id	sid	tid	token	lemma	pos
ejpam-5951	1	1	european	european	PROPN
ejpam-5951	1	2	journal	journal	PROPN
ejpam-5951	1	3	of	of	ADP
ejpam-5951	1	4	pure	pure	ADJ
ejpam-5951	1	5	and	and	CCONJ
ejpam-5951	1	6	applied	applied	ADJ
ejpam-5951	1	7	mathematics	mathematic	NOUN
ejpam-5951	1	8	2025	2025	NUM
ejpam-5951	1	9	,	,	PUNCT
ejpam-5951	1	10	vol	vol	NOUN
ejpam-5951	1	11	.	.	PROPN
ejpam-5951	1	12	18	18	NUM
ejpam-5951	1	13	,	,	PUNCT
ejpam-5951	1	14	issue	issue	NOUN
ejpam-5951	1	15	2	2	NUM
ejpam-5951	1	16	,	,	PUNCT
ejpam-5951	1	17	article	article	NOUN
ejpam-5951	1	18	number	number	NOUN
ejpam-5951	1	19	5951	5951	NUM
ejpam-5951	1	20	issn	issn	PROPN
ejpam-5951	1	21	1307	1307	NUM
ejpam-5951	1	22	-	-	SYM
ejpam-5951	1	23	5543	5543	NUM
ejpam-5951	1	24	–	–	PUNCT
ejpam-5951	1	25	ejpam.com	ejpam.com	X
ejpam-5951	1	26	published	publish	VERB
ejpam-5951	1	27	by	by	ADP
ejpam-5951	1	28	new	new	PROPN
ejpam-5951	1	29	york	york	PROPN
ejpam-5951	1	30	business	business	PROPN
ejpam-5951	1	31	global	global	PROPN
ejpam-5951	1	32	hierarchical	hierarchical	ADJ
ejpam-5951	1	33	fixed	fix	VERB
ejpam-5951	1	34	point	point	NOUN
ejpam-5951	1	35	results	result	NOUN
ejpam-5951	1	36	for	for	ADP
ejpam-5951	1	37	a	a	DET
ejpam-5951	1	38	countable	countable	ADJ
ejpam-5951	1	39	family	family	NOUN
ejpam-5951	1	40	of	of	ADP
ejpam-5951	1	41	strict	strict	ADJ
ejpam-5951	1	42	pseudo	pseudo	NOUN
ejpam-5951	1	43	-	-	ADJ
ejpam-5951	1	44	contractive	contractive	ADJ
ejpam-5951	1	45	mappings	mapping	NOUN
ejpam-5951	1	46	in	in	ADP
ejpam-5951	1	47	hadamard	hadamard	ADJ
ejpam-5951	1	48	manifolds	manifolds	PROPN
ejpam-5951	1	49	prashant	prashant	PROPN
ejpam-5951	1	50	patel1	patel1	PROPN
ejpam-5951	1	51	,	,	PUNCT
ejpam-5951	1	52	rahul	rahul	PROPN
ejpam-5951	1	53	shukla2,∗	shukla2,∗	PROPN
ejpam-5951	1	54	1	1	NUM
ejpam-5951	1	55	department	department	NOUN
ejpam-5951	1	56	of	of	ADP
ejpam-5951	1	57	mathematics	mathematic	NOUN
ejpam-5951	1	58	,	,	PUNCT
ejpam-5951	1	59	school	school	NOUN
ejpam-5951	1	60	of	of	ADP
ejpam-5951	1	61	advanced	advanced	ADJ
ejpam-5951	1	62	sciences	science	NOUN
ejpam-5951	1	63	,	,	PUNCT
ejpam-5951	1	64	vit	vit	PROPN
ejpam-5951	1	65	-	-	PUNCT
ejpam-5951	1	66	ap	ap	PROPN
ejpam-5951	1	67	university	university	PROPN
ejpam-5951	1	68	,	,	PUNCT
ejpam-5951	1	69	inavolu	inavolu	PROPN
ejpam-5951	1	70	,	,	PUNCT
ejpam-5951	1	71	beside	beside	ADP
ejpam-5951	1	72	ap	ap	PROPN
ejpam-5951	1	73	secretariat	secretariat	PROPN
ejpam-5951	1	74	,	,	PUNCT
ejpam-5951	1	75	amaravati	amaravati	PROPN
ejpam-5951	1	76	,	,	PUNCT
ejpam-5951	1	77	522237	522237	NUM
ejpam-5951	1	78	,	,	PUNCT
ejpam-5951	1	79	andhra	andhra	PROPN
ejpam-5951	1	80	pradesh	pradesh	PROPN
ejpam-5951	1	81	,	,	PUNCT
ejpam-5951	1	82	india	india	PROPN
ejpam-5951	1	83	2	2	NUM
ejpam-5951	1	84	department	department	NOUN
ejpam-5951	1	85	of	of	ADP
ejpam-5951	1	86	mathematical	mathematical	ADJ
ejpam-5951	1	87	sciences	sciences	PROPN
ejpam-5951	1	88	&	&	CCONJ
ejpam-5951	1	89	computing	computing	PROPN
ejpam-5951	1	90	,	,	PUNCT
ejpam-5951	1	91	walter	walter	PROPN
ejpam-5951	1	92	sisulu	sisulu	PROPN
ejpam-5951	1	93	university	university	PROPN
ejpam-5951	1	94	,	,	PUNCT
ejpam-5951	1	95	south	south	PROPN
ejpam-5951	1	96	africa	africa	PROPN
ejpam-5951	1	97	abstract	abstract	PROPN
ejpam-5951	1	98	.	.	PUNCT
ejpam-5951	2	1	the	the	DET
ejpam-5951	2	2	aim	aim	NOUN
ejpam-5951	2	3	of	of	ADP
ejpam-5951	2	4	this	this	DET
ejpam-5951	2	5	paper	paper	NOUN
ejpam-5951	2	6	is	be	AUX
ejpam-5951	2	7	to	to	PART
ejpam-5951	2	8	present	present	VERB
ejpam-5951	2	9	convergence	convergence	NOUN
ejpam-5951	2	10	results	result	NOUN
ejpam-5951	2	11	for	for	ADP
ejpam-5951	2	12	a	a	DET
ejpam-5951	2	13	countable	countable	ADJ
ejpam-5951	2	14	family	family	NOUN
ejpam-5951	2	15	of	of	ADP
ejpam-5951	2	16	strict	strict	ADJ
ejpam-5951	2	17	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	2	18	mappings	mapping	NOUN
ejpam-5951	2	19	in	in	ADP
ejpam-5951	2	20	hadamard	hadamard	ADJ
ejpam-5951	2	21	manifolds	manifold	NOUN
ejpam-5951	2	22	.	.	PUNCT
ejpam-5951	3	1	more	more	ADV
ejpam-5951	3	2	precisely	precisely	ADV
ejpam-5951	3	3	,	,	PUNCT
ejpam-5951	3	4	we	we	PRON
ejpam-5951	3	5	employ	employ	VERB
ejpam-5951	3	6	the	the	DET
ejpam-5951	3	7	shrinking	shrink	VERB
ejpam-5951	3	8	projection	projection	NOUN
ejpam-5951	3	9	method	method	NOUN
ejpam-5951	3	10	to	to	PART
ejpam-5951	3	11	approximate	approximate	VERB
ejpam-5951	3	12	common	common	ADJ
ejpam-5951	3	13	hierarchical	hierarchical	ADJ
ejpam-5951	3	14	fixed	fix	VERB
ejpam-5951	3	15	points	point	NOUN
ejpam-5951	3	16	of	of	ADP
ejpam-5951	3	17	a	a	DET
ejpam-5951	3	18	countable	countable	ADJ
ejpam-5951	3	19	family	family	NOUN
ejpam-5951	3	20	of	of	ADP
ejpam-5951	3	21	strict	strict	ADJ
ejpam-5951	3	22	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	3	23	mappings	mapping	NOUN
ejpam-5951	3	24	in	in	ADP
ejpam-5951	3	25	the	the	DET
ejpam-5951	3	26	setting	setting	NOUN
ejpam-5951	3	27	of	of	ADP
ejpam-5951	3	28	hadamard	hadamard	ADJ
ejpam-5951	3	29	manifolds	manifold	NOUN
ejpam-5951	3	30	.	.	PUNCT
ejpam-5951	4	1	we	we	PRON
ejpam-5951	4	2	also	also	ADV
ejpam-5951	4	3	present	present	VERB
ejpam-5951	4	4	some	some	DET
ejpam-5951	4	5	nontrivial	nontrivial	ADJ
ejpam-5951	4	6	examples	example	NOUN
ejpam-5951	4	7	to	to	PART
ejpam-5951	4	8	illustrate	illustrate	VERB
ejpam-5951	4	9	our	our	PRON
ejpam-5951	4	10	result	result	NOUN
ejpam-5951	4	11	.	.	PUNCT
ejpam-5951	5	1	2020	2020	NUM
ejpam-5951	5	2	mathematics	mathematic	NOUN
ejpam-5951	5	3	subject	subject	NOUN
ejpam-5951	5	4	classifications	classification	NOUN
ejpam-5951	5	5	:	:	PUNCT
ejpam-5951	5	6	47h10	47h10	NUM
ejpam-5951	5	7	,	,	PUNCT
ejpam-5951	5	8	47h09	47h09	NUM
ejpam-5951	5	9	key	key	ADJ
ejpam-5951	5	10	words	word	NOUN
ejpam-5951	5	11	and	and	CCONJ
ejpam-5951	5	12	phrases	phrase	NOUN
ejpam-5951	5	13	:	:	PUNCT
ejpam-5951	5	14	hierarchical	hierarchical	ADJ
ejpam-5951	5	15	fixed	fix	VERB
ejpam-5951	5	16	point	point	NOUN
ejpam-5951	5	17	,	,	PUNCT
ejpam-5951	5	18	hadamard	hadamard	NOUN
ejpam-5951	5	19	manifolds	manifold	NOUN
ejpam-5951	5	20	,	,	PUNCT
ejpam-5951	5	21	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	5	22	mappings	mapping	NOUN
ejpam-5951	5	23	1	1	NUM
ejpam-5951	5	24	.	.	PUNCT
ejpam-5951	5	25	introduction	introduction	NOUN
ejpam-5951	5	26	in	in	ADP
ejpam-5951	5	27	1966	1966	NUM
ejpam-5951	5	28	,	,	PUNCT
ejpam-5951	5	29	hartman	hartman	NOUN
ejpam-5951	5	30	and	and	CCONJ
ejpam-5951	5	31	stampacchia	stampacchia	X
ejpam-5951	5	32	[	[	X
ejpam-5951	5	33	1	1	NUM
ejpam-5951	5	34	]	]	PUNCT
ejpam-5951	5	35	introduced	introduce	VERB
ejpam-5951	5	36	variational	variational	ADJ
ejpam-5951	5	37	inequality	inequality	NOUN
ejpam-5951	5	38	theory	theory	NOUN
ejpam-5951	5	39	as	as	ADP
ejpam-5951	5	40	a	a	DET
ejpam-5951	5	41	method	method	NOUN
ejpam-5951	5	42	for	for	ADP
ejpam-5951	5	43	studying	study	VERB
ejpam-5951	5	44	partial	partial	ADJ
ejpam-5951	5	45	differential	differential	ADJ
ejpam-5951	5	46	equations	equation	NOUN
ejpam-5951	5	47	with	with	ADP
ejpam-5951	5	48	applications	application	NOUN
ejpam-5951	5	49	,	,	PUNCT
ejpam-5951	5	50	primarily	primarily	ADV
ejpam-5951	5	51	in	in	ADP
ejpam-5951	5	52	mechanics	mechanic	NOUN
ejpam-5951	5	53	.	.	PUNCT
ejpam-5951	6	1	the	the	DET
ejpam-5951	6	2	variational	variational	ADJ
ejpam-5951	6	3	inequality	inequality	NOUN
ejpam-5951	6	4	problem	problem	NOUN
ejpam-5951	6	5	has	have	VERB
ejpam-5951	6	6	a	a	DET
ejpam-5951	6	7	wide	wide	ADJ
ejpam-5951	6	8	range	range	NOUN
ejpam-5951	6	9	of	of	ADP
ejpam-5951	6	10	applications	application	NOUN
ejpam-5951	6	11	in	in	ADP
ejpam-5951	6	12	some	some	DET
ejpam-5951	6	13	practical	practical	ADJ
ejpam-5951	6	14	problems	problem	NOUN
ejpam-5951	6	15	arising	arise	VERB
ejpam-5951	6	16	in	in	ADP
ejpam-5951	6	17	economics	economic	NOUN
ejpam-5951	6	18	,	,	PUNCT
ejpam-5951	6	19	transportation	transportation	NOUN
ejpam-5951	6	20	,	,	PUNCT
ejpam-5951	6	21	network	network	NOUN
ejpam-5951	6	22	and	and	CCONJ
ejpam-5951	6	23	structural	structural	ADJ
ejpam-5951	6	24	analysis	analysis	NOUN
ejpam-5951	6	25	,	,	PUNCT
ejpam-5951	6	26	elasticity	elasticity	NOUN
ejpam-5951	6	27	,	,	PUNCT
ejpam-5951	6	28	engineering	engineering	NOUN
ejpam-5951	6	29	and	and	CCONJ
ejpam-5951	6	30	mechanics	mechanic	NOUN
ejpam-5951	6	31	,	,	PUNCT
ejpam-5951	6	32	supply	supply	NOUN
ejpam-5951	6	33	chain	chain	NOUN
ejpam-5951	6	34	management	management	NOUN
ejpam-5951	6	35	,	,	PUNCT
ejpam-5951	6	36	finance	finance	NOUN
ejpam-5951	6	37	and	and	CCONJ
ejpam-5951	6	38	game	game	NOUN
ejpam-5951	6	39	theory	theory	NOUN
ejpam-5951	6	40	.	.	PUNCT
ejpam-5951	7	1	in	in	ADP
ejpam-5951	7	2	recent	recent	ADJ
ejpam-5951	7	3	years	year	NOUN
ejpam-5951	7	4	,	,	PUNCT
ejpam-5951	7	5	many	many	ADJ
ejpam-5951	7	6	authors	author	NOUN
ejpam-5951	7	7	discussed	discuss	VERB
ejpam-5951	7	8	variational	variational	ADJ
ejpam-5951	7	9	inequality	inequality	NOUN
ejpam-5951	7	10	problems	problem	NOUN
ejpam-5951	7	11	in	in	ADP
ejpam-5951	7	12	the	the	DET
ejpam-5951	7	13	context	context	NOUN
ejpam-5951	7	14	of	of	ADP
ejpam-5951	7	15	banach	banach	NOUN
ejpam-5951	7	16	and	and	CCONJ
ejpam-5951	7	17	hilbert	hilbert	NOUN
ejpam-5951	7	18	spaces	space	VERB
ejpam-5951	8	1	[	[	X
ejpam-5951	8	2	2–7	2–7	X
ejpam-5951	8	3	]	]	X
ejpam-5951	8	4	.	.	PUNCT
ejpam-5951	9	1	to	to	PART
ejpam-5951	9	2	solve	solve	VERB
ejpam-5951	9	3	environmental	environmental	ADJ
ejpam-5951	9	4	projects	project	NOUN
ejpam-5951	9	5	concerning	concern	VERB
ejpam-5951	9	6	the	the	DET
ejpam-5951	9	7	transmission	transmission	NOUN
ejpam-5951	9	8	of	of	ADP
ejpam-5951	9	9	pollution	pollution	NOUN
ejpam-5951	9	10	in	in	ADP
ejpam-5951	9	11	different	different	ADJ
ejpam-5951	9	12	kind	kind	NOUN
ejpam-5951	9	13	of	of	ADP
ejpam-5951	9	14	media	medium	NOUN
ejpam-5951	9	15	we	we	PRON
ejpam-5951	9	16	need	need	VERB
ejpam-5951	9	17	to	to	PART
ejpam-5951	9	18	transfer	transfer	VERB
ejpam-5951	9	19	pollution	pollution	NOUN
ejpam-5951	9	20	along	along	ADP
ejpam-5951	9	21	certain	certain	ADJ
ejpam-5951	9	22	bounded	bounded	ADJ
ejpam-5951	9	23	surface	surface	NOUN
ejpam-5951	9	24	areas	area	NOUN
ejpam-5951	9	25	.	.	PUNCT
ejpam-5951	10	1	these	these	DET
ejpam-5951	10	2	restrictions	restriction	NOUN
ejpam-5951	10	3	lead	lead	VERB
ejpam-5951	10	4	to	to	ADP
ejpam-5951	10	5	many	many	ADJ
ejpam-5951	10	6	boundary	boundary	ADJ
ejpam-5951	10	7	value	value	NOUN
ejpam-5951	10	8	problems	problem	NOUN
ejpam-5951	10	9	on	on	ADP
ejpam-5951	10	10	manifolds	manifold	NOUN
ejpam-5951	10	11	.	.	PUNCT
ejpam-5951	11	1	to	to	PART
ejpam-5951	11	2	overcome	overcome	VERB
ejpam-5951	11	3	,	,	PUNCT
ejpam-5951	11	4	this	this	DET
ejpam-5951	11	5	situation	situation	NOUN
ejpam-5951	11	6	in	in	ADP
ejpam-5951	11	7	2003	2003	NUM
ejpam-5951	11	8	,	,	PUNCT
ejpam-5951	11	9	nemeth	nemeth	PROPN
ejpam-5951	12	1	[	[	X
ejpam-5951	12	2	8	8	NUM
ejpam-5951	12	3	]	]	PUNCT
ejpam-5951	12	4	introduced	introduce	VERB
ejpam-5951	12	5	the	the	DET
ejpam-5951	12	6	variational	variational	ADJ
ejpam-5951	12	7	inequalities	inequality	NOUN
ejpam-5951	12	8	in	in	ADP
ejpam-5951	12	9	hadamard	hadamard	ADJ
ejpam-5951	12	10	manifolds	manifold	NOUN
ejpam-5951	12	11	.	.	PUNCT
ejpam-5951	13	1	∗corresponding	∗corresponde	VERB
ejpam-5951	13	2	author	author	NOUN
ejpam-5951	13	3	.	.	PUNCT
ejpam-5951	14	1	doi	doi	NOUN
ejpam-5951	14	2	:	:	PUNCT
ejpam-5951	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5951	https://doi.org/10.29020/nybg.ejpam.v18i2.5951	PRON
ejpam-5951	14	4	email	email	NOUN
ejpam-5951	14	5	addresses	address	VERB
ejpam-5951	14	6	:	:	PUNCT
ejpam-5951	14	7	prashant.patel9999@gmail.com	prashant.patel9999@gmail.com	NUM
ejpam-5951	14	8	,	,	PUNCT
ejpam-5951	14	9	prashant.p@vitap.ac.in	prashant.p@vitap.ac.in	PROPN
ejpam-5951	14	10	(	(	PUNCT
ejpam-5951	14	11	p.	p.	NOUN
ejpam-5951	14	12	patel	patel	PROPN
ejpam-5951	14	13	)	)	PUNCT
ejpam-5951	14	14	,	,	PUNCT
ejpam-5951	14	15	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-5951	14	16	(	(	PUNCT
ejpam-5951	14	17	r.	r.	NOUN
ejpam-5951	14	18	shukla	shukla	PROPN
ejpam-5951	14	19	)	)	PUNCT
ejpam-5951	14	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5951	15	1	1	1	NUM
ejpam-5951	15	2	copyright	copyright	NOUN
ejpam-5951	15	3	:	:	PUNCT
ejpam-5951	15	4	©	©	PROPN
ejpam-5951	15	5	2025	2025	NUM
ejpam-5951	15	6	the	the	DET
ejpam-5951	15	7	author(s	author(s	NOUN
ejpam-5951	15	8	)	)	PUNCT
ejpam-5951	15	9	.	.	PUNCT
ejpam-5951	16	1	(	(	PUNCT
ejpam-5951	16	2	cc	cc	NOUN
ejpam-5951	16	3	by	by	ADP
ejpam-5951	16	4	-	-	PUNCT
ejpam-5951	16	5	nc	nc	PROPN
ejpam-5951	16	6	4.0	4.0	NUM
ejpam-5951	16	7	)	)	PUNCT
ejpam-5951	16	8	p.	p.	NOUN
ejpam-5951	16	9	patel	patel	PROPN
ejpam-5951	16	10	,	,	PUNCT
ejpam-5951	16	11	r.	r.	PROPN
ejpam-5951	16	12	shukla	shukla	PROPN
ejpam-5951	16	13	/	/	SYM
ejpam-5951	16	14	eur	eur	PROPN
ejpam-5951	16	15	.	.	PUNCT
ejpam-5951	17	1	j.	j.	PROPN
ejpam-5951	17	2	pure	pure	PROPN
ejpam-5951	17	3	appl	appl	PROPN
ejpam-5951	17	4	.	.	PROPN
ejpam-5951	17	5	math	math	PROPN
ejpam-5951	17	6	,	,	PUNCT
ejpam-5951	17	7	18	18	NUM
ejpam-5951	17	8	(	(	PUNCT
ejpam-5951	17	9	2	2	NUM
ejpam-5951	17	10	)	)	PUNCT
ejpam-5951	17	11	(	(	PUNCT
ejpam-5951	17	12	2025	2025	NUM
ejpam-5951	17	13	)	)	PUNCT
ejpam-5951	17	14	,	,	PUNCT
ejpam-5951	17	15	5951	5951	NUM
ejpam-5951	17	16	2	2	NUM
ejpam-5951	17	17	of	of	ADP
ejpam-5951	17	18	15	15	NUM
ejpam-5951	17	19	a	a	DET
ejpam-5951	17	20	constrained	constrain	VERB
ejpam-5951	17	21	optimization	optimization	NOUN
ejpam-5951	17	22	problem	problem	NOUN
ejpam-5951	17	23	,	,	PUNCT
ejpam-5951	17	24	where	where	SCONJ
ejpam-5951	17	25	the	the	DET
ejpam-5951	17	26	constrained	constrain	VERB
ejpam-5951	17	27	set	set	NOUN
ejpam-5951	17	28	is	be	AUX
ejpam-5951	17	29	the	the	DET
ejpam-5951	17	30	solution	solution	NOUN
ejpam-5951	17	31	set	set	VERB
ejpam-5951	17	32	of	of	ADP
ejpam-5951	17	33	another	another	DET
ejpam-5951	17	34	optimization	optimization	NOUN
ejpam-5951	17	35	problem	problem	NOUN
ejpam-5951	17	36	,	,	PUNCT
ejpam-5951	17	37	is	be	AUX
ejpam-5951	17	38	known	know	VERB
ejpam-5951	17	39	as	as	ADP
ejpam-5951	17	40	a	a	DET
ejpam-5951	17	41	bilevel	bilevel	ADJ
ejpam-5951	17	42	programming	programming	NOUN
ejpam-5951	17	43	problem	problem	NOUN
ejpam-5951	17	44	.	.	PUNCT
ejpam-5951	18	1	over	over	ADP
ejpam-5951	18	2	the	the	DET
ejpam-5951	18	3	past	past	ADJ
ejpam-5951	18	4	thirty	thirty	NUM
ejpam-5951	18	5	years	year	NOUN
ejpam-5951	18	6	,	,	PUNCT
ejpam-5951	18	7	there	there	PRON
ejpam-5951	18	8	has	have	AUX
ejpam-5951	18	9	been	be	AUX
ejpam-5951	18	10	extensive	extensive	ADJ
ejpam-5951	18	11	research	research	NOUN
ejpam-5951	18	12	on	on	ADP
ejpam-5951	18	13	these	these	DET
ejpam-5951	18	14	challenges	challenge	NOUN
ejpam-5951	18	15	due	due	ADP
ejpam-5951	18	16	to	to	ADP
ejpam-5951	18	17	their	their	PRON
ejpam-5951	18	18	relevance	relevance	NOUN
ejpam-5951	18	19	in	in	ADP
ejpam-5951	18	20	domains	domain	NOUN
ejpam-5951	18	21	such	such	ADJ
ejpam-5951	18	22	as	as	ADP
ejpam-5951	18	23	mechanics	mechanic	NOUN
ejpam-5951	18	24	and	and	CCONJ
ejpam-5951	18	25	network	network	NOUN
ejpam-5951	18	26	design	design	NOUN
ejpam-5951	18	27	.	.	PUNCT
ejpam-5951	19	1	if	if	SCONJ
ejpam-5951	19	2	the	the	DET
ejpam-5951	19	3	first	first	ADJ
ejpam-5951	19	4	level	level	NOUN
ejpam-5951	19	5	problem	problem	NOUN
ejpam-5951	19	6	is	be	AUX
ejpam-5951	19	7	one	one	NUM
ejpam-5951	19	8	of	of	ADP
ejpam-5951	19	9	variational	variational	ADJ
ejpam-5951	19	10	inequality	inequality	NOUN
ejpam-5951	19	11	and	and	CCONJ
ejpam-5951	19	12	the	the	DET
ejpam-5951	19	13	second	second	ADJ
ejpam-5951	19	14	level	level	NOUN
ejpam-5951	19	15	problem	problem	NOUN
ejpam-5951	19	16	is	be	AUX
ejpam-5951	19	17	a	a	DET
ejpam-5951	19	18	collection	collection	NOUN
ejpam-5951	19	19	of	of	ADP
ejpam-5951	19	20	fixed	fix	VERB
ejpam-5951	19	21	points	point	NOUN
ejpam-5951	19	22	of	of	ADP
ejpam-5951	19	23	a	a	DET
ejpam-5951	19	24	mapping	mapping	NOUN
ejpam-5951	19	25	,	,	PUNCT
ejpam-5951	19	26	then	then	ADV
ejpam-5951	19	27	the	the	DET
ejpam-5951	19	28	bilevel	bilevel	ADJ
ejpam-5951	19	29	problem	problem	NOUN
ejpam-5951	19	30	is	be	AUX
ejpam-5951	19	31	known	know	VERB
ejpam-5951	19	32	as	as	ADP
ejpam-5951	19	33	a	a	DET
ejpam-5951	19	34	hierarchical	hierarchical	ADJ
ejpam-5951	19	35	variational	variational	ADJ
ejpam-5951	19	36	inequality	inequality	NOUN
ejpam-5951	19	37	problem	problem	NOUN
ejpam-5951	19	38	.	.	PUNCT
ejpam-5951	20	1	stated	state	VERB
ejpam-5951	20	2	otherwise	otherwise	ADV
ejpam-5951	20	3	,	,	PUNCT
ejpam-5951	20	4	a	a	DET
ejpam-5951	20	5	variational	variational	ADJ
ejpam-5951	20	6	inequality	inequality	NOUN
ejpam-5951	20	7	problem	problem	NOUN
ejpam-5951	20	8	defined	define	VERB
ejpam-5951	20	9	over	over	ADP
ejpam-5951	20	10	the	the	DET
ejpam-5951	20	11	set	set	NOUN
ejpam-5951	20	12	of	of	ADP
ejpam-5951	20	13	fixed	fix	VERB
ejpam-5951	20	14	points	point	NOUN
ejpam-5951	20	15	is	be	AUX
ejpam-5951	20	16	a	a	DET
ejpam-5951	20	17	hierarchical	hierarchical	ADJ
ejpam-5951	20	18	variational	variational	ADJ
ejpam-5951	20	19	inequality	inequality	NOUN
ejpam-5951	20	20	problem	problem	NOUN
ejpam-5951	20	21	,	,	PUNCT
ejpam-5951	20	22	sometimes	sometimes	ADV
ejpam-5951	20	23	referred	refer	VERB
ejpam-5951	20	24	to	to	ADP
ejpam-5951	20	25	as	as	ADP
ejpam-5951	20	26	a	a	DET
ejpam-5951	20	27	hierarchical	hierarchical	ADJ
ejpam-5951	20	28	fixed	fix	VERB
ejpam-5951	20	29	point	point	NOUN
ejpam-5951	20	30	problem	problem	NOUN
ejpam-5951	20	31	.	.	PUNCT
ejpam-5951	21	1	in	in	ADP
ejpam-5951	21	2	2006	2006	NUM
ejpam-5951	21	3	,	,	PUNCT
ejpam-5951	21	4	moudafi	moudafi	NOUN
ejpam-5951	21	5	and	and	CCONJ
ejpam-5951	21	6	mainge	mainge	VERB
ejpam-5951	21	7	[	[	X
ejpam-5951	21	8	9	9	NUM
ejpam-5951	21	9	]	]	PUNCT
ejpam-5951	21	10	introduced	introduce	VERB
ejpam-5951	21	11	the	the	DET
ejpam-5951	21	12	hierarchical	hierarchical	ADJ
ejpam-5951	21	13	fixed	fix	VERB
ejpam-5951	21	14	point	point	NOUN
ejpam-5951	21	15	problem	problem	NOUN
ejpam-5951	21	16	in	in	ADP
ejpam-5951	21	17	the	the	DET
ejpam-5951	21	18	setting	setting	NOUN
ejpam-5951	21	19	of	of	ADP
ejpam-5951	21	20	hilbert	hilbert	NOUN
ejpam-5951	21	21	space	space	NOUN
ejpam-5951	21	22	find	find	VERB
ejpam-5951	21	23	ζ	ζ	NOUN
ejpam-5951	21	24	∈	∈	PROPN
ejpam-5951	21	25	f	f	X
ejpam-5951	21	26	(	(	PUNCT
ejpam-5951	21	27	h	h	NOUN
ejpam-5951	21	28	)	)	PUNCT
ejpam-5951	21	29	such	such	ADJ
ejpam-5951	21	30	that	that	DET
ejpam-5951	21	31	⟨ζ	⟨ζ	ADJ
ejpam-5951	21	32	−g(ζ	−g(ζ	NOUN
ejpam-5951	21	33	)	)	PUNCT
ejpam-5951	21	34	,	,	PUNCT
ejpam-5951	21	35	ζ	ζ	NOUN
ejpam-5951	21	36	−	−	NOUN
ejpam-5951	21	37	ν⟩	ν⟩	NOUN
ejpam-5951	21	38	≤	≤	NOUN
ejpam-5951	21	39	0	0	NUM
ejpam-5951	21	40	,	,	PUNCT
ejpam-5951	21	41	for	for	ADP
ejpam-5951	21	42	all	all	PRON
ejpam-5951	21	43	ν	ν	X
ejpam-5951	21	44	∈	∈	PROPN
ejpam-5951	21	45	f	f	X
ejpam-5951	21	46	(	(	PUNCT
ejpam-5951	21	47	g	g	NOUN
ejpam-5951	21	48	)	)	PUNCT
ejpam-5951	21	49	.	.	PUNCT
ejpam-5951	22	1	(	(	PUNCT
ejpam-5951	22	2	1	1	X
ejpam-5951	22	3	)	)	PUNCT
ejpam-5951	22	4	here	here	ADV
ejpam-5951	22	5	g	g	PROPN
ejpam-5951	22	6	,	,	PUNCT
ejpam-5951	22	7	h	h	PROPN
ejpam-5951	22	8	are	be	AUX
ejpam-5951	22	9	nonexpansive	nonexpansive	ADJ
ejpam-5951	22	10	mappings	mapping	NOUN
ejpam-5951	22	11	defined	define	VERB
ejpam-5951	22	12	on	on	ADP
ejpam-5951	22	13	a	a	DET
ejpam-5951	22	14	hilbert	hilbert	NOUN
ejpam-5951	22	15	space	space	NOUN
ejpam-5951	22	16	m.	m.	NOUN
ejpam-5951	22	17	later	later	ADV
ejpam-5951	22	18	in	in	ADP
ejpam-5951	22	19	2010	2010	NUM
ejpam-5951	22	20	,	,	PUNCT
ejpam-5951	22	21	xu	xu	PROPN
ejpam-5951	23	1	[	[	X
ejpam-5951	23	2	10	10	NUM
ejpam-5951	23	3	]	]	PUNCT
ejpam-5951	23	4	extended	extend	VERB
ejpam-5951	23	5	his	his	PRON
ejpam-5951	23	6	work	work	NOUN
ejpam-5951	23	7	in	in	ADP
ejpam-5951	23	8	the	the	DET
ejpam-5951	23	9	context	context	NOUN
ejpam-5951	23	10	of	of	ADP
ejpam-5951	23	11	uniformly	uniformly	ADV
ejpam-5951	23	12	smooth	smooth	ADJ
ejpam-5951	23	13	banach	banach	NOUN
ejpam-5951	23	14	spaces	space	NOUN
ejpam-5951	23	15	.	.	PUNCT
ejpam-5951	24	1	after	after	ADP
ejpam-5951	24	2	that	that	SCONJ
ejpam-5951	24	3	the	the	DET
ejpam-5951	24	4	viscosity	viscosity	NOUN
ejpam-5951	24	5	method	method	NOUN
ejpam-5951	24	6	was	be	AUX
ejpam-5951	24	7	developed	develop	VERB
ejpam-5951	24	8	by	by	ADP
ejpam-5951	24	9	a	a	DET
ejpam-5951	24	10	number	number	NOUN
ejpam-5951	24	11	of	of	ADP
ejpam-5951	24	12	researchers	researcher	NOUN
ejpam-5951	24	13	to	to	PART
ejpam-5951	24	14	solve	solve	VERB
ejpam-5951	24	15	variational	variational	ADJ
ejpam-5951	24	16	inequalities	inequality	NOUN
ejpam-5951	24	17	defined	define	VERB
ejpam-5951	24	18	on	on	ADP
ejpam-5951	24	19	the	the	DET
ejpam-5951	24	20	set	set	NOUN
ejpam-5951	24	21	of	of	ADP
ejpam-5951	24	22	fixed	fix	VERB
ejpam-5951	24	23	points	point	NOUN
ejpam-5951	24	24	of	of	ADP
ejpam-5951	24	25	nonexpansive	nonexpansive	ADJ
ejpam-5951	24	26	mapping	mapping	NOUN
ejpam-5951	24	27	in	in	ADP
ejpam-5951	24	28	the	the	DET
ejpam-5951	24	29	context	context	NOUN
ejpam-5951	24	30	of	of	ADP
ejpam-5951	24	31	hilbert	hilbert	NOUN
ejpam-5951	24	32	or	or	CCONJ
ejpam-5951	24	33	banach	banach	NOUN
ejpam-5951	24	34	spaces	space	VERB
ejpam-5951	24	35	.	.	PUNCT
ejpam-5951	25	1	these	these	DET
ejpam-5951	25	2	researchers	researcher	NOUN
ejpam-5951	25	3	replaced	replace	VERB
ejpam-5951	25	4	contraction	contraction	NOUN
ejpam-5951	25	5	mapping	mapping	NOUN
ejpam-5951	25	6	with	with	ADP
ejpam-5951	25	7	weaker	weak	ADJ
ejpam-5951	25	8	forms	form	NOUN
ejpam-5951	25	9	of	of	ADP
ejpam-5951	25	10	contraction	contraction	NOUN
ejpam-5951	25	11	mappings	mapping	NOUN
ejpam-5951	25	12	,	,	PUNCT
ejpam-5951	25	13	such	such	ADJ
ejpam-5951	25	14	as	as	ADP
ejpam-5951	25	15	pseudo	pseudo	NOUN
ejpam-5951	25	16	-	-	NOUN
ejpam-5951	25	17	contraction	contraction	NOUN
ejpam-5951	25	18	mapping	mapping	NOUN
ejpam-5951	25	19	and	and	CCONJ
ejpam-5951	25	20	weakly	weakly	ADJ
ejpam-5951	25	21	contraction	contraction	NOUN
ejpam-5951	25	22	mapping	mapping	NOUN
ejpam-5951	25	23	[	[	X
ejpam-5951	25	24	3	3	NUM
ejpam-5951	25	25	,	,	PUNCT
ejpam-5951	25	26	4	4	NUM
ejpam-5951	25	27	,	,	PUNCT
ejpam-5951	25	28	11–14	11–14	NUM
ejpam-5951	25	29	]	]	PUNCT
ejpam-5951	25	30	.	.	PUNCT
ejpam-5951	26	1	in	in	ADP
ejpam-5951	26	2	2020	2020	NUM
ejpam-5951	26	3	,	,	PUNCT
ejpam-5951	26	4	al	al	PROPN
ejpam-5951	26	5	-	-	PUNCT
ejpam-5951	26	6	homidan	homidan	PROPN
ejpam-5951	26	7	,	,	PUNCT
ejpam-5951	26	8	presented	present	VERB
ejpam-5951	26	9	a	a	DET
ejpam-5951	26	10	viscosity	viscosity	NOUN
ejpam-5951	26	11	approach	approach	NOUN
ejpam-5951	26	12	to	to	PART
ejpam-5951	26	13	solve	solve	VERB
ejpam-5951	26	14	the	the	DET
ejpam-5951	26	15	hierarchical	hierarchical	ADJ
ejpam-5951	26	16	fixed	fix	VERB
ejpam-5951	26	17	point	point	NOUN
ejpam-5951	26	18	problem	problem	NOUN
ejpam-5951	26	19	in	in	ADP
ejpam-5951	26	20	the	the	DET
ejpam-5951	26	21	context	context	NOUN
ejpam-5951	26	22	of	of	ADP
ejpam-5951	26	23	hadamard	hadamard	ADJ
ejpam-5951	26	24	manifolds	manifold	NOUN
ejpam-5951	26	25	defined	define	VERB
ejpam-5951	26	26	on	on	ADP
ejpam-5951	26	27	the	the	DET
ejpam-5951	26	28	set	set	NOUN
ejpam-5951	26	29	of	of	ADP
ejpam-5951	26	30	fixed	fix	VERB
ejpam-5951	26	31	points	point	NOUN
ejpam-5951	26	32	of	of	ADP
ejpam-5951	26	33	nonexpansive	nonexpansive	ADJ
ejpam-5951	26	34	mapping	mapping	NOUN
ejpam-5951	26	35	and	and	CCONJ
ejpam-5951	26	36	involving	involve	VERB
ejpam-5951	26	37	a	a	DET
ejpam-5951	26	38	nonexpansive	nonexpansive	ADJ
ejpam-5951	26	39	mapping	mapping	NOUN
ejpam-5951	26	40	and	and	CCONJ
ejpam-5951	26	41	another	another	DET
ejpam-5951	26	42	ϕ-contraction	ϕ-contraction	PROPN
ejpam-5951	26	43	mapping	mapping	NOUN
ejpam-5951	26	44	.	.	PUNCT
ejpam-5951	27	1	there	there	PRON
ejpam-5951	27	2	are	be	VERB
ejpam-5951	27	3	many	many	ADJ
ejpam-5951	27	4	authors	author	NOUN
ejpam-5951	27	5	who	who	PRON
ejpam-5951	27	6	presented	present	VERB
ejpam-5951	27	7	a	a	DET
ejpam-5951	27	8	viscosity	viscosity	NOUN
ejpam-5951	27	9	approach	approach	NOUN
ejpam-5951	27	10	for	for	ADP
ejpam-5951	27	11	hierarchical	hierarchical	ADJ
ejpam-5951	27	12	variational	variational	ADJ
ejpam-5951	27	13	inequality	inequality	NOUN
ejpam-5951	27	14	problems	problem	NOUN
ejpam-5951	27	15	in	in	ADP
ejpam-5951	27	16	the	the	DET
ejpam-5951	27	17	context	context	NOUN
ejpam-5951	27	18	of	of	ADP
ejpam-5951	27	19	hadamard	hadamard	ADJ
ejpam-5951	27	20	manifolds	manifold	NOUN
ejpam-5951	27	21	[	[	X
ejpam-5951	27	22	9	9	NUM
ejpam-5951	27	23	,	,	PUNCT
ejpam-5951	27	24	15	15	NUM
ejpam-5951	27	25	]	]	PUNCT
ejpam-5951	27	26	,	,	PUNCT
ejpam-5951	27	27	and	and	CCONJ
ejpam-5951	27	28	references	reference	NOUN
ejpam-5951	27	29	therein	therein	ADV
ejpam-5951	27	30	.	.	PUNCT
ejpam-5951	28	1	motivated	motivate	VERB
ejpam-5951	28	2	by	by	ADP
ejpam-5951	28	3	the	the	DET
ejpam-5951	28	4	above	above	ADJ
ejpam-5951	28	5	works	work	NOUN
ejpam-5951	28	6	,	,	PUNCT
ejpam-5951	28	7	the	the	DET
ejpam-5951	28	8	purpose	purpose	NOUN
ejpam-5951	28	9	of	of	ADP
ejpam-5951	28	10	this	this	DET
ejpam-5951	28	11	paper	paper	NOUN
ejpam-5951	28	12	is	be	AUX
ejpam-5951	28	13	to	to	PART
ejpam-5951	28	14	introduce	introduce	VERB
ejpam-5951	28	15	and	and	CCONJ
ejpam-5951	28	16	analyse	analyse	VERB
ejpam-5951	28	17	a	a	DET
ejpam-5951	28	18	new	new	ADJ
ejpam-5951	28	19	algorithm	algorithm	NOUN
ejpam-5951	28	20	for	for	ADP
ejpam-5951	28	21	solving	solve	VERB
ejpam-5951	28	22	hierarchical	hierarchical	ADJ
ejpam-5951	28	23	variational	variational	ADJ
ejpam-5951	28	24	inequality	inequality	NOUN
ejpam-5951	28	25	problems	problem	NOUN
ejpam-5951	28	26	in	in	ADP
ejpam-5951	28	27	the	the	DET
ejpam-5951	28	28	framework	framework	NOUN
ejpam-5951	28	29	of	of	ADP
ejpam-5951	28	30	hadamard	hadamard	NOUN
ejpam-5951	28	31	manifolds	manifold	NOUN
ejpam-5951	28	32	.	.	PUNCT
ejpam-5951	29	1	in	in	ADP
ejpam-5951	29	2	this	this	DET
ejpam-5951	29	3	paper	paper	NOUN
ejpam-5951	29	4	,	,	PUNCT
ejpam-5951	29	5	we	we	PRON
ejpam-5951	29	6	present	present	VERB
ejpam-5951	29	7	a	a	DET
ejpam-5951	29	8	new	new	ADJ
ejpam-5951	29	9	algorithm	algorithm	NOUN
ejpam-5951	29	10	to	to	PART
ejpam-5951	29	11	solve	solve	VERB
ejpam-5951	29	12	hierarchical	hierarchical	ADJ
ejpam-5951	29	13	fixed	fix	VERB
ejpam-5951	29	14	point	point	NOUN
ejpam-5951	29	15	problem	problem	NOUN
ejpam-5951	29	16	and	and	CCONJ
ejpam-5951	29	17	present	present	ADJ
ejpam-5951	29	18	convergence	convergence	NOUN
ejpam-5951	29	19	result	result	NOUN
ejpam-5951	29	20	for	for	ADP
ejpam-5951	29	21	a	a	DET
ejpam-5951	29	22	finite	finite	ADJ
ejpam-5951	29	23	family	family	NOUN
ejpam-5951	29	24	of	of	ADP
ejpam-5951	29	25	β	β	NOUN
ejpam-5951	29	26	-	-	ADJ
ejpam-5951	29	27	strict	strict	ADJ
ejpam-5951	29	28	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	29	29	mapping	mapping	NOUN
ejpam-5951	29	30	in	in	ADP
ejpam-5951	29	31	hadamard	hadamard	ADJ
ejpam-5951	29	32	manifolds	manifold	NOUN
ejpam-5951	29	33	.	.	PUNCT
ejpam-5951	30	1	the	the	DET
ejpam-5951	30	2	manuscript	manuscript	NOUN
ejpam-5951	30	3	is	be	AUX
ejpam-5951	30	4	presented	present	VERB
ejpam-5951	30	5	as	as	SCONJ
ejpam-5951	30	6	follows	follow	VERB
ejpam-5951	30	7	:	:	PUNCT
ejpam-5951	30	8	section	section	NOUN
ejpam-5951	30	9	2	2	NUM
ejpam-5951	30	10	contains	contain	VERB
ejpam-5951	30	11	basic	basic	ADJ
ejpam-5951	30	12	definitions	definition	NOUN
ejpam-5951	30	13	and	and	CCONJ
ejpam-5951	30	14	facts	fact	NOUN
ejpam-5951	30	15	.	.	PUNCT
ejpam-5951	31	1	section	section	NOUN
ejpam-5951	31	2	3	3	NUM
ejpam-5951	31	3	has	have	VERB
ejpam-5951	31	4	the	the	DET
ejpam-5951	31	5	hierarchical	hierarchical	ADJ
ejpam-5951	31	6	variational	variational	ADJ
ejpam-5951	31	7	inequality	inequality	NOUN
ejpam-5951	31	8	problem	problem	NOUN
ejpam-5951	31	9	and	and	CCONJ
ejpam-5951	31	10	the	the	DET
ejpam-5951	31	11	proposed	propose	VERB
ejpam-5951	31	12	algorithm	algorithm	NOUN
ejpam-5951	31	13	and	and	CCONJ
ejpam-5951	31	14	its	its	PRON
ejpam-5951	31	15	convergence	convergence	NOUN
ejpam-5951	31	16	analysis	analysis	NOUN
ejpam-5951	31	17	.	.	PUNCT
ejpam-5951	32	1	section	section	NOUN
ejpam-5951	32	2	4	4	NUM
ejpam-5951	32	3	has	have	VERB
ejpam-5951	32	4	some	some	DET
ejpam-5951	32	5	numerical	numerical	ADJ
ejpam-5951	32	6	examples	example	NOUN
ejpam-5951	32	7	which	which	PRON
ejpam-5951	32	8	illustrates	illustrate	VERB
ejpam-5951	32	9	the	the	DET
ejpam-5951	32	10	result	result	NOUN
ejpam-5951	32	11	presented	present	VERB
ejpam-5951	32	12	in	in	ADP
ejpam-5951	32	13	the	the	DET
ejpam-5951	32	14	manuscript	manuscript	NOUN
ejpam-5951	32	15	.	.	PUNCT
ejpam-5951	33	1	2	2	X
ejpam-5951	33	2	.	.	X
ejpam-5951	33	3	preliminaries	preliminary	NOUN
ejpam-5951	33	4	now	now	ADV
ejpam-5951	33	5	,	,	PUNCT
ejpam-5951	33	6	we	we	PRON
ejpam-5951	33	7	present	present	VERB
ejpam-5951	33	8	some	some	DET
ejpam-5951	33	9	basic	basic	ADJ
ejpam-5951	33	10	facts	fact	NOUN
ejpam-5951	33	11	and	and	CCONJ
ejpam-5951	33	12	definitions	definition	NOUN
ejpam-5951	33	13	which	which	PRON
ejpam-5951	33	14	are	be	AUX
ejpam-5951	33	15	related	relate	VERB
ejpam-5951	33	16	to	to	ADP
ejpam-5951	33	17	hadamard	hadamard	ADJ
ejpam-5951	33	18	manifolds	manifold	NOUN
ejpam-5951	33	19	.	.	PUNCT
ejpam-5951	34	1	p.	p.	NOUN
ejpam-5951	34	2	patel	patel	PROPN
ejpam-5951	34	3	,	,	PUNCT
ejpam-5951	34	4	r.	r.	PROPN
ejpam-5951	34	5	shukla	shukla	PROPN
ejpam-5951	34	6	/	/	SYM
ejpam-5951	34	7	eur	eur	PROPN
ejpam-5951	34	8	.	.	PUNCT
ejpam-5951	35	1	j.	j.	PROPN
ejpam-5951	35	2	pure	pure	PROPN
ejpam-5951	35	3	appl	appl	PROPN
ejpam-5951	35	4	.	.	PROPN
ejpam-5951	35	5	math	math	PROPN
ejpam-5951	35	6	,	,	PUNCT
ejpam-5951	35	7	18	18	NUM
ejpam-5951	35	8	(	(	PUNCT
ejpam-5951	35	9	2	2	NUM
ejpam-5951	35	10	)	)	PUNCT
ejpam-5951	35	11	(	(	PUNCT
ejpam-5951	35	12	2025	2025	NUM
ejpam-5951	35	13	)	)	PUNCT
ejpam-5951	35	14	,	,	PUNCT
ejpam-5951	35	15	5951	5951	NUM
ejpam-5951	35	16	3	3	NUM
ejpam-5951	35	17	of	of	ADP
ejpam-5951	35	18	15	15	NUM
ejpam-5951	35	19	let	let	VERB
ejpam-5951	35	20	us	we	PRON
ejpam-5951	35	21	consider	consider	VERB
ejpam-5951	35	22	,	,	PUNCT
ejpam-5951	35	23	γ	γ	X
ejpam-5951	35	24	is	be	AUX
ejpam-5951	35	25	the	the	DET
ejpam-5951	35	26	differentiable	differentiable	ADJ
ejpam-5951	35	27	and	and	CCONJ
ejpam-5951	35	28	finite	finite	VERB
ejpam-5951	35	29	dimensional	dimensional	ADJ
ejpam-5951	35	30	manifold	manifold	NOUN
ejpam-5951	35	31	.	.	PUNCT
ejpam-5951	36	1	we	we	PRON
ejpam-5951	36	2	write	write	VERB
ejpam-5951	36	3	the	the	DET
ejpam-5951	36	4	tangent	tangent	ADJ
ejpam-5951	36	5	space	space	NOUN
ejpam-5951	36	6	of	of	ADP
ejpam-5951	36	7	γ	γ	PROPN
ejpam-5951	36	8	,	,	PUNCT
ejpam-5951	36	9	for	for	ADP
ejpam-5951	36	10	all	all	DET
ejpam-5951	36	11	ζ	ζ	PROPN
ejpam-5951	36	12	∈	∈	PROPN
ejpam-5951	36	13	γ	γ	NOUN
ejpam-5951	36	14	as	as	ADP
ejpam-5951	36	15	gζγ	gζγ	NOUN
ejpam-5951	36	16	.	.	PUNCT
ejpam-5951	37	1	this	this	DET
ejpam-5951	37	2	gζγ	gζγ	NOUN
ejpam-5951	37	3	is	be	AUX
ejpam-5951	37	4	also	also	ADV
ejpam-5951	37	5	a	a	DET
ejpam-5951	37	6	vector	vector	NOUN
ejpam-5951	37	7	space	space	NOUN
ejpam-5951	37	8	and	and	CCONJ
ejpam-5951	37	9	its	its	PRON
ejpam-5951	37	10	dimension	dimension	NOUN
ejpam-5951	37	11	is	be	AUX
ejpam-5951	37	12	same	same	ADJ
ejpam-5951	37	13	as	as	ADP
ejpam-5951	37	14	the	the	DET
ejpam-5951	37	15	dimension	dimension	NOUN
ejpam-5951	37	16	of	of	ADP
ejpam-5951	37	17	γ	γ	PROPN
ejpam-5951	37	18	.	.	PROPN
ejpam-5951	38	1	also	also	ADV
ejpam-5951	38	2	,	,	PUNCT
ejpam-5951	38	3	the	the	DET
ejpam-5951	38	4	tangent	tangent	ADJ
ejpam-5951	38	5	bundle	bundle	NOUN
ejpam-5951	38	6	of	of	ADP
ejpam-5951	38	7	γ	γ	PROPN
ejpam-5951	38	8	is	be	AUX
ejpam-5951	38	9	denoted	denote	VERB
ejpam-5951	38	10	by	by	ADP
ejpam-5951	38	11	gγ	gγ	ADP
ejpam-5951	38	12	=	=	SYM
ejpam-5951	38	13	⋃	⋃	NOUN
ejpam-5951	38	14	ζ∈γ	ζ∈γ	VERB
ejpam-5951	38	15	gζγ	gζγ	NOUN
ejpam-5951	38	16	.	.	PUNCT
ejpam-5951	39	1	if	if	SCONJ
ejpam-5951	39	2	we	we	PRON
ejpam-5951	39	3	define	define	VERB
ejpam-5951	39	4	an	an	DET
ejpam-5951	39	5	inner	inner	ADJ
ejpam-5951	39	6	product	product	NOUN
ejpam-5951	39	7	rζ	rζ	NOUN
ejpam-5951	39	8	(	(	PUNCT
ejpam-5951	39	9	·	·	PUNCT
ejpam-5951	39	10	,	,	PUNCT
ejpam-5951	39	11	·	·	PUNCT
ejpam-5951	39	12	)	)	PUNCT
ejpam-5951	39	13	on	on	ADP
ejpam-5951	39	14	the	the	DET
ejpam-5951	39	15	tangent	tangent	ADJ
ejpam-5951	39	16	space	space	NOUN
ejpam-5951	39	17	gζγ	gζγ	NOUN
ejpam-5951	39	18	then	then	ADV
ejpam-5951	39	19	it	it	PRON
ejpam-5951	39	20	is	be	AUX
ejpam-5951	39	21	said	say	VERB
ejpam-5951	39	22	to	to	PART
ejpam-5951	39	23	be	be	AUX
ejpam-5951	39	24	a	a	DET
ejpam-5951	39	25	riemannian	riemannian	ADJ
ejpam-5951	39	26	metric	metric	NOUN
ejpam-5951	39	27	defined	define	VERB
ejpam-5951	39	28	on	on	ADP
ejpam-5951	39	29	gζγ	gζγ	NOUN
ejpam-5951	39	30	.	.	PUNCT
ejpam-5951	40	1	if	if	SCONJ
ejpam-5951	40	2	γ	γ	PROPN
ejpam-5951	40	3	can	can	AUX
ejpam-5951	40	4	be	be	AUX
ejpam-5951	40	5	endowed	endow	VERB
ejpam-5951	40	6	with	with	ADP
ejpam-5951	40	7	a	a	DET
ejpam-5951	40	8	riemannian	riemannian	ADJ
ejpam-5951	40	9	metric	metric	ADJ
ejpam-5951	40	10	rζ	rζ	NOUN
ejpam-5951	40	11	(	(	PUNCT
ejpam-5951	40	12	·	·	PUNCT
ejpam-5951	40	13	,	,	PUNCT
ejpam-5951	40	14	·	·	PUNCT
ejpam-5951	40	15	)	)	PUNCT
ejpam-5951	40	16	then	then	ADV
ejpam-5951	40	17	we	we	PRON
ejpam-5951	40	18	say	say	VERB
ejpam-5951	40	19	γ	γ	NOUN
ejpam-5951	40	20	is	be	AUX
ejpam-5951	40	21	a	a	DET
ejpam-5951	40	22	riemannian	riemannian	ADJ
ejpam-5951	40	23	manifold	manifold	NOUN
ejpam-5951	40	24	.	.	PUNCT
ejpam-5951	41	1	we	we	PRON
ejpam-5951	41	2	denote	denote	VERB
ejpam-5951	41	3	the	the	DET
ejpam-5951	41	4	corresponding	corresponding	ADJ
ejpam-5951	41	5	norm	norm	NOUN
ejpam-5951	41	6	for	for	ADP
ejpam-5951	41	7	the	the	DET
ejpam-5951	41	8	inner	inner	ADJ
ejpam-5951	41	9	product	product	NOUN
ejpam-5951	41	10	on	on	ADP
ejpam-5951	41	11	the	the	DET
ejpam-5951	41	12	tangent	tangent	ADJ
ejpam-5951	41	13	space	space	NOUN
ejpam-5951	41	14	gζγ	gζγ	NOUN
ejpam-5951	41	15	by	by	ADP
ejpam-5951	41	16	∥	∥	X
ejpam-5951	42	1	·	·	PUNCT
ejpam-5951	42	2	∥ζ	∥ζ	NOUN
ejpam-5951	42	3	.	.	PUNCT
ejpam-5951	43	1	a	a	DET
ejpam-5951	43	2	riemannian	riemannian	ADJ
ejpam-5951	43	3	manifold	manifold	NOUN
ejpam-5951	43	4	is	be	AUX
ejpam-5951	43	5	a	a	DET
ejpam-5951	43	6	manifold	manifold	NOUN
ejpam-5951	43	7	,	,	PUNCT
ejpam-5951	43	8	which	which	PRON
ejpam-5951	43	9	is	be	AUX
ejpam-5951	43	10	differentiable	differentiable	ADJ
ejpam-5951	43	11	endowed	endow	VERB
ejpam-5951	43	12	with	with	ADP
ejpam-5951	43	13	a	a	DET
ejpam-5951	43	14	riemannian	riemannian	ADJ
ejpam-5951	43	15	metric	metric	ADJ
ejpam-5951	43	16	r	r	NOUN
ejpam-5951	43	17	(	(	PUNCT
ejpam-5951	43	18	·	·	PUNCT
ejpam-5951	43	19	,	,	PUNCT
ejpam-5951	43	20	·	·	PUNCT
ejpam-5951	43	21	)	)	PUNCT
ejpam-5951	43	22	.	.	PUNCT
ejpam-5951	44	1	the	the	DET
ejpam-5951	44	2	length	length	NOUN
ejpam-5951	44	3	of	of	ADP
ejpam-5951	44	4	piecewise	piecewise	NOUN
ejpam-5951	44	5	smooth	smooth	ADJ
ejpam-5951	44	6	curve	curve	NOUN
ejpam-5951	44	7	υ	υ	NOUN
ejpam-5951	44	8	:	:	PUNCT
ejpam-5951	45	1	[	[	X
ejpam-5951	45	2	0	0	NUM
ejpam-5951	45	3	,	,	PUNCT
ejpam-5951	45	4	1	1	NUM
ejpam-5951	45	5	]	]	PUNCT
ejpam-5951	45	6	→	→	PUNCT
ejpam-5951	45	7	γ	γ	X
ejpam-5951	45	8	joining	join	VERB
ejpam-5951	45	9	ζ	ζ	NOUN
ejpam-5951	45	10	to	to	ADP
ejpam-5951	45	11	η	η	PROPN
ejpam-5951	45	12	(	(	PUNCT
ejpam-5951	45	13	i.e.	i.e.	X
ejpam-5951	45	14	υ(0	υ(0	NOUN
ejpam-5951	45	15	)	)	PUNCT
ejpam-5951	45	16	=	=	SYM
ejpam-5951	45	17	ζ	ζ	NOUN
ejpam-5951	45	18	and	and	CCONJ
ejpam-5951	45	19	υ(1	υ(1	PROPN
ejpam-5951	45	20	)	)	PUNCT
ejpam-5951	45	21	=	=	SYM
ejpam-5951	45	22	η	η	X
ejpam-5951	45	23	)	)	PUNCT
ejpam-5951	45	24	is	be	AUX
ejpam-5951	45	25	given	give	VERB
ejpam-5951	45	26	by	by	ADP
ejpam-5951	45	27	l(υ	l(υ	PROPN
ejpam-5951	45	28	)	)	PUNCT
ejpam-5951	45	29	=	=	PUNCT
ejpam-5951	46	1	1∫	1∫	NUM
ejpam-5951	46	2	0	0	NUM
ejpam-5951	46	3	∥υ′	∥υ′	NOUN
ejpam-5951	46	4	(	(	PUNCT
ejpam-5951	46	5	µ)∥dµ.	µ)∥dµ.	ADV
ejpam-5951	46	6	the	the	DET
ejpam-5951	46	7	riemannian	riemannian	ADJ
ejpam-5951	46	8	distance	distance	NOUN
ejpam-5951	46	9	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	46	10	,	,	PUNCT
ejpam-5951	46	11	η	η	NOUN
ejpam-5951	46	12	)	)	PUNCT
ejpam-5951	46	13	is	be	AUX
ejpam-5951	46	14	the	the	DET
ejpam-5951	46	15	minimal	minimal	ADJ
ejpam-5951	46	16	length	length	NOUN
ejpam-5951	46	17	over	over	ADP
ejpam-5951	46	18	the	the	DET
ejpam-5951	46	19	set	set	NOUN
ejpam-5951	46	20	of	of	ADP
ejpam-5951	46	21	all	all	DET
ejpam-5951	46	22	these	these	DET
ejpam-5951	46	23	curves	curve	NOUN
ejpam-5951	46	24	joining	join	VERB
ejpam-5951	46	25	ζ	ζ	NOUN
ejpam-5951	46	26	to	to	ADP
ejpam-5951	46	27	η	η	PROPN
ejpam-5951	46	28	,	,	PUNCT
ejpam-5951	46	29	which	which	PRON
ejpam-5951	46	30	includes	include	VERB
ejpam-5951	46	31	the	the	DET
ejpam-5951	46	32	original	original	ADJ
ejpam-5951	46	33	topology	topology	NOUN
ejpam-5951	46	34	on	on	ADP
ejpam-5951	46	35	γ	γ	PROPN
ejpam-5951	46	36	.	.	PUNCT
ejpam-5951	46	37	a	a	DET
ejpam-5951	46	38	riemannian	riemannian	ADJ
ejpam-5951	46	39	manifold	manifold	ADJ
ejpam-5951	46	40	γ	γ	NOUN
ejpam-5951	46	41	is	be	AUX
ejpam-5951	46	42	said	say	VERB
ejpam-5951	46	43	to	to	PART
ejpam-5951	46	44	be	be	AUX
ejpam-5951	46	45	complete	complete	ADJ
ejpam-5951	46	46	if	if	SCONJ
ejpam-5951	46	47	for	for	ADP
ejpam-5951	46	48	all	all	DET
ejpam-5951	46	49	ζ	ζ	PROPN
ejpam-5951	46	50	∈	∈	PROPN
ejpam-5951	46	51	γ	γ	NOUN
ejpam-5951	46	52	,	,	PUNCT
ejpam-5951	46	53	all	all	DET
ejpam-5951	46	54	geodesics	geodesic	NOUN
ejpam-5951	46	55	starting	start	VERB
ejpam-5951	46	56	from	from	ADP
ejpam-5951	46	57	ζ	ζ	NOUN
ejpam-5951	46	58	are	be	AUX
ejpam-5951	46	59	defined	define	VERB
ejpam-5951	46	60	for	for	ADP
ejpam-5951	46	61	all	all	DET
ejpam-5951	46	62	µ	µ	PROPN
ejpam-5951	46	63	∈	∈	PROPN
ejpam-5951	46	64	r.	r.	NOUN
ejpam-5951	46	65	a	a	DET
ejpam-5951	46	66	geodesic	geodesic	NOUN
ejpam-5951	46	67	joining	join	VERB
ejpam-5951	46	68	ζ	ζ	NOUN
ejpam-5951	46	69	to	to	ADP
ejpam-5951	46	70	η	η	PROPN
ejpam-5951	46	71	is	be	AUX
ejpam-5951	46	72	said	say	VERB
ejpam-5951	46	73	to	to	PART
ejpam-5951	46	74	be	be	AUX
ejpam-5951	46	75	minimal	minimal	ADJ
ejpam-5951	46	76	in	in	ADP
ejpam-5951	46	77	γ	γ	PROPN
ejpam-5951	46	78	if	if	SCONJ
ejpam-5951	46	79	the	the	DET
ejpam-5951	46	80	length	length	NOUN
ejpam-5951	46	81	of	of	ADP
ejpam-5951	46	82	the	the	DET
ejpam-5951	46	83	geodesic	geodesic	NOUN
ejpam-5951	46	84	is	be	AUX
ejpam-5951	46	85	equal	equal	ADJ
ejpam-5951	46	86	to	to	ADP
ejpam-5951	46	87	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	46	88	,	,	PUNCT
ejpam-5951	46	89	η	η	NOUN
ejpam-5951	46	90	)	)	PUNCT
ejpam-5951	46	91	.	.	PUNCT
ejpam-5951	47	1	the	the	DET
ejpam-5951	47	2	riemannian	riemannian	ADJ
ejpam-5951	47	3	manifold	manifold	ADJ
ejpam-5951	47	4	γ	γ	PROPN
ejpam-5951	47	5	having	have	VERB
ejpam-5951	47	6	the	the	DET
ejpam-5951	47	7	riemannian	riemannian	ADJ
ejpam-5951	47	8	distance	distance	NOUN
ejpam-5951	47	9	ρ	ρ	NOUN
ejpam-5951	47	10	is	be	AUX
ejpam-5951	47	11	also	also	ADV
ejpam-5951	47	12	a	a	DET
ejpam-5951	47	13	metric	metric	ADJ
ejpam-5951	47	14	space	space	NOUN
ejpam-5951	47	15	(	(	PUNCT
ejpam-5951	47	16	γ	γ	X
ejpam-5951	47	17	,	,	PUNCT
ejpam-5951	47	18	ρ	ρ	PROPN
ejpam-5951	47	19	)	)	PUNCT
ejpam-5951	47	20	.	.	PUNCT
ejpam-5951	48	1	definition	definition	NOUN
ejpam-5951	48	2	1	1	NUM
ejpam-5951	48	3	.	.	PUNCT
ejpam-5951	49	1	let	let	VERB
ejpam-5951	49	2	us	we	PRON
ejpam-5951	49	3	consider	consider	VERB
ejpam-5951	49	4	that	that	SCONJ
ejpam-5951	49	5	γ	γ	PROPN
ejpam-5951	49	6	is	be	AUX
ejpam-5951	49	7	a	a	DET
ejpam-5951	49	8	complete	complete	ADJ
ejpam-5951	49	9	riemannian	riemannian	ADJ
ejpam-5951	49	10	manifold	manifold	NOUN
ejpam-5951	49	11	.	.	PUNCT
ejpam-5951	50	1	we	we	PRON
ejpam-5951	50	2	define	define	VERB
ejpam-5951	50	3	the	the	DET
ejpam-5951	50	4	exponential	exponential	ADJ
ejpam-5951	50	5	map	map	NOUN
ejpam-5951	50	6	expζ	expζ	NOUN
ejpam-5951	50	7	:	:	PUNCT
ejpam-5951	50	8	gζγ	gζγ	NOUN
ejpam-5951	50	9	→	→	PUNCT
ejpam-5951	50	10	γ	γ	X
ejpam-5951	50	11	at	at	ADP
ejpam-5951	50	12	point	point	NOUN
ejpam-5951	50	13	ζ	ζ	PROPN
ejpam-5951	50	14	∈	∈	PROPN
ejpam-5951	50	15	γ	γ	X
ejpam-5951	50	16	by	by	ADP
ejpam-5951	50	17	expζ	expζ	PROPN
ejpam-5951	50	18	v	v	NOUN
ejpam-5951	50	19	=	=	SYM
ejpam-5951	50	20	υv(1	υv(1	PROPN
ejpam-5951	50	21	,	,	PUNCT
ejpam-5951	50	22	ζ	ζ	NOUN
ejpam-5951	50	23	)	)	PUNCT
ejpam-5951	50	24	for	for	ADP
ejpam-5951	50	25	all	all	DET
ejpam-5951	50	26	v	v	NOUN
ejpam-5951	50	27	∈	∈	PROPN
ejpam-5951	50	28	gζγ	gζγ	NOUN
ejpam-5951	50	29	,	,	PUNCT
ejpam-5951	50	30	where	where	SCONJ
ejpam-5951	50	31	υv	υv	PART
ejpam-5951	50	32	(	(	PUNCT
ejpam-5951	50	33	·	·	PUNCT
ejpam-5951	50	34	,	,	PUNCT
ejpam-5951	50	35	ζ	ζ	NOUN
ejpam-5951	50	36	)	)	PUNCT
ejpam-5951	50	37	is	be	AUX
ejpam-5951	50	38	the	the	DET
ejpam-5951	50	39	geodesic	geodesic	NOUN
ejpam-5951	50	40	with	with	ADP
ejpam-5951	50	41	the	the	DET
ejpam-5951	50	42	velocity	velocity	NOUN
ejpam-5951	50	43	v	v	NOUN
ejpam-5951	50	44	and	and	CCONJ
ejpam-5951	50	45	starting	start	VERB
ejpam-5951	50	46	from	from	ADP
ejpam-5951	50	47	the	the	DET
ejpam-5951	50	48	point	point	NOUN
ejpam-5951	50	49	ζ	ζ	NOUN
ejpam-5951	50	50	i.e.	i.e.	X
ejpam-5951	50	51	υ′	υ′	DET
ejpam-5951	50	52	v(0	v(0	PROPN
ejpam-5951	50	53	,	,	PUNCT
ejpam-5951	50	54	ζ	ζ	NOUN
ejpam-5951	50	55	)	)	PUNCT
ejpam-5951	50	56	=	=	SYM
ejpam-5951	50	57	v	v	NOUN
ejpam-5951	50	58	and	and	CCONJ
ejpam-5951	50	59	υv(0	υv(0	PROPN
ejpam-5951	50	60	,	,	PUNCT
ejpam-5951	50	61	ζ	ζ	NOUN
ejpam-5951	50	62	)	)	PUNCT
ejpam-5951	50	63	=	=	SYM
ejpam-5951	50	64	ζ	ζ	NOUN
ejpam-5951	51	1	[	[	X
ejpam-5951	51	2	16	16	NUM
ejpam-5951	51	3	]	]	PUNCT
ejpam-5951	51	4	.	.	PUNCT
ejpam-5951	52	1	we	we	PRON
ejpam-5951	52	2	also	also	ADV
ejpam-5951	52	3	know	know	VERB
ejpam-5951	52	4	that	that	SCONJ
ejpam-5951	52	5	for	for	ADP
ejpam-5951	52	6	all	all	DET
ejpam-5951	52	7	µ	µ	PRON
ejpam-5951	52	8	∈	∈	NOUN
ejpam-5951	52	9	r	r	NOUN
ejpam-5951	52	10	the	the	DET
ejpam-5951	52	11	exponential	exponential	ADJ
ejpam-5951	52	12	map	map	NOUN
ejpam-5951	52	13	expζ	expζ	NOUN
ejpam-5951	52	14	µv	µv	NOUN
ejpam-5951	52	15	=	=	SYM
ejpam-5951	52	16	υv(µ	υv(µ	NUM
ejpam-5951	52	17	,	,	PUNCT
ejpam-5951	52	18	ζ	ζ	NOUN
ejpam-5951	52	19	)	)	PUNCT
ejpam-5951	52	20	.	.	PUNCT
ejpam-5951	53	1	here	here	ADV
ejpam-5951	53	2	we	we	PRON
ejpam-5951	53	3	can	can	AUX
ejpam-5951	53	4	also	also	ADV
ejpam-5951	53	5	see	see	VERB
ejpam-5951	53	6	for	for	ADP
ejpam-5951	53	7	all	all	DET
ejpam-5951	53	8	zero	zero	NUM
ejpam-5951	53	9	tangent	tangent	NOUN
ejpam-5951	53	10	vector	vector	NOUN
ejpam-5951	53	11	,	,	PUNCT
ejpam-5951	53	12	exponential	exponential	ADJ
ejpam-5951	53	13	map	map	NOUN
ejpam-5951	53	14	expζ	expζ	NOUN
ejpam-5951	53	15	0	0	NUM
ejpam-5951	54	1	=	=	SYM
ejpam-5951	54	2	υv(0	υv(0	PROPN
ejpam-5951	54	3	,	,	PUNCT
ejpam-5951	54	4	ζ	ζ	NOUN
ejpam-5951	54	5	)	)	PUNCT
ejpam-5951	54	6	=	=	SYM
ejpam-5951	54	7	ζ	ζ	NOUN
ejpam-5951	54	8	.	.	PUNCT
ejpam-5951	55	1	the	the	DET
ejpam-5951	55	2	exponential	exponential	ADJ
ejpam-5951	55	3	map	map	NOUN
ejpam-5951	55	4	expζ	expζ	NOUN
ejpam-5951	55	5	is	be	AUX
ejpam-5951	55	6	differentiable	differentiable	ADJ
ejpam-5951	55	7	on	on	ADP
ejpam-5951	55	8	tζγ	tζγ	NOUN
ejpam-5951	55	9	for	for	ADP
ejpam-5951	55	10	all	all	DET
ejpam-5951	55	11	ζ	ζ	NOUN
ejpam-5951	55	12	∈	∈	NOUN
ejpam-5951	55	13	γ	γ	NOUN
ejpam-5951	55	14	and	and	CCONJ
ejpam-5951	55	15	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	55	16	,	,	PUNCT
ejpam-5951	55	17	η	η	NOUN
ejpam-5951	55	18	)	)	PUNCT
ejpam-5951	55	19	=	=	PUNCT
ejpam-5951	56	1	∥	∥	X
ejpam-5951	56	2	exp−1	exp−1	NOUN
ejpam-5951	56	3	ζ	ζ	NOUN
ejpam-5951	56	4	η∥	η∥	PROPN
ejpam-5951	56	5	for	for	ADP
ejpam-5951	56	6	all	all	DET
ejpam-5951	56	7	ζ	ζ	NOUN
ejpam-5951	56	8	,	,	PUNCT
ejpam-5951	56	9	η	η	PROPN
ejpam-5951	56	10	∈	∈	PROPN
ejpam-5951	56	11	γ	γ	PROPN
ejpam-5951	56	12	.	.	PROPN
ejpam-5951	56	13	definition	definition	NOUN
ejpam-5951	56	14	2	2	NUM
ejpam-5951	56	15	.	.	PUNCT
ejpam-5951	57	1	a	a	DET
ejpam-5951	57	2	riemannian	riemannian	ADJ
ejpam-5951	57	3	manifold	manifold	NOUN
ejpam-5951	57	4	of	of	ADP
ejpam-5951	57	5	non	non	ADJ
ejpam-5951	57	6	positive	positive	ADJ
ejpam-5951	57	7	sectional	sectional	ADJ
ejpam-5951	57	8	curvature	curvature	NOUN
ejpam-5951	57	9	is	be	AUX
ejpam-5951	57	10	said	say	VERB
ejpam-5951	57	11	to	to	PART
ejpam-5951	57	12	be	be	AUX
ejpam-5951	57	13	a	a	DET
ejpam-5951	57	14	hadamard	hadamard	ADJ
ejpam-5951	57	15	manifold	manifold	NOUN
ejpam-5951	57	16	if	if	SCONJ
ejpam-5951	57	17	it	it	PRON
ejpam-5951	57	18	is	be	AUX
ejpam-5951	57	19	complete	complete	ADJ
ejpam-5951	57	20	and	and	CCONJ
ejpam-5951	57	21	simply	simply	ADV
ejpam-5951	57	22	connected	connect	VERB
ejpam-5951	57	23	.	.	PUNCT
ejpam-5951	58	1	lemma	lemma	PROPN
ejpam-5951	58	2	1	1	NUM
ejpam-5951	58	3	.	.	PUNCT
ejpam-5951	59	1	[	[	X
ejpam-5951	59	2	17	17	NUM
ejpam-5951	59	3	]	]	PUNCT
ejpam-5951	59	4	.	.	PUNCT
ejpam-5951	60	1	(	(	PUNCT
ejpam-5951	60	2	1	1	X
ejpam-5951	60	3	)	)	PUNCT
ejpam-5951	60	4	for	for	ADP
ejpam-5951	60	5	all	all	DET
ejpam-5951	60	6	w	w	PROPN
ejpam-5951	60	7	,	,	PUNCT
ejpam-5951	60	8	u	u	NOUN
ejpam-5951	60	9	,	,	PUNCT
ejpam-5951	60	10	ς	ς	PROPN
ejpam-5951	60	11	,	,	PUNCT
ejpam-5951	60	12	η	η	PROPN
ejpam-5951	60	13	,	,	PUNCT
ejpam-5951	60	14	,	,	PUNCT
ejpam-5951	60	15	z	z	PROPN
ejpam-5951	60	16	∈	∈	PROPN
ejpam-5951	60	17	γ	γ	X
ejpam-5951	60	18	,	,	PUNCT
ejpam-5951	60	19	0	0	NUM
ejpam-5951	60	20	≤	≤	NUM
ejpam-5951	61	1	µ	µ	X
ejpam-5951	61	2	≤	≤	NUM
ejpam-5951	61	3	1	1	NUM
ejpam-5951	61	4	,	,	PUNCT
ejpam-5951	61	5	following	follow	VERB
ejpam-5951	61	6	hold	hold	NOUN
ejpam-5951	61	7	:	:	PUNCT
ejpam-5951	61	8	ρ(expη(1−	ρ(expη(1−	NUM
ejpam-5951	61	9	µ	µ	X
ejpam-5951	61	10	)	)	PUNCT
ejpam-5951	61	11	exp−1	exp−1	PROPN
ejpam-5951	61	12	η	η	PROPN
ejpam-5951	61	13	ς	ς	PROPN
ejpam-5951	61	14	,	,	PUNCT
ejpam-5951	61	15	z	z	NOUN
ejpam-5951	61	16	)	)	PUNCT
ejpam-5951	61	17	≤	≤	NOUN
ejpam-5951	61	18	µρ(η	µρ(η	ADP
ejpam-5951	61	19	,	,	PUNCT
ejpam-5951	61	20	z	z	NOUN
ejpam-5951	61	21	)	)	PUNCT
ejpam-5951	61	22	+	+	CCONJ
ejpam-5951	61	23	(	(	PUNCT
ejpam-5951	61	24	1−	1−	NUM
ejpam-5951	61	25	µ)ρ(ς	µ)ρ(ς	ADJ
ejpam-5951	61	26	,	,	PUNCT
ejpam-5951	61	27	z	z	NOUN
ejpam-5951	61	28	)	)	PUNCT
ejpam-5951	61	29	;	;	PUNCT
ejpam-5951	61	30	ρ2(expη(1−	ρ2(expη(1−	PROPN
ejpam-5951	61	31	µ	µ	NOUN
ejpam-5951	61	32	)	)	PUNCT
ejpam-5951	61	33	exp−1	exp−1	PROPN
ejpam-5951	61	34	η	η	PROPN
ejpam-5951	61	35	ς	ς	PROPN
ejpam-5951	61	36	,	,	PUNCT
ejpam-5951	61	37	z	z	NOUN
ejpam-5951	61	38	)	)	PUNCT
ejpam-5951	61	39	≤	≤	NOUN
ejpam-5951	61	40	µρ2(η	µρ2(η	PROPN
ejpam-5951	61	41	,	,	PUNCT
ejpam-5951	61	42	z	z	NOUN
ejpam-5951	61	43	)	)	PUNCT
ejpam-5951	61	44	+	+	CCONJ
ejpam-5951	61	45	(	(	PUNCT
ejpam-5951	61	46	1−	1−	NUM
ejpam-5951	61	47	µ)ρ2(ς	µ)ρ2(ς	NOUN
ejpam-5951	61	48	,	,	PUNCT
ejpam-5951	61	49	z)−	z)−	PROPN
ejpam-5951	61	50	µ(1−	µ(1−	NOUN
ejpam-5951	61	51	µ)ρ2(η	µ)ρ2(η	SYM
ejpam-5951	61	52	,	,	PUNCT
ejpam-5951	61	53	ς	ς	NOUN
ejpam-5951	61	54	)	)	PUNCT
ejpam-5951	61	55	;	;	PUNCT
ejpam-5951	61	56	ρ(expη(1−	ρ(expη(1−	NUM
ejpam-5951	61	57	µ	µ	X
ejpam-5951	61	58	)	)	PUNCT
ejpam-5951	61	59	exp−1	exp−1	PROPN
ejpam-5951	61	60	η	η	PROPN
ejpam-5951	61	61	ς	ς	PROPN
ejpam-5951	61	62	,	,	PUNCT
ejpam-5951	61	63	expu(1−	expu(1−	PROPN
ejpam-5951	61	64	µ	µ	X
ejpam-5951	61	65	)	)	PUNCT
ejpam-5951	61	66	exp−1	exp−1	PROPN
ejpam-5951	61	67	u	u	NOUN
ejpam-5951	61	68	ζ	ζ	NOUN
ejpam-5951	61	69	)	)	PUNCT
ejpam-5951	61	70	≤	≤	NOUN
ejpam-5951	61	71	µρ(η	µρ(η	PROPN
ejpam-5951	61	72	,	,	PUNCT
ejpam-5951	61	73	u	u	NOUN
ejpam-5951	61	74	)	)	PUNCT
ejpam-5951	61	75	+	+	CCONJ
ejpam-5951	61	76	(	(	PUNCT
ejpam-5951	61	77	1−	1−	NUM
ejpam-5951	61	78	µ)ρ(ς	µ)ρ(ς	ADJ
ejpam-5951	61	79	,	,	PUNCT
ejpam-5951	61	80	ζ	ζ	NOUN
ejpam-5951	61	81	)	)	PUNCT
ejpam-5951	61	82	.	.	PUNCT
ejpam-5951	62	1	(	(	PUNCT
ejpam-5951	62	2	2	2	X
ejpam-5951	62	3	)	)	PUNCT
ejpam-5951	62	4	let	let	VERB
ejpam-5951	62	5	υ	υ	NOUN
ejpam-5951	62	6	:	:	PUNCT
ejpam-5951	63	1	[	[	X
ejpam-5951	63	2	0	0	NUM
ejpam-5951	63	3	,	,	PUNCT
ejpam-5951	63	4	1	1	NUM
ejpam-5951	63	5	]	]	PUNCT
ejpam-5951	63	6	→	→	PUNCT
ejpam-5951	63	7	γ	γ	X
ejpam-5951	63	8	be	be	AUX
ejpam-5951	63	9	a	a	DET
ejpam-5951	63	10	geodesic	geodesic	NOUN
ejpam-5951	63	11	joining	join	VERB
ejpam-5951	63	12	points	point	NOUN
ejpam-5951	63	13	η	η	PROPN
ejpam-5951	63	14	to	to	ADP
ejpam-5951	63	15	ς	ς	PROPN
ejpam-5951	63	16	.	.	PUNCT
ejpam-5951	63	17	then	then	ADV
ejpam-5951	63	18	ρ(υ(µ1),υ(µ2	ρ(υ(µ1),υ(µ2	NUM
ejpam-5951	63	19	)	)	PUNCT
ejpam-5951	63	20	)	)	PUNCT
ejpam-5951	64	1	=	=	PUNCT
ejpam-5951	64	2	|µ1	|µ1	VERB
ejpam-5951	64	3	−	−	PROPN
ejpam-5951	64	4	µ2|ρ(η	µ2|ρ(η	PROPN
ejpam-5951	64	5	,	,	PUNCT
ejpam-5951	64	6	ς	ς	NOUN
ejpam-5951	64	7	)	)	PUNCT
ejpam-5951	64	8	for	for	ADP
ejpam-5951	64	9	all	all	DET
ejpam-5951	64	10	µ1	µ1	PROPN
ejpam-5951	64	11	,	,	PUNCT
ejpam-5951	64	12	µ2	µ2	PROPN
ejpam-5951	64	13	∈	∈	PROPN
ejpam-5951	65	1	[	[	X
ejpam-5951	65	2	0	0	NUM
ejpam-5951	65	3	,	,	PUNCT
ejpam-5951	65	4	1	1	NUM
ejpam-5951	65	5	]	]	PUNCT
ejpam-5951	65	6	.	.	PUNCT
ejpam-5951	66	1	p.	p.	NOUN
ejpam-5951	66	2	patel	patel	PROPN
ejpam-5951	66	3	,	,	PUNCT
ejpam-5951	66	4	r.	r.	PROPN
ejpam-5951	66	5	shukla	shukla	PROPN
ejpam-5951	66	6	/	/	SYM
ejpam-5951	66	7	eur	eur	PROPN
ejpam-5951	66	8	.	.	PUNCT
ejpam-5951	67	1	j.	j.	PROPN
ejpam-5951	67	2	pure	pure	PROPN
ejpam-5951	67	3	appl	appl	PROPN
ejpam-5951	67	4	.	.	PROPN
ejpam-5951	67	5	math	math	PROPN
ejpam-5951	67	6	,	,	PUNCT
ejpam-5951	67	7	18	18	NUM
ejpam-5951	67	8	(	(	PUNCT
ejpam-5951	67	9	2	2	NUM
ejpam-5951	67	10	)	)	PUNCT
ejpam-5951	67	11	(	(	PUNCT
ejpam-5951	67	12	2025	2025	NUM
ejpam-5951	67	13	)	)	PUNCT
ejpam-5951	67	14	,	,	PUNCT
ejpam-5951	67	15	5951	5951	NUM
ejpam-5951	67	16	4	4	NUM
ejpam-5951	67	17	of	of	ADP
ejpam-5951	67	18	15	15	NUM
ejpam-5951	67	19	proposition	proposition	NOUN
ejpam-5951	67	20	1	1	NUM
ejpam-5951	67	21	.	.	PUNCT
ejpam-5951	68	1	[	[	X
ejpam-5951	68	2	18	18	NUM
ejpam-5951	68	3	]	]	PUNCT
ejpam-5951	68	4	.	.	PUNCT
ejpam-5951	68	5	expζ	expζ	PROPN
ejpam-5951	68	6	:	:	PUNCT
ejpam-5951	68	7	gζγ	gζγ	NOUN
ejpam-5951	68	8	→	→	PUNCT
ejpam-5951	68	9	γ	γ	X
ejpam-5951	68	10	is	be	AUX
ejpam-5951	68	11	said	say	VERB
ejpam-5951	68	12	to	to	PART
ejpam-5951	68	13	be	be	AUX
ejpam-5951	68	14	a	a	DET
ejpam-5951	68	15	diffeomorphism	diffeomorphism	NOUN
ejpam-5951	68	16	for	for	ADP
ejpam-5951	68	17	all	all	DET
ejpam-5951	68	18	ζ	ζ	PROPN
ejpam-5951	68	19	∈	∈	PROPN
ejpam-5951	68	20	γ	γ	X
ejpam-5951	68	21	,	,	PUNCT
ejpam-5951	68	22	any	any	DET
ejpam-5951	68	23	pair	pair	NOUN
ejpam-5951	68	24	of	of	ADP
ejpam-5951	68	25	points	point	NOUN
ejpam-5951	68	26	ζ	ζ	PROPN
ejpam-5951	68	27	,	,	PUNCT
ejpam-5951	68	28	η	η	PROPN
ejpam-5951	68	29	∈	∈	PROPN
ejpam-5951	68	30	γ	γ	X
ejpam-5951	68	31	,	,	PUNCT
ejpam-5951	68	32	there	there	PRON
ejpam-5951	68	33	exists	exist	VERB
ejpam-5951	68	34	a	a	DET
ejpam-5951	68	35	unique	unique	ADJ
ejpam-5951	68	36	normalized	normalize	VERB
ejpam-5951	68	37	geodesic	geodesic	ADJ
ejpam-5951	68	38	υ	υ	NOUN
ejpam-5951	68	39	:	:	PUNCT
ejpam-5951	69	1	[	[	X
ejpam-5951	69	2	0	0	NUM
ejpam-5951	69	3	,	,	PUNCT
ejpam-5951	69	4	1	1	NUM
ejpam-5951	69	5	]	]	PUNCT
ejpam-5951	69	6	→	→	PUNCT
ejpam-5951	69	7	γ	γ	X
ejpam-5951	69	8	joining	join	VERB
ejpam-5951	69	9	the	the	DET
ejpam-5951	69	10	points	point	NOUN
ejpam-5951	69	11	ζ	ζ	NOUN
ejpam-5951	69	12	=	=	SYM
ejpam-5951	69	13	υ(0	υ(0	PROPN
ejpam-5951	69	14	)	)	PUNCT
ejpam-5951	69	15	to	to	ADP
ejpam-5951	69	16	η	η	PROPN
ejpam-5951	69	17	=	=	PROPN
ejpam-5951	69	18	υ(1	υ(1	PROPN
ejpam-5951	69	19	)	)	PUNCT
ejpam-5951	69	20	,	,	PUNCT
ejpam-5951	69	21	in	in	ADP
ejpam-5951	69	22	fact	fact	NOUN
ejpam-5951	69	23	it	it	PRON
ejpam-5951	69	24	is	be	AUX
ejpam-5951	69	25	a	a	DET
ejpam-5951	69	26	minimal	minimal	ADJ
ejpam-5951	69	27	geodesic	geodesic	NOUN
ejpam-5951	69	28	defined	define	VERB
ejpam-5951	69	29	by	by	ADP
ejpam-5951	69	30	υ(µ	υ(µ	PROPN
ejpam-5951	69	31	)	)	PUNCT
ejpam-5951	69	32	=	=	SYM
ejpam-5951	69	33	expζ	expζ	NOUN
ejpam-5951	69	34	µ	µ	X
ejpam-5951	69	35	exp−1	exp−1	PROPN
ejpam-5951	69	36	ζ	ζ	PROPN
ejpam-5951	69	37	η	η	PROPN
ejpam-5951	69	38	for	for	ADP
ejpam-5951	69	39	all	all	DET
ejpam-5951	69	40	0	0	NUM
ejpam-5951	69	41	≤	≤	NUM
ejpam-5951	69	42	µ	µ	X
ejpam-5951	69	43	≤	≤	NUM
ejpam-5951	69	44	1	1	NUM
ejpam-5951	69	45	.	.	PUNCT
ejpam-5951	70	1	definition	definition	NOUN
ejpam-5951	70	2	3	3	NUM
ejpam-5951	70	3	.	.	PUNCT
ejpam-5951	71	1	the	the	DET
ejpam-5951	71	2	map	map	NOUN
ejpam-5951	71	3	g	g	NOUN
ejpam-5951	71	4	:	:	PUNCT
ejpam-5951	71	5	b	b	X
ejpam-5951	71	6	→	→	SYM
ejpam-5951	71	7	b	b	PROPN
ejpam-5951	71	8	is	be	AUX
ejpam-5951	71	9	called	call	VERB
ejpam-5951	71	10	as	as	ADP
ejpam-5951	71	11	(	(	PUNCT
ejpam-5951	71	12	i	i	NOUN
ejpam-5951	71	13	)	)	PUNCT
ejpam-5951	71	14	nonexpansive	nonexpansive	PROPN
ejpam-5951	71	15	ρ(g(ς	ρ(g(ς	PROPN
ejpam-5951	71	16	)	)	PUNCT
ejpam-5951	71	17	,	,	PUNCT
ejpam-5951	71	18	g(η	g(η	PROPN
ejpam-5951	71	19	)	)	PUNCT
ejpam-5951	71	20	)	)	PUNCT
ejpam-5951	71	21	≤	≤	PROPN
ejpam-5951	71	22	ρ(ς	ρ(ς	PROPN
ejpam-5951	71	23	,	,	PUNCT
ejpam-5951	71	24	η	η	NOUN
ejpam-5951	71	25	)	)	PUNCT
ejpam-5951	71	26	for	for	ADP
ejpam-5951	71	27	all	all	DET
ejpam-5951	71	28	ς	ς	PROPN
ejpam-5951	71	29	,	,	PUNCT
ejpam-5951	71	30	η	η	PROPN
ejpam-5951	71	31	∈	∈	PROPN
ejpam-5951	71	32	b	b	PROPN
ejpam-5951	71	33	,	,	PUNCT
ejpam-5951	71	34	(	(	PUNCT
ejpam-5951	71	35	ii	ii	NOUN
ejpam-5951	71	36	)	)	PUNCT
ejpam-5951	71	37	firmly	firmly	ADV
ejpam-5951	71	38	nonexpansive	nonexpansive	ADJ
ejpam-5951	71	39	,	,	PUNCT
ejpam-5951	71	40	if	if	SCONJ
ejpam-5951	71	41	for	for	ADP
ejpam-5951	71	42	all	all	DET
ejpam-5951	71	43	ς	ς	PROPN
ejpam-5951	71	44	,	,	PUNCT
ejpam-5951	71	45	η	η	PROPN
ejpam-5951	71	46	∈	∈	PROPN
ejpam-5951	71	47	b	b	PROPN
ejpam-5951	71	48	,	,	PUNCT
ejpam-5951	71	49	function	function	NOUN
ejpam-5951	71	50	ϕ	ϕ	NOUN
ejpam-5951	71	51	:	:	PUNCT
ejpam-5951	72	1	[	[	X
ejpam-5951	72	2	0	0	NUM
ejpam-5951	72	3	,	,	PUNCT
ejpam-5951	72	4	1	1	NUM
ejpam-5951	72	5	]	]	PUNCT
ejpam-5951	72	6	→	→	X
ejpam-5951	72	7	[	[	X
ejpam-5951	72	8	0,+∞	0,+∞	NUM
ejpam-5951	72	9	]	]	X
ejpam-5951	72	10	defined	define	VERB
ejpam-5951	72	11	by	by	ADP
ejpam-5951	72	12	ϕ(t	ϕ(t	NUM
ejpam-5951	72	13	)	)	PUNCT
ejpam-5951	73	1	=	=	SYM
ejpam-5951	73	2	ρ	ρ	PROPN
ejpam-5951	73	3	(	(	PUNCT
ejpam-5951	73	4	expη	expη	PROPN
ejpam-5951	73	5	t	t	PROPN
ejpam-5951	73	6	exp	exp	NOUN
ejpam-5951	73	7	−1	−1	PROPN
ejpam-5951	73	8	η	η	PROPN
ejpam-5951	73	9	g(η	g(η	PROPN
ejpam-5951	73	10	)	)	PUNCT
ejpam-5951	73	11	,	,	PUNCT
ejpam-5951	73	12	expς	expς	PROPN
ejpam-5951	73	13	t	t	PROPN
ejpam-5951	73	14	exp	exp	NOUN
ejpam-5951	73	15	−1	−1	NOUN
ejpam-5951	73	16	ς	ς	PROPN
ejpam-5951	73	17	g(ς	g(ς	PROPN
ejpam-5951	73	18	)	)	PUNCT
ejpam-5951	73	19	)	)	PUNCT
ejpam-5951	73	20	for	for	ADP
ejpam-5951	73	21	all	all	PRON
ejpam-5951	73	22	0	0	NUM
ejpam-5951	73	23	≤	≤	NUM
ejpam-5951	73	24	t	t	NOUN
ejpam-5951	73	25	≤	≤	NOUN
ejpam-5951	73	26	1	1	NUM
ejpam-5951	73	27	is	be	AUX
ejpam-5951	73	28	nonincreasing	nonincrease	VERB
ejpam-5951	73	29	[	[	X
ejpam-5951	73	30	18	18	NUM
ejpam-5951	73	31	]	]	PUNCT
ejpam-5951	73	32	.	.	PUNCT
ejpam-5951	74	1	(	(	PUNCT
ejpam-5951	74	2	iii	iii	NOUN
ejpam-5951	74	3	)	)	PUNCT
ejpam-5951	74	4	β	β	NOUN
ejpam-5951	74	5	-	-	ADJ
ejpam-5951	74	6	strict	strict	ADJ
ejpam-5951	74	7	pseudocontractive	pseudocontractive	NOUN
ejpam-5951	74	8	if	if	SCONJ
ejpam-5951	74	9	there	there	PRON
ejpam-5951	74	10	exists	exist	VERB
ejpam-5951	74	11	β	β	X
ejpam-5951	74	12	∈	∈	PROPN
ejpam-5951	75	1	[	[	X
ejpam-5951	75	2	0	0	NUM
ejpam-5951	75	3	,	,	PUNCT
ejpam-5951	75	4	1	1	NUM
ejpam-5951	75	5	)	)	PUNCT
ejpam-5951	75	6	such	such	ADJ
ejpam-5951	75	7	that	that	DET
ejpam-5951	75	8	ρ2(g(η	ρ2(g(η	NUM
ejpam-5951	75	9	)	)	PUNCT
ejpam-5951	75	10	,	,	PUNCT
ejpam-5951	75	11	g(ς	g(ς	PROPN
ejpam-5951	75	12	)	)	PUNCT
ejpam-5951	75	13	)	)	PUNCT
ejpam-5951	76	1	≤	≤	PUNCT
ejpam-5951	77	1	ρ2(η	ρ2(η	NUM
ejpam-5951	77	2	,	,	PUNCT
ejpam-5951	77	3	ς	ς	NOUN
ejpam-5951	77	4	)	)	PUNCT
ejpam-5951	77	5	+	+	CCONJ
ejpam-5951	77	6	β∥pη	β∥pη	NOUN
ejpam-5951	77	7	,	,	PUNCT
ejpam-5951	77	8	ς	ς	PROPN
ejpam-5951	77	9	exp	exp	NOUN
ejpam-5951	77	10	−1	−1	NOUN
ejpam-5951	77	11	ς	ς	PROPN
ejpam-5951	77	12	g(ς)−	g(ς)−	PROPN
ejpam-5951	77	13	exp−1	exp−1	PROPN
ejpam-5951	77	14	η	η	PROPN
ejpam-5951	77	15	g(η)∥2	g(η)∥2	PROPN
ejpam-5951	77	16	,	,	PUNCT
ejpam-5951	77	17	for	for	ADP
ejpam-5951	77	18	all	all	DET
ejpam-5951	77	19	η	η	PROPN
ejpam-5951	77	20	,	,	PUNCT
ejpam-5951	77	21	ς	ς	PROPN
ejpam-5951	77	22	∈	∈	PROPN
ejpam-5951	77	23	b.	b.	PROPN
ejpam-5951	77	24	note	note	VERB
ejpam-5951	77	25	that	that	SCONJ
ejpam-5951	77	26	the	the	DET
ejpam-5951	77	27	mapping	mapping	NOUN
ejpam-5951	77	28	g	g	NOUN
ejpam-5951	77	29	is	be	AUX
ejpam-5951	77	30	nonexpansive	nonexpansive	ADJ
ejpam-5951	77	31	if	if	SCONJ
ejpam-5951	77	32	and	and	CCONJ
ejpam-5951	77	33	only	only	ADV
ejpam-5951	77	34	if	if	SCONJ
ejpam-5951	77	35	it	it	PRON
ejpam-5951	77	36	is	be	AUX
ejpam-5951	77	37	0	0	NUM
ejpam-5951	77	38	-	-	PUNCT
ejpam-5951	77	39	strict	strict	ADJ
ejpam-5951	77	40	pseudocontractive	pseudocontractive	NOUN
ejpam-5951	77	41	.	.	PUNCT
ejpam-5951	77	42	suppose	suppose	VERB
ejpam-5951	77	43	b	b	NOUN
ejpam-5951	77	44	is	be	AUX
ejpam-5951	77	45	a	a	DET
ejpam-5951	77	46	geodesic	geodesic	ADJ
ejpam-5951	77	47	convex	convex	NOUN
ejpam-5951	77	48	and	and	CCONJ
ejpam-5951	77	49	closed	closed	ADJ
ejpam-5951	77	50	subset	subset	NOUN
ejpam-5951	77	51	of	of	ADP
ejpam-5951	77	52	the	the	DET
ejpam-5951	77	53	given	give	VERB
ejpam-5951	77	54	hadamard	hadamard	PROPN
ejpam-5951	77	55	manifold	manifold	ADJ
ejpam-5951	77	56	γ	γ	PROPN
ejpam-5951	77	57	.	.	PUNCT
ejpam-5951	78	1	the	the	DET
ejpam-5951	78	2	projection	projection	NOUN
ejpam-5951	78	3	map	map	NOUN
ejpam-5951	78	4	onto	onto	ADP
ejpam-5951	78	5	the	the	DET
ejpam-5951	78	6	geodesic	geodesic	ADJ
ejpam-5951	78	7	convex	convex	NOUN
ejpam-5951	78	8	and	and	CCONJ
ejpam-5951	78	9	closed	closed	ADJ
ejpam-5951	78	10	sets	set	NOUN
ejpam-5951	78	11	can	can	AUX
ejpam-5951	78	12	also	also	ADV
ejpam-5951	78	13	defined	define	VERB
ejpam-5951	78	14	in	in	ADP
ejpam-5951	78	15	the	the	DET
ejpam-5951	78	16	setting	setting	NOUN
ejpam-5951	78	17	of	of	ADP
ejpam-5951	78	18	linear	linear	ADJ
ejpam-5951	78	19	metric	metric	ADJ
ejpam-5951	78	20	spaces	space	NOUN
ejpam-5951	78	21	.	.	PUNCT
ejpam-5951	79	1	a	a	DET
ejpam-5951	79	2	projection	projection	NOUN
ejpam-5951	79	3	mapping	mapping	NOUN
ejpam-5951	79	4	pb	pb	X
ejpam-5951	79	5	(	(	PUNCT
ejpam-5951	79	6	·	·	PUNCT
ejpam-5951	79	7	)	)	PUNCT
ejpam-5951	79	8	:	:	PUNCT
ejpam-5951	79	9	γ	γ	X
ejpam-5951	79	10	→	→	SYM
ejpam-5951	79	11	b	b	PROPN
ejpam-5951	79	12	is	be	AUX
ejpam-5951	79	13	given	give	VERB
ejpam-5951	79	14	by	by	ADP
ejpam-5951	79	15	for	for	ADP
ejpam-5951	79	16	any	any	DET
ejpam-5951	79	17	ζ	ζ	NOUN
ejpam-5951	79	18	∈	∈	PROPN
ejpam-5951	79	19	γ	γ	NOUN
ejpam-5951	79	20	pb(ζ	pb(ζ	PUNCT
ejpam-5951	79	21	)	)	PUNCT
ejpam-5951	79	22	=	=	PRON
ejpam-5951	79	23	{	{	PUNCT
ejpam-5951	79	24	w	w	PROPN
ejpam-5951	79	25	∈	∈	PROPN
ejpam-5951	79	26	b	b	PROPN
ejpam-5951	79	27	:	:	PUNCT
ejpam-5951	79	28	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	79	29	,	,	PUNCT
ejpam-5951	79	30	w	w	NOUN
ejpam-5951	79	31	)	)	PUNCT
ejpam-5951	79	32	≤	≤	NOUN
ejpam-5951	79	33	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	79	34	,	,	PUNCT
ejpam-5951	79	35	µ	µ	NOUN
ejpam-5951	79	36	)	)	PUNCT
ejpam-5951	79	37	,	,	PUNCT
ejpam-5951	79	38	for	for	ADP
ejpam-5951	79	39	all	all	DET
ejpam-5951	79	40	µ	µ	PRON
ejpam-5951	79	41	∈	∈	ADJ
ejpam-5951	79	42	b	b	NOUN
ejpam-5951	79	43	}	}	PUNCT
ejpam-5951	79	44	.	.	PUNCT
ejpam-5951	80	1	proposition	proposition	NOUN
ejpam-5951	80	2	2	2	NUM
ejpam-5951	80	3	.	.	PUNCT
ejpam-5951	81	1	[	[	X
ejpam-5951	81	2	19	19	NUM
ejpam-5951	81	3	]	]	PUNCT
ejpam-5951	81	4	suppose	suppose	PUNCT
ejpam-5951	81	5	b	b	X
ejpam-5951	81	6	̸=	̸=	PROPN
ejpam-5951	81	7	∅	∅	NOUN
ejpam-5951	81	8	be	be	AUX
ejpam-5951	81	9	closed	close	VERB
ejpam-5951	81	10	and	and	CCONJ
ejpam-5951	81	11	geodesic	geodesic	ADJ
ejpam-5951	81	12	convex	convex	NOUN
ejpam-5951	81	13	subset	subset	NOUN
ejpam-5951	81	14	of	of	ADP
ejpam-5951	81	15	γ	γ	PROPN
ejpam-5951	81	16	.	.	PUNCT
ejpam-5951	82	1	then	then	ADV
ejpam-5951	82	2	we	we	PRON
ejpam-5951	82	3	have	have	VERB
ejpam-5951	82	4	:	:	PUNCT
ejpam-5951	82	5	(	(	PUNCT
ejpam-5951	82	6	1	1	X
ejpam-5951	82	7	)	)	PUNCT
ejpam-5951	82	8	pb	pb	ADP
ejpam-5951	82	9	is	be	AUX
ejpam-5951	82	10	a	a	DET
ejpam-5951	82	11	single	single	ADJ
ejpam-5951	82	12	valued	value	VERB
ejpam-5951	82	13	and	and	CCONJ
ejpam-5951	82	14	firmly	firmly	ADV
ejpam-5951	82	15	nonexpansive	nonexpansive	ADJ
ejpam-5951	82	16	mapping	mapping	NOUN
ejpam-5951	82	17	;	;	PUNCT
ejpam-5951	82	18	(	(	PUNCT
ejpam-5951	82	19	2	2	X
ejpam-5951	82	20	)	)	PUNCT
ejpam-5951	82	21	for	for	ADP
ejpam-5951	82	22	all	all	DET
ejpam-5951	82	23	ζ	ζ	PROPN
ejpam-5951	82	24	∈	∈	PROPN
ejpam-5951	82	25	γ	γ	X
ejpam-5951	82	26	,	,	PUNCT
ejpam-5951	82	27	ω	ω	NOUN
ejpam-5951	82	28	=	=	PUNCT
ejpam-5951	82	29	pb(ζ	pb(ζ	CCONJ
ejpam-5951	82	30	)	)	PUNCT
ejpam-5951	83	1	if	if	SCONJ
ejpam-5951	83	2	and	and	CCONJ
ejpam-5951	83	3	only	only	ADV
ejpam-5951	83	4	if	if	SCONJ
ejpam-5951	83	5	r(exp−1	r(exp−1	PROPN
ejpam-5951	83	6	ω	ω	NUM
ejpam-5951	83	7	ζ	ζ	NOUN
ejpam-5951	83	8	,	,	PUNCT
ejpam-5951	83	9	exp−1	exp−1	PROPN
ejpam-5951	83	10	ω	ω	PROPN
ejpam-5951	83	11	ϑ	ϑ	NOUN
ejpam-5951	83	12	)	)	PUNCT
ejpam-5951	83	13	≤	≤	NOUN
ejpam-5951	83	14	0	0	NUM
ejpam-5951	83	15	,	,	PUNCT
ejpam-5951	83	16	for	for	ADP
ejpam-5951	83	17	all	all	DET
ejpam-5951	83	18	ϑ	ϑ	PRON
ejpam-5951	83	19	∈	∈	PROPN
ejpam-5951	83	20	b	b	NOUN
ejpam-5951	83	21	;	;	PUNCT
ejpam-5951	83	22	(	(	PUNCT
ejpam-5951	83	23	3	3	X
ejpam-5951	83	24	)	)	PUNCT
ejpam-5951	83	25	if	if	SCONJ
ejpam-5951	83	26	pb	pb	ADV
ejpam-5951	83	27	is	be	AUX
ejpam-5951	83	28	firmly	firmly	ADV
ejpam-5951	83	29	nonexpansive	nonexpansive	ADJ
ejpam-5951	83	30	.	.	PUNCT
ejpam-5951	84	1	ρ2(ω	ρ2(ω	NUM
ejpam-5951	84	2	,	,	PUNCT
ejpam-5951	84	3	ν	ν	NOUN
ejpam-5951	84	4	)	)	PUNCT
ejpam-5951	84	5	+	+	NUM
ejpam-5951	85	1	ρ2(ω	ρ2(ω	PROPN
ejpam-5951	85	2	,	,	PUNCT
ejpam-5951	85	3	ζ	ζ	NOUN
ejpam-5951	85	4	)	)	PUNCT
ejpam-5951	85	5	≤	≤	NOUN
ejpam-5951	86	1	ρ2(ζ	ρ2(ζ	PROPN
ejpam-5951	86	2	,	,	PUNCT
ejpam-5951	86	3	ν	ν	NOUN
ejpam-5951	86	4	)	)	PUNCT
ejpam-5951	86	5	,	,	PUNCT
ejpam-5951	86	6	for	for	ADP
ejpam-5951	86	7	all	all	DET
ejpam-5951	86	8	ζ	ζ	PROPN
ejpam-5951	86	9	∈	∈	PROPN
ejpam-5951	86	10	γ	γ	X
ejpam-5951	86	11	,	,	PUNCT
ejpam-5951	86	12	ν	ν	PROPN
ejpam-5951	86	13	∈	∈	PROPN
ejpam-5951	86	14	b	b	NOUN
ejpam-5951	86	15	,	,	PUNCT
ejpam-5951	86	16	here	here	ADV
ejpam-5951	86	17	ω	ω	X
ejpam-5951	86	18	=	=	PUNCT
ejpam-5951	86	19	pb(ζ	pb(ζ	X
ejpam-5951	86	20	)	)	PUNCT
ejpam-5951	86	21	.	.	PUNCT
ejpam-5951	87	1	lemma	lemma	PROPN
ejpam-5951	87	2	2	2	NUM
ejpam-5951	87	3	.	.	PUNCT
ejpam-5951	88	1	[	[	X
ejpam-5951	88	2	20	20	NUM
ejpam-5951	88	3	]	]	PUNCT
ejpam-5951	88	4	suppose	suppose	VERB
ejpam-5951	88	5	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	88	6	,	,	PUNCT
ejpam-5951	88	7	ζ2	ζ2	NOUN
ejpam-5951	88	8	,	,	PUNCT
ejpam-5951	88	9	ζ3	ζ3	NOUN
ejpam-5951	88	10	)	)	PUNCT
ejpam-5951	88	11	is	be	AUX
ejpam-5951	88	12	a	a	DET
ejpam-5951	88	13	geodesic	geodesic	ADJ
ejpam-5951	88	14	triangle	triangle	NOUN
ejpam-5951	88	15	in	in	ADP
ejpam-5951	88	16	γ	γ	PROPN
ejpam-5951	88	17	then	then	ADV
ejpam-5951	88	18	there	there	PRON
ejpam-5951	88	19	exists	exist	VERB
ejpam-5951	88	20	a	a	DET
ejpam-5951	88	21	triangle	triangle	NOUN
ejpam-5951	88	22	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	88	23	,	,	PUNCT
ejpam-5951	88	24	ζ2	ζ2	NOUN
ejpam-5951	88	25	,	,	PUNCT
ejpam-5951	88	26	ζ3	ζ3	NOUN
ejpam-5951	88	27	)	)	PUNCT
ejpam-5951	88	28	in	in	ADP
ejpam-5951	88	29	r2	r2	PROPN
ejpam-5951	88	30	for	for	ADP
ejpam-5951	88	31	∆(ζ1	∆(ζ1	PRON
ejpam-5951	88	32	,	,	PUNCT
ejpam-5951	88	33	ζ2	ζ2	NOUN
ejpam-5951	88	34	,	,	PUNCT
ejpam-5951	88	35	ζ3	ζ3	NOUN
ejpam-5951	88	36	)	)	PUNCT
ejpam-5951	88	37	such	such	ADJ
ejpam-5951	88	38	that	that	SCONJ
ejpam-5951	88	39	ρ(ζi	ρ(ζi	NOUN
ejpam-5951	88	40	,	,	PUNCT
ejpam-5951	88	41	ζi+1	ζi+1	NOUN
ejpam-5951	88	42	)	)	PUNCT
ejpam-5951	88	43	=	=	SYM
ejpam-5951	88	44	∥ζi	∥ζi	PROPN
ejpam-5951	88	45	−	−	NOUN
ejpam-5951	88	46	ζi+1∥	ζi+1∥	NOUN
ejpam-5951	88	47	,	,	PUNCT
ejpam-5951	88	48	indices	index	NOUN
ejpam-5951	88	49	are	be	AUX
ejpam-5951	88	50	taken	take	VERB
ejpam-5951	88	51	modulo	modulo	NOUN
ejpam-5951	88	52	3	3	NUM
ejpam-5951	88	53	;	;	PUNCT
ejpam-5951	88	54	and	and	CCONJ
ejpam-5951	88	55	it	it	PRON
ejpam-5951	88	56	is	be	AUX
ejpam-5951	88	57	unique	unique	ADJ
ejpam-5951	88	58	upto	upto	NOUN
ejpam-5951	88	59	an	an	DET
ejpam-5951	88	60	isometry	isometry	NOUN
ejpam-5951	88	61	of	of	ADP
ejpam-5951	88	62	r2	r2	PROPN
ejpam-5951	88	63	.	.	PUNCT
ejpam-5951	89	1	p.	p.	NOUN
ejpam-5951	89	2	patel	patel	PROPN
ejpam-5951	89	3	,	,	PUNCT
ejpam-5951	89	4	r.	r.	PROPN
ejpam-5951	89	5	shukla	shukla	PROPN
ejpam-5951	89	6	/	/	SYM
ejpam-5951	89	7	eur	eur	PROPN
ejpam-5951	89	8	.	.	PUNCT
ejpam-5951	90	1	j.	j.	PROPN
ejpam-5951	90	2	pure	pure	PROPN
ejpam-5951	90	3	appl	appl	PROPN
ejpam-5951	90	4	.	.	PROPN
ejpam-5951	90	5	math	math	PROPN
ejpam-5951	90	6	,	,	PUNCT
ejpam-5951	90	7	18	18	NUM
ejpam-5951	90	8	(	(	PUNCT
ejpam-5951	90	9	2	2	NUM
ejpam-5951	90	10	)	)	PUNCT
ejpam-5951	90	11	(	(	PUNCT
ejpam-5951	90	12	2025	2025	NUM
ejpam-5951	90	13	)	)	PUNCT
ejpam-5951	90	14	,	,	PUNCT
ejpam-5951	90	15	5951	5951	NUM
ejpam-5951	90	16	5	5	NUM
ejpam-5951	90	17	of	of	ADP
ejpam-5951	90	18	15	15	NUM
ejpam-5951	90	19	proposition	proposition	NOUN
ejpam-5951	90	20	3	3	NUM
ejpam-5951	90	21	.	.	PUNCT
ejpam-5951	91	1	[	[	X
ejpam-5951	91	2	18	18	NUM
ejpam-5951	91	3	]	]	PUNCT
ejpam-5951	91	4	suppose	suppose	VERB
ejpam-5951	91	5	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	91	6	,	,	PUNCT
ejpam-5951	91	7	ζ2	ζ2	NOUN
ejpam-5951	91	8	,	,	PUNCT
ejpam-5951	91	9	ζ3	ζ3	NOUN
ejpam-5951	91	10	)	)	PUNCT
ejpam-5951	91	11	be	be	AUX
ejpam-5951	91	12	a	a	DET
ejpam-5951	91	13	geodesic	geodesic	ADJ
ejpam-5951	91	14	triangle	triangle	NOUN
ejpam-5951	91	15	in	in	ADP
ejpam-5951	91	16	γ	γ	PROPN
ejpam-5951	91	17	.	.	PROPN
ejpam-5951	92	1	then	then	ADV
ejpam-5951	92	2	ρ2(ζ1	ρ2(ζ1	NOUN
ejpam-5951	92	3	,	,	PUNCT
ejpam-5951	92	4	ζ2	ζ2	NOUN
ejpam-5951	92	5	)	)	PUNCT
ejpam-5951	92	6	+	+	CCONJ
ejpam-5951	93	1	ρ2(ζ2	ρ2(ζ2	NUM
ejpam-5951	93	2	,	,	PUNCT
ejpam-5951	93	3	ζ3)−	ζ3)−	PROPN
ejpam-5951	93	4	2r	2r	NUM
ejpam-5951	93	5	(	(	PUNCT
ejpam-5951	93	6	exp−1	exp−1	PROPN
ejpam-5951	93	7	ζ2	ζ2	NOUN
ejpam-5951	93	8	ζ1	ζ1	NOUN
ejpam-5951	93	9	,	,	PUNCT
ejpam-5951	93	10	exp	exp	NOUN
ejpam-5951	93	11	−1	−1	NOUN
ejpam-5951	93	12	ζ2	ζ2	NOUN
ejpam-5951	93	13	ζ3	ζ3	NOUN
ejpam-5951	93	14	)	)	PUNCT
ejpam-5951	93	15	≤	≤	NOUN
ejpam-5951	93	16	ρ2(ζ3	ρ2(ζ3	NUM
ejpam-5951	93	17	,	,	PUNCT
ejpam-5951	93	18	ζ1	ζ1	NOUN
ejpam-5951	93	19	)	)	PUNCT
ejpam-5951	93	20	,	,	PUNCT
ejpam-5951	93	21	(	(	PUNCT
ejpam-5951	93	22	2	2	X
ejpam-5951	93	23	)	)	PUNCT
ejpam-5951	93	24	and	and	CCONJ
ejpam-5951	93	25	ρ2(ζ1	ρ2(ζ1	NOUN
ejpam-5951	93	26	,	,	PUNCT
ejpam-5951	93	27	ζ2	ζ2	NOUN
ejpam-5951	93	28	)	)	PUNCT
ejpam-5951	93	29	≤	≤	NOUN
ejpam-5951	94	1	r	r	NOUN
ejpam-5951	94	2	(	(	PUNCT
ejpam-5951	94	3	exp−1	exp−1	PROPN
ejpam-5951	94	4	ζ1	ζ1	NOUN
ejpam-5951	94	5	ζ3	ζ3	NOUN
ejpam-5951	94	6	,	,	PUNCT
ejpam-5951	94	7	exp	exp	NOUN
ejpam-5951	94	8	−1	−1	NOUN
ejpam-5951	94	9	ζ1	ζ1	NOUN
ejpam-5951	94	10	ζ2	ζ2	NOUN
ejpam-5951	94	11	)	)	PUNCT
ejpam-5951	95	1	+	+	NOUN
ejpam-5951	95	2	r	r	NOUN
ejpam-5951	95	3	(	(	PUNCT
ejpam-5951	95	4	exp−1	exp−1	NOUN
ejpam-5951	95	5	ζ2	ζ2	NOUN
ejpam-5951	95	6	ζ3	ζ3	NOUN
ejpam-5951	95	7	,	,	PUNCT
ejpam-5951	95	8	exp	exp	NOUN
ejpam-5951	95	9	−1	−1	NOUN
ejpam-5951	95	10	ζ2	ζ2	NOUN
ejpam-5951	95	11	ζ1	ζ1	PROPN
ejpam-5951	95	12	)	)	PUNCT
ejpam-5951	95	13	.	.	PUNCT
ejpam-5951	96	1	(	(	PUNCT
ejpam-5951	96	2	3	3	X
ejpam-5951	96	3	)	)	PUNCT
ejpam-5951	96	4	moreover	moreover	ADV
ejpam-5951	96	5	,	,	PUNCT
ejpam-5951	96	6	if	if	SCONJ
ejpam-5951	96	7	θ	θ	PROPN
ejpam-5951	96	8	is	be	AUX
ejpam-5951	96	9	the	the	DET
ejpam-5951	96	10	angle	angle	NOUN
ejpam-5951	96	11	at	at	ADP
ejpam-5951	96	12	ζ1	ζ1	NOUN
ejpam-5951	96	13	,	,	PUNCT
ejpam-5951	96	14	then	then	ADV
ejpam-5951	96	15	we	we	PRON
ejpam-5951	96	16	have	have	VERB
ejpam-5951	96	17	r	r	NOUN
ejpam-5951	96	18	(	(	PUNCT
ejpam-5951	96	19	exp−1	exp−1	PROPN
ejpam-5951	96	20	ζ1	ζ1	NOUN
ejpam-5951	96	21	ζ2	ζ2	NOUN
ejpam-5951	96	22	,	,	PUNCT
ejpam-5951	96	23	exp	exp	NOUN
ejpam-5951	96	24	−1	−1	NOUN
ejpam-5951	96	25	ζ1	ζ1	NOUN
ejpam-5951	96	26	ζ3	ζ3	NOUN
ejpam-5951	96	27	)	)	PUNCT
ejpam-5951	96	28	=	=	PUNCT
ejpam-5951	96	29	ρ(ζ2	ρ(ζ2	NOUN
ejpam-5951	96	30	,	,	PUNCT
ejpam-5951	96	31	ζ1)ρ(ζ1	ζ1)ρ(ζ1	NOUN
ejpam-5951	96	32	,	,	PUNCT
ejpam-5951	96	33	ζ3	ζ3	NOUN
ejpam-5951	96	34	)	)	PUNCT
ejpam-5951	96	35	cos(θ	cos(θ	PROPN
ejpam-5951	96	36	)	)	PUNCT
ejpam-5951	96	37	.	.	PUNCT
ejpam-5951	97	1	lemma	lemma	PROPN
ejpam-5951	97	2	3	3	X
ejpam-5951	97	3	.	.	PUNCT
ejpam-5951	98	1	[	[	X
ejpam-5951	98	2	20	20	NUM
ejpam-5951	98	3	]	]	PUNCT
ejpam-5951	98	4	suppose	suppose	VERB
ejpam-5951	98	5	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	98	6	,	,	PUNCT
ejpam-5951	98	7	ζ2	ζ2	NOUN
ejpam-5951	98	8	,	,	PUNCT
ejpam-5951	98	9	ζ3	ζ3	NOUN
ejpam-5951	98	10	)	)	PUNCT
ejpam-5951	98	11	be	be	AUX
ejpam-5951	98	12	geodesic	geodesic	ADJ
ejpam-5951	98	13	triangle	triangle	NOUN
ejpam-5951	98	14	in	in	ADP
ejpam-5951	98	15	γ	γ	PROPN
ejpam-5951	98	16	,	,	PUNCT
ejpam-5951	98	17	∆(ζ1	∆(ζ1	PRON
ejpam-5951	98	18	,	,	PUNCT
ejpam-5951	98	19	ζ2	ζ2	NOUN
ejpam-5951	98	20	,	,	PUNCT
ejpam-5951	98	21	ζ3	ζ3	NOUN
ejpam-5951	98	22	)	)	PUNCT
ejpam-5951	98	23	its	its	PRON
ejpam-5951	98	24	comparison	comparison	NOUN
ejpam-5951	98	25	triangle	triangle	NOUN
ejpam-5951	98	26	.	.	PUNCT
ejpam-5951	99	1	(	(	PUNCT
ejpam-5951	99	2	1	1	X
ejpam-5951	99	3	)	)	PUNCT
ejpam-5951	99	4	suppose	suppose	VERB
ejpam-5951	99	5	α1	α1	PROPN
ejpam-5951	99	6	,	,	PUNCT
ejpam-5951	99	7	α2	α2	ADJ
ejpam-5951	99	8	,	,	PUNCT
ejpam-5951	99	9	α3	α3	NOUN
ejpam-5951	99	10	and	and	CCONJ
ejpam-5951	99	11	α1	α1	PROPN
ejpam-5951	99	12	,	,	PUNCT
ejpam-5951	99	13	α2	α2	ADJ
ejpam-5951	99	14	,	,	PUNCT
ejpam-5951	99	15	α3	α3	PROPN
ejpam-5951	99	16	be	be	AUX
ejpam-5951	99	17	the	the	DET
ejpam-5951	99	18	angles	angle	NOUN
ejpam-5951	99	19	of	of	ADP
ejpam-5951	99	20	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	99	21	,	,	PUNCT
ejpam-5951	99	22	ζ2	ζ2	NOUN
ejpam-5951	99	23	,	,	PUNCT
ejpam-5951	99	24	ζ3	ζ3	NOUN
ejpam-5951	99	25	)	)	PUNCT
ejpam-5951	99	26	and	and	CCONJ
ejpam-5951	99	27	∆(ζ1	∆(ζ1	NOUN
ejpam-5951	99	28	,	,	PUNCT
ejpam-5951	99	29	ζ2	ζ2	NOUN
ejpam-5951	99	30	,	,	PUNCT
ejpam-5951	99	31	ζ3	ζ3	NOUN
ejpam-5951	99	32	)	)	PUNCT
ejpam-5951	99	33	at	at	ADP
ejpam-5951	99	34	the	the	DET
ejpam-5951	99	35	vertices	vertex	NOUN
ejpam-5951	99	36	ζ1	ζ1	NOUN
ejpam-5951	99	37	,	,	PUNCT
ejpam-5951	99	38	ζ2	ζ2	NOUN
ejpam-5951	99	39	,	,	PUNCT
ejpam-5951	99	40	ζ3	ζ3	NOUN
ejpam-5951	99	41	and	and	CCONJ
ejpam-5951	99	42	ζ1	ζ1	NOUN
ejpam-5951	99	43	,	,	PUNCT
ejpam-5951	99	44	ζ2	ζ2	NOUN
ejpam-5951	99	45	,	,	PUNCT
ejpam-5951	99	46	ζ3	ζ3	NOUN
ejpam-5951	99	47	,	,	PUNCT
ejpam-5951	99	48	respectively	respectively	ADV
ejpam-5951	99	49	.	.	PUNCT
ejpam-5951	100	1	then	then	ADV
ejpam-5951	100	2	α1	α1	PROPN
ejpam-5951	100	3	≤	≤	PROPN
ejpam-5951	100	4	α1	α1	NOUN
ejpam-5951	100	5	,	,	PUNCT
ejpam-5951	100	6	α2	α2	ADJ
ejpam-5951	100	7	≤	≤	ADV
ejpam-5951	100	8	α2	α2	ADJ
ejpam-5951	100	9	and	and	CCONJ
ejpam-5951	100	10	α3	α3	PROPN
ejpam-5951	100	11	≤	≤	NUM
ejpam-5951	100	12	α3	α3	NOUN
ejpam-5951	100	13	.	.	PUNCT
ejpam-5951	101	1	(	(	PUNCT
ejpam-5951	101	2	2	2	X
ejpam-5951	101	3	)	)	PUNCT
ejpam-5951	101	4	suppose	suppose	VERB
ejpam-5951	101	5	µ	µ	X
ejpam-5951	101	6	be	be	AUX
ejpam-5951	101	7	any	any	DET
ejpam-5951	101	8	point	point	NOUN
ejpam-5951	101	9	on	on	ADP
ejpam-5951	101	10	the	the	DET
ejpam-5951	101	11	geodesic	geodesic	NOUN
ejpam-5951	101	12	connecting	connect	VERB
ejpam-5951	101	13	ζ1	ζ1	NOUN
ejpam-5951	101	14	,	,	PUNCT
ejpam-5951	101	15	ζ2	ζ2	NOUN
ejpam-5951	101	16	and	and	CCONJ
ejpam-5951	101	17	µ	µ	PRON
ejpam-5951	101	18	its	its	PRON
ejpam-5951	101	19	comparison	comparison	NOUN
ejpam-5951	101	20	point	point	NOUN
ejpam-5951	101	21	in	in	ADP
ejpam-5951	101	22	interval	interval	NOUN
ejpam-5951	101	23	[	[	X
ejpam-5951	101	24	ζ1	ζ1	NOUN
ejpam-5951	101	25	,	,	PUNCT
ejpam-5951	101	26	ζ2	ζ2	NOUN
ejpam-5951	101	27	]	]	PUNCT
ejpam-5951	101	28	.	.	PUNCT
ejpam-5951	102	1	if	if	SCONJ
ejpam-5951	102	2	ρ(ζ1	ρ(ζ1	NOUN
ejpam-5951	102	3	,	,	PUNCT
ejpam-5951	102	4	µ	µ	NOUN
ejpam-5951	102	5	)	)	PUNCT
ejpam-5951	102	6	=	=	SYM
ejpam-5951	102	7	∥ζ1−µ∥	∥ζ1−µ∥	ADJ
ejpam-5951	102	8	and	and	CCONJ
ejpam-5951	102	9	ρ(ζ2	ρ(ζ2	ADJ
ejpam-5951	102	10	,	,	PUNCT
ejpam-5951	102	11	µ	µ	NOUN
ejpam-5951	102	12	)	)	PUNCT
ejpam-5951	103	1	=	=	SYM
ejpam-5951	103	2	∥ζ2−µ∥	∥ζ2−µ∥	NOUN
ejpam-5951	103	3	then	then	ADV
ejpam-5951	103	4	ρ(ζ3	ρ(ζ3	NOUN
ejpam-5951	103	5	,	,	PUNCT
ejpam-5951	103	6	µ	µ	NOUN
ejpam-5951	103	7	)	)	PUNCT
ejpam-5951	103	8	≤	≤	NOUN
ejpam-5951	103	9	∥ζ3−µ∥.	∥ζ3−µ∥.	VERB
ejpam-5951	103	10	proposition	proposition	NOUN
ejpam-5951	103	11	4	4	NUM
ejpam-5951	103	12	.	.	PUNCT
ejpam-5951	104	1	[	[	X
ejpam-5951	104	2	21	21	NUM
ejpam-5951	104	3	]	]	PUNCT
ejpam-5951	104	4	suppose	suppose	VERB
ejpam-5951	104	5	b	b	X
ejpam-5951	104	6	̸=	̸=	PROPN
ejpam-5951	104	7	∅	∅	NOUN
ejpam-5951	104	8	be	be	AUX
ejpam-5951	104	9	a	a	DET
ejpam-5951	104	10	geodesic	geodesic	ADJ
ejpam-5951	104	11	convex	convex	NOUN
ejpam-5951	104	12	subset	subset	NOUN
ejpam-5951	104	13	of	of	ADP
ejpam-5951	104	14	a	a	DET
ejpam-5951	104	15	hadamard	hadamard	ADJ
ejpam-5951	104	16	manifold	manifold	ADJ
ejpam-5951	104	17	γ	γ	NOUN
ejpam-5951	104	18	and	and	CCONJ
ejpam-5951	104	19	g	g	NOUN
ejpam-5951	104	20	:	:	PUNCT
ejpam-5951	104	21	b	b	X
ejpam-5951	104	22	→	→	SYM
ejpam-5951	104	23	b	b	X
ejpam-5951	104	24	be	be	AUX
ejpam-5951	104	25	a	a	DET
ejpam-5951	104	26	β	β	NOUN
ejpam-5951	104	27	-	-	PUNCT
ejpam-5951	104	28	strictly	strictly	ADV
ejpam-5951	104	29	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	104	30	mapping	mapping	NOUN
ejpam-5951	104	31	with	with	ADP
ejpam-5951	104	32	β	β	X
ejpam-5951	104	33	∈	∈	PROPN
ejpam-5951	104	34	(	(	PUNCT
ejpam-5951	104	35	0	0	NUM
ejpam-5951	104	36	,	,	PUNCT
ejpam-5951	104	37	1	1	NUM
ejpam-5951	104	38	]	]	PUNCT
ejpam-5951	104	39	.	.	PUNCT
ejpam-5951	105	1	then	then	ADV
ejpam-5951	105	2	gλ(ζ	gλ(ζ	X
ejpam-5951	105	3	)	)	PUNCT
ejpam-5951	105	4	=	=	SYM
ejpam-5951	105	5	expζ	expζ	NOUN
ejpam-5951	105	6	λ	λ	X
ejpam-5951	105	7	exp−1	exp−1	PROPN
ejpam-5951	105	8	ζ	ζ	PROPN
ejpam-5951	105	9	g(ζ	g(ζ	PROPN
ejpam-5951	105	10	)	)	PUNCT
ejpam-5951	105	11	is	be	AUX
ejpam-5951	105	12	a	a	DET
ejpam-5951	105	13	nonexpansive	nonexpansive	ADJ
ejpam-5951	105	14	mapping	mapping	NOUN
ejpam-5951	105	15	for	for	ADP
ejpam-5951	105	16	every	every	DET
ejpam-5951	105	17	λ	λ	PROPN
ejpam-5951	105	18	∈	∈	PROPN
ejpam-5951	105	19	(	(	PUNCT
ejpam-5951	105	20	0	0	NUM
ejpam-5951	105	21	,	,	PUNCT
ejpam-5951	105	22	1−	1−	NUM
ejpam-5951	105	23	β	β	X
ejpam-5951	105	24	)	)	PUNCT
ejpam-5951	105	25	.	.	PUNCT
ejpam-5951	106	1	remark	remark	PROPN
ejpam-5951	106	2	1	1	NUM
ejpam-5951	106	3	.	.	PUNCT
ejpam-5951	107	1	if	if	SCONJ
ejpam-5951	107	2	g	g	PROPN
ejpam-5951	107	3	and	and	CCONJ
ejpam-5951	107	4	gλ	gλ	NOUN
ejpam-5951	107	5	are	be	AUX
ejpam-5951	107	6	same	same	ADJ
ejpam-5951	107	7	as	as	ADP
ejpam-5951	107	8	above	above	ADP
ejpam-5951	107	9	proposition	proposition	NOUN
ejpam-5951	107	10	then	then	ADV
ejpam-5951	107	11	f	f	PROPN
ejpam-5951	107	12	(	(	PUNCT
ejpam-5951	107	13	g	g	NOUN
ejpam-5951	107	14	)	)	PUNCT
ejpam-5951	108	1	=	=	SYM
ejpam-5951	108	2	f	f	PROPN
ejpam-5951	108	3	(	(	PUNCT
ejpam-5951	108	4	gλ	gλ	NOUN
ejpam-5951	108	5	)	)	PUNCT
ejpam-5951	108	6	.	.	PUNCT
ejpam-5951	109	1	it	it	PRON
ejpam-5951	109	2	follows	follow	VERB
ejpam-5951	109	3	from	from	ADP
ejpam-5951	109	4	the	the	DET
ejpam-5951	109	5	following	follow	VERB
ejpam-5951	109	6	equivalence	equivalence	NOUN
ejpam-5951	109	7	let	let	VERB
ejpam-5951	109	8	ζ	ζ	NOUN
ejpam-5951	109	9	∈	∈	PROPN
ejpam-5951	109	10	f	f	X
ejpam-5951	109	11	(	(	PUNCT
ejpam-5951	109	12	gλ	gλ	NOUN
ejpam-5951	109	13	)	)	PUNCT
ejpam-5951	109	14	implies	imply	VERB
ejpam-5951	109	15	ζ	ζ	NOUN
ejpam-5951	109	16	=	=	SYM
ejpam-5951	109	17	gλ(ζ	gλ(ζ	X
ejpam-5951	109	18	)	)	PUNCT
ejpam-5951	110	1	⇔	⇔	X
ejpam-5951	110	2	ζ	ζ	X
ejpam-5951	110	3	=	=	SYM
ejpam-5951	110	4	expζ	expζ	NOUN
ejpam-5951	110	5	λ	λ	PROPN
ejpam-5951	110	6	exp	exp	NOUN
ejpam-5951	110	7	−1	−1	NOUN
ejpam-5951	110	8	ζ	ζ	PROPN
ejpam-5951	110	9	g(ζ	g(ζ	PROPN
ejpam-5951	110	10	)	)	PUNCT
ejpam-5951	110	11	⇔	⇔	NOUN
ejpam-5951	110	12	0	0	NUM
ejpam-5951	111	1	=	=	SYM
ejpam-5951	111	2	exp−1	exp−1	PROPN
ejpam-5951	111	3	ζ	ζ	PROPN
ejpam-5951	111	4	g(ζ	g(ζ	PROPN
ejpam-5951	111	5	)	)	PUNCT
ejpam-5951	111	6	⇔	⇔	X
ejpam-5951	111	7	ζ	ζ	X
ejpam-5951	111	8	=	=	SYM
ejpam-5951	111	9	g(ζ	g(ζ	PROPN
ejpam-5951	111	10	)	)	PUNCT
ejpam-5951	111	11	.	.	PUNCT
ejpam-5951	112	1	throughout	throughout	ADP
ejpam-5951	112	2	the	the	DET
ejpam-5951	112	3	article	article	NOUN
ejpam-5951	112	4	we	we	PRON
ejpam-5951	112	5	write	write	VERB
ejpam-5951	112	6	the	the	DET
ejpam-5951	112	7	set	set	NOUN
ejpam-5951	112	8	of	of	ADP
ejpam-5951	112	9	all	all	DET
ejpam-5951	112	10	single	single	ADJ
ejpam-5951	112	11	valued	value	VERB
ejpam-5951	112	12	vector	vector	NOUN
ejpam-5951	112	13	fields	field	NOUN
ejpam-5951	112	14	𭟋	𭟋	ADP
ejpam-5951	112	15	:	:	PUNCT
ejpam-5951	112	16	γ	γ	X
ejpam-5951	112	17	→	→	SYM
ejpam-5951	112	18	gγ	gγ	ADP
ejpam-5951	112	19	as	as	ADP
ejpam-5951	112	20	ξ(γ	ξ(γ	NUM
ejpam-5951	112	21	)	)	PUNCT
ejpam-5951	112	22	such	such	ADJ
ejpam-5951	112	23	that	that	SCONJ
ejpam-5951	112	24	𭟋(ζ	𭟋(ζ	PROPN
ejpam-5951	112	25	)	)	PUNCT
ejpam-5951	112	26	∈	∈	PROPN
ejpam-5951	112	27	gζγ	gζγ	NOUN
ejpam-5951	112	28	for	for	ADP
ejpam-5951	112	29	all	all	DET
ejpam-5951	112	30	ζ	ζ	PROPN
ejpam-5951	112	31	∈	∈	PROPN
ejpam-5951	112	32	γ	γ	X
ejpam-5951	112	33	.	.	PUNCT
ejpam-5951	113	1	let	let	VERB
ejpam-5951	113	2	ψ(γ	ψ(γ	PROPN
ejpam-5951	113	3	)	)	PUNCT
ejpam-5951	114	1	denote	denote	VERB
ejpam-5951	114	2	the	the	DET
ejpam-5951	114	3	set	set	NOUN
ejpam-5951	114	4	of	of	ADP
ejpam-5951	114	5	all	all	DET
ejpam-5951	114	6	multivalued	multivalue	VERB
ejpam-5951	114	7	vector	vector	NOUN
ejpam-5951	114	8	fields	field	NOUN
ejpam-5951	114	9	v	v	NOUN
ejpam-5951	114	10	:	:	PUNCT
ejpam-5951	114	11	γ	γ	X
ejpam-5951	114	12	→	→	SYM
ejpam-5951	114	13	2gγ	2gγ	NOUN
ejpam-5951	114	14	such	such	ADJ
ejpam-5951	114	15	that	that	PRON
ejpam-5951	114	16	v	v	NOUN
ejpam-5951	114	17	(	(	PUNCT
ejpam-5951	114	18	ζ	ζ	NOUN
ejpam-5951	114	19	)	)	PUNCT
ejpam-5951	114	20	⊆	⊆	NUM
ejpam-5951	114	21	gζγ	gζγ	NOUN
ejpam-5951	114	22	for	for	ADP
ejpam-5951	114	23	all	all	DET
ejpam-5951	114	24	ζ	ζ	PROPN
ejpam-5951	114	25	∈	∈	PROPN
ejpam-5951	114	26	γ	γ	X
ejpam-5951	114	27	,	,	PUNCT
ejpam-5951	114	28	and	and	CCONJ
ejpam-5951	114	29	we	we	PRON
ejpam-5951	114	30	denote	denote	VERB
ejpam-5951	114	31	the	the	DET
ejpam-5951	114	32	domain	domain	NOUN
ejpam-5951	114	33	of	of	ADP
ejpam-5951	114	34	v	v	NUM
ejpam-5951	114	35	by	by	ADP
ejpam-5951	114	36	d(v	d(v	PROPN
ejpam-5951	114	37	)	)	PUNCT
ejpam-5951	115	1	=	=	PRON
ejpam-5951	115	2	{	{	PUNCT
ejpam-5951	115	3	ζ	ζ	NOUN
ejpam-5951	115	4	∈	∈	PROPN
ejpam-5951	115	5	γ	γ	X
ejpam-5951	115	6	:	:	PUNCT
ejpam-5951	115	7	v	v	NOUN
ejpam-5951	115	8	(	(	PUNCT
ejpam-5951	115	9	ζ	ζ	NOUN
ejpam-5951	115	10	)	)	PUNCT
ejpam-5951	115	11	̸=	̸=	PROPN
ejpam-5951	115	12	∅	∅	NOUN
ejpam-5951	115	13	}	}	PUNCT
ejpam-5951	115	14	.	.	PUNCT
ejpam-5951	116	1	definition	definition	NOUN
ejpam-5951	116	2	4	4	NUM
ejpam-5951	116	3	.	.	PUNCT
ejpam-5951	117	1	[	[	X
ejpam-5951	117	2	22	22	NUM
ejpam-5951	117	3	]	]	PUNCT
ejpam-5951	117	4	any	any	DET
ejpam-5951	117	5	vector	vector	NOUN
ejpam-5951	117	6	field	field	NOUN
ejpam-5951	117	7	𭟋	𭟋	PROPN
ejpam-5951	117	8	∈	∈	PROPN
ejpam-5951	117	9	ξ(γ	ξ(γ	PROPN
ejpam-5951	117	10	)	)	PUNCT
ejpam-5951	117	11	is	be	AUX
ejpam-5951	117	12	monotone	monotone	ADJ
ejpam-5951	117	13	if	if	SCONJ
ejpam-5951	117	14	it	it	PRON
ejpam-5951	117	15	satisfies	satisfy	VERB
ejpam-5951	117	16	r	r	NOUN
ejpam-5951	117	17	(	(	PUNCT
ejpam-5951	117	18	𭟋(ζ	𭟋(ζ	PROPN
ejpam-5951	117	19	)	)	PUNCT
ejpam-5951	117	20	,	,	PUNCT
ejpam-5951	117	21	exp−1	exp−1	NOUN
ejpam-5951	117	22	ζ	ζ	NOUN
ejpam-5951	117	23	ν	ν	NOUN
ejpam-5951	117	24	)	)	PUNCT
ejpam-5951	118	1	+	+	NOUN
ejpam-5951	118	2	r(𭟋(ν	r(𭟋(ν	NOUN
ejpam-5951	118	3	)	)	PUNCT
ejpam-5951	118	4	,	,	PUNCT
ejpam-5951	118	5	exp−1	exp−1	PROPN
ejpam-5951	118	6	ν	ν	NOUN
ejpam-5951	118	7	ζ	ζ	NOUN
ejpam-5951	118	8	)	)	PUNCT
ejpam-5951	118	9	≤	≤	NOUN
ejpam-5951	118	10	0	0	NUM
ejpam-5951	118	11	,	,	PUNCT
ejpam-5951	118	12	for	for	ADP
ejpam-5951	118	13	all	all	DET
ejpam-5951	118	14	ζ	ζ	NOUN
ejpam-5951	118	15	,	,	PUNCT
ejpam-5951	118	16	ν	ν	PROPN
ejpam-5951	118	17	∈	∈	PROPN
ejpam-5951	118	18	γ	γ	X
ejpam-5951	118	19	.	.	PUNCT
ejpam-5951	119	1	p.	p.	NOUN
ejpam-5951	119	2	patel	patel	PROPN
ejpam-5951	119	3	,	,	PUNCT
ejpam-5951	119	4	r.	r.	PROPN
ejpam-5951	119	5	shukla	shukla	PROPN
ejpam-5951	119	6	/	/	SYM
ejpam-5951	119	7	eur	eur	PROPN
ejpam-5951	119	8	.	.	PUNCT
ejpam-5951	120	1	j.	j.	PROPN
ejpam-5951	120	2	pure	pure	PROPN
ejpam-5951	120	3	appl	appl	PROPN
ejpam-5951	120	4	.	.	PROPN
ejpam-5951	120	5	math	math	PROPN
ejpam-5951	120	6	,	,	PUNCT
ejpam-5951	120	7	18	18	NUM
ejpam-5951	120	8	(	(	PUNCT
ejpam-5951	120	9	2	2	NUM
ejpam-5951	120	10	)	)	PUNCT
ejpam-5951	120	11	(	(	PUNCT
ejpam-5951	120	12	2025	2025	NUM
ejpam-5951	120	13	)	)	PUNCT
ejpam-5951	120	14	,	,	PUNCT
ejpam-5951	120	15	5951	5951	NUM
ejpam-5951	120	16	6	6	NUM
ejpam-5951	120	17	of	of	ADP
ejpam-5951	120	18	15	15	NUM
ejpam-5951	120	19	definition	definition	NOUN
ejpam-5951	120	20	5	5	NUM
ejpam-5951	120	21	.	.	PUNCT
ejpam-5951	121	1	[	[	X
ejpam-5951	121	2	23	23	NUM
ejpam-5951	121	3	]	]	PUNCT
ejpam-5951	121	4	a	a	DET
ejpam-5951	121	5	multivalued	multivalue	VERB
ejpam-5951	121	6	vector	vector	NOUN
ejpam-5951	121	7	field	field	NOUN
ejpam-5951	121	8	v	v	ADP
ejpam-5951	121	9	∈	∈	PROPN
ejpam-5951	121	10	ψ(γ	ψ(γ	PROPN
ejpam-5951	121	11	)	)	PUNCT
ejpam-5951	121	12	is	be	AUX
ejpam-5951	121	13	said	say	VERB
ejpam-5951	121	14	to	to	PART
ejpam-5951	121	15	be	be	AUX
ejpam-5951	121	16	monotone	monotone	ADJ
ejpam-5951	121	17	if	if	SCONJ
ejpam-5951	121	18	for	for	ADP
ejpam-5951	121	19	all	all	DET
ejpam-5951	121	20	ζ	ζ	NOUN
ejpam-5951	121	21	,	,	PUNCT
ejpam-5951	121	22	ν	ν	X
ejpam-5951	121	23	∈	∈	PROPN
ejpam-5951	121	24	d(v	d(v	PROPN
ejpam-5951	121	25	)	)	PUNCT
ejpam-5951	121	26	r	r	NOUN
ejpam-5951	121	27	(	(	PUNCT
ejpam-5951	121	28	u	u	NOUN
ejpam-5951	121	29	,	,	PUNCT
ejpam-5951	121	30	exp−1	exp−1	PROPN
ejpam-5951	121	31	ζ	ζ	NOUN
ejpam-5951	121	32	ν	ν	NOUN
ejpam-5951	121	33	)	)	PUNCT
ejpam-5951	121	34	≤	≤	PUNCT
ejpam-5951	121	35	r(w,−	r(w,−	NOUN
ejpam-5951	121	36	exp−1	exp−1	PROPN
ejpam-5951	121	37	ν	ν	X
ejpam-5951	121	38	ζ	ζ	NOUN
ejpam-5951	121	39	)	)	PUNCT
ejpam-5951	121	40	,	,	PUNCT
ejpam-5951	121	41	for	for	ADP
ejpam-5951	121	42	all	all	PRON
ejpam-5951	121	43	,	,	PUNCT
ejpam-5951	121	44	u	u	PROPN
ejpam-5951	121	45	∈	∈	PROPN
ejpam-5951	121	46	v	v	ADP
ejpam-5951	121	47	(	(	PUNCT
ejpam-5951	121	48	ζ	ζ	NOUN
ejpam-5951	121	49	)	)	PUNCT
ejpam-5951	121	50	,	,	PUNCT
ejpam-5951	121	51	w	w	PROPN
ejpam-5951	121	52	∈	∈	PROPN
ejpam-5951	121	53	v	v	ADP
ejpam-5951	121	54	(	(	PUNCT
ejpam-5951	121	55	ν	ν	NOUN
ejpam-5951	121	56	)	)	PUNCT
ejpam-5951	121	57	;	;	PUNCT
ejpam-5951	121	58	and	and	CCONJ
ejpam-5951	121	59	maximal	maximal	ADJ
ejpam-5951	121	60	monotone	monotone	NOUN
ejpam-5951	121	61	if	if	SCONJ
ejpam-5951	121	62	it	it	PRON
ejpam-5951	121	63	is	be	AUX
ejpam-5951	121	64	already	already	ADV
ejpam-5951	121	65	monotone	monotone	ADJ
ejpam-5951	121	66	,	,	PUNCT
ejpam-5951	121	67	for	for	ADP
ejpam-5951	121	68	all	all	DET
ejpam-5951	121	69	ζ	ζ	PROPN
ejpam-5951	121	70	∈	∈	PROPN
ejpam-5951	121	71	γ	γ	X
ejpam-5951	121	72	,	,	PUNCT
ejpam-5951	121	73	u	u	PROPN
ejpam-5951	121	74	∈	∈	PROPN
ejpam-5951	121	75	gζγ	gζγ	NOUN
ejpam-5951	121	76	,	,	PUNCT
ejpam-5951	121	77	r	r	NOUN
ejpam-5951	121	78	(	(	PUNCT
ejpam-5951	121	79	u	u	NOUN
ejpam-5951	121	80	,	,	PUNCT
ejpam-5951	121	81	exp−1	exp−1	PROPN
ejpam-5951	121	82	ζ	ζ	NOUN
ejpam-5951	121	83	ν	ν	NOUN
ejpam-5951	121	84	)	)	PUNCT
ejpam-5951	121	85	≤	≤	PUNCT
ejpam-5951	121	86	r(w,−	r(w,−	NOUN
ejpam-5951	121	87	exp−1	exp−1	PROPN
ejpam-5951	121	88	ν	ν	X
ejpam-5951	121	89	ζ	ζ	NOUN
ejpam-5951	121	90	)	)	PUNCT
ejpam-5951	121	91	,	,	PUNCT
ejpam-5951	121	92	for	for	ADP
ejpam-5951	121	93	all	all	PRON
ejpam-5951	121	94	,	,	PUNCT
ejpam-5951	121	95	ν	ν	X
ejpam-5951	121	96	∈	∈	PROPN
ejpam-5951	121	97	d(v	d(v	PROPN
ejpam-5951	121	98	)	)	PUNCT
ejpam-5951	121	99	,	,	PUNCT
ejpam-5951	121	100	w	w	PROPN
ejpam-5951	121	101	∈	∈	PROPN
ejpam-5951	121	102	v	v	ADP
ejpam-5951	121	103	(	(	PUNCT
ejpam-5951	121	104	ν	ν	NOUN
ejpam-5951	121	105	)	)	PUNCT
ejpam-5951	121	106	implies	imply	VERB
ejpam-5951	121	107	u	u	PROPN
ejpam-5951	121	108	∈	∈	PROPN
ejpam-5951	121	109	v	v	ADP
ejpam-5951	121	110	(	(	PUNCT
ejpam-5951	121	111	ζ	ζ	NOUN
ejpam-5951	121	112	)	)	PUNCT
ejpam-5951	121	113	.	.	PUNCT
ejpam-5951	122	1	definition	definition	NOUN
ejpam-5951	122	2	6	6	NUM
ejpam-5951	122	3	.	.	PUNCT
ejpam-5951	123	1	[	[	X
ejpam-5951	123	2	22	22	NUM
ejpam-5951	123	3	]	]	PUNCT
ejpam-5951	123	4	suppose	suppose	VERB
ejpam-5951	123	5	g	g	NOUN
ejpam-5951	123	6	:	:	PUNCT
ejpam-5951	123	7	γ	γ	X
ejpam-5951	123	8	→	→	SYM
ejpam-5951	123	9	γ	γ	X
ejpam-5951	123	10	is	be	AUX
ejpam-5951	123	11	a	a	DET
ejpam-5951	123	12	mapping	mapping	NOUN
ejpam-5951	123	13	and	and	CCONJ
ejpam-5951	123	14	vector	vector	NOUN
ejpam-5951	123	15	field	field	NOUN
ejpam-5951	123	16	𭟋	𭟋	PROPN
ejpam-5951	123	17	∈	∈	PROPN
ejpam-5951	123	18	ξ(γ	ξ(γ	PROPN
ejpam-5951	123	19	)	)	PUNCT
ejpam-5951	123	20	is	be	AUX
ejpam-5951	123	21	defined	define	VERB
ejpam-5951	123	22	as	as	ADP
ejpam-5951	123	23	𭟋(ζ	𭟋(ζ	PROPN
ejpam-5951	123	24	)	)	PUNCT
ejpam-5951	123	25	=	=	PUNCT
ejpam-5951	124	1	−	−	PROPN
ejpam-5951	124	2	exp−1	exp−1	NOUN
ejpam-5951	124	3	ζ	ζ	PROPN
ejpam-5951	124	4	g(ζ	g(ζ	PROPN
ejpam-5951	124	5	)	)	PUNCT
ejpam-5951	124	6	,	,	PUNCT
ejpam-5951	124	7	for	for	ADP
ejpam-5951	124	8	all	all	DET
ejpam-5951	124	9	ζ	ζ	PROPN
ejpam-5951	124	10	∈	∈	PROPN
ejpam-5951	124	11	γ	γ	NOUN
ejpam-5951	124	12	,	,	PUNCT
ejpam-5951	124	13	is	be	AUX
ejpam-5951	124	14	the	the	DET
ejpam-5951	124	15	complementary	complementary	ADJ
ejpam-5951	124	16	vector	vector	NOUN
ejpam-5951	124	17	field	field	NOUN
ejpam-5951	124	18	.	.	PUNCT
ejpam-5951	125	1	theorem	theorem	NOUN
ejpam-5951	125	2	1	1	NUM
ejpam-5951	125	3	.	.	PUNCT
ejpam-5951	126	1	[	[	X
ejpam-5951	126	2	22	22	NUM
ejpam-5951	126	3	]	]	PUNCT
ejpam-5951	126	4	the	the	DET
ejpam-5951	126	5	complimentary	complimentary	ADJ
ejpam-5951	126	6	vector	vector	NOUN
ejpam-5951	126	7	field	field	NOUN
ejpam-5951	126	8	𭟋	𭟋	NOUN
ejpam-5951	126	9	=	=	PUNCT
ejpam-5951	126	10	−	−	PROPN
ejpam-5951	126	11	exp−1	exp−1	NOUN
ejpam-5951	126	12	g	g	PROPN
ejpam-5951	126	13	defined	define	VERB
ejpam-5951	126	14	for	for	ADP
ejpam-5951	126	15	any	any	DET
ejpam-5951	126	16	nonexpansive	nonexpansive	ADJ
ejpam-5951	126	17	mapping	mapping	NOUN
ejpam-5951	126	18	g	g	NOUN
ejpam-5951	126	19	:	:	PUNCT
ejpam-5951	126	20	γ	γ	X
ejpam-5951	126	21	→	→	SYM
ejpam-5951	126	22	γ	γ	X
ejpam-5951	126	23	is	be	AUX
ejpam-5951	126	24	always	always	ADV
ejpam-5951	126	25	monotone	monotone	ADJ
ejpam-5951	126	26	.	.	PUNCT
ejpam-5951	127	1	3	3	X
ejpam-5951	127	2	.	.	X
ejpam-5951	127	3	main	main	ADJ
ejpam-5951	127	4	results	result	NOUN
ejpam-5951	127	5	suppose	suppose	VERB
ejpam-5951	127	6	γ	γ	NOUN
ejpam-5951	127	7	is	be	AUX
ejpam-5951	127	8	a	a	DET
ejpam-5951	127	9	hadamard	hadamard	ADJ
ejpam-5951	127	10	manifold	manifold	NOUN
ejpam-5951	127	11	,	,	PUNCT
ejpam-5951	127	12	gi	gi	INTJ
ejpam-5951	127	13	,	,	PUNCT
ejpam-5951	127	14	hi	hi	INTJ
ejpam-5951	127	15	:	:	PUNCT
ejpam-5951	127	16	γ	γ	X
ejpam-5951	127	17	→	→	SYM
ejpam-5951	127	18	γ	γ	X
ejpam-5951	127	19	be	be	AUX
ejpam-5951	127	20	two	two	NUM
ejpam-5951	127	21	countable	countable	ADJ
ejpam-5951	127	22	family	family	NOUN
ejpam-5951	127	23	of	of	ADP
ejpam-5951	127	24	βstrict	βstrict	NOUN
ejpam-5951	127	25	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	127	26	mappings	mapping	NOUN
ejpam-5951	127	27	with	with	ADP
ejpam-5951	127	28	β	β	X
ejpam-5951	127	29	∈	∈	PROPN
ejpam-5951	127	30	(	(	PUNCT
ejpam-5951	127	31	0	0	NUM
ejpam-5951	127	32	,	,	PUNCT
ejpam-5951	127	33	1	1	NUM
ejpam-5951	127	34	]	]	PUNCT
ejpam-5951	127	35	and	and	CCONJ
ejpam-5951	127	36	the	the	DET
ejpam-5951	127	37	set	set	NOUN
ejpam-5951	127	38	of	of	ADP
ejpam-5951	127	39	common	common	ADJ
ejpam-5951	127	40	fixed	fix	VERB
ejpam-5951	127	41	points	point	NOUN
ejpam-5951	127	42	of	of	ADP
ejpam-5951	127	43	mappings	mapping	NOUN
ejpam-5951	127	44	hi	hi	INTJ
ejpam-5951	127	45	and	and	CCONJ
ejpam-5951	127	46	gi	gi	PROPN
ejpam-5951	127	47	are	be	AUX
ejpam-5951	127	48	given	give	VERB
ejpam-5951	127	49	by	by	ADP
ejpam-5951	127	50	⋂	⋂	PROPN
ejpam-5951	127	51	i	i	PROPN
ejpam-5951	127	52	f	f	PROPN
ejpam-5951	127	53	(	(	PUNCT
ejpam-5951	127	54	hi	hi	INTJ
ejpam-5951	127	55	)	)	PUNCT
ejpam-5951	127	56	and	and	CCONJ
ejpam-5951	127	57	⋂	⋂	PROPN
ejpam-5951	128	1	i	i	PRON
ejpam-5951	128	2	f	f	PROPN
ejpam-5951	128	3	(	(	PUNCT
ejpam-5951	128	4	gi	gi	INTJ
ejpam-5951	128	5	)	)	PUNCT
ejpam-5951	128	6	.	.	PUNCT
ejpam-5951	129	1	we	we	PRON
ejpam-5951	129	2	define	define	VERB
ejpam-5951	129	3	the	the	DET
ejpam-5951	129	4	hierarchical	hierarchical	ADJ
ejpam-5951	129	5	fixed	fix	VERB
ejpam-5951	129	6	point	point	NOUN
ejpam-5951	129	7	problem	problem	NOUN
ejpam-5951	129	8	as	as	SCONJ
ejpam-5951	129	9	follows	follow	VERB
ejpam-5951	129	10	find	find	VERB
ejpam-5951	129	11	ζ	ζ	ADJ
ejpam-5951	129	12	∈	∈	ADJ
ejpam-5951	129	13	⋂	⋂	PROPN
ejpam-5951	130	1	i	i	PRON
ejpam-5951	130	2	f	f	PROPN
ejpam-5951	130	3	(	(	PUNCT
ejpam-5951	130	4	hi	hi	INTJ
ejpam-5951	130	5	)	)	PUNCT
ejpam-5951	130	6	:	:	PUNCT
ejpam-5951	131	1	r	r	X
ejpam-5951	131	2	(	(	PUNCT
ejpam-5951	131	3	exp−1	exp−1	PROPN
ejpam-5951	131	4	ζ	ζ	PROPN
ejpam-5951	131	5	gλi	gλi	NOUN
ejpam-5951	131	6	(	(	PUNCT
ejpam-5951	131	7	ζ	ζ	NOUN
ejpam-5951	131	8	)	)	PUNCT
ejpam-5951	131	9	,	,	PUNCT
ejpam-5951	131	10	exp−1	exp−1	NOUN
ejpam-5951	131	11	ζ	ζ	NOUN
ejpam-5951	131	12	ν	ν	NOUN
ejpam-5951	131	13	)	)	PUNCT
ejpam-5951	131	14	≤	≤	NOUN
ejpam-5951	131	15	0	0	NUM
ejpam-5951	131	16	,	,	PUNCT
ejpam-5951	131	17	for	for	ADP
ejpam-5951	131	18	all	all	PRON
ejpam-5951	131	19	ν	ν	NOUN
ejpam-5951	131	20	∈	∈	PROPN
ejpam-5951	131	21	⋂	⋂	PROPN
ejpam-5951	132	1	i	i	PRON
ejpam-5951	132	2	f	f	PROPN
ejpam-5951	132	3	(	(	PUNCT
ejpam-5951	132	4	hi	hi	INTJ
ejpam-5951	132	5	)	)	PUNCT
ejpam-5951	132	6	.	.	PUNCT
ejpam-5951	133	1	(	(	PUNCT
ejpam-5951	133	2	4	4	X
ejpam-5951	133	3	)	)	PUNCT
ejpam-5951	133	4	if	if	SCONJ
ejpam-5951	133	5	⋂	⋂	PROPN
ejpam-5951	133	6	i	i	PRON
ejpam-5951	133	7	f	f	X
ejpam-5951	133	8	(	(	PUNCT
ejpam-5951	133	9	hi	hi	INTJ
ejpam-5951	133	10	)	)	PUNCT
ejpam-5951	133	11	̸=	̸=	NOUN
ejpam-5951	133	12	∅	∅	NOUN
ejpam-5951	133	13	,	,	PUNCT
ejpam-5951	133	14	then	then	ADV
ejpam-5951	133	15	using	use	VERB
ejpam-5951	133	16	proposition	proposition	NOUN
ejpam-5951	133	17	2	2	NUM
ejpam-5951	133	18	(	(	PUNCT
ejpam-5951	133	19	2	2	NUM
ejpam-5951	133	20	)	)	PUNCT
ejpam-5951	133	21	the	the	DET
ejpam-5951	133	22	above	above	ADJ
ejpam-5951	133	23	problem	problem	NOUN
ejpam-5951	133	24	defined	define	VERB
ejpam-5951	133	25	as	as	SCONJ
ejpam-5951	133	26	find	find	VERB
ejpam-5951	133	27	ζ	ζ	NOUN
ejpam-5951	133	28	∈	∈	NOUN
ejpam-5951	133	29	γ	γ	NOUN
ejpam-5951	134	1	such	such	ADJ
ejpam-5951	134	2	that	that	SCONJ
ejpam-5951	134	3	ζ	ζ	NOUN
ejpam-5951	134	4	=	=	SYM
ejpam-5951	134	5	p⋂	p⋂	NOUN
ejpam-5951	135	1	i	i	PRON
ejpam-5951	135	2	f	f	X
ejpam-5951	135	3	(	(	PUNCT
ejpam-5951	135	4	hi)gλi	hi)gλi	X
ejpam-5951	135	5	(	(	PUNCT
ejpam-5951	135	6	ζ	ζ	NOUN
ejpam-5951	135	7	)	)	PUNCT
ejpam-5951	135	8	,	,	PUNCT
ejpam-5951	135	9	(	(	PUNCT
ejpam-5951	135	10	5	5	X
ejpam-5951	135	11	)	)	PUNCT
ejpam-5951	135	12	here	here	ADV
ejpam-5951	135	13	p⋂	p⋂	X
ejpam-5951	136	1	i	i	PRON
ejpam-5951	136	2	f	f	PROPN
ejpam-5951	136	3	(	(	PUNCT
ejpam-5951	136	4	hi	hi	INTJ
ejpam-5951	136	5	)	)	PUNCT
ejpam-5951	136	6	is	be	AUX
ejpam-5951	136	7	the	the	DET
ejpam-5951	136	8	metric	metric	ADJ
ejpam-5951	136	9	projection	projection	NOUN
ejpam-5951	136	10	of	of	ADP
ejpam-5951	136	11	γ	γ	NOUN
ejpam-5951	136	12	onto	onto	ADP
ejpam-5951	136	13	⋂	⋂	PROPN
ejpam-5951	136	14	i	i	PRON
ejpam-5951	136	15	f	f	PROPN
ejpam-5951	137	1	(	(	PUNCT
ejpam-5951	137	2	hi	hi	INTJ
ejpam-5951	137	3	)	)	PUNCT
ejpam-5951	137	4	.	.	PUNCT
ejpam-5951	138	1	we	we	PRON
ejpam-5951	138	2	denote	denote	VERB
ejpam-5951	138	3	the	the	DET
ejpam-5951	138	4	set	set	NOUN
ejpam-5951	138	5	of	of	ADP
ejpam-5951	138	6	solution	solution	NOUN
ejpam-5951	138	7	of	of	ADP
ejpam-5951	138	8	(	(	PUNCT
ejpam-5951	138	9	4	4	NUM
ejpam-5951	138	10	)	)	PUNCT
ejpam-5951	138	11	as	as	ADP
ejpam-5951	138	12	φ	φ	PROPN
ejpam-5951	138	13	=	=	SYM
ejpam-5951	138	14	{	{	PUNCT
ejpam-5951	138	15	ζ†	ζ†	NOUN
ejpam-5951	138	16	∈	∈	PROPN
ejpam-5951	138	17	γ	γ	X
ejpam-5951	138	18	:	:	PUNCT
ejpam-5951	138	19	ζ†	ζ†	NOUN
ejpam-5951	138	20	=	=	SYM
ejpam-5951	138	21	p⋂	p⋂	NOUN
ejpam-5951	139	1	i	i	PRON
ejpam-5951	139	2	f	f	X
ejpam-5951	139	3	(	(	PUNCT
ejpam-5951	139	4	hi)gλi	hi)gλi	X
ejpam-5951	139	5	(	(	PUNCT
ejpam-5951	139	6	ζ†	ζ†	NOUN
ejpam-5951	139	7	)	)	PUNCT
ejpam-5951	139	8	}	}	PUNCT
ejpam-5951	139	9	.	.	PUNCT
ejpam-5951	140	1	hierarchical	hierarchical	ADJ
ejpam-5951	140	2	variational	variational	ADJ
ejpam-5951	140	3	inequality	inequality	NOUN
ejpam-5951	140	4	problem	problem	NOUN
ejpam-5951	140	5	:	:	PUNCT
ejpam-5951	140	6	suppose	suppose	VERB
ejpam-5951	140	7	b	b	X
ejpam-5951	140	8	=	=	NOUN
ejpam-5951	140	9	̸	̸	VERB
ejpam-5951	140	10	∅	∅	NOUN
ejpam-5951	140	11	is	be	AUX
ejpam-5951	140	12	a	a	DET
ejpam-5951	140	13	geodesic	geodesic	ADJ
ejpam-5951	140	14	convex	convex	NOUN
ejpam-5951	140	15	,	,	PUNCT
ejpam-5951	140	16	closed	close	VERB
ejpam-5951	140	17	subset	subset	NOUN
ejpam-5951	140	18	of	of	ADP
ejpam-5951	140	19	γ	γ	PROPN
ejpam-5951	140	20	and	and	CCONJ
ejpam-5951	140	21	𭟋	𭟋	ADP
ejpam-5951	140	22	:	:	PUNCT
ejpam-5951	140	23	b	b	X
ejpam-5951	140	24	→	→	X
ejpam-5951	140	25	hγ	hγ	ADV
ejpam-5951	140	26	be	be	AUX
ejpam-5951	140	27	the	the	DET
ejpam-5951	140	28	monotone	monotone	ADJ
ejpam-5951	140	29	vector	vector	NOUN
ejpam-5951	140	30	field	field	NOUN
ejpam-5951	140	31	.	.	PUNCT
ejpam-5951	141	1	the	the	DET
ejpam-5951	141	2	problem	problem	NOUN
ejpam-5951	141	3	is	be	AUX
ejpam-5951	141	4	to	to	PART
ejpam-5951	141	5	find	find	VERB
ejpam-5951	141	6	ζ	ζ	NOUN
ejpam-5951	141	7	∈	∈	ADJ
ejpam-5951	141	8	b	b	NOUN
ejpam-5951	141	9	:	:	PUNCT
ejpam-5951	141	10	r	r	NOUN
ejpam-5951	141	11	(	(	PUNCT
ejpam-5951	141	12	𭟋(ζ	𭟋(ζ	PROPN
ejpam-5951	141	13	)	)	PUNCT
ejpam-5951	141	14	,	,	PUNCT
ejpam-5951	141	15	exp−1	exp−1	NOUN
ejpam-5951	141	16	ζ	ζ	NOUN
ejpam-5951	141	17	ν	ν	NOUN
ejpam-5951	141	18	)	)	PUNCT
ejpam-5951	141	19	≥	≥	NOUN
ejpam-5951	141	20	0	0	NUM
ejpam-5951	141	21	,	,	PUNCT
ejpam-5951	141	22	for	for	ADP
ejpam-5951	141	23	all	all	DET
ejpam-5951	141	24	ν	ν	X
ejpam-5951	141	25	∈	∈	PROPN
ejpam-5951	141	26	b.	b.	PROPN
ejpam-5951	141	27	(	(	PUNCT
ejpam-5951	141	28	6	6	X
ejpam-5951	141	29	)	)	PUNCT
ejpam-5951	141	30	suppose	suppose	VERB
ejpam-5951	141	31	gi	gi	INTJ
ejpam-5951	141	32	:	:	PUNCT
ejpam-5951	141	33	γ	γ	X
ejpam-5951	141	34	→	→	SYM
ejpam-5951	141	35	γ	γ	X
ejpam-5951	141	36	be	be	AUX
ejpam-5951	141	37	a	a	DET
ejpam-5951	141	38	countable	countable	ADJ
ejpam-5951	141	39	family	family	NOUN
ejpam-5951	141	40	of	of	ADP
ejpam-5951	141	41	β	β	NOUN
ejpam-5951	141	42	-	-	ADJ
ejpam-5951	141	43	strict	strict	ADJ
ejpam-5951	141	44	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	141	45	mappings	mapping	NOUN
ejpam-5951	141	46	.	.	PUNCT
ejpam-5951	142	1	then	then	ADV
ejpam-5951	142	2	the	the	DET
ejpam-5951	142	3	complimentary	complimentary	ADJ
ejpam-5951	142	4	vector	vector	NOUN
ejpam-5951	142	5	field	field	NOUN
ejpam-5951	142	6	of	of	ADP
ejpam-5951	142	7	the	the	DET
ejpam-5951	142	8	corresponding	corresponding	ADJ
ejpam-5951	142	9	family	family	NOUN
ejpam-5951	142	10	of	of	ADP
ejpam-5951	142	11	mappings	mapping	NOUN
ejpam-5951	142	12	gλi	gλi	NOUN
ejpam-5951	142	13	is	be	AUX
ejpam-5951	142	14	monotone	monotone	ADJ
ejpam-5951	142	15	by	by	ADP
ejpam-5951	142	16	theorem	theorem	NOUN
ejpam-5951	142	17	1	1	NUM
ejpam-5951	142	18	.	.	PUNCT
ejpam-5951	143	1	now	now	ADV
ejpam-5951	143	2	,	,	PUNCT
ejpam-5951	143	3	we	we	PRON
ejpam-5951	143	4	can	can	AUX
ejpam-5951	143	5	reduce	reduce	VERB
ejpam-5951	143	6	the	the	DET
ejpam-5951	143	7	problem	problem	NOUN
ejpam-5951	143	8	(	(	PUNCT
ejpam-5951	143	9	4	4	NUM
ejpam-5951	143	10	)	)	PUNCT
ejpam-5951	143	11	as	as	SCONJ
ejpam-5951	143	12	:	:	PUNCT
ejpam-5951	143	13	find	find	VERB
ejpam-5951	143	14	ζ	ζ	NOUN
ejpam-5951	143	15	∈	∈	ADJ
ejpam-5951	144	1	⋂	⋂	PROPN
ejpam-5951	145	1	i	i	PRON
ejpam-5951	145	2	f	f	PROPN
ejpam-5951	145	3	(	(	PUNCT
ejpam-5951	145	4	hi	hi	INTJ
ejpam-5951	145	5	)	)	PUNCT
ejpam-5951	145	6	:	:	PUNCT
ejpam-5951	146	1	r	r	X
ejpam-5951	146	2	(	(	PUNCT
ejpam-5951	146	3	𭟋(ζ	𭟋(ζ	PROPN
ejpam-5951	146	4	)	)	PUNCT
ejpam-5951	146	5	,	,	PUNCT
ejpam-5951	146	6	exp−1	exp−1	NOUN
ejpam-5951	146	7	ζ	ζ	NOUN
ejpam-5951	146	8	ν	ν	NOUN
ejpam-5951	146	9	)	)	PUNCT
ejpam-5951	146	10	≥	≥	NOUN
ejpam-5951	146	11	0	0	NUM
ejpam-5951	146	12	,	,	PUNCT
ejpam-5951	146	13	for	for	ADP
ejpam-5951	146	14	all	all	PRON
ejpam-5951	146	15	ν	ν	NOUN
ejpam-5951	146	16	∈	∈	PROPN
ejpam-5951	146	17	⋂	⋂	PROPN
ejpam-5951	147	1	i	i	PRON
ejpam-5951	147	2	f	f	PROPN
ejpam-5951	147	3	(	(	PUNCT
ejpam-5951	147	4	hi	hi	INTJ
ejpam-5951	147	5	)	)	PUNCT
ejpam-5951	147	6	.	.	PUNCT
ejpam-5951	148	1	(	(	PUNCT
ejpam-5951	148	2	7	7	X
ejpam-5951	148	3	)	)	PUNCT
ejpam-5951	148	4	p.	p.	NOUN
ejpam-5951	148	5	patel	patel	PROPN
ejpam-5951	148	6	,	,	PUNCT
ejpam-5951	148	7	r.	r.	PROPN
ejpam-5951	148	8	shukla	shukla	PROPN
ejpam-5951	148	9	/	/	SYM
ejpam-5951	148	10	eur	eur	PROPN
ejpam-5951	148	11	.	.	PUNCT
ejpam-5951	149	1	j.	j.	PROPN
ejpam-5951	149	2	pure	pure	PROPN
ejpam-5951	149	3	appl	appl	PROPN
ejpam-5951	149	4	.	.	PROPN
ejpam-5951	149	5	math	math	PROPN
ejpam-5951	149	6	,	,	PUNCT
ejpam-5951	149	7	18	18	NUM
ejpam-5951	149	8	(	(	PUNCT
ejpam-5951	149	9	2	2	NUM
ejpam-5951	149	10	)	)	PUNCT
ejpam-5951	149	11	(	(	PUNCT
ejpam-5951	149	12	2025	2025	NUM
ejpam-5951	149	13	)	)	PUNCT
ejpam-5951	149	14	,	,	PUNCT
ejpam-5951	149	15	5951	5951	NUM
ejpam-5951	149	16	7	7	NUM
ejpam-5951	149	17	of	of	ADP
ejpam-5951	149	18	15	15	NUM
ejpam-5951	149	19	where	where	SCONJ
ejpam-5951	149	20	𭟋	𭟋	NOUN
ejpam-5951	149	21	=	=	PUNCT
ejpam-5951	149	22	−	−	PROPN
ejpam-5951	149	23	exp−1gλi	exp−1gλi	NOUN
ejpam-5951	149	24	is	be	AUX
ejpam-5951	149	25	the	the	DET
ejpam-5951	149	26	complimentary	complimentary	ADJ
ejpam-5951	149	27	vector	vector	NOUN
ejpam-5951	149	28	field	field	NOUN
ejpam-5951	149	29	of	of	ADP
ejpam-5951	149	30	gλi	gλi	NOUN
ejpam-5951	149	31	.	.	PUNCT
ejpam-5951	150	1	in	in	ADP
ejpam-5951	150	2	the	the	DET
ejpam-5951	150	3	context	context	NOUN
ejpam-5951	150	4	of	of	ADP
ejpam-5951	150	5	normal	normal	ADJ
ejpam-5951	150	6	cone	cone	NOUN
ejpam-5951	150	7	the	the	DET
ejpam-5951	150	8	set	set	NOUN
ejpam-5951	150	9	⋂	⋂	PROPN
ejpam-5951	150	10	i	i	PRON
ejpam-5951	150	11	f	f	PROPN
ejpam-5951	150	12	(	(	PUNCT
ejpam-5951	150	13	hi	hi	INTJ
ejpam-5951	150	14	)	)	PUNCT
ejpam-5951	150	15	,	,	PUNCT
ejpam-5951	150	16	we	we	PRON
ejpam-5951	150	17	can	can	AUX
ejpam-5951	150	18	easily	easily	ADV
ejpam-5951	150	19	see	see	VERB
ejpam-5951	150	20	that	that	DET
ejpam-5951	150	21	problem	problem	NOUN
ejpam-5951	150	22	(	(	PUNCT
ejpam-5951	150	23	7	7	X
ejpam-5951	150	24	)	)	PUNCT
ejpam-5951	150	25	is	be	AUX
ejpam-5951	150	26	equivalent	equivalent	ADJ
ejpam-5951	150	27	to	to	ADP
ejpam-5951	150	28	the	the	DET
ejpam-5951	150	29	following	follow	VERB
ejpam-5951	150	30	find	find	VERB
ejpam-5951	150	31	ζ	ζ	NOUN
ejpam-5951	150	32	∈	∈	ADJ
ejpam-5951	151	1	⋂	⋂	PROPN
ejpam-5951	152	1	i	i	PRON
ejpam-5951	152	2	f	f	PROPN
ejpam-5951	152	3	(	(	PUNCT
ejpam-5951	152	4	hi	hi	INTJ
ejpam-5951	152	5	)	)	PUNCT
ejpam-5951	152	6	:	:	PUNCT
ejpam-5951	152	7	0	0	NUM
ejpam-5951	152	8	∈	∈	NOUN
ejpam-5951	152	9	−	−	NOUN
ejpam-5951	152	10	exp−1	exp−1	PROPN
ejpam-5951	152	11	ζ	ζ	PROPN
ejpam-5951	152	12	gλi	gλi	NOUN
ejpam-5951	152	13	(	(	PUNCT
ejpam-5951	152	14	ζ	ζ	NOUN
ejpam-5951	152	15	)	)	PUNCT
ejpam-5951	152	16	+	+	NOUN
ejpam-5951	152	17	n⋂	n⋂	NOUN
ejpam-5951	152	18	i	i	PRON
ejpam-5951	152	19	f	f	X
ejpam-5951	152	20	(	(	PUNCT
ejpam-5951	152	21	hi)(ζ	hi)(ζ	ADJ
ejpam-5951	152	22	)	)	PUNCT
ejpam-5951	152	23	.	.	PUNCT
ejpam-5951	153	1	(	(	PUNCT
ejpam-5951	153	2	8)	8)	NUM
ejpam-5951	153	3	here	here	ADV
ejpam-5951	153	4	n⋂	n⋂	VERB
ejpam-5951	154	1	i	i	PRON
ejpam-5951	154	2	f	f	PROPN
ejpam-5951	154	3	(	(	PUNCT
ejpam-5951	154	4	hi	hi	INTJ
ejpam-5951	154	5	)	)	PUNCT
ejpam-5951	154	6	is	be	AUX
ejpam-5951	154	7	normal	normal	ADJ
ejpam-5951	154	8	cone	cone	NOUN
ejpam-5951	154	9	onto	onto	ADP
ejpam-5951	154	10	set	set	NOUN
ejpam-5951	154	11	⋂	⋂	PROPN
ejpam-5951	155	1	i	i	PRON
ejpam-5951	155	2	f	f	PROPN
ejpam-5951	155	3	(	(	PUNCT
ejpam-5951	155	4	hi	hi	INTJ
ejpam-5951	155	5	)	)	PUNCT
ejpam-5951	155	6	at	at	ADP
ejpam-5951	155	7	ζ	ζ	NOUN
ejpam-5951	155	8	∈	∈	PROPN
ejpam-5951	155	9	⋂	⋂	PROPN
ejpam-5951	156	1	i	i	PRON
ejpam-5951	156	2	f	f	PROPN
ejpam-5951	156	3	(	(	PUNCT
ejpam-5951	156	4	hi	hi	INTJ
ejpam-5951	156	5	)	)	PUNCT
ejpam-5951	156	6	,	,	PUNCT
ejpam-5951	156	7	and	and	CCONJ
ejpam-5951	156	8	defined	define	VERB
ejpam-5951	156	9	as	as	ADP
ejpam-5951	156	10	n⋂	n⋂	NOUN
ejpam-5951	156	11	i	i	PRON
ejpam-5951	156	12	f	f	X
ejpam-5951	156	13	(	(	PUNCT
ejpam-5951	156	14	hi)(ζ	hi)(ζ	PUNCT
ejpam-5951	156	15	)	)	PUNCT
ejpam-5951	156	16	=	=	SYM
ejpam-5951	156	17	{	{	PUNCT
ejpam-5951	156	18	µ	µ	PROPN
ejpam-5951	156	19	∈	∈	PROPN
ejpam-5951	156	20	hλiζ	hλiζ	NOUN
ejpam-5951	156	21	γ	γ	NOUN
ejpam-5951	156	22	:	:	PUNCT
ejpam-5951	156	23	r	r	NOUN
ejpam-5951	156	24	(	(	PUNCT
ejpam-5951	156	25	µ	µ	NOUN
ejpam-5951	156	26	,	,	PUNCT
ejpam-5951	156	27	exp−1	exp−1	PROPN
ejpam-5951	156	28	ζ	ζ	NOUN
ejpam-5951	156	29	ν	ν	NOUN
ejpam-5951	156	30	)	)	PUNCT
ejpam-5951	156	31	≤	≤	NOUN
ejpam-5951	156	32	0	0	NUM
ejpam-5951	156	33	,	,	PUNCT
ejpam-5951	156	34	for	for	ADP
ejpam-5951	156	35	all	all	DET
ejpam-5951	156	36	ν	ν	NOUN
ejpam-5951	156	37	∈	∈	PROPN
ejpam-5951	156	38	⋂	⋂	PROPN
ejpam-5951	156	39	i	i	PRON
ejpam-5951	156	40	f	f	PROPN
ejpam-5951	156	41	(	(	PUNCT
ejpam-5951	156	42	hi	hi	INTJ
ejpam-5951	156	43	)	)	PUNCT
ejpam-5951	156	44	}	}	PUNCT
ejpam-5951	156	45	.	.	PUNCT
ejpam-5951	157	1	now	now	ADV
ejpam-5951	157	2	,	,	PUNCT
ejpam-5951	157	3	we	we	PRON
ejpam-5951	157	4	present	present	VERB
ejpam-5951	157	5	a	a	DET
ejpam-5951	157	6	new	new	ADJ
ejpam-5951	157	7	algorithm	algorithm	NOUN
ejpam-5951	157	8	to	to	PART
ejpam-5951	157	9	approximate	approximate	VERB
ejpam-5951	157	10	the	the	DET
ejpam-5951	157	11	solution	solution	NOUN
ejpam-5951	157	12	of	of	ADP
ejpam-5951	157	13	the	the	DET
ejpam-5951	157	14	problem	problem	NOUN
ejpam-5951	157	15	(	(	PUNCT
ejpam-5951	157	16	4	4	NUM
ejpam-5951	157	17	)	)	PUNCT
ejpam-5951	157	18	.	.	PUNCT
ejpam-5951	158	1	suppose	suppose	VERB
ejpam-5951	158	2	γ	γ	NOUN
ejpam-5951	158	3	be	be	AUX
ejpam-5951	158	4	a	a	DET
ejpam-5951	158	5	hadamard	hadamard	ADJ
ejpam-5951	158	6	manifold	manifold	NOUN
ejpam-5951	158	7	and	and	CCONJ
ejpam-5951	158	8	gi	gi	INTJ
ejpam-5951	158	9	,	,	PUNCT
ejpam-5951	158	10	hi	hi	INTJ
ejpam-5951	158	11	:	:	PUNCT
ejpam-5951	158	12	γ	γ	X
ejpam-5951	158	13	→	→	SYM
ejpam-5951	158	14	γ	γ	X
ejpam-5951	158	15	be	be	AUX
ejpam-5951	158	16	two	two	NUM
ejpam-5951	158	17	countable	countable	ADJ
ejpam-5951	158	18	family	family	NOUN
ejpam-5951	158	19	of	of	ADP
ejpam-5951	158	20	β	β	NOUN
ejpam-5951	158	21	-	-	ADJ
ejpam-5951	158	22	strict	strict	ADJ
ejpam-5951	158	23	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	158	24	mappings	mapping	NOUN
ejpam-5951	158	25	with	with	ADP
ejpam-5951	158	26	β	β	X
ejpam-5951	158	27	∈	∈	PROPN
ejpam-5951	158	28	(	(	PUNCT
ejpam-5951	158	29	0	0	NUM
ejpam-5951	158	30	,	,	PUNCT
ejpam-5951	158	31	1	1	NUM
ejpam-5951	158	32	]	]	PUNCT
ejpam-5951	158	33	.	.	PUNCT
ejpam-5951	159	1	assume	assume	VERB
ejpam-5951	159	2	that	that	SCONJ
ejpam-5951	159	3	ζ1	ζ1	PROPN
ejpam-5951	159	4	∈	∈	PROPN
ejpam-5951	159	5	γ	γ	NOUN
ejpam-5951	159	6	and	and	CCONJ
ejpam-5951	159	7	b1	b1	NOUN
ejpam-5951	159	8	=	=	SYM
ejpam-5951	159	9	γ	γ	PROPN
ejpam-5951	159	10	,	,	PUNCT
ejpam-5951	159	11	we	we	PRON
ejpam-5951	159	12	can	can	AUX
ejpam-5951	159	13	generate	generate	VERB
ejpam-5951	159	14	sequences	sequence	NOUN
ejpam-5951	159	15	{	{	PUNCT
ejpam-5951	159	16	ζn	ζn	NOUN
ejpam-5951	159	17	}	}	PUNCT
ejpam-5951	159	18	and	and	CCONJ
ejpam-5951	159	19	{	{	PUNCT
ejpam-5951	159	20	ϑn	ϑn	NOUN
ejpam-5951	159	21	}	}	PUNCT
ejpam-5951	159	22	as	as	ADP
ejpam-5951	159	23	follows:	follows:	NOUN
ejpam-5951	159	24	ϑn	ϑn	NOUN
ejpam-5951	159	25	=	=	NOUN
ejpam-5951	159	26	expgλi	expgλi	NOUN
ejpam-5951	159	27	(	(	PUNCT
ejpam-5951	159	28	ζn)(1−	ζn)(1−	PROPN
ejpam-5951	159	29	δn	δn	NOUN
ejpam-5951	159	30	)	)	PUNCT
ejpam-5951	159	31	exp	exp	NOUN
ejpam-5951	159	32	−1	−1	NOUN
ejpam-5951	159	33	gλi	gλi	NOUN
ejpam-5951	159	34	(	(	PUNCT
ejpam-5951	159	35	ζn	ζn	NOUN
ejpam-5951	159	36	)	)	PUNCT
ejpam-5951	159	37	hλi	hλi	NOUN
ejpam-5951	159	38	(	(	PUNCT
ejpam-5951	159	39	ζn	ζn	NOUN
ejpam-5951	159	40	)	)	PUNCT
ejpam-5951	159	41	,	,	PUNCT
ejpam-5951	159	42	bn+1	bn+1	X
ejpam-5951	159	43	=	=	SYM
ejpam-5951	159	44	{	{	PUNCT
ejpam-5951	159	45	ν	ν	X
ejpam-5951	159	46	∈	∈	PROPN
ejpam-5951	159	47	bn	bn	NOUN
ejpam-5951	159	48	:	:	PUNCT
ejpam-5951	159	49	ρ(ϑn	ρ(ϑn	NUM
ejpam-5951	159	50	,	,	PUNCT
ejpam-5951	159	51	ν	ν	NOUN
ejpam-5951	159	52	)	)	PUNCT
ejpam-5951	159	53	≤	≤	NOUN
ejpam-5951	159	54	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	159	55	,	,	PUNCT
ejpam-5951	159	56	ν	ν	NOUN
ejpam-5951	159	57	)	)	PUNCT
ejpam-5951	159	58	}	}	PUNCT
ejpam-5951	159	59	,	,	PUNCT
ejpam-5951	159	60	ζn+1	ζn+1	ADJ
ejpam-5951	159	61	=	=	SYM
ejpam-5951	159	62	pbn+1(ζ1	pbn+1(ζ1	NOUN
ejpam-5951	159	63	)	)	PUNCT
ejpam-5951	159	64	,	,	PUNCT
ejpam-5951	159	65	for	for	ADP
ejpam-5951	159	66	all	all	DET
ejpam-5951	159	67	n	n	PRON
ejpam-5951	159	68	≥	≥	NOUN
ejpam-5951	159	69	1	1	NUM
ejpam-5951	159	70	.	.	PUNCT
ejpam-5951	160	1	(	(	PUNCT
ejpam-5951	160	2	9	9	NUM
ejpam-5951	160	3	)	)	PUNCT
ejpam-5951	160	4	here	here	ADV
ejpam-5951	160	5	,	,	PUNCT
ejpam-5951	160	6	gλi	gλi	NOUN
ejpam-5951	160	7	(	(	PUNCT
ejpam-5951	160	8	ζ	ζ	NOUN
ejpam-5951	160	9	)	)	PUNCT
ejpam-5951	160	10	=	=	SYM
ejpam-5951	160	11	expζ	expζ	NOUN
ejpam-5951	160	12	λ	λ	AUX
ejpam-5951	160	13	exp−1	exp−1	PROPN
ejpam-5951	160	14	ζ	ζ	X
ejpam-5951	160	15	gi(ζ	gi(ζ	NOUN
ejpam-5951	160	16	)	)	PUNCT
ejpam-5951	160	17	,	,	PUNCT
ejpam-5951	160	18	hλi	hλi	NOUN
ejpam-5951	160	19	(	(	PUNCT
ejpam-5951	160	20	ζ	ζ	NOUN
ejpam-5951	160	21	)	)	PUNCT
ejpam-5951	160	22	=	=	SYM
ejpam-5951	160	23	expζ	expζ	NOUN
ejpam-5951	160	24	λ	λ	X
ejpam-5951	160	25	exp−1	exp−1	PROPN
ejpam-5951	160	26	ζ	ζ	PROPN
ejpam-5951	160	27	hi(ζ	hi(ζ	NOUN
ejpam-5951	160	28	)	)	PUNCT
ejpam-5951	160	29	,	,	PUNCT
ejpam-5951	160	30	{	{	PUNCT
ejpam-5951	160	31	δn	δn	NOUN
ejpam-5951	160	32	}	}	PUNCT
ejpam-5951	160	33	∈	∈	PROPN
ejpam-5951	160	34	(	(	PUNCT
ejpam-5951	160	35	0	0	NUM
ejpam-5951	160	36	,	,	PUNCT
ejpam-5951	160	37	1	1	X
ejpam-5951	160	38	)	)	PUNCT
ejpam-5951	160	39	satisfying	satisfy	VERB
ejpam-5951	160	40	0	0	NUM
ejpam-5951	160	41	<	<	X
ejpam-5951	160	42	δ1	δ1	NOUN
ejpam-5951	160	43	≤	≤	NUM
ejpam-5951	160	44	δn	δn	NOUN
ejpam-5951	160	45	≤	≤	X
ejpam-5951	160	46	δ2	δ2	VERB
ejpam-5951	160	47	<	<	X
ejpam-5951	160	48	1	1	NUM
ejpam-5951	160	49	and	and	CCONJ
ejpam-5951	160	50	lim	lim	PROPN
ejpam-5951	160	51	n→+∞	n→+∞	VERB
ejpam-5951	160	52	δn	δn	NOUN
ejpam-5951	160	53	=	=	SYM
ejpam-5951	160	54	0	0	X
ejpam-5951	160	55	.	.	PUNCT
ejpam-5951	160	56	theorem	theorem	NOUN
ejpam-5951	160	57	2	2	NUM
ejpam-5951	160	58	.	.	PUNCT
ejpam-5951	160	59	suppose	suppose	VERB
ejpam-5951	160	60	γ	γ	X
ejpam-5951	160	61	,	,	PUNCT
ejpam-5951	160	62	gi	gi	INTJ
ejpam-5951	160	63	,	,	PUNCT
ejpam-5951	160	64	hi	hi	INTJ
ejpam-5951	160	65	are	be	AUX
ejpam-5951	160	66	same	same	ADJ
ejpam-5951	160	67	as	as	ADP
ejpam-5951	160	68	defined	define	VERB
ejpam-5951	160	69	above	above	ADV
ejpam-5951	160	70	and	and	CCONJ
ejpam-5951	160	71	π	π	PROPN
ejpam-5951	160	72	=	=	SYM
ejpam-5951	160	73	φ	φ	PROPN
ejpam-5951	160	74	⋂	⋂	PROPN
ejpam-5951	161	1	i	i	PRON
ejpam-5951	161	2	f	f	X
ejpam-5951	161	3	(	(	PUNCT
ejpam-5951	161	4	gi	gi	INTJ
ejpam-5951	161	5	)	)	PUNCT
ejpam-5951	161	6	̸=	̸=	PROPN
ejpam-5951	161	7	∅.	∅.	VERB
ejpam-5951	161	8	for	for	ADP
ejpam-5951	161	9	b1	b1	NOUN
ejpam-5951	161	10	=	=	X
ejpam-5951	161	11	γ	γ	X
ejpam-5951	161	12	the	the	DET
ejpam-5951	161	13	sequence	sequence	NOUN
ejpam-5951	161	14	generated	generate	VERB
ejpam-5951	161	15	by	by	ADP
ejpam-5951	161	16	(	(	PUNCT
ejpam-5951	161	17	9	9	X
ejpam-5951	161	18	)	)	PUNCT
ejpam-5951	161	19	converges	converge	NOUN
ejpam-5951	161	20	to	to	ADP
ejpam-5951	161	21	pπ(ζ1	pπ(ζ1	NOUN
ejpam-5951	161	22	)	)	PUNCT
ejpam-5951	161	23	.	.	PUNCT
ejpam-5951	162	1	proof	proof	NOUN
ejpam-5951	162	2	.	.	PUNCT
ejpam-5951	163	1	since	since	SCONJ
ejpam-5951	163	2	φ	φ	PROPN
ejpam-5951	163	3	=	=	SYM
ejpam-5951	163	4	f	f	PROPN
ejpam-5951	163	5	(	(	PUNCT
ejpam-5951	163	6	p⋂	p⋂	INTJ
ejpam-5951	164	1	i	i	PRON
ejpam-5951	164	2	f	f	X
ejpam-5951	164	3	(	(	PUNCT
ejpam-5951	164	4	hi)gi	hi)gi	NOUN
ejpam-5951	164	5	)	)	PUNCT
ejpam-5951	164	6	̸=	̸=	NOUN
ejpam-5951	164	7	∅	∅	NOUN
ejpam-5951	164	8	,	,	PUNCT
ejpam-5951	164	9	it	it	PRON
ejpam-5951	164	10	can	can	AUX
ejpam-5951	164	11	be	be	AUX
ejpam-5951	164	12	easily	easily	ADV
ejpam-5951	164	13	seen	see	VERB
ejpam-5951	164	14	that	that	SCONJ
ejpam-5951	164	15	φ	φ	PROPN
ejpam-5951	164	16	is	be	AUX
ejpam-5951	164	17	geodesic	geodesic	ADJ
ejpam-5951	164	18	convex	convex	NOUN
ejpam-5951	164	19	and	and	CCONJ
ejpam-5951	164	20	closed	close	VERB
ejpam-5951	164	21	and	and	CCONJ
ejpam-5951	164	22	f	f	X
ejpam-5951	164	23	(	(	PUNCT
ejpam-5951	164	24	gi	gi	INTJ
ejpam-5951	164	25	)	)	PUNCT
ejpam-5951	164	26	is	be	AUX
ejpam-5951	164	27	also	also	ADV
ejpam-5951	164	28	geodesic	geodesic	ADJ
ejpam-5951	164	29	convex	convex	NOUN
ejpam-5951	164	30	and	and	CCONJ
ejpam-5951	164	31	closed	closed	ADJ
ejpam-5951	164	32	.	.	PUNCT
ejpam-5951	165	1	therefore	therefore	ADV
ejpam-5951	165	2	π	π	PROPN
ejpam-5951	165	3	is	be	AUX
ejpam-5951	165	4	also	also	ADV
ejpam-5951	165	5	geodesic	geodesic	ADJ
ejpam-5951	165	6	convex	convex	NOUN
ejpam-5951	165	7	and	and	CCONJ
ejpam-5951	165	8	closed	close	VERB
ejpam-5951	165	9	,	,	PUNCT
ejpam-5951	165	10	indicating	indicate	VERB
ejpam-5951	165	11	that	that	SCONJ
ejpam-5951	165	12	pπ(ζ1	pπ(ζ1	NOUN
ejpam-5951	165	13	)	)	PUNCT
ejpam-5951	165	14	is	be	AUX
ejpam-5951	165	15	well	well	ADV
ejpam-5951	165	16	defined	define	VERB
ejpam-5951	165	17	.	.	PUNCT
ejpam-5951	166	1	now	now	ADV
ejpam-5951	166	2	we	we	PRON
ejpam-5951	166	3	prove	prove	VERB
ejpam-5951	166	4	that	that	SCONJ
ejpam-5951	166	5	the	the	DET
ejpam-5951	166	6	set	set	NOUN
ejpam-5951	166	7	bn	bn	NOUN
ejpam-5951	166	8	is	be	AUX
ejpam-5951	166	9	closed	closed	ADJ
ejpam-5951	166	10	and	and	CCONJ
ejpam-5951	166	11	geodesic	geodesic	ADJ
ejpam-5951	166	12	convex	convex	NOUN
ejpam-5951	166	13	subset	subset	NOUN
ejpam-5951	166	14	of	of	ADP
ejpam-5951	166	15	γ	γ	NOUN
ejpam-5951	166	16	for	for	ADP
ejpam-5951	166	17	all	all	DET
ejpam-5951	166	18	n	n	PRON
ejpam-5951	166	19	≥	≥	NOUN
ejpam-5951	166	20	1	1	NUM
ejpam-5951	166	21	.	.	PUNCT
ejpam-5951	167	1	we	we	PRON
ejpam-5951	167	2	prove	prove	VERB
ejpam-5951	167	3	this	this	PRON
ejpam-5951	167	4	by	by	ADP
ejpam-5951	167	5	mathematical	mathematical	ADJ
ejpam-5951	167	6	induction	induction	NOUN
ejpam-5951	167	7	.	.	PUNCT
ejpam-5951	168	1	if	if	SCONJ
ejpam-5951	168	2	b1	b1	NOUN
ejpam-5951	168	3	=	=	SYM
ejpam-5951	168	4	γ	γ	PROPN
ejpam-5951	168	5	,	,	PUNCT
ejpam-5951	168	6	then	then	ADV
ejpam-5951	168	7	it	it	PRON
ejpam-5951	168	8	is	be	AUX
ejpam-5951	168	9	geodesic	geodesic	ADJ
ejpam-5951	168	10	convex	convex	NOUN
ejpam-5951	168	11	and	and	CCONJ
ejpam-5951	168	12	closed	closed	ADJ
ejpam-5951	168	13	.	.	PUNCT
ejpam-5951	169	1	now	now	ADV
ejpam-5951	169	2	,	,	PUNCT
ejpam-5951	169	3	let	let	VERB
ejpam-5951	169	4	us	we	PRON
ejpam-5951	169	5	assume	assume	VERB
ejpam-5951	169	6	that	that	SCONJ
ejpam-5951	169	7	bn	bn	PRON
ejpam-5951	169	8	is	be	AUX
ejpam-5951	169	9	geodesic	geodesic	ADJ
ejpam-5951	169	10	convex	convex	NOUN
ejpam-5951	169	11	and	and	CCONJ
ejpam-5951	169	12	closed	closed	ADJ
ejpam-5951	169	13	subset	subset	NOUN
ejpam-5951	169	14	in	in	ADP
ejpam-5951	169	15	γ	γ	NOUN
ejpam-5951	169	16	for	for	ADP
ejpam-5951	169	17	some	some	DET
ejpam-5951	169	18	n	n	PRON
ejpam-5951	169	19	≥	≥	NOUN
ejpam-5951	169	20	2	2	NUM
ejpam-5951	169	21	.	.	PUNCT
ejpam-5951	170	1	then	then	ADV
ejpam-5951	170	2	we	we	PRON
ejpam-5951	170	3	need	need	VERB
ejpam-5951	170	4	to	to	PART
ejpam-5951	170	5	prove	prove	VERB
ejpam-5951	170	6	that	that	SCONJ
ejpam-5951	170	7	bn+1	bn+1	PROPN
ejpam-5951	170	8	is	be	AUX
ejpam-5951	170	9	a	a	DET
ejpam-5951	170	10	geodesic	geodesic	ADJ
ejpam-5951	170	11	convex	convex	NOUN
ejpam-5951	170	12	and	and	CCONJ
ejpam-5951	170	13	closed	closed	ADJ
ejpam-5951	170	14	subset	subset	NOUN
ejpam-5951	170	15	of	of	ADP
ejpam-5951	170	16	γ	γ	PROPN
ejpam-5951	170	17	.	.	PROPN
ejpam-5951	170	18	since	since	SCONJ
ejpam-5951	170	19	ν	ν	PROPN
ejpam-5951	170	20	7→	7→	PROPN
ejpam-5951	170	21	ρ(ζ	ρ(ζ	NOUN
ejpam-5951	170	22	,	,	PUNCT
ejpam-5951	170	23	ν	ν	X
ejpam-5951	170	24	)	)	PUNCT
ejpam-5951	170	25	is	be	AUX
ejpam-5951	170	26	a	a	DET
ejpam-5951	170	27	convex	convex	ADJ
ejpam-5951	170	28	geodesic	geodesic	NOUN
ejpam-5951	170	29	function	function	NOUN
ejpam-5951	170	30	,	,	PUNCT
ejpam-5951	170	31	we	we	PRON
ejpam-5951	170	32	can	can	AUX
ejpam-5951	170	33	easily	easily	ADV
ejpam-5951	170	34	say	say	VERB
ejpam-5951	170	35	that	that	SCONJ
ejpam-5951	170	36	bn+1	bn+1	PROPN
ejpam-5951	170	37	is	be	AUX
ejpam-5951	170	38	a	a	DET
ejpam-5951	170	39	closed	closed	ADJ
ejpam-5951	170	40	and	and	CCONJ
ejpam-5951	170	41	geodesic	geodesic	ADJ
ejpam-5951	170	42	convex	convex	NOUN
ejpam-5951	170	43	subset	subset	NOUN
ejpam-5951	170	44	of	of	ADP
ejpam-5951	170	45	γ	γ	PROPN
ejpam-5951	170	46	.	.	PROPN
ejpam-5951	171	1	next	next	ADV
ejpam-5951	171	2	we	we	PRON
ejpam-5951	171	3	prove	prove	VERB
ejpam-5951	171	4	that	that	SCONJ
ejpam-5951	171	5	π	π	PROPN
ejpam-5951	171	6	⊂	⊂	X
ejpam-5951	171	7	bn	bn	PROPN
ejpam-5951	171	8	for	for	ADP
ejpam-5951	171	9	all	all	DET
ejpam-5951	171	10	n	n	PRON
ejpam-5951	171	11	≥	≥	NOUN
ejpam-5951	171	12	1	1	NUM
ejpam-5951	171	13	.	.	PUNCT
ejpam-5951	172	1	we	we	PRON
ejpam-5951	172	2	can	can	AUX
ejpam-5951	172	3	easily	easily	ADV
ejpam-5951	172	4	see	see	VERB
ejpam-5951	172	5	that	that	SCONJ
ejpam-5951	172	6	π	π	PROPN
ejpam-5951	172	7	⊂	⊂	PROPN
ejpam-5951	172	8	b1	b1	PROPN
ejpam-5951	172	9	=	=	SYM
ejpam-5951	172	10	γ	γ	PROPN
ejpam-5951	172	11	.	.	PUNCT
ejpam-5951	173	1	now	now	ADV
ejpam-5951	173	2	we	we	PRON
ejpam-5951	173	3	prove	prove	VERB
ejpam-5951	173	4	that	that	SCONJ
ejpam-5951	173	5	π	π	PROPN
ejpam-5951	173	6	⊂	⊂	X
ejpam-5951	173	7	bn	bn	PROPN
ejpam-5951	173	8	for	for	ADP
ejpam-5951	173	9	all	all	DET
ejpam-5951	173	10	n	n	PRON
ejpam-5951	173	11	≥	≥	NOUN
ejpam-5951	173	12	2	2	NUM
ejpam-5951	173	13	.	.	PUNCT
ejpam-5951	174	1	if	if	SCONJ
ejpam-5951	174	2	ζ†	ζ†	NOUN
ejpam-5951	174	3	∈	∈	PROPN
ejpam-5951	174	4	π	π	PROPN
ejpam-5951	174	5	,	,	PUNCT
ejpam-5951	174	6	then	then	ADV
ejpam-5951	174	7	ζ†	ζ†	PROPN
ejpam-5951	174	8	∈	∈	PROPN
ejpam-5951	174	9	φ	φ	PROPN
ejpam-5951	174	10	and	and	CCONJ
ejpam-5951	174	11	ζ†	ζ†	NOUN
ejpam-5951	174	12	∈	∈	PROPN
ejpam-5951	174	13	⋂	⋂	PROPN
ejpam-5951	175	1	i	i	PRON
ejpam-5951	175	2	f	f	PROPN
ejpam-5951	175	3	(	(	PUNCT
ejpam-5951	175	4	gλi	gλi	PROPN
ejpam-5951	175	5	)	)	PUNCT
ejpam-5951	175	6	.	.	PUNCT
ejpam-5951	176	1	now	now	ADV
ejpam-5951	176	2	let	let	VERB
ejpam-5951	176	3	for	for	ADP
ejpam-5951	176	4	a	a	DET
ejpam-5951	176	5	fix	fix	NOUN
ejpam-5951	176	6	n	n	CCONJ
ejpam-5951	176	7	∈	∈	NOUN
ejpam-5951	176	8	n	n	CCONJ
ejpam-5951	176	9	,	,	PUNCT
ejpam-5951	176	10	∆(gλi	∆(gλi	PROPN
ejpam-5951	176	11	(	(	PUNCT
ejpam-5951	176	12	ζn	ζn	NOUN
ejpam-5951	176	13	)	)	PUNCT
ejpam-5951	176	14	,	,	PUNCT
ejpam-5951	176	15	hλi	hλi	NOUN
ejpam-5951	176	16	(	(	PUNCT
ejpam-5951	176	17	ζn	ζn	NOUN
ejpam-5951	176	18	)	)	PUNCT
ejpam-5951	176	19	,	,	PUNCT
ejpam-5951	176	20	ζ	ζ	PROPN
ejpam-5951	176	21	†	†	NOUN
ejpam-5951	176	22	)	)	PUNCT
ejpam-5951	176	23	⊆	⊆	NUM
ejpam-5951	176	24	γ	γ	X
ejpam-5951	176	25	be	be	VERB
ejpam-5951	176	26	a	a	DET
ejpam-5951	176	27	geodesic	geodesic	ADJ
ejpam-5951	176	28	triangle	triangle	NOUN
ejpam-5951	176	29	with	with	ADP
ejpam-5951	176	30	vertices	vertex	NOUN
ejpam-5951	176	31	gλi	gλi	VERB
ejpam-5951	176	32	(	(	PUNCT
ejpam-5951	176	33	ζn	ζn	NOUN
ejpam-5951	176	34	)	)	PUNCT
ejpam-5951	176	35	,	,	PUNCT
ejpam-5951	176	36	hλi	hλi	NOUN
ejpam-5951	176	37	(	(	PUNCT
ejpam-5951	176	38	ζn	ζn	NOUN
ejpam-5951	176	39	)	)	PUNCT
ejpam-5951	176	40	and	and	CCONJ
ejpam-5951	176	41	ζ†	ζ†	NOUN
ejpam-5951	176	42	,	,	PUNCT
ejpam-5951	176	43	and	and	CCONJ
ejpam-5951	176	44	∆(gλi	∆(gλi	PROPN
ejpam-5951	176	45	(	(	PUNCT
ejpam-5951	176	46	ζn	ζn	NOUN
ejpam-5951	176	47	)	)	PUNCT
ejpam-5951	176	48	,	,	PUNCT
ejpam-5951	176	49	hλi	hλi	NOUN
ejpam-5951	176	50	(	(	PUNCT
ejpam-5951	176	51	ζn	ζn	NOUN
ejpam-5951	176	52	)	)	PUNCT
ejpam-5951	176	53	,	,	PUNCT
ejpam-5951	176	54	ζ†	ζ†	NOUN
ejpam-5951	176	55	)	)	PUNCT
ejpam-5951	176	56	⊆	⊆	NUM
ejpam-5951	176	57	r2	r2	NOUN
ejpam-5951	176	58	a	a	DET
ejpam-5951	176	59	corresponding	correspond	VERB
ejpam-5951	176	60	comparison	comparison	NOUN
ejpam-5951	176	61	triangle	triangle	NOUN
ejpam-5951	176	62	.	.	PUNCT
ejpam-5951	177	1	we	we	PRON
ejpam-5951	177	2	have	have	VERB
ejpam-5951	177	3	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	177	4	(	(	PUNCT
ejpam-5951	177	5	ζn	ζn	NOUN
ejpam-5951	177	6	)	)	PUNCT
ejpam-5951	177	7	−	−	PROPN
ejpam-5951	178	1	hλi	hλi	NOUN
ejpam-5951	178	2	(	(	PUNCT
ejpam-5951	178	3	ζn	ζn	NOUN
ejpam-5951	178	4	)	)	PUNCT
ejpam-5951	178	5	)	)	PUNCT
ejpam-5951	179	1	=	=	SYM
ejpam-5951	179	2	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	179	3	(	(	PUNCT
ejpam-5951	179	4	ζn)−hλi	ζn)−hλi	PROPN
ejpam-5951	179	5	(	(	PUNCT
ejpam-5951	179	6	ζn	ζn	NOUN
ejpam-5951	179	7	)	)	PUNCT
ejpam-5951	179	8	∥∥∥	∥∥∥	PROPN
ejpam-5951	179	9	,	,	PUNCT
ejpam-5951	179	10	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	179	11	(	(	PUNCT
ejpam-5951	179	12	ζn	ζn	PROPN
ejpam-5951	179	13	)	)	PUNCT
ejpam-5951	179	14	,	,	PUNCT
ejpam-5951	179	15	ζ	ζ	PROPN
ejpam-5951	179	16	†	†	NOUN
ejpam-5951	179	17	)	)	PUNCT
ejpam-5951	179	18	=	=	SYM
ejpam-5951	180	1	∥∥∥gλi	∥∥∥gλi	PROPN
ejpam-5951	180	2	(	(	PUNCT
ejpam-5951	180	3	ζn)−	ζn)−	NOUN
ejpam-5951	180	4	ζ†	ζ†	VERB
ejpam-5951	180	5	∥∥∥	∥∥∥	PROPN
ejpam-5951	180	6	,	,	PUNCT
ejpam-5951	180	7	p.	p.	NOUN
ejpam-5951	180	8	patel	patel	PROPN
ejpam-5951	180	9	,	,	PUNCT
ejpam-5951	180	10	r.	r.	PROPN
ejpam-5951	180	11	shukla	shukla	PROPN
ejpam-5951	180	12	/	/	SYM
ejpam-5951	180	13	eur	eur	PROPN
ejpam-5951	180	14	.	.	PUNCT
ejpam-5951	181	1	j.	j.	PROPN
ejpam-5951	181	2	pure	pure	PROPN
ejpam-5951	181	3	appl	appl	PROPN
ejpam-5951	181	4	.	.	PROPN
ejpam-5951	181	5	math	math	PROPN
ejpam-5951	181	6	,	,	PUNCT
ejpam-5951	181	7	18	18	NUM
ejpam-5951	181	8	(	(	PUNCT
ejpam-5951	181	9	2	2	NUM
ejpam-5951	181	10	)	)	PUNCT
ejpam-5951	181	11	(	(	PUNCT
ejpam-5951	181	12	2025	2025	NUM
ejpam-5951	181	13	)	)	PUNCT
ejpam-5951	181	14	,	,	PUNCT
ejpam-5951	181	15	5951	5951	NUM
ejpam-5951	181	16	8	8	NUM
ejpam-5951	181	17	of	of	ADP
ejpam-5951	181	18	15	15	NUM
ejpam-5951	181	19	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	181	20	(	(	PUNCT
ejpam-5951	181	21	ζn	ζn	NOUN
ejpam-5951	181	22	)	)	PUNCT
ejpam-5951	181	23	,	,	PUNCT
ejpam-5951	181	24	ζ	ζ	PROPN
ejpam-5951	181	25	†	†	NOUN
ejpam-5951	181	26	)	)	PUNCT
ejpam-5951	181	27	=	=	SYM
ejpam-5951	182	1	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	182	2	(	(	PUNCT
ejpam-5951	182	3	ζn)−	ζn)−	NOUN
ejpam-5951	182	4	ζ†	ζ†	VERB
ejpam-5951	182	5	∥∥∥.	∥∥∥.	PRON
ejpam-5951	182	6	suppose	suppose	VERB
ejpam-5951	182	7	ϑn	ϑn	NOUN
ejpam-5951	182	8	=	=	SYM
ejpam-5951	182	9	δngλi	δngλi	NOUN
ejpam-5951	182	10	(	(	PUNCT
ejpam-5951	182	11	ζn	ζn	NOUN
ejpam-5951	182	12	)	)	PUNCT
ejpam-5951	182	13	+	+	CCONJ
ejpam-5951	182	14	(	(	PUNCT
ejpam-5951	182	15	1	1	NUM
ejpam-5951	182	16	−	−	PROPN
ejpam-5951	182	17	δn)hλi	δn)hλi	NOUN
ejpam-5951	182	18	(	(	PUNCT
ejpam-5951	182	19	ζn	ζn	X
ejpam-5951	182	20	)	)	PUNCT
ejpam-5951	182	21	is	be	AUX
ejpam-5951	182	22	the	the	DET
ejpam-5951	182	23	comparison	comparison	NOUN
ejpam-5951	182	24	point	point	NOUN
ejpam-5951	182	25	of	of	ADP
ejpam-5951	182	26	ϑn	ϑn	NOUN
ejpam-5951	182	27	.	.	PUNCT
ejpam-5951	183	1	using	use	VERB
ejpam-5951	183	2	the	the	DET
ejpam-5951	183	3	nonexpansiveness	nonexpansiveness	NOUN
ejpam-5951	183	4	of	of	ADP
ejpam-5951	183	5	gλi	gλi	NOUN
ejpam-5951	183	6	,	,	PUNCT
ejpam-5951	183	7	hλi	hλi	NOUN
ejpam-5951	183	8	and	and	CCONJ
ejpam-5951	183	9	lemma	lemma	PROPN
ejpam-5951	183	10	3	3	NUM
ejpam-5951	183	11	(	(	PUNCT
ejpam-5951	183	12	2	2	NUM
ejpam-5951	183	13	)	)	PUNCT
ejpam-5951	183	14	,	,	PUNCT
ejpam-5951	183	15	we	we	PRON
ejpam-5951	183	16	get	get	VERB
ejpam-5951	183	17	ρ2(ϑn	ρ2(ϑn	NUM
ejpam-5951	183	18	,	,	PUNCT
ejpam-5951	183	19	ζ	ζ	NOUN
ejpam-5951	183	20	†	†	NOUN
ejpam-5951	183	21	)	)	PUNCT
ejpam-5951	184	1	=	=	SYM
ejpam-5951	184	2	∥ϑn	∥ϑn	NUM
ejpam-5951	184	3	−	−	PROPN
ejpam-5951	184	4	ζ†∥2	ζ†∥2	NOUN
ejpam-5951	184	5	≤	≤	PUNCT
ejpam-5951	184	6	δn	δn	NOUN
ejpam-5951	184	7	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	184	8	(	(	PUNCT
ejpam-5951	184	9	ζn)−	ζn)−	NOUN
ejpam-5951	184	10	ζ†	ζ†	VERB
ejpam-5951	184	11	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	185	1	+	+	CCONJ
ejpam-5951	186	1	(	(	PUNCT
ejpam-5951	186	2	1−	1−	NUM
ejpam-5951	186	3	δn	δn	NOUN
ejpam-5951	186	4	)	)	PUNCT
ejpam-5951	186	5	∥∥∥hλi	∥∥∥hλi	NOUN
ejpam-5951	186	6	(	(	PUNCT
ejpam-5951	186	7	ζn)−	ζn)−	NOUN
ejpam-5951	186	8	ζ†	ζ†	VERB
ejpam-5951	186	9	∥∥∥	∥∥∥	PROPN
ejpam-5951	186	10	−	−	ADP
ejpam-5951	186	11	δn(1−	δn(1−	ADJ
ejpam-5951	186	12	δn	δn	NOUN
ejpam-5951	186	13	)	)	PUNCT
ejpam-5951	186	14	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	186	15	(	(	PUNCT
ejpam-5951	186	16	ζn)−hλi	ζn)−hλi	PROPN
ejpam-5951	186	17	(	(	PUNCT
ejpam-5951	186	18	ζn	ζn	NOUN
ejpam-5951	186	19	)	)	PUNCT
ejpam-5951	186	20	∥∥∥	∥∥∥	PROPN
ejpam-5951	186	21	=	=	SYM
ejpam-5951	186	22	δnρ	δnρ	X
ejpam-5951	186	23	2	2	NUM
ejpam-5951	186	24	(	(	PUNCT
ejpam-5951	186	25	gλi	gλi	NOUN
ejpam-5951	186	26	(	(	PUNCT
ejpam-5951	186	27	ζn	ζn	NOUN
ejpam-5951	186	28	)	)	PUNCT
ejpam-5951	186	29	,	,	PUNCT
ejpam-5951	186	30	ζ	ζ	X
ejpam-5951	186	31	†	†	PROPN
ejpam-5951	186	32	)	)	PUNCT
ejpam-5951	187	1	+	+	CCONJ
ejpam-5951	187	2	(	(	PUNCT
ejpam-5951	187	3	1−	1−	NUM
ejpam-5951	187	4	δn)ρ	δn)ρ	PROPN
ejpam-5951	187	5	2	2	NUM
ejpam-5951	187	6	(	(	PUNCT
ejpam-5951	187	7	hλi	hλi	NOUN
ejpam-5951	187	8	(	(	PUNCT
ejpam-5951	187	9	ζn	ζn	NOUN
ejpam-5951	187	10	)	)	PUNCT
ejpam-5951	187	11	,	,	PUNCT
ejpam-5951	187	12	ζ	ζ	PROPN
ejpam-5951	187	13	†	†	PROPN
ejpam-5951	187	14	)	)	PUNCT
ejpam-5951	187	15	−	−	PROPN
ejpam-5951	188	1	δn(1−	δn(1−	ADJ
ejpam-5951	188	2	δn)ρ	δn)ρ	PROPN
ejpam-5951	188	3	2	2	NUM
ejpam-5951	188	4	(	(	PUNCT
ejpam-5951	188	5	gλi	gλi	NOUN
ejpam-5951	188	6	(	(	PUNCT
ejpam-5951	188	7	ζn	ζn	NOUN
ejpam-5951	188	8	)	)	PUNCT
ejpam-5951	188	9	,	,	PUNCT
ejpam-5951	188	10	hλi	hλi	NOUN
ejpam-5951	188	11	(	(	PUNCT
ejpam-5951	188	12	ζn	ζn	NOUN
ejpam-5951	188	13	)	)	PUNCT
ejpam-5951	188	14	)	)	PUNCT
ejpam-5951	188	15	≤	≤	NUM
ejpam-5951	188	16	δnρ	δnρ	VERB
ejpam-5951	188	17	2(ζn	2(ζn	NOUN
ejpam-5951	188	18	,	,	PUNCT
ejpam-5951	188	19	ζ	ζ	NOUN
ejpam-5951	188	20	†	†	NOUN
ejpam-5951	188	21	)	)	PUNCT
ejpam-5951	188	22	+	+	CCONJ
ejpam-5951	189	1	(	(	PUNCT
ejpam-5951	189	2	1−	1−	NUM
ejpam-5951	189	3	δn)ρ	δn)ρ	PROPN
ejpam-5951	189	4	2(ζn	2(ζn	NOUN
ejpam-5951	189	5	,	,	PUNCT
ejpam-5951	189	6	ζ	ζ	PROPN
ejpam-5951	189	7	†)−	†)−	PROPN
ejpam-5951	189	8	δn(1−	δn(1−	PROPN
ejpam-5951	189	9	δn)ρ	δn)ρ	PROPN
ejpam-5951	189	10	2	2	NUM
ejpam-5951	189	11	(	(	PUNCT
ejpam-5951	189	12	gλi	gλi	NOUN
ejpam-5951	189	13	(	(	PUNCT
ejpam-5951	189	14	ζn	ζn	NOUN
ejpam-5951	189	15	)	)	PUNCT
ejpam-5951	189	16	,	,	PUNCT
ejpam-5951	189	17	hλi	hλi	NOUN
ejpam-5951	189	18	(	(	PUNCT
ejpam-5951	189	19	ζn	ζn	NOUN
ejpam-5951	189	20	)	)	PUNCT
ejpam-5951	189	21	)	)	PUNCT
ejpam-5951	189	22	≤	≤	NOUN
ejpam-5951	189	23	ρ2(ζn	ρ2(ζn	NUM
ejpam-5951	189	24	,	,	PUNCT
ejpam-5951	189	25	ζ	ζ	PROPN
ejpam-5951	189	26	†)−	†)−	PROPN
ejpam-5951	189	27	δn(1−	δn(1−	PROPN
ejpam-5951	189	28	δn)ρ	δn)ρ	PROPN
ejpam-5951	189	29	2	2	NUM
ejpam-5951	189	30	(	(	PUNCT
ejpam-5951	189	31	gλi	gλi	NOUN
ejpam-5951	189	32	(	(	PUNCT
ejpam-5951	189	33	ζn	ζn	NOUN
ejpam-5951	189	34	)	)	PUNCT
ejpam-5951	189	35	,	,	PUNCT
ejpam-5951	189	36	hλi	hλi	NOUN
ejpam-5951	189	37	(	(	PUNCT
ejpam-5951	189	38	ζn	ζn	NOUN
ejpam-5951	189	39	)	)	PUNCT
ejpam-5951	189	40	)	)	PUNCT
ejpam-5951	189	41	(	(	PUNCT
ejpam-5951	189	42	10	10	NUM
ejpam-5951	189	43	)	)	PUNCT
ejpam-5951	189	44	≤	≤	NOUN
ejpam-5951	189	45	ρ2(ζn	ρ2(ζn	PROPN
ejpam-5951	189	46	,	,	PUNCT
ejpam-5951	189	47	ζ	ζ	NOUN
ejpam-5951	189	48	†	†	NOUN
ejpam-5951	189	49	)	)	PUNCT
ejpam-5951	189	50	.	.	PUNCT
ejpam-5951	190	1	we	we	PRON
ejpam-5951	190	2	can	can	AUX
ejpam-5951	190	3	say	say	VERB
ejpam-5951	190	4	ζ†	ζ†	NOUN
ejpam-5951	190	5	∈	∈	PROPN
ejpam-5951	190	6	bn+1	bn+1	NUM
ejpam-5951	190	7	for	for	ADP
ejpam-5951	190	8	all	all	DET
ejpam-5951	190	9	ζ†	ζ†	NOUN
ejpam-5951	190	10	∈	∈	PROPN
ejpam-5951	190	11	π	π	NOUN
ejpam-5951	190	12	and	and	CCONJ
ejpam-5951	190	13	hence	hence	ADV
ejpam-5951	190	14	π	π	X
ejpam-5951	190	15	⊂	⊂	PROPN
ejpam-5951	190	16	bn	bn	INTJ
ejpam-5951	190	17	for	for	ADP
ejpam-5951	190	18	all	all	PRON
ejpam-5951	190	19	n	n	PRON
ejpam-5951	190	20	≥	≥	NOUN
ejpam-5951	190	21	1	1	NUM
ejpam-5951	190	22	.	.	PUNCT
ejpam-5951	191	1	thus	thus	ADV
ejpam-5951	191	2	bn	bn	PROPN
ejpam-5951	191	3	is	be	AUX
ejpam-5951	191	4	a	a	DET
ejpam-5951	191	5	nonempty	nonempty	ADJ
ejpam-5951	191	6	,	,	PUNCT
ejpam-5951	191	7	geodesic	geodesic	ADJ
ejpam-5951	191	8	convex	convex	NOUN
ejpam-5951	191	9	and	and	CCONJ
ejpam-5951	191	10	closed	closed	ADJ
ejpam-5951	191	11	subset	subset	NOUN
ejpam-5951	191	12	of	of	ADP
ejpam-5951	191	13	γ	γ	PROPN
ejpam-5951	191	14	and	and	CCONJ
ejpam-5951	191	15	π	π	PROPN
ejpam-5951	191	16	⊂	⊂	PROPN
ejpam-5951	191	17	bn+1	bn+1	PROPN
ejpam-5951	191	18	⊂	⊂	PROPN
ejpam-5951	191	19	bn	bn	INTJ
ejpam-5951	191	20	for	for	ADP
ejpam-5951	191	21	all	all	DET
ejpam-5951	191	22	n	n	PRON
ejpam-5951	191	23	≥	≥	NOUN
ejpam-5951	191	24	1	1	NUM
ejpam-5951	191	25	.	.	PUNCT
ejpam-5951	192	1	hence	hence	ADV
ejpam-5951	192	2	sequence	sequence	NOUN
ejpam-5951	192	3	{	{	PUNCT
ejpam-5951	192	4	ζn	ζn	NOUN
ejpam-5951	192	5	}	}	PUNCT
ejpam-5951	192	6	is	be	AUX
ejpam-5951	192	7	well	well	ADV
ejpam-5951	192	8	defined	define	VERB
ejpam-5951	192	9	.	.	PUNCT
ejpam-5951	193	1	now	now	ADV
ejpam-5951	193	2	we	we	PRON
ejpam-5951	193	3	prove	prove	VERB
ejpam-5951	193	4	that	that	SCONJ
ejpam-5951	193	5	lim	lim	PROPN
ejpam-5951	193	6	n→+∞	n→+∞	VERB
ejpam-5951	193	7	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	193	8	,	,	PUNCT
ejpam-5951	193	9	ζ1	ζ1	NOUN
ejpam-5951	193	10	)	)	PUNCT
ejpam-5951	193	11	exists	exist	VERB
ejpam-5951	193	12	and	and	CCONJ
ejpam-5951	193	13	the	the	DET
ejpam-5951	193	14	sequence	sequence	NOUN
ejpam-5951	193	15	{	{	PUNCT
ejpam-5951	193	16	ζn	ζn	NOUN
ejpam-5951	193	17	}	}	PUNCT
ejpam-5951	193	18	is	be	AUX
ejpam-5951	193	19	bounded	bound	VERB
ejpam-5951	193	20	.	.	PUNCT
ejpam-5951	194	1	since	since	SCONJ
ejpam-5951	194	2	we	we	PRON
ejpam-5951	194	3	have	have	VERB
ejpam-5951	194	4	ζn	ζn	PRON
ejpam-5951	194	5	=	=	PUNCT
ejpam-5951	194	6	pbn(ζ1	pbn(ζ1	PROPN
ejpam-5951	194	7	)	)	PUNCT
ejpam-5951	194	8	and	and	CCONJ
ejpam-5951	194	9	using	use	VERB
ejpam-5951	194	10	the	the	DET
ejpam-5951	194	11	fact	fact	NOUN
ejpam-5951	195	1	that	that	SCONJ
ejpam-5951	195	2	π	π	PROPN
ejpam-5951	195	3	⊂	⊂	X
ejpam-5951	195	4	bn+1	bn+1	PROPN
ejpam-5951	195	5	⊂	⊂	PROPN
ejpam-5951	196	1	bn	bn	INTJ
ejpam-5951	196	2	we	we	PRON
ejpam-5951	196	3	get	get	VERB
ejpam-5951	196	4	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	196	5	,	,	PUNCT
ejpam-5951	196	6	ζ1	ζ1	NOUN
ejpam-5951	196	7	)	)	PUNCT
ejpam-5951	196	8	≤	≤	NUM
ejpam-5951	196	9	ρ(ζ†	ρ(ζ†	NUM
ejpam-5951	196	10	,	,	PUNCT
ejpam-5951	196	11	ζ1	ζ1	PROPN
ejpam-5951	196	12	)	)	PUNCT
ejpam-5951	196	13	,	,	PUNCT
ejpam-5951	196	14	for	for	ADP
ejpam-5951	196	15	all	all	DET
ejpam-5951	196	16	ζ†	ζ†	NOUN
ejpam-5951	196	17	∈	∈	PROPN
ejpam-5951	196	18	π	π	PROPN
ejpam-5951	196	19	,	,	PUNCT
ejpam-5951	196	20	n	n	PRON
ejpam-5951	196	21	≥	≥	NOUN
ejpam-5951	196	22	1	1	NUM
ejpam-5951	196	23	.	.	PUNCT
ejpam-5951	197	1	(	(	PUNCT
ejpam-5951	197	2	11	11	NUM
ejpam-5951	197	3	)	)	PUNCT
ejpam-5951	197	4	hence	hence	ADV
ejpam-5951	197	5	,	,	PUNCT
ejpam-5951	197	6	we	we	PRON
ejpam-5951	197	7	get	get	VERB
ejpam-5951	197	8	the	the	DET
ejpam-5951	197	9	sequence	sequence	NOUN
ejpam-5951	197	10	{	{	PUNCT
ejpam-5951	197	11	ζn	ζn	NOUN
ejpam-5951	197	12	}	}	PUNCT
ejpam-5951	197	13	is	be	AUX
ejpam-5951	197	14	bounded	bound	VERB
ejpam-5951	197	15	.	.	PUNCT
ejpam-5951	198	1	since	since	SCONJ
ejpam-5951	198	2	ζn+1	ζn+1	PROPN
ejpam-5951	198	3	∈	∈	PROPN
ejpam-5951	198	4	bn+1	bn+1	NUM
ejpam-5951	198	5	⊂	⊂	X
ejpam-5951	198	6	bn	bn	INTJ
ejpam-5951	199	1	and	and	CCONJ
ejpam-5951	199	2	we	we	PRON
ejpam-5951	199	3	get	get	VERB
ejpam-5951	199	4	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	199	5	,	,	PUNCT
ejpam-5951	199	6	ζ1	ζ1	NOUN
ejpam-5951	199	7	)	)	PUNCT
ejpam-5951	199	8	≤	≤	NOUN
ejpam-5951	199	9	ρ(ζn+1	ρ(ζn+1	PROPN
ejpam-5951	199	10	,	,	PUNCT
ejpam-5951	199	11	ζ1	ζ1	NOUN
ejpam-5951	199	12	)	)	PUNCT
ejpam-5951	199	13	and	and	CCONJ
ejpam-5951	200	1	hence	hence	ADV
ejpam-5951	200	2	lim	lim	PROPN
ejpam-5951	200	3	n→+∞	n→+∞	VERB
ejpam-5951	200	4	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	200	5	,	,	PUNCT
ejpam-5951	200	6	ζ1	ζ1	NOUN
ejpam-5951	200	7	)	)	PUNCT
ejpam-5951	200	8	exists	exist	VERB
ejpam-5951	200	9	.	.	PUNCT
ejpam-5951	201	1	next	next	ADJ
ejpam-5951	201	2	using	use	VERB
ejpam-5951	201	3	proposition	proposition	NOUN
ejpam-5951	201	4	2	2	NUM
ejpam-5951	201	5	(	(	PUNCT
ejpam-5951	201	6	3	3	NUM
ejpam-5951	201	7	)	)	PUNCT
ejpam-5951	201	8	we	we	PRON
ejpam-5951	201	9	get	get	VERB
ejpam-5951	201	10	ρ2(ζn	ρ2(ζn	NOUN
ejpam-5951	201	11	,	,	PUNCT
ejpam-5951	201	12	ζn+1	ζn+1	ADJ
ejpam-5951	201	13	)	)	PUNCT
ejpam-5951	201	14	≤	≤	NOUN
ejpam-5951	201	15	ρ2(ζn+1	ρ2(ζn+1	NOUN
ejpam-5951	201	16	,	,	PUNCT
ejpam-5951	201	17	ζ1)−	ζ1)−	PROPN
ejpam-5951	201	18	ρ2(ζn	ρ2(ζn	PROPN
ejpam-5951	201	19	,	,	PUNCT
ejpam-5951	201	20	ζ1	ζ1	NOUN
ejpam-5951	201	21	)	)	PUNCT
ejpam-5951	201	22	.	.	PUNCT
ejpam-5951	202	1	(	(	PUNCT
ejpam-5951	202	2	12	12	X
ejpam-5951	202	3	)	)	PUNCT
ejpam-5951	202	4	applying	apply	VERB
ejpam-5951	202	5	summation	summation	NOUN
ejpam-5951	202	6	on	on	ADP
ejpam-5951	202	7	(	(	PUNCT
ejpam-5951	202	8	12	12	NUM
ejpam-5951	202	9	)	)	PUNCT
ejpam-5951	202	10	and	and	CCONJ
ejpam-5951	202	11	using	use	VERB
ejpam-5951	202	12	(	(	PUNCT
ejpam-5951	202	13	11	11	NUM
ejpam-5951	202	14	)	)	PUNCT
ejpam-5951	202	15	,	,	PUNCT
ejpam-5951	202	16	we	we	PRON
ejpam-5951	202	17	have	have	VERB
ejpam-5951	202	18	n∑	n∑	NOUN
ejpam-5951	202	19	n=1	n=1	PROPN
ejpam-5951	202	20	ρ2(ζn+1	ρ2(ζn+1	NOUN
ejpam-5951	202	21	,	,	PUNCT
ejpam-5951	202	22	ζn	ζn	NOUN
ejpam-5951	202	23	)	)	PUNCT
ejpam-5951	202	24	≤	≤	NUM
ejpam-5951	202	25	n∑	n∑	PUNCT
ejpam-5951	202	26	n=1	n=1	PROPN
ejpam-5951	202	27	(	(	PUNCT
ejpam-5951	202	28	ρ2(ζn+1	ρ2(ζn+1	ADJ
ejpam-5951	202	29	,	,	PUNCT
ejpam-5951	202	30	ζ1)−	ζ1)−	PROPN
ejpam-5951	202	31	ρ2(ζn	ρ2(ζn	PROPN
ejpam-5951	202	32	,	,	PUNCT
ejpam-5951	202	33	ζ1	ζ1	NOUN
ejpam-5951	202	34	)	)	PUNCT
ejpam-5951	202	35	)	)	PUNCT
ejpam-5951	202	36	≤	≤	NUM
ejpam-5951	202	37	ρ2(ζn+1	ρ2(ζn+1	NOUN
ejpam-5951	202	38	,	,	PUNCT
ejpam-5951	202	39	ζ1)−	ζ1)−	VERB
ejpam-5951	202	40	ρ2(ζ1	ρ2(ζ1	NOUN
ejpam-5951	202	41	,	,	PUNCT
ejpam-5951	202	42	ζ1	ζ1	NOUN
ejpam-5951	202	43	)	)	PUNCT
ejpam-5951	202	44	≤	≤	NOUN
ejpam-5951	202	45	ρ2(ζ†	ρ2(ζ†	PROPN
ejpam-5951	202	46	,	,	PUNCT
ejpam-5951	202	47	ζ1	ζ1	NOUN
ejpam-5951	202	48	)	)	PUNCT
ejpam-5951	202	49	,	,	PUNCT
ejpam-5951	202	50	and	and	CCONJ
ejpam-5951	202	51	it	it	PRON
ejpam-5951	202	52	gives	give	VERB
ejpam-5951	202	53	us	we	PRON
ejpam-5951	202	54	n∑	n∑	ADJ
ejpam-5951	202	55	n=1	n=1	PROPN
ejpam-5951	202	56	ρ2(ζn+1	ρ2(ζn+1	NOUN
ejpam-5951	202	57	,	,	PUNCT
ejpam-5951	202	58	ζn	ζn	NOUN
ejpam-5951	202	59	)	)	PUNCT
ejpam-5951	202	60	is	be	AUX
ejpam-5951	202	61	convergent	convergent	ADJ
ejpam-5951	202	62	and	and	CCONJ
ejpam-5951	202	63	hence	hence	ADV
ejpam-5951	202	64	lim	lim	PROPN
ejpam-5951	202	65	n→+∞	n→+∞	PROPN
ejpam-5951	202	66	ρ(ζn+1	ρ(ζn+1	PROPN
ejpam-5951	202	67	,	,	PUNCT
ejpam-5951	202	68	ζn	ζn	NOUN
ejpam-5951	202	69	)	)	PUNCT
ejpam-5951	202	70	=	=	SYM
ejpam-5951	203	1	0	0	X
ejpam-5951	203	2	.	.	PUNCT
ejpam-5951	204	1	(	(	PUNCT
ejpam-5951	204	2	13	13	NUM
ejpam-5951	204	3	)	)	PUNCT
ejpam-5951	204	4	p.	p.	NOUN
ejpam-5951	204	5	patel	patel	PROPN
ejpam-5951	204	6	,	,	PUNCT
ejpam-5951	204	7	r.	r.	PROPN
ejpam-5951	204	8	shukla	shukla	PROPN
ejpam-5951	204	9	/	/	SYM
ejpam-5951	204	10	eur	eur	PROPN
ejpam-5951	204	11	.	.	PUNCT
ejpam-5951	205	1	j.	j.	PROPN
ejpam-5951	205	2	pure	pure	PROPN
ejpam-5951	205	3	appl	appl	PROPN
ejpam-5951	205	4	.	.	PROPN
ejpam-5951	205	5	math	math	PROPN
ejpam-5951	205	6	,	,	PUNCT
ejpam-5951	205	7	18	18	NUM
ejpam-5951	205	8	(	(	PUNCT
ejpam-5951	205	9	2	2	NUM
ejpam-5951	205	10	)	)	PUNCT
ejpam-5951	205	11	(	(	PUNCT
ejpam-5951	205	12	2025	2025	NUM
ejpam-5951	205	13	)	)	PUNCT
ejpam-5951	205	14	,	,	PUNCT
ejpam-5951	205	15	5951	5951	NUM
ejpam-5951	205	16	9	9	NUM
ejpam-5951	205	17	of	of	ADP
ejpam-5951	205	18	15	15	NUM
ejpam-5951	205	19	since	since	SCONJ
ejpam-5951	205	20	from	from	ADP
ejpam-5951	205	21	(	(	PUNCT
ejpam-5951	205	22	9	9	X
ejpam-5951	205	23	)	)	PUNCT
ejpam-5951	205	24	we	we	PRON
ejpam-5951	205	25	have	have	VERB
ejpam-5951	205	26	ζn+1	ζn+1	ADJ
ejpam-5951	205	27	=	=	SYM
ejpam-5951	205	28	pbn+1(ζ1	pbn+1(ζ1	NOUN
ejpam-5951	205	29	)	)	PUNCT
ejpam-5951	205	30	∈	∈	PROPN
ejpam-5951	205	31	bn+1	bn+1	NUM
ejpam-5951	205	32	,	,	PUNCT
ejpam-5951	205	33	so	so	ADV
ejpam-5951	205	34	using	use	VERB
ejpam-5951	205	35	the	the	DET
ejpam-5951	205	36	definition	definition	NOUN
ejpam-5951	205	37	of	of	ADP
ejpam-5951	205	38	bn+1	bn+1	NUM
ejpam-5951	205	39	we	we	PRON
ejpam-5951	205	40	have	have	VERB
ejpam-5951	205	41	ρ(ϑn	ρ(ϑn	NOUN
ejpam-5951	205	42	,	,	PUNCT
ejpam-5951	205	43	ζn+1	ζn+1	ADJ
ejpam-5951	205	44	)	)	PUNCT
ejpam-5951	205	45	≤	≤	NOUN
ejpam-5951	205	46	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	205	47	,	,	PUNCT
ejpam-5951	205	48	ζn+1	ζn+1	NUM
ejpam-5951	205	49	)	)	PUNCT
ejpam-5951	205	50	.	.	PUNCT
ejpam-5951	206	1	using	use	VERB
ejpam-5951	206	2	the	the	DET
ejpam-5951	206	3	above	above	ADJ
ejpam-5951	206	4	equation	equation	NOUN
ejpam-5951	206	5	,	,	PUNCT
ejpam-5951	206	6	we	we	PRON
ejpam-5951	206	7	have	have	VERB
ejpam-5951	206	8	lim	lim	PROPN
ejpam-5951	206	9	n→+∞	n→+∞	PROPN
ejpam-5951	206	10	ρ(ϑn	ρ(ϑn	PROPN
ejpam-5951	206	11	,	,	PUNCT
ejpam-5951	206	12	ζn+1	ζn+1	NUM
ejpam-5951	206	13	)	)	PUNCT
ejpam-5951	206	14	=	=	SYM
ejpam-5951	207	1	0	0	X
ejpam-5951	207	2	.	.	PUNCT
ejpam-5951	208	1	(	(	PUNCT
ejpam-5951	208	2	14	14	NUM
ejpam-5951	208	3	)	)	PUNCT
ejpam-5951	208	4	now	now	ADV
ejpam-5951	208	5	ρ(ϑn	ρ(ϑn	NUM
ejpam-5951	208	6	,	,	PUNCT
ejpam-5951	208	7	ζn	ζn	NOUN
ejpam-5951	208	8	)	)	PUNCT
ejpam-5951	208	9	≤	≤	NOUN
ejpam-5951	208	10	ρ(ϑn	ρ(ϑn	NOUN
ejpam-5951	208	11	,	,	PUNCT
ejpam-5951	208	12	ζn+1	ζn+1	NUM
ejpam-5951	208	13	)	)	PUNCT
ejpam-5951	208	14	+	+	X
ejpam-5951	208	15	ρ(ζn+1	ρ(ζn+1	ADJ
ejpam-5951	208	16	,	,	PUNCT
ejpam-5951	208	17	ζn	ζn	NOUN
ejpam-5951	208	18	)	)	PUNCT
ejpam-5951	208	19	,	,	PUNCT
ejpam-5951	208	20	applying	apply	VERB
ejpam-5951	208	21	limit	limit	NOUN
ejpam-5951	208	22	n	n	X
ejpam-5951	208	23	→	→	SYM
ejpam-5951	208	24	+	+	NUM
ejpam-5951	208	25	∞	∞	NUM
ejpam-5951	208	26	and	and	CCONJ
ejpam-5951	208	27	using	use	VERB
ejpam-5951	208	28	(	(	PUNCT
ejpam-5951	208	29	13	13	NUM
ejpam-5951	208	30	)	)	PUNCT
ejpam-5951	208	31	and	and	CCONJ
ejpam-5951	208	32	(	(	PUNCT
ejpam-5951	208	33	14	14	NUM
ejpam-5951	208	34	)	)	PUNCT
ejpam-5951	208	35	,	,	PUNCT
ejpam-5951	208	36	we	we	PRON
ejpam-5951	208	37	get	get	VERB
ejpam-5951	208	38	lim	lim	PROPN
ejpam-5951	208	39	n→+∞	n→+∞	PROPN
ejpam-5951	208	40	ρ(ϑn	ρ(ϑn	PROPN
ejpam-5951	208	41	,	,	PUNCT
ejpam-5951	208	42	ζn	ζn	NOUN
ejpam-5951	208	43	)	)	PUNCT
ejpam-5951	208	44	=	=	SYM
ejpam-5951	209	1	0	0	X
ejpam-5951	209	2	.	.	PUNCT
ejpam-5951	210	1	(	(	PUNCT
ejpam-5951	210	2	15	15	X
ejpam-5951	210	3	)	)	PUNCT
ejpam-5951	210	4	using	use	VERB
ejpam-5951	210	5	(	(	PUNCT
ejpam-5951	210	6	10	10	NUM
ejpam-5951	210	7	)	)	PUNCT
ejpam-5951	210	8	,	,	PUNCT
ejpam-5951	210	9	we	we	PRON
ejpam-5951	210	10	will	will	AUX
ejpam-5951	210	11	have	have	VERB
ejpam-5951	210	12	δ1(1−	δ1(1−	VERB
ejpam-5951	210	13	δ2)ρ	δ2)ρ	ADV
ejpam-5951	210	14	2(gλi	2(gλi	NOUN
ejpam-5951	210	15	(	(	PUNCT
ejpam-5951	210	16	ζn	ζn	NOUN
ejpam-5951	210	17	)	)	PUNCT
ejpam-5951	210	18	,	,	PUNCT
ejpam-5951	210	19	hλi	hλi	NOUN
ejpam-5951	210	20	(	(	PUNCT
ejpam-5951	210	21	ζn	ζn	NOUN
ejpam-5951	210	22	)	)	PUNCT
ejpam-5951	210	23	)	)	PUNCT
ejpam-5951	210	24	≤	≤	NOUN
ejpam-5951	211	1	δn(1−	δn(1−	ADJ
ejpam-5951	211	2	δn)ρ	δn)ρ	PROPN
ejpam-5951	211	3	2(gλi	2(gλi	NOUN
ejpam-5951	211	4	(	(	PUNCT
ejpam-5951	211	5	ζn	ζn	NOUN
ejpam-5951	211	6	)	)	PUNCT
ejpam-5951	211	7	,	,	PUNCT
ejpam-5951	211	8	hλi	hλi	NOUN
ejpam-5951	211	9	(	(	PUNCT
ejpam-5951	211	10	ζn	ζn	NOUN
ejpam-5951	211	11	)	)	PUNCT
ejpam-5951	211	12	)	)	PUNCT
ejpam-5951	211	13	≤	≤	NOUN
ejpam-5951	211	14	ρ2(ζn	ρ2(ζn	PROPN
ejpam-5951	211	15	,	,	PUNCT
ejpam-5951	211	16	ζ	ζ	X
ejpam-5951	211	17	†)−	†)−	PROPN
ejpam-5951	211	18	ρ2(ϑn	ρ2(ϑn	PROPN
ejpam-5951	211	19	,	,	PUNCT
ejpam-5951	211	20	ζ	ζ	NOUN
ejpam-5951	211	21	†	†	NOUN
ejpam-5951	211	22	)	)	PUNCT
ejpam-5951	211	23	≤	≤	NUM
ejpam-5951	212	1	c1ρ(ζn	c1ρ(ζn	NOUN
ejpam-5951	212	2	,	,	PUNCT
ejpam-5951	212	3	ϑn	ϑn	NOUN
ejpam-5951	212	4	)	)	PUNCT
ejpam-5951	212	5	.	.	PUNCT
ejpam-5951	213	1	(	(	PUNCT
ejpam-5951	213	2	16	16	NUM
ejpam-5951	213	3	)	)	PUNCT
ejpam-5951	213	4	where	where	SCONJ
ejpam-5951	213	5	c1	c1	NOUN
ejpam-5951	213	6	=	=	NOUN
ejpam-5951	213	7	sup	sup	NOUN
ejpam-5951	213	8	n≥1	n≥1	NOUN
ejpam-5951	213	9	{	{	PUNCT
ejpam-5951	213	10	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	213	11	,	,	PUNCT
ejpam-5951	213	12	ζ†	ζ†	NOUN
ejpam-5951	213	13	)	)	PUNCT
ejpam-5951	213	14	+	+	NUM
ejpam-5951	213	15	ρ(ϑn	ρ(ϑn	PROPN
ejpam-5951	213	16	,	,	PUNCT
ejpam-5951	213	17	ζ	ζ	X
ejpam-5951	213	18	†	†	NOUN
ejpam-5951	213	19	)	)	PUNCT
ejpam-5951	213	20	}	}	PUNCT
ejpam-5951	213	21	.	.	PUNCT
ejpam-5951	214	1	using	use	VERB
ejpam-5951	214	2	(	(	PUNCT
ejpam-5951	214	3	15	15	NUM
ejpam-5951	214	4	)	)	PUNCT
ejpam-5951	214	5	,	,	PUNCT
ejpam-5951	214	6	we	we	PRON
ejpam-5951	214	7	get	get	VERB
ejpam-5951	214	8	lim	lim	PROPN
ejpam-5951	214	9	n→+∞	n→+∞	PROPN
ejpam-5951	214	10	ρ(gλi	ρ(gλi	PROPN
ejpam-5951	214	11	(	(	PUNCT
ejpam-5951	214	12	ζn	ζn	NOUN
ejpam-5951	214	13	)	)	PUNCT
ejpam-5951	214	14	,	,	PUNCT
ejpam-5951	214	15	hλi	hλi	NOUN
ejpam-5951	214	16	(	(	PUNCT
ejpam-5951	214	17	ζn	ζn	NOUN
ejpam-5951	214	18	)	)	PUNCT
ejpam-5951	214	19	)	)	PUNCT
ejpam-5951	215	1	=	=	PUNCT
ejpam-5951	215	2	0	0	X
ejpam-5951	215	3	.	.	PUNCT
ejpam-5951	216	1	(	(	PUNCT
ejpam-5951	216	2	17	17	NUM
ejpam-5951	216	3	)	)	PUNCT
ejpam-5951	216	4	next	next	ADV
ejpam-5951	216	5	we	we	PRON
ejpam-5951	216	6	prove	prove	VERB
ejpam-5951	216	7	that	that	SCONJ
ejpam-5951	216	8	the	the	PRON
ejpam-5951	216	9	{	{	PUNCT
ejpam-5951	216	10	ζn	ζn	NOUN
ejpam-5951	216	11	}	}	PUNCT
ejpam-5951	216	12	is	be	AUX
ejpam-5951	216	13	a	a	DET
ejpam-5951	216	14	cauchy	cauchy	ADJ
ejpam-5951	216	15	sequence	sequence	NOUN
ejpam-5951	216	16	in	in	ADP
ejpam-5951	216	17	γ	γ	PROPN
ejpam-5951	216	18	and	and	CCONJ
ejpam-5951	216	19	{	{	PUNCT
ejpam-5951	216	20	ζn	ζn	NOUN
ejpam-5951	216	21	}	}	PUNCT
ejpam-5951	216	22	converges	converge	NOUN
ejpam-5951	216	23	to	to	ADP
ejpam-5951	216	24	ζ	ζ	SYM
ejpam-5951	216	25	∈	∈	PROPN
ejpam-5951	216	26	π	π	NOUN
ejpam-5951	216	27	.	.	PUNCT
ejpam-5951	217	1	since	since	SCONJ
ejpam-5951	217	2	pbn	pbn	PROPN
ejpam-5951	217	3	is	be	AUX
ejpam-5951	217	4	firmly	firmly	ADV
ejpam-5951	217	5	nonexpansive	nonexpansive	ADJ
ejpam-5951	217	6	,	,	PUNCT
ejpam-5951	217	7	ζm	ζm	ADP
ejpam-5951	217	8	=	=	SYM
ejpam-5951	217	9	pbm(ζ1	pbm(ζ1	PROPN
ejpam-5951	217	10	)	)	PUNCT
ejpam-5951	217	11	∈	∈	PROPN
ejpam-5951	217	12	bm	bm	PROPN
ejpam-5951	217	13	⊂	⊂	PROPN
ejpam-5951	217	14	bn	bn	PROPN
ejpam-5951	217	15	for	for	ADP
ejpam-5951	217	16	any	any	DET
ejpam-5951	217	17	n	n	CCONJ
ejpam-5951	217	18	,	,	PUNCT
ejpam-5951	217	19	m	m	VERB
ejpam-5951	217	20	∈	∈	ADJ
ejpam-5951	217	21	n	n	NOUN
ejpam-5951	217	22	and	and	CCONJ
ejpam-5951	217	23	m	m	ADJ
ejpam-5951	217	24	>	>	X
ejpam-5951	217	25	n.	n.	NOUN
ejpam-5951	217	26	if	if	SCONJ
ejpam-5951	217	27	we	we	PRON
ejpam-5951	217	28	take	take	VERB
ejpam-5951	217	29	b	b	NOUN
ejpam-5951	217	30	=	=	SYM
ejpam-5951	217	31	bn	bn	PROPN
ejpam-5951	217	32	,	,	PUNCT
ejpam-5951	217	33	ζ	ζ	NOUN
ejpam-5951	217	34	=	=	SYM
ejpam-5951	217	35	ζ1	ζ1	PROPN
ejpam-5951	217	36	and	and	CCONJ
ejpam-5951	217	37	ϑ	ϑ	X
ejpam-5951	217	38	=	=	X
ejpam-5951	217	39	ζm	ζm	NOUN
ejpam-5951	217	40	,	,	PUNCT
ejpam-5951	217	41	we	we	PRON
ejpam-5951	217	42	get	get	VERB
ejpam-5951	217	43	ρ2	ρ2	NOUN
ejpam-5951	217	44	(	(	PUNCT
ejpam-5951	217	45	pbnζ1	pbnζ1	PROPN
ejpam-5951	217	46	)	)	PUNCT
ejpam-5951	217	47	=	=	SYM
ejpam-5951	217	48	ρ2(ζn	ρ2(ζn	NOUN
ejpam-5951	217	49	,	,	PUNCT
ejpam-5951	217	50	ζm	ζm	NOUN
ejpam-5951	217	51	)	)	PUNCT
ejpam-5951	217	52	≤	≤	NOUN
ejpam-5951	217	53	ρ2(ζ1	ρ2(ζ1	NOUN
ejpam-5951	217	54	,	,	PUNCT
ejpam-5951	217	55	ζm)−	ζm)−	NUM
ejpam-5951	217	56	ρ2(ζn	ρ2(ζn	PROPN
ejpam-5951	217	57	,	,	PUNCT
ejpam-5951	217	58	ζ1	ζ1	NOUN
ejpam-5951	217	59	)	)	PUNCT
ejpam-5951	217	60	,	,	PUNCT
ejpam-5951	217	61	applying	apply	VERB
ejpam-5951	217	62	limit	limit	NOUN
ejpam-5951	217	63	n	n	CCONJ
ejpam-5951	217	64	,	,	PUNCT
ejpam-5951	217	65	m	m	PROPN
ejpam-5951	217	66	→	→	SYM
ejpam-5951	217	67	+	+	ADJ
ejpam-5951	217	68	∞	∞	NUM
ejpam-5951	217	69	and	and	CCONJ
ejpam-5951	217	70	using	use	VERB
ejpam-5951	217	71	proposition	proposition	NOUN
ejpam-5951	217	72	2	2	NUM
ejpam-5951	217	73	(	(	PUNCT
ejpam-5951	217	74	3	3	NUM
ejpam-5951	217	75	)	)	PUNCT
ejpam-5951	217	76	,	,	PUNCT
ejpam-5951	217	77	we	we	PRON
ejpam-5951	217	78	get	get	VERB
ejpam-5951	217	79	lim	lim	PROPN
ejpam-5951	217	80	n	n	CCONJ
ejpam-5951	217	81	,	,	PUNCT
ejpam-5951	217	82	m→+∞	m→+∞	PROPN
ejpam-5951	217	83	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	217	84	,	,	PUNCT
ejpam-5951	217	85	ζm	ζm	NOUN
ejpam-5951	217	86	)	)	PUNCT
ejpam-5951	217	87	→	→	SYM
ejpam-5951	217	88	0	0	X
ejpam-5951	217	89	.	.	PUNCT
ejpam-5951	218	1	it	it	PRON
ejpam-5951	218	2	gives	give	VERB
ejpam-5951	218	3	us	we	PRON
ejpam-5951	218	4	that	that	SCONJ
ejpam-5951	218	5	the	the	DET
ejpam-5951	218	6	sequence	sequence	NOUN
ejpam-5951	218	7	{	{	PUNCT
ejpam-5951	218	8	ζn	ζn	NOUN
ejpam-5951	218	9	}	}	PUNCT
ejpam-5951	218	10	is	be	AUX
ejpam-5951	218	11	a	a	DET
ejpam-5951	218	12	cauchy	cauchy	ADJ
ejpam-5951	218	13	sequence	sequence	NOUN
ejpam-5951	218	14	and	and	CCONJ
ejpam-5951	218	15	since	since	SCONJ
ejpam-5951	218	16	γ	γ	X
ejpam-5951	218	17	is	be	AUX
ejpam-5951	218	18	complete	complete	ADJ
ejpam-5951	218	19	we	we	PRON
ejpam-5951	218	20	can	can	AUX
ejpam-5951	218	21	assume	assume	VERB
ejpam-5951	218	22	that	that	SCONJ
ejpam-5951	218	23	lim	lim	PROPN
ejpam-5951	218	24	n→+∞	n→+∞	VERB
ejpam-5951	218	25	ζn	ζn	NOUN
ejpam-5951	218	26	=	=	PUNCT
ejpam-5951	218	27	ζ	ζ	NOUN
ejpam-5951	218	28	∈	∈	PROPN
ejpam-5951	218	29	γ	γ	X
ejpam-5951	218	30	.	.	PUNCT
ejpam-5951	219	1	now	now	ADV
ejpam-5951	219	2	we	we	PRON
ejpam-5951	219	3	prove	prove	VERB
ejpam-5951	219	4	that	that	SCONJ
ejpam-5951	219	5	ζ	ζ	PROPN
ejpam-5951	219	6	∈	∈	PROPN
ejpam-5951	219	7	π	π	X
ejpam-5951	219	8	.	.	PUNCT
ejpam-5951	219	9	from	from	ADP
ejpam-5951	219	10	(	(	PUNCT
ejpam-5951	219	11	9	9	X
ejpam-5951	219	12	)	)	PUNCT
ejpam-5951	219	13	we	we	PRON
ejpam-5951	219	14	have	have	VERB
ejpam-5951	219	15	ρ(ϑn	ρ(ϑn	NOUN
ejpam-5951	219	16	,	,	PUNCT
ejpam-5951	219	17	gλi	gλi	NOUN
ejpam-5951	219	18	(	(	PUNCT
ejpam-5951	219	19	ζn	ζn	NOUN
ejpam-5951	219	20	)	)	PUNCT
ejpam-5951	219	21	)	)	PUNCT
ejpam-5951	220	1	=	=	SYM
ejpam-5951	220	2	δnρ(gλi	δnρ(gλi	X
ejpam-5951	220	3	(	(	PUNCT
ejpam-5951	220	4	ζn	ζn	NOUN
ejpam-5951	220	5	)	)	PUNCT
ejpam-5951	220	6	,	,	PUNCT
ejpam-5951	220	7	hλi	hλi	NOUN
ejpam-5951	220	8	(	(	PUNCT
ejpam-5951	220	9	ζn	ζn	NOUN
ejpam-5951	220	10	)	)	PUNCT
ejpam-5951	220	11	)	)	PUNCT
ejpam-5951	220	12	≤	≤	NUM
ejpam-5951	220	13	δ2ρ(gλi	δ2ρ(gλi	NOUN
ejpam-5951	220	14	(	(	PUNCT
ejpam-5951	220	15	ζn	ζn	NOUN
ejpam-5951	220	16	)	)	PUNCT
ejpam-5951	220	17	,	,	PUNCT
ejpam-5951	220	18	hλi	hλi	NOUN
ejpam-5951	220	19	(	(	PUNCT
ejpam-5951	220	20	ζn	ζn	NOUN
ejpam-5951	220	21	)	)	PUNCT
ejpam-5951	220	22	)	)	PUNCT
ejpam-5951	220	23	.	.	PUNCT
ejpam-5951	221	1	applying	apply	VERB
ejpam-5951	221	2	limit	limit	NOUN
ejpam-5951	221	3	n	n	X
ejpam-5951	221	4	→	→	SYM
ejpam-5951	221	5	+	+	NUM
ejpam-5951	221	6	∞	∞	NUM
ejpam-5951	221	7	and	and	CCONJ
ejpam-5951	221	8	using	use	VERB
ejpam-5951	221	9	(	(	PUNCT
ejpam-5951	221	10	17	17	NUM
ejpam-5951	221	11	)	)	PUNCT
ejpam-5951	221	12	,	,	PUNCT
ejpam-5951	221	13	we	we	PRON
ejpam-5951	221	14	get	get	VERB
ejpam-5951	221	15	lim	lim	PROPN
ejpam-5951	221	16	n→+∞	n→+∞	PROPN
ejpam-5951	221	17	ρ(ϑn	ρ(ϑn	PROPN
ejpam-5951	221	18	,	,	PUNCT
ejpam-5951	221	19	gλi	gλi	NOUN
ejpam-5951	221	20	(	(	PUNCT
ejpam-5951	221	21	ζn	ζn	NOUN
ejpam-5951	221	22	)	)	PUNCT
ejpam-5951	221	23	)	)	PUNCT
ejpam-5951	222	1	=	=	PUNCT
ejpam-5951	222	2	0	0	X
ejpam-5951	222	3	.	.	PUNCT
ejpam-5951	223	1	(	(	PUNCT
ejpam-5951	223	2	18	18	NUM
ejpam-5951	223	3	)	)	PUNCT
ejpam-5951	223	4	and	and	CCONJ
ejpam-5951	223	5	ρ(gλi	ρ(gλi	PROPN
ejpam-5951	223	6	(	(	PUNCT
ejpam-5951	223	7	ζn	ζn	PROPN
ejpam-5951	223	8	)	)	PUNCT
ejpam-5951	223	9	,	,	PUNCT
ejpam-5951	223	10	ζn	ζn	NOUN
ejpam-5951	223	11	)	)	PUNCT
ejpam-5951	223	12	≤	≤	NUM
ejpam-5951	223	13	ρ(gλi	ρ(gλi	PROPN
ejpam-5951	223	14	(	(	PUNCT
ejpam-5951	223	15	ζn	ζn	NOUN
ejpam-5951	223	16	)	)	PUNCT
ejpam-5951	223	17	,	,	PUNCT
ejpam-5951	223	18	ϑn	ϑn	NOUN
ejpam-5951	223	19	)	)	PUNCT
ejpam-5951	223	20	+	+	NUM
ejpam-5951	223	21	ρ(ϑn	ρ(ϑn	PROPN
ejpam-5951	223	22	,	,	PUNCT
ejpam-5951	223	23	ζn	ζn	NOUN
ejpam-5951	223	24	)	)	PUNCT
ejpam-5951	223	25	.	.	PUNCT
ejpam-5951	224	1	p.	p.	NOUN
ejpam-5951	224	2	patel	patel	PROPN
ejpam-5951	224	3	,	,	PUNCT
ejpam-5951	224	4	r.	r.	PROPN
ejpam-5951	224	5	shukla	shukla	PROPN
ejpam-5951	224	6	/	/	SYM
ejpam-5951	224	7	eur	eur	PROPN
ejpam-5951	224	8	.	.	PUNCT
ejpam-5951	225	1	j.	j.	PROPN
ejpam-5951	225	2	pure	pure	PROPN
ejpam-5951	225	3	appl	appl	PROPN
ejpam-5951	225	4	.	.	PROPN
ejpam-5951	225	5	math	math	PROPN
ejpam-5951	225	6	,	,	PUNCT
ejpam-5951	225	7	18	18	NUM
ejpam-5951	225	8	(	(	PUNCT
ejpam-5951	225	9	2	2	NUM
ejpam-5951	225	10	)	)	PUNCT
ejpam-5951	225	11	(	(	PUNCT
ejpam-5951	225	12	2025	2025	NUM
ejpam-5951	225	13	)	)	PUNCT
ejpam-5951	225	14	,	,	PUNCT
ejpam-5951	225	15	5951	5951	NUM
ejpam-5951	225	16	10	10	NUM
ejpam-5951	225	17	of	of	ADP
ejpam-5951	225	18	15	15	NUM
ejpam-5951	225	19	applying	apply	VERB
ejpam-5951	225	20	limit	limit	NOUN
ejpam-5951	225	21	n	n	X
ejpam-5951	225	22	→	→	SYM
ejpam-5951	225	23	+	+	PROPN
ejpam-5951	225	24	∞	∞	NUM
ejpam-5951	225	25	to	to	ADP
ejpam-5951	225	26	the	the	DET
ejpam-5951	225	27	above	above	ADJ
ejpam-5951	225	28	equation	equation	NOUN
ejpam-5951	225	29	and	and	CCONJ
ejpam-5951	225	30	using	use	VERB
ejpam-5951	225	31	(	(	PUNCT
ejpam-5951	225	32	18	18	NUM
ejpam-5951	225	33	)	)	PUNCT
ejpam-5951	225	34	and	and	CCONJ
ejpam-5951	225	35	(	(	PUNCT
ejpam-5951	225	36	15	15	NUM
ejpam-5951	225	37	)	)	PUNCT
ejpam-5951	225	38	,	,	PUNCT
ejpam-5951	225	39	we	we	PRON
ejpam-5951	225	40	get	get	VERB
ejpam-5951	225	41	lim	lim	PROPN
ejpam-5951	225	42	n→+∞	n→+∞	PROPN
ejpam-5951	225	43	ρ(gλi	ρ(gλi	PROPN
ejpam-5951	225	44	(	(	PUNCT
ejpam-5951	225	45	ζn	ζn	PROPN
ejpam-5951	225	46	)	)	PUNCT
ejpam-5951	225	47	,	,	PUNCT
ejpam-5951	225	48	ζn	ζn	NOUN
ejpam-5951	225	49	)	)	PUNCT
ejpam-5951	225	50	=	=	SYM
ejpam-5951	226	1	0	0	X
ejpam-5951	226	2	.	.	PUNCT
ejpam-5951	227	1	(	(	PUNCT
ejpam-5951	227	2	19	19	NUM
ejpam-5951	227	3	)	)	PUNCT
ejpam-5951	227	4	similarly	similarly	ADV
ejpam-5951	227	5	,	,	PUNCT
ejpam-5951	227	6	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	227	7	(	(	PUNCT
ejpam-5951	227	8	ζn	ζn	NOUN
ejpam-5951	227	9	)	)	PUNCT
ejpam-5951	227	10	,	,	PUNCT
ejpam-5951	227	11	ζn	ζn	NOUN
ejpam-5951	227	12	)	)	PUNCT
ejpam-5951	227	13	≤	≤	NOUN
ejpam-5951	227	14	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	227	15	(	(	PUNCT
ejpam-5951	227	16	ζn	ζn	NOUN
ejpam-5951	227	17	)	)	PUNCT
ejpam-5951	227	18	,	,	PUNCT
ejpam-5951	227	19	gλi	gλi	NOUN
ejpam-5951	227	20	(	(	PUNCT
ejpam-5951	227	21	ζn	ζn	NOUN
ejpam-5951	227	22	)	)	PUNCT
ejpam-5951	227	23	)	)	PUNCT
ejpam-5951	228	1	+	+	CCONJ
ejpam-5951	228	2	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	228	3	(	(	PUNCT
ejpam-5951	228	4	ζn	ζn	PROPN
ejpam-5951	228	5	)	)	PUNCT
ejpam-5951	228	6	,	,	PUNCT
ejpam-5951	228	7	ζn	ζn	NOUN
ejpam-5951	228	8	)	)	PUNCT
ejpam-5951	228	9	.	.	PUNCT
ejpam-5951	229	1	applying	apply	VERB
ejpam-5951	229	2	limit	limit	NOUN
ejpam-5951	229	3	n	n	X
ejpam-5951	229	4	→	→	SYM
ejpam-5951	229	5	+	+	PROPN
ejpam-5951	229	6	∞	∞	NUM
ejpam-5951	229	7	to	to	ADP
ejpam-5951	229	8	the	the	DET
ejpam-5951	229	9	above	above	ADJ
ejpam-5951	229	10	equation	equation	NOUN
ejpam-5951	229	11	and	and	CCONJ
ejpam-5951	229	12	using	use	VERB
ejpam-5951	229	13	(	(	PUNCT
ejpam-5951	229	14	18	18	NUM
ejpam-5951	229	15	)	)	PUNCT
ejpam-5951	229	16	and	and	CCONJ
ejpam-5951	229	17	(	(	PUNCT
ejpam-5951	229	18	19	19	NUM
ejpam-5951	229	19	)	)	PUNCT
ejpam-5951	229	20	,	,	PUNCT
ejpam-5951	229	21	we	we	PRON
ejpam-5951	229	22	get	get	VERB
ejpam-5951	229	23	lim	lim	PROPN
ejpam-5951	229	24	n→+∞	n→+∞	PROPN
ejpam-5951	229	25	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	229	26	(	(	PUNCT
ejpam-5951	229	27	ζn	ζn	NOUN
ejpam-5951	229	28	)	)	PUNCT
ejpam-5951	229	29	,	,	PUNCT
ejpam-5951	229	30	ζn	ζn	NOUN
ejpam-5951	229	31	)	)	PUNCT
ejpam-5951	229	32	=	=	SYM
ejpam-5951	230	1	0	0	X
ejpam-5951	230	2	.	.	PUNCT
ejpam-5951	231	1	(	(	PUNCT
ejpam-5951	231	2	20	20	NUM
ejpam-5951	231	3	)	)	PUNCT
ejpam-5951	231	4	since	since	SCONJ
ejpam-5951	231	5	hλi	hλi	PROPN
ejpam-5951	231	6	nonexpansive	nonexpansive	PROPN
ejpam-5951	232	1	so	so	ADV
ejpam-5951	232	2	it	it	PRON
ejpam-5951	232	3	is	be	AUX
ejpam-5951	232	4	demiclosed	demiclose	VERB
ejpam-5951	232	5	at	at	ADP
ejpam-5951	232	6	0	0	NUM
ejpam-5951	232	7	and	and	CCONJ
ejpam-5951	232	8	hence	hence	ADV
ejpam-5951	232	9	ζ	ζ	NOUN
ejpam-5951	232	10	∈	∈	NOUN
ejpam-5951	233	1	⋂	⋂	X
ejpam-5951	233	2	i	i	PRON
ejpam-5951	233	3	hi	hi	VERB
ejpam-5951	233	4	,	,	PUNCT
ejpam-5951	233	5	further	far	ADV
ejpam-5951	233	6	from	from	ADP
ejpam-5951	233	7	(	(	PUNCT
ejpam-5951	233	8	19	19	NUM
ejpam-5951	233	9	)	)	PUNCT
ejpam-5951	233	10	we	we	PRON
ejpam-5951	233	11	can	can	AUX
ejpam-5951	233	12	also	also	ADV
ejpam-5951	233	13	say	say	VERB
ejpam-5951	233	14	ζ	ζ	NOUN
ejpam-5951	233	15	∈	∈	PROPN
ejpam-5951	233	16	⋂	⋂	PROPN
ejpam-5951	233	17	i	i	PRON
ejpam-5951	233	18	gi	gi	VERB
ejpam-5951	233	19	.	.	PUNCT
ejpam-5951	234	1	next	next	ADV
ejpam-5951	234	2	we	we	PRON
ejpam-5951	234	3	prove	prove	VERB
ejpam-5951	234	4	that	that	SCONJ
ejpam-5951	234	5	ζ	ζ	PROPN
ejpam-5951	234	6	∈	∈	PROPN
ejpam-5951	234	7	φ	φ	X
ejpam-5951	234	8	.	.	PUNCT
ejpam-5951	234	9	suppose	suppose	VERB
ejpam-5951	235	1	ζ∗	ζ∗	PROPN
ejpam-5951	235	2	∈	∈	PROPN
ejpam-5951	236	1	⋂	⋂	PROPN
ejpam-5951	237	1	i	i	PRON
ejpam-5951	237	2	hi	hi	INTJ
ejpam-5951	237	3	is	be	AUX
ejpam-5951	237	4	arbitrary	arbitrary	ADJ
ejpam-5951	237	5	such	such	ADJ
ejpam-5951	237	6	that	that	SCONJ
ejpam-5951	237	7	ζ	ζ	PROPN
ejpam-5951	237	8	̸=	̸=	PROPN
ejpam-5951	237	9	ζ∗.	ζ∗.	AUX
ejpam-5951	237	10	let	let	VERB
ejpam-5951	237	11	the	the	DET
ejpam-5951	237	12	triangles	triangle	NOUN
ejpam-5951	237	13	∆(gλi	∆(gλi	PROPN
ejpam-5951	237	14	(	(	PUNCT
ejpam-5951	237	15	ζn	ζn	NOUN
ejpam-5951	237	16	)	)	PUNCT
ejpam-5951	237	17	,	,	PUNCT
ejpam-5951	237	18	hλi	hλi	NOUN
ejpam-5951	237	19	(	(	PUNCT
ejpam-5951	237	20	ζn	ζn	NOUN
ejpam-5951	237	21	)	)	PUNCT
ejpam-5951	237	22	,	,	PUNCT
ejpam-5951	237	23	ζ	ζ	NOUN
ejpam-5951	237	24	∗	∗	NOUN
ejpam-5951	237	25	)	)	PUNCT
ejpam-5951	237	26	,	,	PUNCT
ejpam-5951	237	27	∆(gλi	∆(gλi	PROPN
ejpam-5951	237	28	(	(	PUNCT
ejpam-5951	237	29	ζ∗	ζ∗	PROPN
ejpam-5951	237	30	)	)	PUNCT
ejpam-5951	237	31	,	,	PUNCT
ejpam-5951	237	32	hλi	hλi	NOUN
ejpam-5951	237	33	(	(	PUNCT
ejpam-5951	237	34	ζn	ζn	NOUN
ejpam-5951	237	35	)	)	PUNCT
ejpam-5951	237	36	,	,	PUNCT
ejpam-5951	237	37	ζ	ζ	NOUN
ejpam-5951	237	38	∗	∗	NOUN
ejpam-5951	237	39	)	)	PUNCT
ejpam-5951	237	40	and	and	CCONJ
ejpam-5951	237	41	∆(gλi	∆(gλi	PROPN
ejpam-5951	237	42	(	(	PUNCT
ejpam-5951	237	43	ζn	ζn	NOUN
ejpam-5951	237	44	)	)	PUNCT
ejpam-5951	237	45	,	,	PUNCT
ejpam-5951	237	46	gλi	gλi	NOUN
ejpam-5951	237	47	(	(	PUNCT
ejpam-5951	237	48	ζ∗	ζ∗	PROPN
ejpam-5951	237	49	)	)	PUNCT
ejpam-5951	237	50	,	,	PUNCT
ejpam-5951	237	51	hλi	hλi	NOUN
ejpam-5951	237	52	(	(	PUNCT
ejpam-5951	237	53	ζn	ζn	NOUN
ejpam-5951	237	54	)	)	PUNCT
ejpam-5951	237	55	)	)	PUNCT
ejpam-5951	238	1	then	then	ADV
ejpam-5951	238	2	there	there	PRON
ejpam-5951	238	3	exist	exist	VERB
ejpam-5951	238	4	comparison	comparison	NOUN
ejpam-5951	238	5	triangles	triangle	NOUN
ejpam-5951	238	6	∆(gλi	∆(gλi	PROPN
ejpam-5951	238	7	(	(	PUNCT
ejpam-5951	238	8	ζn	ζn	NOUN
ejpam-5951	238	9	)	)	PUNCT
ejpam-5951	238	10	,	,	PUNCT
ejpam-5951	238	11	hλi	hλi	NOUN
ejpam-5951	238	12	(	(	PUNCT
ejpam-5951	238	13	ζn	ζn	NOUN
ejpam-5951	238	14	)	)	PUNCT
ejpam-5951	238	15	,	,	PUNCT
ejpam-5951	238	16	ζ∗	ζ∗	PROPN
ejpam-5951	238	17	)	)	PUNCT
ejpam-5951	238	18	,	,	PUNCT
ejpam-5951	238	19	∆(gλi	∆(gλi	PROPN
ejpam-5951	238	20	(	(	PUNCT
ejpam-5951	238	21	ζ∗	ζ∗	PROPN
ejpam-5951	238	22	)	)	PUNCT
ejpam-5951	238	23	,	,	PUNCT
ejpam-5951	238	24	hλi	hλi	NOUN
ejpam-5951	238	25	(	(	PUNCT
ejpam-5951	238	26	ζn	ζn	NOUN
ejpam-5951	238	27	)	)	PUNCT
ejpam-5951	238	28	,	,	PUNCT
ejpam-5951	238	29	ζ∗	ζ∗	PROPN
ejpam-5951	238	30	)	)	PUNCT
ejpam-5951	238	31	and	and	CCONJ
ejpam-5951	238	32	∆(gλi	∆(gλi	PROPN
ejpam-5951	238	33	(	(	PUNCT
ejpam-5951	238	34	ζn	ζn	NOUN
ejpam-5951	238	35	)	)	PUNCT
ejpam-5951	238	36	,	,	PUNCT
ejpam-5951	238	37	gλi	gλi	NOUN
ejpam-5951	238	38	(	(	PUNCT
ejpam-5951	238	39	ζ∗	ζ∗	PROPN
ejpam-5951	238	40	)	)	PUNCT
ejpam-5951	238	41	,	,	PUNCT
ejpam-5951	238	42	hλi	hλi	NOUN
ejpam-5951	238	43	(	(	PUNCT
ejpam-5951	238	44	ζn	ζn	NOUN
ejpam-5951	238	45	)	)	PUNCT
ejpam-5951	238	46	)	)	PUNCT
ejpam-5951	238	47	such	such	ADJ
ejpam-5951	238	48	that	that	DET
ejpam-5951	238	49	ρ(gλi	ρ(gλi	PROPN
ejpam-5951	238	50	(	(	PUNCT
ejpam-5951	238	51	ζn	ζn	NOUN
ejpam-5951	238	52	)	)	PUNCT
ejpam-5951	238	53	,	,	PUNCT
ejpam-5951	238	54	hλi	hλi	NOUN
ejpam-5951	238	55	(	(	PUNCT
ejpam-5951	238	56	ζn	ζn	NOUN
ejpam-5951	238	57	)	)	PUNCT
ejpam-5951	238	58	)	)	PUNCT
ejpam-5951	239	1	=	=	SYM
ejpam-5951	239	2	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	239	3	(	(	PUNCT
ejpam-5951	239	4	ζn)−hλi	ζn)−hλi	PROPN
ejpam-5951	239	5	(	(	PUNCT
ejpam-5951	239	6	ζn	ζn	NOUN
ejpam-5951	239	7	)	)	PUNCT
ejpam-5951	239	8	∥∥∥	∥∥∥	PROPN
ejpam-5951	239	9	,	,	PUNCT
ejpam-5951	239	10	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	239	11	(	(	PUNCT
ejpam-5951	239	12	ζn	ζn	PROPN
ejpam-5951	239	13	)	)	PUNCT
ejpam-5951	239	14	,	,	PUNCT
ejpam-5951	239	15	ζ	ζ	NOUN
ejpam-5951	239	16	∗	∗	NOUN
ejpam-5951	239	17	)	)	PUNCT
ejpam-5951	239	18	=	=	SYM
ejpam-5951	239	19	∥∥∥gλi	∥∥∥gλi	PUNCT
ejpam-5951	239	20	(	(	PUNCT
ejpam-5951	239	21	ζn)−	ζn)−	NOUN
ejpam-5951	239	22	ζ∗	ζ∗	PROPN
ejpam-5951	239	23	∥∥∥	∥∥∥	PROPN
ejpam-5951	239	24	,	,	PUNCT
ejpam-5951	239	25	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	239	26	(	(	PUNCT
ejpam-5951	239	27	ζn	ζn	NOUN
ejpam-5951	239	28	)	)	PUNCT
ejpam-5951	239	29	,	,	PUNCT
ejpam-5951	239	30	ζ	ζ	NOUN
ejpam-5951	239	31	∗	∗	NOUN
ejpam-5951	239	32	)	)	PUNCT
ejpam-5951	240	1	=	=	NOUN
ejpam-5951	240	2	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	240	3	(	(	PUNCT
ejpam-5951	240	4	ζn)−	ζn)−	NOUN
ejpam-5951	240	5	ζ∗	ζ∗	PROPN
ejpam-5951	240	6	∥∥∥	∥∥∥	PROPN
ejpam-5951	240	7	,	,	PUNCT
ejpam-5951	240	8	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	240	9	(	(	PUNCT
ejpam-5951	240	10	ζ∗	ζ∗	PROPN
ejpam-5951	240	11	)	)	PUNCT
ejpam-5951	240	12	,	,	PUNCT
ejpam-5951	240	13	ζ∗	ζ∗	PROPN
ejpam-5951	240	14	)	)	PUNCT
ejpam-5951	240	15	=	=	SYM
ejpam-5951	241	1	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	241	2	(	(	PUNCT
ejpam-5951	241	3	ζ∗)−	ζ∗)−	ADJ
ejpam-5951	241	4	ζ∗	ζ∗	ADJ
ejpam-5951	241	5	∥∥∥	∥∥∥	NOUN
ejpam-5951	241	6	,	,	PUNCT
ejpam-5951	241	7	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	241	8	(	(	PUNCT
ejpam-5951	241	9	ζn	ζn	NOUN
ejpam-5951	241	10	)	)	PUNCT
ejpam-5951	241	11	,	,	PUNCT
ejpam-5951	241	12	ζ	ζ	NOUN
ejpam-5951	241	13	∗	∗	NOUN
ejpam-5951	241	14	)	)	PUNCT
ejpam-5951	241	15	=	=	SYM
ejpam-5951	242	1	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	242	2	(	(	PUNCT
ejpam-5951	242	3	ζn)−	ζn)−	NOUN
ejpam-5951	242	4	ζ∗	ζ∗	PROPN
ejpam-5951	242	5	∥∥∥	∥∥∥	PROPN
ejpam-5951	242	6	,	,	PUNCT
ejpam-5951	242	7	and	and	CCONJ
ejpam-5951	242	8	ρ(gλi	ρ(gλi	NOUN
ejpam-5951	242	9	(	(	PUNCT
ejpam-5951	242	10	ζn	ζn	NOUN
ejpam-5951	242	11	)	)	PUNCT
ejpam-5951	242	12	,	,	PUNCT
ejpam-5951	242	13	gλi	gλi	NOUN
ejpam-5951	242	14	(	(	PUNCT
ejpam-5951	242	15	ζ∗	ζ∗	PROPN
ejpam-5951	242	16	)	)	PUNCT
ejpam-5951	242	17	)	)	PUNCT
ejpam-5951	243	1	=	=	SYM
ejpam-5951	243	2	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	243	3	(	(	PUNCT
ejpam-5951	243	4	ζn)−gλi	ζn)−gλi	PROPN
ejpam-5951	243	5	(	(	PUNCT
ejpam-5951	243	6	ζ∗	ζ∗	PROPN
ejpam-5951	243	7	)	)	PUNCT
ejpam-5951	243	8	∥∥∥.	∥∥∥.	PUNCT
ejpam-5951	243	9	suppose	suppose	VERB
ejpam-5951	243	10	θ	θ	NOUN
ejpam-5951	243	11	be	be	AUX
ejpam-5951	243	12	the	the	DET
ejpam-5951	243	13	angle	angle	NOUN
ejpam-5951	243	14	at	at	ADP
ejpam-5951	243	15	ζ∗	ζ∗	PROPN
ejpam-5951	243	16	in	in	ADP
ejpam-5951	243	17	the	the	DET
ejpam-5951	243	18	triangle	triangle	NOUN
ejpam-5951	243	19	∆(gλi	∆(gλi	PROPN
ejpam-5951	243	20	(	(	PUNCT
ejpam-5951	243	21	ζ∗	ζ∗	PROPN
ejpam-5951	243	22	)	)	PUNCT
ejpam-5951	243	23	,	,	PUNCT
ejpam-5951	243	24	hλi	hλi	NOUN
ejpam-5951	243	25	(	(	PUNCT
ejpam-5951	243	26	ζn	ζn	NOUN
ejpam-5951	243	27	)	)	PUNCT
ejpam-5951	243	28	,	,	PUNCT
ejpam-5951	243	29	ζ	ζ	NOUN
ejpam-5951	243	30	∗	∗	NOUN
ejpam-5951	243	31	)	)	PUNCT
ejpam-5951	243	32	and	and	CCONJ
ejpam-5951	243	33	θ	θ	PROPN
ejpam-5951	243	34	be	be	VERB
ejpam-5951	243	35	the	the	DET
ejpam-5951	243	36	angle	angle	NOUN
ejpam-5951	243	37	at	at	ADP
ejpam-5951	243	38	ζ∗	ζ∗	PROPN
ejpam-5951	243	39	in	in	ADP
ejpam-5951	243	40	the	the	DET
ejpam-5951	243	41	comparison	comparison	NOUN
ejpam-5951	243	42	triangle	triangle	NOUN
ejpam-5951	243	43	∆(gλi	∆(gλi	PROPN
ejpam-5951	243	44	(	(	PUNCT
ejpam-5951	243	45	ζ∗	ζ∗	PROPN
ejpam-5951	243	46	)	)	PUNCT
ejpam-5951	243	47	,	,	PUNCT
ejpam-5951	243	48	hλi	hλi	NOUN
ejpam-5951	243	49	(	(	PUNCT
ejpam-5951	243	50	ζn	ζn	NOUN
ejpam-5951	243	51	)	)	PUNCT
ejpam-5951	243	52	,	,	PUNCT
ejpam-5951	243	53	ζ∗	ζ∗	PROPN
ejpam-5951	243	54	)	)	PUNCT
ejpam-5951	243	55	.	.	PUNCT
ejpam-5951	244	1	then	then	ADV
ejpam-5951	244	2	θ	θ	X
ejpam-5951	244	3	≤	≤	PROPN
ejpam-5951	244	4	θ	θ	PROPN
ejpam-5951	244	5	,	,	PUNCT
ejpam-5951	244	6	and	and	CCONJ
ejpam-5951	244	7	thus	thus	ADV
ejpam-5951	244	8	,	,	PUNCT
ejpam-5951	244	9	cos(θ	cos(θ	X
ejpam-5951	244	10	)	)	PUNCT
ejpam-5951	244	11	≤	≤	NOUN
ejpam-5951	244	12	cos(θ	cos(θ	X
ejpam-5951	244	13	)	)	PUNCT
ejpam-5951	244	14	.	.	PUNCT
ejpam-5951	245	1	since	since	SCONJ
ejpam-5951	245	2	ϑn	ϑn	NOUN
ejpam-5951	245	3	=	=	SYM
ejpam-5951	245	4	δngλi	δngλi	NOUN
ejpam-5951	245	5	(	(	PUNCT
ejpam-5951	245	6	ζn	ζn	NOUN
ejpam-5951	245	7	)	)	PUNCT
ejpam-5951	245	8	+	+	CCONJ
ejpam-5951	245	9	(	(	PUNCT
ejpam-5951	245	10	1−	1−	NUM
ejpam-5951	245	11	δn)hλi	δn)hλi	NOUN
ejpam-5951	245	12	(	(	PUNCT
ejpam-5951	245	13	ζn	ζn	NOUN
ejpam-5951	245	14	)	)	PUNCT
ejpam-5951	245	15	is	be	AUX
ejpam-5951	245	16	the	the	DET
ejpam-5951	245	17	comparison	comparison	NOUN
ejpam-5951	245	18	point	point	NOUN
ejpam-5951	245	19	of	of	ADP
ejpam-5951	245	20	ϑn	ϑn	NOUN
ejpam-5951	245	21	.	.	PUNCT
ejpam-5951	246	1	using	use	VERB
ejpam-5951	246	2	proposition	proposition	NOUN
ejpam-5951	246	3	3	3	NUM
ejpam-5951	246	4	and	and	CCONJ
ejpam-5951	246	5	lemma	lemma	PROPN
ejpam-5951	246	6	3	3	NUM
ejpam-5951	246	7	(	(	PUNCT
ejpam-5951	246	8	2	2	NUM
ejpam-5951	246	9	)	)	PUNCT
ejpam-5951	246	10	,	,	PUNCT
ejpam-5951	246	11	we	we	PRON
ejpam-5951	246	12	have	have	VERB
ejpam-5951	246	13	ρ2(ϑn	ρ2(ϑn	NUM
ejpam-5951	246	14	,	,	PUNCT
ejpam-5951	246	15	ζ	ζ	NOUN
ejpam-5951	246	16	∗	∗	NOUN
ejpam-5951	246	17	)	)	PUNCT
ejpam-5951	246	18	≤	≤	NUM
ejpam-5951	247	1	∥∥ϑn	∥∥ϑn	NUM
ejpam-5951	247	2	−	−	PROPN
ejpam-5951	247	3	ζ∗	ζ∗	PROPN
ejpam-5951	247	4	∥∥2	∥∥2	PROPN
ejpam-5951	248	1	=	=	SYM
ejpam-5951	248	2	∥∥∥δngλi	∥∥∥δngλi	PROPN
ejpam-5951	248	3	(	(	PUNCT
ejpam-5951	248	4	ζn	ζn	NOUN
ejpam-5951	248	5	)	)	PUNCT
ejpam-5951	248	6	+	+	CCONJ
ejpam-5951	248	7	(	(	PUNCT
ejpam-5951	248	8	1−	1−	NUM
ejpam-5951	248	9	δn)hλi	δn)hλi	NOUN
ejpam-5951	248	10	(	(	PUNCT
ejpam-5951	248	11	ζn)−	ζn)−	NOUN
ejpam-5951	248	12	ζ∗	ζ∗	PROPN
ejpam-5951	248	13	∥∥∥	∥∥∥	PROPN
ejpam-5951	248	14	=	=	SYM
ejpam-5951	248	15	δ2n	δ2n	PROPN
ejpam-5951	248	16	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	248	17	(	(	PUNCT
ejpam-5951	248	18	ζn)−	ζn)−	NOUN
ejpam-5951	248	19	ζ∗	ζ∗	ADJ
ejpam-5951	248	20	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	248	21	+	+	CCONJ
ejpam-5951	248	22	(	(	PUNCT
ejpam-5951	248	23	1−	1−	NUM
ejpam-5951	248	24	δn	δn	NOUN
ejpam-5951	248	25	)	)	PUNCT
ejpam-5951	248	26	2	2	NUM
ejpam-5951	248	27	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	248	28	(	(	PUNCT
ejpam-5951	248	29	ζn)−	ζn)−	NOUN
ejpam-5951	248	30	ζ∗	ζ∗	ADJ
ejpam-5951	248	31	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	249	1	+	+	CCONJ
ejpam-5951	249	2	2δn(1−	2δn(1−	NUM
ejpam-5951	249	3	δn	δn	NOUN
ejpam-5951	249	4	)	)	PUNCT
ejpam-5951	249	5	〈	〈	NOUN
ejpam-5951	249	6	gλi	gλi	NOUN
ejpam-5951	249	7	(	(	PUNCT
ejpam-5951	249	8	ζn)−	ζn)−	NOUN
ejpam-5951	249	9	ζ∗	ζ∗	PROPN
ejpam-5951	249	10	,	,	PUNCT
ejpam-5951	249	11	hλi	hλi	NOUN
ejpam-5951	249	12	(	(	PUNCT
ejpam-5951	249	13	ζn)−	ζn)−	NOUN
ejpam-5951	249	14	ζ∗	ζ∗	PROPN
ejpam-5951	249	15	〉	〉	NOUN
ejpam-5951	249	16	=	=	SYM
ejpam-5951	249	17	δ2n	δ2n	PROPN
ejpam-5951	249	18	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	249	19	(	(	PUNCT
ejpam-5951	249	20	ζn)−	ζn)−	NOUN
ejpam-5951	249	21	ζ∗	ζ∗	ADJ
ejpam-5951	249	22	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	249	23	+	+	CCONJ
ejpam-5951	249	24	(	(	PUNCT
ejpam-5951	249	25	1−	1−	NUM
ejpam-5951	249	26	δn	δn	NOUN
ejpam-5951	249	27	)	)	PUNCT
ejpam-5951	249	28	2	2	NUM
ejpam-5951	249	29	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	249	30	(	(	PUNCT
ejpam-5951	249	31	ζn)−	ζn)−	NOUN
ejpam-5951	249	32	ζ∗	ζ∗	ADJ
ejpam-5951	249	33	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	250	1	+	+	CCONJ
ejpam-5951	250	2	2δn(1−	2δn(1−	NUM
ejpam-5951	250	3	δn	δn	NOUN
ejpam-5951	250	4	)	)	PUNCT
ejpam-5951	250	5	(	(	PUNCT
ejpam-5951	250	6	〈	〈	PROPN
ejpam-5951	250	7	gλi	gλi	NOUN
ejpam-5951	250	8	(	(	PUNCT
ejpam-5951	250	9	ζn)−gλi	ζn)−gλi	PROPN
ejpam-5951	250	10	(	(	PUNCT
ejpam-5951	250	11	ζ∗	ζ∗	PROPN
ejpam-5951	250	12	)	)	PUNCT
ejpam-5951	250	13	,	,	PUNCT
ejpam-5951	250	14	hλi	hλi	NOUN
ejpam-5951	250	15	(	(	PUNCT
ejpam-5951	250	16	ζn)−	ζn)−	NOUN
ejpam-5951	250	17	ζ∗	ζ∗	PROPN
ejpam-5951	250	18	〉	〉	NOUN
ejpam-5951	250	19	+	+	CCONJ
ejpam-5951	250	20	〈	〈	PROPN
ejpam-5951	250	21	gλi	gλi	NOUN
ejpam-5951	250	22	(	(	PUNCT
ejpam-5951	250	23	ζ∗)−	ζ∗)−	ADJ
ejpam-5951	250	24	ζ∗	ζ∗	PROPN
ejpam-5951	250	25	,	,	PUNCT
ejpam-5951	250	26	hλi	hλi	NOUN
ejpam-5951	250	27	(	(	PUNCT
ejpam-5951	250	28	ζn)−	ζn)−	NOUN
ejpam-5951	250	29	ζ∗	ζ∗	PROPN
ejpam-5951	250	30	〉	〉	NOUN
ejpam-5951	250	31	)	)	PUNCT
ejpam-5951	250	32	≤	≤	PUNCT
ejpam-5951	250	33	δ2n	δ2n	PROPN
ejpam-5951	250	34	∥∥∥gλi	∥∥∥gλi	PUNCT
ejpam-5951	251	1	(	(	PUNCT
ejpam-5951	251	2	ζn)−	ζn)−	NOUN
ejpam-5951	251	3	ζ∗	ζ∗	ADJ
ejpam-5951	251	4	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	252	1	+	+	CCONJ
ejpam-5951	252	2	(	(	PUNCT
ejpam-5951	252	3	1−	1−	NUM
ejpam-5951	252	4	δn	δn	NOUN
ejpam-5951	252	5	)	)	PUNCT
ejpam-5951	252	6	2	2	NUM
ejpam-5951	252	7	∥∥∥hλi	∥∥∥hλi	X
ejpam-5951	252	8	(	(	PUNCT
ejpam-5951	252	9	ζn)−	ζn)−	NOUN
ejpam-5951	252	10	ζ∗	ζ∗	ADJ
ejpam-5951	252	11	∥∥∥2	∥∥∥2	NOUN
ejpam-5951	253	1	+	+	CCONJ
ejpam-5951	253	2	2δn(1−	2δn(1−	NUM
ejpam-5951	253	3	δn	δn	NOUN
ejpam-5951	253	4	)	)	PUNCT
ejpam-5951	253	5	(	(	PUNCT
ejpam-5951	253	6	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	253	7	(	(	PUNCT
ejpam-5951	253	8	ζn)−gλi	ζn)−gλi	PROPN
ejpam-5951	253	9	(	(	PUNCT
ejpam-5951	253	10	ζ∗	ζ∗	PROPN
ejpam-5951	253	11	)	)	PUNCT
ejpam-5951	253	12	∥∥∥∥∥∥hλi	∥∥∥∥∥∥hλi	NOUN
ejpam-5951	253	13	(	(	PUNCT
ejpam-5951	253	14	ζn)−	ζn)−	NOUN
ejpam-5951	253	15	ζ∗	ζ∗	PROPN
ejpam-5951	253	16	∥∥∥	∥∥∥	PROPN
ejpam-5951	253	17	+	+	CCONJ
ejpam-5951	253	18	∥∥∥gλi	∥∥∥gλi	X
ejpam-5951	253	19	(	(	PUNCT
ejpam-5951	253	20	ζ∗)−	ζ∗)−	ADJ
ejpam-5951	253	21	ζ∗	ζ∗	ADJ
ejpam-5951	253	22	∥∥∥∥∥∥hλi	∥∥∥∥∥∥hλi	NOUN
ejpam-5951	253	23	(	(	PUNCT
ejpam-5951	253	24	ζn)−	ζn)−	NOUN
ejpam-5951	253	25	ζ∗	ζ∗	PROPN
ejpam-5951	253	26	∥∥∥	∥∥∥	PROPN
ejpam-5951	253	27	cos(θ	cos(θ	PART
ejpam-5951	253	28	)	)	PUNCT
ejpam-5951	253	29	)	)	PUNCT
ejpam-5951	254	1	≤	≤	NUM
ejpam-5951	255	1	δ2nρ	δ2nρ	PUNCT
ejpam-5951	255	2	2	2	NUM
ejpam-5951	255	3	(	(	PUNCT
ejpam-5951	255	4	gλi	gλi	NOUN
ejpam-5951	255	5	(	(	PUNCT
ejpam-5951	255	6	ζn	ζn	NOUN
ejpam-5951	255	7	)	)	PUNCT
ejpam-5951	255	8	,	,	PUNCT
ejpam-5951	255	9	ζ	ζ	NOUN
ejpam-5951	255	10	∗	∗	NOUN
ejpam-5951	255	11	)	)	PUNCT
ejpam-5951	255	12	+	+	CCONJ
ejpam-5951	255	13	(	(	PUNCT
ejpam-5951	255	14	1−	1−	NUM
ejpam-5951	255	15	δn	δn	NOUN
ejpam-5951	255	16	)	)	PUNCT
ejpam-5951	255	17	2ρ2	2ρ2	NUM
ejpam-5951	255	18	(	(	PUNCT
ejpam-5951	255	19	hλi	hλi	NOUN
ejpam-5951	255	20	(	(	PUNCT
ejpam-5951	255	21	ζn	ζn	NOUN
ejpam-5951	255	22	)	)	PUNCT
ejpam-5951	255	23	,	,	PUNCT
ejpam-5951	255	24	ζ	ζ	NOUN
ejpam-5951	255	25	∗	∗	NOUN
ejpam-5951	255	26	)	)	PUNCT
ejpam-5951	256	1	p.	p.	NOUN
ejpam-5951	256	2	patel	patel	PROPN
ejpam-5951	256	3	,	,	PUNCT
ejpam-5951	256	4	r.	r.	PROPN
ejpam-5951	256	5	shukla	shukla	PROPN
ejpam-5951	256	6	/	/	SYM
ejpam-5951	256	7	eur	eur	PROPN
ejpam-5951	256	8	.	.	PUNCT
ejpam-5951	257	1	j.	j.	PROPN
ejpam-5951	257	2	pure	pure	PROPN
ejpam-5951	257	3	appl	appl	PROPN
ejpam-5951	257	4	.	.	PROPN
ejpam-5951	257	5	math	math	PROPN
ejpam-5951	257	6	,	,	PUNCT
ejpam-5951	257	7	18	18	NUM
ejpam-5951	257	8	(	(	PUNCT
ejpam-5951	257	9	2	2	NUM
ejpam-5951	257	10	)	)	PUNCT
ejpam-5951	257	11	(	(	PUNCT
ejpam-5951	257	12	2025	2025	NUM
ejpam-5951	257	13	)	)	PUNCT
ejpam-5951	257	14	,	,	PUNCT
ejpam-5951	257	15	5951	5951	NUM
ejpam-5951	257	16	11	11	NUM
ejpam-5951	257	17	of	of	ADP
ejpam-5951	257	18	15	15	NUM
ejpam-5951	257	19	+	+	CCONJ
ejpam-5951	257	20	2δn(1−	2δn(1−	NUM
ejpam-5951	257	21	δn)ρ	δn)ρ	PROPN
ejpam-5951	257	22	(	(	PUNCT
ejpam-5951	257	23	gλi	gλi	NOUN
ejpam-5951	257	24	(	(	PUNCT
ejpam-5951	257	25	ζn	ζn	NOUN
ejpam-5951	257	26	)	)	PUNCT
ejpam-5951	257	27	,	,	PUNCT
ejpam-5951	257	28	gλi	gλi	NOUN
ejpam-5951	257	29	(	(	PUNCT
ejpam-5951	257	30	ζ∗	ζ∗	PROPN
ejpam-5951	257	31	)	)	PUNCT
ejpam-5951	257	32	)	)	PUNCT
ejpam-5951	258	1	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	258	2	(	(	PUNCT
ejpam-5951	258	3	ζn	ζn	NOUN
ejpam-5951	258	4	)	)	PUNCT
ejpam-5951	258	5	,	,	PUNCT
ejpam-5951	258	6	ζ	ζ	NOUN
ejpam-5951	258	7	∗	∗	NOUN
ejpam-5951	258	8	)	)	PUNCT
ejpam-5951	259	1	+	+	CCONJ
ejpam-5951	259	2	2δn(1−	2δn(1−	NUM
ejpam-5951	259	3	δn)ρ	δn)ρ	PROPN
ejpam-5951	259	4	(	(	PUNCT
ejpam-5951	259	5	gλi	gλi	NOUN
ejpam-5951	259	6	(	(	PUNCT
ejpam-5951	259	7	ζ∗	ζ∗	PROPN
ejpam-5951	259	8	)	)	PUNCT
ejpam-5951	259	9	,	,	PUNCT
ejpam-5951	259	10	ζ∗	ζ∗	PROPN
ejpam-5951	259	11	)	)	PUNCT
ejpam-5951	259	12	ρ(hλi	ρ(hλi	NOUN
ejpam-5951	259	13	(	(	PUNCT
ejpam-5951	259	14	ζn	ζn	NOUN
ejpam-5951	259	15	)	)	PUNCT
ejpam-5951	259	16	,	,	PUNCT
ejpam-5951	259	17	ζ	ζ	NOUN
ejpam-5951	259	18	∗	∗	NOUN
ejpam-5951	259	19	)	)	PUNCT
ejpam-5951	259	20	cos(θ	cos(θ	PART
ejpam-5951	259	21	)	)	PUNCT
ejpam-5951	259	22	ρ2(ϑn	ρ2(ϑn	PROPN
ejpam-5951	259	23	,	,	PUNCT
ejpam-5951	259	24	ζ	ζ	NOUN
ejpam-5951	259	25	∗	∗	NOUN
ejpam-5951	259	26	)	)	PUNCT
ejpam-5951	259	27	≤	≤	NOUN
ejpam-5951	259	28	δ2nρ	δ2nρ	PUNCT
ejpam-5951	259	29	2(gλi	2(gλi	NOUN
ejpam-5951	259	30	(	(	PUNCT
ejpam-5951	259	31	ζn	ζn	NOUN
ejpam-5951	259	32	)	)	PUNCT
ejpam-5951	259	33	,	,	PUNCT
ejpam-5951	259	34	ζ	ζ	NOUN
ejpam-5951	259	35	∗	∗	NOUN
ejpam-5951	259	36	)	)	PUNCT
ejpam-5951	260	1	+	+	CCONJ
ejpam-5951	260	2	(	(	PUNCT
ejpam-5951	260	3	1−	1−	NUM
ejpam-5951	260	4	δn	δn	NOUN
ejpam-5951	260	5	)	)	PUNCT
ejpam-5951	260	6	2ρ2(ζn	2ρ2(ζn	NUM
ejpam-5951	260	7	,	,	PUNCT
ejpam-5951	260	8	ζ	ζ	NOUN
ejpam-5951	260	9	∗	∗	NOUN
ejpam-5951	260	10	)	)	PUNCT
ejpam-5951	261	1	+	+	CCONJ
ejpam-5951	261	2	2δn(1−	2δn(1−	NUM
ejpam-5951	261	3	δn)ρ	δn)ρ	ADJ
ejpam-5951	261	4	2(ζn	2(ζn	NOUN
ejpam-5951	261	5	,	,	PUNCT
ejpam-5951	261	6	ζ	ζ	NOUN
ejpam-5951	261	7	∗	∗	NOUN
ejpam-5951	261	8	)	)	PUNCT
ejpam-5951	262	1	+	+	CCONJ
ejpam-5951	262	2	2δn(1−	2δn(1−	NUM
ejpam-5951	262	3	δn)r	δn)r	PROPN
ejpam-5951	262	4	(	(	PUNCT
ejpam-5951	262	5	exp−1	exp−1	PROPN
ejpam-5951	262	6	ζ∗	ζ∗	PROPN
ejpam-5951	262	7	gλi	gλi	NOUN
ejpam-5951	262	8	(	(	PUNCT
ejpam-5951	262	9	ζ∗	ζ∗	PROPN
ejpam-5951	262	10	)	)	PUNCT
ejpam-5951	262	11	,	,	PUNCT
ejpam-5951	262	12	exp−1	exp−1	PROPN
ejpam-5951	262	13	ζ∗	ζ∗	PROPN
ejpam-5951	262	14	hλi	hλi	NOUN
ejpam-5951	262	15	(	(	PUNCT
ejpam-5951	262	16	ζn	ζn	NOUN
ejpam-5951	262	17	)	)	PUNCT
ejpam-5951	262	18	)	)	PUNCT
ejpam-5951	262	19	=	=	PUNCT
ejpam-5951	263	1	δ2nρ	δ2nρ	X
ejpam-5951	263	2	2(gλi	2(gλi	NOUN
ejpam-5951	263	3	(	(	PUNCT
ejpam-5951	263	4	ζn	ζn	NOUN
ejpam-5951	263	5	)	)	PUNCT
ejpam-5951	263	6	,	,	PUNCT
ejpam-5951	263	7	ζ	ζ	NOUN
ejpam-5951	263	8	∗	∗	NOUN
ejpam-5951	263	9	)	)	PUNCT
ejpam-5951	264	1	+	+	CCONJ
ejpam-5951	264	2	(	(	PUNCT
ejpam-5951	264	3	1−	1−	NUM
ejpam-5951	264	4	δ2n)ρ	δ2n)ρ	PRON
ejpam-5951	264	5	2(ζn	2(ζn	NOUN
ejpam-5951	264	6	,	,	PUNCT
ejpam-5951	264	7	ζ	ζ	NOUN
ejpam-5951	264	8	∗	∗	NOUN
ejpam-5951	264	9	)	)	PUNCT
ejpam-5951	264	10	+	+	CCONJ
ejpam-5951	264	11	2δn(1−	2δn(1−	NUM
ejpam-5951	264	12	δn)r	δn)r	PROPN
ejpam-5951	264	13	(	(	PUNCT
ejpam-5951	264	14	exp−1	exp−1	PROPN
ejpam-5951	264	15	ζ∗	ζ∗	PROPN
ejpam-5951	264	16	gλi	gλi	NOUN
ejpam-5951	264	17	(	(	PUNCT
ejpam-5951	264	18	ζ∗	ζ∗	PROPN
ejpam-5951	264	19	)	)	PUNCT
ejpam-5951	264	20	,	,	PUNCT
ejpam-5951	264	21	exp−1	exp−1	PROPN
ejpam-5951	264	22	ζ∗	ζ∗	PROPN
ejpam-5951	264	23	hλi	hλi	NOUN
ejpam-5951	264	24	(	(	PUNCT
ejpam-5951	264	25	ζn	ζn	NOUN
ejpam-5951	264	26	)	)	PUNCT
ejpam-5951	264	27	)	)	PUNCT
ejpam-5951	264	28	=	=	PUNCT
ejpam-5951	265	1	δ2nρ	δ2nρ	X
ejpam-5951	265	2	2(gλi	2(gλi	NOUN
ejpam-5951	265	3	(	(	PUNCT
ejpam-5951	265	4	ζn	ζn	NOUN
ejpam-5951	265	5	)	)	PUNCT
ejpam-5951	265	6	,	,	PUNCT
ejpam-5951	265	7	ζ	ζ	NOUN
ejpam-5951	265	8	∗	∗	NOUN
ejpam-5951	265	9	)	)	PUNCT
ejpam-5951	265	10	+	+	SYM
ejpam-5951	266	1	ρ2(ζn	ρ2(ζn	NOUN
ejpam-5951	266	2	,	,	PUNCT
ejpam-5951	266	3	ζ	ζ	NOUN
ejpam-5951	266	4	∗	∗	NOUN
ejpam-5951	266	5	)	)	PUNCT
ejpam-5951	267	1	+	+	CCONJ
ejpam-5951	267	2	2δn(1−	2δn(1−	NUM
ejpam-5951	267	3	δn)r	δn)r	PROPN
ejpam-5951	267	4	(	(	PUNCT
ejpam-5951	267	5	exp−1	exp−1	PROPN
ejpam-5951	267	6	ζ∗	ζ∗	PROPN
ejpam-5951	267	7	gλi	gλi	NOUN
ejpam-5951	267	8	(	(	PUNCT
ejpam-5951	267	9	ζ∗	ζ∗	PROPN
ejpam-5951	267	10	)	)	PUNCT
ejpam-5951	267	11	,	,	PUNCT
ejpam-5951	267	12	exp−1	exp−1	PROPN
ejpam-5951	267	13	ζ∗	ζ∗	PROPN
ejpam-5951	267	14	hλi	hλi	NOUN
ejpam-5951	267	15	(	(	PUNCT
ejpam-5951	267	16	ζn	ζn	NOUN
ejpam-5951	267	17	)	)	PUNCT
ejpam-5951	267	18	)	)	PUNCT
ejpam-5951	267	19	,	,	PUNCT
ejpam-5951	267	20	and	and	CCONJ
ejpam-5951	267	21	we	we	PRON
ejpam-5951	267	22	get	get	VERB
ejpam-5951	267	23	0	0	NUM
ejpam-5951	267	24	≤	≤	NOUN
ejpam-5951	267	25	δ2nρ	δ2nρ	PUNCT
ejpam-5951	267	26	2(gλi	2(gλi	NOUN
ejpam-5951	267	27	,	,	PUNCT
ejpam-5951	267	28	ζ∗	ζ∗	PROPN
ejpam-5951	267	29	)	)	PUNCT
ejpam-5951	267	30	+	+	PUNCT
ejpam-5951	268	1	ρ2(ζn	ρ2(ζn	NOUN
ejpam-5951	268	2	,	,	PUNCT
ejpam-5951	268	3	ζ	ζ	NOUN
ejpam-5951	268	4	∗)−	∗)−	ADJ
ejpam-5951	268	5	ρ2(ϑn	ρ2(ϑn	NUM
ejpam-5951	268	6	,	,	PUNCT
ejpam-5951	268	7	ζ	ζ	NOUN
ejpam-5951	268	8	∗	∗	NOUN
ejpam-5951	268	9	)	)	PUNCT
ejpam-5951	268	10	+	+	CCONJ
ejpam-5951	268	11	2δn(1−	2δn(1−	NUM
ejpam-5951	268	12	δn)r	δn)r	PROPN
ejpam-5951	268	13	(	(	PUNCT
ejpam-5951	268	14	exp−1	exp−1	PROPN
ejpam-5951	268	15	ζ∗	ζ∗	PROPN
ejpam-5951	268	16	gλi	gλi	NOUN
ejpam-5951	268	17	(	(	PUNCT
ejpam-5951	268	18	ζ∗	ζ∗	PROPN
ejpam-5951	268	19	)	)	PUNCT
ejpam-5951	268	20	,	,	PUNCT
ejpam-5951	268	21	exp−1	exp−1	PROPN
ejpam-5951	268	22	ζ∗	ζ∗	PROPN
ejpam-5951	268	23	hλi	hλi	NOUN
ejpam-5951	268	24	(	(	PUNCT
ejpam-5951	268	25	ζn	ζn	NOUN
ejpam-5951	268	26	)	)	PUNCT
ejpam-5951	268	27	)	)	PUNCT
ejpam-5951	268	28	≤	≤	NOUN
ejpam-5951	268	29	δ2nρ	δ2nρ	PUNCT
ejpam-5951	268	30	2(gλi	2(gλi	NOUN
ejpam-5951	268	31	(	(	PUNCT
ejpam-5951	268	32	ζn	ζn	NOUN
ejpam-5951	268	33	)	)	PUNCT
ejpam-5951	268	34	,	,	PUNCT
ejpam-5951	268	35	ζ	ζ	NOUN
ejpam-5951	268	36	∗	∗	NOUN
ejpam-5951	268	37	)	)	PUNCT
ejpam-5951	268	38	+	+	NUM
ejpam-5951	268	39	c2ρ(ζn	c2ρ(ζn	NOUN
ejpam-5951	268	40	,	,	PUNCT
ejpam-5951	268	41	ϑn	ϑn	NOUN
ejpam-5951	268	42	)	)	PUNCT
ejpam-5951	268	43	+	+	CCONJ
ejpam-5951	268	44	2δn(1−	2δn(1−	NUM
ejpam-5951	268	45	δn)r	δn)r	PROPN
ejpam-5951	268	46	(	(	PUNCT
ejpam-5951	268	47	exp−1	exp−1	PROPN
ejpam-5951	268	48	ζ∗	ζ∗	PROPN
ejpam-5951	268	49	gλi	gλi	NOUN
ejpam-5951	268	50	(	(	PUNCT
ejpam-5951	268	51	ζ∗	ζ∗	PROPN
ejpam-5951	268	52	)	)	PUNCT
ejpam-5951	268	53	,	,	PUNCT
ejpam-5951	268	54	exp−1	exp−1	PROPN
ejpam-5951	268	55	ζ∗	ζ∗	PROPN
ejpam-5951	268	56	hλi	hλi	NOUN
ejpam-5951	268	57	(	(	PUNCT
ejpam-5951	268	58	ζn	ζn	NOUN
ejpam-5951	268	59	)	)	PUNCT
ejpam-5951	268	60	)	)	PUNCT
ejpam-5951	268	61	.	.	PUNCT
ejpam-5951	269	1	here	here	ADV
ejpam-5951	269	2	c2	c2	PROPN
ejpam-5951	269	3	=	=	PUNCT
ejpam-5951	269	4	sup	sup	NOUN
ejpam-5951	269	5	n≥1	n≥1	NOUN
ejpam-5951	269	6	{	{	PUNCT
ejpam-5951	269	7	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	269	8	,	,	PUNCT
ejpam-5951	269	9	ζ∗)+ρ(ϑn	ζ∗)+ρ(ϑn	PROPN
ejpam-5951	269	10	,	,	PUNCT
ejpam-5951	269	11	ζ	ζ	NOUN
ejpam-5951	269	12	∗	∗	NOUN
ejpam-5951	269	13	)	)	PUNCT
ejpam-5951	269	14	}	}	PUNCT
ejpam-5951	269	15	.	.	PUNCT
ejpam-5951	270	1	since	since	SCONJ
ejpam-5951	270	2	0	0	NUM
ejpam-5951	270	3	<	<	X
ejpam-5951	270	4	δ1	δ1	NOUN
ejpam-5951	270	5	≤	≤	NUM
ejpam-5951	270	6	δn	δn	NOUN
ejpam-5951	270	7	≤	≤	X
ejpam-5951	270	8	δ2	δ2	VERB
ejpam-5951	270	9	<	<	X
ejpam-5951	270	10	1	1	NUM
ejpam-5951	270	11	we	we	PRON
ejpam-5951	270	12	can	can	AUX
ejpam-5951	270	13	have	have	VERB
ejpam-5951	270	14	1	1	NUM
ejpam-5951	270	15	δn	δn	NOUN
ejpam-5951	270	16	≤	≤	NUM
ejpam-5951	270	17	1	1	NUM
ejpam-5951	270	18	δ1	δ1	NOUN
ejpam-5951	270	19	.	.	PUNCT
ejpam-5951	271	1	therefore	therefore	ADV
ejpam-5951	271	2	above	above	ADP
ejpam-5951	271	3	equation	equation	NOUN
ejpam-5951	271	4	becomes	become	VERB
ejpam-5951	271	5	0	0	NUM
ejpam-5951	271	6	≤	≤	NUM
ejpam-5951	271	7	δn	δn	NOUN
ejpam-5951	271	8	2	2	NUM
ejpam-5951	271	9	ρ2(gλi	ρ2(gλi	NOUN
ejpam-5951	271	10	(	(	PUNCT
ejpam-5951	271	11	ζn	ζn	NOUN
ejpam-5951	271	12	)	)	PUNCT
ejpam-5951	271	13	,	,	PUNCT
ejpam-5951	271	14	ζ	ζ	NOUN
ejpam-5951	271	15	∗	∗	NOUN
ejpam-5951	271	16	)	)	PUNCT
ejpam-5951	272	1	+	+	CCONJ
ejpam-5951	272	2	c2	c2	PROPN
ejpam-5951	272	3	2δn	2δn	NOUN
ejpam-5951	272	4	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	272	5	,	,	PUNCT
ejpam-5951	272	6	ϑn	ϑn	NOUN
ejpam-5951	272	7	)	)	PUNCT
ejpam-5951	273	1	+	+	CCONJ
ejpam-5951	273	2	(	(	PUNCT
ejpam-5951	273	3	1−	1−	NUM
ejpam-5951	273	4	δn)r	δn)r	PROPN
ejpam-5951	273	5	(	(	PUNCT
ejpam-5951	273	6	exp−1	exp−1	PROPN
ejpam-5951	273	7	ζ∗	ζ∗	PROPN
ejpam-5951	273	8	gλi	gλi	NOUN
ejpam-5951	273	9	(	(	PUNCT
ejpam-5951	273	10	ζ∗	ζ∗	PROPN
ejpam-5951	273	11	)	)	PUNCT
ejpam-5951	273	12	,	,	PUNCT
ejpam-5951	273	13	exp−1	exp−1	PROPN
ejpam-5951	273	14	ζ∗	ζ∗	PROPN
ejpam-5951	273	15	hλi	hλi	NOUN
ejpam-5951	273	16	(	(	PUNCT
ejpam-5951	273	17	ζn	ζn	NOUN
ejpam-5951	273	18	)	)	PUNCT
ejpam-5951	273	19	)	)	PUNCT
ejpam-5951	273	20	≤	≤	NUM
ejpam-5951	273	21	δn	δn	NOUN
ejpam-5951	273	22	2	2	NUM
ejpam-5951	273	23	ρ2(gλi	ρ2(gλi	NOUN
ejpam-5951	273	24	(	(	PUNCT
ejpam-5951	273	25	ζn	ζn	NOUN
ejpam-5951	273	26	)	)	PUNCT
ejpam-5951	273	27	,	,	PUNCT
ejpam-5951	273	28	ζ	ζ	NOUN
ejpam-5951	273	29	∗	∗	NOUN
ejpam-5951	273	30	)	)	PUNCT
ejpam-5951	273	31	+	+	CCONJ
ejpam-5951	274	1	c2	c2	PROPN
ejpam-5951	274	2	2δ1	2δ1	NUM
ejpam-5951	274	3	ρ(ζn	ρ(ζn	NOUN
ejpam-5951	274	4	,	,	PUNCT
ejpam-5951	274	5	ϑn	ϑn	NOUN
ejpam-5951	274	6	)	)	PUNCT
ejpam-5951	275	1	+	+	CCONJ
ejpam-5951	275	2	(	(	PUNCT
ejpam-5951	275	3	1−	1−	NUM
ejpam-5951	275	4	δn)r	δn)r	PROPN
ejpam-5951	275	5	(	(	PUNCT
ejpam-5951	275	6	exp−1	exp−1	PROPN
ejpam-5951	275	7	ζ∗	ζ∗	PROPN
ejpam-5951	275	8	gλi	gλi	NOUN
ejpam-5951	275	9	(	(	PUNCT
ejpam-5951	275	10	ζ∗	ζ∗	PROPN
ejpam-5951	275	11	)	)	PUNCT
ejpam-5951	275	12	,	,	PUNCT
ejpam-5951	275	13	exp−1	exp−1	PROPN
ejpam-5951	275	14	ζ∗	ζ∗	PROPN
ejpam-5951	275	15	hλi	hλi	NOUN
ejpam-5951	275	16	(	(	PUNCT
ejpam-5951	275	17	ζn	ζn	NOUN
ejpam-5951	275	18	)	)	PUNCT
ejpam-5951	275	19	)	)	PUNCT
ejpam-5951	275	20	since	since	SCONJ
ejpam-5951	275	21	ζ	ζ	NOUN
ejpam-5951	275	22	∈	∈	PROPN
ejpam-5951	276	1	⋂	⋂	PROPN
ejpam-5951	277	1	i	i	PRON
ejpam-5951	277	2	f	f	PROPN
ejpam-5951	277	3	(	(	PUNCT
ejpam-5951	277	4	hλi	hλi	NOUN
ejpam-5951	277	5	)	)	PUNCT
ejpam-5951	277	6	,	,	PUNCT
ejpam-5951	277	7	lim	lim	PROPN
ejpam-5951	277	8	n→+∞	n→+∞	VERB
ejpam-5951	277	9	ζn	ζn	NOUN
ejpam-5951	277	10	=	=	SYM
ejpam-5951	277	11	ζ	ζ	PROPN
ejpam-5951	277	12	and	and	CCONJ
ejpam-5951	277	13	lim	lim	PROPN
ejpam-5951	277	14	n→+∞	n→+∞	VERB
ejpam-5951	277	15	δn	δn	NOUN
ejpam-5951	277	16	=	=	SYM
ejpam-5951	277	17	0	0	NUM
ejpam-5951	277	18	,	,	PUNCT
ejpam-5951	277	19	and	and	CCONJ
ejpam-5951	277	20	using	use	VERB
ejpam-5951	277	21	(	(	PUNCT
ejpam-5951	277	22	14	14	NUM
ejpam-5951	277	23	)	)	PUNCT
ejpam-5951	277	24	,	,	PUNCT
ejpam-5951	277	25	we	we	PRON
ejpam-5951	277	26	get	get	VERB
ejpam-5951	277	27	r	r	NOUN
ejpam-5951	277	28	(	(	PUNCT
ejpam-5951	277	29	exp−1	exp−1	PROPN
ejpam-5951	277	30	ζ∗	ζ∗	PROPN
ejpam-5951	277	31	gλi	gλi	NOUN
ejpam-5951	277	32	(	(	PUNCT
ejpam-5951	277	33	ζ∗),−	ζ∗),−	VERB
ejpam-5951	277	34	exp−1	exp−1	PROPN
ejpam-5951	277	35	ζ∗	ζ∗	ADJ
ejpam-5951	277	36	ζ	ζ	NOUN
ejpam-5951	277	37	)	)	PUNCT
ejpam-5951	277	38	≤	≤	NOUN
ejpam-5951	277	39	0	0	NUM
ejpam-5951	277	40	,	,	PUNCT
ejpam-5951	278	1	i.e.	i.e.	X
ejpam-5951	278	2	r	r	NOUN
ejpam-5951	279	1	(	(	PUNCT
ejpam-5951	279	2	exp−1	exp−1	PROPN
ejpam-5951	279	3	ζ∗	ζ∗	PROPN
ejpam-5951	279	4	gλi	gλi	NOUN
ejpam-5951	279	5	(	(	PUNCT
ejpam-5951	279	6	ζ∗	ζ∗	PROPN
ejpam-5951	279	7	)	)	PUNCT
ejpam-5951	279	8	,	,	PUNCT
ejpam-5951	279	9	pζ∗,ζ	pζ∗,ζ	X
ejpam-5951	279	10	exp	exp	NOUN
ejpam-5951	279	11	−1	−1	NOUN
ejpam-5951	279	12	ζ	ζ	NOUN
ejpam-5951	279	13	ζ∗	ζ∗	PROPN
ejpam-5951	279	14	)	)	PUNCT
ejpam-5951	279	15	≤	≤	NOUN
ejpam-5951	279	16	0	0	NUM
ejpam-5951	279	17	,	,	PUNCT
ejpam-5951	279	18	for	for	ADP
ejpam-5951	279	19	all	all	DET
ejpam-5951	279	20	ζ∗	ζ∗	PROPN
ejpam-5951	279	21	∈	∈	PROPN
ejpam-5951	279	22	⋂	⋂	PROPN
ejpam-5951	280	1	i	i	PRON
ejpam-5951	280	2	f	f	PROPN
ejpam-5951	280	3	(	(	PUNCT
ejpam-5951	280	4	hλi	hλi	NOUN
ejpam-5951	280	5	)	)	PUNCT
ejpam-5951	280	6	.	.	PUNCT
ejpam-5951	281	1	(	(	PUNCT
ejpam-5951	281	2	21	21	NUM
ejpam-5951	281	3	)	)	PUNCT
ejpam-5951	281	4	since	since	SCONJ
ejpam-5951	281	5	ζ	ζ	NOUN
ejpam-5951	281	6	∈	∈	PROPN
ejpam-5951	282	1	⋂	⋂	PROPN
ejpam-5951	283	1	i	i	PRON
ejpam-5951	283	2	f	f	PROPN
ejpam-5951	283	3	(	(	PUNCT
ejpam-5951	283	4	hλi	hλi	NOUN
ejpam-5951	283	5	)	)	PUNCT
ejpam-5951	283	6	,	,	PUNCT
ejpam-5951	283	7	⋂	⋂	PROPN
ejpam-5951	283	8	i	i	PRON
ejpam-5951	283	9	f	f	PROPN
ejpam-5951	283	10	(	(	PUNCT
ejpam-5951	283	11	hλi	hλi	NOUN
ejpam-5951	283	12	)	)	PUNCT
ejpam-5951	283	13	is	be	AUX
ejpam-5951	283	14	geodesic	geodesic	ADJ
ejpam-5951	283	15	convex	convex	NOUN
ejpam-5951	283	16	,	,	PUNCT
ejpam-5951	283	17	we	we	PRON
ejpam-5951	283	18	get	get	VERB
ejpam-5951	283	19	expζ	expζ	PROPN
ejpam-5951	283	20	t	t	PROPN
ejpam-5951	283	21	exp	exp	NOUN
ejpam-5951	283	22	−1	−1	NOUN
ejpam-5951	283	23	ζ	ζ	PROPN
ejpam-5951	283	24	µ	µ	X
ejpam-5951	283	25	∈	∈	NOUN
ejpam-5951	284	1	⋂	⋂	PROPN
ejpam-5951	285	1	i	i	PRON
ejpam-5951	285	2	f	f	PROPN
ejpam-5951	285	3	(	(	PUNCT
ejpam-5951	285	4	hλi	hλi	NOUN
ejpam-5951	285	5	)	)	PUNCT
ejpam-5951	285	6	for	for	ADP
ejpam-5951	285	7	any	any	DET
ejpam-5951	285	8	µ	µ	PROPN
ejpam-5951	285	9	∈	∈	NOUN
ejpam-5951	285	10	⋂	⋂	PROPN
ejpam-5951	286	1	i	i	PRON
ejpam-5951	286	2	f	f	PROPN
ejpam-5951	286	3	(	(	PUNCT
ejpam-5951	286	4	hλi	hλi	NOUN
ejpam-5951	286	5	)	)	PUNCT
ejpam-5951	286	6	and	and	CCONJ
ejpam-5951	286	7	t	t	PROPN
ejpam-5951	286	8	∈	∈	PROPN
ejpam-5951	286	9	(	(	PUNCT
ejpam-5951	286	10	0	0	NUM
ejpam-5951	286	11	,	,	PUNCT
ejpam-5951	286	12	1	1	NUM
ejpam-5951	286	13	)	)	PUNCT
ejpam-5951	286	14	.	.	PUNCT
ejpam-5951	287	1	replacing	replace	VERB
ejpam-5951	287	2	ζ∗	ζ∗	PROPN
ejpam-5951	287	3	by	by	ADP
ejpam-5951	287	4	ut	ut	PROPN
ejpam-5951	287	5	=	=	PROPN
ejpam-5951	287	6	expζ	expζ	PROPN
ejpam-5951	287	7	t	t	PROPN
ejpam-5951	287	8	exp	exp	NOUN
ejpam-5951	287	9	−1	−1	NOUN
ejpam-5951	287	10	ζ	ζ	PROPN
ejpam-5951	287	11	µ	µ	X
ejpam-5951	287	12	∈	∈	NOUN
ejpam-5951	288	1	⋂	⋂	PROPN
ejpam-5951	289	1	i	i	PRON
ejpam-5951	289	2	f	f	PROPN
ejpam-5951	289	3	(	(	PUNCT
ejpam-5951	289	4	hλi	hλi	NOUN
ejpam-5951	289	5	)	)	PUNCT
ejpam-5951	289	6	where	where	SCONJ
ejpam-5951	289	7	µ	µ	X
ejpam-5951	289	8	∈	∈	PROPN
ejpam-5951	289	9	⋂	⋂	PROPN
ejpam-5951	290	1	i	i	PRON
ejpam-5951	290	2	f	f	PROPN
ejpam-5951	290	3	(	(	PUNCT
ejpam-5951	290	4	hλi	hλi	NOUN
ejpam-5951	290	5	)	)	PUNCT
ejpam-5951	290	6	and	and	CCONJ
ejpam-5951	290	7	t	t	PROPN
ejpam-5951	290	8	∈	∈	PROPN
ejpam-5951	290	9	(	(	PUNCT
ejpam-5951	290	10	0	0	NUM
ejpam-5951	290	11	,	,	PUNCT
ejpam-5951	290	12	1	1	NUM
ejpam-5951	290	13	)	)	PUNCT
ejpam-5951	290	14	,	,	PUNCT
ejpam-5951	290	15	in	in	ADP
ejpam-5951	290	16	the	the	DET
ejpam-5951	290	17	equation	equation	NOUN
ejpam-5951	290	18	(	(	PUNCT
ejpam-5951	290	19	21	21	NUM
ejpam-5951	290	20	)	)	PUNCT
ejpam-5951	290	21	,	,	PUNCT
ejpam-5951	290	22	we	we	PRON
ejpam-5951	290	23	get	get	VERB
ejpam-5951	290	24	r	r	NOUN
ejpam-5951	290	25	(	(	PUNCT
ejpam-5951	290	26	exp−1	exp−1	PROPN
ejpam-5951	290	27	expζ	expζ	PROPN
ejpam-5951	290	28	t	t	PROPN
ejpam-5951	290	29	exp	exp	NOUN
ejpam-5951	290	30	−1	−1	NOUN
ejpam-5951	290	31	ζ	ζ	PROPN
ejpam-5951	290	32	µ	µ	X
ejpam-5951	290	33	gλi	gλi	NOUN
ejpam-5951	290	34	(	(	PUNCT
ejpam-5951	290	35	expζ	expζ	PROPN
ejpam-5951	290	36	t	t	PROPN
ejpam-5951	290	37	exp	exp	NOUN
ejpam-5951	290	38	−1	−1	NOUN
ejpam-5951	290	39	ζ	ζ	PROPN
ejpam-5951	290	40	µ	µ	NOUN
ejpam-5951	290	41	)	)	PUNCT
ejpam-5951	290	42	,	,	PUNCT
ejpam-5951	290	43	put	put	VERB
ejpam-5951	290	44	,	,	PUNCT
ejpam-5951	290	45	ζ	ζ	NOUN
ejpam-5951	290	46	exp	exp	NOUN
ejpam-5951	290	47	−1	−1	NOUN
ejpam-5951	290	48	ζ	ζ	NOUN
ejpam-5951	290	49	expζ	expζ	NOUN
ejpam-5951	290	50	t	t	PROPN
ejpam-5951	290	51	exp	exp	NOUN
ejpam-5951	290	52	−1	−1	NOUN
ejpam-5951	290	53	ζ	ζ	PROPN
ejpam-5951	290	54	µ	µ	X
ejpam-5951	290	55	)	)	PUNCT
ejpam-5951	290	56	≤	≤	NOUN
ejpam-5951	290	57	0	0	NUM
ejpam-5951	290	58	,	,	PUNCT
ejpam-5951	290	59	p.	p.	NOUN
ejpam-5951	290	60	patel	patel	PROPN
ejpam-5951	290	61	,	,	PUNCT
ejpam-5951	290	62	r.	r.	PROPN
ejpam-5951	290	63	shukla	shukla	PROPN
ejpam-5951	290	64	/	/	SYM
ejpam-5951	290	65	eur	eur	PROPN
ejpam-5951	290	66	.	.	PUNCT
ejpam-5951	291	1	j.	j.	PROPN
ejpam-5951	291	2	pure	pure	PROPN
ejpam-5951	291	3	appl	appl	PROPN
ejpam-5951	291	4	.	.	PROPN
ejpam-5951	291	5	math	math	PROPN
ejpam-5951	291	6	,	,	PUNCT
ejpam-5951	291	7	18	18	NUM
ejpam-5951	291	8	(	(	PUNCT
ejpam-5951	291	9	2	2	NUM
ejpam-5951	291	10	)	)	PUNCT
ejpam-5951	291	11	(	(	PUNCT
ejpam-5951	291	12	2025	2025	NUM
ejpam-5951	291	13	)	)	PUNCT
ejpam-5951	291	14	,	,	PUNCT
ejpam-5951	291	15	5951	5951	NUM
ejpam-5951	291	16	12	12	NUM
ejpam-5951	291	17	of	of	ADP
ejpam-5951	291	18	15	15	NUM
ejpam-5951	291	19	which	which	PRON
ejpam-5951	291	20	gives	give	VERB
ejpam-5951	291	21	us	we	PRON
ejpam-5951	291	22	r	r	NOUN
ejpam-5951	291	23	(	(	PUNCT
ejpam-5951	291	24	exp−1	exp−1	PROPN
ejpam-5951	291	25	expζ	expζ	PROPN
ejpam-5951	291	26	t	t	PROPN
ejpam-5951	291	27	exp	exp	NOUN
ejpam-5951	291	28	−1	−1	NOUN
ejpam-5951	291	29	ζ	ζ	PROPN
ejpam-5951	291	30	µ	µ	X
ejpam-5951	291	31	gλi	gλi	NOUN
ejpam-5951	291	32	(	(	PUNCT
ejpam-5951	291	33	expζ	expζ	PROPN
ejpam-5951	291	34	t	t	PROPN
ejpam-5951	291	35	exp	exp	NOUN
ejpam-5951	291	36	−1	−1	NOUN
ejpam-5951	291	37	ζ	ζ	PROPN
ejpam-5951	291	38	µ	µ	NOUN
ejpam-5951	291	39	)	)	PUNCT
ejpam-5951	291	40	,	,	PUNCT
ejpam-5951	291	41	put	put	VERB
ejpam-5951	291	42	,	,	PUNCT
ejpam-5951	291	43	ζt	ζt	PROPN
ejpam-5951	291	44	exp	exp	NOUN
ejpam-5951	291	45	−1	−1	NOUN
ejpam-5951	291	46	ζ	ζ	PROPN
ejpam-5951	291	47	µ	µ	X
ejpam-5951	291	48	)	)	PUNCT
ejpam-5951	291	49	≤	≤	NOUN
ejpam-5951	291	50	0	0	NUM
ejpam-5951	291	51	.	.	PUNCT
ejpam-5951	292	1	since	since	SCONJ
ejpam-5951	292	2	the	the	DET
ejpam-5951	292	3	map	map	NOUN
ejpam-5951	292	4	p	p	NOUN
ejpam-5951	292	5	is	be	AUX
ejpam-5951	292	6	linear	linear	ADJ
ejpam-5951	292	7	,	,	PUNCT
ejpam-5951	292	8	we	we	PRON
ejpam-5951	292	9	get	get	VERB
ejpam-5951	292	10	r	r	NOUN
ejpam-5951	292	11	(	(	PUNCT
ejpam-5951	292	12	exp−1	exp−1	PROPN
ejpam-5951	292	13	expζ	expζ	PROPN
ejpam-5951	292	14	t	t	PROPN
ejpam-5951	292	15	exp	exp	NOUN
ejpam-5951	292	16	−1	−1	NOUN
ejpam-5951	292	17	ζ	ζ	PROPN
ejpam-5951	292	18	µ	µ	X
ejpam-5951	292	19	gλi	gλi	NOUN
ejpam-5951	292	20	(	(	PUNCT
ejpam-5951	292	21	expζ	expζ	PROPN
ejpam-5951	292	22	t	t	PROPN
ejpam-5951	292	23	exp	exp	NOUN
ejpam-5951	292	24	−1	−1	NOUN
ejpam-5951	292	25	ζ	ζ	PROPN
ejpam-5951	292	26	µ	µ	NOUN
ejpam-5951	292	27	)	)	PUNCT
ejpam-5951	292	28	,	,	PUNCT
ejpam-5951	292	29	put	put	VERB
ejpam-5951	292	30	,	,	PUNCT
ejpam-5951	292	31	ζ	ζ	NOUN
ejpam-5951	292	32	exp	exp	NOUN
ejpam-5951	292	33	−1	−1	NOUN
ejpam-5951	292	34	ζ	ζ	PROPN
ejpam-5951	292	35	µ	µ	X
ejpam-5951	292	36	)	)	PUNCT
ejpam-5951	292	37	≤	≤	NUM
ejpam-5951	292	38	0	0	NUM
ejpam-5951	292	39	.	.	PUNCT
ejpam-5951	293	1	applying	apply	VERB
ejpam-5951	293	2	t	t	PROPN
ejpam-5951	293	3	→	→	SYM
ejpam-5951	293	4	0	0	NUM
ejpam-5951	293	5	then	then	ADV
ejpam-5951	293	6	ut	ut	PROPN
ejpam-5951	293	7	→	→	SYM
ejpam-5951	293	8	ζ	ζ	X
ejpam-5951	293	9	.	.	PUNCT
ejpam-5951	294	1	since	since	SCONJ
ejpam-5951	294	2	expζ	expζ	NOUN
ejpam-5951	294	3	0	0	NUM
ejpam-5951	294	4	=	=	SYM
ejpam-5951	294	5	ζ	ζ	NOUN
ejpam-5951	294	6	for	for	ADP
ejpam-5951	294	7	all	all	DET
ejpam-5951	294	8	ζ	ζ	PROPN
ejpam-5951	294	9	∈	∈	PROPN
ejpam-5951	294	10	γ	γ	X
ejpam-5951	294	11	,	,	PUNCT
ejpam-5951	294	12	we	we	PRON
ejpam-5951	294	13	get	get	VERB
ejpam-5951	294	14	r	r	NOUN
ejpam-5951	294	15	(	(	PUNCT
ejpam-5951	294	16	exp−1	exp−1	PROPN
ejpam-5951	294	17	ζ	ζ	PROPN
ejpam-5951	294	18	gλi	gλi	NOUN
ejpam-5951	294	19	(	(	PUNCT
ejpam-5951	294	20	ζ	ζ	NOUN
ejpam-5951	294	21	)	)	PUNCT
ejpam-5951	294	22	,	,	PUNCT
ejpam-5951	294	23	pζ	pζ	PROPN
ejpam-5951	294	24	,	,	PUNCT
ejpam-5951	294	25	ζ	ζ	PROPN
ejpam-5951	294	26	exp	exp	NOUN
ejpam-5951	294	27	−1	−1	NOUN
ejpam-5951	294	28	ζ	ζ	PROPN
ejpam-5951	294	29	µ	µ	X
ejpam-5951	294	30	)	)	PUNCT
ejpam-5951	294	31	≤	≤	NUM
ejpam-5951	294	32	0	0	NUM
ejpam-5951	294	33	.	.	PUNCT
ejpam-5951	295	1	thus	thus	ADV
ejpam-5951	295	2	r	r	NOUN
ejpam-5951	295	3	(	(	PUNCT
ejpam-5951	295	4	exp−1	exp−1	PROPN
ejpam-5951	295	5	ζ	ζ	PROPN
ejpam-5951	295	6	gλi	gλi	NOUN
ejpam-5951	295	7	(	(	PUNCT
ejpam-5951	295	8	ζ	ζ	NOUN
ejpam-5951	295	9	)	)	PUNCT
ejpam-5951	295	10	,	,	PUNCT
ejpam-5951	295	11	exp−1	exp−1	PROPN
ejpam-5951	295	12	ζ	ζ	PROPN
ejpam-5951	295	13	µ	µ	X
ejpam-5951	295	14	)	)	PUNCT
ejpam-5951	295	15	≤	≤	NOUN
ejpam-5951	295	16	0	0	NUM
ejpam-5951	295	17	,	,	PUNCT
ejpam-5951	295	18	for	for	ADP
ejpam-5951	295	19	all	all	DET
ejpam-5951	295	20	µ	µ	PRON
ejpam-5951	295	21	∈	∈	NOUN
ejpam-5951	295	22	⋂	⋂	PROPN
ejpam-5951	296	1	i	i	PRON
ejpam-5951	296	2	f	f	PROPN
ejpam-5951	296	3	(	(	PUNCT
ejpam-5951	296	4	hλi	hλi	NOUN
ejpam-5951	296	5	)	)	PUNCT
ejpam-5951	296	6	.	.	PUNCT
ejpam-5951	297	1	(	(	PUNCT
ejpam-5951	297	2	22	22	NUM
ejpam-5951	297	3	)	)	PUNCT
ejpam-5951	297	4	hence	hence	ADV
ejpam-5951	297	5	,	,	PUNCT
ejpam-5951	297	6	ζ	ζ	PROPN
ejpam-5951	297	7	∈	∈	PROPN
ejpam-5951	297	8	φ	φ	NOUN
ejpam-5951	297	9	,	,	PUNCT
ejpam-5951	297	10	and	and	CCONJ
ejpam-5951	297	11	we	we	PRON
ejpam-5951	297	12	have	have	VERB
ejpam-5951	297	13	ζ	ζ	NOUN
ejpam-5951	297	14	∈	∈	PROPN
ejpam-5951	297	15	π	π	NOUN
ejpam-5951	297	16	.	.	PUNCT
ejpam-5951	298	1	now	now	ADV
ejpam-5951	298	2	finally	finally	ADV
ejpam-5951	298	3	we	we	PRON
ejpam-5951	298	4	prove	prove	VERB
ejpam-5951	298	5	that	that	SCONJ
ejpam-5951	298	6	the	the	DET
ejpam-5951	298	7	sequence	sequence	NOUN
ejpam-5951	298	8	{	{	PUNCT
ejpam-5951	298	9	ζn	ζn	NOUN
ejpam-5951	298	10	}	}	PUNCT
ejpam-5951	298	11	converges	converge	NOUN
ejpam-5951	298	12	to	to	ADP
ejpam-5951	298	13	ζ	ζ	NOUN
ejpam-5951	298	14	=	=	SYM
ejpam-5951	298	15	pπ(ζ1	pπ(ζ1	NOUN
ejpam-5951	298	16	)	)	PUNCT
ejpam-5951	298	17	.	.	PUNCT
ejpam-5951	299	1	from	from	ADP
ejpam-5951	299	2	ζn	ζn	PRON
ejpam-5951	299	3	=	=	SYM
ejpam-5951	299	4	pbn(ζ1	pbn(ζ1	PROPN
ejpam-5951	299	5	)	)	PUNCT
ejpam-5951	299	6	,	,	PUNCT
ejpam-5951	299	7	using	use	VERB
ejpam-5951	299	8	proposition	proposition	NOUN
ejpam-5951	299	9	2	2	NUM
ejpam-5951	299	10	(	(	PUNCT
ejpam-5951	299	11	1	1	NUM
ejpam-5951	299	12	)	)	PUNCT
ejpam-5951	299	13	,	,	PUNCT
ejpam-5951	299	14	we	we	PRON
ejpam-5951	299	15	get	get	VERB
ejpam-5951	299	16	r	r	NOUN
ejpam-5951	299	17	(	(	PUNCT
ejpam-5951	299	18	exp−1	exp−1	PROPN
ejpam-5951	299	19	ζn	ζn	DET
ejpam-5951	299	20	ζ1	ζ1	NOUN
ejpam-5951	299	21	,	,	PUNCT
ejpam-5951	299	22	exp	exp	NOUN
ejpam-5951	299	23	−1	−1	NOUN
ejpam-5951	299	24	ζn	ζn	ADP
ejpam-5951	299	25	ν	ν	NOUN
ejpam-5951	299	26	)	)	PUNCT
ejpam-5951	299	27	≤	≤	NOUN
ejpam-5951	299	28	0	0	NUM
ejpam-5951	299	29	,	,	PUNCT
ejpam-5951	299	30	for	for	ADP
ejpam-5951	299	31	all	all	PRON
ejpam-5951	299	32	ν	ν	X
ejpam-5951	299	33	∈	∈	PROPN
ejpam-5951	299	34	bn	bn	NOUN
ejpam-5951	299	35	.	.	PUNCT
ejpam-5951	300	1	using	use	VERB
ejpam-5951	300	2	the	the	DET
ejpam-5951	300	3	fact	fact	NOUN
ejpam-5951	300	4	that	that	SCONJ
ejpam-5951	300	5	π	π	PROPN
ejpam-5951	300	6	⊂	⊂	PROPN
ejpam-5951	300	7	bn	bn	PROPN
ejpam-5951	300	8	,	,	PUNCT
ejpam-5951	300	9	we	we	PRON
ejpam-5951	300	10	get	get	VERB
ejpam-5951	300	11	r	r	NOUN
ejpam-5951	300	12	(	(	PUNCT
ejpam-5951	300	13	exp−1	exp−1	PROPN
ejpam-5951	300	14	ζn	ζn	DET
ejpam-5951	300	15	ζ1	ζ1	NOUN
ejpam-5951	300	16	,	,	PUNCT
ejpam-5951	300	17	exp	exp	NOUN
ejpam-5951	300	18	−1	−1	NOUN
ejpam-5951	300	19	ζn	ζn	ADP
ejpam-5951	300	20	ν	ν	NOUN
ejpam-5951	300	21	)	)	PUNCT
ejpam-5951	300	22	≤	≤	NOUN
ejpam-5951	300	23	0	0	NUM
ejpam-5951	300	24	,	,	PUNCT
ejpam-5951	300	25	for	for	ADP
ejpam-5951	300	26	all	all	PRON
ejpam-5951	300	27	ν	ν	PRON
ejpam-5951	300	28	∈	∈	PROPN
ejpam-5951	300	29	π	π	PROPN
ejpam-5951	300	30	.	.	PUNCT
ejpam-5951	301	1	(	(	PUNCT
ejpam-5951	301	2	23	23	NUM
ejpam-5951	301	3	)	)	PUNCT
ejpam-5951	301	4	applying	apply	VERB
ejpam-5951	301	5	limit	limit	NOUN
ejpam-5951	301	6	n	n	X
ejpam-5951	301	7	→	→	SYM
ejpam-5951	301	8	+	+	NUM
ejpam-5951	301	9	∞	∞	PROPN
ejpam-5951	301	10	in	in	ADP
ejpam-5951	301	11	the	the	DET
ejpam-5951	301	12	above	above	ADJ
ejpam-5951	301	13	equation	equation	NOUN
ejpam-5951	301	14	,	,	PUNCT
ejpam-5951	301	15	we	we	PRON
ejpam-5951	301	16	get	get	VERB
ejpam-5951	301	17	r	r	NOUN
ejpam-5951	301	18	(	(	PUNCT
ejpam-5951	301	19	exp−1	exp−1	PROPN
ejpam-5951	301	20	ζ	ζ	PROPN
ejpam-5951	301	21	ζ1	ζ1	NOUN
ejpam-5951	301	22	,	,	PUNCT
ejpam-5951	301	23	exp	exp	NOUN
ejpam-5951	301	24	−1	−1	NOUN
ejpam-5951	301	25	ζ	ζ	NOUN
ejpam-5951	301	26	ν	ν	NOUN
ejpam-5951	301	27	)	)	PUNCT
ejpam-5951	301	28	≤	≤	NOUN
ejpam-5951	301	29	0	0	NUM
ejpam-5951	301	30	,	,	PUNCT
ejpam-5951	301	31	for	for	ADP
ejpam-5951	301	32	all	all	DET
ejpam-5951	301	33	ν	ν	PRON
ejpam-5951	301	34	∈	∈	PROPN
ejpam-5951	301	35	π	π	PROPN
ejpam-5951	301	36	,	,	PUNCT
ejpam-5951	301	37	i.e.	i.e.	X
ejpam-5951	301	38	lim	lim	PROPN
ejpam-5951	301	39	n→+∞	n→+∞	VERB
ejpam-5951	301	40	ζn	ζn	NOUN
ejpam-5951	301	41	=	=	SYM
ejpam-5951	301	42	ζ	ζ	NOUN
ejpam-5951	301	43	=	=	SYM
ejpam-5951	301	44	pπ(ζ1	pπ(ζ1	NOUN
ejpam-5951	301	45	)	)	PUNCT
ejpam-5951	301	46	.	.	PUNCT
ejpam-5951	302	1	thus	thus	ADV
ejpam-5951	302	2	the	the	DET
ejpam-5951	302	3	proof	proof	NOUN
ejpam-5951	302	4	is	be	AUX
ejpam-5951	302	5	complete	complete	ADJ
ejpam-5951	302	6	.	.	PUNCT
ejpam-5951	303	1	4	4	X
ejpam-5951	303	2	.	.	X
ejpam-5951	303	3	examples	example	NOUN
ejpam-5951	303	4	in	in	ADP
ejpam-5951	303	5	this	this	DET
ejpam-5951	303	6	section	section	NOUN
ejpam-5951	303	7	,	,	PUNCT
ejpam-5951	303	8	we	we	PRON
ejpam-5951	303	9	present	present	VERB
ejpam-5951	303	10	a	a	DET
ejpam-5951	303	11	couple	couple	NOUN
ejpam-5951	303	12	of	of	ADP
ejpam-5951	303	13	examples	example	NOUN
ejpam-5951	303	14	which	which	PRON
ejpam-5951	303	15	are	be	AUX
ejpam-5951	303	16	not	not	PART
ejpam-5951	303	17	nonexpansive	nonexpansive	ADJ
ejpam-5951	303	18	but	but	CCONJ
ejpam-5951	303	19	does	do	AUX
ejpam-5951	303	20	satisfy	satisfy	VERB
ejpam-5951	303	21	strict	strict	ADJ
ejpam-5951	303	22	pseudo	pseudo	NOUN
ejpam-5951	303	23	-	-	NOUN
ejpam-5951	303	24	contraction	contraction	NOUN
ejpam-5951	303	25	.	.	PUNCT
ejpam-5951	304	1	later	later	ADV
ejpam-5951	304	2	,	,	PUNCT
ejpam-5951	304	3	we	we	PRON
ejpam-5951	304	4	also	also	ADV
ejpam-5951	304	5	present	present	VERB
ejpam-5951	304	6	a	a	DET
ejpam-5951	304	7	nontrivial	nontrivial	ADJ
ejpam-5951	304	8	example	example	NOUN
ejpam-5951	304	9	which	which	PRON
ejpam-5951	304	10	illustrates	illustrate	VERB
ejpam-5951	304	11	the	the	DET
ejpam-5951	304	12	theorem	theorem	NOUN
ejpam-5951	304	13	2	2	NUM
ejpam-5951	304	14	.	.	NOUN
ejpam-5951	304	15	example	example	NOUN
ejpam-5951	304	16	1	1	NUM
ejpam-5951	304	17	.	.	PUNCT
ejpam-5951	305	1	[	[	X
ejpam-5951	305	2	24	24	NUM
ejpam-5951	305	3	]	]	PUNCT
ejpam-5951	305	4	let	let	VERB
ejpam-5951	305	5	γ	γ	X
ejpam-5951	305	6	=	=	SYM
ejpam-5951	305	7	r	r	NOUN
ejpam-5951	305	8	and	and	CCONJ
ejpam-5951	305	9	g	g	NOUN
ejpam-5951	305	10	:	:	PUNCT
ejpam-5951	305	11	r	r	NOUN
ejpam-5951	305	12	→	→	SYM
ejpam-5951	305	13	r	r	NOUN
ejpam-5951	305	14	be	be	AUX
ejpam-5951	305	15	a	a	DET
ejpam-5951	305	16	mapping	mapping	NOUN
ejpam-5951	305	17	defined	define	VERB
ejpam-5951	305	18	as	as	ADP
ejpam-5951	305	19	g(ζ	g(ζ	PROPN
ejpam-5951	305	20	)	)	PUNCT
ejpam-5951	306	1	=	=	SYM
ejpam-5951	306	2	−	−	PROPN
ejpam-5951	306	3	(	(	PUNCT
ejpam-5951	306	4	tan−1(ζ	tan−1(ζ	NOUN
ejpam-5951	306	5	)	)	PUNCT
ejpam-5951	306	6	+	+	SYM
ejpam-5951	306	7	sin(ζ	sin(ζ	NOUN
ejpam-5951	306	8	)	)	PUNCT
ejpam-5951	306	9	+	+	CCONJ
ejpam-5951	306	10	cos(ζ	cos(ζ	SYM
ejpam-5951	306	11	)	)	PUNCT
ejpam-5951	306	12	4	4	NUM
ejpam-5951	306	13	)	)	PUNCT
ejpam-5951	306	14	,	,	PUNCT
ejpam-5951	306	15	for	for	ADP
ejpam-5951	306	16	all	all	DET
ejpam-5951	306	17	ζ	ζ	PROPN
ejpam-5951	306	18	∈	∈	PROPN
ejpam-5951	306	19	r.	r.	NOUN
ejpam-5951	306	20	the	the	PRON
ejpam-5951	306	21	,	,	PUNCT
ejpam-5951	306	22	mapping	mapping	NOUN
ejpam-5951	306	23	g	g	NOUN
ejpam-5951	306	24	is	be	AUX
ejpam-5951	306	25	a	a	DET
ejpam-5951	306	26	β	β	NOUN
ejpam-5951	306	27	-	-	ADJ
ejpam-5951	306	28	strict	strict	ADJ
ejpam-5951	306	29	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	306	30	mapping	mapping	NOUN
ejpam-5951	306	31	with	with	ADP
ejpam-5951	306	32	β	β	X
ejpam-5951	306	33	=	=	SYM
ejpam-5951	306	34	5	5	NUM
ejpam-5951	306	35	9	9	NUM
ejpam-5951	306	36	,	,	PUNCT
ejpam-5951	306	37	but	but	CCONJ
ejpam-5951	306	38	it	it	PRON
ejpam-5951	306	39	is	be	AUX
ejpam-5951	306	40	not	not	PART
ejpam-5951	306	41	a	a	DET
ejpam-5951	306	42	nonexpansive	nonexpansive	ADJ
ejpam-5951	306	43	mapping	mapping	NOUN
ejpam-5951	306	44	.	.	PUNCT
ejpam-5951	307	1	p.	p.	NOUN
ejpam-5951	307	2	patel	patel	PROPN
ejpam-5951	307	3	,	,	PUNCT
ejpam-5951	307	4	r.	r.	PROPN
ejpam-5951	307	5	shukla	shukla	PROPN
ejpam-5951	307	6	/	/	SYM
ejpam-5951	307	7	eur	eur	PROPN
ejpam-5951	307	8	.	.	PUNCT
ejpam-5951	308	1	j.	j.	PROPN
ejpam-5951	308	2	pure	pure	PROPN
ejpam-5951	308	3	appl	appl	PROPN
ejpam-5951	308	4	.	.	PROPN
ejpam-5951	308	5	math	math	PROPN
ejpam-5951	308	6	,	,	PUNCT
ejpam-5951	308	7	18	18	NUM
ejpam-5951	308	8	(	(	PUNCT
ejpam-5951	308	9	2	2	NUM
ejpam-5951	308	10	)	)	PUNCT
ejpam-5951	308	11	(	(	PUNCT
ejpam-5951	308	12	2025	2025	NUM
ejpam-5951	308	13	)	)	PUNCT
ejpam-5951	308	14	,	,	PUNCT
ejpam-5951	308	15	5951	5951	NUM
ejpam-5951	308	16	13	13	NUM
ejpam-5951	308	17	of	of	ADP
ejpam-5951	308	18	15	15	NUM
ejpam-5951	308	19	example	example	NOUN
ejpam-5951	308	20	2	2	NUM
ejpam-5951	308	21	.	.	PUNCT
ejpam-5951	309	1	[	[	X
ejpam-5951	309	2	24	24	NUM
ejpam-5951	309	3	]	]	PUNCT
ejpam-5951	309	4	let	let	VERB
ejpam-5951	309	5	γ	γ	X
ejpam-5951	309	6	=	=	SYM
ejpam-5951	309	7	r2	r2	PROPN
ejpam-5951	309	8	and	and	CCONJ
ejpam-5951	309	9	g	g	NOUN
ejpam-5951	309	10	:	:	PUNCT
ejpam-5951	309	11	γ	γ	X
ejpam-5951	309	12	→	→	SYM
ejpam-5951	309	13	γ	γ	X
ejpam-5951	309	14	be	be	AUX
ejpam-5951	309	15	a	a	DET
ejpam-5951	309	16	mapping	mapping	NOUN
ejpam-5951	309	17	defined	define	VERB
ejpam-5951	309	18	as	as	ADP
ejpam-5951	309	19	g(ζ1	g(ζ1	NOUN
ejpam-5951	309	20	,	,	PUNCT
ejpam-5951	309	21	ζ2	ζ2	NOUN
ejpam-5951	309	22	)	)	PUNCT
ejpam-5951	309	23	=	=	PUNCT
ejpam-5951	309	24	(	(	PUNCT
ejpam-5951	309	25	−2	−2	NOUN
ejpam-5951	309	26	tan−1(ζ1	tan−1(ζ1	NOUN
ejpam-5951	309	27	)	)	PUNCT
ejpam-5951	309	28	,	,	PUNCT
ejpam-5951	309	29	2	2	NUM
ejpam-5951	309	30	cot	cot	NOUN
ejpam-5951	309	31	−1(ζ2	−1(ζ2	NOUN
ejpam-5951	309	32	)	)	PUNCT
ejpam-5951	309	33	)	)	PUNCT
ejpam-5951	309	34	,	,	PUNCT
ejpam-5951	309	35	for	for	ADP
ejpam-5951	309	36	all	all	DET
ejpam-5951	309	37	(	(	PUNCT
ejpam-5951	309	38	ζ1	ζ1	NOUN
ejpam-5951	309	39	,	,	PUNCT
ejpam-5951	309	40	ζ2	ζ2	NOUN
ejpam-5951	309	41	)	)	PUNCT
ejpam-5951	309	42	∈	∈	NOUN
ejpam-5951	309	43	r2	r2	NOUN
ejpam-5951	309	44	.	.	PUNCT
ejpam-5951	310	1	the	the	DET
ejpam-5951	310	2	mapping	mapping	NOUN
ejpam-5951	310	3	g	g	NOUN
ejpam-5951	310	4	is	be	AUX
ejpam-5951	310	5	a	a	DET
ejpam-5951	310	6	β	β	NOUN
ejpam-5951	310	7	-	-	ADJ
ejpam-5951	310	8	strict	strict	ADJ
ejpam-5951	310	9	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	310	10	mapping	mapping	NOUN
ejpam-5951	310	11	with	with	ADP
ejpam-5951	310	12	β	β	X
ejpam-5951	310	13	=	=	SYM
ejpam-5951	310	14	3	3	NUM
ejpam-5951	310	15	4	4	NUM
ejpam-5951	311	1	but	but	CCONJ
ejpam-5951	311	2	it	it	PRON
ejpam-5951	311	3	is	be	AUX
ejpam-5951	311	4	not	not	PART
ejpam-5951	311	5	a	a	DET
ejpam-5951	311	6	nonexpansive	nonexpansive	ADJ
ejpam-5951	311	7	mapping	mapping	NOUN
ejpam-5951	311	8	.	.	PUNCT
ejpam-5951	312	1	example	example	NOUN
ejpam-5951	313	1	3	3	NUM
ejpam-5951	313	2	.	.	PUNCT
ejpam-5951	313	3	define	define	VERB
ejpam-5951	313	4	the	the	DET
ejpam-5951	313	5	inner	inner	ADJ
ejpam-5951	313	6	product	product	NOUN
ejpam-5951	313	7	on	on	ADP
ejpam-5951	313	8	r	r	NOUN
ejpam-5951	313	9	as	as	ADP
ejpam-5951	313	10	⟨ϑ	⟨ϑ	NOUN
ejpam-5951	313	11	,	,	PUNCT
ejpam-5951	313	12	ζ⟩	ζ⟩	ADP
ejpam-5951	313	13	=	=	SYM
ejpam-5951	313	14	−ϑζ	−ϑζ	NOUN
ejpam-5951	313	15	for	for	ADP
ejpam-5951	313	16	all	all	DET
ejpam-5951	313	17	ϑ	ϑ	NOUN
ejpam-5951	313	18	,	,	PUNCT
ejpam-5951	313	19	ζ	ζ	PROPN
ejpam-5951	313	20	∈	∈	PROPN
ejpam-5951	313	21	r.	r.	NOUN
ejpam-5951	313	22	define	define	VERB
ejpam-5951	313	23	h	h	NOUN
ejpam-5951	313	24	=	=	PRON
ejpam-5951	313	25	{	{	PUNCT
ejpam-5951	313	26	ζ	ζ	NOUN
ejpam-5951	313	27	∈	∈	NOUN
ejpam-5951	313	28	r	r	NOUN
ejpam-5951	313	29	:	:	PUNCT
ejpam-5951	313	30	⟨ζ	⟨ζ	NUM
ejpam-5951	313	31	,	,	PUNCT
ejpam-5951	313	32	ζ⟩	ζ⟩	PUNCT
ejpam-5951	313	33	=	=	SYM
ejpam-5951	313	34	−1	−1	NOUN
ejpam-5951	313	35	}	}	PUNCT
ejpam-5951	313	36	.	.	PUNCT
ejpam-5951	314	1	then	then	ADV
ejpam-5951	314	2	this	this	DET
ejpam-5951	314	3	inner	inner	ADJ
ejpam-5951	314	4	product	product	NOUN
ejpam-5951	314	5	induces	induce	VERB
ejpam-5951	314	6	riemannian	riemannian	ADJ
ejpam-5951	314	7	metric	metric	ADJ
ejpam-5951	314	8	ρ	ρ	PROPN
ejpam-5951	314	9	,	,	PUNCT
ejpam-5951	314	10	on	on	ADP
ejpam-5951	314	11	tangent	tangent	ADJ
ejpam-5951	314	12	space	space	NOUN
ejpam-5951	314	13	tph	tph	PROPN
ejpam-5951	314	14	⊂	⊂	PROPN
ejpam-5951	314	15	tpr	tpr	PROPN
ejpam-5951	314	16	for	for	ADP
ejpam-5951	314	17	p	p	PROPN
ejpam-5951	314	18	∈	∈	PROPN
ejpam-5951	314	19	h	h	NOUN
ejpam-5951	314	20	defined	define	VERB
ejpam-5951	314	21	by	by	ADP
ejpam-5951	314	22	ρ(ϑ	ρ(ϑ	PROPN
ejpam-5951	314	23	,	,	PUNCT
ejpam-5951	314	24	ζ	ζ	NOUN
ejpam-5951	314	25	)	)	PUNCT
ejpam-5951	314	26	=	=	SYM
ejpam-5951	314	27	cosh−1(−⟨ϑ	cosh−1(−⟨ϑ	NOUN
ejpam-5951	314	28	,	,	PUNCT
ejpam-5951	314	29	ζ⟩	ζ⟩	NOUN
ejpam-5951	314	30	)	)	PUNCT
ejpam-5951	314	31	for	for	ADP
ejpam-5951	314	32	all	all	DET
ejpam-5951	314	33	ϑ	ϑ	NOUN
ejpam-5951	314	34	,	,	PUNCT
ejpam-5951	314	35	ζ	ζ	PROPN
ejpam-5951	314	36	∈	∈	PROPN
ejpam-5951	314	37	h.	h.	NOUN
ejpam-5951	314	38	then	then	ADV
ejpam-5951	314	39	(	(	PUNCT
ejpam-5951	314	40	h	h	NOUN
ejpam-5951	314	41	,	,	PUNCT
ejpam-5951	314	42	ρ	ρ	PROPN
ejpam-5951	314	43	)	)	PUNCT
ejpam-5951	314	44	is	be	AUX
ejpam-5951	314	45	the	the	DET
ejpam-5951	314	46	hadamard	hadamard	PROPN
ejpam-5951	314	47	manifold	manifold	ADJ
ejpam-5951	314	48	with	with	ADP
ejpam-5951	314	49	sectional	sectional	ADJ
ejpam-5951	314	50	curvature	curvature	NOUN
ejpam-5951	314	51	−1	−1	NOUN
ejpam-5951	314	52	at	at	ADP
ejpam-5951	314	53	any	any	DET
ejpam-5951	314	54	point	point	NOUN
ejpam-5951	314	55	.	.	PUNCT
ejpam-5951	315	1	now	now	ADV
ejpam-5951	315	2	,	,	PUNCT
ejpam-5951	315	3	let	let	VERB
ejpam-5951	315	4	γ	γ	X
ejpam-5951	315	5	=	=	SYM
ejpam-5951	315	6	h	h	PROPN
ejpam-5951	315	7	,	,	PUNCT
ejpam-5951	315	8	g1(ζ	g1(ζ	PROPN
ejpam-5951	315	9	)	)	PUNCT
ejpam-5951	316	1	=	=	SYM
ejpam-5951	316	2	−2ζ	−2ζ	PROPN
ejpam-5951	316	3	,	,	PUNCT
ejpam-5951	316	4	g2(ζ	g2(ζ	NOUN
ejpam-5951	316	5	)	)	PUNCT
ejpam-5951	316	6	=	=	SYM
ejpam-5951	316	7	−5ζ	−5ζ	PROPN
ejpam-5951	316	8	and	and	CCONJ
ejpam-5951	316	9	h1(ζ	h1(ζ	PROPN
ejpam-5951	316	10	)	)	PUNCT
ejpam-5951	316	11	=	=	SYM
ejpam-5951	316	12	1	1	NUM
ejpam-5951	316	13	3ζ	3ζ	NOUN
ejpam-5951	316	14	+	+	CCONJ
ejpam-5951	316	15	1	1	NUM
ejpam-5951	316	16	2	2	NUM
ejpam-5951	316	17	sin	sin	NOUN
ejpam-5951	316	18	ζ	ζ	NOUN
ejpam-5951	316	19	,	,	PUNCT
ejpam-5951	316	20	h2(ζ	h2(ζ	PRON
ejpam-5951	316	21	)	)	PUNCT
ejpam-5951	316	22	=	=	SYM
ejpam-5951	317	1	−6ζ	−6ζ	PROPN
ejpam-5951	317	2	.	.	PUNCT
ejpam-5951	318	1	here	here	ADV
ejpam-5951	318	2	mappings	mapping	NOUN
ejpam-5951	318	3	g1	g1	PROPN
ejpam-5951	318	4	,	,	PUNCT
ejpam-5951	318	5	g2	g2	PROPN
ejpam-5951	318	6	are	be	AUX
ejpam-5951	318	7	1	1	NUM
ejpam-5951	318	8	3	3	NUM
ejpam-5951	318	9	,	,	PUNCT
ejpam-5951	318	10	2	2	NUM
ejpam-5951	318	11	3	3	NUM
ejpam-5951	318	12	strict	strict	ADJ
ejpam-5951	318	13	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	318	14	mappings	mapping	NOUN
ejpam-5951	318	15	,	,	PUNCT
ejpam-5951	318	16	respectively	respectively	ADV
ejpam-5951	318	17	.	.	PUNCT
ejpam-5951	319	1	and	and	CCONJ
ejpam-5951	319	2	the	the	DET
ejpam-5951	319	3	mappings	mapping	NOUN
ejpam-5951	319	4	h1	h1	PROPN
ejpam-5951	319	5	,	,	PUNCT
ejpam-5951	319	6	h2	h2	PROPN
ejpam-5951	319	7	are	be	AUX
ejpam-5951	319	8	1	1	NUM
ejpam-5951	319	9	4	4	NUM
ejpam-5951	319	10	,	,	PUNCT
ejpam-5951	319	11	5	5	NUM
ejpam-5951	319	12	7	7	NUM
ejpam-5951	319	13	strict	strict	ADJ
ejpam-5951	319	14	pseudocontractive	pseudocontractive	ADJ
ejpam-5951	319	15	mappings	mapping	NOUN
ejpam-5951	319	16	,	,	PUNCT
ejpam-5951	319	17	respectively	respectively	ADV
ejpam-5951	319	18	.	.	PUNCT
ejpam-5951	320	1	also	also	ADV
ejpam-5951	320	2	2⋂	2⋂	NUM
ejpam-5951	320	3	i=1	i=1	PROPN
ejpam-5951	320	4	f	f	PROPN
ejpam-5951	320	5	(	(	PUNCT
ejpam-5951	320	6	gi	gi	INTJ
ejpam-5951	320	7	)	)	PUNCT
ejpam-5951	320	8	2⋂	2⋂	NOUN
ejpam-5951	321	1	i=1	i=1	PROPN
ejpam-5951	321	2	f	f	PROPN
ejpam-5951	321	3	(	(	PUNCT
ejpam-5951	321	4	hi	hi	INTJ
ejpam-5951	321	5	)	)	PUNCT
ejpam-5951	321	6	⋂	⋂	PROPN
ejpam-5951	321	7	φ	φ	X
ejpam-5951	321	8	=	=	SYM
ejpam-5951	321	9	{	{	PUNCT
ejpam-5951	321	10	0	0	NUM
ejpam-5951	321	11	}	}	PUNCT
ejpam-5951	321	12	.	.	PUNCT
ejpam-5951	322	1	it	it	PRON
ejpam-5951	322	2	satisfies	satisfy	VERB
ejpam-5951	322	3	all	all	DET
ejpam-5951	322	4	the	the	DET
ejpam-5951	322	5	conditions	condition	NOUN
ejpam-5951	322	6	of	of	ADP
ejpam-5951	322	7	the	the	DET
ejpam-5951	322	8	theorem	theorem	NOUN
ejpam-5951	322	9	2	2	NUM
ejpam-5951	322	10	,	,	PUNCT
ejpam-5951	322	11	hence	hence	ADV
ejpam-5951	322	12	for	for	ADP
ejpam-5951	322	13	i	i	PROPN
ejpam-5951	322	14	=	=	SYM
ejpam-5951	322	15	1	1	NUM
ejpam-5951	322	16	,	,	PUNCT
ejpam-5951	322	17	2	2	NUM
ejpam-5951	322	18	the	the	DET
ejpam-5951	322	19	sequence	sequence	NOUN
ejpam-5951	322	20	generated	generate	VERB
ejpam-5951	322	21	by	by	ADP
ejpam-5951	322	22	(	(	PUNCT
ejpam-5951	322	23	9	9	X
ejpam-5951	322	24	)	)	PUNCT
ejpam-5951	322	25	converges	converge	NOUN
ejpam-5951	322	26	to	to	ADP
ejpam-5951	322	27	pπ(ζ1	pπ(ζ1	NOUN
ejpam-5951	322	28	)	)	PUNCT
ejpam-5951	322	29	.	.	PUNCT
ejpam-5951	323	1	acknowledgements	acknowledgement	NOUN
ejpam-5951	323	2	we	we	PRON
ejpam-5951	323	3	are	be	AUX
ejpam-5951	323	4	very	very	ADV
ejpam-5951	323	5	much	much	ADV
ejpam-5951	323	6	thankful	thankful	ADJ
ejpam-5951	323	7	to	to	ADP
ejpam-5951	323	8	the	the	DET
ejpam-5951	323	9	reviewers	reviewer	NOUN
ejpam-5951	323	10	for	for	ADP
ejpam-5951	323	11	their	their	PRON
ejpam-5951	323	12	constructive	constructive	ADJ
ejpam-5951	323	13	comments	comment	NOUN
ejpam-5951	323	14	and	and	CCONJ
ejpam-5951	323	15	suggestions	suggestion	NOUN
ejpam-5951	323	16	which	which	PRON
ejpam-5951	323	17	have	have	AUX
ejpam-5951	323	18	been	be	AUX
ejpam-5951	323	19	useful	useful	ADJ
ejpam-5951	323	20	for	for	ADP
ejpam-5951	323	21	the	the	DET
ejpam-5951	323	22	improvement	improvement	NOUN
ejpam-5951	323	23	of	of	ADP
ejpam-5951	323	24	this	this	DET
ejpam-5951	323	25	paper	paper	NOUN
ejpam-5951	323	26	.	.	PUNCT
ejpam-5951	324	1	conflicts	conflict	NOUN
ejpam-5951	324	2	of	of	ADP
ejpam-5951	324	3	interest	interest	NOUN
ejpam-5951	324	4	the	the	DET
ejpam-5951	324	5	authors	author	NOUN
ejpam-5951	324	6	declare	declare	VERB
ejpam-5951	324	7	that	that	SCONJ
ejpam-5951	324	8	they	they	PRON
ejpam-5951	324	9	have	have	VERB
ejpam-5951	324	10	no	no	DET
ejpam-5951	324	11	conflicts	conflict	NOUN
ejpam-5951	324	12	of	of	ADP
ejpam-5951	324	13	interests	interest	NOUN
ejpam-5951	324	14	.	.	PUNCT
ejpam-5951	325	1	funding	fund	VERB
ejpam-5951	325	2	this	this	DET
ejpam-5951	325	3	work	work	NOUN
ejpam-5951	325	4	was	be	AUX
ejpam-5951	325	5	supported	support	VERB
ejpam-5951	325	6	by	by	ADP
ejpam-5951	325	7	directorate	directorate	NOUN
ejpam-5951	325	8	of	of	ADP
ejpam-5951	325	9	research	research	NOUN
ejpam-5951	325	10	and	and	CCONJ
ejpam-5951	325	11	innovation	innovation	NOUN
ejpam-5951	325	12	,	,	PUNCT
ejpam-5951	325	13	walter	walter	PROPN
ejpam-5951	325	14	sisulu	sisulu	PROPN
ejpam-5951	325	15	university	university	PROPN
ejpam-5951	325	16	,	,	PUNCT
ejpam-5951	325	17	south	south	PROPN
ejpam-5951	325	18	africa	africa	PROPN
ejpam-5951	325	19	.	.	PUNCT
ejpam-5951	326	1	data	datum	NOUN
ejpam-5951	326	2	availability	availability	NOUN
ejpam-5951	326	3	there	there	PRON
ejpam-5951	326	4	is	be	VERB
ejpam-5951	326	5	no	no	DET
ejpam-5951	326	6	any	any	DET
ejpam-5951	326	7	availability	availability	NOUN
ejpam-5951	326	8	of	of	ADP
ejpam-5951	326	9	data	datum	NOUN
ejpam-5951	326	10	.	.	PUNCT
ejpam-5951	327	1	p.	p.	NOUN
ejpam-5951	327	2	patel	patel	PROPN
ejpam-5951	327	3	,	,	PUNCT
ejpam-5951	327	4	r.	r.	PROPN
ejpam-5951	327	5	shukla	shukla	PROPN
ejpam-5951	327	6	/	/	SYM
ejpam-5951	327	7	eur	eur	PROPN
ejpam-5951	327	8	.	.	PUNCT
ejpam-5951	328	1	j.	j.	PROPN
ejpam-5951	328	2	pure	pure	PROPN
ejpam-5951	328	3	appl	appl	PROPN
ejpam-5951	328	4	.	.	PROPN
ejpam-5951	328	5	math	math	PROPN
ejpam-5951	328	6	,	,	PUNCT
ejpam-5951	328	7	18	18	NUM
ejpam-5951	328	8	(	(	PUNCT
ejpam-5951	328	9	2	2	NUM
ejpam-5951	328	10	)	)	PUNCT
ejpam-5951	328	11	(	(	PUNCT
ejpam-5951	328	12	2025	2025	NUM
ejpam-5951	328	13	)	)	PUNCT
ejpam-5951	328	14	,	,	PUNCT
ejpam-5951	328	15	5951	5951	NUM
ejpam-5951	328	16	14	14	NUM
ejpam-5951	328	17	of	of	ADP
ejpam-5951	328	18	15	15	NUM
ejpam-5951	328	19	references	reference	NOUN
ejpam-5951	328	20	[	[	X
ejpam-5951	328	21	1	1	NUM
ejpam-5951	328	22	]	]	PUNCT
ejpam-5951	328	23	p.	p.	PROPN
ejpam-5951	328	24	hartman	hartman	PROPN
ejpam-5951	328	25	and	and	CCONJ
ejpam-5951	328	26	g.	g.	PROPN
ejpam-5951	328	27	stampacchia	stampacchia	PROPN
ejpam-5951	328	28	.	.	PUNCT
ejpam-5951	329	1	on	on	ADP
ejpam-5951	329	2	some	some	DET
ejpam-5951	329	3	non	non	ADJ
ejpam-5951	329	4	-	-	ADJ
ejpam-5951	329	5	linear	linear	ADJ
ejpam-5951	329	6	elliptic	elliptic	ADJ
ejpam-5951	329	7	differential	differential	ADJ
ejpam-5951	329	8	-	-	PUNCT
ejpam-5951	329	9	functional	functional	ADJ
ejpam-5951	329	10	equations	equation	NOUN
ejpam-5951	329	11	.	.	PUNCT
ejpam-5951	330	1	acta	acta	PROPN
ejpam-5951	330	2	math	math	PROPN
ejpam-5951	330	3	.	.	PUNCT
ejpam-5951	330	4	,	,	PUNCT
ejpam-5951	330	5	115:271–310	115:271–310	NUM
ejpam-5951	330	6	,	,	PUNCT
ejpam-5951	330	7	1966	1966	NUM
ejpam-5951	330	8	.	.	PUNCT
ejpam-5951	331	1	[	[	X
ejpam-5951	331	2	2	2	X
ejpam-5951	331	3	]	]	PUNCT
ejpam-5951	331	4	p.	p.	NOUN
ejpam-5951	331	5	patel	patel	PROPN
ejpam-5951	331	6	and	and	CCONJ
ejpam-5951	331	7	r.	r.	PROPN
ejpam-5951	331	8	pant	pant	PROPN
ejpam-5951	331	9	.	.	PUNCT
ejpam-5951	332	1	viscosity	viscosity	NOUN
ejpam-5951	332	2	approximation	approximation	NOUN
ejpam-5951	332	3	methods	method	NOUN
ejpam-5951	332	4	for	for	ADP
ejpam-5951	332	5	quasi	quasi	ADJ
ejpam-5951	332	6	-	-	ADJ
ejpam-5951	332	7	nonexpansive	nonexpansive	ADJ
ejpam-5951	332	8	mappings	mapping	NOUN
ejpam-5951	332	9	in	in	ADP
ejpam-5951	332	10	banach	banach	NOUN
ejpam-5951	332	11	spaces	space	NOUN
ejpam-5951	332	12	.	.	PUNCT
ejpam-5951	333	1	filomat	filomat	NOUN
ejpam-5951	333	2	,	,	PUNCT
ejpam-5951	333	3	35(9):3113–3126	35(9):3113–3126	NOUN
ejpam-5951	333	4	,	,	PUNCT
ejpam-5951	333	5	2021	2021	NUM
ejpam-5951	333	6	.	.	PUNCT
ejpam-5951	334	1	[	[	X
ejpam-5951	334	2	3	3	NUM
ejpam-5951	334	3	]	]	PUNCT
ejpam-5951	334	4	a.	a.	NOUN
ejpam-5951	334	5	moudafi	moudafi	PROPN
ejpam-5951	334	6	.	.	PUNCT
ejpam-5951	335	1	viscosity	viscosity	NOUN
ejpam-5951	335	2	approximation	approximation	NOUN
ejpam-5951	335	3	methods	method	NOUN
ejpam-5951	335	4	for	for	ADP
ejpam-5951	335	5	fixed	fix	VERB
ejpam-5951	335	6	-	-	PUNCT
ejpam-5951	335	7	points	point	NOUN
ejpam-5951	335	8	problems	problem	NOUN
ejpam-5951	335	9	.	.	PUNCT
ejpam-5951	336	1	j.	j.	PROPN
ejpam-5951	336	2	math	math	PROPN
ejpam-5951	336	3	.	.	PUNCT
ejpam-5951	337	1	anal	anal	PROPN
ejpam-5951	337	2	.	.	PUNCT
ejpam-5951	338	1	appl	appl	PROPN
ejpam-5951	338	2	.	.	PROPN
ejpam-5951	338	3	,	,	PUNCT
ejpam-5951	338	4	241(1):46–55	241(1):46–55	NOUN
ejpam-5951	338	5	,	,	PUNCT
ejpam-5951	338	6	2000	2000	NUM
ejpam-5951	338	7	.	.	PUNCT
ejpam-5951	339	1	[	[	X
ejpam-5951	339	2	4	4	X
ejpam-5951	339	3	]	]	PUNCT
ejpam-5951	339	4	h.	h.	PROPN
ejpam-5951	339	5	k.	k.	PROPN
ejpam-5951	339	6	xu	xu	PROPN
ejpam-5951	339	7	.	.	PUNCT
ejpam-5951	340	1	viscosity	viscosity	NOUN
ejpam-5951	340	2	approximation	approximation	NOUN
ejpam-5951	340	3	methods	method	NOUN
ejpam-5951	340	4	for	for	ADP
ejpam-5951	340	5	nonexpansive	nonexpansive	ADJ
ejpam-5951	340	6	mappings	mapping	NOUN
ejpam-5951	340	7	.	.	PUNCT
ejpam-5951	341	1	j.	j.	PROPN
ejpam-5951	341	2	math	math	PROPN
ejpam-5951	341	3	.	.	PUNCT
ejpam-5951	342	1	anal	anal	PROPN
ejpam-5951	342	2	.	.	PUNCT
ejpam-5951	343	1	appl	appl	PROPN
ejpam-5951	343	2	.	.	PROPN
ejpam-5951	343	3	,	,	PUNCT
ejpam-5951	343	4	298(1):279–291	298(1):279–291	PROPN
ejpam-5951	343	5	,	,	PUNCT
ejpam-5951	343	6	2004	2004	NUM
ejpam-5951	343	7	.	.	PUNCT
ejpam-5951	344	1	[	[	X
ejpam-5951	344	2	5	5	X
ejpam-5951	344	3	]	]	PUNCT
ejpam-5951	344	4	v.	v.	ADP
ejpam-5951	344	5	berinde	berinde	NOUN
ejpam-5951	344	6	and	and	CCONJ
ejpam-5951	344	7	m.	m.	NOUN
ejpam-5951	344	8	păcurar	păcurar	NOUN
ejpam-5951	344	9	.	.	PUNCT
ejpam-5951	345	1	krasnoselskij	krasnoselskij	NOUN
ejpam-5951	345	2	-	-	PUNCT
ejpam-5951	345	3	type	type	NOUN
ejpam-5951	345	4	algorithms	algorithms	NOUN
ejpam-5951	345	5	for	for	ADP
ejpam-5951	345	6	fixed	fix	VERB
ejpam-5951	345	7	point	point	NOUN
ejpam-5951	345	8	problems	problem	NOUN
ejpam-5951	345	9	and	and	CCONJ
ejpam-5951	345	10	variational	variational	ADJ
ejpam-5951	345	11	inequality	inequality	NOUN
ejpam-5951	345	12	problems	problem	NOUN
ejpam-5951	345	13	in	in	ADP
ejpam-5951	345	14	banach	banach	NOUN
ejpam-5951	345	15	spaces	space	NOUN
ejpam-5951	345	16	.	.	PUNCT
ejpam-5951	346	1	topology	topology	NOUN
ejpam-5951	346	2	appl	appl	PROPN
ejpam-5951	346	3	.	.	PROPN
ejpam-5951	346	4	,	,	PUNCT
ejpam-5951	346	5	340	340	NUM
ejpam-5951	346	6	:	:	PUNCT
ejpam-5951	346	7	paper	paper	NOUN
ejpam-5951	346	8	no	no	NOUN
ejpam-5951	346	9	.	.	PROPN
ejpam-5951	346	10	108708	108708	NUM
ejpam-5951	346	11	,	,	PUNCT
ejpam-5951	346	12	15	15	NUM
ejpam-5951	346	13	,	,	PUNCT
ejpam-5951	346	14	2023	2023	NUM
ejpam-5951	346	15	.	.	PUNCT
ejpam-5951	347	1	[	[	X
ejpam-5951	347	2	6	6	NUM
ejpam-5951	347	3	]	]	PUNCT
ejpam-5951	347	4	p.	p.	NOUN
ejpam-5951	347	5	patel	patel	PROPN
ejpam-5951	347	6	and	and	CCONJ
ejpam-5951	347	7	r.	r.	PROPN
ejpam-5951	347	8	shukla	shukla	PROPN
ejpam-5951	347	9	.	.	PUNCT
ejpam-5951	348	1	viscosity	viscosity	NOUN
ejpam-5951	348	2	approximation	approximation	NOUN
ejpam-5951	348	3	methods	method	NOUN
ejpam-5951	348	4	for	for	ADP
ejpam-5951	348	5	generalized	generalized	ADJ
ejpam-5951	348	6	modification	modification	NOUN
ejpam-5951	348	7	of	of	ADP
ejpam-5951	348	8	the	the	DET
ejpam-5951	348	9	system	system	NOUN
ejpam-5951	348	10	of	of	ADP
ejpam-5951	348	11	equilibrium	equilibrium	NOUN
ejpam-5951	348	12	problem	problem	NOUN
ejpam-5951	348	13	and	and	CCONJ
ejpam-5951	348	14	fixed	fix	VERB
ejpam-5951	348	15	point	point	NOUN
ejpam-5951	348	16	problems	problem	NOUN
ejpam-5951	348	17	of	of	ADP
ejpam-5951	348	18	an	an	DET
ejpam-5951	348	19	infinite	infinite	ADJ
ejpam-5951	348	20	family	family	NOUN
ejpam-5951	348	21	of	of	ADP
ejpam-5951	348	22	nonexpansive	nonexpansive	ADJ
ejpam-5951	348	23	mappings	mapping	NOUN
ejpam-5951	348	24	.	.	PUNCT
ejpam-5951	349	1	mathematics	mathematic	NOUN
ejpam-5951	349	2	and	and	CCONJ
ejpam-5951	349	3	statistics	statistic	NOUN
ejpam-5951	349	4	,	,	PUNCT
ejpam-5951	349	5	12(4):339–347	12(4):339–347	PROPN
ejpam-5951	349	6	,	,	PUNCT
ejpam-5951	349	7	2024	2024	NUM
ejpam-5951	349	8	.	.	PUNCT
ejpam-5951	350	1	[	[	X
ejpam-5951	350	2	7	7	X
ejpam-5951	350	3	]	]	X
ejpam-5951	350	4	p.	p.	NOUN
ejpam-5951	350	5	patel	patel	PROPN
ejpam-5951	350	6	and	and	CCONJ
ejpam-5951	350	7	r.	r.	PROPN
ejpam-5951	350	8	shukla	shukla	PROPN
ejpam-5951	350	9	.	.	PUNCT
ejpam-5951	351	1	mann	mann	PROPN
ejpam-5951	351	2	-	-	PUNCT
ejpam-5951	351	3	dotson	dotson	PROPN
ejpam-5951	351	4	’s	’s	PART
ejpam-5951	351	5	algorithm	algorithm	NOUN
ejpam-5951	351	6	for	for	ADP
ejpam-5951	351	7	a	a	DET
ejpam-5951	351	8	countable	countable	ADJ
ejpam-5951	351	9	family	family	NOUN
ejpam-5951	351	10	of	of	ADP
ejpam-5951	351	11	non	non	ADJ
ejpam-5951	351	12	-	-	ADJ
ejpam-5951	351	13	self	self	ADJ
ejpam-5951	351	14	strict	strict	ADJ
ejpam-5951	351	15	pseudo	pseudo	NOUN
ejpam-5951	351	16	-	-	ADJ
ejpam-5951	351	17	contractive	contractive	ADJ
ejpam-5951	351	18	mappings	mapping	NOUN
ejpam-5951	351	19	.	.	PUNCT
ejpam-5951	352	1	rend	rend	VERB
ejpam-5951	352	2	.	.	PUNCT
ejpam-5951	353	1	circ	circ	PROPN
ejpam-5951	353	2	.	.	PUNCT
ejpam-5951	354	1	mat	mat	PROPN
ejpam-5951	354	2	.	.	PUNCT
ejpam-5951	354	3	palermo	palermo	PROPN
ejpam-5951	354	4	(	(	PUNCT
ejpam-5951	354	5	2	2	NUM
ejpam-5951	354	6	)	)	PUNCT
ejpam-5951	354	7	,	,	PUNCT
ejpam-5951	354	8	73(1):225–240	73(1):225–240	NOUN
ejpam-5951	354	9	,	,	PUNCT
ejpam-5951	354	10	2024	2024	NUM
ejpam-5951	354	11	.	.	PUNCT
ejpam-5951	355	1	[	[	X
ejpam-5951	355	2	8	8	X
ejpam-5951	355	3	]	]	PUNCT
ejpam-5951	356	1	s.	s.	PROPN
ejpam-5951	356	2	z.	z.	PROPN
ejpam-5951	356	3	németh	németh	PROPN
ejpam-5951	356	4	.	.	PROPN
ejpam-5951	356	5	variational	variational	ADJ
ejpam-5951	356	6	inequalities	inequality	NOUN
ejpam-5951	356	7	on	on	ADP
ejpam-5951	356	8	hadamard	hadamard	ADJ
ejpam-5951	356	9	manifolds	manifold	NOUN
ejpam-5951	356	10	.	.	PUNCT
ejpam-5951	357	1	nonlinear	nonlinear	ADJ
ejpam-5951	357	2	anal	anal	PROPN
ejpam-5951	357	3	.	.	PUNCT
ejpam-5951	357	4	,	,	PUNCT
ejpam-5951	357	5	52(5):1491–1498	52(5):1491–1498	NUM
ejpam-5951	357	6	,	,	PUNCT
ejpam-5951	357	7	2003	2003	NUM
ejpam-5951	357	8	.	.	PUNCT
ejpam-5951	358	1	[	[	X
ejpam-5951	358	2	9	9	NUM
ejpam-5951	358	3	]	]	PUNCT
ejpam-5951	358	4	a.	a.	NOUN
ejpam-5951	358	5	moudafi	moudafi	NOUN
ejpam-5951	358	6	and	and	CCONJ
ejpam-5951	358	7	p.-e	p.-e	PROPN
ejpam-5951	358	8	.	.	PUNCT
ejpam-5951	359	1	maingé.	maingé.	PROPN
ejpam-5951	359	2	towards	towards	ADP
ejpam-5951	359	3	viscosity	viscosity	NOUN
ejpam-5951	359	4	approximations	approximation	NOUN
ejpam-5951	359	5	of	of	ADP
ejpam-5951	359	6	hierarchical	hierarchical	ADJ
ejpam-5951	359	7	fixedpoint	fixedpoint	NOUN
ejpam-5951	359	8	problems	problem	NOUN
ejpam-5951	359	9	.	.	PUNCT
ejpam-5951	360	1	fixed	fix	VERB
ejpam-5951	360	2	point	point	NOUN
ejpam-5951	360	3	theory	theory	NOUN
ejpam-5951	360	4	appl	appl	PROPN
ejpam-5951	360	5	.	.	PROPN
ejpam-5951	360	6	,	,	PUNCT
ejpam-5951	360	7	pages	page	NOUN
ejpam-5951	360	8	art	art	NOUN
ejpam-5951	360	9	.	.	PUNCT
ejpam-5951	361	1	i	i	PRON
ejpam-5951	361	2	d	d	PROPN
ejpam-5951	361	3	95453	95453	NUM
ejpam-5951	361	4	,	,	PUNCT
ejpam-5951	361	5	10	10	NUM
ejpam-5951	361	6	,	,	PUNCT
ejpam-5951	361	7	2006	2006	NUM
ejpam-5951	361	8	.	.	PUNCT
ejpam-5951	362	1	[	[	X
ejpam-5951	362	2	10	10	NUM
ejpam-5951	362	3	]	]	X
ejpam-5951	362	4	h.	h.	PROPN
ejpam-5951	362	5	k.	k.	PROPN
ejpam-5951	362	6	xu	xu	PROPN
ejpam-5951	362	7	.	.	PUNCT
ejpam-5951	363	1	viscosity	viscosity	NOUN
ejpam-5951	363	2	method	method	NOUN
ejpam-5951	363	3	for	for	ADP
ejpam-5951	363	4	hierarchical	hierarchical	ADJ
ejpam-5951	363	5	fixed	fix	VERB
ejpam-5951	363	6	point	point	NOUN
ejpam-5951	363	7	approach	approach	NOUN
ejpam-5951	363	8	to	to	ADP
ejpam-5951	363	9	variational	variational	ADJ
ejpam-5951	363	10	inequalities	inequality	NOUN
ejpam-5951	363	11	.	.	PUNCT
ejpam-5951	364	1	taiwanese	taiwanese	PROPN
ejpam-5951	364	2	j.	j.	PROPN
ejpam-5951	364	3	math	math	PROPN
ejpam-5951	364	4	.	.	PUNCT
ejpam-5951	364	5	,	,	PUNCT
ejpam-5951	364	6	14(2):463–478	14(2):463–478	PROPN
ejpam-5951	364	7	,	,	PUNCT
ejpam-5951	364	8	2010	2010	NUM
ejpam-5951	364	9	.	.	PUNCT
ejpam-5951	365	1	[	[	X
ejpam-5951	365	2	11	11	NUM
ejpam-5951	365	3	]	]	PUNCT
ejpam-5951	365	4	p.	p.	PROPN
ejpam-5951	365	5	e.	e.	PROPN
ejpam-5951	365	6	maingé	maingé	PROPN
ejpam-5951	365	7	and	and	CCONJ
ejpam-5951	365	8	a.	a.	NOUN
ejpam-5951	365	9	moudafi	moudafi	PROPN
ejpam-5951	365	10	.	.	PUNCT
ejpam-5951	366	1	strong	strong	ADJ
ejpam-5951	366	2	convergence	convergence	NOUN
ejpam-5951	366	3	of	of	ADP
ejpam-5951	366	4	an	an	DET
ejpam-5951	366	5	iterative	iterative	NOUN
ejpam-5951	366	6	method	method	NOUN
ejpam-5951	366	7	for	for	ADP
ejpam-5951	366	8	hierarchical	hierarchical	ADJ
ejpam-5951	366	9	fixed	fix	VERB
ejpam-5951	366	10	-	-	PUNCT
ejpam-5951	366	11	point	point	NOUN
ejpam-5951	366	12	problems	problem	NOUN
ejpam-5951	366	13	.	.	PUNCT
ejpam-5951	367	1	pac	pac	PROPN
ejpam-5951	367	2	.	.	PUNCT
ejpam-5951	368	1	j.	j.	PROPN
ejpam-5951	368	2	optim	optim	PROPN
ejpam-5951	368	3	.	.	PROPN
ejpam-5951	368	4	,	,	PUNCT
ejpam-5951	368	5	3(3):529–538	3(3):529–538	NOUN
ejpam-5951	368	6	,	,	PUNCT
ejpam-5951	368	7	2007	2007	NUM
ejpam-5951	368	8	.	.	PUNCT
ejpam-5951	369	1	[	[	X
ejpam-5951	369	2	12	12	NUM
ejpam-5951	369	3	]	]	X
ejpam-5951	369	4	y.	y.	PROPN
ejpam-5951	369	5	zhao	zhao	PROPN
ejpam-5951	369	6	,	,	PUNCT
ejpam-5951	369	7	x.	x.	PROPN
ejpam-5951	369	8	liu	liu	PROPN
ejpam-5951	369	9	,	,	PUNCT
ejpam-5951	369	10	and	and	CCONJ
ejpam-5951	369	11	r.	r.	PROPN
ejpam-5951	369	12	sun	sun	PROPN
ejpam-5951	369	13	.	.	PROPN
ejpam-5951	370	1	iterative	iterative	PROPN
ejpam-5951	370	2	algorithms	algorithm	NOUN
ejpam-5951	370	3	of	of	ADP
ejpam-5951	370	4	common	common	ADJ
ejpam-5951	370	5	solutions	solution	NOUN
ejpam-5951	370	6	for	for	ADP
ejpam-5951	370	7	a	a	DET
ejpam-5951	370	8	hierarchical	hierarchical	ADJ
ejpam-5951	370	9	fixed	fix	VERB
ejpam-5951	370	10	point	point	NOUN
ejpam-5951	370	11	problem	problem	NOUN
ejpam-5951	370	12	,	,	PUNCT
ejpam-5951	370	13	a	a	DET
ejpam-5951	370	14	system	system	NOUN
ejpam-5951	370	15	of	of	ADP
ejpam-5951	370	16	variational	variational	ADJ
ejpam-5951	370	17	inequalities	inequality	NOUN
ejpam-5951	370	18	,	,	PUNCT
ejpam-5951	370	19	and	and	CCONJ
ejpam-5951	370	20	a	a	DET
ejpam-5951	370	21	split	split	ADJ
ejpam-5951	370	22	equilibrium	equilibrium	NOUN
ejpam-5951	370	23	problem	problem	NOUN
ejpam-5951	370	24	in	in	ADP
ejpam-5951	370	25	hilbert	hilbert	PROPN
ejpam-5951	370	26	spaces	space	NOUN
ejpam-5951	370	27	.	.	PUNCT
ejpam-5951	371	1	j.	j.	PROPN
ejpam-5951	371	2	inequal	inequal	PROPN
ejpam-5951	371	3	.	.	PUNCT
ejpam-5951	372	1	appl	appl	PROPN
ejpam-5951	372	2	.	.	PROPN
ejpam-5951	372	3	,	,	PUNCT
ejpam-5951	372	4	pages	page	NOUN
ejpam-5951	372	5	paper	paper	VERB
ejpam-5951	372	6	no	no	NOUN
ejpam-5951	372	7	.	.	NOUN
ejpam-5951	372	8	111	111	NUM
ejpam-5951	372	9	,	,	PUNCT
ejpam-5951	372	10	22	22	NUM
ejpam-5951	372	11	,	,	PUNCT
ejpam-5951	372	12	2021	2021	NUM
ejpam-5951	372	13	.	.	PUNCT
ejpam-5951	373	1	[	[	X
ejpam-5951	373	2	13	13	NUM
ejpam-5951	373	3	]	]	X
ejpam-5951	373	4	y.	y.	PROPN
ejpam-5951	373	5	yao	yao	PROPN
ejpam-5951	373	6	,	,	PUNCT
ejpam-5951	373	7	y.	y.	PROPN
ejpam-5951	373	8	j.	j.	PROPN
ejpam-5951	373	9	cho	cho	PROPN
ejpam-5951	373	10	,	,	PUNCT
ejpam-5951	373	11	and	and	CCONJ
ejpam-5951	373	12	y.	y.	PROPN
ejpam-5951	373	13	c.	c.	PROPN
ejpam-5951	373	14	liou	liou	PROPN
ejpam-5951	373	15	.	.	PUNCT
ejpam-5951	374	1	iterative	iterative	NOUN
ejpam-5951	374	2	algorithms	algorithm	NOUN
ejpam-5951	374	3	for	for	ADP
ejpam-5951	374	4	hierarchical	hierarchical	ADJ
ejpam-5951	374	5	fixed	fix	VERB
ejpam-5951	374	6	points	point	NOUN
ejpam-5951	374	7	problems	problem	NOUN
ejpam-5951	374	8	and	and	CCONJ
ejpam-5951	374	9	variational	variational	ADJ
ejpam-5951	374	10	inequalities	inequality	NOUN
ejpam-5951	374	11	.	.	PUNCT
ejpam-5951	375	1	math	math	NOUN
ejpam-5951	375	2	.	.	PUNCT
ejpam-5951	376	1	comput	comput	NOUN
ejpam-5951	376	2	.	.	PUNCT
ejpam-5951	377	1	modelling	modelling	NOUN
ejpam-5951	377	2	,	,	PUNCT
ejpam-5951	377	3	52(9	52(9	NUM
ejpam-5951	377	4	-	-	PUNCT
ejpam-5951	377	5	10):1697–1705	10):1697–1705	NOUN
ejpam-5951	377	6	,	,	PUNCT
ejpam-5951	377	7	2010	2010	NUM
ejpam-5951	377	8	.	.	PUNCT
ejpam-5951	378	1	[	[	X
ejpam-5951	378	2	14	14	NUM
ejpam-5951	378	3	]	]	X
ejpam-5951	378	4	l.	l.	PROPN
ejpam-5951	378	5	ćirić	ćirić	PROPN
ejpam-5951	378	6	,	,	PUNCT
ejpam-5951	378	7	a.	a.	PROPN
ejpam-5951	378	8	rafiq	rafiq	PROPN
ejpam-5951	378	9	,	,	PUNCT
ejpam-5951	378	10	s.	s.	PROPN
ejpam-5951	378	11	radenović	radenović	VERB
ejpam-5951	378	12	,	,	PUNCT
ejpam-5951	378	13	m.	m.	NOUN
ejpam-5951	378	14	rajović	rajović	NOUN
ejpam-5951	378	15	,	,	PUNCT
ejpam-5951	378	16	and	and	CCONJ
ejpam-5951	378	17	j.	j.	PROPN
ejpam-5951	378	18	s.	s.	PROPN
ejpam-5951	378	19	ume	ume	PROPN
ejpam-5951	378	20	.	.	PROPN
ejpam-5951	379	1	on	on	ADP
ejpam-5951	379	2	mann	mann	PROPN
ejpam-5951	379	3	implicit	implicit	ADJ
ejpam-5951	379	4	iterations	iteration	NOUN
ejpam-5951	379	5	for	for	ADP
ejpam-5951	379	6	strongly	strongly	ADV
ejpam-5951	379	7	accretive	accretive	ADJ
ejpam-5951	379	8	and	and	CCONJ
ejpam-5951	379	9	strongly	strongly	ADV
ejpam-5951	379	10	pseudo	pseudo	ADJ
ejpam-5951	379	11	-	-	ADJ
ejpam-5951	379	12	contractive	contractive	ADJ
ejpam-5951	379	13	mappings	mapping	NOUN
ejpam-5951	379	14	.	.	PUNCT
ejpam-5951	380	1	appl	appl	PROPN
ejpam-5951	380	2	.	.	PROPN
ejpam-5951	380	3	math	math	PROPN
ejpam-5951	380	4	.	.	PUNCT
ejpam-5951	381	1	comput	comput	NOUN
ejpam-5951	381	2	.	.	PUNCT
ejpam-5951	381	3	,	,	PUNCT
ejpam-5951	381	4	198(1):128–137	198(1):128–137	NUM
ejpam-5951	381	5	,	,	PUNCT
ejpam-5951	381	6	2008	2008	NUM
ejpam-5951	381	7	.	.	PUNCT
ejpam-5951	382	1	[	[	X
ejpam-5951	382	2	15	15	NUM
ejpam-5951	382	3	]	]	X
ejpam-5951	382	4	d.	d.	PROPN
ejpam-5951	382	5	filali	filali	PROPN
ejpam-5951	382	6	,	,	PUNCT
ejpam-5951	382	7	m.	m.	NOUN
ejpam-5951	382	8	dilshad	dilshad	PROPN
ejpam-5951	382	9	,	,	PUNCT
ejpam-5951	382	10	m.	m.	NOUN
ejpam-5951	382	11	akram	akram	PROPN
ejpam-5951	382	12	,	,	PUNCT
ejpam-5951	382	13	f.	f.	PROPN
ejpam-5951	382	14	babu	babu	PROPN
ejpam-5951	382	15	,	,	PUNCT
ejpam-5951	382	16	and	and	CCONJ
ejpam-5951	382	17	i.	i.	PROPN
ejpam-5951	382	18	ahmad	ahmad	PROPN
ejpam-5951	382	19	.	.	PUNCT
ejpam-5951	383	1	viscosity	viscosity	NOUN
ejpam-5951	383	2	method	method	NOUN
ejpam-5951	383	3	for	for	ADP
ejpam-5951	383	4	hierarchical	hierarchical	ADJ
ejpam-5951	383	5	variational	variational	ADJ
ejpam-5951	383	6	inequalities	inequality	NOUN
ejpam-5951	383	7	and	and	CCONJ
ejpam-5951	383	8	variational	variational	ADJ
ejpam-5951	383	9	inclusions	inclusion	NOUN
ejpam-5951	383	10	on	on	ADP
ejpam-5951	383	11	hadamard	hadamard	ADJ
ejpam-5951	383	12	manifolds	manifold	NOUN
ejpam-5951	383	13	.	.	PUNCT
ejpam-5951	384	1	j.	j.	PROPN
ejpam-5951	384	2	inequal	inequal	PROPN
ejpam-5951	384	3	.	.	PUNCT
ejpam-5951	385	1	appl	appl	PROPN
ejpam-5951	385	2	.	.	PROPN
ejpam-5951	385	3	,	,	PUNCT
ejpam-5951	385	4	pages	page	NOUN
ejpam-5951	385	5	paper	paper	VERB
ejpam-5951	385	6	no	no	INTJ
ejpam-5951	385	7	.	.	PROPN
ejpam-5951	385	8	66	66	NUM
ejpam-5951	385	9	,	,	PUNCT
ejpam-5951	385	10	20	20	NUM
ejpam-5951	385	11	,	,	PUNCT
ejpam-5951	385	12	2021	2021	NUM
ejpam-5951	385	13	.	.	PUNCT
ejpam-5951	386	1	[	[	X
ejpam-5951	386	2	16	16	NUM
ejpam-5951	386	3	]	]	PUNCT
ejpam-5951	386	4	p.	p.	NOUN
ejpam-5951	386	5	patel	patel	PROPN
ejpam-5951	386	6	and	and	CCONJ
ejpam-5951	386	7	r.	r.	PROPN
ejpam-5951	386	8	shukla	shukla	PROPN
ejpam-5951	386	9	.	.	PUNCT
ejpam-5951	387	1	common	common	ADJ
ejpam-5951	387	2	solution	solution	NOUN
ejpam-5951	387	3	for	for	ADP
ejpam-5951	387	4	a	a	DET
ejpam-5951	387	5	finite	finite	ADJ
ejpam-5951	387	6	family	family	NOUN
ejpam-5951	387	7	of	of	ADP
ejpam-5951	387	8	equilibrium	equilibrium	NOUN
ejpam-5951	387	9	problems	problem	NOUN
ejpam-5951	387	10	,	,	PUNCT
ejpam-5951	387	11	inclusion	inclusion	NOUN
ejpam-5951	387	12	problems	problem	NOUN
ejpam-5951	387	13	and	and	CCONJ
ejpam-5951	387	14	fixed	fix	VERB
ejpam-5951	387	15	points	point	NOUN
ejpam-5951	387	16	of	of	ADP
ejpam-5951	387	17	a	a	DET
ejpam-5951	387	18	finite	finite	ADJ
ejpam-5951	387	19	family	family	NOUN
ejpam-5951	387	20	of	of	ADP
ejpam-5951	387	21	nonexpansive	nonexpansive	ADJ
ejpam-5951	387	22	mappings	mapping	NOUN
ejpam-5951	387	23	in	in	ADP
ejpam-5951	387	24	hadamard	hadamard	ADJ
ejpam-5951	387	25	manifolds	manifold	NOUN
ejpam-5951	387	26	.	.	PUNCT
ejpam-5951	388	1	sahand	sahand	NOUN
ejpam-5951	388	2	communications	communication	NOUN
ejpam-5951	388	3	in	in	ADP
ejpam-5951	388	4	mathematical	mathematical	ADJ
ejpam-5951	388	5	analysis	analysis	NOUN
ejpam-5951	388	6	,	,	PUNCT
ejpam-5951	388	7	21(1):255	21(1):255	NUM
ejpam-5951	388	8	–	–	PUNCT
ejpam-5951	388	9	271	271	NUM
ejpam-5951	388	10	,	,	PUNCT
ejpam-5951	388	11	2024	2024	NUM
ejpam-5951	388	12	.	.	PUNCT
ejpam-5951	389	1	p.	p.	NOUN
ejpam-5951	389	2	patel	patel	PROPN
ejpam-5951	389	3	,	,	PUNCT
ejpam-5951	389	4	r.	r.	PROPN
ejpam-5951	389	5	shukla	shukla	PROPN
ejpam-5951	389	6	/	/	SYM
ejpam-5951	389	7	eur	eur	PROPN
ejpam-5951	389	8	.	.	PUNCT
ejpam-5951	390	1	j.	j.	PROPN
ejpam-5951	390	2	pure	pure	PROPN
ejpam-5951	390	3	appl	appl	PROPN
ejpam-5951	390	4	.	.	PROPN
ejpam-5951	390	5	math	math	PROPN
ejpam-5951	390	6	,	,	PUNCT
ejpam-5951	390	7	18	18	NUM
ejpam-5951	390	8	(	(	PUNCT
ejpam-5951	390	9	2	2	NUM
ejpam-5951	390	10	)	)	PUNCT
ejpam-5951	390	11	(	(	PUNCT
ejpam-5951	390	12	2025	2025	NUM
ejpam-5951	390	13	)	)	PUNCT
ejpam-5951	390	14	,	,	PUNCT
ejpam-5951	390	15	5951	5951	NUM
ejpam-5951	390	16	15	15	NUM
ejpam-5951	390	17	of	of	ADP
ejpam-5951	390	18	15	15	NUM
ejpam-5951	390	19	[	[	SYM
ejpam-5951	390	20	17	17	NUM
ejpam-5951	390	21	]	]	PUNCT
ejpam-5951	390	22	s.	s.	PROPN
ejpam-5951	390	23	chang	chang	PROPN
ejpam-5951	390	24	,	,	PUNCT
ejpam-5951	390	25	j.	j.	PROPN
ejpam-5951	390	26	c.	c.	PROPN
ejpam-5951	390	27	yao	yao	PROPN
ejpam-5951	390	28	,	,	PUNCT
ejpam-5951	390	29	l.	l.	PROPN
ejpam-5951	390	30	yang	yang	PROPN
ejpam-5951	390	31	,	,	PUNCT
ejpam-5951	390	32	c.	c.	PROPN
ejpam-5951	390	33	f.	f.	PROPN
ejpam-5951	390	34	wen	wen	PROPN
ejpam-5951	390	35	,	,	PUNCT
ejpam-5951	390	36	and	and	CCONJ
ejpam-5951	390	37	d.	d.	PROPN
ejpam-5951	390	38	p.	p.	PROPN
ejpam-5951	390	39	wu	wu	PROPN
ejpam-5951	390	40	.	.	PUNCT
ejpam-5951	391	1	convergence	convergence	NOUN
ejpam-5951	391	2	analysis	analysis	NOUN
ejpam-5951	391	3	for	for	ADP
ejpam-5951	391	4	variational	variational	ADJ
ejpam-5951	391	5	inclusion	inclusion	NOUN
ejpam-5951	391	6	problems	problem	NOUN
ejpam-5951	391	7	equilibrium	equilibrium	NOUN
ejpam-5951	391	8	problems	problem	NOUN
ejpam-5951	391	9	and	and	CCONJ
ejpam-5951	391	10	fixed	fix	VERB
ejpam-5951	391	11	point	point	NOUN
ejpam-5951	391	12	in	in	ADP
ejpam-5951	391	13	hadamard	hadamard	ADJ
ejpam-5951	391	14	manifolds	manifold	NOUN
ejpam-5951	391	15	.	.	PUNCT
ejpam-5951	392	1	numer	numer	PROPN
ejpam-5951	392	2	.	.	PUNCT
ejpam-5951	393	1	funct	funct	PROPN
ejpam-5951	393	2	.	.	PUNCT
ejpam-5951	394	1	anal	anal	PROPN
ejpam-5951	394	2	.	.	PUNCT
ejpam-5951	395	1	optim	optim	PROPN
ejpam-5951	395	2	.	.	PROPN
ejpam-5951	395	3	,	,	PUNCT
ejpam-5951	395	4	42(5):567–582	42(5):567–582	PROPN
ejpam-5951	395	5	,	,	PUNCT
ejpam-5951	395	6	2021	2021	NUM
ejpam-5951	395	7	.	.	PUNCT
ejpam-5951	396	1	[	[	X
ejpam-5951	396	2	18	18	NUM
ejpam-5951	396	3	]	]	PUNCT
ejpam-5951	396	4	t.	t.	PROPN
ejpam-5951	396	5	sakai	sakai	PROPN
ejpam-5951	396	6	.	.	PUNCT
ejpam-5951	397	1	riemannian	riemannian	ADJ
ejpam-5951	397	2	geometry	geometry	NOUN
ejpam-5951	397	3	,	,	PUNCT
ejpam-5951	397	4	volume	volume	NOUN
ejpam-5951	397	5	149	149	NUM
ejpam-5951	397	6	of	of	ADP
ejpam-5951	397	7	translations	translation	NOUN
ejpam-5951	397	8	of	of	ADP
ejpam-5951	397	9	mathematical	mathematical	ADJ
ejpam-5951	397	10	monographs	monograph	NOUN
ejpam-5951	397	11	.	.	PUNCT
ejpam-5951	398	1	american	american	PROPN
ejpam-5951	398	2	mathematical	mathematical	PROPN
ejpam-5951	398	3	society	society	NOUN
ejpam-5951	398	4	,	,	PUNCT
ejpam-5951	398	5	providence	providence	NOUN
ejpam-5951	398	6	,	,	PUNCT
ejpam-5951	398	7	ri	ri	NOUN
ejpam-5951	398	8	,	,	PUNCT
ejpam-5951	398	9	1996	1996	NUM
ejpam-5951	398	10	.	.	PUNCT
ejpam-5951	399	1	translated	translate	VERB
ejpam-5951	399	2	from	from	ADP
ejpam-5951	399	3	the	the	DET
ejpam-5951	399	4	1992	1992	NUM
ejpam-5951	399	5	japanese	japanese	PROPN
ejpam-5951	399	6	original	original	NOUN
ejpam-5951	399	7	by	by	ADP
ejpam-5951	399	8	the	the	DET
ejpam-5951	399	9	author	author	NOUN
ejpam-5951	399	10	.	.	PUNCT
ejpam-5951	400	1	[	[	X
ejpam-5951	400	2	19	19	NUM
ejpam-5951	400	3	]	]	X
ejpam-5951	400	4	c.	c.	PROPN
ejpam-5951	400	5	li	li	PROPN
ejpam-5951	400	6	,	,	PUNCT
ejpam-5951	400	7	g.	g.	PROPN
ejpam-5951	400	8	lópez	lópez	PROPN
ejpam-5951	400	9	,	,	PUNCT
ejpam-5951	400	10	v.	v.	ADP
ejpam-5951	400	11	mart́ın	mart́ın	NOUN
ejpam-5951	400	12	-	-	PUNCT
ejpam-5951	400	13	márquez	márquez	NOUN
ejpam-5951	400	14	,	,	PUNCT
ejpam-5951	400	15	and	and	CCONJ
ejpam-5951	400	16	j.	j.	PROPN
ejpam-5951	400	17	h.	h.	PROPN
ejpam-5951	400	18	wang	wang	PROPN
ejpam-5951	400	19	.	.	PUNCT
ejpam-5951	401	1	resolvents	resolvent	NOUN
ejpam-5951	401	2	of	of	ADP
ejpam-5951	401	3	set	set	NOUN
ejpam-5951	401	4	-	-	PUNCT
ejpam-5951	401	5	valued	value	VERB
ejpam-5951	401	6	monotone	monotone	ADJ
ejpam-5951	401	7	vector	vector	NOUN
ejpam-5951	401	8	fields	field	NOUN
ejpam-5951	401	9	in	in	ADP
ejpam-5951	401	10	hadamard	hadamard	ADJ
ejpam-5951	401	11	manifolds	manifold	NOUN
ejpam-5951	401	12	.	.	PUNCT
ejpam-5951	402	1	set	set	NOUN
ejpam-5951	402	2	-	-	PUNCT
ejpam-5951	402	3	valued	value	VERB
ejpam-5951	402	4	var	var	NOUN
ejpam-5951	402	5	.	.	PUNCT
ejpam-5951	403	1	anal	anal	PROPN
ejpam-5951	403	2	.	.	PUNCT
ejpam-5951	403	3	,	,	PUNCT
ejpam-5951	403	4	19(3):361	19(3):361	NOUN
ejpam-5951	403	5	–	–	PUNCT
ejpam-5951	403	6	383	383	NUM
ejpam-5951	403	7	,	,	PUNCT
ejpam-5951	403	8	2011	2011	NUM
ejpam-5951	403	9	.	.	PUNCT
ejpam-5951	404	1	[	[	X
ejpam-5951	404	2	20	20	NUM
ejpam-5951	404	3	]	]	PUNCT
ejpam-5951	404	4	m.	m.	PROPN
ejpam-5951	404	5	r.	r.	PROPN
ejpam-5951	404	6	bridson	bridson	PROPN
ejpam-5951	404	7	and	and	CCONJ
ejpam-5951	404	8	a	a	DET
ejpam-5951	404	9	haefliger	haefliger	NOUN
ejpam-5951	404	10	.	.	PUNCT
ejpam-5951	405	1	metric	metric	ADJ
ejpam-5951	405	2	spaces	space	NOUN
ejpam-5951	405	3	of	of	ADP
ejpam-5951	405	4	non	non	ADJ
ejpam-5951	405	5	-	-	ADJ
ejpam-5951	405	6	positive	positive	ADJ
ejpam-5951	405	7	curvature	curvature	NOUN
ejpam-5951	405	8	,	,	PUNCT
ejpam-5951	405	9	volume	volume	NOUN
ejpam-5951	405	10	319	319	NUM
ejpam-5951	405	11	of	of	ADP
ejpam-5951	405	12	grundlehren	grundlehren	PROPN
ejpam-5951	405	13	der	der	PROPN
ejpam-5951	405	14	mathematischen	mathematischen	PROPN
ejpam-5951	405	15	wissenschaften	wissenschaften	PROPN
ejpam-5951	405	16	[	[	X
ejpam-5951	405	17	fundamental	fundamental	ADJ
ejpam-5951	405	18	principles	principle	NOUN
ejpam-5951	405	19	of	of	ADP
ejpam-5951	405	20	mathematical	mathematical	ADJ
ejpam-5951	405	21	sciences	science	NOUN
ejpam-5951	405	22	]	]	PUNCT
ejpam-5951	405	23	.	.	PUNCT
ejpam-5951	406	1	springer	springer	NOUN
ejpam-5951	406	2	-	-	PUNCT
ejpam-5951	406	3	verlag	verlag	PROPN
ejpam-5951	406	4	,	,	PUNCT
ejpam-5951	406	5	berlin	berlin	PROPN
ejpam-5951	406	6	,	,	PUNCT
ejpam-5951	406	7	1999	1999	NUM
ejpam-5951	406	8	.	.	PUNCT
ejpam-5951	407	1	[	[	X
ejpam-5951	407	2	21	21	NUM
ejpam-5951	407	3	]	]	X
ejpam-5951	407	4	q.	q.	PROPN
ejpam-5951	407	5	h.	h.	PROPN
ejpam-5951	407	6	ansari	ansari	PROPN
ejpam-5951	407	7	,	,	PUNCT
ejpam-5951	407	8	f.	f.	PROPN
ejpam-5951	407	9	babu	babu	PROPN
ejpam-5951	407	10	,	,	PUNCT
ejpam-5951	407	11	and	and	CCONJ
ejpam-5951	407	12	d.	d.	PROPN
ejpam-5951	407	13	r.	r.	PROPN
ejpam-5951	407	14	sahu	sahu	PROPN
ejpam-5951	407	15	.	.	PUNCT
ejpam-5951	408	1	iterative	iterative	ADJ
ejpam-5951	408	2	algorithms	algorithm	NOUN
ejpam-5951	408	3	for	for	ADP
ejpam-5951	408	4	system	system	NOUN
ejpam-5951	408	5	of	of	ADP
ejpam-5951	408	6	variational	variational	ADJ
ejpam-5951	408	7	inclusions	inclusion	NOUN
ejpam-5951	408	8	in	in	ADP
ejpam-5951	408	9	hadamard	hadamard	ADJ
ejpam-5951	408	10	manifolds	manifold	NOUN
ejpam-5951	408	11	.	.	PUNCT
ejpam-5951	409	1	acta	acta	PROPN
ejpam-5951	409	2	math	math	PROPN
ejpam-5951	409	3	.	.	PUNCT
ejpam-5951	410	1	sci	sci	PROPN
ejpam-5951	410	2	.	.	PUNCT
ejpam-5951	410	3	ser	ser	PROPN
ejpam-5951	410	4	.	.	PUNCT
ejpam-5951	411	1	b	b	PROPN
ejpam-5951	411	2	(	(	PUNCT
ejpam-5951	411	3	engl	engl	PROPN
ejpam-5951	411	4	.	.	PUNCT
ejpam-5951	412	1	ed	ed	NOUN
ejpam-5951	412	2	.	.	PUNCT
ejpam-5951	412	3	)	)	PUNCT
ejpam-5951	412	4	,	,	PUNCT
ejpam-5951	412	5	42(4):1333	42(4):1333	PROPN
ejpam-5951	412	6	–	–	PUNCT
ejpam-5951	412	7	1356	1356	NUM
ejpam-5951	412	8	,	,	PUNCT
ejpam-5951	412	9	2022	2022	NUM
ejpam-5951	412	10	.	.	PUNCT
ejpam-5951	413	1	[	[	X
ejpam-5951	413	2	22	22	NUM
ejpam-5951	413	3	]	]	PUNCT
ejpam-5951	414	1	s.	s.	PROPN
ejpam-5951	414	2	z.	z.	PROPN
ejpam-5951	414	3	németh	németh	PROPN
ejpam-5951	414	4	.	.	PROPN
ejpam-5951	414	5	monotonicity	monotonicity	NOUN
ejpam-5951	414	6	of	of	ADP
ejpam-5951	414	7	the	the	DET
ejpam-5951	414	8	complementary	complementary	ADJ
ejpam-5951	414	9	vector	vector	NOUN
ejpam-5951	414	10	field	field	NOUN
ejpam-5951	414	11	of	of	ADP
ejpam-5951	414	12	a	a	DET
ejpam-5951	414	13	nonexpansive	nonexpansive	ADJ
ejpam-5951	414	14	map	map	NOUN
ejpam-5951	414	15	.	.	PUNCT
ejpam-5951	415	1	acta	acta	PROPN
ejpam-5951	415	2	math	math	PROPN
ejpam-5951	415	3	.	.	PUNCT
ejpam-5951	416	1	hungar	hungar	PROPN
ejpam-5951	416	2	.	.	PUNCT
ejpam-5951	416	3	,	,	PUNCT
ejpam-5951	416	4	84(3):189–197	84(3):189–197	PROPN
ejpam-5951	416	5	,	,	PUNCT
ejpam-5951	416	6	1999	1999	NUM
ejpam-5951	416	7	.	.	PUNCT
ejpam-5951	417	1	[	[	X
ejpam-5951	417	2	23	23	NUM
ejpam-5951	417	3	]	]	PUNCT
ejpam-5951	417	4	j.	j.	PROPN
ejpam-5951	417	5	x.	x.	PROPN
ejpam-5951	417	6	da	da	PROPN
ejpam-5951	417	7	cruz	cruz	PROPN
ejpam-5951	417	8	neto	neto	PROPN
ejpam-5951	417	9	,	,	PUNCT
ejpam-5951	417	10	o.	o.	PROPN
ejpam-5951	417	11	p.	p.	PROPN
ejpam-5951	417	12	ferreira	ferreira	PROPN
ejpam-5951	417	13	,	,	PUNCT
ejpam-5951	417	14	and	and	CCONJ
ejpam-5951	417	15	l.	l.	PROPN
ejpam-5951	417	16	r.	r.	PROPN
ejpam-5951	417	17	lucambio	lucambio	PROPN
ejpam-5951	417	18	pérez	pérez	PROPN
ejpam-5951	417	19	.	.	PUNCT
ejpam-5951	418	1	monotone	monotone	ADJ
ejpam-5951	418	2	point	point	NOUN
ejpam-5951	418	3	-	-	PUNCT
ejpam-5951	418	4	to	to	AUX
ejpam-5951	418	5	-	-	PUNCT
ejpam-5951	418	6	set	set	VERB
ejpam-5951	418	7	vector	vector	NOUN
ejpam-5951	418	8	fields	field	NOUN
ejpam-5951	418	9	.	.	PUNCT
ejpam-5951	419	1	balkan	balkan	PROPN
ejpam-5951	419	2	journal	journal	NOUN
ejpam-5951	419	3	of	of	ADP
ejpam-5951	419	4	geometry	geometry	NOUN
ejpam-5951	419	5	and	and	CCONJ
ejpam-5951	419	6	its	its	PRON
ejpam-5951	419	7	applications	application	NOUN
ejpam-5951	419	8	,	,	PUNCT
ejpam-5951	419	9	5(1):69–80	5(1):69–80	NUM
ejpam-5951	419	10	,	,	PUNCT
ejpam-5951	419	11	2000	2000	NUM
ejpam-5951	419	12	.	.	PUNCT
ejpam-5951	420	1	[	[	X
ejpam-5951	420	2	24	24	NUM
ejpam-5951	420	3	]	]	X
ejpam-5951	420	4	s.	s.	PROPN
ejpam-5951	420	5	baiya	baiya	PROPN
ejpam-5951	420	6	and	and	CCONJ
ejpam-5951	420	7	k.	k.	PROPN
ejpam-5951	420	8	ungchittrakool	ungchittrakool	PROPN
ejpam-5951	420	9	.	.	PUNCT
ejpam-5951	421	1	modified	modify	VERB
ejpam-5951	421	2	inertial	inertial	ADJ
ejpam-5951	421	3	mann	mann	PROPN
ejpam-5951	421	4	’s	’s	PART
ejpam-5951	421	5	algorithm	algorithm	NOUN
ejpam-5951	421	6	and	and	CCONJ
ejpam-5951	421	7	inertial	inertial	ADJ
ejpam-5951	421	8	hybrid	hybrid	ADJ
ejpam-5951	421	9	algorithm	algorithm	NOUN
ejpam-5951	421	10	for	for	ADP
ejpam-5951	421	11	k	k	ADJ
ejpam-5951	421	12	-	-	ADJ
ejpam-5951	421	13	strict	strict	ADJ
ejpam-5951	421	14	pseudo	pseudo	NOUN
ejpam-5951	421	15	-	-	ADJ
ejpam-5951	421	16	contractive	contractive	ADJ
ejpam-5951	421	17	mappings	mapping	NOUN
ejpam-5951	421	18	.	.	PUNCT
ejpam-5951	422	1	carpathian	carpathian	PROPN
ejpam-5951	422	2	j.	j.	PROPN
ejpam-5951	422	3	math	math	PROPN
ejpam-5951	422	4	.	.	PUNCT
ejpam-5951	422	5	,	,	PUNCT
ejpam-5951	423	1	39(1):27–43	39(1):27–43	NUM
ejpam-5951	423	2	,	,	PUNCT
ejpam-5951	423	3	2023	2023	NUM
ejpam-5951	423	4	.	.	PUNCT