id	sid	tid	token	lemma	pos
ejpam-6441	1	1	european	european	PROPN
ejpam-6441	1	2	journal	journal	PROPN
ejpam-6441	1	3	of	of	ADP
ejpam-6441	1	4	pure	pure	ADJ
ejpam-6441	1	5	and	and	CCONJ
ejpam-6441	1	6	applied	applied	ADJ
ejpam-6441	1	7	mathematics	mathematic	NOUN
ejpam-6441	1	8	2025	2025	NUM
ejpam-6441	1	9	,	,	PUNCT
ejpam-6441	1	10	vol	vol	NOUN
ejpam-6441	1	11	.	.	PROPN
ejpam-6441	1	12	18	18	NUM
ejpam-6441	1	13	,	,	PUNCT
ejpam-6441	1	14	issue	issue	NOUN
ejpam-6441	1	15	4	4	NUM
ejpam-6441	1	16	,	,	PUNCT
ejpam-6441	1	17	article	article	NOUN
ejpam-6441	1	18	number	number	NOUN
ejpam-6441	1	19	6441	6441	NUM
ejpam-6441	1	20	issn	issn	VERB
ejpam-6441	1	21	1307	1307	NUM
ejpam-6441	1	22	-	-	SYM
ejpam-6441	1	23	5543	5543	NUM
ejpam-6441	1	24	–	–	PUNCT
ejpam-6441	1	25	ejpam.com	ejpam.com	X
ejpam-6441	1	26	published	publish	VERB
ejpam-6441	1	27	by	by	ADP
ejpam-6441	1	28	new	new	PROPN
ejpam-6441	1	29	york	york	PROPN
ejpam-6441	1	30	business	business	PROPN
ejpam-6441	1	31	global	global	PROPN
ejpam-6441	1	32	the	the	DET
ejpam-6441	1	33	existence	existence	NOUN
ejpam-6441	1	34	of	of	ADP
ejpam-6441	1	35	solutions	solution	NOUN
ejpam-6441	1	36	for	for	ADP
ejpam-6441	1	37	second	second	ADJ
ejpam-6441	1	38	-	-	PUNCT
ejpam-6441	1	39	order	order	NOUN
ejpam-6441	1	40	differential	differential	ADJ
ejpam-6441	1	41	inclusions	inclusion	NOUN
ejpam-6441	1	42	under	under	ADP
ejpam-6441	1	43	almost	almost	ADV
ejpam-6441	1	44	fisher	fisher	NOUN
ejpam-6441	1	45	-	-	PUNCT
ejpam-6441	1	46	type	type	NOUN
ejpam-6441	1	47	multivalued	multivalue	VERB
ejpam-6441	1	48	f	f	PROPN
ejpam-6441	1	49	-contractions	-contraction	NOUN
ejpam-6441	1	50	in	in	ADP
ejpam-6441	1	51	metric	metric	ADJ
ejpam-6441	1	52	spaces	space	NOUN
ejpam-6441	1	53	mustafa	mustafa	PROPN
ejpam-6441	1	54	mudhesh1,∗	mudhesh1,∗	PROPN
ejpam-6441	1	55	,	,	PUNCT
ejpam-6441	1	56	muhammad	muhammad	PROPN
ejpam-6441	1	57	arshad1	arshad1	PROPN
ejpam-6441	1	58	,	,	PUNCT
ejpam-6441	1	59	aftab	aftab	PROPN
ejpam-6441	1	60	hussain2	hussain2	PROPN
ejpam-6441	1	61	,	,	PUNCT
ejpam-6441	1	62	hamed	hamed	PROPN
ejpam-6441	1	63	alsulami2	alsulami2	PROPN
ejpam-6441	1	64	1	1	NUM
ejpam-6441	1	65	department	department	NOUN
ejpam-6441	1	66	of	of	ADP
ejpam-6441	1	67	mathematics	mathematic	NOUN
ejpam-6441	1	68	,	,	PUNCT
ejpam-6441	1	69	international	international	ADJ
ejpam-6441	1	70	islamic	islamic	PROPN
ejpam-6441	1	71	university	university	PROPN
ejpam-6441	1	72	,	,	PUNCT
ejpam-6441	1	73	h-10	h-10	PROPN
ejpam-6441	1	74	,	,	PUNCT
ejpam-6441	1	75	islamabad	islamabad	NOUN
ejpam-6441	1	76	44000	44000	NUM
ejpam-6441	1	77	,	,	PUNCT
ejpam-6441	1	78	pakistan	pakistan	PROPN
ejpam-6441	1	79	2	2	NUM
ejpam-6441	1	80	department	department	NOUN
ejpam-6441	1	81	of	of	ADP
ejpam-6441	1	82	mathematics	mathematic	NOUN
ejpam-6441	1	83	,	,	PUNCT
ejpam-6441	1	84	king	king	PROPN
ejpam-6441	1	85	abdulaziz	abdulaziz	PROPN
ejpam-6441	1	86	university	university	PROPN
ejpam-6441	1	87	,	,	PUNCT
ejpam-6441	1	88	jeddah	jeddah	PROPN
ejpam-6441	1	89	,	,	PUNCT
ejpam-6441	1	90	saudi	saudi	PROPN
ejpam-6441	1	91	arabia	arabia	PROPN
ejpam-6441	1	92	abstract	abstract	NOUN
ejpam-6441	1	93	.	.	PUNCT
ejpam-6441	2	1	this	this	DET
ejpam-6441	2	2	paper	paper	NOUN
ejpam-6441	2	3	presents	present	VERB
ejpam-6441	2	4	novel	novel	NOUN
ejpam-6441	2	5	fixed	fix	VERB
ejpam-6441	2	6	point	point	NOUN
ejpam-6441	2	7	(	(	PUNCT
ejpam-6441	2	8	fp	fp	X
ejpam-6441	2	9	)	)	PUNCT
ejpam-6441	2	10	theorems	theorem	NOUN
ejpam-6441	2	11	for	for	ADP
ejpam-6441	2	12	a	a	DET
ejpam-6441	2	13	specific	specific	ADJ
ejpam-6441	2	14	class	class	NOUN
ejpam-6441	2	15	of	of	ADP
ejpam-6441	2	16	multivalued	multivalued	ADJ
ejpam-6441	2	17	contractions	contraction	NOUN
ejpam-6441	2	18	,	,	PUNCT
ejpam-6441	2	19	referred	refer	VERB
ejpam-6441	2	20	to	to	ADP
ejpam-6441	2	21	as	as	ADP
ejpam-6441	2	22	”	"	PUNCT
ejpam-6441	2	23	almost	almost	ADV
ejpam-6441	2	24	fisher	fisher	NOUN
ejpam-6441	2	25	-	-	PUNCT
ejpam-6441	2	26	type	type	NOUN
ejpam-6441	2	27	multivalued	multivalue	VERB
ejpam-6441	2	28	f	f	PROPN
ejpam-6441	2	29	-contractions	-contraction	NOUN
ejpam-6441	2	30	”	"	PUNCT
ejpam-6441	2	31	within	within	ADP
ejpam-6441	2	32	complete	complete	ADJ
ejpam-6441	2	33	metric	metric	ADJ
ejpam-6441	2	34	spaces	space	NOUN
ejpam-6441	2	35	(	(	PUNCT
ejpam-6441	2	36	mss	mss	PROPN
ejpam-6441	2	37	)	)	PUNCT
ejpam-6441	2	38	endowed	endow	VERB
ejpam-6441	2	39	with	with	ADP
ejpam-6441	2	40	a	a	DET
ejpam-6441	2	41	γ	γ	NOUN
ejpam-6441	2	42	-	-	ADJ
ejpam-6441	2	43	transitive	transitive	ADJ
ejpam-6441	2	44	binary	binary	ADJ
ejpam-6441	2	45	relation	relation	NOUN
ejpam-6441	2	46	ℜ.	ℜ.	PROPN
ejpam-6441	2	47	these	these	DET
ejpam-6441	2	48	theorems	theorem	NOUN
ejpam-6441	2	49	establish	establish	VERB
ejpam-6441	2	50	the	the	DET
ejpam-6441	2	51	existence	existence	NOUN
ejpam-6441	2	52	of	of	ADP
ejpam-6441	2	53	fps	fps	NOUN
ejpam-6441	2	54	for	for	ADP
ejpam-6441	2	55	such	such	ADJ
ejpam-6441	2	56	contractions	contraction	NOUN
ejpam-6441	2	57	and	and	CCONJ
ejpam-6441	2	58	explore	explore	VERB
ejpam-6441	2	59	their	their	PRON
ejpam-6441	2	60	intrinsic	intrinsic	ADJ
ejpam-6441	2	61	properties	property	NOUN
ejpam-6441	2	62	.	.	PUNCT
ejpam-6441	3	1	illustrative	illustrative	ADJ
ejpam-6441	3	2	examples	example	NOUN
ejpam-6441	3	3	are	be	AUX
ejpam-6441	3	4	provided	provide	VERB
ejpam-6441	3	5	to	to	PART
ejpam-6441	3	6	demonstrate	demonstrate	VERB
ejpam-6441	3	7	the	the	DET
ejpam-6441	3	8	applicability	applicability	NOUN
ejpam-6441	3	9	and	and	CCONJ
ejpam-6441	3	10	effectiveness	effectiveness	NOUN
ejpam-6441	3	11	of	of	ADP
ejpam-6441	3	12	the	the	DET
ejpam-6441	3	13	proposed	propose	VERB
ejpam-6441	3	14	results	result	NOUN
ejpam-6441	3	15	.	.	PUNCT
ejpam-6441	4	1	an	an	DET
ejpam-6441	4	2	application	application	NOUN
ejpam-6441	4	3	to	to	ADP
ejpam-6441	4	4	second	second	ADJ
ejpam-6441	4	5	-	-	PUNCT
ejpam-6441	4	6	order	order	NOUN
ejpam-6441	4	7	differential	differential	ADJ
ejpam-6441	4	8	inclusions	inclusion	NOUN
ejpam-6441	4	9	(	(	PUNCT
ejpam-6441	4	10	sodis	sodi	NOUN
ejpam-6441	4	11	)	)	PUNCT
ejpam-6441	4	12	is	be	AUX
ejpam-6441	4	13	given	give	VERB
ejpam-6441	4	14	under	under	ADP
ejpam-6441	4	15	these	these	DET
ejpam-6441	4	16	contractions	contraction	NOUN
ejpam-6441	4	17	.	.	PUNCT
ejpam-6441	5	1	2020	2020	NUM
ejpam-6441	5	2	mathematics	mathematic	NOUN
ejpam-6441	5	3	subject	subject	NOUN
ejpam-6441	5	4	classifications	classification	NOUN
ejpam-6441	5	5	:	:	PUNCT
ejpam-6441	5	6	47h10	47h10	NUM
ejpam-6441	5	7	,	,	PUNCT
ejpam-6441	5	8	47h09	47h09	NUM
ejpam-6441	5	9	key	key	ADJ
ejpam-6441	5	10	words	word	NOUN
ejpam-6441	5	11	and	and	CCONJ
ejpam-6441	5	12	phrases	phrase	NOUN
ejpam-6441	5	13	:	:	PUNCT
ejpam-6441	5	14	fixed	fix	VERB
ejpam-6441	5	15	point	point	NOUN
ejpam-6441	5	16	,	,	PUNCT
ejpam-6441	5	17	metric	metric	ADJ
ejpam-6441	5	18	space	space	NOUN
ejpam-6441	5	19	,	,	PUNCT
ejpam-6441	5	20	almost	almost	ADV
ejpam-6441	5	21	fisher	fisher	NOUN
ejpam-6441	5	22	-	-	PUNCT
ejpam-6441	5	23	type	type	NOUN
ejpam-6441	5	24	contraction	contraction	NOUN
ejpam-6441	5	25	,	,	PUNCT
ejpam-6441	5	26	binary	binary	PROPN
ejpam-6441	5	27	relation	relation	NOUN
ejpam-6441	5	28	,	,	PUNCT
ejpam-6441	5	29	second	second	ADJ
ejpam-6441	5	30	-	-	PUNCT
ejpam-6441	5	31	order	order	NOUN
ejpam-6441	5	32	differential	differential	ADJ
ejpam-6441	5	33	inclusion	inclusion	NOUN
ejpam-6441	5	34	1	1	NUM
ejpam-6441	5	35	.	.	PUNCT
ejpam-6441	5	36	introduction	introduction	NOUN
ejpam-6441	5	37	and	and	CCONJ
ejpam-6441	5	38	preliminaries	preliminary	NOUN
ejpam-6441	5	39	in	in	ADP
ejpam-6441	5	40	recent	recent	ADJ
ejpam-6441	5	41	years	year	NOUN
ejpam-6441	5	42	,	,	PUNCT
ejpam-6441	5	43	fixed	fix	VERB
ejpam-6441	5	44	point	point	NOUN
ejpam-6441	5	45	(	(	PUNCT
ejpam-6441	5	46	fp	fp	X
ejpam-6441	5	47	)	)	PUNCT
ejpam-6441	5	48	theory	theory	NOUN
ejpam-6441	5	49	has	have	AUX
ejpam-6441	5	50	undergone	undergo	VERB
ejpam-6441	5	51	substantial	substantial	ADJ
ejpam-6441	5	52	development	development	NOUN
ejpam-6441	5	53	with	with	ADP
ejpam-6441	5	54	various	various	ADJ
ejpam-6441	5	55	generalizations	generalization	NOUN
ejpam-6441	5	56	and	and	CCONJ
ejpam-6441	5	57	refinements	refinement	NOUN
ejpam-6441	5	58	of	of	ADP
ejpam-6441	5	59	the	the	DET
ejpam-6441	5	60	classical	classical	ADJ
ejpam-6441	5	61	banach	banach	NOUN
ejpam-6441	5	62	contraction	contraction	NOUN
ejpam-6441	5	63	principle	principle	NOUN
ejpam-6441	5	64	(	(	PUNCT
ejpam-6441	5	65	bcp	bcp	PROPN
ejpam-6441	5	66	)	)	PUNCT
ejpam-6441	5	67	.	.	PUNCT
ejpam-6441	6	1	in	in	ADP
ejpam-6441	6	2	1977	1977	NUM
ejpam-6441	6	3	,	,	PUNCT
ejpam-6441	6	4	jaggi	jaggi	NOUN
ejpam-6441	6	5	[	[	X
ejpam-6441	6	6	1	1	NUM
ejpam-6441	6	7	]	]	PUNCT
ejpam-6441	6	8	generalized	generalize	VERB
ejpam-6441	6	9	the	the	DET
ejpam-6441	6	10	bcp	bcp	NOUN
ejpam-6441	6	11	in	in	ADP
ejpam-6441	6	12	complete	complete	ADJ
ejpam-6441	6	13	mss	mss	PROPN
ejpam-6441	6	14	with	with	ADP
ejpam-6441	6	15	the	the	DET
ejpam-6441	6	16	condition	condition	NOUN
ejpam-6441	6	17	:	:	PUNCT
ejpam-6441	6	18	∀ς1	∀ς1	NOUN
ejpam-6441	6	19	,	,	PUNCT
ejpam-6441	6	20	ς2	ς2	PROPN
ejpam-6441	6	21	∈	∈	PROPN
ejpam-6441	6	22	∆ℜ	∆ℜ	NOUN
ejpam-6441	6	23	,	,	PUNCT
ejpam-6441	6	24	∃λ1	∃λ1	NOUN
ejpam-6441	6	25	,	,	PUNCT
ejpam-6441	6	26	λ2	λ2	PROPN
ejpam-6441	6	27	∈	∈	PROPN
ejpam-6441	7	1	[	[	X
ejpam-6441	7	2	0,∞	0,∞	NOUN
ejpam-6441	7	3	)	)	PUNCT
ejpam-6441	7	4	with	with	ADP
ejpam-6441	7	5	λ1+λ2	λ1+λ2	PROPN
ejpam-6441	7	6	<	<	X
ejpam-6441	7	7	1	1	NUM
ejpam-6441	8	1	such	such	ADJ
ejpam-6441	8	2	that	that	SCONJ
ejpam-6441	8	3	d	d	NOUN
ejpam-6441	8	4	(	(	PUNCT
ejpam-6441	8	5	γς1,γς2	γς1,γς2	X
ejpam-6441	8	6	)	)	PUNCT
ejpam-6441	8	7	≤	≤	NOUN
ejpam-6441	8	8	λ1d	λ1d	PUNCT
ejpam-6441	8	9	(	(	PUNCT
ejpam-6441	8	10	ς1	ς1	NOUN
ejpam-6441	8	11	,	,	PUNCT
ejpam-6441	8	12	ς2)+λ2	ς2)+λ2	NUM
ejpam-6441	8	13	d(ς1,γς1).d(ς2,γς2	d(ς1,γς1).d(ς2,γς2	PROPN
ejpam-6441	8	14	)	)	PUNCT
ejpam-6441	8	15	d(ς1,ς2	d(ς1,ς2	NOUN
ejpam-6441	8	16	)	)	PUNCT
ejpam-6441	8	17	,	,	PUNCT
ejpam-6441	8	18	where	where	SCONJ
ejpam-6441	8	19	the	the	DET
ejpam-6441	8	20	map	map	NOUN
ejpam-6441	8	21	γ	γ	X
ejpam-6441	8	22	:	:	PUNCT
ejpam-6441	8	23	∆ℜ	∆ℜ	NOUN
ejpam-6441	8	24	→	→	SYM
ejpam-6441	8	25	∆ℜ	∆ℜ	PROPN
ejpam-6441	8	26	has	have	VERB
ejpam-6441	8	27	a	a	DET
ejpam-6441	8	28	unique	unique	ADJ
ejpam-6441	8	29	fixed	fix	VERB
ejpam-6441	8	30	point	point	NOUN
ejpam-6441	8	31	(	(	PUNCT
ejpam-6441	8	32	ufp	ufp	NOUN
ejpam-6441	8	33	)	)	PUNCT
ejpam-6441	8	34	ς∗	ς∗	PROPN
ejpam-6441	8	35	∈	∈	PROPN
ejpam-6441	8	36	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	8	37	karapinar	karapinar	NOUN
ejpam-6441	9	1	[	[	X
ejpam-6441	9	2	2	2	NUM
ejpam-6441	9	3	]	]	PUNCT
ejpam-6441	9	4	further	far	ADV
ejpam-6441	9	5	enriched	enrich	VERB
ejpam-6441	9	6	fp	fp	NOUN
ejpam-6441	9	7	theory	theory	NOUN
ejpam-6441	9	8	by	by	ADP
ejpam-6441	9	9	introducing	introduce	VERB
ejpam-6441	9	10	interpolative	interpolative	ADJ
ejpam-6441	9	11	-	-	PUNCT
ejpam-6441	9	12	type	type	NOUN
ejpam-6441	9	13	contractions	contraction	NOUN
ejpam-6441	9	14	,	,	PUNCT
ejpam-6441	9	15	establishing	establish	VERB
ejpam-6441	9	16	connections	connection	NOUN
ejpam-6441	9	17	with	with	ADP
ejpam-6441	9	18	interpolation	interpolation	NOUN
ejpam-6441	9	19	theory	theory	NOUN
ejpam-6441	9	20	,	,	PUNCT
ejpam-6441	9	21	as	as	SCONJ
ejpam-6441	9	22	explored	explore	VERB
ejpam-6441	9	23	in	in	ADP
ejpam-6441	9	24	related	related	ADJ
ejpam-6441	9	25	works	work	NOUN
ejpam-6441	9	26	,	,	PUNCT
ejpam-6441	9	27	which	which	PRON
ejpam-6441	9	28	was	be	AUX
ejpam-6441	9	29	also	also	ADV
ejpam-6441	9	30	discussed	discuss	VERB
ejpam-6441	9	31	in	in	ADP
ejpam-6441	9	32	[	[	X
ejpam-6441	9	33	3	3	NUM
ejpam-6441	9	34	,	,	PUNCT
ejpam-6441	9	35	4	4	NUM
ejpam-6441	9	36	]	]	PUNCT
ejpam-6441	9	37	.	.	PUNCT
ejpam-6441	10	1	karapinar	karapinar	NOUN
ejpam-6441	10	2	and	and	CCONJ
ejpam-6441	10	3	fulga	fulga	NOUN
ejpam-6441	11	1	[	[	X
ejpam-6441	11	2	5	5	NUM
ejpam-6441	11	3	]	]	PUNCT
ejpam-6441	11	4	introduced	introduce	VERB
ejpam-6441	11	5	a	a	DET
ejpam-6441	11	6	hybrid	hybrid	ADJ
ejpam-6441	11	7	contraction	contraction	NOUN
ejpam-6441	11	8	by	by	ADP
ejpam-6441	11	9	combining	combine	VERB
ejpam-6441	11	10	jaggi	jaggi	NOUN
ejpam-6441	11	11	-	-	PUNCT
ejpam-6441	11	12	type	type	NOUN
ejpam-6441	11	13	and	and	CCONJ
ejpam-6441	11	14	interpolative	interpolative	ADJ
ejpam-6441	11	15	-	-	PUNCT
ejpam-6441	11	16	type	type	NOUN
ejpam-6441	11	17	contractions	contraction	NOUN
ejpam-6441	11	18	.	.	PUNCT
ejpam-6441	12	1	in	in	ADP
ejpam-6441	12	2	2012	2012	NUM
ejpam-6441	12	3	,	,	PUNCT
ejpam-6441	12	4	wardowski	wardowski	VERB
ejpam-6441	12	5	[	[	X
ejpam-6441	12	6	6	6	NUM
ejpam-6441	12	7	]	]	PUNCT
ejpam-6441	12	8	introduced	introduce	VERB
ejpam-6441	12	9	the	the	DET
ejpam-6441	12	10	concept	concept	NOUN
ejpam-6441	12	11	of	of	ADP
ejpam-6441	12	12	f	f	PROPN
ejpam-6441	12	13	-contraction	-contraction	PROPN
ejpam-6441	12	14	as	as	ADP
ejpam-6441	12	15	an	an	DET
ejpam-6441	12	16	extension	extension	NOUN
ejpam-6441	12	17	of	of	ADP
ejpam-6441	12	18	the	the	DET
ejpam-6441	12	19	bcp	bcp	PROPN
ejpam-6441	12	20	.	.	PROPN
ejpam-6441	12	21	subsequent	subsequent	ADJ
ejpam-6441	12	22	works	work	NOUN
ejpam-6441	12	23	in	in	ADP
ejpam-6441	12	24	[	[	X
ejpam-6441	12	25	7	7	NUM
ejpam-6441	12	26	,	,	PUNCT
ejpam-6441	12	27	8	8	NUM
ejpam-6441	12	28	]	]	PUNCT
ejpam-6441	12	29	applied	apply	VERB
ejpam-6441	12	30	∗corresponding	∗corresponde	VERB
ejpam-6441	12	31	author	author	NOUN
ejpam-6441	12	32	.	.	PUNCT
ejpam-6441	13	1	doi	doi	NOUN
ejpam-6441	13	2	:	:	PUNCT
ejpam-6441	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6441	https://doi.org/10.29020/nybg.ejpam.v18i4.6441	PROPN
ejpam-6441	13	4	email	email	NOUN
ejpam-6441	13	5	addresses	address	NOUN
ejpam-6441	13	6	:	:	PUNCT
ejpam-6441	13	7	mustafa.phdma115@iiu.edu.pk	mustafa.phdma115@iiu.edu.pk	NUM
ejpam-6441	13	8	(	(	PUNCT
ejpam-6441	13	9	m.	m.	NOUN
ejpam-6441	13	10	mudhesh	mudhesh	PROPN
ejpam-6441	13	11	)	)	PUNCT
ejpam-6441	13	12	,	,	PUNCT
ejpam-6441	13	13	marshadzia@iiu.edu.pk	marshadzia@iiu.edu.pk	NOUN
ejpam-6441	13	14	(	(	PUNCT
ejpam-6441	13	15	m.	m.	PROPN
ejpam-6441	13	16	arshad	arshad	PROPN
ejpam-6441	13	17	)	)	PUNCT
ejpam-6441	13	18	,	,	PUNCT
ejpam-6441	13	19	aniassuirathka@kau.edu.sa	aniassuirathka@kau.edu.sa	PROPN
ejpam-6441	13	20	(	(	PUNCT
ejpam-6441	13	21	a.	a.	NOUN
ejpam-6441	13	22	hussain	hussain	PROPN
ejpam-6441	13	23	)	)	PUNCT
ejpam-6441	13	24	,	,	PUNCT
ejpam-6441	13	25	hhaalsalmi@kau.edu.sa	hhaalsalmi@kau.edu.sa	PROPN
ejpam-6441	13	26	(	(	PUNCT
ejpam-6441	13	27	h.	h.	PROPN
ejpam-6441	13	28	alsulami	alsulami	PROPN
ejpam-6441	13	29	)	)	PUNCT
ejpam-6441	13	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6441	14	1	1	1	NUM
ejpam-6441	14	2	copyright	copyright	NOUN
ejpam-6441	14	3	:	:	PUNCT
ejpam-6441	14	4	©	©	PROPN
ejpam-6441	14	5	2025	2025	NUM
ejpam-6441	14	6	the	the	DET
ejpam-6441	14	7	author(s	author(s	NOUN
ejpam-6441	14	8	)	)	PUNCT
ejpam-6441	14	9	.	.	PUNCT
ejpam-6441	15	1	(	(	PUNCT
ejpam-6441	15	2	cc	cc	NOUN
ejpam-6441	15	3	by	by	ADP
ejpam-6441	15	4	-	-	PUNCT
ejpam-6441	15	5	nc	nc	PROPN
ejpam-6441	15	6	4.0	4.0	NUM
ejpam-6441	15	7	)	)	PUNCT
ejpam-6441	15	8	m.	m.	NOUN
ejpam-6441	15	9	mudhesh	mudhesh	PROPN
ejpam-6441	15	10	et	et	PROPN
ejpam-6441	15	11	al	al	PROPN
ejpam-6441	15	12	.	.	PUNCT
ejpam-6441	15	13	/	/	SYM
ejpam-6441	15	14	eur	eur	PROPN
ejpam-6441	15	15	.	.	PUNCT
ejpam-6441	16	1	j.	j.	PROPN
ejpam-6441	16	2	pure	pure	PROPN
ejpam-6441	16	3	appl	appl	PROPN
ejpam-6441	16	4	.	.	PROPN
ejpam-6441	16	5	math	math	PROPN
ejpam-6441	16	6	,	,	PUNCT
ejpam-6441	16	7	18	18	NUM
ejpam-6441	16	8	(	(	PUNCT
ejpam-6441	16	9	4	4	NUM
ejpam-6441	16	10	)	)	PUNCT
ejpam-6441	16	11	(	(	PUNCT
ejpam-6441	16	12	2025	2025	NUM
ejpam-6441	16	13	)	)	PUNCT
ejpam-6441	16	14	,	,	PUNCT
ejpam-6441	16	15	6441	6441	NUM
ejpam-6441	16	16	2	2	NUM
ejpam-6441	16	17	of	of	ADP
ejpam-6441	16	18	21	21	NUM
ejpam-6441	16	19	these	these	DET
ejpam-6441	16	20	ideas	idea	NOUN
ejpam-6441	16	21	to	to	PART
ejpam-6441	16	22	combine	combine	VERB
ejpam-6441	16	23	the	the	DET
ejpam-6441	16	24	results	result	NOUN
ejpam-6441	16	25	of	of	ADP
ejpam-6441	16	26	wardowski	wardowski	NOUN
ejpam-6441	16	27	’s	’s	PART
ejpam-6441	16	28	cyclic	cyclic	ADJ
ejpam-6441	16	29	contraction	contraction	NOUN
ejpam-6441	16	30	operators	operator	NOUN
ejpam-6441	16	31	and	and	CCONJ
ejpam-6441	16	32	admissible	admissible	ADJ
ejpam-6441	16	33	mappings	mapping	NOUN
ejpam-6441	16	34	of	of	ADP
ejpam-6441	16	35	geraghty	geraghty	PROPN
ejpam-6441	16	36	f	f	PROPN
ejpam-6441	16	37	-contraction	-contraction	PROPN
ejpam-6441	16	38	,	,	PUNCT
ejpam-6441	16	39	producing	produce	VERB
ejpam-6441	16	40	new	new	ADJ
ejpam-6441	16	41	fp	fp	NOUN
ejpam-6441	16	42	theorems	theorem	NOUN
ejpam-6441	16	43	.	.	PUNCT
ejpam-6441	17	1	ali	ali	PROPN
ejpam-6441	17	2	et	et	PROPN
ejpam-6441	17	3	al	al	PROPN
ejpam-6441	17	4	.	.	PUNCT
ejpam-6441	18	1	[	[	X
ejpam-6441	18	2	9	9	NUM
ejpam-6441	18	3	]	]	PUNCT
ejpam-6441	18	4	discussed	discuss	VERB
ejpam-6441	18	5	new	new	ADJ
ejpam-6441	18	6	fp	fp	NOUN
ejpam-6441	18	7	results	result	NOUN
ejpam-6441	18	8	of	of	ADP
ejpam-6441	18	9	dynamic	dynamic	ADJ
ejpam-6441	18	10	process	process	NOUN
ejpam-6441	18	11	of	of	ADP
ejpam-6441	18	12	integral	integral	ADJ
ejpam-6441	18	13	ciric	ciric	ADJ
ejpam-6441	18	14	-	-	PUNCT
ejpam-6441	18	15	type	type	NOUN
ejpam-6441	18	16	f	f	PROPN
ejpam-6441	18	17	-contractions	-contraction	NOUN
ejpam-6441	18	18	setvalued	setvalue	VERB
ejpam-6441	18	19	mappings	mapping	NOUN
ejpam-6441	18	20	in	in	ADP
ejpam-6441	18	21	mss	mss	PROPN
ejpam-6441	18	22	.	.	PUNCT
ejpam-6441	18	23	nadler	nadler	PROPN
ejpam-6441	19	1	[	[	X
ejpam-6441	19	2	10	10	NUM
ejpam-6441	19	3	]	]	PUNCT
ejpam-6441	19	4	earlier	early	ADV
ejpam-6441	19	5	initiated	initiate	VERB
ejpam-6441	19	6	the	the	DET
ejpam-6441	19	7	study	study	NOUN
ejpam-6441	19	8	of	of	ADP
ejpam-6441	19	9	fps	fps	NOUN
ejpam-6441	19	10	for	for	ADP
ejpam-6441	19	11	multivalued	multivalued	ADJ
ejpam-6441	19	12	mappings	mapping	NOUN
ejpam-6441	19	13	.	.	PUNCT
ejpam-6441	20	1	notably	notably	ADV
ejpam-6441	20	2	,	,	PUNCT
ejpam-6441	20	3	recent	recent	ADJ
ejpam-6441	20	4	articles	article	NOUN
ejpam-6441	20	5	in	in	ADP
ejpam-6441	20	6	the	the	DET
ejpam-6441	20	7	field	field	NOUN
ejpam-6441	20	8	of	of	ADP
ejpam-6441	20	9	fp	fp	PROPN
ejpam-6441	20	10	theory	theory	NOUN
ejpam-6441	20	11	for	for	ADP
ejpam-6441	20	12	multivalued	multivalued	ADJ
ejpam-6441	20	13	mappings	mapping	NOUN
ejpam-6441	20	14	have	have	AUX
ejpam-6441	20	15	been	be	AUX
ejpam-6441	20	16	published	publish	VERB
ejpam-6441	20	17	,	,	PUNCT
ejpam-6441	20	18	providing	provide	VERB
ejpam-6441	20	19	valuable	valuable	ADJ
ejpam-6441	20	20	assistance	assistance	NOUN
ejpam-6441	20	21	to	to	ADP
ejpam-6441	20	22	researchers	researcher	NOUN
ejpam-6441	20	23	.	.	PUNCT
ejpam-6441	21	1	acar	acar	NOUN
ejpam-6441	21	2	and	and	CCONJ
ejpam-6441	21	3	altun	altun	NOUN
ejpam-6441	22	1	[	[	X
ejpam-6441	22	2	11	11	NUM
ejpam-6441	22	3	]	]	PUNCT
ejpam-6441	22	4	extended	extend	VERB
ejpam-6441	22	5	multivalued	multivalued	ADJ
ejpam-6441	22	6	f	f	PROPN
ejpam-6441	22	7	-contractions	-contraction	NOUN
ejpam-6441	22	8	with	with	ADP
ejpam-6441	22	9	δ	δ	NOUN
ejpam-6441	22	10	-	-	PUNCT
ejpam-6441	22	11	distance	distance	NOUN
ejpam-6441	22	12	and	and	CCONJ
ejpam-6441	22	13	established	establish	VERB
ejpam-6441	22	14	fp	fp	NOUN
ejpam-6441	22	15	results	result	NOUN
ejpam-6441	22	16	in	in	ADP
ejpam-6441	22	17	complete	complete	ADJ
ejpam-6441	22	18	mss	mss	PROPN
ejpam-6441	22	19	,	,	PUNCT
ejpam-6441	22	20	(	(	PUNCT
ejpam-6441	22	21	see	see	VERB
ejpam-6441	22	22	[	[	X
ejpam-6441	22	23	12	12	NUM
ejpam-6441	22	24	,	,	PUNCT
ejpam-6441	22	25	13	13	NUM
ejpam-6441	22	26	]	]	PUNCT
ejpam-6441	22	27	)	)	PUNCT
ejpam-6441	22	28	.	.	PUNCT
ejpam-6441	23	1	in	in	ADP
ejpam-6441	23	2	1980	1980	NUM
ejpam-6441	23	3	,	,	PUNCT
ejpam-6441	23	4	fisher	fisher	PROPN
ejpam-6441	23	5	[	[	X
ejpam-6441	23	6	14	14	NUM
ejpam-6441	23	7	]	]	PUNCT
ejpam-6441	23	8	explored	explore	VERB
ejpam-6441	23	9	new	new	ADJ
ejpam-6441	23	10	results	result	NOUN
ejpam-6441	23	11	that	that	PRON
ejpam-6441	23	12	generalized	generalize	VERB
ejpam-6441	23	13	the	the	DET
ejpam-6441	23	14	bcp	bcp	NOUN
ejpam-6441	23	15	by	by	ADP
ejpam-6441	23	16	employing	employ	VERB
ejpam-6441	23	17	a	a	DET
ejpam-6441	23	18	new	new	ADJ
ejpam-6441	23	19	rational	rational	ADJ
ejpam-6441	23	20	inequality	inequality	NOUN
ejpam-6441	23	21	,	,	PUNCT
ejpam-6441	23	22	∀ς1	∀ς1	NOUN
ejpam-6441	23	23	,	,	PUNCT
ejpam-6441	23	24	ς2	ς2	PROPN
ejpam-6441	23	25	∈	∈	PROPN
ejpam-6441	23	26	∆ℜ	∆ℜ	NOUN
ejpam-6441	23	27	,	,	PUNCT
ejpam-6441	23	28	∃λ1	∃λ1	NOUN
ejpam-6441	23	29	,	,	PUNCT
ejpam-6441	23	30	λ2	λ2	PROPN
ejpam-6441	23	31	∈	∈	PROPN
ejpam-6441	24	1	[	[	X
ejpam-6441	24	2	0,∞	0,∞	NOUN
ejpam-6441	24	3	)	)	PUNCT
ejpam-6441	24	4	such	such	ADJ
ejpam-6441	24	5	that	that	SCONJ
ejpam-6441	24	6	d	d	X
ejpam-6441	24	7	(	(	PUNCT
ejpam-6441	24	8	γς1,γς2	γς1,γς2	X
ejpam-6441	24	9	)	)	PUNCT
ejpam-6441	24	10	≤	≤	NOUN
ejpam-6441	24	11	λ1d	λ1d	PUNCT
ejpam-6441	24	12	(	(	PUNCT
ejpam-6441	24	13	ς1	ς1	NOUN
ejpam-6441	24	14	,	,	PUNCT
ejpam-6441	24	15	ς2	ς2	PROPN
ejpam-6441	24	16	)	)	PUNCT
ejpam-6441	24	17	+	+	NUM
ejpam-6441	24	18	λ2	λ2	NOUN
ejpam-6441	24	19	d(ς1,γς1).d(ς2,γς2	d(ς1,γς1).d(ς2,γς2	NOUN
ejpam-6441	24	20	)	)	PUNCT
ejpam-6441	24	21	1+d(ς1,ς2	1+d(ς1,ς2	NUM
ejpam-6441	24	22	)	)	PUNCT
ejpam-6441	24	23	,	,	PUNCT
ejpam-6441	24	24	broadening	broaden	VERB
ejpam-6441	24	25	fixed	fix	VERB
ejpam-6441	24	26	point	point	NOUN
ejpam-6441	24	27	theory	theory	NOUN
ejpam-6441	24	28	and	and	CCONJ
ejpam-6441	24	29	inspiring	inspire	VERB
ejpam-6441	24	30	further	further	ADJ
ejpam-6441	24	31	research	research	NOUN
ejpam-6441	24	32	on	on	ADP
ejpam-6441	24	33	generalized	generalized	ADJ
ejpam-6441	24	34	contractive	contractive	ADJ
ejpam-6441	24	35	mappings	mapping	NOUN
ejpam-6441	24	36	.	.	PUNCT
ejpam-6441	25	1	consequently	consequently	ADV
ejpam-6441	25	2	,	,	PUNCT
ejpam-6441	25	3	fisher	fisher	NOUN
ejpam-6441	25	4	-	-	PUNCT
ejpam-6441	25	5	type	type	NOUN
ejpam-6441	25	6	fcontractions	fcontraction	NOUN
ejpam-6441	25	7	and	and	CCONJ
ejpam-6441	25	8	jaggi	jaggi	NOUN
ejpam-6441	25	9	-	-	PUNCT
ejpam-6441	25	10	type	type	NOUN
ejpam-6441	25	11	f	f	NOUN
ejpam-6441	25	12	-	-	PUNCT
ejpam-6441	25	13	contractions	contraction	NOUN
ejpam-6441	25	14	are	be	AUX
ejpam-6441	25	15	important	important	ADJ
ejpam-6441	25	16	generalizations	generalization	NOUN
ejpam-6441	25	17	of	of	ADP
ejpam-6441	25	18	classical	classical	ADJ
ejpam-6441	25	19	bcs	bc	NOUN
ejpam-6441	25	20	within	within	ADP
ejpam-6441	25	21	fp	fp	PROPN
ejpam-6441	25	22	theory	theory	NOUN
ejpam-6441	25	23	,	,	PUNCT
ejpam-6441	25	24	particularly	particularly	ADV
ejpam-6441	25	25	for	for	ADP
ejpam-6441	25	26	multivalued	multivalued	ADJ
ejpam-6441	25	27	mappings	mapping	NOUN
ejpam-6441	25	28	.	.	PUNCT
ejpam-6441	26	1	by	by	ADP
ejpam-6441	26	2	incorporating	incorporate	VERB
ejpam-6441	26	3	functional	functional	ADJ
ejpam-6441	26	4	inequalities	inequality	NOUN
ejpam-6441	26	5	through	through	ADP
ejpam-6441	26	6	auxiliary	auxiliary	ADJ
ejpam-6441	26	7	functions	function	NOUN
ejpam-6441	26	8	(	(	PUNCT
ejpam-6441	26	9	f	f	NOUN
ejpam-6441	26	10	-	-	PUNCT
ejpam-6441	26	11	functions	function	NOUN
ejpam-6441	26	12	)	)	PUNCT
ejpam-6441	26	13	,	,	PUNCT
ejpam-6441	26	14	they	they	PRON
ejpam-6441	26	15	provide	provide	VERB
ejpam-6441	26	16	greater	great	ADJ
ejpam-6441	26	17	flexibility	flexibility	NOUN
ejpam-6441	26	18	in	in	ADP
ejpam-6441	26	19	defining	define	VERB
ejpam-6441	26	20	contraction	contraction	NOUN
ejpam-6441	26	21	conditions	condition	NOUN
ejpam-6441	26	22	,	,	PUNCT
ejpam-6441	26	23	making	make	VERB
ejpam-6441	26	24	them	they	PRON
ejpam-6441	26	25	applicable	applicable	ADJ
ejpam-6441	26	26	to	to	ADP
ejpam-6441	26	27	a	a	DET
ejpam-6441	26	28	broader	broad	ADJ
ejpam-6441	26	29	class	class	NOUN
ejpam-6441	26	30	of	of	ADP
ejpam-6441	26	31	problems	problem	NOUN
ejpam-6441	26	32	.	.	PUNCT
ejpam-6441	27	1	these	these	DET
ejpam-6441	27	2	contractions	contraction	NOUN
ejpam-6441	27	3	have	have	AUX
ejpam-6441	27	4	proven	prove	VERB
ejpam-6441	27	5	effective	effective	ADJ
ejpam-6441	27	6	in	in	ADP
ejpam-6441	27	7	establishing	establish	VERB
ejpam-6441	27	8	the	the	DET
ejpam-6441	27	9	existence	existence	NOUN
ejpam-6441	27	10	of	of	ADP
ejpam-6441	27	11	solutions	solution	NOUN
ejpam-6441	27	12	to	to	PART
ejpam-6441	27	13	nonlinear	nonlinear	ADJ
ejpam-6441	27	14	integral	integral	ADJ
ejpam-6441	27	15	equations	equation	NOUN
ejpam-6441	27	16	(	(	PUNCT
ejpam-6441	27	17	ies	ies	PROPN
ejpam-6441	27	18	)	)	PUNCT
ejpam-6441	27	19	,	,	PUNCT
ejpam-6441	27	20	differential	differential	ADJ
ejpam-6441	27	21	inclusions	inclusion	NOUN
ejpam-6441	27	22	,	,	PUNCT
ejpam-6441	27	23	and	and	CCONJ
ejpam-6441	27	24	equilibrium	equilibrium	NOUN
ejpam-6441	27	25	problems	problem	NOUN
ejpam-6441	27	26	.	.	PUNCT
ejpam-6441	28	1	they	they	PRON
ejpam-6441	28	2	play	play	VERB
ejpam-6441	28	3	a	a	DET
ejpam-6441	28	4	vital	vital	ADJ
ejpam-6441	28	5	role	role	NOUN
ejpam-6441	28	6	in	in	ADP
ejpam-6441	28	7	optimization	optimization	NOUN
ejpam-6441	28	8	theory	theory	NOUN
ejpam-6441	28	9	,	,	PUNCT
ejpam-6441	28	10	control	control	NOUN
ejpam-6441	28	11	systems	system	NOUN
ejpam-6441	28	12	,	,	PUNCT
ejpam-6441	28	13	fuzzy	fuzzy	ADJ
ejpam-6441	28	14	dynamics	dynamic	NOUN
ejpam-6441	28	15	,	,	PUNCT
ejpam-6441	28	16	game	game	NOUN
ejpam-6441	28	17	theory	theory	NOUN
ejpam-6441	28	18	,	,	PUNCT
ejpam-6441	28	19	and	and	CCONJ
ejpam-6441	28	20	fractal	fractal	ADV
ejpam-6441	28	21	-	-	PUNCT
ejpam-6441	28	22	based	base	VERB
ejpam-6441	28	23	image	image	NOUN
ejpam-6441	28	24	compression	compression	NOUN
ejpam-6441	28	25	.	.	PUNCT
ejpam-6441	29	1	moreover	moreover	ADV
ejpam-6441	29	2	,	,	PUNCT
ejpam-6441	29	3	they	they	PRON
ejpam-6441	29	4	are	be	AUX
ejpam-6441	29	5	instrumental	instrumental	ADJ
ejpam-6441	29	6	in	in	ADP
ejpam-6441	29	7	best	good	ADJ
ejpam-6441	29	8	approximation	approximation	NOUN
ejpam-6441	29	9	problems	problem	NOUN
ejpam-6441	29	10	in	in	ADP
ejpam-6441	29	11	banach	banach	NOUN
ejpam-6441	29	12	spaces	space	NOUN
ejpam-6441	29	13	and	and	CCONJ
ejpam-6441	29	14	in	in	ADP
ejpam-6441	29	15	the	the	DET
ejpam-6441	29	16	study	study	NOUN
ejpam-6441	29	17	of	of	ADP
ejpam-6441	29	18	non	non	ADJ
ejpam-6441	29	19	-	-	ADJ
ejpam-6441	29	20	expansive	expansive	ADJ
ejpam-6441	29	21	multivalued	multivalued	ADJ
ejpam-6441	29	22	mappings	mapping	NOUN
ejpam-6441	29	23	in	in	ADP
ejpam-6441	29	24	geodesic	geodesic	ADJ
ejpam-6441	29	25	spaces	space	NOUN
ejpam-6441	29	26	.	.	PUNCT
ejpam-6441	30	1	extending	extend	VERB
ejpam-6441	30	2	fp	fp	PROPN
ejpam-6441	30	3	theory	theory	NOUN
ejpam-6441	30	4	to	to	ADP
ejpam-6441	30	5	multivalued	multivalued	ADJ
ejpam-6441	30	6	settings	setting	NOUN
ejpam-6441	30	7	through	through	ADP
ejpam-6441	30	8	jaggi	jaggi	NOUN
ejpam-6441	30	9	-	-	PUNCT
ejpam-6441	30	10	type	type	NOUN
ejpam-6441	30	11	contractions	contraction	NOUN
ejpam-6441	30	12	equips	equip	VERB
ejpam-6441	30	13	researchers	researcher	NOUN
ejpam-6441	30	14	with	with	ADP
ejpam-6441	30	15	powerful	powerful	ADJ
ejpam-6441	30	16	tools	tool	NOUN
ejpam-6441	30	17	for	for	ADP
ejpam-6441	30	18	analyzing	analyze	VERB
ejpam-6441	30	19	complex	complex	ADJ
ejpam-6441	30	20	systems	system	NOUN
ejpam-6441	30	21	beyond	beyond	ADP
ejpam-6441	30	22	the	the	DET
ejpam-6441	30	23	scope	scope	NOUN
ejpam-6441	30	24	of	of	ADP
ejpam-6441	30	25	single	single	ADJ
ejpam-6441	30	26	-	-	PUNCT
ejpam-6441	30	27	valued	value	VERB
ejpam-6441	30	28	mappings	mapping	NOUN
ejpam-6441	30	29	.	.	PUNCT
ejpam-6441	31	1	the	the	DET
ejpam-6441	31	2	development	development	NOUN
ejpam-6441	31	3	of	of	ADP
ejpam-6441	31	4	new	new	ADJ
ejpam-6441	31	5	fp	fp	NOUN
ejpam-6441	31	6	theorems	theorem	NOUN
ejpam-6441	31	7	with	with	ADP
ejpam-6441	31	8	sophisticated	sophisticated	ADJ
ejpam-6441	31	9	contractive	contractive	ADJ
ejpam-6441	31	10	conditions	condition	NOUN
ejpam-6441	31	11	on	on	ADP
ejpam-6441	31	12	different	different	ADJ
ejpam-6441	31	13	spaces	space	NOUN
ejpam-6441	31	14	is	be	AUX
ejpam-6441	31	15	essential	essential	ADJ
ejpam-6441	31	16	for	for	ADP
ejpam-6441	31	17	filling	fill	VERB
ejpam-6441	31	18	gaps	gap	NOUN
ejpam-6441	31	19	in	in	ADP
ejpam-6441	31	20	the	the	DET
ejpam-6441	31	21	existing	exist	VERB
ejpam-6441	31	22	literature	literature	NOUN
ejpam-6441	31	23	.	.	PUNCT
ejpam-6441	32	1	by	by	ADP
ejpam-6441	32	2	introducing	introduce	VERB
ejpam-6441	32	3	new	new	ADJ
ejpam-6441	32	4	fp	fp	NOUN
ejpam-6441	32	5	theorems	theorem	NOUN
ejpam-6441	32	6	based	base	VERB
ejpam-6441	32	7	on	on	ADP
ejpam-6441	32	8	this	this	DET
ejpam-6441	32	9	contractive	contractive	ADJ
ejpam-6441	32	10	approach	approach	NOUN
ejpam-6441	32	11	,	,	PUNCT
ejpam-6441	32	12	our	our	PRON
ejpam-6441	32	13	study	study	NOUN
ejpam-6441	32	14	intends	intend	VERB
ejpam-6441	32	15	to	to	PART
ejpam-6441	32	16	address	address	VERB
ejpam-6441	32	17	the	the	DET
ejpam-6441	32	18	gaps	gap	NOUN
ejpam-6441	32	19	in	in	ADP
ejpam-6441	32	20	the	the	DET
ejpam-6441	32	21	literature	literature	NOUN
ejpam-6441	32	22	and	and	CCONJ
ejpam-6441	32	23	provide	provide	VERB
ejpam-6441	32	24	further	further	ADJ
ejpam-6441	32	25	insights	insight	NOUN
ejpam-6441	32	26	into	into	ADP
ejpam-6441	32	27	the	the	DET
ejpam-6441	32	28	theory	theory	NOUN
ejpam-6441	32	29	of	of	ADP
ejpam-6441	32	30	fps	fps	NOUN
ejpam-6441	32	31	for	for	ADP
ejpam-6441	32	32	multivalued	multivalued	ADJ
ejpam-6441	32	33	mappings	mapping	NOUN
ejpam-6441	32	34	.	.	PUNCT
ejpam-6441	33	1	this	this	DET
ejpam-6441	33	2	research	research	NOUN
ejpam-6441	33	3	has	have	VERB
ejpam-6441	33	4	the	the	DET
ejpam-6441	33	5	potential	potential	NOUN
ejpam-6441	33	6	to	to	PART
ejpam-6441	33	7	enhance	enhance	VERB
ejpam-6441	33	8	our	our	PRON
ejpam-6441	33	9	understanding	understanding	NOUN
ejpam-6441	33	10	of	of	ADP
ejpam-6441	33	11	the	the	DET
ejpam-6441	33	12	subject	subject	NOUN
ejpam-6441	33	13	and	and	CCONJ
ejpam-6441	33	14	pave	pave	VERB
ejpam-6441	33	15	the	the	DET
ejpam-6441	33	16	way	way	NOUN
ejpam-6441	33	17	for	for	ADP
ejpam-6441	33	18	future	future	ADJ
ejpam-6441	33	19	developments	development	NOUN
ejpam-6441	33	20	in	in	ADP
ejpam-6441	33	21	the	the	DET
ejpam-6441	33	22	field	field	NOUN
ejpam-6441	33	23	.	.	PUNCT
ejpam-6441	34	1	this	this	DET
ejpam-6441	34	2	approach	approach	NOUN
ejpam-6441	34	3	likely	likely	ADV
ejpam-6441	34	4	incorporates	incorporate	VERB
ejpam-6441	34	5	the	the	DET
ejpam-6441	34	6	almost	almost	ADV
ejpam-6441	34	7	fisher	fisher	NOUN
ejpam-6441	34	8	-	-	PUNCT
ejpam-6441	34	9	type	type	NOUN
ejpam-6441	34	10	multivalued	multivalue	VERB
ejpam-6441	34	11	f	f	PROPN
ejpam-6441	34	12	-contractions	-contraction	NOUN
ejpam-6441	34	13	discussed	discuss	VERB
ejpam-6441	34	14	earlier	early	ADV
ejpam-6441	34	15	,	,	PUNCT
ejpam-6441	34	16	within	within	ADP
ejpam-6441	34	17	the	the	DET
ejpam-6441	34	18	framework	framework	NOUN
ejpam-6441	34	19	of	of	ADP
ejpam-6441	34	20	complete	complete	ADJ
ejpam-6441	34	21	mss	mss	PROPN
ejpam-6441	34	22	endowed	endow	VERB
ejpam-6441	34	23	with	with	ADP
ejpam-6441	34	24	a	a	DET
ejpam-6441	34	25	γ	γ	NOUN
ejpam-6441	34	26	-	-	ADJ
ejpam-6441	34	27	transitive	transitive	ADJ
ejpam-6441	34	28	binary	binary	ADJ
ejpam-6441	34	29	relation	relation	NOUN
ejpam-6441	34	30	ℜ.	ℜ.	PROPN
ejpam-6441	34	31	alam	alam	PROPN
ejpam-6441	34	32	and	and	CCONJ
ejpam-6441	34	33	imdad	imdad	NOUN
ejpam-6441	35	1	[	[	X
ejpam-6441	35	2	15	15	NUM
ejpam-6441	35	3	]	]	PUNCT
ejpam-6441	35	4	introduced	introduce	VERB
ejpam-6441	35	5	the	the	DET
ejpam-6441	35	6	relation	relation	NOUN
ejpam-6441	35	7	-	-	PUNCT
ejpam-6441	35	8	theoretic	theoretic	ADJ
ejpam-6441	35	9	contraction	contraction	NOUN
ejpam-6441	35	10	principle	principle	NOUN
ejpam-6441	35	11	on	on	ADP
ejpam-6441	35	12	ms	ms	PROPN
ejpam-6441	35	13	endowed	endow	VERB
ejpam-6441	35	14	with	with	ADP
ejpam-6441	35	15	an	an	DET
ejpam-6441	35	16	arbitrary	arbitrary	ADJ
ejpam-6441	35	17	binary	binary	ADJ
ejpam-6441	35	18	relation	relation	NOUN
ejpam-6441	35	19	.	.	PUNCT
ejpam-6441	36	1	recently	recently	ADV
ejpam-6441	36	2	,	,	PUNCT
ejpam-6441	36	3	tomar	tomar	NOUN
ejpam-6441	36	4	and	and	CCONJ
ejpam-6441	36	5	joshi	joshi	X
ejpam-6441	37	1	[	[	X
ejpam-6441	37	2	16	16	NUM
ejpam-6441	37	3	]	]	PUNCT
ejpam-6441	37	4	discussed	discuss	VERB
ejpam-6441	37	5	the	the	DET
ejpam-6441	37	6	relation	relation	NOUN
ejpam-6441	37	7	-	-	PUNCT
ejpam-6441	37	8	theoretic	theoretic	NOUN
ejpam-6441	37	9	contractions	contraction	NOUN
ejpam-6441	37	10	in	in	ADP
ejpam-6441	37	11	f	f	PROPN
ejpam-6441	37	12	-mss	-mss	PUNCT
ejpam-6441	37	13	to	to	PART
ejpam-6441	37	14	demonstrate	demonstrate	VERB
ejpam-6441	37	15	the	the	DET
ejpam-6441	37	16	existence	existence	NOUN
ejpam-6441	37	17	of	of	ADP
ejpam-6441	37	18	fp	fp	NOUN
ejpam-6441	37	19	and	and	CCONJ
ejpam-6441	37	20	solved	solve	VERB
ejpam-6441	37	21	a	a	DET
ejpam-6441	37	22	two	two	NUM
ejpam-6441	37	23	-	-	PUNCT
ejpam-6441	37	24	point	point	NOUN
ejpam-6441	37	25	boundary	boundary	ADJ
ejpam-6441	37	26	value	value	NOUN
ejpam-6441	37	27	problem	problem	NOUN
ejpam-6441	37	28	arising	arise	VERB
ejpam-6441	37	29	in	in	ADP
ejpam-6441	37	30	a	a	DET
ejpam-6441	37	31	hanging	hang	VERB
ejpam-6441	37	32	cable	cable	NOUN
ejpam-6441	37	33	problem	problem	NOUN
ejpam-6441	37	34	.	.	PUNCT
ejpam-6441	38	1	alam	alam	PROPN
ejpam-6441	38	2	and	and	CCONJ
ejpam-6441	38	3	imdad	imdad	PROPN
ejpam-6441	39	1	[	[	X
ejpam-6441	39	2	17	17	NUM
ejpam-6441	39	3	,	,	PUNCT
ejpam-6441	39	4	18	18	NUM
ejpam-6441	39	5	]	]	PUNCT
ejpam-6441	39	6	generalized	generalize	VERB
ejpam-6441	39	7	some	some	DET
ejpam-6441	39	8	metrical	metrical	ADJ
ejpam-6441	39	9	notions	notion	NOUN
ejpam-6441	39	10	related	relate	VERB
ejpam-6441	39	11	to	to	ADP
ejpam-6441	39	12	relation	relation	NOUN
ejpam-6441	39	13	-	-	PUNCT
ejpam-6441	39	14	theoretic	theoretic	NOUN
ejpam-6441	39	15	setting	setting	NOUN
ejpam-6441	39	16	and	and	CCONJ
ejpam-6441	39	17	locally	locally	ADV
ejpam-6441	39	18	t	t	NOUN
ejpam-6441	39	19	-transitive	-transitive	ADJ
ejpam-6441	39	20	binary	binary	ADJ
ejpam-6441	39	21	relation	relation	NOUN
ejpam-6441	39	22	with	with	ADP
ejpam-6441	39	23	utilizing	utilize	VERB
ejpam-6441	39	24	these	these	DET
ejpam-6441	39	25	notions	notion	NOUN
ejpam-6441	39	26	to	to	PART
ejpam-6441	39	27	prove	prove	VERB
ejpam-6441	39	28	coincidence	coincidence	NOUN
ejpam-6441	39	29	points	point	NOUN
ejpam-6441	39	30	and	and	CCONJ
ejpam-6441	39	31	fp	fp	PRON
ejpam-6441	39	32	theorems	theorem	NOUN
ejpam-6441	39	33	for	for	ADP
ejpam-6441	39	34	self	self	NOUN
ejpam-6441	39	35	-	-	PUNCT
ejpam-6441	39	36	mappings	mapping	NOUN
ejpam-6441	39	37	on	on	ADP
ejpam-6441	39	38	an	an	DET
ejpam-6441	39	39	ms	ms	PROPN
ejpam-6441	39	40	.	.	PROPN
ejpam-6441	39	41	authors	author	NOUN
ejpam-6441	39	42	in	in	ADP
ejpam-6441	39	43	[	[	X
ejpam-6441	39	44	19–21	19–21	NUM
ejpam-6441	39	45	]	]	X
ejpam-6441	39	46	extended	extend	VERB
ejpam-6441	39	47	the	the	DET
ejpam-6441	39	48	above	above	ADJ
ejpam-6441	39	49	results	result	NOUN
ejpam-6441	39	50	for	for	ADP
ejpam-6441	39	51	set	set	NOUN
ejpam-6441	39	52	-	-	PUNCT
ejpam-6441	39	53	valued	value	VERB
ejpam-6441	39	54	mappings	mapping	NOUN
ejpam-6441	39	55	in	in	ADP
ejpam-6441	39	56	mss	mss	PROPN
ejpam-6441	39	57	.	.	PUNCT
ejpam-6441	40	1	negi	negi	PROPN
ejpam-6441	40	2	and	and	CCONJ
ejpam-6441	40	3	gairola	gairola	PROPN
ejpam-6441	41	1	[	[	X
ejpam-6441	41	2	22	22	NUM
ejpam-6441	41	3	]	]	PUNCT
ejpam-6441	41	4	introduced	introduce	VERB
ejpam-6441	41	5	the	the	DET
ejpam-6441	41	6	notion	notion	NOUN
ejpam-6441	41	7	of	of	ADP
ejpam-6441	41	8	generalized	generalized	ADJ
ejpam-6441	41	9	multivalued	multivalue	VERB
ejpam-6441	41	10	(	(	PUNCT
ejpam-6441	41	11	ψ	ψ	NOUN
ejpam-6441	41	12	-	-	NOUN
ejpam-6441	41	13	fℜ)-contraction	fℜ)-contraction	NOUN
ejpam-6441	41	14	in	in	ADP
ejpam-6441	41	15	pms	pm	NOUN
ejpam-6441	41	16	endowed	endow	VERB
ejpam-6441	41	17	with	with	ADP
ejpam-6441	41	18	an	an	DET
ejpam-6441	41	19	arbitrary	arbitrary	ADJ
ejpam-6441	41	20	binary	binary	ADJ
ejpam-6441	41	21	relation	relation	NOUN
ejpam-6441	41	22	and	and	CCONJ
ejpam-6441	41	23	established	establish	VERB
ejpam-6441	41	24	a	a	DET
ejpam-6441	41	25	new	new	ADJ
ejpam-6441	41	26	fp	fp	NOUN
ejpam-6441	41	27	theorem	theorem	NOUN
ejpam-6441	41	28	,	,	PUNCT
ejpam-6441	41	29	see	see	VERB
ejpam-6441	41	30	[	[	X
ejpam-6441	41	31	23	23	NUM
ejpam-6441	41	32	,	,	PUNCT
ejpam-6441	41	33	24	24	NUM
ejpam-6441	41	34	]	]	PUNCT
ejpam-6441	41	35	.	.	PUNCT
ejpam-6441	42	1	in	in	ADP
ejpam-6441	42	2	line	line	NOUN
ejpam-6441	42	3	with	with	ADP
ejpam-6441	42	4	these	these	DET
ejpam-6441	42	5	advancements	advancement	NOUN
ejpam-6441	42	6	,	,	PUNCT
ejpam-6441	42	7	we	we	PRON
ejpam-6441	42	8	touch	touch	VERB
ejpam-6441	42	9	on	on	ADP
ejpam-6441	42	10	some	some	DET
ejpam-6441	42	11	basics	basic	NOUN
ejpam-6441	42	12	and	and	CCONJ
ejpam-6441	42	13	concepts	concept	NOUN
ejpam-6441	42	14	that	that	PRON
ejpam-6441	42	15	are	be	AUX
ejpam-6441	42	16	far	far	ADV
ejpam-6441	42	17	famed	fame	VERB
ejpam-6441	42	18	in	in	ADP
ejpam-6441	42	19	the	the	DET
ejpam-6441	42	20	literature	literature	NOUN
ejpam-6441	42	21	:	:	PUNCT
ejpam-6441	43	1	m.	m.	NOUN
ejpam-6441	43	2	mudhesh	mudhesh	PROPN
ejpam-6441	43	3	et	et	PROPN
ejpam-6441	43	4	al	al	PROPN
ejpam-6441	43	5	.	.	PUNCT
ejpam-6441	43	6	/	/	SYM
ejpam-6441	43	7	eur	eur	PROPN
ejpam-6441	43	8	.	.	PUNCT
ejpam-6441	44	1	j.	j.	PROPN
ejpam-6441	44	2	pure	pure	PROPN
ejpam-6441	44	3	appl	appl	PROPN
ejpam-6441	44	4	.	.	PROPN
ejpam-6441	44	5	math	math	PROPN
ejpam-6441	44	6	,	,	PUNCT
ejpam-6441	44	7	18	18	NUM
ejpam-6441	44	8	(	(	PUNCT
ejpam-6441	44	9	4	4	NUM
ejpam-6441	44	10	)	)	PUNCT
ejpam-6441	44	11	(	(	PUNCT
ejpam-6441	44	12	2025	2025	NUM
ejpam-6441	44	13	)	)	PUNCT
ejpam-6441	44	14	,	,	PUNCT
ejpam-6441	44	15	6441	6441	NUM
ejpam-6441	44	16	3	3	NUM
ejpam-6441	44	17	of	of	ADP
ejpam-6441	44	18	21	21	NUM
ejpam-6441	44	19	definition	definition	NOUN
ejpam-6441	44	20	1	1	NUM
ejpam-6441	44	21	.	.	PUNCT
ejpam-6441	45	1	[	[	X
ejpam-6441	45	2	6	6	NUM
ejpam-6441	45	3	]	]	PUNCT
ejpam-6441	45	4	let	let	VERB
ejpam-6441	45	5	(	(	PUNCT
ejpam-6441	45	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	45	7	,	,	PUNCT
ejpam-6441	45	8	d	d	NOUN
ejpam-6441	45	9	)	)	PUNCT
ejpam-6441	45	10	be	be	AUX
ejpam-6441	45	11	a	a	DET
ejpam-6441	45	12	ms	ms	PROPN
ejpam-6441	45	13	.	.	PROPN
ejpam-6441	46	1	a	a	DET
ejpam-6441	46	2	map	map	NOUN
ejpam-6441	46	3	γ	γ	X
ejpam-6441	46	4	:	:	PUNCT
ejpam-6441	46	5	∆ℜ	∆ℜ	X
ejpam-6441	46	6	→	→	SYM
ejpam-6441	46	7	∆ℜ	∆ℜ	PROPN
ejpam-6441	46	8	is	be	AUX
ejpam-6441	46	9	said	say	VERB
ejpam-6441	46	10	to	to	PART
ejpam-6441	46	11	be	be	AUX
ejpam-6441	46	12	an	an	DET
ejpam-6441	46	13	f	f	PROPN
ejpam-6441	46	14	-contraction	-contraction	NOUN
ejpam-6441	46	15	if	if	SCONJ
ejpam-6441	46	16	there	there	PRON
ejpam-6441	46	17	exists	exist	VERB
ejpam-6441	46	18	τ	τ	PROPN
ejpam-6441	46	19	∈	∈	PROPN
ejpam-6441	46	20	r+	r+	NOUN
ejpam-6441	46	21	such	such	ADJ
ejpam-6441	46	22	that	that	SCONJ
ejpam-6441	46	23	∀ς1	∀ς1	NOUN
ejpam-6441	46	24	,	,	PUNCT
ejpam-6441	46	25	ς2	ς2	PROPN
ejpam-6441	46	26	∈	∈	PROPN
ejpam-6441	46	27	∆ℜ	∆ℜ	PROPN
ejpam-6441	46	28	,	,	PUNCT
ejpam-6441	46	29	d(γς1,γς2	d(γς1,γς2	PROPN
ejpam-6441	46	30	)	)	PUNCT
ejpam-6441	46	31	>	>	SYM
ejpam-6441	46	32	0	0	PUNCT
ejpam-6441	47	1	⇒	⇒	PROPN
ejpam-6441	47	2	τ	τ	PROPN
ejpam-6441	48	1	+	+	NUM
ejpam-6441	48	2	f	f	X
ejpam-6441	48	3	(	(	PUNCT
ejpam-6441	48	4	γς1,γς2	γς1,γς2	PROPN
ejpam-6441	48	5	)	)	PUNCT
ejpam-6441	48	6	≤	≤	NUM
ejpam-6441	48	7	f	f	X
ejpam-6441	48	8	(	(	PUNCT
ejpam-6441	48	9	d	d	X
ejpam-6441	48	10	(	(	PUNCT
ejpam-6441	48	11	ς1	ς1	NOUN
ejpam-6441	48	12	,	,	PUNCT
ejpam-6441	48	13	ς2	ς2	PROPN
ejpam-6441	48	14	)	)	PUNCT
ejpam-6441	48	15	)	)	PUNCT
ejpam-6441	48	16	,	,	PUNCT
ejpam-6441	48	17	where	where	SCONJ
ejpam-6441	48	18	∆w	∆w	PROPN
ejpam-6441	48	19	is	be	AUX
ejpam-6441	48	20	the	the	DET
ejpam-6441	48	21	family	family	NOUN
ejpam-6441	48	22	of	of	ADP
ejpam-6441	48	23	functions	function	NOUN
ejpam-6441	48	24	f	f	X
ejpam-6441	48	25	:	:	PUNCT
ejpam-6441	48	26	r+	r+	X
ejpam-6441	48	27	→	→	PUNCT
ejpam-6441	48	28	r	r	NOUN
ejpam-6441	48	29	satisfying	satisfy	VERB
ejpam-6441	48	30	the	the	DET
ejpam-6441	48	31	assumptions	assumption	NOUN
ejpam-6441	48	32	below	below	ADV
ejpam-6441	48	33	:	:	PUNCT
ejpam-6441	48	34	(	(	PUNCT
ejpam-6441	48	35	f1	f1	NOUN
ejpam-6441	48	36	)	)	PUNCT
ejpam-6441	48	37	f	f	PROPN
ejpam-6441	48	38	is	be	AUX
ejpam-6441	48	39	strictly	strictly	ADV
ejpam-6441	48	40	increasing	increase	VERB
ejpam-6441	48	41	,	,	PUNCT
ejpam-6441	48	42	i.e.	i.e.	X
ejpam-6441	48	43	,	,	PUNCT
ejpam-6441	48	44	∀ς1	∀ς1	NOUN
ejpam-6441	48	45	,	,	PUNCT
ejpam-6441	48	46	ς2	ς2	PROPN
ejpam-6441	48	47	∈	∈	PROPN
ejpam-6441	48	48	(	(	PUNCT
ejpam-6441	48	49	0,∞	0,∞	NOUN
ejpam-6441	48	50	)	)	PUNCT
ejpam-6441	48	51	,	,	PUNCT
ejpam-6441	48	52	so	so	SCONJ
ejpam-6441	48	53	that	that	SCONJ
ejpam-6441	48	54	ς1	ς1	NOUN
ejpam-6441	48	55	<	<	X
ejpam-6441	48	56	ς2	ς2	PROPN
ejpam-6441	48	57	,	,	PUNCT
ejpam-6441	48	58	then	then	ADV
ejpam-6441	48	59	f	f	PROPN
ejpam-6441	48	60	(	(	PUNCT
ejpam-6441	48	61	ς1	ς1	NOUN
ejpam-6441	48	62	)	)	PUNCT
ejpam-6441	48	63	<	<	X
ejpam-6441	49	1	f	f	X
ejpam-6441	49	2	(	(	PUNCT
ejpam-6441	49	3	ς2	ς2	PROPN
ejpam-6441	49	4	)	)	PUNCT
ejpam-6441	49	5	;	;	PUNCT
ejpam-6441	49	6	(	(	PUNCT
ejpam-6441	49	7	f2	f2	PROPN
ejpam-6441	49	8	)	)	PUNCT
ejpam-6441	49	9	for	for	ADP
ejpam-6441	49	10	{	{	PUNCT
ejpam-6441	49	11	ςȷ}∞ȷ=1	ςȷ}∞ȷ=1	NUM
ejpam-6441	49	12	⊆	⊆	NUM
ejpam-6441	49	13	r+	r+	NOUN
ejpam-6441	49	14	,	,	PUNCT
ejpam-6441	49	15	lim	lim	PROPN
ejpam-6441	49	16	ȷ→∞	ȷ→∞	NUM
ejpam-6441	49	17	ςȷ	ςȷ	PROPN
ejpam-6441	49	18	=	=	SYM
ejpam-6441	49	19	0	0	PROPN
ejpam-6441	49	20	⇔	⇔	PROPN
ejpam-6441	49	21	lim	lim	PROPN
ejpam-6441	49	22	ȷ→∞	ȷ→∞	NUM
ejpam-6441	49	23	f	f	PROPN
ejpam-6441	49	24	(	(	PUNCT
ejpam-6441	49	25	ςȷ	ςȷ	NOUN
ejpam-6441	49	26	)	)	PUNCT
ejpam-6441	49	27	=	=	SYM
ejpam-6441	49	28	−∞	−∞	PROPN
ejpam-6441	49	29	;	;	PUNCT
ejpam-6441	49	30	(	(	PUNCT
ejpam-6441	49	31	f3	f3	ADJ
ejpam-6441	49	32	)	)	PUNCT
ejpam-6441	49	33	∃	∃	PROPN
ejpam-6441	49	34	ℓ	ℓ	PROPN
ejpam-6441	49	35	∈	∈	PROPN
ejpam-6441	49	36	(	(	PUNCT
ejpam-6441	49	37	0	0	NUM
ejpam-6441	49	38	,	,	PUNCT
ejpam-6441	49	39	1	1	NUM
ejpam-6441	49	40	)	)	PUNCT
ejpam-6441	49	41	,	,	PUNCT
ejpam-6441	49	42	so	so	SCONJ
ejpam-6441	49	43	that	that	SCONJ
ejpam-6441	49	44	lim	lim	PROPN
ejpam-6441	49	45	ȷ→∞	ȷ→∞	NUM
ejpam-6441	49	46	ςℓf	ςℓf	NOUN
ejpam-6441	49	47	(	(	PUNCT
ejpam-6441	49	48	ςȷ	ςȷ	NOUN
ejpam-6441	49	49	)	)	PUNCT
ejpam-6441	49	50	=	=	SYM
ejpam-6441	49	51	0	0	X
ejpam-6441	49	52	.	.	PUNCT
ejpam-6441	49	53	theorem	theorem	NOUN
ejpam-6441	49	54	1	1	NUM
ejpam-6441	49	55	.	.	PUNCT
ejpam-6441	50	1	[	[	X
ejpam-6441	50	2	6	6	NUM
ejpam-6441	50	3	]	]	PUNCT
ejpam-6441	50	4	let	let	VERB
ejpam-6441	50	5	(	(	PUNCT
ejpam-6441	50	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	50	7	,	,	PUNCT
ejpam-6441	50	8	d	d	NOUN
ejpam-6441	50	9	)	)	PUNCT
ejpam-6441	50	10	be	be	AUX
ejpam-6441	50	11	a	a	DET
ejpam-6441	50	12	complete	complete	ADJ
ejpam-6441	50	13	ms	ms	NOUN
ejpam-6441	50	14	and	and	CCONJ
ejpam-6441	50	15	γ	γ	NOUN
ejpam-6441	50	16	:	:	PUNCT
ejpam-6441	50	17	∆ℜ	∆ℜ	X
ejpam-6441	50	18	→	→	SYM
ejpam-6441	50	19	∆ℜ	∆ℜ	NOUN
ejpam-6441	50	20	be	be	AUX
ejpam-6441	50	21	an	an	DET
ejpam-6441	50	22	f	f	PROPN
ejpam-6441	50	23	-contraction	-contraction	PROPN
ejpam-6441	50	24	map	map	NOUN
ejpam-6441	50	25	.	.	PUNCT
ejpam-6441	51	1	if	if	SCONJ
ejpam-6441	51	2	∃	∃	PROPN
ejpam-6441	51	3	f	f	PROPN
ejpam-6441	51	4	∈	∈	PROPN
ejpam-6441	51	5	∆w	∆w	PROPN
ejpam-6441	51	6	and	and	CCONJ
ejpam-6441	51	7	τ	τ	PROPN
ejpam-6441	51	8	∈	∈	PROPN
ejpam-6441	51	9	(	(	PUNCT
ejpam-6441	51	10	0,∞	0,∞	NOUN
ejpam-6441	51	11	)	)	PUNCT
ejpam-6441	51	12	.	.	PUNCT
ejpam-6441	52	1	thus	thus	ADV
ejpam-6441	52	2	,	,	PUNCT
ejpam-6441	52	3	γ	γ	PROPN
ejpam-6441	52	4	has	have	VERB
ejpam-6441	52	5	a	a	DET
ejpam-6441	52	6	ufp	ufp	NOUN
ejpam-6441	52	7	.	.	PUNCT
ejpam-6441	53	1	remark	remark	PROPN
ejpam-6441	53	2	1	1	NUM
ejpam-6441	53	3	.	.	PUNCT
ejpam-6441	54	1	[	[	X
ejpam-6441	54	2	3	3	X
ejpam-6441	54	3	]	]	X
ejpam-6441	54	4	if	if	SCONJ
ejpam-6441	54	5	f	f	PROPN
ejpam-6441	54	6	is	be	AUX
ejpam-6441	54	7	right	right	ADV
ejpam-6441	54	8	continuous	continuous	ADJ
ejpam-6441	54	9	and	and	CCONJ
ejpam-6441	54	10	satisfies	satisfie	NOUN
ejpam-6441	54	11	(	(	PUNCT
ejpam-6441	54	12	f2	f2	PROPN
ejpam-6441	54	13	)	)	PUNCT
ejpam-6441	54	14	,	,	PUNCT
ejpam-6441	54	15	then	then	ADV
ejpam-6441	54	16	f	f	X
ejpam-6441	54	17	(	(	PUNCT
ejpam-6441	54	18	inf	inf	PROPN
ejpam-6441	54	19	a	a	NOUN
ejpam-6441	54	20	)	)	PUNCT
ejpam-6441	54	21	=	=	SYM
ejpam-6441	54	22	inf	inf	NOUN
ejpam-6441	54	23	f	f	X
ejpam-6441	54	24	(	(	PUNCT
ejpam-6441	54	25	a	a	NOUN
ejpam-6441	54	26	)	)	PUNCT
ejpam-6441	54	27	,	,	PUNCT
ejpam-6441	54	28	∀a	∀a	X
ejpam-6441	54	29	⊂	⊂	X
ejpam-6441	54	30	(	(	PUNCT
ejpam-6441	54	31	0,∞)with	0,∞)with	PROPN
ejpam-6441	54	32	inf	inf	PROPN
ejpam-6441	54	33	(	(	PUNCT
ejpam-6441	54	34	a	a	NOUN
ejpam-6441	54	35	)	)	PUNCT
ejpam-6441	54	36	>	>	X
ejpam-6441	55	1	0	0	X
ejpam-6441	55	2	.	.	PUNCT
ejpam-6441	56	1	now	now	ADV
ejpam-6441	56	2	,	,	PUNCT
ejpam-6441	56	3	we	we	PRON
ejpam-6441	56	4	introduce	introduce	VERB
ejpam-6441	56	5	some	some	DET
ejpam-6441	56	6	primary	primary	ADJ
ejpam-6441	56	7	debates	debate	NOUN
ejpam-6441	56	8	and	and	CCONJ
ejpam-6441	56	9	terminology	terminology	NOUN
ejpam-6441	56	10	about	about	ADP
ejpam-6441	56	11	ms	ms	PROPN
ejpam-6441	56	12	that	that	PRON
ejpam-6441	56	13	are	be	AUX
ejpam-6441	56	14	well	well	ADV
ejpam-6441	56	15	known	know	VERB
ejpam-6441	56	16	in	in	ADP
ejpam-6441	56	17	the	the	DET
ejpam-6441	56	18	literature	literature	NOUN
ejpam-6441	56	19	.	.	PUNCT
ejpam-6441	57	1	definition	definition	NOUN
ejpam-6441	57	2	2	2	NUM
ejpam-6441	57	3	.	.	PUNCT
ejpam-6441	58	1	[	[	X
ejpam-6441	58	2	6	6	NUM
ejpam-6441	58	3	]	]	PUNCT
ejpam-6441	58	4	let	let	VERB
ejpam-6441	58	5	(	(	PUNCT
ejpam-6441	58	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	58	7	,	,	PUNCT
ejpam-6441	58	8	d	d	NOUN
ejpam-6441	58	9	)	)	PUNCT
ejpam-6441	58	10	be	be	AUX
ejpam-6441	58	11	a	a	DET
ejpam-6441	58	12	ms	ms	NOUN
ejpam-6441	58	13	.	.	PROPN
ejpam-6441	59	1	then	then	ADV
ejpam-6441	59	2	,	,	PUNCT
ejpam-6441	59	3	we	we	PRON
ejpam-6441	59	4	have	have	VERB
ejpam-6441	59	5	(	(	PUNCT
ejpam-6441	59	6	1	1	X
ejpam-6441	59	7	)	)	PUNCT
ejpam-6441	59	8	a	a	DET
ejpam-6441	59	9	sequence	sequence	NOUN
ejpam-6441	59	10	{	{	PUNCT
ejpam-6441	59	11	ςn	ςn	NOUN
ejpam-6441	59	12	}	}	PUNCT
ejpam-6441	59	13	converges	converge	NOUN
ejpam-6441	59	14	to	to	ADP
ejpam-6441	59	15	a	a	DET
ejpam-6441	59	16	point	point	NOUN
ejpam-6441	60	1	ς	ς	PROPN
ejpam-6441	60	2	iff	iff	PROPN
ejpam-6441	60	3	lim	lim	PROPN
ejpam-6441	60	4	n→∞	n→∞	PROPN
ejpam-6441	61	1	d	d	NOUN
ejpam-6441	61	2	(	(	PUNCT
ejpam-6441	61	3	ςn	ςn	PROPN
ejpam-6441	61	4	,	,	PUNCT
ejpam-6441	61	5	ς	ς	PROPN
ejpam-6441	61	6	)	)	PUNCT
ejpam-6441	61	7	=	=	SYM
ejpam-6441	61	8	0	0	X
ejpam-6441	61	9	.	.	PUNCT
ejpam-6441	62	1	(	(	PUNCT
ejpam-6441	62	2	2	2	X
ejpam-6441	62	3	)	)	PUNCT
ejpam-6441	62	4	a	a	DET
ejpam-6441	62	5	sequence	sequence	NOUN
ejpam-6441	62	6	{	{	PUNCT
ejpam-6441	62	7	ςn	ςn	NOUN
ejpam-6441	62	8	}	}	PUNCT
ejpam-6441	62	9	in	in	ADP
ejpam-6441	62	10	∆ℜ	∆ℜ	PROPN
ejpam-6441	62	11	is	be	AUX
ejpam-6441	62	12	said	say	VERB
ejpam-6441	62	13	to	to	PART
ejpam-6441	62	14	be	be	AUX
ejpam-6441	62	15	a	a	DET
ejpam-6441	62	16	cauchy	cauchy	ADJ
ejpam-6441	62	17	sequence	sequence	NOUN
ejpam-6441	62	18	iff	iff	PROPN
ejpam-6441	62	19	lim	lim	PROPN
ejpam-6441	62	20	n	n	CCONJ
ejpam-6441	62	21	,	,	PUNCT
ejpam-6441	62	22	m→∞	m→∞	NOUN
ejpam-6441	62	23	d	d	NOUN
ejpam-6441	62	24	(	(	PUNCT
ejpam-6441	62	25	ςn	ςn	NOUN
ejpam-6441	62	26	,	,	PUNCT
ejpam-6441	62	27	ςm	ςm	NOUN
ejpam-6441	62	28	)	)	PUNCT
ejpam-6441	62	29	=	=	SYM
ejpam-6441	63	1	0	0	X
ejpam-6441	63	2	.	.	PUNCT
ejpam-6441	64	1	(	(	PUNCT
ejpam-6441	64	2	3	3	X
ejpam-6441	64	3	)	)	PUNCT
ejpam-6441	64	4	an	an	DET
ejpam-6441	64	5	ms	ms	NOUN
ejpam-6441	64	6	is	be	AUX
ejpam-6441	64	7	said	say	VERB
ejpam-6441	64	8	to	to	PART
ejpam-6441	64	9	be	be	AUX
ejpam-6441	64	10	complete	complete	ADJ
ejpam-6441	64	11	if	if	SCONJ
ejpam-6441	64	12	every	every	DET
ejpam-6441	64	13	cauchy	cauchy	ADJ
ejpam-6441	64	14	sequence	sequence	NOUN
ejpam-6441	64	15	{	{	PUNCT
ejpam-6441	64	16	ςn	ςn	NOUN
ejpam-6441	64	17	}	}	PUNCT
ejpam-6441	64	18	converges	converge	NOUN
ejpam-6441	64	19	to	to	ADP
ejpam-6441	64	20	a	a	DET
ejpam-6441	64	21	point	point	NOUN
ejpam-6441	64	22	ς	ς	ADP
ejpam-6441	64	23	such	such	ADJ
ejpam-6441	64	24	that	that	SCONJ
ejpam-6441	64	25	lim	lim	PROPN
ejpam-6441	64	26	n→∞	n→∞	X
ejpam-6441	65	1	d	d	NOUN
ejpam-6441	65	2	(	(	PUNCT
ejpam-6441	65	3	ςn	ςn	PROPN
ejpam-6441	65	4	,	,	PUNCT
ejpam-6441	65	5	ς	ς	PROPN
ejpam-6441	65	6	)	)	PUNCT
ejpam-6441	65	7	=	=	NOUN
ejpam-6441	65	8	0	0	X
ejpam-6441	65	9	.	.	PUNCT
ejpam-6441	66	1	if	if	SCONJ
ejpam-6441	66	2	(	(	PUNCT
ejpam-6441	66	3	ς1	ς1	NOUN
ejpam-6441	66	4	,	,	PUNCT
ejpam-6441	66	5	ς2	ς2	PROPN
ejpam-6441	66	6	)	)	PUNCT
ejpam-6441	66	7	∈	∈	PROPN
ejpam-6441	66	8	ℜ	ℜ	PROPN
ejpam-6441	66	9	,	,	PUNCT
ejpam-6441	66	10	then	then	ADV
ejpam-6441	66	11	it	it	PRON
ejpam-6441	66	12	is	be	AUX
ejpam-6441	66	13	said	say	VERB
ejpam-6441	66	14	that	that	SCONJ
ejpam-6441	66	15	ς1	ς1	NOUN
ejpam-6441	66	16	is	be	AUX
ejpam-6441	66	17	related	relate	VERB
ejpam-6441	66	18	to	to	ADP
ejpam-6441	66	19	ς2	ς2	PROPN
ejpam-6441	66	20	.	.	PUNCT
ejpam-6441	67	1	here	here	ADV
ejpam-6441	67	2	,	,	PUNCT
ejpam-6441	67	3	we	we	PRON
ejpam-6441	67	4	take	take	VERB
ejpam-6441	67	5	ℜ	ℜ	PROPN
ejpam-6441	67	6	as	as	ADP
ejpam-6441	67	7	a	a	DET
ejpam-6441	67	8	binary	binary	ADJ
ejpam-6441	67	9	relation	relation	NOUN
ejpam-6441	67	10	on	on	ADP
ejpam-6441	67	11	a	a	DET
ejpam-6441	67	12	nonempty	nonempty	NOUN
ejpam-6441	67	13	subset	subset	VERB
ejpam-6441	67	14	∆ℜ	∆ℜ	PROPN
ejpam-6441	67	15	and	and	CCONJ
ejpam-6441	67	16	(	(	PUNCT
ejpam-6441	67	17	∆ℜ	∆ℜ	PROPN
ejpam-6441	67	18	,	,	PUNCT
ejpam-6441	67	19	d	d	NOUN
ejpam-6441	67	20	)	)	PUNCT
ejpam-6441	67	21	is	be	AUX
ejpam-6441	67	22	a	a	DET
ejpam-6441	67	23	ms	ms	NOUN
ejpam-6441	67	24	equipped	equip	VERB
ejpam-6441	67	25	with	with	ADP
ejpam-6441	67	26	a	a	DET
ejpam-6441	67	27	binary	binary	ADJ
ejpam-6441	67	28	relation	relation	NOUN
ejpam-6441	67	29	ℜ.	ℜ.	PROPN
ejpam-6441	67	30	definition	definition	NOUN
ejpam-6441	67	31	3	3	NUM
ejpam-6441	67	32	.	.	PUNCT
ejpam-6441	68	1	a	a	DET
ejpam-6441	68	2	binary	binary	ADJ
ejpam-6441	68	3	relation	relation	NOUN
ejpam-6441	68	4	ℜ	ℜ	PROPN
ejpam-6441	68	5	on	on	ADP
ejpam-6441	68	6	∆ℜ	∆ℜ	ADJ
ejpam-6441	68	7	̸=	̸=	PROPN
ejpam-6441	68	8	0	0	NUM
ejpam-6441	68	9	is	be	AUX
ejpam-6441	68	10	a	a	DET
ejpam-6441	68	11	subset	subset	NOUN
ejpam-6441	68	12	of	of	ADP
ejpam-6441	68	13	∆ℜ	∆ℜ	ADJ
ejpam-6441	68	14	×∆ℜ	×∆ℜ	NOUN
ejpam-6441	68	15	,	,	PUNCT
ejpam-6441	68	16	we	we	PRON
ejpam-6441	68	17	say	say	VERB
ejpam-6441	68	18	that	that	SCONJ
ejpam-6441	68	19	ς1	ς1	NOUN
ejpam-6441	68	20	is	be	AUX
ejpam-6441	68	21	related	relate	VERB
ejpam-6441	68	22	to	to	ADP
ejpam-6441	68	23	ς2	ς2	PROPN
ejpam-6441	68	24	(	(	PUNCT
ejpam-6441	68	25	i.e.ς1ℜς2	i.e.ς1ℜς2	NOUN
ejpam-6441	68	26	)	)	PUNCT
ejpam-6441	68	27	if	if	SCONJ
ejpam-6441	68	28	and	and	CCONJ
ejpam-6441	68	29	only	only	ADV
ejpam-6441	68	30	if	if	SCONJ
ejpam-6441	68	31	(	(	PUNCT
ejpam-6441	68	32	ς1	ς1	NOUN
ejpam-6441	68	33	,	,	PUNCT
ejpam-6441	68	34	ς2	ς2	PROPN
ejpam-6441	68	35	)	)	PUNCT
ejpam-6441	68	36	∈	∈	PROPN
ejpam-6441	68	37	ℜ.	ℜ.	PROPN
ejpam-6441	68	38	definition	definition	NOUN
ejpam-6441	68	39	4	4	NUM
ejpam-6441	68	40	.	.	PUNCT
ejpam-6441	69	1	[	[	X
ejpam-6441	69	2	15	15	NUM
ejpam-6441	69	3	]	]	PUNCT
ejpam-6441	69	4	let	let	VERB
ejpam-6441	69	5	γ	γ	NOUN
ejpam-6441	69	6	:	:	PUNCT
ejpam-6441	69	7	∆ℜ	∆ℜ	X
ejpam-6441	69	8	→	→	SYM
ejpam-6441	69	9	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	69	10	then	then	ADV
ejpam-6441	69	11	,	,	PUNCT
ejpam-6441	69	12	ℜ	ℜ	PROPN
ejpam-6441	69	13	on	on	ADP
ejpam-6441	69	14	∆ℜ	∆ℜ	PROPN
ejpam-6441	69	15	is	be	AUX
ejpam-6441	69	16	designated	designate	VERB
ejpam-6441	69	17	as	as	ADP
ejpam-6441	69	18	γ	γ	NOUN
ejpam-6441	69	19	-	-	ADJ
ejpam-6441	69	20	closed	closed	ADJ
ejpam-6441	69	21	,	,	PUNCT
ejpam-6441	69	22	if	if	SCONJ
ejpam-6441	69	23	(	(	PUNCT
ejpam-6441	69	24	ς1	ς1	NOUN
ejpam-6441	69	25	,	,	PUNCT
ejpam-6441	69	26	ς2	ς2	PROPN
ejpam-6441	69	27	)	)	PUNCT
ejpam-6441	69	28	∈	∈	PROPN
ejpam-6441	69	29	ℜ	ℜ	PROPN
ejpam-6441	69	30	⇒	⇒	NOUN
ejpam-6441	69	31	(	(	PUNCT
ejpam-6441	69	32	γς1,γς2	γς1,γς2	PROPN
ejpam-6441	69	33	)	)	PUNCT
ejpam-6441	69	34	∈	∈	PROPN
ejpam-6441	69	35	ℜ	ℜ	PROPN
ejpam-6441	69	36	,	,	PUNCT
ejpam-6441	69	37	ς1	ς1	NOUN
ejpam-6441	69	38	,	,	PUNCT
ejpam-6441	69	39	ς2	ς2	PROPN
ejpam-6441	69	40	∈	∈	PROPN
ejpam-6441	69	41	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	69	42	m.	m.	NOUN
ejpam-6441	69	43	mudhesh	mudhesh	PROPN
ejpam-6441	69	44	et	et	PROPN
ejpam-6441	69	45	al	al	PROPN
ejpam-6441	69	46	.	.	PUNCT
ejpam-6441	69	47	/	/	SYM
ejpam-6441	69	48	eur	eur	PROPN
ejpam-6441	69	49	.	.	PUNCT
ejpam-6441	70	1	j.	j.	PROPN
ejpam-6441	70	2	pure	pure	PROPN
ejpam-6441	70	3	appl	appl	PROPN
ejpam-6441	70	4	.	.	PROPN
ejpam-6441	70	5	math	math	PROPN
ejpam-6441	70	6	,	,	PUNCT
ejpam-6441	70	7	18	18	NUM
ejpam-6441	70	8	(	(	PUNCT
ejpam-6441	70	9	4	4	NUM
ejpam-6441	70	10	)	)	PUNCT
ejpam-6441	70	11	(	(	PUNCT
ejpam-6441	70	12	2025	2025	NUM
ejpam-6441	70	13	)	)	PUNCT
ejpam-6441	70	14	,	,	PUNCT
ejpam-6441	70	15	6441	6441	NUM
ejpam-6441	70	16	4	4	NUM
ejpam-6441	70	17	of	of	ADP
ejpam-6441	70	18	21	21	NUM
ejpam-6441	70	19	definition	definition	NOUN
ejpam-6441	70	20	5	5	NUM
ejpam-6441	70	21	.	.	PUNCT
ejpam-6441	71	1	[	[	X
ejpam-6441	71	2	15	15	NUM
ejpam-6441	71	3	]	]	PUNCT
ejpam-6441	71	4	let	let	VERB
ejpam-6441	71	5	ℜ	ℜ	PROPN
ejpam-6441	71	6	be	be	AUX
ejpam-6441	71	7	a	a	DET
ejpam-6441	71	8	binary	binary	ADJ
ejpam-6441	71	9	relation	relation	NOUN
ejpam-6441	71	10	on	on	ADP
ejpam-6441	71	11	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	71	12	then	then	ADV
ejpam-6441	71	13	,	,	PUNCT
ejpam-6441	71	14	a	a	DET
ejpam-6441	71	15	sequence	sequence	NOUN
ejpam-6441	71	16	{	{	PUNCT
ejpam-6441	71	17	ςn	ςn	NOUN
ejpam-6441	71	18	}	}	PUNCT
ejpam-6441	71	19	⊂	⊂	PROPN
ejpam-6441	71	20	∆ℜ	∆ℜ	PROPN
ejpam-6441	71	21	is	be	AUX
ejpam-6441	71	22	designated	designate	VERB
ejpam-6441	71	23	as	as	ADP
ejpam-6441	71	24	ℜ-preserving	ℜ-preserving	PROPN
ejpam-6441	71	25	if	if	SCONJ
ejpam-6441	71	26	∀n	∀n	NUM
ejpam-6441	71	27	∈	∈	PROPN
ejpam-6441	71	28	n	n	CCONJ
ejpam-6441	71	29	,	,	PUNCT
ejpam-6441	71	30	then	then	ADV
ejpam-6441	71	31	(	(	PUNCT
ejpam-6441	71	32	ςn	ςn	PROPN
ejpam-6441	71	33	,	,	PUNCT
ejpam-6441	71	34	ςn+1	ςn+1	NUM
ejpam-6441	71	35	)	)	PUNCT
ejpam-6441	71	36	∈	∈	PROPN
ejpam-6441	71	37	ℜ.	ℜ.	PROPN
ejpam-6441	71	38	definition	definition	NOUN
ejpam-6441	71	39	6	6	NUM
ejpam-6441	71	40	.	.	PUNCT
ejpam-6441	72	1	[	[	X
ejpam-6441	72	2	18	18	NUM
ejpam-6441	72	3	]	]	PUNCT
ejpam-6441	72	4	let	let	VERB
ejpam-6441	72	5	γ	γ	X
ejpam-6441	72	6	:	:	PUNCT
ejpam-6441	72	7	∆ℜ	∆ℜ	X
ejpam-6441	72	8	→	→	SYM
ejpam-6441	72	9	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	72	10	then	then	ADV
ejpam-6441	72	11	,	,	PUNCT
ejpam-6441	72	12	ℜ	ℜ	PROPN
ejpam-6441	72	13	on	on	ADP
ejpam-6441	72	14	∆ℜ	∆ℜ	PROPN
ejpam-6441	72	15	is	be	AUX
ejpam-6441	72	16	designated	designate	VERB
ejpam-6441	72	17	as	as	ADP
ejpam-6441	72	18	γ	γ	NOUN
ejpam-6441	72	19	-	-	NOUN
ejpam-6441	72	20	transitive	transitive	ADJ
ejpam-6441	72	21	,	,	PUNCT
ejpam-6441	72	22	if	if	SCONJ
ejpam-6441	72	23	for	for	ADP
ejpam-6441	72	24	any	any	DET
ejpam-6441	72	25	ς1	ς1	NOUN
ejpam-6441	72	26	,	,	PUNCT
ejpam-6441	72	27	ς2	ς2	PROPN
ejpam-6441	72	28	,	,	PUNCT
ejpam-6441	72	29	ς3	ς3	NOUN
ejpam-6441	72	30	∈	∈	PROPN
ejpam-6441	72	31	∆ℜ	∆ℜ	NOUN
ejpam-6441	72	32	,	,	PUNCT
ejpam-6441	72	33	(	(	PUNCT
ejpam-6441	72	34	γς1,γς2	γς1,γς2	PROPN
ejpam-6441	72	35	)	)	PUNCT
ejpam-6441	72	36	,	,	PUNCT
ejpam-6441	72	37	(	(	PUNCT
ejpam-6441	72	38	γς2,γς3	γς2,γς3	NOUN
ejpam-6441	72	39	)	)	PUNCT
ejpam-6441	72	40	∈	∈	PROPN
ejpam-6441	72	41	ℜ	ℜ	PROPN
ejpam-6441	72	42	⇒	⇒	NOUN
ejpam-6441	72	43	(	(	PUNCT
ejpam-6441	72	44	γς1,γς3	γς1,γς3	NOUN
ejpam-6441	72	45	)	)	PUNCT
ejpam-6441	72	46	∈	∈	PROPN
ejpam-6441	72	47	ℜ.	ℜ.	PROPN
ejpam-6441	72	48	definition	definition	NOUN
ejpam-6441	72	49	7	7	NUM
ejpam-6441	72	50	.	.	PUNCT
ejpam-6441	73	1	[	[	X
ejpam-6441	73	2	25	25	NUM
ejpam-6441	73	3	]	]	PUNCT
ejpam-6441	73	4	an	an	DET
ejpam-6441	73	5	ms	ms	PROPN
ejpam-6441	73	6	(	(	PUNCT
ejpam-6441	73	7	∆ℜ	∆ℜ	PROPN
ejpam-6441	73	8	,	,	PUNCT
ejpam-6441	73	9	d	d	NOUN
ejpam-6441	73	10	)	)	PUNCT
ejpam-6441	73	11	is	be	AUX
ejpam-6441	73	12	ℜ-regular	ℜ-regular	ADJ
ejpam-6441	73	13	if	if	SCONJ
ejpam-6441	73	14	for	for	ADP
ejpam-6441	73	15	every	every	PRON
ejpam-6441	73	16	{	{	PUNCT
ejpam-6441	73	17	ςn}n∈n	ςn}n∈n	NUM
ejpam-6441	73	18	⊂	⊂	PROPN
ejpam-6441	73	19	∆ℜ	∆ℜ	PROPN
ejpam-6441	73	20	,	,	PUNCT
ejpam-6441	73	21	(	(	PUNCT
ejpam-6441	73	22	ςn	ςn	NOUN
ejpam-6441	73	23	,	,	PUNCT
ejpam-6441	73	24	ςn+1	ςn+1	NUM
ejpam-6441	73	25	)	)	PUNCT
ejpam-6441	73	26	∈	∈	PROPN
ejpam-6441	73	27	ℜ	ℜ	PROPN
ejpam-6441	73	28	,	,	PUNCT
ejpam-6441	73	29	ςn	ςn	PROPN
ejpam-6441	73	30	→	→	SYM
ejpam-6441	73	31	ς	ς	PROPN
ejpam-6441	73	32	∈	∈	PROPN
ejpam-6441	73	33	∆ℜ	∆ℜ	ADJ
ejpam-6441	73	34	⇒	⇒	NOUN
ejpam-6441	73	35	(	(	PUNCT
ejpam-6441	73	36	ςn	ςn	PROPN
ejpam-6441	73	37	,	,	PUNCT
ejpam-6441	73	38	ς	ς	PROPN
ejpam-6441	73	39	)	)	PUNCT
ejpam-6441	73	40	∈	∈	PROPN
ejpam-6441	73	41	ℜ.	ℜ.	PROPN
ejpam-6441	73	42	definition	definition	NOUN
ejpam-6441	73	43	8	8	NUM
ejpam-6441	73	44	.	.	PUNCT
ejpam-6441	74	1	[	[	X
ejpam-6441	74	2	17	17	NUM
ejpam-6441	74	3	]	]	PUNCT
ejpam-6441	74	4	let	let	VERB
ejpam-6441	74	5	ℜ	ℜ	PROPN
ejpam-6441	74	6	be	be	AUX
ejpam-6441	74	7	a	a	DET
ejpam-6441	74	8	binary	binary	ADJ
ejpam-6441	74	9	relation	relation	NOUN
ejpam-6441	74	10	in	in	ADP
ejpam-6441	74	11	an	an	DET
ejpam-6441	74	12	ms	ms	NOUN
ejpam-6441	74	13	(	(	PUNCT
ejpam-6441	74	14	∆ℜ	∆ℜ	PROPN
ejpam-6441	74	15	,	,	PUNCT
ejpam-6441	74	16	d	d	NOUN
ejpam-6441	74	17	)	)	PUNCT
ejpam-6441	74	18	and	and	CCONJ
ejpam-6441	74	19	ς∗	ς∗	PROPN
ejpam-6441	74	20	∈	∈	PROPN
ejpam-6441	74	21	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	74	22	a	a	DET
ejpam-6441	74	23	map	map	NOUN
ejpam-6441	74	24	γ	γ	X
ejpam-6441	74	25	:	:	PUNCT
ejpam-6441	74	26	∆ℜ	∆ℜ	X
ejpam-6441	74	27	→	→	SYM
ejpam-6441	74	28	∆ℜ	∆ℜ	PROPN
ejpam-6441	74	29	is	be	AUX
ejpam-6441	74	30	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	74	31	at	at	ADP
ejpam-6441	74	32	ς∗	ς∗	NOUN
ejpam-6441	74	33	if	if	SCONJ
ejpam-6441	74	34	for	for	ADP
ejpam-6441	74	35	any	any	DET
ejpam-6441	74	36	ℜ-preserving	ℜ-preserving	PROPN
ejpam-6441	74	37	sequence	sequence	NOUN
ejpam-6441	74	38	{	{	PUNCT
ejpam-6441	74	39	ςn	ςn	NOUN
ejpam-6441	74	40	}	}	PUNCT
ejpam-6441	74	41	→d	→d	PUNCT
ejpam-6441	74	42	ς∗	ς∗	PROPN
ejpam-6441	74	43	,	,	PUNCT
ejpam-6441	74	44	we	we	PRON
ejpam-6441	74	45	have	have	VERB
ejpam-6441	74	46	γςn	γςn	NOUN
ejpam-6441	74	47	→d	→d	X
ejpam-6441	74	48	γς∗.	γς∗.	NOUN
ejpam-6441	74	49	γ	γ	NOUN
ejpam-6441	74	50	is	be	AUX
ejpam-6441	74	51	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	74	52	if	if	SCONJ
ejpam-6441	74	53	it	it	PRON
ejpam-6441	74	54	is	be	AUX
ejpam-6441	74	55	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	74	56	at	at	ADP
ejpam-6441	74	57	each	each	DET
ejpam-6441	74	58	point	point	NOUN
ejpam-6441	74	59	of	of	ADP
ejpam-6441	74	60	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	74	61	definition	definition	NOUN
ejpam-6441	74	62	9	9	NUM
ejpam-6441	74	63	.	.	PUNCT
ejpam-6441	75	1	[	[	X
ejpam-6441	75	2	22	22	NUM
ejpam-6441	75	3	]	]	PUNCT
ejpam-6441	75	4	let	let	AUX
ejpam-6441	75	5	(	(	PUNCT
ejpam-6441	75	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	75	7	,	,	PUNCT
ejpam-6441	75	8	d	d	NOUN
ejpam-6441	75	9	)	)	PUNCT
ejpam-6441	75	10	be	be	AUX
ejpam-6441	75	11	a	a	DET
ejpam-6441	75	12	partial	partial	ADJ
ejpam-6441	75	13	ms	ms	NOUN
ejpam-6441	75	14	with	with	ADP
ejpam-6441	75	15	a	a	DET
ejpam-6441	75	16	binary	binary	ADJ
ejpam-6441	75	17	relation	relation	NOUN
ejpam-6441	75	18	ℜ	ℜ	PROPN
ejpam-6441	75	19	and	and	CCONJ
ejpam-6441	75	20	γ	γ	X
ejpam-6441	75	21	a	a	DET
ejpam-6441	75	22	multivaluedmaps	multivaluedmap	NOUN
ejpam-6441	75	23	on	on	ADP
ejpam-6441	75	24	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	75	25	then	then	ADV
ejpam-6441	75	26	,	,	PUNCT
ejpam-6441	75	27	(	(	PUNCT
ejpam-6441	75	28	1	1	X
ejpam-6441	75	29	)	)	PUNCT
ejpam-6441	75	30	ℜ	ℜ	NOUN
ejpam-6441	75	31	is	be	AUX
ejpam-6441	75	32	designated	designate	VERB
ejpam-6441	75	33	as	as	ADP
ejpam-6441	75	34	γ	γ	NOUN
ejpam-6441	75	35	-	-	ADJ
ejpam-6441	75	36	closed	closed	ADJ
ejpam-6441	75	37	,	,	PUNCT
ejpam-6441	75	38	if	if	SCONJ
ejpam-6441	75	39	for	for	ADP
ejpam-6441	75	40	any	any	DET
ejpam-6441	75	41	ς1	ς1	NOUN
ejpam-6441	75	42	,	,	PUNCT
ejpam-6441	75	43	ς2	ς2	PROPN
ejpam-6441	75	44	∈	∈	PROPN
ejpam-6441	75	45	∆ℜ	∆ℜ	PROPN
ejpam-6441	75	46	,	,	PUNCT
ejpam-6441	75	47	(	(	PUNCT
ejpam-6441	75	48	ς1	ς1	NOUN
ejpam-6441	75	49	,	,	PUNCT
ejpam-6441	75	50	ς2	ς2	PROPN
ejpam-6441	75	51	)	)	PUNCT
ejpam-6441	75	52	∈	∈	PROPN
ejpam-6441	75	53	ℜ	ℜ	PROPN
ejpam-6441	75	54	⇒	⇒	NOUN
ejpam-6441	75	55	(	(	PUNCT
ejpam-6441	75	56	a	a	DET
ejpam-6441	75	57	,	,	PUNCT
ejpam-6441	75	58	b	b	NOUN
ejpam-6441	75	59	)	)	PUNCT
ejpam-6441	75	60	∈	∈	PROPN
ejpam-6441	75	61	ℜ	ℜ	PROPN
ejpam-6441	75	62	for	for	ADP
ejpam-6441	75	63	some	some	DET
ejpam-6441	75	64	a	a	DET
ejpam-6441	75	65	∈	∈	PROPN
ejpam-6441	75	66	γς1	γς1	NOUN
ejpam-6441	75	67	and	and	CCONJ
ejpam-6441	75	68	b	b	PROPN
ejpam-6441	75	69	∈	∈	PROPN
ejpam-6441	75	70	γς2	γς2	NOUN
ejpam-6441	75	71	.	.	PUNCT
ejpam-6441	76	1	(	(	PUNCT
ejpam-6441	76	2	2	2	X
ejpam-6441	76	3	)	)	PUNCT
ejpam-6441	76	4	γ	γ	NOUN
ejpam-6441	76	5	is	be	AUX
ejpam-6441	76	6	called	call	VERB
ejpam-6441	76	7	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	76	8	at	at	ADP
ejpam-6441	76	9	ς∗	ς∗	PROPN
ejpam-6441	76	10	∈	∈	PROPN
ejpam-6441	76	11	∆ℜ	∆ℜ	PROPN
ejpam-6441	76	12	,	,	PUNCT
ejpam-6441	76	13	if	if	SCONJ
ejpam-6441	76	14	for	for	ADP
ejpam-6441	76	15	any	any	DET
ejpam-6441	76	16	ℜ-preserving	ℜ-preserving	PROPN
ejpam-6441	76	17	sequence	sequence	NOUN
ejpam-6441	76	18	{	{	PUNCT
ejpam-6441	76	19	ςn	ςn	NOUN
ejpam-6441	76	20	}	}	PUNCT
ejpam-6441	76	21	⊂	⊂	PROPN
ejpam-6441	76	22	with	with	ADP
ejpam-6441	76	23	{	{	PUNCT
ejpam-6441	76	24	ςn	ςn	NOUN
ejpam-6441	76	25	}	}	PUNCT
ejpam-6441	76	26	→d	→d	PUNCT
ejpam-6441	76	27	ς∗	ς∗	PROPN
ejpam-6441	76	28	,	,	PUNCT
ejpam-6441	76	29	we	we	PRON
ejpam-6441	76	30	have	have	VERB
ejpam-6441	76	31	γςn	γςn	NOUN
ejpam-6441	76	32	→hd	→hd	X
ejpam-6441	77	1	γς∗	γς∗	PROPN
ejpam-6441	77	2	,	,	PUNCT
ejpam-6441	77	3	we	we	PRON
ejpam-6441	77	4	say	say	VERB
ejpam-6441	77	5	that	that	SCONJ
ejpam-6441	77	6	γ	γ	PROPN
ejpam-6441	77	7	is	be	AUX
ejpam-6441	77	8	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	77	9	if	if	SCONJ
ejpam-6441	77	10	it	it	PRON
ejpam-6441	77	11	is	be	AUX
ejpam-6441	77	12	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	77	13	at	at	ADP
ejpam-6441	77	14	each	each	DET
ejpam-6441	77	15	point	point	NOUN
ejpam-6441	77	16	of	of	ADP
ejpam-6441	77	17	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	77	18	(	(	PUNCT
ejpam-6441	77	19	3	3	X
ejpam-6441	77	20	)	)	PUNCT
ejpam-6441	77	21	ℜ	ℜ	NOUN
ejpam-6441	77	22	is	be	AUX
ejpam-6441	77	23	designated	designate	VERB
ejpam-6441	77	24	as	as	ADP
ejpam-6441	77	25	γ	γ	NOUN
ejpam-6441	77	26	-	-	NOUN
ejpam-6441	77	27	transitive	transitive	ADJ
ejpam-6441	77	28	,	,	PUNCT
ejpam-6441	77	29	if	if	SCONJ
ejpam-6441	77	30	for	for	ADP
ejpam-6441	77	31	any	any	DET
ejpam-6441	77	32	ς1	ς1	NOUN
ejpam-6441	77	33	,	,	PUNCT
ejpam-6441	77	34	ς2	ς2	PROPN
ejpam-6441	77	35	,	,	PUNCT
ejpam-6441	77	36	ς3	ς3	VERB
ejpam-6441	77	37	∈	∈	PROPN
ejpam-6441	77	38	∆ℜ	∆ℜ	NOUN
ejpam-6441	77	39	,	,	PUNCT
ejpam-6441	77	40	a	a	DET
ejpam-6441	77	41	∈	∈	PROPN
ejpam-6441	77	42	γς1	γς1	PROPN
ejpam-6441	77	43	,	,	PUNCT
ejpam-6441	77	44	b	b	PROPN
ejpam-6441	77	45	∈	∈	PROPN
ejpam-6441	77	46	γς2	γς2	NOUN
ejpam-6441	77	47	,	,	PUNCT
ejpam-6441	77	48	c	c	PROPN
ejpam-6441	77	49	∈	∈	PROPN
ejpam-6441	77	50	γς3	γς3	NOUN
ejpam-6441	77	51	,	,	PUNCT
ejpam-6441	77	52	we	we	PRON
ejpam-6441	77	53	have	have	VERB
ejpam-6441	77	54	(	(	PUNCT
ejpam-6441	77	55	a	a	PRON
ejpam-6441	77	56	,	,	PUNCT
ejpam-6441	77	57	b	b	NOUN
ejpam-6441	77	58	)	)	PUNCT
ejpam-6441	77	59	∈	∈	PROPN
ejpam-6441	77	60	ℜ	ℜ	PROPN
ejpam-6441	77	61	,	,	PUNCT
ejpam-6441	77	62	(	(	PUNCT
ejpam-6441	77	63	b	b	X
ejpam-6441	77	64	,	,	PUNCT
ejpam-6441	77	65	c	c	NOUN
ejpam-6441	77	66	)	)	PUNCT
ejpam-6441	77	67	∈	∈	PROPN
ejpam-6441	77	68	ℜ	ℜ	PROPN
ejpam-6441	77	69	⇒	⇒	NOUN
ejpam-6441	77	70	(	(	PUNCT
ejpam-6441	77	71	a	a	PRON
ejpam-6441	77	72	,	,	PUNCT
ejpam-6441	77	73	c	c	NOUN
ejpam-6441	77	74	)	)	PUNCT
ejpam-6441	77	75	∈	∈	PROPN
ejpam-6441	77	76	ℜ.	ℜ.	PROPN
ejpam-6441	77	77	definition	definition	NOUN
ejpam-6441	77	78	10	10	NUM
ejpam-6441	77	79	.	.	PUNCT
ejpam-6441	78	1	[	[	X
ejpam-6441	78	2	19	19	NUM
ejpam-6441	78	3	]	]	PUNCT
ejpam-6441	78	4	let	let	VERB
ejpam-6441	78	5	∆ℜ	∆ℜ	ADJ
ejpam-6441	78	6	̸=	̸=	PROPN
ejpam-6441	78	7	∅	∅	NOUN
ejpam-6441	78	8	and	and	CCONJ
ejpam-6441	78	9	γ	γ	X
ejpam-6441	78	10	:	:	PUNCT
ejpam-6441	78	11	∆ℜ	∆ℜ	X
ejpam-6441	78	12	→	→	SYM
ejpam-6441	78	13	cp	cp	PROPN
ejpam-6441	78	14	(	(	PUNCT
ejpam-6441	78	15	∆ℜ	∆ℜ	NOUN
ejpam-6441	78	16	)	)	PUNCT
ejpam-6441	78	17	.	.	PUNCT
ejpam-6441	79	1	a	a	DET
ejpam-6441	79	2	binary	binary	ADJ
ejpam-6441	79	3	relation	relation	NOUN
ejpam-6441	79	4	ℜ	ℜ	PROPN
ejpam-6441	79	5	on	on	ADP
ejpam-6441	79	6	an	an	DET
ejpam-6441	79	7	ms	ms	PROPN
ejpam-6441	79	8	∆ℜ	∆ℜ	PROPN
ejpam-6441	79	9	is	be	AUX
ejpam-6441	79	10	designated	designate	VERB
ejpam-6441	79	11	as	as	ADP
ejpam-6441	79	12	γ	γ	NOUN
ejpam-6441	79	13	-	-	NOUN
ejpam-6441	79	14	transitive	transitive	ADJ
ejpam-6441	79	15	,	,	PUNCT
ejpam-6441	79	16	if	if	SCONJ
ejpam-6441	79	17	for	for	ADP
ejpam-6441	79	18	any	any	DET
ejpam-6441	79	19	ς1	ς1	NOUN
ejpam-6441	79	20	,	,	PUNCT
ejpam-6441	79	21	ς2	ς2	PROPN
ejpam-6441	79	22	,	,	PUNCT
ejpam-6441	79	23	ς3	ς3	VERB
ejpam-6441	79	24	∈	∈	PROPN
ejpam-6441	79	25	∆ℜ	∆ℜ	NOUN
ejpam-6441	79	26	,	,	PUNCT
ejpam-6441	79	27	a	a	DET
ejpam-6441	79	28	∈	∈	PROPN
ejpam-6441	79	29	γς1	γς1	PROPN
ejpam-6441	79	30	,	,	PUNCT
ejpam-6441	79	31	b	b	PROPN
ejpam-6441	79	32	∈	∈	PROPN
ejpam-6441	79	33	γς2	γς2	NOUN
ejpam-6441	79	34	,	,	PUNCT
ejpam-6441	79	35	c	c	PROPN
ejpam-6441	79	36	∈	∈	PROPN
ejpam-6441	79	37	γς3	γς3	NOUN
ejpam-6441	79	38	,	,	PUNCT
ejpam-6441	79	39	we	we	PRON
ejpam-6441	79	40	have	have	VERB
ejpam-6441	79	41	(	(	PUNCT
ejpam-6441	79	42	a	a	PRON
ejpam-6441	79	43	,	,	PUNCT
ejpam-6441	79	44	b	b	NOUN
ejpam-6441	79	45	)	)	PUNCT
ejpam-6441	79	46	∈	∈	PROPN
ejpam-6441	79	47	ℜ	ℜ	PROPN
ejpam-6441	79	48	,	,	PUNCT
ejpam-6441	79	49	(	(	PUNCT
ejpam-6441	79	50	b	b	X
ejpam-6441	79	51	,	,	PUNCT
ejpam-6441	79	52	c	c	NOUN
ejpam-6441	79	53	)	)	PUNCT
ejpam-6441	79	54	∈	∈	PROPN
ejpam-6441	79	55	ℜ	ℜ	PROPN
ejpam-6441	79	56	⇒	⇒	NOUN
ejpam-6441	79	57	(	(	PUNCT
ejpam-6441	79	58	a	a	PRON
ejpam-6441	79	59	,	,	PUNCT
ejpam-6441	79	60	c	c	NOUN
ejpam-6441	79	61	)	)	PUNCT
ejpam-6441	79	62	∈	∈	PROPN
ejpam-6441	79	63	ℜ.	ℜ.	PROPN
ejpam-6441	79	64	definition	definition	NOUN
ejpam-6441	79	65	11	11	NUM
ejpam-6441	79	66	.	.	PUNCT
ejpam-6441	80	1	[	[	X
ejpam-6441	80	2	26	26	NUM
ejpam-6441	80	3	]	]	X
ejpam-6441	80	4	let	let	VERB
ejpam-6441	80	5	(	(	PUNCT
ejpam-6441	80	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	80	7	,	,	PUNCT
ejpam-6441	80	8	d	d	NOUN
ejpam-6441	80	9	)	)	PUNCT
ejpam-6441	80	10	be	be	AUX
ejpam-6441	80	11	a	a	DET
ejpam-6441	80	12	ms	ms	NOUN
ejpam-6441	80	13	with	with	ADP
ejpam-6441	80	14	a	a	DET
ejpam-6441	80	15	binary	binary	ADJ
ejpam-6441	80	16	relation	relation	NOUN
ejpam-6441	80	17	ℜ	ℜ	PROPN
ejpam-6441	80	18	and	and	CCONJ
ejpam-6441	80	19	γ	γ	X
ejpam-6441	80	20	:	:	PUNCT
ejpam-6441	80	21	∆ℜ	∆ℜ	X
ejpam-6441	80	22	→	→	SYM
ejpam-6441	80	23	cp	cp	PROPN
ejpam-6441	80	24	(	(	PUNCT
ejpam-6441	80	25	∆ℜ	∆ℜ	NOUN
ejpam-6441	80	26	)	)	PUNCT
ejpam-6441	80	27	.	.	PUNCT
ejpam-6441	81	1	then	then	ADV
ejpam-6441	81	2	,	,	PUNCT
ejpam-6441	81	3	ℜ	ℜ	PROPN
ejpam-6441	81	4	is	be	AUX
ejpam-6441	81	5	called	call	VERB
ejpam-6441	81	6	γ	γ	PROPN
ejpam-6441	81	7	-	-	PUNCT
ejpam-6441	81	8	d	d	NOUN
ejpam-6441	81	9	-	-	PUNCT
ejpam-6441	81	10	closed	closed	ADJ
ejpam-6441	81	11	,	,	PUNCT
ejpam-6441	81	12	if	if	SCONJ
ejpam-6441	81	13	(	(	PUNCT
ejpam-6441	81	14	ς1	ς1	NOUN
ejpam-6441	81	15	,	,	PUNCT
ejpam-6441	81	16	ς2	ς2	PROPN
ejpam-6441	81	17	)	)	PUNCT
ejpam-6441	81	18	∈	∈	PROPN
ejpam-6441	81	19	ℜ	ℜ	PROPN
ejpam-6441	81	20	,	,	PUNCT
ejpam-6441	81	21	r	r	NOUN
ejpam-6441	81	22	∈	∈	PROPN
ejpam-6441	81	23	γς1	γς1	PROPN
ejpam-6441	81	24	,	,	PUNCT
ejpam-6441	81	25	s	s	PROPN
ejpam-6441	81	26	∈	∈	PROPN
ejpam-6441	81	27	γς2	γς2	NOUN
ejpam-6441	81	28	,	,	PUNCT
ejpam-6441	81	29	d(r	d(r	PROPN
ejpam-6441	81	30	,	,	PUNCT
ejpam-6441	81	31	s	s	NOUN
ejpam-6441	81	32	)	)	PUNCT
ejpam-6441	81	33	≤	≤	NUM
ejpam-6441	81	34	d(ς1	d(ς1	NOUN
ejpam-6441	81	35	,	,	PUNCT
ejpam-6441	81	36	ς2	ς2	PROPN
ejpam-6441	81	37	)	)	PUNCT
ejpam-6441	81	38	⇒	⇒	NOUN
ejpam-6441	81	39	(	(	PUNCT
ejpam-6441	81	40	r	r	NOUN
ejpam-6441	81	41	,	,	PUNCT
ejpam-6441	81	42	s	s	PART
ejpam-6441	81	43	)	)	PUNCT
ejpam-6441	81	44	∈	∈	PROPN
ejpam-6441	81	45	ℜ.	ℜ.	PROPN
ejpam-6441	81	46	let	let	VERB
ejpam-6441	81	47	(	(	PUNCT
ejpam-6441	81	48	∆ℜ	∆ℜ	NOUN
ejpam-6441	81	49	,	,	PUNCT
ejpam-6441	81	50	d	d	NOUN
ejpam-6441	81	51	)	)	PUNCT
ejpam-6441	81	52	be	be	AUX
ejpam-6441	81	53	a	a	DET
ejpam-6441	81	54	ms	ms	NOUN
ejpam-6441	81	55	.	.	PUNCT
ejpam-6441	82	1	we	we	PRON
ejpam-6441	82	2	shall	shall	AUX
ejpam-6441	82	3	denote	denote	VERB
ejpam-6441	82	4	cb	cb	PROPN
ejpam-6441	82	5	(	(	PUNCT
ejpam-6441	82	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	82	7	)	)	PUNCT
ejpam-6441	82	8	the	the	DET
ejpam-6441	82	9	family	family	NOUN
ejpam-6441	82	10	of	of	ADP
ejpam-6441	82	11	all	all	PRON
ejpam-6441	82	12	bounded	bounded	ADJ
ejpam-6441	82	13	and	and	CCONJ
ejpam-6441	82	14	closed	closed	ADJ
ejpam-6441	82	15	subsets	subset	NOUN
ejpam-6441	82	16	of	of	ADP
ejpam-6441	82	17	∆ℜ	∆ℜ	PROPN
ejpam-6441	82	18	and	and	CCONJ
ejpam-6441	82	19	k	k	PROPN
ejpam-6441	82	20	(	(	PUNCT
ejpam-6441	82	21	∆ℜ	∆ℜ	NOUN
ejpam-6441	82	22	)	)	PUNCT
ejpam-6441	82	23	the	the	DET
ejpam-6441	82	24	class	class	NOUN
ejpam-6441	82	25	of	of	ADP
ejpam-6441	82	26	all	all	DET
ejpam-6441	82	27	compact	compact	ADJ
ejpam-6441	82	28	subsets	subset	NOUN
ejpam-6441	82	29	of	of	ADP
ejpam-6441	82	30	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	82	31	m.	m.	PROPN
ejpam-6441	82	32	mudhesh	mudhesh	PROPN
ejpam-6441	82	33	et	et	PROPN
ejpam-6441	82	34	al	al	PROPN
ejpam-6441	82	35	.	.	PUNCT
ejpam-6441	82	36	/	/	SYM
ejpam-6441	82	37	eur	eur	PROPN
ejpam-6441	82	38	.	.	PUNCT
ejpam-6441	83	1	j.	j.	PROPN
ejpam-6441	83	2	pure	pure	PROPN
ejpam-6441	83	3	appl	appl	PROPN
ejpam-6441	83	4	.	.	PROPN
ejpam-6441	83	5	math	math	PROPN
ejpam-6441	83	6	,	,	PUNCT
ejpam-6441	83	7	18	18	NUM
ejpam-6441	83	8	(	(	PUNCT
ejpam-6441	83	9	4	4	NUM
ejpam-6441	83	10	)	)	PUNCT
ejpam-6441	83	11	(	(	PUNCT
ejpam-6441	83	12	2025	2025	NUM
ejpam-6441	83	13	)	)	PUNCT
ejpam-6441	83	14	,	,	PUNCT
ejpam-6441	83	15	6441	6441	NUM
ejpam-6441	83	16	5	5	NUM
ejpam-6441	83	17	of	of	ADP
ejpam-6441	83	18	21	21	NUM
ejpam-6441	83	19	definition	definition	NOUN
ejpam-6441	83	20	12	12	NUM
ejpam-6441	83	21	.	.	PUNCT
ejpam-6441	84	1	[	[	X
ejpam-6441	84	2	10	10	NUM
ejpam-6441	84	3	]	]	PUNCT
ejpam-6441	84	4	let	let	VERB
ejpam-6441	84	5	h	h	NOUN
ejpam-6441	84	6	:	:	PUNCT
ejpam-6441	84	7	cb	cb	PROPN
ejpam-6441	84	8	(	(	PUNCT
ejpam-6441	84	9	∆ℜ	∆ℜ	NOUN
ejpam-6441	84	10	)	)	PUNCT
ejpam-6441	84	11	×	×	PROPN
ejpam-6441	84	12	cb	cb	PROPN
ejpam-6441	84	13	(	(	PUNCT
ejpam-6441	84	14	∆ℜ	∆ℜ	NOUN
ejpam-6441	84	15	)	)	PUNCT
ejpam-6441	84	16	→	→	PUNCT
ejpam-6441	85	1	[	[	X
ejpam-6441	85	2	0,∞	0,∞	X
ejpam-6441	85	3	)	)	PUNCT
ejpam-6441	85	4	be	be	VERB
ejpam-6441	85	5	the	the	DET
ejpam-6441	85	6	pompeiu	pompeiu	NOUN
ejpam-6441	85	7	-	-	PUNCT
ejpam-6441	85	8	hausdorff	hausdorff	NOUN
ejpam-6441	85	9	metric	metric	NOUN
ejpam-6441	85	10	induced	induce	VERB
ejpam-6441	85	11	by	by	ADP
ejpam-6441	85	12	d	d	PROPN
ejpam-6441	85	13	so	so	SCONJ
ejpam-6441	85	14	that	that	SCONJ
ejpam-6441	85	15	h	h	NOUN
ejpam-6441	85	16	(	(	PUNCT
ejpam-6441	85	17	a	a	DET
ejpam-6441	85	18	,	,	PUNCT
ejpam-6441	85	19	b	b	NOUN
ejpam-6441	85	20	)	)	PUNCT
ejpam-6441	85	21	=	=	SYM
ejpam-6441	85	22	max	max	PROPN
ejpam-6441	85	23	{	{	PUNCT
ejpam-6441	85	24	sup	sup	NOUN
ejpam-6441	85	25	ς1∈a	ς1∈a	PROPN
ejpam-6441	85	26	d	d	X
ejpam-6441	85	27	(	(	PUNCT
ejpam-6441	85	28	ς1	ς1	NOUN
ejpam-6441	85	29	,	,	PUNCT
ejpam-6441	85	30	b	b	NOUN
ejpam-6441	85	31	)	)	PUNCT
ejpam-6441	85	32	,	,	PUNCT
ejpam-6441	85	33	sup	sup	NOUN
ejpam-6441	85	34	ς2∈b	ς2∈b	PROPN
ejpam-6441	85	35	d	d	NOUN
ejpam-6441	85	36	(	(	PUNCT
ejpam-6441	85	37	a	a	PRON
ejpam-6441	85	38	,	,	PUNCT
ejpam-6441	85	39	ς2	ς2	PROPN
ejpam-6441	85	40	)	)	PUNCT
ejpam-6441	85	41	}	}	PUNCT
ejpam-6441	85	42	,	,	PUNCT
ejpam-6441	85	43	where	where	SCONJ
ejpam-6441	85	44	∀ς1	∀ς1	PROPN
ejpam-6441	85	45	∈	∈	PROPN
ejpam-6441	85	46	∆ℜ	∆ℜ	PROPN
ejpam-6441	85	47	and	and	CCONJ
ejpam-6441	85	48	a	a	PRON
ejpam-6441	85	49	,	,	PUNCT
ejpam-6441	85	50	b	b	PROPN
ejpam-6441	85	51	∈	∈	PROPN
ejpam-6441	85	52	cb	cb	X
ejpam-6441	85	53	(	(	PUNCT
ejpam-6441	85	54	∆ℜ	∆ℜ	NOUN
ejpam-6441	85	55	)	)	PUNCT
ejpam-6441	85	56	d	d	NOUN
ejpam-6441	85	57	(	(	PUNCT
ejpam-6441	85	58	ς1	ς1	NOUN
ejpam-6441	85	59	,	,	PUNCT
ejpam-6441	85	60	b	b	NOUN
ejpam-6441	85	61	)	)	PUNCT
ejpam-6441	85	62	=	=	SYM
ejpam-6441	85	63	inf	inf	NOUN
ejpam-6441	85	64	ς2∈b	ς2∈b	PROPN
ejpam-6441	85	65	d	d	NOUN
ejpam-6441	85	66	(	(	PUNCT
ejpam-6441	85	67	ς1	ς1	NOUN
ejpam-6441	85	68	,	,	PUNCT
ejpam-6441	85	69	ς2	ς2	PROPN
ejpam-6441	85	70	)	)	PUNCT
ejpam-6441	85	71	.	.	PUNCT
ejpam-6441	86	1	in	in	ADP
ejpam-6441	86	2	addition	addition	NOUN
ejpam-6441	86	3	,	,	PUNCT
ejpam-6441	86	4	cb	cb	PROPN
ejpam-6441	86	5	(	(	PUNCT
ejpam-6441	86	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	86	7	)	)	PUNCT
ejpam-6441	86	8	,	,	PUNCT
ejpam-6441	86	9	h	h	PROPN
ejpam-6441	86	10	is	be	AUX
ejpam-6441	86	11	known	know	VERB
ejpam-6441	86	12	as	as	ADP
ejpam-6441	86	13	a	a	DET
ejpam-6441	86	14	pompeiu	pompeiu	NOUN
ejpam-6441	86	15	-	-	PUNCT
ejpam-6441	86	16	hausdorff	hausdorff	NOUN
ejpam-6441	86	17	ms	ms	PROPN
ejpam-6441	86	18	.	.	PROPN
ejpam-6441	86	19	here	here	ADV
ejpam-6441	86	20	,	,	PUNCT
ejpam-6441	86	21	we	we	PRON
ejpam-6441	86	22	say	say	VERB
ejpam-6441	86	23	that	that	SCONJ
ejpam-6441	86	24	an	an	DET
ejpam-6441	86	25	element	element	NOUN
ejpam-6441	86	26	a	a	DET
ejpam-6441	86	27	∈	∈	PROPN
ejpam-6441	86	28	∆ℜ	∆ℜ	NOUN
ejpam-6441	86	29	is	be	AUX
ejpam-6441	86	30	an	an	DET
ejpam-6441	86	31	fp	fp	NOUN
ejpam-6441	86	32	of	of	ADP
ejpam-6441	86	33	a	a	DET
ejpam-6441	86	34	multivalued	multivalue	VERB
ejpam-6441	86	35	map	map	NOUN
ejpam-6441	86	36	γ	γ	NOUN
ejpam-6441	86	37	:	:	PUNCT
ejpam-6441	86	38	∆ℜ	∆ℜ	X
ejpam-6441	86	39	→	→	SYM
ejpam-6441	86	40	cb	cb	PROPN
ejpam-6441	86	41	(	(	PUNCT
ejpam-6441	86	42	∆ℜ	∆ℜ	NOUN
ejpam-6441	86	43	)	)	PUNCT
ejpam-6441	86	44	if	if	SCONJ
ejpam-6441	86	45	a	a	DET
ejpam-6441	86	46	∈	∈	PROPN
ejpam-6441	86	47	γa	γa	NOUN
ejpam-6441	86	48	.	.	PUNCT
ejpam-6441	87	1	lemma	lemma	PROPN
ejpam-6441	87	2	1	1	NUM
ejpam-6441	87	3	.	.	PUNCT
ejpam-6441	88	1	[	[	X
ejpam-6441	88	2	10	10	NUM
ejpam-6441	88	3	]	]	X
ejpam-6441	88	4	if	if	SCONJ
ejpam-6441	88	5	a	a	DET
ejpam-6441	88	6	,	,	PUNCT
ejpam-6441	88	7	b	b	PROPN
ejpam-6441	88	8	∈	∈	PROPN
ejpam-6441	88	9	cb	cb	X
ejpam-6441	88	10	(	(	PUNCT
ejpam-6441	88	11	∆ℜ	∆ℜ	NOUN
ejpam-6441	88	12	)	)	PUNCT
ejpam-6441	88	13	,	,	PUNCT
ejpam-6441	88	14	then	then	ADV
ejpam-6441	88	15	d	d	X
ejpam-6441	88	16	(	(	PUNCT
ejpam-6441	88	17	ς	ς	PROPN
ejpam-6441	88	18	,	,	PUNCT
ejpam-6441	88	19	b	b	NOUN
ejpam-6441	88	20	)	)	PUNCT
ejpam-6441	88	21	≤	≤	NUM
ejpam-6441	88	22	h	h	NOUN
ejpam-6441	88	23	(	(	PUNCT
ejpam-6441	88	24	a	a	DET
ejpam-6441	88	25	,	,	PUNCT
ejpam-6441	88	26	b	b	NOUN
ejpam-6441	88	27	)	)	PUNCT
ejpam-6441	88	28	for	for	ADP
ejpam-6441	88	29	every	every	DET
ejpam-6441	88	30	ς	ς	PROPN
ejpam-6441	88	31	∈	∈	PROPN
ejpam-6441	88	32	a.	a.	NOUN
ejpam-6441	88	33	lemma	lemma	PROPN
ejpam-6441	88	34	2	2	X
ejpam-6441	88	35	.	.	PUNCT
ejpam-6441	89	1	[	[	X
ejpam-6441	89	2	10	10	NUM
ejpam-6441	89	3	]	]	X
ejpam-6441	89	4	if	if	SCONJ
ejpam-6441	89	5	a	a	PRON
ejpam-6441	89	6	,	,	PUNCT
ejpam-6441	89	7	b	b	PROPN
ejpam-6441	89	8	∈	∈	PROPN
ejpam-6441	89	9	cb	cb	X
ejpam-6441	89	10	(	(	PUNCT
ejpam-6441	89	11	∆ℜ	∆ℜ	NOUN
ejpam-6441	89	12	)	)	PUNCT
ejpam-6441	89	13	.	.	PUNCT
ejpam-6441	90	1	for	for	ADP
ejpam-6441	90	2	µ	µ	X
ejpam-6441	90	3	>	>	X
ejpam-6441	90	4	0	0	PROPN
ejpam-6441	90	5	,	,	PUNCT
ejpam-6441	90	6	a	a	DET
ejpam-6441	90	7	∈	∈	NOUN
ejpam-6441	90	8	a	a	PRON
ejpam-6441	90	9	there	there	PRON
ejpam-6441	90	10	is	be	VERB
ejpam-6441	90	11	e	e	NOUN
ejpam-6441	90	12	∈	∈	PROPN
ejpam-6441	90	13	b	b	NOUN
ejpam-6441	90	14	such	such	ADJ
ejpam-6441	90	15	that	that	SCONJ
ejpam-6441	90	16	d	d	NOUN
ejpam-6441	90	17	(	(	PUNCT
ejpam-6441	90	18	a	a	DET
ejpam-6441	90	19	,	,	PUNCT
ejpam-6441	90	20	e	e	NOUN
ejpam-6441	90	21	)	)	PUNCT
ejpam-6441	90	22	≤	≤	NUM
ejpam-6441	90	23	h	h	NOUN
ejpam-6441	90	24	(	(	PUNCT
ejpam-6441	90	25	a	a	DET
ejpam-6441	90	26	,	,	PUNCT
ejpam-6441	90	27	b	b	NOUN
ejpam-6441	90	28	)	)	PUNCT
ejpam-6441	91	1	+	+	NOUN
ejpam-6441	91	2	µ.	µ.	ADJ
ejpam-6441	91	3	definition	definition	NOUN
ejpam-6441	91	4	13	13	NUM
ejpam-6441	91	5	.	.	PUNCT
ejpam-6441	92	1	[	[	X
ejpam-6441	92	2	1	1	X
ejpam-6441	92	3	]	]	X
ejpam-6441	92	4	let	let	VERB
ejpam-6441	92	5	(	(	PUNCT
ejpam-6441	92	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	92	7	,	,	PUNCT
ejpam-6441	92	8	d	d	NOUN
ejpam-6441	92	9	)	)	PUNCT
ejpam-6441	92	10	be	be	AUX
ejpam-6441	92	11	an	an	DET
ejpam-6441	92	12	ms	ms	NOUN
ejpam-6441	92	13	and	and	CCONJ
ejpam-6441	92	14	γ	γ	NOUN
ejpam-6441	92	15	:	:	PUNCT
ejpam-6441	92	16	∆ℜ	∆ℜ	X
ejpam-6441	92	17	→	→	SYM
ejpam-6441	92	18	∆ℜ	∆ℜ	NOUN
ejpam-6441	92	19	be	be	AUX
ejpam-6441	92	20	a	a	DET
ejpam-6441	92	21	self	self	NOUN
ejpam-6441	92	22	-	-	PUNCT
ejpam-6441	92	23	map	map	NOUN
ejpam-6441	92	24	,	,	PUNCT
ejpam-6441	92	25	then	then	ADV
ejpam-6441	92	26	γ	γ	PROPN
ejpam-6441	92	27	is	be	AUX
ejpam-6441	92	28	called	call	VERB
ejpam-6441	92	29	a	a	DET
ejpam-6441	92	30	jaggi	jaggi	NOUN
ejpam-6441	92	31	contraction	contraction	NOUN
ejpam-6441	92	32	if	if	SCONJ
ejpam-6441	92	33	there	there	PRON
ejpam-6441	92	34	are	be	VERB
ejpam-6441	92	35	λ1	λ1	ADJ
ejpam-6441	92	36	,	,	PUNCT
ejpam-6441	92	37	λ2	λ2	PROPN
ejpam-6441	92	38	∈	∈	PROPN
ejpam-6441	93	1	[	[	X
ejpam-6441	93	2	0,∞	0,∞	NOUN
ejpam-6441	93	3	)	)	PUNCT
ejpam-6441	93	4	with	with	ADP
ejpam-6441	93	5	λ1	λ1	PROPN
ejpam-6441	94	1	+	+	NUM
ejpam-6441	94	2	λ2	λ2	NOUN
ejpam-6441	94	3	<	<	X
ejpam-6441	94	4	1	1	NUM
ejpam-6441	94	5	such	such	ADJ
ejpam-6441	94	6	that	that	SCONJ
ejpam-6441	94	7	∀ς1	∀ς1	NOUN
ejpam-6441	94	8	,	,	PUNCT
ejpam-6441	94	9	ς2	ς2	PROPN
ejpam-6441	94	10	∈	∈	PROPN
ejpam-6441	95	1	∆ℜ	∆ℜ	PROPN
ejpam-6441	95	2	d	d	X
ejpam-6441	95	3	(	(	PUNCT
ejpam-6441	95	4	γς1,γς2	γς1,γς2	PROPN
ejpam-6441	95	5	)	)	PUNCT
ejpam-6441	95	6	≤	≤	NOUN
ejpam-6441	96	1	λ1d	λ1d	PUNCT
ejpam-6441	96	2	(	(	PUNCT
ejpam-6441	96	3	ς1	ς1	NOUN
ejpam-6441	96	4	,	,	PUNCT
ejpam-6441	96	5	ς2	ς2	PROPN
ejpam-6441	96	6	)	)	PUNCT
ejpam-6441	97	1	+	+	NUM
ejpam-6441	97	2	λ2	λ2	SYM
ejpam-6441	97	3	d	d	NOUN
ejpam-6441	97	4	(	(	PUNCT
ejpam-6441	97	5	ς1,γς1	ς1,γς1	PROPN
ejpam-6441	97	6	)	)	PUNCT
ejpam-6441	97	7	.d	.d	NOUN
ejpam-6441	97	8	(	(	PUNCT
ejpam-6441	97	9	ς2,γς2	ς2,γς2	X
ejpam-6441	97	10	)	)	PUNCT
ejpam-6441	97	11	d	d	NOUN
ejpam-6441	97	12	(	(	PUNCT
ejpam-6441	97	13	ς1	ς1	NOUN
ejpam-6441	97	14	,	,	PUNCT
ejpam-6441	97	15	ς2	ς2	PROPN
ejpam-6441	97	16	)	)	PUNCT
ejpam-6441	97	17	.	.	PUNCT
ejpam-6441	97	18	theorem	theorem	NOUN
ejpam-6441	97	19	2	2	NUM
ejpam-6441	97	20	.	.	PUNCT
ejpam-6441	98	1	[	[	X
ejpam-6441	98	2	1	1	X
ejpam-6441	98	3	]	]	X
ejpam-6441	98	4	let	let	VERB
ejpam-6441	98	5	(	(	PUNCT
ejpam-6441	98	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	98	7	,	,	PUNCT
ejpam-6441	98	8	d	d	NOUN
ejpam-6441	98	9	)	)	PUNCT
ejpam-6441	98	10	be	be	AUX
ejpam-6441	98	11	a	a	DET
ejpam-6441	98	12	complete	complete	ADJ
ejpam-6441	98	13	ms	ms	NOUN
ejpam-6441	98	14	and	and	CCONJ
ejpam-6441	98	15	γ	γ	NOUN
ejpam-6441	98	16	:	:	PUNCT
ejpam-6441	98	17	∆ℜ	∆ℜ	X
ejpam-6441	98	18	→	→	SYM
ejpam-6441	98	19	∆ℜ	∆ℜ	NOUN
ejpam-6441	98	20	be	be	AUX
ejpam-6441	98	21	a	a	DET
ejpam-6441	98	22	jaggi	jaggi	NOUN
ejpam-6441	98	23	contraction	contraction	NOUN
ejpam-6441	98	24	map	map	NOUN
ejpam-6441	98	25	.	.	PUNCT
ejpam-6441	99	1	then	then	ADV
ejpam-6441	99	2	,	,	PUNCT
ejpam-6441	99	3	γ	γ	PROPN
ejpam-6441	99	4	has	have	VERB
ejpam-6441	99	5	a	a	DET
ejpam-6441	99	6	ufp	ufp	NOUN
ejpam-6441	99	7	in	in	ADP
ejpam-6441	99	8	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	99	9	definition	definition	NOUN
ejpam-6441	99	10	14	14	NUM
ejpam-6441	99	11	.	.	PUNCT
ejpam-6441	100	1	[	[	X
ejpam-6441	100	2	2	2	X
ejpam-6441	100	3	]	]	X
ejpam-6441	100	4	let	let	VERB
ejpam-6441	100	5	(	(	PUNCT
ejpam-6441	100	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	100	7	,	,	PUNCT
ejpam-6441	100	8	d	d	NOUN
ejpam-6441	100	9	)	)	PUNCT
ejpam-6441	100	10	be	be	AUX
ejpam-6441	100	11	an	an	DET
ejpam-6441	100	12	ms	ms	NOUN
ejpam-6441	100	13	.	.	PROPN
ejpam-6441	101	1	we	we	PRON
ejpam-6441	101	2	say	say	VERB
ejpam-6441	101	3	that	that	SCONJ
ejpam-6441	101	4	the	the	DET
ejpam-6441	101	5	self	self	NOUN
ejpam-6441	101	6	-	-	PUNCT
ejpam-6441	101	7	mapping	mapping	NOUN
ejpam-6441	101	8	γ	γ	NOUN
ejpam-6441	101	9	:	:	PUNCT
ejpam-6441	101	10	∆ℜ	∆ℜ	X
ejpam-6441	101	11	→	→	SYM
ejpam-6441	101	12	∆ℜ	∆ℜ	PROPN
ejpam-6441	101	13	is	be	AUX
ejpam-6441	101	14	an	an	DET
ejpam-6441	101	15	interpolative	interpolative	ADJ
ejpam-6441	101	16	kannan	kannan	NOUN
ejpam-6441	101	17	-	-	PUNCT
ejpam-6441	101	18	type	type	NOUN
ejpam-6441	101	19	contraction	contraction	NOUN
ejpam-6441	101	20	,	,	PUNCT
ejpam-6441	101	21	if	if	SCONJ
ejpam-6441	101	22	there	there	PRON
ejpam-6441	101	23	exist	exist	VERB
ejpam-6441	101	24	λ	λ	PROPN
ejpam-6441	101	25	∈	∈	PROPN
ejpam-6441	102	1	[	[	X
ejpam-6441	102	2	0,∞	0,∞	NOUN
ejpam-6441	102	3	)	)	PUNCT
ejpam-6441	102	4	and	and	CCONJ
ejpam-6441	102	5	α	α	PRON
ejpam-6441	102	6	∈	∈	PROPN
ejpam-6441	102	7	(	(	PUNCT
ejpam-6441	102	8	0	0	NUM
ejpam-6441	102	9	,	,	PUNCT
ejpam-6441	102	10	1	1	NUM
ejpam-6441	102	11	)	)	PUNCT
ejpam-6441	102	12	,	,	PUNCT
ejpam-6441	102	13	such	such	ADJ
ejpam-6441	102	14	that	that	SCONJ
ejpam-6441	102	15	∀ς1	∀ς1	NOUN
ejpam-6441	102	16	,	,	PUNCT
ejpam-6441	102	17	ς2	ς2	PROPN
ejpam-6441	102	18	∈	∈	PROPN
ejpam-6441	102	19	∆ℜ	∆ℜ	NOUN
ejpam-6441	102	20	with	with	ADP
ejpam-6441	102	21	ς1	ς1	NOUN
ejpam-6441	102	22	̸=	̸=	PROPN
ejpam-6441	102	23	γς1	γς1	NOUN
ejpam-6441	103	1	d	d	X
ejpam-6441	103	2	(	(	PUNCT
ejpam-6441	103	3	γς1,γς2	γς1,γς2	PROPN
ejpam-6441	103	4	)	)	PUNCT
ejpam-6441	103	5	≤	≤	PUNCT
ejpam-6441	104	1	λ	λ	X
ejpam-6441	105	1	[	[	X
ejpam-6441	105	2	d	d	X
ejpam-6441	105	3	(	(	PUNCT
ejpam-6441	105	4	ς1,γς1	ς1,γς1	NOUN
ejpam-6441	105	5	)	)	PUNCT
ejpam-6441	105	6	]	]	PUNCT
ejpam-6441	105	7	α	α	X
ejpam-6441	105	8	.	.	PUNCT
ejpam-6441	106	1	[	[	X
ejpam-6441	106	2	d	d	X
ejpam-6441	106	3	(	(	PUNCT
ejpam-6441	106	4	ς2,γς2	ς2,γς2	X
ejpam-6441	106	5	)	)	PUNCT
ejpam-6441	106	6	]	]	PUNCT
ejpam-6441	106	7	1−α	1−α	NUM
ejpam-6441	106	8	.	.	PUNCT
ejpam-6441	107	1	theorem	theorem	NOUN
ejpam-6441	107	2	3	3	NUM
ejpam-6441	107	3	.	.	PUNCT
ejpam-6441	108	1	[	[	X
ejpam-6441	108	2	2	2	NUM
ejpam-6441	108	3	]	]	X
ejpam-6441	108	4	let	let	VERB
ejpam-6441	108	5	(	(	PUNCT
ejpam-6441	108	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	108	7	,	,	PUNCT
ejpam-6441	108	8	d	d	NOUN
ejpam-6441	108	9	)	)	PUNCT
ejpam-6441	108	10	be	be	AUX
ejpam-6441	108	11	a	a	DET
ejpam-6441	108	12	complete	complete	ADJ
ejpam-6441	108	13	ms	ms	NOUN
ejpam-6441	108	14	and	and	CCONJ
ejpam-6441	108	15	γ	γ	NOUN
ejpam-6441	108	16	:	:	PUNCT
ejpam-6441	108	17	∆ℜ	∆ℜ	X
ejpam-6441	108	18	→	→	SYM
ejpam-6441	108	19	∆ℜ	∆ℜ	NOUN
ejpam-6441	108	20	be	be	AUX
ejpam-6441	108	21	an	an	DET
ejpam-6441	108	22	interpolative	interpolative	ADJ
ejpam-6441	108	23	kannan	kannan	NOUN
ejpam-6441	108	24	-	-	PUNCT
ejpam-6441	108	25	type	type	NOUN
ejpam-6441	108	26	contraction	contraction	NOUN
ejpam-6441	108	27	map	map	NOUN
ejpam-6441	108	28	.	.	PUNCT
ejpam-6441	109	1	then	then	ADV
ejpam-6441	109	2	,	,	PUNCT
ejpam-6441	109	3	γ	γ	PROPN
ejpam-6441	109	4	has	have	VERB
ejpam-6441	109	5	a	a	DET
ejpam-6441	109	6	ufp	ufp	NOUN
ejpam-6441	109	7	in	in	ADP
ejpam-6441	109	8	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	109	9	definition	definition	NOUN
ejpam-6441	109	10	15	15	NUM
ejpam-6441	109	11	.	.	PUNCT
ejpam-6441	110	1	[	[	X
ejpam-6441	110	2	5	5	NUM
ejpam-6441	110	3	]	]	PUNCT
ejpam-6441	110	4	a	a	DET
ejpam-6441	110	5	self	self	NOUN
ejpam-6441	110	6	-	-	PUNCT
ejpam-6441	110	7	mapping	mapping	NOUN
ejpam-6441	110	8	γ	γ	NOUN
ejpam-6441	110	9	on	on	ADP
ejpam-6441	110	10	an	an	DET
ejpam-6441	110	11	ms	ms	NOUN
ejpam-6441	110	12	(	(	PUNCT
ejpam-6441	110	13	∆ℜ	∆ℜ	PROPN
ejpam-6441	110	14	,	,	PUNCT
ejpam-6441	110	15	d	d	NOUN
ejpam-6441	110	16	)	)	PUNCT
ejpam-6441	110	17	is	be	AUX
ejpam-6441	110	18	called	call	VERB
ejpam-6441	110	19	a	a	DET
ejpam-6441	110	20	jaggi	jaggi	NOUN
ejpam-6441	110	21	-	-	PUNCT
ejpam-6441	110	22	type	type	NOUN
ejpam-6441	110	23	hybrid	hybrid	ADJ
ejpam-6441	110	24	contraction	contraction	NOUN
ejpam-6441	110	25	if	if	SCONJ
ejpam-6441	110	26	there	there	PRON
ejpam-6441	110	27	is	be	VERB
ejpam-6441	110	28	ψ	ψ	PRON
ejpam-6441	110	29	∈	∈	NOUN
ejpam-6441	110	30	ψ	ψ	NOUN
ejpam-6441	110	31	so	so	ADV
ejpam-6441	110	32	that	that	SCONJ
ejpam-6441	110	33	d	d	X
ejpam-6441	110	34	(	(	PUNCT
ejpam-6441	110	35	γς1,γς2	γς1,γς2	X
ejpam-6441	110	36	)	)	PUNCT
ejpam-6441	110	37	≤	≤	NOUN
ejpam-6441	110	38	ψ	ψ	X
ejpam-6441	110	39	(	(	PUNCT
ejpam-6441	110	40	mj	mj	PROPN
ejpam-6441	110	41	(	(	PUNCT
ejpam-6441	110	42	ς1	ς1	NOUN
ejpam-6441	110	43	,	,	PUNCT
ejpam-6441	110	44	ς2	ς2	PROPN
ejpam-6441	110	45	)	)	PUNCT
ejpam-6441	110	46	)	)	PUNCT
ejpam-6441	110	47	,	,	PUNCT
ejpam-6441	110	48	where	where	SCONJ
ejpam-6441	110	49	for	for	ADP
ejpam-6441	110	50	s	s	PRON
ejpam-6441	110	51	≥	≥	NOUN
ejpam-6441	110	52	0	0	NUM
ejpam-6441	110	53	,	,	PUNCT
ejpam-6441	110	54	ς1	ς1	NOUN
ejpam-6441	110	55	,	,	PUNCT
ejpam-6441	110	56	ς2	ς2	PROPN
ejpam-6441	110	57	∈	∈	PROPN
ejpam-6441	110	58	∆ℜ	∆ℜ	PROPN
ejpam-6441	110	59	and	and	CCONJ
ejpam-6441	110	60	λi	λi	ADP
ejpam-6441	110	61	≥	≥	NOUN
ejpam-6441	110	62	0	0	NUM
ejpam-6441	110	63	,	,	PUNCT
ejpam-6441	110	64	i	i	PRON
ejpam-6441	110	65	=	=	NOUN
ejpam-6441	110	66	1	1	NUM
ejpam-6441	110	67	,	,	PUNCT
ejpam-6441	110	68	2	2	NUM
ejpam-6441	110	69	,	,	PUNCT
ejpam-6441	110	70	...	...	PUNCT
ejpam-6441	110	71	with	with	ADP
ejpam-6441	110	72	λ1	λ1	PROPN
ejpam-6441	110	73	+	+	CCONJ
ejpam-6441	110	74	λ2	λ2	NOUN
ejpam-6441	110	75	=	=	SYM
ejpam-6441	110	76	1	1	NUM
ejpam-6441	110	77	and	and	CCONJ
ejpam-6441	110	78	mj	mj	PROPN
ejpam-6441	110	79	(	(	PUNCT
ejpam-6441	110	80	ς1	ς1	NOUN
ejpam-6441	110	81	,	,	PUNCT
ejpam-6441	110	82	ς2	ς2	PROPN
ejpam-6441	110	83	)	)	PUNCT
ejpam-6441	110	84	=	=	PUNCT
ejpam-6441	111	1			PUNCT
ejpam-6441	111	2	[	[	PUNCT
ejpam-6441	111	3	λ1	λ1	PROPN
ejpam-6441	111	4	(	(	PUNCT
ejpam-6441	111	5	d(ς1,γς1)d(ς2,γς2	d(ς1,γς1)d(ς2,γς2	PROPN
ejpam-6441	111	6	)	)	PUNCT
ejpam-6441	111	7	d(ς1,ς2	d(ς1,ς2	NOUN
ejpam-6441	111	8	)	)	PUNCT
ejpam-6441	111	9	)	)	PUNCT
ejpam-6441	112	1	s	s	PART
ejpam-6441	113	1	+	+	NUM
ejpam-6441	113	2	λ2	λ2	NOUN
ejpam-6441	113	3	(	(	PUNCT
ejpam-6441	113	4	d	d	X
ejpam-6441	113	5	(	(	PUNCT
ejpam-6441	113	6	ς1	ς1	NOUN
ejpam-6441	113	7	,	,	PUNCT
ejpam-6441	113	8	ς2	ς2	PROPN
ejpam-6441	113	9	)	)	PUNCT
ejpam-6441	113	10	)	)	PUNCT
ejpam-6441	113	11	s	s	VERB
ejpam-6441	113	12	]	]	PUNCT
ejpam-6441	113	13	1	1	NUM
ejpam-6441	113	14	s	s	NOUN
ejpam-6441	113	15	,	,	PUNCT
ejpam-6441	113	16	for	for	ADP
ejpam-6441	113	17	s	s	PROPN
ejpam-6441	113	18	>	>	X
ejpam-6441	113	19	0	0	PROPN
ejpam-6441	113	20	,	,	PUNCT
ejpam-6441	113	21	ς1	ς1	PROPN
ejpam-6441	113	22	̸=	̸=	PROPN
ejpam-6441	113	23	ς2	ς2	PROPN
ejpam-6441	113	24	,	,	PUNCT
ejpam-6441	113	25	(	(	PUNCT
ejpam-6441	113	26	d	d	X
ejpam-6441	113	27	(	(	PUNCT
ejpam-6441	113	28	ς1,γς1	ς1,γς1	NOUN
ejpam-6441	113	29	)	)	PUNCT
ejpam-6441	113	30	)	)	PUNCT
ejpam-6441	114	1	λ1	λ1	PROPN
ejpam-6441	114	2	(	(	PUNCT
ejpam-6441	114	3	d	d	PROPN
ejpam-6441	114	4	(	(	PUNCT
ejpam-6441	114	5	ς2,γς2	ς2,γς2	NUM
ejpam-6441	114	6	)	)	PUNCT
ejpam-6441	114	7	)	)	PUNCT
ejpam-6441	115	1	λ2	λ2	NOUN
ejpam-6441	115	2	for	for	ADP
ejpam-6441	115	3	s	s	NOUN
ejpam-6441	115	4	=	=	SYM
ejpam-6441	115	5	0	0	NUM
ejpam-6441	115	6	,	,	PUNCT
ejpam-6441	115	7	ς1	ς1	NOUN
ejpam-6441	115	8	,	,	PUNCT
ejpam-6441	115	9	ς2	ς2	PROPN
ejpam-6441	115	10	∈	∈	PROPN
ejpam-6441	115	11	∆ℜ\fγ(∆ℜ	∆ℜ\fγ(∆ℜ	PROPN
ejpam-6441	115	12	)	)	PUNCT
ejpam-6441	115	13	,	,	PUNCT
ejpam-6441	115	14	where	where	SCONJ
ejpam-6441	115	15	fγ(∆ℜ	fγ(∆ℜ	NOUN
ejpam-6441	115	16	)	)	PUNCT
ejpam-6441	115	17	=	=	PRON
ejpam-6441	115	18	{	{	PUNCT
ejpam-6441	115	19	ς	ς	PROPN
ejpam-6441	115	20	∈	∈	PROPN
ejpam-6441	115	21	∆ℜ	∆ℜ	NOUN
ejpam-6441	115	22	:	:	PUNCT
ejpam-6441	115	23	γς	γς	PROPN
ejpam-6441	115	24	=	=	SYM
ejpam-6441	115	25	ς	ς	PROPN
ejpam-6441	115	26	}	}	PUNCT
ejpam-6441	115	27	.	.	PUNCT
ejpam-6441	116	1	m.	m.	NOUN
ejpam-6441	116	2	mudhesh	mudhesh	PROPN
ejpam-6441	116	3	et	et	PROPN
ejpam-6441	116	4	al	al	PROPN
ejpam-6441	116	5	.	.	PUNCT
ejpam-6441	116	6	/	/	SYM
ejpam-6441	116	7	eur	eur	PROPN
ejpam-6441	116	8	.	.	PUNCT
ejpam-6441	117	1	j.	j.	PROPN
ejpam-6441	117	2	pure	pure	PROPN
ejpam-6441	117	3	appl	appl	PROPN
ejpam-6441	117	4	.	.	PROPN
ejpam-6441	117	5	math	math	PROPN
ejpam-6441	117	6	,	,	PUNCT
ejpam-6441	117	7	18	18	NUM
ejpam-6441	117	8	(	(	PUNCT
ejpam-6441	117	9	4	4	NUM
ejpam-6441	117	10	)	)	PUNCT
ejpam-6441	117	11	(	(	PUNCT
ejpam-6441	117	12	2025	2025	NUM
ejpam-6441	117	13	)	)	PUNCT
ejpam-6441	117	14	,	,	PUNCT
ejpam-6441	117	15	6441	6441	NUM
ejpam-6441	117	16	6	6	NUM
ejpam-6441	117	17	of	of	ADP
ejpam-6441	117	18	21	21	NUM
ejpam-6441	117	19	theorem	theorem	VERB
ejpam-6441	117	20	4	4	NUM
ejpam-6441	117	21	.	.	PUNCT
ejpam-6441	118	1	[	[	X
ejpam-6441	118	2	5	5	NUM
ejpam-6441	118	3	]	]	X
ejpam-6441	118	4	let	let	AUX
ejpam-6441	118	5	(	(	PUNCT
ejpam-6441	118	6	∆ℜ	∆ℜ	NOUN
ejpam-6441	118	7	,	,	PUNCT
ejpam-6441	118	8	d	d	NOUN
ejpam-6441	118	9	)	)	PUNCT
ejpam-6441	118	10	be	be	AUX
ejpam-6441	118	11	a	a	DET
ejpam-6441	118	12	complete	complete	ADJ
ejpam-6441	118	13	ms	ms	NOUN
ejpam-6441	118	14	and	and	CCONJ
ejpam-6441	118	15	γ	γ	NOUN
ejpam-6441	118	16	:	:	PUNCT
ejpam-6441	118	17	∆ℜ	∆ℜ	X
ejpam-6441	118	18	→	→	SYM
ejpam-6441	118	19	∆ℜ	∆ℜ	NOUN
ejpam-6441	118	20	be	be	AUX
ejpam-6441	118	21	a	a	DET
ejpam-6441	118	22	continuous	continuous	ADJ
ejpam-6441	118	23	jaggitype	jaggitype	NOUN
ejpam-6441	118	24	hybrid	hybrid	NOUN
ejpam-6441	118	25	contraction	contraction	NOUN
ejpam-6441	118	26	.	.	PUNCT
ejpam-6441	119	1	then	then	ADV
ejpam-6441	119	2	,	,	PUNCT
ejpam-6441	119	3	γ	γ	PROPN
ejpam-6441	119	4	has	have	VERB
ejpam-6441	119	5	an	an	DET
ejpam-6441	119	6	fp	fp	NOUN
ejpam-6441	119	7	in	in	ADP
ejpam-6441	119	8	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	119	9	moreover	moreover	ADV
ejpam-6441	119	10	,	,	PUNCT
ejpam-6441	119	11	for	for	ADP
ejpam-6441	119	12	any	any	DET
ejpam-6441	119	13	ς0	ς0	PROPN
ejpam-6441	119	14	∈	∈	PROPN
ejpam-6441	119	15	∆ℜ	∆ℜ	PROPN
ejpam-6441	119	16	,	,	PUNCT
ejpam-6441	119	17	the	the	DET
ejpam-6441	119	18	sequence	sequence	NOUN
ejpam-6441	119	19	{	{	PUNCT
ejpam-6441	119	20	γς0	γς0	NOUN
ejpam-6441	119	21	}	}	PUNCT
ejpam-6441	119	22	converges	converge	NOUN
ejpam-6441	119	23	to	to	ADP
ejpam-6441	119	24	ς	ς	PROPN
ejpam-6441	119	25	.	.	PUNCT
ejpam-6441	119	26	definition	definition	NOUN
ejpam-6441	119	27	16	16	NUM
ejpam-6441	119	28	.	.	PUNCT
ejpam-6441	120	1	[	[	X
ejpam-6441	120	2	27	27	NUM
ejpam-6441	120	3	]	]	PUNCT
ejpam-6441	120	4	a	a	DET
ejpam-6441	120	5	self	self	NOUN
ejpam-6441	120	6	-	-	PUNCT
ejpam-6441	120	7	mapping	mapping	NOUN
ejpam-6441	120	8	γ	γ	NOUN
ejpam-6441	120	9	on	on	ADP
ejpam-6441	120	10	a	a	DET
ejpam-6441	120	11	graphical	graphical	ADJ
ejpam-6441	120	12	b	b	NOUN
ejpam-6441	120	13	-	-	PUNCT
ejpam-6441	120	14	ms	ms	NOUN
ejpam-6441	120	15	(	(	PUNCT
ejpam-6441	120	16	∆ℜ	∆ℜ	PROPN
ejpam-6441	120	17	,	,	PUNCT
ejpam-6441	120	18	d	d	NOUN
ejpam-6441	120	19	)	)	PUNCT
ejpam-6441	120	20	with	with	ADP
ejpam-6441	120	21	s	s	PRON
ejpam-6441	120	22	≥	≥	NUM
ejpam-6441	120	23	1	1	NUM
ejpam-6441	120	24	is	be	AUX
ejpam-6441	120	25	called	call	VERB
ejpam-6441	120	26	a	a	DET
ejpam-6441	120	27	fisher	fisher	NOUN
ejpam-6441	120	28	-	-	PUNCT
ejpam-6441	120	29	type	type	NOUN
ejpam-6441	120	30	graph	graph	NOUN
ejpam-6441	120	31	contraction	contraction	NOUN
ejpam-6441	120	32	for	for	SCONJ
ejpam-6441	120	33	hg	hg	PROPN
ejpam-6441	120	34	on	on	ADP
ejpam-6441	120	35	(	(	PUNCT
ejpam-6441	120	36	∆ℜ	∆ℜ	PROPN
ejpam-6441	120	37	,	,	PUNCT
ejpam-6441	120	38	d	d	PROPN
ejpam-6441	120	39	)	)	PUNCT
ejpam-6441	120	40	if	if	SCONJ
ejpam-6441	120	41	hg	hg	PROPN
ejpam-6441	120	42	is	be	AUX
ejpam-6441	120	43	graph	graph	NOUN
ejpam-6441	120	44	preserving	preserve	VERB
ejpam-6441	120	45	and	and	CCONJ
ejpam-6441	120	46	if	if	SCONJ
ejpam-6441	120	47	there	there	PRON
ejpam-6441	120	48	exist	exist	VERB
ejpam-6441	120	49	nonnegative	nonnegative	ADJ
ejpam-6441	120	50	constants	constant	NOUN
ejpam-6441	120	51	λ1	λ1	ADJ
ejpam-6441	120	52	,	,	PUNCT
ejpam-6441	120	53	λ2	λ2	PROPN
ejpam-6441	120	54	with	with	ADP
ejpam-6441	120	55	λ1	λ1	PROPN
ejpam-6441	121	1	+	+	CCONJ
ejpam-6441	121	2	λ2	λ2	NOUN
ejpam-6441	121	3	<	<	X
ejpam-6441	121	4	1	1	NUM
ejpam-6441	121	5	s	s	VERB
ejpam-6441	121	6	so	so	SCONJ
ejpam-6441	121	7	that	that	SCONJ
ejpam-6441	121	8	for	for	ADP
ejpam-6441	121	9	every	every	DET
ejpam-6441	121	10	ς1	ς1	NOUN
ejpam-6441	121	11	,	,	PUNCT
ejpam-6441	121	12	ς2	ς2	PROPN
ejpam-6441	121	13	∈	∈	PROPN
ejpam-6441	122	1	∆ℜ	∆ℜ	NOUN
ejpam-6441	122	2	with	with	ADP
ejpam-6441	122	3	(	(	PUNCT
ejpam-6441	122	4	ς1	ς1	NOUN
ejpam-6441	122	5	,	,	PUNCT
ejpam-6441	122	6	ς2	ς2	PROPN
ejpam-6441	122	7	)	)	PUNCT
ejpam-6441	122	8	∈	∈	PROPN
ejpam-6441	122	9	e(hg	e(hg	NOUN
ejpam-6441	122	10	)	)	PUNCT
ejpam-6441	122	11	,	,	PUNCT
ejpam-6441	122	12	we	we	PRON
ejpam-6441	122	13	have	have	VERB
ejpam-6441	122	14	d	d	X
ejpam-6441	122	15	(	(	PUNCT
ejpam-6441	122	16	γς1,γς2	γς1,γς2	X
ejpam-6441	122	17	)	)	PUNCT
ejpam-6441	122	18	≤	≤	NOUN
ejpam-6441	123	1	λ1d	λ1d	PUNCT
ejpam-6441	123	2	(	(	PUNCT
ejpam-6441	123	3	ς1	ς1	NOUN
ejpam-6441	123	4	,	,	PUNCT
ejpam-6441	123	5	ς2	ς2	PROPN
ejpam-6441	123	6	)	)	PUNCT
ejpam-6441	124	1	+	+	NUM
ejpam-6441	124	2	λ2	λ2	SYM
ejpam-6441	124	3	d	d	NOUN
ejpam-6441	124	4	(	(	PUNCT
ejpam-6441	124	5	ς1,γς1	ς1,γς1	PROPN
ejpam-6441	124	6	)	)	PUNCT
ejpam-6441	124	7	d	d	NOUN
ejpam-6441	124	8	(	(	PUNCT
ejpam-6441	124	9	ς2,γς2	ς2,γς2	X
ejpam-6441	124	10	)	)	PUNCT
ejpam-6441	124	11	1	1	NUM
ejpam-6441	125	1	+	+	CCONJ
ejpam-6441	125	2	d	d	X
ejpam-6441	125	3	(	(	PUNCT
ejpam-6441	125	4	ς1	ς1	NOUN
ejpam-6441	125	5	,	,	PUNCT
ejpam-6441	125	6	ς2	ς2	PROPN
ejpam-6441	125	7	)	)	PUNCT
ejpam-6441	125	8	.	.	PUNCT
ejpam-6441	126	1	2	2	X
ejpam-6441	126	2	.	.	X
ejpam-6441	126	3	main	main	ADJ
ejpam-6441	126	4	result	result	NOUN
ejpam-6441	126	5	in	in	ADP
ejpam-6441	126	6	this	this	DET
ejpam-6441	126	7	part	part	NOUN
ejpam-6441	126	8	,	,	PUNCT
ejpam-6441	126	9	we	we	PRON
ejpam-6441	126	10	study	study	VERB
ejpam-6441	126	11	the	the	DET
ejpam-6441	126	12	existence	existence	NOUN
ejpam-6441	126	13	of	of	ADP
ejpam-6441	126	14	fps	fps	NOUN
ejpam-6441	126	15	for	for	ADP
ejpam-6441	126	16	an	an	DET
ejpam-6441	126	17	almost	almost	ADV
ejpam-6441	126	18	fisher	fisher	NOUN
ejpam-6441	126	19	-	-	PUNCT
ejpam-6441	126	20	type	type	NOUN
ejpam-6441	126	21	multivalued	multivalue	VERB
ejpam-6441	126	22	f	f	PROPN
ejpam-6441	126	23	-contraction	-contraction	PROPN
ejpam-6441	126	24	mappings	mapping	NOUN
ejpam-6441	126	25	endowed	endow	VERB
ejpam-6441	126	26	with	with	ADP
ejpam-6441	126	27	a	a	DET
ejpam-6441	126	28	γ	γ	NOUN
ejpam-6441	126	29	-	-	ADJ
ejpam-6441	126	30	transitive	transitive	ADJ
ejpam-6441	126	31	binary	binary	ADJ
ejpam-6441	126	32	relation	relation	NOUN
ejpam-6441	126	33	ℜ	ℜ	PROPN
ejpam-6441	126	34	into	into	ADP
ejpam-6441	126	35	a	a	DET
ejpam-6441	126	36	ms	ms	PROPN
ejpam-6441	126	37	.	.	PROPN
ejpam-6441	126	38	definition	definition	NOUN
ejpam-6441	126	39	17	17	NUM
ejpam-6441	126	40	.	.	PUNCT
ejpam-6441	127	1	let	let	AUX
ejpam-6441	127	2	(	(	PUNCT
ejpam-6441	127	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	127	4	,	,	PUNCT
ejpam-6441	127	5	d	d	NOUN
ejpam-6441	127	6	)	)	PUNCT
ejpam-6441	127	7	be	be	AUX
ejpam-6441	127	8	a	a	DET
ejpam-6441	127	9	ms	ms	PROPN
ejpam-6441	127	10	.	.	PROPN
ejpam-6441	128	1	a	a	DET
ejpam-6441	128	2	map	map	NOUN
ejpam-6441	128	3	γ	γ	X
ejpam-6441	128	4	:	:	PUNCT
ejpam-6441	128	5	∆ℜ	∆ℜ	PROPN
ejpam-6441	128	6	→	→	SYM
ejpam-6441	128	7	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	128	8	)	)	PUNCT
ejpam-6441	128	9	is	be	AUX
ejpam-6441	128	10	called	call	VERB
ejpam-6441	128	11	an	an	DET
ejpam-6441	128	12	almost	almost	ADV
ejpam-6441	128	13	fisher	fisher	NOUN
ejpam-6441	128	14	-	-	PUNCT
ejpam-6441	128	15	type	type	NOUN
ejpam-6441	128	16	multivalued	multivalue	VERB
ejpam-6441	128	17	f	f	PROPN
ejpam-6441	128	18	-contraction	-contraction	PROPN
ejpam-6441	128	19	endowed	endow	VERB
ejpam-6441	128	20	with	with	ADP
ejpam-6441	128	21	a	a	DET
ejpam-6441	128	22	γ	γ	NOUN
ejpam-6441	128	23	-	-	ADJ
ejpam-6441	128	24	transitive	transitive	ADJ
ejpam-6441	128	25	binary	binary	ADJ
ejpam-6441	128	26	relation	relation	PROPN
ejpam-6441	128	27	ℜ	ℜ	PROPN
ejpam-6441	128	28	,	,	PUNCT
ejpam-6441	128	29	if	if	SCONJ
ejpam-6441	128	30	there	there	PRON
ejpam-6441	128	31	exist	exist	VERB
ejpam-6441	128	32	τ	τ	PROPN
ejpam-6441	128	33	∈	∈	PROPN
ejpam-6441	128	34	r+	r+	NOUN
ejpam-6441	128	35	,	,	PUNCT
ejpam-6441	128	36	f	f	PROPN
ejpam-6441	128	37	∈	∈	PROPN
ejpam-6441	128	38	∆w	∆w	PROPN
ejpam-6441	128	39	and	and	CCONJ
ejpam-6441	128	40	λ1	λ1	ADJ
ejpam-6441	128	41	,	,	PUNCT
ejpam-6441	128	42	λ2	λ2	PROPN
ejpam-6441	128	43	,	,	PUNCT
ejpam-6441	128	44	l	l	NOUN
ejpam-6441	128	45	≥	≥	NOUN
ejpam-6441	128	46	0	0	NUM
ejpam-6441	128	47	with	with	ADP
ejpam-6441	128	48	λ1	λ1	PROPN
ejpam-6441	128	49	+	+	CCONJ
ejpam-6441	128	50	λ2	λ2	NOUN
ejpam-6441	128	51	≤	≤	NUM
ejpam-6441	128	52	1	1	NUM
ejpam-6441	128	53	such	such	ADJ
ejpam-6441	128	54	that	that	PRON
ejpam-6441	128	55	for	for	ADP
ejpam-6441	128	56	all	all	PRON
ejpam-6441	128	57	(	(	PUNCT
ejpam-6441	128	58	ς1	ς1	NOUN
ejpam-6441	128	59	,	,	PUNCT
ejpam-6441	128	60	ς2	ς2	PROPN
ejpam-6441	128	61	)	)	PUNCT
ejpam-6441	128	62	∈	∈	PROPN
ejpam-6441	128	63	ℜ∗	ℜ∗	PROPN
ejpam-6441	129	1	=	=	PRON
ejpam-6441	129	2	{	{	PUNCT
ejpam-6441	129	3	(	(	PUNCT
ejpam-6441	129	4	ς1	ς1	NOUN
ejpam-6441	129	5	,	,	PUNCT
ejpam-6441	129	6	ς2	ς2	PROPN
ejpam-6441	129	7	)	)	PUNCT
ejpam-6441	129	8	∈	∈	PROPN
ejpam-6441	129	9	ℜ	ℜ	PROPN
ejpam-6441	129	10	:	:	PUNCT
ejpam-6441	129	11	ς1	ς1	NOUN
ejpam-6441	129	12	,	,	PUNCT
ejpam-6441	129	13	ς2	ς2	PROPN
ejpam-6441	129	14	∈	∈	PROPN
ejpam-6441	129	15	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	129	16	(	(	PUNCT
ejpam-6441	129	17	γ	γ	NOUN
ejpam-6441	129	18	)	)	PUNCT
ejpam-6441	129	19	}	}	PUNCT
ejpam-6441	129	20	,	,	PUNCT
ejpam-6441	129	21	we	we	PRON
ejpam-6441	129	22	have	have	VERB
ejpam-6441	129	23	τ	τ	PROPN
ejpam-6441	130	1	+	+	NUM
ejpam-6441	130	2	f	f	X
ejpam-6441	130	3	(	(	PUNCT
ejpam-6441	130	4	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	130	5	)	)	PUNCT
ejpam-6441	130	6	)	)	PUNCT
ejpam-6441	130	7	≤	≤	NUM
ejpam-6441	130	8	f	f	X
ejpam-6441	130	9	(	(	PUNCT
ejpam-6441	130	10	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	130	11	,	,	PUNCT
ejpam-6441	130	12	ς2	ς2	PROPN
ejpam-6441	130	13	)	)	PUNCT
ejpam-6441	130	14	)	)	PUNCT
ejpam-6441	131	1	+	+	CCONJ
ejpam-6441	131	2	lnℜ	lnℜ	NOUN
ejpam-6441	131	3	(	(	PUNCT
ejpam-6441	131	4	ς1	ς1	NOUN
ejpam-6441	131	5	,	,	PUNCT
ejpam-6441	131	6	ς2	ς2	PROPN
ejpam-6441	131	7	)	)	PUNCT
ejpam-6441	131	8	,	,	PUNCT
ejpam-6441	131	9	(	(	PUNCT
ejpam-6441	131	10	1	1	X
ejpam-6441	131	11	)	)	PUNCT
ejpam-6441	131	12	where	where	SCONJ
ejpam-6441	131	13	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	131	14	,	,	PUNCT
ejpam-6441	131	15	ς2	ς2	PROPN
ejpam-6441	131	16	)	)	PUNCT
ejpam-6441	131	17	=	=	SYM
ejpam-6441	132	1			PROPN
ejpam-6441	132	2	[	[	PUNCT
ejpam-6441	132	3	λ1	λ1	PROPN
ejpam-6441	132	4	(	(	PUNCT
ejpam-6441	132	5	d(ς1,γς1)d(ς2,γς2	d(ς1,γς1)d(ς2,γς2	PROPN
ejpam-6441	132	6	)	)	PUNCT
ejpam-6441	132	7	1+d(ς1,ς2	1+d(ς1,ς2	NUM
ejpam-6441	132	8	)	)	PUNCT
ejpam-6441	132	9	)	)	PUNCT
ejpam-6441	133	1	β	β	X
ejpam-6441	134	1	+	+	NUM
ejpam-6441	134	2	λ2	λ2	NOUN
ejpam-6441	134	3	(	(	PUNCT
ejpam-6441	134	4	d(ς1	d(ς1	NOUN
ejpam-6441	134	5	,	,	PUNCT
ejpam-6441	134	6	ς2	ς2	PROPN
ejpam-6441	134	7	)	)	PUNCT
ejpam-6441	134	8	)	)	PUNCT
ejpam-6441	134	9	β	β	X
ejpam-6441	134	10	]	]	PUNCT
ejpam-6441	134	11	1	1	NUM
ejpam-6441	134	12	β	β	NOUN
ejpam-6441	134	13	if	if	SCONJ
ejpam-6441	134	14	β	β	X
ejpam-6441	134	15	>	>	X
ejpam-6441	134	16	0	0	NUM
ejpam-6441	134	17	;	;	PUNCT
ejpam-6441	134	18	(	(	PUNCT
ejpam-6441	134	19	d	d	X
ejpam-6441	134	20	(	(	PUNCT
ejpam-6441	134	21	ς1,γς1	ς1,γς1	NOUN
ejpam-6441	134	22	)	)	PUNCT
ejpam-6441	134	23	)	)	PUNCT
ejpam-6441	135	1	λ1	λ1	PROPN
ejpam-6441	135	2	(	(	PUNCT
ejpam-6441	135	3	d	d	PROPN
ejpam-6441	135	4	(	(	PUNCT
ejpam-6441	135	5	ς2,γς2	ς2,γς2	NUM
ejpam-6441	135	6	)	)	PUNCT
ejpam-6441	135	7	)	)	PUNCT
ejpam-6441	136	1	λ2	λ2	NOUN
ejpam-6441	136	2	if	if	SCONJ
ejpam-6441	136	3	β	β	X
ejpam-6441	136	4	=	=	SYM
ejpam-6441	136	5	0	0	NUM
ejpam-6441	136	6	,	,	PUNCT
ejpam-6441	136	7	(	(	PUNCT
ejpam-6441	136	8	2	2	NUM
ejpam-6441	136	9	)	)	PUNCT
ejpam-6441	136	10	and	and	CCONJ
ejpam-6441	136	11	nℜ(ς1	nℜ(ς1	PROPN
ejpam-6441	136	12	,	,	PUNCT
ejpam-6441	136	13	ς2	ς2	PROPN
ejpam-6441	136	14	)	)	PUNCT
ejpam-6441	136	15	=	=	SYM
ejpam-6441	136	16	min	min	NOUN
ejpam-6441	136	17	{	{	PUNCT
ejpam-6441	136	18	d	d	X
ejpam-6441	136	19	(	(	PUNCT
ejpam-6441	136	20	ς1,γς1	ς1,γς1	PROPN
ejpam-6441	136	21	)	)	PUNCT
ejpam-6441	136	22	,	,	PUNCT
ejpam-6441	136	23	d	d	X
ejpam-6441	136	24	(	(	PUNCT
ejpam-6441	136	25	ς2,γς2	ς2,γς2	X
ejpam-6441	136	26	)	)	PUNCT
ejpam-6441	136	27	,	,	PUNCT
ejpam-6441	137	1	d	d	X
ejpam-6441	137	2	(	(	PUNCT
ejpam-6441	137	3	ς1,γς2	ς1,γς2	NUM
ejpam-6441	137	4	)	)	PUNCT
ejpam-6441	137	5	,	,	PUNCT
ejpam-6441	138	1	d	d	X
ejpam-6441	138	2	(	(	PUNCT
ejpam-6441	138	3	ς2,γς1	ς2,γς1	NUM
ejpam-6441	138	4	)	)	PUNCT
ejpam-6441	138	5	}	}	PUNCT
ejpam-6441	138	6	.	.	PUNCT
ejpam-6441	139	1	(	(	PUNCT
ejpam-6441	139	2	3	3	X
ejpam-6441	139	3	)	)	PUNCT
ejpam-6441	139	4	theorem	theorem	NOUN
ejpam-6441	139	5	5	5	NUM
ejpam-6441	139	6	.	.	PUNCT
ejpam-6441	140	1	let	let	AUX
ejpam-6441	140	2	(	(	PUNCT
ejpam-6441	140	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	140	4	,	,	PUNCT
ejpam-6441	140	5	d	d	NOUN
ejpam-6441	140	6	)	)	PUNCT
ejpam-6441	140	7	be	be	AUX
ejpam-6441	140	8	an	an	DET
ejpam-6441	140	9	ℜ-complete	ℜ-complete	PROPN
ejpam-6441	140	10	ms	ms	NOUN
ejpam-6441	140	11	,	,	PUNCT
ejpam-6441	140	12	and	and	CCONJ
ejpam-6441	140	13	let	let	VERB
ejpam-6441	140	14	γ	γ	X
ejpam-6441	140	15	:	:	PUNCT
ejpam-6441	140	16	∆ℜ	∆ℜ	PROPN
ejpam-6441	140	17	→	→	SYM
ejpam-6441	140	18	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	140	19	)	)	PUNCT
ejpam-6441	140	20	be	be	VERB
ejpam-6441	140	21	an	an	DET
ejpam-6441	140	22	almost	almost	ADV
ejpam-6441	140	23	fisher	fisher	NOUN
ejpam-6441	140	24	-	-	PUNCT
ejpam-6441	140	25	type	type	NOUN
ejpam-6441	140	26	multivalued	multivalue	VERB
ejpam-6441	140	27	f	f	PROPN
ejpam-6441	140	28	-contraction	-contraction	PROPN
ejpam-6441	140	29	mapping	mapping	NOUN
ejpam-6441	140	30	endowed	endow	VERB
ejpam-6441	140	31	with	with	ADP
ejpam-6441	140	32	a	a	DET
ejpam-6441	140	33	γ	γ	NOUN
ejpam-6441	140	34	-	-	ADJ
ejpam-6441	140	35	transitive	transitive	ADJ
ejpam-6441	140	36	binary	binary	ADJ
ejpam-6441	140	37	relation	relation	NOUN
ejpam-6441	140	38	ℜ.	ℜ.	PROPN
ejpam-6441	140	39	assume	assume	VERB
ejpam-6441	140	40	that	that	SCONJ
ejpam-6441	140	41	(	(	PUNCT
ejpam-6441	140	42	t1	t1	NOUN
ejpam-6441	140	43	)	)	PUNCT
ejpam-6441	141	1	∆ℜ	∆ℜ	NOUN
ejpam-6441	141	2	(	(	PUNCT
ejpam-6441	141	3	γ,ℜ	γ,ℜ	ADJ
ejpam-6441	141	4	)	)	PUNCT
ejpam-6441	141	5	=	=	PRON
ejpam-6441	141	6	{	{	PUNCT
ejpam-6441	141	7	ς	ς	PROPN
ejpam-6441	141	8	∈	∈	PROPN
ejpam-6441	141	9	∆ℜ	∆ℜ	NOUN
ejpam-6441	141	10	:	:	PUNCT
ejpam-6441	141	11	(	(	PUNCT
ejpam-6441	141	12	ς	ς	PROPN
ejpam-6441	141	13	,	,	PUNCT
ejpam-6441	141	14	γς	γς	ADJ
ejpam-6441	141	15	)	)	PUNCT
ejpam-6441	141	16	∈	∈	PROPN
ejpam-6441	141	17	ℜ	ℜ	PROPN
ejpam-6441	141	18	}	}	PUNCT
ejpam-6441	141	19	̸=	̸=	PROPN
ejpam-6441	141	20	∅	∅	NOUN
ejpam-6441	141	21	;	;	PUNCT
ejpam-6441	141	22	(	(	PUNCT
ejpam-6441	141	23	t2	t2	NOUN
ejpam-6441	141	24	)	)	PUNCT
ejpam-6441	141	25	ℜ	ℜ	PROPN
ejpam-6441	141	26	is	be	AUX
ejpam-6441	141	27	γ	γ	PRON
ejpam-6441	141	28	-	-	ADJ
ejpam-6441	141	29	closed	closed	ADJ
ejpam-6441	141	30	;	;	PUNCT
ejpam-6441	141	31	(	(	PUNCT
ejpam-6441	141	32	t3	t3	NOUN
ejpam-6441	141	33	)	)	PUNCT
ejpam-6441	141	34	γ	γ	NOUN
ejpam-6441	141	35	is	be	AUX
ejpam-6441	141	36	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	141	37	or	or	CCONJ
ejpam-6441	141	38	(	(	PUNCT
ejpam-6441	141	39	∆ℜ	∆ℜ	NOUN
ejpam-6441	141	40	,	,	PUNCT
ejpam-6441	141	41	d	d	NOUN
ejpam-6441	141	42	)	)	PUNCT
ejpam-6441	141	43	is	be	AUX
ejpam-6441	141	44	ℜ-regular	ℜ-regular	ADJ
ejpam-6441	141	45	space	space	NOUN
ejpam-6441	141	46	.	.	PUNCT
ejpam-6441	142	1	then	then	ADV
ejpam-6441	142	2	,	,	PUNCT
ejpam-6441	142	3	γ	γ	PROPN
ejpam-6441	142	4	has	have	VERB
ejpam-6441	142	5	a	a	DET
ejpam-6441	142	6	fp	fp	PROPN
ejpam-6441	142	7	ς∗	ς∗	PROPN
ejpam-6441	142	8	∈	∈	PROPN
ejpam-6441	142	9	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	142	10	proof	proof	NOUN
ejpam-6441	142	11	.	.	PUNCT
ejpam-6441	143	1	from	from	ADP
ejpam-6441	143	2	(	(	PUNCT
ejpam-6441	143	3	t1	t1	NOUN
ejpam-6441	143	4	)	)	PUNCT
ejpam-6441	143	5	∃	∃	PROPN
ejpam-6441	143	6	ς0	ς0	PROPN
ejpam-6441	143	7	∈	∈	PROPN
ejpam-6441	143	8	∆ℜ	∆ℜ	ADJ
ejpam-6441	143	9	such	such	ADJ
ejpam-6441	143	10	that	that	PRON
ejpam-6441	143	11	(	(	PUNCT
ejpam-6441	143	12	ς0,γς0	ς0,γς0	NOUN
ejpam-6441	143	13	)	)	PUNCT
ejpam-6441	143	14	∈	∈	PROPN
ejpam-6441	143	15	ℜ	ℜ	PROPN
ejpam-6441	143	16	and	and	CCONJ
ejpam-6441	143	17	from	from	ADP
ejpam-6441	143	18	(	(	PUNCT
ejpam-6441	143	19	t2	t2	NOUN
ejpam-6441	143	20	)	)	PUNCT
ejpam-6441	143	21	we	we	PRON
ejpam-6441	143	22	have	have	VERB
ejpam-6441	143	23	(	(	PUNCT
ejpam-6441	143	24	γς0,γ	γς0,γ	NOUN
ejpam-6441	143	25	2ς0	2ς0	NUM
ejpam-6441	143	26	)	)	PUNCT
ejpam-6441	143	27	∈	∈	PROPN
ejpam-6441	143	28	ℜ.	ℜ.	PROPN
ejpam-6441	143	29	since	since	SCONJ
ejpam-6441	143	30	γς0	γς0	NOUN
ejpam-6441	143	31	̸=	̸=	PROPN
ejpam-6441	143	32	∅	∅	NOUN
ejpam-6441	143	33	and	and	CCONJ
ejpam-6441	143	34	closed	close	VERB
ejpam-6441	143	35	∃	∃	PROPN
ejpam-6441	143	36	ς1	ς1	PROPN
ejpam-6441	143	37	∈	∈	NOUN
ejpam-6441	144	1	∆ℜ	∆ℜ	NOUN
ejpam-6441	144	2	such	such	ADJ
ejpam-6441	144	3	that	that	SCONJ
ejpam-6441	144	4	ς1	ς1	PROPN
ejpam-6441	144	5	∈	∈	PROPN
ejpam-6441	144	6	γς0	γς0	NOUN
ejpam-6441	145	1	⊂	⊂	PROPN
ejpam-6441	145	2	∆ℜ	∆ℜ	ADJ
ejpam-6441	145	3	such	such	ADJ
ejpam-6441	145	4	that	that	SCONJ
ejpam-6441	145	5	(	(	PUNCT
ejpam-6441	145	6	ς1,γς1	ς1,γς1	PROPN
ejpam-6441	145	7	)	)	PUNCT
ejpam-6441	145	8	∈	∈	PROPN
ejpam-6441	145	9	ℜ	ℜ	PROPN
ejpam-6441	145	10	and	and	CCONJ
ejpam-6441	145	11	from	from	ADP
ejpam-6441	145	12	(	(	PUNCT
ejpam-6441	145	13	t2	t2	PROPN
ejpam-6441	145	14	)	)	PUNCT
ejpam-6441	145	15	,	,	PUNCT
ejpam-6441	145	16	we	we	PRON
ejpam-6441	145	17	have	have	VERB
ejpam-6441	145	18	(	(	PUNCT
ejpam-6441	145	19	γ2ς0,γ	γ2ς0,γ	PROPN
ejpam-6441	145	20	3ς0	3ς0	NUM
ejpam-6441	145	21	)	)	PUNCT
ejpam-6441	146	1	∈	∈	PROPN
ejpam-6441	146	2	ℜ.	ℜ.	PROPN
ejpam-6441	146	3	continuing	continue	VERB
ejpam-6441	146	4	in	in	ADP
ejpam-6441	146	5	this	this	DET
ejpam-6441	146	6	way	way	NOUN
ejpam-6441	146	7	,	,	PUNCT
ejpam-6441	146	8	we	we	PRON
ejpam-6441	146	9	construct	construct	VERB
ejpam-6441	146	10	a	a	DET
ejpam-6441	146	11	sequence	sequence	NOUN
ejpam-6441	146	12	{	{	PUNCT
ejpam-6441	146	13	ςn	ςn	NOUN
ejpam-6441	146	14	}	}	PUNCT
ejpam-6441	146	15	by	by	ADP
ejpam-6441	146	16	ςn	ςn	PROPN
ejpam-6441	146	17	∈	∈	PROPN
ejpam-6441	146	18	γςn−1	γςn−1	PROPN
ejpam-6441	146	19	=	=	PUNCT
ejpam-6441	146	20	γnς0	γnς0	NOUN
ejpam-6441	146	21	∀n	∀n	X
ejpam-6441	146	22	∈	∈	PROPN
ejpam-6441	146	23	n0	n0	PROPN
ejpam-6441	146	24	.	.	PUNCT
ejpam-6441	147	1	if	if	SCONJ
ejpam-6441	147	2	ςn	ςn	PROPN
ejpam-6441	147	3	∈	∈	PROPN
ejpam-6441	147	4	γςn	γςn	NOUN
ejpam-6441	147	5	for	for	ADP
ejpam-6441	147	6	some	some	DET
ejpam-6441	147	7	n	n	PRON
ejpam-6441	147	8	∈	∈	PROPN
ejpam-6441	147	9	n0	n0	NOUN
ejpam-6441	147	10	then	then	ADV
ejpam-6441	147	11	ςn	ςn	PROPN
ejpam-6441	147	12	becomes	become	VERB
ejpam-6441	147	13	a	a	DET
ejpam-6441	147	14	fp	fp	NOUN
ejpam-6441	147	15	of	of	ADP
ejpam-6441	147	16	γ	γ	PROPN
ejpam-6441	147	17	m.	m.	PROPN
ejpam-6441	147	18	mudhesh	mudhesh	PROPN
ejpam-6441	147	19	et	et	PROPN
ejpam-6441	147	20	al	al	PROPN
ejpam-6441	147	21	.	.	PUNCT
ejpam-6441	147	22	/	/	SYM
ejpam-6441	147	23	eur	eur	PROPN
ejpam-6441	147	24	.	.	PUNCT
ejpam-6441	148	1	j.	j.	PROPN
ejpam-6441	148	2	pure	pure	PROPN
ejpam-6441	148	3	appl	appl	PROPN
ejpam-6441	148	4	.	.	PROPN
ejpam-6441	148	5	math	math	PROPN
ejpam-6441	148	6	,	,	PUNCT
ejpam-6441	148	7	18	18	NUM
ejpam-6441	148	8	(	(	PUNCT
ejpam-6441	148	9	4	4	NUM
ejpam-6441	148	10	)	)	PUNCT
ejpam-6441	148	11	(	(	PUNCT
ejpam-6441	148	12	2025	2025	NUM
ejpam-6441	148	13	)	)	PUNCT
ejpam-6441	148	14	,	,	PUNCT
ejpam-6441	148	15	6441	6441	NUM
ejpam-6441	148	16	7	7	NUM
ejpam-6441	148	17	of	of	ADP
ejpam-6441	148	18	21	21	NUM
ejpam-6441	148	19	and	and	CCONJ
ejpam-6441	148	20	the	the	DET
ejpam-6441	148	21	proof	proof	NOUN
ejpam-6441	148	22	is	be	AUX
ejpam-6441	148	23	done	do	VERB
ejpam-6441	148	24	.	.	PUNCT
ejpam-6441	149	1	so	so	ADV
ejpam-6441	149	2	,	,	PUNCT
ejpam-6441	149	3	we	we	PRON
ejpam-6441	149	4	assume	assume	VERB
ejpam-6441	149	5	that	that	SCONJ
ejpam-6441	149	6	ςn	ςn	PROPN
ejpam-6441	149	7	/∈	/∈	PUNCT
ejpam-6441	150	1	γςn	γςn	NOUN
ejpam-6441	150	2	∀	∀	NOUN
ejpam-6441	151	1	n	n	PRON
ejpam-6441	151	2	∈	∈	PROPN
ejpam-6441	151	3	n0	n0	NOUN
ejpam-6441	151	4	then	then	ADV
ejpam-6441	151	5	d	d	X
ejpam-6441	151	6	(	(	PUNCT
ejpam-6441	151	7	ςn	ςn	PROPN
ejpam-6441	151	8	,	,	PUNCT
ejpam-6441	151	9	γςn	γςn	PROPN
ejpam-6441	151	10	)	)	PUNCT
ejpam-6441	151	11	>	>	X
ejpam-6441	151	12	0	0	PUNCT
ejpam-6441	152	1	and	and	CCONJ
ejpam-6441	152	2	by	by	ADP
ejpam-6441	152	3	lemma	lemma	PROPN
ejpam-6441	152	4	1.15	1.15	NUM
ejpam-6441	152	5	,	,	PUNCT
ejpam-6441	152	6	we	we	PRON
ejpam-6441	152	7	have	have	VERB
ejpam-6441	152	8	0	0	NUM
ejpam-6441	153	1	<	<	X
ejpam-6441	154	1	d	d	X
ejpam-6441	154	2	(	(	PUNCT
ejpam-6441	154	3	ςn	ςn	PROPN
ejpam-6441	154	4	,	,	PUNCT
ejpam-6441	154	5	γςn	γςn	PROPN
ejpam-6441	154	6	)	)	PUNCT
ejpam-6441	154	7	≤	≤	NUM
ejpam-6441	155	1	h	h	NOUN
ejpam-6441	155	2	(	(	PUNCT
ejpam-6441	155	3	γςn−1,γςn	γςn−1,γςn	PROPN
ejpam-6441	155	4	)	)	PUNCT
ejpam-6441	155	5	∀	∀	PUNCT
ejpam-6441	155	6	n	n	PRON
ejpam-6441	155	7	∈	∈	PROPN
ejpam-6441	155	8	n0	n0	X
ejpam-6441	155	9	(	(	PUNCT
ejpam-6441	155	10	4	4	NUM
ejpam-6441	155	11	)	)	PUNCT
ejpam-6441	155	12	since	since	SCONJ
ejpam-6441	155	13	(	(	PUNCT
ejpam-6441	155	14	ς0,γς0	ς0,γς0	NOUN
ejpam-6441	155	15	)	)	PUNCT
ejpam-6441	155	16	∈	∈	PROPN
ejpam-6441	155	17	ℜ	ℜ	PROPN
ejpam-6441	155	18	and	and	CCONJ
ejpam-6441	155	19	from	from	ADP
ejpam-6441	155	20	(	(	PUNCT
ejpam-6441	155	21	t2	t2	PROPN
ejpam-6441	155	22	)	)	PUNCT
ejpam-6441	155	23	,	,	PUNCT
ejpam-6441	155	24	we	we	PRON
ejpam-6441	155	25	conclude	conclude	VERB
ejpam-6441	155	26	that	that	SCONJ
ejpam-6441	155	27	(	(	PUNCT
ejpam-6441	155	28	γnς0,γ	γnς0,γ	PROPN
ejpam-6441	155	29	n+1ς0	n+1ς0	PROPN
ejpam-6441	155	30	)	)	PUNCT
ejpam-6441	155	31	∈	∈	PROPN
ejpam-6441	155	32	ℜ	ℜ	PROPN
ejpam-6441	155	33	∀n	∀n	NUM
ejpam-6441	155	34	∈	∈	PROPN
ejpam-6441	155	35	n0	n0	PROPN
ejpam-6441	155	36	.	.	PUNCT
ejpam-6441	156	1	that	that	ADV
ejpam-6441	156	2	is	is	ADV
ejpam-6441	156	3	(	(	PUNCT
ejpam-6441	156	4	ςn	ςn	PROPN
ejpam-6441	156	5	,	,	PUNCT
ejpam-6441	156	6	ςn+1	ςn+1	NUM
ejpam-6441	156	7	)	)	PUNCT
ejpam-6441	156	8	∈	∈	PROPN
ejpam-6441	156	9	ℜ	ℜ	PROPN
ejpam-6441	156	10	∀n	∀n	NUM
ejpam-6441	156	11	∈	∈	PROPN
ejpam-6441	156	12	n0	n0	PROPN
ejpam-6441	156	13	.	.	PUNCT
ejpam-6441	157	1	(	(	PUNCT
ejpam-6441	157	2	5	5	NUM
ejpam-6441	157	3	)	)	PUNCT
ejpam-6441	157	4	now	now	ADV
ejpam-6441	157	5	,	,	PUNCT
ejpam-6441	157	6	from	from	ADP
ejpam-6441	157	7	(	(	PUNCT
ejpam-6441	157	8	4	4	NUM
ejpam-6441	157	9	)	)	PUNCT
ejpam-6441	157	10	and	and	CCONJ
ejpam-6441	157	11	(	(	PUNCT
ejpam-6441	157	12	5	5	NUM
ejpam-6441	157	13	)	)	PUNCT
ejpam-6441	157	14	,	,	PUNCT
ejpam-6441	157	15	we	we	PRON
ejpam-6441	157	16	have	have	VERB
ejpam-6441	157	17	(	(	PUNCT
ejpam-6441	157	18	ςn−1	ςn−1	NOUN
ejpam-6441	157	19	,	,	PUNCT
ejpam-6441	157	20	ςn	ςn	NOUN
ejpam-6441	157	21	)	)	PUNCT
ejpam-6441	157	22	∈	∈	PROPN
ejpam-6441	157	23	ℜ∗	ℜ∗	PROPN
ejpam-6441	158	1	∀n	∀n	NUM
ejpam-6441	158	2	∈	∈	PROPN
ejpam-6441	158	3	n0.utilizing	n0.utilize	VERB
ejpam-6441	158	4	(	(	PUNCT
ejpam-6441	158	5	f1	f1	NOUN
ejpam-6441	158	6	)	)	PUNCT
ejpam-6441	158	7	in	in	ADP
ejpam-6441	158	8	(	(	PUNCT
ejpam-6441	158	9	4	4	NUM
ejpam-6441	158	10	)	)	PUNCT
ejpam-6441	158	11	and	and	CCONJ
ejpam-6441	158	12	applying	apply	VERB
ejpam-6441	158	13	remark	remark	NOUN
ejpam-6441	158	14	1.3	1.3	NUM
ejpam-6441	158	15	together	together	ADV
ejpam-6441	158	16	with	with	ADP
ejpam-6441	158	17	(	(	PUNCT
ejpam-6441	158	18	1	1	NUM
ejpam-6441	158	19	)	)	PUNCT
ejpam-6441	158	20	,	,	PUNCT
ejpam-6441	158	21	we	we	PRON
ejpam-6441	158	22	get	get	VERB
ejpam-6441	158	23	f	f	X
ejpam-6441	158	24	(	(	PUNCT
ejpam-6441	158	25	d(ςn	d(ςn	PROPN
ejpam-6441	158	26	,	,	PUNCT
ejpam-6441	158	27	ςn+1	ςn+1	NUM
ejpam-6441	158	28	)	)	PUNCT
ejpam-6441	158	29	)	)	PUNCT
ejpam-6441	159	1	=	=	SYM
ejpam-6441	159	2	f	f	PROPN
ejpam-6441	159	3	(	(	PUNCT
ejpam-6441	159	4	d(ςn	d(ςn	PROPN
ejpam-6441	159	5	,	,	PUNCT
ejpam-6441	159	6	γςn	γςn	PROPN
ejpam-6441	159	7	)	)	PUNCT
ejpam-6441	159	8	)	)	PUNCT
ejpam-6441	160	1	≤	≤	NUM
ejpam-6441	160	2	f	f	X
ejpam-6441	160	3	(	(	PUNCT
ejpam-6441	160	4	h(γςn−1,γςn	h(γςn−1,γςn	PROPN
ejpam-6441	160	5	)	)	PUNCT
ejpam-6441	160	6	)	)	PUNCT
ejpam-6441	160	7	(	(	PUNCT
ejpam-6441	160	8	6	6	X
ejpam-6441	160	9	)	)	PUNCT
ejpam-6441	160	10	≤	≤	NUM
ejpam-6441	160	11	f	f	X
ejpam-6441	160	12	(	(	PUNCT
ejpam-6441	160	13	mℜ(ςn−1	mℜ(ςn−1	PROPN
ejpam-6441	160	14	,	,	PUNCT
ejpam-6441	160	15	ςn	ςn	NOUN
ejpam-6441	160	16	)	)	PUNCT
ejpam-6441	160	17	)	)	PUNCT
ejpam-6441	161	1	+	+	CCONJ
ejpam-6441	161	2	lnℜ(ςn−1	lnℜ(ςn−1	ADJ
ejpam-6441	161	3	,	,	PUNCT
ejpam-6441	161	4	ςn)−	ςn)−	NUM
ejpam-6441	161	5	τ	τ	PROPN
ejpam-6441	161	6	,	,	PUNCT
ejpam-6441	161	7	where	where	SCONJ
ejpam-6441	161	8	if	if	SCONJ
ejpam-6441	161	9	β	β	X
ejpam-6441	161	10	>	>	X
ejpam-6441	161	11	0	0	NUM
ejpam-6441	161	12	,	,	PUNCT
ejpam-6441	161	13	then	then	ADV
ejpam-6441	161	14	mℜ(ςn−1	mℜ(ςn−1	ADJ
ejpam-6441	161	15	,	,	PUNCT
ejpam-6441	161	16	ςn	ςn	NOUN
ejpam-6441	161	17	)	)	PUNCT
ejpam-6441	161	18	=	=	PUNCT
ejpam-6441	162	1	[	[	PUNCT
ejpam-6441	162	2	λ1	λ1	PROPN
ejpam-6441	162	3	(	(	PUNCT
ejpam-6441	162	4	d	d	X
ejpam-6441	162	5	(	(	PUNCT
ejpam-6441	162	6	ςn−1,γςn−1)d	ςn−1,γςn−1)d	NUM
ejpam-6441	162	7	(	(	PUNCT
ejpam-6441	162	8	ςn	ςn	PROPN
ejpam-6441	162	9	,	,	PUNCT
ejpam-6441	162	10	γςn	γςn	PROPN
ejpam-6441	162	11	)	)	PUNCT
ejpam-6441	162	12	1	1	NUM
ejpam-6441	163	1	+	+	CCONJ
ejpam-6441	163	2	d	d	X
ejpam-6441	163	3	(	(	PUNCT
ejpam-6441	163	4	ςn−1	ςn−1	PROPN
ejpam-6441	163	5	,	,	PUNCT
ejpam-6441	163	6	ςn	ςn	NOUN
ejpam-6441	163	7	)	)	PUNCT
ejpam-6441	163	8	)	)	PUNCT
ejpam-6441	164	1	β	β	X
ejpam-6441	164	2	+	+	NUM
ejpam-6441	164	3	λ2	λ2	NOUN
ejpam-6441	164	4	(	(	PUNCT
ejpam-6441	164	5	d(ςn−1	d(ςn−1	PROPN
ejpam-6441	164	6	,	,	PUNCT
ejpam-6441	164	7	ςn	ςn	NOUN
ejpam-6441	164	8	)	)	PUNCT
ejpam-6441	164	9	)	)	PUNCT
ejpam-6441	165	1	β	β	X
ejpam-6441	165	2	]	]	PUNCT
ejpam-6441	165	3	1	1	NUM
ejpam-6441	165	4	β	β	X
ejpam-6441	165	5	=	=	SYM
ejpam-6441	165	6	[	[	PUNCT
ejpam-6441	165	7	λ1	λ1	PROPN
ejpam-6441	165	8	(	(	PUNCT
ejpam-6441	165	9	d	d	X
ejpam-6441	165	10	(	(	PUNCT
ejpam-6441	165	11	ςn−1	ςn−1	PROPN
ejpam-6441	165	12	,	,	PUNCT
ejpam-6441	165	13	ςn	ςn	NOUN
ejpam-6441	165	14	)	)	PUNCT
ejpam-6441	165	15	d	d	NOUN
ejpam-6441	165	16	(	(	PUNCT
ejpam-6441	165	17	ςn	ςn	PROPN
ejpam-6441	165	18	,	,	PUNCT
ejpam-6441	165	19	ςn+1	ςn+1	NUM
ejpam-6441	165	20	)	)	PUNCT
ejpam-6441	165	21	1	1	NUM
ejpam-6441	166	1	+	+	CCONJ
ejpam-6441	166	2	d	d	X
ejpam-6441	166	3	(	(	PUNCT
ejpam-6441	166	4	ςn−1	ςn−1	PROPN
ejpam-6441	166	5	,	,	PUNCT
ejpam-6441	166	6	ςn	ςn	NOUN
ejpam-6441	166	7	)	)	PUNCT
ejpam-6441	166	8	)	)	PUNCT
ejpam-6441	167	1	β	β	X
ejpam-6441	167	2	+	+	NUM
ejpam-6441	167	3	λ2	λ2	NOUN
ejpam-6441	167	4	(	(	PUNCT
ejpam-6441	167	5	d(ςn−1	d(ςn−1	PROPN
ejpam-6441	167	6	,	,	PUNCT
ejpam-6441	167	7	ςn	ςn	NOUN
ejpam-6441	167	8	)	)	PUNCT
ejpam-6441	167	9	)	)	PUNCT
ejpam-6441	168	1	β	β	X
ejpam-6441	168	2	]	]	PUNCT
ejpam-6441	168	3	1	1	NUM
ejpam-6441	168	4	β	β	X
ejpam-6441	168	5	≤	≤	X
ejpam-6441	168	6	[	[	PUNCT
ejpam-6441	168	7	λ1	λ1	PROPN
ejpam-6441	168	8	(	(	PUNCT
ejpam-6441	168	9	d	d	X
ejpam-6441	168	10	(	(	PUNCT
ejpam-6441	168	11	ςn−1	ςn−1	PROPN
ejpam-6441	168	12	,	,	PUNCT
ejpam-6441	168	13	ςn	ςn	NOUN
ejpam-6441	168	14	)	)	PUNCT
ejpam-6441	168	15	d	d	NOUN
ejpam-6441	168	16	(	(	PUNCT
ejpam-6441	168	17	ςn	ςn	PROPN
ejpam-6441	168	18	,	,	PUNCT
ejpam-6441	168	19	ςn+1	ςn+1	NUM
ejpam-6441	168	20	)	)	PUNCT
ejpam-6441	168	21	d	d	NOUN
ejpam-6441	168	22	(	(	PUNCT
ejpam-6441	168	23	ςn−1	ςn−1	PROPN
ejpam-6441	168	24	,	,	PUNCT
ejpam-6441	168	25	ςn	ςn	NOUN
ejpam-6441	168	26	)	)	PUNCT
ejpam-6441	168	27	)	)	PUNCT
ejpam-6441	169	1	β	β	X
ejpam-6441	169	2	+	+	NUM
ejpam-6441	169	3	λ2	λ2	NOUN
ejpam-6441	169	4	(	(	PUNCT
ejpam-6441	169	5	d(ςn−1	d(ςn−1	PROPN
ejpam-6441	169	6	,	,	PUNCT
ejpam-6441	169	7	ςn	ςn	NOUN
ejpam-6441	169	8	)	)	PUNCT
ejpam-6441	169	9	)	)	PUNCT
ejpam-6441	170	1	β	β	X
ejpam-6441	170	2	]	]	PUNCT
ejpam-6441	170	3	1	1	NUM
ejpam-6441	170	4	β	β	X
ejpam-6441	170	5	=	=	SYM
ejpam-6441	170	6	[	[	PUNCT
ejpam-6441	170	7	λ1	λ1	PROPN
ejpam-6441	170	8	(	(	PUNCT
ejpam-6441	170	9	d	d	PROPN
ejpam-6441	170	10	(	(	PUNCT
ejpam-6441	170	11	ςn	ςn	PROPN
ejpam-6441	170	12	,	,	PUNCT
ejpam-6441	170	13	ςn+1	ςn+1	NUM
ejpam-6441	170	14	)	)	PUNCT
ejpam-6441	170	15	)	)	PUNCT
ejpam-6441	170	16	β	β	X
ejpam-6441	171	1	+	+	NUM
ejpam-6441	171	2	λ2	λ2	NOUN
ejpam-6441	171	3	(	(	PUNCT
ejpam-6441	171	4	d(ςn−1	d(ςn−1	PROPN
ejpam-6441	171	5	,	,	PUNCT
ejpam-6441	171	6	ςn	ςn	NOUN
ejpam-6441	171	7	)	)	PUNCT
ejpam-6441	171	8	)	)	PUNCT
ejpam-6441	172	1	β	β	X
ejpam-6441	172	2	]	]	PUNCT
ejpam-6441	172	3	1	1	NUM
ejpam-6441	172	4	β	β	X
ejpam-6441	172	5	.	.	PUNCT
ejpam-6441	173	1	assume	assume	VERB
ejpam-6441	173	2	that	that	SCONJ
ejpam-6441	173	3	d	d	PROPN
ejpam-6441	173	4	(	(	PUNCT
ejpam-6441	173	5	ςn−1	ςn−1	PROPN
ejpam-6441	173	6	,	,	PUNCT
ejpam-6441	173	7	ςn	ςn	NOUN
ejpam-6441	173	8	)	)	PUNCT
ejpam-6441	173	9	≤	≤	NUM
ejpam-6441	173	10	d	d	PROPN
ejpam-6441	173	11	(	(	PUNCT
ejpam-6441	173	12	ςn	ςn	PROPN
ejpam-6441	173	13	,	,	PUNCT
ejpam-6441	173	14	ςn+1	ςn+1	NUM
ejpam-6441	173	15	)	)	PUNCT
ejpam-6441	173	16	,	,	PUNCT
ejpam-6441	173	17	then	then	ADV
ejpam-6441	173	18	we	we	PRON
ejpam-6441	173	19	get	get	VERB
ejpam-6441	173	20	mℜ(ςn−1	mℜ(ςn−1	ADJ
ejpam-6441	173	21	,	,	PUNCT
ejpam-6441	173	22	ςn	ςn	NOUN
ejpam-6441	173	23	)	)	PUNCT
ejpam-6441	173	24	≤	≤	NOUN
ejpam-6441	173	25	[	[	PUNCT
ejpam-6441	173	26	λ1	λ1	PROPN
ejpam-6441	173	27	(	(	PUNCT
ejpam-6441	173	28	d	d	PROPN
ejpam-6441	173	29	(	(	PUNCT
ejpam-6441	173	30	ςn	ςn	PROPN
ejpam-6441	173	31	,	,	PUNCT
ejpam-6441	173	32	ςn+1	ςn+1	NUM
ejpam-6441	173	33	)	)	PUNCT
ejpam-6441	173	34	)	)	PUNCT
ejpam-6441	174	1	β	β	X
ejpam-6441	175	1	+	+	NUM
ejpam-6441	175	2	λ2	λ2	NOUN
ejpam-6441	175	3	(	(	PUNCT
ejpam-6441	175	4	d	d	X
ejpam-6441	175	5	(	(	PUNCT
ejpam-6441	175	6	ςn	ςn	PROPN
ejpam-6441	175	7	,	,	PUNCT
ejpam-6441	175	8	ςn+1	ςn+1	NUM
ejpam-6441	175	9	)	)	PUNCT
ejpam-6441	175	10	)	)	PUNCT
ejpam-6441	175	11	β	β	X
ejpam-6441	175	12	]	]	PUNCT
ejpam-6441	175	13	1	1	NUM
ejpam-6441	175	14	β	β	X
ejpam-6441	175	15	(	(	PUNCT
ejpam-6441	175	16	7	7	NUM
ejpam-6441	175	17	)	)	PUNCT
ejpam-6441	175	18	=	=	NOUN
ejpam-6441	176	1	[	[	PUNCT
ejpam-6441	176	2	(	(	PUNCT
ejpam-6441	176	3	λ1	λ1	ADJ
ejpam-6441	176	4	+	+	SYM
ejpam-6441	176	5	λ2	λ2	NOUN
ejpam-6441	176	6	)	)	PUNCT
ejpam-6441	176	7	(	(	PUNCT
ejpam-6441	176	8	d	d	X
ejpam-6441	176	9	(	(	PUNCT
ejpam-6441	176	10	ςn	ςn	PROPN
ejpam-6441	176	11	,	,	PUNCT
ejpam-6441	176	12	ςn+1	ςn+1	NUM
ejpam-6441	176	13	)	)	PUNCT
ejpam-6441	176	14	)	)	PUNCT
ejpam-6441	177	1	β	β	X
ejpam-6441	177	2	]	]	PUNCT
ejpam-6441	177	3	1	1	NUM
ejpam-6441	177	4	β	β	X
ejpam-6441	177	5	<	<	X
ejpam-6441	177	6	d	d	X
ejpam-6441	177	7	(	(	PUNCT
ejpam-6441	177	8	ςn	ςn	PROPN
ejpam-6441	177	9	,	,	PUNCT
ejpam-6441	177	10	ςn+1	ςn+1	NUM
ejpam-6441	177	11	)	)	PUNCT
ejpam-6441	177	12	and	and	CCONJ
ejpam-6441	177	13	nℜ(ςn−1	nℜ(ςn−1	PRON
ejpam-6441	177	14	,	,	PUNCT
ejpam-6441	177	15	ςn	ςn	NOUN
ejpam-6441	177	16	)	)	PUNCT
ejpam-6441	178	1	=	=	SYM
ejpam-6441	178	2	min	min	NOUN
ejpam-6441	178	3	{	{	PUNCT
ejpam-6441	178	4	d	d	X
ejpam-6441	178	5	(	(	PUNCT
ejpam-6441	178	6	xn−1	xn−1	PROPN
ejpam-6441	178	7	,	,	PUNCT
ejpam-6441	178	8	xn	xn	PROPN
ejpam-6441	178	9	)	)	PUNCT
ejpam-6441	178	10	,	,	PUNCT
ejpam-6441	179	1	d	d	X
ejpam-6441	179	2	(	(	PUNCT
ejpam-6441	179	3	ςn	ςn	PROPN
ejpam-6441	179	4	,	,	PUNCT
ejpam-6441	179	5	ςn+1	ςn+1	NUM
ejpam-6441	179	6	)	)	PUNCT
ejpam-6441	179	7	,	,	PUNCT
ejpam-6441	179	8	d	d	X
ejpam-6441	179	9	(	(	PUNCT
ejpam-6441	179	10	ςn−1	ςn−1	PROPN
ejpam-6441	179	11	,	,	PUNCT
ejpam-6441	179	12	ςn+1	ςn+1	NUM
ejpam-6441	179	13	)	)	PUNCT
ejpam-6441	179	14	,	,	PUNCT
ejpam-6441	180	1	d	d	X
ejpam-6441	180	2	(	(	PUNCT
ejpam-6441	180	3	ςn	ςn	NOUN
ejpam-6441	180	4	,	,	PUNCT
ejpam-6441	180	5	ςn	ςn	NOUN
ejpam-6441	180	6	)	)	PUNCT
ejpam-6441	180	7	}	}	PUNCT
ejpam-6441	180	8	=	=	PUNCT
ejpam-6441	181	1	0	0	X
ejpam-6441	181	2	.	.	PUNCT
ejpam-6441	181	3	then	then	ADV
ejpam-6441	181	4	from	from	ADP
ejpam-6441	181	5	(	(	PUNCT
ejpam-6441	181	6	6	6	NUM
ejpam-6441	181	7	)	)	PUNCT
ejpam-6441	181	8	,	,	PUNCT
ejpam-6441	181	9	we	we	PRON
ejpam-6441	181	10	have	have	VERB
ejpam-6441	181	11	f	f	X
ejpam-6441	181	12	(	(	PUNCT
ejpam-6441	181	13	d(ςn	d(ςn	PROPN
ejpam-6441	181	14	,	,	PUNCT
ejpam-6441	181	15	ςn+1	ςn+1	NUM
ejpam-6441	181	16	)	)	PUNCT
ejpam-6441	181	17	)	)	PUNCT
ejpam-6441	182	1	≤	≤	NUM
ejpam-6441	182	2	f	f	X
ejpam-6441	182	3	(	(	PUNCT
ejpam-6441	182	4	d	d	X
ejpam-6441	182	5	(	(	PUNCT
ejpam-6441	182	6	ςn	ςn	NOUN
ejpam-6441	182	7	,	,	PUNCT
ejpam-6441	182	8	ςn+1))−	ςn+1))−	NOUN
ejpam-6441	182	9	τ	τ	X
ejpam-6441	182	10	<	<	X
ejpam-6441	182	11	f	f	X
ejpam-6441	182	12	(	(	PUNCT
ejpam-6441	182	13	d	d	X
ejpam-6441	182	14	(	(	PUNCT
ejpam-6441	182	15	ςn	ςn	PROPN
ejpam-6441	182	16	,	,	PUNCT
ejpam-6441	182	17	ςn+1	ςn+1	NUM
ejpam-6441	182	18	)	)	PUNCT
ejpam-6441	182	19	)	)	PUNCT
ejpam-6441	182	20	.	.	PUNCT
ejpam-6441	183	1	m.	m.	NOUN
ejpam-6441	183	2	mudhesh	mudhesh	PROPN
ejpam-6441	183	3	et	et	PROPN
ejpam-6441	183	4	al	al	PROPN
ejpam-6441	183	5	.	.	PUNCT
ejpam-6441	183	6	/	/	SYM
ejpam-6441	183	7	eur	eur	PROPN
ejpam-6441	183	8	.	.	PUNCT
ejpam-6441	184	1	j.	j.	PROPN
ejpam-6441	184	2	pure	pure	PROPN
ejpam-6441	184	3	appl	appl	PROPN
ejpam-6441	184	4	.	.	PROPN
ejpam-6441	184	5	math	math	PROPN
ejpam-6441	184	6	,	,	PUNCT
ejpam-6441	184	7	18	18	NUM
ejpam-6441	184	8	(	(	PUNCT
ejpam-6441	184	9	4	4	NUM
ejpam-6441	184	10	)	)	PUNCT
ejpam-6441	184	11	(	(	PUNCT
ejpam-6441	184	12	2025	2025	NUM
ejpam-6441	184	13	)	)	PUNCT
ejpam-6441	184	14	,	,	PUNCT
ejpam-6441	184	15	6441	6441	NUM
ejpam-6441	184	16	8	8	NUM
ejpam-6441	184	17	of	of	ADP
ejpam-6441	184	18	21	21	NUM
ejpam-6441	184	19	a	a	DET
ejpam-6441	184	20	contradiction	contradiction	NOUN
ejpam-6441	184	21	.	.	PUNCT
ejpam-6441	185	1	therefore	therefore	ADV
ejpam-6441	185	2	,	,	PUNCT
ejpam-6441	185	3	d	d	X
ejpam-6441	185	4	(	(	PUNCT
ejpam-6441	185	5	ςn−1	ςn−1	PROPN
ejpam-6441	185	6	,	,	PUNCT
ejpam-6441	185	7	ςn	ςn	NOUN
ejpam-6441	185	8	)	)	PUNCT
ejpam-6441	185	9	>	>	X
ejpam-6441	185	10	d	d	X
ejpam-6441	185	11	(	(	PUNCT
ejpam-6441	185	12	xn	xn	PROPN
ejpam-6441	185	13	,	,	PUNCT
ejpam-6441	185	14	xn+1	xn+1	NUM
ejpam-6441	185	15	)	)	PUNCT
ejpam-6441	185	16	,	,	PUNCT
ejpam-6441	185	17	which	which	PRON
ejpam-6441	185	18	implies	imply	VERB
ejpam-6441	185	19	that	that	SCONJ
ejpam-6441	185	20	mℜ(ςn−1	mℜ(ςn−1	PROPN
ejpam-6441	185	21	,	,	PUNCT
ejpam-6441	185	22	ςn	ςn	NOUN
ejpam-6441	185	23	)	)	PUNCT
ejpam-6441	185	24	≤	≤	NOUN
ejpam-6441	185	25	[	[	PUNCT
ejpam-6441	185	26	λ1	λ1	PROPN
ejpam-6441	185	27	(	(	PUNCT
ejpam-6441	185	28	d	d	X
ejpam-6441	185	29	(	(	PUNCT
ejpam-6441	185	30	ςn−1	ςn−1	PROPN
ejpam-6441	185	31	,	,	PUNCT
ejpam-6441	185	32	ςn	ςn	NOUN
ejpam-6441	185	33	)	)	PUNCT
ejpam-6441	185	34	)	)	PUNCT
ejpam-6441	186	1	β	β	X
ejpam-6441	187	1	+	+	NUM
ejpam-6441	187	2	λ2	λ2	NOUN
ejpam-6441	187	3	(	(	PUNCT
ejpam-6441	187	4	d	d	X
ejpam-6441	187	5	(	(	PUNCT
ejpam-6441	187	6	ςn−1	ςn−1	PROPN
ejpam-6441	187	7	,	,	PUNCT
ejpam-6441	187	8	ςn	ςn	NOUN
ejpam-6441	187	9	)	)	PUNCT
ejpam-6441	187	10	)	)	PUNCT
ejpam-6441	187	11	β	β	X
ejpam-6441	187	12	]	]	PUNCT
ejpam-6441	187	13	1	1	NUM
ejpam-6441	187	14	β	β	X
ejpam-6441	187	15	=	=	SYM
ejpam-6441	187	16	[	[	PUNCT
ejpam-6441	187	17	(	(	PUNCT
ejpam-6441	187	18	λ1	λ1	ADJ
ejpam-6441	187	19	+	+	SYM
ejpam-6441	187	20	λ2	λ2	NOUN
ejpam-6441	187	21	)	)	PUNCT
ejpam-6441	187	22	(	(	PUNCT
ejpam-6441	187	23	d	d	X
ejpam-6441	187	24	(	(	PUNCT
ejpam-6441	187	25	ςn−1	ςn−1	PROPN
ejpam-6441	187	26	,	,	PUNCT
ejpam-6441	187	27	ςn	ςn	NOUN
ejpam-6441	187	28	)	)	PUNCT
ejpam-6441	187	29	)	)	PUNCT
ejpam-6441	188	1	β	β	X
ejpam-6441	188	2	]	]	PUNCT
ejpam-6441	188	3	1	1	NUM
ejpam-6441	188	4	β	β	X
ejpam-6441	188	5	<	<	X
ejpam-6441	188	6	d	d	X
ejpam-6441	188	7	(	(	PUNCT
ejpam-6441	188	8	ςn−1	ςn−1	PROPN
ejpam-6441	188	9	,	,	PUNCT
ejpam-6441	188	10	ςn	ςn	NOUN
ejpam-6441	188	11	)	)	PUNCT
ejpam-6441	188	12	.	.	PUNCT
ejpam-6441	189	1	then	then	ADV
ejpam-6441	189	2	from	from	ADP
ejpam-6441	189	3	(	(	PUNCT
ejpam-6441	189	4	6	6	NUM
ejpam-6441	189	5	)	)	PUNCT
ejpam-6441	189	6	,	,	PUNCT
ejpam-6441	189	7	we	we	PRON
ejpam-6441	189	8	have	have	VERB
ejpam-6441	189	9	f	f	X
ejpam-6441	189	10	(	(	PUNCT
ejpam-6441	189	11	d(ςn	d(ςn	PROPN
ejpam-6441	189	12	,	,	PUNCT
ejpam-6441	189	13	ςn+1	ςn+1	NUM
ejpam-6441	189	14	)	)	PUNCT
ejpam-6441	189	15	)	)	PUNCT
ejpam-6441	190	1	≤	≤	NUM
ejpam-6441	191	1	f	f	X
ejpam-6441	191	2	(	(	PUNCT
ejpam-6441	191	3	d	d	X
ejpam-6441	191	4	(	(	PUNCT
ejpam-6441	191	5	ςn−1	ςn−1	PROPN
ejpam-6441	191	6	,	,	PUNCT
ejpam-6441	191	7	ςn))−	ςn))−	ADV
ejpam-6441	191	8	τ	τ	X
ejpam-6441	191	9	(	(	PUNCT
ejpam-6441	191	10	8)	8)	NUM
ejpam-6441	191	11	<	<	X
ejpam-6441	191	12	f	f	X
ejpam-6441	191	13	(	(	PUNCT
ejpam-6441	191	14	d	d	X
ejpam-6441	191	15	(	(	PUNCT
ejpam-6441	191	16	ςn−1	ςn−1	PROPN
ejpam-6441	191	17	,	,	PUNCT
ejpam-6441	191	18	ςn	ςn	NOUN
ejpam-6441	191	19	)	)	PUNCT
ejpam-6441	191	20	)	)	PUNCT
ejpam-6441	191	21	.	.	PUNCT
ejpam-6441	192	1	thus	thus	ADV
ejpam-6441	192	2	,	,	PUNCT
ejpam-6441	192	3	the	the	DET
ejpam-6441	192	4	sequence	sequence	NOUN
ejpam-6441	192	5	{	{	PUNCT
ejpam-6441	192	6	d(ςn	d(ςn	NOUN
ejpam-6441	192	7	,	,	PUNCT
ejpam-6441	192	8	ςn+1	ςn+1	NUM
ejpam-6441	192	9	)	)	PUNCT
ejpam-6441	192	10	}	}	PUNCT
ejpam-6441	192	11	is	be	AUX
ejpam-6441	192	12	decreasing	decrease	VERB
ejpam-6441	192	13	and	and	CCONJ
ejpam-6441	192	14	convergent	convergent	NOUN
ejpam-6441	192	15	.	.	PUNCT
ejpam-6441	193	1	by	by	ADP
ejpam-6441	193	2	induction	induction	NOUN
ejpam-6441	193	3	on	on	ADP
ejpam-6441	193	4	n	n	CCONJ
ejpam-6441	193	5	,	,	PUNCT
ejpam-6441	193	6	we	we	PRON
ejpam-6441	193	7	obtain	obtain	VERB
ejpam-6441	193	8	f	f	X
ejpam-6441	193	9	(	(	PUNCT
ejpam-6441	193	10	d(ςn	d(ςn	PROPN
ejpam-6441	193	11	,	,	PUNCT
ejpam-6441	193	12	ςn+1	ςn+1	NUM
ejpam-6441	193	13	)	)	PUNCT
ejpam-6441	193	14	)	)	PUNCT
ejpam-6441	194	1	≤	≤	NUM
ejpam-6441	195	1	f	f	X
ejpam-6441	195	2	(	(	PUNCT
ejpam-6441	195	3	d	d	X
ejpam-6441	195	4	(	(	PUNCT
ejpam-6441	195	5	ςn−1	ςn−1	PROPN
ejpam-6441	195	6	,	,	PUNCT
ejpam-6441	195	7	ςn))−	ςn))−	X
ejpam-6441	195	8	τ	τ	X
ejpam-6441	195	9	<	<	X
ejpam-6441	195	10	...	...	PUNCT
ejpam-6441	196	1	<	<	X
ejpam-6441	196	2	f	f	X
ejpam-6441	196	3	(	(	PUNCT
ejpam-6441	196	4	d	d	X
ejpam-6441	196	5	(	(	PUNCT
ejpam-6441	196	6	ς0	ς0	VERB
ejpam-6441	196	7	,	,	PUNCT
ejpam-6441	196	8	ς1))−	ς1))−	PRON
ejpam-6441	196	9	nτ	nτ	ADJ
ejpam-6441	196	10	.	.	PUNCT
ejpam-6441	197	1	taking	take	VERB
ejpam-6441	197	2	limit	limit	NOUN
ejpam-6441	197	3	as	as	ADP
ejpam-6441	197	4	n→	n→	PROPN
ejpam-6441	197	5	∞	∞	PROPN
ejpam-6441	197	6	above	above	ADV
ejpam-6441	197	7	,	,	PUNCT
ejpam-6441	197	8	we	we	PRON
ejpam-6441	197	9	get	get	VERB
ejpam-6441	197	10	lim	lim	PROPN
ejpam-6441	197	11	n→∞	n→∞	X
ejpam-6441	197	12	f	f	X
ejpam-6441	197	13	(	(	PUNCT
ejpam-6441	197	14	d(ςn	d(ςn	PROPN
ejpam-6441	197	15	,	,	PUNCT
ejpam-6441	197	16	ςn+1	ςn+1	NUM
ejpam-6441	197	17	)	)	PUNCT
ejpam-6441	197	18	)	)	PUNCT
ejpam-6441	198	1	=	=	SYM
ejpam-6441	198	2	−∞.	−∞.	ADJ
ejpam-6441	198	3	by	by	ADP
ejpam-6441	198	4	(	(	PUNCT
ejpam-6441	198	5	f2	f2	PROPN
ejpam-6441	198	6	)	)	PUNCT
ejpam-6441	198	7	,	,	PUNCT
ejpam-6441	198	8	we	we	PRON
ejpam-6441	198	9	have	have	VERB
ejpam-6441	198	10	lim	lim	PROPN
ejpam-6441	198	11	n→∞	n→∞	NUM
ejpam-6441	198	12	d(ςn	d(ςn	NOUN
ejpam-6441	198	13	,	,	PUNCT
ejpam-6441	198	14	ςn+1	ςn+1	NUM
ejpam-6441	198	15	)	)	PUNCT
ejpam-6441	198	16	=	=	SYM
ejpam-6441	198	17	0	0	X
ejpam-6441	198	18	.	.	PUNCT
ejpam-6441	199	1	(	(	PUNCT
ejpam-6441	199	2	9	9	X
ejpam-6441	199	3	)	)	PUNCT
ejpam-6441	199	4	we	we	PRON
ejpam-6441	199	5	claim	claim	VERB
ejpam-6441	199	6	that	that	SCONJ
ejpam-6441	199	7	{	{	PUNCT
ejpam-6441	199	8	ςn	ςn	NOUN
ejpam-6441	199	9	}	}	PUNCT
ejpam-6441	199	10	is	be	AUX
ejpam-6441	199	11	a	a	DET
ejpam-6441	199	12	cauchy	cauchy	ADJ
ejpam-6441	199	13	sequence	sequence	NOUN
ejpam-6441	199	14	,	,	PUNCT
ejpam-6441	199	15	by	by	ADP
ejpam-6441	199	16	supposing	suppose	VERB
ejpam-6441	199	17	on	on	ADP
ejpam-6441	199	18	the	the	DET
ejpam-6441	199	19	contrary	contrary	NOUN
ejpam-6441	199	20	that	that	SCONJ
ejpam-6441	199	21	it	it	PRON
ejpam-6441	199	22	is	be	AUX
ejpam-6441	199	23	not	not	PART
ejpam-6441	199	24	.	.	PUNCT
ejpam-6441	200	1	then	then	ADV
ejpam-6441	200	2	∃	∃	PROPN
ejpam-6441	200	3	ε	ε	PROPN
ejpam-6441	200	4	>	>	X
ejpam-6441	200	5	0	0	PUNCT
ejpam-6441	201	1	and	and	CCONJ
ejpam-6441	201	2	subsequences	subsequence	NOUN
ejpam-6441	201	3	{	{	PUNCT
ejpam-6441	201	4	ςln	ςln	NOUN
ejpam-6441	201	5	}	}	PUNCT
ejpam-6441	201	6	and	and	CCONJ
ejpam-6441	201	7	{	{	PUNCT
ejpam-6441	201	8	ςqn	ςqn	NOUN
ejpam-6441	201	9	}	}	PUNCT
ejpam-6441	201	10	so	so	SCONJ
ejpam-6441	201	11	that	that	SCONJ
ejpam-6441	201	12	for	for	ADP
ejpam-6441	201	13	ln	ln	PROPN
ejpam-6441	201	14	>	>	X
ejpam-6441	201	15	qn	qn	PROPN
ejpam-6441	201	16	>	>	X
ejpam-6441	201	17	n	n	CCONJ
ejpam-6441	201	18	,	,	PUNCT
ejpam-6441	201	19	we	we	PRON
ejpam-6441	201	20	have	have	VERB
ejpam-6441	201	21	d(ςln	d(ςln	NOUN
ejpam-6441	201	22	,	,	PUNCT
ejpam-6441	201	23	ςqn	ςqn	PROPN
ejpam-6441	201	24	)	)	PUNCT
ejpam-6441	201	25	≥	≥	NOUN
ejpam-6441	201	26	ε	ε	PROPN
ejpam-6441	201	27	and	and	CCONJ
ejpam-6441	201	28	d(ςln−1	d(ςln−1	PROPN
ejpam-6441	201	29	,	,	PUNCT
ejpam-6441	201	30	ςqn	ςqn	PROPN
ejpam-6441	201	31	)	)	PUNCT
ejpam-6441	201	32	<	<	X
ejpam-6441	201	33	ε	ε	X
ejpam-6441	201	34	∀	∀	X
ejpam-6441	201	35	n	n	PRON
ejpam-6441	201	36	∈	∈	PROPN
ejpam-6441	201	37	n.	n.	NOUN
ejpam-6441	201	38	(	(	PUNCT
ejpam-6441	201	39	10	10	NUM
ejpam-6441	201	40	)	)	PUNCT
ejpam-6441	201	41	by	by	ADP
ejpam-6441	201	42	triangle	triangle	NOUN
ejpam-6441	201	43	inequality	inequality	NOUN
ejpam-6441	201	44	,	,	PUNCT
ejpam-6441	201	45	we	we	PRON
ejpam-6441	201	46	have	have	AUX
ejpam-6441	201	47	ε	ε	PROPN
ejpam-6441	201	48	≤	≤	ADJ
ejpam-6441	201	49	d(ςln	d(ςln	NOUN
ejpam-6441	201	50	,	,	PUNCT
ejpam-6441	201	51	ςqn	ςqn	NOUN
ejpam-6441	201	52	)	)	PUNCT
ejpam-6441	201	53	≤	≤	NOUN
ejpam-6441	201	54	d(ςln	d(ςln	NOUN
ejpam-6441	201	55	,	,	PUNCT
ejpam-6441	201	56	ςln−1	ςln−1	PROPN
ejpam-6441	201	57	)	)	PUNCT
ejpam-6441	202	1	+	+	CCONJ
ejpam-6441	202	2	d(ςln−1	d(ςln−1	ADJ
ejpam-6441	202	3	,	,	PUNCT
ejpam-6441	202	4	ςqn	ςqn	PROPN
ejpam-6441	202	5	)	)	PUNCT
ejpam-6441	202	6	.	.	PUNCT
ejpam-6441	203	1	taking	take	VERB
ejpam-6441	203	2	limit	limit	NOUN
ejpam-6441	203	3	as	as	ADP
ejpam-6441	203	4	n→	n→	ADV
ejpam-6441	203	5	∞	∞	PROPN
ejpam-6441	203	6	and	and	CCONJ
ejpam-6441	203	7	using	use	VERB
ejpam-6441	203	8	(	(	PUNCT
ejpam-6441	203	9	9	9	NUM
ejpam-6441	203	10	)	)	PUNCT
ejpam-6441	203	11	and	and	CCONJ
ejpam-6441	203	12	(	(	PUNCT
ejpam-6441	203	13	10	10	NUM
ejpam-6441	203	14	)	)	PUNCT
ejpam-6441	203	15	,	,	PUNCT
ejpam-6441	203	16	we	we	PRON
ejpam-6441	203	17	get	get	VERB
ejpam-6441	203	18	lim	lim	PROPN
ejpam-6441	203	19	n→∞	n→∞	PRON
ejpam-6441	203	20	d(ςln	d(ςln	PROPN
ejpam-6441	203	21	,	,	PUNCT
ejpam-6441	203	22	ςqn	ςqn	PROPN
ejpam-6441	203	23	)	)	PUNCT
ejpam-6441	203	24	=	=	SYM
ejpam-6441	203	25	ε	ε	PROPN
ejpam-6441	203	26	.	.	PUNCT
ejpam-6441	204	1	(	(	PUNCT
ejpam-6441	204	2	11	11	NUM
ejpam-6441	204	3	)	)	PUNCT
ejpam-6441	204	4	using	use	VERB
ejpam-6441	204	5	triangle	triangle	NOUN
ejpam-6441	204	6	inequality	inequality	NOUN
ejpam-6441	204	7	again	again	ADV
ejpam-6441	204	8	,	,	PUNCT
ejpam-6441	204	9	we	we	PRON
ejpam-6441	204	10	get	get	VERB
ejpam-6441	204	11	d(ςlm	d(ςlm	NOUN
ejpam-6441	204	12	,	,	PUNCT
ejpam-6441	204	13	ςqm+1	ςqm+1	PROPN
ejpam-6441	204	14	)	)	PUNCT
ejpam-6441	204	15	≤	≤	NOUN
ejpam-6441	204	16	d(ςlm	d(ςlm	NOUN
ejpam-6441	204	17	,	,	PUNCT
ejpam-6441	204	18	ςqm	ςqm	PROPN
ejpam-6441	204	19	)	)	PUNCT
ejpam-6441	205	1	+	+	CCONJ
ejpam-6441	205	2	d(ςqm	d(ςqm	PROPN
ejpam-6441	205	3	,	,	PUNCT
ejpam-6441	205	4	ςqm+1	ςqm+1	PROPN
ejpam-6441	205	5	)	)	PUNCT
ejpam-6441	205	6	.	.	PUNCT
ejpam-6441	206	1	taking	take	VERB
ejpam-6441	206	2	limit	limit	NOUN
ejpam-6441	206	3	as	as	ADP
ejpam-6441	206	4	m→	m→	NOUN
ejpam-6441	206	5	∞	∞	PROPN
ejpam-6441	206	6	above	above	ADP
ejpam-6441	206	7	and	and	CCONJ
ejpam-6441	206	8	using	use	VERB
ejpam-6441	206	9	(	(	PUNCT
ejpam-6441	206	10	9	9	NUM
ejpam-6441	206	11	)	)	PUNCT
ejpam-6441	206	12	and	and	CCONJ
ejpam-6441	206	13	(	(	PUNCT
ejpam-6441	206	14	11	11	NUM
ejpam-6441	206	15	)	)	PUNCT
ejpam-6441	206	16	,	,	PUNCT
ejpam-6441	206	17	we	we	PRON
ejpam-6441	206	18	get	get	VERB
ejpam-6441	206	19	lim	lim	PROPN
ejpam-6441	206	20	m→∞	m→∞	NUM
ejpam-6441	206	21	d(ςlm	d(ςlm	NOUN
ejpam-6441	206	22	,	,	PUNCT
ejpam-6441	206	23	ςqm+1	ςqm+1	PROPN
ejpam-6441	206	24	)	)	PUNCT
ejpam-6441	206	25	≤	≤	NUM
ejpam-6441	206	26	ε	ε	PROPN
ejpam-6441	206	27	.	.	PUNCT
ejpam-6441	207	1	(	(	PUNCT
ejpam-6441	207	2	12	12	NUM
ejpam-6441	207	3	)	)	PUNCT
ejpam-6441	207	4	similarly	similarly	ADV
ejpam-6441	207	5	,	,	PUNCT
ejpam-6441	207	6	we	we	PRON
ejpam-6441	207	7	have	have	VERB
ejpam-6441	207	8	ε	ε	PROPN
ejpam-6441	207	9	≤	≤	PROPN
ejpam-6441	207	10	d(ςlm	d(ςlm	NOUN
ejpam-6441	207	11	,	,	PUNCT
ejpam-6441	207	12	ςqm	ςqm	ADJ
ejpam-6441	207	13	)	)	PUNCT
ejpam-6441	207	14	≤	≤	NOUN
ejpam-6441	207	15	d(ςlm	d(ςlm	NOUN
ejpam-6441	207	16	,	,	PUNCT
ejpam-6441	207	17	xqm+1	xqm+1	PROPN
ejpam-6441	207	18	)	)	PUNCT
ejpam-6441	207	19	+	+	CCONJ
ejpam-6441	207	20	d(ςqm+1	d(ςqm+1	X
ejpam-6441	207	21	,	,	PUNCT
ejpam-6441	207	22	ςqm	ςqm	PROPN
ejpam-6441	207	23	)	)	PUNCT
ejpam-6441	207	24	.	.	PUNCT
ejpam-6441	208	1	m.	m.	NOUN
ejpam-6441	208	2	mudhesh	mudhesh	PROPN
ejpam-6441	208	3	et	et	PROPN
ejpam-6441	208	4	al	al	PROPN
ejpam-6441	208	5	.	.	PUNCT
ejpam-6441	208	6	/	/	SYM
ejpam-6441	208	7	eur	eur	PROPN
ejpam-6441	208	8	.	.	PUNCT
ejpam-6441	209	1	j.	j.	PROPN
ejpam-6441	209	2	pure	pure	PROPN
ejpam-6441	209	3	appl	appl	PROPN
ejpam-6441	209	4	.	.	PROPN
ejpam-6441	209	5	math	math	PROPN
ejpam-6441	209	6	,	,	PUNCT
ejpam-6441	209	7	18	18	NUM
ejpam-6441	209	8	(	(	PUNCT
ejpam-6441	209	9	4	4	NUM
ejpam-6441	209	10	)	)	PUNCT
ejpam-6441	209	11	(	(	PUNCT
ejpam-6441	209	12	2025	2025	NUM
ejpam-6441	209	13	)	)	PUNCT
ejpam-6441	209	14	,	,	PUNCT
ejpam-6441	209	15	6441	6441	NUM
ejpam-6441	209	16	9	9	NUM
ejpam-6441	209	17	of	of	ADP
ejpam-6441	209	18	21	21	NUM
ejpam-6441	209	19	taking	taking	NOUN
ejpam-6441	209	20	limit	limit	NOUN
ejpam-6441	209	21	as	as	ADP
ejpam-6441	209	22	m→	m→	NOUN
ejpam-6441	209	23	∞	∞	PROPN
ejpam-6441	209	24	above	above	ADP
ejpam-6441	209	25	and	and	CCONJ
ejpam-6441	209	26	using	use	VERB
ejpam-6441	209	27	(	(	PUNCT
ejpam-6441	209	28	9	9	NUM
ejpam-6441	209	29	)	)	PUNCT
ejpam-6441	209	30	and	and	CCONJ
ejpam-6441	209	31	(	(	PUNCT
ejpam-6441	209	32	11	11	NUM
ejpam-6441	209	33	)	)	PUNCT
ejpam-6441	209	34	,	,	PUNCT
ejpam-6441	209	35	we	we	PRON
ejpam-6441	209	36	get	get	VERB
ejpam-6441	209	37	lim	lim	PROPN
ejpam-6441	209	38	m→∞	m→∞	NUM
ejpam-6441	209	39	d(ςlm	d(ςlm	NOUN
ejpam-6441	209	40	,	,	PUNCT
ejpam-6441	209	41	ςqm+1	ςqm+1	PROPN
ejpam-6441	209	42	)	)	PUNCT
ejpam-6441	209	43	≥	≥	NOUN
ejpam-6441	210	1	ε	ε	PROPN
ejpam-6441	211	1	.	.	PUNCT
ejpam-6441	212	1	(	(	PUNCT
ejpam-6441	212	2	13	13	NUM
ejpam-6441	212	3	)	)	PUNCT
ejpam-6441	212	4	therefore	therefore	ADV
ejpam-6441	212	5	,	,	PUNCT
ejpam-6441	212	6	from	from	ADP
ejpam-6441	212	7	(	(	PUNCT
ejpam-6441	212	8	12	12	NUM
ejpam-6441	212	9	)	)	PUNCT
ejpam-6441	212	10	and	and	CCONJ
ejpam-6441	212	11	(	(	PUNCT
ejpam-6441	212	12	13	13	NUM
ejpam-6441	212	13	)	)	PUNCT
ejpam-6441	212	14	,	,	PUNCT
ejpam-6441	212	15	we	we	PRON
ejpam-6441	212	16	get	get	VERB
ejpam-6441	212	17	lim	lim	PROPN
ejpam-6441	212	18	m→∞	m→∞	NUM
ejpam-6441	212	19	d(ςlm	d(ςlm	NOUN
ejpam-6441	212	20	,	,	PUNCT
ejpam-6441	212	21	ςqm+1	ςqm+1	PROPN
ejpam-6441	212	22	)	)	PUNCT
ejpam-6441	212	23	=	=	SYM
ejpam-6441	212	24	ε	ε	PROPN
ejpam-6441	212	25	.	.	PUNCT
ejpam-6441	212	26	by	by	ADP
ejpam-6441	212	27	similar	similar	ADJ
ejpam-6441	212	28	way	way	NOUN
ejpam-6441	212	29	,	,	PUNCT
ejpam-6441	212	30	we	we	PRON
ejpam-6441	212	31	conclude	conclude	VERB
ejpam-6441	212	32	lim	lim	PROPN
ejpam-6441	212	33	m→∞	m→∞	NOUN
ejpam-6441	212	34	d(ςqm	d(ςqm	PROPN
ejpam-6441	212	35	,	,	PUNCT
ejpam-6441	212	36	ςlm+1	ςlm+1	NOUN
ejpam-6441	212	37	)	)	PUNCT
ejpam-6441	212	38	=	=	SYM
ejpam-6441	212	39	ε	ε	PROPN
ejpam-6441	212	40	.	.	PUNCT
ejpam-6441	213	1	next	next	ADV
ejpam-6441	213	2	,	,	PUNCT
ejpam-6441	213	3	we	we	PRON
ejpam-6441	213	4	claim	claim	VERB
ejpam-6441	213	5	that	that	SCONJ
ejpam-6441	213	6	d(ςln+1	d(ςln+1	VERB
ejpam-6441	213	7	,	,	PUNCT
ejpam-6441	213	8	ςqn+1	ςqn+1	PROPN
ejpam-6441	213	9	)	)	PUNCT
ejpam-6441	213	10	>	>	SYM
ejpam-6441	213	11	0	0	NUM
ejpam-6441	213	12	∀	∀	PUNCT
ejpam-6441	213	13	n	n	PRON
ejpam-6441	213	14	∈	∈	PROPN
ejpam-6441	213	15	n.	n.	NOUN
ejpam-6441	213	16	(	(	PUNCT
ejpam-6441	213	17	14	14	NUM
ejpam-6441	213	18	)	)	PUNCT
ejpam-6441	213	19	arguing	argue	VERB
ejpam-6441	213	20	by	by	ADP
ejpam-6441	213	21	contradiction	contradiction	NOUN
ejpam-6441	213	22	,	,	PUNCT
ejpam-6441	213	23	there	there	PRON
ejpam-6441	213	24	exists	exist	VERB
ejpam-6441	213	25	m	m	PROPN
ejpam-6441	213	26	∈	∈	PROPN
ejpam-6441	213	27	n	n	CCONJ
ejpam-6441	213	28	,	,	PUNCT
ejpam-6441	213	29	such	such	ADJ
ejpam-6441	213	30	that	that	SCONJ
ejpam-6441	213	31	d(ςlm+1	d(ςlm+1	PROPN
ejpam-6441	213	32	,	,	PUNCT
ejpam-6441	213	33	ςqm+1	ςqm+1	X
ejpam-6441	213	34	)	)	PUNCT
ejpam-6441	213	35	=	=	SYM
ejpam-6441	214	1	0	0	X
ejpam-6441	214	2	.	.	PUNCT
ejpam-6441	215	1	(	(	PUNCT
ejpam-6441	215	2	15	15	X
ejpam-6441	215	3	)	)	PUNCT
ejpam-6441	215	4	using	use	VERB
ejpam-6441	215	5	triangle	triangle	NOUN
ejpam-6441	215	6	inequality	inequality	NOUN
ejpam-6441	215	7	,	,	PUNCT
ejpam-6441	215	8	we	we	PRON
ejpam-6441	215	9	have	have	VERB
ejpam-6441	215	10	ε	ε	PROPN
ejpam-6441	215	11	≤	≤	PROPN
ejpam-6441	215	12	d(ςlm	d(ςlm	NOUN
ejpam-6441	215	13	,	,	PUNCT
ejpam-6441	215	14	ςqm	ςqm	ADJ
ejpam-6441	215	15	)	)	PUNCT
ejpam-6441	215	16	≤	≤	NOUN
ejpam-6441	215	17	d(ςlm	d(ςlm	NOUN
ejpam-6441	215	18	,	,	PUNCT
ejpam-6441	215	19	ςlm+1	ςlm+1	PROPN
ejpam-6441	215	20	)	)	PUNCT
ejpam-6441	215	21	+	+	CCONJ
ejpam-6441	215	22	d(ςlm+1	d(ςlm+1	PRON
ejpam-6441	215	23	,	,	PUNCT
ejpam-6441	215	24	ςqm	ςqm	ADJ
ejpam-6441	215	25	)	)	PUNCT
ejpam-6441	215	26	≤	≤	NOUN
ejpam-6441	215	27	d(ςlm	d(ςlm	NOUN
ejpam-6441	215	28	,	,	PUNCT
ejpam-6441	215	29	ςlm+1	ςlm+1	PROPN
ejpam-6441	215	30	)	)	PUNCT
ejpam-6441	215	31	+	+	CCONJ
ejpam-6441	215	32	d(ςlm+1	d(ςlm+1	PROPN
ejpam-6441	215	33	,	,	PUNCT
ejpam-6441	215	34	ςqm+1	ςqm+1	PROPN
ejpam-6441	215	35	)	)	PUNCT
ejpam-6441	215	36	+	+	CCONJ
ejpam-6441	215	37	d(ςqm+1	d(ςqm+1	X
ejpam-6441	215	38	,	,	PUNCT
ejpam-6441	215	39	ςqm	ςqm	ADJ
ejpam-6441	215	40	)	)	PUNCT
ejpam-6441	215	41	.	.	PUNCT
ejpam-6441	216	1	taking	take	VERB
ejpam-6441	216	2	limit	limit	NOUN
ejpam-6441	216	3	as	as	ADP
ejpam-6441	216	4	m→	m→	NOUN
ejpam-6441	216	5	∞	∞	PROPN
ejpam-6441	216	6	above	above	ADP
ejpam-6441	216	7	and	and	CCONJ
ejpam-6441	216	8	from	from	ADP
ejpam-6441	216	9	(	(	PUNCT
ejpam-6441	216	10	9	9	NUM
ejpam-6441	216	11	)	)	PUNCT
ejpam-6441	216	12	and	and	CCONJ
ejpam-6441	216	13	(	(	PUNCT
ejpam-6441	216	14	15	15	NUM
ejpam-6441	216	15	)	)	PUNCT
ejpam-6441	216	16	,	,	PUNCT
ejpam-6441	216	17	we	we	PRON
ejpam-6441	216	18	get	get	VERB
ejpam-6441	216	19	a	a	DET
ejpam-6441	216	20	contradiction	contradiction	NOUN
ejpam-6441	216	21	.	.	PUNCT
ejpam-6441	217	1	hence	hence	ADV
ejpam-6441	217	2	(	(	PUNCT
ejpam-6441	217	3	14	14	NUM
ejpam-6441	217	4	)	)	PUNCT
ejpam-6441	217	5	hold	hold	VERB
ejpam-6441	217	6	true	true	ADJ
ejpam-6441	217	7	.	.	PUNCT
ejpam-6441	218	1	now	now	ADV
ejpam-6441	218	2	,	,	PUNCT
ejpam-6441	218	3	we	we	PRON
ejpam-6441	218	4	have	have	VERB
ejpam-6441	218	5	0	0	NUM
ejpam-6441	218	6	<	<	X
ejpam-6441	218	7	d(ςlm+1	d(ςlm+1	PROPN
ejpam-6441	218	8	,	,	PUNCT
ejpam-6441	218	9	ςqm+1	ςqm+1	NOUN
ejpam-6441	218	10	)	)	PUNCT
ejpam-6441	218	11	=	=	SYM
ejpam-6441	218	12	d(ςlm+1,γςqm	d(ςlm+1,γςqm	PROPN
ejpam-6441	218	13	)	)	PUNCT
ejpam-6441	218	14	≤	≤	NOUN
ejpam-6441	218	15	h(γςlm	h(γςlm	NOUN
ejpam-6441	218	16	,	,	PUNCT
ejpam-6441	218	17	γςqm	γςqm	PROPN
ejpam-6441	218	18	)	)	PUNCT
ejpam-6441	218	19	.	.	PUNCT
ejpam-6441	219	1	(	(	PUNCT
ejpam-6441	219	2	16	16	NUM
ejpam-6441	219	3	)	)	PUNCT
ejpam-6441	219	4	since	since	SCONJ
ejpam-6441	219	5	{	{	PUNCT
ejpam-6441	219	6	ςn	ςn	NOUN
ejpam-6441	219	7	}	}	PUNCT
ejpam-6441	219	8	is	be	AUX
ejpam-6441	219	9	ℜ-preserving	ℜ-preserving	NOUN
ejpam-6441	219	10	sequence	sequence	NOUN
ejpam-6441	219	11	,	,	PUNCT
ejpam-6441	219	12	then	then	ADV
ejpam-6441	219	13	by	by	ADP
ejpam-6441	219	14	γ	γ	NOUN
ejpam-6441	219	15	-	-	NOUN
ejpam-6441	219	16	transitivity	transitivity	NOUN
ejpam-6441	219	17	of	of	ADP
ejpam-6441	219	18	ℜ	ℜ	NOUN
ejpam-6441	219	19	we	we	PRON
ejpam-6441	219	20	have	have	VERB
ejpam-6441	219	21	(	(	PUNCT
ejpam-6441	219	22	ςln	ςln	NOUN
ejpam-6441	219	23	,	,	PUNCT
ejpam-6441	219	24	ςqn	ςqn	NOUN
ejpam-6441	219	25	)	)	PUNCT
ejpam-6441	219	26	∈	∈	PROPN
ejpam-6441	219	27	ℜ	ℜ	PROPN
ejpam-6441	219	28	and	and	CCONJ
ejpam-6441	219	29	from	from	ADP
ejpam-6441	219	30	(	(	PUNCT
ejpam-6441	219	31	16	16	NUM
ejpam-6441	219	32	)	)	PUNCT
ejpam-6441	219	33	,	,	PUNCT
ejpam-6441	219	34	we	we	PRON
ejpam-6441	219	35	have	have	VERB
ejpam-6441	219	36	(	(	PUNCT
ejpam-6441	219	37	ςln	ςln	NOUN
ejpam-6441	219	38	,	,	PUNCT
ejpam-6441	219	39	ςqn	ςqn	NOUN
ejpam-6441	219	40	)	)	PUNCT
ejpam-6441	219	41	∈	∈	NOUN
ejpam-6441	219	42	ℜ∗.	ℜ∗.	NOUN
ejpam-6441	219	43	utilizing	utilize	VERB
ejpam-6441	219	44	(	(	PUNCT
ejpam-6441	219	45	f1	f1	NOUN
ejpam-6441	219	46	)	)	PUNCT
ejpam-6441	219	47	in	in	ADP
ejpam-6441	219	48	(	(	PUNCT
ejpam-6441	219	49	16	16	NUM
ejpam-6441	219	50	)	)	PUNCT
ejpam-6441	219	51	and	and	CCONJ
ejpam-6441	219	52	applying	apply	VERB
ejpam-6441	219	53	(	(	PUNCT
ejpam-6441	219	54	1	1	NUM
ejpam-6441	219	55	)	)	PUNCT
ejpam-6441	219	56	,	,	PUNCT
ejpam-6441	219	57	we	we	PRON
ejpam-6441	219	58	obtain	obtain	VERB
ejpam-6441	219	59	f	f	PROPN
ejpam-6441	219	60	(	(	PUNCT
ejpam-6441	219	61	d(ςlm+1	d(ςlm+1	PROPN
ejpam-6441	219	62	,	,	PUNCT
ejpam-6441	219	63	ςqm+1	ςqm+1	PROPN
ejpam-6441	219	64	)	)	PUNCT
ejpam-6441	219	65	)	)	PUNCT
ejpam-6441	220	1	≤	≤	NUM
ejpam-6441	220	2	f	f	X
ejpam-6441	220	3	(	(	PUNCT
ejpam-6441	220	4	h(γςlm	h(γςlm	NOUN
ejpam-6441	220	5	,	,	PUNCT
ejpam-6441	220	6	γςqm	γςqm	PROPN
ejpam-6441	220	7	)	)	PUNCT
ejpam-6441	220	8	)	)	PUNCT
ejpam-6441	220	9	(	(	PUNCT
ejpam-6441	220	10	17	17	NUM
ejpam-6441	220	11	)	)	PUNCT
ejpam-6441	220	12	≤	≤	NUM
ejpam-6441	220	13	f	f	X
ejpam-6441	220	14	(	(	PUNCT
ejpam-6441	220	15	mℜ(ςlm	mℜ(ςlm	NOUN
ejpam-6441	220	16	,	,	PUNCT
ejpam-6441	220	17	ςqm	ςqm	PROPN
ejpam-6441	220	18	)	)	PUNCT
ejpam-6441	220	19	)	)	PUNCT
ejpam-6441	221	1	+	+	CCONJ
ejpam-6441	221	2	lnℜ(ςlm	lnℜ(ςlm	PROPN
ejpam-6441	221	3	,	,	PUNCT
ejpam-6441	221	4	ςqm)−	ςqm)−	PROPN
ejpam-6441	221	5	τ	τ	PROPN
ejpam-6441	221	6	,	,	PUNCT
ejpam-6441	221	7	where	where	SCONJ
ejpam-6441	221	8	mℜ(ςlm	mℜ(ςlm	NOUN
ejpam-6441	221	9	,	,	PUNCT
ejpam-6441	221	10	ςqm	ςqm	ADJ
ejpam-6441	221	11	)	)	PUNCT
ejpam-6441	222	1	=	=	PUNCT
ejpam-6441	222	2	[	[	PUNCT
ejpam-6441	222	3	λ1	λ1	X
ejpam-6441	222	4	(	(	PUNCT
ejpam-6441	222	5	d(ςlm	d(ςlm	NOUN
ejpam-6441	222	6	,	,	PUNCT
ejpam-6441	222	7	γςlm)d(ςqm	γςlm)d(ςqm	PROPN
ejpam-6441	222	8	,	,	PUNCT
ejpam-6441	222	9	γςqm	γςqm	PROPN
ejpam-6441	222	10	)	)	PUNCT
ejpam-6441	222	11	1	1	NUM
ejpam-6441	223	1	+	+	CCONJ
ejpam-6441	223	2	d(ςlm	d(ςlm	NOUN
ejpam-6441	223	3	,	,	PUNCT
ejpam-6441	223	4	ςqm	ςqm	PROPN
ejpam-6441	223	5	)	)	PUNCT
ejpam-6441	223	6	)	)	PUNCT
ejpam-6441	224	1	β	β	X
ejpam-6441	225	1	+	+	NUM
ejpam-6441	225	2	λ2	λ2	NOUN
ejpam-6441	225	3	(	(	PUNCT
ejpam-6441	225	4	d(ςlm	d(ςlm	NOUN
ejpam-6441	225	5	,	,	PUNCT
ejpam-6441	225	6	ςqm	ςqm	PROPN
ejpam-6441	225	7	)	)	PUNCT
ejpam-6441	225	8	)	)	PUNCT
ejpam-6441	225	9	β	β	X
ejpam-6441	225	10	]	]	PUNCT
ejpam-6441	225	11	1	1	NUM
ejpam-6441	225	12	β	β	X
ejpam-6441	225	13	=	=	SYM
ejpam-6441	225	14	[	[	PUNCT
ejpam-6441	225	15	λ1	λ1	X
ejpam-6441	225	16	(	(	PUNCT
ejpam-6441	225	17	d(ςlm	d(ςlm	NOUN
ejpam-6441	225	18	,	,	PUNCT
ejpam-6441	225	19	ςlm+1)d(ςqm	ςlm+1)d(ςqm	X
ejpam-6441	225	20	,	,	PUNCT
ejpam-6441	225	21	ςqm+1	ςqm+1	PROPN
ejpam-6441	225	22	)	)	PUNCT
ejpam-6441	225	23	1	1	NUM
ejpam-6441	225	24	+	+	CCONJ
ejpam-6441	225	25	d(ςlm	d(ςlm	NOUN
ejpam-6441	225	26	,	,	PUNCT
ejpam-6441	225	27	ςqm	ςqm	PROPN
ejpam-6441	225	28	)	)	PUNCT
ejpam-6441	225	29	)	)	PUNCT
ejpam-6441	225	30	β	β	X
ejpam-6441	226	1	+	+	NUM
ejpam-6441	226	2	λ2	λ2	NOUN
ejpam-6441	226	3	(	(	PUNCT
ejpam-6441	226	4	d(ςlm	d(ςlm	NOUN
ejpam-6441	226	5	,	,	PUNCT
ejpam-6441	226	6	ςqm	ςqm	PROPN
ejpam-6441	226	7	)	)	PUNCT
ejpam-6441	226	8	)	)	PUNCT
ejpam-6441	226	9	β	β	X
ejpam-6441	226	10	]	]	PUNCT
ejpam-6441	226	11	1	1	NUM
ejpam-6441	226	12	β	β	X
ejpam-6441	226	13	and	and	CCONJ
ejpam-6441	226	14	nℜ(ςlm	nℜ(ςlm	NOUN
ejpam-6441	226	15	,	,	PUNCT
ejpam-6441	226	16	ςqm	ςqm	ADJ
ejpam-6441	226	17	)	)	PUNCT
ejpam-6441	226	18	=	=	SYM
ejpam-6441	226	19	min	min	NOUN
ejpam-6441	226	20	{	{	PUNCT
ejpam-6441	226	21	d(ςlm	d(ςlm	NOUN
ejpam-6441	226	22	,	,	PUNCT
ejpam-6441	226	23	γςlm	γςlm	NOUN
ejpam-6441	226	24	)	)	PUNCT
ejpam-6441	226	25	,	,	PUNCT
ejpam-6441	226	26	d(ςqm	d(ςqm	PROPN
ejpam-6441	226	27	,	,	PUNCT
ejpam-6441	226	28	γςqm	γςqm	PROPN
ejpam-6441	226	29	)	)	PUNCT
ejpam-6441	226	30	,	,	PUNCT
ejpam-6441	226	31	d(ςlm	d(ςlm	NOUN
ejpam-6441	226	32	,	,	PUNCT
ejpam-6441	226	33	γςqm	γςqm	PROPN
ejpam-6441	226	34	)	)	PUNCT
ejpam-6441	226	35	,	,	PUNCT
ejpam-6441	226	36	d(ςqm	d(ςqm	PROPN
ejpam-6441	226	37	,	,	PUNCT
ejpam-6441	226	38	γςlm	γςlm	NOUN
ejpam-6441	226	39	)	)	PUNCT
ejpam-6441	226	40	}	}	PUNCT
ejpam-6441	226	41	m.	m.	NOUN
ejpam-6441	226	42	mudhesh	mudhesh	PROPN
ejpam-6441	226	43	et	et	PROPN
ejpam-6441	226	44	al	al	PROPN
ejpam-6441	226	45	.	.	PUNCT
ejpam-6441	226	46	/	/	SYM
ejpam-6441	226	47	eur	eur	PROPN
ejpam-6441	226	48	.	.	PUNCT
ejpam-6441	227	1	j.	j.	PROPN
ejpam-6441	227	2	pure	pure	PROPN
ejpam-6441	227	3	appl	appl	PROPN
ejpam-6441	227	4	.	.	PROPN
ejpam-6441	227	5	math	math	PROPN
ejpam-6441	227	6	,	,	PUNCT
ejpam-6441	227	7	18	18	NUM
ejpam-6441	227	8	(	(	PUNCT
ejpam-6441	227	9	4	4	NUM
ejpam-6441	227	10	)	)	PUNCT
ejpam-6441	227	11	(	(	PUNCT
ejpam-6441	227	12	2025	2025	NUM
ejpam-6441	227	13	)	)	PUNCT
ejpam-6441	227	14	,	,	PUNCT
ejpam-6441	227	15	6441	6441	NUM
ejpam-6441	227	16	10	10	NUM
ejpam-6441	227	17	of	of	ADP
ejpam-6441	227	18	21	21	NUM
ejpam-6441	227	19	=	=	SYM
ejpam-6441	227	20	min	min	NOUN
ejpam-6441	227	21	{	{	PUNCT
ejpam-6441	227	22	d(ςlm	d(ςlm	NOUN
ejpam-6441	227	23	,	,	PUNCT
ejpam-6441	227	24	ςlm+1	ςlm+1	PROPN
ejpam-6441	227	25	)	)	PUNCT
ejpam-6441	227	26	,	,	PUNCT
ejpam-6441	227	27	d(ςqm	d(ςqm	PROPN
ejpam-6441	227	28	,	,	PUNCT
ejpam-6441	227	29	ςqm+1	ςqm+1	PROPN
ejpam-6441	227	30	)	)	PUNCT
ejpam-6441	227	31	,	,	PUNCT
ejpam-6441	227	32	d(ςlm	d(ςlm	NOUN
ejpam-6441	227	33	,	,	PUNCT
ejpam-6441	227	34	ςqm+1	ςqm+1	PROPN
ejpam-6441	227	35	)	)	PUNCT
ejpam-6441	227	36	,	,	PUNCT
ejpam-6441	227	37	d(ςqm	d(ςqm	PROPN
ejpam-6441	227	38	,	,	PUNCT
ejpam-6441	227	39	ςlm+1	ςlm+1	NOUN
ejpam-6441	227	40	)	)	PUNCT
ejpam-6441	227	41	}	}	PUNCT
ejpam-6441	227	42	.	.	PUNCT
ejpam-6441	228	1	as	as	SCONJ
ejpam-6441	228	2	f	f	PROPN
ejpam-6441	228	3	is	be	AUX
ejpam-6441	228	4	continuous	continuous	ADJ
ejpam-6441	228	5	then	then	ADV
ejpam-6441	228	6	taking	take	VERB
ejpam-6441	228	7	limit	limit	NOUN
ejpam-6441	228	8	as	as	ADP
ejpam-6441	228	9	m→	m→	NOUN
ejpam-6441	228	10	∞	∞	PROPN
ejpam-6441	228	11	in	in	ADP
ejpam-6441	228	12	(	(	PUNCT
ejpam-6441	228	13	17	17	NUM
ejpam-6441	228	14	)	)	PUNCT
ejpam-6441	228	15	,	,	PUNCT
ejpam-6441	228	16	we	we	PRON
ejpam-6441	228	17	get	get	VERB
ejpam-6441	228	18	f	f	PROPN
ejpam-6441	228	19	(	(	PUNCT
ejpam-6441	228	20	ε	ε	PROPN
ejpam-6441	228	21	)	)	PUNCT
ejpam-6441	228	22	≤	≤	NOUN
ejpam-6441	228	23	f	f	PROPN
ejpam-6441	228	24	(	(	PUNCT
ejpam-6441	228	25	β	β	NOUN
ejpam-6441	228	26	√	√	ADP
ejpam-6441	228	27	λ2ε	λ2ε	PRON
ejpam-6441	228	28	)	)	PUNCT
ejpam-6441	229	1	+	+	NUM
ejpam-6441	229	2	l	l	NOUN
ejpam-6441	229	3	(	(	PUNCT
ejpam-6441	229	4	0)−	0)−	NUM
ejpam-6441	229	5	τ	τ	PROPN
ejpam-6441	229	6	<	<	X
ejpam-6441	229	7	f	f	X
ejpam-6441	229	8	(	(	PUNCT
ejpam-6441	229	9	ε	ε	PROPN
ejpam-6441	229	10	)	)	PUNCT
ejpam-6441	229	11	,	,	PUNCT
ejpam-6441	229	12	which	which	PRON
ejpam-6441	229	13	gives	give	VERB
ejpam-6441	229	14	a	a	DET
ejpam-6441	229	15	contradiction	contradiction	NOUN
ejpam-6441	229	16	.	.	PUNCT
ejpam-6441	230	1	so	so	ADV
ejpam-6441	230	2	,	,	PUNCT
ejpam-6441	230	3	{	{	PUNCT
ejpam-6441	230	4	ςn	ςn	NOUN
ejpam-6441	230	5	}	}	PUNCT
ejpam-6441	230	6	is	be	AUX
ejpam-6441	230	7	ℜ-cauchy	ℜ-cauchy	ADJ
ejpam-6441	230	8	sequence	sequence	NOUN
ejpam-6441	230	9	in	in	ADP
ejpam-6441	230	10	an	an	DET
ejpam-6441	230	11	ℜ-complete	ℜ-complete	PROPN
ejpam-6441	230	12	ms	ms	NOUN
ejpam-6441	230	13	such	such	ADJ
ejpam-6441	230	14	that	that	SCONJ
ejpam-6441	230	15	∃	∃	PROPN
ejpam-6441	230	16	ς∗	ς∗	PROPN
ejpam-6441	230	17	∈	∈	PROPN
ejpam-6441	230	18	∆ℜ	∆ℜ	NOUN
ejpam-6441	230	19	implies	imply	VERB
ejpam-6441	230	20	that	that	SCONJ
ejpam-6441	230	21	lim	lim	PROPN
ejpam-6441	230	22	n→∞	n→∞	X
ejpam-6441	230	23	ςn	ςn	PROPN
ejpam-6441	230	24	=	=	NOUN
ejpam-6441	230	25	ς∗.	ς∗.	NOUN
ejpam-6441	230	26	to	to	ADP
ejpam-6441	230	27	proof	proof	NOUN
ejpam-6441	230	28	that	that	SCONJ
ejpam-6441	230	29	ς∗	ς∗	PROPN
ejpam-6441	230	30	∈	∈	PROPN
ejpam-6441	230	31	γς∗	γς∗	NOUN
ejpam-6441	230	32	,	,	PUNCT
ejpam-6441	230	33	we	we	PRON
ejpam-6441	230	34	claim	claim	VERB
ejpam-6441	230	35	that	that	SCONJ
ejpam-6441	230	36	d	d	X
ejpam-6441	230	37	(	(	PUNCT
ejpam-6441	230	38	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	230	39	)	)	PUNCT
ejpam-6441	230	40	>	>	X
ejpam-6441	230	41	0	0	PUNCT
ejpam-6441	230	42	and	and	CCONJ
ejpam-6441	230	43	by	by	ADP
ejpam-6441	230	44	using	use	VERB
ejpam-6441	230	45	(	(	PUNCT
ejpam-6441	230	46	1	1	NUM
ejpam-6441	230	47	)	)	PUNCT
ejpam-6441	230	48	,	,	PUNCT
ejpam-6441	230	49	lemma	lemma	PROPN
ejpam-6441	230	50	1.15	1.15	NUM
ejpam-6441	230	51	and	and	CCONJ
ejpam-6441	230	52	(	(	PUNCT
ejpam-6441	230	53	t3	t3	PROPN
ejpam-6441	230	54	)	)	PUNCT
ejpam-6441	230	55	,	,	PUNCT
ejpam-6441	230	56	we	we	PRON
ejpam-6441	230	57	write	write	VERB
ejpam-6441	230	58	f	f	PROPN
ejpam-6441	230	59	(	(	PUNCT
ejpam-6441	230	60	d	d	X
ejpam-6441	230	61	(	(	PUNCT
ejpam-6441	230	62	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	230	63	)	)	PUNCT
ejpam-6441	230	64	)	)	PUNCT
ejpam-6441	231	1	≤	≤	PROPN
ejpam-6441	231	2	lim	lim	PROPN
ejpam-6441	231	3	n→∞	n→∞	PRON
ejpam-6441	231	4	f	f	X
ejpam-6441	231	5	(	(	PUNCT
ejpam-6441	231	6	d	d	X
ejpam-6441	231	7	(	(	PUNCT
ejpam-6441	231	8	ςn	ςn	NOUN
ejpam-6441	231	9	,	,	PUNCT
ejpam-6441	231	10	γς	γς	ADV
ejpam-6441	231	11	∗	∗	NOUN
ejpam-6441	231	12	)	)	PUNCT
ejpam-6441	231	13	)	)	PUNCT
ejpam-6441	231	14	(	(	PUNCT
ejpam-6441	231	15	18	18	NUM
ejpam-6441	231	16	)	)	PUNCT
ejpam-6441	231	17	≤	≤	NOUN
ejpam-6441	231	18	lim	lim	PROPN
ejpam-6441	231	19	n→∞	n→∞	PRON
ejpam-6441	231	20	f	f	PROPN
ejpam-6441	231	21	(	(	PUNCT
ejpam-6441	231	22	h	h	PROPN
ejpam-6441	231	23	(	(	PUNCT
ejpam-6441	231	24	γςn−1,γς	γςn−1,γς	PROPN
ejpam-6441	231	25	∗	∗	NOUN
ejpam-6441	231	26	)	)	PUNCT
ejpam-6441	231	27	)	)	PUNCT
ejpam-6441	231	28	≤	≤	PROPN
ejpam-6441	232	1	lim	lim	PROPN
ejpam-6441	232	2	n→∞	n→∞	PRON
ejpam-6441	232	3	f	f	NOUN
ejpam-6441	232	4	(	(	PUNCT
ejpam-6441	232	5	mℜ	mℜ	NOUN
ejpam-6441	232	6	(	(	PUNCT
ejpam-6441	232	7	ςn−1	ςn−1	PROPN
ejpam-6441	232	8	,	,	PUNCT
ejpam-6441	232	9	ς	ς	PROPN
ejpam-6441	232	10	∗	∗	NOUN
ejpam-6441	232	11	)	)	PUNCT
ejpam-6441	232	12	)	)	PUNCT
ejpam-6441	233	1	+	+	CCONJ
ejpam-6441	233	2	lim	lim	PROPN
ejpam-6441	233	3	n→∞	n→∞	PRON
ejpam-6441	233	4	lnℜ	lnℜ	PROPN
ejpam-6441	233	5	(	(	PUNCT
ejpam-6441	233	6	ςn−1	ςn−1	PROPN
ejpam-6441	233	7	,	,	PUNCT
ejpam-6441	233	8	ς	ς	PROPN
ejpam-6441	233	9	∗)−	∗)−	ADV
ejpam-6441	233	10	τ	τ	PROPN
ejpam-6441	233	11	,	,	PUNCT
ejpam-6441	233	12	where	where	SCONJ
ejpam-6441	233	13	mℜ	mℜ	NOUN
ejpam-6441	233	14	(	(	PUNCT
ejpam-6441	233	15	ςn−1	ςn−1	PROPN
ejpam-6441	233	16	,	,	PUNCT
ejpam-6441	233	17	ς	ς	NOUN
ejpam-6441	233	18	∗	∗	NOUN
ejpam-6441	233	19	)	)	PUNCT
ejpam-6441	233	20	=	=	SYM
ejpam-6441	234	1	[	[	PUNCT
ejpam-6441	234	2	λ1	λ1	PROPN
ejpam-6441	234	3	(	(	PUNCT
ejpam-6441	234	4	d	d	X
ejpam-6441	234	5	(	(	PUNCT
ejpam-6441	234	6	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	234	7	∗)d	∗)d	PROPN
ejpam-6441	234	8	(	(	PUNCT
ejpam-6441	234	9	ς∗,γςn−1	ς∗,γςn−1	NUM
ejpam-6441	234	10	)	)	PUNCT
ejpam-6441	234	11	1	1	NUM
ejpam-6441	235	1	+	+	NOUN
ejpam-6441	235	2	d	d	PROPN
ejpam-6441	235	3	(	(	PUNCT
ejpam-6441	235	4	ςn−1	ςn−1	PROPN
ejpam-6441	235	5	,	,	PUNCT
ejpam-6441	235	6	ς∗	ς∗	NOUN
ejpam-6441	235	7	)	)	PUNCT
ejpam-6441	235	8	)	)	PUNCT
ejpam-6441	235	9	β	β	X
ejpam-6441	236	1	+	+	PUNCT
ejpam-6441	236	2	λ2d	λ2d	PUNCT
ejpam-6441	236	3	(	(	PUNCT
ejpam-6441	236	4	ςn−1	ςn−1	PROPN
ejpam-6441	236	5	,	,	PUNCT
ejpam-6441	236	6	ς	ς	PROPN
ejpam-6441	236	7	∗)β	∗)β	PROPN
ejpam-6441	236	8	]	]	PUNCT
ejpam-6441	236	9	1	1	NUM
ejpam-6441	236	10	β	β	X
ejpam-6441	236	11	=	=	SYM
ejpam-6441	236	12	[	[	PUNCT
ejpam-6441	236	13	λ1	λ1	PROPN
ejpam-6441	236	14	(	(	PUNCT
ejpam-6441	236	15	d	d	X
ejpam-6441	236	16	(	(	PUNCT
ejpam-6441	236	17	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	236	18	∗	∗	NOUN
ejpam-6441	236	19	)	)	PUNCT
ejpam-6441	236	20	d	d	NOUN
ejpam-6441	236	21	(	(	PUNCT
ejpam-6441	236	22	ς∗	ς∗	PROPN
ejpam-6441	236	23	,	,	PUNCT
ejpam-6441	236	24	ςn	ςn	NOUN
ejpam-6441	236	25	)	)	PUNCT
ejpam-6441	236	26	1	1	NUM
ejpam-6441	237	1	+	+	CCONJ
ejpam-6441	237	2	d	d	X
ejpam-6441	237	3	(	(	PUNCT
ejpam-6441	237	4	ςn−1	ςn−1	PROPN
ejpam-6441	237	5	,	,	PUNCT
ejpam-6441	237	6	ς∗	ς∗	NOUN
ejpam-6441	237	7	)	)	PUNCT
ejpam-6441	237	8	)	)	PUNCT
ejpam-6441	238	1	β	β	X
ejpam-6441	239	1	+	+	PUNCT
ejpam-6441	239	2	λ2d	λ2d	PUNCT
ejpam-6441	239	3	(	(	PUNCT
ejpam-6441	239	4	γxn−2	γxn−2	PROPN
ejpam-6441	239	5	,	,	PUNCT
ejpam-6441	239	6	x	x	X
ejpam-6441	239	7	∗)β	∗)β	NOUN
ejpam-6441	239	8	]	]	PUNCT
ejpam-6441	239	9	1	1	NUM
ejpam-6441	239	10	β	β	NOUN
ejpam-6441	239	11	,	,	PUNCT
ejpam-6441	239	12	and	and	CCONJ
ejpam-6441	239	13	nℜ	nℜ	PROPN
ejpam-6441	239	14	(	(	PUNCT
ejpam-6441	239	15	ςn−1	ςn−1	PROPN
ejpam-6441	239	16	,	,	PUNCT
ejpam-6441	239	17	ς	ς	NOUN
ejpam-6441	239	18	∗	∗	NOUN
ejpam-6441	239	19	)	)	PUNCT
ejpam-6441	239	20	=	=	SYM
ejpam-6441	239	21	min	min	NOUN
ejpam-6441	239	22	{	{	PUNCT
ejpam-6441	239	23	d	d	X
ejpam-6441	239	24	(	(	PUNCT
ejpam-6441	239	25	ςn−1,γςn−1	ςn−1,γςn−1	NUM
ejpam-6441	239	26	)	)	PUNCT
ejpam-6441	239	27	,	,	PUNCT
ejpam-6441	239	28	d	d	X
ejpam-6441	239	29	(	(	PUNCT
ejpam-6441	239	30	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	239	31	)	)	PUNCT
ejpam-6441	239	32	,	,	PUNCT
ejpam-6441	239	33	d	d	X
ejpam-6441	239	34	(	(	PUNCT
ejpam-6441	239	35	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	239	36	∗	∗	NOUN
ejpam-6441	239	37	)	)	PUNCT
ejpam-6441	239	38	,	,	PUNCT
ejpam-6441	239	39	d	d	X
ejpam-6441	239	40	(	(	PUNCT
ejpam-6441	239	41	ς∗,γςn−1	ς∗,γςn−1	NUM
ejpam-6441	239	42	)	)	PUNCT
ejpam-6441	239	43	}	}	PUNCT
ejpam-6441	239	44	=	=	SYM
ejpam-6441	239	45	min	min	NOUN
ejpam-6441	239	46	{	{	PUNCT
ejpam-6441	239	47	d	d	X
ejpam-6441	239	48	(	(	PUNCT
ejpam-6441	239	49	ςn−1	ςn−1	PROPN
ejpam-6441	239	50	,	,	PUNCT
ejpam-6441	239	51	ςn	ςn	NOUN
ejpam-6441	239	52	)	)	PUNCT
ejpam-6441	239	53	,	,	PUNCT
ejpam-6441	240	1	d	d	X
ejpam-6441	240	2	(	(	PUNCT
ejpam-6441	240	3	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	240	4	)	)	PUNCT
ejpam-6441	240	5	,	,	PUNCT
ejpam-6441	240	6	d	d	X
ejpam-6441	240	7	(	(	PUNCT
ejpam-6441	240	8	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	240	9	∗	∗	NOUN
ejpam-6441	240	10	)	)	PUNCT
ejpam-6441	240	11	,	,	PUNCT
ejpam-6441	240	12	d	d	X
ejpam-6441	240	13	(	(	PUNCT
ejpam-6441	240	14	ς∗	ς∗	PROPN
ejpam-6441	240	15	,	,	PUNCT
ejpam-6441	240	16	ςn	ςn	NOUN
ejpam-6441	240	17	)	)	PUNCT
ejpam-6441	240	18	}	}	PUNCT
ejpam-6441	240	19	.	.	PUNCT
ejpam-6441	241	1	taking	take	VERB
ejpam-6441	241	2	limit	limit	NOUN
ejpam-6441	241	3	as	as	ADP
ejpam-6441	241	4	n→	n→	PROPN
ejpam-6441	241	5	∞	∞	PROPN
ejpam-6441	241	6	in	in	ADP
ejpam-6441	241	7	(	(	PUNCT
ejpam-6441	241	8	18	18	NUM
ejpam-6441	241	9	)	)	PUNCT
ejpam-6441	241	10	with	with	ADP
ejpam-6441	241	11	continuity	continuity	NOUN
ejpam-6441	241	12	of	of	ADP
ejpam-6441	241	13	f	f	PROPN
ejpam-6441	241	14	,	,	PUNCT
ejpam-6441	241	15	we	we	PRON
ejpam-6441	241	16	have	have	VERB
ejpam-6441	241	17	f	f	X
ejpam-6441	241	18	(	(	PUNCT
ejpam-6441	241	19	d	d	X
ejpam-6441	241	20	(	(	PUNCT
ejpam-6441	241	21	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	241	22	)	)	PUNCT
ejpam-6441	241	23	)	)	PUNCT
ejpam-6441	242	1	≤	≤	NUM
ejpam-6441	242	2	f	f	X
ejpam-6441	242	3	(	(	PUNCT
ejpam-6441	242	4	β	β	NOUN
ejpam-6441	242	5	√	√	NUM
ejpam-6441	242	6	λ2d	λ2d	PUNCT
ejpam-6441	242	7	(	(	PUNCT
ejpam-6441	242	8	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	242	9	)	)	PUNCT
ejpam-6441	242	10	)	)	PUNCT
ejpam-6441	243	1	+	+	PUNCT
ejpam-6441	243	2	l	l	NOUN
ejpam-6441	243	3	(	(	PUNCT
ejpam-6441	243	4	0)−	0)−	NUM
ejpam-6441	243	5	τ	τ	X
ejpam-6441	243	6	<	<	X
ejpam-6441	243	7	f	f	X
ejpam-6441	243	8	(	(	PUNCT
ejpam-6441	243	9	d	d	X
ejpam-6441	243	10	(	(	PUNCT
ejpam-6441	243	11	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	243	12	)	)	PUNCT
ejpam-6441	243	13	)	)	PUNCT
ejpam-6441	243	14	.	.	PUNCT
ejpam-6441	244	1	a	a	DET
ejpam-6441	244	2	contradiction	contradiction	NOUN
ejpam-6441	244	3	,	,	PUNCT
ejpam-6441	244	4	thence	thence	NOUN
ejpam-6441	244	5	d	d	NOUN
ejpam-6441	244	6	(	(	PUNCT
ejpam-6441	244	7	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	244	8	)	)	PUNCT
ejpam-6441	244	9	=	=	SYM
ejpam-6441	244	10	0	0	NUM
ejpam-6441	244	11	and	and	CCONJ
ejpam-6441	244	12	ς∗	ς∗	PROPN
ejpam-6441	244	13	∈	∈	PROPN
ejpam-6441	244	14	γς∗	γς∗	NOUN
ejpam-6441	244	15	is	be	AUX
ejpam-6441	244	16	a	a	DET
ejpam-6441	244	17	fp	fp	NOUN
ejpam-6441	244	18	of	of	ADP
ejpam-6441	244	19	γ	γ	PROPN
ejpam-6441	244	20	.	.	PUNCT
ejpam-6441	245	1	now	now	ADV
ejpam-6441	245	2	,	,	PUNCT
ejpam-6441	245	3	if	if	SCONJ
ejpam-6441	245	4	β	β	X
ejpam-6441	245	5	=	=	SYM
ejpam-6441	245	6	0	0	NUM
ejpam-6441	245	7	,	,	PUNCT
ejpam-6441	245	8	then	then	ADV
ejpam-6441	245	9	mℜ(ςn−1	mℜ(ςn−1	ADJ
ejpam-6441	245	10	,	,	PUNCT
ejpam-6441	245	11	ςn	ςn	NOUN
ejpam-6441	245	12	)	)	PUNCT
ejpam-6441	246	1	=	=	SYM
ejpam-6441	246	2	d	d	X
ejpam-6441	246	3	(	(	PUNCT
ejpam-6441	246	4	ςn−1,γςn−1	ςn−1,γςn−1	NOUN
ejpam-6441	246	5	)	)	PUNCT
ejpam-6441	246	6	λ1	λ1	PROPN
ejpam-6441	246	7	d	d	X
ejpam-6441	246	8	(	(	PUNCT
ejpam-6441	246	9	ςn	ςn	PROPN
ejpam-6441	246	10	,	,	PUNCT
ejpam-6441	246	11	γςn	γςn	PROPN
ejpam-6441	246	12	)	)	PUNCT
ejpam-6441	247	1	λ2	λ2	NOUN
ejpam-6441	247	2	(	(	PUNCT
ejpam-6441	247	3	19	19	NUM
ejpam-6441	247	4	)	)	PUNCT
ejpam-6441	247	5	=	=	SYM
ejpam-6441	248	1	d	d	PROPN
ejpam-6441	248	2	(	(	PUNCT
ejpam-6441	248	3	ςn−1	ςn−1	PROPN
ejpam-6441	248	4	,	,	PUNCT
ejpam-6441	248	5	ςn	ςn	NOUN
ejpam-6441	248	6	)	)	PUNCT
ejpam-6441	248	7	λ1	λ1	PROPN
ejpam-6441	248	8	d	d	X
ejpam-6441	248	9	(	(	PUNCT
ejpam-6441	248	10	ςn	ςn	PROPN
ejpam-6441	248	11	,	,	PUNCT
ejpam-6441	248	12	ςn+1	ςn+1	NOUN
ejpam-6441	248	13	)	)	PUNCT
ejpam-6441	248	14	λ2	λ2	NOUN
ejpam-6441	248	15	.	.	PUNCT
ejpam-6441	248	16	assume	assume	VERB
ejpam-6441	248	17	that	that	SCONJ
ejpam-6441	248	18	d	d	PROPN
ejpam-6441	248	19	(	(	PUNCT
ejpam-6441	248	20	ςn−1	ςn−1	PROPN
ejpam-6441	248	21	,	,	PUNCT
ejpam-6441	248	22	ςn	ςn	NOUN
ejpam-6441	248	23	)	)	PUNCT
ejpam-6441	248	24	≤	≤	NUM
ejpam-6441	248	25	d	d	PROPN
ejpam-6441	248	26	(	(	PUNCT
ejpam-6441	248	27	ςn	ςn	PROPN
ejpam-6441	248	28	,	,	PUNCT
ejpam-6441	248	29	ςn+1	ςn+1	NUM
ejpam-6441	248	30	)	)	PUNCT
ejpam-6441	248	31	,	,	PUNCT
ejpam-6441	248	32	then	then	ADV
ejpam-6441	248	33	(	(	PUNCT
ejpam-6441	248	34	19	19	NUM
ejpam-6441	248	35	)	)	PUNCT
ejpam-6441	248	36	becomes	become	VERB
ejpam-6441	248	37	mℜ(ςn−1	mℜ(ςn−1	PROPN
ejpam-6441	248	38	,	,	PUNCT
ejpam-6441	248	39	ςn	ςn	NOUN
ejpam-6441	248	40	)	)	PUNCT
ejpam-6441	248	41	≤	≤	NUM
ejpam-6441	249	1	d	d	PROPN
ejpam-6441	249	2	(	(	PUNCT
ejpam-6441	249	3	ςn	ςn	PROPN
ejpam-6441	249	4	,	,	PUNCT
ejpam-6441	249	5	ςn+1	ςn+1	NUM
ejpam-6441	249	6	)	)	PUNCT
ejpam-6441	249	7	λ1	λ1	PROPN
ejpam-6441	249	8	d	d	X
ejpam-6441	249	9	(	(	PUNCT
ejpam-6441	249	10	ςn	ςn	PROPN
ejpam-6441	249	11	,	,	PUNCT
ejpam-6441	249	12	ςn+1	ςn+1	NOUN
ejpam-6441	249	13	)	)	PUNCT
ejpam-6441	249	14	λ2	λ2	NOUN
ejpam-6441	249	15	(	(	PUNCT
ejpam-6441	249	16	20	20	NUM
ejpam-6441	249	17	)	)	PUNCT
ejpam-6441	249	18	=	=	SYM
ejpam-6441	250	1	d	d	PROPN
ejpam-6441	250	2	(	(	PUNCT
ejpam-6441	250	3	ςn	ςn	PROPN
ejpam-6441	250	4	,	,	PUNCT
ejpam-6441	250	5	ςn+1	ςn+1	NUM
ejpam-6441	250	6	)	)	PUNCT
ejpam-6441	251	1	λ1+λ2	λ1+λ2	PROPN
ejpam-6441	251	2	m.	m.	NOUN
ejpam-6441	251	3	mudhesh	mudhesh	PROPN
ejpam-6441	251	4	et	et	PROPN
ejpam-6441	251	5	al	al	PROPN
ejpam-6441	251	6	.	.	PUNCT
ejpam-6441	251	7	/	/	SYM
ejpam-6441	251	8	eur	eur	PROPN
ejpam-6441	251	9	.	.	PUNCT
ejpam-6441	252	1	j.	j.	PROPN
ejpam-6441	252	2	pure	pure	PROPN
ejpam-6441	252	3	appl	appl	PROPN
ejpam-6441	252	4	.	.	PROPN
ejpam-6441	252	5	math	math	PROPN
ejpam-6441	252	6	,	,	PUNCT
ejpam-6441	252	7	18	18	NUM
ejpam-6441	252	8	(	(	PUNCT
ejpam-6441	252	9	4	4	NUM
ejpam-6441	252	10	)	)	PUNCT
ejpam-6441	252	11	(	(	PUNCT
ejpam-6441	252	12	2025	2025	NUM
ejpam-6441	252	13	)	)	PUNCT
ejpam-6441	252	14	,	,	PUNCT
ejpam-6441	252	15	6441	6441	NUM
ejpam-6441	252	16	11	11	NUM
ejpam-6441	252	17	of	of	ADP
ejpam-6441	252	18	21	21	NUM
ejpam-6441	252	19	=	=	SYM
ejpam-6441	252	20	d	d	PROPN
ejpam-6441	252	21	(	(	PUNCT
ejpam-6441	252	22	ςn	ςn	PROPN
ejpam-6441	252	23	,	,	PUNCT
ejpam-6441	252	24	ςn+1	ςn+1	NUM
ejpam-6441	252	25	)	)	PUNCT
ejpam-6441	252	26	.	.	PUNCT
ejpam-6441	253	1	thereafter	thereafter	ADV
ejpam-6441	253	2	,	,	PUNCT
ejpam-6441	253	3	from	from	ADP
ejpam-6441	253	4	(	(	PUNCT
ejpam-6441	253	5	6	6	NUM
ejpam-6441	253	6	)	)	PUNCT
ejpam-6441	253	7	and	and	CCONJ
ejpam-6441	253	8	(	(	PUNCT
ejpam-6441	253	9	20	20	NUM
ejpam-6441	253	10	)	)	PUNCT
ejpam-6441	253	11	,	,	PUNCT
ejpam-6441	253	12	we	we	PRON
ejpam-6441	253	13	get	get	VERB
ejpam-6441	253	14	a	a	DET
ejpam-6441	253	15	contradiction	contradiction	NOUN
ejpam-6441	253	16	.	.	PUNCT
ejpam-6441	254	1	thus	thus	ADV
ejpam-6441	254	2	,	,	PUNCT
ejpam-6441	254	3	d	d	X
ejpam-6441	254	4	(	(	PUNCT
ejpam-6441	254	5	ςn−1	ςn−1	PROPN
ejpam-6441	254	6	,	,	PUNCT
ejpam-6441	254	7	ςn	ςn	NOUN
ejpam-6441	254	8	)	)	PUNCT
ejpam-6441	254	9	>	>	PUNCT
ejpam-6441	254	10	d	d	X
ejpam-6441	254	11	(	(	PUNCT
ejpam-6441	254	12	ςn	ςn	PROPN
ejpam-6441	254	13	,	,	PUNCT
ejpam-6441	254	14	ςn+1	ςn+1	NUM
ejpam-6441	254	15	)	)	PUNCT
ejpam-6441	254	16	and	and	CCONJ
ejpam-6441	254	17	(	(	PUNCT
ejpam-6441	254	18	19	19	NUM
ejpam-6441	254	19	)	)	PUNCT
ejpam-6441	254	20	becomes	become	VERB
ejpam-6441	254	21	mℜ(ςn−1	mℜ(ςn−1	PROPN
ejpam-6441	254	22	,	,	PUNCT
ejpam-6441	254	23	ςn	ςn	NOUN
ejpam-6441	254	24	)	)	PUNCT
ejpam-6441	254	25	<	<	X
ejpam-6441	255	1	d	d	X
ejpam-6441	255	2	(	(	PUNCT
ejpam-6441	255	3	ςn−1	ςn−1	PROPN
ejpam-6441	255	4	,	,	PUNCT
ejpam-6441	255	5	ςn	ςn	NOUN
ejpam-6441	255	6	)	)	PUNCT
ejpam-6441	255	7	(	(	PUNCT
ejpam-6441	255	8	21	21	NUM
ejpam-6441	255	9	)	)	PUNCT
ejpam-6441	255	10	applying	apply	VERB
ejpam-6441	255	11	(	(	PUNCT
ejpam-6441	255	12	21	21	NUM
ejpam-6441	255	13	)	)	PUNCT
ejpam-6441	255	14	in	in	ADP
ejpam-6441	255	15	(	(	PUNCT
ejpam-6441	255	16	6	6	NUM
ejpam-6441	255	17	)	)	PUNCT
ejpam-6441	255	18	and	and	CCONJ
ejpam-6441	255	19	following	follow	VERB
ejpam-6441	255	20	the	the	DET
ejpam-6441	255	21	same	same	ADJ
ejpam-6441	255	22	steps	step	NOUN
ejpam-6441	255	23	from	from	ADP
ejpam-6441	255	24	(	(	PUNCT
ejpam-6441	255	25	8)	8)	NUM
ejpam-6441	255	26	till	till	SCONJ
ejpam-6441	255	27	(	(	PUNCT
ejpam-6441	255	28	17	17	NUM
ejpam-6441	255	29	)	)	PUNCT
ejpam-6441	255	30	,	,	PUNCT
ejpam-6441	255	31	we	we	PRON
ejpam-6441	255	32	get	get	VERB
ejpam-6441	255	33	mℜ(ςlm	mℜ(ςlm	NOUN
ejpam-6441	255	34	,	,	PUNCT
ejpam-6441	255	35	ςqm	ςqm	ADJ
ejpam-6441	255	36	)	)	PUNCT
ejpam-6441	256	1	=	=	SYM
ejpam-6441	256	2	d(ςlm	d(ςlm	NOUN
ejpam-6441	256	3	,	,	PUNCT
ejpam-6441	256	4	γςlm	γςlm	NOUN
ejpam-6441	256	5	)	)	PUNCT
ejpam-6441	256	6	λ1d(ςqm	λ1d(ςqm	X
ejpam-6441	256	7	,	,	PUNCT
ejpam-6441	256	8	γςqm	γςqm	ADJ
ejpam-6441	256	9	)	)	PUNCT
ejpam-6441	256	10	λ2	λ2	NOUN
ejpam-6441	256	11	=	=	PUNCT
ejpam-6441	256	12	d(ςlm	d(ςlm	NOUN
ejpam-6441	256	13	,	,	PUNCT
ejpam-6441	256	14	ςlm+1	ςlm+1	PROPN
ejpam-6441	256	15	)	)	PUNCT
ejpam-6441	256	16	λ1d(ςqm	λ1d(ςqm	NOUN
ejpam-6441	256	17	,	,	PUNCT
ejpam-6441	256	18	ςqm+1	ςqm+1	PROPN
ejpam-6441	256	19	)	)	PUNCT
ejpam-6441	256	20	λ2	λ2	NOUN
ejpam-6441	256	21	and	and	CCONJ
ejpam-6441	256	22	nℜ(ςlm	nℜ(ςlm	NOUN
ejpam-6441	256	23	,	,	PUNCT
ejpam-6441	256	24	ςqm	ςqm	ADJ
ejpam-6441	256	25	)	)	PUNCT
ejpam-6441	257	1	=	=	SYM
ejpam-6441	257	2	min	min	NOUN
ejpam-6441	257	3	{	{	PUNCT
ejpam-6441	257	4	d(ςlm	d(ςlm	NOUN
ejpam-6441	257	5	,	,	PUNCT
ejpam-6441	257	6	γςlm	γςlm	NOUN
ejpam-6441	257	7	)	)	PUNCT
ejpam-6441	257	8	,	,	PUNCT
ejpam-6441	257	9	d(ςqm	d(ςqm	PROPN
ejpam-6441	257	10	,	,	PUNCT
ejpam-6441	257	11	γςqm	γςqm	PROPN
ejpam-6441	257	12	)	)	PUNCT
ejpam-6441	257	13	,	,	PUNCT
ejpam-6441	257	14	d(ςlm	d(ςlm	NOUN
ejpam-6441	257	15	,	,	PUNCT
ejpam-6441	257	16	γςqm	γςqm	PROPN
ejpam-6441	257	17	)	)	PUNCT
ejpam-6441	257	18	,	,	PUNCT
ejpam-6441	257	19	d(ςqm	d(ςqm	PROPN
ejpam-6441	257	20	,	,	PUNCT
ejpam-6441	257	21	γςlm	γςlm	NOUN
ejpam-6441	257	22	)	)	PUNCT
ejpam-6441	257	23	}	}	PUNCT
ejpam-6441	257	24	=	=	SYM
ejpam-6441	257	25	min	min	NOUN
ejpam-6441	257	26	{	{	PUNCT
ejpam-6441	257	27	d(ςlm	d(ςlm	NOUN
ejpam-6441	257	28	,	,	PUNCT
ejpam-6441	257	29	ςlm+1	ςlm+1	PROPN
ejpam-6441	257	30	)	)	PUNCT
ejpam-6441	257	31	,	,	PUNCT
ejpam-6441	257	32	d(ςqm	d(ςqm	PROPN
ejpam-6441	257	33	,	,	PUNCT
ejpam-6441	257	34	ςqm+1	ςqm+1	PROPN
ejpam-6441	257	35	)	)	PUNCT
ejpam-6441	257	36	,	,	PUNCT
ejpam-6441	257	37	d(ςlm	d(ςlm	NOUN
ejpam-6441	257	38	,	,	PUNCT
ejpam-6441	257	39	ςqm+1	ςqm+1	PROPN
ejpam-6441	257	40	)	)	PUNCT
ejpam-6441	257	41	,	,	PUNCT
ejpam-6441	257	42	d(ςqm	d(ςqm	PROPN
ejpam-6441	257	43	,	,	PUNCT
ejpam-6441	257	44	ςlm+1	ςlm+1	NOUN
ejpam-6441	257	45	)	)	PUNCT
ejpam-6441	257	46	}	}	PUNCT
ejpam-6441	257	47	.	.	PUNCT
ejpam-6441	258	1	as	as	SCONJ
ejpam-6441	258	2	f	f	PROPN
ejpam-6441	258	3	is	be	AUX
ejpam-6441	258	4	continuous	continuous	ADJ
ejpam-6441	258	5	then	then	ADV
ejpam-6441	258	6	taking	take	VERB
ejpam-6441	258	7	limit	limit	NOUN
ejpam-6441	258	8	as	as	ADP
ejpam-6441	258	9	m→	m→	NOUN
ejpam-6441	258	10	∞	∞	PROPN
ejpam-6441	258	11	in	in	ADP
ejpam-6441	258	12	(	(	PUNCT
ejpam-6441	258	13	17	17	NUM
ejpam-6441	258	14	)	)	PUNCT
ejpam-6441	258	15	,	,	PUNCT
ejpam-6441	258	16	we	we	PRON
ejpam-6441	258	17	get	get	VERB
ejpam-6441	258	18	f	f	PROPN
ejpam-6441	258	19	(	(	PUNCT
ejpam-6441	258	20	ε	ε	PROPN
ejpam-6441	258	21	)	)	PUNCT
ejpam-6441	258	22	<	<	X
ejpam-6441	258	23	f	f	X
ejpam-6441	258	24	(	(	PUNCT
ejpam-6441	258	25	0	0	NUM
ejpam-6441	258	26	)	)	PUNCT
ejpam-6441	259	1	+	+	NUM
ejpam-6441	259	2	l	l	NOUN
ejpam-6441	259	3	(	(	PUNCT
ejpam-6441	259	4	0)−	0)−	NUM
ejpam-6441	259	5	τ	τ	PROPN
ejpam-6441	259	6	which	which	PRON
ejpam-6441	259	7	gives	give	VERB
ejpam-6441	259	8	a	a	DET
ejpam-6441	259	9	contradiction	contradiction	NOUN
ejpam-6441	259	10	again	again	ADV
ejpam-6441	259	11	.	.	PUNCT
ejpam-6441	260	1	so	so	ADV
ejpam-6441	260	2	,	,	PUNCT
ejpam-6441	260	3	{	{	PUNCT
ejpam-6441	260	4	ςn	ςn	NOUN
ejpam-6441	260	5	}	}	PUNCT
ejpam-6441	260	6	is	be	AUX
ejpam-6441	260	7	ℜ-cauchy	ℜ-cauchy	ADJ
ejpam-6441	260	8	sequence	sequence	NOUN
ejpam-6441	260	9	in	in	ADP
ejpam-6441	260	10	an	an	DET
ejpam-6441	260	11	ℜ-complete	ℜ-complete	PROPN
ejpam-6441	260	12	ms	ms	NOUN
ejpam-6441	260	13	such	such	ADJ
ejpam-6441	260	14	that	that	SCONJ
ejpam-6441	260	15	∃	∃	PROPN
ejpam-6441	260	16	ς∗	ς∗	PROPN
ejpam-6441	260	17	∈	∈	PROPN
ejpam-6441	260	18	∆ℜ	∆ℜ	NOUN
ejpam-6441	260	19	implies	imply	VERB
ejpam-6441	260	20	that	that	SCONJ
ejpam-6441	260	21	lim	lim	PROPN
ejpam-6441	260	22	n→∞	n→∞	X
ejpam-6441	260	23	ςn	ςn	PROPN
ejpam-6441	260	24	=	=	NOUN
ejpam-6441	260	25	ς∗.	ς∗.	NOUN
ejpam-6441	260	26	to	to	ADP
ejpam-6441	260	27	proof	proof	NOUN
ejpam-6441	260	28	that	that	SCONJ
ejpam-6441	260	29	ς∗	ς∗	PROPN
ejpam-6441	260	30	∈	∈	PROPN
ejpam-6441	260	31	γς∗	γς∗	NOUN
ejpam-6441	260	32	,	,	PUNCT
ejpam-6441	260	33	we	we	PRON
ejpam-6441	260	34	claim	claim	VERB
ejpam-6441	260	35	that	that	SCONJ
ejpam-6441	260	36	d	d	X
ejpam-6441	260	37	(	(	PUNCT
ejpam-6441	260	38	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	260	39	)	)	PUNCT
ejpam-6441	260	40	>	>	X
ejpam-6441	260	41	0	0	PUNCT
ejpam-6441	260	42	and	and	CCONJ
ejpam-6441	260	43	by	by	ADP
ejpam-6441	260	44	using	use	VERB
ejpam-6441	260	45	(	(	PUNCT
ejpam-6441	260	46	1	1	NUM
ejpam-6441	260	47	)	)	PUNCT
ejpam-6441	260	48	,	,	PUNCT
ejpam-6441	260	49	lemma	lemma	PROPN
ejpam-6441	260	50	1.15	1.15	NUM
ejpam-6441	260	51	and	and	CCONJ
ejpam-6441	260	52	(	(	PUNCT
ejpam-6441	260	53	t3	t3	PROPN
ejpam-6441	260	54	)	)	PUNCT
ejpam-6441	260	55	,	,	PUNCT
ejpam-6441	260	56	we	we	PRON
ejpam-6441	260	57	write	write	VERB
ejpam-6441	260	58	f	f	PROPN
ejpam-6441	260	59	(	(	PUNCT
ejpam-6441	260	60	d	d	X
ejpam-6441	260	61	(	(	PUNCT
ejpam-6441	260	62	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	260	63	)	)	PUNCT
ejpam-6441	260	64	)	)	PUNCT
ejpam-6441	261	1	≤	≤	PROPN
ejpam-6441	261	2	lim	lim	PROPN
ejpam-6441	261	3	n→∞	n→∞	PRON
ejpam-6441	261	4	f	f	X
ejpam-6441	261	5	(	(	PUNCT
ejpam-6441	261	6	d	d	X
ejpam-6441	261	7	(	(	PUNCT
ejpam-6441	261	8	ςn	ςn	NOUN
ejpam-6441	261	9	,	,	PUNCT
ejpam-6441	261	10	γς	γς	ADV
ejpam-6441	261	11	∗	∗	NOUN
ejpam-6441	261	12	)	)	PUNCT
ejpam-6441	261	13	)	)	PUNCT
ejpam-6441	261	14	(	(	PUNCT
ejpam-6441	261	15	22	22	NUM
ejpam-6441	261	16	)	)	PUNCT
ejpam-6441	261	17	≤	≤	NOUN
ejpam-6441	261	18	lim	lim	PROPN
ejpam-6441	261	19	n→∞	n→∞	PRON
ejpam-6441	261	20	f	f	PROPN
ejpam-6441	261	21	(	(	PUNCT
ejpam-6441	261	22	h	h	PROPN
ejpam-6441	261	23	(	(	PUNCT
ejpam-6441	261	24	γςn−1,γς	γςn−1,γς	PROPN
ejpam-6441	261	25	∗	∗	NOUN
ejpam-6441	261	26	)	)	PUNCT
ejpam-6441	261	27	)	)	PUNCT
ejpam-6441	261	28	≤	≤	PROPN
ejpam-6441	262	1	lim	lim	PROPN
ejpam-6441	262	2	n→∞	n→∞	PRON
ejpam-6441	262	3	f	f	NOUN
ejpam-6441	262	4	(	(	PUNCT
ejpam-6441	262	5	mℜ	mℜ	NOUN
ejpam-6441	262	6	(	(	PUNCT
ejpam-6441	262	7	ςn−1	ςn−1	PROPN
ejpam-6441	262	8	,	,	PUNCT
ejpam-6441	262	9	ς	ς	PROPN
ejpam-6441	262	10	∗	∗	NOUN
ejpam-6441	262	11	)	)	PUNCT
ejpam-6441	262	12	)	)	PUNCT
ejpam-6441	263	1	+	+	CCONJ
ejpam-6441	263	2	lim	lim	PROPN
ejpam-6441	263	3	n→∞	n→∞	PRON
ejpam-6441	263	4	lnℜ	lnℜ	PROPN
ejpam-6441	263	5	(	(	PUNCT
ejpam-6441	263	6	ςn−1	ςn−1	PROPN
ejpam-6441	263	7	,	,	PUNCT
ejpam-6441	263	8	ς	ς	PROPN
ejpam-6441	263	9	∗)−	∗)−	ADV
ejpam-6441	263	10	τ	τ	PROPN
ejpam-6441	263	11	,	,	PUNCT
ejpam-6441	263	12	where	where	SCONJ
ejpam-6441	263	13	mℜ	mℜ	NOUN
ejpam-6441	263	14	(	(	PUNCT
ejpam-6441	263	15	ςn−1	ςn−1	PROPN
ejpam-6441	263	16	,	,	PUNCT
ejpam-6441	263	17	ς	ς	NOUN
ejpam-6441	263	18	∗	∗	NOUN
ejpam-6441	263	19	)	)	PUNCT
ejpam-6441	263	20	=	=	SYM
ejpam-6441	264	1	d	d	PROPN
ejpam-6441	264	2	(	(	PUNCT
ejpam-6441	264	3	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	264	4	∗)λ1	∗)λ1	PROPN
ejpam-6441	264	5	d	d	PROPN
ejpam-6441	264	6	(	(	PUNCT
ejpam-6441	264	7	ς∗,γςn−1	ς∗,γςn−1	NUM
ejpam-6441	264	8	)	)	PUNCT
ejpam-6441	264	9	λ2	λ2	NOUN
ejpam-6441	264	10	=	=	SYM
ejpam-6441	264	11	d	d	PROPN
ejpam-6441	264	12	(	(	PUNCT
ejpam-6441	264	13	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	264	14	∗)λ1	∗)λ1	PROPN
ejpam-6441	264	15	d	d	PROPN
ejpam-6441	264	16	(	(	PUNCT
ejpam-6441	264	17	ς∗	ς∗	PROPN
ejpam-6441	264	18	,	,	PUNCT
ejpam-6441	264	19	ςn	ςn	NOUN
ejpam-6441	264	20	)	)	PUNCT
ejpam-6441	264	21	λ2	λ2	NOUN
ejpam-6441	264	22	,	,	PUNCT
ejpam-6441	264	23	and	and	CCONJ
ejpam-6441	264	24	nℜ	nℜ	PROPN
ejpam-6441	264	25	(	(	PUNCT
ejpam-6441	264	26	ςn−1	ςn−1	PROPN
ejpam-6441	264	27	,	,	PUNCT
ejpam-6441	264	28	ς	ς	NOUN
ejpam-6441	264	29	∗	∗	NOUN
ejpam-6441	264	30	)	)	PUNCT
ejpam-6441	264	31	=	=	SYM
ejpam-6441	264	32	min	min	NOUN
ejpam-6441	264	33	{	{	PUNCT
ejpam-6441	264	34	d	d	X
ejpam-6441	264	35	(	(	PUNCT
ejpam-6441	264	36	ςn−1,γςn−1	ςn−1,γςn−1	NUM
ejpam-6441	264	37	)	)	PUNCT
ejpam-6441	264	38	,	,	PUNCT
ejpam-6441	264	39	d	d	X
ejpam-6441	264	40	(	(	PUNCT
ejpam-6441	264	41	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	264	42	)	)	PUNCT
ejpam-6441	264	43	,	,	PUNCT
ejpam-6441	265	1	d	d	X
ejpam-6441	265	2	(	(	PUNCT
ejpam-6441	265	3	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	265	4	∗	∗	NOUN
ejpam-6441	265	5	)	)	PUNCT
ejpam-6441	265	6	,	,	PUNCT
ejpam-6441	265	7	d	d	X
ejpam-6441	265	8	(	(	PUNCT
ejpam-6441	265	9	ς∗,γςn−1	ς∗,γςn−1	NUM
ejpam-6441	265	10	)	)	PUNCT
ejpam-6441	265	11	}	}	PUNCT
ejpam-6441	265	12	=	=	SYM
ejpam-6441	265	13	min	min	NOUN
ejpam-6441	265	14	{	{	PUNCT
ejpam-6441	265	15	d	d	X
ejpam-6441	265	16	(	(	PUNCT
ejpam-6441	265	17	ςn−1	ςn−1	PROPN
ejpam-6441	265	18	,	,	PUNCT
ejpam-6441	265	19	ςn	ςn	NOUN
ejpam-6441	265	20	)	)	PUNCT
ejpam-6441	265	21	,	,	PUNCT
ejpam-6441	266	1	d	d	X
ejpam-6441	266	2	(	(	PUNCT
ejpam-6441	266	3	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	266	4	)	)	PUNCT
ejpam-6441	266	5	,	,	PUNCT
ejpam-6441	266	6	d	d	X
ejpam-6441	266	7	(	(	PUNCT
ejpam-6441	266	8	ςn−1,γς	ςn−1,γς	PROPN
ejpam-6441	266	9	∗	∗	NOUN
ejpam-6441	266	10	)	)	PUNCT
ejpam-6441	266	11	,	,	PUNCT
ejpam-6441	266	12	d	d	X
ejpam-6441	266	13	(	(	PUNCT
ejpam-6441	266	14	ς∗	ς∗	PROPN
ejpam-6441	266	15	,	,	PUNCT
ejpam-6441	266	16	ςn	ςn	NOUN
ejpam-6441	266	17	)	)	PUNCT
ejpam-6441	266	18	}	}	PUNCT
ejpam-6441	266	19	.	.	PUNCT
ejpam-6441	267	1	taking	take	VERB
ejpam-6441	267	2	limit	limit	NOUN
ejpam-6441	267	3	as	as	ADP
ejpam-6441	267	4	n→	n→	PROPN
ejpam-6441	267	5	∞	∞	PROPN
ejpam-6441	267	6	in	in	ADP
ejpam-6441	267	7	(	(	PUNCT
ejpam-6441	267	8	22	22	NUM
ejpam-6441	267	9	)	)	PUNCT
ejpam-6441	267	10	with	with	ADP
ejpam-6441	267	11	continuity	continuity	NOUN
ejpam-6441	267	12	of	of	ADP
ejpam-6441	267	13	f	f	PROPN
ejpam-6441	267	14	,	,	PUNCT
ejpam-6441	267	15	we	we	PRON
ejpam-6441	267	16	have	have	VERB
ejpam-6441	267	17	f	f	X
ejpam-6441	267	18	(	(	PUNCT
ejpam-6441	267	19	d	d	X
ejpam-6441	267	20	(	(	PUNCT
ejpam-6441	267	21	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	267	22	)	)	PUNCT
ejpam-6441	267	23	)	)	PUNCT
ejpam-6441	268	1	≤	≤	NUM
ejpam-6441	268	2	f	f	X
ejpam-6441	268	3	(	(	PUNCT
ejpam-6441	268	4	0	0	NUM
ejpam-6441	268	5	)	)	PUNCT
ejpam-6441	268	6	+	+	NUM
ejpam-6441	268	7	l	l	NOUN
ejpam-6441	268	8	(	(	PUNCT
ejpam-6441	268	9	0)−	0)−	NUM
ejpam-6441	268	10	τ	τ	PROPN
ejpam-6441	268	11	,	,	PUNCT
ejpam-6441	268	12	this	this	PRON
ejpam-6441	268	13	implies	imply	VERB
ejpam-6441	268	14	that	that	SCONJ
ejpam-6441	269	1	d	d	X
ejpam-6441	269	2	(	(	PUNCT
ejpam-6441	269	3	ς∗,γς∗	ς∗,γς∗	PROPN
ejpam-6441	269	4	)	)	PUNCT
ejpam-6441	269	5	=	=	SYM
ejpam-6441	269	6	0	0	NUM
ejpam-6441	269	7	and	and	CCONJ
ejpam-6441	269	8	ς∗	ς∗	PROPN
ejpam-6441	269	9	∈	∈	PROPN
ejpam-6441	269	10	γς∗	γς∗	NOUN
ejpam-6441	269	11	is	be	AUX
ejpam-6441	269	12	a	a	DET
ejpam-6441	269	13	fp	fp	NOUN
ejpam-6441	269	14	of	of	ADP
ejpam-6441	269	15	γ	γ	PROPN
ejpam-6441	269	16	.	.	PROPN
ejpam-6441	269	17	m.	m.	PROPN
ejpam-6441	269	18	mudhesh	mudhesh	PROPN
ejpam-6441	269	19	et	et	PROPN
ejpam-6441	269	20	al	al	PROPN
ejpam-6441	269	21	.	.	PUNCT
ejpam-6441	269	22	/	/	SYM
ejpam-6441	269	23	eur	eur	PROPN
ejpam-6441	269	24	.	.	PUNCT
ejpam-6441	270	1	j.	j.	PROPN
ejpam-6441	270	2	pure	pure	PROPN
ejpam-6441	270	3	appl	appl	PROPN
ejpam-6441	270	4	.	.	PROPN
ejpam-6441	270	5	math	math	PROPN
ejpam-6441	270	6	,	,	PUNCT
ejpam-6441	270	7	18	18	NUM
ejpam-6441	270	8	(	(	PUNCT
ejpam-6441	270	9	4	4	NUM
ejpam-6441	270	10	)	)	PUNCT
ejpam-6441	270	11	(	(	PUNCT
ejpam-6441	270	12	2025	2025	NUM
ejpam-6441	270	13	)	)	PUNCT
ejpam-6441	270	14	,	,	PUNCT
ejpam-6441	270	15	6441	6441	NUM
ejpam-6441	270	16	12	12	NUM
ejpam-6441	270	17	of	of	ADP
ejpam-6441	270	18	21	21	NUM
ejpam-6441	270	19	example	example	NOUN
ejpam-6441	270	20	1	1	NUM
ejpam-6441	270	21	.	.	PUNCT
ejpam-6441	271	1	let	let	VERB
ejpam-6441	271	2	∆ℜ	∆ℜ	NOUN
ejpam-6441	271	3	=	=	PUNCT
ejpam-6441	272	1	[	[	X
ejpam-6441	272	2	0,∞	0,∞	NOUN
ejpam-6441	272	3	)	)	PUNCT
ejpam-6441	272	4	equipped	equip	VERB
ejpam-6441	272	5	with	with	ADP
ejpam-6441	272	6	a	a	DET
ejpam-6441	272	7	usual	usual	ADJ
ejpam-6441	272	8	metric	metric	NOUN
ejpam-6441	272	9	.	.	PUNCT
ejpam-6441	273	1	take	take	VERB
ejpam-6441	273	2	a	a	DET
ejpam-6441	273	3	sequence	sequence	NOUN
ejpam-6441	273	4	{	{	PUNCT
ejpam-6441	273	5	ςn	ςn	NOUN
ejpam-6441	273	6	}	}	PUNCT
ejpam-6441	273	7	⊂	⊂	PROPN
ejpam-6441	274	1	∆ℜ	∆ℜ	NOUN
ejpam-6441	274	2	given	give	VERB
ejpam-6441	274	3	by	by	ADP
ejpam-6441	274	4	ςn	ςn	NOUN
ejpam-6441	274	5	=	=	NOUN
ejpam-6441	274	6	n2(n+1)2	n2(n+1)2	NUM
ejpam-6441	274	7	4	4	NUM
ejpam-6441	274	8	∀	∀	NOUN
ejpam-6441	274	9	n	n	PRON
ejpam-6441	274	10	≥	≥	NOUN
ejpam-6441	274	11	1	1	NUM
ejpam-6441	274	12	.	.	PUNCT
ejpam-6441	274	13	set	set	VERB
ejpam-6441	274	14	ℜ	ℜ	NOUN
ejpam-6441	274	15	=	=	PRON
ejpam-6441	274	16	{	{	PUNCT
ejpam-6441	274	17	(	(	PUNCT
ejpam-6441	274	18	ςn	ςn	NOUN
ejpam-6441	274	19	,	,	PUNCT
ejpam-6441	274	20	ςn	ςn	NOUN
ejpam-6441	274	21	)	)	PUNCT
ejpam-6441	274	22	,	,	PUNCT
ejpam-6441	274	23	(	(	PUNCT
ejpam-6441	274	24	ςn	ςn	NOUN
ejpam-6441	274	25	,	,	PUNCT
ejpam-6441	274	26	ςn+1	ςn+1	NUM
ejpam-6441	274	27	)	)	PUNCT
ejpam-6441	274	28	,	,	PUNCT
ejpam-6441	274	29	(	(	PUNCT
ejpam-6441	274	30	ςn	ςn	NOUN
ejpam-6441	274	31	,	,	PUNCT
ejpam-6441	274	32	ςn+2	ςn+2	NUM
ejpam-6441	274	33	)	)	PUNCT
ejpam-6441	274	34	:	:	PUNCT
ejpam-6441	274	35	n	n	NOUN
ejpam-6441	274	36	=	=	SYM
ejpam-6441	274	37	1	1	NUM
ejpam-6441	274	38	,	,	PUNCT
ejpam-6441	274	39	2	2	NUM
ejpam-6441	274	40	,	,	PUNCT
ejpam-6441	274	41	...	...	PUNCT
ejpam-6441	274	42	}	}	PUNCT
ejpam-6441	274	43	,	,	PUNCT
ejpam-6441	274	44	and	and	CCONJ
ejpam-6441	274	45	γ	γ	X
ejpam-6441	274	46	:	:	PUNCT
ejpam-6441	274	47	∆ℜ	∆ℜ	X
ejpam-6441	274	48	→	→	SYM
ejpam-6441	274	49	cb	cb	PROPN
ejpam-6441	274	50	(	(	PUNCT
ejpam-6441	274	51	∆ℜ	∆ℜ	NOUN
ejpam-6441	274	52	)	)	PUNCT
ejpam-6441	274	53	by	by	ADP
ejpam-6441	274	54	γx	γx	NOUN
ejpam-6441	274	55	=	=	SYM
ejpam-6441	274	56			PROPN
ejpam-6441	274	57	{	{	PUNCT
ejpam-6441	274	58	3x	3x	NUM
ejpam-6441	274	59	}	}	PUNCT
ejpam-6441	274	60	if	if	SCONJ
ejpam-6441	274	61	0	0	NUM
ejpam-6441	274	62	≤	≤	NUM
ejpam-6441	274	63	x	x	SYM
ejpam-6441	274	64	≤	≤	NUM
ejpam-6441	274	65	ς1	ς1	NOUN
ejpam-6441	274	66	{	{	PUNCT
ejpam-6441	274	67	0	0	NUM
ejpam-6441	274	68	,	,	PUNCT
ejpam-6441	274	69	ς1	ς1	NOUN
ejpam-6441	274	70	}	}	PUNCT
ejpam-6441	274	71	if	if	SCONJ
ejpam-6441	274	72	ς1	ς1	NOUN
ejpam-6441	274	73	≤	≤	NUM
ejpam-6441	274	74	x	x	PUNCT
ejpam-6441	274	75	≤	≤	NUM
ejpam-6441	274	76	ς2	ς2	PROPN
ejpam-6441	274	77	{	{	PUNCT
ejpam-6441	274	78	ςn−1	ςn−1	PROPN
ejpam-6441	274	79	+	+	CCONJ
ejpam-6441	274	80	(	(	PUNCT
ejpam-6441	274	81	ςn−ςn−1	ςn−ςn−1	ADJ
ejpam-6441	274	82	ςn+1−ςn	ςn+1−ςn	PROPN
ejpam-6441	274	83	)	)	PUNCT
ejpam-6441	274	84	(	(	PUNCT
ejpam-6441	274	85	x−	x−	PROPN
ejpam-6441	274	86	ςn	ςn	PROPN
ejpam-6441	274	87	)	)	PUNCT
ejpam-6441	274	88	}	}	PUNCT
ejpam-6441	274	89	if	if	SCONJ
ejpam-6441	274	90	ςn	ςn	PROPN
ejpam-6441	274	91	≤	≤	NUM
ejpam-6441	274	92	x	x	SYM
ejpam-6441	274	93	≤	≤	NOUN
ejpam-6441	274	94	ςn+1	ςn+1	NUM
ejpam-6441	274	95	,	,	PUNCT
ejpam-6441	274	96	n	n	NOUN
ejpam-6441	274	97	=	=	SYM
ejpam-6441	274	98	2	2	NUM
ejpam-6441	274	99	,	,	PUNCT
ejpam-6441	274	100	...	...	PUNCT
ejpam-6441	274	101	.	.	PUNCT
ejpam-6441	275	1	then	then	ADV
ejpam-6441	275	2	,	,	PUNCT
ejpam-6441	275	3	(	(	PUNCT
ejpam-6441	275	4	∆ℜ	∆ℜ	X
ejpam-6441	275	5	,	,	PUNCT
ejpam-6441	275	6	d	d	NOUN
ejpam-6441	275	7	)	)	PUNCT
ejpam-6441	275	8	is	be	AUX
ejpam-6441	275	9	a	a	DET
ejpam-6441	275	10	complete	complete	ADJ
ejpam-6441	275	11	ms	ms	NOUN
ejpam-6441	275	12	,	,	PUNCT
ejpam-6441	275	13	∆ℜ	∆ℜ	PROPN
ejpam-6441	275	14	(	(	PUNCT
ejpam-6441	275	15	γ,ℜ	γ,ℜ	ADJ
ejpam-6441	275	16	)	)	PUNCT
ejpam-6441	275	17	̸=	̸=	PROPN
ejpam-6441	275	18	∅	∅	NOUN
ejpam-6441	275	19	as	as	ADP
ejpam-6441	275	20	ς1	ς1	NOUN
ejpam-6441	275	21	=	=	SYM
ejpam-6441	275	22	1	1	NUM
ejpam-6441	275	23	∈	∈	PROPN
ejpam-6441	275	24	∆ℜ	∆ℜ	NOUN
ejpam-6441	275	25	,	,	PUNCT
ejpam-6441	275	26	1	1	NUM
ejpam-6441	275	27	∈	∈	PROPN
ejpam-6441	275	28	γς1	γς1	NOUN
ejpam-6441	275	29	=	=	SYM
ejpam-6441	275	30	γ1	γ1	PROPN
ejpam-6441	275	31	=	=	SYM
ejpam-6441	275	32	{	{	PUNCT
ejpam-6441	275	33	0	0	NUM
ejpam-6441	275	34	,	,	PUNCT
ejpam-6441	275	35	1	1	NUM
ejpam-6441	275	36	}	}	PUNCT
ejpam-6441	275	37	and	and	CCONJ
ejpam-6441	275	38	(	(	PUNCT
ejpam-6441	275	39	1	1	NUM
ejpam-6441	275	40	,	,	PUNCT
ejpam-6441	275	41	1	1	NUM
ejpam-6441	275	42	)	)	PUNCT
ejpam-6441	275	43	∈	∈	PROPN
ejpam-6441	275	44	ℜ.	ℜ.	PROPN
ejpam-6441	275	45	also	also	ADV
ejpam-6441	275	46	it	it	PRON
ejpam-6441	275	47	is	be	AUX
ejpam-6441	275	48	easy	easy	ADJ
ejpam-6441	275	49	to	to	PART
ejpam-6441	275	50	check	check	VERB
ejpam-6441	275	51	that	that	PRON
ejpam-6441	275	52	ℜ	ℜ	PROPN
ejpam-6441	275	53	is	be	AUX
ejpam-6441	275	54	γ	γ	X
ejpam-6441	275	55	-	-	ADJ
ejpam-6441	275	56	transitive	transitive	ADJ
ejpam-6441	275	57	and	and	CCONJ
ejpam-6441	275	58	γ	γ	X
ejpam-6441	275	59	is	be	AUX
ejpam-6441	275	60	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	275	61	or	or	CCONJ
ejpam-6441	275	62	(	(	PUNCT
ejpam-6441	275	63	∆ℜ	∆ℜ	NOUN
ejpam-6441	275	64	,	,	PUNCT
ejpam-6441	275	65	d	d	NOUN
ejpam-6441	275	66	)	)	PUNCT
ejpam-6441	275	67	is	be	AUX
ejpam-6441	275	68	ℜ-regular	ℜ-regular	ADJ
ejpam-6441	275	69	space	space	NOUN
ejpam-6441	275	70	.	.	PUNCT
ejpam-6441	276	1	now	now	ADV
ejpam-6441	276	2	,	,	PUNCT
ejpam-6441	276	3	for	for	ADP
ejpam-6441	276	4	n	n	NOUN
ejpam-6441	276	5	=	=	SYM
ejpam-6441	276	6	2	2	NUM
ejpam-6441	276	7	,	,	PUNCT
ejpam-6441	276	8	...	...	PUNCT
ejpam-6441	276	9	,	,	PUNCT
ejpam-6441	276	10	we	we	PRON
ejpam-6441	276	11	have	have	VERB
ejpam-6441	276	12	h	h	NOUN
ejpam-6441	276	13	(	(	PUNCT
ejpam-6441	276	14	γςn	γςn	PROPN
ejpam-6441	276	15	,	,	PUNCT
ejpam-6441	276	16	γςn+1	γςn+1	ADJ
ejpam-6441	276	17	)	)	PUNCT
ejpam-6441	277	1	=	=	SYM
ejpam-6441	277	2	max	max	PROPN
ejpam-6441	277	3	{	{	PUNCT
ejpam-6441	277	4	sup	sup	PROPN
ejpam-6441	277	5	r∈γςn	r∈γςn	PROPN
ejpam-6441	277	6	d	d	NOUN
ejpam-6441	277	7	(	(	PUNCT
ejpam-6441	277	8	r	r	NOUN
ejpam-6441	277	9	,	,	PUNCT
ejpam-6441	277	10	γςn+1	γςn+1	ADJ
ejpam-6441	277	11	)	)	PUNCT
ejpam-6441	277	12	,	,	PUNCT
ejpam-6441	277	13	sup	sup	NOUN
ejpam-6441	277	14	s∈γξn+1	s∈γξn+1	PROPN
ejpam-6441	277	15	d	d	X
ejpam-6441	277	16	(	(	PUNCT
ejpam-6441	277	17	γςn	γςn	PROPN
ejpam-6441	277	18	,	,	PUNCT
ejpam-6441	277	19	s	s	NOUN
ejpam-6441	277	20	)	)	PUNCT
ejpam-6441	277	21	}	}	PUNCT
ejpam-6441	277	22	=	=	SYM
ejpam-6441	277	23	max	max	X
ejpam-6441	277	24	{	{	PUNCT
ejpam-6441	277	25	d	d	X
ejpam-6441	277	26	(	(	PUNCT
ejpam-6441	277	27	ςn−1	ςn−1	PROPN
ejpam-6441	277	28	,	,	PUNCT
ejpam-6441	277	29	ςn	ςn	NOUN
ejpam-6441	277	30	)	)	PUNCT
ejpam-6441	277	31	,	,	PUNCT
ejpam-6441	278	1	d	d	X
ejpam-6441	278	2	(	(	PUNCT
ejpam-6441	278	3	ςn−1	ςn−1	PROPN
ejpam-6441	278	4	,	,	PUNCT
ejpam-6441	278	5	ςn	ςn	NOUN
ejpam-6441	278	6	)	)	PUNCT
ejpam-6441	278	7	}	}	PUNCT
ejpam-6441	279	1	=	=	SYM
ejpam-6441	279	2	d	d	X
ejpam-6441	279	3	(	(	PUNCT
ejpam-6441	279	4	ςn	ςn	PROPN
ejpam-6441	279	5	,	,	PUNCT
ejpam-6441	279	6	ςn−1	ςn−1	PROPN
ejpam-6441	279	7	)	)	PUNCT
ejpam-6441	279	8	.	.	PUNCT
ejpam-6441	280	1	from	from	ADP
ejpam-6441	280	2	(	(	PUNCT
ejpam-6441	280	3	2	2	NUM
ejpam-6441	280	4	)	)	PUNCT
ejpam-6441	280	5	and	and	CCONJ
ejpam-6441	280	6	(	(	PUNCT
ejpam-6441	280	7	3	3	X
ejpam-6441	280	8	)	)	PUNCT
ejpam-6441	280	9	with	with	ADP
ejpam-6441	280	10	β	β	X
ejpam-6441	280	11	≥	≥	NOUN
ejpam-6441	280	12	0	0	NUM
ejpam-6441	280	13	,	,	PUNCT
ejpam-6441	280	14	we	we	PRON
ejpam-6441	280	15	get	get	VERB
ejpam-6441	280	16	mℜ	mℜ	NOUN
ejpam-6441	280	17	(	(	PUNCT
ejpam-6441	280	18	ςn	ςn	PROPN
ejpam-6441	280	19	,	,	PUNCT
ejpam-6441	280	20	ςn+1	ςn+1	NUM
ejpam-6441	280	21	)	)	PUNCT
ejpam-6441	280	22	=	=	SYM
ejpam-6441	281	1	d	d	PROPN
ejpam-6441	281	2	(	(	PUNCT
ejpam-6441	281	3	ςn+1	ςn+1	PROPN
ejpam-6441	281	4	,	,	PUNCT
ejpam-6441	281	5	ςn	ςn	NOUN
ejpam-6441	281	6	)	)	PUNCT
ejpam-6441	281	7	and	and	CCONJ
ejpam-6441	281	8	nℜ	nℜ	PROPN
ejpam-6441	281	9	(	(	PUNCT
ejpam-6441	281	10	ςn	ςn	PROPN
ejpam-6441	281	11	,	,	PUNCT
ejpam-6441	281	12	ςn+1	ςn+1	NUM
ejpam-6441	281	13	)	)	PUNCT
ejpam-6441	281	14	=	=	SYM
ejpam-6441	281	15	0	0	X
ejpam-6441	281	16	.	.	PUNCT
ejpam-6441	282	1	then	then	ADV
ejpam-6441	282	2	,	,	PUNCT
ejpam-6441	282	3	utilizing	utilize	VERB
ejpam-6441	282	4	(	(	PUNCT
ejpam-6441	282	5	1	1	NUM
ejpam-6441	282	6	)	)	PUNCT
ejpam-6441	282	7	,	,	PUNCT
ejpam-6441	282	8	we	we	PRON
ejpam-6441	282	9	have	have	VERB
ejpam-6441	282	10	τ	τ	PROPN
ejpam-6441	283	1	+	+	NUM
ejpam-6441	283	2	f	f	X
ejpam-6441	283	3	(	(	PUNCT
ejpam-6441	283	4	h	h	PROPN
ejpam-6441	283	5	(	(	PUNCT
ejpam-6441	283	6	γςn	γςn	PROPN
ejpam-6441	283	7	,	,	PUNCT
ejpam-6441	283	8	γςn+1	γςn+1	PROPN
ejpam-6441	283	9	)	)	PUNCT
ejpam-6441	283	10	)	)	PUNCT
ejpam-6441	284	1	=	=	PUNCT
ejpam-6441	285	1	τ	τ	X
ejpam-6441	286	1	+	+	NUM
ejpam-6441	286	2	f	f	X
ejpam-6441	286	3	(	(	PUNCT
ejpam-6441	286	4	d	d	X
ejpam-6441	286	5	(	(	PUNCT
ejpam-6441	286	6	ςn	ςn	PROPN
ejpam-6441	286	7	,	,	PUNCT
ejpam-6441	286	8	ςn−1	ςn−1	NOUN
ejpam-6441	286	9	)	)	PUNCT
ejpam-6441	286	10	)	)	PUNCT
ejpam-6441	286	11	(	(	PUNCT
ejpam-6441	286	12	23	23	NUM
ejpam-6441	286	13	)	)	PUNCT
ejpam-6441	286	14	=	=	SYM
ejpam-6441	287	1	τ	τ	PROPN
ejpam-6441	288	1	+	+	X
ejpam-6441	288	2	ln	ln	INTJ
ejpam-6441	288	3	(	(	PUNCT
ejpam-6441	288	4	d	d	X
ejpam-6441	288	5	(	(	PUNCT
ejpam-6441	288	6	ςn	ςn	PROPN
ejpam-6441	288	7	,	,	PUNCT
ejpam-6441	288	8	ςn−1	ςn−1	NOUN
ejpam-6441	288	9	)	)	PUNCT
ejpam-6441	288	10	)	)	PUNCT
ejpam-6441	288	11	,	,	PUNCT
ejpam-6441	288	12	and	and	CCONJ
ejpam-6441	288	13	f	f	PROPN
ejpam-6441	288	14	(	(	PUNCT
ejpam-6441	288	15	mℜ	mℜ	NOUN
ejpam-6441	288	16	(	(	PUNCT
ejpam-6441	288	17	ςn	ςn	PROPN
ejpam-6441	288	18	,	,	PUNCT
ejpam-6441	288	19	ςn+1	ςn+1	NUM
ejpam-6441	288	20	)	)	PUNCT
ejpam-6441	288	21	)	)	PUNCT
ejpam-6441	289	1	+	+	CCONJ
ejpam-6441	289	2	lnℜ	lnℜ	NOUN
ejpam-6441	289	3	(	(	PUNCT
ejpam-6441	289	4	ςn	ςn	PROPN
ejpam-6441	289	5	,	,	PUNCT
ejpam-6441	289	6	ςn+1	ςn+1	NUM
ejpam-6441	289	7	)	)	PUNCT
ejpam-6441	289	8	(	(	PUNCT
ejpam-6441	289	9	24	24	NUM
ejpam-6441	289	10	)	)	PUNCT
ejpam-6441	289	11	≤	≤	NUM
ejpam-6441	289	12	f	f	X
ejpam-6441	289	13	(	(	PUNCT
ejpam-6441	289	14	d	d	X
ejpam-6441	289	15	(	(	PUNCT
ejpam-6441	289	16	ςn+1	ςn+1	PROPN
ejpam-6441	289	17	,	,	PUNCT
ejpam-6441	289	18	ςn	ςn	NOUN
ejpam-6441	289	19	)	)	PUNCT
ejpam-6441	289	20	)	)	PUNCT
ejpam-6441	290	1	+	+	CCONJ
ejpam-6441	290	2	l	l	NOUN
ejpam-6441	290	3	(	(	PUNCT
ejpam-6441	290	4	0	0	NUM
ejpam-6441	290	5	)	)	PUNCT
ejpam-6441	290	6	=	=	SYM
ejpam-6441	291	1	ln	ln	ADJ
ejpam-6441	291	2	(	(	PUNCT
ejpam-6441	291	3	d	d	X
ejpam-6441	291	4	(	(	PUNCT
ejpam-6441	291	5	ςn+1	ςn+1	PROPN
ejpam-6441	291	6	,	,	PUNCT
ejpam-6441	291	7	ςn	ςn	NOUN
ejpam-6441	291	8	)	)	PUNCT
ejpam-6441	291	9	)	)	PUNCT
ejpam-6441	291	10	.	.	PUNCT
ejpam-6441	292	1	from	from	ADP
ejpam-6441	292	2	(	(	PUNCT
ejpam-6441	292	3	23	23	NUM
ejpam-6441	292	4	)	)	PUNCT
ejpam-6441	292	5	and	and	CCONJ
ejpam-6441	292	6	(	(	PUNCT
ejpam-6441	292	7	24	24	NUM
ejpam-6441	292	8	)	)	PUNCT
ejpam-6441	292	9	,	,	PUNCT
ejpam-6441	292	10	we	we	PRON
ejpam-6441	292	11	deduce	deduce	VERB
ejpam-6441	292	12	that	that	SCONJ
ejpam-6441	292	13	τ	τ	PROPN
ejpam-6441	293	1	+	+	X
ejpam-6441	293	2	ln	ln	ADJ
ejpam-6441	293	3	(	(	PUNCT
ejpam-6441	293	4	d	d	X
ejpam-6441	293	5	(	(	PUNCT
ejpam-6441	293	6	ςn	ςn	PROPN
ejpam-6441	293	7	,	,	PUNCT
ejpam-6441	293	8	ςn−1	ςn−1	NOUN
ejpam-6441	293	9	)	)	PUNCT
ejpam-6441	293	10	)	)	PUNCT
ejpam-6441	293	11	≤	≤	NUM
ejpam-6441	293	12	ln	ln	ADV
ejpam-6441	293	13	(	(	PUNCT
ejpam-6441	293	14	d	d	X
ejpam-6441	293	15	(	(	PUNCT
ejpam-6441	293	16	ςn+1	ςn+1	PROPN
ejpam-6441	293	17	,	,	PUNCT
ejpam-6441	293	18	ςn	ςn	NOUN
ejpam-6441	293	19	)	)	PUNCT
ejpam-6441	293	20	)	)	PUNCT
ejpam-6441	293	21	,	,	PUNCT
ejpam-6441	293	22	implies	imply	VERB
ejpam-6441	293	23	that	that	SCONJ
ejpam-6441	293	24	τ	τ	PROPN
ejpam-6441	293	25	≤	≤	PROPN
ejpam-6441	293	26	ln	ln	ADV
ejpam-6441	293	27	(	(	PUNCT
ejpam-6441	293	28	d	d	X
ejpam-6441	293	29	(	(	PUNCT
ejpam-6441	293	30	ςn+1	ςn+1	ADJ
ejpam-6441	293	31	,	,	PUNCT
ejpam-6441	293	32	ςn	ςn	NOUN
ejpam-6441	293	33	)	)	PUNCT
ejpam-6441	293	34	d	d	NOUN
ejpam-6441	293	35	(	(	PUNCT
ejpam-6441	293	36	ςn	ςn	NOUN
ejpam-6441	293	37	,	,	PUNCT
ejpam-6441	293	38	ςn−1	ςn−1	NOUN
ejpam-6441	293	39	)	)	PUNCT
ejpam-6441	293	40	)	)	PUNCT
ejpam-6441	293	41	.	.	PUNCT
ejpam-6441	294	1	(	(	PUNCT
ejpam-6441	294	2	25	25	NUM
ejpam-6441	294	3	)	)	PUNCT
ejpam-6441	294	4	let	let	VERB
ejpam-6441	294	5	f	f	PROPN
ejpam-6441	294	6	(	(	PUNCT
ejpam-6441	294	7	n	n	CCONJ
ejpam-6441	294	8	)	)	PUNCT
ejpam-6441	294	9	=	=	SYM
ejpam-6441	295	1	ln	ln	ADJ
ejpam-6441	295	2	(	(	PUNCT
ejpam-6441	295	3	|ςn+1	|ςn+1	ADP
ejpam-6441	295	4	−	−	VERB
ejpam-6441	295	5	ςn|	ςn|	NOUN
ejpam-6441	295	6	|ςn	|ςn	PRON
ejpam-6441	295	7	−	−	PROPN
ejpam-6441	295	8	ςn−1|	ςn−1|	NOUN
ejpam-6441	295	9	)	)	PUNCT
ejpam-6441	295	10	.	.	PUNCT
ejpam-6441	296	1	(	(	PUNCT
ejpam-6441	296	2	26	26	NUM
ejpam-6441	296	3	)	)	PUNCT
ejpam-6441	296	4	m.	m.	NOUN
ejpam-6441	296	5	mudhesh	mudhesh	PROPN
ejpam-6441	296	6	et	et	PROPN
ejpam-6441	296	7	al	al	PROPN
ejpam-6441	296	8	.	.	PUNCT
ejpam-6441	296	9	/	/	SYM
ejpam-6441	296	10	eur	eur	PROPN
ejpam-6441	296	11	.	.	PUNCT
ejpam-6441	297	1	j.	j.	PROPN
ejpam-6441	297	2	pure	pure	PROPN
ejpam-6441	297	3	appl	appl	PROPN
ejpam-6441	297	4	.	.	PROPN
ejpam-6441	297	5	math	math	PROPN
ejpam-6441	297	6	,	,	PUNCT
ejpam-6441	297	7	18	18	NUM
ejpam-6441	297	8	(	(	PUNCT
ejpam-6441	297	9	4	4	NUM
ejpam-6441	297	10	)	)	PUNCT
ejpam-6441	297	11	(	(	PUNCT
ejpam-6441	297	12	2025	2025	NUM
ejpam-6441	297	13	)	)	PUNCT
ejpam-6441	297	14	,	,	PUNCT
ejpam-6441	297	15	6441	6441	NUM
ejpam-6441	297	16	13	13	NUM
ejpam-6441	297	17	of	of	ADP
ejpam-6441	297	18	21	21	NUM
ejpam-6441	297	19	table	table	NOUN
ejpam-6441	297	20	1	1	NUM
ejpam-6441	297	21	:	:	PUNCT
ejpam-6441	297	22	iteration	iteration	NOUN
ejpam-6441	297	23	and	and	CCONJ
ejpam-6441	297	24	f(n	f(n	PROPN
ejpam-6441	297	25	)	)	PUNCT
ejpam-6441	297	26	iter	iter	PROPN
ejpam-6441	297	27	f(n	f(n	PROPN
ejpam-6441	297	28	)	)	PUNCT
ejpam-6441	297	29	iter	iter	PROPN
ejpam-6441	297	30	f(n	f(n	PROPN
ejpam-6441	297	31	)	)	PUNCT
ejpam-6441	297	32	n=2	n=2	ADV
ejpam-6441	297	33	1.21	1.21	NUM
ejpam-6441	297	34	n=11	n=11	NOUN
ejpam-6441	297	35	0.26	0.26	NUM
ejpam-6441	297	36	n=3	n=3	SYM
ejpam-6441	297	37	0.86	0.86	NUM
ejpam-6441	297	38	n=12	n=12	ADV
ejpam-6441	297	39	0.24	0.24	NUM
ejpam-6441	297	40	n=4	n=4	SYM
ejpam-6441	297	41	0.66	0.66	NUM
ejpam-6441	297	42	n=13	n=13	PROPN
ejpam-6441	297	43	0.22	0.22	NUM
ejpam-6441	297	44	n=5	n=5	NUM
ejpam-6441	297	45	0.55	0.55	NUM
ejpam-6441	297	46	n=14	n=14	NUM
ejpam-6441	297	47	0.20	0.20	NUM
ejpam-6441	297	48	n=6	n=6	NOUN
ejpam-6441	297	49	0.46	0.46	NUM
ejpam-6441	297	50	n=15	n=15	ADV
ejpam-6441	297	51	0.19	0.19	NUM
ejpam-6441	297	52	n=7	n=7	PROPN
ejpam-6441	297	53	0.40	0.40	NUM
ejpam-6441	297	54	n=16	n=16	NOUN
ejpam-6441	297	55	0.18	0.18	NUM
ejpam-6441	297	56	n=8	n=8	SYM
ejpam-6441	297	57	0.35	0.35	NUM
ejpam-6441	297	58	n=17	n=17	NOUN
ejpam-6441	297	59	0.17	0.17	NUM
ejpam-6441	297	60	n=9	n=9	PROPN
ejpam-6441	297	61	0.31	0.31	NUM
ejpam-6441	297	62	...	...	PUNCT
ejpam-6441	297	63	...	...	PUNCT
ejpam-6441	298	1	n=10	n=10	PRON
ejpam-6441	298	2	0.28	0.28	NUM
ejpam-6441	298	3	n=50	n=50	ADJ
ejpam-6441	298	4	0.059	0.059	NUM
ejpam-6441	298	5	0	0	NUM
ejpam-6441	298	6	10	10	NUM
ejpam-6441	298	7	20	20	NUM
ejpam-6441	298	8	30	30	NUM
ejpam-6441	298	9	40	40	NUM
ejpam-6441	298	10	50	50	NUM
ejpam-6441	298	11	0	0	NUM
ejpam-6441	298	12	0.2	0.2	NUM
ejpam-6441	298	13	0.4	0.4	NUM
ejpam-6441	298	14	0.6	0.6	NUM
ejpam-6441	298	15	0.8	0.8	NUM
ejpam-6441	298	16	1	1	NUM
ejpam-6441	298	17	1.2	1.2	NUM
ejpam-6441	298	18	n	n	NUM
ejpam-6441	298	19	f	f	PROPN
ejpam-6441	298	20	(	(	PUNCT
ejpam-6441	298	21	n	n	CCONJ
ejpam-6441	298	22	)	)	PUNCT
ejpam-6441	298	23	figure	figure	NOUN
ejpam-6441	298	24	1	1	NUM
ejpam-6441	298	25	:	:	PUNCT
ejpam-6441	298	26	behavior	behavior	NOUN
ejpam-6441	298	27	of	of	ADP
ejpam-6441	298	28	f(n	f(n	PROPN
ejpam-6441	298	29	)	)	PUNCT
ejpam-6441	298	30	for	for	ADP
ejpam-6441	298	31	n	n	DET
ejpam-6441	298	32	∈	∈	NOUN
ejpam-6441	299	1	[	[	X
ejpam-6441	299	2	2	2	NUM
ejpam-6441	299	3	,	,	PUNCT
ejpam-6441	299	4	50	50	NUM
ejpam-6441	299	5	]	]	PUNCT
ejpam-6441	299	6	.	.	PUNCT
ejpam-6441	300	1	in	in	ADP
ejpam-6441	300	2	view	view	NOUN
ejpam-6441	300	3	of	of	ADP
ejpam-6441	300	4	table1	table1	PROPN
ejpam-6441	300	5	and	and	CCONJ
ejpam-6441	300	6	figure1	figure1	PROPN
ejpam-6441	300	7	,	,	PUNCT
ejpam-6441	300	8	since	since	SCONJ
ejpam-6441	300	9	the	the	DET
ejpam-6441	300	10	sequence	sequence	NOUN
ejpam-6441	300	11	{	{	PUNCT
ejpam-6441	300	12	f	f	PROPN
ejpam-6441	300	13	(	(	PUNCT
ejpam-6441	300	14	n)}n≥2	n)}n≥2	NOUN
ejpam-6441	300	15	is	be	AUX
ejpam-6441	300	16	decreasing	decrease	VERB
ejpam-6441	300	17	and	and	CCONJ
ejpam-6441	300	18	discontinuous	discontinuous	ADJ
ejpam-6441	300	19	,	,	PUNCT
ejpam-6441	300	20	the	the	DET
ejpam-6441	300	21	smallest	small	ADJ
ejpam-6441	300	22	value	value	NOUN
ejpam-6441	300	23	in	in	ADP
ejpam-6441	300	24	(	(	PUNCT
ejpam-6441	300	25	26	26	NUM
ejpam-6441	300	26	)	)	PUNCT
ejpam-6441	300	27	is	be	AUX
ejpam-6441	300	28	0.059	0.059	NUM
ejpam-6441	300	29	.	.	PUNCT
ejpam-6441	301	1	therefore	therefore	ADV
ejpam-6441	301	2	,	,	PUNCT
ejpam-6441	301	3	the	the	DET
ejpam-6441	301	4	eq	eq	NOUN
ejpam-6441	301	5	(	(	PUNCT
ejpam-6441	301	6	25	25	NUM
ejpam-6441	301	7	)	)	PUNCT
ejpam-6441	301	8	holds	hold	VERB
ejpam-6441	301	9	for	for	ADP
ejpam-6441	301	10	0	0	NUM
ejpam-6441	301	11	<	<	X
ejpam-6441	301	12	ς	ς	X
ejpam-6441	301	13	<	<	X
ejpam-6441	301	14	0.059	0.059	NUM
ejpam-6441	301	15	.	.	PUNCT
ejpam-6441	302	1	so	so	ADV
ejpam-6441	302	2	,	,	PUNCT
ejpam-6441	302	3	the	the	DET
ejpam-6441	302	4	contraction	contraction	NOUN
ejpam-6441	302	5	(	(	PUNCT
ejpam-6441	302	6	1	1	X
ejpam-6441	302	7	)	)	PUNCT
ejpam-6441	302	8	is	be	AUX
ejpam-6441	302	9	satisfied	satisfied	ADJ
ejpam-6441	302	10	for	for	ADP
ejpam-6441	302	11	all	all	DET
ejpam-6441	302	12	ς1	ς1	NOUN
ejpam-6441	302	13	,	,	PUNCT
ejpam-6441	302	14	ς2	ς2	PROPN
ejpam-6441	302	15	∈	∈	PROPN
ejpam-6441	302	16	∆ℜ	∆ℜ	ADJ
ejpam-6441	302	17	such	such	ADJ
ejpam-6441	302	18	that	that	PRON
ejpam-6441	302	19	(	(	PUNCT
ejpam-6441	302	20	ς1	ς1	NOUN
ejpam-6441	302	21	,	,	PUNCT
ejpam-6441	302	22	ς2	ς2	PROPN
ejpam-6441	302	23	)	)	PUNCT
ejpam-6441	302	24	∈	∈	PROPN
ejpam-6441	302	25	ℜ∗.	ℜ∗.	NOUN
ejpam-6441	302	26	hence	hence	ADV
ejpam-6441	302	27	,	,	PUNCT
ejpam-6441	302	28	γ	γ	PROPN
ejpam-6441	302	29	has	have	VERB
ejpam-6441	302	30	infinite	infinite	PROPN
ejpam-6441	302	31	fps	fps	PROPN
ejpam-6441	302	32	.	.	PUNCT
ejpam-6441	302	33	example	example	NOUN
ejpam-6441	303	1	2	2	NUM
ejpam-6441	303	2	.	.	PUNCT
ejpam-6441	303	3	let	let	VERB
ejpam-6441	303	4	∆ℜ	∆ℜ	NOUN
ejpam-6441	303	5	=	=	PUNCT
ejpam-6441	303	6	{	{	PUNCT
ejpam-6441	303	7	1	1	NUM
ejpam-6441	303	8	,	,	PUNCT
ejpam-6441	303	9	2	2	NUM
ejpam-6441	303	10	,	,	PUNCT
ejpam-6441	303	11	3	3	NUM
ejpam-6441	303	12	,	,	PUNCT
ejpam-6441	303	13	4	4	NUM
ejpam-6441	303	14	}	}	PUNCT
ejpam-6441	303	15	and	and	CCONJ
ejpam-6441	303	16	d	d	NOUN
ejpam-6441	303	17	:	:	PUNCT
ejpam-6441	303	18	∆ℜ	∆ℜ	NOUN
ejpam-6441	303	19	×∆ℜ	×∆ℜ	PROPN
ejpam-6441	303	20	→	→	SYM
ejpam-6441	304	1	[	[	X
ejpam-6441	304	2	0,∞	0,∞	X
ejpam-6441	304	3	)	)	PUNCT
ejpam-6441	304	4	be	be	AUX
ejpam-6441	304	5	a	a	DET
ejpam-6441	304	6	metric	metric	NOUN
ejpam-6441	304	7	on	on	ADP
ejpam-6441	304	8	∆ℜ	∆ℜ	NOUN
ejpam-6441	304	9	defined	define	VERB
ejpam-6441	304	10	as	as	ADP
ejpam-6441	304	11	d	d	PROPN
ejpam-6441	304	12	(	(	PUNCT
ejpam-6441	304	13	1	1	NUM
ejpam-6441	304	14	,	,	PUNCT
ejpam-6441	304	15	2	2	NUM
ejpam-6441	304	16	)	)	PUNCT
ejpam-6441	304	17	=	=	SYM
ejpam-6441	304	18	4	4	NUM
ejpam-6441	304	19	,	,	PUNCT
ejpam-6441	304	20	d	d	X
ejpam-6441	304	21	(	(	PUNCT
ejpam-6441	304	22	1	1	NUM
ejpam-6441	304	23	,	,	PUNCT
ejpam-6441	304	24	3	3	NUM
ejpam-6441	304	25	)	)	PUNCT
ejpam-6441	304	26	=	=	SYM
ejpam-6441	304	27	6	6	NUM
ejpam-6441	304	28	,	,	PUNCT
ejpam-6441	304	29	d	d	X
ejpam-6441	304	30	(	(	PUNCT
ejpam-6441	304	31	1	1	NUM
ejpam-6441	304	32	,	,	PUNCT
ejpam-6441	304	33	4	4	NUM
ejpam-6441	304	34	)	)	PUNCT
ejpam-6441	304	35	=	=	SYM
ejpam-6441	304	36	3	3	NUM
ejpam-6441	304	37	,	,	PUNCT
ejpam-6441	304	38	d	d	X
ejpam-6441	304	39	(	(	PUNCT
ejpam-6441	304	40	2	2	NUM
ejpam-6441	304	41	,	,	PUNCT
ejpam-6441	304	42	3	3	NUM
ejpam-6441	304	43	)	)	PUNCT
ejpam-6441	304	44	=	=	SYM
ejpam-6441	304	45	4	4	NUM
ejpam-6441	304	46	,	,	PUNCT
ejpam-6441	304	47	d	d	X
ejpam-6441	304	48	(	(	PUNCT
ejpam-6441	304	49	2	2	NUM
ejpam-6441	304	50	,	,	PUNCT
ejpam-6441	304	51	4	4	NUM
ejpam-6441	304	52	)	)	PUNCT
ejpam-6441	304	53	=	=	SYM
ejpam-6441	304	54	3	3	NUM
ejpam-6441	304	55	,	,	PUNCT
ejpam-6441	304	56	d	d	X
ejpam-6441	304	57	(	(	PUNCT
ejpam-6441	304	58	3	3	NUM
ejpam-6441	304	59	,	,	PUNCT
ejpam-6441	304	60	4	4	NUM
ejpam-6441	304	61	)	)	PUNCT
ejpam-6441	304	62	=	=	SYM
ejpam-6441	304	63	5	5	NUM
ejpam-6441	304	64	,	,	PUNCT
ejpam-6441	304	65	d	d	X
ejpam-6441	304	66	(	(	PUNCT
ejpam-6441	304	67	ς1	ς1	NOUN
ejpam-6441	304	68	,	,	PUNCT
ejpam-6441	304	69	ς2	ς2	PROPN
ejpam-6441	304	70	)	)	PUNCT
ejpam-6441	305	1	=	=	SYM
ejpam-6441	305	2	d	d	PROPN
ejpam-6441	305	3	(	(	PUNCT
ejpam-6441	305	4	ς2	ς2	PROPN
ejpam-6441	305	5	,	,	PUNCT
ejpam-6441	305	6	ς1	ς1	NOUN
ejpam-6441	305	7	)	)	PUNCT
ejpam-6441	305	8	and	and	CCONJ
ejpam-6441	305	9	d	d	X
ejpam-6441	305	10	(	(	PUNCT
ejpam-6441	305	11	ς1	ς1	NOUN
ejpam-6441	305	12	,	,	PUNCT
ejpam-6441	305	13	ς1	ς1	NOUN
ejpam-6441	305	14	)	)	PUNCT
ejpam-6441	305	15	=	=	SYM
ejpam-6441	305	16	0	0	NUM
ejpam-6441	305	17	,	,	PUNCT
ejpam-6441	305	18	∀ς1	∀ς1	NOUN
ejpam-6441	305	19	,	,	PUNCT
ejpam-6441	305	20	ς2	ς2	PROPN
ejpam-6441	305	21	∈	∈	PROPN
ejpam-6441	305	22	∆ℜ.	∆ℜ.	NOUN
ejpam-6441	305	23	we	we	PRON
ejpam-6441	305	24	define	define	VERB
ejpam-6441	305	25	a	a	DET
ejpam-6441	305	26	binary	binary	ADJ
ejpam-6441	305	27	relation	relation	NOUN
ejpam-6441	305	28	on	on	ADP
ejpam-6441	305	29	∆ℜ	∆ℜ	NOUN
ejpam-6441	305	30	as	as	ADP
ejpam-6441	305	31	ℜ	ℜ	NOUN
ejpam-6441	305	32	=	=	NOUN
ejpam-6441	305	33	{	{	PUNCT
ejpam-6441	305	34	(	(	PUNCT
ejpam-6441	305	35	1	1	NUM
ejpam-6441	305	36	,	,	PUNCT
ejpam-6441	305	37	1	1	NUM
ejpam-6441	305	38	)	)	PUNCT
ejpam-6441	305	39	,	,	PUNCT
ejpam-6441	305	40	(	(	PUNCT
ejpam-6441	305	41	1	1	NUM
ejpam-6441	305	42	,	,	PUNCT
ejpam-6441	305	43	2	2	NUM
ejpam-6441	305	44	)	)	PUNCT
ejpam-6441	305	45	,	,	PUNCT
ejpam-6441	305	46	(	(	PUNCT
ejpam-6441	305	47	1	1	NUM
ejpam-6441	305	48	,	,	PUNCT
ejpam-6441	305	49	3	3	NUM
ejpam-6441	305	50	)	)	PUNCT
ejpam-6441	305	51	,	,	PUNCT
ejpam-6441	305	52	(	(	PUNCT
ejpam-6441	305	53	1	1	NUM
ejpam-6441	305	54	,	,	PUNCT
ejpam-6441	305	55	4	4	NUM
ejpam-6441	305	56	)	)	PUNCT
ejpam-6441	305	57	,	,	PUNCT
ejpam-6441	305	58	(	(	PUNCT
ejpam-6441	305	59	4	4	NUM
ejpam-6441	305	60	,	,	PUNCT
ejpam-6441	305	61	1	1	NUM
ejpam-6441	305	62	)	)	PUNCT
ejpam-6441	305	63	,	,	PUNCT
ejpam-6441	305	64	(	(	PUNCT
ejpam-6441	305	65	2	2	NUM
ejpam-6441	305	66	,	,	PUNCT
ejpam-6441	305	67	1	1	NUM
ejpam-6441	305	68	)	)	PUNCT
ejpam-6441	305	69	,	,	PUNCT
ejpam-6441	305	70	(	(	PUNCT
ejpam-6441	305	71	2	2	NUM
ejpam-6441	305	72	,	,	PUNCT
ejpam-6441	305	73	2	2	NUM
ejpam-6441	305	74	)	)	PUNCT
ejpam-6441	305	75	,	,	PUNCT
ejpam-6441	305	76	(	(	PUNCT
ejpam-6441	305	77	2	2	NUM
ejpam-6441	305	78	,	,	PUNCT
ejpam-6441	305	79	4	4	NUM
ejpam-6441	305	80	)	)	PUNCT
ejpam-6441	305	81	,	,	PUNCT
ejpam-6441	305	82	(	(	PUNCT
ejpam-6441	305	83	3	3	NUM
ejpam-6441	305	84	,	,	PUNCT
ejpam-6441	305	85	1	1	NUM
ejpam-6441	305	86	)	)	PUNCT
ejpam-6441	305	87	,	,	PUNCT
ejpam-6441	305	88	(	(	PUNCT
ejpam-6441	305	89	4	4	NUM
ejpam-6441	305	90	,	,	PUNCT
ejpam-6441	305	91	3	3	NUM
ejpam-6441	305	92	)	)	PUNCT
ejpam-6441	305	93	}	}	PUNCT
ejpam-6441	305	94	.	.	PUNCT
ejpam-6441	306	1	m.	m.	NOUN
ejpam-6441	306	2	mudhesh	mudhesh	PROPN
ejpam-6441	306	3	et	et	PROPN
ejpam-6441	306	4	al	al	PROPN
ejpam-6441	306	5	.	.	PUNCT
ejpam-6441	306	6	/	/	SYM
ejpam-6441	306	7	eur	eur	PROPN
ejpam-6441	306	8	.	.	PUNCT
ejpam-6441	307	1	j.	j.	PROPN
ejpam-6441	307	2	pure	pure	PROPN
ejpam-6441	307	3	appl	appl	PROPN
ejpam-6441	307	4	.	.	PROPN
ejpam-6441	307	5	math	math	PROPN
ejpam-6441	307	6	,	,	PUNCT
ejpam-6441	307	7	18	18	NUM
ejpam-6441	307	8	(	(	PUNCT
ejpam-6441	307	9	4	4	NUM
ejpam-6441	307	10	)	)	PUNCT
ejpam-6441	307	11	(	(	PUNCT
ejpam-6441	307	12	2025	2025	NUM
ejpam-6441	307	13	)	)	PUNCT
ejpam-6441	307	14	,	,	PUNCT
ejpam-6441	307	15	6441	6441	NUM
ejpam-6441	307	16	14	14	NUM
ejpam-6441	307	17	of	of	ADP
ejpam-6441	307	18	21	21	NUM
ejpam-6441	307	19	consider	consider	VERB
ejpam-6441	307	20	a	a	DET
ejpam-6441	307	21	mapping	mapping	NOUN
ejpam-6441	307	22	γ	γ	NOUN
ejpam-6441	307	23	:	:	PUNCT
ejpam-6441	307	24	∆ℜ	∆ℜ	X
ejpam-6441	307	25	→	→	SYM
ejpam-6441	307	26	cb	cb	PROPN
ejpam-6441	307	27	(	(	PUNCT
ejpam-6441	307	28	∆ℜ	∆ℜ	NOUN
ejpam-6441	307	29	)	)	PUNCT
ejpam-6441	307	30	as	as	ADP
ejpam-6441	307	31	γς	γς	ADV
ejpam-6441	307	32	=	=	PUNCT
ejpam-6441	307	33			PUNCT
ejpam-6441	307	34	{	{	PUNCT
ejpam-6441	307	35	3	3	NUM
ejpam-6441	307	36	,	,	PUNCT
ejpam-6441	307	37	4	4	NUM
ejpam-6441	307	38	}	}	PUNCT
ejpam-6441	307	39	,	,	PUNCT
ejpam-6441	307	40	ς	ς	PROPN
ejpam-6441	307	41	∈	∈	PROPN
ejpam-6441	307	42	{	{	PUNCT
ejpam-6441	307	43	1	1	NUM
ejpam-6441	307	44	,	,	PUNCT
ejpam-6441	307	45	4	4	NUM
ejpam-6441	307	46	}	}	PUNCT
ejpam-6441	307	47	;	;	PUNCT
ejpam-6441	307	48	{	{	PUNCT
ejpam-6441	307	49	3	3	X
ejpam-6441	307	50	}	}	PUNCT
ejpam-6441	307	51	,	,	PUNCT
ejpam-6441	307	52	ς	ς	PROPN
ejpam-6441	307	53	=	=	SYM
ejpam-6441	307	54	2	2	NUM
ejpam-6441	307	55	;	;	PUNCT
ejpam-6441	307	56	{	{	PUNCT
ejpam-6441	307	57	4	4	NUM
ejpam-6441	307	58	}	}	PUNCT
ejpam-6441	307	59	,	,	PUNCT
ejpam-6441	307	60	ς	ς	PROPN
ejpam-6441	307	61	=	=	SYM
ejpam-6441	307	62	3	3	X
ejpam-6441	307	63	.	.	PUNCT
ejpam-6441	308	1	then	then	ADV
ejpam-6441	308	2	,	,	PUNCT
ejpam-6441	308	3	∆ℜ	∆ℜ	X
ejpam-6441	308	4	(	(	PUNCT
ejpam-6441	308	5	γ,ℜ	γ,ℜ	ADJ
ejpam-6441	308	6	)	)	PUNCT
ejpam-6441	308	7	̸=	̸=	PROPN
ejpam-6441	308	8	∅	∅	NOUN
ejpam-6441	308	9	as	as	ADP
ejpam-6441	308	10	4	4	NUM
ejpam-6441	308	11	∈	∈	PROPN
ejpam-6441	308	12	∆ℜ	∆ℜ	NOUN
ejpam-6441	308	13	,	,	PUNCT
ejpam-6441	308	14	4	4	NUM
ejpam-6441	308	15	∈	∈	NOUN
ejpam-6441	308	16	γ3	γ3	NOUN
ejpam-6441	308	17	=	=	SYM
ejpam-6441	308	18	{	{	PUNCT
ejpam-6441	308	19	4	4	NUM
ejpam-6441	308	20	}	}	PUNCT
ejpam-6441	308	21	and	and	CCONJ
ejpam-6441	308	22	(	(	PUNCT
ejpam-6441	308	23	4	4	NUM
ejpam-6441	308	24	,	,	PUNCT
ejpam-6441	308	25	3	3	X
ejpam-6441	308	26	)	)	PUNCT
ejpam-6441	308	27	∈	∈	NOUN
ejpam-6441	308	28	ℜ.	ℜ.	PROPN
ejpam-6441	308	29	also	also	ADV
ejpam-6441	308	30	it	it	PRON
ejpam-6441	308	31	is	be	AUX
ejpam-6441	308	32	easy	easy	ADJ
ejpam-6441	308	33	to	to	PART
ejpam-6441	308	34	check	check	VERB
ejpam-6441	308	35	that	that	PRON
ejpam-6441	308	36	ℜ	ℜ	PROPN
ejpam-6441	308	37	is	be	AUX
ejpam-6441	308	38	γ	γ	X
ejpam-6441	308	39	-	-	ADJ
ejpam-6441	308	40	transitive	transitive	ADJ
ejpam-6441	308	41	and	and	CCONJ
ejpam-6441	308	42	γ	γ	X
ejpam-6441	308	43	is	be	AUX
ejpam-6441	308	44	ℜ-continuous	ℜ-continuous	ADJ
ejpam-6441	308	45	or	or	CCONJ
ejpam-6441	308	46	(	(	PUNCT
ejpam-6441	308	47	∆ℜ	∆ℜ	NOUN
ejpam-6441	308	48	,	,	PUNCT
ejpam-6441	308	49	d	d	NOUN
ejpam-6441	308	50	)	)	PUNCT
ejpam-6441	308	51	is	be	AUX
ejpam-6441	308	52	ℜ-regular	ℜ-regular	ADJ
ejpam-6441	308	53	space	space	NOUN
ejpam-6441	308	54	.	.	PUNCT
ejpam-6441	309	1	now	now	ADV
ejpam-6441	309	2	,	,	PUNCT
ejpam-6441	309	3	for	for	ADP
ejpam-6441	309	4	all	all	DET
ejpam-6441	309	5	λ1	λ1	VERB
ejpam-6441	309	6	=	=	SYM
ejpam-6441	309	7	1	1	NUM
ejpam-6441	309	8	5	5	NUM
ejpam-6441	309	9	,	,	PUNCT
ejpam-6441	309	10	λ2	λ2	NOUN
ejpam-6441	309	11	=	=	SYM
ejpam-6441	309	12	3	3	NUM
ejpam-6441	309	13	5	5	NUM
ejpam-6441	309	14	,	,	PUNCT
ejpam-6441	309	15	β	β	X
ejpam-6441	309	16	=	=	SYM
ejpam-6441	309	17	2	2	NUM
ejpam-6441	309	18	,	,	PUNCT
ejpam-6441	309	19	l	l	NOUN
ejpam-6441	309	20	=	=	SYM
ejpam-6441	309	21	1	1	NUM
ejpam-6441	309	22	5	5	NUM
ejpam-6441	309	23	and	and	CCONJ
ejpam-6441	309	24	(	(	PUNCT
ejpam-6441	309	25	ς1	ς1	NOUN
ejpam-6441	309	26	,	,	PUNCT
ejpam-6441	309	27	ς2	ς2	PROPN
ejpam-6441	309	28	)	)	PUNCT
ejpam-6441	309	29	∈	∈	PROPN
ejpam-6441	309	30	ℜ∗	ℜ∗	PROPN
ejpam-6441	310	1	=	=	PRON
ejpam-6441	310	2	{	{	PUNCT
ejpam-6441	310	3	(	(	PUNCT
ejpam-6441	310	4	1	1	NUM
ejpam-6441	310	5	,	,	PUNCT
ejpam-6441	310	6	1	1	NUM
ejpam-6441	310	7	)	)	PUNCT
ejpam-6441	310	8	,	,	PUNCT
ejpam-6441	310	9	(	(	PUNCT
ejpam-6441	310	10	1	1	NUM
ejpam-6441	310	11	,	,	PUNCT
ejpam-6441	310	12	2	2	NUM
ejpam-6441	310	13	)	)	PUNCT
ejpam-6441	310	14	,	,	PUNCT
ejpam-6441	310	15	(	(	PUNCT
ejpam-6441	310	16	1	1	NUM
ejpam-6441	310	17	,	,	PUNCT
ejpam-6441	310	18	3	3	NUM
ejpam-6441	310	19	)	)	PUNCT
ejpam-6441	310	20	,	,	PUNCT
ejpam-6441	310	21	(	(	PUNCT
ejpam-6441	310	22	3	3	NUM
ejpam-6441	310	23	,	,	PUNCT
ejpam-6441	310	24	1	1	NUM
ejpam-6441	310	25	)	)	PUNCT
ejpam-6441	310	26	,	,	PUNCT
ejpam-6441	310	27	(	(	PUNCT
ejpam-6441	310	28	2	2	NUM
ejpam-6441	310	29	,	,	PUNCT
ejpam-6441	310	30	2	2	NUM
ejpam-6441	310	31	)	)	PUNCT
ejpam-6441	310	32	,	,	PUNCT
ejpam-6441	310	33	(	(	PUNCT
ejpam-6441	310	34	2	2	NUM
ejpam-6441	310	35	,	,	PUNCT
ejpam-6441	310	36	1	1	NUM
ejpam-6441	310	37	)	)	PUNCT
ejpam-6441	310	38	}	}	PUNCT
ejpam-6441	310	39	,	,	PUNCT
ejpam-6441	310	40	we	we	PRON
ejpam-6441	310	41	have	have	VERB
ejpam-6441	310	42	for	for	ADP
ejpam-6441	310	43	(	(	PUNCT
ejpam-6441	310	44	ς1	ς1	NOUN
ejpam-6441	310	45	,	,	PUNCT
ejpam-6441	310	46	ς2	ς2	PROPN
ejpam-6441	310	47	)	)	PUNCT
ejpam-6441	310	48	=	=	PUNCT
ejpam-6441	311	1	(	(	PUNCT
ejpam-6441	311	2	1	1	NUM
ejpam-6441	311	3	,	,	PUNCT
ejpam-6441	311	4	2	2	NUM
ejpam-6441	311	5	)	)	PUNCT
ejpam-6441	311	6	h	h	NOUN
ejpam-6441	311	7	(	(	PUNCT
ejpam-6441	311	8	γ1,γ2	γ1,γ2	PROPN
ejpam-6441	311	9	)	)	PUNCT
ejpam-6441	312	1	=	=	SYM
ejpam-6441	312	2	max	max	PROPN
ejpam-6441	312	3	{	{	PUNCT
ejpam-6441	312	4	sup	sup	NOUN
ejpam-6441	312	5	a∈γ1	a∈γ1	INTJ
ejpam-6441	313	1	d	d	NOUN
ejpam-6441	313	2	(	(	PUNCT
ejpam-6441	313	3	a	a	DET
ejpam-6441	313	4	,	,	PUNCT
ejpam-6441	313	5	γ2	γ2	NOUN
ejpam-6441	313	6	)	)	PUNCT
ejpam-6441	313	7	,	,	PUNCT
ejpam-6441	313	8	sup	sup	NOUN
ejpam-6441	313	9	b∈γ2	b∈γ2	NOUN
ejpam-6441	313	10	d	d	NOUN
ejpam-6441	313	11	(	(	PUNCT
ejpam-6441	313	12	γ1	γ1	PROPN
ejpam-6441	313	13	,	,	PUNCT
ejpam-6441	313	14	b	b	NOUN
ejpam-6441	313	15	)	)	PUNCT
ejpam-6441	313	16	}	}	PUNCT
ejpam-6441	313	17	=	=	SYM
ejpam-6441	313	18	max	max	X
ejpam-6441	313	19	{	{	PUNCT
ejpam-6441	313	20	d	d	X
ejpam-6441	313	21	(	(	PUNCT
ejpam-6441	313	22	4	4	NUM
ejpam-6441	313	23	,	,	PUNCT
ejpam-6441	313	24	3	3	NUM
ejpam-6441	313	25	)	)	PUNCT
ejpam-6441	313	26	,	,	PUNCT
ejpam-6441	313	27	d	d	X
ejpam-6441	313	28	(	(	PUNCT
ejpam-6441	313	29	3	3	NUM
ejpam-6441	313	30	,	,	PUNCT
ejpam-6441	313	31	3	3	NUM
ejpam-6441	313	32	)	)	PUNCT
ejpam-6441	313	33	}	}	PUNCT
ejpam-6441	313	34	=	=	SYM
ejpam-6441	313	35	max	max	X
ejpam-6441	313	36	{	{	PUNCT
ejpam-6441	313	37	5	5	NUM
ejpam-6441	313	38	,	,	PUNCT
ejpam-6441	313	39	0	0	NUM
ejpam-6441	313	40	}	}	PUNCT
ejpam-6441	313	41	=	=	SYM
ejpam-6441	313	42	5	5	NUM
ejpam-6441	313	43	,	,	PUNCT
ejpam-6441	313	44	where	where	SCONJ
ejpam-6441	313	45	mℜ	mℜ	NOUN
ejpam-6441	313	46	(	(	PUNCT
ejpam-6441	313	47	1	1	NUM
ejpam-6441	313	48	,	,	PUNCT
ejpam-6441	313	49	2	2	NUM
ejpam-6441	313	50	)	)	PUNCT
ejpam-6441	313	51	=	=	NOUN
ejpam-6441	314	1	[	[	PUNCT
ejpam-6441	314	2	λ1	λ1	PROPN
ejpam-6441	314	3	(	(	PUNCT
ejpam-6441	314	4	d	d	X
ejpam-6441	314	5	(	(	PUNCT
ejpam-6441	314	6	1,γ1)d	1,γ1)d	PROPN
ejpam-6441	314	7	(	(	PUNCT
ejpam-6441	314	8	2,γ2	2,γ2	NUM
ejpam-6441	314	9	)	)	PUNCT
ejpam-6441	314	10	1	1	NUM
ejpam-6441	315	1	+	+	CCONJ
ejpam-6441	315	2	d	d	X
ejpam-6441	315	3	(	(	PUNCT
ejpam-6441	315	4	1	1	NUM
ejpam-6441	315	5	,	,	PUNCT
ejpam-6441	315	6	2	2	NUM
ejpam-6441	315	7	)	)	PUNCT
ejpam-6441	315	8	)	)	PUNCT
ejpam-6441	316	1	β	β	X
ejpam-6441	317	1	+	+	NUM
ejpam-6441	317	2	λ2	λ2	NOUN
ejpam-6441	317	3	(	(	PUNCT
ejpam-6441	317	4	d	d	NOUN
ejpam-6441	317	5	(	(	PUNCT
ejpam-6441	317	6	1	1	NUM
ejpam-6441	317	7	,	,	PUNCT
ejpam-6441	317	8	2	2	NUM
ejpam-6441	317	9	)	)	PUNCT
ejpam-6441	317	10	)	)	PUNCT
ejpam-6441	317	11	β	β	X
ejpam-6441	317	12	]	]	PUNCT
ejpam-6441	317	13	1	1	NUM
ejpam-6441	317	14	β	β	X
ejpam-6441	317	15	=	=	SYM
ejpam-6441	317	16	[	[	PUNCT
ejpam-6441	317	17	λ1	λ1	PROPN
ejpam-6441	317	18	(	(	PUNCT
ejpam-6441	317	19	d	d	X
ejpam-6441	317	20	(	(	PUNCT
ejpam-6441	317	21	1	1	NUM
ejpam-6441	317	22	,	,	PUNCT
ejpam-6441	317	23	3	3	X
ejpam-6441	317	24	)	)	PUNCT
ejpam-6441	317	25	d	d	NOUN
ejpam-6441	317	26	(	(	PUNCT
ejpam-6441	317	27	2	2	NUM
ejpam-6441	317	28	,	,	PUNCT
ejpam-6441	317	29	3	3	NUM
ejpam-6441	317	30	)	)	PUNCT
ejpam-6441	317	31	1	1	NUM
ejpam-6441	318	1	+	+	CCONJ
ejpam-6441	318	2	d	d	X
ejpam-6441	318	3	(	(	PUNCT
ejpam-6441	318	4	1	1	NUM
ejpam-6441	318	5	,	,	PUNCT
ejpam-6441	318	6	2	2	NUM
ejpam-6441	318	7	)	)	PUNCT
ejpam-6441	318	8	)	)	PUNCT
ejpam-6441	319	1	β	β	X
ejpam-6441	320	1	+	+	NUM
ejpam-6441	320	2	λ2	λ2	NOUN
ejpam-6441	320	3	(	(	PUNCT
ejpam-6441	320	4	d	d	NOUN
ejpam-6441	320	5	(	(	PUNCT
ejpam-6441	320	6	1	1	NUM
ejpam-6441	320	7	,	,	PUNCT
ejpam-6441	320	8	2	2	NUM
ejpam-6441	320	9	)	)	PUNCT
ejpam-6441	320	10	)	)	PUNCT
ejpam-6441	320	11	β	β	X
ejpam-6441	320	12	]	]	PUNCT
ejpam-6441	320	13	1	1	NUM
ejpam-6441	320	14	β	β	X
ejpam-6441	320	15	=	=	SYM
ejpam-6441	320	16	[	[	PUNCT
ejpam-6441	320	17	λ1	λ1	PROPN
ejpam-6441	320	18	(	(	PUNCT
ejpam-6441	320	19	6×	6×	NOUN
ejpam-6441	320	20	4	4	NUM
ejpam-6441	320	21	1	1	NUM
ejpam-6441	320	22	+	+	NUM
ejpam-6441	320	23	4	4	NUM
ejpam-6441	320	24	)	)	PUNCT
ejpam-6441	320	25	β	β	NOUN
ejpam-6441	320	26	+	+	CCONJ
ejpam-6441	320	27	λ2	λ2	NOUN
ejpam-6441	320	28	(	(	PUNCT
ejpam-6441	320	29	4	4	NUM
ejpam-6441	320	30	)	)	PUNCT
ejpam-6441	320	31	β	β	NOUN
ejpam-6441	320	32	]	]	PUNCT
ejpam-6441	320	33	1	1	NUM
ejpam-6441	320	34	β	β	X
ejpam-6441	320	35	≤	≤	X
ejpam-6441	320	36	[	[	PUNCT
ejpam-6441	320	37	1	1	NUM
ejpam-6441	320	38	3	3	NUM
ejpam-6441	320	39	(	(	PUNCT
ejpam-6441	320	40	24	24	NUM
ejpam-6441	320	41	5	5	NUM
ejpam-6441	320	42	)	)	PUNCT
ejpam-6441	320	43	2	2	NUM
ejpam-6441	320	44	+	+	CCONJ
ejpam-6441	320	45	2	2	NUM
ejpam-6441	320	46	3	3	NUM
ejpam-6441	320	47	(	(	PUNCT
ejpam-6441	320	48	4)2	4)2	X
ejpam-6441	320	49	]	]	SYM
ejpam-6441	320	50	1	1	NUM
ejpam-6441	320	51	2	2	NUM
ejpam-6441	320	52	=	=	SYM
ejpam-6441	320	53	(	(	PUNCT
ejpam-6441	320	54	86	86	NUM
ejpam-6441	320	55	75	75	NUM
ejpam-6441	320	56	)	)	PUNCT
ejpam-6441	320	57	1	1	NUM
ejpam-6441	320	58	2	2	NUM
ejpam-6441	320	59	×	×	NOUN
ejpam-6441	320	60	4	4	NUM
ejpam-6441	320	61	=	=	SYM
ejpam-6441	320	62	4.283300908	4.283300908	NUM
ejpam-6441	320	63	,	,	PUNCT
ejpam-6441	320	64	and	and	CCONJ
ejpam-6441	320	65	nℜ	nℜ	PROPN
ejpam-6441	320	66	(	(	PUNCT
ejpam-6441	320	67	1	1	NUM
ejpam-6441	320	68	,	,	PUNCT
ejpam-6441	320	69	2	2	NUM
ejpam-6441	320	70	)	)	PUNCT
ejpam-6441	320	71	=	=	SYM
ejpam-6441	320	72	min	min	NOUN
ejpam-6441	320	73	{	{	PUNCT
ejpam-6441	320	74	d	d	X
ejpam-6441	320	75	(	(	PUNCT
ejpam-6441	320	76	1,γ1	1,γ1	NUM
ejpam-6441	320	77	)	)	PUNCT
ejpam-6441	320	78	,	,	PUNCT
ejpam-6441	320	79	d	d	X
ejpam-6441	320	80	(	(	PUNCT
ejpam-6441	320	81	2,γ2	2,γ2	NUM
ejpam-6441	320	82	)	)	PUNCT
ejpam-6441	320	83	,	,	PUNCT
ejpam-6441	321	1	d	d	X
ejpam-6441	321	2	(	(	PUNCT
ejpam-6441	321	3	1,γ2	1,γ2	NUM
ejpam-6441	321	4	)	)	PUNCT
ejpam-6441	321	5	,	,	PUNCT
ejpam-6441	321	6	d	d	X
ejpam-6441	321	7	(	(	PUNCT
ejpam-6441	321	8	2,γ1	2,γ1	NUM
ejpam-6441	321	9	)	)	PUNCT
ejpam-6441	321	10	}	}	PUNCT
ejpam-6441	321	11	=	=	SYM
ejpam-6441	321	12	min	min	NOUN
ejpam-6441	321	13	{	{	PUNCT
ejpam-6441	321	14	d	d	X
ejpam-6441	321	15	(	(	PUNCT
ejpam-6441	321	16	1	1	NUM
ejpam-6441	321	17	,	,	PUNCT
ejpam-6441	321	18	3	3	NUM
ejpam-6441	321	19	)	)	PUNCT
ejpam-6441	321	20	,	,	PUNCT
ejpam-6441	321	21	d	d	X
ejpam-6441	321	22	(	(	PUNCT
ejpam-6441	321	23	2	2	NUM
ejpam-6441	321	24	,	,	PUNCT
ejpam-6441	321	25	3	3	NUM
ejpam-6441	321	26	)	)	PUNCT
ejpam-6441	321	27	,	,	PUNCT
ejpam-6441	321	28	d	d	X
ejpam-6441	321	29	(	(	PUNCT
ejpam-6441	321	30	1	1	NUM
ejpam-6441	321	31	,	,	PUNCT
ejpam-6441	321	32	3	3	NUM
ejpam-6441	321	33	)	)	PUNCT
ejpam-6441	321	34	,	,	PUNCT
ejpam-6441	321	35	d	d	X
ejpam-6441	321	36	(	(	PUNCT
ejpam-6441	321	37	2	2	NUM
ejpam-6441	321	38	,	,	PUNCT
ejpam-6441	321	39	3	3	NUM
ejpam-6441	321	40	)	)	PUNCT
ejpam-6441	321	41	}	}	PUNCT
ejpam-6441	321	42	=	=	SYM
ejpam-6441	321	43	min	min	NOUN
ejpam-6441	321	44	{	{	PUNCT
ejpam-6441	321	45	6	6	NUM
ejpam-6441	321	46	,	,	PUNCT
ejpam-6441	321	47	4	4	NUM
ejpam-6441	321	48	,	,	PUNCT
ejpam-6441	321	49	6	6	NUM
ejpam-6441	321	50	,	,	PUNCT
ejpam-6441	321	51	4	4	NUM
ejpam-6441	321	52	}	}	PUNCT
ejpam-6441	321	53	=	=	SYM
ejpam-6441	321	54	4	4	X
ejpam-6441	321	55	.	.	X
ejpam-6441	321	56	for	for	ADP
ejpam-6441	321	57	β	β	X
ejpam-6441	321	58	=	=	SYM
ejpam-6441	321	59	0	0	NUM
ejpam-6441	321	60	,	,	PUNCT
ejpam-6441	321	61	we	we	PRON
ejpam-6441	321	62	get	get	VERB
ejpam-6441	321	63	mℜ	mℜ	NOUN
ejpam-6441	321	64	(	(	PUNCT
ejpam-6441	321	65	1	1	NUM
ejpam-6441	321	66	,	,	PUNCT
ejpam-6441	321	67	2	2	NUM
ejpam-6441	321	68	)	)	PUNCT
ejpam-6441	322	1	=	=	SYM
ejpam-6441	322	2	d	d	X
ejpam-6441	322	3	(	(	PUNCT
ejpam-6441	322	4	1,γ1	1,γ1	NUM
ejpam-6441	322	5	)	)	PUNCT
ejpam-6441	322	6	1	1	NUM
ejpam-6441	322	7	5	5	NUM
ejpam-6441	322	8	d	d	NOUN
ejpam-6441	322	9	(	(	PUNCT
ejpam-6441	322	10	2,γ2	2,γ2	NUM
ejpam-6441	322	11	)	)	PUNCT
ejpam-6441	322	12	3	3	NUM
ejpam-6441	322	13	5	5	NUM
ejpam-6441	322	14	=	=	SYM
ejpam-6441	322	15	d	d	NOUN
ejpam-6441	322	16	(	(	PUNCT
ejpam-6441	322	17	1	1	NUM
ejpam-6441	322	18	,	,	PUNCT
ejpam-6441	322	19	3	3	NUM
ejpam-6441	322	20	)	)	PUNCT
ejpam-6441	322	21	1	1	NUM
ejpam-6441	322	22	5	5	NUM
ejpam-6441	322	23	d	d	NOUN
ejpam-6441	322	24	(	(	PUNCT
ejpam-6441	322	25	2	2	NUM
ejpam-6441	322	26	,	,	PUNCT
ejpam-6441	322	27	3	3	NUM
ejpam-6441	322	28	)	)	PUNCT
ejpam-6441	322	29	3	3	NUM
ejpam-6441	322	30	5	5	NUM
ejpam-6441	322	31	m.	m.	NOUN
ejpam-6441	322	32	mudhesh	mudhesh	NOUN
ejpam-6441	322	33	et	et	PROPN
ejpam-6441	322	34	al	al	PROPN
ejpam-6441	322	35	.	.	PUNCT
ejpam-6441	322	36	/	/	SYM
ejpam-6441	322	37	eur	eur	PROPN
ejpam-6441	322	38	.	.	PUNCT
ejpam-6441	323	1	j.	j.	PROPN
ejpam-6441	323	2	pure	pure	PROPN
ejpam-6441	323	3	appl	appl	PROPN
ejpam-6441	323	4	.	.	PROPN
ejpam-6441	323	5	math	math	PROPN
ejpam-6441	323	6	,	,	PUNCT
ejpam-6441	323	7	18	18	NUM
ejpam-6441	323	8	(	(	PUNCT
ejpam-6441	323	9	4	4	NUM
ejpam-6441	323	10	)	)	PUNCT
ejpam-6441	323	11	(	(	PUNCT
ejpam-6441	323	12	2025	2025	NUM
ejpam-6441	323	13	)	)	PUNCT
ejpam-6441	323	14	,	,	PUNCT
ejpam-6441	323	15	6441	6441	NUM
ejpam-6441	323	16	15	15	NUM
ejpam-6441	323	17	of	of	ADP
ejpam-6441	323	18	21	21	NUM
ejpam-6441	323	19	=	=	SYM
ejpam-6441	323	20	6	6	NUM
ejpam-6441	323	21	1	1	NUM
ejpam-6441	323	22	5	5	NUM
ejpam-6441	323	23	×	×	NOUN
ejpam-6441	323	24	4	4	NUM
ejpam-6441	323	25	3	3	NUM
ejpam-6441	323	26	5	5	NUM
ejpam-6441	323	27	≈	≈	PROPN
ejpam-6441	323	28	3.3	3.3	NUM
ejpam-6441	323	29	.	.	PUNCT
ejpam-6441	324	1	therefore	therefore	ADV
ejpam-6441	324	2	,	,	PUNCT
ejpam-6441	324	3	τ	τ	PROPN
ejpam-6441	325	1	+	+	NUM
ejpam-6441	325	2	f	f	X
ejpam-6441	325	3	(	(	PUNCT
ejpam-6441	325	4	5	5	NUM
ejpam-6441	325	5	)	)	PUNCT
ejpam-6441	325	6	≤	≤	NUM
ejpam-6441	325	7	f	f	X
ejpam-6441	325	8	(	(	PUNCT
ejpam-6441	325	9	4	4	NUM
ejpam-6441	325	10	)	)	PUNCT
ejpam-6441	325	11	+	+	CCONJ
ejpam-6441	325	12	4	4	NUM
ejpam-6441	325	13	5	5	NUM
ejpam-6441	325	14	and	and	CCONJ
ejpam-6441	325	15	for	for	ADP
ejpam-6441	325	16	β	β	X
ejpam-6441	325	17	=	=	SYM
ejpam-6441	325	18	0	0	NUM
ejpam-6441	325	19	,	,	PUNCT
ejpam-6441	325	20	we	we	PRON
ejpam-6441	325	21	get	get	VERB
ejpam-6441	325	22	τ	τ	PROPN
ejpam-6441	325	23	+	+	NUM
ejpam-6441	325	24	f	f	X
ejpam-6441	325	25	(	(	PUNCT
ejpam-6441	325	26	5	5	NUM
ejpam-6441	325	27	)	)	PUNCT
ejpam-6441	325	28	≤	≤	NUM
ejpam-6441	325	29	f	f	X
ejpam-6441	325	30	(	(	PUNCT
ejpam-6441	325	31	3.3	3.3	NUM
ejpam-6441	325	32	)	)	PUNCT
ejpam-6441	326	1	+	+	CCONJ
ejpam-6441	326	2	4	4	NUM
ejpam-6441	326	3	5	5	NUM
ejpam-6441	326	4	.	.	PUNCT
ejpam-6441	327	1	for	for	ADP
ejpam-6441	327	2	(	(	PUNCT
ejpam-6441	327	3	ς1	ς1	NOUN
ejpam-6441	327	4	,	,	PUNCT
ejpam-6441	327	5	ς2	ς2	PROPN
ejpam-6441	327	6	)	)	PUNCT
ejpam-6441	327	7	=	=	PUNCT
ejpam-6441	327	8	(	(	PUNCT
ejpam-6441	327	9	1	1	NUM
ejpam-6441	327	10	,	,	PUNCT
ejpam-6441	327	11	3	3	NUM
ejpam-6441	327	12	)	)	PUNCT
ejpam-6441	327	13	,	,	PUNCT
ejpam-6441	327	14	we	we	PRON
ejpam-6441	327	15	have	have	VERB
ejpam-6441	327	16	h	h	NOUN
ejpam-6441	327	17	(	(	PUNCT
ejpam-6441	327	18	γ1,γ3	γ1,γ3	PROPN
ejpam-6441	327	19	)	)	PUNCT
ejpam-6441	327	20	=	=	SYM
ejpam-6441	327	21	5	5	NUM
ejpam-6441	327	22	,	,	PUNCT
ejpam-6441	327	23	mℜ	mℜ	NOUN
ejpam-6441	327	24	(	(	PUNCT
ejpam-6441	327	25	1	1	NUM
ejpam-6441	327	26	,	,	PUNCT
ejpam-6441	327	27	3	3	NUM
ejpam-6441	327	28	)	)	PUNCT
ejpam-6441	327	29	=	=	SYM
ejpam-6441	327	30	5.488	5.488	NUM
ejpam-6441	327	31	,	,	PUNCT
ejpam-6441	327	32	and	and	CCONJ
ejpam-6441	327	33	nℜ	nℜ	PROPN
ejpam-6441	327	34	(	(	PUNCT
ejpam-6441	327	35	1	1	NUM
ejpam-6441	327	36	,	,	PUNCT
ejpam-6441	327	37	3	3	NUM
ejpam-6441	327	38	)	)	PUNCT
ejpam-6441	327	39	=	=	SYM
ejpam-6441	328	1	0	0	X
ejpam-6441	328	2	.	.	PUNCT
ejpam-6441	328	3	therefore	therefore	ADV
ejpam-6441	328	4	τ	τ	PROPN
ejpam-6441	329	1	+	+	NUM
ejpam-6441	329	2	f	f	X
ejpam-6441	329	3	(	(	PUNCT
ejpam-6441	329	4	5	5	NUM
ejpam-6441	329	5	)	)	PUNCT
ejpam-6441	329	6	≤	≤	NUM
ejpam-6441	329	7	f	f	X
ejpam-6441	329	8	(	(	PUNCT
ejpam-6441	329	9	5.488	5.488	NUM
ejpam-6441	329	10	)	)	PUNCT
ejpam-6441	330	1	+	+	CCONJ
ejpam-6441	330	2	0	0	NUM
ejpam-6441	330	3	for	for	ADP
ejpam-6441	330	4	(	(	PUNCT
ejpam-6441	330	5	ς1	ς1	NOUN
ejpam-6441	330	6	,	,	PUNCT
ejpam-6441	330	7	ς2	ς2	PROPN
ejpam-6441	330	8	)	)	PUNCT
ejpam-6441	330	9	=	=	PUNCT
ejpam-6441	330	10	(	(	PUNCT
ejpam-6441	330	11	1	1	NUM
ejpam-6441	330	12	,	,	PUNCT
ejpam-6441	330	13	1	1	NUM
ejpam-6441	330	14	)	)	PUNCT
ejpam-6441	330	15	,	,	PUNCT
ejpam-6441	330	16	we	we	PRON
ejpam-6441	330	17	have	have	VERB
ejpam-6441	330	18	h	h	NOUN
ejpam-6441	330	19	(	(	PUNCT
ejpam-6441	330	20	γ1,γ1	γ1,γ1	PROPN
ejpam-6441	330	21	)	)	PUNCT
ejpam-6441	330	22	=	=	SYM
ejpam-6441	330	23	5	5	NUM
ejpam-6441	330	24	,	,	PUNCT
ejpam-6441	330	25	mℜ	mℜ	NOUN
ejpam-6441	330	26	(	(	PUNCT
ejpam-6441	330	27	1	1	NUM
ejpam-6441	330	28	,	,	PUNCT
ejpam-6441	330	29	1	1	NUM
ejpam-6441	330	30	)	)	PUNCT
ejpam-6441	330	31	=	=	SYM
ejpam-6441	331	1	12	12	NUM
ejpam-6441	331	2	√	√	NUM
ejpam-6441	331	3	3	3	NUM
ejpam-6441	331	4	and	and	CCONJ
ejpam-6441	331	5	nℜ	nℜ	PROPN
ejpam-6441	331	6	(	(	PUNCT
ejpam-6441	331	7	1	1	NUM
ejpam-6441	331	8	,	,	PUNCT
ejpam-6441	331	9	1	1	NUM
ejpam-6441	331	10	)	)	PUNCT
ejpam-6441	331	11	=	=	SYM
ejpam-6441	332	1	6	6	X
ejpam-6441	332	2	.	.	PUNCT
ejpam-6441	332	3	therefore	therefore	ADV
ejpam-6441	332	4	τ	τ	PROPN
ejpam-6441	332	5	+	+	NUM
ejpam-6441	332	6	f	f	X
ejpam-6441	332	7	(	(	PUNCT
ejpam-6441	332	8	5	5	NUM
ejpam-6441	332	9	)	)	PUNCT
ejpam-6441	333	1	≤	≤	NUM
ejpam-6441	333	2	f	f	X
ejpam-6441	333	3	(	(	PUNCT
ejpam-6441	333	4	12	12	NUM
ejpam-6441	333	5	√	√	NUM
ejpam-6441	333	6	3	3	NUM
ejpam-6441	333	7	)	)	PUNCT
ejpam-6441	333	8	+	+	CCONJ
ejpam-6441	333	9	6	6	NUM
ejpam-6441	333	10	5	5	NUM
ejpam-6441	333	11	.	.	PUNCT
ejpam-6441	334	1	for	for	ADP
ejpam-6441	334	2	(	(	PUNCT
ejpam-6441	334	3	ς1	ς1	NOUN
ejpam-6441	334	4	,	,	PUNCT
ejpam-6441	334	5	ς2	ς2	PROPN
ejpam-6441	334	6	)	)	PUNCT
ejpam-6441	334	7	=	=	PUNCT
ejpam-6441	334	8	(	(	PUNCT
ejpam-6441	334	9	2	2	NUM
ejpam-6441	334	10	,	,	PUNCT
ejpam-6441	334	11	2	2	NUM
ejpam-6441	334	12	)	)	PUNCT
ejpam-6441	334	13	,	,	PUNCT
ejpam-6441	334	14	we	we	PRON
ejpam-6441	334	15	have	have	VERB
ejpam-6441	334	16	h	h	NOUN
ejpam-6441	334	17	(	(	PUNCT
ejpam-6441	334	18	γ2,γ2	γ2,γ2	PROPN
ejpam-6441	334	19	)	)	PUNCT
ejpam-6441	334	20	=	=	SYM
ejpam-6441	335	1	0	0	NUM
ejpam-6441	335	2	,	,	PUNCT
ejpam-6441	335	3	where	where	SCONJ
ejpam-6441	335	4	mℜ	mℜ	NOUN
ejpam-6441	335	5	(	(	PUNCT
ejpam-6441	335	6	2	2	NUM
ejpam-6441	335	7	,	,	PUNCT
ejpam-6441	335	8	2	2	NUM
ejpam-6441	335	9	)	)	PUNCT
ejpam-6441	335	10	=	=	SYM
ejpam-6441	336	1	16√	16√	NUM
ejpam-6441	336	2	3	3	NUM
ejpam-6441	336	3	,	,	PUNCT
ejpam-6441	336	4	and	and	CCONJ
ejpam-6441	336	5	nℜ	nℜ	PROPN
ejpam-6441	336	6	(	(	PUNCT
ejpam-6441	336	7	2	2	NUM
ejpam-6441	336	8	,	,	PUNCT
ejpam-6441	336	9	2	2	NUM
ejpam-6441	336	10	)	)	PUNCT
ejpam-6441	336	11	=	=	SYM
ejpam-6441	337	1	4	4	X
ejpam-6441	337	2	.	.	PUNCT
ejpam-6441	337	3	therefore	therefore	ADV
ejpam-6441	337	4	τ	τ	PROPN
ejpam-6441	338	1	+	+	NUM
ejpam-6441	338	2	f	f	X
ejpam-6441	338	3	(	(	PUNCT
ejpam-6441	338	4	0	0	NUM
ejpam-6441	338	5	)	)	PUNCT
ejpam-6441	338	6	≤	≤	NUM
ejpam-6441	338	7	f	f	X
ejpam-6441	338	8	(	(	PUNCT
ejpam-6441	338	9	16√	16√	NUM
ejpam-6441	338	10	3	3	NUM
ejpam-6441	338	11	)	)	PUNCT
ejpam-6441	338	12	+	+	CCONJ
ejpam-6441	338	13	4	4	NUM
ejpam-6441	338	14	5	5	NUM
ejpam-6441	338	15	.	.	PUNCT
ejpam-6441	339	1	hence	hence	ADV
ejpam-6441	339	2	,	,	PUNCT
ejpam-6441	339	3	for	for	ADP
ejpam-6441	339	4	all	all	DET
ejpam-6441	339	5	(	(	PUNCT
ejpam-6441	339	6	ς1	ς1	NOUN
ejpam-6441	339	7	,	,	PUNCT
ejpam-6441	339	8	ς2	ς2	PROPN
ejpam-6441	339	9	)	)	PUNCT
ejpam-6441	339	10	∈	∈	PROPN
ejpam-6441	339	11	ℜ∗	ℜ∗	PROPN
ejpam-6441	339	12	,	,	PUNCT
ejpam-6441	339	13	we	we	PRON
ejpam-6441	339	14	find	find	VERB
ejpam-6441	339	15	that	that	SCONJ
ejpam-6441	339	16	(	(	PUNCT
ejpam-6441	339	17	1	1	X
ejpam-6441	339	18	)	)	PUNCT
ejpam-6441	339	19	is	be	AUX
ejpam-6441	339	20	achieved	achieve	VERB
ejpam-6441	339	21	and	and	CCONJ
ejpam-6441	339	22	all	all	DET
ejpam-6441	339	23	the	the	DET
ejpam-6441	339	24	conditions	condition	NOUN
ejpam-6441	339	25	of	of	ADP
ejpam-6441	339	26	theorem	theorem	NOUN
ejpam-6441	339	27	5	5	NUM
ejpam-6441	339	28	are	be	AUX
ejpam-6441	339	29	satisfied	satisfied	ADJ
ejpam-6441	339	30	so	so	SCONJ
ejpam-6441	339	31	that	that	SCONJ
ejpam-6441	339	32	γ	γ	PROPN
ejpam-6441	339	33	has	have	VERB
ejpam-6441	339	34	an	an	DET
ejpam-6441	339	35	fp	fp	PROPN
ejpam-6441	339	36	4	4	NUM
ejpam-6441	339	37	∈	∈	PROPN
ejpam-6441	339	38	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	339	39	3	3	NUM
ejpam-6441	340	1	.	.	PUNCT
ejpam-6441	340	2	corollaries	corollary	NOUN
ejpam-6441	340	3	corollary	corollary	ADJ
ejpam-6441	340	4	1	1	NUM
ejpam-6441	340	5	.	.	PUNCT
ejpam-6441	341	1	let	let	AUX
ejpam-6441	341	2	(	(	PUNCT
ejpam-6441	341	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	341	4	,	,	PUNCT
ejpam-6441	341	5	d	d	NOUN
ejpam-6441	341	6	)	)	PUNCT
ejpam-6441	341	7	be	be	AUX
ejpam-6441	341	8	a	a	DET
ejpam-6441	341	9	ms	ms	PROPN
ejpam-6441	341	10	.	.	PROPN
ejpam-6441	342	1	a	a	DET
ejpam-6441	342	2	map	map	NOUN
ejpam-6441	342	3	γ	γ	X
ejpam-6441	342	4	:	:	PUNCT
ejpam-6441	342	5	∆ℜ	∆ℜ	X
ejpam-6441	342	6	→	→	SYM
ejpam-6441	342	7	∆ℜ	∆ℜ	PROPN
ejpam-6441	342	8	is	be	AUX
ejpam-6441	342	9	called	call	VERB
ejpam-6441	342	10	an	an	DET
ejpam-6441	342	11	almost	almost	ADV
ejpam-6441	342	12	fishertype	fishertype	NOUN
ejpam-6441	342	13	f	f	PROPN
ejpam-6441	342	14	-contraction	-contraction	PROPN
ejpam-6441	342	15	endowed	endow	VERB
ejpam-6441	342	16	with	with	ADP
ejpam-6441	342	17	a	a	DET
ejpam-6441	342	18	γ	γ	NOUN
ejpam-6441	342	19	-	-	ADJ
ejpam-6441	342	20	transitive	transitive	ADJ
ejpam-6441	342	21	binary	binary	ADJ
ejpam-6441	342	22	relation	relation	PROPN
ejpam-6441	342	23	ℜ	ℜ	PROPN
ejpam-6441	342	24	,	,	PUNCT
ejpam-6441	342	25	if	if	SCONJ
ejpam-6441	342	26	there	there	PRON
ejpam-6441	342	27	exist	exist	VERB
ejpam-6441	342	28	τ	τ	PROPN
ejpam-6441	342	29	∈	∈	PROPN
ejpam-6441	342	30	r+	r+	NOUN
ejpam-6441	342	31	,	,	PUNCT
ejpam-6441	342	32	f	f	PROPN
ejpam-6441	342	33	∈	∈	PROPN
ejpam-6441	342	34	∆w	∆w	PROPN
ejpam-6441	342	35	and	and	CCONJ
ejpam-6441	342	36	λ1	λ1	ADJ
ejpam-6441	342	37	,	,	PUNCT
ejpam-6441	342	38	λ2	λ2	PROPN
ejpam-6441	342	39	,	,	PUNCT
ejpam-6441	342	40	l	l	NOUN
ejpam-6441	342	41	≥	≥	NOUN
ejpam-6441	342	42	0	0	NUM
ejpam-6441	342	43	with	with	ADP
ejpam-6441	342	44	λ1	λ1	PROPN
ejpam-6441	342	45	+	+	CCONJ
ejpam-6441	342	46	λ2	λ2	NOUN
ejpam-6441	342	47	≤	≤	NUM
ejpam-6441	342	48	1	1	NUM
ejpam-6441	342	49	such	such	ADJ
ejpam-6441	342	50	that	that	PRON
ejpam-6441	342	51	for	for	ADP
ejpam-6441	342	52	all	all	PRON
ejpam-6441	342	53	(	(	PUNCT
ejpam-6441	342	54	ς1	ς1	NOUN
ejpam-6441	342	55	,	,	PUNCT
ejpam-6441	342	56	ς2	ς2	PROPN
ejpam-6441	342	57	)	)	PUNCT
ejpam-6441	342	58	∈	∈	PROPN
ejpam-6441	342	59	ℜ∗	ℜ∗	PROPN
ejpam-6441	343	1	=	=	PRON
ejpam-6441	343	2	{	{	PUNCT
ejpam-6441	343	3	(	(	PUNCT
ejpam-6441	343	4	ς1	ς1	NOUN
ejpam-6441	343	5	,	,	PUNCT
ejpam-6441	343	6	ς2	ς2	PROPN
ejpam-6441	343	7	)	)	PUNCT
ejpam-6441	343	8	∈	∈	PROPN
ejpam-6441	343	9	ℜ	ℜ	PROPN
ejpam-6441	343	10	:	:	PUNCT
ejpam-6441	343	11	ς1	ς1	NOUN
ejpam-6441	343	12	,	,	PUNCT
ejpam-6441	343	13	ς2	ς2	PROPN
ejpam-6441	343	14	∈	∈	PROPN
ejpam-6441	343	15	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	343	16	(	(	PUNCT
ejpam-6441	343	17	γ	γ	NOUN
ejpam-6441	343	18	)	)	PUNCT
ejpam-6441	343	19	}	}	PUNCT
ejpam-6441	343	20	,	,	PUNCT
ejpam-6441	343	21	we	we	PRON
ejpam-6441	343	22	have	have	VERB
ejpam-6441	343	23	τ	τ	PROPN
ejpam-6441	344	1	+	+	NUM
ejpam-6441	344	2	f	f	X
ejpam-6441	344	3	(	(	PUNCT
ejpam-6441	344	4	d(γς1,γς2	d(γς1,γς2	PROPN
ejpam-6441	344	5	)	)	PUNCT
ejpam-6441	344	6	)	)	PUNCT
ejpam-6441	344	7	≤	≤	NUM
ejpam-6441	344	8	f	f	X
ejpam-6441	344	9	(	(	PUNCT
ejpam-6441	344	10	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	344	11	,	,	PUNCT
ejpam-6441	344	12	ς2	ς2	PROPN
ejpam-6441	344	13	)	)	PUNCT
ejpam-6441	344	14	)	)	PUNCT
ejpam-6441	345	1	+	+	CCONJ
ejpam-6441	345	2	lnℜ	lnℜ	NOUN
ejpam-6441	345	3	(	(	PUNCT
ejpam-6441	345	4	ς1	ς1	NOUN
ejpam-6441	345	5	,	,	PUNCT
ejpam-6441	345	6	ς2	ς2	PROPN
ejpam-6441	345	7	)	)	PUNCT
ejpam-6441	345	8	,	,	PUNCT
ejpam-6441	345	9	(	(	PUNCT
ejpam-6441	345	10	27	27	NUM
ejpam-6441	345	11	)	)	PUNCT
ejpam-6441	345	12	where	where	SCONJ
ejpam-6441	345	13	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	345	14	,	,	PUNCT
ejpam-6441	345	15	ς2	ς2	PROPN
ejpam-6441	345	16	)	)	PUNCT
ejpam-6441	345	17	and	and	CCONJ
ejpam-6441	345	18	nℜ	nℜ	PROPN
ejpam-6441	345	19	(	(	PUNCT
ejpam-6441	345	20	ς1	ς1	NOUN
ejpam-6441	345	21	,	,	PUNCT
ejpam-6441	345	22	ς2	ς2	PROPN
ejpam-6441	345	23	)	)	PUNCT
ejpam-6441	345	24	are	be	AUX
ejpam-6441	345	25	defined	define	VERB
ejpam-6441	345	26	as	as	ADP
ejpam-6441	345	27	in	in	ADP
ejpam-6441	345	28	(	(	PUNCT
ejpam-6441	345	29	2	2	NUM
ejpam-6441	345	30	)	)	PUNCT
ejpam-6441	345	31	and	and	CCONJ
ejpam-6441	345	32	(	(	PUNCT
ejpam-6441	345	33	3	3	X
ejpam-6441	345	34	)	)	PUNCT
ejpam-6441	345	35	respectively	respectively	ADV
ejpam-6441	345	36	.	.	PUNCT
ejpam-6441	346	1	hence	hence	ADV
ejpam-6441	346	2	,	,	PUNCT
ejpam-6441	346	3	γ	γ	PROPN
ejpam-6441	346	4	has	have	VERB
ejpam-6441	346	5	an	an	DET
ejpam-6441	346	6	fp	fp	NOUN
ejpam-6441	346	7	ς∗	ς∗	PROPN
ejpam-6441	346	8	∈	∈	PROPN
ejpam-6441	346	9	∆ℜ	∆ℜ	PROPN
ejpam-6441	346	10	.	.	PUNCT
ejpam-6441	347	1	corollary	corollary	ADJ
ejpam-6441	347	2	2	2	NUM
ejpam-6441	347	3	.	.	PUNCT
ejpam-6441	348	1	let	let	AUX
ejpam-6441	348	2	(	(	PUNCT
ejpam-6441	348	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	348	4	,	,	PUNCT
ejpam-6441	348	5	d	d	NOUN
ejpam-6441	348	6	)	)	PUNCT
ejpam-6441	348	7	be	be	AUX
ejpam-6441	348	8	a	a	DET
ejpam-6441	348	9	ms	ms	PROPN
ejpam-6441	348	10	.	.	PROPN
ejpam-6441	349	1	a	a	DET
ejpam-6441	349	2	map	map	NOUN
ejpam-6441	349	3	γ	γ	X
ejpam-6441	349	4	:	:	PUNCT
ejpam-6441	349	5	∆ℜ	∆ℜ	PROPN
ejpam-6441	349	6	→	→	SYM
ejpam-6441	349	7	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	349	8	)	)	PUNCT
ejpam-6441	349	9	is	be	AUX
ejpam-6441	349	10	called	call	VERB
ejpam-6441	349	11	an	an	DET
ejpam-6441	349	12	almost	almost	ADV
ejpam-6441	349	13	fishertype	fishertype	NOUN
ejpam-6441	349	14	multivalued	multivalue	VERB
ejpam-6441	349	15	f	f	PROPN
ejpam-6441	349	16	-contraction	-contraction	PROPN
ejpam-6441	349	17	endowed	endow	VERB
ejpam-6441	349	18	with	with	ADP
ejpam-6441	349	19	a	a	DET
ejpam-6441	349	20	γ	γ	NOUN
ejpam-6441	349	21	-	-	ADJ
ejpam-6441	349	22	transitive	transitive	ADJ
ejpam-6441	349	23	binary	binary	ADJ
ejpam-6441	349	24	relation	relation	PROPN
ejpam-6441	349	25	ℜ	ℜ	PROPN
ejpam-6441	349	26	,	,	PUNCT
ejpam-6441	349	27	if	if	SCONJ
ejpam-6441	349	28	there	there	PRON
ejpam-6441	349	29	exist	exist	VERB
ejpam-6441	349	30	τ	τ	PROPN
ejpam-6441	349	31	∈	∈	PROPN
ejpam-6441	349	32	r+	r+	NOUN
ejpam-6441	349	33	,	,	PUNCT
ejpam-6441	349	34	f	f	PROPN
ejpam-6441	349	35	∈	∈	PROPN
ejpam-6441	349	36	∆w	∆w	PROPN
ejpam-6441	349	37	and	and	CCONJ
ejpam-6441	349	38	λ1	λ1	ADJ
ejpam-6441	349	39	,	,	PUNCT
ejpam-6441	349	40	λ2	λ2	PROPN
ejpam-6441	349	41	,	,	PUNCT
ejpam-6441	349	42	l	l	NOUN
ejpam-6441	349	43	≥	≥	NOUN
ejpam-6441	349	44	0	0	NUM
ejpam-6441	349	45	with	with	ADP
ejpam-6441	349	46	λ1	λ1	PROPN
ejpam-6441	349	47	+	+	CCONJ
ejpam-6441	349	48	λ2	λ2	NOUN
ejpam-6441	349	49	≤	≤	NUM
ejpam-6441	349	50	1	1	NUM
ejpam-6441	349	51	such	such	ADJ
ejpam-6441	349	52	that	that	PRON
ejpam-6441	349	53	for	for	ADP
ejpam-6441	349	54	all	all	PRON
ejpam-6441	349	55	(	(	PUNCT
ejpam-6441	349	56	ς1	ς1	NOUN
ejpam-6441	349	57	,	,	PUNCT
ejpam-6441	349	58	ς2	ς2	PROPN
ejpam-6441	349	59	)	)	PUNCT
ejpam-6441	349	60	∈	∈	PROPN
ejpam-6441	349	61	ℜ∗	ℜ∗	PROPN
ejpam-6441	350	1	=	=	PRON
ejpam-6441	350	2	{	{	PUNCT
ejpam-6441	350	3	(	(	PUNCT
ejpam-6441	350	4	ς1	ς1	NOUN
ejpam-6441	350	5	,	,	PUNCT
ejpam-6441	350	6	ς2	ς2	PROPN
ejpam-6441	350	7	)	)	PUNCT
ejpam-6441	350	8	∈	∈	PROPN
ejpam-6441	350	9	ℜ	ℜ	PROPN
ejpam-6441	350	10	:	:	PUNCT
ejpam-6441	350	11	ς1	ς1	NOUN
ejpam-6441	350	12	,	,	PUNCT
ejpam-6441	350	13	ς2	ς2	PROPN
ejpam-6441	350	14	∈	∈	PROPN
ejpam-6441	350	15	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	350	16	(	(	PUNCT
ejpam-6441	350	17	γ	γ	NOUN
ejpam-6441	350	18	)	)	PUNCT
ejpam-6441	350	19	}	}	PUNCT
ejpam-6441	350	20	,	,	PUNCT
ejpam-6441	350	21	we	we	PRON
ejpam-6441	350	22	have	have	VERB
ejpam-6441	350	23	τ	τ	PROPN
ejpam-6441	351	1	+	+	NUM
ejpam-6441	351	2	f	f	X
ejpam-6441	351	3	(	(	PUNCT
ejpam-6441	351	4	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	351	5	)	)	PUNCT
ejpam-6441	351	6	)	)	PUNCT
ejpam-6441	351	7	≤	≤	NUM
ejpam-6441	351	8	f	f	X
ejpam-6441	351	9	(	(	PUNCT
ejpam-6441	351	10	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	351	11	,	,	PUNCT
ejpam-6441	351	12	ς2	ς2	PROPN
ejpam-6441	351	13	)	)	PUNCT
ejpam-6441	351	14	)	)	PUNCT
ejpam-6441	352	1	+	+	CCONJ
ejpam-6441	352	2	ld	ld	PROPN
ejpam-6441	352	3	(	(	PUNCT
ejpam-6441	352	4	ς2,γς1	ς2,γς1	NUM
ejpam-6441	352	5	)	)	PUNCT
ejpam-6441	352	6	,	,	PUNCT
ejpam-6441	352	7	(	(	PUNCT
ejpam-6441	352	8	28	28	NUM
ejpam-6441	352	9	)	)	PUNCT
ejpam-6441	352	10	where	where	SCONJ
ejpam-6441	352	11	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	352	12	,	,	PUNCT
ejpam-6441	352	13	ς2	ς2	PROPN
ejpam-6441	352	14	)	)	PUNCT
ejpam-6441	352	15	is	be	AUX
ejpam-6441	352	16	defind	defind	NOUN
ejpam-6441	352	17	as	as	ADP
ejpam-6441	352	18	in	in	ADP
ejpam-6441	352	19	(	(	PUNCT
ejpam-6441	352	20	2	2	NUM
ejpam-6441	352	21	)	)	PUNCT
ejpam-6441	352	22	.	.	PUNCT
ejpam-6441	353	1	hence	hence	ADV
ejpam-6441	353	2	,	,	PUNCT
ejpam-6441	353	3	γ	γ	PROPN
ejpam-6441	353	4	has	have	VERB
ejpam-6441	353	5	an	an	DET
ejpam-6441	353	6	fp	fp	NOUN
ejpam-6441	353	7	in	in	ADP
ejpam-6441	353	8	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	353	9	corollary	corollary	NOUN
ejpam-6441	353	10	3	3	X
ejpam-6441	353	11	.	.	PUNCT
ejpam-6441	354	1	let	let	AUX
ejpam-6441	354	2	(	(	PUNCT
ejpam-6441	354	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	354	4	,	,	PUNCT
ejpam-6441	354	5	d	d	NOUN
ejpam-6441	354	6	)	)	PUNCT
ejpam-6441	354	7	be	be	AUX
ejpam-6441	354	8	a	a	DET
ejpam-6441	354	9	ms	ms	PROPN
ejpam-6441	354	10	.	.	PROPN
ejpam-6441	355	1	a	a	DET
ejpam-6441	355	2	map	map	NOUN
ejpam-6441	355	3	γ	γ	X
ejpam-6441	355	4	:	:	PUNCT
ejpam-6441	355	5	∆ℜ	∆ℜ	X
ejpam-6441	355	6	→	→	SYM
ejpam-6441	355	7	∆ℜ	∆ℜ	PROPN
ejpam-6441	355	8	is	be	AUX
ejpam-6441	355	9	called	call	VERB
ejpam-6441	355	10	an	an	DET
ejpam-6441	355	11	almost	almost	ADV
ejpam-6441	355	12	fishertype	fishertype	NOUN
ejpam-6441	355	13	f	f	PROPN
ejpam-6441	355	14	-contraction	-contraction	PROPN
ejpam-6441	355	15	endowed	endow	VERB
ejpam-6441	355	16	with	with	ADP
ejpam-6441	355	17	a	a	DET
ejpam-6441	355	18	γ	γ	NOUN
ejpam-6441	355	19	-	-	ADJ
ejpam-6441	355	20	transitive	transitive	ADJ
ejpam-6441	355	21	binary	binary	ADJ
ejpam-6441	355	22	relation	relation	PROPN
ejpam-6441	355	23	ℜ	ℜ	PROPN
ejpam-6441	355	24	,	,	PUNCT
ejpam-6441	355	25	if	if	SCONJ
ejpam-6441	355	26	there	there	PRON
ejpam-6441	355	27	exist	exist	VERB
ejpam-6441	355	28	τ	τ	PROPN
ejpam-6441	355	29	∈	∈	PROPN
ejpam-6441	355	30	r+	r+	NOUN
ejpam-6441	355	31	,	,	PUNCT
ejpam-6441	355	32	f	f	PROPN
ejpam-6441	355	33	∈	∈	PROPN
ejpam-6441	355	34	∆w	∆w	PROPN
ejpam-6441	355	35	and	and	CCONJ
ejpam-6441	355	36	λ1	λ1	ADJ
ejpam-6441	355	37	,	,	PUNCT
ejpam-6441	355	38	λ2	λ2	PROPN
ejpam-6441	355	39	,	,	PUNCT
ejpam-6441	355	40	l	l	NOUN
ejpam-6441	355	41	≥	≥	NOUN
ejpam-6441	355	42	0	0	NUM
ejpam-6441	355	43	with	with	ADP
ejpam-6441	355	44	λ1	λ1	PROPN
ejpam-6441	355	45	+	+	CCONJ
ejpam-6441	355	46	λ2	λ2	NOUN
ejpam-6441	355	47	≤	≤	NUM
ejpam-6441	355	48	1	1	NUM
ejpam-6441	355	49	such	such	ADJ
ejpam-6441	355	50	that	that	PRON
ejpam-6441	355	51	for	for	ADP
ejpam-6441	355	52	all	all	PRON
ejpam-6441	355	53	(	(	PUNCT
ejpam-6441	355	54	ς1	ς1	NOUN
ejpam-6441	355	55	,	,	PUNCT
ejpam-6441	355	56	ς2	ς2	PROPN
ejpam-6441	355	57	)	)	PUNCT
ejpam-6441	355	58	∈	∈	PROPN
ejpam-6441	355	59	ℜ∗	ℜ∗	PROPN
ejpam-6441	356	1	=	=	PRON
ejpam-6441	356	2	{	{	PUNCT
ejpam-6441	356	3	(	(	PUNCT
ejpam-6441	356	4	ς1	ς1	NOUN
ejpam-6441	356	5	,	,	PUNCT
ejpam-6441	356	6	ς2	ς2	PROPN
ejpam-6441	356	7	)	)	PUNCT
ejpam-6441	356	8	∈	∈	PROPN
ejpam-6441	356	9	ℜ	ℜ	PROPN
ejpam-6441	356	10	:	:	PUNCT
ejpam-6441	356	11	ς1	ς1	NOUN
ejpam-6441	356	12	,	,	PUNCT
ejpam-6441	356	13	ς2	ς2	PROPN
ejpam-6441	356	14	∈	∈	PROPN
ejpam-6441	356	15	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	356	16	(	(	PUNCT
ejpam-6441	356	17	γ	γ	NOUN
ejpam-6441	356	18	)	)	PUNCT
ejpam-6441	356	19	}	}	PUNCT
ejpam-6441	356	20	,	,	PUNCT
ejpam-6441	356	21	we	we	PRON
ejpam-6441	356	22	have	have	VERB
ejpam-6441	356	23	τ	τ	PROPN
ejpam-6441	357	1	+	+	NUM
ejpam-6441	357	2	f	f	X
ejpam-6441	357	3	(	(	PUNCT
ejpam-6441	357	4	d(γς1,γς2	d(γς1,γς2	PROPN
ejpam-6441	357	5	)	)	PUNCT
ejpam-6441	357	6	)	)	PUNCT
ejpam-6441	357	7	≤	≤	NUM
ejpam-6441	357	8	f	f	X
ejpam-6441	357	9	(	(	PUNCT
ejpam-6441	357	10	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	357	11	,	,	PUNCT
ejpam-6441	357	12	ς2	ς2	PROPN
ejpam-6441	357	13	)	)	PUNCT
ejpam-6441	357	14	)	)	PUNCT
ejpam-6441	358	1	+	+	CCONJ
ejpam-6441	358	2	ld	ld	PROPN
ejpam-6441	358	3	(	(	PUNCT
ejpam-6441	358	4	ς2,γς1	ς2,γς1	NUM
ejpam-6441	358	5	)	)	PUNCT
ejpam-6441	358	6	,	,	PUNCT
ejpam-6441	358	7	(	(	PUNCT
ejpam-6441	358	8	29	29	NUM
ejpam-6441	358	9	)	)	PUNCT
ejpam-6441	358	10	where	where	SCONJ
ejpam-6441	358	11	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	358	12	,	,	PUNCT
ejpam-6441	358	13	ς2	ς2	PROPN
ejpam-6441	358	14	)	)	PUNCT
ejpam-6441	358	15	is	be	AUX
ejpam-6441	358	16	defined	define	VERB
ejpam-6441	358	17	as	as	ADP
ejpam-6441	358	18	in	in	ADP
ejpam-6441	358	19	(	(	PUNCT
ejpam-6441	358	20	2	2	NUM
ejpam-6441	358	21	)	)	PUNCT
ejpam-6441	358	22	.	.	PUNCT
ejpam-6441	359	1	m.	m.	NOUN
ejpam-6441	359	2	mudhesh	mudhesh	PROPN
ejpam-6441	359	3	et	et	PROPN
ejpam-6441	359	4	al	al	PROPN
ejpam-6441	359	5	.	.	PUNCT
ejpam-6441	359	6	/	/	SYM
ejpam-6441	359	7	eur	eur	PROPN
ejpam-6441	359	8	.	.	PUNCT
ejpam-6441	360	1	j.	j.	PROPN
ejpam-6441	360	2	pure	pure	PROPN
ejpam-6441	360	3	appl	appl	PROPN
ejpam-6441	360	4	.	.	PROPN
ejpam-6441	360	5	math	math	PROPN
ejpam-6441	360	6	,	,	PUNCT
ejpam-6441	360	7	18	18	NUM
ejpam-6441	360	8	(	(	PUNCT
ejpam-6441	360	9	4	4	NUM
ejpam-6441	360	10	)	)	PUNCT
ejpam-6441	360	11	(	(	PUNCT
ejpam-6441	360	12	2025	2025	NUM
ejpam-6441	360	13	)	)	PUNCT
ejpam-6441	360	14	,	,	PUNCT
ejpam-6441	360	15	6441	6441	NUM
ejpam-6441	360	16	16	16	NUM
ejpam-6441	360	17	of	of	ADP
ejpam-6441	360	18	21	21	NUM
ejpam-6441	360	19	hence	hence	ADV
ejpam-6441	360	20	,	,	PUNCT
ejpam-6441	360	21	γ	γ	PROPN
ejpam-6441	360	22	has	have	VERB
ejpam-6441	360	23	an	an	DET
ejpam-6441	360	24	fp	fp	NOUN
ejpam-6441	360	25	in	in	ADP
ejpam-6441	360	26	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	360	27	corollary	corollary	ADJ
ejpam-6441	360	28	4	4	NUM
ejpam-6441	360	29	.	.	PUNCT
ejpam-6441	361	1	let	let	AUX
ejpam-6441	361	2	(	(	PUNCT
ejpam-6441	361	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	361	4	,	,	PUNCT
ejpam-6441	361	5	d	d	NOUN
ejpam-6441	361	6	)	)	PUNCT
ejpam-6441	361	7	be	be	AUX
ejpam-6441	361	8	a	a	DET
ejpam-6441	361	9	ms	ms	PROPN
ejpam-6441	361	10	.	.	PROPN
ejpam-6441	362	1	a	a	DET
ejpam-6441	362	2	map	map	NOUN
ejpam-6441	362	3	γ	γ	X
ejpam-6441	362	4	:	:	PUNCT
ejpam-6441	362	5	∆ℜ	∆ℜ	PROPN
ejpam-6441	362	6	→	→	SYM
ejpam-6441	362	7	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	362	8	)	)	PUNCT
ejpam-6441	362	9	is	be	AUX
ejpam-6441	362	10	called	call	VERB
ejpam-6441	362	11	an	an	DET
ejpam-6441	362	12	almost	almost	ADV
ejpam-6441	362	13	multivalued	multivalue	VERB
ejpam-6441	362	14	f	f	PROPN
ejpam-6441	362	15	-contraction	-contraction	PROPN
ejpam-6441	362	16	endowed	endow	VERB
ejpam-6441	362	17	with	with	ADP
ejpam-6441	362	18	a	a	DET
ejpam-6441	362	19	γ	γ	NOUN
ejpam-6441	362	20	-	-	ADJ
ejpam-6441	362	21	transitive	transitive	ADJ
ejpam-6441	362	22	binary	binary	ADJ
ejpam-6441	362	23	relation	relation	PROPN
ejpam-6441	362	24	ℜ	ℜ	PROPN
ejpam-6441	362	25	,	,	PUNCT
ejpam-6441	362	26	if	if	SCONJ
ejpam-6441	362	27	there	there	PRON
ejpam-6441	362	28	exist	exist	VERB
ejpam-6441	362	29	τ	τ	PROPN
ejpam-6441	362	30	∈	∈	PROPN
ejpam-6441	362	31	r+	r+	NOUN
ejpam-6441	362	32	,	,	PUNCT
ejpam-6441	362	33	f	f	PROPN
ejpam-6441	362	34	∈	∈	PROPN
ejpam-6441	362	35	∆w	∆w	PROPN
ejpam-6441	362	36	and	and	CCONJ
ejpam-6441	362	37	λ	λ	PROPN
ejpam-6441	362	38	,	,	PUNCT
ejpam-6441	362	39	l	l	NOUN
ejpam-6441	362	40	≥	≥	NOUN
ejpam-6441	362	41	0	0	NUM
ejpam-6441	362	42	with	with	ADP
ejpam-6441	362	43	λ	λ	PROPN
ejpam-6441	362	44	+	+	CCONJ
ejpam-6441	362	45	l	l	NOUN
ejpam-6441	362	46	≤	≤	NUM
ejpam-6441	362	47	1	1	NUM
ejpam-6441	362	48	such	such	ADJ
ejpam-6441	362	49	that	that	PRON
ejpam-6441	362	50	for	for	ADP
ejpam-6441	362	51	all	all	PRON
ejpam-6441	362	52	(	(	PUNCT
ejpam-6441	362	53	ς1	ς1	NOUN
ejpam-6441	362	54	,	,	PUNCT
ejpam-6441	362	55	ς2	ς2	PROPN
ejpam-6441	362	56	)	)	PUNCT
ejpam-6441	362	57	∈	∈	PROPN
ejpam-6441	362	58	ℜ∗	ℜ∗	PROPN
ejpam-6441	363	1	=	=	PRON
ejpam-6441	363	2	{	{	PUNCT
ejpam-6441	363	3	(	(	PUNCT
ejpam-6441	363	4	ς1	ς1	NOUN
ejpam-6441	363	5	,	,	PUNCT
ejpam-6441	363	6	ς2	ς2	PROPN
ejpam-6441	363	7	)	)	PUNCT
ejpam-6441	363	8	∈	∈	PROPN
ejpam-6441	363	9	ℜ	ℜ	PROPN
ejpam-6441	363	10	:	:	PUNCT
ejpam-6441	363	11	ς1	ς1	NOUN
ejpam-6441	363	12	,	,	PUNCT
ejpam-6441	363	13	ς2	ς2	PROPN
ejpam-6441	363	14	∈	∈	PROPN
ejpam-6441	363	15	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	363	16	(	(	PUNCT
ejpam-6441	363	17	γ	γ	NOUN
ejpam-6441	363	18	)	)	PUNCT
ejpam-6441	363	19	}	}	PUNCT
ejpam-6441	363	20	,	,	PUNCT
ejpam-6441	363	21	we	we	PRON
ejpam-6441	363	22	have	have	VERB
ejpam-6441	363	23	τ	τ	PROPN
ejpam-6441	364	1	+	+	NUM
ejpam-6441	364	2	f	f	X
ejpam-6441	364	3	(	(	PUNCT
ejpam-6441	364	4	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	364	5	)	)	PUNCT
ejpam-6441	364	6	)	)	PUNCT
ejpam-6441	364	7	≤	≤	NUM
ejpam-6441	364	8	f	f	X
ejpam-6441	364	9	(	(	PUNCT
ejpam-6441	364	10	λd(ς1	λd(ς1	NOUN
ejpam-6441	364	11	,	,	PUNCT
ejpam-6441	364	12	ς2	ς2	PROPN
ejpam-6441	364	13	)	)	PUNCT
ejpam-6441	364	14	)	)	PUNCT
ejpam-6441	365	1	+	+	CCONJ
ejpam-6441	365	2	ld	ld	PROPN
ejpam-6441	365	3	(	(	PUNCT
ejpam-6441	365	4	ς1	ς1	NOUN
ejpam-6441	365	5	,	,	PUNCT
ejpam-6441	365	6	ς2	ς2	PROPN
ejpam-6441	365	7	)	)	PUNCT
ejpam-6441	365	8	.	.	PUNCT
ejpam-6441	366	1	(	(	PUNCT
ejpam-6441	366	2	30	30	NUM
ejpam-6441	366	3	)	)	PUNCT
ejpam-6441	366	4	then	then	ADV
ejpam-6441	366	5	,	,	PUNCT
ejpam-6441	366	6	γ	γ	PROPN
ejpam-6441	366	7	has	have	VERB
ejpam-6441	366	8	an	an	DET
ejpam-6441	366	9	fp	fp	NOUN
ejpam-6441	366	10	in	in	ADP
ejpam-6441	366	11	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	366	12	corollary	corollary	NOUN
ejpam-6441	366	13	5	5	NUM
ejpam-6441	366	14	.	.	PUNCT
ejpam-6441	367	1	let	let	AUX
ejpam-6441	367	2	(	(	PUNCT
ejpam-6441	367	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	367	4	,	,	PUNCT
ejpam-6441	367	5	d	d	NOUN
ejpam-6441	367	6	)	)	PUNCT
ejpam-6441	367	7	be	be	AUX
ejpam-6441	367	8	a	a	DET
ejpam-6441	367	9	ms	ms	PROPN
ejpam-6441	367	10	.	.	PROPN
ejpam-6441	368	1	a	a	DET
ejpam-6441	368	2	map	map	NOUN
ejpam-6441	368	3	γ	γ	X
ejpam-6441	368	4	:	:	PUNCT
ejpam-6441	368	5	∆ℜ	∆ℜ	X
ejpam-6441	368	6	→	→	SYM
ejpam-6441	368	7	∆ℜ	∆ℜ	PROPN
ejpam-6441	368	8	is	be	AUX
ejpam-6441	368	9	called	call	VERB
ejpam-6441	368	10	fisher	fisher	NOUN
ejpam-6441	368	11	-	-	PUNCT
ejpam-6441	368	12	type	type	NOUN
ejpam-6441	368	13	f	f	PROPN
ejpam-6441	368	14	contraction	contraction	NOUN
ejpam-6441	368	15	,	,	PUNCT
ejpam-6441	368	16	if	if	SCONJ
ejpam-6441	368	17	there	there	PRON
ejpam-6441	368	18	exist	exist	VERB
ejpam-6441	368	19	τ	τ	PROPN
ejpam-6441	368	20	∈	∈	PROPN
ejpam-6441	368	21	r+	r+	NOUN
ejpam-6441	368	22	,	,	PUNCT
ejpam-6441	368	23	f	f	PROPN
ejpam-6441	368	24	∈	∈	PROPN
ejpam-6441	368	25	∆w	∆w	PROPN
ejpam-6441	368	26	and	and	CCONJ
ejpam-6441	368	27	λ1	λ1	PROPN
ejpam-6441	368	28	,	,	PUNCT
ejpam-6441	368	29	λ2	λ2	NOUN
ejpam-6441	368	30	≥	≥	NOUN
ejpam-6441	368	31	0	0	NUM
ejpam-6441	368	32	with	with	ADP
ejpam-6441	368	33	λ1	λ1	PROPN
ejpam-6441	368	34	+	+	CCONJ
ejpam-6441	368	35	λ2	λ2	NOUN
ejpam-6441	368	36	≤	≤	NUM
ejpam-6441	368	37	1	1	NUM
ejpam-6441	368	38	such	such	ADJ
ejpam-6441	368	39	that	that	PRON
ejpam-6441	368	40	for	for	ADP
ejpam-6441	368	41	all	all	DET
ejpam-6441	368	42	ς1	ς1	NOUN
ejpam-6441	368	43	,	,	PUNCT
ejpam-6441	368	44	ς2	ς2	PROPN
ejpam-6441	368	45	∈	∈	PROPN
ejpam-6441	368	46	∆ℜ\fix	∆ℜ\fix	PROPN
ejpam-6441	368	47	(	(	PUNCT
ejpam-6441	368	48	γ	γ	PROPN
ejpam-6441	368	49	)	)	PUNCT
ejpam-6441	368	50	,	,	PUNCT
ejpam-6441	368	51	we	we	PRON
ejpam-6441	368	52	have	have	VERB
ejpam-6441	368	53	τ	τ	PROPN
ejpam-6441	369	1	+	+	NUM
ejpam-6441	369	2	f	f	X
ejpam-6441	369	3	(	(	PUNCT
ejpam-6441	369	4	d(γς1,γς2	d(γς1,γς2	PROPN
ejpam-6441	369	5	)	)	PUNCT
ejpam-6441	369	6	)	)	PUNCT
ejpam-6441	369	7	≤	≤	NUM
ejpam-6441	369	8	f	f	X
ejpam-6441	369	9	(	(	PUNCT
ejpam-6441	369	10	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	369	11	,	,	PUNCT
ejpam-6441	369	12	ς2	ς2	PROPN
ejpam-6441	369	13	)	)	PUNCT
ejpam-6441	369	14	)	)	PUNCT
ejpam-6441	369	15	,	,	PUNCT
ejpam-6441	369	16	where	where	SCONJ
ejpam-6441	369	17	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	369	18	,	,	PUNCT
ejpam-6441	369	19	ς2	ς2	PROPN
ejpam-6441	369	20	)	)	PUNCT
ejpam-6441	369	21	=	=	SYM
ejpam-6441	370	1			PROPN
ejpam-6441	370	2	[	[	PUNCT
ejpam-6441	370	3	λ1	λ1	PROPN
ejpam-6441	370	4	(	(	PUNCT
ejpam-6441	370	5	d(ς1,γς1)d(ς2,γς2	d(ς1,γς1)d(ς2,γς2	PROPN
ejpam-6441	370	6	)	)	PUNCT
ejpam-6441	370	7	1+d(ς1,ς2	1+d(ς1,ς2	NUM
ejpam-6441	370	8	)	)	PUNCT
ejpam-6441	370	9	)	)	PUNCT
ejpam-6441	371	1	β	β	X
ejpam-6441	372	1	+	+	NUM
ejpam-6441	372	2	λ2	λ2	NOUN
ejpam-6441	372	3	(	(	PUNCT
ejpam-6441	372	4	d(ς1	d(ς1	NOUN
ejpam-6441	372	5	,	,	PUNCT
ejpam-6441	372	6	ς2	ς2	PROPN
ejpam-6441	372	7	)	)	PUNCT
ejpam-6441	372	8	)	)	PUNCT
ejpam-6441	372	9	β	β	X
ejpam-6441	372	10	]	]	PUNCT
ejpam-6441	372	11	1	1	NUM
ejpam-6441	372	12	β	β	NOUN
ejpam-6441	372	13	if	if	SCONJ
ejpam-6441	372	14	β	β	X
ejpam-6441	372	15	>	>	X
ejpam-6441	372	16	0	0	NUM
ejpam-6441	372	17	;	;	PUNCT
ejpam-6441	372	18	(	(	PUNCT
ejpam-6441	372	19	d	d	X
ejpam-6441	372	20	(	(	PUNCT
ejpam-6441	372	21	ς1,γς1	ς1,γς1	NOUN
ejpam-6441	372	22	)	)	PUNCT
ejpam-6441	372	23	)	)	PUNCT
ejpam-6441	373	1	λ1	λ1	PROPN
ejpam-6441	373	2	(	(	PUNCT
ejpam-6441	373	3	d	d	PROPN
ejpam-6441	373	4	(	(	PUNCT
ejpam-6441	373	5	ς2,γς2	ς2,γς2	NUM
ejpam-6441	373	6	)	)	PUNCT
ejpam-6441	373	7	)	)	PUNCT
ejpam-6441	374	1	λ2	λ2	NOUN
ejpam-6441	374	2	if	if	SCONJ
ejpam-6441	374	3	β	β	X
ejpam-6441	374	4	=	=	NOUN
ejpam-6441	374	5	0	0	X
ejpam-6441	374	6	.	.	PUNCT
ejpam-6441	375	1	hence	hence	ADV
ejpam-6441	375	2	,	,	PUNCT
ejpam-6441	375	3	γ	γ	PROPN
ejpam-6441	375	4	has	have	VERB
ejpam-6441	375	5	an	an	DET
ejpam-6441	375	6	fp	fp	NOUN
ejpam-6441	375	7	in	in	ADP
ejpam-6441	375	8	∆ℜ.	∆ℜ.	PROPN
ejpam-6441	375	9	4	4	NUM
ejpam-6441	375	10	.	.	PUNCT
ejpam-6441	376	1	an	an	DET
ejpam-6441	376	2	application	application	NOUN
ejpam-6441	376	3	to	to	ADP
ejpam-6441	376	4	second	second	ADJ
ejpam-6441	376	5	-	-	PUNCT
ejpam-6441	376	6	order	order	NOUN
ejpam-6441	376	7	differential	differential	ADJ
ejpam-6441	376	8	inclusions	inclusion	NOUN
ejpam-6441	376	9	in	in	ADP
ejpam-6441	376	10	this	this	DET
ejpam-6441	376	11	section	section	NOUN
ejpam-6441	376	12	,	,	PUNCT
ejpam-6441	376	13	we	we	PRON
ejpam-6441	376	14	apply	apply	VERB
ejpam-6441	376	15	the	the	DET
ejpam-6441	376	16	previous	previous	ADJ
ejpam-6441	376	17	theoretical	theoretical	ADJ
ejpam-6441	376	18	results	result	NOUN
ejpam-6441	376	19	to	to	PART
ejpam-6441	376	20	study	study	VERB
ejpam-6441	376	21	the	the	DET
ejpam-6441	376	22	existence	existence	NOUN
ejpam-6441	376	23	of	of	ADP
ejpam-6441	376	24	solutions	solution	NOUN
ejpam-6441	376	25	for	for	ADP
ejpam-6441	376	26	the	the	DET
ejpam-6441	376	27	following	follow	VERB
ejpam-6441	376	28	sodi	sodi	NOUN
ejpam-6441	376	29	.	.	PUNCT
ejpam-6441	377	1	in	in	ADP
ejpam-6441	377	2	line	line	NOUN
ejpam-6441	377	3	with	with	ADP
ejpam-6441	377	4	[	[	X
ejpam-6441	377	5	28–31	28–31	NUM
ejpam-6441	377	6	]	]	PUNCT
ejpam-6441	377	7	,	,	PUNCT
ejpam-6441	377	8	we	we	PRON
ejpam-6441	377	9	consider	consider	VERB
ejpam-6441	377	10	the	the	DET
ejpam-6441	377	11	boundary	boundary	ADJ
ejpam-6441	377	12	value	value	NOUN
ejpam-6441	377	13	problem	problem	NOUN
ejpam-6441	377	14	(	(	PUNCT
ejpam-6441	377	15	bvp	bvp	NOUN
ejpam-6441	377	16	)	)	PUNCT
ejpam-6441	377	17	on	on	ADP
ejpam-6441	377	18	[	[	X
ejpam-6441	377	19	0	0	NUM
ejpam-6441	377	20	,	,	PUNCT
ejpam-6441	377	21	1	1	NUM
ejpam-6441	377	22	]	]	NUM
ejpam-6441	377	23	:	:	PUNCT
ejpam-6441	377	24	{	{	PUNCT
ejpam-6441	377	25	ς	ς	PROPN
ejpam-6441	377	26	′′(t	′′(t	PROPN
ejpam-6441	377	27	)	)	PUNCT
ejpam-6441	377	28	∈	∈	PROPN
ejpam-6441	377	29	π(t	π(t	PROPN
ejpam-6441	377	30	,	,	PUNCT
ejpam-6441	377	31	ς(t	ς(t	PROPN
ejpam-6441	377	32	)	)	PUNCT
ejpam-6441	377	33	,	,	PUNCT
ejpam-6441	377	34	ς	ς	PROPN
ejpam-6441	377	35	′(t	′(t	NOUN
ejpam-6441	377	36	)	)	PUNCT
ejpam-6441	377	37	)	)	PUNCT
ejpam-6441	377	38	,	,	PUNCT
ejpam-6441	377	39	t	t	PROPN
ejpam-6441	377	40	∈	∈	PROPN
ejpam-6441	378	1	[	[	X
ejpam-6441	378	2	0	0	NUM
ejpam-6441	378	3	,	,	PUNCT
ejpam-6441	378	4	1	1	NUM
ejpam-6441	378	5	]	]	PUNCT
ejpam-6441	378	6	,	,	PUNCT
ejpam-6441	378	7	ς(0	ς(0	PROPN
ejpam-6441	378	8	)	)	PUNCT
ejpam-6441	378	9	=	=	SYM
ejpam-6441	378	10	0	0	NUM
ejpam-6441	378	11	,	,	PUNCT
ejpam-6441	378	12	ς(1	ς(1	NOUN
ejpam-6441	378	13	)	)	PUNCT
ejpam-6441	378	14	=	=	SYM
ejpam-6441	378	15	0	0	NUM
ejpam-6441	378	16	,	,	PUNCT
ejpam-6441	378	17	(	(	PUNCT
ejpam-6441	378	18	31	31	NUM
ejpam-6441	378	19	)	)	PUNCT
ejpam-6441	378	20	where	where	SCONJ
ejpam-6441	378	21	π	π	NOUN
ejpam-6441	378	22	:	:	PUNCT
ejpam-6441	379	1	[	[	X
ejpam-6441	379	2	0	0	NUM
ejpam-6441	379	3	,	,	PUNCT
ejpam-6441	379	4	1	1	NUM
ejpam-6441	379	5	]	]	SYM
ejpam-6441	379	6	×	×	NOUN
ejpam-6441	379	7	r2	r2	PROPN
ejpam-6441	379	8	→	→	SYM
ejpam-6441	379	9	cb(r	cb(r	PROPN
ejpam-6441	379	10	)	)	PUNCT
ejpam-6441	379	11	has	have	AUX
ejpam-6441	379	12	nonempty	nonempty	X
ejpam-6441	379	13	,	,	PUNCT
ejpam-6441	379	14	closed	closed	ADJ
ejpam-6441	379	15	and	and	CCONJ
ejpam-6441	379	16	compact	compact	ADJ
ejpam-6441	379	17	values	value	NOUN
ejpam-6441	379	18	and	and	CCONJ
ejpam-6441	379	19	satisfies	satisfy	VERB
ejpam-6441	379	20	measurability	measurability	NOUN
ejpam-6441	379	21	hypotheses	hypothesis	NOUN
ejpam-6441	379	22	to	to	PART
ejpam-6441	379	23	ensure	ensure	VERB
ejpam-6441	379	24	selections	selection	NOUN
ejpam-6441	379	25	.	.	PUNCT
ejpam-6441	380	1	let	let	VERB
ejpam-6441	380	2	∆ℜ	∆ℜ	NOUN
ejpam-6441	380	3	=	=	SYM
ejpam-6441	380	4	c1([0	c1([0	NOUN
ejpam-6441	380	5	,	,	PUNCT
ejpam-6441	380	6	1],r	1],r	NUM
ejpam-6441	380	7	)	)	PUNCT
ejpam-6441	380	8	with	with	ADP
ejpam-6441	380	9	norm	norm	NOUN
ejpam-6441	380	10	∥ς∥	∥ς∥	NOUN
ejpam-6441	380	11	=	=	SYM
ejpam-6441	380	12	supt	supt	PROPN
ejpam-6441	380	13	|ς(t)|+	|ς(t)|+	VERB
ejpam-6441	380	14	supt	supt	ADJ
ejpam-6441	380	15	|ς	|ς	PROPN
ejpam-6441	381	1	′(t)|	′(t)|	NOUN
ejpam-6441	381	2	and	and	CCONJ
ejpam-6441	381	3	metric	metric	ADJ
ejpam-6441	381	4	d(ς1	d(ς1	NOUN
ejpam-6441	381	5	,	,	PUNCT
ejpam-6441	381	6	ς2	ς2	PROPN
ejpam-6441	381	7	)	)	PUNCT
ejpam-6441	381	8	=	=	PRON
ejpam-6441	381	9	∥ς1	∥ς1	VERB
ejpam-6441	381	10	−	−	PROPN
ejpam-6441	381	11	ς2∥.	ς2∥.	PROPN
ejpam-6441	381	12	denote	denote	NOUN
ejpam-6441	381	13	by	by	ADP
ejpam-6441	381	14	g(t	g(t	PROPN
ejpam-6441	381	15	,	,	PUNCT
ejpam-6441	381	16	s	s	PART
ejpam-6441	381	17	)	)	PUNCT
ejpam-6441	381	18	the	the	DET
ejpam-6441	381	19	green	green	ADJ
ejpam-6441	381	20	function	function	NOUN
ejpam-6441	381	21	for	for	ADP
ejpam-6441	381	22	the	the	DET
ejpam-6441	381	23	homogeneous	homogeneous	ADJ
ejpam-6441	381	24	dirichlet	dirichlet	PROPN
ejpam-6441	381	25	problem	problem	NOUN
ejpam-6441	381	26	:	:	PUNCT
ejpam-6441	382	1	g(t	g(t	PROPN
ejpam-6441	382	2	,	,	PUNCT
ejpam-6441	382	3	s	s	PART
ejpam-6441	382	4	)	)	PUNCT
ejpam-6441	382	5	=	=	SYM
ejpam-6441	382	6	{	{	PUNCT
ejpam-6441	382	7	t(1−	t(1−	PROPN
ejpam-6441	382	8	s	s	PART
ejpam-6441	382	9	)	)	PUNCT
ejpam-6441	382	10	,	,	PUNCT
ejpam-6441	382	11	t	t	VERB
ejpam-6441	382	12	≤	≤	PROPN
ejpam-6441	382	13	s	s	PROPN
ejpam-6441	382	14	,	,	PUNCT
ejpam-6441	382	15	s(1−	s(1−	PROPN
ejpam-6441	382	16	t	t	PROPN
ejpam-6441	382	17	)	)	PUNCT
ejpam-6441	382	18	,	,	PUNCT
ejpam-6441	382	19	t	t	PROPN
ejpam-6441	382	20	>	>	X
ejpam-6441	382	21	s.	s.	PROPN
ejpam-6441	382	22	define	define	VERB
ejpam-6441	382	23	the	the	DET
ejpam-6441	382	24	multivalued	multivalue	VERB
ejpam-6441	382	25	operator	operator	NOUN
ejpam-6441	382	26	γ	γ	NOUN
ejpam-6441	382	27	:	:	PUNCT
ejpam-6441	382	28	∆ℜ	∆ℜ	PROPN
ejpam-6441	382	29	→	→	SYM
ejpam-6441	382	30	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	382	31	)	)	PUNCT
ejpam-6441	382	32	by	by	ADP
ejpam-6441	382	33	γ(ς	γ(ς	NOUN
ejpam-6441	382	34	)	)	PUNCT
ejpam-6441	383	1	=	=	PRON
ejpam-6441	383	2	{	{	PUNCT
ejpam-6441	383	3	υ	υ	PROPN
ejpam-6441	383	4	∈	∈	PROPN
ejpam-6441	383	5	c1([0	c1([0	PROPN
ejpam-6441	383	6	,	,	PUNCT
ejpam-6441	383	7	1	1	NUM
ejpam-6441	383	8	]	]	PUNCT
ejpam-6441	383	9	)	)	PUNCT
ejpam-6441	383	10	:	:	PUNCT
ejpam-6441	383	11	υ(t	υ(t	NOUN
ejpam-6441	383	12	)	)	PUNCT
ejpam-6441	383	13	=	=	SYM
ejpam-6441	384	1	∫	∫	PROPN
ejpam-6441	384	2	1	1	NUM
ejpam-6441	384	3	0	0	NUM
ejpam-6441	384	4	g(t	g(t	PROPN
ejpam-6441	384	5	,	,	PUNCT
ejpam-6441	384	6	s)f(s	s)f(	NOUN
ejpam-6441	384	7	)	)	PUNCT
ejpam-6441	384	8	ds	ds	NOUN
ejpam-6441	384	9	,	,	PUNCT
ejpam-6441	384	10	f(s	f(s	ADV
ejpam-6441	384	11	)	)	PUNCT
ejpam-6441	384	12	∈	∈	PROPN
ejpam-6441	384	13	π(s	π(s	PROPN
ejpam-6441	384	14	,	,	PUNCT
ejpam-6441	384	15	ς(s	ς(s	PROPN
ejpam-6441	384	16	)	)	PUNCT
ejpam-6441	384	17	,	,	PUNCT
ejpam-6441	384	18	ς	ς	PROPN
ejpam-6441	384	19	′(s	′(s	NOUN
ejpam-6441	384	20	)	)	PUNCT
ejpam-6441	384	21	)	)	PUNCT
ejpam-6441	384	22	}	}	PUNCT
ejpam-6441	384	23	}	}	PUNCT
ejpam-6441	384	24	.	.	PUNCT
ejpam-6441	385	1	(	(	PUNCT
ejpam-6441	385	2	32	32	NUM
ejpam-6441	385	3	)	)	PUNCT
ejpam-6441	385	4	m.	m.	NOUN
ejpam-6441	385	5	mudhesh	mudhesh	PROPN
ejpam-6441	385	6	et	et	PROPN
ejpam-6441	385	7	al	al	PROPN
ejpam-6441	385	8	.	.	PUNCT
ejpam-6441	385	9	/	/	SYM
ejpam-6441	385	10	eur	eur	PROPN
ejpam-6441	385	11	.	.	PUNCT
ejpam-6441	386	1	j.	j.	PROPN
ejpam-6441	386	2	pure	pure	PROPN
ejpam-6441	386	3	appl	appl	PROPN
ejpam-6441	386	4	.	.	PROPN
ejpam-6441	386	5	math	math	PROPN
ejpam-6441	386	6	,	,	PUNCT
ejpam-6441	386	7	18	18	NUM
ejpam-6441	386	8	(	(	PUNCT
ejpam-6441	386	9	4	4	NUM
ejpam-6441	386	10	)	)	PUNCT
ejpam-6441	386	11	(	(	PUNCT
ejpam-6441	386	12	2025	2025	NUM
ejpam-6441	386	13	)	)	PUNCT
ejpam-6441	386	14	,	,	PUNCT
ejpam-6441	386	15	6441	6441	NUM
ejpam-6441	386	16	17	17	NUM
ejpam-6441	386	17	of	of	ADP
ejpam-6441	386	18	21	21	NUM
ejpam-6441	386	19	a	a	DET
ejpam-6441	386	20	fixed	fix	VERB
ejpam-6441	386	21	point	point	NOUN
ejpam-6441	386	22	ς∗	ς∗	NOUN
ejpam-6441	386	23	∈	∈	PROPN
ejpam-6441	386	24	γς∗	γς∗	NOUN
ejpam-6441	386	25	is	be	AUX
ejpam-6441	386	26	a	a	DET
ejpam-6441	386	27	solution	solution	NOUN
ejpam-6441	386	28	of	of	ADP
ejpam-6441	386	29	(	(	PUNCT
ejpam-6441	386	30	31	31	NUM
ejpam-6441	386	31	)	)	PUNCT
ejpam-6441	386	32	.	.	PUNCT
ejpam-6441	387	1	compute	compute	NOUN
ejpam-6441	387	2	k	k	NOUN
ejpam-6441	388	1	=	=	PUNCT
ejpam-6441	388	2	sup	sup	NOUN
ejpam-6441	388	3	t∈[0,1	t∈[0,1	NOUN
ejpam-6441	388	4	]	]	PUNCT
ejpam-6441	388	5	∫	∫	PROPN
ejpam-6441	389	1	1	1	NUM
ejpam-6441	389	2	0	0	NUM
ejpam-6441	389	3	g(t	g(t	PROPN
ejpam-6441	389	4	,	,	PUNCT
ejpam-6441	389	5	s	s	X
ejpam-6441	389	6	)	)	PUNCT
ejpam-6441	389	7	ds	ds	NOUN
ejpam-6441	389	8	=	=	SYM
ejpam-6441	389	9	1	1	NUM
ejpam-6441	389	10	8	8	NUM
ejpam-6441	389	11	,	,	PUNCT
ejpam-6441	389	12	m	m	VERB
ejpam-6441	389	13	=	=	VERB
ejpam-6441	389	14	sup	sup	NOUN
ejpam-6441	389	15	t∈[0,1	t∈[0,1	NOUN
ejpam-6441	389	16	]	]	PUNCT
ejpam-6441	389	17	∫	∫	PROPN
ejpam-6441	389	18	1	1	NUM
ejpam-6441	389	19	0	0	NUM
ejpam-6441	389	20	∣∣∂tg(t	∣∣∂tg(t	NOUN
ejpam-6441	389	21	,	,	PUNCT
ejpam-6441	389	22	s)∣∣	s)∣∣	VERB
ejpam-6441	389	23	ds	ds	ADJ
ejpam-6441	389	24	=	=	SYM
ejpam-6441	389	25	1	1	NUM
ejpam-6441	389	26	2	2	NUM
ejpam-6441	389	27	,	,	PUNCT
ejpam-6441	389	28	so	so	SCONJ
ejpam-6441	389	29	k	k	PROPN
ejpam-6441	390	1	+	+	PROPN
ejpam-6441	390	2	m	m	VERB
ejpam-6441	390	3	≤	≤	NOUN
ejpam-6441	390	4	5/8	5/8	NUM
ejpam-6441	390	5	.	.	PUNCT
ejpam-6441	391	1	we	we	PRON
ejpam-6441	391	2	assume	assume	VERB
ejpam-6441	391	3	π	π	PROPN
ejpam-6441	391	4	satisfies	satisfy	VERB
ejpam-6441	391	5	the	the	DET
ejpam-6441	391	6	following	follow	VERB
ejpam-6441	391	7	pointwise	pointwise	NOUN
ejpam-6441	391	8	control	control	NOUN
ejpam-6441	391	9	:	:	PUNCT
ejpam-6441	391	10	(	(	PUNCT
ejpam-6441	391	11	p1	p1	NOUN
ejpam-6441	391	12	)	)	PUNCT
ejpam-6441	391	13	there	there	PRON
ejpam-6441	391	14	exist	exist	VERB
ejpam-6441	391	15	measurable	measurable	ADJ
ejpam-6441	391	16	functions	function	NOUN
ejpam-6441	391	17	a(s	a(	NOUN
ejpam-6441	391	18	)	)	PUNCT
ejpam-6441	391	19	,	,	PUNCT
ejpam-6441	391	20	b(s	b(	NOUN
ejpam-6441	391	21	)	)	PUNCT
ejpam-6441	391	22	≥	≥	NOUN
ejpam-6441	391	23	0	0	NUM
ejpam-6441	391	24	and	and	CCONJ
ejpam-6441	391	25	constants	constant	NOUN
ejpam-6441	391	26	λ1	λ1	ADJ
ejpam-6441	391	27	,	,	PUNCT
ejpam-6441	391	28	λ2	λ2	PROPN
ejpam-6441	391	29	≥	≥	NUM
ejpam-6441	391	30	0	0	NUM
ejpam-6441	391	31	,	,	PUNCT
ejpam-6441	392	1	0	0	NUM
ejpam-6441	392	2	≤	≤	NOUN
ejpam-6441	392	3	λ1	λ1	ADJ
ejpam-6441	392	4	+	+	NUM
ejpam-6441	392	5	λ2	λ2	NOUN
ejpam-6441	392	6	≤	≤	NUM
ejpam-6441	392	7	1	1	NUM
ejpam-6441	392	8	,	,	PUNCT
ejpam-6441	392	9	and	and	CCONJ
ejpam-6441	392	10	β	β	X
ejpam-6441	392	11	∈	∈	PROPN
ejpam-6441	392	12	(	(	PUNCT
ejpam-6441	392	13	0	0	NUM
ejpam-6441	392	14	,	,	PUNCT
ejpam-6441	392	15	1	1	NUM
ejpam-6441	392	16	]	]	PUNCT
ejpam-6441	392	17	such	such	ADJ
ejpam-6441	392	18	that	that	SCONJ
ejpam-6441	392	19	∀	∀	NOUN
ejpam-6441	392	20	s	s	PART
ejpam-6441	392	21	∈	∈	NOUN
ejpam-6441	393	1	[	[	X
ejpam-6441	393	2	0	0	NUM
ejpam-6441	393	3	,	,	PUNCT
ejpam-6441	393	4	1	1	NUM
ejpam-6441	393	5	]	]	PUNCT
ejpam-6441	393	6	and	and	CCONJ
ejpam-6441	393	7	all	all	DET
ejpam-6441	393	8	ui	ui	PROPN
ejpam-6441	393	9	∈	∈	PROPN
ejpam-6441	393	10	π(s	π(s	PROPN
ejpam-6441	393	11	,	,	PUNCT
ejpam-6441	393	12	ςi(s	ςi(s	NUM
ejpam-6441	393	13	)	)	PUNCT
ejpam-6441	393	14	,	,	PUNCT
ejpam-6441	393	15	ς	ς	PROPN
ejpam-6441	393	16	′	′	NUM
ejpam-6441	393	17	i(s	i(s	NOUN
ejpam-6441	393	18	)	)	PUNCT
ejpam-6441	393	19	)	)	PUNCT
ejpam-6441	393	20	(	(	PUNCT
ejpam-6441	393	21	for	for	ADP
ejpam-6441	393	22	i	i	PRON
ejpam-6441	393	23	=	=	SYM
ejpam-6441	393	24	1	1	NUM
ejpam-6441	393	25	,	,	PUNCT
ejpam-6441	393	26	2	2	NUM
ejpam-6441	393	27	)	)	PUNCT
ejpam-6441	393	28	,	,	PUNCT
ejpam-6441	393	29	one	one	PRON
ejpam-6441	393	30	has	have	VERB
ejpam-6441	393	31	|u1	|u1	VERB
ejpam-6441	393	32	−	−	PROPN
ejpam-6441	393	33	u2|β	u2|β	PROPN
ejpam-6441	393	34	≤	≤	PUNCT
ejpam-6441	393	35	a(s	a(s	PROPN
ejpam-6441	393	36	)	)	PUNCT
ejpam-6441	393	37	(	(	PUNCT
ejpam-6441	393	38	|ς1(s)−	|ς1(s)−	PROPN
ejpam-6441	393	39	ς2(s)|β	ς2(s)|β	X
ejpam-6441	394	1	+	+	CCONJ
ejpam-6441	394	2	|ς	|ς	PROPN
ejpam-6441	394	3	′1(s)−	′1(s)−	PROPN
ejpam-6441	394	4	ς	ς	PROPN
ejpam-6441	394	5	′2(s)|β	′2(s)|β	PROPN
ejpam-6441	394	6	)	)	PUNCT
ejpam-6441	395	1	+	+	NUM
ejpam-6441	395	2	b(s)ds(ς1	b(s)ds(ς1	NOUN
ejpam-6441	395	3	,	,	PUNCT
ejpam-6441	395	4	ς2	ς2	PROPN
ejpam-6441	395	5	)	)	PUNCT
ejpam-6441	395	6	,	,	PUNCT
ejpam-6441	395	7	(	(	PUNCT
ejpam-6441	395	8	33	33	NUM
ejpam-6441	395	9	)	)	PUNCT
ejpam-6441	395	10	where	where	SCONJ
ejpam-6441	395	11	ds(ς1	ds(ς1	NOUN
ejpam-6441	395	12	,	,	PUNCT
ejpam-6441	395	13	ς2	ς2	PROPN
ejpam-6441	395	14	)	)	PUNCT
ejpam-6441	395	15	stands	stand	VERB
ejpam-6441	395	16	for	for	ADP
ejpam-6441	395	17	combinations	combination	NOUN
ejpam-6441	395	18	of	of	ADP
ejpam-6441	395	19	pointwise	pointwise	NOUN
ejpam-6441	395	20	“	"	PUNCT
ejpam-6441	395	21	distances	distance	NOUN
ejpam-6441	395	22	-	-	PUNCT
ejpam-6441	395	23	to	to	ADP
ejpam-6441	395	24	-	-	PUNCT
ejpam-6441	395	25	value	value	NOUN
ejpam-6441	395	26	-	-	PUNCT
ejpam-6441	395	27	sets	set	NOUN
ejpam-6441	395	28	”	"	PUNCT
ejpam-6441	395	29	(	(	PUNCT
ejpam-6441	395	30	these	these	PRON
ejpam-6441	395	31	will	will	AUX
ejpam-6441	395	32	produce	produce	VERB
ejpam-6441	395	33	the	the	DET
ejpam-6441	395	34	d(·,γ(·))-type	d(·,γ(·))-type	ADJ
ejpam-6441	395	35	terms	term	NOUN
ejpam-6441	395	36	appearing	appear	VERB
ejpam-6441	395	37	in	in	ADP
ejpam-6441	395	38	(	(	PUNCT
ejpam-6441	395	39	2	2	NUM
ejpam-6441	395	40	)	)	PUNCT
ejpam-6441	395	41	)	)	PUNCT
ejpam-6441	395	42	.	.	PUNCT
ejpam-6441	396	1	this	this	PRON
ejpam-6441	396	2	is	be	AUX
ejpam-6441	396	3	an	an	DET
ejpam-6441	396	4	abstract	abstract	ADJ
ejpam-6441	396	5	but	but	CCONJ
ejpam-6441	396	6	standard	standard	ADJ
ejpam-6441	396	7	assumption	assumption	NOUN
ejpam-6441	396	8	,	,	PUNCT
ejpam-6441	396	9	it	it	PRON
ejpam-6441	396	10	generalizes	generalize	VERB
ejpam-6441	396	11	the	the	DET
ejpam-6441	396	12	hausdorff	hausdorff	NOUN
ejpam-6441	396	13	–	–	PUNCT
ejpam-6441	396	14	lipschitz	lipschitz	NOUN
ejpam-6441	396	15	condition	condition	NOUN
ejpam-6441	396	16	and	and	CCONJ
ejpam-6441	396	17	allows	allow	VERB
ejpam-6441	396	18	us	we	PRON
ejpam-6441	396	19	to	to	PART
ejpam-6441	396	20	produce	produce	VERB
ejpam-6441	396	21	the	the	DET
ejpam-6441	396	22	more	more	ADV
ejpam-6441	396	23	general	general	ADJ
ejpam-6441	396	24	mℜ-term	mℜ-term	NOUN
ejpam-6441	396	25	.	.	PUNCT
ejpam-6441	397	1	(	(	PUNCT
ejpam-6441	397	2	p2	p2	PROPN
ejpam-6441	397	3	)	)	PUNCT
ejpam-6441	397	4	fix	fix	NOUN
ejpam-6441	397	5	ς1	ς1	NOUN
ejpam-6441	397	6	,	,	PUNCT
ejpam-6441	397	7	ς2	ς2	PROPN
ejpam-6441	397	8	∈	∈	PROPN
ejpam-6441	397	9	∆ℜ.	∆ℜ.	NOUN
ejpam-6441	397	10	let	let	VERB
ejpam-6441	397	11	f	f	X
ejpam-6441	397	12	(	(	PUNCT
ejpam-6441	397	13	·	·	PUNCT
ejpam-6441	397	14	)	)	PUNCT
ejpam-6441	397	15	be	be	AUX
ejpam-6441	397	16	a	a	DET
ejpam-6441	397	17	measurable	measurable	ADJ
ejpam-6441	397	18	selection	selection	NOUN
ejpam-6441	397	19	from	from	ADP
ejpam-6441	397	20	π	π	PROPN
ejpam-6441	397	21	(	(	PUNCT
ejpam-6441	397	22	·	·	PUNCT
ejpam-6441	397	23	,	,	PUNCT
ejpam-6441	397	24	ς1	ς1	NOUN
ejpam-6441	397	25	(	(	PUNCT
ejpam-6441	397	26	·	·	PUNCT
ejpam-6441	397	27	)	)	PUNCT
ejpam-6441	397	28	,	,	PUNCT
ejpam-6441	397	29	ς	ς	PROPN
ejpam-6441	397	30	′1	′1	X
ejpam-6441	397	31	(	(	PUNCT
ejpam-6441	397	32	·	·	PUNCT
ejpam-6441	397	33	)	)	PUNCT
ejpam-6441	397	34	)	)	PUNCT
ejpam-6441	397	35	and	and	CCONJ
ejpam-6441	397	36	g	g	PROPN
ejpam-6441	397	37	(	(	PUNCT
ejpam-6441	397	38	·	·	PUNCT
ejpam-6441	397	39	)	)	PUNCT
ejpam-6441	397	40	from	from	ADP
ejpam-6441	397	41	π	π	PROPN
ejpam-6441	397	42	(	(	PUNCT
ejpam-6441	397	43	·	·	PUNCT
ejpam-6441	397	44	,	,	PUNCT
ejpam-6441	397	45	ς2	ς2	PROPN
ejpam-6441	397	46	(	(	PUNCT
ejpam-6441	397	47	·	·	PUNCT
ejpam-6441	397	48	)	)	PUNCT
ejpam-6441	397	49	,	,	PUNCT
ejpam-6441	397	50	ς	ς	PROPN
ejpam-6441	397	51	′2	′2	X
ejpam-6441	397	52	(	(	PUNCT
ejpam-6441	397	53	·	·	PUNCT
ejpam-6441	397	54	)	)	PUNCT
ejpam-6441	397	55	)	)	PUNCT
ejpam-6441	397	56	.	.	PUNCT
ejpam-6441	398	1	for	for	ADP
ejpam-6441	398	2	η	η	PROPN
ejpam-6441	398	3	=	=	PROPN
ejpam-6441	398	4	∫	∫	PROPN
ejpam-6441	398	5	g(t	g(t	PROPN
ejpam-6441	398	6	,	,	PUNCT
ejpam-6441	398	7	s)f(s	s)f(s	PROPN
ejpam-6441	398	8	)	)	PUNCT
ejpam-6441	398	9	∈	∈	PROPN
ejpam-6441	398	10	γ(ς1	γ(ς1	NOUN
ejpam-6441	398	11	)	)	PUNCT
ejpam-6441	398	12	and	and	CCONJ
ejpam-6441	398	13	ζ	ζ	NOUN
ejpam-6441	398	14	=	=	SYM
ejpam-6441	398	15	∫	∫	PROPN
ejpam-6441	398	16	g(t	g(t	PROPN
ejpam-6441	398	17	,	,	PUNCT
ejpam-6441	398	18	s)g(s	s)g(s	NOUN
ejpam-6441	398	19	)	)	PUNCT
ejpam-6441	398	20	∈	∈	PROPN
ejpam-6441	398	21	γ(ς2	γ(ς2	ADV
ejpam-6441	398	22	)	)	PUNCT
ejpam-6441	398	23	we	we	PRON
ejpam-6441	398	24	have	have	VERB
ejpam-6441	398	25	,	,	PUNCT
ejpam-6441	398	26	for	for	ADP
ejpam-6441	398	27	any	any	DET
ejpam-6441	398	28	t	t	PROPN
ejpam-6441	398	29	,	,	PUNCT
ejpam-6441	398	30	|η(t)−	|η(t)−	PROPN
ejpam-6441	398	31	ζ(t)|	ζ(t)|	PROPN
ejpam-6441	398	32	≤	≤	NUM
ejpam-6441	399	1	∫	∫	PROPN
ejpam-6441	399	2	1	1	NUM
ejpam-6441	399	3	0	0	NUM
ejpam-6441	399	4	g(t	g(t	PROPN
ejpam-6441	399	5	,	,	PUNCT
ejpam-6441	399	6	s	s	PART
ejpam-6441	399	7	)	)	PUNCT
ejpam-6441	399	8	|f(s)−	|f(s)−	NUM
ejpam-6441	399	9	g(s)|	g(s)|	PROPN
ejpam-6441	399	10	ds	ds	PROPN
ejpam-6441	399	11	.	.	PUNCT
ejpam-6441	400	1	(	(	PUNCT
ejpam-6441	400	2	34	34	NUM
ejpam-6441	400	3	)	)	PUNCT
ejpam-6441	400	4	theorem	theorem	VERB
ejpam-6441	400	5	6	6	NUM
ejpam-6441	400	6	.	.	PUNCT
ejpam-6441	401	1	under	under	ADP
ejpam-6441	401	2	the	the	DET
ejpam-6441	401	3	two	two	NUM
ejpam-6441	401	4	assumptions	assumption	NOUN
ejpam-6441	401	5	above	above	ADV
ejpam-6441	401	6	,	,	PUNCT
ejpam-6441	401	7	sodi	sodi	NOUN
ejpam-6441	401	8	(	(	PUNCT
ejpam-6441	401	9	31	31	NUM
ejpam-6441	401	10	)	)	PUNCT
ejpam-6441	401	11	has	have	VERB
ejpam-6441	401	12	at	at	ADV
ejpam-6441	401	13	least	least	ADV
ejpam-6441	401	14	one	one	NUM
ejpam-6441	401	15	solution	solution	NOUN
ejpam-6441	401	16	ς∗	ς∗	NOUN
ejpam-6441	401	17	∈	∈	PROPN
ejpam-6441	401	18	∆ℜ	∆ℜ	NOUN
ejpam-6441	401	19	iff	iff	PROPN
ejpam-6441	401	20	γ	γ	PROPN
ejpam-6441	401	21	has	have	VERB
ejpam-6441	401	22	an	an	DET
ejpam-6441	401	23	fp	fp	NOUN
ejpam-6441	401	24	.	.	NOUN
ejpam-6441	401	25	proof	proof	NOUN
ejpam-6441	401	26	.	.	PUNCT
ejpam-6441	402	1	the	the	DET
ejpam-6441	402	2	set	set	NOUN
ejpam-6441	402	3	∆ℜ	∆ℜ	NOUN
ejpam-6441	402	4	=	=	SYM
ejpam-6441	402	5	c1([0	c1([0	PROPN
ejpam-6441	402	6	,	,	PUNCT
ejpam-6441	402	7	1],r	1],r	NUM
ejpam-6441	402	8	)	)	PUNCT
ejpam-6441	402	9	is	be	AUX
ejpam-6441	402	10	a	a	DET
ejpam-6441	402	11	complete	complete	ADJ
ejpam-6441	402	12	ms	ms	PROPN
ejpam-6441	402	13	.	.	PROPN
ejpam-6441	402	14	define	define	VERB
ejpam-6441	402	15	the	the	DET
ejpam-6441	402	16	multivalued	multivalue	VERB
ejpam-6441	402	17	operator	operator	NOUN
ejpam-6441	402	18	γ	γ	NOUN
ejpam-6441	402	19	:	:	PUNCT
ejpam-6441	402	20	∆ℜ	∆ℜ	PROPN
ejpam-6441	402	21	→	→	SYM
ejpam-6441	402	22	cb(∆ℜ	cb(∆ℜ	PROPN
ejpam-6441	402	23	)	)	PUNCT
ejpam-6441	402	24	as	as	ADP
ejpam-6441	402	25	in	in	ADP
ejpam-6441	402	26	(	(	PUNCT
ejpam-6441	402	27	32	32	NUM
ejpam-6441	402	28	)	)	PUNCT
ejpam-6441	402	29	and	and	CCONJ
ejpam-6441	402	30	from	from	ADP
ejpam-6441	402	31	(	(	PUNCT
ejpam-6441	402	32	p2	p2	NOUN
ejpam-6441	402	33	)	)	PUNCT
ejpam-6441	402	34	,	,	PUNCT
ejpam-6441	402	35	we	we	PRON
ejpam-6441	402	36	raise	raise	VERB
ejpam-6441	402	37	to	to	ADP
ejpam-6441	402	38	the	the	DET
ejpam-6441	402	39	power	power	NOUN
ejpam-6441	402	40	β	β	X
ejpam-6441	402	41	∈	∈	PROPN
ejpam-6441	402	42	(	(	PUNCT
ejpam-6441	402	43	0	0	NUM
ejpam-6441	402	44	,	,	PUNCT
ejpam-6441	402	45	1	1	NUM
ejpam-6441	402	46	]	]	PUNCT
ejpam-6441	402	47	in	in	ADP
ejpam-6441	402	48	(	(	PUNCT
ejpam-6441	402	49	34	34	NUM
ejpam-6441	402	50	)	)	PUNCT
ejpam-6441	402	51	and	and	CCONJ
ejpam-6441	402	52	use	use	VERB
ejpam-6441	402	53	jensen	jensen	PROPN
ejpam-6441	402	54	(	(	PUNCT
ejpam-6441	402	55	or	or	CCONJ
ejpam-6441	402	56	generalized	generalized	ADJ
ejpam-6441	402	57	hölder	hölder	NOUN
ejpam-6441	402	58	)	)	PUNCT
ejpam-6441	402	59	to	to	PART
ejpam-6441	402	60	obtain	obtain	VERB
ejpam-6441	402	61	|η(t)−	|η(t)−	PROPN
ejpam-6441	402	62	ζ(t)|β	ζ(t)|β	PROPN
ejpam-6441	402	63	≤	≤	PROPN
ejpam-6441	402	64	∫	∫	PROPN
ejpam-6441	403	1	1	1	NUM
ejpam-6441	403	2	0	0	NUM
ejpam-6441	403	3	g(t	g(t	PROPN
ejpam-6441	403	4	,	,	PUNCT
ejpam-6441	403	5	s)β	s)β	PROPN
ejpam-6441	403	6	|f(s)−	|f(s)−	NUM
ejpam-6441	403	7	g(s)|β	g(s)|β	PROPN
ejpam-6441	403	8	ds	ds	PROPN
ejpam-6441	403	9	.	.	NOUN
ejpam-6441	403	10	taking	take	VERB
ejpam-6441	403	11	supremum	supremum	ADV
ejpam-6441	403	12	in	in	ADP
ejpam-6441	403	13	t	t	PROPN
ejpam-6441	403	14	and	and	CCONJ
ejpam-6441	403	15	using	use	VERB
ejpam-6441	403	16	c1	c1	PROPN
ejpam-6441	403	17	=	=	PROPN
ejpam-6441	403	18	supt	supt	PROPN
ejpam-6441	404	1	∫	∫	PROPN
ejpam-6441	404	2	1	1	NUM
ejpam-6441	404	3	0	0	NUM
ejpam-6441	404	4	g(t	g(t	PROPN
ejpam-6441	404	5	,	,	PUNCT
ejpam-6441	404	6	s	s	PART
ejpam-6441	404	7	)	)	PUNCT
ejpam-6441	404	8	βds	βds	PROPN
ejpam-6441	404	9	,	,	PUNCT
ejpam-6441	404	10	c2	c2	PROPN
ejpam-6441	404	11	=	=	PUNCT
ejpam-6441	404	12	supt	supt	PROPN
ejpam-6441	404	13	∫	∫	PROPN
ejpam-6441	404	14	1	1	NUM
ejpam-6441	404	15	0	0	NUM
ejpam-6441	404	16	|∂tg(t	|∂tg(t	NUM
ejpam-6441	404	17	,	,	PUNCT
ejpam-6441	404	18	s)|βds	s)|βds	PROPN
ejpam-6441	404	19	,	,	PUNCT
ejpam-6441	404	20	we	we	PRON
ejpam-6441	404	21	get	get	VERB
ejpam-6441	404	22	∥η	∥η	PROPN
ejpam-6441	404	23	−	−	PROPN
ejpam-6441	404	24	ζ∥β	ζ∥β	NOUN
ejpam-6441	404	25	≤	≤	PROPN
ejpam-6441	404	26	(	(	PUNCT
ejpam-6441	404	27	c1	c1	PROPN
ejpam-6441	404	28	+	+	CCONJ
ejpam-6441	404	29	c2	c2	PROPN
ejpam-6441	404	30	)	)	PUNCT
ejpam-6441	404	31	∫	∫	PROPN
ejpam-6441	404	32	1	1	NUM
ejpam-6441	404	33	0	0	NUM
ejpam-6441	404	34	|f(s)−	|f(s)−	NUM
ejpam-6441	404	35	g(s)|β	g(s)|β	PROPN
ejpam-6441	404	36	ds	ds	PROPN
ejpam-6441	404	37	.	.	PROPN
ejpam-6441	405	1	from	from	ADP
ejpam-6441	405	2	(	(	PUNCT
ejpam-6441	405	3	p2	p2	X
ejpam-6441	405	4	)	)	PUNCT
ejpam-6441	405	5	and	and	CCONJ
ejpam-6441	405	6	applying	apply	VERB
ejpam-6441	405	7	the	the	DET
ejpam-6441	405	8	structural	structural	ADJ
ejpam-6441	405	9	bound	bind	VERB
ejpam-6441	405	10	(	(	PUNCT
ejpam-6441	405	11	33	33	NUM
ejpam-6441	405	12	)	)	PUNCT
ejpam-6441	405	13	to	to	ADP
ejpam-6441	405	14	the	the	DET
ejpam-6441	405	15	integrand	integrand	NOUN
ejpam-6441	405	16	and	and	CCONJ
ejpam-6441	405	17	integrate(∫	integrate(∫	ADP
ejpam-6441	405	18	1	1	NUM
ejpam-6441	405	19	0	0	NUM
ejpam-6441	405	20	|f	|f	PROPN
ejpam-6441	405	21	−	−	PROPN
ejpam-6441	405	22	g|β	g|β	NOUN
ejpam-6441	405	23	)	)	PUNCT
ejpam-6441	405	24	1	1	NUM
ejpam-6441	405	25	/	/	SYM
ejpam-6441	405	26	β	β	X
ejpam-6441	405	27	≤	≤	NUM
ejpam-6441	405	28	ad(ς1	ad(ς1	NOUN
ejpam-6441	405	29	,	,	PUNCT
ejpam-6441	405	30	ς2	ς2	PROPN
ejpam-6441	405	31	)	)	PUNCT
ejpam-6441	406	1	+	+	NOUN
ejpam-6441	406	2	bmℜ(ς1	bmℜ(ς1	NOUN
ejpam-6441	406	3	,	,	PUNCT
ejpam-6441	406	4	ς2	ς2	PROPN
ejpam-6441	406	5	)	)	PUNCT
ejpam-6441	406	6	,	,	PUNCT
ejpam-6441	406	7	m.	m.	NOUN
ejpam-6441	406	8	mudhesh	mudhesh	PROPN
ejpam-6441	406	9	et	et	PROPN
ejpam-6441	406	10	al	al	PROPN
ejpam-6441	406	11	.	.	PUNCT
ejpam-6441	406	12	/	/	SYM
ejpam-6441	406	13	eur	eur	PROPN
ejpam-6441	406	14	.	.	PUNCT
ejpam-6441	407	1	j.	j.	PROPN
ejpam-6441	407	2	pure	pure	PROPN
ejpam-6441	407	3	appl	appl	PROPN
ejpam-6441	407	4	.	.	PROPN
ejpam-6441	407	5	math	math	PROPN
ejpam-6441	407	6	,	,	PUNCT
ejpam-6441	407	7	18	18	NUM
ejpam-6441	407	8	(	(	PUNCT
ejpam-6441	407	9	4	4	NUM
ejpam-6441	407	10	)	)	PUNCT
ejpam-6441	407	11	(	(	PUNCT
ejpam-6441	407	12	2025	2025	NUM
ejpam-6441	407	13	)	)	PUNCT
ejpam-6441	407	14	,	,	PUNCT
ejpam-6441	407	15	6441	6441	NUM
ejpam-6441	407	16	18	18	NUM
ejpam-6441	407	17	of	of	ADP
ejpam-6441	407	18	21	21	NUM
ejpam-6441	407	19	for	for	ADP
ejpam-6441	407	20	appropriate	appropriate	ADJ
ejpam-6441	407	21	constants	constant	NOUN
ejpam-6441	407	22	a	a	PRON
ejpam-6441	407	23	,	,	PUNCT
ejpam-6441	407	24	b	b	PROPN
ejpam-6441	407	25	≥	≥	NOUN
ejpam-6441	407	26	0	0	NUM
ejpam-6441	408	1	depending	depend	VERB
ejpam-6441	408	2	on	on	ADP
ejpam-6441	408	3	a	a	DET
ejpam-6441	408	4	(	(	PUNCT
ejpam-6441	408	5	·	·	PUNCT
ejpam-6441	408	6	)	)	PUNCT
ejpam-6441	408	7	,	,	PUNCT
ejpam-6441	408	8	b	b	X
ejpam-6441	408	9	(	(	PUNCT
ejpam-6441	408	10	·	·	PUNCT
ejpam-6441	408	11	)	)	PUNCT
ejpam-6441	408	12	,	,	PUNCT
ejpam-6441	408	13	c1	c1	PROPN
ejpam-6441	408	14	,	,	PUNCT
ejpam-6441	408	15	c2	c2	PROPN
ejpam-6441	408	16	,	,	PUNCT
ejpam-6441	408	17	wheremℜ(ς1	wheremℜ(ς1	NOUN
ejpam-6441	408	18	,	,	PUNCT
ejpam-6441	408	19	ς2	ς2	PROPN
ejpam-6441	408	20	)	)	PUNCT
ejpam-6441	408	21	denotes	denote	VERB
ejpam-6441	408	22	a	a	DET
ejpam-6441	408	23	combination	combination	NOUN
ejpam-6441	408	24	of	of	ADP
ejpam-6441	408	25	distances	distance	NOUN
ejpam-6441	408	26	-	-	PUNCT
ejpam-6441	408	27	to	to	ADP
ejpam-6441	408	28	-	-	PUNCT
ejpam-6441	408	29	value	value	NOUN
ejpam-6441	408	30	-	-	PUNCT
ejpam-6441	408	31	sets	set	NOUN
ejpam-6441	408	32	of	of	ADP
ejpam-6441	408	33	the	the	DET
ejpam-6441	408	34	type	type	NOUN
ejpam-6441	408	35	appearing	appear	VERB
ejpam-6441	408	36	in	in	ADP
ejpam-6441	408	37	(	(	PUNCT
ejpam-6441	408	38	2	2	NUM
ejpam-6441	408	39	)	)	PUNCT
ejpam-6441	408	40	.	.	PUNCT
ejpam-6441	409	1	concretely	concretely	ADV
ejpam-6441	409	2	one	one	PRON
ejpam-6441	409	3	may	may	AUX
ejpam-6441	409	4	choose	choose	VERB
ejpam-6441	409	5	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	409	6	,	,	PUNCT
ejpam-6441	409	7	ς2	ς2	PROPN
ejpam-6441	409	8	)	)	PUNCT
ejpam-6441	409	9	=	=	PUNCT
ejpam-6441	410	1	[	[	PUNCT
ejpam-6441	410	2	λ1	λ1	PROPN
ejpam-6441	410	3	(	(	PUNCT
ejpam-6441	410	4	d(ς1,γς1)d(ς2,γς2	d(ς1,γς1)d(ς2,γς2	PROPN
ejpam-6441	410	5	)	)	PUNCT
ejpam-6441	410	6	1	1	NUM
ejpam-6441	411	1	+	+	NOUN
ejpam-6441	411	2	d(ς1	d(ς1	NOUN
ejpam-6441	411	3	,	,	PUNCT
ejpam-6441	411	4	ς2	ς2	PROPN
ejpam-6441	411	5	)	)	PUNCT
ejpam-6441	411	6	)	)	PUNCT
ejpam-6441	412	1	β	β	X
ejpam-6441	413	1	+	+	NUM
ejpam-6441	413	2	λ2	λ2	NOUN
ejpam-6441	413	3	(	(	PUNCT
ejpam-6441	413	4	d(ς1	d(ς1	NOUN
ejpam-6441	413	5	,	,	PUNCT
ejpam-6441	413	6	ς2	ς2	PROPN
ejpam-6441	413	7	)	)	PUNCT
ejpam-6441	413	8	)	)	PUNCT
ejpam-6441	413	9	β]1	β]1	NUM
ejpam-6441	413	10	/	/	SYM
ejpam-6441	413	11	β	β	X
ejpam-6441	413	12	,	,	PUNCT
ejpam-6441	413	13	combining	combine	VERB
ejpam-6441	413	14	the	the	DET
ejpam-6441	413	15	previous	previous	ADJ
ejpam-6441	413	16	two	two	NUM
ejpam-6441	413	17	displayed	display	VERB
ejpam-6441	413	18	bounds	bound	NOUN
ejpam-6441	413	19	yields	yield	NOUN
ejpam-6441	413	20	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	413	21	)	)	PUNCT
ejpam-6441	413	22	≤	≤	PROPN
ejpam-6441	413	23	c1	c1	PROPN
ejpam-6441	413	24	/	/	SYM
ejpam-6441	413	25	β	β	PROPN
ejpam-6441	413	26	(	(	PUNCT
ejpam-6441	413	27	ad(ς1	ad(ς1	PROPN
ejpam-6441	413	28	,	,	PUNCT
ejpam-6441	413	29	ς2	ς2	PROPN
ejpam-6441	413	30	)	)	PUNCT
ejpam-6441	414	1	+	+	NOUN
ejpam-6441	414	2	bmℜ(ς1	bmℜ(ς1	NOUN
ejpam-6441	414	3	,	,	PUNCT
ejpam-6441	414	4	ς2	ς2	PROPN
ejpam-6441	414	5	)	)	PUNCT
ejpam-6441	414	6	)	)	PUNCT
ejpam-6441	415	1	,	,	PUNCT
ejpam-6441	415	2	where	where	SCONJ
ejpam-6441	415	3	c	c	NOUN
ejpam-6441	415	4	=	=	PROPN
ejpam-6441	415	5	c1	c1	PROPN
ejpam-6441	415	6	+	+	CCONJ
ejpam-6441	415	7	c2	c2	PROPN
ejpam-6441	415	8	.	.	PUNCT
ejpam-6441	416	1	now	now	ADV
ejpam-6441	416	2	choose	choose	VERB
ejpam-6441	416	3	τ	τ	PROPN
ejpam-6441	416	4	=	=	SYM
ejpam-6441	416	5	0	0	PROPN
ejpam-6441	416	6	,	,	PUNCT
ejpam-6441	416	7	f	f	PROPN
ejpam-6441	416	8	(	(	PUNCT
ejpam-6441	416	9	t	t	PROPN
ejpam-6441	416	10	)	)	PUNCT
ejpam-6441	417	1	=	=	SYM
ejpam-6441	417	2	t	t	PROPN
ejpam-6441	417	3	(	(	PUNCT
ejpam-6441	417	4	t	t	PROPN
ejpam-6441	417	5	≥	≥	PROPN
ejpam-6441	417	6	0	0	NUM
ejpam-6441	417	7	)	)	PUNCT
ejpam-6441	417	8	,	,	PUNCT
ejpam-6441	417	9	nℜ(ς1	nℜ(ς1	NOUN
ejpam-6441	417	10	,	,	PUNCT
ejpam-6441	417	11	ς2	ς2	PROPN
ejpam-6441	417	12	)	)	PUNCT
ejpam-6441	417	13	=	=	SYM
ejpam-6441	417	14	d(ς1	d(ς1	NOUN
ejpam-6441	417	15	,	,	PUNCT
ejpam-6441	417	16	ς2	ς2	PROPN
ejpam-6441	417	17	)	)	PUNCT
ejpam-6441	417	18	,	,	PUNCT
ejpam-6441	417	19	and	and	CCONJ
ejpam-6441	417	20	define	define	VERB
ejpam-6441	417	21	the	the	DET
ejpam-6441	417	22	constant	constant	ADJ
ejpam-6441	417	23	l	l	NOUN
ejpam-6441	417	24	=	=	SYM
ejpam-6441	417	25	c1	c1	PROPN
ejpam-6441	417	26	/	/	SYM
ejpam-6441	417	27	βa	βa	PROPN
ejpam-6441	417	28	and	and	CCONJ
ejpam-6441	417	29	note	note	VERB
ejpam-6441	417	30	that	that	SCONJ
ejpam-6441	417	31	f	f	PROPN
ejpam-6441	417	32	(	(	PUNCT
ejpam-6441	417	33	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	417	34	,	,	PUNCT
ejpam-6441	417	35	ς2	ς2	PROPN
ejpam-6441	417	36	)	)	PUNCT
ejpam-6441	417	37	)	)	PUNCT
ejpam-6441	417	38	can	can	AUX
ejpam-6441	417	39	absorb	absorb	VERB
ejpam-6441	417	40	the	the	DET
ejpam-6441	417	41	other	other	ADJ
ejpam-6441	417	42	piece	piece	NOUN
ejpam-6441	417	43	c1	c1	PROPN
ejpam-6441	417	44	/	/	SYM
ejpam-6441	417	45	βbmℜ.	βbmℜ.	PROPN
ejpam-6441	417	46	with	with	ADP
ejpam-6441	417	47	these	these	DET
ejpam-6441	417	48	choice	choice	NOUN
ejpam-6441	417	49	the	the	DET
ejpam-6441	417	50	bound	bind	VERB
ejpam-6441	417	51	becomes	become	VERB
ejpam-6441	417	52	exactly	exactly	ADV
ejpam-6441	417	53	of	of	ADP
ejpam-6441	417	54	the	the	DET
ejpam-6441	417	55	form	form	NOUN
ejpam-6441	417	56	τ	τ	X
ejpam-6441	417	57	+	+	NUM
ejpam-6441	417	58	f	f	X
ejpam-6441	417	59	(	(	PUNCT
ejpam-6441	417	60	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	417	61	)	)	PUNCT
ejpam-6441	417	62	)	)	PUNCT
ejpam-6441	418	1	≤	≤	NUM
ejpam-6441	418	2	f	f	X
ejpam-6441	418	3	(	(	PUNCT
ejpam-6441	418	4	mℜ(ς1	mℜ(ς1	PROPN
ejpam-6441	418	5	,	,	PUNCT
ejpam-6441	418	6	ς2	ς2	PROPN
ejpam-6441	418	7	)	)	PUNCT
ejpam-6441	418	8	)	)	PUNCT
ejpam-6441	419	1	+	+	CCONJ
ejpam-6441	419	2	lnℜ(ς1	lnℜ(ς1	NOUN
ejpam-6441	419	3	,	,	PUNCT
ejpam-6441	419	4	ς2	ς2	PROPN
ejpam-6441	419	5	)	)	PUNCT
ejpam-6441	419	6	,	,	PUNCT
ejpam-6441	419	7	which	which	PRON
ejpam-6441	419	8	is	be	AUX
ejpam-6441	419	9	equation	equation	NOUN
ejpam-6441	419	10	(	(	PUNCT
ejpam-6441	419	11	1	1	NUM
ejpam-6441	419	12	)	)	PUNCT
ejpam-6441	419	13	.	.	PUNCT
ejpam-6441	420	1	we	we	PRON
ejpam-6441	420	2	now	now	ADV
ejpam-6441	420	3	show	show	VERB
ejpam-6441	420	4	that	that	SCONJ
ejpam-6441	420	5	the	the	DET
ejpam-6441	420	6	conditions	condition	NOUN
ejpam-6441	420	7	(	(	PUNCT
ejpam-6441	420	8	t1)–(t3	t1)–(t3	ADJ
ejpam-6441	420	9	)	)	PUNCT
ejpam-6441	420	10	in	in	ADP
ejpam-6441	420	11	theorem	theorem	NOUN
ejpam-6441	420	12	5	5	NUM
ejpam-6441	420	13	can	can	AUX
ejpam-6441	420	14	be	be	AUX
ejpam-6441	420	15	satisfied	satisfied	ADJ
ejpam-6441	420	16	by	by	ADP
ejpam-6441	420	17	natural	natural	ADJ
ejpam-6441	420	18	choices	choice	NOUN
ejpam-6441	420	19	.	.	PUNCT
ejpam-6441	421	1	•	•	NUM
ejpam-6441	421	2	choose	choose	VERB
ejpam-6441	421	3	the	the	DET
ejpam-6441	421	4	binary	binary	PROPN
ejpam-6441	421	5	relation	relation	NOUN
ejpam-6441	421	6	ℜ	ℜ	PROPN
ejpam-6441	421	7	=	=	PUNCT
ejpam-6441	421	8	∆ℜ	∆ℜ	NOUN
ejpam-6441	421	9	×	×	PROPN
ejpam-6441	421	10	∆ℜ	∆ℜ	PROPN
ejpam-6441	421	11	(	(	PUNCT
ejpam-6441	421	12	the	the	DET
ejpam-6441	421	13	universal	universal	ADJ
ejpam-6441	421	14	relation	relation	PROPN
ejpam-6441	421	15	)	)	PUNCT
ejpam-6441	421	16	.	.	PUNCT
ejpam-6441	422	1	it	it	PRON
ejpam-6441	422	2	is	be	AUX
ejpam-6441	422	3	clearly	clearly	ADV
ejpam-6441	422	4	transitive	transitive	ADJ
ejpam-6441	422	5	and	and	CCONJ
ejpam-6441	422	6	closed	closed	ADJ
ejpam-6441	422	7	.	.	PUNCT
ejpam-6441	423	1	•	•	NUM
ejpam-6441	423	2	(	(	PUNCT
ejpam-6441	423	3	t1	t1	NOUN
ejpam-6441	423	4	)	)	PUNCT
ejpam-6441	423	5	the	the	DET
ejpam-6441	423	6	set	set	NOUN
ejpam-6441	423	7	∆ℜ(γ,ℜ	∆ℜ(γ,ℜ	ADV
ejpam-6441	423	8	)	)	PUNCT
ejpam-6441	423	9	=	=	PRON
ejpam-6441	423	10	{	{	PUNCT
ejpam-6441	423	11	ς	ς	PROPN
ejpam-6441	423	12	∈	∈	PROPN
ejpam-6441	423	13	∆ℜ	∆ℜ	NOUN
ejpam-6441	423	14	:	:	PUNCT
ejpam-6441	423	15	(	(	PUNCT
ejpam-6441	423	16	ς	ς	PROPN
ejpam-6441	423	17	,	,	PUNCT
ejpam-6441	423	18	γς	γς	ADJ
ejpam-6441	423	19	)	)	PUNCT
ejpam-6441	423	20	∈	∈	PROPN
ejpam-6441	423	21	ℜ	ℜ	PROPN
ejpam-6441	423	22	}	}	PUNCT
ejpam-6441	423	23	is	be	AUX
ejpam-6441	423	24	equal	equal	ADJ
ejpam-6441	423	25	to	to	ADP
ejpam-6441	423	26	∆ℜ	∆ℜ	PROPN
ejpam-6441	423	27	(	(	PUNCT
ejpam-6441	423	28	hence	hence	ADV
ejpam-6441	423	29	nonempty	nonempty	VERB
ejpam-6441	423	30	)	)	PUNCT
ejpam-6441	423	31	because	because	SCONJ
ejpam-6441	423	32	ℜ	ℜ	PROPN
ejpam-6441	423	33	is	be	AUX
ejpam-6441	423	34	universal	universal	ADJ
ejpam-6441	423	35	.	.	PUNCT
ejpam-6441	424	1	•	•	NUM
ejpam-6441	424	2	(	(	PUNCT
ejpam-6441	424	3	t2	t2	NOUN
ejpam-6441	424	4	)	)	PUNCT
ejpam-6441	424	5	ℜ	ℜ	PROPN
ejpam-6441	424	6	is	be	AUX
ejpam-6441	424	7	γ	γ	X
ejpam-6441	424	8	-	-	ADJ
ejpam-6441	424	9	closed	closed	ADJ
ejpam-6441	424	10	trivially	trivially	ADV
ejpam-6441	424	11	.	.	PUNCT
ejpam-6441	425	1	•	•	NUM
ejpam-6441	425	2	(	(	PUNCT
ejpam-6441	425	3	t3	t3	NOUN
ejpam-6441	425	4	)	)	PUNCT
ejpam-6441	425	5	is	be	AUX
ejpam-6441	425	6	satisfied	satisfied	ADJ
ejpam-6441	425	7	because	because	SCONJ
ejpam-6441	425	8	under	under	ADP
ejpam-6441	425	9	the	the	DET
ejpam-6441	425	10	compactness	compactness	NOUN
ejpam-6441	425	11	of	of	ADP
ejpam-6441	425	12	values	value	NOUN
ejpam-6441	425	13	and	and	CCONJ
ejpam-6441	425	14	the	the	DET
ejpam-6441	425	15	structural	structural	ADJ
ejpam-6441	425	16	bounds	bound	NOUN
ejpam-6441	425	17	we	we	PRON
ejpam-6441	425	18	can	can	AUX
ejpam-6441	425	19	show	show	VERB
ejpam-6441	425	20	upper	upper	ADJ
ejpam-6441	425	21	semicontinuity	semicontinuity	NOUN
ejpam-6441	425	22	of	of	ADP
ejpam-6441	425	23	γ	γ	PROPN
ejpam-6441	425	24	in	in	ADP
ejpam-6441	425	25	the	the	DET
ejpam-6441	425	26	hausdorff	hausdorff	NOUN
ejpam-6441	425	27	metric	metric	NOUN
ejpam-6441	425	28	;	;	PUNCT
ejpam-6441	425	29	hence	hence	ADV
ejpam-6441	425	30	γ	γ	PROPN
ejpam-6441	425	31	is	be	AUX
ejpam-6441	425	32	ℜcontinuous	ℜcontinuous	ADJ
ejpam-6441	425	33	or	or	CCONJ
ejpam-6441	425	34	the	the	DET
ejpam-6441	425	35	space	space	NOUN
ejpam-6441	425	36	(	(	PUNCT
ejpam-6441	425	37	∆ℜ	∆ℜ	NOUN
ejpam-6441	425	38	,	,	PUNCT
ejpam-6441	425	39	d	d	NOUN
ejpam-6441	425	40	)	)	PUNCT
ejpam-6441	425	41	is	be	AUX
ejpam-6441	425	42	ℜ-regular	ℜ-regular	PROPN
ejpam-6441	425	43	.	.	PUNCT
ejpam-6441	426	1	hence	hence	ADV
ejpam-6441	426	2	,	,	PUNCT
ejpam-6441	426	3	with	with	ADP
ejpam-6441	426	4	the	the	DET
ejpam-6441	426	5	above	above	ADJ
ejpam-6441	426	6	matching	matching	NOUN
ejpam-6441	426	7	of	of	ADP
ejpam-6441	426	8	parameters	parameter	NOUN
ejpam-6441	426	9	and	and	CCONJ
ejpam-6441	426	10	the	the	DET
ejpam-6441	426	11	structural	structural	ADJ
ejpam-6441	426	12	pointwise	pointwise	NOUN
ejpam-6441	426	13	control	control	NOUN
ejpam-6441	426	14	(	(	PUNCT
ejpam-6441	426	15	33	33	NUM
ejpam-6441	426	16	)	)	PUNCT
ejpam-6441	426	17	,	,	PUNCT
ejpam-6441	426	18	all	all	DET
ejpam-6441	426	19	hypotheses	hypothesis	NOUN
ejpam-6441	426	20	of	of	ADP
ejpam-6441	426	21	theorem	theorem	ADJ
ejpam-6441	426	22	2	2	NUM
ejpam-6441	426	23	are	be	AUX
ejpam-6441	426	24	satisfied	satisfied	ADJ
ejpam-6441	426	25	and	and	CCONJ
ejpam-6441	426	26	yields	yield	NOUN
ejpam-6441	426	27	existence	existence	NOUN
ejpam-6441	426	28	of	of	ADP
ejpam-6441	426	29	a	a	DET
ejpam-6441	426	30	fixed	fix	VERB
ejpam-6441	426	31	point	point	NOUN
ejpam-6441	426	32	ς∗	ς∗	PROPN
ejpam-6441	426	33	∈	∈	PROPN
ejpam-6441	426	34	∆ℜ	∆ℜ	NOUN
ejpam-6441	426	35	of	of	ADP
ejpam-6441	426	36	γ	γ	PROPN
ejpam-6441	426	37	,	,	PUNCT
ejpam-6441	426	38	which	which	PRON
ejpam-6441	426	39	is	be	AUX
ejpam-6441	426	40	a	a	DET
ejpam-6441	426	41	solution	solution	NOUN
ejpam-6441	426	42	of	of	ADP
ejpam-6441	426	43	(	(	PUNCT
ejpam-6441	426	44	31	31	NUM
ejpam-6441	426	45	)	)	PUNCT
ejpam-6441	426	46	.	.	PUNCT
ejpam-6441	427	1	example	example	NOUN
ejpam-6441	428	1	3	3	X
ejpam-6441	428	2	.	.	X
ejpam-6441	428	3	take	take	VERB
ejpam-6441	428	4	π(t	π(t	PROPN
ejpam-6441	428	5	,	,	PUNCT
ejpam-6441	428	6	u	u	NOUN
ejpam-6441	428	7	,	,	PUNCT
ejpam-6441	428	8	v	v	NOUN
ejpam-6441	428	9	)	)	PUNCT
ejpam-6441	428	10	=	=	PUNCT
ejpam-6441	429	1	[	[	PUNCT
ejpam-6441	429	2	1	1	NUM
ejpam-6441	429	3	4(u+	4(u+	NUM
ejpam-6441	429	4	v	v	NOUN
ejpam-6441	429	5	)	)	PUNCT
ejpam-6441	429	6	,	,	PUNCT
ejpam-6441	429	7	1	1	NUM
ejpam-6441	429	8	2(u+	2(u+	NUM
ejpam-6441	429	9	v	v	NOUN
ejpam-6441	429	10	)	)	PUNCT
ejpam-6441	429	11	]	]	PUNCT
ejpam-6441	429	12	,	,	PUNCT
ejpam-6441	429	13	t	t	PROPN
ejpam-6441	429	14	∈	∈	PROPN
ejpam-6441	430	1	[	[	X
ejpam-6441	430	2	0	0	NUM
ejpam-6441	430	3	,	,	PUNCT
ejpam-6441	430	4	1	1	NUM
ejpam-6441	430	5	]	]	PUNCT
ejpam-6441	430	6	.	.	PUNCT
ejpam-6441	431	1	pointwise	pointwise	PROPN
ejpam-6441	431	2	one	one	PRON
ejpam-6441	431	3	has	have	VERB
ejpam-6441	431	4	for	for	ADP
ejpam-6441	431	5	any	any	DET
ejpam-6441	431	6	ui	ui	PROPN
ejpam-6441	431	7	∈	∈	PROPN
ejpam-6441	431	8	π(t	π(t	PROPN
ejpam-6441	431	9	,	,	PUNCT
ejpam-6441	431	10	u∗i	u∗i	PUNCT
ejpam-6441	431	11	,	,	PUNCT
ejpam-6441	431	12	v	v	X
ejpam-6441	431	13	∗	∗	NOUN
ejpam-6441	431	14	i	i	PRON
ejpam-6441	431	15	)	)	PUNCT
ejpam-6441	431	16	|u1	|u1	NOUN
ejpam-6441	432	1	−	−	ADP
ejpam-6441	432	2	u2|	u2|	ADJ
ejpam-6441	432	3	≤	≤	NOUN
ejpam-6441	432	4	1	1	NUM
ejpam-6441	432	5	2(|u	2(|u	NUM
ejpam-6441	432	6	∗	∗	NOUN
ejpam-6441	432	7	1	1	NUM
ejpam-6441	432	8	−	−	PROPN
ejpam-6441	432	9	u∗2|+	u∗2|+	ADJ
ejpam-6441	432	10	|v∗1	|v∗1	ADJ
ejpam-6441	432	11	−	−	NOUN
ejpam-6441	432	12	v∗2|	v∗2|	NOUN
ejpam-6441	432	13	)	)	PUNCT
ejpam-6441	432	14	,	,	PUNCT
ejpam-6441	432	15	so	so	ADV
ejpam-6441	432	16	setting	set	VERB
ejpam-6441	432	17	β	β	NOUN
ejpam-6441	432	18	=	=	SYM
ejpam-6441	432	19	1	1	NUM
ejpam-6441	432	20	and	and	CCONJ
ejpam-6441	432	21	integrating	integrate	VERB
ejpam-6441	432	22	the	the	DET
ejpam-6441	432	23	previous	previous	ADJ
ejpam-6441	432	24	estimates	estimate	NOUN
ejpam-6441	432	25	yields	yield	VERB
ejpam-6441	432	26	the	the	DET
ejpam-6441	432	27	linear	linear	PROPN
ejpam-6441	432	28	contraction	contraction	NOUN
ejpam-6441	432	29	estimate	estimate	VERB
ejpam-6441	432	30	h(γς1,γς2	h(γς1,γς2	PROPN
ejpam-6441	432	31	)	)	PUNCT
ejpam-6441	432	32	≤	≤	NOUN
ejpam-6441	432	33	(	(	PUNCT
ejpam-6441	432	34	k	k	PROPN
ejpam-6441	432	35	+	+	PROPN
ejpam-6441	432	36	m)12	m)12	PROPN
ejpam-6441	432	37	d(ς1	d(ς1	NOUN
ejpam-6441	432	38	,	,	PUNCT
ejpam-6441	432	39	ς2	ς2	PROPN
ejpam-6441	432	40	)	)	PUNCT
ejpam-6441	432	41	,	,	PUNCT
ejpam-6441	432	42	with	with	ADP
ejpam-6441	432	43	(	(	PUNCT
ejpam-6441	432	44	k	k	X
ejpam-6441	432	45	+	+	PROPN
ejpam-6441	432	46	m)12	m)12	NOUN
ejpam-6441	432	47	=	=	PUNCT
ejpam-6441	433	1	5	5	NUM
ejpam-6441	433	2	16	16	NUM
ejpam-6441	433	3	<	<	X
ejpam-6441	433	4	1	1	NUM
ejpam-6441	433	5	.	.	PUNCT
ejpam-6441	434	1	in	in	ADP
ejpam-6441	434	2	the	the	DET
ejpam-6441	434	3	view	view	NOUN
ejpam-6441	434	4	of	of	ADP
ejpam-6441	434	5	definition	definition	NOUN
ejpam-6441	434	6	1	1	NUM
ejpam-6441	434	7	this	this	PRON
ejpam-6441	434	8	corresponds	correspond	VERB
ejpam-6441	434	9	to	to	ADP
ejpam-6441	434	10	taking	take	VERB
ejpam-6441	434	11	mℜ	mℜ	NOUN
ejpam-6441	434	12	negligible	negligible	ADJ
ejpam-6441	434	13	(	(	PUNCT
ejpam-6441	434	14	or	or	CCONJ
ejpam-6441	434	15	explicitly	explicitly	ADV
ejpam-6441	434	16	zero	zero	NUM
ejpam-6441	434	17	)	)	PUNCT
ejpam-6441	434	18	and	and	CCONJ
ejpam-6441	434	19	l	l	NOUN
ejpam-6441	434	20	=	=	SYM
ejpam-6441	434	21	(	(	PUNCT
ejpam-6441	434	22	k	k	PROPN
ejpam-6441	434	23	+	+	PROPN
ejpam-6441	434	24	m	m	NOUN
ejpam-6441	434	25	)	)	PUNCT
ejpam-6441	434	26	·	·	PUNCT
ejpam-6441	434	27	1	1	NUM
ejpam-6441	434	28	2	2	NUM
ejpam-6441	434	29	;	;	PUNCT
ejpam-6441	434	30	the	the	DET
ejpam-6441	434	31	inequality	inequality	NOUN
ejpam-6441	434	32	(	(	PUNCT
ejpam-6441	434	33	1	1	X
ejpam-6441	434	34	)	)	PUNCT
ejpam-6441	434	35	is	be	AUX
ejpam-6441	434	36	thus	thus	ADV
ejpam-6441	434	37	satisfied	satisfied	ADJ
ejpam-6441	434	38	and	and	CCONJ
ejpam-6441	434	39	theorem	theorem	VERB
ejpam-6441	434	40	2	2	NUM
ejpam-6441	434	41	gives	give	VERB
ejpam-6441	434	42	existence	existence	NOUN
ejpam-6441	434	43	of	of	ADP
ejpam-6441	434	44	the	the	DET
ejpam-6441	434	45	bvp	bvp	NOUN
ejpam-6441	434	46	’s	’s	PART
ejpam-6441	434	47	solution	solution	NOUN
ejpam-6441	434	48	.	.	PUNCT
ejpam-6441	435	1	m.	m.	NOUN
ejpam-6441	435	2	mudhesh	mudhesh	PROPN
ejpam-6441	435	3	et	et	PROPN
ejpam-6441	435	4	al	al	PROPN
ejpam-6441	435	5	.	.	PUNCT
ejpam-6441	435	6	/	/	SYM
ejpam-6441	435	7	eur	eur	PROPN
ejpam-6441	435	8	.	.	PUNCT
ejpam-6441	436	1	j.	j.	PROPN
ejpam-6441	436	2	pure	pure	PROPN
ejpam-6441	436	3	appl	appl	PROPN
ejpam-6441	436	4	.	.	PROPN
ejpam-6441	436	5	math	math	PROPN
ejpam-6441	436	6	,	,	PUNCT
ejpam-6441	436	7	18	18	NUM
ejpam-6441	436	8	(	(	PUNCT
ejpam-6441	436	9	4	4	NUM
ejpam-6441	436	10	)	)	PUNCT
ejpam-6441	436	11	(	(	PUNCT
ejpam-6441	436	12	2025	2025	NUM
ejpam-6441	436	13	)	)	PUNCT
ejpam-6441	436	14	,	,	PUNCT
ejpam-6441	436	15	6441	6441	NUM
ejpam-6441	436	16	19	19	NUM
ejpam-6441	436	17	of	of	ADP
ejpam-6441	436	18	21	21	NUM
ejpam-6441	436	19	5	5	NUM
ejpam-6441	436	20	.	.	PUNCT
ejpam-6441	437	1	conclusions	conclusion	NOUN
ejpam-6441	437	2	in	in	ADP
ejpam-6441	437	3	this	this	DET
ejpam-6441	437	4	article	article	NOUN
ejpam-6441	437	5	,	,	PUNCT
ejpam-6441	437	6	we	we	PRON
ejpam-6441	437	7	have	have	AUX
ejpam-6441	437	8	introduced	introduce	VERB
ejpam-6441	437	9	and	and	CCONJ
ejpam-6441	437	10	studied	study	VERB
ejpam-6441	437	11	a	a	DET
ejpam-6441	437	12	new	new	ADJ
ejpam-6441	437	13	class	class	NOUN
ejpam-6441	437	14	of	of	ADP
ejpam-6441	437	15	contractions	contraction	NOUN
ejpam-6441	437	16	,	,	PUNCT
ejpam-6441	437	17	namely	namely	ADV
ejpam-6441	437	18	almost	almost	ADV
ejpam-6441	437	19	fisher	fisher	NOUN
ejpam-6441	437	20	-	-	PUNCT
ejpam-6441	437	21	type	type	NOUN
ejpam-6441	437	22	multivalued	multivalue	VERB
ejpam-6441	437	23	f	f	PROPN
ejpam-6441	437	24	-contractions	-contraction	NOUN
ejpam-6441	437	25	equipped	equip	VERB
ejpam-6441	437	26	with	with	ADP
ejpam-6441	437	27	a	a	DET
ejpam-6441	437	28	γ	γ	NOUN
ejpam-6441	437	29	-	-	ADJ
ejpam-6441	437	30	transitive	transitive	ADJ
ejpam-6441	437	31	binary	binary	ADJ
ejpam-6441	437	32	relation	relation	NOUN
ejpam-6441	437	33	.	.	PUNCT
ejpam-6441	438	1	within	within	ADP
ejpam-6441	438	2	this	this	DET
ejpam-6441	438	3	framework	framework	NOUN
ejpam-6441	438	4	,	,	PUNCT
ejpam-6441	438	5	we	we	PRON
ejpam-6441	438	6	proved	prove	VERB
ejpam-6441	438	7	several	several	ADJ
ejpam-6441	438	8	fixed	fix	VERB
ejpam-6441	438	9	-	-	PUNCT
ejpam-6441	438	10	point	point	NOUN
ejpam-6441	438	11	results	result	NOUN
ejpam-6441	438	12	which	which	PRON
ejpam-6441	438	13	extend	extend	VERB
ejpam-6441	438	14	and	and	CCONJ
ejpam-6441	438	15	unify	unify	VERB
ejpam-6441	438	16	a	a	DET
ejpam-6441	438	17	number	number	NOUN
ejpam-6441	438	18	of	of	ADP
ejpam-6441	438	19	existing	exist	VERB
ejpam-6441	438	20	theorems	theorem	NOUN
ejpam-6441	438	21	in	in	ADP
ejpam-6441	438	22	the	the	DET
ejpam-6441	438	23	literature	literature	NOUN
ejpam-6441	438	24	on	on	ADP
ejpam-6441	438	25	multivalued	multivalued	ADJ
ejpam-6441	438	26	contractions	contraction	NOUN
ejpam-6441	438	27	.	.	PUNCT
ejpam-6441	439	1	the	the	DET
ejpam-6441	439	2	obtained	obtain	VERB
ejpam-6441	439	3	results	result	NOUN
ejpam-6441	439	4	highlight	highlight	VERB
ejpam-6441	439	5	the	the	DET
ejpam-6441	439	6	flexibility	flexibility	NOUN
ejpam-6441	439	7	of	of	ADP
ejpam-6441	439	8	the	the	DET
ejpam-6441	439	9	proposed	propose	VERB
ejpam-6441	439	10	approach	approach	NOUN
ejpam-6441	439	11	,	,	PUNCT
ejpam-6441	439	12	as	as	SCONJ
ejpam-6441	439	13	they	they	PRON
ejpam-6441	439	14	recover	recover	VERB
ejpam-6441	439	15	wellknown	wellknown	ADJ
ejpam-6441	439	16	outcomes	outcome	NOUN
ejpam-6441	439	17	as	as	ADP
ejpam-6441	439	18	special	special	ADJ
ejpam-6441	439	19	cases	case	NOUN
ejpam-6441	439	20	and	and	CCONJ
ejpam-6441	439	21	,	,	PUNCT
ejpam-6441	439	22	at	at	ADP
ejpam-6441	439	23	the	the	DET
ejpam-6441	439	24	same	same	ADJ
ejpam-6441	439	25	time	time	NOUN
ejpam-6441	439	26	,	,	PUNCT
ejpam-6441	439	27	yield	yield	VERB
ejpam-6441	439	28	genuinely	genuinely	ADV
ejpam-6441	439	29	new	new	ADJ
ejpam-6441	439	30	contributions	contribution	NOUN
ejpam-6441	439	31	.	.	PUNCT
ejpam-6441	440	1	to	to	PART
ejpam-6441	440	2	illustrate	illustrate	VERB
ejpam-6441	440	3	the	the	DET
ejpam-6441	440	4	applicability	applicability	NOUN
ejpam-6441	440	5	of	of	ADP
ejpam-6441	440	6	our	our	PRON
ejpam-6441	440	7	theory	theory	NOUN
ejpam-6441	440	8	,	,	PUNCT
ejpam-6441	440	9	we	we	PRON
ejpam-6441	440	10	provided	provide	VERB
ejpam-6441	440	11	explicit	explicit	ADJ
ejpam-6441	440	12	examples	example	NOUN
ejpam-6441	440	13	and	and	CCONJ
ejpam-6441	440	14	developed	develop	VERB
ejpam-6441	440	15	an	an	DET
ejpam-6441	440	16	application	application	NOUN
ejpam-6441	440	17	to	to	ADP
ejpam-6441	440	18	second	second	ADJ
ejpam-6441	440	19	-	-	PUNCT
ejpam-6441	440	20	order	order	NOUN
ejpam-6441	440	21	differential	differential	ADJ
ejpam-6441	440	22	inclusions	inclusion	NOUN
ejpam-6441	440	23	.	.	PUNCT
ejpam-6441	441	1	this	this	DET
ejpam-6441	441	2	application	application	NOUN
ejpam-6441	441	3	shows	show	VERB
ejpam-6441	441	4	how	how	SCONJ
ejpam-6441	441	5	the	the	DET
ejpam-6441	441	6	abstract	abstract	ADJ
ejpam-6441	441	7	fixed	fix	VERB
ejpam-6441	441	8	point	point	NOUN
ejpam-6441	441	9	results	result	NOUN
ejpam-6441	441	10	can	can	AUX
ejpam-6441	441	11	be	be	AUX
ejpam-6441	441	12	effectively	effectively	ADV
ejpam-6441	441	13	employed	employ	VERB
ejpam-6441	441	14	to	to	PART
ejpam-6441	441	15	guarantee	guarantee	VERB
ejpam-6441	441	16	the	the	DET
ejpam-6441	441	17	existence	existence	NOUN
ejpam-6441	441	18	of	of	ADP
ejpam-6441	441	19	solutions	solution	NOUN
ejpam-6441	441	20	to	to	ADP
ejpam-6441	441	21	nonlinear	nonlinear	ADJ
ejpam-6441	441	22	problems	problem	NOUN
ejpam-6441	441	23	.	.	PUNCT
ejpam-6441	442	1	in	in	ADP
ejpam-6441	442	2	particular	particular	ADJ
ejpam-6441	442	3	,	,	PUNCT
ejpam-6441	442	4	it	it	PRON
ejpam-6441	442	5	demonstrates	demonstrate	VERB
ejpam-6441	442	6	that	that	SCONJ
ejpam-6441	442	7	the	the	DET
ejpam-6441	442	8	almost	almost	ADV
ejpam-6441	442	9	fisher	fisher	NOUN
ejpam-6441	442	10	-	-	PUNCT
ejpam-6441	442	11	type	type	NOUN
ejpam-6441	442	12	multivalued	multivalue	VERB
ejpam-6441	442	13	f	f	PROPN
ejpam-6441	442	14	-contraction	-contraction	PROPN
ejpam-6441	442	15	framework	framework	NOUN
ejpam-6441	442	16	can	can	AUX
ejpam-6441	442	17	serve	serve	VERB
ejpam-6441	442	18	as	as	ADP
ejpam-6441	442	19	a	a	DET
ejpam-6441	442	20	powerful	powerful	ADJ
ejpam-6441	442	21	tool	tool	NOUN
ejpam-6441	442	22	in	in	ADP
ejpam-6441	442	23	the	the	DET
ejpam-6441	442	24	analysis	analysis	NOUN
ejpam-6441	442	25	of	of	ADP
ejpam-6441	442	26	integral	integral	ADJ
ejpam-6441	442	27	and	and	CCONJ
ejpam-6441	442	28	differential	differential	ADJ
ejpam-6441	442	29	inclusions	inclusion	NOUN
ejpam-6441	442	30	.	.	PUNCT
ejpam-6441	443	1	data	datum	NOUN
ejpam-6441	443	2	availability	availability	NOUN
ejpam-6441	443	3	statement	statement	NOUN
ejpam-6441	443	4	all	all	DET
ejpam-6441	443	5	data	datum	NOUN
ejpam-6441	443	6	generated	generate	VERB
ejpam-6441	443	7	or	or	CCONJ
ejpam-6441	443	8	analyzed	analyze	VERB
ejpam-6441	443	9	during	during	ADP
ejpam-6441	443	10	this	this	DET
ejpam-6441	443	11	study	study	NOUN
ejpam-6441	443	12	are	be	AUX
ejpam-6441	443	13	included	include	VERB
ejpam-6441	443	14	in	in	ADP
ejpam-6441	443	15	this	this	DET
ejpam-6441	443	16	manuscript	manuscript	NOUN
ejpam-6441	443	17	.	.	PUNCT
ejpam-6441	444	1	conflict	conflict	NOUN
ejpam-6441	444	2	of	of	ADP
ejpam-6441	444	3	interests	interest	NOUN
ejpam-6441	444	4	the	the	DET
ejpam-6441	444	5	authors	author	NOUN
ejpam-6441	444	6	declare	declare	VERB
ejpam-6441	444	7	that	that	SCONJ
ejpam-6441	444	8	they	they	PRON
ejpam-6441	444	9	have	have	VERB
ejpam-6441	444	10	no	no	DET
ejpam-6441	444	11	competing	compete	VERB
ejpam-6441	444	12	interests	interest	NOUN
ejpam-6441	444	13	.	.	PUNCT
ejpam-6441	445	1	funding	fund	VERB
ejpam-6441	445	2	no	no	DET
ejpam-6441	445	3	funding	funding	NOUN
ejpam-6441	445	4	was	be	AUX
ejpam-6441	445	5	received	receive	VERB
ejpam-6441	445	6	for	for	ADP
ejpam-6441	445	7	this	this	DET
ejpam-6441	445	8	research	research	NOUN
ejpam-6441	445	9	.	.	PUNCT
ejpam-6441	446	1	authors	author	NOUN
ejpam-6441	446	2	’	’	PART
ejpam-6441	446	3	contributions	contribution	NOUN
ejpam-6441	446	4	mmwas	mmwa	VERB
ejpam-6441	446	5	responsible	responsible	ADJ
ejpam-6441	446	6	for	for	ADP
ejpam-6441	446	7	conceptualization	conceptualization	NOUN
ejpam-6441	446	8	,	,	PUNCT
ejpam-6441	446	9	methodology	methodology	NOUN
ejpam-6441	446	10	,	,	PUNCT
ejpam-6441	446	11	software	software	NOUN
ejpam-6441	446	12	,	,	PUNCT
ejpam-6441	446	13	original	original	ADJ
ejpam-6441	446	14	draft	draft	NOUN
ejpam-6441	446	15	preparation	preparation	NOUN
ejpam-6441	446	16	and	and	CCONJ
ejpam-6441	446	17	editing	editing	NOUN
ejpam-6441	446	18	.	.	PUNCT
ejpam-6441	447	1	ma	ma	PROPN
ejpam-6441	447	2	was	be	AUX
ejpam-6441	447	3	responsible	responsible	ADJ
ejpam-6441	447	4	for	for	ADP
ejpam-6441	447	5	supervision	supervision	NOUN
ejpam-6441	447	6	,	,	PUNCT
ejpam-6441	447	7	investigation	investigation	NOUN
ejpam-6441	447	8	,	,	PUNCT
ejpam-6441	447	9	and	and	CCONJ
ejpam-6441	447	10	resources	resource	NOUN
ejpam-6441	447	11	.	.	PUNCT
ejpam-6441	448	1	ah	ah	INTJ
ejpam-6441	448	2	was	be	AUX
ejpam-6441	448	3	responsible	responsible	ADJ
ejpam-6441	448	4	for	for	ADP
ejpam-6441	448	5	validation	validation	NOUN
ejpam-6441	448	6	,	,	PUNCT
ejpam-6441	448	7	formal	formal	ADJ
ejpam-6441	448	8	analysis	analysis	NOUN
ejpam-6441	448	9	,	,	PUNCT
ejpam-6441	448	10	data	data	NOUN
ejpam-6441	448	11	curation	curation	NOUN
ejpam-6441	448	12	,	,	PUNCT
ejpam-6441	448	13	and	and	CCONJ
ejpam-6441	448	14	review	review	NOUN
ejpam-6441	448	15	.	.	PUNCT
ejpam-6441	449	1	ha	ha	INTJ
ejpam-6441	449	2	was	be	AUX
ejpam-6441	449	3	responsible	responsible	ADJ
ejpam-6441	449	4	for	for	ADP
ejpam-6441	449	5	project	project	NOUN
ejpam-6441	449	6	administration	administration	NOUN
ejpam-6441	449	7	,	,	PUNCT
ejpam-6441	449	8	resources	resource	NOUN
ejpam-6441	449	9	,	,	PUNCT
ejpam-6441	449	10	and	and	CCONJ
ejpam-6441	449	11	funding	funding	NOUN
ejpam-6441	449	12	acquisition	acquisition	NOUN
ejpam-6441	449	13	.	.	PUNCT
ejpam-6441	450	1	all	all	DET
ejpam-6441	450	2	authors	author	NOUN
ejpam-6441	450	3	have	have	AUX
ejpam-6441	450	4	read	read	VERB
ejpam-6441	450	5	and	and	CCONJ
ejpam-6441	450	6	agreed	agree	VERB
ejpam-6441	450	7	to	to	PART
ejpam-6441	450	8	be	be	AUX
ejpam-6441	450	9	responsible	responsible	ADJ
ejpam-6441	450	10	for	for	ADP
ejpam-6441	450	11	the	the	DET
ejpam-6441	450	12	content	content	NOUN
ejpam-6441	450	13	and	and	CCONJ
ejpam-6441	450	14	conclusions	conclusion	NOUN
ejpam-6441	450	15	of	of	ADP
ejpam-6441	450	16	the	the	DET
ejpam-6441	450	17	article	article	NOUN
ejpam-6441	450	18	.	.	PUNCT
ejpam-6441	451	1	references	reference	NOUN
ejpam-6441	451	2	[	[	X
ejpam-6441	451	3	1	1	X
ejpam-6441	451	4	]	]	PUNCT
ejpam-6441	451	5	d.	d.	PROPN
ejpam-6441	451	6	s.	s.	PROPN
ejpam-6441	451	7	jaggi	jaggi	PROPN
ejpam-6441	451	8	.	.	PUNCT
ejpam-6441	452	1	some	some	DET
ejpam-6441	452	2	unique	unique	ADJ
ejpam-6441	452	3	fixed	fix	VERB
ejpam-6441	452	4	point	point	NOUN
ejpam-6441	452	5	theorems	theorem	NOUN
ejpam-6441	452	6	.	.	PUNCT
ejpam-6441	452	7	indian	indian	PROPN
ejpam-6441	452	8	journal	journal	PROPN
ejpam-6441	452	9	of	of	ADP
ejpam-6441	452	10	pure	pure	ADJ
ejpam-6441	452	11	and	and	CCONJ
ejpam-6441	452	12	applied	applied	ADJ
ejpam-6441	452	13	mathematics	mathematic	NOUN
ejpam-6441	452	14	,	,	PUNCT
ejpam-6441	452	15	8:223–230	8:223–230	NUM
ejpam-6441	452	16	,	,	PUNCT
ejpam-6441	452	17	1977	1977	NUM
ejpam-6441	452	18	.	.	PUNCT
ejpam-6441	453	1	[	[	X
ejpam-6441	453	2	2	2	X
ejpam-6441	453	3	]	]	PUNCT
ejpam-6441	453	4	e.	e.	PROPN
ejpam-6441	453	5	karapinar	karapinar	PROPN
ejpam-6441	453	6	.	.	PUNCT
ejpam-6441	454	1	revisiting	revisit	VERB
ejpam-6441	454	2	the	the	DET
ejpam-6441	454	3	kannan	kannan	PROPN
ejpam-6441	454	4	type	type	NOUN
ejpam-6441	454	5	contractions	contraction	NOUN
ejpam-6441	454	6	via	via	ADP
ejpam-6441	454	7	interpolation	interpolation	NOUN
ejpam-6441	454	8	.	.	PUNCT
ejpam-6441	455	1	advances	advance	NOUN
ejpam-6441	455	2	in	in	ADP
ejpam-6441	455	3	theory	theory	NOUN
ejpam-6441	455	4	of	of	ADP
ejpam-6441	455	5	nonlinear	nonlinear	ADJ
ejpam-6441	455	6	analysis	analysis	NOUN
ejpam-6441	455	7	and	and	CCONJ
ejpam-6441	455	8	applications	application	NOUN
ejpam-6441	455	9	,	,	PUNCT
ejpam-6441	455	10	2(2):85–87	2(2):85–87	NUM
ejpam-6441	455	11	,	,	PUNCT
ejpam-6441	455	12	2018	2018	NUM
ejpam-6441	455	13	.	.	PUNCT
ejpam-6441	456	1	[	[	X
ejpam-6441	456	2	3	3	X
ejpam-6441	456	3	]	]	X
ejpam-6441	456	4	e.	e.	PROPN
ejpam-6441	456	5	karapınar	karapınar	PROPN
ejpam-6441	456	6	,	,	PUNCT
ejpam-6441	456	7	o.	o.	PROPN
ejpam-6441	456	8	alqahtani	alqahtani	PROPN
ejpam-6441	456	9	,	,	PUNCT
ejpam-6441	456	10	and	and	CCONJ
ejpam-6441	456	11	h.	h.	PROPN
ejpam-6441	456	12	aydi	aydi	VERB
ejpam-6441	456	13	.	.	PUNCT
ejpam-6441	457	1	on	on	ADP
ejpam-6441	457	2	interpolative	interpolative	ADJ
ejpam-6441	457	3	hardy?rogers	hardy?roger	NOUN
ejpam-6441	457	4	type	type	NOUN
ejpam-6441	457	5	contractions	contraction	NOUN
ejpam-6441	457	6	.	.	PUNCT
ejpam-6441	458	1	symmetry	symmetry	NOUN
ejpam-6441	458	2	,	,	PUNCT
ejpam-6441	458	3	11(1):1–7	11(1):1–7	NUM
ejpam-6441	458	4	,	,	PUNCT
ejpam-6441	458	5	2019	2019	NUM
ejpam-6441	458	6	.	.	PUNCT
ejpam-6441	459	1	m.	m.	NOUN
ejpam-6441	459	2	mudhesh	mudhesh	PROPN
ejpam-6441	459	3	et	et	PROPN
ejpam-6441	459	4	al	al	PROPN
ejpam-6441	459	5	.	.	PUNCT
ejpam-6441	459	6	/	/	SYM
ejpam-6441	459	7	eur	eur	PROPN
ejpam-6441	459	8	.	.	PUNCT
ejpam-6441	460	1	j.	j.	PROPN
ejpam-6441	460	2	pure	pure	PROPN
ejpam-6441	460	3	appl	appl	PROPN
ejpam-6441	460	4	.	.	PROPN
ejpam-6441	460	5	math	math	PROPN
ejpam-6441	460	6	,	,	PUNCT
ejpam-6441	460	7	18	18	NUM
ejpam-6441	460	8	(	(	PUNCT
ejpam-6441	460	9	4	4	NUM
ejpam-6441	460	10	)	)	PUNCT
ejpam-6441	460	11	(	(	PUNCT
ejpam-6441	460	12	2025	2025	NUM
ejpam-6441	460	13	)	)	PUNCT
ejpam-6441	460	14	,	,	PUNCT
ejpam-6441	460	15	6441	6441	NUM
ejpam-6441	460	16	20	20	NUM
ejpam-6441	460	17	of	of	ADP
ejpam-6441	460	18	21	21	NUM
ejpam-6441	461	1	[	[	SYM
ejpam-6441	461	2	4	4	NUM
ejpam-6441	461	3	]	]	X
ejpam-6441	461	4	h.	h.	PROPN
ejpam-6441	461	5	aydi	aydi	PROPN
ejpam-6441	461	6	,	,	PUNCT
ejpam-6441	461	7	c.	c.	PROPN
ejpam-6441	461	8	m.	m.	PROPN
ejpam-6441	461	9	chen	chen	PROPN
ejpam-6441	461	10	,	,	PUNCT
ejpam-6441	461	11	and	and	CCONJ
ejpam-6441	461	12	e.	e.	PROPN
ejpam-6441	461	13	karapınar	karapınar	PROPN
ejpam-6441	461	14	.	.	PUNCT
ejpam-6441	462	1	interpolative	interpolative	ADJ
ejpam-6441	462	2	çirić–reich	çirić–reich	PROPN
ejpam-6441	462	3	–	–	PUNCT
ejpam-6441	462	4	rus	rus	NOUN
ejpam-6441	462	5	type	type	NOUN
ejpam-6441	462	6	contractions	contraction	NOUN
ejpam-6441	462	7	via	via	ADP
ejpam-6441	462	8	the	the	DET
ejpam-6441	462	9	branciari	branciari	ADJ
ejpam-6441	462	10	distance	distance	NOUN
ejpam-6441	462	11	.	.	PUNCT
ejpam-6441	463	1	mathematics	mathematic	NOUN
ejpam-6441	463	2	,	,	PUNCT
ejpam-6441	463	3	7(1):1–7	7(1):1–7	NUM
ejpam-6441	463	4	,	,	PUNCT
ejpam-6441	463	5	2019	2019	NUM
ejpam-6441	463	6	.	.	PUNCT
ejpam-6441	464	1	[	[	X
ejpam-6441	464	2	5	5	X
ejpam-6441	464	3	]	]	PUNCT
ejpam-6441	464	4	e.	e.	PROPN
ejpam-6441	464	5	karapınar	karapınar	PROPN
ejpam-6441	464	6	and	and	CCONJ
ejpam-6441	464	7	a.	a.	NOUN
ejpam-6441	464	8	fulga	fulga	NOUN
ejpam-6441	464	9	.	.	PUNCT
ejpam-6441	465	1	a	a	DET
ejpam-6441	465	2	hybrid	hybrid	ADJ
ejpam-6441	465	3	contraction	contraction	NOUN
ejpam-6441	465	4	that	that	PRON
ejpam-6441	465	5	involves	involve	VERB
ejpam-6441	465	6	jaggi	jaggi	NOUN
ejpam-6441	465	7	type	type	NOUN
ejpam-6441	465	8	.	.	PUNCT
ejpam-6441	466	1	symmetry	symmetry	NOUN
ejpam-6441	466	2	,	,	PUNCT
ejpam-6441	466	3	11(5):1–9	11(5):1–9	NUM
ejpam-6441	466	4	,	,	PUNCT
ejpam-6441	466	5	2019	2019	NUM
ejpam-6441	466	6	.	.	PUNCT
ejpam-6441	467	1	[	[	X
ejpam-6441	467	2	6	6	NUM
ejpam-6441	467	3	]	]	X
ejpam-6441	467	4	d.	d.	PROPN
ejpam-6441	467	5	wardowski	wardowski	PROPN
ejpam-6441	467	6	.	.	PUNCT
ejpam-6441	468	1	fixed	fix	VERB
ejpam-6441	468	2	points	point	NOUN
ejpam-6441	468	3	of	of	ADP
ejpam-6441	468	4	a	a	DET
ejpam-6441	468	5	new	new	ADJ
ejpam-6441	468	6	type	type	NOUN
ejpam-6441	468	7	of	of	ADP
ejpam-6441	468	8	contractive	contractive	ADJ
ejpam-6441	468	9	mappings	mapping	NOUN
ejpam-6441	468	10	in	in	ADP
ejpam-6441	468	11	complete	complete	ADJ
ejpam-6441	468	12	metric	metric	ADJ
ejpam-6441	468	13	spaces	space	NOUN
ejpam-6441	468	14	.	.	PUNCT
ejpam-6441	469	1	fixed	fix	VERB
ejpam-6441	469	2	point	point	NOUN
ejpam-6441	469	3	theory	theory	NOUN
ejpam-6441	469	4	and	and	CCONJ
ejpam-6441	469	5	applications	application	NOUN
ejpam-6441	469	6	,	,	PUNCT
ejpam-6441	469	7	2012(94):1–6	2012(94):1–6	NUM
ejpam-6441	469	8	,	,	PUNCT
ejpam-6441	469	9	2012	2012	NUM
ejpam-6441	469	10	.	.	PUNCT
ejpam-6441	470	1	[	[	X
ejpam-6441	470	2	7	7	X
ejpam-6441	470	3	]	]	X
ejpam-6441	470	4	m.	m.	NOUN
ejpam-6441	470	5	arshad	arshad	PROPN
ejpam-6441	470	6	,	,	PUNCT
ejpam-6441	470	7	m.	m.	NOUN
ejpam-6441	470	8	mudhesh	mudhesh	NOUN
ejpam-6441	470	9	,	,	PUNCT
ejpam-6441	470	10	a.	a.	NOUN
ejpam-6441	470	11	hussain	hussain	PROPN
ejpam-6441	470	12	,	,	PUNCT
ejpam-6441	470	13	and	and	CCONJ
ejpam-6441	470	14	e.	e.	PROPN
ejpam-6441	470	15	ameer	ameer	PROPN
ejpam-6441	470	16	.	.	PUNCT
ejpam-6441	471	1	recent	recent	ADJ
ejpam-6441	471	2	thought	thought	NOUN
ejpam-6441	471	3	of	of	ADP
ejpam-6441	471	4	α∗-geraghty	α∗-geraghty	PROPN
ejpam-6441	471	5	f	f	PROPN
ejpam-6441	471	6	contraction	contraction	NOUN
ejpam-6441	471	7	with	with	ADP
ejpam-6441	471	8	application	application	NOUN
ejpam-6441	471	9	.	.	PUNCT
ejpam-6441	472	1	journal	journal	PROPN
ejpam-6441	472	2	of	of	ADP
ejpam-6441	472	3	mathematical	mathematical	ADJ
ejpam-6441	472	4	extension	extension	NOUN
ejpam-6441	472	5	,	,	PUNCT
ejpam-6441	472	6	(	(	PUNCT
ejpam-6441	472	7	7):1–28	7):1–28	NOUN
ejpam-6441	472	8	)	)	PUNCT
ejpam-6441	472	9	,	,	PUNCT
ejpam-6441	472	10	volume	volume	NOUN
ejpam-6441	472	11	=	=	PUNCT
ejpam-6441	472	12	16	16	NUM
ejpam-6441	472	13	,	,	PUNCT
ejpam-6441	472	14	2022	2022	NUM
ejpam-6441	472	15	.	.	PUNCT
ejpam-6441	473	1	[	[	X
ejpam-6441	473	2	8	8	NUM
ejpam-6441	473	3	]	]	X
ejpam-6441	473	4	m.	m.	NOUN
ejpam-6441	473	5	mudhesh	mudhesh	NOUN
ejpam-6441	473	6	,	,	PUNCT
ejpam-6441	473	7	h.	h.	PROPN
ejpam-6441	473	8	a.	a.	PROPN
ejpam-6441	473	9	hammad	hammad	PROPN
ejpam-6441	473	10	,	,	PUNCT
ejpam-6441	473	11	e.	e.	PROPN
ejpam-6441	473	12	ameer	ameer	PROPN
ejpam-6441	473	13	,	,	PUNCT
ejpam-6441	473	14	m.	m.	PROPN
ejpam-6441	473	15	arshad	arshad	PROPN
ejpam-6441	473	16	,	,	PUNCT
ejpam-6441	473	17	and	and	CCONJ
ejpam-6441	473	18	f.	f.	PROPN
ejpam-6441	473	19	jarad	jarad	PROPN
ejpam-6441	473	20	.	.	PUNCT
ejpam-6441	474	1	novel	novel	ADJ
ejpam-6441	474	2	results	result	NOUN
ejpam-6441	474	3	on	on	ADP
ejpam-6441	474	4	fixed	fix	VERB
ejpam-6441	474	5	-	-	PUNCT
ejpam-6441	474	6	point	point	NOUN
ejpam-6441	474	7	methodologies	methodology	NOUN
ejpam-6441	474	8	for	for	ADP
ejpam-6441	474	9	hybrid	hybrid	ADJ
ejpam-6441	474	10	contraction	contraction	NOUN
ejpam-6441	474	11	mappings	mapping	NOUN
ejpam-6441	474	12	in	in	ADP
ejpam-6441	474	13	mb	mb	ADJ
ejpam-6441	474	14	-	-	ADJ
ejpam-6441	474	15	metric	metric	ADJ
ejpam-6441	474	16	spaces	space	NOUN
ejpam-6441	474	17	with	with	ADP
ejpam-6441	474	18	an	an	DET
ejpam-6441	474	19	application	application	NOUN
ejpam-6441	474	20	.	.	PUNCT
ejpam-6441	475	1	aims	aim	VERB
ejpam-6441	475	2	mathematics	mathematic	NOUN
ejpam-6441	475	3	,	,	PUNCT
ejpam-6441	475	4	8(1):1530–1549	8(1):1530–1549	PROPN
ejpam-6441	475	5	,	,	PUNCT
ejpam-6441	475	6	2023	2023	NUM
ejpam-6441	475	7	.	.	PUNCT
ejpam-6441	476	1	[	[	X
ejpam-6441	476	2	9	9	NUM
ejpam-6441	476	3	]	]	PUNCT
ejpam-6441	476	4	a.	a.	PROPN
ejpam-6441	476	5	ali	ali	PROPN
ejpam-6441	476	6	,	,	PUNCT
ejpam-6441	476	7	e.	e.	PROPN
ejpam-6441	476	8	ameer	ameer	PROPN
ejpam-6441	476	9	,	,	PUNCT
ejpam-6441	476	10	m.	m.	PROPN
ejpam-6441	476	11	arshad	arshad	PROPN
ejpam-6441	476	12	,	,	PUNCT
ejpam-6441	476	13	h.	h.	PROPN
ejpam-6441	476	14	işık	işık	PROPN
ejpam-6441	476	15	,	,	PUNCT
ejpam-6441	476	16	and	and	CCONJ
ejpam-6441	476	17	m.	m.	NOUN
ejpam-6441	476	18	mudhesh	mudhesh	PROPN
ejpam-6441	476	19	.	.	PUNCT
ejpam-6441	477	1	fixed	fix	VERB
ejpam-6441	477	2	point	point	NOUN
ejpam-6441	477	3	results	result	NOUN
ejpam-6441	477	4	of	of	ADP
ejpam-6441	477	5	dynamic	dynamic	ADJ
ejpam-6441	477	6	process	process	NOUN
ejpam-6441	477	7	d̆(υ	d̆(υ	NOUN
ejpam-6441	477	8	,	,	PUNCT
ejpam-6441	477	9	µ0	µ0	PROPN
ejpam-6441	477	10	)	)	PUNCT
ejpam-6441	477	11	through	through	ADP
ejpam-6441	477	12	fci	fci	PROPN
ejpam-6441	477	13	-contractions	-contraction	NOUN
ejpam-6441	477	14	with	with	ADP
ejpam-6441	477	15	applications	application	NOUN
ejpam-6441	477	16	.	.	PUNCT
ejpam-6441	478	1	complexity	complexity	NOUN
ejpam-6441	478	2	,	,	PUNCT
ejpam-6441	478	3	2022(1):1–8	2022(1):1–8	NUM
ejpam-6441	478	4	,	,	PUNCT
ejpam-6441	478	5	2022	2022	NUM
ejpam-6441	478	6	.	.	PUNCT
ejpam-6441	479	1	[	[	X
ejpam-6441	479	2	10	10	NUM
ejpam-6441	479	3	]	]	PUNCT
ejpam-6441	479	4	s.	s.	PROPN
ejpam-6441	479	5	b.	b.	PROPN
ejpam-6441	479	6	nadler	nadler	PROPN
ejpam-6441	479	7	.	.	PUNCT
ejpam-6441	479	8	multivalued	multivalue	VERB
ejpam-6441	479	9	contraction	contraction	NOUN
ejpam-6441	479	10	mappings	mapping	NOUN
ejpam-6441	479	11	.	.	PUNCT
ejpam-6441	480	1	pacific	pacific	PROPN
ejpam-6441	480	2	journal	journal	PROPN
ejpam-6441	480	3	of	of	ADP
ejpam-6441	480	4	mathematics	mathematic	NOUN
ejpam-6441	480	5	,	,	PUNCT
ejpam-6441	480	6	30(2):475–488	30(2):475–488	PROPN
ejpam-6441	480	7	,	,	PUNCT
ejpam-6441	480	8	1969	1969	NUM
ejpam-6441	480	9	.	.	PUNCT
ejpam-6441	481	1	[	[	X
ejpam-6441	481	2	11	11	NUM
ejpam-6441	481	3	]	]	PUNCT
ejpam-6441	481	4	ö.	ö.	PROPN
ejpam-6441	481	5	acar	acar	NOUN
ejpam-6441	481	6	and	and	CCONJ
ejpam-6441	481	7	i.	i.	NOUN
ejpam-6441	481	8	altun	altun	PROPN
ejpam-6441	481	9	.	.	PUNCT
ejpam-6441	482	1	a	a	DET
ejpam-6441	482	2	fixed	fix	VERB
ejpam-6441	482	3	point	point	NOUN
ejpam-6441	482	4	theorem	theorem	NOUN
ejpam-6441	482	5	for	for	ADP
ejpam-6441	482	6	multivalued	multivalued	ADJ
ejpam-6441	482	7	mappings	mapping	NOUN
ejpam-6441	482	8	with	with	ADP
ejpam-6441	482	9	δ	δ	NOUN
ejpam-6441	482	10	-	-	PUNCT
ejpam-6441	482	11	distance	distance	NOUN
ejpam-6441	482	12	.	.	PUNCT
ejpam-6441	483	1	abstract	abstract	ADJ
ejpam-6441	483	2	and	and	CCONJ
ejpam-6441	483	3	applied	apply	VERB
ejpam-6441	483	4	analysis	analysis	NOUN
ejpam-6441	483	5	,	,	PUNCT
ejpam-6441	483	6	2014(497092):1–5	2014(497092):1–5	NUM
ejpam-6441	483	7	,	,	PUNCT
ejpam-6441	483	8	2014	2014	NUM
ejpam-6441	483	9	.	.	PUNCT
ejpam-6441	484	1	[	[	X
ejpam-6441	484	2	12	12	NUM
ejpam-6441	484	3	]	]	X
ejpam-6441	484	4	ö.	ö.	PROPN
ejpam-6441	484	5	acar	acar	NOUN
ejpam-6441	484	6	,	,	PUNCT
ejpam-6441	484	7	g.	g.	PROPN
ejpam-6441	484	8	durmaz	durmaz	PROPN
ejpam-6441	484	9	,	,	PUNCT
ejpam-6441	484	10	and	and	CCONJ
ejpam-6441	484	11	g.	g.	PROPN
ejpam-6441	484	12	minak	minak	PROPN
ejpam-6441	484	13	.	.	PUNCT
ejpam-6441	485	1	generalized	generalize	VERB
ejpam-6441	485	2	multivalued	multivalued	ADJ
ejpam-6441	485	3	f	f	PROPN
ejpam-6441	485	4	-contractions	-contraction	NOUN
ejpam-6441	485	5	on	on	ADP
ejpam-6441	485	6	complete	complete	ADJ
ejpam-6441	485	7	metric	metric	ADJ
ejpam-6441	485	8	spaces	space	NOUN
ejpam-6441	485	9	.	.	PUNCT
ejpam-6441	486	1	bulletin	bulletin	NOUN
ejpam-6441	486	2	of	of	ADP
ejpam-6441	486	3	the	the	DET
ejpam-6441	486	4	iranian	iranian	PROPN
ejpam-6441	486	5	mathematical	mathematical	PROPN
ejpam-6441	486	6	society	society	NOUN
ejpam-6441	486	7	,	,	PUNCT
ejpam-6441	486	8	40(6):1469	40(6):1469	NUM
ejpam-6441	486	9	–	–	PUNCT
ejpam-6441	486	10	1478	1478	NUM
ejpam-6441	486	11	,	,	PUNCT
ejpam-6441	486	12	2014	2014	NUM
ejpam-6441	486	13	.	.	PUNCT
ejpam-6441	487	1	[	[	X
ejpam-6441	487	2	13	13	NUM
ejpam-6441	487	3	]	]	PUNCT
ejpam-6441	487	4	m.	m.	NOUN
ejpam-6441	487	5	u.	u.	PROPN
ejpam-6441	487	6	ali	ali	PROPN
ejpam-6441	487	7	and	and	CCONJ
ejpam-6441	487	8	t.	t.	PROPN
ejpam-6441	487	9	kamran	kamran	PROPN
ejpam-6441	487	10	.	.	PUNCT
ejpam-6441	488	1	multivalued	multivalued	PROPN
ejpam-6441	488	2	f	f	PROPN
ejpam-6441	488	3	-contractions	-contractions	PROPN
ejpam-6441	488	4	and	and	CCONJ
ejpam-6441	488	5	related	relate	VERB
ejpam-6441	488	6	fixed	fix	VERB
ejpam-6441	488	7	point	point	NOUN
ejpam-6441	488	8	theorems	theorem	NOUN
ejpam-6441	488	9	with	with	ADP
ejpam-6441	488	10	an	an	DET
ejpam-6441	488	11	application	application	NOUN
ejpam-6441	488	12	.	.	PUNCT
ejpam-6441	489	1	filomat	filomat	NOUN
ejpam-6441	489	2	,	,	PUNCT
ejpam-6441	489	3	30(14):3779–3793	30(14):3779–3793	NUM
ejpam-6441	489	4	,	,	PUNCT
ejpam-6441	489	5	2016	2016	NUM
ejpam-6441	489	6	.	.	PUNCT
ejpam-6441	490	1	[	[	X
ejpam-6441	490	2	14	14	NUM
ejpam-6441	490	3	]	]	X
ejpam-6441	490	4	b.	b.	PROPN
ejpam-6441	490	5	fisher	fisher	PROPN
ejpam-6441	490	6	.	.	PUNCT
ejpam-6441	491	1	mappings	mapping	NOUN
ejpam-6441	491	2	satisfying	satisfy	VERB
ejpam-6441	491	3	a	a	DET
ejpam-6441	491	4	rational	rational	ADJ
ejpam-6441	491	5	inequality	inequality	NOUN
ejpam-6441	491	6	.	.	PUNCT
ejpam-6441	492	1	bulletin	bulletin	NOUN
ejpam-6441	492	2	of	of	ADP
ejpam-6441	492	3	the	the	DET
ejpam-6441	492	4	mathematical	mathematical	ADJ
ejpam-6441	492	5	society	society	NOUN
ejpam-6441	492	6	of	of	ADP
ejpam-6441	492	7	the	the	DET
ejpam-6441	492	8	sciences	sciences	PROPN
ejpam-6441	492	9	mathematical	mathematical	PROPN
ejpam-6441	492	10	of	of	ADP
ejpam-6441	492	11	roumanie	roumanie	PROPN
ejpam-6441	492	12	(	(	PUNCT
ejpam-6441	492	13	n.s	n.s	PROPN
ejpam-6441	492	14	.	.	PROPN
ejpam-6441	492	15	)	)	PUNCT
ejpam-6441	492	16	,	,	PUNCT
ejpam-6441	492	17	24(72):247–251	24(72):247–251	NUM
ejpam-6441	492	18	,	,	PUNCT
ejpam-6441	492	19	1980	1980	NUM
ejpam-6441	492	20	.	.	PUNCT
ejpam-6441	493	1	[	[	X
ejpam-6441	493	2	15	15	NUM
ejpam-6441	493	3	]	]	X
ejpam-6441	493	4	a.	a.	NOUN
ejpam-6441	493	5	alam	alam	PROPN
ejpam-6441	493	6	and	and	CCONJ
ejpam-6441	493	7	m.	m.	PROPN
ejpam-6441	493	8	imdad	imdad	PROPN
ejpam-6441	493	9	.	.	PUNCT
ejpam-6441	494	1	relation	relation	NOUN
ejpam-6441	494	2	-	-	PUNCT
ejpam-6441	494	3	theoretic	theoretic	NOUN
ejpam-6441	494	4	contraction	contraction	NOUN
ejpam-6441	494	5	principle	principle	NOUN
ejpam-6441	494	6	.	.	PUNCT
ejpam-6441	495	1	journal	journal	NOUN
ejpam-6441	495	2	of	of	ADP
ejpam-6441	495	3	fixed	fix	VERB
ejpam-6441	495	4	point	point	NOUN
ejpam-6441	495	5	theory	theory	NOUN
ejpam-6441	495	6	and	and	CCONJ
ejpam-6441	495	7	applications	application	NOUN
ejpam-6441	495	8	,	,	PUNCT
ejpam-6441	495	9	17(4):693–702	17(4):693–702	NUM
ejpam-6441	495	10	,	,	PUNCT
ejpam-6441	495	11	2015	2015	NUM
ejpam-6441	495	12	.	.	PUNCT
ejpam-6441	496	1	[	[	X
ejpam-6441	496	2	16	16	NUM
ejpam-6441	496	3	]	]	PUNCT
ejpam-6441	496	4	a.	a.	NOUN
ejpam-6441	496	5	tomar	tomar	PROPN
ejpam-6441	496	6	and	and	CCONJ
ejpam-6441	496	7	m.	m.	PROPN
ejpam-6441	496	8	joshi	joshi	PROPN
ejpam-6441	496	9	.	.	PUNCT
ejpam-6441	497	1	relation	relation	NOUN
ejpam-6441	497	2	-	-	PUNCT
ejpam-6441	497	3	theoretic	theoretic	NOUN
ejpam-6441	497	4	nonlinear	nonlinear	ADJ
ejpam-6441	497	5	contractions	contraction	NOUN
ejpam-6441	497	6	in	in	ADP
ejpam-6441	497	7	an	an	DET
ejpam-6441	497	8	f	f	PROPN
ejpam-6441	497	9	-metric	-metric	ADJ
ejpam-6441	497	10	space	space	NOUN
ejpam-6441	497	11	and	and	CCONJ
ejpam-6441	497	12	applications	application	NOUN
ejpam-6441	497	13	.	.	PUNCT
ejpam-6441	498	1	rendiconti	rendiconti	ADJ
ejpam-6441	498	2	del	del	PROPN
ejpam-6441	498	3	circolo	circolo	PROPN
ejpam-6441	498	4	matematico	matematico	NOUN
ejpam-6441	498	5	di	di	PROPN
ejpam-6441	498	6	palermo	palermo	PROPN
ejpam-6441	498	7	series	series	PROPN
ejpam-6441	498	8	2	2	NUM
ejpam-6441	498	9	,	,	PUNCT
ejpam-6441	498	10	70(2):835	70(2):835	NOUN
ejpam-6441	498	11	–	–	PUNCT
ejpam-6441	498	12	852	852	NUM
ejpam-6441	498	13	,	,	PUNCT
ejpam-6441	498	14	2021	2021	NUM
ejpam-6441	498	15	.	.	PUNCT
ejpam-6441	499	1	[	[	X
ejpam-6441	499	2	17	17	NUM
ejpam-6441	499	3	]	]	PUNCT
ejpam-6441	499	4	a.	a.	NOUN
ejpam-6441	499	5	alam	alam	PROPN
ejpam-6441	499	6	and	and	CCONJ
ejpam-6441	499	7	m.	m.	PROPN
ejpam-6441	499	8	imdad	imdad	PROPN
ejpam-6441	499	9	.	.	PUNCT
ejpam-6441	500	1	relation	relation	NOUN
ejpam-6441	500	2	-	-	PUNCT
ejpam-6441	500	3	theoretic	theoretic	NOUN
ejpam-6441	500	4	metrical	metrical	ADJ
ejpam-6441	500	5	coincidence	coincidence	NOUN
ejpam-6441	500	6	theorems	theorem	NOUN
ejpam-6441	500	7	.	.	PUNCT
ejpam-6441	501	1	filomat	filomat	PROPN
ejpam-6441	501	2	,	,	PUNCT
ejpam-6441	501	3	31(14):4421–4439	31(14):4421–4439	NUM
ejpam-6441	501	4	,	,	PUNCT
ejpam-6441	501	5	2017	2017	NUM
ejpam-6441	501	6	.	.	PUNCT
ejpam-6441	502	1	[	[	X
ejpam-6441	502	2	18	18	NUM
ejpam-6441	502	3	]	]	PUNCT
ejpam-6441	502	4	a.	a.	NOUN
ejpam-6441	502	5	alam	alam	PROPN
ejpam-6441	502	6	and	and	CCONJ
ejpam-6441	502	7	m.	m.	PROPN
ejpam-6441	502	8	imdad	imdad	PROPN
ejpam-6441	502	9	.	.	PUNCT
ejpam-6441	503	1	nonlinear	nonlinear	ADJ
ejpam-6441	503	2	contractions	contraction	NOUN
ejpam-6441	503	3	in	in	ADP
ejpam-6441	503	4	metric	metric	ADJ
ejpam-6441	503	5	spaces	space	NOUN
ejpam-6441	503	6	under	under	ADP
ejpam-6441	503	7	locally	locally	ADV
ejpam-6441	503	8	ttransitive	ttransitive	ADJ
ejpam-6441	503	9	binary	binary	ADJ
ejpam-6441	503	10	relations	relation	NOUN
ejpam-6441	503	11	.	.	PUNCT
ejpam-6441	504	1	fixed	fix	VERB
ejpam-6441	504	2	point	point	NOUN
ejpam-6441	504	3	theory	theory	NOUN
ejpam-6441	504	4	,	,	PUNCT
ejpam-6441	504	5	2018(19):13–24	2018(19):13–24	NOUN
ejpam-6441	504	6	,	,	PUNCT
ejpam-6441	504	7	2018	2018	NUM
ejpam-6441	504	8	.	.	PUNCT
ejpam-6441	505	1	[	[	X
ejpam-6441	505	2	19	19	NUM
ejpam-6441	505	3	]	]	X
ejpam-6441	505	4	s.	s.	PROPN
ejpam-6441	505	5	antal	antal	PROPN
ejpam-6441	505	6	,	,	PUNCT
ejpam-6441	505	7	d.	d.	PROPN
ejpam-6441	505	8	khantwal	khantwal	PROPN
ejpam-6441	505	9	,	,	PUNCT
ejpam-6441	505	10	and	and	CCONJ
ejpam-6441	505	11	u.	u.	PROPN
ejpam-6441	505	12	c.	c.	PROPN
ejpam-6441	505	13	gairola	gairola	PROPN
ejpam-6441	505	14	.	.	PUNCT
ejpam-6441	506	1	fixed	fix	VERB
ejpam-6441	506	2	point	point	NOUN
ejpam-6441	506	3	theorems	theorem	NOUN
ejpam-6441	506	4	for	for	ADP
ejpam-6441	506	5	multivalued	multivalued	ADJ
ejpam-6441	506	6	suzuki	suzuki	NOUN
ejpam-6441	506	7	type	type	NOUN
ejpam-6441	506	8	zℜ-contraction	zℜ-contraction	NOUN
ejpam-6441	506	9	in	in	ADP
ejpam-6441	506	10	relational	relational	ADJ
ejpam-6441	506	11	metric	metric	ADJ
ejpam-6441	506	12	space	space	NOUN
ejpam-6441	506	13	.	.	PUNCT
ejpam-6441	507	1	in	in	ADP
ejpam-6441	507	2	anita	anita	PROPN
ejpam-6441	507	3	tomar	tomar	PROPN
ejpam-6441	507	4	and	and	CCONJ
ejpam-6441	507	5	m.	m.	PROPN
ejpam-6441	507	6	c.	c.	PROPN
ejpam-6441	507	7	joshi	joshi	PROPN
ejpam-6441	507	8	,	,	PUNCT
ejpam-6441	507	9	editors	editor	NOUN
ejpam-6441	507	10	,	,	PUNCT
ejpam-6441	507	11	fixed	fix	VERB
ejpam-6441	507	12	point	point	NOUN
ejpam-6441	507	13	theory	theory	NOUN
ejpam-6441	507	14	and	and	CCONJ
ejpam-6441	507	15	its	its	PRON
ejpam-6441	507	16	applications	application	NOUN
ejpam-6441	507	17	to	to	ADP
ejpam-6441	507	18	real	real	ADJ
ejpam-6441	507	19	world	world	NOUN
ejpam-6441	507	20	problems	problem	NOUN
ejpam-6441	507	21	.	.	PUNCT
ejpam-6441	508	1	nova	nova	PROPN
ejpam-6441	508	2	science	science	NOUN
ejpam-6441	508	3	publishers	publisher	NOUN
ejpam-6441	508	4	,	,	PUNCT
ejpam-6441	508	5	inc	inc	PROPN
ejpam-6441	508	6	.	.	PROPN
ejpam-6441	508	7	,	,	PUNCT
ejpam-6441	508	8	2021	2021	NUM
ejpam-6441	508	9	.	.	PUNCT
ejpam-6441	509	1	[	[	X
ejpam-6441	509	2	20	20	NUM
ejpam-6441	509	3	]	]	PUNCT
ejpam-6441	509	4	m.	m.	PROPN
ejpam-6441	509	5	d.	d.	PROPN
ejpam-6441	509	6	hasanuzzaman	hasanuzzaman	PROPN
ejpam-6441	509	7	,	,	PUNCT
ejpam-6441	509	8	s.	s.	PROPN
ejpam-6441	509	9	sessa	sessa	PROPN
ejpam-6441	509	10	,	,	PUNCT
ejpam-6441	509	11	m.	m.	NOUN
ejpam-6441	509	12	imdad	imdad	PROPN
ejpam-6441	509	13	,	,	PUNCT
ejpam-6441	509	14	and	and	CCONJ
ejpam-6441	509	15	w.	w.	PROPN
ejpam-6441	509	16	m.	m.	PROPN
ejpam-6441	509	17	alfaqih	alfaqih	PROPN
ejpam-6441	509	18	.	.	PUNCT
ejpam-6441	510	1	fixed	fix	VERB
ejpam-6441	510	2	point	point	NOUN
ejpam-6441	510	3	results	result	NOUN
ejpam-6441	510	4	for	for	ADP
ejpam-6441	510	5	a	a	DET
ejpam-6441	510	6	selected	select	VERB
ejpam-6441	510	7	class	class	NOUN
ejpam-6441	510	8	of	of	ADP
ejpam-6441	510	9	multi	multi	ADJ
ejpam-6441	510	10	-	-	ADJ
ejpam-6441	510	11	valued	value	VERB
ejpam-6441	510	12	mappings	mapping	NOUN
ejpam-6441	510	13	under	under	ADP
ejpam-6441	510	14	(	(	PUNCT
ejpam-6441	510	15	θ	θ	NOUN
ejpam-6441	510	16	,	,	PUNCT
ejpam-6441	510	17	)	)	PUNCT
ejpam-6441	510	18	-contractions	-contraction	NOUN
ejpam-6441	510	19	with	with	ADP
ejpam-6441	510	20	an	an	DET
ejpam-6441	510	21	application	application	NOUN
ejpam-6441	510	22	.	.	PUNCT
ejpam-6441	511	1	mathematics	mathematic	NOUN
ejpam-6441	511	2	,	,	PUNCT
ejpam-6441	511	3	8(5):1–17	8(5):1–17	NUM
ejpam-6441	511	4	,	,	PUNCT
ejpam-6441	511	5	2020	2020	NUM
ejpam-6441	511	6	.	.	PUNCT
ejpam-6441	512	1	[	[	X
ejpam-6441	512	2	21	21	NUM
ejpam-6441	512	3	]	]	PUNCT
ejpam-6441	512	4	a.	a.	PROPN
ejpam-6441	512	5	malhotra	malhotra	PROPN
ejpam-6441	512	6	and	and	CCONJ
ejpam-6441	512	7	d.	d.	PROPN
ejpam-6441	512	8	kumar	kumar	PROPN
ejpam-6441	512	9	.	.	PROPN
ejpam-6441	512	10	fixed	fix	VERB
ejpam-6441	512	11	point	point	NOUN
ejpam-6441	512	12	results	result	NOUN
ejpam-6441	512	13	for	for	ADP
ejpam-6441	512	14	multivalued	multivalued	ADJ
ejpam-6441	512	15	mapping	mapping	NOUN
ejpam-6441	512	16	in	in	ADP
ejpam-6441	512	17	r	r	NOUN
ejpam-6441	512	18	-	-	PUNCT
ejpam-6441	512	19	metric	metric	ADJ
ejpam-6441	512	20	m.	m.	NOUN
ejpam-6441	512	21	mudhesh	mudhesh	PROPN
ejpam-6441	512	22	et	et	PROPN
ejpam-6441	512	23	al	al	PROPN
ejpam-6441	512	24	.	.	PUNCT
ejpam-6441	512	25	/	/	SYM
ejpam-6441	512	26	eur	eur	PROPN
ejpam-6441	512	27	.	.	PUNCT
ejpam-6441	513	1	j.	j.	PROPN
ejpam-6441	513	2	pure	pure	PROPN
ejpam-6441	513	3	appl	appl	PROPN
ejpam-6441	513	4	.	.	PROPN
ejpam-6441	513	5	math	math	PROPN
ejpam-6441	513	6	,	,	PUNCT
ejpam-6441	513	7	18	18	NUM
ejpam-6441	513	8	(	(	PUNCT
ejpam-6441	513	9	4	4	NUM
ejpam-6441	513	10	)	)	PUNCT
ejpam-6441	513	11	(	(	PUNCT
ejpam-6441	513	12	2025	2025	NUM
ejpam-6441	513	13	)	)	PUNCT
ejpam-6441	513	14	,	,	PUNCT
ejpam-6441	513	15	6441	6441	NUM
ejpam-6441	513	16	21	21	NUM
ejpam-6441	513	17	of	of	ADP
ejpam-6441	513	18	21	21	NUM
ejpam-6441	513	19	space	space	NOUN
ejpam-6441	513	20	.	.	PUNCT
ejpam-6441	514	1	sahand	sahand	NOUN
ejpam-6441	514	2	communications	communication	NOUN
ejpam-6441	514	3	in	in	ADP
ejpam-6441	514	4	mathematical	mathematical	ADJ
ejpam-6441	514	5	analysis	analysis	NOUN
ejpam-6441	514	6	,	,	PUNCT
ejpam-6441	514	7	20(2):109–121	20(2):109–121	PROPN
ejpam-6441	514	8	,	,	PUNCT
ejpam-6441	514	9	2023	2023	NUM
ejpam-6441	514	10	.	.	PUNCT
ejpam-6441	515	1	[	[	X
ejpam-6441	515	2	22	22	NUM
ejpam-6441	515	3	]	]	PUNCT
ejpam-6441	515	4	s.	s.	PROPN
ejpam-6441	515	5	negi	negi	PROPN
ejpam-6441	515	6	and	and	CCONJ
ejpam-6441	515	7	u.	u.	PROPN
ejpam-6441	515	8	c.	c.	PROPN
ejpam-6441	515	9	gairola	gairola	PROPN
ejpam-6441	515	10	.	.	PUNCT
ejpam-6441	516	1	existence	existence	NOUN
ejpam-6441	516	2	of	of	ADP
ejpam-6441	516	3	fixed	fix	VERB
ejpam-6441	516	4	point	point	NOUN
ejpam-6441	516	5	under	under	ADP
ejpam-6441	516	6	generalized	generalize	VERB
ejpam-6441	516	7	multivalued	multivalue	VERB
ejpam-6441	516	8	(	(	PUNCT
ejpam-6441	516	9	ψ	ψ	NOUN
ejpam-6441	516	10	-	-	NOUN
ejpam-6441	516	11	fℜ)-contraction	fℜ)-contraction	NOUN
ejpam-6441	516	12	in	in	ADP
ejpam-6441	516	13	partial	partial	ADJ
ejpam-6441	516	14	metric	metric	ADJ
ejpam-6441	516	15	spaces	space	NOUN
ejpam-6441	516	16	.	.	PUNCT
ejpam-6441	517	1	journal	journal	NOUN
ejpam-6441	517	2	of	of	ADP
ejpam-6441	517	3	mountain	mountain	NOUN
ejpam-6441	517	4	research	research	NOUN
ejpam-6441	517	5	,	,	PUNCT
ejpam-6441	517	6	16(1):169	16(1):169	NUM
ejpam-6441	517	7	–	–	PUNCT
ejpam-6441	517	8	179	179	NUM
ejpam-6441	517	9	,	,	PUNCT
ejpam-6441	517	10	2021	2021	NUM
ejpam-6441	517	11	.	.	PUNCT
ejpam-6441	518	1	[	[	X
ejpam-6441	518	2	23	23	NUM
ejpam-6441	518	3	]	]	PUNCT
ejpam-6441	518	4	m.	m.	PROPN
ejpam-6441	518	5	b.	b.	PROPN
ejpam-6441	518	6	zada	zada	PROPN
ejpam-6441	518	7	and	and	CCONJ
ejpam-6441	518	8	m.	m.	PROPN
ejpam-6441	518	9	sarwar	sarwar	PROPN
ejpam-6441	518	10	.	.	PUNCT
ejpam-6441	519	1	common	common	ADJ
ejpam-6441	519	2	fixed	fix	VERB
ejpam-6441	519	3	point	point	NOUN
ejpam-6441	519	4	theorems	theorem	NOUN
ejpam-6441	519	5	for	for	ADP
ejpam-6441	519	6	rational	rational	ADJ
ejpam-6441	519	7	fℜ-contractive	fℜ-contractive	ADJ
ejpam-6441	519	8	pairs	pair	NOUN
ejpam-6441	519	9	of	of	ADP
ejpam-6441	519	10	mappings	mapping	NOUN
ejpam-6441	519	11	with	with	ADP
ejpam-6441	519	12	applications	application	NOUN
ejpam-6441	519	13	.	.	PUNCT
ejpam-6441	520	1	journal	journal	PROPN
ejpam-6441	520	2	of	of	ADP
ejpam-6441	520	3	inequalities	inequality	NOUN
ejpam-6441	520	4	and	and	CCONJ
ejpam-6441	520	5	applications	application	NOUN
ejpam-6441	520	6	,	,	PUNCT
ejpam-6441	520	7	2019(11):1–14	2019(11):1–14	PROPN
ejpam-6441	520	8	,	,	PUNCT
ejpam-6441	520	9	2019	2019	NUM
ejpam-6441	520	10	.	.	PUNCT
ejpam-6441	521	1	[	[	X
ejpam-6441	521	2	24	24	NUM
ejpam-6441	521	3	]	]	PUNCT
ejpam-6441	521	4	i.	i.	NOUN
ejpam-6441	521	5	altun	altun	PROPN
ejpam-6441	521	6	,	,	PUNCT
ejpam-6441	521	7	g.	g.	PROPN
ejpam-6441	521	8	minak	minak	PROPN
ejpam-6441	521	9	,	,	PUNCT
ejpam-6441	521	10	and	and	CCONJ
ejpam-6441	521	11	h.	h.	PROPN
ejpam-6441	521	12	dag	dag	PROPN
ejpam-6441	521	13	.	.	PUNCT
ejpam-6441	522	1	multivalued	multivalued	PROPN
ejpam-6441	522	2	f	f	PROPN
ejpam-6441	522	3	-contractions	-contraction	NOUN
ejpam-6441	522	4	on	on	ADP
ejpam-6441	522	5	complete	complete	ADJ
ejpam-6441	522	6	metric	metric	ADJ
ejpam-6441	522	7	spaces	space	NOUN
ejpam-6441	522	8	.	.	PUNCT
ejpam-6441	523	1	journal	journal	PROPN
ejpam-6441	523	2	of	of	ADP
ejpam-6441	523	3	nonlinear	nonlinear	ADJ
ejpam-6441	523	4	and	and	CCONJ
ejpam-6441	523	5	convex	convex	ADJ
ejpam-6441	523	6	analysis	analysis	NOUN
ejpam-6441	523	7	,	,	PUNCT
ejpam-6441	523	8	16(4):659–666	16(4):659–666	PROPN
ejpam-6441	523	9	,	,	PUNCT
ejpam-6441	523	10	2015	2015	NUM
ejpam-6441	523	11	.	.	PUNCT
ejpam-6441	524	1	[	[	X
ejpam-6441	524	2	25	25	NUM
ejpam-6441	524	3	]	]	PUNCT
ejpam-6441	524	4	a.	a.	NOUN
ejpam-6441	524	5	f.	f.	PROPN
ejpam-6441	524	6	roldán	roldán	PROPN
ejpam-6441	524	7	lópez	lópez	PROPN
ejpam-6441	524	8	de	de	PROPN
ejpam-6441	524	9	hierro	hierro	PROPN
ejpam-6441	524	10	.	.	PROPN
ejpam-6441	525	1	a	a	DET
ejpam-6441	525	2	unified	unified	ADJ
ejpam-6441	525	3	version	version	NOUN
ejpam-6441	525	4	of	of	ADP
ejpam-6441	525	5	ran	ran	NOUN
ejpam-6441	525	6	and	and	CCONJ
ejpam-6441	525	7	reurings	reuring	NOUN
ejpam-6441	525	8	’	'	PUNCT
ejpam-6441	525	9	theorem	theorem	NOUN
ejpam-6441	525	10	and	and	CCONJ
ejpam-6441	525	11	nieto	nieto	PROPN
ejpam-6441	525	12	and	and	CCONJ
ejpam-6441	525	13	rodŕıguez	rodŕıguez	NOUN
ejpam-6441	525	14	-	-	PUNCT
ejpam-6441	525	15	lópez	lópez	ADV
ejpam-6441	525	16	’s	’s	PART
ejpam-6441	525	17	theorem	theorem	ADJ
ejpam-6441	525	18	and	and	CCONJ
ejpam-6441	525	19	low	low	ADJ
ejpam-6441	525	20	-	-	PUNCT
ejpam-6441	525	21	dimensional	dimensional	ADJ
ejpam-6441	525	22	generalizations	generalization	NOUN
ejpam-6441	525	23	.	.	PUNCT
ejpam-6441	526	1	applied	apply	VERB
ejpam-6441	526	2	mathematics	mathematics	PROPN
ejpam-6441	526	3	&	&	CCONJ
ejpam-6441	526	4	information	information	NOUN
ejpam-6441	526	5	sciences	sciences	PROPN
ejpam-6441	526	6	,	,	PUNCT
ejpam-6441	526	7	10(2):383–393	10(2):383–393	PROPN
ejpam-6441	526	8	,	,	PUNCT
ejpam-6441	526	9	2016	2016	NUM
ejpam-6441	526	10	.	.	PUNCT
ejpam-6441	527	1	[	[	X
ejpam-6441	527	2	26	26	NUM
ejpam-6441	527	3	]	]	X
ejpam-6441	527	4	s.	s.	PROPN
ejpam-6441	527	5	shukla	shukla	PROPN
ejpam-6441	527	6	and	and	CCONJ
ejpam-6441	527	7	r.	r.	PROPN
ejpam-6441	527	8	rodŕıguez	rodŕıguez	PROPN
ejpam-6441	527	9	-	-	PUNCT
ejpam-6441	527	10	lópez	lópez	ADV
ejpam-6441	527	11	.	.	PUNCT
ejpam-6441	528	1	fixed	fix	VERB
ejpam-6441	528	2	points	point	NOUN
ejpam-6441	528	3	of	of	ADP
ejpam-6441	528	4	multi	multi	ADJ
ejpam-6441	528	5	-	-	ADJ
ejpam-6441	528	6	valued	value	VERB
ejpam-6441	528	7	relation	relation	NOUN
ejpam-6441	528	8	-	-	PUNCT
ejpam-6441	528	9	theoretic	theoretic	NOUN
ejpam-6441	528	10	contractions	contraction	NOUN
ejpam-6441	528	11	in	in	ADP
ejpam-6441	528	12	metric	metric	ADJ
ejpam-6441	528	13	spaces	space	NOUN
ejpam-6441	528	14	and	and	CCONJ
ejpam-6441	528	15	application	application	NOUN
ejpam-6441	528	16	.	.	PUNCT
ejpam-6441	529	1	quaestiones	quaestione	NOUN
ejpam-6441	529	2	mathematicae	mathematicae	PROPN
ejpam-6441	529	3	,	,	PUNCT
ejpam-6441	529	4	43(3):409	43(3):409	NUM
ejpam-6441	529	5	–	–	PUNCT
ejpam-6441	529	6	424	424	NUM
ejpam-6441	529	7	,	,	PUNCT
ejpam-6441	529	8	2019	2019	NUM
ejpam-6441	529	9	.	.	PUNCT
ejpam-6441	530	1	[	[	X
ejpam-6441	530	2	27	27	NUM
ejpam-6441	530	3	]	]	PUNCT
ejpam-6441	530	4	a.	a.	PROPN
ejpam-6441	530	5	h.	h.	PROPN
ejpam-6441	530	6	albargi	albargi	PROPN
ejpam-6441	530	7	and	and	CCONJ
ejpam-6441	530	8	v.	v.	ADP
ejpam-6441	530	9	obukhovskii	obukhovskii	PROPN
ejpam-6441	530	10	.	.	PUNCT
ejpam-6441	531	1	fixed	fix	VERB
ejpam-6441	531	2	-	-	PUNCT
ejpam-6441	531	3	point	point	NOUN
ejpam-6441	531	4	results	result	NOUN
ejpam-6441	531	5	for	for	ADP
ejpam-6441	531	6	generalized	generalized	ADJ
ejpam-6441	531	7	rational	rational	ADJ
ejpam-6441	531	8	contractions	contraction	NOUN
ejpam-6441	531	9	in	in	ADP
ejpam-6441	531	10	graphical	graphical	ADJ
ejpam-6441	531	11	b	b	NOUN
ejpam-6441	531	12	-	-	ADJ
ejpam-6441	531	13	metric	metric	ADJ
ejpam-6441	531	14	spaces	space	NOUN
ejpam-6441	531	15	with	with	ADP
ejpam-6441	531	16	applications	application	NOUN
ejpam-6441	531	17	.	.	PUNCT
ejpam-6441	532	1	journal	journal	NOUN
ejpam-6441	532	2	of	of	ADP
ejpam-6441	532	3	mathematics	mathematic	NOUN
ejpam-6441	532	4	,	,	PUNCT
ejpam-6441	532	5	(	(	PUNCT
ejpam-6441	532	6	1	1	NUM
ejpam-6441	532	7	)	)	PUNCT
ejpam-6441	532	8	,	,	PUNCT
ejpam-6441	532	9	2023	2023	NUM
ejpam-6441	532	10	.	.	PUNCT
ejpam-6441	533	1	[	[	X
ejpam-6441	533	2	28	28	NUM
ejpam-6441	533	3	]	]	X
ejpam-6441	533	4	h.	h.	PROPN
ejpam-6441	533	5	k.	k.	PROPN
ejpam-6441	533	6	jassim	jassim	PROPN
ejpam-6441	533	7	,	,	PUNCT
ejpam-6441	533	8	h.	h.	PROPN
ejpam-6441	533	9	ahmad	ahmad	PROPN
ejpam-6441	533	10	,	,	PUNCT
ejpam-6441	533	11	a.	a.	NOUN
ejpam-6441	533	12	shamaoon	shamaoon	NOUN
ejpam-6441	533	13	,	,	PUNCT
ejpam-6441	533	14	and	and	CCONJ
ejpam-6441	533	15	c.	c.	PROPN
ejpam-6441	533	16	cesarano	cesarano	PROPN
ejpam-6441	533	17	.	.	PUNCT
ejpam-6441	534	1	an	an	DET
ejpam-6441	534	2	efficient	efficient	ADJ
ejpam-6441	534	3	hybrid	hybrid	NOUN
ejpam-6441	534	4	technique	technique	NOUN
ejpam-6441	534	5	for	for	ADP
ejpam-6441	534	6	the	the	DET
ejpam-6441	534	7	solution	solution	NOUN
ejpam-6441	534	8	of	of	ADP
ejpam-6441	534	9	fractional	fractional	ADJ
ejpam-6441	534	10	-	-	PUNCT
ejpam-6441	534	11	order	order	NOUN
ejpam-6441	534	12	partial	partial	ADJ
ejpam-6441	534	13	differential	differential	NOUN
ejpam-6441	534	14	equations	equation	NOUN
ejpam-6441	534	15	.	.	PUNCT
ejpam-6441	535	1	carpathian	carpathian	ADJ
ejpam-6441	535	2	mathematical	mathematical	ADJ
ejpam-6441	535	3	publications	publication	NOUN
ejpam-6441	535	4	,	,	PUNCT
ejpam-6441	535	5	13(3):790–804	13(3):790–804	PROPN
ejpam-6441	535	6	,	,	PUNCT
ejpam-6441	535	7	2021	2021	NUM
ejpam-6441	535	8	.	.	PUNCT
ejpam-6441	536	1	[	[	X
ejpam-6441	536	2	29	29	NUM
ejpam-6441	536	3	]	]	PUNCT
ejpam-6441	536	4	m.	m.	NOUN
ejpam-6441	536	5	zakarya	zakarya	PROPN
ejpam-6441	536	6	,	,	PUNCT
ejpam-6441	536	7	m.	m.	NOUN
ejpam-6441	536	8	altanji	altanji	NOUN
ejpam-6441	536	9	,	,	PUNCT
ejpam-6441	536	10	g.	g.	PROPN
ejpam-6441	536	11	alnemer	alnemer	PROPN
ejpam-6441	536	12	,	,	PUNCT
ejpam-6441	536	13	h.	h.	PROPN
ejpam-6441	536	14	a.	a.	PROPN
ejpam-6441	536	15	abd	abd	PROPN
ejpam-6441	536	16	el	el	PROPN
ejpam-6441	536	17	-	-	PUNCT
ejpam-6441	536	18	hamid	hamid	PROPN
ejpam-6441	536	19	,	,	PUNCT
ejpam-6441	536	20	c.	c.	PROPN
ejpam-6441	536	21	cesarano	cesarano	PROPN
ejpam-6441	536	22	,	,	PUNCT
ejpam-6441	536	23	and	and	CCONJ
ejpam-6441	536	24	h.	h.	PROPN
ejpam-6441	536	25	m.	m.	PROPN
ejpam-6441	536	26	rezk	rezk	PROPN
ejpam-6441	536	27	.	.	PUNCT
ejpam-6441	537	1	fractional	fractional	ADJ
ejpam-6441	537	2	reverse	reverse	ADJ
ejpam-6441	537	3	copsons	copson	NOUN
ejpam-6441	537	4	inequalities	inequality	NOUN
ejpam-6441	537	5	via	via	ADP
ejpam-6441	537	6	conformable	conformable	ADJ
ejpam-6441	537	7	calculus	calculus	NOUN
ejpam-6441	537	8	on	on	ADP
ejpam-6441	537	9	time	time	NOUN
ejpam-6441	537	10	scales	scale	NOUN
ejpam-6441	537	11	.	.	PUNCT
ejpam-6441	538	1	symmetry	symmetry	NOUN
ejpam-6441	538	2	,	,	PUNCT
ejpam-6441	538	3	13(4):1–16	13(4):1–16	PROPN
ejpam-6441	538	4	,	,	PUNCT
ejpam-6441	538	5	2021	2021	NUM
ejpam-6441	538	6	.	.	PUNCT
ejpam-6441	539	1	[	[	X
ejpam-6441	539	2	30	30	NUM
ejpam-6441	539	3	]	]	X
ejpam-6441	539	4	a.	a.	NOUN
ejpam-6441	539	5	azam	azam	PROPN
ejpam-6441	539	6	,	,	PUNCT
ejpam-6441	539	7	m.	m.	NOUN
ejpam-6441	539	8	rashid	rashid	PROPN
ejpam-6441	539	9	,	,	PUNCT
ejpam-6441	539	10	and	and	CCONJ
ejpam-6441	539	11	n.	n.	PROPN
ejpam-6441	539	12	mehmood	mehmood	PROPN
ejpam-6441	539	13	.	.	PUNCT
ejpam-6441	540	1	set	set	PROPN
ejpam-6441	540	2	-	-	PUNCT
ejpam-6441	540	3	valued	value	VERB
ejpam-6441	540	4	(	(	PUNCT
ejpam-6441	540	5	ψ	ψ	X
ejpam-6441	540	6	,	,	PUNCT
ejpam-6441	540	7	ϕ	ϕ	NOUN
ejpam-6441	540	8	)	)	PUNCT
ejpam-6441	540	9	−	−	PROPN
ejpam-6441	540	10	θ	θ	PROPN
ejpam-6441	540	11	ordered	order	VERB
ejpam-6441	540	12	contractions	contraction	NOUN
ejpam-6441	540	13	with	with	ADP
ejpam-6441	540	14	applications	application	NOUN
ejpam-6441	540	15	in	in	ADP
ejpam-6441	540	16	differential	differential	ADJ
ejpam-6441	540	17	inclusions	inclusion	NOUN
ejpam-6441	540	18	.	.	PUNCT
ejpam-6441	541	1	the	the	DET
ejpam-6441	541	2	journal	journal	NOUN
ejpam-6441	541	3	of	of	ADP
ejpam-6441	541	4	analysis	analysis	NOUN
ejpam-6441	541	5	,	,	PUNCT
ejpam-6441	541	6	27(3):673–695	27(3):673–695	NUM
ejpam-6441	541	7	,	,	PUNCT
ejpam-6441	541	8	2019	2019	NUM
ejpam-6441	541	9	.	.	PUNCT
ejpam-6441	542	1	[	[	X
ejpam-6441	542	2	31	31	NUM
ejpam-6441	542	3	]	]	PUNCT
ejpam-6441	542	4	l.	l.	PROPN
ejpam-6441	542	5	shahid	shahid	PROPN
ejpam-6441	542	6	,	,	PUNCT
ejpam-6441	542	7	m.	m.	NOUN
ejpam-6441	542	8	rashid	rashid	PROPN
ejpam-6441	542	9	,	,	PUNCT
ejpam-6441	542	10	a.	a.	PROPN
ejpam-6441	542	11	azam	azam	PROPN
ejpam-6441	542	12	,	,	PUNCT
ejpam-6441	542	13	and	and	CCONJ
ejpam-6441	542	14	f.	f.	PROPN
ejpam-6441	542	15	ali	ali	PROPN
ejpam-6441	542	16	.	.	PROPN
ejpam-6441	543	1	existence	existence	PROPN
ejpam-6441	543	2	results	result	VERB
ejpam-6441	543	3	for	for	ADP
ejpam-6441	543	4	nonlinear	nonlinear	ADJ
ejpam-6441	543	5	fractional	fractional	ADJ
ejpam-6441	543	6	differential	differential	ADJ
ejpam-6441	543	7	inclusions	inclusion	NOUN
ejpam-6441	543	8	via	via	ADP
ejpam-6441	543	9	q	q	ADJ
ejpam-6441	543	10	-	-	PUNCT
ejpam-6441	543	11	rof	rof	NOUN
ejpam-6441	543	12	fixed	fix	VERB
ejpam-6441	543	13	point	point	NOUN
ejpam-6441	543	14	.	.	PUNCT
ejpam-6441	544	1	fractal	fractal	ADJ
ejpam-6441	544	2	and	and	CCONJ
ejpam-6441	544	3	fractional	fractional	ADJ
ejpam-6441	544	4	,	,	PUNCT
ejpam-6441	544	5	7(1):1–12	7(1):1–12	NUM
ejpam-6441	544	6	,	,	PUNCT
ejpam-6441	544	7	2022	2022	NUM
ejpam-6441	544	8	.	.	PUNCT