id	sid	tid	token	lemma	pos
ejpam-6847	1	1	european	european	PROPN
ejpam-6847	1	2	journal	journal	PROPN
ejpam-6847	1	3	of	of	ADP
ejpam-6847	1	4	pure	pure	ADJ
ejpam-6847	1	5	and	and	CCONJ
ejpam-6847	1	6	applied	applied	ADJ
ejpam-6847	1	7	mathematics	mathematic	NOUN
ejpam-6847	1	8	2025	2025	NUM
ejpam-6847	1	9	,	,	PUNCT
ejpam-6847	1	10	vol	vol	NOUN
ejpam-6847	1	11	.	.	PROPN
ejpam-6847	1	12	18	18	NUM
ejpam-6847	1	13	,	,	PUNCT
ejpam-6847	1	14	issue	issue	NOUN
ejpam-6847	1	15	4	4	NUM
ejpam-6847	1	16	,	,	PUNCT
ejpam-6847	1	17	article	article	NOUN
ejpam-6847	1	18	number	number	NOUN
ejpam-6847	1	19	6847	6847	NUM
ejpam-6847	1	20	issn	issn	VERB
ejpam-6847	1	21	1307	1307	NUM
ejpam-6847	1	22	-	-	SYM
ejpam-6847	1	23	5543	5543	NUM
ejpam-6847	1	24	–	–	PUNCT
ejpam-6847	1	25	ejpam.com	ejpam.com	X
ejpam-6847	1	26	published	publish	VERB
ejpam-6847	1	27	by	by	ADP
ejpam-6847	1	28	new	new	PROPN
ejpam-6847	1	29	york	york	PROPN
ejpam-6847	1	30	business	business	PROPN
ejpam-6847	1	31	global	global	ADJ
ejpam-6847	1	32	extending	extend	VERB
ejpam-6847	1	33	f	f	NOUN
ejpam-6847	1	34	-	-	PUNCT
ejpam-6847	1	35	contraction	contraction	NOUN
ejpam-6847	1	36	theory	theory	NOUN
ejpam-6847	1	37	:	:	PUNCT
ejpam-6847	1	38	fixed	fix	VERB
ejpam-6847	1	39	points	point	NOUN
ejpam-6847	1	40	in	in	ADP
ejpam-6847	1	41	triple	triple	ADV
ejpam-6847	1	42	-	-	PUNCT
ejpam-6847	1	43	controlled	control	VERB
ejpam-6847	1	44	s	s	ADJ
ejpam-6847	1	45	-	-	ADJ
ejpam-6847	1	46	metric	metric	ADJ
ejpam-6847	1	47	spaces	space	NOUN
ejpam-6847	1	48	fatima	fatima	PROPN
ejpam-6847	1	49	m.	m.	PROPN
ejpam-6847	1	50	azmi1,∗	azmi1,∗	PROPN
ejpam-6847	1	51	,	,	PUNCT
ejpam-6847	1	52	arsalan	arsalan	PROPN
ejpam-6847	1	53	hojjat	hojjat	PROPN
ejpam-6847	1	54	ansari2	ansari2	PROPN
ejpam-6847	1	55	,	,	PUNCT
ejpam-6847	1	56	seyyed	seyye	VERB
ejpam-6847	1	57	h.	h.	PROPN
ejpam-6847	1	58	j.	j.	PROPN
ejpam-6847	1	59	petroudi3	petroudi3	PROPN
ejpam-6847	1	60	1	1	NUM
ejpam-6847	1	61	department	department	NOUN
ejpam-6847	1	62	of	of	ADP
ejpam-6847	1	63	mathematics	mathematic	NOUN
ejpam-6847	1	64	and	and	CCONJ
ejpam-6847	1	65	sciences	science	NOUN
ejpam-6847	1	66	,	,	PUNCT
ejpam-6847	1	67	prince	prince	PROPN
ejpam-6847	1	68	sultan	sultan	PROPN
ejpam-6847	1	69	university	university	PROPN
ejpam-6847	1	70	,	,	PUNCT
ejpam-6847	1	71	riyadh	riyadh	PROPN
ejpam-6847	1	72	11586	11586	NUM
ejpam-6847	1	73	,	,	PUNCT
ejpam-6847	1	74	saudi	saudi	PROPN
ejpam-6847	1	75	arabia	arabia	PROPN
ejpam-6847	1	76	2	2	NUM
ejpam-6847	1	77	department	department	NOUN
ejpam-6847	1	78	of	of	ADP
ejpam-6847	1	79	mathematics	mathematics	PROPN
ejpam-6847	1	80	,	,	PUNCT
ejpam-6847	1	81	karaj	karaj	PROPN
ejpam-6847	1	82	branch	branch	PROPN
ejpam-6847	1	83	,	,	PUNCT
ejpam-6847	1	84	islamic	islamic	PROPN
ejpam-6847	1	85	azad	azad	PROPN
ejpam-6847	1	86	university	university	PROPN
ejpam-6847	1	87	,	,	PUNCT
ejpam-6847	1	88	karaj	karaj	PROPN
ejpam-6847	1	89	,	,	PUNCT
ejpam-6847	1	90	iran	iran	PROPN
ejpam-6847	1	91	3	3	NUM
ejpam-6847	1	92	department	department	NOUN
ejpam-6847	1	93	of	of	ADP
ejpam-6847	1	94	mathematics	mathematic	NOUN
ejpam-6847	1	95	,	,	PUNCT
ejpam-6847	1	96	payame	payame	NOUN
ejpam-6847	1	97	noor	noor	PROPN
ejpam-6847	1	98	university	university	PROPN
ejpam-6847	1	99	,	,	PUNCT
ejpam-6847	1	100	p.o	p.o	PROPN
ejpam-6847	1	101	.	.	PROPN
ejpam-6847	1	102	box	box	PROPN
ejpam-6847	1	103	19395	19395	NUM
ejpam-6847	1	104	-	-	SYM
ejpam-6847	1	105	3697	3697	NUM
ejpam-6847	1	106	,	,	PUNCT
ejpam-6847	1	107	tehran	tehran	PROPN
ejpam-6847	1	108	,	,	PUNCT
ejpam-6847	1	109	iran	iran	PROPN
ejpam-6847	1	110	abstract	abstract	ADJ
ejpam-6847	1	111	.	.	PUNCT
ejpam-6847	2	1	this	this	DET
ejpam-6847	2	2	paper	paper	NOUN
ejpam-6847	2	3	explores	explore	VERB
ejpam-6847	2	4	the	the	DET
ejpam-6847	2	5	landscape	landscape	NOUN
ejpam-6847	2	6	of	of	ADP
ejpam-6847	2	7	fixed	fix	VERB
ejpam-6847	2	8	point	point	NOUN
ejpam-6847	2	9	theory	theory	NOUN
ejpam-6847	2	10	by	by	ADP
ejpam-6847	2	11	introducing	introduce	VERB
ejpam-6847	2	12	two	two	NUM
ejpam-6847	2	13	novel	novel	ADJ
ejpam-6847	2	14	classes	class	NOUN
ejpam-6847	2	15	of	of	ADP
ejpam-6847	2	16	contraction	contraction	NOUN
ejpam-6847	2	17	mappings	mapping	NOUN
ejpam-6847	2	18	:	:	PUNCT
ejpam-6847	2	19	the	the	DET
ejpam-6847	2	20	(	(	PUNCT
ejpam-6847	2	21	αs	αs	PROPN
ejpam-6847	2	22	,	,	PUNCT
ejpam-6847	2	23	νs	νs	NOUN
ejpam-6847	2	24	,	,	PUNCT
ejpam-6847	2	25	(	(	PUNCT
ejpam-6847	2	26	q	q	NOUN
ejpam-6847	2	27	,	,	PUNCT
ejpam-6847	2	28	h)-f)-contraction	h)-f)-contraction	NOUN
ejpam-6847	2	29	and	and	CCONJ
ejpam-6847	2	30	the	the	DET
ejpam-6847	2	31	(	(	PUNCT
ejpam-6847	2	32	αs	αs	PROPN
ejpam-6847	2	33	,	,	PUNCT
ejpam-6847	2	34	ηs	ηs	PROPN
ejpam-6847	2	35	,	,	PUNCT
ejpam-6847	2	36	νs	νs	NOUN
ejpam-6847	2	37	,	,	PUNCT
ejpam-6847	2	38	(	(	PUNCT
ejpam-6847	2	39	q	q	X
ejpam-6847	2	40	,	,	PUNCT
ejpam-6847	2	41	h)-f)contraction	h)-f)contraction	NOUN
ejpam-6847	2	42	,	,	PUNCT
ejpam-6847	2	43	defined	define	VERB
ejpam-6847	2	44	within	within	ADP
ejpam-6847	2	45	the	the	DET
ejpam-6847	2	46	rich	rich	ADJ
ejpam-6847	2	47	structure	structure	NOUN
ejpam-6847	2	48	of	of	ADP
ejpam-6847	2	49	triple	triple	ADJ
ejpam-6847	2	50	-	-	PUNCT
ejpam-6847	2	51	controlled	control	VERB
ejpam-6847	2	52	s	s	ADJ
ejpam-6847	2	53	-	-	ADJ
ejpam-6847	2	54	metric	metric	ADJ
ejpam-6847	2	55	type	type	NOUN
ejpam-6847	2	56	spaces	space	NOUN
ejpam-6847	2	57	.	.	PUNCT
ejpam-6847	3	1	these	these	DET
ejpam-6847	3	2	mappings	mapping	NOUN
ejpam-6847	3	3	are	be	AUX
ejpam-6847	3	4	constructed	construct	VERB
ejpam-6847	3	5	using	use	VERB
ejpam-6847	3	6	a	a	DET
ejpam-6847	3	7	blend	blend	NOUN
ejpam-6847	3	8	of	of	ADP
ejpam-6847	3	9	αsand	αsand	NOUN
ejpam-6847	3	10	ηs	ηs	NOUN
ejpam-6847	3	11	-	-	PUNCT
ejpam-6847	3	12	admissibility	admissibility	NOUN
ejpam-6847	3	13	,	,	PUNCT
ejpam-6847	3	14	νs	νs	NOUN
ejpam-6847	3	15	-	-	PUNCT
ejpam-6847	3	16	subadmissibility	subadmissibility	NOUN
ejpam-6847	3	17	,	,	PUNCT
ejpam-6847	3	18	and	and	CCONJ
ejpam-6847	3	19	a	a	DET
ejpam-6847	3	20	pair	pair	NOUN
ejpam-6847	3	21	of	of	ADP
ejpam-6847	3	22	upper	upper	ADJ
ejpam-6847	3	23	-	-	PUNCT
ejpam-6847	3	24	class	class	NOUN
ejpam-6847	3	25	functions	function	NOUN
ejpam-6847	3	26	(	(	PUNCT
ejpam-6847	3	27	q	q	NOUN
ejpam-6847	3	28	,	,	PUNCT
ejpam-6847	3	29	h	h	NOUN
ejpam-6847	3	30	)	)	PUNCT
ejpam-6847	3	31	,	,	PUNCT
ejpam-6847	3	32	integrated	integrate	VERB
ejpam-6847	3	33	with	with	ADP
ejpam-6847	3	34	wardowski	wardowski	PROPN
ejpam-6847	3	35	’s	’s	PART
ejpam-6847	3	36	powerful	powerful	ADJ
ejpam-6847	3	37	f	f	NOUN
ejpam-6847	3	38	-	-	PUNCT
ejpam-6847	3	39	contraction	contraction	NOUN
ejpam-6847	3	40	approach	approach	NOUN
ejpam-6847	3	41	.	.	PUNCT
ejpam-6847	4	1	our	our	PRON
ejpam-6847	4	2	results	result	NOUN
ejpam-6847	4	3	significantly	significantly	ADV
ejpam-6847	4	4	extend	extend	VERB
ejpam-6847	4	5	the	the	DET
ejpam-6847	4	6	classical	classical	ADJ
ejpam-6847	4	7	(	(	PUNCT
ejpam-6847	4	8	αs	αs	ADJ
ejpam-6847	4	9	-	-	PUNCT
ejpam-6847	4	10	f)-contraction	f)-contraction	NOUN
ejpam-6847	4	11	framework	framework	NOUN
ejpam-6847	4	12	by	by	ADP
ejpam-6847	4	13	proving	prove	VERB
ejpam-6847	4	14	the	the	DET
ejpam-6847	4	15	existence	existence	NOUN
ejpam-6847	4	16	and	and	CCONJ
ejpam-6847	4	17	uniqueness	uniqueness	NOUN
ejpam-6847	4	18	of	of	ADP
ejpam-6847	4	19	fixed	fix	VERB
ejpam-6847	4	20	points	point	NOUN
ejpam-6847	4	21	under	under	ADP
ejpam-6847	4	22	these	these	DET
ejpam-6847	4	23	generalized	generalized	ADJ
ejpam-6847	4	24	settings	setting	NOUN
ejpam-6847	4	25	.	.	PUNCT
ejpam-6847	5	1	furthermore	furthermore	ADV
ejpam-6847	5	2	,	,	PUNCT
ejpam-6847	5	3	we	we	PRON
ejpam-6847	5	4	derive	derive	VERB
ejpam-6847	5	5	meaningful	meaningful	ADJ
ejpam-6847	5	6	corollaries	corollary	NOUN
ejpam-6847	5	7	by	by	ADP
ejpam-6847	5	8	specifying	specify	VERB
ejpam-6847	5	9	various	various	ADJ
ejpam-6847	5	10	(	(	PUNCT
ejpam-6847	5	11	q	q	ADJ
ejpam-6847	5	12	,	,	PUNCT
ejpam-6847	5	13	h	h	NOUN
ejpam-6847	5	14	)	)	PUNCT
ejpam-6847	5	15	pairs	pair	NOUN
ejpam-6847	5	16	,	,	PUNCT
ejpam-6847	5	17	illustrating	illustrate	VERB
ejpam-6847	5	18	the	the	DET
ejpam-6847	5	19	versatility	versatility	NOUN
ejpam-6847	5	20	and	and	CCONJ
ejpam-6847	5	21	depth	depth	NOUN
ejpam-6847	5	22	of	of	ADP
ejpam-6847	5	23	the	the	DET
ejpam-6847	5	24	proposed	propose	VERB
ejpam-6847	5	25	theory	theory	NOUN
ejpam-6847	5	26	and	and	CCONJ
ejpam-6847	5	27	its	its	PRON
ejpam-6847	5	28	contribution	contribution	NOUN
ejpam-6847	5	29	to	to	ADP
ejpam-6847	5	30	the	the	DET
ejpam-6847	5	31	advancement	advancement	NOUN
ejpam-6847	5	32	of	of	ADP
ejpam-6847	5	33	fixed	fix	VERB
ejpam-6847	5	34	point	point	NOUN
ejpam-6847	5	35	results	result	NOUN
ejpam-6847	5	36	in	in	ADP
ejpam-6847	5	37	generalized	generalized	ADJ
ejpam-6847	5	38	metric	metric	ADJ
ejpam-6847	5	39	environments	environment	NOUN
ejpam-6847	5	40	.	.	PUNCT
ejpam-6847	6	1	2020	2020	NUM
ejpam-6847	6	2	mathematics	mathematic	NOUN
ejpam-6847	6	3	subject	subject	NOUN
ejpam-6847	6	4	classifications	classification	NOUN
ejpam-6847	6	5	:	:	PUNCT
ejpam-6847	6	6	47h10	47h10	NUM
ejpam-6847	6	7	,	,	PUNCT
ejpam-6847	6	8	54h25	54h25	NUM
ejpam-6847	6	9	key	key	ADJ
ejpam-6847	6	10	words	word	NOUN
ejpam-6847	6	11	and	and	CCONJ
ejpam-6847	6	12	phrases	phrase	NOUN
ejpam-6847	6	13	:	:	PUNCT
ejpam-6847	6	14	fixed	fix	VERB
ejpam-6847	6	15	point	point	NOUN
ejpam-6847	6	16	,	,	PUNCT
ejpam-6847	6	17	triple	triple	ADV
ejpam-6847	6	18	controlled	control	VERB
ejpam-6847	6	19	s	s	NOUN
ejpam-6847	6	20	-	-	ADJ
ejpam-6847	6	21	metric	metric	ADJ
ejpam-6847	6	22	type	type	NOUN
ejpam-6847	6	23	spaces	space	NOUN
ejpam-6847	6	24	,	,	PUNCT
ejpam-6847	6	25	(	(	PUNCT
ejpam-6847	6	26	αs	αs	INTJ
ejpam-6847	6	27	,	,	PUNCT
ejpam-6847	6	28	µs	µs	NOUN
ejpam-6847	6	29	,	,	PUNCT
ejpam-6847	6	30	(	(	PUNCT
ejpam-6847	6	31	q	q	X
ejpam-6847	6	32	,	,	PUNCT
ejpam-6847	6	33	h)−	h)−	PROPN
ejpam-6847	6	34	f)-contraction	f)-contraction	NOUN
ejpam-6847	6	35	,	,	PUNCT
ejpam-6847	6	36	s	s	NOUN
ejpam-6847	6	37	-	-	ADJ
ejpam-6847	6	38	metric	metric	ADJ
ejpam-6847	6	39	spaces	space	NOUN
ejpam-6847	6	40	,	,	PUNCT
ejpam-6847	6	41	pair	pair	NOUN
ejpam-6847	6	42	(	(	PUNCT
ejpam-6847	6	43	q	q	NOUN
ejpam-6847	6	44	,	,	PUNCT
ejpam-6847	6	45	h	h	NOUN
ejpam-6847	6	46	)	)	PUNCT
ejpam-6847	6	47	upper	upper	ADJ
ejpam-6847	6	48	class	class	NOUN
ejpam-6847	6	49	1	1	NUM
ejpam-6847	6	50	.	.	PUNCT
ejpam-6847	6	51	introduction	introduction	NOUN
ejpam-6847	6	52	the	the	DET
ejpam-6847	6	53	study	study	NOUN
ejpam-6847	6	54	of	of	ADP
ejpam-6847	6	55	fixed	fix	VERB
ejpam-6847	6	56	point	point	NOUN
ejpam-6847	6	57	theory	theory	NOUN
ejpam-6847	6	58	has	have	VERB
ejpam-6847	6	59	a	a	DET
ejpam-6847	6	60	rich	rich	ADJ
ejpam-6847	6	61	and	and	CCONJ
ejpam-6847	6	62	influential	influential	ADJ
ejpam-6847	6	63	history	history	NOUN
ejpam-6847	6	64	,	,	PUNCT
ejpam-6847	6	65	tracing	trace	VERB
ejpam-6847	6	66	back	back	ADV
ejpam-6847	6	67	to	to	ADP
ejpam-6847	6	68	the	the	DET
ejpam-6847	6	69	foundational	foundational	ADJ
ejpam-6847	6	70	work	work	NOUN
ejpam-6847	6	71	of	of	ADP
ejpam-6847	6	72	banach	banach	NOUN
ejpam-6847	6	73	(	(	PUNCT
ejpam-6847	6	74	1922	1922	NUM
ejpam-6847	6	75	)	)	PUNCT
ejpam-6847	7	1	[	[	X
ejpam-6847	7	2	1	1	NUM
ejpam-6847	7	3	]	]	PUNCT
ejpam-6847	7	4	,	,	PUNCT
ejpam-6847	7	5	whose	whose	DET
ejpam-6847	7	6	pioneering	pioneering	ADJ
ejpam-6847	7	7	contributions	contribution	NOUN
ejpam-6847	7	8	to	to	ADP
ejpam-6847	7	9	metric	metric	ADJ
ejpam-6847	7	10	fixed	fix	VERB
ejpam-6847	7	11	point	point	NOUN
ejpam-6847	7	12	theory	theory	NOUN
ejpam-6847	7	13	culminated	culminate	VERB
ejpam-6847	7	14	in	in	ADP
ejpam-6847	7	15	the	the	DET
ejpam-6847	7	16	celebrated	celebrate	VERB
ejpam-6847	7	17	banach	banach	NOUN
ejpam-6847	7	18	contraction	contraction	NOUN
ejpam-6847	7	19	principle	principle	NOUN
ejpam-6847	7	20	.	.	PUNCT
ejpam-6847	8	1	this	this	DET
ejpam-6847	8	2	cornerstone	cornerstone	NOUN
ejpam-6847	8	3	result	result	NOUN
ejpam-6847	8	4	has	have	AUX
ejpam-6847	8	5	inspired	inspire	VERB
ejpam-6847	8	6	extensive	extensive	ADJ
ejpam-6847	8	7	research	research	NOUN
ejpam-6847	8	8	across	across	ADP
ejpam-6847	8	9	diverse	diverse	ADJ
ejpam-6847	8	10	branches	branch	NOUN
ejpam-6847	8	11	of	of	ADP
ejpam-6847	8	12	mathematics	mathematic	NOUN
ejpam-6847	8	13	and	and	CCONJ
ejpam-6847	8	14	numerous	numerous	ADJ
ejpam-6847	8	15	scientific	scientific	ADJ
ejpam-6847	8	16	fields	field	NOUN
ejpam-6847	8	17	,	,	PUNCT
ejpam-6847	8	18	including	include	VERB
ejpam-6847	8	19	computer	computer	NOUN
ejpam-6847	8	20	science	science	NOUN
ejpam-6847	8	21	,	,	PUNCT
ejpam-6847	8	22	engineering	engineering	NOUN
ejpam-6847	8	23	,	,	PUNCT
ejpam-6847	8	24	physics	physics	NOUN
ejpam-6847	8	25	,	,	PUNCT
ejpam-6847	8	26	and	and	CCONJ
ejpam-6847	8	27	economics	economic	NOUN
ejpam-6847	8	28	.	.	PUNCT
ejpam-6847	9	1	by	by	ADP
ejpam-6847	9	2	its	its	PRON
ejpam-6847	9	3	very	very	ADJ
ejpam-6847	9	4	nature	nature	NOUN
ejpam-6847	9	5	,	,	PUNCT
ejpam-6847	9	6	fixed	fix	VERB
ejpam-6847	9	7	point	point	NOUN
ejpam-6847	9	8	theory	theory	NOUN
ejpam-6847	9	9	draws	draw	VERB
ejpam-6847	9	10	upon	upon	SCONJ
ejpam-6847	9	11	ideas	idea	NOUN
ejpam-6847	9	12	from	from	ADP
ejpam-6847	9	13	topology	topology	NOUN
ejpam-6847	9	14	,	,	PUNCT
ejpam-6847	9	15	analysis	analysis	NOUN
ejpam-6847	9	16	,	,	PUNCT
ejpam-6847	9	17	and	and	CCONJ
ejpam-6847	9	18	geometry	geometry	NOUN
ejpam-6847	9	19	∗corresponding	∗corresponding	NOUN
ejpam-6847	9	20	author	author	NOUN
ejpam-6847	9	21	.	.	PUNCT
ejpam-6847	10	1	doi	doi	NOUN
ejpam-6847	10	2	:	:	PUNCT
ejpam-6847	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6847	https://doi.org/10.29020/nybg.ejpam.v18i4.6847	PROPN
ejpam-6847	10	4	email	email	NOUN
ejpam-6847	10	5	addresses	address	NOUN
ejpam-6847	10	6	:	:	PUNCT
ejpam-6847	10	7	fazmi@psu.edu.sa	fazmi@psu.edu.sa	PROPN
ejpam-6847	10	8	,	,	PUNCT
ejpam-6847	10	9	fazmi1996@gmail.com	fazmi1996@gmail.com	X
ejpam-6847	10	10	(	(	PUNCT
ejpam-6847	10	11	f.	f.	PROPN
ejpam-6847	10	12	m.	m.	PROPN
ejpam-6847	10	13	azmi	azmi	PROPN
ejpam-6847	10	14	)	)	PUNCT
ejpam-6847	10	15	,	,	PUNCT
ejpam-6847	10	16	analsisamirmath2@gmail.com	analsisamirmath2@gmail.com	PROPN
ejpam-6847	10	17	,	,	PUNCT
ejpam-6847	10	18	mathanalsisamir4@gmail.com	mathanalsisamir4@gmail.com	X
ejpam-6847	10	19	(	(	PUNCT
ejpam-6847	10	20	a.	a.	NOUN
ejpam-6847	10	21	h.	h.	PROPN
ejpam-6847	10	22	ansari	ansari	PROPN
ejpam-6847	10	23	)	)	PUNCT
ejpam-6847	10	24	,	,	PUNCT
ejpam-6847	10	25	petroudi@pnu.ac.ir	petroudi@pnu.ac.ir	NOUN
ejpam-6847	10	26	(	(	PUNCT
ejpam-6847	10	27	s.	s.	PROPN
ejpam-6847	10	28	h.	h.	PROPN
ejpam-6847	10	29	j.	j.	PROPN
ejpam-6847	10	30	petroudi	petroudi	PROPN
ejpam-6847	10	31	)	)	PUNCT
ejpam-6847	10	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6847	10	33	1	1	NUM
ejpam-6847	10	34	copyright	copyright	NOUN
ejpam-6847	10	35	:	:	PUNCT
ejpam-6847	11	1	©	©	PROPN
ejpam-6847	11	2	2025	2025	NUM
ejpam-6847	11	3	the	the	DET
ejpam-6847	11	4	author(s	author(s	NOUN
ejpam-6847	11	5	)	)	PUNCT
ejpam-6847	11	6	.	.	PUNCT
ejpam-6847	12	1	(	(	PUNCT
ejpam-6847	12	2	cc	cc	NOUN
ejpam-6847	12	3	by	by	ADP
ejpam-6847	12	4	-	-	PUNCT
ejpam-6847	12	5	nc	nc	PROPN
ejpam-6847	12	6	4.0	4.0	NUM
ejpam-6847	12	7	)	)	PUNCT
ejpam-6847	12	8	f.	f.	PROPN
ejpam-6847	12	9	m.	m.	PROPN
ejpam-6847	12	10	azmi	azmi	PROPN
ejpam-6847	12	11	,	,	PUNCT
ejpam-6847	12	12	a.	a.	PROPN
ejpam-6847	12	13	h.	h.	PROPN
ejpam-6847	12	14	ansari	ansari	PROPN
ejpam-6847	12	15	,	,	PUNCT
ejpam-6847	12	16	s.	s.	PROPN
ejpam-6847	12	17	h.	h.	PROPN
ejpam-6847	12	18	j.	j.	PROPN
ejpam-6847	12	19	petroudi	petroudi	PROPN
ejpam-6847	12	20	/	/	SYM
ejpam-6847	12	21	eur	eur	PROPN
ejpam-6847	12	22	.	.	PUNCT
ejpam-6847	13	1	j.	j.	PROPN
ejpam-6847	13	2	pure	pure	PROPN
ejpam-6847	13	3	appl	appl	PROPN
ejpam-6847	13	4	.	.	PROPN
ejpam-6847	13	5	math	math	PROPN
ejpam-6847	13	6	,	,	PUNCT
ejpam-6847	13	7	18	18	NUM
ejpam-6847	13	8	(	(	PUNCT
ejpam-6847	13	9	4	4	NUM
ejpam-6847	13	10	)	)	PUNCT
ejpam-6847	13	11	(	(	PUNCT
ejpam-6847	13	12	2025	2025	NUM
ejpam-6847	13	13	)	)	PUNCT
ejpam-6847	13	14	,	,	PUNCT
ejpam-6847	13	15	6847	6847	NUM
ejpam-6847	13	16	2	2	NUM
ejpam-6847	13	17	of	of	ADP
ejpam-6847	13	18	26	26	NUM
ejpam-6847	13	19	to	to	PART
ejpam-6847	13	20	investigate	investigate	VERB
ejpam-6847	13	21	the	the	DET
ejpam-6847	13	22	existence	existence	NOUN
ejpam-6847	13	23	and	and	CCONJ
ejpam-6847	13	24	uniqueness	uniqueness	NOUN
ejpam-6847	13	25	of	of	ADP
ejpam-6847	13	26	fixed	fix	VERB
ejpam-6847	13	27	points	point	NOUN
ejpam-6847	13	28	of	of	ADP
ejpam-6847	13	29	mappings	mapping	NOUN
ejpam-6847	13	30	—	—	PUNCT
ejpam-6847	13	31	an	an	DET
ejpam-6847	13	32	endeavor	endeavor	NOUN
ejpam-6847	13	33	that	that	PRON
ejpam-6847	13	34	has	have	AUX
ejpam-6847	13	35	generated	generate	VERB
ejpam-6847	13	36	profound	profound	ADJ
ejpam-6847	13	37	theoretical	theoretical	ADJ
ejpam-6847	13	38	insights	insight	NOUN
ejpam-6847	13	39	as	as	ADV
ejpam-6847	13	40	well	well	ADV
ejpam-6847	13	41	as	as	ADP
ejpam-6847	13	42	practical	practical	ADJ
ejpam-6847	13	43	applications	application	NOUN
ejpam-6847	13	44	.	.	PUNCT
ejpam-6847	14	1	over	over	ADP
ejpam-6847	14	2	the	the	DET
ejpam-6847	14	3	decades	decade	NOUN
ejpam-6847	14	4	,	,	PUNCT
ejpam-6847	14	5	the	the	DET
ejpam-6847	14	6	banach	banach	ADV
ejpam-6847	14	7	fixed	fix	VERB
ejpam-6847	14	8	point	point	NOUN
ejpam-6847	14	9	theorem	theorem	NOUN
ejpam-6847	14	10	has	have	AUX
ejpam-6847	14	11	undergone	undergo	VERB
ejpam-6847	14	12	significant	significant	ADJ
ejpam-6847	14	13	generalizations	generalization	NOUN
ejpam-6847	14	14	,	,	PUNCT
ejpam-6847	14	15	particularly	particularly	ADV
ejpam-6847	14	16	through	through	ADP
ejpam-6847	14	17	the	the	DET
ejpam-6847	14	18	development	development	NOUN
ejpam-6847	14	19	of	of	ADP
ejpam-6847	14	20	new	new	ADJ
ejpam-6847	14	21	classes	class	NOUN
ejpam-6847	14	22	of	of	ADP
ejpam-6847	14	23	metric	metric	ADJ
ejpam-6847	14	24	spaces	space	NOUN
ejpam-6847	14	25	.	.	PUNCT
ejpam-6847	15	1	for	for	ADP
ejpam-6847	15	2	instance	instance	NOUN
ejpam-6847	15	3	,	,	PUNCT
ejpam-6847	15	4	bakhtin	bakhtin	NOUN
ejpam-6847	15	5	[	[	X
ejpam-6847	15	6	2	2	NUM
ejpam-6847	15	7	]	]	PUNCT
ejpam-6847	15	8	introduced	introduce	VERB
ejpam-6847	15	9	the	the	DET
ejpam-6847	15	10	concept	concept	NOUN
ejpam-6847	15	11	of	of	ADP
ejpam-6847	15	12	b	b	NOUN
ejpam-6847	15	13	-	-	PUNCT
ejpam-6847	15	14	metric	metric	ADJ
ejpam-6847	15	15	spaces	space	NOUN
ejpam-6847	15	16	,	,	PUNCT
ejpam-6847	15	17	which	which	PRON
ejpam-6847	15	18	was	be	AUX
ejpam-6847	15	19	subsequently	subsequently	ADV
ejpam-6847	15	20	extended	extend	VERB
ejpam-6847	15	21	into	into	ADP
ejpam-6847	15	22	extended	extended	ADJ
ejpam-6847	15	23	b	b	X
ejpam-6847	15	24	-	-	ADJ
ejpam-6847	15	25	metric	metric	ADJ
ejpam-6847	15	26	spaces	space	NOUN
ejpam-6847	15	27	[	[	X
ejpam-6847	15	28	3	3	NUM
ejpam-6847	15	29	]	]	PUNCT
ejpam-6847	15	30	.	.	PUNCT
ejpam-6847	16	1	researchers	researcher	NOUN
ejpam-6847	16	2	further	far	ADV
ejpam-6847	16	3	expanded	expand	VERB
ejpam-6847	16	4	this	this	DET
ejpam-6847	16	5	framework	framework	NOUN
ejpam-6847	16	6	to	to	PART
ejpam-6847	16	7	include	include	VERB
ejpam-6847	16	8	controlled	control	VERB
ejpam-6847	16	9	metric	metric	ADJ
ejpam-6847	16	10	spaces	space	NOUN
ejpam-6847	16	11	[	[	X
ejpam-6847	16	12	4	4	NUM
ejpam-6847	16	13	]	]	PUNCT
ejpam-6847	16	14	,	,	PUNCT
ejpam-6847	16	15	and	and	CCONJ
ejpam-6847	16	16	later	later	ADV
ejpam-6847	16	17	to	to	ADP
ejpam-6847	16	18	more	more	ADV
ejpam-6847	16	19	complex	complex	ADJ
ejpam-6847	16	20	structures	structure	NOUN
ejpam-6847	16	21	such	such	ADJ
ejpam-6847	16	22	as	as	ADV
ejpam-6847	16	23	double	double	ADJ
ejpam-6847	16	24	and	and	CCONJ
ejpam-6847	16	25	triple	triple	ADV
ejpam-6847	16	26	controlled	control	VERB
ejpam-6847	16	27	metric	metric	ADJ
ejpam-6847	16	28	spaces	space	NOUN
ejpam-6847	16	29	[	[	X
ejpam-6847	16	30	5	5	NUM
ejpam-6847	16	31	]	]	PUNCT
ejpam-6847	16	32	,	,	PUNCT
ejpam-6847	16	33	[	[	X
ejpam-6847	16	34	6	6	NUM
ejpam-6847	16	35	]	]	PUNCT
ejpam-6847	16	36	,	,	PUNCT
ejpam-6847	16	37	[	[	X
ejpam-6847	16	38	7	7	NUM
ejpam-6847	16	39	]	]	PUNCT
ejpam-6847	16	40	,	,	PUNCT
ejpam-6847	16	41	[	[	X
ejpam-6847	16	42	8	8	NUM
ejpam-6847	16	43	]	]	PUNCT
ejpam-6847	16	44	,	,	PUNCT
ejpam-6847	16	45	[	[	X
ejpam-6847	16	46	9],[10	9],[10	NUM
ejpam-6847	16	47	]	]	X
ejpam-6847	16	48	.	.	PUNCT
ejpam-6847	17	1	in	in	ADP
ejpam-6847	17	2	parallel	parallel	NOUN
ejpam-6847	17	3	,	,	PUNCT
ejpam-6847	17	4	sedghi	sedghi	VERB
ejpam-6847	17	5	et	et	PROPN
ejpam-6847	17	6	al	al	PROPN
ejpam-6847	17	7	.	.	PUNCT
ejpam-6847	18	1	[	[	X
ejpam-6847	18	2	11	11	NUM
ejpam-6847	18	3	]	]	PUNCT
ejpam-6847	18	4	introduced	introduce	VERB
ejpam-6847	18	5	the	the	DET
ejpam-6847	18	6	concept	concept	NOUN
ejpam-6847	18	7	of	of	ADP
ejpam-6847	18	8	s	s	NOUN
ejpam-6847	18	9	-	-	ADJ
ejpam-6847	18	10	metric	metric	ADJ
ejpam-6847	18	11	spaces	space	NOUN
ejpam-6847	18	12	as	as	ADP
ejpam-6847	18	13	a	a	DET
ejpam-6847	18	14	broad	broad	ADJ
ejpam-6847	18	15	generalization	generalization	NOUN
ejpam-6847	18	16	of	of	ADP
ejpam-6847	18	17	classical	classical	ADJ
ejpam-6847	18	18	metric	metric	ADJ
ejpam-6847	18	19	spaces	space	NOUN
ejpam-6847	18	20	.	.	PUNCT
ejpam-6847	19	1	although	although	SCONJ
ejpam-6847	19	2	sedghi	sedghi	VERB
ejpam-6847	19	3	et	et	PROPN
ejpam-6847	19	4	al	al	PROPN
ejpam-6847	19	5	.	.	PROPN
ejpam-6847	19	6	later	later	ADV
ejpam-6847	19	7	demonstrated	demonstrate	VERB
ejpam-6847	19	8	in	in	ADP
ejpam-6847	19	9	[	[	X
ejpam-6847	19	10	12	12	NUM
ejpam-6847	19	11	]	]	PUNCT
ejpam-6847	19	12	that	that	SCONJ
ejpam-6847	19	13	every	every	DET
ejpam-6847	19	14	standard	standard	ADJ
ejpam-6847	19	15	metric	metric	ADJ
ejpam-6847	19	16	d	d	PROPN
ejpam-6847	19	17	induces	induce	VERB
ejpam-6847	19	18	an	an	DET
ejpam-6847	19	19	s	s	NOUN
ejpam-6847	19	20	-	-	ADJ
ejpam-6847	19	21	metric	metric	ADJ
ejpam-6847	19	22	and	and	CCONJ
ejpam-6847	19	23	conversely	conversely	ADV
ejpam-6847	19	24	,	,	PUNCT
ejpam-6847	19	25	that	that	SCONJ
ejpam-6847	19	26	a	a	DET
ejpam-6847	19	27	standard	standard	ADJ
ejpam-6847	19	28	metric	metric	NOUN
ejpam-6847	19	29	can	can	AUX
ejpam-6847	19	30	be	be	AUX
ejpam-6847	19	31	defined	define	VERB
ejpam-6847	19	32	from	from	ADP
ejpam-6847	19	33	an	an	DET
ejpam-6847	19	34	s	s	NOUN
ejpam-6847	19	35	-	-	NOUN
ejpam-6847	19	36	metric	metric	ADJ
ejpam-6847	19	37	,	,	PUNCT
ejpam-6847	19	38	researchers	researcher	NOUN
ejpam-6847	19	39	have	have	AUX
ejpam-6847	19	40	continued	continue	VERB
ejpam-6847	19	41	to	to	PART
ejpam-6847	19	42	work	work	VERB
ejpam-6847	19	43	extensively	extensively	ADV
ejpam-6847	19	44	with	with	ADP
ejpam-6847	19	45	s	s	ADJ
ejpam-6847	19	46	-	-	ADJ
ejpam-6847	19	47	metric	metric	ADJ
ejpam-6847	19	48	spaces	space	NOUN
ejpam-6847	19	49	(	(	PUNCT
ejpam-6847	19	50	see	see	VERB
ejpam-6847	19	51	[	[	X
ejpam-6847	19	52	13	13	NUM
ejpam-6847	19	53	]	]	PUNCT
ejpam-6847	19	54	,	,	PUNCT
ejpam-6847	20	1	[	[	X
ejpam-6847	20	2	14	14	NUM
ejpam-6847	20	3	]	]	PUNCT
ejpam-6847	20	4	)	)	PUNCT
ejpam-6847	20	5	.	.	PUNCT
ejpam-6847	21	1	this	this	PRON
ejpam-6847	21	2	is	be	AUX
ejpam-6847	21	3	because	because	SCONJ
ejpam-6847	21	4	many	many	ADJ
ejpam-6847	21	5	fixed	fix	VERB
ejpam-6847	21	6	point	point	NOUN
ejpam-6847	21	7	results	result	NOUN
ejpam-6847	21	8	admit	admit	VERB
ejpam-6847	21	9	clearer	clear	ADJ
ejpam-6847	21	10	and	and	CCONJ
ejpam-6847	21	11	more	more	ADJ
ejpam-6847	21	12	natural	natural	ADJ
ejpam-6847	21	13	formulations	formulation	NOUN
ejpam-6847	21	14	within	within	ADP
ejpam-6847	21	15	the	the	DET
ejpam-6847	21	16	s	s	NOUN
ejpam-6847	21	17	-	-	ADJ
ejpam-6847	21	18	metric	metric	ADJ
ejpam-6847	21	19	framework	framework	NOUN
ejpam-6847	21	20	.	.	PUNCT
ejpam-6847	22	1	moreover	moreover	ADV
ejpam-6847	22	2	,	,	PUNCT
ejpam-6847	22	3	s	s	ADJ
ejpam-6847	22	4	-	-	ADJ
ejpam-6847	22	5	metric	metric	ADJ
ejpam-6847	22	6	spaces	space	NOUN
ejpam-6847	22	7	unify	unify	VERB
ejpam-6847	22	8	and	and	CCONJ
ejpam-6847	22	9	generalize	generalize	VERB
ejpam-6847	22	10	several	several	ADJ
ejpam-6847	22	11	other	other	ADJ
ejpam-6847	22	12	structures	structure	NOUN
ejpam-6847	22	13	,	,	PUNCT
ejpam-6847	22	14	such	such	ADJ
ejpam-6847	22	15	as	as	ADP
ejpam-6847	22	16	g	g	NOUN
ejpam-6847	22	17	-	-	PUNCT
ejpam-6847	22	18	metrics	metric	NOUN
ejpam-6847	22	19	,	,	PUNCT
ejpam-6847	22	20	and	and	CCONJ
ejpam-6847	22	21	admissibility	admissibility	NOUN
ejpam-6847	22	22	conditions	condition	NOUN
ejpam-6847	22	23	,	,	PUNCT
ejpam-6847	22	24	as	as	ADV
ejpam-6847	22	25	well	well	ADV
ejpam-6847	22	26	as	as	ADP
ejpam-6847	22	27	contraction	contraction	NOUN
ejpam-6847	22	28	mappings	mapping	NOUN
ejpam-6847	22	29	may	may	AUX
ejpam-6847	22	30	behave	behave	VERB
ejpam-6847	22	31	differently	differently	ADV
ejpam-6847	22	32	in	in	ADP
ejpam-6847	22	33	s	s	NOUN
ejpam-6847	22	34	-	-	ADJ
ejpam-6847	22	35	metric	metric	ADJ
ejpam-6847	22	36	settings	setting	NOUN
ejpam-6847	22	37	,	,	PUNCT
ejpam-6847	22	38	yielding	yield	VERB
ejpam-6847	22	39	genuinely	genuinely	ADV
ejpam-6847	22	40	new	new	ADJ
ejpam-6847	22	41	fixed	fix	VERB
ejpam-6847	22	42	point	point	NOUN
ejpam-6847	22	43	results	result	NOUN
ejpam-6847	22	44	.	.	PUNCT
ejpam-6847	23	1	these	these	DET
ejpam-6847	23	2	developments	development	NOUN
ejpam-6847	23	3	have	have	AUX
ejpam-6847	23	4	further	far	ADV
ejpam-6847	23	5	stimulated	stimulate	VERB
ejpam-6847	23	6	generalizations	generalization	NOUN
ejpam-6847	23	7	,	,	PUNCT
ejpam-6847	23	8	leading	lead	VERB
ejpam-6847	23	9	to	to	ADP
ejpam-6847	23	10	structures	structure	NOUN
ejpam-6847	23	11	such	such	ADJ
ejpam-6847	23	12	as	as	ADP
ejpam-6847	23	13	sb	sb	NOUN
ejpam-6847	23	14	-	-	ADJ
ejpam-6847	23	15	metric	metric	ADJ
ejpam-6847	23	16	spaces	space	NOUN
ejpam-6847	23	17	[	[	X
ejpam-6847	23	18	15	15	NUM
ejpam-6847	23	19	]	]	PUNCT
ejpam-6847	23	20	,	,	PUNCT
ejpam-6847	23	21	[	[	X
ejpam-6847	23	22	16	16	NUM
ejpam-6847	23	23	]	]	X
ejpam-6847	23	24	partial	partial	ADJ
ejpam-6847	23	25	s	s	X
ejpam-6847	23	26	metric	metric	ADJ
ejpam-6847	23	27	space	space	NOUN
ejpam-6847	23	28	[	[	X
ejpam-6847	23	29	17	17	NUM
ejpam-6847	23	30	]	]	PUNCT
ejpam-6847	23	31	,	,	PUNCT
ejpam-6847	23	32	extended	extend	VERB
ejpam-6847	23	33	s	s	X
ejpam-6847	23	34	metric	metric	ADJ
ejpam-6847	23	35	space	space	NOUN
ejpam-6847	23	36	[	[	X
ejpam-6847	23	37	18	18	NUM
ejpam-6847	23	38	]	]	PUNCT
ejpam-6847	23	39	,	,	PUNCT
ejpam-6847	23	40	and	and	CCONJ
ejpam-6847	23	41	controlled	control	VERB
ejpam-6847	23	42	s	s	ADJ
ejpam-6847	23	43	-	-	ADJ
ejpam-6847	23	44	metric	metric	ADJ
ejpam-6847	23	45	spaces	space	NOUN
ejpam-6847	23	46	[	[	X
ejpam-6847	23	47	19	19	NUM
ejpam-6847	23	48	]	]	PUNCT
ejpam-6847	23	49	,	,	PUNCT
ejpam-6847	23	50	[	[	X
ejpam-6847	23	51	20	20	NUM
ejpam-6847	23	52	]	]	PUNCT
ejpam-6847	23	53	,	,	PUNCT
ejpam-6847	23	54	and	and	CCONJ
ejpam-6847	23	55	recently	recently	ADV
ejpam-6847	23	56	,	,	PUNCT
ejpam-6847	23	57	controlled	control	VERB
ejpam-6847	23	58	orthogonal	orthogonal	ADJ
ejpam-6847	23	59	s	s	NOUN
ejpam-6847	23	60	-	-	ADJ
ejpam-6847	23	61	metric	metric	ADJ
ejpam-6847	23	62	spaces	space	NOUN
ejpam-6847	23	63	[	[	X
ejpam-6847	23	64	21	21	NUM
ejpam-6847	23	65	]	]	PUNCT
ejpam-6847	23	66	,	,	PUNCT
ejpam-6847	23	67	[	[	X
ejpam-6847	23	68	22	22	NUM
ejpam-6847	23	69	]	]	PUNCT
ejpam-6847	23	70	.	.	PUNCT
ejpam-6847	24	1	collectively	collectively	ADV
ejpam-6847	24	2	,	,	PUNCT
ejpam-6847	24	3	these	these	DET
ejpam-6847	24	4	advances	advance	NOUN
ejpam-6847	24	5	underscore	underscore	VERB
ejpam-6847	24	6	the	the	DET
ejpam-6847	24	7	dynamic	dynamic	ADJ
ejpam-6847	24	8	evolution	evolution	NOUN
ejpam-6847	24	9	of	of	ADP
ejpam-6847	24	10	fixed	fix	VERB
ejpam-6847	24	11	point	point	NOUN
ejpam-6847	24	12	theory	theory	NOUN
ejpam-6847	24	13	,	,	PUNCT
ejpam-6847	24	14	which	which	PRON
ejpam-6847	24	15	continues	continue	VERB
ejpam-6847	24	16	to	to	PART
ejpam-6847	24	17	broaden	broaden	VERB
ejpam-6847	24	18	in	in	ADP
ejpam-6847	24	19	scope	scope	NOUN
ejpam-6847	24	20	and	and	CCONJ
ejpam-6847	24	21	enrich	enrich	VERB
ejpam-6847	24	22	its	its	PRON
ejpam-6847	24	23	applications	application	NOUN
ejpam-6847	24	24	.	.	PUNCT
ejpam-6847	25	1	building	build	VERB
ejpam-6847	25	2	on	on	ADP
ejpam-6847	25	3	this	this	DET
ejpam-6847	25	4	tradition	tradition	NOUN
ejpam-6847	25	5	,	,	PUNCT
ejpam-6847	25	6	recent	recent	ADJ
ejpam-6847	25	7	research	research	NOUN
ejpam-6847	25	8	has	have	AUX
ejpam-6847	25	9	focused	focus	VERB
ejpam-6847	25	10	on	on	ADP
ejpam-6847	25	11	both	both	CCONJ
ejpam-6847	25	12	new	new	ADJ
ejpam-6847	25	13	spaces	space	NOUN
ejpam-6847	25	14	and	and	CCONJ
ejpam-6847	25	15	novel	novel	ADJ
ejpam-6847	25	16	contraction	contraction	NOUN
ejpam-6847	25	17	conditions	condition	NOUN
ejpam-6847	25	18	.	.	PUNCT
ejpam-6847	26	1	for	for	ADP
ejpam-6847	26	2	example	example	NOUN
ejpam-6847	26	3	,	,	PUNCT
ejpam-6847	26	4	azmi	azmi	PROPN
ejpam-6847	26	5	[	[	X
ejpam-6847	26	6	20	20	NUM
ejpam-6847	26	7	]	]	PUNCT
ejpam-6847	26	8	introduced	introduce	VERB
ejpam-6847	26	9	triple	triple	ADV
ejpam-6847	26	10	controlled	control	VERB
ejpam-6847	26	11	s	s	NOUN
ejpam-6847	26	12	-	-	ADJ
ejpam-6847	26	13	metric	metric	ADJ
ejpam-6847	26	14	type	type	NOUN
ejpam-6847	26	15	spaces	space	NOUN
ejpam-6847	26	16	and	and	CCONJ
ejpam-6847	26	17	established	establish	VERB
ejpam-6847	26	18	corresponding	corresponding	ADJ
ejpam-6847	26	19	fixed	fix	VERB
ejpam-6847	26	20	point	point	NOUN
ejpam-6847	26	21	results	result	NOUN
ejpam-6847	26	22	,	,	PUNCT
ejpam-6847	26	23	thereby	thereby	ADV
ejpam-6847	26	24	extending	extend	VERB
ejpam-6847	26	25	the	the	DET
ejpam-6847	26	26	framework	framework	NOUN
ejpam-6847	26	27	of	of	ADP
ejpam-6847	26	28	controlled	control	VERB
ejpam-6847	26	29	metric	metric	ADJ
ejpam-6847	26	30	-	-	PUNCT
ejpam-6847	26	31	type	type	NOUN
ejpam-6847	26	32	spaces	space	NOUN
ejpam-6847	26	33	.	.	PUNCT
ejpam-6847	27	1	this	this	PRON
ejpam-6847	27	2	illustrates	illustrate	VERB
ejpam-6847	27	3	how	how	SCONJ
ejpam-6847	27	4	the	the	DET
ejpam-6847	27	5	theory	theory	NOUN
ejpam-6847	27	6	has	have	AUX
ejpam-6847	27	7	gradually	gradually	ADV
ejpam-6847	27	8	shifted	shift	VERB
ejpam-6847	27	9	from	from	ADP
ejpam-6847	27	10	classical	classical	ADJ
ejpam-6847	27	11	metric	metric	ADJ
ejpam-6847	27	12	settings	setting	NOUN
ejpam-6847	27	13	to	to	ADP
ejpam-6847	27	14	highly	highly	ADV
ejpam-6847	27	15	generalized	generalize	VERB
ejpam-6847	27	16	structures	structure	NOUN
ejpam-6847	27	17	to	to	PART
ejpam-6847	27	18	address	address	VERB
ejpam-6847	27	19	broader	broad	ADJ
ejpam-6847	27	20	classes	class	NOUN
ejpam-6847	27	21	of	of	ADP
ejpam-6847	27	22	mappings	mapping	NOUN
ejpam-6847	27	23	.	.	PUNCT
ejpam-6847	28	1	a	a	DET
ejpam-6847	28	2	parallel	parallel	ADJ
ejpam-6847	28	3	stream	stream	NOUN
ejpam-6847	28	4	of	of	ADP
ejpam-6847	28	5	research	research	NOUN
ejpam-6847	28	6	has	have	AUX
ejpam-6847	28	7	centered	center	VERB
ejpam-6847	28	8	on	on	ADP
ejpam-6847	28	9	the	the	DET
ejpam-6847	28	10	development	development	NOUN
ejpam-6847	28	11	of	of	ADP
ejpam-6847	28	12	generalized	generalized	ADJ
ejpam-6847	28	13	contractions	contraction	NOUN
ejpam-6847	28	14	.	.	PUNCT
ejpam-6847	29	1	a	a	DET
ejpam-6847	29	2	milestone	milestone	NOUN
ejpam-6847	29	3	in	in	ADP
ejpam-6847	29	4	this	this	DET
ejpam-6847	29	5	direction	direction	NOUN
ejpam-6847	29	6	was	be	AUX
ejpam-6847	29	7	the	the	DET
ejpam-6847	29	8	introduction	introduction	NOUN
ejpam-6847	29	9	of	of	ADP
ejpam-6847	29	10	the	the	DET
ejpam-6847	29	11	f	f	NOUN
ejpam-6847	29	12	-	-	PUNCT
ejpam-6847	29	13	contraction	contraction	NOUN
ejpam-6847	29	14	by	by	ADP
ejpam-6847	29	15	wardowski	wardowski	PROPN
ejpam-6847	29	16	(	(	PUNCT
ejpam-6847	29	17	2012	2012	NUM
ejpam-6847	29	18	)	)	PUNCT
ejpam-6847	30	1	[	[	X
ejpam-6847	30	2	23	23	NUM
ejpam-6847	30	3	]	]	PUNCT
ejpam-6847	30	4	,	,	PUNCT
ejpam-6847	30	5	which	which	PRON
ejpam-6847	30	6	generated	generate	VERB
ejpam-6847	30	7	significant	significant	ADJ
ejpam-6847	30	8	interest	interest	NOUN
ejpam-6847	30	9	.	.	PUNCT
ejpam-6847	31	1	subsequent	subsequent	ADJ
ejpam-6847	31	2	studies	study	NOUN
ejpam-6847	31	3	have	have	AUX
ejpam-6847	31	4	examined	examine	VERB
ejpam-6847	31	5	f	f	NUM
ejpam-6847	31	6	-	-	PUNCT
ejpam-6847	31	7	contraction	contraction	NOUN
ejpam-6847	31	8	mappings	mapping	NOUN
ejpam-6847	31	9	in	in	ADP
ejpam-6847	31	10	various	various	ADJ
ejpam-6847	31	11	contexts	contexts	NOUN
ejpam-6847	31	12	—	—	PUNCT
ejpam-6847	31	13	for	for	ADP
ejpam-6847	31	14	instance	instance	NOUN
ejpam-6847	31	15	,	,	PUNCT
ejpam-6847	31	16	multi	multi	ADJ
ejpam-6847	31	17	-	-	ADJ
ejpam-6847	31	18	valued	value	VERB
ejpam-6847	31	19	f	f	PROPN
ejpam-6847	31	20	contraction	contraction	NOUN
ejpam-6847	31	21	[	[	X
ejpam-6847	31	22	24	24	NUM
ejpam-6847	31	23	]	]	PUNCT
ejpam-6847	31	24	,	,	PUNCT
ejpam-6847	31	25	[	[	X
ejpam-6847	31	26	25	25	NUM
ejpam-6847	31	27	]	]	PUNCT
ejpam-6847	31	28	,	,	PUNCT
ejpam-6847	31	29	modified	modify	VERB
ejpam-6847	31	30	f	f	NOUN
ejpam-6847	31	31	-	-	PUNCT
ejpam-6847	31	32	contraction	contraction	NOUN
ejpam-6847	31	33	[	[	X
ejpam-6847	31	34	26	26	NUM
ejpam-6847	31	35	]	]	PUNCT
ejpam-6847	31	36	.	.	PUNCT
ejpam-6847	32	1	karapinar	karapinar	PROPN
ejpam-6847	32	2	et	et	PROPN
ejpam-6847	32	3	al	al	PROPN
ejpam-6847	32	4	.	.	PROPN
ejpam-6847	32	5	provided	provide	VERB
ejpam-6847	32	6	a	a	DET
ejpam-6847	32	7	nice	nice	ADJ
ejpam-6847	32	8	survey	survey	NOUN
ejpam-6847	32	9	on	on	ADP
ejpam-6847	32	10	f	f	NOUN
ejpam-6847	32	11	-	-	PUNCT
ejpam-6847	32	12	contractions	contraction	NOUN
ejpam-6847	33	1	[	[	X
ejpam-6847	33	2	27	27	NUM
ejpam-6847	33	3	]	]	PUNCT
ejpam-6847	33	4	.	.	PUNCT
ejpam-6847	34	1	for	for	ADP
ejpam-6847	34	2	broader	broad	ADJ
ejpam-6847	34	3	treatments	treatment	NOUN
ejpam-6847	34	4	and	and	CCONJ
ejpam-6847	34	5	further	further	ADJ
ejpam-6847	34	6	generalizations	generalization	NOUN
ejpam-6847	34	7	of	of	ADP
ejpam-6847	34	8	f	f	NOUN
ejpam-6847	34	9	-	-	PUNCT
ejpam-6847	34	10	contractions	contraction	NOUN
ejpam-6847	34	11	,	,	PUNCT
ejpam-6847	34	12	we	we	PRON
ejpam-6847	34	13	refer	refer	VERB
ejpam-6847	34	14	to	to	ADP
ejpam-6847	34	15	[	[	X
ejpam-6847	34	16	28	28	NUM
ejpam-6847	34	17	]	]	PUNCT
ejpam-6847	34	18	,	,	PUNCT
ejpam-6847	34	19	[	[	X
ejpam-6847	34	20	29	29	NUM
ejpam-6847	34	21	]	]	PUNCT
ejpam-6847	34	22	,	,	PUNCT
ejpam-6847	34	23	[	[	X
ejpam-6847	34	24	30	30	NUM
ejpam-6847	34	25	]	]	PUNCT
ejpam-6847	34	26	,	,	PUNCT
ejpam-6847	34	27	and	and	CCONJ
ejpam-6847	34	28	[	[	X
ejpam-6847	34	29	31	31	NUM
ejpam-6847	34	30	]	]	PUNCT
ejpam-6847	34	31	.	.	PUNCT
ejpam-6847	35	1	additionally	additionally	ADV
ejpam-6847	35	2	,	,	PUNCT
ejpam-6847	35	3	samet	samet	PROPN
ejpam-6847	35	4	et	et	PROPN
ejpam-6847	35	5	al	al	PROPN
ejpam-6847	35	6	.	.	PUNCT
ejpam-6847	36	1	[	[	X
ejpam-6847	36	2	32	32	NUM
ejpam-6847	36	3	]	]	PUNCT
ejpam-6847	36	4	introduced	introduce	VERB
ejpam-6847	36	5	the	the	DET
ejpam-6847	36	6	concept	concept	NOUN
ejpam-6847	36	7	of	of	ADP
ejpam-6847	36	8	α	α	NOUN
ejpam-6847	36	9	-	-	PUNCT
ejpam-6847	36	10	admissible	admissible	ADJ
ejpam-6847	36	11	mappings	mapping	NOUN
ejpam-6847	36	12	in	in	ADP
ejpam-6847	36	13	metric	metric	ADJ
ejpam-6847	36	14	spaces	space	NOUN
ejpam-6847	36	15	,	,	PUNCT
ejpam-6847	36	16	which	which	PRON
ejpam-6847	36	17	was	be	AUX
ejpam-6847	36	18	later	later	ADV
ejpam-6847	36	19	developed	develop	VERB
ejpam-6847	36	20	by	by	ADP
ejpam-6847	36	21	gopal	gopal	PROPN
ejpam-6847	36	22	et	et	PROPN
ejpam-6847	36	23	al	al	PROPN
ejpam-6847	36	24	.	.	PUNCT
ejpam-6847	37	1	[	[	X
ejpam-6847	37	2	33	33	NUM
ejpam-6847	37	3	]	]	PUNCT
ejpam-6847	37	4	into	into	ADP
ejpam-6847	37	5	(	(	PUNCT
ejpam-6847	37	6	α	α	NUM
ejpam-6847	37	7	-	-	PUNCT
ejpam-6847	37	8	f)-contractive	f)-contractive	NUM
ejpam-6847	37	9	mappings	mapping	NOUN
ejpam-6847	37	10	in	in	ADP
ejpam-6847	37	11	2016	2016	NUM
ejpam-6847	37	12	.	.	PUNCT
ejpam-6847	38	1	these	these	DET
ejpam-6847	38	2	mappings	mapping	NOUN
ejpam-6847	38	3	have	have	AUX
ejpam-6847	38	4	proven	prove	VERB
ejpam-6847	38	5	crucial	crucial	ADJ
ejpam-6847	38	6	in	in	ADP
ejpam-6847	38	7	extending	extend	VERB
ejpam-6847	38	8	fixed	fix	VERB
ejpam-6847	38	9	point	point	NOUN
ejpam-6847	38	10	theorems	theorem	NOUN
ejpam-6847	38	11	to	to	ADP
ejpam-6847	38	12	various	various	ADJ
ejpam-6847	38	13	complete	complete	ADJ
ejpam-6847	38	14	metric	metric	ADJ
ejpam-6847	38	15	spaces	space	NOUN
ejpam-6847	38	16	(	(	PUNCT
ejpam-6847	38	17	see	see	VERB
ejpam-6847	38	18	also	also	ADV
ejpam-6847	38	19	[	[	X
ejpam-6847	38	20	34	34	NUM
ejpam-6847	38	21	]	]	PUNCT
ejpam-6847	38	22	,	,	PUNCT
ejpam-6847	38	23	[	[	X
ejpam-6847	38	24	35	35	NUM
ejpam-6847	38	25	]	]	PUNCT
ejpam-6847	38	26	,	,	PUNCT
ejpam-6847	38	27	[	[	X
ejpam-6847	38	28	36	36	NUM
ejpam-6847	38	29	]	]	NUM
ejpam-6847	38	30	)	)	PUNCT
ejpam-6847	38	31	.	.	PUNCT
ejpam-6847	39	1	subsequently	subsequently	ADV
ejpam-6847	39	2	,	,	PUNCT
ejpam-6847	39	3	priyobarta	priyobarta	NOUN
ejpam-6847	39	4	et	et	PROPN
ejpam-6847	39	5	al	al	PROPN
ejpam-6847	39	6	.	.	PROPN
ejpam-6847	39	7	generalized	generalize	VERB
ejpam-6847	39	8	the	the	DET
ejpam-6847	39	9	idea	idea	NOUN
ejpam-6847	39	10	to	to	ADP
ejpam-6847	39	11	αs	αs	ADJ
ejpam-6847	39	12	-	-	ADJ
ejpam-6847	39	13	admissible	admissible	ADJ
ejpam-6847	39	14	mappings	mapping	NOUN
ejpam-6847	39	15	in	in	ADP
ejpam-6847	39	16	s	s	NOUN
ejpam-6847	39	17	-	-	ADJ
ejpam-6847	39	18	metric	metric	ADJ
ejpam-6847	39	19	spaces	space	NOUN
ejpam-6847	39	20	[	[	X
ejpam-6847	39	21	37	37	NUM
ejpam-6847	39	22	]	]	PUNCT
ejpam-6847	39	23	.	.	PUNCT
ejpam-6847	40	1	more	more	ADV
ejpam-6847	40	2	recently	recently	ADV
ejpam-6847	40	3	,	,	PUNCT
ejpam-6847	40	4	azmi	azmi	PROPN
ejpam-6847	40	5	[	[	X
ejpam-6847	40	6	20	20	NUM
ejpam-6847	40	7	]	]	X
ejpam-6847	40	8	advanced	advance	VERB
ejpam-6847	40	9	this	this	DET
ejpam-6847	40	10	concept	concept	NOUN
ejpam-6847	40	11	by	by	ADP
ejpam-6847	40	12	defining	define	VERB
ejpam-6847	40	13	such	such	ADJ
ejpam-6847	40	14	mappings	mapping	NOUN
ejpam-6847	40	15	in	in	ADP
ejpam-6847	40	16	the	the	DET
ejpam-6847	40	17	context	context	NOUN
ejpam-6847	40	18	of	of	ADP
ejpam-6847	40	19	triple	triple	ADJ
ejpam-6847	40	20	controlled	control	VERB
ejpam-6847	40	21	s	s	NOUN
ejpam-6847	40	22	-	-	ADJ
ejpam-6847	40	23	metric	metric	ADJ
ejpam-6847	40	24	spaces	space	NOUN
ejpam-6847	40	25	and	and	CCONJ
ejpam-6847	40	26	deriving	derive	VERB
ejpam-6847	40	27	new	new	ADJ
ejpam-6847	40	28	fixed	fix	VERB
ejpam-6847	40	29	point	point	NOUN
ejpam-6847	40	30	results	result	NOUN
ejpam-6847	40	31	.	.	PUNCT
ejpam-6847	41	1	f.	f.	PROPN
ejpam-6847	41	2	m.	m.	PROPN
ejpam-6847	41	3	azmi	azmi	PROPN
ejpam-6847	41	4	,	,	PUNCT
ejpam-6847	41	5	a.	a.	PROPN
ejpam-6847	41	6	h.	h.	PROPN
ejpam-6847	41	7	ansari	ansari	PROPN
ejpam-6847	41	8	,	,	PUNCT
ejpam-6847	41	9	s.	s.	PROPN
ejpam-6847	41	10	h.	h.	PROPN
ejpam-6847	41	11	j.	j.	PROPN
ejpam-6847	41	12	petroudi	petroudi	PROPN
ejpam-6847	41	13	/	/	SYM
ejpam-6847	41	14	eur	eur	PROPN
ejpam-6847	41	15	.	.	PUNCT
ejpam-6847	42	1	j.	j.	PROPN
ejpam-6847	42	2	pure	pure	PROPN
ejpam-6847	42	3	appl	appl	PROPN
ejpam-6847	42	4	.	.	PROPN
ejpam-6847	42	5	math	math	PROPN
ejpam-6847	42	6	,	,	PUNCT
ejpam-6847	42	7	18	18	NUM
ejpam-6847	42	8	(	(	PUNCT
ejpam-6847	42	9	4	4	NUM
ejpam-6847	42	10	)	)	PUNCT
ejpam-6847	42	11	(	(	PUNCT
ejpam-6847	42	12	2025	2025	NUM
ejpam-6847	42	13	)	)	PUNCT
ejpam-6847	42	14	,	,	PUNCT
ejpam-6847	42	15	6847	6847	NUM
ejpam-6847	42	16	3	3	NUM
ejpam-6847	42	17	of	of	ADP
ejpam-6847	42	18	26	26	NUM
ejpam-6847	42	19	motivated	motivate	VERB
ejpam-6847	42	20	by	by	ADP
ejpam-6847	42	21	these	these	DET
ejpam-6847	42	22	developments	development	NOUN
ejpam-6847	42	23	,	,	PUNCT
ejpam-6847	42	24	this	this	DET
ejpam-6847	42	25	paper	paper	NOUN
ejpam-6847	42	26	introduces	introduce	VERB
ejpam-6847	42	27	the	the	DET
ejpam-6847	42	28	concept	concept	NOUN
ejpam-6847	42	29	of	of	ADP
ejpam-6847	42	30	(	(	PUNCT
ejpam-6847	42	31	αs	αs	PROPN
ejpam-6847	42	32	,	,	PUNCT
ejpam-6847	42	33	νs	νs	NOUN
ejpam-6847	42	34	,	,	PUNCT
ejpam-6847	42	35	(	(	PUNCT
ejpam-6847	42	36	q	q	X
ejpam-6847	42	37	,	,	PUNCT
ejpam-6847	42	38	h)−	h)−	PROPN
ejpam-6847	42	39	f)-contraction	f)-contraction	NOUN
ejpam-6847	42	40	mappings	mapping	NOUN
ejpam-6847	42	41	tailored	tailor	VERB
ejpam-6847	42	42	for	for	ADP
ejpam-6847	42	43	triple	triple	ADV
ejpam-6847	42	44	-	-	PUNCT
ejpam-6847	42	45	controlled	control	VERB
ejpam-6847	42	46	s	s	NOUN
ejpam-6847	42	47	-	-	ADJ
ejpam-6847	42	48	metric	metric	ADJ
ejpam-6847	42	49	spaces	space	NOUN
ejpam-6847	42	50	.	.	PUNCT
ejpam-6847	43	1	these	these	DET
ejpam-6847	43	2	mappings	mapping	NOUN
ejpam-6847	43	3	rely	rely	VERB
ejpam-6847	43	4	on	on	ADP
ejpam-6847	43	5	αsand	αsand	ADJ
ejpam-6847	43	6	ηs	ηs	NOUN
ejpam-6847	43	7	-	-	PUNCT
ejpam-6847	43	8	admissible	admissible	ADJ
ejpam-6847	43	9	mappings	mapping	NOUN
ejpam-6847	43	10	,	,	PUNCT
ejpam-6847	43	11	νs	νs	NOUN
ejpam-6847	43	12	-	-	PUNCT
ejpam-6847	43	13	subadmissible	subadmissible	ADJ
ejpam-6847	43	14	mappings	mapping	NOUN
ejpam-6847	43	15	,	,	PUNCT
ejpam-6847	43	16	a	a	DET
ejpam-6847	43	17	set	set	NOUN
ejpam-6847	43	18	of	of	ADP
ejpam-6847	43	19	upper	upper	ADJ
ejpam-6847	43	20	-	-	PUNCT
ejpam-6847	43	21	class	class	NOUN
ejpam-6847	43	22	functions	function	NOUN
ejpam-6847	43	23	(	(	PUNCT
ejpam-6847	43	24	q	q	NOUN
ejpam-6847	43	25	,	,	PUNCT
ejpam-6847	43	26	h	h	NOUN
ejpam-6847	43	27	)	)	PUNCT
ejpam-6847	43	28	,	,	PUNCT
ejpam-6847	43	29	and	and	CCONJ
ejpam-6847	43	30	wardowski	wardowski	VERB
ejpam-6847	43	31	’s	’s	PART
ejpam-6847	43	32	f	f	NOUN
ejpam-6847	43	33	-	-	PUNCT
ejpam-6847	43	34	contraction	contraction	NOUN
ejpam-6847	43	35	.	.	PUNCT
ejpam-6847	44	1	building	build	VERB
ejpam-6847	44	2	on	on	ADP
ejpam-6847	44	3	the	the	DET
ejpam-6847	44	4	(	(	PUNCT
ejpam-6847	44	5	αs	αs	INTJ
ejpam-6847	44	6	−	−	PROPN
ejpam-6847	44	7	f)-contraction	f)-contraction	NOUN
ejpam-6847	44	8	framework	framework	NOUN
ejpam-6847	44	9	proposed	propose	VERB
ejpam-6847	44	10	by	by	ADP
ejpam-6847	44	11	azmi	azmi	PROPN
ejpam-6847	44	12	[	[	X
ejpam-6847	44	13	20	20	NUM
ejpam-6847	44	14	]	]	PUNCT
ejpam-6847	44	15	,	,	PUNCT
ejpam-6847	44	16	we	we	PRON
ejpam-6847	44	17	demonstrate	demonstrate	VERB
ejpam-6847	44	18	the	the	DET
ejpam-6847	44	19	existence	existence	NOUN
ejpam-6847	44	20	and	and	CCONJ
ejpam-6847	44	21	uniqueness	uniqueness	NOUN
ejpam-6847	44	22	of	of	ADP
ejpam-6847	44	23	fixed	fix	VERB
ejpam-6847	44	24	points	point	NOUN
ejpam-6847	44	25	in	in	ADP
ejpam-6847	44	26	complete	complete	ADJ
ejpam-6847	44	27	triple	triple	ADV
ejpam-6847	44	28	-	-	PUNCT
ejpam-6847	44	29	controlled	control	VERB
ejpam-6847	44	30	s	s	ADJ
ejpam-6847	44	31	-	-	ADJ
ejpam-6847	44	32	metric	metric	ADJ
ejpam-6847	44	33	spaces	space	NOUN
ejpam-6847	44	34	and	and	CCONJ
ejpam-6847	44	35	provide	provide	VERB
ejpam-6847	44	36	an	an	DET
ejpam-6847	44	37	example	example	NOUN
ejpam-6847	44	38	to	to	PART
ejpam-6847	44	39	illustrate	illustrate	VERB
ejpam-6847	44	40	our	our	PRON
ejpam-6847	44	41	findings	finding	NOUN
ejpam-6847	44	42	.	.	PUNCT
ejpam-6847	45	1	furthermore	furthermore	ADV
ejpam-6847	45	2	,	,	PUNCT
ejpam-6847	45	3	we	we	PRON
ejpam-6847	45	4	derive	derive	VERB
ejpam-6847	45	5	meaningful	meaningful	ADJ
ejpam-6847	45	6	corollaries	corollary	NOUN
ejpam-6847	45	7	by	by	ADP
ejpam-6847	45	8	specifying	specify	VERB
ejpam-6847	45	9	various	various	ADJ
ejpam-6847	45	10	(	(	PUNCT
ejpam-6847	45	11	q	q	ADJ
ejpam-6847	45	12	,	,	PUNCT
ejpam-6847	45	13	h	h	NOUN
ejpam-6847	45	14	)	)	PUNCT
ejpam-6847	45	15	pairs	pair	NOUN
ejpam-6847	45	16	,	,	PUNCT
ejpam-6847	45	17	illustrating	illustrate	VERB
ejpam-6847	45	18	the	the	DET
ejpam-6847	45	19	versatility	versatility	NOUN
ejpam-6847	45	20	and	and	CCONJ
ejpam-6847	45	21	depth	depth	NOUN
ejpam-6847	45	22	of	of	ADP
ejpam-6847	45	23	the	the	DET
ejpam-6847	45	24	proposed	propose	VERB
ejpam-6847	45	25	theory	theory	NOUN
ejpam-6847	45	26	and	and	CCONJ
ejpam-6847	45	27	its	its	PRON
ejpam-6847	45	28	contribution	contribution	NOUN
ejpam-6847	45	29	to	to	ADP
ejpam-6847	45	30	the	the	DET
ejpam-6847	45	31	advancement	advancement	NOUN
ejpam-6847	45	32	of	of	ADP
ejpam-6847	45	33	fixed	fix	VERB
ejpam-6847	45	34	point	point	NOUN
ejpam-6847	45	35	results	result	NOUN
ejpam-6847	45	36	in	in	ADP
ejpam-6847	45	37	generalized	generalized	ADJ
ejpam-6847	45	38	metric	metric	ADJ
ejpam-6847	45	39	environments	environment	NOUN
ejpam-6847	45	40	.	.	PUNCT
ejpam-6847	46	1	2	2	X
ejpam-6847	46	2	.	.	X
ejpam-6847	46	3	preliminaries	preliminary	NOUN
ejpam-6847	46	4	in	in	ADP
ejpam-6847	46	5	this	this	DET
ejpam-6847	46	6	section	section	NOUN
ejpam-6847	46	7	,	,	PUNCT
ejpam-6847	46	8	we	we	PRON
ejpam-6847	46	9	will	will	AUX
ejpam-6847	46	10	first	first	ADV
ejpam-6847	46	11	review	review	VERB
ejpam-6847	46	12	some	some	DET
ejpam-6847	46	13	key	key	ADJ
ejpam-6847	46	14	results	result	NOUN
ejpam-6847	46	15	and	and	CCONJ
ejpam-6847	46	16	definitions	definition	NOUN
ejpam-6847	46	17	of	of	ADP
ejpam-6847	46	18	s	s	NOUN
ejpam-6847	46	19	-	-	ADJ
ejpam-6847	46	20	metric	metric	ADJ
ejpam-6847	46	21	spaces	space	NOUN
ejpam-6847	46	22	introduced	introduce	VERB
ejpam-6847	46	23	by	by	ADP
ejpam-6847	46	24	sedghi	sedghi	PROPN
ejpam-6847	46	25	et	et	PROPN
ejpam-6847	46	26	al	al	PROPN
ejpam-6847	46	27	.	.	PUNCT
ejpam-6847	47	1	[	[	X
ejpam-6847	47	2	11	11	NUM
ejpam-6847	47	3	]	]	PUNCT
ejpam-6847	47	4	.	.	PUNCT
ejpam-6847	48	1	definition	definition	NOUN
ejpam-6847	48	2	1	1	NUM
ejpam-6847	48	3	.	.	PUNCT
ejpam-6847	49	1	[	[	X
ejpam-6847	49	2	11	11	NUM
ejpam-6847	49	3	]	]	PUNCT
ejpam-6847	49	4	let	let	VERB
ejpam-6847	49	5	x	x	SYM
ejpam-6847	49	6	6=	6=	ADP
ejpam-6847	49	7	∅	∅	NOUN
ejpam-6847	49	8	,	,	PUNCT
ejpam-6847	49	9	and	and	CCONJ
ejpam-6847	49	10	let	let	VERB
ejpam-6847	49	11	s	s	PRON
ejpam-6847	49	12	:	:	PUNCT
ejpam-6847	49	13	x3	x3	ADJ
ejpam-6847	49	14	→	→	SYM
ejpam-6847	50	1	[	[	X
ejpam-6847	50	2	0,+∞	0,+∞	NUM
ejpam-6847	50	3	)	)	PUNCT
ejpam-6847	50	4	be	be	VERB
ejpam-6847	50	5	a	a	DET
ejpam-6847	50	6	mapping	mapping	NOUN
ejpam-6847	50	7	satistfying	satistfye	VERB
ejpam-6847	50	8	the	the	DET
ejpam-6847	50	9	following	follow	VERB
ejpam-6847	50	10	conditions	condition	NOUN
ejpam-6847	50	11	,	,	PUNCT
ejpam-6847	50	12	for	for	ADP
ejpam-6847	50	13	all	all	DET
ejpam-6847	50	14	x	x	NOUN
ejpam-6847	50	15	,	,	PUNCT
ejpam-6847	50	16	y	y	PROPN
ejpam-6847	50	17	,	,	PUNCT
ejpam-6847	50	18	z	z	NOUN
ejpam-6847	50	19	∈	∈	PROPN
ejpam-6847	50	20	x	x	X
ejpam-6847	50	21	and	and	CCONJ
ejpam-6847	50	22	a	a	DET
ejpam-6847	50	23	∈	∈	NOUN
ejpam-6847	50	24	x	x	X
ejpam-6847	50	25	:	:	PUNCT
ejpam-6847	50	26	(	(	PUNCT
ejpam-6847	50	27	i	i	NOUN
ejpam-6847	50	28	)	)	PUNCT
ejpam-6847	50	29	s(x	s(x	PROPN
ejpam-6847	50	30	,	,	PUNCT
ejpam-6847	50	31	y	y	PROPN
ejpam-6847	50	32	,	,	PUNCT
ejpam-6847	50	33	z	z	NOUN
ejpam-6847	50	34	)	)	PUNCT
ejpam-6847	51	1	=	=	SYM
ejpam-6847	51	2	0	0	NUM
ejpam-6847	51	3	iff	iff	NOUN
ejpam-6847	51	4	x	x	PROPN
ejpam-6847	51	5	=	=	SYM
ejpam-6847	51	6	y	y	PROPN
ejpam-6847	51	7	=	=	SYM
ejpam-6847	51	8	z	z	PROPN
ejpam-6847	51	9	,	,	PUNCT
ejpam-6847	51	10	(	(	PUNCT
ejpam-6847	51	11	ii	ii	NOUN
ejpam-6847	51	12	)	)	PUNCT
ejpam-6847	51	13	s(x	s(x	PROPN
ejpam-6847	51	14	,	,	PUNCT
ejpam-6847	51	15	y	y	PROPN
ejpam-6847	51	16	,	,	PUNCT
ejpam-6847	51	17	z	z	NOUN
ejpam-6847	51	18	)	)	PUNCT
ejpam-6847	51	19	≤	≤	NOUN
ejpam-6847	51	20	s(x	s(x	NOUN
ejpam-6847	51	21	,	,	PUNCT
ejpam-6847	51	22	x	x	X
ejpam-6847	51	23	,	,	PUNCT
ejpam-6847	51	24	a	a	PRON
ejpam-6847	51	25	)	)	PUNCT
ejpam-6847	51	26	+	+	CCONJ
ejpam-6847	52	1	s(y	s(y	PROPN
ejpam-6847	52	2	,	,	PUNCT
ejpam-6847	52	3	y	y	PROPN
ejpam-6847	52	4	,	,	PUNCT
ejpam-6847	52	5	a	a	PRON
ejpam-6847	52	6	)	)	PUNCT
ejpam-6847	53	1	+	+	PROPN
ejpam-6847	53	2	s(z	s(z	PROPN
ejpam-6847	53	3	,	,	PUNCT
ejpam-6847	53	4	z	z	PROPN
ejpam-6847	53	5	,	,	PUNCT
ejpam-6847	53	6	a	a	PRON
ejpam-6847	53	7	)	)	PUNCT
ejpam-6847	53	8	.	.	PUNCT
ejpam-6847	54	1	then	then	ADV
ejpam-6847	54	2	,	,	PUNCT
ejpam-6847	54	3	(	(	PUNCT
ejpam-6847	54	4	x	x	X
ejpam-6847	54	5	,	,	PUNCT
ejpam-6847	54	6	s	s	PART
ejpam-6847	54	7	)	)	PUNCT
ejpam-6847	54	8	is	be	AUX
ejpam-6847	54	9	called	call	VERB
ejpam-6847	54	10	an	an	DET
ejpam-6847	54	11	smetric	smetric	ADJ
ejpam-6847	54	12	space	space	NOUN
ejpam-6847	54	13	.	.	PUNCT
ejpam-6847	55	1	definition	definition	NOUN
ejpam-6847	55	2	2	2	NUM
ejpam-6847	55	3	.	.	PUNCT
ejpam-6847	56	1	[	[	X
ejpam-6847	56	2	15	15	NUM
ejpam-6847	56	3	]	]	X
ejpam-6847	56	4	let	let	VERB
ejpam-6847	56	5	x	x	SYM
ejpam-6847	56	6	6=	6=	ADP
ejpam-6847	56	7	∅	∅	NOUN
ejpam-6847	56	8	and	and	CCONJ
ejpam-6847	56	9	b	b	NOUN
ejpam-6847	56	10	≥	≥	NUM
ejpam-6847	56	11	1	1	NUM
ejpam-6847	56	12	.	.	PUNCT
ejpam-6847	57	1	let	let	VERB
ejpam-6847	57	2	s	s	PRON
ejpam-6847	57	3	:	:	PUNCT
ejpam-6847	57	4	x3	x3	ADJ
ejpam-6847	57	5	→	→	SYM
ejpam-6847	57	6	[	[	X
ejpam-6847	57	7	0,∞	0,∞	X
ejpam-6847	57	8	)	)	PUNCT
ejpam-6847	57	9	be	be	VERB
ejpam-6847	57	10	a	a	DET
ejpam-6847	57	11	mapping	mapping	NOUN
ejpam-6847	57	12	satisfying	satisfy	VERB
ejpam-6847	57	13	the	the	DET
ejpam-6847	57	14	following	follow	VERB
ejpam-6847	57	15	conditions	condition	NOUN
ejpam-6847	57	16	,	,	PUNCT
ejpam-6847	57	17	for	for	ADP
ejpam-6847	57	18	all	all	DET
ejpam-6847	57	19	x	x	NOUN
ejpam-6847	57	20	,	,	PUNCT
ejpam-6847	57	21	y	y	PROPN
ejpam-6847	57	22	,	,	PUNCT
ejpam-6847	57	23	z	z	PROPN
ejpam-6847	57	24	∈	∈	PROPN
ejpam-6847	57	25	x	x	X
ejpam-6847	57	26	:	:	PUNCT
ejpam-6847	57	27	(	(	PUNCT
ejpam-6847	57	28	i	i	NOUN
ejpam-6847	57	29	)	)	PUNCT
ejpam-6847	57	30	s(x	s(x	PROPN
ejpam-6847	57	31	,	,	PUNCT
ejpam-6847	57	32	y	y	PROPN
ejpam-6847	57	33	,	,	PUNCT
ejpam-6847	57	34	z	z	NOUN
ejpam-6847	57	35	)	)	PUNCT
ejpam-6847	58	1	=	=	SYM
ejpam-6847	58	2	0	0	NUM
ejpam-6847	58	3	iff	iff	NOUN
ejpam-6847	58	4	x	x	PROPN
ejpam-6847	58	5	=	=	SYM
ejpam-6847	58	6	y	y	PROPN
ejpam-6847	58	7	=	=	SYM
ejpam-6847	58	8	z	z	PROPN
ejpam-6847	58	9	;	;	PUNCT
ejpam-6847	58	10	(	(	PUNCT
ejpam-6847	58	11	ii	ii	NOUN
ejpam-6847	58	12	)	)	PUNCT
ejpam-6847	58	13	s(x	s(x	PROPN
ejpam-6847	58	14	,	,	PUNCT
ejpam-6847	58	15	y	y	PROPN
ejpam-6847	58	16	,	,	PUNCT
ejpam-6847	58	17	y	y	PROPN
ejpam-6847	58	18	)	)	PUNCT
ejpam-6847	58	19	=	=	SYM
ejpam-6847	59	1	s(y	s(y	PROPN
ejpam-6847	59	2	,	,	PUNCT
ejpam-6847	59	3	x	x	X
ejpam-6847	59	4	,	,	PUNCT
ejpam-6847	59	5	x	x	X
ejpam-6847	59	6	)	)	PUNCT
ejpam-6847	59	7	(	(	PUNCT
ejpam-6847	59	8	iii	iii	NOUN
ejpam-6847	59	9	)	)	PUNCT
ejpam-6847	59	10	s(x	s(x	PROPN
ejpam-6847	59	11	,	,	PUNCT
ejpam-6847	59	12	y	y	PROPN
ejpam-6847	59	13	,	,	PUNCT
ejpam-6847	59	14	z	z	NOUN
ejpam-6847	59	15	)	)	PUNCT
ejpam-6847	59	16	≤	≤	NUM
ejpam-6847	59	17	b[s(x	b[s(x	X
ejpam-6847	59	18	,	,	PUNCT
ejpam-6847	59	19	x	x	X
ejpam-6847	59	20	,	,	PUNCT
ejpam-6847	59	21	a	a	PRON
ejpam-6847	59	22	)	)	PUNCT
ejpam-6847	59	23	+	+	CCONJ
ejpam-6847	60	1	s(y	s(y	PROPN
ejpam-6847	60	2	,	,	PUNCT
ejpam-6847	60	3	y	y	PROPN
ejpam-6847	60	4	,	,	PUNCT
ejpam-6847	60	5	a	a	PRON
ejpam-6847	60	6	)	)	PUNCT
ejpam-6847	61	1	+	+	PROPN
ejpam-6847	61	2	s(z	s(z	PROPN
ejpam-6847	61	3	,	,	PUNCT
ejpam-6847	61	4	z	z	PROPN
ejpam-6847	61	5	,	,	PUNCT
ejpam-6847	61	6	a	a	NOUN
ejpam-6847	61	7	)	)	PUNCT
ejpam-6847	61	8	]	]	PUNCT
ejpam-6847	61	9	.	.	PUNCT
ejpam-6847	62	1	the	the	DET
ejpam-6847	62	2	pair	pair	NOUN
ejpam-6847	62	3	(	(	PUNCT
ejpam-6847	62	4	x	x	X
ejpam-6847	62	5	,	,	PUNCT
ejpam-6847	62	6	s	s	PART
ejpam-6847	62	7	)	)	PUNCT
ejpam-6847	62	8	is	be	AUX
ejpam-6847	62	9	called	call	VERB
ejpam-6847	62	10	an	an	DET
ejpam-6847	62	11	sbmetric	sbmetric	ADJ
ejpam-6847	62	12	space	space	NOUN
ejpam-6847	62	13	.	.	PUNCT
ejpam-6847	63	1	definition	definition	NOUN
ejpam-6847	63	2	3	3	NUM
ejpam-6847	63	3	.	.	PUNCT
ejpam-6847	64	1	[	[	X
ejpam-6847	64	2	16	16	NUM
ejpam-6847	64	3	]	]	X
ejpam-6847	64	4	let	let	VERB
ejpam-6847	64	5	s	s	PRON
ejpam-6847	64	6	:	:	PUNCT
ejpam-6847	64	7	x3	x3	ADJ
ejpam-6847	64	8	→	→	SYM
ejpam-6847	64	9	[	[	X
ejpam-6847	64	10	0,∞	0,∞	X
ejpam-6847	64	11	)	)	PUNCT
ejpam-6847	64	12	be	be	VERB
ejpam-6847	64	13	a	a	DET
ejpam-6847	64	14	mapping	mapping	NOUN
ejpam-6847	64	15	,	,	PUNCT
ejpam-6847	64	16	where	where	SCONJ
ejpam-6847	64	17	x	x	PRON
ejpam-6847	64	18	is	be	AUX
ejpam-6847	64	19	a	a	DET
ejpam-6847	64	20	non	non	ADJ
ejpam-6847	64	21	-	-	ADJ
ejpam-6847	64	22	void	void	ADJ
ejpam-6847	64	23	set	set	NOUN
ejpam-6847	64	24	,	,	PUNCT
ejpam-6847	64	25	and	and	CCONJ
ejpam-6847	64	26	consider	consider	VERB
ejpam-6847	64	27	a	a	DET
ejpam-6847	64	28	function	function	NOUN
ejpam-6847	64	29	θ	θ	NOUN
ejpam-6847	64	30	:	:	PUNCT
ejpam-6847	64	31	x3	x3	ADJ
ejpam-6847	64	32	→	→	SYM
ejpam-6847	64	33	[	[	X
ejpam-6847	64	34	1,+∞	1,+∞	NUM
ejpam-6847	64	35	)	)	PUNCT
ejpam-6847	64	36	,	,	PUNCT
ejpam-6847	64	37	satisfying	satisfy	VERB
ejpam-6847	64	38	the	the	DET
ejpam-6847	64	39	following	follow	VERB
ejpam-6847	64	40	conditions	condition	NOUN
ejpam-6847	64	41	,	,	PUNCT
ejpam-6847	64	42	for	for	ADP
ejpam-6847	64	43	all	all	DET
ejpam-6847	64	44	x	x	NOUN
ejpam-6847	64	45	,	,	PUNCT
ejpam-6847	64	46	y	y	PROPN
ejpam-6847	64	47	,	,	PUNCT
ejpam-6847	64	48	z	z	PROPN
ejpam-6847	64	49	∈	∈	PROPN
ejpam-6847	64	50	x	x	X
ejpam-6847	64	51	:	:	PUNCT
ejpam-6847	64	52	(	(	PUNCT
ejpam-6847	64	53	i	i	NOUN
ejpam-6847	64	54	)	)	PUNCT
ejpam-6847	64	55	s(x	s(x	PROPN
ejpam-6847	64	56	,	,	PUNCT
ejpam-6847	64	57	y	y	PROPN
ejpam-6847	64	58	,	,	PUNCT
ejpam-6847	64	59	z	z	NOUN
ejpam-6847	64	60	)	)	PUNCT
ejpam-6847	64	61	=	=	SYM
ejpam-6847	64	62	0	0	NUM
ejpam-6847	65	1	iff	iff	NOUN
ejpam-6847	65	2	x	x	PROPN
ejpam-6847	65	3	=	=	SYM
ejpam-6847	65	4	y	y	PROPN
ejpam-6847	65	5	=	=	SYM
ejpam-6847	65	6	z	z	PROPN
ejpam-6847	65	7	;	;	PUNCT
ejpam-6847	65	8	(	(	PUNCT
ejpam-6847	65	9	ii	ii	NOUN
ejpam-6847	65	10	)	)	PUNCT
ejpam-6847	65	11	s(x	s(x	PROPN
ejpam-6847	65	12	,	,	PUNCT
ejpam-6847	65	13	y	y	PROPN
ejpam-6847	65	14	,	,	PUNCT
ejpam-6847	65	15	z	z	NOUN
ejpam-6847	65	16	)	)	PUNCT
ejpam-6847	65	17	≤	≤	NOUN
ejpam-6847	65	18	θ(x	θ(x	PROPN
ejpam-6847	65	19	,	,	PUNCT
ejpam-6847	65	20	y	y	PROPN
ejpam-6847	65	21	,	,	PUNCT
ejpam-6847	65	22	z)[s(x	z)[s(x	NUM
ejpam-6847	65	23	,	,	PUNCT
ejpam-6847	65	24	x	x	X
ejpam-6847	65	25	,	,	PUNCT
ejpam-6847	65	26	a	a	PRON
ejpam-6847	65	27	)	)	PUNCT
ejpam-6847	66	1	+	+	CCONJ
ejpam-6847	66	2	s(y	s(y	PROPN
ejpam-6847	66	3	,	,	PUNCT
ejpam-6847	66	4	y	y	PROPN
ejpam-6847	66	5	,	,	PUNCT
ejpam-6847	66	6	a	a	PRON
ejpam-6847	66	7	)	)	PUNCT
ejpam-6847	66	8	+	+	PROPN
ejpam-6847	66	9	s(z	s(z	PROPN
ejpam-6847	66	10	,	,	PUNCT
ejpam-6847	66	11	z	z	PROPN
ejpam-6847	66	12	,	,	PUNCT
ejpam-6847	66	13	a	a	NOUN
ejpam-6847	66	14	)	)	PUNCT
ejpam-6847	66	15	]	]	PUNCT
ejpam-6847	66	16	.	.	PUNCT
ejpam-6847	67	1	f.	f.	PROPN
ejpam-6847	67	2	m.	m.	PROPN
ejpam-6847	67	3	azmi	azmi	PROPN
ejpam-6847	67	4	,	,	PUNCT
ejpam-6847	67	5	a.	a.	PROPN
ejpam-6847	67	6	h.	h.	PROPN
ejpam-6847	67	7	ansari	ansari	PROPN
ejpam-6847	67	8	,	,	PUNCT
ejpam-6847	67	9	s.	s.	PROPN
ejpam-6847	67	10	h.	h.	PROPN
ejpam-6847	67	11	j.	j.	PROPN
ejpam-6847	67	12	petroudi	petroudi	PROPN
ejpam-6847	67	13	/	/	SYM
ejpam-6847	67	14	eur	eur	PROPN
ejpam-6847	67	15	.	.	PUNCT
ejpam-6847	68	1	j.	j.	PROPN
ejpam-6847	68	2	pure	pure	PROPN
ejpam-6847	68	3	appl	appl	PROPN
ejpam-6847	68	4	.	.	PROPN
ejpam-6847	68	5	math	math	PROPN
ejpam-6847	68	6	,	,	PUNCT
ejpam-6847	68	7	18	18	NUM
ejpam-6847	68	8	(	(	PUNCT
ejpam-6847	68	9	4	4	NUM
ejpam-6847	68	10	)	)	PUNCT
ejpam-6847	68	11	(	(	PUNCT
ejpam-6847	68	12	2025	2025	NUM
ejpam-6847	68	13	)	)	PUNCT
ejpam-6847	68	14	,	,	PUNCT
ejpam-6847	68	15	6847	6847	NUM
ejpam-6847	68	16	4	4	NUM
ejpam-6847	68	17	of	of	ADP
ejpam-6847	68	18	26	26	NUM
ejpam-6847	68	19	the	the	DET
ejpam-6847	68	20	pair	pair	NOUN
ejpam-6847	68	21	(	(	PUNCT
ejpam-6847	68	22	x	x	X
ejpam-6847	68	23	,	,	PUNCT
ejpam-6847	68	24	s	s	PART
ejpam-6847	68	25	)	)	PUNCT
ejpam-6847	68	26	is	be	AUX
ejpam-6847	68	27	known	know	VERB
ejpam-6847	68	28	as	as	ADP
ejpam-6847	68	29	an	an	DET
ejpam-6847	68	30	extended	extended	ADJ
ejpam-6847	68	31	sbmetric	sbmetric	ADJ
ejpam-6847	68	32	space	space	NOUN
ejpam-6847	68	33	.	.	PUNCT
ejpam-6847	69	1	ekiz	ekiz	PROPN
ejpam-6847	69	2	et	et	PROPN
ejpam-6847	69	3	al	al	PROPN
ejpam-6847	69	4	.	.	PUNCT
ejpam-6847	70	1	[	[	X
ejpam-6847	70	2	19	19	NUM
ejpam-6847	70	3	]	]	PUNCT
ejpam-6847	70	4	presented	present	VERB
ejpam-6847	70	5	the	the	DET
ejpam-6847	70	6	concept	concept	NOUN
ejpam-6847	70	7	of	of	ADP
ejpam-6847	70	8	controlled	control	VERB
ejpam-6847	70	9	s	s	PROPN
ejpam-6847	70	10	-	-	ADJ
ejpam-6847	70	11	metric	metric	ADJ
ejpam-6847	70	12	type	type	NOUN
ejpam-6847	70	13	spaces	space	NOUN
ejpam-6847	70	14	in	in	ADP
ejpam-6847	70	15	the	the	DET
ejpam-6847	70	16	following	following	ADJ
ejpam-6847	70	17	way	way	NOUN
ejpam-6847	70	18	.	.	PUNCT
ejpam-6847	71	1	definition	definition	NOUN
ejpam-6847	71	2	4	4	NUM
ejpam-6847	71	3	.	.	PUNCT
ejpam-6847	72	1	[	[	X
ejpam-6847	72	2	19	19	NUM
ejpam-6847	72	3	]	]	X
ejpam-6847	72	4	let	let	VERB
ejpam-6847	72	5	s	s	PRON
ejpam-6847	72	6	:	:	PUNCT
ejpam-6847	72	7	x3	x3	ADJ
ejpam-6847	72	8	→	→	SYM
ejpam-6847	72	9	[	[	X
ejpam-6847	72	10	0,+∞	0,+∞	NUM
ejpam-6847	72	11	)	)	PUNCT
ejpam-6847	72	12	be	be	AUX
ejpam-6847	72	13	a	a	DET
ejpam-6847	72	14	mapping	mapping	NOUN
ejpam-6847	72	15	,	,	PUNCT
ejpam-6847	72	16	where	where	SCONJ
ejpam-6847	72	17	x	x	PRON
ejpam-6847	72	18	be	be	AUX
ejpam-6847	72	19	a	a	DET
ejpam-6847	72	20	non	non	ADJ
ejpam-6847	72	21	-	-	ADJ
ejpam-6847	72	22	void	void	ADJ
ejpam-6847	72	23	set	set	NOUN
ejpam-6847	72	24	and	and	CCONJ
ejpam-6847	72	25	suppose	suppose	VERB
ejpam-6847	72	26	α	α	X
ejpam-6847	72	27	:	:	PUNCT
ejpam-6847	73	1	x2	x2	PROPN
ejpam-6847	73	2	→	→	PUNCT
ejpam-6847	74	1	[	[	X
ejpam-6847	74	2	1,+∞	1,+∞	NUM
ejpam-6847	74	3	)	)	PUNCT
ejpam-6847	74	4	is	be	AUX
ejpam-6847	74	5	a	a	DET
ejpam-6847	74	6	function	function	NOUN
ejpam-6847	74	7	,	,	PUNCT
ejpam-6847	74	8	such	such	ADJ
ejpam-6847	74	9	that	that	PRON
ejpam-6847	74	10	for	for	ADP
ejpam-6847	74	11	all	all	DET
ejpam-6847	74	12	x	x	NOUN
ejpam-6847	74	13	,	,	PUNCT
ejpam-6847	74	14	y	y	PROPN
ejpam-6847	74	15	,	,	PUNCT
ejpam-6847	74	16	z	z	PROPN
ejpam-6847	74	17	,	,	PUNCT
ejpam-6847	74	18	a	a	DET
ejpam-6847	74	19	∈	∈	PROPN
ejpam-6847	74	20	x	x	NOUN
ejpam-6847	74	21	,	,	PUNCT
ejpam-6847	74	22	the	the	DET
ejpam-6847	74	23	following	follow	VERB
ejpam-6847	74	24	conditions	condition	NOUN
ejpam-6847	74	25	hold	hold	VERB
ejpam-6847	74	26	:	:	PUNCT
ejpam-6847	74	27	(	(	PUNCT
ejpam-6847	74	28	i	i	NOUN
ejpam-6847	74	29	)	)	PUNCT
ejpam-6847	74	30	s(x	s(x	PROPN
ejpam-6847	74	31	,	,	PUNCT
ejpam-6847	74	32	y	y	PROPN
ejpam-6847	74	33	,	,	PUNCT
ejpam-6847	74	34	z	z	NOUN
ejpam-6847	74	35	)	)	PUNCT
ejpam-6847	74	36	=	=	SYM
ejpam-6847	74	37	0	0	NUM
ejpam-6847	75	1	iff	iff	NOUN
ejpam-6847	75	2	x	x	PROPN
ejpam-6847	75	3	=	=	SYM
ejpam-6847	75	4	y	y	PROPN
ejpam-6847	75	5	=	=	SYM
ejpam-6847	75	6	z	z	PROPN
ejpam-6847	75	7	;	;	PUNCT
ejpam-6847	75	8	(	(	PUNCT
ejpam-6847	75	9	ii	ii	NOUN
ejpam-6847	75	10	)	)	PUNCT
ejpam-6847	75	11	s(x	s(x	PROPN
ejpam-6847	75	12	,	,	PUNCT
ejpam-6847	75	13	y	y	PROPN
ejpam-6847	75	14	,	,	PUNCT
ejpam-6847	75	15	z	z	NOUN
ejpam-6847	75	16	)	)	PUNCT
ejpam-6847	75	17	≤	≤	ADJ
ejpam-6847	75	18	α(x	α(x	NOUN
ejpam-6847	75	19	,	,	PUNCT
ejpam-6847	75	20	a)s(x	a)s(x	NOUN
ejpam-6847	75	21	,	,	PUNCT
ejpam-6847	75	22	x	x	X
ejpam-6847	75	23	,	,	PUNCT
ejpam-6847	75	24	a	a	PRON
ejpam-6847	75	25	)	)	PUNCT
ejpam-6847	76	1	+	+	CCONJ
ejpam-6847	76	2	α(y	α(y	NOUN
ejpam-6847	76	3	,	,	PUNCT
ejpam-6847	76	4	a)s(y	a)s(y	ADJ
ejpam-6847	76	5	,	,	PUNCT
ejpam-6847	76	6	y	y	PROPN
ejpam-6847	76	7	,	,	PUNCT
ejpam-6847	76	8	a	a	PRON
ejpam-6847	76	9	)	)	PUNCT
ejpam-6847	76	10	+	+	NOUN
ejpam-6847	77	1	α(z	α(z	NOUN
ejpam-6847	77	2	,	,	PUNCT
ejpam-6847	77	3	a)s(z	a)s(z	PROPN
ejpam-6847	77	4	,	,	PUNCT
ejpam-6847	77	5	z	z	PROPN
ejpam-6847	77	6	,	,	PUNCT
ejpam-6847	77	7	a	a	PRON
ejpam-6847	77	8	)	)	PUNCT
ejpam-6847	77	9	.	.	PUNCT
ejpam-6847	78	1	then	then	ADV
ejpam-6847	78	2	,	,	PUNCT
ejpam-6847	78	3	the	the	DET
ejpam-6847	78	4	pair	pair	NOUN
ejpam-6847	78	5	(	(	PUNCT
ejpam-6847	78	6	x	x	X
ejpam-6847	78	7	,	,	PUNCT
ejpam-6847	78	8	s	s	AUX
ejpam-6847	78	9	)	)	PUNCT
ejpam-6847	78	10	is	be	AUX
ejpam-6847	78	11	referred	refer	VERB
ejpam-6847	78	12	to	to	ADP
ejpam-6847	78	13	as	as	ADP
ejpam-6847	78	14	a	a	DET
ejpam-6847	78	15	controlled	control	VERB
ejpam-6847	78	16	s	s	ADJ
ejpam-6847	78	17	-	-	ADJ
ejpam-6847	78	18	metric	metric	ADJ
ejpam-6847	78	19	type	type	NOUN
ejpam-6847	78	20	space	space	NOUN
ejpam-6847	78	21	.	.	PUNCT
ejpam-6847	79	1	we	we	PRON
ejpam-6847	79	2	will	will	AUX
ejpam-6847	79	3	now	now	ADV
ejpam-6847	79	4	present	present	VERB
ejpam-6847	79	5	the	the	DET
ejpam-6847	79	6	idea	idea	NOUN
ejpam-6847	79	7	of	of	ADP
ejpam-6847	79	8	triple	triple	ADV
ejpam-6847	79	9	controlled	control	VERB
ejpam-6847	79	10	s	s	NOUN
ejpam-6847	79	11	-	-	ADJ
ejpam-6847	79	12	metric	metric	ADJ
ejpam-6847	79	13	type	type	NOUN
ejpam-6847	79	14	spaces	space	NOUN
ejpam-6847	79	15	as	as	SCONJ
ejpam-6847	79	16	introduced	introduce	VERB
ejpam-6847	79	17	by	by	ADP
ejpam-6847	79	18	azmi	azmi	PROPN
ejpam-6847	79	19	[	[	X
ejpam-6847	79	20	20	20	NUM
ejpam-6847	79	21	]	]	PUNCT
ejpam-6847	79	22	.	.	PUNCT
ejpam-6847	80	1	definition	definition	NOUN
ejpam-6847	80	2	5	5	NUM
ejpam-6847	80	3	.	.	PUNCT
ejpam-6847	81	1	[	[	X
ejpam-6847	81	2	20	20	NUM
ejpam-6847	81	3	]	]	PUNCT
ejpam-6847	81	4	consider	consider	VERB
ejpam-6847	81	5	a	a	DET
ejpam-6847	81	6	mapping	mapping	NOUN
ejpam-6847	81	7	s	s	PART
ejpam-6847	81	8	:	:	PUNCT
ejpam-6847	81	9	x3	x3	ADJ
ejpam-6847	81	10	→	→	SYM
ejpam-6847	81	11	[	[	X
ejpam-6847	81	12	0,+∞	0,+∞	NUM
ejpam-6847	81	13	)	)	PUNCT
ejpam-6847	81	14	with	with	ADP
ejpam-6847	81	15	x	x	PUNCT
ejpam-6847	81	16	being	be	AUX
ejpam-6847	81	17	a	a	DET
ejpam-6847	81	18	non	non	ADJ
ejpam-6847	81	19	-	-	ADJ
ejpam-6847	81	20	void	void	ADJ
ejpam-6847	81	21	set	set	NOUN
ejpam-6847	81	22	,	,	PUNCT
ejpam-6847	81	23	and	and	CCONJ
ejpam-6847	81	24	suppose	suppose	VERB
ejpam-6847	81	25	β	β	X
ejpam-6847	81	26	,	,	PUNCT
ejpam-6847	81	27	µ	µ	NOUN
ejpam-6847	81	28	,	,	PUNCT
ejpam-6847	81	29	γ	γ	X
ejpam-6847	81	30	:	:	PUNCT
ejpam-6847	81	31	x2	x2	PROPN
ejpam-6847	81	32	→	→	PUNCT
ejpam-6847	81	33	[	[	X
ejpam-6847	81	34	1,+∞	1,+∞	NUM
ejpam-6847	81	35	)	)	PUNCT
ejpam-6847	81	36	are	be	AUX
ejpam-6847	81	37	functions	function	NOUN
ejpam-6847	81	38	such	such	ADJ
ejpam-6847	81	39	that	that	PRON
ejpam-6847	81	40	for	for	ADP
ejpam-6847	81	41	all	all	DET
ejpam-6847	81	42	x	x	NOUN
ejpam-6847	81	43	,	,	PUNCT
ejpam-6847	81	44	y	y	PROPN
ejpam-6847	81	45	,	,	PUNCT
ejpam-6847	81	46	z	z	PROPN
ejpam-6847	81	47	,	,	PUNCT
ejpam-6847	81	48	a	a	DET
ejpam-6847	81	49	∈	∈	PROPN
ejpam-6847	81	50	x	x	NOUN
ejpam-6847	81	51	,	,	PUNCT
ejpam-6847	81	52	the	the	DET
ejpam-6847	81	53	following	follow	VERB
ejpam-6847	81	54	conditions	condition	NOUN
ejpam-6847	81	55	are	be	AUX
ejpam-6847	81	56	fulfilled	fulfil	VERB
ejpam-6847	81	57	:	:	PUNCT
ejpam-6847	81	58	(	(	PUNCT
ejpam-6847	81	59	t1	t1	NOUN
ejpam-6847	81	60	)	)	PUNCT
ejpam-6847	81	61	s(x	s(x	PROPN
ejpam-6847	81	62	,	,	PUNCT
ejpam-6847	81	63	y	y	PROPN
ejpam-6847	81	64	,	,	PUNCT
ejpam-6847	81	65	z	z	NOUN
ejpam-6847	81	66	)	)	PUNCT
ejpam-6847	81	67	=	=	SYM
ejpam-6847	81	68	0	0	NUM
ejpam-6847	81	69	iff	iff	NOUN
ejpam-6847	81	70	x	x	PROPN
ejpam-6847	81	71	=	=	SYM
ejpam-6847	81	72	y	y	PROPN
ejpam-6847	81	73	=	=	SYM
ejpam-6847	81	74	z	z	PROPN
ejpam-6847	81	75	;	;	PUNCT
ejpam-6847	81	76	(	(	PUNCT
ejpam-6847	81	77	t2	t2	NOUN
ejpam-6847	81	78	)	)	PUNCT
ejpam-6847	81	79	s(x	s(x	PROPN
ejpam-6847	81	80	,	,	PUNCT
ejpam-6847	81	81	x	x	X
ejpam-6847	81	82	,	,	PUNCT
ejpam-6847	81	83	z	z	NOUN
ejpam-6847	81	84	)	)	PUNCT
ejpam-6847	81	85	=	=	SYM
ejpam-6847	81	86	s(z	s(z	PROPN
ejpam-6847	81	87	,	,	PUNCT
ejpam-6847	81	88	z	z	NOUN
ejpam-6847	81	89	,	,	PUNCT
ejpam-6847	81	90	x	x	NOUN
ejpam-6847	81	91	)	)	PUNCT
ejpam-6847	81	92	;	;	PUNCT
ejpam-6847	81	93	,	,	PUNCT
ejpam-6847	81	94	for	for	ADP
ejpam-6847	81	95	all	all	DET
ejpam-6847	81	96	x	x	NOUN
ejpam-6847	81	97	,	,	PUNCT
ejpam-6847	81	98	z	z	PROPN
ejpam-6847	81	99	∈	∈	PROPN
ejpam-6847	82	1	x	x	X
ejpam-6847	82	2	;	;	PUNCT
ejpam-6847	82	3	(	(	PUNCT
ejpam-6847	82	4	t3	t3	NOUN
ejpam-6847	82	5	)	)	PUNCT
ejpam-6847	82	6	s(x	s(x	PROPN
ejpam-6847	82	7	,	,	PUNCT
ejpam-6847	82	8	y	y	PROPN
ejpam-6847	82	9	,	,	PUNCT
ejpam-6847	82	10	z	z	NOUN
ejpam-6847	82	11	)	)	PUNCT
ejpam-6847	82	12	≤	≤	NOUN
ejpam-6847	82	13	β(x	β(x	NOUN
ejpam-6847	82	14	,	,	PUNCT
ejpam-6847	82	15	a)s(x	a)s(x	NOUN
ejpam-6847	82	16	,	,	PUNCT
ejpam-6847	82	17	x	x	X
ejpam-6847	82	18	,	,	PUNCT
ejpam-6847	82	19	a	a	PRON
ejpam-6847	82	20	)	)	PUNCT
ejpam-6847	83	1	+	+	SYM
ejpam-6847	83	2	µ(y	µ(y	PROPN
ejpam-6847	83	3	,	,	PUNCT
ejpam-6847	83	4	a)s(y	a)s(y	ADJ
ejpam-6847	83	5	,	,	PUNCT
ejpam-6847	83	6	y	y	PROPN
ejpam-6847	83	7	,	,	PUNCT
ejpam-6847	83	8	a	a	PRON
ejpam-6847	83	9	)	)	PUNCT
ejpam-6847	83	10	+	+	CCONJ
ejpam-6847	83	11	γ(z	γ(z	PROPN
ejpam-6847	83	12	,	,	PUNCT
ejpam-6847	83	13	a)s(z	a)s(z	PROPN
ejpam-6847	83	14	,	,	PUNCT
ejpam-6847	83	15	z	z	PROPN
ejpam-6847	83	16	,	,	PUNCT
ejpam-6847	83	17	a	a	PRON
ejpam-6847	83	18	)	)	PUNCT
ejpam-6847	83	19	.	.	PUNCT
ejpam-6847	84	1	then	then	ADV
ejpam-6847	84	2	,	,	PUNCT
ejpam-6847	84	3	the	the	DET
ejpam-6847	84	4	pair	pair	NOUN
ejpam-6847	84	5	(	(	PUNCT
ejpam-6847	84	6	x	x	X
ejpam-6847	84	7	,	,	PUNCT
ejpam-6847	84	8	s	s	AUX
ejpam-6847	84	9	)	)	PUNCT
ejpam-6847	84	10	is	be	AUX
ejpam-6847	84	11	referred	refer	VERB
ejpam-6847	84	12	to	to	ADP
ejpam-6847	84	13	as	as	ADP
ejpam-6847	84	14	a	a	DET
ejpam-6847	84	15	triple	triple	ADV
ejpam-6847	84	16	controlled	control	VERB
ejpam-6847	84	17	s	s	NOUN
ejpam-6847	84	18	-	-	ADJ
ejpam-6847	84	19	metric	metric	ADJ
ejpam-6847	84	20	type	type	NOUN
ejpam-6847	84	21	space	space	NOUN
ejpam-6847	84	22	,	,	PUNCT
ejpam-6847	84	23	abbreviated	abbreviate	VERB
ejpam-6847	84	24	as	as	ADP
ejpam-6847	84	25	t	t	PROPN
ejpam-6847	84	26	c	c	PROPN
ejpam-6847	84	27	-	-	PUNCT
ejpam-6847	84	28	s	s	PROPN
ejpam-6847	84	29	-	-	PUNCT
ejpam-6847	84	30	mt	mt	PROPN
ejpam-6847	84	31	s.	s.	PROPN
ejpam-6847	84	32	remark	remark	PROPN
ejpam-6847	84	33	1	1	NUM
ejpam-6847	84	34	.	.	PUNCT
ejpam-6847	85	1	[	[	X
ejpam-6847	85	2	20	20	NUM
ejpam-6847	85	3	]	]	PUNCT
ejpam-6847	85	4	by	by	ADP
ejpam-6847	85	5	setting	set	VERB
ejpam-6847	85	6	β	β	X
ejpam-6847	85	7	=	=	SYM
ejpam-6847	85	8	µ	µ	X
ejpam-6847	85	9	=	=	PUNCT
ejpam-6847	85	10	γ	γ	X
ejpam-6847	85	11	in	in	ADP
ejpam-6847	85	12	definition	definition	NOUN
ejpam-6847	85	13	5	5	NUM
ejpam-6847	85	14	,	,	PUNCT
ejpam-6847	85	15	we	we	PRON
ejpam-6847	85	16	get	get	VERB
ejpam-6847	85	17	a	a	DET
ejpam-6847	85	18	controlled	control	VERB
ejpam-6847	85	19	s	s	ADJ
ejpam-6847	85	20	-	-	ADJ
ejpam-6847	85	21	metric	metric	ADJ
ejpam-6847	85	22	type	type	NOUN
ejpam-6847	85	23	space	space	NOUN
ejpam-6847	85	24	,	,	PUNCT
ejpam-6847	85	25	as	as	SCONJ
ejpam-6847	85	26	described	describe	VERB
ejpam-6847	85	27	in	in	ADP
ejpam-6847	85	28	definition	definition	NOUN
ejpam-6847	85	29	4	4	NUM
ejpam-6847	85	30	.	.	PUNCT
ejpam-6847	86	1	therefore	therefore	ADV
ejpam-6847	86	2	,	,	PUNCT
ejpam-6847	86	3	the	the	DET
ejpam-6847	86	4	definition	definition	NOUN
ejpam-6847	86	5	of	of	ADP
ejpam-6847	86	6	t	t	PROPN
ejpam-6847	86	7	c	c	PROPN
ejpam-6847	86	8	-	-	PUNCT
ejpam-6847	86	9	s	s	PROPN
ejpam-6847	86	10	-	-	PUNCT
ejpam-6847	86	11	mt	mt	PROPN
ejpam-6847	86	12	s	s	PART
ejpam-6847	86	13	is	be	AUX
ejpam-6847	86	14	a	a	DET
ejpam-6847	86	15	generalization	generalization	NOUN
ejpam-6847	86	16	of	of	ADP
ejpam-6847	86	17	the	the	DET
ejpam-6847	86	18	controlled	control	VERB
ejpam-6847	86	19	s	s	PROPN
ejpam-6847	86	20	-	-	ADJ
ejpam-6847	86	21	metric	metric	ADJ
ejpam-6847	86	22	type	type	NOUN
ejpam-6847	86	23	space	space	NOUN
ejpam-6847	86	24	.	.	PUNCT
ejpam-6847	87	1	additionally	additionally	ADV
ejpam-6847	87	2	,	,	PUNCT
ejpam-6847	87	3	if	if	SCONJ
ejpam-6847	87	4	we	we	PRON
ejpam-6847	87	5	set	set	VERB
ejpam-6847	87	6	β	β	X
ejpam-6847	87	7	=	=	SYM
ejpam-6847	87	8	µ	µ	X
ejpam-6847	87	9	=	=	SYM
ejpam-6847	87	10	γ	γ	X
ejpam-6847	87	11	=	=	SYM
ejpam-6847	87	12	1	1	NUM
ejpam-6847	87	13	,	,	PUNCT
ejpam-6847	87	14	the	the	DET
ejpam-6847	87	15	definition	definition	NOUN
ejpam-6847	87	16	of	of	ADP
ejpam-6847	87	17	t	t	PROPN
ejpam-6847	87	18	c	c	PROPN
ejpam-6847	87	19	-	-	PUNCT
ejpam-6847	87	20	s	s	PROPN
ejpam-6847	87	21	-	-	PUNCT
ejpam-6847	87	22	mt	mt	NOUN
ejpam-6847	87	23	s	s	PRON
ejpam-6847	87	24	turns	turn	VERB
ejpam-6847	87	25	into	into	ADP
ejpam-6847	87	26	an	an	DET
ejpam-6847	87	27	s	s	NOUN
ejpam-6847	87	28	-	-	ADJ
ejpam-6847	87	29	metric	metric	ADJ
ejpam-6847	87	30	space	space	NOUN
ejpam-6847	87	31	,	,	PUNCT
ejpam-6847	87	32	as	as	SCONJ
ejpam-6847	87	33	outlined	outline	VERB
ejpam-6847	87	34	in	in	ADP
ejpam-6847	87	35	definition	definition	NOUN
ejpam-6847	87	36	1	1	NUM
ejpam-6847	87	37	.	.	PUNCT
ejpam-6847	88	1	the	the	DET
ejpam-6847	88	2	following	follow	VERB
ejpam-6847	88	3	example	example	NOUN
ejpam-6847	88	4	demonstrates	demonstrate	VERB
ejpam-6847	88	5	that	that	SCONJ
ejpam-6847	88	6	a	a	DET
ejpam-6847	88	7	triple	triple	ADV
ejpam-6847	88	8	controlled	control	VERB
ejpam-6847	88	9	s	s	NOUN
ejpam-6847	88	10	-	-	ADJ
ejpam-6847	88	11	metric	metric	ADJ
ejpam-6847	88	12	type	type	NOUN
ejpam-6847	88	13	space	space	NOUN
ejpam-6847	88	14	is	be	AUX
ejpam-6847	88	15	different	different	ADJ
ejpam-6847	88	16	from	from	ADP
ejpam-6847	88	17	a	a	DET
ejpam-6847	88	18	controlled	control	VERB
ejpam-6847	88	19	s	s	ADJ
ejpam-6847	88	20	-	-	ADJ
ejpam-6847	88	21	metric	metric	ADJ
ejpam-6847	88	22	type	type	NOUN
ejpam-6847	88	23	space	space	NOUN
ejpam-6847	88	24	[	[	X
ejpam-6847	88	25	20	20	NUM
ejpam-6847	88	26	]	]	PUNCT
ejpam-6847	88	27	.	.	PUNCT
ejpam-6847	89	1	example	example	NOUN
ejpam-6847	90	1	1	1	NUM
ejpam-6847	90	2	.	.	PUNCT
ejpam-6847	91	1	[	[	X
ejpam-6847	91	2	20	20	NUM
ejpam-6847	91	3	]	]	PUNCT
ejpam-6847	91	4	let	let	VERB
ejpam-6847	91	5	x	x	PUNCT
ejpam-6847	91	6	=	=	PUNCT
ejpam-6847	91	7	{	{	PUNCT
ejpam-6847	91	8	0	0	NUM
ejpam-6847	91	9	,	,	PUNCT
ejpam-6847	91	10	1	1	NUM
ejpam-6847	91	11	,	,	PUNCT
ejpam-6847	91	12	2	2	NUM
ejpam-6847	91	13	}	}	PUNCT
ejpam-6847	91	14	,	,	PUNCT
ejpam-6847	91	15	and	and	CCONJ
ejpam-6847	91	16	define	define	VERB
ejpam-6847	91	17	s	s	VERB
ejpam-6847	91	18	:	:	PUNCT
ejpam-6847	91	19	x3	x3	ADJ
ejpam-6847	91	20	→	→	SYM
ejpam-6847	91	21	[	[	X
ejpam-6847	91	22	0,+∞	0,+∞	NUM
ejpam-6847	91	23	)	)	PUNCT
ejpam-6847	91	24	by	by	ADP
ejpam-6847	91	25	s(x	s(x	PROPN
ejpam-6847	91	26	,	,	PUNCT
ejpam-6847	91	27	y	y	PROPN
ejpam-6847	91	28	,	,	PUNCT
ejpam-6847	91	29	z	z	NOUN
ejpam-6847	91	30	)	)	PUNCT
ejpam-6847	91	31	=	=	SYM
ejpam-6847	92	1			NOUN
ejpam-6847	92	2	0	0	PUNCT
ejpam-6847	93	1	if	if	SCONJ
ejpam-6847	93	2	x	x	X
ejpam-6847	93	3	=	=	PUNCT
ejpam-6847	93	4	y	y	PROPN
ejpam-6847	93	5	=	=	SYM
ejpam-6847	93	6	z	z	PROPN
ejpam-6847	93	7	,	,	PUNCT
ejpam-6847	93	8	1	1	NUM
ejpam-6847	93	9	if	if	SCONJ
ejpam-6847	93	10	x	x	PROPN
ejpam-6847	93	11	6=	6=	NUM
ejpam-6847	93	12	y	y	PROPN
ejpam-6847	93	13	6=	6=	PROPN
ejpam-6847	94	1	z	z	PROPN
ejpam-6847	94	2	,	,	PUNCT
ejpam-6847	94	3	3	3	NUM
ejpam-6847	94	4	2	2	NUM
ejpam-6847	94	5	if	if	SCONJ
ejpam-6847	94	6	x	x	X
ejpam-6847	94	7	=	=	SYM
ejpam-6847	94	8	y	y	PROPN
ejpam-6847	94	9	,	,	PUNCT
ejpam-6847	94	10	y	y	PROPN
ejpam-6847	94	11	6=	6=	PROPN
ejpam-6847	94	12	z.	z.	PROPN
ejpam-6847	94	13	f.	f.	PROPN
ejpam-6847	94	14	m.	m.	PROPN
ejpam-6847	94	15	azmi	azmi	PROPN
ejpam-6847	94	16	,	,	PUNCT
ejpam-6847	94	17	a.	a.	PROPN
ejpam-6847	94	18	h.	h.	PROPN
ejpam-6847	94	19	ansari	ansari	PROPN
ejpam-6847	94	20	,	,	PUNCT
ejpam-6847	94	21	s.	s.	PROPN
ejpam-6847	94	22	h.	h.	PROPN
ejpam-6847	94	23	j.	j.	PROPN
ejpam-6847	94	24	petroudi	petroudi	PROPN
ejpam-6847	94	25	/	/	SYM
ejpam-6847	94	26	eur	eur	PROPN
ejpam-6847	94	27	.	.	PUNCT
ejpam-6847	95	1	j.	j.	PROPN
ejpam-6847	95	2	pure	pure	PROPN
ejpam-6847	95	3	appl	appl	PROPN
ejpam-6847	95	4	.	.	PROPN
ejpam-6847	95	5	math	math	PROPN
ejpam-6847	95	6	,	,	PUNCT
ejpam-6847	95	7	18	18	NUM
ejpam-6847	95	8	(	(	PUNCT
ejpam-6847	95	9	4	4	NUM
ejpam-6847	95	10	)	)	PUNCT
ejpam-6847	95	11	(	(	PUNCT
ejpam-6847	95	12	2025	2025	NUM
ejpam-6847	95	13	)	)	PUNCT
ejpam-6847	95	14	,	,	PUNCT
ejpam-6847	95	15	6847	6847	NUM
ejpam-6847	95	16	5	5	NUM
ejpam-6847	95	17	of	of	ADP
ejpam-6847	95	18	26	26	NUM
ejpam-6847	95	19	let	let	VERB
ejpam-6847	95	20	β	β	NOUN
ejpam-6847	95	21	,	,	PUNCT
ejpam-6847	95	22	µ	µ	NUM
ejpam-6847	95	23	,	,	PUNCT
ejpam-6847	95	24	γ	γ	X
ejpam-6847	95	25	:	:	PUNCT
ejpam-6847	95	26	x2	x2	PROPN
ejpam-6847	95	27	→	→	PUNCT
ejpam-6847	96	1	[	[	X
ejpam-6847	96	2	1,+∞	1,+∞	NUM
ejpam-6847	96	3	)	)	PUNCT
ejpam-6847	96	4	be	be	AUX
ejpam-6847	96	5	defined	define	VERB
ejpam-6847	96	6	as	as	SCONJ
ejpam-6847	96	7	follows	follow	VERB
ejpam-6847	96	8	:	:	PUNCT
ejpam-6847	96	9	β(x	β(x	NOUN
ejpam-6847	96	10	,	,	PUNCT
ejpam-6847	96	11	y	y	NOUN
ejpam-6847	96	12	)	)	PUNCT
ejpam-6847	96	13	=	=	SYM
ejpam-6847	96	14	1	1	NUM
ejpam-6847	96	15	+	+	CCONJ
ejpam-6847	96	16	x+	x+	ADJ
ejpam-6847	96	17	y	y	PROPN
ejpam-6847	96	18	,	,	PUNCT
ejpam-6847	96	19	µ(x	µ(x	NOUN
ejpam-6847	96	20	,	,	PUNCT
ejpam-6847	96	21	y	y	NOUN
ejpam-6847	96	22	)	)	PUNCT
ejpam-6847	96	23	=	=	SYM
ejpam-6847	96	24	1	1	NUM
ejpam-6847	96	25	+	+	CCONJ
ejpam-6847	96	26	xy	xy	PROPN
ejpam-6847	96	27	,	,	PUNCT
ejpam-6847	96	28	and	and	CCONJ
ejpam-6847	96	29	γ(x	γ(x	PROPN
ejpam-6847	96	30	,	,	PUNCT
ejpam-6847	96	31	y	y	NOUN
ejpam-6847	96	32	)	)	PUNCT
ejpam-6847	96	33	=	=	SYM
ejpam-6847	96	34	2	2	NUM
ejpam-6847	96	35	+	+	CCONJ
ejpam-6847	97	1	x+	x+	ADJ
ejpam-6847	97	2	y.	y.	NOUN
ejpam-6847	97	3	it	it	PRON
ejpam-6847	97	4	is	be	AUX
ejpam-6847	97	5	evident	evident	ADJ
ejpam-6847	97	6	that	that	SCONJ
ejpam-6847	97	7	(	(	PUNCT
ejpam-6847	97	8	x	x	X
ejpam-6847	97	9	,	,	PUNCT
ejpam-6847	97	10	s	s	PART
ejpam-6847	97	11	)	)	PUNCT
ejpam-6847	97	12	is	be	AUX
ejpam-6847	97	13	a	a	DET
ejpam-6847	97	14	t	t	NOUN
ejpam-6847	97	15	c	c	X
ejpam-6847	97	16	-	-	PUNCT
ejpam-6847	97	17	s	s	PROPN
ejpam-6847	97	18	-	-	PUNCT
ejpam-6847	97	19	mt	mt	NOUN
ejpam-6847	97	20	s	s	PROPN
ejpam-6847	97	21	,	,	PUNCT
ejpam-6847	97	22	since	since	SCONJ
ejpam-6847	97	23	β	β	X
ejpam-6847	97	24	6=	6=	ADP
ejpam-6847	97	25	µ	µ	PROPN
ejpam-6847	97	26	6=	6=	ADP
ejpam-6847	97	27	γ	γ	X
ejpam-6847	97	28	,	,	PUNCT
ejpam-6847	97	29	this	this	PRON
ejpam-6847	97	30	indicates	indicate	VERB
ejpam-6847	97	31	that	that	SCONJ
ejpam-6847	97	32	(	(	PUNCT
ejpam-6847	97	33	x	x	X
ejpam-6847	97	34	,	,	PUNCT
ejpam-6847	97	35	s	s	PART
ejpam-6847	97	36	)	)	PUNCT
ejpam-6847	97	37	is	be	AUX
ejpam-6847	97	38	not	not	PART
ejpam-6847	97	39	a	a	DET
ejpam-6847	97	40	controlled	control	VERB
ejpam-6847	97	41	s	s	ADJ
ejpam-6847	97	42	-	-	ADJ
ejpam-6847	97	43	metric	metric	ADJ
ejpam-6847	97	44	type	type	NOUN
ejpam-6847	97	45	space	space	NOUN
ejpam-6847	97	46	.	.	PUNCT
ejpam-6847	98	1	we	we	PRON
ejpam-6847	98	2	recall	recall	VERB
ejpam-6847	98	3	the	the	DET
ejpam-6847	98	4	concepts	concept	NOUN
ejpam-6847	98	5	of	of	ADP
ejpam-6847	98	6	cauchy	cauchy	NOUN
ejpam-6847	98	7	and	and	CCONJ
ejpam-6847	98	8	convergent	convergent	ADJ
ejpam-6847	98	9	sequences	sequence	NOUN
ejpam-6847	98	10	,	,	PUNCT
ejpam-6847	98	11	completeness	completeness	NOUN
ejpam-6847	98	12	,	,	PUNCT
ejpam-6847	98	13	and	and	CCONJ
ejpam-6847	98	14	the	the	DET
ejpam-6847	98	15	concept	concept	NOUN
ejpam-6847	98	16	of	of	ADP
ejpam-6847	98	17	the	the	DET
ejpam-6847	98	18	open	open	ADJ
ejpam-6847	98	19	ball	ball	NOUN
ejpam-6847	98	20	in	in	ADP
ejpam-6847	98	21	t	t	PROPN
ejpam-6847	98	22	c	c	PROPN
ejpam-6847	98	23	-	-	PUNCT
ejpam-6847	98	24	s	s	PROPN
ejpam-6847	98	25	-	-	PUNCT
ejpam-6847	98	26	mt	mt	NOUN
ejpam-6847	98	27	s	s	PROPN
ejpam-6847	98	28	,	,	PUNCT
ejpam-6847	98	29	as	as	SCONJ
ejpam-6847	98	30	defined	define	VERB
ejpam-6847	98	31	in	in	ADP
ejpam-6847	98	32	[	[	X
ejpam-6847	98	33	20	20	NUM
ejpam-6847	98	34	]	]	PUNCT
ejpam-6847	98	35	.	.	PUNCT
ejpam-6847	99	1	definition	definition	NOUN
ejpam-6847	99	2	6	6	NUM
ejpam-6847	99	3	.	.	PUNCT
ejpam-6847	100	1	[	[	X
ejpam-6847	100	2	20	20	NUM
ejpam-6847	100	3	]	]	X
ejpam-6847	100	4	let	let	AUX
ejpam-6847	100	5	(	(	PUNCT
ejpam-6847	100	6	x	x	X
ejpam-6847	100	7	,	,	PUNCT
ejpam-6847	100	8	s	s	PART
ejpam-6847	100	9	)	)	PUNCT
ejpam-6847	100	10	be	be	AUX
ejpam-6847	100	11	a	a	DET
ejpam-6847	100	12	t	t	NOUN
ejpam-6847	100	13	c	c	X
ejpam-6847	100	14	-	-	PUNCT
ejpam-6847	100	15	s	s	PROPN
ejpam-6847	100	16	-	-	PUNCT
ejpam-6847	100	17	mt	mt	NOUN
ejpam-6847	100	18	s	s	PART
ejpam-6847	100	19	and	and	CCONJ
ejpam-6847	100	20	let	let	VERB
ejpam-6847	100	21	{	{	PUNCT
ejpam-6847	100	22	xn	xn	VERB
ejpam-6847	100	23	}	}	PUNCT
ejpam-6847	100	24	be	be	AUX
ejpam-6847	100	25	any	any	DET
ejpam-6847	100	26	sequence	sequence	NOUN
ejpam-6847	100	27	in	in	ADP
ejpam-6847	100	28	x.	x.	PROPN
ejpam-6847	100	29	(	(	PUNCT
ejpam-6847	100	30	1	1	NUM
ejpam-6847	100	31	)	)	PUNCT
ejpam-6847	100	32	for	for	ADP
ejpam-6847	100	33	x	x	SYM
ejpam-6847	100	34	∈	∈	PROPN
ejpam-6847	100	35	x	x	PUNCT
ejpam-6847	100	36	with	with	ADP
ejpam-6847	100	37	ε	ε	PROPN
ejpam-6847	100	38	>	>	X
ejpam-6847	100	39	0	0	PROPN
ejpam-6847	100	40	.	.	PUNCT
ejpam-6847	101	1	then	then	ADV
ejpam-6847	101	2	,	,	PUNCT
ejpam-6847	101	3	b(x	b(x	NOUN
ejpam-6847	101	4	,	,	PUNCT
ejpam-6847	101	5	ε	ε	PROPN
ejpam-6847	101	6	)	)	PUNCT
ejpam-6847	101	7	=	=	PRON
ejpam-6847	101	8	{	{	PUNCT
ejpam-6847	101	9	w	w	NOUN
ejpam-6847	101	10	∈	∈	PROPN
ejpam-6847	101	11	x	x	NOUN
ejpam-6847	101	12	,	,	PUNCT
ejpam-6847	101	13	s(w	s(w	NOUN
ejpam-6847	101	14	,	,	PUNCT
ejpam-6847	101	15	w	w	NOUN
ejpam-6847	101	16	,	,	PUNCT
ejpam-6847	101	17	x	x	NOUN
ejpam-6847	101	18	)	)	PUNCT
ejpam-6847	101	19	<	<	X
ejpam-6847	101	20	ε	ε	X
ejpam-6847	101	21	}	}	PUNCT
ejpam-6847	101	22	,	,	PUNCT
ejpam-6847	101	23	denotes	denote	VERB
ejpam-6847	101	24	the	the	DET
ejpam-6847	101	25	open	open	ADJ
ejpam-6847	101	26	ball	ball	NOUN
ejpam-6847	101	27	.	.	PUNCT
ejpam-6847	102	1	(	(	PUNCT
ejpam-6847	102	2	2	2	X
ejpam-6847	102	3	)	)	PUNCT
ejpam-6847	102	4	{	{	PUNCT
ejpam-6847	102	5	xn	xn	X
ejpam-6847	102	6	}	}	PUNCT
ejpam-6847	102	7	converges	converge	NOUN
ejpam-6847	102	8	to	to	ADP
ejpam-6847	102	9	a	a	DET
ejpam-6847	102	10	point	point	NOUN
ejpam-6847	102	11	w	w	NOUN
ejpam-6847	102	12	in	in	ADP
ejpam-6847	102	13	x	x	SYM
ejpam-6847	102	14	,	,	PUNCT
ejpam-6847	102	15	if	if	SCONJ
ejpam-6847	102	16	for	for	ADP
ejpam-6847	102	17	every	every	DET
ejpam-6847	102	18	ε	ε	PROPN
ejpam-6847	102	19	>	>	X
ejpam-6847	102	20	0	0	PROPN
ejpam-6847	102	21	,	,	PUNCT
ejpam-6847	102	22	there	there	PRON
ejpam-6847	102	23	exists	exist	VERB
ejpam-6847	102	24	an	an	DET
ejpam-6847	102	25	n	n	NUM
ejpam-6847	102	26	∈	∈	PROPN
ejpam-6847	102	27	n	n	CCONJ
ejpam-6847	102	28	,	,	PUNCT
ejpam-6847	102	29	such	such	ADJ
ejpam-6847	102	30	s(xn	s(xn	PROPN
ejpam-6847	102	31	,	,	PUNCT
ejpam-6847	102	32	xn	xn	PROPN
ejpam-6847	102	33	,	,	PUNCT
ejpam-6847	102	34	w	w	NOUN
ejpam-6847	102	35	)	)	PUNCT
ejpam-6847	102	36	<	<	X
ejpam-6847	102	37	ε	ε	PROPN
ejpam-6847	102	38	for	for	ADP
ejpam-6847	102	39	all	all	DET
ejpam-6847	102	40	n	n	PRON
ejpam-6847	102	41	≥	≥	NOUN
ejpam-6847	102	42	n.	n.	NOUN
ejpam-6847	102	43	(	(	PUNCT
ejpam-6847	102	44	3	3	NUM
ejpam-6847	102	45	)	)	PUNCT
ejpam-6847	102	46	{	{	PUNCT
ejpam-6847	102	47	xn	xn	X
ejpam-6847	102	48	}	}	PUNCT
ejpam-6847	102	49	is	be	AUX
ejpam-6847	102	50	referred	refer	VERB
ejpam-6847	102	51	to	to	ADP
ejpam-6847	102	52	as	as	ADP
ejpam-6847	102	53	a	a	DET
ejpam-6847	102	54	cauchy	cauchy	ADJ
ejpam-6847	102	55	sequence	sequence	NOUN
ejpam-6847	102	56	if	if	SCONJ
ejpam-6847	102	57	for	for	ADP
ejpam-6847	102	58	every	every	DET
ejpam-6847	102	59	ε	ε	PROPN
ejpam-6847	102	60	>	>	X
ejpam-6847	102	61	0	0	PROPN
ejpam-6847	102	62	,	,	PUNCT
ejpam-6847	102	63	there	there	PRON
ejpam-6847	102	64	exists	exist	VERB
ejpam-6847	102	65	an	an	DET
ejpam-6847	102	66	n	n	NOUN
ejpam-6847	102	67	∈	∈	NOUN
ejpam-6847	102	68	n	n	NOUN
ejpam-6847	102	69	such	such	ADJ
ejpam-6847	102	70	that	that	SCONJ
ejpam-6847	102	71	s(xn	s(xn	NOUN
ejpam-6847	102	72	,	,	PUNCT
ejpam-6847	102	73	xn	xn	PROPN
ejpam-6847	102	74	,	,	PUNCT
ejpam-6847	102	75	xm	xm	PROPN
ejpam-6847	102	76	)	)	PUNCT
ejpam-6847	102	77	<	<	X
ejpam-6847	102	78	ε	ε	PROPN
ejpam-6847	102	79	for	for	ADP
ejpam-6847	102	80	all	all	DET
ejpam-6847	102	81	m	m	PROPN
ejpam-6847	102	82	,	,	PUNCT
ejpam-6847	102	83	n	n	PRON
ejpam-6847	102	84	≥	≥	NOUN
ejpam-6847	102	85	n.	n.	NOUN
ejpam-6847	102	86	(	(	PUNCT
ejpam-6847	102	87	4	4	NUM
ejpam-6847	102	88	)	)	PUNCT
ejpam-6847	102	89	the	the	DET
ejpam-6847	102	90	space	space	NOUN
ejpam-6847	102	91	(	(	PUNCT
ejpam-6847	102	92	x	x	X
ejpam-6847	102	93	,	,	PUNCT
ejpam-6847	102	94	s	s	PART
ejpam-6847	102	95	)	)	PUNCT
ejpam-6847	102	96	is	be	AUX
ejpam-6847	102	97	called	call	VERB
ejpam-6847	102	98	complete	complete	ADJ
ejpam-6847	102	99	if	if	SCONJ
ejpam-6847	102	100	every	every	DET
ejpam-6847	102	101	cauchy	cauchy	ADJ
ejpam-6847	102	102	sequence	sequence	NOUN
ejpam-6847	102	103	in	in	ADP
ejpam-6847	102	104	x	x	PROPN
ejpam-6847	102	105	is	be	AUX
ejpam-6847	102	106	convergent	convergent	ADJ
ejpam-6847	102	107	.	.	PUNCT
ejpam-6847	103	1	lemma	lemma	PROPN
ejpam-6847	103	2	1	1	NUM
ejpam-6847	103	3	.	.	PUNCT
ejpam-6847	104	1	[	[	X
ejpam-6847	104	2	20	20	NUM
ejpam-6847	104	3	]	]	X
ejpam-6847	104	4	let	let	VERB
ejpam-6847	104	5	(	(	PUNCT
ejpam-6847	104	6	x	x	X
ejpam-6847	104	7	,	,	PUNCT
ejpam-6847	104	8	s	s	PART
ejpam-6847	104	9	)	)	PUNCT
ejpam-6847	104	10	be	be	AUX
ejpam-6847	104	11	a	a	DET
ejpam-6847	104	12	t	t	NOUN
ejpam-6847	104	13	c	c	X
ejpam-6847	104	14	-	-	PUNCT
ejpam-6847	104	15	s	s	PROPN
ejpam-6847	104	16	-	-	PUNCT
ejpam-6847	104	17	mt	mt	NOUN
ejpam-6847	104	18	s	s	PART
ejpam-6847	104	19	and	and	CCONJ
ejpam-6847	104	20	let	let	VERB
ejpam-6847	104	21	β	β	NOUN
ejpam-6847	104	22	,	,	PUNCT
ejpam-6847	104	23	µ	µ	NUM
ejpam-6847	104	24	,	,	PUNCT
ejpam-6847	104	25	γ	γ	X
ejpam-6847	104	26	:	:	PUNCT
ejpam-6847	104	27	x2	x2	PROPN
ejpam-6847	104	28	→	→	PUNCT
ejpam-6847	105	1	[	[	X
ejpam-6847	105	2	1,+∞	1,+∞	NUM
ejpam-6847	105	3	)	)	PUNCT
ejpam-6847	105	4	be	be	VERB
ejpam-6847	105	5	mappings	mapping	NOUN
ejpam-6847	105	6	.	.	PUNCT
ejpam-6847	106	1	if	if	SCONJ
ejpam-6847	106	2	the	the	DET
ejpam-6847	106	3	sequence	sequence	NOUN
ejpam-6847	106	4	{	{	PUNCT
ejpam-6847	106	5	xn	xn	NOUN
ejpam-6847	106	6	}	}	PUNCT
ejpam-6847	106	7	in	in	ADP
ejpam-6847	106	8	x	x	SYM
ejpam-6847	106	9	is	be	AUX
ejpam-6847	106	10	convergent	convergent	ADJ
ejpam-6847	106	11	,	,	PUNCT
ejpam-6847	106	12	then	then	ADV
ejpam-6847	106	13	the	the	DET
ejpam-6847	106	14	limit	limit	NOUN
ejpam-6847	106	15	is	be	AUX
ejpam-6847	106	16	unique	unique	ADJ
ejpam-6847	106	17	.	.	PUNCT
ejpam-6847	107	1	samet	samet	PROPN
ejpam-6847	107	2	et	et	PROPN
ejpam-6847	107	3	al	al	PROPN
ejpam-6847	107	4	.	.	PUNCT
ejpam-6847	108	1	[	[	X
ejpam-6847	108	2	32	32	NUM
ejpam-6847	108	3	]	]	PUNCT
ejpam-6847	108	4	initially	initially	ADV
ejpam-6847	108	5	presented	present	VERB
ejpam-6847	108	6	the	the	DET
ejpam-6847	108	7	class	class	NOUN
ejpam-6847	108	8	of	of	ADP
ejpam-6847	108	9	αs	αs	PRON
ejpam-6847	108	10	-admissible	-admissible	ADJ
ejpam-6847	108	11	mappings	mapping	NOUN
ejpam-6847	108	12	.	.	PUNCT
ejpam-6847	109	1	for	for	ADP
ejpam-6847	109	2	more	more	ADJ
ejpam-6847	109	3	details	detail	NOUN
ejpam-6847	109	4	,	,	PUNCT
ejpam-6847	109	5	refer	refer	VERB
ejpam-6847	109	6	to	to	ADP
ejpam-6847	109	7	[	[	X
ejpam-6847	109	8	38	38	NUM
ejpam-6847	109	9	]	]	PUNCT
ejpam-6847	109	10	and	and	CCONJ
ejpam-6847	109	11	[	[	X
ejpam-6847	109	12	32	32	NUM
ejpam-6847	109	13	]	]	PUNCT
ejpam-6847	109	14	.	.	PUNCT
ejpam-6847	110	1	definition	definition	NOUN
ejpam-6847	110	2	7	7	NUM
ejpam-6847	110	3	.	.	PUNCT
ejpam-6847	111	1	let	let	VERB
ejpam-6847	111	2	t	t	NOUN
ejpam-6847	111	3	:	:	PUNCT
ejpam-6847	111	4	x	x	PUNCT
ejpam-6847	111	5	−→	−→	NOUN
ejpam-6847	111	6	x	x	VERB
ejpam-6847	111	7	be	be	AUX
ejpam-6847	111	8	a	a	DET
ejpam-6847	111	9	mapping	mapping	NOUN
ejpam-6847	111	10	with	with	ADP
ejpam-6847	111	11	x	x	DET
ejpam-6847	111	12	a	a	DET
ejpam-6847	111	13	non	non	ADJ
ejpam-6847	111	14	-	-	ADJ
ejpam-6847	111	15	void	void	ADJ
ejpam-6847	111	16	set	set	NOUN
ejpam-6847	111	17	,	,	PUNCT
ejpam-6847	111	18	and	and	CCONJ
ejpam-6847	111	19	let	let	VERB
ejpam-6847	111	20	αs	αs	INTJ
ejpam-6847	111	21	:	:	PUNCT
ejpam-6847	111	22	x	x	PROPN
ejpam-6847	111	23	×x	×x	X
ejpam-6847	111	24	→	→	SYM
ejpam-6847	111	25	[	[	X
ejpam-6847	111	26	0,+∞	0,+∞	NUM
ejpam-6847	111	27	)	)	PUNCT
ejpam-6847	111	28	be	be	AUX
ejpam-6847	111	29	a	a	DET
ejpam-6847	111	30	function	function	NOUN
ejpam-6847	111	31	.	.	PUNCT
ejpam-6847	112	1	t	t	PROPN
ejpam-6847	112	2	is	be	AUX
ejpam-6847	112	3	called	call	VERB
ejpam-6847	112	4	an	an	DET
ejpam-6847	112	5	αs	αs	ADV
ejpam-6847	112	6	-admissible	-admissible	ADJ
ejpam-6847	112	7	,	,	PUNCT
ejpam-6847	112	8	if	if	SCONJ
ejpam-6847	112	9	whenever	whenever	SCONJ
ejpam-6847	112	10	αs	αs	INTJ
ejpam-6847	112	11	(	(	PUNCT
ejpam-6847	112	12	x̂	x̂	NUM
ejpam-6847	112	13	,	,	PUNCT
ejpam-6847	112	14	ŷ	ŷ	NUM
ejpam-6847	112	15	)	)	PUNCT
ejpam-6847	112	16	≥	≥	PROPN
ejpam-6847	112	17	1	1	NUM
ejpam-6847	112	18	implies	imply	VERB
ejpam-6847	112	19	αs(t	αs(t	NUM
ejpam-6847	112	20	x̂	x̂	NUM
ejpam-6847	112	21	,	,	PUNCT
ejpam-6847	112	22	t	t	NOUN
ejpam-6847	112	23	ŷ	ŷ	NUM
ejpam-6847	112	24	)	)	PUNCT
ejpam-6847	112	25	≥	≥	NOUN
ejpam-6847	112	26	1	1	NUM
ejpam-6847	112	27	,	,	PUNCT
ejpam-6847	112	28	for	for	ADP
ejpam-6847	112	29	all	all	DET
ejpam-6847	112	30	x̂	x̂	NUM
ejpam-6847	112	31	,	,	PUNCT
ejpam-6847	112	32	ŷ	ŷ	X
ejpam-6847	112	33	∈	∈	PROPN
ejpam-6847	112	34	x.	x.	NOUN
ejpam-6847	112	35	on	on	ADP
ejpam-6847	112	36	the	the	DET
ejpam-6847	112	37	other	other	ADJ
ejpam-6847	112	38	hand	hand	NOUN
ejpam-6847	112	39	,	,	PUNCT
ejpam-6847	112	40	priyobarta	priyobarta	NOUN
ejpam-6847	112	41	et	et	NOUN
ejpam-6847	112	42	al	al	PROPN
ejpam-6847	112	43	.	.	PUNCT
ejpam-6847	113	1	[	[	X
ejpam-6847	113	2	37	37	NUM
ejpam-6847	113	3	]	]	PUNCT
ejpam-6847	113	4	extended	extend	VERB
ejpam-6847	113	5	the	the	DET
ejpam-6847	113	6	class	class	NOUN
ejpam-6847	113	7	of	of	ADP
ejpam-6847	113	8	αs	αs	PRON
ejpam-6847	113	9	-admissible	-admissible	ADJ
ejpam-6847	113	10	mappings	mapping	NOUN
ejpam-6847	113	11	in	in	ADP
ejpam-6847	113	12	the	the	DET
ejpam-6847	113	13	framework	framework	NOUN
ejpam-6847	113	14	of	of	ADP
ejpam-6847	113	15	s	s	NOUN
ejpam-6847	113	16	-metric	-metric	ADJ
ejpam-6847	113	17	space	space	NOUN
ejpam-6847	113	18	as	as	SCONJ
ejpam-6847	113	19	demonstrated	demonstrate	VERB
ejpam-6847	113	20	below	below	ADP
ejpam-6847	113	21	:	:	PUNCT
ejpam-6847	113	22	definition	definition	NOUN
ejpam-6847	113	23	8	8	NUM
ejpam-6847	113	24	.	.	PUNCT
ejpam-6847	114	1	[	[	X
ejpam-6847	114	2	37	37	NUM
ejpam-6847	114	3	]	]	PUNCT
ejpam-6847	114	4	consider	consider	VERB
ejpam-6847	114	5	the	the	DET
ejpam-6847	114	6	mapping	mapping	NOUN
ejpam-6847	114	7	t	t	NOUN
ejpam-6847	114	8	:	:	PUNCT
ejpam-6847	115	1	x	x	PUNCT
ejpam-6847	115	2	−→	−→	NOUN
ejpam-6847	115	3	x	x	PUNCT
ejpam-6847	115	4	and	and	CCONJ
ejpam-6847	115	5	let	let	VERB
ejpam-6847	115	6	αs	αs	INTJ
ejpam-6847	115	7	:	:	PUNCT
ejpam-6847	115	8	x3	x3	VERB
ejpam-6847	115	9	→	→	SYM
ejpam-6847	115	10	[	[	X
ejpam-6847	115	11	0,+∞	0,+∞	NUM
ejpam-6847	115	12	)	)	PUNCT
ejpam-6847	115	13	be	be	AUX
ejpam-6847	115	14	a	a	DET
ejpam-6847	115	15	function	function	NOUN
ejpam-6847	115	16	,	,	PUNCT
ejpam-6847	115	17	with	with	ADP
ejpam-6847	115	18	x	x	DET
ejpam-6847	115	19	a	a	DET
ejpam-6847	115	20	non	non	ADJ
ejpam-6847	115	21	-	-	ADJ
ejpam-6847	115	22	void	void	ADJ
ejpam-6847	115	23	set	set	NOUN
ejpam-6847	115	24	.	.	PUNCT
ejpam-6847	116	1	t	t	PROPN
ejpam-6847	116	2	is	be	AUX
ejpam-6847	116	3	referred	refer	VERB
ejpam-6847	116	4	to	to	ADP
ejpam-6847	116	5	as	as	ADP
ejpam-6847	116	6	αs	αs	ADJ
ejpam-6847	116	7	-	-	ADJ
ejpam-6847	116	8	admissible	admissible	ADJ
ejpam-6847	116	9	mapping	mapping	NOUN
ejpam-6847	116	10	,	,	PUNCT
ejpam-6847	116	11	if	if	SCONJ
ejpam-6847	116	12	for	for	ADP
ejpam-6847	116	13	all	all	DET
ejpam-6847	116	14	x̂	x̂	NUM
ejpam-6847	116	15	,	,	PUNCT
ejpam-6847	116	16	ŷ	ŷ	NUM
ejpam-6847	116	17	,	,	PUNCT
ejpam-6847	116	18	ẑ	ẑ	PROPN
ejpam-6847	116	19	∈	∈	PROPN
ejpam-6847	116	20	x	x	X
ejpam-6847	116	21	,	,	PUNCT
ejpam-6847	116	22	we	we	PRON
ejpam-6847	116	23	have	have	VERB
ejpam-6847	116	24	αs(x̂	αs(x̂	NOUN
ejpam-6847	116	25	,	,	PUNCT
ejpam-6847	116	26	ŷ	ŷ	NUM
ejpam-6847	116	27	,	,	PUNCT
ejpam-6847	116	28	ẑ	ẑ	NUM
ejpam-6847	116	29	)	)	PUNCT
ejpam-6847	116	30	≥	≥	NOUN
ejpam-6847	117	1	1	1	NUM
ejpam-6847	117	2	=	=	NOUN
ejpam-6847	117	3	⇒	⇒	NOUN
ejpam-6847	117	4	αs(t	αs(t	NUM
ejpam-6847	117	5	x̂	x̂	NUM
ejpam-6847	117	6	,	,	PUNCT
ejpam-6847	117	7	t	t	PROPN
ejpam-6847	117	8	ŷ	ŷ	NUM
ejpam-6847	117	9	,	,	PUNCT
ejpam-6847	117	10	t	t	PROPN
ejpam-6847	117	11	ẑ	ẑ	NUM
ejpam-6847	117	12	)	)	PUNCT
ejpam-6847	117	13	≥	≥	NOUN
ejpam-6847	117	14	1	1	NUM
ejpam-6847	117	15	.	.	PUNCT
ejpam-6847	117	16	(	(	PUNCT
ejpam-6847	117	17	1	1	X
ejpam-6847	117	18	)	)	PUNCT
ejpam-6847	117	19	example	example	NOUN
ejpam-6847	117	20	2	2	NUM
ejpam-6847	117	21	.	.	PUNCT
ejpam-6847	118	1	[	[	X
ejpam-6847	118	2	37	37	NUM
ejpam-6847	118	3	]	]	PUNCT
ejpam-6847	118	4	assume	assume	VERB
ejpam-6847	118	5	x	x	X
ejpam-6847	118	6	=	=	PUNCT
ejpam-6847	119	1	[	[	X
ejpam-6847	119	2	0,+∞	0,+∞	NUM
ejpam-6847	119	3	)	)	PUNCT
ejpam-6847	119	4	,	,	PUNCT
ejpam-6847	119	5	the	the	DET
ejpam-6847	119	6	mappings	mapping	NOUN
ejpam-6847	119	7	t	t	NOUN
ejpam-6847	119	8	:	:	PUNCT
ejpam-6847	119	9	x	x	PUNCT
ejpam-6847	119	10	−→	−→	NOUN
ejpam-6847	119	11	x	x	NOUN
ejpam-6847	119	12	,	,	PUNCT
ejpam-6847	119	13	and	and	CCONJ
ejpam-6847	119	14	αs	αs	INTJ
ejpam-6847	119	15	:	:	PUNCT
ejpam-6847	119	16	x3	x3	VERB
ejpam-6847	119	17	→	→	SYM
ejpam-6847	120	1	[	[	X
ejpam-6847	120	2	0,+∞	0,+∞	NUM
ejpam-6847	120	3	)	)	PUNCT
ejpam-6847	120	4	be	be	AUX
ejpam-6847	120	5	defined	define	VERB
ejpam-6847	120	6	by	by	ADP
ejpam-6847	120	7	t	t	PROPN
ejpam-6847	120	8	(	(	PUNCT
ejpam-6847	120	9	u	u	NOUN
ejpam-6847	120	10	)	)	PUNCT
ejpam-6847	120	11	=	=	SYM
ejpam-6847	120	12	4u	4u	NOUN
ejpam-6847	120	13	,	,	PUNCT
ejpam-6847	120	14	for	for	ADP
ejpam-6847	120	15	all	all	DET
ejpam-6847	120	16	u	u	NOUN
ejpam-6847	120	17	∈	∈	PROPN
ejpam-6847	120	18	x	x	NOUN
ejpam-6847	120	19	,	,	PUNCT
ejpam-6847	120	20	and	and	CCONJ
ejpam-6847	120	21	αs(x	αs(x	NUM
ejpam-6847	120	22	,	,	PUNCT
ejpam-6847	120	23	y	y	PROPN
ejpam-6847	120	24	,	,	PUNCT
ejpam-6847	120	25	z	z	NOUN
ejpam-6847	120	26	)	)	PUNCT
ejpam-6847	120	27	=	=	PUNCT
ejpam-6847	121	1	e	e	X
ejpam-6847	121	2	z	z	NOUN
ejpam-6847	121	3	xy	xy	INTJ
ejpam-6847	121	4	if	if	SCONJ
ejpam-6847	121	5	x	x	PROPN
ejpam-6847	121	6	≥	≥	NUM
ejpam-6847	121	7	y	y	PROPN
ejpam-6847	121	8	≥	≥	PROPN
ejpam-6847	121	9	z	z	NOUN
ejpam-6847	121	10	,	,	PUNCT
ejpam-6847	121	11	x	x	PROPN
ejpam-6847	121	12	6=	6=	ADP
ejpam-6847	121	13	0	0	NUM
ejpam-6847	121	14	,	,	PUNCT
ejpam-6847	121	15	y	y	PROPN
ejpam-6847	121	16	6=	6=	PROPN
ejpam-6847	121	17	0	0	NUM
ejpam-6847	121	18	,	,	PUNCT
ejpam-6847	121	19	and	and	CCONJ
ejpam-6847	121	20	αs(x	αs(x	NUM
ejpam-6847	121	21	,	,	PUNCT
ejpam-6847	121	22	y	y	PROPN
ejpam-6847	121	23	,	,	PUNCT
ejpam-6847	121	24	z	z	NOUN
ejpam-6847	121	25	)	)	PUNCT
ejpam-6847	121	26	=	=	SYM
ejpam-6847	121	27	0	0	NUM
ejpam-6847	121	28	,	,	PUNCT
ejpam-6847	121	29	if	if	SCONJ
ejpam-6847	121	30	x	x	PUNCT
ejpam-6847	121	31	<	<	X
ejpam-6847	121	32	y	y	X
ejpam-6847	121	33	<	<	X
ejpam-6847	121	34	z.	z.	PROPN
ejpam-6847	122	1	then	then	ADV
ejpam-6847	122	2	,	,	PUNCT
ejpam-6847	122	3	t	t	PROPN
ejpam-6847	122	4	is	be	AUX
ejpam-6847	122	5	an	an	DET
ejpam-6847	122	6	αs	αs	ADJ
ejpam-6847	122	7	-	-	PUNCT
ejpam-6847	122	8	admissible	admissible	ADJ
ejpam-6847	122	9	mapping	mapping	NOUN
ejpam-6847	122	10	.	.	PUNCT
ejpam-6847	123	1	f.	f.	PROPN
ejpam-6847	123	2	m.	m.	PROPN
ejpam-6847	123	3	azmi	azmi	PROPN
ejpam-6847	123	4	,	,	PUNCT
ejpam-6847	123	5	a.	a.	PROPN
ejpam-6847	123	6	h.	h.	PROPN
ejpam-6847	123	7	ansari	ansari	PROPN
ejpam-6847	123	8	,	,	PUNCT
ejpam-6847	123	9	s.	s.	PROPN
ejpam-6847	123	10	h.	h.	PROPN
ejpam-6847	123	11	j.	j.	PROPN
ejpam-6847	123	12	petroudi	petroudi	PROPN
ejpam-6847	123	13	/	/	SYM
ejpam-6847	123	14	eur	eur	PROPN
ejpam-6847	123	15	.	.	PUNCT
ejpam-6847	124	1	j.	j.	PROPN
ejpam-6847	124	2	pure	pure	PROPN
ejpam-6847	124	3	appl	appl	PROPN
ejpam-6847	124	4	.	.	PROPN
ejpam-6847	124	5	math	math	PROPN
ejpam-6847	124	6	,	,	PUNCT
ejpam-6847	124	7	18	18	NUM
ejpam-6847	124	8	(	(	PUNCT
ejpam-6847	124	9	4	4	NUM
ejpam-6847	124	10	)	)	PUNCT
ejpam-6847	124	11	(	(	PUNCT
ejpam-6847	124	12	2025	2025	NUM
ejpam-6847	124	13	)	)	PUNCT
ejpam-6847	124	14	,	,	PUNCT
ejpam-6847	124	15	6847	6847	NUM
ejpam-6847	124	16	6	6	NUM
ejpam-6847	124	17	of	of	ADP
ejpam-6847	124	18	26	26	NUM
ejpam-6847	124	19	definition	definition	NOUN
ejpam-6847	124	20	9	9	NUM
ejpam-6847	124	21	.	.	PUNCT
ejpam-6847	125	1	[	[	X
ejpam-6847	125	2	34	34	NUM
ejpam-6847	125	3	]	]	PUNCT
ejpam-6847	125	4	consider	consider	VERB
ejpam-6847	125	5	the	the	DET
ejpam-6847	125	6	mapping	mapping	NOUN
ejpam-6847	125	7	t	t	NOUN
ejpam-6847	125	8	:	:	PUNCT
ejpam-6847	125	9	x	x	PUNCT
ejpam-6847	125	10	−→	−→	NOUN
ejpam-6847	125	11	x	x	PUNCT
ejpam-6847	125	12	and	and	CCONJ
ejpam-6847	125	13	let	let	VERB
ejpam-6847	125	14	νs	νs	PRON
ejpam-6847	125	15	:	:	PUNCT
ejpam-6847	125	16	x3	x3	VERB
ejpam-6847	125	17	→	→	SYM
ejpam-6847	126	1	[	[	X
ejpam-6847	126	2	0,+∞	0,+∞	NUM
ejpam-6847	126	3	)	)	PUNCT
ejpam-6847	126	4	be	be	AUX
ejpam-6847	126	5	a	a	DET
ejpam-6847	126	6	function	function	NOUN
ejpam-6847	126	7	,	,	PUNCT
ejpam-6847	126	8	with	with	ADP
ejpam-6847	126	9	x	x	DET
ejpam-6847	126	10	a	a	DET
ejpam-6847	126	11	non	non	ADJ
ejpam-6847	126	12	-	-	ADJ
ejpam-6847	126	13	void	void	ADJ
ejpam-6847	126	14	set	set	NOUN
ejpam-6847	126	15	.	.	PUNCT
ejpam-6847	127	1	t	t	PROPN
ejpam-6847	127	2	is	be	AUX
ejpam-6847	127	3	referred	refer	VERB
ejpam-6847	127	4	to	to	ADP
ejpam-6847	127	5	as	as	ADP
ejpam-6847	127	6	νs	νs	NOUN
ejpam-6847	127	7	-	-	PUNCT
ejpam-6847	127	8	subadmissible	subadmissible	ADJ
ejpam-6847	127	9	mapping	mapping	NOUN
ejpam-6847	127	10	,	,	PUNCT
ejpam-6847	127	11	if	if	SCONJ
ejpam-6847	127	12	for	for	ADP
ejpam-6847	127	13	all	all	DET
ejpam-6847	127	14	x̂	x̂	NUM
ejpam-6847	127	15	,	,	PUNCT
ejpam-6847	127	16	ŷ	ŷ	NUM
ejpam-6847	127	17	,	,	PUNCT
ejpam-6847	127	18	ẑ	ẑ	PROPN
ejpam-6847	127	19	∈	∈	PROPN
ejpam-6847	127	20	x	x	X
ejpam-6847	127	21	,	,	PUNCT
ejpam-6847	127	22	we	we	PRON
ejpam-6847	127	23	have	have	VERB
ejpam-6847	127	24	νs(x̂	νs(x̂	NOUN
ejpam-6847	127	25	,	,	PUNCT
ejpam-6847	127	26	ŷ	ŷ	NUM
ejpam-6847	127	27	,	,	PUNCT
ejpam-6847	127	28	ẑ	ẑ	NUM
ejpam-6847	127	29	)	)	PUNCT
ejpam-6847	127	30	≤	≤	NOUN
ejpam-6847	128	1	1	1	NUM
ejpam-6847	128	2	=	=	NOUN
ejpam-6847	128	3	⇒	⇒	NOUN
ejpam-6847	128	4	νs(t	νs(t	PUNCT
ejpam-6847	128	5	x̂	x̂	NUM
ejpam-6847	128	6	,	,	PUNCT
ejpam-6847	128	7	t	t	PROPN
ejpam-6847	128	8	ŷ	ŷ	NUM
ejpam-6847	128	9	,	,	PUNCT
ejpam-6847	128	10	t	t	PROPN
ejpam-6847	128	11	ẑ	ẑ	NUM
ejpam-6847	128	12	)	)	PUNCT
ejpam-6847	128	13	≤	≤	NUM
ejpam-6847	128	14	1	1	NUM
ejpam-6847	128	15	.	.	PUNCT
ejpam-6847	129	1	(	(	PUNCT
ejpam-6847	129	2	2	2	X
ejpam-6847	129	3	)	)	PUNCT
ejpam-6847	129	4	we	we	PRON
ejpam-6847	129	5	will	will	AUX
ejpam-6847	129	6	now	now	ADV
ejpam-6847	129	7	provide	provide	VERB
ejpam-6847	129	8	definitions	definition	NOUN
ejpam-6847	129	9	for	for	ADP
ejpam-6847	129	10	the	the	DET
ejpam-6847	129	11	functions	function	NOUN
ejpam-6847	129	12	associated	associate	VERB
ejpam-6847	129	13	with	with	ADP
ejpam-6847	129	14	a	a	DET
ejpam-6847	129	15	subclass	subclass	NOUN
ejpam-6847	129	16	of	of	ADP
ejpam-6847	129	17	types	type	NOUN
ejpam-6847	129	18	i	i	PRON
ejpam-6847	129	19	and	and	CCONJ
ejpam-6847	129	20	ii	ii	PROPN
ejpam-6847	129	21	,	,	PUNCT
ejpam-6847	129	22	as	as	ADV
ejpam-6847	129	23	well	well	ADV
ejpam-6847	129	24	as	as	ADP
ejpam-6847	129	25	for	for	ADP
ejpam-6847	129	26	the	the	DET
ejpam-6847	129	27	pairs	pair	NOUN
ejpam-6847	129	28	belonging	belong	VERB
ejpam-6847	129	29	to	to	ADP
ejpam-6847	129	30	the	the	DET
ejpam-6847	129	31	upper	upper	ADJ
ejpam-6847	129	32	class	class	NOUN
ejpam-6847	129	33	of	of	ADP
ejpam-6847	129	34	types	type	NOUN
ejpam-6847	129	35	i	i	PRON
ejpam-6847	129	36	and	and	CCONJ
ejpam-6847	129	37	ii	ii	PROPN
ejpam-6847	129	38	.	.	PUNCT
ejpam-6847	130	1	for	for	ADP
ejpam-6847	130	2	more	more	ADJ
ejpam-6847	130	3	information	information	NOUN
ejpam-6847	130	4	,	,	PUNCT
ejpam-6847	130	5	see	see	VERB
ejpam-6847	130	6	[	[	X
ejpam-6847	130	7	30	30	NUM
ejpam-6847	130	8	,	,	PUNCT
ejpam-6847	130	9	39	39	NUM
ejpam-6847	130	10	]	]	PUNCT
ejpam-6847	130	11	.	.	PUNCT
ejpam-6847	131	1	definition	definition	NOUN
ejpam-6847	131	2	10	10	NUM
ejpam-6847	131	3	.	.	PUNCT
ejpam-6847	132	1	(	(	PUNCT
ejpam-6847	132	2	[	[	X
ejpam-6847	132	3	30	30	NUM
ejpam-6847	132	4	,	,	PUNCT
ejpam-6847	132	5	39	39	NUM
ejpam-6847	132	6	]	]	PUNCT
ejpam-6847	132	7	)	)	PUNCT
ejpam-6847	132	8	we	we	PRON
ejpam-6847	132	9	say	say	VERB
ejpam-6847	132	10	that	that	SCONJ
ejpam-6847	132	11	the	the	DET
ejpam-6847	132	12	function	function	NOUN
ejpam-6847	132	13	h	h	NOUN
ejpam-6847	132	14	:	:	PUNCT
ejpam-6847	132	15	r+	r+	NOUN
ejpam-6847	132	16	×	×	NOUN
ejpam-6847	132	17	r+	r+	NOUN
ejpam-6847	132	18	→	→	PUNCT
ejpam-6847	132	19	r	r	NOUN
ejpam-6847	132	20	is	be	AUX
ejpam-6847	132	21	of	of	ADP
ejpam-6847	132	22	subclass	subclass	NOUN
ejpam-6847	132	23	of	of	ADP
ejpam-6847	132	24	type	type	NOUN
ejpam-6847	132	25	i	i	PRON
ejpam-6847	132	26	,	,	PUNCT
ejpam-6847	132	27	if	if	SCONJ
ejpam-6847	132	28	x	x	X
ejpam-6847	132	29	≥	≥	NOUN
ejpam-6847	132	30	1	1	NUM
ejpam-6847	132	31	=	=	NOUN
ejpam-6847	132	32	⇒	⇒	NOUN
ejpam-6847	132	33	h(1	h(1	PROPN
ejpam-6847	132	34	,	,	PUNCT
ejpam-6847	132	35	y	y	PROPN
ejpam-6847	132	36	)	)	PUNCT
ejpam-6847	132	37	≤	≤	NOUN
ejpam-6847	132	38	h(x	h(x	PROPN
ejpam-6847	132	39	,	,	PUNCT
ejpam-6847	132	40	y	y	PROPN
ejpam-6847	132	41	)	)	PUNCT
ejpam-6847	132	42	,	,	PUNCT
ejpam-6847	132	43	for	for	SCONJ
ejpam-6847	132	44	all	all	DET
ejpam-6847	132	45	x	x	NOUN
ejpam-6847	132	46	,	,	PUNCT
ejpam-6847	132	47	y	y	PROPN
ejpam-6847	132	48	∈	∈	PROPN
ejpam-6847	132	49	r+	r+	X
ejpam-6847	132	50	.	.	PUNCT
ejpam-6847	133	1	next	next	ADV
ejpam-6847	133	2	,	,	PUNCT
ejpam-6847	133	3	we	we	PRON
ejpam-6847	133	4	present	present	VERB
ejpam-6847	133	5	examples	example	NOUN
ejpam-6847	133	6	of	of	ADP
ejpam-6847	133	7	functions	function	NOUN
ejpam-6847	133	8	belonging	belong	VERB
ejpam-6847	133	9	to	to	ADP
ejpam-6847	133	10	the	the	DET
ejpam-6847	133	11	subclass	subclass	NOUN
ejpam-6847	133	12	of	of	ADP
ejpam-6847	133	13	type	type	NOUN
ejpam-6847	133	14	i	i	PRON
ejpam-6847	133	15	as	as	SCONJ
ejpam-6847	133	16	discussed	discuss	VERB
ejpam-6847	133	17	in	in	ADP
ejpam-6847	133	18	[	[	X
ejpam-6847	133	19	30	30	NUM
ejpam-6847	133	20	,	,	PUNCT
ejpam-6847	133	21	39	39	NUM
ejpam-6847	133	22	]	]	PUNCT
ejpam-6847	133	23	.	.	PUNCT
ejpam-6847	134	1	example	example	NOUN
ejpam-6847	135	1	3	3	NUM
ejpam-6847	135	2	.	.	PUNCT
ejpam-6847	136	1	[	[	X
ejpam-6847	136	2	30	30	NUM
ejpam-6847	136	3	,	,	PUNCT
ejpam-6847	136	4	39	39	NUM
ejpam-6847	136	5	]	]	PUNCT
ejpam-6847	136	6	(	(	PUNCT
ejpam-6847	136	7	1	1	X
ejpam-6847	136	8	)	)	PUNCT
ejpam-6847	136	9	let	let	VERB
ejpam-6847	136	10	h(x	h(x	PROPN
ejpam-6847	136	11	,	,	PUNCT
ejpam-6847	136	12	y	y	PROPN
ejpam-6847	136	13	)	)	PUNCT
ejpam-6847	136	14	=	=	SYM
ejpam-6847	137	1	(	(	PUNCT
ejpam-6847	137	2	y	y	PROPN
ejpam-6847	137	3	+	+	CCONJ
ejpam-6847	137	4	l)x	l)x	ADJ
ejpam-6847	137	5	,	,	PUNCT
ejpam-6847	137	6	with	with	ADP
ejpam-6847	137	7	l	l	PROPN
ejpam-6847	137	8	>	>	X
ejpam-6847	137	9	1	1	X
ejpam-6847	137	10	.	.	PUNCT
ejpam-6847	138	1	(	(	PUNCT
ejpam-6847	138	2	2	2	X
ejpam-6847	138	3	)	)	PUNCT
ejpam-6847	138	4	let	let	VERB
ejpam-6847	138	5	h(x	h(x	PROPN
ejpam-6847	138	6	,	,	PUNCT
ejpam-6847	138	7	y	y	PROPN
ejpam-6847	138	8	)	)	PUNCT
ejpam-6847	138	9	=	=	SYM
ejpam-6847	139	1	(	(	PUNCT
ejpam-6847	139	2	x+	x+	X
ejpam-6847	139	3	l)y	l)y	NOUN
ejpam-6847	139	4	,	,	PUNCT
ejpam-6847	139	5	with	with	ADP
ejpam-6847	139	6	l	l	PROPN
ejpam-6847	139	7	>	>	X
ejpam-6847	139	8	0	0	X
ejpam-6847	139	9	.	.	PUNCT
ejpam-6847	140	1	(	(	PUNCT
ejpam-6847	140	2	3	3	X
ejpam-6847	140	3	)	)	PUNCT
ejpam-6847	140	4	let	let	VERB
ejpam-6847	140	5	h(x	h(x	PROPN
ejpam-6847	140	6	,	,	PUNCT
ejpam-6847	140	7	y	y	PROPN
ejpam-6847	140	8	)	)	PUNCT
ejpam-6847	140	9	=	=	SYM
ejpam-6847	140	10	xnyk	xnyk	PROPN
ejpam-6847	140	11	,	,	PUNCT
ejpam-6847	140	12	such	such	ADJ
ejpam-6847	140	13	that	that	SCONJ
ejpam-6847	140	14	k	k	PROPN
ejpam-6847	140	15	>	>	X
ejpam-6847	140	16	0	0	PROPN
ejpam-6847	140	17	,	,	PUNCT
ejpam-6847	140	18	n	n	PRON
ejpam-6847	140	19	∈	∈	PROPN
ejpam-6847	140	20	n∪{0	n∪{0	NOUN
ejpam-6847	140	21	}	}	PUNCT
ejpam-6847	140	22	.	.	PUNCT
ejpam-6847	141	1	(	(	PUNCT
ejpam-6847	141	2	4	4	X
ejpam-6847	141	3	)	)	PUNCT
ejpam-6847	141	4	let	let	VERB
ejpam-6847	141	5	h(x	h(x	PROPN
ejpam-6847	141	6	,	,	PUNCT
ejpam-6847	141	7	y	y	PROPN
ejpam-6847	141	8	)	)	PUNCT
ejpam-6847	141	9	=	=	SYM
ejpam-6847	142	1	xn+xn−1+	xn+xn−1+	PROPN
ejpam-6847	142	2	...	...	PUNCT
ejpam-6847	142	3	+x+1	+x+1	PROPN
ejpam-6847	142	4	n+1	n+1	PROPN
ejpam-6847	142	5	y.	y.	NOUN
ejpam-6847	142	6	(	(	PUNCT
ejpam-6847	142	7	5	5	X
ejpam-6847	142	8	)	)	PUNCT
ejpam-6847	142	9	let	let	VERB
ejpam-6847	142	10	h(x	h(x	PROPN
ejpam-6847	142	11	,	,	PUNCT
ejpam-6847	142	12	y	y	PROPN
ejpam-6847	142	13	)	)	PUNCT
ejpam-6847	142	14	=	=	PRON
ejpam-6847	143	1	(	(	PUNCT
ejpam-6847	143	2	x	x	SYM
ejpam-6847	143	3	n+xn−1+	n+xn−1+	ADV
ejpam-6847	143	4	...	...	PUNCT
ejpam-6847	143	5	+x+1	+x+1	PROPN
ejpam-6847	143	6	n+1	n+1	X
ejpam-6847	143	7	+	+	NUM
ejpam-6847	143	8	l)y	l)y	NOUN
ejpam-6847	143	9	,	,	PUNCT
ejpam-6847	143	10	and	and	CCONJ
ejpam-6847	143	11	l	l	NOUN
ejpam-6847	143	12	>	>	X
ejpam-6847	143	13	1	1	X
ejpam-6847	143	14	.	.	PUNCT
ejpam-6847	143	15	(	(	PUNCT
ejpam-6847	143	16	6	6	X
ejpam-6847	143	17	)	)	PUNCT
ejpam-6847	143	18	let	let	VERB
ejpam-6847	143	19	h(x	h(x	PROPN
ejpam-6847	143	20	,	,	PUNCT
ejpam-6847	143	21	y	y	PROPN
ejpam-6847	143	22	)	)	PUNCT
ejpam-6847	143	23	=	=	SYM
ejpam-6847	144	1	mx+n	mx+n	NOUN
ejpam-6847	144	2	m+n	m+n	NOUN
ejpam-6847	144	3	y	y	NOUN
ejpam-6847	144	4	,	,	PUNCT
ejpam-6847	144	5	such	such	ADJ
ejpam-6847	144	6	that	that	SCONJ
ejpam-6847	144	7	m	m	PROPN
ejpam-6847	144	8	,	,	PUNCT
ejpam-6847	144	9	n	n	PROPN
ejpam-6847	144	10	∈	∈	PROPN
ejpam-6847	144	11	n	n	X
ejpam-6847	144	12	.	.	PUNCT
ejpam-6847	145	1	remark	remark	PROPN
ejpam-6847	145	2	2	2	NUM
ejpam-6847	145	3	.	.	PUNCT
ejpam-6847	145	4	from	from	ADP
ejpam-6847	145	5	definition	definition	NOUN
ejpam-6847	145	6	10	10	NUM
ejpam-6847	145	7	,	,	PUNCT
ejpam-6847	145	8	we	we	PRON
ejpam-6847	145	9	observe	observe	VERB
ejpam-6847	145	10	that	that	SCONJ
ejpam-6847	145	11	y	y	PROPN
ejpam-6847	145	12	≤	≤	PROPN
ejpam-6847	145	13	h(1	h(1	PROPN
ejpam-6847	145	14	,	,	PUNCT
ejpam-6847	145	15	y	y	PROPN
ejpam-6847	145	16	)	)	PUNCT
ejpam-6847	145	17	.	.	PUNCT
ejpam-6847	146	1	definition	definition	NOUN
ejpam-6847	146	2	11	11	NUM
ejpam-6847	146	3	.	.	PUNCT
ejpam-6847	147	1	[	[	X
ejpam-6847	147	2	30	30	NUM
ejpam-6847	147	3	,	,	PUNCT
ejpam-6847	147	4	39	39	NUM
ejpam-6847	147	5	]	]	PUNCT
ejpam-6847	147	6	a	a	DET
ejpam-6847	147	7	function	function	NOUN
ejpam-6847	147	8	h	h	NOUN
ejpam-6847	147	9	:	:	PUNCT
ejpam-6847	147	10	r+	r+	NOUN
ejpam-6847	147	11	×	×	NOUN
ejpam-6847	147	12	r+	r+	NOUN
ejpam-6847	147	13	×	×	NOUN
ejpam-6847	147	14	r+	r+	NOUN
ejpam-6847	147	15	→	→	PUNCT
ejpam-6847	147	16	r	r	NOUN
ejpam-6847	147	17	is	be	AUX
ejpam-6847	147	18	said	say	VERB
ejpam-6847	147	19	to	to	PART
ejpam-6847	147	20	be	be	AUX
ejpam-6847	147	21	of	of	ADP
ejpam-6847	147	22	subclass	subclass	NOUN
ejpam-6847	147	23	of	of	ADP
ejpam-6847	147	24	type	type	NOUN
ejpam-6847	147	25	ii	ii	PROPN
ejpam-6847	147	26	,	,	PUNCT
ejpam-6847	147	27	if	if	SCONJ
ejpam-6847	147	28	x	x	NOUN
ejpam-6847	147	29	,	,	PUNCT
ejpam-6847	147	30	y	y	PROPN
ejpam-6847	147	31	≥	≥	NUM
ejpam-6847	147	32	1	1	NUM
ejpam-6847	147	33	=	=	NOUN
ejpam-6847	147	34	⇒	⇒	NOUN
ejpam-6847	147	35	h(1	h(1	PROPN
ejpam-6847	147	36	,	,	PUNCT
ejpam-6847	147	37	1	1	NUM
ejpam-6847	147	38	,	,	PUNCT
ejpam-6847	147	39	z	z	NOUN
ejpam-6847	147	40	)	)	PUNCT
ejpam-6847	147	41	≤	≤	NOUN
ejpam-6847	148	1	h(x	h(x	PROPN
ejpam-6847	148	2	,	,	PUNCT
ejpam-6847	148	3	y	y	PROPN
ejpam-6847	148	4	,	,	PUNCT
ejpam-6847	148	5	z	z	NOUN
ejpam-6847	148	6	)	)	PUNCT
ejpam-6847	148	7	,	,	PUNCT
ejpam-6847	148	8	for	for	ADP
ejpam-6847	148	9	all	all	DET
ejpam-6847	148	10	x	x	NOUN
ejpam-6847	148	11	,	,	PUNCT
ejpam-6847	148	12	y	y	PROPN
ejpam-6847	148	13	,	,	PUNCT
ejpam-6847	148	14	z	z	PROPN
ejpam-6847	148	15	∈	∈	PROPN
ejpam-6847	148	16	r+	r+	X
ejpam-6847	148	17	.	.	PUNCT
ejpam-6847	148	18	example	example	NOUN
ejpam-6847	149	1	4	4	NUM
ejpam-6847	149	2	.	.	PUNCT
ejpam-6847	150	1	[	[	X
ejpam-6847	150	2	30	30	NUM
ejpam-6847	150	3	,	,	PUNCT
ejpam-6847	150	4	39	39	NUM
ejpam-6847	150	5	]	]	PUNCT
ejpam-6847	150	6	the	the	DET
ejpam-6847	150	7	following	follow	VERB
ejpam-6847	150	8	functions	function	NOUN
ejpam-6847	150	9	are	be	AUX
ejpam-6847	150	10	examples	example	NOUN
ejpam-6847	150	11	of	of	ADP
ejpam-6847	150	12	a	a	DET
ejpam-6847	150	13	subclass	subclass	NOUN
ejpam-6847	150	14	of	of	ADP
ejpam-6847	150	15	type	type	NOUN
ejpam-6847	150	16	ii	ii	PROPN
ejpam-6847	150	17	.	.	PUNCT
ejpam-6847	151	1	(	(	PUNCT
ejpam-6847	151	2	1	1	X
ejpam-6847	151	3	)	)	PUNCT
ejpam-6847	151	4	h(x	h(x	PROPN
ejpam-6847	151	5	,	,	PUNCT
ejpam-6847	151	6	y	y	PROPN
ejpam-6847	151	7	,	,	PUNCT
ejpam-6847	151	8	z	z	NOUN
ejpam-6847	151	9	)	)	PUNCT
ejpam-6847	151	10	=	=	PUNCT
ejpam-6847	151	11	(	(	PUNCT
ejpam-6847	151	12	z	z	NOUN
ejpam-6847	151	13	+	+	CCONJ
ejpam-6847	151	14	l)xy	l)xy	PROPN
ejpam-6847	151	15	,	,	PUNCT
ejpam-6847	151	16	and	and	CCONJ
ejpam-6847	151	17	l	l	NOUN
ejpam-6847	151	18	>	>	X
ejpam-6847	151	19	1	1	X
ejpam-6847	151	20	.	.	PUNCT
ejpam-6847	151	21	(	(	PUNCT
ejpam-6847	151	22	2	2	X
ejpam-6847	151	23	)	)	PUNCT
ejpam-6847	151	24	h(x	h(x	PROPN
ejpam-6847	151	25	,	,	PUNCT
ejpam-6847	151	26	y	y	PROPN
ejpam-6847	151	27	,	,	PUNCT
ejpam-6847	151	28	z	z	NOUN
ejpam-6847	151	29	)	)	PUNCT
ejpam-6847	151	30	=	=	SYM
ejpam-6847	151	31	(	(	PUNCT
ejpam-6847	151	32	xy	xy	NOUN
ejpam-6847	151	33	+	+	NOUN
ejpam-6847	151	34	l)z	l)z	NOUN
ejpam-6847	151	35	,	,	PUNCT
ejpam-6847	151	36	with	with	ADP
ejpam-6847	151	37	l	l	PROPN
ejpam-6847	151	38	>	>	X
ejpam-6847	151	39	0	0	X
ejpam-6847	151	40	.	.	PUNCT
ejpam-6847	152	1	(	(	PUNCT
ejpam-6847	152	2	3	3	X
ejpam-6847	152	3	)	)	PUNCT
ejpam-6847	152	4	h(x	h(x	PROPN
ejpam-6847	152	5	,	,	PUNCT
ejpam-6847	152	6	y	y	PROPN
ejpam-6847	152	7	,	,	PUNCT
ejpam-6847	152	8	z	z	NOUN
ejpam-6847	152	9	)	)	PUNCT
ejpam-6847	152	10	=	=	SYM
ejpam-6847	152	11	xmynzp	xmynzp	PROPN
ejpam-6847	152	12	,	,	PUNCT
ejpam-6847	152	13	such	such	ADJ
ejpam-6847	152	14	that	that	SCONJ
ejpam-6847	152	15	m	m	PROPN
ejpam-6847	152	16	,	,	PUNCT
ejpam-6847	152	17	n	n	PROPN
ejpam-6847	152	18	∈	∈	PROPN
ejpam-6847	152	19	n∪{0	n∪{0	NOUN
ejpam-6847	152	20	}	}	PUNCT
ejpam-6847	152	21	,	,	PUNCT
ejpam-6847	152	22	p	p	X
ejpam-6847	152	23	>	>	X
ejpam-6847	152	24	0	0	NUM
ejpam-6847	152	25	.	.	PUNCT
ejpam-6847	153	1	(	(	PUNCT
ejpam-6847	153	2	4	4	X
ejpam-6847	153	3	)	)	PUNCT
ejpam-6847	153	4	h(x	h(x	PROPN
ejpam-6847	153	5	,	,	PUNCT
ejpam-6847	153	6	y	y	PROPN
ejpam-6847	153	7	,	,	PUNCT
ejpam-6847	153	8	z	z	NOUN
ejpam-6847	153	9	)	)	PUNCT
ejpam-6847	153	10	=	=	SYM
ejpam-6847	154	1	(	(	PUNCT
ejpam-6847	154	2	n∑	n∑	NOUN
ejpam-6847	154	3	i=0	i=0	PROPN
ejpam-6847	154	4	xn−iyi	xn−iyi	NOUN
ejpam-6847	154	5	n+1	n+1	X
ejpam-6847	154	6	)	)	PUNCT
ejpam-6847	154	7	z.	z.	PROPN
ejpam-6847	154	8	(	(	PUNCT
ejpam-6847	154	9	5	5	X
ejpam-6847	154	10	)	)	PUNCT
ejpam-6847	154	11	h(x	h(x	PROPN
ejpam-6847	154	12	,	,	PUNCT
ejpam-6847	154	13	y	y	PROPN
ejpam-6847	154	14	,	,	PUNCT
ejpam-6847	154	15	z	z	NOUN
ejpam-6847	154	16	)	)	PUNCT
ejpam-6847	154	17	=	=	SYM
ejpam-6847	155	1	(	(	PUNCT
ejpam-6847	155	2	n∑	n∑	NOUN
ejpam-6847	155	3	i=0	i=0	PROPN
ejpam-6847	155	4	xn−iyi	xn−iyi	X
ejpam-6847	155	5	n+1	n+1	PROPN
ejpam-6847	156	1	+	+	PUNCT
ejpam-6847	156	2	l)z	l)z	NOUN
ejpam-6847	156	3	,	,	PUNCT
ejpam-6847	156	4	and	and	CCONJ
ejpam-6847	156	5	l	l	NOUN
ejpam-6847	156	6	>	>	X
ejpam-6847	156	7	1	1	X
ejpam-6847	156	8	.	.	PUNCT
ejpam-6847	156	9	(	(	PUNCT
ejpam-6847	156	10	6	6	NUM
ejpam-6847	156	11	)	)	PUNCT
ejpam-6847	156	12	h(x	h(x	PROPN
ejpam-6847	156	13	,	,	PUNCT
ejpam-6847	156	14	y	y	PROPN
ejpam-6847	156	15	,	,	PUNCT
ejpam-6847	156	16	z	z	NOUN
ejpam-6847	156	17	)	)	PUNCT
ejpam-6847	156	18	=	=	SYM
ejpam-6847	156	19	xm+xnyp+yq	xm+xnyp+yq	PROPN
ejpam-6847	156	20	3	3	NUM
ejpam-6847	156	21	zk	zk	PROPN
ejpam-6847	156	22	,	,	PUNCT
ejpam-6847	156	23	with	with	ADP
ejpam-6847	156	24	the	the	DET
ejpam-6847	156	25	assumption	assumption	NOUN
ejpam-6847	156	26	m	m	PROPN
ejpam-6847	156	27	,	,	PUNCT
ejpam-6847	156	28	n	n	CCONJ
ejpam-6847	156	29	,	,	PUNCT
ejpam-6847	156	30	p	p	X
ejpam-6847	156	31	,	,	PUNCT
ejpam-6847	156	32	q	q	X
ejpam-6847	156	33	,	,	PUNCT
ejpam-6847	156	34	k	k	PROPN
ejpam-6847	156	35	∈	∈	PROPN
ejpam-6847	156	36	n.	n.	NOUN
ejpam-6847	156	37	remark	remark	NOUN
ejpam-6847	156	38	3	3	NUM
ejpam-6847	156	39	.	.	PUNCT
ejpam-6847	156	40	by	by	ADP
ejpam-6847	156	41	definition	definition	NOUN
ejpam-6847	156	42	11	11	NUM
ejpam-6847	156	43	,	,	PUNCT
ejpam-6847	156	44	we	we	PRON
ejpam-6847	156	45	observe	observe	VERB
ejpam-6847	156	46	that	that	SCONJ
ejpam-6847	156	47	z	z	NOUN
ejpam-6847	156	48	≤	≤	PUNCT
ejpam-6847	157	1	h(1	h(1	PROPN
ejpam-6847	157	2	,	,	PUNCT
ejpam-6847	157	3	1	1	NUM
ejpam-6847	157	4	,	,	PUNCT
ejpam-6847	157	5	z	z	NOUN
ejpam-6847	157	6	)	)	PUNCT
ejpam-6847	157	7	.	.	PUNCT
ejpam-6847	158	1	f.	f.	PROPN
ejpam-6847	158	2	m.	m.	PROPN
ejpam-6847	158	3	azmi	azmi	PROPN
ejpam-6847	158	4	,	,	PUNCT
ejpam-6847	158	5	a.	a.	PROPN
ejpam-6847	158	6	h.	h.	PROPN
ejpam-6847	158	7	ansari	ansari	PROPN
ejpam-6847	158	8	,	,	PUNCT
ejpam-6847	158	9	s.	s.	PROPN
ejpam-6847	158	10	h.	h.	PROPN
ejpam-6847	158	11	j.	j.	PROPN
ejpam-6847	158	12	petroudi	petroudi	PROPN
ejpam-6847	158	13	/	/	SYM
ejpam-6847	158	14	eur	eur	PROPN
ejpam-6847	158	15	.	.	PUNCT
ejpam-6847	159	1	j.	j.	PROPN
ejpam-6847	159	2	pure	pure	PROPN
ejpam-6847	159	3	appl	appl	PROPN
ejpam-6847	159	4	.	.	PROPN
ejpam-6847	159	5	math	math	PROPN
ejpam-6847	159	6	,	,	PUNCT
ejpam-6847	159	7	18	18	NUM
ejpam-6847	159	8	(	(	PUNCT
ejpam-6847	159	9	4	4	NUM
ejpam-6847	159	10	)	)	PUNCT
ejpam-6847	159	11	(	(	PUNCT
ejpam-6847	159	12	2025	2025	NUM
ejpam-6847	159	13	)	)	PUNCT
ejpam-6847	159	14	,	,	PUNCT
ejpam-6847	159	15	6847	6847	NUM
ejpam-6847	159	16	7	7	NUM
ejpam-6847	159	17	of	of	ADP
ejpam-6847	159	18	26	26	NUM
ejpam-6847	159	19	definition	definition	NOUN
ejpam-6847	159	20	12	12	NUM
ejpam-6847	159	21	.	.	PUNCT
ejpam-6847	160	1	(	(	PUNCT
ejpam-6847	160	2	[	[	X
ejpam-6847	160	3	30	30	NUM
ejpam-6847	160	4	,	,	PUNCT
ejpam-6847	160	5	39	39	NUM
ejpam-6847	160	6	]	]	PUNCT
ejpam-6847	160	7	)	)	PUNCT
ejpam-6847	160	8	let	let	VERB
ejpam-6847	160	9	h	h	NOUN
ejpam-6847	160	10	,	,	PUNCT
ejpam-6847	160	11	q	q	NOUN
ejpam-6847	160	12	:	:	PUNCT
ejpam-6847	160	13	r+×r+	r+×r+	NOUN
ejpam-6847	160	14	→	→	PUNCT
ejpam-6847	160	15	r	r	NOUN
ejpam-6847	160	16	be	be	NOUN
ejpam-6847	160	17	functions	function	NOUN
ejpam-6847	160	18	.	.	PUNCT
ejpam-6847	161	1	we	we	PRON
ejpam-6847	161	2	say	say	VERB
ejpam-6847	161	3	the	the	DET
ejpam-6847	161	4	pair	pair	NOUN
ejpam-6847	161	5	(	(	PUNCT
ejpam-6847	161	6	q	q	NOUN
ejpam-6847	161	7	,	,	PUNCT
ejpam-6847	161	8	h	h	NOUN
ejpam-6847	161	9	)	)	PUNCT
ejpam-6847	161	10	is	be	AUX
ejpam-6847	161	11	an	an	DET
ejpam-6847	161	12	upper	upper	ADJ
ejpam-6847	161	13	class	class	NOUN
ejpam-6847	161	14	of	of	ADP
ejpam-6847	161	15	type	type	NOUN
ejpam-6847	161	16	i	i	PRON
ejpam-6847	161	17	,	,	PUNCT
ejpam-6847	161	18	if	if	SCONJ
ejpam-6847	161	19	h	h	NOUN
ejpam-6847	161	20	is	be	AUX
ejpam-6847	161	21	a	a	DET
ejpam-6847	161	22	subclass	subclass	NOUN
ejpam-6847	161	23	of	of	ADP
ejpam-6847	161	24	type	type	NOUN
ejpam-6847	161	25	i	i	PROPN
ejpam-6847	161	26	,	,	PUNCT
ejpam-6847	161	27	and	and	CCONJ
ejpam-6847	161	28	satisfies	satisfy	VERB
ejpam-6847	161	29	the	the	DET
ejpam-6847	161	30	following	follow	VERB
ejpam-6847	161	31	conditions	condition	NOUN
ejpam-6847	161	32	:	:	PUNCT
ejpam-6847	161	33	(	(	PUNCT
ejpam-6847	161	34	i	i	NOUN
ejpam-6847	161	35	)	)	PUNCT
ejpam-6847	161	36	0	0	NUM
ejpam-6847	162	1	≤	≤	NUM
ejpam-6847	162	2	s	s	PART
ejpam-6847	162	3	≤	≤	NUM
ejpam-6847	162	4	1	1	NUM
ejpam-6847	162	5	=	=	NOUN
ejpam-6847	162	6	⇒	⇒	NOUN
ejpam-6847	162	7	q(s	q(s	PROPN
ejpam-6847	162	8	,	,	PUNCT
ejpam-6847	162	9	t	t	PROPN
ejpam-6847	162	10	)	)	PUNCT
ejpam-6847	162	11	≤	≤	NOUN
ejpam-6847	162	12	q(1	q(1	PROPN
ejpam-6847	162	13	,	,	PUNCT
ejpam-6847	162	14	t	t	PROPN
ejpam-6847	162	15	)	)	PUNCT
ejpam-6847	162	16	,	,	PUNCT
ejpam-6847	162	17	(	(	PUNCT
ejpam-6847	162	18	ii	ii	NOUN
ejpam-6847	162	19	)	)	PUNCT
ejpam-6847	162	20	h(1	h(1	PROPN
ejpam-6847	162	21	,	,	PUNCT
ejpam-6847	162	22	y	y	NOUN
ejpam-6847	162	23	)	)	PUNCT
ejpam-6847	162	24	≤	≤	NOUN
ejpam-6847	162	25	q(s	q(s	PROPN
ejpam-6847	162	26	,	,	PUNCT
ejpam-6847	162	27	t	t	NOUN
ejpam-6847	162	28	)	)	PUNCT
ejpam-6847	162	29	=	=	AUX
ejpam-6847	162	30	⇒	⇒	X
ejpam-6847	162	31	y	y	PROPN
ejpam-6847	162	32	≤	≤	PROPN
ejpam-6847	162	33	st	st	PROPN
ejpam-6847	162	34	,	,	PUNCT
ejpam-6847	162	35	for	for	ADP
ejpam-6847	162	36	all	all	DET
ejpam-6847	162	37	x	x	NOUN
ejpam-6847	162	38	,	,	PUNCT
ejpam-6847	162	39	y	y	PROPN
ejpam-6847	162	40	,	,	PUNCT
ejpam-6847	162	41	s	s	PROPN
ejpam-6847	162	42	,	,	PUNCT
ejpam-6847	162	43	t	t	PROPN
ejpam-6847	162	44	∈	∈	PROPN
ejpam-6847	162	45	r+	r+	NOUN
ejpam-6847	162	46	.	.	PUNCT
ejpam-6847	163	1	when	when	SCONJ
ejpam-6847	163	2	we	we	PRON
ejpam-6847	163	3	set	set	VERB
ejpam-6847	163	4	s	s	X
ejpam-6847	163	5	=	=	NOUN
ejpam-6847	163	6	1	1	NUM
ejpam-6847	163	7	in	in	ADP
ejpam-6847	163	8	(	(	PUNCT
ejpam-6847	163	9	2	2	NUM
ejpam-6847	163	10	)	)	PUNCT
ejpam-6847	163	11	,	,	PUNCT
ejpam-6847	163	12	the	the	DET
ejpam-6847	163	13	pair	pair	NOUN
ejpam-6847	163	14	(	(	PUNCT
ejpam-6847	163	15	q	q	NOUN
ejpam-6847	163	16	,	,	PUNCT
ejpam-6847	163	17	h	h	NOUN
ejpam-6847	163	18	)	)	PUNCT
ejpam-6847	163	19	is	be	AUX
ejpam-6847	163	20	referred	refer	VERB
ejpam-6847	163	21	to	to	ADP
ejpam-6847	163	22	as	as	ADP
ejpam-6847	163	23	a	a	DET
ejpam-6847	163	24	special	special	ADJ
ejpam-6847	163	25	upper	upper	ADJ
ejpam-6847	163	26	class	class	NOUN
ejpam-6847	163	27	of	of	ADP
ejpam-6847	163	28	type	type	NOUN
ejpam-6847	163	29	i.	i.	PROPN
ejpam-6847	163	30	example	example	NOUN
ejpam-6847	163	31	5	5	NUM
ejpam-6847	163	32	.	.	PUNCT
ejpam-6847	164	1	[	[	X
ejpam-6847	164	2	30	30	NUM
ejpam-6847	164	3	,	,	PUNCT
ejpam-6847	164	4	39	39	NUM
ejpam-6847	164	5	]	]	PUNCT
ejpam-6847	164	6	examples	example	NOUN
ejpam-6847	164	7	of	of	ADP
ejpam-6847	164	8	functions	function	NOUN
ejpam-6847	164	9	belonging	belong	VERB
ejpam-6847	164	10	to	to	ADP
ejpam-6847	164	11	the	the	DET
ejpam-6847	164	12	upper	upper	ADJ
ejpam-6847	164	13	class	class	NOUN
ejpam-6847	164	14	of	of	ADP
ejpam-6847	164	15	type	type	NOUN
ejpam-6847	164	16	i	i	PRON
ejpam-6847	164	17	are	be	AUX
ejpam-6847	164	18	given	give	VERB
ejpam-6847	164	19	below	below	ADV
ejpam-6847	164	20	.	.	PUNCT
ejpam-6847	165	1	(	(	PUNCT
ejpam-6847	165	2	1)let	1)let	NUM
ejpam-6847	165	3	h(x	h(x	PROPN
ejpam-6847	165	4	,	,	PUNCT
ejpam-6847	165	5	y	y	PROPN
ejpam-6847	165	6	)	)	PUNCT
ejpam-6847	165	7	=	=	SYM
ejpam-6847	165	8	(	(	PUNCT
ejpam-6847	165	9	y	y	PROPN
ejpam-6847	165	10	+	+	CCONJ
ejpam-6847	165	11	l)x	l)x	ADJ
ejpam-6847	165	12	,	,	PUNCT
ejpam-6847	165	13	with	with	ADP
ejpam-6847	165	14	l	l	NOUN
ejpam-6847	165	15	>	>	X
ejpam-6847	165	16	1	1	NUM
ejpam-6847	165	17	and	and	CCONJ
ejpam-6847	165	18	,	,	PUNCT
ejpam-6847	165	19	q(s	q(s	PROPN
ejpam-6847	165	20	,	,	PUNCT
ejpam-6847	165	21	t	t	PROPN
ejpam-6847	165	22	)	)	PUNCT
ejpam-6847	165	23	=	=	SYM
ejpam-6847	165	24	st+	st+	PROPN
ejpam-6847	165	25	l.	l.	PROPN
ejpam-6847	165	26	(	(	PUNCT
ejpam-6847	165	27	2	2	X
ejpam-6847	165	28	)	)	PUNCT
ejpam-6847	165	29	let	let	VERB
ejpam-6847	165	30	h(x	h(x	PROPN
ejpam-6847	165	31	,	,	PUNCT
ejpam-6847	165	32	y	y	PROPN
ejpam-6847	165	33	)	)	PUNCT
ejpam-6847	165	34	=	=	SYM
ejpam-6847	166	1	(	(	PUNCT
ejpam-6847	166	2	x+	x+	X
ejpam-6847	166	3	l)y	l)y	NOUN
ejpam-6847	166	4	,	,	PUNCT
ejpam-6847	166	5	l	l	NOUN
ejpam-6847	166	6	>	>	X
ejpam-6847	166	7	0	0	NUM
ejpam-6847	166	8	,	,	PUNCT
ejpam-6847	166	9	and	and	CCONJ
ejpam-6847	166	10	q(s	q(s	PROPN
ejpam-6847	166	11	,	,	PUNCT
ejpam-6847	166	12	t	t	PROPN
ejpam-6847	166	13	)	)	PUNCT
ejpam-6847	166	14	=	=	PUNCT
ejpam-6847	166	15	(	(	PUNCT
ejpam-6847	166	16	1	1	NUM
ejpam-6847	166	17	+	+	NUM
ejpam-6847	166	18	l)st	l)st	NOUN
ejpam-6847	166	19	.	.	PUNCT
ejpam-6847	167	1	(	(	PUNCT
ejpam-6847	167	2	3	3	X
ejpam-6847	167	3	)	)	PUNCT
ejpam-6847	167	4	let	let	VERB
ejpam-6847	168	1	h(x	h(x	PROPN
ejpam-6847	168	2	,	,	PUNCT
ejpam-6847	168	3	y	y	PROPN
ejpam-6847	168	4	)	)	PUNCT
ejpam-6847	168	5	=	=	SYM
ejpam-6847	168	6	xnyk	xnyk	NOUN
ejpam-6847	168	7	,	,	PUNCT
ejpam-6847	168	8	and	and	CCONJ
ejpam-6847	168	9	q(s	q(s	PROPN
ejpam-6847	168	10	,	,	PUNCT
ejpam-6847	168	11	t	t	NOUN
ejpam-6847	168	12	)	)	PUNCT
ejpam-6847	168	13	=	=	SYM
ejpam-6847	168	14	smtk	smtk	NOUN
ejpam-6847	168	15	,	,	PUNCT
ejpam-6847	168	16	k	k	PROPN
ejpam-6847	168	17	>	>	X
ejpam-6847	168	18	0	0	X
ejpam-6847	168	19	.	.	PUNCT
ejpam-6847	168	20	(	(	PUNCT
ejpam-6847	168	21	4	4	X
ejpam-6847	168	22	)	)	PUNCT
ejpam-6847	168	23	let	let	VERB
ejpam-6847	168	24	h(x	h(x	PROPN
ejpam-6847	168	25	,	,	PUNCT
ejpam-6847	168	26	y	y	PROPN
ejpam-6847	168	27	)	)	PUNCT
ejpam-6847	168	28	=	=	SYM
ejpam-6847	169	1	mx+n	mx+n	NOUN
ejpam-6847	169	2	m+n	m+n	NOUN
ejpam-6847	169	3	y	y	NOUN
ejpam-6847	169	4	,	,	PUNCT
ejpam-6847	169	5	with	with	ADP
ejpam-6847	169	6	m	m	PROPN
ejpam-6847	169	7	,	,	PUNCT
ejpam-6847	169	8	n	n	PROPN
ejpam-6847	169	9	∈	∈	PROPN
ejpam-6847	169	10	n	n	CCONJ
ejpam-6847	169	11	,	,	PUNCT
ejpam-6847	169	12	and	and	CCONJ
ejpam-6847	169	13	q(s	q(s	PROPN
ejpam-6847	169	14	,	,	PUNCT
ejpam-6847	169	15	t	t	PROPN
ejpam-6847	169	16	)	)	PUNCT
ejpam-6847	169	17	=	=	SYM
ejpam-6847	170	1	st	st	PROPN
ejpam-6847	170	2	.	.	PROPN
ejpam-6847	170	3	(	(	PUNCT
ejpam-6847	170	4	5	5	X
ejpam-6847	170	5	)	)	PUNCT
ejpam-6847	170	6	let	let	VERB
ejpam-6847	170	7	h(x	h(x	PROPN
ejpam-6847	170	8	,	,	PUNCT
ejpam-6847	170	9	y	y	PROPN
ejpam-6847	170	10	)	)	PUNCT
ejpam-6847	170	11	=	=	PRON
ejpam-6847	171	1	(	(	PUNCT
ejpam-6847	171	2	x	x	SYM
ejpam-6847	171	3	n+xn−1+	n+xn−1+	ADV
ejpam-6847	171	4	...	...	PUNCT
ejpam-6847	171	5	+x+1	+x+1	PROPN
ejpam-6847	171	6	n+1	n+1	X
ejpam-6847	171	7	+	+	NUM
ejpam-6847	171	8	l)y	l)y	NOUN
ejpam-6847	171	9	,	,	PUNCT
ejpam-6847	171	10	l	l	NOUN
ejpam-6847	171	11	>	>	X
ejpam-6847	171	12	1	1	NUM
ejpam-6847	171	13	,	,	PUNCT
ejpam-6847	171	14	and	and	CCONJ
ejpam-6847	171	15	q(s	q(s	PROPN
ejpam-6847	171	16	,	,	PUNCT
ejpam-6847	171	17	t	t	PROPN
ejpam-6847	171	18	)	)	PUNCT
ejpam-6847	171	19	=	=	PUNCT
ejpam-6847	171	20	(	(	PUNCT
ejpam-6847	171	21	1	1	NUM
ejpam-6847	171	22	+	+	NUM
ejpam-6847	171	23	l)st	l)st	NOUN
ejpam-6847	171	24	.	.	PUNCT
ejpam-6847	172	1	(	(	PUNCT
ejpam-6847	172	2	6	6	X
ejpam-6847	172	3	)	)	PUNCT
ejpam-6847	172	4	let	let	VERB
ejpam-6847	172	5	h(x	h(x	PROPN
ejpam-6847	172	6	,	,	PUNCT
ejpam-6847	172	7	y	y	PROPN
ejpam-6847	172	8	)	)	PUNCT
ejpam-6847	172	9	=	=	SYM
ejpam-6847	173	1	(	(	PUNCT
ejpam-6847	173	2	y	y	PROPN
ejpam-6847	173	3	+	+	CCONJ
ejpam-6847	173	4	l)x	l)x	X
ejpam-6847	173	5	,	,	PUNCT
ejpam-6847	173	6	l	l	NOUN
ejpam-6847	173	7	>	>	X
ejpam-6847	173	8	1	1	NUM
ejpam-6847	173	9	and	and	CCONJ
ejpam-6847	173	10	q(s	q(s	PROPN
ejpam-6847	173	11	,	,	PUNCT
ejpam-6847	173	12	t	t	PROPN
ejpam-6847	173	13	)	)	PUNCT
ejpam-6847	173	14	=	=	SYM
ejpam-6847	174	1	st+	st+	PROPN
ejpam-6847	174	2	l	l	PROPN
ejpam-6847	174	3	k	k	PROPN
ejpam-6847	174	4	,	,	PUNCT
ejpam-6847	174	5	k	k	PROPN
ejpam-6847	174	6	≥	≥	NUM
ejpam-6847	174	7	1	1	NUM
ejpam-6847	174	8	.	.	PUNCT
ejpam-6847	174	9	definition	definition	NOUN
ejpam-6847	174	10	13	13	NUM
ejpam-6847	174	11	.	.	PUNCT
ejpam-6847	175	1	(	(	PUNCT
ejpam-6847	175	2	[	[	X
ejpam-6847	175	3	30	30	NUM
ejpam-6847	175	4	,	,	PUNCT
ejpam-6847	175	5	39	39	NUM
ejpam-6847	175	6	]	]	PUNCT
ejpam-6847	175	7	)	)	PUNCT
ejpam-6847	175	8	let	let	VERB
ejpam-6847	175	9	h	h	NOUN
ejpam-6847	175	10	:	:	PUNCT
ejpam-6847	175	11	r+	r+	NOUN
ejpam-6847	175	12	×	×	NOUN
ejpam-6847	175	13	r+	r+	NOUN
ejpam-6847	175	14	×	×	NOUN
ejpam-6847	175	15	r+	r+	NOUN
ejpam-6847	175	16	→	→	PUNCT
ejpam-6847	175	17	r	r	NOUN
ejpam-6847	175	18	and	and	CCONJ
ejpam-6847	175	19	q	q	NOUN
ejpam-6847	175	20	:	:	PUNCT
ejpam-6847	175	21	r+	r+	NOUN
ejpam-6847	175	22	×	×	NOUN
ejpam-6847	175	23	r+	r+	NOUN
ejpam-6847	175	24	→	→	PUNCT
ejpam-6847	175	25	r	r	NOUN
ejpam-6847	175	26	be	be	NOUN
ejpam-6847	175	27	functions	function	NOUN
ejpam-6847	175	28	.	.	PUNCT
ejpam-6847	176	1	we	we	PRON
ejpam-6847	176	2	say	say	VERB
ejpam-6847	176	3	the	the	DET
ejpam-6847	176	4	pair	pair	NOUN
ejpam-6847	176	5	(	(	PUNCT
ejpam-6847	176	6	q	q	NOUN
ejpam-6847	176	7	,	,	PUNCT
ejpam-6847	176	8	h	h	NOUN
ejpam-6847	176	9	)	)	PUNCT
ejpam-6847	176	10	is	be	AUX
ejpam-6847	176	11	an	an	DET
ejpam-6847	176	12	upper	upper	ADJ
ejpam-6847	176	13	class	class	NOUN
ejpam-6847	176	14	of	of	ADP
ejpam-6847	176	15	type	type	NOUN
ejpam-6847	176	16	ii	ii	PROPN
ejpam-6847	176	17	,	,	PUNCT
ejpam-6847	176	18	if	if	SCONJ
ejpam-6847	176	19	h	h	NOUN
ejpam-6847	176	20	is	be	AUX
ejpam-6847	176	21	a	a	DET
ejpam-6847	176	22	subclass	subclass	NOUN
ejpam-6847	176	23	of	of	ADP
ejpam-6847	176	24	type	type	NOUN
ejpam-6847	176	25	ii	ii	PROPN
ejpam-6847	176	26	,	,	PUNCT
ejpam-6847	176	27	and	and	CCONJ
ejpam-6847	176	28	satisfies	satisfy	VERB
ejpam-6847	176	29	the	the	DET
ejpam-6847	176	30	following	follow	VERB
ejpam-6847	176	31	conditions	condition	NOUN
ejpam-6847	176	32	:	:	PUNCT
ejpam-6847	176	33	(	(	PUNCT
ejpam-6847	176	34	i	i	NOUN
ejpam-6847	176	35	)	)	PUNCT
ejpam-6847	176	36	0	0	NUM
ejpam-6847	177	1	≤	≤	NUM
ejpam-6847	177	2	s	s	PART
ejpam-6847	177	3	≤	≤	NUM
ejpam-6847	177	4	1	1	NUM
ejpam-6847	177	5	=	=	NOUN
ejpam-6847	177	6	⇒	⇒	NOUN
ejpam-6847	177	7	q(s	q(s	PROPN
ejpam-6847	177	8	,	,	PUNCT
ejpam-6847	177	9	t	t	PROPN
ejpam-6847	177	10	)	)	PUNCT
ejpam-6847	177	11	≤	≤	NOUN
ejpam-6847	177	12	q(1	q(1	PROPN
ejpam-6847	177	13	,	,	PUNCT
ejpam-6847	177	14	t	t	PROPN
ejpam-6847	177	15	)	)	PUNCT
ejpam-6847	177	16	.	.	PUNCT
ejpam-6847	178	1	(	(	PUNCT
ejpam-6847	178	2	ii	ii	NOUN
ejpam-6847	178	3	)	)	PUNCT
ejpam-6847	178	4	h(1	h(1	PROPN
ejpam-6847	178	5	,	,	PUNCT
ejpam-6847	178	6	1	1	NUM
ejpam-6847	178	7	,	,	PUNCT
ejpam-6847	178	8	z	z	NOUN
ejpam-6847	178	9	)	)	PUNCT
ejpam-6847	178	10	≤	≤	NOUN
ejpam-6847	178	11	q(s	q(s	PROPN
ejpam-6847	178	12	,	,	PUNCT
ejpam-6847	178	13	t	t	NOUN
ejpam-6847	178	14	)	)	PUNCT
ejpam-6847	178	15	=	=	NOUN
ejpam-6847	178	16	⇒	⇒	NOUN
ejpam-6847	178	17	z	z	PROPN
ejpam-6847	178	18	≤	≤	PROPN
ejpam-6847	178	19	st	st	PROPN
ejpam-6847	178	20	,	,	PUNCT
ejpam-6847	178	21	for	for	ADP
ejpam-6847	178	22	all	all	DET
ejpam-6847	178	23	z	z	PROPN
ejpam-6847	178	24	,	,	PUNCT
ejpam-6847	178	25	s	s	PROPN
ejpam-6847	178	26	,	,	PUNCT
ejpam-6847	178	27	t	t	PROPN
ejpam-6847	178	28	∈	∈	PROPN
ejpam-6847	178	29	r+	r+	NOUN
ejpam-6847	178	30	.	.	PUNCT
ejpam-6847	179	1	when	when	SCONJ
ejpam-6847	179	2	we	we	PRON
ejpam-6847	179	3	set	set	VERB
ejpam-6847	179	4	s	s	X
ejpam-6847	179	5	=	=	NOUN
ejpam-6847	179	6	1	1	NUM
ejpam-6847	179	7	in	in	ADP
ejpam-6847	179	8	(	(	PUNCT
ejpam-6847	179	9	2	2	NUM
ejpam-6847	179	10	)	)	PUNCT
ejpam-6847	179	11	,	,	PUNCT
ejpam-6847	179	12	the	the	DET
ejpam-6847	179	13	pair	pair	NOUN
ejpam-6847	179	14	(	(	PUNCT
ejpam-6847	179	15	q	q	NOUN
ejpam-6847	179	16	,	,	PUNCT
ejpam-6847	179	17	h	h	NOUN
ejpam-6847	179	18	)	)	PUNCT
ejpam-6847	179	19	is	be	AUX
ejpam-6847	179	20	referred	refer	VERB
ejpam-6847	179	21	to	to	ADP
ejpam-6847	179	22	as	as	ADP
ejpam-6847	179	23	a	a	DET
ejpam-6847	179	24	special	special	ADJ
ejpam-6847	179	25	upper	upper	ADJ
ejpam-6847	179	26	class	class	NOUN
ejpam-6847	179	27	of	of	ADP
ejpam-6847	179	28	type	type	PROPN
ejpam-6847	179	29	ii	ii	PROPN
ejpam-6847	179	30	.	.	PROPN
ejpam-6847	179	31	example	example	NOUN
ejpam-6847	180	1	6	6	NUM
ejpam-6847	180	2	.	.	PUNCT
ejpam-6847	181	1	[	[	X
ejpam-6847	181	2	30	30	NUM
ejpam-6847	181	3	,	,	PUNCT
ejpam-6847	181	4	39	39	NUM
ejpam-6847	181	5	]	]	PUNCT
ejpam-6847	181	6	examples	example	NOUN
ejpam-6847	181	7	of	of	ADP
ejpam-6847	181	8	functions	function	NOUN
ejpam-6847	181	9	belonging	belong	VERB
ejpam-6847	181	10	to	to	ADP
ejpam-6847	181	11	the	the	DET
ejpam-6847	181	12	upper	upper	ADJ
ejpam-6847	181	13	class	class	NOUN
ejpam-6847	181	14	of	of	ADP
ejpam-6847	181	15	type	type	NOUN
ejpam-6847	181	16	ii	ii	PROPN
ejpam-6847	181	17	are	be	AUX
ejpam-6847	181	18	given	give	VERB
ejpam-6847	181	19	below	below	ADV
ejpam-6847	181	20	.	.	PUNCT
ejpam-6847	182	1	(	(	PUNCT
ejpam-6847	182	2	1	1	X
ejpam-6847	182	3	)	)	PUNCT
ejpam-6847	182	4	h(x	h(x	PROPN
ejpam-6847	182	5	,	,	PUNCT
ejpam-6847	182	6	y	y	PROPN
ejpam-6847	182	7	,	,	PUNCT
ejpam-6847	182	8	z	z	NOUN
ejpam-6847	182	9	)	)	PUNCT
ejpam-6847	182	10	=	=	PUNCT
ejpam-6847	182	11	(	(	PUNCT
ejpam-6847	182	12	z	z	NOUN
ejpam-6847	182	13	+	+	CCONJ
ejpam-6847	182	14	l)xy	l)xy	PROPN
ejpam-6847	182	15	,	,	PUNCT
ejpam-6847	182	16	l	l	NOUN
ejpam-6847	182	17	>	>	X
ejpam-6847	182	18	1	1	NUM
ejpam-6847	182	19	,	,	PUNCT
ejpam-6847	182	20	and	and	CCONJ
ejpam-6847	182	21	q(s	q(s	PROPN
ejpam-6847	182	22	,	,	PUNCT
ejpam-6847	182	23	t	t	PROPN
ejpam-6847	182	24	)	)	PUNCT
ejpam-6847	182	25	=	=	SYM
ejpam-6847	182	26	st+	st+	PROPN
ejpam-6847	182	27	l.	l.	PROPN
ejpam-6847	182	28	(	(	PUNCT
ejpam-6847	182	29	2	2	NUM
ejpam-6847	182	30	)	)	PUNCT
ejpam-6847	182	31	h(x	h(x	PROPN
ejpam-6847	182	32	,	,	PUNCT
ejpam-6847	182	33	y	y	PROPN
ejpam-6847	182	34	,	,	PUNCT
ejpam-6847	182	35	z	z	NOUN
ejpam-6847	182	36	)	)	PUNCT
ejpam-6847	182	37	=	=	SYM
ejpam-6847	182	38	(	(	PUNCT
ejpam-6847	182	39	xy	xy	NOUN
ejpam-6847	182	40	+	+	NOUN
ejpam-6847	182	41	l)z	l)z	NOUN
ejpam-6847	182	42	,	,	PUNCT
ejpam-6847	182	43	with	with	ADP
ejpam-6847	182	44	l	l	PROPN
ejpam-6847	182	45	>	>	X
ejpam-6847	182	46	0	0	NUM
ejpam-6847	182	47	,	,	PUNCT
ejpam-6847	182	48	and	and	CCONJ
ejpam-6847	182	49	q(s	q(s	PROPN
ejpam-6847	182	50	,	,	PUNCT
ejpam-6847	182	51	t	t	PROPN
ejpam-6847	182	52	)	)	PUNCT
ejpam-6847	182	53	=	=	PUNCT
ejpam-6847	182	54	(	(	PUNCT
ejpam-6847	182	55	1	1	NUM
ejpam-6847	182	56	+	+	NUM
ejpam-6847	182	57	l)st	l)st	NOUN
ejpam-6847	182	58	.	.	PUNCT
ejpam-6847	183	1	(	(	PUNCT
ejpam-6847	183	2	3	3	X
ejpam-6847	183	3	)	)	PUNCT
ejpam-6847	183	4	h(x	h(x	PROPN
ejpam-6847	183	5	,	,	PUNCT
ejpam-6847	183	6	y	y	PROPN
ejpam-6847	183	7	,	,	PUNCT
ejpam-6847	183	8	z	z	NOUN
ejpam-6847	183	9	)	)	PUNCT
ejpam-6847	183	10	=	=	SYM
ejpam-6847	183	11	xmynzp	xmynzp	PROPN
ejpam-6847	183	12	,	,	PUNCT
ejpam-6847	183	13	q(s	q(s	PROPN
ejpam-6847	183	14	,	,	PUNCT
ejpam-6847	183	15	t	t	PROPN
ejpam-6847	183	16	)	)	PUNCT
ejpam-6847	183	17	=	=	PUNCT
ejpam-6847	183	18	sptp	sptp	PROPN
ejpam-6847	183	19	,	,	PUNCT
ejpam-6847	183	20	such	such	ADJ
ejpam-6847	183	21	that	that	SCONJ
ejpam-6847	183	22	m	m	PROPN
ejpam-6847	183	23	,	,	PUNCT
ejpam-6847	183	24	n	n	PROPN
ejpam-6847	183	25	∈	∈	PROPN
ejpam-6847	183	26	n∪{0	n∪{0	NOUN
ejpam-6847	183	27	}	}	PUNCT
ejpam-6847	183	28	and	and	CCONJ
ejpam-6847	183	29	p	p	X
ejpam-6847	183	30	>	>	X
ejpam-6847	183	31	0	0	NUM
ejpam-6847	183	32	.	.	PUNCT
ejpam-6847	184	1	(	(	PUNCT
ejpam-6847	184	2	4	4	X
ejpam-6847	184	3	)	)	PUNCT
ejpam-6847	184	4	h(x	h(x	PROPN
ejpam-6847	184	5	,	,	PUNCT
ejpam-6847	184	6	y	y	PROPN
ejpam-6847	184	7	,	,	PUNCT
ejpam-6847	184	8	z	z	NOUN
ejpam-6847	184	9	)	)	PUNCT
ejpam-6847	184	10	=	=	SYM
ejpam-6847	184	11	xm+xnyp+yq	xm+xnyp+yq	PROPN
ejpam-6847	184	12	3	3	NUM
ejpam-6847	184	13	zk	zk	PROPN
ejpam-6847	184	14	,	,	PUNCT
ejpam-6847	184	15	with	with	ADP
ejpam-6847	184	16	m	m	PROPN
ejpam-6847	184	17	,	,	PUNCT
ejpam-6847	184	18	n	n	CCONJ
ejpam-6847	184	19	,	,	PUNCT
ejpam-6847	184	20	p	p	X
ejpam-6847	184	21	,	,	PUNCT
ejpam-6847	184	22	q	q	X
ejpam-6847	184	23	,	,	PUNCT
ejpam-6847	184	24	k	k	PROPN
ejpam-6847	184	25	∈	∈	PROPN
ejpam-6847	184	26	n	n	ADV
ejpam-6847	184	27	and	and	CCONJ
ejpam-6847	184	28	q(s	q(s	PROPN
ejpam-6847	184	29	,	,	PUNCT
ejpam-6847	184	30	t	t	PROPN
ejpam-6847	184	31	)	)	PUNCT
ejpam-6847	184	32	=	=	SYM
ejpam-6847	184	33	(	(	PUNCT
ejpam-6847	184	34	st)k	st)k	ADJ
ejpam-6847	184	35	.	.	PUNCT
ejpam-6847	185	1	(	(	PUNCT
ejpam-6847	185	2	5	5	X
ejpam-6847	185	3	)	)	PUNCT
ejpam-6847	185	4	h(x	h(x	PROPN
ejpam-6847	185	5	,	,	PUNCT
ejpam-6847	185	6	y	y	PROPN
ejpam-6847	185	7	,	,	PUNCT
ejpam-6847	185	8	z	z	NOUN
ejpam-6847	185	9	)	)	PUNCT
ejpam-6847	185	10	=	=	SYM
ejpam-6847	186	1	(	(	PUNCT
ejpam-6847	186	2	n∑	n∑	NOUN
ejpam-6847	186	3	i=0	i=0	PROPN
ejpam-6847	186	4	xn−iyi	xn−iyi	X
ejpam-6847	186	5	n+1	n+1	PROPN
ejpam-6847	187	1	+	+	PUNCT
ejpam-6847	187	2	l)z	l)z	NOUN
ejpam-6847	187	3	,	,	PUNCT
ejpam-6847	187	4	l	l	NOUN
ejpam-6847	187	5	>	>	X
ejpam-6847	187	6	1	1	NUM
ejpam-6847	187	7	,	,	PUNCT
ejpam-6847	187	8	and	and	CCONJ
ejpam-6847	187	9	q(s	q(s	PROPN
ejpam-6847	187	10	,	,	PUNCT
ejpam-6847	187	11	t	t	PROPN
ejpam-6847	187	12	)	)	PUNCT
ejpam-6847	187	13	=	=	PUNCT
ejpam-6847	188	1	(	(	PUNCT
ejpam-6847	188	2	1	1	NUM
ejpam-6847	188	3	+	+	NUM
ejpam-6847	188	4	l)st	l)st	NOUN
ejpam-6847	188	5	.	.	PUNCT
ejpam-6847	189	1	(	(	PUNCT
ejpam-6847	189	2	6	6	NUM
ejpam-6847	189	3	)	)	PUNCT
ejpam-6847	189	4	h(x	h(x	PROPN
ejpam-6847	189	5	,	,	PUNCT
ejpam-6847	189	6	y	y	PROPN
ejpam-6847	189	7	,	,	PUNCT
ejpam-6847	189	8	z	z	NOUN
ejpam-6847	189	9	)	)	PUNCT
ejpam-6847	189	10	=	=	SYM
ejpam-6847	190	1	(	(	PUNCT
ejpam-6847	190	2	n∑	n∑	NOUN
ejpam-6847	190	3	i=0	i=0	PROPN
ejpam-6847	190	4	xn−iyi	xn−iyi	NOUN
ejpam-6847	190	5	n+1	n+1	X
ejpam-6847	190	6	)	)	PUNCT
ejpam-6847	190	7	z	z	NOUN
ejpam-6847	190	8	,	,	PUNCT
ejpam-6847	190	9	and	and	CCONJ
ejpam-6847	190	10	q(s	q(s	PROPN
ejpam-6847	190	11	,	,	PUNCT
ejpam-6847	190	12	t	t	PROPN
ejpam-6847	190	13	)	)	PUNCT
ejpam-6847	190	14	=	=	SYM
ejpam-6847	190	15	st	st	PROPN
ejpam-6847	190	16	.	.	PROPN
ejpam-6847	190	17	(	(	PUNCT
ejpam-6847	190	18	7	7	X
ejpam-6847	190	19	)	)	PUNCT
ejpam-6847	190	20	h(x	h(x	PROPN
ejpam-6847	190	21	,	,	PUNCT
ejpam-6847	190	22	y	y	PROPN
ejpam-6847	190	23	,	,	PUNCT
ejpam-6847	190	24	z	z	NOUN
ejpam-6847	190	25	)	)	PUNCT
ejpam-6847	190	26	=	=	PUNCT
ejpam-6847	190	27	(	(	PUNCT
ejpam-6847	190	28	z	z	NOUN
ejpam-6847	190	29	+	+	CCONJ
ejpam-6847	190	30	l)xy	l)xy	PROPN
ejpam-6847	190	31	,	,	PUNCT
ejpam-6847	190	32	l	l	NOUN
ejpam-6847	190	33	>	>	X
ejpam-6847	190	34	1	1	NUM
ejpam-6847	190	35	,	,	PUNCT
ejpam-6847	190	36	and	and	CCONJ
ejpam-6847	190	37	q(s	q(s	PROPN
ejpam-6847	190	38	,	,	PUNCT
ejpam-6847	190	39	t	t	PROPN
ejpam-6847	190	40	)	)	PUNCT
ejpam-6847	190	41	=	=	SYM
ejpam-6847	191	1	st+	st+	PROPN
ejpam-6847	191	2	l	l	PROPN
ejpam-6847	191	3	k	k	PROPN
ejpam-6847	191	4	,	,	PUNCT
ejpam-6847	191	5	k	k	PROPN
ejpam-6847	191	6	≥	≥	NUM
ejpam-6847	191	7	1	1	NUM
ejpam-6847	191	8	.	.	PUNCT
ejpam-6847	192	1	f.	f.	PROPN
ejpam-6847	192	2	m.	m.	PROPN
ejpam-6847	192	3	azmi	azmi	PROPN
ejpam-6847	192	4	,	,	PUNCT
ejpam-6847	192	5	a.	a.	PROPN
ejpam-6847	192	6	h.	h.	PROPN
ejpam-6847	192	7	ansari	ansari	PROPN
ejpam-6847	192	8	,	,	PUNCT
ejpam-6847	192	9	s.	s.	PROPN
ejpam-6847	192	10	h.	h.	PROPN
ejpam-6847	192	11	j.	j.	PROPN
ejpam-6847	192	12	petroudi	petroudi	PROPN
ejpam-6847	192	13	/	/	SYM
ejpam-6847	192	14	eur	eur	PROPN
ejpam-6847	192	15	.	.	PUNCT
ejpam-6847	193	1	j.	j.	PROPN
ejpam-6847	193	2	pure	pure	PROPN
ejpam-6847	193	3	appl	appl	PROPN
ejpam-6847	193	4	.	.	PROPN
ejpam-6847	193	5	math	math	PROPN
ejpam-6847	193	6	,	,	PUNCT
ejpam-6847	193	7	18	18	NUM
ejpam-6847	193	8	(	(	PUNCT
ejpam-6847	193	9	4	4	NUM
ejpam-6847	193	10	)	)	PUNCT
ejpam-6847	193	11	(	(	PUNCT
ejpam-6847	193	12	2025	2025	NUM
ejpam-6847	193	13	)	)	PUNCT
ejpam-6847	193	14	,	,	PUNCT
ejpam-6847	193	15	6847	6847	NUM
ejpam-6847	193	16	8	8	NUM
ejpam-6847	193	17	of	of	ADP
ejpam-6847	193	18	26	26	NUM
ejpam-6847	193	19	wardowski	wardowski	NOUN
ejpam-6847	193	20	[	[	X
ejpam-6847	193	21	23	23	NUM
ejpam-6847	193	22	]	]	PUNCT
ejpam-6847	193	23	introduced	introduce	VERB
ejpam-6847	193	24	the	the	DET
ejpam-6847	193	25	notion	notion	NOUN
ejpam-6847	193	26	of	of	ADP
ejpam-6847	193	27	f−contraction	f−contraction	PROPN
ejpam-6847	193	28	and	and	CCONJ
ejpam-6847	193	29	developed	develop	VERB
ejpam-6847	193	30	new	new	ADJ
ejpam-6847	193	31	fixed	fix	VERB
ejpam-6847	193	32	point	point	NOUN
ejpam-6847	193	33	theorems	theorem	NOUN
ejpam-6847	193	34	applicable	applicable	ADJ
ejpam-6847	193	35	to	to	PART
ejpam-6847	193	36	complete	complete	VERB
ejpam-6847	193	37	metric	metric	ADJ
ejpam-6847	193	38	spaces	space	NOUN
ejpam-6847	193	39	.	.	PUNCT
ejpam-6847	194	1	the	the	DET
ejpam-6847	194	2	definition	definition	NOUN
ejpam-6847	194	3	is	be	AUX
ejpam-6847	194	4	provided	provide	VERB
ejpam-6847	194	5	below	below	ADP
ejpam-6847	194	6	.	.	PUNCT
ejpam-6847	195	1	definition	definition	NOUN
ejpam-6847	195	2	14	14	NUM
ejpam-6847	195	3	.	.	PUNCT
ejpam-6847	196	1	[	[	X
ejpam-6847	196	2	23	23	NUM
ejpam-6847	196	3	]	]	PUNCT
ejpam-6847	196	4	let	let	VERB
ejpam-6847	196	5	f	f	PROPN
ejpam-6847	196	6	represents	represent	VERB
ejpam-6847	196	7	the	the	DET
ejpam-6847	196	8	family	family	NOUN
ejpam-6847	196	9	of	of	ADP
ejpam-6847	196	10	all	all	DET
ejpam-6847	196	11	functions	function	NOUN
ejpam-6847	196	12	f	f	X
ejpam-6847	196	13	:	:	PUNCT
ejpam-6847	196	14	(	(	PUNCT
ejpam-6847	196	15	0	0	NUM
ejpam-6847	196	16	,	,	PUNCT
ejpam-6847	196	17	+	+	NOUN
ejpam-6847	196	18	∞	∞	NOUN
ejpam-6847	196	19	)	)	PUNCT
ejpam-6847	196	20	→	→	SYM
ejpam-6847	196	21	(	(	PUNCT
ejpam-6847	196	22	−∞,+∞	−∞,+∞	ADV
ejpam-6847	196	23	)	)	PUNCT
ejpam-6847	196	24	satisfying	satisfy	VERB
ejpam-6847	196	25	the	the	DET
ejpam-6847	196	26	following	follow	VERB
ejpam-6847	196	27	conditions	condition	NOUN
ejpam-6847	196	28	:	:	PUNCT
ejpam-6847	196	29	(	(	PUNCT
ejpam-6847	196	30	w1	w1	NOUN
ejpam-6847	196	31	)	)	PUNCT
ejpam-6847	196	32	f	f	PROPN
ejpam-6847	196	33	is	be	AUX
ejpam-6847	196	34	an	an	DET
ejpam-6847	196	35	strictly	strictly	ADV
ejpam-6847	196	36	increasing	increase	VERB
ejpam-6847	196	37	function	function	NOUN
ejpam-6847	196	38	.	.	PUNCT
ejpam-6847	197	1	(	(	PUNCT
ejpam-6847	197	2	w2	w2	NOUN
ejpam-6847	197	3	)	)	PUNCT
ejpam-6847	197	4	let	let	VERB
ejpam-6847	197	5	{	{	PUNCT
ejpam-6847	197	6	tn	tn	NOUN
ejpam-6847	197	7	}	}	PUNCT
ejpam-6847	197	8	be	be	VERB
ejpam-6847	197	9	any	any	DET
ejpam-6847	197	10	sequence	sequence	NOUN
ejpam-6847	197	11	of	of	ADP
ejpam-6847	197	12	positive	positive	ADJ
ejpam-6847	197	13	real	real	ADJ
ejpam-6847	197	14	numbers	number	NOUN
ejpam-6847	197	15	,	,	PUNCT
ejpam-6847	197	16	then	then	ADV
ejpam-6847	197	17	lim	lim	PROPN
ejpam-6847	197	18	n→+∞	n→+∞	VERB
ejpam-6847	197	19	tn	tn	PROPN
ejpam-6847	197	20	=	=	SYM
ejpam-6847	197	21	0	0	NUM
ejpam-6847	198	1	iff	iff	PROPN
ejpam-6847	198	2	lim	lim	PROPN
ejpam-6847	198	3	n→+∞	n→+∞	PROPN
ejpam-6847	198	4	f	f	PROPN
ejpam-6847	198	5	(	(	PUNCT
ejpam-6847	198	6	tn	tn	PROPN
ejpam-6847	198	7	)	)	PUNCT
ejpam-6847	198	8	=	=	SYM
ejpam-6847	198	9	−∞.	−∞.	PROPN
ejpam-6847	198	10	(	(	PUNCT
ejpam-6847	198	11	w3	w3	PROPN
ejpam-6847	198	12	)	)	PUNCT
ejpam-6847	198	13	limt→0	limt→0	PROPN
ejpam-6847	198	14	+	+	CCONJ
ejpam-6847	198	15	tkf	tkf	NOUN
ejpam-6847	198	16	(	(	PUNCT
ejpam-6847	198	17	t	t	NOUN
ejpam-6847	198	18	)	)	PUNCT
ejpam-6847	198	19	=	=	SYM
ejpam-6847	198	20	0	0	NUM
ejpam-6847	198	21	,	,	PUNCT
ejpam-6847	198	22	for	for	ADP
ejpam-6847	198	23	some	some	DET
ejpam-6847	198	24	k	k	PROPN
ejpam-6847	198	25	∈	∈	PROPN
ejpam-6847	198	26	(	(	PUNCT
ejpam-6847	198	27	0	0	NUM
ejpam-6847	198	28	,	,	PUNCT
ejpam-6847	198	29	1	1	NUM
ejpam-6847	198	30	)	)	PUNCT
ejpam-6847	198	31	.	.	PUNCT
ejpam-6847	199	1	then	then	ADV
ejpam-6847	199	2	,	,	PUNCT
ejpam-6847	199	3	f	f	PROPN
ejpam-6847	199	4	is	be	AUX
ejpam-6847	199	5	referred	refer	VERB
ejpam-6847	199	6	to	to	ADP
ejpam-6847	199	7	as	as	ADP
ejpam-6847	199	8	an	an	DET
ejpam-6847	199	9	f	f	NOUN
ejpam-6847	199	10	-	-	PUNCT
ejpam-6847	199	11	contraction	contraction	NOUN
ejpam-6847	199	12	mapping	mapping	NOUN
ejpam-6847	199	13	.	.	PUNCT
ejpam-6847	200	1	numerous	numerous	ADJ
ejpam-6847	200	2	researchers	researcher	NOUN
ejpam-6847	200	3	have	have	AUX
ejpam-6847	200	4	adapted	adapt	VERB
ejpam-6847	200	5	the	the	DET
ejpam-6847	200	6	f	f	PROPN
ejpam-6847	200	7	-contraction	-contraction	PROPN
ejpam-6847	200	8	mapping	mapping	NOUN
ejpam-6847	200	9	initially	initially	ADV
ejpam-6847	200	10	proposed	propose	VERB
ejpam-6847	200	11	by	by	ADP
ejpam-6847	200	12	wardowski	wardowski	PROPN
ejpam-6847	200	13	[	[	X
ejpam-6847	200	14	23	23	NUM
ejpam-6847	200	15	]	]	PUNCT
ejpam-6847	200	16	to	to	PART
ejpam-6847	200	17	fit	fit	VERB
ejpam-6847	200	18	various	various	ADJ
ejpam-6847	200	19	metric	metric	ADJ
ejpam-6847	200	20	space	space	NOUN
ejpam-6847	200	21	contexts	contexts	NOUN
ejpam-6847	200	22	,	,	PUNCT
ejpam-6847	200	23	as	as	SCONJ
ejpam-6847	200	24	discussed	discuss	VERB
ejpam-6847	200	25	in	in	ADP
ejpam-6847	200	26	[	[	X
ejpam-6847	200	27	26	26	NUM
ejpam-6847	200	28	]	]	PUNCT
ejpam-6847	200	29	and	and	CCONJ
ejpam-6847	200	30	[	[	X
ejpam-6847	200	31	29	29	NUM
ejpam-6847	200	32	]	]	PUNCT
ejpam-6847	200	33	.	.	PUNCT
ejpam-6847	201	1	additionally	additionally	ADV
ejpam-6847	201	2	,	,	PUNCT
ejpam-6847	201	3	azmi	azmi	PROPN
ejpam-6847	201	4	[	[	X
ejpam-6847	201	5	20	20	NUM
ejpam-6847	201	6	]	]	PUNCT
ejpam-6847	201	7	introduced	introduce	VERB
ejpam-6847	201	8	a	a	DET
ejpam-6847	201	9	modified	modified	ADJ
ejpam-6847	201	10	f	f	NOUN
ejpam-6847	201	11	-	-	PUNCT
ejpam-6847	201	12	contraction	contraction	NOUN
ejpam-6847	201	13	mapping	mapping	NOUN
ejpam-6847	201	14	specifically	specifically	ADV
ejpam-6847	201	15	designed	design	VERB
ejpam-6847	201	16	for	for	ADP
ejpam-6847	201	17	s	s	ADJ
ejpam-6847	201	18	-	-	ADJ
ejpam-6847	201	19	metric	metric	ADJ
ejpam-6847	201	20	type	type	NOUN
ejpam-6847	201	21	spaces	space	NOUN
ejpam-6847	201	22	.	.	PUNCT
ejpam-6847	202	1	definition	definition	NOUN
ejpam-6847	202	2	15	15	NUM
ejpam-6847	202	3	.	.	PUNCT
ejpam-6847	203	1	[	[	X
ejpam-6847	203	2	20	20	NUM
ejpam-6847	203	3	]	]	PUNCT
ejpam-6847	203	4	assume	assume	VERB
ejpam-6847	203	5	(	(	PUNCT
ejpam-6847	203	6	x	x	X
ejpam-6847	203	7	,	,	PUNCT
ejpam-6847	203	8	s	s	PART
ejpam-6847	203	9	)	)	PUNCT
ejpam-6847	203	10	is	be	AUX
ejpam-6847	203	11	a	a	DET
ejpam-6847	203	12	t	t	NOUN
ejpam-6847	203	13	c	c	X
ejpam-6847	203	14	-	-	PUNCT
ejpam-6847	203	15	s	s	PROPN
ejpam-6847	203	16	-	-	PUNCT
ejpam-6847	203	17	mt	mt	NOUN
ejpam-6847	203	18	s	s	PROPN
ejpam-6847	203	19	,	,	PUNCT
ejpam-6847	203	20	where	where	SCONJ
ejpam-6847	203	21	x	x	PUNCT
ejpam-6847	203	22	6=	6=	ADP
ejpam-6847	203	23	∅.	∅.	ADP
ejpam-6847	203	24	the	the	DET
ejpam-6847	203	25	mapping	mapping	NOUN
ejpam-6847	203	26	t	t	NOUN
ejpam-6847	203	27	:	:	PUNCT
ejpam-6847	203	28	x	x	X
ejpam-6847	203	29	→	→	PUNCT
ejpam-6847	203	30	x	x	X
ejpam-6847	203	31	is	be	AUX
ejpam-6847	203	32	referred	refer	VERB
ejpam-6847	203	33	to	to	ADP
ejpam-6847	203	34	as	as	ADP
ejpam-6847	203	35	a	a	DET
ejpam-6847	203	36	modified	modified	ADJ
ejpam-6847	203	37	f	f	NOUN
ejpam-6847	203	38	-	-	PUNCT
ejpam-6847	203	39	contraction	contraction	NOUN
ejpam-6847	203	40	mapping	mapping	NOUN
ejpam-6847	203	41	,	,	PUNCT
ejpam-6847	203	42	if	if	SCONJ
ejpam-6847	203	43	there	there	PRON
ejpam-6847	203	44	exists	exist	VERB
ejpam-6847	203	45	a	a	DET
ejpam-6847	203	46	function	function	NOUN
ejpam-6847	203	47	f	f	PROPN
ejpam-6847	203	48	∈	∈	PROPN
ejpam-6847	203	49	f	f	PROPN
ejpam-6847	203	50	and	and	CCONJ
ejpam-6847	203	51	a	a	DET
ejpam-6847	203	52	constant	constant	ADJ
ejpam-6847	203	53	τ	τ	X
ejpam-6847	203	54	>	>	X
ejpam-6847	203	55	0	0	PROPN
ejpam-6847	203	56	,	,	PUNCT
ejpam-6847	203	57	such	such	ADJ
ejpam-6847	203	58	that	that	SCONJ
ejpam-6847	203	59	the	the	DET
ejpam-6847	203	60	following	follow	VERB
ejpam-6847	203	61	condition	condition	NOUN
ejpam-6847	203	62	holds	hold	VERB
ejpam-6847	203	63	:	:	PUNCT
ejpam-6847	203	64	s(tx	s(tx	NUM
ejpam-6847	203	65	,	,	PUNCT
ejpam-6847	203	66	ty	ty	INTJ
ejpam-6847	203	67	,	,	PUNCT
ejpam-6847	203	68	tz	tz	PROPN
ejpam-6847	203	69	)	)	PUNCT
ejpam-6847	203	70	>	>	X
ejpam-6847	203	71	0	0	PUNCT
ejpam-6847	204	1	=	=	AUX
ejpam-6847	204	2	⇒	⇒	X
ejpam-6847	204	3	τ	τ	PROPN
ejpam-6847	205	1	+	+	NUM
ejpam-6847	205	2	f	f	X
ejpam-6847	205	3	(	(	PUNCT
ejpam-6847	205	4	s(tx	s(tx	PROPN
ejpam-6847	205	5	,	,	PUNCT
ejpam-6847	205	6	ty	ty	INTJ
ejpam-6847	205	7	,	,	PUNCT
ejpam-6847	205	8	tz	tz	NOUN
ejpam-6847	205	9	)	)	PUNCT
ejpam-6847	205	10	)	)	PUNCT
ejpam-6847	205	11	≤	≤	NUM
ejpam-6847	205	12	f	f	X
ejpam-6847	205	13	(	(	PUNCT
ejpam-6847	205	14	s(x	s(x	PROPN
ejpam-6847	205	15	,	,	PUNCT
ejpam-6847	205	16	y	y	PROPN
ejpam-6847	205	17	,	,	PUNCT
ejpam-6847	205	18	z	z	NOUN
ejpam-6847	205	19	)	)	PUNCT
ejpam-6847	205	20	)	)	PUNCT
ejpam-6847	205	21	,	,	PUNCT
ejpam-6847	205	22	(	(	PUNCT
ejpam-6847	205	23	3	3	X
ejpam-6847	205	24	)	)	PUNCT
ejpam-6847	205	25	for	for	ADP
ejpam-6847	205	26	allx	allx	NOUN
ejpam-6847	205	27	,	,	PUNCT
ejpam-6847	205	28	y	y	PROPN
ejpam-6847	205	29	,	,	PUNCT
ejpam-6847	205	30	z	z	NOUN
ejpam-6847	205	31	∈	∈	NOUN
ejpam-6847	205	32	x.	x.	NOUN
ejpam-6847	205	33	3	3	X
ejpam-6847	205	34	.	.	X
ejpam-6847	205	35	main	main	ADJ
ejpam-6847	205	36	results	result	NOUN
ejpam-6847	205	37	in	in	ADP
ejpam-6847	205	38	this	this	DET
ejpam-6847	205	39	section	section	NOUN
ejpam-6847	205	40	,	,	PUNCT
ejpam-6847	205	41	we	we	PRON
ejpam-6847	205	42	demonstrate	demonstrate	VERB
ejpam-6847	205	43	the	the	DET
ejpam-6847	205	44	existence	existence	NOUN
ejpam-6847	205	45	and	and	CCONJ
ejpam-6847	205	46	uniqueness	uniqueness	NOUN
ejpam-6847	205	47	of	of	ADP
ejpam-6847	205	48	fixed	fix	VERB
ejpam-6847	205	49	points	point	NOUN
ejpam-6847	205	50	within	within	ADP
ejpam-6847	205	51	a	a	DET
ejpam-6847	205	52	complete	complete	ADJ
ejpam-6847	205	53	t	t	NOUN
ejpam-6847	205	54	c	c	X
ejpam-6847	205	55	-	-	PUNCT
ejpam-6847	205	56	s	s	PROPN
ejpam-6847	205	57	-	-	PUNCT
ejpam-6847	205	58	mt	mt	PROPN
ejpam-6847	205	59	s	s	PART
ejpam-6847	205	60	space	space	NOUN
ejpam-6847	205	61	by	by	ADP
ejpam-6847	205	62	employing	employ	VERB
ejpam-6847	205	63	two	two	NUM
ejpam-6847	205	64	different	different	ADJ
ejpam-6847	205	65	contraction	contraction	NOUN
ejpam-6847	205	66	mappings	mapping	NOUN
ejpam-6847	205	67	.	.	PUNCT
ejpam-6847	206	1	definition	definition	NOUN
ejpam-6847	206	2	16	16	NUM
ejpam-6847	206	3	.	.	PUNCT
ejpam-6847	207	1	[	[	X
ejpam-6847	207	2	20	20	NUM
ejpam-6847	207	3	]	]	PUNCT
ejpam-6847	207	4	assume	assume	VERB
ejpam-6847	207	5	(	(	PUNCT
ejpam-6847	207	6	x	x	X
ejpam-6847	207	7	,	,	PUNCT
ejpam-6847	207	8	s	s	PART
ejpam-6847	207	9	)	)	PUNCT
ejpam-6847	207	10	is	be	AUX
ejpam-6847	207	11	a	a	DET
ejpam-6847	207	12	t	t	NOUN
ejpam-6847	207	13	c	c	X
ejpam-6847	207	14	-	-	PUNCT
ejpam-6847	207	15	s	s	PROPN
ejpam-6847	207	16	-	-	PUNCT
ejpam-6847	207	17	mt	mt	NOUN
ejpam-6847	207	18	s	s	PROPN
ejpam-6847	207	19	,	,	PUNCT
ejpam-6847	207	20	where	where	SCONJ
ejpam-6847	207	21	x	x	PUNCT
ejpam-6847	207	22	6=	6=	ADP
ejpam-6847	207	23	∅.	∅.	ADP
ejpam-6847	207	24	a	a	DET
ejpam-6847	207	25	mapping	mapping	NOUN
ejpam-6847	207	26	t	t	NOUN
ejpam-6847	207	27	:	:	PUNCT
ejpam-6847	207	28	x	x	X
ejpam-6847	207	29	→	→	PUNCT
ejpam-6847	207	30	x	x	X
ejpam-6847	207	31	is	be	AUX
ejpam-6847	207	32	said	say	VERB
ejpam-6847	207	33	to	to	PART
ejpam-6847	207	34	be	be	AUX
ejpam-6847	207	35	an	an	DET
ejpam-6847	207	36	(	(	PUNCT
ejpam-6847	207	37	αs	αs	ADJ
ejpam-6847	207	38	-	-	PUNCT
ejpam-6847	207	39	f)-contraction	f)-contraction	NOUN
ejpam-6847	207	40	mapping	mapping	NOUN
ejpam-6847	207	41	,	,	PUNCT
ejpam-6847	207	42	if	if	SCONJ
ejpam-6847	207	43	there	there	PRON
ejpam-6847	207	44	exists	exist	VERB
ejpam-6847	207	45	a	a	DET
ejpam-6847	207	46	function	function	NOUN
ejpam-6847	207	47	αs	αs	INTJ
ejpam-6847	207	48	:	:	PUNCT
ejpam-6847	207	49	x	x	SYM
ejpam-6847	207	50	3	3	X
ejpam-6847	207	51	→	→	SYM
ejpam-6847	207	52	[	[	X
ejpam-6847	207	53	0,+∞	0,+∞	NUM
ejpam-6847	207	54	)	)	PUNCT
ejpam-6847	208	1	,	,	PUNCT
ejpam-6847	208	2	f	f	PROPN
ejpam-6847	208	3	∈	∈	PROPN
ejpam-6847	208	4	f	f	PROPN
ejpam-6847	208	5	,	,	PUNCT
ejpam-6847	208	6	and	and	CCONJ
ejpam-6847	208	7	a	a	DET
ejpam-6847	208	8	constant	constant	ADJ
ejpam-6847	208	9	τ	τ	X
ejpam-6847	208	10	>	>	X
ejpam-6847	208	11	0	0	NUM
ejpam-6847	208	12	such	such	ADJ
ejpam-6847	208	13	that	that	SCONJ
ejpam-6847	208	14	the	the	DET
ejpam-6847	208	15	following	follow	VERB
ejpam-6847	208	16	inequality	inequality	NOUN
ejpam-6847	208	17	holds	hold	VERB
ejpam-6847	208	18	:	:	PUNCT
ejpam-6847	208	19	τ	τ	PROPN
ejpam-6847	208	20	+	+	CCONJ
ejpam-6847	208	21	αs(x	αs(x	NUM
ejpam-6847	208	22	,	,	PUNCT
ejpam-6847	208	23	y	y	PROPN
ejpam-6847	208	24	,	,	PUNCT
ejpam-6847	208	25	z)f	z)f	X
ejpam-6847	208	26	(	(	PUNCT
ejpam-6847	208	27	s(tx	s(tx	X
ejpam-6847	208	28	,	,	PUNCT
ejpam-6847	208	29	ty	ty	INTJ
ejpam-6847	208	30	,	,	PUNCT
ejpam-6847	208	31	tz	tz	NOUN
ejpam-6847	208	32	)	)	PUNCT
ejpam-6847	208	33	)	)	PUNCT
ejpam-6847	209	1	≤	≤	NUM
ejpam-6847	209	2	f	f	X
ejpam-6847	209	3	(	(	PUNCT
ejpam-6847	209	4	s(x	s(x	PROPN
ejpam-6847	209	5	,	,	PUNCT
ejpam-6847	209	6	y	y	PROPN
ejpam-6847	209	7	,	,	PUNCT
ejpam-6847	209	8	z	z	NOUN
ejpam-6847	209	9	)	)	PUNCT
ejpam-6847	209	10	)	)	PUNCT
ejpam-6847	209	11	,	,	PUNCT
ejpam-6847	209	12	for	for	ADP
ejpam-6847	209	13	x	x	SYM
ejpam-6847	209	14	,	,	PUNCT
ejpam-6847	209	15	y	y	PROPN
ejpam-6847	209	16	,	,	PUNCT
ejpam-6847	209	17	z	z	PROPN
ejpam-6847	209	18	∈	∈	PROPN
ejpam-6847	209	19	x	x	X
ejpam-6847	209	20	,	,	PUNCT
ejpam-6847	209	21	with	with	ADP
ejpam-6847	209	22	s(tx	s(tx	PROPN
ejpam-6847	209	23	,	,	PUNCT
ejpam-6847	209	24	ty	ty	INTJ
ejpam-6847	209	25	,	,	PUNCT
ejpam-6847	209	26	tz	tz	PROPN
ejpam-6847	209	27	)	)	PUNCT
ejpam-6847	209	28	>	>	X
ejpam-6847	209	29	0	0	X
ejpam-6847	209	30	.	.	PUNCT
ejpam-6847	210	1	we	we	PRON
ejpam-6847	210	2	now	now	ADV
ejpam-6847	210	3	introduce	introduce	VERB
ejpam-6847	210	4	our	our	PRON
ejpam-6847	210	5	new	new	ADJ
ejpam-6847	210	6	(	(	PUNCT
ejpam-6847	210	7	αs	αs	PROPN
ejpam-6847	210	8	,	,	PUNCT
ejpam-6847	210	9	νs	νs	NOUN
ejpam-6847	210	10	,	,	PUNCT
ejpam-6847	210	11	(	(	PUNCT
ejpam-6847	210	12	q	q	X
ejpam-6847	210	13	,	,	PUNCT
ejpam-6847	210	14	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	210	15	mapping	mapping	NOUN
ejpam-6847	210	16	on	on	ADP
ejpam-6847	210	17	t	t	PROPN
ejpam-6847	210	18	c	c	PROPN
ejpam-6847	210	19	-	-	PUNCT
ejpam-6847	210	20	s	s	PROPN
ejpam-6847	210	21	-	-	PUNCT
ejpam-6847	210	22	mt	mt	NOUN
ejpam-6847	210	23	s	s	PROPN
ejpam-6847	210	24	,	,	PUNCT
ejpam-6847	210	25	detailed	detail	VERB
ejpam-6847	210	26	as	as	SCONJ
ejpam-6847	210	27	follows	follow	VERB
ejpam-6847	210	28	.	.	PUNCT
ejpam-6847	211	1	f.	f.	PROPN
ejpam-6847	211	2	m.	m.	PROPN
ejpam-6847	211	3	azmi	azmi	PROPN
ejpam-6847	211	4	,	,	PUNCT
ejpam-6847	211	5	a.	a.	PROPN
ejpam-6847	211	6	h.	h.	PROPN
ejpam-6847	211	7	ansari	ansari	PROPN
ejpam-6847	211	8	,	,	PUNCT
ejpam-6847	211	9	s.	s.	PROPN
ejpam-6847	211	10	h.	h.	PROPN
ejpam-6847	211	11	j.	j.	PROPN
ejpam-6847	211	12	petroudi	petroudi	PROPN
ejpam-6847	211	13	/	/	SYM
ejpam-6847	211	14	eur	eur	PROPN
ejpam-6847	211	15	.	.	PUNCT
ejpam-6847	212	1	j.	j.	PROPN
ejpam-6847	212	2	pure	pure	PROPN
ejpam-6847	212	3	appl	appl	PROPN
ejpam-6847	212	4	.	.	PROPN
ejpam-6847	212	5	math	math	PROPN
ejpam-6847	212	6	,	,	PUNCT
ejpam-6847	212	7	18	18	NUM
ejpam-6847	212	8	(	(	PUNCT
ejpam-6847	212	9	4	4	NUM
ejpam-6847	212	10	)	)	PUNCT
ejpam-6847	212	11	(	(	PUNCT
ejpam-6847	212	12	2025	2025	NUM
ejpam-6847	212	13	)	)	PUNCT
ejpam-6847	212	14	,	,	PUNCT
ejpam-6847	212	15	6847	6847	NUM
ejpam-6847	212	16	9	9	NUM
ejpam-6847	212	17	of	of	ADP
ejpam-6847	212	18	26	26	NUM
ejpam-6847	212	19	definition	definition	NOUN
ejpam-6847	212	20	17	17	NUM
ejpam-6847	212	21	.	.	PUNCT
ejpam-6847	212	22	assume	assume	VERB
ejpam-6847	212	23	that	that	SCONJ
ejpam-6847	212	24	(	(	PUNCT
ejpam-6847	212	25	x	x	X
ejpam-6847	212	26	,	,	PUNCT
ejpam-6847	212	27	s	s	PART
ejpam-6847	212	28	)	)	PUNCT
ejpam-6847	212	29	is	be	AUX
ejpam-6847	212	30	a	a	DET
ejpam-6847	212	31	t	t	NOUN
ejpam-6847	212	32	c	c	X
ejpam-6847	212	33	-	-	PUNCT
ejpam-6847	212	34	s	s	PROPN
ejpam-6847	212	35	-	-	PUNCT
ejpam-6847	212	36	mt	mt	NOUN
ejpam-6847	212	37	s	s	PROPN
ejpam-6847	212	38	,	,	PUNCT
ejpam-6847	212	39	where	where	SCONJ
ejpam-6847	212	40	x	x	PUNCT
ejpam-6847	212	41	6=	6=	ADP
ejpam-6847	212	42	∅	∅	NOUN
ejpam-6847	212	43	,	,	PUNCT
ejpam-6847	212	44	and	and	CCONJ
ejpam-6847	212	45	let	let	VERB
ejpam-6847	212	46	the	the	DET
ejpam-6847	212	47	pair	pair	NOUN
ejpam-6847	212	48	(	(	PUNCT
ejpam-6847	212	49	q	q	NOUN
ejpam-6847	212	50	,	,	PUNCT
ejpam-6847	212	51	h	h	NOUN
ejpam-6847	212	52	)	)	PUNCT
ejpam-6847	212	53	be	be	VERB
ejpam-6847	212	54	an	an	DET
ejpam-6847	212	55	upper	upper	ADJ
ejpam-6847	212	56	class	class	NOUN
ejpam-6847	212	57	of	of	ADP
ejpam-6847	212	58	type	type	NOUN
ejpam-6847	212	59	i.	i.	PROPN
ejpam-6847	212	60	a	a	DET
ejpam-6847	212	61	mapping	mapping	NOUN
ejpam-6847	212	62	t	t	NOUN
ejpam-6847	212	63	:	:	PUNCT
ejpam-6847	212	64	x	x	X
ejpam-6847	212	65	→	→	PUNCT
ejpam-6847	212	66	x	x	X
ejpam-6847	212	67	is	be	AUX
ejpam-6847	212	68	said	say	VERB
ejpam-6847	212	69	to	to	PART
ejpam-6847	212	70	be	be	AUX
ejpam-6847	212	71	an	an	DET
ejpam-6847	212	72	(	(	PUNCT
ejpam-6847	212	73	αs	αs	PROPN
ejpam-6847	212	74	,	,	PUNCT
ejpam-6847	212	75	νs	νs	NOUN
ejpam-6847	212	76	,	,	PUNCT
ejpam-6847	212	77	(	(	PUNCT
ejpam-6847	212	78	q	q	X
ejpam-6847	212	79	,	,	PUNCT
ejpam-6847	212	80	h	h	NOUN
ejpam-6847	212	81	)	)	PUNCT
ejpam-6847	212	82	−	−	PROPN
ejpam-6847	212	83	f)−contraction	f)−contraction	NOUN
ejpam-6847	212	84	mapping	mapping	NOUN
ejpam-6847	212	85	,	,	PUNCT
ejpam-6847	212	86	if	if	SCONJ
ejpam-6847	212	87	there	there	PRON
ejpam-6847	212	88	exist	exist	VERB
ejpam-6847	212	89	functions	function	NOUN
ejpam-6847	213	1	αs	αs	X
ejpam-6847	213	2	:	:	PUNCT
ejpam-6847	213	3	x3	x3	VERB
ejpam-6847	213	4	→	→	SYM
ejpam-6847	214	1	[	[	X
ejpam-6847	214	2	0,+∞	0,+∞	NUM
ejpam-6847	214	3	)	)	PUNCT
ejpam-6847	214	4	and	and	CCONJ
ejpam-6847	214	5	νs	νs	PRON
ejpam-6847	214	6	:	:	PUNCT
ejpam-6847	214	7	x3	x3	VERB
ejpam-6847	214	8	→	→	SYM
ejpam-6847	215	1	[	[	X
ejpam-6847	215	2	0,+∞	0,+∞	NUM
ejpam-6847	215	3	)	)	PUNCT
ejpam-6847	215	4	,	,	PUNCT
ejpam-6847	215	5	as	as	ADP
ejpam-6847	215	6	in	in	ADP
ejpam-6847	215	7	definitions	definition	NOUN
ejpam-6847	215	8	8	8	NUM
ejpam-6847	215	9	and	and	CCONJ
ejpam-6847	215	10	9	9	NUM
ejpam-6847	215	11	,	,	PUNCT
ejpam-6847	215	12	with	with	ADP
ejpam-6847	215	13	f	f	PROPN
ejpam-6847	215	14	∈	∈	PROPN
ejpam-6847	215	15	f	f	PROPN
ejpam-6847	215	16	,	,	PUNCT
ejpam-6847	215	17	and	and	CCONJ
ejpam-6847	215	18	some	some	DET
ejpam-6847	215	19	constant	constant	ADJ
ejpam-6847	215	20	τ	τ	X
ejpam-6847	215	21	>	>	X
ejpam-6847	215	22	0	0	PROPN
ejpam-6847	215	23	,	,	PUNCT
ejpam-6847	215	24	such	such	ADJ
ejpam-6847	215	25	that	that	SCONJ
ejpam-6847	215	26	subsequent	subsequent	ADJ
ejpam-6847	215	27	inequality	inequality	NOUN
ejpam-6847	215	28	holds	hold	VERB
ejpam-6847	215	29	:	:	PUNCT
ejpam-6847	215	30	h	h	NOUN
ejpam-6847	215	31	(	(	PUNCT
ejpam-6847	215	32	αs(x	αs(x	PROPN
ejpam-6847	215	33	,	,	PUNCT
ejpam-6847	215	34	y	y	PROPN
ejpam-6847	215	35	,	,	PUNCT
ejpam-6847	215	36	z	z	PROPN
ejpam-6847	215	37	)	)	PUNCT
ejpam-6847	215	38	,	,	PUNCT
ejpam-6847	215	39	τ	τ	PROPN
ejpam-6847	216	1	+	+	NUM
ejpam-6847	216	2	f	f	X
ejpam-6847	216	3	(	(	PUNCT
ejpam-6847	216	4	s(tx	s(tx	PROPN
ejpam-6847	216	5	,	,	PUNCT
ejpam-6847	216	6	ty	ty	INTJ
ejpam-6847	216	7	,	,	PUNCT
ejpam-6847	216	8	tz	tz	PROPN
ejpam-6847	216	9	)	)	PUNCT
ejpam-6847	216	10	)	)	PUNCT
ejpam-6847	216	11	≤	≤	NUM
ejpam-6847	216	12	q	q	X
ejpam-6847	216	13	(	(	PUNCT
ejpam-6847	216	14	νs(x	νs(x	PROPN
ejpam-6847	216	15	,	,	PUNCT
ejpam-6847	216	16	y	y	PROPN
ejpam-6847	216	17	,	,	PUNCT
ejpam-6847	216	18	z	z	NOUN
ejpam-6847	216	19	)	)	PUNCT
ejpam-6847	216	20	,	,	PUNCT
ejpam-6847	216	21	f	f	PROPN
ejpam-6847	216	22	(	(	PUNCT
ejpam-6847	216	23	s(x	s(x	PROPN
ejpam-6847	216	24	,	,	PUNCT
ejpam-6847	216	25	y	y	PROPN
ejpam-6847	216	26	,	,	PUNCT
ejpam-6847	216	27	z	z	NOUN
ejpam-6847	216	28	)	)	PUNCT
ejpam-6847	216	29	)	)	PUNCT
ejpam-6847	216	30	)	)	PUNCT
ejpam-6847	216	31	,	,	PUNCT
ejpam-6847	216	32	(	(	PUNCT
ejpam-6847	216	33	4	4	X
ejpam-6847	216	34	)	)	PUNCT
ejpam-6847	216	35	for	for	ADP
ejpam-6847	216	36	x	x	PROPN
ejpam-6847	216	37	,	,	PUNCT
ejpam-6847	216	38	y	y	PROPN
ejpam-6847	216	39	,	,	PUNCT
ejpam-6847	216	40	z	z	PROPN
ejpam-6847	216	41	∈	∈	PROPN
ejpam-6847	216	42	x	x	X
ejpam-6847	216	43	,	,	PUNCT
ejpam-6847	216	44	with	with	ADP
ejpam-6847	216	45	s(tx	s(tx	PROPN
ejpam-6847	216	46	,	,	PUNCT
ejpam-6847	216	47	ty	ty	INTJ
ejpam-6847	216	48	,	,	PUNCT
ejpam-6847	216	49	tz	tz	PROPN
ejpam-6847	216	50	)	)	PUNCT
ejpam-6847	216	51	>	>	X
ejpam-6847	216	52	0	0	PUNCT
ejpam-6847	216	53	.	.	PUNCT
ejpam-6847	217	1	we	we	PRON
ejpam-6847	217	2	present	present	VERB
ejpam-6847	217	3	our	our	PRON
ejpam-6847	217	4	first	first	ADJ
ejpam-6847	217	5	main	main	ADJ
ejpam-6847	217	6	result	result	NOUN
ejpam-6847	217	7	.	.	PUNCT
ejpam-6847	218	1	theorem	theorem	NOUN
ejpam-6847	218	2	1	1	X
ejpam-6847	218	3	.	.	PUNCT
ejpam-6847	219	1	let	let	AUX
ejpam-6847	219	2	(	(	PUNCT
ejpam-6847	219	3	x	x	NOUN
ejpam-6847	219	4	,	,	PUNCT
ejpam-6847	219	5	s	s	PART
ejpam-6847	219	6	)	)	PUNCT
ejpam-6847	219	7	be	be	AUX
ejpam-6847	219	8	a	a	DET
ejpam-6847	219	9	complete	complete	ADJ
ejpam-6847	219	10	t	t	NOUN
ejpam-6847	219	11	c	c	X
ejpam-6847	219	12	-	-	PUNCT
ejpam-6847	219	13	s	s	PROPN
ejpam-6847	219	14	-	-	PUNCT
ejpam-6847	219	15	mt	mt	NOUN
ejpam-6847	219	16	s	s	PROPN
ejpam-6847	219	17	,	,	PUNCT
ejpam-6847	219	18	where	where	SCONJ
ejpam-6847	219	19	x	x	PUNCT
ejpam-6847	220	1	6=	6=	AUX
ejpam-6847	220	2	∅.	∅.	NOUN
ejpam-6847	220	3	let	let	VERB
ejpam-6847	220	4	the	the	DET
ejpam-6847	220	5	pair	pair	NOUN
ejpam-6847	220	6	(	(	PUNCT
ejpam-6847	220	7	q	q	NOUN
ejpam-6847	220	8	,	,	PUNCT
ejpam-6847	220	9	h	h	NOUN
ejpam-6847	220	10	)	)	PUNCT
ejpam-6847	220	11	be	be	VERB
ejpam-6847	220	12	an	an	DET
ejpam-6847	220	13	upper	upper	ADJ
ejpam-6847	220	14	class	class	NOUN
ejpam-6847	220	15	of	of	ADP
ejpam-6847	220	16	type	type	NOUN
ejpam-6847	220	17	i	i	PRON
ejpam-6847	220	18	and	and	CCONJ
ejpam-6847	220	19	let	let	VERB
ejpam-6847	220	20	t	t	NOUN
ejpam-6847	220	21	:	:	PUNCT
ejpam-6847	220	22	x	x	X
ejpam-6847	220	23	→	→	PUNCT
ejpam-6847	220	24	x	x	X
ejpam-6847	220	25	be	be	AUX
ejpam-6847	220	26	(	(	PUNCT
ejpam-6847	220	27	αs	αs	PROPN
ejpam-6847	220	28	,	,	PUNCT
ejpam-6847	220	29	νs	νs	NOUN
ejpam-6847	220	30	,	,	PUNCT
ejpam-6847	220	31	(	(	PUNCT
ejpam-6847	220	32	q	q	X
ejpam-6847	220	33	,	,	PUNCT
ejpam-6847	220	34	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	220	35	mapping	mapping	NOUN
ejpam-6847	220	36	.	.	PUNCT
ejpam-6847	221	1	assume	assume	VERB
ejpam-6847	221	2	the	the	DET
ejpam-6847	221	3	following	follow	VERB
ejpam-6847	221	4	conditions	condition	NOUN
ejpam-6847	221	5	hold	hold	VERB
ejpam-6847	221	6	:	:	PUNCT
ejpam-6847	221	7	(	(	PUNCT
ejpam-6847	221	8	1	1	X
ejpam-6847	221	9	)	)	PUNCT
ejpam-6847	221	10	t	t	PROPN
ejpam-6847	221	11	is	be	AUX
ejpam-6847	221	12	αs	αs	ADJ
ejpam-6847	221	13	-	-	ADJ
ejpam-6847	221	14	admissible	admissible	ADJ
ejpam-6847	221	15	and	and	CCONJ
ejpam-6847	221	16	νs	νs	NOUN
ejpam-6847	221	17	-	-	PUNCT
ejpam-6847	221	18	subadmissible	subadmissible	ADJ
ejpam-6847	221	19	mapping	mapping	NOUN
ejpam-6847	221	20	.	.	PUNCT
ejpam-6847	222	1	(	(	PUNCT
ejpam-6847	222	2	2	2	X
ejpam-6847	222	3	)	)	PUNCT
ejpam-6847	222	4	there	there	PRON
ejpam-6847	222	5	is	be	VERB
ejpam-6847	222	6	x0	x0	PROPN
ejpam-6847	222	7	∈	∈	PROPN
ejpam-6847	222	8	x	x	NOUN
ejpam-6847	222	9	,	,	PUNCT
ejpam-6847	222	10	such	such	ADJ
ejpam-6847	222	11	that	that	DET
ejpam-6847	222	12	αs(x0	αs(x0	NOUN
ejpam-6847	222	13	,	,	PUNCT
ejpam-6847	222	14	x0	x0	PROPN
ejpam-6847	222	15	,	,	PUNCT
ejpam-6847	222	16	tx0	tx0	PROPN
ejpam-6847	222	17	)	)	PUNCT
ejpam-6847	222	18	≥	≥	NOUN
ejpam-6847	222	19	1	1	NUM
ejpam-6847	222	20	,	,	PUNCT
ejpam-6847	222	21	νs(x0	νs(x0	PROPN
ejpam-6847	222	22	,	,	PUNCT
ejpam-6847	222	23	x0	x0	PROPN
ejpam-6847	222	24	,	,	PUNCT
ejpam-6847	222	25	tx0	tx0	NOUN
ejpam-6847	222	26	)	)	PUNCT
ejpam-6847	222	27	≤	≤	NOUN
ejpam-6847	222	28	1	1	NUM
ejpam-6847	222	29	.	.	PUNCT
ejpam-6847	223	1	(	(	PUNCT
ejpam-6847	223	2	3	3	X
ejpam-6847	223	3	)	)	PUNCT
ejpam-6847	223	4	for	for	ADP
ejpam-6847	223	5	x0	x0	PROPN
ejpam-6847	223	6	∈	∈	PROPN
ejpam-6847	223	7	x	x	PRON
ejpam-6847	223	8	,	,	PUNCT
ejpam-6847	223	9	the	the	DET
ejpam-6847	223	10	sequence	sequence	NOUN
ejpam-6847	223	11	{	{	PUNCT
ejpam-6847	223	12	xn	xn	NUM
ejpam-6847	223	13	}	}	PUNCT
ejpam-6847	223	14	,	,	PUNCT
ejpam-6847	223	15	is	be	AUX
ejpam-6847	223	16	defined	define	VERB
ejpam-6847	223	17	by	by	ADP
ejpam-6847	223	18	xn	xn	PROPN
ejpam-6847	223	19	=	=	SYM
ejpam-6847	223	20	tnx0	tnx0	PROPN
ejpam-6847	223	21	,	,	PUNCT
ejpam-6847	223	22	and	and	CCONJ
ejpam-6847	223	23	the	the	DET
ejpam-6847	223	24	following	follow	VERB
ejpam-6847	223	25	inequality	inequality	NOUN
ejpam-6847	223	26	holds	hold	VERB
ejpam-6847	223	27	:	:	PUNCT
ejpam-6847	223	28	sup	sup	PROPN
ejpam-6847	223	29	m≥1	m≥1	PROPN
ejpam-6847	223	30	lim	lim	PROPN
ejpam-6847	223	31	n→+∞	n→+∞	PROPN
ejpam-6847	223	32	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	223	33	,	,	PUNCT
ejpam-6847	223	34	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	223	35	,	,	PUNCT
ejpam-6847	223	36	xn+2	xn+2	NUM
ejpam-6847	223	37	)	)	PUNCT
ejpam-6847	224	1	+	+	CCONJ
ejpam-6847	224	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	224	3	,	,	PUNCT
ejpam-6847	224	4	xn+2	xn+2	NUM
ejpam-6847	224	5	)	)	PUNCT
ejpam-6847	224	6	]	]	PUNCT
ejpam-6847	225	1	[	[	X
ejpam-6847	225	2	β(xn	β(xn	NOUN
ejpam-6847	225	3	,	,	PUNCT
ejpam-6847	225	4	xn+1	xn+1	NUM
ejpam-6847	225	5	)	)	PUNCT
ejpam-6847	225	6	+	+	CCONJ
ejpam-6847	225	7	µ(xn	µ(xn	PROPN
ejpam-6847	225	8	,	,	PUNCT
ejpam-6847	225	9	xn+1	xn+1	NUM
ejpam-6847	225	10	)	)	PUNCT
ejpam-6847	225	11	]	]	PUNCT
ejpam-6847	225	12	<	<	X
ejpam-6847	225	13	1	1	X
ejpam-6847	225	14	.	.	PUNCT
ejpam-6847	225	15	(	(	PUNCT
ejpam-6847	225	16	5	5	NUM
ejpam-6847	225	17	)	)	PUNCT
ejpam-6847	225	18	for	for	SCONJ
ejpam-6847	225	19	every	every	DET
ejpam-6847	225	20	x	x	SYM
ejpam-6847	225	21	∈	∈	PROPN
ejpam-6847	225	22	x	x	NOUN
ejpam-6847	225	23	,	,	PUNCT
ejpam-6847	225	24	the	the	DET
ejpam-6847	225	25	following	follow	VERB
ejpam-6847	225	26	limits	limit	NOUN
ejpam-6847	225	27	exist	exist	VERB
ejpam-6847	225	28	and	and	CCONJ
ejpam-6847	225	29	are	be	AUX
ejpam-6847	225	30	finite	finite	ADJ
ejpam-6847	225	31	;	;	PUNCT
ejpam-6847	225	32	lim	lim	PROPN
ejpam-6847	225	33	n→+∞	n→+∞	PROPN
ejpam-6847	225	34	β(x	β(x	PROPN
ejpam-6847	225	35	,	,	PUNCT
ejpam-6847	225	36	xn	xn	PROPN
ejpam-6847	225	37	)	)	PUNCT
ejpam-6847	225	38	,	,	PUNCT
ejpam-6847	225	39	lim	lim	PROPN
ejpam-6847	225	40	n→+∞	n→+∞	VERB
ejpam-6847	225	41	µ(xn	µ(xn	PROPN
ejpam-6847	225	42	,	,	PUNCT
ejpam-6847	225	43	x	x	NOUN
ejpam-6847	225	44	)	)	PUNCT
ejpam-6847	225	45	and	and	CCONJ
ejpam-6847	225	46	lim	lim	PROPN
ejpam-6847	225	47	n→+∞	n→+∞	VERB
ejpam-6847	225	48	γ(xn	γ(xn	PROPN
ejpam-6847	225	49	,	,	PUNCT
ejpam-6847	225	50	x	x	NOUN
ejpam-6847	225	51	)	)	PUNCT
ejpam-6847	225	52	.	.	PUNCT
ejpam-6847	226	1	(	(	PUNCT
ejpam-6847	226	2	6	6	NUM
ejpam-6847	226	3	)	)	PUNCT
ejpam-6847	226	4	then	then	ADV
ejpam-6847	226	5	,	,	PUNCT
ejpam-6847	226	6	t	t	PROPN
ejpam-6847	226	7	has	have	VERB
ejpam-6847	226	8	a	a	DET
ejpam-6847	226	9	fixed	fix	VERB
ejpam-6847	226	10	point	point	NOUN
ejpam-6847	226	11	.	.	PUNCT
ejpam-6847	227	1	for	for	ADP
ejpam-6847	227	2	the	the	DET
ejpam-6847	227	3	uniqueness	uniqueness	NOUN
ejpam-6847	227	4	of	of	ADP
ejpam-6847	227	5	the	the	DET
ejpam-6847	227	6	fixed	fix	VERB
ejpam-6847	227	7	point	point	NOUN
ejpam-6847	227	8	,	,	PUNCT
ejpam-6847	227	9	assume	assume	VERB
ejpam-6847	227	10	both	both	DET
ejpam-6847	227	11	u	u	NOUN
ejpam-6847	227	12	,	,	PUNCT
ejpam-6847	227	13	and	and	CCONJ
ejpam-6847	227	14	v	v	NOUN
ejpam-6847	227	15	are	be	AUX
ejpam-6847	227	16	fixed	fix	VERB
ejpam-6847	227	17	points	point	NOUN
ejpam-6847	227	18	such	such	ADJ
ejpam-6847	227	19	that	that	PRON
ejpam-6847	227	20	αs(u	αs(u	NUM
ejpam-6847	227	21	,	,	PUNCT
ejpam-6847	227	22	u	u	NOUN
ejpam-6847	227	23	,	,	PUNCT
ejpam-6847	227	24	v	v	NOUN
ejpam-6847	227	25	)	)	PUNCT
ejpam-6847	227	26	≥	≥	NOUN
ejpam-6847	227	27	1	1	NUM
ejpam-6847	227	28	,	,	PUNCT
ejpam-6847	227	29	and	and	CCONJ
ejpam-6847	227	30	νs(u	νs(u	NUM
ejpam-6847	227	31	,	,	PUNCT
ejpam-6847	227	32	u	u	NOUN
ejpam-6847	227	33	,	,	PUNCT
ejpam-6847	227	34	v	v	NOUN
ejpam-6847	227	35	)	)	PUNCT
ejpam-6847	227	36	≤	≤	NUM
ejpam-6847	227	37	1	1	NUM
ejpam-6847	227	38	,	,	PUNCT
ejpam-6847	227	39	then	then	ADV
ejpam-6847	227	40	t	t	PROPN
ejpam-6847	227	41	has	have	VERB
ejpam-6847	227	42	a	a	DET
ejpam-6847	227	43	unique	unique	ADJ
ejpam-6847	227	44	fixed	fix	VERB
ejpam-6847	227	45	point	point	NOUN
ejpam-6847	227	46	in	in	ADP
ejpam-6847	227	47	x.	x.	NOUN
ejpam-6847	227	48	proof	proof	NOUN
ejpam-6847	227	49	.	.	PUNCT
ejpam-6847	228	1	select	select	VERB
ejpam-6847	228	2	x0	x0	PROPN
ejpam-6847	228	3	∈	∈	PROPN
ejpam-6847	228	4	x	x	PUNCT
ejpam-6847	228	5	such	such	ADJ
ejpam-6847	228	6	that	that	SCONJ
ejpam-6847	228	7	,	,	PUNCT
ejpam-6847	228	8	αs(x0	αs(x0	PROPN
ejpam-6847	228	9	,	,	PUNCT
ejpam-6847	228	10	x0	x0	PROPN
ejpam-6847	228	11	,	,	PUNCT
ejpam-6847	228	12	tx0	tx0	PROPN
ejpam-6847	228	13	)	)	PUNCT
ejpam-6847	228	14	≥	≥	NOUN
ejpam-6847	228	15	1	1	NUM
ejpam-6847	228	16	,	,	PUNCT
ejpam-6847	228	17	and	and	CCONJ
ejpam-6847	228	18	νs(x0	νs(x0	PROPN
ejpam-6847	228	19	,	,	PUNCT
ejpam-6847	228	20	x0	x0	PROPN
ejpam-6847	228	21	,	,	PUNCT
ejpam-6847	228	22	tx0	tx0	NOUN
ejpam-6847	228	23	)	)	PUNCT
ejpam-6847	228	24	≤	≤	NUM
ejpam-6847	228	25	1	1	NUM
ejpam-6847	228	26	.	.	PUNCT
ejpam-6847	229	1	a	a	DET
ejpam-6847	229	2	sequence	sequence	NOUN
ejpam-6847	229	3	{	{	PUNCT
ejpam-6847	229	4	xn	xn	NOUN
ejpam-6847	229	5	}	}	PUNCT
ejpam-6847	229	6	is	be	AUX
ejpam-6847	229	7	formed	form	VERB
ejpam-6847	229	8	by	by	ADP
ejpam-6847	229	9	tx0	tx0	NOUN
ejpam-6847	229	10	=	=	SYM
ejpam-6847	229	11	x1	x1	PROPN
ejpam-6847	229	12	,	,	PUNCT
ejpam-6847	229	13	t	t	PROPN
ejpam-6847	229	14	2x0	2x0	NUM
ejpam-6847	229	15	=	=	SYM
ejpam-6847	229	16	tx1	tx1	NOUN
ejpam-6847	229	17	=	=	SYM
ejpam-6847	229	18	x2	x2	PROPN
ejpam-6847	229	19	.	.	PUNCT
ejpam-6847	230	1	therefore	therefore	ADV
ejpam-6847	230	2	,	,	PUNCT
ejpam-6847	230	3	for	for	ADP
ejpam-6847	230	4	any	any	DET
ejpam-6847	230	5	n	n	PRON
ejpam-6847	230	6	∈	∈	PROPN
ejpam-6847	230	7	n	n	CCONJ
ejpam-6847	230	8	,	,	PUNCT
ejpam-6847	230	9	we	we	PRON
ejpam-6847	230	10	have	have	VERB
ejpam-6847	230	11	tnx0	tnx0	NOUN
ejpam-6847	230	12	=	=	SYM
ejpam-6847	230	13	tn−1x1	tn−1x1	X
ejpam-6847	230	14	=	=	X
ejpam-6847	230	15	·	·	PUNCT
ejpam-6847	230	16	·	·	PUNCT
ejpam-6847	230	17	·	·	PUNCT
ejpam-6847	231	1	=	=	PUNCT
ejpam-6847	231	2	txn−1	txn−1	PROPN
ejpam-6847	231	3	=	=	PUNCT
ejpam-6847	232	1	xn	xn	PROPN
ejpam-6847	232	2	.	.	PUNCT
ejpam-6847	233	1	in	in	ADP
ejpam-6847	233	2	addition	addition	NOUN
ejpam-6847	233	3	,	,	PUNCT
ejpam-6847	233	4	tnx0	tnx0	PROPN
ejpam-6847	233	5	6=	6=	PROPN
ejpam-6847	233	6	tn+1x0	tn+1x0	PROPN
ejpam-6847	233	7	holds	hold	VERB
ejpam-6847	233	8	for	for	ADP
ejpam-6847	233	9	all	all	DET
ejpam-6847	233	10	n	n	PRON
ejpam-6847	233	11	≥	≥	NOUN
ejpam-6847	233	12	0	0	NUM
ejpam-6847	233	13	.	.	PUNCT
ejpam-6847	234	1	utilizing	utilize	VERB
ejpam-6847	234	2	the	the	DET
ejpam-6847	234	3	fact	fact	NOUN
ejpam-6847	234	4	that	that	SCONJ
ejpam-6847	234	5	t	t	PROPN
ejpam-6847	234	6	is	be	AUX
ejpam-6847	234	7	an	an	DET
ejpam-6847	234	8	(	(	PUNCT
ejpam-6847	234	9	αs	αs	ADJ
ejpam-6847	234	10	,	,	PUNCT
ejpam-6847	234	11	µs	µs	NOUN
ejpam-6847	234	12	,	,	PUNCT
ejpam-6847	234	13	(	(	PUNCT
ejpam-6847	234	14	q	q	X
ejpam-6847	234	15	,	,	PUNCT
ejpam-6847	234	16	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	234	17	mapping	mapping	NOUN
ejpam-6847	234	18	and	and	CCONJ
ejpam-6847	234	19	referring	refer	VERB
ejpam-6847	234	20	to	to	ADP
ejpam-6847	234	21	definition	definition	NOUN
ejpam-6847	234	22	12	12	NUM
ejpam-6847	234	23	,	,	PUNCT
ejpam-6847	234	24	we	we	PRON
ejpam-6847	234	25	can	can	AUX
ejpam-6847	234	26	derive	derive	VERB
ejpam-6847	234	27	:	:	PUNCT
ejpam-6847	235	1	h	h	NOUN
ejpam-6847	235	2	(	(	PUNCT
ejpam-6847	235	3	1	1	NUM
ejpam-6847	235	4	,	,	PUNCT
ejpam-6847	235	5	τ	τ	PROPN
ejpam-6847	236	1	+	+	NUM
ejpam-6847	236	2	f	f	X
ejpam-6847	236	3	(	(	PUNCT
ejpam-6847	236	4	s(xn	s(xn	PROPN
ejpam-6847	236	5	,	,	PUNCT
ejpam-6847	236	6	xn	xn	PROPN
ejpam-6847	236	7	,	,	PUNCT
ejpam-6847	236	8	xn+1	xn+1	NUM
ejpam-6847	236	9	)	)	PUNCT
ejpam-6847	236	10	)	)	PUNCT
ejpam-6847	236	11	)	)	PUNCT
ejpam-6847	237	1	=	=	PUNCT
ejpam-6847	237	2	h	h	NOUN
ejpam-6847	237	3	(	(	PUNCT
ejpam-6847	237	4	1	1	NUM
ejpam-6847	237	5	,	,	PUNCT
ejpam-6847	237	6	τ	τ	PROPN
ejpam-6847	238	1	+	+	NUM
ejpam-6847	238	2	f	f	X
ejpam-6847	238	3	(	(	PUNCT
ejpam-6847	238	4	s(t	s(t	PROPN
ejpam-6847	238	5	xn−1	xn−1	PROPN
ejpam-6847	238	6	,	,	PUNCT
ejpam-6847	238	7	t	t	PROPN
ejpam-6847	238	8	xn−1	xn−1	PROPN
ejpam-6847	238	9	,	,	PUNCT
ejpam-6847	238	10	t	t	PROPN
ejpam-6847	238	11	xn	xn	PROPN
ejpam-6847	238	12	)	)	PUNCT
ejpam-6847	238	13	)	)	PUNCT
ejpam-6847	238	14	)	)	PUNCT
ejpam-6847	238	15	.	.	PUNCT
ejpam-6847	239	1	≤	≤	NUM
ejpam-6847	239	2	h	h	NOUN
ejpam-6847	239	3	(	(	PUNCT
ejpam-6847	239	4	αs(xn−1	αs(xn−1	PROPN
ejpam-6847	239	5	,	,	PUNCT
ejpam-6847	239	6	xn−1	xn−1	PROPN
ejpam-6847	239	7	,	,	PUNCT
ejpam-6847	239	8	xn	xn	PROPN
ejpam-6847	239	9	)	)	PUNCT
ejpam-6847	239	10	,	,	PUNCT
ejpam-6847	239	11	τ	τ	PROPN
ejpam-6847	240	1	+	+	NUM
ejpam-6847	240	2	f	f	X
ejpam-6847	240	3	(	(	PUNCT
ejpam-6847	240	4	s(t	s(t	PROPN
ejpam-6847	240	5	xn−1	xn−1	PROPN
ejpam-6847	240	6	,	,	PUNCT
ejpam-6847	240	7	t	t	PROPN
ejpam-6847	240	8	xn−1	xn−1	PROPN
ejpam-6847	240	9	,	,	PUNCT
ejpam-6847	240	10	t	t	PROPN
ejpam-6847	240	11	xn	xn	PROPN
ejpam-6847	240	12	)	)	PUNCT
ejpam-6847	240	13	)	)	PUNCT
ejpam-6847	240	14	)	)	PUNCT
ejpam-6847	240	15	.	.	PUNCT
ejpam-6847	241	1	f.	f.	PROPN
ejpam-6847	241	2	m.	m.	PROPN
ejpam-6847	241	3	azmi	azmi	PROPN
ejpam-6847	241	4	,	,	PUNCT
ejpam-6847	241	5	a.	a.	PROPN
ejpam-6847	241	6	h.	h.	PROPN
ejpam-6847	241	7	ansari	ansari	PROPN
ejpam-6847	241	8	,	,	PUNCT
ejpam-6847	241	9	s.	s.	PROPN
ejpam-6847	241	10	h.	h.	PROPN
ejpam-6847	241	11	j.	j.	PROPN
ejpam-6847	241	12	petroudi	petroudi	PROPN
ejpam-6847	241	13	/	/	SYM
ejpam-6847	241	14	eur	eur	PROPN
ejpam-6847	241	15	.	.	PUNCT
ejpam-6847	242	1	j.	j.	PROPN
ejpam-6847	242	2	pure	pure	PROPN
ejpam-6847	242	3	appl	appl	PROPN
ejpam-6847	242	4	.	.	PROPN
ejpam-6847	242	5	math	math	PROPN
ejpam-6847	242	6	,	,	PUNCT
ejpam-6847	242	7	18	18	NUM
ejpam-6847	242	8	(	(	PUNCT
ejpam-6847	242	9	4	4	NUM
ejpam-6847	242	10	)	)	PUNCT
ejpam-6847	242	11	(	(	PUNCT
ejpam-6847	242	12	2025	2025	NUM
ejpam-6847	242	13	)	)	PUNCT
ejpam-6847	242	14	,	,	PUNCT
ejpam-6847	242	15	6847	6847	NUM
ejpam-6847	242	16	10	10	NUM
ejpam-6847	242	17	of	of	ADP
ejpam-6847	242	18	26	26	NUM
ejpam-6847	242	19	≤	≤	NUM
ejpam-6847	242	20	q	q	NOUN
ejpam-6847	242	21	(	(	PUNCT
ejpam-6847	242	22	νs(xn−1	νs(xn−1	PROPN
ejpam-6847	242	23	,	,	PUNCT
ejpam-6847	242	24	xn−1	xn−1	PROPN
ejpam-6847	242	25	,	,	PUNCT
ejpam-6847	242	26	xn	xn	PROPN
ejpam-6847	242	27	)	)	PUNCT
ejpam-6847	242	28	,	,	PUNCT
ejpam-6847	242	29	f	f	PROPN
ejpam-6847	242	30	(	(	PUNCT
ejpam-6847	242	31	s(xn−1	s(xn−1	PROPN
ejpam-6847	242	32	,	,	PUNCT
ejpam-6847	242	33	xn−1	xn−1	PROPN
ejpam-6847	242	34	,	,	PUNCT
ejpam-6847	242	35	xn	xn	PROPN
ejpam-6847	242	36	)	)	PUNCT
ejpam-6847	242	37	)	)	PUNCT
ejpam-6847	242	38	)	)	PUNCT
ejpam-6847	242	39	.	.	PUNCT
ejpam-6847	243	1	≤	≤	ADJ
ejpam-6847	244	1	q	q	NOUN
ejpam-6847	244	2	(	(	PUNCT
ejpam-6847	244	3	1	1	NUM
ejpam-6847	244	4	,	,	PUNCT
ejpam-6847	244	5	f	f	X
ejpam-6847	244	6	(	(	PUNCT
ejpam-6847	244	7	s(xn−1	s(xn−1	PROPN
ejpam-6847	244	8	,	,	PUNCT
ejpam-6847	244	9	xn−1	xn−1	PROPN
ejpam-6847	244	10	,	,	PUNCT
ejpam-6847	244	11	xn	xn	PROPN
ejpam-6847	244	12	)	)	PUNCT
ejpam-6847	244	13	)	)	PUNCT
ejpam-6847	244	14	)	)	PUNCT
ejpam-6847	244	15	.	.	PUNCT
ejpam-6847	245	1	as	as	SCONJ
ejpam-6847	245	2	the	the	DET
ejpam-6847	245	3	pair	pair	NOUN
ejpam-6847	245	4	(	(	PUNCT
ejpam-6847	245	5	q	q	NOUN
ejpam-6847	245	6	,	,	PUNCT
ejpam-6847	245	7	h	h	NOUN
ejpam-6847	245	8	)	)	PUNCT
ejpam-6847	245	9	is	be	AUX
ejpam-6847	245	10	an	an	DET
ejpam-6847	245	11	upper	upper	ADJ
ejpam-6847	245	12	class	class	NOUN
ejpam-6847	245	13	of	of	ADP
ejpam-6847	245	14	type	type	NOUN
ejpam-6847	245	15	i	i	PRON
ejpam-6847	245	16	,	,	PUNCT
ejpam-6847	245	17	hence	hence	ADV
ejpam-6847	245	18	we	we	PRON
ejpam-6847	245	19	have	have	VERB
ejpam-6847	245	20	τ	τ	PROPN
ejpam-6847	246	1	+	+	NUM
ejpam-6847	246	2	f	f	X
ejpam-6847	246	3	(	(	PUNCT
ejpam-6847	246	4	s(xn	s(xn	PROPN
ejpam-6847	246	5	,	,	PUNCT
ejpam-6847	246	6	xn	xn	PROPN
ejpam-6847	246	7	,	,	PUNCT
ejpam-6847	246	8	xn+1	xn+1	NUM
ejpam-6847	246	9	)	)	PUNCT
ejpam-6847	246	10	)	)	PUNCT
ejpam-6847	246	11	≤	≤	NUM
ejpam-6847	246	12	f	f	X
ejpam-6847	246	13	(	(	PUNCT
ejpam-6847	246	14	s(xn−1	s(xn−1	PROPN
ejpam-6847	246	15	,	,	PUNCT
ejpam-6847	246	16	xn−1	xn−1	PROPN
ejpam-6847	246	17	,	,	PUNCT
ejpam-6847	246	18	xn	xn	PROPN
ejpam-6847	246	19	)	)	PUNCT
ejpam-6847	246	20	)	)	PUNCT
ejpam-6847	246	21	,	,	PUNCT
ejpam-6847	246	22	which	which	PRON
ejpam-6847	246	23	implies	imply	VERB
ejpam-6847	246	24	f	f	PROPN
ejpam-6847	246	25	(	(	PUNCT
ejpam-6847	246	26	s(xn	s(xn	PROPN
ejpam-6847	246	27	,	,	PUNCT
ejpam-6847	246	28	xn	xn	PROPN
ejpam-6847	246	29	,	,	PUNCT
ejpam-6847	246	30	xn+1	xn+1	NUM
ejpam-6847	246	31	)	)	PUNCT
ejpam-6847	246	32	)	)	PUNCT
ejpam-6847	247	1	≤	≤	NUM
ejpam-6847	247	2	f	f	X
ejpam-6847	247	3	(	(	PUNCT
ejpam-6847	247	4	s(xn−1	s(xn−1	PROPN
ejpam-6847	247	5	,	,	PUNCT
ejpam-6847	247	6	xn−1	xn−1	PROPN
ejpam-6847	247	7	,	,	PUNCT
ejpam-6847	247	8	xn))−	xn))−	PROPN
ejpam-6847	247	9	τ	τ	X
ejpam-6847	247	10	.	.	PUNCT
ejpam-6847	247	11	(	(	PUNCT
ejpam-6847	247	12	7	7	X
ejpam-6847	247	13	)	)	PUNCT
ejpam-6847	247	14	≤	≤	NUM
ejpam-6847	247	15	f	f	X
ejpam-6847	247	16	(	(	PUNCT
ejpam-6847	247	17	s(xn−2	s(xn−2	PROPN
ejpam-6847	247	18	,	,	PUNCT
ejpam-6847	247	19	xn−2	xn−2	PROPN
ejpam-6847	247	20	,	,	PUNCT
ejpam-6847	247	21	xn−1))−	xn−1))−	NUM
ejpam-6847	247	22	2τ	2τ	NOUN
ejpam-6847	247	23	.	.	PUNCT
ejpam-6847	248	1	≤	≤	NUM
ejpam-6847	248	2	·	·	PUNCT
ejpam-6847	248	3	·	·	PUNCT
ejpam-6847	248	4	·	·	PUNCT
ejpam-6847	249	1	≤	≤	NUM
ejpam-6847	249	2	f	f	X
ejpam-6847	249	3	(	(	PUNCT
ejpam-6847	249	4	s(x0	s(x0	ADV
ejpam-6847	249	5	,	,	PUNCT
ejpam-6847	249	6	x0	x0	PROPN
ejpam-6847	249	7	,	,	PUNCT
ejpam-6847	249	8	x1))−	x1))−	PROPN
ejpam-6847	249	9	nτ	nτ	NOUN
ejpam-6847	249	10	.	.	PUNCT
ejpam-6847	250	1	letting	let	VERB
ejpam-6847	250	2	n→	n→	ADV
ejpam-6847	250	3	+	+	ADJ
ejpam-6847	250	4	∞	∞	NUM
ejpam-6847	250	5	in	in	ADP
ejpam-6847	250	6	equation	equation	NOUN
ejpam-6847	250	7	7	7	NUM
ejpam-6847	250	8	,	,	PUNCT
ejpam-6847	250	9	and	and	CCONJ
ejpam-6847	250	10	with	with	ADP
ejpam-6847	250	11	τ	τ	PROPN
ejpam-6847	250	12	>	>	X
ejpam-6847	250	13	0	0	PROPN
ejpam-6847	250	14	,	,	PUNCT
ejpam-6847	250	15	we	we	PRON
ejpam-6847	250	16	have	have	VERB
ejpam-6847	250	17	lim	lim	PROPN
ejpam-6847	250	18	n→+∞	n→+∞	PROPN
ejpam-6847	250	19	f	f	PROPN
ejpam-6847	250	20	(	(	PUNCT
ejpam-6847	250	21	s(xn	s(xn	PROPN
ejpam-6847	250	22	,	,	PUNCT
ejpam-6847	250	23	xn	xn	PROPN
ejpam-6847	250	24	,	,	PUNCT
ejpam-6847	250	25	xn+1	xn+1	NUM
ejpam-6847	250	26	)	)	PUNCT
ejpam-6847	250	27	)	)	PUNCT
ejpam-6847	251	1	=	=	SYM
ejpam-6847	251	2	−∞.	−∞.	NOUN
ejpam-6847	251	3	(	(	PUNCT
ejpam-6847	251	4	8)	8)	NUM
ejpam-6847	251	5	as	as	ADP
ejpam-6847	251	6	f	f	PROPN
ejpam-6847	251	7	∈	∈	PROPN
ejpam-6847	251	8	f	f	PROPN
ejpam-6847	251	9	,	,	PUNCT
ejpam-6847	251	10	utilizing	utilize	VERB
ejpam-6847	251	11	(	(	PUNCT
ejpam-6847	251	12	w2	w2	NOUN
ejpam-6847	251	13	)	)	PUNCT
ejpam-6847	251	14	of	of	ADP
ejpam-6847	251	15	definition	definition	NOUN
ejpam-6847	251	16	14	14	NUM
ejpam-6847	251	17	,	,	PUNCT
ejpam-6847	251	18	we	we	PRON
ejpam-6847	251	19	deduce	deduce	VERB
ejpam-6847	251	20	that	that	PRON
ejpam-6847	251	21	limn→+∞	limn→+∞	VERB
ejpam-6847	251	22	s(xn	s(xn	NOUN
ejpam-6847	251	23	,	,	PUNCT
ejpam-6847	251	24	xn	xn	PROPN
ejpam-6847	251	25	,	,	PUNCT
ejpam-6847	251	26	xn+1	xn+1	NUM
ejpam-6847	251	27	)	)	PUNCT
ejpam-6847	251	28	=	=	SYM
ejpam-6847	251	29	0	0	NUM
ejpam-6847	251	30	,	,	PUNCT
ejpam-6847	251	31	and	and	CCONJ
ejpam-6847	251	32	by	by	ADP
ejpam-6847	251	33	(	(	PUNCT
ejpam-6847	251	34	w3	w3	PROPN
ejpam-6847	251	35	)	)	PUNCT
ejpam-6847	251	36	,	,	PUNCT
ejpam-6847	251	37	there	there	PRON
ejpam-6847	251	38	exists	exist	VERB
ejpam-6847	251	39	k	k	PROPN
ejpam-6847	251	40	∈	∈	PROPN
ejpam-6847	251	41	(	(	PUNCT
ejpam-6847	251	42	0	0	NUM
ejpam-6847	251	43	,	,	PUNCT
ejpam-6847	251	44	1	1	NUM
ejpam-6847	251	45	)	)	PUNCT
ejpam-6847	251	46	such	such	ADJ
ejpam-6847	251	47	that	that	SCONJ
ejpam-6847	251	48	lim	lim	PROPN
ejpam-6847	251	49	n→+∞	n→+∞	PROPN
ejpam-6847	251	50	(	(	PUNCT
ejpam-6847	251	51	s(xn	s(xn	PROPN
ejpam-6847	251	52	,	,	PUNCT
ejpam-6847	251	53	xn	xn	PROPN
ejpam-6847	251	54	,	,	PUNCT
ejpam-6847	251	55	xn+1	xn+1	NUM
ejpam-6847	251	56	)	)	PUNCT
ejpam-6847	251	57	)	)	PUNCT
ejpam-6847	252	1	kf	kf	INTJ
ejpam-6847	252	2	(	(	PUNCT
ejpam-6847	252	3	(	(	PUNCT
ejpam-6847	252	4	s(xn	s(xn	X
ejpam-6847	252	5	,	,	PUNCT
ejpam-6847	252	6	xn	xn	PROPN
ejpam-6847	252	7	,	,	PUNCT
ejpam-6847	252	8	xn+1	xn+1	NUM
ejpam-6847	252	9	)	)	PUNCT
ejpam-6847	252	10	)	)	PUNCT
ejpam-6847	253	1	=	=	PUNCT
ejpam-6847	253	2	0	0	X
ejpam-6847	253	3	.	.	PUNCT
ejpam-6847	253	4	(	(	PUNCT
ejpam-6847	253	5	9	9	NUM
ejpam-6847	253	6	)	)	PUNCT
ejpam-6847	253	7	from	from	ADP
ejpam-6847	253	8	equation	equation	NOUN
ejpam-6847	253	9	7	7	NUM
ejpam-6847	253	10	,	,	PUNCT
ejpam-6847	253	11	we	we	PRON
ejpam-6847	253	12	obtain	obtain	VERB
ejpam-6847	253	13	f	f	X
ejpam-6847	253	14	(	(	PUNCT
ejpam-6847	253	15	s(xn	s(xn	PROPN
ejpam-6847	253	16	,	,	PUNCT
ejpam-6847	253	17	xn	xn	PROPN
ejpam-6847	253	18	,	,	PUNCT
ejpam-6847	253	19	xn+1))−	xn+1))−	PROPN
ejpam-6847	253	20	f	f	X
ejpam-6847	253	21	(	(	PUNCT
ejpam-6847	253	22	s(x0	s(x0	PROPN
ejpam-6847	253	23	,	,	PUNCT
ejpam-6847	253	24	x0	x0	PROPN
ejpam-6847	253	25	,	,	PUNCT
ejpam-6847	253	26	x1	x1	PROPN
ejpam-6847	253	27	)	)	PUNCT
ejpam-6847	253	28	)	)	PUNCT
ejpam-6847	253	29	≤	≤	PUNCT
ejpam-6847	254	1	−nτ	−nτ	NOUN
ejpam-6847	254	2	.	.	PUNCT
ejpam-6847	255	1	thus	thus	ADV
ejpam-6847	255	2	for	for	ADP
ejpam-6847	255	3	any	any	DET
ejpam-6847	255	4	n	n	CCONJ
ejpam-6847	255	5	,	,	PUNCT
ejpam-6847	255	6	we	we	PRON
ejpam-6847	255	7	have	have	VERB
ejpam-6847	255	8	(	(	PUNCT
ejpam-6847	255	9	s(xn	s(xn	X
ejpam-6847	255	10	,	,	PUNCT
ejpam-6847	255	11	xn	xn	PROPN
ejpam-6847	255	12	,	,	PUNCT
ejpam-6847	255	13	xn+1	xn+1	NUM
ejpam-6847	255	14	)	)	PUNCT
ejpam-6847	255	15	)	)	PUNCT
ejpam-6847	256	1	kf	kf	PROPN
ejpam-6847	256	2	(	(	PUNCT
ejpam-6847	256	3	s(xn	s(xn	PROPN
ejpam-6847	256	4	,	,	PUNCT
ejpam-6847	256	5	xn	xn	PROPN
ejpam-6847	256	6	,	,	PUNCT
ejpam-6847	256	7	xn+1)−	xn+1)−	PROPN
ejpam-6847	256	8	(	(	PUNCT
ejpam-6847	256	9	s(xn	s(xn	PROPN
ejpam-6847	256	10	,	,	PUNCT
ejpam-6847	256	11	xn	xn	PROPN
ejpam-6847	256	12	,	,	PUNCT
ejpam-6847	256	13	xn+1	xn+1	NUM
ejpam-6847	256	14	)	)	PUNCT
ejpam-6847	256	15	kf	kf	PROPN
ejpam-6847	256	16	(	(	PUNCT
ejpam-6847	256	17	s(x0	s(x0	PROPN
ejpam-6847	256	18	,	,	PUNCT
ejpam-6847	256	19	x0	x0	PROPN
ejpam-6847	256	20	,	,	PUNCT
ejpam-6847	256	21	x1	x1	PROPN
ejpam-6847	256	22	)	)	PUNCT
ejpam-6847	256	23	)	)	PUNCT
ejpam-6847	256	24	≤	≤	NUM
ejpam-6847	257	1	−nτ(s(xn	−nτ(s(xn	PROPN
ejpam-6847	257	2	,	,	PUNCT
ejpam-6847	257	3	xn	xn	PROPN
ejpam-6847	257	4	,	,	PUNCT
ejpam-6847	257	5	xn+1	xn+1	NUM
ejpam-6847	257	6	)	)	PUNCT
ejpam-6847	257	7	)	)	PUNCT
ejpam-6847	258	1	k	k	PROPN
ejpam-6847	258	2	≤	≤	ADV
ejpam-6847	258	3	0	0	NUM
ejpam-6847	258	4	.	.	PUNCT
ejpam-6847	259	1	(	(	PUNCT
ejpam-6847	259	2	10	10	NUM
ejpam-6847	259	3	)	)	PUNCT
ejpam-6847	259	4	as	as	ADP
ejpam-6847	259	5	n	n	NUM
ejpam-6847	259	6	approaches	approach	NOUN
ejpam-6847	259	7	infinity	infinity	NOUN
ejpam-6847	259	8	in	in	ADP
ejpam-6847	259	9	equation	equation	NOUN
ejpam-6847	259	10	10	10	NUM
ejpam-6847	259	11	,	,	PUNCT
ejpam-6847	259	12	we	we	PRON
ejpam-6847	259	13	find	find	VERB
ejpam-6847	259	14	that	that	SCONJ
ejpam-6847	259	15	lim	lim	PROPN
ejpam-6847	259	16	n→+∞	n→+∞	PROPN
ejpam-6847	259	17	n(s(xn	n(s(xn	PROPN
ejpam-6847	259	18	,	,	PUNCT
ejpam-6847	259	19	xn	xn	PROPN
ejpam-6847	259	20	,	,	PUNCT
ejpam-6847	259	21	xn+1	xn+1	NUM
ejpam-6847	259	22	)	)	PUNCT
ejpam-6847	259	23	)	)	PUNCT
ejpam-6847	260	1	k	k	X
ejpam-6847	260	2	=	=	PUNCT
ejpam-6847	260	3	0	0	PROPN
ejpam-6847	260	4	.	.	PUNCT
ejpam-6847	261	1	(	(	PUNCT
ejpam-6847	261	2	11	11	NUM
ejpam-6847	261	3	)	)	PUNCT
ejpam-6847	261	4	this	this	PRON
ejpam-6847	261	5	gives	give	VERB
ejpam-6847	261	6	,	,	PUNCT
ejpam-6847	261	7	limn→+∞	limn→+∞	VERB
ejpam-6847	261	8	n1	n1	NOUN
ejpam-6847	261	9	/	/	SYM
ejpam-6847	261	10	k(s(xn	k(s(xn	PROPN
ejpam-6847	261	11	,	,	PUNCT
ejpam-6847	261	12	xn	xn	PROPN
ejpam-6847	261	13	,	,	PUNCT
ejpam-6847	261	14	xn+1	xn+1	NUM
ejpam-6847	261	15	)	)	PUNCT
ejpam-6847	261	16	)	)	PUNCT
ejpam-6847	262	1	=	=	PUNCT
ejpam-6847	262	2	0	0	NUM
ejpam-6847	262	3	,	,	PUNCT
ejpam-6847	262	4	hence	hence	ADV
ejpam-6847	262	5	there	there	PRON
ejpam-6847	262	6	exists	exist	VERB
ejpam-6847	262	7	some	some	DET
ejpam-6847	262	8	n0	n0	PROPN
ejpam-6847	262	9	∈	∈	PROPN
ejpam-6847	262	10	n	n	CCONJ
ejpam-6847	262	11	,	,	PUNCT
ejpam-6847	262	12	such	such	ADJ
ejpam-6847	262	13	that	that	SCONJ
ejpam-6847	262	14	s(xn	s(xn	NOUN
ejpam-6847	262	15	,	,	PUNCT
ejpam-6847	262	16	xn	xn	PROPN
ejpam-6847	262	17	,	,	PUNCT
ejpam-6847	262	18	xn+1	xn+1	NUM
ejpam-6847	262	19	)	)	PUNCT
ejpam-6847	262	20	≤	≤	NOUN
ejpam-6847	262	21	1	1	NUM
ejpam-6847	262	22	n1	n1	NOUN
ejpam-6847	262	23	/	/	SYM
ejpam-6847	262	24	k	k	PROPN
ejpam-6847	262	25	,	,	PUNCT
ejpam-6847	262	26	for	for	ADP
ejpam-6847	262	27	alln	alln	PROPN
ejpam-6847	262	28	≥	≥	PROPN
ejpam-6847	262	29	n0	n0	PROPN
ejpam-6847	262	30	.	.	PUNCT
ejpam-6847	263	1	(	(	PUNCT
ejpam-6847	263	2	12	12	NUM
ejpam-6847	263	3	)	)	PUNCT
ejpam-6847	263	4	to	to	PART
ejpam-6847	263	5	show	show	VERB
ejpam-6847	263	6	that	that	SCONJ
ejpam-6847	263	7	the	the	DET
ejpam-6847	263	8	sequence	sequence	NOUN
ejpam-6847	263	9	{	{	PUNCT
ejpam-6847	263	10	xn	xn	PROPN
ejpam-6847	263	11	}	}	PUNCT
ejpam-6847	263	12	is	be	AUX
ejpam-6847	263	13	a	a	DET
ejpam-6847	263	14	cauchy	cauchy	ADJ
ejpam-6847	263	15	sequence	sequence	NOUN
ejpam-6847	263	16	,	,	PUNCT
ejpam-6847	263	17	we	we	PRON
ejpam-6847	263	18	consider	consider	VERB
ejpam-6847	263	19	any	any	DET
ejpam-6847	263	20	natural	natural	ADJ
ejpam-6847	263	21	numbers	number	NOUN
ejpam-6847	263	22	m	m	VERB
ejpam-6847	263	23	and	and	CCONJ
ejpam-6847	263	24	n	n	PRON
ejpam-6847	263	25	such	such	ADJ
ejpam-6847	263	26	that	that	SCONJ
ejpam-6847	263	27	n	n	NOUN
ejpam-6847	263	28	<	<	X
ejpam-6847	263	29	m.	m.	NOUN
ejpam-6847	263	30	we	we	PRON
ejpam-6847	263	31	find	find	VERB
ejpam-6847	263	32	that	that	SCONJ
ejpam-6847	263	33	:	:	PUNCT
ejpam-6847	263	34	s(xn	s(xn	NOUN
ejpam-6847	263	35	,	,	PUNCT
ejpam-6847	263	36	xn	xn	PROPN
ejpam-6847	263	37	,	,	PUNCT
ejpam-6847	263	38	xm	xm	NOUN
ejpam-6847	263	39	)	)	PUNCT
ejpam-6847	263	40	≤	≤	NOUN
ejpam-6847	263	41	β(xn	β(xn	NOUN
ejpam-6847	263	42	,	,	PUNCT
ejpam-6847	263	43	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	263	44	,	,	PUNCT
ejpam-6847	263	45	xn	xn	PROPN
ejpam-6847	263	46	,	,	PUNCT
ejpam-6847	263	47	xn+1	xn+1	NUM
ejpam-6847	263	48	)	)	PUNCT
ejpam-6847	264	1	+	+	CCONJ
ejpam-6847	264	2	µ(xn	µ(xn	PROPN
ejpam-6847	264	3	,	,	PUNCT
ejpam-6847	264	4	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	264	5	,	,	PUNCT
ejpam-6847	264	6	xn	xn	PROPN
ejpam-6847	264	7	,	,	PUNCT
ejpam-6847	264	8	xn+1	xn+1	NUM
ejpam-6847	264	9	)	)	PUNCT
ejpam-6847	264	10	f.	f.	PROPN
ejpam-6847	264	11	m.	m.	PROPN
ejpam-6847	264	12	azmi	azmi	PROPN
ejpam-6847	264	13	,	,	PUNCT
ejpam-6847	264	14	a.	a.	PROPN
ejpam-6847	264	15	h.	h.	PROPN
ejpam-6847	264	16	ansari	ansari	PROPN
ejpam-6847	264	17	,	,	PUNCT
ejpam-6847	264	18	s.	s.	PROPN
ejpam-6847	264	19	h.	h.	PROPN
ejpam-6847	264	20	j.	j.	PROPN
ejpam-6847	264	21	petroudi	petroudi	PROPN
ejpam-6847	264	22	/	/	SYM
ejpam-6847	264	23	eur	eur	PROPN
ejpam-6847	264	24	.	.	PUNCT
ejpam-6847	265	1	j.	j.	PROPN
ejpam-6847	265	2	pure	pure	PROPN
ejpam-6847	265	3	appl	appl	PROPN
ejpam-6847	265	4	.	.	PROPN
ejpam-6847	265	5	math	math	PROPN
ejpam-6847	265	6	,	,	PUNCT
ejpam-6847	265	7	18	18	NUM
ejpam-6847	265	8	(	(	PUNCT
ejpam-6847	265	9	4	4	NUM
ejpam-6847	265	10	)	)	PUNCT
ejpam-6847	265	11	(	(	PUNCT
ejpam-6847	265	12	2025	2025	NUM
ejpam-6847	265	13	)	)	PUNCT
ejpam-6847	265	14	,	,	PUNCT
ejpam-6847	265	15	6847	6847	NUM
ejpam-6847	265	16	11	11	NUM
ejpam-6847	265	17	of	of	ADP
ejpam-6847	265	18	26	26	NUM
ejpam-6847	265	19	+	+	CCONJ
ejpam-6847	265	20	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	265	21	,	,	PUNCT
ejpam-6847	265	22	xm)s(xn+1	xm)s(xn+1	PROPN
ejpam-6847	265	23	,	,	PUNCT
ejpam-6847	265	24	xn+1	xn+1	PROPN
ejpam-6847	265	25	,	,	PUNCT
ejpam-6847	265	26	xm	xm	PROPN
ejpam-6847	265	27	)	)	PUNCT
ejpam-6847	265	28	.	.	PUNCT
ejpam-6847	266	1	≤	≤	NOUN
ejpam-6847	266	2	β(xn	β(xn	NOUN
ejpam-6847	266	3	,	,	PUNCT
ejpam-6847	266	4	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	266	5	,	,	PUNCT
ejpam-6847	266	6	xn	xn	PROPN
ejpam-6847	266	7	,	,	PUNCT
ejpam-6847	266	8	xn+1	xn+1	NUM
ejpam-6847	266	9	)	)	PUNCT
ejpam-6847	267	1	+	+	CCONJ
ejpam-6847	267	2	µ(xn	µ(xn	PROPN
ejpam-6847	267	3	,	,	PUNCT
ejpam-6847	267	4	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	267	5	,	,	PUNCT
ejpam-6847	267	6	xn	xn	PROPN
ejpam-6847	267	7	,	,	PUNCT
ejpam-6847	267	8	xn+1	xn+1	NUM
ejpam-6847	267	9	)	)	PUNCT
ejpam-6847	267	10	+	+	X
ejpam-6847	267	11	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	267	12	,	,	PUNCT
ejpam-6847	267	13	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	267	14	,	,	PUNCT
ejpam-6847	267	15	xn+2)s(xn+1	xn+2)s(xn+1	PROPN
ejpam-6847	267	16	,	,	PUNCT
ejpam-6847	267	17	xn+1	xn+1	PROPN
ejpam-6847	267	18	,	,	PUNCT
ejpam-6847	267	19	xn+2	xn+2	NUM
ejpam-6847	267	20	)	)	PUNCT
ejpam-6847	267	21	+	+	PUNCT
ejpam-6847	267	22	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	267	23	,	,	PUNCT
ejpam-6847	267	24	xn+2)s(xn+1	xn+2)s(xn+1	PROPN
ejpam-6847	267	25	,	,	PUNCT
ejpam-6847	267	26	xn+1	xn+1	PROPN
ejpam-6847	267	27	,	,	PUNCT
ejpam-6847	267	28	xn+2	xn+2	NUM
ejpam-6847	267	29	)	)	PUNCT
ejpam-6847	267	30	+	+	CCONJ
ejpam-6847	267	31	γ(xn+2	γ(xn+2	NUM
ejpam-6847	267	32	,	,	PUNCT
ejpam-6847	267	33	xm)s(xn+2	xm)s(xn+2	PROPN
ejpam-6847	267	34	,	,	PUNCT
ejpam-6847	267	35	xn+2	xn+2	NUM
ejpam-6847	267	36	,	,	PUNCT
ejpam-6847	267	37	xm	xm	PROPN
ejpam-6847	267	38	)	)	PUNCT
ejpam-6847	267	39	]	]	PUNCT
ejpam-6847	267	40	.	.	PUNCT
ejpam-6847	268	1	≤	≤	NOUN
ejpam-6847	268	2	β(xn	β(xn	NOUN
ejpam-6847	268	3	,	,	PUNCT
ejpam-6847	268	4	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	268	5	,	,	PUNCT
ejpam-6847	268	6	xn	xn	PROPN
ejpam-6847	268	7	,	,	PUNCT
ejpam-6847	268	8	xn+1	xn+1	NUM
ejpam-6847	268	9	)	)	PUNCT
ejpam-6847	269	1	+	+	CCONJ
ejpam-6847	269	2	µ(xn	µ(xn	PROPN
ejpam-6847	269	3	,	,	PUNCT
ejpam-6847	269	4	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	269	5	,	,	PUNCT
ejpam-6847	269	6	xn	xn	PROPN
ejpam-6847	269	7	,	,	PUNCT
ejpam-6847	269	8	xn+1	xn+1	NUM
ejpam-6847	269	9	)	)	PUNCT
ejpam-6847	269	10	+	+	X
ejpam-6847	269	11	γ(xn+1	γ(xn+1	ADJ
ejpam-6847	269	12	,	,	PUNCT
ejpam-6847	269	13	xm)β(xn+1	xm)β(xn+1	ADJ
ejpam-6847	269	14	,	,	PUNCT
ejpam-6847	269	15	xn+2)s(xn+1	xn+2)s(xn+1	PROPN
ejpam-6847	269	16	,	,	PUNCT
ejpam-6847	269	17	xn+1	xn+1	PROPN
ejpam-6847	269	18	,	,	PUNCT
ejpam-6847	269	19	xn+2	xn+2	NUM
ejpam-6847	269	20	)	)	PUNCT
ejpam-6847	269	21	+	+	CCONJ
ejpam-6847	269	22	γ(xn+1	γ(xn+1	ADJ
ejpam-6847	269	23	,	,	PUNCT
ejpam-6847	269	24	xm)µ(xn+1	xm)µ(xn+1	PROPN
ejpam-6847	269	25	,	,	PUNCT
ejpam-6847	269	26	xn+2)s(xn+1	xn+2)s(xn+1	PROPN
ejpam-6847	269	27	,	,	PUNCT
ejpam-6847	269	28	xn+1	xn+1	PROPN
ejpam-6847	269	29	,	,	PUNCT
ejpam-6847	269	30	xn+2	xn+2	NUM
ejpam-6847	269	31	)	)	PUNCT
ejpam-6847	269	32	+	+	PUNCT
ejpam-6847	269	33	γ(xn+1	γ(xn+1	ADJ
ejpam-6847	269	34	,	,	PUNCT
ejpam-6847	269	35	xm)γ(xn+2	xm)γ(xn+2	PROPN
ejpam-6847	269	36	,	,	PUNCT
ejpam-6847	269	37	xm)[β(xn+2	xm)[β(xn+2	PROPN
ejpam-6847	269	38	,	,	PUNCT
ejpam-6847	269	39	xn+3)s(xn+2	xn+3)s(xn+2	PROPN
ejpam-6847	269	40	,	,	PUNCT
ejpam-6847	269	41	xn+2	xn+2	NUM
ejpam-6847	269	42	,	,	PUNCT
ejpam-6847	269	43	xn+3	xn+3	PROPN
ejpam-6847	269	44	)	)	PUNCT
ejpam-6847	269	45	+	+	CCONJ
ejpam-6847	269	46	µ(xn+2	µ(xn+2	PROPN
ejpam-6847	269	47	,	,	PUNCT
ejpam-6847	269	48	xn+3)s(xn+2	xn+3)s(xn+2	PROPN
ejpam-6847	269	49	,	,	PUNCT
ejpam-6847	269	50	xn+2	xn+2	NUM
ejpam-6847	269	51	,	,	PUNCT
ejpam-6847	269	52	xn+3	xn+3	PROPN
ejpam-6847	269	53	)	)	PUNCT
ejpam-6847	270	1	+	+	CCONJ
ejpam-6847	270	2	γ(xn+3	γ(xn+3	PROPN
ejpam-6847	270	3	,	,	PUNCT
ejpam-6847	270	4	xm)s(xn+3	xm)s(xn+3	PROPN
ejpam-6847	270	5	,	,	PUNCT
ejpam-6847	270	6	xn+3	xn+3	PROPN
ejpam-6847	270	7	,	,	PUNCT
ejpam-6847	270	8	xm	xm	PROPN
ejpam-6847	270	9	)	)	PUNCT
ejpam-6847	270	10	]	]	PUNCT
ejpam-6847	270	11	.	.	PUNCT
ejpam-6847	271	1	...	...	PUNCT
ejpam-6847	272	1	hence	hence	ADV
ejpam-6847	272	2	,	,	PUNCT
ejpam-6847	272	3	we	we	PRON
ejpam-6847	272	4	get	get	VERB
ejpam-6847	272	5	s(xn	s(xn	NOUN
ejpam-6847	272	6	,	,	PUNCT
ejpam-6847	272	7	xn	xn	PROPN
ejpam-6847	272	8	,	,	PUNCT
ejpam-6847	272	9	xm	xm	NOUN
ejpam-6847	272	10	)	)	PUNCT
ejpam-6847	272	11	≤	≤	NOUN
ejpam-6847	272	12	β(xn	β(xn	NOUN
ejpam-6847	272	13	,	,	PUNCT
ejpam-6847	272	14	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	272	15	,	,	PUNCT
ejpam-6847	272	16	xn	xn	PROPN
ejpam-6847	272	17	,	,	PUNCT
ejpam-6847	272	18	xn+1	xn+1	NUM
ejpam-6847	272	19	)	)	PUNCT
ejpam-6847	272	20	+	+	CCONJ
ejpam-6847	273	1	µ(xn	µ(xn	PROPN
ejpam-6847	273	2	,	,	PUNCT
ejpam-6847	273	3	xn+1)s(xn	xn+1)s(xn	PROPN
ejpam-6847	273	4	,	,	PUNCT
ejpam-6847	273	5	xn	xn	PROPN
ejpam-6847	273	6	,	,	PUNCT
ejpam-6847	273	7	xn+1	xn+1	PUNCT
ejpam-6847	273	8	)	)	PUNCT
ejpam-6847	274	1	+	+	CCONJ
ejpam-6847	274	2	m−2∑	m−2∑	NUM
ejpam-6847	274	3	i	i	PRON
ejpam-6847	274	4	=	=	NOUN
ejpam-6847	274	5	n+1	n+1	PROPN
ejpam-6847	274	6	[	[	X
ejpam-6847	274	7	β(xi	β(xi	PROPN
ejpam-6847	274	8	,	,	PUNCT
ejpam-6847	274	9	xi+1	xi+1	NOUN
ejpam-6847	274	10	)	)	PUNCT
ejpam-6847	274	11	+	+	X
ejpam-6847	274	12	µ(xi	µ(xi	NUM
ejpam-6847	274	13	,	,	PUNCT
ejpam-6847	274	14	xi+1)]s(xi	xi+1)]s(xi	PROPN
ejpam-6847	274	15	,	,	PUNCT
ejpam-6847	274	16	xi	xi	PROPN
ejpam-6847	274	17	,	,	PUNCT
ejpam-6847	274	18	xi+1	xi+1	NOUN
ejpam-6847	274	19	)	)	PUNCT
ejpam-6847	274	20			PROPN
ejpam-6847	274	21	i∏	i∏	PROPN
ejpam-6847	274	22	j	j	NOUN
ejpam-6847	274	23	=	=	NOUN
ejpam-6847	274	24	n+1	n+1	PROPN
ejpam-6847	274	25	γ(xj	γ(xj	PROPN
ejpam-6847	274	26	,	,	PUNCT
ejpam-6847	274	27	xm	xm	PROPN
ejpam-6847	274	28	)	)	PUNCT
ejpam-6847	275	1			PROPN
ejpam-6847	276	1	+	+	CCONJ
ejpam-6847	276	2	m−1∏	m−1∏	PROPN
ejpam-6847	276	3	i	i	PROPN
ejpam-6847	276	4	=	=	PROPN
ejpam-6847	276	5	n+1	n+1	PROPN
ejpam-6847	276	6	γ(xi	γ(xi	PROPN
ejpam-6847	276	7	,	,	PUNCT
ejpam-6847	276	8	xm)s(xm−1	xm)s(xm−1	PROPN
ejpam-6847	276	9	,	,	PUNCT
ejpam-6847	276	10	xm−1	xm−1	PROPN
ejpam-6847	276	11	,	,	PUNCT
ejpam-6847	276	12	xm	xm	PROPN
ejpam-6847	276	13	)	)	PUNCT
ejpam-6847	276	14	.	.	PUNCT
ejpam-6847	277	1	therefore	therefore	ADV
ejpam-6847	277	2	,	,	PUNCT
ejpam-6847	277	3	s(xn	s(xn	PROPN
ejpam-6847	277	4	,	,	PUNCT
ejpam-6847	277	5	xn	xn	PROPN
ejpam-6847	277	6	,	,	PUNCT
ejpam-6847	277	7	xm	xm	PROPN
ejpam-6847	277	8	)	)	PUNCT
ejpam-6847	277	9	≤	≤	NOUN
ejpam-6847	278	1	[	[	X
ejpam-6847	278	2	β(xn	β(xn	NOUN
ejpam-6847	278	3	,	,	PUNCT
ejpam-6847	278	4	xn+1	xn+1	NUM
ejpam-6847	278	5	)	)	PUNCT
ejpam-6847	278	6	+	+	CCONJ
ejpam-6847	278	7	µ(xn	µ(xn	PROPN
ejpam-6847	278	8	,	,	PUNCT
ejpam-6847	278	9	xn+1)]s(xn	xn+1)]s(xn	PROPN
ejpam-6847	278	10	,	,	PUNCT
ejpam-6847	278	11	xn	xn	PROPN
ejpam-6847	278	12	,	,	PUNCT
ejpam-6847	278	13	xn+1	xn+1	NUM
ejpam-6847	278	14	)	)	PUNCT
ejpam-6847	279	1	+	+	CCONJ
ejpam-6847	280	1	m−1∑	m−1∑	NUM
ejpam-6847	280	2	i	i	NOUN
ejpam-6847	280	3	=	=	NOUN
ejpam-6847	280	4	n+1	n+1	PROPN
ejpam-6847	280	5	[	[	X
ejpam-6847	280	6	β(xi	β(xi	PROPN
ejpam-6847	280	7	,	,	PUNCT
ejpam-6847	280	8	xi+1	xi+1	NOUN
ejpam-6847	280	9	)	)	PUNCT
ejpam-6847	280	10	+	+	X
ejpam-6847	280	11	µ(xi	µ(xi	NUM
ejpam-6847	280	12	,	,	PUNCT
ejpam-6847	280	13	xi+1)]s(xi	xi+1)]s(xi	PROPN
ejpam-6847	280	14	,	,	PUNCT
ejpam-6847	280	15	xi	xi	PROPN
ejpam-6847	280	16	,	,	PUNCT
ejpam-6847	280	17	xi+1	xi+1	NOUN
ejpam-6847	280	18	)	)	PUNCT
ejpam-6847	280	19			PROPN
ejpam-6847	280	20	i∏	i∏	PROPN
ejpam-6847	280	21	j	j	NOUN
ejpam-6847	280	22	=	=	NOUN
ejpam-6847	280	23	n+1	n+1	PROPN
ejpam-6847	280	24	γ(xj	γ(xj	PROPN
ejpam-6847	280	25	,	,	PUNCT
ejpam-6847	280	26	xm	xm	PROPN
ejpam-6847	280	27	)	)	PUNCT
ejpam-6847	281	1			PROPN
ejpam-6847	281	2	(	(	PUNCT
ejpam-6847	281	3	13	13	NUM
ejpam-6847	281	4	)	)	PUNCT
ejpam-6847	281	5	applying	apply	VERB
ejpam-6847	281	6	equation	equation	NOUN
ejpam-6847	281	7	12	12	NUM
ejpam-6847	281	8	into	into	ADP
ejpam-6847	281	9	inequality	inequality	NOUN
ejpam-6847	281	10	13	13	NUM
ejpam-6847	281	11	,	,	PUNCT
ejpam-6847	281	12	it	it	PRON
ejpam-6847	281	13	becomes	become	VERB
ejpam-6847	281	14	s(xn	s(xn	NOUN
ejpam-6847	281	15	,	,	PUNCT
ejpam-6847	281	16	xn	xn	PROPN
ejpam-6847	281	17	,	,	PUNCT
ejpam-6847	281	18	xm	xm	PROPN
ejpam-6847	281	19	)	)	PUNCT
ejpam-6847	281	20	≤	≤	NOUN
ejpam-6847	282	1	[	[	X
ejpam-6847	282	2	β(xn	β(xn	NOUN
ejpam-6847	282	3	,	,	PUNCT
ejpam-6847	282	4	xn+1	xn+1	NUM
ejpam-6847	282	5	)	)	PUNCT
ejpam-6847	282	6	+	+	CCONJ
ejpam-6847	282	7	µ(xn	µ(xn	PROPN
ejpam-6847	282	8	,	,	PUNCT
ejpam-6847	282	9	xn+1	xn+1	NUM
ejpam-6847	282	10	)	)	PUNCT
ejpam-6847	282	11	]	]	PUNCT
ejpam-6847	282	12	(	(	PUNCT
ejpam-6847	282	13	1	1	NUM
ejpam-6847	282	14	n1	n1	NOUN
ejpam-6847	282	15	/	/	SYM
ejpam-6847	282	16	k	k	NOUN
ejpam-6847	282	17	)	)	PUNCT
ejpam-6847	283	1	+	+	CCONJ
ejpam-6847	284	1	m−1∑	m−1∑	NUM
ejpam-6847	284	2	i	i	NOUN
ejpam-6847	284	3	=	=	NOUN
ejpam-6847	284	4	n+1	n+1	PROPN
ejpam-6847	284	5	[	[	X
ejpam-6847	284	6	β(xi	β(xi	PROPN
ejpam-6847	284	7	,	,	PUNCT
ejpam-6847	284	8	xi+1	xi+1	NOUN
ejpam-6847	284	9	)	)	PUNCT
ejpam-6847	284	10	+	+	X
ejpam-6847	284	11	µ(xi	µ(xi	NUM
ejpam-6847	284	12	,	,	PUNCT
ejpam-6847	284	13	xi+1	xi+1	NUM
ejpam-6847	284	14	)	)	PUNCT
ejpam-6847	284	15	]	]	X
ejpam-6847	284	16	(	(	PUNCT
ejpam-6847	284	17	1	1	NUM
ejpam-6847	284	18	i1	i1	PROPN
ejpam-6847	284	19	/	/	SYM
ejpam-6847	284	20	k	k	PROPN
ejpam-6847	284	21	)	)	PUNCT
ejpam-6847	285	1			PROPN
ejpam-6847	285	2	i∏	i∏	PROPN
ejpam-6847	285	3	j	j	NOUN
ejpam-6847	285	4	=	=	NOUN
ejpam-6847	285	5	n+1	n+1	PROPN
ejpam-6847	285	6	γ(xj	γ(xj	PROPN
ejpam-6847	285	7	,	,	PUNCT
ejpam-6847	285	8	xm	xm	PROPN
ejpam-6847	285	9	)	)	PUNCT
ejpam-6847	285	10			PROPN
ejpam-6847	285	11	.	.	PUNCT
ejpam-6847	286	1	≤	≤	NOUN
ejpam-6847	287	1	[	[	X
ejpam-6847	287	2	β(xn	β(xn	NOUN
ejpam-6847	287	3	,	,	PUNCT
ejpam-6847	287	4	xn+1	xn+1	NUM
ejpam-6847	287	5	)	)	PUNCT
ejpam-6847	287	6	+	+	CCONJ
ejpam-6847	287	7	µ(xn	µ(xn	PROPN
ejpam-6847	287	8	,	,	PUNCT
ejpam-6847	287	9	xn+1	xn+1	NUM
ejpam-6847	287	10	)	)	PUNCT
ejpam-6847	287	11	]	]	PUNCT
ejpam-6847	287	12	(	(	PUNCT
ejpam-6847	287	13	1	1	NUM
ejpam-6847	287	14	n1	n1	NOUN
ejpam-6847	287	15	/	/	SYM
ejpam-6847	287	16	k	k	NOUN
ejpam-6847	287	17	)	)	PUNCT
ejpam-6847	288	1	+	+	CCONJ
ejpam-6847	289	1	m−1∑	m−1∑	NUM
ejpam-6847	289	2	i=1	i=1	X
ejpam-6847	290	1	[	[	X
ejpam-6847	290	2	β(xi	β(xi	PROPN
ejpam-6847	290	3	,	,	PUNCT
ejpam-6847	290	4	xi+1	xi+1	NOUN
ejpam-6847	290	5	)	)	PUNCT
ejpam-6847	290	6	+	+	X
ejpam-6847	290	7	µ(xi	µ(xi	NUM
ejpam-6847	290	8	,	,	PUNCT
ejpam-6847	290	9	xi+1	xi+1	NUM
ejpam-6847	290	10	)	)	PUNCT
ejpam-6847	290	11	]	]	X
ejpam-6847	290	12	(	(	PUNCT
ejpam-6847	290	13	1	1	NUM
ejpam-6847	290	14	i1	i1	PROPN
ejpam-6847	290	15	/	/	SYM
ejpam-6847	290	16	k	k	PROPN
ejpam-6847	290	17	)	)	PUNCT
ejpam-6847	291	1			PROPN
ejpam-6847	291	2	i∏	i∏	PROPN
ejpam-6847	291	3	j=1	j=1	NOUN
ejpam-6847	291	4	γ(xj	γ(xj	ADV
ejpam-6847	291	5	,	,	PUNCT
ejpam-6847	291	6	xm	xm	PROPN
ejpam-6847	291	7	)	)	PUNCT
ejpam-6847	291	8			PROPN
ejpam-6847	291	9	.	.	PUNCT
ejpam-6847	292	1	f.	f.	PROPN
ejpam-6847	292	2	m.	m.	PROPN
ejpam-6847	292	3	azmi	azmi	PROPN
ejpam-6847	292	4	,	,	PUNCT
ejpam-6847	292	5	a.	a.	PROPN
ejpam-6847	292	6	h.	h.	PROPN
ejpam-6847	292	7	ansari	ansari	PROPN
ejpam-6847	292	8	,	,	PUNCT
ejpam-6847	292	9	s.	s.	PROPN
ejpam-6847	292	10	h.	h.	PROPN
ejpam-6847	292	11	j.	j.	PROPN
ejpam-6847	292	12	petroudi	petroudi	PROPN
ejpam-6847	292	13	/	/	SYM
ejpam-6847	292	14	eur	eur	PROPN
ejpam-6847	292	15	.	.	PUNCT
ejpam-6847	293	1	j.	j.	PROPN
ejpam-6847	293	2	pure	pure	PROPN
ejpam-6847	293	3	appl	appl	PROPN
ejpam-6847	293	4	.	.	PROPN
ejpam-6847	293	5	math	math	PROPN
ejpam-6847	293	6	,	,	PUNCT
ejpam-6847	293	7	18	18	NUM
ejpam-6847	293	8	(	(	PUNCT
ejpam-6847	293	9	4	4	NUM
ejpam-6847	293	10	)	)	PUNCT
ejpam-6847	293	11	(	(	PUNCT
ejpam-6847	293	12	2025	2025	NUM
ejpam-6847	293	13	)	)	PUNCT
ejpam-6847	293	14	,	,	PUNCT
ejpam-6847	293	15	6847	6847	NUM
ejpam-6847	293	16	12	12	NUM
ejpam-6847	293	17	of	of	ADP
ejpam-6847	293	18	26	26	NUM
ejpam-6847	293	19	(	(	PUNCT
ejpam-6847	293	20	14	14	NUM
ejpam-6847	293	21	)	)	PUNCT
ejpam-6847	293	22	let	let	VERB
ejpam-6847	293	23	lp	lp	NOUN
ejpam-6847	293	24	=	=	PUNCT
ejpam-6847	293	25	∑p−1	∑p−1	X
ejpam-6847	294	1	i=1	i=1	X
ejpam-6847	295	1	[	[	X
ejpam-6847	295	2	β(xi	β(xi	PROPN
ejpam-6847	295	3	,	,	PUNCT
ejpam-6847	295	4	xi+1	xi+1	NOUN
ejpam-6847	295	5	)	)	PUNCT
ejpam-6847	295	6	+	+	X
ejpam-6847	295	7	µ(xi	µ(xi	NUM
ejpam-6847	295	8	,	,	PUNCT
ejpam-6847	295	9	xi+1	xi+1	NUM
ejpam-6847	295	10	)	)	PUNCT
ejpam-6847	295	11	]	]	X
ejpam-6847	295	12	(	(	PUNCT
ejpam-6847	295	13	1	1	NUM
ejpam-6847	295	14	i1	i1	PROPN
ejpam-6847	295	15	/	/	SYM
ejpam-6847	295	16	k	k	PROPN
ejpam-6847	295	17	)	)	PUNCT
ejpam-6847	296	1	(	(	PUNCT
ejpam-6847	296	2	∏p	∏p	NOUN
ejpam-6847	296	3	j=1	j=1	NOUN
ejpam-6847	296	4	γ(xj	γ(xj	ADV
ejpam-6847	296	5	,	,	PUNCT
ejpam-6847	296	6	xm	xm	PROPN
ejpam-6847	296	7	)	)	PUNCT
ejpam-6847	296	8	)	)	PUNCT
ejpam-6847	296	9	.	.	PUNCT
ejpam-6847	297	1	therefore	therefore	ADV
ejpam-6847	297	2	,	,	PUNCT
ejpam-6847	297	3	inequality	inequality	NOUN
ejpam-6847	297	4	14	14	NUM
ejpam-6847	297	5	can	can	AUX
ejpam-6847	297	6	be	be	AUX
ejpam-6847	297	7	expressed	express	VERB
ejpam-6847	297	8	as	as	ADP
ejpam-6847	297	9	:	:	PUNCT
ejpam-6847	297	10	s(xn	s(xn	NOUN
ejpam-6847	297	11	,	,	PUNCT
ejpam-6847	297	12	xn	xn	PROPN
ejpam-6847	297	13	,	,	PUNCT
ejpam-6847	297	14	xm	xm	PROPN
ejpam-6847	297	15	)	)	PUNCT
ejpam-6847	297	16	≤	≤	NOUN
ejpam-6847	298	1	[	[	X
ejpam-6847	298	2	β(xn	β(xn	NOUN
ejpam-6847	298	3	,	,	PUNCT
ejpam-6847	298	4	xn+1	xn+1	NUM
ejpam-6847	298	5	)	)	PUNCT
ejpam-6847	298	6	+	+	CCONJ
ejpam-6847	298	7	µ(xn	µ(xn	PROPN
ejpam-6847	298	8	,	,	PUNCT
ejpam-6847	298	9	xn+1	xn+1	NUM
ejpam-6847	298	10	)	)	PUNCT
ejpam-6847	298	11	]	]	PUNCT
ejpam-6847	298	12	(	(	PUNCT
ejpam-6847	298	13	1	1	NUM
ejpam-6847	298	14	n1	n1	NOUN
ejpam-6847	298	15	/	/	SYM
ejpam-6847	298	16	k	k	NOUN
ejpam-6847	298	17	)	)	PUNCT
ejpam-6847	299	1	+	+	CCONJ
ejpam-6847	299	2	(	(	PUNCT
ejpam-6847	299	3	lm−1	lm−1	PROPN
ejpam-6847	299	4	−	−	PROPN
ejpam-6847	299	5	ln	ln	ADJ
ejpam-6847	299	6	)	)	PUNCT
ejpam-6847	299	7	.	.	PUNCT
ejpam-6847	300	1	(	(	PUNCT
ejpam-6847	300	2	15	15	X
ejpam-6847	300	3	)	)	PUNCT
ejpam-6847	300	4	the	the	DET
ejpam-6847	300	5	application	application	NOUN
ejpam-6847	300	6	of	of	ADP
ejpam-6847	300	7	the	the	DET
ejpam-6847	300	8	ratio	ratio	NOUN
ejpam-6847	300	9	test	test	NOUN
ejpam-6847	300	10	to	to	ADP
ejpam-6847	300	11	inequality	inequality	NOUN
ejpam-6847	300	12	15	15	NUM
ejpam-6847	300	13	,	,	PUNCT
ejpam-6847	300	14	followed	follow	VERB
ejpam-6847	300	15	by	by	ADP
ejpam-6847	300	16	taking	take	VERB
ejpam-6847	300	17	the	the	DET
ejpam-6847	300	18	limit	limit	NOUN
ejpam-6847	300	19	as	as	ADP
ejpam-6847	300	20	both	both	CCONJ
ejpam-6847	300	21	n	n	NOUN
ejpam-6847	300	22	and	and	CCONJ
ejpam-6847	300	23	m	m	VERB
ejpam-6847	300	24	approach	approach	NOUN
ejpam-6847	300	25	infinity	infinity	NOUN
ejpam-6847	300	26	while	while	SCONJ
ejpam-6847	300	27	utilizing	utilize	VERB
ejpam-6847	300	28	equations	equation	NOUN
ejpam-6847	300	29	5	5	NUM
ejpam-6847	300	30	,	,	PUNCT
ejpam-6847	300	31	leads	lead	VERB
ejpam-6847	300	32	us	we	PRON
ejpam-6847	300	33	to	to	ADP
ejpam-6847	300	34	the	the	DET
ejpam-6847	300	35	conclusion	conclusion	NOUN
ejpam-6847	300	36	that	that	SCONJ
ejpam-6847	300	37	limn	limn	NOUN
ejpam-6847	300	38	,	,	PUNCT
ejpam-6847	300	39	m→+∞[lm−1−ln	m→+∞[lm−1−ln	X
ejpam-6847	300	40	]	]	X
ejpam-6847	300	41	=	=	SYM
ejpam-6847	300	42	0	0	X
ejpam-6847	300	43	.	.	PUNCT
ejpam-6847	301	1	furthermore	furthermore	ADV
ejpam-6847	301	2	,	,	PUNCT
ejpam-6847	301	3	the	the	DET
ejpam-6847	301	4	use	use	NOUN
ejpam-6847	301	5	of	of	ADP
ejpam-6847	301	6	6	6	NUM
ejpam-6847	301	7	indicates	indicate	VERB
ejpam-6847	301	8	that	that	SCONJ
ejpam-6847	301	9	limn→+∞[β(xn	limn→+∞[β(xn	PROPN
ejpam-6847	301	10	,	,	PUNCT
ejpam-6847	301	11	xn+1)+	xn+1)+	PROPN
ejpam-6847	301	12	µ(xn	µ(xn	PROPN
ejpam-6847	301	13	,	,	PUNCT
ejpam-6847	301	14	xn+1	xn+1	NUM
ejpam-6847	301	15	)	)	PUNCT
ejpam-6847	301	16	]	]	PUNCT
ejpam-6847	301	17	(	(	PUNCT
ejpam-6847	301	18	1	1	NUM
ejpam-6847	301	19	n1	n1	NOUN
ejpam-6847	301	20	/	/	SYM
ejpam-6847	301	21	k	k	NOUN
ejpam-6847	301	22	)	)	PUNCT
ejpam-6847	301	23	=	=	PUNCT
ejpam-6847	302	1	0	0	X
ejpam-6847	302	2	.	.	PUNCT
ejpam-6847	303	1	thus	thus	ADV
ejpam-6847	303	2	,	,	PUNCT
ejpam-6847	303	3	we	we	PRON
ejpam-6847	303	4	have	have	AUX
ejpam-6847	303	5	demonstrated	demonstrate	VERB
ejpam-6847	303	6	that	that	SCONJ
ejpam-6847	303	7	:	:	PUNCT
ejpam-6847	303	8	lim	lim	PROPN
ejpam-6847	303	9	n	n	CCONJ
ejpam-6847	303	10	,	,	PUNCT
ejpam-6847	303	11	m→+∞	m→+∞	PROPN
ejpam-6847	303	12	s(xn	s(xn	NOUN
ejpam-6847	303	13	,	,	PUNCT
ejpam-6847	303	14	xn	xn	PROPN
ejpam-6847	303	15	,	,	PUNCT
ejpam-6847	303	16	xm	xm	PROPN
ejpam-6847	303	17	)	)	PUNCT
ejpam-6847	303	18	=	=	SYM
ejpam-6847	304	1	0	0	X
ejpam-6847	304	2	.	.	PUNCT
ejpam-6847	305	1	we	we	PRON
ejpam-6847	305	2	deduce	deduce	VERB
ejpam-6847	305	3	that	that	SCONJ
ejpam-6847	305	4	the	the	DET
ejpam-6847	305	5	sequence	sequence	NOUN
ejpam-6847	305	6	{	{	PUNCT
ejpam-6847	305	7	xn	xn	PROPN
ejpam-6847	305	8	}	}	PUNCT
ejpam-6847	305	9	is	be	AUX
ejpam-6847	305	10	a	a	DET
ejpam-6847	305	11	cauchy	cauchy	ADJ
ejpam-6847	305	12	sequence	sequence	NOUN
ejpam-6847	305	13	.	.	PUNCT
ejpam-6847	306	1	given	give	VERB
ejpam-6847	306	2	the	the	DET
ejpam-6847	306	3	completeness	completeness	NOUN
ejpam-6847	306	4	of	of	ADP
ejpam-6847	306	5	the	the	DET
ejpam-6847	306	6	space	space	NOUN
ejpam-6847	306	7	(	(	PUNCT
ejpam-6847	306	8	x	x	X
ejpam-6847	306	9	,	,	PUNCT
ejpam-6847	306	10	s	s	PART
ejpam-6847	306	11	)	)	PUNCT
ejpam-6847	306	12	,	,	PUNCT
ejpam-6847	306	13	it	it	PRON
ejpam-6847	306	14	follows	follow	VERB
ejpam-6847	306	15	that	that	SCONJ
ejpam-6847	306	16	this	this	DET
ejpam-6847	306	17	sequence	sequence	NOUN
ejpam-6847	306	18	must	must	AUX
ejpam-6847	306	19	converge	converge	VERB
ejpam-6847	306	20	to	to	ADP
ejpam-6847	306	21	a	a	DET
ejpam-6847	306	22	limit	limit	NOUN
ejpam-6847	307	1	u	u	NOUN
ejpam-6847	307	2	∈	∈	PROPN
ejpam-6847	307	3	x	x	NOUN
ejpam-6847	307	4	,	,	PUNCT
ejpam-6847	307	5	i.e.	i.e.	X
ejpam-6847	307	6	lim	lim	PROPN
ejpam-6847	307	7	n→+∞	n→+∞	VERB
ejpam-6847	307	8	s(xn	s(xn	PROPN
ejpam-6847	307	9	,	,	PUNCT
ejpam-6847	307	10	xn	xn	PROPN
ejpam-6847	307	11	,	,	PUNCT
ejpam-6847	307	12	u	u	NOUN
ejpam-6847	307	13	)	)	PUNCT
ejpam-6847	307	14	=	=	SYM
ejpam-6847	307	15	0	0	X
ejpam-6847	307	16	.	.	PUNCT
ejpam-6847	308	1	(	(	PUNCT
ejpam-6847	308	2	16	16	NUM
ejpam-6847	308	3	)	)	PUNCT
ejpam-6847	308	4	assume	assume	VERB
ejpam-6847	308	5	that	that	SCONJ
ejpam-6847	308	6	s(t	s(t	PROPN
ejpam-6847	308	7	xn	xn	PROPN
ejpam-6847	308	8	,	,	PUNCT
ejpam-6847	308	9	t	t	PROPN
ejpam-6847	308	10	xn	xn	PROPN
ejpam-6847	308	11	,	,	PUNCT
ejpam-6847	308	12	tu	tu	PROPN
ejpam-6847	308	13	)	)	PUNCT
ejpam-6847	308	14	>	>	PUNCT
ejpam-6847	309	1	0for	0for	ADP
ejpam-6847	309	2	all	all	DET
ejpam-6847	309	3	n.	n.	NOUN
ejpam-6847	309	4	by	by	ADP
ejpam-6847	309	5	definition	definition	NOUN
ejpam-6847	309	6	15	15	NUM
ejpam-6847	309	7	,	,	PUNCT
ejpam-6847	309	8	we	we	PRON
ejpam-6847	309	9	have	have	VERB
ejpam-6847	309	10	h	h	NOUN
ejpam-6847	309	11	(	(	PUNCT
ejpam-6847	309	12	1	1	NUM
ejpam-6847	309	13	,	,	PUNCT
ejpam-6847	309	14	τ	τ	PROPN
ejpam-6847	310	1	+	+	NUM
ejpam-6847	310	2	f	f	PROPN
ejpam-6847	310	3	(	(	PUNCT
ejpam-6847	310	4	s(txn	s(txn	PROPN
ejpam-6847	310	5	,	,	PUNCT
ejpam-6847	310	6	txn	txn	PROPN
ejpam-6847	310	7	,	,	PUNCT
ejpam-6847	310	8	tu	tu	PROPN
ejpam-6847	310	9	)	)	PUNCT
ejpam-6847	310	10	)	)	PUNCT
ejpam-6847	310	11	)	)	PUNCT
ejpam-6847	310	12	≤	≤	NUM
ejpam-6847	310	13	h	h	NOUN
ejpam-6847	310	14	(	(	PUNCT
ejpam-6847	310	15	αs(xn	αs(xn	PROPN
ejpam-6847	310	16	,	,	PUNCT
ejpam-6847	310	17	xn	xn	PROPN
ejpam-6847	310	18	,	,	PUNCT
ejpam-6847	310	19	u	u	NOUN
ejpam-6847	310	20	)	)	PUNCT
ejpam-6847	310	21	,	,	PUNCT
ejpam-6847	310	22	τ	τ	PROPN
ejpam-6847	310	23	+	+	NUM
ejpam-6847	310	24	f	f	PROPN
ejpam-6847	310	25	(	(	PUNCT
ejpam-6847	310	26	s(txn	s(txn	PROPN
ejpam-6847	310	27	,	,	PUNCT
ejpam-6847	310	28	txn	txn	PROPN
ejpam-6847	310	29	,	,	PUNCT
ejpam-6847	310	30	tu	tu	PROPN
ejpam-6847	310	31	)	)	PUNCT
ejpam-6847	310	32	)	)	PUNCT
ejpam-6847	310	33	)	)	PUNCT
ejpam-6847	311	1	≤	≤	NUM
ejpam-6847	312	1	q	q	NOUN
ejpam-6847	312	2	(	(	PUNCT
ejpam-6847	312	3	νs(xn	νs(xn	PROPN
ejpam-6847	312	4	,	,	PUNCT
ejpam-6847	312	5	xn	xn	PROPN
ejpam-6847	312	6	,	,	PUNCT
ejpam-6847	312	7	u	u	NOUN
ejpam-6847	312	8	)	)	PUNCT
ejpam-6847	312	9	,	,	PUNCT
ejpam-6847	312	10	f	f	PROPN
ejpam-6847	312	11	(	(	PUNCT
ejpam-6847	312	12	s(xn	s(xn	PROPN
ejpam-6847	312	13	,	,	PUNCT
ejpam-6847	312	14	xn	xn	PROPN
ejpam-6847	312	15	,	,	PUNCT
ejpam-6847	312	16	u	u	NOUN
ejpam-6847	312	17	)	)	PUNCT
ejpam-6847	312	18	)	)	PUNCT
ejpam-6847	312	19	)	)	PUNCT
ejpam-6847	313	1	≤	≤	PROPN
ejpam-6847	313	2	q(1	q(1	PROPN
ejpam-6847	313	3	,	,	PUNCT
ejpam-6847	313	4	f	f	PROPN
ejpam-6847	313	5	(	(	PUNCT
ejpam-6847	313	6	s(xn	s(xn	PROPN
ejpam-6847	313	7	,	,	PUNCT
ejpam-6847	313	8	xn	xn	PROPN
ejpam-6847	313	9	,	,	PUNCT
ejpam-6847	313	10	u	u	NOUN
ejpam-6847	313	11	)	)	PUNCT
ejpam-6847	313	12	)	)	PUNCT
ejpam-6847	313	13	)	)	PUNCT
ejpam-6847	313	14	.	.	PUNCT
ejpam-6847	314	1	as	as	SCONJ
ejpam-6847	314	2	the	the	DET
ejpam-6847	314	3	pair	pair	NOUN
ejpam-6847	314	4	(	(	PUNCT
ejpam-6847	314	5	q	q	NOUN
ejpam-6847	314	6	,	,	PUNCT
ejpam-6847	314	7	h	h	NOUN
ejpam-6847	314	8	)	)	PUNCT
ejpam-6847	314	9	is	be	AUX
ejpam-6847	314	10	an	an	DET
ejpam-6847	314	11	upper	upper	ADJ
ejpam-6847	314	12	class	class	NOUN
ejpam-6847	314	13	of	of	ADP
ejpam-6847	314	14	type	type	NOUN
ejpam-6847	314	15	i	i	PRON
ejpam-6847	314	16	,	,	PUNCT
ejpam-6847	314	17	hence	hence	ADV
ejpam-6847	314	18	the	the	DET
ejpam-6847	314	19	following	follow	VERB
ejpam-6847	314	20	inequality	inequality	NOUN
ejpam-6847	314	21	holds	hold	VERB
ejpam-6847	314	22	:	:	PUNCT
ejpam-6847	314	23	τ	τ	PROPN
ejpam-6847	315	1	+	+	NUM
ejpam-6847	315	2	f	f	PROPN
ejpam-6847	315	3	(	(	PUNCT
ejpam-6847	315	4	s(txn	s(txn	PROPN
ejpam-6847	315	5	,	,	PUNCT
ejpam-6847	315	6	txn	txn	PROPN
ejpam-6847	315	7	,	,	PUNCT
ejpam-6847	315	8	tu	tu	PROPN
ejpam-6847	315	9	)	)	PUNCT
ejpam-6847	315	10	)	)	PUNCT
ejpam-6847	315	11	≤	≤	NUM
ejpam-6847	315	12	f	f	X
ejpam-6847	315	13	(	(	PUNCT
ejpam-6847	315	14	s(xn	s(xn	PROPN
ejpam-6847	315	15	,	,	PUNCT
ejpam-6847	315	16	xn	xn	PROPN
ejpam-6847	315	17	,	,	PUNCT
ejpam-6847	315	18	u	u	NOUN
ejpam-6847	315	19	)	)	PUNCT
ejpam-6847	315	20	)	)	PUNCT
ejpam-6847	315	21	.	.	PUNCT
ejpam-6847	316	1	(	(	PUNCT
ejpam-6847	316	2	17	17	X
ejpam-6847	316	3	)	)	PUNCT
ejpam-6847	316	4	taking	take	VERB
ejpam-6847	316	5	the	the	DET
ejpam-6847	316	6	limit	limit	NOUN
ejpam-6847	316	7	as	as	ADP
ejpam-6847	316	8	n	n	NOUN
ejpam-6847	316	9	approaches	approach	NOUN
ejpam-6847	316	10	infinity	infinity	NOUN
ejpam-6847	316	11	in	in	ADP
ejpam-6847	316	12	equation	equation	NOUN
ejpam-6847	316	13	17	17	NUM
ejpam-6847	316	14	,	,	PUNCT
ejpam-6847	316	15	and	and	CCONJ
ejpam-6847	316	16	applying	apply	VERB
ejpam-6847	316	17	equation	equation	NOUN
ejpam-6847	316	18	16	16	NUM
ejpam-6847	316	19	along	along	ADP
ejpam-6847	316	20	with	with	ADP
ejpam-6847	316	21	(	(	PUNCT
ejpam-6847	316	22	w2	w2	NOUN
ejpam-6847	316	23	)	)	PUNCT
ejpam-6847	316	24	from	from	ADP
ejpam-6847	316	25	definition	definition	NOUN
ejpam-6847	316	26	14	14	NUM
ejpam-6847	316	27	,	,	PUNCT
ejpam-6847	316	28	we	we	PRON
ejpam-6847	316	29	find	find	VERB
ejpam-6847	316	30	that	that	PRON
ejpam-6847	316	31	limn→+∞	limn→+∞	ADP
ejpam-6847	316	32	f	f	PROPN
ejpam-6847	316	33	(	(	PUNCT
ejpam-6847	316	34	s(txn	s(txn	PROPN
ejpam-6847	316	35	,	,	PUNCT
ejpam-6847	316	36	txn	txn	PROPN
ejpam-6847	316	37	,	,	PUNCT
ejpam-6847	316	38	tu	tu	PROPN
ejpam-6847	316	39	)	)	PUNCT
ejpam-6847	316	40	)	)	PUNCT
ejpam-6847	317	1	=	=	SYM
ejpam-6847	317	2	−∞.	−∞.	PROPN
ejpam-6847	317	3	according	accord	VERB
ejpam-6847	317	4	to	to	ADP
ejpam-6847	317	5	definition	definition	NOUN
ejpam-6847	317	6	14	14	NUM
ejpam-6847	317	7	,	,	PUNCT
ejpam-6847	317	8	this	this	PRON
ejpam-6847	317	9	means	mean	VERB
ejpam-6847	317	10	that	that	SCONJ
ejpam-6847	317	11	limn→+∞	limn→+∞	VERB
ejpam-6847	317	12	s(txn	s(txn	PROPN
ejpam-6847	317	13	,	,	PUNCT
ejpam-6847	317	14	txn	txn	PROPN
ejpam-6847	317	15	,	,	PUNCT
ejpam-6847	317	16	tu	tu	PROPN
ejpam-6847	317	17	)	)	PUNCT
ejpam-6847	317	18	=	=	SYM
ejpam-6847	318	1	0	0	X
ejpam-6847	318	2	.	.	PUNCT
ejpam-6847	318	3	taking	take	VERB
ejpam-6847	318	4	the	the	DET
ejpam-6847	318	5	limit	limit	NOUN
ejpam-6847	318	6	as	as	SCONJ
ejpam-6847	318	7	n	n	PRON
ejpam-6847	318	8	tends	tend	VERB
ejpam-6847	318	9	to	to	PART
ejpam-6847	318	10	infinity	infinity	VERB
ejpam-6847	318	11	in	in	ADP
ejpam-6847	318	12	equation	equation	NOUN
ejpam-6847	318	13	17	17	NUM
ejpam-6847	318	14	,	,	PUNCT
ejpam-6847	318	15	and	and	CCONJ
ejpam-6847	318	16	using	use	VERB
ejpam-6847	318	17	equation	equation	NOUN
ejpam-6847	318	18	16	16	NUM
ejpam-6847	318	19	,	,	PUNCT
ejpam-6847	318	20	and	and	CCONJ
ejpam-6847	318	21	(	(	PUNCT
ejpam-6847	318	22	w2	w2	NOUN
ejpam-6847	318	23	)	)	PUNCT
ejpam-6847	318	24	from	from	ADP
ejpam-6847	318	25	definition	definition	NOUN
ejpam-6847	318	26	14	14	NUM
ejpam-6847	318	27	,	,	PUNCT
ejpam-6847	318	28	we	we	PRON
ejpam-6847	318	29	obtain	obtain	VERB
ejpam-6847	318	30	limn→+∞	limn→+∞	ADP
ejpam-6847	318	31	f	f	PROPN
ejpam-6847	318	32	(	(	PUNCT
ejpam-6847	318	33	s(txn	s(txn	PROPN
ejpam-6847	318	34	,	,	PUNCT
ejpam-6847	318	35	txn	txn	PROPN
ejpam-6847	318	36	,	,	PUNCT
ejpam-6847	318	37	tu	tu	PROPN
ejpam-6847	318	38	)	)	PUNCT
ejpam-6847	318	39	)	)	PUNCT
ejpam-6847	319	1	=	=	SYM
ejpam-6847	319	2	−∞.	−∞.	ADJ
ejpam-6847	319	3	again	again	ADV
ejpam-6847	319	4	,	,	PUNCT
ejpam-6847	319	5	by	by	ADP
ejpam-6847	319	6	definition	definition	NOUN
ejpam-6847	319	7	14	14	NUM
ejpam-6847	319	8	this	this	PRON
ejpam-6847	319	9	implies	imply	VERB
ejpam-6847	319	10	limn→+∞	limn→+∞	VERB
ejpam-6847	319	11	s(txn	s(txn	PROPN
ejpam-6847	319	12	,	,	PUNCT
ejpam-6847	319	13	txn	txn	PROPN
ejpam-6847	319	14	,	,	PUNCT
ejpam-6847	319	15	tu	tu	PROPN
ejpam-6847	319	16	)	)	PUNCT
ejpam-6847	319	17	=	=	SYM
ejpam-6847	320	1	0	0	X
ejpam-6847	320	2	.	.	PUNCT
ejpam-6847	320	3	f.	f.	PROPN
ejpam-6847	320	4	m.	m.	PROPN
ejpam-6847	320	5	azmi	azmi	PROPN
ejpam-6847	320	6	,	,	PUNCT
ejpam-6847	320	7	a.	a.	PROPN
ejpam-6847	320	8	h.	h.	PROPN
ejpam-6847	320	9	ansari	ansari	PROPN
ejpam-6847	320	10	,	,	PUNCT
ejpam-6847	320	11	s.	s.	PROPN
ejpam-6847	320	12	h.	h.	PROPN
ejpam-6847	320	13	j.	j.	PROPN
ejpam-6847	320	14	petroudi	petroudi	PROPN
ejpam-6847	320	15	/	/	SYM
ejpam-6847	320	16	eur	eur	PROPN
ejpam-6847	320	17	.	.	PUNCT
ejpam-6847	321	1	j.	j.	PROPN
ejpam-6847	321	2	pure	pure	PROPN
ejpam-6847	321	3	appl	appl	PROPN
ejpam-6847	321	4	.	.	PROPN
ejpam-6847	321	5	math	math	PROPN
ejpam-6847	321	6	,	,	PUNCT
ejpam-6847	321	7	18	18	NUM
ejpam-6847	321	8	(	(	PUNCT
ejpam-6847	321	9	4	4	NUM
ejpam-6847	321	10	)	)	PUNCT
ejpam-6847	321	11	(	(	PUNCT
ejpam-6847	321	12	2025	2025	NUM
ejpam-6847	321	13	)	)	PUNCT
ejpam-6847	321	14	,	,	PUNCT
ejpam-6847	321	15	6847	6847	NUM
ejpam-6847	321	16	13	13	NUM
ejpam-6847	321	17	of	of	ADP
ejpam-6847	321	18	26	26	NUM
ejpam-6847	321	19	to	to	PART
ejpam-6847	321	20	show	show	VERB
ejpam-6847	321	21	that	that	SCONJ
ejpam-6847	321	22	u	u	PRON
ejpam-6847	321	23	is	be	AUX
ejpam-6847	321	24	a	a	DET
ejpam-6847	321	25	fixed	fix	VERB
ejpam-6847	321	26	point	point	NOUN
ejpam-6847	321	27	,	,	PUNCT
ejpam-6847	321	28	note	note	VERB
ejpam-6847	321	29	that	that	SCONJ
ejpam-6847	321	30	;	;	PUNCT
ejpam-6847	321	31	s(tu	s(tu	PROPN
ejpam-6847	321	32	,	,	PUNCT
ejpam-6847	321	33	tu	tu	PROPN
ejpam-6847	321	34	,	,	PUNCT
ejpam-6847	321	35	u	u	NOUN
ejpam-6847	321	36	)	)	PUNCT
ejpam-6847	321	37	=	=	SYM
ejpam-6847	321	38	s(u	s(u	PROPN
ejpam-6847	321	39	,	,	PUNCT
ejpam-6847	321	40	u	u	NOUN
ejpam-6847	321	41	,	,	PUNCT
ejpam-6847	321	42	tu	tu	PROPN
ejpam-6847	321	43	)	)	PUNCT
ejpam-6847	321	44	≤	≤	NOUN
ejpam-6847	321	45	β(u	β(u	PROPN
ejpam-6847	321	46	,	,	PUNCT
ejpam-6847	321	47	xn+1)s(u	xn+1)s(u	PROPN
ejpam-6847	321	48	,	,	PUNCT
ejpam-6847	321	49	u	u	NOUN
ejpam-6847	321	50	,	,	PUNCT
ejpam-6847	321	51	xn+1	xn+1	NUM
ejpam-6847	321	52	)	)	PUNCT
ejpam-6847	322	1	+	+	CCONJ
ejpam-6847	322	2	µ(u	µ(u	NOUN
ejpam-6847	322	3	,	,	PUNCT
ejpam-6847	322	4	xn+1)s(u	xn+1)s(u	NUM
ejpam-6847	322	5	,	,	PUNCT
ejpam-6847	322	6	u	u	NOUN
ejpam-6847	322	7	,	,	PUNCT
ejpam-6847	322	8	xn+1	xn+1	NUM
ejpam-6847	322	9	)	)	PUNCT
ejpam-6847	323	1	+	+	CCONJ
ejpam-6847	323	2	γ(tu	γ(tu	PROPN
ejpam-6847	323	3	,	,	PUNCT
ejpam-6847	323	4	xn+1)s(tu	xn+1)s(tu	PROPN
ejpam-6847	323	5	,	,	PUNCT
ejpam-6847	323	6	tu	tu	PROPN
ejpam-6847	323	7	,	,	PUNCT
ejpam-6847	323	8	txn	txn	PROPN
ejpam-6847	323	9	)	)	PUNCT
ejpam-6847	323	10	.	.	PUNCT
ejpam-6847	324	1	≤	≤	PROPN
ejpam-6847	324	2	β(u	β(u	PROPN
ejpam-6847	324	3	,	,	PUNCT
ejpam-6847	324	4	xn+1)s(u	xn+1)s(u	PROPN
ejpam-6847	324	5	,	,	PUNCT
ejpam-6847	324	6	u	u	NOUN
ejpam-6847	324	7	,	,	PUNCT
ejpam-6847	324	8	xn+1	xn+1	NUM
ejpam-6847	324	9	)	)	PUNCT
ejpam-6847	325	1	+	+	CCONJ
ejpam-6847	325	2	µ(u	µ(u	NOUN
ejpam-6847	325	3	,	,	PUNCT
ejpam-6847	325	4	xn+1)s(u	xn+1)s(u	NUM
ejpam-6847	325	5	,	,	PUNCT
ejpam-6847	325	6	u	u	NOUN
ejpam-6847	325	7	,	,	PUNCT
ejpam-6847	325	8	xn+1	xn+1	NUM
ejpam-6847	325	9	)	)	PUNCT
ejpam-6847	326	1	+	+	CCONJ
ejpam-6847	326	2	γ(tu	γ(tu	PROPN
ejpam-6847	326	3	,	,	PUNCT
ejpam-6847	326	4	xn+1)s(txn	xn+1)s(txn	PROPN
ejpam-6847	326	5	,	,	PUNCT
ejpam-6847	326	6	txn	txn	PROPN
ejpam-6847	326	7	,	,	PUNCT
ejpam-6847	326	8	tu	tu	PROPN
ejpam-6847	326	9	)	)	PUNCT
ejpam-6847	326	10	.	.	PUNCT
ejpam-6847	327	1	as	as	SCONJ
ejpam-6847	327	2	n	n	PRON
ejpam-6847	327	3	tends	tend	VERB
ejpam-6847	327	4	to	to	ADP
ejpam-6847	327	5	+	+	NOUN
ejpam-6847	327	6	∞	∞	PROPN
ejpam-6847	327	7	in	in	ADP
ejpam-6847	327	8	the	the	DET
ejpam-6847	327	9	preceding	precede	VERB
ejpam-6847	327	10	inequality	inequality	NOUN
ejpam-6847	327	11	,	,	PUNCT
ejpam-6847	327	12	we	we	PRON
ejpam-6847	327	13	conclude	conclude	VERB
ejpam-6847	327	14	that	that	SCONJ
ejpam-6847	327	15	s(tu	s(tu	PROPN
ejpam-6847	327	16	,	,	PUNCT
ejpam-6847	327	17	tu	tu	PROPN
ejpam-6847	327	18	,	,	PUNCT
ejpam-6847	327	19	u	u	NOUN
ejpam-6847	327	20	)	)	PUNCT
ejpam-6847	327	21	=	=	SYM
ejpam-6847	327	22	0	0	NUM
ejpam-6847	327	23	,	,	PUNCT
ejpam-6847	327	24	implying	imply	VERB
ejpam-6847	327	25	tu	tu	PROPN
ejpam-6847	327	26	=	=	PUNCT
ejpam-6847	327	27	u.	u.	PROPN
ejpam-6847	327	28	now	now	ADV
ejpam-6847	327	29	,	,	PUNCT
ejpam-6847	327	30	we	we	PRON
ejpam-6847	327	31	proceed	proceed	VERB
ejpam-6847	327	32	to	to	PART
ejpam-6847	327	33	establish	establish	VERB
ejpam-6847	327	34	the	the	DET
ejpam-6847	327	35	uniqueness	uniqueness	NOUN
ejpam-6847	327	36	of	of	ADP
ejpam-6847	327	37	the	the	DET
ejpam-6847	327	38	fixed	fix	VERB
ejpam-6847	327	39	point	point	NOUN
ejpam-6847	327	40	.	.	PUNCT
ejpam-6847	328	1	suppose	suppose	VERB
ejpam-6847	328	2	there	there	PRON
ejpam-6847	328	3	exist	exist	VERB
ejpam-6847	328	4	two	two	NUM
ejpam-6847	328	5	fixed	fix	VERB
ejpam-6847	328	6	points	point	NOUN
ejpam-6847	328	7	,	,	PUNCT
ejpam-6847	328	8	u	u	NOUN
ejpam-6847	328	9	and	and	CCONJ
ejpam-6847	328	10	v	v	NOUN
ejpam-6847	328	11	,	,	PUNCT
ejpam-6847	328	12	with	with	ADP
ejpam-6847	328	13	u	u	PROPN
ejpam-6847	328	14	6=	6=	PROPN
ejpam-6847	328	15	v	v	ADP
ejpam-6847	328	16	such	such	ADJ
ejpam-6847	328	17	that	that	DET
ejpam-6847	328	18	αs(u	αs(u	PROPN
ejpam-6847	328	19	,	,	PUNCT
ejpam-6847	328	20	u	u	NOUN
ejpam-6847	328	21	,	,	PUNCT
ejpam-6847	328	22	v	v	NOUN
ejpam-6847	328	23	)	)	PUNCT
ejpam-6847	328	24	≥	≥	NOUN
ejpam-6847	328	25	1	1	NUM
ejpam-6847	328	26	,	,	PUNCT
ejpam-6847	328	27	and	and	CCONJ
ejpam-6847	328	28	µs(u	µs(u	NOUN
ejpam-6847	328	29	,	,	PUNCT
ejpam-6847	328	30	u	u	NOUN
ejpam-6847	328	31	,	,	PUNCT
ejpam-6847	328	32	v	v	NOUN
ejpam-6847	328	33	)	)	PUNCT
ejpam-6847	328	34	≤	≤	NOUN
ejpam-6847	328	35	1	1	NUM
ejpam-6847	328	36	.	.	PUNCT
ejpam-6847	329	1	since	since	SCONJ
ejpam-6847	329	2	tu	tu	PROPN
ejpam-6847	329	3	=	=	SYM
ejpam-6847	329	4	u	u	PROPN
ejpam-6847	329	5	6=	6=	PROPN
ejpam-6847	329	6	v	v	NOUN
ejpam-6847	329	7	=	=	SYM
ejpam-6847	329	8	tv	tv	NOUN
ejpam-6847	329	9	,	,	PUNCT
ejpam-6847	329	10	it	it	PRON
ejpam-6847	329	11	implies	imply	VERB
ejpam-6847	329	12	that	that	SCONJ
ejpam-6847	329	13	s(tu	s(tu	PROPN
ejpam-6847	329	14	,	,	PUNCT
ejpam-6847	329	15	tu	tu	PROPN
ejpam-6847	329	16	,	,	PUNCT
ejpam-6847	329	17	tv	tv	NOUN
ejpam-6847	329	18	)	)	PUNCT
ejpam-6847	329	19	>	>	X
ejpam-6847	330	1	0	0	X
ejpam-6847	330	2	.	.	PUNCT
ejpam-6847	330	3	given	give	VERB
ejpam-6847	330	4	that	that	DET
ejpam-6847	330	5	t	t	PROPN
ejpam-6847	330	6	is	be	AUX
ejpam-6847	330	7	an	an	DET
ejpam-6847	330	8	(	(	PUNCT
ejpam-6847	330	9	αs	αs	ADJ
ejpam-6847	330	10	,	,	PUNCT
ejpam-6847	330	11	µs	µs	NOUN
ejpam-6847	330	12	,	,	PUNCT
ejpam-6847	330	13	(	(	PUNCT
ejpam-6847	330	14	q	q	X
ejpam-6847	330	15	,	,	PUNCT
ejpam-6847	330	16	h)−f)-contraction	h)−f)-contraction	NOUN
ejpam-6847	330	17	mapping	mapping	NOUN
ejpam-6847	330	18	,	,	PUNCT
ejpam-6847	330	19	utilizing	utilize	VERB
ejpam-6847	330	20	equation	equation	NOUN
ejpam-6847	330	21	4	4	NUM
ejpam-6847	330	22	,	,	PUNCT
ejpam-6847	330	23	we	we	PRON
ejpam-6847	330	24	obtain	obtain	VERB
ejpam-6847	330	25	h	h	NOUN
ejpam-6847	330	26	(	(	PUNCT
ejpam-6847	330	27	1	1	NUM
ejpam-6847	330	28	,	,	PUNCT
ejpam-6847	330	29	τ	τ	PROPN
ejpam-6847	331	1	+	+	NUM
ejpam-6847	331	2	f	f	X
ejpam-6847	331	3	(	(	PUNCT
ejpam-6847	331	4	s(tu	s(tu	PROPN
ejpam-6847	331	5	,	,	PUNCT
ejpam-6847	331	6	tu	tu	PROPN
ejpam-6847	331	7	,	,	PUNCT
ejpam-6847	331	8	tv	tv	NOUN
ejpam-6847	331	9	)	)	PUNCT
ejpam-6847	331	10	)	)	PUNCT
ejpam-6847	331	11	)	)	PUNCT
ejpam-6847	331	12	≤	≤	NUM
ejpam-6847	331	13	h	h	NOUN
ejpam-6847	331	14	(	(	PUNCT
ejpam-6847	331	15	αs(u	αs(u	PROPN
ejpam-6847	331	16	,	,	PUNCT
ejpam-6847	331	17	u	u	NOUN
ejpam-6847	331	18	,	,	PUNCT
ejpam-6847	331	19	v	v	NOUN
ejpam-6847	331	20	)	)	PUNCT
ejpam-6847	331	21	,	,	PUNCT
ejpam-6847	331	22	τ	τ	PROPN
ejpam-6847	331	23	+	+	NUM
ejpam-6847	331	24	f	f	X
ejpam-6847	331	25	(	(	PUNCT
ejpam-6847	331	26	s(tu	s(tu	PROPN
ejpam-6847	331	27	,	,	PUNCT
ejpam-6847	331	28	tu	tu	PROPN
ejpam-6847	331	29	,	,	PUNCT
ejpam-6847	331	30	tv	tv	NOUN
ejpam-6847	331	31	)	)	PUNCT
ejpam-6847	331	32	)	)	PUNCT
ejpam-6847	331	33	)	)	PUNCT
ejpam-6847	332	1	≤	≤	NUM
ejpam-6847	332	2	q	q	PUNCT
ejpam-6847	332	3	(	(	PUNCT
ejpam-6847	332	4	νs(u	νs(u	X
ejpam-6847	332	5	,	,	PUNCT
ejpam-6847	332	6	u	u	NOUN
ejpam-6847	332	7	,	,	PUNCT
ejpam-6847	332	8	v	v	NOUN
ejpam-6847	332	9	)	)	PUNCT
ejpam-6847	332	10	,	,	PUNCT
ejpam-6847	332	11	f	f	PROPN
ejpam-6847	332	12	(	(	PUNCT
ejpam-6847	332	13	s(u	s(u	PROPN
ejpam-6847	332	14	,	,	PUNCT
ejpam-6847	332	15	u	u	NOUN
ejpam-6847	332	16	,	,	PUNCT
ejpam-6847	332	17	v	v	NOUN
ejpam-6847	332	18	)	)	PUNCT
ejpam-6847	332	19	)	)	PUNCT
ejpam-6847	332	20	)	)	PUNCT
ejpam-6847	333	1	≤	≤	NUM
ejpam-6847	334	1	q	q	NOUN
ejpam-6847	334	2	(	(	PUNCT
ejpam-6847	334	3	1	1	NUM
ejpam-6847	334	4	,	,	PUNCT
ejpam-6847	334	5	f	f	PROPN
ejpam-6847	334	6	(	(	PUNCT
ejpam-6847	334	7	s(u	s(u	PROPN
ejpam-6847	334	8	,	,	PUNCT
ejpam-6847	334	9	u	u	NOUN
ejpam-6847	334	10	,	,	PUNCT
ejpam-6847	334	11	v	v	NOUN
ejpam-6847	334	12	)	)	PUNCT
ejpam-6847	334	13	)	)	PUNCT
ejpam-6847	334	14	)	)	PUNCT
ejpam-6847	334	15	.	.	PUNCT
ejpam-6847	335	1	since	since	SCONJ
ejpam-6847	335	2	the	the	DET
ejpam-6847	335	3	pair(q	pair(q	PROPN
ejpam-6847	335	4	,	,	PUNCT
ejpam-6847	335	5	h	h	NOUN
ejpam-6847	335	6	)	)	PUNCT
ejpam-6847	335	7	is	be	AUX
ejpam-6847	335	8	an	an	DET
ejpam-6847	335	9	upper	upper	ADJ
ejpam-6847	335	10	class	class	NOUN
ejpam-6847	335	11	of	of	ADP
ejpam-6847	335	12	type	type	NOUN
ejpam-6847	335	13	i	i	PRON
ejpam-6847	335	14	,	,	PUNCT
ejpam-6847	335	15	we	we	PRON
ejpam-6847	335	16	get	get	VERB
ejpam-6847	335	17	τ	τ	PROPN
ejpam-6847	335	18	+	+	NUM
ejpam-6847	335	19	f	f	X
ejpam-6847	335	20	(	(	PUNCT
ejpam-6847	335	21	s(tu	s(tu	PROPN
ejpam-6847	335	22	,	,	PUNCT
ejpam-6847	335	23	tu	tu	PROPN
ejpam-6847	335	24	,	,	PUNCT
ejpam-6847	335	25	tv	tv	NOUN
ejpam-6847	335	26	)	)	PUNCT
ejpam-6847	335	27	)	)	PUNCT
ejpam-6847	336	1	≤	≤	NUM
ejpam-6847	336	2	τ	τ	PROPN
ejpam-6847	337	1	+	+	SYM
ejpam-6847	337	2	αs(u	αs(u	PROPN
ejpam-6847	337	3	,	,	PUNCT
ejpam-6847	337	4	u	u	NOUN
ejpam-6847	337	5	,	,	PUNCT
ejpam-6847	337	6	v)f	v)f	NOUN
ejpam-6847	337	7	(	(	PUNCT
ejpam-6847	337	8	s(tu	s(tu	PROPN
ejpam-6847	337	9	,	,	PUNCT
ejpam-6847	337	10	tu	tu	PROPN
ejpam-6847	337	11	,	,	PUNCT
ejpam-6847	337	12	tv	tv	NOUN
ejpam-6847	337	13	)	)	PUNCT
ejpam-6847	337	14	)	)	PUNCT
ejpam-6847	338	1	≤	≤	NUM
ejpam-6847	338	2	f	f	X
ejpam-6847	338	3	(	(	PUNCT
ejpam-6847	338	4	s(u	s(u	PROPN
ejpam-6847	338	5	,	,	PUNCT
ejpam-6847	338	6	u	u	NOUN
ejpam-6847	338	7	,	,	PUNCT
ejpam-6847	338	8	v	v	NOUN
ejpam-6847	338	9	)	)	PUNCT
ejpam-6847	338	10	)	)	PUNCT
ejpam-6847	339	1	=	=	SYM
ejpam-6847	339	2	f	f	PROPN
ejpam-6847	339	3	(	(	PUNCT
ejpam-6847	339	4	s(tu	s(tu	PROPN
ejpam-6847	339	5	,	,	PUNCT
ejpam-6847	339	6	tu	tu	PROPN
ejpam-6847	339	7	,	,	PUNCT
ejpam-6847	339	8	tv	tv	NOUN
ejpam-6847	339	9	)	)	PUNCT
ejpam-6847	339	10	)	)	PUNCT
ejpam-6847	339	11	.	.	PUNCT
ejpam-6847	340	1	this	this	PRON
ejpam-6847	340	2	implies	imply	VERB
ejpam-6847	340	3	τ	τ	PROPN
ejpam-6847	340	4	≤	≤	NUM
ejpam-6847	340	5	0	0	NUM
ejpam-6847	340	6	,	,	PUNCT
ejpam-6847	340	7	leading	lead	VERB
ejpam-6847	340	8	to	to	ADP
ejpam-6847	340	9	a	a	DET
ejpam-6847	340	10	contradiction	contradiction	NOUN
ejpam-6847	340	11	.	.	PUNCT
ejpam-6847	341	1	therefore	therefore	ADV
ejpam-6847	341	2	,	,	PUNCT
ejpam-6847	341	3	u	u	PROPN
ejpam-6847	341	4	=	=	PROPN
ejpam-6847	341	5	v	v	NOUN
ejpam-6847	341	6	,	,	PUNCT
ejpam-6847	341	7	implying	imply	VERB
ejpam-6847	341	8	the	the	DET
ejpam-6847	341	9	uniqueness	uniqueness	NOUN
ejpam-6847	341	10	of	of	ADP
ejpam-6847	341	11	the	the	DET
ejpam-6847	341	12	fixed	fix	VERB
ejpam-6847	341	13	point	point	NOUN
ejpam-6847	341	14	.	.	PUNCT
ejpam-6847	342	1	we	we	PRON
ejpam-6847	342	2	will	will	AUX
ejpam-6847	342	3	now	now	ADV
ejpam-6847	342	4	provide	provide	VERB
ejpam-6847	342	5	an	an	DET
ejpam-6847	342	6	example	example	NOUN
ejpam-6847	342	7	that	that	SCONJ
ejpam-6847	342	8	supports	support	VERB
ejpam-6847	342	9	theorem	theorem	NOUN
ejpam-6847	342	10	1	1	NUM
ejpam-6847	342	11	,	,	PUNCT
ejpam-6847	342	12	based	base	VERB
ejpam-6847	342	13	on	on	ADP
ejpam-6847	342	14	the	the	DET
ejpam-6847	342	15	work	work	NOUN
ejpam-6847	342	16	of	of	ADP
ejpam-6847	342	17	azmi	azmi	PROPN
ejpam-6847	342	18	[	[	X
ejpam-6847	342	19	9	9	NUM
ejpam-6847	342	20	]	]	PUNCT
ejpam-6847	342	21	.	.	PUNCT
ejpam-6847	342	22	example	example	NOUN
ejpam-6847	343	1	7	7	X
ejpam-6847	343	2	.	.	PUNCT
ejpam-6847	344	1	let	let	VERB
ejpam-6847	344	2	x	x	PUNCT
ejpam-6847	344	3	=	=	PUNCT
ejpam-6847	345	1	[	[	X
ejpam-6847	345	2	0,+∞	0,+∞	NUM
ejpam-6847	345	3	)	)	PUNCT
ejpam-6847	345	4	,	,	PUNCT
ejpam-6847	345	5	and	and	CCONJ
ejpam-6847	345	6	consider	consider	VERB
ejpam-6847	345	7	the	the	DET
ejpam-6847	345	8	mapping	mapping	NOUN
ejpam-6847	345	9	s	s	PART
ejpam-6847	345	10	:	:	PUNCT
ejpam-6847	345	11	x3	x3	ADJ
ejpam-6847	345	12	→	→	PUNCT
ejpam-6847	345	13	[	[	X
ejpam-6847	345	14	0,+∞	0,+∞	NUM
ejpam-6847	345	15	)	)	PUNCT
ejpam-6847	345	16	,	,	PUNCT
ejpam-6847	345	17	defined	define	VERB
ejpam-6847	345	18	by	by	ADP
ejpam-6847	345	19	s(x	s(x	PROPN
ejpam-6847	345	20	,	,	PUNCT
ejpam-6847	345	21	y	y	PROPN
ejpam-6847	345	22	,	,	PUNCT
ejpam-6847	345	23	z	z	NOUN
ejpam-6847	345	24	)	)	PUNCT
ejpam-6847	345	25	=	=	SYM
ejpam-6847	345	26	|x−y|+	|x−y|+	PRON
ejpam-6847	345	27	|y−z|	|y−z|	NOUN
ejpam-6847	345	28	.	.	PUNCT
ejpam-6847	346	1	then	then	ADV
ejpam-6847	346	2	(	(	PUNCT
ejpam-6847	346	3	x	x	X
ejpam-6847	346	4	,	,	PUNCT
ejpam-6847	346	5	s	s	PART
ejpam-6847	346	6	)	)	PUNCT
ejpam-6847	346	7	is	be	AUX
ejpam-6847	346	8	a	a	DET
ejpam-6847	346	9	complete	complete	ADJ
ejpam-6847	346	10	t	t	NOUN
ejpam-6847	346	11	c	c	X
ejpam-6847	346	12	-	-	PUNCT
ejpam-6847	346	13	s	s	PROPN
ejpam-6847	346	14	-	-	PUNCT
ejpam-6847	346	15	mt	mt	NOUN
ejpam-6847	346	16	s	s	PROPN
ejpam-6847	346	17	,	,	PUNCT
ejpam-6847	346	18	where	where	SCONJ
ejpam-6847	346	19	β	β	X
ejpam-6847	346	20	,	,	PUNCT
ejpam-6847	346	21	µ	µ	NOUN
ejpam-6847	346	22	,	,	PUNCT
ejpam-6847	346	23	γ	γ	X
ejpam-6847	346	24	:	:	PUNCT
ejpam-6847	346	25	x2	x2	PROPN
ejpam-6847	346	26	→	→	PUNCT
ejpam-6847	347	1	[	[	X
ejpam-6847	347	2	1,+∞	1,+∞	NUM
ejpam-6847	347	3	)	)	PUNCT
ejpam-6847	347	4	are	be	AUX
ejpam-6847	347	5	defined	define	VERB
ejpam-6847	347	6	by	by	ADP
ejpam-6847	347	7	β(x	β(x	PROPN
ejpam-6847	347	8	,	,	PUNCT
ejpam-6847	347	9	y	y	NOUN
ejpam-6847	347	10	)	)	PUNCT
ejpam-6847	347	11	=	=	SYM
ejpam-6847	347	12	max{x	max{x	PROPN
ejpam-6847	347	13	,	,	PUNCT
ejpam-6847	347	14	y}+	y}+	PROPN
ejpam-6847	347	15	1	1	NUM
ejpam-6847	347	16	,	,	PUNCT
ejpam-6847	347	17	µ(x	µ(x	ADJ
ejpam-6847	347	18	,	,	PUNCT
ejpam-6847	347	19	y	y	NOUN
ejpam-6847	347	20	)	)	PUNCT
ejpam-6847	347	21	=	=	SYM
ejpam-6847	347	22	max{x	max{x	PROPN
ejpam-6847	347	23	,	,	PUNCT
ejpam-6847	347	24	y}+	y}+	PROPN
ejpam-6847	347	25	2	2	NUM
ejpam-6847	347	26	,	,	PUNCT
ejpam-6847	347	27	and	and	CCONJ
ejpam-6847	347	28	γ(x	γ(x	PROPN
ejpam-6847	347	29	,	,	PUNCT
ejpam-6847	347	30	y	y	NOUN
ejpam-6847	347	31	)	)	PUNCT
ejpam-6847	348	1	=	=	PRON
ejpam-6847	348	2	{	{	PUNCT
ejpam-6847	348	3	x+	x+	INTJ
ejpam-6847	348	4	y	y	NOUN
ejpam-6847	348	5	if	if	SCONJ
ejpam-6847	348	6	x	x	X
ejpam-6847	348	7	∈	∈	PROPN
ejpam-6847	349	1	[	[	X
ejpam-6847	349	2	0	0	NUM
ejpam-6847	349	3	,	,	PUNCT
ejpam-6847	349	4	1	1	NUM
ejpam-6847	349	5	]	]	PUNCT
ejpam-6847	349	6	,	,	PUNCT
ejpam-6847	349	7	1	1	NUM
ejpam-6847	349	8	if	if	SCONJ
ejpam-6847	349	9	x	x	PROPN
ejpam-6847	349	10	>	>	X
ejpam-6847	349	11	1	1	NUM
ejpam-6847	349	12	.	.	PUNCT
ejpam-6847	350	1	the	the	DET
ejpam-6847	350	2	mapping	mapping	NOUN
ejpam-6847	350	3	t	t	NOUN
ejpam-6847	350	4	:	:	PUNCT
ejpam-6847	350	5	x	x	X
ejpam-6847	350	6	→	→	SYM
ejpam-6847	350	7	x	x	X
ejpam-6847	350	8	,	,	PUNCT
ejpam-6847	350	9	is	be	AUX
ejpam-6847	350	10	defined	define	VERB
ejpam-6847	350	11	by	by	ADP
ejpam-6847	350	12	t	t	PROPN
ejpam-6847	350	13	(	(	PUNCT
ejpam-6847	350	14	x	x	NOUN
ejpam-6847	350	15	)	)	PUNCT
ejpam-6847	350	16	=	=	PRON
ejpam-6847	350	17	{	{	PUNCT
ejpam-6847	350	18	x	x	SYM
ejpam-6847	350	19	3	3	NUM
ejpam-6847	350	20	if	if	SCONJ
ejpam-6847	350	21	x	x	X
ejpam-6847	350	22	∈	∈	PROPN
ejpam-6847	351	1	[	[	X
ejpam-6847	351	2	0	0	NUM
ejpam-6847	351	3	,	,	PUNCT
ejpam-6847	351	4	1	1	NUM
ejpam-6847	351	5	]	]	PUNCT
ejpam-6847	351	6	,	,	PUNCT
ejpam-6847	351	7	2x−	2x−	NUM
ejpam-6847	351	8	5	5	NUM
ejpam-6847	351	9	3	3	NUM
ejpam-6847	351	10	if	if	SCONJ
ejpam-6847	351	11	x	x	PROPN
ejpam-6847	351	12	>	>	X
ejpam-6847	351	13	1	1	NUM
ejpam-6847	351	14	.	.	PUNCT
ejpam-6847	351	15	f.	f.	PROPN
ejpam-6847	351	16	m.	m.	PROPN
ejpam-6847	351	17	azmi	azmi	PROPN
ejpam-6847	351	18	,	,	PUNCT
ejpam-6847	351	19	a.	a.	PROPN
ejpam-6847	351	20	h.	h.	PROPN
ejpam-6847	351	21	ansari	ansari	PROPN
ejpam-6847	351	22	,	,	PUNCT
ejpam-6847	351	23	s.	s.	PROPN
ejpam-6847	351	24	h.	h.	PROPN
ejpam-6847	351	25	j.	j.	PROPN
ejpam-6847	351	26	petroudi	petroudi	PROPN
ejpam-6847	351	27	/	/	SYM
ejpam-6847	351	28	eur	eur	PROPN
ejpam-6847	351	29	.	.	PUNCT
ejpam-6847	352	1	j.	j.	PROPN
ejpam-6847	352	2	pure	pure	PROPN
ejpam-6847	352	3	appl	appl	PROPN
ejpam-6847	352	4	.	.	PROPN
ejpam-6847	352	5	math	math	PROPN
ejpam-6847	352	6	,	,	PUNCT
ejpam-6847	352	7	18	18	NUM
ejpam-6847	352	8	(	(	PUNCT
ejpam-6847	352	9	4	4	NUM
ejpam-6847	352	10	)	)	PUNCT
ejpam-6847	352	11	(	(	PUNCT
ejpam-6847	352	12	2025	2025	NUM
ejpam-6847	352	13	)	)	PUNCT
ejpam-6847	352	14	,	,	PUNCT
ejpam-6847	352	15	6847	6847	NUM
ejpam-6847	352	16	14	14	NUM
ejpam-6847	352	17	of	of	ADP
ejpam-6847	352	18	26	26	NUM
ejpam-6847	352	19	let	let	VERB
ejpam-6847	352	20	αs	αs	PROPN
ejpam-6847	352	21	,	,	PUNCT
ejpam-6847	352	22	νs	νs	X
ejpam-6847	352	23	:	:	PUNCT
ejpam-6847	352	24	x	x	SYM
ejpam-6847	352	25	3	3	NUM
ejpam-6847	352	26	→	→	SYM
ejpam-6847	352	27	(	(	PUNCT
ejpam-6847	352	28	−∞,+∞	−∞,+∞	NUM
ejpam-6847	352	29	)	)	PUNCT
ejpam-6847	352	30	,	,	PUNCT
ejpam-6847	352	31	and	and	CCONJ
ejpam-6847	352	32	f	f	X
ejpam-6847	352	33	:	:	PUNCT
ejpam-6847	352	34	(	(	PUNCT
ejpam-6847	352	35	0,+∞	0,+∞	NUM
ejpam-6847	352	36	)	)	PUNCT
ejpam-6847	352	37	→	→	SYM
ejpam-6847	352	38	(	(	PUNCT
ejpam-6847	352	39	−∞,+∞	−∞,+∞	ADV
ejpam-6847	352	40	)	)	PUNCT
ejpam-6847	352	41	be	be	AUX
ejpam-6847	352	42	defined	define	VERB
ejpam-6847	352	43	by	by	ADP
ejpam-6847	352	44	,	,	PUNCT
ejpam-6847	352	45	αs(x	αs(x	NUM
ejpam-6847	352	46	,	,	PUNCT
ejpam-6847	352	47	y	y	PROPN
ejpam-6847	352	48	,	,	PUNCT
ejpam-6847	352	49	z	z	NOUN
ejpam-6847	352	50	)	)	PUNCT
ejpam-6847	352	51	=	=	PRON
ejpam-6847	352	52	{	{	PUNCT
ejpam-6847	352	53	1	1	NUM
ejpam-6847	352	54	if	if	SCONJ
ejpam-6847	352	55	x	x	PROPN
ejpam-6847	352	56	,	,	PUNCT
ejpam-6847	352	57	y	y	PROPN
ejpam-6847	352	58	,	,	PUNCT
ejpam-6847	352	59	z	z	NOUN
ejpam-6847	352	60	∈	∈	PROPN
ejpam-6847	353	1	[	[	X
ejpam-6847	353	2	0	0	NUM
ejpam-6847	353	3	,	,	PUNCT
ejpam-6847	353	4	1	1	NUM
ejpam-6847	353	5	]	]	PUNCT
ejpam-6847	353	6	,	,	PUNCT
ejpam-6847	353	7	0	0	NUM
ejpam-6847	353	8	otherwise	otherwise	ADV
ejpam-6847	353	9	.	.	PUNCT
ejpam-6847	354	1	νs(x	νs(x	PROPN
ejpam-6847	354	2	,	,	PUNCT
ejpam-6847	354	3	y	y	PROPN
ejpam-6847	354	4	,	,	PUNCT
ejpam-6847	354	5	z	z	NOUN
ejpam-6847	354	6	)	)	PUNCT
ejpam-6847	354	7	=	=	PRON
ejpam-6847	354	8	{	{	PUNCT
ejpam-6847	354	9	1	1	NUM
ejpam-6847	354	10	if	if	SCONJ
ejpam-6847	354	11	x	x	PROPN
ejpam-6847	354	12	,	,	PUNCT
ejpam-6847	354	13	y	y	PROPN
ejpam-6847	354	14	,	,	PUNCT
ejpam-6847	354	15	z	z	NOUN
ejpam-6847	354	16	∈	∈	PROPN
ejpam-6847	355	1	[	[	X
ejpam-6847	355	2	0	0	NUM
ejpam-6847	355	3	,	,	PUNCT
ejpam-6847	355	4	1	1	NUM
ejpam-6847	355	5	]	]	PUNCT
ejpam-6847	355	6	,	,	PUNCT
ejpam-6847	355	7	2	2	NUM
ejpam-6847	355	8	otherwise	otherwise	ADV
ejpam-6847	355	9	.	.	PUNCT
ejpam-6847	356	1	and	and	CCONJ
ejpam-6847	356	2	f	f	PROPN
ejpam-6847	356	3	(	(	PUNCT
ejpam-6847	356	4	t	t	PROPN
ejpam-6847	356	5	)	)	PUNCT
ejpam-6847	356	6	=	=	NOUN
ejpam-6847	356	7	ln(t	ln(t	PRON
ejpam-6847	356	8	)	)	PUNCT
ejpam-6847	356	9	.	.	PUNCT
ejpam-6847	357	1	to	to	PART
ejpam-6847	357	2	show	show	VERB
ejpam-6847	357	3	t	t	PROPN
ejpam-6847	357	4	is	be	AUX
ejpam-6847	357	5	(	(	PUNCT
ejpam-6847	357	6	αs	αs	PROPN
ejpam-6847	357	7	,	,	PUNCT
ejpam-6847	357	8	νs	νs	NOUN
ejpam-6847	357	9	,	,	PUNCT
ejpam-6847	357	10	(	(	PUNCT
ejpam-6847	357	11	q	q	X
ejpam-6847	357	12	,	,	PUNCT
ejpam-6847	357	13	h	h	NOUN
ejpam-6847	357	14	)	)	PUNCT
ejpam-6847	357	15	−	−	PROPN
ejpam-6847	357	16	f)-contraction	f)-contraction	NOUN
ejpam-6847	357	17	mapping	mapping	NOUN
ejpam-6847	357	18	;	;	PUNCT
ejpam-6847	357	19	we	we	PRON
ejpam-6847	357	20	only	only	ADV
ejpam-6847	357	21	need	need	VERB
ejpam-6847	357	22	to	to	PART
ejpam-6847	357	23	consider	consider	VERB
ejpam-6847	357	24	the	the	DET
ejpam-6847	357	25	case	case	NOUN
ejpam-6847	357	26	when	when	SCONJ
ejpam-6847	357	27	x	x	X
ejpam-6847	357	28	,	,	PUNCT
ejpam-6847	357	29	y	y	PROPN
ejpam-6847	357	30	,	,	PUNCT
ejpam-6847	357	31	z	z	NOUN
ejpam-6847	357	32	∈	∈	PROPN
ejpam-6847	358	1	[	[	X
ejpam-6847	358	2	0	0	NUM
ejpam-6847	358	3	,	,	PUNCT
ejpam-6847	358	4	1	1	NUM
ejpam-6847	358	5	]	]	PUNCT
ejpam-6847	358	6	.	.	PUNCT
ejpam-6847	359	1	note	note	VERB
ejpam-6847	359	2	that	that	SCONJ
ejpam-6847	359	3	s(tx	s(tx	NOUN
ejpam-6847	359	4	,	,	PUNCT
ejpam-6847	359	5	ty	ty	INTJ
ejpam-6847	359	6	,	,	PUNCT
ejpam-6847	359	7	tz	tz	NOUN
ejpam-6847	359	8	)	)	PUNCT
ejpam-6847	359	9	=	=	NOUN
ejpam-6847	359	10	|tx−	|tx−	NUM
ejpam-6847	359	11	ty|+	ty|+	PROPN
ejpam-6847	359	12	|ty	|ty	AUX
ejpam-6847	359	13	−	−	NOUN
ejpam-6847	359	14	tz|	tz|	NOUN
ejpam-6847	359	15	=	=	SYM
ejpam-6847	359	16	1	1	NUM
ejpam-6847	359	17	3	3	NUM
ejpam-6847	359	18	|x−	|x−	NOUN
ejpam-6847	359	19	y|+	y|+	PROPN
ejpam-6847	359	20	1	1	NUM
ejpam-6847	359	21	3	3	NUM
ejpam-6847	359	22	|y	|y	NOUN
ejpam-6847	359	23	−	−	PRON
ejpam-6847	359	24	z|	z|	PRON
ejpam-6847	359	25	=	=	SYM
ejpam-6847	359	26	1	1	NUM
ejpam-6847	359	27	3	3	NUM
ejpam-6847	359	28	s(x	s(x	PROPN
ejpam-6847	359	29	,	,	PUNCT
ejpam-6847	359	30	y	y	PROPN
ejpam-6847	359	31	,	,	PUNCT
ejpam-6847	359	32	z	z	NOUN
ejpam-6847	359	33	)	)	PUNCT
ejpam-6847	359	34	<	<	X
ejpam-6847	359	35	2	2	NUM
ejpam-6847	359	36	3	3	NUM
ejpam-6847	359	37	s(x	s(x	NOUN
ejpam-6847	359	38	,	,	PUNCT
ejpam-6847	359	39	y	y	PROPN
ejpam-6847	359	40	,	,	PUNCT
ejpam-6847	359	41	z	z	NOUN
ejpam-6847	359	42	)	)	PUNCT
ejpam-6847	359	43	.	.	PUNCT
ejpam-6847	360	1	hence	hence	ADV
ejpam-6847	360	2	,	,	PUNCT
ejpam-6847	360	3	the	the	DET
ejpam-6847	360	4	following	follow	VERB
ejpam-6847	360	5	inequality	inequality	NOUN
ejpam-6847	360	6	holds	hold	VERB
ejpam-6847	360	7	:	:	PUNCT
ejpam-6847	360	8	αs(x	αs(x	NUM
ejpam-6847	360	9	,	,	PUNCT
ejpam-6847	360	10	y	y	NOUN
ejpam-6847	360	11	,	,	PUNCT
ejpam-6847	360	12	z)(ln	z)(ln	NOUN
ejpam-6847	360	13	(	(	PUNCT
ejpam-6847	360	14	3	3	NUM
ejpam-6847	360	15	2	2	NUM
ejpam-6847	360	16	)	)	PUNCT
ejpam-6847	361	1	+	+	ADP
ejpam-6847	361	2	ln(s(tx	ln(s(tx	PROPN
ejpam-6847	361	3	,	,	PUNCT
ejpam-6847	361	4	ty	ty	INTJ
ejpam-6847	361	5	,	,	PUNCT
ejpam-6847	361	6	tz	tz	NOUN
ejpam-6847	361	7	)	)	PUNCT
ejpam-6847	361	8	)	)	PUNCT
ejpam-6847	361	9	)	)	PUNCT
ejpam-6847	362	1	≤	≤	NOUN
ejpam-6847	363	1	ln	ln	ADJ
ejpam-6847	363	2	(	(	PUNCT
ejpam-6847	363	3	3	3	NUM
ejpam-6847	363	4	2	2	NUM
ejpam-6847	363	5	)	)	PUNCT
ejpam-6847	364	1	+	+	ADP
ejpam-6847	364	2	ln(s(tx	ln(s(tx	PROPN
ejpam-6847	364	3	,	,	PUNCT
ejpam-6847	364	4	ty	ty	INTJ
ejpam-6847	364	5	,	,	PUNCT
ejpam-6847	364	6	tz	tz	NOUN
ejpam-6847	364	7	)	)	PUNCT
ejpam-6847	364	8	)	)	PUNCT
ejpam-6847	364	9	≤	≤	NOUN
ejpam-6847	364	10	νs(x	νs(x	NOUN
ejpam-6847	364	11	,	,	PUNCT
ejpam-6847	364	12	y	y	PROPN
ejpam-6847	364	13	,	,	PUNCT
ejpam-6847	364	14	z)ln(s(x	z)ln(s(x	PROPN
ejpam-6847	364	15	,	,	PUNCT
ejpam-6847	364	16	y	y	PROPN
ejpam-6847	364	17	,	,	PUNCT
ejpam-6847	364	18	z	z	NOUN
ejpam-6847	364	19	)	)	PUNCT
ejpam-6847	364	20	)	)	PUNCT
ejpam-6847	364	21	.	.	PUNCT
ejpam-6847	365	1	(	(	PUNCT
ejpam-6847	365	2	18	18	NUM
ejpam-6847	365	3	)	)	PUNCT
ejpam-6847	365	4	by	by	ADP
ejpam-6847	365	5	taking	take	VERB
ejpam-6847	365	6	τ	τ	X
ejpam-6847	365	7	=	=	SYM
ejpam-6847	365	8	ln(32	ln(32	PROPN
ejpam-6847	365	9	)	)	PUNCT
ejpam-6847	365	10	>	>	X
ejpam-6847	365	11	0	0	NUM
ejpam-6847	365	12	,	,	PUNCT
ejpam-6847	365	13	in	in	ADP
ejpam-6847	365	14	18	18	NUM
ejpam-6847	365	15	,	,	PUNCT
ejpam-6847	365	16	we	we	PRON
ejpam-6847	365	17	find	find	VERB
ejpam-6847	365	18	that	that	SCONJ
ejpam-6847	365	19	αs(x	αs(x	NUM
ejpam-6847	365	20	,	,	PUNCT
ejpam-6847	365	21	y	y	NOUN
ejpam-6847	365	22	,	,	PUNCT
ejpam-6847	365	23	z)(τ	z)(τ	PROPN
ejpam-6847	366	1	+	+	CCONJ
ejpam-6847	366	2	f	f	X
ejpam-6847	366	3	(	(	PUNCT
ejpam-6847	366	4	s(tx	s(tx	PROPN
ejpam-6847	366	5	,	,	PUNCT
ejpam-6847	366	6	ty	ty	INTJ
ejpam-6847	366	7	,	,	PUNCT
ejpam-6847	366	8	tz	tz	NOUN
ejpam-6847	366	9	)	)	PUNCT
ejpam-6847	366	10	)	)	PUNCT
ejpam-6847	366	11	)	)	PUNCT
ejpam-6847	367	1	≤	≤	NOUN
ejpam-6847	367	2	νs(x	νs(x	NOUN
ejpam-6847	367	3	,	,	PUNCT
ejpam-6847	367	4	y	y	PROPN
ejpam-6847	367	5	,	,	PUNCT
ejpam-6847	367	6	z)f	z)f	X
ejpam-6847	367	7	(	(	PUNCT
ejpam-6847	367	8	s(x	s(x	PROPN
ejpam-6847	367	9	,	,	PUNCT
ejpam-6847	367	10	y	y	PROPN
ejpam-6847	367	11	,	,	PUNCT
ejpam-6847	367	12	z	z	NOUN
ejpam-6847	367	13	)	)	PUNCT
ejpam-6847	367	14	)	)	PUNCT
ejpam-6847	367	15	.	.	PUNCT
ejpam-6847	368	1	therefore	therefore	ADV
ejpam-6847	368	2	,	,	PUNCT
ejpam-6847	368	3	we	we	PRON
ejpam-6847	368	4	have	have	VERB
ejpam-6847	368	5	h	h	NOUN
ejpam-6847	368	6	(	(	PUNCT
ejpam-6847	368	7	αs(x	αs(x	NUM
ejpam-6847	368	8	,	,	PUNCT
ejpam-6847	368	9	y	y	PROPN
ejpam-6847	368	10	,	,	PUNCT
ejpam-6847	368	11	z	z	PROPN
ejpam-6847	368	12	)	)	PUNCT
ejpam-6847	368	13	,	,	PUNCT
ejpam-6847	368	14	τ	τ	PROPN
ejpam-6847	369	1	+	+	NUM
ejpam-6847	369	2	f	f	X
ejpam-6847	369	3	(	(	PUNCT
ejpam-6847	369	4	s(tx	s(tx	PROPN
ejpam-6847	369	5	,	,	PUNCT
ejpam-6847	369	6	ty	ty	INTJ
ejpam-6847	369	7	,	,	PUNCT
ejpam-6847	369	8	tz	tz	PROPN
ejpam-6847	369	9	)	)	PUNCT
ejpam-6847	369	10	)	)	PUNCT
ejpam-6847	369	11	≤	≤	NUM
ejpam-6847	369	12	q	q	X
ejpam-6847	369	13	(	(	PUNCT
ejpam-6847	369	14	νs(x	νs(x	PROPN
ejpam-6847	369	15	,	,	PUNCT
ejpam-6847	369	16	y	y	PROPN
ejpam-6847	369	17	,	,	PUNCT
ejpam-6847	369	18	z	z	NOUN
ejpam-6847	369	19	)	)	PUNCT
ejpam-6847	369	20	,	,	PUNCT
ejpam-6847	369	21	f	f	PROPN
ejpam-6847	369	22	(	(	PUNCT
ejpam-6847	369	23	s(x	s(x	PROPN
ejpam-6847	369	24	,	,	PUNCT
ejpam-6847	369	25	y	y	PROPN
ejpam-6847	369	26	,	,	PUNCT
ejpam-6847	369	27	z	z	NOUN
ejpam-6847	369	28	)	)	PUNCT
ejpam-6847	369	29	)	)	PUNCT
ejpam-6847	369	30	)	)	PUNCT
ejpam-6847	370	1	,	,	PUNCT
ejpam-6847	370	2	which	which	PRON
ejpam-6847	370	3	implies	imply	VERB
ejpam-6847	370	4	that	that	SCONJ
ejpam-6847	370	5	t	t	PROPN
ejpam-6847	370	6	is	be	AUX
ejpam-6847	370	7	(	(	PUNCT
ejpam-6847	370	8	αs	αs	PROPN
ejpam-6847	370	9	,	,	PUNCT
ejpam-6847	370	10	νs	νs	NOUN
ejpam-6847	370	11	,	,	PUNCT
ejpam-6847	370	12	(	(	PUNCT
ejpam-6847	370	13	q	q	X
ejpam-6847	370	14	,	,	PUNCT
ejpam-6847	370	15	h	h	NOUN
ejpam-6847	370	16	)	)	PUNCT
ejpam-6847	370	17	−	−	PROPN
ejpam-6847	370	18	f)-contraction	f)-contraction	NOUN
ejpam-6847	370	19	mapping	mapping	NOUN
ejpam-6847	370	20	.	.	PUNCT
ejpam-6847	371	1	let	let	VERB
ejpam-6847	371	2	x0	x0	PROPN
ejpam-6847	371	3	=	=	SYM
ejpam-6847	371	4	1	1	NUM
ejpam-6847	371	5	,	,	PUNCT
ejpam-6847	371	6	then	then	ADV
ejpam-6847	371	7	αs(x0	αs(x0	PROPN
ejpam-6847	371	8	,	,	PUNCT
ejpam-6847	371	9	x0	x0	PROPN
ejpam-6847	371	10	,	,	PUNCT
ejpam-6847	371	11	tx0	tx0	PROPN
ejpam-6847	371	12	)	)	PUNCT
ejpam-6847	371	13	≥	≥	NOUN
ejpam-6847	371	14	1	1	NUM
ejpam-6847	371	15	,	,	PUNCT
ejpam-6847	371	16	νs(x0	νs(x0	PROPN
ejpam-6847	371	17	,	,	PUNCT
ejpam-6847	371	18	x0	x0	PROPN
ejpam-6847	371	19	,	,	PUNCT
ejpam-6847	371	20	tx0	tx0	NOUN
ejpam-6847	371	21	)	)	PUNCT
ejpam-6847	371	22	≤	≤	NOUN
ejpam-6847	372	1	1	1	NUM
ejpam-6847	372	2	.	.	PUNCT
ejpam-6847	373	1	we	we	PRON
ejpam-6847	373	2	form	form	VERB
ejpam-6847	373	3	a	a	DET
ejpam-6847	373	4	sequence	sequence	NOUN
ejpam-6847	373	5	by	by	ADP
ejpam-6847	373	6	x1	x1	PROPN
ejpam-6847	373	7	=	=	SYM
ejpam-6847	373	8	t	t	PROPN
ejpam-6847	373	9	(	(	PUNCT
ejpam-6847	373	10	x0	x0	PROPN
ejpam-6847	373	11	)	)	PUNCT
ejpam-6847	373	12	=	=	SYM
ejpam-6847	373	13	t	t	PROPN
ejpam-6847	373	14	(	(	PUNCT
ejpam-6847	373	15	1	1	NUM
ejpam-6847	373	16	)	)	PUNCT
ejpam-6847	373	17	=	=	SYM
ejpam-6847	373	18	1	1	NUM
ejpam-6847	373	19	3	3	NUM
ejpam-6847	373	20	,	,	PUNCT
ejpam-6847	373	21	hence	hence	ADV
ejpam-6847	373	22	xn	xn	PUNCT
ejpam-6847	374	1	=	=	SYM
ejpam-6847	374	2	tn(x0	tn(x0	NOUN
ejpam-6847	374	3	)	)	PUNCT
ejpam-6847	374	4	=	=	SYM
ejpam-6847	374	5	tn(1	tn(1	NOUN
ejpam-6847	374	6	)	)	PUNCT
ejpam-6847	374	7	=	=	SYM
ejpam-6847	374	8	1	1	NUM
ejpam-6847	374	9	3n	3n	NUM
ejpam-6847	374	10	for	for	ADP
ejpam-6847	374	11	all	all	DET
ejpam-6847	374	12	n	n	PRON
ejpam-6847	374	13	≥	≥	NOUN
ejpam-6847	374	14	1	1	NUM
ejpam-6847	374	15	.	.	PUNCT
ejpam-6847	375	1	finally	finally	ADV
ejpam-6847	375	2	,	,	PUNCT
ejpam-6847	375	3	to	to	PART
ejpam-6847	375	4	show	show	VERB
ejpam-6847	375	5	that	that	SCONJ
ejpam-6847	375	6	the	the	DET
ejpam-6847	375	7	equation	equation	NOUN
ejpam-6847	375	8	5	5	NUM
ejpam-6847	375	9	holds	hold	NOUN
ejpam-6847	375	10	,	,	PUNCT
ejpam-6847	375	11	consider	consider	VERB
ejpam-6847	375	12	that	that	PRON
ejpam-6847	375	13	sup	sup	NOUN
ejpam-6847	375	14	m≥1	m≥1	PROPN
ejpam-6847	375	15	lim	lim	PROPN
ejpam-6847	375	16	n→+∞	n→+∞	PROPN
ejpam-6847	375	17	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	375	18	,	,	PUNCT
ejpam-6847	375	19	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	375	20	,	,	PUNCT
ejpam-6847	375	21	xn+2	xn+2	NUM
ejpam-6847	375	22	)	)	PUNCT
ejpam-6847	376	1	+	+	CCONJ
ejpam-6847	376	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	376	3	,	,	PUNCT
ejpam-6847	376	4	xn+2	xn+2	NUM
ejpam-6847	376	5	)	)	PUNCT
ejpam-6847	376	6	]	]	PUNCT
ejpam-6847	377	1	[	[	X
ejpam-6847	377	2	β(xn	β(xn	NOUN
ejpam-6847	377	3	,	,	PUNCT
ejpam-6847	377	4	xn+1	xn+1	NUM
ejpam-6847	377	5	)	)	PUNCT
ejpam-6847	377	6	+	+	CCONJ
ejpam-6847	377	7	µ(xn	µ(xn	PROPN
ejpam-6847	377	8	,	,	PUNCT
ejpam-6847	377	9	xn+1	xn+1	NUM
ejpam-6847	377	10	)	)	PUNCT
ejpam-6847	377	11	]	]	PUNCT
ejpam-6847	378	1	=	=	PUNCT
ejpam-6847	378	2	sup	sup	NOUN
ejpam-6847	378	3	m≥1	m≥1	PROPN
ejpam-6847	378	4	lim	lim	PROPN
ejpam-6847	378	5	n→+∞	n→+∞	PROPN
ejpam-6847	378	6	(	(	PUNCT
ejpam-6847	378	7	(	(	PUNCT
ejpam-6847	378	8	[	[	X
ejpam-6847	378	9	max	max	X
ejpam-6847	378	10	{	{	PUNCT
ejpam-6847	378	11	1	1	NUM
ejpam-6847	378	12	3n+1	3n+1	PROPN
ejpam-6847	378	13	,	,	PUNCT
ejpam-6847	378	14	1	1	NUM
ejpam-6847	378	15	3n+2	3n+2	NUM
ejpam-6847	378	16	}	}	PUNCT
ejpam-6847	378	17	+	+	CCONJ
ejpam-6847	378	18	1	1	X
ejpam-6847	378	19	)	)	PUNCT
ejpam-6847	378	20	+	+	CCONJ
ejpam-6847	378	21	max	max	PROPN
ejpam-6847	378	22	{	{	PUNCT
ejpam-6847	378	23	1	1	NUM
ejpam-6847	378	24	3n+1	3n+1	PROPN
ejpam-6847	378	25	,	,	PUNCT
ejpam-6847	378	26	1	1	NUM
ejpam-6847	378	27	3n+2	3n+2	NUM
ejpam-6847	378	28	}	}	PUNCT
ejpam-6847	378	29	+	+	PUNCT
ejpam-6847	378	30	2	2	NUM
ejpam-6847	378	31	)	)	PUNCT
ejpam-6847	378	32	]	]	PUNCT
ejpam-6847	379	1	[	[	X
ejpam-6847	379	2	(	(	PUNCT
ejpam-6847	379	3	max	max	PROPN
ejpam-6847	379	4	{	{	PUNCT
ejpam-6847	379	5	1	1	NUM
ejpam-6847	379	6	3n	3n	NUM
ejpam-6847	379	7	,	,	PUNCT
ejpam-6847	379	8	1	1	NUM
ejpam-6847	379	9	3n+1	3n+1	NUM
ejpam-6847	379	10	}	}	PUNCT
ejpam-6847	379	11	+	+	CCONJ
ejpam-6847	379	12	1	1	X
ejpam-6847	379	13	)	)	PUNCT
ejpam-6847	380	1	+	+	CCONJ
ejpam-6847	380	2	(	(	PUNCT
ejpam-6847	380	3	max	max	PROPN
ejpam-6847	380	4	{	{	PUNCT
ejpam-6847	380	5	1	1	NUM
ejpam-6847	380	6	3n	3n	NUM
ejpam-6847	380	7	,	,	PUNCT
ejpam-6847	380	8	1	1	NUM
ejpam-6847	380	9	3n+1	3n+1	NUM
ejpam-6847	380	10	}	}	PUNCT
ejpam-6847	380	11	+	+	CCONJ
ejpam-6847	380	12	2	2	NUM
ejpam-6847	380	13	]	]	NUM
ejpam-6847	380	14	)	)	PUNCT
ejpam-6847	380	15	)	)	PUNCT
ejpam-6847	380	16	(	(	PUNCT
ejpam-6847	380	17	1	1	NUM
ejpam-6847	380	18	3n+1	3n+1	NUM
ejpam-6847	380	19	+	+	CCONJ
ejpam-6847	380	20	1	1	NUM
ejpam-6847	380	21	3	3	NUM
ejpam-6847	380	22	m	m	NOUN
ejpam-6847	380	23	)	)	PUNCT
ejpam-6847	381	1	<	<	X
ejpam-6847	381	2	1	1	X
ejpam-6847	381	3	.	.	PUNCT
ejpam-6847	382	1	moreover	moreover	ADV
ejpam-6847	382	2	,	,	PUNCT
ejpam-6847	382	3	for	for	ADP
ejpam-6847	382	4	any	any	DET
ejpam-6847	382	5	x	x	SYM
ejpam-6847	382	6	∈	∈	PROPN
ejpam-6847	382	7	x	x	NOUN
ejpam-6847	382	8	,	,	PUNCT
ejpam-6847	382	9	all	all	DET
ejpam-6847	382	10	the	the	DET
ejpam-6847	382	11	following	follow	VERB
ejpam-6847	382	12	limits	limit	NOUN
ejpam-6847	382	13	limn→+∞	limn→+∞	VERB
ejpam-6847	382	14	β(x	β(x	NOUN
ejpam-6847	382	15	,	,	PUNCT
ejpam-6847	382	16	xn	xn	PROPN
ejpam-6847	382	17	)	)	PUNCT
ejpam-6847	382	18	,	,	PUNCT
ejpam-6847	382	19	limn→+∞	limn→+∞	VERB
ejpam-6847	382	20	µ(xn	µ(xn	PROPN
ejpam-6847	382	21	,	,	PUNCT
ejpam-6847	382	22	x	x	NOUN
ejpam-6847	382	23	)	)	PUNCT
ejpam-6847	382	24	,	,	PUNCT
ejpam-6847	382	25	and	and	CCONJ
ejpam-6847	382	26	limn→+∞	limn→+∞	VERB
ejpam-6847	382	27	γ(xn	γ(xn	NUM
ejpam-6847	382	28	,	,	PUNCT
ejpam-6847	382	29	x	x	PRON
ejpam-6847	382	30	)	)	PUNCT
ejpam-6847	382	31	exists	exist	VERB
ejpam-6847	382	32	and	and	CCONJ
ejpam-6847	382	33	are	be	AUX
ejpam-6847	382	34	finite	finite	ADJ
ejpam-6847	382	35	.	.	PUNCT
ejpam-6847	383	1	therefore	therefore	ADV
ejpam-6847	383	2	,	,	PUNCT
ejpam-6847	383	3	t	t	PROPN
ejpam-6847	383	4	fulfills	fulfill	VERB
ejpam-6847	383	5	all	all	DET
ejpam-6847	383	6	the	the	DET
ejpam-6847	383	7	hypotheses	hypothesis	NOUN
ejpam-6847	383	8	of	of	ADP
ejpam-6847	383	9	theorem	theorem	NOUN
ejpam-6847	383	10	1	1	NUM
ejpam-6847	383	11	.	.	PUNCT
ejpam-6847	383	12	consequently	consequently	ADV
ejpam-6847	383	13	,	,	PUNCT
ejpam-6847	383	14	t	t	PROPN
ejpam-6847	383	15	has	have	VERB
ejpam-6847	383	16	a	a	DET
ejpam-6847	383	17	fixed	fix	VERB
ejpam-6847	383	18	point	point	NOUN
ejpam-6847	383	19	,	,	PUNCT
ejpam-6847	383	20	which	which	PRON
ejpam-6847	383	21	is	be	AUX
ejpam-6847	383	22	x	x	X
ejpam-6847	383	23	=	=	SYM
ejpam-6847	383	24	0	0	PROPN
ejpam-6847	383	25	.	.	PUNCT
ejpam-6847	384	1	f.	f.	PROPN
ejpam-6847	384	2	m.	m.	PROPN
ejpam-6847	384	3	azmi	azmi	PROPN
ejpam-6847	384	4	,	,	PUNCT
ejpam-6847	384	5	a.	a.	PROPN
ejpam-6847	384	6	h.	h.	PROPN
ejpam-6847	384	7	ansari	ansari	PROPN
ejpam-6847	384	8	,	,	PUNCT
ejpam-6847	384	9	s.	s.	PROPN
ejpam-6847	384	10	h.	h.	PROPN
ejpam-6847	384	11	j.	j.	PROPN
ejpam-6847	384	12	petroudi	petroudi	PROPN
ejpam-6847	384	13	/	/	SYM
ejpam-6847	384	14	eur	eur	PROPN
ejpam-6847	384	15	.	.	PUNCT
ejpam-6847	385	1	j.	j.	PROPN
ejpam-6847	385	2	pure	pure	PROPN
ejpam-6847	385	3	appl	appl	PROPN
ejpam-6847	385	4	.	.	PROPN
ejpam-6847	385	5	math	math	PROPN
ejpam-6847	385	6	,	,	PUNCT
ejpam-6847	385	7	18	18	NUM
ejpam-6847	385	8	(	(	PUNCT
ejpam-6847	385	9	4	4	NUM
ejpam-6847	385	10	)	)	PUNCT
ejpam-6847	385	11	(	(	PUNCT
ejpam-6847	385	12	2025	2025	NUM
ejpam-6847	385	13	)	)	PUNCT
ejpam-6847	385	14	,	,	PUNCT
ejpam-6847	385	15	6847	6847	NUM
ejpam-6847	385	16	15	15	NUM
ejpam-6847	385	17	of	of	ADP
ejpam-6847	385	18	26	26	NUM
ejpam-6847	385	19	remark	remark	NOUN
ejpam-6847	385	20	4	4	NUM
ejpam-6847	385	21	.	.	PUNCT
ejpam-6847	386	1	in	in	ADP
ejpam-6847	386	2	example	example	NOUN
ejpam-6847	386	3	7	7	NUM
ejpam-6847	386	4	,	,	PUNCT
ejpam-6847	386	5	if	if	SCONJ
ejpam-6847	386	6	the	the	DET
ejpam-6847	386	7	mapping	mapping	NOUN
ejpam-6847	386	8	t	t	NOUN
ejpam-6847	386	9	is	be	AUX
ejpam-6847	386	10	not	not	PART
ejpam-6847	386	11	regarded	regard	VERB
ejpam-6847	386	12	as	as	ADP
ejpam-6847	386	13	αs	αs	ADJ
ejpam-6847	386	14	-	-	ADJ
ejpam-6847	386	15	admissible	admissible	ADJ
ejpam-6847	386	16	and	and	CCONJ
ejpam-6847	386	17	νssubadmissible	νssubadmissible	ADJ
ejpam-6847	386	18	,	,	PUNCT
ejpam-6847	386	19	it	it	PRON
ejpam-6847	386	20	follows	follow	VERB
ejpam-6847	386	21	that	that	SCONJ
ejpam-6847	386	22	t	t	PROPN
ejpam-6847	386	23	can	can	AUX
ejpam-6847	386	24	not	not	PART
ejpam-6847	386	25	be	be	AUX
ejpam-6847	386	26	classified	classify	VERB
ejpam-6847	386	27	as	as	ADP
ejpam-6847	386	28	a	a	DET
ejpam-6847	386	29	contraction	contraction	NOUN
ejpam-6847	386	30	mapping	mapping	NOUN
ejpam-6847	386	31	.	.	PUNCT
ejpam-6847	387	1	it	it	PRON
ejpam-6847	387	2	is	be	AUX
ejpam-6847	387	3	important	important	ADJ
ejpam-6847	387	4	to	to	PART
ejpam-6847	387	5	observe	observe	VERB
ejpam-6847	387	6	that	that	SCONJ
ejpam-6847	387	7	for	for	ADP
ejpam-6847	387	8	any	any	DET
ejpam-6847	387	9	x	x	NOUN
ejpam-6847	387	10	,	,	PUNCT
ejpam-6847	387	11	y	y	PROPN
ejpam-6847	387	12	,	,	PUNCT
ejpam-6847	387	13	z	z	PROPN
ejpam-6847	387	14	∈	∈	PROPN
ejpam-6847	387	15	(	(	PUNCT
ejpam-6847	387	16	1,+∞	1,+∞	NUM
ejpam-6847	387	17	)	)	PUNCT
ejpam-6847	387	18	,	,	PUNCT
ejpam-6847	387	19	the	the	DET
ejpam-6847	387	20	following	follow	VERB
ejpam-6847	387	21	expression	expression	NOUN
ejpam-6847	387	22	holds	hold	VERB
ejpam-6847	387	23	:	:	PUNCT
ejpam-6847	387	24	s(tx	s(tx	NUM
ejpam-6847	387	25	,	,	PUNCT
ejpam-6847	387	26	ty	ty	INTJ
ejpam-6847	387	27	,	,	PUNCT
ejpam-6847	387	28	tz	tz	NOUN
ejpam-6847	387	29	)	)	PUNCT
ejpam-6847	387	30	=	=	NOUN
ejpam-6847	388	1	|tx−	|tx−	NUM
ejpam-6847	388	2	ty|+	ty|+	PROPN
ejpam-6847	388	3	|ty	|ty	AUX
ejpam-6847	388	4	−	−	NOUN
ejpam-6847	388	5	tz|	tz|	NOUN
ejpam-6847	388	6	=	=	SYM
ejpam-6847	388	7	2(|x−	2(|x−	NUM
ejpam-6847	388	8	y|+	y|+	PROPN
ejpam-6847	388	9	|y	|y	NOUN
ejpam-6847	388	10	−	−	PROPN
ejpam-6847	388	11	z|	z|	PROPN
ejpam-6847	388	12	)	)	PUNCT
ejpam-6847	388	13	=	=	SYM
ejpam-6847	388	14	2s(x	2s(x	PROPN
ejpam-6847	388	15	,	,	PUNCT
ejpam-6847	388	16	y	y	PROPN
ejpam-6847	388	17	,	,	PUNCT
ejpam-6847	388	18	z	z	NOUN
ejpam-6847	388	19	)	)	PUNCT
ejpam-6847	388	20	>	>	X
ejpam-6847	389	1	s(x	s(x	PROPN
ejpam-6847	389	2	,	,	PUNCT
ejpam-6847	389	3	y	y	PROPN
ejpam-6847	389	4	,	,	PUNCT
ejpam-6847	389	5	z	z	NOUN
ejpam-6847	389	6	)	)	PUNCT
ejpam-6847	389	7	,	,	PUNCT
ejpam-6847	389	8	which	which	PRON
ejpam-6847	389	9	implies	imply	VERB
ejpam-6847	389	10	that	that	SCONJ
ejpam-6847	389	11	t	t	PROPN
ejpam-6847	389	12	is	be	AUX
ejpam-6847	389	13	not	not	PART
ejpam-6847	389	14	a	a	DET
ejpam-6847	389	15	contraction	contraction	NOUN
ejpam-6847	389	16	.	.	PUNCT
ejpam-6847	390	1	remark	remark	NOUN
ejpam-6847	390	2	5	5	NUM
ejpam-6847	390	3	.	.	PUNCT
ejpam-6847	391	1	let	let	AUX
ejpam-6847	391	2	(	(	PUNCT
ejpam-6847	391	3	x	x	X
ejpam-6847	391	4	,	,	PUNCT
ejpam-6847	391	5	s	s	PART
ejpam-6847	391	6	)	)	PUNCT
ejpam-6847	391	7	be	be	AUX
ejpam-6847	391	8	a	a	DET
ejpam-6847	391	9	t	t	NOUN
ejpam-6847	391	10	c	c	X
ejpam-6847	391	11	-	-	PUNCT
ejpam-6847	391	12	s	s	PROPN
ejpam-6847	391	13	-	-	PUNCT
ejpam-6847	391	14	mt	mt	NOUN
ejpam-6847	391	15	s	s	PROPN
ejpam-6847	391	16	,	,	PUNCT
ejpam-6847	391	17	as	as	SCONJ
ejpam-6847	391	18	stated	state	VERB
ejpam-6847	391	19	in	in	ADP
ejpam-6847	391	20	theorem	theorem	NOUN
ejpam-6847	391	21	1	1	NUM
ejpam-6847	391	22	.	.	PUNCT
ejpam-6847	392	1	if	if	SCONJ
ejpam-6847	392	2	β	β	PROPN
ejpam-6847	392	3	=	=	SYM
ejpam-6847	392	4	µ	µ	X
ejpam-6847	392	5	=	=	SYM
ejpam-6847	392	6	γ	γ	X
ejpam-6847	392	7	,	,	PUNCT
ejpam-6847	392	8	then	then	ADV
ejpam-6847	392	9	(	(	PUNCT
ejpam-6847	392	10	x	x	X
ejpam-6847	392	11	,	,	PUNCT
ejpam-6847	392	12	s	s	PART
ejpam-6847	392	13	)	)	PUNCT
ejpam-6847	392	14	becomes	become	VERB
ejpam-6847	392	15	a	a	DET
ejpam-6847	392	16	controlled	control	VERB
ejpam-6847	392	17	s	s	ADJ
ejpam-6847	392	18	-	-	ADJ
ejpam-6847	392	19	metric	metric	ADJ
ejpam-6847	392	20	type	type	NOUN
ejpam-6847	392	21	space	space	NOUN
ejpam-6847	392	22	according	accord	VERB
ejpam-6847	392	23	to	to	ADP
ejpam-6847	392	24	definition	definition	NOUN
ejpam-6847	392	25	4	4	NUM
ejpam-6847	392	26	.	.	PUNCT
ejpam-6847	393	1	therefore	therefore	ADV
ejpam-6847	393	2	,	,	PUNCT
ejpam-6847	393	3	we	we	PRON
ejpam-6847	393	4	arrive	arrive	VERB
ejpam-6847	393	5	at	at	ADP
ejpam-6847	393	6	our	our	PRON
ejpam-6847	393	7	next	next	ADJ
ejpam-6847	393	8	result	result	NOUN
ejpam-6847	393	9	.	.	PUNCT
ejpam-6847	394	1	theorem	theorem	ADJ
ejpam-6847	394	2	2	2	NUM
ejpam-6847	395	1	.	.	X
ejpam-6847	395	2	assume	assume	VERB
ejpam-6847	395	3	that	that	SCONJ
ejpam-6847	395	4	(	(	PUNCT
ejpam-6847	395	5	x	x	X
ejpam-6847	395	6	,	,	PUNCT
ejpam-6847	395	7	s	s	PART
ejpam-6847	395	8	)	)	PUNCT
ejpam-6847	395	9	is	be	AUX
ejpam-6847	395	10	a	a	DET
ejpam-6847	395	11	complete	complete	ADJ
ejpam-6847	395	12	controlled	control	VERB
ejpam-6847	395	13	s	s	ADJ
ejpam-6847	395	14	-	-	ADJ
ejpam-6847	395	15	metric	metric	ADJ
ejpam-6847	395	16	type	type	NOUN
ejpam-6847	395	17	space	space	NOUN
ejpam-6847	395	18	,	,	PUNCT
ejpam-6847	395	19	where	where	SCONJ
ejpam-6847	395	20	x	x	PRON
ejpam-6847	395	21	is	be	AUX
ejpam-6847	395	22	a	a	DET
ejpam-6847	395	23	nonempty	nonempty	ADV
ejpam-6847	395	24	set	set	VERB
ejpam-6847	395	25	.	.	PUNCT
ejpam-6847	396	1	let	let	VERB
ejpam-6847	396	2	t	t	NOUN
ejpam-6847	396	3	:	:	PUNCT
ejpam-6847	396	4	x	x	X
ejpam-6847	396	5	→	→	PUNCT
ejpam-6847	396	6	x	x	PUNCT
ejpam-6847	396	7	be	be	AUX
ejpam-6847	396	8	an	an	DET
ejpam-6847	396	9	(	(	PUNCT
ejpam-6847	396	10	αs	αs	PROPN
ejpam-6847	396	11	,	,	PUNCT
ejpam-6847	396	12	νs	νs	NOUN
ejpam-6847	396	13	,	,	PUNCT
ejpam-6847	396	14	(	(	PUNCT
ejpam-6847	396	15	q	q	X
ejpam-6847	396	16	,	,	PUNCT
ejpam-6847	396	17	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	396	18	mapping	mapping	NOUN
ejpam-6847	396	19	,	,	PUNCT
ejpam-6847	396	20	such	such	ADJ
ejpam-6847	396	21	that	that	SCONJ
ejpam-6847	396	22	the	the	DET
ejpam-6847	396	23	following	follow	VERB
ejpam-6847	396	24	conditions	condition	NOUN
ejpam-6847	396	25	hold	hold	VERB
ejpam-6847	396	26	:	:	PUNCT
ejpam-6847	396	27	(	(	PUNCT
ejpam-6847	396	28	1	1	X
ejpam-6847	396	29	)	)	PUNCT
ejpam-6847	396	30	t	t	PROPN
ejpam-6847	396	31	is	be	AUX
ejpam-6847	396	32	αs	αs	ADJ
ejpam-6847	396	33	-	-	ADJ
ejpam-6847	396	34	admissible	admissible	ADJ
ejpam-6847	396	35	and	and	CCONJ
ejpam-6847	396	36	νs	νs	NOUN
ejpam-6847	396	37	-	-	PUNCT
ejpam-6847	396	38	subadmissible	subadmissible	ADJ
ejpam-6847	396	39	mapping	mapping	NOUN
ejpam-6847	396	40	.	.	PUNCT
ejpam-6847	397	1	(	(	PUNCT
ejpam-6847	397	2	2	2	X
ejpam-6847	397	3	)	)	PUNCT
ejpam-6847	397	4	there	there	PRON
ejpam-6847	397	5	is	be	VERB
ejpam-6847	397	6	x0	x0	PROPN
ejpam-6847	397	7	∈	∈	PROPN
ejpam-6847	397	8	x	x	NOUN
ejpam-6847	397	9	,	,	PUNCT
ejpam-6847	397	10	such	such	ADJ
ejpam-6847	397	11	that	that	DET
ejpam-6847	397	12	αs(x0	αs(x0	NOUN
ejpam-6847	397	13	,	,	PUNCT
ejpam-6847	397	14	x0	x0	PROPN
ejpam-6847	397	15	,	,	PUNCT
ejpam-6847	397	16	tx0	tx0	PROPN
ejpam-6847	397	17	)	)	PUNCT
ejpam-6847	397	18	≥	≥	NOUN
ejpam-6847	397	19	1	1	NUM
ejpam-6847	397	20	,	,	PUNCT
ejpam-6847	397	21	and	and	CCONJ
ejpam-6847	397	22	νs(x0	νs(x0	PROPN
ejpam-6847	397	23	,	,	PUNCT
ejpam-6847	397	24	x0	x0	PROPN
ejpam-6847	397	25	,	,	PUNCT
ejpam-6847	397	26	tx0	tx0	NOUN
ejpam-6847	397	27	)	)	PUNCT
ejpam-6847	397	28	≤	≤	NOUN
ejpam-6847	397	29	1	1	NUM
ejpam-6847	397	30	.	.	PUNCT
ejpam-6847	398	1	(	(	PUNCT
ejpam-6847	398	2	3	3	X
ejpam-6847	398	3	)	)	PUNCT
ejpam-6847	398	4	for	for	ADP
ejpam-6847	398	5	x0	x0	PROPN
ejpam-6847	398	6	∈	∈	PROPN
ejpam-6847	398	7	x	x	PRON
ejpam-6847	398	8	,	,	PUNCT
ejpam-6847	398	9	the	the	DET
ejpam-6847	398	10	sequence	sequence	NOUN
ejpam-6847	398	11	{	{	PUNCT
ejpam-6847	398	12	xn	xn	NUM
ejpam-6847	398	13	}	}	PUNCT
ejpam-6847	398	14	,	,	PUNCT
ejpam-6847	398	15	is	be	AUX
ejpam-6847	398	16	defined	define	VERB
ejpam-6847	398	17	by	by	ADP
ejpam-6847	398	18	xn	xn	PROPN
ejpam-6847	398	19	=	=	SYM
ejpam-6847	398	20	tnx0	tnx0	PROPN
ejpam-6847	398	21	,	,	PUNCT
ejpam-6847	398	22	moreover	moreover	ADV
ejpam-6847	398	23	,	,	PUNCT
ejpam-6847	398	24	assume	assume	VERB
ejpam-6847	398	25	these	these	DET
ejpam-6847	398	26	hold	hold	NOUN
ejpam-6847	398	27	sup	sup	NOUN
ejpam-6847	398	28	m≥1	m≥1	PROPN
ejpam-6847	398	29	lim	lim	PROPN
ejpam-6847	398	30	n→+∞	n→+∞	PROPN
ejpam-6847	398	31	β(xn+1	β(xn+1	PROPN
ejpam-6847	398	32	,	,	PUNCT
ejpam-6847	398	33	xm)β(xn+1	xm)β(xn+1	ADJ
ejpam-6847	398	34	,	,	PUNCT
ejpam-6847	398	35	xn+2	xn+2	NUM
ejpam-6847	398	36	)	)	PUNCT
ejpam-6847	398	37	β(xn	β(xn	NOUN
ejpam-6847	398	38	,	,	PUNCT
ejpam-6847	398	39	xn+1	xn+1	NUM
ejpam-6847	398	40	)	)	PUNCT
ejpam-6847	398	41	<	<	X
ejpam-6847	399	1	1	1	X
ejpam-6847	399	2	.	.	PUNCT
ejpam-6847	399	3	(	(	PUNCT
ejpam-6847	399	4	19	19	NUM
ejpam-6847	399	5	)	)	PUNCT
ejpam-6847	400	1	and	and	CCONJ
ejpam-6847	400	2	suppose	suppose	VERB
ejpam-6847	400	3	that	that	SCONJ
ejpam-6847	400	4	,	,	PUNCT
ejpam-6847	400	5	lim	lim	PROPN
ejpam-6847	400	6	n→+∞	n→+∞	VERB
ejpam-6847	400	7	β(x	β(x	PROPN
ejpam-6847	400	8	,	,	PUNCT
ejpam-6847	400	9	xn	xn	PROPN
ejpam-6847	400	10	)	)	PUNCT
ejpam-6847	400	11	,	,	PUNCT
ejpam-6847	400	12	exists	exist	VERB
ejpam-6847	400	13	and	and	CCONJ
ejpam-6847	400	14	finite	finite	PROPN
ejpam-6847	400	15	.	.	PUNCT
ejpam-6847	401	1	(	(	PUNCT
ejpam-6847	401	2	20	20	NUM
ejpam-6847	401	3	)	)	PUNCT
ejpam-6847	401	4	then	then	ADV
ejpam-6847	401	5	,	,	PUNCT
ejpam-6847	401	6	t	t	PROPN
ejpam-6847	401	7	has	have	VERB
ejpam-6847	401	8	a	a	DET
ejpam-6847	401	9	fixed	fix	VERB
ejpam-6847	401	10	point	point	NOUN
ejpam-6847	401	11	.	.	PUNCT
ejpam-6847	402	1	furthermore	furthermore	ADV
ejpam-6847	402	2	,	,	PUNCT
ejpam-6847	402	3	if	if	SCONJ
ejpam-6847	402	4	there	there	PRON
ejpam-6847	402	5	are	be	VERB
ejpam-6847	402	6	two	two	NUM
ejpam-6847	402	7	fixed	fix	VERB
ejpam-6847	402	8	points	point	NOUN
ejpam-6847	402	9	of	of	ADP
ejpam-6847	402	10	t	t	PROPN
ejpam-6847	402	11	in	in	ADP
ejpam-6847	402	12	the	the	DET
ejpam-6847	402	13	space	space	NOUN
ejpam-6847	402	14	x	x	NOUN
ejpam-6847	402	15	,	,	PUNCT
ejpam-6847	402	16	labeled	label	VERB
ejpam-6847	402	17	as	as	ADP
ejpam-6847	402	18	u	u	NOUN
ejpam-6847	402	19	and	and	CCONJ
ejpam-6847	402	20	v	v	NOUN
ejpam-6847	402	21	,	,	PUNCT
ejpam-6847	402	22	such	such	ADJ
ejpam-6847	402	23	that	that	DET
ejpam-6847	402	24	αs(u	αs(u	NUM
ejpam-6847	402	25	,	,	PUNCT
ejpam-6847	402	26	u	u	NOUN
ejpam-6847	402	27	,	,	PUNCT
ejpam-6847	402	28	v	v	NOUN
ejpam-6847	402	29	)	)	PUNCT
ejpam-6847	402	30	≥	≥	NOUN
ejpam-6847	402	31	1	1	NUM
ejpam-6847	402	32	and	and	CCONJ
ejpam-6847	402	33	νs(u	νs(u	NUM
ejpam-6847	402	34	,	,	PUNCT
ejpam-6847	402	35	u	u	NOUN
ejpam-6847	402	36	,	,	PUNCT
ejpam-6847	402	37	v	v	NOUN
ejpam-6847	402	38	)	)	PUNCT
ejpam-6847	402	39	≤	≤	NUM
ejpam-6847	402	40	1	1	NUM
ejpam-6847	402	41	,	,	PUNCT
ejpam-6847	402	42	it	it	PRON
ejpam-6847	402	43	follows	follow	VERB
ejpam-6847	402	44	that	that	SCONJ
ejpam-6847	402	45	t	t	PROPN
ejpam-6847	402	46	has	have	VERB
ejpam-6847	402	47	a	a	DET
ejpam-6847	402	48	unique	unique	ADJ
ejpam-6847	402	49	fixed	fix	VERB
ejpam-6847	402	50	point	point	NOUN
ejpam-6847	402	51	within	within	ADP
ejpam-6847	402	52	x.	x.	NOUN
ejpam-6847	402	53	proof	proof	NOUN
ejpam-6847	402	54	.	.	PUNCT
ejpam-6847	403	1	the	the	DET
ejpam-6847	403	2	proof	proof	NOUN
ejpam-6847	403	3	is	be	AUX
ejpam-6847	403	4	completed	complete	VERB
ejpam-6847	403	5	by	by	ADP
ejpam-6847	403	6	following	follow	VERB
ejpam-6847	403	7	a	a	DET
ejpam-6847	403	8	similar	similar	ADJ
ejpam-6847	403	9	approach	approach	NOUN
ejpam-6847	403	10	to	to	ADP
ejpam-6847	403	11	theorem	theorem	NOUN
ejpam-6847	403	12	1	1	NUM
ejpam-6847	403	13	,	,	PUNCT
ejpam-6847	403	14	using	use	VERB
ejpam-6847	403	15	β	β	X
ejpam-6847	403	16	=	=	SYM
ejpam-6847	403	17	µ	µ	X
ejpam-6847	403	18	=	=	SYM
ejpam-6847	403	19	γ	γ	PROPN
ejpam-6847	403	20	.	.	PROPN
ejpam-6847	403	21	definition	definition	NOUN
ejpam-6847	403	22	18	18	NUM
ejpam-6847	403	23	.	.	PUNCT
ejpam-6847	404	1	assume	assume	VERB
ejpam-6847	404	2	that	that	SCONJ
ejpam-6847	404	3	(	(	PUNCT
ejpam-6847	404	4	x	x	X
ejpam-6847	404	5	,	,	PUNCT
ejpam-6847	404	6	s	s	PART
ejpam-6847	404	7	)	)	PUNCT
ejpam-6847	404	8	is	be	AUX
ejpam-6847	404	9	a	a	DET
ejpam-6847	404	10	t	t	NOUN
ejpam-6847	404	11	c	c	X
ejpam-6847	404	12	-	-	PUNCT
ejpam-6847	404	13	s	s	PROPN
ejpam-6847	404	14	-	-	PUNCT
ejpam-6847	404	15	mt	mt	NOUN
ejpam-6847	404	16	s	s	PROPN
ejpam-6847	404	17	,	,	PUNCT
ejpam-6847	404	18	where	where	SCONJ
ejpam-6847	404	19	x	x	PUNCT
ejpam-6847	404	20	6=	6=	AUX
ejpam-6847	404	21	∅.	∅.	NOUN
ejpam-6847	404	22	let	let	VERB
ejpam-6847	404	23	the	the	DET
ejpam-6847	404	24	pair	pair	NOUN
ejpam-6847	404	25	(	(	PUNCT
ejpam-6847	404	26	q	q	NOUN
ejpam-6847	404	27	,	,	PUNCT
ejpam-6847	404	28	h	h	NOUN
ejpam-6847	404	29	)	)	PUNCT
ejpam-6847	404	30	represent	represent	VERB
ejpam-6847	404	31	an	an	DET
ejpam-6847	404	32	upper	upper	ADJ
ejpam-6847	404	33	class	class	NOUN
ejpam-6847	404	34	of	of	ADP
ejpam-6847	404	35	type	type	PROPN
ejpam-6847	404	36	ii	ii	PROPN
ejpam-6847	404	37	.	.	PUNCT
ejpam-6847	405	1	a	a	DET
ejpam-6847	405	2	mapping	mapping	NOUN
ejpam-6847	405	3	t	t	NOUN
ejpam-6847	405	4	:	:	PUNCT
ejpam-6847	405	5	x	x	X
ejpam-6847	405	6	→	→	PUNCT
ejpam-6847	405	7	x	x	X
ejpam-6847	405	8	is	be	AUX
ejpam-6847	405	9	defined	define	VERB
ejpam-6847	405	10	as	as	ADP
ejpam-6847	405	11	an	an	DET
ejpam-6847	405	12	(	(	PUNCT
ejpam-6847	405	13	αs	αs	PROPN
ejpam-6847	405	14	,	,	PUNCT
ejpam-6847	405	15	ηs	ηs	PROPN
ejpam-6847	405	16	,	,	PUNCT
ejpam-6847	405	17	νs	νs	NOUN
ejpam-6847	405	18	,	,	PUNCT
ejpam-6847	405	19	(	(	PUNCT
ejpam-6847	405	20	q	q	X
ejpam-6847	405	21	,	,	PUNCT
ejpam-6847	405	22	h)−f)-contraction	h)−f)-contraction	NOUN
ejpam-6847	405	23	mapping	mapping	NOUN
ejpam-6847	405	24	if	if	SCONJ
ejpam-6847	405	25	there	there	PRON
ejpam-6847	405	26	are	be	VERB
ejpam-6847	405	27	functions	function	NOUN
ejpam-6847	405	28	αs	αs	ADJ
ejpam-6847	405	29	,	,	PUNCT
ejpam-6847	405	30	ηs	ηs	PROPN
ejpam-6847	405	31	,	,	PUNCT
ejpam-6847	405	32	νs	νs	X
ejpam-6847	405	33	:	:	PUNCT
ejpam-6847	405	34	x	x	SYM
ejpam-6847	405	35	3	3	X
ejpam-6847	405	36	→	→	SYM
ejpam-6847	405	37	[	[	X
ejpam-6847	405	38	0,+∞	0,+∞	NUM
ejpam-6847	405	39	)	)	PUNCT
ejpam-6847	405	40	,	,	PUNCT
ejpam-6847	405	41	a	a	DET
ejpam-6847	405	42	function	function	NOUN
ejpam-6847	405	43	f	f	PROPN
ejpam-6847	405	44	∈	∈	PROPN
ejpam-6847	405	45	f	f	PROPN
ejpam-6847	405	46	,	,	PUNCT
ejpam-6847	405	47	and	and	CCONJ
ejpam-6847	405	48	a	a	DET
ejpam-6847	405	49	constant	constant	ADJ
ejpam-6847	405	50	τ	τ	X
ejpam-6847	405	51	>	>	X
ejpam-6847	405	52	0	0	NUM
ejpam-6847	405	53	such	such	ADJ
ejpam-6847	405	54	that	that	SCONJ
ejpam-6847	405	55	the	the	DET
ejpam-6847	405	56	following	follow	VERB
ejpam-6847	405	57	condition	condition	NOUN
ejpam-6847	405	58	holds	hold	VERB
ejpam-6847	405	59	:	:	PUNCT
ejpam-6847	405	60	h	h	NOUN
ejpam-6847	405	61	(	(	PUNCT
ejpam-6847	405	62	αs(x	αs(x	PROPN
ejpam-6847	405	63	,	,	PUNCT
ejpam-6847	405	64	y	y	PROPN
ejpam-6847	405	65	,	,	PUNCT
ejpam-6847	405	66	z	z	NOUN
ejpam-6847	405	67	)	)	PUNCT
ejpam-6847	405	68	,	,	PUNCT
ejpam-6847	405	69	ηs(x	ηs(x	NUM
ejpam-6847	405	70	,	,	PUNCT
ejpam-6847	405	71	y	y	PROPN
ejpam-6847	405	72	,	,	PUNCT
ejpam-6847	405	73	z	z	PROPN
ejpam-6847	405	74	)	)	PUNCT
ejpam-6847	405	75	,	,	PUNCT
ejpam-6847	405	76	τ	τ	PROPN
ejpam-6847	406	1	+	+	NUM
ejpam-6847	406	2	f	f	X
ejpam-6847	406	3	(	(	PUNCT
ejpam-6847	406	4	s(tx	s(tx	PROPN
ejpam-6847	406	5	,	,	PUNCT
ejpam-6847	406	6	ty	ty	INTJ
ejpam-6847	406	7	,	,	PUNCT
ejpam-6847	406	8	tz	tz	NOUN
ejpam-6847	406	9	)	)	PUNCT
ejpam-6847	406	10	)	)	PUNCT
ejpam-6847	406	11	)	)	PUNCT
ejpam-6847	406	12	≤	≤	NUM
ejpam-6847	406	13	q	q	X
ejpam-6847	406	14	(	(	PUNCT
ejpam-6847	406	15	νs(x	νs(x	PROPN
ejpam-6847	406	16	,	,	PUNCT
ejpam-6847	406	17	y	y	PROPN
ejpam-6847	406	18	,	,	PUNCT
ejpam-6847	406	19	z	z	NOUN
ejpam-6847	406	20	)	)	PUNCT
ejpam-6847	406	21	,	,	PUNCT
ejpam-6847	406	22	f	f	PROPN
ejpam-6847	406	23	(	(	PUNCT
ejpam-6847	406	24	s(x	s(x	PROPN
ejpam-6847	406	25	,	,	PUNCT
ejpam-6847	406	26	y	y	PROPN
ejpam-6847	406	27	,	,	PUNCT
ejpam-6847	406	28	z	z	NOUN
ejpam-6847	406	29	)	)	PUNCT
ejpam-6847	406	30	)	)	PUNCT
ejpam-6847	406	31	)	)	PUNCT
ejpam-6847	406	32	,	,	PUNCT
ejpam-6847	406	33	for	for	ADP
ejpam-6847	406	34	all	all	DET
ejpam-6847	406	35	x	x	NOUN
ejpam-6847	406	36	,	,	PUNCT
ejpam-6847	406	37	y	y	PROPN
ejpam-6847	406	38	,	,	PUNCT
ejpam-6847	406	39	z	z	PROPN
ejpam-6847	406	40	∈	∈	PROPN
ejpam-6847	406	41	x	x	X
ejpam-6847	406	42	,	,	PUNCT
ejpam-6847	406	43	with	with	ADP
ejpam-6847	406	44	s(tx	s(tx	PROPN
ejpam-6847	406	45	,	,	PUNCT
ejpam-6847	406	46	ty	ty	INTJ
ejpam-6847	406	47	,	,	PUNCT
ejpam-6847	406	48	tz	tz	PROPN
ejpam-6847	406	49	)	)	PUNCT
ejpam-6847	406	50	>	>	X
ejpam-6847	406	51	0	0	X
ejpam-6847	406	52	.	.	PUNCT
ejpam-6847	406	53	f.	f.	PROPN
ejpam-6847	406	54	m.	m.	PROPN
ejpam-6847	406	55	azmi	azmi	PROPN
ejpam-6847	406	56	,	,	PUNCT
ejpam-6847	406	57	a.	a.	PROPN
ejpam-6847	406	58	h.	h.	PROPN
ejpam-6847	406	59	ansari	ansari	PROPN
ejpam-6847	406	60	,	,	PUNCT
ejpam-6847	406	61	s.	s.	PROPN
ejpam-6847	406	62	h.	h.	PROPN
ejpam-6847	406	63	j.	j.	PROPN
ejpam-6847	406	64	petroudi	petroudi	PROPN
ejpam-6847	406	65	/	/	SYM
ejpam-6847	406	66	eur	eur	PROPN
ejpam-6847	406	67	.	.	PUNCT
ejpam-6847	407	1	j.	j.	PROPN
ejpam-6847	407	2	pure	pure	PROPN
ejpam-6847	407	3	appl	appl	PROPN
ejpam-6847	407	4	.	.	PROPN
ejpam-6847	407	5	math	math	PROPN
ejpam-6847	407	6	,	,	PUNCT
ejpam-6847	407	7	18	18	NUM
ejpam-6847	407	8	(	(	PUNCT
ejpam-6847	407	9	4	4	NUM
ejpam-6847	407	10	)	)	PUNCT
ejpam-6847	407	11	(	(	PUNCT
ejpam-6847	407	12	2025	2025	NUM
ejpam-6847	407	13	)	)	PUNCT
ejpam-6847	407	14	,	,	PUNCT
ejpam-6847	407	15	6847	6847	NUM
ejpam-6847	407	16	16	16	NUM
ejpam-6847	407	17	of	of	ADP
ejpam-6847	407	18	26	26	NUM
ejpam-6847	407	19	theorem	theorem	NOUN
ejpam-6847	407	20	3	3	X
ejpam-6847	407	21	.	.	PUNCT
ejpam-6847	408	1	let	let	AUX
ejpam-6847	408	2	(	(	PUNCT
ejpam-6847	408	3	x	x	NOUN
ejpam-6847	408	4	,	,	PUNCT
ejpam-6847	408	5	s	s	PART
ejpam-6847	408	6	)	)	PUNCT
ejpam-6847	408	7	be	be	AUX
ejpam-6847	408	8	a	a	DET
ejpam-6847	408	9	complete	complete	ADJ
ejpam-6847	408	10	t	t	NOUN
ejpam-6847	408	11	c	c	X
ejpam-6847	408	12	-	-	PUNCT
ejpam-6847	408	13	s	s	PROPN
ejpam-6847	408	14	-	-	PUNCT
ejpam-6847	408	15	mt	mt	NOUN
ejpam-6847	408	16	s	s	PROPN
ejpam-6847	408	17	,	,	PUNCT
ejpam-6847	408	18	where	where	SCONJ
ejpam-6847	408	19	x	x	PUNCT
ejpam-6847	409	1	6=	6=	AUX
ejpam-6847	409	2	∅.	∅.	NOUN
ejpam-6847	409	3	let	let	VERB
ejpam-6847	409	4	t	t	NOUN
ejpam-6847	409	5	:	:	PUNCT
ejpam-6847	409	6	x	x	X
ejpam-6847	409	7	→	→	PUNCT
ejpam-6847	409	8	x	x	PUNCT
ejpam-6847	409	9	be	be	AUX
ejpam-6847	409	10	an	an	DET
ejpam-6847	409	11	(	(	PUNCT
ejpam-6847	409	12	αs	αs	PROPN
ejpam-6847	409	13	,	,	PUNCT
ejpam-6847	409	14	ηs	ηs	PROPN
ejpam-6847	409	15	,	,	PUNCT
ejpam-6847	409	16	νs	νs	NOUN
ejpam-6847	409	17	,	,	PUNCT
ejpam-6847	409	18	(	(	PUNCT
ejpam-6847	409	19	q	q	X
ejpam-6847	409	20	,	,	PUNCT
ejpam-6847	409	21	h)−	h)−	PROPN
ejpam-6847	409	22	f)−contraction	f)−contraction	PROPN
ejpam-6847	409	23	mapping	mapping	NOUN
ejpam-6847	409	24	.	.	PUNCT
ejpam-6847	410	1	assume	assume	VERB
ejpam-6847	410	2	that	that	SCONJ
ejpam-6847	410	3	the	the	DET
ejpam-6847	410	4	following	follow	VERB
ejpam-6847	410	5	conditions	condition	NOUN
ejpam-6847	410	6	hold	hold	VERB
ejpam-6847	410	7	:	:	PUNCT
ejpam-6847	410	8	(	(	PUNCT
ejpam-6847	410	9	1	1	X
ejpam-6847	410	10	)	)	PUNCT
ejpam-6847	410	11	t	t	PROPN
ejpam-6847	410	12	is	be	AUX
ejpam-6847	410	13	αs	αs	ADJ
ejpam-6847	410	14	-	-	ADJ
ejpam-6847	410	15	admissible	admissible	ADJ
ejpam-6847	410	16	,	,	PUNCT
ejpam-6847	410	17	ηs	ηs	NOUN
ejpam-6847	410	18	-	-	PUNCT
ejpam-6847	410	19	admissible	admissible	ADJ
ejpam-6847	410	20	and	and	CCONJ
ejpam-6847	410	21	νs	νs	NOUN
ejpam-6847	410	22	-	-	PUNCT
ejpam-6847	410	23	subadmissible	subadmissible	ADJ
ejpam-6847	410	24	mapping	mapping	NOUN
ejpam-6847	410	25	.	.	PUNCT
ejpam-6847	411	1	(	(	PUNCT
ejpam-6847	411	2	2	2	X
ejpam-6847	411	3	)	)	PUNCT
ejpam-6847	411	4	there	there	PRON
ejpam-6847	411	5	is	be	VERB
ejpam-6847	411	6	x0	x0	PROPN
ejpam-6847	411	7	∈	∈	PROPN
ejpam-6847	411	8	x	x	NOUN
ejpam-6847	411	9	,	,	PUNCT
ejpam-6847	411	10	such	such	ADJ
ejpam-6847	411	11	that	that	DET
ejpam-6847	411	12	αs(x0	αs(x0	NOUN
ejpam-6847	411	13	,	,	PUNCT
ejpam-6847	411	14	x0	x0	PROPN
ejpam-6847	411	15	,	,	PUNCT
ejpam-6847	411	16	tx0	tx0	PROPN
ejpam-6847	411	17	)	)	PUNCT
ejpam-6847	411	18	≥	≥	NOUN
ejpam-6847	411	19	1	1	NUM
ejpam-6847	411	20	,	,	PUNCT
ejpam-6847	411	21	ηs(x0	ηs(x0	NOUN
ejpam-6847	411	22	,	,	PUNCT
ejpam-6847	411	23	x0	x0	PROPN
ejpam-6847	411	24	,	,	PUNCT
ejpam-6847	411	25	tx0	tx0	PROPN
ejpam-6847	411	26	)	)	PUNCT
ejpam-6847	411	27	≥	≥	NOUN
ejpam-6847	411	28	1	1	NUM
ejpam-6847	411	29	,	,	PUNCT
ejpam-6847	411	30	and	and	CCONJ
ejpam-6847	411	31	νs(x0	νs(x0	PROPN
ejpam-6847	411	32	,	,	PUNCT
ejpam-6847	411	33	x0	x0	PROPN
ejpam-6847	411	34	,	,	PUNCT
ejpam-6847	411	35	tx0	tx0	NOUN
ejpam-6847	411	36	)	)	PUNCT
ejpam-6847	411	37	≤	≤	NOUN
ejpam-6847	411	38	1	1	NUM
ejpam-6847	411	39	.	.	PUNCT
ejpam-6847	412	1	(	(	PUNCT
ejpam-6847	412	2	3	3	X
ejpam-6847	412	3	)	)	PUNCT
ejpam-6847	412	4	for	for	ADP
ejpam-6847	412	5	x0	x0	PROPN
ejpam-6847	412	6	∈	∈	PROPN
ejpam-6847	412	7	x	x	PRON
ejpam-6847	412	8	,	,	PUNCT
ejpam-6847	412	9	the	the	DET
ejpam-6847	412	10	sequence	sequence	NOUN
ejpam-6847	412	11	{	{	PUNCT
ejpam-6847	412	12	xn	xn	NUM
ejpam-6847	412	13	}	}	PUNCT
ejpam-6847	412	14	,	,	PUNCT
ejpam-6847	412	15	is	be	AUX
ejpam-6847	412	16	defined	define	VERB
ejpam-6847	412	17	by	by	ADP
ejpam-6847	412	18	xn	xn	PROPN
ejpam-6847	412	19	=	=	SYM
ejpam-6847	412	20	tnx0	tnx0	PROPN
ejpam-6847	412	21	,	,	PUNCT
ejpam-6847	412	22	and	and	CCONJ
ejpam-6847	412	23	the	the	DET
ejpam-6847	412	24	following	following	ADJ
ejpam-6847	412	25	inequalityholds	inequalityhold	NOUN
ejpam-6847	412	26	:	:	PUNCT
ejpam-6847	412	27	sup	sup	PROPN
ejpam-6847	412	28	m≥1	m≥1	PROPN
ejpam-6847	412	29	lim	lim	PROPN
ejpam-6847	412	30	n→+∞	n→+∞	PROPN
ejpam-6847	412	31	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	412	32	,	,	PUNCT
ejpam-6847	412	33	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	412	34	,	,	PUNCT
ejpam-6847	412	35	xn+2	xn+2	NUM
ejpam-6847	412	36	)	)	PUNCT
ejpam-6847	413	1	+	+	CCONJ
ejpam-6847	413	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	413	3	,	,	PUNCT
ejpam-6847	413	4	xn+2	xn+2	NUM
ejpam-6847	413	5	)	)	PUNCT
ejpam-6847	413	6	]	]	PUNCT
ejpam-6847	414	1	[	[	X
ejpam-6847	414	2	β(xn	β(xn	NOUN
ejpam-6847	414	3	,	,	PUNCT
ejpam-6847	414	4	xn+1	xn+1	NUM
ejpam-6847	414	5	)	)	PUNCT
ejpam-6847	414	6	+	+	CCONJ
ejpam-6847	414	7	µ(xn	µ(xn	PROPN
ejpam-6847	414	8	,	,	PUNCT
ejpam-6847	414	9	xn+1	xn+1	NUM
ejpam-6847	414	10	)	)	PUNCT
ejpam-6847	414	11	]	]	PUNCT
ejpam-6847	414	12	<	<	X
ejpam-6847	414	13	1	1	X
ejpam-6847	414	14	.	.	PUNCT
ejpam-6847	414	15	(	(	PUNCT
ejpam-6847	414	16	21	21	NUM
ejpam-6847	414	17	)	)	PUNCT
ejpam-6847	414	18	in	in	ADP
ejpam-6847	414	19	addition	addition	NOUN
ejpam-6847	414	20	,	,	PUNCT
ejpam-6847	414	21	for	for	SCONJ
ejpam-6847	414	22	every	every	DET
ejpam-6847	414	23	x	x	SYM
ejpam-6847	414	24	∈	∈	PROPN
ejpam-6847	414	25	x	x	NOUN
ejpam-6847	414	26	,	,	PUNCT
ejpam-6847	414	27	the	the	DET
ejpam-6847	414	28	following	follow	VERB
ejpam-6847	414	29	limits	limit	NOUN
ejpam-6847	414	30	exist	exist	VERB
ejpam-6847	414	31	and	and	CCONJ
ejpam-6847	414	32	are	be	AUX
ejpam-6847	414	33	finite	finite	ADJ
ejpam-6847	414	34	:	:	PUNCT
ejpam-6847	414	35	lim	lim	PROPN
ejpam-6847	414	36	n→+∞	n→+∞	PROPN
ejpam-6847	414	37	β(x	β(x	PROPN
ejpam-6847	414	38	,	,	PUNCT
ejpam-6847	414	39	xn	xn	PROPN
ejpam-6847	414	40	)	)	PUNCT
ejpam-6847	414	41	,	,	PUNCT
ejpam-6847	414	42	lim	lim	PROPN
ejpam-6847	414	43	n→+∞	n→+∞	VERB
ejpam-6847	414	44	µ(xn	µ(xn	PROPN
ejpam-6847	414	45	,	,	PUNCT
ejpam-6847	414	46	x	x	NOUN
ejpam-6847	414	47	)	)	PUNCT
ejpam-6847	414	48	and	and	CCONJ
ejpam-6847	414	49	lim	lim	PROPN
ejpam-6847	414	50	n→+∞	n→+∞	VERB
ejpam-6847	414	51	γ(xn	γ(xn	PROPN
ejpam-6847	414	52	,	,	PUNCT
ejpam-6847	414	53	x	x	NOUN
ejpam-6847	414	54	)	)	PUNCT
ejpam-6847	414	55	.	.	PUNCT
ejpam-6847	415	1	(	(	PUNCT
ejpam-6847	415	2	22	22	NUM
ejpam-6847	415	3	)	)	PUNCT
ejpam-6847	415	4	then	then	ADV
ejpam-6847	415	5	,	,	PUNCT
ejpam-6847	415	6	t	t	PROPN
ejpam-6847	415	7	has	have	VERB
ejpam-6847	415	8	a	a	DET
ejpam-6847	415	9	fixed	fix	VERB
ejpam-6847	415	10	point	point	NOUN
ejpam-6847	415	11	.	.	PUNCT
ejpam-6847	416	1	for	for	ADP
ejpam-6847	416	2	the	the	DET
ejpam-6847	416	3	uniqueness	uniqueness	NOUN
ejpam-6847	416	4	of	of	ADP
ejpam-6847	416	5	the	the	DET
ejpam-6847	416	6	fixed	fix	VERB
ejpam-6847	416	7	point	point	NOUN
ejpam-6847	416	8	,	,	PUNCT
ejpam-6847	416	9	assume	assume	VERB
ejpam-6847	416	10	both	both	DET
ejpam-6847	416	11	u	u	NOUN
ejpam-6847	416	12	,	,	PUNCT
ejpam-6847	416	13	and	and	CCONJ
ejpam-6847	416	14	v	v	NOUN
ejpam-6847	416	15	are	be	AUX
ejpam-6847	416	16	fixed	fix	VERB
ejpam-6847	416	17	points	point	NOUN
ejpam-6847	416	18	such	such	ADJ
ejpam-6847	416	19	that	that	PRON
ejpam-6847	416	20	αs(u	αs(u	NUM
ejpam-6847	416	21	,	,	PUNCT
ejpam-6847	416	22	u	u	NOUN
ejpam-6847	416	23	,	,	PUNCT
ejpam-6847	416	24	v	v	NOUN
ejpam-6847	416	25	)	)	PUNCT
ejpam-6847	416	26	≥	≥	NOUN
ejpam-6847	416	27	1	1	NUM
ejpam-6847	416	28	,	,	PUNCT
ejpam-6847	416	29	ηs(u	ηs(u	NOUN
ejpam-6847	416	30	,	,	PUNCT
ejpam-6847	416	31	u	u	NOUN
ejpam-6847	416	32	,	,	PUNCT
ejpam-6847	416	33	v	v	NOUN
ejpam-6847	416	34	)	)	PUNCT
ejpam-6847	416	35	≥	≥	NOUN
ejpam-6847	416	36	1	1	NUM
ejpam-6847	416	37	,	,	PUNCT
ejpam-6847	416	38	and	and	CCONJ
ejpam-6847	416	39	νs(u	νs(u	NUM
ejpam-6847	416	40	,	,	PUNCT
ejpam-6847	416	41	u	u	NOUN
ejpam-6847	416	42	,	,	PUNCT
ejpam-6847	416	43	v	v	NOUN
ejpam-6847	416	44	)	)	PUNCT
ejpam-6847	416	45	≤	≤	NUM
ejpam-6847	416	46	1	1	NUM
ejpam-6847	416	47	,	,	PUNCT
ejpam-6847	416	48	then	then	ADV
ejpam-6847	416	49	t	t	PROPN
ejpam-6847	416	50	has	have	VERB
ejpam-6847	416	51	a	a	DET
ejpam-6847	416	52	unique	unique	ADJ
ejpam-6847	416	53	fixed	fix	VERB
ejpam-6847	416	54	point	point	NOUN
ejpam-6847	416	55	in	in	ADP
ejpam-6847	416	56	x.	x.	NOUN
ejpam-6847	416	57	proof	proof	NOUN
ejpam-6847	416	58	.	.	PUNCT
ejpam-6847	417	1	select	select	VERB
ejpam-6847	417	2	x0	x0	PROPN
ejpam-6847	417	3	∈	∈	PROPN
ejpam-6847	417	4	x	x	PUNCT
ejpam-6847	417	5	so	so	ADV
ejpam-6847	417	6	αs(x0	αs(x0	PROPN
ejpam-6847	417	7	,	,	PUNCT
ejpam-6847	417	8	x0	x0	PROPN
ejpam-6847	417	9	,	,	PUNCT
ejpam-6847	417	10	tx0	tx0	PROPN
ejpam-6847	417	11	)	)	PUNCT
ejpam-6847	417	12	≥	≥	NOUN
ejpam-6847	417	13	1	1	NUM
ejpam-6847	417	14	,	,	PUNCT
ejpam-6847	417	15	ηs(x0	ηs(x0	NOUN
ejpam-6847	417	16	,	,	PUNCT
ejpam-6847	417	17	x0	x0	PROPN
ejpam-6847	417	18	,	,	PUNCT
ejpam-6847	417	19	tx0	tx0	PROPN
ejpam-6847	417	20	)	)	PUNCT
ejpam-6847	417	21	≥	≥	NOUN
ejpam-6847	417	22	1	1	NUM
ejpam-6847	417	23	,	,	PUNCT
ejpam-6847	417	24	νs(x0	νs(x0	PROPN
ejpam-6847	417	25	,	,	PUNCT
ejpam-6847	417	26	x0	x0	PROPN
ejpam-6847	417	27	,	,	PUNCT
ejpam-6847	417	28	tx0	tx0	NOUN
ejpam-6847	417	29	)	)	PUNCT
ejpam-6847	417	30	≤	≤	NUM
ejpam-6847	417	31	1	1	NUM
ejpam-6847	417	32	.	.	PUNCT
ejpam-6847	418	1	a	a	DET
ejpam-6847	418	2	sequence	sequence	NOUN
ejpam-6847	418	3	{	{	PUNCT
ejpam-6847	418	4	xn	xn	NOUN
ejpam-6847	418	5	}	}	PUNCT
ejpam-6847	418	6	is	be	AUX
ejpam-6847	418	7	formed	form	VERB
ejpam-6847	418	8	by	by	ADP
ejpam-6847	418	9	tx0	tx0	NOUN
ejpam-6847	418	10	=	=	SYM
ejpam-6847	418	11	x1	x1	PROPN
ejpam-6847	418	12	,	,	PUNCT
ejpam-6847	418	13	t	t	PROPN
ejpam-6847	418	14	2x0	2x0	NUM
ejpam-6847	418	15	=	=	SYM
ejpam-6847	418	16	tx1	tx1	NOUN
ejpam-6847	418	17	=	=	SYM
ejpam-6847	418	18	x2	x2	PROPN
ejpam-6847	418	19	.	.	PUNCT
ejpam-6847	419	1	therefore	therefore	ADV
ejpam-6847	419	2	,	,	PUNCT
ejpam-6847	419	3	for	for	ADP
ejpam-6847	419	4	any	any	DET
ejpam-6847	419	5	n	n	PRON
ejpam-6847	419	6	∈	∈	PROPN
ejpam-6847	419	7	n	n	CCONJ
ejpam-6847	419	8	,	,	PUNCT
ejpam-6847	419	9	we	we	PRON
ejpam-6847	419	10	have	have	VERB
ejpam-6847	419	11	tnx0	tnx0	NOUN
ejpam-6847	419	12	=	=	SYM
ejpam-6847	419	13	tn−1x1	tn−1x1	X
ejpam-6847	419	14	=	=	X
ejpam-6847	419	15	·	·	PUNCT
ejpam-6847	419	16	·	·	PUNCT
ejpam-6847	419	17	·	·	PUNCT
ejpam-6847	420	1	=	=	PUNCT
ejpam-6847	420	2	txn−1	txn−1	PROPN
ejpam-6847	420	3	=	=	PUNCT
ejpam-6847	421	1	xn	xn	PROPN
ejpam-6847	421	2	.	.	PUNCT
ejpam-6847	422	1	in	in	ADP
ejpam-6847	422	2	addition	addition	NOUN
ejpam-6847	422	3	,	,	PUNCT
ejpam-6847	422	4	tnx0	tnx0	PROPN
ejpam-6847	422	5	6=	6=	PROPN
ejpam-6847	422	6	tn+1x0	tn+1x0	PROPN
ejpam-6847	422	7	holds	hold	VERB
ejpam-6847	422	8	for	for	ADP
ejpam-6847	422	9	all	all	DET
ejpam-6847	422	10	n	n	PRON
ejpam-6847	422	11	≥	≥	NOUN
ejpam-6847	422	12	0	0	NUM
ejpam-6847	422	13	.	.	PUNCT
ejpam-6847	423	1	as	as	SCONJ
ejpam-6847	423	2	t	t	PROPN
ejpam-6847	423	3	is	be	AUX
ejpam-6847	423	4	an	an	DET
ejpam-6847	423	5	αs	αs	ADJ
ejpam-6847	423	6	-	-	PUNCT
ejpam-6847	423	7	admissible	admissible	ADJ
ejpam-6847	423	8	mapping	mapping	NOUN
ejpam-6847	423	9	and	and	CCONJ
ejpam-6847	423	10	νs	νs	NOUN
ejpam-6847	423	11	-	-	PUNCT
ejpam-6847	423	12	subadmissible	subadmissible	ADJ
ejpam-6847	423	13	mapping	mapping	NOUN
ejpam-6847	423	14	,	,	PUNCT
ejpam-6847	423	15	this	this	PRON
ejpam-6847	423	16	implies	imply	VERB
ejpam-6847	423	17	that	that	SCONJ
ejpam-6847	423	18	αs(xn	αs(xn	PROPN
ejpam-6847	423	19	,	,	PUNCT
ejpam-6847	423	20	xn	xn	PROPN
ejpam-6847	423	21	,	,	PUNCT
ejpam-6847	423	22	xn+1	xn+1	NUM
ejpam-6847	423	23	)	)	PUNCT
ejpam-6847	423	24	≥	≥	NOUN
ejpam-6847	423	25	1	1	NUM
ejpam-6847	423	26	,	,	PUNCT
ejpam-6847	423	27	νs(xn	νs(xn	PROPN
ejpam-6847	423	28	,	,	PUNCT
ejpam-6847	423	29	xn	xn	PROPN
ejpam-6847	423	30	,	,	PUNCT
ejpam-6847	423	31	xn+1	xn+1	NUM
ejpam-6847	423	32	)	)	PUNCT
ejpam-6847	423	33	≤	≤	NUM
ejpam-6847	423	34	1	1	NUM
ejpam-6847	423	35	,	,	PUNCT
ejpam-6847	423	36	for	for	ADP
ejpam-6847	423	37	all	all	PRON
ejpam-6847	423	38	n	n	DET
ejpam-6847	423	39	∈	∈	PROPN
ejpam-6847	423	40	n.	n.	NOUN
ejpam-6847	423	41	since	since	SCONJ
ejpam-6847	423	42	t	t	PROPN
ejpam-6847	423	43	is	be	AUX
ejpam-6847	423	44	(	(	PUNCT
ejpam-6847	423	45	αs	αs	INTJ
ejpam-6847	423	46	,	,	PUNCT
ejpam-6847	423	47	ηs	ηs	PROPN
ejpam-6847	423	48	,	,	PUNCT
ejpam-6847	423	49	νs	νs	NOUN
ejpam-6847	423	50	,	,	PUNCT
ejpam-6847	423	51	(	(	PUNCT
ejpam-6847	423	52	q	q	X
ejpam-6847	423	53	,	,	PUNCT
ejpam-6847	423	54	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	423	55	mapping	mapping	NOUN
ejpam-6847	423	56	,	,	PUNCT
ejpam-6847	423	57	we	we	PRON
ejpam-6847	423	58	obtain	obtain	VERB
ejpam-6847	423	59	h	h	NOUN
ejpam-6847	423	60	(	(	PUNCT
ejpam-6847	423	61	1	1	NUM
ejpam-6847	423	62	,	,	PUNCT
ejpam-6847	423	63	1	1	NUM
ejpam-6847	423	64	,	,	PUNCT
ejpam-6847	423	65	τ	τ	PROPN
ejpam-6847	424	1	+	+	NUM
ejpam-6847	424	2	f	f	X
ejpam-6847	424	3	(	(	PUNCT
ejpam-6847	424	4	s(xn	s(xn	PROPN
ejpam-6847	424	5	,	,	PUNCT
ejpam-6847	424	6	xn	xn	PROPN
ejpam-6847	424	7	,	,	PUNCT
ejpam-6847	424	8	xn+1	xn+1	NUM
ejpam-6847	424	9	)	)	PUNCT
ejpam-6847	424	10	)	)	PUNCT
ejpam-6847	424	11	)	)	PUNCT
ejpam-6847	425	1	=	=	NOUN
ejpam-6847	425	2	h	h	NOUN
ejpam-6847	425	3	(	(	PUNCT
ejpam-6847	425	4	1	1	NUM
ejpam-6847	425	5	,	,	PUNCT
ejpam-6847	425	6	1	1	NUM
ejpam-6847	425	7	,	,	PUNCT
ejpam-6847	425	8	τ	τ	PROPN
ejpam-6847	425	9	+	+	NUM
ejpam-6847	425	10	f	f	X
ejpam-6847	425	11	(	(	PUNCT
ejpam-6847	425	12	s(t	s(t	PROPN
ejpam-6847	425	13	xn−1	xn−1	PROPN
ejpam-6847	425	14	,	,	PUNCT
ejpam-6847	425	15	t	t	PROPN
ejpam-6847	425	16	xn−1	xn−1	PROPN
ejpam-6847	425	17	,	,	PUNCT
ejpam-6847	425	18	t	t	PROPN
ejpam-6847	425	19	xn	xn	PROPN
ejpam-6847	425	20	)	)	PUNCT
ejpam-6847	425	21	)	)	PUNCT
ejpam-6847	425	22	)	)	PUNCT
ejpam-6847	426	1	≤	≤	NUM
ejpam-6847	426	2	h	h	NOUN
ejpam-6847	426	3	(	(	PUNCT
ejpam-6847	426	4	αs(xn−1	αs(xn−1	PROPN
ejpam-6847	426	5	,	,	PUNCT
ejpam-6847	426	6	xn−1	xn−1	PROPN
ejpam-6847	426	7	,	,	PUNCT
ejpam-6847	426	8	xn	xn	PROPN
ejpam-6847	426	9	)	)	PUNCT
ejpam-6847	426	10	,	,	PUNCT
ejpam-6847	426	11	ηs(xn−1	ηs(xn−1	PROPN
ejpam-6847	426	12	,	,	PUNCT
ejpam-6847	426	13	xn−1	xn−1	PROPN
ejpam-6847	426	14	,	,	PUNCT
ejpam-6847	426	15	xn	xn	PROPN
ejpam-6847	426	16	)	)	PUNCT
ejpam-6847	426	17	,	,	PUNCT
ejpam-6847	426	18	τ	τ	PROPN
ejpam-6847	427	1	+	+	NUM
ejpam-6847	427	2	f	f	X
ejpam-6847	427	3	(	(	PUNCT
ejpam-6847	427	4	s(t	s(t	PROPN
ejpam-6847	427	5	xn−1	xn−1	PROPN
ejpam-6847	427	6	,	,	PUNCT
ejpam-6847	427	7	t	t	PROPN
ejpam-6847	427	8	xn−1	xn−1	PROPN
ejpam-6847	427	9	,	,	PUNCT
ejpam-6847	427	10	t	t	PROPN
ejpam-6847	427	11	xn	xn	PROPN
ejpam-6847	427	12	)	)	PUNCT
ejpam-6847	427	13	)	)	PUNCT
ejpam-6847	427	14	)	)	PUNCT
ejpam-6847	427	15	≤	≤	NUM
ejpam-6847	428	1	q	q	NOUN
ejpam-6847	428	2	(	(	PUNCT
ejpam-6847	428	3	νs(xn−1	νs(xn−1	PROPN
ejpam-6847	428	4	,	,	PUNCT
ejpam-6847	428	5	xn−1	xn−1	PROPN
ejpam-6847	428	6	,	,	PUNCT
ejpam-6847	428	7	xn	xn	PROPN
ejpam-6847	428	8	)	)	PUNCT
ejpam-6847	428	9	,	,	PUNCT
ejpam-6847	428	10	f	f	PROPN
ejpam-6847	428	11	(	(	PUNCT
ejpam-6847	428	12	s(xn−1	s(xn−1	PROPN
ejpam-6847	428	13	,	,	PUNCT
ejpam-6847	428	14	xn−1	xn−1	PROPN
ejpam-6847	428	15	,	,	PUNCT
ejpam-6847	428	16	xn	xn	PROPN
ejpam-6847	428	17	)	)	PUNCT
ejpam-6847	428	18	)	)	PUNCT
ejpam-6847	428	19	)	)	PUNCT
ejpam-6847	429	1	≤	≤	NUM
ejpam-6847	430	1	q	q	NOUN
ejpam-6847	430	2	(	(	PUNCT
ejpam-6847	430	3	1	1	NUM
ejpam-6847	430	4	,	,	PUNCT
ejpam-6847	430	5	f	f	X
ejpam-6847	430	6	(	(	PUNCT
ejpam-6847	430	7	s(xn−1	s(xn−1	PROPN
ejpam-6847	430	8	,	,	PUNCT
ejpam-6847	430	9	xn−1	xn−1	PROPN
ejpam-6847	430	10	,	,	PUNCT
ejpam-6847	430	11	xn	xn	PROPN
ejpam-6847	430	12	)	)	PUNCT
ejpam-6847	430	13	)	)	PUNCT
ejpam-6847	430	14	)	)	PUNCT
ejpam-6847	430	15	.	.	PUNCT
ejpam-6847	431	1	f.	f.	PROPN
ejpam-6847	431	2	m.	m.	PROPN
ejpam-6847	431	3	azmi	azmi	PROPN
ejpam-6847	431	4	,	,	PUNCT
ejpam-6847	431	5	a.	a.	PROPN
ejpam-6847	431	6	h.	h.	PROPN
ejpam-6847	431	7	ansari	ansari	PROPN
ejpam-6847	431	8	,	,	PUNCT
ejpam-6847	431	9	s.	s.	PROPN
ejpam-6847	431	10	h.	h.	PROPN
ejpam-6847	431	11	j.	j.	PROPN
ejpam-6847	431	12	petroudi	petroudi	PROPN
ejpam-6847	431	13	/	/	SYM
ejpam-6847	431	14	eur	eur	PROPN
ejpam-6847	431	15	.	.	PUNCT
ejpam-6847	432	1	j.	j.	PROPN
ejpam-6847	432	2	pure	pure	PROPN
ejpam-6847	432	3	appl	appl	PROPN
ejpam-6847	432	4	.	.	PROPN
ejpam-6847	432	5	math	math	PROPN
ejpam-6847	432	6	,	,	PUNCT
ejpam-6847	432	7	18	18	NUM
ejpam-6847	432	8	(	(	PUNCT
ejpam-6847	432	9	4	4	NUM
ejpam-6847	432	10	)	)	PUNCT
ejpam-6847	432	11	(	(	PUNCT
ejpam-6847	432	12	2025	2025	NUM
ejpam-6847	432	13	)	)	PUNCT
ejpam-6847	432	14	,	,	PUNCT
ejpam-6847	432	15	6847	6847	NUM
ejpam-6847	432	16	17	17	NUM
ejpam-6847	432	17	of	of	ADP
ejpam-6847	432	18	26	26	NUM
ejpam-6847	432	19	as	as	ADP
ejpam-6847	432	20	(	(	PUNCT
ejpam-6847	432	21	q	q	ADJ
ejpam-6847	432	22	,	,	PUNCT
ejpam-6847	432	23	h	h	NOUN
ejpam-6847	432	24	)	)	PUNCT
ejpam-6847	432	25	is	be	AUX
ejpam-6847	432	26	an	an	DET
ejpam-6847	432	27	upper	upper	ADJ
ejpam-6847	432	28	class	class	NOUN
ejpam-6847	432	29	pair	pair	NOUN
ejpam-6847	432	30	of	of	ADP
ejpam-6847	432	31	typeii	typeii	NOUN
ejpam-6847	432	32	,	,	PUNCT
ejpam-6847	432	33	the	the	DET
ejpam-6847	432	34	following	follow	VERB
ejpam-6847	432	35	inequality	inequality	NOUN
ejpam-6847	432	36	holds	hold	VERB
ejpam-6847	432	37	:	:	PUNCT
ejpam-6847	433	1	τ	τ	PROPN
ejpam-6847	433	2	+	+	NUM
ejpam-6847	433	3	f	f	X
ejpam-6847	433	4	(	(	PUNCT
ejpam-6847	433	5	s(xn	s(xn	PROPN
ejpam-6847	433	6	,	,	PUNCT
ejpam-6847	433	7	xn	xn	PROPN
ejpam-6847	433	8	,	,	PUNCT
ejpam-6847	433	9	xn+1	xn+1	NUM
ejpam-6847	433	10	)	)	PUNCT
ejpam-6847	433	11	)	)	PUNCT
ejpam-6847	434	1	≤	≤	NUM
ejpam-6847	434	2	f	f	X
ejpam-6847	434	3	(	(	PUNCT
ejpam-6847	434	4	s(xn−1	s(xn−1	PROPN
ejpam-6847	434	5	,	,	PUNCT
ejpam-6847	434	6	xn−1	xn−1	PROPN
ejpam-6847	434	7	,	,	PUNCT
ejpam-6847	434	8	xn	xn	PROPN
ejpam-6847	434	9	)	)	PUNCT
ejpam-6847	434	10	)	)	PUNCT
ejpam-6847	434	11	,	,	PUNCT
ejpam-6847	434	12	which	which	PRON
ejpam-6847	434	13	implies	imply	VERB
ejpam-6847	434	14	that	that	SCONJ
ejpam-6847	434	15	f	f	PROPN
ejpam-6847	434	16	(	(	PUNCT
ejpam-6847	434	17	s(xn	s(xn	PROPN
ejpam-6847	434	18	,	,	PUNCT
ejpam-6847	434	19	xn	xn	PROPN
ejpam-6847	434	20	,	,	PUNCT
ejpam-6847	434	21	xn+1	xn+1	NUM
ejpam-6847	434	22	)	)	PUNCT
ejpam-6847	434	23	)	)	PUNCT
ejpam-6847	434	24	≤	≤	NUM
ejpam-6847	435	1	f	f	X
ejpam-6847	435	2	(	(	PUNCT
ejpam-6847	435	3	s(xn−1	s(xn−1	PROPN
ejpam-6847	435	4	,	,	PUNCT
ejpam-6847	435	5	xn−1	xn−1	PROPN
ejpam-6847	435	6	,	,	PUNCT
ejpam-6847	435	7	xn))−	xn))−	PROPN
ejpam-6847	435	8	τ	τ	PROPN
ejpam-6847	435	9	.	.	PUNCT
ejpam-6847	436	1	(	(	PUNCT
ejpam-6847	436	2	23	23	NUM
ejpam-6847	436	3	)	)	PUNCT
ejpam-6847	436	4	≤	≤	NUM
ejpam-6847	436	5	f	f	X
ejpam-6847	436	6	(	(	PUNCT
ejpam-6847	436	7	s(xn−2	s(xn−2	PROPN
ejpam-6847	436	8	,	,	PUNCT
ejpam-6847	436	9	xn−2	xn−2	PROPN
ejpam-6847	436	10	,	,	PUNCT
ejpam-6847	436	11	xn−1))−	xn−1))−	NUM
ejpam-6847	436	12	2τ	2τ	NOUN
ejpam-6847	436	13	.	.	PUNCT
ejpam-6847	437	1	≤	≤	NUM
ejpam-6847	437	2	·	·	PUNCT
ejpam-6847	437	3	·	·	PUNCT
ejpam-6847	437	4	·	·	PUNCT
ejpam-6847	438	1	≤	≤	NUM
ejpam-6847	438	2	f	f	X
ejpam-6847	438	3	(	(	PUNCT
ejpam-6847	438	4	s(x0	s(x0	ADV
ejpam-6847	438	5	,	,	PUNCT
ejpam-6847	438	6	x0	x0	PROPN
ejpam-6847	438	7	,	,	PUNCT
ejpam-6847	438	8	x1))−	x1))−	PROPN
ejpam-6847	438	9	nτ	nτ	NOUN
ejpam-6847	438	10	.	.	PUNCT
ejpam-6847	439	1	letting	let	VERB
ejpam-6847	439	2	n→	n→	ADV
ejpam-6847	439	3	+	+	ADJ
ejpam-6847	439	4	∞	∞	NUM
ejpam-6847	439	5	in	in	ADP
ejpam-6847	439	6	equation	equation	NOUN
ejpam-6847	439	7	23	23	NUM
ejpam-6847	439	8	,	,	PUNCT
ejpam-6847	439	9	and	and	CCONJ
ejpam-6847	439	10	with	with	ADP
ejpam-6847	439	11	τ	τ	PROPN
ejpam-6847	439	12	>	>	X
ejpam-6847	439	13	0	0	PROPN
ejpam-6847	439	14	,	,	PUNCT
ejpam-6847	439	15	we	we	PRON
ejpam-6847	439	16	have	have	VERB
ejpam-6847	439	17	lim	lim	PROPN
ejpam-6847	439	18	n→+∞	n→+∞	PROPN
ejpam-6847	439	19	f	f	PROPN
ejpam-6847	439	20	(	(	PUNCT
ejpam-6847	439	21	s(xn	s(xn	PROPN
ejpam-6847	439	22	,	,	PUNCT
ejpam-6847	439	23	xn	xn	PROPN
ejpam-6847	439	24	,	,	PUNCT
ejpam-6847	439	25	xn+1	xn+1	NUM
ejpam-6847	439	26	)	)	PUNCT
ejpam-6847	439	27	)	)	PUNCT
ejpam-6847	440	1	=	=	SYM
ejpam-6847	440	2	−∞.	−∞.	NOUN
ejpam-6847	440	3	(	(	PUNCT
ejpam-6847	440	4	24	24	NUM
ejpam-6847	440	5	)	)	PUNCT
ejpam-6847	440	6	as	as	ADP
ejpam-6847	440	7	f	f	PROPN
ejpam-6847	440	8	∈	∈	PROPN
ejpam-6847	440	9	f	f	PROPN
ejpam-6847	440	10	,	,	PUNCT
ejpam-6847	440	11	utilizing	utilize	VERB
ejpam-6847	440	12	(	(	PUNCT
ejpam-6847	440	13	w2	w2	NOUN
ejpam-6847	440	14	)	)	PUNCT
ejpam-6847	440	15	of	of	ADP
ejpam-6847	440	16	definition	definition	NOUN
ejpam-6847	440	17	14	14	NUM
ejpam-6847	440	18	,	,	PUNCT
ejpam-6847	440	19	we	we	PRON
ejpam-6847	440	20	deduce	deduce	VERB
ejpam-6847	440	21	that	that	PRON
ejpam-6847	440	22	limn→+∞	limn→+∞	VERB
ejpam-6847	440	23	s(xn	s(xn	NOUN
ejpam-6847	440	24	,	,	PUNCT
ejpam-6847	440	25	xn	xn	PROPN
ejpam-6847	440	26	,	,	PUNCT
ejpam-6847	440	27	xn+1	xn+1	NUM
ejpam-6847	440	28	)	)	PUNCT
ejpam-6847	440	29	=	=	SYM
ejpam-6847	440	30	0	0	NUM
ejpam-6847	440	31	,	,	PUNCT
ejpam-6847	440	32	and	and	CCONJ
ejpam-6847	440	33	by	by	ADP
ejpam-6847	440	34	(	(	PUNCT
ejpam-6847	440	35	w3	w3	PROPN
ejpam-6847	440	36	)	)	PUNCT
ejpam-6847	440	37	,	,	PUNCT
ejpam-6847	440	38	there	there	PRON
ejpam-6847	440	39	exists	exist	VERB
ejpam-6847	440	40	k	k	PROPN
ejpam-6847	440	41	∈	∈	PROPN
ejpam-6847	440	42	(	(	PUNCT
ejpam-6847	440	43	0	0	NUM
ejpam-6847	440	44	,	,	PUNCT
ejpam-6847	440	45	1	1	NUM
ejpam-6847	440	46	)	)	PUNCT
ejpam-6847	440	47	such	such	ADJ
ejpam-6847	440	48	that	that	SCONJ
ejpam-6847	440	49	lim	lim	PROPN
ejpam-6847	440	50	n→+∞	n→+∞	PROPN
ejpam-6847	440	51	(	(	PUNCT
ejpam-6847	440	52	s(xn	s(xn	PROPN
ejpam-6847	440	53	,	,	PUNCT
ejpam-6847	440	54	xn	xn	PROPN
ejpam-6847	440	55	,	,	PUNCT
ejpam-6847	440	56	xn+1	xn+1	NUM
ejpam-6847	440	57	)	)	PUNCT
ejpam-6847	440	58	)	)	PUNCT
ejpam-6847	441	1	kf	kf	INTJ
ejpam-6847	441	2	(	(	PUNCT
ejpam-6847	441	3	(	(	PUNCT
ejpam-6847	441	4	s(xn	s(xn	X
ejpam-6847	441	5	,	,	PUNCT
ejpam-6847	441	6	xn	xn	PROPN
ejpam-6847	441	7	,	,	PUNCT
ejpam-6847	441	8	xn+1	xn+1	NUM
ejpam-6847	441	9	)	)	PUNCT
ejpam-6847	441	10	)	)	PUNCT
ejpam-6847	442	1	=	=	PUNCT
ejpam-6847	442	2	0	0	X
ejpam-6847	442	3	.	.	PUNCT
ejpam-6847	443	1	(	(	PUNCT
ejpam-6847	443	2	25	25	NUM
ejpam-6847	443	3	)	)	PUNCT
ejpam-6847	443	4	from	from	ADP
ejpam-6847	443	5	equation	equation	NOUN
ejpam-6847	443	6	23	23	NUM
ejpam-6847	443	7	,	,	PUNCT
ejpam-6847	443	8	we	we	PRON
ejpam-6847	443	9	obtain	obtain	VERB
ejpam-6847	443	10	f	f	X
ejpam-6847	443	11	(	(	PUNCT
ejpam-6847	443	12	s(xn	s(xn	PROPN
ejpam-6847	443	13	,	,	PUNCT
ejpam-6847	443	14	xn	xn	PROPN
ejpam-6847	443	15	,	,	PUNCT
ejpam-6847	443	16	xn+1))−	xn+1))−	PROPN
ejpam-6847	443	17	f	f	X
ejpam-6847	443	18	(	(	PUNCT
ejpam-6847	443	19	s(x0	s(x0	PROPN
ejpam-6847	443	20	,	,	PUNCT
ejpam-6847	443	21	x0	x0	PROPN
ejpam-6847	443	22	,	,	PUNCT
ejpam-6847	443	23	x1	x1	PROPN
ejpam-6847	443	24	)	)	PUNCT
ejpam-6847	443	25	)	)	PUNCT
ejpam-6847	443	26	≤	≤	PUNCT
ejpam-6847	444	1	−nτ	−nτ	NOUN
ejpam-6847	444	2	.	.	PUNCT
ejpam-6847	445	1	thus	thus	ADV
ejpam-6847	445	2	for	for	ADP
ejpam-6847	445	3	any	any	DET
ejpam-6847	445	4	n	n	CCONJ
ejpam-6847	445	5	,	,	PUNCT
ejpam-6847	445	6	we	we	PRON
ejpam-6847	445	7	have	have	VERB
ejpam-6847	445	8	(	(	PUNCT
ejpam-6847	445	9	s(xn	s(xn	X
ejpam-6847	445	10	,	,	PUNCT
ejpam-6847	445	11	xn	xn	PROPN
ejpam-6847	445	12	,	,	PUNCT
ejpam-6847	445	13	xn+1	xn+1	NUM
ejpam-6847	445	14	)	)	PUNCT
ejpam-6847	445	15	)	)	PUNCT
ejpam-6847	446	1	kf	kf	PROPN
ejpam-6847	446	2	(	(	PUNCT
ejpam-6847	446	3	s(xn	s(xn	PROPN
ejpam-6847	446	4	,	,	PUNCT
ejpam-6847	446	5	xn	xn	PROPN
ejpam-6847	446	6	,	,	PUNCT
ejpam-6847	446	7	xn+1)−	xn+1)−	PROPN
ejpam-6847	446	8	(	(	PUNCT
ejpam-6847	446	9	s(xn	s(xn	PROPN
ejpam-6847	446	10	,	,	PUNCT
ejpam-6847	446	11	xn	xn	PROPN
ejpam-6847	446	12	,	,	PUNCT
ejpam-6847	446	13	xn+1	xn+1	NUM
ejpam-6847	446	14	)	)	PUNCT
ejpam-6847	446	15	kf	kf	PROPN
ejpam-6847	446	16	(	(	PUNCT
ejpam-6847	446	17	s(x0	s(x0	PROPN
ejpam-6847	446	18	,	,	PUNCT
ejpam-6847	446	19	x0	x0	PROPN
ejpam-6847	446	20	,	,	PUNCT
ejpam-6847	446	21	x1	x1	PROPN
ejpam-6847	446	22	)	)	PUNCT
ejpam-6847	446	23	)	)	PUNCT
ejpam-6847	446	24	≤	≤	NUM
ejpam-6847	447	1	−nτ(s(xn	−nτ(s(xn	PROPN
ejpam-6847	447	2	,	,	PUNCT
ejpam-6847	447	3	xn	xn	PROPN
ejpam-6847	447	4	,	,	PUNCT
ejpam-6847	447	5	xn+1	xn+1	NUM
ejpam-6847	447	6	)	)	PUNCT
ejpam-6847	447	7	)	)	PUNCT
ejpam-6847	448	1	k	k	PROPN
ejpam-6847	448	2	≤	≤	ADV
ejpam-6847	448	3	0	0	NUM
ejpam-6847	448	4	.	.	PUNCT
ejpam-6847	449	1	(	(	PUNCT
ejpam-6847	449	2	26	26	NUM
ejpam-6847	449	3	)	)	PUNCT
ejpam-6847	449	4	as	as	ADP
ejpam-6847	449	5	n	n	NUM
ejpam-6847	449	6	approaches	approach	NOUN
ejpam-6847	449	7	infinity	infinity	NOUN
ejpam-6847	449	8	in	in	ADP
ejpam-6847	449	9	equation	equation	NOUN
ejpam-6847	449	10	26	26	NUM
ejpam-6847	449	11	,	,	PUNCT
ejpam-6847	449	12	we	we	PRON
ejpam-6847	449	13	find	find	VERB
ejpam-6847	449	14	that	that	SCONJ
ejpam-6847	449	15	lim	lim	PROPN
ejpam-6847	449	16	n→+∞	n→+∞	PROPN
ejpam-6847	449	17	n(s(xn	n(s(xn	PROPN
ejpam-6847	449	18	,	,	PUNCT
ejpam-6847	449	19	xn	xn	PROPN
ejpam-6847	449	20	,	,	PUNCT
ejpam-6847	449	21	xn+1	xn+1	NUM
ejpam-6847	449	22	)	)	PUNCT
ejpam-6847	449	23	)	)	PUNCT
ejpam-6847	450	1	k	k	X
ejpam-6847	450	2	=	=	PUNCT
ejpam-6847	450	3	0	0	PROPN
ejpam-6847	450	4	.	.	PUNCT
ejpam-6847	451	1	(	(	PUNCT
ejpam-6847	451	2	27	27	NUM
ejpam-6847	451	3	)	)	PUNCT
ejpam-6847	451	4	this	this	PRON
ejpam-6847	451	5	leads	lead	VERB
ejpam-6847	451	6	to	to	ADP
ejpam-6847	451	7	the	the	DET
ejpam-6847	451	8	conclusion	conclusion	NOUN
ejpam-6847	451	9	that	that	PRON
ejpam-6847	451	10	limn→+∞	limn→+∞	VERB
ejpam-6847	451	11	n1	n1	PROPN
ejpam-6847	451	12	/	/	SYM
ejpam-6847	451	13	k(s(xn	k(s(xn	PROPN
ejpam-6847	451	14	,	,	PUNCT
ejpam-6847	451	15	xn	xn	PROPN
ejpam-6847	451	16	,	,	PUNCT
ejpam-6847	451	17	xn+1	xn+1	NUM
ejpam-6847	451	18	)	)	PUNCT
ejpam-6847	451	19	)	)	PUNCT
ejpam-6847	452	1	=	=	PUNCT
ejpam-6847	452	2	0	0	X
ejpam-6847	452	3	.	.	PUNCT
ejpam-6847	452	4	consequently	consequently	ADV
ejpam-6847	452	5	,	,	PUNCT
ejpam-6847	452	6	there	there	PRON
ejpam-6847	452	7	exists	exist	VERB
ejpam-6847	452	8	a	a	DET
ejpam-6847	452	9	natural	natural	ADJ
ejpam-6847	452	10	number	number	NOUN
ejpam-6847	452	11	n0	n0	NOUN
ejpam-6847	452	12	such	such	ADJ
ejpam-6847	452	13	that	that	SCONJ
ejpam-6847	452	14	the	the	DET
ejpam-6847	452	15	following	follow	VERB
ejpam-6847	452	16	inequality	inequality	NOUN
ejpam-6847	452	17	holds	hold	VERB
ejpam-6847	452	18	:	:	PUNCT
ejpam-6847	452	19	s(xn	s(xn	NOUN
ejpam-6847	452	20	,	,	PUNCT
ejpam-6847	452	21	xn	xn	PROPN
ejpam-6847	452	22	,	,	PUNCT
ejpam-6847	452	23	xn+1	xn+1	NUM
ejpam-6847	452	24	)	)	PUNCT
ejpam-6847	452	25	≤	≤	NOUN
ejpam-6847	452	26	1	1	NUM
ejpam-6847	452	27	n1	n1	NOUN
ejpam-6847	452	28	/	/	SYM
ejpam-6847	452	29	k	k	PROPN
ejpam-6847	452	30	,	,	PUNCT
ejpam-6847	452	31	for	for	ADP
ejpam-6847	452	32	alln	alln	PROPN
ejpam-6847	452	33	≥	≥	PROPN
ejpam-6847	452	34	n0	n0	PROPN
ejpam-6847	452	35	.	.	PUNCT
ejpam-6847	453	1	(	(	PUNCT
ejpam-6847	453	2	28	28	NUM
ejpam-6847	453	3	)	)	PUNCT
ejpam-6847	453	4	to	to	PART
ejpam-6847	453	5	show	show	VERB
ejpam-6847	453	6	that	that	SCONJ
ejpam-6847	453	7	{	{	PUNCT
ejpam-6847	453	8	xn	xn	X
ejpam-6847	453	9	}	}	PUNCT
ejpam-6847	453	10	is	be	AUX
ejpam-6847	453	11	a	a	DET
ejpam-6847	453	12	cauchy	cauchy	ADJ
ejpam-6847	453	13	sequence	sequence	NOUN
ejpam-6847	453	14	,	,	PUNCT
ejpam-6847	453	15	we	we	PRON
ejpam-6847	453	16	will	will	AUX
ejpam-6847	453	17	use	use	VERB
ejpam-6847	453	18	the	the	DET
ejpam-6847	453	19	same	same	ADJ
ejpam-6847	453	20	approach	approach	NOUN
ejpam-6847	453	21	as	as	ADP
ejpam-6847	453	22	in	in	ADP
ejpam-6847	453	23	the	the	DET
ejpam-6847	453	24	proof	proof	NOUN
ejpam-6847	453	25	of	of	ADP
ejpam-6847	453	26	theorem	theorem	NOUN
ejpam-6847	453	27	1	1	NUM
ejpam-6847	453	28	.	.	PUNCT
ejpam-6847	454	1	this	this	PRON
ejpam-6847	454	2	leads	lead	VERB
ejpam-6847	454	3	us	we	PRON
ejpam-6847	454	4	to	to	ADP
ejpam-6847	454	5	the	the	DET
ejpam-6847	454	6	conclusion	conclusion	NOUN
ejpam-6847	454	7	that	that	SCONJ
ejpam-6847	454	8	lim	lim	PROPN
ejpam-6847	454	9	n	n	CCONJ
ejpam-6847	454	10	,	,	PUNCT
ejpam-6847	454	11	m→+∞	m→+∞	PROPN
ejpam-6847	454	12	s(xn	s(xn	NOUN
ejpam-6847	454	13	,	,	PUNCT
ejpam-6847	454	14	xn	xn	PROPN
ejpam-6847	454	15	,	,	PUNCT
ejpam-6847	454	16	xm	xm	PROPN
ejpam-6847	454	17	)	)	PUNCT
ejpam-6847	455	1	=	=	SYM
ejpam-6847	455	2	0	0	X
ejpam-6847	455	3	.	.	PUNCT
ejpam-6847	456	1	consequently	consequently	ADV
ejpam-6847	456	2	,	,	PUNCT
ejpam-6847	456	3	{	{	PUNCT
ejpam-6847	456	4	xn	xn	X
ejpam-6847	456	5	}	}	PUNCT
ejpam-6847	456	6	is	be	AUX
ejpam-6847	456	7	a	a	DET
ejpam-6847	456	8	cauchy	cauchy	ADJ
ejpam-6847	456	9	sequence	sequence	NOUN
ejpam-6847	456	10	.	.	PUNCT
ejpam-6847	457	1	from	from	ADP
ejpam-6847	457	2	the	the	DET
ejpam-6847	457	3	completeness	completeness	NOUN
ejpam-6847	457	4	of	of	ADP
ejpam-6847	457	5	(	(	PUNCT
ejpam-6847	457	6	x	x	X
ejpam-6847	457	7	,	,	PUNCT
ejpam-6847	457	8	s	s	PART
ejpam-6847	457	9	)	)	PUNCT
ejpam-6847	457	10	,	,	PUNCT
ejpam-6847	457	11	therefore	therefore	ADV
ejpam-6847	457	12	the	the	DET
ejpam-6847	457	13	sequence	sequence	NOUN
ejpam-6847	457	14	converges	converge	VERB
ejpam-6847	457	15	to	to	ADP
ejpam-6847	457	16	a	a	DET
ejpam-6847	457	17	point	point	NOUN
ejpam-6847	458	1	u	u	NOUN
ejpam-6847	458	2	∈	∈	PROPN
ejpam-6847	458	3	x.	x.	NOUN
ejpam-6847	458	4	this	this	PRON
ejpam-6847	458	5	means	mean	VERB
ejpam-6847	458	6	that	that	SCONJ
ejpam-6847	458	7	lim	lim	PROPN
ejpam-6847	458	8	n→+∞	n→+∞	VERB
ejpam-6847	458	9	s(xn	s(xn	PROPN
ejpam-6847	458	10	,	,	PUNCT
ejpam-6847	458	11	xn	xn	PROPN
ejpam-6847	458	12	,	,	PUNCT
ejpam-6847	458	13	u	u	NOUN
ejpam-6847	458	14	)	)	PUNCT
ejpam-6847	458	15	=	=	SYM
ejpam-6847	459	1	0	0	X
ejpam-6847	459	2	.	.	PUNCT
ejpam-6847	460	1	(	(	PUNCT
ejpam-6847	460	2	29	29	NUM
ejpam-6847	460	3	)	)	PUNCT
ejpam-6847	460	4	f.	f.	PROPN
ejpam-6847	460	5	m.	m.	PROPN
ejpam-6847	460	6	azmi	azmi	PROPN
ejpam-6847	460	7	,	,	PUNCT
ejpam-6847	460	8	a.	a.	PROPN
ejpam-6847	460	9	h.	h.	PROPN
ejpam-6847	460	10	ansari	ansari	PROPN
ejpam-6847	460	11	,	,	PUNCT
ejpam-6847	460	12	s.	s.	PROPN
ejpam-6847	460	13	h.	h.	PROPN
ejpam-6847	460	14	j.	j.	PROPN
ejpam-6847	460	15	petroudi	petroudi	PROPN
ejpam-6847	460	16	/	/	SYM
ejpam-6847	460	17	eur	eur	PROPN
ejpam-6847	460	18	.	.	PUNCT
ejpam-6847	461	1	j.	j.	PROPN
ejpam-6847	461	2	pure	pure	PROPN
ejpam-6847	461	3	appl	appl	PROPN
ejpam-6847	461	4	.	.	PROPN
ejpam-6847	461	5	math	math	PROPN
ejpam-6847	461	6	,	,	PUNCT
ejpam-6847	461	7	18	18	NUM
ejpam-6847	461	8	(	(	PUNCT
ejpam-6847	461	9	4	4	NUM
ejpam-6847	461	10	)	)	PUNCT
ejpam-6847	461	11	(	(	PUNCT
ejpam-6847	461	12	2025	2025	NUM
ejpam-6847	461	13	)	)	PUNCT
ejpam-6847	461	14	,	,	PUNCT
ejpam-6847	461	15	6847	6847	NUM
ejpam-6847	461	16	18	18	NUM
ejpam-6847	461	17	of	of	ADP
ejpam-6847	461	18	26	26	NUM
ejpam-6847	461	19	in	in	ADP
ejpam-6847	461	20	the	the	DET
ejpam-6847	461	21	next	next	ADJ
ejpam-6847	461	22	paragraph	paragraph	NOUN
ejpam-6847	461	23	,	,	PUNCT
ejpam-6847	461	24	we	we	PRON
ejpam-6847	461	25	will	will	AUX
ejpam-6847	461	26	demonstrate	demonstrate	VERB
ejpam-6847	461	27	that	that	SCONJ
ejpam-6847	461	28	u	u	PROPN
ejpam-6847	461	29	is	be	AUX
ejpam-6847	461	30	a	a	DET
ejpam-6847	461	31	fixed	fix	VERB
ejpam-6847	461	32	point	point	NOUN
ejpam-6847	461	33	of	of	ADP
ejpam-6847	461	34	the	the	DET
ejpam-6847	461	35	mapping	mapping	NOUN
ejpam-6847	461	36	t	t	NOUN
ejpam-6847	461	37	,	,	PUNCT
ejpam-6847	461	38	meaning	mean	VERB
ejpam-6847	461	39	that	that	SCONJ
ejpam-6847	461	40	tu	tu	PROPN
ejpam-6847	461	41	=	=	PUNCT
ejpam-6847	461	42	u.	u.	PROPN
ejpam-6847	461	43	first	first	ADV
ejpam-6847	461	44	,	,	PUNCT
ejpam-6847	461	45	we	we	PRON
ejpam-6847	461	46	will	will	AUX
ejpam-6847	461	47	prove	prove	VERB
ejpam-6847	461	48	that	that	PRON
ejpam-6847	461	49	limn→+∞	limn→+∞	VERB
ejpam-6847	461	50	s(txn	s(txn	PROPN
ejpam-6847	461	51	,	,	PUNCT
ejpam-6847	461	52	txn	txn	PROPN
ejpam-6847	461	53	,	,	PUNCT
ejpam-6847	461	54	tu	tu	PROPN
ejpam-6847	461	55	)	)	PUNCT
ejpam-6847	461	56	=	=	SYM
ejpam-6847	462	1	0	0	X
ejpam-6847	462	2	.	.	PUNCT
ejpam-6847	462	3	assume	assume	VERB
ejpam-6847	462	4	that	that	SCONJ
ejpam-6847	462	5	s(t	s(t	PROPN
ejpam-6847	462	6	xn	xn	PROPN
ejpam-6847	462	7	,	,	PUNCT
ejpam-6847	462	8	t	t	PROPN
ejpam-6847	462	9	xn	xn	PROPN
ejpam-6847	462	10	,	,	PUNCT
ejpam-6847	462	11	tu	tu	PROPN
ejpam-6847	462	12	)	)	PUNCT
ejpam-6847	462	13	>	>	X
ejpam-6847	462	14	0	0	NUM
ejpam-6847	462	15	,	,	PUNCT
ejpam-6847	462	16	for	for	ADP
ejpam-6847	462	17	all	all	DET
ejpam-6847	462	18	naturan	naturan	ADJ
ejpam-6847	462	19	number	number	NOUN
ejpam-6847	462	20	n.	n.	NOUN
ejpam-6847	462	21	by	by	ADP
ejpam-6847	462	22	definition	definition	NOUN
ejpam-6847	462	23	15	15	NUM
ejpam-6847	462	24	,	,	PUNCT
ejpam-6847	462	25	we	we	PRON
ejpam-6847	462	26	have	have	VERB
ejpam-6847	462	27	h	h	NOUN
ejpam-6847	462	28	(	(	PUNCT
ejpam-6847	462	29	1	1	NUM
ejpam-6847	462	30	,	,	PUNCT
ejpam-6847	462	31	1	1	NUM
ejpam-6847	462	32	,	,	PUNCT
ejpam-6847	462	33	τ	τ	PROPN
ejpam-6847	463	1	+	+	NUM
ejpam-6847	463	2	f	f	PROPN
ejpam-6847	463	3	(	(	PUNCT
ejpam-6847	463	4	s(txn	s(txn	PROPN
ejpam-6847	463	5	,	,	PUNCT
ejpam-6847	463	6	txn	txn	PROPN
ejpam-6847	463	7	,	,	PUNCT
ejpam-6847	463	8	tu	tu	PROPN
ejpam-6847	463	9	)	)	PUNCT
ejpam-6847	463	10	)	)	PUNCT
ejpam-6847	463	11	)	)	PUNCT
ejpam-6847	463	12	≤	≤	NUM
ejpam-6847	463	13	h	h	NOUN
ejpam-6847	463	14	(	(	PUNCT
ejpam-6847	463	15	αs(xn	αs(xn	PROPN
ejpam-6847	463	16	,	,	PUNCT
ejpam-6847	463	17	xn	xn	PROPN
ejpam-6847	463	18	,	,	PUNCT
ejpam-6847	463	19	u	u	NOUN
ejpam-6847	463	20	)	)	PUNCT
ejpam-6847	463	21	,	,	PUNCT
ejpam-6847	463	22	ηs(xn	ηs(xn	PROPN
ejpam-6847	463	23	,	,	PUNCT
ejpam-6847	463	24	xn	xn	PROPN
ejpam-6847	463	25	,	,	PUNCT
ejpam-6847	463	26	u	u	NOUN
ejpam-6847	463	27	)	)	PUNCT
ejpam-6847	463	28	,	,	PUNCT
ejpam-6847	463	29	τ	τ	PROPN
ejpam-6847	463	30	+	+	NUM
ejpam-6847	463	31	f	f	PROPN
ejpam-6847	463	32	(	(	PUNCT
ejpam-6847	463	33	s(txn	s(txn	PROPN
ejpam-6847	463	34	,	,	PUNCT
ejpam-6847	463	35	txn	txn	PROPN
ejpam-6847	463	36	,	,	PUNCT
ejpam-6847	463	37	tu	tu	PROPN
ejpam-6847	463	38	)	)	PUNCT
ejpam-6847	463	39	)	)	PUNCT
ejpam-6847	463	40	)	)	PUNCT
ejpam-6847	464	1	≤	≤	NUM
ejpam-6847	465	1	q	q	NOUN
ejpam-6847	465	2	(	(	PUNCT
ejpam-6847	465	3	νs(xn	νs(xn	PROPN
ejpam-6847	465	4	,	,	PUNCT
ejpam-6847	465	5	xn	xn	PROPN
ejpam-6847	465	6	,	,	PUNCT
ejpam-6847	465	7	u	u	NOUN
ejpam-6847	465	8	)	)	PUNCT
ejpam-6847	465	9	,	,	PUNCT
ejpam-6847	465	10	f	f	PROPN
ejpam-6847	465	11	(	(	PUNCT
ejpam-6847	465	12	s(xn	s(xn	PROPN
ejpam-6847	465	13	,	,	PUNCT
ejpam-6847	465	14	xn	xn	PROPN
ejpam-6847	465	15	,	,	PUNCT
ejpam-6847	465	16	u	u	NOUN
ejpam-6847	465	17	)	)	PUNCT
ejpam-6847	465	18	)	)	PUNCT
ejpam-6847	465	19	)	)	PUNCT
ejpam-6847	466	1	≤	≤	NUM
ejpam-6847	467	1	q	q	NOUN
ejpam-6847	467	2	(	(	PUNCT
ejpam-6847	467	3	1	1	NUM
ejpam-6847	467	4	,	,	PUNCT
ejpam-6847	467	5	f	f	PROPN
ejpam-6847	467	6	(	(	PUNCT
ejpam-6847	467	7	s(xn	s(xn	PROPN
ejpam-6847	467	8	,	,	PUNCT
ejpam-6847	467	9	xn	xn	PROPN
ejpam-6847	467	10	,	,	PUNCT
ejpam-6847	467	11	u	u	NOUN
ejpam-6847	467	12	)	)	PUNCT
ejpam-6847	467	13	)	)	PUNCT
ejpam-6847	467	14	)	)	PUNCT
ejpam-6847	467	15	.	.	PUNCT
ejpam-6847	468	1	as	as	SCONJ
ejpam-6847	468	2	the	the	DET
ejpam-6847	468	3	pair(q	pair(q	PROPN
ejpam-6847	468	4	,	,	PUNCT
ejpam-6847	468	5	h	h	NOUN
ejpam-6847	468	6	)	)	PUNCT
ejpam-6847	468	7	is	be	AUX
ejpam-6847	468	8	an	an	DET
ejpam-6847	468	9	upper	upper	ADJ
ejpam-6847	468	10	class	class	NOUN
ejpam-6847	468	11	of	of	ADP
ejpam-6847	468	12	typeii	typeii	NOUN
ejpam-6847	468	13	,	,	PUNCT
ejpam-6847	468	14	hence	hence	ADV
ejpam-6847	468	15	we	we	PRON
ejpam-6847	468	16	find	find	VERB
ejpam-6847	468	17	that	that	SCONJ
ejpam-6847	468	18	τ	τ	PROPN
ejpam-6847	468	19	+	+	NUM
ejpam-6847	468	20	f	f	X
ejpam-6847	468	21	(	(	PUNCT
ejpam-6847	468	22	s(txn	s(txn	PROPN
ejpam-6847	468	23	,	,	PUNCT
ejpam-6847	468	24	txn	txn	PROPN
ejpam-6847	468	25	,	,	PUNCT
ejpam-6847	468	26	tu	tu	PROPN
ejpam-6847	468	27	)	)	PUNCT
ejpam-6847	468	28	)	)	PUNCT
ejpam-6847	469	1	≤	≤	NUM
ejpam-6847	469	2	f	f	X
ejpam-6847	469	3	(	(	PUNCT
ejpam-6847	469	4	s(xn	s(xn	PROPN
ejpam-6847	469	5	,	,	PUNCT
ejpam-6847	469	6	xn	xn	PROPN
ejpam-6847	469	7	,	,	PUNCT
ejpam-6847	469	8	u	u	NOUN
ejpam-6847	469	9	)	)	PUNCT
ejpam-6847	469	10	)	)	PUNCT
ejpam-6847	469	11	.	.	PUNCT
ejpam-6847	470	1	(	(	PUNCT
ejpam-6847	470	2	30	30	X
ejpam-6847	470	3	)	)	PUNCT
ejpam-6847	470	4	taking	take	VERB
ejpam-6847	470	5	the	the	DET
ejpam-6847	470	6	limit	limit	NOUN
ejpam-6847	470	7	as	as	ADP
ejpam-6847	470	8	n	n	NOUN
ejpam-6847	470	9	approaches	approach	NOUN
ejpam-6847	470	10	infinity	infinity	NOUN
ejpam-6847	470	11	in	in	ADP
ejpam-6847	470	12	equation	equation	NOUN
ejpam-6847	470	13	30	30	NUM
ejpam-6847	470	14	,	,	PUNCT
ejpam-6847	470	15	and	and	CCONJ
ejpam-6847	470	16	applying	apply	VERB
ejpam-6847	470	17	equation	equation	NOUN
ejpam-6847	470	18	29	29	NUM
ejpam-6847	470	19	along	along	ADP
ejpam-6847	470	20	with	with	ADP
ejpam-6847	470	21	(	(	PUNCT
ejpam-6847	470	22	w2	w2	NOUN
ejpam-6847	470	23	)	)	PUNCT
ejpam-6847	470	24	from	from	ADP
ejpam-6847	470	25	definition	definition	NOUN
ejpam-6847	470	26	14	14	NUM
ejpam-6847	470	27	,	,	PUNCT
ejpam-6847	470	28	we	we	PRON
ejpam-6847	470	29	find	find	VERB
ejpam-6847	470	30	that	that	PRON
ejpam-6847	470	31	limn→+∞	limn→+∞	ADP
ejpam-6847	470	32	f	f	PROPN
ejpam-6847	470	33	(	(	PUNCT
ejpam-6847	470	34	s(txn	s(txn	PROPN
ejpam-6847	470	35	,	,	PUNCT
ejpam-6847	470	36	txn	txn	PROPN
ejpam-6847	470	37	,	,	PUNCT
ejpam-6847	470	38	tu	tu	PROPN
ejpam-6847	470	39	)	)	PUNCT
ejpam-6847	470	40	)	)	PUNCT
ejpam-6847	471	1	=	=	SYM
ejpam-6847	471	2	−∞.	−∞.	PROPN
ejpam-6847	471	3	furthermore	furthermore	ADV
ejpam-6847	471	4	,	,	PUNCT
ejpam-6847	471	5	according	accord	VERB
ejpam-6847	471	6	to	to	ADP
ejpam-6847	471	7	definition	definition	NOUN
ejpam-6847	471	8	14	14	NUM
ejpam-6847	471	9	,	,	PUNCT
ejpam-6847	471	10	this	this	PRON
ejpam-6847	471	11	means	mean	VERB
ejpam-6847	471	12	that	that	SCONJ
ejpam-6847	471	13	limn→+∞	limn→+∞	VERB
ejpam-6847	471	14	s(txn	s(txn	PROPN
ejpam-6847	471	15	,	,	PUNCT
ejpam-6847	471	16	txn	txn	PROPN
ejpam-6847	471	17	,	,	PUNCT
ejpam-6847	471	18	tu	tu	PROPN
ejpam-6847	471	19	)	)	PUNCT
ejpam-6847	471	20	=	=	PUNCT
ejpam-6847	472	1	0	0	X
ejpam-6847	472	2	.	.	PUNCT
ejpam-6847	472	3	to	to	PART
ejpam-6847	472	4	prove	prove	VERB
ejpam-6847	472	5	that	that	SCONJ
ejpam-6847	472	6	u	u	NOUN
ejpam-6847	472	7	is	be	AUX
ejpam-6847	472	8	a	a	DET
ejpam-6847	472	9	fixed	fix	VERB
ejpam-6847	472	10	point	point	NOUN
ejpam-6847	472	11	,	,	PUNCT
ejpam-6847	472	12	note	note	VERB
ejpam-6847	472	13	the	the	DET
ejpam-6847	472	14	following	following	NOUN
ejpam-6847	472	15	;	;	PUNCT
ejpam-6847	472	16	s(tu	s(tu	PROPN
ejpam-6847	472	17	,	,	PUNCT
ejpam-6847	472	18	tu	tu	PROPN
ejpam-6847	472	19	,	,	PUNCT
ejpam-6847	472	20	u	u	NOUN
ejpam-6847	472	21	)	)	PUNCT
ejpam-6847	472	22	=	=	SYM
ejpam-6847	472	23	s(u	s(u	PROPN
ejpam-6847	472	24	,	,	PUNCT
ejpam-6847	472	25	u	u	NOUN
ejpam-6847	472	26	,	,	PUNCT
ejpam-6847	472	27	tu	tu	PROPN
ejpam-6847	472	28	)	)	PUNCT
ejpam-6847	472	29	≤	≤	NOUN
ejpam-6847	472	30	β(u	β(u	PROPN
ejpam-6847	472	31	,	,	PUNCT
ejpam-6847	472	32	xn+1)s(u	xn+1)s(u	PROPN
ejpam-6847	472	33	,	,	PUNCT
ejpam-6847	472	34	u	u	NOUN
ejpam-6847	472	35	,	,	PUNCT
ejpam-6847	472	36	xn+1	xn+1	NUM
ejpam-6847	472	37	)	)	PUNCT
ejpam-6847	473	1	+	+	CCONJ
ejpam-6847	473	2	µ(u	µ(u	NOUN
ejpam-6847	473	3	,	,	PUNCT
ejpam-6847	473	4	xn+1)s(u	xn+1)s(u	NUM
ejpam-6847	473	5	,	,	PUNCT
ejpam-6847	473	6	u	u	NOUN
ejpam-6847	473	7	,	,	PUNCT
ejpam-6847	473	8	xn+1	xn+1	NUM
ejpam-6847	473	9	)	)	PUNCT
ejpam-6847	474	1	+	+	CCONJ
ejpam-6847	474	2	γ(tu	γ(tu	PROPN
ejpam-6847	474	3	,	,	PUNCT
ejpam-6847	474	4	xn+1)s(tu	xn+1)s(tu	PROPN
ejpam-6847	474	5	,	,	PUNCT
ejpam-6847	474	6	tu	tu	PROPN
ejpam-6847	474	7	,	,	PUNCT
ejpam-6847	474	8	txn	txn	PROPN
ejpam-6847	474	9	)	)	PUNCT
ejpam-6847	474	10	.	.	PUNCT
ejpam-6847	475	1	≤	≤	PROPN
ejpam-6847	475	2	β(u	β(u	PROPN
ejpam-6847	475	3	,	,	PUNCT
ejpam-6847	475	4	xn+1)s(u	xn+1)s(u	PROPN
ejpam-6847	475	5	,	,	PUNCT
ejpam-6847	475	6	u	u	NOUN
ejpam-6847	475	7	,	,	PUNCT
ejpam-6847	475	8	xn+1	xn+1	NUM
ejpam-6847	475	9	)	)	PUNCT
ejpam-6847	476	1	+	+	CCONJ
ejpam-6847	476	2	µ(u	µ(u	NOUN
ejpam-6847	476	3	,	,	PUNCT
ejpam-6847	476	4	xn+1)s(u	xn+1)s(u	NUM
ejpam-6847	476	5	,	,	PUNCT
ejpam-6847	476	6	u	u	NOUN
ejpam-6847	476	7	,	,	PUNCT
ejpam-6847	476	8	xn+1	xn+1	NUM
ejpam-6847	476	9	)	)	PUNCT
ejpam-6847	477	1	+	+	CCONJ
ejpam-6847	477	2	γ(tu	γ(tu	PROPN
ejpam-6847	477	3	,	,	PUNCT
ejpam-6847	477	4	xn+1)s(txn	xn+1)s(txn	PROPN
ejpam-6847	477	5	,	,	PUNCT
ejpam-6847	477	6	txn	txn	PROPN
ejpam-6847	477	7	,	,	PUNCT
ejpam-6847	477	8	tu	tu	PROPN
ejpam-6847	477	9	)	)	PUNCT
ejpam-6847	477	10	.	.	PUNCT
ejpam-6847	478	1	as	as	SCONJ
ejpam-6847	478	2	n	n	NOUN
ejpam-6847	478	3	approaches	approach	NOUN
ejpam-6847	478	4	infinity	infinity	NOUN
ejpam-6847	478	5	in	in	ADP
ejpam-6847	478	6	the	the	DET
ejpam-6847	478	7	previous	previous	ADJ
ejpam-6847	478	8	inequality	inequality	NOUN
ejpam-6847	478	9	,	,	PUNCT
ejpam-6847	478	10	we	we	PRON
ejpam-6847	478	11	find	find	VERB
ejpam-6847	478	12	that	that	SCONJ
ejpam-6847	478	13	s(tu	s(tu	PROPN
ejpam-6847	478	14	,	,	PUNCT
ejpam-6847	478	15	tu	tu	PROPN
ejpam-6847	478	16	,	,	PUNCT
ejpam-6847	478	17	u	u	NOUN
ejpam-6847	478	18	)	)	PUNCT
ejpam-6847	478	19	=	=	SYM
ejpam-6847	478	20	0	0	NUM
ejpam-6847	478	21	,	,	PUNCT
ejpam-6847	478	22	which	which	PRON
ejpam-6847	478	23	means	mean	VERB
ejpam-6847	478	24	tu	tu	PROPN
ejpam-6847	478	25	=	=	PUNCT
ejpam-6847	478	26	u.	u.	PROPN
ejpam-6847	478	27	next	next	ADV
ejpam-6847	478	28	,	,	PUNCT
ejpam-6847	478	29	we	we	PRON
ejpam-6847	478	30	will	will	AUX
ejpam-6847	478	31	show	show	VERB
ejpam-6847	478	32	that	that	SCONJ
ejpam-6847	478	33	the	the	DET
ejpam-6847	478	34	fixed	fix	VERB
ejpam-6847	478	35	point	point	NOUN
ejpam-6847	478	36	is	be	AUX
ejpam-6847	478	37	unique	unique	ADJ
ejpam-6847	478	38	.	.	PUNCT
ejpam-6847	479	1	assume	assume	VERB
ejpam-6847	479	2	there	there	PRON
ejpam-6847	479	3	are	be	VERB
ejpam-6847	479	4	two	two	NUM
ejpam-6847	479	5	fixed	fix	VERB
ejpam-6847	479	6	points	point	NOUN
ejpam-6847	479	7	,	,	PUNCT
ejpam-6847	479	8	u	u	NOUN
ejpam-6847	479	9	and	and	CCONJ
ejpam-6847	479	10	v	v	NOUN
ejpam-6847	479	11	,	,	PUNCT
ejpam-6847	479	12	where	where	SCONJ
ejpam-6847	479	13	u	u	PROPN
ejpam-6847	479	14	6=	6=	PROPN
ejpam-6847	479	15	v	v	NUM
ejpam-6847	479	16	and	and	CCONJ
ejpam-6847	479	17	αs(u	αs(u	NUM
ejpam-6847	479	18	,	,	PUNCT
ejpam-6847	479	19	u	u	NOUN
ejpam-6847	479	20	,	,	PUNCT
ejpam-6847	479	21	v	v	NOUN
ejpam-6847	479	22	)	)	PUNCT
ejpam-6847	479	23	≥	≥	NOUN
ejpam-6847	479	24	1	1	NUM
ejpam-6847	479	25	,	,	PUNCT
ejpam-6847	479	26	ηs(u	ηs(u	NOUN
ejpam-6847	479	27	,	,	PUNCT
ejpam-6847	479	28	u	u	NOUN
ejpam-6847	479	29	,	,	PUNCT
ejpam-6847	479	30	v	v	NOUN
ejpam-6847	479	31	)	)	PUNCT
ejpam-6847	479	32	≥	≥	NOUN
ejpam-6847	479	33	1	1	NUM
ejpam-6847	479	34	,	,	PUNCT
ejpam-6847	479	35	νs(u	νs(u	NUM
ejpam-6847	479	36	,	,	PUNCT
ejpam-6847	479	37	u	u	NOUN
ejpam-6847	479	38	,	,	PUNCT
ejpam-6847	479	39	v	v	NOUN
ejpam-6847	479	40	)	)	PUNCT
ejpam-6847	479	41	≤	≤	NOUN
ejpam-6847	479	42	1	1	NUM
ejpam-6847	479	43	.	.	PUNCT
ejpam-6847	480	1	since	since	SCONJ
ejpam-6847	480	2	tu	tu	PROPN
ejpam-6847	480	3	=	=	SYM
ejpam-6847	480	4	u	u	PROPN
ejpam-6847	480	5	and	and	CCONJ
ejpam-6847	480	6	v	v	NOUN
ejpam-6847	480	7	=	=	SYM
ejpam-6847	480	8	tv	tv	NOUN
ejpam-6847	480	9	,	,	PUNCT
ejpam-6847	480	10	it	it	PRON
ejpam-6847	480	11	follows	follow	VERB
ejpam-6847	480	12	that	that	SCONJ
ejpam-6847	480	13	s(tu	s(tu	PROPN
ejpam-6847	480	14	,	,	PUNCT
ejpam-6847	480	15	tu	tu	PROPN
ejpam-6847	480	16	,	,	PUNCT
ejpam-6847	480	17	tv	tv	NOUN
ejpam-6847	480	18	)	)	PUNCT
ejpam-6847	480	19	>	>	X
ejpam-6847	481	1	0	0	X
ejpam-6847	481	2	.	.	PUNCT
ejpam-6847	481	3	given	give	VERB
ejpam-6847	481	4	that	that	DET
ejpam-6847	481	5	t	t	PROPN
ejpam-6847	481	6	is	be	AUX
ejpam-6847	481	7	an	an	DET
ejpam-6847	481	8	(	(	PUNCT
ejpam-6847	481	9	αs	αs	PROPN
ejpam-6847	481	10	,	,	PUNCT
ejpam-6847	481	11	ηs	ηs	PROPN
ejpam-6847	481	12	,	,	PUNCT
ejpam-6847	481	13	νs	νs	NOUN
ejpam-6847	481	14	,	,	PUNCT
ejpam-6847	481	15	(	(	PUNCT
ejpam-6847	481	16	q	q	X
ejpam-6847	481	17	,	,	PUNCT
ejpam-6847	481	18	h)−f)−contraction	h)−f)−contraction	PROPN
ejpam-6847	481	19	mapping	mapping	NOUN
ejpam-6847	481	20	,	,	PUNCT
ejpam-6847	481	21	we	we	PRON
ejpam-6847	481	22	obtain	obtain	VERB
ejpam-6847	481	23	h	h	NOUN
ejpam-6847	481	24	(	(	PUNCT
ejpam-6847	481	25	1	1	NUM
ejpam-6847	481	26	,	,	PUNCT
ejpam-6847	481	27	1	1	NUM
ejpam-6847	481	28	,	,	PUNCT
ejpam-6847	481	29	τ	τ	PROPN
ejpam-6847	482	1	+	+	NUM
ejpam-6847	482	2	f	f	X
ejpam-6847	482	3	(	(	PUNCT
ejpam-6847	482	4	s(tu	s(tu	PROPN
ejpam-6847	482	5	,	,	PUNCT
ejpam-6847	482	6	tu	tu	PROPN
ejpam-6847	482	7	,	,	PUNCT
ejpam-6847	482	8	tv	tv	NOUN
ejpam-6847	482	9	)	)	PUNCT
ejpam-6847	482	10	)	)	PUNCT
ejpam-6847	482	11	)	)	PUNCT
ejpam-6847	482	12	≤	≤	NUM
ejpam-6847	482	13	h	h	NOUN
ejpam-6847	482	14	(	(	PUNCT
ejpam-6847	482	15	αs(u	αs(u	PROPN
ejpam-6847	482	16	,	,	PUNCT
ejpam-6847	482	17	u	u	NOUN
ejpam-6847	482	18	,	,	PUNCT
ejpam-6847	482	19	v	v	NOUN
ejpam-6847	482	20	)	)	PUNCT
ejpam-6847	482	21	,	,	PUNCT
ejpam-6847	482	22	ηs(u	ηs(u	X
ejpam-6847	482	23	,	,	PUNCT
ejpam-6847	482	24	u	u	NOUN
ejpam-6847	482	25	,	,	PUNCT
ejpam-6847	482	26	v	v	NOUN
ejpam-6847	482	27	)	)	PUNCT
ejpam-6847	482	28	,	,	PUNCT
ejpam-6847	482	29	τ	τ	PROPN
ejpam-6847	482	30	+	+	NUM
ejpam-6847	482	31	f	f	X
ejpam-6847	482	32	(	(	PUNCT
ejpam-6847	482	33	s(tu	s(tu	PROPN
ejpam-6847	482	34	,	,	PUNCT
ejpam-6847	482	35	tu	tu	PROPN
ejpam-6847	482	36	,	,	PUNCT
ejpam-6847	482	37	tv	tv	NOUN
ejpam-6847	482	38	)	)	PUNCT
ejpam-6847	482	39	)	)	PUNCT
ejpam-6847	482	40	)	)	PUNCT
ejpam-6847	483	1	≤	≤	NUM
ejpam-6847	483	2	q	q	PUNCT
ejpam-6847	483	3	(	(	PUNCT
ejpam-6847	483	4	νs(u	νs(u	X
ejpam-6847	483	5	,	,	PUNCT
ejpam-6847	483	6	u	u	NOUN
ejpam-6847	483	7	,	,	PUNCT
ejpam-6847	483	8	v	v	NOUN
ejpam-6847	483	9	)	)	PUNCT
ejpam-6847	483	10	,	,	PUNCT
ejpam-6847	483	11	f	f	PROPN
ejpam-6847	483	12	(	(	PUNCT
ejpam-6847	483	13	s(u	s(u	PROPN
ejpam-6847	483	14	,	,	PUNCT
ejpam-6847	483	15	u	u	NOUN
ejpam-6847	483	16	,	,	PUNCT
ejpam-6847	483	17	v	v	NOUN
ejpam-6847	483	18	)	)	PUNCT
ejpam-6847	483	19	)	)	PUNCT
ejpam-6847	483	20	)	)	PUNCT
ejpam-6847	484	1	f.	f.	PROPN
ejpam-6847	484	2	m.	m.	PROPN
ejpam-6847	484	3	azmi	azmi	PROPN
ejpam-6847	484	4	,	,	PUNCT
ejpam-6847	484	5	a.	a.	PROPN
ejpam-6847	484	6	h.	h.	PROPN
ejpam-6847	484	7	ansari	ansari	PROPN
ejpam-6847	484	8	,	,	PUNCT
ejpam-6847	484	9	s.	s.	PROPN
ejpam-6847	484	10	h.	h.	PROPN
ejpam-6847	484	11	j.	j.	PROPN
ejpam-6847	484	12	petroudi	petroudi	PROPN
ejpam-6847	484	13	/	/	SYM
ejpam-6847	484	14	eur	eur	PROPN
ejpam-6847	484	15	.	.	PUNCT
ejpam-6847	485	1	j.	j.	PROPN
ejpam-6847	485	2	pure	pure	PROPN
ejpam-6847	485	3	appl	appl	PROPN
ejpam-6847	485	4	.	.	PROPN
ejpam-6847	485	5	math	math	PROPN
ejpam-6847	485	6	,	,	PUNCT
ejpam-6847	485	7	18	18	NUM
ejpam-6847	485	8	(	(	PUNCT
ejpam-6847	485	9	4	4	NUM
ejpam-6847	485	10	)	)	PUNCT
ejpam-6847	485	11	(	(	PUNCT
ejpam-6847	485	12	2025	2025	NUM
ejpam-6847	485	13	)	)	PUNCT
ejpam-6847	485	14	,	,	PUNCT
ejpam-6847	485	15	6847	6847	NUM
ejpam-6847	485	16	19	19	NUM
ejpam-6847	485	17	of	of	ADP
ejpam-6847	485	18	26	26	NUM
ejpam-6847	485	19	≤	≤	NUM
ejpam-6847	485	20	q	q	PUNCT
ejpam-6847	485	21	(	(	PUNCT
ejpam-6847	485	22	1	1	NUM
ejpam-6847	485	23	,	,	PUNCT
ejpam-6847	485	24	f	f	PROPN
ejpam-6847	485	25	(	(	PUNCT
ejpam-6847	485	26	s(u	s(u	PROPN
ejpam-6847	485	27	,	,	PUNCT
ejpam-6847	485	28	u	u	NOUN
ejpam-6847	485	29	,	,	PUNCT
ejpam-6847	485	30	v	v	NOUN
ejpam-6847	485	31	)	)	PUNCT
ejpam-6847	485	32	)	)	PUNCT
ejpam-6847	485	33	)	)	PUNCT
ejpam-6847	485	34	.	.	PUNCT
ejpam-6847	486	1	by	by	ADP
ejpam-6847	486	2	the	the	DET
ejpam-6847	486	3	property	property	NOUN
ejpam-6847	486	4	of	of	ADP
ejpam-6847	486	5	the	the	DET
ejpam-6847	486	6	pair(q	pair(q	PROPN
ejpam-6847	486	7	,	,	PUNCT
ejpam-6847	486	8	h	h	NOUN
ejpam-6847	486	9	)	)	PUNCT
ejpam-6847	486	10	being	be	AUX
ejpam-6847	486	11	an	an	DET
ejpam-6847	486	12	upper	upper	ADJ
ejpam-6847	486	13	class	class	NOUN
ejpam-6847	486	14	of	of	ADP
ejpam-6847	486	15	typeii	typeii	NOUN
ejpam-6847	486	16	,	,	PUNCT
ejpam-6847	486	17	allows	allow	VERB
ejpam-6847	486	18	to	to	PART
ejpam-6847	486	19	say	say	VERB
ejpam-6847	486	20	that	that	SCONJ
ejpam-6847	486	21	τ	τ	PROPN
ejpam-6847	486	22	+	+	NUM
ejpam-6847	486	23	f	f	X
ejpam-6847	486	24	(	(	PUNCT
ejpam-6847	486	25	s(tu	s(tu	PROPN
ejpam-6847	486	26	,	,	PUNCT
ejpam-6847	486	27	tu	tu	PROPN
ejpam-6847	486	28	,	,	PUNCT
ejpam-6847	486	29	tv	tv	NOUN
ejpam-6847	486	30	)	)	PUNCT
ejpam-6847	486	31	)	)	PUNCT
ejpam-6847	487	1	≤	≤	NUM
ejpam-6847	487	2	f	f	X
ejpam-6847	487	3	(	(	PUNCT
ejpam-6847	487	4	s(u	s(u	PROPN
ejpam-6847	487	5	,	,	PUNCT
ejpam-6847	487	6	u	u	NOUN
ejpam-6847	487	7	,	,	PUNCT
ejpam-6847	487	8	v	v	NOUN
ejpam-6847	487	9	)	)	PUNCT
ejpam-6847	487	10	)	)	PUNCT
ejpam-6847	488	1	=	=	SYM
ejpam-6847	488	2	f	f	PROPN
ejpam-6847	488	3	(	(	PUNCT
ejpam-6847	488	4	s(tu	s(tu	PROPN
ejpam-6847	488	5	,	,	PUNCT
ejpam-6847	488	6	tu	tu	PROPN
ejpam-6847	488	7	,	,	PUNCT
ejpam-6847	488	8	tv	tv	NOUN
ejpam-6847	488	9	)	)	PUNCT
ejpam-6847	488	10	)	)	PUNCT
ejpam-6847	488	11	.	.	PUNCT
ejpam-6847	489	1	this	this	PRON
ejpam-6847	489	2	implies	imply	VERB
ejpam-6847	489	3	τ	τ	PROPN
ejpam-6847	489	4	≤	≤	NUM
ejpam-6847	489	5	0	0	NUM
ejpam-6847	489	6	,	,	PUNCT
ejpam-6847	489	7	leading	lead	VERB
ejpam-6847	489	8	to	to	ADP
ejpam-6847	489	9	a	a	DET
ejpam-6847	489	10	contradiction	contradiction	NOUN
ejpam-6847	489	11	.	.	PUNCT
ejpam-6847	490	1	consequently	consequently	ADV
ejpam-6847	490	2	,	,	PUNCT
ejpam-6847	490	3	it	it	PRON
ejpam-6847	490	4	follows	follow	VERB
ejpam-6847	490	5	that	that	SCONJ
ejpam-6847	490	6	u	u	NOUN
ejpam-6847	490	7	=	=	PROPN
ejpam-6847	490	8	v	v	PROPN
ejpam-6847	490	9	,	,	PUNCT
ejpam-6847	490	10	which	which	PRON
ejpam-6847	490	11	indicates	indicate	VERB
ejpam-6847	490	12	the	the	DET
ejpam-6847	490	13	uniqueness	uniqueness	NOUN
ejpam-6847	490	14	of	of	ADP
ejpam-6847	490	15	the	the	DET
ejpam-6847	490	16	fixed	fix	VERB
ejpam-6847	490	17	point	point	NOUN
ejpam-6847	490	18	.	.	PUNCT
ejpam-6847	491	1	4	4	X
ejpam-6847	491	2	.	.	X
ejpam-6847	491	3	corollaries	corollary	NOUN
ejpam-6847	491	4	this	this	DET
ejpam-6847	491	5	section	section	NOUN
ejpam-6847	491	6	presents	present	VERB
ejpam-6847	491	7	several	several	ADJ
ejpam-6847	491	8	corollaries	corollary	NOUN
ejpam-6847	491	9	derived	derive	VERB
ejpam-6847	491	10	from	from	ADP
ejpam-6847	491	11	theorem	theorem	ADJ
ejpam-6847	491	12	1	1	NUM
ejpam-6847	491	13	.	.	PUNCT
ejpam-6847	491	14	as	as	SCONJ
ejpam-6847	491	15	introduced	introduce	VERB
ejpam-6847	491	16	in	in	ADP
ejpam-6847	491	17	definition	definition	NOUN
ejpam-6847	491	18	17	17	NUM
ejpam-6847	491	19	,	,	PUNCT
ejpam-6847	491	20	we	we	PRON
ejpam-6847	491	21	have	have	AUX
ejpam-6847	491	22	established	establish	VERB
ejpam-6847	491	23	an	an	DET
ejpam-6847	491	24	(	(	PUNCT
ejpam-6847	491	25	αs	αs	ADJ
ejpam-6847	491	26	,	,	PUNCT
ejpam-6847	491	27	µs	µs	NOUN
ejpam-6847	491	28	,	,	PUNCT
ejpam-6847	491	29	(	(	PUNCT
ejpam-6847	491	30	q	q	ADJ
ejpam-6847	491	31	,	,	PUNCT
ejpam-6847	491	32	h	h	NOUN
ejpam-6847	491	33	)	)	PUNCT
ejpam-6847	491	34	−	−	PROPN
ejpam-6847	491	35	f	f	X
ejpam-6847	491	36	)	)	PUNCT
ejpam-6847	491	37	contraction	contraction	NOUN
ejpam-6847	491	38	mapping	mapping	NOUN
ejpam-6847	491	39	denoted	denote	VERB
ejpam-6847	491	40	as	as	ADP
ejpam-6847	491	41	t	t	PROPN
ejpam-6847	491	42	in	in	ADP
ejpam-6847	491	43	the	the	DET
ejpam-6847	491	44	framework	framework	NOUN
ejpam-6847	491	45	of	of	ADP
ejpam-6847	491	46	the	the	DET
ejpam-6847	491	47	space	space	NOUN
ejpam-6847	492	1	t	t	PROPN
ejpam-6847	492	2	c	c	X
ejpam-6847	492	3	-	-	PUNCT
ejpam-6847	492	4	s	s	PROPN
ejpam-6847	492	5	-	-	PUNCT
ejpam-6847	492	6	mt	mt	NOUN
ejpam-6847	492	7	s	s	PART
ejpam-6847	492	8	(	(	PUNCT
ejpam-6847	492	9	x	x	X
ejpam-6847	492	10	,	,	PUNCT
ejpam-6847	492	11	s	s	PART
ejpam-6847	492	12	)	)	PUNCT
ejpam-6847	492	13	,	,	PUNCT
ejpam-6847	492	14	that	that	PRON
ejpam-6847	492	15	satisfies	satisfy	VERB
ejpam-6847	492	16	the	the	DET
ejpam-6847	492	17	condition	condition	NOUN
ejpam-6847	492	18	4	4	NUM
ejpam-6847	492	19	.	.	PUNCT
ejpam-6847	493	1	here	here	ADV
ejpam-6847	493	2	,	,	PUNCT
ejpam-6847	493	3	(	(	PUNCT
ejpam-6847	493	4	q	q	X
ejpam-6847	493	5	,	,	PUNCT
ejpam-6847	493	6	h	h	NOUN
ejpam-6847	493	7	)	)	PUNCT
ejpam-6847	493	8	represents	represent	VERB
ejpam-6847	493	9	a	a	DET
ejpam-6847	493	10	pair	pair	NOUN
ejpam-6847	493	11	from	from	ADP
ejpam-6847	493	12	the	the	DET
ejpam-6847	493	13	upper	upper	ADJ
ejpam-6847	493	14	class	class	NOUN
ejpam-6847	493	15	of	of	ADP
ejpam-6847	493	16	type	type	NOUN
ejpam-6847	493	17	i.	i.	NOUN
ejpam-6847	493	18	we	we	PRON
ejpam-6847	493	19	will	will	AUX
ejpam-6847	493	20	now	now	ADV
ejpam-6847	493	21	provide	provide	VERB
ejpam-6847	493	22	specific	specific	ADJ
ejpam-6847	493	23	examples	example	NOUN
ejpam-6847	493	24	of	of	ADP
ejpam-6847	493	25	such	such	ADJ
ejpam-6847	493	26	pairs	pair	NOUN
ejpam-6847	493	27	(	(	PUNCT
ejpam-6847	493	28	q	q	NOUN
ejpam-6847	493	29	,	,	PUNCT
ejpam-6847	493	30	h	h	NOUN
ejpam-6847	493	31	)	)	PUNCT
ejpam-6847	493	32	belonging	belong	VERB
ejpam-6847	493	33	to	to	ADP
ejpam-6847	493	34	this	this	DET
ejpam-6847	493	35	upper	upper	ADJ
ejpam-6847	493	36	class	class	NOUN
ejpam-6847	493	37	.	.	PUNCT
ejpam-6847	494	1	by	by	ADP
ejpam-6847	494	2	applying	apply	VERB
ejpam-6847	494	3	a	a	DET
ejpam-6847	494	4	similar	similar	ADJ
ejpam-6847	494	5	approach	approach	NOUN
ejpam-6847	494	6	with	with	ADP
ejpam-6847	494	7	a	a	DET
ejpam-6847	494	8	pair	pair	NOUN
ejpam-6847	494	9	(	(	PUNCT
ejpam-6847	494	10	q	q	NOUN
ejpam-6847	494	11	,	,	PUNCT
ejpam-6847	494	12	h	h	NOUN
ejpam-6847	494	13	)	)	PUNCT
ejpam-6847	494	14	from	from	ADP
ejpam-6847	494	15	the	the	DET
ejpam-6847	494	16	upper	upper	ADJ
ejpam-6847	494	17	class	class	NOUN
ejpam-6847	494	18	of	of	ADP
ejpam-6847	494	19	type	type	PROPN
ejpam-6847	494	20	ii	ii	PROPN
ejpam-6847	494	21	,	,	PUNCT
ejpam-6847	494	22	one	one	PRON
ejpam-6847	494	23	can	can	AUX
ejpam-6847	494	24	derive	derive	VERB
ejpam-6847	494	25	corollaries	corollary	NOUN
ejpam-6847	494	26	for	for	ADP
ejpam-6847	494	27	theorem	theorem	NOUN
ejpam-6847	494	28	3	3	NUM
ejpam-6847	494	29	.	.	PUNCT
ejpam-6847	494	30	by	by	ADP
ejpam-6847	494	31	selecting	select	VERB
ejpam-6847	494	32	the	the	DET
ejpam-6847	494	33	pair	pair	NOUN
ejpam-6847	494	34	(	(	PUNCT
ejpam-6847	494	35	q	q	NOUN
ejpam-6847	494	36	,	,	PUNCT
ejpam-6847	494	37	h	h	NOUN
ejpam-6847	494	38	)	)	PUNCT
ejpam-6847	494	39	of	of	ADP
ejpam-6847	494	40	upper	upper	ADJ
ejpam-6847	494	41	class	class	NOUN
ejpam-6847	494	42	of	of	ADP
ejpam-6847	494	43	type	type	NOUN
ejpam-6847	494	44	i	i	PRON
ejpam-6847	494	45	,	,	PUNCT
ejpam-6847	495	1	where	where	SCONJ
ejpam-6847	495	2	h(x	h(x	PROPN
ejpam-6847	495	3	,	,	PUNCT
ejpam-6847	495	4	y	y	PROPN
ejpam-6847	495	5	)	)	PUNCT
ejpam-6847	495	6	=	=	SYM
ejpam-6847	495	7	xnyk	xnyk	NOUN
ejpam-6847	495	8	,	,	PUNCT
ejpam-6847	495	9	q(s	q(s	PROPN
ejpam-6847	495	10	,	,	PUNCT
ejpam-6847	495	11	t	t	NOUN
ejpam-6847	495	12	)	)	PUNCT
ejpam-6847	495	13	=	=	SYM
ejpam-6847	495	14	smtk	smtk	NOUN
ejpam-6847	495	15	,	,	PUNCT
ejpam-6847	495	16	m	m	PROPN
ejpam-6847	495	17	,	,	PUNCT
ejpam-6847	495	18	n	n	PRON
ejpam-6847	495	19	∈	∈	PROPN
ejpam-6847	495	20	n∪{0	n∪{0	NOUN
ejpam-6847	495	21	}	}	PUNCT
ejpam-6847	495	22	,	,	PUNCT
ejpam-6847	495	23	k	k	X
ejpam-6847	495	24	>	>	X
ejpam-6847	495	25	0	0	NUM
ejpam-6847	495	26	,	,	PUNCT
ejpam-6847	495	27	we	we	PRON
ejpam-6847	495	28	drive	drive	VERB
ejpam-6847	495	29	the	the	DET
ejpam-6847	495	30	following	follow	VERB
ejpam-6847	495	31	corollary	corollary	NOUN
ejpam-6847	495	32	from	from	ADP
ejpam-6847	495	33	theorem	theorem	ADJ
ejpam-6847	495	34	1	1	NUM
ejpam-6847	495	35	.	.	PUNCT
ejpam-6847	495	36	corollary	corollary	ADJ
ejpam-6847	495	37	1	1	NUM
ejpam-6847	495	38	.	.	PUNCT
ejpam-6847	496	1	let	let	VERB
ejpam-6847	496	2	(	(	PUNCT
ejpam-6847	496	3	x	x	NOUN
ejpam-6847	496	4	,	,	PUNCT
ejpam-6847	496	5	s	s	PART
ejpam-6847	496	6	)	)	PUNCT
ejpam-6847	496	7	be	be	AUX
ejpam-6847	496	8	a	a	DET
ejpam-6847	496	9	complete	complete	ADJ
ejpam-6847	496	10	t	t	NOUN
ejpam-6847	496	11	c	c	X
ejpam-6847	496	12	-	-	PUNCT
ejpam-6847	496	13	s	s	PROPN
ejpam-6847	496	14	-	-	PUNCT
ejpam-6847	496	15	mt	mt	NOUN
ejpam-6847	496	16	s	s	PROPN
ejpam-6847	496	17	,	,	PUNCT
ejpam-6847	496	18	where	where	SCONJ
ejpam-6847	496	19	x	x	PUNCT
ejpam-6847	496	20	6=	6=	ADP
ejpam-6847	496	21	∅.	∅.	AUX
ejpam-6847	496	22	let	let	VERB
ejpam-6847	496	23	αs(x	αs(x	NUM
ejpam-6847	496	24	,	,	PUNCT
ejpam-6847	496	25	y	y	PROPN
ejpam-6847	496	26	,	,	PUNCT
ejpam-6847	496	27	z	z	NOUN
ejpam-6847	496	28	)	)	PUNCT
ejpam-6847	497	1	n(τ	n(τ	PROPN
ejpam-6847	498	1	+	+	NUM
ejpam-6847	498	2	f	f	X
ejpam-6847	498	3	(	(	PUNCT
ejpam-6847	498	4	s(tx	s(tx	PROPN
ejpam-6847	498	5	,	,	PUNCT
ejpam-6847	498	6	ty	ty	INTJ
ejpam-6847	498	7	,	,	PUNCT
ejpam-6847	498	8	tz)))k	tz)))k	DET
ejpam-6847	498	9	≤	≤	NOUN
ejpam-6847	498	10	νs(x	νs(x	PROPN
ejpam-6847	498	11	,	,	PUNCT
ejpam-6847	498	12	y	y	PROPN
ejpam-6847	498	13	,	,	PUNCT
ejpam-6847	498	14	z	z	NOUN
ejpam-6847	498	15	)	)	PUNCT
ejpam-6847	498	16	mf	mf	X
ejpam-6847	498	17	(	(	PUNCT
ejpam-6847	498	18	s(x	s(x	PROPN
ejpam-6847	498	19	,	,	PUNCT
ejpam-6847	498	20	y	y	PROPN
ejpam-6847	498	21	,	,	PUNCT
ejpam-6847	498	22	z))k	z))k	PROPN
ejpam-6847	498	23	,	,	PUNCT
ejpam-6847	498	24	where	where	SCONJ
ejpam-6847	498	25	,	,	PUNCT
ejpam-6847	498	26	m	m	PROPN
ejpam-6847	498	27	,	,	PUNCT
ejpam-6847	498	28	n	n	PROPN
ejpam-6847	498	29	∈	∈	PROPN
ejpam-6847	498	30	n∪{0	n∪{0	NOUN
ejpam-6847	498	31	}	}	PUNCT
ejpam-6847	498	32	,	,	PUNCT
ejpam-6847	498	33	k	k	PROPN
ejpam-6847	498	34	>	>	X
ejpam-6847	498	35	0	0	PUNCT
ejpam-6847	498	36	.	.	PUNCT
ejpam-6847	499	1	assume	assume	VERB
ejpam-6847	499	2	the	the	DET
ejpam-6847	499	3	following	follow	VERB
ejpam-6847	499	4	conditions	condition	NOUN
ejpam-6847	499	5	hold	hold	VERB
ejpam-6847	499	6	:	:	PUNCT
ejpam-6847	499	7	(	(	PUNCT
ejpam-6847	499	8	i	i	NOUN
ejpam-6847	499	9	)	)	PUNCT
ejpam-6847	499	10	t	t	PROPN
ejpam-6847	499	11	is	be	AUX
ejpam-6847	499	12	αs	αs	ADJ
ejpam-6847	499	13	-	-	ADJ
ejpam-6847	499	14	admissible	admissible	ADJ
ejpam-6847	499	15	and	and	CCONJ
ejpam-6847	499	16	µs	µs	NOUN
ejpam-6847	499	17	-	-	PUNCT
ejpam-6847	499	18	subadmissible	subadmissible	ADJ
ejpam-6847	499	19	mapping	mapping	NOUN
ejpam-6847	499	20	.	.	PUNCT
ejpam-6847	500	1	(	(	PUNCT
ejpam-6847	500	2	ii	ii	NOUN
ejpam-6847	500	3	)	)	PUNCT
ejpam-6847	500	4	there	there	PRON
ejpam-6847	500	5	is	be	VERB
ejpam-6847	500	6	x0	x0	PROPN
ejpam-6847	500	7	∈	∈	PROPN
ejpam-6847	500	8	x	x	NOUN
ejpam-6847	500	9	,	,	PUNCT
ejpam-6847	500	10	such	such	ADJ
ejpam-6847	500	11	that	that	DET
ejpam-6847	500	12	αs(x0	αs(x0	NOUN
ejpam-6847	500	13	,	,	PUNCT
ejpam-6847	500	14	x0	x0	PROPN
ejpam-6847	500	15	,	,	PUNCT
ejpam-6847	500	16	tx0	tx0	PROPN
ejpam-6847	500	17	)	)	PUNCT
ejpam-6847	500	18	≥	≥	NOUN
ejpam-6847	500	19	1	1	NUM
ejpam-6847	500	20	,	,	PUNCT
ejpam-6847	500	21	νs(x0	νs(x0	PROPN
ejpam-6847	500	22	,	,	PUNCT
ejpam-6847	500	23	x0	x0	PROPN
ejpam-6847	500	24	,	,	PUNCT
ejpam-6847	500	25	tx0	tx0	NOUN
ejpam-6847	500	26	)	)	PUNCT
ejpam-6847	500	27	≤	≤	NOUN
ejpam-6847	500	28	1	1	NUM
ejpam-6847	500	29	.	.	PUNCT
ejpam-6847	501	1	(	(	PUNCT
ejpam-6847	501	2	iii	iii	NOUN
ejpam-6847	501	3	)	)	PUNCT
ejpam-6847	501	4	for	for	ADP
ejpam-6847	501	5	x0	x0	PROPN
ejpam-6847	501	6	∈	∈	PROPN
ejpam-6847	502	1	x	x	PRON
ejpam-6847	502	2	,	,	PUNCT
ejpam-6847	502	3	the	the	DET
ejpam-6847	502	4	sequence	sequence	NOUN
ejpam-6847	502	5	{	{	PUNCT
ejpam-6847	502	6	xn	xn	NUM
ejpam-6847	502	7	}	}	PUNCT
ejpam-6847	502	8	,	,	PUNCT
ejpam-6847	502	9	is	be	AUX
ejpam-6847	502	10	defined	define	VERB
ejpam-6847	502	11	by	by	ADP
ejpam-6847	502	12	xn	xn	PROPN
ejpam-6847	502	13	=	=	SYM
ejpam-6847	502	14	tnx0	tnx0	PROPN
ejpam-6847	502	15	,	,	PUNCT
ejpam-6847	502	16	and	and	CCONJ
ejpam-6847	502	17	the	the	DET
ejpam-6847	502	18	following	follow	VERB
ejpam-6847	502	19	inequality	inequality	NOUN
ejpam-6847	502	20	holds	hold	VERB
ejpam-6847	502	21	:	:	PUNCT
ejpam-6847	502	22	sup	sup	PROPN
ejpam-6847	502	23	m≥1	m≥1	PROPN
ejpam-6847	502	24	lim	lim	PROPN
ejpam-6847	502	25	n→+∞	n→+∞	PROPN
ejpam-6847	502	26	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	502	27	,	,	PUNCT
ejpam-6847	502	28	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	502	29	,	,	PUNCT
ejpam-6847	502	30	xn+2	xn+2	NUM
ejpam-6847	502	31	)	)	PUNCT
ejpam-6847	503	1	+	+	CCONJ
ejpam-6847	503	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	503	3	,	,	PUNCT
ejpam-6847	503	4	xn+2	xn+2	NUM
ejpam-6847	503	5	)	)	PUNCT
ejpam-6847	503	6	]	]	PUNCT
ejpam-6847	504	1	[	[	X
ejpam-6847	504	2	β(xn	β(xn	NOUN
ejpam-6847	504	3	,	,	PUNCT
ejpam-6847	504	4	xn+1	xn+1	NUM
ejpam-6847	504	5	)	)	PUNCT
ejpam-6847	504	6	+	+	CCONJ
ejpam-6847	504	7	µ(xn	µ(xn	PROPN
ejpam-6847	504	8	,	,	PUNCT
ejpam-6847	504	9	xn+1	xn+1	NUM
ejpam-6847	504	10	)	)	PUNCT
ejpam-6847	504	11	]	]	PUNCT
ejpam-6847	504	12	<	<	X
ejpam-6847	504	13	1	1	X
ejpam-6847	504	14	.	.	PUNCT
ejpam-6847	505	1	in	in	ADP
ejpam-6847	505	2	addition	addition	NOUN
ejpam-6847	505	3	,	,	PUNCT
ejpam-6847	505	4	for	for	SCONJ
ejpam-6847	505	5	every	every	DET
ejpam-6847	505	6	x	x	SYM
ejpam-6847	505	7	∈	∈	PROPN
ejpam-6847	505	8	x	x	NOUN
ejpam-6847	505	9	,	,	PUNCT
ejpam-6847	505	10	the	the	DET
ejpam-6847	505	11	following	follow	VERB
ejpam-6847	505	12	limits	limit	NOUN
ejpam-6847	505	13	exist	exist	VERB
ejpam-6847	505	14	and	and	CCONJ
ejpam-6847	505	15	are	be	AUX
ejpam-6847	505	16	finite	finite	ADJ
ejpam-6847	505	17	:	:	PUNCT
ejpam-6847	505	18	lim	lim	PROPN
ejpam-6847	505	19	n→+∞	n→+∞	PROPN
ejpam-6847	505	20	β(x	β(x	PROPN
ejpam-6847	505	21	,	,	PUNCT
ejpam-6847	505	22	xn	xn	PROPN
ejpam-6847	505	23	)	)	PUNCT
ejpam-6847	505	24	,	,	PUNCT
ejpam-6847	505	25	lim	lim	PROPN
ejpam-6847	505	26	n→+∞	n→+∞	VERB
ejpam-6847	505	27	µ(xn	µ(xn	PROPN
ejpam-6847	505	28	,	,	PUNCT
ejpam-6847	505	29	x	x	NOUN
ejpam-6847	505	30	)	)	PUNCT
ejpam-6847	505	31	and	and	CCONJ
ejpam-6847	505	32	lim	lim	PROPN
ejpam-6847	505	33	n→+∞	n→+∞	VERB
ejpam-6847	505	34	γ(xn	γ(xn	PROPN
ejpam-6847	505	35	,	,	PUNCT
ejpam-6847	505	36	x	x	NOUN
ejpam-6847	505	37	)	)	PUNCT
ejpam-6847	505	38	.	.	PUNCT
ejpam-6847	506	1	then	then	ADV
ejpam-6847	506	2	,	,	PUNCT
ejpam-6847	506	3	t	t	PROPN
ejpam-6847	506	4	has	have	VERB
ejpam-6847	506	5	a	a	DET
ejpam-6847	506	6	fixed	fix	VERB
ejpam-6847	506	7	point	point	NOUN
ejpam-6847	506	8	.	.	PUNCT
ejpam-6847	507	1	for	for	ADP
ejpam-6847	507	2	the	the	DET
ejpam-6847	507	3	uniqueness	uniqueness	NOUN
ejpam-6847	507	4	of	of	ADP
ejpam-6847	507	5	the	the	DET
ejpam-6847	507	6	fixed	fix	VERB
ejpam-6847	507	7	point	point	NOUN
ejpam-6847	507	8	,	,	PUNCT
ejpam-6847	507	9	assume	assume	VERB
ejpam-6847	507	10	both	both	DET
ejpam-6847	507	11	u	u	NOUN
ejpam-6847	507	12	,	,	PUNCT
ejpam-6847	507	13	and	and	CCONJ
ejpam-6847	507	14	v	v	NOUN
ejpam-6847	507	15	are	be	AUX
ejpam-6847	507	16	fixed	fix	VERB
ejpam-6847	507	17	points	point	NOUN
ejpam-6847	507	18	such	such	ADJ
ejpam-6847	507	19	that	that	PRON
ejpam-6847	507	20	αs(u	αs(u	NUM
ejpam-6847	507	21	,	,	PUNCT
ejpam-6847	507	22	u	u	NOUN
ejpam-6847	507	23	,	,	PUNCT
ejpam-6847	507	24	v	v	NOUN
ejpam-6847	507	25	)	)	PUNCT
ejpam-6847	507	26	≥	≥	NOUN
ejpam-6847	507	27	1	1	NUM
ejpam-6847	507	28	,	,	PUNCT
ejpam-6847	507	29	and	and	CCONJ
ejpam-6847	507	30	νs(u	νs(u	NUM
ejpam-6847	507	31	,	,	PUNCT
ejpam-6847	507	32	u	u	NOUN
ejpam-6847	507	33	,	,	PUNCT
ejpam-6847	507	34	v	v	NOUN
ejpam-6847	507	35	)	)	PUNCT
ejpam-6847	507	36	≤	≤	NUM
ejpam-6847	507	37	1	1	NUM
ejpam-6847	507	38	,	,	PUNCT
ejpam-6847	507	39	then	then	ADV
ejpam-6847	507	40	t	t	PROPN
ejpam-6847	507	41	has	have	VERB
ejpam-6847	507	42	a	a	DET
ejpam-6847	507	43	unique	unique	ADJ
ejpam-6847	507	44	fixed	fix	VERB
ejpam-6847	507	45	point	point	NOUN
ejpam-6847	507	46	in	in	ADP
ejpam-6847	507	47	x.	x.	PROPN
ejpam-6847	507	48	f.	f.	PROPN
ejpam-6847	507	49	m.	m.	PROPN
ejpam-6847	507	50	azmi	azmi	PROPN
ejpam-6847	507	51	,	,	PUNCT
ejpam-6847	507	52	a.	a.	PROPN
ejpam-6847	507	53	h.	h.	PROPN
ejpam-6847	507	54	ansari	ansari	PROPN
ejpam-6847	507	55	,	,	PUNCT
ejpam-6847	507	56	s.	s.	PROPN
ejpam-6847	507	57	h.	h.	PROPN
ejpam-6847	507	58	j.	j.	PROPN
ejpam-6847	507	59	petroudi	petroudi	PROPN
ejpam-6847	507	60	/	/	SYM
ejpam-6847	507	61	eur	eur	PROPN
ejpam-6847	507	62	.	.	PUNCT
ejpam-6847	508	1	j.	j.	PROPN
ejpam-6847	508	2	pure	pure	PROPN
ejpam-6847	508	3	appl	appl	PROPN
ejpam-6847	508	4	.	.	PROPN
ejpam-6847	508	5	math	math	PROPN
ejpam-6847	508	6	,	,	PUNCT
ejpam-6847	508	7	18	18	NUM
ejpam-6847	508	8	(	(	PUNCT
ejpam-6847	508	9	4	4	NUM
ejpam-6847	508	10	)	)	PUNCT
ejpam-6847	508	11	(	(	PUNCT
ejpam-6847	508	12	2025	2025	NUM
ejpam-6847	508	13	)	)	PUNCT
ejpam-6847	508	14	,	,	PUNCT
ejpam-6847	508	15	6847	6847	NUM
ejpam-6847	508	16	20	20	NUM
ejpam-6847	508	17	of	of	ADP
ejpam-6847	508	18	26	26	NUM
ejpam-6847	508	19	it	it	PRON
ejpam-6847	508	20	is	be	AUX
ejpam-6847	508	21	important	important	ADJ
ejpam-6847	508	22	to	to	PART
ejpam-6847	508	23	observe	observe	VERB
ejpam-6847	508	24	that	that	SCONJ
ejpam-6847	508	25	by	by	ADP
ejpam-6847	508	26	selecting	select	VERB
ejpam-6847	508	27	n	n	NOUN
ejpam-6847	508	28	=	=	SYM
ejpam-6847	508	29	m	m	PROPN
ejpam-6847	508	30	=	=	SYM
ejpam-6847	508	31	k	k	NOUN
ejpam-6847	508	32	=	=	SYM
ejpam-6847	508	33	1	1	NUM
ejpam-6847	508	34	in	in	ADP
ejpam-6847	508	35	corollary	corollary	ADJ
ejpam-6847	508	36	1	1	NUM
ejpam-6847	508	37	,	,	PUNCT
ejpam-6847	508	38	we	we	PRON
ejpam-6847	508	39	obtain	obtain	VERB
ejpam-6847	508	40	the	the	DET
ejpam-6847	508	41	subsequent	subsequent	ADJ
ejpam-6847	508	42	corollary	corollary	NOUN
ejpam-6847	508	43	,	,	PUNCT
ejpam-6847	508	44	as	as	SCONJ
ejpam-6847	508	45	illustrated	illustrate	VERB
ejpam-6847	508	46	in	in	ADP
ejpam-6847	508	47	example	example	NOUN
ejpam-6847	508	48	7	7	NUM
ejpam-6847	508	49	.	.	PUNCT
ejpam-6847	508	50	corollary	corollary	ADJ
ejpam-6847	508	51	2	2	NUM
ejpam-6847	508	52	.	.	PUNCT
ejpam-6847	509	1	let	let	AUX
ejpam-6847	509	2	(	(	PUNCT
ejpam-6847	509	3	x	x	NOUN
ejpam-6847	509	4	,	,	PUNCT
ejpam-6847	509	5	s	s	PART
ejpam-6847	509	6	)	)	PUNCT
ejpam-6847	509	7	be	be	AUX
ejpam-6847	509	8	a	a	DET
ejpam-6847	509	9	complete	complete	ADJ
ejpam-6847	509	10	t	t	NOUN
ejpam-6847	509	11	c	c	X
ejpam-6847	509	12	-	-	PUNCT
ejpam-6847	509	13	s	s	PROPN
ejpam-6847	509	14	-	-	PUNCT
ejpam-6847	509	15	mt	mt	NOUN
ejpam-6847	509	16	s	s	PROPN
ejpam-6847	509	17	,	,	PUNCT
ejpam-6847	509	18	where	where	SCONJ
ejpam-6847	509	19	x	x	PUNCT
ejpam-6847	510	1	6=	6=	ADP
ejpam-6847	510	2	∅.	∅.	AUX
ejpam-6847	510	3	let	let	VERB
ejpam-6847	510	4	αs(x	αs(x	NOUN
ejpam-6847	510	5	,	,	PUNCT
ejpam-6847	510	6	y	y	PROPN
ejpam-6847	510	7	,	,	PUNCT
ejpam-6847	510	8	z)(τ	z)(τ	PROPN
ejpam-6847	511	1	+	+	CCONJ
ejpam-6847	511	2	f	f	X
ejpam-6847	511	3	(	(	PUNCT
ejpam-6847	511	4	s(tx	s(tx	PROPN
ejpam-6847	511	5	,	,	PUNCT
ejpam-6847	511	6	ty	ty	INTJ
ejpam-6847	511	7	,	,	PUNCT
ejpam-6847	511	8	tz	tz	NOUN
ejpam-6847	511	9	)	)	PUNCT
ejpam-6847	511	10	)	)	PUNCT
ejpam-6847	511	11	)	)	PUNCT
ejpam-6847	511	12	≤	≤	NOUN
ejpam-6847	511	13	νs(x	νs(x	NOUN
ejpam-6847	511	14	,	,	PUNCT
ejpam-6847	511	15	y	y	PROPN
ejpam-6847	511	16	,	,	PUNCT
ejpam-6847	511	17	z)f	z)f	X
ejpam-6847	511	18	(	(	PUNCT
ejpam-6847	511	19	s(x	s(x	PROPN
ejpam-6847	511	20	,	,	PUNCT
ejpam-6847	511	21	y	y	PROPN
ejpam-6847	511	22	,	,	PUNCT
ejpam-6847	511	23	z	z	NOUN
ejpam-6847	511	24	)	)	PUNCT
ejpam-6847	511	25	)	)	PUNCT
ejpam-6847	511	26	.	.	PUNCT
ejpam-6847	512	1	assume	assume	VERB
ejpam-6847	512	2	the	the	DET
ejpam-6847	512	3	following	follow	VERB
ejpam-6847	512	4	conditions	condition	NOUN
ejpam-6847	512	5	hold	hold	VERB
ejpam-6847	512	6	:	:	PUNCT
ejpam-6847	512	7	(	(	PUNCT
ejpam-6847	512	8	i	i	NOUN
ejpam-6847	512	9	)	)	PUNCT
ejpam-6847	512	10	t	t	PROPN
ejpam-6847	512	11	is	be	AUX
ejpam-6847	512	12	αs	αs	ADJ
ejpam-6847	512	13	-	-	ADJ
ejpam-6847	512	14	admissible	admissible	ADJ
ejpam-6847	512	15	and	and	CCONJ
ejpam-6847	512	16	νs	νs	NOUN
ejpam-6847	512	17	-	-	PUNCT
ejpam-6847	512	18	subadmissible	subadmissible	ADJ
ejpam-6847	512	19	mapping	mapping	NOUN
ejpam-6847	512	20	.	.	PUNCT
ejpam-6847	513	1	(	(	PUNCT
ejpam-6847	513	2	ii	ii	NOUN
ejpam-6847	513	3	)	)	PUNCT
ejpam-6847	513	4	there	there	PRON
ejpam-6847	513	5	is	be	VERB
ejpam-6847	513	6	x0	x0	PROPN
ejpam-6847	513	7	∈	∈	PROPN
ejpam-6847	513	8	x	x	NOUN
ejpam-6847	513	9	,	,	PUNCT
ejpam-6847	513	10	such	such	ADJ
ejpam-6847	513	11	that	that	DET
ejpam-6847	513	12	αs(x0	αs(x0	NOUN
ejpam-6847	513	13	,	,	PUNCT
ejpam-6847	513	14	x0	x0	PROPN
ejpam-6847	513	15	,	,	PUNCT
ejpam-6847	513	16	tx0	tx0	PROPN
ejpam-6847	513	17	)	)	PUNCT
ejpam-6847	513	18	≥	≥	NOUN
ejpam-6847	513	19	1	1	NUM
ejpam-6847	513	20	,	,	PUNCT
ejpam-6847	513	21	νs(x0	νs(x0	PROPN
ejpam-6847	513	22	,	,	PUNCT
ejpam-6847	513	23	x0	x0	PROPN
ejpam-6847	513	24	,	,	PUNCT
ejpam-6847	513	25	tx0	tx0	NOUN
ejpam-6847	513	26	)	)	PUNCT
ejpam-6847	513	27	≤	≤	NOUN
ejpam-6847	513	28	1	1	NUM
ejpam-6847	513	29	.	.	PUNCT
ejpam-6847	514	1	(	(	PUNCT
ejpam-6847	514	2	iii	iii	NOUN
ejpam-6847	514	3	)	)	PUNCT
ejpam-6847	514	4	for	for	ADP
ejpam-6847	514	5	x0	x0	PROPN
ejpam-6847	514	6	∈	∈	PROPN
ejpam-6847	515	1	x	x	PRON
ejpam-6847	515	2	,	,	PUNCT
ejpam-6847	515	3	the	the	DET
ejpam-6847	515	4	sequence	sequence	NOUN
ejpam-6847	515	5	{	{	PUNCT
ejpam-6847	515	6	xn	xn	NUM
ejpam-6847	515	7	}	}	PUNCT
ejpam-6847	515	8	,	,	PUNCT
ejpam-6847	515	9	is	be	AUX
ejpam-6847	515	10	defined	define	VERB
ejpam-6847	515	11	by	by	ADP
ejpam-6847	515	12	xn	xn	PROPN
ejpam-6847	515	13	=	=	SYM
ejpam-6847	515	14	tnx0	tnx0	PROPN
ejpam-6847	515	15	,	,	PUNCT
ejpam-6847	515	16	and	and	CCONJ
ejpam-6847	515	17	the	the	DET
ejpam-6847	515	18	following	follow	VERB
ejpam-6847	515	19	inequality	inequality	NOUN
ejpam-6847	515	20	holds	hold	VERB
ejpam-6847	515	21	:	:	PUNCT
ejpam-6847	515	22	sup	sup	PROPN
ejpam-6847	515	23	m≥1	m≥1	PROPN
ejpam-6847	515	24	lim	lim	PROPN
ejpam-6847	515	25	n→+∞	n→+∞	PROPN
ejpam-6847	515	26	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	515	27	,	,	PUNCT
ejpam-6847	515	28	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	515	29	,	,	PUNCT
ejpam-6847	515	30	xn+2	xn+2	NUM
ejpam-6847	515	31	)	)	PUNCT
ejpam-6847	516	1	+	+	CCONJ
ejpam-6847	516	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	516	3	,	,	PUNCT
ejpam-6847	516	4	xn+2	xn+2	NUM
ejpam-6847	516	5	)	)	PUNCT
ejpam-6847	516	6	]	]	PUNCT
ejpam-6847	517	1	[	[	X
ejpam-6847	517	2	β(xn	β(xn	NOUN
ejpam-6847	517	3	,	,	PUNCT
ejpam-6847	517	4	xn+1	xn+1	NUM
ejpam-6847	517	5	)	)	PUNCT
ejpam-6847	517	6	+	+	CCONJ
ejpam-6847	517	7	µ(xn	µ(xn	PROPN
ejpam-6847	517	8	,	,	PUNCT
ejpam-6847	517	9	xn+1	xn+1	NUM
ejpam-6847	517	10	)	)	PUNCT
ejpam-6847	517	11	]	]	PUNCT
ejpam-6847	517	12	<	<	X
ejpam-6847	517	13	1	1	X
ejpam-6847	517	14	.	.	PUNCT
ejpam-6847	518	1	in	in	ADP
ejpam-6847	518	2	addition	addition	NOUN
ejpam-6847	518	3	,	,	PUNCT
ejpam-6847	518	4	for	for	SCONJ
ejpam-6847	518	5	every	every	DET
ejpam-6847	518	6	x	x	NOUN
ejpam-6847	518	7	in	in	ADP
ejpam-6847	518	8	x	x	PRON
ejpam-6847	518	9	,	,	PUNCT
ejpam-6847	518	10	the	the	DET
ejpam-6847	518	11	following	follow	VERB
ejpam-6847	518	12	limits	limit	NOUN
ejpam-6847	518	13	exist	exist	VERB
ejpam-6847	518	14	and	and	CCONJ
ejpam-6847	518	15	are	be	AUX
ejpam-6847	518	16	finite	finite	ADJ
ejpam-6847	518	17	:	:	PUNCT
ejpam-6847	518	18	lim	lim	PROPN
ejpam-6847	518	19	n→+∞	n→+∞	PROPN
ejpam-6847	518	20	β(x	β(x	PROPN
ejpam-6847	518	21	,	,	PUNCT
ejpam-6847	518	22	xn	xn	PROPN
ejpam-6847	518	23	)	)	PUNCT
ejpam-6847	518	24	,	,	PUNCT
ejpam-6847	518	25	lim	lim	PROPN
ejpam-6847	518	26	n→+∞	n→+∞	VERB
ejpam-6847	518	27	µ(xn	µ(xn	PROPN
ejpam-6847	518	28	,	,	PUNCT
ejpam-6847	518	29	x	x	NOUN
ejpam-6847	518	30	)	)	PUNCT
ejpam-6847	518	31	and	and	CCONJ
ejpam-6847	518	32	lim	lim	PROPN
ejpam-6847	518	33	n→+∞	n→+∞	VERB
ejpam-6847	518	34	γ(xn	γ(xn	PROPN
ejpam-6847	518	35	,	,	PUNCT
ejpam-6847	518	36	x	x	NOUN
ejpam-6847	518	37	)	)	PUNCT
ejpam-6847	518	38	.	.	PUNCT
ejpam-6847	519	1	then	then	ADV
ejpam-6847	519	2	,	,	PUNCT
ejpam-6847	519	3	t	t	PROPN
ejpam-6847	519	4	has	have	VERB
ejpam-6847	519	5	a	a	DET
ejpam-6847	519	6	fixed	fix	VERB
ejpam-6847	519	7	point	point	NOUN
ejpam-6847	519	8	.	.	PUNCT
ejpam-6847	520	1	for	for	ADP
ejpam-6847	520	2	the	the	DET
ejpam-6847	520	3	uniqueness	uniqueness	NOUN
ejpam-6847	520	4	of	of	ADP
ejpam-6847	520	5	the	the	DET
ejpam-6847	520	6	fixed	fix	VERB
ejpam-6847	520	7	point	point	NOUN
ejpam-6847	520	8	,	,	PUNCT
ejpam-6847	520	9	assume	assume	VERB
ejpam-6847	520	10	both	both	DET
ejpam-6847	520	11	u	u	NOUN
ejpam-6847	520	12	,	,	PUNCT
ejpam-6847	520	13	and	and	CCONJ
ejpam-6847	520	14	v	v	NOUN
ejpam-6847	520	15	are	be	AUX
ejpam-6847	520	16	fixed	fix	VERB
ejpam-6847	520	17	points	point	NOUN
ejpam-6847	520	18	such	such	ADJ
ejpam-6847	520	19	that	that	PRON
ejpam-6847	520	20	αs(u	αs(u	NUM
ejpam-6847	520	21	,	,	PUNCT
ejpam-6847	520	22	u	u	NOUN
ejpam-6847	520	23	,	,	PUNCT
ejpam-6847	520	24	v	v	NOUN
ejpam-6847	520	25	)	)	PUNCT
ejpam-6847	520	26	≥	≥	NOUN
ejpam-6847	520	27	1	1	NUM
ejpam-6847	520	28	,	,	PUNCT
ejpam-6847	520	29	and	and	CCONJ
ejpam-6847	520	30	νs(u	νs(u	NUM
ejpam-6847	520	31	,	,	PUNCT
ejpam-6847	520	32	u	u	NOUN
ejpam-6847	520	33	,	,	PUNCT
ejpam-6847	520	34	v	v	NOUN
ejpam-6847	520	35	)	)	PUNCT
ejpam-6847	520	36	≤	≤	NUM
ejpam-6847	520	37	1	1	NUM
ejpam-6847	520	38	,	,	PUNCT
ejpam-6847	520	39	then	then	ADV
ejpam-6847	520	40	t	t	PROPN
ejpam-6847	520	41	has	have	VERB
ejpam-6847	520	42	a	a	DET
ejpam-6847	520	43	unique	unique	ADJ
ejpam-6847	520	44	fixed	fix	VERB
ejpam-6847	520	45	point	point	NOUN
ejpam-6847	520	46	in	in	ADP
ejpam-6847	520	47	x.	x.	NOUN
ejpam-6847	520	48	by	by	ADP
ejpam-6847	520	49	selecting	select	VERB
ejpam-6847	520	50	the	the	DET
ejpam-6847	520	51	pair	pair	NOUN
ejpam-6847	520	52	(	(	PUNCT
ejpam-6847	520	53	q	q	NOUN
ejpam-6847	520	54	,	,	PUNCT
ejpam-6847	520	55	h	h	NOUN
ejpam-6847	520	56	)	)	PUNCT
ejpam-6847	520	57	of	of	ADP
ejpam-6847	520	58	upper	upper	ADJ
ejpam-6847	520	59	class	class	NOUN
ejpam-6847	520	60	of	of	ADP
ejpam-6847	520	61	type	type	NOUN
ejpam-6847	520	62	i	i	PRON
ejpam-6847	520	63	,	,	PUNCT
ejpam-6847	520	64	where	where	SCONJ
ejpam-6847	520	65	,	,	PUNCT
ejpam-6847	520	66	h(x	h(x	PROPN
ejpam-6847	520	67	,	,	PUNCT
ejpam-6847	520	68	y	y	PROPN
ejpam-6847	520	69	)	)	PUNCT
ejpam-6847	521	1	=	=	SYM
ejpam-6847	521	2	(	(	PUNCT
ejpam-6847	521	3	y	y	PROPN
ejpam-6847	521	4	+	+	CCONJ
ejpam-6847	521	5	l)x	l)x	X
ejpam-6847	521	6	,	,	PUNCT
ejpam-6847	521	7	l	l	NOUN
ejpam-6847	521	8	>	>	X
ejpam-6847	521	9	1	1	NUM
ejpam-6847	521	10	,	,	PUNCT
ejpam-6847	521	11	and	and	CCONJ
ejpam-6847	521	12	q(s	q(s	PROPN
ejpam-6847	521	13	,	,	PUNCT
ejpam-6847	521	14	t	t	PROPN
ejpam-6847	521	15	)	)	PUNCT
ejpam-6847	521	16	=	=	SYM
ejpam-6847	522	1	st+	st+	PROPN
ejpam-6847	522	2	l	l	NOUN
ejpam-6847	522	3	,	,	PUNCT
ejpam-6847	522	4	we	we	PRON
ejpam-6847	522	5	drive	drive	VERB
ejpam-6847	522	6	the	the	DET
ejpam-6847	522	7	following	follow	VERB
ejpam-6847	522	8	corollary	corollary	NOUN
ejpam-6847	522	9	from	from	ADP
ejpam-6847	522	10	theorem	theorem	ADJ
ejpam-6847	522	11	1	1	NUM
ejpam-6847	522	12	.	.	PUNCT
ejpam-6847	522	13	corollary	corollary	ADJ
ejpam-6847	522	14	3	3	X
ejpam-6847	522	15	.	.	PUNCT
ejpam-6847	523	1	let	let	AUX
ejpam-6847	523	2	(	(	PUNCT
ejpam-6847	523	3	x	x	NOUN
ejpam-6847	523	4	,	,	PUNCT
ejpam-6847	523	5	s	s	PART
ejpam-6847	523	6	)	)	PUNCT
ejpam-6847	523	7	be	be	AUX
ejpam-6847	523	8	a	a	DET
ejpam-6847	523	9	complete	complete	ADJ
ejpam-6847	523	10	t	t	NOUN
ejpam-6847	523	11	c	c	X
ejpam-6847	523	12	-	-	PUNCT
ejpam-6847	523	13	s	s	PROPN
ejpam-6847	523	14	-	-	PUNCT
ejpam-6847	523	15	mt	mt	NOUN
ejpam-6847	523	16	s	s	PROPN
ejpam-6847	523	17	,	,	PUNCT
ejpam-6847	523	18	where	where	SCONJ
ejpam-6847	523	19	x	x	PUNCT
ejpam-6847	523	20	6=	6=	AUX
ejpam-6847	523	21	∅.	∅.	ADV
ejpam-6847	523	22	let	let	VERB
ejpam-6847	523	23	(	(	PUNCT
ejpam-6847	523	24	τ	τ	PROPN
ejpam-6847	524	1	+	+	NUM
ejpam-6847	524	2	f	f	X
ejpam-6847	524	3	(	(	PUNCT
ejpam-6847	524	4	s(tx	s(tx	PROPN
ejpam-6847	524	5	,	,	PUNCT
ejpam-6847	524	6	ty	ty	INTJ
ejpam-6847	524	7	,	,	PUNCT
ejpam-6847	524	8	tz	tz	NOUN
ejpam-6847	524	9	)	)	PUNCT
ejpam-6847	524	10	)	)	PUNCT
ejpam-6847	525	1	+	+	CCONJ
ejpam-6847	525	2	l)αs(x	l)αs(x	NOUN
ejpam-6847	525	3	,	,	PUNCT
ejpam-6847	525	4	y	y	PROPN
ejpam-6847	525	5	,	,	PUNCT
ejpam-6847	525	6	z	z	NOUN
ejpam-6847	525	7	)	)	PUNCT
ejpam-6847	525	8	≤	≤	NOUN
ejpam-6847	525	9	νs(x	νs(x	NOUN
ejpam-6847	525	10	,	,	PUNCT
ejpam-6847	525	11	y	y	PROPN
ejpam-6847	525	12	,	,	PUNCT
ejpam-6847	525	13	z)f	z)f	X
ejpam-6847	525	14	(	(	PUNCT
ejpam-6847	525	15	s(x	s(x	PROPN
ejpam-6847	525	16	,	,	PUNCT
ejpam-6847	525	17	y	y	PROPN
ejpam-6847	525	18	,	,	PUNCT
ejpam-6847	525	19	z	z	NOUN
ejpam-6847	525	20	)	)	PUNCT
ejpam-6847	525	21	)	)	PUNCT
ejpam-6847	526	1	+	+	CCONJ
ejpam-6847	526	2	l	l	NOUN
ejpam-6847	526	3	,	,	PUNCT
ejpam-6847	526	4	where	where	SCONJ
ejpam-6847	526	5	,	,	PUNCT
ejpam-6847	526	6	l	l	PROPN
ejpam-6847	526	7	>	>	X
ejpam-6847	526	8	1	1	X
ejpam-6847	526	9	.	.	PUNCT
ejpam-6847	526	10	assume	assume	VERB
ejpam-6847	526	11	the	the	DET
ejpam-6847	526	12	following	follow	VERB
ejpam-6847	526	13	conditions	condition	NOUN
ejpam-6847	526	14	hold	hold	VERB
ejpam-6847	526	15	:	:	PUNCT
ejpam-6847	526	16	(	(	PUNCT
ejpam-6847	526	17	i	i	NOUN
ejpam-6847	526	18	)	)	PUNCT
ejpam-6847	526	19	t	t	PROPN
ejpam-6847	526	20	is	be	AUX
ejpam-6847	526	21	αs	αs	ADJ
ejpam-6847	526	22	-	-	ADJ
ejpam-6847	526	23	admissible	admissible	ADJ
ejpam-6847	526	24	and	and	CCONJ
ejpam-6847	526	25	νs	νs	NOUN
ejpam-6847	526	26	-	-	PUNCT
ejpam-6847	526	27	subadmissible	subadmissible	ADJ
ejpam-6847	526	28	mapping	mapping	NOUN
ejpam-6847	526	29	.	.	PUNCT
ejpam-6847	527	1	(	(	PUNCT
ejpam-6847	527	2	ii	ii	NOUN
ejpam-6847	527	3	)	)	PUNCT
ejpam-6847	527	4	there	there	PRON
ejpam-6847	527	5	is	be	VERB
ejpam-6847	527	6	x0	x0	PROPN
ejpam-6847	527	7	∈	∈	PROPN
ejpam-6847	527	8	x	x	NOUN
ejpam-6847	527	9	,	,	PUNCT
ejpam-6847	527	10	such	such	ADJ
ejpam-6847	527	11	that	that	DET
ejpam-6847	527	12	αs(x0	αs(x0	NOUN
ejpam-6847	527	13	,	,	PUNCT
ejpam-6847	527	14	x0	x0	PROPN
ejpam-6847	527	15	,	,	PUNCT
ejpam-6847	527	16	tx0	tx0	PROPN
ejpam-6847	527	17	)	)	PUNCT
ejpam-6847	527	18	≥	≥	NOUN
ejpam-6847	527	19	1	1	NUM
ejpam-6847	527	20	,	,	PUNCT
ejpam-6847	527	21	νs(x0	νs(x0	PROPN
ejpam-6847	527	22	,	,	PUNCT
ejpam-6847	527	23	x0	x0	PROPN
ejpam-6847	527	24	,	,	PUNCT
ejpam-6847	527	25	tx0	tx0	NOUN
ejpam-6847	527	26	)	)	PUNCT
ejpam-6847	527	27	≤	≤	NOUN
ejpam-6847	527	28	1	1	NUM
ejpam-6847	527	29	.	.	PUNCT
ejpam-6847	528	1	(	(	PUNCT
ejpam-6847	528	2	iii	iii	NOUN
ejpam-6847	528	3	)	)	PUNCT
ejpam-6847	528	4	for	for	ADP
ejpam-6847	528	5	x0	x0	PROPN
ejpam-6847	528	6	∈	∈	PROPN
ejpam-6847	529	1	x	x	PRON
ejpam-6847	529	2	,	,	PUNCT
ejpam-6847	529	3	the	the	DET
ejpam-6847	529	4	sequence	sequence	NOUN
ejpam-6847	529	5	{	{	PUNCT
ejpam-6847	529	6	xn	xn	NUM
ejpam-6847	529	7	}	}	PUNCT
ejpam-6847	529	8	,	,	PUNCT
ejpam-6847	529	9	is	be	AUX
ejpam-6847	529	10	defined	define	VERB
ejpam-6847	529	11	by	by	ADP
ejpam-6847	529	12	xn	xn	PROPN
ejpam-6847	529	13	=	=	SYM
ejpam-6847	529	14	tnx0	tnx0	PROPN
ejpam-6847	529	15	,	,	PUNCT
ejpam-6847	529	16	and	and	CCONJ
ejpam-6847	529	17	the	the	DET
ejpam-6847	529	18	following	follow	VERB
ejpam-6847	529	19	inequality	inequality	NOUN
ejpam-6847	529	20	holds	hold	VERB
ejpam-6847	529	21	:	:	PUNCT
ejpam-6847	529	22	sup	sup	PROPN
ejpam-6847	529	23	m≥1	m≥1	PROPN
ejpam-6847	529	24	lim	lim	PROPN
ejpam-6847	529	25	n→+∞	n→+∞	PROPN
ejpam-6847	529	26	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	529	27	,	,	PUNCT
ejpam-6847	529	28	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	529	29	,	,	PUNCT
ejpam-6847	529	30	xn+2	xn+2	NUM
ejpam-6847	529	31	)	)	PUNCT
ejpam-6847	530	1	+	+	CCONJ
ejpam-6847	530	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	530	3	,	,	PUNCT
ejpam-6847	530	4	xn+2	xn+2	NUM
ejpam-6847	530	5	)	)	PUNCT
ejpam-6847	530	6	]	]	PUNCT
ejpam-6847	531	1	[	[	X
ejpam-6847	531	2	β(xn	β(xn	NOUN
ejpam-6847	531	3	,	,	PUNCT
ejpam-6847	531	4	xn+1	xn+1	NUM
ejpam-6847	531	5	)	)	PUNCT
ejpam-6847	531	6	+	+	CCONJ
ejpam-6847	531	7	µ(xn	µ(xn	PROPN
ejpam-6847	531	8	,	,	PUNCT
ejpam-6847	531	9	xn+1	xn+1	NUM
ejpam-6847	531	10	)	)	PUNCT
ejpam-6847	531	11	]	]	PUNCT
ejpam-6847	531	12	<	<	X
ejpam-6847	531	13	1	1	X
ejpam-6847	531	14	.	.	PUNCT
ejpam-6847	531	15	f.	f.	PROPN
ejpam-6847	531	16	m.	m.	PROPN
ejpam-6847	531	17	azmi	azmi	PROPN
ejpam-6847	531	18	,	,	PUNCT
ejpam-6847	531	19	a.	a.	PROPN
ejpam-6847	531	20	h.	h.	PROPN
ejpam-6847	531	21	ansari	ansari	PROPN
ejpam-6847	531	22	,	,	PUNCT
ejpam-6847	531	23	s.	s.	PROPN
ejpam-6847	531	24	h.	h.	PROPN
ejpam-6847	531	25	j.	j.	PROPN
ejpam-6847	531	26	petroudi	petroudi	PROPN
ejpam-6847	531	27	/	/	SYM
ejpam-6847	531	28	eur	eur	PROPN
ejpam-6847	531	29	.	.	PUNCT
ejpam-6847	532	1	j.	j.	PROPN
ejpam-6847	532	2	pure	pure	PROPN
ejpam-6847	532	3	appl	appl	PROPN
ejpam-6847	532	4	.	.	PROPN
ejpam-6847	532	5	math	math	PROPN
ejpam-6847	532	6	,	,	PUNCT
ejpam-6847	532	7	18	18	NUM
ejpam-6847	532	8	(	(	PUNCT
ejpam-6847	532	9	4	4	NUM
ejpam-6847	532	10	)	)	PUNCT
ejpam-6847	532	11	(	(	PUNCT
ejpam-6847	532	12	2025	2025	NUM
ejpam-6847	532	13	)	)	PUNCT
ejpam-6847	532	14	,	,	PUNCT
ejpam-6847	532	15	6847	6847	NUM
ejpam-6847	532	16	21	21	NUM
ejpam-6847	532	17	of	of	ADP
ejpam-6847	532	18	26	26	NUM
ejpam-6847	532	19	in	in	ADP
ejpam-6847	532	20	addition	addition	NOUN
ejpam-6847	532	21	,	,	PUNCT
ejpam-6847	532	22	for	for	ADP
ejpam-6847	532	23	every	every	DET
ejpam-6847	532	24	x	x	SYM
ejpam-6847	532	25	∈	∈	PROPN
ejpam-6847	532	26	x	x	NOUN
ejpam-6847	532	27	,	,	PUNCT
ejpam-6847	532	28	the	the	DET
ejpam-6847	532	29	following	follow	VERB
ejpam-6847	532	30	limits	limit	NOUN
ejpam-6847	532	31	exist	exist	VERB
ejpam-6847	532	32	and	and	CCONJ
ejpam-6847	532	33	are	be	AUX
ejpam-6847	532	34	finite	finite	ADJ
ejpam-6847	532	35	:	:	PUNCT
ejpam-6847	532	36	lim	lim	PROPN
ejpam-6847	532	37	n→+∞	n→+∞	PROPN
ejpam-6847	532	38	β(x	β(x	PROPN
ejpam-6847	532	39	,	,	PUNCT
ejpam-6847	532	40	xn	xn	PROPN
ejpam-6847	532	41	)	)	PUNCT
ejpam-6847	532	42	,	,	PUNCT
ejpam-6847	532	43	lim	lim	PROPN
ejpam-6847	532	44	n→+∞	n→+∞	VERB
ejpam-6847	532	45	µ(xn	µ(xn	PROPN
ejpam-6847	532	46	,	,	PUNCT
ejpam-6847	532	47	x	x	NOUN
ejpam-6847	532	48	)	)	PUNCT
ejpam-6847	532	49	and	and	CCONJ
ejpam-6847	532	50	lim	lim	PROPN
ejpam-6847	532	51	n→+∞	n→+∞	VERB
ejpam-6847	532	52	γ(xn	γ(xn	PROPN
ejpam-6847	532	53	,	,	PUNCT
ejpam-6847	532	54	x	x	NOUN
ejpam-6847	532	55	)	)	PUNCT
ejpam-6847	532	56	.	.	PUNCT
ejpam-6847	533	1	then	then	ADV
ejpam-6847	533	2	,	,	PUNCT
ejpam-6847	533	3	t	t	PROPN
ejpam-6847	533	4	has	have	VERB
ejpam-6847	533	5	a	a	DET
ejpam-6847	533	6	fixed	fix	VERB
ejpam-6847	533	7	point	point	NOUN
ejpam-6847	533	8	.	.	PUNCT
ejpam-6847	534	1	for	for	ADP
ejpam-6847	534	2	the	the	DET
ejpam-6847	534	3	uniqueness	uniqueness	NOUN
ejpam-6847	534	4	of	of	ADP
ejpam-6847	534	5	the	the	DET
ejpam-6847	534	6	fixed	fix	VERB
ejpam-6847	534	7	point	point	NOUN
ejpam-6847	534	8	,	,	PUNCT
ejpam-6847	534	9	assume	assume	VERB
ejpam-6847	534	10	both	both	DET
ejpam-6847	534	11	u	u	NOUN
ejpam-6847	534	12	,	,	PUNCT
ejpam-6847	534	13	and	and	CCONJ
ejpam-6847	534	14	v	v	NOUN
ejpam-6847	534	15	are	be	AUX
ejpam-6847	534	16	fixed	fix	VERB
ejpam-6847	534	17	points	point	NOUN
ejpam-6847	534	18	such	such	ADJ
ejpam-6847	534	19	that	that	PRON
ejpam-6847	534	20	αs(u	αs(u	NUM
ejpam-6847	534	21	,	,	PUNCT
ejpam-6847	534	22	u	u	NOUN
ejpam-6847	534	23	,	,	PUNCT
ejpam-6847	534	24	v	v	NOUN
ejpam-6847	534	25	)	)	PUNCT
ejpam-6847	534	26	≥	≥	NOUN
ejpam-6847	534	27	1	1	NUM
ejpam-6847	534	28	,	,	PUNCT
ejpam-6847	534	29	and	and	CCONJ
ejpam-6847	534	30	νs(u	νs(u	NUM
ejpam-6847	534	31	,	,	PUNCT
ejpam-6847	534	32	u	u	NOUN
ejpam-6847	534	33	,	,	PUNCT
ejpam-6847	534	34	v	v	NOUN
ejpam-6847	534	35	)	)	PUNCT
ejpam-6847	534	36	≤	≤	NUM
ejpam-6847	534	37	1	1	NUM
ejpam-6847	534	38	,	,	PUNCT
ejpam-6847	534	39	then	then	ADV
ejpam-6847	534	40	t	t	PROPN
ejpam-6847	534	41	has	have	VERB
ejpam-6847	534	42	a	a	DET
ejpam-6847	534	43	unique	unique	ADJ
ejpam-6847	534	44	fixed	fix	VERB
ejpam-6847	534	45	point	point	NOUN
ejpam-6847	534	46	in	in	ADP
ejpam-6847	534	47	x.	x.	NOUN
ejpam-6847	534	48	by	by	ADP
ejpam-6847	534	49	selecting	select	VERB
ejpam-6847	534	50	the	the	DET
ejpam-6847	534	51	pair	pair	NOUN
ejpam-6847	534	52	(	(	PUNCT
ejpam-6847	534	53	q	q	NOUN
ejpam-6847	534	54	,	,	PUNCT
ejpam-6847	534	55	h	h	NOUN
ejpam-6847	534	56	)	)	PUNCT
ejpam-6847	534	57	of	of	ADP
ejpam-6847	534	58	upper	upper	ADJ
ejpam-6847	534	59	class	class	NOUN
ejpam-6847	534	60	of	of	ADP
ejpam-6847	534	61	type	type	NOUN
ejpam-6847	534	62	i	i	PRON
ejpam-6847	534	63	,	,	PUNCT
ejpam-6847	534	64	where	where	SCONJ
ejpam-6847	534	65	h(x	h(x	PROPN
ejpam-6847	534	66	,	,	PUNCT
ejpam-6847	534	67	y	y	PROPN
ejpam-6847	534	68	)	)	PUNCT
ejpam-6847	534	69	=	=	SYM
ejpam-6847	535	1	(	(	PUNCT
ejpam-6847	535	2	x	x	SYM
ejpam-6847	535	3	+	+	SYM
ejpam-6847	535	4	l)y	l)y	ADJ
ejpam-6847	535	5	,	,	PUNCT
ejpam-6847	535	6	l	l	NOUN
ejpam-6847	535	7	>	>	X
ejpam-6847	535	8	0	0	NUM
ejpam-6847	535	9	,	,	PUNCT
ejpam-6847	535	10	and	and	CCONJ
ejpam-6847	535	11	q(s	q(s	PROPN
ejpam-6847	535	12	,	,	PUNCT
ejpam-6847	535	13	t	t	PROPN
ejpam-6847	535	14	)	)	PUNCT
ejpam-6847	535	15	=	=	PUNCT
ejpam-6847	536	1	(	(	PUNCT
ejpam-6847	536	2	1	1	NUM
ejpam-6847	536	3	+	+	X
ejpam-6847	536	4	l)st	l)st	PROPN
ejpam-6847	536	5	,	,	PUNCT
ejpam-6847	536	6	we	we	PRON
ejpam-6847	536	7	drive	drive	VERB
ejpam-6847	536	8	the	the	DET
ejpam-6847	536	9	following	follow	VERB
ejpam-6847	536	10	corollary	corollary	NOUN
ejpam-6847	536	11	from	from	ADP
ejpam-6847	536	12	theorem	theorem	ADJ
ejpam-6847	536	13	1	1	NUM
ejpam-6847	536	14	.	.	PUNCT
ejpam-6847	536	15	corollary	corollary	ADJ
ejpam-6847	536	16	4	4	NUM
ejpam-6847	536	17	.	.	PUNCT
ejpam-6847	537	1	let	let	VERB
ejpam-6847	537	2	(	(	PUNCT
ejpam-6847	537	3	x	x	NOUN
ejpam-6847	537	4	,	,	PUNCT
ejpam-6847	537	5	s	s	PART
ejpam-6847	537	6	)	)	PUNCT
ejpam-6847	537	7	be	be	AUX
ejpam-6847	537	8	a	a	DET
ejpam-6847	537	9	complete	complete	ADJ
ejpam-6847	537	10	t	t	NOUN
ejpam-6847	537	11	c	c	X
ejpam-6847	537	12	-	-	PUNCT
ejpam-6847	537	13	s	s	PROPN
ejpam-6847	537	14	-	-	PUNCT
ejpam-6847	537	15	mt	mt	NOUN
ejpam-6847	537	16	s	s	PROPN
ejpam-6847	537	17	,	,	PUNCT
ejpam-6847	537	18	where	where	SCONJ
ejpam-6847	537	19	,	,	PUNCT
ejpam-6847	537	20	x	x	SYM
ejpam-6847	537	21	6=	6=	ADP
ejpam-6847	537	22	∅.	∅.	ADV
ejpam-6847	537	23	let	let	VERB
ejpam-6847	537	24	(	(	PUNCT
ejpam-6847	537	25	τ	τ	PROPN
ejpam-6847	537	26	+	+	NUM
ejpam-6847	537	27	f	f	X
ejpam-6847	537	28	(	(	PUNCT
ejpam-6847	537	29	s(tx	s(tx	PROPN
ejpam-6847	537	30	,	,	PUNCT
ejpam-6847	537	31	ty	ty	INTJ
ejpam-6847	537	32	,	,	PUNCT
ejpam-6847	537	33	tz	tz	NOUN
ejpam-6847	537	34	)	)	PUNCT
ejpam-6847	537	35	)	)	PUNCT
ejpam-6847	538	1	+	+	CCONJ
ejpam-6847	538	2	l)αs(x	l)αs(x	NOUN
ejpam-6847	538	3	,	,	PUNCT
ejpam-6847	538	4	y	y	PROPN
ejpam-6847	538	5	,	,	PUNCT
ejpam-6847	538	6	z	z	NOUN
ejpam-6847	538	7	)	)	PUNCT
ejpam-6847	538	8	≤	≤	NOUN
ejpam-6847	538	9	(	(	PUNCT
ejpam-6847	538	10	1	1	NUM
ejpam-6847	538	11	+	+	CCONJ
ejpam-6847	538	12	l)νs(x	l)νs(x	PROPN
ejpam-6847	538	13	,	,	PUNCT
ejpam-6847	538	14	y	y	NOUN
ejpam-6847	538	15	,	,	PUNCT
ejpam-6847	538	16	z)f	z)f	X
ejpam-6847	538	17	(	(	PUNCT
ejpam-6847	538	18	s(x	s(x	PROPN
ejpam-6847	538	19	,	,	PUNCT
ejpam-6847	538	20	y	y	PROPN
ejpam-6847	538	21	,	,	PUNCT
ejpam-6847	538	22	z	z	NOUN
ejpam-6847	538	23	)	)	PUNCT
ejpam-6847	538	24	,	,	PUNCT
ejpam-6847	538	25	where	where	SCONJ
ejpam-6847	538	26	,	,	PUNCT
ejpam-6847	538	27	l	l	PROPN
ejpam-6847	538	28	>	>	X
ejpam-6847	538	29	0	0	X
ejpam-6847	538	30	.	.	PUNCT
ejpam-6847	538	31	assume	assume	VERB
ejpam-6847	538	32	the	the	DET
ejpam-6847	538	33	following	follow	VERB
ejpam-6847	538	34	conditions	condition	NOUN
ejpam-6847	538	35	hold	hold	VERB
ejpam-6847	538	36	:	:	PUNCT
ejpam-6847	538	37	(	(	PUNCT
ejpam-6847	538	38	i	i	NOUN
ejpam-6847	538	39	)	)	PUNCT
ejpam-6847	538	40	t	t	PROPN
ejpam-6847	538	41	is	be	AUX
ejpam-6847	538	42	αs	αs	ADJ
ejpam-6847	538	43	-	-	ADJ
ejpam-6847	538	44	admissible	admissible	ADJ
ejpam-6847	538	45	and	and	CCONJ
ejpam-6847	538	46	νs	νs	NOUN
ejpam-6847	538	47	-	-	PUNCT
ejpam-6847	538	48	subadmissible	subadmissible	ADJ
ejpam-6847	538	49	mapping	mapping	NOUN
ejpam-6847	538	50	.	.	PUNCT
ejpam-6847	539	1	(	(	PUNCT
ejpam-6847	539	2	ii	ii	NOUN
ejpam-6847	539	3	)	)	PUNCT
ejpam-6847	539	4	there	there	PRON
ejpam-6847	539	5	is	be	VERB
ejpam-6847	539	6	x0	x0	PROPN
ejpam-6847	539	7	∈	∈	PROPN
ejpam-6847	539	8	x	x	NOUN
ejpam-6847	539	9	,	,	PUNCT
ejpam-6847	539	10	such	such	ADJ
ejpam-6847	539	11	that	that	DET
ejpam-6847	539	12	αs(x0	αs(x0	NOUN
ejpam-6847	539	13	,	,	PUNCT
ejpam-6847	539	14	x0	x0	PROPN
ejpam-6847	539	15	,	,	PUNCT
ejpam-6847	539	16	tx0	tx0	PROPN
ejpam-6847	539	17	)	)	PUNCT
ejpam-6847	539	18	≥	≥	NOUN
ejpam-6847	539	19	1	1	NUM
ejpam-6847	539	20	,	,	PUNCT
ejpam-6847	539	21	νs(x0	νs(x0	PROPN
ejpam-6847	539	22	,	,	PUNCT
ejpam-6847	539	23	x0	x0	PROPN
ejpam-6847	539	24	,	,	PUNCT
ejpam-6847	539	25	tx0	tx0	NOUN
ejpam-6847	539	26	)	)	PUNCT
ejpam-6847	539	27	≤	≤	NOUN
ejpam-6847	539	28	1	1	NUM
ejpam-6847	539	29	.	.	PUNCT
ejpam-6847	540	1	(	(	PUNCT
ejpam-6847	540	2	iii	iii	NOUN
ejpam-6847	540	3	)	)	PUNCT
ejpam-6847	540	4	for	for	ADP
ejpam-6847	540	5	x0	x0	PROPN
ejpam-6847	540	6	∈	∈	PROPN
ejpam-6847	541	1	x	x	PRON
ejpam-6847	541	2	,	,	PUNCT
ejpam-6847	541	3	the	the	DET
ejpam-6847	541	4	sequence	sequence	NOUN
ejpam-6847	541	5	{	{	PUNCT
ejpam-6847	541	6	xn	xn	NUM
ejpam-6847	541	7	}	}	PUNCT
ejpam-6847	541	8	,	,	PUNCT
ejpam-6847	541	9	is	be	AUX
ejpam-6847	541	10	defined	define	VERB
ejpam-6847	541	11	by	by	ADP
ejpam-6847	541	12	xn	xn	PROPN
ejpam-6847	541	13	=	=	SYM
ejpam-6847	541	14	tnx0	tnx0	PROPN
ejpam-6847	541	15	,	,	PUNCT
ejpam-6847	541	16	and	and	CCONJ
ejpam-6847	541	17	the	the	DET
ejpam-6847	541	18	following	follow	VERB
ejpam-6847	541	19	inequality	inequality	NOUN
ejpam-6847	541	20	holds	hold	VERB
ejpam-6847	541	21	:	:	PUNCT
ejpam-6847	541	22	sup	sup	PROPN
ejpam-6847	541	23	m≥1	m≥1	PROPN
ejpam-6847	541	24	lim	lim	PROPN
ejpam-6847	541	25	n→+∞	n→+∞	PROPN
ejpam-6847	541	26	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	541	27	,	,	PUNCT
ejpam-6847	541	28	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	541	29	,	,	PUNCT
ejpam-6847	541	30	xn+2	xn+2	NUM
ejpam-6847	541	31	)	)	PUNCT
ejpam-6847	542	1	+	+	CCONJ
ejpam-6847	542	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	542	3	,	,	PUNCT
ejpam-6847	542	4	xn+2	xn+2	NUM
ejpam-6847	542	5	)	)	PUNCT
ejpam-6847	542	6	]	]	PUNCT
ejpam-6847	543	1	[	[	X
ejpam-6847	543	2	β(xn	β(xn	NOUN
ejpam-6847	543	3	,	,	PUNCT
ejpam-6847	543	4	xn+1	xn+1	NUM
ejpam-6847	543	5	)	)	PUNCT
ejpam-6847	543	6	+	+	CCONJ
ejpam-6847	543	7	µ(xn	µ(xn	PROPN
ejpam-6847	543	8	,	,	PUNCT
ejpam-6847	543	9	xn+1	xn+1	NUM
ejpam-6847	543	10	)	)	PUNCT
ejpam-6847	543	11	]	]	PUNCT
ejpam-6847	543	12	<	<	X
ejpam-6847	543	13	1	1	X
ejpam-6847	543	14	.	.	PUNCT
ejpam-6847	544	1	in	in	ADP
ejpam-6847	544	2	addition	addition	NOUN
ejpam-6847	544	3	,	,	PUNCT
ejpam-6847	544	4	for	for	SCONJ
ejpam-6847	544	5	every	every	DET
ejpam-6847	544	6	x	x	SYM
ejpam-6847	544	7	∈	∈	PROPN
ejpam-6847	544	8	x	x	NOUN
ejpam-6847	544	9	,	,	PUNCT
ejpam-6847	544	10	the	the	DET
ejpam-6847	544	11	following	follow	VERB
ejpam-6847	544	12	limits	limit	NOUN
ejpam-6847	544	13	exist	exist	VERB
ejpam-6847	544	14	and	and	CCONJ
ejpam-6847	544	15	are	be	AUX
ejpam-6847	544	16	finite	finite	ADJ
ejpam-6847	544	17	:	:	PUNCT
ejpam-6847	544	18	lim	lim	PROPN
ejpam-6847	544	19	n→+∞	n→+∞	PROPN
ejpam-6847	544	20	β(x	β(x	PROPN
ejpam-6847	544	21	,	,	PUNCT
ejpam-6847	544	22	xn	xn	PROPN
ejpam-6847	544	23	)	)	PUNCT
ejpam-6847	544	24	,	,	PUNCT
ejpam-6847	544	25	lim	lim	PROPN
ejpam-6847	544	26	n→+∞	n→+∞	VERB
ejpam-6847	544	27	µ(xn	µ(xn	PROPN
ejpam-6847	544	28	,	,	PUNCT
ejpam-6847	544	29	x	x	NOUN
ejpam-6847	544	30	)	)	PUNCT
ejpam-6847	544	31	and	and	CCONJ
ejpam-6847	544	32	lim	lim	PROPN
ejpam-6847	544	33	n→+∞	n→+∞	VERB
ejpam-6847	544	34	γ(xn	γ(xn	PROPN
ejpam-6847	544	35	,	,	PUNCT
ejpam-6847	544	36	x	x	NOUN
ejpam-6847	544	37	)	)	PUNCT
ejpam-6847	544	38	.	.	PUNCT
ejpam-6847	545	1	then	then	ADV
ejpam-6847	545	2	,	,	PUNCT
ejpam-6847	545	3	t	t	PROPN
ejpam-6847	545	4	has	have	VERB
ejpam-6847	545	5	a	a	DET
ejpam-6847	545	6	fixed	fix	VERB
ejpam-6847	545	7	point	point	NOUN
ejpam-6847	545	8	.	.	PUNCT
ejpam-6847	546	1	for	for	ADP
ejpam-6847	546	2	the	the	DET
ejpam-6847	546	3	uniqueness	uniqueness	NOUN
ejpam-6847	546	4	of	of	ADP
ejpam-6847	546	5	the	the	DET
ejpam-6847	546	6	fixed	fix	VERB
ejpam-6847	546	7	point	point	NOUN
ejpam-6847	546	8	,	,	PUNCT
ejpam-6847	546	9	assume	assume	VERB
ejpam-6847	546	10	both	both	DET
ejpam-6847	546	11	u	u	NOUN
ejpam-6847	546	12	,	,	PUNCT
ejpam-6847	546	13	and	and	CCONJ
ejpam-6847	546	14	v	v	NOUN
ejpam-6847	546	15	are	be	AUX
ejpam-6847	546	16	fixed	fix	VERB
ejpam-6847	546	17	points	point	NOUN
ejpam-6847	546	18	such	such	ADJ
ejpam-6847	546	19	that	that	PRON
ejpam-6847	546	20	αs(u	αs(u	NUM
ejpam-6847	546	21	,	,	PUNCT
ejpam-6847	546	22	u	u	NOUN
ejpam-6847	546	23	,	,	PUNCT
ejpam-6847	546	24	v	v	NOUN
ejpam-6847	546	25	)	)	PUNCT
ejpam-6847	546	26	≥	≥	NOUN
ejpam-6847	546	27	1	1	NUM
ejpam-6847	546	28	,	,	PUNCT
ejpam-6847	546	29	and	and	CCONJ
ejpam-6847	546	30	νs(u	νs(u	NUM
ejpam-6847	546	31	,	,	PUNCT
ejpam-6847	546	32	u	u	NOUN
ejpam-6847	546	33	,	,	PUNCT
ejpam-6847	546	34	v	v	NOUN
ejpam-6847	546	35	)	)	PUNCT
ejpam-6847	546	36	≤	≤	NUM
ejpam-6847	546	37	1	1	NUM
ejpam-6847	546	38	,	,	PUNCT
ejpam-6847	546	39	then	then	ADV
ejpam-6847	546	40	t	t	PROPN
ejpam-6847	546	41	has	have	VERB
ejpam-6847	546	42	a	a	DET
ejpam-6847	546	43	unique	unique	ADJ
ejpam-6847	546	44	fixed	fix	VERB
ejpam-6847	546	45	point	point	NOUN
ejpam-6847	546	46	in	in	ADP
ejpam-6847	546	47	x.	x.	NOUN
ejpam-6847	546	48	by	by	ADP
ejpam-6847	546	49	selecting	select	VERB
ejpam-6847	546	50	the	the	DET
ejpam-6847	546	51	pair	pair	NOUN
ejpam-6847	546	52	(	(	PUNCT
ejpam-6847	546	53	q	q	NOUN
ejpam-6847	546	54	,	,	PUNCT
ejpam-6847	546	55	h	h	NOUN
ejpam-6847	546	56	)	)	PUNCT
ejpam-6847	546	57	of	of	ADP
ejpam-6847	546	58	upper	upper	ADJ
ejpam-6847	546	59	class	class	NOUN
ejpam-6847	546	60	of	of	ADP
ejpam-6847	546	61	type	type	NOUN
ejpam-6847	546	62	i	i	PRON
ejpam-6847	546	63	,	,	PUNCT
ejpam-6847	547	1	where	where	SCONJ
ejpam-6847	547	2	h(x	h(x	PROPN
ejpam-6847	547	3	,	,	PUNCT
ejpam-6847	547	4	y	y	PROPN
ejpam-6847	547	5	)	)	PUNCT
ejpam-6847	547	6	=	=	SYM
ejpam-6847	547	7	mx+n	mx+n	NOUN
ejpam-6847	547	8	m+n	m+n	PROPN
ejpam-6847	547	9	y	y	PROPN
ejpam-6847	547	10	,	,	PUNCT
ejpam-6847	547	11	withm	withm	PROPN
ejpam-6847	547	12	,	,	PUNCT
ejpam-6847	547	13	n	n	PROPN
ejpam-6847	547	14	∈	∈	PROPN
ejpam-6847	547	15	n	n	CCONJ
ejpam-6847	547	16	,	,	PUNCT
ejpam-6847	547	17	and	and	CCONJ
ejpam-6847	547	18	q(s	q(s	PROPN
ejpam-6847	547	19	,	,	PUNCT
ejpam-6847	547	20	t	t	PROPN
ejpam-6847	547	21	)	)	PUNCT
ejpam-6847	547	22	=	=	SYM
ejpam-6847	547	23	st	st	PROPN
ejpam-6847	547	24	,	,	PUNCT
ejpam-6847	547	25	we	we	PRON
ejpam-6847	547	26	drive	drive	VERB
ejpam-6847	547	27	the	the	DET
ejpam-6847	547	28	following	follow	VERB
ejpam-6847	547	29	corollary	corollary	NOUN
ejpam-6847	547	30	from	from	ADP
ejpam-6847	547	31	theorem	theorem	ADJ
ejpam-6847	547	32	1	1	NUM
ejpam-6847	547	33	.	.	PUNCT
ejpam-6847	547	34	f.	f.	PROPN
ejpam-6847	547	35	m.	m.	PROPN
ejpam-6847	547	36	azmi	azmi	PROPN
ejpam-6847	547	37	,	,	PUNCT
ejpam-6847	547	38	a.	a.	PROPN
ejpam-6847	547	39	h.	h.	PROPN
ejpam-6847	547	40	ansari	ansari	PROPN
ejpam-6847	547	41	,	,	PUNCT
ejpam-6847	547	42	s.	s.	PROPN
ejpam-6847	547	43	h.	h.	PROPN
ejpam-6847	547	44	j.	j.	PROPN
ejpam-6847	547	45	petroudi	petroudi	PROPN
ejpam-6847	547	46	/	/	SYM
ejpam-6847	547	47	eur	eur	PROPN
ejpam-6847	547	48	.	.	PUNCT
ejpam-6847	548	1	j.	j.	PROPN
ejpam-6847	548	2	pure	pure	PROPN
ejpam-6847	548	3	appl	appl	PROPN
ejpam-6847	548	4	.	.	PROPN
ejpam-6847	548	5	math	math	PROPN
ejpam-6847	548	6	,	,	PUNCT
ejpam-6847	548	7	18	18	NUM
ejpam-6847	548	8	(	(	PUNCT
ejpam-6847	548	9	4	4	NUM
ejpam-6847	548	10	)	)	PUNCT
ejpam-6847	548	11	(	(	PUNCT
ejpam-6847	548	12	2025	2025	NUM
ejpam-6847	548	13	)	)	PUNCT
ejpam-6847	548	14	,	,	PUNCT
ejpam-6847	548	15	6847	6847	NUM
ejpam-6847	548	16	22	22	NUM
ejpam-6847	548	17	of	of	ADP
ejpam-6847	548	18	26	26	NUM
ejpam-6847	548	19	corollary	corollary	ADJ
ejpam-6847	548	20	5	5	NUM
ejpam-6847	548	21	.	.	PUNCT
ejpam-6847	549	1	let	let	VERB
ejpam-6847	549	2	(	(	PUNCT
ejpam-6847	549	3	x	x	NOUN
ejpam-6847	549	4	,	,	PUNCT
ejpam-6847	549	5	s	s	PART
ejpam-6847	549	6	)	)	PUNCT
ejpam-6847	549	7	be	be	AUX
ejpam-6847	549	8	a	a	DET
ejpam-6847	549	9	complete	complete	ADJ
ejpam-6847	549	10	t	t	NOUN
ejpam-6847	549	11	c	c	X
ejpam-6847	549	12	-	-	PUNCT
ejpam-6847	549	13	s	s	PROPN
ejpam-6847	549	14	-	-	PUNCT
ejpam-6847	549	15	mt	mt	NOUN
ejpam-6847	549	16	s	s	PROPN
ejpam-6847	549	17	,	,	PUNCT
ejpam-6847	549	18	where	where	SCONJ
ejpam-6847	549	19	x	x	PUNCT
ejpam-6847	549	20	6=	6=	AUX
ejpam-6847	549	21	∅.	∅.	ADV
ejpam-6847	549	22	let	let	VERB
ejpam-6847	549	23	mαs(x	mαs(x	PROPN
ejpam-6847	549	24	,	,	PUNCT
ejpam-6847	549	25	y	y	PROPN
ejpam-6847	549	26	,	,	PUNCT
ejpam-6847	549	27	z	z	NOUN
ejpam-6847	549	28	)	)	PUNCT
ejpam-6847	550	1	+	+	CCONJ
ejpam-6847	550	2	n	n	CCONJ
ejpam-6847	550	3	m+	m+	NUM
ejpam-6847	550	4	n	n	PROPN
ejpam-6847	550	5	(	(	PUNCT
ejpam-6847	550	6	τ	τ	PROPN
ejpam-6847	551	1	+	+	NUM
ejpam-6847	551	2	f	f	X
ejpam-6847	551	3	(	(	PUNCT
ejpam-6847	551	4	s(tx	s(tx	PROPN
ejpam-6847	551	5	,	,	PUNCT
ejpam-6847	551	6	ty	ty	INTJ
ejpam-6847	551	7	,	,	PUNCT
ejpam-6847	551	8	tz	tz	NOUN
ejpam-6847	551	9	)	)	PUNCT
ejpam-6847	551	10	)	)	PUNCT
ejpam-6847	551	11	≤	≤	NOUN
ejpam-6847	551	12	νs(x	νs(x	NOUN
ejpam-6847	551	13	,	,	PUNCT
ejpam-6847	551	14	y	y	PROPN
ejpam-6847	551	15	,	,	PUNCT
ejpam-6847	551	16	z)f	z)f	X
ejpam-6847	551	17	(	(	PUNCT
ejpam-6847	551	18	s(x	s(x	PROPN
ejpam-6847	551	19	,	,	PUNCT
ejpam-6847	551	20	y	y	PROPN
ejpam-6847	551	21	,	,	PUNCT
ejpam-6847	551	22	z	z	NOUN
ejpam-6847	551	23	)	)	PUNCT
ejpam-6847	551	24	.	.	PUNCT
ejpam-6847	552	1	where	where	SCONJ
ejpam-6847	552	2	m	m	VERB
ejpam-6847	552	3	∈	∈	PROPN
ejpam-6847	552	4	n	n	CCONJ
ejpam-6847	552	5	,	,	PUNCT
ejpam-6847	552	6	n	n	PROPN
ejpam-6847	552	7	∈	∈	PROPN
ejpam-6847	552	8	n	n	NOUN
ejpam-6847	552	9	∪	∪	X
ejpam-6847	552	10	{	{	PUNCT
ejpam-6847	552	11	0}ȧssume	0}ȧssume	NOUN
ejpam-6847	552	12	the	the	DET
ejpam-6847	552	13	following	follow	VERB
ejpam-6847	552	14	conditions	condition	NOUN
ejpam-6847	552	15	hold	hold	VERB
ejpam-6847	552	16	:	:	PUNCT
ejpam-6847	552	17	(	(	PUNCT
ejpam-6847	552	18	i	i	NOUN
ejpam-6847	552	19	)	)	PUNCT
ejpam-6847	552	20	t	t	PROPN
ejpam-6847	552	21	is	be	AUX
ejpam-6847	552	22	αs	αs	ADJ
ejpam-6847	552	23	-	-	ADJ
ejpam-6847	552	24	admissible	admissible	ADJ
ejpam-6847	552	25	and	and	CCONJ
ejpam-6847	552	26	νs	νs	NOUN
ejpam-6847	552	27	-	-	PUNCT
ejpam-6847	552	28	subadmissible	subadmissible	ADJ
ejpam-6847	552	29	mapping	mapping	NOUN
ejpam-6847	552	30	.	.	PUNCT
ejpam-6847	553	1	(	(	PUNCT
ejpam-6847	553	2	ii	ii	NOUN
ejpam-6847	553	3	)	)	PUNCT
ejpam-6847	553	4	there	there	PRON
ejpam-6847	553	5	is	be	VERB
ejpam-6847	553	6	x0	x0	PROPN
ejpam-6847	553	7	∈	∈	PROPN
ejpam-6847	553	8	x	x	NOUN
ejpam-6847	553	9	,	,	PUNCT
ejpam-6847	553	10	such	such	ADJ
ejpam-6847	553	11	that	that	DET
ejpam-6847	553	12	αs(x0	αs(x0	NOUN
ejpam-6847	553	13	,	,	PUNCT
ejpam-6847	553	14	x0	x0	PROPN
ejpam-6847	553	15	,	,	PUNCT
ejpam-6847	553	16	tx0	tx0	PROPN
ejpam-6847	553	17	)	)	PUNCT
ejpam-6847	553	18	≥	≥	NOUN
ejpam-6847	553	19	1	1	NUM
ejpam-6847	553	20	,	,	PUNCT
ejpam-6847	553	21	νs(x0	νs(x0	PROPN
ejpam-6847	553	22	,	,	PUNCT
ejpam-6847	553	23	x0	x0	PROPN
ejpam-6847	553	24	,	,	PUNCT
ejpam-6847	553	25	tx0	tx0	NOUN
ejpam-6847	553	26	)	)	PUNCT
ejpam-6847	553	27	≤	≤	NOUN
ejpam-6847	553	28	1	1	NUM
ejpam-6847	553	29	.	.	PUNCT
ejpam-6847	554	1	(	(	PUNCT
ejpam-6847	554	2	iii	iii	NOUN
ejpam-6847	554	3	)	)	PUNCT
ejpam-6847	554	4	for	for	ADP
ejpam-6847	554	5	x0	x0	PROPN
ejpam-6847	554	6	∈	∈	PROPN
ejpam-6847	555	1	x	x	PRON
ejpam-6847	555	2	,	,	PUNCT
ejpam-6847	555	3	the	the	DET
ejpam-6847	555	4	sequence	sequence	NOUN
ejpam-6847	555	5	{	{	PUNCT
ejpam-6847	555	6	xn	xn	NUM
ejpam-6847	555	7	}	}	PUNCT
ejpam-6847	555	8	,	,	PUNCT
ejpam-6847	555	9	is	be	AUX
ejpam-6847	555	10	defined	define	VERB
ejpam-6847	555	11	by	by	ADP
ejpam-6847	555	12	xn	xn	PROPN
ejpam-6847	555	13	=	=	SYM
ejpam-6847	555	14	tnx0	tnx0	PROPN
ejpam-6847	555	15	,	,	PUNCT
ejpam-6847	555	16	and	and	CCONJ
ejpam-6847	555	17	the	the	DET
ejpam-6847	555	18	following	follow	VERB
ejpam-6847	555	19	inequality	inequality	NOUN
ejpam-6847	555	20	holds	hold	VERB
ejpam-6847	555	21	:	:	PUNCT
ejpam-6847	555	22	sup	sup	PROPN
ejpam-6847	555	23	m≥1	m≥1	PROPN
ejpam-6847	555	24	lim	lim	PROPN
ejpam-6847	555	25	n→+∞	n→+∞	PROPN
ejpam-6847	555	26	γ(xn+1	γ(xn+1	PROPN
ejpam-6847	555	27	,	,	PUNCT
ejpam-6847	555	28	xm)[β(xn+1	xm)[β(xn+1	PROPN
ejpam-6847	555	29	,	,	PUNCT
ejpam-6847	555	30	xn+2	xn+2	NUM
ejpam-6847	555	31	)	)	PUNCT
ejpam-6847	556	1	+	+	CCONJ
ejpam-6847	556	2	µ(xn+1	µ(xn+1	ADJ
ejpam-6847	556	3	,	,	PUNCT
ejpam-6847	556	4	xn+2	xn+2	NUM
ejpam-6847	556	5	)	)	PUNCT
ejpam-6847	556	6	]	]	PUNCT
ejpam-6847	557	1	[	[	X
ejpam-6847	557	2	β(xn	β(xn	NOUN
ejpam-6847	557	3	,	,	PUNCT
ejpam-6847	557	4	xn+1	xn+1	NUM
ejpam-6847	557	5	)	)	PUNCT
ejpam-6847	557	6	+	+	CCONJ
ejpam-6847	557	7	µ(xn	µ(xn	PROPN
ejpam-6847	557	8	,	,	PUNCT
ejpam-6847	557	9	xn+1	xn+1	NUM
ejpam-6847	557	10	)	)	PUNCT
ejpam-6847	557	11	]	]	PUNCT
ejpam-6847	557	12	<	<	X
ejpam-6847	557	13	1	1	X
ejpam-6847	557	14	.	.	PUNCT
ejpam-6847	558	1	in	in	ADP
ejpam-6847	558	2	addition	addition	NOUN
ejpam-6847	558	3	,	,	PUNCT
ejpam-6847	558	4	for	for	SCONJ
ejpam-6847	558	5	every	every	DET
ejpam-6847	558	6	x	x	SYM
ejpam-6847	558	7	∈	∈	PROPN
ejpam-6847	558	8	x	x	NOUN
ejpam-6847	558	9	,	,	PUNCT
ejpam-6847	558	10	the	the	DET
ejpam-6847	558	11	following	follow	VERB
ejpam-6847	558	12	limits	limit	NOUN
ejpam-6847	558	13	exist	exist	VERB
ejpam-6847	558	14	and	and	CCONJ
ejpam-6847	558	15	are	be	AUX
ejpam-6847	558	16	finite	finite	ADJ
ejpam-6847	558	17	:	:	PUNCT
ejpam-6847	558	18	lim	lim	PROPN
ejpam-6847	558	19	n→+∞	n→+∞	PROPN
ejpam-6847	558	20	β(x	β(x	PROPN
ejpam-6847	558	21	,	,	PUNCT
ejpam-6847	558	22	xn	xn	PROPN
ejpam-6847	558	23	)	)	PUNCT
ejpam-6847	558	24	,	,	PUNCT
ejpam-6847	558	25	lim	lim	PROPN
ejpam-6847	558	26	n→+∞	n→+∞	VERB
ejpam-6847	558	27	µ(xn	µ(xn	PROPN
ejpam-6847	558	28	,	,	PUNCT
ejpam-6847	558	29	x	x	NOUN
ejpam-6847	558	30	)	)	PUNCT
ejpam-6847	558	31	and	and	CCONJ
ejpam-6847	558	32	lim	lim	PROPN
ejpam-6847	558	33	n→+∞	n→+∞	VERB
ejpam-6847	558	34	γ(xn	γ(xn	PROPN
ejpam-6847	558	35	,	,	PUNCT
ejpam-6847	558	36	x	x	NOUN
ejpam-6847	558	37	)	)	PUNCT
ejpam-6847	558	38	.	.	PUNCT
ejpam-6847	559	1	then	then	ADV
ejpam-6847	559	2	,	,	PUNCT
ejpam-6847	559	3	t	t	PROPN
ejpam-6847	559	4	has	have	VERB
ejpam-6847	559	5	a	a	DET
ejpam-6847	559	6	fixed	fix	VERB
ejpam-6847	559	7	point	point	NOUN
ejpam-6847	559	8	.	.	PUNCT
ejpam-6847	560	1	for	for	ADP
ejpam-6847	560	2	the	the	DET
ejpam-6847	560	3	uniqueness	uniqueness	NOUN
ejpam-6847	560	4	of	of	ADP
ejpam-6847	560	5	the	the	DET
ejpam-6847	560	6	fixed	fix	VERB
ejpam-6847	560	7	point	point	NOUN
ejpam-6847	560	8	,	,	PUNCT
ejpam-6847	560	9	assume	assume	VERB
ejpam-6847	560	10	both	both	DET
ejpam-6847	560	11	u	u	NOUN
ejpam-6847	560	12	,	,	PUNCT
ejpam-6847	560	13	and	and	CCONJ
ejpam-6847	560	14	v	v	NOUN
ejpam-6847	560	15	are	be	AUX
ejpam-6847	560	16	fixed	fix	VERB
ejpam-6847	560	17	points	point	NOUN
ejpam-6847	560	18	such	such	ADJ
ejpam-6847	560	19	that	that	PRON
ejpam-6847	560	20	αs(u	αs(u	NUM
ejpam-6847	560	21	,	,	PUNCT
ejpam-6847	560	22	u	u	NOUN
ejpam-6847	560	23	,	,	PUNCT
ejpam-6847	560	24	v	v	NOUN
ejpam-6847	560	25	)	)	PUNCT
ejpam-6847	560	26	≥	≥	NOUN
ejpam-6847	560	27	1	1	NUM
ejpam-6847	560	28	,	,	PUNCT
ejpam-6847	560	29	and	and	CCONJ
ejpam-6847	560	30	νs(u	νs(u	NUM
ejpam-6847	560	31	,	,	PUNCT
ejpam-6847	560	32	u	u	NOUN
ejpam-6847	560	33	,	,	PUNCT
ejpam-6847	560	34	v	v	NOUN
ejpam-6847	560	35	)	)	PUNCT
ejpam-6847	560	36	≤	≤	NUM
ejpam-6847	560	37	1	1	NUM
ejpam-6847	560	38	,	,	PUNCT
ejpam-6847	560	39	then	then	ADV
ejpam-6847	560	40	t	t	PROPN
ejpam-6847	560	41	has	have	VERB
ejpam-6847	560	42	a	a	DET
ejpam-6847	560	43	unique	unique	ADJ
ejpam-6847	560	44	fixed	fix	VERB
ejpam-6847	560	45	point	point	NOUN
ejpam-6847	560	46	in	in	ADP
ejpam-6847	560	47	x.	x.	NOUN
ejpam-6847	560	48	remark	remark	PROPN
ejpam-6847	560	49	6	6	NUM
ejpam-6847	560	50	.	.	PUNCT
ejpam-6847	561	1	it	it	PRON
ejpam-6847	561	2	is	be	AUX
ejpam-6847	561	3	important	important	ADJ
ejpam-6847	561	4	to	to	PART
ejpam-6847	561	5	observe	observe	VERB
ejpam-6847	561	6	that	that	SCONJ
ejpam-6847	561	7	by	by	ADP
ejpam-6847	561	8	selecting	select	VERB
ejpam-6847	561	9	n	n	NOUN
ejpam-6847	561	10	=	=	SYM
ejpam-6847	561	11	0	0	NUM
ejpam-6847	561	12	in	in	ADP
ejpam-6847	561	13	corollary	corollary	ADJ
ejpam-6847	561	14	5	5	NUM
ejpam-6847	561	15	,	,	PUNCT
ejpam-6847	561	16	we	we	PRON
ejpam-6847	561	17	obtain	obtain	VERB
ejpam-6847	561	18	corollary	corollary	ADJ
ejpam-6847	561	19	2	2	NUM
ejpam-6847	561	20	.	.	NOUN
ejpam-6847	561	21	5	5	NUM
ejpam-6847	561	22	.	.	X
ejpam-6847	561	23	application	application	NOUN
ejpam-6847	561	24	this	this	DET
ejpam-6847	561	25	section	section	NOUN
ejpam-6847	561	26	demonstrates	demonstrate	VERB
ejpam-6847	561	27	the	the	DET
ejpam-6847	561	28	application	application	NOUN
ejpam-6847	561	29	of	of	ADP
ejpam-6847	561	30	the	the	DET
ejpam-6847	561	31	main	main	ADJ
ejpam-6847	561	32	theorem	theorem	NOUN
ejpam-6847	561	33	presented	present	VERB
ejpam-6847	561	34	earlier	early	ADV
ejpam-6847	561	35	,	,	PUNCT
ejpam-6847	561	36	with	with	ADP
ejpam-6847	561	37	a	a	DET
ejpam-6847	561	38	particular	particular	ADJ
ejpam-6847	561	39	focus	focus	NOUN
ejpam-6847	561	40	on	on	ADP
ejpam-6847	561	41	theorem	theorem	NOUN
ejpam-6847	561	42	1	1	NUM
ejpam-6847	561	43	,	,	PUNCT
ejpam-6847	561	44	which	which	PRON
ejpam-6847	561	45	plays	play	VERB
ejpam-6847	561	46	a	a	DET
ejpam-6847	561	47	crucial	crucial	ADJ
ejpam-6847	561	48	role	role	NOUN
ejpam-6847	561	49	in	in	ADP
ejpam-6847	561	50	establishing	establish	VERB
ejpam-6847	561	51	the	the	DET
ejpam-6847	561	52	existence	existence	NOUN
ejpam-6847	561	53	of	of	ADP
ejpam-6847	561	54	a	a	DET
ejpam-6847	561	55	unique	unique	ADJ
ejpam-6847	561	56	real	real	ADJ
ejpam-6847	561	57	solution	solution	NOUN
ejpam-6847	561	58	for	for	ADP
ejpam-6847	561	59	an	an	DET
ejpam-6847	561	60	mth	mth	NOUN
ejpam-6847	561	61	-	-	PUNCT
ejpam-6847	561	62	degree	degree	NOUN
ejpam-6847	561	63	polynomial	polynomial	NOUN
ejpam-6847	561	64	.	.	PUNCT
ejpam-6847	562	1	while	while	SCONJ
ejpam-6847	562	2	various	various	ADJ
ejpam-6847	562	3	approaches	approach	NOUN
ejpam-6847	562	4	exist	exist	VERB
ejpam-6847	562	5	for	for	ADP
ejpam-6847	562	6	solving	solve	VERB
ejpam-6847	562	7	root	root	NOUN
ejpam-6847	562	8	-	-	PUNCT
ejpam-6847	562	9	finding	find	VERB
ejpam-6847	562	10	problems	problem	NOUN
ejpam-6847	562	11	—	—	PUNCT
ejpam-6847	562	12	especially	especially	ADV
ejpam-6847	562	13	numerical	numerical	ADJ
ejpam-6847	562	14	techniques	technique	NOUN
ejpam-6847	562	15	—	—	PUNCT
ejpam-6847	562	16	the	the	DET
ejpam-6847	562	17	use	use	NOUN
ejpam-6847	562	18	of	of	ADP
ejpam-6847	562	19	fixed	fix	VERB
ejpam-6847	562	20	point	point	NOUN
ejpam-6847	562	21	theory	theory	NOUN
ejpam-6847	562	22	,	,	PUNCT
ejpam-6847	562	23	as	as	SCONJ
ejpam-6847	562	24	outlined	outline	VERB
ejpam-6847	562	25	below	below	ADV
ejpam-6847	562	26	,	,	PUNCT
ejpam-6847	562	27	provides	provide	VERB
ejpam-6847	562	28	a	a	DET
ejpam-6847	562	29	clear	clear	ADJ
ejpam-6847	562	30	and	and	CCONJ
ejpam-6847	562	31	effective	effective	ADJ
ejpam-6847	562	32	alternative	alternative	NOUN
ejpam-6847	562	33	.	.	PUNCT
ejpam-6847	563	1	we	we	PRON
ejpam-6847	563	2	begin	begin	VERB
ejpam-6847	563	3	with	with	ADP
ejpam-6847	563	4	the	the	DET
ejpam-6847	563	5	following	follow	VERB
ejpam-6847	563	6	theorem	theorem	NOUN
ejpam-6847	563	7	.	.	PUNCT
ejpam-6847	564	1	the	the	DET
ejpam-6847	564	2	application	application	NOUN
ejpam-6847	564	3	of	of	ADP
ejpam-6847	564	4	fixed	fix	VERB
ejpam-6847	564	5	point	point	NOUN
ejpam-6847	564	6	results	result	NOUN
ejpam-6847	564	7	offers	offer	VERB
ejpam-6847	564	8	a	a	DET
ejpam-6847	564	9	direct	direct	ADJ
ejpam-6847	564	10	and	and	CCONJ
ejpam-6847	564	11	elegant	elegant	ADJ
ejpam-6847	564	12	method	method	NOUN
ejpam-6847	564	13	for	for	ADP
ejpam-6847	564	14	proving	prove	VERB
ejpam-6847	564	15	theorem	theorem	NOUN
ejpam-6847	564	16	1	1	NUM
ejpam-6847	564	17	.	.	PUNCT
ejpam-6847	565	1	since	since	SCONJ
ejpam-6847	565	2	the	the	DET
ejpam-6847	565	3	proof	proof	NOUN
ejpam-6847	565	4	closely	closely	ADV
ejpam-6847	565	5	follows	follow	VERB
ejpam-6847	565	6	the	the	DET
ejpam-6847	565	7	arguments	argument	NOUN
ejpam-6847	565	8	of	of	ADP
ejpam-6847	565	9	theorem	theorem	NOUN
ejpam-6847	565	10	4.1	4.1	NUM
ejpam-6847	565	11	in	in	ADP
ejpam-6847	565	12	[	[	X
ejpam-6847	565	13	20	20	NUM
ejpam-6847	565	14	]	]	PUNCT
ejpam-6847	565	15	,	,	PUNCT
ejpam-6847	565	16	we	we	PRON
ejpam-6847	565	17	omit	omit	VERB
ejpam-6847	565	18	it	it	PRON
ejpam-6847	565	19	here	here	ADV
ejpam-6847	565	20	.	.	PUNCT
ejpam-6847	566	1	theorem	theorem	VERB
ejpam-6847	566	2	4	4	NUM
ejpam-6847	566	3	.	.	PUNCT
ejpam-6847	567	1	[	[	X
ejpam-6847	567	2	20	20	NUM
ejpam-6847	567	3	]	]	PUNCT
ejpam-6847	567	4	for	for	ADP
ejpam-6847	567	5	any	any	DET
ejpam-6847	567	6	natural	natural	ADJ
ejpam-6847	567	7	number	number	NOUN
ejpam-6847	567	8	m	m	PROPN
ejpam-6847	567	9	≥	≥	NOUN
ejpam-6847	567	10	3	3	NUM
ejpam-6847	567	11	,	,	PUNCT
ejpam-6847	567	12	the	the	DET
ejpam-6847	567	13	following	follow	VERB
ejpam-6847	567	14	equation	equation	NOUN
ejpam-6847	567	15	xm	xm	PROPN
ejpam-6847	567	16	−	−	PROPN
ejpam-6847	567	17	(	(	PUNCT
ejpam-6847	567	18	m4	m4	PROPN
ejpam-6847	567	19	−	−	PROPN
ejpam-6847	567	20	1)xm+1	1)xm+1	PROPN
ejpam-6847	567	21	−m4x+	−m4x+	NOUN
ejpam-6847	567	22	1	1	NUM
ejpam-6847	567	23	=	=	SYM
ejpam-6847	567	24	0	0	NUM
ejpam-6847	567	25	,	,	PUNCT
ejpam-6847	567	26	(	(	PUNCT
ejpam-6847	567	27	31	31	NUM
ejpam-6847	567	28	)	)	PUNCT
ejpam-6847	567	29	has	have	VERB
ejpam-6847	567	30	exactly	exactly	ADV
ejpam-6847	567	31	one	one	NUM
ejpam-6847	567	32	solution	solution	NOUN
ejpam-6847	567	33	in	in	ADP
ejpam-6847	567	34	the	the	DET
ejpam-6847	567	35	interval	interval	NOUN
ejpam-6847	567	36	[	[	X
ejpam-6847	567	37	−1	−1	NOUN
ejpam-6847	567	38	,	,	PUNCT
ejpam-6847	567	39	1	1	NUM
ejpam-6847	567	40	]	]	PUNCT
ejpam-6847	567	41	.	.	PUNCT
ejpam-6847	568	1	f.	f.	PROPN
ejpam-6847	568	2	m.	m.	PROPN
ejpam-6847	568	3	azmi	azmi	PROPN
ejpam-6847	568	4	,	,	PUNCT
ejpam-6847	568	5	a.	a.	PROPN
ejpam-6847	568	6	h.	h.	PROPN
ejpam-6847	568	7	ansari	ansari	PROPN
ejpam-6847	568	8	,	,	PUNCT
ejpam-6847	568	9	s.	s.	PROPN
ejpam-6847	568	10	h.	h.	PROPN
ejpam-6847	568	11	j.	j.	PROPN
ejpam-6847	568	12	petroudi	petroudi	PROPN
ejpam-6847	568	13	/	/	SYM
ejpam-6847	568	14	eur	eur	PROPN
ejpam-6847	568	15	.	.	PUNCT
ejpam-6847	569	1	j.	j.	PROPN
ejpam-6847	569	2	pure	pure	PROPN
ejpam-6847	569	3	appl	appl	PROPN
ejpam-6847	569	4	.	.	PROPN
ejpam-6847	569	5	math	math	PROPN
ejpam-6847	569	6	,	,	PUNCT
ejpam-6847	569	7	18	18	NUM
ejpam-6847	569	8	(	(	PUNCT
ejpam-6847	569	9	4	4	NUM
ejpam-6847	569	10	)	)	PUNCT
ejpam-6847	569	11	(	(	PUNCT
ejpam-6847	569	12	2025	2025	NUM
ejpam-6847	569	13	)	)	PUNCT
ejpam-6847	569	14	,	,	PUNCT
ejpam-6847	569	15	6847	6847	NUM
ejpam-6847	569	16	23	23	NUM
ejpam-6847	569	17	of	of	ADP
ejpam-6847	569	18	26	26	NUM
ejpam-6847	569	19	theorem	theorem	NOUN
ejpam-6847	569	20	5	5	NUM
ejpam-6847	569	21	.	.	X
ejpam-6847	570	1	for	for	ADP
ejpam-6847	570	2	any	any	DET
ejpam-6847	570	3	natural	natural	ADJ
ejpam-6847	570	4	number	number	NOUN
ejpam-6847	570	5	m	m	PROPN
ejpam-6847	570	6	≥	≥	NOUN
ejpam-6847	570	7	3	3	NUM
ejpam-6847	570	8	,	,	PUNCT
ejpam-6847	570	9	the	the	DET
ejpam-6847	570	10	following	follow	VERB
ejpam-6847	570	11	equation	equation	NOUN
ejpam-6847	570	12	sinm	sinm	ADJ
ejpam-6847	570	13	x−	x−	PROPN
ejpam-6847	570	14	(	(	PUNCT
ejpam-6847	570	15	m4	m4	PROPN
ejpam-6847	570	16	−	−	NOUN
ejpam-6847	570	17	1	1	NUM
ejpam-6847	570	18	)	)	PUNCT
ejpam-6847	570	19	sinm+1	sinm+1	NOUN
ejpam-6847	570	20	x−m4	x−m4	PRON
ejpam-6847	570	21	sinx+	sinx+	PROPN
ejpam-6847	570	22	1	1	NUM
ejpam-6847	570	23	=	=	SYM
ejpam-6847	570	24	0	0	NUM
ejpam-6847	570	25	,	,	PUNCT
ejpam-6847	570	26	(	(	PUNCT
ejpam-6847	570	27	32	32	NUM
ejpam-6847	570	28	)	)	PUNCT
ejpam-6847	570	29	has	have	VERB
ejpam-6847	570	30	a	a	DET
ejpam-6847	570	31	unique	unique	ADJ
ejpam-6847	570	32	solution	solution	NOUN
ejpam-6847	570	33	in	in	ADP
ejpam-6847	570	34	the	the	DET
ejpam-6847	570	35	interval	interval	NOUN
ejpam-6847	570	36	[	[	X
ejpam-6847	570	37	−1	−1	NOUN
ejpam-6847	570	38	,	,	PUNCT
ejpam-6847	570	39	1	1	NUM
ejpam-6847	570	40	]	]	PUNCT
ejpam-6847	570	41	.	.	PUNCT
ejpam-6847	571	1	proof	proof	NOUN
ejpam-6847	571	2	.	.	PUNCT
ejpam-6847	572	1	let	let	VERB
ejpam-6847	572	2	y	y	PROPN
ejpam-6847	572	3	=	=	PUNCT
ejpam-6847	572	4	sinx	sinx	PROPN
ejpam-6847	572	5	.	.	PUNCT
ejpam-6847	573	1	thus	thus	ADV
ejpam-6847	573	2	,	,	PUNCT
ejpam-6847	573	3	|y|	|y|	ADJ
ejpam-6847	573	4	≤	≤	ADV
ejpam-6847	573	5	1	1	NUM
ejpam-6847	573	6	.	.	PUNCT
ejpam-6847	573	7	now	now	ADV
ejpam-6847	573	8	apply	apply	VERB
ejpam-6847	573	9	theorem	theorem	ADJ
ejpam-6847	573	10	4	4	NUM
ejpam-6847	573	11	.	.	PUNCT
ejpam-6847	573	12	definition	definition	NOUN
ejpam-6847	573	13	19	19	NUM
ejpam-6847	573	14	.	.	PUNCT
ejpam-6847	574	1	[	[	X
ejpam-6847	574	2	40	40	NUM
ejpam-6847	574	3	]	]	PUNCT
ejpam-6847	574	4	the	the	DET
ejpam-6847	574	5	functions	function	NOUN
ejpam-6847	574	6	p	p	X
ejpam-6847	574	7	tani	tani	PROPN
ejpam-6847	574	8	j	j	PROPN
ejpam-6847	574	9	,	,	PUNCT
ejpam-6847	574	10	p	p	PROPN
ejpam-6847	574	11	tanhi	tanhi	PROPN
ejpam-6847	574	12	j	j	NOUN
ejpam-6847	574	13	:	:	PUNCT
ejpam-6847	574	14	r	r	NOUN
ejpam-6847	574	15	→	→	SYM
ejpam-6847	574	16	r	r	NOUN
ejpam-6847	574	17	,	,	PUNCT
ejpam-6847	574	18	i	i	PRON
ejpam-6847	574	19	,	,	PUNCT
ejpam-6847	574	20	j	j	PROPN
ejpam-6847	574	21	=	=	SYM
ejpam-6847	574	22	0	0	NUM
ejpam-6847	574	23	,	,	PUNCT
ejpam-6847	574	24	1	1	NUM
ejpam-6847	574	25	,	,	PUNCT
ejpam-6847	574	26	2	2	NUM
ejpam-6847	574	27	,	,	PUNCT
ejpam-6847	574	28	·	·	PUNCT
ejpam-6847	574	29	·	·	PUNCT
ejpam-6847	574	30	·	·	PUNCT
ejpam-6847	574	31	,	,	PUNCT
ejpam-6847	575	1	p−	p−	NOUN
ejpam-6847	575	2	1	1	NUM
ejpam-6847	575	3	,	,	PUNCT
ejpam-6847	575	4	p	p	PROPN
ejpam-6847	575	5	∈	∈	PROPN
ejpam-6847	575	6	n	n	CCONJ
ejpam-6847	575	7	,	,	PUNCT
ejpam-6847	575	8	i	i	PROPN
ejpam-6847	575	9	6=	6=	PROPN
ejpam-6847	575	10	j	j	PROPN
ejpam-6847	575	11	are	be	AUX
ejpam-6847	575	12	defined	define	VERB
ejpam-6847	575	13	as	as	SCONJ
ejpam-6847	575	14	follows	follow	VERB
ejpam-6847	575	15	:	:	PUNCT
ejpam-6847	575	16	p	p	X
ejpam-6847	575	17	tani	tani	X
ejpam-6847	575	18	j(t	j(t	PROPN
ejpam-6847	575	19	)	)	PUNCT
ejpam-6847	575	20	=	=	SYM
ejpam-6847	575	21	tp	tp	ADP
ejpam-6847	575	22	i(t	i(t	PROPN
ejpam-6847	575	23	)	)	PUNCT
ejpam-6847	575	24	tp	tp	ADP
ejpam-6847	575	25	j(t	j(t	PROPN
ejpam-6847	575	26	)	)	PUNCT
ejpam-6847	575	27	,	,	PUNCT
ejpam-6847	575	28	p	p	PRON
ejpam-6847	575	29	tanhi	tanhi	PROPN
ejpam-6847	575	30	j(t	j(t	PROPN
ejpam-6847	575	31	)	)	PUNCT
ejpam-6847	575	32	=	=	SYM
ejpam-6847	575	33	hp	hp	PROPN
ejpam-6847	575	34	i(t	i(t	PROPN
ejpam-6847	575	35	)	)	PUNCT
ejpam-6847	575	36	hp	hp	PROPN
ejpam-6847	575	37	j(t	j(t	PROPN
ejpam-6847	575	38	)	)	PUNCT
ejpam-6847	575	39	.	.	PUNCT
ejpam-6847	576	1	=	=	PRON
ejpam-6847	576	2	⇒	⇒	VERB
ejpam-6847	576	3	p	p	PROPN
ejpam-6847	576	4	tan1	tan1	PROPN
ejpam-6847	576	5	0(t	0(t	NUM
ejpam-6847	576	6	)	)	PUNCT
ejpam-6847	577	1	=	=	NOUN
ejpam-6847	577	2	tp	tp	NOUN
ejpam-6847	577	3	1(t	1(t	NUM
ejpam-6847	577	4	)	)	PUNCT
ejpam-6847	577	5	tp	tp	ADP
ejpam-6847	577	6	0(t	0(t	NUM
ejpam-6847	577	7	)	)	PUNCT
ejpam-6847	577	8	,	,	PUNCT
ejpam-6847	577	9	p	p	X
ejpam-6847	577	10	tanh1	tanh1	NOUN
ejpam-6847	577	11	0(t	0(t	NUM
ejpam-6847	577	12	)	)	PUNCT
ejpam-6847	577	13	=	=	PRON
ejpam-6847	577	14	hp	hp	ADJ
ejpam-6847	577	15	1(t	1(t	NUM
ejpam-6847	577	16	)	)	PUNCT
ejpam-6847	577	17	hp	hp	PROPN
ejpam-6847	577	18	0(t	0(t	NUM
ejpam-6847	577	19	)	)	PUNCT
ejpam-6847	577	20	.	.	PUNCT
ejpam-6847	578	1	where	where	SCONJ
ejpam-6847	578	2	tp	tp	PROPN
ejpam-6847	578	3	j	j	PROPN
ejpam-6847	578	4	,	,	PUNCT
ejpam-6847	578	5	hp	hp	PROPN
ejpam-6847	578	6	j	j	NOUN
ejpam-6847	578	7	:	:	PUNCT
ejpam-6847	578	8	r	r	NOUN
ejpam-6847	578	9	→	→	SYM
ejpam-6847	578	10	r	r	NOUN
ejpam-6847	578	11	,	,	PUNCT
ejpam-6847	578	12	j	j	NOUN
ejpam-6847	578	13	=	=	SYM
ejpam-6847	578	14	0	0	NUM
ejpam-6847	578	15	,	,	PUNCT
ejpam-6847	578	16	1	1	NUM
ejpam-6847	578	17	,	,	PUNCT
ejpam-6847	578	18	2	2	NUM
ejpam-6847	578	19	,	,	PUNCT
ejpam-6847	578	20	·	·	PUNCT
ejpam-6847	578	21	·	·	PUNCT
ejpam-6847	578	22	·	·	PUNCT
ejpam-6847	578	23	,	,	PUNCT
ejpam-6847	578	24	p−	p−	NOUN
ejpam-6847	578	25	1	1	NUM
ejpam-6847	578	26	,	,	PUNCT
ejpam-6847	578	27	p	p	PROPN
ejpam-6847	578	28	∈	∈	PROPN
ejpam-6847	578	29	n	n	CCONJ
ejpam-6847	578	30	,	,	PUNCT
ejpam-6847	578	31	are	be	AUX
ejpam-6847	578	32	nested	nested	ADJ
ejpam-6847	578	33	functions	function	NOUN
ejpam-6847	578	34	defined	define	VERB
ejpam-6847	578	35	by	by	ADP
ejpam-6847	578	36	:	:	PUNCT
ejpam-6847	578	37	tp	tp	PART
ejpam-6847	578	38	j(t	j(t	PROPN
ejpam-6847	578	39	)	)	PUNCT
ejpam-6847	578	40	=	=	PUNCT
ejpam-6847	579	1	+	+	ADP
ejpam-6847	579	2	∞∑	∞∑	NUM
ejpam-6847	579	3	n=0	n=0	PRON
ejpam-6847	579	4	(	(	PUNCT
ejpam-6847	579	5	−1)ntpn+j	−1)ntpn+j	NOUN
ejpam-6847	579	6	(	(	PUNCT
ejpam-6847	579	7	pn+	pn+	NOUN
ejpam-6847	579	8	j	j	PROPN
ejpam-6847	579	9	)	)	PUNCT
ejpam-6847	579	10	!	!	PUNCT
ejpam-6847	579	11	,	,	PUNCT
ejpam-6847	579	12	hp	hp	PROPN
ejpam-6847	579	13	j(t	j(t	PROPN
ejpam-6847	579	14	)	)	PUNCT
ejpam-6847	579	15	=	=	PUNCT
ejpam-6847	580	1	+	+	ADP
ejpam-6847	580	2	∞∑	∞∑	NUM
ejpam-6847	580	3	n=0	n=0	NUM
ejpam-6847	580	4	tpn+j	tpn+j	PROPN
ejpam-6847	580	5	(	(	PUNCT
ejpam-6847	580	6	pn+	pn+	NOUN
ejpam-6847	580	7	j	j	PROPN
ejpam-6847	580	8	)	)	PUNCT
ejpam-6847	580	9	!	!	PUNCT
ejpam-6847	580	10	.	.	PUNCT
ejpam-6847	581	1	consult	consult	VERB
ejpam-6847	582	1	[	[	X
ejpam-6847	582	2	41	41	NUM
ejpam-6847	582	3	]	]	PUNCT
ejpam-6847	582	4	and	and	CCONJ
ejpam-6847	583	1	[	[	X
ejpam-6847	583	2	42	42	NUM
ejpam-6847	583	3	]	]	PUNCT
ejpam-6847	583	4	for	for	ADP
ejpam-6847	583	5	more	more	ADJ
ejpam-6847	583	6	details	detail	NOUN
ejpam-6847	583	7	on	on	ADP
ejpam-6847	583	8	the	the	DET
ejpam-6847	583	9	nested	nested	ADJ
ejpam-6847	583	10	functions	function	NOUN
ejpam-6847	583	11	.	.	PUNCT
ejpam-6847	584	1	theorem	theorem	VERB
ejpam-6847	584	2	6	6	NUM
ejpam-6847	584	3	.	.	PUNCT
ejpam-6847	585	1	for	for	ADP
ejpam-6847	585	2	m	m	PROPN
ejpam-6847	585	3	≥	≥	NUM
ejpam-6847	585	4	3	3	NUM
ejpam-6847	585	5	any	any	DET
ejpam-6847	585	6	natural	natural	ADJ
ejpam-6847	585	7	number	number	NOUN
ejpam-6847	585	8	m	m	PROPN
ejpam-6847	585	9	,	,	PUNCT
ejpam-6847	585	10	the	the	DET
ejpam-6847	585	11	following	follow	VERB
ejpam-6847	585	12	equation	equation	NOUN
ejpam-6847	585	13	p	p	PROPN
ejpam-6847	585	14	tanhi0(x	tanhi0(x	NOUN
ejpam-6847	585	15	)	)	PUNCT
ejpam-6847	585	16	xi	xi	ADP
ejpam-6847	585	17	m	m	PROPN
ejpam-6847	585	18	−	−	PROPN
ejpam-6847	585	19	(	(	PUNCT
ejpam-6847	585	20	m4	m4	VERB
ejpam-6847	585	21	−	−	NOUN
ejpam-6847	585	22	1	1	NUM
ejpam-6847	585	23	)	)	PUNCT
ejpam-6847	585	24	p	p	NOUN
ejpam-6847	585	25	tanhi0(x	tanhi0(x	NOUN
ejpam-6847	585	26	)	)	PUNCT
ejpam-6847	585	27	xi	xi	VERB
ejpam-6847	586	1	m+1	m+1	NUM
ejpam-6847	586	2	−m4	−m4	PROPN
ejpam-6847	586	3	p	p	PROPN
ejpam-6847	586	4	tanhi0(x	tanhi0(x	PROPN
ejpam-6847	586	5	)	)	PUNCT
ejpam-6847	586	6	xi	xi	VERB
ejpam-6847	587	1	+	+	CCONJ
ejpam-6847	587	2	1	1	NUM
ejpam-6847	587	3	=	=	SYM
ejpam-6847	587	4	0	0	NUM
ejpam-6847	587	5	,	,	PUNCT
ejpam-6847	587	6	(	(	PUNCT
ejpam-6847	587	7	33	33	NUM
ejpam-6847	587	8	)	)	PUNCT
ejpam-6847	587	9	has	have	VERB
ejpam-6847	587	10	a	a	DET
ejpam-6847	587	11	unique	unique	ADJ
ejpam-6847	587	12	solution	solution	NOUN
ejpam-6847	587	13	in	in	ADP
ejpam-6847	587	14	the	the	DET
ejpam-6847	587	15	interval	interval	NOUN
ejpam-6847	587	16	[	[	X
ejpam-6847	587	17	−1	−1	NOUN
ejpam-6847	587	18	,	,	PUNCT
ejpam-6847	587	19	1	1	NUM
ejpam-6847	587	20	]	]	PUNCT
ejpam-6847	587	21	.	.	PUNCT
ejpam-6847	588	1	proof	proof	NOUN
ejpam-6847	588	2	.	.	PUNCT
ejpam-6847	589	1	let	let	VERB
ejpam-6847	589	2	y	y	NOUN
ejpam-6847	589	3	=	=	PUNCT
ejpam-6847	589	4	p	p	PROPN
ejpam-6847	589	5	tanhi0(x	tanhi0(x	NOUN
ejpam-6847	589	6	)	)	PUNCT
ejpam-6847	589	7	xi	xi	X
ejpam-6847	589	8	;	;	PUNCT
ejpam-6847	589	9	thus	thus	ADV
ejpam-6847	589	10	,	,	PUNCT
ejpam-6847	589	11	|y|	|y|	ADJ
ejpam-6847	589	12	≤	≤	ADV
ejpam-6847	589	13	1	1	NUM
ejpam-6847	589	14	.	.	PUNCT
ejpam-6847	590	1	now	now	ADV
ejpam-6847	590	2	,	,	PUNCT
ejpam-6847	590	3	apply	apply	VERB
ejpam-6847	590	4	theorem	theorem	NOUN
ejpam-6847	590	5	4	4	NUM
ejpam-6847	590	6	.	.	NOUN
ejpam-6847	590	7	6	6	NUM
ejpam-6847	590	8	.	.	X
ejpam-6847	590	9	conclusion	conclusion	NOUN
ejpam-6847	590	10	this	this	DET
ejpam-6847	590	11	paper	paper	NOUN
ejpam-6847	590	12	presents	present	VERB
ejpam-6847	590	13	two	two	NUM
ejpam-6847	590	14	new	new	ADJ
ejpam-6847	590	15	types	type	NOUN
ejpam-6847	590	16	of	of	ADP
ejpam-6847	590	17	contraction	contraction	NOUN
ejpam-6847	590	18	mappings	mapping	NOUN
ejpam-6847	590	19	:	:	PUNCT
ejpam-6847	590	20	(	(	PUNCT
ejpam-6847	590	21	αs	αs	INTJ
ejpam-6847	590	22	,	,	PUNCT
ejpam-6847	590	23	νs	νs	NOUN
ejpam-6847	590	24	,	,	PUNCT
ejpam-6847	590	25	(	(	PUNCT
ejpam-6847	590	26	q	q	X
ejpam-6847	590	27	,	,	PUNCT
ejpam-6847	590	28	h	h	NOUN
ejpam-6847	590	29	)	)	PUNCT
ejpam-6847	590	30	−	−	PROPN
ejpam-6847	590	31	f)contraction	f)contraction	NOUN
ejpam-6847	590	32	and	and	CCONJ
ejpam-6847	590	33	(	(	PUNCT
ejpam-6847	590	34	αs	αs	INTJ
ejpam-6847	590	35	,	,	PUNCT
ejpam-6847	590	36	ηs	ηs	PROPN
ejpam-6847	590	37	,	,	PUNCT
ejpam-6847	590	38	νs	νs	NOUN
ejpam-6847	590	39	,	,	PUNCT
ejpam-6847	590	40	(	(	PUNCT
ejpam-6847	590	41	q	q	NOUN
ejpam-6847	590	42	,	,	PUNCT
ejpam-6847	590	43	h)−f)-contraction	h)−f)-contraction	NOUN
ejpam-6847	590	44	,	,	PUNCT
ejpam-6847	590	45	within	within	ADP
ejpam-6847	590	46	the	the	DET
ejpam-6847	590	47	framework	framework	NOUN
ejpam-6847	590	48	of	of	ADP
ejpam-6847	590	49	triple	triple	ADJ
ejpam-6847	590	50	-	-	PUNCT
ejpam-6847	590	51	controlled	control	VERB
ejpam-6847	590	52	s	s	NOUN
ejpam-6847	590	53	-	-	ADJ
ejpam-6847	590	54	metric	metric	ADJ
ejpam-6847	590	55	spaces	space	NOUN
ejpam-6847	590	56	.	.	PUNCT
ejpam-6847	591	1	these	these	DET
ejpam-6847	591	2	mappings	mapping	NOUN
ejpam-6847	591	3	are	be	AUX
ejpam-6847	591	4	based	base	VERB
ejpam-6847	591	5	on	on	ADP
ejpam-6847	591	6	αs	αs	ADP
ejpam-6847	591	7	and	and	CCONJ
ejpam-6847	591	8	ηs	ηs	NOUN
ejpam-6847	591	9	-	-	PUNCT
ejpam-6847	591	10	admissible	admissible	ADJ
ejpam-6847	591	11	mappings	mapping	NOUN
ejpam-6847	591	12	,	,	PUNCT
ejpam-6847	591	13	νssubadmissible	νssubadmissible	ADJ
ejpam-6847	591	14	mappings	mapping	NOUN
ejpam-6847	591	15	,	,	PUNCT
ejpam-6847	591	16	upper	upper	ADJ
ejpam-6847	591	17	-	-	PUNCT
ejpam-6847	591	18	class	class	NOUN
ejpam-6847	591	19	functions	function	NOUN
ejpam-6847	591	20	(	(	PUNCT
ejpam-6847	591	21	q	q	NOUN
ejpam-6847	591	22	,	,	PUNCT
ejpam-6847	591	23	h	h	NOUN
ejpam-6847	591	24	)	)	PUNCT
ejpam-6847	591	25	,	,	PUNCT
ejpam-6847	591	26	and	and	CCONJ
ejpam-6847	591	27	wardowski	wardowski	VERB
ejpam-6847	591	28	’s	’s	PART
ejpam-6847	591	29	f	f	NOUN
ejpam-6847	591	30	-	-	PUNCT
ejpam-6847	591	31	contraction	contraction	NOUN
ejpam-6847	591	32	.	.	PUNCT
ejpam-6847	592	1	by	by	ADP
ejpam-6847	592	2	expanding	expand	VERB
ejpam-6847	592	3	the	the	DET
ejpam-6847	592	4	(	(	PUNCT
ejpam-6847	592	5	αs	αs	INTJ
ejpam-6847	592	6	−	−	PROPN
ejpam-6847	592	7	f)-contraction	f)-contraction	NOUN
ejpam-6847	592	8	,	,	PUNCT
ejpam-6847	592	9	we	we	PRON
ejpam-6847	592	10	have	have	AUX
ejpam-6847	592	11	shown	show	VERB
ejpam-6847	592	12	that	that	SCONJ
ejpam-6847	592	13	fixed	fix	VERB
ejpam-6847	592	14	points	point	NOUN
ejpam-6847	592	15	exist	exist	VERB
ejpam-6847	592	16	uniquely	uniquely	ADV
ejpam-6847	592	17	in	in	ADP
ejpam-6847	592	18	complete	complete	ADJ
ejpam-6847	592	19	triple	triple	ADV
ejpam-6847	592	20	-	-	PUNCT
ejpam-6847	592	21	controlled	control	VERB
ejpam-6847	592	22	s	s	NOUN
ejpam-6847	592	23	-	-	ADJ
ejpam-6847	592	24	metric	metric	ADJ
ejpam-6847	592	25	spaces	space	NOUN
ejpam-6847	592	26	.	.	PUNCT
ejpam-6847	593	1	furthermore	furthermore	ADV
ejpam-6847	593	2	,	,	PUNCT
ejpam-6847	593	3	we	we	PRON
ejpam-6847	593	4	provided	provide	VERB
ejpam-6847	593	5	several	several	ADJ
ejpam-6847	593	6	corollaries	corollary	NOUN
ejpam-6847	593	7	of	of	ADP
ejpam-6847	593	8	theorem	theorem	NOUN
ejpam-6847	593	9	1	1	NUM
ejpam-6847	593	10	using	use	VERB
ejpam-6847	593	11	specific	specific	ADJ
ejpam-6847	593	12	examples	example	NOUN
ejpam-6847	593	13	of	of	ADP
ejpam-6847	593	14	pairs	pair	NOUN
ejpam-6847	593	15	(	(	PUNCT
ejpam-6847	593	16	q	q	NOUN
ejpam-6847	593	17	,	,	PUNCT
ejpam-6847	593	18	h	h	NOUN
ejpam-6847	593	19	)	)	PUNCT
ejpam-6847	593	20	from	from	ADP
ejpam-6847	593	21	the	the	DET
ejpam-6847	593	22	upper	upper	ADJ
ejpam-6847	593	23	class	class	NOUN
ejpam-6847	593	24	of	of	ADP
ejpam-6847	593	25	type	type	NOUN
ejpam-6847	593	26	i.	i.	NOUN
ejpam-6847	593	27	the	the	DET
ejpam-6847	593	28	findings	finding	NOUN
ejpam-6847	593	29	of	of	ADP
ejpam-6847	593	30	this	this	DET
ejpam-6847	593	31	paper	paper	NOUN
ejpam-6847	593	32	enhance	enhance	VERB
ejpam-6847	593	33	the	the	DET
ejpam-6847	593	34	understanding	understanding	NOUN
ejpam-6847	593	35	of	of	ADP
ejpam-6847	593	36	fixed	fix	VERB
ejpam-6847	593	37	point	point	NOUN
ejpam-6847	593	38	theory	theory	NOUN
ejpam-6847	593	39	in	in	ADP
ejpam-6847	593	40	generalized	generalized	ADJ
ejpam-6847	593	41	metric	metric	ADJ
ejpam-6847	593	42	spaces	space	NOUN
ejpam-6847	593	43	and	and	CCONJ
ejpam-6847	593	44	lay	lie	VERB
ejpam-6847	593	45	the	the	DET
ejpam-6847	593	46	groundwork	groundwork	NOUN
ejpam-6847	593	47	for	for	ADP
ejpam-6847	593	48	future	future	ADJ
ejpam-6847	593	49	studies	study	NOUN
ejpam-6847	593	50	in	in	ADP
ejpam-6847	593	51	this	this	DET
ejpam-6847	593	52	field	field	NOUN
ejpam-6847	593	53	.	.	PUNCT
ejpam-6847	594	1	f.	f.	PROPN
ejpam-6847	594	2	m.	m.	PROPN
ejpam-6847	594	3	azmi	azmi	PROPN
ejpam-6847	594	4	,	,	PUNCT
ejpam-6847	594	5	a.	a.	PROPN
ejpam-6847	594	6	h.	h.	PROPN
ejpam-6847	594	7	ansari	ansari	PROPN
ejpam-6847	594	8	,	,	PUNCT
ejpam-6847	594	9	s.	s.	PROPN
ejpam-6847	594	10	h.	h.	PROPN
ejpam-6847	594	11	j.	j.	PROPN
ejpam-6847	594	12	petroudi	petroudi	PROPN
ejpam-6847	594	13	/	/	SYM
ejpam-6847	594	14	eur	eur	PROPN
ejpam-6847	594	15	.	.	PUNCT
ejpam-6847	595	1	j.	j.	PROPN
ejpam-6847	595	2	pure	pure	PROPN
ejpam-6847	595	3	appl	appl	PROPN
ejpam-6847	595	4	.	.	PROPN
ejpam-6847	595	5	math	math	PROPN
ejpam-6847	595	6	,	,	PUNCT
ejpam-6847	595	7	18	18	NUM
ejpam-6847	595	8	(	(	PUNCT
ejpam-6847	595	9	4	4	NUM
ejpam-6847	595	10	)	)	PUNCT
ejpam-6847	595	11	(	(	PUNCT
ejpam-6847	595	12	2025	2025	NUM
ejpam-6847	595	13	)	)	PUNCT
ejpam-6847	595	14	,	,	PUNCT
ejpam-6847	595	15	6847	6847	NUM
ejpam-6847	595	16	24	24	NUM
ejpam-6847	595	17	of	of	ADP
ejpam-6847	595	18	26	26	NUM
ejpam-6847	595	19	statement	statement	NOUN
ejpam-6847	595	20	of	of	ADP
ejpam-6847	595	21	funding	fund	VERB
ejpam-6847	595	22	no	no	DET
ejpam-6847	595	23	funding	funding	NOUN
ejpam-6847	595	24	was	be	AUX
ejpam-6847	595	25	received	receive	VERB
ejpam-6847	595	26	for	for	ADP
ejpam-6847	595	27	conducting	conduct	VERB
ejpam-6847	595	28	this	this	DET
ejpam-6847	595	29	study	study	NOUN
ejpam-6847	595	30	.	.	PUNCT
ejpam-6847	596	1	conflict	conflict	NOUN
ejpam-6847	596	2	of	of	ADP
ejpam-6847	596	3	interest	interest	NOUN
ejpam-6847	596	4	the	the	DET
ejpam-6847	596	5	authors	author	NOUN
ejpam-6847	596	6	declare	declare	VERB
ejpam-6847	596	7	no	no	DET
ejpam-6847	596	8	conflict	conflict	NOUN
ejpam-6847	596	9	of	of	ADP
ejpam-6847	596	10	interest	interest	NOUN
ejpam-6847	596	11	.	.	PUNCT
ejpam-6847	597	1	acknowledgments	acknowledgment	NOUN
ejpam-6847	597	2	the	the	DET
ejpam-6847	597	3	first	first	ADJ
ejpam-6847	597	4	author	author	NOUN
ejpam-6847	597	5	,	,	PUNCT
ejpam-6847	597	6	f.	f.	PROPN
ejpam-6847	597	7	m.	m.	PROPN
ejpam-6847	597	8	azmi	azmi	PROPN
ejpam-6847	597	9	,	,	PUNCT
ejpam-6847	597	10	would	would	AUX
ejpam-6847	597	11	like	like	VERB
ejpam-6847	597	12	to	to	PART
ejpam-6847	597	13	thank	thank	VERB
ejpam-6847	597	14	prince	prince	PROPN
ejpam-6847	597	15	sultan	sultan	PROPN
ejpam-6847	597	16	university	university	PROPN
ejpam-6847	597	17	for	for	ADP
ejpam-6847	597	18	covering	cover	VERB
ejpam-6847	597	19	the	the	DET
ejpam-6847	597	20	article	article	NOUN
ejpam-6847	597	21	publication	publication	NOUN
ejpam-6847	597	22	fees	fee	NOUN
ejpam-6847	597	23	through	through	ADP
ejpam-6847	597	24	the	the	DET
ejpam-6847	597	25	tas	tas	PROPN
ejpam-6847	597	26	research	research	NOUN
ejpam-6847	597	27	lab	lab	NOUN
ejpam-6847	597	28	.	.	PUNCT
ejpam-6847	598	1	references	reference	NOUN
ejpam-6847	598	2	[	[	X
ejpam-6847	598	3	1	1	X
ejpam-6847	598	4	]	]	X
ejpam-6847	598	5	stefan	stefan	PROPN
ejpam-6847	598	6	banach	banach	PROPN
ejpam-6847	598	7	.	.	PUNCT
ejpam-6847	599	1	sur	sur	PROPN
ejpam-6847	599	2	les	les	PROPN
ejpam-6847	599	3	operations	operation	NOUN
ejpam-6847	599	4	dans	dan	NOUN
ejpam-6847	599	5	les	les	X
ejpam-6847	599	6	ensembles	ensemble	NOUN
ejpam-6847	599	7	et	et	PROPN
ejpam-6847	599	8	leur	leur	X
ejpam-6847	599	9	application	application	PROPN
ejpam-6847	599	10	aux	aux	PROPN
ejpam-6847	599	11	equation	equation	NOUN
ejpam-6847	599	12	sitegrales	sitegrale	NOUN
ejpam-6847	599	13	.	.	PUNCT
ejpam-6847	600	1	fundam	fundam	PROPN
ejpam-6847	600	2	.	.	PUNCT
ejpam-6847	600	3	math	math	NOUN
ejpam-6847	600	4	.	.	PUNCT
ejpam-6847	600	5	,	,	PUNCT
ejpam-6847	600	6	3:133–181	3:133–181	NUM
ejpam-6847	600	7	,	,	PUNCT
ejpam-6847	600	8	1922	1922	NUM
ejpam-6847	600	9	.	.	PUNCT
ejpam-6847	601	1	[	[	X
ejpam-6847	601	2	2	2	NUM
ejpam-6847	601	3	]	]	PUNCT
ejpam-6847	601	4	a.	a.	NOUN
ejpam-6847	601	5	bakhtin	bakhtin	NOUN
ejpam-6847	601	6	.	.	PUNCT
ejpam-6847	602	1	the	the	DET
ejpam-6847	602	2	contractive	contractive	ADJ
ejpam-6847	602	3	mapping	mapping	NOUN
ejpam-6847	602	4	principle	principle	NOUN
ejpam-6847	602	5	in	in	ADP
ejpam-6847	602	6	almost	almost	ADV
ejpam-6847	602	7	metric	metric	ADJ
ejpam-6847	602	8	spaces	space	NOUN
ejpam-6847	602	9	.	.	PUNCT
ejpam-6847	603	1	funct	funct	ADJ
ejpam-6847	603	2	.	.	PUNCT
ejpam-6847	604	1	anal	anal	PROPN
ejpam-6847	604	2	.	.	PROPN
ejpam-6847	604	3	,	,	PUNCT
ejpam-6847	604	4	gos	gos	PROPN
ejpam-6847	604	5	.	.	PUNCT
ejpam-6847	604	6	ped	ped	PROPN
ejpam-6847	604	7	.	.	PROPN
ejpam-6847	604	8	inst	inst	PROPN
ejpam-6847	604	9	.	.	PUNCT
ejpam-6847	605	1	unianowsk	unianowsk	PROPN
ejpam-6847	605	2	.	.	PUNCT
ejpam-6847	605	3	,	,	PUNCT
ejpam-6847	605	4	30:26–37	30:26–37	PROPN
ejpam-6847	605	5	,	,	PUNCT
ejpam-6847	605	6	1989	1989	NUM
ejpam-6847	605	7	.	.	PUNCT
ejpam-6847	606	1	[	[	X
ejpam-6847	606	2	3	3	X
ejpam-6847	606	3	]	]	PUNCT
ejpam-6847	606	4	t.	t.	PROPN
ejpam-6847	606	5	kamran	kamran	PROPN
ejpam-6847	606	6	,	,	PUNCT
ejpam-6847	606	7	m.	m.	NOUN
ejpam-6847	606	8	samreen	samreen	PROPN
ejpam-6847	606	9	,	,	PUNCT
ejpam-6847	606	10	and	and	CCONJ
ejpam-6847	606	11	q.	q.	PROPN
ejpam-6847	606	12	ain	ain	PROPN
ejpam-6847	606	13	.	.	PUNCT
ejpam-6847	607	1	a	a	DET
ejpam-6847	607	2	generalization	generalization	NOUN
ejpam-6847	607	3	of	of	ADP
ejpam-6847	607	4	b	b	NOUN
ejpam-6847	607	5	-	-	PUNCT
ejpam-6847	607	6	metric	metric	ADJ
ejpam-6847	607	7	space	space	NOUN
ejpam-6847	607	8	and	and	CCONJ
ejpam-6847	607	9	some	some	DET
ejpam-6847	607	10	fixed	fix	VERB
ejpam-6847	607	11	point	point	NOUN
ejpam-6847	607	12	theorems	theorem	NOUN
ejpam-6847	607	13	.	.	PUNCT
ejpam-6847	608	1	mathematics	mathematic	NOUN
ejpam-6847	608	2	,	,	PUNCT
ejpam-6847	608	3	5(19):1–7	5(19):1–7	NUM
ejpam-6847	608	4	,	,	PUNCT
ejpam-6847	608	5	2017	2017	NUM
ejpam-6847	608	6	.	.	PUNCT
ejpam-6847	609	1	[	[	X
ejpam-6847	609	2	4	4	NUM
ejpam-6847	609	3	]	]	X
ejpam-6847	609	4	n.	n.	PROPN
ejpam-6847	609	5	mlaiki	mlaiki	PROPN
ejpam-6847	609	6	,	,	PUNCT
ejpam-6847	609	7	h.	h.	PROPN
ejpam-6847	609	8	aydi	aydi	PROPN
ejpam-6847	609	9	,	,	PUNCT
ejpam-6847	609	10	n.	n.	NOUN
ejpam-6847	609	11	souayah	souayah	NOUN
ejpam-6847	609	12	,	,	PUNCT
ejpam-6847	609	13	and	and	CCONJ
ejpam-6847	609	14	t.	t.	PROPN
ejpam-6847	609	15	abdeljawad	abdeljawad	NOUN
ejpam-6847	609	16	.	.	PUNCT
ejpam-6847	610	1	controlled	control	VERB
ejpam-6847	610	2	metric	metric	ADJ
ejpam-6847	610	3	type	type	NOUN
ejpam-6847	610	4	spaces	space	NOUN
ejpam-6847	610	5	and	and	CCONJ
ejpam-6847	610	6	the	the	DET
ejpam-6847	610	7	related	relate	VERB
ejpam-6847	610	8	contractive	contractive	ADJ
ejpam-6847	610	9	principle	principle	NOUN
ejpam-6847	610	10	.	.	PUNCT
ejpam-6847	611	1	mathematics	mathematic	NOUN
ejpam-6847	611	2	,	,	PUNCT
ejpam-6847	611	3	6(10):194	6(10):194	PROPN
ejpam-6847	611	4	,	,	PUNCT
ejpam-6847	611	5	2018	2018	NUM
ejpam-6847	611	6	.	.	PUNCT
ejpam-6847	612	1	[	[	X
ejpam-6847	612	2	5	5	X
ejpam-6847	612	3	]	]	PUNCT
ejpam-6847	612	4	t.	t.	NOUN
ejpam-6847	612	5	abdeljawad	abdeljawad	PROPN
ejpam-6847	612	6	,	,	PUNCT
ejpam-6847	612	7	n.	n.	PROPN
ejpam-6847	612	8	mlaiki	mlaiki	PROPN
ejpam-6847	612	9	,	,	PUNCT
ejpam-6847	612	10	h.	h.	PROPN
ejpam-6847	612	11	aydi	aydi	PROPN
ejpam-6847	612	12	,	,	PUNCT
ejpam-6847	612	13	and	and	CCONJ
ejpam-6847	612	14	n.	n.	NOUN
ejpam-6847	612	15	souayah	souayah	NOUN
ejpam-6847	612	16	.	.	PUNCT
ejpam-6847	613	1	double	double	PROPN
ejpam-6847	613	2	controlled	control	VERB
ejpam-6847	613	3	metric	metric	ADJ
ejpam-6847	613	4	type	type	NOUN
ejpam-6847	613	5	spaces	space	NOUN
ejpam-6847	613	6	and	and	CCONJ
ejpam-6847	613	7	some	some	DET
ejpam-6847	613	8	fixed	fix	VERB
ejpam-6847	613	9	point	point	NOUN
ejpam-6847	613	10	results	result	NOUN
ejpam-6847	613	11	.	.	PUNCT
ejpam-6847	614	1	mathematics	mathematic	NOUN
ejpam-6847	614	2	,	,	PUNCT
ejpam-6847	614	3	6(12):320	6(12):320	PROPN
ejpam-6847	614	4	,	,	PUNCT
ejpam-6847	614	5	2018	2018	NUM
ejpam-6847	614	6	.	.	PUNCT
ejpam-6847	615	1	[	[	X
ejpam-6847	615	2	6	6	NUM
ejpam-6847	615	3	]	]	PUNCT
ejpam-6847	615	4	k.	k.	NOUN
ejpam-6847	615	5	gopalan	gopalan	PROPN
ejpam-6847	615	6	,	,	PUNCT
ejpam-6847	615	7	s.	s.	PROPN
ejpam-6847	615	8	zubair	zubair	PROPN
ejpam-6847	615	9	,	,	PUNCT
ejpam-6847	615	10	t.	t.	NOUN
ejpam-6847	615	11	abdeljawad	abdeljawad	NOUN
ejpam-6847	615	12	,	,	PUNCT
ejpam-6847	615	13	and	and	CCONJ
ejpam-6847	615	14	n.	n.	PROPN
ejpam-6847	615	15	mlaiki	mlaiki	PROPN
ejpam-6847	615	16	.	.	PUNCT
ejpam-6847	616	1	new	new	ADJ
ejpam-6847	616	2	fixed	fix	VERB
ejpam-6847	616	3	point	point	NOUN
ejpam-6847	616	4	theorem	theorem	VERB
ejpam-6847	616	5	on	on	ADP
ejpam-6847	616	6	triple	triple	ADJ
ejpam-6847	616	7	controlled	control	VERB
ejpam-6847	616	8	metric	metric	ADJ
ejpam-6847	616	9	type	type	NOUN
ejpam-6847	616	10	spaces	space	NOUN
ejpam-6847	616	11	with	with	ADP
ejpam-6847	616	12	applications	application	NOUN
ejpam-6847	616	13	to	to	ADP
ejpam-6847	616	14	volterra	volterra	PROPN
ejpam-6847	616	15	fredholm	fredholm	VERB
ejpam-6847	616	16	integrodynamic	integrodynamic	ADJ
ejpam-6847	616	17	equations	equation	NOUN
ejpam-6847	616	18	.	.	PUNCT
ejpam-6847	617	1	axioms	axiom	NOUN
ejpam-6847	617	2	,	,	PUNCT
ejpam-6847	617	3	11(1):19	11(1):19	NUM
ejpam-6847	617	4	,	,	PUNCT
ejpam-6847	617	5	2022	2022	NUM
ejpam-6847	617	6	.	.	PUNCT
ejpam-6847	618	1	[	[	X
ejpam-6847	618	2	7	7	X
ejpam-6847	618	3	]	]	PUNCT
ejpam-6847	618	4	j.	j.	PROPN
ejpam-6847	618	5	ahmad	ahmad	PROPN
ejpam-6847	618	6	,	,	PUNCT
ejpam-6847	618	7	a.	a.	PROPN
ejpam-6847	618	8	al	al	PROPN
ejpam-6847	618	9	-	-	PUNCT
ejpam-6847	618	10	mazrooei	mazrooei	PROPN
ejpam-6847	618	11	,	,	PUNCT
ejpam-6847	618	12	h.	h.	PROPN
ejpam-6847	618	13	aydi	aydi	PROPN
ejpam-6847	618	14	,	,	PUNCT
ejpam-6847	618	15	and	and	CCONJ
ejpam-6847	618	16	m.	m.	PROPN
ejpam-6847	618	17	de	de	PROPN
ejpam-6847	618	18	la	la	PROPN
ejpam-6847	618	19	sen	sen	PROPN
ejpam-6847	618	20	.	.	PROPN
ejpam-6847	619	1	on	on	ADP
ejpam-6847	619	2	fixed	fix	VERB
ejpam-6847	619	3	point	point	NOUN
ejpam-6847	619	4	results	result	NOUN
ejpam-6847	619	5	in	in	ADP
ejpam-6847	619	6	controlled	control	VERB
ejpam-6847	619	7	metric	metric	ADJ
ejpam-6847	619	8	spaces	space	NOUN
ejpam-6847	619	9	.	.	PUNCT
ejpam-6847	620	1	journal	journal	NOUN
ejpam-6847	620	2	of	of	ADP
ejpam-6847	620	3	function	function	NOUN
ejpam-6847	620	4	spaces	space	NOUN
ejpam-6847	620	5	,	,	PUNCT
ejpam-6847	620	6	2020	2020	NUM
ejpam-6847	620	7	.	.	PUNCT
ejpam-6847	621	1	[	[	X
ejpam-6847	621	2	8	8	NUM
ejpam-6847	621	3	]	]	X
ejpam-6847	621	4	f.	f.	PROPN
ejpam-6847	621	5	m.	m.	PROPN
ejpam-6847	621	6	azmi	azmi	PROPN
ejpam-6847	621	7	.	.	PUNCT
ejpam-6847	622	1	new	new	ADJ
ejpam-6847	622	2	contractive	contractive	ADJ
ejpam-6847	622	3	mappings	mapping	NOUN
ejpam-6847	622	4	and	and	CCONJ
ejpam-6847	622	5	solutions	solution	NOUN
ejpam-6847	622	6	to	to	ADP
ejpam-6847	622	7	boundary	boundary	ADJ
ejpam-6847	622	8	-	-	PUNCT
ejpam-6847	622	9	value	value	NOUN
ejpam-6847	622	10	problems	problem	NOUN
ejpam-6847	622	11	in	in	ADP
ejpam-6847	622	12	triple	triple	ADJ
ejpam-6847	622	13	controlled	control	VERB
ejpam-6847	622	14	metric	metric	ADJ
ejpam-6847	622	15	type	type	NOUN
ejpam-6847	622	16	spaces	space	NOUN
ejpam-6847	622	17	.	.	PUNCT
ejpam-6847	623	1	symmetry	symmetry	NOUN
ejpam-6847	623	2	,	,	PUNCT
ejpam-6847	623	3	14(11):2270	14(11):2270	NUM
ejpam-6847	623	4	,	,	PUNCT
ejpam-6847	623	5	2022	2022	NUM
ejpam-6847	623	6	.	.	PUNCT
ejpam-6847	624	1	[	[	X
ejpam-6847	624	2	9	9	NUM
ejpam-6847	624	3	]	]	PUNCT
ejpam-6847	624	4	f.	f.	PROPN
ejpam-6847	624	5	m.	m.	PROPN
ejpam-6847	624	6	azmi	azmi	PROPN
ejpam-6847	624	7	.	.	PUNCT
ejpam-6847	625	1	new	new	ADJ
ejpam-6847	625	2	fixed	fix	VERB
ejpam-6847	625	3	point	point	NOUN
ejpam-6847	625	4	results	result	NOUN
ejpam-6847	625	5	in	in	ADP
ejpam-6847	625	6	double	double	ADJ
ejpam-6847	625	7	controlled	control	VERB
ejpam-6847	625	8	metric	metric	ADJ
ejpam-6847	625	9	type	type	NOUN
ejpam-6847	625	10	spaces	space	NOUN
ejpam-6847	625	11	with	with	ADP
ejpam-6847	625	12	applications	application	NOUN
ejpam-6847	625	13	.	.	PUNCT
ejpam-6847	626	1	aims	aim	VERB
ejpam-6847	626	2	mathematics	mathematic	NOUN
ejpam-6847	626	3	,	,	PUNCT
ejpam-6847	626	4	2023	2023	NUM
ejpam-6847	626	5	.	.	PUNCT
ejpam-6847	627	1	[	[	X
ejpam-6847	627	2	10	10	NUM
ejpam-6847	627	3	]	]	PUNCT
ejpam-6847	627	4	z.	z.	PROPN
ejpam-6847	627	5	s.	s.	PROPN
ejpam-6847	627	6	tasneem	tasneem	PROPN
ejpam-6847	627	7	,	,	PUNCT
ejpam-6847	627	8	g.	g.	PROPN
ejpam-6847	627	9	kalpana	kalpana	PROPN
ejpam-6847	627	10	,	,	PUNCT
ejpam-6847	627	11	and	and	CCONJ
ejpam-6847	627	12	t.	t.	PROPN
ejpam-6847	627	13	abdeljawad	abdeljawad	NOUN
ejpam-6847	627	14	.	.	PUNCT
ejpam-6847	628	1	a	a	DET
ejpam-6847	628	2	different	different	ADJ
ejpam-6847	628	3	approach	approach	NOUN
ejpam-6847	628	4	to	to	ADP
ejpam-6847	628	5	fixed	fix	VERB
ejpam-6847	628	6	point	point	NOUN
ejpam-6847	628	7	theorems	theorem	NOUN
ejpam-6847	628	8	on	on	ADP
ejpam-6847	628	9	triple	triple	ADJ
ejpam-6847	628	10	controlled	control	VERB
ejpam-6847	628	11	metric	metric	ADJ
ejpam-6847	628	12	type	type	NOUN
ejpam-6847	628	13	spaces	space	NOUN
ejpam-6847	628	14	with	with	ADP
ejpam-6847	628	15	a	a	DET
ejpam-6847	628	16	numerical	numerical	ADJ
ejpam-6847	628	17	experiment	experiment	NOUN
ejpam-6847	628	18	.	.	PUNCT
ejpam-6847	629	1	dyn	dyn	NOUN
ejpam-6847	629	2	.	.	PUNCT
ejpam-6847	630	1	syst	syst	PROPN
ejpam-6847	630	2	.	.	PUNCT
ejpam-6847	631	1	appl	appl	PROPN
ejpam-6847	631	2	.	.	PROPN
ejpam-6847	631	3	,	,	PUNCT
ejpam-6847	631	4	30:111–130	30:111–130	PROPN
ejpam-6847	631	5	,	,	PUNCT
ejpam-6847	631	6	2021	2021	NUM
ejpam-6847	631	7	.	.	PUNCT
ejpam-6847	632	1	[	[	X
ejpam-6847	632	2	11	11	NUM
ejpam-6847	632	3	]	]	X
ejpam-6847	632	4	s.	s.	PROPN
ejpam-6847	632	5	sedghi	sedghi	PROPN
ejpam-6847	632	6	,	,	PUNCT
ejpam-6847	632	7	n.	n.	PROPN
ejpam-6847	632	8	shobe	shobe	PROPN
ejpam-6847	632	9	,	,	PUNCT
ejpam-6847	632	10	and	and	CCONJ
ejpam-6847	632	11	a.	a.	NOUN
ejpam-6847	632	12	aliouche	aliouche	PROPN
ejpam-6847	632	13	.	.	PUNCT
ejpam-6847	633	1	a	a	DET
ejpam-6847	633	2	generalization	generalization	NOUN
ejpam-6847	633	3	of	of	ADP
ejpam-6847	633	4	fixed	fix	VERB
ejpam-6847	633	5	point	point	NOUN
ejpam-6847	633	6	theorems	theorem	NOUN
ejpam-6847	633	7	in	in	ADP
ejpam-6847	633	8	s	s	NOUN
ejpam-6847	633	9	-	-	ADJ
ejpam-6847	633	10	metric	metric	ADJ
ejpam-6847	633	11	spaces	space	NOUN
ejpam-6847	633	12	.	.	PUNCT
ejpam-6847	634	1	mat	mat	NOUN
ejpam-6847	634	2	.	.	PUNCT
ejpam-6847	634	3	vesn	vesn	PROPN
ejpam-6847	634	4	.	.	PUNCT
ejpam-6847	634	5	,	,	PUNCT
ejpam-6847	635	1	64:258–266	64:258–266	NOUN
ejpam-6847	635	2	,	,	PUNCT
ejpam-6847	635	3	2012	2012	NUM
ejpam-6847	635	4	.	.	PUNCT
ejpam-6847	636	1	[	[	X
ejpam-6847	636	2	12	12	NUM
ejpam-6847	636	3	]	]	X
ejpam-6847	636	4	shaban	shaban	PROPN
ejpam-6847	636	5	sedghi	sedghi	PROPN
ejpam-6847	636	6	and	and	CCONJ
ejpam-6847	636	7	nguyen	nguyen	PROPN
ejpam-6847	636	8	van	van	PROPN
ejpam-6847	636	9	dung	dung	PROPN
ejpam-6847	636	10	.	.	PUNCT
ejpam-6847	637	1	fixed	fix	VERB
ejpam-6847	637	2	point	point	NOUN
ejpam-6847	637	3	theorems	theorem	NOUN
ejpam-6847	637	4	on	on	ADP
ejpam-6847	637	5	s	s	NOUN
ejpam-6847	637	6	-	-	ADJ
ejpam-6847	637	7	metric	metric	ADJ
ejpam-6847	637	8	spaces	space	NOUN
ejpam-6847	637	9	.	.	PUNCT
ejpam-6847	638	1	mat	mat	PROPN
ejpam-6847	638	2	.	.	PUNCT
ejpam-6847	638	3	vesnik	vesnik	PROPN
ejpam-6847	638	4	,	,	PUNCT
ejpam-6847	638	5	66(1	66(1	NOUN
ejpam-6847	638	6	)	)	PUNCT
ejpam-6847	638	7	,	,	PUNCT
ejpam-6847	638	8	2014	2014	NUM
ejpam-6847	638	9	.	.	PUNCT
ejpam-6847	639	1	[	[	X
ejpam-6847	639	2	13	13	NUM
ejpam-6847	639	3	]	]	PUNCT
ejpam-6847	639	4	m.	m.	NOUN
ejpam-6847	639	5	shahraki	shahraki	PROPN
ejpam-6847	639	6	,	,	PUNCT
ejpam-6847	639	7	s.	s.	PROPN
ejpam-6847	639	8	sedghi	sedghi	PROPN
ejpam-6847	639	9	,	,	PUNCT
ejpam-6847	639	10	s.	s.	PROPN
ejpam-6847	639	11	m.	m.	PROPN
ejpam-6847	639	12	a.	a.	NOUN
ejpam-6847	639	13	aleomraninejad	aleomraninejad	NOUN
ejpam-6847	639	14	,	,	PUNCT
ejpam-6847	639	15	and	and	CCONJ
ejpam-6847	639	16	zoran	zoran	PROPN
ejpam-6847	639	17	d.	d.	PROPN
ejpam-6847	639	18	mitrović	mitrović	VERB
ejpam-6847	639	19	.	.	PUNCT
ejpam-6847	640	1	some	some	DET
ejpam-6847	640	2	fixed	fix	VERB
ejpam-6847	640	3	point	point	NOUN
ejpam-6847	640	4	results	result	NOUN
ejpam-6847	640	5	on	on	ADP
ejpam-6847	640	6	s	s	NOUN
ejpam-6847	640	7	-	-	ADJ
ejpam-6847	640	8	metric	metric	ADJ
ejpam-6847	640	9	spaces	space	NOUN
ejpam-6847	640	10	.	.	PUNCT
ejpam-6847	641	1	acta	acta	PROPN
ejpam-6847	641	2	univ	univ	PROPN
ejpam-6847	641	3	.	.	PUNCT
ejpam-6847	642	1	sapientiae	sapientiae	PROPN
ejpam-6847	642	2	,	,	PUNCT
ejpam-6847	642	3	math	math	NOUN
ejpam-6847	642	4	.	.	PUNCT
ejpam-6847	642	5	,	,	PUNCT
ejpam-6847	642	6	12(2):347–357	12(2):347–357	PROPN
ejpam-6847	642	7	,	,	PUNCT
ejpam-6847	642	8	2020	2020	NUM
ejpam-6847	642	9	.	.	PUNCT
ejpam-6847	643	1	f.	f.	PROPN
ejpam-6847	643	2	m.	m.	PROPN
ejpam-6847	643	3	azmi	azmi	PROPN
ejpam-6847	643	4	,	,	PUNCT
ejpam-6847	643	5	a.	a.	PROPN
ejpam-6847	643	6	h.	h.	PROPN
ejpam-6847	643	7	ansari	ansari	PROPN
ejpam-6847	643	8	,	,	PUNCT
ejpam-6847	643	9	s.	s.	PROPN
ejpam-6847	643	10	h.	h.	PROPN
ejpam-6847	643	11	j.	j.	PROPN
ejpam-6847	643	12	petroudi	petroudi	PROPN
ejpam-6847	643	13	/	/	SYM
ejpam-6847	643	14	eur	eur	PROPN
ejpam-6847	643	15	.	.	PUNCT
ejpam-6847	644	1	j.	j.	PROPN
ejpam-6847	644	2	pure	pure	PROPN
ejpam-6847	644	3	appl	appl	PROPN
ejpam-6847	644	4	.	.	PROPN
ejpam-6847	644	5	math	math	PROPN
ejpam-6847	644	6	,	,	PUNCT
ejpam-6847	644	7	18	18	NUM
ejpam-6847	644	8	(	(	PUNCT
ejpam-6847	644	9	4	4	NUM
ejpam-6847	644	10	)	)	PUNCT
ejpam-6847	644	11	(	(	PUNCT
ejpam-6847	644	12	2025	2025	NUM
ejpam-6847	644	13	)	)	PUNCT
ejpam-6847	644	14	,	,	PUNCT
ejpam-6847	644	15	6847	6847	NUM
ejpam-6847	644	16	25	25	NUM
ejpam-6847	644	17	of	of	ADP
ejpam-6847	644	18	26	26	NUM
ejpam-6847	644	19	[	[	X
ejpam-6847	644	20	14	14	NUM
ejpam-6847	644	21	]	]	PUNCT
ejpam-6847	644	22	m.	m.	NOUN
ejpam-6847	644	23	simkhah	simkhah	NOUN
ejpam-6847	644	24	asil	asil	PROPN
ejpam-6847	644	25	,	,	PUNCT
ejpam-6847	644	26	sh	sh	PROPN
ejpam-6847	644	27	.	.	PROPN
ejpam-6847	644	28	sedghi	sedghi	PROPN
ejpam-6847	644	29	,	,	PUNCT
ejpam-6847	644	30	n.	n.	PROPN
ejpam-6847	644	31	shobe	shobe	PROPN
ejpam-6847	644	32	,	,	PUNCT
ejpam-6847	644	33	and	and	CCONJ
ejpam-6847	644	34	z.	z.	PROPN
ejpam-6847	644	35	d.	d.	PROPN
ejpam-6847	644	36	mitrović	mitrović	PROPN
ejpam-6847	644	37	.	.	PUNCT
ejpam-6847	645	1	s	s	X
ejpam-6847	645	2	-	-	ADJ
ejpam-6847	645	3	metric	metric	ADJ
ejpam-6847	645	4	and	and	CCONJ
ejpam-6847	645	5	fixed	fix	VERB
ejpam-6847	645	6	point	point	NOUN
ejpam-6847	645	7	theorem	theorem	VERB
ejpam-6847	645	8	.	.	PUNCT
ejpam-6847	646	1	j.	j.	PROPN
ejpam-6847	646	2	linear	linear	PROPN
ejpam-6847	646	3	topol	topol	PROPN
ejpam-6847	646	4	.	.	PUNCT
ejpam-6847	647	1	algebra	algebra	NOUN
ejpam-6847	647	2	,	,	PUNCT
ejpam-6847	647	3	9(3):213–220	9(3):213–220	NOUN
ejpam-6847	647	4	,	,	PUNCT
ejpam-6847	647	5	2020	2020	NUM
ejpam-6847	647	6	.	.	PUNCT
ejpam-6847	648	1	[	[	X
ejpam-6847	648	2	15	15	NUM
ejpam-6847	648	3	]	]	X
ejpam-6847	648	4	n.	n.	NOUN
ejpam-6847	648	5	souayah	souayah	NOUN
ejpam-6847	648	6	and	and	CCONJ
ejpam-6847	648	7	n.	n.	PROPN
ejpam-6847	648	8	mlaiki	mlaiki	PROPN
ejpam-6847	648	9	.	.	PUNCT
ejpam-6847	649	1	a	a	DET
ejpam-6847	649	2	fixed	fix	VERB
ejpam-6847	649	3	point	point	NOUN
ejpam-6847	649	4	theorem	theorem	VERB
ejpam-6847	649	5	in	in	ADP
ejpam-6847	649	6	sb	sb	NOUN
ejpam-6847	649	7	-	-	ADJ
ejpam-6847	649	8	metric	metric	ADJ
ejpam-6847	649	9	spaces	space	NOUN
ejpam-6847	649	10	.	.	PUNCT
ejpam-6847	650	1	j.	j.	PROPN
ejpam-6847	650	2	math	math	PROPN
ejpam-6847	650	3	.	.	PUNCT
ejpam-6847	651	1	comput	comput	NOUN
ejpam-6847	651	2	.	.	PUNCT
ejpam-6847	652	1	sci	sci	PROPN
ejpam-6847	652	2	.	.	PROPN
ejpam-6847	652	3	,	,	PUNCT
ejpam-6847	652	4	16:131–139	16:131–139	NUM
ejpam-6847	652	5	,	,	PUNCT
ejpam-6847	652	6	2016	2016	NUM
ejpam-6847	652	7	.	.	PUNCT
ejpam-6847	653	1	[	[	X
ejpam-6847	653	2	16	16	NUM
ejpam-6847	653	3	]	]	X
ejpam-6847	653	4	n.	n.	PROPN
ejpam-6847	653	5	mlaiki	mlaiki	PROPN
ejpam-6847	653	6	.	.	PROPN
ejpam-6847	654	1	extended	extend	VERB
ejpam-6847	654	2	sb	sb	NOUN
ejpam-6847	654	3	-	-	ADJ
ejpam-6847	654	4	metric	metric	ADJ
ejpam-6847	654	5	spaces	space	NOUN
ejpam-6847	654	6	.	.	PUNCT
ejpam-6847	655	1	j.	j.	PROPN
ejpam-6847	655	2	math	math	PROPN
ejpam-6847	655	3	.	.	PUNCT
ejpam-6847	656	1	anal	anal	PROPN
ejpam-6847	656	2	.	.	PROPN
ejpam-6847	656	3	,	,	PUNCT
ejpam-6847	656	4	9:124–135	9:124–135	PROPN
ejpam-6847	656	5	,	,	PUNCT
ejpam-6847	656	6	2018	2018	NUM
ejpam-6847	656	7	.	.	PUNCT
ejpam-6847	657	1	[	[	X
ejpam-6847	657	2	17	17	NUM
ejpam-6847	657	3	]	]	PUNCT
ejpam-6847	657	4	m.	m.	NOUN
ejpam-6847	657	5	simkhah	simkhah	NOUN
ejpam-6847	657	6	asil	asil	PROPN
ejpam-6847	657	7	,	,	PUNCT
ejpam-6847	657	8	shaban	shaban	PROPN
ejpam-6847	657	9	sedghi	sedghi	PROPN
ejpam-6847	657	10	,	,	PUNCT
ejpam-6847	657	11	and	and	CCONJ
ejpam-6847	657	12	zoran	zoran	PROPN
ejpam-6847	657	13	d.	d.	PROPN
ejpam-6847	657	14	mitrović	mitrović	PROPN
ejpam-6847	657	15	.	.	PUNCT
ejpam-6847	658	1	partial	partial	ADJ
ejpam-6847	658	2	s	s	NOUN
ejpam-6847	658	3	-	-	ADJ
ejpam-6847	658	4	metric	metric	ADJ
ejpam-6847	658	5	spaces	space	NOUN
ejpam-6847	658	6	and	and	CCONJ
ejpam-6847	658	7	coincidence	coincidence	NOUN
ejpam-6847	658	8	points	point	NOUN
ejpam-6847	658	9	.	.	PUNCT
ejpam-6847	659	1	filomat	filomat	NOUN
ejpam-6847	659	2	,	,	PUNCT
ejpam-6847	659	3	33(14):4613–4626	33(14):4613–4626	NUM
ejpam-6847	659	4	,	,	PUNCT
ejpam-6847	659	5	2019	2019	NUM
ejpam-6847	659	6	.	.	PUNCT
ejpam-6847	660	1	[	[	X
ejpam-6847	660	2	18	18	NUM
ejpam-6847	660	3	]	]	X
ejpam-6847	660	4	r.	r.	PROPN
ejpam-6847	660	5	qaralleh	qaralleh	PROPN
ejpam-6847	660	6	,	,	PUNCT
ejpam-6847	660	7	a.	a.	NOUN
ejpam-6847	660	8	tallafha	tallafha	NOUN
ejpam-6847	660	9	,	,	PUNCT
ejpam-6847	660	10	and	and	CCONJ
ejpam-6847	660	11	w.	w.	PROPN
ejpam-6847	660	12	shatanawi	shatanawi	PROPN
ejpam-6847	660	13	.	.	PUNCT
ejpam-6847	661	1	some	some	DET
ejpam-6847	661	2	fixed	fix	VERB
ejpam-6847	661	3	-	-	PUNCT
ejpam-6847	661	4	point	point	NOUN
ejpam-6847	661	5	results	result	NOUN
ejpam-6847	661	6	in	in	ADP
ejpam-6847	661	7	extended	extended	ADJ
ejpam-6847	661	8	s	s	NOUN
ejpam-6847	661	9	-	-	ADJ
ejpam-6847	661	10	metric	metric	ADJ
ejpam-6847	661	11	space	space	NOUN
ejpam-6847	661	12	of	of	ADP
ejpam-6847	661	13	type	type	NOUN
ejpam-6847	661	14	(	(	PUNCT
ejpam-6847	661	15	α	α	NOUN
ejpam-6847	661	16	,	,	PUNCT
ejpam-6847	661	17	β	β	NOUN
ejpam-6847	661	18	)	)	PUNCT
ejpam-6847	661	19	.	.	PUNCT
ejpam-6847	662	1	symmetry	symmetry	NOUN
ejpam-6847	662	2	,	,	PUNCT
ejpam-6847	662	3	2023	2023	NUM
ejpam-6847	662	4	.	.	PUNCT
ejpam-6847	663	1	[	[	X
ejpam-6847	663	2	19	19	NUM
ejpam-6847	663	3	]	]	X
ejpam-6847	663	4	n.	n.	PROPN
ejpam-6847	663	5	e.	e.	PROPN
ejpam-6847	663	6	yazici	yazici	PROPN
ejpam-6847	663	7	,	,	PUNCT
ejpam-6847	663	8	o.	o.	PROPN
ejpam-6847	663	9	ege	ege	PROPN
ejpam-6847	663	10	,	,	PUNCT
ejpam-6847	663	11	n.	n.	PROPN
ejpam-6847	663	12	mlaiki	mlaiki	PROPN
ejpam-6847	663	13	,	,	PUNCT
ejpam-6847	663	14	and	and	CCONJ
ejpam-6847	663	15	a.	a.	NOUN
ejpam-6847	663	16	mukheimer	mukheimer	PROPN
ejpam-6847	663	17	.	.	PROPN
ejpam-6847	663	18	controlled	control	VERB
ejpam-6847	663	19	s	s	X
ejpam-6847	663	20	-	-	ADJ
ejpam-6847	663	21	metric	metric	ADJ
ejpam-6847	663	22	-	-	PUNCT
ejpam-6847	663	23	type	type	NOUN
ejpam-6847	663	24	spaces	space	NOUN
ejpam-6847	663	25	and	and	CCONJ
ejpam-6847	663	26	applications	application	NOUN
ejpam-6847	663	27	to	to	ADP
ejpam-6847	663	28	fractional	fractional	ADJ
ejpam-6847	663	29	integrals	integral	NOUN
ejpam-6847	663	30	.	.	PUNCT
ejpam-6847	664	1	symmetry	symmetry	NOUN
ejpam-6847	664	2	,	,	PUNCT
ejpam-6847	664	3	2023	2023	NUM
ejpam-6847	664	4	.	.	PUNCT
ejpam-6847	665	1	[	[	X
ejpam-6847	665	2	20	20	NUM
ejpam-6847	665	3	]	]	PUNCT
ejpam-6847	665	4	f.	f.	PROPN
ejpam-6847	665	5	m.	m.	PROPN
ejpam-6847	665	6	azmi	azmi	PROPN
ejpam-6847	665	7	.	.	PUNCT
ejpam-6847	666	1	wardowski	wardowski	PROPN
ejpam-6847	666	2	contraction	contraction	NOUN
ejpam-6847	666	3	on	on	ADP
ejpam-6847	666	4	controlled	control	VERB
ejpam-6847	666	5	s	s	ADJ
ejpam-6847	666	6	-	-	ADJ
ejpam-6847	666	7	metric	metric	ADJ
ejpam-6847	666	8	type	type	NOUN
ejpam-6847	666	9	spaces	space	NOUN
ejpam-6847	666	10	with	with	ADP
ejpam-6847	666	11	fixed	fix	VERB
ejpam-6847	666	12	point	point	NOUN
ejpam-6847	666	13	results	result	NOUN
ejpam-6847	666	14	.	.	PUNCT
ejpam-6847	667	1	int	int	NOUN
ejpam-6847	667	2	.	.	PUNCT
ejpam-6847	668	1	j.	j.	PROPN
ejpam-6847	668	2	anal	anal	PROPN
ejpam-6847	668	3	.	.	PUNCT
ejpam-6847	669	1	appl	appl	PROPN
ejpam-6847	669	2	.	.	PROPN
ejpam-6847	669	3	,	,	PUNCT
ejpam-6847	669	4	2024	2024	NUM
ejpam-6847	669	5	.	.	PUNCT
ejpam-6847	670	1	[	[	X
ejpam-6847	670	2	21	21	NUM
ejpam-6847	670	3	]	]	X
ejpam-6847	670	4	b.	b.	PROPN
ejpam-6847	670	5	w.	w.	PROPN
ejpam-6847	670	6	samuel	samuel	PROPN
ejpam-6847	670	7	,	,	PUNCT
ejpam-6847	670	8	g.	g.	PROPN
ejpam-6847	670	9	mani	mani	PROPN
ejpam-6847	670	10	,	,	PUNCT
ejpam-6847	670	11	s.	s.	PROPN
ejpam-6847	670	12	s.	s.	PROPN
ejpam-6847	670	13	ramulu	ramulu	PROPN
ejpam-6847	670	14	,	,	PUNCT
ejpam-6847	670	15	et	et	PROPN
ejpam-6847	670	16	al	al	PROPN
ejpam-6847	670	17	.	.	PROPN
ejpam-6847	670	18	integral	integral	ADJ
ejpam-6847	670	19	-	-	PUNCT
ejpam-6847	670	20	type	type	NOUN
ejpam-6847	670	21	contraction	contraction	NOUN
ejpam-6847	670	22	on	on	ADP
ejpam-6847	670	23	orthogonal	orthogonal	ADJ
ejpam-6847	670	24	s	s	NOUN
ejpam-6847	670	25	-	-	ADJ
ejpam-6847	670	26	metric	metric	ADJ
ejpam-6847	670	27	spaces	space	NOUN
ejpam-6847	670	28	with	with	ADP
ejpam-6847	670	29	common	common	ADJ
ejpam-6847	670	30	fixed	fix	VERB
ejpam-6847	670	31	-	-	PUNCT
ejpam-6847	670	32	point	point	NOUN
ejpam-6847	670	33	results	result	NOUN
ejpam-6847	670	34	and	and	CCONJ
ejpam-6847	670	35	applications	application	NOUN
ejpam-6847	670	36	to	to	PART
ejpam-6847	670	37	fractional	fractional	ADJ
ejpam-6847	670	38	integral	integral	ADJ
ejpam-6847	670	39	equations	equation	NOUN
ejpam-6847	670	40	.	.	PUNCT
ejpam-6847	671	1	fixed	fix	VERB
ejpam-6847	671	2	point	point	NOUN
ejpam-6847	671	3	theory	theory	NOUN
ejpam-6847	671	4	and	and	CCONJ
ejpam-6847	671	5	algorithms	algorithm	NOUN
ejpam-6847	671	6	for	for	ADP
ejpam-6847	671	7	sciences	science	NOUN
ejpam-6847	671	8	and	and	CCONJ
ejpam-6847	671	9	engineering	engineering	NOUN
ejpam-6847	671	10	,	,	PUNCT
ejpam-6847	671	11	2025:10	2025:10	NUM
ejpam-6847	671	12	,	,	PUNCT
ejpam-6847	671	13	2025	2025	NUM
ejpam-6847	671	14	.	.	PUNCT
ejpam-6847	672	1	[	[	X
ejpam-6847	672	2	22	22	NUM
ejpam-6847	672	3	]	]	X
ejpam-6847	672	4	b.	b.	PROPN
ejpam-6847	672	5	w.	w.	PROPN
ejpam-6847	672	6	samuel	samuel	PROPN
ejpam-6847	672	7	,	,	PUNCT
ejpam-6847	672	8	g.	g.	PROPN
ejpam-6847	672	9	mani	mani	PROPN
ejpam-6847	672	10	,	,	PUNCT
ejpam-6847	672	11	p.	p.	PROPN
ejpam-6847	672	12	ganesh	ganesh	PROPN
ejpam-6847	672	13	,	,	PUNCT
ejpam-6847	672	14	s.	s.	PROPN
ejpam-6847	672	15	t.	t.	PROPN
ejpam-6847	672	16	m.	m.	PROPN
ejpam-6847	672	17	thabet	thabet	PROPN
ejpam-6847	672	18	,	,	PUNCT
ejpam-6847	672	19	i.	i.	PROPN
ejpam-6847	672	20	kedim	kedim	PROPN
ejpam-6847	672	21	,	,	PUNCT
ejpam-6847	672	22	and	and	CCONJ
ejpam-6847	672	23	m.	m.	NOUN
ejpam-6847	672	24	vivascortez	vivascortez	PROPN
ejpam-6847	672	25	.	.	PUNCT
ejpam-6847	673	1	new	new	ADJ
ejpam-6847	673	2	common	common	ADJ
ejpam-6847	673	3	fixed	fix	VERB
ejpam-6847	673	4	point	point	NOUN
ejpam-6847	673	5	theorems	theorem	NOUN
ejpam-6847	673	6	for	for	ADP
ejpam-6847	673	7	quartet	quartet	NOUN
ejpam-6847	673	8	mappings	mapping	NOUN
ejpam-6847	673	9	on	on	ADP
ejpam-6847	673	10	orthogonal	orthogonal	ADJ
ejpam-6847	673	11	smetric	smetric	ADJ
ejpam-6847	673	12	spaces	space	NOUN
ejpam-6847	673	13	with	with	ADP
ejpam-6847	673	14	applications	application	NOUN
ejpam-6847	673	15	.	.	PUNCT
ejpam-6847	674	1	j.	j.	PROPN
ejpam-6847	674	2	math	math	PROPN
ejpam-6847	674	3	.	.	PUNCT
ejpam-6847	675	1	comput	comput	NOUN
ejpam-6847	675	2	.	.	PUNCT
ejpam-6847	676	1	sci	sci	PROPN
ejpam-6847	676	2	.	.	PROPN
ejpam-6847	676	3	,	,	PUNCT
ejpam-6847	676	4	38(1):80–97	38(1):80–97	NUM
ejpam-6847	676	5	,	,	PUNCT
ejpam-6847	676	6	2025	2025	NUM
ejpam-6847	676	7	.	.	PUNCT
ejpam-6847	677	1	[	[	X
ejpam-6847	677	2	23	23	NUM
ejpam-6847	677	3	]	]	X
ejpam-6847	677	4	w.	w.	PROPN
ejpam-6847	677	5	wardowski	wardowski	PROPN
ejpam-6847	677	6	.	.	PUNCT
ejpam-6847	678	1	fixed	fix	VERB
ejpam-6847	678	2	points	point	NOUN
ejpam-6847	678	3	of	of	ADP
ejpam-6847	678	4	a	a	DET
ejpam-6847	678	5	new	new	ADJ
ejpam-6847	678	6	type	type	NOUN
ejpam-6847	678	7	of	of	ADP
ejpam-6847	678	8	contractive	contractive	ADJ
ejpam-6847	678	9	mappings	mapping	NOUN
ejpam-6847	678	10	in	in	ADP
ejpam-6847	678	11	complete	complete	ADJ
ejpam-6847	678	12	metric	metric	ADJ
ejpam-6847	678	13	spaces	space	NOUN
ejpam-6847	678	14	.	.	PUNCT
ejpam-6847	679	1	fixed	fix	VERB
ejpam-6847	679	2	point	point	NOUN
ejpam-6847	679	3	theory	theory	NOUN
ejpam-6847	679	4	appl	appl	PROPN
ejpam-6847	679	5	.	.	PROPN
ejpam-6847	679	6	,	,	PUNCT
ejpam-6847	679	7	2012	2012	NUM
ejpam-6847	679	8	.	.	PUNCT
ejpam-6847	680	1	[	[	X
ejpam-6847	680	2	24	24	NUM
ejpam-6847	680	3	]	]	PUNCT
ejpam-6847	680	4	m.	m.	NOUN
ejpam-6847	680	5	u.	u.	PROPN
ejpam-6847	680	6	ali	ali	PROPN
ejpam-6847	680	7	and	and	CCONJ
ejpam-6847	680	8	t.	t.	PROPN
ejpam-6847	680	9	kamran	kamran	PROPN
ejpam-6847	680	10	.	.	PUNCT
ejpam-6847	681	1	multivalued	multivalue	VERB
ejpam-6847	682	1	f	f	X
ejpam-6847	682	2	-	-	PUNCT
ejpam-6847	682	3	contractions	contraction	NOUN
ejpam-6847	682	4	and	and	CCONJ
ejpam-6847	682	5	related	relate	VERB
ejpam-6847	682	6	fixed	fix	VERB
ejpam-6847	682	7	point	point	NOUN
ejpam-6847	682	8	theorems	theorem	NOUN
ejpam-6847	682	9	with	with	ADP
ejpam-6847	682	10	an	an	DET
ejpam-6847	682	11	application	application	NOUN
ejpam-6847	682	12	.	.	PUNCT
ejpam-6847	683	1	filomat	filomat	NOUN
ejpam-6847	683	2	,	,	PUNCT
ejpam-6847	683	3	30:3779–3793	30:3779–3793	NUM
ejpam-6847	683	4	,	,	PUNCT
ejpam-6847	683	5	2016	2016	NUM
ejpam-6847	683	6	.	.	PUNCT
ejpam-6847	684	1	[	[	X
ejpam-6847	684	2	25	25	NUM
ejpam-6847	684	3	]	]	X
ejpam-6847	684	4	o.	o.	NOUN
ejpam-6847	684	5	acar	acar	NOUN
ejpam-6847	684	6	and	and	CCONJ
ejpam-6847	684	7	i̇.	i̇.	VERB
ejpam-6847	684	8	altun	altun	NOUN
ejpam-6847	684	9	.	.	PUNCT
ejpam-6847	685	1	multivalued	multivalue	VERB
ejpam-6847	685	2	f	f	X
ejpam-6847	685	3	-	-	PUNCT
ejpam-6847	685	4	contractive	contractive	ADJ
ejpam-6847	685	5	mappings	mapping	NOUN
ejpam-6847	685	6	with	with	ADP
ejpam-6847	685	7	a	a	DET
ejpam-6847	685	8	graph	graph	NOUN
ejpam-6847	685	9	and	and	CCONJ
ejpam-6847	685	10	some	some	DET
ejpam-6847	685	11	fixed	fix	VERB
ejpam-6847	685	12	point	point	NOUN
ejpam-6847	685	13	results	result	NOUN
ejpam-6847	685	14	.	.	PUNCT
ejpam-6847	686	1	publ	publ	NOUN
ejpam-6847	686	2	.	.	PUNCT
ejpam-6847	687	1	math	math	NOUN
ejpam-6847	687	2	.	.	PUNCT
ejpam-6847	688	1	(	(	PUNCT
ejpam-6847	688	2	debr	debr	NOUN
ejpam-6847	688	3	.	.	PUNCT
ejpam-6847	688	4	)	)	PUNCT
ejpam-6847	689	1	,	,	PUNCT
ejpam-6847	689	2	88:305–317	88:305–317	NUM
ejpam-6847	689	3	,	,	PUNCT
ejpam-6847	689	4	2016	2016	NUM
ejpam-6847	689	5	.	.	PUNCT
ejpam-6847	690	1	[	[	X
ejpam-6847	690	2	26	26	NUM
ejpam-6847	690	3	]	]	X
ejpam-6847	690	4	h.	h.	PROPN
ejpam-6847	690	5	aydi	aydi	PROPN
ejpam-6847	690	6	,	,	PUNCT
ejpam-6847	690	7	e.	e.	PROPN
ejpam-6847	690	8	karapinar	karapinar	PROPN
ejpam-6847	690	9	,	,	PUNCT
ejpam-6847	690	10	and	and	CCONJ
ejpam-6847	690	11	h.	h.	PROPN
ejpam-6847	690	12	yazidi	yazidi	PROPN
ejpam-6847	690	13	.	.	PUNCT
ejpam-6847	691	1	modified	modify	VERB
ejpam-6847	691	2	f	f	PROPN
ejpam-6847	691	3	-contractions	-contraction	NOUN
ejpam-6847	691	4	via	via	ADP
ejpam-6847	691	5	α	α	DET
ejpam-6847	691	6	-	-	PUNCT
ejpam-6847	691	7	admissible	admissible	ADJ
ejpam-6847	691	8	mappings	mapping	NOUN
ejpam-6847	691	9	and	and	CCONJ
ejpam-6847	691	10	application	application	NOUN
ejpam-6847	691	11	to	to	ADP
ejpam-6847	691	12	integral	integral	ADJ
ejpam-6847	691	13	equations	equation	NOUN
ejpam-6847	691	14	.	.	PUNCT
ejpam-6847	692	1	filomat	filomat	NOUN
ejpam-6847	692	2	,	,	PUNCT
ejpam-6847	692	3	31:1141–1148	31:1141–1148	NUM
ejpam-6847	692	4	,	,	PUNCT
ejpam-6847	692	5	2017	2017	NUM
ejpam-6847	692	6	.	.	PUNCT
ejpam-6847	693	1	[	[	X
ejpam-6847	693	2	27	27	NUM
ejpam-6847	693	3	]	]	X
ejpam-6847	693	4	e.	e.	PROPN
ejpam-6847	693	5	karapinar	karapinar	PROPN
ejpam-6847	693	6	,	,	PUNCT
ejpam-6847	693	7	a.	a.	NOUN
ejpam-6847	693	8	fulga	fulga	NOUN
ejpam-6847	693	9	,	,	PUNCT
ejpam-6847	693	10	and	and	CCONJ
ejpam-6847	693	11	r.	r.	PROPN
ejpam-6847	693	12	p.	p.	PROPN
ejpam-6847	693	13	agarwal	agarwal	PROPN
ejpam-6847	693	14	.	.	PUNCT
ejpam-6847	694	1	a	a	DET
ejpam-6847	694	2	survey	survey	NOUN
ejpam-6847	694	3	:	:	PUNCT
ejpam-6847	694	4	f	f	PROPN
ejpam-6847	694	5	-contractions	-contraction	NOUN
ejpam-6847	694	6	with	with	ADP
ejpam-6847	694	7	related	related	ADJ
ejpam-6847	694	8	fixed	fix	VERB
ejpam-6847	694	9	point	point	NOUN
ejpam-6847	694	10	results	result	NOUN
ejpam-6847	694	11	.	.	PUNCT
ejpam-6847	695	1	j.	j.	PROPN
ejpam-6847	695	2	fixed	fix	VERB
ejpam-6847	695	3	point	point	PROPN
ejpam-6847	695	4	theory	theory	NOUN
ejpam-6847	695	5	appl	appl	PROPN
ejpam-6847	695	6	.	.	PROPN
ejpam-6847	695	7	,	,	PUNCT
ejpam-6847	695	8	2020	2020	NUM
ejpam-6847	695	9	.	.	PUNCT
ejpam-6847	696	1	[	[	X
ejpam-6847	696	2	28	28	NUM
ejpam-6847	696	3	]	]	X
ejpam-6847	696	4	r.	r.	PROPN
ejpam-6847	696	5	p.	p.	PROPN
ejpam-6847	696	6	agarwal	agarwal	PROPN
ejpam-6847	696	7	,	,	PUNCT
ejpam-6847	696	8	u.	u.	PROPN
ejpam-6847	696	9	aksoy	aksoy	PROPN
ejpam-6847	696	10	,	,	PUNCT
ejpam-6847	696	11	e.	e.	PROPN
ejpam-6847	696	12	karapinar	karapinar	PROPN
ejpam-6847	696	13	,	,	PUNCT
ejpam-6847	696	14	and	and	CCONJ
ejpam-6847	696	15	i.	i.	PROPN
ejpam-6847	696	16	m.	m.	PROPN
ejpam-6847	696	17	erhan	erhan	PROPN
ejpam-6847	696	18	.	.	PUNCT
ejpam-6847	697	1	f	f	PROPN
ejpam-6847	697	2	-contraction	-contraction	PROPN
ejpam-6847	697	3	mappings	mapping	NOUN
ejpam-6847	697	4	on	on	ADP
ejpam-6847	697	5	metric	metric	ADJ
ejpam-6847	697	6	-	-	PUNCT
ejpam-6847	697	7	like	like	ADJ
ejpam-6847	697	8	spaces	space	NOUN
ejpam-6847	697	9	in	in	ADP
ejpam-6847	697	10	connection	connection	NOUN
ejpam-6847	697	11	with	with	ADP
ejpam-6847	697	12	integral	integral	ADJ
ejpam-6847	697	13	equations	equation	NOUN
ejpam-6847	697	14	on	on	ADP
ejpam-6847	697	15	time	time	NOUN
ejpam-6847	697	16	scales	scale	NOUN
ejpam-6847	697	17	.	.	PUNCT
ejpam-6847	698	1	racsam	racsam	PROPN
ejpam-6847	698	2	,	,	PUNCT
ejpam-6847	698	3	114:147	114:147	NUM
ejpam-6847	698	4	,	,	PUNCT
ejpam-6847	698	5	2020	2020	NUM
ejpam-6847	698	6	.	.	PUNCT
ejpam-6847	699	1	[	[	X
ejpam-6847	699	2	29	29	NUM
ejpam-6847	699	3	]	]	PUNCT
ejpam-6847	699	4	k.	k.	PROPN
ejpam-6847	699	5	m.	m.	PROPN
ejpam-6847	699	6	devi	devi	PROPN
ejpam-6847	699	7	,	,	PUNCT
ejpam-6847	699	8	y.	y.	PROPN
ejpam-6847	699	9	rohen	rohen	PROPN
ejpam-6847	699	10	,	,	PUNCT
ejpam-6847	699	11	and	and	CCONJ
ejpam-6847	699	12	k.	k.	PROPN
ejpam-6847	699	13	a.	a.	PROPN
ejpam-6847	699	14	singh	singh	PROPN
ejpam-6847	699	15	.	.	PUNCT
ejpam-6847	700	1	fixed	fix	VERB
ejpam-6847	700	2	points	point	NOUN
ejpam-6847	700	3	of	of	ADP
ejpam-6847	700	4	modified	modified	ADJ
ejpam-6847	700	5	f	f	PROPN
ejpam-6847	700	6	-contractions	-contraction	NOUN
ejpam-6847	700	7	in	in	ADP
ejpam-6847	700	8	s	s	NOUN
ejpam-6847	700	9	-	-	ADJ
ejpam-6847	700	10	metric	metric	ADJ
ejpam-6847	700	11	spaces	space	NOUN
ejpam-6847	700	12	.	.	PUNCT
ejpam-6847	701	1	j.	j.	PROPN
ejpam-6847	701	2	math	math	PROPN
ejpam-6847	701	3	.	.	PUNCT
ejpam-6847	702	1	comput	comput	NOUN
ejpam-6847	702	2	.	.	PUNCT
ejpam-6847	703	1	sci	sci	PROPN
ejpam-6847	703	2	.	.	PROPN
ejpam-6847	703	3	,	,	PUNCT
ejpam-6847	703	4	2022	2022	NUM
ejpam-6847	703	5	.	.	PUNCT
ejpam-6847	704	1	[	[	X
ejpam-6847	704	2	30	30	NUM
ejpam-6847	704	3	]	]	PUNCT
ejpam-6847	704	4	a.	a.	NOUN
ejpam-6847	704	5	h.	h.	PROPN
ejpam-6847	704	6	ansari	ansari	PROPN
ejpam-6847	704	7	and	and	CCONJ
ejpam-6847	704	8	s.	s.	PROPN
ejpam-6847	704	9	shukla	shukla	PROPN
ejpam-6847	704	10	.	.	PUNCT
ejpam-6847	705	1	some	some	DET
ejpam-6847	705	2	fixed	fix	VERB
ejpam-6847	705	3	point	point	NOUN
ejpam-6847	705	4	theorems	theorem	NOUN
ejpam-6847	705	5	for	for	ADP
ejpam-6847	705	6	ordered	order	VERB
ejpam-6847	705	7	f	f	PROPN
ejpam-6847	705	8	-(f	-(f	PUNCT
ejpam-6847	705	9	,	,	PUNCT
ejpam-6847	705	10	h)contraction	h)contraction	NOUN
ejpam-6847	705	11	and	and	CCONJ
ejpam-6847	705	12	subcontractions	subcontraction	NOUN
ejpam-6847	705	13	in	in	ADP
ejpam-6847	705	14	0	0	NUM
ejpam-6847	705	15	-	-	SYM
ejpam-6847	705	16	f	f	NOUN
ejpam-6847	705	17	-orbitally	-orbitally	NOUN
ejpam-6847	705	18	complete	complete	ADJ
ejpam-6847	705	19	partial	partial	ADJ
ejpam-6847	705	20	metric	metric	ADJ
ejpam-6847	705	21	spaces	space	NOUN
ejpam-6847	705	22	.	.	PUNCT
ejpam-6847	706	1	j.	j.	PROPN
ejpam-6847	706	2	adv	adv	PROPN
ejpam-6847	706	3	.	.	PUNCT
ejpam-6847	706	4	math	math	PROPN
ejpam-6847	706	5	.	.	PUNCT
ejpam-6847	707	1	stud	stud	PROPN
ejpam-6847	707	2	.	.	PUNCT
ejpam-6847	707	3	,	,	PUNCT
ejpam-6847	707	4	9(1):37–53	9(1):37–53	NUM
ejpam-6847	707	5	,	,	PUNCT
ejpam-6847	707	6	2016	2016	NUM
ejpam-6847	707	7	.	.	PUNCT
ejpam-6847	708	1	[	[	X
ejpam-6847	708	2	31	31	NUM
ejpam-6847	708	3	]	]	PUNCT
ejpam-6847	708	4	gunaseelan	gunaseelan	PROPN
ejpam-6847	708	5	mani	mani	PROPN
ejpam-6847	708	6	,	,	PUNCT
ejpam-6847	708	7	rajagopalan	rajagopalan	VERB
ejpam-6847	708	8	ramaswamy	ramaswamy	ADJ
ejpam-6847	708	9	,	,	PUNCT
ejpam-6847	708	10	arul	arul	PROPN
ejpam-6847	708	11	joseph	joseph	PROPN
ejpam-6847	708	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6847	708	13	,	,	PUNCT
ejpam-6847	708	14	vuk	vuk	PROPN
ejpam-6847	708	15	stojiljković	stojiljković	PROPN
ejpam-6847	708	16	,	,	PUNCT
ejpam-6847	708	17	zaid	zaid	PROPN
ejpam-6847	708	18	m.	m.	PROPN
ejpam-6847	708	19	fadail	fadail	PROPN
ejpam-6847	708	20	,	,	PUNCT
ejpam-6847	708	21	and	and	CCONJ
ejpam-6847	708	22	stojan	stojan	ADP
ejpam-6847	708	23	radenović	radenović	PROPN
ejpam-6847	708	24	.	.	PUNCT
ejpam-6847	709	1	application	application	NOUN
ejpam-6847	709	2	of	of	ADP
ejpam-6847	709	3	fixed	fix	VERB
ejpam-6847	709	4	-	-	PUNCT
ejpam-6847	709	5	point	point	NOUN
ejpam-6847	709	6	results	result	NOUN
ejpam-6847	709	7	in	in	ADP
ejpam-6847	709	8	the	the	DET
ejpam-6847	709	9	setting	setting	NOUN
ejpam-6847	709	10	of	of	ADP
ejpam-6847	709	11	f	f	PROPN
ejpam-6847	709	12	-contraction	-contraction	PROPN
ejpam-6847	709	13	and	and	CCONJ
ejpam-6847	709	14	simulation	simulation	NOUN
ejpam-6847	709	15	function	function	NOUN
ejpam-6847	709	16	in	in	ADP
ejpam-6847	709	17	the	the	DET
ejpam-6847	709	18	setting	setting	NOUN
ejpam-6847	709	19	of	of	ADP
ejpam-6847	709	20	bipolar	bipolar	ADJ
ejpam-6847	709	21	metric	metric	ADJ
ejpam-6847	709	22	space	space	NOUN
ejpam-6847	709	23	.	.	PUNCT
ejpam-6847	710	1	aims	aim	VERB
ejpam-6847	710	2	mathematics	mathematic	NOUN
ejpam-6847	710	3	,	,	PUNCT
ejpam-6847	710	4	8(2):3269–3285	8(2):3269–3285	NUM
ejpam-6847	710	5	,	,	PUNCT
ejpam-6847	710	6	2023	2023	NUM
ejpam-6847	710	7	.	.	PUNCT
ejpam-6847	711	1	[	[	X
ejpam-6847	711	2	32	32	NUM
ejpam-6847	711	3	]	]	PUNCT
ejpam-6847	711	4	b.	b.	PROPN
ejpam-6847	711	5	samet	samet	PROPN
ejpam-6847	711	6	,	,	PUNCT
ejpam-6847	711	7	c.	c.	PROPN
ejpam-6847	711	8	vetro	vetro	PROPN
ejpam-6847	711	9	,	,	PUNCT
ejpam-6847	711	10	and	and	CCONJ
ejpam-6847	711	11	p.	p.	PROPN
ejpam-6847	711	12	vetro	vetro	PROPN
ejpam-6847	711	13	.	.	PUNCT
ejpam-6847	712	1	fixed	fix	VERB
ejpam-6847	712	2	points	point	NOUN
ejpam-6847	712	3	theorems	theorem	NOUN
ejpam-6847	712	4	for	for	ADP
ejpam-6847	712	5	α	α	NOUN
ejpam-6847	712	6	-	-	PUNCT
ejpam-6847	712	7	ψ	ψ	NOUN
ejpam-6847	712	8	-	-	ADJ
ejpam-6847	712	9	contractive	contractive	ADJ
ejpam-6847	712	10	type	type	NOUN
ejpam-6847	712	11	f.	f.	PROPN
ejpam-6847	712	12	m.	m.	PROPN
ejpam-6847	712	13	azmi	azmi	PROPN
ejpam-6847	712	14	,	,	PUNCT
ejpam-6847	712	15	a.	a.	PROPN
ejpam-6847	712	16	h.	h.	PROPN
ejpam-6847	712	17	ansari	ansari	PROPN
ejpam-6847	712	18	,	,	PUNCT
ejpam-6847	712	19	s.	s.	PROPN
ejpam-6847	712	20	h.	h.	PROPN
ejpam-6847	712	21	j.	j.	PROPN
ejpam-6847	712	22	petroudi	petroudi	PROPN
ejpam-6847	712	23	/	/	SYM
ejpam-6847	712	24	eur	eur	PROPN
ejpam-6847	712	25	.	.	PUNCT
ejpam-6847	713	1	j.	j.	PROPN
ejpam-6847	713	2	pure	pure	PROPN
ejpam-6847	713	3	appl	appl	PROPN
ejpam-6847	713	4	.	.	PROPN
ejpam-6847	713	5	math	math	PROPN
ejpam-6847	713	6	,	,	PUNCT
ejpam-6847	713	7	18	18	NUM
ejpam-6847	713	8	(	(	PUNCT
ejpam-6847	713	9	4	4	NUM
ejpam-6847	713	10	)	)	PUNCT
ejpam-6847	713	11	(	(	PUNCT
ejpam-6847	713	12	2025	2025	NUM
ejpam-6847	713	13	)	)	PUNCT
ejpam-6847	713	14	,	,	PUNCT
ejpam-6847	713	15	6847	6847	NUM
ejpam-6847	713	16	26	26	NUM
ejpam-6847	713	17	of	of	ADP
ejpam-6847	713	18	26	26	NUM
ejpam-6847	713	19	mappings	mapping	NOUN
ejpam-6847	713	20	.	.	PUNCT
ejpam-6847	714	1	nonlinear	nonlinear	ADJ
ejpam-6847	714	2	analysis	analysis	NOUN
ejpam-6847	714	3	:	:	PUNCT
ejpam-6847	714	4	theory	theory	NOUN
ejpam-6847	714	5	,	,	PUNCT
ejpam-6847	714	6	methods	method	NOUN
ejpam-6847	714	7	and	and	CCONJ
ejpam-6847	714	8	applications	application	NOUN
ejpam-6847	714	9	,	,	PUNCT
ejpam-6847	714	10	75(4):2154–2165	75(4):2154–2165	NOUN
ejpam-6847	714	11	,	,	PUNCT
ejpam-6847	714	12	2012	2012	NUM
ejpam-6847	714	13	.	.	PUNCT
ejpam-6847	715	1	[	[	X
ejpam-6847	715	2	33	33	NUM
ejpam-6847	715	3	]	]	PUNCT
ejpam-6847	715	4	d.	d.	PROPN
ejpam-6847	715	5	gopal	gopal	PROPN
ejpam-6847	715	6	,	,	PUNCT
ejpam-6847	715	7	m.	m.	NOUN
ejpam-6847	715	8	abbas	abbas	PROPN
ejpam-6847	715	9	,	,	PUNCT
ejpam-6847	715	10	d.	d.	PROPN
ejpam-6847	715	11	k.	k.	PROPN
ejpam-6847	715	12	patel	patel	PROPN
ejpam-6847	715	13	,	,	PUNCT
ejpam-6847	715	14	and	and	CCONJ
ejpam-6847	715	15	c.	c.	PROPN
ejpam-6847	715	16	vetro	vetro	PROPN
ejpam-6847	715	17	.	.	PUNCT
ejpam-6847	716	1	fixed	fix	VERB
ejpam-6847	716	2	points	point	NOUN
ejpam-6847	716	3	of	of	ADP
ejpam-6847	716	4	α	α	NOUN
ejpam-6847	716	5	-	-	PUNCT
ejpam-6847	716	6	type	type	NOUN
ejpam-6847	716	7	f	f	NOUN
ejpam-6847	716	8	-contractive	-contractive	ADJ
ejpam-6847	716	9	mappings	mapping	NOUN
ejpam-6847	716	10	with	with	ADP
ejpam-6847	716	11	an	an	DET
ejpam-6847	716	12	application	application	NOUN
ejpam-6847	716	13	to	to	ADP
ejpam-6847	716	14	nonlinear	nonlinear	ADJ
ejpam-6847	716	15	fractional	fractional	ADJ
ejpam-6847	716	16	differential	differential	NOUN
ejpam-6847	716	17	equation	equation	NOUN
ejpam-6847	716	18	.	.	PUNCT
ejpam-6847	717	1	acta	acta	PROPN
ejpam-6847	717	2	mathematica	mathematica	PROPN
ejpam-6847	717	3	scientia	scientia	PROPN
ejpam-6847	717	4	,	,	PUNCT
ejpam-6847	717	5	2016	2016	NUM
ejpam-6847	717	6	.	.	PUNCT
ejpam-6847	718	1	[	[	X
ejpam-6847	718	2	34	34	NUM
ejpam-6847	718	3	]	]	PUNCT
ejpam-6847	718	4	a.	a.	NOUN
ejpam-6847	718	5	h.	h.	PROPN
ejpam-6847	718	6	ansari	ansari	PROPN
ejpam-6847	718	7	,	,	PUNCT
ejpam-6847	718	8	s.	s.	PROPN
ejpam-6847	718	9	chandok	chandok	PROPN
ejpam-6847	718	10	,	,	PUNCT
ejpam-6847	718	11	n.	n.	NOUN
ejpam-6847	718	12	hussain	hussain	PROPN
ejpam-6847	718	13	,	,	PUNCT
ejpam-6847	718	14	and	and	CCONJ
ejpam-6847	718	15	m.	m.	NOUN
ejpam-6847	718	16	m.	m.	NOUN
ejpam-6847	718	17	jaradat	jaradat	PROPN
ejpam-6847	718	18	.	.	PUNCT
ejpam-6847	719	1	some	some	DET
ejpam-6847	719	2	common	common	ADJ
ejpam-6847	719	3	fixed	fix	VERB
ejpam-6847	719	4	point	point	NOUN
ejpam-6847	719	5	theorems	theorem	NOUN
ejpam-6847	719	6	for	for	ADP
ejpam-6847	719	7	weakly	weakly	ADJ
ejpam-6847	719	8	α	α	NOUN
ejpam-6847	719	9	-	-	ADJ
ejpam-6847	719	10	admissible	admissible	ADJ
ejpam-6847	719	11	pairs	pair	NOUN
ejpam-6847	719	12	in	in	ADP
ejpam-6847	719	13	g	g	NOUN
ejpam-6847	719	14	-	-	PUNCT
ejpam-6847	719	15	metric	metric	ADJ
ejpam-6847	719	16	spaces	space	NOUN
ejpam-6847	719	17	with	with	ADP
ejpam-6847	719	18	auxiliary	auxiliary	ADJ
ejpam-6847	719	19	functions	function	NOUN
ejpam-6847	719	20	.	.	PUNCT
ejpam-6847	720	1	journal	journal	PROPN
ejpam-6847	720	2	of	of	ADP
ejpam-6847	720	3	mathematical	mathematical	ADJ
ejpam-6847	720	4	analysis	analysis	NOUN
ejpam-6847	720	5	,	,	PUNCT
ejpam-6847	720	6	8(3):80–107	8(3):80–107	NUM
ejpam-6847	720	7	,	,	PUNCT
ejpam-6847	720	8	2017	2017	NUM
ejpam-6847	720	9	.	.	PUNCT
ejpam-6847	721	1	[	[	X
ejpam-6847	721	2	35	35	NUM
ejpam-6847	721	3	]	]	PUNCT
ejpam-6847	721	4	a.	a.	PROPN
ejpam-6847	721	5	al	al	PROPN
ejpam-6847	721	6	-	-	PUNCT
ejpam-6847	721	7	rawashdeh	rawashdeh	PROPN
ejpam-6847	721	8	,	,	PUNCT
ejpam-6847	721	9	h.	h.	PROPN
ejpam-6847	721	10	aydi	aydi	PROPN
ejpam-6847	721	11	,	,	PUNCT
ejpam-6847	721	12	a.	a.	PROPN
ejpam-6847	721	13	felhi	felhi	PROPN
ejpam-6847	721	14	,	,	PUNCT
ejpam-6847	721	15	s.	s.	PROPN
ejpam-6847	721	16	sahmim	sahmim	PROPN
ejpam-6847	721	17	,	,	PUNCT
ejpam-6847	721	18	and	and	CCONJ
ejpam-6847	721	19	w.	w.	PROPN
ejpam-6847	721	20	shatanawi	shatanawi	PROPN
ejpam-6847	721	21	.	.	PUNCT
ejpam-6847	722	1	on	on	ADP
ejpam-6847	722	2	common	common	ADJ
ejpam-6847	722	3	fixed	fix	VERB
ejpam-6847	722	4	points	point	NOUN
ejpam-6847	722	5	for	for	ADP
ejpam-6847	722	6	α	α	NOUN
ejpam-6847	722	7	-	-	PUNCT
ejpam-6847	722	8	f	f	NOUN
ejpam-6847	722	9	-	-	PUNCT
ejpam-6847	722	10	contractives	contractive	NOUN
ejpam-6847	722	11	and	and	CCONJ
ejpam-6847	722	12	applications	application	NOUN
ejpam-6847	722	13	.	.	PUNCT
ejpam-6847	723	1	journal	journal	PROPN
ejpam-6847	723	2	of	of	ADP
ejpam-6847	723	3	nonlinear	nonlinear	ADJ
ejpam-6847	723	4	science	science	NOUN
ejpam-6847	723	5	and	and	CCONJ
ejpam-6847	723	6	applications	application	NOUN
ejpam-6847	723	7	,	,	PUNCT
ejpam-6847	723	8	9:3445–3458	9:3445–3458	NUM
ejpam-6847	723	9	,	,	PUNCT
ejpam-6847	723	10	2016	2016	NUM
ejpam-6847	723	11	.	.	PUNCT
ejpam-6847	724	1	[	[	X
ejpam-6847	724	2	36	36	NUM
ejpam-6847	724	3	]	]	X
ejpam-6847	724	4	h.	h.	NOUN
ejpam-6847	724	5	faraji	faraji	PROPN
ejpam-6847	724	6	,	,	PUNCT
ejpam-6847	724	7	n.	n.	PROPN
ejpam-6847	724	8	mirkov	mirkov	PROPN
ejpam-6847	724	9	,	,	PUNCT
ejpam-6847	724	10	z.	z.	PROPN
ejpam-6847	724	11	d.	d.	PROPN
ejpam-6847	724	12	mitrović	mitrović	PROPN
ejpam-6847	724	13	,	,	PUNCT
ejpam-6847	724	14	r.	r.	PROPN
ejpam-6847	724	15	ramaswamy	ramaswamy	PROPN
ejpam-6847	724	16	,	,	PUNCT
ejpam-6847	724	17	o.	o.	PROPN
ejpam-6847	724	18	a.	a.	PROPN
ejpam-6847	724	19	a.	a.	PROPN
ejpam-6847	724	20	abdelnaby	abdelnaby	PROPN
ejpam-6847	724	21	,	,	PUNCT
ejpam-6847	724	22	and	and	CCONJ
ejpam-6847	724	23	s.	s.	PROPN
ejpam-6847	724	24	radenović	radenović	PROPN
ejpam-6847	724	25	.	.	PUNCT
ejpam-6847	725	1	some	some	DET
ejpam-6847	725	2	new	new	ADJ
ejpam-6847	725	3	results	result	NOUN
ejpam-6847	725	4	for	for	ADP
ejpam-6847	725	5	(	(	PUNCT
ejpam-6847	725	6	α	α	X
ejpam-6847	725	7	,	,	PUNCT
ejpam-6847	725	8	β)-admissible	β)-admissible	PUNCT
ejpam-6847	725	9	mappings	mapping	NOUN
ejpam-6847	725	10	in	in	ADP
ejpam-6847	725	11	f	f	ADJ
ejpam-6847	725	12	-	-	PUNCT
ejpam-6847	725	13	metric	metric	ADJ
ejpam-6847	725	14	spaces	space	NOUN
ejpam-6847	725	15	with	with	ADP
ejpam-6847	725	16	applications	application	NOUN
ejpam-6847	725	17	to	to	ADP
ejpam-6847	725	18	integral	integral	ADJ
ejpam-6847	725	19	equations	equation	NOUN
ejpam-6847	725	20	.	.	PUNCT
ejpam-6847	726	1	symmetry	symmetry	PROPN
ejpam-6847	726	2	,	,	PUNCT
ejpam-6847	726	3	14:2429	14:2429	NUM
ejpam-6847	726	4	,	,	PUNCT
ejpam-6847	726	5	2022	2022	NUM
ejpam-6847	726	6	.	.	PUNCT
ejpam-6847	727	1	[	[	X
ejpam-6847	727	2	37	37	NUM
ejpam-6847	727	3	]	]	X
ejpam-6847	727	4	n.	n.	NOUN
ejpam-6847	727	5	priyobarta	priyobarta	PROPN
ejpam-6847	727	6	,	,	PUNCT
ejpam-6847	727	7	y.	y.	PROPN
ejpam-6847	727	8	rohen	rohen	PROPN
ejpam-6847	727	9	,	,	PUNCT
ejpam-6847	727	10	and	and	CCONJ
ejpam-6847	727	11	th	th	X
ejpam-6847	727	12	.	.	PUNCT
ejpam-6847	727	13	stephen	stephen	PROPN
ejpam-6847	727	14	.	.	PUNCT
ejpam-6847	728	1	some	some	DET
ejpam-6847	728	2	remarks	remark	NOUN
ejpam-6847	728	3	on	on	ADP
ejpam-6847	728	4	α	α	NOUN
ejpam-6847	728	5	-	-	NOUN
ejpam-6847	728	6	admissibility	admissibility	NOUN
ejpam-6847	728	7	in	in	ADP
ejpam-6847	728	8	s	s	NOUN
ejpam-6847	728	9	-	-	ADJ
ejpam-6847	728	10	metric	metric	ADJ
ejpam-6847	728	11	spaces	space	NOUN
ejpam-6847	728	12	.	.	PUNCT
ejpam-6847	729	1	journal	journal	PROPN
ejpam-6847	729	2	of	of	ADP
ejpam-6847	729	3	inequalities	inequality	NOUN
ejpam-6847	729	4	and	and	CCONJ
ejpam-6847	729	5	applications	application	NOUN
ejpam-6847	729	6	,	,	PUNCT
ejpam-6847	729	7	2022	2022	NUM
ejpam-6847	729	8	.	.	PUNCT
ejpam-6847	730	1	[	[	X
ejpam-6847	730	2	38	38	NUM
ejpam-6847	730	3	]	]	PUNCT
ejpam-6847	730	4	e.	e.	PROPN
ejpam-6847	730	5	karapinar	karapinar	PROPN
ejpam-6847	730	6	,	,	PUNCT
ejpam-6847	730	7	a.	a.	NOUN
ejpam-6847	730	8	petrusel	petrusel	NOUN
ejpam-6847	730	9	,	,	PUNCT
ejpam-6847	730	10	and	and	CCONJ
ejpam-6847	730	11	g.	g.	PROPN
ejpam-6847	730	12	petrusel	petrusel	NOUN
ejpam-6847	730	13	.	.	PUNCT
ejpam-6847	731	1	on	on	ADP
ejpam-6847	731	2	admissible	admissible	ADJ
ejpam-6847	731	3	hybrid	hybrid	ADJ
ejpam-6847	731	4	geraghty	geraghty	VERB
ejpam-6847	731	5	contractives	contractive	NOUN
ejpam-6847	731	6	.	.	PUNCT
ejpam-6847	732	1	carpathian	carpathian	PROPN
ejpam-6847	732	2	j.	j.	PROPN
ejpam-6847	732	3	math	math	PROPN
ejpam-6847	732	4	.	.	PUNCT
ejpam-6847	732	5	,	,	PUNCT
ejpam-6847	732	6	36(3):433–442	36(3):433–442	NUM
ejpam-6847	732	7	,	,	PUNCT
ejpam-6847	732	8	2020	2020	NUM
ejpam-6847	732	9	.	.	PUNCT
ejpam-6847	733	1	[	[	X
ejpam-6847	733	2	39	39	NUM
ejpam-6847	733	3	]	]	PUNCT
ejpam-6847	733	4	a.	a.	NOUN
ejpam-6847	733	5	h.	h.	PROPN
ejpam-6847	733	6	ansari	ansari	PROPN
ejpam-6847	733	7	.	.	PUNCT
ejpam-6847	734	1	note	note	NOUN
ejpam-6847	734	2	on	on	ADP
ejpam-6847	734	3	“	"	PUNCT
ejpam-6847	734	4	α	α	NUM
ejpam-6847	734	5	-	-	PUNCT
ejpam-6847	734	6	admissible	admissible	ADJ
ejpam-6847	734	7	mappings	mapping	NOUN
ejpam-6847	734	8	and	and	CCONJ
ejpam-6847	734	9	related	relate	VERB
ejpam-6847	734	10	fixed	fix	VERB
ejpam-6847	734	11	point	point	NOUN
ejpam-6847	734	12	theorems	theorem	NOUN
ejpam-6847	734	13	”	"	PUNCT
ejpam-6847	734	14	.	.	PUNCT
ejpam-6847	735	1	in	in	ADP
ejpam-6847	735	2	the	the	DET
ejpam-6847	735	3	2nd	2nd	ADJ
ejpam-6847	735	4	regional	regional	ADJ
ejpam-6847	735	5	conference	conference	NOUN
ejpam-6847	735	6	on	on	ADP
ejpam-6847	735	7	mathematics	mathematic	NOUN
ejpam-6847	735	8	and	and	CCONJ
ejpam-6847	735	9	applications	application	NOUN
ejpam-6847	735	10	,	,	PUNCT
ejpam-6847	735	11	pages	page	NOUN
ejpam-6847	735	12	373–376	373–376	NUM
ejpam-6847	735	13	,	,	PUNCT
ejpam-6847	735	14	payame	payame	NOUN
ejpam-6847	735	15	noor	noor	PROPN
ejpam-6847	735	16	university	university	PROPN
ejpam-6847	735	17	,	,	PUNCT
ejpam-6847	735	18	tonekabon	tonekabon	NOUN
ejpam-6847	735	19	,	,	PUNCT
ejpam-6847	735	20	iran	iran	PROPN
ejpam-6847	735	21	,	,	PUNCT
ejpam-6847	735	22	september	september	PROPN
ejpam-6847	735	23	2014	2014	NUM
ejpam-6847	735	24	.	.	PUNCT
ejpam-6847	736	1	[	[	X
ejpam-6847	736	2	40	40	NUM
ejpam-6847	736	3	]	]	PUNCT
ejpam-6847	736	4	s.	s.	PROPN
ejpam-6847	736	5	h.	h.	PROPN
ejpam-6847	736	6	j.	j.	PROPN
ejpam-6847	736	7	petroudi	petroudi	PROPN
ejpam-6847	736	8	,	,	PUNCT
ejpam-6847	736	9	a.	a.	PROPN
ejpam-6847	736	10	h.	h.	PROPN
ejpam-6847	736	11	ansari	ansari	PROPN
ejpam-6847	736	12	,	,	PUNCT
ejpam-6847	736	13	and	and	CCONJ
ejpam-6847	736	14	c.	c.	PROPN
ejpam-6847	736	15	park	park	PROPN
ejpam-6847	736	16	.	.	PUNCT
ejpam-6847	737	1	generalized	generalize	VERB
ejpam-6847	737	2	nested	nested	ADJ
ejpam-6847	737	3	functions	function	NOUN
ejpam-6847	737	4	and	and	CCONJ
ejpam-6847	737	5	some	some	DET
ejpam-6847	737	6	generalizations	generalization	NOUN
ejpam-6847	737	7	of	of	ADP
ejpam-6847	737	8	wilker	wilker	NOUN
ejpam-6847	737	9	and	and	CCONJ
ejpam-6847	737	10	huygen	huygen	PROPN
ejpam-6847	737	11	’s	’s	PART
ejpam-6847	737	12	inequalities	inequality	NOUN
ejpam-6847	737	13	.	.	PUNCT
ejpam-6847	738	1	int	int	NOUN
ejpam-6847	738	2	.	.	PUNCT
ejpam-6847	739	1	j.	j.	PROPN
ejpam-6847	739	2	appl	appl	PROPN
ejpam-6847	739	3	.	.	PROPN
ejpam-6847	739	4	math	math	PROPN
ejpam-6847	739	5	.	.	PUNCT
ejpam-6847	739	6	,	,	PUNCT
ejpam-6847	739	7	2024	2024	NUM
ejpam-6847	739	8	.	.	PUNCT
ejpam-6847	740	1	[	[	X
ejpam-6847	740	2	41	41	NUM
ejpam-6847	740	3	]	]	PUNCT
ejpam-6847	740	4	a.	a.	NOUN
ejpam-6847	740	5	h.	h.	PROPN
ejpam-6847	740	6	ansari	ansari	PROPN
ejpam-6847	740	7	,	,	PUNCT
ejpam-6847	740	8	x.	x.	PROPN
ejpam-6847	740	9	liu	liu	PROPN
ejpam-6847	740	10	,	,	PUNCT
ejpam-6847	740	11	and	and	CCONJ
ejpam-6847	740	12	v.	v.	ADP
ejpam-6847	740	13	n.	n.	PROPN
ejpam-6847	740	14	mishra	mishra	PROPN
ejpam-6847	740	15	.	.	PROPN
ejpam-6847	741	1	on	on	ADP
ejpam-6847	741	2	mittag	mittag	ADJ
ejpam-6847	741	3	-	-	PUNCT
ejpam-6847	741	4	leffler	leffler	NOUN
ejpam-6847	741	5	function	function	NOUN
ejpam-6847	741	6	and	and	CCONJ
ejpam-6847	741	7	beyond	beyond	ADP
ejpam-6847	741	8	.	.	PUNCT
ejpam-6847	742	1	nonlinear	nonlinear	PROPN
ejpam-6847	742	2	sci	sci	PROPN
ejpam-6847	742	3	.	.	PROPN
ejpam-6847	742	4	lett	lett	PROPN
ejpam-6847	742	5	.	.	PUNCT
ejpam-6847	743	1	a	a	DET
ejpam-6847	743	2	,	,	PUNCT
ejpam-6847	743	3	8(2):187–199	8(2):187–199	NOUN
ejpam-6847	743	4	,	,	PUNCT
ejpam-6847	743	5	2017	2017	NUM
ejpam-6847	743	6	.	.	PUNCT
ejpam-6847	744	1	[	[	X
ejpam-6847	744	2	42	42	NUM
ejpam-6847	744	3	]	]	PUNCT
ejpam-6847	744	4	a.	a.	NOUN
ejpam-6847	744	5	h.	h.	PROPN
ejpam-6847	744	6	ansari	ansari	PROPN
ejpam-6847	744	7	,	,	PUNCT
ejpam-6847	744	8	s.	s.	PROPN
ejpam-6847	744	9	maksimovic	maksimovic	PROPN
ejpam-6847	744	10	,	,	PUNCT
ejpam-6847	744	11	l.	l.	PROPN
ejpam-6847	744	12	guran	guran	PROPN
ejpam-6847	744	13	,	,	PUNCT
ejpam-6847	744	14	and	and	CCONJ
ejpam-6847	744	15	m.	m.	PROPN
ejpam-6847	744	16	zhou	zhou	PROPN
ejpam-6847	744	17	.	.	PUNCT
ejpam-6847	745	1	nested	nested	ADJ
ejpam-6847	745	2	functions	function	NOUN
ejpam-6847	745	3	of	of	ADP
ejpam-6847	745	4	type	type	NOUN
ejpam-6847	745	5	supertrigonometric	supertrigonometric	ADJ
ejpam-6847	745	6	and	and	CCONJ
ejpam-6847	745	7	superhyperbolic	superhyperbolic	ADJ
ejpam-6847	745	8	via	via	ADP
ejpam-6847	745	9	mittag	mittag	ADJ
ejpam-6847	745	10	-	-	PUNCT
ejpam-6847	745	11	leffler	leffler	NOUN
ejpam-6847	745	12	functions	function	NOUN
ejpam-6847	745	13	.	.	PUNCT
ejpam-6847	746	1	ser	ser	NOUN
ejpam-6847	746	2	.	.	PUNCT
ejpam-6847	747	1	a	a	DET
ejpam-6847	747	2	:	:	PUNCT
ejpam-6847	747	3	appl	appl	PROPN
ejpam-6847	747	4	.	.	PROPN
ejpam-6847	747	5	math	math	PROPN
ejpam-6847	747	6	.	.	PUNCT
ejpam-6847	748	1	inform	inform	NOUN
ejpam-6847	748	2	.	.	PUNCT
ejpam-6847	749	1	and	and	CCONJ
ejpam-6847	749	2	mech	mech	NOUN
ejpam-6847	749	3	.	.	PUNCT
ejpam-6847	749	4	,	,	PUNCT
ejpam-6847	749	5	15(2):109–120	15(2):109–120	NUM
ejpam-6847	749	6	,	,	PUNCT
ejpam-6847	749	7	2023	2023	NUM
ejpam-6847	749	8	.	.	PUNCT