id	sid	tid	token	lemma	pos
ejpam-5268	1	1	european	european	PROPN
ejpam-5268	1	2	journal	journal	PROPN
ejpam-5268	1	3	of	of	ADP
ejpam-5268	1	4	pure	pure	ADJ
ejpam-5268	1	5	and	and	CCONJ
ejpam-5268	1	6	applied	apply	VERB
ejpam-5268	1	7	mathematics	mathematic	NOUN
ejpam-5268	1	8	vol	vol	NOUN
ejpam-5268	1	9	.	.	PROPN
ejpam-5268	2	1	17	17	NUM
ejpam-5268	2	2	,	,	PUNCT
ejpam-5268	2	3	no	no	INTJ
ejpam-5268	2	4	.	.	NOUN
ejpam-5268	2	5	3	3	NUM
ejpam-5268	2	6	,	,	PUNCT
ejpam-5268	2	7	2024	2024	NUM
ejpam-5268	2	8	,	,	PUNCT
ejpam-5268	2	9	1877	1877	NUM
ejpam-5268	2	10	-	-	SYM
ejpam-5268	2	11	1893	1893	NUM
ejpam-5268	2	12	issn	issn	VERB
ejpam-5268	2	13	1307	1307	NUM
ejpam-5268	2	14	-	-	SYM
ejpam-5268	2	15	5543	5543	NUM
ejpam-5268	2	16	–	–	PUNCT
ejpam-5268	2	17	ejpam.com	ejpam.com	X
ejpam-5268	2	18	published	publish	VERB
ejpam-5268	2	19	by	by	ADP
ejpam-5268	2	20	new	new	PROPN
ejpam-5268	2	21	york	york	PROPN
ejpam-5268	2	22	business	business	PROPN
ejpam-5268	2	23	global	global	ADJ
ejpam-5268	2	24	enhanced	enhance	VERB
ejpam-5268	2	25	results	result	NOUN
ejpam-5268	2	26	in	in	ADP
ejpam-5268	2	27	common	common	ADJ
ejpam-5268	2	28	and	and	CCONJ
ejpam-5268	2	29	coincidence	coincidence	NOUN
ejpam-5268	2	30	fixed	fix	VERB
ejpam-5268	2	31	point	point	NOUN
ejpam-5268	2	32	theory	theory	NOUN
ejpam-5268	2	33	with	with	ADP
ejpam-5268	2	34	applications	application	NOUN
ejpam-5268	2	35	to	to	ADP
ejpam-5268	2	36	simulation	simulation	NOUN
ejpam-5268	2	37	mappings	mapping	NOUN
ejpam-5268	2	38	nassar	nassar	PROPN
ejpam-5268	2	39	aiman	aiman	PROPN
ejpam-5268	2	40	majid1,2,∗	majid1,2,∗	PROPN
ejpam-5268	2	41	,	,	PUNCT
ejpam-5268	2	42	alaa	alaa	PROPN
ejpam-5268	2	43	al	al	PROPN
ejpam-5268	2	44	jumaili3	jumaili3	PROPN
ejpam-5268	2	45	,	,	PUNCT
ejpam-5268	2	46	zhen	zhen	PROPN
ejpam-5268	2	47	chuan	chuan	PROPN
ejpam-5268	2	48	ng1	ng1	PROPN
ejpam-5268	2	49	,	,	PUNCT
ejpam-5268	2	50	see	see	VERB
ejpam-5268	2	51	keong	keong	PROPN
ejpam-5268	2	52	lee1	lee1	PROPN
ejpam-5268	2	53	1	1	NUM
ejpam-5268	2	54	school	school	NOUN
ejpam-5268	2	55	of	of	ADP
ejpam-5268	2	56	mathematical	mathematical	ADJ
ejpam-5268	2	57	sciences	science	NOUN
ejpam-5268	2	58	,	,	PUNCT
ejpam-5268	2	59	universiti	universiti	PROPN
ejpam-5268	2	60	sains	sain	NOUN
ejpam-5268	2	61	malaysia	malaysia	PROPN
ejpam-5268	2	62	,	,	PUNCT
ejpam-5268	2	63	11800	11800	NUM
ejpam-5268	2	64	,	,	PUNCT
ejpam-5268	2	65	penang	penang	PROPN
ejpam-5268	2	66	,	,	PUNCT
ejpam-5268	2	67	malaysia	malaysia	PROPN
ejpam-5268	2	68	2	2	NUM
ejpam-5268	2	69	department	department	NOUN
ejpam-5268	2	70	of	of	ADP
ejpam-5268	2	71	ecology	ecology	NOUN
ejpam-5268	2	72	sciences	sciences	PROPN
ejpam-5268	2	73	,	,	PUNCT
ejpam-5268	2	74	college	college	NOUN
ejpam-5268	2	75	of	of	ADP
ejpam-5268	2	76	applied	apply	VERB
ejpam-5268	2	77	sciences	science	NOUN
ejpam-5268	2	78	-	-	PUNCT
ejpam-5268	2	79	hit	hit	VERB
ejpam-5268	2	80	,	,	PUNCT
ejpam-5268	2	81	university	university	NOUN
ejpam-5268	2	82	of	of	ADP
ejpam-5268	2	83	anbar	anbar	NOUN
ejpam-5268	2	84	,	,	PUNCT
ejpam-5268	2	85	31001	31001	NUM
ejpam-5268	2	86	,	,	PUNCT
ejpam-5268	2	87	ramadi	ramadi	PROPN
ejpam-5268	2	88	,	,	PUNCT
ejpam-5268	2	89	iraq	iraq	PROPN
ejpam-5268	2	90	3	3	NUM
ejpam-5268	2	91	department	department	NOUN
ejpam-5268	2	92	of	of	ADP
ejpam-5268	2	93	mathematics	mathematics	PROPN
ejpam-5268	2	94	,	,	PUNCT
ejpam-5268	2	95	college	college	NOUN
ejpam-5268	2	96	of	of	ADP
ejpam-5268	2	97	education	education	NOUN
ejpam-5268	2	98	for	for	ADP
ejpam-5268	2	99	pure	pure	ADJ
ejpam-5268	2	100	sciences	science	NOUN
ejpam-5268	2	101	,	,	PUNCT
ejpam-5268	2	102	university	university	NOUN
ejpam-5268	2	103	of	of	ADP
ejpam-5268	2	104	anbar	anbar	NOUN
ejpam-5268	2	105	,	,	PUNCT
ejpam-5268	2	106	31001	31001	NUM
ejpam-5268	2	107	,	,	PUNCT
ejpam-5268	2	108	ramadi	ramadi	PROPN
ejpam-5268	2	109	,	,	PUNCT
ejpam-5268	2	110	iraq	iraq	PROPN
ejpam-5268	2	111	abstract	abstract	NOUN
ejpam-5268	2	112	.	.	PUNCT
ejpam-5268	3	1	in	in	ADP
ejpam-5268	3	2	this	this	DET
ejpam-5268	3	3	manuscript	manuscript	NOUN
ejpam-5268	3	4	,	,	PUNCT
ejpam-5268	3	5	we	we	PRON
ejpam-5268	3	6	apply	apply	VERB
ejpam-5268	3	7	the	the	DET
ejpam-5268	3	8	simulation	simulation	NOUN
ejpam-5268	3	9	mappings	mapping	NOUN
ejpam-5268	3	10	to	to	PART
ejpam-5268	3	11	present	present	VERB
ejpam-5268	3	12	and	and	CCONJ
ejpam-5268	3	13	verify	verify	VERB
ejpam-5268	3	14	several	several	ADJ
ejpam-5268	3	15	original	original	ADJ
ejpam-5268	3	16	results	result	NOUN
ejpam-5268	3	17	of	of	ADP
ejpam-5268	3	18	common	common	ADJ
ejpam-5268	3	19	and	and	CCONJ
ejpam-5268	3	20	coincidence	coincidence	NOUN
ejpam-5268	3	21	fixed	fix	VERB
ejpam-5268	3	22	point	point	NOUN
ejpam-5268	3	23	in	in	ADP
ejpam-5268	3	24	complete	complete	ADJ
ejpam-5268	3	25	s	s	NOUN
ejpam-5268	3	26	-	-	ADJ
ejpam-5268	3	27	metric	metric	ADJ
ejpam-5268	3	28	spaces	space	NOUN
ejpam-5268	3	29	.	.	PUNCT
ejpam-5268	4	1	moreover	moreover	ADV
ejpam-5268	4	2	,	,	PUNCT
ejpam-5268	4	3	using	use	VERB
ejpam-5268	4	4	s	s	NOUN
ejpam-5268	4	5	-	-	ADJ
ejpam-5268	4	6	metric	metric	ADJ
ejpam-5268	4	7	to	to	PART
ejpam-5268	4	8	expand	expand	VERB
ejpam-5268	4	9	and	and	CCONJ
ejpam-5268	4	10	generalized	generalize	VERB
ejpam-5268	4	11	diverse	diverse	ADJ
ejpam-5268	4	12	results	result	NOUN
ejpam-5268	4	13	in	in	ADP
ejpam-5268	4	14	the	the	DET
ejpam-5268	4	15	literature	literature	NOUN
ejpam-5268	4	16	involving	involve	VERB
ejpam-5268	4	17	simulation	simulation	NOUN
ejpam-5268	4	18	mappings	mapping	NOUN
ejpam-5268	4	19	.	.	PUNCT
ejpam-5268	5	1	on	on	ADP
ejpam-5268	5	2	the	the	DET
ejpam-5268	5	3	other	other	ADJ
ejpam-5268	5	4	hand	hand	NOUN
ejpam-5268	5	5	,	,	PUNCT
ejpam-5268	5	6	we	we	PRON
ejpam-5268	5	7	apply	apply	VERB
ejpam-5268	5	8	our	our	PRON
ejpam-5268	5	9	major	major	ADJ
ejpam-5268	5	10	results	result	NOUN
ejpam-5268	5	11	to	to	PART
ejpam-5268	5	12	derive	derive	VERB
ejpam-5268	5	13	several	several	ADJ
ejpam-5268	5	14	common	common	ADJ
ejpam-5268	5	15	and	and	CCONJ
ejpam-5268	5	16	coincidence	coincidence	NOUN
ejpam-5268	5	17	fixed	fix	VERB
ejpam-5268	5	18	point	point	NOUN
ejpam-5268	5	19	theorems	theorem	NOUN
ejpam-5268	5	20	for	for	ADP
ejpam-5268	5	21	right	right	ADJ
ejpam-5268	5	22	monotone	monotone	ADJ
ejpam-5268	5	23	simulation	simulation	NOUN
ejpam-5268	5	24	map	map	NOUN
ejpam-5268	5	25	in	in	ADP
ejpam-5268	5	26	complete	complete	ADJ
ejpam-5268	5	27	s	s	NOUN
ejpam-5268	5	28	-	-	NOUN
ejpam-5268	5	29	metric	metric	ADJ
ejpam-5268	5	30	.	.	PUNCT
ejpam-5268	6	1	as	as	ADP
ejpam-5268	6	2	implementations	implementation	NOUN
ejpam-5268	6	3	,	,	PUNCT
ejpam-5268	6	4	various	various	ADJ
ejpam-5268	6	5	related	related	ADJ
ejpam-5268	6	6	outcomes	outcome	NOUN
ejpam-5268	6	7	of	of	ADP
ejpam-5268	6	8	fixed	fix	VERB
ejpam-5268	6	9	-	-	PUNCT
ejpam-5268	6	10	point	point	NOUN
ejpam-5268	6	11	theory	theory	NOUN
ejpam-5268	6	12	via	via	ADP
ejpam-5268	6	13	specific	specific	ADJ
ejpam-5268	6	14	simulation	simulation	NOUN
ejpam-5268	6	15	mappings	mapping	NOUN
ejpam-5268	6	16	are	be	AUX
ejpam-5268	6	17	obtained	obtain	VERB
ejpam-5268	6	18	in	in	ADP
ejpam-5268	6	19	complete	complete	ADJ
ejpam-5268	6	20	s	s	NOUN
ejpam-5268	6	21	-	-	ADJ
ejpam-5268	6	22	metric	metric	ADJ
ejpam-5268	6	23	spaces	space	NOUN
ejpam-5268	6	24	.	.	PUNCT
ejpam-5268	7	1	additionally	additionally	ADV
ejpam-5268	7	2	,	,	PUNCT
ejpam-5268	7	3	illustrative	illustrative	ADJ
ejpam-5268	7	4	examples	example	NOUN
ejpam-5268	7	5	and	and	CCONJ
ejpam-5268	7	6	some	some	DET
ejpam-5268	7	7	applications	application	NOUN
ejpam-5268	7	8	to	to	PART
ejpam-5268	7	9	solve	solve	VERB
ejpam-5268	7	10	an	an	DET
ejpam-5268	7	11	integral	integral	ADJ
ejpam-5268	7	12	equation	equation	NOUN
ejpam-5268	7	13	are	be	AUX
ejpam-5268	7	14	introduced	introduce	VERB
ejpam-5268	7	15	to	to	PART
ejpam-5268	7	16	support	support	VERB
ejpam-5268	7	17	our	our	PRON
ejpam-5268	7	18	major	major	ADJ
ejpam-5268	7	19	results	result	NOUN
ejpam-5268	7	20	.	.	PUNCT
ejpam-5268	8	1	2020	2020	NUM
ejpam-5268	8	2	mathematics	mathematic	NOUN
ejpam-5268	8	3	subject	subject	NOUN
ejpam-5268	8	4	classifications	classification	NOUN
ejpam-5268	8	5	:	:	PUNCT
ejpam-5268	8	6	46b45	46b45	NUM
ejpam-5268	8	7	,	,	PUNCT
ejpam-5268	8	8	30l15	30l15	NUM
ejpam-5268	8	9	,	,	PUNCT
ejpam-5268	8	10	54e50	54e50	NUM
ejpam-5268	8	11	key	key	ADJ
ejpam-5268	8	12	words	word	NOUN
ejpam-5268	8	13	and	and	CCONJ
ejpam-5268	8	14	phrases	phrase	NOUN
ejpam-5268	8	15	:	:	PUNCT
ejpam-5268	8	16	s	s	X
ejpam-5268	8	17	-	-	ADJ
ejpam-5268	8	18	metric	metric	ADJ
ejpam-5268	8	19	spaces	space	NOUN
ejpam-5268	8	20	,	,	PUNCT
ejpam-5268	8	21	simulation	simulation	NOUN
ejpam-5268	8	22	mappings	mapping	NOUN
ejpam-5268	8	23	,	,	PUNCT
ejpam-5268	8	24	common	common	ADJ
ejpam-5268	8	25	and	and	CCONJ
ejpam-5268	8	26	coincidence	coincidence	NOUN
ejpam-5268	8	27	fixed	fix	VERB
ejpam-5268	8	28	points	point	NOUN
ejpam-5268	8	29	,	,	PUNCT
ejpam-5268	8	30	symmetrical	symmetrical	ADJ
ejpam-5268	8	31	complete	complete	ADJ
ejpam-5268	8	32	s	s	NOUN
ejpam-5268	8	33	-	-	ADJ
ejpam-5268	8	34	metric	metric	ADJ
ejpam-5268	8	35	1	1	NUM
ejpam-5268	8	36	.	.	PUNCT
ejpam-5268	8	37	introduction	introduction	NOUN
ejpam-5268	8	38	and	and	CCONJ
ejpam-5268	8	39	preliminaries	preliminary	NOUN
ejpam-5268	8	40	most	most	ADV
ejpam-5268	8	41	significant	significant	ADJ
ejpam-5268	8	42	results	result	NOUN
ejpam-5268	8	43	in	in	ADP
ejpam-5268	8	44	fixed	fix	VERB
ejpam-5268	8	45	point	point	NOUN
ejpam-5268	8	46	theory	theory	NOUN
ejpam-5268	8	47	is	be	AUX
ejpam-5268	8	48	banach	banach	NOUN
ejpam-5268	8	49	contraction	contraction	NOUN
ejpam-5268	8	50	principle	principle	NOUN
ejpam-5268	8	51	{	{	PUNCT
ejpam-5268	8	52	assume	assume	VERB
ejpam-5268	8	53	(	(	PUNCT
ejpam-5268	8	54	x	x	X
ejpam-5268	8	55	,	,	PUNCT
ejpam-5268	8	56	d	d	NOUN
ejpam-5268	8	57	)	)	PUNCT
ejpam-5268	8	58	is	be	AUX
ejpam-5268	8	59	a	a	DET
ejpam-5268	8	60	complete	complete	ADJ
ejpam-5268	8	61	metric	metric	ADJ
ejpam-5268	8	62	space	space	NOUN
ejpam-5268	8	63	.	.	PUNCT
ejpam-5268	9	1	t	t	NOUN
ejpam-5268	9	2	:	:	PUNCT
ejpam-5268	9	3	x	x	X
ejpam-5268	9	4	→	→	PUNCT
ejpam-5268	9	5	x	x	X
ejpam-5268	9	6	is	be	AUX
ejpam-5268	9	7	contraction	contraction	NOUN
ejpam-5268	9	8	map	map	NOUN
ejpam-5268	9	9	if	if	SCONJ
ejpam-5268	9	10	∃	∃	PROPN
ejpam-5268	9	11	q	q	X
ejpam-5268	9	12	∈	∈	PROPN
ejpam-5268	9	13	(	(	PUNCT
ejpam-5268	9	14	0	0	NUM
ejpam-5268	9	15	,	,	PUNCT
ejpam-5268	9	16	1	1	NUM
ejpam-5268	9	17	)	)	PUNCT
ejpam-5268	9	18	(	(	PUNCT
ejpam-5268	9	19	s.t	s.t	PROPN
ejpam-5268	9	20	)	)	PUNCT
ejpam-5268	9	21	,	,	PUNCT
ejpam-5268	10	1	d	d	X
ejpam-5268	10	2	(	(	PUNCT
ejpam-5268	10	3	t	t	PROPN
ejpam-5268	10	4	(	(	PUNCT
ejpam-5268	10	5	x	x	NOUN
ejpam-5268	10	6	)	)	PUNCT
ejpam-5268	10	7	,	,	PUNCT
ejpam-5268	10	8	t	t	PROPN
ejpam-5268	10	9	(	(	PUNCT
ejpam-5268	10	10	y	y	NOUN
ejpam-5268	10	11	)	)	PUNCT
ejpam-5268	10	12	)	)	PUNCT
ejpam-5268	10	13	≤	≤	NUM
ejpam-5268	10	14	qd	qd	ADP
ejpam-5268	10	15	(	(	PUNCT
ejpam-5268	10	16	x	x	NOUN
ejpam-5268	10	17	,	,	PUNCT
ejpam-5268	10	18	y	y	PROPN
ejpam-5268	10	19	)	)	PUNCT
ejpam-5268	10	20	,	,	PUNCT
ejpam-5268	10	21	∀	∀	X
ejpam-5268	10	22	x	x	NOUN
ejpam-5268	10	23	,	,	PUNCT
ejpam-5268	10	24	y	y	PROPN
ejpam-5268	10	25	∈	∈	PROPN
ejpam-5268	10	26	x	x	X
ejpam-5268	10	27	}	}	PUNCT
ejpam-5268	10	28	.	.	PUNCT
ejpam-5268	11	1	in	in	ADP
ejpam-5268	11	2	that	that	DET
ejpam-5268	11	3	case	case	NOUN
ejpam-5268	11	4	,	,	PUNCT
ejpam-5268	11	5	banach	banach	ADV
ejpam-5268	11	6	fixed	fix	VERB
ejpam-5268	11	7	point	point	NOUN
ejpam-5268	11	8	theorem	theorem	NOUN
ejpam-5268	11	9	(	(	PUNCT
ejpam-5268	11	10	b.	b.	PROPN
ejpam-5268	11	11	f.	f.	PROPN
ejpam-5268	11	12	p.	p.	PROPN
ejpam-5268	11	13	th	th	PART
ejpam-5268	11	14	)	)	PUNCT
ejpam-5268	11	15	illustrates	illustrate	VERB
ejpam-5268	11	16	that	that	SCONJ
ejpam-5268	11	17	t	t	PROPN
ejpam-5268	11	18	permanently	permanently	ADV
ejpam-5268	11	19	has	have	VERB
ejpam-5268	11	20	unique	unique	ADJ
ejpam-5268	11	21	fixed	fix	VERB
ejpam-5268	11	22	point	point	NOUN
ejpam-5268	11	23	.	.	PUNCT
ejpam-5268	12	1	after	after	ADP
ejpam-5268	12	2	witnessing	witness	VERB
ejpam-5268	12	3	the	the	DET
ejpam-5268	12	4	applications	application	NOUN
ejpam-5268	12	5	of	of	ADP
ejpam-5268	12	6	(	(	PUNCT
ejpam-5268	12	7	b.	b.	PROPN
ejpam-5268	12	8	f.	f.	PROPN
ejpam-5268	12	9	p.	p.	PROPN
ejpam-5268	12	10	th	th	X
ejpam-5268	12	11	)	)	PUNCT
ejpam-5268	12	12	in	in	ADP
ejpam-5268	12	13	giving	give	VERB
ejpam-5268	12	14	the	the	DET
ejpam-5268	12	15	existence	existence	NOUN
ejpam-5268	12	16	and	and	CCONJ
ejpam-5268	12	17	uniqueness	uniqueness	ADJ
ejpam-5268	12	18	solutions	solution	NOUN
ejpam-5268	12	19	for	for	ADP
ejpam-5268	12	20	a	a	DET
ejpam-5268	12	21	lot	lot	NOUN
ejpam-5268	12	22	of	of	ADP
ejpam-5268	12	23	differential	differential	ADJ
ejpam-5268	12	24	and	and	CCONJ
ejpam-5268	12	25	integral	integral	ADJ
ejpam-5268	12	26	equations	equation	NOUN
ejpam-5268	12	27	,	,	PUNCT
ejpam-5268	12	28	diverse	diverse	ADJ
ejpam-5268	12	29	extensions	extension	NOUN
ejpam-5268	12	30	of	of	ADP
ejpam-5268	12	31	(	(	PUNCT
ejpam-5268	12	32	b.	b.	PROPN
ejpam-5268	12	33	f.	f.	PROPN
ejpam-5268	12	34	p.	p.	PROPN
ejpam-5268	12	35	th	th	PROPN
ejpam-5268	12	36	)	)	PUNCT
ejpam-5268	12	37	were	be	AUX
ejpam-5268	12	38	completed	complete	VERB
ejpam-5268	12	39	.	.	PUNCT
ejpam-5268	13	1	due	due	ADP
ejpam-5268	13	2	to	to	ADP
ejpam-5268	13	3	applications	application	NOUN
ejpam-5268	13	4	of	of	ADP
ejpam-5268	13	5	banach	banach	NOUN
ejpam-5268	13	6	contraction	contraction	NOUN
ejpam-5268	13	7	principle	principle	NOUN
ejpam-5268	13	8	in	in	ADP
ejpam-5268	13	9	all	all	DET
ejpam-5268	13	10	branch	branch	NOUN
ejpam-5268	13	11	of	of	ADP
ejpam-5268	13	12	pure	pure	ADJ
ejpam-5268	13	13	and	and	CCONJ
ejpam-5268	13	14	applied	applied	ADJ
ejpam-5268	13	15	mathematics	mathematic	NOUN
ejpam-5268	13	16	as	as	ADV
ejpam-5268	13	17	well	well	ADV
ejpam-5268	13	18	in	in	ADP
ejpam-5268	13	19	other	other	ADJ
ejpam-5268	13	20	various	various	ADJ
ejpam-5268	13	21	sciences	science	NOUN
ejpam-5268	13	22	,	,	PUNCT
ejpam-5268	13	23	numerous	numerous	ADJ
ejpam-5268	13	24	researchers	researcher	NOUN
ejpam-5268	13	25	have	have	AUX
ejpam-5268	13	26	expanded	expand	VERB
ejpam-5268	13	27	it	it	PRON
ejpam-5268	13	28	in	in	ADP
ejpam-5268	13	29	nonlinear	nonlinear	ADJ
ejpam-5268	13	30	analysis	analysis	NOUN
ejpam-5268	13	31	(	(	PUNCT
ejpam-5268	13	32	see	see	VERB
ejpam-5268	13	33	[	[	X
ejpam-5268	13	34	2	2	NUM
ejpam-5268	13	35	,	,	PUNCT
ejpam-5268	13	36	13	13	NUM
ejpam-5268	13	37	,	,	PUNCT
ejpam-5268	13	38	17	17	NUM
ejpam-5268	13	39	]	]	PUNCT
ejpam-5268	13	40	)	)	PUNCT
ejpam-5268	13	41	.	.	PUNCT
ejpam-5268	14	1	∗corresponding	∗corresponde	VERB
ejpam-5268	14	2	author	author	NOUN
ejpam-5268	14	3	.	.	PUNCT
ejpam-5268	15	1	doi	doi	NOUN
ejpam-5268	15	2	:	:	PUNCT
ejpam-5268	15	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5268	https://doi.org/10.29020/nybg.ejpam.v17i3.5268	NUM
ejpam-5268	15	4	email	email	NOUN
ejpam-5268	15	5	addresses	address	NOUN
ejpam-5268	15	6	:	:	PUNCT
ejpam-5268	15	7	aimanalhity@uoanbar.edu.iq	aimanalhity@uoanbar.edu.iq	PROPN
ejpam-5268	15	8	(	(	PUNCT
ejpam-5268	15	9	n.	n.	PROPN
ejpam-5268	15	10	a.	a.	PROPN
ejpam-5268	15	11	majid	majid	PROPN
ejpam-5268	15	12	)	)	PUNCT
ejpam-5268	15	13	,	,	PUNCT
ejpam-5268	15	14	eps.alaamahmood.farhan@uoanbar.edu.iq	eps.alaamahmood.farhan@uoanbar.edu.iq	X
ejpam-5268	15	15	(	(	PUNCT
ejpam-5268	15	16	a.	a.	PROPN
ejpam-5268	15	17	al	al	PROPN
ejpam-5268	15	18	jumaili	jumaili	PROPN
ejpam-5268	15	19	)	)	PUNCT
ejpam-5268	15	20	,	,	PUNCT
ejpam-5268	15	21	zhenchuanng@usm.my	zhenchuanng@usm.my	PROPN
ejpam-5268	15	22	(	(	PUNCT
ejpam-5268	15	23	z.	z.	PROPN
ejpam-5268	15	24	c.	c.	PROPN
ejpam-5268	15	25	ng	ng	PROPN
ejpam-5268	15	26	)	)	PUNCT
ejpam-5268	15	27	,	,	PUNCT
ejpam-5268	15	28	sklee@usm.my	sklee@usm.my	PROPN
ejpam-5268	15	29	(	(	PUNCT
ejpam-5268	15	30	s.	s.	PROPN
ejpam-5268	15	31	k.	k.	PROPN
ejpam-5268	15	32	lee	lee	PROPN
ejpam-5268	15	33	)	)	PUNCT
ejpam-5268	15	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5268	15	35	1877	1877	NUM
ejpam-5268	16	1	©	©	ADP
ejpam-5268	16	2	2024	2024	NUM
ejpam-5268	16	3	ejpam	ejpam	NOUN
ejpam-5268	16	4	all	all	DET
ejpam-5268	16	5	rights	right	NOUN
ejpam-5268	16	6	reserved	reserve	VERB
ejpam-5268	16	7	.	.	PUNCT
ejpam-5268	17	1	n.	n.	PROPN
ejpam-5268	17	2	a.	a.	PROPN
ejpam-5268	17	3	majid	majid	PROPN
ejpam-5268	17	4	et	et	PROPN
ejpam-5268	17	5	al	al	PROPN
ejpam-5268	17	6	.	.	PUNCT
ejpam-5268	17	7	/	/	SYM
ejpam-5268	17	8	eur	eur	PROPN
ejpam-5268	17	9	.	.	PUNCT
ejpam-5268	18	1	j.	j.	PROPN
ejpam-5268	18	2	pure	pure	PROPN
ejpam-5268	18	3	appl	appl	PROPN
ejpam-5268	18	4	.	.	PROPN
ejpam-5268	18	5	math	math	PROPN
ejpam-5268	18	6	,	,	PUNCT
ejpam-5268	18	7	17	17	NUM
ejpam-5268	18	8	(	(	PUNCT
ejpam-5268	18	9	3	3	NUM
ejpam-5268	18	10	)	)	PUNCT
ejpam-5268	18	11	(	(	PUNCT
ejpam-5268	18	12	2024	2024	NUM
ejpam-5268	18	13	)	)	PUNCT
ejpam-5268	18	14	,	,	PUNCT
ejpam-5268	18	15	1877	1877	NUM
ejpam-5268	18	16	-	-	SYM
ejpam-5268	18	17	1893	1893	NUM
ejpam-5268	18	18	1878	1878	NUM
ejpam-5268	18	19	newly	newly	ADJ
ejpam-5268	18	20	,	,	PUNCT
ejpam-5268	18	21	khojasteh	khojasteh	PROPN
ejpam-5268	18	22	et	et	PROPN
ejpam-5268	18	23	al	al	PROPN
ejpam-5268	18	24	,	,	PUNCT
ejpam-5268	18	25	in	in	ADP
ejpam-5268	18	26	[	[	X
ejpam-5268	18	27	18	18	NUM
ejpam-5268	18	28	]	]	PUNCT
ejpam-5268	18	29	,	,	PUNCT
ejpam-5268	18	30	offered	offer	VERB
ejpam-5268	18	31	the	the	DET
ejpam-5268	18	32	concept	concept	NOUN
ejpam-5268	18	33	of	of	ADP
ejpam-5268	18	34	simulation	simulation	NOUN
ejpam-5268	18	35	mappings	mapping	NOUN
ejpam-5268	18	36	to	to	PART
ejpam-5268	18	37	express	express	VERB
ejpam-5268	18	38	diverse	diverse	ADJ
ejpam-5268	18	39	contractivity	contractivity	NOUN
ejpam-5268	18	40	situations	situation	NOUN
ejpam-5268	18	41	in	in	ADP
ejpam-5268	18	42	unified	unified	ADJ
ejpam-5268	18	43	method	method	NOUN
ejpam-5268	18	44	.	.	PUNCT
ejpam-5268	19	1	this	this	DET
ejpam-5268	19	2	class	class	NOUN
ejpam-5268	19	3	of	of	ADP
ejpam-5268	19	4	contraction	contraction	NOUN
ejpam-5268	19	5	simplifies	simplify	VERB
ejpam-5268	19	6	the	the	DET
ejpam-5268	19	7	banach	banach	NOUN
ejpam-5268	19	8	contraction	contraction	NOUN
ejpam-5268	19	9	and	and	CCONJ
ejpam-5268	19	10	verifies	verifie	NOUN
ejpam-5268	19	11	some	some	DET
ejpam-5268	19	12	kinds	kind	NOUN
ejpam-5268	19	13	of	of	ADP
ejpam-5268	19	14	non	non	ADJ
ejpam-5268	19	15	-	-	ADJ
ejpam-5268	19	16	linear	linear	ADJ
ejpam-5268	19	17	contractions	contraction	NOUN
ejpam-5268	19	18	.	.	PUNCT
ejpam-5268	20	1	in	in	ADP
ejpam-5268	20	2	the	the	DET
ejpam-5268	20	3	same	same	ADJ
ejpam-5268	20	4	year	year	NOUN
ejpam-5268	20	5	,	,	PUNCT
ejpam-5268	20	6	the	the	DET
ejpam-5268	20	7	authors	author	NOUN
ejpam-5268	20	8	in	in	ADP
ejpam-5268	20	9	[	[	X
ejpam-5268	20	10	4	4	NUM
ejpam-5268	20	11	,	,	PUNCT
ejpam-5268	20	12	5	5	NUM
ejpam-5268	20	13	]	]	PUNCT
ejpam-5268	20	14	,	,	PUNCT
ejpam-5268	20	15	independently	independently	ADV
ejpam-5268	20	16	improved	improve	VERB
ejpam-5268	20	17	the	the	DET
ejpam-5268	20	18	idea	idea	NOUN
ejpam-5268	20	19	of	of	ADP
ejpam-5268	20	20	simulation	simulation	NOUN
ejpam-5268	20	21	maps	map	NOUN
ejpam-5268	20	22	and	and	CCONJ
ejpam-5268	20	23	established	establish	VERB
ejpam-5268	20	24	various	various	ADJ
ejpam-5268	20	25	common	common	ADJ
ejpam-5268	20	26	and	and	CCONJ
ejpam-5268	20	27	coincidence	coincidence	NOUN
ejpam-5268	20	28	fixed	fix	VERB
ejpam-5268	20	29	point	point	NOUN
ejpam-5268	20	30	results	result	NOUN
ejpam-5268	20	31	involving	involve	VERB
ejpam-5268	20	32	the	the	DET
ejpam-5268	20	33	most	most	ADV
ejpam-5268	20	34	recent	recent	ADJ
ejpam-5268	20	35	type	type	NOUN
ejpam-5268	20	36	of	of	ADP
ejpam-5268	20	37	simulation	simulation	NOUN
ejpam-5268	20	38	mappings	mapping	NOUN
ejpam-5268	20	39	.	.	PUNCT
ejpam-5268	21	1	recently	recently	ADV
ejpam-5268	21	2	,	,	PUNCT
ejpam-5268	21	3	many	many	ADJ
ejpam-5268	21	4	results	result	NOUN
ejpam-5268	21	5	involving	involve	VERB
ejpam-5268	21	6	fixed	fix	VERB
ejpam-5268	21	7	point	point	NOUN
ejpam-5268	21	8	,	,	PUNCT
ejpam-5268	21	9	common	common	ADJ
ejpam-5268	21	10	and	and	CCONJ
ejpam-5268	21	11	coincidence	coincidence	NOUN
ejpam-5268	21	12	fixed	fix	VERB
ejpam-5268	21	13	point	point	NOUN
ejpam-5268	21	14	are	be	AUX
ejpam-5268	21	15	established	establish	VERB
ejpam-5268	21	16	endowed	endow	VERB
ejpam-5268	21	17	with	with	ADP
ejpam-5268	21	18	various	various	ADJ
ejpam-5268	21	19	kinds	kind	NOUN
ejpam-5268	21	20	of	of	ADP
ejpam-5268	21	21	binary	binary	ADJ
ejpam-5268	21	22	relations	relation	NOUN
ejpam-5268	21	23	(	(	PUNCT
ejpam-5268	21	24	[	[	X
ejpam-5268	21	25	6	6	NUM
ejpam-5268	21	26	,	,	PUNCT
ejpam-5268	21	27	12	12	NUM
ejpam-5268	21	28	,	,	PUNCT
ejpam-5268	21	29	23	23	NUM
ejpam-5268	21	30	]	]	PUNCT
ejpam-5268	21	31	)	)	PUNCT
ejpam-5268	21	32	.	.	PUNCT
ejpam-5268	22	1	in	in	ADP
ejpam-5268	22	2	2010	2010	NUM
ejpam-5268	22	3	,	,	PUNCT
ejpam-5268	22	4	imdad	imdad	PROPN
ejpam-5268	22	5	and	and	CCONJ
ejpam-5268	22	6	soliman	soliman	NOUN
ejpam-5268	22	7	[	[	X
ejpam-5268	22	8	14	14	NUM
ejpam-5268	22	9	]	]	X
ejpam-5268	22	10	,	,	PUNCT
ejpam-5268	22	11	as	as	ADV
ejpam-5268	22	12	well	well	ADV
ejpam-5268	22	13	soliman	soliman	NOUN
ejpam-5268	22	14	et	et	PROPN
ejpam-5268	22	15	al	al	PROPN
ejpam-5268	22	16	.	.	PUNCT
ejpam-5268	23	1	[	[	X
ejpam-5268	23	2	24	24	NUM
ejpam-5268	23	3	]	]	PUNCT
ejpam-5268	23	4	expanded	expand	VERB
ejpam-5268	23	5	some	some	DET
ejpam-5268	23	6	outcomes	outcome	NOUN
ejpam-5268	23	7	in	in	ADP
ejpam-5268	23	8	the	the	DET
ejpam-5268	23	9	literature	literature	NOUN
ejpam-5268	23	10	to	to	ADP
ejpam-5268	23	11	symmetric	symmetric	ADJ
ejpam-5268	23	12	spaces	space	NOUN
ejpam-5268	23	13	using	use	VERB
ejpam-5268	23	14	the	the	DET
ejpam-5268	23	15	notion	notion	NOUN
ejpam-5268	23	16	of	of	ADP
ejpam-5268	23	17	weakly	weakly	ADJ
ejpam-5268	23	18	compatible	compatible	ADJ
ejpam-5268	23	19	pair	pair	NOUN
ejpam-5268	23	20	maps	map	NOUN
ejpam-5268	23	21	together	together	ADV
ejpam-5268	23	22	with	with	ADP
ejpam-5268	23	23	common	common	ADJ
ejpam-5268	23	24	(	(	PUNCT
ejpam-5268	23	25	e.a	e.a	PROPN
ejpam-5268	23	26	)	)	PUNCT
ejpam-5268	23	27	property	property	NOUN
ejpam-5268	23	28	(	(	PUNCT
ejpam-5268	23	29	idea	idea	NOUN
ejpam-5268	23	30	due	due	ADP
ejpam-5268	23	31	to	to	ADP
ejpam-5268	23	32	liu	liu	PROPN
ejpam-5268	23	33	et	et	PROPN
ejpam-5268	23	34	al	al	PROPN
ejpam-5268	23	35	.	.	PUNCT
ejpam-5268	24	1	[	[	X
ejpam-5268	24	2	20	20	NUM
ejpam-5268	24	3	]	]	NUM
ejpam-5268	24	4	)	)	PUNCT
ejpam-5268	24	5	,	,	PUNCT
ejpam-5268	24	6	for	for	ADP
ejpam-5268	24	7	additional	additional	ADJ
ejpam-5268	24	8	information	information	NOUN
ejpam-5268	24	9	on	on	ADP
ejpam-5268	24	10	advance	advance	NOUN
ejpam-5268	24	11	of	of	ADP
ejpam-5268	24	12	common	common	ADJ
ejpam-5268	24	13	fixed	fix	VERB
ejpam-5268	24	14	point	point	NOUN
ejpam-5268	24	15	theory	theory	NOUN
ejpam-5268	24	16	in	in	ADP
ejpam-5268	24	17	symmetric	symmetric	ADJ
ejpam-5268	24	18	spaces	space	NOUN
ejpam-5268	24	19	refer	refer	VERB
ejpam-5268	24	20	authors	author	NOUN
ejpam-5268	24	21	to	to	ADP
ejpam-5268	24	22	[	[	X
ejpam-5268	24	23	1	1	NUM
ejpam-5268	24	24	,	,	PUNCT
ejpam-5268	24	25	8	8	NUM
ejpam-5268	24	26	,	,	PUNCT
ejpam-5268	24	27	10	10	NUM
ejpam-5268	24	28	,	,	PUNCT
ejpam-5268	24	29	11	11	NUM
ejpam-5268	24	30	,	,	PUNCT
ejpam-5268	24	31	16	16	NUM
ejpam-5268	24	32	]	]	PUNCT
ejpam-5268	24	33	.	.	PUNCT
ejpam-5268	25	1	recent	recent	ADJ
ejpam-5268	25	2	,	,	PUNCT
ejpam-5268	25	3	b.	b.	PROPN
ejpam-5268	25	4	alqahtani	alqahtani	PROPN
ejpam-5268	25	5	et	et	PROPN
ejpam-5268	25	6	al	al	PROPN
ejpam-5268	25	7	.	.	PUNCT
ejpam-5268	26	1	[	[	X
ejpam-5268	26	2	3	3	NUM
ejpam-5268	26	3	]	]	PUNCT
ejpam-5268	26	4	,	,	PUNCT
ejpam-5268	26	5	scrutinized	scrutinize	VERB
ejpam-5268	26	6	the	the	DET
ejpam-5268	26	7	existence	existence	NOUN
ejpam-5268	26	8	and	and	CCONJ
ejpam-5268	26	9	uniqueness	uniqueness	NOUN
ejpam-5268	26	10	of	of	ADP
ejpam-5268	26	11	fixed	fix	VERB
ejpam-5268	26	12	point	point	NOUN
ejpam-5268	26	13	in	in	ADP
ejpam-5268	26	14	∆-symmetric	∆-symmetric	ADJ
ejpam-5268	26	15	quasi	quasi	ADJ
ejpam-5268	26	16	-	-	ADJ
ejpam-5268	26	17	metric	metric	ADJ
ejpam-5268	26	18	spaces	space	NOUN
ejpam-5268	26	19	utilizing	utilize	VERB
ejpam-5268	26	20	simulation	simulation	NOUN
ejpam-5268	26	21	mappings	mapping	NOUN
ejpam-5268	26	22	.	.	PUNCT
ejpam-5268	27	1	after	after	ADP
ejpam-5268	27	2	that	that	PRON
ejpam-5268	27	3	,	,	PUNCT
ejpam-5268	27	4	m.	m.	NOUN
ejpam-5268	27	5	kumar	kumar	PROPN
ejpam-5268	27	6	et	et	PROPN
ejpam-5268	27	7	al	al	PROPN
ejpam-5268	27	8	.	.	PUNCT
ejpam-5268	28	1	[	[	X
ejpam-5268	28	2	19	19	NUM
ejpam-5268	28	3	]	]	PUNCT
ejpam-5268	28	4	offered	offer	VERB
ejpam-5268	28	5	and	and	CCONJ
ejpam-5268	28	6	established	establish	VERB
ejpam-5268	28	7	various	various	ADJ
ejpam-5268	28	8	common	common	ADJ
ejpam-5268	28	9	and	and	CCONJ
ejpam-5268	28	10	coincidence	coincidence	NOUN
ejpam-5268	28	11	fixed	fix	VERB
ejpam-5268	28	12	-	-	PUNCT
ejpam-5268	28	13	point	point	NOUN
ejpam-5268	28	14	results	result	NOUN
ejpam-5268	28	15	in	in	ADP
ejpam-5268	28	16	symmetrical	symmetrical	ADJ
ejpam-5268	28	17	g	g	NOUN
ejpam-5268	28	18	-	-	PUNCT
ejpam-5268	28	19	metric	metric	ADJ
ejpam-5268	28	20	utilizing	utilize	VERB
ejpam-5268	28	21	the	the	DET
ejpam-5268	28	22	simulation	simulation	NOUN
ejpam-5268	28	23	mappings	mapping	NOUN
ejpam-5268	28	24	.	.	PUNCT
ejpam-5268	29	1	soon	soon	ADV
ejpam-5268	29	2	,	,	PUNCT
ejpam-5268	29	3	t.	t.	NOUN
ejpam-5268	29	4	hamaizia	hamaizia	PROPN
ejpam-5268	29	5	and	and	CCONJ
ejpam-5268	29	6	p.p	p.p	PROPN
ejpam-5268	29	7	.	.	PROPN
ejpam-5268	29	8	murthy	murthy	PROPN
ejpam-5268	30	1	[	[	X
ejpam-5268	30	2	9	9	NUM
ejpam-5268	30	3	]	]	PUNCT
ejpam-5268	30	4	verified	verify	VERB
ejpam-5268	30	5	some	some	DET
ejpam-5268	30	6	common	common	ADJ
ejpam-5268	30	7	fixed	fix	VERB
ejpam-5268	30	8	-	-	PUNCT
ejpam-5268	30	9	point	point	NOUN
ejpam-5268	30	10	results	result	NOUN
ejpam-5268	30	11	for	for	ADP
ejpam-5268	30	12	two	two	NUM
ejpam-5268	30	13	pairs	pair	NOUN
ejpam-5268	30	14	of	of	ADP
ejpam-5268	30	15	maps	map	NOUN
ejpam-5268	30	16	under	under	ADP
ejpam-5268	30	17	the	the	DET
ejpam-5268	30	18	extended	extended	ADJ
ejpam-5268	30	19	z	z	NOUN
ejpam-5268	30	20	-	-	PUNCT
ejpam-5268	30	21	contraction	contraction	NOUN
ejpam-5268	30	22	with	with	ADP
ejpam-5268	30	23	related	related	ADJ
ejpam-5268	30	24	to	to	ADP
ejpam-5268	30	25	the	the	DET
ejpam-5268	30	26	idea	idea	NOUN
ejpam-5268	30	27	of	of	ADP
ejpam-5268	30	28	simulation	simulation	NOUN
ejpam-5268	30	29	mappings	mapping	NOUN
ejpam-5268	30	30	in	in	ADP
ejpam-5268	30	31	b	b	NOUN
ejpam-5268	30	32	-	-	ADJ
ejpam-5268	30	33	metric	metric	ADJ
ejpam-5268	30	34	spaces	space	NOUN
ejpam-5268	30	35	.	.	PUNCT
ejpam-5268	31	1	s.shaban	s.shaban	PROPN
ejpam-5268	31	2	,	,	PUNCT
ejpam-5268	31	3	et	et	PROPN
ejpam-5268	31	4	al	al	PROPN
ejpam-5268	31	5	.	.	PUNCT
ejpam-5268	32	1	[	[	X
ejpam-5268	32	2	22	22	NUM
ejpam-5268	32	3	]	]	PUNCT
ejpam-5268	32	4	introduced	introduce	VERB
ejpam-5268	32	5	the	the	DET
ejpam-5268	32	6	idea	idea	NOUN
ejpam-5268	32	7	of	of	ADP
ejpam-5268	32	8	d∗-metric	d∗-metric	NOUN
ejpam-5268	32	9	-	-	PUNCT
ejpam-5268	32	10	sps	sps	NOUN
ejpam-5268	32	11	.	.	PUNCT
ejpam-5268	33	1	in	in	ADP
ejpam-5268	33	2	[	[	X
ejpam-5268	33	3	15	15	NUM
ejpam-5268	33	4	]	]	PUNCT
ejpam-5268	33	5	a.	a.	NOUN
ejpam-5268	33	6	al	al	PROPN
ejpam-5268	33	7	.	.	PROPN
ejpam-5268	33	8	jumaili	jumaili	PROPN
ejpam-5268	33	9	,	,	PUNCT
ejpam-5268	33	10	employed	employ	VERB
ejpam-5268	33	11	the	the	DET
ejpam-5268	33	12	idea	idea	NOUN
ejpam-5268	33	13	of	of	ADP
ejpam-5268	33	14	d∗metric	d∗metric	ADJ
ejpam-5268	33	15	-	-	PUNCT
ejpam-5268	33	16	sps	sps	NOUN
ejpam-5268	33	17	and	and	CCONJ
ejpam-5268	33	18	proved	prove	VERB
ejpam-5268	33	19	various	various	ADJ
ejpam-5268	33	20	coincidence	coincidence	NOUN
ejpam-5268	33	21	fixed	fix	VERB
ejpam-5268	33	22	point	point	NOUN
ejpam-5268	33	23	results	result	NOUN
ejpam-5268	33	24	for	for	ADP
ejpam-5268	33	25	mappings	mapping	NOUN
ejpam-5268	33	26	satisfying	satisfy	VERB
ejpam-5268	33	27	contractive	contractive	ADJ
ejpam-5268	33	28	conditions	condition	NOUN
ejpam-5268	33	29	relating	relate	VERB
ejpam-5268	33	30	to	to	ADP
ejpam-5268	33	31	nondecreasing	nondecrease	VERB
ejpam-5268	33	32	φ	φ	NOUN
ejpam-5268	33	33	-	-	NOUN
ejpam-5268	33	34	maps	map	NOUN
ejpam-5268	33	35	in	in	ADP
ejpam-5268	33	36	partially	partially	ADV
ejpam-5268	33	37	ordered	order	VERB
ejpam-5268	33	38	d∗-metric	d∗-metric	NOUN
ejpam-5268	33	39	.	.	PUNCT
ejpam-5268	34	1	in	in	ADP
ejpam-5268	34	2	this	this	DET
ejpam-5268	34	3	article	article	NOUN
ejpam-5268	34	4	we	we	PRON
ejpam-5268	34	5	introduce	introduce	VERB
ejpam-5268	34	6	another	another	DET
ejpam-5268	34	7	extension	extension	NOUN
ejpam-5268	34	8	al	al	PROPN
ejpam-5268	34	9	-	-	PUNCT
ejpam-5268	34	10	argoubi	argoubi	PROPN
ejpam-5268	34	11	outcomes	outcome	NOUN
ejpam-5268	34	12	in	in	ADP
ejpam-5268	34	13	[	[	X
ejpam-5268	34	14	4	4	X
ejpam-5268	34	15	]	]	PUNCT
ejpam-5268	34	16	utilizing	utilize	VERB
ejpam-5268	34	17	the	the	DET
ejpam-5268	34	18	idea	idea	NOUN
ejpam-5268	34	19	of	of	ADP
ejpam-5268	34	20	s	s	NOUN
ejpam-5268	34	21	-	-	ADJ
ejpam-5268	34	22	metric	metric	ADJ
ejpam-5268	34	23	spaces	space	NOUN
ejpam-5268	34	24	.	.	PUNCT
ejpam-5268	35	1	several	several	ADJ
ejpam-5268	35	2	basic	basic	ADJ
ejpam-5268	35	3	definitions	definition	NOUN
ejpam-5268	35	4	and	and	CCONJ
ejpam-5268	35	5	essential	essential	ADJ
ejpam-5268	35	6	conclusions	conclusion	NOUN
ejpam-5268	35	7	under	under	ADP
ejpam-5268	35	8	the	the	DET
ejpam-5268	35	9	idea	idea	NOUN
ejpam-5268	35	10	of	of	ADP
ejpam-5268	35	11	s	s	NOUN
ejpam-5268	35	12	-	-	ADJ
ejpam-5268	35	13	metric	metric	ADJ
ejpam-5268	35	14	spaces	space	NOUN
ejpam-5268	35	15	and	and	CCONJ
ejpam-5268	35	16	simulation	simulation	NOUN
ejpam-5268	35	17	mappings	mapping	NOUN
ejpam-5268	35	18	have	have	AUX
ejpam-5268	35	19	been	be	AUX
ejpam-5268	35	20	presented	present	VERB
ejpam-5268	35	21	in	in	ADP
ejpam-5268	35	22	the	the	DET
ejpam-5268	35	23	beginning	beginning	NOUN
ejpam-5268	35	24	.	.	PUNCT
ejpam-5268	36	1	a	a	DET
ejpam-5268	36	2	novel	novel	ADJ
ejpam-5268	36	3	concept	concept	NOUN
ejpam-5268	36	4	of	of	ADP
ejpam-5268	36	5	extended	extend	VERB
ejpam-5268	36	6	metric	metric	ADJ
ejpam-5268	36	7	spaces	space	NOUN
ejpam-5268	36	8	introduced	introduce	VERB
ejpam-5268	36	9	via	via	ADP
ejpam-5268	36	10	s.	s.	PROPN
ejpam-5268	36	11	shaban	shaban	PROPN
ejpam-5268	36	12	,	,	PUNCT
ejpam-5268	36	13	et	et	PROPN
ejpam-5268	36	14	al	al	PROPN
ejpam-5268	36	15	.	.	PUNCT
ejpam-5268	37	1	[	[	X
ejpam-5268	37	2	22	22	NUM
ejpam-5268	37	3	]	]	PUNCT
ejpam-5268	37	4	as	as	SCONJ
ejpam-5268	37	5	follows	follow	VERB
ejpam-5268	37	6	:	:	PUNCT
ejpam-5268	37	7	definition	definition	NOUN
ejpam-5268	37	8	1	1	NUM
ejpam-5268	37	9	.	.	PUNCT
ejpam-5268	38	1	[	[	X
ejpam-5268	38	2	22	22	NUM
ejpam-5268	38	3	]	]	PUNCT
ejpam-5268	38	4	suppose	suppose	VERB
ejpam-5268	38	5	x	x	PUNCT
ejpam-5268	38	6	̸=	̸=	PROPN
ejpam-5268	38	7	∅.	∅.	ADP
ejpam-5268	38	8	a	a	DET
ejpam-5268	38	9	d∗-metric	d∗-metric	NOUN
ejpam-5268	38	10	is	be	AUX
ejpam-5268	38	11	a	a	DET
ejpam-5268	38	12	mapping	mapping	NOUN
ejpam-5268	38	13	,	,	PUNCT
ejpam-5268	38	14	d∗	d∗	NOUN
ejpam-5268	38	15	:	:	PUNCT
ejpam-5268	38	16	x3	x3	ADJ
ejpam-5268	38	17	→	→	SYM
ejpam-5268	38	18	[	[	X
ejpam-5268	38	19	0	0	NUM
ejpam-5268	38	20	,	,	PUNCT
ejpam-5268	38	21	+	+	NOUN
ejpam-5268	38	22	∞	∞	NOUN
ejpam-5268	38	23	)	)	PUNCT
ejpam-5268	38	24	,	,	PUNCT
ejpam-5268	38	25	that	that	PRON
ejpam-5268	38	26	satisfies	satisfy	VERB
ejpam-5268	38	27	the	the	DET
ejpam-5268	38	28	next	next	ADJ
ejpam-5268	38	29	statements	statement	NOUN
ejpam-5268	38	30	∀	∀	X
ejpam-5268	38	31	x	x	NOUN
ejpam-5268	38	32	,	,	PUNCT
ejpam-5268	38	33	y	y	PROPN
ejpam-5268	38	34	,	,	PUNCT
ejpam-5268	38	35	z	z	PROPN
ejpam-5268	38	36	,	,	PUNCT
ejpam-5268	38	37	b	b	X
ejpam-5268	38	38	∈	∈	PROPN
ejpam-5268	38	39	x	x	X
ejpam-5268	38	40	:	:	PUNCT
ejpam-5268	38	41	(	(	PUNCT
ejpam-5268	38	42	d∗	d∗	PROPN
ejpam-5268	38	43	1	1	NUM
ejpam-5268	38	44	)	)	PUNCT
ejpam-5268	38	45	d∗	d∗	NOUN
ejpam-5268	38	46	(	(	PUNCT
ejpam-5268	38	47	x	x	X
ejpam-5268	38	48	,	,	PUNCT
ejpam-5268	38	49	y	y	PROPN
ejpam-5268	38	50	,	,	PUNCT
ejpam-5268	38	51	z	z	NOUN
ejpam-5268	38	52	)	)	PUNCT
ejpam-5268	38	53	≥	≥	NOUN
ejpam-5268	38	54	0	0	NUM
ejpam-5268	38	55	,	,	PUNCT
ejpam-5268	38	56	∀	∀	X
ejpam-5268	38	57	x	x	NOUN
ejpam-5268	38	58	,	,	PUNCT
ejpam-5268	38	59	y	y	PROPN
ejpam-5268	38	60	,	,	PUNCT
ejpam-5268	38	61	z	z	PROPN
ejpam-5268	38	62	∈	∈	PROPN
ejpam-5268	38	63	x	x	X
ejpam-5268	38	64	;	;	PUNCT
ejpam-5268	38	65	(	(	PUNCT
ejpam-5268	38	66	d∗	d∗	PROPN
ejpam-5268	38	67	2	2	NUM
ejpam-5268	38	68	)	)	PUNCT
ejpam-5268	38	69	d∗	d∗	NOUN
ejpam-5268	38	70	(	(	PUNCT
ejpam-5268	38	71	x	x	X
ejpam-5268	38	72	,	,	PUNCT
ejpam-5268	38	73	y	y	PROPN
ejpam-5268	38	74	,	,	PUNCT
ejpam-5268	38	75	z	z	NOUN
ejpam-5268	38	76	)	)	PUNCT
ejpam-5268	39	1	=	=	SYM
ejpam-5268	39	2	0	0	NUM
ejpam-5268	39	3	⇐	⇐	ADJ
ejpam-5268	39	4	⇒	⇒	NOUN
ejpam-5268	39	5	x	x	PUNCT
ejpam-5268	40	1	=	=	SYM
ejpam-5268	40	2	y	y	PROPN
ejpam-5268	40	3	=	=	SYM
ejpam-5268	40	4	z	z	PROPN
ejpam-5268	40	5	;	;	PUNCT
ejpam-5268	40	6	(	(	PUNCT
ejpam-5268	40	7	d∗	d∗	PROPN
ejpam-5268	40	8	3	3	NUM
ejpam-5268	40	9	)	)	PUNCT
ejpam-5268	40	10	d∗	d∗	NOUN
ejpam-5268	40	11	(	(	PUNCT
ejpam-5268	40	12	x	x	X
ejpam-5268	40	13	,	,	PUNCT
ejpam-5268	40	14	y	y	PROPN
ejpam-5268	40	15	,	,	PUNCT
ejpam-5268	40	16	z	z	NOUN
ejpam-5268	40	17	)	)	PUNCT
ejpam-5268	40	18	=	=	SYM
ejpam-5268	40	19	d∗	d∗	NOUN
ejpam-5268	40	20	(	(	PUNCT
ejpam-5268	40	21	p	p	X
ejpam-5268	40	22	{	{	PUNCT
ejpam-5268	40	23	x	x	PROPN
ejpam-5268	40	24	,	,	PUNCT
ejpam-5268	40	25	y	y	PROPN
ejpam-5268	40	26	,	,	PUNCT
ejpam-5268	40	27	z	z	NOUN
ejpam-5268	40	28	}	}	PUNCT
ejpam-5268	40	29	)	)	PUNCT
ejpam-5268	40	30	,	,	PUNCT
ejpam-5268	40	31	(	(	PUNCT
ejpam-5268	40	32	symmetry	symmetry	NOUN
ejpam-5268	40	33	)	)	PUNCT
ejpam-5268	40	34	where	where	SCONJ
ejpam-5268	40	35	p	p	NOUN
ejpam-5268	40	36	is	be	AUX
ejpam-5268	40	37	permutation	permutation	NOUN
ejpam-5268	40	38	mapping	mapping	NOUN
ejpam-5268	40	39	;	;	PUNCT
ejpam-5268	40	40	(	(	PUNCT
ejpam-5268	40	41	d∗	d∗	PROPN
ejpam-5268	40	42	4	4	NUM
ejpam-5268	40	43	)	)	PUNCT
ejpam-5268	40	44	d∗	d∗	NOUN
ejpam-5268	40	45	(	(	PUNCT
ejpam-5268	40	46	x	x	X
ejpam-5268	40	47	,	,	PUNCT
ejpam-5268	40	48	y	y	PROPN
ejpam-5268	40	49	,	,	PUNCT
ejpam-5268	40	50	z	z	NOUN
ejpam-5268	40	51	)	)	PUNCT
ejpam-5268	40	52	≤	≤	NUM
ejpam-5268	40	53	d∗	d∗	NOUN
ejpam-5268	40	54	(	(	PUNCT
ejpam-5268	40	55	x	x	X
ejpam-5268	40	56	,	,	PUNCT
ejpam-5268	40	57	y	y	PROPN
ejpam-5268	40	58	,	,	PUNCT
ejpam-5268	40	59	b	b	NOUN
ejpam-5268	40	60	)	)	PUNCT
ejpam-5268	41	1	+	+	NOUN
ejpam-5268	41	2	d∗	d∗	NOUN
ejpam-5268	41	3	(	(	PUNCT
ejpam-5268	41	4	b	b	NOUN
ejpam-5268	41	5	,	,	PUNCT
ejpam-5268	41	6	z	z	PROPN
ejpam-5268	41	7	,	,	PUNCT
ejpam-5268	41	8	z	z	NOUN
ejpam-5268	41	9	)	)	PUNCT
ejpam-5268	41	10	.	.	PUNCT
ejpam-5268	42	1	in	in	ADP
ejpam-5268	42	2	that	that	DET
ejpam-5268	42	3	case	case	NOUN
ejpam-5268	42	4	the	the	DET
ejpam-5268	42	5	map	map	NOUN
ejpam-5268	42	6	d∗	d∗	NOUN
ejpam-5268	42	7	is	be	AUX
ejpam-5268	42	8	called	call	VERB
ejpam-5268	42	9	d∗-metric	d∗-metric	ADJ
ejpam-5268	42	10	and	and	CCONJ
ejpam-5268	42	11	(	(	PUNCT
ejpam-5268	42	12	x	x	NOUN
ejpam-5268	42	13	,	,	PUNCT
ejpam-5268	42	14	d∗	d∗	PROPN
ejpam-5268	42	15	)	)	PUNCT
ejpam-5268	42	16	is	be	AUX
ejpam-5268	42	17	namely	namely	ADV
ejpam-5268	42	18	,	,	PUNCT
ejpam-5268	42	19	d∗-metric	d∗-metric	NOUN
ejpam-5268	42	20	.	.	PUNCT
ejpam-5268	42	21	example	example	NOUN
ejpam-5268	43	1	1	1	NUM
ejpam-5268	43	2	.	.	PUNCT
ejpam-5268	44	1	[	[	X
ejpam-5268	44	2	22	22	NUM
ejpam-5268	44	3	]	]	PUNCT
ejpam-5268	44	4	(	(	PUNCT
ejpam-5268	44	5	i	i	NOUN
ejpam-5268	44	6	)	)	PUNCT
ejpam-5268	44	7	let	let	AUX
ejpam-5268	44	8	(	(	PUNCT
ejpam-5268	44	9	x	x	NOUN
ejpam-5268	44	10	,	,	PUNCT
ejpam-5268	44	11	d	d	NOUN
ejpam-5268	44	12	)	)	PUNCT
ejpam-5268	44	13	be	be	AUX
ejpam-5268	44	14	a	a	DET
ejpam-5268	44	15	metric	metric	ADJ
ejpam-5268	44	16	space	space	NOUN
ejpam-5268	44	17	,	,	PUNCT
ejpam-5268	44	18	then	then	ADV
ejpam-5268	44	19	(	(	PUNCT
ejpam-5268	44	20	x	x	X
ejpam-5268	44	21	,	,	PUNCT
ejpam-5268	44	22	d∗	d∗	PROPN
ejpam-5268	44	23	)	)	PUNCT
ejpam-5268	44	24	,	,	PUNCT
ejpam-5268	44	25	with	with	ADP
ejpam-5268	44	26	a	a	DET
ejpam-5268	44	27	mapping	mapping	NOUN
ejpam-5268	44	28	d∗	d∗	NOUN
ejpam-5268	44	29	:	:	PUNCT
ejpam-5268	44	30	x3	x3	ADJ
ejpam-5268	44	31	→	→	SYM
ejpam-5268	44	32	[	[	X
ejpam-5268	44	33	0	0	NUM
ejpam-5268	44	34	,	,	PUNCT
ejpam-5268	44	35	+	+	NOUN
ejpam-5268	44	36	∞	∞	NOUN
ejpam-5268	44	37	)	)	PUNCT
ejpam-5268	44	38	be	be	AUX
ejpam-5268	44	39	defined	define	VERB
ejpam-5268	44	40	as	as	SCONJ
ejpam-5268	44	41	follows	follow	VERB
ejpam-5268	44	42	:	:	PUNCT
ejpam-5268	44	43	(	(	PUNCT
ejpam-5268	44	44	a	a	X
ejpam-5268	44	45	)	)	PUNCT
ejpam-5268	44	46	d∗	d∗	NOUN
ejpam-5268	44	47	(	(	PUNCT
ejpam-5268	44	48	x	x	X
ejpam-5268	44	49	,	,	PUNCT
ejpam-5268	44	50	y	y	PROPN
ejpam-5268	44	51	,	,	PUNCT
ejpam-5268	44	52	z	z	NOUN
ejpam-5268	44	53	)	)	PUNCT
ejpam-5268	45	1	=	=	SYM
ejpam-5268	45	2	d	d	X
ejpam-5268	45	3	(	(	PUNCT
ejpam-5268	45	4	x	x	NOUN
ejpam-5268	45	5	,	,	PUNCT
ejpam-5268	45	6	y	y	PROPN
ejpam-5268	45	7	)	)	PUNCT
ejpam-5268	46	1	+	+	CCONJ
ejpam-5268	46	2	d	d	X
ejpam-5268	46	3	(	(	PUNCT
ejpam-5268	46	4	y	y	PROPN
ejpam-5268	46	5	,	,	PUNCT
ejpam-5268	46	6	z	z	NOUN
ejpam-5268	46	7	)	)	PUNCT
ejpam-5268	47	1	+	+	CCONJ
ejpam-5268	47	2	d	d	X
ejpam-5268	47	3	(	(	PUNCT
ejpam-5268	47	4	z	z	NOUN
ejpam-5268	47	5	,	,	PUNCT
ejpam-5268	47	6	x	x	NOUN
ejpam-5268	47	7	)	)	PUNCT
ejpam-5268	47	8	.	.	PUNCT
ejpam-5268	48	1	n.	n.	PROPN
ejpam-5268	48	2	a.	a.	PROPN
ejpam-5268	48	3	majid	majid	PROPN
ejpam-5268	48	4	et	et	PROPN
ejpam-5268	48	5	al	al	PROPN
ejpam-5268	48	6	.	.	PUNCT
ejpam-5268	48	7	/	/	SYM
ejpam-5268	48	8	eur	eur	PROPN
ejpam-5268	48	9	.	.	PUNCT
ejpam-5268	49	1	j.	j.	PROPN
ejpam-5268	49	2	pure	pure	PROPN
ejpam-5268	49	3	appl	appl	PROPN
ejpam-5268	49	4	.	.	PROPN
ejpam-5268	49	5	math	math	PROPN
ejpam-5268	49	6	,	,	PUNCT
ejpam-5268	49	7	17	17	NUM
ejpam-5268	49	8	(	(	PUNCT
ejpam-5268	49	9	3	3	NUM
ejpam-5268	49	10	)	)	PUNCT
ejpam-5268	49	11	(	(	PUNCT
ejpam-5268	49	12	2024	2024	NUM
ejpam-5268	49	13	)	)	PUNCT
ejpam-5268	49	14	,	,	PUNCT
ejpam-5268	49	15	1877	1877	NUM
ejpam-5268	49	16	-	-	SYM
ejpam-5268	49	17	1893	1893	NUM
ejpam-5268	49	18	1879	1879	NUM
ejpam-5268	49	19	(	(	PUNCT
ejpam-5268	49	20	b	b	X
ejpam-5268	49	21	)	)	PUNCT
ejpam-5268	49	22	d∗	d∗	PROPN
ejpam-5268	49	23	(	(	PUNCT
ejpam-5268	49	24	x	x	X
ejpam-5268	49	25	,	,	PUNCT
ejpam-5268	49	26	y	y	PROPN
ejpam-5268	49	27	,	,	PUNCT
ejpam-5268	49	28	z	z	NOUN
ejpam-5268	49	29	)	)	PUNCT
ejpam-5268	49	30	=	=	SYM
ejpam-5268	49	31	max	max	PROPN
ejpam-5268	49	32	{	{	PUNCT
ejpam-5268	49	33	d	d	X
ejpam-5268	49	34	(	(	PUNCT
ejpam-5268	49	35	x	x	NOUN
ejpam-5268	49	36	,	,	PUNCT
ejpam-5268	49	37	y	y	PROPN
ejpam-5268	49	38	)	)	PUNCT
ejpam-5268	49	39	,	,	PUNCT
ejpam-5268	50	1	d	d	X
ejpam-5268	50	2	(	(	PUNCT
ejpam-5268	50	3	y	y	PROPN
ejpam-5268	50	4	,	,	PUNCT
ejpam-5268	50	5	z	z	NOUN
ejpam-5268	50	6	)	)	PUNCT
ejpam-5268	50	7	,	,	PUNCT
ejpam-5268	51	1	d	d	X
ejpam-5268	51	2	(	(	PUNCT
ejpam-5268	51	3	z	z	NOUN
ejpam-5268	51	4	,	,	PUNCT
ejpam-5268	51	5	x	x	NOUN
ejpam-5268	51	6	)	)	PUNCT
ejpam-5268	51	7	}	}	PUNCT
ejpam-5268	51	8	.	.	PUNCT
ejpam-5268	51	9	∀	∀	PUNCT
ejpam-5268	52	1	x	x	X
ejpam-5268	52	2	,	,	PUNCT
ejpam-5268	52	3	y	y	PROPN
ejpam-5268	52	4	,	,	PUNCT
ejpam-5268	52	5	z	z	PROPN
ejpam-5268	52	6	∈	∈	PROPN
ejpam-5268	52	7	x	x	X
ejpam-5268	52	8	,	,	PUNCT
ejpam-5268	52	9	is	be	AUX
ejpam-5268	52	10	d∗-metric	d∗-metric	ADJ
ejpam-5268	52	11	.	.	PUNCT
ejpam-5268	53	1	(	(	PUNCT
ejpam-5268	53	2	ii	ii	NOUN
ejpam-5268	53	3	)	)	PUNCT
ejpam-5268	53	4	if	if	SCONJ
ejpam-5268	53	5	x	x	X
ejpam-5268	53	6	=	=	SYM
ejpam-5268	53	7	r	r	NOUN
ejpam-5268	53	8	,	,	PUNCT
ejpam-5268	53	9	then	then	ADV
ejpam-5268	53	10	we	we	PRON
ejpam-5268	53	11	define	define	VERB
ejpam-5268	53	12	:	:	PUNCT
ejpam-5268	53	13	d∗	d∗	PROPN
ejpam-5268	53	14	(	(	PUNCT
ejpam-5268	53	15	x	x	X
ejpam-5268	53	16	,	,	PUNCT
ejpam-5268	53	17	y	y	PROPN
ejpam-5268	53	18	,	,	PUNCT
ejpam-5268	53	19	z	z	NOUN
ejpam-5268	53	20	)	)	PUNCT
ejpam-5268	53	21	=	=	PRON
ejpam-5268	53	22	{	{	PUNCT
ejpam-5268	53	23	0	0	NUM
ejpam-5268	53	24	,	,	PUNCT
ejpam-5268	53	25	if	if	SCONJ
ejpam-5268	53	26	x	x	ADP
ejpam-5268	53	27	=	=	PUNCT
ejpam-5268	53	28	y	y	PROPN
ejpam-5268	53	29	=	=	SYM
ejpam-5268	53	30	z	z	PROPN
ejpam-5268	53	31	max	max	PROPN
ejpam-5268	53	32	{	{	PUNCT
ejpam-5268	53	33	x	x	PROPN
ejpam-5268	53	34	,	,	PUNCT
ejpam-5268	53	35	y	y	PROPN
ejpam-5268	53	36	,	,	PUNCT
ejpam-5268	53	37	z	z	NOUN
ejpam-5268	53	38	}	}	PUNCT
ejpam-5268	53	39	,	,	PUNCT
ejpam-5268	53	40	otherwise	otherwise	ADV
ejpam-5268	53	41	.	.	PUNCT
ejpam-5268	54	1	for	for	ADP
ejpam-5268	54	2	all	all	DET
ejpam-5268	54	3	x	x	PROPN
ejpam-5268	54	4	,	,	PUNCT
ejpam-5268	54	5	y	y	PROPN
ejpam-5268	54	6	,	,	PUNCT
ejpam-5268	54	7	z	z	PROPN
ejpam-5268	54	8	∈	∈	PROPN
ejpam-5268	54	9	x	x	X
ejpam-5268	54	10	,	,	PUNCT
ejpam-5268	54	11	(	(	PUNCT
ejpam-5268	54	12	x	x	NOUN
ejpam-5268	54	13	,	,	PUNCT
ejpam-5268	54	14	d∗	d∗	PROPN
ejpam-5268	54	15	)	)	PUNCT
ejpam-5268	54	16	is	be	AUX
ejpam-5268	54	17	d∗-metric	d∗-metric	VERB
ejpam-5268	54	18	.	.	PUNCT
ejpam-5268	55	1	in	in	ADP
ejpam-5268	55	2	2012	2012	NUM
ejpam-5268	55	3	,	,	PUNCT
ejpam-5268	55	4	s.	s.	PROPN
ejpam-5268	55	5	shaban	shaban	PROPN
ejpam-5268	55	6	,	,	PUNCT
ejpam-5268	55	7	et	et	PROPN
ejpam-5268	55	8	al	al	PROPN
ejpam-5268	55	9	.	.	PUNCT
ejpam-5268	56	1	[	[	X
ejpam-5268	56	2	21	21	NUM
ejpam-5268	56	3	]	]	PUNCT
ejpam-5268	56	4	categorizing	categorize	VERB
ejpam-5268	56	5	symmetry	symmetry	NOUN
ejpam-5268	56	6	condition	condition	NOUN
ejpam-5268	56	7	as	as	ADP
ejpam-5268	56	8	common	common	ADJ
ejpam-5268	56	9	weakness	weakness	NOUN
ejpam-5268	56	10	of	of	ADP
ejpam-5268	56	11	g	g	NOUN
ejpam-5268	56	12	-	-	PUNCT
ejpam-5268	56	13	metric	metric	ADJ
ejpam-5268	56	14	&	&	CCONJ
ejpam-5268	56	15	d∗-metric	d∗-metric	ADJ
ejpam-5268	56	16	.	.	PUNCT
ejpam-5268	57	1	therefore	therefore	ADV
ejpam-5268	57	2	,	,	PUNCT
ejpam-5268	57	3	s.	s.	PROPN
ejpam-5268	57	4	shaban	shaban	PROPN
ejpam-5268	57	5	,	,	PUNCT
ejpam-5268	57	6	et	et	PROPN
ejpam-5268	57	7	al	al	PROPN
ejpam-5268	57	8	.	.	PUNCT
ejpam-5268	58	1	[	[	X
ejpam-5268	58	2	21	21	NUM
ejpam-5268	58	3	]	]	PUNCT
ejpam-5268	58	4	studied	study	VERB
ejpam-5268	58	5	and	and	CCONJ
ejpam-5268	58	6	established	establish	VERB
ejpam-5268	58	7	a	a	DET
ejpam-5268	58	8	novel	novel	ADJ
ejpam-5268	58	9	meaning	meaning	NOUN
ejpam-5268	58	10	of	of	ADP
ejpam-5268	58	11	generalized	generalized	ADJ
ejpam-5268	58	12	metric	metric	ADJ
ejpam-5268	58	13	space	space	NOUN
ejpam-5268	58	14	namely	namely	ADV
ejpam-5268	58	15	,	,	PUNCT
ejpam-5268	58	16	(	(	PUNCT
ejpam-5268	58	17	s	s	NOUN
ejpam-5268	58	18	-	-	ADJ
ejpam-5268	58	19	metric	metric	ADJ
ejpam-5268	58	20	space	space	NOUN
ejpam-5268	58	21	)	)	PUNCT
ejpam-5268	59	1	which	which	PRON
ejpam-5268	59	2	as	as	ADP
ejpam-5268	59	3	potential	potential	ADJ
ejpam-5268	59	4	improvement	improvement	NOUN
ejpam-5268	59	5	of	of	ADP
ejpam-5268	59	6	d∗-metric	d∗-metric	ADJ
ejpam-5268	59	7	which	which	PRON
ejpam-5268	59	8	was	be	AUX
ejpam-5268	59	9	studied	study	VERB
ejpam-5268	59	10	via	via	ADP
ejpam-5268	59	11	s.	s.	PROPN
ejpam-5268	59	12	shaban	shaban	PROPN
ejpam-5268	59	13	,	,	PUNCT
ejpam-5268	59	14	et	et	PROPN
ejpam-5268	59	15	al	al	PROPN
ejpam-5268	60	1	.	.	PUNCT
ejpam-5268	61	1	[	[	X
ejpam-5268	61	2	22	22	NUM
ejpam-5268	61	3	]	]	PUNCT
ejpam-5268	61	4	and	and	CCONJ
ejpam-5268	61	5	gave	give	VERB
ejpam-5268	61	6	some	some	PRON
ejpam-5268	61	7	of	of	ADP
ejpam-5268	61	8	their	their	PRON
ejpam-5268	61	9	properties	property	NOUN
ejpam-5268	61	10	.	.	PUNCT
ejpam-5268	62	1	definition	definition	NOUN
ejpam-5268	62	2	2	2	NUM
ejpam-5268	62	3	.	.	PUNCT
ejpam-5268	63	1	[	[	X
ejpam-5268	63	2	21	21	NUM
ejpam-5268	63	3	]	]	X
ejpam-5268	63	4	assume	assume	VERB
ejpam-5268	63	5	x	x	X
ejpam-5268	63	6	̸=	̸=	PROPN
ejpam-5268	63	7	∅.as	∅.as	NOUN
ejpam-5268	63	8	–	–	PUNCT
ejpam-5268	63	9	metric	metric	ADJ
ejpam-5268	63	10	on	on	ADP
ejpam-5268	63	11	x	x	SYM
ejpam-5268	63	12	is	be	AUX
ejpam-5268	63	13	s	s	PART
ejpam-5268	63	14	:	:	PUNCT
ejpam-5268	63	15	x3	x3	VERB
ejpam-5268	63	16	−→	−→	NOUN
ejpam-5268	63	17	[	[	X
ejpam-5268	63	18	0	0	NUM
ejpam-5268	63	19	,	,	PUNCT
ejpam-5268	63	20	+	+	NOUN
ejpam-5268	63	21	∞	∞	NOUN
ejpam-5268	63	22	)	)	PUNCT
ejpam-5268	63	23	,	,	PUNCT
ejpam-5268	63	24	satisfies	satisfy	VERB
ejpam-5268	63	25	the	the	DET
ejpam-5268	63	26	next	next	ADJ
ejpam-5268	63	27	statements	statement	NOUN
ejpam-5268	63	28	∀	∀	X
ejpam-5268	63	29	x	x	NOUN
ejpam-5268	63	30	,	,	PUNCT
ejpam-5268	63	31	y	y	PROPN
ejpam-5268	63	32	,	,	PUNCT
ejpam-5268	63	33	z	z	PROPN
ejpam-5268	63	34	,	,	PUNCT
ejpam-5268	63	35	a	a	DET
ejpam-5268	63	36	∈	∈	PROPN
ejpam-5268	63	37	x	x	X
ejpam-5268	63	38	,	,	PUNCT
ejpam-5268	63	39	(	(	PUNCT
ejpam-5268	63	40	s1	s1	NOUN
ejpam-5268	63	41	)	)	PUNCT
ejpam-5268	63	42	s	s	PART
ejpam-5268	63	43	(	(	PUNCT
ejpam-5268	63	44	x	x	NOUN
ejpam-5268	63	45	,	,	PUNCT
ejpam-5268	63	46	y	y	PROPN
ejpam-5268	63	47	,	,	PUNCT
ejpam-5268	63	48	z	z	NOUN
ejpam-5268	63	49	)	)	PUNCT
ejpam-5268	63	50	≥	≥	NOUN
ejpam-5268	63	51	0	0	NUM
ejpam-5268	63	52	;	;	PUNCT
ejpam-5268	63	53	(	(	PUNCT
ejpam-5268	63	54	s2)s	s2)s	NOUN
ejpam-5268	63	55	(	(	PUNCT
ejpam-5268	63	56	x	x	NOUN
ejpam-5268	63	57	,	,	PUNCT
ejpam-5268	63	58	y	y	PROPN
ejpam-5268	63	59	,	,	PUNCT
ejpam-5268	63	60	z	z	NOUN
ejpam-5268	63	61	)	)	PUNCT
ejpam-5268	63	62	=	=	SYM
ejpam-5268	63	63	0	0	NUM
ejpam-5268	63	64	⇐	⇐	ADJ
ejpam-5268	63	65	⇒	⇒	NOUN
ejpam-5268	63	66	x	x	PUNCT
ejpam-5268	64	1	=	=	SYM
ejpam-5268	64	2	y	y	PROPN
ejpam-5268	64	3	=	=	SYM
ejpam-5268	64	4	z	z	PROPN
ejpam-5268	64	5	;	;	PUNCT
ejpam-5268	64	6	(	(	PUNCT
ejpam-5268	64	7	s3)s	s3)s	NOUN
ejpam-5268	64	8	(	(	PUNCT
ejpam-5268	64	9	x	x	X
ejpam-5268	64	10	,	,	PUNCT
ejpam-5268	64	11	y	y	PROPN
ejpam-5268	64	12	,	,	PUNCT
ejpam-5268	64	13	z	z	NOUN
ejpam-5268	64	14	)	)	PUNCT
ejpam-5268	64	15	≤	≤	NOUN
ejpam-5268	64	16	s	s	PART
ejpam-5268	64	17	(	(	PUNCT
ejpam-5268	64	18	x	x	X
ejpam-5268	64	19	,	,	PUNCT
ejpam-5268	64	20	x	x	NOUN
ejpam-5268	64	21	,	,	PUNCT
ejpam-5268	64	22	a	a	PRON
ejpam-5268	64	23	)	)	PUNCT
ejpam-5268	65	1	+	+	SYM
ejpam-5268	65	2	s	s	X
ejpam-5268	65	3	(	(	PUNCT
ejpam-5268	65	4	y	y	PROPN
ejpam-5268	65	5	,	,	PUNCT
ejpam-5268	65	6	y	y	PROPN
ejpam-5268	65	7	,	,	PUNCT
ejpam-5268	65	8	a	a	PRON
ejpam-5268	65	9	)	)	PUNCT
ejpam-5268	65	10	+	+	SYM
ejpam-5268	65	11	s	s	X
ejpam-5268	65	12	(	(	PUNCT
ejpam-5268	65	13	z	z	NOUN
ejpam-5268	65	14	,	,	PUNCT
ejpam-5268	65	15	z	z	PROPN
ejpam-5268	65	16	,	,	PUNCT
ejpam-5268	65	17	a	a	PRON
ejpam-5268	65	18	)	)	PUNCT
ejpam-5268	65	19	.	.	PUNCT
ejpam-5268	66	1	then	then	ADV
ejpam-5268	66	2	,	,	PUNCT
ejpam-5268	66	3	(	(	PUNCT
ejpam-5268	66	4	x	x	X
ejpam-5268	66	5	,	,	PUNCT
ejpam-5268	66	6	s	s	PART
ejpam-5268	66	7	)	)	PUNCT
ejpam-5268	66	8	is	be	AUX
ejpam-5268	66	9	said	say	VERB
ejpam-5268	66	10	s	s	NOUN
ejpam-5268	66	11	–	–	PUNCT
ejpam-5268	66	12	metric	metric	ADJ
ejpam-5268	66	13	space	space	NOUN
ejpam-5268	66	14	.	.	PUNCT
ejpam-5268	67	1	example	example	NOUN
ejpam-5268	68	1	2	2	NUM
ejpam-5268	68	2	.	.	PUNCT
ejpam-5268	69	1	[	[	X
ejpam-5268	69	2	21	21	NUM
ejpam-5268	69	3	]	]	X
ejpam-5268	69	4	direct	direct	ADJ
ejpam-5268	69	5	examples	example	NOUN
ejpam-5268	69	6	of	of	ADP
ejpam-5268	69	7	such	such	ADJ
ejpam-5268	69	8	s	s	NOUN
ejpam-5268	69	9	-	-	ADJ
ejpam-5268	69	10	metric	metric	ADJ
ejpam-5268	69	11	spaces	space	NOUN
ejpam-5268	69	12	are	be	AUX
ejpam-5268	69	13	:	:	PUNCT
ejpam-5268	69	14	(	(	PUNCT
ejpam-5268	69	15	i	i	NOUN
ejpam-5268	69	16	)	)	PUNCT
ejpam-5268	69	17	assume	assume	VERB
ejpam-5268	69	18	x	x	X
ejpam-5268	69	19	=	=	SYM
ejpam-5268	69	20	rn	rn	PROPN
ejpam-5268	69	21	with	with	ADP
ejpam-5268	69	22	∥.∥	∥.∥	PROPN
ejpam-5268	69	23	is	be	AUX
ejpam-5268	69	24	a	a	DET
ejpam-5268	69	25	norm	norm	NOUN
ejpam-5268	69	26	,	,	PUNCT
ejpam-5268	69	27	consequently	consequently	ADV
ejpam-5268	69	28	s	s	VERB
ejpam-5268	69	29	=	=	PUNCT
ejpam-5268	69	30	(	(	PUNCT
ejpam-5268	69	31	x	x	X
ejpam-5268	69	32	,	,	PUNCT
ejpam-5268	69	33	y	y	PROPN
ejpam-5268	69	34	,	,	PUNCT
ejpam-5268	69	35	z	z	NOUN
ejpam-5268	69	36	)	)	PUNCT
ejpam-5268	69	37	=	=	SYM
ejpam-5268	70	1	∥x−	∥x−	PROPN
ejpam-5268	70	2	z∥+∥y	z∥+∥y	NOUN
ejpam-5268	70	3	−	−	PROPN
ejpam-5268	70	4	z∥	z∥	NUM
ejpam-5268	70	5	is	be	AUX
ejpam-5268	70	6	s	s	NOUN
ejpam-5268	70	7	-	-	NOUN
ejpam-5268	70	8	metric	metric	ADJ
ejpam-5268	70	9	.	.	PUNCT
ejpam-5268	71	1	(	(	PUNCT
ejpam-5268	71	2	ii	ii	NOUN
ejpam-5268	71	3	)	)	PUNCT
ejpam-5268	71	4	assume	assume	VERB
ejpam-5268	71	5	x	x	X
ejpam-5268	71	6	̸=	̸=	NOUN
ejpam-5268	71	7	∅	∅	NOUN
ejpam-5268	71	8	,	,	PUNCT
ejpam-5268	71	9	d	d	NOUN
ejpam-5268	71	10	is	be	AUX
ejpam-5268	71	11	ordinary	ordinary	ADJ
ejpam-5268	71	12	metric	metric	ADJ
ejpam-5268	71	13	,	,	PUNCT
ejpam-5268	72	1	so	so	CCONJ
ejpam-5268	72	2	s	s	X
ejpam-5268	72	3	(	(	PUNCT
ejpam-5268	72	4	x	x	X
ejpam-5268	72	5	,	,	PUNCT
ejpam-5268	72	6	y	y	PROPN
ejpam-5268	72	7	,	,	PUNCT
ejpam-5268	72	8	z	z	NOUN
ejpam-5268	72	9	)	)	PUNCT
ejpam-5268	72	10	=	=	SYM
ejpam-5268	73	1	d	d	X
ejpam-5268	73	2	(	(	PUNCT
ejpam-5268	73	3	x	x	X
ejpam-5268	73	4	,	,	PUNCT
ejpam-5268	73	5	z	z	NOUN
ejpam-5268	73	6	)	)	PUNCT
ejpam-5268	74	1	+	+	CCONJ
ejpam-5268	74	2	d	d	X
ejpam-5268	74	3	(	(	PUNCT
ejpam-5268	74	4	y	y	PROPN
ejpam-5268	74	5	,	,	PUNCT
ejpam-5268	74	6	z	z	NOUN
ejpam-5268	74	7	)	)	PUNCT
ejpam-5268	74	8	is	be	AUX
ejpam-5268	74	9	s	s	NOUN
ejpam-5268	74	10	-	-	ADJ
ejpam-5268	74	11	metric	metric	ADJ
ejpam-5268	74	12	.	.	PUNCT
ejpam-5268	75	1	remark	remark	NOUN
ejpam-5268	75	2	1	1	NUM
ejpam-5268	75	3	.	.	PUNCT
ejpam-5268	76	1	[	[	X
ejpam-5268	76	2	21	21	NUM
ejpam-5268	76	3	]	]	X
ejpam-5268	76	4	it	it	PRON
ejpam-5268	76	5	’s	’	VERB
ejpam-5268	76	6	clear	clear	ADJ
ejpam-5268	76	7	to	to	PART
ejpam-5268	76	8	see	see	VERB
ejpam-5268	76	9	each	each	DET
ejpam-5268	76	10	d*-metric	d*-metric	NOUN
ejpam-5268	76	11	-	-	PUNCT
ejpam-5268	76	12	sp	sp	NOUN
ejpam-5268	76	13	is	be	AUX
ejpam-5268	76	14	s	s	NOUN
ejpam-5268	76	15	-	-	ADJ
ejpam-5268	76	16	metric	metric	ADJ
ejpam-5268	76	17	,	,	PUNCT
ejpam-5268	76	18	the	the	DET
ejpam-5268	76	19	converse	converse	NOUN
ejpam-5268	76	20	not	not	PART
ejpam-5268	76	21	true	true	ADJ
ejpam-5268	76	22	in	in	ADP
ejpam-5268	76	23	general	general	ADJ
ejpam-5268	76	24	,	,	PUNCT
ejpam-5268	76	25	as	as	SCONJ
ejpam-5268	76	26	shown	show	VERB
ejpam-5268	76	27	in	in	ADP
ejpam-5268	76	28	the	the	DET
ejpam-5268	76	29	example	example	NOUN
ejpam-5268	76	30	below	below	ADV
ejpam-5268	76	31	.	.	PUNCT
ejpam-5268	77	1	example	example	NOUN
ejpam-5268	78	1	3	3	NUM
ejpam-5268	78	2	.	.	PUNCT
ejpam-5268	79	1	[	[	X
ejpam-5268	79	2	21	21	NUM
ejpam-5268	79	3	]	]	PUNCT
ejpam-5268	79	4	suppose	suppose	VERB
ejpam-5268	79	5	x	x	SYM
ejpam-5268	79	6	=	=	SYM
ejpam-5268	79	7	rn	rn	PROPN
ejpam-5268	79	8	with	with	ADP
ejpam-5268	79	9	∥.∥	∥.∥	PROPN
ejpam-5268	79	10	a	a	DET
ejpam-5268	79	11	norm	norm	NOUN
ejpam-5268	79	12	on	on	ADP
ejpam-5268	79	13	x	x	NOUN
ejpam-5268	79	14	,	,	PUNCT
ejpam-5268	79	15	consequently	consequently	ADV
ejpam-5268	79	16	s	s	VERB
ejpam-5268	79	17	=	=	PUNCT
ejpam-5268	79	18	(	(	PUNCT
ejpam-5268	79	19	x	x	X
ejpam-5268	79	20	,	,	PUNCT
ejpam-5268	79	21	y	y	PROPN
ejpam-5268	79	22	,	,	PUNCT
ejpam-5268	79	23	z	z	NOUN
ejpam-5268	79	24	)	)	PUNCT
ejpam-5268	79	25	=	=	SYM
ejpam-5268	79	26	∥y	∥y	PROPN
ejpam-5268	79	27	+	+	CCONJ
ejpam-5268	79	28	z	z	NOUN
ejpam-5268	79	29	−	−	PROPN
ejpam-5268	79	30	2x∥+	2x∥+	NUM
ejpam-5268	79	31	∥y	∥y	PROPN
ejpam-5268	79	32	−	−	PROPN
ejpam-5268	79	33	z∥	z∥	NUM
ejpam-5268	79	34	is	be	AUX
ejpam-5268	79	35	s	s	NOUN
ejpam-5268	79	36	-	-	NOUN
ejpam-5268	79	37	metric	metric	ADJ
ejpam-5268	79	38	,	,	PUNCT
ejpam-5268	79	39	but	but	CCONJ
ejpam-5268	79	40	it	it	PRON
ejpam-5268	79	41	is	be	AUX
ejpam-5268	79	42	n’t	not	PART
ejpam-5268	79	43	d∗-metric	d∗-metric	ADJ
ejpam-5268	79	44	since	since	SCONJ
ejpam-5268	79	45	it	it	PRON
ejpam-5268	79	46	is	be	AUX
ejpam-5268	79	47	n’t	not	PART
ejpam-5268	79	48	symmetric	symmetric	ADJ
ejpam-5268	79	49	.	.	PUNCT
ejpam-5268	80	1	example	example	NOUN
ejpam-5268	81	1	4	4	NUM
ejpam-5268	81	2	.	.	PUNCT
ejpam-5268	82	1	[	[	X
ejpam-5268	82	2	21	21	NUM
ejpam-5268	82	3	]	]	PUNCT
ejpam-5268	82	4	suppose	suppose	VERB
ejpam-5268	82	5	x	x	SYM
ejpam-5268	82	6	=	=	SYM
ejpam-5268	82	7	r2	r2	NOUN
ejpam-5268	82	8	,	,	PUNCT
ejpam-5268	82	9	and	and	CCONJ
ejpam-5268	82	10	d	d	NOUN
ejpam-5268	82	11	is	be	AUX
ejpam-5268	82	12	ordinary	ordinary	ADJ
ejpam-5268	82	13	metric	metric	ADJ
ejpam-5268	82	14	,	,	PUNCT
ejpam-5268	82	15	consequently	consequently	ADV
ejpam-5268	82	16	,	,	PUNCT
ejpam-5268	82	17	s	s	X
ejpam-5268	82	18	(	(	PUNCT
ejpam-5268	82	19	x	x	NOUN
ejpam-5268	82	20	,	,	PUNCT
ejpam-5268	82	21	y	y	PROPN
ejpam-5268	82	22	,	,	PUNCT
ejpam-5268	82	23	z	z	NOUN
ejpam-5268	82	24	)	)	PUNCT
ejpam-5268	83	1	=	=	SYM
ejpam-5268	83	2	d	d	X
ejpam-5268	83	3	(	(	PUNCT
ejpam-5268	83	4	x	x	NOUN
ejpam-5268	83	5	,	,	PUNCT
ejpam-5268	83	6	y)+d	y)+d	PROPN
ejpam-5268	83	7	(	(	PUNCT
ejpam-5268	83	8	x	x	NOUN
ejpam-5268	83	9	,	,	PUNCT
ejpam-5268	83	10	z)+d	z)+d	PROPN
ejpam-5268	83	11	(	(	PUNCT
ejpam-5268	83	12	y	y	PROPN
ejpam-5268	83	13	,	,	PUNCT
ejpam-5268	83	14	z	z	NOUN
ejpam-5268	83	15	)	)	PUNCT
ejpam-5268	83	16	is	be	AUX
ejpam-5268	83	17	s	s	NOUN
ejpam-5268	83	18	-	-	ADJ
ejpam-5268	83	19	metric	metric	ADJ
ejpam-5268	83	20	on	on	ADP
ejpam-5268	83	21	x.	x.	NOUN
ejpam-5268	83	22	if	if	SCONJ
ejpam-5268	83	23	connect	connect	VERB
ejpam-5268	83	24	the	the	DET
ejpam-5268	83	25	points	point	NOUN
ejpam-5268	83	26	x	x	NOUN
ejpam-5268	83	27	,	,	PUNCT
ejpam-5268	83	28	y	y	PROPN
ejpam-5268	83	29	,	,	PUNCT
ejpam-5268	83	30	z	z	NOUN
ejpam-5268	83	31	via	via	ADP
ejpam-5268	83	32	a	a	DET
ejpam-5268	83	33	line	line	NOUN
ejpam-5268	83	34	,	,	PUNCT
ejpam-5268	83	35	we	we	PRON
ejpam-5268	83	36	have	have	VERB
ejpam-5268	83	37	triangle	triangle	NOUN
ejpam-5268	83	38	and	and	CCONJ
ejpam-5268	83	39	select	select	VERB
ejpam-5268	83	40	a	a	DET
ejpam-5268	83	41	point	point	NOUN
ejpam-5268	83	42	mediating	mediate	VERB
ejpam-5268	83	43	this	this	DET
ejpam-5268	83	44	triangle	triangle	NOUN
ejpam-5268	83	45	in	in	ADP
ejpam-5268	83	46	that	that	DET
ejpam-5268	83	47	case	case	NOUN
ejpam-5268	83	48	s	s	X
ejpam-5268	83	49	(	(	PUNCT
ejpam-5268	83	50	x	x	NOUN
ejpam-5268	83	51	,	,	PUNCT
ejpam-5268	83	52	y	y	PROPN
ejpam-5268	83	53	,	,	PUNCT
ejpam-5268	83	54	z	z	NOUN
ejpam-5268	83	55	)	)	PUNCT
ejpam-5268	83	56	≤	≤	NOUN
ejpam-5268	83	57	s	s	PART
ejpam-5268	83	58	(	(	PUNCT
ejpam-5268	83	59	x	x	X
ejpam-5268	83	60	,	,	PUNCT
ejpam-5268	83	61	x	x	NOUN
ejpam-5268	83	62	,	,	PUNCT
ejpam-5268	83	63	a	a	PRON
ejpam-5268	83	64	)	)	PUNCT
ejpam-5268	84	1	+	+	SYM
ejpam-5268	84	2	s	s	X
ejpam-5268	84	3	(	(	PUNCT
ejpam-5268	84	4	y	y	PROPN
ejpam-5268	84	5	,	,	PUNCT
ejpam-5268	84	6	y	y	PROPN
ejpam-5268	84	7	,	,	PUNCT
ejpam-5268	84	8	a	a	PRON
ejpam-5268	84	9	)	)	PUNCT
ejpam-5268	84	10	+	+	SYM
ejpam-5268	84	11	s	s	X
ejpam-5268	84	12	(	(	PUNCT
ejpam-5268	84	13	z	z	NOUN
ejpam-5268	84	14	,	,	PUNCT
ejpam-5268	84	15	z	z	PROPN
ejpam-5268	84	16	,	,	PUNCT
ejpam-5268	84	17	a	a	PRON
ejpam-5268	84	18	)	)	PUNCT
ejpam-5268	84	19	holds	hold	NOUN
ejpam-5268	84	20	.	.	PUNCT
ejpam-5268	85	1	in	in	ADP
ejpam-5268	85	2	fact	fact	NOUN
ejpam-5268	85	3	s	s	X
ejpam-5268	85	4	(	(	PUNCT
ejpam-5268	85	5	x	x	X
ejpam-5268	85	6	,	,	PUNCT
ejpam-5268	85	7	y	y	PROPN
ejpam-5268	85	8	,	,	PUNCT
ejpam-5268	85	9	z	z	NOUN
ejpam-5268	85	10	)	)	PUNCT
ejpam-5268	85	11	=	=	SYM
ejpam-5268	86	1	d	d	X
ejpam-5268	86	2	(	(	PUNCT
ejpam-5268	86	3	x	x	NOUN
ejpam-5268	86	4	,	,	PUNCT
ejpam-5268	86	5	y	y	PROPN
ejpam-5268	86	6	)	)	PUNCT
ejpam-5268	87	1	+	+	CCONJ
ejpam-5268	87	2	d	d	X
ejpam-5268	87	3	(	(	PUNCT
ejpam-5268	87	4	x	x	X
ejpam-5268	87	5	,	,	PUNCT
ejpam-5268	87	6	z	z	NOUN
ejpam-5268	87	7	)	)	PUNCT
ejpam-5268	88	1	+	+	CCONJ
ejpam-5268	88	2	d	d	X
ejpam-5268	88	3	(	(	PUNCT
ejpam-5268	88	4	y	y	PROPN
ejpam-5268	88	5	,	,	PUNCT
ejpam-5268	88	6	z	z	NOUN
ejpam-5268	88	7	)	)	PUNCT
ejpam-5268	88	8	≤	≤	NUM
ejpam-5268	89	1	d	d	NOUN
ejpam-5268	89	2	(	(	PUNCT
ejpam-5268	89	3	x	x	X
ejpam-5268	89	4	,	,	PUNCT
ejpam-5268	89	5	a	a	NOUN
ejpam-5268	89	6	)	)	PUNCT
ejpam-5268	89	7	+	+	NOUN
ejpam-5268	89	8	d	d	X
ejpam-5268	89	9	(	(	PUNCT
ejpam-5268	89	10	a	a	DET
ejpam-5268	89	11	,	,	PUNCT
ejpam-5268	89	12	y	y	NOUN
ejpam-5268	89	13	)	)	PUNCT
ejpam-5268	89	14	+	+	CCONJ
ejpam-5268	90	1	d	d	X
ejpam-5268	90	2	(	(	PUNCT
ejpam-5268	90	3	x	x	X
ejpam-5268	90	4	,	,	PUNCT
ejpam-5268	90	5	a	a	NOUN
ejpam-5268	90	6	)	)	PUNCT
ejpam-5268	90	7	+	+	NOUN
ejpam-5268	90	8	d	d	X
ejpam-5268	90	9	(	(	PUNCT
ejpam-5268	90	10	a	a	PRON
ejpam-5268	90	11	,	,	PUNCT
ejpam-5268	90	12	z	z	NOUN
ejpam-5268	90	13	)	)	PUNCT
ejpam-5268	90	14	+	+	CCONJ
ejpam-5268	91	1	d	d	X
ejpam-5268	91	2	(	(	PUNCT
ejpam-5268	91	3	y	y	PROPN
ejpam-5268	91	4	,	,	PUNCT
ejpam-5268	91	5	a	a	NOUN
ejpam-5268	91	6	)	)	PUNCT
ejpam-5268	91	7	+	+	NOUN
ejpam-5268	91	8	d	d	X
ejpam-5268	91	9	(	(	PUNCT
ejpam-5268	91	10	z	z	NOUN
ejpam-5268	91	11	,	,	PUNCT
ejpam-5268	91	12	a	a	NOUN
ejpam-5268	91	13	)	)	PUNCT
ejpam-5268	91	14	=	=	SYM
ejpam-5268	91	15	s	s	X
ejpam-5268	91	16	(	(	PUNCT
ejpam-5268	91	17	x	x	X
ejpam-5268	91	18	,	,	PUNCT
ejpam-5268	91	19	x	x	NOUN
ejpam-5268	91	20	,	,	PUNCT
ejpam-5268	91	21	a	a	PRON
ejpam-5268	91	22	)	)	PUNCT
ejpam-5268	91	23	+	+	SYM
ejpam-5268	91	24	s	s	X
ejpam-5268	91	25	(	(	PUNCT
ejpam-5268	91	26	y	y	PROPN
ejpam-5268	91	27	,	,	PUNCT
ejpam-5268	91	28	y	y	PROPN
ejpam-5268	91	29	,	,	PUNCT
ejpam-5268	91	30	a	a	PRON
ejpam-5268	91	31	)	)	PUNCT
ejpam-5268	91	32	+	+	SYM
ejpam-5268	91	33	s	s	X
ejpam-5268	91	34	(	(	PUNCT
ejpam-5268	91	35	z	z	NOUN
ejpam-5268	91	36	,	,	PUNCT
ejpam-5268	91	37	z	z	PROPN
ejpam-5268	91	38	,	,	PUNCT
ejpam-5268	91	39	a	a	PRON
ejpam-5268	91	40	)	)	PUNCT
ejpam-5268	91	41	.	.	PUNCT
ejpam-5268	92	1	n.	n.	PROPN
ejpam-5268	92	2	a.	a.	PROPN
ejpam-5268	92	3	majid	majid	PROPN
ejpam-5268	92	4	et	et	PROPN
ejpam-5268	92	5	al	al	PROPN
ejpam-5268	92	6	.	.	PUNCT
ejpam-5268	92	7	/	/	SYM
ejpam-5268	92	8	eur	eur	PROPN
ejpam-5268	92	9	.	.	PUNCT
ejpam-5268	93	1	j.	j.	PROPN
ejpam-5268	93	2	pure	pure	PROPN
ejpam-5268	93	3	appl	appl	PROPN
ejpam-5268	93	4	.	.	PROPN
ejpam-5268	93	5	math	math	PROPN
ejpam-5268	93	6	,	,	PUNCT
ejpam-5268	93	7	17	17	NUM
ejpam-5268	93	8	(	(	PUNCT
ejpam-5268	93	9	3	3	NUM
ejpam-5268	93	10	)	)	PUNCT
ejpam-5268	93	11	(	(	PUNCT
ejpam-5268	93	12	2024	2024	NUM
ejpam-5268	93	13	)	)	PUNCT
ejpam-5268	93	14	,	,	PUNCT
ejpam-5268	93	15	1877	1877	NUM
ejpam-5268	93	16	-	-	SYM
ejpam-5268	93	17	1893	1893	NUM
ejpam-5268	93	18	1880	1880	NUM
ejpam-5268	93	19	lemma	lemma	PROPN
ejpam-5268	93	20	1	1	NUM
ejpam-5268	93	21	.	.	PUNCT
ejpam-5268	94	1	[	[	X
ejpam-5268	94	2	21	21	NUM
ejpam-5268	94	3	]	]	PUNCT
ejpam-5268	94	4	in	in	ADP
ejpam-5268	94	5	s	s	ADJ
ejpam-5268	94	6	-	-	ADJ
ejpam-5268	94	7	metric	metric	ADJ
ejpam-5268	94	8	-	-	PUNCT
ejpam-5268	94	9	space	space	NOUN
ejpam-5268	94	10	,	,	PUNCT
ejpam-5268	94	11	s	s	PART
ejpam-5268	94	12	(	(	PUNCT
ejpam-5268	94	13	x	x	X
ejpam-5268	94	14	,	,	PUNCT
ejpam-5268	94	15	x	x	NOUN
ejpam-5268	94	16	,	,	PUNCT
ejpam-5268	94	17	y	y	PROPN
ejpam-5268	94	18	)	)	PUNCT
ejpam-5268	95	1	=	=	SYM
ejpam-5268	95	2	s	s	X
ejpam-5268	95	3	(	(	PUNCT
ejpam-5268	95	4	y	y	PROPN
ejpam-5268	95	5	,	,	PUNCT
ejpam-5268	95	6	y	y	PROPN
ejpam-5268	95	7	,	,	PUNCT
ejpam-5268	95	8	x	x	NOUN
ejpam-5268	95	9	)	)	PUNCT
ejpam-5268	95	10	,	,	PUNCT
ejpam-5268	95	11	∀	∀	X
ejpam-5268	95	12	x	x	NOUN
ejpam-5268	95	13	,	,	PUNCT
ejpam-5268	95	14	y	y	PROPN
ejpam-5268	95	15	∈	∈	PROPN
ejpam-5268	95	16	x.	x.	NOUN
ejpam-5268	95	17	definition	definition	NOUN
ejpam-5268	95	18	3	3	NUM
ejpam-5268	95	19	.	.	PUNCT
ejpam-5268	96	1	[	[	X
ejpam-5268	96	2	21	21	NUM
ejpam-5268	96	3	]	]	PUNCT
ejpam-5268	96	4	suppose	suppose	VERB
ejpam-5268	96	5	(	(	PUNCT
ejpam-5268	96	6	x	x	X
ejpam-5268	96	7	,	,	PUNCT
ejpam-5268	96	8	s	s	PART
ejpam-5268	96	9	)	)	PUNCT
ejpam-5268	96	10	is	be	AUX
ejpam-5268	96	11	s	s	NOUN
ejpam-5268	96	12	-	-	ADJ
ejpam-5268	96	13	metric	metric	ADJ
ejpam-5268	96	14	and	and	CCONJ
ejpam-5268	96	15	a	a	DET
ejpam-5268	96	16	⊆	⊆	NUM
ejpam-5268	96	17	x.	x.	NOUN
ejpam-5268	96	18	(	(	PUNCT
ejpam-5268	96	19	i	i	NOUN
ejpam-5268	96	20	)	)	PUNCT
ejpam-5268	96	21	a	a	PRON
ejpam-5268	96	22	is	be	AUX
ejpam-5268	96	23	said	say	VERB
ejpam-5268	96	24	to	to	ADP
ejpam-5268	96	25	s	s	VERB
ejpam-5268	96	26	-	-	PUNCT
ejpam-5268	96	27	bounded	bound	VERB
ejpam-5268	96	28	if	if	SCONJ
ejpam-5268	96	29	∃	∃	PROPN
ejpam-5268	96	30	r	r	NOUN
ejpam-5268	96	31	>	>	X
ejpam-5268	96	32	0(s.t),s	0(s.t),s	NOUN
ejpam-5268	96	33	(	(	PUNCT
ejpam-5268	96	34	x	x	X
ejpam-5268	96	35	,	,	PUNCT
ejpam-5268	96	36	x	x	NOUN
ejpam-5268	96	37	,	,	PUNCT
ejpam-5268	96	38	y	y	PROPN
ejpam-5268	96	39	)	)	PUNCT
ejpam-5268	96	40	<	<	X
ejpam-5268	96	41	r	r	NOUN
ejpam-5268	96	42	,	,	PUNCT
ejpam-5268	96	43	∀	∀	X
ejpam-5268	96	44	x	x	NOUN
ejpam-5268	96	45	,	,	PUNCT
ejpam-5268	96	46	y	y	PROPN
ejpam-5268	96	47	∈	∈	PROPN
ejpam-5268	96	48	a.	a.	NOUN
ejpam-5268	96	49	(	(	PUNCT
ejpam-5268	96	50	ii	ii	NOUN
ejpam-5268	96	51	)	)	PUNCT
ejpam-5268	96	52	a	a	DET
ejpam-5268	96	53	sequence	sequence	NOUN
ejpam-5268	96	54	{	{	PUNCT
ejpam-5268	96	55	xs	xs	NOUN
ejpam-5268	96	56	}	}	PUNCT
ejpam-5268	96	57	in	in	ADP
ejpam-5268	96	58	x	x	PROPN
ejpam-5268	96	59	is	be	AUX
ejpam-5268	96	60	called	call	VERB
ejpam-5268	96	61	s	s	NOUN
ejpam-5268	96	62	-	-	PUNCT
ejpam-5268	96	63	converges	converge	NOUN
ejpam-5268	96	64	to	to	ADP
ejpam-5268	96	65	x	x	SYM
ejpam-5268	96	66	∈	∈	PROPN
ejpam-5268	96	67	x	x	X
ejpam-5268	96	68	⇐	⇐	ADJ
ejpam-5268	96	69	⇒	⇒	NOUN
ejpam-5268	96	70	s	s	PART
ejpam-5268	96	71	(	(	PUNCT
ejpam-5268	96	72	xs	xs	PROPN
ejpam-5268	96	73	,	,	PUNCT
ejpam-5268	96	74	xs	xs	PROPN
ejpam-5268	96	75	,	,	PUNCT
ejpam-5268	96	76	x	x	NOUN
ejpam-5268	96	77	)	)	PUNCT
ejpam-5268	96	78	→	→	SYM
ejpam-5268	96	79	0	0	NUM
ejpam-5268	96	80	since	since	SCONJ
ejpam-5268	96	81	s	s	PRON
ejpam-5268	96	82	→	→	SYM
ejpam-5268	96	83	+	+	PROPN
ejpam-5268	96	84	∞.	∞.	PROPN
ejpam-5268	96	85	(	(	PUNCT
ejpam-5268	96	86	i.e	i.e	NOUN
ejpam-5268	96	87	)	)	PUNCT
ejpam-5268	96	88	∀	∀	PUNCT
ejpam-5268	97	1	ε	ε	X
ejpam-5268	97	2	>	>	X
ejpam-5268	97	3	0	0	PROPN
ejpam-5268	97	4	,	,	PUNCT
ejpam-5268	97	5	∃	∃	PROPN
ejpam-5268	97	6	s0	s0	PROPN
ejpam-5268	97	7	∈	∈	PROPN
ejpam-5268	97	8	n	n	PROPN
ejpam-5268	97	9	(	(	PUNCT
ejpam-5268	97	10	s.t	s.t	PROPN
ejpam-5268	97	11	)	)	PUNCT
ejpam-5268	97	12	,	,	PUNCT
ejpam-5268	97	13	∀	∀	X
ejpam-5268	97	14	s	s	PART
ejpam-5268	97	15	≥	≥	NOUN
ejpam-5268	97	16	s0	s0	NOUN
ejpam-5268	97	17	=	=	NOUN
ejpam-5268	97	18	⇒	⇒	PROPN
ejpam-5268	97	19	s	s	PART
ejpam-5268	97	20	(	(	PUNCT
ejpam-5268	97	21	xs	xs	PROPN
ejpam-5268	97	22	,	,	PUNCT
ejpam-5268	97	23	xs	xs	PROPN
ejpam-5268	97	24	,	,	PUNCT
ejpam-5268	97	25	x	x	X
ejpam-5268	97	26	)	)	PUNCT
ejpam-5268	97	27	<	<	X
ejpam-5268	97	28	ε	ε	PROPN
ejpam-5268	97	29	,	,	PUNCT
ejpam-5268	97	30	and	and	CCONJ
ejpam-5268	97	31	denote	denote	VERB
ejpam-5268	97	32	this	this	PRON
ejpam-5268	97	33	via	via	ADP
ejpam-5268	97	34	lims→+∞	lims→+∞	PROPN
ejpam-5268	97	35	xs	xs	PROPN
ejpam-5268	97	36	=	=	PUNCT
ejpam-5268	97	37	x.	x.	PROPN
ejpam-5268	97	38	(	(	PUNCT
ejpam-5268	97	39	iii	iii	NOUN
ejpam-5268	97	40	)	)	PUNCT
ejpam-5268	97	41	{	{	PUNCT
ejpam-5268	97	42	xs	xs	NOUN
ejpam-5268	97	43	}	}	PUNCT
ejpam-5268	97	44	in	in	ADP
ejpam-5268	97	45	x	x	PROPN
ejpam-5268	97	46	is	be	AUX
ejpam-5268	97	47	called	call	VERB
ejpam-5268	97	48	s	s	PART
ejpam-5268	97	49	-	-	PUNCT
ejpam-5268	97	50	cauchy	cauchy	ADJ
ejpam-5268	97	51	sequence	sequence	NOUN
ejpam-5268	97	52	if	if	SCONJ
ejpam-5268	97	53	∀	∀	NOUN
ejpam-5268	97	54	ε	ε	VERB
ejpam-5268	97	55	>	>	X
ejpam-5268	97	56	0,∃	0,∃	NUM
ejpam-5268	97	57	s0	s0	PROPN
ejpam-5268	97	58	∈	∈	PROPN
ejpam-5268	97	59	n(s	n(s	PROPN
ejpam-5268	97	60	.	.	PROPN
ejpam-5268	97	61	t	t	PROPN
ejpam-5268	97	62	)	)	PUNCT
ejpam-5268	97	63	,	,	PUNCT
ejpam-5268	97	64	s	s	X
ejpam-5268	97	65	(	(	PUNCT
ejpam-5268	97	66	xs	xs	PROPN
ejpam-5268	97	67	,	,	PUNCT
ejpam-5268	97	68	xs	xs	PROPN
ejpam-5268	97	69	,	,	PUNCT
ejpam-5268	97	70	xr	xr	PROPN
ejpam-5268	97	71	)	)	PUNCT
ejpam-5268	97	72	<	<	X
ejpam-5268	97	73	ε	ε	PROPN
ejpam-5268	97	74	,	,	PUNCT
ejpam-5268	97	75	∀	∀	X
ejpam-5268	97	76	s	s	PART
ejpam-5268	97	77	,	,	PUNCT
ejpam-5268	97	78	r	r	NOUN
ejpam-5268	97	79	≥	≥	NUM
ejpam-5268	97	80	s0	s0	PROPN
ejpam-5268	97	81	.	.	PUNCT
ejpam-5268	98	1	(	(	PUNCT
ejpam-5268	98	2	iv	iv	X
ejpam-5268	98	3	)	)	PUNCT
ejpam-5268	98	4	x	x	X
ejpam-5268	98	5	is	be	AUX
ejpam-5268	98	6	complete	complete	ADJ
ejpam-5268	98	7	if	if	SCONJ
ejpam-5268	98	8	each	each	DET
ejpam-5268	98	9	s	s	NOUN
ejpam-5268	98	10	-	-	ADJ
ejpam-5268	98	11	cauchy	cauchy	ADJ
ejpam-5268	98	12	sequence	sequence	NOUN
ejpam-5268	98	13	of	of	ADP
ejpam-5268	98	14	(	(	PUNCT
ejpam-5268	98	15	x	x	NOUN
ejpam-5268	98	16	,	,	PUNCT
ejpam-5268	98	17	s	s	PART
ejpam-5268	98	18	)	)	PUNCT
ejpam-5268	98	19	is	be	AUX
ejpam-5268	98	20	convergent	convergent	ADJ
ejpam-5268	98	21	.	.	PUNCT
ejpam-5268	99	1	now	now	ADV
ejpam-5268	99	2	,	,	PUNCT
ejpam-5268	99	3	we	we	PRON
ejpam-5268	99	4	mention	mention	VERB
ejpam-5268	99	5	the	the	DET
ejpam-5268	99	6	concept	concept	NOUN
ejpam-5268	99	7	of	of	ADP
ejpam-5268	99	8	simulation	simulation	NOUN
ejpam-5268	99	9	mappings	mapping	NOUN
ejpam-5268	99	10	which	which	PRON
ejpam-5268	99	11	presented	present	VERB
ejpam-5268	99	12	via	via	ADP
ejpam-5268	99	13	khojasteh	khojasteh	PROPN
ejpam-5268	99	14	et	et	PROPN
ejpam-5268	99	15	al	al	PROPN
ejpam-5268	100	1	[	[	X
ejpam-5268	100	2	18	18	NUM
ejpam-5268	100	3	]	]	PUNCT
ejpam-5268	100	4	,	,	PUNCT
ejpam-5268	100	5	as	as	SCONJ
ejpam-5268	100	6	follows	follow	VERB
ejpam-5268	100	7	:	:	PUNCT
ejpam-5268	100	8	definition	definition	NOUN
ejpam-5268	100	9	4	4	NUM
ejpam-5268	100	10	.	.	PUNCT
ejpam-5268	101	1	ξ	ξ	X
ejpam-5268	101	2	:	:	PUNCT
ejpam-5268	102	1	[	[	X
ejpam-5268	102	2	0	0	NUM
ejpam-5268	102	3	,	,	PUNCT
ejpam-5268	102	4	+	+	NOUN
ejpam-5268	102	5	∞)×	∞)×	NOUN
ejpam-5268	102	6	[	[	X
ejpam-5268	102	7	0	0	NUM
ejpam-5268	102	8	,	,	PUNCT
ejpam-5268	102	9	+	+	NOUN
ejpam-5268	102	10	∞	∞	NOUN
ejpam-5268	102	11	)	)	PUNCT
ejpam-5268	102	12	→	→	SYM
ejpam-5268	102	13	r	r	NOUN
ejpam-5268	102	14	is	be	AUX
ejpam-5268	102	15	said	say	VERB
ejpam-5268	102	16	to	to	PART
ejpam-5268	102	17	be	be	AUX
ejpam-5268	102	18	simulation	simulation	NOUN
ejpam-5268	102	19	map	map	NOUN
ejpam-5268	102	20	if	if	SCONJ
ejpam-5268	102	21	it	it	PRON
ejpam-5268	102	22	’s	’s	AUX
ejpam-5268	102	23	satisfying	satisfy	VERB
ejpam-5268	102	24	the	the	DET
ejpam-5268	102	25	next	next	ADJ
ejpam-5268	102	26	statements	statement	NOUN
ejpam-5268	102	27	:	:	PUNCT
ejpam-5268	102	28	(	(	PUNCT
ejpam-5268	102	29	ξ1	ξ1	NOUN
ejpam-5268	102	30	)	)	PUNCT
ejpam-5268	102	31	ξ	ξ	PROPN
ejpam-5268	102	32	(	(	PUNCT
ejpam-5268	102	33	0	0	NUM
ejpam-5268	102	34	,	,	PUNCT
ejpam-5268	102	35	0	0	NUM
ejpam-5268	102	36	)	)	PUNCT
ejpam-5268	102	37	=	=	SYM
ejpam-5268	102	38	0	0	NUM
ejpam-5268	102	39	,	,	PUNCT
ejpam-5268	102	40	(	(	PUNCT
ejpam-5268	102	41	ξ2	ξ2	NOUN
ejpam-5268	102	42	)	)	PUNCT
ejpam-5268	102	43	ξ	ξ	PROPN
ejpam-5268	102	44	(	(	PUNCT
ejpam-5268	102	45	t	t	PROPN
ejpam-5268	102	46	,	,	PUNCT
ejpam-5268	102	47	w	w	PROPN
ejpam-5268	102	48	)	)	PUNCT
ejpam-5268	102	49	<	<	X
ejpam-5268	102	50	w	w	PROPN
ejpam-5268	102	51	−	−	PROPN
ejpam-5268	102	52	t	t	PROPN
ejpam-5268	102	53	,	,	PUNCT
ejpam-5268	102	54	∀	∀	X
ejpam-5268	102	55	,	,	PUNCT
ejpam-5268	102	56	w	w	PROPN
ejpam-5268	102	57	,	,	PUNCT
ejpam-5268	102	58	t	t	X
ejpam-5268	102	59	>	>	X
ejpam-5268	102	60	0	0	NUM
ejpam-5268	102	61	,	,	PUNCT
ejpam-5268	102	62	(	(	PUNCT
ejpam-5268	102	63	ξ3	ξ3	NOUN
ejpam-5268	102	64	)	)	PUNCT
ejpam-5268	102	65	if	if	SCONJ
ejpam-5268	102	66	{	{	PUNCT
ejpam-5268	102	67	tn	tn	NOUN
ejpam-5268	102	68	}	}	PUNCT
ejpam-5268	102	69	&	&	CCONJ
ejpam-5268	102	70	{	{	PUNCT
ejpam-5268	102	71	wn	wn	PROPN
ejpam-5268	102	72	}	}	PUNCT
ejpam-5268	102	73	⊆	⊆	NUM
ejpam-5268	102	74	(	(	PUNCT
ejpam-5268	102	75	0	0	NUM
ejpam-5268	102	76	,	,	PUNCT
ejpam-5268	102	77	+	+	NOUN
ejpam-5268	102	78	∞	∞	NOUN
ejpam-5268	102	79	)	)	PUNCT
ejpam-5268	102	80	satisfying	satisfy	VERB
ejpam-5268	102	81	lim	lim	PROPN
ejpam-5268	102	82	n−→+∞	n−→+∞	PROPN
ejpam-5268	102	83	{	{	PUNCT
ejpam-5268	102	84	tn	tn	PROPN
ejpam-5268	102	85	}	}	PUNCT
ejpam-5268	102	86	=	=	PROPN
ejpam-5268	102	87	lim	lim	PROPN
ejpam-5268	102	88	n−→+∞	n−→+∞	PROPN
ejpam-5268	102	89	{	{	PUNCT
ejpam-5268	102	90	wn	wn	PROPN
ejpam-5268	102	91	}	}	PUNCT
ejpam-5268	102	92	=	=	PUNCT
ejpam-5268	102	93	l	l	NOUN
ejpam-5268	102	94	∈	∈	PROPN
ejpam-5268	102	95	(	(	PUNCT
ejpam-5268	102	96	0	0	NUM
ejpam-5268	102	97	,	,	PUNCT
ejpam-5268	102	98	+	+	NOUN
ejpam-5268	102	99	∞	∞	NOUN
ejpam-5268	102	100	)	)	PUNCT
ejpam-5268	102	101	,	,	PUNCT
ejpam-5268	102	102	so	so	ADV
ejpam-5268	102	103	lim	lim	PROPN
ejpam-5268	102	104	n−→+∞	n−→+∞	PROPN
ejpam-5268	102	105	supξ(tn	supξ(tn	PROPN
ejpam-5268	102	106	,	,	PUNCT
ejpam-5268	102	107	wn	wn	PROPN
ejpam-5268	102	108	)	)	PUNCT
ejpam-5268	102	109	<	<	X
ejpam-5268	102	110	0	0	X
ejpam-5268	102	111	.	.	PUNCT
ejpam-5268	102	112	remark	remark	PROPN
ejpam-5268	102	113	2	2	NUM
ejpam-5268	102	114	.	.	PUNCT
ejpam-5268	103	1	the	the	DET
ejpam-5268	103	2	authors	author	NOUN
ejpam-5268	103	3	in	in	ADP
ejpam-5268	103	4	[	[	X
ejpam-5268	103	5	5	5	NUM
ejpam-5268	103	6	]	]	PUNCT
ejpam-5268	103	7	modified	modify	VERB
ejpam-5268	103	8	the	the	DET
ejpam-5268	103	9	condition	condition	NOUN
ejpam-5268	103	10	(	(	PUNCT
ejpam-5268	103	11	ξ3	ξ3	NOUN
ejpam-5268	103	12	)	)	PUNCT
ejpam-5268	103	13	of	of	ADP
ejpam-5268	103	14	simulation	simulation	NOUN
ejpam-5268	103	15	mappings	mapping	NOUN
ejpam-5268	103	16	as	as	ADP
ejpam-5268	103	17	:	:	PUNCT
ejpam-5268	103	18	(	(	PUNCT
ejpam-5268	103	19	ξ∗3	ξ∗3	NOUN
ejpam-5268	103	20	)	)	PUNCT
ejpam-5268	103	21	if	if	SCONJ
ejpam-5268	103	22	{	{	PUNCT
ejpam-5268	103	23	tn	tn	NOUN
ejpam-5268	103	24	}	}	PUNCT
ejpam-5268	103	25	&	&	CCONJ
ejpam-5268	103	26	{	{	PUNCT
ejpam-5268	103	27	wn	wn	PROPN
ejpam-5268	103	28	}	}	PUNCT
ejpam-5268	103	29	⊆	⊆	NUM
ejpam-5268	103	30	(	(	PUNCT
ejpam-5268	103	31	0	0	NUM
ejpam-5268	103	32	,	,	PUNCT
ejpam-5268	103	33	∞	∞	NUM
ejpam-5268	103	34	)	)	PUNCT
ejpam-5268	103	35	satisfying	satisfy	VERB
ejpam-5268	103	36	limn−→+∞{tn	limn−→+∞{tn	NOUN
ejpam-5268	103	37	}	}	PUNCT
ejpam-5268	103	38	=	=	SYM
ejpam-5268	103	39	limn−→+∞{wn	limn−→+∞{wn	ADJ
ejpam-5268	103	40	}	}	PUNCT
ejpam-5268	103	41	=	=	PUNCT
ejpam-5268	103	42	l	l	NOUN
ejpam-5268	103	43	∈	∈	PROPN
ejpam-5268	103	44	(	(	PUNCT
ejpam-5268	103	45	0	0	NUM
ejpam-5268	103	46	,	,	PUNCT
ejpam-5268	103	47	+	+	NOUN
ejpam-5268	103	48	∞	∞	NOUN
ejpam-5268	103	49	)	)	PUNCT
ejpam-5268	103	50	,	,	PUNCT
ejpam-5268	103	51	and	and	CCONJ
ejpam-5268	103	52	tn	tn	NOUN
ejpam-5268	103	53	<	<	X
ejpam-5268	103	54	wn	wn	PROPN
ejpam-5268	103	55	,	,	PUNCT
ejpam-5268	103	56	∀	∀	VERB
ejpam-5268	103	57	n	n	PRON
ejpam-5268	103	58	∈	∈	PROPN
ejpam-5268	103	59	n	n	CCONJ
ejpam-5268	103	60	,	,	PUNCT
ejpam-5268	103	61	so	so	ADV
ejpam-5268	103	62	lim	lim	PROPN
ejpam-5268	103	63	n−→+∞	n−→+∞	PROPN
ejpam-5268	103	64	supξ(tn	supξ(tn	PROPN
ejpam-5268	103	65	,	,	PUNCT
ejpam-5268	103	66	wn	wn	PROPN
ejpam-5268	103	67	)	)	PUNCT
ejpam-5268	103	68	<	<	X
ejpam-5268	103	69	0	0	X
ejpam-5268	103	70	.	.	PUNCT
ejpam-5268	103	71	to	to	PART
ejpam-5268	103	72	see	see	VERB
ejpam-5268	103	73	various	various	ADJ
ejpam-5268	103	74	examples	example	NOUN
ejpam-5268	103	75	of	of	ADP
ejpam-5268	103	76	simulation	simulation	NOUN
ejpam-5268	103	77	mappings	mapping	NOUN
ejpam-5268	103	78	we	we	PRON
ejpam-5268	103	79	refer	refer	VERB
ejpam-5268	103	80	the	the	DET
ejpam-5268	103	81	authors	author	NOUN
ejpam-5268	103	82	to	to	ADP
ejpam-5268	103	83	[	[	X
ejpam-5268	103	84	5	5	NUM
ejpam-5268	103	85	,	,	PUNCT
ejpam-5268	103	86	7	7	NUM
ejpam-5268	103	87	,	,	PUNCT
ejpam-5268	103	88	18	18	NUM
ejpam-5268	103	89	]	]	PUNCT
ejpam-5268	103	90	.	.	PUNCT
ejpam-5268	104	1	the	the	DET
ejpam-5268	104	2	main	main	ADJ
ejpam-5268	104	3	objective	objective	NOUN
ejpam-5268	104	4	of	of	ADP
ejpam-5268	104	5	this	this	DET
ejpam-5268	104	6	article	article	NOUN
ejpam-5268	104	7	is	be	AUX
ejpam-5268	104	8	to	to	PART
ejpam-5268	104	9	investigate	investigate	VERB
ejpam-5268	104	10	and	and	CCONJ
ejpam-5268	104	11	verify	verify	VERB
ejpam-5268	104	12	another	another	DET
ejpam-5268	104	13	original	original	ADJ
ejpam-5268	104	14	common	common	ADJ
ejpam-5268	104	15	and	and	CCONJ
ejpam-5268	104	16	coincidence	coincidence	NOUN
ejpam-5268	104	17	fixed	fix	VERB
ejpam-5268	104	18	point	point	NOUN
ejpam-5268	104	19	theorems	theorem	NOUN
ejpam-5268	104	20	in	in	ADP
ejpam-5268	104	21	symmetrical	symmetrical	ADJ
ejpam-5268	104	22	complete	complete	ADJ
ejpam-5268	104	23	s	s	NOUN
ejpam-5268	104	24	-	-	ADJ
ejpam-5268	104	25	metric	metric	ADJ
ejpam-5268	104	26	spaces	space	NOUN
ejpam-5268	104	27	involving	involve	VERB
ejpam-5268	104	28	simulation	simulation	NOUN
ejpam-5268	104	29	mappings	mapping	NOUN
ejpam-5268	104	30	.	.	PUNCT
ejpam-5268	105	1	furthermore	furthermore	ADV
ejpam-5268	105	2	,	,	PUNCT
ejpam-5268	105	3	by	by	ADP
ejpam-5268	105	4	applying	apply	VERB
ejpam-5268	105	5	our	our	PRON
ejpam-5268	105	6	outcomes	outcome	NOUN
ejpam-5268	105	7	to	to	PART
ejpam-5268	105	8	derive	derive	VERB
ejpam-5268	105	9	various	various	ADJ
ejpam-5268	105	10	common	common	ADJ
ejpam-5268	105	11	&	&	CCONJ
ejpam-5268	105	12	coincidence	coincidence	NOUN
ejpam-5268	105	13	fixed	fix	VERB
ejpam-5268	105	14	point	point	NOUN
ejpam-5268	105	15	theorems	theorem	NOUN
ejpam-5268	105	16	for	for	ADP
ejpam-5268	105	17	right	right	ADJ
ejpam-5268	105	18	monotone	monotone	ADJ
ejpam-5268	105	19	simulation	simulation	NOUN
ejpam-5268	105	20	maps	map	NOUN
ejpam-5268	105	21	in	in	ADP
ejpam-5268	105	22	generalized	generalized	ADJ
ejpam-5268	105	23	metric	metric	NOUN
ejpam-5268	105	24	.	.	PUNCT
ejpam-5268	106	1	additionally	additionally	ADV
ejpam-5268	106	2	,	,	PUNCT
ejpam-5268	106	3	suitable	suitable	ADJ
ejpam-5268	106	4	examples	example	NOUN
ejpam-5268	106	5	,	,	PUNCT
ejpam-5268	106	6	and	and	CCONJ
ejpam-5268	106	7	some	some	DET
ejpam-5268	106	8	implementations	implementation	NOUN
ejpam-5268	106	9	to	to	PART
ejpam-5268	106	10	solve	solve	VERB
ejpam-5268	106	11	an	an	DET
ejpam-5268	106	12	integral	integral	ADJ
ejpam-5268	106	13	equation	equation	NOUN
ejpam-5268	106	14	are	be	AUX
ejpam-5268	106	15	given	give	VERB
ejpam-5268	106	16	to	to	PART
ejpam-5268	106	17	support	support	VERB
ejpam-5268	106	18	our	our	PRON
ejpam-5268	106	19	major	major	ADJ
ejpam-5268	106	20	results	result	NOUN
ejpam-5268	106	21	.	.	PUNCT
ejpam-5268	107	1	n.	n.	PROPN
ejpam-5268	107	2	a.	a.	PROPN
ejpam-5268	107	3	majid	majid	PROPN
ejpam-5268	107	4	et	et	PROPN
ejpam-5268	107	5	al	al	PROPN
ejpam-5268	107	6	.	.	PUNCT
ejpam-5268	107	7	/	/	SYM
ejpam-5268	107	8	eur	eur	PROPN
ejpam-5268	107	9	.	.	PUNCT
ejpam-5268	108	1	j.	j.	PROPN
ejpam-5268	108	2	pure	pure	PROPN
ejpam-5268	108	3	appl	appl	PROPN
ejpam-5268	108	4	.	.	PROPN
ejpam-5268	108	5	math	math	PROPN
ejpam-5268	108	6	,	,	PUNCT
ejpam-5268	108	7	17	17	NUM
ejpam-5268	108	8	(	(	PUNCT
ejpam-5268	108	9	3	3	NUM
ejpam-5268	108	10	)	)	PUNCT
ejpam-5268	108	11	(	(	PUNCT
ejpam-5268	108	12	2024	2024	NUM
ejpam-5268	108	13	)	)	PUNCT
ejpam-5268	108	14	,	,	PUNCT
ejpam-5268	108	15	1877	1877	NUM
ejpam-5268	108	16	-	-	SYM
ejpam-5268	108	17	1893	1893	NUM
ejpam-5268	108	18	1881	1881	NUM
ejpam-5268	108	19	2	2	NUM
ejpam-5268	108	20	.	.	PUNCT
ejpam-5268	109	1	some	some	DET
ejpam-5268	109	2	common	common	ADJ
ejpam-5268	109	3	and	and	CCONJ
ejpam-5268	109	4	coincidence	coincidence	NOUN
ejpam-5268	109	5	fixed	fix	VERB
ejpam-5268	109	6	point	point	NOUN
ejpam-5268	109	7	results	result	NOUN
ejpam-5268	109	8	by	by	ADP
ejpam-5268	109	9	means	mean	NOUN
ejpam-5268	109	10	of	of	ADP
ejpam-5268	109	11	simulation	simulation	NOUN
ejpam-5268	109	12	mappings	mapping	NOUN
ejpam-5268	109	13	in	in	ADP
ejpam-5268	109	14	this	this	DET
ejpam-5268	109	15	part	part	NOUN
ejpam-5268	109	16	,	,	PUNCT
ejpam-5268	109	17	we	we	PRON
ejpam-5268	109	18	introduce	introduce	VERB
ejpam-5268	109	19	and	and	CCONJ
ejpam-5268	109	20	investigate	investigate	VERB
ejpam-5268	109	21	several	several	ADJ
ejpam-5268	109	22	common	common	ADJ
ejpam-5268	109	23	and	and	CCONJ
ejpam-5268	109	24	coincidence	coincidence	NOUN
ejpam-5268	109	25	fixed	fix	VERB
ejpam-5268	109	26	point	point	NOUN
ejpam-5268	109	27	outcomes	outcome	NOUN
ejpam-5268	109	28	utilizing	utilize	VERB
ejpam-5268	109	29	simulation	simulation	NOUN
ejpam-5268	109	30	mappings	mapping	NOUN
ejpam-5268	109	31	in	in	ADP
ejpam-5268	109	32	complete	complete	ADJ
ejpam-5268	109	33	s	s	NOUN
ejpam-5268	109	34	-	-	NOUN
ejpam-5268	109	35	metric	metric	ADJ
ejpam-5268	109	36	.	.	PUNCT
ejpam-5268	110	1	in	in	ADP
ejpam-5268	110	2	the	the	DET
ejpam-5268	110	3	beginning	beginning	NOUN
ejpam-5268	110	4	,	,	PUNCT
ejpam-5268	110	5	generalized	generalize	VERB
ejpam-5268	110	6	several	several	ADJ
ejpam-5268	110	7	fundamental	fundamental	ADJ
ejpam-5268	110	8	propositions	proposition	NOUN
ejpam-5268	110	9	in	in	ADP
ejpam-5268	110	10	the	the	DET
ejpam-5268	110	11	literature	literature	NOUN
ejpam-5268	110	12	,	,	PUNCT
ejpam-5268	110	13	which	which	PRON
ejpam-5268	110	14	are	be	AUX
ejpam-5268	110	15	needed	need	VERB
ejpam-5268	110	16	throughout	throughout	ADP
ejpam-5268	110	17	this	this	DET
ejpam-5268	110	18	work	work	NOUN
ejpam-5268	110	19	.	.	PUNCT
ejpam-5268	111	1	proposition	proposition	NOUN
ejpam-5268	111	2	1	1	NUM
ejpam-5268	111	3	.	.	PUNCT
ejpam-5268	112	1	if	if	SCONJ
ejpam-5268	112	2	f	f	PROPN
ejpam-5268	112	3	,	,	PUNCT
ejpam-5268	112	4	t	t	X
ejpam-5268	112	5	:	:	PUNCT
ejpam-5268	112	6	(	(	PUNCT
ejpam-5268	112	7	x	x	X
ejpam-5268	112	8	,	,	PUNCT
ejpam-5268	112	9	s	s	PART
ejpam-5268	112	10	)	)	PUNCT
ejpam-5268	112	11	→	→	SYM
ejpam-5268	112	12	(	(	PUNCT
ejpam-5268	112	13	x	x	X
ejpam-5268	112	14	,	,	PUNCT
ejpam-5268	112	15	s	s	PART
ejpam-5268	112	16	)	)	PUNCT
ejpam-5268	112	17	are	be	AUX
ejpam-5268	112	18	self	self	NOUN
ejpam-5268	112	19	mappings	mapping	NOUN
ejpam-5268	112	20	and	and	CCONJ
ejpam-5268	112	21	f	f	PROPN
ejpam-5268	112	22	is	be	AUX
ejpam-5268	112	23	t	t	PROPN
ejpam-5268	112	24	-	-	PUNCT
ejpam-5268	112	25	non	non	NOUN
ejpam-5268	112	26	-	-	ADJ
ejpam-5268	112	27	decreasing	decrease	VERB
ejpam-5268	112	28	in	in	ADP
ejpam-5268	112	29	a	a	DET
ejpam-5268	112	30	s	s	NOUN
ejpam-5268	113	1	-	-	ADJ
ejpam-5268	113	2	metric	metric	ADJ
ejpam-5268	113	3	(	(	PUNCT
ejpam-5268	113	4	x	x	NOUN
ejpam-5268	113	5	,	,	PUNCT
ejpam-5268	113	6	s	s	PART
ejpam-5268	113	7	)	)	PUNCT
ejpam-5268	113	8	and	and	CCONJ
ejpam-5268	113	9	satisfies	satisfy	VERB
ejpam-5268	113	10	the	the	DET
ejpam-5268	113	11	next	next	ADJ
ejpam-5268	113	12	cases	case	NOUN
ejpam-5268	113	13	:	:	PUNCT
ejpam-5268	113	14	(	(	PUNCT
ejpam-5268	113	15	i	i	NOUN
ejpam-5268	113	16	)	)	PUNCT
ejpam-5268	113	17	if	if	SCONJ
ejpam-5268	113	18	t	t	PROPN
ejpam-5268	113	19	(	(	PUNCT
ejpam-5268	113	20	x	x	NOUN
ejpam-5268	113	21	)	)	PUNCT
ejpam-5268	113	22	closed	closed	ADJ
ejpam-5268	113	23	and	and	CCONJ
ejpam-5268	113	24	f(x	f(x	PROPN
ejpam-5268	113	25	)	)	PUNCT
ejpam-5268	114	1	⊂	⊂	PROPN
ejpam-5268	115	1	t(x	t(x	PROPN
ejpam-5268	115	2	)	)	PUNCT
ejpam-5268	115	3	,	,	PUNCT
ejpam-5268	115	4	then	then	ADV
ejpam-5268	115	5	∃	∃	PROPN
ejpam-5268	115	6	x∗	x∗	PROPN
ejpam-5268	115	7	∈	∈	PROPN
ejpam-5268	115	8	x	x	PUNCT
ejpam-5268	115	9	with	with	ADP
ejpam-5268	115	10	tx∗	tx∗	NOUN
ejpam-5268	115	11	≤	≤	NUM
ejpam-5268	115	12	fx∗.	fx∗.	ADV
ejpam-5268	115	13	furthermore	furthermore	ADV
ejpam-5268	115	14	,	,	PUNCT
ejpam-5268	115	15	if	if	SCONJ
ejpam-5268	115	16	{	{	PUNCT
ejpam-5268	115	17	txs	txs	NOUN
ejpam-5268	115	18	}	}	PUNCT
ejpam-5268	115	19	⊂	⊂	PROPN
ejpam-5268	115	20	x	x	X
ejpam-5268	115	21	is	be	AUX
ejpam-5268	115	22	non	non	ADJ
ejpam-5268	115	23	-	-	ADJ
ejpam-5268	115	24	decreasing	decrease	VERB
ejpam-5268	115	25	sequence	sequence	NOUN
ejpam-5268	115	26	;	;	PUNCT
ejpam-5268	115	27	(	(	PUNCT
ejpam-5268	115	28	w.	w.	PROPN
ejpam-5268	115	29	r.	r.	PROPN
ejpam-5268	115	30	t.	t.	PROPN
ejpam-5268	115	31	≤	≤	PROPN
ejpam-5268	115	32	)	)	PUNCT
ejpam-5268	115	33	with	with	ADP
ejpam-5268	115	34	txs	txs	NOUN
ejpam-5268	115	35	→	→	SYM
ejpam-5268	115	36	tz	tz	PROPN
ejpam-5268	115	37	of	of	ADP
ejpam-5268	115	38	t	t	PROPN
ejpam-5268	115	39	(	(	PUNCT
ejpam-5268	115	40	x	x	NOUN
ejpam-5268	115	41	)	)	PUNCT
ejpam-5268	115	42	,	,	PUNCT
ejpam-5268	115	43	so	so	SCONJ
ejpam-5268	115	44	tp	tp	ADP
ejpam-5268	115	45	≤	≤	PROPN
ejpam-5268	115	46	t	t	PROPN
ejpam-5268	115	47	(	(	PUNCT
ejpam-5268	115	48	tp	tp	NOUN
ejpam-5268	115	49	)	)	PUNCT
ejpam-5268	115	50	&	&	CCONJ
ejpam-5268	115	51	txs	txs	NOUN
ejpam-5268	115	52	≤	≤	PROPN
ejpam-5268	115	53	(	(	PUNCT
ejpam-5268	115	54	tp	tp	NOUN
ejpam-5268	115	55	)	)	PUNCT
ejpam-5268	115	56	,	,	PUNCT
ejpam-5268	115	57	∀	∀	X
ejpam-5268	115	58	s	s	NOUN
ejpam-5268	115	59	∈	∈	PROPN
ejpam-5268	115	60	n.	n.	NOUN
ejpam-5268	115	61	(	(	PUNCT
ejpam-5268	115	62	ii	ii	NOUN
ejpam-5268	115	63	)	)	PUNCT
ejpam-5268	115	64	if	if	SCONJ
ejpam-5268	115	65	there	there	PRON
ejpam-5268	115	66	exists	exist	VERB
ejpam-5268	115	67	simulation	simulation	NOUN
ejpam-5268	115	68	mapping	mapping	PROPN
ejpam-5268	115	69	ξ	ξ	PROPN
ejpam-5268	115	70	;	;	PUNCT
ejpam-5268	115	71	(	(	PUNCT
ejpam-5268	115	72	s.t	s.t	PROPN
ejpam-5268	115	73	)	)	PUNCT
ejpam-5268	115	74	,	,	PUNCT
ejpam-5268	115	75	∀	∀	X
ejpam-5268	115	76	(	(	PUNCT
ejpam-5268	115	77	x	x	NOUN
ejpam-5268	115	78	,	,	PUNCT
ejpam-5268	115	79	y	y	NOUN
ejpam-5268	115	80	)	)	PUNCT
ejpam-5268	115	81	∈	∈	PROPN
ejpam-5268	115	82	x	x	X
ejpam-5268	115	83	×x	×x	X
ejpam-5268	115	84	&	&	CCONJ
ejpam-5268	115	85	tx	tx	VERB
ejpam-5268	115	86	≤	≤	PROPN
ejpam-5268	116	1	ty	ty	NUM
ejpam-5268	116	2	,	,	PUNCT
ejpam-5268	116	3	we	we	PRON
ejpam-5268	116	4	have	have	VERB
ejpam-5268	116	5	ξ	ξ	X
ejpam-5268	116	6	(	(	PUNCT
ejpam-5268	116	7	s	s	X
ejpam-5268	116	8	(	(	PUNCT
ejpam-5268	116	9	fx	fx	PROPN
ejpam-5268	116	10	,	,	PUNCT
ejpam-5268	116	11	fy	fy	PROPN
ejpam-5268	116	12	,	,	PUNCT
ejpam-5268	116	13	fz	fz	PROPN
ejpam-5268	116	14	)	)	PUNCT
ejpam-5268	116	15	,	,	PUNCT
ejpam-5268	116	16	m1	m1	PROPN
ejpam-5268	116	17	(	(	PUNCT
ejpam-5268	116	18	f	f	PROPN
ejpam-5268	116	19	,	,	PUNCT
ejpam-5268	116	20	t	t	PROPN
ejpam-5268	116	21	,	,	PUNCT
ejpam-5268	116	22	x	x	X
ejpam-5268	116	23	,	,	PUNCT
ejpam-5268	116	24	y	y	PROPN
ejpam-5268	116	25	,	,	PUNCT
ejpam-5268	116	26	z	z	NOUN
ejpam-5268	116	27	)	)	PUNCT
ejpam-5268	116	28	)	)	PUNCT
ejpam-5268	116	29	≥	≥	NOUN
ejpam-5268	116	30	0	0	NUM
ejpam-5268	116	31	,	,	PUNCT
ejpam-5268	116	32	(	(	PUNCT
ejpam-5268	116	33	1	1	X
ejpam-5268	116	34	)	)	PUNCT
ejpam-5268	116	35	where	where	SCONJ
ejpam-5268	116	36	(	(	PUNCT
ejpam-5268	116	37	ξ1	ξ1	NOUN
ejpam-5268	116	38	)	)	PUNCT
ejpam-5268	116	39	ξ	ξ	PROPN
ejpam-5268	116	40	(	(	PUNCT
ejpam-5268	116	41	0	0	NUM
ejpam-5268	116	42	,	,	PUNCT
ejpam-5268	116	43	0	0	NUM
ejpam-5268	116	44	)	)	PUNCT
ejpam-5268	116	45	=	=	SYM
ejpam-5268	116	46	0	0	NUM
ejpam-5268	116	47	,	,	PUNCT
ejpam-5268	116	48	(	(	PUNCT
ejpam-5268	116	49	ξ2	ξ2	NOUN
ejpam-5268	117	1	)	)	PUNCT
ejpam-5268	117	2	ξ	ξ	PROPN
ejpam-5268	117	3	(	(	PUNCT
ejpam-5268	117	4	t	t	PROPN
ejpam-5268	117	5	,	,	PUNCT
ejpam-5268	117	6	w	w	PROPN
ejpam-5268	117	7	)	)	PUNCT
ejpam-5268	117	8	<	<	X
ejpam-5268	117	9	w	w	PROPN
ejpam-5268	117	10	−	−	PROPN
ejpam-5268	117	11	t	t	PROPN
ejpam-5268	117	12	,	,	PUNCT
ejpam-5268	117	13	∀	∀	X
ejpam-5268	117	14	,	,	PUNCT
ejpam-5268	117	15	w	w	PROPN
ejpam-5268	117	16	,	,	PUNCT
ejpam-5268	117	17	t	t	X
ejpam-5268	117	18	>	>	X
ejpam-5268	117	19	0	0	NUM
ejpam-5268	117	20	,	,	PUNCT
ejpam-5268	117	21	(	(	PUNCT
ejpam-5268	117	22	ξ3	ξ3	NOUN
ejpam-5268	117	23	)	)	PUNCT
ejpam-5268	117	24	if	if	SCONJ
ejpam-5268	117	25	{	{	PUNCT
ejpam-5268	117	26	tn	tn	NOUN
ejpam-5268	117	27	}	}	PUNCT
ejpam-5268	117	28	&	&	CCONJ
ejpam-5268	117	29	{	{	PUNCT
ejpam-5268	117	30	wn	wn	PROPN
ejpam-5268	117	31	}	}	PUNCT
ejpam-5268	117	32	⊆	⊆	NUM
ejpam-5268	117	33	(	(	PUNCT
ejpam-5268	117	34	0	0	NUM
ejpam-5268	117	35	,	,	PUNCT
ejpam-5268	117	36	+	+	NOUN
ejpam-5268	117	37	∞	∞	NOUN
ejpam-5268	117	38	)	)	PUNCT
ejpam-5268	117	39	m1	m1	NOUN
ejpam-5268	117	40	(	(	PUNCT
ejpam-5268	117	41	f	f	X
ejpam-5268	117	42	,	,	PUNCT
ejpam-5268	117	43	t	t	PROPN
ejpam-5268	117	44	,	,	PUNCT
ejpam-5268	117	45	x	x	X
ejpam-5268	117	46	,	,	PUNCT
ejpam-5268	117	47	y	y	PROPN
ejpam-5268	117	48	,	,	PUNCT
ejpam-5268	117	49	z	z	NOUN
ejpam-5268	117	50	)	)	PUNCT
ejpam-5268	117	51	=	=	SYM
ejpam-5268	117	52	max	max	X
ejpam-5268	117	53	{	{	PUNCT
ejpam-5268	117	54	s	s	X
ejpam-5268	117	55	(	(	PUNCT
ejpam-5268	117	56	tx	tx	PROPN
ejpam-5268	117	57	,	,	PUNCT
ejpam-5268	117	58	ty	ty	INTJ
ejpam-5268	117	59	,	,	PUNCT
ejpam-5268	117	60	tz	tz	PROPN
ejpam-5268	117	61	)	)	PUNCT
ejpam-5268	117	62	,	,	PUNCT
ejpam-5268	117	63	s	s	PART
ejpam-5268	117	64	(	(	PUNCT
ejpam-5268	117	65	tx	tx	PROPN
ejpam-5268	117	66	,	,	PUNCT
ejpam-5268	117	67	fy	fy	PROPN
ejpam-5268	117	68	,	,	PUNCT
ejpam-5268	117	69	tz	tz	PROPN
ejpam-5268	117	70	)	)	PUNCT
ejpam-5268	117	71	,	,	PUNCT
ejpam-5268	117	72	s	s	X
ejpam-5268	117	73	(	(	PUNCT
ejpam-5268	117	74	ty	ty	INTJ
ejpam-5268	117	75	,	,	PUNCT
ejpam-5268	117	76	fx	fx	PROPN
ejpam-5268	117	77	,	,	PUNCT
ejpam-5268	117	78	tz	tz	PROPN
ejpam-5268	117	79	)	)	PUNCT
ejpam-5268	117	80	,	,	PUNCT
ejpam-5268	117	81	s	s	PART
ejpam-5268	117	82	(	(	PUNCT
ejpam-5268	117	83	tx	tx	PROPN
ejpam-5268	117	84	,	,	PUNCT
ejpam-5268	117	85	fx	fx	PROPN
ejpam-5268	117	86	,	,	PUNCT
ejpam-5268	117	87	tz	tz	PROPN
ejpam-5268	117	88	)	)	PUNCT
ejpam-5268	117	89	,	,	PUNCT
ejpam-5268	117	90	s	s	X
ejpam-5268	117	91	(	(	PUNCT
ejpam-5268	117	92	ty	ty	INTJ
ejpam-5268	117	93	,	,	PUNCT
ejpam-5268	117	94	fy	fy	PROPN
ejpam-5268	117	95	,	,	PUNCT
ejpam-5268	117	96	tz	tz	PROPN
ejpam-5268	117	97	)	)	PUNCT
ejpam-5268	117	98	}	}	PUNCT
ejpam-5268	117	99	let	let	VERB
ejpam-5268	117	100	xs	xs	PROPN
ejpam-5268	117	101	be	be	AUX
ejpam-5268	117	102	sequence	sequence	NOUN
ejpam-5268	117	103	in	in	ADP
ejpam-5268	117	104	x	x	PROPN
ejpam-5268	117	105	(	(	PUNCT
ejpam-5268	117	106	s.	s.	PROPN
ejpam-5268	117	107	t	t	PROPN
ejpam-5268	117	108	)	)	PUNCT
ejpam-5268	117	109	,	,	PUNCT
ejpam-5268	117	110	txs+1	txs+1	PROPN
ejpam-5268	117	111	=	=	SYM
ejpam-5268	117	112	fxs	fxs	NOUN
ejpam-5268	117	113	,	,	PUNCT
ejpam-5268	117	114	∀	∀	PUNCT
ejpam-5268	117	115	s	s	NOUN
ejpam-5268	117	116	∈	∈	PROPN
ejpam-5268	117	117	n.	n.	NOUN
ejpam-5268	117	118	if	if	SCONJ
ejpam-5268	117	119	txs	txs	NOUN
ejpam-5268	117	120	̸=	̸=	PROPN
ejpam-5268	117	121	txs+1∀	txs+1∀	NOUN
ejpam-5268	117	122	s	s	NOUN
ejpam-5268	117	123	∈	∈	PROPN
ejpam-5268	117	124	n	n	CCONJ
ejpam-5268	117	125	,	,	PUNCT
ejpam-5268	117	126	so	so	ADV
ejpam-5268	117	127	lim	lim	PROPN
ejpam-5268	117	128	s→+∞	s→+∞	PROPN
ejpam-5268	117	129	s	s	PROPN
ejpam-5268	117	130	(	(	PUNCT
ejpam-5268	117	131	txs	txs	NOUN
ejpam-5268	117	132	,	,	PUNCT
ejpam-5268	117	133	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	117	134	)	)	PUNCT
ejpam-5268	117	135	=	=	SYM
ejpam-5268	118	1	0	0	X
ejpam-5268	118	2	.	.	PUNCT
ejpam-5268	119	1	proof	proof	NOUN
ejpam-5268	119	2	.	.	PUNCT
ejpam-5268	120	1	at	at	ADP
ejpam-5268	120	2	the	the	DET
ejpam-5268	120	3	beginning	beginning	NOUN
ejpam-5268	120	4	,	,	PUNCT
ejpam-5268	120	5	observe	observe	VERB
ejpam-5268	120	6	that	that	SCONJ
ejpam-5268	120	7	from	from	ADP
ejpam-5268	120	8	the	the	DET
ejpam-5268	120	9	hypothesis	hypothesis	NOUN
ejpam-5268	120	10	,	,	PUNCT
ejpam-5268	120	11	we	we	PRON
ejpam-5268	120	12	have	have	VERB
ejpam-5268	120	13	tx0	tx0	ADJ
ejpam-5268	120	14	≤	≤	NUM
ejpam-5268	120	15	tx1	tx1	NOUN
ejpam-5268	120	16	≤	≤	ADJ
ejpam-5268	120	17	tx2	tx2	NOUN
ejpam-5268	120	18	≤	≤	NOUN
ejpam-5268	120	19	.	.	PUNCT
ejpam-5268	120	20	.	.	PUNCT
ejpam-5268	120	21	.	.	PUNCT
ejpam-5268	121	1	≤	≤	NUM
ejpam-5268	121	2	txs	txs	NOUN
ejpam-5268	121	3	≤	≤	NOUN
ejpam-5268	121	4	txs+1	txs+1	NOUN
ejpam-5268	121	5	.	.	PUNCT
ejpam-5268	122	1	it	it	PRON
ejpam-5268	122	2	follows	follow	VERB
ejpam-5268	122	3	from	from	ADP
ejpam-5268	122	4	part	part	NOUN
ejpam-5268	122	5	(	(	PUNCT
ejpam-5268	122	6	vi	vi	NOUN
ejpam-5268	122	7	)	)	PUNCT
ejpam-5268	122	8	that	that	SCONJ
ejpam-5268	122	9	for	for	ADP
ejpam-5268	122	10	all	all	PRON
ejpam-5268	122	11	s	s	PART
ejpam-5268	122	12	≥	≥	NOUN
ejpam-5268	122	13	1	1	NUM
ejpam-5268	122	14	,	,	PUNCT
ejpam-5268	122	15	we	we	PRON
ejpam-5268	122	16	have	have	VERB
ejpam-5268	122	17	0	0	NUM
ejpam-5268	122	18	≤	≤	NUM
ejpam-5268	122	19	ξ(s(fxs−1	ξ(s(fxs−1	NOUN
ejpam-5268	122	20	,	,	PUNCT
ejpam-5268	122	21	fxs	fxs	NOUN
ejpam-5268	122	22	,	,	PUNCT
ejpam-5268	122	23	fxs	fxs	PROPN
ejpam-5268	122	24	)	)	PUNCT
ejpam-5268	122	25	,	,	PUNCT
ejpam-5268	122	26	m1(f	m1(f	PROPN
ejpam-5268	122	27	,	,	PUNCT
ejpam-5268	122	28	t	t	PROPN
ejpam-5268	122	29	,	,	PUNCT
ejpam-5268	122	30	xs−1	xs−1	PROPN
ejpam-5268	122	31	,	,	PUNCT
ejpam-5268	122	32	xs	xs	PROPN
ejpam-5268	122	33	,	,	PUNCT
ejpam-5268	122	34	xs	xs	PROPN
ejpam-5268	122	35	)	)	PUNCT
ejpam-5268	122	36	)	)	PUNCT
ejpam-5268	122	37	,	,	PUNCT
ejpam-5268	122	38	that	that	ADV
ejpam-5268	122	39	is	is	ADV
ejpam-5268	122	40	,	,	PUNCT
ejpam-5268	122	41	0	0	NUM
ejpam-5268	122	42	≤	≤	NUM
ejpam-5268	123	1	ξ	ξ	X
ejpam-5268	123	2	(	(	PUNCT
ejpam-5268	123	3	s	s	X
ejpam-5268	123	4	(	(	PUNCT
ejpam-5268	123	5	txs	txs	NOUN
ejpam-5268	123	6	,	,	PUNCT
ejpam-5268	123	7	txs−1,txs+1	txs−1,txs+1	NOUN
ejpam-5268	123	8	)	)	PUNCT
ejpam-5268	123	9	,	,	PUNCT
ejpam-5268	123	10	m1	m1	PROPN
ejpam-5268	123	11	(	(	PUNCT
ejpam-5268	123	12	f	f	PROPN
ejpam-5268	123	13	,	,	PUNCT
ejpam-5268	123	14	t	t	PROPN
ejpam-5268	123	15	,	,	PUNCT
ejpam-5268	123	16	xs−1,xs	xs−1,xs	PROPN
ejpam-5268	123	17	,	,	PUNCT
ejpam-5268	123	18	xs	xs	PROPN
ejpam-5268	123	19	)	)	PUNCT
ejpam-5268	123	20	)	)	PUNCT
ejpam-5268	124	1	where	where	SCONJ
ejpam-5268	124	2	,	,	PUNCT
ejpam-5268	124	3	m1	m1	PROPN
ejpam-5268	124	4	(	(	PUNCT
ejpam-5268	124	5	f	f	PROPN
ejpam-5268	124	6	,	,	PUNCT
ejpam-5268	124	7	t	t	PROPN
ejpam-5268	124	8	,	,	PUNCT
ejpam-5268	124	9	xs−1,xs	xs−1,xs	PROPN
ejpam-5268	124	10	,	,	PUNCT
ejpam-5268	124	11	xs	xs	PROPN
ejpam-5268	124	12	)	)	PUNCT
ejpam-5268	124	13	=	=	SYM
ejpam-5268	124	14	max	max	X
ejpam-5268	124	15	{	{	PUNCT
ejpam-5268	124	16	s	s	X
ejpam-5268	124	17	(	(	PUNCT
ejpam-5268	124	18	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	124	19	,	,	PUNCT
ejpam-5268	124	20	txs	txs	PROPN
ejpam-5268	124	21	)	)	PUNCT
ejpam-5268	124	22	,	,	PUNCT
ejpam-5268	124	23	s	s	X
ejpam-5268	124	24	(	(	PUNCT
ejpam-5268	124	25	txs−1,fxs−1,txs	txs−1,fxs−1,txs	NOUN
ejpam-5268	124	26	)	)	PUNCT
ejpam-5268	124	27	,	,	PUNCT
ejpam-5268	124	28	s	s	X
ejpam-5268	124	29	(	(	PUNCT
ejpam-5268	124	30	txs−1,fxs−1,txs	txs−1,fxs−1,txs	NOUN
ejpam-5268	124	31	)	)	PUNCT
ejpam-5268	124	32	,	,	PUNCT
ejpam-5268	124	33	s	s	X
ejpam-5268	124	34	(	(	PUNCT
ejpam-5268	124	35	txs−1,fxs−1,txs	txs−1,fxs−1,txs	NOUN
ejpam-5268	124	36	)	)	PUNCT
ejpam-5268	124	37	,	,	PUNCT
ejpam-5268	124	38	s	s	X
ejpam-5268	124	39	(	(	PUNCT
ejpam-5268	124	40	txs−1,fxs−1,txs	txs−1,fxs−1,txs	NOUN
ejpam-5268	124	41	)	)	PUNCT
ejpam-5268	124	42	}	}	PUNCT
ejpam-5268	124	43	.	.	PUNCT
ejpam-5268	125	1	n.	n.	PROPN
ejpam-5268	125	2	a.	a.	PROPN
ejpam-5268	125	3	majid	majid	PROPN
ejpam-5268	125	4	et	et	PROPN
ejpam-5268	125	5	al	al	PROPN
ejpam-5268	125	6	.	.	PUNCT
ejpam-5268	125	7	/	/	SYM
ejpam-5268	125	8	eur	eur	PROPN
ejpam-5268	125	9	.	.	PUNCT
ejpam-5268	126	1	j.	j.	PROPN
ejpam-5268	126	2	pure	pure	PROPN
ejpam-5268	126	3	appl	appl	PROPN
ejpam-5268	126	4	.	.	PROPN
ejpam-5268	126	5	math	math	PROPN
ejpam-5268	126	6	,	,	PUNCT
ejpam-5268	126	7	17	17	NUM
ejpam-5268	126	8	(	(	PUNCT
ejpam-5268	126	9	3	3	NUM
ejpam-5268	126	10	)	)	PUNCT
ejpam-5268	126	11	(	(	PUNCT
ejpam-5268	126	12	2024	2024	NUM
ejpam-5268	126	13	)	)	PUNCT
ejpam-5268	126	14	,	,	PUNCT
ejpam-5268	126	15	1877	1877	NUM
ejpam-5268	126	16	-	-	SYM
ejpam-5268	126	17	1893	1893	NUM
ejpam-5268	126	18	1882	1882	NUM
ejpam-5268	126	19	furthermore	furthermore	ADV
ejpam-5268	126	20	,	,	PUNCT
ejpam-5268	126	21	by	by	ADP
ejpam-5268	126	22	utilizing	utilize	VERB
ejpam-5268	126	23	the	the	DET
ejpam-5268	126	24	assumptions	assumption	NOUN
ejpam-5268	126	25	,	,	PUNCT
ejpam-5268	126	26	we	we	PRON
ejpam-5268	126	27	have	have	VERB
ejpam-5268	126	28	m1	m1	NOUN
ejpam-5268	126	29	(	(	PUNCT
ejpam-5268	126	30	f	f	PROPN
ejpam-5268	126	31	,	,	PUNCT
ejpam-5268	126	32	t	t	PROPN
ejpam-5268	126	33	,	,	PUNCT
ejpam-5268	126	34	xs−1	xs−1	PROPN
ejpam-5268	126	35	,	,	PUNCT
ejpam-5268	126	36	xs	xs	PROPN
ejpam-5268	126	37	,	,	PUNCT
ejpam-5268	126	38	xs	xs	PROPN
ejpam-5268	126	39	)	)	PUNCT
ejpam-5268	127	1	=	=	SYM
ejpam-5268	127	2	max	max	X
ejpam-5268	127	3	{	{	PUNCT
ejpam-5268	127	4	s	s	X
ejpam-5268	127	5	(	(	PUNCT
ejpam-5268	127	6	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	127	7	,	,	PUNCT
ejpam-5268	127	8	txs	txs	PROPN
ejpam-5268	127	9	)	)	PUNCT
ejpam-5268	127	10	,	,	PUNCT
ejpam-5268	127	11	s	s	X
ejpam-5268	127	12	(	(	PUNCT
ejpam-5268	127	13	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	127	14	,	,	PUNCT
ejpam-5268	127	15	txs	txs	PROPN
ejpam-5268	127	16	)	)	PUNCT
ejpam-5268	127	17	,	,	PUNCT
ejpam-5268	127	18	s	s	X
ejpam-5268	127	19	(	(	PUNCT
ejpam-5268	127	20	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	127	21	,	,	PUNCT
ejpam-5268	127	22	txs	txs	PROPN
ejpam-5268	127	23	)	)	PUNCT
ejpam-5268	127	24	,	,	PUNCT
ejpam-5268	127	25	s	s	X
ejpam-5268	127	26	(	(	PUNCT
ejpam-5268	127	27	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	127	28	,	,	PUNCT
ejpam-5268	127	29	txs	txs	PROPN
ejpam-5268	127	30	)	)	PUNCT
ejpam-5268	127	31	,	,	PUNCT
ejpam-5268	127	32	s	s	X
ejpam-5268	127	33	(	(	PUNCT
ejpam-5268	127	34	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	127	35	,	,	PUNCT
ejpam-5268	127	36	txs	txs	NOUN
ejpam-5268	127	37	)	)	PUNCT
ejpam-5268	127	38	}	}	PUNCT
ejpam-5268	127	39	.	.	PUNCT
ejpam-5268	128	1	=	=	PRON
ejpam-5268	128	2	max	max	PROPN
ejpam-5268	128	3	{	{	PUNCT
ejpam-5268	128	4	s	s	X
ejpam-5268	128	5	(	(	PUNCT
ejpam-5268	128	6	txs−1,txs−1,txs	txs−1,txs−1,txs	NOUN
ejpam-5268	128	7	)	)	PUNCT
ejpam-5268	128	8	,	,	PUNCT
ejpam-5268	128	9	s	s	X
ejpam-5268	128	10	(	(	PUNCT
ejpam-5268	128	11	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	128	12	,	,	PUNCT
ejpam-5268	128	13	txs	txs	NOUN
ejpam-5268	128	14	)	)	PUNCT
ejpam-5268	128	15	}	}	PUNCT
ejpam-5268	128	16	.	.	PUNCT
ejpam-5268	129	1	since	since	SCONJ
ejpam-5268	129	2	(	(	PUNCT
ejpam-5268	129	3	x	x	X
ejpam-5268	129	4	,	,	PUNCT
ejpam-5268	129	5	s	s	PART
ejpam-5268	129	6	)	)	PUNCT
ejpam-5268	129	7	is	be	AUX
ejpam-5268	129	8	s	s	NOUN
ejpam-5268	129	9	-	-	ADJ
ejpam-5268	129	10	metric	metric	ADJ
ejpam-5268	129	11	,	,	PUNCT
ejpam-5268	129	12	so	so	SCONJ
ejpam-5268	129	13	we	we	PRON
ejpam-5268	129	14	get	get	VERB
ejpam-5268	129	15	m1	m1	PROPN
ejpam-5268	129	16	(	(	PUNCT
ejpam-5268	129	17	f	f	PROPN
ejpam-5268	129	18	,	,	PUNCT
ejpam-5268	129	19	t	t	PROPN
ejpam-5268	129	20	,	,	PUNCT
ejpam-5268	129	21	xs−1	xs−1	PROPN
ejpam-5268	129	22	,	,	PUNCT
ejpam-5268	129	23	xs	xs	PROPN
ejpam-5268	129	24	,	,	PUNCT
ejpam-5268	129	25	xs	xs	PROPN
ejpam-5268	129	26	)	)	PUNCT
ejpam-5268	130	1	=	=	SYM
ejpam-5268	130	2	s	s	X
ejpam-5268	130	3	(	(	PUNCT
ejpam-5268	130	4	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	130	5	,	,	PUNCT
ejpam-5268	130	6	txs	txs	NOUN
ejpam-5268	130	7	)	)	PUNCT
ejpam-5268	130	8	.	.	PUNCT
ejpam-5268	131	1	from	from	ADP
ejpam-5268	131	2	the	the	DET
ejpam-5268	131	3	condition	condition	NOUN
ejpam-5268	131	4	(	(	PUNCT
ejpam-5268	131	5	ξ2	ξ2	NOUN
ejpam-5268	131	6	)	)	PUNCT
ejpam-5268	131	7	of	of	ADP
ejpam-5268	131	8	simulation	simulation	NOUN
ejpam-5268	131	9	mapping	mapping	NOUN
ejpam-5268	131	10	we	we	PRON
ejpam-5268	131	11	obtain	obtain	VERB
ejpam-5268	131	12	:	:	PUNCT
ejpam-5268	131	13	0	0	NUM
ejpam-5268	131	14	≤	≤	NUM
ejpam-5268	131	15	ξ	ξ	X
ejpam-5268	131	16	(	(	PUNCT
ejpam-5268	131	17	s	s	X
ejpam-5268	131	18	(	(	PUNCT
ejpam-5268	131	19	txs	txs	NOUN
ejpam-5268	131	20	,	,	PUNCT
ejpam-5268	131	21	txs+1,txs+1	txs+1,txs+1	ADJ
ejpam-5268	131	22	)	)	PUNCT
ejpam-5268	131	23	,	,	PUNCT
ejpam-5268	131	24	s	s	X
ejpam-5268	131	25	(	(	PUNCT
ejpam-5268	131	26	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	131	27	,	,	PUNCT
ejpam-5268	131	28	txs	txs	NOUN
ejpam-5268	131	29	)	)	PUNCT
ejpam-5268	131	30	)	)	PUNCT
ejpam-5268	132	1	<	<	X
ejpam-5268	132	2	s	s	X
ejpam-5268	132	3	(	(	PUNCT
ejpam-5268	132	4	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	132	5	,	,	PUNCT
ejpam-5268	132	6	txs)−	txs)−	PROPN
ejpam-5268	132	7	s	s	PART
ejpam-5268	132	8	(	(	PUNCT
ejpam-5268	132	9	txs	txs	NOUN
ejpam-5268	132	10	,	,	PUNCT
ejpam-5268	132	11	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	132	12	)	)	PUNCT
ejpam-5268	132	13	thus	thus	ADV
ejpam-5268	132	14	,	,	PUNCT
ejpam-5268	132	15	s	s	X
ejpam-5268	132	16	(	(	PUNCT
ejpam-5268	132	17	txs	txs	NOUN
ejpam-5268	132	18	,	,	PUNCT
ejpam-5268	132	19	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	132	20	)	)	PUNCT
ejpam-5268	132	21	<	<	X
ejpam-5268	132	22	s	s	X
ejpam-5268	132	23	(	(	PUNCT
ejpam-5268	132	24	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	132	25	,	,	PUNCT
ejpam-5268	132	26	txs	txs	NOUN
ejpam-5268	132	27	)	)	PUNCT
ejpam-5268	132	28	.	.	PUNCT
ejpam-5268	133	1	which	which	PRON
ejpam-5268	133	2	implies	imply	VERB
ejpam-5268	133	3	that	that	SCONJ
ejpam-5268	133	4	{	{	PUNCT
ejpam-5268	133	5	s	s	X
ejpam-5268	133	6	(	(	PUNCT
ejpam-5268	133	7	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	133	8	,	,	PUNCT
ejpam-5268	133	9	txs	txs	NOUN
ejpam-5268	133	10	)	)	PUNCT
ejpam-5268	133	11	}	}	PUNCT
ejpam-5268	133	12	monotonically	monotonically	ADV
ejpam-5268	133	13	decreasing	decrease	VERB
ejpam-5268	133	14	of	of	ADP
ejpam-5268	133	15	non	non	ADJ
ejpam-5268	133	16	-	-	ADJ
ejpam-5268	133	17	negative	negative	ADJ
ejpam-5268	133	18	real	real	ADJ
ejpam-5268	133	19	numbers	number	NOUN
ejpam-5268	133	20	and	and	CCONJ
ejpam-5268	133	21	thus	thus	ADV
ejpam-5268	133	22	it	it	PRON
ejpam-5268	133	23	should	should	AUX
ejpam-5268	133	24	be	be	AUX
ejpam-5268	133	25	convergent	convergent	ADJ
ejpam-5268	133	26	.	.	PUNCT
ejpam-5268	134	1	therefore	therefore	ADV
ejpam-5268	134	2	,	,	PUNCT
ejpam-5268	134	3	∃	∃	PROPN
ejpam-5268	134	4	p	p	PROPN
ejpam-5268	134	5	≥	≥	PROPN
ejpam-5268	134	6	0	0	NUM
ejpam-5268	135	1	where	where	SCONJ
ejpam-5268	135	2	:	:	PUNCT
ejpam-5268	135	3	lims→+∞s	lims→+∞s	NOUN
ejpam-5268	135	4	(	(	PUNCT
ejpam-5268	135	5	txs	txs	NOUN
ejpam-5268	135	6	,	,	PUNCT
ejpam-5268	135	7	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	135	8	)	)	PUNCT
ejpam-5268	135	9	=	=	PUNCT
ejpam-5268	136	1	p.	p.	NOUN
ejpam-5268	136	2	suppose	suppose	VERB
ejpam-5268	136	3	that	that	SCONJ
ejpam-5268	136	4	p	p	PROPN
ejpam-5268	136	5	>	>	X
ejpam-5268	136	6	0	0	X
ejpam-5268	136	7	.	.	PUNCT
ejpam-5268	136	8	utilizing	utilize	VERB
ejpam-5268	136	9	the	the	DET
ejpam-5268	136	10	condition	condition	NOUN
ejpam-5268	136	11	(	(	PUNCT
ejpam-5268	136	12	ξ3	ξ3	NOUN
ejpam-5268	136	13	)	)	PUNCT
ejpam-5268	136	14	we	we	PRON
ejpam-5268	136	15	get	get	VERB
ejpam-5268	136	16	0	0	NUM
ejpam-5268	136	17	≤	≤	NUM
ejpam-5268	136	18	sup	sup	NOUN
ejpam-5268	136	19	ξ(s	ξ(s	PROPN
ejpam-5268	136	20	(	(	PUNCT
ejpam-5268	136	21	txs	txs	NOUN
ejpam-5268	136	22	,	,	PUNCT
ejpam-5268	136	23	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	136	24	)	)	PUNCT
ejpam-5268	136	25	,	,	PUNCT
ejpam-5268	136	26	s	s	X
ejpam-5268	136	27	(	(	PUNCT
ejpam-5268	136	28	txs−1,txs	txs−1,txs	NOUN
ejpam-5268	136	29	,	,	PUNCT
ejpam-5268	136	30	txs	txs	NOUN
ejpam-5268	136	31	)	)	PUNCT
ejpam-5268	136	32	)	)	PUNCT
ejpam-5268	137	1	<	<	X
ejpam-5268	137	2	0	0	NUM
ejpam-5268	137	3	,	,	PUNCT
ejpam-5268	137	4	this	this	PRON
ejpam-5268	137	5	is	be	AUX
ejpam-5268	137	6	a	a	DET
ejpam-5268	137	7	contraction	contraction	NOUN
ejpam-5268	137	8	.	.	PUNCT
ejpam-5268	138	1	then	then	ADV
ejpam-5268	138	2	,	,	PUNCT
ejpam-5268	138	3	we	we	PRON
ejpam-5268	138	4	conclude	conclude	VERB
ejpam-5268	138	5	that	that	SCONJ
ejpam-5268	138	6	p	p	X
ejpam-5268	138	7	=	=	NOUN
ejpam-5268	138	8	0	0	NUM
ejpam-5268	138	9	.	.	PUNCT
ejpam-5268	139	1	therefore	therefore	ADV
ejpam-5268	139	2	,	,	PUNCT
ejpam-5268	139	3	lim	lim	PROPN
ejpam-5268	139	4	s→+∞	s→+∞	PROPN
ejpam-5268	139	5	s	s	PROPN
ejpam-5268	139	6	(	(	PUNCT
ejpam-5268	139	7	txs	txs	NOUN
ejpam-5268	139	8	,	,	PUNCT
ejpam-5268	139	9	txs+1,txs+1	txs+1,txs+1	NOUN
ejpam-5268	139	10	)	)	PUNCT
ejpam-5268	139	11	=	=	SYM
ejpam-5268	139	12	0	0	NUM
ejpam-5268	139	13	,	,	PUNCT
ejpam-5268	139	14	proposition	proposition	NOUN
ejpam-5268	139	15	2	2	NUM
ejpam-5268	139	16	.	.	PUNCT
ejpam-5268	140	1	if	if	SCONJ
ejpam-5268	140	2	f	f	PROPN
ejpam-5268	140	3	,	,	PUNCT
ejpam-5268	140	4	t	t	X
ejpam-5268	140	5	:	:	PUNCT
ejpam-5268	140	6	(	(	PUNCT
ejpam-5268	140	7	x	x	X
ejpam-5268	140	8	,	,	PUNCT
ejpam-5268	140	9	s	s	PART
ejpam-5268	140	10	)	)	PUNCT
ejpam-5268	140	11	→	→	SYM
ejpam-5268	140	12	(	(	PUNCT
ejpam-5268	140	13	x	x	X
ejpam-5268	140	14	,	,	PUNCT
ejpam-5268	140	15	s	s	PART
ejpam-5268	140	16	)	)	PUNCT
ejpam-5268	140	17	are	be	AUX
ejpam-5268	140	18	self	self	NOUN
ejpam-5268	140	19	maps	map	NOUN
ejpam-5268	140	20	and	and	CCONJ
ejpam-5268	140	21	f	f	PROPN
ejpam-5268	140	22	is	be	AUX
ejpam-5268	140	23	t	t	PROPN
ejpam-5268	140	24	-	-	PUNCT
ejpam-5268	140	25	non	non	NOUN
ejpam-5268	140	26	-	-	ADJ
ejpam-5268	140	27	decreasing	decrease	VERB
ejpam-5268	140	28	in	in	ADP
ejpam-5268	140	29	s	s	NOUN
ejpam-5268	140	30	-	-	ADJ
ejpam-5268	140	31	metric	metric	ADJ
ejpam-5268	140	32	(	(	PUNCT
ejpam-5268	140	33	x	x	NOUN
ejpam-5268	140	34	,	,	PUNCT
ejpam-5268	140	35	s	s	PART
ejpam-5268	140	36	)	)	PUNCT
ejpam-5268	140	37	and	and	CCONJ
ejpam-5268	140	38	satisfies	satisfy	VERB
ejpam-5268	140	39	the	the	DET
ejpam-5268	140	40	cases	case	NOUN
ejpam-5268	140	41	(	(	PUNCT
ejpam-5268	140	42	(	(	PUNCT
ejpam-5268	140	43	i	i	NOUN
ejpam-5268	140	44	)	)	PUNCT
ejpam-5268	140	45	&	&	CCONJ
ejpam-5268	140	46	(	(	PUNCT
ejpam-5268	140	47	ii	ii	NOUN
ejpam-5268	140	48	)	)	PUNCT
ejpam-5268	140	49	)	)	PUNCT
ejpam-5268	140	50	of	of	ADP
ejpam-5268	140	51	proposition	proposition	NOUN
ejpam-5268	140	52	1	1	NUM
ejpam-5268	140	53	.	.	PUNCT
ejpam-5268	141	1	if	if	SCONJ
ejpam-5268	141	2	xs	xs	PROPN
ejpam-5268	141	3	is	be	AUX
ejpam-5268	141	4	sequence	sequence	NOUN
ejpam-5268	141	5	(	(	PUNCT
ejpam-5268	141	6	s.	s.	PROPN
ejpam-5268	141	7	t	t	PROPN
ejpam-5268	141	8	)	)	PUNCT
ejpam-5268	141	9	txs+1	txs+1	PROPN
ejpam-5268	141	10	̸=	̸=	PROPN
ejpam-5268	141	11	txs,∀	txs,∀	VERB
ejpam-5268	141	12	s	s	PROPN
ejpam-5268	141	13	∈	∈	PROPN
ejpam-5268	141	14	n.	n.	NOUN
ejpam-5268	141	15	then	then	ADV
ejpam-5268	141	16	,	,	PUNCT
ejpam-5268	141	17	txs	txs	PROPN
ejpam-5268	141	18	is	be	AUX
ejpam-5268	141	19	bounded	bounded	ADJ
ejpam-5268	141	20	sequence	sequence	NOUN
ejpam-5268	141	21	.	.	PUNCT
ejpam-5268	142	1	proof	proof	NOUN
ejpam-5268	142	2	.	.	PUNCT
ejpam-5268	143	1	suppose	suppose	VERB
ejpam-5268	143	2	txs	txs	NOUN
ejpam-5268	143	3	is	be	AUX
ejpam-5268	143	4	not	not	PART
ejpam-5268	143	5	bounded	bound	VERB
ejpam-5268	143	6	.	.	PUNCT
ejpam-5268	144	1	in	in	ADP
ejpam-5268	144	2	that	that	DET
ejpam-5268	144	3	case	case	NOUN
ejpam-5268	144	4	there	there	PRON
ejpam-5268	144	5	exists	exist	VERB
ejpam-5268	144	6	subsequence	subsequence	NOUN
ejpam-5268	144	7	{	{	PUNCT
ejpam-5268	144	8	xsk	xsk	PROPN
ejpam-5268	144	9	}	}	PUNCT
ejpam-5268	144	10	of	of	ADP
ejpam-5268	144	11	xs	xs	PROPN
ejpam-5268	144	12	(	(	PUNCT
ejpam-5268	144	13	s.	s.	PROPN
ejpam-5268	144	14	t	t	PROPN
ejpam-5268	144	15	)	)	PUNCT
ejpam-5268	144	16	s1	s1	NOUN
ejpam-5268	144	17	=	=	SYM
ejpam-5268	144	18	1	1	NUM
ejpam-5268	144	19	and	and	CCONJ
ejpam-5268	144	20	∀	∀	NUM
ejpam-5268	144	21	j	j	PROPN
ejpam-5268	144	22	∈	∈	PROPN
ejpam-5268	144	23	n	n	CCONJ
ejpam-5268	144	24	,	,	PUNCT
ejpam-5268	144	25	sk+1	sk+1	NUM
ejpam-5268	144	26	is	be	AUX
ejpam-5268	144	27	minimum	minimum	ADJ
ejpam-5268	144	28	integer	integer	NOUN
ejpam-5268	144	29	satisfying	satisfy	VERB
ejpam-5268	144	30	s(txsk+1	s(txsk+1	NOUN
ejpam-5268	144	31	,	,	PUNCT
ejpam-5268	144	32	txsk+1	txsk+1	PRON
ejpam-5268	144	33	,	,	PUNCT
ejpam-5268	144	34	txsk	txsk	NOUN
ejpam-5268	144	35	)	)	PUNCT
ejpam-5268	144	36	>	>	X
ejpam-5268	145	1	1	1	NUM
ejpam-5268	145	2	,	,	PUNCT
ejpam-5268	145	3	and	and	CCONJ
ejpam-5268	145	4	s(txj	s(txj	PROPN
ejpam-5268	145	5	,	,	PUNCT
ejpam-5268	145	6	txj	txj	NOUN
ejpam-5268	145	7	,	,	PUNCT
ejpam-5268	145	8	txsk	txsk	NOUN
ejpam-5268	145	9	)	)	PUNCT
ejpam-5268	145	10	≤	≤	NUM
ejpam-5268	145	11	1	1	NUM
ejpam-5268	145	12	,	,	PUNCT
ejpam-5268	145	13	for	for	ADP
ejpam-5268	145	14	sk	sk	NOUN
ejpam-5268	145	15	≤	≤	NUM
ejpam-5268	145	16	j	j	PROPN
ejpam-5268	145	17	≤	≤	NOUN
ejpam-5268	145	18	sk+1	sk+1	NUM
ejpam-5268	145	19	−	−	PROPN
ejpam-5268	145	20	1	1	NUM
ejpam-5268	145	21	.	.	PUNCT
ejpam-5268	145	22	utilizing	utilize	VERB
ejpam-5268	145	23	triangle	triangle	NOUN
ejpam-5268	145	24	inequality	inequality	NOUN
ejpam-5268	145	25	,	,	PUNCT
ejpam-5268	145	26	get	get	VERB
ejpam-5268	145	27	1	1	NUM
ejpam-5268	145	28	<	<	X
ejpam-5268	145	29	s	s	X
ejpam-5268	145	30	(	(	PUNCT
ejpam-5268	145	31	txsk+1,txsk+1,txsk	txsk+1,txsk+1,txsk	NOUN
ejpam-5268	145	32	)	)	PUNCT
ejpam-5268	145	33	n.	n.	PROPN
ejpam-5268	145	34	a.	a.	PROPN
ejpam-5268	145	35	majid	majid	PROPN
ejpam-5268	145	36	et	et	PROPN
ejpam-5268	145	37	al	al	PROPN
ejpam-5268	145	38	.	.	PUNCT
ejpam-5268	145	39	/	/	SYM
ejpam-5268	145	40	eur	eur	PROPN
ejpam-5268	145	41	.	.	PUNCT
ejpam-5268	146	1	j.	j.	PROPN
ejpam-5268	146	2	pure	pure	PROPN
ejpam-5268	146	3	appl	appl	PROPN
ejpam-5268	146	4	.	.	PROPN
ejpam-5268	146	5	math	math	PROPN
ejpam-5268	146	6	,	,	PUNCT
ejpam-5268	146	7	17	17	NUM
ejpam-5268	146	8	(	(	PUNCT
ejpam-5268	146	9	3	3	NUM
ejpam-5268	146	10	)	)	PUNCT
ejpam-5268	146	11	(	(	PUNCT
ejpam-5268	146	12	2024	2024	NUM
ejpam-5268	146	13	)	)	PUNCT
ejpam-5268	146	14	,	,	PUNCT
ejpam-5268	146	15	1877	1877	NUM
ejpam-5268	146	16	-	-	SYM
ejpam-5268	146	17	1893	1893	NUM
ejpam-5268	146	18	1883	1883	NUM
ejpam-5268	146	19	≤	≤	NOUN
ejpam-5268	147	1	2s	2s	NUM
ejpam-5268	147	2	(	(	PUNCT
ejpam-5268	147	3	txsk+1,txsk+1,txsk+1−1	txsk+1,txsk+1,txsk+1−1	PROPN
ejpam-5268	147	4	)	)	PUNCT
ejpam-5268	147	5	+	+	NUM
ejpam-5268	147	6	s(txsk	s(txsk	NOUN
ejpam-5268	147	7	,	,	PUNCT
ejpam-5268	147	8	txsk	txsk	NOUN
ejpam-5268	147	9	,	,	PUNCT
ejpam-5268	147	10	txsk+1−1	txsk+1−1	NUM
ejpam-5268	147	11	)	)	PUNCT
ejpam-5268	147	12	≤	≤	NOUN
ejpam-5268	148	1	2s	2s	NUM
ejpam-5268	148	2	(	(	PUNCT
ejpam-5268	148	3	txsk+1,txsk+1,txsk+1−1	txsk+1,txsk+1,txsk+1−1	PROPN
ejpam-5268	148	4	)	)	PUNCT
ejpam-5268	149	1	+	+	NOUN
ejpam-5268	149	2	1	1	X
ejpam-5268	149	3	.	.	X
ejpam-5268	149	4	letting	let	VERB
ejpam-5268	149	5	k	k	X
ejpam-5268	149	6	→	→	SYM
ejpam-5268	149	7	∞	∞	PROPN
ejpam-5268	149	8	in	in	ADP
ejpam-5268	149	9	the	the	DET
ejpam-5268	149	10	above	above	ADJ
ejpam-5268	149	11	inequality	inequality	NOUN
ejpam-5268	149	12	and	and	CCONJ
ejpam-5268	149	13	utilizing	utilize	VERB
ejpam-5268	149	14	proposition	proposition	NOUN
ejpam-5268	149	15	1	1	NUM
ejpam-5268	149	16	,	,	PUNCT
ejpam-5268	149	17	we	we	PRON
ejpam-5268	149	18	get	get	VERB
ejpam-5268	149	19	s	s	NOUN
ejpam-5268	149	20	(	(	PUNCT
ejpam-5268	149	21	txsk+1,txsk+1,txsk	txsk+1,txsk+1,txsk	INTJ
ejpam-5268	149	22	)	)	PUNCT
ejpam-5268	150	1	=	=	SYM
ejpam-5268	150	2	1	1	X
ejpam-5268	150	3	.	.	X
ejpam-5268	150	4	utilizing	utilize	VERB
ejpam-5268	150	5	the	the	DET
ejpam-5268	150	6	triangle	triangle	NOUN
ejpam-5268	150	7	inequality	inequality	NOUN
ejpam-5268	150	8	,	,	PUNCT
ejpam-5268	150	9	we	we	PRON
ejpam-5268	150	10	obtain	obtain	VERB
ejpam-5268	150	11	1	1	NUM
ejpam-5268	150	12	<	<	X
ejpam-5268	150	13	s	s	X
ejpam-5268	150	14	(	(	PUNCT
ejpam-5268	150	15	txsk+1,txsk+1,txsk	txsk+1,txsk+1,txsk	NOUN
ejpam-5268	150	16	)	)	PUNCT
ejpam-5268	150	17	≤	≤	NOUN
ejpam-5268	150	18	s	s	PART
ejpam-5268	150	19	(	(	PUNCT
ejpam-5268	150	20	txsk+1−1,txsk+1−1,txsk−1	txsk+1−1,txsk+1−1,txsk−1	PROPN
ejpam-5268	150	21	)	)	PUNCT
ejpam-5268	150	22	≤	≤	PUNCT
ejpam-5268	151	1	2s	2s	NUM
ejpam-5268	151	2	(	(	PUNCT
ejpam-5268	151	3	txsk+1−1,txsk+1−1,txsk	txsk+1−1,txsk+1−1,txsk	NOUN
ejpam-5268	151	4	)	)	PUNCT
ejpam-5268	152	1	+	+	NUM
ejpam-5268	152	2	s(txsk−1,txsk−1,txsk	s(txsk−1,txsk−1,txsk	NOUN
ejpam-5268	152	3	)	)	PUNCT
ejpam-5268	152	4	≤	≤	NOUN
ejpam-5268	152	5	2	2	NUM
ejpam-5268	152	6	+	+	NUM
ejpam-5268	152	7	s(txsk−1,txsk−1,txsk	s(txsk−1,txsk−1,txsk	NOUN
ejpam-5268	152	8	)	)	PUNCT
ejpam-5268	152	9	.	.	PUNCT
ejpam-5268	153	1	letting	let	VERB
ejpam-5268	153	2	k	k	PRON
ejpam-5268	153	3	→	→	PUNCT
ejpam-5268	153	4	+	+	NUM
ejpam-5268	153	5	∞	∞	PROPN
ejpam-5268	153	6	in	in	ADP
ejpam-5268	153	7	the	the	DET
ejpam-5268	153	8	above	above	ADJ
ejpam-5268	153	9	inequality	inequality	NOUN
ejpam-5268	153	10	and	and	CCONJ
ejpam-5268	153	11	utilizing	utilize	VERB
ejpam-5268	153	12	proposition	proposition	NOUN
ejpam-5268	153	13	1	1	NUM
ejpam-5268	153	14	,	,	PUNCT
ejpam-5268	153	15	we	we	PRON
ejpam-5268	153	16	obtain	obtain	VERB
ejpam-5268	153	17	lim	lim	PROPN
ejpam-5268	153	18	k→+∞	k→+∞	PROPN
ejpam-5268	153	19	s	s	PROPN
ejpam-5268	153	20	(	(	PUNCT
ejpam-5268	153	21	txsk+1−1,txsk+1−1,txsk−1	txsk+1−1,txsk+1−1,txsk−1	PROPN
ejpam-5268	153	22	)	)	PUNCT
ejpam-5268	154	1	=	=	SYM
ejpam-5268	154	2	1	1	X
ejpam-5268	154	3	.	.	PUNCT
ejpam-5268	154	4	(	(	PUNCT
ejpam-5268	154	5	2	2	X
ejpam-5268	154	6	)	)	PUNCT
ejpam-5268	154	7	again	again	ADV
ejpam-5268	154	8	,	,	PUNCT
ejpam-5268	154	9	due	due	ADP
ejpam-5268	154	10	to	to	ADP
ejpam-5268	154	11	the	the	DET
ejpam-5268	154	12	triangle	triangle	NOUN
ejpam-5268	154	13	inequality	inequality	NOUN
ejpam-5268	154	14	yields∣∣s	yields∣∣s	PROPN
ejpam-5268	154	15	(	(	PUNCT
ejpam-5268	154	16	txsk+1−1,txsk+1−1,txsk	txsk+1−1,txsk+1−1,txsk	NOUN
ejpam-5268	154	17	)	)	PUNCT
ejpam-5268	155	1	−	−	PROPN
ejpam-5268	155	2	s	s	PART
ejpam-5268	155	3	(	(	PUNCT
ejpam-5268	155	4	txsk	txsk	NOUN
ejpam-5268	155	5	,	,	PUNCT
ejpam-5268	155	6	txsk	txsk	NOUN
ejpam-5268	155	7	,	,	PUNCT
ejpam-5268	155	8	txsk+1	txsk+1	NOUN
ejpam-5268	155	9	)	)	PUNCT
ejpam-5268	155	10	∣∣	∣∣	NUM
ejpam-5268	155	11	≤	≤	PROPN
ejpam-5268	155	12	s	s	PART
ejpam-5268	155	13	(	(	PUNCT
ejpam-5268	155	14	txsk+1−1,txsk+1−1,txsk+1	txsk+1−1,txsk+1−1,txsk+1	NOUN
ejpam-5268	155	15	)	)	PUNCT
ejpam-5268	155	16	.	.	PUNCT
ejpam-5268	156	1	permitting	permit	VERB
ejpam-5268	156	2	k	k	X
ejpam-5268	156	3	→	→	PUNCT
ejpam-5268	156	4	+	+	ADJ
ejpam-5268	156	5	∞	∞	PROPN
ejpam-5268	156	6	in	in	ADP
ejpam-5268	156	7	the	the	DET
ejpam-5268	156	8	above	above	ADJ
ejpam-5268	156	9	inequality	inequality	NOUN
ejpam-5268	156	10	and	and	CCONJ
ejpam-5268	156	11	utilizing	utilize	VERB
ejpam-5268	156	12	proposition	proposition	NOUN
ejpam-5268	156	13	1	1	NUM
ejpam-5268	156	14	,	,	PUNCT
ejpam-5268	156	15	we	we	PRON
ejpam-5268	156	16	obtain	obtain	VERB
ejpam-5268	156	17	lim	lim	PROPN
ejpam-5268	156	18	k→+∞	k→+∞	PROPN
ejpam-5268	156	19	s	s	PROPN
ejpam-5268	156	20	(	(	PUNCT
ejpam-5268	156	21	txsk+1−1,txsk+1−1,txsk	txsk+1−1,txsk+1−1,txsk	NOUN
ejpam-5268	156	22	)	)	PUNCT
ejpam-5268	156	23	=	=	PUNCT
ejpam-5268	157	1	1	1	X
ejpam-5268	157	2	.	.	PUNCT
ejpam-5268	157	3	(	(	PUNCT
ejpam-5268	157	4	3	3	NUM
ejpam-5268	157	5	)	)	PUNCT
ejpam-5268	157	6	via	via	ADP
ejpam-5268	157	7	similar	similar	ADJ
ejpam-5268	157	8	method	method	NOUN
ejpam-5268	157	9	,	,	PUNCT
ejpam-5268	157	10	we	we	PRON
ejpam-5268	157	11	get∣∣s	get∣∣s	NOUN
ejpam-5268	157	12	(	(	PUNCT
ejpam-5268	157	13	txsk−1,txsk−1,txsk+1	txsk−1,txsk−1,txsk+1	PROPN
ejpam-5268	157	14	)	)	PUNCT
ejpam-5268	157	15	−	−	PROPN
ejpam-5268	157	16	s	s	X
ejpam-5268	157	17	(	(	PUNCT
ejpam-5268	157	18	txsk−1,txsk−1,txsk+1−1	txsk−1,txsk−1,txsk+1−1	ADV
ejpam-5268	157	19	)	)	PUNCT
ejpam-5268	157	20	∣∣	∣∣	X
ejpam-5268	157	21	≤	≤	X
ejpam-5268	157	22	s	s	PART
ejpam-5268	157	23	(	(	PUNCT
ejpam-5268	157	24	txsk+1	txsk+1	PRON
ejpam-5268	157	25	,	,	PUNCT
ejpam-5268	157	26	txsk+1	txsk+1	PRON
ejpam-5268	157	27	,	,	PUNCT
ejpam-5268	157	28	txsk+1−1	txsk+1−1	NOUN
ejpam-5268	157	29	)	)	PUNCT
ejpam-5268	157	30	.	.	PUNCT
ejpam-5268	158	1	permitting	permit	VERB
ejpam-5268	158	2	k	k	PROPN
ejpam-5268	158	3	→	→	SYM
ejpam-5268	158	4	∞	∞	PROPN
ejpam-5268	158	5	in	in	ADP
ejpam-5268	158	6	the	the	DET
ejpam-5268	158	7	above	above	ADJ
ejpam-5268	158	8	inequality	inequality	NOUN
ejpam-5268	158	9	and	and	CCONJ
ejpam-5268	158	10	utilizing	utilize	VERB
ejpam-5268	158	11	proposition	proposition	NOUN
ejpam-5268	158	12	1	1	NUM
ejpam-5268	158	13	,	,	PUNCT
ejpam-5268	158	14	we	we	PRON
ejpam-5268	158	15	get	get	VERB
ejpam-5268	158	16	lim	lim	PROPN
ejpam-5268	158	17	k→+∞	k→+∞	PROPN
ejpam-5268	158	18	s	s	PROPN
ejpam-5268	158	19	(	(	PUNCT
ejpam-5268	158	20	txsk−1,txsk−1,txsk+1	txsk−1,txsk−1,txsk+1	NOUN
ejpam-5268	158	21	)	)	PUNCT
ejpam-5268	158	22	=	=	SYM
ejpam-5268	159	1	1	1	X
ejpam-5268	159	2	.	.	PUNCT
ejpam-5268	159	3	(	(	PUNCT
ejpam-5268	159	4	4	4	X
ejpam-5268	159	5	)	)	PUNCT
ejpam-5268	159	6	now	now	ADV
ejpam-5268	159	7	,	,	PUNCT
ejpam-5268	159	8	utilizing	utilize	VERB
ejpam-5268	159	9	equations	equation	NOUN
ejpam-5268	159	10	2	2	NUM
ejpam-5268	159	11	,	,	PUNCT
ejpam-5268	159	12	3	3	NUM
ejpam-5268	159	13	,	,	PUNCT
ejpam-5268	159	14	4	4	NUM
ejpam-5268	159	15	and	and	CCONJ
ejpam-5268	159	16	proposition	proposition	NOUN
ejpam-5268	159	17	1	1	NUM
ejpam-5268	159	18	,	,	PUNCT
ejpam-5268	159	19	we	we	PRON
ejpam-5268	159	20	obtain	obtain	VERB
ejpam-5268	159	21	m1	m1	PROPN
ejpam-5268	159	22	(	(	PUNCT
ejpam-5268	159	23	f	f	X
ejpam-5268	159	24	,	,	PUNCT
ejpam-5268	159	25	t	t	PROPN
ejpam-5268	159	26	,	,	PUNCT
ejpam-5268	159	27	xsk+1−1	xsk+1−1	PROPN
ejpam-5268	159	28	,	,	PUNCT
ejpam-5268	159	29	xsk+1−1	xsk+1−1	PROPN
ejpam-5268	159	30	,	,	PUNCT
ejpam-5268	159	31	xsk−1	xsk−1	PROPN
ejpam-5268	159	32	)	)	PUNCT
ejpam-5268	160	1	=	=	PUNCT
ejpam-5268	160	2	1	1	X
ejpam-5268	160	3	.	.	PUNCT
ejpam-5268	160	4	(	(	PUNCT
ejpam-5268	160	5	5	5	X
ejpam-5268	160	6	)	)	PUNCT
ejpam-5268	160	7	using	use	VERB
ejpam-5268	160	8	equations	equation	NOUN
ejpam-5268	160	9	1	1	NUM
ejpam-5268	160	10	,	,	PUNCT
ejpam-5268	160	11	2	2	NUM
ejpam-5268	160	12	,	,	PUNCT
ejpam-5268	160	13	3	3	NUM
ejpam-5268	160	14	,	,	PUNCT
ejpam-5268	160	15	4	4	NUM
ejpam-5268	160	16	,	,	PUNCT
ejpam-5268	160	17	5	5	NUM
ejpam-5268	160	18	and	and	CCONJ
ejpam-5268	160	19	the	the	DET
ejpam-5268	160	20	condition	condition	NOUN
ejpam-5268	160	21	(	(	PUNCT
ejpam-5268	160	22	ξ3	ξ3	NOUN
ejpam-5268	160	23	)	)	PUNCT
ejpam-5268	160	24	of	of	ADP
ejpam-5268	160	25	definition	definition	NOUN
ejpam-5268	160	26	4	4	NUM
ejpam-5268	160	27	,	,	PUNCT
ejpam-5268	160	28	we	we	PRON
ejpam-5268	160	29	obtain	obtain	VERB
ejpam-5268	160	30	0	0	NUM
ejpam-5268	160	31	≤	≤	NOUN
ejpam-5268	160	32	lim	lim	PROPN
ejpam-5268	160	33	k→+∞	k→+∞	PROPN
ejpam-5268	160	34	sup	sup	NOUN
ejpam-5268	160	35	ξ(s	ξ(s	PROPN
ejpam-5268	160	36	(	(	PUNCT
ejpam-5268	160	37	txsk+1,txsk+1,txsk	txsk+1,txsk+1,txsk	PROPN
ejpam-5268	160	38	)	)	PUNCT
ejpam-5268	160	39	,	,	PUNCT
ejpam-5268	160	40	m1(f	m1(f	X
ejpam-5268	160	41	,	,	PUNCT
ejpam-5268	160	42	t	t	PROPN
ejpam-5268	160	43	,	,	PUNCT
ejpam-5268	160	44	xsk+1−1,xsk+1−1,xsk−1	xsk+1−1,xsk+1−1,xsk−1	PROPN
ejpam-5268	160	45	)	)	PUNCT
ejpam-5268	160	46	)	)	PUNCT
ejpam-5268	161	1	<	<	X
ejpam-5268	161	2	0	0	NUM
ejpam-5268	161	3	,	,	PUNCT
ejpam-5268	161	4	this	this	PRON
ejpam-5268	161	5	is	be	AUX
ejpam-5268	161	6	contradiction	contradiction	NOUN
ejpam-5268	161	7	.	.	PUNCT
ejpam-5268	162	1	this	this	PRON
ejpam-5268	162	2	completes	complete	VERB
ejpam-5268	162	3	the	the	DET
ejpam-5268	162	4	evidence	evidence	NOUN
ejpam-5268	162	5	.	.	PUNCT
ejpam-5268	163	1	proposition	proposition	NOUN
ejpam-5268	163	2	3	3	NUM
ejpam-5268	163	3	.	.	PUNCT
ejpam-5268	164	1	if	if	SCONJ
ejpam-5268	164	2	f	f	PROPN
ejpam-5268	164	3	,	,	PUNCT
ejpam-5268	164	4	t	t	X
ejpam-5268	164	5	:	:	PUNCT
ejpam-5268	164	6	(	(	PUNCT
ejpam-5268	164	7	x	x	X
ejpam-5268	164	8	,	,	PUNCT
ejpam-5268	164	9	s	s	PART
ejpam-5268	164	10	)	)	PUNCT
ejpam-5268	164	11	→	→	SYM
ejpam-5268	164	12	(	(	PUNCT
ejpam-5268	164	13	x	x	X
ejpam-5268	164	14	,	,	PUNCT
ejpam-5268	164	15	s	s	PART
ejpam-5268	164	16	)	)	PUNCT
ejpam-5268	164	17	are	be	AUX
ejpam-5268	164	18	self	self	NOUN
ejpam-5268	164	19	mappings	mapping	NOUN
ejpam-5268	164	20	and	and	CCONJ
ejpam-5268	164	21	f	f	PROPN
ejpam-5268	164	22	is	be	AUX
ejpam-5268	164	23	t	t	PROPN
ejpam-5268	164	24	-	-	PUNCT
ejpam-5268	164	25	non	non	ADJ
ejpam-5268	164	26	-	-	ADJ
ejpam-5268	164	27	decreasing	decrease	VERB
ejpam-5268	164	28	ins	in	NOUN
ejpam-5268	164	29	-	-	ADJ
ejpam-5268	164	30	metric	metric	ADJ
ejpam-5268	164	31	(	(	PUNCT
ejpam-5268	164	32	x	x	NOUN
ejpam-5268	164	33	,	,	PUNCT
ejpam-5268	164	34	s	s	PART
ejpam-5268	164	35	)	)	PUNCT
ejpam-5268	164	36	and	and	CCONJ
ejpam-5268	164	37	satisfies	satisfy	VERB
ejpam-5268	164	38	the	the	DET
ejpam-5268	164	39	cases	case	NOUN
ejpam-5268	164	40	(	(	PUNCT
ejpam-5268	164	41	(	(	PUNCT
ejpam-5268	164	42	i	i	NOUN
ejpam-5268	164	43	)	)	PUNCT
ejpam-5268	164	44	&	&	CCONJ
ejpam-5268	164	45	(	(	PUNCT
ejpam-5268	164	46	ii	ii	NOUN
ejpam-5268	164	47	)	)	PUNCT
ejpam-5268	164	48	)	)	PUNCT
ejpam-5268	164	49	of	of	ADP
ejpam-5268	164	50	proposition	proposition	NOUN
ejpam-5268	164	51	1	1	NUM
ejpam-5268	164	52	.	.	PUNCT
ejpam-5268	165	1	if	if	SCONJ
ejpam-5268	165	2	xs	xs	PROPN
ejpam-5268	165	3	is	be	AUX
ejpam-5268	165	4	sequence	sequence	NOUN
ejpam-5268	165	5	(	(	PUNCT
ejpam-5268	165	6	s.	s.	PROPN
ejpam-5268	165	7	t	t	PROPN
ejpam-5268	165	8	)	)	PUNCT
ejpam-5268	165	9	,	,	PUNCT
ejpam-5268	165	10	txs+1	txs+1	PROPN
ejpam-5268	165	11	=	=	SYM
ejpam-5268	165	12	fxs	fxs	PROPN
ejpam-5268	165	13	,	,	PUNCT
ejpam-5268	165	14	&	&	CCONJ
ejpam-5268	165	15	txs+1	txs+1	PROPN
ejpam-5268	165	16	̸=	̸=	PROPN
ejpam-5268	165	17	txs	txs	PROPN
ejpam-5268	165	18	,	,	PUNCT
ejpam-5268	165	19	∀	∀	NOUN
ejpam-5268	165	20	s	s	NOUN
ejpam-5268	165	21	∈	∈	PROPN
ejpam-5268	165	22	n	n	CCONJ
ejpam-5268	165	23	,	,	PUNCT
ejpam-5268	165	24	then	then	ADV
ejpam-5268	165	25	txs	txs	NOUN
ejpam-5268	165	26	is	be	AUX
ejpam-5268	165	27	cauchy	cauchy	ADJ
ejpam-5268	165	28	sequence	sequence	NOUN
ejpam-5268	165	29	.	.	PUNCT
ejpam-5268	166	1	n.	n.	PROPN
ejpam-5268	166	2	a.	a.	PROPN
ejpam-5268	166	3	majid	majid	PROPN
ejpam-5268	166	4	et	et	PROPN
ejpam-5268	166	5	al	al	PROPN
ejpam-5268	166	6	.	.	PUNCT
ejpam-5268	166	7	/	/	SYM
ejpam-5268	166	8	eur	eur	PROPN
ejpam-5268	166	9	.	.	PUNCT
ejpam-5268	167	1	j.	j.	PROPN
ejpam-5268	167	2	pure	pure	PROPN
ejpam-5268	167	3	appl	appl	PROPN
ejpam-5268	167	4	.	.	PROPN
ejpam-5268	167	5	math	math	PROPN
ejpam-5268	167	6	,	,	PUNCT
ejpam-5268	167	7	17	17	NUM
ejpam-5268	167	8	(	(	PUNCT
ejpam-5268	167	9	3	3	NUM
ejpam-5268	167	10	)	)	PUNCT
ejpam-5268	167	11	(	(	PUNCT
ejpam-5268	167	12	2024	2024	NUM
ejpam-5268	167	13	)	)	PUNCT
ejpam-5268	167	14	,	,	PUNCT
ejpam-5268	167	15	1877	1877	NUM
ejpam-5268	167	16	-	-	SYM
ejpam-5268	167	17	1893	1893	NUM
ejpam-5268	167	18	1884	1884	NUM
ejpam-5268	167	19	proof	proof	NOUN
ejpam-5268	167	20	.	.	PUNCT
ejpam-5268	168	1	presume	presume	VERB
ejpam-5268	168	2	as	as	ADP
ejpam-5268	168	3	=	=	PRON
ejpam-5268	168	4	sup	sup	X
ejpam-5268	168	5	{	{	PUNCT
ejpam-5268	168	6	s	s	X
ejpam-5268	168	7	(	(	PUNCT
ejpam-5268	168	8	txu	txu	PROPN
ejpam-5268	168	9	,	,	PUNCT
ejpam-5268	168	10	txu	txu	PROPN
ejpam-5268	168	11	,	,	PUNCT
ejpam-5268	168	12	txv	txv	NOUN
ejpam-5268	168	13	)	)	PUNCT
ejpam-5268	168	14	:	:	PUNCT
ejpam-5268	169	1	u	u	NOUN
ejpam-5268	169	2	,	,	PUNCT
ejpam-5268	169	3	v	v	PRON
ejpam-5268	169	4	≥	≥	NOUN
ejpam-5268	169	5	s	s	PART
ejpam-5268	169	6	}	}	PUNCT
ejpam-5268	169	7	.	.	PUNCT
ejpam-5268	170	1	from	from	ADP
ejpam-5268	170	2	proposition	proposition	NOUN
ejpam-5268	170	3	2	2	NUM
ejpam-5268	170	4	,	,	PUNCT
ejpam-5268	170	5	we	we	PRON
ejpam-5268	170	6	know	know	VERB
ejpam-5268	170	7	that	that	SCONJ
ejpam-5268	170	8	the	the	DET
ejpam-5268	170	9	sequence	sequence	NOUN
ejpam-5268	170	10	txs	txs	NOUN
ejpam-5268	170	11	is	be	AUX
ejpam-5268	170	12	bounded	bound	VERB
ejpam-5268	170	13	.	.	PUNCT
ejpam-5268	171	1	hence	hence	ADV
ejpam-5268	171	2	,	,	PUNCT
ejpam-5268	171	3	as	as	ADP
ejpam-5268	171	4	<	<	X
ejpam-5268	171	5	∞	∞	PROPN
ejpam-5268	171	6	,	,	PUNCT
ejpam-5268	171	7	for	for	ADP
ejpam-5268	171	8	all	all	DET
ejpam-5268	171	9	s	s	PART
ejpam-5268	171	10	∈	∈	PROPN
ejpam-5268	171	11	n	n	PRON
ejpam-5268	171	12	which	which	PRON
ejpam-5268	171	13	implies	imply	VERB
ejpam-5268	171	14	that	that	SCONJ
ejpam-5268	171	15	,	,	PUNCT
ejpam-5268	171	16	as	as	SCONJ
ejpam-5268	171	17	is	be	AUX
ejpam-5268	171	18	bounded	bound	VERB
ejpam-5268	171	19	and	and	CCONJ
ejpam-5268	171	20	monotonically	monotonically	ADV
ejpam-5268	171	21	decreasing	decrease	VERB
ejpam-5268	171	22	sequence	sequence	NOUN
ejpam-5268	171	23	,	,	PUNCT
ejpam-5268	171	24	thus	thus	ADV
ejpam-5268	171	25	is	be	AUX
ejpam-5268	171	26	convergent	convergent	ADJ
ejpam-5268	171	27	.	.	PUNCT
ejpam-5268	172	1	consequently	consequently	ADV
ejpam-5268	172	2	,	,	PUNCT
ejpam-5268	172	3	∃	∃	PROPN
ejpam-5268	172	4	a	a	DET
ejpam-5268	172	5	≥	≥	NOUN
ejpam-5268	172	6	0	0	NUM
ejpam-5268	172	7	were	be	AUX
ejpam-5268	172	8	lims→+∞as	lims→+∞as	X
ejpam-5268	172	9	=	=	PUNCT
ejpam-5268	172	10	a.	a.	NOUN
ejpam-5268	172	11	next	next	ADV
ejpam-5268	172	12	establish	establish	VERB
ejpam-5268	172	13	a	a	DET
ejpam-5268	172	14	=	=	NOUN
ejpam-5268	172	15	0	0	NUM
ejpam-5268	172	16	,	,	PUNCT
ejpam-5268	172	17	to	to	PART
ejpam-5268	172	18	show	show	VERB
ejpam-5268	172	19	that	that	SCONJ
ejpam-5268	172	20	txs	txs	NOUN
ejpam-5268	172	21	is	be	AUX
ejpam-5268	172	22	a	a	DET
ejpam-5268	172	23	cauchy	cauchy	ADJ
ejpam-5268	172	24	sequence	sequence	NOUN
ejpam-5268	172	25	.	.	PUNCT
ejpam-5268	173	1	assume	assume	VERB
ejpam-5268	173	2	a	a	DET
ejpam-5268	173	3	>	>	X
ejpam-5268	173	4	0	0	NUM
ejpam-5268	173	5	.	.	PUNCT
ejpam-5268	174	1	via	via	ADP
ejpam-5268	174	2	definition	definition	NOUN
ejpam-5268	174	3	of	of	ADP
ejpam-5268	174	4	as	as	ADP
ejpam-5268	174	5	,	,	PUNCT
ejpam-5268	174	6	∀	∀	X
ejpam-5268	174	7	k	k	NOUN
ejpam-5268	174	8	∈	∈	PROPN
ejpam-5268	174	9	n	n	CCONJ
ejpam-5268	174	10	∃	∃	PROPN
ejpam-5268	174	11	sk	sk	NOUN
ejpam-5268	174	12	,	,	PUNCT
ejpam-5268	174	13	rk	rk	NOUN
ejpam-5268	174	14	∈	∈	PROPN
ejpam-5268	174	15	n	n	CCONJ
ejpam-5268	174	16	,	,	PUNCT
ejpam-5268	174	17	(	(	PUNCT
ejpam-5268	174	18	s.t	s.t	PROPN
ejpam-5268	174	19	)	)	PUNCT
ejpam-5268	174	20	,	,	PUNCT
ejpam-5268	174	21	rk	rk	PROPN
ejpam-5268	174	22	>	>	X
ejpam-5268	174	23	sk	sk	PROPN
ejpam-5268	174	24	≥	≥	PROPN
ejpam-5268	174	25	kand	kand	PROPN
ejpam-5268	174	26	k	k	PROPN
ejpam-5268	174	27	ak−1	ak−1	PROPN
ejpam-5268	175	1	k	k	PROPN
ejpam-5268	175	2	<	<	X
ejpam-5268	175	3	s	s	X
ejpam-5268	175	4	(	(	PUNCT
ejpam-5268	175	5	txrk	txrk	ADJ
ejpam-5268	175	6	,	,	PUNCT
ejpam-5268	175	7	txrk	txrk	ADJ
ejpam-5268	175	8	,	,	PUNCT
ejpam-5268	175	9	txsk	txsk	NOUN
ejpam-5268	175	10	)	)	PUNCT
ejpam-5268	175	11	≤	≤	PROPN
ejpam-5268	176	1	ak	ak	PROPN
ejpam-5268	176	2	.	.	PROPN
ejpam-5268	177	1	therefore	therefore	ADV
ejpam-5268	177	2	,	,	PUNCT
ejpam-5268	177	3	lim	lim	PROPN
ejpam-5268	177	4	k→+∞	k→+∞	PROPN
ejpam-5268	177	5	s	s	PART
ejpam-5268	177	6	(	(	PUNCT
ejpam-5268	177	7	txrk	txrk	ADJ
ejpam-5268	177	8	,	,	PUNCT
ejpam-5268	177	9	txrk	txrk	ADJ
ejpam-5268	177	10	,	,	PUNCT
ejpam-5268	177	11	txsk	txsk	NOUN
ejpam-5268	177	12	)	)	PUNCT
ejpam-5268	178	1	=	=	SYM
ejpam-5268	178	2	a.	a.	NOUN
ejpam-5268	178	3	(	(	PUNCT
ejpam-5268	178	4	6	6	NUM
ejpam-5268	178	5	)	)	PUNCT
ejpam-5268	178	6	utilizing	utilize	VERB
ejpam-5268	178	7	triangle	triangle	NOUN
ejpam-5268	178	8	inequality	inequality	NOUN
ejpam-5268	178	9	,	,	PUNCT
ejpam-5268	178	10	lemma	lemma	PROPN
ejpam-5268	178	11	1	1	NUM
ejpam-5268	178	12	and	and	CCONJ
ejpam-5268	178	13	proposition	proposition	NOUN
ejpam-5268	178	14	2	2	NUM
ejpam-5268	178	15	,	,	PUNCT
ejpam-5268	178	16	we	we	PRON
ejpam-5268	178	17	obtain	obtain	VERB
ejpam-5268	178	18	:	:	PUNCT
ejpam-5268	178	19	s	s	X
ejpam-5268	178	20	(	(	PUNCT
ejpam-5268	178	21	txrk	txrk	ADJ
ejpam-5268	178	22	,	,	PUNCT
ejpam-5268	178	23	txrk	txrk	ADJ
ejpam-5268	178	24	,	,	PUNCT
ejpam-5268	178	25	txsk	txsk	NOUN
ejpam-5268	178	26	)	)	PUNCT
ejpam-5268	178	27	≤	≤	NUM
ejpam-5268	179	1	s	s	PART
ejpam-5268	179	2	(	(	PUNCT
ejpam-5268	179	3	txrk−1	txrk−1	PROPN
ejpam-5268	179	4	,	,	PUNCT
ejpam-5268	179	5	txrk−1	txrk−1	PRON
ejpam-5268	179	6	,	,	PUNCT
ejpam-5268	179	7	txsk−1	txsk−1	PROPN
ejpam-5268	179	8	)	)	PUNCT
ejpam-5268	179	9	≤	≤	PUNCT
ejpam-5268	180	1	2s	2s	NUM
ejpam-5268	180	2	(	(	PUNCT
ejpam-5268	180	3	txrk−1	txrk−1	NOUN
ejpam-5268	180	4	,	,	PUNCT
ejpam-5268	180	5	txrk−1	txrk−1	PRON
ejpam-5268	180	6	,	,	PUNCT
ejpam-5268	180	7	txrk	txrk	VERB
ejpam-5268	180	8	)	)	PUNCT
ejpam-5268	181	1	+	+	CCONJ
ejpam-5268	181	2	2s	2s	NUM
ejpam-5268	181	3	(	(	PUNCT
ejpam-5268	181	4	txsk	txsk	NOUN
ejpam-5268	181	5	,	,	PUNCT
ejpam-5268	181	6	txsk	txsk	NOUN
ejpam-5268	181	7	,	,	PUNCT
ejpam-5268	181	8	txsk−1	txsk−1	PROPN
ejpam-5268	181	9	)	)	PUNCT
ejpam-5268	182	1	+	+	SYM
ejpam-5268	182	2	s	s	X
ejpam-5268	182	3	(	(	PUNCT
ejpam-5268	182	4	txrk	txrk	NOUN
ejpam-5268	182	5	,	,	PUNCT
ejpam-5268	182	6	txrk	txrk	ADJ
ejpam-5268	182	7	,	,	PUNCT
ejpam-5268	182	8	txsk	txsk	NOUN
ejpam-5268	182	9	)	)	PUNCT
ejpam-5268	182	10	.	.	PUNCT
ejpam-5268	183	1	utilizing	utilize	VERB
ejpam-5268	183	2	proposition	proposition	NOUN
ejpam-5268	183	3	2	2	NUM
ejpam-5268	183	4	,	,	PUNCT
ejpam-5268	183	5	and	and	CCONJ
ejpam-5268	183	6	equation	equation	NOUN
ejpam-5268	183	7	6	6	NUM
ejpam-5268	183	8	and	and	CCONJ
ejpam-5268	183	9	letting	let	VERB
ejpam-5268	183	10	k	k	X
ejpam-5268	183	11	→	→	SYM
ejpam-5268	183	12	+	+	PROPN
ejpam-5268	183	13	∞	∞	PROPN
ejpam-5268	183	14	,	,	PUNCT
ejpam-5268	183	15	we	we	PRON
ejpam-5268	183	16	get	get	VERB
ejpam-5268	183	17	lim	lim	PROPN
ejpam-5268	183	18	k→+∞	k→+∞	PROPN
ejpam-5268	183	19	s	s	PROPN
ejpam-5268	183	20	(	(	PUNCT
ejpam-5268	183	21	txrk−1	txrk−1	PROPN
ejpam-5268	183	22	,	,	PUNCT
ejpam-5268	183	23	txrk−1	txrk−1	PRON
ejpam-5268	183	24	,	,	PUNCT
ejpam-5268	183	25	txsk−1	txsk−1	PROPN
ejpam-5268	183	26	)	)	PUNCT
ejpam-5268	183	27	=	=	SYM
ejpam-5268	184	1	a.	a.	NOUN
ejpam-5268	184	2	(	(	PUNCT
ejpam-5268	184	3	7	7	NUM
ejpam-5268	184	4	)	)	PUNCT
ejpam-5268	184	5	similarly	similarly	ADV
ejpam-5268	184	6	,	,	PUNCT
ejpam-5268	184	7	we	we	PRON
ejpam-5268	184	8	can	can	AUX
ejpam-5268	184	9	prove	prove	VERB
ejpam-5268	184	10	that	that	SCONJ
ejpam-5268	184	11	lim	lim	PROPN
ejpam-5268	184	12	k→+∞	k→+∞	PROPN
ejpam-5268	184	13	s	s	PROPN
ejpam-5268	184	14	(	(	PUNCT
ejpam-5268	184	15	txrk−1	txrk−1	PROPN
ejpam-5268	184	16	,	,	PUNCT
ejpam-5268	184	17	txrk−1	txrk−1	PRON
ejpam-5268	184	18	,	,	PUNCT
ejpam-5268	184	19	txsk	txsk	NOUN
ejpam-5268	184	20	)	)	PUNCT
ejpam-5268	185	1	=	=	PUNCT
ejpam-5268	185	2	a.	a.	NOUN
ejpam-5268	185	3	(	(	PUNCT
ejpam-5268	185	4	8)	8)	NUM
ejpam-5268	185	5	and	and	CCONJ
ejpam-5268	185	6	lim	lim	PROPN
ejpam-5268	186	1	k→+∞	k→+∞	PROPN
ejpam-5268	186	2	s	s	PROPN
ejpam-5268	186	3	(	(	PUNCT
ejpam-5268	186	4	txsk−1	txsk−1	PROPN
ejpam-5268	186	5	,	,	PUNCT
ejpam-5268	186	6	txsk−1	txsk−1	NUM
ejpam-5268	186	7	,	,	PUNCT
ejpam-5268	186	8	txrk	txrk	NOUN
ejpam-5268	186	9	)	)	PUNCT
ejpam-5268	186	10	=	=	SYM
ejpam-5268	186	11	a.	a.	NOUN
ejpam-5268	186	12	(	(	PUNCT
ejpam-5268	186	13	9	9	X
ejpam-5268	186	14	)	)	PUNCT
ejpam-5268	186	15	utilizing	utilize	VERB
ejpam-5268	186	16	propositions	proposition	NOUN
ejpam-5268	186	17	2	2	NUM
ejpam-5268	186	18	and	and	CCONJ
ejpam-5268	186	19	equations	equation	NOUN
ejpam-5268	186	20	7	7	NUM
ejpam-5268	186	21	,	,	PUNCT
ejpam-5268	186	22	8	8	NUM
ejpam-5268	186	23	,	,	PUNCT
ejpam-5268	186	24	9	9	NUM
ejpam-5268	186	25	,	,	PUNCT
ejpam-5268	186	26	we	we	PRON
ejpam-5268	186	27	obtain	obtain	VERB
ejpam-5268	186	28	lim	lim	PROPN
ejpam-5268	186	29	k→+∞	k→+∞	PROPN
ejpam-5268	186	30	m1	m1	PROPN
ejpam-5268	186	31	(	(	PUNCT
ejpam-5268	186	32	f	f	X
ejpam-5268	186	33	,	,	PUNCT
ejpam-5268	186	34	t	t	PROPN
ejpam-5268	186	35	,	,	PUNCT
ejpam-5268	186	36	xrk−1,xrk−1,xsk−1	xrk−1,xrk−1,xsk−1	X
ejpam-5268	186	37	)	)	PUNCT
ejpam-5268	186	38	=	=	SYM
ejpam-5268	186	39	a.	a.	NOUN
ejpam-5268	186	40	(	(	PUNCT
ejpam-5268	186	41	10	10	NUM
ejpam-5268	186	42	)	)	PUNCT
ejpam-5268	186	43	utilizing	utilize	VERB
ejpam-5268	186	44	the	the	DET
ejpam-5268	186	45	condition	condition	NOUN
ejpam-5268	186	46	of	of	ADP
ejpam-5268	186	47	simulation	simulation	NOUN
ejpam-5268	186	48	mapping	mapping	PROPN
ejpam-5268	186	49	(	(	PUNCT
ejpam-5268	186	50	ξ3	ξ3	NOUN
ejpam-5268	186	51	)	)	PUNCT
ejpam-5268	186	52	and	and	CCONJ
ejpam-5268	186	53	1,6,10	1,6,10	NUM
ejpam-5268	186	54	,	,	PUNCT
ejpam-5268	186	55	we	we	PRON
ejpam-5268	186	56	get	get	VERB
ejpam-5268	186	57	0	0	NUM
ejpam-5268	186	58	≤	≤	NOUN
ejpam-5268	186	59	lim	lim	PROPN
ejpam-5268	186	60	k→+∞	k→+∞	PROPN
ejpam-5268	186	61	supξ(s	supξ(s	PROPN
ejpam-5268	186	62	(	(	PUNCT
ejpam-5268	186	63	txrk	txrk	NOUN
ejpam-5268	186	64	,	,	PUNCT
ejpam-5268	186	65	txrk	txrk	ADJ
ejpam-5268	186	66	,	,	PUNCT
ejpam-5268	186	67	txsk	txsk	NOUN
ejpam-5268	186	68	)	)	PUNCT
ejpam-5268	186	69	,	,	PUNCT
ejpam-5268	186	70	m1(f	m1(f	X
ejpam-5268	186	71	,	,	PUNCT
ejpam-5268	186	72	t	t	PROPN
ejpam-5268	186	73	,	,	PUNCT
ejpam-5268	186	74	xrk−1,xrk−1,xsk−1	xrk−1,xrk−1,xsk−1	PROPN
ejpam-5268	186	75	)	)	PUNCT
ejpam-5268	186	76	)	)	PUNCT
ejpam-5268	187	1	<	<	X
ejpam-5268	187	2	0	0	X
ejpam-5268	187	3	.	.	PUNCT
ejpam-5268	188	1	this	this	PRON
ejpam-5268	188	2	is	be	AUX
ejpam-5268	188	3	a	a	DET
ejpam-5268	188	4	contradiction	contradiction	NOUN
ejpam-5268	188	5	.	.	PUNCT
ejpam-5268	189	1	therefore	therefore	ADV
ejpam-5268	189	2	,	,	PUNCT
ejpam-5268	189	3	we	we	PRON
ejpam-5268	189	4	have	have	VERB
ejpam-5268	189	5	a	a	DET
ejpam-5268	189	6	=	=	SYM
ejpam-5268	189	7	0	0	NUM
ejpam-5268	189	8	,	,	PUNCT
ejpam-5268	189	9	that	that	ADV
ejpam-5268	189	10	is	is	ADV
ejpam-5268	189	11	,	,	PUNCT
ejpam-5268	189	12	lims→+∞as	lims→+∞as	X
ejpam-5268	189	13	=	=	SYM
ejpam-5268	189	14	a.	a.	NOUN
ejpam-5268	189	15	thus	thus	ADV
ejpam-5268	189	16	,	,	PUNCT
ejpam-5268	189	17	this	this	PRON
ejpam-5268	189	18	proves	prove	VERB
ejpam-5268	189	19	txs	txs	NOUN
ejpam-5268	189	20	is	be	AUX
ejpam-5268	189	21	cauchy	cauchy	ADJ
ejpam-5268	189	22	sequence	sequence	NOUN
ejpam-5268	189	23	.	.	PUNCT
ejpam-5268	190	1	next	next	ADV
ejpam-5268	190	2	,	,	PUNCT
ejpam-5268	190	3	introduce	introduce	VERB
ejpam-5268	190	4	the	the	DET
ejpam-5268	190	5	first	first	ADJ
ejpam-5268	190	6	major	major	ADJ
ejpam-5268	190	7	outcome	outcome	NOUN
ejpam-5268	190	8	in	in	ADP
ejpam-5268	190	9	our	our	PRON
ejpam-5268	190	10	article	article	NOUN
ejpam-5268	190	11	.	.	PUNCT
ejpam-5268	191	1	theorem	theorem	NOUN
ejpam-5268	191	2	1	1	NUM
ejpam-5268	191	3	.	.	PUNCT
ejpam-5268	192	1	if	if	SCONJ
ejpam-5268	192	2	f	f	PROPN
ejpam-5268	192	3	,	,	PUNCT
ejpam-5268	192	4	t	t	X
ejpam-5268	192	5	:	:	PUNCT
ejpam-5268	192	6	(	(	PUNCT
ejpam-5268	192	7	x	x	X
ejpam-5268	192	8	,	,	PUNCT
ejpam-5268	192	9	s	s	PART
ejpam-5268	192	10	)	)	PUNCT
ejpam-5268	192	11	→	→	SYM
ejpam-5268	192	12	(	(	PUNCT
ejpam-5268	192	13	x	x	X
ejpam-5268	192	14	,	,	PUNCT
ejpam-5268	192	15	s	s	PART
ejpam-5268	192	16	)	)	PUNCT
ejpam-5268	192	17	are	be	AUX
ejpam-5268	192	18	self	self	NOUN
ejpam-5268	192	19	maps	map	NOUN
ejpam-5268	192	20	and	and	CCONJ
ejpam-5268	192	21	f	f	PROPN
ejpam-5268	192	22	is	be	AUX
ejpam-5268	192	23	t	t	PROPN
ejpam-5268	192	24	-	-	PUNCT
ejpam-5268	192	25	non	non	NOUN
ejpam-5268	192	26	-	-	ADJ
ejpam-5268	192	27	decreasing	decrease	VERB
ejpam-5268	192	28	in	in	ADP
ejpam-5268	192	29	complete	complete	ADJ
ejpam-5268	192	30	s	s	NOUN
ejpam-5268	192	31	-	-	ADJ
ejpam-5268	192	32	metric	metric	ADJ
ejpam-5268	192	33	(	(	PUNCT
ejpam-5268	192	34	x	x	NOUN
ejpam-5268	192	35	,	,	PUNCT
ejpam-5268	192	36	s	s	PART
ejpam-5268	192	37	)	)	PUNCT
ejpam-5268	192	38	and	and	CCONJ
ejpam-5268	192	39	satisfies	satisfy	VERB
ejpam-5268	192	40	each	each	DET
ejpam-5268	192	41	cases	case	NOUN
ejpam-5268	192	42	of	of	ADP
ejpam-5268	192	43	proposition	proposition	NOUN
ejpam-5268	192	44	1	1	NUM
ejpam-5268	192	45	.	.	PUNCT
ejpam-5268	193	1	if	if	SCONJ
ejpam-5268	193	2	there	there	PRON
ejpam-5268	193	3	exists	exist	VERB
ejpam-5268	193	4	simulation	simulation	NOUN
ejpam-5268	193	5	map	map	NOUN
ejpam-5268	193	6	;	;	PUNCT
ejpam-5268	193	7	(	(	PUNCT
ejpam-5268	193	8	s.	s.	PROPN
ejpam-5268	193	9	t	t	PROPN
ejpam-5268	193	10	)	)	PUNCT
ejpam-5268	193	11	,	,	PUNCT
ejpam-5268	193	12	∀	∀	X
ejpam-5268	193	13	(	(	PUNCT
ejpam-5268	193	14	x	x	NOUN
ejpam-5268	193	15	,	,	PUNCT
ejpam-5268	193	16	y	y	NOUN
ejpam-5268	193	17	)	)	PUNCT
ejpam-5268	193	18	∈	∈	PROPN
ejpam-5268	193	19	x	x	X
ejpam-5268	193	20	×x	×x	X
ejpam-5268	193	21	and	and	CCONJ
ejpam-5268	193	22	tx	tx	VERB
ejpam-5268	193	23	≤	≤	NUM
ejpam-5268	193	24	ty	ty	NUM
ejpam-5268	193	25	,	,	PUNCT
ejpam-5268	193	26	we	we	PRON
ejpam-5268	193	27	have	have	VERB
ejpam-5268	193	28	ξ	ξ	X
ejpam-5268	193	29	(	(	PUNCT
ejpam-5268	193	30	s	s	X
ejpam-5268	193	31	(	(	PUNCT
ejpam-5268	193	32	fx	fx	PROPN
ejpam-5268	193	33	,	,	PUNCT
ejpam-5268	193	34	fy	fy	PROPN
ejpam-5268	193	35	,	,	PUNCT
ejpam-5268	193	36	fz	fz	PROPN
ejpam-5268	193	37	)	)	PUNCT
ejpam-5268	193	38	,	,	PUNCT
ejpam-5268	193	39	m1	m1	PROPN
ejpam-5268	193	40	(	(	PUNCT
ejpam-5268	193	41	f	f	PROPN
ejpam-5268	193	42	,	,	PUNCT
ejpam-5268	193	43	t	t	PROPN
ejpam-5268	193	44	,	,	PUNCT
ejpam-5268	193	45	x	x	X
ejpam-5268	193	46	,	,	PUNCT
ejpam-5268	193	47	y	y	PROPN
ejpam-5268	193	48	,	,	PUNCT
ejpam-5268	193	49	z	z	NOUN
ejpam-5268	193	50	)	)	PUNCT
ejpam-5268	193	51	)	)	PUNCT
ejpam-5268	193	52	≥	≥	NOUN
ejpam-5268	193	53	0	0	NUM
ejpam-5268	193	54	.	.	PUNCT
ejpam-5268	194	1	n.	n.	PROPN
ejpam-5268	194	2	a.	a.	PROPN
ejpam-5268	194	3	majid	majid	PROPN
ejpam-5268	194	4	et	et	PROPN
ejpam-5268	194	5	al	al	PROPN
ejpam-5268	194	6	.	.	PUNCT
ejpam-5268	194	7	/	/	SYM
ejpam-5268	194	8	eur	eur	PROPN
ejpam-5268	194	9	.	.	PUNCT
ejpam-5268	195	1	j.	j.	PROPN
ejpam-5268	195	2	pure	pure	PROPN
ejpam-5268	195	3	appl	appl	PROPN
ejpam-5268	195	4	.	.	PROPN
ejpam-5268	195	5	math	math	PROPN
ejpam-5268	195	6	,	,	PUNCT
ejpam-5268	195	7	17	17	NUM
ejpam-5268	195	8	(	(	PUNCT
ejpam-5268	195	9	3	3	NUM
ejpam-5268	195	10	)	)	PUNCT
ejpam-5268	195	11	(	(	PUNCT
ejpam-5268	195	12	2024	2024	NUM
ejpam-5268	195	13	)	)	PUNCT
ejpam-5268	195	14	,	,	PUNCT
ejpam-5268	195	15	1877	1877	NUM
ejpam-5268	195	16	-	-	SYM
ejpam-5268	195	17	1893	1893	NUM
ejpam-5268	195	18	1885	1885	NUM
ejpam-5268	196	1	where	where	SCONJ
ejpam-5268	196	2	,	,	PUNCT
ejpam-5268	196	3	m1	m1	PROPN
ejpam-5268	196	4	(	(	PUNCT
ejpam-5268	196	5	f	f	PROPN
ejpam-5268	196	6	,	,	PUNCT
ejpam-5268	196	7	t	t	PROPN
ejpam-5268	196	8	,	,	PUNCT
ejpam-5268	196	9	x	x	X
ejpam-5268	196	10	,	,	PUNCT
ejpam-5268	196	11	y	y	PROPN
ejpam-5268	196	12	,	,	PUNCT
ejpam-5268	196	13	z	z	NOUN
ejpam-5268	196	14	)	)	PUNCT
ejpam-5268	197	1	=	=	NOUN
ejpam-5268	197	2	max	max	X
ejpam-5268	197	3	{	{	PUNCT
ejpam-5268	197	4	s	s	X
ejpam-5268	197	5	(	(	PUNCT
ejpam-5268	197	6	tx	tx	PROPN
ejpam-5268	197	7	,	,	PUNCT
ejpam-5268	197	8	ty	ty	INTJ
ejpam-5268	197	9	,	,	PUNCT
ejpam-5268	197	10	tz	tz	PROPN
ejpam-5268	197	11	)	)	PUNCT
ejpam-5268	197	12	,	,	PUNCT
ejpam-5268	197	13	s	s	PART
ejpam-5268	197	14	(	(	PUNCT
ejpam-5268	197	15	tx	tx	PROPN
ejpam-5268	197	16	,	,	PUNCT
ejpam-5268	197	17	fy	fy	PROPN
ejpam-5268	197	18	,	,	PUNCT
ejpam-5268	197	19	tz	tz	PROPN
ejpam-5268	197	20	)	)	PUNCT
ejpam-5268	197	21	,	,	PUNCT
ejpam-5268	197	22	s	s	X
ejpam-5268	197	23	(	(	PUNCT
ejpam-5268	197	24	ty	ty	INTJ
ejpam-5268	197	25	,	,	PUNCT
ejpam-5268	197	26	fx	fx	PROPN
ejpam-5268	197	27	,	,	PUNCT
ejpam-5268	197	28	tz	tz	PROPN
ejpam-5268	197	29	)	)	PUNCT
ejpam-5268	197	30	,	,	PUNCT
ejpam-5268	197	31	s	s	PART
ejpam-5268	197	32	(	(	PUNCT
ejpam-5268	197	33	tx	tx	PROPN
ejpam-5268	197	34	,	,	PUNCT
ejpam-5268	197	35	fx	fx	PROPN
ejpam-5268	197	36	,	,	PUNCT
ejpam-5268	197	37	tz	tz	PROPN
ejpam-5268	197	38	)	)	PUNCT
ejpam-5268	197	39	,	,	PUNCT
ejpam-5268	197	40	s	s	X
ejpam-5268	197	41	(	(	PUNCT
ejpam-5268	197	42	ty	ty	INTJ
ejpam-5268	197	43	,	,	PUNCT
ejpam-5268	197	44	fy	fy	PROPN
ejpam-5268	197	45	,	,	PUNCT
ejpam-5268	197	46	tz	tz	PROPN
ejpam-5268	197	47	)	)	PUNCT
ejpam-5268	197	48	}	}	PUNCT
ejpam-5268	197	49	.	.	PUNCT
ejpam-5268	198	1	so	so	ADV
ejpam-5268	198	2	,	,	PUNCT
ejpam-5268	198	3	f	f	PROPN
ejpam-5268	198	4	&	&	CCONJ
ejpam-5268	198	5	t	t	PROPN
ejpam-5268	198	6	have	have	VERB
ejpam-5268	198	7	coincidence	coincidence	NOUN
ejpam-5268	198	8	point	point	NOUN
ejpam-5268	198	9	.	.	PUNCT
ejpam-5268	199	1	additional	additional	ADJ
ejpam-5268	199	2	,	,	PUNCT
ejpam-5268	199	3	if	if	SCONJ
ejpam-5268	199	4	f	f	PROPN
ejpam-5268	199	5	&	&	CCONJ
ejpam-5268	199	6	t	t	PROPN
ejpam-5268	199	7	commute	commute	NOUN
ejpam-5268	199	8	,	,	PUNCT
ejpam-5268	199	9	in	in	ADP
ejpam-5268	199	10	that	that	DET
ejpam-5268	199	11	case	case	NOUN
ejpam-5268	199	12	f	f	PROPN
ejpam-5268	199	13	&	&	CCONJ
ejpam-5268	199	14	t	t	PROPN
ejpam-5268	199	15	have	have	VERB
ejpam-5268	199	16	common	common	ADJ
ejpam-5268	199	17	fixed	fix	VERB
ejpam-5268	199	18	point	point	NOUN
ejpam-5268	199	19	.	.	PUNCT
ejpam-5268	200	1	proof	proof	NOUN
ejpam-5268	200	2	.	.	PUNCT
ejpam-5268	201	1	via	via	ADP
ejpam-5268	201	2	proposition	proposition	NOUN
ejpam-5268	201	3	3	3	NUM
ejpam-5268	201	4	,	,	PUNCT
ejpam-5268	201	5	we	we	PRON
ejpam-5268	201	6	have	have	VERB
ejpam-5268	201	7	txs	txs	NOUN
ejpam-5268	201	8	is	be	AUX
ejpam-5268	201	9	cauchy	cauchy	ADJ
ejpam-5268	201	10	and	and	CCONJ
ejpam-5268	201	11	via	via	ADP
ejpam-5268	201	12	the	the	DET
ejpam-5268	201	13	completeness	completeness	NOUN
ejpam-5268	201	14	of	of	ADP
ejpam-5268	201	15	x	x	PROPN
ejpam-5268	201	16	∃	∃	PROPN
ejpam-5268	202	1	some	some	DET
ejpam-5268	202	2	p	p	PROPN
ejpam-5268	202	3	∈	∈	PROPN
ejpam-5268	202	4	x	x	X
ejpam-5268	202	5	satisfying	satisfying	NOUN
ejpam-5268	202	6	,	,	PUNCT
ejpam-5268	202	7	txs	txs	NOUN
ejpam-5268	202	8	→	→	SYM
ejpam-5268	202	9	tp	tp	NOUN
ejpam-5268	202	10	,	,	PUNCT
ejpam-5268	202	11	when	when	SCONJ
ejpam-5268	202	12	s→	s→	PROPN
ejpam-5268	203	1	+	+	NOUN
ejpam-5268	203	2	∞.	∞.	PROPN
ejpam-5268	203	3	(	(	PUNCT
ejpam-5268	203	4	11	11	NUM
ejpam-5268	203	5	)	)	PUNCT
ejpam-5268	203	6	now	now	ADV
ejpam-5268	203	7	,	,	PUNCT
ejpam-5268	203	8	explain	explain	VERB
ejpam-5268	203	9	p	p	NOUN
ejpam-5268	203	10	is	be	AUX
ejpam-5268	203	11	coincidence	coincidence	NOUN
ejpam-5268	203	12	point	point	NOUN
ejpam-5268	203	13	of	of	ADP
ejpam-5268	203	14	f	f	PROPN
ejpam-5268	203	15	&	&	CCONJ
ejpam-5268	203	16	t.	t.	PROPN
ejpam-5268	203	17	presume	presume	PROPN
ejpam-5268	203	18	s	s	PART
ejpam-5268	203	19	(	(	PUNCT
ejpam-5268	203	20	fp	fp	INTJ
ejpam-5268	203	21	,	,	PUNCT
ejpam-5268	203	22	fp	fp	NOUN
ejpam-5268	203	23	,	,	PUNCT
ejpam-5268	203	24	tp	tp	NOUN
ejpam-5268	203	25	)	)	PUNCT
ejpam-5268	203	26	>	>	X
ejpam-5268	204	1	0	0	X
ejpam-5268	204	2	.	.	PUNCT
ejpam-5268	204	3	letting	let	VERB
ejpam-5268	204	4	s→	s→	PUNCT
ejpam-5268	205	1	+	+	NOUN
ejpam-5268	205	2	∞	∞	PROPN
ejpam-5268	205	3	,	,	PUNCT
ejpam-5268	205	4	and	and	CCONJ
ejpam-5268	205	5	utilizing	utilize	VERB
ejpam-5268	205	6	11	11	NUM
ejpam-5268	205	7	)	)	PUNCT
ejpam-5268	205	8	we	we	PRON
ejpam-5268	205	9	get	get	VERB
ejpam-5268	205	10	:	:	PUNCT
ejpam-5268	205	11	m1	m1	PROPN
ejpam-5268	205	12	(	(	PUNCT
ejpam-5268	205	13	f	f	X
ejpam-5268	205	14	,	,	PUNCT
ejpam-5268	205	15	t	t	PROPN
ejpam-5268	205	16	,	,	PUNCT
ejpam-5268	205	17	xs	xs	PROPN
ejpam-5268	205	18	,	,	PUNCT
ejpam-5268	205	19	xs	xs	PROPN
ejpam-5268	205	20	,	,	PUNCT
ejpam-5268	205	21	p	p	X
ejpam-5268	205	22	)	)	PUNCT
ejpam-5268	205	23	=	=	NOUN
ejpam-5268	205	24	max	max	X
ejpam-5268	205	25	{	{	PUNCT
ejpam-5268	205	26	s	s	PROPN
ejpam-5268	205	27	(	(	PUNCT
ejpam-5268	205	28	fxs	fxs	PROPN
ejpam-5268	205	29	,	,	PUNCT
ejpam-5268	205	30	fxs	fxs	PROPN
ejpam-5268	205	31	,	,	PUNCT
ejpam-5268	205	32	fp	fp	NOUN
ejpam-5268	205	33	)	)	PUNCT
ejpam-5268	205	34	,	,	PUNCT
ejpam-5268	205	35	s	s	X
ejpam-5268	205	36	(	(	PUNCT
ejpam-5268	205	37	fxs	fxs	NOUN
ejpam-5268	205	38	,	,	PUNCT
ejpam-5268	205	39	tp	tp	NOUN
ejpam-5268	205	40	,	,	PUNCT
ejpam-5268	205	41	fp	fp	NOUN
ejpam-5268	205	42	)	)	PUNCT
ejpam-5268	205	43	,	,	PUNCT
ejpam-5268	205	44	s	s	X
ejpam-5268	205	45	(	(	PUNCT
ejpam-5268	205	46	fp	fp	INTJ
ejpam-5268	205	47	,	,	PUNCT
ejpam-5268	205	48	txs	txs	PROPN
ejpam-5268	205	49	,	,	PUNCT
ejpam-5268	205	50	fp	fp	NOUN
ejpam-5268	205	51	)	)	PUNCT
ejpam-5268	205	52	,	,	PUNCT
ejpam-5268	205	53	s	s	X
ejpam-5268	205	54	(	(	PUNCT
ejpam-5268	205	55	fxs	fxs	PROPN
ejpam-5268	205	56	,	,	PUNCT
ejpam-5268	205	57	txs	txs	PROPN
ejpam-5268	205	58	,	,	PUNCT
ejpam-5268	205	59	fp	fp	NOUN
ejpam-5268	205	60	)	)	PUNCT
ejpam-5268	205	61	,	,	PUNCT
ejpam-5268	205	62	s	s	X
ejpam-5268	205	63	(	(	PUNCT
ejpam-5268	205	64	fp	fp	INTJ
ejpam-5268	205	65	,	,	PUNCT
ejpam-5268	205	66	tp	tp	NOUN
ejpam-5268	205	67	,	,	PUNCT
ejpam-5268	205	68	fp	fp	PROPN
ejpam-5268	205	69	)	)	PUNCT
ejpam-5268	205	70	}	}	PUNCT
ejpam-5268	206	1	=	=	SYM
ejpam-5268	206	2	max	max	X
ejpam-5268	206	3	{	{	PUNCT
ejpam-5268	206	4	s	s	X
ejpam-5268	206	5	(	(	PUNCT
ejpam-5268	206	6	fp	fp	INTJ
ejpam-5268	206	7	,	,	PUNCT
ejpam-5268	206	8	fp	fp	NOUN
ejpam-5268	206	9	,	,	PUNCT
ejpam-5268	206	10	fp	fp	NOUN
ejpam-5268	206	11	)	)	PUNCT
ejpam-5268	206	12	,	,	PUNCT
ejpam-5268	206	13	s	s	X
ejpam-5268	206	14	(	(	PUNCT
ejpam-5268	206	15	fp	fp	INTJ
ejpam-5268	206	16	,	,	PUNCT
ejpam-5268	206	17	tp	tp	NOUN
ejpam-5268	206	18	,	,	PUNCT
ejpam-5268	206	19	fp	fp	NOUN
ejpam-5268	206	20	)	)	PUNCT
ejpam-5268	206	21	,	,	PUNCT
ejpam-5268	206	22	s	s	X
ejpam-5268	206	23	(	(	PUNCT
ejpam-5268	206	24	fp	fp	INTJ
ejpam-5268	206	25	,	,	PUNCT
ejpam-5268	206	26	tp	tp	NOUN
ejpam-5268	206	27	,	,	PUNCT
ejpam-5268	206	28	fp	fp	NOUN
ejpam-5268	206	29	)	)	PUNCT
ejpam-5268	206	30	,	,	PUNCT
ejpam-5268	206	31	s	s	X
ejpam-5268	206	32	(	(	PUNCT
ejpam-5268	206	33	fp	fp	INTJ
ejpam-5268	206	34	,	,	PUNCT
ejpam-5268	206	35	tp	tp	NOUN
ejpam-5268	206	36	,	,	PUNCT
ejpam-5268	206	37	fp	fp	NOUN
ejpam-5268	206	38	)	)	PUNCT
ejpam-5268	206	39	,	,	PUNCT
ejpam-5268	206	40	s	s	X
ejpam-5268	206	41	(	(	PUNCT
ejpam-5268	206	42	fp	fp	INTJ
ejpam-5268	206	43	,	,	PUNCT
ejpam-5268	206	44	tp	tp	NOUN
ejpam-5268	206	45	,	,	PUNCT
ejpam-5268	206	46	fp	fp	PROPN
ejpam-5268	206	47	)	)	PUNCT
ejpam-5268	206	48	}	}	PUNCT
ejpam-5268	207	1	=	=	SYM
ejpam-5268	207	2	s	s	X
ejpam-5268	207	3	(	(	PUNCT
ejpam-5268	207	4	fp	fp	INTJ
ejpam-5268	207	5	,	,	PUNCT
ejpam-5268	207	6	fp	fp	NOUN
ejpam-5268	207	7	,	,	PUNCT
ejpam-5268	207	8	tp	tp	NOUN
ejpam-5268	207	9	)	)	PUNCT
ejpam-5268	207	10	>	>	X
ejpam-5268	207	11	0	0	X
ejpam-5268	207	12	.	.	PUNCT
ejpam-5268	208	1	on	on	ADP
ejpam-5268	208	2	the	the	DET
ejpam-5268	208	3	other	other	ADJ
ejpam-5268	208	4	hand	hand	NOUN
ejpam-5268	208	5	,	,	PUNCT
ejpam-5268	208	6	utilizing	utilize	VERB
ejpam-5268	208	7	1	1	NUM
ejpam-5268	208	8	,	,	PUNCT
ejpam-5268	208	9	11	11	NUM
ejpam-5268	208	10	and	and	CCONJ
ejpam-5268	208	11	the	the	DET
ejpam-5268	208	12	case	case	NOUN
ejpam-5268	208	13	(	(	PUNCT
ejpam-5268	208	14	ξ3	ξ3	NOUN
ejpam-5268	208	15	)	)	PUNCT
ejpam-5268	208	16	,	,	PUNCT
ejpam-5268	208	17	obtain	obtain	VERB
ejpam-5268	208	18	:	:	PUNCT
ejpam-5268	208	19	0	0	NUM
ejpam-5268	208	20	≤	≤	NUM
ejpam-5268	208	21	limk→+∞supξ(s	limk→+∞supξ(s	X
ejpam-5268	208	22	(	(	PUNCT
ejpam-5268	208	23	fp	fp	INTJ
ejpam-5268	208	24	,	,	PUNCT
ejpam-5268	208	25	fp	fp	ADJ
ejpam-5268	208	26	,	,	PUNCT
ejpam-5268	208	27	txs+1	txs+1	NOUN
ejpam-5268	208	28	)	)	PUNCT
ejpam-5268	208	29	,	,	PUNCT
ejpam-5268	208	30	m1(f	m1(f	X
ejpam-5268	208	31	,	,	PUNCT
ejpam-5268	208	32	t	t	PROPN
ejpam-5268	208	33	,	,	PUNCT
ejpam-5268	208	34	xs	xs	PROPN
ejpam-5268	208	35	,	,	PUNCT
ejpam-5268	208	36	xs	xs	PROPN
ejpam-5268	208	37	,	,	PUNCT
ejpam-5268	208	38	p	p	NOUN
ejpam-5268	208	39	)	)	PUNCT
ejpam-5268	208	40	)	)	PUNCT
ejpam-5268	209	1	<	<	X
ejpam-5268	209	2	0	0	X
ejpam-5268	209	3	.	.	PUNCT
ejpam-5268	210	1	this	this	PRON
ejpam-5268	210	2	is	be	AUX
ejpam-5268	210	3	a	a	DET
ejpam-5268	210	4	contradiction	contradiction	NOUN
ejpam-5268	210	5	.	.	PUNCT
ejpam-5268	211	1	hence	hence	ADV
ejpam-5268	211	2	,	,	PUNCT
ejpam-5268	211	3	we	we	PRON
ejpam-5268	211	4	have	have	VERB
ejpam-5268	211	5	s	s	NOUN
ejpam-5268	211	6	(	(	PUNCT
ejpam-5268	211	7	fp	fp	INTJ
ejpam-5268	211	8	,	,	PUNCT
ejpam-5268	211	9	fp	fp	NOUN
ejpam-5268	211	10	,	,	PUNCT
ejpam-5268	211	11	tp	tp	NOUN
ejpam-5268	211	12	)	)	PUNCT
ejpam-5268	211	13	=	=	SYM
ejpam-5268	211	14	0	0	X
ejpam-5268	211	15	.	.	PUNCT
ejpam-5268	212	1	thus	thus	ADV
ejpam-5268	212	2	,	,	PUNCT
ejpam-5268	212	3	p	p	NOUN
ejpam-5268	212	4	is	be	AUX
ejpam-5268	212	5	coincident	coincident	ADJ
ejpam-5268	212	6	point	point	NOUN
ejpam-5268	212	7	of	of	ADP
ejpam-5268	212	8	f	f	PROPN
ejpam-5268	212	9	&	&	CCONJ
ejpam-5268	212	10	t.	t.	PROPN
ejpam-5268	212	11	now	now	ADV
ejpam-5268	212	12	,	,	PUNCT
ejpam-5268	212	13	assume	assume	VERB
ejpam-5268	212	14	f	f	PROPN
ejpam-5268	212	15	&	&	CCONJ
ejpam-5268	212	16	t	t	PROPN
ejpam-5268	212	17	commute	commute	NOUN
ejpam-5268	212	18	at	at	ADP
ejpam-5268	212	19	their	their	PRON
ejpam-5268	212	20	coincident	coincident	ADJ
ejpam-5268	212	21	point	point	NOUN
ejpam-5268	212	22	p.	p.	NOUN
ejpam-5268	212	23	put	put	VERB
ejpam-5268	212	24	q	q	NOUN
ejpam-5268	213	1	=	=	PUNCT
ejpam-5268	213	2	tp	tp	NOUN
ejpam-5268	213	3	=	=	SYM
ejpam-5268	213	4	fp	fp	PROPN
ejpam-5268	213	5	.	.	PUNCT
ejpam-5268	213	6	then	then	ADV
ejpam-5268	213	7	,	,	PUNCT
ejpam-5268	213	8	fq	fq	PROPN
ejpam-5268	213	9	=	=	PROPN
ejpam-5268	213	10	f	f	PROPN
ejpam-5268	213	11	(	(	PUNCT
ejpam-5268	213	12	tp	tp	NOUN
ejpam-5268	213	13	)	)	PUNCT
ejpam-5268	213	14	=	=	SYM
ejpam-5268	213	15	t	t	PROPN
ejpam-5268	213	16	(	(	PUNCT
ejpam-5268	213	17	fp	fp	X
ejpam-5268	213	18	)	)	PUNCT
ejpam-5268	213	19	=	=	PUNCT
ejpam-5268	213	20	tq	tq	ADP
ejpam-5268	213	21	.	.	PUNCT
ejpam-5268	214	1	via	via	ADP
ejpam-5268	214	2	part	part	NOUN
ejpam-5268	214	3	(	(	PUNCT
ejpam-5268	214	4	v	v	NOUN
ejpam-5268	214	5	)	)	PUNCT
ejpam-5268	214	6	,	,	PUNCT
ejpam-5268	214	7	we	we	PRON
ejpam-5268	214	8	have	have	VERB
ejpam-5268	214	9	tp	tp	ADP
ejpam-5268	214	10	≤	≤	NUM
ejpam-5268	214	11	t	t	PROPN
ejpam-5268	214	12	(	(	PUNCT
ejpam-5268	214	13	tp	tp	NOUN
ejpam-5268	214	14	)	)	PUNCT
ejpam-5268	214	15	=	=	PUNCT
ejpam-5268	215	1	tq	tq	X
ejpam-5268	215	2	.	.	PUNCT
ejpam-5268	216	1	m1	m1	PROPN
ejpam-5268	216	2	(	(	PUNCT
ejpam-5268	216	3	f	f	X
ejpam-5268	216	4	,	,	PUNCT
ejpam-5268	216	5	t	t	PROPN
ejpam-5268	216	6	,	,	PUNCT
ejpam-5268	216	7	q	q	NOUN
ejpam-5268	216	8	,	,	PUNCT
ejpam-5268	216	9	q	q	ADJ
ejpam-5268	216	10	,	,	PUNCT
ejpam-5268	216	11	p	p	NOUN
ejpam-5268	216	12	)	)	PUNCT
ejpam-5268	216	13	=	=	SYM
ejpam-5268	216	14	max	max	PROPN
ejpam-5268	216	15	{	{	PUNCT
ejpam-5268	216	16	s(tq	s(tq	PROPN
ejpam-5268	216	17	,	,	PUNCT
ejpam-5268	216	18	tq	tq	ADV
ejpam-5268	216	19	,	,	PUNCT
ejpam-5268	216	20	tp),s	tp),s	X
ejpam-5268	216	21	(	(	PUNCT
ejpam-5268	216	22	tq	tq	INTJ
ejpam-5268	216	23	,	,	PUNCT
ejpam-5268	216	24	fq	fq	PROPN
ejpam-5268	216	25	,	,	PUNCT
ejpam-5268	216	26	tp	tp	NOUN
ejpam-5268	216	27	)	)	PUNCT
ejpam-5268	216	28	,	,	PUNCT
ejpam-5268	216	29	s	s	X
ejpam-5268	216	30	(	(	PUNCT
ejpam-5268	216	31	tp	tp	PROPN
ejpam-5268	216	32	,	,	PUNCT
ejpam-5268	216	33	fq	fq	PROPN
ejpam-5268	216	34	,	,	PUNCT
ejpam-5268	216	35	tp	tp	NOUN
ejpam-5268	216	36	)	)	PUNCT
ejpam-5268	216	37	,	,	PUNCT
ejpam-5268	216	38	s	s	X
ejpam-5268	216	39	(	(	PUNCT
ejpam-5268	216	40	tq	tq	INTJ
ejpam-5268	216	41	,	,	PUNCT
ejpam-5268	216	42	fq	fq	PROPN
ejpam-5268	216	43	,	,	PUNCT
ejpam-5268	216	44	tp	tp	NOUN
ejpam-5268	216	45	)	)	PUNCT
ejpam-5268	216	46	,	,	PUNCT
ejpam-5268	216	47	s	s	X
ejpam-5268	216	48	(	(	PUNCT
ejpam-5268	216	49	tp	tp	PROPN
ejpam-5268	216	50	,	,	PUNCT
ejpam-5268	216	51	fp	fp	X
ejpam-5268	216	52	,	,	PUNCT
ejpam-5268	216	53	tp	tp	NOUN
ejpam-5268	216	54	)	)	PUNCT
ejpam-5268	216	55	}	}	PUNCT
ejpam-5268	216	56	=	=	SYM
ejpam-5268	216	57	maxs	max	NOUN
ejpam-5268	216	58	(	(	PUNCT
ejpam-5268	216	59	tq	tq	INTJ
ejpam-5268	216	60	,	,	PUNCT
ejpam-5268	216	61	tq	tq	INTJ
ejpam-5268	216	62	,	,	PUNCT
ejpam-5268	216	63	q	q	NOUN
ejpam-5268	216	64	)	)	PUNCT
ejpam-5268	216	65	,	,	PUNCT
ejpam-5268	216	66	s	s	X
ejpam-5268	216	67	(	(	PUNCT
ejpam-5268	216	68	tq	tq	INTJ
ejpam-5268	216	69	,	,	PUNCT
ejpam-5268	216	70	tq	tq	INTJ
ejpam-5268	216	71	,	,	PUNCT
ejpam-5268	216	72	q	q	NOUN
ejpam-5268	216	73	)	)	PUNCT
ejpam-5268	216	74	,	,	PUNCT
ejpam-5268	216	75	s	s	X
ejpam-5268	216	76	(	(	PUNCT
ejpam-5268	216	77	q	q	PROPN
ejpam-5268	216	78	,	,	PUNCT
ejpam-5268	216	79	fq	fq	PROPN
ejpam-5268	216	80	,	,	PUNCT
ejpam-5268	216	81	q	q	NOUN
ejpam-5268	216	82	)	)	PUNCT
ejpam-5268	216	83	,	,	PUNCT
ejpam-5268	216	84	s	s	X
ejpam-5268	216	85	(	(	PUNCT
ejpam-5268	216	86	tq	tq	INTJ
ejpam-5268	216	87	,	,	PUNCT
ejpam-5268	216	88	fq	fq	PROPN
ejpam-5268	216	89	,	,	PUNCT
ejpam-5268	216	90	q	q	NOUN
ejpam-5268	216	91	)	)	PUNCT
ejpam-5268	216	92	,	,	PUNCT
ejpam-5268	216	93	s	s	X
ejpam-5268	216	94	(	(	PUNCT
ejpam-5268	216	95	q	q	ADJ
ejpam-5268	216	96	,	,	PUNCT
ejpam-5268	216	97	q	q	ADJ
ejpam-5268	216	98	,	,	PUNCT
ejpam-5268	216	99	q	q	NOUN
ejpam-5268	216	100	)	)	PUNCT
ejpam-5268	216	101	since	since	SCONJ
ejpam-5268	216	102	,	,	PUNCT
ejpam-5268	216	103	(	(	PUNCT
ejpam-5268	216	104	x	x	X
ejpam-5268	216	105	,	,	PUNCT
ejpam-5268	216	106	s	s	PART
ejpam-5268	216	107	)	)	PUNCT
ejpam-5268	216	108	is	be	AUX
ejpam-5268	216	109	s	s	NOUN
ejpam-5268	216	110	-	-	NOUN
ejpam-5268	216	111	metric	metric	ADJ
ejpam-5268	216	112	.	.	PUNCT
ejpam-5268	217	1	thus	thus	ADV
ejpam-5268	217	2	,	,	PUNCT
ejpam-5268	217	3	m1	m1	PROPN
ejpam-5268	217	4	(	(	PUNCT
ejpam-5268	217	5	f	f	PROPN
ejpam-5268	217	6	,	,	PUNCT
ejpam-5268	217	7	t	t	PROPN
ejpam-5268	217	8	,	,	PUNCT
ejpam-5268	217	9	q	q	NOUN
ejpam-5268	217	10	,	,	PUNCT
ejpam-5268	217	11	q	q	ADJ
ejpam-5268	217	12	,	,	PUNCT
ejpam-5268	217	13	p	p	NOUN
ejpam-5268	217	14	)	)	PUNCT
ejpam-5268	217	15	=	=	SYM
ejpam-5268	217	16	s	s	X
ejpam-5268	217	17	(	(	PUNCT
ejpam-5268	217	18	tq	tq	INTJ
ejpam-5268	217	19	,	,	PUNCT
ejpam-5268	217	20	tq	tq	INTJ
ejpam-5268	217	21	,	,	PUNCT
ejpam-5268	217	22	q	q	NOUN
ejpam-5268	217	23	)	)	PUNCT
ejpam-5268	217	24	.	.	PUNCT
ejpam-5268	218	1	via	via	ADP
ejpam-5268	218	2	1	1	NUM
ejpam-5268	218	3	and	and	CCONJ
ejpam-5268	218	4	the	the	DET
ejpam-5268	218	5	condition	condition	NOUN
ejpam-5268	218	6	(	(	PUNCT
ejpam-5268	218	7	ξ3	ξ3	NOUN
ejpam-5268	218	8	)	)	PUNCT
ejpam-5268	218	9	,	,	PUNCT
ejpam-5268	218	10	we	we	PRON
ejpam-5268	218	11	obtain	obtain	VERB
ejpam-5268	218	12	0	0	NUM
ejpam-5268	218	13	≤	≤	NOUN
ejpam-5268	218	14	lim	lim	PROPN
ejpam-5268	218	15	k→+∞	k→+∞	PROPN
ejpam-5268	218	16	sup	sup	NOUN
ejpam-5268	218	17	ξ(s	ξ(s	PROPN
ejpam-5268	218	18	(	(	PUNCT
ejpam-5268	218	19	fq	fq	PROPN
ejpam-5268	218	20	,	,	PUNCT
ejpam-5268	218	21	fq	fq	PROPN
ejpam-5268	218	22	,	,	PUNCT
ejpam-5268	218	23	fp	fp	PROPN
ejpam-5268	218	24	)	)	PUNCT
ejpam-5268	218	25	,	,	PUNCT
ejpam-5268	218	26	m1(f	m1(f	X
ejpam-5268	218	27	,	,	PUNCT
ejpam-5268	218	28	t	t	PROPN
ejpam-5268	218	29	,	,	PUNCT
ejpam-5268	218	30	q	q	NOUN
ejpam-5268	218	31	,	,	PUNCT
ejpam-5268	218	32	q	q	ADJ
ejpam-5268	218	33	,	,	PUNCT
ejpam-5268	218	34	p	p	NOUN
ejpam-5268	218	35	)	)	PUNCT
ejpam-5268	218	36	)	)	PUNCT
ejpam-5268	219	1	=	=	SYM
ejpam-5268	219	2	limk→+∞sup	limk→+∞sup	NOUN
ejpam-5268	219	3	ξ(s	ξ(s	PROPN
ejpam-5268	219	4	(	(	PUNCT
ejpam-5268	219	5	fq	fq	PROPN
ejpam-5268	219	6	,	,	PUNCT
ejpam-5268	219	7	fq	fq	PROPN
ejpam-5268	219	8	,	,	PUNCT
ejpam-5268	219	9	q	q	NOUN
ejpam-5268	219	10	)	)	PUNCT
ejpam-5268	219	11	,	,	PUNCT
ejpam-5268	219	12	s	s	X
ejpam-5268	219	13	(	(	PUNCT
ejpam-5268	219	14	fq	fq	PROPN
ejpam-5268	219	15	,	,	PUNCT
ejpam-5268	219	16	fq	fq	PROPN
ejpam-5268	219	17	,	,	PUNCT
ejpam-5268	219	18	q	q	NOUN
ejpam-5268	219	19	)	)	PUNCT
ejpam-5268	219	20	)	)	PUNCT
ejpam-5268	219	21	<	<	X
ejpam-5268	219	22	0	0	NUM
ejpam-5268	219	23	,	,	PUNCT
ejpam-5268	219	24	this	this	PRON
ejpam-5268	219	25	is	be	AUX
ejpam-5268	219	26	a	a	DET
ejpam-5268	219	27	contradiction	contradiction	NOUN
ejpam-5268	219	28	.	.	PUNCT
ejpam-5268	220	1	thus	thus	ADV
ejpam-5268	220	2	,	,	PUNCT
ejpam-5268	220	3	we	we	PRON
ejpam-5268	220	4	have	have	VERB
ejpam-5268	220	5	s	s	NOUN
ejpam-5268	220	6	(	(	PUNCT
ejpam-5268	220	7	tq	tq	INTJ
ejpam-5268	220	8	,	,	PUNCT
ejpam-5268	220	9	tq	tq	INTJ
ejpam-5268	220	10	,	,	PUNCT
ejpam-5268	220	11	q	q	NOUN
ejpam-5268	220	12	)	)	PUNCT
ejpam-5268	220	13	=	=	SYM
ejpam-5268	221	1	0,=⇒	0,=⇒	PROPN
ejpam-5268	221	2	tq	tq	ADP
ejpam-5268	221	3	=	=	SYM
ejpam-5268	221	4	fq	fq	PROPN
ejpam-5268	221	5	=	=	NOUN
ejpam-5268	221	6	q.	q.	PROPN
ejpam-5268	221	7	in	in	ADP
ejpam-5268	221	8	that	that	DET
ejpam-5268	221	9	case	case	NOUN
ejpam-5268	221	10	,	,	PUNCT
ejpam-5268	221	11	the	the	DET
ejpam-5268	221	12	common	common	ADJ
ejpam-5268	221	13	fixed	fix	VERB
ejpam-5268	221	14	point	point	NOUN
ejpam-5268	221	15	of	of	ADP
ejpam-5268	221	16	f	f	PROPN
ejpam-5268	221	17	&	&	CCONJ
ejpam-5268	221	18	tisq	tisq	PROPN
ejpam-5268	221	19	.	.	PUNCT
ejpam-5268	222	1	now	now	ADV
ejpam-5268	222	2	,	,	PUNCT
ejpam-5268	222	3	via	via	ADP
ejpam-5268	222	4	means	mean	NOUN
ejpam-5268	222	5	of	of	ADP
ejpam-5268	222	6	simulation	simulation	NOUN
ejpam-5268	222	7	mapping	mapping	NOUN
ejpam-5268	222	8	and	and	CCONJ
ejpam-5268	222	9	theorem	theorem	VERB
ejpam-5268	222	10	1	1	NUM
ejpam-5268	222	11	,	,	PUNCT
ejpam-5268	222	12	can	can	AUX
ejpam-5268	222	13	present	present	VERB
ejpam-5268	222	14	numerous	numerous	ADJ
ejpam-5268	222	15	outcomes	outcome	NOUN
ejpam-5268	222	16	of	of	ADP
ejpam-5268	222	17	common	common	ADJ
ejpam-5268	222	18	and	and	CCONJ
ejpam-5268	222	19	coincidence	coincidence	NOUN
ejpam-5268	222	20	fixed	fix	VERB
ejpam-5268	222	21	point	point	NOUN
ejpam-5268	222	22	.	.	PUNCT
ejpam-5268	223	1	n.	n.	PROPN
ejpam-5268	223	2	a.	a.	PROPN
ejpam-5268	223	3	majid	majid	PROPN
ejpam-5268	223	4	et	et	PROPN
ejpam-5268	223	5	al	al	PROPN
ejpam-5268	223	6	.	.	PUNCT
ejpam-5268	223	7	/	/	SYM
ejpam-5268	223	8	eur	eur	PROPN
ejpam-5268	223	9	.	.	PUNCT
ejpam-5268	224	1	j.	j.	PROPN
ejpam-5268	224	2	pure	pure	PROPN
ejpam-5268	224	3	appl	appl	PROPN
ejpam-5268	224	4	.	.	PROPN
ejpam-5268	224	5	math	math	PROPN
ejpam-5268	224	6	,	,	PUNCT
ejpam-5268	224	7	17	17	NUM
ejpam-5268	224	8	(	(	PUNCT
ejpam-5268	224	9	3	3	NUM
ejpam-5268	224	10	)	)	PUNCT
ejpam-5268	224	11	(	(	PUNCT
ejpam-5268	224	12	2024	2024	NUM
ejpam-5268	224	13	)	)	PUNCT
ejpam-5268	224	14	,	,	PUNCT
ejpam-5268	224	15	1877	1877	NUM
ejpam-5268	224	16	-	-	SYM
ejpam-5268	224	17	1893	1893	NUM
ejpam-5268	224	18	1886	1886	NUM
ejpam-5268	224	19	corollary	corollary	NOUN
ejpam-5268	224	20	1	1	NUM
ejpam-5268	224	21	.	.	PUNCT
ejpam-5268	225	1	if	if	SCONJ
ejpam-5268	225	2	f	f	PROPN
ejpam-5268	225	3	,	,	PUNCT
ejpam-5268	225	4	t	t	X
ejpam-5268	225	5	:	:	PUNCT
ejpam-5268	225	6	(	(	PUNCT
ejpam-5268	225	7	x	x	X
ejpam-5268	225	8	,	,	PUNCT
ejpam-5268	225	9	s	s	PART
ejpam-5268	225	10	)	)	PUNCT
ejpam-5268	225	11	→	→	SYM
ejpam-5268	225	12	(	(	PUNCT
ejpam-5268	225	13	x	x	X
ejpam-5268	225	14	,	,	PUNCT
ejpam-5268	225	15	s	s	PART
ejpam-5268	225	16	)	)	PUNCT
ejpam-5268	225	17	are	be	AUX
ejpam-5268	225	18	self	self	NOUN
ejpam-5268	225	19	mappings	mapping	NOUN
ejpam-5268	225	20	and	and	CCONJ
ejpam-5268	225	21	f	f	PROPN
ejpam-5268	225	22	is	be	AUX
ejpam-5268	225	23	t	t	PROPN
ejpam-5268	225	24	-	-	PUNCT
ejpam-5268	225	25	non	non	NOUN
ejpam-5268	225	26	-	-	ADJ
ejpam-5268	225	27	decreasing	decrease	VERB
ejpam-5268	225	28	in	in	ADP
ejpam-5268	225	29	complete	complete	ADJ
ejpam-5268	225	30	s	s	NOUN
ejpam-5268	225	31	-	-	ADJ
ejpam-5268	225	32	metric	metric	ADJ
ejpam-5268	225	33	(	(	PUNCT
ejpam-5268	225	34	x	x	NOUN
ejpam-5268	225	35	,	,	PUNCT
ejpam-5268	225	36	s	s	PART
ejpam-5268	225	37	)	)	PUNCT
ejpam-5268	225	38	and	and	CCONJ
ejpam-5268	225	39	satisfies	satisfy	VERB
ejpam-5268	225	40	the	the	DET
ejpam-5268	225	41	cases	case	NOUN
ejpam-5268	225	42	(	(	PUNCT
ejpam-5268	225	43	(	(	PUNCT
ejpam-5268	225	44	i	i	NOUN
ejpam-5268	225	45	)	)	PUNCT
ejpam-5268	225	46	&	&	CCONJ
ejpam-5268	225	47	(	(	PUNCT
ejpam-5268	225	48	ii	ii	NOUN
ejpam-5268	225	49	)	)	PUNCT
ejpam-5268	225	50	)	)	PUNCT
ejpam-5268	225	51	of	of	ADP
ejpam-5268	225	52	proposition	proposition	NOUN
ejpam-5268	225	53	1	1	NUM
ejpam-5268	225	54	.	.	PUNCT
ejpam-5268	226	1	if	if	SCONJ
ejpam-5268	226	2	there	there	PRON
ejpam-5268	226	3	exists	exist	VERB
ejpam-5268	226	4	monotone	monotone	ADJ
ejpam-5268	226	5	simulation	simulation	NOUN
ejpam-5268	226	6	mapping	mapping	NOUN
ejpam-5268	226	7	ξ	ξ	PROPN
ejpam-5268	226	8	;	;	PUNCT
ejpam-5268	226	9	(	(	PUNCT
ejpam-5268	226	10	s.	s.	PROPN
ejpam-5268	226	11	t	t	PROPN
ejpam-5268	226	12	)	)	PUNCT
ejpam-5268	226	13	∀	∀	X
ejpam-5268	226	14	(	(	PUNCT
ejpam-5268	226	15	x	x	X
ejpam-5268	226	16	,	,	PUNCT
ejpam-5268	226	17	y	y	NOUN
ejpam-5268	226	18	)	)	PUNCT
ejpam-5268	226	19	∈	∈	PROPN
ejpam-5268	226	20	x	x	X
ejpam-5268	226	21	×x	×x	X
ejpam-5268	226	22	&	&	CCONJ
ejpam-5268	226	23	tx	tx	VERB
ejpam-5268	226	24	≤	≤	PROPN
ejpam-5268	226	25	ty	ty	NUM
ejpam-5268	226	26	,	,	PUNCT
ejpam-5268	226	27	we	we	PRON
ejpam-5268	226	28	have	have	VERB
ejpam-5268	226	29	ξ	ξ	X
ejpam-5268	226	30	(	(	PUNCT
ejpam-5268	226	31	s	s	X
ejpam-5268	226	32	(	(	PUNCT
ejpam-5268	226	33	fx	fx	PROPN
ejpam-5268	226	34	,	,	PUNCT
ejpam-5268	226	35	fy	fy	PROPN
ejpam-5268	226	36	,	,	PUNCT
ejpam-5268	226	37	fz	fz	PROPN
ejpam-5268	226	38	)	)	PUNCT
ejpam-5268	226	39	,	,	PUNCT
ejpam-5268	226	40	s	s	PART
ejpam-5268	226	41	(	(	PUNCT
ejpam-5268	226	42	tx	tx	PROPN
ejpam-5268	226	43	,	,	PUNCT
ejpam-5268	226	44	ty	ty	INTJ
ejpam-5268	226	45	,	,	PUNCT
ejpam-5268	226	46	tz	tz	NOUN
ejpam-5268	226	47	)	)	PUNCT
ejpam-5268	226	48	)	)	PUNCT
ejpam-5268	226	49	≥	≥	NOUN
ejpam-5268	226	50	0	0	NUM
ejpam-5268	226	51	.	.	PUNCT
ejpam-5268	227	1	so	so	ADV
ejpam-5268	227	2	,	,	PUNCT
ejpam-5268	227	3	f	f	PROPN
ejpam-5268	227	4	&	&	CCONJ
ejpam-5268	227	5	t	t	PROPN
ejpam-5268	227	6	have	have	VERB
ejpam-5268	227	7	coincidence	coincidence	NOUN
ejpam-5268	227	8	point	point	NOUN
ejpam-5268	227	9	.	.	PUNCT
ejpam-5268	228	1	additional	additional	ADJ
ejpam-5268	228	2	,	,	PUNCT
ejpam-5268	228	3	if	if	SCONJ
ejpam-5268	228	4	f	f	PROPN
ejpam-5268	228	5	&	&	CCONJ
ejpam-5268	228	6	t	t	PROPN
ejpam-5268	228	7	commute	commute	PROPN
ejpam-5268	228	8	,	,	PUNCT
ejpam-5268	228	9	so	so	PROPN
ejpam-5268	228	10	f	f	PROPN
ejpam-5268	228	11	&	&	CCONJ
ejpam-5268	228	12	t	t	PROPN
ejpam-5268	228	13	have	have	VERB
ejpam-5268	228	14	a	a	DET
ejpam-5268	228	15	common	common	ADJ
ejpam-5268	228	16	fixed	fix	VERB
ejpam-5268	228	17	point	point	NOUN
ejpam-5268	228	18	.	.	PUNCT
ejpam-5268	229	1	proof	proof	NOUN
ejpam-5268	229	2	.	.	PUNCT
ejpam-5268	230	1	for	for	ADP
ejpam-5268	230	2	all	all	DET
ejpam-5268	230	3	x	x	PROPN
ejpam-5268	230	4	,	,	PUNCT
ejpam-5268	230	5	y	y	PROPN
ejpam-5268	230	6	,	,	PUNCT
ejpam-5268	230	7	z	z	NOUN
ejpam-5268	230	8	∈	∈	PROPN
ejpam-5268	230	9	x	x	X
ejpam-5268	230	10	s	s	X
ejpam-5268	230	11	(	(	PUNCT
ejpam-5268	230	12	tx	tx	PROPN
ejpam-5268	230	13	,	,	PUNCT
ejpam-5268	230	14	ty	ty	INTJ
ejpam-5268	230	15	,	,	PUNCT
ejpam-5268	230	16	tz	tz	NOUN
ejpam-5268	230	17	)	)	PUNCT
ejpam-5268	230	18	≤	≤	NOUN
ejpam-5268	230	19	m1	m1	NOUN
ejpam-5268	230	20	(	(	PUNCT
ejpam-5268	230	21	f	f	X
ejpam-5268	230	22	,	,	PUNCT
ejpam-5268	230	23	t	t	PROPN
ejpam-5268	230	24	,	,	PUNCT
ejpam-5268	230	25	x	x	X
ejpam-5268	230	26	,	,	PUNCT
ejpam-5268	230	27	y	y	PROPN
ejpam-5268	230	28	,	,	PUNCT
ejpam-5268	230	29	z	z	NOUN
ejpam-5268	230	30	)	)	PUNCT
ejpam-5268	230	31	.	.	PUNCT
ejpam-5268	231	1	(	(	PUNCT
ejpam-5268	231	2	12	12	X
ejpam-5268	231	3	)	)	PUNCT
ejpam-5268	231	4	suppose	suppose	VERB
ejpam-5268	231	5	that	that	SCONJ
ejpam-5268	231	6	ξ	ξ	X
ejpam-5268	231	7	:	:	PUNCT
ejpam-5268	231	8	x	x	SYM
ejpam-5268	231	9	×x	×x	NUM
ejpam-5268	231	10	→	→	SYM
ejpam-5268	231	11	r	r	NOUN
ejpam-5268	231	12	is	be	AUX
ejpam-5268	231	13	described	describe	VERB
ejpam-5268	231	14	as	as	ADP
ejpam-5268	231	15	:	:	PUNCT
ejpam-5268	231	16	ξ	ξ	X
ejpam-5268	231	17	(	(	PUNCT
ejpam-5268	231	18	t	t	PROPN
ejpam-5268	231	19	,	,	PUNCT
ejpam-5268	231	20	w	w	NOUN
ejpam-5268	231	21	)	)	PUNCT
ejpam-5268	231	22	=	=	NOUN
ejpam-5268	231	23	λw	λw	ADP
ejpam-5268	231	24	−	−	PROPN
ejpam-5268	231	25	t	t	PROPN
ejpam-5268	231	26	,	,	PUNCT
ejpam-5268	231	27	for	for	ADP
ejpam-5268	231	28	λ	λ	PROPN
ejpam-5268	231	29	∈	∈	PROPN
ejpam-5268	232	1	[	[	X
ejpam-5268	232	2	0	0	NUM
ejpam-5268	232	3	,	,	PUNCT
ejpam-5268	232	4	1	1	NUM
ejpam-5268	232	5	)	)	PUNCT
ejpam-5268	232	6	.	.	PUNCT
ejpam-5268	233	1	utilizing	utilize	VERB
ejpam-5268	233	2	the	the	DET
ejpam-5268	233	3	given	give	VERB
ejpam-5268	233	4	supposing	supposing	NOUN
ejpam-5268	233	5	,	,	PUNCT
ejpam-5268	233	6	we	we	PRON
ejpam-5268	233	7	obtain	obtain	VERB
ejpam-5268	233	8	0	0	NUM
ejpam-5268	233	9	≤	≤	NUM
ejpam-5268	233	10	ξ(s(fx	ξ(s(fx	NOUN
ejpam-5268	233	11	,	,	PUNCT
ejpam-5268	233	12	fy	fy	PROPN
ejpam-5268	233	13	,	,	PUNCT
ejpam-5268	233	14	fz	fz	PROPN
ejpam-5268	233	15	)	)	PUNCT
ejpam-5268	233	16	,	,	PUNCT
ejpam-5268	233	17	s(tx	s(tx	PROPN
ejpam-5268	233	18	,	,	PUNCT
ejpam-5268	233	19	ty	ty	INTJ
ejpam-5268	233	20	,	,	PUNCT
ejpam-5268	233	21	tz	tz	PROPN
ejpam-5268	233	22	)	)	PUNCT
ejpam-5268	233	23	<	<	X
ejpam-5268	233	24	s	s	X
ejpam-5268	233	25	(	(	PUNCT
ejpam-5268	233	26	tx	tx	PROPN
ejpam-5268	233	27	,	,	PUNCT
ejpam-5268	233	28	ty	ty	INTJ
ejpam-5268	233	29	,	,	PUNCT
ejpam-5268	233	30	tz)−	tz)−	NOUN
ejpam-5268	233	31	s	s	PART
ejpam-5268	233	32	(	(	PUNCT
ejpam-5268	233	33	fx	fx	PROPN
ejpam-5268	233	34	,	,	PUNCT
ejpam-5268	233	35	fy	fy	PROPN
ejpam-5268	233	36	,	,	PUNCT
ejpam-5268	233	37	fz	fz	PROPN
ejpam-5268	233	38	)	)	PUNCT
ejpam-5268	233	39	by	by	ADP
ejpam-5268	233	40	using	use	VERB
ejpam-5268	233	41	12	12	NUM
ejpam-5268	233	42	,	,	PUNCT
ejpam-5268	233	43	we	we	PRON
ejpam-5268	233	44	get	get	VERB
ejpam-5268	233	45	s	s	PRON
ejpam-5268	233	46	(	(	PUNCT
ejpam-5268	233	47	fx	fx	PROPN
ejpam-5268	233	48	,	,	PUNCT
ejpam-5268	233	49	fy	fy	PROPN
ejpam-5268	233	50	,	,	PUNCT
ejpam-5268	233	51	fz	fz	PROPN
ejpam-5268	233	52	)	)	PUNCT
ejpam-5268	233	53	<	<	X
ejpam-5268	233	54	s	s	X
ejpam-5268	233	55	(	(	PUNCT
ejpam-5268	233	56	tx	tx	PROPN
ejpam-5268	233	57	,	,	PUNCT
ejpam-5268	233	58	ty	ty	INTJ
ejpam-5268	233	59	,	,	PUNCT
ejpam-5268	233	60	tz	tz	NOUN
ejpam-5268	233	61	)	)	PUNCT
ejpam-5268	233	62	≤	≤	NOUN
ejpam-5268	233	63	m1	m1	NOUN
ejpam-5268	233	64	(	(	PUNCT
ejpam-5268	233	65	f	f	X
ejpam-5268	233	66	,	,	PUNCT
ejpam-5268	233	67	t	t	PROPN
ejpam-5268	233	68	,	,	PUNCT
ejpam-5268	233	69	x	x	PROPN
ejpam-5268	233	70	,	,	PUNCT
ejpam-5268	233	71	y	y	PROPN
ejpam-5268	233	72	,	,	PUNCT
ejpam-5268	233	73	z	z	NOUN
ejpam-5268	233	74	)	)	PUNCT
ejpam-5268	233	75	,	,	PUNCT
ejpam-5268	233	76	this	this	PRON
ejpam-5268	233	77	implies	imply	VERB
ejpam-5268	233	78	that	that	SCONJ
ejpam-5268	233	79	ξ(s(fx	ξ(s(fx	NOUN
ejpam-5268	233	80	,	,	PUNCT
ejpam-5268	233	81	fy	fy	PROPN
ejpam-5268	233	82	,	,	PUNCT
ejpam-5268	233	83	fz	fz	PROPN
ejpam-5268	233	84	)	)	PUNCT
ejpam-5268	233	85	,	,	PUNCT
ejpam-5268	233	86	m1	m1	PROPN
ejpam-5268	233	87	(	(	PUNCT
ejpam-5268	233	88	f	f	PROPN
ejpam-5268	233	89	,	,	PUNCT
ejpam-5268	233	90	t	t	PROPN
ejpam-5268	233	91	,	,	PUNCT
ejpam-5268	233	92	x	x	X
ejpam-5268	233	93	,	,	PUNCT
ejpam-5268	233	94	y	y	PROPN
ejpam-5268	233	95	,	,	PUNCT
ejpam-5268	233	96	z	z	NOUN
ejpam-5268	233	97	)	)	PUNCT
ejpam-5268	233	98	≥	≥	NOUN
ejpam-5268	233	99	0	0	NUM
ejpam-5268	233	100	.	.	PUNCT
ejpam-5268	234	1	consequently	consequently	ADV
ejpam-5268	234	2	,	,	PUNCT
ejpam-5268	234	3	via	via	ADP
ejpam-5268	234	4	theorem	theorem	ADJ
ejpam-5268	234	5	1	1	NUM
ejpam-5268	234	6	f	f	PROPN
ejpam-5268	234	7	&	&	CCONJ
ejpam-5268	234	8	t	t	PROPN
ejpam-5268	234	9	have	have	VERB
ejpam-5268	234	10	common	common	ADJ
ejpam-5268	234	11	point	point	NOUN
ejpam-5268	234	12	and	and	CCONJ
ejpam-5268	234	13	coincidence	coincidence	NOUN
ejpam-5268	234	14	fixed	fix	VERB
ejpam-5268	234	15	point	point	NOUN
ejpam-5268	234	16	.	.	PUNCT
ejpam-5268	235	1	corollary	corollary	ADJ
ejpam-5268	235	2	2	2	NUM
ejpam-5268	235	3	.	.	PUNCT
ejpam-5268	236	1	assume	assume	VERB
ejpam-5268	236	2	f	f	X
ejpam-5268	236	3	:	:	PUNCT
ejpam-5268	236	4	(	(	PUNCT
ejpam-5268	236	5	x	x	X
ejpam-5268	236	6	,	,	PUNCT
ejpam-5268	236	7	s	s	PART
ejpam-5268	236	8	)	)	PUNCT
ejpam-5268	236	9	→	→	SYM
ejpam-5268	236	10	(	(	PUNCT
ejpam-5268	236	11	x	x	X
ejpam-5268	236	12	,	,	PUNCT
ejpam-5268	236	13	s	s	PART
ejpam-5268	236	14	)	)	PUNCT
ejpam-5268	236	15	is	be	AUX
ejpam-5268	236	16	self	self	NOUN
ejpam-5268	236	17	map	map	NOUN
ejpam-5268	236	18	in	in	ADP
ejpam-5268	236	19	complete	complete	ADJ
ejpam-5268	236	20	s−metric	s−metric	PROPN
ejpam-5268	236	21	(	(	PUNCT
ejpam-5268	236	22	x	x	X
ejpam-5268	236	23	,	,	PUNCT
ejpam-5268	236	24	s	s	PART
ejpam-5268	236	25	)	)	PUNCT
ejpam-5268	236	26	,	,	PUNCT
ejpam-5268	236	27	so	so	ADV
ejpam-5268	236	28	exists	exist	VERB
ejpam-5268	236	29	x∗	x∗	PROPN
ejpam-5268	236	30	∈	∈	PROPN
ejpam-5268	236	31	x	x	X
ejpam-5268	236	32	(	(	PUNCT
ejpam-5268	236	33	s.	s.	PROPN
ejpam-5268	236	34	t	t	PROPN
ejpam-5268	236	35	)	)	PUNCT
ejpam-5268	236	36	,	,	PUNCT
ejpam-5268	236	37	x∗	x∗	PROPN
ejpam-5268	236	38	≤	≤	PUNCT
ejpam-5268	236	39	fx∗	fx∗	VERB
ejpam-5268	236	40	;	;	PUNCT
ejpam-5268	236	41	if	if	SCONJ
ejpam-5268	236	42	(	(	PUNCT
ejpam-5268	236	43	x	x	NOUN
ejpam-5268	236	44	,	,	PUNCT
ejpam-5268	236	45	y	y	PROPN
ejpam-5268	236	46	)	)	PUNCT
ejpam-5268	236	47	∈	∈	PROPN
ejpam-5268	236	48	x×x	x×x	PROPN
ejpam-5268	236	49	,	,	PUNCT
ejpam-5268	236	50	x	x	PUNCT
ejpam-5268	236	51	≤	≤	ADJ
ejpam-5268	236	52	y	y	PROPN
ejpam-5268	236	53	=	=	AUX
ejpam-5268	236	54	⇒	⇒	NOUN
ejpam-5268	236	55	fx	fx	VERB
ejpam-5268	236	56	≤	≤	PROPN
ejpam-5268	236	57	fy	fy	PROPN
ejpam-5268	236	58	;	;	PUNCT
ejpam-5268	236	59	additionally	additionally	ADV
ejpam-5268	236	60	,	,	PUNCT
ejpam-5268	236	61	if	if	SCONJ
ejpam-5268	236	62	{	{	PUNCT
ejpam-5268	236	63	xs	xs	NOUN
ejpam-5268	236	64	}	}	PUNCT
ejpam-5268	236	65	⊂	⊂	PROPN
ejpam-5268	236	66	x	x	X
ejpam-5268	236	67	is	be	AUX
ejpam-5268	236	68	nondecreasing	nondecrease	VERB
ejpam-5268	236	69	;	;	PUNCT
ejpam-5268	236	70	(	(	PUNCT
ejpam-5268	236	71	w.	w.	PROPN
ejpam-5268	236	72	r.	r.	PROPN
ejpam-5268	236	73	t.	t.	PROPN
ejpam-5268	236	74	≤	≤	PROPN
ejpam-5268	236	75	)	)	PUNCT
ejpam-5268	236	76	with	with	ADP
ejpam-5268	236	77	xs	xs	PROPN
ejpam-5268	236	78	→	→	SYM
ejpam-5268	236	79	p	p	X
ejpam-5268	236	80	,	,	PUNCT
ejpam-5268	236	81	∀s	∀s	PROPN
ejpam-5268	236	82	∈	∈	PROPN
ejpam-5268	237	1	n	n	ADV
ejpam-5268	237	2	and	and	CCONJ
ejpam-5268	237	3	there	there	PRON
ejpam-5268	237	4	exists	exist	VERB
ejpam-5268	237	5	monotone	monotone	ADJ
ejpam-5268	237	6	simulation	simulation	NOUN
ejpam-5268	237	7	map	map	NOUN
ejpam-5268	237	8	ξ	ξ	PROPN
ejpam-5268	237	9	;	;	PUNCT
ejpam-5268	237	10	(	(	PUNCT
ejpam-5268	237	11	s.	s.	PROPN
ejpam-5268	237	12	t	t	PROPN
ejpam-5268	237	13	)	)	PUNCT
ejpam-5268	237	14	,	,	PUNCT
ejpam-5268	237	15	∀	∀	X
ejpam-5268	238	1	(	(	PUNCT
ejpam-5268	238	2	x	x	NOUN
ejpam-5268	238	3	,	,	PUNCT
ejpam-5268	238	4	y	y	NOUN
ejpam-5268	238	5	)	)	PUNCT
ejpam-5268	238	6	∈	∈	PROPN
ejpam-5268	238	7	x	x	X
ejpam-5268	238	8	×x	×x	X
ejpam-5268	238	9	&	&	CCONJ
ejpam-5268	238	10	x	x	PROPN
ejpam-5268	238	11	≤	≤	PROPN
ejpam-5268	238	12	y	y	PROPN
ejpam-5268	238	13	,	,	PUNCT
ejpam-5268	238	14	we	we	PRON
ejpam-5268	238	15	get	get	VERB
ejpam-5268	238	16	ξ	ξ	X
ejpam-5268	238	17	(	(	PUNCT
ejpam-5268	238	18	s	s	X
ejpam-5268	238	19	(	(	PUNCT
ejpam-5268	238	20	fx	fx	PROPN
ejpam-5268	238	21	,	,	PUNCT
ejpam-5268	238	22	fy	fy	PROPN
ejpam-5268	238	23	,	,	PUNCT
ejpam-5268	238	24	fz	fz	PROPN
ejpam-5268	238	25	)	)	PUNCT
ejpam-5268	238	26	,	,	PUNCT
ejpam-5268	238	27	m2	m2	PROPN
ejpam-5268	238	28	(	(	PUNCT
ejpam-5268	238	29	f	f	PROPN
ejpam-5268	238	30	,	,	PUNCT
ejpam-5268	238	31	x	x	PROPN
ejpam-5268	238	32	,	,	PUNCT
ejpam-5268	238	33	y	y	PROPN
ejpam-5268	238	34	,	,	PUNCT
ejpam-5268	238	35	z	z	NOUN
ejpam-5268	238	36	)	)	PUNCT
ejpam-5268	238	37	)	)	PUNCT
ejpam-5268	238	38	≥	≥	NOUN
ejpam-5268	238	39	0	0	NUM
ejpam-5268	238	40	where	where	SCONJ
ejpam-5268	238	41	m2	m2	PROPN
ejpam-5268	238	42	(	(	PUNCT
ejpam-5268	238	43	f	f	PROPN
ejpam-5268	238	44	,	,	PUNCT
ejpam-5268	238	45	x	x	PROPN
ejpam-5268	238	46	,	,	PUNCT
ejpam-5268	238	47	y	y	PROPN
ejpam-5268	238	48	,	,	PUNCT
ejpam-5268	238	49	z	z	NOUN
ejpam-5268	238	50	)	)	PUNCT
ejpam-5268	238	51	=	=	SYM
ejpam-5268	238	52	max	max	PROPN
ejpam-5268	238	53	{	{	PUNCT
ejpam-5268	238	54	s(x	s(x	PROPN
ejpam-5268	238	55	,	,	PUNCT
ejpam-5268	238	56	y	y	PROPN
ejpam-5268	238	57	,	,	PUNCT
ejpam-5268	238	58	z	z	NOUN
ejpam-5268	238	59	)	)	PUNCT
ejpam-5268	238	60	,	,	PUNCT
ejpam-5268	238	61	s(x	s(x	PROPN
ejpam-5268	238	62	,	,	PUNCT
ejpam-5268	238	63	fy	fy	PROPN
ejpam-5268	238	64	,	,	PUNCT
ejpam-5268	238	65	z),s	z),s	X
ejpam-5268	238	66	(	(	PUNCT
ejpam-5268	238	67	y	y	PROPN
ejpam-5268	238	68	,	,	PUNCT
ejpam-5268	238	69	fx	fx	PROPN
ejpam-5268	238	70	,	,	PUNCT
ejpam-5268	238	71	z	z	PROPN
ejpam-5268	238	72	)	)	PUNCT
ejpam-5268	238	73	,	,	PUNCT
ejpam-5268	238	74	s	s	X
ejpam-5268	238	75	(	(	PUNCT
ejpam-5268	238	76	x	x	NOUN
ejpam-5268	238	77	,	,	PUNCT
ejpam-5268	238	78	fx	fx	PROPN
ejpam-5268	238	79	,	,	PUNCT
ejpam-5268	238	80	z	z	PROPN
ejpam-5268	238	81	)	)	PUNCT
ejpam-5268	238	82	,	,	PUNCT
ejpam-5268	238	83	s	s	X
ejpam-5268	238	84	(	(	PUNCT
ejpam-5268	238	85	y	y	PROPN
ejpam-5268	238	86	,	,	PUNCT
ejpam-5268	238	87	fy	fy	PROPN
ejpam-5268	238	88	,	,	PUNCT
ejpam-5268	238	89	z	z	NOUN
ejpam-5268	238	90	)	)	PUNCT
ejpam-5268	238	91	}	}	PUNCT
ejpam-5268	238	92	.	.	PUNCT
ejpam-5268	239	1	then	then	ADV
ejpam-5268	239	2	,	,	PUNCT
ejpam-5268	239	3	{	{	PUNCT
ejpam-5268	239	4	fsx0	fsx0	PROPN
ejpam-5268	239	5	}	}	PUNCT
ejpam-5268	239	6	converges	converge	VERB
ejpam-5268	239	7	to	to	ADP
ejpam-5268	239	8	fixed	fix	VERB
ejpam-5268	239	9	point	point	NOUN
ejpam-5268	239	10	in	in	ADP
ejpam-5268	239	11	f.	f.	PROPN
ejpam-5268	239	12	proof	proof	PROPN
ejpam-5268	239	13	.	.	PUNCT
ejpam-5268	240	1	consequence	consequence	NOUN
ejpam-5268	240	2	immediately	immediately	ADV
ejpam-5268	240	3	of	of	ADP
ejpam-5268	240	4	theorem	theorem	ADJ
ejpam-5268	240	5	1	1	NUM
ejpam-5268	240	6	via	via	ADP
ejpam-5268	240	7	choosing	choose	VERB
ejpam-5268	240	8	t	t	PROPN
ejpam-5268	240	9	as	as	ADP
ejpam-5268	240	10	the	the	DET
ejpam-5268	240	11	identity	identity	NOUN
ejpam-5268	240	12	map	map	NOUN
ejpam-5268	240	13	.	.	PUNCT
ejpam-5268	241	1	now	now	ADV
ejpam-5268	241	2	,	,	PUNCT
ejpam-5268	241	3	introduce	introduce	VERB
ejpam-5268	241	4	instructive	instructive	ADJ
ejpam-5268	241	5	example	example	NOUN
ejpam-5268	241	6	,	,	PUNCT
ejpam-5268	241	7	which	which	PRON
ejpam-5268	241	8	displays	display	VERB
ejpam-5268	241	9	the	the	DET
ejpam-5268	241	10	interest	interest	NOUN
ejpam-5268	241	11	of	of	ADP
ejpam-5268	241	12	theorem	theorem	NOUN
ejpam-5268	241	13	1	1	NUM
ejpam-5268	241	14	.	.	PUNCT
ejpam-5268	241	15	n.	n.	PROPN
ejpam-5268	241	16	a.	a.	PROPN
ejpam-5268	241	17	majid	majid	PROPN
ejpam-5268	241	18	et	et	PROPN
ejpam-5268	241	19	al	al	PROPN
ejpam-5268	241	20	.	.	PUNCT
ejpam-5268	241	21	/	/	SYM
ejpam-5268	241	22	eur	eur	PROPN
ejpam-5268	241	23	.	.	PUNCT
ejpam-5268	242	1	j.	j.	PROPN
ejpam-5268	242	2	pure	pure	PROPN
ejpam-5268	242	3	appl	appl	PROPN
ejpam-5268	242	4	.	.	PROPN
ejpam-5268	242	5	math	math	PROPN
ejpam-5268	242	6	,	,	PUNCT
ejpam-5268	242	7	17	17	NUM
ejpam-5268	242	8	(	(	PUNCT
ejpam-5268	242	9	3	3	NUM
ejpam-5268	242	10	)	)	PUNCT
ejpam-5268	242	11	(	(	PUNCT
ejpam-5268	242	12	2024	2024	NUM
ejpam-5268	242	13	)	)	PUNCT
ejpam-5268	242	14	,	,	PUNCT
ejpam-5268	242	15	1877	1877	NUM
ejpam-5268	242	16	-	-	SYM
ejpam-5268	242	17	1893	1893	NUM
ejpam-5268	242	18	1887	1887	NUM
ejpam-5268	242	19	example	example	NOUN
ejpam-5268	242	20	5	5	NUM
ejpam-5268	242	21	(	(	PUNCT
ejpam-5268	242	22	23	23	NUM
ejpam-5268	242	23	)	)	PUNCT
ejpam-5268	242	24	.	.	PUNCT
ejpam-5268	243	1	assume	assume	VERB
ejpam-5268	243	2	that	that	SCONJ
ejpam-5268	243	3	x	x	X
ejpam-5268	244	1	=	=	PUNCT
ejpam-5268	245	1	[	[	X
ejpam-5268	245	2	0	0	NUM
ejpam-5268	245	3	,	,	PUNCT
ejpam-5268	245	4	1	1	NUM
ejpam-5268	245	5	]	]	PUNCT
ejpam-5268	245	6	with	with	ADP
ejpam-5268	245	7	s	s	ADJ
ejpam-5268	245	8	-	-	ADJ
ejpam-5268	245	9	metric	metric	ADJ
ejpam-5268	245	10	described	describe	VERB
ejpam-5268	245	11	via	via	ADP
ejpam-5268	245	12	s	s	PRON
ejpam-5268	245	13	(	(	PUNCT
ejpam-5268	245	14	x	x	X
ejpam-5268	245	15	,	,	PUNCT
ejpam-5268	245	16	y	y	PROPN
ejpam-5268	245	17	,	,	PUNCT
ejpam-5268	245	18	z	z	NOUN
ejpam-5268	245	19	)	)	PUNCT
ejpam-5268	245	20	=	=	SYM
ejpam-5268	245	21	max	max	PROPN
ejpam-5268	245	22	{	{	PUNCT
ejpam-5268	245	23	|z	|z	PROPN
ejpam-5268	245	24	−	−	PROPN
ejpam-5268	245	25	x|	x|	PROPN
ejpam-5268	245	26	,	,	PUNCT
ejpam-5268	245	27	|x−	|x−	NOUN
ejpam-5268	245	28	y|	y|	NOUN
ejpam-5268	245	29	,	,	PUNCT
ejpam-5268	245	30	|y−	|y−	NOUN
ejpam-5268	245	31	z|	z|	PROPN
ejpam-5268	245	32	}	}	PUNCT
ejpam-5268	245	33	for	for	ADP
ejpam-5268	245	34	each	each	DET
ejpam-5268	245	35	x	x	PROPN
ejpam-5268	245	36	,	,	PUNCT
ejpam-5268	245	37	y	y	PROPN
ejpam-5268	245	38	,	,	PUNCT
ejpam-5268	245	39	z	z	PROPN
ejpam-5268	245	40	∈	∈	PROPN
ejpam-5268	245	41	x.	x.	NOUN
ejpam-5268	245	42	suppose	suppose	VERB
ejpam-5268	245	43	,	,	PUNCT
ejpam-5268	245	44	z	z	NOUN
ejpam-5268	245	45	≤	≤	NUM
ejpam-5268	245	46	y	y	PROPN
ejpam-5268	245	47	≤	≤	PROPN
ejpam-5268	245	48	x.	x.	PUNCT
ejpam-5268	246	1	consequently	consequently	ADV
ejpam-5268	246	2	,	,	PUNCT
ejpam-5268	246	3	s	s	X
ejpam-5268	246	4	(	(	PUNCT
ejpam-5268	246	5	x	x	NOUN
ejpam-5268	246	6	,	,	PUNCT
ejpam-5268	246	7	y	y	PROPN
ejpam-5268	246	8	,	,	PUNCT
ejpam-5268	246	9	z	z	NOUN
ejpam-5268	246	10	)	)	PUNCT
ejpam-5268	246	11	=	=	SYM
ejpam-5268	246	12	|x	|x	NOUN
ejpam-5268	246	13	−	−	PROPN
ejpam-5268	246	14	z|	z|	PROPN
ejpam-5268	246	15	.	.	PUNCT
ejpam-5268	246	16	define	define	VERB
ejpam-5268	246	17	the	the	DET
ejpam-5268	246	18	mappings	mapping	NOUN
ejpam-5268	246	19	f	f	X
ejpam-5268	246	20	,	,	PUNCT
ejpam-5268	246	21	t	t	X
ejpam-5268	246	22	:	:	PUNCT
ejpam-5268	246	23	(	(	PUNCT
ejpam-5268	246	24	x	x	X
ejpam-5268	246	25	,	,	PUNCT
ejpam-5268	246	26	s	s	PART
ejpam-5268	246	27	)	)	PUNCT
ejpam-5268	246	28	→	→	SYM
ejpam-5268	246	29	(	(	PUNCT
ejpam-5268	246	30	x	x	X
ejpam-5268	246	31	,	,	PUNCT
ejpam-5268	246	32	s	s	PART
ejpam-5268	246	33	)	)	PUNCT
ejpam-5268	246	34	by	by	ADP
ejpam-5268	246	35	fx	fx	NOUN
ejpam-5268	246	36	=	=	SYM
ejpam-5268	246	37	1	1	NUM
ejpam-5268	246	38	25x	25x	PROPN
ejpam-5268	246	39	&	&	CCONJ
ejpam-5268	246	40	tx	tx	PROPN
ejpam-5268	246	41	=	=	NOUN
ejpam-5268	246	42	1	1	NUM
ejpam-5268	246	43	5x	5x	NUM
ejpam-5268	246	44	,	,	PUNCT
ejpam-5268	246	45	∀	∀	X
ejpam-5268	246	46	x	x	SYM
ejpam-5268	246	47	∈	∈	NOUN
ejpam-5268	246	48	x.	x.	NOUN
ejpam-5268	246	49	obviously	obviously	ADV
ejpam-5268	246	50	,	,	PUNCT
ejpam-5268	246	51	the	the	DET
ejpam-5268	246	52	cases	case	NOUN
ejpam-5268	246	53	(	(	PUNCT
ejpam-5268	246	54	i	i	NOUN
ejpam-5268	246	55	)	)	PUNCT
ejpam-5268	246	56	to	to	ADP
ejpam-5268	246	57	(	(	PUNCT
ejpam-5268	246	58	v	v	NOUN
ejpam-5268	246	59	)	)	PUNCT
ejpam-5268	246	60	of	of	ADP
ejpam-5268	246	61	theorem	theorem	NOUN
ejpam-5268	246	62	1	1	NUM
ejpam-5268	246	63	are	be	AUX
ejpam-5268	246	64	satisfied	satisfied	ADJ
ejpam-5268	246	65	at	at	ADP
ejpam-5268	246	66	x∗	x∗	PROPN
ejpam-5268	246	67	=	=	SYM
ejpam-5268	246	68	0	0	X
ejpam-5268	246	69	.	.	PUNCT
ejpam-5268	246	70	presume	presume	VERB
ejpam-5268	246	71	ξ	ξ	X
ejpam-5268	246	72	:	:	PUNCT
ejpam-5268	246	73	x	x	PROPN
ejpam-5268	246	74	×x	×x	ADP
ejpam-5268	246	75	→	→	SYM
ejpam-5268	246	76	r	r	NOUN
ejpam-5268	246	77	given	give	VERB
ejpam-5268	246	78	via	via	ADP
ejpam-5268	246	79	ξ	ξ	PROPN
ejpam-5268	246	80	(	(	PUNCT
ejpam-5268	246	81	t	t	PROPN
ejpam-5268	246	82	,	,	PUNCT
ejpam-5268	246	83	w	w	NOUN
ejpam-5268	246	84	)	)	PUNCT
ejpam-5268	246	85	=	=	NOUN
ejpam-5268	246	86	λw	λw	ADP
ejpam-5268	246	87	−	−	PROPN
ejpam-5268	246	88	t	t	PROPN
ejpam-5268	246	89	,	,	PUNCT
ejpam-5268	246	90	for	for	ADP
ejpam-5268	246	91	,	,	PUNCT
ejpam-5268	246	92	λ	λ	PROPN
ejpam-5268	246	93	∈	∈	PROPN
ejpam-5268	247	1	[	[	X
ejpam-5268	247	2	0	0	NUM
ejpam-5268	247	3	,	,	PUNCT
ejpam-5268	247	4	1	1	NUM
ejpam-5268	247	5	)	)	PUNCT
ejpam-5268	247	6	.	.	PUNCT
ejpam-5268	248	1	certainly	certainly	ADV
ejpam-5268	248	2	∀	∀	X
ejpam-5268	248	3	x	x	X
ejpam-5268	248	4	̸=	̸=	PROPN
ejpam-5268	248	5	y	y	PROPN
ejpam-5268	248	6	̸=	̸=	PROPN
ejpam-5268	248	7	z	z	PROPN
ejpam-5268	248	8	,	,	PUNCT
ejpam-5268	248	9	get	get	VERB
ejpam-5268	248	10	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	248	11	,	,	PUNCT
ejpam-5268	248	12	fy	fy	PROPN
ejpam-5268	248	13	,	,	PUNCT
ejpam-5268	248	14	fz	fz	PROPN
ejpam-5268	248	15	)	)	PUNCT
ejpam-5268	248	16	,	,	PUNCT
ejpam-5268	248	17	m1(f	m1(f	X
ejpam-5268	248	18	,	,	PUNCT
ejpam-5268	248	19	t	t	PROPN
ejpam-5268	248	20	,	,	PUNCT
ejpam-5268	248	21	x	x	PROPN
ejpam-5268	248	22	,	,	PUNCT
ejpam-5268	248	23	y	y	PROPN
ejpam-5268	248	24	,	,	PUNCT
ejpam-5268	248	25	z	z	NOUN
ejpam-5268	248	26	)	)	PUNCT
ejpam-5268	248	27	)	)	PUNCT
ejpam-5268	249	1	=	=	SYM
ejpam-5268	249	2	λm1(f	λm1(f	PROPN
ejpam-5268	249	3	,	,	PUNCT
ejpam-5268	249	4	t	t	PROPN
ejpam-5268	249	5	,	,	PUNCT
ejpam-5268	249	6	x	x	X
ejpam-5268	249	7	,	,	PUNCT
ejpam-5268	249	8	y	y	PROPN
ejpam-5268	249	9	,	,	PUNCT
ejpam-5268	249	10	z)−	z)−	PROPN
ejpam-5268	249	11	s(fx	s(fx	PROPN
ejpam-5268	249	12	,	,	PUNCT
ejpam-5268	249	13	fy	fy	PROPN
ejpam-5268	249	14	,	,	PUNCT
ejpam-5268	249	15	fz	fz	PROPN
ejpam-5268	249	16	)	)	PUNCT
ejpam-5268	249	17	.	.	PUNCT
ejpam-5268	250	1	in	in	ADP
ejpam-5268	250	2	particular	particular	ADJ
ejpam-5268	250	3	if	if	SCONJ
ejpam-5268	250	4	we	we	PRON
ejpam-5268	250	5	select	select	VERB
ejpam-5268	250	6	,	,	PUNCT
ejpam-5268	250	7	λ	λ	X
ejpam-5268	250	8	=	=	NOUN
ejpam-5268	250	9	1	1	NUM
ejpam-5268	250	10	3	3	NUM
ejpam-5268	250	11	,	,	PUNCT
ejpam-5268	250	12	we	we	PRON
ejpam-5268	250	13	find	find	VERB
ejpam-5268	250	14	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	250	15	,	,	PUNCT
ejpam-5268	250	16	fy	fy	PROPN
ejpam-5268	250	17	,	,	PUNCT
ejpam-5268	250	18	fz	fz	PROPN
ejpam-5268	250	19	)	)	PUNCT
ejpam-5268	250	20	,	,	PUNCT
ejpam-5268	250	21	m1(f	m1(f	X
ejpam-5268	250	22	,	,	PUNCT
ejpam-5268	250	23	t	t	PROPN
ejpam-5268	250	24	,	,	PUNCT
ejpam-5268	250	25	x	x	PROPN
ejpam-5268	250	26	,	,	PUNCT
ejpam-5268	250	27	y	y	PROPN
ejpam-5268	250	28	,	,	PUNCT
ejpam-5268	250	29	z	z	NOUN
ejpam-5268	250	30	)	)	PUNCT
ejpam-5268	250	31	)	)	PUNCT
ejpam-5268	251	1	=	=	SYM
ejpam-5268	251	2	1	1	NUM
ejpam-5268	251	3	3	3	NUM
ejpam-5268	251	4	m1(f	m1(f	PROPN
ejpam-5268	251	5	,	,	PUNCT
ejpam-5268	251	6	t	t	PROPN
ejpam-5268	251	7	,	,	PUNCT
ejpam-5268	251	8	x	x	PROPN
ejpam-5268	251	9	,	,	PUNCT
ejpam-5268	251	10	y	y	PROPN
ejpam-5268	251	11	,	,	PUNCT
ejpam-5268	251	12	z)−	z)−	PROPN
ejpam-5268	251	13	s(fx	s(fx	PROPN
ejpam-5268	251	14	,	,	PUNCT
ejpam-5268	251	15	fy	fy	PROPN
ejpam-5268	251	16	,	,	PUNCT
ejpam-5268	251	17	fz	fz	PROPN
ejpam-5268	251	18	)	)	PUNCT
ejpam-5268	251	19	.	.	PUNCT
ejpam-5268	252	1	(	(	PUNCT
ejpam-5268	252	2	13	13	NUM
ejpam-5268	252	3	)	)	PUNCT
ejpam-5268	252	4	∀	∀	X
ejpam-5268	253	1	x	x	NOUN
ejpam-5268	253	2	,	,	PUNCT
ejpam-5268	253	3	y	y	PROPN
ejpam-5268	253	4	,	,	PUNCT
ejpam-5268	253	5	z	z	NOUN
ejpam-5268	253	6	∈	∈	PROPN
ejpam-5268	253	7	x.	x.	NOUN
ejpam-5268	253	8	we	we	PRON
ejpam-5268	253	9	have	have	VERB
ejpam-5268	253	10	s	s	NOUN
ejpam-5268	253	11	(	(	PUNCT
ejpam-5268	253	12	fx	fx	PROPN
ejpam-5268	253	13	,	,	PUNCT
ejpam-5268	253	14	fy	fy	PROPN
ejpam-5268	253	15	,	,	PUNCT
ejpam-5268	253	16	fz	fz	PROPN
ejpam-5268	253	17	)	)	PUNCT
ejpam-5268	254	1	=	=	SYM
ejpam-5268	254	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	254	3	125x−	125x−	NUM
ejpam-5268	254	4	1	1	NUM
ejpam-5268	254	5	25	25	NUM
ejpam-5268	254	6	z	z	NOUN
ejpam-5268	254	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	254	8	≤	≤	NUM
ejpam-5268	254	9	1	1	NUM
ejpam-5268	254	10	4	4	NUM
ejpam-5268	254	11	∣∣∣∣15x	∣∣∣∣15x	ADP
ejpam-5268	254	12	−	−	NOUN
ejpam-5268	254	13	1	1	NUM
ejpam-5268	254	14	5	5	NUM
ejpam-5268	254	15	z	z	NOUN
ejpam-5268	254	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	254	17	=	=	NOUN
ejpam-5268	254	18	1	1	NUM
ejpam-5268	254	19	4	4	NUM
ejpam-5268	254	20	s(tx	s(tx	NOUN
ejpam-5268	254	21	,	,	PUNCT
ejpam-5268	254	22	ty	ty	INTJ
ejpam-5268	254	23	,	,	PUNCT
ejpam-5268	254	24	tz	tz	NOUN
ejpam-5268	254	25	)	)	PUNCT
ejpam-5268	254	26	≤	≤	NUM
ejpam-5268	254	27	1	1	NUM
ejpam-5268	254	28	3	3	NUM
ejpam-5268	254	29	m1(f	m1(f	PROPN
ejpam-5268	254	30	,	,	PUNCT
ejpam-5268	254	31	t	t	PROPN
ejpam-5268	254	32	,	,	PUNCT
ejpam-5268	254	33	x	x	X
ejpam-5268	254	34	,	,	PUNCT
ejpam-5268	254	35	y	y	PROPN
ejpam-5268	254	36	,	,	PUNCT
ejpam-5268	254	37	z	z	NOUN
ejpam-5268	254	38	)	)	PUNCT
ejpam-5268	254	39	this	this	PRON
ejpam-5268	254	40	means	mean	VERB
ejpam-5268	254	41	,	,	PUNCT
ejpam-5268	254	42	1	1	NUM
ejpam-5268	254	43	3	3	NUM
ejpam-5268	254	44	m1	m1	NOUN
ejpam-5268	254	45	(	(	PUNCT
ejpam-5268	254	46	f	f	PROPN
ejpam-5268	254	47	,	,	PUNCT
ejpam-5268	254	48	t	t	PROPN
ejpam-5268	254	49	,	,	PUNCT
ejpam-5268	254	50	x	x	X
ejpam-5268	254	51	,	,	PUNCT
ejpam-5268	254	52	y	y	PROPN
ejpam-5268	254	53	,	,	PUNCT
ejpam-5268	254	54	z)−	z)−	PROPN
ejpam-5268	254	55	s(fx	s(fx	PROPN
ejpam-5268	254	56	,	,	PUNCT
ejpam-5268	254	57	fy	fy	PROPN
ejpam-5268	254	58	,	,	PUNCT
ejpam-5268	254	59	fz	fz	PROPN
ejpam-5268	254	60	)	)	PUNCT
ejpam-5268	254	61	≥	≥	NOUN
ejpam-5268	254	62	0	0	NUM
ejpam-5268	254	63	.	.	PUNCT
ejpam-5268	255	1	(	(	PUNCT
ejpam-5268	255	2	14	14	NUM
ejpam-5268	255	3	)	)	PUNCT
ejpam-5268	255	4	utilizing	utilizing	NOUN
ejpam-5268	255	5	of	of	ADP
ejpam-5268	255	6	13	13	NUM
ejpam-5268	255	7	and	and	CCONJ
ejpam-5268	255	8	14	14	NUM
ejpam-5268	255	9	,	,	PUNCT
ejpam-5268	255	10	we	we	PRON
ejpam-5268	255	11	get	get	VERB
ejpam-5268	255	12	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	255	13	,	,	PUNCT
ejpam-5268	255	14	fy	fy	PROPN
ejpam-5268	255	15	,	,	PUNCT
ejpam-5268	255	16	fz	fz	PROPN
ejpam-5268	255	17	)	)	PUNCT
ejpam-5268	255	18	,	,	PUNCT
ejpam-5268	255	19	m1(f	m1(f	X
ejpam-5268	255	20	,	,	PUNCT
ejpam-5268	255	21	t	t	PROPN
ejpam-5268	255	22	,	,	PUNCT
ejpam-5268	255	23	x	x	PROPN
ejpam-5268	255	24	,	,	PUNCT
ejpam-5268	255	25	y	y	PROPN
ejpam-5268	255	26	,	,	PUNCT
ejpam-5268	255	27	z	z	NOUN
ejpam-5268	255	28	)	)	PUNCT
ejpam-5268	255	29	)	)	PUNCT
ejpam-5268	255	30	≥	≥	NOUN
ejpam-5268	256	1	0	0	NUM
ejpam-5268	256	2	.	.	PUNCT
ejpam-5268	257	1	then	then	ADV
ejpam-5268	257	2	,	,	PUNCT
ejpam-5268	257	3	all	all	DET
ejpam-5268	257	4	suppositions	supposition	NOUN
ejpam-5268	257	5	of	of	ADP
ejpam-5268	257	6	theorem	theorem	ADJ
ejpam-5268	257	7	1	1	NUM
ejpam-5268	257	8	satisfied	satisfied	ADJ
ejpam-5268	257	9	.	.	PUNCT
ejpam-5268	258	1	therefore	therefore	ADV
ejpam-5268	258	2	,	,	PUNCT
ejpam-5268	258	3	f	f	PROPN
ejpam-5268	258	4	&	&	CCONJ
ejpam-5268	258	5	t	t	PROPN
ejpam-5268	258	6	have	have	VERB
ejpam-5268	258	7	coincident	coincident	NOUN
ejpam-5268	258	8	(	(	PUNCT
ejpam-5268	258	9	0	0	NUM
ejpam-5268	258	10	∈	∈	PROPN
ejpam-5268	258	11	x	x	NOUN
ejpam-5268	258	12	)	)	PUNCT
ejpam-5268	258	13	.	.	PUNCT
ejpam-5268	259	1	moreover	moreover	ADV
ejpam-5268	259	2	,	,	PUNCT
ejpam-5268	259	3	f	f	PROPN
ejpam-5268	259	4	&	&	CCONJ
ejpam-5268	259	5	t	t	PROPN
ejpam-5268	259	6	commute	commute	NOUN
ejpam-5268	259	7	at	at	ADP
ejpam-5268	259	8	point	point	NOUN
ejpam-5268	259	9	0	0	NUM
ejpam-5268	259	10	,	,	PUNCT
ejpam-5268	259	11	which	which	PRON
ejpam-5268	259	12	illustrate	illustrate	VERB
ejpam-5268	259	13	0	0	NUM
ejpam-5268	259	14	unique	unique	ADJ
ejpam-5268	259	15	common	common	ADJ
ejpam-5268	259	16	fixed	fix	VERB
ejpam-5268	259	17	point	point	NOUN
ejpam-5268	259	18	of	of	ADP
ejpam-5268	259	19	a	a	DET
ejpam-5268	259	20	maps	map	NOUN
ejpam-5268	259	21	f	f	PROPN
ejpam-5268	259	22	&	&	CCONJ
ejpam-5268	259	23	t.	t.	PROPN
ejpam-5268	259	24	3	3	NUM
ejpam-5268	259	25	.	.	PUNCT
ejpam-5268	259	26	various	various	ADJ
ejpam-5268	259	27	common	common	ADJ
ejpam-5268	259	28	and	and	CCONJ
ejpam-5268	259	29	coincidence	coincidence	NOUN
ejpam-5268	259	30	fixed	fix	VERB
ejpam-5268	259	31	point	point	NOUN
ejpam-5268	259	32	results	result	NOUN
ejpam-5268	259	33	utilize	utilize	VERB
ejpam-5268	259	34	right	right	ADJ
ejpam-5268	259	35	monotone	monotone	ADJ
ejpam-5268	259	36	simulation	simulation	NOUN
ejpam-5268	259	37	maps	map	NOUN
ejpam-5268	259	38	in	in	ADP
ejpam-5268	259	39	this	this	DET
ejpam-5268	259	40	section	section	NOUN
ejpam-5268	259	41	,	,	PUNCT
ejpam-5268	259	42	utilize	utilize	VERB
ejpam-5268	259	43	right	right	ADJ
ejpam-5268	259	44	monotone	monotone	ADJ
ejpam-5268	259	45	simulation	simulation	NOUN
ejpam-5268	259	46	mappings	mapping	NOUN
ejpam-5268	259	47	to	to	PART
ejpam-5268	259	48	deduce	deduce	VERB
ejpam-5268	259	49	various	various	ADJ
ejpam-5268	259	50	common	common	ADJ
ejpam-5268	259	51	and	and	CCONJ
ejpam-5268	259	52	coincidence	coincidence	NOUN
ejpam-5268	259	53	fixed	fix	VERB
ejpam-5268	259	54	point	point	NOUN
ejpam-5268	259	55	outcomes	outcome	NOUN
ejpam-5268	259	56	in	in	ADP
ejpam-5268	259	57	symmetrical	symmetrical	ADJ
ejpam-5268	259	58	complete	complete	ADJ
ejpam-5268	259	59	s	s	NOUN
ejpam-5268	259	60	-	-	NOUN
ejpam-5268	259	61	metric	metric	ADJ
ejpam-5268	259	62	.	.	PUNCT
ejpam-5268	260	1	definition	definition	NOUN
ejpam-5268	260	2	5	5	NUM
ejpam-5268	260	3	.	.	PUNCT
ejpam-5268	261	1	[	[	X
ejpam-5268	261	2	4	4	NUM
ejpam-5268	261	3	]	]	SYM
ejpam-5268	261	4	ξ	ξ	NOUN
ejpam-5268	261	5	:	:	PUNCT
ejpam-5268	262	1	[	[	X
ejpam-5268	262	2	0,+∞	0,+∞	NUM
ejpam-5268	262	3	)	)	PUNCT
ejpam-5268	262	4	×	×	NOUN
ejpam-5268	263	1	[	[	X
ejpam-5268	263	2	0,+∞	0,+∞	NUM
ejpam-5268	263	3	)	)	PUNCT
ejpam-5268	263	4	→	→	SYM
ejpam-5268	263	5	r	r	X
ejpam-5268	263	6	,	,	PUNCT
ejpam-5268	263	7	is	be	AUX
ejpam-5268	263	8	called	call	VERB
ejpam-5268	263	9	right	right	ADJ
ejpam-5268	263	10	-	-	PUNCT
ejpam-5268	263	11	monotone	monotone	ADJ
ejpam-5268	263	12	simulation	simulation	NOUN
ejpam-5268	263	13	mapping	mapping	NOUN
ejpam-5268	263	14	,	,	PUNCT
ejpam-5268	263	15	if	if	SCONJ
ejpam-5268	263	16	it	it	PRON
ejpam-5268	263	17	’s	’	VERB
ejpam-5268	263	18	a	a	DET
ejpam-5268	263	19	simulation	simulation	NOUN
ejpam-5268	263	20	mapping	mapping	NOUN
ejpam-5268	263	21	that	that	PRON
ejpam-5268	263	22	satisfies	satisfy	VERB
ejpam-5268	263	23	for	for	ADP
ejpam-5268	263	24	each	each	DET
ejpam-5268	263	25	t	t	PROPN
ejpam-5268	263	26	,	,	PUNCT
ejpam-5268	263	27	w1,w2	w1,w2	PROPN
ejpam-5268	263	28	≥	≥	PROPN
ejpam-5268	263	29	0	0	NUM
ejpam-5268	263	30	,	,	PUNCT
ejpam-5268	263	31	ifw1	ifw1	PROPN
ejpam-5268	263	32	≤	≤	PROPN
ejpam-5268	263	33	w2	w2	NOUN
ejpam-5268	263	34	,	,	PUNCT
ejpam-5268	263	35	then	then	ADV
ejpam-5268	263	36	ξ	ξ	PROPN
ejpam-5268	263	37	(	(	PUNCT
ejpam-5268	263	38	t	t	PROPN
ejpam-5268	263	39	,	,	PUNCT
ejpam-5268	263	40	w1	w1	NOUN
ejpam-5268	263	41	)	)	PUNCT
ejpam-5268	264	1	≤	≤	NOUN
ejpam-5268	265	1	ξ	ξ	PROPN
ejpam-5268	265	2	(	(	PUNCT
ejpam-5268	265	3	t	t	PROPN
ejpam-5268	265	4	,	,	PUNCT
ejpam-5268	265	5	w2	w2	NOUN
ejpam-5268	265	6	)	)	PUNCT
ejpam-5268	265	7	,	,	PUNCT
ejpam-5268	265	8	example	example	NOUN
ejpam-5268	265	9	6	6	NUM
ejpam-5268	265	10	.	.	PUNCT
ejpam-5268	265	11	suppose	suppose	VERB
ejpam-5268	265	12	that	that	SCONJ
ejpam-5268	265	13	ξ	ξ	X
ejpam-5268	265	14	:	:	PUNCT
ejpam-5268	266	1	[	[	X
ejpam-5268	266	2	0,+∞)×	0,+∞)×	NOUN
ejpam-5268	267	1	[	[	X
ejpam-5268	267	2	0,+∞	0,+∞	NUM
ejpam-5268	267	3	)	)	PUNCT
ejpam-5268	267	4	→	→	SYM
ejpam-5268	267	5	r	r	NOUN
ejpam-5268	267	6	be	be	VERB
ejpam-5268	267	7	a	a	DET
ejpam-5268	267	8	mapping	mapping	NOUN
ejpam-5268	267	9	described	describe	VERB
ejpam-5268	267	10	as	as	ADP
ejpam-5268	267	11	follows	follow	VERB
ejpam-5268	267	12	:	:	PUNCT
ejpam-5268	267	13	ξ	ξ	PROPN
ejpam-5268	267	14	(	(	PUNCT
ejpam-5268	267	15	t	t	PROPN
ejpam-5268	267	16	,	,	PUNCT
ejpam-5268	267	17	w	w	NOUN
ejpam-5268	267	18	)	)	PUNCT
ejpam-5268	267	19	=	=	PUNCT
ejpam-5268	268	1	w	w	PROPN
ejpam-5268	268	2	−	−	PROPN
ejpam-5268	268	3	t	t	NOUN
ejpam-5268	268	4	+	+	CCONJ
ejpam-5268	268	5	2	2	NUM
ejpam-5268	268	6	t	t	NOUN
ejpam-5268	268	7	+	+	CCONJ
ejpam-5268	268	8	1	1	NUM
ejpam-5268	268	9	t	t	NOUN
ejpam-5268	268	10	,	,	PUNCT
ejpam-5268	268	11	∀	∀	X
ejpam-5268	268	12	t	t	PROPN
ejpam-5268	268	13	,	,	PUNCT
ejpam-5268	268	14	w	w	PROPN
ejpam-5268	268	15	≥	≥	NOUN
ejpam-5268	268	16	0	0	NUM
ejpam-5268	268	17	.	.	PUNCT
ejpam-5268	269	1	so	so	ADV
ejpam-5268	269	2	,	,	PUNCT
ejpam-5268	269	3	ξ	ξ	PROPN
ejpam-5268	269	4	is	be	AUX
ejpam-5268	269	5	right	right	ADJ
ejpam-5268	269	6	-	-	PUNCT
ejpam-5268	269	7	monotone	monotone	ADJ
ejpam-5268	269	8	simulation	simulation	NOUN
ejpam-5268	269	9	mapping	mapping	NOUN
ejpam-5268	269	10	.	.	PUNCT
ejpam-5268	270	1	n.	n.	PROPN
ejpam-5268	270	2	a.	a.	PROPN
ejpam-5268	270	3	majid	majid	PROPN
ejpam-5268	270	4	et	et	PROPN
ejpam-5268	270	5	al	al	PROPN
ejpam-5268	270	6	.	.	PUNCT
ejpam-5268	270	7	/	/	SYM
ejpam-5268	270	8	eur	eur	PROPN
ejpam-5268	270	9	.	.	PUNCT
ejpam-5268	271	1	j.	j.	PROPN
ejpam-5268	271	2	pure	pure	PROPN
ejpam-5268	271	3	appl	appl	PROPN
ejpam-5268	271	4	.	.	PROPN
ejpam-5268	271	5	math	math	PROPN
ejpam-5268	271	6	,	,	PUNCT
ejpam-5268	271	7	17	17	NUM
ejpam-5268	271	8	(	(	PUNCT
ejpam-5268	271	9	3	3	NUM
ejpam-5268	271	10	)	)	PUNCT
ejpam-5268	271	11	(	(	PUNCT
ejpam-5268	271	12	2024	2024	NUM
ejpam-5268	271	13	)	)	PUNCT
ejpam-5268	271	14	,	,	PUNCT
ejpam-5268	271	15	1877	1877	NUM
ejpam-5268	271	16	-	-	SYM
ejpam-5268	271	17	1893	1893	NUM
ejpam-5268	271	18	1888	1888	NUM
ejpam-5268	271	19	remark	remark	NOUN
ejpam-5268	271	20	3	3	NUM
ejpam-5268	271	21	.	.	PUNCT
ejpam-5268	272	1	it	it	PRON
ejpam-5268	272	2	’s	’	VERB
ejpam-5268	272	3	clear	clear	ADJ
ejpam-5268	272	4	that	that	SCONJ
ejpam-5268	272	5	each	each	DET
ejpam-5268	272	6	right	right	ADJ
ejpam-5268	272	7	-	-	PUNCT
ejpam-5268	272	8	monotone	monotone	NOUN
ejpam-5268	272	9	simulation	simulation	NOUN
ejpam-5268	272	10	mapping	mapping	NOUN
ejpam-5268	272	11	is	be	AUX
ejpam-5268	272	12	simulation	simulation	NOUN
ejpam-5268	272	13	mapping	mapping	NOUN
ejpam-5268	272	14	;	;	PUNCT
ejpam-5268	272	15	the	the	DET
ejpam-5268	272	16	converse	converse	NOUN
ejpam-5268	272	17	need	need	VERB
ejpam-5268	272	18	n’t	not	PART
ejpam-5268	272	19	to	to	PART
ejpam-5268	272	20	be	be	AUX
ejpam-5268	272	21	true	true	ADJ
ejpam-5268	272	22	in	in	ADP
ejpam-5268	272	23	general	general	ADJ
ejpam-5268	272	24	.	.	PUNCT
ejpam-5268	272	25	example	example	NOUN
ejpam-5268	273	1	7	7	X
ejpam-5268	273	2	.	.	PUNCT
ejpam-5268	273	3	suppose	suppose	VERB
ejpam-5268	273	4	ξ	ξ	X
ejpam-5268	273	5	:	:	PUNCT
ejpam-5268	274	1	[	[	X
ejpam-5268	274	2	0,+∞)×	0,+∞)×	NOUN
ejpam-5268	274	3	[	[	X
ejpam-5268	274	4	0,+∞	0,+∞	NUM
ejpam-5268	274	5	)	)	PUNCT
ejpam-5268	274	6	→	→	SYM
ejpam-5268	274	7	r	r	X
ejpam-5268	274	8	,	,	PUNCT
ejpam-5268	274	9	is	be	AUX
ejpam-5268	274	10	mapping	mapping	NOUN
ejpam-5268	274	11	described	describe	VERB
ejpam-5268	274	12	as	as	ADP
ejpam-5268	274	13	:	:	PUNCT
ejpam-5268	274	14	ξ	ξ	X
ejpam-5268	274	15	(	(	PUNCT
ejpam-5268	274	16	t	t	PROPN
ejpam-5268	274	17	,	,	PUNCT
ejpam-5268	274	18	w	w	NOUN
ejpam-5268	274	19	)	)	PUNCT
ejpam-5268	274	20	=	=	SYM
ejpam-5268	274	21	|sint|	|sint|	PROPN
ejpam-5268	274	22	−	−	PROPN
ejpam-5268	274	23	w	w	NOUN
ejpam-5268	274	24	,	,	PUNCT
ejpam-5268	274	25	∀	∀	X
ejpam-5268	274	26	t	t	NOUN
ejpam-5268	274	27	,	,	PUNCT
ejpam-5268	274	28	w	w	PROPN
ejpam-5268	274	29	≥	≥	NOUN
ejpam-5268	274	30	0	0	NUM
ejpam-5268	274	31	.	.	PUNCT
ejpam-5268	275	1	in	in	ADP
ejpam-5268	275	2	that	that	DET
ejpam-5268	275	3	case	case	NOUN
ejpam-5268	275	4	,	,	PUNCT
ejpam-5268	275	5	ξ	ξ	PROPN
ejpam-5268	275	6	is	be	AUX
ejpam-5268	275	7	simulation	simulation	NOUN
ejpam-5268	275	8	mapping	mapping	NOUN
ejpam-5268	275	9	,	,	PUNCT
ejpam-5268	275	10	but	but	CCONJ
ejpam-5268	275	11	it	it	PRON
ejpam-5268	275	12	is	be	AUX
ejpam-5268	275	13	n’t	not	PART
ejpam-5268	275	14	right	right	ADV
ejpam-5268	275	15	monotone	monotone	ADJ
ejpam-5268	275	16	simulation	simulation	NOUN
ejpam-5268	275	17	mapping	mapping	NOUN
ejpam-5268	275	18	.	.	PUNCT
ejpam-5268	276	1	theorem	theorem	VERB
ejpam-5268	276	2	2	2	NUM
ejpam-5268	276	3	.	.	PUNCT
ejpam-5268	277	1	if	if	SCONJ
ejpam-5268	277	2	f	f	PROPN
ejpam-5268	277	3	,	,	PUNCT
ejpam-5268	277	4	t	t	X
ejpam-5268	277	5	:	:	PUNCT
ejpam-5268	277	6	(	(	PUNCT
ejpam-5268	277	7	x	x	X
ejpam-5268	277	8	,	,	PUNCT
ejpam-5268	277	9	s	s	PART
ejpam-5268	277	10	)	)	PUNCT
ejpam-5268	277	11	→	→	SYM
ejpam-5268	277	12	(	(	PUNCT
ejpam-5268	277	13	x	x	X
ejpam-5268	277	14	,	,	PUNCT
ejpam-5268	277	15	s	s	PART
ejpam-5268	277	16	)	)	PUNCT
ejpam-5268	277	17	are	be	AUX
ejpam-5268	277	18	self	self	NOUN
ejpam-5268	277	19	maps	map	NOUN
ejpam-5268	277	20	and	and	CCONJ
ejpam-5268	277	21	f	f	PROPN
ejpam-5268	277	22	is	be	AUX
ejpam-5268	277	23	t	t	PROPN
ejpam-5268	277	24	-	-	PUNCT
ejpam-5268	277	25	non	non	NOUN
ejpam-5268	277	26	-	-	ADJ
ejpam-5268	277	27	decreasing	decrease	VERB
ejpam-5268	277	28	in	in	ADP
ejpam-5268	277	29	s	s	NOUN
ejpam-5268	277	30	-	-	ADJ
ejpam-5268	277	31	metric	metric	ADJ
ejpam-5268	277	32	(	(	PUNCT
ejpam-5268	277	33	x	x	NOUN
ejpam-5268	277	34	,	,	PUNCT
ejpam-5268	277	35	s	s	PART
ejpam-5268	277	36	)	)	PUNCT
ejpam-5268	277	37	and	and	CCONJ
ejpam-5268	277	38	satisfies	satisfy	VERB
ejpam-5268	277	39	the	the	DET
ejpam-5268	277	40	case	case	NOUN
ejpam-5268	277	41	(	(	PUNCT
ejpam-5268	277	42	i	i	NOUN
ejpam-5268	277	43	)	)	PUNCT
ejpam-5268	277	44	of	of	ADP
ejpam-5268	277	45	proposition	proposition	NOUN
ejpam-5268	277	46	1	1	NUM
ejpam-5268	277	47	.	.	PUNCT
ejpam-5268	278	1	if	if	SCONJ
ejpam-5268	278	2	there	there	PRON
ejpam-5268	278	3	exists	exist	VERB
ejpam-5268	278	4	right	right	ADV
ejpam-5268	278	5	monotone	monotone	ADJ
ejpam-5268	278	6	simulation	simulation	NOUN
ejpam-5268	278	7	mapping	mapping	NOUN
ejpam-5268	278	8	ξ	ξ	PROPN
ejpam-5268	278	9	;	;	PUNCT
ejpam-5268	278	10	(	(	PUNCT
ejpam-5268	278	11	s.	s.	PROPN
ejpam-5268	278	12	t	t	PROPN
ejpam-5268	278	13	)	)	PUNCT
ejpam-5268	278	14	,	,	PUNCT
ejpam-5268	278	15	∀	∀	X
ejpam-5268	278	16	(	(	PUNCT
ejpam-5268	278	17	x	x	NOUN
ejpam-5268	278	18	,	,	PUNCT
ejpam-5268	278	19	y	y	NOUN
ejpam-5268	278	20	)	)	PUNCT
ejpam-5268	278	21	∈	∈	PROPN
ejpam-5268	278	22	x	x	X
ejpam-5268	278	23	×	×	NOUN
ejpam-5268	278	24	x	x	NOUN
ejpam-5268	278	25	,	,	PUNCT
ejpam-5268	278	26	and	and	CCONJ
ejpam-5268	278	27	tx	tx	VERB
ejpam-5268	278	28	≤	≤	NUM
ejpam-5268	278	29	ty	ty	NUM
ejpam-5268	278	30	,	,	PUNCT
ejpam-5268	278	31	we	we	PRON
ejpam-5268	278	32	have	have	VERB
ejpam-5268	278	33	ξ	ξ	X
ejpam-5268	278	34	(	(	PUNCT
ejpam-5268	278	35	s	s	X
ejpam-5268	278	36	(	(	PUNCT
ejpam-5268	278	37	fx	fx	PROPN
ejpam-5268	278	38	,	,	PUNCT
ejpam-5268	278	39	fy	fy	PROPN
ejpam-5268	278	40	,	,	PUNCT
ejpam-5268	278	41	fz	fz	VERB
ejpam-5268	278	42	)	)	PUNCT
ejpam-5268	278	43	,	,	PUNCT
ejpam-5268	278	44	s	s	X
ejpam-5268	278	45	(	(	PUNCT
ejpam-5268	278	46	tx	tx	PROPN
ejpam-5268	278	47	,	,	PUNCT
ejpam-5268	278	48	ty	ty	INTJ
ejpam-5268	278	49	,	,	PUNCT
ejpam-5268	278	50	tz	tz	PROPN
ejpam-5268	278	51	)	)	PUNCT
ejpam-5268	278	52	)	)	PUNCT
ejpam-5268	278	53	≥	≥	NOUN
ejpam-5268	278	54	0	0	NUM
ejpam-5268	278	55	,	,	PUNCT
ejpam-5268	278	56	so	so	ADV
ejpam-5268	278	57	,	,	PUNCT
ejpam-5268	278	58	f	f	PROPN
ejpam-5268	278	59	&	&	CCONJ
ejpam-5268	278	60	t	t	PROPN
ejpam-5268	278	61	have	have	VERB
ejpam-5268	278	62	coincidence	coincidence	NOUN
ejpam-5268	278	63	point	point	NOUN
ejpam-5268	278	64	.	.	PUNCT
ejpam-5268	279	1	additional	additional	ADJ
ejpam-5268	279	2	,	,	PUNCT
ejpam-5268	279	3	if	if	SCONJ
ejpam-5268	279	4	f	f	PROPN
ejpam-5268	279	5	&	&	CCONJ
ejpam-5268	279	6	t	t	PROPN
ejpam-5268	279	7	commute	commute	PROPN
ejpam-5268	279	8	,	,	PUNCT
ejpam-5268	279	9	so	so	PROPN
ejpam-5268	279	10	f	f	PROPN
ejpam-5268	279	11	&	&	CCONJ
ejpam-5268	279	12	t	t	PROPN
ejpam-5268	279	13	have	have	VERB
ejpam-5268	279	14	common	common	ADJ
ejpam-5268	279	15	fixed	fix	VERB
ejpam-5268	279	16	point	point	NOUN
ejpam-5268	279	17	.	.	PUNCT
ejpam-5268	280	1	proof	proof	NOUN
ejpam-5268	280	2	.	.	PUNCT
ejpam-5268	281	1	choosing	choose	VERB
ejpam-5268	281	2	t	t	PROPN
ejpam-5268	281	3	=	=	SYM
ejpam-5268	281	4	s	s	X
ejpam-5268	281	5	(	(	PUNCT
ejpam-5268	281	6	fx	fx	PROPN
ejpam-5268	281	7	,	,	PUNCT
ejpam-5268	281	8	fy	fy	PROPN
ejpam-5268	281	9	,	,	PUNCT
ejpam-5268	281	10	fz	fz	PROPN
ejpam-5268	281	11	)	)	PUNCT
ejpam-5268	281	12	,	,	PUNCT
ejpam-5268	281	13	w1	w1	NOUN
ejpam-5268	281	14	=	=	SYM
ejpam-5268	281	15	s	s	X
ejpam-5268	281	16	(	(	PUNCT
ejpam-5268	281	17	tx	tx	PROPN
ejpam-5268	281	18	,	,	PUNCT
ejpam-5268	281	19	ty	ty	INTJ
ejpam-5268	281	20	,	,	PUNCT
ejpam-5268	281	21	tz	tz	PROPN
ejpam-5268	281	22	)	)	PUNCT
ejpam-5268	281	23	and	and	CCONJ
ejpam-5268	281	24	w2	w2	NOUN
ejpam-5268	281	25	=	=	PROPN
ejpam-5268	281	26	m1	m1	PROPN
ejpam-5268	281	27	(	(	PUNCT
ejpam-5268	281	28	f	f	X
ejpam-5268	281	29	,	,	PUNCT
ejpam-5268	281	30	t	t	PROPN
ejpam-5268	281	31	,	,	PUNCT
ejpam-5268	281	32	x	x	PROPN
ejpam-5268	281	33	,	,	PUNCT
ejpam-5268	281	34	y	y	PROPN
ejpam-5268	281	35	,	,	PUNCT
ejpam-5268	281	36	z	z	NOUN
ejpam-5268	281	37	)	)	PUNCT
ejpam-5268	281	38	.	.	PUNCT
ejpam-5268	282	1	due	due	ADP
ejpam-5268	282	2	to	to	ADP
ejpam-5268	282	3	the	the	DET
ejpam-5268	282	4	given	give	VERB
ejpam-5268	282	5	supposition	supposition	NOUN
ejpam-5268	282	6	,	,	PUNCT
ejpam-5268	282	7	we	we	PRON
ejpam-5268	282	8	have	have	VERB
ejpam-5268	282	9	ξ	ξ	X
ejpam-5268	282	10	(	(	PUNCT
ejpam-5268	282	11	s	s	X
ejpam-5268	282	12	(	(	PUNCT
ejpam-5268	282	13	fx	fx	PROPN
ejpam-5268	282	14	,	,	PUNCT
ejpam-5268	282	15	fy	fy	PROPN
ejpam-5268	282	16	,	,	PUNCT
ejpam-5268	282	17	fz	fz	PROPN
ejpam-5268	282	18	)	)	PUNCT
ejpam-5268	282	19	,	,	PUNCT
ejpam-5268	282	20	s	s	PART
ejpam-5268	282	21	(	(	PUNCT
ejpam-5268	282	22	tx	tx	PROPN
ejpam-5268	282	23	,	,	PUNCT
ejpam-5268	282	24	ty	ty	INTJ
ejpam-5268	282	25	,	,	PUNCT
ejpam-5268	282	26	tz	tz	NOUN
ejpam-5268	282	27	)	)	PUNCT
ejpam-5268	282	28	)	)	PUNCT
ejpam-5268	282	29	(	(	PUNCT
ejpam-5268	282	30	15	15	X
ejpam-5268	282	31	)	)	PUNCT
ejpam-5268	282	32	we	we	PRON
ejpam-5268	282	33	know	know	VERB
ejpam-5268	282	34	that	that	SCONJ
ejpam-5268	282	35	s(tx	s(tx	PROPN
ejpam-5268	282	36	,	,	PUNCT
ejpam-5268	282	37	ty	ty	INTJ
ejpam-5268	282	38	,	,	PUNCT
ejpam-5268	282	39	tz	tz	NOUN
ejpam-5268	282	40	)	)	PUNCT
ejpam-5268	282	41	≤	≤	NOUN
ejpam-5268	282	42	m1	m1	NOUN
ejpam-5268	282	43	(	(	PUNCT
ejpam-5268	282	44	f	f	X
ejpam-5268	282	45	,	,	PUNCT
ejpam-5268	282	46	t	t	PROPN
ejpam-5268	282	47	,	,	PUNCT
ejpam-5268	282	48	x	x	PROPN
ejpam-5268	282	49	,	,	PUNCT
ejpam-5268	282	50	y	y	PROPN
ejpam-5268	282	51	,	,	PUNCT
ejpam-5268	282	52	z	z	NOUN
ejpam-5268	282	53	)	)	PUNCT
ejpam-5268	282	54	(	(	PUNCT
ejpam-5268	282	55	16	16	NUM
ejpam-5268	282	56	)	)	PUNCT
ejpam-5268	282	57	by	by	ADP
ejpam-5268	282	58	utilizing	utilize	VERB
ejpam-5268	282	59	of	of	ADP
ejpam-5268	282	60	16	16	NUM
ejpam-5268	282	61	and	and	CCONJ
ejpam-5268	282	62	the	the	DET
ejpam-5268	282	63	part	part	NOUN
ejpam-5268	282	64	ξ4	ξ4	NOUN
ejpam-5268	282	65	of	of	ADP
ejpam-5268	282	66	right	right	ADJ
ejpam-5268	282	67	-	-	PUNCT
ejpam-5268	282	68	monotone	monotone	NOUN
ejpam-5268	282	69	simulation	simulation	NOUN
ejpam-5268	282	70	map	map	NOUN
ejpam-5268	282	71	of	of	ADP
ejpam-5268	282	72	definition	definition	NOUN
ejpam-5268	282	73	5	5	NUM
ejpam-5268	282	74	,	,	PUNCT
ejpam-5268	282	75	get	get	VERB
ejpam-5268	282	76	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	282	77	,	,	PUNCT
ejpam-5268	282	78	fy	fy	PROPN
ejpam-5268	282	79	,	,	PUNCT
ejpam-5268	282	80	fz	fz	PROPN
ejpam-5268	282	81	)	)	PUNCT
ejpam-5268	282	82	,	,	PUNCT
ejpam-5268	282	83	s	s	PART
ejpam-5268	282	84	(	(	PUNCT
ejpam-5268	282	85	tx	tx	PROPN
ejpam-5268	282	86	,	,	PUNCT
ejpam-5268	282	87	ty	ty	INTJ
ejpam-5268	282	88	,	,	PUNCT
ejpam-5268	282	89	tz	tz	NOUN
ejpam-5268	282	90	)	)	PUNCT
ejpam-5268	282	91	)	)	PUNCT
ejpam-5268	282	92	≤	≤	NOUN
ejpam-5268	282	93	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	282	94	,	,	PUNCT
ejpam-5268	282	95	fy	fy	PROPN
ejpam-5268	282	96	,	,	PUNCT
ejpam-5268	282	97	fz	fz	PROPN
ejpam-5268	282	98	)	)	PUNCT
ejpam-5268	282	99	,	,	PUNCT
ejpam-5268	282	100	m1	m1	PROPN
ejpam-5268	282	101	(	(	PUNCT
ejpam-5268	282	102	f	f	PROPN
ejpam-5268	282	103	,	,	PUNCT
ejpam-5268	282	104	t	t	PROPN
ejpam-5268	282	105	,	,	PUNCT
ejpam-5268	282	106	x	x	PROPN
ejpam-5268	282	107	,	,	PUNCT
ejpam-5268	282	108	y	y	PROPN
ejpam-5268	282	109	,	,	PUNCT
ejpam-5268	282	110	z	z	NOUN
ejpam-5268	282	111	)	)	PUNCT
ejpam-5268	282	112	)	)	PUNCT
ejpam-5268	282	113	.	.	PUNCT
ejpam-5268	283	1	(	(	PUNCT
ejpam-5268	283	2	17	17	NUM
ejpam-5268	283	3	)	)	PUNCT
ejpam-5268	283	4	by	by	ADP
ejpam-5268	283	5	using	use	VERB
ejpam-5268	283	6	15	15	NUM
ejpam-5268	283	7	and	and	CCONJ
ejpam-5268	283	8	17	17	NUM
ejpam-5268	283	9	,	,	PUNCT
ejpam-5268	283	10	we	we	PRON
ejpam-5268	283	11	obtain	obtain	VERB
ejpam-5268	283	12	ξ(s(fx	ξ(s(fx	ADP
ejpam-5268	283	13	,	,	PUNCT
ejpam-5268	283	14	fy	fy	PROPN
ejpam-5268	283	15	,	,	PUNCT
ejpam-5268	283	16	fz	fz	PROPN
ejpam-5268	283	17	)	)	PUNCT
ejpam-5268	283	18	,	,	PUNCT
ejpam-5268	283	19	m1	m1	PROPN
ejpam-5268	283	20	(	(	PUNCT
ejpam-5268	283	21	f	f	PROPN
ejpam-5268	283	22	,	,	PUNCT
ejpam-5268	283	23	t	t	PROPN
ejpam-5268	283	24	,	,	PUNCT
ejpam-5268	283	25	x	x	PROPN
ejpam-5268	283	26	,	,	PUNCT
ejpam-5268	283	27	y	y	PROPN
ejpam-5268	283	28	,	,	PUNCT
ejpam-5268	283	29	z	z	NOUN
ejpam-5268	283	30	)	)	PUNCT
ejpam-5268	283	31	)	)	PUNCT
ejpam-5268	283	32	≥	≥	NOUN
ejpam-5268	283	33	0	0	NUM
ejpam-5268	283	34	.	.	PUNCT
ejpam-5268	284	1	next	next	ADV
ejpam-5268	284	2	,	,	PUNCT
ejpam-5268	284	3	by	by	ADP
ejpam-5268	284	4	similar	similar	ADJ
ejpam-5268	284	5	procedure	procedure	NOUN
ejpam-5268	284	6	of	of	ADP
ejpam-5268	284	7	theorem	theorem	NOUN
ejpam-5268	284	8	1	1	NUM
ejpam-5268	284	9	,	,	PUNCT
ejpam-5268	284	10	acquire	acquire	VERB
ejpam-5268	284	11	common	common	ADJ
ejpam-5268	284	12	fixed	fix	VERB
ejpam-5268	284	13	and	and	CCONJ
ejpam-5268	284	14	coincidence	coincidence	NOUN
ejpam-5268	284	15	point	point	NOUN
ejpam-5268	284	16	of	of	ADP
ejpam-5268	284	17	f	f	PROPN
ejpam-5268	284	18	&	&	CCONJ
ejpam-5268	284	19	t.	t.	PROPN
ejpam-5268	284	20	corollary	corollary	PROPN
ejpam-5268	284	21	3	3	PROPN
ejpam-5268	284	22	.	.	PUNCT
ejpam-5268	284	23	suppose	suppose	VERB
ejpam-5268	284	24	f	f	X
ejpam-5268	284	25	,	,	PUNCT
ejpam-5268	284	26	t	t	X
ejpam-5268	284	27	:	:	PUNCT
ejpam-5268	284	28	(	(	PUNCT
ejpam-5268	284	29	x	x	X
ejpam-5268	284	30	,	,	PUNCT
ejpam-5268	284	31	s	s	PART
ejpam-5268	284	32	)	)	PUNCT
ejpam-5268	284	33	→	→	SYM
ejpam-5268	284	34	(	(	PUNCT
ejpam-5268	284	35	x	x	X
ejpam-5268	284	36	,	,	PUNCT
ejpam-5268	284	37	s	s	PART
ejpam-5268	284	38	)	)	PUNCT
ejpam-5268	284	39	are	be	AUX
ejpam-5268	284	40	self	self	NOUN
ejpam-5268	284	41	mappings	mapping	NOUN
ejpam-5268	284	42	and	and	CCONJ
ejpam-5268	284	43	f	f	PROPN
ejpam-5268	284	44	is	be	AUX
ejpam-5268	284	45	t	t	PROPN
ejpam-5268	284	46	-	-	PUNCT
ejpam-5268	284	47	nondecreasing	nondecrease	VERB
ejpam-5268	284	48	in	in	ADP
ejpam-5268	284	49	complete	complete	ADJ
ejpam-5268	284	50	s	s	NOUN
ejpam-5268	284	51	-	-	ADJ
ejpam-5268	284	52	metric	metric	ADJ
ejpam-5268	284	53	(	(	PUNCT
ejpam-5268	284	54	x	x	NOUN
ejpam-5268	284	55	,	,	PUNCT
ejpam-5268	284	56	s	s	PART
ejpam-5268	284	57	)	)	PUNCT
ejpam-5268	284	58	and	and	CCONJ
ejpam-5268	284	59	satisfies	satisfy	VERB
ejpam-5268	284	60	the	the	DET
ejpam-5268	284	61	case	case	NOUN
ejpam-5268	284	62	(	(	PUNCT
ejpam-5268	284	63	i	i	NOUN
ejpam-5268	284	64	)	)	PUNCT
ejpam-5268	284	65	of	of	ADP
ejpam-5268	284	66	proposition	proposition	NOUN
ejpam-5268	284	67	1	1	NUM
ejpam-5268	284	68	.	.	PUNCT
ejpam-5268	285	1	if	if	SCONJ
ejpam-5268	285	2	there	there	PRON
ejpam-5268	285	3	exists	exist	VERB
ejpam-5268	285	4	a	a	DET
ejpam-5268	285	5	monotone	monotone	ADJ
ejpam-5268	285	6	simulation	simulation	NOUN
ejpam-5268	285	7	mapping	mapping	NOUN
ejpam-5268	285	8	ξ	ξ	PROPN
ejpam-5268	285	9	;	;	PUNCT
ejpam-5268	285	10	(	(	PUNCT
ejpam-5268	285	11	s.	s.	PROPN
ejpam-5268	285	12	t	t	PROPN
ejpam-5268	285	13	)	)	PUNCT
ejpam-5268	285	14	∀	∀	X
ejpam-5268	285	15	(	(	PUNCT
ejpam-5268	285	16	x	x	X
ejpam-5268	285	17	,	,	PUNCT
ejpam-5268	285	18	y	y	NOUN
ejpam-5268	285	19	)	)	PUNCT
ejpam-5268	285	20	∈	∈	PROPN
ejpam-5268	285	21	x	x	X
ejpam-5268	285	22	×x	×x	X
ejpam-5268	285	23	&	&	CCONJ
ejpam-5268	285	24	tx	tx	VERB
ejpam-5268	285	25	≤	≤	PROPN
ejpam-5268	285	26	ty	ty	NUM
ejpam-5268	285	27	,	,	PUNCT
ejpam-5268	285	28	we	we	PRON
ejpam-5268	285	29	have	have	VERB
ejpam-5268	285	30	ξ	ξ	X
ejpam-5268	285	31	(	(	PUNCT
ejpam-5268	285	32	s	s	X
ejpam-5268	285	33	(	(	PUNCT
ejpam-5268	285	34	fx	fx	PROPN
ejpam-5268	285	35	,	,	PUNCT
ejpam-5268	285	36	fy	fy	PROPN
ejpam-5268	285	37	,	,	PUNCT
ejpam-5268	285	38	fz	fz	PROPN
ejpam-5268	285	39	)	)	PUNCT
ejpam-5268	285	40	,	,	PUNCT
ejpam-5268	285	41	m3	m3	PROPN
ejpam-5268	285	42	(	(	PUNCT
ejpam-5268	285	43	f	f	PROPN
ejpam-5268	285	44	,	,	PUNCT
ejpam-5268	285	45	t	t	PROPN
ejpam-5268	285	46	,	,	PUNCT
ejpam-5268	285	47	x	x	PROPN
ejpam-5268	285	48	,	,	PUNCT
ejpam-5268	285	49	y	y	PROPN
ejpam-5268	285	50	,	,	PUNCT
ejpam-5268	285	51	z	z	NOUN
ejpam-5268	285	52	)	)	PUNCT
ejpam-5268	285	53	)	)	PUNCT
ejpam-5268	285	54	≥	≥	NOUN
ejpam-5268	285	55	0	0	NUM
ejpam-5268	285	56	,	,	PUNCT
ejpam-5268	285	57	where	where	SCONJ
ejpam-5268	285	58	m3	m3	PROPN
ejpam-5268	285	59	(	(	PUNCT
ejpam-5268	285	60	f	f	PROPN
ejpam-5268	285	61	,	,	PUNCT
ejpam-5268	285	62	t	t	PROPN
ejpam-5268	285	63	,	,	PUNCT
ejpam-5268	285	64	x	x	PROPN
ejpam-5268	285	65	,	,	PUNCT
ejpam-5268	285	66	y	y	PROPN
ejpam-5268	285	67	,	,	PUNCT
ejpam-5268	285	68	z	z	NOUN
ejpam-5268	285	69	)	)	PUNCT
ejpam-5268	285	70	=	=	SYM
ejpam-5268	285	71	max	max	PROPN
ejpam-5268	285	72	{	{	PUNCT
ejpam-5268	285	73	s(tx	s(tx	PROPN
ejpam-5268	285	74	,	,	PUNCT
ejpam-5268	285	75	fx	fx	PROPN
ejpam-5268	285	76	,	,	PUNCT
ejpam-5268	285	77	tz	tz	PROPN
ejpam-5268	285	78	)	)	PUNCT
ejpam-5268	285	79	,	,	PUNCT
ejpam-5268	285	80	s(ty	s(ty	PROPN
ejpam-5268	285	81	,	,	PUNCT
ejpam-5268	285	82	fy	fy	PROPN
ejpam-5268	285	83	,	,	PUNCT
ejpam-5268	285	84	tz	tz	PROPN
ejpam-5268	285	85	)	)	PUNCT
ejpam-5268	285	86	}	}	PUNCT
ejpam-5268	285	87	.	.	PUNCT
ejpam-5268	286	1	so	so	ADV
ejpam-5268	286	2	,	,	PUNCT
ejpam-5268	286	3	f	f	PROPN
ejpam-5268	286	4	&	&	CCONJ
ejpam-5268	286	5	t	t	PROPN
ejpam-5268	286	6	have	have	VERB
ejpam-5268	286	7	coincidence	coincidence	NOUN
ejpam-5268	286	8	point	point	NOUN
ejpam-5268	286	9	.	.	PUNCT
ejpam-5268	287	1	additional	additional	ADJ
ejpam-5268	287	2	,	,	PUNCT
ejpam-5268	287	3	if	if	SCONJ
ejpam-5268	287	4	f	f	PROPN
ejpam-5268	287	5	&	&	CCONJ
ejpam-5268	287	6	t	t	PROPN
ejpam-5268	287	7	commute	commute	PROPN
ejpam-5268	287	8	,	,	PUNCT
ejpam-5268	287	9	so	so	PROPN
ejpam-5268	287	10	f	f	PROPN
ejpam-5268	287	11	&	&	CCONJ
ejpam-5268	287	12	t	t	PROPN
ejpam-5268	287	13	have	have	VERB
ejpam-5268	287	14	common	common	ADJ
ejpam-5268	287	15	fixed	fix	VERB
ejpam-5268	287	16	point	point	NOUN
ejpam-5268	287	17	.	.	PUNCT
ejpam-5268	288	1	n.	n.	PROPN
ejpam-5268	288	2	a.	a.	PROPN
ejpam-5268	288	3	majid	majid	PROPN
ejpam-5268	288	4	et	et	PROPN
ejpam-5268	288	5	al	al	PROPN
ejpam-5268	288	6	.	.	PUNCT
ejpam-5268	288	7	/	/	SYM
ejpam-5268	288	8	eur	eur	PROPN
ejpam-5268	288	9	.	.	PUNCT
ejpam-5268	289	1	j.	j.	PROPN
ejpam-5268	289	2	pure	pure	PROPN
ejpam-5268	289	3	appl	appl	PROPN
ejpam-5268	289	4	.	.	PROPN
ejpam-5268	289	5	math	math	PROPN
ejpam-5268	289	6	,	,	PUNCT
ejpam-5268	289	7	17	17	NUM
ejpam-5268	289	8	(	(	PUNCT
ejpam-5268	289	9	3	3	NUM
ejpam-5268	289	10	)	)	PUNCT
ejpam-5268	289	11	(	(	PUNCT
ejpam-5268	289	12	2024	2024	NUM
ejpam-5268	289	13	)	)	PUNCT
ejpam-5268	289	14	,	,	PUNCT
ejpam-5268	289	15	1877	1877	NUM
ejpam-5268	289	16	-	-	SYM
ejpam-5268	289	17	1893	1893	NUM
ejpam-5268	289	18	1889	1889	NUM
ejpam-5268	289	19	proof	proof	NOUN
ejpam-5268	289	20	.	.	PUNCT
ejpam-5268	290	1	it	it	PRON
ejpam-5268	290	2	can	can	AUX
ejpam-5268	290	3	be	be	AUX
ejpam-5268	290	4	established	establish	VERB
ejpam-5268	290	5	independently	independently	ADV
ejpam-5268	290	6	via	via	ADP
ejpam-5268	290	7	choosing	choose	VERB
ejpam-5268	290	8	the	the	DET
ejpam-5268	290	9	following	follow	VERB
ejpam-5268	290	10	right	right	ADJ
ejpam-5268	290	11	monotone	monotone	ADJ
ejpam-5268	290	12	simulation	simulation	NOUN
ejpam-5268	290	13	mapping	mapping	NOUN
ejpam-5268	290	14	ξ	ξ	X
ejpam-5268	290	15	:	:	PUNCT
ejpam-5268	291	1	[	[	X
ejpam-5268	291	2	0,+∞)×	0,+∞)×	NOUN
ejpam-5268	292	1	[	[	X
ejpam-5268	292	2	0,+∞	0,+∞	NUM
ejpam-5268	292	3	)	)	PUNCT
ejpam-5268	292	4	→	→	SYM
ejpam-5268	292	5	r	r	X
ejpam-5268	292	6	,	,	PUNCT
ejpam-5268	292	7	where	where	SCONJ
ejpam-5268	292	8	ξ	ξ	X
ejpam-5268	292	9	(	(	PUNCT
ejpam-5268	292	10	t	t	PROPN
ejpam-5268	292	11	,	,	PUNCT
ejpam-5268	292	12	w	w	NOUN
ejpam-5268	292	13	)	)	PUNCT
ejpam-5268	292	14	=	=	PUNCT
ejpam-5268	292	15	w	w	PROPN
ejpam-5268	292	16	−	−	PROPN
ejpam-5268	292	17	t	t	NOUN
ejpam-5268	292	18	+	+	CCONJ
ejpam-5268	292	19	2	2	NUM
ejpam-5268	292	20	t	t	NOUN
ejpam-5268	292	21	+	+	CCONJ
ejpam-5268	292	22	1	1	NUM
ejpam-5268	292	23	t	t	PROPN
ejpam-5268	292	24	,	,	PUNCT
ejpam-5268	292	25	∀	∀	X
ejpam-5268	292	26	t	t	PROPN
ejpam-5268	292	27	,	,	PUNCT
ejpam-5268	292	28	w	w	PROPN
ejpam-5268	292	29	≥	≥	NOUN
ejpam-5268	292	30	0	0	NUM
ejpam-5268	292	31	.	.	PUNCT
ejpam-5268	292	32	corollary	corollary	ADJ
ejpam-5268	292	33	4	4	NUM
ejpam-5268	292	34	.	.	PUNCT
ejpam-5268	292	35	suppose	suppose	VERB
ejpam-5268	292	36	f	f	X
ejpam-5268	292	37	,	,	PUNCT
ejpam-5268	292	38	t	t	X
ejpam-5268	292	39	:	:	PUNCT
ejpam-5268	292	40	(	(	PUNCT
ejpam-5268	292	41	x	x	X
ejpam-5268	292	42	,	,	PUNCT
ejpam-5268	292	43	s	s	PART
ejpam-5268	292	44	)	)	PUNCT
ejpam-5268	292	45	→	→	SYM
ejpam-5268	292	46	(	(	PUNCT
ejpam-5268	292	47	x	x	X
ejpam-5268	292	48	,	,	PUNCT
ejpam-5268	292	49	s	s	PART
ejpam-5268	292	50	)	)	PUNCT
ejpam-5268	292	51	are	be	AUX
ejpam-5268	292	52	self	self	NOUN
ejpam-5268	292	53	mappings	mapping	NOUN
ejpam-5268	292	54	and	and	CCONJ
ejpam-5268	292	55	f	f	PROPN
ejpam-5268	292	56	is	be	AUX
ejpam-5268	292	57	t	t	PROPN
ejpam-5268	292	58	-	-	PUNCT
ejpam-5268	292	59	nondecreasing	nondecrease	VERB
ejpam-5268	292	60	in	in	ADP
ejpam-5268	292	61	complete	complete	ADJ
ejpam-5268	292	62	s	s	NOUN
ejpam-5268	292	63	-	-	ADJ
ejpam-5268	292	64	metric	metric	ADJ
ejpam-5268	292	65	(	(	PUNCT
ejpam-5268	292	66	x	x	NOUN
ejpam-5268	292	67	,	,	PUNCT
ejpam-5268	292	68	s	s	PART
ejpam-5268	292	69	)	)	PUNCT
ejpam-5268	292	70	satisfies	satisfy	VERB
ejpam-5268	292	71	the	the	DET
ejpam-5268	292	72	case	case	NOUN
ejpam-5268	292	73	(	(	PUNCT
ejpam-5268	292	74	i	i	NOUN
ejpam-5268	292	75	)	)	PUNCT
ejpam-5268	292	76	of	of	ADP
ejpam-5268	292	77	proposition	proposition	NOUN
ejpam-5268	292	78	1	1	NUM
ejpam-5268	292	79	.	.	PUNCT
ejpam-5268	293	1	if	if	SCONJ
ejpam-5268	293	2	there	there	PRON
ejpam-5268	293	3	exists	exist	VERB
ejpam-5268	293	4	a	a	DET
ejpam-5268	293	5	monotone	monotone	ADJ
ejpam-5268	293	6	simulation	simulation	NOUN
ejpam-5268	293	7	mapping	mapping	NOUN
ejpam-5268	293	8	ξ	ξ	PROPN
ejpam-5268	293	9	;	;	PUNCT
ejpam-5268	293	10	(	(	PUNCT
ejpam-5268	293	11	s.	s.	PROPN
ejpam-5268	293	12	t	t	PROPN
ejpam-5268	293	13	)	)	PUNCT
ejpam-5268	293	14	∀	∀	X
ejpam-5268	293	15	(	(	PUNCT
ejpam-5268	293	16	x	x	X
ejpam-5268	293	17	,	,	PUNCT
ejpam-5268	293	18	y	y	NOUN
ejpam-5268	293	19	)	)	PUNCT
ejpam-5268	293	20	∈	∈	PROPN
ejpam-5268	293	21	x	x	X
ejpam-5268	293	22	×x	×x	X
ejpam-5268	293	23	&	&	CCONJ
ejpam-5268	293	24	tx	tx	VERB
ejpam-5268	293	25	≤	≤	PROPN
ejpam-5268	293	26	ty	ty	NUM
ejpam-5268	293	27	,	,	PUNCT
ejpam-5268	293	28	we	we	PRON
ejpam-5268	293	29	have	have	VERB
ejpam-5268	293	30	ξ	ξ	X
ejpam-5268	293	31	(	(	PUNCT
ejpam-5268	293	32	s	s	X
ejpam-5268	293	33	(	(	PUNCT
ejpam-5268	293	34	fx	fx	PROPN
ejpam-5268	293	35	,	,	PUNCT
ejpam-5268	293	36	fy	fy	PROPN
ejpam-5268	293	37	,	,	PUNCT
ejpam-5268	293	38	fz	fz	PROPN
ejpam-5268	293	39	)	)	PUNCT
ejpam-5268	293	40	,	,	PUNCT
ejpam-5268	293	41	m4	m4	PROPN
ejpam-5268	293	42	(	(	PUNCT
ejpam-5268	293	43	f	f	PROPN
ejpam-5268	293	44	,	,	PUNCT
ejpam-5268	293	45	t	t	PROPN
ejpam-5268	293	46	,	,	PUNCT
ejpam-5268	293	47	x	x	PROPN
ejpam-5268	293	48	,	,	PUNCT
ejpam-5268	293	49	y	y	PROPN
ejpam-5268	293	50	,	,	PUNCT
ejpam-5268	293	51	z	z	NOUN
ejpam-5268	293	52	)	)	PUNCT
ejpam-5268	293	53	)	)	PUNCT
ejpam-5268	293	54	≥	≥	NOUN
ejpam-5268	293	55	0	0	NUM
ejpam-5268	293	56	,	,	PUNCT
ejpam-5268	293	57	where	where	SCONJ
ejpam-5268	293	58	m4	m4	PROPN
ejpam-5268	293	59	(	(	PUNCT
ejpam-5268	293	60	f	f	PROPN
ejpam-5268	293	61	,	,	PUNCT
ejpam-5268	293	62	t	t	PROPN
ejpam-5268	293	63	,	,	PUNCT
ejpam-5268	293	64	x	x	X
ejpam-5268	293	65	,	,	PUNCT
ejpam-5268	293	66	y	y	PROPN
ejpam-5268	293	67	,	,	PUNCT
ejpam-5268	293	68	z	z	NOUN
ejpam-5268	293	69	)	)	PUNCT
ejpam-5268	293	70	=	=	SYM
ejpam-5268	293	71	max	max	PROPN
ejpam-5268	293	72	{	{	PUNCT
ejpam-5268	293	73	s(tx	s(tx	PROPN
ejpam-5268	293	74	,	,	PUNCT
ejpam-5268	293	75	ty	ty	INTJ
ejpam-5268	293	76	,	,	PUNCT
ejpam-5268	293	77	tz	tz	PROPN
ejpam-5268	293	78	)	)	PUNCT
ejpam-5268	293	79	,	,	PUNCT
ejpam-5268	293	80	s(tx	s(tx	PROPN
ejpam-5268	293	81	,	,	PUNCT
ejpam-5268	293	82	fy	fy	PROPN
ejpam-5268	293	83	,	,	PUNCT
ejpam-5268	293	84	tz),s(ty	tz),s(ty	ADJ
ejpam-5268	293	85	,	,	PUNCT
ejpam-5268	293	86	fx	fx	PROPN
ejpam-5268	293	87	,	,	PUNCT
ejpam-5268	293	88	tz	tz	NOUN
ejpam-5268	293	89	)	)	PUNCT
ejpam-5268	293	90	}	}	PUNCT
ejpam-5268	293	91	.	.	PUNCT
ejpam-5268	294	1	so	so	ADV
ejpam-5268	294	2	,	,	PUNCT
ejpam-5268	294	3	f	f	PROPN
ejpam-5268	294	4	&	&	CCONJ
ejpam-5268	294	5	t	t	PROPN
ejpam-5268	294	6	have	have	VERB
ejpam-5268	294	7	coincidence	coincidence	NOUN
ejpam-5268	294	8	point	point	NOUN
ejpam-5268	294	9	.	.	PUNCT
ejpam-5268	295	1	additional	additional	ADJ
ejpam-5268	295	2	,	,	PUNCT
ejpam-5268	295	3	if	if	SCONJ
ejpam-5268	295	4	f	f	PROPN
ejpam-5268	295	5	&	&	CCONJ
ejpam-5268	295	6	t	t	PROPN
ejpam-5268	295	7	commute	commute	PROPN
ejpam-5268	295	8	,	,	PUNCT
ejpam-5268	295	9	so	so	PROPN
ejpam-5268	295	10	f	f	PROPN
ejpam-5268	295	11	&	&	CCONJ
ejpam-5268	295	12	t	t	PROPN
ejpam-5268	295	13	have	have	VERB
ejpam-5268	295	14	common	common	ADJ
ejpam-5268	295	15	fixed	fix	VERB
ejpam-5268	295	16	point	point	NOUN
ejpam-5268	295	17	.	.	PUNCT
ejpam-5268	296	1	proof	proof	NOUN
ejpam-5268	296	2	.	.	PUNCT
ejpam-5268	297	1	it	it	PRON
ejpam-5268	297	2	can	can	AUX
ejpam-5268	297	3	be	be	AUX
ejpam-5268	297	4	established	establish	VERB
ejpam-5268	297	5	independently	independently	ADV
ejpam-5268	297	6	via	via	ADP
ejpam-5268	297	7	choosing	choose	VERB
ejpam-5268	297	8	the	the	DET
ejpam-5268	297	9	following	follow	VERB
ejpam-5268	297	10	right	right	ADJ
ejpam-5268	297	11	monotone	monotone	ADJ
ejpam-5268	297	12	simulation	simulation	NOUN
ejpam-5268	297	13	mapping	mapping	NOUN
ejpam-5268	297	14	ξ	ξ	X
ejpam-5268	297	15	:	:	PUNCT
ejpam-5268	298	1	[	[	X
ejpam-5268	298	2	0,+∞)×	0,+∞)×	NOUN
ejpam-5268	299	1	[	[	X
ejpam-5268	299	2	0,+∞	0,+∞	NUM
ejpam-5268	299	3	)	)	PUNCT
ejpam-5268	299	4	→	→	SYM
ejpam-5268	299	5	r	r	X
ejpam-5268	299	6	,	,	PUNCT
ejpam-5268	299	7	where	where	SCONJ
ejpam-5268	299	8	ξ	ξ	X
ejpam-5268	299	9	(	(	PUNCT
ejpam-5268	299	10	t	t	PROPN
ejpam-5268	299	11	,	,	PUNCT
ejpam-5268	299	12	w	w	NOUN
ejpam-5268	299	13	)	)	PUNCT
ejpam-5268	299	14	=	=	PUNCT
ejpam-5268	299	15	w	w	PROPN
ejpam-5268	299	16	−	−	PROPN
ejpam-5268	299	17	t	t	NOUN
ejpam-5268	299	18	+	+	CCONJ
ejpam-5268	299	19	2	2	NUM
ejpam-5268	299	20	t	t	NOUN
ejpam-5268	299	21	+	+	CCONJ
ejpam-5268	299	22	1	1	NUM
ejpam-5268	299	23	t	t	PROPN
ejpam-5268	299	24	,	,	PUNCT
ejpam-5268	299	25	∀	∀	X
ejpam-5268	299	26	t	t	PROPN
ejpam-5268	299	27	,	,	PUNCT
ejpam-5268	299	28	w	w	PROPN
ejpam-5268	299	29	≥	≥	NOUN
ejpam-5268	299	30	0	0	NUM
ejpam-5268	299	31	.	.	PROPN
ejpam-5268	299	32	4	4	NUM
ejpam-5268	299	33	.	.	X
ejpam-5268	299	34	applications	application	NOUN
ejpam-5268	299	35	of	of	ADP
ejpam-5268	299	36	integral	integral	ADJ
ejpam-5268	299	37	equations	equation	NOUN
ejpam-5268	299	38	this	this	DET
ejpam-5268	299	39	segment	segment	NOUN
ejpam-5268	299	40	devoted	devote	VERB
ejpam-5268	299	41	to	to	PART
ejpam-5268	299	42	introduce	introduce	VERB
ejpam-5268	299	43	an	an	DET
ejpam-5268	299	44	application	application	NOUN
ejpam-5268	299	45	to	to	PART
ejpam-5268	299	46	explain	explain	VERB
ejpam-5268	299	47	the	the	DET
ejpam-5268	299	48	existence	existence	NOUN
ejpam-5268	299	49	and	and	CCONJ
ejpam-5268	299	50	uniqueness	uniqueness	ADJ
ejpam-5268	299	51	problem	problem	NOUN
ejpam-5268	299	52	of	of	ADP
ejpam-5268	299	53	the	the	DET
ejpam-5268	299	54	solution	solution	NOUN
ejpam-5268	299	55	to	to	ADP
ejpam-5268	299	56	an	an	DET
ejpam-5268	299	57	integral	integral	ADJ
ejpam-5268	299	58	equation	equation	NOUN
ejpam-5268	299	59	of	of	ADP
ejpam-5268	299	60	the	the	DET
ejpam-5268	299	61	following	follow	VERB
ejpam-5268	299	62	structure	structure	NOUN
ejpam-5268	299	63	in	in	ADP
ejpam-5268	299	64	s	s	NOUN
ejpam-5268	299	65	-	-	ADJ
ejpam-5268	299	66	metric	metric	ADJ
ejpam-5268	299	67	spaces	space	NOUN
ejpam-5268	299	68	:	:	PUNCT
ejpam-5268	299	69	δ	δ	PROPN
ejpam-5268	299	70	(	(	PUNCT
ejpam-5268	299	71	q	q	X
ejpam-5268	299	72	)	)	PUNCT
ejpam-5268	299	73	=	=	SYM
ejpam-5268	299	74	j(q	j(q	NOUN
ejpam-5268	299	75	)	)	PUNCT
ejpam-5268	300	1	+	+	CCONJ
ejpam-5268	300	2	λ	λ	X
ejpam-5268	300	3	∫	∫	PROPN
ejpam-5268	300	4	s	s	PART
ejpam-5268	300	5	r	r	NOUN
ejpam-5268	300	6	ψ	ψ	X
ejpam-5268	300	7	(	(	PUNCT
ejpam-5268	300	8	q	q	INTJ
ejpam-5268	300	9	,	,	PUNCT
ejpam-5268	300	10	p	p	X
ejpam-5268	300	11	,	,	PUNCT
ejpam-5268	300	12	p)µ	p)µ	NOUN
ejpam-5268	300	13	(	(	PUNCT
ejpam-5268	300	14	p	p	X
ejpam-5268	300	15	,	,	PUNCT
ejpam-5268	300	16	η	η	PROPN
ejpam-5268	300	17	(	(	PUNCT
ejpam-5268	300	18	p	p	NOUN
ejpam-5268	300	19	)	)	PUNCT
ejpam-5268	300	20	,	,	PUNCT
ejpam-5268	300	21	η	η	PROPN
ejpam-5268	300	22	(	(	PUNCT
ejpam-5268	300	23	p	p	NOUN
ejpam-5268	300	24	)	)	PUNCT
ejpam-5268	300	25	)	)	PUNCT
ejpam-5268	300	26	dp	dp	NOUN
ejpam-5268	300	27	(	(	PUNCT
ejpam-5268	300	28	18	18	NUM
ejpam-5268	300	29	)	)	PUNCT
ejpam-5268	300	30	assume	assume	VERB
ejpam-5268	300	31	f(x	f(x	PROPN
ejpam-5268	300	32	,	,	PUNCT
ejpam-5268	300	33	s	s	PART
ejpam-5268	300	34	)	)	PUNCT
ejpam-5268	300	35	→	→	SYM
ejpam-5268	300	36	(	(	PUNCT
ejpam-5268	300	37	x	x	X
ejpam-5268	300	38	,	,	PUNCT
ejpam-5268	300	39	s	s	PART
ejpam-5268	300	40	)	)	PUNCT
ejpam-5268	300	41	a	a	DET
ejpam-5268	300	42	self	self	NOUN
ejpam-5268	300	43	-	-	PUNCT
ejpam-5268	300	44	map	map	NOUN
ejpam-5268	300	45	defined	define	VERB
ejpam-5268	300	46	as	as	SCONJ
ejpam-5268	300	47	follows	follow	VERB
ejpam-5268	300	48	:	:	PUNCT
ejpam-5268	300	49	fδ	fδ	PART
ejpam-5268	300	50	(	(	PUNCT
ejpam-5268	300	51	q	q	X
ejpam-5268	300	52	)	)	PUNCT
ejpam-5268	300	53	=	=	SYM
ejpam-5268	300	54	j(q	j(q	NOUN
ejpam-5268	300	55	)	)	PUNCT
ejpam-5268	301	1	+	+	CCONJ
ejpam-5268	301	2	λ	λ	X
ejpam-5268	301	3	∫	∫	PROPN
ejpam-5268	301	4	s	s	PART
ejpam-5268	301	5	r	r	NOUN
ejpam-5268	301	6	ψ	ψ	X
ejpam-5268	301	7	(	(	PUNCT
ejpam-5268	301	8	q	q	INTJ
ejpam-5268	301	9	,	,	PUNCT
ejpam-5268	301	10	p	p	X
ejpam-5268	301	11	,	,	PUNCT
ejpam-5268	301	12	p)µ	p)µ	NOUN
ejpam-5268	301	13	(	(	PUNCT
ejpam-5268	301	14	p	p	X
ejpam-5268	301	15	,	,	PUNCT
ejpam-5268	301	16	δ	δ	PROPN
ejpam-5268	301	17	(	(	PUNCT
ejpam-5268	301	18	p	p	NOUN
ejpam-5268	301	19	)	)	PUNCT
ejpam-5268	301	20	,	,	PUNCT
ejpam-5268	301	21	δ	δ	PROPN
ejpam-5268	301	22	(	(	PUNCT
ejpam-5268	301	23	p	p	NOUN
ejpam-5268	301	24	)	)	PUNCT
ejpam-5268	301	25	)	)	PUNCT
ejpam-5268	301	26	dp	dp	NOUN
ejpam-5268	301	27	let	let	VERB
ejpam-5268	301	28	x	x	PRON
ejpam-5268	301	29	be	be	AUX
ejpam-5268	301	30	provided	provide	VERB
ejpam-5268	301	31	with	with	ADP
ejpam-5268	301	32	s	s	NOUN
ejpam-5268	301	33	-	-	ADJ
ejpam-5268	301	34	metric	metric	ADJ
ejpam-5268	301	35	which	which	PRON
ejpam-5268	301	36	is	be	AUX
ejpam-5268	301	37	described	describe	VERB
ejpam-5268	301	38	as	as	ADP
ejpam-5268	301	39	s	s	PROPN
ejpam-5268	301	40	(	(	PUNCT
ejpam-5268	301	41	δ	δ	PROPN
ejpam-5268	301	42	,	,	PUNCT
ejpam-5268	301	43	j	j	PROPN
ejpam-5268	301	44	,	,	PUNCT
ejpam-5268	301	45	j	j	PROPN
ejpam-5268	301	46	)	)	PUNCT
ejpam-5268	301	47	=	=	SYM
ejpam-5268	301	48	2	2	NUM
ejpam-5268	301	49	sup	sup	NOUN
ejpam-5268	301	50	|δ	|δ	NOUN
ejpam-5268	301	51	(	(	PUNCT
ejpam-5268	301	52	q)−	q)−	PROPN
ejpam-5268	301	53	j(q)|	j(q)|	PROPN
ejpam-5268	301	54	.	.	PUNCT
ejpam-5268	302	1	where	where	SCONJ
ejpam-5268	302	2	,	,	PUNCT
ejpam-5268	302	3	q	q	NOUN
ejpam-5268	302	4	∈	∈	PROPN
ejpam-5268	302	5	[	[	X
ejpam-5268	302	6	r	r	X
ejpam-5268	302	7	,	,	PUNCT
ejpam-5268	302	8	s	s	PART
ejpam-5268	302	9	]	]	X
ejpam-5268	302	10	,	,	PUNCT
ejpam-5268	302	11	and	and	CCONJ
ejpam-5268	302	12	η	η	PROPN
ejpam-5268	302	13	:	:	PUNCT
ejpam-5268	303	1	[	[	X
ejpam-5268	303	2	0	0	NUM
ejpam-5268	303	3	,	,	PUNCT
ejpam-5268	303	4	1]×	1]×	NUM
ejpam-5268	303	5	r×	r×	NOUN
ejpam-5268	303	6	r	r	NOUN
ejpam-5268	303	7	→	→	SYM
ejpam-5268	303	8	r	r	NOUN
ejpam-5268	303	9	theorem	theorem	NOUN
ejpam-5268	303	10	3	3	X
ejpam-5268	303	11	.	.	PUNCT
ejpam-5268	304	1	let	let	VERB
ejpam-5268	304	2	the	the	DET
ejpam-5268	304	3	following	follow	VERB
ejpam-5268	304	4	suppositions	supposition	NOUN
ejpam-5268	304	5	hold	hold	VERB
ejpam-5268	304	6	:	:	PUNCT
ejpam-5268	304	7	(	(	PUNCT
ejpam-5268	304	8	i	i	NOUN
ejpam-5268	304	9	)	)	PUNCT
ejpam-5268	305	1	sup	sup	NOUN
ejpam-5268	305	2	∫	∫	PROPN
ejpam-5268	305	3	s	s	PART
ejpam-5268	305	4	r	r	NOUN
ejpam-5268	305	5	ψ	ψ	X
ejpam-5268	305	6	(	(	PUNCT
ejpam-5268	305	7	q	q	INTJ
ejpam-5268	305	8	,	,	PUNCT
ejpam-5268	305	9	p	p	X
ejpam-5268	305	10	,	,	PUNCT
ejpam-5268	305	11	p	p	NOUN
ejpam-5268	305	12	)	)	PUNCT
ejpam-5268	305	13	dp	dp	NOUN
ejpam-5268	305	14	≤	≤	NUM
ejpam-5268	305	15	1	1	NUM
ejpam-5268	305	16	2(s−r	2(s−r	NUM
ejpam-5268	305	17	)	)	PUNCT
ejpam-5268	305	18	,	,	PUNCT
ejpam-5268	305	19	(	(	PUNCT
ejpam-5268	305	20	ii	ii	NOUN
ejpam-5268	305	21	)	)	PUNCT
ejpam-5268	305	22	s	s	PART
ejpam-5268	305	23	(	(	PUNCT
ejpam-5268	305	24	p	p	X
ejpam-5268	305	25	,	,	PUNCT
ejpam-5268	305	26	δ	δ	PROPN
ejpam-5268	305	27	,	,	PUNCT
ejpam-5268	305	28	δ)−	δ)−	PROPN
ejpam-5268	305	29	s	s	X
ejpam-5268	305	30	(	(	PUNCT
ejpam-5268	305	31	p	p	PROPN
ejpam-5268	305	32	,	,	PUNCT
ejpam-5268	305	33	j	j	PROPN
ejpam-5268	305	34	,	,	PUNCT
ejpam-5268	305	35	j	j	PROPN
ejpam-5268	305	36	)	)	PUNCT
ejpam-5268	305	37	≤	≤	PROPN
ejpam-5268	305	38	φ	φ	PROPN
ejpam-5268	305	39	(	(	PUNCT
ejpam-5268	305	40	|δ	|δ	NOUN
ejpam-5268	305	41	−	−	PROPN
ejpam-5268	305	42	j|	j|	PROPN
ejpam-5268	305	43	)	)	PUNCT
ejpam-5268	305	44	;	;	PUNCT
ejpam-5268	306	1	n.	n.	PROPN
ejpam-5268	306	2	a.	a.	PROPN
ejpam-5268	306	3	majid	majid	PROPN
ejpam-5268	306	4	et	et	PROPN
ejpam-5268	306	5	al	al	PROPN
ejpam-5268	306	6	.	.	PUNCT
ejpam-5268	306	7	/	/	SYM
ejpam-5268	306	8	eur	eur	PROPN
ejpam-5268	306	9	.	.	PUNCT
ejpam-5268	307	1	j.	j.	PROPN
ejpam-5268	307	2	pure	pure	PROPN
ejpam-5268	307	3	appl	appl	PROPN
ejpam-5268	307	4	.	.	PROPN
ejpam-5268	307	5	math	math	PROPN
ejpam-5268	307	6	,	,	PUNCT
ejpam-5268	307	7	17	17	NUM
ejpam-5268	307	8	(	(	PUNCT
ejpam-5268	307	9	3	3	NUM
ejpam-5268	307	10	)	)	PUNCT
ejpam-5268	307	11	(	(	PUNCT
ejpam-5268	307	12	2024	2024	NUM
ejpam-5268	307	13	)	)	PUNCT
ejpam-5268	307	14	,	,	PUNCT
ejpam-5268	307	15	1877	1877	NUM
ejpam-5268	307	16	-	-	SYM
ejpam-5268	307	17	1893	1893	NUM
ejpam-5268	307	18	1890	1890	NUM
ejpam-5268	307	19	(	(	PUNCT
ejpam-5268	307	20	iii	iii	X
ejpam-5268	307	21	)	)	PUNCT
ejpam-5268	307	22	|λ|	|λ|	NOUN
ejpam-5268	307	23	≤	≤	NUM
ejpam-5268	307	24	1	1	NUM
ejpam-5268	307	25	,	,	PUNCT
ejpam-5268	307	26	where	where	SCONJ
ejpam-5268	307	27	φ	φ	PROPN
ejpam-5268	307	28	is	be	AUX
ejpam-5268	307	29	nondecreasing	nondecrease	VERB
ejpam-5268	307	30	continuous	continuous	ADJ
ejpam-5268	307	31	mapping	mapping	NOUN
ejpam-5268	307	32	having	have	VERB
ejpam-5268	307	33	φ	φ	PROPN
ejpam-5268	307	34	(	(	PUNCT
ejpam-5268	307	35	n	n	CCONJ
ejpam-5268	307	36	)	)	PUNCT
ejpam-5268	307	37	<	<	X
ejpam-5268	307	38	n	n	CCONJ
ejpam-5268	307	39	,	,	PUNCT
ejpam-5268	307	40	∀	∀	X
ejpam-5268	307	41	n	n	CCONJ
ejpam-5268	307	42	>	>	X
ejpam-5268	307	43	0	0	X
ejpam-5268	307	44	.	.	PUNCT
ejpam-5268	308	1	so	so	ADV
ejpam-5268	308	2	,	,	PUNCT
ejpam-5268	308	3	integral	integral	ADJ
ejpam-5268	308	4	equation	equation	NOUN
ejpam-5268	308	5	18	18	NUM
ejpam-5268	308	6	has	have	VERB
ejpam-5268	308	7	unique	unique	ADJ
ejpam-5268	308	8	solution	solution	NOUN
ejpam-5268	308	9	.	.	PUNCT
ejpam-5268	309	1	proof	proof	NOUN
ejpam-5268	309	2	.	.	PUNCT
ejpam-5268	310	1	for	for	ADP
ejpam-5268	310	2	δ1	δ1	NOUN
ejpam-5268	310	3	,	,	PUNCT
ejpam-5268	310	4	δ2	δ2	VERB
ejpam-5268	310	5	∈	∈	PROPN
ejpam-5268	310	6	x	x	PRON
ejpam-5268	310	7	,	,	PUNCT
ejpam-5268	310	8	we	we	PRON
ejpam-5268	310	9	have	have	VERB
ejpam-5268	310	10	s	s	NOUN
ejpam-5268	310	11	(	(	PUNCT
ejpam-5268	310	12	fδ1,fδ2,fδ2	fδ1,fδ2,fδ2	NOUN
ejpam-5268	310	13	)	)	PUNCT
ejpam-5268	310	14	=	=	SYM
ejpam-5268	310	15	2	2	NUM
ejpam-5268	310	16	sup	sup	NOUN
ejpam-5268	310	17	|fδ1	|fδ1	VERB
ejpam-5268	310	18	(	(	PUNCT
ejpam-5268	310	19	q)−fδ2(q)|	q)−fδ2(q)|	NOUN
ejpam-5268	310	20	=	=	SYM
ejpam-5268	310	21	2sup	2sup	NUM
ejpam-5268	310	22	∣∣∣∣j	∣∣∣∣j	NOUN
ejpam-5268	310	23	(	(	PUNCT
ejpam-5268	310	24	q	q	X
ejpam-5268	310	25	)	)	PUNCT
ejpam-5268	311	1	+	+	CCONJ
ejpam-5268	311	2	λ	λ	X
ejpam-5268	311	3	∫	∫	PROPN
ejpam-5268	311	4	s	s	PART
ejpam-5268	311	5	r	r	NOUN
ejpam-5268	311	6	ψ	ψ	X
ejpam-5268	311	7	(	(	PUNCT
ejpam-5268	311	8	q	q	INTJ
ejpam-5268	311	9	,	,	PUNCT
ejpam-5268	311	10	p	p	X
ejpam-5268	311	11	,	,	PUNCT
ejpam-5268	311	12	p)µ	p)µ	NOUN
ejpam-5268	311	13	(	(	PUNCT
ejpam-5268	311	14	p	p	X
ejpam-5268	311	15	,	,	PUNCT
ejpam-5268	311	16	δ1	δ1	NOUN
ejpam-5268	311	17	(	(	PUNCT
ejpam-5268	311	18	p	p	NOUN
ejpam-5268	311	19	)	)	PUNCT
ejpam-5268	311	20	,	,	PUNCT
ejpam-5268	311	21	δ1	δ1	NOUN
ejpam-5268	311	22	(	(	PUNCT
ejpam-5268	311	23	p	p	NOUN
ejpam-5268	311	24	)	)	PUNCT
ejpam-5268	311	25	)	)	PUNCT
ejpam-5268	312	1	dp−	dp−	PROPN
ejpam-5268	312	2	j	j	PROPN
ejpam-5268	312	3	(	(	PUNCT
ejpam-5268	312	4	q)−	q)−	PROPN
ejpam-5268	312	5	λ	λ	PROPN
ejpam-5268	312	6	∫	∫	PROPN
ejpam-5268	312	7	s	s	PART
ejpam-5268	312	8	r	r	NOUN
ejpam-5268	312	9	ψ	ψ	X
ejpam-5268	312	10	(	(	PUNCT
ejpam-5268	312	11	q	q	INTJ
ejpam-5268	312	12	,	,	PUNCT
ejpam-5268	312	13	p	p	X
ejpam-5268	312	14	,	,	PUNCT
ejpam-5268	312	15	p)µ	p)µ	NOUN
ejpam-5268	312	16	(	(	PUNCT
ejpam-5268	312	17	p	p	X
ejpam-5268	312	18	,	,	PUNCT
ejpam-5268	312	19	δ2	δ2	VERB
ejpam-5268	312	20	(	(	PUNCT
ejpam-5268	312	21	p	p	NOUN
ejpam-5268	312	22	)	)	PUNCT
ejpam-5268	312	23	,	,	PUNCT
ejpam-5268	312	24	δ2	δ2	VERB
ejpam-5268	312	25	(	(	PUNCT
ejpam-5268	312	26	p	p	NOUN
ejpam-5268	312	27	)	)	PUNCT
ejpam-5268	312	28	)	)	PUNCT
ejpam-5268	312	29	dp	dp	NOUN
ejpam-5268	312	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	312	31	=	=	SYM
ejpam-5268	312	32	2	2	NUM
ejpam-5268	312	33	|λ|	|λ|	NOUN
ejpam-5268	312	34	sup	sup	NOUN
ejpam-5268	312	35	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5268	312	36	s	s	PART
ejpam-5268	312	37	r	r	NOUN
ejpam-5268	312	38	ψ	ψ	X
ejpam-5268	312	39	(	(	PUNCT
ejpam-5268	312	40	q	q	INTJ
ejpam-5268	312	41	,	,	PUNCT
ejpam-5268	312	42	p	p	X
ejpam-5268	312	43	,	,	PUNCT
ejpam-5268	312	44	p)µ	p)µ	NOUN
ejpam-5268	312	45	(	(	PUNCT
ejpam-5268	312	46	p	p	X
ejpam-5268	312	47	,	,	PUNCT
ejpam-5268	312	48	δ1	δ1	NOUN
ejpam-5268	312	49	(	(	PUNCT
ejpam-5268	312	50	p	p	NOUN
ejpam-5268	312	51	)	)	PUNCT
ejpam-5268	312	52	,	,	PUNCT
ejpam-5268	312	53	δ1	δ1	NOUN
ejpam-5268	312	54	(	(	PUNCT
ejpam-5268	312	55	p))−	p))−	PROPN
ejpam-5268	312	56	µ	µ	X
ejpam-5268	312	57	(	(	PUNCT
ejpam-5268	312	58	p	p	X
ejpam-5268	312	59	,	,	PUNCT
ejpam-5268	312	60	δ2	δ2	VERB
ejpam-5268	312	61	(	(	PUNCT
ejpam-5268	312	62	p	p	NOUN
ejpam-5268	312	63	)	)	PUNCT
ejpam-5268	312	64	,	,	PUNCT
ejpam-5268	312	65	δ2	δ2	VERB
ejpam-5268	312	66	(	(	PUNCT
ejpam-5268	312	67	p	p	NOUN
ejpam-5268	312	68	)	)	PUNCT
ejpam-5268	312	69	)	)	PUNCT
ejpam-5268	312	70	dp	dp	PROPN
ejpam-5268	312	71	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	312	72	≤	≤	ADV
ejpam-5268	312	73	2	2	NUM
ejpam-5268	312	74	|λ|	|λ|	NOUN
ejpam-5268	312	75	sup	sup	NOUN
ejpam-5268	313	1	[	[	X
ejpam-5268	313	2	∫	∫	X
ejpam-5268	313	3	s	s	PART
ejpam-5268	313	4	r	r	NOUN
ejpam-5268	313	5	ψ	ψ	X
ejpam-5268	313	6	(	(	PUNCT
ejpam-5268	313	7	q	q	INTJ
ejpam-5268	313	8	,	,	PUNCT
ejpam-5268	313	9	p	p	X
ejpam-5268	313	10	,	,	PUNCT
ejpam-5268	313	11	p	p	NOUN
ejpam-5268	313	12	)	)	PUNCT
ejpam-5268	313	13	dp	dp	NOUN
ejpam-5268	314	1	∫	∫	PROPN
ejpam-5268	314	2	s	s	PART
ejpam-5268	314	3	r	r	NOUN
ejpam-5268	314	4	(	(	PUNCT
ejpam-5268	314	5	µ	µ	X
ejpam-5268	314	6	(	(	PUNCT
ejpam-5268	314	7	p	p	NOUN
ejpam-5268	314	8	,	,	PUNCT
ejpam-5268	314	9	δ1	δ1	NOUN
ejpam-5268	314	10	(	(	PUNCT
ejpam-5268	314	11	p	p	NOUN
ejpam-5268	314	12	)	)	PUNCT
ejpam-5268	314	13	,	,	PUNCT
ejpam-5268	314	14	δ1	δ1	NOUN
ejpam-5268	314	15	(	(	PUNCT
ejpam-5268	314	16	p))−	p))−	PROPN
ejpam-5268	314	17	µ	µ	X
ejpam-5268	314	18	(	(	PUNCT
ejpam-5268	314	19	p	p	X
ejpam-5268	314	20	,	,	PUNCT
ejpam-5268	314	21	δ2	δ2	VERB
ejpam-5268	314	22	(	(	PUNCT
ejpam-5268	314	23	p	p	NOUN
ejpam-5268	314	24	)	)	PUNCT
ejpam-5268	314	25	,	,	PUNCT
ejpam-5268	314	26	δ2	δ2	VERB
ejpam-5268	314	27	(	(	PUNCT
ejpam-5268	314	28	p	p	NOUN
ejpam-5268	314	29	)	)	PUNCT
ejpam-5268	314	30	)	)	PUNCT
ejpam-5268	314	31	dp	dp	NOUN
ejpam-5268	314	32	]	]	PUNCT
ejpam-5268	314	33	≤	≤	NOUN
ejpam-5268	314	34	2	2	NUM
ejpam-5268	314	35	|λ|	|λ|	NOUN
ejpam-5268	314	36	2(s−	2(s−	NUM
ejpam-5268	314	37	r	r	NOUN
ejpam-5268	314	38	)	)	PUNCT
ejpam-5268	315	1	[	[	X
ejpam-5268	315	2	∫	∫	X
ejpam-5268	315	3	s	s	PART
ejpam-5268	315	4	r	r	NOUN
ejpam-5268	315	5	φ(|δ1	φ(|δ1	NOUN
ejpam-5268	315	6	(	(	PUNCT
ejpam-5268	315	7	p)−	p)−	NOUN
ejpam-5268	315	8	δ2	δ2	VERB
ejpam-5268	315	9	(	(	PUNCT
ejpam-5268	315	10	p)|)dp	p)|)dp	NOUN
ejpam-5268	315	11	]	]	PUNCT
ejpam-5268	315	12	≤	≤	NUM
ejpam-5268	315	13	|λ|	|λ|	PROPN
ejpam-5268	315	14	s−	s−	PROPN
ejpam-5268	315	15	r	r	PROPN
ejpam-5268	316	1	[	[	X
ejpam-5268	316	2	∫	∫	X
ejpam-5268	316	3	s	s	PART
ejpam-5268	316	4	r	r	NOUN
ejpam-5268	316	5	φ(s(δ1	φ(s(δ1	PROPN
ejpam-5268	316	6	,	,	PUNCT
ejpam-5268	316	7	δ2	δ2	VERB
ejpam-5268	316	8	,	,	PUNCT
ejpam-5268	316	9	δ2))dp	δ2))dp	NOUN
ejpam-5268	316	10	]	]	PUNCT
ejpam-5268	316	11	=	=	PUNCT
ejpam-5268	316	12	|λ|	|λ|	PROPN
ejpam-5268	316	13	s−	s−	PROPN
ejpam-5268	316	14	r	r	PROPN
ejpam-5268	316	15	φ(s(δ1	φ(s(δ1	PROPN
ejpam-5268	316	16	,	,	PUNCT
ejpam-5268	316	17	δ2	δ2	VERB
ejpam-5268	316	18	,	,	PUNCT
ejpam-5268	316	19	δ2))×	δ2))×	PROPN
ejpam-5268	316	20	s−	s−	PROPN
ejpam-5268	316	21	r	r	NOUN
ejpam-5268	316	22	=	=	PUNCT
ejpam-5268	316	23	|λ|	|λ|	NOUN
ejpam-5268	316	24	φ(s(δ1	φ(s(δ1	PROPN
ejpam-5268	316	25	,	,	PUNCT
ejpam-5268	316	26	δ2	δ2	VERB
ejpam-5268	316	27	,	,	PUNCT
ejpam-5268	316	28	δ2	δ2	PROPN
ejpam-5268	316	29	)	)	PUNCT
ejpam-5268	316	30	)	)	PUNCT
ejpam-5268	316	31	≤	≤	PUNCT
ejpam-5268	317	1	φ(s(δ1	φ(s(δ1	PROPN
ejpam-5268	317	2	,	,	PUNCT
ejpam-5268	317	3	δ2	δ2	VERB
ejpam-5268	317	4	,	,	PUNCT
ejpam-5268	317	5	δ2	δ2	PROPN
ejpam-5268	317	6	)	)	PUNCT
ejpam-5268	317	7	)	)	PUNCT
ejpam-5268	317	8	.	.	PUNCT
ejpam-5268	318	1	consequently	consequently	ADV
ejpam-5268	318	2	,	,	PUNCT
ejpam-5268	318	3	f	f	PROPN
ejpam-5268	318	4	has	have	VERB
ejpam-5268	318	5	unique	unique	ADJ
ejpam-5268	318	6	solution	solution	NOUN
ejpam-5268	318	7	,	,	PUNCT
ejpam-5268	318	8	which	which	PRON
ejpam-5268	318	9	means	mean	VERB
ejpam-5268	318	10	that	that	SCONJ
ejpam-5268	318	11	equation	equation	NOUN
ejpam-5268	318	12	18	18	NUM
ejpam-5268	318	13	has	have	VERB
ejpam-5268	318	14	unique	unique	ADJ
ejpam-5268	318	15	solution	solution	NOUN
ejpam-5268	318	16	in	in	ADP
ejpam-5268	318	17	x.	x.	NOUN
ejpam-5268	318	18	now	now	ADV
ejpam-5268	318	19	,	,	PUNCT
ejpam-5268	318	20	introduce	introduce	VERB
ejpam-5268	318	21	an	an	DET
ejpam-5268	318	22	application	application	NOUN
ejpam-5268	318	23	to	to	PART
ejpam-5268	318	24	explain	explain	VERB
ejpam-5268	318	25	the	the	DET
ejpam-5268	318	26	existence	existence	NOUN
ejpam-5268	318	27	and	and	CCONJ
ejpam-5268	318	28	uniqueness	uniqueness	ADJ
ejpam-5268	318	29	problem	problem	NOUN
ejpam-5268	318	30	of	of	ADP
ejpam-5268	318	31	the	the	DET
ejpam-5268	318	32	solution	solution	NOUN
ejpam-5268	318	33	to	to	ADP
ejpam-5268	318	34	an	an	DET
ejpam-5268	318	35	integral	integral	ADJ
ejpam-5268	318	36	equation	equation	NOUN
ejpam-5268	318	37	of	of	ADP
ejpam-5268	318	38	the	the	DET
ejpam-5268	318	39	following	follow	VERB
ejpam-5268	318	40	form	form	NOUN
ejpam-5268	318	41	in	in	ADP
ejpam-5268	318	42	s	s	NOUN
ejpam-5268	318	43	-	-	ADJ
ejpam-5268	318	44	metric	metric	ADJ
ejpam-5268	318	45	spaces	space	NOUN
ejpam-5268	318	46	:	:	PUNCT
ejpam-5268	318	47	δ	δ	PROPN
ejpam-5268	318	48	(	(	PUNCT
ejpam-5268	318	49	q	q	X
ejpam-5268	318	50	)	)	PUNCT
ejpam-5268	319	1	=	=	SYM
ejpam-5268	319	2	j	j	PROPN
ejpam-5268	319	3	(	(	PUNCT
ejpam-5268	319	4	q	q	X
ejpam-5268	319	5	)	)	PUNCT
ejpam-5268	319	6	+	+	CCONJ
ejpam-5268	319	7	∫	∫	PROPN
ejpam-5268	319	8	1	1	NUM
ejpam-5268	319	9	0	0	NUM
ejpam-5268	319	10	ψ	ψ	X
ejpam-5268	319	11	(	(	PUNCT
ejpam-5268	319	12	q	q	INTJ
ejpam-5268	319	13	,	,	PUNCT
ejpam-5268	319	14	p	p	X
ejpam-5268	319	15	,	,	PUNCT
ejpam-5268	319	16	u	u	NOUN
ejpam-5268	319	17	(	(	PUNCT
ejpam-5268	319	18	p	p	NOUN
ejpam-5268	319	19	)	)	PUNCT
ejpam-5268	319	20	)	)	PUNCT
ejpam-5268	320	1	dp	dp	NOUN
ejpam-5268	320	2	,	,	PUNCT
ejpam-5268	320	3	q	q	NOUN
ejpam-5268	320	4	∈	∈	PROPN
ejpam-5268	321	1	[	[	X
ejpam-5268	321	2	0	0	NUM
ejpam-5268	321	3	,	,	PUNCT
ejpam-5268	321	4	1	1	NUM
ejpam-5268	321	5	]	]	PUNCT
ejpam-5268	321	6	.	.	PUNCT
ejpam-5268	322	1	(	(	PUNCT
ejpam-5268	322	2	19	19	NUM
ejpam-5268	322	3	)	)	PUNCT
ejpam-5268	322	4	assume	assume	VERB
ejpam-5268	322	5	f	f	X
ejpam-5268	322	6	:	:	PUNCT
ejpam-5268	322	7	(	(	PUNCT
ejpam-5268	322	8	x	x	X
ejpam-5268	322	9	,	,	PUNCT
ejpam-5268	322	10	s	s	PART
ejpam-5268	322	11	)	)	PUNCT
ejpam-5268	322	12	→	→	SYM
ejpam-5268	322	13	(	(	PUNCT
ejpam-5268	322	14	x	x	X
ejpam-5268	322	15	,	,	PUNCT
ejpam-5268	322	16	s	s	PART
ejpam-5268	322	17	)	)	PUNCT
ejpam-5268	322	18	is	be	AUX
ejpam-5268	322	19	self	self	NOUN
ejpam-5268	322	20	-	-	PUNCT
ejpam-5268	322	21	mapping	mapping	NOUN
ejpam-5268	322	22	defined	define	VERB
ejpam-5268	322	23	as	as	SCONJ
ejpam-5268	322	24	follows	follow	VERB
ejpam-5268	322	25	:	:	PUNCT
ejpam-5268	322	26	fδ	fδ	PART
ejpam-5268	322	27	(	(	PUNCT
ejpam-5268	322	28	q	q	X
ejpam-5268	322	29	)	)	PUNCT
ejpam-5268	323	1	=	=	SYM
ejpam-5268	323	2	j	j	PROPN
ejpam-5268	323	3	(	(	PUNCT
ejpam-5268	323	4	q	q	X
ejpam-5268	323	5	)	)	PUNCT
ejpam-5268	323	6	+	+	CCONJ
ejpam-5268	323	7	∫	∫	PROPN
ejpam-5268	323	8	1	1	NUM
ejpam-5268	323	9	0	0	NUM
ejpam-5268	323	10	ψ	ψ	X
ejpam-5268	323	11	(	(	PUNCT
ejpam-5268	323	12	q	q	INTJ
ejpam-5268	323	13	,	,	PUNCT
ejpam-5268	323	14	p	p	X
ejpam-5268	323	15	,	,	PUNCT
ejpam-5268	323	16	δ	δ	PROPN
ejpam-5268	323	17	(	(	PUNCT
ejpam-5268	323	18	p	p	NOUN
ejpam-5268	323	19	)	)	PUNCT
ejpam-5268	323	20	)	)	PUNCT
ejpam-5268	324	1	dp	dp	NOUN
ejpam-5268	324	2	,	,	PUNCT
ejpam-5268	324	3	q	q	NOUN
ejpam-5268	324	4	∈	∈	PROPN
ejpam-5268	325	1	[	[	X
ejpam-5268	325	2	0	0	NUM
ejpam-5268	325	3	,	,	PUNCT
ejpam-5268	325	4	1	1	NUM
ejpam-5268	325	5	]	]	PUNCT
ejpam-5268	325	6	.	.	PUNCT
ejpam-5268	326	1	resume	resume	VERB
ejpam-5268	326	2	x	x	X
ejpam-5268	327	1	=	=	SYM
ejpam-5268	327	2	c([0	c([0	PROPN
ejpam-5268	327	3	,	,	PUNCT
ejpam-5268	327	4	1	1	NUM
ejpam-5268	327	5	]	]	NUM
ejpam-5268	327	6	)	)	PUNCT
ejpam-5268	327	7	space	space	NOUN
ejpam-5268	327	8	of	of	ADP
ejpam-5268	327	9	real	real	ADJ
ejpam-5268	327	10	continuous	continuous	ADJ
ejpam-5268	327	11	mappings	mapping	NOUN
ejpam-5268	327	12	described	describe	VERB
ejpam-5268	327	13	on	on	ADP
ejpam-5268	327	14	[	[	X
ejpam-5268	327	15	0,1	0,1	NUM
ejpam-5268	327	16	]	]	PUNCT
ejpam-5268	327	17	,	,	PUNCT
ejpam-5268	327	18	and	and	CCONJ
ejpam-5268	327	19	let	let	VERB
ejpam-5268	327	20	x	x	PRON
ejpam-5268	327	21	equipped	equip	VERB
ejpam-5268	327	22	with	with	ADP
ejpam-5268	327	23	s	s	NOUN
ejpam-5268	327	24	-	-	ADJ
ejpam-5268	327	25	metric	metric	ADJ
ejpam-5268	327	26	which	which	PRON
ejpam-5268	327	27	is	be	AUX
ejpam-5268	327	28	described	describe	VERB
ejpam-5268	327	29	as	as	SCONJ
ejpam-5268	327	30	follows	follow	VERB
ejpam-5268	327	31	:	:	PUNCT
ejpam-5268	327	32	s	s	X
ejpam-5268	327	33	(	(	PUNCT
ejpam-5268	327	34	δ	δ	PROPN
ejpam-5268	327	35	,	,	PUNCT
ejpam-5268	327	36	α	α	X
ejpam-5268	327	37	,	,	PUNCT
ejpam-5268	327	38	β	β	NOUN
ejpam-5268	327	39	)	)	PUNCT
ejpam-5268	327	40	=	=	SYM
ejpam-5268	327	41	sup	sup	NOUN
ejpam-5268	327	42	q∈[0,1	q∈[0,1	PROPN
ejpam-5268	327	43	]	]	PUNCT
ejpam-5268	327	44	|δ	|δ	NOUN
ejpam-5268	327	45	(	(	PUNCT
ejpam-5268	327	46	q)−	q)−	PROPN
ejpam-5268	327	47	α(q)|+	α(q)|+	PROPN
ejpam-5268	327	48	sup	sup	NOUN
ejpam-5268	327	49	q∈[0,1	q∈[0,1	PROPN
ejpam-5268	327	50	]	]	PUNCT
ejpam-5268	327	51	|α	|α	NOUN
ejpam-5268	327	52	(	(	PUNCT
ejpam-5268	327	53	q)−	q)−	PROPN
ejpam-5268	327	54	β(q)|+	β(q)|+	ADP
ejpam-5268	327	55	sup	sup	NOUN
ejpam-5268	327	56	q∈[0,1	q∈[0,1	PROPN
ejpam-5268	327	57	]	]	PUNCT
ejpam-5268	327	58	|β	|β	VERB
ejpam-5268	327	59	(	(	PUNCT
ejpam-5268	327	60	q)−	q)−	PROPN
ejpam-5268	327	61	δ(q)|	δ(q)|	NOUN
ejpam-5268	327	62	is	be	AUX
ejpam-5268	327	63	complete	complete	ADJ
ejpam-5268	327	64	s	s	NOUN
ejpam-5268	327	65	-	-	ADJ
ejpam-5268	327	66	metric	metric	ADJ
ejpam-5268	327	67	-	-	PUNCT
ejpam-5268	327	68	space	space	NOUN
ejpam-5268	327	69	.	.	PUNCT
ejpam-5268	328	1	theorem	theorem	NOUN
ejpam-5268	328	2	4	4	NUM
ejpam-5268	328	3	.	.	PUNCT
ejpam-5268	329	1	if	if	SCONJ
ejpam-5268	329	2	the	the	DET
ejpam-5268	329	3	following	follow	VERB
ejpam-5268	329	4	suppositions	supposition	NOUN
ejpam-5268	329	5	hold	hold	VERB
ejpam-5268	329	6	:	:	PUNCT
ejpam-5268	329	7	(	(	PUNCT
ejpam-5268	329	8	i	i	NOUN
ejpam-5268	329	9	)	)	PUNCT
ejpam-5268	329	10	ψ	ψ	X
ejpam-5268	329	11	:	:	PUNCT
ejpam-5268	330	1	[	[	X
ejpam-5268	330	2	0	0	NUM
ejpam-5268	330	3	,	,	PUNCT
ejpam-5268	330	4	1]×	1]×	NUM
ejpam-5268	330	5	[	[	X
ejpam-5268	330	6	0	0	NUM
ejpam-5268	330	7	,	,	PUNCT
ejpam-5268	330	8	1]×	1]×	NUM
ejpam-5268	330	9	r	r	NOUN
ejpam-5268	330	10	→	→	SYM
ejpam-5268	330	11	r	r	NOUN
ejpam-5268	330	12	and	and	CCONJ
ejpam-5268	330	13	j	j	NOUN
ejpam-5268	330	14	:	:	PUNCT
ejpam-5268	330	15	r	r	NOUN
ejpam-5268	330	16	→	→	SYM
ejpam-5268	330	17	r	r	NOUN
ejpam-5268	330	18	are	be	AUX
ejpam-5268	330	19	continuous	continuous	ADJ
ejpam-5268	330	20	mappings	mapping	NOUN
ejpam-5268	330	21	,	,	PUNCT
ejpam-5268	330	22	(	(	PUNCT
ejpam-5268	330	23	ii	ii	NOUN
ejpam-5268	330	24	)	)	PUNCT
ejpam-5268	330	25	there	there	PRON
ejpam-5268	330	26	exists	exist	VERB
ejpam-5268	330	27	φ	φ	NOUN
ejpam-5268	330	28	:	:	PUNCT
ejpam-5268	331	1	[	[	X
ejpam-5268	331	2	0	0	NUM
ejpam-5268	331	3	,	,	PUNCT
ejpam-5268	331	4	1]×	1]×	NUM
ejpam-5268	331	5	[	[	X
ejpam-5268	331	6	0	0	NUM
ejpam-5268	331	7	,	,	PUNCT
ejpam-5268	331	8	1	1	NUM
ejpam-5268	331	9	]	]	PUNCT
ejpam-5268	331	10	→	→	X
ejpam-5268	331	11	[	[	X
ejpam-5268	331	12	0,∞	0,∞	NUM
ejpam-5268	331	13	)	)	PUNCT
ejpam-5268	331	14	such	such	ADJ
ejpam-5268	331	15	that	that	SCONJ
ejpam-5268	331	16	1	1	NUM
ejpam-5268	331	17	3s	3s	NUM
ejpam-5268	331	18	(	(	PUNCT
ejpam-5268	331	19	δ	δ	PROPN
ejpam-5268	331	20	,	,	PUNCT
ejpam-5268	331	21	fδ	fδ	NOUN
ejpam-5268	331	22	,	,	PUNCT
ejpam-5268	331	23	fδ	fδ	NOUN
ejpam-5268	331	24	)	)	PUNCT
ejpam-5268	331	25	≤	≤	NOUN
ejpam-5268	331	26	s	s	PART
ejpam-5268	331	27	(	(	PUNCT
ejpam-5268	331	28	δ	δ	PROPN
ejpam-5268	331	29	,	,	PUNCT
ejpam-5268	331	30	α	α	PROPN
ejpam-5268	331	31	,	,	PUNCT
ejpam-5268	331	32	α	α	NOUN
ejpam-5268	331	33	)	)	PUNCT
ejpam-5268	331	34	implies	imply	VERB
ejpam-5268	331	35	that	that	SCONJ
ejpam-5268	331	36	|ψ	|ψ	X
ejpam-5268	331	37	(	(	PUNCT
ejpam-5268	331	38	q	q	ADJ
ejpam-5268	331	39	,	,	PUNCT
ejpam-5268	331	40	p	p	X
ejpam-5268	331	41	,	,	PUNCT
ejpam-5268	331	42	u)−	u)−	PROPN
ejpam-5268	331	43	ψ	ψ	X
ejpam-5268	331	44	(	(	PUNCT
ejpam-5268	331	45	q	q	INTJ
ejpam-5268	331	46	,	,	PUNCT
ejpam-5268	331	47	p	p	X
ejpam-5268	331	48	,	,	PUNCT
ejpam-5268	331	49	v)|	v)|	NOUN
ejpam-5268	331	50	≤	≤	PUNCT
ejpam-5268	331	51	φ	φ	PROPN
ejpam-5268	331	52	(	(	PUNCT
ejpam-5268	331	53	q	q	NOUN
ejpam-5268	331	54	,	,	PUNCT
ejpam-5268	331	55	p	p	NOUN
ejpam-5268	331	56	)	)	PUNCT
ejpam-5268	331	57	|u	|u	ADJ
ejpam-5268	331	58	−	−	PROPN
ejpam-5268	331	59	v|	v|	NOUN
ejpam-5268	331	60	.	.	PUNCT
ejpam-5268	332	1	for	for	ADP
ejpam-5268	332	2	all	all	DET
ejpam-5268	332	3	distinct	distinct	PROPN
ejpam-5268	332	4	δ	δ	PROPN
ejpam-5268	332	5	,	,	PUNCT
ejpam-5268	332	6	α	α	PROPN
ejpam-5268	332	7	∈	∈	PROPN
ejpam-5268	332	8	x	x	SYM
ejpam-5268	332	9	,	,	PUNCT
ejpam-5268	332	10	q	q	INTJ
ejpam-5268	332	11	,	,	PUNCT
ejpam-5268	332	12	p	p	NOUN
ejpam-5268	332	13	∈	∈	PROPN
ejpam-5268	333	1	[	[	X
ejpam-5268	333	2	0	0	NUM
ejpam-5268	333	3	,	,	PUNCT
ejpam-5268	333	4	1	1	NUM
ejpam-5268	333	5	]	]	PUNCT
ejpam-5268	333	6	with	with	ADP
ejpam-5268	333	7	u	u	NOUN
ejpam-5268	333	8	,	,	PUNCT
ejpam-5268	333	9	v	v	NOUN
ejpam-5268	333	10	∈	∈	NOUN
ejpam-5268	333	11	r	r	NOUN
ejpam-5268	333	12	,	,	PUNCT
ejpam-5268	333	13	n.	n.	NOUN
ejpam-5268	333	14	a.	a.	PROPN
ejpam-5268	333	15	majid	majid	PROPN
ejpam-5268	333	16	et	et	PROPN
ejpam-5268	333	17	al	al	PROPN
ejpam-5268	333	18	.	.	PUNCT
ejpam-5268	333	19	/	/	SYM
ejpam-5268	333	20	eur	eur	PROPN
ejpam-5268	333	21	.	.	PUNCT
ejpam-5268	334	1	j.	j.	PROPN
ejpam-5268	334	2	pure	pure	PROPN
ejpam-5268	334	3	appl	appl	PROPN
ejpam-5268	334	4	.	.	PROPN
ejpam-5268	334	5	math	math	PROPN
ejpam-5268	334	6	,	,	PUNCT
ejpam-5268	334	7	17	17	NUM
ejpam-5268	334	8	(	(	PUNCT
ejpam-5268	334	9	3	3	NUM
ejpam-5268	334	10	)	)	PUNCT
ejpam-5268	334	11	(	(	PUNCT
ejpam-5268	334	12	2024	2024	NUM
ejpam-5268	334	13	)	)	PUNCT
ejpam-5268	334	14	,	,	PUNCT
ejpam-5268	334	15	1877	1877	NUM
ejpam-5268	334	16	-	-	SYM
ejpam-5268	334	17	1893	1893	NUM
ejpam-5268	334	18	1891	1891	NUM
ejpam-5268	334	19	(	(	PUNCT
ejpam-5268	334	20	iii	iii	NOUN
ejpam-5268	334	21	)	)	PUNCT
ejpam-5268	334	22	sup	sup	NOUN
ejpam-5268	334	23	q∈[0,1	q∈[0,1	PROPN
ejpam-5268	334	24	]	]	PUNCT
ejpam-5268	334	25	∫	∫	PROPN
ejpam-5268	334	26	1	1	NUM
ejpam-5268	334	27	0	0	NUM
ejpam-5268	334	28	φ	φ	PROPN
ejpam-5268	334	29	(	(	PUNCT
ejpam-5268	334	30	q	q	NOUN
ejpam-5268	334	31	,	,	PUNCT
ejpam-5268	334	32	p	p	NOUN
ejpam-5268	334	33	)	)	PUNCT
ejpam-5268	334	34	dp	dp	NOUN
ejpam-5268	334	35	<	<	X
ejpam-5268	334	36	φ	φ	PROPN
ejpam-5268	334	37	,	,	PUNCT
ejpam-5268	334	38	where	where	SCONJ
ejpam-5268	334	39	φ	φ	PROPN
ejpam-5268	334	40	∈	∈	PROPN
ejpam-5268	334	41	(	(	PUNCT
ejpam-5268	334	42	0	0	NUM
ejpam-5268	334	43	,	,	PUNCT
ejpam-5268	334	44	1	1	NUM
ejpam-5268	334	45	)	)	PUNCT
ejpam-5268	334	46	.	.	PUNCT
ejpam-5268	335	1	so	so	ADV
ejpam-5268	335	2	,	,	PUNCT
ejpam-5268	335	3	integral	integral	ADJ
ejpam-5268	335	4	equation	equation	NOUN
ejpam-5268	335	5	19	19	NUM
ejpam-5268	335	6	has	have	VERB
ejpam-5268	335	7	unique	unique	ADJ
ejpam-5268	335	8	solution	solution	NOUN
ejpam-5268	335	9	.	.	PUNCT
ejpam-5268	336	1	proof	proof	NOUN
ejpam-5268	336	2	.	.	PUNCT
ejpam-5268	337	1	for	for	ADP
ejpam-5268	337	2	δ	δ	PROPN
ejpam-5268	337	3	,	,	PUNCT
ejpam-5268	337	4	α	α	PROPN
ejpam-5268	337	5	∈	∈	PROPN
ejpam-5268	337	6	x	x	X
ejpam-5268	337	7	,	,	PUNCT
ejpam-5268	337	8	we	we	PRON
ejpam-5268	337	9	have	have	VERB
ejpam-5268	337	10	s	s	NOUN
ejpam-5268	337	11	(	(	PUNCT
ejpam-5268	337	12	fδ	fδ	PART
ejpam-5268	337	13	,	,	PUNCT
ejpam-5268	337	14	fα	fα	NOUN
ejpam-5268	337	15	,	,	PUNCT
ejpam-5268	337	16	fα	fα	NOUN
ejpam-5268	337	17	)	)	PUNCT
ejpam-5268	337	18	=	=	SYM
ejpam-5268	338	1	sup	sup	NOUN
ejpam-5268	338	2	q	q	NOUN
ejpam-5268	338	3	∈	∈	PROPN
ejpam-5268	339	1	[	[	X
ejpam-5268	339	2	0	0	NUM
ejpam-5268	339	3	,	,	PUNCT
ejpam-5268	339	4	1	1	NUM
ejpam-5268	339	5	]	]	SYM
ejpam-5268	339	6	|fδ	|fδ	PROPN
ejpam-5268	339	7	(	(	PUNCT
ejpam-5268	339	8	q)−fα(q)|	q)−fα(q)|	NOUN
ejpam-5268	339	9	=	=	SYM
ejpam-5268	339	10	2	2	NUM
ejpam-5268	339	11	sup	sup	NOUN
ejpam-5268	339	12	q	q	NOUN
ejpam-5268	339	13	∈	∈	PROPN
ejpam-5268	340	1	[	[	X
ejpam-5268	340	2	0	0	NUM
ejpam-5268	340	3	,	,	PUNCT
ejpam-5268	340	4	1	1	NUM
ejpam-5268	340	5	]	]	SYM
ejpam-5268	340	6	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-5268	340	7	1	1	NUM
ejpam-5268	340	8	0	0	NUM
ejpam-5268	340	9	ψ	ψ	X
ejpam-5268	340	10	(	(	PUNCT
ejpam-5268	340	11	q	q	INTJ
ejpam-5268	340	12	,	,	PUNCT
ejpam-5268	340	13	p	p	X
ejpam-5268	340	14	,	,	PUNCT
ejpam-5268	340	15	δ	δ	PROPN
ejpam-5268	340	16	(	(	PUNCT
ejpam-5268	340	17	p))−	p))−	NOUN
ejpam-5268	340	18	ψ	ψ	X
ejpam-5268	340	19	(	(	PUNCT
ejpam-5268	340	20	q	q	X
ejpam-5268	340	21	,	,	PUNCT
ejpam-5268	340	22	p	p	X
ejpam-5268	340	23	,	,	PUNCT
ejpam-5268	340	24	α	α	X
ejpam-5268	340	25	(	(	PUNCT
ejpam-5268	340	26	p	p	NOUN
ejpam-5268	340	27	)	)	PUNCT
ejpam-5268	340	28	)	)	PUNCT
ejpam-5268	340	29	dp	dp	PROPN
ejpam-5268	340	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5268	340	31	≤	≤	NUM
ejpam-5268	340	32	2	2	NUM
ejpam-5268	340	33	sup	sup	NOUN
ejpam-5268	340	34	q	q	NOUN
ejpam-5268	340	35	∈	∈	PROPN
ejpam-5268	341	1	[	[	X
ejpam-5268	341	2	0	0	NUM
ejpam-5268	341	3	,	,	PUNCT
ejpam-5268	341	4	1	1	NUM
ejpam-5268	341	5	]	]	PUNCT
ejpam-5268	341	6	∫	∫	PROPN
ejpam-5268	341	7	1	1	NUM
ejpam-5268	341	8	0	0	NUM
ejpam-5268	341	9	|ψ	|ψ	NOUN
ejpam-5268	341	10	(	(	PUNCT
ejpam-5268	341	11	q	q	NOUN
ejpam-5268	341	12	,	,	PUNCT
ejpam-5268	341	13	p	p	X
ejpam-5268	341	14	,	,	PUNCT
ejpam-5268	341	15	δ	δ	PROPN
ejpam-5268	341	16	(	(	PUNCT
ejpam-5268	341	17	p))−	p))−	NOUN
ejpam-5268	341	18	ψ	ψ	X
ejpam-5268	341	19	(	(	PUNCT
ejpam-5268	341	20	q	q	X
ejpam-5268	341	21	,	,	PUNCT
ejpam-5268	341	22	p	p	X
ejpam-5268	341	23	,	,	PUNCT
ejpam-5268	341	24	α	α	PROPN
ejpam-5268	341	25	(	(	PUNCT
ejpam-5268	341	26	p))|	p))|	PROPN
ejpam-5268	341	27	dp	dp	VERB
ejpam-5268	341	28	≤	≤	ADJ
ejpam-5268	341	29	2	2	NUM
ejpam-5268	341	30	sup	sup	NOUN
ejpam-5268	341	31	q	q	NOUN
ejpam-5268	341	32	∈	∈	PROPN
ejpam-5268	342	1	[	[	X
ejpam-5268	342	2	0	0	NUM
ejpam-5268	342	3	,	,	PUNCT
ejpam-5268	342	4	1	1	NUM
ejpam-5268	342	5	]	]	PUNCT
ejpam-5268	342	6	∫	∫	PROPN
ejpam-5268	342	7	1	1	NUM
ejpam-5268	342	8	0	0	NUM
ejpam-5268	342	9	φ	φ	PROPN
ejpam-5268	342	10	(	(	PUNCT
ejpam-5268	342	11	q	q	NOUN
ejpam-5268	342	12	,	,	PUNCT
ejpam-5268	342	13	p	p	NOUN
ejpam-5268	342	14	)	)	PUNCT
ejpam-5268	342	15	|δ	|δ	NOUN
ejpam-5268	342	16	(	(	PUNCT
ejpam-5268	342	17	p)−	p)−	NOUN
ejpam-5268	342	18	α	α	X
ejpam-5268	342	19	(	(	PUNCT
ejpam-5268	342	20	p)|	p)|	NOUN
ejpam-5268	342	21	dp	dp	NOUN
ejpam-5268	342	22	≤	≤	NUM
ejpam-5268	342	23	2	2	NUM
ejpam-5268	342	24	sup	sup	NOUN
ejpam-5268	342	25	q	q	NOUN
ejpam-5268	342	26	∈	∈	PROPN
ejpam-5268	343	1	[	[	X
ejpam-5268	343	2	0	0	NUM
ejpam-5268	343	3	,	,	PUNCT
ejpam-5268	343	4	1	1	NUM
ejpam-5268	343	5	]	]	PUNCT
ejpam-5268	343	6	|δ	|δ	NOUN
ejpam-5268	343	7	(	(	PUNCT
ejpam-5268	343	8	q)−	q)−	ADJ
ejpam-5268	343	9	α	α	NOUN
ejpam-5268	343	10	(	(	PUNCT
ejpam-5268	343	11	q)|	q)|	INTJ
ejpam-5268	343	12	sup	sup	NOUN
ejpam-5268	343	13	q	q	PROPN
ejpam-5268	343	14	∈	∈	PROPN
ejpam-5268	344	1	[	[	X
ejpam-5268	344	2	0	0	NUM
ejpam-5268	344	3	,	,	PUNCT
ejpam-5268	344	4	1	1	NUM
ejpam-5268	344	5	]	]	PUNCT
ejpam-5268	344	6	∫	∫	PROPN
ejpam-5268	344	7	1	1	NUM
ejpam-5268	344	8	0	0	NUM
ejpam-5268	344	9	φ	φ	PROPN
ejpam-5268	344	10	(	(	PUNCT
ejpam-5268	344	11	q	q	NOUN
ejpam-5268	344	12	,	,	PUNCT
ejpam-5268	344	13	p	p	NOUN
ejpam-5268	344	14	)	)	PUNCT
ejpam-5268	344	15	dp	dp	NOUN
ejpam-5268	344	16	≤	≤	NOUN
ejpam-5268	344	17	φ(s	φ(s	NOUN
ejpam-5268	344	18	(	(	PUNCT
ejpam-5268	344	19	δ	δ	PROPN
ejpam-5268	344	20	,	,	PUNCT
ejpam-5268	344	21	α	α	PROPN
ejpam-5268	344	22	,	,	PUNCT
ejpam-5268	344	23	α	α	NOUN
ejpam-5268	344	24	)	)	PUNCT
ejpam-5268	344	25	)	)	PUNCT
ejpam-5268	344	26	consequently	consequently	ADV
ejpam-5268	344	27	,	,	PUNCT
ejpam-5268	344	28	f	f	PROPN
ejpam-5268	344	29	has	have	VERB
ejpam-5268	344	30	unique	unique	ADJ
ejpam-5268	344	31	solution	solution	NOUN
ejpam-5268	344	32	,	,	PUNCT
ejpam-5268	344	33	which	which	PRON
ejpam-5268	344	34	means	mean	VERB
ejpam-5268	344	35	that	that	SCONJ
ejpam-5268	344	36	equation	equation	NOUN
ejpam-5268	344	37	4.2	4.2	NUM
ejpam-5268	344	38	has	have	VERB
ejpam-5268	344	39	unique	unique	ADJ
ejpam-5268	344	40	solution	solution	NOUN
ejpam-5268	344	41	in	in	ADP
ejpam-5268	344	42	x.	x.	NOUN
ejpam-5268	344	43	5	5	NUM
ejpam-5268	344	44	.	.	PUNCT
ejpam-5268	344	45	conclusion	conclusion	NOUN
ejpam-5268	344	46	fixed	fix	VERB
ejpam-5268	344	47	point	point	NOUN
ejpam-5268	344	48	theory	theory	NOUN
ejpam-5268	344	49	plays	play	VERB
ejpam-5268	344	50	a	a	DET
ejpam-5268	344	51	significant	significant	ADJ
ejpam-5268	344	52	role	role	NOUN
ejpam-5268	344	53	in	in	ADP
ejpam-5268	344	54	various	various	ADJ
ejpam-5268	344	55	fields	field	NOUN
ejpam-5268	344	56	of	of	ADP
ejpam-5268	344	57	pure	pure	ADJ
ejpam-5268	344	58	and	and	CCONJ
ejpam-5268	344	59	applied	apply	VERB
ejpam-5268	344	60	mathematical	mathematical	ADJ
ejpam-5268	344	61	analysis	analysis	NOUN
ejpam-5268	344	62	and	and	CCONJ
ejpam-5268	344	63	scientific	scientific	ADJ
ejpam-5268	344	64	implementations	implementation	NOUN
ejpam-5268	344	65	,	,	PUNCT
ejpam-5268	344	66	as	as	ADV
ejpam-5268	344	67	well	well	ADV
ejpam-5268	344	68	provides	provide	VERB
ejpam-5268	344	69	a	a	DET
ejpam-5268	344	70	technique	technique	NOUN
ejpam-5268	344	71	for	for	ADP
ejpam-5268	344	72	solving	solve	VERB
ejpam-5268	344	73	a	a	DET
ejpam-5268	344	74	variety	variety	NOUN
ejpam-5268	344	75	of	of	ADP
ejpam-5268	344	76	pure	pure	ADJ
ejpam-5268	344	77	and	and	CCONJ
ejpam-5268	344	78	applied	applied	ADJ
ejpam-5268	344	79	issues	issue	NOUN
ejpam-5268	344	80	in	in	ADP
ejpam-5268	344	81	mathematics	mathematic	NOUN
ejpam-5268	344	82	,	,	PUNCT
ejpam-5268	344	83	physics	physics	NOUN
ejpam-5268	344	84	,	,	PUNCT
ejpam-5268	344	85	and	and	CCONJ
ejpam-5268	344	86	other	other	ADJ
ejpam-5268	344	87	sciences	science	NOUN
ejpam-5268	344	88	and	and	CCONJ
ejpam-5268	344	89	has	have	AUX
ejpam-5268	344	90	been	be	AUX
ejpam-5268	344	91	expanded	expand	VERB
ejpam-5268	344	92	and	and	CCONJ
ejpam-5268	344	93	enhanced	enhance	VERB
ejpam-5268	344	94	in	in	ADP
ejpam-5268	344	95	various	various	ADJ
ejpam-5268	344	96	directions	direction	NOUN
ejpam-5268	344	97	.	.	PUNCT
ejpam-5268	345	1	therefore	therefore	ADV
ejpam-5268	345	2	,	,	PUNCT
ejpam-5268	345	3	in	in	ADP
ejpam-5268	345	4	this	this	DET
ejpam-5268	345	5	article	article	NOUN
ejpam-5268	345	6	several	several	ADJ
ejpam-5268	345	7	results	result	NOUN
ejpam-5268	345	8	were	be	AUX
ejpam-5268	345	9	concluded	conclude	VERB
ejpam-5268	345	10	,	,	PUNCT
ejpam-5268	345	11	firstly	firstly	ADV
ejpam-5268	345	12	,	,	PUNCT
ejpam-5268	345	13	it	it	PRON
ejpam-5268	345	14	is	be	AUX
ejpam-5268	345	15	possible	possible	ADJ
ejpam-5268	345	16	to	to	PART
ejpam-5268	345	17	get	get	VERB
ejpam-5268	345	18	coincidence	coincidence	NOUN
ejpam-5268	345	19	and	and	CCONJ
ejpam-5268	345	20	common	common	ADJ
ejpam-5268	345	21	fixed	fix	VERB
ejpam-5268	345	22	point	point	NOUN
ejpam-5268	345	23	results	result	NOUN
ejpam-5268	345	24	if	if	SCONJ
ejpam-5268	345	25	the	the	DET
ejpam-5268	345	26	maps	map	NOUN
ejpam-5268	345	27	used	use	VERB
ejpam-5268	345	28	are	be	AUX
ejpam-5268	345	29	non	non	ADJ
ejpam-5268	345	30	-	-	ADJ
ejpam-5268	345	31	decreasing	decrease	VERB
ejpam-5268	345	32	in	in	ADP
ejpam-5268	345	33	generalized	generalized	ADJ
ejpam-5268	345	34	complete	complete	ADJ
ejpam-5268	345	35	s	s	NOUN
ejpam-5268	345	36	-	-	ADJ
ejpam-5268	345	37	metric	metric	ADJ
ejpam-5268	345	38	spaces	space	NOUN
ejpam-5268	345	39	,	,	PUNCT
ejpam-5268	345	40	as	as	ADV
ejpam-5268	345	41	well	well	ADV
ejpam-5268	345	42	as	as	ADP
ejpam-5268	345	43	if	if	SCONJ
ejpam-5268	345	44	there	there	PRON
ejpam-5268	345	45	are	be	VERB
ejpam-5268	345	46	a	a	DET
ejpam-5268	345	47	simulation	simulation	NOUN
ejpam-5268	345	48	and	and	CCONJ
ejpam-5268	345	49	right	right	ADJ
ejpam-5268	345	50	monotone	monotone	ADJ
ejpam-5268	345	51	simulation	simulation	NOUN
ejpam-5268	345	52	mappings	mapping	NOUN
ejpam-5268	345	53	(	(	PUNCT
ejpam-5268	345	54	ξ	ξ	NOUN
ejpam-5268	345	55	)	)	PUNCT
ejpam-5268	345	56	.	.	PUNCT
ejpam-5268	346	1	secondly	secondly	ADV
ejpam-5268	346	2	,	,	PUNCT
ejpam-5268	346	3	the	the	DET
ejpam-5268	346	4	relationship	relationship	NOUN
ejpam-5268	346	5	between	between	ADP
ejpam-5268	346	6	simulation	simulation	NOUN
ejpam-5268	346	7	mapping	mapping	NOUN
ejpam-5268	346	8	and	and	CCONJ
ejpam-5268	346	9	right	right	ADJ
ejpam-5268	346	10	monotone	monotone	ADJ
ejpam-5268	346	11	simulation	simulation	NOUN
ejpam-5268	346	12	mapping	mapping	NOUN
ejpam-5268	346	13	was	be	AUX
ejpam-5268	346	14	clarified	clarify	VERB
ejpam-5268	346	15	.	.	PUNCT
ejpam-5268	347	1	it	it	PRON
ejpam-5268	347	2	was	be	AUX
ejpam-5268	347	3	concluded	conclude	VERB
ejpam-5268	347	4	that	that	SCONJ
ejpam-5268	347	5	each	each	DET
ejpam-5268	347	6	right	right	ADJ
ejpam-5268	347	7	monotone	monotone	ADJ
ejpam-5268	347	8	simulation	simulation	NOUN
ejpam-5268	347	9	mapping	mapping	NOUN
ejpam-5268	347	10	is	be	AUX
ejpam-5268	347	11	simulation	simulation	NOUN
ejpam-5268	347	12	mapping	mapping	NOUN
ejpam-5268	347	13	,	,	PUNCT
ejpam-5268	347	14	but	but	CCONJ
ejpam-5268	347	15	the	the	DET
ejpam-5268	347	16	converse	converse	NOUN
ejpam-5268	347	17	need	need	AUX
ejpam-5268	347	18	not	not	PART
ejpam-5268	347	19	be	be	AUX
ejpam-5268	347	20	true	true	ADJ
ejpam-5268	347	21	in	in	ADP
ejpam-5268	347	22	general	general	ADJ
ejpam-5268	347	23	.	.	PUNCT
ejpam-5268	348	1	these	these	DET
ejpam-5268	348	2	conclusions	conclusion	NOUN
ejpam-5268	348	3	were	be	AUX
ejpam-5268	348	4	supported	support	VERB
ejpam-5268	348	5	by	by	ADP
ejpam-5268	348	6	appropriate	appropriate	ADJ
ejpam-5268	348	7	examples	example	NOUN
ejpam-5268	348	8	.	.	PUNCT
ejpam-5268	349	1	third	third	ADJ
ejpam-5268	349	2	,	,	PUNCT
ejpam-5268	349	3	various	various	ADJ
ejpam-5268	349	4	common	common	ADJ
ejpam-5268	349	5	and	and	CCONJ
ejpam-5268	349	6	coincidence	coincidence	NOUN
ejpam-5268	349	7	fixed	fix	VERB
ejpam-5268	349	8	point	point	NOUN
ejpam-5268	349	9	results	result	NOUN
ejpam-5268	349	10	in	in	ADP
ejpam-5268	349	11	symmetrical	symmetrical	ADJ
ejpam-5268	349	12	complete	complete	ADJ
ejpam-5268	349	13	s	s	NOUN
ejpam-5268	349	14	-	-	ADJ
ejpam-5268	349	15	metric	metric	ADJ
ejpam-5268	349	16	have	have	AUX
ejpam-5268	349	17	been	be	AUX
ejpam-5268	349	18	deduced	deduce	VERB
ejpam-5268	349	19	.	.	PUNCT
ejpam-5268	350	1	on	on	ADP
ejpam-5268	350	2	the	the	DET
ejpam-5268	350	3	other	other	ADJ
ejpam-5268	350	4	hand	hand	NOUN
ejpam-5268	350	5	,	,	PUNCT
ejpam-5268	350	6	through	through	ADP
ejpam-5268	350	7	the	the	DET
ejpam-5268	350	8	applications	application	NOUN
ejpam-5268	350	9	presented	present	VERB
ejpam-5268	350	10	in	in	ADP
ejpam-5268	350	11	the	the	DET
ejpam-5268	350	12	fourth	fourth	ADJ
ejpam-5268	350	13	section	section	NOUN
ejpam-5268	350	14	,	,	PUNCT
ejpam-5268	350	15	it	it	PRON
ejpam-5268	350	16	was	be	AUX
ejpam-5268	350	17	verified	verify	VERB
ejpam-5268	350	18	existence	existence	NOUN
ejpam-5268	350	19	and	and	CCONJ
ejpam-5268	350	20	uniqueness	uniqueness	NOUN
ejpam-5268	350	21	of	of	ADP
ejpam-5268	350	22	the	the	DET
ejpam-5268	350	23	solution	solution	NOUN
ejpam-5268	350	24	for	for	ADP
ejpam-5268	350	25	some	some	DET
ejpam-5268	350	26	nonlinear	nonlinear	ADJ
ejpam-5268	350	27	integral	integral	ADJ
ejpam-5268	350	28	equations	equation	NOUN
ejpam-5268	350	29	in	in	ADP
ejpam-5268	350	30	generalized	generalized	ADJ
ejpam-5268	350	31	s	s	NOUN
ejpam-5268	350	32	-	-	NOUN
ejpam-5268	350	33	metric	metric	ADJ
ejpam-5268	350	34	.	.	PUNCT
ejpam-5268	351	1	finally	finally	ADV
ejpam-5268	351	2	,	,	PUNCT
ejpam-5268	351	3	the	the	DET
ejpam-5268	351	4	obtained	obtain	VERB
ejpam-5268	351	5	results	result	NOUN
ejpam-5268	351	6	may	may	AUX
ejpam-5268	351	7	be	be	AUX
ejpam-5268	351	8	beneficial	beneficial	ADJ
ejpam-5268	351	9	for	for	ADP
ejpam-5268	351	10	further	further	ADJ
ejpam-5268	351	11	research	research	NOUN
ejpam-5268	351	12	on	on	ADP
ejpam-5268	351	13	extended	extended	ADJ
ejpam-5268	351	14	metric	metric	ADJ
ejpam-5268	351	15	spaces	space	NOUN
ejpam-5268	351	16	,	,	PUNCT
ejpam-5268	351	17	providing	provide	VERB
ejpam-5268	351	18	a	a	DET
ejpam-5268	351	19	foundation	foundation	NOUN
ejpam-5268	351	20	for	for	ADP
ejpam-5268	351	21	practical	practical	ADJ
ejpam-5268	351	22	applications	application	NOUN
ejpam-5268	351	23	in	in	ADP
ejpam-5268	351	24	engineering	engineering	NOUN
ejpam-5268	351	25	and	and	CCONJ
ejpam-5268	351	26	various	various	ADJ
ejpam-5268	351	27	kinds	kind	NOUN
ejpam-5268	351	28	of	of	ADP
ejpam-5268	351	29	general	general	ADJ
ejpam-5268	351	30	dynamical	dynamical	ADJ
ejpam-5268	351	31	systems	system	NOUN
ejpam-5268	351	32	.	.	PUNCT
ejpam-5268	352	1	acknowledgements	acknowledgement	NOUN
ejpam-5268	352	2	the	the	DET
ejpam-5268	352	3	authors	author	NOUN
ejpam-5268	352	4	express	express	VERB
ejpam-5268	352	5	their	their	PRON
ejpam-5268	352	6	gratitude	gratitude	NOUN
ejpam-5268	352	7	to	to	ADP
ejpam-5268	352	8	the	the	DET
ejpam-5268	352	9	reviewers	reviewer	NOUN
ejpam-5268	352	10	and	and	CCONJ
ejpam-5268	352	11	the	the	DET
ejpam-5268	352	12	editor	editor	NOUN
ejpam-5268	352	13	for	for	ADP
ejpam-5268	352	14	their	their	PRON
ejpam-5268	352	15	invaluable	invaluable	ADJ
ejpam-5268	352	16	comments	comment	NOUN
ejpam-5268	352	17	.	.	PUNCT
ejpam-5268	353	1	references	reference	NOUN
ejpam-5268	353	2	1892	1892	NUM
ejpam-5268	353	3	references	reference	NOUN
ejpam-5268	353	4	[	[	X
ejpam-5268	353	5	1	1	NUM
ejpam-5268	353	6	]	]	X
ejpam-5268	353	7	m	m	VERB
ejpam-5268	353	8	abbas	abbas	NOUN
ejpam-5268	353	9	and	and	CCONJ
ejpam-5268	353	10	a	a	DET
ejpam-5268	353	11	r	r	NOUN
ejpam-5268	353	12	khan	khan	PROPN
ejpam-5268	353	13	.	.	PUNCT
ejpam-5268	354	1	common	common	ADJ
ejpam-5268	354	2	fixed	fix	VERB
ejpam-5268	354	3	points	point	NOUN
ejpam-5268	354	4	of	of	ADP
ejpam-5268	354	5	generalized	generalized	ADJ
ejpam-5268	354	6	contractive	contractive	ADJ
ejpam-5268	354	7	hybrid	hybrid	ADJ
ejpam-5268	354	8	pairs	pair	NOUN
ejpam-5268	354	9	in	in	ADP
ejpam-5268	354	10	symmetric	symmetric	ADJ
ejpam-5268	354	11	spaces	space	NOUN
ejpam-5268	354	12	.	.	PUNCT
ejpam-5268	355	1	fixed	fix	VERB
ejpam-5268	355	2	point	point	NOUN
ejpam-5268	355	3	theory	theory	NOUN
ejpam-5268	355	4	and	and	CCONJ
ejpam-5268	355	5	applications	application	NOUN
ejpam-5268	355	6	,	,	PUNCT
ejpam-5268	355	7	2009:1–11	2009:1–11	NUM
ejpam-5268	355	8	,	,	PUNCT
ejpam-5268	355	9	2009	2009	NUM
ejpam-5268	355	10	.	.	PUNCT
ejpam-5268	356	1	[	[	X
ejpam-5268	356	2	2	2	NUM
ejpam-5268	356	3	]	]	X
ejpam-5268	356	4	r	r	NOUN
ejpam-5268	356	5	p	p	PROPN
ejpam-5268	356	6	agarwal	agarwal	PROPN
ejpam-5268	356	7	,	,	PUNCT
ejpam-5268	356	8	e	e	NOUN
ejpam-5268	356	9	karapınar	karapınar	NOUN
ejpam-5268	356	10	,	,	PUNCT
ejpam-5268	356	11	and	and	CCONJ
ejpam-5268	356	12	a	a	DET
ejpam-5268	356	13	f	f	NOUN
ejpam-5268	356	14	roldán	roldán	PROPN
ejpam-5268	356	15	lópez	lópez	PROPN
ejpam-5268	356	16	de	de	PROPN
ejpam-5268	356	17	hierro	hierro	PROPN
ejpam-5268	356	18	.	.	PROPN
ejpam-5268	357	1	last	last	ADJ
ejpam-5268	357	2	remarks	remark	NOUN
ejpam-5268	357	3	on	on	ADP
ejpam-5268	357	4	g	g	NOUN
ejpam-5268	357	5	-	-	PUNCT
ejpam-5268	357	6	metric	metric	ADJ
ejpam-5268	357	7	spaces	space	NOUN
ejpam-5268	357	8	and	and	CCONJ
ejpam-5268	357	9	related	relate	VERB
ejpam-5268	357	10	fixed	fix	VERB
ejpam-5268	357	11	point	point	NOUN
ejpam-5268	357	12	theorems	theorem	NOUN
ejpam-5268	357	13	.	.	PUNCT
ejpam-5268	358	1	revista	revista	PROPN
ejpam-5268	358	2	de	de	X
ejpam-5268	358	3	la	la	PROPN
ejpam-5268	358	4	real	real	PROPN
ejpam-5268	358	5	academia	academia	PROPN
ejpam-5268	358	6	de	de	PROPN
ejpam-5268	358	7	ciencias	ciencias	PROPN
ejpam-5268	358	8	exactas	exacta	NOUN
ejpam-5268	358	9	,	,	PUNCT
ejpam-5268	358	10	f́ısicas	f́ısicas	PROPN
ejpam-5268	358	11	y	y	PROPN
ejpam-5268	358	12	naturales	naturale	NOUN
ejpam-5268	358	13	.	.	PUNCT
ejpam-5268	359	1	serie	serie	PROPN
ejpam-5268	359	2	a.	a.	PROPN
ejpam-5268	359	3	matemáticas	matemáticas	PROPN
ejpam-5268	359	4	,	,	PUNCT
ejpam-5268	359	5	110:433–456	110:433–456	NUM
ejpam-5268	359	6	,	,	PUNCT
ejpam-5268	359	7	2016	2016	NUM
ejpam-5268	359	8	.	.	PUNCT
ejpam-5268	360	1	[	[	X
ejpam-5268	360	2	3	3	NUM
ejpam-5268	360	3	]	]	X
ejpam-5268	360	4	b	b	X
ejpam-5268	360	5	alqahtani	alqahtani	ADJ
ejpam-5268	360	6	,	,	PUNCT
ejpam-5268	360	7	a	a	DET
ejpam-5268	360	8	fulga	fulga	NOUN
ejpam-5268	360	9	,	,	PUNCT
ejpam-5268	360	10	and	and	CCONJ
ejpam-5268	360	11	e	e	PROPN
ejpam-5268	360	12	karapınar	karapınar	NOUN
ejpam-5268	360	13	.	.	PUNCT
ejpam-5268	361	1	fixed	fix	VERB
ejpam-5268	361	2	point	point	NOUN
ejpam-5268	361	3	results	result	NOUN
ejpam-5268	361	4	on	on	ADP
ejpam-5268	361	5	δ	δ	NOUN
ejpam-5268	361	6	-	-	PUNCT
ejpam-5268	361	7	symmetric	symmetric	ADJ
ejpam-5268	361	8	quasimetric	quasimetric	ADJ
ejpam-5268	361	9	space	space	NOUN
ejpam-5268	361	10	via	via	ADP
ejpam-5268	361	11	simulation	simulation	NOUN
ejpam-5268	361	12	function	function	NOUN
ejpam-5268	361	13	with	with	ADP
ejpam-5268	361	14	an	an	DET
ejpam-5268	361	15	application	application	NOUN
ejpam-5268	361	16	to	to	ADP
ejpam-5268	361	17	ulam	ulam	PROPN
ejpam-5268	361	18	stability	stability	NOUN
ejpam-5268	361	19	.	.	PUNCT
ejpam-5268	362	1	mathematics	mathematic	NOUN
ejpam-5268	362	2	,	,	PUNCT
ejpam-5268	362	3	6(10):208	6(10):208	NOUN
ejpam-5268	362	4	,	,	PUNCT
ejpam-5268	362	5	2018	2018	NUM
ejpam-5268	362	6	.	.	PUNCT
ejpam-5268	363	1	[	[	X
ejpam-5268	363	2	4	4	X
ejpam-5268	363	3	]	]	X
ejpam-5268	363	4	h	h	NOUN
ejpam-5268	363	5	argoubi	argoubi	ADV
ejpam-5268	363	6	,	,	PUNCT
ejpam-5268	363	7	b	b	NOUN
ejpam-5268	363	8	samet	samet	NOUN
ejpam-5268	363	9	,	,	PUNCT
ejpam-5268	363	10	and	and	CCONJ
ejpam-5268	363	11	c	c	PROPN
ejpam-5268	363	12	vetro	vetro	X
ejpam-5268	363	13	.	.	PUNCT
ejpam-5268	364	1	nonlinear	nonlinear	ADJ
ejpam-5268	364	2	contractions	contraction	NOUN
ejpam-5268	364	3	involving	involve	VERB
ejpam-5268	364	4	simulation	simulation	NOUN
ejpam-5268	364	5	functions	function	NOUN
ejpam-5268	364	6	in	in	ADP
ejpam-5268	364	7	a	a	DET
ejpam-5268	364	8	metric	metric	ADJ
ejpam-5268	364	9	space	space	NOUN
ejpam-5268	364	10	with	with	ADP
ejpam-5268	364	11	a	a	DET
ejpam-5268	364	12	partial	partial	ADJ
ejpam-5268	364	13	order	order	NOUN
ejpam-5268	364	14	.	.	PUNCT
ejpam-5268	365	1	j.	j.	PROPN
ejpam-5268	365	2	nonlinear	nonlinear	PROPN
ejpam-5268	365	3	sci	sci	PROPN
ejpam-5268	365	4	.	.	PUNCT
ejpam-5268	365	5	appl	appl	PROPN
ejpam-5268	365	6	,	,	PUNCT
ejpam-5268	365	7	8(6):1082–1094	8(6):1082–1094	PROPN
ejpam-5268	365	8	,	,	PUNCT
ejpam-5268	365	9	2015	2015	NUM
ejpam-5268	365	10	.	.	PUNCT
ejpam-5268	366	1	[	[	X
ejpam-5268	366	2	5	5	NUM
ejpam-5268	366	3	]	]	PUNCT
ejpam-5268	366	4	a	a	DET
ejpam-5268	366	5	f	f	NOUN
ejpam-5268	366	6	roldán	roldán	NOUN
ejpam-5268	366	7	-	-	PUNCT
ejpam-5268	366	8	lópez	lópez	ADV
ejpam-5268	366	9	de	de	X
ejpam-5268	366	10	hierro	hierro	PROPN
ejpam-5268	366	11	,	,	PUNCT
ejpam-5268	366	12	e	e	NOUN
ejpam-5268	366	13	karapınar	karapınar	NOUN
ejpam-5268	366	14	,	,	PUNCT
ejpam-5268	366	15	c	c	NOUN
ejpam-5268	366	16	roldán	roldán	NOUN
ejpam-5268	366	17	-	-	PUNCT
ejpam-5268	366	18	lópez	lópez	ADV
ejpam-5268	366	19	de	de	X
ejpam-5268	366	20	hierro	hierro	PROPN
ejpam-5268	366	21	,	,	PUNCT
ejpam-5268	366	22	and	and	CCONJ
ejpam-5268	366	23	j	j	PROPN
ejpam-5268	366	24	mart́ınez	mart́ınez	PROPN
ejpam-5268	366	25	-	-	PUNCT
ejpam-5268	366	26	moreno	moreno	PROPN
ejpam-5268	366	27	.	.	PUNCT
ejpam-5268	367	1	coincidence	coincidence	NOUN
ejpam-5268	367	2	point	point	NOUN
ejpam-5268	367	3	theorems	theorem	NOUN
ejpam-5268	367	4	on	on	ADP
ejpam-5268	367	5	metric	metric	ADJ
ejpam-5268	367	6	spaces	space	NOUN
ejpam-5268	367	7	via	via	ADP
ejpam-5268	367	8	simulation	simulation	NOUN
ejpam-5268	367	9	functions	function	NOUN
ejpam-5268	367	10	.	.	PUNCT
ejpam-5268	368	1	journal	journal	NOUN
ejpam-5268	368	2	of	of	ADP
ejpam-5268	368	3	computational	computational	ADJ
ejpam-5268	368	4	and	and	CCONJ
ejpam-5268	368	5	applied	applied	ADJ
ejpam-5268	368	6	mathematics	mathematic	NOUN
ejpam-5268	368	7	,	,	PUNCT
ejpam-5268	368	8	275:345–355	275:345–355	NUM
ejpam-5268	368	9	,	,	PUNCT
ejpam-5268	368	10	2015	2015	NUM
ejpam-5268	368	11	.	.	PUNCT
ejpam-5268	369	1	[	[	X
ejpam-5268	369	2	6	6	NUM
ejpam-5268	369	3	]	]	PUNCT
ejpam-5268	369	4	a	a	DET
ejpam-5268	369	5	f	f	X
ejpam-5268	369	6	roldán	roldán	NOUN
ejpam-5268	369	7	-	-	PUNCT
ejpam-5268	369	8	lópez	lópez	X
ejpam-5268	369	9	de	de	X
ejpam-5268	369	10	hierro	hierro	PROPN
ejpam-5268	369	11	and	and	CCONJ
ejpam-5268	369	12	n	n	PRON
ejpam-5268	369	13	shahzad	shahzad	PROPN
ejpam-5268	369	14	.	.	PUNCT
ejpam-5268	370	1	common	common	ADJ
ejpam-5268	370	2	fixed	fix	VERB
ejpam-5268	370	3	point	point	NOUN
ejpam-5268	370	4	theorems	theorem	NOUN
ejpam-5268	370	5	under	under	ADP
ejpam-5268	370	6	(	(	PUNCT
ejpam-5268	370	7	r	r	NOUN
ejpam-5268	370	8	,	,	PUNCT
ejpam-5268	370	9	s)-contractivity	s)-contractivity	NOUN
ejpam-5268	370	10	conditions	condition	NOUN
ejpam-5268	370	11	.	.	PUNCT
ejpam-5268	371	1	fixed	fix	VERB
ejpam-5268	371	2	point	point	NOUN
ejpam-5268	371	3	theory	theory	NOUN
ejpam-5268	371	4	and	and	CCONJ
ejpam-5268	371	5	applications	application	NOUN
ejpam-5268	371	6	,	,	PUNCT
ejpam-5268	371	7	2016(1):55	2016(1):55	NUM
ejpam-5268	371	8	,	,	PUNCT
ejpam-5268	371	9	2016	2016	NUM
ejpam-5268	371	10	.	.	PUNCT
ejpam-5268	372	1	[	[	X
ejpam-5268	372	2	7	7	X
ejpam-5268	372	3	]	]	SYM
ejpam-5268	372	4	n	n	X
ejpam-5268	372	5	fetouci	fetouci	ADJ
ejpam-5268	372	6	and	and	CCONJ
ejpam-5268	372	7	s	s	VERB
ejpam-5268	372	8	radenović.	radenović.	PROPN
ejpam-5268	372	9	on	on	ADP
ejpam-5268	372	10	some	some	DET
ejpam-5268	372	11	fixed	fix	VERB
ejpam-5268	372	12	point	point	NOUN
ejpam-5268	372	13	results	result	NOUN
ejpam-5268	372	14	for	for	ADP
ejpam-5268	372	15	expansive	expansive	ADJ
ejpam-5268	372	16	mappings	mapping	NOUN
ejpam-5268	372	17	in	in	ADP
ejpam-5268	372	18	s	s	NOUN
ejpam-5268	372	19	-	-	ADJ
ejpam-5268	372	20	metric	metric	ADJ
ejpam-5268	372	21	spaces	space	NOUN
ejpam-5268	372	22	.	.	PUNCT
ejpam-5268	373	1	military	military	ADJ
ejpam-5268	373	2	technical	technical	ADJ
ejpam-5268	373	3	courier	courier	NOUN
ejpam-5268	373	4	,	,	PUNCT
ejpam-5268	373	5	pages	page	NOUN
ejpam-5268	373	6	3–16	3–16	NOUN
ejpam-5268	373	7	,	,	PUNCT
ejpam-5268	373	8	2024	2024	NUM
ejpam-5268	373	9	.	.	PUNCT
ejpam-5268	374	1	in	in	ADP
ejpam-5268	374	2	press	press	NOUN
ejpam-5268	374	3	.	.	PUNCT
ejpam-5268	375	1	[	[	X
ejpam-5268	375	2	8	8	NUM
ejpam-5268	375	3	]	]	X
ejpam-5268	375	4	d	d	X
ejpam-5268	375	5	gopal	gopal	NOUN
ejpam-5268	375	6	,	,	PUNCT
ejpam-5268	375	7	m	m	PROPN
ejpam-5268	375	8	imdad	imdad	NOUN
ejpam-5268	375	9	,	,	PUNCT
ejpam-5268	375	10	and	and	CCONJ
ejpam-5268	375	11	c	c	X
ejpam-5268	375	12	vetro	vetro	X
ejpam-5268	375	13	.	.	PUNCT
ejpam-5268	376	1	common	common	ADJ
ejpam-5268	376	2	fixed	fix	VERB
ejpam-5268	376	3	point	point	NOUN
ejpam-5268	376	4	theorems	theorem	NOUN
ejpam-5268	376	5	for	for	ADP
ejpam-5268	376	6	mappings	mapping	NOUN
ejpam-5268	376	7	satisfying	satisfy	VERB
ejpam-5268	376	8	common	common	ADJ
ejpam-5268	376	9	property	property	NOUN
ejpam-5268	376	10	(	(	PUNCT
ejpam-5268	376	11	ea	ea	NOUN
ejpam-5268	376	12	)	)	PUNCT
ejpam-5268	376	13	in	in	ADP
ejpam-5268	376	14	symmetric	symmetric	ADJ
ejpam-5268	376	15	spaces	space	NOUN
ejpam-5268	376	16	.	.	PUNCT
ejpam-5268	377	1	filomat	filomat	NOUN
ejpam-5268	377	2	,	,	PUNCT
ejpam-5268	377	3	25(2):59–78	25(2):59–78	NUM
ejpam-5268	377	4	,	,	PUNCT
ejpam-5268	377	5	2011	2011	NUM
ejpam-5268	377	6	.	.	PUNCT
ejpam-5268	378	1	[	[	X
ejpam-5268	378	2	9	9	NUM
ejpam-5268	378	3	]	]	PUNCT
ejpam-5268	378	4	t	t	NOUN
ejpam-5268	378	5	hamaizia	hamaizia	NOUN
ejpam-5268	378	6	and	and	CCONJ
ejpam-5268	378	7	p	p	X
ejpam-5268	378	8	p	p	PROPN
ejpam-5268	378	9	murthy	murthy	ADJ
ejpam-5268	378	10	.	.	PUNCT
ejpam-5268	379	1	z	z	NOUN
ejpam-5268	379	2	-	-	PUNCT
ejpam-5268	379	3	contraction	contraction	NOUN
ejpam-5268	379	4	condition	condition	NOUN
ejpam-5268	379	5	involving	involve	VERB
ejpam-5268	379	6	simulation	simulation	NOUN
ejpam-5268	379	7	function	function	NOUN
ejpam-5268	379	8	in	in	ADP
ejpam-5268	379	9	b	b	NOUN
ejpam-5268	379	10	-	-	ADJ
ejpam-5268	379	11	metric	metric	ADJ
ejpam-5268	379	12	space	space	NOUN
ejpam-5268	379	13	under	under	ADP
ejpam-5268	379	14	fixed	fix	VERB
ejpam-5268	379	15	points	point	NOUN
ejpam-5268	379	16	considerations	consideration	NOUN
ejpam-5268	379	17	.	.	PUNCT
ejpam-5268	380	1	mathematica	mathematica	PROPN
ejpam-5268	380	2	moravica	moravica	PROPN
ejpam-5268	380	3	,	,	PUNCT
ejpam-5268	380	4	25(2):43–52	25(2):43–52	NUM
ejpam-5268	380	5	,	,	PUNCT
ejpam-5268	380	6	2021	2021	NUM
ejpam-5268	380	7	.	.	PUNCT
ejpam-5268	381	1	[	[	X
ejpam-5268	381	2	10	10	NUM
ejpam-5268	381	3	]	]	PUNCT
ejpam-5268	381	4	n	n	X
ejpam-5268	381	5	hussain	hussain	NOUN
ejpam-5268	381	6	and	and	CCONJ
ejpam-5268	381	7	m	m	PROPN
ejpam-5268	381	8	abbas	abbas	NOUN
ejpam-5268	381	9	.	.	PUNCT
ejpam-5268	382	1	common	common	ADJ
ejpam-5268	382	2	fixed	fix	VERB
ejpam-5268	382	3	point	point	NOUN
ejpam-5268	382	4	results	result	NOUN
ejpam-5268	382	5	for	for	ADP
ejpam-5268	382	6	two	two	NUM
ejpam-5268	382	7	new	new	ADJ
ejpam-5268	382	8	classes	class	NOUN
ejpam-5268	382	9	of	of	ADP
ejpam-5268	382	10	hybrid	hybrid	ADJ
ejpam-5268	382	11	pairs	pair	NOUN
ejpam-5268	382	12	in	in	ADP
ejpam-5268	382	13	symmetric	symmetric	ADJ
ejpam-5268	382	14	spaces	space	NOUN
ejpam-5268	382	15	.	.	PUNCT
ejpam-5268	383	1	applied	apply	VERB
ejpam-5268	383	2	mathematics	mathematic	NOUN
ejpam-5268	383	3	and	and	CCONJ
ejpam-5268	383	4	computation	computation	NOUN
ejpam-5268	383	5	,	,	PUNCT
ejpam-5268	383	6	218(2):542–547	218(2):542–547	NUM
ejpam-5268	383	7	,	,	PUNCT
ejpam-5268	383	8	2011	2011	NUM
ejpam-5268	383	9	.	.	PUNCT
ejpam-5268	384	1	[	[	X
ejpam-5268	384	2	11	11	NUM
ejpam-5268	384	3	]	]	X
ejpam-5268	384	4	n	n	X
ejpam-5268	384	5	hussain	hussain	NOUN
ejpam-5268	384	6	,	,	PUNCT
ejpam-5268	384	7	m	m	VERB
ejpam-5268	384	8	a	a	DET
ejpam-5268	384	9	khamsi	khamsi	NOUN
ejpam-5268	384	10	,	,	PUNCT
ejpam-5268	384	11	and	and	CCONJ
ejpam-5268	384	12	a	a	DET
ejpam-5268	384	13	latif	latif	PROPN
ejpam-5268	384	14	.	.	PUNCT
ejpam-5268	385	1	common	common	ADJ
ejpam-5268	385	2	fixed	fix	VERB
ejpam-5268	385	3	points	point	NOUN
ejpam-5268	385	4	for	for	ADP
ejpam-5268	385	5	jh	jh	PROPN
ejpam-5268	385	6	-	-	PUNCT
ejpam-5268	385	7	operators	operator	NOUN
ejpam-5268	385	8	and	and	CCONJ
ejpam-5268	385	9	occasionally	occasionally	ADV
ejpam-5268	385	10	weakly	weakly	ADJ
ejpam-5268	385	11	biased	biased	ADJ
ejpam-5268	385	12	pairs	pair	NOUN
ejpam-5268	385	13	under	under	ADP
ejpam-5268	385	14	relaxed	relaxed	ADJ
ejpam-5268	385	15	conditions	condition	NOUN
ejpam-5268	385	16	.	.	PUNCT
ejpam-5268	386	1	nonlinear	nonlinear	ADJ
ejpam-5268	386	2	analysis	analysis	NOUN
ejpam-5268	386	3	:	:	PUNCT
ejpam-5268	386	4	theory	theory	NOUN
ejpam-5268	386	5	,	,	PUNCT
ejpam-5268	386	6	methods	method	NOUN
ejpam-5268	386	7	&	&	CCONJ
ejpam-5268	386	8	applications	application	NOUN
ejpam-5268	386	9	,	,	PUNCT
ejpam-5268	386	10	74(6):2133–2140	74(6):2133–2140	NUM
ejpam-5268	386	11	,	,	PUNCT
ejpam-5268	386	12	2011	2011	NUM
ejpam-5268	386	13	.	.	PUNCT
ejpam-5268	387	1	[	[	X
ejpam-5268	387	2	12	12	NUM
ejpam-5268	387	3	]	]	X
ejpam-5268	387	4	m	m	VERB
ejpam-5268	387	5	imdad	imdad	NOUN
ejpam-5268	387	6	and	and	CCONJ
ejpam-5268	387	7	w	w	PROPN
ejpam-5268	387	8	m	m	VERB
ejpam-5268	387	9	alfaqih	alfaqih	NOUN
ejpam-5268	387	10	.	.	PUNCT
ejpam-5268	388	1	a	a	DET
ejpam-5268	388	2	relation	relation	NOUN
ejpam-5268	388	3	-	-	PUNCT
ejpam-5268	388	4	theoretic	theoretic	ADJ
ejpam-5268	388	5	expansion	expansion	NOUN
ejpam-5268	388	6	principle	principle	NOUN
ejpam-5268	388	7	.	.	PUNCT
ejpam-5268	389	1	acta	acta	PROPN
ejpam-5268	389	2	univ	univ	PROPN
ejpam-5268	389	3	.	.	PUNCT
ejpam-5268	390	1	apulensis	apulensis	NOUN
ejpam-5268	390	2	,	,	PUNCT
ejpam-5268	390	3	54:55–69	54:55–69	NUM
ejpam-5268	390	4	,	,	PUNCT
ejpam-5268	390	5	2018	2018	NUM
ejpam-5268	390	6	.	.	PUNCT
ejpam-5268	391	1	[	[	X
ejpam-5268	391	2	13	13	NUM
ejpam-5268	391	3	]	]	SYM
ejpam-5268	391	4	m	m	VERB
ejpam-5268	391	5	imdad	imdad	PROPN
ejpam-5268	391	6	,	,	PUNCT
ejpam-5268	391	7	w	w	PROPN
ejpam-5268	391	8	m	m	VERB
ejpam-5268	391	9	alfaqih	alfaqih	NOUN
ejpam-5268	391	10	,	,	PUNCT
ejpam-5268	391	11	and	and	CCONJ
ejpam-5268	391	12	i	i	PRON
ejpam-5268	391	13	a	a	DET
ejpam-5268	391	14	khan	khan	PROPN
ejpam-5268	391	15	.	.	PUNCT
ejpam-5268	392	1	weak	weak	ADJ
ejpam-5268	392	2	θ	θ	NOUN
ejpam-5268	392	3	-	-	PUNCT
ejpam-5268	392	4	contractions	contraction	NOUN
ejpam-5268	392	5	and	and	CCONJ
ejpam-5268	392	6	some	some	DET
ejpam-5268	392	7	fixed	fix	VERB
ejpam-5268	392	8	point	point	NOUN
ejpam-5268	392	9	results	result	NOUN
ejpam-5268	392	10	with	with	ADP
ejpam-5268	392	11	applications	application	NOUN
ejpam-5268	392	12	to	to	ADP
ejpam-5268	392	13	fractal	fractal	ADJ
ejpam-5268	392	14	theory	theory	NOUN
ejpam-5268	392	15	.	.	PUNCT
ejpam-5268	393	1	advances	advance	NOUN
ejpam-5268	393	2	in	in	ADP
ejpam-5268	393	3	difference	difference	NOUN
ejpam-5268	393	4	equations	equation	NOUN
ejpam-5268	393	5	,	,	PUNCT
ejpam-5268	393	6	2018:1	2018:1	NUM
ejpam-5268	393	7	–	–	PUNCT
ejpam-5268	393	8	18	18	NUM
ejpam-5268	393	9	,	,	PUNCT
ejpam-5268	393	10	2018	2018	NUM
ejpam-5268	393	11	.	.	PUNCT
ejpam-5268	394	1	references	reference	NOUN
ejpam-5268	394	2	1893	1893	NUM
ejpam-5268	395	1	[	[	X
ejpam-5268	395	2	14	14	NUM
ejpam-5268	395	3	]	]	X
ejpam-5268	395	4	m	m	VERB
ejpam-5268	395	5	imdad	imdad	NOUN
ejpam-5268	395	6	and	and	CCONJ
ejpam-5268	395	7	a	a	DET
ejpam-5268	395	8	h	h	NOUN
ejpam-5268	395	9	soliman	soliman	NOUN
ejpam-5268	395	10	.	.	PUNCT
ejpam-5268	396	1	some	some	DET
ejpam-5268	396	2	common	common	ADJ
ejpam-5268	396	3	fixed	fix	VERB
ejpam-5268	396	4	point	point	NOUN
ejpam-5268	396	5	theorems	theorem	NOUN
ejpam-5268	396	6	for	for	ADP
ejpam-5268	396	7	a	a	DET
ejpam-5268	396	8	pair	pair	NOUN
ejpam-5268	396	9	of	of	ADP
ejpam-5268	396	10	tangential	tangential	ADJ
ejpam-5268	396	11	mappings	mapping	NOUN
ejpam-5268	396	12	in	in	ADP
ejpam-5268	396	13	symmetric	symmetric	ADJ
ejpam-5268	396	14	spaces	space	NOUN
ejpam-5268	396	15	.	.	PUNCT
ejpam-5268	397	1	applied	apply	VERB
ejpam-5268	397	2	mathematics	mathematics	NOUN
ejpam-5268	397	3	letters	letter	NOUN
ejpam-5268	397	4	,	,	PUNCT
ejpam-5268	397	5	23(4):351–355	23(4):351–355	NUM
ejpam-5268	397	6	,	,	PUNCT
ejpam-5268	397	7	2010	2010	NUM
ejpam-5268	397	8	.	.	PUNCT
ejpam-5268	398	1	[	[	X
ejpam-5268	398	2	15	15	NUM
ejpam-5268	398	3	]	]	X
ejpam-5268	398	4	a	a	DET
ejpam-5268	398	5	m	m	NOUN
ejpam-5268	398	6	al	al	PROPN
ejpam-5268	398	7	jumaili	jumaili	PROPN
ejpam-5268	398	8	.	.	PUNCT
ejpam-5268	399	1	some	some	DET
ejpam-5268	399	2	coincidence	coincidence	NOUN
ejpam-5268	399	3	and	and	CCONJ
ejpam-5268	399	4	fixed	fix	VERB
ejpam-5268	399	5	point	point	NOUN
ejpam-5268	399	6	results	result	NOUN
ejpam-5268	399	7	in	in	ADP
ejpam-5268	399	8	partially	partially	ADV
ejpam-5268	399	9	ordered	order	VERB
ejpam-5268	399	10	complete	complete	ADJ
ejpam-5268	399	11	generalized	generalize	VERB
ejpam-5268	399	12	d∗-metric	d∗-metric	ADJ
ejpam-5268	399	13	spaces	space	NOUN
ejpam-5268	399	14	.	.	PUNCT
ejpam-5268	400	1	european	european	ADJ
ejpam-5268	400	2	journal	journal	PROPN
ejpam-5268	400	3	of	of	ADP
ejpam-5268	400	4	pure	pure	ADJ
ejpam-5268	400	5	and	and	CCONJ
ejpam-5268	400	6	applied	applied	ADJ
ejpam-5268	400	7	mathematics	mathematic	NOUN
ejpam-5268	400	8	,	,	PUNCT
ejpam-5268	400	9	10(5):1023–1034	10(5):1023–1034	NUM
ejpam-5268	400	10	,	,	PUNCT
ejpam-5268	400	11	2017	2017	NUM
ejpam-5268	400	12	.	.	PUNCT
ejpam-5268	401	1	[	[	X
ejpam-5268	401	2	16	16	NUM
ejpam-5268	401	3	]	]	X
ejpam-5268	401	4	e	e	X
ejpam-5268	401	5	karapinar	karapinar	PROPN
ejpam-5268	401	6	,	,	PUNCT
ejpam-5268	401	7	d	d	PROPN
ejpam-5268	401	8	k	k	PROPN
ejpam-5268	401	9	patel	patel	PROPN
ejpam-5268	401	10	,	,	PUNCT
ejpam-5268	401	11	m	m	VERB
ejpam-5268	401	12	imdad	imdad	NOUN
ejpam-5268	401	13	,	,	PUNCT
ejpam-5268	401	14	and	and	CCONJ
ejpam-5268	401	15	d	d	ADP
ejpam-5268	401	16	gopal	gopal	NOUN
ejpam-5268	401	17	.	.	PUNCT
ejpam-5268	402	1	some	some	DET
ejpam-5268	402	2	nonunique	nonunique	ADJ
ejpam-5268	402	3	common	common	ADJ
ejpam-5268	402	4	fixed	fix	VERB
ejpam-5268	402	5	point	point	NOUN
ejpam-5268	402	6	theorems	theorem	NOUN
ejpam-5268	402	7	in	in	ADP
ejpam-5268	402	8	symmetric	symmetric	ADJ
ejpam-5268	402	9	spaces	space	NOUN
ejpam-5268	402	10	through	through	ADP
ejpam-5268	402	11	clr	clr	PROPN
ejpam-5268	402	12	(	(	PUNCT
ejpam-5268	402	13	s	s	PROPN
ejpam-5268	402	14	,	,	PUNCT
ejpam-5268	402	15	t	t	NOUN
ejpam-5268	402	16	)	)	PUNCT
ejpam-5268	402	17	property	property	NOUN
ejpam-5268	402	18	.	.	PUNCT
ejpam-5268	403	1	international	international	ADJ
ejpam-5268	403	2	journal	journal	PROPN
ejpam-5268	403	3	of	of	ADP
ejpam-5268	403	4	mathematics	mathematics	PROPN
ejpam-5268	403	5	and	and	CCONJ
ejpam-5268	403	6	mathematical	mathematical	ADJ
ejpam-5268	403	7	sciences	science	NOUN
ejpam-5268	403	8	,	,	PUNCT
ejpam-5268	403	9	2013	2013	NUM
ejpam-5268	403	10	,	,	PUNCT
ejpam-5268	403	11	2013	2013	NUM
ejpam-5268	403	12	.	.	PUNCT
ejpam-5268	404	1	[	[	X
ejpam-5268	404	2	17	17	NUM
ejpam-5268	404	3	]	]	X
ejpam-5268	404	4	e	e	X
ejpam-5268	404	5	karapιnar	karapιnar	PROPN
ejpam-5268	404	6	,	,	PUNCT
ejpam-5268	404	7	a	a	DET
ejpam-5268	404	8	f	f	NOUN
ejpam-5268	404	9	roldán	roldán	NOUN
ejpam-5268	404	10	-	-	PUNCT
ejpam-5268	404	11	lópez	lópez	ADV
ejpam-5268	404	12	de	de	X
ejpam-5268	404	13	hierro	hierro	PROPN
ejpam-5268	404	14	,	,	PUNCT
ejpam-5268	404	15	and	and	CCONJ
ejpam-5268	404	16	b	b	X
ejpam-5268	404	17	samet	samet	NOUN
ejpam-5268	404	18	.	.	PUNCT
ejpam-5268	405	1	matkowski	matkowski	PROPN
ejpam-5268	405	2	theorems	theorem	NOUN
ejpam-5268	405	3	in	in	ADP
ejpam-5268	405	4	the	the	DET
ejpam-5268	405	5	context	context	NOUN
ejpam-5268	405	6	of	of	ADP
ejpam-5268	405	7	quasi	quasi	ADJ
ejpam-5268	405	8	-	-	ADJ
ejpam-5268	405	9	metric	metric	ADJ
ejpam-5268	405	10	spaces	space	NOUN
ejpam-5268	405	11	and	and	CCONJ
ejpam-5268	405	12	consequences	consequence	NOUN
ejpam-5268	405	13	on	on	ADP
ejpam-5268	405	14	g	g	NOUN
ejpam-5268	405	15	-	-	PUNCT
ejpam-5268	405	16	metric	metric	ADJ
ejpam-5268	405	17	spaces	space	NOUN
ejpam-5268	405	18	.	.	PUNCT
ejpam-5268	406	1	analele	analele	ADP
ejpam-5268	406	2	ştiinţifice	ştiinţifice	PROPN
ejpam-5268	406	3	ale	ale	NOUN
ejpam-5268	406	4	universităţii	universităţii	PROPN
ejpam-5268	406	5	”	"	PUNCT
ejpam-5268	406	6	ovidius	ovidius	ADJ
ejpam-5268	406	7	”	"	PUNCT
ejpam-5268	406	8	constanţa	constanţa	NOUN
ejpam-5268	406	9	.	.	PUNCT
ejpam-5268	407	1	seria	seria	PROPN
ejpam-5268	407	2	matematică	matematică	PROPN
ejpam-5268	407	3	,	,	PUNCT
ejpam-5268	407	4	24(1):309–333	24(1):309–333	AUX
ejpam-5268	407	5	,	,	PUNCT
ejpam-5268	407	6	2016	2016	NUM
ejpam-5268	407	7	.	.	PUNCT
ejpam-5268	408	1	[	[	X
ejpam-5268	408	2	18	18	NUM
ejpam-5268	408	3	]	]	X
ejpam-5268	408	4	f	f	PROPN
ejpam-5268	408	5	khojasteh	khojasteh	PROPN
ejpam-5268	408	6	,	,	PUNCT
ejpam-5268	408	7	s	s	NOUN
ejpam-5268	408	8	shukla	shukla	NOUN
ejpam-5268	408	9	,	,	PUNCT
ejpam-5268	408	10	and	and	CCONJ
ejpam-5268	408	11	s	s	VERB
ejpam-5268	409	1	radenović.	radenović.	PRON
ejpam-5268	409	2	a	a	DET
ejpam-5268	409	3	new	new	ADJ
ejpam-5268	409	4	approach	approach	NOUN
ejpam-5268	409	5	to	to	ADP
ejpam-5268	409	6	the	the	DET
ejpam-5268	409	7	study	study	NOUN
ejpam-5268	409	8	of	of	ADP
ejpam-5268	409	9	fixed	fix	VERB
ejpam-5268	409	10	point	point	NOUN
ejpam-5268	409	11	theory	theory	NOUN
ejpam-5268	409	12	for	for	ADP
ejpam-5268	409	13	simulation	simulation	NOUN
ejpam-5268	409	14	functions	function	NOUN
ejpam-5268	409	15	.	.	PUNCT
ejpam-5268	410	1	filomat	filomat	NOUN
ejpam-5268	410	2	,	,	PUNCT
ejpam-5268	410	3	29(6):1189–1194	29(6):1189–1194	PROPN
ejpam-5268	410	4	,	,	PUNCT
ejpam-5268	410	5	2015	2015	NUM
ejpam-5268	410	6	.	.	PUNCT
ejpam-5268	411	1	[	[	X
ejpam-5268	411	2	19	19	NUM
ejpam-5268	411	3	]	]	X
ejpam-5268	411	4	m	m	PROPN
ejpam-5268	411	5	kumar	kumar	PROPN
ejpam-5268	411	6	,	,	PUNCT
ejpam-5268	411	7	s	s	PROPN
ejpam-5268	411	8	arora	arora	PROPN
ejpam-5268	411	9	,	,	PUNCT
ejpam-5268	411	10	m	m	VERB
ejpam-5268	411	11	imdad	imdad	NOUN
ejpam-5268	411	12	,	,	PUNCT
ejpam-5268	411	13	and	and	CCONJ
ejpam-5268	411	14	w	w	NOUN
ejpam-5268	411	15	m	m	VERB
ejpam-5268	411	16	alfaqih	alfaqih	NOUN
ejpam-5268	411	17	.	.	PUNCT
ejpam-5268	412	1	coincidence	coincidence	NOUN
ejpam-5268	412	2	and	and	CCONJ
ejpam-5268	412	3	common	common	ADJ
ejpam-5268	412	4	fixed	fix	VERB
ejpam-5268	412	5	point	point	NOUN
ejpam-5268	412	6	results	result	NOUN
ejpam-5268	412	7	via	via	ADP
ejpam-5268	412	8	simulation	simulation	NOUN
ejpam-5268	412	9	functions	function	NOUN
ejpam-5268	412	10	in	in	ADP
ejpam-5268	412	11	g	g	NOUN
ejpam-5268	412	12	-	-	PUNCT
ejpam-5268	412	13	metric	metric	ADJ
ejpam-5268	412	14	spaces	space	NOUN
ejpam-5268	412	15	.	.	PUNCT
ejpam-5268	413	1	journal	journal	NOUN
ejpam-5268	413	2	of	of	ADP
ejpam-5268	413	3	mathematics	mathematic	NOUN
ejpam-5268	413	4	and	and	CCONJ
ejpam-5268	413	5	computer	computer	NOUN
ejpam-5268	413	6	science	science	NOUN
ejpam-5268	413	7	,	,	PUNCT
ejpam-5268	413	8	19(4):288–300	19(4):288–300	PROPN
ejpam-5268	413	9	,	,	PUNCT
ejpam-5268	413	10	2019	2019	NUM
ejpam-5268	413	11	.	.	PUNCT
ejpam-5268	414	1	[	[	X
ejpam-5268	414	2	20	20	NUM
ejpam-5268	414	3	]	]	X
ejpam-5268	414	4	y	y	PROPN
ejpam-5268	414	5	liu	liu	PROPN
ejpam-5268	414	6	,	,	PUNCT
ejpam-5268	414	7	j	j	PROPN
ejpam-5268	414	8	wu	wu	PROPN
ejpam-5268	414	9	,	,	PUNCT
ejpam-5268	414	10	and	and	CCONJ
ejpam-5268	414	11	z	z	PROPN
ejpam-5268	414	12	li	li	PROPN
ejpam-5268	414	13	.	.	PROPN
ejpam-5268	414	14	common	common	ADJ
ejpam-5268	414	15	fixed	fix	VERB
ejpam-5268	414	16	points	point	NOUN
ejpam-5268	414	17	of	of	ADP
ejpam-5268	414	18	single	single	ADV
ejpam-5268	414	19	-	-	PUNCT
ejpam-5268	414	20	valued	value	VERB
ejpam-5268	414	21	and	and	CCONJ
ejpam-5268	414	22	multivalued	multivalued	ADJ
ejpam-5268	414	23	maps	map	NOUN
ejpam-5268	414	24	.	.	PUNCT
ejpam-5268	415	1	international	international	ADJ
ejpam-5268	415	2	journal	journal	PROPN
ejpam-5268	415	3	of	of	ADP
ejpam-5268	415	4	mathematics	mathematics	PROPN
ejpam-5268	415	5	and	and	CCONJ
ejpam-5268	415	6	mathematical	mathematical	ADJ
ejpam-5268	415	7	sciences	science	NOUN
ejpam-5268	415	8	,	,	PUNCT
ejpam-5268	415	9	2005(19):3045	2005(19):3045	NUM
ejpam-5268	415	10	–	–	PUNCT
ejpam-5268	415	11	3055	3055	NUM
ejpam-5268	415	12	,	,	PUNCT
ejpam-5268	415	13	2005	2005	NUM
ejpam-5268	415	14	.	.	PUNCT
ejpam-5268	416	1	[	[	X
ejpam-5268	416	2	21	21	NUM
ejpam-5268	416	3	]	]	X
ejpam-5268	416	4	s	s	PART
ejpam-5268	416	5	sedghi	sedghi	X
ejpam-5268	416	6	,	,	PUNCT
ejpam-5268	416	7	n	n	PRON
ejpam-5268	416	8	shobe	shobe	NOUN
ejpam-5268	416	9	,	,	PUNCT
ejpam-5268	416	10	and	and	CCONJ
ejpam-5268	416	11	a	a	DET
ejpam-5268	416	12	aliouche	aliouche	NOUN
ejpam-5268	416	13	.	.	PUNCT
ejpam-5268	417	1	a	a	DET
ejpam-5268	417	2	generalization	generalization	NOUN
ejpam-5268	417	3	of	of	ADP
ejpam-5268	417	4	fixed	fix	VERB
ejpam-5268	417	5	point	point	NOUN
ejpam-5268	417	6	theorems	theorem	NOUN
ejpam-5268	417	7	in	in	ADP
ejpam-5268	417	8	s	s	NOUN
ejpam-5268	417	9	-	-	ADJ
ejpam-5268	417	10	metric	metric	ADJ
ejpam-5268	417	11	spaces	space	NOUN
ejpam-5268	417	12	.	.	PUNCT
ejpam-5268	418	1	matematički	matematički	PROPN
ejpam-5268	418	2	vesnik	vesnik	PROPN
ejpam-5268	418	3	,	,	PUNCT
ejpam-5268	418	4	64(249):258–266	64(249):258–266	PROPN
ejpam-5268	418	5	,	,	PUNCT
ejpam-5268	418	6	2012	2012	NUM
ejpam-5268	418	7	.	.	PUNCT
ejpam-5268	419	1	[	[	X
ejpam-5268	419	2	22	22	NUM
ejpam-5268	419	3	]	]	X
ejpam-5268	419	4	s	s	VERB
ejpam-5268	419	5	shaban	shaban	PROPN
ejpam-5268	419	6	,	,	PUNCT
ejpam-5268	419	7	s	s	NOUN
ejpam-5268	419	8	nabi	nabi	NOUN
ejpam-5268	419	9	,	,	PUNCT
ejpam-5268	419	10	and	and	CCONJ
ejpam-5268	419	11	z	z	NOUN
ejpam-5268	419	12	haiyun	haiyun	NOUN
ejpam-5268	419	13	.	.	PUNCT
ejpam-5268	420	1	a	a	DET
ejpam-5268	420	2	common	common	ADJ
ejpam-5268	420	3	fixed	fix	VERB
ejpam-5268	420	4	point	point	NOUN
ejpam-5268	420	5	theorem	theorem	VERB
ejpam-5268	420	6	in	in	ADP
ejpam-5268	420	7	d*-metric	d*-metric	ADJ
ejpam-5268	420	8	spaces	space	NOUN
ejpam-5268	420	9	.	.	PUNCT
ejpam-5268	421	1	hindawi	hindawi	ADJ
ejpam-5268	421	2	publishing	publishing	NOUN
ejpam-5268	421	3	corporation	corporation	NOUN
ejpam-5268	421	4	.	.	PUNCT
ejpam-5268	422	1	fixed	fix	VERB
ejpam-5268	422	2	point	point	NOUN
ejpam-5268	422	3	theory	theory	NOUN
ejpam-5268	422	4	and	and	CCONJ
ejpam-5268	422	5	applications	application	NOUN
ejpam-5268	422	6	,	,	PUNCT
ejpam-5268	422	7	2007:13	2007:13	NUM
ejpam-5268	422	8	,	,	PUNCT
ejpam-5268	422	9	2007	2007	NUM
ejpam-5268	422	10	.	.	PUNCT
ejpam-5268	423	1	[	[	X
ejpam-5268	423	2	23	23	NUM
ejpam-5268	423	3	]	]	PUNCT
ejpam-5268	423	4	n	n	CCONJ
ejpam-5268	423	5	shahzad	shahzad	PROPN
ejpam-5268	423	6	,	,	PUNCT
ejpam-5268	423	7	a	a	DET
ejpam-5268	423	8	f	f	X
ejpam-5268	423	9	roldán	roldán	NOUN
ejpam-5268	423	10	-	-	PUNCT
ejpam-5268	423	11	lópez	lópez	ADV
ejpam-5268	423	12	de	de	X
ejpam-5268	423	13	hierro	hierro	PROPN
ejpam-5268	423	14	,	,	PUNCT
ejpam-5268	423	15	and	and	CCONJ
ejpam-5268	423	16	f	f	PROPN
ejpam-5268	423	17	khojasteh	khojasteh	NOUN
ejpam-5268	423	18	.	.	PUNCT
ejpam-5268	424	1	some	some	DET
ejpam-5268	424	2	new	new	ADJ
ejpam-5268	424	3	fixed	fix	VERB
ejpam-5268	424	4	point	point	NOUN
ejpam-5268	424	5	theorems	theorem	NOUN
ejpam-5268	424	6	under	under	ADP
ejpam-5268	424	7	(	(	PUNCT
ejpam-5268	424	8	a	a	PRON
ejpam-5268	424	9	,	,	PUNCT
ejpam-5268	424	10	s)(a	s)(a	NUM
ejpam-5268	424	11	,	,	PUNCT
ejpam-5268	424	12	s)-contractivity	s)-contractivity	NOUN
ejpam-5268	424	13	conditions	condition	NOUN
ejpam-5268	424	14	.	.	PUNCT
ejpam-5268	425	1	revista	revista	PROPN
ejpam-5268	425	2	de	de	X
ejpam-5268	425	3	la	la	PROPN
ejpam-5268	425	4	real	real	PROPN
ejpam-5268	425	5	academia	academia	PROPN
ejpam-5268	425	6	de	de	PROPN
ejpam-5268	425	7	ciencias	ciencias	PROPN
ejpam-5268	425	8	exactas	exacta	NOUN
ejpam-5268	425	9	,	,	PUNCT
ejpam-5268	425	10	fisicas	fisicas	PROPN
ejpam-5268	425	11	y	y	PROPN
ejpam-5268	425	12	naturales	naturales	PROPN
ejpam-5268	425	13	.	.	PUNCT
ejpam-5268	426	1	serie	serie	PROPN
ejpam-5268	426	2	a.	a.	PROPN
ejpam-5268	426	3	matematicas	matematicas	PROPN
ejpam-5268	426	4	,	,	PUNCT
ejpam-5268	426	5	111:307–324	111:307–324	NUM
ejpam-5268	426	6	,	,	PUNCT
ejpam-5268	426	7	2017	2017	NUM
ejpam-5268	426	8	.	.	PUNCT
ejpam-5268	427	1	[	[	X
ejpam-5268	427	2	24	24	NUM
ejpam-5268	427	3	]	]	PUNCT
ejpam-5268	427	4	a	a	DET
ejpam-5268	427	5	h	h	NOUN
ejpam-5268	427	6	soliman	soliman	NOUN
ejpam-5268	427	7	,	,	PUNCT
ejpam-5268	427	8	m	m	PROPN
ejpam-5268	427	9	imdad	imdad	NOUN
ejpam-5268	427	10	,	,	PUNCT
ejpam-5268	427	11	and	and	CCONJ
ejpam-5268	427	12	m	m	PROPN
ejpam-5268	427	13	hasan	hasan	PROPN
ejpam-5268	427	14	.	.	PUNCT
ejpam-5268	428	1	proving	prove	VERB
ejpam-5268	428	2	unified	unified	ADJ
ejpam-5268	428	3	common	common	ADJ
ejpam-5268	428	4	fixed	fix	VERB
ejpam-5268	428	5	point	point	NOUN
ejpam-5268	428	6	theorems	theorem	NOUN
ejpam-5268	428	7	via	via	ADP
ejpam-5268	428	8	common	common	ADJ
ejpam-5268	428	9	property	property	NOUN
ejpam-5268	428	10	(	(	PUNCT
ejpam-5268	428	11	ea	ea	NOUN
ejpam-5268	428	12	)	)	PUNCT
ejpam-5268	428	13	in	in	ADP
ejpam-5268	428	14	symmetric	symmetric	ADJ
ejpam-5268	428	15	spaces	space	NOUN
ejpam-5268	428	16	.	.	PUNCT
ejpam-5268	429	1	communications	communication	NOUN
ejpam-5268	429	2	of	of	ADP
ejpam-5268	429	3	the	the	DET
ejpam-5268	429	4	korean	korean	ADJ
ejpam-5268	429	5	mathematical	mathematical	ADJ
ejpam-5268	429	6	society	society	NOUN
ejpam-5268	429	7	,	,	PUNCT
ejpam-5268	429	8	25(4):629–645	25(4):629–645	PROPN
ejpam-5268	429	9	,	,	PUNCT
ejpam-5268	429	10	2010	2010	NUM
ejpam-5268	429	11	.	.	PUNCT