id	sid	tid	token	lemma	pos
ejpam-6810	1	1	european	european	PROPN
ejpam-6810	1	2	journal	journal	PROPN
ejpam-6810	1	3	of	of	ADP
ejpam-6810	1	4	pure	pure	ADJ
ejpam-6810	1	5	and	and	CCONJ
ejpam-6810	1	6	applied	applied	ADJ
ejpam-6810	1	7	mathematics	mathematic	NOUN
ejpam-6810	1	8	2025	2025	NUM
ejpam-6810	1	9	,	,	PUNCT
ejpam-6810	1	10	vol	vol	NOUN
ejpam-6810	1	11	.	.	PROPN
ejpam-6810	1	12	18	18	NUM
ejpam-6810	1	13	,	,	PUNCT
ejpam-6810	1	14	issue	issue	NOUN
ejpam-6810	1	15	4	4	NUM
ejpam-6810	1	16	,	,	PUNCT
ejpam-6810	1	17	article	article	NOUN
ejpam-6810	1	18	number	number	NOUN
ejpam-6810	1	19	6810	6810	NUM
ejpam-6810	1	20	issn	issn	VERB
ejpam-6810	1	21	1307	1307	NUM
ejpam-6810	1	22	-	-	SYM
ejpam-6810	1	23	5543	5543	NUM
ejpam-6810	1	24	–	–	PUNCT
ejpam-6810	1	25	ejpam.com	ejpam.com	X
ejpam-6810	1	26	published	publish	VERB
ejpam-6810	1	27	by	by	ADP
ejpam-6810	1	28	new	new	PROPN
ejpam-6810	1	29	york	york	PROPN
ejpam-6810	1	30	business	business	PROPN
ejpam-6810	1	31	global	global	ADJ
ejpam-6810	1	32	fixed	fix	VERB
ejpam-6810	1	33	point	point	NOUN
ejpam-6810	1	34	theorems	theorem	NOUN
ejpam-6810	1	35	for	for	ADP
ejpam-6810	1	36	mappings	mapping	NOUN
ejpam-6810	1	37	contracting	contract	VERB
ejpam-6810	1	38	perimeter	perimeter	NOUN
ejpam-6810	1	39	of	of	ADP
ejpam-6810	1	40	triangles	triangle	NOUN
ejpam-6810	1	41	embedded	embed	VERB
ejpam-6810	1	42	with	with	ADP
ejpam-6810	1	43	f	f	NOUN
ejpam-6810	1	44	-	-	PUNCT
ejpam-6810	1	45	contractions	contraction	NOUN
ejpam-6810	1	46	in	in	ADP
ejpam-6810	1	47	b	b	NOUN
ejpam-6810	1	48	-	-	ADJ
ejpam-6810	1	49	metric	metric	ADJ
ejpam-6810	1	50	spaces	space	NOUN
ejpam-6810	1	51	samina	samina	PROPN
ejpam-6810	1	52	batul1	batul1	PROPN
ejpam-6810	1	53	,	,	PUNCT
ejpam-6810	1	54	haitham	haitham	PROPN
ejpam-6810	1	55	qawaqneh2	qawaqneh2	PROPN
ejpam-6810	1	56	,	,	PUNCT
ejpam-6810	1	57	hira	hira	PROPN
ejpam-6810	1	58	ulfat1	ulfat1	PROPN
ejpam-6810	1	59	,	,	PUNCT
ejpam-6810	1	60	dur	dur	PROPN
ejpam-6810	1	61	-	-	PUNCT
ejpam-6810	1	62	e	e	ADJ
ejpam-6810	1	63	-	-	ADJ
ejpam-6810	1	64	shehwar	shehwar	ADJ
ejpam-6810	1	65	sagheer1	sagheer1	NOUN
ejpam-6810	1	66	,	,	PUNCT
ejpam-6810	1	67	hassen	hassen	NOUN
ejpam-6810	1	68	aydi3,4,∗	aydi3,4,∗	ADJ
ejpam-6810	1	69	1	1	NUM
ejpam-6810	1	70	department	department	NOUN
ejpam-6810	1	71	of	of	ADP
ejpam-6810	1	72	mathematics	mathematic	NOUN
ejpam-6810	1	73	,	,	PUNCT
ejpam-6810	1	74	capital	capital	NOUN
ejpam-6810	1	75	university	university	PROPN
ejpam-6810	1	76	of	of	ADP
ejpam-6810	1	77	science	science	NOUN
ejpam-6810	1	78	and	and	CCONJ
ejpam-6810	1	79	technology	technology	NOUN
ejpam-6810	1	80	,	,	PUNCT
ejpam-6810	1	81	islamabad	islamabad	PROPN
ejpam-6810	1	82	,	,	PUNCT
ejpam-6810	1	83	pakistan	pakistan	PROPN
ejpam-6810	1	84	2	2	NUM
ejpam-6810	1	85	al	al	PROPN
ejpam-6810	1	86	-	-	PUNCT
ejpam-6810	1	87	zaytoonah	zaytoonah	PROPN
ejpam-6810	1	88	university	university	PROPN
ejpam-6810	1	89	of	of	ADP
ejpam-6810	1	90	jordan	jordan	PROPN
ejpam-6810	1	91	,	,	PUNCT
ejpam-6810	1	92	amman	amman	PROPN
ejpam-6810	1	93	11733	11733	NUM
ejpam-6810	1	94	,	,	PUNCT
ejpam-6810	1	95	jordan	jordan	PROPN
ejpam-6810	1	96	3	3	NUM
ejpam-6810	1	97	université	université	PROPN
ejpam-6810	1	98	de	de	X
ejpam-6810	1	99	sousse	sousse	PROPN
ejpam-6810	1	100	,	,	PUNCT
ejpam-6810	1	101	institut	institut	PROPN
ejpam-6810	1	102	supérieur	supérieur	PROPN
ejpam-6810	1	103	d’informatique	d’informatique	PROPN
ejpam-6810	1	104	et	et	PROPN
ejpam-6810	1	105	des	des	X
ejpam-6810	1	106	techniques	techniques	X
ejpam-6810	1	107	de	de	X
ejpam-6810	1	108	communication	communication	NOUN
ejpam-6810	1	109	,	,	PUNCT
ejpam-6810	1	110	h.	h.	PROPN
ejpam-6810	1	111	sousse	sousse	PROPN
ejpam-6810	1	112	4000	4000	NUM
ejpam-6810	1	113	,	,	PUNCT
ejpam-6810	1	114	tunisia	tunisia	PROPN
ejpam-6810	1	115	4	4	NUM
ejpam-6810	1	116	department	department	NOUN
ejpam-6810	1	117	of	of	ADP
ejpam-6810	1	118	mathematics	mathematic	NOUN
ejpam-6810	1	119	,	,	PUNCT
ejpam-6810	1	120	sefako	sefako	VERB
ejpam-6810	1	121	makgatho	makgatho	PROPN
ejpam-6810	1	122	health	health	PROPN
ejpam-6810	1	123	sciences	sciences	PROPN
ejpam-6810	1	124	university	university	PROPN
ejpam-6810	1	125	,	,	PUNCT
ejpam-6810	1	126	ga	ga	PROPN
ejpam-6810	1	127	-	-	NOUN
ejpam-6810	1	128	rankuwa	rankuwa	PROPN
ejpam-6810	1	129	,	,	PUNCT
ejpam-6810	1	130	south	south	PROPN
ejpam-6810	1	131	africa	africa	PROPN
ejpam-6810	1	132	abstract	abstract	PROPN
ejpam-6810	1	133	.	.	PUNCT
ejpam-6810	2	1	in	in	ADP
ejpam-6810	2	2	this	this	DET
ejpam-6810	2	3	article	article	NOUN
ejpam-6810	2	4	,	,	PUNCT
ejpam-6810	2	5	the	the	DET
ejpam-6810	2	6	concept	concept	NOUN
ejpam-6810	2	7	of	of	ADP
ejpam-6810	2	8	a	a	DET
ejpam-6810	2	9	mapping	mapping	NOUN
ejpam-6810	2	10	contracting	contract	VERB
ejpam-6810	2	11	perimeter	perimeter	NOUN
ejpam-6810	2	12	of	of	ADP
ejpam-6810	2	13	triangles	triangle	NOUN
ejpam-6810	2	14	embedded	embed	VERB
ejpam-6810	2	15	with	with	ADP
ejpam-6810	2	16	f	f	NOUN
ejpam-6810	2	17	-	-	PUNCT
ejpam-6810	2	18	contractions	contraction	NOUN
ejpam-6810	2	19	in	in	ADP
ejpam-6810	2	20	the	the	DET
ejpam-6810	2	21	framework	framework	NOUN
ejpam-6810	2	22	of	of	ADP
ejpam-6810	2	23	b	b	NOUN
ejpam-6810	2	24	-	-	PUNCT
ejpam-6810	2	25	metric	metric	ADJ
ejpam-6810	2	26	spaces	space	NOUN
ejpam-6810	2	27	is	be	AUX
ejpam-6810	2	28	introduced	introduce	VERB
ejpam-6810	2	29	.	.	PUNCT
ejpam-6810	3	1	some	some	DET
ejpam-6810	3	2	related	related	ADJ
ejpam-6810	3	3	fixed	fix	VERB
ejpam-6810	3	4	point	point	NOUN
ejpam-6810	3	5	results	result	NOUN
ejpam-6810	3	6	are	be	AUX
ejpam-6810	3	7	established	establish	VERB
ejpam-6810	3	8	.	.	PUNCT
ejpam-6810	4	1	banach	banach	NOUN
ejpam-6810	4	2	contraction	contraction	NOUN
ejpam-6810	4	3	principle	principle	NOUN
ejpam-6810	4	4	is	be	AUX
ejpam-6810	4	5	derived	derive	VERB
ejpam-6810	4	6	as	as	ADP
ejpam-6810	4	7	a	a	DET
ejpam-6810	4	8	corollary	corollary	NOUN
ejpam-6810	4	9	of	of	ADP
ejpam-6810	4	10	main	main	ADJ
ejpam-6810	4	11	result	result	NOUN
ejpam-6810	4	12	.	.	PUNCT
ejpam-6810	5	1	additionally	additionally	ADV
ejpam-6810	5	2	,	,	PUNCT
ejpam-6810	5	3	we	we	PRON
ejpam-6810	5	4	construct	construct	VERB
ejpam-6810	5	5	examples	example	NOUN
ejpam-6810	5	6	of	of	ADP
ejpam-6810	5	7	mappings	mapping	NOUN
ejpam-6810	5	8	contracting	contract	VERB
ejpam-6810	5	9	perimeters	perimeter	NOUN
ejpam-6810	5	10	of	of	ADP
ejpam-6810	5	11	triangles	triangle	NOUN
ejpam-6810	5	12	embedded	embed	VERB
ejpam-6810	5	13	with	with	ADP
ejpam-6810	5	14	f	f	PROPN
ejpam-6810	5	15	-	-	PUNCT
ejpam-6810	5	16	contractions	contraction	NOUN
ejpam-6810	5	17	which	which	PRON
ejpam-6810	5	18	are	be	AUX
ejpam-6810	5	19	not	not	PART
ejpam-6810	5	20	contraction	contraction	NOUN
ejpam-6810	5	21	mappings	mapping	NOUN
ejpam-6810	5	22	in	in	ADP
ejpam-6810	5	23	the	the	DET
ejpam-6810	5	24	framework	framework	NOUN
ejpam-6810	5	25	of	of	ADP
ejpam-6810	5	26	b	b	NOUN
ejpam-6810	5	27	-	-	PUNCT
ejpam-6810	5	28	metric	metric	ADJ
ejpam-6810	5	29	spaces	space	NOUN
ejpam-6810	5	30	.	.	PUNCT
ejpam-6810	6	1	the	the	DET
ejpam-6810	6	2	results	result	NOUN
ejpam-6810	6	3	of	of	ADP
ejpam-6810	6	4	this	this	DET
ejpam-6810	6	5	article	article	NOUN
ejpam-6810	6	6	are	be	AUX
ejpam-6810	6	7	the	the	DET
ejpam-6810	6	8	extensions	extension	NOUN
ejpam-6810	6	9	of	of	ADP
ejpam-6810	6	10	some	some	DET
ejpam-6810	6	11	already	already	ADV
ejpam-6810	6	12	established	establish	VERB
ejpam-6810	6	13	results	result	NOUN
ejpam-6810	6	14	in	in	ADP
ejpam-6810	6	15	literature	literature	NOUN
ejpam-6810	6	16	.	.	PUNCT
ejpam-6810	7	1	2020	2020	NUM
ejpam-6810	7	2	mathematics	mathematics	PROPN
ejpam-6810	7	3	subject	subject	NOUN
ejpam-6810	7	4	classifications	classification	NOUN
ejpam-6810	7	5	:	:	PUNCT
ejpam-6810	7	6	47h10	47h10	NUM
ejpam-6810	7	7	,	,	PUNCT
ejpam-6810	7	8	54h25	54h25	NUM
ejpam-6810	7	9	key	key	ADJ
ejpam-6810	7	10	words	word	NOUN
ejpam-6810	7	11	and	and	CCONJ
ejpam-6810	7	12	phrases	phrase	NOUN
ejpam-6810	7	13	:	:	PUNCT
ejpam-6810	7	14	fixed	fixed	ADJ
ejpam-6810	7	15	point	point	NOUN
ejpam-6810	7	16	(	(	PUNCT
ejpam-6810	7	17	fp	fp	X
ejpam-6810	7	18	)	)	PUNCT
ejpam-6810	7	19	,	,	PUNCT
ejpam-6810	7	20	banach	banach	NOUN
ejpam-6810	7	21	contraction	contraction	NOUN
ejpam-6810	7	22	principle	principle	NOUN
ejpam-6810	7	23	(	(	PUNCT
ejpam-6810	7	24	bcp	bcp	PROPN
ejpam-6810	7	25	)	)	PUNCT
ejpam-6810	7	26	,	,	PUNCT
ejpam-6810	7	27	metric	metric	ADJ
ejpam-6810	7	28	space	space	NOUN
ejpam-6810	7	29	(	(	PUNCT
ejpam-6810	7	30	ms	ms	NOUN
ejpam-6810	7	31	)	)	PUNCT
ejpam-6810	7	32	,	,	PUNCT
ejpam-6810	7	33	b	b	X
ejpam-6810	7	34	-	-	PUNCT
ejpam-6810	7	35	metric	metric	ADJ
ejpam-6810	7	36	space	space	NOUN
ejpam-6810	7	37	(	(	PUNCT
ejpam-6810	7	38	b	b	X
ejpam-6810	7	39	-	-	PUNCT
ejpam-6810	7	40	ms	ms	NOUN
ejpam-6810	7	41	)	)	PUNCT
ejpam-6810	7	42	,	,	PUNCT
ejpam-6810	7	43	mapping	map	VERB
ejpam-6810	7	44	contracting	contracting	NOUN
ejpam-6810	7	45	perimeters	perimeter	NOUN
ejpam-6810	7	46	of	of	ADP
ejpam-6810	7	47	triangle	triangle	NOUN
ejpam-6810	7	48	(	(	PUNCT
ejpam-6810	7	49	mcpt	mcpt	NOUN
ejpam-6810	7	50	)	)	PUNCT
ejpam-6810	7	51	1	1	NUM
ejpam-6810	7	52	.	.	PUNCT
ejpam-6810	8	1	introduction	introduction	NOUN
ejpam-6810	8	2	and	and	CCONJ
ejpam-6810	8	3	preliminaries	preliminary	NOUN
ejpam-6810	8	4	fixed	fix	VERB
ejpam-6810	8	5	point	point	NOUN
ejpam-6810	8	6	(	(	PUNCT
ejpam-6810	8	7	fp	fp	X
ejpam-6810	8	8	)	)	PUNCT
ejpam-6810	8	9	theory	theory	NOUN
ejpam-6810	8	10	is	be	AUX
ejpam-6810	8	11	a	a	DET
ejpam-6810	8	12	significant	significant	ADJ
ejpam-6810	8	13	and	and	CCONJ
ejpam-6810	8	14	highly	highly	ADV
ejpam-6810	8	15	active	active	ADJ
ejpam-6810	8	16	area	area	NOUN
ejpam-6810	8	17	within	within	ADP
ejpam-6810	8	18	functional	functional	ADJ
ejpam-6810	8	19	analysis	analysis	NOUN
ejpam-6810	8	20	.	.	PUNCT
ejpam-6810	9	1	it	it	PRON
ejpam-6810	9	2	offers	offer	VERB
ejpam-6810	9	3	crucial	crucial	ADJ
ejpam-6810	9	4	methods	method	NOUN
ejpam-6810	9	5	for	for	ADP
ejpam-6810	9	6	addressing	address	VERB
ejpam-6810	9	7	problems	problem	NOUN
ejpam-6810	9	8	encountered	encounter	VERB
ejpam-6810	9	9	across	across	ADP
ejpam-6810	9	10	multiple	multiple	ADJ
ejpam-6810	9	11	fields	field	NOUN
ejpam-6810	9	12	of	of	ADP
ejpam-6810	9	13	mathematical	mathematical	ADJ
ejpam-6810	9	14	analysis	analysis	NOUN
ejpam-6810	9	15	.	.	PUNCT
ejpam-6810	10	1	this	this	DET
ejpam-6810	10	2	theory	theory	NOUN
ejpam-6810	10	3	plays	play	VERB
ejpam-6810	10	4	a	a	DET
ejpam-6810	10	5	key	key	ADJ
ejpam-6810	10	6	role	role	NOUN
ejpam-6810	10	7	in	in	ADP
ejpam-6810	10	8	ensuring	ensure	VERB
ejpam-6810	10	9	both	both	CCONJ
ejpam-6810	10	10	the	the	DET
ejpam-6810	10	11	existence	existence	NOUN
ejpam-6810	10	12	and	and	CCONJ
ejpam-6810	10	13	uniqueness	uniqueness	NOUN
ejpam-6810	10	14	of	of	ADP
ejpam-6810	10	15	solutions	solution	NOUN
ejpam-6810	10	16	to	to	ADP
ejpam-6810	10	17	integral	integral	ADJ
ejpam-6810	10	18	and	and	CCONJ
ejpam-6810	10	19	differential	differential	ADJ
ejpam-6810	10	20	equations	equation	NOUN
ejpam-6810	10	21	.	.	PUNCT
ejpam-6810	11	1	for	for	ADP
ejpam-6810	11	2	more	more	ADJ
ejpam-6810	11	3	details	detail	NOUN
ejpam-6810	11	4	,	,	PUNCT
ejpam-6810	11	5	see	see	VERB
ejpam-6810	11	6	[	[	X
ejpam-6810	11	7	1–9	1–9	NOUN
ejpam-6810	11	8	]	]	X
ejpam-6810	11	9	.	.	PUNCT
ejpam-6810	12	1	in	in	ADP
ejpam-6810	12	2	1922	1922	NUM
ejpam-6810	12	3	,	,	PUNCT
ejpam-6810	12	4	the	the	DET
ejpam-6810	12	5	polish	polish	ADJ
ejpam-6810	12	6	mathematician	mathematician	NOUN
ejpam-6810	12	7	banach	banach	NOUN
ejpam-6810	12	8	[	[	X
ejpam-6810	12	9	10	10	NUM
ejpam-6810	12	10	]	]	PUNCT
ejpam-6810	12	11	introduced	introduce	VERB
ejpam-6810	12	12	the	the	DET
ejpam-6810	12	13	contraction	contraction	NOUN
ejpam-6810	12	14	principle	principle	NOUN
ejpam-6810	12	15	,	,	PUNCT
ejpam-6810	12	16	which	which	PRON
ejpam-6810	12	17	has	have	AUX
ejpam-6810	12	18	become	become	VERB
ejpam-6810	12	19	one	one	NUM
ejpam-6810	12	20	of	of	ADP
ejpam-6810	12	21	the	the	DET
ejpam-6810	12	22	most	most	ADV
ejpam-6810	12	23	renowned	renowned	ADJ
ejpam-6810	12	24	and	and	CCONJ
ejpam-6810	12	25	influential	influential	ADJ
ejpam-6810	12	26	results	result	NOUN
ejpam-6810	12	27	in	in	ADP
ejpam-6810	12	28	mathematics	mathematic	NOUN
ejpam-6810	12	29	.	.	PUNCT
ejpam-6810	13	1	in	in	ADP
ejpam-6810	13	2	∗corresponding	∗corresponde	VERB
ejpam-6810	13	3	author	author	NOUN
ejpam-6810	13	4	.	.	PUNCT
ejpam-6810	14	1	doi	doi	NOUN
ejpam-6810	14	2	:	:	PUNCT
ejpam-6810	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6810	https://doi.org/10.29020/nybg.ejpam.v18i4.6810	ADP
ejpam-6810	14	4	email	email	NOUN
ejpam-6810	14	5	addresses	address	NOUN
ejpam-6810	14	6	:	:	PUNCT
ejpam-6810	14	7	samina.batul@cust.edu.pk	samina.batul@cust.edu.pk	PROPN
ejpam-6810	14	8	(	(	PUNCT
ejpam-6810	14	9	s.	s.	PROPN
ejpam-6810	14	10	batul	batul	PROPN
ejpam-6810	14	11	)	)	PUNCT
ejpam-6810	14	12	,	,	PUNCT
ejpam-6810	14	13	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6810	14	14	(	(	PUNCT
ejpam-6810	14	15	h.	h.	PROPN
ejpam-6810	14	16	qawaqneh	qawaqneh	PROPN
ejpam-6810	14	17	)	)	PUNCT
ejpam-6810	14	18	,	,	PUNCT
ejpam-6810	14	19	hiraulfat786@gmail.com	hiraulfat786@gmail.com	X
ejpam-6810	14	20	(	(	PUNCT
ejpam-6810	14	21	h.	h.	NOUN
ejpam-6810	14	22	ulfat	ulfat	PROPN
ejpam-6810	14	23	)	)	PUNCT
ejpam-6810	14	24	,	,	PUNCT
ejpam-6810	14	25	d.e.shehwar@cust.edu.pk	d.e.shehwar@cust.edu.pk	PROPN
ejpam-6810	14	26	(	(	PUNCT
ejpam-6810	14	27	d.	d.	PROPN
ejpam-6810	14	28	e.	e.	PROPN
ejpam-6810	14	29	shehwar	shehwar	PROPN
ejpam-6810	14	30	sagheer	sagheer	PROPN
ejpam-6810	14	31	)	)	PUNCT
ejpam-6810	14	32	,	,	PUNCT
ejpam-6810	15	1	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	INTJ
ejpam-6810	15	2	(	(	PUNCT
ejpam-6810	15	3	h.	h.	PROPN
ejpam-6810	15	4	aydi	aydi	ADJ
ejpam-6810	15	5	)	)	PUNCT
ejpam-6810	15	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6810	15	7	1	1	NUM
ejpam-6810	15	8	copyright	copyright	NOUN
ejpam-6810	15	9	:	:	PUNCT
ejpam-6810	15	10	©	©	PROPN
ejpam-6810	15	11	2025	2025	NUM
ejpam-6810	15	12	the	the	DET
ejpam-6810	15	13	author(s	author(s	NOUN
ejpam-6810	15	14	)	)	PUNCT
ejpam-6810	15	15	.	.	PUNCT
ejpam-6810	16	1	(	(	PUNCT
ejpam-6810	16	2	cc	cc	NOUN
ejpam-6810	16	3	by	by	ADP
ejpam-6810	16	4	-	-	PUNCT
ejpam-6810	16	5	nc	nc	PROPN
ejpam-6810	16	6	4.0	4.0	NUM
ejpam-6810	16	7	)	)	PUNCT
ejpam-6810	16	8	s.	s.	PROPN
ejpam-6810	16	9	batul	batul	PROPN
ejpam-6810	16	10	et	et	PROPN
ejpam-6810	16	11	al	al	PROPN
ejpam-6810	16	12	.	.	PUNCT
ejpam-6810	16	13	/	/	SYM
ejpam-6810	16	14	eur	eur	PROPN
ejpam-6810	16	15	.	.	PUNCT
ejpam-6810	17	1	j.	j.	PROPN
ejpam-6810	17	2	pure	pure	PROPN
ejpam-6810	17	3	appl	appl	PROPN
ejpam-6810	17	4	.	.	PROPN
ejpam-6810	17	5	math	math	PROPN
ejpam-6810	17	6	,	,	PUNCT
ejpam-6810	17	7	18	18	NUM
ejpam-6810	17	8	(	(	PUNCT
ejpam-6810	17	9	4	4	NUM
ejpam-6810	17	10	)	)	PUNCT
ejpam-6810	17	11	(	(	PUNCT
ejpam-6810	17	12	2025	2025	NUM
ejpam-6810	17	13	)	)	PUNCT
ejpam-6810	17	14	,	,	PUNCT
ejpam-6810	17	15	6810	6810	NUM
ejpam-6810	17	16	2	2	NUM
ejpam-6810	17	17	of	of	ADP
ejpam-6810	17	18	23	23	NUM
ejpam-6810	17	19	the	the	DET
ejpam-6810	17	20	existing	exist	VERB
ejpam-6810	17	21	literature	literature	NOUN
ejpam-6810	17	22	,	,	PUNCT
ejpam-6810	17	23	the	the	DET
ejpam-6810	17	24	banach	banach	NOUN
ejpam-6810	17	25	contraction	contraction	NOUN
ejpam-6810	17	26	principle	principle	NOUN
ejpam-6810	17	27	(	(	PUNCT
ejpam-6810	17	28	bcp	bcp	NOUN
ejpam-6810	17	29	)	)	PUNCT
ejpam-6810	17	30	has	have	AUX
ejpam-6810	17	31	been	be	AUX
ejpam-6810	17	32	generalized	generalize	VERB
ejpam-6810	17	33	in	in	ADP
ejpam-6810	17	34	two	two	NUM
ejpam-6810	17	35	main	main	ADJ
ejpam-6810	17	36	ways	way	NOUN
ejpam-6810	17	37	:	:	PUNCT
ejpam-6810	17	38	either	either	CCONJ
ejpam-6810	17	39	by	by	ADP
ejpam-6810	17	40	modifying	modify	VERB
ejpam-6810	17	41	the	the	DET
ejpam-6810	17	42	contraction	contraction	NOUN
ejpam-6810	17	43	condition	condition	NOUN
ejpam-6810	17	44	,	,	PUNCT
ejpam-6810	17	45	or	or	CCONJ
ejpam-6810	17	46	by	by	ADP
ejpam-6810	17	47	altering	alter	VERB
ejpam-6810	17	48	the	the	DET
ejpam-6810	17	49	structure	structure	NOUN
ejpam-6810	17	50	of	of	ADP
ejpam-6810	17	51	the	the	DET
ejpam-6810	17	52	metric	metric	ADJ
ejpam-6810	17	53	space	space	NOUN
ejpam-6810	17	54	(	(	PUNCT
ejpam-6810	17	55	ms	ms	NOUN
ejpam-6810	17	56	)	)	PUNCT
ejpam-6810	17	57	.	.	PUNCT
ejpam-6810	18	1	within	within	ADP
ejpam-6810	18	2	fp	fp	PROPN
ejpam-6810	18	3	theory	theory	NOUN
ejpam-6810	18	4	,	,	PUNCT
ejpam-6810	18	5	numerous	numerous	ADJ
ejpam-6810	18	6	types	type	NOUN
ejpam-6810	18	7	of	of	ADP
ejpam-6810	18	8	contractions	contraction	NOUN
ejpam-6810	18	9	have	have	AUX
ejpam-6810	18	10	been	be	AUX
ejpam-6810	18	11	formulated	formulate	VERB
ejpam-6810	18	12	in	in	ADP
ejpam-6810	18	13	a	a	DET
ejpam-6810	18	14	ms	ms	NOUN
ejpam-6810	18	15	,	,	PUNCT
ejpam-6810	18	16	including	include	VERB
ejpam-6810	18	17	boyd	boyd	PROPN
ejpam-6810	18	18	and	and	CCONJ
ejpam-6810	18	19	wong	wong	PROPN
ejpam-6810	18	20	nonlinear	nonlinear	PROPN
ejpam-6810	18	21	contraction	contraction	PROPN
ejpam-6810	18	22	[	[	X
ejpam-6810	18	23	11	11	NUM
ejpam-6810	18	24	]	]	PUNCT
ejpam-6810	18	25	,	,	PUNCT
ejpam-6810	18	26	the	the	DET
ejpam-6810	18	27	meir	meir	PROPN
ejpam-6810	18	28	-	-	PUNCT
ejpam-6810	18	29	keeler	keeler	PROPN
ejpam-6810	18	30	contraction	contraction	NOUN
ejpam-6810	18	31	[	[	X
ejpam-6810	18	32	12	12	NUM
ejpam-6810	18	33	,	,	PUNCT
ejpam-6810	18	34	13	13	NUM
ejpam-6810	18	35	]	]	PUNCT
ejpam-6810	18	36	,	,	PUNCT
ejpam-6810	18	37	suzuki	suzuki	PROPN
ejpam-6810	18	38	contraction	contraction	NOUN
ejpam-6810	19	1	[	[	X
ejpam-6810	19	2	14	14	NUM
ejpam-6810	19	3	]	]	PUNCT
ejpam-6810	19	4	,	,	PUNCT
ejpam-6810	19	5	kannan	kannan	PROPN
ejpam-6810	19	6	contraction	contraction	PROPN
ejpam-6810	20	1	[	[	X
ejpam-6810	20	2	15	15	NUM
ejpam-6810	20	3	]	]	PUNCT
ejpam-6810	20	4	,	,	PUNCT
ejpam-6810	20	5	ćirić	ćirić	NOUN
ejpam-6810	20	6	generalized	generalize	VERB
ejpam-6810	20	7	contraction	contraction	NOUN
ejpam-6810	21	1	[	[	X
ejpam-6810	21	2	16	16	NUM
ejpam-6810	21	3	]	]	PUNCT
ejpam-6810	21	4	and	and	CCONJ
ejpam-6810	21	5	quasi	quasi	ADJ
ejpam-6810	21	6	contraction	contraction	NOUN
ejpam-6810	21	7	[	[	X
ejpam-6810	21	8	17	17	NUM
ejpam-6810	21	9	]	]	PUNCT
ejpam-6810	21	10	,	,	PUNCT
ejpam-6810	21	11	weak	weak	ADJ
ejpam-6810	21	12	contraction	contraction	NOUN
ejpam-6810	21	13	[	[	X
ejpam-6810	21	14	18	18	NUM
ejpam-6810	21	15	]	]	PUNCT
ejpam-6810	21	16	,	,	PUNCT
ejpam-6810	21	17	chatterjea	chatterjea	PROPN
ejpam-6810	21	18	contraction	contraction	NOUN
ejpam-6810	21	19	[	[	X
ejpam-6810	21	20	19	19	NUM
ejpam-6810	21	21	]	]	PUNCT
ejpam-6810	21	22	,	,	PUNCT
ejpam-6810	21	23	zamfirescu	zamfirescu	PROPN
ejpam-6810	21	24	contraction	contraction	PROPN
ejpam-6810	22	1	[	[	X
ejpam-6810	22	2	20	20	NUM
ejpam-6810	22	3	]	]	PUNCT
ejpam-6810	22	4	,	,	PUNCT
ejpam-6810	22	5	the	the	DET
ejpam-6810	22	6	f	f	PROPN
ejpam-6810	22	7	-	-	PUNCT
ejpam-6810	22	8	suzuki	suzuki	PROPN
ejpam-6810	22	9	contraction	contraction	NOUN
ejpam-6810	23	1	[	[	X
ejpam-6810	23	2	21	21	NUM
ejpam-6810	23	3	]	]	PUNCT
ejpam-6810	23	4	,	,	PUNCT
ejpam-6810	23	5	and	and	CCONJ
ejpam-6810	23	6	among	among	ADP
ejpam-6810	23	7	others	other	NOUN
ejpam-6810	24	1	[	[	X
ejpam-6810	24	2	22	22	NUM
ejpam-6810	24	3	,	,	PUNCT
ejpam-6810	24	4	23	23	NUM
ejpam-6810	24	5	]	]	PUNCT
ejpam-6810	24	6	.	.	PUNCT
ejpam-6810	25	1	a	a	DET
ejpam-6810	25	2	ms	ms	PROPN
ejpam-6810	25	3	is	be	AUX
ejpam-6810	25	4	a	a	DET
ejpam-6810	25	5	vast	vast	ADJ
ejpam-6810	25	6	concept	concept	NOUN
ejpam-6810	25	7	,	,	PUNCT
ejpam-6810	25	8	and	and	CCONJ
ejpam-6810	25	9	even	even	ADV
ejpam-6810	25	10	small	small	ADJ
ejpam-6810	25	11	modifications	modification	NOUN
ejpam-6810	25	12	to	to	ADP
ejpam-6810	25	13	its	its	PRON
ejpam-6810	25	14	axioms	axiom	NOUN
ejpam-6810	25	15	can	can	AUX
ejpam-6810	25	16	lead	lead	VERB
ejpam-6810	25	17	to	to	ADP
ejpam-6810	25	18	the	the	DET
ejpam-6810	25	19	creation	creation	NOUN
ejpam-6810	25	20	of	of	ADP
ejpam-6810	25	21	different	different	ADJ
ejpam-6810	25	22	structures	structure	NOUN
ejpam-6810	25	23	,	,	PUNCT
ejpam-6810	25	24	such	such	ADJ
ejpam-6810	25	25	as	as	ADP
ejpam-6810	25	26	a	a	DET
ejpam-6810	25	27	2	2	NUM
ejpam-6810	25	28	-	-	PUNCT
ejpam-6810	25	29	ms	ms	NOUN
ejpam-6810	25	30	[	[	X
ejpam-6810	25	31	24	24	NUM
ejpam-6810	25	32	]	]	PUNCT
ejpam-6810	25	33	,	,	PUNCT
ejpam-6810	26	1	a	a	DET
ejpam-6810	26	2	cone	cone	NOUN
ejpam-6810	26	3	ms	ms	NOUN
ejpam-6810	27	1	[	[	X
ejpam-6810	27	2	25	25	NUM
ejpam-6810	27	3	]	]	PUNCT
ejpam-6810	27	4	,	,	PUNCT
ejpam-6810	27	5	and	and	CCONJ
ejpam-6810	27	6	many	many	ADJ
ejpam-6810	27	7	others	other	NOUN
ejpam-6810	27	8	.	.	PUNCT
ejpam-6810	28	1	the	the	DET
ejpam-6810	28	2	notion	notion	NOUN
ejpam-6810	28	3	of	of	ADP
ejpam-6810	28	4	a	a	DET
ejpam-6810	28	5	b	b	NOUN
ejpam-6810	28	6	-	-	PUNCT
ejpam-6810	28	7	metric	metric	ADJ
ejpam-6810	28	8	space	space	NOUN
ejpam-6810	28	9	(	(	PUNCT
ejpam-6810	28	10	b	b	X
ejpam-6810	28	11	-	-	PUNCT
ejpam-6810	28	12	ms	ms	NOUN
ejpam-6810	28	13	)	)	PUNCT
ejpam-6810	28	14	was	be	AUX
ejpam-6810	28	15	pioneered	pioneer	VERB
ejpam-6810	28	16	by	by	ADP
ejpam-6810	28	17	bakhtin	bakhtin	NOUN
ejpam-6810	28	18	[	[	X
ejpam-6810	28	19	26	26	NUM
ejpam-6810	28	20	]	]	PUNCT
ejpam-6810	28	21	in	in	ADP
ejpam-6810	28	22	1989	1989	NUM
ejpam-6810	28	23	,	,	PUNCT
ejpam-6810	28	24	and	and	CCONJ
ejpam-6810	28	25	later	later	ADV
ejpam-6810	28	26	refined	refine	VERB
ejpam-6810	28	27	by	by	ADP
ejpam-6810	28	28	czerwik	czerwik	PROPN
ejpam-6810	28	29	[	[	X
ejpam-6810	28	30	27	27	NUM
ejpam-6810	28	31	]	]	PUNCT
ejpam-6810	28	32	in	in	ADP
ejpam-6810	28	33	1993	1993	NUM
ejpam-6810	28	34	.	.	PUNCT
ejpam-6810	29	1	this	this	DET
ejpam-6810	29	2	innovation	innovation	NOUN
ejpam-6810	29	3	introduced	introduce	VERB
ejpam-6810	29	4	a	a	DET
ejpam-6810	29	5	new	new	ADJ
ejpam-6810	29	6	coefficient	coefficient	NOUN
ejpam-6810	29	7	in	in	ADP
ejpam-6810	29	8	the	the	DET
ejpam-6810	29	9	triangular	triangular	NOUN
ejpam-6810	29	10	inequality	inequality	NOUN
ejpam-6810	29	11	of	of	ADP
ejpam-6810	29	12	a	a	DET
ejpam-6810	29	13	ms	ms	NOUN
ejpam-6810	29	14	,	,	PUNCT
ejpam-6810	29	15	laying	lay	VERB
ejpam-6810	29	16	the	the	DET
ejpam-6810	29	17	groundwork	groundwork	NOUN
ejpam-6810	29	18	for	for	ADP
ejpam-6810	29	19	the	the	DET
ejpam-6810	29	20	development	development	NOUN
ejpam-6810	29	21	of	of	ADP
ejpam-6810	29	22	b	b	PROPN
ejpam-6810	29	23	-	-	PUNCT
ejpam-6810	29	24	mss	mss	NOUN
ejpam-6810	29	25	.	.	PUNCT
ejpam-6810	30	1	researchers	researcher	NOUN
ejpam-6810	30	2	have	have	AUX
ejpam-6810	30	3	developed	develop	VERB
ejpam-6810	30	4	a	a	DET
ejpam-6810	30	5	wide	wide	ADJ
ejpam-6810	30	6	range	range	NOUN
ejpam-6810	30	7	of	of	ADP
ejpam-6810	30	8	fp	fp	PROPN
ejpam-6810	30	9	results	result	NOUN
ejpam-6810	30	10	utilizing	utilize	VERB
ejpam-6810	30	11	the	the	DET
ejpam-6810	30	12	framework	framework	NOUN
ejpam-6810	30	13	of	of	ADP
ejpam-6810	30	14	b	b	PROPN
ejpam-6810	30	15	-	-	PUNCT
ejpam-6810	30	16	ms	ms	PROPN
ejpam-6810	30	17	.	.	PROPN
ejpam-6810	30	18	karapinar	karapinar	PROPN
ejpam-6810	31	1	[	[	X
ejpam-6810	31	2	28	28	NUM
ejpam-6810	31	3	]	]	PUNCT
ejpam-6810	31	4	discusses	discuss	VERB
ejpam-6810	31	5	foundational	foundational	ADJ
ejpam-6810	31	6	aspects	aspect	NOUN
ejpam-6810	31	7	and	and	CCONJ
ejpam-6810	31	8	key	key	ADJ
ejpam-6810	31	9	contributions	contribution	NOUN
ejpam-6810	31	10	in	in	ADP
ejpam-6810	31	11	fp	fp	NOUN
ejpam-6810	31	12	theory	theory	NOUN
ejpam-6810	31	13	within	within	ADP
ejpam-6810	31	14	the	the	DET
ejpam-6810	31	15	framework	framework	NOUN
ejpam-6810	31	16	of	of	ADP
ejpam-6810	31	17	b	b	PROPN
ejpam-6810	31	18	-	-	PUNCT
ejpam-6810	31	19	ms	ms	NOUN
ejpam-6810	31	20	.	.	PROPN
ejpam-6810	31	21	in	in	ADP
ejpam-6810	31	22	2022	2022	NUM
ejpam-6810	31	23	,	,	PUNCT
ejpam-6810	31	24	berinde	berinde	NOUN
ejpam-6810	31	25	and	and	CCONJ
ejpam-6810	31	26	păcurar	păcurar	NOUN
ejpam-6810	31	27	[	[	X
ejpam-6810	31	28	29	29	NUM
ejpam-6810	31	29	]	]	PUNCT
ejpam-6810	31	30	survey	survey	NOUN
ejpam-6810	31	31	the	the	DET
ejpam-6810	31	32	early	early	ADJ
ejpam-6810	31	33	progress	progress	NOUN
ejpam-6810	31	34	and	and	CCONJ
ejpam-6810	31	35	key	key	ADJ
ejpam-6810	31	36	issues	issue	NOUN
ejpam-6810	31	37	in	in	ADP
ejpam-6810	31	38	fp	fp	NOUN
ejpam-6810	31	39	theory	theory	NOUN
ejpam-6810	31	40	within	within	ADP
ejpam-6810	31	41	b	b	PROPN
ejpam-6810	31	42	-	-	PUNCT
ejpam-6810	31	43	ms	ms	PROPN
ejpam-6810	31	44	.	.	PROPN
ejpam-6810	31	45	ma	ma	PROPN
ejpam-6810	31	46	et	et	PROPN
ejpam-6810	31	47	al	al	PROPN
ejpam-6810	31	48	.	.	PUNCT
ejpam-6810	32	1	[	[	X
ejpam-6810	32	2	30	30	NUM
ejpam-6810	32	3	]	]	PUNCT
ejpam-6810	32	4	introduced	introduce	VERB
ejpam-6810	32	5	the	the	DET
ejpam-6810	32	6	concept	concept	NOUN
ejpam-6810	32	7	of	of	ADP
ejpam-6810	32	8	c∗-algebra	c∗-algebra	PROPN
ejpam-6810	32	9	-	-	PUNCT
ejpam-6810	32	10	valued	value	VERB
ejpam-6810	32	11	contraction	contraction	NOUN
ejpam-6810	32	12	mappings	mapping	NOUN
ejpam-6810	32	13	.	.	PUNCT
ejpam-6810	33	1	building	build	VERB
ejpam-6810	33	2	on	on	ADP
ejpam-6810	33	3	this	this	PRON
ejpam-6810	33	4	,	,	PUNCT
ejpam-6810	33	5	batul	batul	PROPN
ejpam-6810	33	6	et	et	PROPN
ejpam-6810	33	7	al	al	PROPN
ejpam-6810	33	8	.	.	PUNCT
ejpam-6810	34	1	[	[	X
ejpam-6810	34	2	31	31	NUM
ejpam-6810	34	3	]	]	PUNCT
ejpam-6810	34	4	generalized	generalize	VERB
ejpam-6810	34	5	the	the	DET
ejpam-6810	34	6	idea	idea	NOUN
ejpam-6810	34	7	by	by	ADP
ejpam-6810	34	8	relaxing	relax	VERB
ejpam-6810	34	9	the	the	DET
ejpam-6810	34	10	contraction	contraction	NOUN
ejpam-6810	34	11	condition	condition	NOUN
ejpam-6810	34	12	initially	initially	ADV
ejpam-6810	34	13	proposed	propose	VERB
ejpam-6810	34	14	in	in	ADP
ejpam-6810	34	15	[	[	X
ejpam-6810	34	16	30	30	NUM
ejpam-6810	34	17	]	]	PUNCT
ejpam-6810	34	18	.	.	PUNCT
ejpam-6810	35	1	in	in	ADP
ejpam-6810	35	2	another	another	DET
ejpam-6810	35	3	development	development	NOUN
ejpam-6810	35	4	,	,	PUNCT
ejpam-6810	35	5	shehwar	shehwar	NOUN
ejpam-6810	35	6	et	et	PROPN
ejpam-6810	35	7	al	al	PROPN
ejpam-6810	35	8	.	.	PUNCT
ejpam-6810	36	1	[	[	X
ejpam-6810	36	2	32	32	NUM
ejpam-6810	36	3	]	]	PUNCT
ejpam-6810	36	4	extended	extend	VERB
ejpam-6810	36	5	caristi	caristi	PROPN
ejpam-6810	36	6	fp	fp	X
ejpam-6810	36	7	theorem	theorem	VERB
ejpam-6810	36	8	to	to	PART
ejpam-6810	36	9	mappings	mapping	NOUN
ejpam-6810	36	10	defined	define	VERB
ejpam-6810	36	11	on	on	ADP
ejpam-6810	36	12	c∗-algebra	c∗-algebra	PROPN
ejpam-6810	36	13	-	-	PUNCT
ejpam-6810	36	14	valued	value	VERB
ejpam-6810	36	15	mss	mss	PROPN
ejpam-6810	36	16	.	.	PUNCT
ejpam-6810	37	1	they	they	PRON
ejpam-6810	37	2	demonstrated	demonstrate	VERB
ejpam-6810	37	3	the	the	DET
ejpam-6810	37	4	existence	existence	NOUN
ejpam-6810	37	5	of	of	ADP
ejpam-6810	37	6	fps	fps	NOUN
ejpam-6810	37	7	by	by	ADP
ejpam-6810	37	8	employing	employ	VERB
ejpam-6810	37	9	the	the	DET
ejpam-6810	37	10	concept	concept	NOUN
ejpam-6810	37	11	of	of	ADP
ejpam-6810	37	12	minimal	minimal	ADJ
ejpam-6810	37	13	elements	element	NOUN
ejpam-6810	37	14	within	within	ADP
ejpam-6810	37	15	these	these	DET
ejpam-6810	37	16	spaces	space	NOUN
ejpam-6810	37	17	and	and	CCONJ
ejpam-6810	37	18	introduced	introduce	VERB
ejpam-6810	37	19	a	a	DET
ejpam-6810	37	20	partial	partial	ADJ
ejpam-6810	37	21	order	order	NOUN
ejpam-6810	37	22	on	on	ADP
ejpam-6810	37	23	the	the	DET
ejpam-6810	37	24	set	set	ADJ
ejpam-6810	37	25	u	u	NOUN
ejpam-6810	37	26	.	.	PUNCT
ejpam-6810	38	1	recently	recently	ADV
ejpam-6810	38	2	,	,	PUNCT
ejpam-6810	38	3	pasicki	pasicki	NOUN
ejpam-6810	38	4	[	[	X
ejpam-6810	38	5	33	33	NUM
ejpam-6810	38	6	]	]	PUNCT
ejpam-6810	38	7	explores	explore	VERB
ejpam-6810	38	8	the	the	DET
ejpam-6810	38	9	characteristics	characteristic	NOUN
ejpam-6810	38	10	of	of	ADP
ejpam-6810	38	11	cauchy	cauchy	ADJ
ejpam-6810	38	12	sequences	sequence	NOUN
ejpam-6810	38	13	in	in	ADP
ejpam-6810	38	14	b	b	PROPN
ejpam-6810	38	15	-	-	PUNCT
ejpam-6810	38	16	ms	ms	NOUN
ejpam-6810	38	17	,	,	PUNCT
ejpam-6810	38	18	contributing	contribute	VERB
ejpam-6810	38	19	to	to	ADP
ejpam-6810	38	20	a	a	DET
ejpam-6810	38	21	deeper	deep	ADJ
ejpam-6810	38	22	understanding	understanding	NOUN
ejpam-6810	38	23	of	of	ADP
ejpam-6810	38	24	their	their	PRON
ejpam-6810	38	25	convergence	convergence	NOUN
ejpam-6810	38	26	properties	property	NOUN
ejpam-6810	38	27	.	.	PUNCT
ejpam-6810	39	1	in	in	ADP
ejpam-6810	39	2	2012	2012	NUM
ejpam-6810	39	3	,	,	PUNCT
ejpam-6810	39	4	wardowski	wardowski	VERB
ejpam-6810	39	5	[	[	X
ejpam-6810	39	6	34	34	NUM
ejpam-6810	39	7	]	]	PUNCT
ejpam-6810	39	8	introduced	introduce	VERB
ejpam-6810	39	9	a	a	DET
ejpam-6810	39	10	novel	novel	ADJ
ejpam-6810	39	11	type	type	NOUN
ejpam-6810	39	12	of	of	ADP
ejpam-6810	39	13	contractions	contraction	NOUN
ejpam-6810	39	14	,	,	PUNCT
ejpam-6810	39	15	known	know	VERB
ejpam-6810	39	16	as	as	ADP
ejpam-6810	39	17	an	an	DET
ejpam-6810	39	18	f	f	NOUN
ejpam-6810	39	19	-	-	PUNCT
ejpam-6810	39	20	contraction	contraction	NOUN
ejpam-6810	39	21	,	,	PUNCT
ejpam-6810	39	22	for	for	ADP
ejpam-6810	39	23	real	real	ADV
ejpam-6810	39	24	-	-	PUNCT
ejpam-6810	39	25	valued	value	VERB
ejpam-6810	39	26	functions	function	NOUN
ejpam-6810	39	27	defined	define	VERB
ejpam-6810	39	28	on	on	ADP
ejpam-6810	39	29	the	the	DET
ejpam-6810	39	30	set	set	NOUN
ejpam-6810	39	31	of	of	ADP
ejpam-6810	39	32	positive	positive	ADJ
ejpam-6810	39	33	real	real	ADJ
ejpam-6810	39	34	numbers	number	NOUN
ejpam-6810	39	35	and	and	CCONJ
ejpam-6810	39	36	satisfying	satisfy	VERB
ejpam-6810	39	37	specific	specific	ADJ
ejpam-6810	39	38	conditions	condition	NOUN
ejpam-6810	39	39	.	.	PUNCT
ejpam-6810	40	1	he	he	PRON
ejpam-6810	40	2	also	also	ADV
ejpam-6810	40	3	established	establish	VERB
ejpam-6810	40	4	a	a	DET
ejpam-6810	40	5	fixed	fix	VERB
ejpam-6810	40	6	point	point	NOUN
ejpam-6810	40	7	theorem	theorem	NOUN
ejpam-6810	40	8	for	for	ADP
ejpam-6810	40	9	this	this	DET
ejpam-6810	40	10	class	class	NOUN
ejpam-6810	40	11	of	of	ADP
ejpam-6810	40	12	contractions	contraction	NOUN
ejpam-6810	40	13	.	.	PUNCT
ejpam-6810	41	1	since	since	SCONJ
ejpam-6810	41	2	then	then	ADV
ejpam-6810	41	3	,	,	PUNCT
ejpam-6810	41	4	numerous	numerous	ADJ
ejpam-6810	41	5	researchers	researcher	NOUN
ejpam-6810	41	6	have	have	AUX
ejpam-6810	41	7	extended	extend	VERB
ejpam-6810	41	8	and	and	CCONJ
ejpam-6810	41	9	explored	explore	VERB
ejpam-6810	41	10	f	f	NOUN
ejpam-6810	41	11	-	-	PUNCT
ejpam-6810	41	12	contraction	contraction	NOUN
ejpam-6810	41	13	mappings	mapping	NOUN
ejpam-6810	41	14	within	within	ADP
ejpam-6810	41	15	various	various	ADJ
ejpam-6810	41	16	types	type	NOUN
ejpam-6810	41	17	of	of	ADP
ejpam-6810	41	18	ms	ms	PROPN
ejpam-6810	41	19	.	.	PROPN
ejpam-6810	41	20	fabiano	fabiano	PROPN
ejpam-6810	41	21	et	et	PROPN
ejpam-6810	41	22	al	al	PROPN
ejpam-6810	41	23	.	.	PUNCT
ejpam-6810	42	1	[	[	X
ejpam-6810	42	2	35	35	NUM
ejpam-6810	42	3	]	]	PUNCT
ejpam-6810	42	4	present	present	NOUN
ejpam-6810	42	5	an	an	DET
ejpam-6810	42	6	in	in	ADP
ejpam-6810	42	7	-	-	PUNCT
ejpam-6810	42	8	depth	depth	NOUN
ejpam-6810	42	9	overview	overview	NOUN
ejpam-6810	42	10	of	of	ADP
ejpam-6810	42	11	f	f	NOUN
ejpam-6810	42	12	-	-	PUNCT
ejpam-6810	42	13	contractions	contraction	NOUN
ejpam-6810	42	14	,	,	PUNCT
ejpam-6810	42	15	focusing	focus	VERB
ejpam-6810	42	16	on	on	ADP
ejpam-6810	42	17	their	their	PRON
ejpam-6810	42	18	origins	origin	NOUN
ejpam-6810	42	19	,	,	PUNCT
ejpam-6810	42	20	theoretical	theoretical	ADJ
ejpam-6810	42	21	advancements	advancement	NOUN
ejpam-6810	42	22	and	and	CCONJ
ejpam-6810	42	23	applications	application	NOUN
ejpam-6810	42	24	in	in	ADP
ejpam-6810	42	25	generalized	generalized	ADJ
ejpam-6810	42	26	ms	ms	PROPN
ejpam-6810	42	27	.	.	PROPN
ejpam-6810	42	28	petrov	petrov	PROPN
ejpam-6810	42	29	[	[	X
ejpam-6810	42	30	36	36	NUM
ejpam-6810	42	31	]	]	PUNCT
ejpam-6810	42	32	obtained	obtain	VERB
ejpam-6810	42	33	some	some	DET
ejpam-6810	42	34	fp	fp	NOUN
ejpam-6810	42	35	theorems	theorem	NOUN
ejpam-6810	42	36	for	for	ADP
ejpam-6810	42	37	“	"	PUNCT
ejpam-6810	42	38	mappings	mapping	NOUN
ejpam-6810	42	39	contracting	contract	VERB
ejpam-6810	42	40	perimeters	perimeter	NOUN
ejpam-6810	42	41	of	of	ADP
ejpam-6810	42	42	triangles	triangle	NOUN
ejpam-6810	42	43	”	"	PUNCT
ejpam-6810	42	44	(	(	PUNCT
ejpam-6810	42	45	mcpts	mcpt	NOUN
ejpam-6810	42	46	)	)	PUNCT
ejpam-6810	42	47	in	in	ADP
ejpam-6810	42	48	the	the	DET
ejpam-6810	42	49	framework	framework	NOUN
ejpam-6810	42	50	of	of	ADP
ejpam-6810	42	51	mss	mss	PROPN
ejpam-6810	42	52	.	.	PUNCT
ejpam-6810	43	1	in	in	ADP
ejpam-6810	43	2	this	this	DET
ejpam-6810	43	3	paper	paper	NOUN
ejpam-6810	43	4	,	,	PUNCT
ejpam-6810	43	5	the	the	DET
ejpam-6810	43	6	author	author	NOUN
ejpam-6810	43	7	[	[	X
ejpam-6810	43	8	36	36	NUM
ejpam-6810	43	9	]	]	PUNCT
ejpam-6810	43	10	introduced	introduce	VERB
ejpam-6810	43	11	a	a	DET
ejpam-6810	43	12	new	new	ADJ
ejpam-6810	43	13	type	type	NOUN
ejpam-6810	43	14	of	of	ADP
ejpam-6810	43	15	mappings	mapping	NOUN
ejpam-6810	43	16	in	in	ADP
ejpam-6810	43	17	mss	mss	PROPN
ejpam-6810	43	18	which	which	PRON
ejpam-6810	43	19	can	can	AUX
ejpam-6810	43	20	be	be	AUX
ejpam-6810	43	21	characterized	characterize	VERB
ejpam-6810	43	22	as	as	ADP
ejpam-6810	43	23	a	a	DET
ejpam-6810	43	24	mcpt	mcpt	NOUN
ejpam-6810	43	25	.	.	PUNCT
ejpam-6810	44	1	influenced	influence	VERB
ejpam-6810	44	2	by	by	ADP
ejpam-6810	44	3	the	the	DET
ejpam-6810	44	4	work	work	NOUN
ejpam-6810	44	5	of	of	ADP
ejpam-6810	44	6	petrov	petrov	PROPN
ejpam-6810	44	7	,	,	PUNCT
ejpam-6810	44	8	we	we	PRON
ejpam-6810	44	9	bring	bring	VERB
ejpam-6810	44	10	to	to	PART
ejpam-6810	44	11	light	light	VERB
ejpam-6810	44	12	some	some	DET
ejpam-6810	44	13	fp	fp	NOUN
ejpam-6810	44	14	theorems	theorem	NOUN
ejpam-6810	44	15	for	for	ADP
ejpam-6810	44	16	mcpts	mcpt	NOUN
ejpam-6810	44	17	embedded	embed	VERB
ejpam-6810	44	18	with	with	ADP
ejpam-6810	44	19	f	f	NOUN
ejpam-6810	44	20	-	-	PUNCT
ejpam-6810	44	21	contractions	contraction	NOUN
ejpam-6810	44	22	in	in	ADP
ejpam-6810	44	23	the	the	DET
ejpam-6810	44	24	framework	framework	NOUN
ejpam-6810	44	25	of	of	ADP
ejpam-6810	44	26	b	b	PROPN
ejpam-6810	44	27	-	-	PUNCT
ejpam-6810	44	28	mss	mss	PROPN
ejpam-6810	44	29	.	.	PUNCT
ejpam-6810	45	1	standard	standard	ADJ
ejpam-6810	45	2	contraction	contraction	NOUN
ejpam-6810	45	3	mappings	mapping	NOUN
ejpam-6810	45	4	represent	represent	VERB
ejpam-6810	45	5	a	a	DET
ejpam-6810	45	6	notable	notable	ADJ
ejpam-6810	45	7	subclass	subclass	NOUN
ejpam-6810	45	8	within	within	ADP
ejpam-6810	45	9	this	this	DET
ejpam-6810	45	10	broader	broad	ADJ
ejpam-6810	45	11	framework	framework	NOUN
ejpam-6810	45	12	,	,	PUNCT
ejpam-6810	45	13	enabling	enable	VERB
ejpam-6810	45	14	us	we	PRON
ejpam-6810	45	15	to	to	PART
ejpam-6810	45	16	recover	recover	VERB
ejpam-6810	45	17	banach	banach	ADV
ejpam-6810	45	18	classical	classical	ADJ
ejpam-6810	45	19	result	result	NOUN
ejpam-6810	45	20	as	as	ADP
ejpam-6810	45	21	a	a	DET
ejpam-6810	45	22	straightforward	straightforward	ADJ
ejpam-6810	45	23	corollary	corollary	NOUN
ejpam-6810	45	24	.	.	PUNCT
ejpam-6810	46	1	furthermore	furthermore	ADV
ejpam-6810	46	2	,	,	PUNCT
ejpam-6810	46	3	we	we	PRON
ejpam-6810	46	4	provide	provide	VERB
ejpam-6810	46	5	examples	example	NOUN
ejpam-6810	46	6	of	of	ADP
ejpam-6810	46	7	mappings	mapping	NOUN
ejpam-6810	46	8	that	that	PRON
ejpam-6810	46	9	contract	contract	VERB
ejpam-6810	46	10	the	the	DET
ejpam-6810	46	11	perimeters	perimeter	NOUN
ejpam-6810	46	12	of	of	ADP
ejpam-6810	46	13	triangles	triangle	NOUN
ejpam-6810	46	14	embedded	embed	VERB
ejpam-6810	46	15	with	with	ADP
ejpam-6810	46	16	f	f	NOUN
ejpam-6810	46	17	-	-	PUNCT
ejpam-6810	46	18	contractions	contraction	NOUN
ejpam-6810	46	19	in	in	ADP
ejpam-6810	46	20	b	b	PROPN
ejpam-6810	46	21	-	-	PUNCT
ejpam-6810	46	22	mss	mss	NOUN
ejpam-6810	46	23	,	,	PUNCT
ejpam-6810	46	24	but	but	CCONJ
ejpam-6810	46	25	do	do	AUX
ejpam-6810	46	26	not	not	PART
ejpam-6810	46	27	qualify	qualify	VERB
ejpam-6810	46	28	as	as	ADP
ejpam-6810	46	29	contraction	contraction	NOUN
ejpam-6810	46	30	mappings	mapping	NOUN
ejpam-6810	46	31	in	in	ADP
ejpam-6810	46	32	the	the	DET
ejpam-6810	46	33	traditional	traditional	ADJ
ejpam-6810	46	34	sense	sense	NOUN
ejpam-6810	46	35	.	.	PUNCT
ejpam-6810	47	1	the	the	DET
ejpam-6810	47	2	following	follow	VERB
ejpam-6810	47	3	are	be	AUX
ejpam-6810	47	4	some	some	DET
ejpam-6810	47	5	definitions	definition	NOUN
ejpam-6810	47	6	and	and	CCONJ
ejpam-6810	47	7	results	result	NOUN
ejpam-6810	47	8	which	which	PRON
ejpam-6810	47	9	are	be	AUX
ejpam-6810	47	10	useful	useful	ADJ
ejpam-6810	47	11	for	for	ADP
ejpam-6810	47	12	the	the	DET
ejpam-6810	47	13	proof	proof	NOUN
ejpam-6810	47	14	of	of	ADP
ejpam-6810	47	15	main	main	ADJ
ejpam-6810	47	16	theorems	theorem	NOUN
ejpam-6810	47	17	.	.	PUNCT
ejpam-6810	48	1	definition	definition	NOUN
ejpam-6810	48	2	1	1	NUM
ejpam-6810	48	3	.	.	PUNCT
ejpam-6810	49	1	[	[	X
ejpam-6810	49	2	26	26	NUM
ejpam-6810	49	3	]	]	PUNCT
ejpam-6810	49	4	let	let	VERB
ejpam-6810	49	5	u	u	PRON
ejpam-6810	49	6	be	be	AUX
ejpam-6810	49	7	a	a	DET
ejpam-6810	49	8	nonempty	nonempty	ADV
ejpam-6810	49	9	set	set	VERB
ejpam-6810	49	10	and	and	CCONJ
ejpam-6810	49	11	let	let	VERB
ejpam-6810	49	12	s	s	PRON
ejpam-6810	49	13	≥	≥	X
ejpam-6810	49	14	1	1	NUM
ejpam-6810	49	15	be	be	AUX
ejpam-6810	49	16	a	a	DET
ejpam-6810	49	17	given	give	VERB
ejpam-6810	49	18	real	real	ADJ
ejpam-6810	49	19	number	number	NOUN
ejpam-6810	49	20	.	.	PUNCT
ejpam-6810	50	1	a	a	DET
ejpam-6810	50	2	s.	s.	PROPN
ejpam-6810	50	3	batul	batul	PROPN
ejpam-6810	50	4	et	et	PROPN
ejpam-6810	50	5	al	al	PROPN
ejpam-6810	50	6	.	.	PUNCT
ejpam-6810	50	7	/	/	SYM
ejpam-6810	50	8	eur	eur	PROPN
ejpam-6810	50	9	.	.	PUNCT
ejpam-6810	51	1	j.	j.	PROPN
ejpam-6810	51	2	pure	pure	PROPN
ejpam-6810	51	3	appl	appl	PROPN
ejpam-6810	51	4	.	.	PROPN
ejpam-6810	51	5	math	math	PROPN
ejpam-6810	51	6	,	,	PUNCT
ejpam-6810	51	7	18	18	NUM
ejpam-6810	51	8	(	(	PUNCT
ejpam-6810	51	9	4	4	NUM
ejpam-6810	51	10	)	)	PUNCT
ejpam-6810	51	11	(	(	PUNCT
ejpam-6810	51	12	2025	2025	NUM
ejpam-6810	51	13	)	)	PUNCT
ejpam-6810	51	14	,	,	PUNCT
ejpam-6810	51	15	6810	6810	NUM
ejpam-6810	51	16	3	3	NUM
ejpam-6810	51	17	of	of	ADP
ejpam-6810	51	18	23	23	NUM
ejpam-6810	51	19	function	function	NOUN
ejpam-6810	51	20	σb	σb	ADP
ejpam-6810	51	21	:	:	PUNCT
ejpam-6810	51	22	u	u	NOUN
ejpam-6810	51	23	×	×	PROPN
ejpam-6810	51	24	u	u	X
ejpam-6810	51	25	→	→	PUNCT
ejpam-6810	51	26	r+	r+	PRON
ejpam-6810	51	27	is	be	AUX
ejpam-6810	51	28	called	call	VERB
ejpam-6810	51	29	a	a	DET
ejpam-6810	51	30	b	b	NOUN
ejpam-6810	51	31	-	-	ADJ
ejpam-6810	51	32	metric	metric	ADJ
ejpam-6810	51	33	provided	provide	VERB
ejpam-6810	51	34	that	that	SCONJ
ejpam-6810	51	35	,	,	PUNCT
ejpam-6810	51	36	for	for	ADP
ejpam-6810	51	37	all	all	DET
ejpam-6810	51	38	η	η	PROPN
ejpam-6810	51	39	,	,	PUNCT
ejpam-6810	51	40	ξ	ξ	PROPN
ejpam-6810	51	41	,	,	PUNCT
ejpam-6810	51	42	ζ	ζ	PROPN
ejpam-6810	51	43	∈	∈	PROPN
ejpam-6810	51	44	u	u	NOUN
ejpam-6810	51	45	,	,	PUNCT
ejpam-6810	51	46	(	(	PUNCT
ejpam-6810	51	47	mb1	mb1	NOUN
ejpam-6810	51	48	):	):	PUNCT
ejpam-6810	51	49	σb(η	σb(η	PROPN
ejpam-6810	51	50	,	,	PUNCT
ejpam-6810	51	51	ξ	ξ	NOUN
ejpam-6810	51	52	)	)	PUNCT
ejpam-6810	51	53	≥	≥	NOUN
ejpam-6810	51	54	0	0	NUM
ejpam-6810	51	55	,	,	PUNCT
ejpam-6810	51	56	(	(	PUNCT
ejpam-6810	51	57	mb2	mb2	PROPN
ejpam-6810	51	58	):	):	PUNCT
ejpam-6810	51	59	σb(η	σb(η	PROPN
ejpam-6810	51	60	,	,	PUNCT
ejpam-6810	51	61	ξ	ξ	X
ejpam-6810	51	62	)	)	PUNCT
ejpam-6810	51	63	=	=	SYM
ejpam-6810	51	64	0	0	PUNCT
ejpam-6810	52	1	if	if	SCONJ
ejpam-6810	52	2	and	and	CCONJ
ejpam-6810	52	3	only	only	ADV
ejpam-6810	52	4	if	if	SCONJ
ejpam-6810	52	5	η	η	PROPN
ejpam-6810	52	6	=	=	SYM
ejpam-6810	52	7	ξ	ξ	PROPN
ejpam-6810	52	8	,	,	PUNCT
ejpam-6810	52	9	(	(	PUNCT
ejpam-6810	52	10	mb3	mb3	NOUN
ejpam-6810	52	11	):	):	PUNCT
ejpam-6810	52	12	σb(η	σb(η	PROPN
ejpam-6810	52	13	,	,	PUNCT
ejpam-6810	52	14	ξ	ξ	X
ejpam-6810	52	15	)	)	PUNCT
ejpam-6810	52	16	=	=	SYM
ejpam-6810	52	17	σb(ξ	σb(ξ	PROPN
ejpam-6810	52	18	,	,	PUNCT
ejpam-6810	52	19	η	η	NOUN
ejpam-6810	52	20	)	)	PUNCT
ejpam-6810	52	21	,	,	PUNCT
ejpam-6810	52	22	(	(	PUNCT
ejpam-6810	52	23	mb4	mb4	PROPN
ejpam-6810	52	24	):	):	PUNCT
ejpam-6810	52	25	σb(η	σb(η	PROPN
ejpam-6810	52	26	,	,	PUNCT
ejpam-6810	52	27	ζ	ζ	NOUN
ejpam-6810	52	28	)	)	PUNCT
ejpam-6810	52	29	≤	≤	NOUN
ejpam-6810	52	30	s	s	PART
ejpam-6810	53	1	[	[	X
ejpam-6810	53	2	σb(η	σb(η	PRON
ejpam-6810	53	3	,	,	PUNCT
ejpam-6810	53	4	ξ	ξ	NOUN
ejpam-6810	53	5	)	)	PUNCT
ejpam-6810	53	6	+	+	CCONJ
ejpam-6810	53	7	σb(ξ	σb(ξ	ADJ
ejpam-6810	53	8	,	,	PUNCT
ejpam-6810	53	9	ζ	ζ	NOUN
ejpam-6810	53	10	)	)	PUNCT
ejpam-6810	53	11	]	]	PUNCT
ejpam-6810	53	12	.	.	PUNCT
ejpam-6810	54	1	the	the	DET
ejpam-6810	54	2	pair	pair	NOUN
ejpam-6810	54	3	(	(	PUNCT
ejpam-6810	54	4	u	u	NOUN
ejpam-6810	54	5	,	,	PUNCT
ejpam-6810	54	6	σb	σb	ADP
ejpam-6810	54	7	)	)	PUNCT
ejpam-6810	54	8	is	be	AUX
ejpam-6810	54	9	called	call	VERB
ejpam-6810	54	10	a	a	DET
ejpam-6810	54	11	b	b	PROPN
ejpam-6810	54	12	-	-	PUNCT
ejpam-6810	54	13	ms	ms	NOUN
ejpam-6810	54	14	.	.	PROPN
ejpam-6810	54	15	in	in	ADP
ejpam-6810	54	16	general	general	ADJ
ejpam-6810	54	17	,	,	PUNCT
ejpam-6810	54	18	a	a	DET
ejpam-6810	54	19	b	b	X
ejpam-6810	54	20	-	-	ADJ
ejpam-6810	54	21	metric	metric	ADJ
ejpam-6810	54	22	is	be	AUX
ejpam-6810	54	23	not	not	PART
ejpam-6810	54	24	a	a	DET
ejpam-6810	54	25	continuous	continuous	ADJ
ejpam-6810	54	26	function	function	NOUN
ejpam-6810	54	27	.	.	PUNCT
ejpam-6810	55	1	however	however	ADV
ejpam-6810	55	2	,	,	PUNCT
ejpam-6810	55	3	throughout	throughout	ADP
ejpam-6810	55	4	the	the	DET
ejpam-6810	55	5	article	article	NOUN
ejpam-6810	55	6	,	,	PUNCT
ejpam-6810	55	7	we	we	PRON
ejpam-6810	55	8	will	will	AUX
ejpam-6810	55	9	assume	assume	VERB
ejpam-6810	55	10	that	that	SCONJ
ejpam-6810	55	11	the	the	DET
ejpam-6810	55	12	b	b	X
ejpam-6810	55	13	-	-	ADJ
ejpam-6810	55	14	metric	metric	ADJ
ejpam-6810	55	15	is	be	AUX
ejpam-6810	55	16	continuous	continuous	ADJ
ejpam-6810	55	17	.	.	PUNCT
ejpam-6810	55	18	example	example	NOUN
ejpam-6810	56	1	1	1	NUM
ejpam-6810	56	2	.	.	PUNCT
ejpam-6810	56	3	let	let	VERB
ejpam-6810	56	4	u	u	NOUN
ejpam-6810	56	5	=	=	NOUN
ejpam-6810	56	6	n.	n.	NOUN
ejpam-6810	56	7	define	define	VERB
ejpam-6810	56	8	σb	σb	ADP
ejpam-6810	56	9	:	:	PUNCT
ejpam-6810	56	10	u	u	PROPN
ejpam-6810	56	11	×	×	PROPN
ejpam-6810	56	12	u	u	X
ejpam-6810	56	13	→	→	PUNCT
ejpam-6810	56	14	[	[	X
ejpam-6810	56	15	0,+∞	0,+∞	NUM
ejpam-6810	56	16	)	)	PUNCT
ejpam-6810	56	17	by	by	ADP
ejpam-6810	56	18	σb(η	σb(η	NUM
ejpam-6810	56	19	,	,	PUNCT
ejpam-6810	56	20	ξ	ξ	X
ejpam-6810	56	21	)	)	PUNCT
ejpam-6810	56	22	=	=	SYM
ejpam-6810	57	1			NOUN
ejpam-6810	57	2	0	0	NUM
ejpam-6810	57	3	,	,	PUNCT
ejpam-6810	57	4	if	if	SCONJ
ejpam-6810	57	5	η	η	PROPN
ejpam-6810	57	6	=	=	SYM
ejpam-6810	57	7	ξ	ξ	PROPN
ejpam-6810	57	8	,	,	PUNCT
ejpam-6810	57	9	4α	4α	NOUN
ejpam-6810	57	10	,	,	PUNCT
ejpam-6810	57	11	if	if	SCONJ
ejpam-6810	57	12	η	η	PROPN
ejpam-6810	57	13	,	,	PUNCT
ejpam-6810	57	14	ξ	ξ	PROPN
ejpam-6810	57	15	∈	∈	PROPN
ejpam-6810	57	16	{	{	PUNCT
ejpam-6810	57	17	1	1	NUM
ejpam-6810	57	18	,	,	PUNCT
ejpam-6810	57	19	2	2	NUM
ejpam-6810	57	20	}	}	PUNCT
ejpam-6810	57	21	,	,	PUNCT
ejpam-6810	57	22	α	α	INTJ
ejpam-6810	57	23	,	,	PUNCT
ejpam-6810	57	24	if	if	SCONJ
ejpam-6810	57	25	η	η	PROPN
ejpam-6810	57	26	or	or	CCONJ
ejpam-6810	57	27	ξ	ξ	PROPN
ejpam-6810	57	28	/∈	/∈	PUNCT
ejpam-6810	57	29	{	{	PUNCT
ejpam-6810	57	30	1	1	NUM
ejpam-6810	57	31	,	,	PUNCT
ejpam-6810	57	32	2	2	NUM
ejpam-6810	57	33	}	}	PUNCT
ejpam-6810	57	34	and	and	CCONJ
ejpam-6810	57	35	η	η	PROPN
ejpam-6810	57	36	6=	6=	PROPN
ejpam-6810	57	37	ξ	ξ	PROPN
ejpam-6810	57	38	,	,	PUNCT
ejpam-6810	57	39	where	where	SCONJ
ejpam-6810	57	40	α	α	PROPN
ejpam-6810	57	41	>	>	X
ejpam-6810	57	42	0	0	PUNCT
ejpam-6810	57	43	is	be	AUX
ejpam-6810	57	44	a	a	DET
ejpam-6810	57	45	constant	constant	ADJ
ejpam-6810	57	46	.	.	PUNCT
ejpam-6810	58	1	here	here	ADV
ejpam-6810	58	2	(	(	PUNCT
ejpam-6810	58	3	u	u	NOUN
ejpam-6810	58	4	,	,	PUNCT
ejpam-6810	58	5	σb	σb	PROPN
ejpam-6810	58	6	)	)	PUNCT
ejpam-6810	58	7	is	be	AUX
ejpam-6810	58	8	a	a	DET
ejpam-6810	58	9	b	b	NOUN
ejpam-6810	58	10	-	-	PUNCT
ejpam-6810	58	11	ms	ms	NOUN
ejpam-6810	58	12	with	with	ADP
ejpam-6810	58	13	s	s	NOUN
ejpam-6810	58	14	=	=	SYM
ejpam-6810	58	15	3	3	X
ejpam-6810	58	16	.	.	NOUN
ejpam-6810	58	17	definition	definition	NOUN
ejpam-6810	58	18	2	2	NUM
ejpam-6810	58	19	.	.	PUNCT
ejpam-6810	59	1	[	[	X
ejpam-6810	59	2	34	34	NUM
ejpam-6810	59	3	]	]	PUNCT
ejpam-6810	59	4	suppose	suppose	VERB
ejpam-6810	59	5	f	f	X
ejpam-6810	59	6	:	:	PUNCT
ejpam-6810	59	7	r+	r+	X
ejpam-6810	59	8	→	→	PUNCT
ejpam-6810	59	9	r	r	NOUN
ejpam-6810	59	10	is	be	AUX
ejpam-6810	59	11	a	a	DET
ejpam-6810	59	12	function	function	NOUN
ejpam-6810	59	13	that	that	PRON
ejpam-6810	59	14	satisfies	satisfy	VERB
ejpam-6810	59	15	the	the	DET
ejpam-6810	59	16	following	following	NOUN
ejpam-6810	59	17	:	:	PUNCT
ejpam-6810	59	18	(	(	PUNCT
ejpam-6810	59	19	f-1	f-1	NOUN
ejpam-6810	59	20	):	):	PUNCT
ejpam-6810	59	21	f	f	PROPN
ejpam-6810	59	22	is	be	AUX
ejpam-6810	59	23	increasing	increase	VERB
ejpam-6810	59	24	,	,	PUNCT
ejpam-6810	59	25	i.e.	i.e.	X
ejpam-6810	59	26	,	,	PUNCT
ejpam-6810	59	27	for	for	ADP
ejpam-6810	59	28	all	all	DET
ejpam-6810	59	29	η	η	PROPN
ejpam-6810	59	30	,	,	PUNCT
ejpam-6810	59	31	ξ	ξ	PROPN
ejpam-6810	59	32	∈	∈	PROPN
ejpam-6810	59	33	r+	r+	NOUN
ejpam-6810	59	34	such	such	ADJ
ejpam-6810	59	35	that	that	SCONJ
ejpam-6810	59	36	η	η	PROPN
ejpam-6810	59	37	<	<	X
ejpam-6810	59	38	ξ	ξ	PROPN
ejpam-6810	59	39	,	,	PUNCT
ejpam-6810	59	40	⇒	⇒	PROPN
ejpam-6810	59	41	f(η	f(η	PROPN
ejpam-6810	59	42	)	)	PUNCT
ejpam-6810	59	43	<	<	X
ejpam-6810	59	44	f(ξ	f(ξ	NOUN
ejpam-6810	59	45	)	)	PUNCT
ejpam-6810	59	46	.	.	PUNCT
ejpam-6810	60	1	(	(	PUNCT
ejpam-6810	60	2	f-2	f-2	ADV
ejpam-6810	60	3	):	):	PUNCT
ejpam-6810	60	4	for	for	ADP
ejpam-6810	60	5	any	any	DET
ejpam-6810	60	6	sequence	sequence	NOUN
ejpam-6810	60	7	{	{	PUNCT
ejpam-6810	60	8	ηn}∞n=1	ηn}∞n=1	X
ejpam-6810	60	9	of	of	ADP
ejpam-6810	60	10	positive	positive	ADJ
ejpam-6810	60	11	real	real	ADJ
ejpam-6810	60	12	numbers	number	NOUN
ejpam-6810	60	13	,	,	PUNCT
ejpam-6810	60	14	lim	lim	PROPN
ejpam-6810	60	15	n→+∞	n→+∞	VERB
ejpam-6810	60	16	ηn	ηn	PROPN
ejpam-6810	61	1	=	=	NOUN
ejpam-6810	61	2	0	0	PUNCT
ejpam-6810	62	1	if	if	SCONJ
ejpam-6810	62	2	and	and	CCONJ
ejpam-6810	62	3	only	only	ADV
ejpam-6810	62	4	if	if	SCONJ
ejpam-6810	62	5	lim	lim	PROPN
ejpam-6810	62	6	n→+∞	n→+∞	VERB
ejpam-6810	62	7	f(ηn	f(ηn	PROPN
ejpam-6810	62	8	)	)	PUNCT
ejpam-6810	62	9	=	=	SYM
ejpam-6810	62	10	−∞.	−∞.	NOUN
ejpam-6810	62	11	(	(	PUNCT
ejpam-6810	62	12	f-3	f-3	PROPN
ejpam-6810	62	13	):	):	PUNCT
ejpam-6810	62	14	there	there	PRON
ejpam-6810	62	15	exists	exist	VERB
ejpam-6810	62	16	k	k	PROPN
ejpam-6810	62	17	∈	∈	PROPN
ejpam-6810	62	18	(	(	PUNCT
ejpam-6810	62	19	0	0	NUM
ejpam-6810	62	20	,	,	PUNCT
ejpam-6810	62	21	1	1	NUM
ejpam-6810	62	22	)	)	PUNCT
ejpam-6810	62	23	such	such	ADJ
ejpam-6810	62	24	that	that	SCONJ
ejpam-6810	62	25	lim	lim	PROPN
ejpam-6810	62	26	α→0	α→0	PROPN
ejpam-6810	62	27	+	+	CCONJ
ejpam-6810	62	28	αkf(α	αkf(α	NOUN
ejpam-6810	62	29	)	)	PUNCT
ejpam-6810	62	30	=	=	NOUN
ejpam-6810	63	1	0	0	X
ejpam-6810	63	2	.	.	PUNCT
ejpam-6810	63	3	definition	definition	NOUN
ejpam-6810	63	4	3	3	NUM
ejpam-6810	63	5	.	.	PUNCT
ejpam-6810	64	1	[	[	X
ejpam-6810	64	2	34	34	NUM
ejpam-6810	64	3	]	]	X
ejpam-6810	64	4	let	let	NOUN
ejpam-6810	64	5	(	(	PUNCT
ejpam-6810	64	6	u	u	NOUN
ejpam-6810	64	7	,	,	PUNCT
ejpam-6810	64	8	σ	σ	PROPN
ejpam-6810	64	9	)	)	PUNCT
ejpam-6810	64	10	be	be	VERB
ejpam-6810	64	11	a	a	DET
ejpam-6810	64	12	ms	ms	PROPN
ejpam-6810	64	13	.	.	PROPN
ejpam-6810	65	1	a	a	DET
ejpam-6810	65	2	mapping	mapping	NOUN
ejpam-6810	65	3	υ	υ	NOUN
ejpam-6810	65	4	:	:	PUNCT
ejpam-6810	65	5	u	u	NOUN
ejpam-6810	65	6	→	→	SYM
ejpam-6810	65	7	u	u	NOUN
ejpam-6810	65	8	is	be	AUX
ejpam-6810	65	9	said	say	VERB
ejpam-6810	65	10	to	to	PART
ejpam-6810	65	11	be	be	AUX
ejpam-6810	65	12	a	a	DET
ejpam-6810	65	13	wardowski	wardowski	NOUN
ejpam-6810	65	14	f	f	NOUN
ejpam-6810	65	15	-	-	PUNCT
ejpam-6810	65	16	contraction	contraction	NOUN
ejpam-6810	65	17	if	if	SCONJ
ejpam-6810	65	18	there	there	PRON
ejpam-6810	65	19	are	be	VERB
ejpam-6810	65	20	f	f	PROPN
ejpam-6810	65	21	∈	∈	PROPN
ejpam-6810	65	22	f	f	PROPN
ejpam-6810	65	23	and	and	CCONJ
ejpam-6810	65	24	τ	τ	PROPN
ejpam-6810	65	25	>	>	X
ejpam-6810	65	26	0	0	NUM
ejpam-6810	65	27	such	such	ADJ
ejpam-6810	65	28	that	that	SCONJ
ejpam-6810	65	29	η	η	PROPN
ejpam-6810	65	30	,	,	PUNCT
ejpam-6810	65	31	ξ	ξ	PROPN
ejpam-6810	65	32	∈	∈	PROPN
ejpam-6810	65	33	u	u	NOUN
ejpam-6810	65	34	,	,	PUNCT
ejpam-6810	65	35	σ(υη	σ(υη	PROPN
ejpam-6810	65	36	,	,	PUNCT
ejpam-6810	65	37	υξ	υξ	NOUN
ejpam-6810	65	38	)	)	PUNCT
ejpam-6810	65	39	>	>	SYM
ejpam-6810	65	40	0	0	PUNCT
ejpam-6810	65	41	⇒	⇒	PROPN
ejpam-6810	65	42	τ	τ	PROPN
ejpam-6810	65	43	+	+	SYM
ejpam-6810	65	44	f(σ(υη	f(σ(υη	PROPN
ejpam-6810	65	45	,	,	PUNCT
ejpam-6810	65	46	υξ	υξ	NOUN
ejpam-6810	65	47	)	)	PUNCT
ejpam-6810	65	48	)	)	PUNCT
ejpam-6810	65	49	≤	≤	NUM
ejpam-6810	66	1	f(σ(η	f(σ(η	PROPN
ejpam-6810	66	2	,	,	PUNCT
ejpam-6810	66	3	ξ	ξ	NOUN
ejpam-6810	66	4	)	)	PUNCT
ejpam-6810	66	5	)	)	PUNCT
ejpam-6810	66	6	.	.	PUNCT
ejpam-6810	67	1	in	in	ADP
ejpam-6810	67	2	2015	2015	NUM
ejpam-6810	67	3	,	,	PUNCT
ejpam-6810	67	4	cosentine	cosentine	VERB
ejpam-6810	67	5	et	et	PROPN
ejpam-6810	67	6	al	al	PROPN
ejpam-6810	67	7	.	.	PUNCT
ejpam-6810	68	1	[	[	X
ejpam-6810	68	2	37	37	NUM
ejpam-6810	68	3	]	]	PUNCT
ejpam-6810	68	4	introduced	introduce	VERB
ejpam-6810	68	5	a	a	DET
ejpam-6810	68	6	new	new	ADJ
ejpam-6810	68	7	condition	condition	NOUN
ejpam-6810	68	8	in	in	ADP
ejpam-6810	68	9	definition	definition	NOUN
ejpam-6810	68	10	2	2	NUM
ejpam-6810	68	11	to	to	PART
ejpam-6810	68	12	derive	derive	VERB
ejpam-6810	68	13	certain	certain	ADJ
ejpam-6810	68	14	fixed	fix	VERB
ejpam-6810	68	15	point	point	NOUN
ejpam-6810	68	16	results	result	NOUN
ejpam-6810	68	17	in	in	ADP
ejpam-6810	68	18	b	b	PROPN
ejpam-6810	68	19	-	-	PUNCT
ejpam-6810	68	20	mss	mss	NOUN
ejpam-6810	68	21	.	.	PUNCT
ejpam-6810	69	1	in	in	ADP
ejpam-6810	69	2	this	this	DET
ejpam-6810	69	3	article	article	NOUN
ejpam-6810	69	4	,	,	PUNCT
ejpam-6810	69	5	we	we	PRON
ejpam-6810	69	6	further	far	ADV
ejpam-6810	69	7	extend	extend	VERB
ejpam-6810	69	8	this	this	DET
ejpam-6810	69	9	definition	definition	NOUN
ejpam-6810	69	10	by	by	ADP
ejpam-6810	69	11	incorporating	incorporate	VERB
ejpam-6810	69	12	an	an	DET
ejpam-6810	69	13	additional	additional	ADJ
ejpam-6810	69	14	condition	condition	NOUN
ejpam-6810	69	15	into	into	ADP
ejpam-6810	69	16	definition	definition	NOUN
ejpam-6810	69	17	2	2	NUM
ejpam-6810	69	18	.	.	PUNCT
ejpam-6810	70	1	(	(	PUNCT
ejpam-6810	70	2	f	f	X
ejpam-6810	70	3	−	−	PROPN
ejpam-6810	70	4	4	4	NUM
ejpam-6810	70	5	):	):	PUNCT
ejpam-6810	70	6	let	let	VERB
ejpam-6810	70	7	s	s	PRON
ejpam-6810	70	8	≥	≥	X
ejpam-6810	70	9	1	1	NUM
ejpam-6810	70	10	be	be	AUX
ejpam-6810	70	11	a	a	DET
ejpam-6810	70	12	real	real	ADJ
ejpam-6810	70	13	number	number	NOUN
ejpam-6810	70	14	.	.	PUNCT
ejpam-6810	71	1	for	for	ADP
ejpam-6810	71	2	each	each	DET
ejpam-6810	71	3	sequence	sequence	NOUN
ejpam-6810	71	4	{	{	PUNCT
ejpam-6810	71	5	βn}n∈n	βn}n∈n	X
ejpam-6810	71	6	of	of	ADP
ejpam-6810	71	7	positive	positive	ADJ
ejpam-6810	71	8	real	real	ADJ
ejpam-6810	71	9	numbers	number	NOUN
ejpam-6810	71	10	such	such	ADJ
ejpam-6810	71	11	that	that	SCONJ
ejpam-6810	71	12	τ	τ	PROPN
ejpam-6810	71	13	+	+	CCONJ
ejpam-6810	71	14	f(s2βn	f(s2βn	NOUN
ejpam-6810	71	15	)	)	PUNCT
ejpam-6810	71	16	≤	≤	NOUN
ejpam-6810	71	17	f(βn−1	f(βn−1	NUM
ejpam-6810	71	18	)	)	PUNCT
ejpam-6810	71	19	(	(	PUNCT
ejpam-6810	71	20	1	1	X
ejpam-6810	71	21	)	)	PUNCT
ejpam-6810	71	22	for	for	ADP
ejpam-6810	71	23	all	all	PRON
ejpam-6810	71	24	n	n	PRON
ejpam-6810	71	25	∈	∈	NOUN
ejpam-6810	71	26	n	n	NOUN
ejpam-6810	71	27	and	and	CCONJ
ejpam-6810	71	28	some	some	PRON
ejpam-6810	71	29	τ	τ	PROPN
ejpam-6810	71	30	>	>	X
ejpam-6810	71	31	0	0	PROPN
ejpam-6810	71	32	,	,	PUNCT
ejpam-6810	71	33	then	then	ADV
ejpam-6810	71	34	τ	τ	PROPN
ejpam-6810	71	35	+	+	CCONJ
ejpam-6810	71	36	f(snβn	f(snβn	NOUN
ejpam-6810	71	37	)	)	PUNCT
ejpam-6810	71	38	≤	≤	NUM
ejpam-6810	71	39	f(sn−2βn−1	f(sn−2βn−1	PROPN
ejpam-6810	71	40	)	)	PUNCT
ejpam-6810	71	41	.	.	PUNCT
ejpam-6810	72	1	(	(	PUNCT
ejpam-6810	72	2	2	2	X
ejpam-6810	72	3	)	)	PUNCT
ejpam-6810	72	4	throughout	throughout	ADP
ejpam-6810	72	5	the	the	DET
ejpam-6810	72	6	paper	paper	NOUN
ejpam-6810	72	7	,	,	PUNCT
ejpam-6810	72	8	f	f	PROPN
ejpam-6810	72	9	denotes	denote	VERB
ejpam-6810	72	10	the	the	DET
ejpam-6810	72	11	collection	collection	NOUN
ejpam-6810	72	12	of	of	ADP
ejpam-6810	72	13	mappings	mapping	NOUN
ejpam-6810	72	14	that	that	PRON
ejpam-6810	72	15	satisfy	satisfy	VERB
ejpam-6810	72	16	(	(	PUNCT
ejpam-6810	72	17	f−1	f−1	PROPN
ejpam-6810	72	18	)	)	PUNCT
ejpam-6810	72	19	to	to	ADP
ejpam-6810	72	20	(	(	PUNCT
ejpam-6810	72	21	f−4	f−4	NOUN
ejpam-6810	72	22	)	)	PUNCT
ejpam-6810	72	23	.	.	PUNCT
ejpam-6810	73	1	s.	s.	PROPN
ejpam-6810	73	2	batul	batul	PROPN
ejpam-6810	73	3	et	et	PROPN
ejpam-6810	73	4	al	al	PROPN
ejpam-6810	73	5	.	.	PUNCT
ejpam-6810	73	6	/	/	SYM
ejpam-6810	73	7	eur	eur	PROPN
ejpam-6810	73	8	.	.	PUNCT
ejpam-6810	74	1	j.	j.	PROPN
ejpam-6810	74	2	pure	pure	PROPN
ejpam-6810	74	3	appl	appl	PROPN
ejpam-6810	74	4	.	.	PROPN
ejpam-6810	74	5	math	math	PROPN
ejpam-6810	74	6	,	,	PUNCT
ejpam-6810	74	7	18	18	NUM
ejpam-6810	74	8	(	(	PUNCT
ejpam-6810	74	9	4	4	NUM
ejpam-6810	74	10	)	)	PUNCT
ejpam-6810	74	11	(	(	PUNCT
ejpam-6810	74	12	2025	2025	NUM
ejpam-6810	74	13	)	)	PUNCT
ejpam-6810	74	14	,	,	PUNCT
ejpam-6810	74	15	6810	6810	NUM
ejpam-6810	74	16	4	4	NUM
ejpam-6810	74	17	of	of	ADP
ejpam-6810	74	18	23	23	NUM
ejpam-6810	74	19	2	2	NUM
ejpam-6810	74	20	.	.	PUNCT
ejpam-6810	74	21	main	main	ADJ
ejpam-6810	74	22	results	result	NOUN
ejpam-6810	74	23	the	the	DET
ejpam-6810	74	24	following	follow	VERB
ejpam-6810	74	25	section	section	NOUN
ejpam-6810	74	26	is	be	AUX
ejpam-6810	74	27	concerned	concern	VERB
ejpam-6810	74	28	with	with	ADP
ejpam-6810	74	29	the	the	DET
ejpam-6810	74	30	principal	principal	ADJ
ejpam-6810	74	31	results	result	NOUN
ejpam-6810	74	32	of	of	ADP
ejpam-6810	74	33	this	this	DET
ejpam-6810	74	34	paper	paper	NOUN
ejpam-6810	74	35	.	.	PUNCT
ejpam-6810	75	1	definition	definition	NOUN
ejpam-6810	75	2	4	4	NUM
ejpam-6810	75	3	.	.	PUNCT
ejpam-6810	75	4	consider	consider	VERB
ejpam-6810	75	5	a	a	DET
ejpam-6810	75	6	b	b	NOUN
ejpam-6810	75	7	-	-	PUNCT
ejpam-6810	75	8	ms	ms	ADJ
ejpam-6810	75	9	(	(	PUNCT
ejpam-6810	75	10	u	u	NOUN
ejpam-6810	75	11	,	,	PUNCT
ejpam-6810	75	12	σb	σb	ADP
ejpam-6810	75	13	)	)	PUNCT
ejpam-6810	75	14	and	and	CCONJ
ejpam-6810	75	15	(	(	PUNCT
ejpam-6810	75	16	s	s	X
ejpam-6810	75	17	≥	≥	NOUN
ejpam-6810	75	18	1	1	NUM
ejpam-6810	75	19	)	)	PUNCT
ejpam-6810	75	20	with	with	ADP
ejpam-6810	75	21	at	at	ADV
ejpam-6810	75	22	least	least	ADV
ejpam-6810	75	23	three	three	NUM
ejpam-6810	75	24	elements	element	NOUN
ejpam-6810	75	25	,	,	PUNCT
ejpam-6810	75	26	i.e.	i.e.	X
ejpam-6810	75	27	,	,	PUNCT
ejpam-6810	75	28	|u|	|u|	X
ejpam-6810	75	29	≥	≥	NOUN
ejpam-6810	75	30	3	3	NUM
ejpam-6810	75	31	.	.	PUNCT
ejpam-6810	76	1	a	a	DET
ejpam-6810	76	2	mapping	mapping	NOUN
ejpam-6810	76	3	υ	υ	NOUN
ejpam-6810	76	4	:	:	PUNCT
ejpam-6810	76	5	u	u	NOUN
ejpam-6810	76	6	−→	−→	NOUN
ejpam-6810	76	7	u	u	NOUN
ejpam-6810	76	8	is	be	AUX
ejpam-6810	76	9	said	say	VERB
ejpam-6810	76	10	to	to	PART
ejpam-6810	76	11	be	be	AUX
ejpam-6810	76	12	a	a	DET
ejpam-6810	76	13	mcpt	mcpt	NOUN
ejpam-6810	76	14	embedded	embed	VERB
ejpam-6810	76	15	with	with	ADP
ejpam-6810	76	16	an	an	DET
ejpam-6810	76	17	f	f	NOUN
ejpam-6810	76	18	-	-	PUNCT
ejpam-6810	76	19	contraction	contraction	NOUN
ejpam-6810	76	20	on	on	ADP
ejpam-6810	76	21	u	u	PRON
ejpam-6810	76	22	if	if	SCONJ
ejpam-6810	76	23	there	there	PRON
ejpam-6810	76	24	exist	exist	VERB
ejpam-6810	76	25	f	f	PROPN
ejpam-6810	76	26	∈	∈	PROPN
ejpam-6810	76	27	f	f	PROPN
ejpam-6810	76	28	and	and	CCONJ
ejpam-6810	76	29	τ	τ	PROPN
ejpam-6810	76	30	>	>	X
ejpam-6810	76	31	0	0	NUM
ejpam-6810	76	32	such	such	ADJ
ejpam-6810	76	33	that	that	SCONJ
ejpam-6810	76	34	the	the	DET
ejpam-6810	76	35	following	follow	VERB
ejpam-6810	76	36	inequality	inequality	NOUN
ejpam-6810	76	37	τ	τ	PROPN
ejpam-6810	76	38	+	+	NUM
ejpam-6810	76	39	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	76	40	,	,	PUNCT
ejpam-6810	76	41	υξ	υξ	X
ejpam-6810	76	42	)	)	PUNCT
ejpam-6810	77	1	+	+	CCONJ
ejpam-6810	77	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	77	3	,	,	PUNCT
ejpam-6810	77	4	υζ	υζ	NOUN
ejpam-6810	77	5	)	)	PUNCT
ejpam-6810	77	6	+	+	CCONJ
ejpam-6810	77	7	σb(υη	σb(υη	PROPN
ejpam-6810	77	8	,	,	PUNCT
ejpam-6810	77	9	υζ	υζ	NOUN
ejpam-6810	77	10	)	)	PUNCT
ejpam-6810	77	11	)	)	PUNCT
ejpam-6810	77	12	≤	≤	NUM
ejpam-6810	77	13	f	f	X
ejpam-6810	77	14	(	(	PUNCT
ejpam-6810	77	15	1	1	NUM
ejpam-6810	77	16	s2	s2	NOUN
ejpam-6810	77	17	(	(	PUNCT
ejpam-6810	77	18	σb(η	σb(η	PROPN
ejpam-6810	77	19	,	,	PUNCT
ejpam-6810	77	20	ξ	ξ	NOUN
ejpam-6810	77	21	)	)	PUNCT
ejpam-6810	77	22	+	+	CCONJ
ejpam-6810	77	23	σb(ξ	σb(ξ	ADJ
ejpam-6810	77	24	,	,	PUNCT
ejpam-6810	77	25	ζ	ζ	NOUN
ejpam-6810	77	26	)	)	PUNCT
ejpam-6810	77	27	+	+	NUM
ejpam-6810	77	28	σb(η	σb(η	NUM
ejpam-6810	77	29	,	,	PUNCT
ejpam-6810	77	30	ζ	ζ	NOUN
ejpam-6810	77	31	)	)	PUNCT
ejpam-6810	77	32	)	)	PUNCT
ejpam-6810	77	33	)	)	PUNCT
ejpam-6810	77	34	,	,	PUNCT
ejpam-6810	77	35	(	(	PUNCT
ejpam-6810	77	36	3	3	X
ejpam-6810	77	37	)	)	PUNCT
ejpam-6810	77	38	holds	hold	VERB
ejpam-6810	77	39	for	for	ADP
ejpam-6810	77	40	all	all	DET
ejpam-6810	77	41	possible	possible	ADJ
ejpam-6810	77	42	combinations	combination	NOUN
ejpam-6810	77	43	of	of	ADP
ejpam-6810	77	44	three	three	NUM
ejpam-6810	77	45	pairwise	pairwise	NOUN
ejpam-6810	77	46	distinct	distinct	ADJ
ejpam-6810	77	47	points	point	NOUN
ejpam-6810	77	48	η	η	PROPN
ejpam-6810	77	49	,	,	PUNCT
ejpam-6810	77	50	ξ	ξ	PROPN
ejpam-6810	77	51	,	,	PUNCT
ejpam-6810	77	52	ζ	ζ	NOUN
ejpam-6810	77	53	in	in	ADP
ejpam-6810	77	54	u	u	PROPN
ejpam-6810	77	55	.	.	PUNCT
ejpam-6810	78	1	proposition	proposition	NOUN
ejpam-6810	78	2	1	1	NUM
ejpam-6810	78	3	.	.	PUNCT
ejpam-6810	79	1	let	let	AUX
ejpam-6810	79	2	(	(	PUNCT
ejpam-6810	79	3	u	u	NOUN
ejpam-6810	79	4	,	,	PUNCT
ejpam-6810	79	5	σb	σb	PROPN
ejpam-6810	79	6	)	)	PUNCT
ejpam-6810	79	7	be	be	AUX
ejpam-6810	79	8	a	a	DET
ejpam-6810	79	9	complete	complete	ADJ
ejpam-6810	79	10	b	b	NOUN
ejpam-6810	79	11	-	-	PUNCT
ejpam-6810	79	12	ms	ms	NOUN
ejpam-6810	79	13	and	and	CCONJ
ejpam-6810	79	14	υ	υ	NOUN
ejpam-6810	79	15	:	:	PUNCT
ejpam-6810	79	16	u	u	NOUN
ejpam-6810	79	17	−→	−→	NOUN
ejpam-6810	79	18	u	u	NOUN
ejpam-6810	79	19	be	be	VERB
ejpam-6810	79	20	a	a	DET
ejpam-6810	79	21	mcpt	mcpt	NOUN
ejpam-6810	79	22	embedded	embed	VERB
ejpam-6810	79	23	with	with	ADP
ejpam-6810	79	24	an	an	DET
ejpam-6810	79	25	f	f	NOUN
ejpam-6810	79	26	-	-	PUNCT
ejpam-6810	79	27	contraction	contraction	NOUN
ejpam-6810	79	28	.	.	PUNCT
ejpam-6810	80	1	then	then	ADV
ejpam-6810	80	2	υ	υ	PROPN
ejpam-6810	80	3	is	be	AUX
ejpam-6810	80	4	continuous	continuous	ADJ
ejpam-6810	80	5	.	.	PUNCT
ejpam-6810	81	1	proof	proof	NOUN
ejpam-6810	81	2	.	.	PUNCT
ejpam-6810	82	1	suppose	suppose	VERB
ejpam-6810	82	2	that	that	SCONJ
ejpam-6810	82	3	(	(	PUNCT
ejpam-6810	82	4	u	u	NOUN
ejpam-6810	82	5	,	,	PUNCT
ejpam-6810	82	6	σb	σb	PROPN
ejpam-6810	82	7	)	)	PUNCT
ejpam-6810	82	8	is	be	AUX
ejpam-6810	82	9	a	a	DET
ejpam-6810	82	10	b	b	NOUN
ejpam-6810	82	11	-	-	PUNCT
ejpam-6810	82	12	ms	ms	NOUN
ejpam-6810	82	13	with	with	ADP
ejpam-6810	82	14	|u|	|u|	PROPN
ejpam-6810	82	15	≥3	≥3	PROPN
ejpam-6810	82	16	,	,	PUNCT
ejpam-6810	82	17	υ	υ	NOUN
ejpam-6810	82	18	:	:	PUNCT
ejpam-6810	82	19	u	u	NOUN
ejpam-6810	82	20	−→	−→	NOUN
ejpam-6810	82	21	u	u	NOUN
ejpam-6810	82	22	is	be	AUX
ejpam-6810	82	23	a	a	DET
ejpam-6810	82	24	mcpt	mcpt	NOUN
ejpam-6810	82	25	embedded	embed	VERB
ejpam-6810	82	26	with	with	ADP
ejpam-6810	82	27	an	an	DET
ejpam-6810	82	28	f	f	NOUN
ejpam-6810	82	29	-	-	PUNCT
ejpam-6810	82	30	contraction	contraction	NOUN
ejpam-6810	82	31	on	on	ADP
ejpam-6810	82	32	u	u	NOUN
ejpam-6810	82	33	and	and	CCONJ
ejpam-6810	82	34	let	let	VERB
ejpam-6810	82	35	η0	η0	NOUN
ejpam-6810	82	36	be	be	AUX
ejpam-6810	82	37	an	an	DET
ejpam-6810	82	38	isolated	isolated	ADJ
ejpam-6810	82	39	point	point	NOUN
ejpam-6810	82	40	in	in	ADP
ejpam-6810	82	41	u	u	PROPN
ejpam-6810	82	42	.	.	PUNCT
ejpam-6810	83	1	then	then	ADV
ejpam-6810	83	2	,	,	PUNCT
ejpam-6810	83	3	clearly	clearly	ADV
ejpam-6810	83	4	,	,	PUNCT
ejpam-6810	83	5	υ	υ	PROPN
ejpam-6810	83	6	is	be	AUX
ejpam-6810	83	7	continuous	continuous	ADJ
ejpam-6810	83	8	at	at	ADP
ejpam-6810	83	9	η0	η0	NOUN
ejpam-6810	83	10	.	.	PUNCT
ejpam-6810	84	1	let	let	AUX
ejpam-6810	84	2	suppose	suppose	VERB
ejpam-6810	84	3	that	that	SCONJ
ejpam-6810	84	4	η0	η0	NOUN
ejpam-6810	84	5	be	be	VERB
ejpam-6810	84	6	a	a	DET
ejpam-6810	84	7	limit	limit	NOUN
ejpam-6810	84	8	point	point	NOUN
ejpam-6810	84	9	of	of	ADP
ejpam-6810	84	10	u	u	NOUN
ejpam-6810	84	11	.	.	PUNCT
ejpam-6810	85	1	now	now	ADV
ejpam-6810	85	2	,	,	PUNCT
ejpam-6810	85	3	we	we	PRON
ejpam-6810	85	4	show	show	VERB
ejpam-6810	85	5	that	that	SCONJ
ejpam-6810	85	6	for	for	ADP
ejpam-6810	85	7	every	every	DET
ejpam-6810	85	8	ε	ε	PROPN
ejpam-6810	85	9	>	>	X
ejpam-6810	85	10	0	0	PROPN
ejpam-6810	85	11	,	,	PUNCT
ejpam-6810	85	12	there	there	PRON
ejpam-6810	85	13	exists	exist	VERB
ejpam-6810	85	14	δ	δ	PROPN
ejpam-6810	85	15	>	>	X
ejpam-6810	85	16	0	0	NUM
ejpam-6810	85	17	such	such	ADJ
ejpam-6810	85	18	that	that	DET
ejpam-6810	85	19	σb(υη0,υη	σb(υη0,υη	NOUN
ejpam-6810	85	20	)	)	PUNCT
ejpam-6810	85	21	<	<	X
ejpam-6810	85	22	ε	ε	PROPN
ejpam-6810	85	23	whenever	whenever	SCONJ
ejpam-6810	85	24	σb(η0	σb(η0	X
ejpam-6810	85	25	,	,	PUNCT
ejpam-6810	85	26	η	η	NOUN
ejpam-6810	85	27	)	)	PUNCT
ejpam-6810	85	28	<	<	X
ejpam-6810	85	29	δ	δ	PROPN
ejpam-6810	85	30	.	.	PUNCT
ejpam-6810	86	1	since	since	SCONJ
ejpam-6810	86	2	η0	η0	NOUN
ejpam-6810	86	3	is	be	AUX
ejpam-6810	86	4	a	a	DET
ejpam-6810	86	5	limit	limit	NOUN
ejpam-6810	86	6	point	point	NOUN
ejpam-6810	86	7	,	,	PUNCT
ejpam-6810	86	8	for	for	ADP
ejpam-6810	86	9	every	every	DET
ejpam-6810	86	10	δ	δ	PROPN
ejpam-6810	86	11	>	>	X
ejpam-6810	86	12	0	0	PUNCT
ejpam-6810	86	13	there	there	PRON
ejpam-6810	86	14	exists	exist	VERB
ejpam-6810	86	15	ξ	ξ	PROPN
ejpam-6810	86	16	∈	∈	PROPN
ejpam-6810	86	17	u	u	NOUN
ejpam-6810	86	18	such	such	ADJ
ejpam-6810	86	19	that	that	PRON
ejpam-6810	86	20	σb(η0	σb(η0	NOUN
ejpam-6810	86	21	,	,	PUNCT
ejpam-6810	86	22	ξ	ξ	X
ejpam-6810	86	23	)	)	PUNCT
ejpam-6810	86	24	<	<	X
ejpam-6810	86	25	δ	δ	PROPN
ejpam-6810	86	26	.	.	PUNCT
ejpam-6810	87	1	using	use	VERB
ejpam-6810	87	2	(	(	PUNCT
ejpam-6810	87	3	3	3	NUM
ejpam-6810	87	4	)	)	PUNCT
ejpam-6810	87	5	,	,	PUNCT
ejpam-6810	87	6	we	we	PRON
ejpam-6810	87	7	have	have	VERB
ejpam-6810	87	8	f(σb(υη0,υη	f(σb(υη0,υη	NOUN
ejpam-6810	87	9	)	)	PUNCT
ejpam-6810	87	10	)	)	PUNCT
ejpam-6810	88	1	≤	≤	NUM
ejpam-6810	88	2	τ	τ	PUNCT
ejpam-6810	89	1	+	+	NUM
ejpam-6810	89	2	f(σb(υη0,υη	f(σb(υη0,υη	PROPN
ejpam-6810	89	3	)	)	PUNCT
ejpam-6810	89	4	)	)	PUNCT
ejpam-6810	89	5	,	,	PUNCT
ejpam-6810	89	6	≤	≤	NUM
ejpam-6810	89	7	τ	τ	PROPN
ejpam-6810	89	8	+	+	NUM
ejpam-6810	89	9	f(σb(υη0,υη	f(σb(υη0,υη	PROPN
ejpam-6810	89	10	)	)	PUNCT
ejpam-6810	89	11	+	+	SYM
ejpam-6810	89	12	σb(υη0,υξ	σb(υη0,υξ	NOUN
ejpam-6810	89	13	)	)	PUNCT
ejpam-6810	89	14	+	+	CCONJ
ejpam-6810	90	1	σb(υη	σb(υη	PROPN
ejpam-6810	90	2	,	,	PUNCT
ejpam-6810	90	3	υξ	υξ	NOUN
ejpam-6810	90	4	)	)	PUNCT
ejpam-6810	90	5	)	)	PUNCT
ejpam-6810	91	1	≤	≤	NUM
ejpam-6810	92	1	f	f	X
ejpam-6810	92	2	(	(	PUNCT
ejpam-6810	92	3	1	1	NUM
ejpam-6810	92	4	s2	s2	NOUN
ejpam-6810	92	5	(	(	PUNCT
ejpam-6810	92	6	σb(η0	σb(η0	PROPN
ejpam-6810	92	7	,	,	PUNCT
ejpam-6810	92	8	η	η	NOUN
ejpam-6810	92	9	)	)	PUNCT
ejpam-6810	92	10	+	+	CCONJ
ejpam-6810	92	11	σb(η0	σb(η0	X
ejpam-6810	92	12	,	,	PUNCT
ejpam-6810	92	13	ξ	ξ	NOUN
ejpam-6810	92	14	)	)	PUNCT
ejpam-6810	92	15	+	+	NUM
ejpam-6810	92	16	σb(η	σb(η	PROPN
ejpam-6810	92	17	,	,	PUNCT
ejpam-6810	92	18	ξ	ξ	NOUN
ejpam-6810	92	19	)	)	PUNCT
ejpam-6810	92	20	)	)	PUNCT
ejpam-6810	92	21	)	)	PUNCT
ejpam-6810	93	1	≤	≤	NUM
ejpam-6810	93	2	f	f	X
ejpam-6810	93	3	(	(	PUNCT
ejpam-6810	93	4	1	1	NUM
ejpam-6810	93	5	s2	s2	NOUN
ejpam-6810	93	6	(	(	PUNCT
ejpam-6810	93	7	σb(η0	σb(η0	PROPN
ejpam-6810	93	8	,	,	PUNCT
ejpam-6810	93	9	η	η	NOUN
ejpam-6810	93	10	)	)	PUNCT
ejpam-6810	93	11	+	+	CCONJ
ejpam-6810	93	12	σb(η0	σb(η0	X
ejpam-6810	93	13	,	,	PUNCT
ejpam-6810	93	14	ξ	ξ	NOUN
ejpam-6810	93	15	)	)	PUNCT
ejpam-6810	93	16	+	+	NUM
ejpam-6810	93	17	s(σb(η0	s(σb(η0	ADJ
ejpam-6810	93	18	,	,	PUNCT
ejpam-6810	93	19	η	η	NOUN
ejpam-6810	93	20	)	)	PUNCT
ejpam-6810	93	21	+	+	CCONJ
ejpam-6810	93	22	σb(η0	σb(η0	NOUN
ejpam-6810	93	23	,	,	PUNCT
ejpam-6810	93	24	ξ	ξ	NOUN
ejpam-6810	93	25	)	)	PUNCT
ejpam-6810	93	26	)	)	PUNCT
ejpam-6810	93	27	)	)	PUNCT
ejpam-6810	93	28	)	)	PUNCT
ejpam-6810	94	1	≤	≤	NUM
ejpam-6810	94	2	f	f	X
ejpam-6810	94	3	(	(	PUNCT
ejpam-6810	94	4	1	1	NUM
ejpam-6810	94	5	s2	s2	NOUN
ejpam-6810	94	6	(	(	PUNCT
ejpam-6810	94	7	1	1	NUM
ejpam-6810	94	8	+	+	CCONJ
ejpam-6810	94	9	s)(σb(η0	s)(σb(η0	PROPN
ejpam-6810	94	10	,	,	PUNCT
ejpam-6810	94	11	η	η	NOUN
ejpam-6810	94	12	)	)	PUNCT
ejpam-6810	94	13	+	+	CCONJ
ejpam-6810	94	14	σb(η0	σb(η0	NOUN
ejpam-6810	94	15	,	,	PUNCT
ejpam-6810	94	16	ξ	ξ	NOUN
ejpam-6810	94	17	)	)	PUNCT
ejpam-6810	94	18	)	)	PUNCT
ejpam-6810	94	19	)	)	PUNCT
ejpam-6810	95	1	<	<	X
ejpam-6810	95	2	f	f	X
ejpam-6810	95	3	(	(	PUNCT
ejpam-6810	95	4	1	1	NUM
ejpam-6810	95	5	s2	s2	NOUN
ejpam-6810	95	6	(	(	PUNCT
ejpam-6810	95	7	1	1	NUM
ejpam-6810	95	8	+	+	NUM
ejpam-6810	95	9	s)(δ	s)(δ	X
ejpam-6810	95	10	+	+	CCONJ
ejpam-6810	95	11	δ	δ	NOUN
ejpam-6810	95	12	)	)	PUNCT
ejpam-6810	95	13	)	)	PUNCT
ejpam-6810	96	1	=	=	PUNCT
ejpam-6810	96	2	f	f	PROPN
ejpam-6810	96	3	(	(	PUNCT
ejpam-6810	96	4	2	2	NUM
ejpam-6810	96	5	1	1	NUM
ejpam-6810	96	6	s2	s2	NOUN
ejpam-6810	96	7	(	(	PUNCT
ejpam-6810	96	8	1	1	NUM
ejpam-6810	96	9	+	+	CCONJ
ejpam-6810	96	10	s)δ	s)δ	ADJ
ejpam-6810	96	11	)	)	PUNCT
ejpam-6810	96	12	.	.	PUNCT
ejpam-6810	97	1	(	(	PUNCT
ejpam-6810	97	2	4	4	X
ejpam-6810	97	3	)	)	PUNCT
ejpam-6810	97	4	setting	set	VERB
ejpam-6810	97	5	δ	δ	NOUN
ejpam-6810	97	6	=	=	PUNCT
ejpam-6810	97	7	εs2	εs2	NOUN
ejpam-6810	97	8	2(1	2(1	NUM
ejpam-6810	97	9	+	+	SYM
ejpam-6810	97	10	s	s	X
ejpam-6810	97	11	)	)	PUNCT
ejpam-6810	97	12	,	,	PUNCT
ejpam-6810	97	13	then	then	ADV
ejpam-6810	97	14	equation	equation	NOUN
ejpam-6810	97	15	(	(	PUNCT
ejpam-6810	97	16	4	4	X
ejpam-6810	97	17	)	)	PUNCT
ejpam-6810	97	18	becomes	become	VERB
ejpam-6810	97	19	f(σb(υη0,υη	f(σb(υη0,υη	NOUN
ejpam-6810	97	20	)	)	PUNCT
ejpam-6810	97	21	)	)	PUNCT
ejpam-6810	97	22	<	<	X
ejpam-6810	97	23	f(ε	f(ε	NOUN
ejpam-6810	97	24	)	)	PUNCT
ejpam-6810	97	25	.	.	PUNCT
ejpam-6810	98	1	since	since	SCONJ
ejpam-6810	98	2	f	f	PROPN
ejpam-6810	98	3	in	in	ADP
ejpam-6810	98	4	increasing	increase	VERB
ejpam-6810	98	5	,	,	PUNCT
ejpam-6810	98	6	one	one	PRON
ejpam-6810	98	7	has	have	VERB
ejpam-6810	98	8	σb(υη0,υη	σb(υη0,υη	PROPN
ejpam-6810	98	9	)	)	PUNCT
ejpam-6810	98	10	)	)	PUNCT
ejpam-6810	99	1	<	<	X
ejpam-6810	99	2	ε	ε	PROPN
ejpam-6810	99	3	.	.	PUNCT
ejpam-6810	99	4	hence	hence	ADV
ejpam-6810	99	5	,	,	PUNCT
ejpam-6810	99	6	the	the	DET
ejpam-6810	99	7	mcpt	mcpt	NOUN
ejpam-6810	99	8	embedded	embed	VERB
ejpam-6810	99	9	with	with	ADP
ejpam-6810	99	10	an	an	DET
ejpam-6810	99	11	f	f	NOUN
ejpam-6810	99	12	-	-	PUNCT
ejpam-6810	99	13	contraction	contraction	NOUN
ejpam-6810	99	14	is	be	AUX
ejpam-6810	99	15	continuous	continuous	ADJ
ejpam-6810	99	16	.	.	PUNCT
ejpam-6810	100	1	s.	s.	PROPN
ejpam-6810	100	2	batul	batul	PROPN
ejpam-6810	100	3	et	et	PROPN
ejpam-6810	100	4	al	al	PROPN
ejpam-6810	100	5	.	.	PUNCT
ejpam-6810	100	6	/	/	SYM
ejpam-6810	100	7	eur	eur	PROPN
ejpam-6810	100	8	.	.	PUNCT
ejpam-6810	101	1	j.	j.	PROPN
ejpam-6810	101	2	pure	pure	PROPN
ejpam-6810	101	3	appl	appl	PROPN
ejpam-6810	101	4	.	.	PROPN
ejpam-6810	101	5	math	math	PROPN
ejpam-6810	101	6	,	,	PUNCT
ejpam-6810	101	7	18	18	NUM
ejpam-6810	101	8	(	(	PUNCT
ejpam-6810	101	9	4	4	NUM
ejpam-6810	101	10	)	)	PUNCT
ejpam-6810	101	11	(	(	PUNCT
ejpam-6810	101	12	2025	2025	NUM
ejpam-6810	101	13	)	)	PUNCT
ejpam-6810	101	14	,	,	PUNCT
ejpam-6810	101	15	6810	6810	NUM
ejpam-6810	101	16	5	5	NUM
ejpam-6810	101	17	of	of	ADP
ejpam-6810	101	18	23	23	NUM
ejpam-6810	101	19	definition	definition	NOUN
ejpam-6810	101	20	5	5	NUM
ejpam-6810	101	21	.	.	PUNCT
ejpam-6810	101	22	consider	consider	VERB
ejpam-6810	101	23	a	a	DET
ejpam-6810	101	24	mapping	mapping	NOUN
ejpam-6810	101	25	υ	υ	NOUN
ejpam-6810	101	26	on	on	ADP
ejpam-6810	101	27	the	the	DET
ejpam-6810	101	28	b	b	NOUN
ejpam-6810	101	29	-	-	PUNCT
ejpam-6810	101	30	ms	ms	NOUN
ejpam-6810	101	31	u	u	PROPN
ejpam-6810	101	32	.	.	PUNCT
ejpam-6810	102	1	a	a	DET
ejpam-6810	102	2	point	point	NOUN
ejpam-6810	102	3	η	η	PROPN
ejpam-6810	102	4	∈	∈	PROPN
ejpam-6810	102	5	u	u	NOUN
ejpam-6810	102	6	is	be	AUX
ejpam-6810	102	7	said	say	VERB
ejpam-6810	102	8	to	to	PART
ejpam-6810	102	9	be	be	AUX
ejpam-6810	102	10	a	a	DET
ejpam-6810	102	11	periodic	periodic	ADJ
ejpam-6810	102	12	point	point	NOUN
ejpam-6810	102	13	of	of	ADP
ejpam-6810	102	14	period	period	NOUN
ejpam-6810	102	15	n	n	CCONJ
ejpam-6810	102	16	if	if	SCONJ
ejpam-6810	102	17	υn(η	υn(η	NUM
ejpam-6810	102	18	)	)	PUNCT
ejpam-6810	102	19	=	=	SYM
ejpam-6810	102	20	η	η	PROPN
ejpam-6810	102	21	,	,	PUNCT
ejpam-6810	102	22	where	where	SCONJ
ejpam-6810	102	23	n	n	PRON
ejpam-6810	102	24	is	be	AUX
ejpam-6810	102	25	the	the	DET
ejpam-6810	102	26	least	least	ADV
ejpam-6810	102	27	positive	positive	ADJ
ejpam-6810	102	28	integer	integer	NOUN
ejpam-6810	102	29	for	for	ADP
ejpam-6810	102	30	which	which	PRON
ejpam-6810	102	31	υn(η	υn(η	PUNCT
ejpam-6810	102	32	)	)	PUNCT
ejpam-6810	102	33	=	=	SYM
ejpam-6810	102	34	η	η	PROPN
ejpam-6810	102	35	,	,	PUNCT
ejpam-6810	102	36	such	such	DET
ejpam-6810	102	37	a	a	DET
ejpam-6810	102	38	positive	positive	ADJ
ejpam-6810	102	39	integer	integer	NOUN
ejpam-6810	102	40	n	n	NUM
ejpam-6810	102	41	is	be	AUX
ejpam-6810	102	42	called	call	VERB
ejpam-6810	102	43	the	the	DET
ejpam-6810	102	44	prime	prime	ADJ
ejpam-6810	102	45	period	period	NOUN
ejpam-6810	102	46	of	of	ADP
ejpam-6810	102	47	η	η	PROPN
ejpam-6810	102	48	.	.	PROPN
ejpam-6810	102	49	theorem	theorem	PROPN
ejpam-6810	102	50	1	1	X
ejpam-6810	102	51	.	.	X
ejpam-6810	102	52	consider	consider	VERB
ejpam-6810	102	53	a	a	DET
ejpam-6810	102	54	complete	complete	ADJ
ejpam-6810	102	55	b	b	NOUN
ejpam-6810	102	56	-	-	PUNCT
ejpam-6810	102	57	ms	ms	ADJ
ejpam-6810	102	58	(	(	PUNCT
ejpam-6810	102	59	u	u	NOUN
ejpam-6810	102	60	,	,	PUNCT
ejpam-6810	102	61	σb	σb	ADP
ejpam-6810	102	62	)	)	PUNCT
ejpam-6810	102	63	with	with	ADP
ejpam-6810	102	64	at	at	ADV
ejpam-6810	102	65	least	least	ADV
ejpam-6810	102	66	three	three	NUM
ejpam-6810	102	67	elements	element	NOUN
ejpam-6810	102	68	,	,	PUNCT
ejpam-6810	102	69	i.e.	i.e.	X
ejpam-6810	102	70	,	,	PUNCT
ejpam-6810	102	71	|u|	|u|	X
ejpam-6810	102	72	≥	≥	NOUN
ejpam-6810	102	73	3	3	X
ejpam-6810	102	74	.	.	PUNCT
ejpam-6810	102	75	assume	assume	VERB
ejpam-6810	102	76	that	that	SCONJ
ejpam-6810	102	77	the	the	DET
ejpam-6810	102	78	mapping	mapping	NOUN
ejpam-6810	102	79	υ	υ	NOUN
ejpam-6810	102	80	:	:	PUNCT
ejpam-6810	102	81	u	u	NOUN
ejpam-6810	102	82	−→	−→	NOUN
ejpam-6810	102	83	u	u	NOUN
ejpam-6810	102	84	satisfies	satisfy	VERB
ejpam-6810	102	85	a	a	DET
ejpam-6810	102	86	mcpt	mcpt	NOUN
ejpam-6810	102	87	embedded	embed	VERB
ejpam-6810	102	88	with	with	ADP
ejpam-6810	102	89	f	f	PROPN
ejpam-6810	102	90	-	-	PUNCT
ejpam-6810	102	91	contraction	contraction	NOUN
ejpam-6810	102	92	condition	condition	NOUN
ejpam-6810	102	93	on	on	ADP
ejpam-6810	102	94	u	u	PROPN
ejpam-6810	102	95	.	.	PUNCT
ejpam-6810	103	1	then	then	ADV
ejpam-6810	103	2	the	the	DET
ejpam-6810	103	3	following	follow	VERB
ejpam-6810	103	4	statements	statement	NOUN
ejpam-6810	103	5	are	be	AUX
ejpam-6810	103	6	true	true	ADJ
ejpam-6810	103	7	:	:	PUNCT
ejpam-6810	103	8	i	i	X
ejpam-6810	103	9	)	)	PUNCT
ejpam-6810	103	10	the	the	DET
ejpam-6810	103	11	mapping	mapping	NOUN
ejpam-6810	103	12	υ	υ	NOUN
ejpam-6810	103	13	has	have	VERB
ejpam-6810	103	14	a	a	DET
ejpam-6810	103	15	fp	fp	NOUN
ejpam-6810	103	16	if	if	SCONJ
ejpam-6810	103	17	and	and	CCONJ
ejpam-6810	103	18	only	only	ADV
ejpam-6810	103	19	if	if	SCONJ
ejpam-6810	103	20	it	it	PRON
ejpam-6810	103	21	does	do	AUX
ejpam-6810	103	22	not	not	PART
ejpam-6810	103	23	have	have	VERB
ejpam-6810	103	24	periodic	periodic	ADJ
ejpam-6810	103	25	points	point	NOUN
ejpam-6810	103	26	with	with	ADP
ejpam-6810	103	27	a	a	DET
ejpam-6810	103	28	prime	prime	ADJ
ejpam-6810	103	29	period	period	NOUN
ejpam-6810	103	30	2	2	NUM
ejpam-6810	103	31	.	.	X
ejpam-6810	103	32	ii	ii	PROPN
ejpam-6810	103	33	)	)	PUNCT
ejpam-6810	103	34	υ	υ	PROPN
ejpam-6810	103	35	possesses	possesse	NOUN
ejpam-6810	103	36	at	at	ADP
ejpam-6810	103	37	most	most	ADV
ejpam-6810	103	38	two	two	NUM
ejpam-6810	103	39	fps	fps	PROPN
ejpam-6810	103	40	.	.	PUNCT
ejpam-6810	104	1	proof	proof	NOUN
ejpam-6810	104	2	.	.	PUNCT
ejpam-6810	105	1	suppose	suppose	VERB
ejpam-6810	105	2	that	that	SCONJ
ejpam-6810	105	3	no	no	DET
ejpam-6810	105	4	point	point	NOUN
ejpam-6810	105	5	is	be	AUX
ejpam-6810	105	6	periodic	periodic	ADJ
ejpam-6810	105	7	with	with	ADP
ejpam-6810	105	8	prime	prime	ADJ
ejpam-6810	105	9	period	period	NOUN
ejpam-6810	105	10	2	2	NUM
ejpam-6810	105	11	under	under	ADP
ejpam-6810	105	12	the	the	DET
ejpam-6810	105	13	mapping	mapping	NOUN
ejpam-6810	105	14	υ	υ	NOUN
ejpam-6810	105	15	.	.	PUNCT
ejpam-6810	106	1	our	our	PRON
ejpam-6810	106	2	objective	objective	NOUN
ejpam-6810	106	3	is	be	AUX
ejpam-6810	106	4	to	to	PART
ejpam-6810	106	5	show	show	VERB
ejpam-6810	106	6	that	that	SCONJ
ejpam-6810	106	7	υ	υ	PROPN
ejpam-6810	106	8	has	have	VERB
ejpam-6810	106	9	a	a	DET
ejpam-6810	106	10	fp	fp	X
ejpam-6810	106	11	.	.	PUNCT
ejpam-6810	107	1	let	let	VERB
ejpam-6810	107	2	η0	η0	PROPN
ejpam-6810	107	3	∈	∈	PROPN
ejpam-6810	107	4	υ	υ	NOUN
ejpam-6810	108	1	and	and	CCONJ
ejpam-6810	108	2	,	,	PUNCT
ejpam-6810	108	3	υη0	υη0	X
ejpam-6810	108	4	=	=	PUNCT
ejpam-6810	108	5	η1,υη1	η1,υη1	PROPN
ejpam-6810	108	6	=	=	SYM
ejpam-6810	108	7	η2	η2	PROPN
ejpam-6810	108	8	,	,	PUNCT
ejpam-6810	108	9	·	·	PUNCT
ejpam-6810	108	10	·	·	PUNCT
ejpam-6810	108	11	·	·	PUNCT
ejpam-6810	108	12	,	,	PUNCT
ejpam-6810	108	13	υηn	υηn	NOUN
ejpam-6810	108	14	=	=	SYM
ejpam-6810	108	15	ηn+1	ηn+1	PROPN
ejpam-6810	108	16	,	,	PUNCT
ejpam-6810	108	17	·	·	PUNCT
ejpam-6810	108	18	·	·	PUNCT
ejpam-6810	108	19	·	·	PUNCT
ejpam-6810	108	20	.	.	PUNCT
ejpam-6810	109	1	assume	assume	VERB
ejpam-6810	109	2	that	that	SCONJ
ejpam-6810	109	3	,	,	PUNCT
ejpam-6810	109	4	for	for	ADP
ejpam-6810	109	5	all	all	DET
ejpam-6810	109	6	i	i	NOUN
ejpam-6810	109	7	=	=	NOUN
ejpam-6810	109	8	0	0	NUM
ejpam-6810	109	9	,	,	PUNCT
ejpam-6810	109	10	1	1	NUM
ejpam-6810	109	11	,	,	PUNCT
ejpam-6810	109	12	2	2	NUM
ejpam-6810	109	13	,	,	PUNCT
ejpam-6810	109	14	·	·	PUNCT
ejpam-6810	109	15	·	·	PUNCT
ejpam-6810	109	16	·	·	PUNCT
ejpam-6810	109	17	,	,	PUNCT
ejpam-6810	109	18	there	there	PRON
ejpam-6810	109	19	are	be	VERB
ejpam-6810	109	20	no	no	DET
ejpam-6810	109	21	fp	fp	NOUN
ejpam-6810	109	22	of	of	ADP
ejpam-6810	109	23	the	the	DET
ejpam-6810	109	24	mapping	mapping	NOUN
ejpam-6810	109	25	υ	υ	NOUN
ejpam-6810	109	26	among	among	ADP
ejpam-6810	109	27	the	the	DET
ejpam-6810	109	28	points	point	NOUN
ejpam-6810	109	29	ηi	ηi	NOUN
ejpam-6810	109	30	.	.	PUNCT
ejpam-6810	110	1	our	our	PRON
ejpam-6810	110	2	goal	goal	NOUN
ejpam-6810	110	3	is	be	AUX
ejpam-6810	110	4	to	to	PART
ejpam-6810	110	5	demonstrate	demonstrate	VERB
ejpam-6810	110	6	the	the	DET
ejpam-6810	110	7	distinctness	distinctness	NOUN
ejpam-6810	110	8	of	of	ADP
ejpam-6810	110	9	every	every	DET
ejpam-6810	110	10	point	point	NOUN
ejpam-6810	110	11	ηi	ηi	NOUN
ejpam-6810	110	12	.	.	PUNCT
ejpam-6810	111	1	we	we	PRON
ejpam-6810	111	2	have	have	VERB
ejpam-6810	111	3	ηi	ηi	PROPN
ejpam-6810	111	4	6=	6=	NUM
ejpam-6810	111	5	ηi+1	ηi+1	NOUN
ejpam-6810	111	6	=	=	PUNCT
ejpam-6810	111	7	υηi	υηi	VERB
ejpam-6810	111	8	because	because	SCONJ
ejpam-6810	111	9	ηi	ηi	PROPN
ejpam-6810	111	10	is	be	AUX
ejpam-6810	111	11	not	not	PART
ejpam-6810	111	12	a	a	DET
ejpam-6810	111	13	fp	fp	NOUN
ejpam-6810	111	14	.	.	PUNCT
ejpam-6810	112	1	we	we	PRON
ejpam-6810	112	2	also	also	ADV
ejpam-6810	112	3	know	know	VERB
ejpam-6810	112	4	that	that	SCONJ
ejpam-6810	112	5	ηi+2	ηi+2	VERB
ejpam-6810	112	6	=	=	SYM
ejpam-6810	112	7	υ(υ(ηi	υ(υ(ηi	PROPN
ejpam-6810	112	8	)	)	PUNCT
ejpam-6810	112	9	)	)	PUNCT
ejpam-6810	113	1	6=	6=	NUM
ejpam-6810	113	2	ηi	ηi	NOUN
ejpam-6810	113	3	since	since	SCONJ
ejpam-6810	113	4	υ	υ	PRON
ejpam-6810	113	5	lacks	lack	VERB
ejpam-6810	113	6	any	any	DET
ejpam-6810	113	7	periodic	periodic	ADJ
ejpam-6810	113	8	points	point	NOUN
ejpam-6810	113	9	of	of	ADP
ejpam-6810	113	10	prime	prime	ADJ
ejpam-6810	113	11	period	period	NOUN
ejpam-6810	113	12	2	2	NUM
ejpam-6810	113	13	.	.	PUNCT
ejpam-6810	114	1	moreover	moreover	ADV
ejpam-6810	114	2	,	,	PUNCT
ejpam-6810	114	3	ηi+1	ηi+1	PROPN
ejpam-6810	114	4	6=	6=	ADP
ejpam-6810	114	5	ηi+2	ηi+2	NOUN
ejpam-6810	114	6	=	=	SYM
ejpam-6810	114	7	υηi+1	υηi+1	ADP
ejpam-6810	114	8	since	since	SCONJ
ejpam-6810	114	9	ηi+1	ηi+1	NUM
ejpam-6810	114	10	is	be	AUX
ejpam-6810	114	11	not	not	PART
ejpam-6810	114	12	a	a	DET
ejpam-6810	114	13	fp	fp	X
ejpam-6810	114	14	.	.	PROPN
ejpam-6810	115	1	as	as	ADP
ejpam-6810	115	2	a	a	DET
ejpam-6810	115	3	result	result	NOUN
ejpam-6810	115	4	,	,	PUNCT
ejpam-6810	115	5	pairwise	pairwise	NOUN
ejpam-6810	115	6	distinct	distinct	ADJ
ejpam-6810	115	7	points	point	NOUN
ejpam-6810	115	8	are	be	AUX
ejpam-6810	115	9	ηi	ηi	NOUN
ejpam-6810	115	10	,	,	PUNCT
ejpam-6810	115	11	ηi+1	ηi+1	PROPN
ejpam-6810	115	12	,	,	PUNCT
ejpam-6810	115	13	and	and	CCONJ
ejpam-6810	115	14	ηi+2	ηi+2	NOUN
ejpam-6810	115	15	.	.	PUNCT
ejpam-6810	116	1	furthermore	furthermore	ADV
ejpam-6810	116	2	,	,	PUNCT
ejpam-6810	116	3	suppose	suppose	VERB
ejpam-6810	116	4	that	that	SCONJ
ejpam-6810	116	5	γ0	γ0	NOUN
ejpam-6810	116	6	=	=	SYM
ejpam-6810	116	7	σb(η0	σb(η0	NOUN
ejpam-6810	116	8	,	,	PUNCT
ejpam-6810	116	9	η1	η1	NOUN
ejpam-6810	116	10	)	)	PUNCT
ejpam-6810	116	11	+	+	CCONJ
ejpam-6810	116	12	σb(η1	σb(η1	NOUN
ejpam-6810	116	13	,	,	PUNCT
ejpam-6810	116	14	η2	η2	X
ejpam-6810	116	15	)	)	PUNCT
ejpam-6810	116	16	+	+	CCONJ
ejpam-6810	116	17	σb(η2	σb(η2	NOUN
ejpam-6810	116	18	,	,	PUNCT
ejpam-6810	116	19	η0	η0	NOUN
ejpam-6810	116	20	)	)	PUNCT
ejpam-6810	116	21	,	,	PUNCT
ejpam-6810	116	22	γ1	γ1	PROPN
ejpam-6810	116	23	=	=	SYM
ejpam-6810	116	24	σb(η1	σb(η1	PROPN
ejpam-6810	116	25	,	,	PUNCT
ejpam-6810	116	26	η2	η2	X
ejpam-6810	116	27	)	)	PUNCT
ejpam-6810	116	28	+	+	CCONJ
ejpam-6810	116	29	σb(η2	σb(η2	NOUN
ejpam-6810	116	30	,	,	PUNCT
ejpam-6810	116	31	η3	η3	NOUN
ejpam-6810	116	32	)	)	PUNCT
ejpam-6810	116	33	+	+	CCONJ
ejpam-6810	116	34	σb(η3	σb(η3	NOUN
ejpam-6810	116	35	,	,	PUNCT
ejpam-6810	116	36	η1	η1	NOUN
ejpam-6810	116	37	)	)	PUNCT
ejpam-6810	116	38	,	,	PUNCT
ejpam-6810	116	39	...	...	PUNCT
ejpam-6810	116	40	γn	γn	X
ejpam-6810	116	41	=	=	SYM
ejpam-6810	116	42	σb(ηn	σb(ηn	PROPN
ejpam-6810	116	43	,	,	PUNCT
ejpam-6810	116	44	ηn+1	ηn+1	NUM
ejpam-6810	116	45	)	)	PUNCT
ejpam-6810	116	46	+	+	X
ejpam-6810	116	47	σb(ηn+1	σb(ηn+1	ADJ
ejpam-6810	116	48	,	,	PUNCT
ejpam-6810	116	49	ηn+2	ηn+2	ADV
ejpam-6810	116	50	)	)	PUNCT
ejpam-6810	116	51	+	+	CCONJ
ejpam-6810	117	1	σb(ηn+2	σb(ηn+2	PROPN
ejpam-6810	117	2	,	,	PUNCT
ejpam-6810	117	3	ηn	ηn	ADJ
ejpam-6810	117	4	)	)	PUNCT
ejpam-6810	117	5	,	,	PUNCT
ejpam-6810	117	6	...	...	PUNCT
ejpam-6810	117	7	applying	apply	VERB
ejpam-6810	117	8	the	the	DET
ejpam-6810	117	9	contraction	contraction	NOUN
ejpam-6810	117	10	condition	condition	NOUN
ejpam-6810	117	11	to	to	ADP
ejpam-6810	117	12	the	the	DET
ejpam-6810	117	13	pairwise	pairwise	NOUN
ejpam-6810	117	14	distinct	distinct	ADJ
ejpam-6810	117	15	points	point	NOUN
ejpam-6810	117	16	ηi	ηi	PROPN
ejpam-6810	117	17	,	,	PUNCT
ejpam-6810	117	18	ηi+1	ηi+1	PROPN
ejpam-6810	117	19	,	,	PUNCT
ejpam-6810	117	20	and	and	CCONJ
ejpam-6810	117	21	ηi+2	ηi+2	NUM
ejpam-6810	117	22	,	,	PUNCT
ejpam-6810	117	23	we	we	PRON
ejpam-6810	117	24	obtain	obtain	VERB
ejpam-6810	117	25	f	f	PROPN
ejpam-6810	117	26	(	(	PUNCT
ejpam-6810	117	27	σb(η1	σb(η1	PROPN
ejpam-6810	117	28	,	,	PUNCT
ejpam-6810	117	29	η2	η2	X
ejpam-6810	117	30	)	)	PUNCT
ejpam-6810	117	31	+	+	CCONJ
ejpam-6810	117	32	σb(η2	σb(η2	NOUN
ejpam-6810	117	33	,	,	PUNCT
ejpam-6810	117	34	η3	η3	NOUN
ejpam-6810	117	35	)	)	PUNCT
ejpam-6810	117	36	+	+	CCONJ
ejpam-6810	117	37	σb(η1	σb(η1	PROPN
ejpam-6810	117	38	,	,	PUNCT
ejpam-6810	117	39	η3	η3	NOUN
ejpam-6810	117	40	)	)	PUNCT
ejpam-6810	117	41	)	)	PUNCT
ejpam-6810	118	1	=	=	SYM
ejpam-6810	118	2	f	f	X
ejpam-6810	118	3	(	(	PUNCT
ejpam-6810	118	4	σb(υη0,υη1	σb(υη0,υη1	PROPN
ejpam-6810	118	5	)	)	PUNCT
ejpam-6810	118	6	+	+	CCONJ
ejpam-6810	119	1	σb(υη1,υη2	σb(υη1,υη2	PROPN
ejpam-6810	119	2	)	)	PUNCT
ejpam-6810	119	3	+	+	NUM
ejpam-6810	119	4	σb(υη0,υη2	σb(υη0,υη2	PROPN
ejpam-6810	119	5	)	)	PUNCT
ejpam-6810	119	6	)	)	PUNCT
ejpam-6810	119	7	,	,	PUNCT
ejpam-6810	119	8	≤	≤	NUM
ejpam-6810	119	9	f	f	X
ejpam-6810	119	10	(	(	PUNCT
ejpam-6810	119	11	1	1	NUM
ejpam-6810	119	12	s2	s2	NOUN
ejpam-6810	119	13	(	(	PUNCT
ejpam-6810	119	14	(	(	PUNCT
ejpam-6810	119	15	σb(η0	σb(η0	X
ejpam-6810	119	16	,	,	PUNCT
ejpam-6810	119	17	η1	η1	NOUN
ejpam-6810	119	18	)	)	PUNCT
ejpam-6810	119	19	+	+	CCONJ
ejpam-6810	119	20	σb(η1	σb(η1	NOUN
ejpam-6810	119	21	,	,	PUNCT
ejpam-6810	119	22	η2	η2	X
ejpam-6810	119	23	)	)	PUNCT
ejpam-6810	119	24	+	+	CCONJ
ejpam-6810	119	25	σb(η0	σb(η0	NOUN
ejpam-6810	119	26	,	,	PUNCT
ejpam-6810	119	27	η2	η2	NOUN
ejpam-6810	119	28	)	)	PUNCT
ejpam-6810	119	29	)	)	PUNCT
ejpam-6810	119	30	)	)	PUNCT
ejpam-6810	120	1	−	−	PROPN
ejpam-6810	120	2	τ	τ	PROPN
ejpam-6810	120	3	,	,	PUNCT
ejpam-6810	120	4	f(γ1	f(γ1	X
ejpam-6810	120	5	)	)	PUNCT
ejpam-6810	120	6	≤	≤	NUM
ejpam-6810	120	7	f	f	X
ejpam-6810	120	8	(	(	PUNCT
ejpam-6810	120	9	1	1	NUM
ejpam-6810	120	10	s2	s2	NOUN
ejpam-6810	120	11	(	(	PUNCT
ejpam-6810	120	12	γ0	γ0	PROPN
ejpam-6810	120	13	)	)	PUNCT
ejpam-6810	120	14	)	)	PUNCT
ejpam-6810	120	15	−	−	PROPN
ejpam-6810	121	1	τ	τ	X
ejpam-6810	121	2	.	.	PUNCT
ejpam-6810	122	1	since	since	SCONJ
ejpam-6810	122	2	f	f	PROPN
ejpam-6810	122	3	is	be	AUX
ejpam-6810	122	4	increasing	increase	VERB
ejpam-6810	122	5	,	,	PUNCT
ejpam-6810	122	6	we	we	PRON
ejpam-6810	122	7	can	can	AUX
ejpam-6810	122	8	write	write	VERB
ejpam-6810	122	9	above	above	ADP
ejpam-6810	122	10	equation	equation	NOUN
ejpam-6810	122	11	as	as	ADP
ejpam-6810	122	12	f(s2γ1	f(s2γ1	NOUN
ejpam-6810	122	13	)	)	PUNCT
ejpam-6810	122	14	≤	≤	NOUN
ejpam-6810	123	1	f(γ0)−	f(γ0)−	PROPN
ejpam-6810	123	2	τ	τ	PROPN
ejpam-6810	123	3	.	.	PUNCT
ejpam-6810	124	1	similarly	similarly	ADV
ejpam-6810	124	2	,	,	PUNCT
ejpam-6810	124	3	f(s2γ2	f(s2γ2	NOUN
ejpam-6810	124	4	)	)	PUNCT
ejpam-6810	124	5	≤	≤	PUNCT
ejpam-6810	124	6	f(γ1)−	f(γ1)−	PROPN
ejpam-6810	124	7	τ	τ	PROPN
ejpam-6810	124	8	,	,	PUNCT
ejpam-6810	124	9	f(s2γ3	f(s2γ3	NOUN
ejpam-6810	124	10	)	)	PUNCT
ejpam-6810	124	11	≤	≤	NOUN
ejpam-6810	124	12	f(γ2)−	f(γ2)−	VERB
ejpam-6810	124	13	τ	τ	PROPN
ejpam-6810	124	14	,	,	PUNCT
ejpam-6810	124	15	...	...	PUNCT
ejpam-6810	124	16	f(s2γn	f(s2γn	NUM
ejpam-6810	124	17	)	)	PUNCT
ejpam-6810	124	18	≤	≤	PUNCT
ejpam-6810	125	1	f(γn−1)−	f(γn−1)−	PROPN
ejpam-6810	125	2	τ	τ	PROPN
ejpam-6810	125	3	,	,	PUNCT
ejpam-6810	125	4	s.	s.	PROPN
ejpam-6810	125	5	batul	batul	PROPN
ejpam-6810	125	6	et	et	PROPN
ejpam-6810	125	7	al	al	PROPN
ejpam-6810	125	8	.	.	PUNCT
ejpam-6810	125	9	/	/	SYM
ejpam-6810	125	10	eur	eur	PROPN
ejpam-6810	125	11	.	.	PUNCT
ejpam-6810	126	1	j.	j.	PROPN
ejpam-6810	126	2	pure	pure	PROPN
ejpam-6810	126	3	appl	appl	PROPN
ejpam-6810	126	4	.	.	PROPN
ejpam-6810	126	5	math	math	PROPN
ejpam-6810	126	6	,	,	PUNCT
ejpam-6810	126	7	18	18	NUM
ejpam-6810	126	8	(	(	PUNCT
ejpam-6810	126	9	4	4	NUM
ejpam-6810	126	10	)	)	PUNCT
ejpam-6810	126	11	(	(	PUNCT
ejpam-6810	126	12	2025	2025	NUM
ejpam-6810	126	13	)	)	PUNCT
ejpam-6810	126	14	,	,	PUNCT
ejpam-6810	126	15	6810	6810	NUM
ejpam-6810	126	16	6	6	NUM
ejpam-6810	126	17	of	of	ADP
ejpam-6810	126	18	23	23	NUM
ejpam-6810	126	19	f(s2γn+1	f(s2γn+1	NUM
ejpam-6810	126	20	)	)	PUNCT
ejpam-6810	126	21	≤	≤	NOUN
ejpam-6810	126	22	f(γn)−	f(γn)−	NOUN
ejpam-6810	126	23	τ	τ	X
ejpam-6810	126	24	.	.	PUNCT
ejpam-6810	127	1	(	(	PUNCT
ejpam-6810	127	2	5	5	NUM
ejpam-6810	127	3	)	)	PUNCT
ejpam-6810	127	4	since	since	SCONJ
ejpam-6810	127	5	s	s	PRON
ejpam-6810	127	6	≥	≥	NUM
ejpam-6810	127	7	1	1	NUM
ejpam-6810	127	8	,	,	PUNCT
ejpam-6810	127	9	one	one	PRON
ejpam-6810	127	10	has	have	VERB
ejpam-6810	127	11	γ0	γ0	PROPN
ejpam-6810	127	12	>	>	X
ejpam-6810	127	13	γ1	γ1	PROPN
ejpam-6810	127	14	>	>	X
ejpam-6810	127	15	·	·	PUNCT
ejpam-6810	127	16	·	·	PUNCT
ejpam-6810	127	17	·	·	PUNCT
ejpam-6810	128	1	>	>	X
ejpam-6810	128	2	γn	γn	ADP
ejpam-6810	128	3	>	>	X
ejpam-6810	128	4	·	·	PUNCT
ejpam-6810	128	5	·	·	PUNCT
ejpam-6810	128	6	·	·	PUNCT
ejpam-6810	128	7	.	.	PUNCT
ejpam-6810	129	1	(	(	PUNCT
ejpam-6810	129	2	6	6	X
ejpam-6810	129	3	)	)	PUNCT
ejpam-6810	129	4	assume	assume	VERB
ejpam-6810	129	5	that	that	SCONJ
ejpam-6810	129	6	j	j	PROPN
ejpam-6810	129	7	≥	≥	NUM
ejpam-6810	129	8	3	3	NUM
ejpam-6810	129	9	is	be	AUX
ejpam-6810	129	10	the	the	DET
ejpam-6810	129	11	smallest	small	ADJ
ejpam-6810	129	12	natural	natural	ADJ
ejpam-6810	129	13	number	number	NOUN
ejpam-6810	129	14	such	such	ADJ
ejpam-6810	129	15	that	that	PRON
ejpam-6810	129	16	ηj	ηj	NOUN
ejpam-6810	129	17	=	=	PUNCT
ejpam-6810	129	18	ηi	ηi	PROPN
ejpam-6810	129	19	for	for	ADP
ejpam-6810	129	20	some	some	PRON
ejpam-6810	129	21	i	i	PRON
ejpam-6810	129	22	satisfying	satisfy	VERB
ejpam-6810	130	1	0	0	NUM
ejpam-6810	130	2	≤	≤	NUM
ejpam-6810	131	1	i	i	PRON
ejpam-6810	131	2	<	<	X
ejpam-6810	131	3	j	j	PROPN
ejpam-6810	132	1	−	−	NOUN
ejpam-6810	132	2	2	2	NUM
ejpam-6810	132	3	.	.	PUNCT
ejpam-6810	133	1	then	then	ADV
ejpam-6810	133	2	,	,	PUNCT
ejpam-6810	133	3	we	we	PRON
ejpam-6810	133	4	have	have	VERB
ejpam-6810	133	5	ηj+1	ηj+1	PRON
ejpam-6810	133	6	=	=	SYM
ejpam-6810	133	7	ηi+1	ηi+1	NUM
ejpam-6810	133	8	and	and	CCONJ
ejpam-6810	133	9	ηj+2	ηj+2	NOUN
ejpam-6810	133	10	=	=	SYM
ejpam-6810	133	11	ηi+2	ηi+2	PROPN
ejpam-6810	133	12	.	.	PUNCT
ejpam-6810	134	1	consequently	consequently	ADV
ejpam-6810	134	2	,	,	PUNCT
ejpam-6810	134	3	γi	γi	PROPN
ejpam-6810	134	4	=	=	SYM
ejpam-6810	134	5	γj	γj	PROPN
ejpam-6810	134	6	which	which	PRON
ejpam-6810	134	7	contradicts	contradict	VERB
ejpam-6810	134	8	(	(	PUNCT
ejpam-6810	134	9	6	6	NUM
ejpam-6810	134	10	)	)	PUNCT
ejpam-6810	134	11	,	,	PUNCT
ejpam-6810	134	12	this	this	PRON
ejpam-6810	134	13	shows	show	VERB
ejpam-6810	134	14	that	that	SCONJ
ejpam-6810	134	15	all	all	DET
ejpam-6810	134	16	ηi	ηi	NOUN
ejpam-6810	134	17	’s	’s	PART
ejpam-6810	134	18	are	be	AUX
ejpam-6810	134	19	distinct	distinct	ADJ
ejpam-6810	134	20	.	.	PUNCT
ejpam-6810	135	1	further	far	ADV
ejpam-6810	135	2	,	,	PUNCT
ejpam-6810	135	3	we	we	PRON
ejpam-6810	135	4	have	have	VERB
ejpam-6810	135	5	to	to	PART
ejpam-6810	135	6	show	show	VERB
ejpam-6810	135	7	that	that	SCONJ
ejpam-6810	135	8	{	{	PUNCT
ejpam-6810	135	9	ηn	ηn	ADJ
ejpam-6810	135	10	}	}	PUNCT
ejpam-6810	135	11	is	be	AUX
ejpam-6810	135	12	a	a	DET
ejpam-6810	135	13	cauchy	cauchy	ADJ
ejpam-6810	135	14	sequence	sequence	NOUN
ejpam-6810	135	15	.	.	PUNCT
ejpam-6810	136	1	it	it	PRON
ejpam-6810	136	2	is	be	AUX
ejpam-6810	136	3	clear	clear	ADJ
ejpam-6810	136	4	that	that	SCONJ
ejpam-6810	136	5	f(s2γn+1	f(s2γn+1	NOUN
ejpam-6810	136	6	)	)	PUNCT
ejpam-6810	136	7	≤	≤	NOUN
ejpam-6810	136	8	f(γn)−	f(γn)−	NOUN
ejpam-6810	136	9	τ	τ	X
ejpam-6810	136	10	.	.	PUNCT
ejpam-6810	137	1	using	use	VERB
ejpam-6810	137	2	(	(	PUNCT
ejpam-6810	137	3	f	f	NOUN
ejpam-6810	137	4	−	−	PROPN
ejpam-6810	137	5	2	2	NUM
ejpam-6810	137	6	)	)	PUNCT
ejpam-6810	137	7	,	,	PUNCT
ejpam-6810	137	8	f(sn+2γn+1	f(sn+2γn+1	PROPN
ejpam-6810	137	9	)	)	PUNCT
ejpam-6810	137	10	≤	≤	NUM
ejpam-6810	137	11	f(snγn)−	f(snγn)−	NOUN
ejpam-6810	137	12	τ	τ	X
ejpam-6810	137	13	.	.	PUNCT
ejpam-6810	138	1	(	(	PUNCT
ejpam-6810	138	2	7	7	X
ejpam-6810	138	3	)	)	PUNCT
ejpam-6810	138	4	it	it	PRON
ejpam-6810	138	5	follows	follow	VERB
ejpam-6810	138	6	by	by	ADP
ejpam-6810	138	7	induction	induction	NOUN
ejpam-6810	138	8	that	that	SCONJ
ejpam-6810	138	9	f(snγn	f(snγn	NOUN
ejpam-6810	138	10	)	)	PUNCT
ejpam-6810	138	11	≤	≤	NOUN
ejpam-6810	139	1	f(sn−2γn−1)−	f(sn−2γn−1)−	VERB
ejpam-6810	139	2	τ	τ	X
ejpam-6810	139	3	,	,	PUNCT
ejpam-6810	139	4	≤	≤	NUM
ejpam-6810	139	5	f(sn−4γn−2)−	f(sn−4γn−2)−	VERB
ejpam-6810	139	6	2τ	2τ	NUM
ejpam-6810	139	7	,	,	PUNCT
ejpam-6810	139	8	≤	≤	NUM
ejpam-6810	139	9	f(sn−6γn−3)−	f(sn−6γn−3)−	NOUN
ejpam-6810	139	10	3τ	3τ	NUM
ejpam-6810	139	11	.	.	PUNCT
ejpam-6810	140	1	by	by	ADP
ejpam-6810	140	2	continuing	continue	VERB
ejpam-6810	140	3	this	this	DET
ejpam-6810	140	4	process	process	NOUN
ejpam-6810	140	5	,	,	PUNCT
ejpam-6810	140	6	one	one	PRON
ejpam-6810	140	7	can	can	AUX
ejpam-6810	140	8	obtain	obtain	VERB
ejpam-6810	140	9	f(snγn	f(snγn	NOUN
ejpam-6810	140	10	)	)	PUNCT
ejpam-6810	140	11	≤	≤	NOUN
ejpam-6810	140	12	f(γ0)−	f(γ0)−	PROPN
ejpam-6810	140	13	nτ	nτ	NOUN
ejpam-6810	140	14	.	.	PUNCT
ejpam-6810	141	1	(	(	PUNCT
ejpam-6810	141	2	8)	8)	NUM
ejpam-6810	141	3	taking	take	VERB
ejpam-6810	141	4	limit	limit	NOUN
ejpam-6810	141	5	as	as	ADP
ejpam-6810	141	6	n	n	PROPN
ejpam-6810	141	7	→	→	SYM
ejpam-6810	141	8	+	+	NOUN
ejpam-6810	141	9	∞	∞	PROPN
ejpam-6810	141	10	in	in	ADP
ejpam-6810	141	11	(	(	PUNCT
ejpam-6810	141	12	8)	8)	NUM
ejpam-6810	141	13	to	to	PART
ejpam-6810	141	14	obtain	obtain	VERB
ejpam-6810	141	15	lim	lim	PROPN
ejpam-6810	141	16	n→+∞	n→+∞	VERB
ejpam-6810	141	17	f(snγn	f(snγn	NOUN
ejpam-6810	141	18	)	)	PUNCT
ejpam-6810	141	19	→	→	PUNCT
ejpam-6810	141	20	−+∞	−+∞	PRON
ejpam-6810	141	21	which	which	PRON
ejpam-6810	141	22	together	together	ADV
ejpam-6810	141	23	with	with	ADP
ejpam-6810	141	24	(	(	PUNCT
ejpam-6810	141	25	f	f	NOUN
ejpam-6810	141	26	−	−	PROPN
ejpam-6810	141	27	2	2	NUM
ejpam-6810	141	28	)	)	PUNCT
ejpam-6810	141	29	yield	yield	NOUN
ejpam-6810	141	30	that	that	PRON
ejpam-6810	141	31	lim	lim	PROPN
ejpam-6810	141	32	n→+∞	n→+∞	PROPN
ejpam-6810	141	33	snγn	snγn	NOUN
ejpam-6810	141	34	=	=	SYM
ejpam-6810	141	35	0	0	X
ejpam-6810	141	36	.	.	PUNCT
ejpam-6810	142	1	according	accord	VERB
ejpam-6810	142	2	to	to	ADP
ejpam-6810	142	3	(	(	PUNCT
ejpam-6810	142	4	f	f	PROPN
ejpam-6810	142	5	−	−	PROPN
ejpam-6810	142	6	3	3	NUM
ejpam-6810	142	7	)	)	PUNCT
ejpam-6810	142	8	,	,	PUNCT
ejpam-6810	142	9	there	there	PRON
ejpam-6810	142	10	is	be	VERB
ejpam-6810	142	11	k	k	PROPN
ejpam-6810	142	12	∈	∈	PROPN
ejpam-6810	142	13	(	(	PUNCT
ejpam-6810	142	14	0,1	0,1	NOUN
ejpam-6810	142	15	)	)	PUNCT
ejpam-6810	142	16	such	such	ADJ
ejpam-6810	142	17	that	that	SCONJ
ejpam-6810	142	18	lim	lim	PROPN
ejpam-6810	142	19	n→+∞	n→+∞	PROPN
ejpam-6810	142	20	(	(	PUNCT
ejpam-6810	142	21	snγn	snγn	NOUN
ejpam-6810	142	22	)	)	PUNCT
ejpam-6810	142	23	kf(snγn	kf(snγn	NOUN
ejpam-6810	142	24	)	)	PUNCT
ejpam-6810	142	25	=	=	SYM
ejpam-6810	143	1	0	0	X
ejpam-6810	143	2	.	.	X
ejpam-6810	143	3	multiplying	multiply	VERB
ejpam-6810	143	4	(	(	PUNCT
ejpam-6810	143	5	8)	8)	NUM
ejpam-6810	143	6	by	by	ADP
ejpam-6810	143	7	(	(	PUNCT
ejpam-6810	143	8	snγn	snγn	NOUN
ejpam-6810	143	9	)	)	PUNCT
ejpam-6810	144	1	k	k	PROPN
ejpam-6810	144	2	leads	lead	VERB
ejpam-6810	144	3	to	to	ADP
ejpam-6810	144	4	0	0	NUM
ejpam-6810	144	5	≤	≤	NOUN
ejpam-6810	144	6	(	(	PUNCT
ejpam-6810	144	7	snγn	snγn	NOUN
ejpam-6810	144	8	)	)	PUNCT
ejpam-6810	144	9	kf(snγn	kf(snγn	NOUN
ejpam-6810	144	10	)	)	PUNCT
ejpam-6810	145	1	+	+	CCONJ
ejpam-6810	145	2	(	(	PUNCT
ejpam-6810	145	3	snγn	snγn	NOUN
ejpam-6810	145	4	)	)	PUNCT
ejpam-6810	145	5	knτ	knτ	PROPN
ejpam-6810	145	6	≤	≤	PROPN
ejpam-6810	145	7	(	(	PUNCT
ejpam-6810	145	8	snγn	snγn	NOUN
ejpam-6810	145	9	)	)	PUNCT
ejpam-6810	145	10	kf(γ0	kf(γ0	NOUN
ejpam-6810	145	11	)	)	PUNCT
ejpam-6810	145	12	.	.	PUNCT
ejpam-6810	146	1	taking	take	VERB
ejpam-6810	146	2	limit	limit	NOUN
ejpam-6810	146	3	as	as	ADP
ejpam-6810	146	4	n	n	PROPN
ejpam-6810	146	5	→	→	SYM
ejpam-6810	146	6	+	+	NOUN
ejpam-6810	146	7	∞	∞	PROPN
ejpam-6810	146	8	,	,	PUNCT
ejpam-6810	146	9	we	we	PRON
ejpam-6810	146	10	get	get	VERB
ejpam-6810	146	11	lim	lim	PROPN
ejpam-6810	146	12	n→+∞	n→+∞	PROPN
ejpam-6810	146	13	(	(	PUNCT
ejpam-6810	146	14	snγn	snγn	NOUN
ejpam-6810	146	15	)	)	PUNCT
ejpam-6810	147	1	kn	kn	PROPN
ejpam-6810	147	2	=	=	NOUN
ejpam-6810	147	3	0	0	PROPN
ejpam-6810	147	4	.	.	PUNCT
ejpam-6810	148	1	as	as	ADP
ejpam-6810	148	2	a	a	DET
ejpam-6810	148	3	result	result	NOUN
ejpam-6810	148	4	,	,	PUNCT
ejpam-6810	148	5	it	it	PRON
ejpam-6810	148	6	can	can	AUX
ejpam-6810	148	7	be	be	AUX
ejpam-6810	148	8	concluded	conclude	VERB
ejpam-6810	148	9	that	that	SCONJ
ejpam-6810	148	10	there	there	PRON
ejpam-6810	148	11	is	be	VERB
ejpam-6810	148	12	n1	n1	ADJ
ejpam-6810	148	13	∈	∈	NOUN
ejpam-6810	148	14	n	n	PRON
ejpam-6810	148	15	such	such	ADJ
ejpam-6810	148	16	that	that	SCONJ
ejpam-6810	148	17	(	(	PUNCT
ejpam-6810	148	18	snγn	snγn	NOUN
ejpam-6810	148	19	)	)	PUNCT
ejpam-6810	148	20	kn	kn	PROPN
ejpam-6810	148	21	≤	≤	PROPN
ejpam-6810	148	22	1	1	NUM
ejpam-6810	148	23	,	,	PUNCT
ejpam-6810	148	24	forall	forall	NOUN
ejpam-6810	148	25	n	n	CCONJ
ejpam-6810	148	26	≥	≥	NOUN
ejpam-6810	148	27	n1	n1	PROPN
ejpam-6810	148	28	.	.	PUNCT
ejpam-6810	149	1	s.	s.	PROPN
ejpam-6810	149	2	batul	batul	PROPN
ejpam-6810	149	3	et	et	PROPN
ejpam-6810	149	4	al	al	PROPN
ejpam-6810	149	5	.	.	PUNCT
ejpam-6810	149	6	/	/	SYM
ejpam-6810	149	7	eur	eur	PROPN
ejpam-6810	149	8	.	.	PUNCT
ejpam-6810	150	1	j.	j.	PROPN
ejpam-6810	150	2	pure	pure	PROPN
ejpam-6810	150	3	appl	appl	PROPN
ejpam-6810	150	4	.	.	PROPN
ejpam-6810	150	5	math	math	PROPN
ejpam-6810	150	6	,	,	PUNCT
ejpam-6810	150	7	18	18	NUM
ejpam-6810	150	8	(	(	PUNCT
ejpam-6810	150	9	4	4	NUM
ejpam-6810	150	10	)	)	PUNCT
ejpam-6810	150	11	(	(	PUNCT
ejpam-6810	150	12	2025	2025	NUM
ejpam-6810	150	13	)	)	PUNCT
ejpam-6810	150	14	,	,	PUNCT
ejpam-6810	150	15	6810	6810	NUM
ejpam-6810	150	16	7	7	NUM
ejpam-6810	150	17	of	of	ADP
ejpam-6810	150	18	23	23	NUM
ejpam-6810	150	19	therefore	therefore	ADV
ejpam-6810	150	20	,	,	PUNCT
ejpam-6810	150	21	(	(	PUNCT
ejpam-6810	150	22	snγn	snγn	NOUN
ejpam-6810	150	23	)	)	PUNCT
ejpam-6810	151	1	k	k	PROPN
ejpam-6810	151	2	≤	≤	ADV
ejpam-6810	151	3	1	1	NUM
ejpam-6810	151	4	n	n	NOUN
ejpam-6810	151	5	,	,	PUNCT
ejpam-6810	151	6	forall	forall	NOUN
ejpam-6810	151	7	n	n	CCONJ
ejpam-6810	151	8	≥	≥	NOUN
ejpam-6810	151	9	n1	n1	NOUN
ejpam-6810	151	10	.	.	PUNCT
ejpam-6810	152	1	it	it	PRON
ejpam-6810	152	2	implies	imply	VERB
ejpam-6810	152	3	snγn	snγn	NOUN
ejpam-6810	152	4	≤	≤	NUM
ejpam-6810	152	5	1	1	NUM
ejpam-6810	152	6	n	n	NUM
ejpam-6810	152	7	1	1	NUM
ejpam-6810	152	8	k	k	NOUN
ejpam-6810	152	9	,	,	PUNCT
ejpam-6810	152	10	forall	forall	NOUN
ejpam-6810	152	11	n	n	CCONJ
ejpam-6810	152	12	≥	≥	NOUN
ejpam-6810	152	13	n1	n1	NOUN
ejpam-6810	152	14	.	.	PUNCT
ejpam-6810	153	1	(	(	PUNCT
ejpam-6810	153	2	9	9	X
ejpam-6810	153	3	)	)	PUNCT
ejpam-6810	153	4	this	this	PRON
ejpam-6810	153	5	implies	imply	VERB
ejpam-6810	153	6	that	that	SCONJ
ejpam-6810	153	7	the	the	DET
ejpam-6810	153	8	series	series	NOUN
ejpam-6810	153	9	+	+	PROPN
ejpam-6810	153	10	∞∑	∞∑	NUM
ejpam-6810	153	11	i=1	i=1	PROPN
ejpam-6810	153	12	siγi	siγi	NOUN
ejpam-6810	153	13	converges	converge	NOUN
ejpam-6810	153	14	.	.	PUNCT
ejpam-6810	154	1	now	now	ADV
ejpam-6810	154	2	,	,	PUNCT
ejpam-6810	154	3	by	by	ADP
ejpam-6810	154	4	the	the	DET
ejpam-6810	154	5	triangular	triangular	NOUN
ejpam-6810	154	6	inequality	inequality	NOUN
ejpam-6810	154	7	,	,	PUNCT
ejpam-6810	154	8	for	for	ADP
ejpam-6810	154	9	all	all	DET
ejpam-6810	154	10	n	n	CCONJ
ejpam-6810	154	11	,	,	PUNCT
ejpam-6810	154	12	p	p	PROPN
ejpam-6810	154	13	∈	∈	PROPN
ejpam-6810	154	14	n	n	CCONJ
ejpam-6810	154	15	,	,	PUNCT
ejpam-6810	154	16	σb(ηn	σb(ηn	PROPN
ejpam-6810	154	17	,	,	PUNCT
ejpam-6810	154	18	ηn+p	ηn+p	PROPN
ejpam-6810	154	19	)	)	PUNCT
ejpam-6810	154	20	≤s(σb(ηn	≤s(σb(ηn	PROPN
ejpam-6810	154	21	,	,	PUNCT
ejpam-6810	154	22	ηn+1	ηn+1	ADV
ejpam-6810	154	23	)	)	PUNCT
ejpam-6810	155	1	+	+	X
ejpam-6810	155	2	σb(ηn+1	σb(ηn+1	ADJ
ejpam-6810	155	3	,	,	PUNCT
ejpam-6810	155	4	ηn+p	ηn+p	PROPN
ejpam-6810	155	5	)	)	PUNCT
ejpam-6810	155	6	)	)	PUNCT
ejpam-6810	155	7	.	.	PUNCT
ejpam-6810	156	1	that	that	PRON
ejpam-6810	156	2	is	be	AUX
ejpam-6810	156	3	,	,	PUNCT
ejpam-6810	156	4	σb(ηn	σb(ηn	PROPN
ejpam-6810	156	5	,	,	PUNCT
ejpam-6810	156	6	ηn+p	ηn+p	PROPN
ejpam-6810	156	7	)	)	PUNCT
ejpam-6810	156	8	≤sσb(ηn	≤sσb(ηn	PROPN
ejpam-6810	156	9	,	,	PUNCT
ejpam-6810	156	10	ηn+1	ηn+1	NUM
ejpam-6810	156	11	)	)	PUNCT
ejpam-6810	157	1	+	+	X
ejpam-6810	157	2	s2(σb(ηn+1	s2(σb(ηn+1	X
ejpam-6810	157	3	,	,	PUNCT
ejpam-6810	157	4	ηn+2	ηn+2	NOUN
ejpam-6810	157	5	)	)	PUNCT
ejpam-6810	157	6	+	+	CCONJ
ejpam-6810	157	7	σb(ηn+2	σb(ηn+2	PROPN
ejpam-6810	157	8	,	,	PUNCT
ejpam-6810	157	9	ηn+p	ηn+p	PROPN
ejpam-6810	157	10	)	)	PUNCT
ejpam-6810	157	11	)	)	PUNCT
ejpam-6810	157	12	.	.	PUNCT
ejpam-6810	158	1	continuing	continue	VERB
ejpam-6810	158	2	in	in	ADP
ejpam-6810	158	3	this	this	DET
ejpam-6810	158	4	way	way	NOUN
ejpam-6810	158	5	,	,	PUNCT
ejpam-6810	158	6	σb(ηn	σb(ηn	PROPN
ejpam-6810	158	7	,	,	PUNCT
ejpam-6810	158	8	ηn+p	ηn+p	PROPN
ejpam-6810	158	9	)	)	PUNCT
ejpam-6810	158	10	≤	≤	NOUN
ejpam-6810	158	11	sσb(ηn	sσb(ηn	AUX
ejpam-6810	158	12	,	,	PUNCT
ejpam-6810	158	13	ηn+1	ηn+1	NUM
ejpam-6810	158	14	)	)	PUNCT
ejpam-6810	159	1	+	+	CCONJ
ejpam-6810	159	2	s2σb(ηn+1	s2σb(ηn+1	ADJ
ejpam-6810	159	3	,	,	PUNCT
ejpam-6810	159	4	ηn+2	ηn+2	ADV
ejpam-6810	159	5	)	)	PUNCT
ejpam-6810	160	1	+	+	X
ejpam-6810	160	2	s3σb(ηn+2	s3σb(ηn+2	ADJ
ejpam-6810	160	3	,	,	PUNCT
ejpam-6810	160	4	ηn+3	ηn+3	NOUN
ejpam-6810	160	5	)	)	PUNCT
ejpam-6810	161	1	+	+	CCONJ
ejpam-6810	161	2	·	·	PUNCT
ejpam-6810	161	3	·	·	PUNCT
ejpam-6810	161	4	·	·	PUNCT
ejpam-6810	161	5	+	+	NUM
ejpam-6810	161	6	spσb(ηn+p−1	spσb(ηn+p−1	PROPN
ejpam-6810	161	7	,	,	PUNCT
ejpam-6810	161	8	ηn+p	ηn+p	PROPN
ejpam-6810	161	9	)	)	PUNCT
ejpam-6810	161	10	.	.	PUNCT
ejpam-6810	162	1	(	(	PUNCT
ejpam-6810	162	2	10	10	X
ejpam-6810	162	3	)	)	PUNCT
ejpam-6810	162	4	putting	put	VERB
ejpam-6810	162	5	n	n	PRON
ejpam-6810	162	6	=	=	NOUN
ejpam-6810	162	7	0	0	NUM
ejpam-6810	162	8	in	in	ADP
ejpam-6810	162	9	(	(	PUNCT
ejpam-6810	162	10	7	7	NUM
ejpam-6810	162	11	)	)	PUNCT
ejpam-6810	162	12	,	,	PUNCT
ejpam-6810	162	13	f(s2γ1	f(s2γ1	PROPN
ejpam-6810	162	14	)	)	PUNCT
ejpam-6810	162	15	≤	≤	NOUN
ejpam-6810	162	16	f(γ0)−	f(γ0)−	PROPN
ejpam-6810	162	17	τ	τ	PROPN
ejpam-6810	162	18	.	.	PUNCT
ejpam-6810	163	1	(	(	PUNCT
ejpam-6810	163	2	11	11	NUM
ejpam-6810	163	3	)	)	PUNCT
ejpam-6810	163	4	as	as	ADP
ejpam-6810	163	5	γ1	γ1	NOUN
ejpam-6810	163	6	=	=	SYM
ejpam-6810	163	7	σb(η1	σb(η1	X
ejpam-6810	163	8	,	,	PUNCT
ejpam-6810	163	9	η2	η2	X
ejpam-6810	163	10	)	)	PUNCT
ejpam-6810	164	1	+	+	CCONJ
ejpam-6810	164	2	σb(η2	σb(η2	NOUN
ejpam-6810	164	3	,	,	PUNCT
ejpam-6810	164	4	η3	η3	NOUN
ejpam-6810	164	5	)	)	PUNCT
ejpam-6810	164	6	+	+	CCONJ
ejpam-6810	164	7	σb(η3	σb(η3	NOUN
ejpam-6810	164	8	,	,	PUNCT
ejpam-6810	164	9	η1	η1	NOUN
ejpam-6810	164	10	)	)	PUNCT
ejpam-6810	164	11	,	,	PUNCT
ejpam-6810	164	12	(	(	PUNCT
ejpam-6810	164	13	11	11	NUM
ejpam-6810	164	14	)	)	PUNCT
ejpam-6810	164	15	becomes	become	VERB
ejpam-6810	164	16	,	,	PUNCT
ejpam-6810	164	17	f(s2(σb(η1	f(s2(σb(η1	NUM
ejpam-6810	164	18	,	,	PUNCT
ejpam-6810	164	19	η2	η2	X
ejpam-6810	164	20	)	)	PUNCT
ejpam-6810	165	1	+	+	CCONJ
ejpam-6810	165	2	σb(η2	σb(η2	NOUN
ejpam-6810	165	3	,	,	PUNCT
ejpam-6810	165	4	η3	η3	NOUN
ejpam-6810	165	5	)	)	PUNCT
ejpam-6810	165	6	+	+	CCONJ
ejpam-6810	165	7	σb(η3	σb(η3	NOUN
ejpam-6810	165	8	,	,	PUNCT
ejpam-6810	165	9	η1	η1	NOUN
ejpam-6810	165	10	)	)	PUNCT
ejpam-6810	165	11	)	)	PUNCT
ejpam-6810	165	12	)	)	PUNCT
ejpam-6810	166	1	≤	≤	PROPN
ejpam-6810	166	2	f(γ0)−	f(γ0)−	PROPN
ejpam-6810	166	3	τ	τ	PROPN
ejpam-6810	166	4	.	.	PUNCT
ejpam-6810	167	1	that	that	PRON
ejpam-6810	167	2	is	be	AUX
ejpam-6810	167	3	,	,	PUNCT
ejpam-6810	167	4	f(s2(σb(η1	f(s2(σb(η1	NUM
ejpam-6810	167	5	,	,	PUNCT
ejpam-6810	167	6	η2	η2	X
ejpam-6810	167	7	)	)	PUNCT
ejpam-6810	168	1	+	+	CCONJ
ejpam-6810	168	2	σb(η2	σb(η2	NOUN
ejpam-6810	168	3	,	,	PUNCT
ejpam-6810	168	4	η3	η3	NOUN
ejpam-6810	168	5	)	)	PUNCT
ejpam-6810	168	6	+	+	CCONJ
ejpam-6810	168	7	σb(η3	σb(η3	NOUN
ejpam-6810	168	8	,	,	PUNCT
ejpam-6810	168	9	η1	η1	NOUN
ejpam-6810	168	10	)	)	PUNCT
ejpam-6810	168	11	)	)	PUNCT
ejpam-6810	168	12	)	)	PUNCT
ejpam-6810	169	1	≤	≤	NUM
ejpam-6810	169	2	f(γ0	f(γ0	NOUN
ejpam-6810	169	3	)	)	PUNCT
ejpam-6810	169	4	.	.	PUNCT
ejpam-6810	170	1	since	since	SCONJ
ejpam-6810	170	2	f	f	PROPN
ejpam-6810	170	3	is	be	AUX
ejpam-6810	170	4	increasing	increase	VERB
ejpam-6810	170	5	and	and	CCONJ
ejpam-6810	170	6	s	s	VERB
ejpam-6810	170	7	≥1	≥1	NUM
ejpam-6810	170	8	,	,	PUNCT
ejpam-6810	170	9	σb(η1	σb(η1	NOUN
ejpam-6810	170	10	,	,	PUNCT
ejpam-6810	170	11	η2	η2	X
ejpam-6810	170	12	)	)	PUNCT
ejpam-6810	170	13	+	+	CCONJ
ejpam-6810	170	14	σb(η2	σb(η2	NOUN
ejpam-6810	170	15	,	,	PUNCT
ejpam-6810	170	16	η3	η3	NOUN
ejpam-6810	170	17	)	)	PUNCT
ejpam-6810	170	18	+	+	CCONJ
ejpam-6810	170	19	σb(η3	σb(η3	NOUN
ejpam-6810	170	20	,	,	PUNCT
ejpam-6810	170	21	η1	η1	NOUN
ejpam-6810	170	22	)	)	PUNCT
ejpam-6810	170	23	)	)	PUNCT
ejpam-6810	170	24	≤	≤	NUM
ejpam-6810	170	25	γ0	γ0	NOUN
ejpam-6810	170	26	.	.	PUNCT
ejpam-6810	171	1	thus	thus	ADV
ejpam-6810	171	2	,	,	PUNCT
ejpam-6810	171	3	σb(η1	σb(η1	NOUN
ejpam-6810	171	4	,	,	PUNCT
ejpam-6810	171	5	η2	η2	X
ejpam-6810	171	6	)	)	PUNCT
ejpam-6810	171	7	≤	≤	NOUN
ejpam-6810	171	8	γ0	γ0	NOUN
ejpam-6810	171	9	.	.	PUNCT
ejpam-6810	172	1	continuing	continue	VERB
ejpam-6810	172	2	the	the	DET
ejpam-6810	172	3	same	same	ADJ
ejpam-6810	172	4	process	process	NOUN
ejpam-6810	172	5	,	,	PUNCT
ejpam-6810	172	6	we	we	PRON
ejpam-6810	172	7	obtain	obtain	VERB
ejpam-6810	172	8	σb(η2	σb(η2	NOUN
ejpam-6810	172	9	,	,	PUNCT
ejpam-6810	172	10	η3	η3	NOUN
ejpam-6810	172	11	)	)	PUNCT
ejpam-6810	172	12	≤	≤	NUM
ejpam-6810	172	13	γ1	γ1	NOUN
ejpam-6810	172	14	,	,	PUNCT
ejpam-6810	172	15	σb(η3	σb(η3	INTJ
ejpam-6810	172	16	,	,	PUNCT
ejpam-6810	172	17	η4	η4	VERB
ejpam-6810	172	18	)	)	PUNCT
ejpam-6810	172	19	≤	≤	NOUN
ejpam-6810	172	20	γ2	γ2	NOUN
ejpam-6810	172	21	,	,	PUNCT
ejpam-6810	172	22	...	...	PUNCT
ejpam-6810	173	1	σb(ηn	σb(ηn	PROPN
ejpam-6810	173	2	,	,	PUNCT
ejpam-6810	173	3	ηn+1	ηn+1	NUM
ejpam-6810	173	4	)	)	PUNCT
ejpam-6810	173	5	≤	≤	PUNCT
ejpam-6810	173	6	γn−1	γn−1	PROPN
ejpam-6810	173	7	,	,	PUNCT
ejpam-6810	173	8	σb(ηn+1	σb(ηn+1	PROPN
ejpam-6810	173	9	,	,	PUNCT
ejpam-6810	173	10	ηn+2	ηn+2	NOUN
ejpam-6810	173	11	)	)	PUNCT
ejpam-6810	173	12	≤	≤	NOUN
ejpam-6810	173	13	γn	γn	ADP
ejpam-6810	173	14	,	,	PUNCT
ejpam-6810	173	15	...	...	PUNCT
ejpam-6810	173	16	s.	s.	PROPN
ejpam-6810	173	17	batul	batul	PROPN
ejpam-6810	173	18	et	et	PROPN
ejpam-6810	173	19	al	al	PROPN
ejpam-6810	173	20	.	.	PUNCT
ejpam-6810	173	21	/	/	SYM
ejpam-6810	173	22	eur	eur	PROPN
ejpam-6810	173	23	.	.	PUNCT
ejpam-6810	174	1	j.	j.	PROPN
ejpam-6810	174	2	pure	pure	PROPN
ejpam-6810	174	3	appl	appl	PROPN
ejpam-6810	174	4	.	.	PROPN
ejpam-6810	174	5	math	math	PROPN
ejpam-6810	174	6	,	,	PUNCT
ejpam-6810	174	7	18	18	NUM
ejpam-6810	174	8	(	(	PUNCT
ejpam-6810	174	9	4	4	NUM
ejpam-6810	174	10	)	)	PUNCT
ejpam-6810	174	11	(	(	PUNCT
ejpam-6810	174	12	2025	2025	NUM
ejpam-6810	174	13	)	)	PUNCT
ejpam-6810	174	14	,	,	PUNCT
ejpam-6810	174	15	6810	6810	NUM
ejpam-6810	174	16	8	8	NUM
ejpam-6810	174	17	of	of	ADP
ejpam-6810	174	18	23	23	NUM
ejpam-6810	174	19	substituting	substituting	NOUN
ejpam-6810	174	20	in	in	ADP
ejpam-6810	174	21	(	(	PUNCT
ejpam-6810	174	22	10	10	NUM
ejpam-6810	174	23	)	)	PUNCT
ejpam-6810	174	24	,	,	PUNCT
ejpam-6810	174	25	σb(ηn	σb(ηn	PROPN
ejpam-6810	174	26	,	,	PUNCT
ejpam-6810	174	27	ηn+p	ηn+p	PROPN
ejpam-6810	174	28	)	)	PUNCT
ejpam-6810	174	29	≤	≤	PUNCT
ejpam-6810	174	30	sγn−1	sγn−1	PROPN
ejpam-6810	174	31	+	+	CCONJ
ejpam-6810	174	32	s2γn	s2γn	PUNCT
ejpam-6810	175	1	+	+	NUM
ejpam-6810	175	2	s3γn+1	s3γn+1	ADJ
ejpam-6810	175	3	+	+	X
ejpam-6810	175	4	·	·	PUNCT
ejpam-6810	175	5	·	·	PUNCT
ejpam-6810	175	6	·	·	PUNCT
ejpam-6810	175	7	+	+	NUM
ejpam-6810	175	8	spγn+p−2	spγn+p−2	NOUN
ejpam-6810	175	9	,	,	PUNCT
ejpam-6810	175	10	≤	≤	X
ejpam-6810	175	11	s(γn−1	s(γn−1	X
ejpam-6810	175	12	+	+	CCONJ
ejpam-6810	175	13	sγn	sγn	NOUN
ejpam-6810	175	14	+	+	CCONJ
ejpam-6810	175	15	s2γn+1	s2γn+1	NOUN
ejpam-6810	175	16	+	+	X
ejpam-6810	175	17	·	·	PUNCT
ejpam-6810	175	18	·	·	PUNCT
ejpam-6810	175	19	·	·	PUNCT
ejpam-6810	175	20	+	+	NUM
ejpam-6810	175	21	sp−1γn+p−2	sp−1γn+p−2	NOUN
ejpam-6810	175	22	)	)	PUNCT
ejpam-6810	175	23	,	,	PUNCT
ejpam-6810	175	24	≤	≤	PROPN
ejpam-6810	175	25	s	s	VERB
ejpam-6810	175	26	sn−1	sn−1	PROPN
ejpam-6810	175	27	(	(	PUNCT
ejpam-6810	175	28	sn−1γn−1	sn−1γn−1	PROPN
ejpam-6810	175	29	+	+	NUM
ejpam-6810	175	30	snγn	snγn	NOUN
ejpam-6810	175	31	+	+	CCONJ
ejpam-6810	175	32	sn+1γn+1	sn+1γn+1	NOUN
ejpam-6810	175	33	+	+	X
ejpam-6810	175	34	·	·	PUNCT
ejpam-6810	175	35	·	·	PUNCT
ejpam-6810	175	36	·	·	PUNCT
ejpam-6810	175	37	+	+	NUM
ejpam-6810	175	38	sn+p−2γn+p−2	sn+p−2γn+p−2	NUM
ejpam-6810	175	39	)	)	PUNCT
ejpam-6810	175	40	,	,	PUNCT
ejpam-6810	175	41	≤	≤	NUM
ejpam-6810	175	42	1	1	NUM
ejpam-6810	175	43	sn−2	sn−2	ADV
ejpam-6810	175	44	(	(	PUNCT
ejpam-6810	175	45	n+p−2∑	n+p−2∑	PROPN
ejpam-6810	175	46	i	i	PROPN
ejpam-6810	175	47	=	=	PROPN
ejpam-6810	175	48	n−1	n−1	PROPN
ejpam-6810	175	49	siγi	siγi	NOUN
ejpam-6810	175	50	)	)	PUNCT
ejpam-6810	175	51	,	,	PUNCT
ejpam-6810	175	52	≤	≤	NUM
ejpam-6810	175	53	1	1	NUM
ejpam-6810	175	54	sn−2	sn−2	ADV
ejpam-6810	175	55	(	(	PUNCT
ejpam-6810	175	56	+	+	ADP
ejpam-6810	175	57	∞∑	∞∑	NUM
ejpam-6810	175	58	i	i	PROPN
ejpam-6810	175	59	=	=	ADJ
ejpam-6810	175	60	n−1	n−1	PROPN
ejpam-6810	175	61	siγi	siγi	NOUN
ejpam-6810	175	62	)	)	PUNCT
ejpam-6810	175	63	.	.	PUNCT
ejpam-6810	176	1	therefore	therefore	ADV
ejpam-6810	176	2	,	,	PUNCT
ejpam-6810	176	3	for	for	ADP
ejpam-6810	176	4	all	all	DET
ejpam-6810	176	5	n	n	PRON
ejpam-6810	176	6	≥	≥	NOUN
ejpam-6810	176	7	n1	n1	PROPN
ejpam-6810	176	8	and	and	CCONJ
ejpam-6810	176	9	p	p	NOUN
ejpam-6810	176	10	∈	∈	PROPN
ejpam-6810	176	11	n	n	CCONJ
ejpam-6810	176	12	,	,	PUNCT
ejpam-6810	176	13	(	(	PUNCT
ejpam-6810	176	14	9	9	NUM
ejpam-6810	176	15	)	)	PUNCT
ejpam-6810	176	16	implies	imply	VERB
ejpam-6810	176	17	that	that	SCONJ
ejpam-6810	176	18	σb(ηn	σb(ηn	PROPN
ejpam-6810	176	19	,	,	PUNCT
ejpam-6810	176	20	ηn+p	ηn+p	PROPN
ejpam-6810	176	21	)	)	PUNCT
ejpam-6810	176	22	≤	≤	NUM
ejpam-6810	176	23	1	1	NUM
ejpam-6810	176	24	sn−2	sn−2	ADV
ejpam-6810	176	25	(	(	PUNCT
ejpam-6810	176	26	+	+	ADP
ejpam-6810	176	27	∞∑	∞∑	NUM
ejpam-6810	176	28	i	i	PROPN
ejpam-6810	176	29	=	=	ADJ
ejpam-6810	176	30	n−1	n−1	PROPN
ejpam-6810	176	31	siγi	siγi	NOUN
ejpam-6810	176	32	)	)	PUNCT
ejpam-6810	176	33	≤	≤	NOUN
ejpam-6810	176	34	1	1	NUM
ejpam-6810	176	35	sn−2	sn−2	ADV
ejpam-6810	176	36	(	(	PUNCT
ejpam-6810	176	37	+	+	ADP
ejpam-6810	176	38	∞∑	∞∑	NUM
ejpam-6810	176	39	i	i	PRON
ejpam-6810	176	40	=	=	NOUN
ejpam-6810	176	41	n−1	n−1	PROPN
ejpam-6810	176	42	1	1	NUM
ejpam-6810	176	43	i	i	NOUN
ejpam-6810	176	44	1	1	NUM
ejpam-6810	176	45	k	k	NOUN
ejpam-6810	176	46	)	)	PUNCT
ejpam-6810	176	47	.	.	PUNCT
ejpam-6810	177	1	taking	take	VERB
ejpam-6810	177	2	limit	limit	NOUN
ejpam-6810	177	3	as	as	ADP
ejpam-6810	177	4	n	n	ADV
ejpam-6810	177	5	−→	−→	NOUN
ejpam-6810	177	6	+	+	ADJ
ejpam-6810	177	7	∞	∞	PROPN
ejpam-6810	177	8	,	,	PUNCT
ejpam-6810	177	9	σb(ηn	σb(ηn	PROPN
ejpam-6810	177	10	,	,	PUNCT
ejpam-6810	177	11	ηn+p	ηn+p	PROPN
ejpam-6810	177	12	)	)	PUNCT
ejpam-6810	177	13	−→	−→	NOUN
ejpam-6810	177	14	0	0	NUM
ejpam-6810	177	15	.	.	PUNCT
ejpam-6810	178	1	it	it	PRON
ejpam-6810	178	2	follows	follow	VERB
ejpam-6810	178	3	that	that	SCONJ
ejpam-6810	178	4	{	{	PUNCT
ejpam-6810	178	5	ηn	ηn	ADJ
ejpam-6810	178	6	}	}	PUNCT
ejpam-6810	178	7	is	be	AUX
ejpam-6810	178	8	a	a	DET
ejpam-6810	178	9	cauchy	cauchy	ADJ
ejpam-6810	178	10	sequence	sequence	NOUN
ejpam-6810	178	11	in	in	ADP
ejpam-6810	178	12	u	u	PROPN
ejpam-6810	178	13	.	.	PUNCT
ejpam-6810	179	1	as	as	SCONJ
ejpam-6810	179	2	(	(	PUNCT
ejpam-6810	179	3	u	u	NOUN
ejpam-6810	179	4	,	,	PUNCT
ejpam-6810	179	5	σb	σb	NOUN
ejpam-6810	179	6	)	)	PUNCT
ejpam-6810	179	7	is	be	AUX
ejpam-6810	179	8	complete	complete	ADJ
ejpam-6810	179	9	,	,	PUNCT
ejpam-6810	179	10	{	{	PUNCT
ejpam-6810	179	11	ηn	ηn	ADJ
ejpam-6810	179	12	}	}	PUNCT
ejpam-6810	179	13	has	have	VERB
ejpam-6810	179	14	a	a	DET
ejpam-6810	179	15	limit	limit	NOUN
ejpam-6810	179	16	η∗	η∗	NOUN
ejpam-6810	179	17	in	in	ADP
ejpam-6810	179	18	u	u	PROPN
ejpam-6810	179	19	.	.	PUNCT
ejpam-6810	180	1	to	to	PART
ejpam-6810	180	2	show	show	VERB
ejpam-6810	180	3	that	that	SCONJ
ejpam-6810	180	4	υη∗	υη∗	NOUN
ejpam-6810	180	5	=	=	SYM
ejpam-6810	180	6	η∗	η∗	NOUN
ejpam-6810	180	7	,	,	PUNCT
ejpam-6810	180	8	we	we	PRON
ejpam-6810	180	9	apply	apply	VERB
ejpam-6810	180	10	the	the	DET
ejpam-6810	180	11	triangular	triangular	NOUN
ejpam-6810	180	12	inequality	inequality	NOUN
ejpam-6810	180	13	and	and	CCONJ
ejpam-6810	180	14	inequality	inequality	NOUN
ejpam-6810	180	15	(	(	PUNCT
ejpam-6810	180	16	3	3	NUM
ejpam-6810	180	17	)	)	PUNCT
ejpam-6810	180	18	.	.	PUNCT
ejpam-6810	181	1	for	for	ADP
ejpam-6810	181	2	this	this	PRON
ejpam-6810	181	3	,	,	PUNCT
ejpam-6810	181	4	σb(η	σb(η	PRON
ejpam-6810	181	5	∗,υη∗	∗,υη∗	NOUN
ejpam-6810	181	6	)	)	PUNCT
ejpam-6810	182	1	≤s(σb(η	≤s(σb(η	PROPN
ejpam-6810	182	2	∗	∗	NOUN
ejpam-6810	182	3	,	,	PUNCT
ejpam-6810	182	4	ηn	ηn	ADJ
ejpam-6810	182	5	)	)	PUNCT
ejpam-6810	182	6	+	+	CCONJ
ejpam-6810	182	7	σb(ηn	σb(ηn	ADJ
ejpam-6810	182	8	,	,	PUNCT
ejpam-6810	182	9	υη∗	υη∗	NOUN
ejpam-6810	182	10	)	)	PUNCT
ejpam-6810	182	11	)	)	PUNCT
ejpam-6810	182	12	,	,	PUNCT
ejpam-6810	182	13	=	=	SYM
ejpam-6810	182	14	sσb(η	sσb(η	PROPN
ejpam-6810	182	15	∗	∗	NOUN
ejpam-6810	182	16	,	,	PUNCT
ejpam-6810	182	17	ηn	ηn	ADJ
ejpam-6810	182	18	)	)	PUNCT
ejpam-6810	182	19	+	+	NUM
ejpam-6810	182	20	sσb(υηn−1,υη∗	sσb(υηn−1,υη∗	NOUN
ejpam-6810	182	21	)	)	PUNCT
ejpam-6810	182	22	,	,	PUNCT
ejpam-6810	182	23	≤sσb(η	≤sσb(η	ADJ
ejpam-6810	182	24	∗	∗	NOUN
ejpam-6810	182	25	,	,	PUNCT
ejpam-6810	182	26	ηn	ηn	ADJ
ejpam-6810	182	27	)	)	PUNCT
ejpam-6810	182	28	+	+	NUM
ejpam-6810	182	29	s(σb(υηn−1,υη∗	s(σb(υηn−1,υη∗	NOUN
ejpam-6810	182	30	)	)	PUNCT
ejpam-6810	183	1	+	+	X
ejpam-6810	183	2	σb(υηn−1,υηn	σb(υηn−1,υηn	ADJ
ejpam-6810	183	3	)	)	PUNCT
ejpam-6810	184	1	+	+	CCONJ
ejpam-6810	184	2	σb(υηn	σb(υηn	NOUN
ejpam-6810	184	3	,	,	PUNCT
ejpam-6810	184	4	υη∗	υη∗	NOUN
ejpam-6810	184	5	)	)	PUNCT
ejpam-6810	184	6	)	)	PUNCT
ejpam-6810	184	7	,	,	PUNCT
ejpam-6810	184	8	≤sσb(η	≤sσb(η	ADJ
ejpam-6810	184	9	∗	∗	NOUN
ejpam-6810	184	10	,	,	PUNCT
ejpam-6810	184	11	ηn	ηn	ADJ
ejpam-6810	184	12	)	)	PUNCT
ejpam-6810	184	13	+	+	SYM
ejpam-6810	185	1	s	s	X
ejpam-6810	185	2	(	(	PUNCT
ejpam-6810	185	3	1	1	NUM
ejpam-6810	185	4	s2	s2	NOUN
ejpam-6810	185	5	(	(	PUNCT
ejpam-6810	185	6	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	185	7	,	,	PUNCT
ejpam-6810	185	8	η	η	NOUN
ejpam-6810	185	9	∗	∗	NOUN
ejpam-6810	185	10	)	)	PUNCT
ejpam-6810	185	11	+	+	CCONJ
ejpam-6810	185	12	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	185	13	,	,	PUNCT
ejpam-6810	185	14	ηn	ηn	ADJ
ejpam-6810	185	15	)	)	PUNCT
ejpam-6810	185	16	+	+	CCONJ
ejpam-6810	185	17	σb(ηn	σb(ηn	PROPN
ejpam-6810	185	18	,	,	PUNCT
ejpam-6810	185	19	η	η	NOUN
ejpam-6810	185	20	∗	∗	NOUN
ejpam-6810	185	21	)	)	PUNCT
ejpam-6810	185	22	)	)	PUNCT
ejpam-6810	185	23	)	)	PUNCT
ejpam-6810	185	24	,	,	PUNCT
ejpam-6810	185	25	≤sσb(η	≤sσb(η	ADJ
ejpam-6810	185	26	∗	∗	NOUN
ejpam-6810	185	27	,	,	PUNCT
ejpam-6810	185	28	ηn	ηn	ADJ
ejpam-6810	185	29	)	)	PUNCT
ejpam-6810	186	1	+	+	SYM
ejpam-6810	186	2	s	s	X
ejpam-6810	186	3	(	(	PUNCT
ejpam-6810	186	4	1	1	NUM
ejpam-6810	186	5	s2	s2	NOUN
ejpam-6810	186	6	(	(	PUNCT
ejpam-6810	186	7	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	186	8	,	,	PUNCT
ejpam-6810	186	9	η	η	NOUN
ejpam-6810	186	10	∗	∗	NOUN
ejpam-6810	186	11	)	)	PUNCT
ejpam-6810	186	12	+	+	CCONJ
ejpam-6810	186	13	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	186	14	,	,	PUNCT
ejpam-6810	186	15	ηn	ηn	ADJ
ejpam-6810	186	16	)	)	PUNCT
ejpam-6810	186	17	+	+	CCONJ
ejpam-6810	186	18	σb(ηn	σb(ηn	PROPN
ejpam-6810	186	19	,	,	PUNCT
ejpam-6810	186	20	η	η	NOUN
ejpam-6810	186	21	∗	∗	NOUN
ejpam-6810	186	22	)	)	PUNCT
ejpam-6810	186	23	)	)	PUNCT
ejpam-6810	186	24	,	,	PUNCT
ejpam-6810	186	25	)	)	PUNCT
ejpam-6810	186	26	≤sσb(η	≤sσb(η	ADJ
ejpam-6810	186	27	∗	∗	NOUN
ejpam-6810	186	28	,	,	PUNCT
ejpam-6810	186	29	ηn	ηn	ADJ
ejpam-6810	186	30	)	)	PUNCT
ejpam-6810	186	31	+	+	CCONJ
ejpam-6810	186	32	(	(	PUNCT
ejpam-6810	186	33	1	1	NUM
ejpam-6810	186	34	s	s	PART
ejpam-6810	186	35	(	(	PUNCT
ejpam-6810	186	36	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	186	37	,	,	PUNCT
ejpam-6810	186	38	η	η	NOUN
ejpam-6810	186	39	∗	∗	NOUN
ejpam-6810	186	40	)	)	PUNCT
ejpam-6810	186	41	+	+	CCONJ
ejpam-6810	186	42	σb(ηn−1	σb(ηn−1	PROPN
ejpam-6810	186	43	,	,	PUNCT
ejpam-6810	186	44	ηn	ηn	ADJ
ejpam-6810	186	45	)	)	PUNCT
ejpam-6810	186	46	+	+	CCONJ
ejpam-6810	186	47	σb(ηn	σb(ηn	PROPN
ejpam-6810	186	48	,	,	PUNCT
ejpam-6810	186	49	η	η	NOUN
ejpam-6810	186	50	∗	∗	NOUN
ejpam-6810	186	51	)	)	PUNCT
ejpam-6810	186	52	)	)	PUNCT
ejpam-6810	186	53	)	)	PUNCT
ejpam-6810	186	54	.	.	PUNCT
ejpam-6810	187	1	taking	take	VERB
ejpam-6810	187	2	the	the	DET
ejpam-6810	187	3	limit	limit	NOUN
ejpam-6810	187	4	as	as	ADP
ejpam-6810	187	5	n	n	PROPN
ejpam-6810	187	6	→	→	SYM
ejpam-6810	187	7	+	+	NOUN
ejpam-6810	187	8	∞	∞	PROPN
ejpam-6810	187	9	,	,	PUNCT
ejpam-6810	187	10	we	we	PRON
ejpam-6810	187	11	note	note	VERB
ejpam-6810	187	12	that	that	SCONJ
ejpam-6810	187	13	each	each	DET
ejpam-6810	187	14	term	term	NOUN
ejpam-6810	187	15	in	in	ADP
ejpam-6810	187	16	the	the	DET
ejpam-6810	187	17	preceding	precede	VERB
ejpam-6810	187	18	sum	sum	NOUN
ejpam-6810	187	19	vanishes	vanish	VERB
ejpam-6810	187	20	,	,	PUNCT
ejpam-6810	187	21	and	and	CCONJ
ejpam-6810	187	22	so	so	ADV
ejpam-6810	187	23	σb(η	σb(η	PUNCT
ejpam-6810	187	24	∗,υη∗	∗,υη∗	NOUN
ejpam-6810	187	25	)	)	PUNCT
ejpam-6810	187	26	=	=	PUNCT
ejpam-6810	188	1	0	0	X
ejpam-6810	188	2	.	.	PUNCT
ejpam-6810	189	1	therefore	therefore	ADV
ejpam-6810	189	2	,	,	PUNCT
ejpam-6810	189	3	we	we	PRON
ejpam-6810	189	4	conclude	conclude	VERB
ejpam-6810	189	5	that	that	SCONJ
ejpam-6810	189	6	υη∗	υη∗	NOUN
ejpam-6810	189	7	=	=	PUNCT
ejpam-6810	189	8	η∗.	η∗.	NOUN
ejpam-6810	189	9	in	in	ADP
ejpam-6810	189	10	order	order	NOUN
ejpam-6810	189	11	to	to	PART
ejpam-6810	189	12	prove	prove	VERB
ejpam-6810	189	13	there	there	PRON
ejpam-6810	189	14	exists	exist	VERB
ejpam-6810	189	15	at	at	ADP
ejpam-6810	189	16	most	most	ADV
ejpam-6810	189	17	two	two	NUM
ejpam-6810	189	18	fps	fps	PROPN
ejpam-6810	189	19	.	.	PUNCT
ejpam-6810	190	1	assume	assume	VERB
ejpam-6810	190	2	by	by	ADP
ejpam-6810	190	3	contradiction	contradiction	NOUN
ejpam-6810	190	4	that	that	PRON
ejpam-6810	190	5	υ	υ	PROPN
ejpam-6810	190	6	has	have	VERB
ejpam-6810	190	7	at	at	ADV
ejpam-6810	190	8	least	least	ADV
ejpam-6810	190	9	three	three	NUM
ejpam-6810	190	10	pairwise	pairwise	NOUN
ejpam-6810	190	11	distinct	distinct	PROPN
ejpam-6810	190	12	fps	fps	PROPN
ejpam-6810	190	13	,	,	PUNCT
ejpam-6810	190	14	say	say	VERB
ejpam-6810	190	15	η	η	PROPN
ejpam-6810	190	16	,	,	PUNCT
ejpam-6810	190	17	ξ	ξ	PROPN
ejpam-6810	190	18	,	,	PUNCT
ejpam-6810	190	19	and	and	CCONJ
ejpam-6810	190	20	ζ	ζ	NOUN
ejpam-6810	190	21	.	.	PUNCT
ejpam-6810	191	1	that	that	PRON
ejpam-6810	191	2	is	be	AUX
ejpam-6810	191	3	,	,	PUNCT
ejpam-6810	191	4	υη	υη	PROPN
ejpam-6810	191	5	=	=	PROPN
ejpam-6810	191	6	η	η	PROPN
ejpam-6810	191	7	,	,	PUNCT
ejpam-6810	191	8	υξ	υξ	VERB
ejpam-6810	191	9	=	=	SYM
ejpam-6810	191	10	ξ	ξ	PROPN
ejpam-6810	191	11	and	and	CCONJ
ejpam-6810	191	12	υζ	υζ	NOUN
ejpam-6810	191	13	=	=	SYM
ejpam-6810	191	14	ζ	ζ	PROPN
ejpam-6810	191	15	.	.	PUNCT
ejpam-6810	192	1	then	then	ADV
ejpam-6810	192	2	by	by	ADP
ejpam-6810	192	3	contraction	contraction	NOUN
ejpam-6810	192	4	condition	condition	NOUN
ejpam-6810	192	5	,	,	PUNCT
ejpam-6810	192	6	τ	τ	PROPN
ejpam-6810	192	7	+	+	NUM
ejpam-6810	192	8	f	f	X
ejpam-6810	192	9	(	(	PUNCT
ejpam-6810	192	10	σb(η	σb(η	PROPN
ejpam-6810	192	11	,	,	PUNCT
ejpam-6810	192	12	ξ	ξ	NOUN
ejpam-6810	192	13	)	)	PUNCT
ejpam-6810	192	14	+	+	CCONJ
ejpam-6810	192	15	σb(ξ	σb(ξ	ADJ
ejpam-6810	192	16	,	,	PUNCT
ejpam-6810	192	17	ζ	ζ	NOUN
ejpam-6810	192	18	)	)	PUNCT
ejpam-6810	192	19	+	+	NUM
ejpam-6810	192	20	σb(η	σb(η	NUM
ejpam-6810	192	21	,	,	PUNCT
ejpam-6810	192	22	ζ	ζ	NOUN
ejpam-6810	192	23	)	)	PUNCT
ejpam-6810	192	24	)	)	PUNCT
ejpam-6810	193	1	=	=	PUNCT
ejpam-6810	194	1	τ	τ	X
ejpam-6810	194	2	+	+	NUM
ejpam-6810	194	3	f	f	X
ejpam-6810	194	4	(	(	PUNCT
ejpam-6810	194	5	σb(υη	σb(υη	PROPN
ejpam-6810	194	6	,	,	PUNCT
ejpam-6810	194	7	υξ	υξ	NOUN
ejpam-6810	194	8	)	)	PUNCT
ejpam-6810	195	1	+	+	CCONJ
ejpam-6810	195	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	195	3	,	,	PUNCT
ejpam-6810	195	4	υζ	υζ	NOUN
ejpam-6810	195	5	)	)	PUNCT
ejpam-6810	195	6	+	+	CCONJ
ejpam-6810	195	7	σb(υη	σb(υη	PROPN
ejpam-6810	195	8	,	,	PUNCT
ejpam-6810	195	9	υζ	υζ	NOUN
ejpam-6810	195	10	)	)	PUNCT
ejpam-6810	195	11	)	)	PUNCT
ejpam-6810	195	12	,	,	PUNCT
ejpam-6810	195	13	≤	≤	NUM
ejpam-6810	195	14	f	f	X
ejpam-6810	195	15	(	(	PUNCT
ejpam-6810	195	16	1	1	NUM
ejpam-6810	195	17	s2	s2	NOUN
ejpam-6810	195	18	(	(	PUNCT
ejpam-6810	195	19	σb(η	σb(η	PROPN
ejpam-6810	195	20	,	,	PUNCT
ejpam-6810	195	21	ξ	ξ	NOUN
ejpam-6810	195	22	)	)	PUNCT
ejpam-6810	195	23	+	+	CCONJ
ejpam-6810	195	24	σb(ξ	σb(ξ	ADJ
ejpam-6810	195	25	,	,	PUNCT
ejpam-6810	195	26	ζ	ζ	NOUN
ejpam-6810	195	27	)	)	PUNCT
ejpam-6810	195	28	+	+	NUM
ejpam-6810	195	29	σb(η	σb(η	NUM
ejpam-6810	195	30	,	,	PUNCT
ejpam-6810	195	31	ζ	ζ	NOUN
ejpam-6810	195	32	)	)	PUNCT
ejpam-6810	195	33	)	)	PUNCT
ejpam-6810	195	34	)	)	PUNCT
ejpam-6810	195	35	.	.	PUNCT
ejpam-6810	196	1	s.	s.	PROPN
ejpam-6810	196	2	batul	batul	PROPN
ejpam-6810	196	3	et	et	PROPN
ejpam-6810	196	4	al	al	PROPN
ejpam-6810	196	5	.	.	PUNCT
ejpam-6810	196	6	/	/	SYM
ejpam-6810	196	7	eur	eur	PROPN
ejpam-6810	196	8	.	.	PUNCT
ejpam-6810	197	1	j.	j.	PROPN
ejpam-6810	197	2	pure	pure	PROPN
ejpam-6810	197	3	appl	appl	PROPN
ejpam-6810	197	4	.	.	PROPN
ejpam-6810	197	5	math	math	PROPN
ejpam-6810	197	6	,	,	PUNCT
ejpam-6810	197	7	18	18	NUM
ejpam-6810	197	8	(	(	PUNCT
ejpam-6810	197	9	4	4	NUM
ejpam-6810	197	10	)	)	PUNCT
ejpam-6810	197	11	(	(	PUNCT
ejpam-6810	197	12	2025	2025	NUM
ejpam-6810	197	13	)	)	PUNCT
ejpam-6810	197	14	,	,	PUNCT
ejpam-6810	197	15	6810	6810	NUM
ejpam-6810	197	16	9	9	NUM
ejpam-6810	197	17	of	of	ADP
ejpam-6810	197	18	23	23	NUM
ejpam-6810	197	19	since	since	SCONJ
ejpam-6810	197	20	f	f	PROPN
ejpam-6810	197	21	is	be	AUX
ejpam-6810	197	22	increasing	increase	VERB
ejpam-6810	197	23	,	,	PUNCT
ejpam-6810	197	24	σb(η	σb(η	NUM
ejpam-6810	197	25	,	,	PUNCT
ejpam-6810	197	26	ξ	ξ	NOUN
ejpam-6810	197	27	)	)	PUNCT
ejpam-6810	197	28	+	+	CCONJ
ejpam-6810	197	29	σb(ξ	σb(ξ	ADJ
ejpam-6810	197	30	,	,	PUNCT
ejpam-6810	197	31	ζ	ζ	NOUN
ejpam-6810	197	32	)	)	PUNCT
ejpam-6810	197	33	+	+	NUM
ejpam-6810	197	34	σb(η	σb(η	NUM
ejpam-6810	197	35	,	,	PUNCT
ejpam-6810	197	36	ζ	ζ	NOUN
ejpam-6810	197	37	)	)	PUNCT
ejpam-6810	197	38	≤	≤	NOUN
ejpam-6810	197	39	1	1	NUM
ejpam-6810	197	40	s2	s2	NOUN
ejpam-6810	197	41	(	(	PUNCT
ejpam-6810	197	42	σb(η	σb(η	PROPN
ejpam-6810	197	43	,	,	PUNCT
ejpam-6810	197	44	ξ	ξ	NOUN
ejpam-6810	197	45	)	)	PUNCT
ejpam-6810	197	46	+	+	CCONJ
ejpam-6810	197	47	σb(ξ	σb(ξ	ADJ
ejpam-6810	197	48	,	,	PUNCT
ejpam-6810	197	49	ζ	ζ	NOUN
ejpam-6810	197	50	)	)	PUNCT
ejpam-6810	197	51	+	+	NUM
ejpam-6810	197	52	σb(η	σb(η	NUM
ejpam-6810	197	53	,	,	PUNCT
ejpam-6810	197	54	ζ	ζ	NOUN
ejpam-6810	197	55	)	)	PUNCT
ejpam-6810	197	56	)	)	PUNCT
ejpam-6810	197	57	,	,	PUNCT
ejpam-6810	197	58	which	which	PRON
ejpam-6810	197	59	is	be	AUX
ejpam-6810	197	60	a	a	DET
ejpam-6810	197	61	contradiction	contradiction	NOUN
ejpam-6810	197	62	,	,	PUNCT
ejpam-6810	197	63	since	since	SCONJ
ejpam-6810	197	64	s2	s2	PROPN
ejpam-6810	197	65	≥	≥	NUM
ejpam-6810	197	66	1	1	NUM
ejpam-6810	197	67	.	.	PUNCT
ejpam-6810	198	1	thus	thus	ADV
ejpam-6810	198	2	,	,	PUNCT
ejpam-6810	198	3	we	we	PRON
ejpam-6810	198	4	conclude	conclude	VERB
ejpam-6810	198	5	that	that	SCONJ
ejpam-6810	198	6	υ	υ	PROPN
ejpam-6810	198	7	possesses	possess	VERB
ejpam-6810	198	8	at	at	ADP
ejpam-6810	198	9	most	most	ADV
ejpam-6810	198	10	two	two	NUM
ejpam-6810	198	11	fps	fps	PROPN
ejpam-6810	198	12	.	.	PUNCT
ejpam-6810	199	1	conversely	conversely	ADV
ejpam-6810	199	2	,	,	PUNCT
ejpam-6810	199	3	suppose	suppose	VERB
ejpam-6810	199	4	that	that	SCONJ
ejpam-6810	199	5	υ	υ	PROPN
ejpam-6810	199	6	possesses	possess	VERB
ejpam-6810	199	7	a	a	DET
ejpam-6810	199	8	fp	fp	INTJ
ejpam-6810	199	9	η∗.	η∗.	NOUN
ejpam-6810	199	10	we	we	PRON
ejpam-6810	199	11	have	have	VERB
ejpam-6810	199	12	to	to	PART
ejpam-6810	199	13	prove	prove	VERB
ejpam-6810	199	14	that	that	SCONJ
ejpam-6810	199	15	there	there	PRON
ejpam-6810	199	16	are	be	VERB
ejpam-6810	199	17	no	no	DET
ejpam-6810	199	18	periodic	periodic	ADJ
ejpam-6810	199	19	point	point	NOUN
ejpam-6810	199	20	in	in	ADP
ejpam-6810	199	21	υ	υ	NOUN
ejpam-6810	199	22	with	with	ADP
ejpam-6810	199	23	a	a	DET
ejpam-6810	199	24	prime	prime	ADJ
ejpam-6810	199	25	period	period	NOUN
ejpam-6810	199	26	2	2	NUM
ejpam-6810	199	27	.	.	PUNCT
ejpam-6810	200	1	for	for	ADP
ejpam-6810	200	2	this	this	PRON
ejpam-6810	200	3	,	,	PUNCT
ejpam-6810	200	4	suppose	suppose	VERB
ejpam-6810	200	5	by	by	ADP
ejpam-6810	200	6	contradiction	contradiction	NOUN
ejpam-6810	200	7	that	that	PRON
ejpam-6810	200	8	υ	υ	PROPN
ejpam-6810	200	9	has	have	AUX
ejpam-6810	200	10	a	a	DET
ejpam-6810	200	11	periodic	periodic	ADJ
ejpam-6810	200	12	point	point	NOUN
ejpam-6810	200	13	η	η	PROPN
ejpam-6810	200	14	of	of	ADP
ejpam-6810	200	15	prime	prime	ADJ
ejpam-6810	200	16	period	period	NOUN
ejpam-6810	200	17	2	2	NUM
ejpam-6810	200	18	,	,	PUNCT
ejpam-6810	200	19	that	that	ADV
ejpam-6810	200	20	is	is	ADV
ejpam-6810	200	21	,	,	PUNCT
ejpam-6810	200	22	υ(υη	υ(υη	X
ejpam-6810	200	23	)	)	PUNCT
ejpam-6810	200	24	=	=	SYM
ejpam-6810	200	25	η	η	PROPN
ejpam-6810	200	26	.	.	PROPN
ejpam-6810	200	27	define	define	VERB
ejpam-6810	200	28	ξ	ξ	PROPN
ejpam-6810	200	29	=	=	SYM
ejpam-6810	200	30	υη	υη	PROPN
ejpam-6810	200	31	and	and	CCONJ
ejpam-6810	200	32	η	η	PROPN
ejpam-6810	200	33	=	=	SYM
ejpam-6810	200	34	υξ	υξ	PROPN
ejpam-6810	200	35	.	.	PUNCT
ejpam-6810	201	1	then	then	ADV
ejpam-6810	201	2	τ	τ	PROPN
ejpam-6810	201	3	+	+	NUM
ejpam-6810	201	4	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	201	5	,	,	PUNCT
ejpam-6810	201	6	υξ	υξ	X
ejpam-6810	201	7	)	)	PUNCT
ejpam-6810	201	8	+	+	CCONJ
ejpam-6810	201	9	σb(υξ	σb(υξ	PROPN
ejpam-6810	201	10	,	,	PUNCT
ejpam-6810	201	11	υη∗	υη∗	NOUN
ejpam-6810	201	12	)	)	PUNCT
ejpam-6810	201	13	+	+	CCONJ
ejpam-6810	201	14	σb(υη	σb(υη	PROPN
ejpam-6810	201	15	,	,	PUNCT
ejpam-6810	201	16	υη∗	υη∗	NOUN
ejpam-6810	201	17	)	)	PUNCT
ejpam-6810	201	18	)	)	PUNCT
ejpam-6810	202	1	=	=	SYM
ejpam-6810	202	2	f(σb(ξ	f(σb(ξ	NUM
ejpam-6810	202	3	,	,	PUNCT
ejpam-6810	202	4	η	η	NOUN
ejpam-6810	202	5	)	)	PUNCT
ejpam-6810	202	6	+	+	CCONJ
ejpam-6810	202	7	σb(η	σb(η	PROPN
ejpam-6810	202	8	,	,	PUNCT
ejpam-6810	202	9	η	η	NOUN
ejpam-6810	202	10	∗	∗	NOUN
ejpam-6810	202	11	)	)	PUNCT
ejpam-6810	202	12	+	+	CCONJ
ejpam-6810	202	13	σb(ξ	σb(ξ	NUM
ejpam-6810	202	14	,	,	PUNCT
ejpam-6810	202	15	η	η	NOUN
ejpam-6810	202	16	∗	∗	NOUN
ejpam-6810	202	17	)	)	PUNCT
ejpam-6810	202	18	)	)	PUNCT
ejpam-6810	202	19	,	,	PUNCT
ejpam-6810	202	20	which	which	PRON
ejpam-6810	202	21	contradicts	contradict	VERB
ejpam-6810	202	22	(	(	PUNCT
ejpam-6810	202	23	3	3	NUM
ejpam-6810	202	24	)	)	PUNCT
ejpam-6810	202	25	.	.	PUNCT
ejpam-6810	203	1	thus	thus	ADV
ejpam-6810	203	2	,	,	PUNCT
ejpam-6810	203	3	υ	υ	PROPN
ejpam-6810	203	4	does	do	AUX
ejpam-6810	203	5	not	not	PART
ejpam-6810	203	6	have	have	VERB
ejpam-6810	203	7	periodic	periodic	ADJ
ejpam-6810	203	8	points	point	NOUN
ejpam-6810	203	9	with	with	ADP
ejpam-6810	203	10	a	a	DET
ejpam-6810	203	11	prime	prime	ADJ
ejpam-6810	203	12	period	period	NOUN
ejpam-6810	203	13	2	2	NUM
ejpam-6810	203	14	.	.	PUNCT
ejpam-6810	203	15	remark	remark	NOUN
ejpam-6810	203	16	1	1	NUM
ejpam-6810	203	17	.	.	PUNCT
ejpam-6810	204	1	in	in	ADP
ejpam-6810	204	2	the	the	DET
ejpam-6810	204	3	assumption	assumption	NOUN
ejpam-6810	204	4	of	of	ADP
ejpam-6810	204	5	theorem	theorem	NOUN
ejpam-6810	204	6	1	1	NUM
ejpam-6810	204	7	,	,	PUNCT
ejpam-6810	204	8	if	if	SCONJ
ejpam-6810	204	9	we	we	PRON
ejpam-6810	204	10	add	add	VERB
ejpam-6810	204	11	an	an	DET
ejpam-6810	204	12	extra	extra	ADJ
ejpam-6810	204	13	condition	condition	NOUN
ejpam-6810	204	14	that	that	SCONJ
ejpam-6810	204	15	the	the	DET
ejpam-6810	204	16	fp	fp	PROPN
ejpam-6810	204	17	η∗	η∗	PROPN
ejpam-6810	204	18	is	be	AUX
ejpam-6810	204	19	the	the	DET
ejpam-6810	204	20	limit	limit	NOUN
ejpam-6810	204	21	of	of	ADP
ejpam-6810	204	22	some	some	DET
ejpam-6810	204	23	iterative	iterative	NOUN
ejpam-6810	204	24	sequence	sequence	NOUN
ejpam-6810	204	25	,	,	PUNCT
ejpam-6810	204	26	then	then	ADV
ejpam-6810	204	27	υ	υ	PROPN
ejpam-6810	204	28	has	have	VERB
ejpam-6810	204	29	a	a	DET
ejpam-6810	204	30	unique	unique	ADJ
ejpam-6810	204	31	fp	fp	NOUN
ejpam-6810	204	32	.	.	PUNCT
ejpam-6810	205	1	now	now	ADV
ejpam-6810	205	2	,	,	PUNCT
ejpam-6810	205	3	we	we	PRON
ejpam-6810	205	4	show	show	VERB
ejpam-6810	205	5	that	that	SCONJ
ejpam-6810	205	6	ηn	ηn	PROPN
ejpam-6810	205	7	6=	6=	ADJ
ejpam-6810	205	8	η∗foralln	η∗foralln	ADV
ejpam-6810	205	9	=	=	SYM
ejpam-6810	205	10	1,2	1,2	NUM
ejpam-6810	205	11	,	,	PUNCT
ejpam-6810	205	12	·	·	PUNCT
ejpam-6810	205	13	·	·	PUNCT
ejpam-6810	205	14	·	·	PUNCT
ejpam-6810	205	15	.	.	PUNCT
ejpam-6810	206	1	for	for	ADP
ejpam-6810	206	2	this	this	PRON
ejpam-6810	206	3	,	,	PUNCT
ejpam-6810	206	4	let	let	VERB
ejpam-6810	206	5	η0	η0	NOUN
ejpam-6810	206	6	be	be	AUX
ejpam-6810	206	7	an	an	DET
ejpam-6810	206	8	initial	initial	ADJ
ejpam-6810	206	9	point	point	NOUN
ejpam-6810	206	10	,	,	PUNCT
ejpam-6810	206	11	and	and	CCONJ
ejpam-6810	206	12	iterative	iterative	NOUN
ejpam-6810	206	13	sequence	sequence	NOUN
ejpam-6810	206	14	will	will	AUX
ejpam-6810	206	15	be	be	AUX
ejpam-6810	206	16	η1	η1	NOUN
ejpam-6810	206	17	=	=	SYM
ejpam-6810	206	18	υη0	υη0	PROPN
ejpam-6810	206	19	,	,	PUNCT
ejpam-6810	206	20	η2	η2	X
ejpam-6810	206	21	=	=	SYM
ejpam-6810	206	22	υη1	υη1	PROPN
ejpam-6810	206	23	,	,	PUNCT
ejpam-6810	206	24	·	·	PUNCT
ejpam-6810	206	25	·	·	PUNCT
ejpam-6810	206	26	·	·	PUNCT
ejpam-6810	206	27	.	.	PUNCT
ejpam-6810	207	1	in	in	ADP
ejpam-6810	207	2	that	that	DET
ejpam-6810	207	3	case	case	NOUN
ejpam-6810	207	4	,	,	PUNCT
ejpam-6810	207	5	there	there	PRON
ejpam-6810	207	6	is	be	VERB
ejpam-6810	207	7	only	only	ADV
ejpam-6810	207	8	one	one	NUM
ejpam-6810	207	9	fp	fp	NOUN
ejpam-6810	207	10	η∗.	η∗.	NOUN
ejpam-6810	207	11	assume	assume	VERB
ejpam-6810	207	12	in	in	ADP
ejpam-6810	207	13	fact	fact	NOUN
ejpam-6810	207	14	that	that	SCONJ
ejpam-6810	207	15	υ	υ	PROPN
ejpam-6810	207	16	has	have	AUX
ejpam-6810	207	17	another	another	DET
ejpam-6810	207	18	fp	fp	X
ejpam-6810	207	19	x∗∗.	x∗∗.	PROPN
ejpam-6810	207	20	for	for	ADP
ejpam-6810	207	21	every	every	DET
ejpam-6810	207	22	n	n	NOUN
ejpam-6810	207	23	=	=	SYM
ejpam-6810	207	24	1,2	1,2	NUM
ejpam-6810	207	25	,	,	PUNCT
ejpam-6810	207	26	·	·	PUNCT
ejpam-6810	207	27	·	·	PUNCT
ejpam-6810	207	28	·	·	PUNCT
ejpam-6810	207	29	,	,	PUNCT
ejpam-6810	207	30	it	it	PRON
ejpam-6810	207	31	is	be	AUX
ejpam-6810	207	32	evident	evident	ADJ
ejpam-6810	207	33	that	that	SCONJ
ejpam-6810	207	34	xn	xn	PROPN
ejpam-6810	207	35	6=	6=	PROPN
ejpam-6810	207	36	η∗∗.	η∗∗.	PROPN
ejpam-6810	207	37	thus	thus	ADV
ejpam-6810	207	38	,	,	PUNCT
ejpam-6810	207	39	for	for	ADP
ejpam-6810	207	40	every	every	DET
ejpam-6810	207	41	n	n	NOUN
ejpam-6810	207	42	=	=	SYM
ejpam-6810	207	43	1,2	1,2	NUM
ejpam-6810	207	44	,	,	PUNCT
ejpam-6810	207	45	·	·	PUNCT
ejpam-6810	207	46	·	·	PUNCT
ejpam-6810	207	47	·	·	PUNCT
ejpam-6810	207	48	,	,	PUNCT
ejpam-6810	207	49	we	we	PRON
ejpam-6810	207	50	have	have	VERB
ejpam-6810	207	51	that	that	SCONJ
ejpam-6810	207	52	the	the	DET
ejpam-6810	207	53	points	point	NOUN
ejpam-6810	207	54	η∗	η∗	PROPN
ejpam-6810	207	55	,	,	PUNCT
ejpam-6810	207	56	η∗∗	η∗∗	ADV
ejpam-6810	207	57	,	,	PUNCT
ejpam-6810	207	58	and	and	CCONJ
ejpam-6810	207	59	ηn	ηn	PROPN
ejpam-6810	207	60	are	be	AUX
ejpam-6810	207	61	pairwise	pairwise	NOUN
ejpam-6810	207	62	distinct	distinct	ADJ
ejpam-6810	207	63	.	.	PUNCT
ejpam-6810	208	1	now	now	ADV
ejpam-6810	208	2	,	,	PUNCT
ejpam-6810	208	3	by	by	ADP
ejpam-6810	208	4	contraction	contraction	NOUN
ejpam-6810	208	5	condition	condition	NOUN
ejpam-6810	208	6	,	,	PUNCT
ejpam-6810	208	7	τ	τ	PROPN
ejpam-6810	208	8	+	+	CCONJ
ejpam-6810	208	9	f(σb(η	f(σb(η	PROPN
ejpam-6810	208	10	∗	∗	NOUN
ejpam-6810	208	11	,	,	PUNCT
ejpam-6810	208	12	η∗∗	η∗∗	ADV
ejpam-6810	208	13	)	)	PUNCT
ejpam-6810	209	1	+	+	CCONJ
ejpam-6810	209	2	σb(η	σb(η	NUM
ejpam-6810	209	3	∗	∗	NOUN
ejpam-6810	209	4	,	,	PUNCT
ejpam-6810	209	5	ηn+1	ηn+1	NUM
ejpam-6810	209	6	)	)	PUNCT
ejpam-6810	210	1	+	+	NUM
ejpam-6810	210	2	σb(η	σb(η	X
ejpam-6810	210	3	∗∗	∗∗	NOUN
ejpam-6810	210	4	,	,	PUNCT
ejpam-6810	210	5	ηn+1	ηn+1	NUM
ejpam-6810	210	6	)	)	PUNCT
ejpam-6810	210	7	)	)	PUNCT
ejpam-6810	211	1	=	=	PUNCT
ejpam-6810	211	2	τ	τ	PROPN
ejpam-6810	211	3	+	+	NUM
ejpam-6810	211	4	f(σb(υη∗,υη∗∗	f(σb(υη∗,υη∗∗	NOUN
ejpam-6810	211	5	)	)	PUNCT
ejpam-6810	211	6	+	+	SYM
ejpam-6810	211	7	σb(υη∗,υηn	σb(υη∗,υηn	PROPN
ejpam-6810	211	8	)	)	PUNCT
ejpam-6810	211	9	+	+	NUM
ejpam-6810	211	10	σb(υη∗∗,υηn	σb(υη∗∗,υηn	PROPN
ejpam-6810	211	11	)	)	PUNCT
ejpam-6810	211	12	)	)	PUNCT
ejpam-6810	212	1	≤	≤	NUM
ejpam-6810	212	2	f	f	X
ejpam-6810	212	3	(	(	PUNCT
ejpam-6810	212	4	1	1	NUM
ejpam-6810	212	5	s2	s2	NOUN
ejpam-6810	212	6	(	(	PUNCT
ejpam-6810	212	7	σb(η	σb(η	NUM
ejpam-6810	212	8	∗	∗	NOUN
ejpam-6810	212	9	,	,	PUNCT
ejpam-6810	212	10	η∗∗	η∗∗	ADV
ejpam-6810	212	11	)	)	PUNCT
ejpam-6810	212	12	+	+	CCONJ
ejpam-6810	212	13	σb(η	σb(η	NUM
ejpam-6810	212	14	∗	∗	NOUN
ejpam-6810	212	15	,	,	PUNCT
ejpam-6810	212	16	ηn	ηn	ADJ
ejpam-6810	212	17	)	)	PUNCT
ejpam-6810	212	18	+	+	NUM
ejpam-6810	212	19	σb(η	σb(η	X
ejpam-6810	212	20	∗∗	∗∗	NOUN
ejpam-6810	212	21	,	,	PUNCT
ejpam-6810	212	22	ηn	ηn	ADJ
ejpam-6810	212	23	)	)	PUNCT
ejpam-6810	212	24	)	)	PUNCT
ejpam-6810	212	25	)	)	PUNCT
ejpam-6810	212	26	.	.	PUNCT
ejpam-6810	213	1	as	as	ADP
ejpam-6810	213	2	n	n	PROPN
ejpam-6810	213	3	−→0	−→0	PROPN
ejpam-6810	213	4	,	,	PUNCT
ejpam-6810	213	5	we	we	PRON
ejpam-6810	213	6	get	get	VERB
ejpam-6810	213	7	σb(η∗	σb(η∗	NOUN
ejpam-6810	213	8	,	,	PUNCT
ejpam-6810	213	9	ηn+1	ηn+1	NUM
ejpam-6810	213	10	)	)	PUNCT
ejpam-6810	213	11	−→	−→	NOUN
ejpam-6810	213	12	0	0	NUM
ejpam-6810	213	13	,	,	PUNCT
ejpam-6810	213	14	σb(η∗	σb(η∗	NUM
ejpam-6810	213	15	,	,	PUNCT
ejpam-6810	213	16	ηn	ηn	ADJ
ejpam-6810	213	17	)	)	PUNCT
ejpam-6810	213	18	−→	−→	NOUN
ejpam-6810	213	19	0	0	NUM
ejpam-6810	213	20	,	,	PUNCT
ejpam-6810	213	21	σb(η∗∗	σb(η∗∗	PROPN
ejpam-6810	213	22	,	,	PUNCT
ejpam-6810	213	23	ηn+1	ηn+1	NUM
ejpam-6810	213	24	)	)	PUNCT
ejpam-6810	213	25	−→	−→	NOUN
ejpam-6810	213	26	σb(x	σb(x	ADJ
ejpam-6810	213	27	∗∗	∗∗	PROPN
ejpam-6810	213	28	,	,	PUNCT
ejpam-6810	213	29	x∗	x∗	PROPN
ejpam-6810	213	30	)	)	PUNCT
ejpam-6810	213	31	and	and	CCONJ
ejpam-6810	213	32	σb(η	σb(η	X
ejpam-6810	214	1	∗∗	∗∗	NOUN
ejpam-6810	214	2	,	,	PUNCT
ejpam-6810	214	3	ηn	ηn	ADJ
ejpam-6810	214	4	)	)	PUNCT
ejpam-6810	214	5	−→	−→	NOUN
ejpam-6810	214	6	σb(η	σb(η	X
ejpam-6810	214	7	∗∗	∗∗	NOUN
ejpam-6810	214	8	,	,	PUNCT
ejpam-6810	214	9	η∗	η∗	NOUN
ejpam-6810	214	10	)	)	PUNCT
ejpam-6810	214	11	.	.	PUNCT
ejpam-6810	215	1	hence	hence	ADV
ejpam-6810	215	2	,	,	PUNCT
ejpam-6810	215	3	τ	τ	PROPN
ejpam-6810	215	4	+	+	CCONJ
ejpam-6810	215	5	f(2σb(η	f(2σb(η	ADJ
ejpam-6810	215	6	∗	∗	NOUN
ejpam-6810	215	7	,	,	PUNCT
ejpam-6810	215	8	η∗∗	η∗∗	NOUN
ejpam-6810	215	9	)	)	PUNCT
ejpam-6810	215	10	)	)	PUNCT
ejpam-6810	215	11	≤	≤	NUM
ejpam-6810	216	1	f	f	X
ejpam-6810	216	2	(	(	PUNCT
ejpam-6810	216	3	1	1	NUM
ejpam-6810	216	4	s2	s2	NOUN
ejpam-6810	216	5	2σb(η	2σb(η	NUM
ejpam-6810	216	6	∗	∗	NOUN
ejpam-6810	216	7	,	,	PUNCT
ejpam-6810	216	8	η∗∗	η∗∗	NOUN
ejpam-6810	216	9	)	)	PUNCT
ejpam-6810	216	10	)	)	PUNCT
ejpam-6810	216	11	,	,	PUNCT
ejpam-6810	216	12	implies	imply	VERB
ejpam-6810	216	13	f(2σb(η	f(2σb(η	ADJ
ejpam-6810	216	14	∗	∗	NOUN
ejpam-6810	216	15	,	,	PUNCT
ejpam-6810	216	16	η∗∗	η∗∗	NOUN
ejpam-6810	216	17	)	)	PUNCT
ejpam-6810	216	18	)	)	PUNCT
ejpam-6810	217	1	≤	≤	NUM
ejpam-6810	218	1	f	f	X
ejpam-6810	218	2	(	(	PUNCT
ejpam-6810	218	3	2	2	NUM
ejpam-6810	218	4	s2	s2	NOUN
ejpam-6810	218	5	σb(η	σb(η	NUM
ejpam-6810	218	6	∗	∗	NOUN
ejpam-6810	218	7	,	,	PUNCT
ejpam-6810	218	8	η∗∗	η∗∗	NOUN
ejpam-6810	218	9	)	)	PUNCT
ejpam-6810	218	10	)	)	PUNCT
ejpam-6810	218	11	.	.	PUNCT
ejpam-6810	219	1	since	since	SCONJ
ejpam-6810	219	2	f	f	PROPN
ejpam-6810	219	3	is	be	AUX
ejpam-6810	219	4	increasing	increase	VERB
ejpam-6810	219	5	,	,	PUNCT
ejpam-6810	219	6	2σb(η	2σb(η	NUM
ejpam-6810	219	7	∗	∗	NOUN
ejpam-6810	219	8	,	,	PUNCT
ejpam-6810	219	9	η∗∗	η∗∗	NOUN
ejpam-6810	219	10	)	)	PUNCT
ejpam-6810	219	11	≤	≤	NOUN
ejpam-6810	219	12	2	2	NUM
ejpam-6810	219	13	s2	s2	NOUN
ejpam-6810	219	14	σb(η	σb(η	NUM
ejpam-6810	219	15	∗	∗	NOUN
ejpam-6810	219	16	,	,	PUNCT
ejpam-6810	219	17	η∗∗	η∗∗	NOUN
ejpam-6810	219	18	)	)	PUNCT
ejpam-6810	219	19	.	.	PUNCT
ejpam-6810	220	1	which	which	PRON
ejpam-6810	220	2	is	be	AUX
ejpam-6810	220	3	a	a	DET
ejpam-6810	220	4	contradiction	contradiction	NOUN
ejpam-6810	220	5	as	as	ADP
ejpam-6810	220	6	s	s	PRON
ejpam-6810	220	7	≥	≥	NOUN
ejpam-6810	220	8	1	1	NUM
ejpam-6810	220	9	.	.	PUNCT
ejpam-6810	221	1	this	this	PRON
ejpam-6810	221	2	shows	show	VERB
ejpam-6810	221	3	that	that	SCONJ
ejpam-6810	221	4	η∗	η∗	PROPN
ejpam-6810	221	5	=	=	PROPN
ejpam-6810	221	6	η∗∗.	η∗∗.	PROPN
ejpam-6810	221	7	therefore	therefore	ADV
ejpam-6810	221	8	,	,	PUNCT
ejpam-6810	221	9	υ	υ	PROPN
ejpam-6810	221	10	has	have	VERB
ejpam-6810	221	11	a	a	DET
ejpam-6810	221	12	unique	unique	ADJ
ejpam-6810	221	13	fp	fp	NOUN
ejpam-6810	221	14	.	.	PUNCT
ejpam-6810	222	1	the	the	DET
ejpam-6810	222	2	followings	following	NOUN
ejpam-6810	222	3	are	be	AUX
ejpam-6810	222	4	examples	example	NOUN
ejpam-6810	222	5	of	of	ADP
ejpam-6810	222	6	a	a	DET
ejpam-6810	222	7	mcpt	mcpt	NOUN
ejpam-6810	222	8	embedded	embed	VERB
ejpam-6810	222	9	with	with	ADP
ejpam-6810	222	10	f	f	NOUN
ejpam-6810	222	11	-	-	PUNCT
ejpam-6810	222	12	contraction	contraction	NOUN
ejpam-6810	222	13	with	with	ADP
ejpam-6810	222	14	exactly	exactly	ADV
ejpam-6810	222	15	two	two	NUM
ejpam-6810	222	16	fps	fps	PROPN
ejpam-6810	222	17	.	.	PUNCT
ejpam-6810	222	18	example	example	NOUN
ejpam-6810	223	1	2	2	NUM
ejpam-6810	223	2	.	.	PUNCT
ejpam-6810	223	3	let	let	VERB
ejpam-6810	223	4	u	u	PRON
ejpam-6810	223	5	=	=	PUNCT
ejpam-6810	223	6	{	{	PUNCT
ejpam-6810	223	7	2	2	NUM
ejpam-6810	223	8	,	,	PUNCT
ejpam-6810	223	9	3	3	NUM
ejpam-6810	223	10	,	,	PUNCT
ejpam-6810	223	11	10	10	NUM
ejpam-6810	223	12	}	}	PUNCT
ejpam-6810	223	13	.	.	PUNCT
ejpam-6810	224	1	let	let	VERB
ejpam-6810	224	2	σb	σb	INTJ
ejpam-6810	224	3	:	:	PUNCT
ejpam-6810	224	4	u	u	NOUN
ejpam-6810	224	5	×	×	NOUN
ejpam-6810	224	6	u	u	NOUN
ejpam-6810	224	7	−→	−→	NOUN
ejpam-6810	224	8	r	r	NOUN
ejpam-6810	224	9	be	be	AUX
ejpam-6810	224	10	defined	define	VERB
ejpam-6810	224	11	as	as	ADP
ejpam-6810	224	12	:	:	PUNCT
ejpam-6810	224	13	σb(η	σb(η	NUM
ejpam-6810	224	14	,	,	PUNCT
ejpam-6810	224	15	ξ	ξ	X
ejpam-6810	224	16	)	)	PUNCT
ejpam-6810	224	17	=	=	SYM
ejpam-6810	224	18	(	(	PUNCT
ejpam-6810	224	19	η	η	PROPN
ejpam-6810	224	20	−	−	PROPN
ejpam-6810	224	21	ξ)2	ξ)2	PROPN
ejpam-6810	224	22	,	,	PUNCT
ejpam-6810	224	23	for	for	ADP
ejpam-6810	224	24	all	all	DET
ejpam-6810	224	25	η	η	PROPN
ejpam-6810	224	26	,	,	PUNCT
ejpam-6810	224	27	ξ	ξ	PROPN
ejpam-6810	224	28	∈	∈	PROPN
ejpam-6810	224	29	u	u	NOUN
ejpam-6810	224	30	.	.	PUNCT
ejpam-6810	225	1	s.	s.	PROPN
ejpam-6810	225	2	batul	batul	PROPN
ejpam-6810	225	3	et	et	PROPN
ejpam-6810	225	4	al	al	PROPN
ejpam-6810	225	5	.	.	PUNCT
ejpam-6810	225	6	/	/	SYM
ejpam-6810	225	7	eur	eur	PROPN
ejpam-6810	225	8	.	.	PUNCT
ejpam-6810	226	1	j.	j.	PROPN
ejpam-6810	226	2	pure	pure	PROPN
ejpam-6810	226	3	appl	appl	PROPN
ejpam-6810	226	4	.	.	PROPN
ejpam-6810	226	5	math	math	PROPN
ejpam-6810	226	6	,	,	PUNCT
ejpam-6810	226	7	18	18	NUM
ejpam-6810	226	8	(	(	PUNCT
ejpam-6810	226	9	4	4	NUM
ejpam-6810	226	10	)	)	PUNCT
ejpam-6810	226	11	(	(	PUNCT
ejpam-6810	226	12	2025	2025	NUM
ejpam-6810	226	13	)	)	PUNCT
ejpam-6810	226	14	,	,	PUNCT
ejpam-6810	226	15	6810	6810	NUM
ejpam-6810	226	16	10	10	NUM
ejpam-6810	226	17	of	of	ADP
ejpam-6810	226	18	23	23	NUM
ejpam-6810	226	19	then	then	ADV
ejpam-6810	226	20	(	(	PUNCT
ejpam-6810	226	21	u	u	NOUN
ejpam-6810	226	22	,	,	PUNCT
ejpam-6810	226	23	σb	σb	PROPN
ejpam-6810	226	24	)	)	PUNCT
ejpam-6810	226	25	is	be	AUX
ejpam-6810	226	26	a	a	DET
ejpam-6810	226	27	b	b	NOUN
ejpam-6810	226	28	-	-	PUNCT
ejpam-6810	226	29	ms	ms	NOUN
ejpam-6810	226	30	with	with	ADP
ejpam-6810	226	31	s	s	NOUN
ejpam-6810	226	32	=	=	SYM
ejpam-6810	226	33	2	2	X
ejpam-6810	226	34	.	.	PUNCT
ejpam-6810	226	35	define	define	VERB
ejpam-6810	226	36	υ	υ	NOUN
ejpam-6810	226	37	:	:	PUNCT
ejpam-6810	226	38	u	u	VERB
ejpam-6810	226	39	−→	−→	NOUN
ejpam-6810	226	40	u	u	NOUN
ejpam-6810	226	41	by	by	ADP
ejpam-6810	226	42	υη	υη	PROPN
ejpam-6810	226	43	=	=	SYM
ejpam-6810	226	44	η	η	PROPN
ejpam-6810	226	45	,	,	PUNCT
ejpam-6810	226	46	υξ	υξ	VERB
ejpam-6810	226	47	=	=	SYM
ejpam-6810	226	48	ξ	ξ	PROPN
ejpam-6810	226	49	and	and	CCONJ
ejpam-6810	226	50	υζ	υζ	NOUN
ejpam-6810	226	51	=	=	SYM
ejpam-6810	226	52	η	η	PROPN
ejpam-6810	226	53	.	.	PROPN
ejpam-6810	226	54	consider	consider	VERB
ejpam-6810	226	55	τ	τ	PROPN
ejpam-6810	226	56	+	+	NUM
ejpam-6810	226	57	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	226	58	,	,	PUNCT
ejpam-6810	226	59	υξ	υξ	X
ejpam-6810	226	60	)	)	PUNCT
ejpam-6810	227	1	+	+	CCONJ
ejpam-6810	227	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	227	3	,	,	PUNCT
ejpam-6810	227	4	υζ	υζ	NOUN
ejpam-6810	227	5	)	)	PUNCT
ejpam-6810	227	6	+	+	CCONJ
ejpam-6810	227	7	σb(υη	σb(υη	PROPN
ejpam-6810	227	8	,	,	PUNCT
ejpam-6810	227	9	υζ	υζ	NOUN
ejpam-6810	227	10	)	)	PUNCT
ejpam-6810	227	11	)	)	PUNCT
ejpam-6810	228	1	=	=	PUNCT
ejpam-6810	229	1	τ	τ	X
ejpam-6810	230	1	+	+	X
ejpam-6810	230	2	f(σb(η	f(σb(η	PROPN
ejpam-6810	230	3	,	,	PUNCT
ejpam-6810	230	4	ξ	ξ	X
ejpam-6810	230	5	)	)	PUNCT
ejpam-6810	230	6	+	+	CCONJ
ejpam-6810	230	7	σb(ξ	σb(ξ	ADJ
ejpam-6810	230	8	,	,	PUNCT
ejpam-6810	230	9	ζ	ζ	NOUN
ejpam-6810	230	10	)	)	PUNCT
ejpam-6810	230	11	+	+	CCONJ
ejpam-6810	230	12	σb(η	σb(η	PROPN
ejpam-6810	230	13	,	,	PUNCT
ejpam-6810	230	14	η	η	NOUN
ejpam-6810	230	15	)	)	PUNCT
ejpam-6810	230	16	)	)	PUNCT
ejpam-6810	230	17	,	,	PUNCT
ejpam-6810	231	1	=	=	PUNCT
ejpam-6810	231	2	τ	τ	X
ejpam-6810	231	3	+	+	X
ejpam-6810	231	4	f(σb(η	f(σb(η	PROPN
ejpam-6810	231	5	,	,	PUNCT
ejpam-6810	231	6	ξ	ξ	X
ejpam-6810	231	7	)	)	PUNCT
ejpam-6810	231	8	+	+	CCONJ
ejpam-6810	231	9	σb(ξ	σb(ξ	NUM
ejpam-6810	231	10	,	,	PUNCT
ejpam-6810	231	11	η	η	NOUN
ejpam-6810	231	12	)	)	PUNCT
ejpam-6810	231	13	+	+	CCONJ
ejpam-6810	231	14	σb(η	σb(η	PROPN
ejpam-6810	231	15	,	,	PUNCT
ejpam-6810	231	16	η	η	NOUN
ejpam-6810	231	17	)	)	PUNCT
ejpam-6810	231	18	)	)	PUNCT
ejpam-6810	231	19	,	,	PUNCT
ejpam-6810	231	20	=	=	PUNCT
ejpam-6810	231	21	τ	τ	PROPN
ejpam-6810	231	22	+	+	NUM
ejpam-6810	231	23	f(2σb(η	f(2σb(η	PROPN
ejpam-6810	231	24	,	,	PUNCT
ejpam-6810	231	25	ξ	ξ	NOUN
ejpam-6810	231	26	)	)	PUNCT
ejpam-6810	231	27	)	)	PUNCT
ejpam-6810	231	28	,	,	PUNCT
ejpam-6810	232	1	=	=	PUNCT
ejpam-6810	232	2	τ	τ	X
ejpam-6810	232	3	+	+	NUM
ejpam-6810	232	4	f(2(η	f(2(η	PRON
ejpam-6810	232	5	−	−	NOUN
ejpam-6810	232	6	ξ)2	ξ)2	NOUN
ejpam-6810	232	7	)	)	PUNCT
ejpam-6810	232	8	,	,	PUNCT
ejpam-6810	233	1	=	=	PUNCT
ejpam-6810	233	2	τ	τ	X
ejpam-6810	234	1	+	+	CCONJ
ejpam-6810	234	2	f(2(2−	f(2(2−	PROPN
ejpam-6810	234	3	3)2	3)2	NUM
ejpam-6810	234	4	)	)	PUNCT
ejpam-6810	234	5	,	,	PUNCT
ejpam-6810	234	6	τ	τ	PROPN
ejpam-6810	234	7	+	+	NUM
ejpam-6810	234	8	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	234	9	,	,	PUNCT
ejpam-6810	234	10	υξ	υξ	X
ejpam-6810	234	11	)	)	PUNCT
ejpam-6810	235	1	+	+	CCONJ
ejpam-6810	235	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	235	3	,	,	PUNCT
ejpam-6810	235	4	υζ	υζ	NOUN
ejpam-6810	235	5	)	)	PUNCT
ejpam-6810	235	6	+	+	CCONJ
ejpam-6810	235	7	σb(υη	σb(υη	PROPN
ejpam-6810	235	8	,	,	PUNCT
ejpam-6810	235	9	υζ	υζ	NOUN
ejpam-6810	235	10	)	)	PUNCT
ejpam-6810	235	11	)	)	PUNCT
ejpam-6810	236	1	=	=	PUNCT
ejpam-6810	236	2	τ	τ	PROPN
ejpam-6810	236	3	+	+	NUM
ejpam-6810	236	4	f(2	f(2	PROPN
ejpam-6810	236	5	)	)	PUNCT
ejpam-6810	236	6	.	.	PUNCT
ejpam-6810	237	1	(	(	PUNCT
ejpam-6810	237	2	12	12	NUM
ejpam-6810	237	3	)	)	PUNCT
ejpam-6810	237	4	now	now	ADV
ejpam-6810	237	5	,	,	PUNCT
ejpam-6810	237	6	f	f	PROPN
ejpam-6810	237	7	(	(	PUNCT
ejpam-6810	237	8	1	1	NUM
ejpam-6810	237	9	s2	s2	NOUN
ejpam-6810	237	10	(	(	PUNCT
ejpam-6810	237	11	σb(η	σb(η	PROPN
ejpam-6810	237	12	,	,	PUNCT
ejpam-6810	237	13	ξ	ξ	NOUN
ejpam-6810	237	14	)	)	PUNCT
ejpam-6810	237	15	+	+	CCONJ
ejpam-6810	237	16	σb(ξ	σb(ξ	ADJ
ejpam-6810	237	17	,	,	PUNCT
ejpam-6810	237	18	ζ	ζ	NOUN
ejpam-6810	237	19	)	)	PUNCT
ejpam-6810	237	20	+	+	NUM
ejpam-6810	237	21	σb(η	σb(η	NUM
ejpam-6810	237	22	,	,	PUNCT
ejpam-6810	237	23	ζ	ζ	NOUN
ejpam-6810	237	24	)	)	PUNCT
ejpam-6810	237	25	)	)	PUNCT
ejpam-6810	237	26	)	)	PUNCT
ejpam-6810	238	1	=	=	PRON
ejpam-6810	238	2	f	f	X
ejpam-6810	238	3	(	(	PUNCT
ejpam-6810	238	4	1	1	NUM
ejpam-6810	238	5	s2	s2	NOUN
ejpam-6810	238	6	(	(	PUNCT
ejpam-6810	238	7	(	(	PUNCT
ejpam-6810	238	8	η	η	PROPN
ejpam-6810	238	9	−	−	PROPN
ejpam-6810	238	10	ξ)2	ξ)2	PROPN
ejpam-6810	238	11	+	+	CCONJ
ejpam-6810	238	12	(	(	PUNCT
ejpam-6810	238	13	ξ	ξ	X
ejpam-6810	238	14	−	−	NOUN
ejpam-6810	238	15	ζ)2	ζ)2	VERB
ejpam-6810	238	16	+	+	CCONJ
ejpam-6810	238	17	(	(	PUNCT
ejpam-6810	238	18	η	η	PROPN
ejpam-6810	238	19	−	−	PROPN
ejpam-6810	238	20	ζ)2	ζ)2	PROPN
ejpam-6810	238	21	)	)	PUNCT
ejpam-6810	238	22	)	)	PUNCT
ejpam-6810	238	23	,	,	PUNCT
ejpam-6810	239	1	=	=	PRON
ejpam-6810	239	2	f	f	X
ejpam-6810	239	3	(	(	PUNCT
ejpam-6810	239	4	1	1	NUM
ejpam-6810	239	5	22	22	NUM
ejpam-6810	239	6	(	(	PUNCT
ejpam-6810	239	7	(	(	PUNCT
ejpam-6810	239	8	2−	2−	NUM
ejpam-6810	239	9	3)2	3)2	NUM
ejpam-6810	239	10	+	+	PUNCT
ejpam-6810	239	11	(	(	PUNCT
ejpam-6810	239	12	3−	3−	NUM
ejpam-6810	239	13	10)2	10)2	NUM
ejpam-6810	239	14	+	+	CCONJ
ejpam-6810	239	15	(	(	PUNCT
ejpam-6810	239	16	2−	2−	NUM
ejpam-6810	239	17	10)2	10)2	NUM
ejpam-6810	239	18	)	)	PUNCT
ejpam-6810	239	19	.	.	PUNCT
ejpam-6810	239	20	by	by	ADP
ejpam-6810	239	21	simplifying	simplify	VERB
ejpam-6810	239	22	,	,	PUNCT
ejpam-6810	239	23	one	one	PRON
ejpam-6810	239	24	can	can	AUX
ejpam-6810	239	25	get	get	VERB
ejpam-6810	239	26	f	f	X
ejpam-6810	239	27	(	(	PUNCT
ejpam-6810	239	28	1	1	NUM
ejpam-6810	239	29	s2	s2	NOUN
ejpam-6810	239	30	(	(	PUNCT
ejpam-6810	239	31	σb(η	σb(η	PROPN
ejpam-6810	239	32	,	,	PUNCT
ejpam-6810	239	33	ξ	ξ	NOUN
ejpam-6810	239	34	)	)	PUNCT
ejpam-6810	240	1	+	+	CCONJ
ejpam-6810	240	2	σb(ξ	σb(ξ	ADJ
ejpam-6810	240	3	,	,	PUNCT
ejpam-6810	240	4	ζ	ζ	NOUN
ejpam-6810	240	5	)	)	PUNCT
ejpam-6810	240	6	+	+	NUM
ejpam-6810	240	7	σb(η	σb(η	NUM
ejpam-6810	240	8	,	,	PUNCT
ejpam-6810	240	9	ζ	ζ	NOUN
ejpam-6810	240	10	)	)	PUNCT
ejpam-6810	240	11	)	)	PUNCT
ejpam-6810	240	12	)	)	PUNCT
ejpam-6810	241	1	=	=	SYM
ejpam-6810	241	2	f(28.5	f(28.5	X
ejpam-6810	241	3	)	)	PUNCT
ejpam-6810	241	4	.	.	PUNCT
ejpam-6810	242	1	(	(	PUNCT
ejpam-6810	242	2	13	13	NUM
ejpam-6810	242	3	)	)	PUNCT
ejpam-6810	242	4	hence	hence	ADV
ejpam-6810	242	5	,	,	PUNCT
ejpam-6810	242	6	by	by	ADP
ejpam-6810	242	7	(	(	PUNCT
ejpam-6810	242	8	12	12	NUM
ejpam-6810	242	9	)	)	PUNCT
ejpam-6810	242	10	and	and	CCONJ
ejpam-6810	242	11	(	(	PUNCT
ejpam-6810	242	12	13	13	NUM
ejpam-6810	242	13	)	)	PUNCT
ejpam-6810	242	14	,	,	PUNCT
ejpam-6810	242	15	we	we	PRON
ejpam-6810	242	16	conclude	conclude	VERB
ejpam-6810	242	17	that	that	SCONJ
ejpam-6810	242	18	τ	τ	PROPN
ejpam-6810	242	19	+	+	NUM
ejpam-6810	242	20	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	242	21	,	,	PUNCT
ejpam-6810	242	22	υξ	υξ	X
ejpam-6810	242	23	)	)	PUNCT
ejpam-6810	243	1	+	+	CCONJ
ejpam-6810	243	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	243	3	,	,	PUNCT
ejpam-6810	243	4	υζ	υζ	NOUN
ejpam-6810	243	5	)	)	PUNCT
ejpam-6810	243	6	+	+	CCONJ
ejpam-6810	243	7	σb(υη	σb(υη	PROPN
ejpam-6810	243	8	,	,	PUNCT
ejpam-6810	243	9	υζ	υζ	NOUN
ejpam-6810	243	10	)	)	PUNCT
ejpam-6810	243	11	)	)	PUNCT
ejpam-6810	243	12	≤	≤	NUM
ejpam-6810	243	13	f	f	X
ejpam-6810	243	14	(	(	PUNCT
ejpam-6810	243	15	1	1	NUM
ejpam-6810	243	16	s2	s2	NOUN
ejpam-6810	243	17	(	(	PUNCT
ejpam-6810	243	18	σb(η	σb(η	PROPN
ejpam-6810	243	19	,	,	PUNCT
ejpam-6810	243	20	ξ	ξ	NOUN
ejpam-6810	243	21	)	)	PUNCT
ejpam-6810	243	22	+	+	CCONJ
ejpam-6810	243	23	σb(ξ	σb(ξ	ADJ
ejpam-6810	243	24	,	,	PUNCT
ejpam-6810	243	25	ζ	ζ	NOUN
ejpam-6810	243	26	)	)	PUNCT
ejpam-6810	243	27	+	+	NUM
ejpam-6810	243	28	σb(η	σb(η	NUM
ejpam-6810	243	29	,	,	PUNCT
ejpam-6810	243	30	ζ	ζ	NOUN
ejpam-6810	243	31	)	)	PUNCT
ejpam-6810	243	32	)	)	PUNCT
ejpam-6810	243	33	)	)	PUNCT
ejpam-6810	243	34	,	,	PUNCT
ejpam-6810	243	35	with	with	ADP
ejpam-6810	243	36	f(η	f(η	NOUN
ejpam-6810	243	37	)	)	PUNCT
ejpam-6810	243	38	=	=	PUNCT
ejpam-6810	243	39	ln(η	ln(η	X
ejpam-6810	243	40	)	)	PUNCT
ejpam-6810	243	41	and	and	CCONJ
ejpam-6810	243	42	τ	τ	PROPN
ejpam-6810	243	43	=	=	SYM
ejpam-6810	243	44	1	1	X
ejpam-6810	243	45	.	.	PUNCT
ejpam-6810	244	1	also	also	ADV
ejpam-6810	244	2	,	,	PUNCT
ejpam-6810	244	3	υ	υ	PROPN
ejpam-6810	244	4	has	have	VERB
ejpam-6810	244	5	no	no	DET
ejpam-6810	244	6	periodic	periodic	ADJ
ejpam-6810	244	7	point	point	NOUN
ejpam-6810	244	8	of	of	ADP
ejpam-6810	244	9	prime	prime	ADJ
ejpam-6810	244	10	period	period	NOUN
ejpam-6810	244	11	2	2	NUM
ejpam-6810	244	12	.	.	PUNCT
ejpam-6810	245	1	take	take	VERB
ejpam-6810	245	2	υζ	υζ	NOUN
ejpam-6810	245	3	=	=	SYM
ejpam-6810	245	4	η	η	PROPN
ejpam-6810	245	5	,	,	PUNCT
ejpam-6810	245	6	υ(υζ	υ(υζ	ADJ
ejpam-6810	245	7	)	)	PUNCT
ejpam-6810	245	8	=	=	SYM
ejpam-6810	245	9	υ(η	υ(η	PROPN
ejpam-6810	245	10	)	)	PUNCT
ejpam-6810	245	11	,	,	PUNCT
ejpam-6810	245	12	υ2(ζ	υ2(ζ	PROPN
ejpam-6810	245	13	)	)	PUNCT
ejpam-6810	245	14	=	=	SYM
ejpam-6810	245	15	η	η	PROPN
ejpam-6810	245	16	.	.	PROPN
ejpam-6810	245	17	hence	hence	ADV
ejpam-6810	245	18	,	,	PUNCT
ejpam-6810	245	19	υ	υ	PROPN
ejpam-6810	245	20	has	have	VERB
ejpam-6810	245	21	no	no	DET
ejpam-6810	245	22	periodic	periodic	ADJ
ejpam-6810	245	23	point	point	NOUN
ejpam-6810	245	24	with	with	ADP
ejpam-6810	245	25	prime	prime	ADJ
ejpam-6810	245	26	period	period	NOUN
ejpam-6810	245	27	2	2	NUM
ejpam-6810	245	28	.	.	PUNCT
ejpam-6810	246	1	therefore	therefore	ADV
ejpam-6810	246	2	,	,	PUNCT
ejpam-6810	246	3	all	all	DET
ejpam-6810	246	4	the	the	DET
ejpam-6810	246	5	assumptions	assumption	NOUN
ejpam-6810	246	6	of	of	ADP
ejpam-6810	246	7	theorem	theorem	NOUN
ejpam-6810	246	8	(	(	PUNCT
ejpam-6810	246	9	1	1	NUM
ejpam-6810	246	10	)	)	PUNCT
ejpam-6810	246	11	are	be	AUX
ejpam-6810	246	12	true	true	ADJ
ejpam-6810	246	13	.	.	PUNCT
ejpam-6810	247	1	thus	thus	ADV
ejpam-6810	247	2	,	,	PUNCT
ejpam-6810	247	3	υ	υ	PROPN
ejpam-6810	247	4	has	have	VERB
ejpam-6810	247	5	exactly	exactly	ADV
ejpam-6810	247	6	two	two	NUM
ejpam-6810	247	7	fps	fps	PROPN
ejpam-6810	247	8	,	,	PUNCT
ejpam-6810	247	9	namely	namely	ADV
ejpam-6810	247	10	η	η	PROPN
ejpam-6810	247	11	and	and	CCONJ
ejpam-6810	247	12	ξ	ξ	PROPN
ejpam-6810	247	13	.	.	PUNCT
ejpam-6810	247	14	note	note	NOUN
ejpam-6810	247	15	:	:	PUNCT
ejpam-6810	247	16	in	in	ADP
ejpam-6810	247	17	the	the	DET
ejpam-6810	247	18	previous	previous	ADJ
ejpam-6810	247	19	example	example	NOUN
ejpam-6810	247	20	,	,	PUNCT
ejpam-6810	247	21	we	we	PRON
ejpam-6810	247	22	verified	verify	VERB
ejpam-6810	247	23	the	the	DET
ejpam-6810	247	24	conditions	condition	NOUN
ejpam-6810	247	25	of	of	ADP
ejpam-6810	247	26	theorem	theorem	NOUN
ejpam-6810	247	27	(	(	PUNCT
ejpam-6810	247	28	1	1	X
ejpam-6810	247	29	)	)	PUNCT
ejpam-6810	247	30	using	use	VERB
ejpam-6810	247	31	a	a	DET
ejpam-6810	247	32	continuous	continuous	ADJ
ejpam-6810	247	33	b	b	NOUN
ejpam-6810	247	34	-	-	PUNCT
ejpam-6810	247	35	ms	ms	NOUN
ejpam-6810	247	36	.	.	PROPN
ejpam-6810	248	1	now	now	ADV
ejpam-6810	248	2	,	,	PUNCT
ejpam-6810	248	3	in	in	ADP
ejpam-6810	248	4	the	the	DET
ejpam-6810	248	5	next	next	ADJ
ejpam-6810	248	6	example	example	NOUN
ejpam-6810	248	7	,	,	PUNCT
ejpam-6810	248	8	we	we	PRON
ejpam-6810	248	9	will	will	AUX
ejpam-6810	248	10	use	use	VERB
ejpam-6810	248	11	a	a	DET
ejpam-6810	248	12	discontinuous	discontinuous	ADJ
ejpam-6810	248	13	b	b	NOUN
ejpam-6810	248	14	-	-	PUNCT
ejpam-6810	248	15	ms	ms	NOUN
ejpam-6810	248	16	to	to	PART
ejpam-6810	248	17	verify	verify	VERB
ejpam-6810	248	18	theorem	theorem	NOUN
ejpam-6810	248	19	1	1	NUM
ejpam-6810	248	20	.	.	PUNCT
ejpam-6810	248	21	s.	s.	PROPN
ejpam-6810	248	22	batul	batul	PROPN
ejpam-6810	248	23	et	et	PROPN
ejpam-6810	248	24	al	al	PROPN
ejpam-6810	248	25	.	.	PUNCT
ejpam-6810	248	26	/	/	SYM
ejpam-6810	248	27	eur	eur	PROPN
ejpam-6810	248	28	.	.	PUNCT
ejpam-6810	249	1	j.	j.	PROPN
ejpam-6810	249	2	pure	pure	PROPN
ejpam-6810	249	3	appl	appl	PROPN
ejpam-6810	249	4	.	.	PROPN
ejpam-6810	249	5	math	math	PROPN
ejpam-6810	249	6	,	,	PUNCT
ejpam-6810	249	7	18	18	NUM
ejpam-6810	249	8	(	(	PUNCT
ejpam-6810	249	9	4	4	NUM
ejpam-6810	249	10	)	)	PUNCT
ejpam-6810	249	11	(	(	PUNCT
ejpam-6810	249	12	2025	2025	NUM
ejpam-6810	249	13	)	)	PUNCT
ejpam-6810	249	14	,	,	PUNCT
ejpam-6810	249	15	6810	6810	NUM
ejpam-6810	249	16	11	11	NUM
ejpam-6810	249	17	of	of	ADP
ejpam-6810	249	18	23	23	NUM
ejpam-6810	249	19	example	example	NOUN
ejpam-6810	249	20	3	3	NUM
ejpam-6810	249	21	.	.	PUNCT
ejpam-6810	250	1	let	let	VERB
ejpam-6810	250	2	u	u	PRON
ejpam-6810	250	3	=	=	PUNCT
ejpam-6810	250	4	{	{	PUNCT
ejpam-6810	250	5	2	2	NUM
ejpam-6810	250	6	,	,	PUNCT
ejpam-6810	250	7	3	3	NUM
ejpam-6810	250	8	,	,	PUNCT
ejpam-6810	250	9	10	10	NUM
ejpam-6810	250	10	}	}	PUNCT
ejpam-6810	250	11	.	.	PUNCT
ejpam-6810	251	1	let	let	VERB
ejpam-6810	251	2	σb	σb	INTJ
ejpam-6810	251	3	:	:	PUNCT
ejpam-6810	251	4	u	u	NOUN
ejpam-6810	251	5	×	×	NOUN
ejpam-6810	251	6	u	u	NOUN
ejpam-6810	251	7	−→	−→	NOUN
ejpam-6810	251	8	r	r	NOUN
ejpam-6810	251	9	be	be	AUX
ejpam-6810	251	10	defined	define	VERB
ejpam-6810	251	11	for	for	SCONJ
ejpam-6810	251	12	all	all	DET
ejpam-6810	251	13	η	η	PROPN
ejpam-6810	251	14	,	,	PUNCT
ejpam-6810	251	15	ξ	ξ	PROPN
ejpam-6810	251	16	∈	∈	PROPN
ejpam-6810	251	17	u	u	NOUN
ejpam-6810	251	18	as	as	SCONJ
ejpam-6810	251	19	follows	follow	VERB
ejpam-6810	251	20	:	:	PUNCT
ejpam-6810	251	21	σb	σb	ADP
ejpam-6810	251	22	=	=	PUNCT
ejpam-6810	251	23			PROPN
ejpam-6810	251	24	0	0	PUNCT
ejpam-6810	252	1	if	if	SCONJ
ejpam-6810	252	2	η	η	PROPN
ejpam-6810	252	3	=	=	SYM
ejpam-6810	252	4	ξ	ξ	PROPN
ejpam-6810	252	5	,	,	PUNCT
ejpam-6810	252	6	1	1	NUM
ejpam-6810	252	7	if	if	SCONJ
ejpam-6810	252	8	|η	|η	NOUN
ejpam-6810	252	9	−	−	PROPN
ejpam-6810	252	10	ξ|	ξ|	PROPN
ejpam-6810	252	11	=	=	SYM
ejpam-6810	252	12	1	1	NUM
ejpam-6810	252	13	,	,	PUNCT
ejpam-6810	252	14	5	5	NUM
ejpam-6810	252	15	if	if	SCONJ
ejpam-6810	252	16	|η	|η	ADP
ejpam-6810	252	17	−	−	PROPN
ejpam-6810	252	18	ξ|	ξ|	PROPN
ejpam-6810	252	19	>	>	X
ejpam-6810	253	1	1	1	NUM
ejpam-6810	253	2	.	.	PUNCT
ejpam-6810	254	1	then	then	ADV
ejpam-6810	254	2	,	,	PUNCT
ejpam-6810	254	3	one	one	PRON
ejpam-6810	254	4	can	can	AUX
ejpam-6810	254	5	easily	easily	ADV
ejpam-6810	254	6	verify	verify	VERB
ejpam-6810	254	7	that	that	SCONJ
ejpam-6810	254	8	(	(	PUNCT
ejpam-6810	254	9	u	u	NOUN
ejpam-6810	254	10	,	,	PUNCT
ejpam-6810	254	11	σb	σb	PROPN
ejpam-6810	254	12	)	)	PUNCT
ejpam-6810	254	13	is	be	AUX
ejpam-6810	254	14	a	a	DET
ejpam-6810	254	15	b	b	NOUN
ejpam-6810	254	16	-	-	PUNCT
ejpam-6810	254	17	ms	ms	NOUN
ejpam-6810	254	18	with	with	ADP
ejpam-6810	254	19	s	s	NOUN
ejpam-6810	254	20	=	=	SYM
ejpam-6810	254	21	2	2	X
ejpam-6810	254	22	.	.	PUNCT
ejpam-6810	254	23	define	define	VERB
ejpam-6810	254	24	υ	υ	NOUN
ejpam-6810	254	25	:	:	PUNCT
ejpam-6810	254	26	u	u	VERB
ejpam-6810	254	27	−→	−→	NOUN
ejpam-6810	254	28	u	u	NOUN
ejpam-6810	254	29	by	by	ADP
ejpam-6810	254	30	υη	υη	PROPN
ejpam-6810	254	31	=	=	SYM
ejpam-6810	254	32	η	η	PROPN
ejpam-6810	254	33	,	,	PUNCT
ejpam-6810	254	34	υξ	υξ	VERB
ejpam-6810	254	35	=	=	SYM
ejpam-6810	254	36	ξ	ξ	PROPN
ejpam-6810	254	37	and	and	CCONJ
ejpam-6810	254	38	υζ	υζ	NOUN
ejpam-6810	254	39	=	=	SYM
ejpam-6810	254	40	η	η	PROPN
ejpam-6810	254	41	.	.	PROPN
ejpam-6810	254	42	consider	consider	VERB
ejpam-6810	254	43	τ	τ	PROPN
ejpam-6810	254	44	+	+	NUM
ejpam-6810	254	45	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	254	46	,	,	PUNCT
ejpam-6810	254	47	υξ	υξ	X
ejpam-6810	254	48	)	)	PUNCT
ejpam-6810	255	1	+	+	CCONJ
ejpam-6810	255	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	255	3	,	,	PUNCT
ejpam-6810	255	4	υζ	υζ	NOUN
ejpam-6810	255	5	)	)	PUNCT
ejpam-6810	255	6	+	+	CCONJ
ejpam-6810	255	7	σb(υη	σb(υη	PROPN
ejpam-6810	255	8	,	,	PUNCT
ejpam-6810	255	9	υζ	υζ	NOUN
ejpam-6810	255	10	)	)	PUNCT
ejpam-6810	255	11	)	)	PUNCT
ejpam-6810	256	1	=	=	PUNCT
ejpam-6810	257	1	τ	τ	X
ejpam-6810	258	1	+	+	X
ejpam-6810	258	2	f(σb(η	f(σb(η	PROPN
ejpam-6810	258	3	,	,	PUNCT
ejpam-6810	258	4	ξ	ξ	X
ejpam-6810	258	5	)	)	PUNCT
ejpam-6810	258	6	+	+	CCONJ
ejpam-6810	258	7	σb(ξ	σb(ξ	ADJ
ejpam-6810	258	8	,	,	PUNCT
ejpam-6810	258	9	ζ	ζ	NOUN
ejpam-6810	258	10	)	)	PUNCT
ejpam-6810	258	11	+	+	CCONJ
ejpam-6810	258	12	σb(η	σb(η	PROPN
ejpam-6810	258	13	,	,	PUNCT
ejpam-6810	258	14	η	η	NOUN
ejpam-6810	258	15	)	)	PUNCT
ejpam-6810	258	16	)	)	PUNCT
ejpam-6810	258	17	,	,	PUNCT
ejpam-6810	259	1	=	=	PUNCT
ejpam-6810	259	2	τ	τ	X
ejpam-6810	259	3	+	+	X
ejpam-6810	259	4	f(σb(η	f(σb(η	PROPN
ejpam-6810	259	5	,	,	PUNCT
ejpam-6810	259	6	ξ	ξ	X
ejpam-6810	259	7	)	)	PUNCT
ejpam-6810	259	8	+	+	CCONJ
ejpam-6810	259	9	σb(ξ	σb(ξ	NUM
ejpam-6810	259	10	,	,	PUNCT
ejpam-6810	259	11	η	η	NOUN
ejpam-6810	259	12	)	)	PUNCT
ejpam-6810	259	13	+	+	CCONJ
ejpam-6810	259	14	σb(η	σb(η	PROPN
ejpam-6810	259	15	,	,	PUNCT
ejpam-6810	259	16	η	η	NOUN
ejpam-6810	259	17	)	)	PUNCT
ejpam-6810	259	18	)	)	PUNCT
ejpam-6810	259	19	,	,	PUNCT
ejpam-6810	259	20	=	=	PUNCT
ejpam-6810	259	21	τ	τ	PROPN
ejpam-6810	259	22	+	+	NUM
ejpam-6810	259	23	f(2σb(η	f(2σb(η	PROPN
ejpam-6810	259	24	,	,	PUNCT
ejpam-6810	259	25	ξ	ξ	NOUN
ejpam-6810	259	26	)	)	PUNCT
ejpam-6810	259	27	)	)	PUNCT
ejpam-6810	259	28	,	,	PUNCT
ejpam-6810	260	1	=	=	PUNCT
ejpam-6810	260	2	τ	τ	PROPN
ejpam-6810	260	3	+	+	NUM
ejpam-6810	260	4	f(2(1	f(2(1	NOUN
ejpam-6810	260	5	)	)	PUNCT
ejpam-6810	260	6	)	)	PUNCT
ejpam-6810	260	7	,	,	PUNCT
ejpam-6810	260	8	τ	τ	PROPN
ejpam-6810	260	9	+	+	NUM
ejpam-6810	260	10	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	260	11	,	,	PUNCT
ejpam-6810	260	12	υξ	υξ	X
ejpam-6810	260	13	)	)	PUNCT
ejpam-6810	261	1	+	+	CCONJ
ejpam-6810	261	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	261	3	,	,	PUNCT
ejpam-6810	261	4	υζ	υζ	NOUN
ejpam-6810	261	5	)	)	PUNCT
ejpam-6810	261	6	+	+	CCONJ
ejpam-6810	261	7	σb(υη	σb(υη	PROPN
ejpam-6810	261	8	,	,	PUNCT
ejpam-6810	261	9	υζ	υζ	NOUN
ejpam-6810	261	10	)	)	PUNCT
ejpam-6810	261	11	)	)	PUNCT
ejpam-6810	262	1	=	=	PUNCT
ejpam-6810	262	2	τ	τ	PROPN
ejpam-6810	262	3	+	+	NUM
ejpam-6810	262	4	f(2	f(2	PROPN
ejpam-6810	262	5	)	)	PUNCT
ejpam-6810	262	6	.	.	PUNCT
ejpam-6810	263	1	(	(	PUNCT
ejpam-6810	263	2	14	14	NUM
ejpam-6810	263	3	)	)	PUNCT
ejpam-6810	263	4	now	now	ADV
ejpam-6810	263	5	,	,	PUNCT
ejpam-6810	263	6	f	f	PROPN
ejpam-6810	263	7	(	(	PUNCT
ejpam-6810	263	8	1	1	NUM
ejpam-6810	263	9	s2	s2	NOUN
ejpam-6810	263	10	(	(	PUNCT
ejpam-6810	263	11	σb(η	σb(η	PROPN
ejpam-6810	263	12	,	,	PUNCT
ejpam-6810	263	13	ξ	ξ	NOUN
ejpam-6810	263	14	)	)	PUNCT
ejpam-6810	263	15	+	+	CCONJ
ejpam-6810	263	16	σb(ξ	σb(ξ	ADJ
ejpam-6810	263	17	,	,	PUNCT
ejpam-6810	263	18	ζ	ζ	NOUN
ejpam-6810	263	19	)	)	PUNCT
ejpam-6810	263	20	+	+	NUM
ejpam-6810	263	21	σb(η	σb(η	NUM
ejpam-6810	263	22	,	,	PUNCT
ejpam-6810	263	23	ζ	ζ	NOUN
ejpam-6810	263	24	)	)	PUNCT
ejpam-6810	263	25	)	)	PUNCT
ejpam-6810	263	26	)	)	PUNCT
ejpam-6810	264	1	=	=	PRON
ejpam-6810	264	2	f	f	X
ejpam-6810	264	3	(	(	PUNCT
ejpam-6810	264	4	1	1	NUM
ejpam-6810	264	5	22	22	NUM
ejpam-6810	264	6	(	(	PUNCT
ejpam-6810	264	7	(	(	PUNCT
ejpam-6810	264	8	1	1	NUM
ejpam-6810	264	9	)	)	PUNCT
ejpam-6810	264	10	+	+	CCONJ
ejpam-6810	264	11	(	(	PUNCT
ejpam-6810	264	12	5	5	NUM
ejpam-6810	264	13	)	)	PUNCT
ejpam-6810	264	14	+	+	CCONJ
ejpam-6810	264	15	(	(	PUNCT
ejpam-6810	264	16	5	5	NUM
ejpam-6810	264	17	)	)	PUNCT
ejpam-6810	264	18	)	)	PUNCT
ejpam-6810	264	19	,	,	PUNCT
ejpam-6810	264	20	=	=	PRON
ejpam-6810	264	21	f	f	X
ejpam-6810	264	22	(	(	PUNCT
ejpam-6810	264	23	11	11	NUM
ejpam-6810	264	24	4	4	NUM
ejpam-6810	264	25	)	)	PUNCT
ejpam-6810	264	26	.	.	PUNCT
ejpam-6810	265	1	by	by	ADP
ejpam-6810	265	2	simplifying	simplify	VERB
ejpam-6810	265	3	,	,	PUNCT
ejpam-6810	265	4	one	one	PRON
ejpam-6810	265	5	can	can	AUX
ejpam-6810	265	6	get	get	VERB
ejpam-6810	265	7	f	f	X
ejpam-6810	265	8	(	(	PUNCT
ejpam-6810	265	9	1	1	NUM
ejpam-6810	265	10	s2	s2	NOUN
ejpam-6810	265	11	(	(	PUNCT
ejpam-6810	265	12	σb(η	σb(η	PROPN
ejpam-6810	265	13	,	,	PUNCT
ejpam-6810	265	14	ξ	ξ	NOUN
ejpam-6810	265	15	)	)	PUNCT
ejpam-6810	266	1	+	+	CCONJ
ejpam-6810	266	2	σb(ξ	σb(ξ	ADJ
ejpam-6810	266	3	,	,	PUNCT
ejpam-6810	266	4	ζ	ζ	NOUN
ejpam-6810	266	5	)	)	PUNCT
ejpam-6810	266	6	+	+	NUM
ejpam-6810	266	7	σb(η	σb(η	NUM
ejpam-6810	266	8	,	,	PUNCT
ejpam-6810	266	9	ζ	ζ	NOUN
ejpam-6810	266	10	)	)	PUNCT
ejpam-6810	266	11	)	)	PUNCT
ejpam-6810	266	12	)	)	PUNCT
ejpam-6810	267	1	=	=	SYM
ejpam-6810	267	2	f(2.75	f(2.75	ADJ
ejpam-6810	267	3	)	)	PUNCT
ejpam-6810	267	4	.	.	PUNCT
ejpam-6810	268	1	(	(	PUNCT
ejpam-6810	268	2	15	15	NUM
ejpam-6810	268	3	)	)	PUNCT
ejpam-6810	268	4	hence	hence	ADV
ejpam-6810	268	5	,	,	PUNCT
ejpam-6810	268	6	by	by	ADP
ejpam-6810	268	7	(	(	PUNCT
ejpam-6810	268	8	14	14	NUM
ejpam-6810	268	9	)	)	PUNCT
ejpam-6810	268	10	and	and	CCONJ
ejpam-6810	268	11	(	(	PUNCT
ejpam-6810	268	12	15	15	NUM
ejpam-6810	268	13	)	)	PUNCT
ejpam-6810	268	14	,	,	PUNCT
ejpam-6810	268	15	we	we	PRON
ejpam-6810	268	16	conclude	conclude	VERB
ejpam-6810	268	17	that	that	SCONJ
ejpam-6810	268	18	τ	τ	PROPN
ejpam-6810	268	19	+	+	NUM
ejpam-6810	268	20	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	268	21	,	,	PUNCT
ejpam-6810	268	22	υξ	υξ	X
ejpam-6810	268	23	)	)	PUNCT
ejpam-6810	269	1	+	+	CCONJ
ejpam-6810	269	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	269	3	,	,	PUNCT
ejpam-6810	269	4	υζ	υζ	NOUN
ejpam-6810	269	5	)	)	PUNCT
ejpam-6810	269	6	+	+	CCONJ
ejpam-6810	269	7	σb(υη	σb(υη	PROPN
ejpam-6810	269	8	,	,	PUNCT
ejpam-6810	269	9	υζ	υζ	NOUN
ejpam-6810	269	10	)	)	PUNCT
ejpam-6810	269	11	)	)	PUNCT
ejpam-6810	269	12	≤	≤	NUM
ejpam-6810	269	13	f	f	X
ejpam-6810	269	14	(	(	PUNCT
ejpam-6810	269	15	1	1	NUM
ejpam-6810	269	16	s2	s2	NOUN
ejpam-6810	269	17	(	(	PUNCT
ejpam-6810	269	18	σb(η	σb(η	PROPN
ejpam-6810	269	19	,	,	PUNCT
ejpam-6810	269	20	ξ	ξ	NOUN
ejpam-6810	269	21	)	)	PUNCT
ejpam-6810	269	22	+	+	CCONJ
ejpam-6810	269	23	σb(ξ	σb(ξ	ADJ
ejpam-6810	269	24	,	,	PUNCT
ejpam-6810	269	25	ζ	ζ	NOUN
ejpam-6810	269	26	)	)	PUNCT
ejpam-6810	269	27	+	+	NUM
ejpam-6810	269	28	σb(η	σb(η	NUM
ejpam-6810	269	29	,	,	PUNCT
ejpam-6810	269	30	ζ	ζ	NOUN
ejpam-6810	269	31	)	)	PUNCT
ejpam-6810	269	32	)	)	PUNCT
ejpam-6810	269	33	)	)	PUNCT
ejpam-6810	269	34	,	,	PUNCT
ejpam-6810	269	35	with	with	ADP
ejpam-6810	269	36	f(η	f(η	NOUN
ejpam-6810	269	37	)	)	PUNCT
ejpam-6810	269	38	=	=	PUNCT
ejpam-6810	269	39	ln(η	ln(η	X
ejpam-6810	269	40	)	)	PUNCT
ejpam-6810	269	41	and	and	CCONJ
ejpam-6810	269	42	τ	τ	PROPN
ejpam-6810	269	43	=	=	NOUN
ejpam-6810	269	44	0.01	0.01	NUM
ejpam-6810	269	45	.	.	PUNCT
ejpam-6810	270	1	also	also	ADV
ejpam-6810	270	2	,	,	PUNCT
ejpam-6810	270	3	υ	υ	PROPN
ejpam-6810	270	4	has	have	VERB
ejpam-6810	270	5	no	no	DET
ejpam-6810	270	6	periodic	periodic	ADJ
ejpam-6810	270	7	point	point	NOUN
ejpam-6810	270	8	of	of	ADP
ejpam-6810	270	9	prime	prime	ADJ
ejpam-6810	270	10	period	period	NOUN
ejpam-6810	270	11	2	2	NUM
ejpam-6810	270	12	.	.	PUNCT
ejpam-6810	271	1	take	take	VERB
ejpam-6810	271	2	υζ	υζ	NOUN
ejpam-6810	271	3	=	=	SYM
ejpam-6810	271	4	η	η	PROPN
ejpam-6810	271	5	,	,	PUNCT
ejpam-6810	271	6	υ(υζ	υ(υζ	ADJ
ejpam-6810	271	7	)	)	PUNCT
ejpam-6810	271	8	=	=	SYM
ejpam-6810	271	9	υ(η	υ(η	PROPN
ejpam-6810	271	10	)	)	PUNCT
ejpam-6810	271	11	,	,	PUNCT
ejpam-6810	271	12	υ2(ζ	υ2(ζ	PROPN
ejpam-6810	271	13	)	)	PUNCT
ejpam-6810	271	14	=	=	SYM
ejpam-6810	271	15	η	η	PROPN
ejpam-6810	271	16	.	.	PROPN
ejpam-6810	271	17	hence	hence	ADV
ejpam-6810	271	18	,	,	PUNCT
ejpam-6810	271	19	υ	υ	PROPN
ejpam-6810	271	20	has	have	VERB
ejpam-6810	271	21	no	no	DET
ejpam-6810	271	22	periodic	periodic	ADJ
ejpam-6810	271	23	point	point	NOUN
ejpam-6810	271	24	with	with	ADP
ejpam-6810	271	25	prime	prime	ADJ
ejpam-6810	271	26	period	period	NOUN
ejpam-6810	271	27	2	2	NUM
ejpam-6810	271	28	.	.	PUNCT
ejpam-6810	272	1	therefore	therefore	ADV
ejpam-6810	272	2	,	,	PUNCT
ejpam-6810	272	3	all	all	DET
ejpam-6810	272	4	the	the	DET
ejpam-6810	272	5	assumptions	assumption	NOUN
ejpam-6810	272	6	of	of	ADP
ejpam-6810	272	7	theorem	theorem	NOUN
ejpam-6810	272	8	(	(	PUNCT
ejpam-6810	272	9	1	1	NUM
ejpam-6810	272	10	)	)	PUNCT
ejpam-6810	272	11	are	be	AUX
ejpam-6810	272	12	true	true	ADJ
ejpam-6810	272	13	.	.	PUNCT
ejpam-6810	273	1	thus	thus	ADV
ejpam-6810	273	2	,	,	PUNCT
ejpam-6810	273	3	υ	υ	PROPN
ejpam-6810	273	4	has	have	VERB
ejpam-6810	273	5	exactly	exactly	ADV
ejpam-6810	273	6	two	two	NUM
ejpam-6810	273	7	fps	fps	PROPN
ejpam-6810	273	8	,	,	PUNCT
ejpam-6810	273	9	namely	namely	ADV
ejpam-6810	273	10	η	η	PROPN
ejpam-6810	273	11	and	and	CCONJ
ejpam-6810	273	12	ξ	ξ	PROPN
ejpam-6810	273	13	.	.	PUNCT
ejpam-6810	274	1	in	in	ADP
ejpam-6810	274	2	next	next	ADJ
ejpam-6810	274	3	example	example	NOUN
ejpam-6810	274	4	,	,	PUNCT
ejpam-6810	274	5	we	we	PRON
ejpam-6810	274	6	prove	prove	VERB
ejpam-6810	274	7	that	that	SCONJ
ejpam-6810	274	8	if	if	SCONJ
ejpam-6810	274	9	υ	υ	NOUN
ejpam-6810	274	10	has	have	VERB
ejpam-6810	274	11	periodic	periodic	ADJ
ejpam-6810	274	12	points	point	NOUN
ejpam-6810	274	13	of	of	ADP
ejpam-6810	274	14	prime	prime	ADJ
ejpam-6810	274	15	period	period	NOUN
ejpam-6810	274	16	2	2	NUM
ejpam-6810	274	17	,	,	PUNCT
ejpam-6810	274	18	then	then	ADV
ejpam-6810	274	19	υ	υ	PROPN
ejpam-6810	274	20	has	have	VERB
ejpam-6810	274	21	no	no	DET
ejpam-6810	274	22	fp	fp	NOUN
ejpam-6810	274	23	.	.	PUNCT
ejpam-6810	274	24	s.	s.	PROPN
ejpam-6810	274	25	batul	batul	PROPN
ejpam-6810	274	26	et	et	PROPN
ejpam-6810	274	27	al	al	PROPN
ejpam-6810	274	28	.	.	PUNCT
ejpam-6810	274	29	/	/	SYM
ejpam-6810	274	30	eur	eur	PROPN
ejpam-6810	274	31	.	.	PUNCT
ejpam-6810	275	1	j.	j.	PROPN
ejpam-6810	275	2	pure	pure	PROPN
ejpam-6810	275	3	appl	appl	PROPN
ejpam-6810	275	4	.	.	PROPN
ejpam-6810	275	5	math	math	PROPN
ejpam-6810	275	6	,	,	PUNCT
ejpam-6810	275	7	18	18	NUM
ejpam-6810	275	8	(	(	PUNCT
ejpam-6810	275	9	4	4	NUM
ejpam-6810	275	10	)	)	PUNCT
ejpam-6810	275	11	(	(	PUNCT
ejpam-6810	275	12	2025	2025	NUM
ejpam-6810	275	13	)	)	PUNCT
ejpam-6810	275	14	,	,	PUNCT
ejpam-6810	275	15	6810	6810	NUM
ejpam-6810	275	16	12	12	NUM
ejpam-6810	275	17	of	of	ADP
ejpam-6810	275	18	23	23	NUM
ejpam-6810	275	19	example	example	NOUN
ejpam-6810	276	1	4	4	NUM
ejpam-6810	276	2	.	.	PUNCT
ejpam-6810	277	1	let	let	VERB
ejpam-6810	277	2	u	u	PRON
ejpam-6810	277	3	=	=	X
ejpam-6810	277	4	{	{	PUNCT
ejpam-6810	277	5	η	η	PROPN
ejpam-6810	277	6	,	,	PUNCT
ejpam-6810	277	7	ξ	ξ	PROPN
ejpam-6810	277	8	,	,	PUNCT
ejpam-6810	277	9	ζ	ζ	NOUN
ejpam-6810	277	10	}	}	PUNCT
ejpam-6810	277	11	.	.	PUNCT
ejpam-6810	278	1	define	define	VERB
ejpam-6810	278	2	σb	σb	ADP
ejpam-6810	278	3	:	:	PUNCT
ejpam-6810	278	4	u	u	NOUN
ejpam-6810	278	5	×	×	NOUN
ejpam-6810	278	6	u	u	NOUN
ejpam-6810	278	7	−→	−→	NOUN
ejpam-6810	278	8	r	r	NOUN
ejpam-6810	278	9	as	as	ADP
ejpam-6810	278	10	σb(η	σb(η	NUM
ejpam-6810	278	11	,	,	PUNCT
ejpam-6810	278	12	ξ	ξ	NOUN
ejpam-6810	278	13	)	)	PUNCT
ejpam-6810	278	14	=	=	SYM
ejpam-6810	278	15	(	(	PUNCT
ejpam-6810	278	16	η	η	PROPN
ejpam-6810	278	17	−	−	PROPN
ejpam-6810	278	18	ξ)2	ξ)2	PROPN
ejpam-6810	278	19	,	,	PUNCT
ejpam-6810	278	20	for	for	ADP
ejpam-6810	278	21	all	all	DET
ejpam-6810	278	22	η	η	PROPN
ejpam-6810	278	23	,	,	PUNCT
ejpam-6810	278	24	ξ	ξ	PROPN
ejpam-6810	278	25	∈	∈	PROPN
ejpam-6810	278	26	u	u	NOUN
ejpam-6810	278	27	.	.	PUNCT
ejpam-6810	279	1	then	then	ADV
ejpam-6810	279	2	one	one	PRON
ejpam-6810	279	3	can	can	AUX
ejpam-6810	279	4	prove	prove	VERB
ejpam-6810	279	5	that	that	SCONJ
ejpam-6810	279	6	(	(	PUNCT
ejpam-6810	279	7	u	u	NOUN
ejpam-6810	279	8	,	,	PUNCT
ejpam-6810	279	9	σb	σb	PROPN
ejpam-6810	279	10	)	)	PUNCT
ejpam-6810	279	11	is	be	AUX
ejpam-6810	279	12	a	a	DET
ejpam-6810	279	13	b	b	NOUN
ejpam-6810	279	14	-	-	PUNCT
ejpam-6810	279	15	ms	ms	NOUN
ejpam-6810	279	16	with	with	ADP
ejpam-6810	279	17	s=	s=	NOUN
ejpam-6810	279	18	2	2	NUM
ejpam-6810	279	19	.	.	PUNCT
ejpam-6810	280	1	now	now	ADV
ejpam-6810	280	2	,	,	PUNCT
ejpam-6810	280	3	define	define	VERB
ejpam-6810	280	4	υ	υ	X
ejpam-6810	280	5	:	:	PUNCT
ejpam-6810	280	6	u	u	VERB
ejpam-6810	280	7	−→	−→	NOUN
ejpam-6810	280	8	u	u	NOUN
ejpam-6810	280	9	by	by	ADP
ejpam-6810	280	10	υη	υη	X
ejpam-6810	280	11	=	=	SYM
ejpam-6810	280	12	ξ	ξ	PROPN
ejpam-6810	280	13	,	,	PUNCT
ejpam-6810	280	14	υξ	υξ	VERB
ejpam-6810	280	15	=	=	SYM
ejpam-6810	280	16	η	η	PROPN
ejpam-6810	280	17	and	and	CCONJ
ejpam-6810	280	18	υζ	υζ	NOUN
ejpam-6810	280	19	=	=	SYM
ejpam-6810	280	20	η	η	PROPN
ejpam-6810	280	21	.	.	PROPN
ejpam-6810	281	1	then	then	ADV
ejpam-6810	281	2	υ	υ	PROPN
ejpam-6810	281	3	has	have	VERB
ejpam-6810	281	4	no	no	DET
ejpam-6810	281	5	fp	fp	NOUN
ejpam-6810	281	6	.	.	PUNCT
ejpam-6810	282	1	here	here	ADV
ejpam-6810	282	2	,	,	PUNCT
ejpam-6810	282	3	η	η	PROPN
ejpam-6810	282	4	and	and	CCONJ
ejpam-6810	282	5	ξ	ξ	PROPN
ejpam-6810	282	6	are	be	AUX
ejpam-6810	282	7	periodic	periodic	ADJ
ejpam-6810	282	8	points	point	NOUN
ejpam-6810	282	9	with	with	ADP
ejpam-6810	282	10	prime	prime	ADJ
ejpam-6810	282	11	period	period	NOUN
ejpam-6810	282	12	2	2	NUM
ejpam-6810	282	13	.	.	PUNCT
ejpam-6810	283	1	consider	consider	VERB
ejpam-6810	283	2	υη	υη	X
ejpam-6810	283	3	=	=	SYM
ejpam-6810	283	4	ξ	ξ	PROPN
ejpam-6810	283	5	,	,	PUNCT
ejpam-6810	283	6	υ(υη	υ(υη	X
ejpam-6810	283	7	)	)	PUNCT
ejpam-6810	283	8	=	=	SYM
ejpam-6810	283	9	υ(ξ	υ(ξ	X
ejpam-6810	283	10	)	)	PUNCT
ejpam-6810	283	11	,	,	PUNCT
ejpam-6810	283	12	υ2(η	υ2(η	NUM
ejpam-6810	283	13	)	)	PUNCT
ejpam-6810	283	14	=	=	SYM
ejpam-6810	284	1	η	η	PROPN
ejpam-6810	284	2	.	.	PROPN
ejpam-6810	284	3	also	also	ADV
ejpam-6810	284	4	,	,	PUNCT
ejpam-6810	284	5	υξ	υξ	PROPN
ejpam-6810	284	6	=	=	SYM
ejpam-6810	284	7	η	η	PROPN
ejpam-6810	284	8	,	,	PUNCT
ejpam-6810	284	9	υ(υξ	υ(υξ	PROPN
ejpam-6810	284	10	)	)	PUNCT
ejpam-6810	284	11	=	=	SYM
ejpam-6810	284	12	υ(η	υ(η	PROPN
ejpam-6810	284	13	)	)	PUNCT
ejpam-6810	284	14	,	,	PUNCT
ejpam-6810	284	15	υ2(ξ	υ2(ξ	NOUN
ejpam-6810	284	16	)	)	PUNCT
ejpam-6810	284	17	=	=	SYM
ejpam-6810	284	18	ξ	ξ	X
ejpam-6810	284	19	.	.	PUNCT
ejpam-6810	284	20	definition	definition	NOUN
ejpam-6810	284	21	6	6	NUM
ejpam-6810	284	22	.	.	PUNCT
ejpam-6810	285	1	let	let	AUX
ejpam-6810	285	2	(	(	PUNCT
ejpam-6810	285	3	u	u	NOUN
ejpam-6810	285	4	,	,	PUNCT
ejpam-6810	285	5	σb	σb	PROPN
ejpam-6810	285	6	)	)	PUNCT
ejpam-6810	285	7	be	be	AUX
ejpam-6810	285	8	a	a	DET
ejpam-6810	285	9	b	b	PROPN
ejpam-6810	285	10	-	-	PUNCT
ejpam-6810	285	11	ms	ms	NOUN
ejpam-6810	285	12	.	.	PROPN
ejpam-6810	286	1	then	then	ADV
ejpam-6810	286	2	a	a	DET
ejpam-6810	286	3	f	f	NOUN
ejpam-6810	286	4	-	-	PUNCT
ejpam-6810	286	5	mapping	mapping	NOUN
ejpam-6810	286	6	υ	υ	NOUN
ejpam-6810	286	7	:	:	PUNCT
ejpam-6810	286	8	u	u	NOUN
ejpam-6810	286	9	−→	−→	NOUN
ejpam-6810	286	10	u	u	NOUN
ejpam-6810	286	11	is	be	AUX
ejpam-6810	286	12	called	call	VERB
ejpam-6810	286	13	an	an	DET
ejpam-6810	286	14	fcontraction	fcontraction	NOUN
ejpam-6810	286	15	mapping	mapping	NOUN
ejpam-6810	286	16	on	on	ADP
ejpam-6810	286	17	u	u	PRON
ejpam-6810	286	18	if	if	SCONJ
ejpam-6810	286	19	there	there	PRON
ejpam-6810	286	20	exist	exist	VERB
ejpam-6810	286	21	a	a	DET
ejpam-6810	286	22	positive	positive	ADJ
ejpam-6810	286	23	real	real	ADJ
ejpam-6810	286	24	number	number	NOUN
ejpam-6810	286	25	s	s	PART
ejpam-6810	286	26	≥	≥	NOUN
ejpam-6810	286	27	1	1	NUM
ejpam-6810	286	28	and	and	CCONJ
ejpam-6810	286	29	τ	τ	PROPN
ejpam-6810	286	30	>	>	X
ejpam-6810	286	31	0	0	NUM
ejpam-6810	287	1	such	such	ADJ
ejpam-6810	287	2	that	that	SCONJ
ejpam-6810	287	3	τ	τ	PROPN
ejpam-6810	287	4	+	+	NUM
ejpam-6810	287	5	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	287	6	,	,	PUNCT
ejpam-6810	287	7	υξ	υξ	NOUN
ejpam-6810	287	8	)	)	PUNCT
ejpam-6810	287	9	)	)	PUNCT
ejpam-6810	287	10	≤	≤	NUM
ejpam-6810	287	11	f	f	X
ejpam-6810	287	12	(	(	PUNCT
ejpam-6810	287	13	1	1	NUM
ejpam-6810	287	14	s2	s2	NOUN
ejpam-6810	287	15	σb(η	σb(η	NUM
ejpam-6810	287	16	,	,	PUNCT
ejpam-6810	287	17	ξ	ξ	NOUN
ejpam-6810	287	18	)	)	PUNCT
ejpam-6810	287	19	)	)	PUNCT
ejpam-6810	287	20	,	,	PUNCT
ejpam-6810	287	21	where	where	SCONJ
ejpam-6810	287	22	f	f	PROPN
ejpam-6810	287	23	∈	∈	PROPN
ejpam-6810	287	24	f	f	PROPN
ejpam-6810	287	25	and	and	CCONJ
ejpam-6810	287	26	for	for	ADP
ejpam-6810	287	27	all	all	DET
ejpam-6810	287	28	η	η	PROPN
ejpam-6810	287	29	,	,	PUNCT
ejpam-6810	287	30	ξ	ξ	PROPN
ejpam-6810	287	31	∈	∈	PROPN
ejpam-6810	287	32	u	u	NOUN
ejpam-6810	287	33	.	.	PUNCT
ejpam-6810	288	1	(	(	PUNCT
ejpam-6810	288	2	16	16	NUM
ejpam-6810	288	3	)	)	PUNCT
ejpam-6810	288	4	the	the	DET
ejpam-6810	288	5	following	follow	VERB
ejpam-6810	288	6	corollary	corollary	NOUN
ejpam-6810	288	7	provides	provide	VERB
ejpam-6810	288	8	a	a	DET
ejpam-6810	288	9	simple	simple	ADJ
ejpam-6810	288	10	and	and	CCONJ
ejpam-6810	288	11	direct	direct	ADJ
ejpam-6810	288	12	proof	proof	NOUN
ejpam-6810	288	13	of	of	ADP
ejpam-6810	288	14	banach	banach	NOUN
ejpam-6810	288	15	fp	fp	X
ejpam-6810	288	16	theorem	theorem	PROPN
ejpam-6810	288	17	,	,	PUNCT
ejpam-6810	288	18	in	in	ADP
ejpam-6810	288	19	the	the	DET
ejpam-6810	288	20	framework	framework	NOUN
ejpam-6810	288	21	of	of	ADP
ejpam-6810	288	22	a	a	DET
ejpam-6810	288	23	b	b	PROPN
ejpam-6810	288	24	-	-	PUNCT
ejpam-6810	288	25	ms	ms	PROPN
ejpam-6810	288	26	.	.	PROPN
ejpam-6810	288	27	corollary	corollary	NOUN
ejpam-6810	288	28	1	1	PROPN
ejpam-6810	288	29	.	.	PUNCT
ejpam-6810	288	30	suppose	suppose	VERB
ejpam-6810	288	31	that	that	SCONJ
ejpam-6810	288	32	(	(	PUNCT
ejpam-6810	288	33	u	u	NOUN
ejpam-6810	288	34	,	,	PUNCT
ejpam-6810	288	35	σb	σb	PROPN
ejpam-6810	288	36	)	)	PUNCT
ejpam-6810	288	37	is	be	AUX
ejpam-6810	288	38	a	a	DET
ejpam-6810	288	39	complete	complete	ADJ
ejpam-6810	288	40	b	b	NOUN
ejpam-6810	288	41	-	-	PUNCT
ejpam-6810	288	42	ms	ms	NOUN
ejpam-6810	288	43	,	,	PUNCT
ejpam-6810	288	44	where	where	SCONJ
ejpam-6810	288	45	u	u	PROPN
ejpam-6810	288	46	6=	6=	PROPN
ejpam-6810	288	47	∅.	∅.	ADP
ejpam-6810	288	48	then	then	ADV
ejpam-6810	288	49	the	the	DET
ejpam-6810	288	50	fcontraction	fcontraction	NOUN
ejpam-6810	288	51	mapping	mapping	NOUN
ejpam-6810	288	52	υ	υ	NOUN
ejpam-6810	288	53	:	:	PUNCT
ejpam-6810	288	54	u	u	NOUN
ejpam-6810	288	55	→	→	SYM
ejpam-6810	288	56	u	u	NOUN
ejpam-6810	288	57	guarantees	guarantee	VERB
ejpam-6810	288	58	that	that	SCONJ
ejpam-6810	288	59	υ	υ	PROPN
ejpam-6810	288	60	has	have	VERB
ejpam-6810	288	61	a	a	DET
ejpam-6810	288	62	unique	unique	ADJ
ejpam-6810	288	63	fp	fp	NOUN
ejpam-6810	288	64	.	.	NOUN
ejpam-6810	288	65	proof	proof	NOUN
ejpam-6810	288	66	.	.	PUNCT
ejpam-6810	289	1	suppose	suppose	VERB
ejpam-6810	289	2	that	that	SCONJ
ejpam-6810	289	3	u	u	PROPN
ejpam-6810	289	4	is	be	AUX
ejpam-6810	289	5	a	a	DET
ejpam-6810	289	6	complete	complete	ADJ
ejpam-6810	289	7	b	b	NOUN
ejpam-6810	289	8	-	-	PUNCT
ejpam-6810	289	9	ms	ms	NOUN
ejpam-6810	289	10	and	and	CCONJ
ejpam-6810	289	11	|u|	|u|	PROPN
ejpam-6810	289	12	=	=	SYM
ejpam-6810	289	13	1	1	X
ejpam-6810	289	14	.	.	PUNCT
ejpam-6810	290	1	let	let	VERB
ejpam-6810	290	2	u	u	PRON
ejpam-6810	290	3	=	=	PUNCT
ejpam-6810	290	4	{	{	PUNCT
ejpam-6810	290	5	u	u	NOUN
ejpam-6810	290	6	}	}	PUNCT
ejpam-6810	290	7	.	.	PUNCT
ejpam-6810	291	1	in	in	ADP
ejpam-6810	291	2	this	this	DET
ejpam-6810	291	3	case	case	NOUN
ejpam-6810	291	4	,	,	PUNCT
ejpam-6810	291	5	since	since	SCONJ
ejpam-6810	291	6	u	u	NOUN
ejpam-6810	291	7	has	have	VERB
ejpam-6810	291	8	only	only	ADV
ejpam-6810	291	9	one	one	NUM
ejpam-6810	291	10	element	element	PROPN
ejpam-6810	291	11	η	η	PROPN
ejpam-6810	291	12	,	,	PUNCT
ejpam-6810	291	13	the	the	DET
ejpam-6810	291	14	mapping	mapping	NOUN
ejpam-6810	291	15	υ	υ	NOUN
ejpam-6810	291	16	must	must	AUX
ejpam-6810	291	17	map	map	VERB
ejpam-6810	291	18	η	η	PROPN
ejpam-6810	291	19	to	to	ADP
ejpam-6810	291	20	itself	itself	PRON
ejpam-6810	291	21	.	.	PUNCT
ejpam-6810	292	1	that	that	PRON
ejpam-6810	292	2	is	be	AUX
ejpam-6810	292	3	,	,	PUNCT
ejpam-6810	292	4	υη	υη	PROPN
ejpam-6810	292	5	=	=	SYM
ejpam-6810	292	6	η	η	PROPN
ejpam-6810	292	7	.	.	PROPN
ejpam-6810	293	1	this	this	PRON
ejpam-6810	293	2	is	be	AUX
ejpam-6810	293	3	because	because	SCONJ
ejpam-6810	293	4	there	there	PRON
ejpam-6810	293	5	are	be	VERB
ejpam-6810	293	6	no	no	DET
ejpam-6810	293	7	other	other	ADJ
ejpam-6810	293	8	element	element	NOUN
ejpam-6810	293	9	in	in	ADP
ejpam-6810	293	10	u	u	PROPN
ejpam-6810	293	11	for	for	SCONJ
ejpam-6810	293	12	υη	υη	PROPN
ejpam-6810	293	13	to	to	PART
ejpam-6810	293	14	map	map	VERB
ejpam-6810	293	15	.	.	PUNCT
ejpam-6810	294	1	so	so	ADV
ejpam-6810	294	2	,	,	PUNCT
ejpam-6810	294	3	we	we	PRON
ejpam-6810	294	4	can	can	AUX
ejpam-6810	294	5	see	see	VERB
ejpam-6810	294	6	that	that	SCONJ
ejpam-6810	294	7	η	η	PROPN
ejpam-6810	294	8	is	be	AUX
ejpam-6810	294	9	indeed	indeed	ADV
ejpam-6810	294	10	a	a	DET
ejpam-6810	294	11	fp	fp	X
ejpam-6810	294	12	of	of	ADP
ejpam-6810	294	13	υ	υ	PROPN
ejpam-6810	294	14	,	,	PUNCT
ejpam-6810	294	15	and	and	CCONJ
ejpam-6810	294	16	it	it	PRON
ejpam-6810	294	17	is	be	AUX
ejpam-6810	294	18	unique	unique	ADJ
ejpam-6810	294	19	.	.	PUNCT
ejpam-6810	295	1	therefore	therefore	ADV
ejpam-6810	295	2	,	,	PUNCT
ejpam-6810	295	3	the	the	DET
ejpam-6810	295	4	banach	banach	NOUN
ejpam-6810	295	5	fp	fp	X
ejpam-6810	295	6	theorem	theorem	NOUN
ejpam-6810	295	7	holds	hold	VERB
ejpam-6810	295	8	trivially	trivially	ADV
ejpam-6810	295	9	for	for	ADP
ejpam-6810	295	10	a	a	DET
ejpam-6810	295	11	set	set	ADJ
ejpam-6810	295	12	u	u	NOUN
ejpam-6810	295	13	of	of	ADP
ejpam-6810	295	14	order	order	NOUN
ejpam-6810	295	15	1	1	X
ejpam-6810	295	16	.	.	PUNCT
ejpam-6810	296	1	now	now	ADV
ejpam-6810	296	2	,	,	PUNCT
ejpam-6810	296	3	if	if	SCONJ
ejpam-6810	296	4	|u|	|u|	ADJ
ejpam-6810	296	5	=	=	SYM
ejpam-6810	296	6	2	2	NUM
ejpam-6810	296	7	,	,	PUNCT
ejpam-6810	296	8	suppose	suppose	VERB
ejpam-6810	296	9	that	that	SCONJ
ejpam-6810	296	10	u	u	PRON
ejpam-6810	296	11	=	=	PUNCT
ejpam-6810	296	12	{	{	PUNCT
ejpam-6810	296	13	u	u	NOUN
ejpam-6810	296	14	,	,	PUNCT
ejpam-6810	296	15	v	v	NOUN
ejpam-6810	296	16	}	}	PUNCT
ejpam-6810	296	17	and	and	CCONJ
ejpam-6810	296	18	υ	υ	NOUN
ejpam-6810	296	19	:	:	PUNCT
ejpam-6810	296	20	u	u	NOUN
ejpam-6810	296	21	−→	−→	NOUN
ejpam-6810	296	22	u	u	NOUN
ejpam-6810	296	23	is	be	AUX
ejpam-6810	296	24	an	an	DET
ejpam-6810	296	25	f	f	NUM
ejpam-6810	296	26	-	-	PUNCT
ejpam-6810	296	27	contraction	contraction	NOUN
ejpam-6810	296	28	mapping	mapping	NOUN
ejpam-6810	296	29	.	.	PUNCT
ejpam-6810	297	1	assume	assume	VERB
ejpam-6810	297	2	,	,	PUNCT
ejpam-6810	297	3	if	if	SCONJ
ejpam-6810	297	4	possible	possible	ADJ
ejpam-6810	297	5	,	,	PUNCT
ejpam-6810	297	6	that	that	SCONJ
ejpam-6810	297	7	υ	υ	PROPN
ejpam-6810	297	8	has	have	VERB
ejpam-6810	297	9	two	two	NUM
ejpam-6810	297	10	distinct	distinct	ADJ
ejpam-6810	297	11	fps	fps	PROPN
ejpam-6810	297	12	η	η	PROPN
ejpam-6810	297	13	and	and	CCONJ
ejpam-6810	297	14	ξ	ξ	PROPN
ejpam-6810	297	15	.	.	PUNCT
ejpam-6810	298	1	then	then	ADV
ejpam-6810	298	2	,	,	PUNCT
ejpam-6810	298	3	υη	υη	PROPN
ejpam-6810	298	4	=	=	PROPN
ejpam-6810	298	5	η	η	PROPN
ejpam-6810	298	6	and	and	CCONJ
ejpam-6810	298	7	υξ	υξ	PRON
ejpam-6810	298	8	=	=	SYM
ejpam-6810	298	9	ξ	ξ	PROPN
ejpam-6810	298	10	.	.	PUNCT
ejpam-6810	299	1	by	by	ADP
ejpam-6810	299	2	the	the	DET
ejpam-6810	299	3	definition	definition	NOUN
ejpam-6810	299	4	of	of	ADP
ejpam-6810	299	5	an	an	DET
ejpam-6810	299	6	f	f	PROPN
ejpam-6810	299	7	-	-	PUNCT
ejpam-6810	299	8	contraction	contraction	NOUN
ejpam-6810	299	9	mapping	mapping	NOUN
ejpam-6810	299	10	,	,	PUNCT
ejpam-6810	299	11	we	we	PRON
ejpam-6810	299	12	have	have	VERB
ejpam-6810	299	13	τ	τ	PROPN
ejpam-6810	299	14	+	+	NUM
ejpam-6810	299	15	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	299	16	,	,	PUNCT
ejpam-6810	299	17	υξ	υξ	NOUN
ejpam-6810	299	18	)	)	PUNCT
ejpam-6810	299	19	)	)	PUNCT
ejpam-6810	299	20	≤	≤	NUM
ejpam-6810	300	1	f	f	X
ejpam-6810	300	2	(	(	PUNCT
ejpam-6810	300	3	1	1	NUM
ejpam-6810	300	4	s2	s2	NOUN
ejpam-6810	300	5	σb(η	σb(η	NUM
ejpam-6810	300	6	,	,	PUNCT
ejpam-6810	300	7	ξ	ξ	NOUN
ejpam-6810	300	8	)	)	PUNCT
ejpam-6810	300	9	)	)	PUNCT
ejpam-6810	300	10	that	that	ADV
ejpam-6810	300	11	is	be	AUX
ejpam-6810	300	12	,	,	PUNCT
ejpam-6810	300	13	f(σb(η	f(σb(η	PROPN
ejpam-6810	300	14	,	,	PUNCT
ejpam-6810	300	15	ξ	ξ	NOUN
ejpam-6810	300	16	)	)	PUNCT
ejpam-6810	300	17	)	)	PUNCT
ejpam-6810	300	18	≤	≤	NUM
ejpam-6810	301	1	f	f	X
ejpam-6810	301	2	(	(	PUNCT
ejpam-6810	301	3	1	1	NUM
ejpam-6810	301	4	s2	s2	NOUN
ejpam-6810	301	5	σb(η	σb(η	NUM
ejpam-6810	301	6	,	,	PUNCT
ejpam-6810	301	7	ξ))−	ξ))−	NUM
ejpam-6810	301	8	τ	τ	X
ejpam-6810	301	9	.	.	PUNCT
ejpam-6810	302	1	s.	s.	PROPN
ejpam-6810	302	2	batul	batul	PROPN
ejpam-6810	302	3	et	et	PROPN
ejpam-6810	302	4	al	al	PROPN
ejpam-6810	302	5	.	.	PUNCT
ejpam-6810	302	6	/	/	SYM
ejpam-6810	302	7	eur	eur	PROPN
ejpam-6810	302	8	.	.	PUNCT
ejpam-6810	303	1	j.	j.	PROPN
ejpam-6810	303	2	pure	pure	PROPN
ejpam-6810	303	3	appl	appl	PROPN
ejpam-6810	303	4	.	.	PROPN
ejpam-6810	303	5	math	math	PROPN
ejpam-6810	303	6	,	,	PUNCT
ejpam-6810	303	7	18	18	NUM
ejpam-6810	303	8	(	(	PUNCT
ejpam-6810	303	9	4	4	NUM
ejpam-6810	303	10	)	)	PUNCT
ejpam-6810	303	11	(	(	PUNCT
ejpam-6810	303	12	2025	2025	NUM
ejpam-6810	303	13	)	)	PUNCT
ejpam-6810	303	14	,	,	PUNCT
ejpam-6810	303	15	6810	6810	NUM
ejpam-6810	303	16	13	13	NUM
ejpam-6810	303	17	of	of	ADP
ejpam-6810	303	18	23	23	NUM
ejpam-6810	303	19	hence	hence	ADV
ejpam-6810	303	20	,	,	PUNCT
ejpam-6810	303	21	f(σb(η	f(σb(η	PROPN
ejpam-6810	303	22	,	,	PUNCT
ejpam-6810	303	23	ξ	ξ	NOUN
ejpam-6810	303	24	)	)	PUNCT
ejpam-6810	303	25	)	)	PUNCT
ejpam-6810	303	26	≤	≤	NUM
ejpam-6810	304	1	f	f	X
ejpam-6810	304	2	(	(	PUNCT
ejpam-6810	304	3	1	1	NUM
ejpam-6810	304	4	s2	s2	NOUN
ejpam-6810	304	5	σb(η	σb(η	NUM
ejpam-6810	304	6	,	,	PUNCT
ejpam-6810	304	7	ξ	ξ	NOUN
ejpam-6810	304	8	)	)	PUNCT
ejpam-6810	304	9	)	)	PUNCT
ejpam-6810	304	10	.	.	PUNCT
ejpam-6810	305	1	f	f	PROPN
ejpam-6810	305	2	is	be	AUX
ejpam-6810	305	3	increasing	increase	VERB
ejpam-6810	305	4	,	,	PUNCT
ejpam-6810	305	5	so	so	SCONJ
ejpam-6810	305	6	σb(η	σb(η	PROPN
ejpam-6810	305	7	,	,	PUNCT
ejpam-6810	305	8	ξ	ξ	NOUN
ejpam-6810	305	9	)	)	PUNCT
ejpam-6810	305	10	≤	≤	NOUN
ejpam-6810	305	11	1	1	NUM
ejpam-6810	305	12	s2	s2	NOUN
ejpam-6810	305	13	σb(η	σb(η	NUM
ejpam-6810	305	14	,	,	PUNCT
ejpam-6810	305	15	ξ	ξ	NOUN
ejpam-6810	305	16	)	)	PUNCT
ejpam-6810	305	17	.	.	PUNCT
ejpam-6810	306	1	this	this	PRON
ejpam-6810	306	2	is	be	AUX
ejpam-6810	306	3	a	a	DET
ejpam-6810	306	4	contradiction	contradiction	NOUN
ejpam-6810	306	5	since	since	SCONJ
ejpam-6810	306	6	s	s	PRON
ejpam-6810	306	7	≥	≥	NOUN
ejpam-6810	306	8	1	1	NUM
ejpam-6810	306	9	.	.	PUNCT
ejpam-6810	307	1	therefore	therefore	ADV
ejpam-6810	307	2	,	,	PUNCT
ejpam-6810	307	3	our	our	PRON
ejpam-6810	307	4	assumption	assumption	NOUN
ejpam-6810	307	5	that	that	SCONJ
ejpam-6810	307	6	υ	υ	PROPN
ejpam-6810	307	7	has	have	AUX
ejpam-6810	307	8	two	two	NUM
ejpam-6810	307	9	distinct	distinct	ADJ
ejpam-6810	307	10	fps	fps	NOUN
ejpam-6810	307	11	is	be	AUX
ejpam-6810	307	12	false	false	ADJ
ejpam-6810	307	13	.	.	PUNCT
ejpam-6810	308	1	hence	hence	ADV
ejpam-6810	308	2	,	,	PUNCT
ejpam-6810	308	3	υ	υ	PROPN
ejpam-6810	308	4	can	can	AUX
ejpam-6810	308	5	have	have	VERB
ejpam-6810	308	6	at	at	ADP
ejpam-6810	308	7	most	most	ADV
ejpam-6810	308	8	one	one	NUM
ejpam-6810	308	9	fp	fp	NOUN
ejpam-6810	308	10	.	.	PUNCT
ejpam-6810	309	1	so	so	ADV
ejpam-6810	309	2	,	,	PUNCT
ejpam-6810	309	3	for	for	ADP
ejpam-6810	309	4	|u|	|u|	NOUN
ejpam-6810	309	5	=	=	SYM
ejpam-6810	309	6	1	1	NUM
ejpam-6810	309	7	,	,	PUNCT
ejpam-6810	309	8	2	2	NUM
ejpam-6810	309	9	the	the	DET
ejpam-6810	309	10	proof	proof	NOUN
ejpam-6810	309	11	is	be	AUX
ejpam-6810	309	12	complete	complete	ADJ
ejpam-6810	309	13	.	.	PUNCT
ejpam-6810	310	1	assume	assume	VERB
ejpam-6810	310	2	u	u	NOUN
ejpam-6810	310	3	has	have	VERB
ejpam-6810	310	4	at	at	ADV
ejpam-6810	310	5	least	least	ADV
ejpam-6810	310	6	three	three	NUM
ejpam-6810	310	7	elements	element	NOUN
ejpam-6810	310	8	,	,	PUNCT
ejpam-6810	310	9	i.e.	i.e.	X
ejpam-6810	310	10	,	,	PUNCT
ejpam-6810	310	11	|u|	|u|	PROPN
ejpam-6810	310	12	≥3	≥3	PROPN
ejpam-6810	310	13	,	,	PUNCT
ejpam-6810	310	14	if	if	SCONJ
ejpam-6810	310	15	υ	υ	NOUN
ejpam-6810	310	16	has	have	VERB
ejpam-6810	310	17	some	some	DET
ejpam-6810	310	18	η	η	PROPN
ejpam-6810	310	19	∈	∈	PROPN
ejpam-6810	310	20	u	u	NOUN
ejpam-6810	310	21	with	with	ADP
ejpam-6810	310	22	prime	prime	ADJ
ejpam-6810	310	23	period	period	NOUN
ejpam-6810	310	24	2	2	NUM
ejpam-6810	310	25	,	,	PUNCT
ejpam-6810	310	26	i.e.	i.e.	X
ejpam-6810	310	27	,	,	PUNCT
ejpam-6810	310	28	υ(υ(η	υ(υ(η	NOUN
ejpam-6810	310	29	)	)	PUNCT
ejpam-6810	310	30	)	)	PUNCT
ejpam-6810	311	1	=	=	SYM
ejpam-6810	311	2	η	η	PROPN
ejpam-6810	311	3	,	,	PUNCT
ejpam-6810	311	4	then	then	ADV
ejpam-6810	311	5	σb(η	σb(η	NUM
ejpam-6810	311	6	,	,	PUNCT
ejpam-6810	311	7	υη	υη	NOUN
ejpam-6810	311	8	)	)	PUNCT
ejpam-6810	311	9	=	=	SYM
ejpam-6810	312	1	σb(υη	σb(υη	PROPN
ejpam-6810	312	2	,	,	PUNCT
ejpam-6810	312	3	η	η	NOUN
ejpam-6810	312	4	)	)	PUNCT
ejpam-6810	312	5	=	=	SYM
ejpam-6810	312	6	σb(υη	σb(υη	PROPN
ejpam-6810	312	7	,	,	PUNCT
ejpam-6810	312	8	υ(υη	υ(υη	PROPN
ejpam-6810	312	9	)	)	PUNCT
ejpam-6810	312	10	)	)	PUNCT
ejpam-6810	312	11	.	.	PUNCT
ejpam-6810	313	1	which	which	PRON
ejpam-6810	313	2	is	be	AUX
ejpam-6810	313	3	contradiction	contradiction	NOUN
ejpam-6810	313	4	with	with	ADP
ejpam-6810	313	5	(	(	PUNCT
ejpam-6810	313	6	16	16	NUM
ejpam-6810	313	7	)	)	PUNCT
ejpam-6810	313	8	.	.	PUNCT
ejpam-6810	314	1	it	it	PRON
ejpam-6810	314	2	follows	follow	VERB
ejpam-6810	314	3	that	that	SCONJ
ejpam-6810	314	4	υ	υ	PROPN
ejpam-6810	314	5	has	have	VERB
ejpam-6810	314	6	no	no	DET
ejpam-6810	314	7	periodic	periodic	ADJ
ejpam-6810	314	8	point	point	NOUN
ejpam-6810	314	9	with	with	ADP
ejpam-6810	314	10	prime	prime	ADJ
ejpam-6810	314	11	period	period	NOUN
ejpam-6810	314	12	2	2	NUM
ejpam-6810	314	13	.	.	PUNCT
ejpam-6810	314	14	considering	consider	VERB
ejpam-6810	314	15	pairwise	pairwise	NOUN
ejpam-6810	314	16	distinct	distinct	ADJ
ejpam-6810	314	17	elements	element	NOUN
ejpam-6810	314	18	η	η	PROPN
ejpam-6810	314	19	,	,	PUNCT
ejpam-6810	314	20	ξ	ξ	PROPN
ejpam-6810	314	21	,	,	PUNCT
ejpam-6810	314	22	ζ	ζ	PROPN
ejpam-6810	314	23	∈	∈	PROPN
ejpam-6810	314	24	u	u	NOUN
ejpam-6810	314	25	,	,	PUNCT
ejpam-6810	314	26	and	and	CCONJ
ejpam-6810	314	27	applying	apply	VERB
ejpam-6810	314	28	(	(	PUNCT
ejpam-6810	314	29	16	16	NUM
ejpam-6810	314	30	)	)	PUNCT
ejpam-6810	314	31	,	,	PUNCT
ejpam-6810	314	32	we	we	PRON
ejpam-6810	314	33	have	have	VERB
ejpam-6810	314	34	τ	τ	PROPN
ejpam-6810	314	35	+	+	CCONJ
ejpam-6810	314	36	f(σb(υ(η),υ(ξ	f(σb(υ(η),υ(ξ	NUM
ejpam-6810	314	37	)	)	PUNCT
ejpam-6810	314	38	)	)	PUNCT
ejpam-6810	314	39	)	)	PUNCT
ejpam-6810	315	1	≤	≤	NUM
ejpam-6810	316	1	f	f	X
ejpam-6810	316	2	(	(	PUNCT
ejpam-6810	316	3	1	1	NUM
ejpam-6810	316	4	s2	s2	NOUN
ejpam-6810	316	5	σb(η	σb(η	NUM
ejpam-6810	316	6	,	,	PUNCT
ejpam-6810	316	7	ξ	ξ	NOUN
ejpam-6810	316	8	)	)	PUNCT
ejpam-6810	316	9	)	)	PUNCT
ejpam-6810	316	10	.	.	PUNCT
ejpam-6810	317	1	let	let	VERB
ejpam-6810	317	2	f(η	f(η	X
ejpam-6810	317	3	)	)	PUNCT
ejpam-6810	318	1	=	=	SYM
ejpam-6810	318	2	ln(η	ln(η	X
ejpam-6810	318	3	)	)	PUNCT
ejpam-6810	318	4	,	,	PUNCT
ejpam-6810	318	5	so	so	ADV
ejpam-6810	318	6	τ	τ	PROPN
ejpam-6810	318	7	+	+	NUM
ejpam-6810	318	8	ln(σb(υ(η),υ(ξ	ln(σb(υ(η),υ(ξ	PROPN
ejpam-6810	318	9	)	)	PUNCT
ejpam-6810	318	10	)	)	PUNCT
ejpam-6810	318	11	)	)	PUNCT
ejpam-6810	319	1	≤	≤	NOUN
ejpam-6810	320	1	ln	ln	ADJ
ejpam-6810	320	2	(	(	PUNCT
ejpam-6810	320	3	1	1	NUM
ejpam-6810	320	4	s2	s2	NOUN
ejpam-6810	320	5	σb(η	σb(η	NUM
ejpam-6810	320	6	,	,	PUNCT
ejpam-6810	320	7	ξ	ξ	NOUN
ejpam-6810	320	8	)	)	PUNCT
ejpam-6810	320	9	)	)	PUNCT
ejpam-6810	320	10	.	.	PUNCT
ejpam-6810	321	1	that	that	PRON
ejpam-6810	321	2	is	be	AUX
ejpam-6810	321	3	,	,	PUNCT
ejpam-6810	321	4	eτσb(υ(η),υ(ξ	eτσb(υ(η),υ(ξ	X
ejpam-6810	321	5	)	)	PUNCT
ejpam-6810	321	6	)	)	PUNCT
ejpam-6810	321	7	≤	≤	NOUN
ejpam-6810	321	8	1	1	NUM
ejpam-6810	321	9	s2	s2	NOUN
ejpam-6810	321	10	σb(η	σb(η	NUM
ejpam-6810	321	11	,	,	PUNCT
ejpam-6810	321	12	ξ	ξ	NOUN
ejpam-6810	321	13	)	)	PUNCT
ejpam-6810	321	14	.	.	PUNCT
ejpam-6810	322	1	that	that	PRON
ejpam-6810	322	2	is	is	ADV
ejpam-6810	322	3	,	,	PUNCT
ejpam-6810	322	4	σb(υ(η),υ(ξ	σb(υ(η),υ(ξ	X
ejpam-6810	322	5	)	)	PUNCT
ejpam-6810	322	6	)	)	PUNCT
ejpam-6810	322	7	≤	≤	NUM
ejpam-6810	322	8	e−τ	e−τ	NOUN
ejpam-6810	322	9	s2	s2	NOUN
ejpam-6810	322	10	σb(η	σb(η	NUM
ejpam-6810	322	11	,	,	PUNCT
ejpam-6810	322	12	ξ	ξ	NOUN
ejpam-6810	322	13	)	)	PUNCT
ejpam-6810	322	14	.	.	PUNCT
ejpam-6810	323	1	(	(	PUNCT
ejpam-6810	323	2	17	17	NUM
ejpam-6810	323	3	)	)	PUNCT
ejpam-6810	323	4	similarly	similarly	ADV
ejpam-6810	323	5	,	,	PUNCT
ejpam-6810	323	6	one	one	PRON
ejpam-6810	323	7	can	can	AUX
ejpam-6810	323	8	get	get	VERB
ejpam-6810	323	9	τ	τ	NOUN
ejpam-6810	323	10	+	+	X
ejpam-6810	323	11	f(σb(υ(ξ),υ(ζ	f(σb(υ(ξ),υ(ζ	NOUN
ejpam-6810	323	12	)	)	PUNCT
ejpam-6810	323	13	)	)	PUNCT
ejpam-6810	323	14	)	)	PUNCT
ejpam-6810	324	1	≤	≤	NUM
ejpam-6810	325	1	f	f	X
ejpam-6810	325	2	(	(	PUNCT
ejpam-6810	325	3	1	1	NUM
ejpam-6810	325	4	s2	s2	NOUN
ejpam-6810	325	5	σb(ξ	σb(ξ	NOUN
ejpam-6810	325	6	,	,	PUNCT
ejpam-6810	325	7	ζ	ζ	NOUN
ejpam-6810	325	8	)	)	PUNCT
ejpam-6810	325	9	)	)	PUNCT
ejpam-6810	325	10	implying	imply	VERB
ejpam-6810	325	11	σb(υ(ξ),υ(ζ	σb(υ(ξ),υ(ζ	NOUN
ejpam-6810	325	12	)	)	PUNCT
ejpam-6810	325	13	)	)	PUNCT
ejpam-6810	325	14	≤	≤	NUM
ejpam-6810	325	15	e−τ	e−τ	NOUN
ejpam-6810	325	16	s2	s2	NOUN
ejpam-6810	325	17	σb(ξ	σb(ξ	NOUN
ejpam-6810	325	18	,	,	PUNCT
ejpam-6810	325	19	ζ	ζ	NOUN
ejpam-6810	325	20	)	)	PUNCT
ejpam-6810	325	21	.	.	PUNCT
ejpam-6810	326	1	(	(	PUNCT
ejpam-6810	326	2	18	18	NUM
ejpam-6810	326	3	)	)	PUNCT
ejpam-6810	326	4	and	and	CCONJ
ejpam-6810	326	5	τ	τ	PROPN
ejpam-6810	326	6	+	+	CCONJ
ejpam-6810	326	7	f(σb(υ(η),υ(ζ	f(σb(υ(η),υ(ζ	NOUN
ejpam-6810	326	8	)	)	PUNCT
ejpam-6810	326	9	)	)	PUNCT
ejpam-6810	326	10	)	)	PUNCT
ejpam-6810	327	1	≤	≤	NUM
ejpam-6810	328	1	f	f	X
ejpam-6810	328	2	(	(	PUNCT
ejpam-6810	328	3	1	1	NUM
ejpam-6810	328	4	s2	s2	NOUN
ejpam-6810	328	5	σb(η	σb(η	PRON
ejpam-6810	328	6	,	,	PUNCT
ejpam-6810	328	7	ζ	ζ	NOUN
ejpam-6810	328	8	)	)	PUNCT
ejpam-6810	328	9	)	)	PUNCT
ejpam-6810	328	10	.	.	PUNCT
ejpam-6810	329	1	thus	thus	ADV
ejpam-6810	329	2	,	,	PUNCT
ejpam-6810	329	3	σb(υ(η),υ(ζ	σb(υ(η),υ(ζ	NOUN
ejpam-6810	329	4	)	)	PUNCT
ejpam-6810	329	5	)	)	PUNCT
ejpam-6810	329	6	≤	≤	NUM
ejpam-6810	329	7	e−τ	e−τ	NOUN
ejpam-6810	329	8	s2	s2	NOUN
ejpam-6810	329	9	σb(η	σb(η	PRON
ejpam-6810	329	10	,	,	PUNCT
ejpam-6810	329	11	ζ	ζ	NOUN
ejpam-6810	329	12	)	)	PUNCT
ejpam-6810	329	13	.	.	PUNCT
ejpam-6810	330	1	(	(	PUNCT
ejpam-6810	330	2	19	19	NUM
ejpam-6810	330	3	)	)	PUNCT
ejpam-6810	330	4	s.	s.	PROPN
ejpam-6810	330	5	batul	batul	PROPN
ejpam-6810	330	6	et	et	PROPN
ejpam-6810	330	7	al	al	PROPN
ejpam-6810	330	8	.	.	PUNCT
ejpam-6810	330	9	/	/	SYM
ejpam-6810	330	10	eur	eur	PROPN
ejpam-6810	330	11	.	.	PUNCT
ejpam-6810	331	1	j.	j.	PROPN
ejpam-6810	331	2	pure	pure	PROPN
ejpam-6810	331	3	appl	appl	PROPN
ejpam-6810	331	4	.	.	PROPN
ejpam-6810	331	5	math	math	PROPN
ejpam-6810	331	6	,	,	PUNCT
ejpam-6810	331	7	18	18	NUM
ejpam-6810	331	8	(	(	PUNCT
ejpam-6810	331	9	4	4	NUM
ejpam-6810	331	10	)	)	PUNCT
ejpam-6810	331	11	(	(	PUNCT
ejpam-6810	331	12	2025	2025	NUM
ejpam-6810	331	13	)	)	PUNCT
ejpam-6810	331	14	,	,	PUNCT
ejpam-6810	331	15	6810	6810	NUM
ejpam-6810	331	16	14	14	NUM
ejpam-6810	331	17	of	of	ADP
ejpam-6810	331	18	23	23	NUM
ejpam-6810	331	19	adding	add	VERB
ejpam-6810	331	20	(	(	PUNCT
ejpam-6810	331	21	17	17	NUM
ejpam-6810	331	22	)	)	PUNCT
ejpam-6810	331	23	,	,	PUNCT
ejpam-6810	331	24	(	(	PUNCT
ejpam-6810	331	25	18	18	NUM
ejpam-6810	331	26	)	)	PUNCT
ejpam-6810	331	27	and	and	CCONJ
ejpam-6810	331	28	(	(	PUNCT
ejpam-6810	331	29	19	19	NUM
ejpam-6810	331	30	)	)	PUNCT
ejpam-6810	331	31	,	,	PUNCT
ejpam-6810	331	32	one	one	PRON
ejpam-6810	331	33	has	have	AUX
ejpam-6810	331	34	σb(υ(η),υ(ξ	σb(υ(η),υ(ξ	X
ejpam-6810	331	35	)	)	PUNCT
ejpam-6810	331	36	)	)	PUNCT
ejpam-6810	332	1	+	+	CCONJ
ejpam-6810	332	2	σb(υ(ξ),υ(ζ	σb(υ(ξ),υ(ζ	NOUN
ejpam-6810	332	3	)	)	PUNCT
ejpam-6810	332	4	)	)	PUNCT
ejpam-6810	333	1	+	+	PUNCT
ejpam-6810	333	2	σb(υ(η),υ(ζ	σb(υ(η),υ(ζ	NOUN
ejpam-6810	333	3	)	)	PUNCT
ejpam-6810	333	4	)	)	PUNCT
ejpam-6810	333	5	≤	≤	NUM
ejpam-6810	333	6	e−τ	e−τ	NOUN
ejpam-6810	333	7	s2	s2	NOUN
ejpam-6810	333	8	(	(	PUNCT
ejpam-6810	333	9	σb(η	σb(η	PROPN
ejpam-6810	333	10	,	,	PUNCT
ejpam-6810	333	11	ξ	ξ	NOUN
ejpam-6810	333	12	)	)	PUNCT
ejpam-6810	333	13	+	+	CCONJ
ejpam-6810	333	14	σb(ξ	σb(ξ	ADJ
ejpam-6810	333	15	,	,	PUNCT
ejpam-6810	333	16	ζ	ζ	NOUN
ejpam-6810	333	17	)	)	PUNCT
ejpam-6810	333	18	+	+	NUM
ejpam-6810	333	19	σb(η	σb(η	NUM
ejpam-6810	333	20	,	,	PUNCT
ejpam-6810	333	21	ζ	ζ	NOUN
ejpam-6810	333	22	)	)	PUNCT
ejpam-6810	333	23	)	)	PUNCT
ejpam-6810	333	24	,	,	PUNCT
ejpam-6810	333	25	with	with	ADP
ejpam-6810	333	26	α	α	NOUN
ejpam-6810	333	27	=	=	SYM
ejpam-6810	333	28	e−τ	e−τ	NOUN
ejpam-6810	333	29	.	.	PUNCT
ejpam-6810	334	1	hence	hence	ADV
ejpam-6810	334	2	,	,	PUNCT
ejpam-6810	334	3	υ	υ	PROPN
ejpam-6810	334	4	is	be	AUX
ejpam-6810	334	5	a	a	DET
ejpam-6810	334	6	mcpt	mcpt	NOUN
ejpam-6810	334	7	embedded	embed	VERB
ejpam-6810	334	8	with	with	ADP
ejpam-6810	334	9	an	an	DET
ejpam-6810	334	10	f	f	NOUN
ejpam-6810	334	11	-	-	PUNCT
ejpam-6810	334	12	contraction	contraction	NOUN
ejpam-6810	334	13	on	on	ADP
ejpam-6810	334	14	u	u	PROPN
ejpam-6810	334	15	.	.	PUNCT
ejpam-6810	335	1	by	by	ADP
ejpam-6810	335	2	theorem	theorem	NOUN
ejpam-6810	335	3	1	1	NUM
ejpam-6810	335	4	,	,	PUNCT
ejpam-6810	335	5	a	a	DET
ejpam-6810	335	6	fp	fp	PROPN
ejpam-6810	335	7	exists	exist	VERB
ejpam-6810	335	8	for	for	ADP
ejpam-6810	335	9	the	the	DET
ejpam-6810	335	10	mapping	mapping	NOUN
ejpam-6810	335	11	υ	υ	NOUN
ejpam-6810	335	12	.	.	PUNCT
ejpam-6810	335	13	for	for	ADP
ejpam-6810	335	14	the	the	DET
ejpam-6810	335	15	uniqueness	uniqueness	NOUN
ejpam-6810	335	16	,	,	PUNCT
ejpam-6810	335	17	suppose	suppose	VERB
ejpam-6810	335	18	that	that	SCONJ
ejpam-6810	335	19	υ	υ	PROPN
ejpam-6810	335	20	has	have	VERB
ejpam-6810	335	21	two	two	NUM
ejpam-6810	335	22	fps	fps	PROPN
ejpam-6810	335	23	η	η	PROPN
ejpam-6810	335	24	and	and	CCONJ
ejpam-6810	335	25	η∗	η∗	PROPN
ejpam-6810	335	26	,	,	PUNCT
ejpam-6810	335	27	i.e	i.e	PROPN
ejpam-6810	335	28	,	,	PUNCT
ejpam-6810	335	29	υη	υη	PROPN
ejpam-6810	335	30	=	=	PROPN
ejpam-6810	335	31	η	η	PROPN
ejpam-6810	335	32	and	and	CCONJ
ejpam-6810	335	33	υη∗	υη∗	NOUN
ejpam-6810	335	34	=	=	NOUN
ejpam-6810	335	35	η∗.	η∗.	NOUN
ejpam-6810	335	36	now	now	ADV
ejpam-6810	335	37	,	,	PUNCT
ejpam-6810	335	38	by	by	ADP
ejpam-6810	335	39	the	the	DET
ejpam-6810	335	40	definition	definition	NOUN
ejpam-6810	335	41	of	of	ADP
ejpam-6810	335	42	a	a	DET
ejpam-6810	335	43	b	b	NOUN
ejpam-6810	335	44	-	-	ADJ
ejpam-6810	335	45	metric	metric	ADJ
ejpam-6810	335	46	and	and	CCONJ
ejpam-6810	335	47	the	the	DET
ejpam-6810	335	48	given	give	VERB
ejpam-6810	335	49	assumption	assumption	NOUN
ejpam-6810	335	50	,	,	PUNCT
ejpam-6810	335	51	one	one	NUM
ejpam-6810	335	52	writes	write	VERB
ejpam-6810	335	53	0	0	NUM
ejpam-6810	335	54	<	<	X
ejpam-6810	335	55	f(σb(η	f(σb(η	PROPN
ejpam-6810	335	56	,	,	PUNCT
ejpam-6810	335	57	η	η	NOUN
ejpam-6810	335	58	∗	∗	NOUN
ejpam-6810	335	59	)	)	PUNCT
ejpam-6810	335	60	)	)	PUNCT
ejpam-6810	336	1	=	=	SYM
ejpam-6810	336	2	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	336	3	,	,	PUNCT
ejpam-6810	336	4	υη∗	υη∗	NOUN
ejpam-6810	336	5	)	)	PUNCT
ejpam-6810	336	6	)	)	PUNCT
ejpam-6810	336	7	,	,	PUNCT
ejpam-6810	336	8	<	<	X
ejpam-6810	336	9	τ	τ	PROPN
ejpam-6810	336	10	+	+	NUM
ejpam-6810	336	11	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	336	12	,	,	PUNCT
ejpam-6810	336	13	υη∗	υη∗	NOUN
ejpam-6810	336	14	)	)	PUNCT
ejpam-6810	336	15	)	)	PUNCT
ejpam-6810	336	16	,	,	PUNCT
ejpam-6810	336	17	f(σb(η	f(σb(η	PROPN
ejpam-6810	336	18	,	,	PUNCT
ejpam-6810	336	19	η	η	NOUN
ejpam-6810	336	20	∗	∗	NOUN
ejpam-6810	336	21	)	)	PUNCT
ejpam-6810	336	22	)	)	PUNCT
ejpam-6810	337	1	≤	≤	NUM
ejpam-6810	338	1	f	f	X
ejpam-6810	338	2	(	(	PUNCT
ejpam-6810	338	3	1	1	NUM
ejpam-6810	338	4	s2	s2	NOUN
ejpam-6810	338	5	σb(η	σb(η	NUM
ejpam-6810	338	6	,	,	PUNCT
ejpam-6810	338	7	η	η	NOUN
ejpam-6810	338	8	∗	∗	NOUN
ejpam-6810	338	9	)	)	PUNCT
ejpam-6810	338	10	)	)	PUNCT
ejpam-6810	338	11	,	,	PUNCT
ejpam-6810	338	12	since	since	SCONJ
ejpam-6810	338	13	f	f	PROPN
ejpam-6810	338	14	is	be	AUX
ejpam-6810	338	15	increasing	increase	VERB
ejpam-6810	338	16	,	,	PUNCT
ejpam-6810	338	17	σb(η	σb(η	NUM
ejpam-6810	338	18	,	,	PUNCT
ejpam-6810	338	19	η	η	NOUN
ejpam-6810	338	20	∗	∗	NOUN
ejpam-6810	338	21	)	)	PUNCT
ejpam-6810	338	22	≤	≤	NOUN
ejpam-6810	338	23	(	(	PUNCT
ejpam-6810	338	24	1	1	NUM
ejpam-6810	338	25	s2	s2	NOUN
ejpam-6810	338	26	σb(η	σb(η	NUM
ejpam-6810	338	27	,	,	PUNCT
ejpam-6810	338	28	η	η	NOUN
ejpam-6810	338	29	∗	∗	NOUN
ejpam-6810	338	30	)	)	PUNCT
ejpam-6810	338	31	)	)	PUNCT
ejpam-6810	338	32	,	,	PUNCT
ejpam-6810	338	33	where	where	SCONJ
ejpam-6810	338	34	s	s	VERB
ejpam-6810	338	35	≥	≥	NOUN
ejpam-6810	338	36	1	1	NUM
ejpam-6810	338	37	,	,	PUNCT
ejpam-6810	338	38	which	which	PRON
ejpam-6810	338	39	is	be	AUX
ejpam-6810	338	40	only	only	ADV
ejpam-6810	338	41	possible	possible	ADJ
ejpam-6810	338	42	when	when	SCONJ
ejpam-6810	338	43	σb(η	σb(η	NUM
ejpam-6810	338	44	,	,	PUNCT
ejpam-6810	338	45	η	η	NOUN
ejpam-6810	338	46	∗	∗	NOUN
ejpam-6810	338	47	)	)	PUNCT
ejpam-6810	338	48	=	=	SYM
ejpam-6810	338	49	0	0	X
ejpam-6810	338	50	.	.	PUNCT
ejpam-6810	339	1	thus	thus	ADV
ejpam-6810	339	2	,	,	PUNCT
ejpam-6810	339	3	η	η	PROPN
ejpam-6810	339	4	=	=	NOUN
ejpam-6810	339	5	η∗.	η∗.	NOUN
ejpam-6810	339	6	hence	hence	ADV
ejpam-6810	339	7	,	,	PUNCT
ejpam-6810	339	8	υ	υ	PROPN
ejpam-6810	339	9	has	have	AUX
ejpam-6810	339	10	a	a	DET
ejpam-6810	339	11	unique	unique	ADJ
ejpam-6810	339	12	fp	fp	NOUN
ejpam-6810	339	13	.	.	PUNCT
ejpam-6810	339	14	proposition	proposition	NOUN
ejpam-6810	339	15	2	2	NUM
ejpam-6810	339	16	.	.	PUNCT
ejpam-6810	339	17	consider	consider	VERB
ejpam-6810	339	18	a	a	DET
ejpam-6810	339	19	b	b	NOUN
ejpam-6810	339	20	-	-	PUNCT
ejpam-6810	339	21	ms	ms	ADJ
ejpam-6810	339	22	(	(	PUNCT
ejpam-6810	339	23	u	u	NOUN
ejpam-6810	339	24	,	,	PUNCT
ejpam-6810	339	25	σb	σb	ADP
ejpam-6810	339	26	)	)	PUNCT
ejpam-6810	339	27	with	with	ADP
ejpam-6810	339	28	at	at	ADV
ejpam-6810	339	29	least	least	ADV
ejpam-6810	339	30	three	three	NUM
ejpam-6810	339	31	elements	element	NOUN
ejpam-6810	339	32	,	,	PUNCT
ejpam-6810	339	33	i.e	i.e	PROPN
ejpam-6810	339	34	,	,	PUNCT
ejpam-6810	339	35	|u|	|u|	PROPN
ejpam-6810	339	36	≥3	≥3	PROPN
ejpam-6810	339	37	,	,	PUNCT
ejpam-6810	339	38	and	and	CCONJ
ejpam-6810	339	39	υ	υ	NOUN
ejpam-6810	339	40	:	:	PUNCT
ejpam-6810	339	41	u	u	PROPN
ejpam-6810	339	42	→	→	SYM
ejpam-6810	339	43	u	u	PROPN
ejpam-6810	339	44	is	be	AUX
ejpam-6810	339	45	a	a	DET
ejpam-6810	339	46	mcpt	mcpt	NOUN
ejpam-6810	339	47	embedded	embed	VERB
ejpam-6810	339	48	with	with	ADP
ejpam-6810	339	49	an	an	DET
ejpam-6810	339	50	f	f	NOUN
ejpam-6810	339	51	-	-	PUNCT
ejpam-6810	339	52	contraction	contraction	NOUN
ejpam-6810	339	53	.	.	PUNCT
ejpam-6810	340	1	then	then	ADV
ejpam-6810	340	2	,	,	PUNCT
ejpam-6810	340	3	for	for	ADP
ejpam-6810	340	4	all	all	DET
ejpam-6810	340	5	points	point	NOUN
ejpam-6810	340	6	ξ	ξ	X
ejpam-6810	340	7	∈	∈	PROPN
ejpam-6810	340	8	u	u	NOUN
ejpam-6810	340	9	,	,	PUNCT
ejpam-6810	340	10	υ	υ	PROPN
ejpam-6810	340	11	is	be	AUX
ejpam-6810	340	12	an	an	DET
ejpam-6810	340	13	f	f	NOUN
ejpam-6810	340	14	-	-	PUNCT
ejpam-6810	340	15	contraction	contraction	NOUN
ejpam-6810	340	16	mapping	mapping	NOUN
ejpam-6810	340	17	if	if	SCONJ
ejpam-6810	340	18	η	η	PROPN
ejpam-6810	340	19	is	be	AUX
ejpam-6810	340	20	a	a	DET
ejpam-6810	340	21	limit	limit	NOUN
ejpam-6810	340	22	point	point	NOUN
ejpam-6810	340	23	of	of	ADP
ejpam-6810	340	24	u	u	NOUN
ejpam-6810	340	25	.	.	PUNCT
ejpam-6810	341	1	proof	proof	NOUN
ejpam-6810	341	2	.	.	PUNCT
ejpam-6810	342	1	consider	consider	VERB
ejpam-6810	342	2	an	an	DET
ejpam-6810	342	3	accumulation	accumulation	NOUN
ejpam-6810	342	4	point	point	NOUN
ejpam-6810	342	5	η	η	PROPN
ejpam-6810	342	6	∈	∈	PROPN
ejpam-6810	342	7	u	u	NOUN
ejpam-6810	342	8	and	and	CCONJ
ejpam-6810	342	9	any	any	DET
ejpam-6810	342	10	point	point	NOUN
ejpam-6810	342	11	ξ	ξ	X
ejpam-6810	342	12	∈	∈	PROPN
ejpam-6810	342	13	u	u	NOUN
ejpam-6810	342	14	.	.	PUNCT
ejpam-6810	343	1	if	if	SCONJ
ejpam-6810	343	2	ξ	ξ	PROPN
ejpam-6810	343	3	=	=	SYM
ejpam-6810	343	4	η	η	PROPN
ejpam-6810	343	5	,	,	PUNCT
ejpam-6810	343	6	then	then	ADV
ejpam-6810	343	7	(	(	PUNCT
ejpam-6810	343	8	16	16	NUM
ejpam-6810	343	9	)	)	PUNCT
ejpam-6810	343	10	is	be	AUX
ejpam-6810	343	11	obviously	obviously	ADV
ejpam-6810	343	12	satisfied	satisfied	ADJ
ejpam-6810	343	13	.	.	PUNCT
ejpam-6810	344	1	now	now	ADV
ejpam-6810	344	2	,	,	PUNCT
ejpam-6810	344	3	consider	consider	VERB
ejpam-6810	344	4	the	the	DET
ejpam-6810	344	5	case	case	NOUN
ejpam-6810	344	6	where	where	SCONJ
ejpam-6810	344	7	ξ	ξ	PROPN
ejpam-6810	344	8	6=	6=	PROPN
ejpam-6810	344	9	η	η	PROPN
ejpam-6810	344	10	.	.	PROPN
ejpam-6810	344	11	as	as	SCONJ
ejpam-6810	344	12	η	η	PROPN
ejpam-6810	344	13	is	be	AUX
ejpam-6810	344	14	a	a	DET
ejpam-6810	344	15	limit	limit	NOUN
ejpam-6810	344	16	point	point	NOUN
ejpam-6810	344	17	,	,	PUNCT
ejpam-6810	344	18	which	which	PRON
ejpam-6810	344	19	implies	imply	VERB
ejpam-6810	344	20	the	the	DET
ejpam-6810	344	21	existence	existence	NOUN
ejpam-6810	344	22	of	of	ADP
ejpam-6810	344	23	a	a	DET
ejpam-6810	344	24	sequence	sequence	NOUN
ejpam-6810	344	25	{	{	PUNCT
ejpam-6810	344	26	ζn	ζn	NOUN
ejpam-6810	344	27	}	}	PUNCT
ejpam-6810	344	28	converging	converge	VERB
ejpam-6810	344	29	to	to	ADP
ejpam-6810	344	30	η	η	PROPN
ejpam-6810	344	31	,	,	PUNCT
ejpam-6810	344	32	satisfying	satisfy	VERB
ejpam-6810	344	33	ζn	ζn	ADP
ejpam-6810	344	34	6=	6=	PROPN
ejpam-6810	344	35	x	x	PROPN
ejpam-6810	344	36	,	,	PUNCT
ejpam-6810	344	37	ζn	ζn	PROPN
ejpam-6810	344	38	6=	6=	SYM
ejpam-6810	344	39	ξ	ξ	NOUN
ejpam-6810	344	40	with	with	ADP
ejpam-6810	344	41	all	all	DET
ejpam-6810	344	42	distinct	distinct	ADJ
ejpam-6810	344	43	elements	element	NOUN
ejpam-6810	344	44	ζn	ζn	PRON
ejpam-6810	344	45	.	.	PUNCT
ejpam-6810	345	1	consequently	consequently	ADV
ejpam-6810	345	2	,	,	PUNCT
ejpam-6810	345	3	applying	apply	VERB
ejpam-6810	345	4	(	(	PUNCT
ejpam-6810	345	5	3	3	NUM
ejpam-6810	345	6	)	)	PUNCT
ejpam-6810	345	7	establishes	establish	VERB
ejpam-6810	345	8	the	the	DET
ejpam-6810	345	9	following	follow	VERB
ejpam-6810	345	10	τ	τ	PROPN
ejpam-6810	345	11	+	+	NUM
ejpam-6810	345	12	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	345	13	,	,	PUNCT
ejpam-6810	345	14	υξ	υξ	X
ejpam-6810	345	15	)	)	PUNCT
ejpam-6810	346	1	+	+	CCONJ
ejpam-6810	346	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	346	3	,	,	PUNCT
ejpam-6810	346	4	υζn	υζn	PROPN
ejpam-6810	346	5	)	)	PUNCT
ejpam-6810	347	1	+	+	CCONJ
ejpam-6810	347	2	σb(υη	σb(υη	PROPN
ejpam-6810	347	3	,	,	PUNCT
ejpam-6810	347	4	υζn	υζn	PROPN
ejpam-6810	347	5	)	)	PUNCT
ejpam-6810	347	6	)	)	PUNCT
ejpam-6810	348	1	≤	≤	NUM
ejpam-6810	349	1	f	f	X
ejpam-6810	349	2	(	(	PUNCT
ejpam-6810	349	3	1	1	NUM
ejpam-6810	349	4	s2	s2	NOUN
ejpam-6810	349	5	(	(	PUNCT
ejpam-6810	349	6	σb(η	σb(η	PROPN
ejpam-6810	349	7	,	,	PUNCT
ejpam-6810	349	8	ξ	ξ	NOUN
ejpam-6810	349	9	)	)	PUNCT
ejpam-6810	349	10	+	+	CCONJ
ejpam-6810	349	11	σb(ξ	σb(ξ	NOUN
ejpam-6810	349	12	,	,	PUNCT
ejpam-6810	349	13	ζn	ζn	NOUN
ejpam-6810	349	14	)	)	PUNCT
ejpam-6810	349	15	+	+	CCONJ
ejpam-6810	349	16	σb(η	σb(η	NUM
ejpam-6810	349	17	,	,	PUNCT
ejpam-6810	349	18	ζn	ζn	NOUN
ejpam-6810	349	19	)	)	PUNCT
ejpam-6810	349	20	)	)	PUNCT
ejpam-6810	349	21	)	)	PUNCT
ejpam-6810	349	22	,	,	PUNCT
ejpam-6810	349	23	(	(	PUNCT
ejpam-6810	349	24	20	20	NUM
ejpam-6810	349	25	)	)	PUNCT
ejpam-6810	349	26	which	which	PRON
ejpam-6810	349	27	is	be	AUX
ejpam-6810	349	28	satisfied	satisfied	ADJ
ejpam-6810	349	29	for	for	ADP
ejpam-6810	349	30	all	all	PRON
ejpam-6810	349	31	n	n	DET
ejpam-6810	349	32	∈	∈	PROPN
ejpam-6810	349	33	n.	n.	NOUN
ejpam-6810	349	34	as	as	ADP
ejpam-6810	349	35	σb(η	σb(η	PROPN
ejpam-6810	349	36	,	,	PUNCT
ejpam-6810	349	37	ζn	ζn	NOUN
ejpam-6810	349	38	)	)	PUNCT
ejpam-6810	349	39	−→	−→	NOUN
ejpam-6810	349	40	0	0	NUM
ejpam-6810	349	41	,	,	PUNCT
ejpam-6810	349	42	ζn	ζn	ADV
ejpam-6810	349	43	−→	−→	NOUN
ejpam-6810	349	44	x	x	X
ejpam-6810	349	45	and	and	CCONJ
ejpam-6810	349	46	the	the	DET
ejpam-6810	349	47	continuity	continuity	NOUN
ejpam-6810	349	48	of	of	ADP
ejpam-6810	349	49	b	b	NOUN
ejpam-6810	349	50	-	-	PUNCT
ejpam-6810	349	51	ms	ms	PROPN
ejpam-6810	349	52	implies	imply	VERB
ejpam-6810	349	53	σb(ξ	σb(ξ	PROPN
ejpam-6810	349	54	,	,	PUNCT
ejpam-6810	349	55	ζn	ζn	NOUN
ejpam-6810	349	56	)	)	PUNCT
ejpam-6810	349	57	→	→	SYM
ejpam-6810	349	58	σb(η	σb(η	PROPN
ejpam-6810	349	59	,	,	PUNCT
ejpam-6810	349	60	ξ	ξ	NOUN
ejpam-6810	349	61	)	)	PUNCT
ejpam-6810	349	62	.	.	PUNCT
ejpam-6810	350	1	by	by	ADP
ejpam-6810	350	2	continuity	continuity	NOUN
ejpam-6810	350	3	of	of	ADP
ejpam-6810	350	4	υ	υ	PROPN
ejpam-6810	350	5	,	,	PUNCT
ejpam-6810	350	6	σb(υη	σb(υη	PROPN
ejpam-6810	350	7	,	,	PUNCT
ejpam-6810	350	8	υζn	υζn	PROPN
ejpam-6810	350	9	)	)	PUNCT
ejpam-6810	350	10	→	→	SYM
ejpam-6810	350	11	σb(υη	σb(υη	PROPN
ejpam-6810	350	12	,	,	PUNCT
ejpam-6810	350	13	υη	υη	PROPN
ejpam-6810	350	14	)	)	PUNCT
ejpam-6810	350	15	=	=	SYM
ejpam-6810	350	16	0	0	NUM
ejpam-6810	350	17	and	and	CCONJ
ejpam-6810	350	18	σb(υξ	σb(υξ	PROPN
ejpam-6810	350	19	,	,	PUNCT
ejpam-6810	350	20	υζn	υζn	PROPN
ejpam-6810	350	21	)	)	PUNCT
ejpam-6810	350	22	→	→	SYM
ejpam-6810	350	23	σb(υη	σb(υη	PROPN
ejpam-6810	350	24	,	,	PUNCT
ejpam-6810	350	25	υξ	υξ	NOUN
ejpam-6810	350	26	)	)	PUNCT
ejpam-6810	350	27	.	.	PUNCT
ejpam-6810	351	1	taking	take	VERB
ejpam-6810	351	2	limit	limit	NOUN
ejpam-6810	351	3	n	n	NOUN
ejpam-6810	351	4	→	→	SYM
ejpam-6810	351	5	+	+	NOUN
ejpam-6810	351	6	∞	∞	PROPN
ejpam-6810	351	7	in	in	ADP
ejpam-6810	351	8	(	(	PUNCT
ejpam-6810	351	9	20	20	NUM
ejpam-6810	351	10	)	)	PUNCT
ejpam-6810	351	11	gives	give	VERB
ejpam-6810	351	12	τ	τ	PROPN
ejpam-6810	351	13	+	+	NUM
ejpam-6810	351	14	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	351	15	,	,	PUNCT
ejpam-6810	351	16	υξ	υξ	X
ejpam-6810	351	17	)	)	PUNCT
ejpam-6810	352	1	+	+	CCONJ
ejpam-6810	352	2	σb(υη	σb(υη	PROPN
ejpam-6810	352	3	,	,	PUNCT
ejpam-6810	352	4	υξ	υξ	NOUN
ejpam-6810	352	5	)	)	PUNCT
ejpam-6810	352	6	)	)	PUNCT
ejpam-6810	352	7	≤	≤	NUM
ejpam-6810	353	1	f	f	X
ejpam-6810	353	2	(	(	PUNCT
ejpam-6810	353	3	1	1	NUM
ejpam-6810	353	4	s2	s2	NOUN
ejpam-6810	353	5	(	(	PUNCT
ejpam-6810	353	6	σb(η	σb(η	PROPN
ejpam-6810	353	7	,	,	PUNCT
ejpam-6810	353	8	ξ	ξ	NOUN
ejpam-6810	353	9	)	)	PUNCT
ejpam-6810	353	10	+	+	NUM
ejpam-6810	353	11	σb(η	σb(η	PROPN
ejpam-6810	353	12	,	,	PUNCT
ejpam-6810	353	13	ξ	ξ	NOUN
ejpam-6810	353	14	)	)	PUNCT
ejpam-6810	353	15	)	)	PUNCT
ejpam-6810	353	16	)	)	PUNCT
ejpam-6810	353	17	,	,	PUNCT
ejpam-6810	353	18	τ	τ	PROPN
ejpam-6810	353	19	+	+	NUM
ejpam-6810	353	20	f(2σb(υη	f(2σb(υη	PROPN
ejpam-6810	353	21	,	,	PUNCT
ejpam-6810	353	22	υξ	υξ	NOUN
ejpam-6810	353	23	)	)	PUNCT
ejpam-6810	353	24	)	)	PUNCT
ejpam-6810	353	25	≤	≤	NUM
ejpam-6810	354	1	f	f	X
ejpam-6810	354	2	(	(	PUNCT
ejpam-6810	354	3	2	2	NUM
ejpam-6810	354	4	s2	s2	NOUN
ejpam-6810	354	5	σb(η	σb(η	NUM
ejpam-6810	354	6	,	,	PUNCT
ejpam-6810	354	7	ξ	ξ	NOUN
ejpam-6810	354	8	)	)	PUNCT
ejpam-6810	354	9	)	)	PUNCT
ejpam-6810	354	10	,	,	PUNCT
ejpam-6810	354	11	τ	τ	PROPN
ejpam-6810	354	12	+	+	NUM
ejpam-6810	354	13	f(σb(υη	f(σb(υη	PROPN
ejpam-6810	354	14	,	,	PUNCT
ejpam-6810	354	15	υξ	υξ	NOUN
ejpam-6810	354	16	)	)	PUNCT
ejpam-6810	354	17	)	)	PUNCT
ejpam-6810	354	18	≤	≤	NUM
ejpam-6810	355	1	f	f	X
ejpam-6810	355	2	(	(	PUNCT
ejpam-6810	355	3	1	1	NUM
ejpam-6810	355	4	s2	s2	NOUN
ejpam-6810	355	5	σb(η	σb(η	NUM
ejpam-6810	355	6	,	,	PUNCT
ejpam-6810	355	7	ξ	ξ	NOUN
ejpam-6810	355	8	)	)	PUNCT
ejpam-6810	355	9	)	)	PUNCT
ejpam-6810	355	10	.	.	PUNCT
ejpam-6810	356	1	hence	hence	ADV
ejpam-6810	356	2	,	,	PUNCT
ejpam-6810	356	3	if	if	SCONJ
ejpam-6810	356	4	η	η	PROPN
ejpam-6810	356	5	is	be	AUX
ejpam-6810	356	6	a	a	DET
ejpam-6810	356	7	limit	limit	NOUN
ejpam-6810	356	8	point	point	NOUN
ejpam-6810	356	9	of	of	ADP
ejpam-6810	356	10	u	u	PROPN
ejpam-6810	356	11	,	,	PUNCT
ejpam-6810	356	12	then	then	ADV
ejpam-6810	356	13	υ	υ	PROPN
ejpam-6810	356	14	is	be	AUX
ejpam-6810	356	15	an	an	DET
ejpam-6810	356	16	f	f	NOUN
ejpam-6810	356	17	-	-	PUNCT
ejpam-6810	356	18	contraction	contraction	NOUN
ejpam-6810	356	19	.	.	PUNCT
ejpam-6810	357	1	s.	s.	PROPN
ejpam-6810	357	2	batul	batul	PROPN
ejpam-6810	357	3	et	et	PROPN
ejpam-6810	357	4	al	al	PROPN
ejpam-6810	357	5	.	.	PUNCT
ejpam-6810	357	6	/	/	SYM
ejpam-6810	357	7	eur	eur	PROPN
ejpam-6810	357	8	.	.	PUNCT
ejpam-6810	358	1	j.	j.	PROPN
ejpam-6810	358	2	pure	pure	PROPN
ejpam-6810	358	3	appl	appl	PROPN
ejpam-6810	358	4	.	.	PROPN
ejpam-6810	358	5	math	math	PROPN
ejpam-6810	358	6	,	,	PUNCT
ejpam-6810	358	7	18	18	NUM
ejpam-6810	358	8	(	(	PUNCT
ejpam-6810	358	9	4	4	NUM
ejpam-6810	358	10	)	)	PUNCT
ejpam-6810	358	11	(	(	PUNCT
ejpam-6810	358	12	2025	2025	NUM
ejpam-6810	358	13	)	)	PUNCT
ejpam-6810	358	14	,	,	PUNCT
ejpam-6810	358	15	6810	6810	NUM
ejpam-6810	358	16	15	15	NUM
ejpam-6810	358	17	of	of	ADP
ejpam-6810	358	18	23	23	NUM
ejpam-6810	358	19	corollary	corollary	ADJ
ejpam-6810	358	20	2	2	NUM
ejpam-6810	358	21	.	.	PUNCT
ejpam-6810	358	22	consider	consider	VERB
ejpam-6810	358	23	υ	υ	NOUN
ejpam-6810	358	24	:	:	PUNCT
ejpam-6810	358	25	u	u	VERB
ejpam-6810	358	26	−→	−→	NOUN
ejpam-6810	358	27	u	u	NOUN
ejpam-6810	358	28	is	be	AUX
ejpam-6810	358	29	a	a	DET
ejpam-6810	358	30	mcpt	mcpt	NOUN
ejpam-6810	358	31	embedded	embed	VERB
ejpam-6810	358	32	with	with	ADP
ejpam-6810	358	33	an	an	DET
ejpam-6810	358	34	f	f	NOUN
ejpam-6810	358	35	-	-	PUNCT
ejpam-6810	358	36	contraction	contraction	NOUN
ejpam-6810	358	37	,	,	PUNCT
ejpam-6810	358	38	and	and	CCONJ
ejpam-6810	358	39	(	(	PUNCT
ejpam-6810	358	40	u	u	NOUN
ejpam-6810	358	41	,	,	PUNCT
ejpam-6810	358	42	σb	σb	PROPN
ejpam-6810	358	43	)	)	PUNCT
ejpam-6810	358	44	is	be	AUX
ejpam-6810	358	45	a	a	DET
ejpam-6810	358	46	b	b	NOUN
ejpam-6810	358	47	-	-	PUNCT
ejpam-6810	358	48	ms	ms	NOUN
ejpam-6810	358	49	with	with	ADP
ejpam-6810	358	50	at	at	ADV
ejpam-6810	358	51	least	least	ADV
ejpam-6810	358	52	three	three	NUM
ejpam-6810	358	53	points	point	NOUN
ejpam-6810	358	54	,	,	PUNCT
ejpam-6810	358	55	i.e	i.e	X
ejpam-6810	358	56	,	,	PUNCT
ejpam-6810	358	57	|u	|u	ADJ
ejpam-6810	358	58	|	|	ADP
ejpam-6810	358	59	≥3	≥3	PROPN
ejpam-6810	358	60	.	.	PUNCT
ejpam-6810	359	1	then	then	ADV
ejpam-6810	359	2	υ	υ	PROPN
ejpam-6810	359	3	is	be	AUX
ejpam-6810	359	4	an	an	DET
ejpam-6810	359	5	f	f	NOUN
ejpam-6810	359	6	-	-	PUNCT
ejpam-6810	359	7	contracting	contract	VERB
ejpam-6810	359	8	mapping	mapping	NOUN
ejpam-6810	359	9	whenever	whenever	SCONJ
ejpam-6810	359	10	every	every	DET
ejpam-6810	359	11	element	element	NOUN
ejpam-6810	359	12	of	of	ADP
ejpam-6810	359	13	u	u	NOUN
ejpam-6810	359	14	is	be	AUX
ejpam-6810	359	15	an	an	DET
ejpam-6810	359	16	accumulation	accumulation	NOUN
ejpam-6810	359	17	point	point	NOUN
ejpam-6810	359	18	of	of	ADP
ejpam-6810	359	19	u	u	PROPN
ejpam-6810	359	20	.	.	PUNCT
ejpam-6810	360	1	in	in	ADP
ejpam-6810	360	2	a	a	DET
ejpam-6810	360	3	ms	ms	NOUN
ejpam-6810	360	4	(	(	PUNCT
ejpam-6810	360	5	u	u	NOUN
ejpam-6810	360	6	,	,	PUNCT
ejpam-6810	360	7	σb	σb	ADP
ejpam-6810	360	8	)	)	PUNCT
ejpam-6810	360	9	,	,	PUNCT
ejpam-6810	360	10	ξ	ξ	PROPN
ejpam-6810	360	11	is	be	AUX
ejpam-6810	360	12	an	an	DET
ejpam-6810	360	13	intermediate	intermediate	ADJ
ejpam-6810	360	14	point	point	NOUN
ejpam-6810	360	15	for	for	ADP
ejpam-6810	360	16	η	η	PROPN
ejpam-6810	360	17	and	and	CCONJ
ejpam-6810	360	18	ζ	ζ	NOUN
ejpam-6810	360	19	,	,	PUNCT
ejpam-6810	360	20	whenever	whenever	SCONJ
ejpam-6810	360	21	σb(η	σb(η	NUM
ejpam-6810	360	22	,	,	PUNCT
ejpam-6810	360	23	ζ	ζ	NOUN
ejpam-6810	360	24	)	)	PUNCT
ejpam-6810	360	25	=	=	SYM
ejpam-6810	360	26	σb(η	σb(η	PROPN
ejpam-6810	360	27	,	,	PUNCT
ejpam-6810	360	28	ξ	ξ	NOUN
ejpam-6810	360	29	)	)	PUNCT
ejpam-6810	361	1	+	+	CCONJ
ejpam-6810	361	2	σb(ξ	σb(ξ	ADJ
ejpam-6810	361	3	,	,	PUNCT
ejpam-6810	361	4	ζ	ζ	NOUN
ejpam-6810	361	5	)	)	PUNCT
ejpam-6810	361	6	where	where	SCONJ
ejpam-6810	361	7	η	η	PROPN
ejpam-6810	361	8	,	,	PUNCT
ejpam-6810	361	9	ξ	ξ	PROPN
ejpam-6810	361	10	,	,	PUNCT
ejpam-6810	361	11	ζ	ζ	PROPN
ejpam-6810	361	12	∈	∈	PROPN
ejpam-6810	361	13	u	u	NOUN
ejpam-6810	361	14	.	.	PUNCT
ejpam-6810	362	1	(	(	PUNCT
ejpam-6810	362	2	21	21	NUM
ejpam-6810	362	3	)	)	PUNCT
ejpam-6810	362	4	let	let	VERB
ejpam-6810	362	5	us	we	PRON
ejpam-6810	362	6	develop	develop	VERB
ejpam-6810	362	7	an	an	DET
ejpam-6810	362	8	example	example	NOUN
ejpam-6810	362	9	demonstrating	demonstrate	VERB
ejpam-6810	362	10	the	the	DET
ejpam-6810	362	11	distinction	distinction	NOUN
ejpam-6810	362	12	between	between	ADP
ejpam-6810	362	13	a	a	DET
ejpam-6810	362	14	mcpt	mcpt	NOUN
ejpam-6810	362	15	embedded	embed	VERB
ejpam-6810	362	16	with	with	ADP
ejpam-6810	362	17	an	an	DET
ejpam-6810	362	18	f	f	NOUN
ejpam-6810	362	19	-	-	PUNCT
ejpam-6810	362	20	contraction	contraction	NOUN
ejpam-6810	362	21	and	and	CCONJ
ejpam-6810	362	22	an	an	DET
ejpam-6810	362	23	f	f	NOUN
ejpam-6810	362	24	-	-	PUNCT
ejpam-6810	362	25	contraction	contraction	NOUN
ejpam-6810	362	26	in	in	ADP
ejpam-6810	362	27	the	the	DET
ejpam-6810	362	28	framework	framework	NOUN
ejpam-6810	362	29	of	of	ADP
ejpam-6810	362	30	a	a	DET
ejpam-6810	362	31	b	b	PROPN
ejpam-6810	362	32	-	-	PUNCT
ejpam-6810	362	33	ms	ms	PROPN
ejpam-6810	362	34	.	.	PROPN
ejpam-6810	362	35	example	example	NOUN
ejpam-6810	363	1	5	5	NUM
ejpam-6810	363	2	.	.	PUNCT
ejpam-6810	363	3	suppose	suppose	VERB
ejpam-6810	363	4	u	u	NOUN
ejpam-6810	363	5	has	have	VERB
ejpam-6810	363	6	countably	countably	ADV
ejpam-6810	363	7	infinite	infinite	ADJ
ejpam-6810	363	8	elements	element	NOUN
ejpam-6810	363	9	,	,	PUNCT
ejpam-6810	363	10	|u|	|u|	PROPN
ejpam-6810	363	11	=	=	SYM
ejpam-6810	363	12	ℵ0	ℵ0	PROPN
ejpam-6810	363	13	,	,	PUNCT
ejpam-6810	363	14	specifically	specifically	ADV
ejpam-6810	363	15	u	u	NOUN
ejpam-6810	363	16	=	=	NOUN
ejpam-6810	363	17	{	{	PUNCT
ejpam-6810	363	18	η∗	η∗	PROPN
ejpam-6810	363	19	,	,	PUNCT
ejpam-6810	363	20	η0	η0	NOUN
ejpam-6810	363	21	,	,	PUNCT
ejpam-6810	363	22	η1	η1	NOUN
ejpam-6810	363	23	,	,	PUNCT
ejpam-6810	363	24	.	.	PUNCT
ejpam-6810	363	25	.	.	PUNCT
ejpam-6810	363	26	.	.	PUNCT
ejpam-6810	363	27	}	}	PUNCT
ejpam-6810	363	28	.	.	PUNCT
ejpam-6810	364	1	consider	consider	VERB
ejpam-6810	364	2	a	a	DET
ejpam-6810	364	3	mapping	mapping	NOUN
ejpam-6810	364	4	υ	υ	NOUN
ejpam-6810	364	5	:	:	PUNCT
ejpam-6810	364	6	u	u	NOUN
ejpam-6810	364	7	−→	−→	NOUN
ejpam-6810	364	8	u	u	NOUN
ejpam-6810	364	9	,	,	PUNCT
ejpam-6810	364	10	that	that	ADV
ejpam-6810	364	11	is	is	ADV
ejpam-6810	364	12	,	,	PUNCT
ejpam-6810	364	13	a	a	DET
ejpam-6810	364	14	mcpt	mcpt	NOUN
ejpam-6810	364	15	embedded	embed	VERB
ejpam-6810	364	16	with	with	ADP
ejpam-6810	364	17	an	an	DET
ejpam-6810	364	18	f	f	NOUN
ejpam-6810	364	19	-	-	PUNCT
ejpam-6810	364	20	contraction	contraction	NOUN
ejpam-6810	364	21	,	,	PUNCT
ejpam-6810	364	22	but	but	CCONJ
ejpam-6810	364	23	exhibits	exhibit	VERB
ejpam-6810	364	24	non	non	ADJ
ejpam-6810	364	25	-	-	ADJ
ejpam-6810	364	26	contracting	contracting	ADJ
ejpam-6810	364	27	behavior	behavior	NOUN
ejpam-6810	364	28	in	in	ADP
ejpam-6810	364	29	a	a	DET
ejpam-6810	364	30	b	b	NOUN
ejpam-6810	364	31	-	-	PUNCT
ejpam-6810	364	32	ms	ms	PROPN
ejpam-6810	364	33	u	u	PROPN
ejpam-6810	364	34	.	.	PUNCT
ejpam-6810	365	1	figure	figure	NOUN
ejpam-6810	365	2	1	1	NUM
ejpam-6810	365	3	:	:	PUNCT
ejpam-6810	365	4	the	the	DET
ejpam-6810	365	5	points	point	NOUN
ejpam-6810	365	6	of	of	ADP
ejpam-6810	365	7	the	the	DET
ejpam-6810	365	8	space	space	NOUN
ejpam-6810	365	9	(	(	PUNCT
ejpam-6810	365	10	u	u	NOUN
ejpam-6810	365	11	,	,	PUNCT
ejpam-6810	365	12	σb	σb	ADP
ejpam-6810	365	13	)	)	PUNCT
ejpam-6810	365	14	with	with	ADP
ejpam-6810	365	15	consecutive	consecutive	ADJ
ejpam-6810	365	16	distances	distance	NOUN
ejpam-6810	365	17	between	between	ADP
ejpam-6810	365	18	them	they	PRON
ejpam-6810	365	19	let	let	VERB
ejpam-6810	365	20	a	a	PRON
ejpam-6810	365	21	be	be	AUX
ejpam-6810	365	22	a	a	DET
ejpam-6810	365	23	positive	positive	ADJ
ejpam-6810	365	24	real	real	ADJ
ejpam-6810	365	25	number	number	NOUN
ejpam-6810	365	26	.	.	PUNCT
ejpam-6810	366	1	define	define	VERB
ejpam-6810	366	2	σb	σb	ADP
ejpam-6810	366	3	on	on	ADP
ejpam-6810	366	4	u	u	PRON
ejpam-6810	366	5	×	×	PROPN
ejpam-6810	366	6	u	u	NOUN
ejpam-6810	366	7	as	as	SCONJ
ejpam-6810	366	8	follows	follow	VERB
ejpam-6810	366	9	:	:	PUNCT
ejpam-6810	366	10	σb(η	σb(η	NUM
ejpam-6810	366	11	,	,	PUNCT
ejpam-6810	366	12	ξ	ξ	X
ejpam-6810	366	13	)	)	PUNCT
ejpam-6810	366	14	=	=	SYM
ejpam-6810	367	1			NUM
ejpam-6810	367	2	a2/2bi/2c	a2/2bi/2c	NOUN
ejpam-6810	367	3	,	,	PUNCT
ejpam-6810	367	4	if	if	SCONJ
ejpam-6810	367	5	η	η	PROPN
ejpam-6810	367	6	=	=	PROPN
ejpam-6810	367	7	ηi	ηi	PROPN
ejpam-6810	367	8	,	,	PUNCT
ejpam-6810	367	9	ξ	ξ	X
ejpam-6810	367	10	=	=	SYM
ejpam-6810	367	11	ηi+1	ηi+1	PROPN
ejpam-6810	367	12	,	,	PUNCT
ejpam-6810	367	13	i	i	PRON
ejpam-6810	367	14	=	=	NOUN
ejpam-6810	367	15	1	1	NUM
ejpam-6810	367	16	,	,	PUNCT
ejpam-6810	367	17	2	2	NUM
ejpam-6810	367	18	,	,	PUNCT
ejpam-6810	367	19	3	3	NUM
ejpam-6810	367	20	,	,	PUNCT
ejpam-6810	367	21	·	·	PUNCT
ejpam-6810	367	22	·	·	PUNCT
ejpam-6810	367	23	·	·	PUNCT
ejpam-6810	367	24	.	.	PUNCT
ejpam-6810	367	25	,	,	PUNCT
ejpam-6810	367	26	σb(ηi	σb(ηi	PROPN
ejpam-6810	367	27	,	,	PUNCT
ejpam-6810	367	28	ηi+1	ηi+1	NOUN
ejpam-6810	367	29	)	)	PUNCT
ejpam-6810	367	30	+	+	CCONJ
ejpam-6810	367	31	·	·	PUNCT
ejpam-6810	367	32	·	·	PUNCT
ejpam-6810	367	33	·	·	PUNCT
ejpam-6810	368	1	+	+	NUM
ejpam-6810	368	2	σb(ηj−1	σb(ηj−1	NOUN
ejpam-6810	368	3	,	,	PUNCT
ejpam-6810	368	4	ηj	ηj	NOUN
ejpam-6810	368	5	)	)	PUNCT
ejpam-6810	368	6	,	,	PUNCT
ejpam-6810	368	7	if	if	SCONJ
ejpam-6810	368	8	η	η	PROPN
ejpam-6810	368	9	=	=	PROPN
ejpam-6810	368	10	ηi	ηi	PROPN
ejpam-6810	368	11	,	,	PUNCT
ejpam-6810	368	12	ξ	ξ	X
ejpam-6810	368	13	=	=	SYM
ejpam-6810	368	14	ηj	ηj	NOUN
ejpam-6810	368	15	,	,	PUNCT
ejpam-6810	368	16	i+	i+	X
ejpam-6810	368	17	1	1	NUM
ejpam-6810	368	18	<	<	X
ejpam-6810	368	19	j	j	PROPN
ejpam-6810	368	20	,	,	PUNCT
ejpam-6810	368	21	4a2	4a2	NUM
ejpam-6810	368	22	−	−	PROPN
ejpam-6810	368	23	σb(η0	σb(η0	NOUN
ejpam-6810	368	24	,	,	PUNCT
ejpam-6810	368	25	ηi	ηi	PROPN
ejpam-6810	368	26	)	)	PUNCT
ejpam-6810	368	27	,	,	PUNCT
ejpam-6810	368	28	if	if	SCONJ
ejpam-6810	368	29	η	η	PROPN
ejpam-6810	368	30	=	=	PROPN
ejpam-6810	368	31	ηi	ηi	PROPN
ejpam-6810	368	32	,	,	PUNCT
ejpam-6810	368	33	ξ	ξ	X
ejpam-6810	368	34	=	=	SYM
ejpam-6810	368	35	η∗	η∗	PROPN
ejpam-6810	368	36	,	,	PUNCT
ejpam-6810	368	37	0	0	NUM
ejpam-6810	368	38	,	,	PUNCT
ejpam-6810	368	39	if	if	SCONJ
ejpam-6810	368	40	η	η	PROPN
ejpam-6810	368	41	=	=	SYM
ejpam-6810	368	42	ξ	ξ	PROPN
ejpam-6810	368	43	,	,	PUNCT
ejpam-6810	368	44	where	where	SCONJ
ejpam-6810	368	45	b·c	b·c	NOUN
ejpam-6810	368	46	is	be	AUX
ejpam-6810	368	47	the	the	DET
ejpam-6810	368	48	floor	floor	NOUN
ejpam-6810	368	49	function	function	NOUN
ejpam-6810	368	50	defined	define	VERB
ejpam-6810	368	51	as	as	ADP
ejpam-6810	368	52	the	the	DET
ejpam-6810	368	53	greatest	great	ADJ
ejpam-6810	368	54	integer	integer	NOUN
ejpam-6810	368	55	less	less	ADJ
ejpam-6810	368	56	than	than	ADP
ejpam-6810	368	57	or	or	CCONJ
ejpam-6810	368	58	equal	equal	ADJ
ejpam-6810	368	59	to	to	ADP
ejpam-6810	368	60	a	a	DET
ejpam-6810	368	61	given	give	VERB
ejpam-6810	368	62	number	number	NOUN
ejpam-6810	368	63	.	.	PUNCT
ejpam-6810	369	1	clearly	clearly	ADV
ejpam-6810	369	2	,	,	PUNCT
ejpam-6810	369	3	for	for	ADP
ejpam-6810	369	4	every	every	DET
ejpam-6810	369	5	triplet	triplet	NOUN
ejpam-6810	369	6	of	of	ADP
ejpam-6810	369	7	distinct	distinct	ADJ
ejpam-6810	369	8	points	point	NOUN
ejpam-6810	369	9	in	in	ADP
ejpam-6810	369	10	u	u	NOUN
ejpam-6810	369	11	,	,	PUNCT
ejpam-6810	369	12	one	one	NUM
ejpam-6810	369	13	point	point	NOUN
ejpam-6810	369	14	is	be	AUX
ejpam-6810	369	15	situated	situate	VERB
ejpam-6810	369	16	between	between	ADP
ejpam-6810	369	17	the	the	DET
ejpam-6810	369	18	remaining	remain	VERB
ejpam-6810	369	19	two	two	NUM
ejpam-6810	369	20	,	,	PUNCT
ejpam-6810	369	21	we	we	PRON
ejpam-6810	369	22	can	can	AUX
ejpam-6810	369	23	see	see	VERB
ejpam-6810	369	24	in	in	ADP
ejpam-6810	369	25	fig.1	fig.1	PROPN
ejpam-6810	369	26	.	.	PUNCT
ejpam-6810	370	1	furthermore	furthermore	ADV
ejpam-6810	370	2	,	,	PUNCT
ejpam-6810	370	3	the	the	DET
ejpam-6810	370	4	space	space	NOUN
ejpam-6810	370	5	has	have	VERB
ejpam-6810	370	6	a	a	DET
ejpam-6810	370	7	single	single	ADJ
ejpam-6810	370	8	accumulation	accumulation	NOUN
ejpam-6810	370	9	point	point	NOUN
ejpam-6810	370	10	η∗	η∗	NOUN
ejpam-6810	370	11	,	,	PUNCT
ejpam-6810	370	12	and	and	CCONJ
ejpam-6810	370	13	so	so	ADV
ejpam-6810	370	14	it	it	PRON
ejpam-6810	370	15	is	be	AUX
ejpam-6810	370	16	complete	complete	ADJ
ejpam-6810	370	17	.	.	PUNCT
ejpam-6810	371	1	define	define	VERB
ejpam-6810	371	2	the	the	DET
ejpam-6810	371	3	mapping	mapping	NOUN
ejpam-6810	371	4	υ	υ	NOUN
ejpam-6810	371	5	:	:	PUNCT
ejpam-6810	371	6	u	u	PROPN
ejpam-6810	371	7	→	→	SYM
ejpam-6810	371	8	u	u	X
ejpam-6810	371	9	given	give	VERB
ejpam-6810	371	10	by	by	ADP
ejpam-6810	371	11	υ(ηi	υ(ηi	NOUN
ejpam-6810	371	12	)	)	PUNCT
ejpam-6810	371	13	=	=	SYM
ejpam-6810	371	14	ηi+1	ηi+1	PROPN
ejpam-6810	371	15	for	for	ADP
ejpam-6810	371	16	all	all	PRON
ejpam-6810	371	17	i	i	PRON
ejpam-6810	371	18	∈	∈	VERB
ejpam-6810	371	19	n	n	PART
ejpam-6810	371	20	∪	∪	X
ejpam-6810	371	21	{	{	PUNCT
ejpam-6810	371	22	0	0	NUM
ejpam-6810	371	23	}	}	PUNCT
ejpam-6810	371	24	,	,	PUNCT
ejpam-6810	371	25	and	and	CCONJ
ejpam-6810	371	26	υ(η∗	υ(η∗	NOUN
ejpam-6810	371	27	)	)	PUNCT
ejpam-6810	371	28	=	=	NOUN
ejpam-6810	371	29	η∗.	η∗.	NOUN
ejpam-6810	371	30	we	we	PRON
ejpam-6810	371	31	can	can	AUX
ejpam-6810	371	32	see	see	VERB
ejpam-6810	371	33	that	that	SCONJ
ejpam-6810	371	34	υ	υ	NOUN
ejpam-6810	371	35	is	be	AUX
ejpam-6810	371	36	not	not	PART
ejpam-6810	371	37	an	an	DET
ejpam-6810	371	38	f	f	NUM
ejpam-6810	371	39	-	-	PUNCT
ejpam-6810	371	40	contraction	contraction	NOUN
ejpam-6810	371	41	mapping	mapping	NOUN
ejpam-6810	371	42	.	.	PUNCT
ejpam-6810	372	1	indeed	indeed	ADV
ejpam-6810	372	2	,	,	PUNCT
ejpam-6810	372	3	σb(η2n	σb(η2n	PROPN
ejpam-6810	372	4	,	,	PUNCT
ejpam-6810	372	5	η2n+1	η2n+1	PROPN
ejpam-6810	372	6	)	)	PUNCT
ejpam-6810	372	7	=	=	SYM
ejpam-6810	372	8	σb(υη2n	σb(υη2n	NOUN
ejpam-6810	372	9	,	,	PUNCT
ejpam-6810	372	10	υη2n+1	υη2n+1	PROPN
ejpam-6810	372	11	)	)	PUNCT
ejpam-6810	372	12	,	,	PUNCT
ejpam-6810	372	13	for	for	ADP
ejpam-6810	372	14	all	all	DET
ejpam-6810	372	15	n	n	NOUN
ejpam-6810	372	16	=	=	NOUN
ejpam-6810	372	17	0,1,2	0,1,2	NUM
ejpam-6810	372	18	,	,	PUNCT
ejpam-6810	372	19	·	·	PUNCT
ejpam-6810	372	20	·	·	PUNCT
ejpam-6810	372	21	·	·	PUNCT
ejpam-6810	372	22	.	.	PUNCT
ejpam-6810	373	1	now	now	ADV
ejpam-6810	373	2	,	,	PUNCT
ejpam-6810	373	3	we	we	PRON
ejpam-6810	373	4	prove	prove	VERB
ejpam-6810	373	5	that	that	SCONJ
ejpam-6810	373	6	υ	υ	PROPN
ejpam-6810	373	7	is	be	AUX
ejpam-6810	373	8	a	a	DET
ejpam-6810	373	9	mcpt	mcpt	NOUN
ejpam-6810	373	10	embedded	embed	VERB
ejpam-6810	373	11	with	with	ADP
ejpam-6810	373	12	an	an	DET
ejpam-6810	373	13	f	f	NOUN
ejpam-6810	373	14	-	-	PUNCT
ejpam-6810	373	15	contraction	contraction	NOUN
ejpam-6810	373	16	.	.	PUNCT
ejpam-6810	374	1	consider	consider	VERB
ejpam-6810	374	2	the	the	DET
ejpam-6810	374	3	first	first	ADJ
ejpam-6810	374	4	triplets	triplet	NOUN
ejpam-6810	374	5	of	of	ADP
ejpam-6810	374	6	points	point	NOUN
ejpam-6810	374	7	ηi	ηi	PROPN
ejpam-6810	374	8	,	,	PUNCT
ejpam-6810	374	9	ηj	ηj	PROPN
ejpam-6810	374	10	,	,	PUNCT
ejpam-6810	374	11	η	η	PROPN
ejpam-6810	374	12	∗	∗	PROPN
ejpam-6810	374	13	∈	∈	PROPN
ejpam-6810	374	14	u	u	NOUN
ejpam-6810	374	15	with	with	ADP
ejpam-6810	374	16	0	0	NUM
ejpam-6810	374	17	≤	≤	NUM
ejpam-6810	375	1	i	i	PRON
ejpam-6810	375	2	<	<	X
ejpam-6810	375	3	j.	j.	PROPN
ejpam-6810	375	4	according	accord	VERB
ejpam-6810	375	5	to	to	ADP
ejpam-6810	375	6	the	the	DET
ejpam-6810	375	7	definition	definition	NOUN
ejpam-6810	375	8	of	of	ADP
ejpam-6810	375	9	the	the	DET
ejpam-6810	375	10	σb	σb	NOUN
ejpam-6810	375	11	given	give	VERB
ejpam-6810	375	12	above	above	ADP
ejpam-6810	375	13	σb(ηi	σb(ηi	PROPN
ejpam-6810	375	14	,	,	PUNCT
ejpam-6810	375	15	ηj	ηj	NOUN
ejpam-6810	375	16	)	)	PUNCT
ejpam-6810	376	1	+	+	CCONJ
ejpam-6810	376	2	σb(ηj	σb(ηj	PROPN
ejpam-6810	376	3	,	,	PUNCT
ejpam-6810	376	4	η	η	NOUN
ejpam-6810	376	5	∗	∗	NOUN
ejpam-6810	376	6	)	)	PUNCT
ejpam-6810	377	1	=	=	SYM
ejpam-6810	377	2	σb(ηi	σb(ηi	PROPN
ejpam-6810	377	3	,	,	PUNCT
ejpam-6810	377	4	η	η	NOUN
ejpam-6810	377	5	∗	∗	NOUN
ejpam-6810	377	6	)	)	PUNCT
ejpam-6810	377	7	.	.	PUNCT
ejpam-6810	378	1	and	and	CCONJ
ejpam-6810	378	2	adding	add	VERB
ejpam-6810	378	3	σb(ηi	σb(ηi	PROPN
ejpam-6810	378	4	,	,	PUNCT
ejpam-6810	378	5	η	η	NOUN
ejpam-6810	378	6	∗	∗	NOUN
ejpam-6810	378	7	)	)	PUNCT
ejpam-6810	378	8	in	in	ADP
ejpam-6810	378	9	both	both	DET
ejpam-6810	378	10	sides	side	NOUN
ejpam-6810	378	11	,	,	PUNCT
ejpam-6810	378	12	one	one	NUM
ejpam-6810	378	13	writes	write	VERB
ejpam-6810	378	14	σb(ηi	σb(ηi	PROPN
ejpam-6810	378	15	,	,	PUNCT
ejpam-6810	378	16	ηj	ηj	NOUN
ejpam-6810	378	17	)	)	PUNCT
ejpam-6810	379	1	+	+	CCONJ
ejpam-6810	379	2	σb(ηj	σb(ηj	PROPN
ejpam-6810	379	3	,	,	PUNCT
ejpam-6810	379	4	η	η	NOUN
ejpam-6810	379	5	∗	∗	NOUN
ejpam-6810	379	6	)	)	PUNCT
ejpam-6810	380	1	+	+	CCONJ
ejpam-6810	380	2	σb(ηi	σb(ηi	PROPN
ejpam-6810	380	3	,	,	PUNCT
ejpam-6810	380	4	η	η	NOUN
ejpam-6810	380	5	∗	∗	NOUN
ejpam-6810	380	6	)	)	PUNCT
ejpam-6810	380	7	=	=	SYM
ejpam-6810	380	8	2σb(ηi	2σb(ηi	NUM
ejpam-6810	380	9	,	,	PUNCT
ejpam-6810	380	10	η	η	NOUN
ejpam-6810	380	11	∗	∗	NOUN
ejpam-6810	380	12	)	)	PUNCT
ejpam-6810	380	13	,	,	PUNCT
ejpam-6810	380	14	=	=	SYM
ejpam-6810	380	15	2(4a2	2(4a2	NUM
ejpam-6810	381	1	−	−	PROPN
ejpam-6810	381	2	σb(η0	σb(η0	PROPN
ejpam-6810	381	3	,	,	PUNCT
ejpam-6810	381	4	ηi	ηi	NOUN
ejpam-6810	381	5	)	)	PUNCT
ejpam-6810	381	6	)	)	PUNCT
ejpam-6810	381	7	,	,	PUNCT
ejpam-6810	381	8	=	=	NOUN
ejpam-6810	381	9	8a2	8a2	NUM
ejpam-6810	381	10	−	−	NUM
ejpam-6810	381	11	2σb(η0	2σb(η0	NUM
ejpam-6810	381	12	,	,	PUNCT
ejpam-6810	381	13	ηi	ηi	PROPN
ejpam-6810	381	14	)	)	PUNCT
ejpam-6810	381	15	.	.	PUNCT
ejpam-6810	382	1	s.	s.	PROPN
ejpam-6810	382	2	batul	batul	PROPN
ejpam-6810	382	3	et	et	PROPN
ejpam-6810	382	4	al	al	PROPN
ejpam-6810	382	5	.	.	PUNCT
ejpam-6810	382	6	/	/	SYM
ejpam-6810	382	7	eur	eur	PROPN
ejpam-6810	382	8	.	.	PUNCT
ejpam-6810	383	1	j.	j.	PROPN
ejpam-6810	383	2	pure	pure	PROPN
ejpam-6810	383	3	appl	appl	PROPN
ejpam-6810	383	4	.	.	PROPN
ejpam-6810	383	5	math	math	PROPN
ejpam-6810	383	6	,	,	PUNCT
ejpam-6810	383	7	18	18	NUM
ejpam-6810	383	8	(	(	PUNCT
ejpam-6810	383	9	4	4	NUM
ejpam-6810	383	10	)	)	PUNCT
ejpam-6810	383	11	(	(	PUNCT
ejpam-6810	383	12	2025	2025	NUM
ejpam-6810	383	13	)	)	PUNCT
ejpam-6810	383	14	,	,	PUNCT
ejpam-6810	383	15	6810	6810	NUM
ejpam-6810	383	16	16	16	NUM
ejpam-6810	383	17	of	of	ADP
ejpam-6810	383	18	23	23	NUM
ejpam-6810	383	19	also	also	ADV
ejpam-6810	383	20	,	,	PUNCT
ejpam-6810	383	21	σb(υηi	σb(υηi	ADJ
ejpam-6810	383	22	,	,	PUNCT
ejpam-6810	383	23	υηj	υηj	NOUN
ejpam-6810	383	24	)	)	PUNCT
ejpam-6810	384	1	+	+	CCONJ
ejpam-6810	384	2	σb(υηj	σb(υηj	ADJ
ejpam-6810	384	3	,	,	PUNCT
ejpam-6810	384	4	υη∗	υη∗	NOUN
ejpam-6810	384	5	)	)	PUNCT
ejpam-6810	385	1	=	=	NOUN
ejpam-6810	385	2	σb(υηi	σb(υηi	ADJ
ejpam-6810	385	3	,	,	PUNCT
ejpam-6810	385	4	υη∗	υη∗	NOUN
ejpam-6810	385	5	)	)	PUNCT
ejpam-6810	385	6	.	.	PUNCT
ejpam-6810	386	1	adding	add	VERB
ejpam-6810	386	2	σb(υηi	σb(υηi	NOUN
ejpam-6810	386	3	,	,	PUNCT
ejpam-6810	386	4	υη∗	υη∗	NOUN
ejpam-6810	386	5	)	)	PUNCT
ejpam-6810	386	6	in	in	ADP
ejpam-6810	386	7	both	both	DET
ejpam-6810	386	8	sides	side	NOUN
ejpam-6810	386	9	,	,	PUNCT
ejpam-6810	386	10	σb(υηi	σb(υηi	NOUN
ejpam-6810	386	11	,	,	PUNCT
ejpam-6810	386	12	υηj	υηj	NOUN
ejpam-6810	386	13	)	)	PUNCT
ejpam-6810	387	1	+	+	CCONJ
ejpam-6810	387	2	σb(υηj	σb(υηj	ADJ
ejpam-6810	387	3	,	,	PUNCT
ejpam-6810	387	4	υη∗	υη∗	NOUN
ejpam-6810	387	5	)	)	PUNCT
ejpam-6810	388	1	+	+	X
ejpam-6810	388	2	σb(υηi	σb(υηi	ADJ
ejpam-6810	388	3	,	,	PUNCT
ejpam-6810	388	4	υη∗	υη∗	NOUN
ejpam-6810	388	5	)	)	PUNCT
ejpam-6810	389	1	=	=	SYM
ejpam-6810	389	2	2σb(υηi	2σb(υηi	NUM
ejpam-6810	389	3	,	,	PUNCT
ejpam-6810	389	4	υη∗	υη∗	NOUN
ejpam-6810	389	5	)	)	PUNCT
ejpam-6810	389	6	,	,	PUNCT
ejpam-6810	389	7	=	=	SYM
ejpam-6810	389	8	2(σb(ηi+1	2(σb(ηi+1	NUM
ejpam-6810	389	9	,	,	PUNCT
ejpam-6810	389	10	η	η	NOUN
ejpam-6810	389	11	∗	∗	NOUN
ejpam-6810	389	12	)	)	PUNCT
ejpam-6810	389	13	)	)	PUNCT
ejpam-6810	389	14	,	,	PUNCT
ejpam-6810	390	1	=	=	NOUN
ejpam-6810	390	2	2(4a2	2(4a2	NUM
ejpam-6810	390	3	−	−	PROPN
ejpam-6810	390	4	σb(η0	σb(η0	PROPN
ejpam-6810	390	5	,	,	PUNCT
ejpam-6810	390	6	ηi+1	ηi+1	PROPN
ejpam-6810	390	7	)	)	PUNCT
ejpam-6810	390	8	)	)	PUNCT
ejpam-6810	390	9	,	,	PUNCT
ejpam-6810	391	1	=	=	NOUN
ejpam-6810	391	2	8a2	8a2	NUM
ejpam-6810	391	3	−	−	ADP
ejpam-6810	391	4	2σb(η0	2σb(η0	NUM
ejpam-6810	391	5	,	,	PUNCT
ejpam-6810	391	6	ηi+1	ηi+1	PROPN
ejpam-6810	391	7	)	)	PUNCT
ejpam-6810	391	8	.	.	PUNCT
ejpam-6810	392	1	using	use	VERB
ejpam-6810	392	2	the	the	DET
ejpam-6810	392	3	formula	formula	NOUN
ejpam-6810	392	4	for	for	ADP
ejpam-6810	392	5	the	the	DET
ejpam-6810	392	6	sum	sum	NOUN
ejpam-6810	392	7	of	of	ADP
ejpam-6810	392	8	a	a	DET
ejpam-6810	392	9	geometric	geometric	ADJ
ejpam-6810	392	10	series	series	NOUN
ejpam-6810	392	11	with	with	ADP
ejpam-6810	392	12	n	n	PRON
ejpam-6810	392	13	terms	term	NOUN
ejpam-6810	392	14	,	,	PUNCT
ejpam-6810	392	15	we	we	PRON
ejpam-6810	392	16	get	get	VERB
ejpam-6810	392	17	σb(η0	σb(η0	NOUN
ejpam-6810	392	18	,	,	PUNCT
ejpam-6810	392	19	ηi	ηi	X
ejpam-6810	392	20	)	)	PUNCT
ejpam-6810	392	21	=	=	PUNCT
ejpam-6810	393	1			NOUN
ejpam-6810	393	2	4a2	4a2	NUM
ejpam-6810	394	1	(	(	PUNCT
ejpam-6810	394	2	1−	1−	NUM
ejpam-6810	394	3	(	(	PUNCT
ejpam-6810	394	4	1	1	NUM
ejpam-6810	394	5	2	2	NUM
ejpam-6810	394	6	)	)	PUNCT
ejpam-6810	394	7	n	n	CCONJ
ejpam-6810	394	8	)	)	PUNCT
ejpam-6810	394	9	,	,	PUNCT
ejpam-6810	394	10	if	if	SCONJ
ejpam-6810	394	11	i	i	PRON
ejpam-6810	394	12	=	=	SYM
ejpam-6810	394	13	2n	2n	NUM
ejpam-6810	394	14	,	,	PUNCT
ejpam-6810	394	15	4a2	4a2	NUM
ejpam-6810	394	16	(	(	PUNCT
ejpam-6810	394	17	1−	1−	NUM
ejpam-6810	394	18	(	(	PUNCT
ejpam-6810	394	19	1	1	NUM
ejpam-6810	394	20	2	2	NUM
ejpam-6810	394	21	)	)	PUNCT
ejpam-6810	394	22	n	n	CCONJ
ejpam-6810	394	23	)	)	PUNCT
ejpam-6810	394	24	−	−	PROPN
ejpam-6810	394	25	a2	a2	PROPN
ejpam-6810	394	26	2n−1	2n−1	NUM
ejpam-6810	394	27	,	,	PUNCT
ejpam-6810	394	28	if	if	SCONJ
ejpam-6810	394	29	i	i	PRON
ejpam-6810	394	30	=	=	PUNCT
ejpam-6810	395	1	2n−	2n−	PROPN
ejpam-6810	395	2	1	1	NUM
ejpam-6810	395	3	.	.	PUNCT
ejpam-6810	396	1	n	n	NOUN
ejpam-6810	396	2	=	=	SYM
ejpam-6810	396	3	1	1	NUM
ejpam-6810	396	4	,	,	PUNCT
ejpam-6810	396	5	2	2	NUM
ejpam-6810	396	6	,	,	PUNCT
ejpam-6810	396	7	·	·	PUNCT
ejpam-6810	396	8	·	·	PUNCT
ejpam-6810	396	9	·	·	PUNCT
ejpam-6810	396	10	.	.	PUNCT
ejpam-6810	397	1	by	by	ADP
ejpam-6810	397	2	the	the	DET
ejpam-6810	397	3	equation	equation	NOUN
ejpam-6810	397	4	(	(	PUNCT
ejpam-6810	397	5	21	21	NUM
ejpam-6810	397	6	)	)	PUNCT
ejpam-6810	397	7	,	,	PUNCT
ejpam-6810	397	8	σb(η0	σb(η0	NOUN
ejpam-6810	397	9	,	,	PUNCT
ejpam-6810	397	10	ηi+1	ηi+1	NOUN
ejpam-6810	397	11	)	)	PUNCT
ejpam-6810	397	12	=	=	SYM
ejpam-6810	397	13	σb(η0	σb(η0	NOUN
ejpam-6810	397	14	,	,	PUNCT
ejpam-6810	397	15	ηi	ηi	X
ejpam-6810	397	16	)	)	PUNCT
ejpam-6810	397	17	+	+	CCONJ
ejpam-6810	397	18	σb(ηi	σb(ηi	PROPN
ejpam-6810	397	19	,	,	PUNCT
ejpam-6810	397	20	ηi+1	ηi+1	PROPN
ejpam-6810	397	21	)	)	PUNCT
ejpam-6810	397	22	,	,	PUNCT
ejpam-6810	397	23	=	=	SYM
ejpam-6810	397	24	σb(η0	σb(η0	X
ejpam-6810	397	25	,	,	PUNCT
ejpam-6810	397	26	ηi	ηi	PROPN
ejpam-6810	397	27	)	)	PUNCT
ejpam-6810	397	28	+	+	NUM
ejpam-6810	397	29	a2	a2	PROPN
ejpam-6810	397	30	(	(	PUNCT
ejpam-6810	397	31	2bi/2c	2bi/2c	NOUN
ejpam-6810	397	32	)	)	PUNCT
ejpam-6810	397	33	.	.	PUNCT
ejpam-6810	398	1	now	now	ADV
ejpam-6810	398	2	,	,	PUNCT
ejpam-6810	398	3	σb(υηi	σb(υηi	ADJ
ejpam-6810	398	4	,	,	PUNCT
ejpam-6810	398	5	υηj	υηj	NOUN
ejpam-6810	398	6	)	)	PUNCT
ejpam-6810	399	1	+	+	CCONJ
ejpam-6810	399	2	σb(υηj	σb(υηj	ADJ
ejpam-6810	399	3	,	,	PUNCT
ejpam-6810	399	4	υη∗	υη∗	NOUN
ejpam-6810	399	5	)	)	PUNCT
ejpam-6810	400	1	+	+	X
ejpam-6810	400	2	σb(υηi	σb(υηi	ADJ
ejpam-6810	400	3	,	,	PUNCT
ejpam-6810	400	4	υη∗	υη∗	NOUN
ejpam-6810	400	5	)	)	PUNCT
ejpam-6810	400	6	σb(ηi	σb(ηi	PROPN
ejpam-6810	400	7	,	,	PUNCT
ejpam-6810	400	8	ηj	ηj	NOUN
ejpam-6810	400	9	)	)	PUNCT
ejpam-6810	400	10	+	+	CCONJ
ejpam-6810	400	11	σb(ηj	σb(ηj	NOUN
ejpam-6810	400	12	,	,	PUNCT
ejpam-6810	400	13	η∗	η∗	NOUN
ejpam-6810	400	14	)	)	PUNCT
ejpam-6810	401	1	+	+	X
ejpam-6810	401	2	σb(ηi	σb(ηi	ADJ
ejpam-6810	401	3	,	,	PUNCT
ejpam-6810	401	4	η∗	η∗	NOUN
ejpam-6810	401	5	)	)	PUNCT
ejpam-6810	401	6	=	=	SYM
ejpam-6810	402	1	8a2	8a2	NUM
ejpam-6810	402	2	−	−	NUM
ejpam-6810	402	3	2σb(η0	2σb(η0	NUM
ejpam-6810	402	4	,	,	PUNCT
ejpam-6810	402	5	ηi+1	ηi+1	PROPN
ejpam-6810	402	6	)	)	PUNCT
ejpam-6810	402	7	8a2	8a2	NUM
ejpam-6810	402	8	−	−	PROPN
ejpam-6810	402	9	2σb(η0	2σb(η0	NUM
ejpam-6810	402	10	,	,	PUNCT
ejpam-6810	402	11	ηi	ηi	PROPN
ejpam-6810	402	12	)	)	PUNCT
ejpam-6810	402	13	,	,	PUNCT
ejpam-6810	402	14	=	=	NOUN
ejpam-6810	402	15	4a2	4a2	NUM
ejpam-6810	402	16	−	−	NOUN
ejpam-6810	402	17	σb(η0	σb(η0	NOUN
ejpam-6810	402	18	,	,	PUNCT
ejpam-6810	402	19	ηi)−	ηi)−	NOUN
ejpam-6810	402	20	a2	a2	PROPN
ejpam-6810	402	21	(	(	PUNCT
ejpam-6810	402	22	2bi/2c	2bi/2c	NOUN
ejpam-6810	402	23	)	)	PUNCT
ejpam-6810	403	1	4a−	4a−	NUM
ejpam-6810	403	2	σb(η0	σb(η0	NOUN
ejpam-6810	403	3	,	,	PUNCT
ejpam-6810	403	4	ηi	ηi	PROPN
ejpam-6810	403	5	)	)	PUNCT
ejpam-6810	403	6	,	,	PUNCT
ejpam-6810	403	7	=	=	PUNCT
ejpam-6810	403	8			PROPN
ejpam-6810	403	9	4a2	4a2	NUM
ejpam-6810	404	1	−	−	NOUN
ejpam-6810	404	2	4a2	4a2	NUM
ejpam-6810	405	1	(	(	PUNCT
ejpam-6810	405	2	1−	1−	NUM
ejpam-6810	405	3	(	(	PUNCT
ejpam-6810	405	4	1	1	NUM
ejpam-6810	405	5	2	2	NUM
ejpam-6810	405	6	)	)	PUNCT
ejpam-6810	405	7	n	n	CCONJ
ejpam-6810	405	8	)	)	PUNCT
ejpam-6810	405	9	−	−	PROPN
ejpam-6810	405	10	a2	a2	PROPN
ejpam-6810	405	11	(	(	PUNCT
ejpam-6810	405	12	2bi/2c	2bi/2c	NOUN
ejpam-6810	405	13	)	)	PUNCT
ejpam-6810	405	14	4a2	4a2	NUM
ejpam-6810	406	1	−	−	PROPN
ejpam-6810	407	1	4a2(1−	4a2(1−	NUM
ejpam-6810	407	2	(	(	PUNCT
ejpam-6810	407	3	1	1	NUM
ejpam-6810	407	4	2	2	NUM
ejpam-6810	407	5	)	)	PUNCT
ejpam-6810	407	6	n	n	CCONJ
ejpam-6810	407	7	)	)	PUNCT
ejpam-6810	407	8	,	,	PUNCT
ejpam-6810	407	9	if	if	SCONJ
ejpam-6810	407	10	i	i	PRON
ejpam-6810	407	11	=	=	SYM
ejpam-6810	407	12	2n	2n	NUM
ejpam-6810	407	13	,	,	PUNCT
ejpam-6810	407	14	4a2	4a2	NUM
ejpam-6810	407	15	−	−	NOUN
ejpam-6810	407	16	4a2	4a2	NUM
ejpam-6810	407	17	(	(	PUNCT
ejpam-6810	407	18	1−	1−	NUM
ejpam-6810	407	19	(	(	PUNCT
ejpam-6810	407	20	1	1	NUM
ejpam-6810	407	21	2	2	NUM
ejpam-6810	407	22	)	)	PUNCT
ejpam-6810	407	23	n	n	CCONJ
ejpam-6810	407	24	)	)	PUNCT
ejpam-6810	407	25	+	+	CCONJ
ejpam-6810	407	26	a2	a2	PROPN
ejpam-6810	407	27	2n−1	2n−1	NUM
ejpam-6810	407	28	−	−	PROPN
ejpam-6810	407	29	a2	a2	PROPN
ejpam-6810	407	30	(	(	PUNCT
ejpam-6810	407	31	2bi/2c	2bi/2c	NOUN
ejpam-6810	407	32	)	)	PUNCT
ejpam-6810	407	33	4a2	4a2	NUM
ejpam-6810	408	1	−	−	PROPN
ejpam-6810	408	2	4a2(1−	4a2(1−	NUM
ejpam-6810	408	3	(	(	PUNCT
ejpam-6810	408	4	1	1	NUM
ejpam-6810	408	5	2	2	NUM
ejpam-6810	408	6	)	)	PUNCT
ejpam-6810	408	7	n	n	CCONJ
ejpam-6810	408	8	)	)	PUNCT
ejpam-6810	409	1	+	+	CCONJ
ejpam-6810	409	2	a2	a2	PROPN
ejpam-6810	409	3	2n−1	2n−1	NUM
ejpam-6810	409	4	,	,	PUNCT
ejpam-6810	409	5	if	if	SCONJ
ejpam-6810	409	6	i	i	PRON
ejpam-6810	409	7	=	=	PUNCT
ejpam-6810	410	1	2n−	2n−	NUM
ejpam-6810	410	2	1	1	NUM
ejpam-6810	410	3	,	,	PUNCT
ejpam-6810	410	4	=	=	PUNCT
ejpam-6810	410	5			PROPN
ejpam-6810	410	6	3	3	NUM
ejpam-6810	410	7	4	4	NUM
ejpam-6810	410	8	,	,	PUNCT
ejpam-6810	410	9	if	if	SCONJ
ejpam-6810	410	10	i	i	PRON
ejpam-6810	410	11	=	=	SYM
ejpam-6810	410	12	2n	2n	NUM
ejpam-6810	410	13	,	,	PUNCT
ejpam-6810	410	14	2	2	NUM
ejpam-6810	410	15	3	3	NUM
ejpam-6810	410	16	,	,	PUNCT
ejpam-6810	410	17	if	if	SCONJ
ejpam-6810	410	18	i	i	PRON
ejpam-6810	410	19	=	=	PUNCT
ejpam-6810	411	1	2n−	2n−	PROPN
ejpam-6810	411	2	1	1	NUM
ejpam-6810	411	3	.	.	PUNCT
ejpam-6810	412	1	(	(	PUNCT
ejpam-6810	412	2	22	22	NUM
ejpam-6810	412	3	)	)	PUNCT
ejpam-6810	412	4	s.	s.	PROPN
ejpam-6810	412	5	batul	batul	PROPN
ejpam-6810	412	6	et	et	PROPN
ejpam-6810	412	7	al	al	PROPN
ejpam-6810	412	8	.	.	PUNCT
ejpam-6810	412	9	/	/	SYM
ejpam-6810	412	10	eur	eur	PROPN
ejpam-6810	412	11	.	.	PUNCT
ejpam-6810	413	1	j.	j.	PROPN
ejpam-6810	413	2	pure	pure	PROPN
ejpam-6810	413	3	appl	appl	PROPN
ejpam-6810	413	4	.	.	PROPN
ejpam-6810	413	5	math	math	PROPN
ejpam-6810	413	6	,	,	PUNCT
ejpam-6810	413	7	18	18	NUM
ejpam-6810	413	8	(	(	PUNCT
ejpam-6810	413	9	4	4	NUM
ejpam-6810	413	10	)	)	PUNCT
ejpam-6810	413	11	(	(	PUNCT
ejpam-6810	413	12	2025	2025	NUM
ejpam-6810	413	13	)	)	PUNCT
ejpam-6810	413	14	,	,	PUNCT
ejpam-6810	413	15	6810	6810	NUM
ejpam-6810	413	16	17	17	NUM
ejpam-6810	413	17	of	of	ADP
ejpam-6810	413	18	23	23	NUM
ejpam-6810	413	19	considering	consider	VERB
ejpam-6810	413	20	ηi	ηi	PROPN
ejpam-6810	413	21	,	,	PUNCT
ejpam-6810	413	22	ηj	ηj	NOUN
ejpam-6810	413	23	,	,	PUNCT
ejpam-6810	413	24	ηk	ηk	PROPN
ejpam-6810	413	25	∈	∈	PROPN
ejpam-6810	413	26	u	u	NOUN
ejpam-6810	413	27	with	with	ADP
ejpam-6810	413	28	0	0	NUM
ejpam-6810	413	29	≤	≤	NUM
ejpam-6810	414	1	i	i	PRON
ejpam-6810	414	2	<	<	X
ejpam-6810	414	3	j	j	X
ejpam-6810	414	4	<	<	X
ejpam-6810	414	5	k	k	X
ejpam-6810	414	6	,	,	PUNCT
ejpam-6810	414	7	fig.1	fig.1	PROPN
ejpam-6810	414	8	illustrates	illustrate	VERB
ejpam-6810	414	9	that	that	SCONJ
ejpam-6810	414	10	σb(ηi	σb(ηi	PROPN
ejpam-6810	414	11	,	,	PUNCT
ejpam-6810	414	12	ηj	ηj	NOUN
ejpam-6810	414	13	)	)	PUNCT
ejpam-6810	414	14	=	=	SYM
ejpam-6810	414	15	σb(ηi	σb(ηi	PROPN
ejpam-6810	414	16	,	,	PUNCT
ejpam-6810	414	17	ηi+1	ηi+1	NOUN
ejpam-6810	414	18	)	)	PUNCT
ejpam-6810	414	19	+	+	CCONJ
ejpam-6810	415	1	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	415	2	,	,	PUNCT
ejpam-6810	415	3	ηi+2	ηi+2	NUM
ejpam-6810	415	4	)	)	PUNCT
ejpam-6810	415	5	+	+	CCONJ
ejpam-6810	415	6	·	·	PUNCT
ejpam-6810	415	7	·	·	PUNCT
ejpam-6810	415	8	·	·	PUNCT
ejpam-6810	416	1	+	+	NUM
ejpam-6810	416	2	σb(ηj−1	σb(ηj−1	NOUN
ejpam-6810	416	3	,	,	PUNCT
ejpam-6810	416	4	ηj	ηj	NOUN
ejpam-6810	416	5	)	)	PUNCT
ejpam-6810	416	6	,	,	PUNCT
ejpam-6810	416	7	(	(	PUNCT
ejpam-6810	416	8	23	23	X
ejpam-6810	416	9	)	)	PUNCT
ejpam-6810	416	10	σb(ηj	σb(ηj	PROPN
ejpam-6810	416	11	,	,	PUNCT
ejpam-6810	416	12	ηk	ηk	NOUN
ejpam-6810	416	13	)	)	PUNCT
ejpam-6810	416	14	=	=	SYM
ejpam-6810	416	15	σb(ηj	σb(ηj	PROPN
ejpam-6810	416	16	,	,	PUNCT
ejpam-6810	416	17	ηj+1	ηj+1	PROPN
ejpam-6810	416	18	)	)	PUNCT
ejpam-6810	417	1	+	+	CCONJ
ejpam-6810	417	2	σb(ηj+1	σb(ηj+1	PROPN
ejpam-6810	417	3	,	,	PUNCT
ejpam-6810	417	4	ηj+2	ηj+2	NUM
ejpam-6810	417	5	)	)	PUNCT
ejpam-6810	417	6	+	+	NUM
ejpam-6810	417	7	·	·	PUNCT
ejpam-6810	417	8	·	·	PUNCT
ejpam-6810	417	9	·	·	PUNCT
ejpam-6810	417	10	+	+	CCONJ
ejpam-6810	417	11	σb(ηk−1	σb(ηk−1	NUM
ejpam-6810	417	12	,	,	PUNCT
ejpam-6810	417	13	ηk	ηk	NOUN
ejpam-6810	417	14	)	)	PUNCT
ejpam-6810	417	15	,	,	PUNCT
ejpam-6810	417	16	(	(	PUNCT
ejpam-6810	417	17	24	24	NUM
ejpam-6810	417	18	)	)	PUNCT
ejpam-6810	417	19	and	and	CCONJ
ejpam-6810	417	20	σb(ηi	σb(ηi	PROPN
ejpam-6810	417	21	,	,	PUNCT
ejpam-6810	417	22	ηk	ηk	X
ejpam-6810	417	23	)	)	PUNCT
ejpam-6810	417	24	=	=	SYM
ejpam-6810	417	25	σb(ηi	σb(ηi	PROPN
ejpam-6810	417	26	,	,	PUNCT
ejpam-6810	417	27	ηi+1	ηi+1	NOUN
ejpam-6810	417	28	)	)	PUNCT
ejpam-6810	417	29	+	+	CCONJ
ejpam-6810	417	30	·	·	PUNCT
ejpam-6810	417	31	·	·	PUNCT
ejpam-6810	417	32	·	·	PUNCT
ejpam-6810	417	33	+	+	NUM
ejpam-6810	417	34	σb(ηj−1	σb(ηj−1	NOUN
ejpam-6810	417	35	,	,	PUNCT
ejpam-6810	417	36	ηj	ηj	NOUN
ejpam-6810	417	37	)	)	PUNCT
ejpam-6810	417	38	+	+	CCONJ
ejpam-6810	417	39	·	·	PUNCT
ejpam-6810	417	40	·	·	PUNCT
ejpam-6810	417	41	·	·	PUNCT
ejpam-6810	417	42	+	+	CCONJ
ejpam-6810	417	43	σb(ηk−1	σb(ηk−1	NUM
ejpam-6810	417	44	,	,	PUNCT
ejpam-6810	417	45	ηk	ηk	NOUN
ejpam-6810	417	46	)	)	PUNCT
ejpam-6810	417	47	.	.	PUNCT
ejpam-6810	418	1	(	(	PUNCT
ejpam-6810	418	2	25	25	NUM
ejpam-6810	418	3	)	)	PUNCT
ejpam-6810	418	4	adding	add	VERB
ejpam-6810	418	5	(	(	PUNCT
ejpam-6810	418	6	23	23	NUM
ejpam-6810	418	7	)	)	PUNCT
ejpam-6810	418	8	,	,	PUNCT
ejpam-6810	418	9	(	(	PUNCT
ejpam-6810	418	10	24	24	NUM
ejpam-6810	418	11	)	)	PUNCT
ejpam-6810	418	12	and	and	CCONJ
ejpam-6810	418	13	(	(	PUNCT
ejpam-6810	418	14	25	25	NUM
ejpam-6810	418	15	)	)	PUNCT
ejpam-6810	418	16	yields	yield	NOUN
ejpam-6810	418	17	that	that	PRON
ejpam-6810	418	18	σb(ηi	σb(ηi	PROPN
ejpam-6810	418	19	,	,	PUNCT
ejpam-6810	418	20	ηj	ηj	NOUN
ejpam-6810	418	21	)	)	PUNCT
ejpam-6810	419	1	+	+	CCONJ
ejpam-6810	420	1	σb(ηj	σb(ηj	NOUN
ejpam-6810	420	2	,	,	PUNCT
ejpam-6810	420	3	ηk	ηk	X
ejpam-6810	420	4	)	)	PUNCT
ejpam-6810	420	5	+	+	CCONJ
ejpam-6810	420	6	σb(ηi	σb(ηi	PROPN
ejpam-6810	420	7	,	,	PUNCT
ejpam-6810	420	8	ηk	ηk	NOUN
ejpam-6810	420	9	)	)	PUNCT
ejpam-6810	420	10	=	=	SYM
ejpam-6810	420	11	2(σb(ηi	2(σb(ηi	NUM
ejpam-6810	420	12	,	,	PUNCT
ejpam-6810	420	13	ηi+1	ηi+1	NOUN
ejpam-6810	420	14	)	)	PUNCT
ejpam-6810	420	15	+	+	CCONJ
ejpam-6810	420	16	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	420	17	,	,	PUNCT
ejpam-6810	420	18	ηi+2	ηi+2	NUM
ejpam-6810	420	19	)	)	PUNCT
ejpam-6810	420	20	+	+	CCONJ
ejpam-6810	420	21	·	·	PUNCT
ejpam-6810	420	22	·	·	PUNCT
ejpam-6810	420	23	·	·	PUNCT
ejpam-6810	420	24	+	+	CCONJ
ejpam-6810	420	25	σb(ηk−1	σb(ηk−1	NUM
ejpam-6810	420	26	,	,	PUNCT
ejpam-6810	420	27	ηk	ηk	NOUN
ejpam-6810	420	28	)	)	PUNCT
ejpam-6810	420	29	)	)	PUNCT
ejpam-6810	420	30	.	.	PUNCT
ejpam-6810	421	1	(	(	PUNCT
ejpam-6810	421	2	26	26	NUM
ejpam-6810	421	3	)	)	PUNCT
ejpam-6810	421	4	now	now	ADV
ejpam-6810	421	5	,	,	PUNCT
ejpam-6810	421	6	by	by	ADP
ejpam-6810	421	7	the	the	DET
ejpam-6810	421	8	definition	definition	NOUN
ejpam-6810	421	9	of	of	ADP
ejpam-6810	421	10	σb	σb	ADP
ejpam-6810	421	11	,	,	PUNCT
ejpam-6810	421	12	σb(υηi	σb(υηi	NOUN
ejpam-6810	421	13	,	,	PUNCT
ejpam-6810	421	14	υηj	υηj	NOUN
ejpam-6810	421	15	)	)	PUNCT
ejpam-6810	421	16	=	=	SYM
ejpam-6810	421	17	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	421	18	,	,	PUNCT
ejpam-6810	421	19	ηj+1	ηj+1	PROPN
ejpam-6810	421	20	)	)	PUNCT
ejpam-6810	421	21	=	=	SYM
ejpam-6810	421	22	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	421	23	,	,	PUNCT
ejpam-6810	421	24	ηi+2	ηi+2	NUM
ejpam-6810	421	25	)	)	PUNCT
ejpam-6810	421	26	+	+	CCONJ
ejpam-6810	421	27	·	·	PUNCT
ejpam-6810	421	28	·	·	PUNCT
ejpam-6810	421	29	·	·	PUNCT
ejpam-6810	422	1	+	+	NUM
ejpam-6810	422	2	σb(ηj−1	σb(ηj−1	NOUN
ejpam-6810	422	3	,	,	PUNCT
ejpam-6810	422	4	ηj	ηj	NOUN
ejpam-6810	422	5	)	)	PUNCT
ejpam-6810	422	6	,	,	PUNCT
ejpam-6810	422	7	(	(	PUNCT
ejpam-6810	422	8	27	27	NUM
ejpam-6810	422	9	)	)	PUNCT
ejpam-6810	422	10	σb(υηj	σb(υηj	ADV
ejpam-6810	422	11	,	,	PUNCT
ejpam-6810	422	12	υηk	υηk	NOUN
ejpam-6810	422	13	)	)	PUNCT
ejpam-6810	422	14	=	=	SYM
ejpam-6810	422	15	σb(ηj+1	σb(ηj+1	PROPN
ejpam-6810	422	16	,	,	PUNCT
ejpam-6810	422	17	ηk+1	ηk+1	X
ejpam-6810	422	18	)	)	PUNCT
ejpam-6810	422	19	=	=	SYM
ejpam-6810	422	20	σb(ηj+1	σb(ηj+1	PROPN
ejpam-6810	422	21	,	,	PUNCT
ejpam-6810	422	22	ηj+2	ηj+2	NOUN
ejpam-6810	422	23	)	)	PUNCT
ejpam-6810	422	24	+	+	NUM
ejpam-6810	422	25	·	·	PUNCT
ejpam-6810	422	26	·	·	PUNCT
ejpam-6810	422	27	·	·	PUNCT
ejpam-6810	423	1	+	+	CCONJ
ejpam-6810	423	2	σb(ηk	σb(ηk	ADJ
ejpam-6810	423	3	,	,	PUNCT
ejpam-6810	423	4	ηk+1	ηk+1	NOUN
ejpam-6810	423	5	)	)	PUNCT
ejpam-6810	423	6	,	,	PUNCT
ejpam-6810	423	7	(	(	PUNCT
ejpam-6810	423	8	28	28	NUM
ejpam-6810	423	9	)	)	PUNCT
ejpam-6810	423	10	and	and	CCONJ
ejpam-6810	423	11	σb(υηi	σb(υηi	NOUN
ejpam-6810	423	12	,	,	PUNCT
ejpam-6810	423	13	υηk	υηk	NOUN
ejpam-6810	423	14	)	)	PUNCT
ejpam-6810	423	15	=	=	SYM
ejpam-6810	423	16	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	423	17	,	,	PUNCT
ejpam-6810	423	18	ηk+1	ηk+1	X
ejpam-6810	423	19	)	)	PUNCT
ejpam-6810	423	20	=	=	SYM
ejpam-6810	423	21	σb(ηi+1	σb(ηi+1	NOUN
ejpam-6810	423	22	,	,	PUNCT
ejpam-6810	423	23	ηi+2	ηi+2	NUM
ejpam-6810	423	24	)	)	PUNCT
ejpam-6810	423	25	+	+	CCONJ
ejpam-6810	423	26	·	·	PUNCT
ejpam-6810	423	27	·	·	PUNCT
ejpam-6810	424	1	·	·	PUNCT
ejpam-6810	424	2	+	+	CCONJ
ejpam-6810	424	3	σb(ηk	σb(ηk	ADJ
ejpam-6810	424	4	,	,	PUNCT
ejpam-6810	424	5	ηk+1	ηk+1	NOUN
ejpam-6810	424	6	)	)	PUNCT
ejpam-6810	424	7	.	.	PUNCT
ejpam-6810	425	1	(	(	PUNCT
ejpam-6810	425	2	29	29	NUM
ejpam-6810	425	3	)	)	PUNCT
ejpam-6810	425	4	adding	add	VERB
ejpam-6810	425	5	(	(	PUNCT
ejpam-6810	425	6	27	27	NUM
ejpam-6810	425	7	)	)	PUNCT
ejpam-6810	425	8	,	,	PUNCT
ejpam-6810	425	9	(	(	PUNCT
ejpam-6810	425	10	28	28	NUM
ejpam-6810	425	11	)	)	PUNCT
ejpam-6810	425	12	and	and	CCONJ
ejpam-6810	425	13	(	(	PUNCT
ejpam-6810	425	14	29	29	NUM
ejpam-6810	425	15	)	)	PUNCT
ejpam-6810	425	16	leads	lead	VERB
ejpam-6810	425	17	to	to	ADP
ejpam-6810	425	18	σb(υηi	σb(υηi	NOUN
ejpam-6810	425	19	,	,	PUNCT
ejpam-6810	425	20	υηj	υηj	NOUN
ejpam-6810	425	21	)	)	PUNCT
ejpam-6810	426	1	+	+	CCONJ
ejpam-6810	426	2	σb(υηj	σb(υηj	X
ejpam-6810	426	3	,	,	PUNCT
ejpam-6810	426	4	υηk	υηk	NOUN
ejpam-6810	426	5	)	)	PUNCT
ejpam-6810	427	1	+	+	SYM
ejpam-6810	427	2	σb(υηi	σb(υηi	NOUN
ejpam-6810	427	3	,	,	PUNCT
ejpam-6810	427	4	υηk	υηk	NOUN
ejpam-6810	427	5	)	)	PUNCT
ejpam-6810	427	6	=	=	SYM
ejpam-6810	428	1	2(σb(ηi+1	2(σb(ηi+1	NUM
ejpam-6810	428	2	,	,	PUNCT
ejpam-6810	428	3	ηi+2	ηi+2	NUM
ejpam-6810	428	4	)	)	PUNCT
ejpam-6810	428	5	+	+	CCONJ
ejpam-6810	428	6	·	·	PUNCT
ejpam-6810	428	7	·	·	PUNCT
ejpam-6810	428	8	·	·	PUNCT
ejpam-6810	429	1	+	+	CCONJ
ejpam-6810	429	2	σb(ηk−1	σb(ηk−1	NUM
ejpam-6810	429	3	,	,	PUNCT
ejpam-6810	429	4	ηk	ηk	X
ejpam-6810	429	5	)	)	PUNCT
ejpam-6810	430	1	+	+	CCONJ
ejpam-6810	430	2	σb(ηk	σb(ηk	ADJ
ejpam-6810	430	3	,	,	PUNCT
ejpam-6810	430	4	ηk+1	ηk+1	NOUN
ejpam-6810	430	5	)	)	PUNCT
ejpam-6810	430	6	)	)	PUNCT
ejpam-6810	430	7	.	.	PUNCT
ejpam-6810	431	1	(	(	PUNCT
ejpam-6810	431	2	30	30	NUM
ejpam-6810	431	3	)	)	PUNCT
ejpam-6810	431	4	by	by	ADP
ejpam-6810	431	5	subtracting	subtract	VERB
ejpam-6810	431	6	(	(	PUNCT
ejpam-6810	431	7	26	26	NUM
ejpam-6810	431	8	)	)	PUNCT
ejpam-6810	431	9	and	and	CCONJ
ejpam-6810	431	10	(	(	PUNCT
ejpam-6810	431	11	30	30	NUM
ejpam-6810	431	12	)	)	PUNCT
ejpam-6810	431	13	,	,	PUNCT
ejpam-6810	431	14	one	one	PRON
ejpam-6810	431	15	gets	get	VERB
ejpam-6810	431	16	σb(ηi	σb(ηi	ADJ
ejpam-6810	431	17	,	,	PUNCT
ejpam-6810	431	18	ηj	ηj	NOUN
ejpam-6810	431	19	)	)	PUNCT
ejpam-6810	432	1	+	+	CCONJ
ejpam-6810	432	2	σb(ηj	σb(ηj	NOUN
ejpam-6810	432	3	,	,	PUNCT
ejpam-6810	432	4	ηk	ηk	X
ejpam-6810	432	5	)	)	PUNCT
ejpam-6810	432	6	+	+	CCONJ
ejpam-6810	432	7	σb(ηi	σb(ηi	ADJ
ejpam-6810	432	8	,	,	PUNCT
ejpam-6810	432	9	ηk)−	ηk)−	PRON
ejpam-6810	432	10	(	(	PUNCT
ejpam-6810	432	11	σb(υηi	σb(υηi	ADJ
ejpam-6810	432	12	,	,	PUNCT
ejpam-6810	432	13	υηj	υηj	NOUN
ejpam-6810	432	14	)	)	PUNCT
ejpam-6810	433	1	+	+	CCONJ
ejpam-6810	433	2	σb(υηj	σb(υηj	X
ejpam-6810	433	3	,	,	PUNCT
ejpam-6810	433	4	υηk	υηk	NOUN
ejpam-6810	433	5	)	)	PUNCT
ejpam-6810	433	6	+	+	SYM
ejpam-6810	433	7	σb(υηi	σb(υηi	NOUN
ejpam-6810	433	8	,	,	PUNCT
ejpam-6810	433	9	υηk	υηk	NOUN
ejpam-6810	433	10	)	)	PUNCT
ejpam-6810	433	11	)	)	PUNCT
ejpam-6810	433	12	,	,	PUNCT
ejpam-6810	434	1	=	=	PUNCT
ejpam-6810	434	2	2(σb(ηi	2(σb(ηi	NUM
ejpam-6810	434	3	,	,	PUNCT
ejpam-6810	434	4	ηi+1	ηi+1	NOUN
ejpam-6810	434	5	)	)	PUNCT
ejpam-6810	434	6	+	+	CCONJ
ejpam-6810	434	7	σb(ηk	σb(ηk	ADJ
ejpam-6810	434	8	,	,	PUNCT
ejpam-6810	434	9	ηk+1	ηk+1	NOUN
ejpam-6810	434	10	)	)	PUNCT
ejpam-6810	434	11	)	)	PUNCT
ejpam-6810	434	12	,	,	PUNCT
ejpam-6810	434	13	=	=	SYM
ejpam-6810	434	14	2	2	NUM
ejpam-6810	434	15	(	(	PUNCT
ejpam-6810	434	16	a2	a2	PROPN
ejpam-6810	434	17	(	(	PUNCT
ejpam-6810	434	18	2bi/2c	2bi/2c	NOUN
ejpam-6810	434	19	)	)	PUNCT
ejpam-6810	434	20	−	−	PROPN
ejpam-6810	434	21	a2	a2	PROPN
ejpam-6810	434	22	(	(	PUNCT
ejpam-6810	434	23	2bk/2c	2bk/2c	NOUN
ejpam-6810	434	24	)	)	PUNCT
ejpam-6810	434	25	)	)	PUNCT
ejpam-6810	434	26	.	.	PUNCT
ejpam-6810	435	1	rearranging	rearrange	VERB
ejpam-6810	435	2	this	this	DET
ejpam-6810	435	3	equation	equation	NOUN
ejpam-6810	435	4	,	,	PUNCT
ejpam-6810	435	5	σb(υηi	σb(υηi	NOUN
ejpam-6810	435	6	,	,	PUNCT
ejpam-6810	435	7	υηj)+σb(υηj	υηj)+σb(υηj	NOUN
ejpam-6810	435	8	,	,	PUNCT
ejpam-6810	435	9	υηk)+σb(υηi	υηk)+σb(υηi	X
ejpam-6810	435	10	,	,	PUNCT
ejpam-6810	435	11	υηk	υηk	NOUN
ejpam-6810	435	12	)	)	PUNCT
ejpam-6810	435	13	=	=	SYM
ejpam-6810	435	14	σb(ηi	σb(ηi	PROPN
ejpam-6810	435	15	,	,	PUNCT
ejpam-6810	435	16	ηj)+σb(ηj	ηj)+σb(ηj	PROPN
ejpam-6810	435	17	,	,	PUNCT
ejpam-6810	435	18	ηk)+σb(ηi	ηk)+σb(ηi	PROPN
ejpam-6810	435	19	,	,	PUNCT
ejpam-6810	435	20	ηk)−2	ηk)−2	ADJ
ejpam-6810	435	21	(	(	PUNCT
ejpam-6810	435	22	a2	a2	PROPN
ejpam-6810	435	23	(	(	PUNCT
ejpam-6810	435	24	2bi/2c	2bi/2c	NOUN
ejpam-6810	435	25	)	)	PUNCT
ejpam-6810	435	26	−	−	PROPN
ejpam-6810	435	27	a2	a2	PROPN
ejpam-6810	435	28	(	(	PUNCT
ejpam-6810	435	29	2bk/2c	2bk/2c	NOUN
ejpam-6810	435	30	)	)	PUNCT
ejpam-6810	435	31	)	)	PUNCT
ejpam-6810	435	32	.	.	PUNCT
ejpam-6810	436	1	(	(	PUNCT
ejpam-6810	436	2	31	31	NUM
ejpam-6810	436	3	)	)	PUNCT
ejpam-6810	436	4	we	we	PRON
ejpam-6810	436	5	can	can	AUX
ejpam-6810	436	6	see	see	VERB
ejpam-6810	436	7	that	that	SCONJ
ejpam-6810	436	8	i+	i+	NOUN
ejpam-6810	436	9	1	1	NUM
ejpam-6810	436	10	<	<	X
ejpam-6810	436	11	k	k	X
ejpam-6810	436	12	,	,	PUNCT
ejpam-6810	436	13	which	which	PRON
ejpam-6810	436	14	implies	imply	VERB
ejpam-6810	436	15	that	that	SCONJ
ejpam-6810	436	16	2bi/2	2bi/2	NUM
ejpam-6810	436	17	+	+	NOUN
ejpam-6810	436	18	1c	1c	NOUN
ejpam-6810	436	19	<	<	X
ejpam-6810	436	20	2bk/2c	2bk/2c	NOUN
ejpam-6810	436	21	,	,	PUNCT
ejpam-6810	436	22	⇒	⇒	VERB
ejpam-6810	436	23	2.2bi/2c	2.2bi/2c	NOUN
ejpam-6810	436	24	<	<	X
ejpam-6810	436	25	2bk/2c	2bk/2c	NOUN
ejpam-6810	436	26	,	,	PUNCT
ejpam-6810	436	27	⇒	⇒	PROPN
ejpam-6810	436	28	a2	a2	PROPN
ejpam-6810	436	29	2bk/2c	2bk/2c	PROPN
ejpam-6810	436	30	≤	≤	PROPN
ejpam-6810	436	31	a2	a2	PROPN
ejpam-6810	436	32	(	(	PUNCT
ejpam-6810	436	33	2.2bi/2c	2.2bi/2c	NUM
ejpam-6810	436	34	)	)	PUNCT
ejpam-6810	436	35	.	.	PUNCT
ejpam-6810	437	1	using	use	VERB
ejpam-6810	437	2	this	this	PRON
ejpam-6810	437	3	in	in	ADP
ejpam-6810	437	4	(	(	PUNCT
ejpam-6810	437	5	31	31	NUM
ejpam-6810	437	6	)	)	PUNCT
ejpam-6810	437	7	to	to	PART
ejpam-6810	437	8	obtain	obtain	VERB
ejpam-6810	437	9	σb(υηi	σb(υηi	NOUN
ejpam-6810	437	10	,	,	PUNCT
ejpam-6810	437	11	υηj	υηj	NOUN
ejpam-6810	437	12	)	)	PUNCT
ejpam-6810	437	13	+	+	CCONJ
ejpam-6810	437	14	σb(υηj	σb(υηj	X
ejpam-6810	437	15	,	,	PUNCT
ejpam-6810	437	16	υηk	υηk	NOUN
ejpam-6810	437	17	)	)	PUNCT
ejpam-6810	437	18	+	+	SYM
ejpam-6810	437	19	σb(υηi	σb(υηi	ADJ
ejpam-6810	437	20	,	,	PUNCT
ejpam-6810	437	21	υηk	υηk	NOUN
ejpam-6810	437	22	)	)	PUNCT
ejpam-6810	437	23	≤	≤	NOUN
ejpam-6810	437	24	σb(ηi	σb(ηi	PROPN
ejpam-6810	437	25	,	,	PUNCT
ejpam-6810	437	26	ηj	ηj	NOUN
ejpam-6810	437	27	)	)	PUNCT
ejpam-6810	438	1	+	+	CCONJ
ejpam-6810	438	2	σb(ηj	σb(ηj	NOUN
ejpam-6810	438	3	,	,	PUNCT
ejpam-6810	438	4	ηk	ηk	X
ejpam-6810	438	5	)	)	PUNCT
ejpam-6810	438	6	+	+	CCONJ
ejpam-6810	438	7	σb(ηi	σb(ηi	ADJ
ejpam-6810	438	8	,	,	PUNCT
ejpam-6810	438	9	ηk)−	ηk)−	ADJ
ejpam-6810	438	10	2a2	2a2	NUM
ejpam-6810	438	11	2bi/2c	2bi/2c	NOUN
ejpam-6810	439	1	+	+	NUM
ejpam-6810	439	2	a2	a2	PROPN
ejpam-6810	439	3	2bi/2c	2bi/2c	PROPN
ejpam-6810	439	4	s.	s.	PROPN
ejpam-6810	439	5	batul	batul	PROPN
ejpam-6810	439	6	et	et	PROPN
ejpam-6810	439	7	al	al	PROPN
ejpam-6810	439	8	.	.	PUNCT
ejpam-6810	439	9	/	/	SYM
ejpam-6810	439	10	eur	eur	PROPN
ejpam-6810	439	11	.	.	PUNCT
ejpam-6810	440	1	j.	j.	PROPN
ejpam-6810	440	2	pure	pure	PROPN
ejpam-6810	440	3	appl	appl	PROPN
ejpam-6810	440	4	.	.	PROPN
ejpam-6810	440	5	math	math	PROPN
ejpam-6810	440	6	,	,	PUNCT
ejpam-6810	440	7	18	18	NUM
ejpam-6810	440	8	(	(	PUNCT
ejpam-6810	440	9	4	4	NUM
ejpam-6810	440	10	)	)	PUNCT
ejpam-6810	440	11	(	(	PUNCT
ejpam-6810	440	12	2025	2025	NUM
ejpam-6810	440	13	)	)	PUNCT
ejpam-6810	440	14	,	,	PUNCT
ejpam-6810	440	15	6810	6810	NUM
ejpam-6810	440	16	18	18	NUM
ejpam-6810	440	17	of	of	ADP
ejpam-6810	440	18	23	23	NUM
ejpam-6810	440	19	⇒	⇒	NOUN
ejpam-6810	440	20	σb(υηi	σb(υηi	NOUN
ejpam-6810	440	21	,	,	PUNCT
ejpam-6810	440	22	υηj	υηj	NOUN
ejpam-6810	440	23	)	)	PUNCT
ejpam-6810	441	1	+	+	CCONJ
ejpam-6810	441	2	σb(υηj	σb(υηj	X
ejpam-6810	441	3	,	,	PUNCT
ejpam-6810	441	4	υηk	υηk	NOUN
ejpam-6810	441	5	)	)	PUNCT
ejpam-6810	441	6	+	+	SYM
ejpam-6810	442	1	σb(υηi	σb(υηi	ADJ
ejpam-6810	442	2	,	,	PUNCT
ejpam-6810	442	3	υηk	υηk	NOUN
ejpam-6810	442	4	)	)	PUNCT
ejpam-6810	442	5	≤	≤	NOUN
ejpam-6810	442	6	σb(ηi	σb(ηi	PROPN
ejpam-6810	442	7	,	,	PUNCT
ejpam-6810	442	8	ηj	ηj	NOUN
ejpam-6810	442	9	)	)	PUNCT
ejpam-6810	442	10	+	+	CCONJ
ejpam-6810	442	11	σb(ηj	σb(ηj	NOUN
ejpam-6810	442	12	,	,	PUNCT
ejpam-6810	442	13	ηk	ηk	X
ejpam-6810	442	14	)	)	PUNCT
ejpam-6810	442	15	+	+	CCONJ
ejpam-6810	442	16	σb(ηi	σb(ηi	ADJ
ejpam-6810	442	17	,	,	PUNCT
ejpam-6810	442	18	ηk)−	ηk)−	PROPN
ejpam-6810	442	19	a2	a2	PROPN
ejpam-6810	442	20	2bi/2c	2bi/2c	NOUN
ejpam-6810	442	21	.	.	PUNCT
ejpam-6810	443	1	(	(	PUNCT
ejpam-6810	443	2	32	32	NUM
ejpam-6810	443	3	)	)	PUNCT
ejpam-6810	443	4	one	one	NOUN
ejpam-6810	443	5	can	can	AUX
ejpam-6810	443	6	show	show	VERB
ejpam-6810	443	7	that	that	SCONJ
ejpam-6810	443	8	σb(ηi	σb(ηi	ADJ
ejpam-6810	443	9	,	,	PUNCT
ejpam-6810	443	10	η∗	η∗	NOUN
ejpam-6810	443	11	)	)	PUNCT
ejpam-6810	443	12	≤	≤	NOUN
ejpam-6810	443	13	4σb(ηi	4σb(ηi	NUM
ejpam-6810	443	14	,	,	PUNCT
ejpam-6810	443	15	ηi+1	ηi+1	PROPN
ejpam-6810	443	16	)	)	PUNCT
ejpam-6810	443	17	.	.	PUNCT
ejpam-6810	444	1	we	we	PRON
ejpam-6810	444	2	have	have	AUX
ejpam-6810	444	3	σb(ηi	σb(ηi	PROPN
ejpam-6810	444	4	,	,	PUNCT
ejpam-6810	444	5	ηk	ηk	NOUN
ejpam-6810	444	6	)	)	PUNCT
ejpam-6810	444	7	≤	≤	NOUN
ejpam-6810	444	8	σb(ηi	σb(ηi	PROPN
ejpam-6810	444	9	,	,	PUNCT
ejpam-6810	444	10	η	η	NOUN
ejpam-6810	444	11	∗	∗	NOUN
ejpam-6810	444	12	)	)	PUNCT
ejpam-6810	444	13	.	.	PUNCT
ejpam-6810	445	1	consequently	consequently	ADV
ejpam-6810	445	2	,	,	PUNCT
ejpam-6810	445	3	we	we	PRON
ejpam-6810	445	4	obtain	obtain	VERB
ejpam-6810	445	5	σb(ηi	σb(ηi	PROPN
ejpam-6810	445	6	,	,	PUNCT
ejpam-6810	445	7	ηk	ηk	NOUN
ejpam-6810	445	8	)	)	PUNCT
ejpam-6810	445	9	≤	≤	NOUN
ejpam-6810	445	10	4σb(ηi	4σb(ηi	NUM
ejpam-6810	445	11	,	,	PUNCT
ejpam-6810	445	12	ηi+1	ηi+1	PROPN
ejpam-6810	445	13	)	)	PUNCT
ejpam-6810	445	14	.	.	PUNCT
ejpam-6810	446	1	using	use	VERB
ejpam-6810	446	2	equality	equality	NOUN
ejpam-6810	446	3	(	(	PUNCT
ejpam-6810	446	4	23	23	NUM
ejpam-6810	446	5	)	)	PUNCT
ejpam-6810	446	6	and	and	CCONJ
ejpam-6810	446	7	the	the	DET
ejpam-6810	446	8	preceding	precede	VERB
ejpam-6810	446	9	inequality	inequality	NOUN
ejpam-6810	446	10	,	,	PUNCT
ejpam-6810	446	11	we	we	PRON
ejpam-6810	446	12	obtain	obtain	VERB
ejpam-6810	446	13	σb(ηi	σb(ηi	ADJ
ejpam-6810	446	14	,	,	PUNCT
ejpam-6810	446	15	ηj	ηj	NOUN
ejpam-6810	446	16	)	)	PUNCT
ejpam-6810	447	1	+	+	CCONJ
ejpam-6810	447	2	σb(ηj	σb(ηj	NOUN
ejpam-6810	447	3	,	,	PUNCT
ejpam-6810	447	4	ηk	ηk	X
ejpam-6810	447	5	)	)	PUNCT
ejpam-6810	447	6	+	+	CCONJ
ejpam-6810	447	7	σb(ηi	σb(ηi	PROPN
ejpam-6810	447	8	,	,	PUNCT
ejpam-6810	447	9	ηk	ηk	NOUN
ejpam-6810	447	10	)	)	PUNCT
ejpam-6810	447	11	=	=	SYM
ejpam-6810	447	12	2σb(ηi	2σb(ηi	NUM
ejpam-6810	447	13	,	,	PUNCT
ejpam-6810	447	14	ηk	ηk	PROPN
ejpam-6810	447	15	)	)	PUNCT
ejpam-6810	447	16	,	,	PUNCT
ejpam-6810	447	17	≤	≤	PROPN
ejpam-6810	447	18	8σb(ηi	8σb(ηi	NUM
ejpam-6810	447	19	,	,	PUNCT
ejpam-6810	447	20	ηi+1	ηi+1	PROPN
ejpam-6810	447	21	)	)	PUNCT
ejpam-6810	447	22	,	,	PUNCT
ejpam-6810	447	23	=	=	SYM
ejpam-6810	447	24	8	8	NUM
ejpam-6810	447	25	a2	a2	PROPN
ejpam-6810	447	26	(	(	PUNCT
ejpam-6810	447	27	2bi/2c	2bi/2c	NOUN
ejpam-6810	447	28	)	)	PUNCT
ejpam-6810	447	29	.	.	PUNCT
ejpam-6810	448	1	by	by	ADP
ejpam-6810	448	2	putting	put	VERB
ejpam-6810	448	3	this	this	DET
ejpam-6810	448	4	inequality	inequality	NOUN
ejpam-6810	448	5	in	in	ADP
ejpam-6810	448	6	(	(	PUNCT
ejpam-6810	448	7	32	32	NUM
ejpam-6810	448	8	)	)	PUNCT
ejpam-6810	448	9	,	,	PUNCT
ejpam-6810	448	10	yields	yield	NOUN
ejpam-6810	448	11	σb(υηi	σb(υηi	NOUN
ejpam-6810	448	12	,	,	PUNCT
ejpam-6810	448	13	υηj	υηj	NOUN
ejpam-6810	448	14	)	)	PUNCT
ejpam-6810	448	15	+	+	CCONJ
ejpam-6810	448	16	σb(υηj	σb(υηj	X
ejpam-6810	448	17	,	,	PUNCT
ejpam-6810	448	18	υηk	υηk	NOUN
ejpam-6810	448	19	)	)	PUNCT
ejpam-6810	448	20	+	+	SYM
ejpam-6810	448	21	σb(υηi	σb(υηi	ADJ
ejpam-6810	448	22	,	,	PUNCT
ejpam-6810	448	23	υηk	υηk	NOUN
ejpam-6810	448	24	)	)	PUNCT
ejpam-6810	448	25	≤	≤	NOUN
ejpam-6810	448	26	σb(ηi	σb(ηi	PROPN
ejpam-6810	448	27	,	,	PUNCT
ejpam-6810	448	28	ηj	ηj	NOUN
ejpam-6810	448	29	)	)	PUNCT
ejpam-6810	449	1	+	+	CCONJ
ejpam-6810	449	2	σb(ηj	σb(ηj	NOUN
ejpam-6810	449	3	,	,	PUNCT
ejpam-6810	449	4	ηk	ηk	X
ejpam-6810	449	5	)	)	PUNCT
ejpam-6810	449	6	+	+	CCONJ
ejpam-6810	449	7	σb(ηi	σb(ηi	ADJ
ejpam-6810	449	8	,	,	PUNCT
ejpam-6810	449	9	ηk)−	ηk)−	ADJ
ejpam-6810	449	10	1	1	NUM
ejpam-6810	449	11	8	8	NUM
ejpam-6810	449	12	(	(	PUNCT
ejpam-6810	449	13	σb(ηi	σb(ηi	PROPN
ejpam-6810	449	14	,	,	PUNCT
ejpam-6810	449	15	ηj	ηj	NOUN
ejpam-6810	449	16	)	)	PUNCT
ejpam-6810	449	17	+	+	CCONJ
ejpam-6810	449	18	σb(ηj	σb(ηj	NOUN
ejpam-6810	449	19	,	,	PUNCT
ejpam-6810	449	20	ηk	ηk	X
ejpam-6810	449	21	)	)	PUNCT
ejpam-6810	449	22	+	+	CCONJ
ejpam-6810	449	23	σb(ηi	σb(ηi	PROPN
ejpam-6810	449	24	,	,	PUNCT
ejpam-6810	449	25	ηk	ηk	NOUN
ejpam-6810	449	26	)	)	PUNCT
ejpam-6810	449	27	)	)	PUNCT
ejpam-6810	449	28	σb(υηi	σb(υηi	NOUN
ejpam-6810	449	29	,	,	PUNCT
ejpam-6810	449	30	υηj	υηj	NOUN
ejpam-6810	449	31	)	)	PUNCT
ejpam-6810	450	1	+	+	CCONJ
ejpam-6810	450	2	σb(υηj	σb(υηj	X
ejpam-6810	450	3	,	,	PUNCT
ejpam-6810	450	4	υηk	υηk	NOUN
ejpam-6810	450	5	)	)	PUNCT
ejpam-6810	451	1	+	+	SYM
ejpam-6810	451	2	σb(υηi	σb(υηi	ADJ
ejpam-6810	451	3	,	,	PUNCT
ejpam-6810	451	4	υηk	υηk	NOUN
ejpam-6810	451	5	)	)	PUNCT
ejpam-6810	451	6	≤	≤	NOUN
ejpam-6810	451	7	7	7	NUM
ejpam-6810	451	8	8	8	NUM
ejpam-6810	451	9	(	(	PUNCT
ejpam-6810	451	10	σb(ηi	σb(ηi	PROPN
ejpam-6810	451	11	,	,	PUNCT
ejpam-6810	451	12	ηj	ηj	NOUN
ejpam-6810	451	13	)	)	PUNCT
ejpam-6810	452	1	+	+	CCONJ
ejpam-6810	452	2	σb(ηj	σb(ηj	NOUN
ejpam-6810	452	3	,	,	PUNCT
ejpam-6810	452	4	ηk	ηk	X
ejpam-6810	452	5	)	)	PUNCT
ejpam-6810	452	6	+	+	CCONJ
ejpam-6810	452	7	σb(ηi	σb(ηi	PROPN
ejpam-6810	452	8	,	,	PUNCT
ejpam-6810	452	9	ηk	ηk	NOUN
ejpam-6810	452	10	)	)	PUNCT
ejpam-6810	452	11	)	)	PUNCT
ejpam-6810	452	12	.	.	PUNCT
ejpam-6810	453	1	(	(	PUNCT
ejpam-6810	453	2	33	33	NUM
ejpam-6810	453	3	)	)	PUNCT
ejpam-6810	453	4	by	by	ADP
ejpam-6810	453	5	equations	equation	NOUN
ejpam-6810	453	6	(	(	PUNCT
ejpam-6810	453	7	22	22	NUM
ejpam-6810	453	8	)	)	PUNCT
ejpam-6810	453	9	and	and	CCONJ
ejpam-6810	453	10	(	(	PUNCT
ejpam-6810	453	11	33	33	NUM
ejpam-6810	453	12	)	)	PUNCT
ejpam-6810	453	13	,	,	PUNCT
ejpam-6810	453	14	inequality	inequality	NOUN
ejpam-6810	453	15	(	(	PUNCT
ejpam-6810	453	16	3	3	X
ejpam-6810	453	17	)	)	PUNCT
ejpam-6810	453	18	satisfies	satisfie	NOUN
ejpam-6810	453	19	for	for	ADP
ejpam-6810	453	20	any	any	DET
ejpam-6810	453	21	three	three	NUM
ejpam-6810	453	22	pairwise	pairwise	NOUN
ejpam-6810	453	23	distinct	distinct	ADJ
ejpam-6810	453	24	points	point	NOUN
ejpam-6810	453	25	from	from	ADP
ejpam-6810	453	26	the	the	DET
ejpam-6810	453	27	space	space	NOUN
ejpam-6810	453	28	u	u	NOUN
ejpam-6810	453	29	with	with	ADP
ejpam-6810	453	30	f(η	f(η	NOUN
ejpam-6810	453	31	)	)	PUNCT
ejpam-6810	453	32	=	=	PUNCT
ejpam-6810	453	33	ln(η	ln(η	X
ejpam-6810	453	34	)	)	PUNCT
ejpam-6810	453	35	and	and	CCONJ
ejpam-6810	453	36	e−τ	e−τ	NOUN
ejpam-6810	453	37	s2	s2	NOUN
ejpam-6810	453	38	=	=	NOUN
ejpam-6810	453	39	7	7	NUM
ejpam-6810	453	40	8	8	NUM
ejpam-6810	453	41	=	=	SYM
ejpam-6810	453	42	max	max	NOUN
ejpam-6810	453	43	{	{	PUNCT
ejpam-6810	453	44	2	2	NUM
ejpam-6810	453	45	3	3	NUM
ejpam-6810	453	46	,	,	PUNCT
ejpam-6810	453	47	3	3	NUM
ejpam-6810	453	48	4	4	NUM
ejpam-6810	453	49	,	,	PUNCT
ejpam-6810	453	50	7	7	NUM
ejpam-6810	453	51	8	8	NUM
ejpam-6810	453	52	}	}	PUNCT
ejpam-6810	453	53	.	.	PUNCT
ejpam-6810	454	1	it	it	PRON
ejpam-6810	454	2	should	should	AUX
ejpam-6810	454	3	be	be	AUX
ejpam-6810	454	4	noted	note	VERB
ejpam-6810	454	5	that	that	SCONJ
ejpam-6810	454	6	the	the	DET
ejpam-6810	454	7	sequence	sequence	NOUN
ejpam-6810	454	8	of	of	ADP
ejpam-6810	454	9	iterates	iterate	NOUN
ejpam-6810	454	10	of	of	ADP
ejpam-6810	454	11	any	any	DET
ejpam-6810	454	12	two	two	NUM
ejpam-6810	454	13	points	point	NOUN
ejpam-6810	454	14	,	,	PUNCT
ejpam-6810	454	15	ηi	ηi	PROPN
ejpam-6810	454	16	and	and	CCONJ
ejpam-6810	454	17	ηj	ηj	NOUN
ejpam-6810	454	18	,	,	PUNCT
ejpam-6810	454	19	in	in	ADP
ejpam-6810	454	20	the	the	DET
ejpam-6810	454	21	preceding	precede	VERB
ejpam-6810	454	22	example	example	NOUN
ejpam-6810	454	23	overlap	overlap	NOUN
ejpam-6810	454	24	sets	set	NOUN
ejpam-6810	454	25	.	.	PUNCT
ejpam-6810	455	1	let	let	VERB
ejpam-6810	455	2	’s	’s	NOUN
ejpam-6810	455	3	create	create	VERB
ejpam-6810	455	4	an	an	DET
ejpam-6810	455	5	example	example	NOUN
ejpam-6810	455	6	of	of	ADP
ejpam-6810	455	7	a	a	DET
ejpam-6810	455	8	mapping	mapping	NOUN
ejpam-6810	455	9	υ	υ	NOUN
ejpam-6810	455	10	:	:	PUNCT
ejpam-6810	455	11	u	u	VERB
ejpam-6810	455	12	−→	−→	ADJ
ejpam-6810	455	13	u	u	NOUN
ejpam-6810	455	14	that	that	PRON
ejpam-6810	455	15	is	be	AUX
ejpam-6810	455	16	a	a	DET
ejpam-6810	455	17	mcpt	mcpt	NOUN
ejpam-6810	455	18	embedded	embed	VERB
ejpam-6810	455	19	with	with	ADP
ejpam-6810	455	20	an	an	DET
ejpam-6810	455	21	f	f	NOUN
ejpam-6810	455	22	-	-	PUNCT
ejpam-6810	455	23	contraction	contraction	NOUN
ejpam-6810	455	24	and	and	CCONJ
ejpam-6810	455	25	is	be	AUX
ejpam-6810	455	26	not	not	PART
ejpam-6810	455	27	a	a	DET
ejpam-6810	455	28	an	an	DET
ejpam-6810	455	29	f	f	NUM
ejpam-6810	455	30	-	-	PUNCT
ejpam-6810	455	31	contraction	contraction	NOUN
ejpam-6810	455	32	mapping	mapping	NOUN
ejpam-6810	455	33	.	.	PUNCT
ejpam-6810	456	1	it	it	PRON
ejpam-6810	456	2	has	have	VERB
ejpam-6810	456	3	the	the	DET
ejpam-6810	456	4	feature	feature	NOUN
ejpam-6810	456	5	that	that	SCONJ
ejpam-6810	456	6	there	there	PRON
ejpam-6810	456	7	are	be	VERB
ejpam-6810	456	8	an	an	DET
ejpam-6810	456	9	infinite	infinite	ADJ
ejpam-6810	456	10	number	number	NOUN
ejpam-6810	456	11	of	of	ADP
ejpam-6810	456	12	points	point	NOUN
ejpam-6810	456	13	such	such	ADJ
ejpam-6810	456	14	that	that	SCONJ
ejpam-6810	456	15	the	the	DET
ejpam-6810	456	16	iteration	iteration	NOUN
ejpam-6810	456	17	sequences	sequence	NOUN
ejpam-6810	456	18	of	of	ADP
ejpam-6810	456	19	these	these	DET
ejpam-6810	456	20	points	point	NOUN
ejpam-6810	456	21	are	be	AUX
ejpam-6810	456	22	disjoint	disjoint	NOUN
ejpam-6810	456	23	sets	set	NOUN
ejpam-6810	456	24	.	.	PUNCT
ejpam-6810	457	1	example	example	NOUN
ejpam-6810	457	2	6	6	NUM
ejpam-6810	457	3	.	.	PUNCT
ejpam-6810	457	4	consider	consider	VERB
ejpam-6810	457	5	the	the	DET
ejpam-6810	457	6	subset	subset	NOUN
ejpam-6810	457	7	u	u	NOUN
ejpam-6810	457	8	⊆	⊆	NUM
ejpam-6810	457	9	r	r	NOUN
ejpam-6810	457	10	consisting	consisting	NOUN
ejpam-6810	457	11	of	of	ADP
ejpam-6810	457	12	{	{	PUNCT
ejpam-6810	457	13	η0	η0	PROPN
ejpam-6810	457	14	,	,	PUNCT
ejpam-6810	457	15	η1	η1	NOUN
ejpam-6810	457	16	,	,	PUNCT
ejpam-6810	457	17	...	...	PUNCT
ejpam-6810	457	18	}	}	PUNCT
ejpam-6810	457	19	∪[0	∪[0	PRON
ejpam-6810	457	20	,	,	PUNCT
ejpam-6810	457	21	1	1	NUM
ejpam-6810	457	22	]	]	PUNCT
ejpam-6810	457	23	,	,	PUNCT
ejpam-6810	457	24	where	where	SCONJ
ejpam-6810	457	25	η2k	η2k	PROPN
ejpam-6810	457	26	=	=	SYM
ejpam-6810	457	27	−4	−4	X
ejpam-6810	457	28	2k	2k	NUM
ejpam-6810	457	29	and	and	CCONJ
ejpam-6810	457	30	η2k+1	η2k+1	NOUN
ejpam-6810	457	31	=	=	SYM
ejpam-6810	457	32	−3	−3	NOUN
ejpam-6810	457	33	2k	2k	NOUN
ejpam-6810	457	34	for	for	ADP
ejpam-6810	457	35	k	k	PROPN
ejpam-6810	457	36	≥	≥	PROPN
ejpam-6810	457	37	0	0	NUM
ejpam-6810	457	38	,	,	PUNCT
ejpam-6810	457	39	illustrated	illustrate	VERB
ejpam-6810	457	40	in	in	ADP
ejpam-6810	457	41	fig.2	fig.2	PROPN
ejpam-6810	457	42	.	.	PUNCT
ejpam-6810	458	1	figure	figure	NOUN
ejpam-6810	458	2	2	2	NUM
ejpam-6810	458	3	:	:	PUNCT
ejpam-6810	458	4	the	the	DET
ejpam-6810	458	5	b	b	X
ejpam-6810	458	6	-	-	PUNCT
ejpam-6810	458	7	ms	ms	ADJ
ejpam-6810	458	8	(	(	PUNCT
ejpam-6810	458	9	u	u	NOUN
ejpam-6810	458	10	,	,	PUNCT
ejpam-6810	458	11	σb	σb	ADP
ejpam-6810	458	12	)	)	PUNCT
ejpam-6810	458	13	.	.	PUNCT
ejpam-6810	459	1	let	let	VERB
ejpam-6810	459	2	υ	υ	PRON
ejpam-6810	459	3	:	:	PUNCT
ejpam-6810	459	4	u	u	VERB
ejpam-6810	459	5	−→	−→	NOUN
ejpam-6810	459	6	u	u	NOUN
ejpam-6810	459	7	be	be	AUX
ejpam-6810	459	8	defined	define	VERB
ejpam-6810	459	9	by	by	ADP
ejpam-6810	459	10	υηi	υηi	NOUN
ejpam-6810	459	11	=	=	SYM
ejpam-6810	459	12	ηi+1	ηi+1	PROPN
ejpam-6810	459	13	for	for	ADP
ejpam-6810	459	14	all	all	PRON
ejpam-6810	459	15	i	i	PRON
ejpam-6810	459	16	∈	∈	PROPN
ejpam-6810	459	17	{	{	PUNCT
ejpam-6810	459	18	0	0	NUM
ejpam-6810	459	19	}	}	PUNCT
ejpam-6810	459	20	∪	∪	NOUN
ejpam-6810	459	21	n	n	CCONJ
ejpam-6810	459	22	and	and	CCONJ
ejpam-6810	459	23	υη	υη	PROPN
ejpam-6810	459	24	=	=	PROPN
ejpam-6810	459	25	η	η	PROPN
ejpam-6810	459	26	2	2	NUM
ejpam-6810	459	27	for	for	ADP
ejpam-6810	459	28	η	η	PROPN
ejpam-6810	459	29	∈	∈	PROPN
ejpam-6810	460	1	[	[	X
ejpam-6810	460	2	0	0	NUM
ejpam-6810	460	3	,	,	PUNCT
ejpam-6810	460	4	1	1	NUM
ejpam-6810	460	5	]	]	PUNCT
ejpam-6810	460	6	.	.	PUNCT
ejpam-6810	461	1	s.	s.	PROPN
ejpam-6810	461	2	batul	batul	PROPN
ejpam-6810	461	3	et	et	PROPN
ejpam-6810	461	4	al	al	PROPN
ejpam-6810	461	5	.	.	PUNCT
ejpam-6810	461	6	/	/	SYM
ejpam-6810	461	7	eur	eur	PROPN
ejpam-6810	461	8	.	.	PUNCT
ejpam-6810	462	1	j.	j.	PROPN
ejpam-6810	462	2	pure	pure	PROPN
ejpam-6810	462	3	appl	appl	PROPN
ejpam-6810	462	4	.	.	PROPN
ejpam-6810	462	5	math	math	PROPN
ejpam-6810	462	6	,	,	PUNCT
ejpam-6810	462	7	18	18	NUM
ejpam-6810	462	8	(	(	PUNCT
ejpam-6810	462	9	4	4	NUM
ejpam-6810	462	10	)	)	PUNCT
ejpam-6810	462	11	(	(	PUNCT
ejpam-6810	462	12	2025	2025	NUM
ejpam-6810	462	13	)	)	PUNCT
ejpam-6810	462	14	,	,	PUNCT
ejpam-6810	462	15	6810	6810	NUM
ejpam-6810	462	16	19	19	NUM
ejpam-6810	462	17	of	of	ADP
ejpam-6810	462	18	23	23	NUM
ejpam-6810	462	19	the	the	DET
ejpam-6810	462	20	mapping	mapping	NOUN
ejpam-6810	463	1	υ	υ	NOUN
ejpam-6810	463	2	satisfies	satisfy	VERB
ejpam-6810	463	3	the	the	DET
ejpam-6810	463	4	required	require	VERB
ejpam-6810	463	5	condition	condition	NOUN
ejpam-6810	463	6	for	for	ADP
ejpam-6810	463	7	sequences	sequence	NOUN
ejpam-6810	463	8	of	of	ADP
ejpam-6810	463	9	iterates	iterate	NOUN
ejpam-6810	463	10	of	of	ADP
ejpam-6810	463	11	points	point	NOUN
ejpam-6810	463	12	in	in	ADP
ejpam-6810	463	13	[	[	X
ejpam-6810	463	14	0,1	0,1	NUM
ejpam-6810	463	15	]	]	PUNCT
ejpam-6810	463	16	of	of	ADP
ejpam-6810	463	17	the	the	DET
ejpam-6810	463	18	form	form	NOUN
ejpam-6810	463	19	p	p	NOUN
ejpam-6810	463	20	2k	2k	NOUN
ejpam-6810	463	21	,	,	PUNCT
ejpam-6810	463	22	where	where	SCONJ
ejpam-6810	463	23	p	p	NOUN
ejpam-6810	463	24	is	be	AUX
ejpam-6810	463	25	a	a	DET
ejpam-6810	463	26	prime	prime	ADJ
ejpam-6810	463	27	number	number	NOUN
ejpam-6810	463	28	greater	great	ADJ
ejpam-6810	463	29	than	than	ADP
ejpam-6810	463	30	or	or	CCONJ
ejpam-6810	463	31	equal	equal	ADJ
ejpam-6810	463	32	to	to	ADP
ejpam-6810	463	33	3	3	NUM
ejpam-6810	463	34	and	and	CCONJ
ejpam-6810	463	35	k	k	PROPN
ejpam-6810	463	36	is	be	AUX
ejpam-6810	463	37	the	the	DET
ejpam-6810	463	38	smallest	small	ADJ
ejpam-6810	463	39	natural	natural	ADJ
ejpam-6810	463	40	number	number	NOUN
ejpam-6810	463	41	ensuring	ensure	VERB
ejpam-6810	463	42	p	p	NOUN
ejpam-6810	463	43	2k	2k	NOUN
ejpam-6810	463	44	⊆	⊆	NUM
ejpam-6810	463	45	[	[	X
ejpam-6810	463	46	0	0	NUM
ejpam-6810	463	47	,	,	PUNCT
ejpam-6810	463	48	1	1	NUM
ejpam-6810	463	49	]	]	PUNCT
ejpam-6810	463	50	.	.	PUNCT
ejpam-6810	464	1	setting	set	VERB
ejpam-6810	464	2	s	s	X
ejpam-6810	464	3	=	=	SYM
ejpam-6810	464	4	1	1	NUM
ejpam-6810	464	5	establishes	establish	VERB
ejpam-6810	464	6	an	an	DET
ejpam-6810	464	7	isometry	isometry	NOUN
ejpam-6810	464	8	between	between	ADP
ejpam-6810	464	9	the	the	DET
ejpam-6810	464	10	previous	previous	ADJ
ejpam-6810	464	11	example	example	NOUN
ejpam-6810	464	12	’s	’s	PART
ejpam-6810	464	13	b	b	NOUN
ejpam-6810	464	14	-	-	PUNCT
ejpam-6810	464	15	ms	ms	NOUN
ejpam-6810	464	16	and	and	CCONJ
ejpam-6810	464	17	the	the	DET
ejpam-6810	464	18	subspace	subspace	NOUN
ejpam-6810	464	19	(	(	PUNCT
ejpam-6810	464	20	{	{	PUNCT
ejpam-6810	464	21	0	0	NUM
ejpam-6810	464	22	,	,	PUNCT
ejpam-6810	464	23	η0	η0	NOUN
ejpam-6810	464	24	,	,	PUNCT
ejpam-6810	464	25	η1	η1	NOUN
ejpam-6810	464	26	,	,	PUNCT
ejpam-6810	464	27	·	·	PUNCT
ejpam-6810	464	28	·	·	PUNCT
ejpam-6810	464	29	·	·	PUNCT
ejpam-6810	465	1	}	}	PUNCT
ejpam-6810	465	2	,	,	PUNCT
ejpam-6810	465	3	σb	σb	ADP
ejpam-6810	465	4	)	)	PUNCT
ejpam-6810	465	5	within	within	ADP
ejpam-6810	465	6	(	(	PUNCT
ejpam-6810	465	7	u	u	NOUN
ejpam-6810	465	8	,	,	PUNCT
ejpam-6810	465	9	σb	σb	ADP
ejpam-6810	465	10	)	)	PUNCT
ejpam-6810	465	11	.	.	PUNCT
ejpam-6810	466	1	the	the	DET
ejpam-6810	466	2	f	f	NOUN
ejpam-6810	466	3	-	-	PUNCT
ejpam-6810	466	4	mapping	mapping	NOUN
ejpam-6810	466	5	υ	υ	NOUN
ejpam-6810	466	6	is	be	AUX
ejpam-6810	466	7	defined	define	VERB
ejpam-6810	466	8	in	in	ADP
ejpam-6810	466	9	a	a	DET
ejpam-6810	466	10	similar	similar	ADJ
ejpam-6810	466	11	manner	manner	NOUN
ejpam-6810	466	12	for	for	ADP
ejpam-6810	466	13	this	this	DET
ejpam-6810	466	14	subspace	subspace	NOUN
ejpam-6810	466	15	,	,	PUNCT
ejpam-6810	466	16	and	and	CCONJ
ejpam-6810	466	17	it	it	PRON
ejpam-6810	466	18	follows	follow	VERB
ejpam-6810	466	19	that	that	SCONJ
ejpam-6810	466	20	υ	υ	NOUN
ejpam-6810	466	21	is	be	AUX
ejpam-6810	466	22	not	not	PART
ejpam-6810	466	23	an	an	DET
ejpam-6810	466	24	f	f	NUM
ejpam-6810	466	25	-	-	PUNCT
ejpam-6810	466	26	contraction	contraction	NOUN
ejpam-6810	466	27	mapping	mapping	NOUN
ejpam-6810	466	28	.	.	PUNCT
ejpam-6810	467	1	we	we	PRON
ejpam-6810	467	2	will	will	AUX
ejpam-6810	467	3	demonstrate	demonstrate	VERB
ejpam-6810	467	4	that	that	SCONJ
ejpam-6810	467	5	for	for	SCONJ
ejpam-6810	467	6	each	each	PRON
ejpam-6810	467	7	of	of	ADP
ejpam-6810	467	8	the	the	DET
ejpam-6810	467	9	three	three	NUM
ejpam-6810	467	10	pairwise	pairwise	NOUN
ejpam-6810	467	11	distinct	distinct	ADJ
ejpam-6810	467	12	points	point	NOUN
ejpam-6810	467	13	from	from	ADP
ejpam-6810	467	14	the	the	DET
ejpam-6810	467	15	space	space	NOUN
ejpam-6810	467	16	(	(	PUNCT
ejpam-6810	467	17	u	u	NOUN
ejpam-6810	467	18	,	,	PUNCT
ejpam-6810	467	19	σb	σb	ADP
ejpam-6810	467	20	)	)	PUNCT
ejpam-6810	467	21	,	,	PUNCT
ejpam-6810	467	22	inequality	inequality	NOUN
ejpam-6810	467	23	(	(	PUNCT
ejpam-6810	467	24	3	3	NUM
ejpam-6810	467	25	)	)	PUNCT
ejpam-6810	467	26	is	be	AUX
ejpam-6810	467	27	satisfied	satisfied	ADJ
ejpam-6810	467	28	.	.	PUNCT
ejpam-6810	468	1	the	the	DET
ejpam-6810	468	2	validity	validity	NOUN
ejpam-6810	468	3	of	of	ADP
ejpam-6810	468	4	this	this	DET
ejpam-6810	468	5	property	property	NOUN
ejpam-6810	468	6	for	for	ADP
ejpam-6810	468	7	all	all	DET
ejpam-6810	468	8	distinct	distinct	ADJ
ejpam-6810	468	9	triplets	triplet	NOUN
ejpam-6810	468	10	in	in	ADP
ejpam-6810	468	11	(	(	PUNCT
ejpam-6810	468	12	{	{	PUNCT
ejpam-6810	468	13	0	0	NUM
ejpam-6810	468	14	,	,	PUNCT
ejpam-6810	468	15	η0	η0	NOUN
ejpam-6810	468	16	,	,	PUNCT
ejpam-6810	468	17	η1	η1	NOUN
ejpam-6810	468	18	,	,	PUNCT
ejpam-6810	468	19	·	·	PUNCT
ejpam-6810	468	20	·	·	PUNCT
ejpam-6810	468	21	·	·	PUNCT
ejpam-6810	468	22	}	}	PUNCT
ejpam-6810	468	23	,	,	PUNCT
ejpam-6810	468	24	σb	σb	ADP
ejpam-6810	468	25	)	)	PUNCT
ejpam-6810	468	26	has	have	AUX
ejpam-6810	468	27	been	be	AUX
ejpam-6810	468	28	previously	previously	ADV
ejpam-6810	468	29	established	establish	VERB
ejpam-6810	468	30	.	.	PUNCT
ejpam-6810	469	1	since	since	SCONJ
ejpam-6810	469	2	the	the	DET
ejpam-6810	469	3	b	b	NOUN
ejpam-6810	469	4	-	-	PUNCT
ejpam-6810	469	5	metric	metric	ADJ
ejpam-6810	469	6	σb	σb	NOUN
ejpam-6810	469	7	is	be	AUX
ejpam-6810	469	8	contractive	contractive	ADJ
ejpam-6810	469	9	on	on	ADP
ejpam-6810	469	10	(	(	PUNCT
ejpam-6810	469	11	[	[	X
ejpam-6810	469	12	0	0	NUM
ejpam-6810	469	13	,	,	PUNCT
ejpam-6810	469	14	1	1	NUM
ejpam-6810	469	15	]	]	PUNCT
ejpam-6810	469	16	,	,	PUNCT
ejpam-6810	469	17	σb	σb	ADP
ejpam-6810	469	18	)	)	PUNCT
ejpam-6810	469	19	,	,	PUNCT
ejpam-6810	469	20	and	and	CCONJ
ejpam-6810	469	21	every	every	DET
ejpam-6810	469	22	f	f	NOUN
ejpam-6810	469	23	-	-	PUNCT
ejpam-6810	469	24	contraction	contraction	NOUN
ejpam-6810	469	25	reduces	reduce	VERB
ejpam-6810	469	26	to	to	PART
ejpam-6810	469	27	triangle	triangle	VERB
ejpam-6810	469	28	perimeters	perimeter	NOUN
ejpam-6810	469	29	,	,	PUNCT
ejpam-6810	469	30	we	we	PRON
ejpam-6810	469	31	only	only	ADV
ejpam-6810	469	32	need	need	VERB
ejpam-6810	469	33	to	to	PART
ejpam-6810	469	34	prove	prove	VERB
ejpam-6810	469	35	inequality	inequality	NOUN
ejpam-6810	469	36	(	(	PUNCT
ejpam-6810	469	37	3	3	NUM
ejpam-6810	469	38	)	)	PUNCT
ejpam-6810	469	39	for	for	ADP
ejpam-6810	469	40	three	three	NUM
ejpam-6810	469	41	pairwise	pairwise	NOUN
ejpam-6810	469	42	distinct	distinct	ADJ
ejpam-6810	469	43	points	point	NOUN
ejpam-6810	469	44	η	η	PROPN
ejpam-6810	469	45	,	,	PUNCT
ejpam-6810	469	46	ξ	ξ	PROPN
ejpam-6810	469	47	,	,	PUNCT
ejpam-6810	469	48	ζ	ζ	PROPN
ejpam-6810	469	49	∈	∈	NOUN
ejpam-6810	469	50	u	u	NOUN
ejpam-6810	469	51	satisfying	satisfying	NOUN
ejpam-6810	469	52	:	:	PUNCT
ejpam-6810	469	53	η	η	X
ejpam-6810	469	54	<	<	X
ejpam-6810	469	55	ξ	ξ	X
ejpam-6810	469	56	<	<	X
ejpam-6810	469	57	ζ	ζ	X
ejpam-6810	469	58	where	where	SCONJ
ejpam-6810	469	59	,	,	PUNCT
ejpam-6810	469	60	η	η	PROPN
ejpam-6810	469	61	∈	∈	PROPN
ejpam-6810	469	62	{	{	PUNCT
ejpam-6810	469	63	η0	η0	NOUN
ejpam-6810	469	64	,	,	PUNCT
ejpam-6810	469	65	η1	η1	NOUN
ejpam-6810	469	66	,	,	PUNCT
ejpam-6810	469	67	·	·	PUNCT
ejpam-6810	469	68	·	·	PUNCT
ejpam-6810	469	69	·	·	PUNCT
ejpam-6810	469	70	}	}	PUNCT
ejpam-6810	469	71	and	and	CCONJ
ejpam-6810	469	72	ζ	ζ	NOUN
ejpam-6810	469	73	∈	∈	NOUN
ejpam-6810	469	74	(	(	PUNCT
ejpam-6810	469	75	0	0	NUM
ejpam-6810	469	76	,	,	PUNCT
ejpam-6810	469	77	1	1	NUM
ejpam-6810	469	78	]	]	PUNCT
ejpam-6810	469	79	.	.	PUNCT
ejpam-6810	470	1	we	we	PRON
ejpam-6810	470	2	begin	begin	VERB
ejpam-6810	470	3	by	by	ADP
ejpam-6810	470	4	considering	consider	VERB
ejpam-6810	470	5	η	η	PROPN
ejpam-6810	470	6	=	=	PROPN
ejpam-6810	470	7	η2k	η2k	PROPN
ejpam-6810	470	8	=	=	SYM
ejpam-6810	470	9	−4	−4	PROPN
ejpam-6810	470	10	2k	2k	NUM
ejpam-6810	470	11	.	.	PUNCT
ejpam-6810	471	1	subsequently	subsequently	ADV
ejpam-6810	471	2	,	,	PUNCT
ejpam-6810	471	3	σb(η	σb(η	PROPN
ejpam-6810	471	4	,	,	PUNCT
ejpam-6810	471	5	ξ	ξ	NOUN
ejpam-6810	471	6	)	)	PUNCT
ejpam-6810	471	7	+	+	CCONJ
ejpam-6810	471	8	σb(ξ	σb(ξ	ADJ
ejpam-6810	471	9	,	,	PUNCT
ejpam-6810	471	10	ζ	ζ	NOUN
ejpam-6810	471	11	)	)	PUNCT
ejpam-6810	471	12	+	+	NUM
ejpam-6810	471	13	σb(η	σb(η	NUM
ejpam-6810	471	14	,	,	PUNCT
ejpam-6810	471	15	ζ	ζ	NOUN
ejpam-6810	471	16	)	)	PUNCT
ejpam-6810	471	17	=	=	SYM
ejpam-6810	471	18	2σb(η	2σb(η	NUM
ejpam-6810	471	19	,	,	PUNCT
ejpam-6810	471	20	ζ	ζ	NOUN
ejpam-6810	471	21	)	)	PUNCT
ejpam-6810	471	22	=	=	SYM
ejpam-6810	471	23	2	2	NUM
ejpam-6810	471	24	(	(	PUNCT
ejpam-6810	471	25	4	4	NUM
ejpam-6810	471	26	2k	2k	NUM
ejpam-6810	471	27	+	+	CCONJ
ejpam-6810	471	28	ζ	ζ	NOUN
ejpam-6810	471	29	)	)	PUNCT
ejpam-6810	471	30	2	2	NUM
ejpam-6810	471	31	.	.	PUNCT
ejpam-6810	472	1	(	(	PUNCT
ejpam-6810	472	2	34	34	NUM
ejpam-6810	472	3	)	)	PUNCT
ejpam-6810	472	4	from	from	ADP
ejpam-6810	472	5	υη	υη	PROPN
ejpam-6810	472	6	=	=	SYM
ejpam-6810	472	7	υη2k	υη2k	PROPN
ejpam-6810	472	8	,	,	PUNCT
ejpam-6810	472	9	it	it	PRON
ejpam-6810	472	10	follows	follow	VERB
ejpam-6810	472	11	that	that	SCONJ
ejpam-6810	472	12	υη2k	υη2k	PROPN
ejpam-6810	472	13	=	=	PRON
ejpam-6810	472	14	η2k+1	η2k+1	VERB
ejpam-6810	472	15	=	=	PUNCT
ejpam-6810	472	16	−3	−3	NOUN
ejpam-6810	472	17	2k	2k	PROPN
ejpam-6810	472	18	.	.	PUNCT
ejpam-6810	473	1	which	which	PRON
ejpam-6810	473	2	implies	imply	VERB
ejpam-6810	473	3	that	that	SCONJ
ejpam-6810	473	4	σb(υη	σb(υη	PROPN
ejpam-6810	473	5	,	,	PUNCT
ejpam-6810	473	6	υξ	υξ	NOUN
ejpam-6810	473	7	)	)	PUNCT
ejpam-6810	473	8	+	+	CCONJ
ejpam-6810	473	9	σb(υξ	σb(υξ	PROPN
ejpam-6810	473	10	,	,	PUNCT
ejpam-6810	473	11	υζ	υζ	NOUN
ejpam-6810	473	12	)	)	PUNCT
ejpam-6810	473	13	+	+	CCONJ
ejpam-6810	473	14	σb(υη	σb(υη	PROPN
ejpam-6810	473	15	,	,	PUNCT
ejpam-6810	473	16	υζ	υζ	NOUN
ejpam-6810	473	17	)	)	PUNCT
ejpam-6810	473	18	=	=	SYM
ejpam-6810	473	19	2σb(υη	2σb(υη	NUM
ejpam-6810	473	20	,	,	PUNCT
ejpam-6810	473	21	υζ	υζ	NOUN
ejpam-6810	473	22	)	)	PUNCT
ejpam-6810	473	23	=	=	SYM
ejpam-6810	473	24	2	2	NUM
ejpam-6810	473	25	(	(	PUNCT
ejpam-6810	473	26	3	3	NUM
ejpam-6810	473	27	2k	2k	NUM
ejpam-6810	473	28	+	+	CCONJ
ejpam-6810	473	29	ζ	ζ	SYM
ejpam-6810	473	30	2	2	NUM
ejpam-6810	473	31	)	)	PUNCT
ejpam-6810	473	32	2	2	NUM
ejpam-6810	473	33	,	,	PUNCT
ejpam-6810	473	34	=	=	NOUN
ejpam-6810	473	35	32	32	NUM
ejpam-6810	473	36	×	×	NOUN
ejpam-6810	473	37	2	2	NUM
ejpam-6810	473	38	(	(	PUNCT
ejpam-6810	473	39	1	1	NUM
ejpam-6810	473	40	2k	2k	NUM
ejpam-6810	473	41	+	+	CCONJ
ejpam-6810	473	42	ζ	ζ	NOUN
ejpam-6810	473	43	6	6	NUM
ejpam-6810	473	44	)	)	SYM
ejpam-6810	473	45	2	2	NUM
ejpam-6810	473	46	,	,	PUNCT
ejpam-6810	473	47	=	=	NOUN
ejpam-6810	473	48	9	9	NUM
ejpam-6810	473	49	16	16	NUM
ejpam-6810	473	50	×	×	NOUN
ejpam-6810	473	51	2	2	NUM
ejpam-6810	473	52	(	(	PUNCT
ejpam-6810	473	53	4	4	NUM
ejpam-6810	473	54	2k	2k	NUM
ejpam-6810	473	55	+	+	CCONJ
ejpam-6810	473	56	4ζ	4ζ	NUM
ejpam-6810	473	57	6	6	NUM
ejpam-6810	473	58	)	)	SYM
ejpam-6810	473	59	2	2	NUM
ejpam-6810	473	60	,	,	PUNCT
ejpam-6810	473	61	≤	≤	NUM
ejpam-6810	473	62	9	9	NUM
ejpam-6810	473	63	16	16	NUM
ejpam-6810	473	64	×	×	NOUN
ejpam-6810	473	65	2	2	NUM
ejpam-6810	473	66	(	(	PUNCT
ejpam-6810	473	67	4	4	NUM
ejpam-6810	473	68	2k	2k	NUM
ejpam-6810	473	69	+	+	CCONJ
ejpam-6810	473	70	ζ	ζ	NOUN
ejpam-6810	473	71	)	)	PUNCT
ejpam-6810	473	72	2	2	NUM
ejpam-6810	473	73	.	.	PUNCT
ejpam-6810	474	1	by	by	ADP
ejpam-6810	474	2	equation	equation	NOUN
ejpam-6810	474	3	(	(	PUNCT
ejpam-6810	474	4	34	34	NUM
ejpam-6810	474	5	)	)	PUNCT
ejpam-6810	474	6	,	,	PUNCT
ejpam-6810	474	7	one	one	PRON
ejpam-6810	474	8	writes	write	VERB
ejpam-6810	474	9	σb(υη	σb(υη	PROPN
ejpam-6810	474	10	,	,	PUNCT
ejpam-6810	474	11	υξ	υξ	NOUN
ejpam-6810	474	12	)	)	PUNCT
ejpam-6810	475	1	+	+	CCONJ
ejpam-6810	475	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	475	3	,	,	PUNCT
ejpam-6810	475	4	υζ	υζ	NOUN
ejpam-6810	475	5	)	)	PUNCT
ejpam-6810	475	6	+	+	CCONJ
ejpam-6810	475	7	σb(υη	σb(υη	PROPN
ejpam-6810	475	8	,	,	PUNCT
ejpam-6810	475	9	υζ	υζ	NOUN
ejpam-6810	475	10	)	)	PUNCT
ejpam-6810	475	11	≤	≤	NOUN
ejpam-6810	475	12	9	9	NUM
ejpam-6810	475	13	16	16	NUM
ejpam-6810	475	14	(	(	PUNCT
ejpam-6810	475	15	σb(η	σb(η	PROPN
ejpam-6810	475	16	,	,	PUNCT
ejpam-6810	475	17	ξ	ξ	NOUN
ejpam-6810	475	18	)	)	PUNCT
ejpam-6810	475	19	+	+	CCONJ
ejpam-6810	475	20	σb(ξ	σb(ξ	ADJ
ejpam-6810	475	21	,	,	PUNCT
ejpam-6810	475	22	ζ	ζ	NOUN
ejpam-6810	475	23	)	)	PUNCT
ejpam-6810	475	24	+	+	NUM
ejpam-6810	475	25	σb(η	σb(η	NUM
ejpam-6810	475	26	,	,	PUNCT
ejpam-6810	475	27	ζ	ζ	NOUN
ejpam-6810	475	28	)	)	PUNCT
ejpam-6810	475	29	)	)	PUNCT
ejpam-6810	475	30	.	.	PUNCT
ejpam-6810	476	1	we	we	PRON
ejpam-6810	476	2	can	can	AUX
ejpam-6810	476	3	see	see	VERB
ejpam-6810	476	4	that	that	SCONJ
ejpam-6810	476	5	it	it	PRON
ejpam-6810	476	6	satisfies	satisfy	VERB
ejpam-6810	476	7	the	the	DET
ejpam-6810	476	8	inequality	inequality	NOUN
ejpam-6810	476	9	(	(	PUNCT
ejpam-6810	476	10	3	3	NUM
ejpam-6810	476	11	)	)	PUNCT
ejpam-6810	476	12	.	.	PUNCT
ejpam-6810	477	1	similarly	similarly	ADV
ejpam-6810	477	2	,	,	PUNCT
ejpam-6810	477	3	for	for	ADP
ejpam-6810	477	4	η	η	PROPN
ejpam-6810	477	5	=	=	PRON
ejpam-6810	477	6	η2k+1	η2k+1	VERB
ejpam-6810	477	7	=	=	PUNCT
ejpam-6810	477	8	−3	−3	NOUN
ejpam-6810	477	9	2k	2k	NOUN
ejpam-6810	477	10	,	,	PUNCT
ejpam-6810	477	11	we	we	PRON
ejpam-6810	477	12	have	have	VERB
ejpam-6810	477	13	σb(η	σb(η	NUM
ejpam-6810	477	14	,	,	PUNCT
ejpam-6810	477	15	ξ	ξ	X
ejpam-6810	477	16	)	)	PUNCT
ejpam-6810	478	1	+	+	CCONJ
ejpam-6810	478	2	σb(ξ	σb(ξ	ADJ
ejpam-6810	478	3	,	,	PUNCT
ejpam-6810	478	4	ζ	ζ	NOUN
ejpam-6810	478	5	)	)	PUNCT
ejpam-6810	478	6	+	+	NUM
ejpam-6810	478	7	σb(η	σb(η	NUM
ejpam-6810	478	8	,	,	PUNCT
ejpam-6810	478	9	ζ	ζ	NOUN
ejpam-6810	478	10	)	)	PUNCT
ejpam-6810	478	11	=	=	SYM
ejpam-6810	478	12	2σb(η	2σb(η	NUM
ejpam-6810	478	13	,	,	PUNCT
ejpam-6810	478	14	ζ	ζ	NOUN
ejpam-6810	478	15	)	)	PUNCT
ejpam-6810	478	16	=	=	SYM
ejpam-6810	478	17	2	2	NUM
ejpam-6810	478	18	(	(	PUNCT
ejpam-6810	478	19	3	3	NUM
ejpam-6810	478	20	2k	2k	NOUN
ejpam-6810	478	21	+	+	CCONJ
ejpam-6810	478	22	ζ	ζ	NOUN
ejpam-6810	478	23	)	)	PUNCT
ejpam-6810	478	24	2	2	NUM
ejpam-6810	478	25	.	.	PUNCT
ejpam-6810	479	1	(	(	PUNCT
ejpam-6810	479	2	35	35	NUM
ejpam-6810	479	3	)	)	PUNCT
ejpam-6810	479	4	s.	s.	PROPN
ejpam-6810	479	5	batul	batul	PROPN
ejpam-6810	479	6	et	et	PROPN
ejpam-6810	479	7	al	al	PROPN
ejpam-6810	479	8	.	.	PUNCT
ejpam-6810	479	9	/	/	SYM
ejpam-6810	479	10	eur	eur	PROPN
ejpam-6810	479	11	.	.	PUNCT
ejpam-6810	480	1	j.	j.	PROPN
ejpam-6810	480	2	pure	pure	PROPN
ejpam-6810	480	3	appl	appl	PROPN
ejpam-6810	480	4	.	.	PROPN
ejpam-6810	480	5	math	math	PROPN
ejpam-6810	480	6	,	,	PUNCT
ejpam-6810	480	7	18	18	NUM
ejpam-6810	480	8	(	(	PUNCT
ejpam-6810	480	9	4	4	NUM
ejpam-6810	480	10	)	)	PUNCT
ejpam-6810	480	11	(	(	PUNCT
ejpam-6810	480	12	2025	2025	NUM
ejpam-6810	480	13	)	)	PUNCT
ejpam-6810	480	14	,	,	PUNCT
ejpam-6810	480	15	6810	6810	NUM
ejpam-6810	480	16	20	20	NUM
ejpam-6810	480	17	of	of	ADP
ejpam-6810	480	18	23	23	NUM
ejpam-6810	480	19	applying	apply	VERB
ejpam-6810	480	20	υ	υ	NOUN
ejpam-6810	480	21	to	to	ADP
ejpam-6810	480	22	η2k+1	η2k+1	ADJ
ejpam-6810	480	23	yields	yield	NOUN
ejpam-6810	480	24	υη2k+1	υη2k+1	VERB
ejpam-6810	480	25	=	=	SYM
ejpam-6810	480	26	η2(k+1	η2(k+1	NOUN
ejpam-6810	480	27	)	)	PUNCT
ejpam-6810	480	28	=	=	SYM
ejpam-6810	481	1	−4	−4	X
ejpam-6810	482	1	2k+1	2k+1	NOUN
ejpam-6810	482	2	.	.	PUNCT
ejpam-6810	483	1	we	we	PRON
ejpam-6810	483	2	get	get	VERB
ejpam-6810	483	3	σb(υη	σb(υη	PROPN
ejpam-6810	483	4	,	,	PUNCT
ejpam-6810	483	5	υξ	υξ	NOUN
ejpam-6810	483	6	)	)	PUNCT
ejpam-6810	484	1	+	+	CCONJ
ejpam-6810	484	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	484	3	,	,	PUNCT
ejpam-6810	484	4	υζ	υζ	NOUN
ejpam-6810	484	5	)	)	PUNCT
ejpam-6810	484	6	+	+	CCONJ
ejpam-6810	484	7	σb(υη	σb(υη	PROPN
ejpam-6810	484	8	,	,	PUNCT
ejpam-6810	484	9	υζ	υζ	NOUN
ejpam-6810	484	10	)	)	PUNCT
ejpam-6810	484	11	=	=	SYM
ejpam-6810	484	12	2σb(υη	2σb(υη	NUM
ejpam-6810	484	13	,	,	PUNCT
ejpam-6810	484	14	υζ	υζ	NOUN
ejpam-6810	484	15	)	)	PUNCT
ejpam-6810	484	16	,	,	PUNCT
ejpam-6810	484	17	=	=	SYM
ejpam-6810	484	18	2	2	NUM
ejpam-6810	484	19	(	(	PUNCT
ejpam-6810	484	20	4	4	NUM
ejpam-6810	484	21	2k+1	2k+1	NOUN
ejpam-6810	484	22	+	+	CCONJ
ejpam-6810	484	23	ζ	ζ	SYM
ejpam-6810	484	24	2	2	NUM
ejpam-6810	484	25	)	)	PUNCT
ejpam-6810	484	26	2	2	NUM
ejpam-6810	484	27	,	,	PUNCT
ejpam-6810	484	28	=	=	NOUN
ejpam-6810	484	29	2	2	NUM
ejpam-6810	484	30	(	(	PUNCT
ejpam-6810	484	31	4	4	NUM
ejpam-6810	484	32	2.2k	2.2k	NUM
ejpam-6810	484	33	+	+	CCONJ
ejpam-6810	484	34	ζ	ζ	NOUN
ejpam-6810	484	35	2	2	NUM
ejpam-6810	484	36	)	)	PUNCT
ejpam-6810	484	37	2	2	NUM
ejpam-6810	484	38	,	,	PUNCT
ejpam-6810	484	39	=	=	SYM
ejpam-6810	484	40	4×	4×	NOUN
ejpam-6810	484	41	2	2	NUM
ejpam-6810	484	42	(	(	PUNCT
ejpam-6810	484	43	1	1	NUM
ejpam-6810	484	44	2k	2k	NUM
ejpam-6810	484	45	+	+	CCONJ
ejpam-6810	484	46	ζ	ζ	SYM
ejpam-6810	484	47	4	4	NUM
ejpam-6810	484	48	)	)	SYM
ejpam-6810	484	49	2	2	NUM
ejpam-6810	484	50	,	,	PUNCT
ejpam-6810	484	51	=	=	NOUN
ejpam-6810	484	52	4	4	NUM
ejpam-6810	484	53	9	9	NUM
ejpam-6810	484	54	×	×	NOUN
ejpam-6810	484	55	2	2	NUM
ejpam-6810	484	56	(	(	PUNCT
ejpam-6810	484	57	3	3	NUM
ejpam-6810	484	58	2k	2k	NUM
ejpam-6810	484	59	+	+	CCONJ
ejpam-6810	484	60	3ζ	3ζ	NOUN
ejpam-6810	484	61	4	4	NUM
ejpam-6810	484	62	)	)	SYM
ejpam-6810	484	63	2	2	NUM
ejpam-6810	484	64	,	,	PUNCT
ejpam-6810	484	65	≤	≤	NUM
ejpam-6810	484	66	4	4	NUM
ejpam-6810	484	67	9	9	NUM
ejpam-6810	484	68	×	×	NOUN
ejpam-6810	484	69	2	2	NUM
ejpam-6810	484	70	(	(	PUNCT
ejpam-6810	484	71	3	3	NUM
ejpam-6810	484	72	2k	2k	NUM
ejpam-6810	484	73	+	+	CCONJ
ejpam-6810	484	74	2ζ	2ζ	NUM
ejpam-6810	484	75	)	)	PUNCT
ejpam-6810	484	76	2	2	NUM
ejpam-6810	484	77	.	.	PUNCT
ejpam-6810	485	1	now	now	ADV
ejpam-6810	485	2	,	,	PUNCT
ejpam-6810	485	3	by	by	ADP
ejpam-6810	485	4	equation	equation	NOUN
ejpam-6810	485	5	(	(	PUNCT
ejpam-6810	485	6	35	35	NUM
ejpam-6810	485	7	)	)	PUNCT
ejpam-6810	485	8	,	,	PUNCT
ejpam-6810	485	9	we	we	PRON
ejpam-6810	485	10	obtain	obtain	VERB
ejpam-6810	485	11	σb(υη	σb(υη	PROPN
ejpam-6810	485	12	,	,	PUNCT
ejpam-6810	485	13	υξ	υξ	NOUN
ejpam-6810	485	14	)	)	PUNCT
ejpam-6810	486	1	+	+	CCONJ
ejpam-6810	486	2	σb(υξ	σb(υξ	PROPN
ejpam-6810	486	3	,	,	PUNCT
ejpam-6810	486	4	υζ	υζ	NOUN
ejpam-6810	486	5	)	)	PUNCT
ejpam-6810	486	6	+	+	CCONJ
ejpam-6810	486	7	σb(υη	σb(υη	PROPN
ejpam-6810	486	8	,	,	PUNCT
ejpam-6810	486	9	υζ	υζ	NOUN
ejpam-6810	486	10	)	)	PUNCT
ejpam-6810	486	11	≤	≤	NUM
ejpam-6810	486	12	2	2	NUM
ejpam-6810	486	13	3	3	NUM
ejpam-6810	486	14	(	(	PUNCT
ejpam-6810	486	15	σb(η	σb(η	NUM
ejpam-6810	486	16	,	,	PUNCT
ejpam-6810	486	17	ξ	ξ	NOUN
ejpam-6810	486	18	)	)	PUNCT
ejpam-6810	486	19	+	+	CCONJ
ejpam-6810	486	20	σb(ξ	σb(ξ	ADJ
ejpam-6810	486	21	,	,	PUNCT
ejpam-6810	486	22	ζ	ζ	NOUN
ejpam-6810	486	23	)	)	PUNCT
ejpam-6810	486	24	+	+	NUM
ejpam-6810	486	25	σb(η	σb(η	NUM
ejpam-6810	486	26	,	,	PUNCT
ejpam-6810	486	27	ζ	ζ	NOUN
ejpam-6810	486	28	)	)	PUNCT
ejpam-6810	486	29	)	)	PUNCT
ejpam-6810	486	30	,	,	PUNCT
ejpam-6810	487	1	which	which	PRON
ejpam-6810	487	2	implies	imply	VERB
ejpam-6810	487	3	that	that	SCONJ
ejpam-6810	487	4	inequality	inequality	NOUN
ejpam-6810	487	5	(	(	PUNCT
ejpam-6810	487	6	3	3	X
ejpam-6810	487	7	)	)	PUNCT
ejpam-6810	487	8	holds	hold	VERB
ejpam-6810	487	9	with	with	ADP
ejpam-6810	487	10	f(η	f(η	NOUN
ejpam-6810	487	11	)	)	PUNCT
ejpam-6810	488	1	=	=	PUNCT
ejpam-6810	488	2	ln(η	ln(η	X
ejpam-6810	488	3	)	)	PUNCT
ejpam-6810	488	4	.	.	PUNCT
ejpam-6810	489	1	3	3	X
ejpam-6810	489	2	.	.	X
ejpam-6810	489	3	conclusion	conclusion	NOUN
ejpam-6810	489	4	using	use	VERB
ejpam-6810	489	5	some	some	DET
ejpam-6810	489	6	well	well	ADV
ejpam-6810	489	7	established	establish	VERB
ejpam-6810	489	8	results	result	NOUN
ejpam-6810	489	9	for	for	ADP
ejpam-6810	489	10	“	"	PUNCT
ejpam-6810	489	11	mappings	mapping	NOUN
ejpam-6810	489	12	contracting	contract	VERB
ejpam-6810	489	13	perimeter	perimeter	NOUN
ejpam-6810	489	14	of	of	ADP
ejpam-6810	489	15	triangles	triangle	NOUN
ejpam-6810	489	16	”	"	PUNCT
ejpam-6810	489	17	the	the	DET
ejpam-6810	489	18	notion	notion	NOUN
ejpam-6810	489	19	of	of	ADP
ejpam-6810	489	20	a	a	DET
ejpam-6810	489	21	“	"	PUNCT
ejpam-6810	489	22	mapping	mapping	NOUN
ejpam-6810	489	23	contracting	contracting	NOUN
ejpam-6810	489	24	perimeters	perimeter	NOUN
ejpam-6810	489	25	of	of	ADP
ejpam-6810	489	26	triangles	triangle	NOUN
ejpam-6810	489	27	(	(	PUNCT
ejpam-6810	489	28	mcpt	mcpt	NOUN
ejpam-6810	489	29	)	)	PUNCT
ejpam-6810	489	30	embedded	embed	VERB
ejpam-6810	489	31	with	with	ADP
ejpam-6810	489	32	an	an	DET
ejpam-6810	489	33	f	f	NOUN
ejpam-6810	489	34	-	-	PUNCT
ejpam-6810	489	35	contraction	contraction	NOUN
ejpam-6810	489	36	in	in	ADP
ejpam-6810	489	37	a	a	DET
ejpam-6810	489	38	b	b	NOUN
ejpam-6810	489	39	-	-	PUNCT
ejpam-6810	489	40	metric	metric	ADJ
ejpam-6810	489	41	space	space	NOUN
ejpam-6810	489	42	(	(	PUNCT
ejpam-6810	489	43	b	b	X
ejpam-6810	489	44	-	-	PUNCT
ejpam-6810	489	45	ms	ms	NOUN
ejpam-6810	489	46	)	)	PUNCT
ejpam-6810	489	47	”	"	PUNCT
ejpam-6810	489	48	has	have	AUX
ejpam-6810	489	49	been	be	AUX
ejpam-6810	489	50	introduced	introduce	VERB
ejpam-6810	489	51	.	.	PUNCT
ejpam-6810	490	1	the	the	DET
ejpam-6810	490	2	fp	fp	PROPN
ejpam-6810	490	3	theorem	theorem	NOUN
ejpam-6810	490	4	has	have	AUX
ejpam-6810	490	5	been	be	AUX
ejpam-6810	490	6	proved	prove	VERB
ejpam-6810	490	7	and	and	CCONJ
ejpam-6810	490	8	classical	classical	ADJ
ejpam-6810	490	9	banach	banach	NOUN
ejpam-6810	490	10	fp	fp	PROPN
ejpam-6810	490	11	theorem	theorem	NOUN
ejpam-6810	490	12	is	be	AUX
ejpam-6810	490	13	derived	derive	VERB
ejpam-6810	490	14	as	as	ADP
ejpam-6810	490	15	a	a	DET
ejpam-6810	490	16	simple	simple	ADJ
ejpam-6810	490	17	corollary	corollary	NOUN
ejpam-6810	490	18	.	.	PUNCT
ejpam-6810	491	1	examples	example	NOUN
ejpam-6810	491	2	of	of	ADP
ejpam-6810	491	3	a	a	DET
ejpam-6810	491	4	mcpt	mcpt	NOUN
ejpam-6810	491	5	embedded	embed	VERB
ejpam-6810	491	6	with	with	ADP
ejpam-6810	491	7	an	an	DET
ejpam-6810	491	8	f	f	NOUN
ejpam-6810	491	9	-	-	PUNCT
ejpam-6810	491	10	contraction	contraction	NOUN
ejpam-6810	491	11	which	which	PRON
ejpam-6810	491	12	are	be	AUX
ejpam-6810	491	13	not	not	PART
ejpam-6810	491	14	contraction	contraction	NOUN
ejpam-6810	491	15	mappings	mapping	NOUN
ejpam-6810	491	16	in	in	ADP
ejpam-6810	491	17	the	the	DET
ejpam-6810	491	18	framework	framework	NOUN
ejpam-6810	491	19	of	of	ADP
ejpam-6810	491	20	a	a	DET
ejpam-6810	491	21	b	b	NOUN
ejpam-6810	491	22	-	-	PUNCT
ejpam-6810	491	23	ms	ms	NOUN
ejpam-6810	491	24	have	have	AUX
ejpam-6810	491	25	been	be	AUX
ejpam-6810	491	26	established	establish	VERB
ejpam-6810	491	27	.	.	PUNCT
ejpam-6810	492	1	these	these	DET
ejpam-6810	492	2	results	result	NOUN
ejpam-6810	492	3	open	open	VERB
ejpam-6810	492	4	avenues	avenue	NOUN
ejpam-6810	492	5	for	for	ADP
ejpam-6810	492	6	further	further	ADJ
ejpam-6810	492	7	research	research	NOUN
ejpam-6810	492	8	.	.	PUNCT
ejpam-6810	493	1	future	future	ADJ
ejpam-6810	493	2	work	work	NOUN
ejpam-6810	493	3	may	may	AUX
ejpam-6810	493	4	explore	explore	VERB
ejpam-6810	493	5	the	the	DET
ejpam-6810	493	6	application	application	NOUN
ejpam-6810	493	7	of	of	ADP
ejpam-6810	493	8	this	this	DET
ejpam-6810	493	9	framework	framework	NOUN
ejpam-6810	493	10	in	in	ADP
ejpam-6810	493	11	controlled	control	VERB
ejpam-6810	493	12	,	,	PUNCT
ejpam-6810	493	13	double	double	PROPN
ejpam-6810	493	14	controlled	control	VERB
ejpam-6810	493	15	,	,	PUNCT
ejpam-6810	493	16	partial	partial	ADJ
ejpam-6810	493	17	and	and	CCONJ
ejpam-6810	493	18	cone	cone	NOUN
ejpam-6810	493	19	b	b	PROPN
ejpam-6810	493	20	-	-	PUNCT
ejpam-6810	493	21	mss	mss	PROPN
ejpam-6810	493	22	.	.	PUNCT
ejpam-6810	494	1	authors	author	NOUN
ejpam-6810	494	2	’	'	PUNCT
ejpam-6810	494	3	contributions	contribution	NOUN
ejpam-6810	494	4	all	all	DET
ejpam-6810	494	5	authors	author	NOUN
ejpam-6810	494	6	contribute	contribute	VERB
ejpam-6810	494	7	equally	equally	ADV
ejpam-6810	494	8	in	in	ADP
ejpam-6810	494	9	this	this	DET
ejpam-6810	494	10	paper	paper	NOUN
ejpam-6810	494	11	.	.	PUNCT
ejpam-6810	495	1	acknowledgements	acknowledgement	NOUN
ejpam-6810	495	2	we	we	PRON
ejpam-6810	495	3	acknowledge	acknowledge	VERB
ejpam-6810	495	4	the	the	DET
ejpam-6810	495	5	support	support	NOUN
ejpam-6810	495	6	of	of	ADP
ejpam-6810	495	7	this	this	DET
ejpam-6810	495	8	research	research	NOUN
ejpam-6810	495	9	from	from	ADP
ejpam-6810	495	10	al	al	PROPN
ejpam-6810	495	11	-	-	PROPN
ejpam-6810	495	12	zaytoonah	zaytoonah	PROPN
ejpam-6810	495	13	university	university	PROPN
ejpam-6810	495	14	.	.	PUNCT
ejpam-6810	496	1	s.	s.	PROPN
ejpam-6810	496	2	batul	batul	PROPN
ejpam-6810	496	3	et	et	PROPN
ejpam-6810	496	4	al	al	PROPN
ejpam-6810	496	5	.	.	PUNCT
ejpam-6810	496	6	/	/	SYM
ejpam-6810	496	7	eur	eur	PROPN
ejpam-6810	496	8	.	.	PUNCT
ejpam-6810	497	1	j.	j.	PROPN
ejpam-6810	497	2	pure	pure	PROPN
ejpam-6810	497	3	appl	appl	PROPN
ejpam-6810	497	4	.	.	PROPN
ejpam-6810	497	5	math	math	PROPN
ejpam-6810	497	6	,	,	PUNCT
ejpam-6810	497	7	18	18	NUM
ejpam-6810	497	8	(	(	PUNCT
ejpam-6810	497	9	4	4	NUM
ejpam-6810	497	10	)	)	PUNCT
ejpam-6810	497	11	(	(	PUNCT
ejpam-6810	497	12	2025	2025	NUM
ejpam-6810	497	13	)	)	PUNCT
ejpam-6810	497	14	,	,	PUNCT
ejpam-6810	497	15	6810	6810	NUM
ejpam-6810	497	16	21	21	NUM
ejpam-6810	497	17	of	of	ADP
ejpam-6810	497	18	23	23	NUM
ejpam-6810	497	19	conflict	conflict	NOUN
ejpam-6810	497	20	of	of	ADP
ejpam-6810	497	21	interest	interest	NOUN
ejpam-6810	497	22	the	the	DET
ejpam-6810	497	23	authors	author	NOUN
ejpam-6810	497	24	declare	declare	VERB
ejpam-6810	497	25	that	that	SCONJ
ejpam-6810	497	26	they	they	PRON
ejpam-6810	497	27	have	have	VERB
ejpam-6810	497	28	no	no	DET
ejpam-6810	497	29	conflict	conflict	NOUN
ejpam-6810	497	30	of	of	ADP
ejpam-6810	497	31	interest	interest	NOUN
ejpam-6810	497	32	.	.	PUNCT
ejpam-6810	498	1	references	reference	NOUN
ejpam-6810	498	2	[	[	X
ejpam-6810	498	3	1	1	X
ejpam-6810	498	4	]	]	PUNCT
ejpam-6810	498	5	d.	d.	PROPN
ejpam-6810	498	6	judeh	judeh	PROPN
ejpam-6810	498	7	and	and	CCONJ
ejpam-6810	498	8	m.	m.	PROPN
ejpam-6810	498	9	abu	abu	PROPN
ejpam-6810	498	10	hammad	hammad	PROPN
ejpam-6810	498	11	.	.	PUNCT
ejpam-6810	499	1	applications	application	NOUN
ejpam-6810	499	2	of	of	ADP
ejpam-6810	499	3	conformable	conformable	ADJ
ejpam-6810	499	4	fractional	fractional	ADJ
ejpam-6810	499	5	pareto	pareto	ADJ
ejpam-6810	499	6	probability	probability	NOUN
ejpam-6810	499	7	distribution	distribution	NOUN
ejpam-6810	499	8	.	.	PUNCT
ejpam-6810	500	1	international	international	ADJ
ejpam-6810	500	2	journal	journal	NOUN
ejpam-6810	500	3	of	of	ADP
ejpam-6810	500	4	advances	advance	NOUN
ejpam-6810	500	5	in	in	ADP
ejpam-6810	500	6	soft	soft	ADJ
ejpam-6810	500	7	computing	computing	NOUN
ejpam-6810	500	8	and	and	CCONJ
ejpam-6810	500	9	its	its	PRON
ejpam-6810	500	10	applications	application	NOUN
ejpam-6810	500	11	,	,	PUNCT
ejpam-6810	500	12	14(2):116–124	14(2):116–124	PROPN
ejpam-6810	500	13	,	,	PUNCT
ejpam-6810	500	14	2022	2022	NUM
ejpam-6810	500	15	.	.	PUNCT
ejpam-6810	501	1	[	[	X
ejpam-6810	501	2	2	2	X
ejpam-6810	501	3	]	]	PUNCT
ejpam-6810	501	4	t.	t.	PROPN
ejpam-6810	501	5	kanan	kanan	PROPN
ejpam-6810	501	6	,	,	PUNCT
ejpam-6810	501	7	m.	m.	NOUN
ejpam-6810	501	8	elbes	elbes	PROPN
ejpam-6810	501	9	,	,	PUNCT
ejpam-6810	501	10	k.	k.	PROPN
ejpam-6810	501	11	abu	abu	PROPN
ejpam-6810	501	12	maria	maria	PROPN
ejpam-6810	501	13	,	,	PUNCT
ejpam-6810	501	14	and	and	CCONJ
ejpam-6810	501	15	m.	m.	NOUN
ejpam-6810	501	16	alia	alia	PROPN
ejpam-6810	501	17	.	.	PUNCT
ejpam-6810	502	1	exploring	explore	VERB
ejpam-6810	502	2	the	the	DET
ejpam-6810	502	3	potential	potential	NOUN
ejpam-6810	502	4	of	of	ADP
ejpam-6810	502	5	iotbased	iotbase	VERB
ejpam-6810	502	6	learning	learn	VERB
ejpam-6810	502	7	environments	environment	NOUN
ejpam-6810	502	8	in	in	ADP
ejpam-6810	502	9	education	education	NOUN
ejpam-6810	502	10	.	.	PUNCT
ejpam-6810	503	1	international	international	ADJ
ejpam-6810	503	2	journal	journal	NOUN
ejpam-6810	503	3	of	of	ADP
ejpam-6810	503	4	advances	advance	NOUN
ejpam-6810	503	5	in	in	ADP
ejpam-6810	503	6	soft	soft	ADJ
ejpam-6810	503	7	computing	computing	NOUN
ejpam-6810	503	8	and	and	CCONJ
ejpam-6810	503	9	its	its	PRON
ejpam-6810	503	10	applications	application	NOUN
ejpam-6810	503	11	,	,	PUNCT
ejpam-6810	503	12	15(2	15(2	NUM
ejpam-6810	503	13	)	)	PUNCT
ejpam-6810	503	14	,	,	PUNCT
ejpam-6810	503	15	2023	2023	NUM
ejpam-6810	503	16	.	.	PUNCT
ejpam-6810	504	1	[	[	X
ejpam-6810	504	2	3	3	X
ejpam-6810	504	3	]	]	X
ejpam-6810	504	4	h.	h.	PROPN
ejpam-6810	504	5	qawaqneh	qawaqneh	PROPN
ejpam-6810	504	6	,	,	PUNCT
ejpam-6810	504	7	m.	m.	PROPN
ejpam-6810	504	8	s.	s.	PROPN
ejpam-6810	504	9	noorani	noorani	PROPN
ejpam-6810	504	10	,	,	PUNCT
ejpam-6810	504	11	h.	h.	PROPN
ejpam-6810	504	12	aydi	aydi	PROPN
ejpam-6810	504	13	,	,	PUNCT
ejpam-6810	504	14	a.	a.	NOUN
ejpam-6810	504	15	zraiqat	zraiqat	PROPN
ejpam-6810	504	16	,	,	PUNCT
ejpam-6810	504	17	and	and	CCONJ
ejpam-6810	504	18	a.	a.	NOUN
ejpam-6810	504	19	h.	h.	PROPN
ejpam-6810	504	20	ansari	ansari	PROPN
ejpam-6810	504	21	.	.	PUNCT
ejpam-6810	505	1	on	on	ADP
ejpam-6810	505	2	fixed	fix	VERB
ejpam-6810	505	3	pointresults	pointresult	NOUN
ejpam-6810	505	4	in	in	ADP
ejpam-6810	505	5	partial	partial	ADJ
ejpam-6810	505	6	b	b	NOUN
ejpam-6810	505	7	-	-	PUNCT
ejpam-6810	505	8	metric	metric	ADJ
ejpam-6810	505	9	spaces	space	NOUN
ejpam-6810	505	10	.	.	PUNCT
ejpam-6810	506	1	journal	journal	NOUN
ejpam-6810	506	2	of	of	ADP
ejpam-6810	506	3	function	function	NOUN
ejpam-6810	506	4	spaces	space	NOUN
ejpam-6810	506	5	,	,	PUNCT
ejpam-6810	506	6	8769190:9	8769190:9	NUM
ejpam-6810	506	7	pages	page	NOUN
ejpam-6810	506	8	,	,	PUNCT
ejpam-6810	506	9	2021	2021	NUM
ejpam-6810	506	10	.	.	PUNCT
ejpam-6810	507	1	[	[	X
ejpam-6810	507	2	4	4	X
ejpam-6810	507	3	]	]	X
ejpam-6810	507	4	h.	h.	PROPN
ejpam-6810	507	5	qawaqneh	qawaqneh	PROPN
ejpam-6810	507	6	,	,	PUNCT
ejpam-6810	507	7	m.	m.	PROPN
ejpam-6810	507	8	s.	s.	PROPN
ejpam-6810	507	9	noorani	noorani	PROPN
ejpam-6810	507	10	,	,	PUNCT
ejpam-6810	507	11	and	and	CCONJ
ejpam-6810	507	12	h.	h.	PROPN
ejpam-6810	507	13	aydi	aydi	VERB
ejpam-6810	507	14	.	.	PUNCT
ejpam-6810	508	1	some	some	DET
ejpam-6810	508	2	new	new	ADJ
ejpam-6810	508	3	characterizations	characterization	NOUN
ejpam-6810	508	4	and	and	CCONJ
ejpam-6810	508	5	results	result	NOUN
ejpam-6810	508	6	for	for	ADP
ejpam-6810	508	7	fuzzy	fuzzy	ADJ
ejpam-6810	508	8	contractions	contraction	NOUN
ejpam-6810	508	9	in	in	ADP
ejpam-6810	508	10	fuzzy	fuzzy	ADJ
ejpam-6810	508	11	b	b	X
ejpam-6810	508	12	-	-	PUNCT
ejpam-6810	508	13	metric	metric	ADJ
ejpam-6810	508	14	spaces	space	NOUN
ejpam-6810	508	15	and	and	CCONJ
ejpam-6810	508	16	applications	application	NOUN
ejpam-6810	508	17	.	.	PUNCT
ejpam-6810	509	1	aims	aim	VERB
ejpam-6810	509	2	mathematics	mathematic	NOUN
ejpam-6810	509	3	,	,	PUNCT
ejpam-6810	509	4	8:6682–6696	8:6682–6696	NUM
ejpam-6810	509	5	,	,	PUNCT
ejpam-6810	509	6	2023	2023	NUM
ejpam-6810	509	7	.	.	PUNCT
ejpam-6810	510	1	[	[	X
ejpam-6810	510	2	5	5	X
ejpam-6810	510	3	]	]	PUNCT
ejpam-6810	510	4	h.	h.	PROPN
ejpam-6810	510	5	qawaqneh	qawaqneh	PROPN
ejpam-6810	510	6	,	,	PUNCT
ejpam-6810	510	7	h.	h.	PROPN
ejpam-6810	510	8	a.	a.	PROPN
ejpam-6810	510	9	hammad	hammad	PROPN
ejpam-6810	510	10	,	,	PUNCT
ejpam-6810	510	11	and	and	CCONJ
ejpam-6810	510	12	h.	h.	PROPN
ejpam-6810	510	13	aydi	aydi	VERB
ejpam-6810	510	14	.	.	PUNCT
ejpam-6810	511	1	exploring	explore	VERB
ejpam-6810	511	2	new	new	ADJ
ejpam-6810	511	3	geometric	geometric	ADJ
ejpam-6810	511	4	contraction	contraction	NOUN
ejpam-6810	511	5	mappings	mapping	NOUN
ejpam-6810	511	6	and	and	CCONJ
ejpam-6810	511	7	their	their	PRON
ejpam-6810	511	8	applications	application	NOUN
ejpam-6810	511	9	in	in	ADP
ejpam-6810	511	10	fractional	fractional	ADJ
ejpam-6810	511	11	metric	metric	ADJ
ejpam-6810	511	12	spaces	space	NOUN
ejpam-6810	511	13	.	.	PUNCT
ejpam-6810	512	1	aims	aim	VERB
ejpam-6810	512	2	mathematics	mathematic	NOUN
ejpam-6810	512	3	,	,	PUNCT
ejpam-6810	512	4	9:521–541	9:521–541	NUM
ejpam-6810	512	5	,	,	PUNCT
ejpam-6810	512	6	2024	2024	NUM
ejpam-6810	512	7	.	.	PUNCT
ejpam-6810	513	1	[	[	X
ejpam-6810	513	2	6	6	NUM
ejpam-6810	513	3	]	]	PUNCT
ejpam-6810	513	4	m.	m.	NOUN
ejpam-6810	513	5	nazam	nazam	PROPN
ejpam-6810	513	6	,	,	PUNCT
ejpam-6810	513	7	h.	h.	PROPN
ejpam-6810	513	8	aydi	aydi	PROPN
ejpam-6810	513	9	,	,	PUNCT
ejpam-6810	513	10	m.s	m.s	PROPN
ejpam-6810	513	11	.	.	PROPN
ejpam-6810	513	12	noorani	noorani	PROPN
ejpam-6810	513	13	,	,	PUNCT
ejpam-6810	513	14	and	and	CCONJ
ejpam-6810	513	15	h.	h.	PROPN
ejpam-6810	513	16	qawaqneh	qawaqneh	PROPN
ejpam-6810	513	17	.	.	PUNCT
ejpam-6810	514	1	existence	existence	NOUN
ejpam-6810	514	2	of	of	ADP
ejpam-6810	514	3	fixed	fix	VERB
ejpam-6810	514	4	points	point	NOUN
ejpam-6810	514	5	of	of	ADP
ejpam-6810	514	6	four	four	NUM
ejpam-6810	514	7	maps	map	NOUN
ejpam-6810	514	8	for	for	ADP
ejpam-6810	514	9	a	a	DET
ejpam-6810	514	10	new	new	ADJ
ejpam-6810	514	11	generalized	generalized	ADJ
ejpam-6810	514	12	f−contraction	f−contraction	NOUN
ejpam-6810	514	13	and	and	CCONJ
ejpam-6810	514	14	an	an	DET
ejpam-6810	514	15	application	application	NOUN
ejpam-6810	514	16	.	.	PUNCT
ejpam-6810	515	1	journal	journal	NOUN
ejpam-6810	515	2	of	of	ADP
ejpam-6810	515	3	function	function	NOUN
ejpam-6810	515	4	spaces	space	NOUN
ejpam-6810	515	5	,	,	PUNCT
ejpam-6810	515	6	5980312:8	5980312:8	NUM
ejpam-6810	515	7	pages	page	NOUN
ejpam-6810	515	8	,	,	PUNCT
ejpam-6810	515	9	2019	2019	NUM
ejpam-6810	515	10	.	.	PUNCT
ejpam-6810	516	1	[	[	X
ejpam-6810	516	2	7	7	X
ejpam-6810	516	3	]	]	X
ejpam-6810	516	4	h.	h.	PROPN
ejpam-6810	516	5	qawaqneh	qawaqneh	PROPN
ejpam-6810	516	6	,	,	PUNCT
ejpam-6810	516	7	m.	m.	PROPN
ejpam-6810	516	8	s.	s.	PROPN
ejpam-6810	516	9	noorani	noorani	PROPN
ejpam-6810	516	10	,	,	PUNCT
ejpam-6810	516	11	h.	h.	PROPN
ejpam-6810	516	12	aydi	aydi	PROPN
ejpam-6810	516	13	,	,	PUNCT
ejpam-6810	516	14	and	and	CCONJ
ejpam-6810	516	15	w.	w.	PROPN
ejpam-6810	516	16	shatanawi	shatanawi	PROPN
ejpam-6810	516	17	.	.	PUNCT
ejpam-6810	517	1	on	on	ADP
ejpam-6810	517	2	common	common	ADJ
ejpam-6810	517	3	fixed	fix	VERB
ejpam-6810	517	4	point	point	NOUN
ejpam-6810	517	5	results	result	NOUN
ejpam-6810	517	6	for	for	ADP
ejpam-6810	517	7	new	new	ADJ
ejpam-6810	517	8	contractions	contraction	NOUN
ejpam-6810	517	9	with	with	ADP
ejpam-6810	517	10	applications	application	NOUN
ejpam-6810	517	11	to	to	PART
ejpam-6810	517	12	graph	graph	VERB
ejpam-6810	517	13	and	and	CCONJ
ejpam-6810	517	14	integral	integral	ADJ
ejpam-6810	517	15	equations	equation	NOUN
ejpam-6810	517	16	.	.	PUNCT
ejpam-6810	518	1	mathematics	mathematic	NOUN
ejpam-6810	518	2	,	,	PUNCT
ejpam-6810	518	3	7:1082	7:1082	NUM
ejpam-6810	518	4	,	,	PUNCT
ejpam-6810	518	5	2019	2019	NUM
ejpam-6810	518	6	.	.	PUNCT
ejpam-6810	519	1	[	[	X
ejpam-6810	519	2	8	8	NUM
ejpam-6810	519	3	]	]	X
ejpam-6810	519	4	m.	m.	NOUN
ejpam-6810	519	5	elbes	elbes	PROPN
ejpam-6810	519	6	,	,	PUNCT
ejpam-6810	519	7	kanan	kanan	PROPN
ejpam-6810	519	8	t.	t.	PROPN
ejpam-6810	519	9	,	,	PUNCT
ejpam-6810	519	10	m.	m.	NOUN
ejpam-6810	519	11	alia	alia	PROPN
ejpam-6810	519	12	,	,	PUNCT
ejpam-6810	519	13	and	and	CCONJ
ejpam-6810	519	14	ziad	ziad	PROPN
ejpam-6810	519	15	m.	m.	NOUN
ejpam-6810	519	16	covd-19	covd-19	PROPN
ejpam-6810	519	17	detection	detection	NOUN
ejpam-6810	519	18	platform	platform	NOUN
ejpam-6810	519	19	from	from	ADP
ejpam-6810	519	20	x	x	ADJ
ejpam-6810	519	21	-	-	NOUN
ejpam-6810	519	22	ray	ray	NOUN
ejpam-6810	519	23	images	image	NOUN
ejpam-6810	519	24	using	use	VERB
ejpam-6810	519	25	deep	deep	ADJ
ejpam-6810	519	26	learning	learning	NOUN
ejpam-6810	519	27	.	.	PUNCT
ejpam-6810	520	1	international	international	ADJ
ejpam-6810	520	2	journal	journal	NOUN
ejpam-6810	520	3	of	of	ADP
ejpam-6810	520	4	advances	advance	NOUN
ejpam-6810	520	5	in	in	ADP
ejpam-6810	520	6	soft	soft	ADJ
ejpam-6810	520	7	computing	computing	NOUN
ejpam-6810	520	8	and	and	CCONJ
ejpam-6810	520	9	its	its	PRON
ejpam-6810	520	10	applications	application	NOUN
ejpam-6810	520	11	,	,	PUNCT
ejpam-6810	520	12	14(1	14(1	NUM
ejpam-6810	520	13	)	)	PUNCT
ejpam-6810	520	14	,	,	PUNCT
ejpam-6810	520	15	2022	2022	NUM
ejpam-6810	520	16	.	.	PUNCT
ejpam-6810	521	1	[	[	X
ejpam-6810	521	2	9	9	NUM
ejpam-6810	521	3	]	]	PUNCT
ejpam-6810	521	4	haitham	haitham	PROPN
ejpam-6810	521	5	qawaqneh	qawaqneh	PROPN
ejpam-6810	521	6	.	.	PUNCT
ejpam-6810	522	1	new	new	ADJ
ejpam-6810	522	2	functions	function	NOUN
ejpam-6810	522	3	for	for	ADP
ejpam-6810	522	4	fixed	fix	VERB
ejpam-6810	522	5	point	point	NOUN
ejpam-6810	522	6	results	result	NOUN
ejpam-6810	522	7	in	in	ADP
ejpam-6810	522	8	metric	metric	ADJ
ejpam-6810	522	9	spaces	space	NOUN
ejpam-6810	522	10	with	with	ADP
ejpam-6810	522	11	some	some	DET
ejpam-6810	522	12	applications	application	NOUN
ejpam-6810	522	13	.	.	PUNCT
ejpam-6810	523	1	indian	indian	ADJ
ejpam-6810	523	2	journal	journal	PROPN
ejpam-6810	523	3	of	of	ADP
ejpam-6810	523	4	mathematics	mathematic	NOUN
ejpam-6810	523	5	,	,	PUNCT
ejpam-6810	523	6	66(1):55–84	66(1):55–84	NOUN
ejpam-6810	523	7	,	,	PUNCT
ejpam-6810	523	8	2024	2024	NUM
ejpam-6810	523	9	.	.	PUNCT
ejpam-6810	524	1	[	[	X
ejpam-6810	524	2	10	10	NUM
ejpam-6810	524	3	]	]	X
ejpam-6810	524	4	stefan	stefan	PROPN
ejpam-6810	524	5	banach	banach	PROPN
ejpam-6810	524	6	.	.	PUNCT
ejpam-6810	525	1	sur	sur	PROPN
ejpam-6810	525	2	les	les	PROPN
ejpam-6810	525	3	opérations	opération	NOUN
ejpam-6810	525	4	dans	dan	NOUN
ejpam-6810	525	5	les	les	X
ejpam-6810	525	6	ensembles	ensemble	NOUN
ejpam-6810	525	7	abstraits	abstrait	NOUN
ejpam-6810	525	8	et	et	PROPN
ejpam-6810	525	9	leur	leur	X
ejpam-6810	525	10	application	application	PROPN
ejpam-6810	525	11	aux	aux	PROPN
ejpam-6810	525	12	équations	équations	PROPN
ejpam-6810	525	13	intégrales	intégrale	NOUN
ejpam-6810	525	14	.	.	PUNCT
ejpam-6810	526	1	fundamenta	fundamenta	PROPN
ejpam-6810	526	2	mathematicae	mathematicae	PROPN
ejpam-6810	526	3	,	,	PUNCT
ejpam-6810	526	4	3:133–181	3:133–181	NUM
ejpam-6810	526	5	,	,	PUNCT
ejpam-6810	526	6	1922	1922	NUM
ejpam-6810	526	7	.	.	PUNCT
ejpam-6810	527	1	[	[	X
ejpam-6810	527	2	11	11	NUM
ejpam-6810	527	3	]	]	X
ejpam-6810	527	4	david	david	PROPN
ejpam-6810	527	5	william	william	PROPN
ejpam-6810	527	6	boyd	boyd	PROPN
ejpam-6810	527	7	and	and	CCONJ
ejpam-6810	527	8	james	james	PROPN
ejpam-6810	527	9	sw	sw	PROPN
ejpam-6810	527	10	wong	wong	PROPN
ejpam-6810	527	11	.	.	PUNCT
ejpam-6810	528	1	on	on	ADP
ejpam-6810	528	2	nonlinear	nonlinear	ADJ
ejpam-6810	528	3	contractions	contraction	NOUN
ejpam-6810	528	4	.	.	PUNCT
ejpam-6810	529	1	proceedings	proceeding	NOUN
ejpam-6810	529	2	of	of	ADP
ejpam-6810	529	3	the	the	DET
ejpam-6810	529	4	american	american	PROPN
ejpam-6810	529	5	mathematical	mathematical	PROPN
ejpam-6810	529	6	society	society	NOUN
ejpam-6810	529	7	,	,	PUNCT
ejpam-6810	529	8	20(2):458–464	20(2):458–464	NUM
ejpam-6810	529	9	,	,	PUNCT
ejpam-6810	529	10	1969	1969	NUM
ejpam-6810	529	11	.	.	PUNCT
ejpam-6810	530	1	[	[	X
ejpam-6810	530	2	12	12	NUM
ejpam-6810	530	3	]	]	X
ejpam-6810	530	4	mehdi	mehdi	NOUN
ejpam-6810	530	5	asadi	asadi	NOUN
ejpam-6810	530	6	.	.	PUNCT
ejpam-6810	531	1	fixed	fix	VERB
ejpam-6810	531	2	point	point	NOUN
ejpam-6810	531	3	theorems	theorem	NOUN
ejpam-6810	531	4	for	for	ADP
ejpam-6810	531	5	meir	meir	PROPN
ejpam-6810	531	6	-	-	PUNCT
ejpam-6810	531	7	keeler	keeler	PROPN
ejpam-6810	531	8	type	type	NOUN
ejpam-6810	531	9	mappings	mapping	NOUN
ejpam-6810	531	10	in	in	ADP
ejpam-6810	531	11	m	m	ADJ
ejpam-6810	531	12	-	-	ADJ
ejpam-6810	531	13	metric	metric	ADJ
ejpam-6810	531	14	spaces	space	NOUN
ejpam-6810	531	15	with	with	ADP
ejpam-6810	531	16	applications	application	NOUN
ejpam-6810	531	17	.	.	PUNCT
ejpam-6810	532	1	fixed	fix	VERB
ejpam-6810	532	2	point	point	NOUN
ejpam-6810	532	3	theory	theory	NOUN
ejpam-6810	532	4	and	and	CCONJ
ejpam-6810	532	5	applications	application	NOUN
ejpam-6810	532	6	,	,	PUNCT
ejpam-6810	532	7	2015(1):210	2015(1):210	NUM
ejpam-6810	532	8	,	,	PUNCT
ejpam-6810	532	9	2015	2015	NUM
ejpam-6810	532	10	.	.	PUNCT
ejpam-6810	533	1	[	[	X
ejpam-6810	533	2	13	13	NUM
ejpam-6810	533	3	]	]	PUNCT
ejpam-6810	533	4	emmett	emmett	PROPN
ejpam-6810	533	5	keeler	keeler	PROPN
ejpam-6810	533	6	and	and	CCONJ
ejpam-6810	533	7	a	a	DET
ejpam-6810	533	8	meir	meir	PROPN
ejpam-6810	533	9	.	.	PUNCT
ejpam-6810	534	1	a	a	DET
ejpam-6810	534	2	theorem	theorem	NOUN
ejpam-6810	534	3	on	on	ADP
ejpam-6810	534	4	contraction	contraction	NOUN
ejpam-6810	534	5	mappings	mapping	NOUN
ejpam-6810	534	6	.	.	PUNCT
ejpam-6810	535	1	j.	j.	PROPN
ejpam-6810	535	2	math	math	PROPN
ejpam-6810	535	3	.	.	PUNCT
ejpam-6810	536	1	anal	anal	PROPN
ejpam-6810	536	2	.	.	PUNCT
ejpam-6810	537	1	appl	appl	PROPN
ejpam-6810	537	2	,	,	PUNCT
ejpam-6810	537	3	28(1):326–329	28(1):326–329	PROPN
ejpam-6810	537	4	,	,	PUNCT
ejpam-6810	537	5	1969	1969	NUM
ejpam-6810	537	6	.	.	PUNCT
ejpam-6810	538	1	[	[	X
ejpam-6810	538	2	14	14	NUM
ejpam-6810	538	3	]	]	X
ejpam-6810	538	4	tomonari	tomonari	PROPN
ejpam-6810	538	5	suzuki	suzuki	PROPN
ejpam-6810	538	6	.	.	PUNCT
ejpam-6810	539	1	generalized	generalized	ADJ
ejpam-6810	539	2	distance	distance	NOUN
ejpam-6810	539	3	and	and	CCONJ
ejpam-6810	539	4	existence	existence	NOUN
ejpam-6810	539	5	theorems	theorem	VERB
ejpam-6810	539	6	in	in	ADP
ejpam-6810	539	7	complete	complete	ADJ
ejpam-6810	539	8	metric	metric	ADJ
ejpam-6810	539	9	spaces	space	NOUN
ejpam-6810	539	10	.	.	PUNCT
ejpam-6810	540	1	journal	journal	NOUN
ejpam-6810	540	2	of	of	ADP
ejpam-6810	540	3	mathematical	mathematical	ADJ
ejpam-6810	540	4	analysis	analysis	NOUN
ejpam-6810	540	5	and	and	CCONJ
ejpam-6810	540	6	applications	application	NOUN
ejpam-6810	540	7	,	,	PUNCT
ejpam-6810	540	8	253(2):440–458	253(2):440–458	NUM
ejpam-6810	540	9	,	,	PUNCT
ejpam-6810	540	10	2001	2001	NUM
ejpam-6810	540	11	.	.	PUNCT
ejpam-6810	541	1	s.	s.	PROPN
ejpam-6810	541	2	batul	batul	PROPN
ejpam-6810	541	3	et	et	PROPN
ejpam-6810	541	4	al	al	PROPN
ejpam-6810	541	5	.	.	PUNCT
ejpam-6810	541	6	/	/	SYM
ejpam-6810	541	7	eur	eur	PROPN
ejpam-6810	541	8	.	.	PUNCT
ejpam-6810	542	1	j.	j.	PROPN
ejpam-6810	542	2	pure	pure	PROPN
ejpam-6810	542	3	appl	appl	PROPN
ejpam-6810	542	4	.	.	PROPN
ejpam-6810	542	5	math	math	PROPN
ejpam-6810	542	6	,	,	PUNCT
ejpam-6810	542	7	18	18	NUM
ejpam-6810	542	8	(	(	PUNCT
ejpam-6810	542	9	4	4	NUM
ejpam-6810	542	10	)	)	PUNCT
ejpam-6810	542	11	(	(	PUNCT
ejpam-6810	542	12	2025	2025	NUM
ejpam-6810	542	13	)	)	PUNCT
ejpam-6810	542	14	,	,	PUNCT
ejpam-6810	542	15	6810	6810	NUM
ejpam-6810	542	16	22	22	NUM
ejpam-6810	542	17	of	of	ADP
ejpam-6810	542	18	23	23	NUM
ejpam-6810	543	1	[	[	SYM
ejpam-6810	543	2	15	15	NUM
ejpam-6810	543	3	]	]	X
ejpam-6810	543	4	rangachary	rangachary	PROPN
ejpam-6810	543	5	kannan	kannan	PROPN
ejpam-6810	543	6	.	.	PUNCT
ejpam-6810	544	1	some	some	DET
ejpam-6810	544	2	results	result	NOUN
ejpam-6810	544	3	on	on	ADP
ejpam-6810	544	4	fixed	fix	VERB
ejpam-6810	544	5	points	point	NOUN
ejpam-6810	544	6	.	.	PUNCT
ejpam-6810	545	1	bull	bull	NOUN
ejpam-6810	545	2	.	.	PUNCT
ejpam-6810	546	1	cal	cal	PROPN
ejpam-6810	546	2	.	.	PUNCT
ejpam-6810	547	1	math	math	NOUN
ejpam-6810	547	2	.	.	PUNCT
ejpam-6810	548	1	soc	soc	PROPN
ejpam-6810	548	2	.	.	PUNCT
ejpam-6810	548	3	,	,	PUNCT
ejpam-6810	548	4	60:71–76	60:71–76	NUM
ejpam-6810	548	5	,	,	PUNCT
ejpam-6810	548	6	1968	1968	NUM
ejpam-6810	548	7	.	.	PUNCT
ejpam-6810	549	1	[	[	X
ejpam-6810	549	2	16	16	NUM
ejpam-6810	549	3	]	]	X
ejpam-6810	549	4	ljubomir	ljubomir	PROPN
ejpam-6810	549	5	b	b	PROPN
ejpam-6810	549	6	ciric	ciric	ADJ
ejpam-6810	549	7	.	.	PUNCT
ejpam-6810	550	1	generalized	generalized	ADJ
ejpam-6810	550	2	contractions	contraction	NOUN
ejpam-6810	550	3	and	and	CCONJ
ejpam-6810	550	4	fixed	fix	VERB
ejpam-6810	550	5	-	-	PUNCT
ejpam-6810	550	6	point	point	NOUN
ejpam-6810	550	7	theorems	theorem	NOUN
ejpam-6810	550	8	.	.	PUNCT
ejpam-6810	551	1	publ	publ	PROPN
ejpam-6810	551	2	.	.	PUNCT
ejpam-6810	552	1	inst	inst	PROPN
ejpam-6810	552	2	.	.	PUNCT
ejpam-6810	552	3	math	math	NOUN
ejpam-6810	552	4	,	,	PUNCT
ejpam-6810	552	5	12(26):19–26	12(26):19–26	NUM
ejpam-6810	552	6	,	,	PUNCT
ejpam-6810	552	7	1971	1971	NUM
ejpam-6810	552	8	.	.	PUNCT
ejpam-6810	553	1	[	[	X
ejpam-6810	553	2	17	17	NUM
ejpam-6810	553	3	]	]	X
ejpam-6810	553	4	lj	lj	PROPN
ejpam-6810	553	5	b	b	NOUN
ejpam-6810	553	6	ćirić	ćirić	NOUN
ejpam-6810	553	7	.	.	PUNCT
ejpam-6810	554	1	a	a	DET
ejpam-6810	554	2	generalization	generalization	NOUN
ejpam-6810	554	3	of	of	ADP
ejpam-6810	554	4	banach	banach	NOUN
ejpam-6810	554	5	’s	’s	PART
ejpam-6810	554	6	contraction	contraction	NOUN
ejpam-6810	554	7	principle	principle	NOUN
ejpam-6810	554	8	.	.	PUNCT
ejpam-6810	555	1	proceedings	proceeding	NOUN
ejpam-6810	555	2	of	of	ADP
ejpam-6810	555	3	the	the	DET
ejpam-6810	555	4	american	american	PROPN
ejpam-6810	555	5	mathematical	mathematical	PROPN
ejpam-6810	555	6	society	society	NOUN
ejpam-6810	555	7	,	,	PUNCT
ejpam-6810	555	8	45(2):267–273	45(2):267–273	PROPN
ejpam-6810	555	9	,	,	PUNCT
ejpam-6810	555	10	1974	1974	NUM
ejpam-6810	555	11	.	.	PUNCT
ejpam-6810	556	1	[	[	X
ejpam-6810	556	2	18	18	NUM
ejpam-6810	556	3	]	]	PUNCT
ejpam-6810	556	4	simeon	simeon	PROPN
ejpam-6810	556	5	reich	reich	PROPN
ejpam-6810	556	6	.	.	PUNCT
ejpam-6810	557	1	some	some	DET
ejpam-6810	557	2	remarks	remark	NOUN
ejpam-6810	557	3	concerning	concern	VERB
ejpam-6810	557	4	contraction	contraction	NOUN
ejpam-6810	557	5	mappings	mapping	NOUN
ejpam-6810	557	6	.	.	PUNCT
ejpam-6810	558	1	canadian	canadian	ADJ
ejpam-6810	558	2	mathematical	mathematical	ADJ
ejpam-6810	558	3	bulletin	bulletin	NOUN
ejpam-6810	558	4	,	,	PUNCT
ejpam-6810	558	5	14(1):121–124	14(1):121–124	PROPN
ejpam-6810	558	6	,	,	PUNCT
ejpam-6810	558	7	1971	1971	NUM
ejpam-6810	558	8	.	.	PUNCT
ejpam-6810	559	1	[	[	X
ejpam-6810	559	2	19	19	NUM
ejpam-6810	559	3	]	]	PUNCT
ejpam-6810	559	4	s.	s.	PROPN
ejpam-6810	559	5	k.	k.	PROPN
ejpam-6810	559	6	chatterjee	chatterjee	PROPN
ejpam-6810	559	7	.	.	PUNCT
ejpam-6810	560	1	fixed	fix	VERB
ejpam-6810	560	2	point	point	NOUN
ejpam-6810	560	3	theorems	theorem	NOUN
ejpam-6810	560	4	.	.	PUNCT
ejpam-6810	561	1	c.	c.	PROPN
ejpam-6810	561	2	r.	r.	PROPN
ejpam-6810	561	3	acad	acad	PROPN
ejpam-6810	561	4	.	.	PUNCT
ejpam-6810	562	1	bulgare	bulgare	PROPN
ejpam-6810	562	2	sci	sci	PROPN
ejpam-6810	562	3	,	,	PUNCT
ejpam-6810	562	4	1972	1972	NUM
ejpam-6810	562	5	.	.	PUNCT
ejpam-6810	563	1	[	[	X
ejpam-6810	563	2	20	20	NUM
ejpam-6810	563	3	]	]	PUNCT
ejpam-6810	563	4	tudor	tudor	PROPN
ejpam-6810	563	5	zamfirescu	zamfirescu	PROPN
ejpam-6810	563	6	.	.	PUNCT
ejpam-6810	564	1	fixed	fix	VERB
ejpam-6810	564	2	point	point	NOUN
ejpam-6810	564	3	theorems	theorem	NOUN
ejpam-6810	564	4	in	in	ADP
ejpam-6810	564	5	metric	metric	ADJ
ejpam-6810	564	6	spaces	space	NOUN
ejpam-6810	564	7	.	.	PUNCT
ejpam-6810	565	1	archiv	archiv	PROPN
ejpam-6810	565	2	der	der	PROPN
ejpam-6810	565	3	mathematik	mathematik	PROPN
ejpam-6810	565	4	,	,	PUNCT
ejpam-6810	565	5	23(1):292–298	23(1):292–298	PROPN
ejpam-6810	565	6	,	,	PUNCT
ejpam-6810	565	7	1972	1972	NUM
ejpam-6810	565	8	.	.	PUNCT
ejpam-6810	566	1	[	[	X
ejpam-6810	566	2	21	21	NUM
ejpam-6810	566	3	]	]	X
ejpam-6810	566	4	hossein	hossein	PROPN
ejpam-6810	566	5	piri	piri	NOUN
ejpam-6810	566	6	and	and	CCONJ
ejpam-6810	566	7	poom	poom	NOUN
ejpam-6810	566	8	kumam	kumam	NOUN
ejpam-6810	566	9	.	.	PUNCT
ejpam-6810	567	1	some	some	DET
ejpam-6810	567	2	fixed	fix	VERB
ejpam-6810	567	3	point	point	NOUN
ejpam-6810	567	4	theorems	theorem	NOUN
ejpam-6810	567	5	concerning	concern	VERB
ejpam-6810	567	6	f	f	NOUN
ejpam-6810	567	7	-	-	PUNCT
ejpam-6810	567	8	contraction	contraction	NOUN
ejpam-6810	567	9	in	in	ADP
ejpam-6810	567	10	complete	complete	ADJ
ejpam-6810	567	11	metric	metric	ADJ
ejpam-6810	567	12	spaces	space	NOUN
ejpam-6810	567	13	.	.	PUNCT
ejpam-6810	568	1	fixed	fix	VERB
ejpam-6810	568	2	point	point	NOUN
ejpam-6810	568	3	theory	theory	NOUN
ejpam-6810	568	4	and	and	CCONJ
ejpam-6810	568	5	applications	application	NOUN
ejpam-6810	568	6	,	,	PUNCT
ejpam-6810	568	7	2014(1):210	2014(1):210	NUM
ejpam-6810	568	8	,	,	PUNCT
ejpam-6810	568	9	2014	2014	NUM
ejpam-6810	568	10	.	.	PUNCT
ejpam-6810	569	1	[	[	X
ejpam-6810	569	2	22	22	NUM
ejpam-6810	569	3	]	]	X
ejpam-6810	569	4	mustafa	mustafa	PROPN
ejpam-6810	569	5	aslantas	aslanta	NOUN
ejpam-6810	569	6	,	,	PUNCT
ejpam-6810	569	7	hakan	hakan	PROPN
ejpam-6810	569	8	sahin	sahin	PROPN
ejpam-6810	569	9	,	,	PUNCT
ejpam-6810	569	10	and	and	CCONJ
ejpam-6810	569	11	duran	duran	PROPN
ejpam-6810	569	12	turkoglu	turkoglu	PROPN
ejpam-6810	569	13	.	.	PUNCT
ejpam-6810	570	1	some	some	DET
ejpam-6810	570	2	caristi	caristi	PROPN
ejpam-6810	570	3	type	type	NOUN
ejpam-6810	570	4	fixed	fix	VERB
ejpam-6810	570	5	point	point	NOUN
ejpam-6810	570	6	theorems	theorem	NOUN
ejpam-6810	570	7	.	.	PUNCT
ejpam-6810	571	1	the	the	DET
ejpam-6810	571	2	journal	journal	NOUN
ejpam-6810	571	3	of	of	ADP
ejpam-6810	571	4	analysis	analysis	NOUN
ejpam-6810	571	5	,	,	PUNCT
ejpam-6810	571	6	29(1):89–103	29(1):89–103	NUM
ejpam-6810	571	7	,	,	PUNCT
ejpam-6810	571	8	2021	2021	NUM
ejpam-6810	571	9	.	.	PUNCT
ejpam-6810	572	1	[	[	X
ejpam-6810	572	2	23	23	NUM
ejpam-6810	572	3	]	]	X
ejpam-6810	572	4	wudthichai	wudthichai	PROPN
ejpam-6810	572	5	onsod	onsod	PROPN
ejpam-6810	572	6	,	,	PUNCT
ejpam-6810	572	7	poom	poom	NOUN
ejpam-6810	572	8	kumam	kumam	NOUN
ejpam-6810	572	9	,	,	PUNCT
ejpam-6810	572	10	and	and	CCONJ
ejpam-6810	572	11	yeol	yeol	PROPN
ejpam-6810	572	12	je	je	PROPN
ejpam-6810	572	13	cho	cho	PROPN
ejpam-6810	572	14	.	.	PUNCT
ejpam-6810	573	1	fixed	fix	VERB
ejpam-6810	573	2	points	point	NOUN
ejpam-6810	573	3	of	of	ADP
ejpam-6810	573	4	α	α	NOUN
ejpam-6810	573	5	-	-	ADJ
ejpam-6810	573	6	θgeraghty	θgeraghty	ADJ
ejpam-6810	573	7	type	type	NOUN
ejpam-6810	573	8	and	and	CCONJ
ejpam-6810	573	9	θ	θ	NOUN
ejpam-6810	573	10	-	-	PUNCT
ejpam-6810	573	11	geraghty	geraghty	VERB
ejpam-6810	573	12	graphic	graphic	ADJ
ejpam-6810	573	13	type	type	NOUN
ejpam-6810	573	14	contractionss	contractionss	NOUN
ejpam-6810	573	15	.	.	PUNCT
ejpam-6810	574	1	applied	apply	VERB
ejpam-6810	574	2	general	general	ADJ
ejpam-6810	574	3	topology	topology	NOUN
ejpam-6810	574	4	,	,	PUNCT
ejpam-6810	574	5	18(1):153–171	18(1):153–171	PROPN
ejpam-6810	574	6	,	,	PUNCT
ejpam-6810	574	7	2017	2017	NUM
ejpam-6810	574	8	.	.	PUNCT
ejpam-6810	575	1	[	[	X
ejpam-6810	575	2	24	24	NUM
ejpam-6810	575	3	]	]	X
ejpam-6810	575	4	siegfried	siegfried	ADJ
ejpam-6810	575	5	gähler	gähler	NOUN
ejpam-6810	575	6	.	.	PUNCT
ejpam-6810	576	1	2	2	NUM
ejpam-6810	576	2	-	-	PUNCT
ejpam-6810	576	3	metrische	metrische	NOUN
ejpam-6810	576	4	räume	räume	PROPN
ejpam-6810	576	5	und	und	VERB
ejpam-6810	576	6	ihre	ihre	NOUN
ejpam-6810	576	7	topologische	topologische	NOUN
ejpam-6810	576	8	struktur	struktur	PROPN
ejpam-6810	576	9	.	.	PUNCT
ejpam-6810	577	1	mathematische	mathematische	PROPN
ejpam-6810	577	2	nachrichten	nachrichten	PROPN
ejpam-6810	577	3	,	,	PUNCT
ejpam-6810	577	4	26(1	26(1	NUM
ejpam-6810	577	5	-	-	SYM
ejpam-6810	577	6	4):115–148	4):115–148	NUM
ejpam-6810	577	7	,	,	PUNCT
ejpam-6810	577	8	1963	1963	NUM
ejpam-6810	577	9	.	.	PUNCT
ejpam-6810	578	1	[	[	X
ejpam-6810	578	2	25	25	NUM
ejpam-6810	578	3	]	]	X
ejpam-6810	578	4	huang	huang	PROPN
ejpam-6810	578	5	long	long	PROPN
ejpam-6810	578	6	-	-	PUNCT
ejpam-6810	578	7	guang	guang	PROPN
ejpam-6810	578	8	and	and	CCONJ
ejpam-6810	578	9	zhang	zhang	PROPN
ejpam-6810	578	10	xian	xian	PROPN
ejpam-6810	578	11	.	.	PUNCT
ejpam-6810	579	1	cone	cone	PROPN
ejpam-6810	579	2	metric	metric	ADJ
ejpam-6810	579	3	spaces	space	NOUN
ejpam-6810	579	4	and	and	CCONJ
ejpam-6810	579	5	fixed	fix	VERB
ejpam-6810	579	6	point	point	NOUN
ejpam-6810	579	7	theorems	theorem	NOUN
ejpam-6810	579	8	of	of	ADP
ejpam-6810	579	9	contractive	contractive	ADJ
ejpam-6810	579	10	mappings	mapping	NOUN
ejpam-6810	579	11	.	.	PUNCT
ejpam-6810	580	1	j.	j.	PROPN
ejpam-6810	580	2	math	math	PROPN
ejpam-6810	580	3	.	.	PUNCT
ejpam-6810	581	1	anal	anal	PROPN
ejpam-6810	581	2	.	.	PUNCT
ejpam-6810	582	1	appl	appl	PROPN
ejpam-6810	582	2	,	,	PUNCT
ejpam-6810	582	3	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-6810	582	4	,	,	PUNCT
ejpam-6810	582	5	2007	2007	NUM
ejpam-6810	582	6	.	.	PUNCT
ejpam-6810	583	1	[	[	X
ejpam-6810	583	2	26	26	NUM
ejpam-6810	583	3	]	]	X
ejpam-6810	583	4	i.a	i.a	PROPN
ejpam-6810	583	5	bakhtin	bakhtin	NOUN
ejpam-6810	583	6	.	.	PUNCT
ejpam-6810	584	1	the	the	DET
ejpam-6810	584	2	contraction	contraction	NOUN
ejpam-6810	584	3	mapping	map	VERB
ejpam-6810	584	4	principle	principle	NOUN
ejpam-6810	584	5	in	in	ADP
ejpam-6810	584	6	quasimetric	quasimetric	ADJ
ejpam-6810	584	7	spaces	space	NOUN
ejpam-6810	584	8	.	.	PUNCT
ejpam-6810	585	1	functional	functional	ADJ
ejpam-6810	585	2	analysis	analysis	NOUN
ejpam-6810	585	3	,	,	PUNCT
ejpam-6810	585	4	30:26–37	30:26–37	PROPN
ejpam-6810	585	5	,	,	PUNCT
ejpam-6810	585	6	1989	1989	NUM
ejpam-6810	585	7	.	.	PUNCT
ejpam-6810	586	1	[	[	X
ejpam-6810	586	2	27	27	NUM
ejpam-6810	586	3	]	]	X
ejpam-6810	586	4	stefan	stefan	PROPN
ejpam-6810	586	5	czerwik	czerwik	PROPN
ejpam-6810	586	6	.	.	PUNCT
ejpam-6810	587	1	contraction	contraction	NOUN
ejpam-6810	587	2	mappings	mapping	NOUN
ejpam-6810	587	3	in	in	ADP
ejpam-6810	587	4	b	b	NOUN
ejpam-6810	587	5	-	-	ADJ
ejpam-6810	587	6	metric	metric	ADJ
ejpam-6810	587	7	spaces	space	NOUN
ejpam-6810	587	8	.	.	PUNCT
ejpam-6810	588	1	acta	acta	PROPN
ejpam-6810	588	2	mathematica	mathematica	PROPN
ejpam-6810	588	3	et	et	PROPN
ejpam-6810	588	4	informatica	informatica	PROPN
ejpam-6810	588	5	universitatis	universitatis	PROPN
ejpam-6810	588	6	ostraviensis	ostraviensis	PROPN
ejpam-6810	588	7	,	,	PUNCT
ejpam-6810	588	8	1(1):5–11	1(1):5–11	NUM
ejpam-6810	588	9	,	,	PUNCT
ejpam-6810	588	10	1993	1993	NUM
ejpam-6810	588	11	.	.	PUNCT
ejpam-6810	589	1	[	[	X
ejpam-6810	589	2	28	28	NUM
ejpam-6810	589	3	]	]	X
ejpam-6810	589	4	erdal	erdal	PROPN
ejpam-6810	589	5	karapınar	karapınar	PROPN
ejpam-6810	589	6	.	.	PUNCT
ejpam-6810	590	1	a	a	DET
ejpam-6810	590	2	short	short	ADJ
ejpam-6810	590	3	survey	survey	NOUN
ejpam-6810	590	4	on	on	ADP
ejpam-6810	590	5	the	the	DET
ejpam-6810	590	6	recent	recent	ADJ
ejpam-6810	590	7	fixed	fix	VERB
ejpam-6810	590	8	point	point	NOUN
ejpam-6810	590	9	results	result	NOUN
ejpam-6810	590	10	on	on	ADP
ejpam-6810	590	11	b	b	NOUN
ejpam-6810	590	12	-	-	PUNCT
ejpam-6810	590	13	metric	metric	ADJ
ejpam-6810	590	14	spaces	space	NOUN
ejpam-6810	590	15	.	.	PUNCT
ejpam-6810	591	1	constructive	constructive	ADJ
ejpam-6810	591	2	mathematical	mathematical	ADJ
ejpam-6810	591	3	analysis	analysis	NOUN
ejpam-6810	591	4	,	,	PUNCT
ejpam-6810	591	5	1(1):15–44	1(1):15–44	NUM
ejpam-6810	591	6	,	,	PUNCT
ejpam-6810	591	7	2018	2018	NUM
ejpam-6810	591	8	.	.	PUNCT
ejpam-6810	592	1	[	[	X
ejpam-6810	592	2	29	29	NUM
ejpam-6810	592	3	]	]	X
ejpam-6810	592	4	vasile	vasile	NOUN
ejpam-6810	592	5	berinde	berinde	NOUN
ejpam-6810	592	6	and	and	CCONJ
ejpam-6810	592	7	mădalina	mădalina	NOUN
ejpam-6810	592	8	păcurar	păcurar	NOUN
ejpam-6810	592	9	.	.	PUNCT
ejpam-6810	593	1	the	the	DET
ejpam-6810	593	2	early	early	ADJ
ejpam-6810	593	3	developments	development	NOUN
ejpam-6810	593	4	in	in	ADP
ejpam-6810	593	5	fixed	fix	VERB
ejpam-6810	593	6	point	point	NOUN
ejpam-6810	593	7	theory	theory	NOUN
ejpam-6810	593	8	on	on	ADP
ejpam-6810	593	9	b	b	NOUN
ejpam-6810	593	10	-	-	ADJ
ejpam-6810	593	11	metric	metric	ADJ
ejpam-6810	593	12	spaces	space	NOUN
ejpam-6810	593	13	.	.	PUNCT
ejpam-6810	594	1	carpathian	carpathian	ADJ
ejpam-6810	594	2	journal	journal	PROPN
ejpam-6810	594	3	of	of	ADP
ejpam-6810	594	4	mathematics	mathematics	PROPN
ejpam-6810	594	5	,	,	PUNCT
ejpam-6810	594	6	38(3):523–538	38(3):523–538	PROPN
ejpam-6810	594	7	,	,	PUNCT
ejpam-6810	594	8	2022	2022	NUM
ejpam-6810	594	9	.	.	PUNCT
ejpam-6810	595	1	[	[	X
ejpam-6810	595	2	30	30	NUM
ejpam-6810	595	3	]	]	PUNCT
ejpam-6810	595	4	zhenhua	zhenhua	PROPN
ejpam-6810	595	5	ma	ma	PROPN
ejpam-6810	595	6	and	and	CCONJ
ejpam-6810	595	7	lining	lining	PROPN
ejpam-6810	595	8	jiang	jiang	PROPN
ejpam-6810	595	9	.	.	PUNCT
ejpam-6810	596	1	c∗-algebra	c∗-algebra	PROPN
ejpam-6810	596	2	-	-	PUNCT
ejpam-6810	596	3	valued	value	VERB
ejpam-6810	596	4	b	b	NOUN
ejpam-6810	596	5	-	-	PUNCT
ejpam-6810	596	6	metric	metric	ADJ
ejpam-6810	596	7	spaces	space	NOUN
ejpam-6810	596	8	and	and	CCONJ
ejpam-6810	596	9	related	relate	VERB
ejpam-6810	596	10	fixed	fix	VERB
ejpam-6810	596	11	point	point	NOUN
ejpam-6810	596	12	theorems	theorem	NOUN
ejpam-6810	596	13	.	.	PUNCT
ejpam-6810	597	1	fixed	fix	VERB
ejpam-6810	597	2	point	point	NOUN
ejpam-6810	597	3	theory	theory	NOUN
ejpam-6810	597	4	and	and	CCONJ
ejpam-6810	597	5	applications	application	NOUN
ejpam-6810	597	6	,	,	PUNCT
ejpam-6810	597	7	2015(1):222	2015(1):222	NUM
ejpam-6810	597	8	,	,	PUNCT
ejpam-6810	597	9	2015	2015	NUM
ejpam-6810	597	10	.	.	PUNCT
ejpam-6810	598	1	[	[	X
ejpam-6810	598	2	31	31	NUM
ejpam-6810	598	3	]	]	X
ejpam-6810	598	4	samina	samina	PROPN
ejpam-6810	598	5	batul	batul	PROPN
ejpam-6810	598	6	and	and	CCONJ
ejpam-6810	598	7	tayyab	tayyab	PROPN
ejpam-6810	598	8	kamran	kamran	PROPN
ejpam-6810	598	9	.	.	PUNCT
ejpam-6810	599	1	c∗-valued	c∗-value	VERB
ejpam-6810	599	2	contractive	contractive	ADJ
ejpam-6810	599	3	type	type	NOUN
ejpam-6810	599	4	mappings	mapping	NOUN
ejpam-6810	599	5	.	.	PUNCT
ejpam-6810	600	1	fixed	fix	VERB
ejpam-6810	600	2	point	point	NOUN
ejpam-6810	600	3	theory	theory	NOUN
ejpam-6810	600	4	and	and	CCONJ
ejpam-6810	600	5	applications	application	NOUN
ejpam-6810	600	6	,	,	PUNCT
ejpam-6810	600	7	2015(1):142	2015(1):142	NUM
ejpam-6810	600	8	,	,	PUNCT
ejpam-6810	600	9	2015	2015	NUM
ejpam-6810	600	10	.	.	PUNCT
ejpam-6810	601	1	[	[	X
ejpam-6810	601	2	32	32	NUM
ejpam-6810	601	3	]	]	X
ejpam-6810	601	4	dur	dur	PROPN
ejpam-6810	601	5	e	e	NOUN
ejpam-6810	601	6	shehwar	shehwar	NOUN
ejpam-6810	601	7	,	,	PUNCT
ejpam-6810	601	8	samina	samina	PROPN
ejpam-6810	601	9	batul	batul	PROPN
ejpam-6810	601	10	,	,	PUNCT
ejpam-6810	601	11	tayyab	tayyab	PROPN
ejpam-6810	601	12	kamran	kamran	PROPN
ejpam-6810	601	13	,	,	PUNCT
ejpam-6810	601	14	and	and	CCONJ
ejpam-6810	601	15	adrian	adrian	PROPN
ejpam-6810	601	16	ghiura	ghiura	NOUN
ejpam-6810	601	17	.	.	PUNCT
ejpam-6810	602	1	caristi	caristi	PROPN
ejpam-6810	602	2	’s	’s	PART
ejpam-6810	602	3	fixed	fix	VERB
ejpam-6810	602	4	point	point	NOUN
ejpam-6810	602	5	theorem	theorem	VERB
ejpam-6810	602	6	on	on	ADP
ejpam-6810	602	7	c∗-algebra	c∗-algebra	PROPN
ejpam-6810	602	8	valued	value	VERB
ejpam-6810	602	9	metric	metric	ADJ
ejpam-6810	602	10	spaces	space	NOUN
ejpam-6810	602	11	.	.	PUNCT
ejpam-6810	603	1	journal	journal	PROPN
ejpam-6810	603	2	of	of	ADP
ejpam-6810	603	3	nonlinear	nonlinear	PROPN
ejpam-6810	603	4	sciences	sciences	PROPN
ejpam-6810	603	5	and	and	CCONJ
ejpam-6810	603	6	applications	application	NOUN
ejpam-6810	603	7	,	,	PUNCT
ejpam-6810	603	8	9(2):584–588	9(2):584–588	NUM
ejpam-6810	603	9	,	,	PUNCT
ejpam-6810	603	10	2016	2016	NUM
ejpam-6810	603	11	.	.	PUNCT
ejpam-6810	604	1	[	[	X
ejpam-6810	604	2	33	33	NUM
ejpam-6810	604	3	]	]	PUNCT
ejpam-6810	604	4	lech	lech	PROPN
ejpam-6810	604	5	pasicki	pasicki	NOUN
ejpam-6810	604	6	.	.	PUNCT
ejpam-6810	605	1	cauchy	cauchy	PROPN
ejpam-6810	605	2	sequences	sequence	NOUN
ejpam-6810	605	3	in	in	ADP
ejpam-6810	605	4	b	b	NOUN
ejpam-6810	605	5	-	-	PUNCT
ejpam-6810	605	6	metric	metric	ADJ
ejpam-6810	605	7	spaces	space	NOUN
ejpam-6810	605	8	.	.	PUNCT
ejpam-6810	605	9	topology	topology	NOUN
ejpam-6810	605	10	and	and	CCONJ
ejpam-6810	605	11	its	its	PRON
ejpam-6810	605	12	applications	application	NOUN
ejpam-6810	605	13	,	,	PUNCT
ejpam-6810	605	14	page	page	NOUN
ejpam-6810	605	15	109477	109477	NUM
ejpam-6810	605	16	,	,	PUNCT
ejpam-6810	605	17	2025	2025	NUM
ejpam-6810	605	18	.	.	PUNCT
ejpam-6810	606	1	[	[	X
ejpam-6810	606	2	34	34	NUM
ejpam-6810	606	3	]	]	X
ejpam-6810	606	4	dariusz	dariusz	NOUN
ejpam-6810	606	5	wardowski	wardowski	VERB
ejpam-6810	606	6	.	.	PUNCT
ejpam-6810	607	1	fixed	fix	VERB
ejpam-6810	607	2	points	point	NOUN
ejpam-6810	607	3	of	of	ADP
ejpam-6810	607	4	a	a	DET
ejpam-6810	607	5	new	new	ADJ
ejpam-6810	607	6	type	type	NOUN
ejpam-6810	607	7	of	of	ADP
ejpam-6810	607	8	contractive	contractive	ADJ
ejpam-6810	607	9	mappings	mapping	NOUN
ejpam-6810	607	10	in	in	ADP
ejpam-6810	607	11	complete	complete	ADJ
ejpam-6810	607	12	metric	metric	ADJ
ejpam-6810	607	13	spaces	space	NOUN
ejpam-6810	607	14	.	.	PUNCT
ejpam-6810	608	1	fixed	fix	VERB
ejpam-6810	608	2	point	point	NOUN
ejpam-6810	608	3	theory	theory	NOUN
ejpam-6810	608	4	and	and	CCONJ
ejpam-6810	608	5	applications	application	NOUN
ejpam-6810	608	6	,	,	PUNCT
ejpam-6810	608	7	2012(1):94	2012(1):94	NUM
ejpam-6810	608	8	,	,	PUNCT
ejpam-6810	608	9	2012	2012	NUM
ejpam-6810	608	10	.	.	PUNCT
ejpam-6810	609	1	[	[	X
ejpam-6810	609	2	35	35	NUM
ejpam-6810	609	3	]	]	X
ejpam-6810	609	4	nicola	nicola	PROPN
ejpam-6810	609	5	fabiano	fabiano	PROPN
ejpam-6810	609	6	,	,	PUNCT
ejpam-6810	609	7	zoran	zoran	PROPN
ejpam-6810	609	8	kadelburg	kadelburg	PROPN
ejpam-6810	609	9	,	,	PUNCT
ejpam-6810	609	10	nikola	nikola	PROPN
ejpam-6810	609	11	mirkov	mirkov	PROPN
ejpam-6810	609	12	,	,	PUNCT
ejpam-6810	609	13	vesna	vesna	PROPN
ejpam-6810	609	14	šešum	šešum	PROPN
ejpam-6810	609	15	čavić	čavić	PROPN
ejpam-6810	609	16	,	,	PUNCT
ejpam-6810	609	17	and	and	CCONJ
ejpam-6810	609	18	stojan	stojan	ADP
ejpam-6810	609	19	radenović	radenović	NOUN
ejpam-6810	609	20	.	.	PUNCT
ejpam-6810	610	1	on	on	ADP
ejpam-6810	610	2	f	f	NOUN
ejpam-6810	610	3	-	-	PUNCT
ejpam-6810	610	4	contractions	contraction	NOUN
ejpam-6810	610	5	:	:	PUNCT
ejpam-6810	610	6	a	a	DET
ejpam-6810	610	7	survey	survey	NOUN
ejpam-6810	610	8	.	.	PUNCT
ejpam-6810	611	1	contemporary	contemporary	ADJ
ejpam-6810	611	2	mathematics	mathematic	NOUN
ejpam-6810	611	3	,	,	PUNCT
ejpam-6810	611	4	pages	page	NOUN
ejpam-6810	611	5	327–342	327–342	NUM
ejpam-6810	611	6	,	,	PUNCT
ejpam-6810	611	7	s.	s.	PROPN
ejpam-6810	611	8	batul	batul	PROPN
ejpam-6810	611	9	et	et	PROPN
ejpam-6810	611	10	al	al	PROPN
ejpam-6810	611	11	.	.	PUNCT
ejpam-6810	611	12	/	/	SYM
ejpam-6810	611	13	eur	eur	PROPN
ejpam-6810	611	14	.	.	PUNCT
ejpam-6810	612	1	j.	j.	PROPN
ejpam-6810	612	2	pure	pure	PROPN
ejpam-6810	612	3	appl	appl	PROPN
ejpam-6810	612	4	.	.	PROPN
ejpam-6810	612	5	math	math	PROPN
ejpam-6810	612	6	,	,	PUNCT
ejpam-6810	612	7	18	18	NUM
ejpam-6810	612	8	(	(	PUNCT
ejpam-6810	612	9	4	4	NUM
ejpam-6810	612	10	)	)	PUNCT
ejpam-6810	612	11	(	(	PUNCT
ejpam-6810	612	12	2025	2025	NUM
ejpam-6810	612	13	)	)	PUNCT
ejpam-6810	612	14	,	,	PUNCT
ejpam-6810	612	15	6810	6810	NUM
ejpam-6810	612	16	23	23	NUM
ejpam-6810	612	17	of	of	ADP
ejpam-6810	612	18	23	23	NUM
ejpam-6810	612	19	2022	2022	NUM
ejpam-6810	612	20	.	.	PUNCT
ejpam-6810	613	1	[	[	X
ejpam-6810	613	2	36	36	NUM
ejpam-6810	613	3	]	]	X
ejpam-6810	613	4	evgeniy	evgeniy	ADJ
ejpam-6810	613	5	petrov	petrov	PROPN
ejpam-6810	613	6	.	.	PUNCT
ejpam-6810	613	7	fixed	fix	VERB
ejpam-6810	613	8	point	point	NOUN
ejpam-6810	613	9	theorem	theorem	NOUN
ejpam-6810	613	10	for	for	ADP
ejpam-6810	613	11	mappings	mapping	NOUN
ejpam-6810	613	12	contracting	contract	VERB
ejpam-6810	613	13	perimeters	perimeter	NOUN
ejpam-6810	613	14	of	of	ADP
ejpam-6810	613	15	triangles	triangle	NOUN
ejpam-6810	613	16	.	.	PUNCT
ejpam-6810	614	1	journal	journal	NOUN
ejpam-6810	614	2	of	of	ADP
ejpam-6810	614	3	fixed	fix	VERB
ejpam-6810	614	4	point	point	NOUN
ejpam-6810	614	5	theory	theory	NOUN
ejpam-6810	614	6	and	and	CCONJ
ejpam-6810	614	7	applications	application	NOUN
ejpam-6810	614	8	,	,	PUNCT
ejpam-6810	614	9	25(3):74	25(3):74	NUM
ejpam-6810	614	10	,	,	PUNCT
ejpam-6810	614	11	2023	2023	NUM
ejpam-6810	614	12	.	.	PUNCT
ejpam-6810	615	1	[	[	X
ejpam-6810	615	2	37	37	NUM
ejpam-6810	615	3	]	]	X
ejpam-6810	615	4	monica	monica	PROPN
ejpam-6810	615	5	cosentino	cosentino	PROPN
ejpam-6810	615	6	,	,	PUNCT
ejpam-6810	615	7	mohamed	mohamed	PROPN
ejpam-6810	615	8	jleli	jleli	PROPN
ejpam-6810	615	9	,	,	PUNCT
ejpam-6810	615	10	bessem	bessem	NOUN
ejpam-6810	615	11	samet	samet	NOUN
ejpam-6810	615	12	,	,	PUNCT
ejpam-6810	615	13	and	and	CCONJ
ejpam-6810	615	14	calogero	calogero	PROPN
ejpam-6810	615	15	vetro	vetro	PROPN
ejpam-6810	615	16	.	.	PUNCT
ejpam-6810	616	1	solvability	solvability	NOUN
ejpam-6810	616	2	of	of	ADP
ejpam-6810	616	3	integrodifferential	integrodifferential	ADJ
ejpam-6810	616	4	problems	problem	NOUN
ejpam-6810	616	5	via	via	ADP
ejpam-6810	616	6	fixed	fix	VERB
ejpam-6810	616	7	point	point	NOUN
ejpam-6810	616	8	theory	theory	NOUN
ejpam-6810	616	9	in	in	ADP
ejpam-6810	616	10	b	b	NOUN
ejpam-6810	616	11	-	-	ADJ
ejpam-6810	616	12	metric	metric	ADJ
ejpam-6810	616	13	spaces	space	NOUN
ejpam-6810	616	14	.	.	PUNCT
ejpam-6810	617	1	fixed	fix	VERB
ejpam-6810	617	2	point	point	NOUN
ejpam-6810	617	3	theory	theory	NOUN
ejpam-6810	617	4	and	and	CCONJ
ejpam-6810	617	5	applications	application	NOUN
ejpam-6810	617	6	,	,	PUNCT
ejpam-6810	617	7	2015(1):70	2015(1):70	NUM
ejpam-6810	617	8	,	,	PUNCT
ejpam-6810	617	9	2015	2015	NUM
ejpam-6810	617	10	.	.	PUNCT