id	sid	tid	token	lemma	pos
ejpam-5794	1	1	european	european	PROPN
ejpam-5794	1	2	journal	journal	PROPN
ejpam-5794	1	3	of	of	ADP
ejpam-5794	1	4	pure	pure	ADJ
ejpam-5794	1	5	and	and	CCONJ
ejpam-5794	1	6	applied	applied	ADJ
ejpam-5794	1	7	mathematics	mathematic	NOUN
ejpam-5794	1	8	2025	2025	NUM
ejpam-5794	1	9	,	,	PUNCT
ejpam-5794	1	10	vol	vol	NOUN
ejpam-5794	1	11	.	.	PROPN
ejpam-5794	1	12	18	18	NUM
ejpam-5794	1	13	,	,	PUNCT
ejpam-5794	1	14	issue	issue	NOUN
ejpam-5794	1	15	1	1	NUM
ejpam-5794	1	16	,	,	PUNCT
ejpam-5794	1	17	article	article	NOUN
ejpam-5794	1	18	number	number	NOUN
ejpam-5794	1	19	5794	5794	NUM
ejpam-5794	1	20	issn	issn	VERB
ejpam-5794	1	21	1307	1307	NUM
ejpam-5794	1	22	-	-	SYM
ejpam-5794	1	23	5543	5543	NUM
ejpam-5794	1	24	–	–	PUNCT
ejpam-5794	1	25	ejpam.com	ejpam.com	X
ejpam-5794	1	26	published	publish	VERB
ejpam-5794	1	27	by	by	ADP
ejpam-5794	1	28	new	new	PROPN
ejpam-5794	1	29	york	york	PROPN
ejpam-5794	1	30	business	business	PROPN
ejpam-5794	1	31	global	global	ADJ
ejpam-5794	1	32	fixed	fix	VERB
ejpam-5794	1	33	point	point	NOUN
ejpam-5794	1	34	theorems	theorem	NOUN
ejpam-5794	1	35	in	in	ADP
ejpam-5794	1	36	controlled	control	VERB
ejpam-5794	1	37	rectangular	rectangular	ADJ
ejpam-5794	1	38	modular	modular	ADJ
ejpam-5794	1	39	metric	metric	ADJ
ejpam-5794	1	40	spaces	space	NOUN
ejpam-5794	1	41	with	with	ADP
ejpam-5794	1	42	solution	solution	NOUN
ejpam-5794	1	43	of	of	ADP
ejpam-5794	1	44	fractional	fractional	ADJ
ejpam-5794	1	45	differential	differential	ADJ
ejpam-5794	1	46	equations	equation	NOUN
ejpam-5794	1	47	umar	umar	PROPN
ejpam-5794	1	48	ishtiaq1	ishtiaq1	PROPN
ejpam-5794	1	49	,	,	PUNCT
ejpam-5794	1	50	naeem	naeem	PROPN
ejpam-5794	1	51	saleem2,3,∗	saleem2,3,∗	PROPN
ejpam-5794	1	52	,	,	PUNCT
ejpam-5794	1	53	muhammad	muhammad	PROPN
ejpam-5794	1	54	farhan4	farhan4	PROPN
ejpam-5794	1	55	,	,	PUNCT
ejpam-5794	1	56	maggie	maggie	NOUN
ejpam-5794	1	57	aphane3	aphane3	PROPN
ejpam-5794	1	58	,	,	PUNCT
ejpam-5794	1	59	mohammad	mohammad	PROPN
ejpam-5794	1	60	s.	s.	PROPN
ejpam-5794	1	61	r.	r.	PROPN
ejpam-5794	1	62	chowdhury5	chowdhury5	PROPN
ejpam-5794	1	63	1	1	NUM
ejpam-5794	1	64	office	office	NOUN
ejpam-5794	1	65	of	of	ADP
ejpam-5794	1	66	research	research	NOUN
ejpam-5794	1	67	,	,	PUNCT
ejpam-5794	1	68	innovation	innovation	NOUN
ejpam-5794	1	69	and	and	CCONJ
ejpam-5794	1	70	commercialization	commercialization	NOUN
ejpam-5794	1	71	,	,	PUNCT
ejpam-5794	1	72	university	university	NOUN
ejpam-5794	1	73	of	of	ADP
ejpam-5794	1	74	management	management	NOUN
ejpam-5794	1	75	and	and	CCONJ
ejpam-5794	1	76	technology	technology	NOUN
ejpam-5794	1	77	,	,	PUNCT
ejpam-5794	1	78	lahore	lahore	NOUN
ejpam-5794	1	79	54770	54770	NUM
ejpam-5794	1	80	,	,	PUNCT
ejpam-5794	1	81	pakistan	pakistan	PROPN
ejpam-5794	1	82	2	2	NUM
ejpam-5794	1	83	department	department	NOUN
ejpam-5794	1	84	of	of	ADP
ejpam-5794	1	85	mathematics	mathematic	NOUN
ejpam-5794	1	86	,	,	PUNCT
ejpam-5794	1	87	university	university	NOUN
ejpam-5794	1	88	of	of	ADP
ejpam-5794	1	89	management	management	NOUN
ejpam-5794	1	90	and	and	CCONJ
ejpam-5794	1	91	technology	technology	NOUN
ejpam-5794	1	92	,	,	PUNCT
ejpam-5794	1	93	lahore	lahore	NOUN
ejpam-5794	1	94	,	,	PUNCT
ejpam-5794	1	95	pakistan	pakistan	PROPN
ejpam-5794	1	96	3	3	NUM
ejpam-5794	1	97	department	department	NOUN
ejpam-5794	1	98	of	of	ADP
ejpam-5794	1	99	mathematics	mathematic	NOUN
ejpam-5794	1	100	and	and	CCONJ
ejpam-5794	1	101	applied	apply	VERB
ejpam-5794	1	102	mathematics	mathematic	NOUN
ejpam-5794	1	103	,	,	PUNCT
ejpam-5794	1	104	sefako	sefako	VERB
ejpam-5794	1	105	makgatho	makgatho	PROPN
ejpam-5794	1	106	health	health	PROPN
ejpam-5794	1	107	sciences	sciences	PROPN
ejpam-5794	1	108	university	university	PROPN
ejpam-5794	1	109	,	,	PUNCT
ejpam-5794	1	110	ga	ga	PROPN
ejpam-5794	1	111	-	-	NOUN
ejpam-5794	1	112	rankuwa	rankuwa	ADJ
ejpam-5794	1	113	,	,	PUNCT
ejpam-5794	1	114	pretoria	pretoria	NOUN
ejpam-5794	1	115	,	,	PUNCT
ejpam-5794	1	116	medunsa-0204	medunsa-0204	ADJ
ejpam-5794	1	117	,	,	PUNCT
ejpam-5794	1	118	south	south	PROPN
ejpam-5794	1	119	africa	africa	PROPN
ejpam-5794	1	120	4	4	NUM
ejpam-5794	1	121	department	department	NOUN
ejpam-5794	1	122	of	of	ADP
ejpam-5794	1	123	mathematics	mathematic	NOUN
ejpam-5794	1	124	,	,	PUNCT
ejpam-5794	1	125	numl	numl	PROPN
ejpam-5794	1	126	university	university	PROPN
ejpam-5794	1	127	multan	multan	PROPN
ejpam-5794	1	128	campus	campus	PROPN
ejpam-5794	1	129	,	,	PUNCT
ejpam-5794	1	130	multan	multan	PROPN
ejpam-5794	1	131	,	,	PUNCT
ejpam-5794	1	132	pakistan	pakistan	PROPN
ejpam-5794	1	133	5	5	NUM
ejpam-5794	1	134	department	department	NOUN
ejpam-5794	1	135	of	of	ADP
ejpam-5794	1	136	mathematics	mathematic	NOUN
ejpam-5794	1	137	and	and	CCONJ
ejpam-5794	1	138	statistics	statistic	NOUN
ejpam-5794	1	139	,	,	PUNCT
ejpam-5794	1	140	the	the	DET
ejpam-5794	1	141	university	university	NOUN
ejpam-5794	1	142	of	of	ADP
ejpam-5794	1	143	lahore	lahore	PROPN
ejpam-5794	1	144	,	,	PUNCT
ejpam-5794	1	145	lahore	lahore	NOUN
ejpam-5794	1	146	,	,	PUNCT
ejpam-5794	1	147	pakistan	pakistan	PROPN
ejpam-5794	1	148	abstract	abstract	NOUN
ejpam-5794	1	149	.	.	PUNCT
ejpam-5794	2	1	in	in	ADP
ejpam-5794	2	2	this	this	DET
ejpam-5794	2	3	paper	paper	NOUN
ejpam-5794	2	4	,	,	PUNCT
ejpam-5794	2	5	we	we	PRON
ejpam-5794	2	6	establish	establish	VERB
ejpam-5794	2	7	the	the	DET
ejpam-5794	2	8	notion	notion	NOUN
ejpam-5794	2	9	of	of	ADP
ejpam-5794	2	10	controlled	control	VERB
ejpam-5794	2	11	rectangular	rectangular	ADJ
ejpam-5794	2	12	modular	modular	ADJ
ejpam-5794	2	13	metric	metric	ADJ
ejpam-5794	2	14	space	space	NOUN
ejpam-5794	2	15	as	as	ADP
ejpam-5794	2	16	a	a	DET
ejpam-5794	2	17	generalization	generalization	NOUN
ejpam-5794	2	18	of	of	ADP
ejpam-5794	2	19	modular	modular	ADJ
ejpam-5794	2	20	b−metric	b−metric	ADJ
ejpam-5794	2	21	space	space	NOUN
ejpam-5794	2	22	and	and	CCONJ
ejpam-5794	2	23	rectangular	rectangular	ADJ
ejpam-5794	2	24	b−metric	b−metric	ADJ
ejpam-5794	2	25	space	space	NOUN
ejpam-5794	2	26	.	.	PUNCT
ejpam-5794	3	1	we	we	PRON
ejpam-5794	3	2	used	use	VERB
ejpam-5794	3	3	contraction	contraction	NOUN
ejpam-5794	3	4	mappings	mapping	NOUN
ejpam-5794	3	5	to	to	PART
ejpam-5794	3	6	find	find	VERB
ejpam-5794	3	7	the	the	DET
ejpam-5794	3	8	existence	existence	NOUN
ejpam-5794	3	9	and	and	CCONJ
ejpam-5794	3	10	uniqueness	uniqueness	NOUN
ejpam-5794	3	11	of	of	ADP
ejpam-5794	3	12	a	a	DET
ejpam-5794	3	13	fixed	fix	VERB
ejpam-5794	3	14	point	point	NOUN
ejpam-5794	3	15	in	in	ADP
ejpam-5794	3	16	the	the	DET
ejpam-5794	3	17	framework	framework	NOUN
ejpam-5794	3	18	of	of	ADP
ejpam-5794	3	19	controlled	control	VERB
ejpam-5794	3	20	rectangular	rectangular	ADJ
ejpam-5794	3	21	modular	modular	ADJ
ejpam-5794	3	22	metric	metric	ADJ
ejpam-5794	3	23	space	space	NOUN
ejpam-5794	3	24	.	.	PUNCT
ejpam-5794	4	1	we	we	PRON
ejpam-5794	4	2	give	give	VERB
ejpam-5794	4	3	several	several	ADJ
ejpam-5794	4	4	non	non	ADJ
ejpam-5794	4	5	-	-	ADJ
ejpam-5794	4	6	trivial	trivial	ADJ
ejpam-5794	4	7	examples	example	NOUN
ejpam-5794	4	8	and	and	CCONJ
ejpam-5794	4	9	show	show	VERB
ejpam-5794	4	10	the	the	DET
ejpam-5794	4	11	validity	validity	NOUN
ejpam-5794	4	12	of	of	ADP
ejpam-5794	4	13	contraction	contraction	NOUN
ejpam-5794	4	14	mappings	mapping	NOUN
ejpam-5794	4	15	via	via	ADP
ejpam-5794	4	16	graphs	graph	NOUN
ejpam-5794	4	17	.	.	PUNCT
ejpam-5794	5	1	at	at	ADP
ejpam-5794	5	2	the	the	DET
ejpam-5794	5	3	end	end	NOUN
ejpam-5794	5	4	,	,	PUNCT
ejpam-5794	5	5	we	we	PRON
ejpam-5794	5	6	utilize	utilize	VERB
ejpam-5794	5	7	our	our	PRON
ejpam-5794	5	8	main	main	ADJ
ejpam-5794	5	9	result	result	NOUN
ejpam-5794	5	10	to	to	PART
ejpam-5794	5	11	solve	solve	VERB
ejpam-5794	5	12	a	a	DET
ejpam-5794	5	13	non	non	ADJ
ejpam-5794	5	14	-	-	ADJ
ejpam-5794	5	15	linear	linear	ADJ
ejpam-5794	5	16	fractional	fractional	ADJ
ejpam-5794	5	17	differential	differential	NOUN
ejpam-5794	5	18	equation	equation	NOUN
ejpam-5794	5	19	.	.	PUNCT
ejpam-5794	6	1	2020	2020	NUM
ejpam-5794	6	2	mathematics	mathematic	NOUN
ejpam-5794	6	3	subject	subject	NOUN
ejpam-5794	6	4	classifications	classification	NOUN
ejpam-5794	6	5	:	:	PUNCT
ejpam-5794	6	6	47h10	47h10	NUM
ejpam-5794	6	7	,	,	PUNCT
ejpam-5794	6	8	54h25	54h25	NUM
ejpam-5794	6	9	key	key	ADJ
ejpam-5794	6	10	words	word	NOUN
ejpam-5794	6	11	and	and	CCONJ
ejpam-5794	6	12	phrases	phrase	NOUN
ejpam-5794	6	13	:	:	PUNCT
ejpam-5794	6	14	controlled	control	VERB
ejpam-5794	6	15	metric	metric	ADJ
ejpam-5794	6	16	space	space	NOUN
ejpam-5794	6	17	,	,	PUNCT
ejpam-5794	6	18	modular	modular	ADJ
ejpam-5794	6	19	metric	metric	ADJ
ejpam-5794	6	20	space	space	NOUN
ejpam-5794	6	21	,	,	PUNCT
ejpam-5794	6	22	fixed	fix	VERB
ejpam-5794	6	23	point	point	NOUN
ejpam-5794	6	24	;	;	PUNCT
ejpam-5794	6	25	existence	existence	NOUN
ejpam-5794	6	26	and	and	CCONJ
ejpam-5794	6	27	uniqueness	uniqueness	NOUN
ejpam-5794	6	28	,	,	PUNCT
ejpam-5794	6	29	non	non	ADJ
ejpam-5794	6	30	-	-	ADJ
ejpam-5794	6	31	linear	linear	ADJ
ejpam-5794	6	32	fractional	fractional	ADJ
ejpam-5794	6	33	differential	differential	ADJ
ejpam-5794	6	34	equations	equation	NOUN
ejpam-5794	6	35	1	1	NUM
ejpam-5794	6	36	.	.	PUNCT
ejpam-5794	7	1	introduction	introduction	NOUN
ejpam-5794	7	2	and	and	CCONJ
ejpam-5794	7	3	preliminaries	preliminary	NOUN
ejpam-5794	7	4	the	the	DET
ejpam-5794	7	5	banach	banach	ADV
ejpam-5794	7	6	fixed	fix	VERB
ejpam-5794	7	7	-	-	PUNCT
ejpam-5794	7	8	point	point	NOUN
ejpam-5794	7	9	theorem	theorem	NOUN
ejpam-5794	7	10	[	[	X
ejpam-5794	7	11	10	10	NUM
ejpam-5794	7	12	]	]	PUNCT
ejpam-5794	7	13	ensures	ensure	VERB
ejpam-5794	7	14	the	the	DET
ejpam-5794	7	15	existence	existence	NOUN
ejpam-5794	7	16	and	and	CCONJ
ejpam-5794	7	17	uniqueness	uniqueness	NOUN
ejpam-5794	7	18	of	of	ADP
ejpam-5794	7	19	fixed	fix	VERB
ejpam-5794	7	20	points	point	NOUN
ejpam-5794	7	21	of	of	ADP
ejpam-5794	7	22	particular	particular	ADJ
ejpam-5794	7	23	self	self	NOUN
ejpam-5794	7	24	-	-	PUNCT
ejpam-5794	7	25	maps	map	NOUN
ejpam-5794	7	26	of	of	ADP
ejpam-5794	7	27	metric	metric	ADJ
ejpam-5794	7	28	spaces	space	NOUN
ejpam-5794	7	29	(	(	PUNCT
ejpam-5794	7	30	mss	mss	PROPN
ejpam-5794	7	31	)	)	PUNCT
ejpam-5794	7	32	and	and	CCONJ
ejpam-5794	7	33	provides	provide	VERB
ejpam-5794	7	34	a	a	DET
ejpam-5794	7	35	constructive	constructive	ADJ
ejpam-5794	7	36	approach	approach	NOUN
ejpam-5794	7	37	to	to	PART
ejpam-5794	7	38	identify	identify	VERB
ejpam-5794	7	39	those	those	DET
ejpam-5794	7	40	fixed	fix	VERB
ejpam-5794	7	41	points	point	NOUN
ejpam-5794	7	42	.	.	PUNCT
ejpam-5794	8	1	picard	picard	PROPN
ejpam-5794	8	2	’s	’s	PART
ejpam-5794	8	3	method	method	NOUN
ejpam-5794	8	4	[	[	X
ejpam-5794	8	5	20	20	NUM
ejpam-5794	8	6	]	]	PUNCT
ejpam-5794	8	7	of	of	ADP
ejpam-5794	8	8	consecutive	consecutive	ADJ
ejpam-5794	8	9	approximations	approximation	NOUN
ejpam-5794	8	10	might	might	AUX
ejpam-5794	8	11	be	be	AUX
ejpam-5794	8	12	viewed	view	VERB
ejpam-5794	8	13	as	as	ADP
ejpam-5794	8	14	an	an	DET
ejpam-5794	8	15	abstract	abstract	ADJ
ejpam-5794	8	16	formulation	formulation	NOUN
ejpam-5794	8	17	of	of	ADP
ejpam-5794	8	18	this	this	DET
ejpam-5794	8	19	method	method	NOUN
ejpam-5794	8	20	.	.	PUNCT
ejpam-5794	9	1	in	in	ADP
ejpam-5794	9	2	1922	1922	NUM
ejpam-5794	9	3	banach	banach	NOUN
ejpam-5794	9	4	established	establish	VERB
ejpam-5794	9	5	the	the	DET
ejpam-5794	9	6	following	following	ADJ
ejpam-5794	9	7	famous	famous	ADJ
ejpam-5794	9	8	result	result	NOUN
ejpam-5794	9	9	.	.	PUNCT
ejpam-5794	10	1	∗corresponding	∗corresponde	VERB
ejpam-5794	10	2	author	author	NOUN
ejpam-5794	10	3	.	.	PUNCT
ejpam-5794	11	1	doi	doi	NOUN
ejpam-5794	11	2	:	:	PUNCT
ejpam-5794	11	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5794	https://doi.org/10.29020/nybg.ejpam.v18i1.5794	NOUN
ejpam-5794	11	4	email	email	NOUN
ejpam-5794	11	5	addresses	address	NOUN
ejpam-5794	11	6	:	:	PUNCT
ejpam-5794	11	7	umarishtiaq000@gmail.com	umarishtiaq000@gmail.com	X
ejpam-5794	11	8	(	(	PUNCT
ejpam-5794	11	9	u.	u.	PROPN
ejpam-5794	11	10	ishtiaq	ishtiaq	PROPN
ejpam-5794	11	11	)	)	PUNCT
ejpam-5794	11	12	,	,	PUNCT
ejpam-5794	11	13	naeem.saleem2@gmail.com	naeem.saleem2@gmail.com	X
ejpam-5794	11	14	(	(	PUNCT
ejpam-5794	11	15	n.	n.	NOUN
ejpam-5794	11	16	saleem	saleem	PROPN
ejpam-5794	11	17	)	)	PUNCT
ejpam-5794	11	18	,	,	PUNCT
ejpam-5794	11	19	maggie.aphane@smu.ac.za	maggie.aphane@smu.ac.za	PROPN
ejpam-5794	11	20	(	(	PUNCT
ejpam-5794	11	21	m.	m.	NOUN
ejpam-5794	11	22	aphane	aphane	PROPN
ejpam-5794	11	23	)	)	PUNCT
ejpam-5794	11	24	,	,	PUNCT
ejpam-5794	11	25	muhammadfarhan@numl.edu.pk	muhammadfarhan@numl.edu.pk	INTJ
ejpam-5794	11	26	(	(	PUNCT
ejpam-5794	11	27	m.	m.	NOUN
ejpam-5794	11	28	farhan	farhan	PROPN
ejpam-5794	11	29	)	)	PUNCT
ejpam-5794	11	30	,	,	PUNCT
ejpam-5794	12	1	msrchowdhury@hotmail.com	msrchowdhury@hotmail.com	PROPN
ejpam-5794	12	2	showkat.rahim@math.uol.edu.pk	showkat.rahim@math.uol.edu.pk	PROPN
ejpam-5794	12	3	(	(	PUNCT
ejpam-5794	12	4	m	m	PROPN
ejpam-5794	12	5	s.	s.	PROPN
ejpam-5794	12	6	r.	r.	PROPN
ejpam-5794	12	7	chowdhury	chowdhury	PROPN
ejpam-5794	12	8	)	)	PUNCT
ejpam-5794	12	9	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5794	13	1	1	1	NUM
ejpam-5794	13	2	copyright	copyright	NOUN
ejpam-5794	13	3	:	:	PUNCT
ejpam-5794	13	4	©	©	PROPN
ejpam-5794	13	5	2025	2025	NUM
ejpam-5794	13	6	the	the	DET
ejpam-5794	13	7	author(s	author(s	NOUN
ejpam-5794	13	8	)	)	PUNCT
ejpam-5794	13	9	.	.	PUNCT
ejpam-5794	14	1	(	(	PUNCT
ejpam-5794	14	2	cc	cc	NOUN
ejpam-5794	14	3	by	by	ADP
ejpam-5794	14	4	-	-	PUNCT
ejpam-5794	14	5	nc	nc	PROPN
ejpam-5794	14	6	4.0	4.0	NUM
ejpam-5794	14	7	)	)	PUNCT
ejpam-5794	14	8	u.	u.	PROPN
ejpam-5794	14	9	ishtiaq	ishtiaq	PROPN
ejpam-5794	14	10	et	et	PROPN
ejpam-5794	14	11	al	al	PROPN
ejpam-5794	14	12	.	.	PUNCT
ejpam-5794	14	13	/	/	SYM
ejpam-5794	14	14	eur	eur	PROPN
ejpam-5794	14	15	.	.	PUNCT
ejpam-5794	15	1	j.	j.	PROPN
ejpam-5794	15	2	pure	pure	PROPN
ejpam-5794	15	3	appl	appl	PROPN
ejpam-5794	15	4	.	.	PROPN
ejpam-5794	15	5	math	math	PROPN
ejpam-5794	15	6	,	,	PUNCT
ejpam-5794	15	7	18	18	NUM
ejpam-5794	15	8	(	(	PUNCT
ejpam-5794	15	9	1	1	NUM
ejpam-5794	15	10	)	)	PUNCT
ejpam-5794	15	11	(	(	PUNCT
ejpam-5794	15	12	2025	2025	NUM
ejpam-5794	15	13	)	)	PUNCT
ejpam-5794	15	14	,	,	PUNCT
ejpam-5794	15	15	5794	5794	NUM
ejpam-5794	15	16	2	2	NUM
ejpam-5794	15	17	of	of	ADP
ejpam-5794	15	18	20	20	NUM
ejpam-5794	15	19	definition	definition	NOUN
ejpam-5794	15	20	1	1	NUM
ejpam-5794	15	21	.	.	PUNCT
ejpam-5794	16	1	[	[	X
ejpam-5794	16	2	10	10	NUM
ejpam-5794	16	3	]	]	PUNCT
ejpam-5794	16	4	suppose	suppose	VERB
ejpam-5794	16	5	(	(	PUNCT
ejpam-5794	16	6	ℵ,∆	ℵ,∆	PROPN
ejpam-5794	16	7	)	)	PUNCT
ejpam-5794	16	8	be	be	VERB
ejpam-5794	16	9	a	a	DET
ejpam-5794	16	10	ms	ms	PROPN
ejpam-5794	16	11	.	.	PROPN
ejpam-5794	17	1	then	then	ADV
ejpam-5794	17	2	a	a	DET
ejpam-5794	17	3	mapping	mapping	NOUN
ejpam-5794	17	4	t	t	NOUN
ejpam-5794	17	5	:	:	PUNCT
ejpam-5794	17	6	ℵ	ℵ	X
ejpam-5794	17	7	→	→	SYM
ejpam-5794	17	8	ℵ	ℵ	NOUN
ejpam-5794	17	9	is	be	AUX
ejpam-5794	17	10	known	know	VERB
ejpam-5794	17	11	as	as	ADP
ejpam-5794	17	12	contraction	contraction	NOUN
ejpam-5794	17	13	mapping	mapping	NOUN
ejpam-5794	17	14	on	on	ADP
ejpam-5794	17	15	ℵ	ℵ	NOUN
ejpam-5794	17	16	if	if	SCONJ
ejpam-5794	17	17	there	there	PRON
ejpam-5794	17	18	exists	exist	VERB
ejpam-5794	17	19	q	q	PROPN
ejpam-5794	17	20	∈	∈	PROPN
ejpam-5794	18	1	[	[	X
ejpam-5794	18	2	0	0	NUM
ejpam-5794	18	3	,	,	PUNCT
ejpam-5794	18	4	1	1	NUM
ejpam-5794	18	5	)	)	PUNCT
ejpam-5794	18	6	such	such	ADJ
ejpam-5794	18	7	that	that	SCONJ
ejpam-5794	18	8	∆(tϑ	∆(tϑ	NOUN
ejpam-5794	18	9	,	,	PUNCT
ejpam-5794	18	10	ty	ty	NOUN
ejpam-5794	18	11	)	)	PUNCT
ejpam-5794	18	12	≤	≤	NOUN
ejpam-5794	18	13	q∆(ϑ	q∆(ϑ	NOUN
ejpam-5794	18	14	,	,	PUNCT
ejpam-5794	18	15	y	y	NOUN
ejpam-5794	18	16	)	)	PUNCT
ejpam-5794	18	17	for	for	ADP
ejpam-5794	18	18	all	all	DET
ejpam-5794	18	19	ϑ	ϑ	X
ejpam-5794	18	20	,	,	PUNCT
ejpam-5794	18	21	y	y	PROPN
ejpam-5794	18	22	∈	∈	PROPN
ejpam-5794	18	23	ℵ.	ℵ.	PROPN
ejpam-5794	18	24	theorem	theorem	VERB
ejpam-5794	18	25	1	1	NUM
ejpam-5794	18	26	.	.	PUNCT
ejpam-5794	19	1	[	[	X
ejpam-5794	19	2	10	10	NUM
ejpam-5794	19	3	]	]	X
ejpam-5794	19	4	let	let	VERB
ejpam-5794	19	5	(	(	PUNCT
ejpam-5794	19	6	ℵ,∆	ℵ,∆	X
ejpam-5794	19	7	)	)	PUNCT
ejpam-5794	19	8	be	be	AUX
ejpam-5794	19	9	a	a	DET
ejpam-5794	19	10	complete	complete	ADJ
ejpam-5794	19	11	ms	ms	NOUN
ejpam-5794	19	12	and	and	CCONJ
ejpam-5794	19	13	t	t	PROPN
ejpam-5794	19	14	:	:	PUNCT
ejpam-5794	19	15	ℵ	ℵ	X
ejpam-5794	19	16	→	→	SYM
ejpam-5794	19	17	ℵ	ℵ	ADJ
ejpam-5794	19	18	be	be	VERB
ejpam-5794	19	19	a	a	DET
ejpam-5794	19	20	contraction	contraction	NOUN
ejpam-5794	19	21	mapping	mapping	NOUN
ejpam-5794	19	22	.	.	PUNCT
ejpam-5794	20	1	then	then	ADV
ejpam-5794	20	2	t	t	PROPN
ejpam-5794	20	3	has	have	VERB
ejpam-5794	20	4	a	a	DET
ejpam-5794	20	5	unique	unique	ADJ
ejpam-5794	20	6	fixed	fix	VERB
ejpam-5794	20	7	point	point	NOUN
ejpam-5794	20	8	ϑ	ϑ	ADP
ejpam-5794	20	9	∗	∗	NOUN
ejpam-5794	20	10	in	in	ADP
ejpam-5794	20	11	ℵ.	ℵ.	PROPN
ejpam-5794	21	1	many	many	ADJ
ejpam-5794	21	2	authors	author	NOUN
ejpam-5794	21	3	established	establish	VERB
ejpam-5794	21	4	various	various	ADJ
ejpam-5794	21	5	kinds	kind	NOUN
ejpam-5794	21	6	of	of	ADP
ejpam-5794	21	7	contraction	contraction	NOUN
ejpam-5794	21	8	inequalities	inequality	NOUN
ejpam-5794	21	9	in	in	ADP
ejpam-5794	21	10	an	an	DET
ejpam-5794	21	11	attempt	attempt	NOUN
ejpam-5794	21	12	to	to	PART
ejpam-5794	21	13	generalize	generalize	VERB
ejpam-5794	21	14	the	the	DET
ejpam-5794	21	15	famous	famous	ADJ
ejpam-5794	21	16	banach	banach	NOUN
ejpam-5794	21	17	contraction	contraction	NOUN
ejpam-5794	21	18	principle	principle	NOUN
ejpam-5794	21	19	by	by	ADP
ejpam-5794	21	20	using	use	VERB
ejpam-5794	21	21	different	different	ADJ
ejpam-5794	21	22	generalizations	generalization	NOUN
ejpam-5794	21	23	of	of	ADP
ejpam-5794	21	24	chistyakov	chistyakov	NOUN
ejpam-5794	21	25	[	[	X
ejpam-5794	21	26	13	13	NUM
ejpam-5794	21	27	]	]	PUNCT
ejpam-5794	21	28	established	establish	VERB
ejpam-5794	21	29	the	the	DET
ejpam-5794	21	30	notion	notion	NOUN
ejpam-5794	21	31	of	of	ADP
ejpam-5794	21	32	modular	modular	ADJ
ejpam-5794	21	33	ms	ms	NOUN
ejpam-5794	21	34	and	and	CCONJ
ejpam-5794	21	35	proved	prove	VERB
ejpam-5794	21	36	some	some	DET
ejpam-5794	21	37	new	new	ADJ
ejpam-5794	21	38	results	result	NOUN
ejpam-5794	21	39	.	.	PUNCT
ejpam-5794	22	1	definition	definition	NOUN
ejpam-5794	22	2	2	2	NUM
ejpam-5794	22	3	.	.	PUNCT
ejpam-5794	23	1	let	let	VERB
ejpam-5794	23	2	ℵ	ℵ	NOUN
ejpam-5794	23	3	be	be	AUX
ejpam-5794	23	4	a	a	DET
ejpam-5794	23	5	non	non	ADJ
ejpam-5794	23	6	-	-	ADJ
ejpam-5794	23	7	empty	empty	ADJ
ejpam-5794	23	8	set	set	NOUN
ejpam-5794	23	9	and	and	CCONJ
ejpam-5794	23	10	the	the	DET
ejpam-5794	23	11	function	function	NOUN
ejpam-5794	23	12	∆ξ	∆ξ	NOUN
ejpam-5794	23	13	:	:	PUNCT
ejpam-5794	23	14	(	(	PUNCT
ejpam-5794	23	15	0,+∞)×ℵ×ℵ	0,+∞)×ℵ×ℵ	NUM
ejpam-5794	23	16	→	→	SYM
ejpam-5794	23	17	[	[	X
ejpam-5794	23	18	0,+∞	0,+∞	NUM
ejpam-5794	23	19	]	]	PUNCT
ejpam-5794	23	20	,	,	PUNCT
ejpam-5794	23	21	which	which	PRON
ejpam-5794	23	22	satisfies	satisfy	VERB
ejpam-5794	23	23	the	the	DET
ejpam-5794	23	24	following	follow	VERB
ejpam-5794	23	25	axioms	axiom	NOUN
ejpam-5794	23	26	for	for	ADP
ejpam-5794	23	27	all	all	DET
ejpam-5794	23	28	µ	µ	NUM
ejpam-5794	23	29	,	,	PUNCT
ejpam-5794	23	30	κ	κ	NOUN
ejpam-5794	23	31	,	,	PUNCT
ejpam-5794	23	32	ϑ	ϑ	X
ejpam-5794	23	33	∈	∈	PROPN
ejpam-5794	23	34	ℵ	ℵ	NOUN
ejpam-5794	23	35	:	:	PUNCT
ejpam-5794	23	36	(	(	PUNCT
ejpam-5794	23	37	m1	m1	NOUN
ejpam-5794	23	38	)	)	PUNCT
ejpam-5794	23	39	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	23	40	,	,	PUNCT
ejpam-5794	23	41	κ	κ	NOUN
ejpam-5794	23	42	)	)	PUNCT
ejpam-5794	23	43	=	=	SYM
ejpam-5794	23	44	0	0	NUM
ejpam-5794	23	45	for	for	ADP
ejpam-5794	23	46	all	all	PRON
ejpam-5794	23	47	ξ	ξ	X
ejpam-5794	23	48	>	>	PUNCT
ejpam-5794	23	49	0	0	PUNCT
ejpam-5794	24	1	if	if	SCONJ
ejpam-5794	24	2	and	and	CCONJ
ejpam-5794	24	3	only	only	ADV
ejpam-5794	24	4	if	if	SCONJ
ejpam-5794	24	5	µ	µ	X
ejpam-5794	24	6	=	=	SYM
ejpam-5794	24	7	κ	κ	NOUN
ejpam-5794	24	8	;	;	PUNCT
ejpam-5794	24	9	(	(	PUNCT
ejpam-5794	24	10	m2	m2	PROPN
ejpam-5794	24	11	)	)	PUNCT
ejpam-5794	24	12	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	24	13	,	,	PUNCT
ejpam-5794	24	14	κ	κ	NOUN
ejpam-5794	24	15	)	)	PUNCT
ejpam-5794	24	16	=	=	SYM
ejpam-5794	24	17	∆ξ(κ	∆ξ(κ	PROPN
ejpam-5794	24	18	,	,	PUNCT
ejpam-5794	24	19	µ	µ	NOUN
ejpam-5794	24	20	)	)	PUNCT
ejpam-5794	24	21	for	for	ADP
ejpam-5794	24	22	all	all	PRON
ejpam-5794	24	23	ξ	ξ	X
ejpam-5794	24	24	>	>	X
ejpam-5794	24	25	0	0	NUM
ejpam-5794	24	26	;	;	PUNCT
ejpam-5794	24	27	(	(	PUNCT
ejpam-5794	24	28	m3	m3	PROPN
ejpam-5794	24	29	)	)	PUNCT
ejpam-5794	24	30	∆ξ+ρ(µ	∆ξ+ρ(µ	PROPN
ejpam-5794	24	31	,	,	PUNCT
ejpam-5794	24	32	κ	κ	NOUN
ejpam-5794	24	33	)	)	PUNCT
ejpam-5794	24	34	≤	≤	NOUN
ejpam-5794	24	35	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	24	36	,	,	PUNCT
ejpam-5794	24	37	ϑ	ϑ	NOUN
ejpam-5794	24	38	)	)	PUNCT
ejpam-5794	24	39	+	+	CCONJ
ejpam-5794	24	40	∆ρ(ϑ	∆ρ(ϑ	PROPN
ejpam-5794	24	41	,	,	PUNCT
ejpam-5794	24	42	κ	κ	NOUN
ejpam-5794	24	43	)	)	PUNCT
ejpam-5794	24	44	for	for	ADP
ejpam-5794	24	45	all	all	DET
ejpam-5794	24	46	ξ	ξ	PROPN
ejpam-5794	24	47	,	,	PUNCT
ejpam-5794	24	48	ρ	ρ	PROPN
ejpam-5794	24	49	>	>	X
ejpam-5794	24	50	0	0	PROPN
ejpam-5794	24	51	.	.	PUNCT
ejpam-5794	25	1	then	then	ADV
ejpam-5794	25	2	∆ξ	∆ξ	PROPN
ejpam-5794	25	3	be	be	AUX
ejpam-5794	25	4	known	know	VERB
ejpam-5794	25	5	as	as	ADP
ejpam-5794	25	6	a	a	DET
ejpam-5794	25	7	modular	modular	ADJ
ejpam-5794	25	8	metric	metric	NOUN
ejpam-5794	25	9	on	on	ADP
ejpam-5794	25	10	ℵ.	ℵ.	PROPN
ejpam-5794	25	11	recently	recently	ADV
ejpam-5794	25	12	,	,	PUNCT
ejpam-5794	25	13	abdou	abdou	PROPN
ejpam-5794	26	1	[	[	X
ejpam-5794	26	2	3	3	NUM
ejpam-5794	26	3	,	,	PUNCT
ejpam-5794	26	4	4	4	NUM
ejpam-5794	26	5	]	]	PUNCT
ejpam-5794	26	6	proved	prove	VERB
ejpam-5794	26	7	various	various	ADJ
ejpam-5794	26	8	interesting	interesting	ADJ
ejpam-5794	26	9	fixed	fix	VERB
ejpam-5794	26	10	point	point	NOUN
ejpam-5794	26	11	results	result	NOUN
ejpam-5794	26	12	in	in	ADP
ejpam-5794	26	13	the	the	DET
ejpam-5794	26	14	sense	sense	NOUN
ejpam-5794	26	15	of	of	ADP
ejpam-5794	26	16	modular	modular	ADJ
ejpam-5794	26	17	ms	ms	PROPN
ejpam-5794	26	18	.	.	PROPN
ejpam-5794	26	19	in	in	ADP
ejpam-5794	26	20	2018	2018	NUM
ejpam-5794	26	21	,	,	PUNCT
ejpam-5794	26	22	mlaiki	mlaiki	PROPN
ejpam-5794	26	23	et	et	PROPN
ejpam-5794	26	24	al	al	PROPN
ejpam-5794	26	25	.	.	PUNCT
ejpam-5794	27	1	[	[	X
ejpam-5794	27	2	21	21	NUM
ejpam-5794	27	3	]	]	PUNCT
ejpam-5794	27	4	established	establish	VERB
ejpam-5794	27	5	the	the	DET
ejpam-5794	27	6	notion	notion	NOUN
ejpam-5794	27	7	of	of	ADP
ejpam-5794	27	8	controlled	control	VERB
ejpam-5794	27	9	type	type	NOUN
ejpam-5794	27	10	ms	ms	NOUN
ejpam-5794	27	11	as	as	SCONJ
ejpam-5794	27	12	follows	follow	VERB
ejpam-5794	27	13	:	:	PUNCT
ejpam-5794	27	14	definition	definition	NOUN
ejpam-5794	27	15	3	3	NUM
ejpam-5794	27	16	.	.	PUNCT
ejpam-5794	27	17	consider	consider	VERB
ejpam-5794	27	18	a	a	DET
ejpam-5794	27	19	non	non	ADJ
ejpam-5794	27	20	-	-	ADJ
ejpam-5794	27	21	empty	empty	ADJ
ejpam-5794	27	22	set	set	ADJ
ejpam-5794	27	23	ℵ	ℵ	NOUN
ejpam-5794	27	24	and	and	CCONJ
ejpam-5794	27	25	the	the	DET
ejpam-5794	27	26	function	function	NOUN
ejpam-5794	27	27	α	α	NOUN
ejpam-5794	27	28	:	:	PUNCT
ejpam-5794	27	29	ℵ	ℵ	PROPN
ejpam-5794	27	30	×	×	NOUN
ejpam-5794	27	31	ℵ	ℵ	X
ejpam-5794	27	32	→	→	SYM
ejpam-5794	27	33	[	[	X
ejpam-5794	27	34	0,+∞	0,+∞	NUM
ejpam-5794	27	35	)	)	PUNCT
ejpam-5794	27	36	.	.	PUNCT
ejpam-5794	28	1	then	then	ADV
ejpam-5794	28	2	a	a	DET
ejpam-5794	28	3	function	function	NOUN
ejpam-5794	28	4	∆	∆	PROPN
ejpam-5794	28	5	:	:	PUNCT
ejpam-5794	28	6	ℵ	ℵ	X
ejpam-5794	28	7	×	×	NOUN
ejpam-5794	28	8	ℵ	ℵ	X
ejpam-5794	28	9	→	→	SYM
ejpam-5794	28	10	[	[	X
ejpam-5794	28	11	0,+∞	0,+∞	NUM
ejpam-5794	28	12	)	)	PUNCT
ejpam-5794	28	13	is	be	AUX
ejpam-5794	28	14	said	say	VERB
ejpam-5794	28	15	to	to	PART
ejpam-5794	28	16	be	be	AUX
ejpam-5794	28	17	controlled	control	VERB
ejpam-5794	28	18	ms	ms	NOUN
ejpam-5794	28	19	if	if	SCONJ
ejpam-5794	28	20	the	the	DET
ejpam-5794	28	21	following	follow	VERB
ejpam-5794	28	22	axioms	axiom	NOUN
ejpam-5794	28	23	holds	hold	VERB
ejpam-5794	28	24	for	for	ADP
ejpam-5794	28	25	all	all	DET
ejpam-5794	28	26	µ	µ	NUM
ejpam-5794	28	27	,	,	PUNCT
ejpam-5794	28	28	κ	κ	NOUN
ejpam-5794	28	29	,	,	PUNCT
ejpam-5794	28	30	ϑ	ϑ	X
ejpam-5794	28	31	∈	∈	PROPN
ejpam-5794	28	32	ℵ	ℵ	NOUN
ejpam-5794	28	33	:	:	PUNCT
ejpam-5794	28	34	(	(	PUNCT
ejpam-5794	28	35	c1	c1	NOUN
ejpam-5794	28	36	)	)	PUNCT
ejpam-5794	29	1	∆(µ	∆(µ	PROPN
ejpam-5794	29	2	,	,	PUNCT
ejpam-5794	29	3	κ	κ	NOUN
ejpam-5794	29	4	)	)	PUNCT
ejpam-5794	29	5	=	=	SYM
ejpam-5794	29	6	0	0	PUNCT
ejpam-5794	30	1	if	if	SCONJ
ejpam-5794	30	2	and	and	CCONJ
ejpam-5794	30	3	only	only	ADV
ejpam-5794	30	4	if	if	SCONJ
ejpam-5794	30	5	µ	µ	X
ejpam-5794	30	6	=	=	SYM
ejpam-5794	30	7	κ	κ	NOUN
ejpam-5794	30	8	;	;	PUNCT
ejpam-5794	30	9	(	(	PUNCT
ejpam-5794	30	10	c2	c2	PROPN
ejpam-5794	30	11	)	)	PUNCT
ejpam-5794	30	12	∆(µ	∆(µ	PROPN
ejpam-5794	30	13	,	,	PUNCT
ejpam-5794	30	14	κ	κ	NOUN
ejpam-5794	30	15	)	)	PUNCT
ejpam-5794	30	16	=	=	SYM
ejpam-5794	30	17	∆(κ	∆(κ	NOUN
ejpam-5794	30	18	,	,	PUNCT
ejpam-5794	30	19	µ	µ	NOUN
ejpam-5794	30	20	)	)	PUNCT
ejpam-5794	30	21	;	;	PUNCT
ejpam-5794	30	22	(	(	PUNCT
ejpam-5794	30	23	c3	c3	NOUN
ejpam-5794	30	24	)	)	PUNCT
ejpam-5794	30	25	∆(µ	∆(µ	PROPN
ejpam-5794	30	26	,	,	PUNCT
ejpam-5794	30	27	κ	κ	NOUN
ejpam-5794	30	28	)	)	PUNCT
ejpam-5794	30	29	≤	≤	NOUN
ejpam-5794	30	30	α(µ	α(µ	ADV
ejpam-5794	30	31	,	,	PUNCT
ejpam-5794	30	32	ϑ)∆(µ	ϑ)∆(µ	PROPN
ejpam-5794	30	33	,	,	PUNCT
ejpam-5794	30	34	ϑ	ϑ	NOUN
ejpam-5794	30	35	)	)	PUNCT
ejpam-5794	30	36	+	+	CCONJ
ejpam-5794	30	37	α(ϑ	α(ϑ	PROPN
ejpam-5794	30	38	,	,	PUNCT
ejpam-5794	30	39	κ)∆(y	κ)∆(y	PROPN
ejpam-5794	30	40	,	,	PUNCT
ejpam-5794	30	41	κ	κ	NOUN
ejpam-5794	30	42	)	)	PUNCT
ejpam-5794	30	43	.	.	PUNCT
ejpam-5794	31	1	then	then	ADV
ejpam-5794	31	2	the	the	DET
ejpam-5794	31	3	pair	pair	NOUN
ejpam-5794	31	4	(	(	PUNCT
ejpam-5794	31	5	∆,ℵ	∆,ℵ	CCONJ
ejpam-5794	31	6	)	)	PUNCT
ejpam-5794	31	7	is	be	AUX
ejpam-5794	31	8	called	call	VERB
ejpam-5794	31	9	a	a	DET
ejpam-5794	31	10	controlled	control	VERB
ejpam-5794	31	11	ms	ms	NOUN
ejpam-5794	31	12	.	.	PROPN
ejpam-5794	31	13	in	in	ADP
ejpam-5794	31	14	addition	addition	NOUN
ejpam-5794	31	15	,	,	PUNCT
ejpam-5794	31	16	mlaiki	mlaiki	PROPN
ejpam-5794	31	17	et	et	PROPN
ejpam-5794	31	18	al	al	PROPN
ejpam-5794	31	19	.	.	PUNCT
ejpam-5794	32	1	[	[	X
ejpam-5794	32	2	21	21	NUM
ejpam-5794	32	3	]	]	PUNCT
ejpam-5794	32	4	generalized	generalize	VERB
ejpam-5794	32	5	the	the	DET
ejpam-5794	32	6	banach	banach	ADV
ejpam-5794	32	7	fixed	fix	VERB
ejpam-5794	32	8	point	point	NOUN
ejpam-5794	32	9	theorem	theorem	VERB
ejpam-5794	32	10	.	.	PUNCT
ejpam-5794	33	1	in	in	ADP
ejpam-5794	33	2	2000	2000	NUM
ejpam-5794	33	3	,	,	PUNCT
ejpam-5794	33	4	branciari	branciari	NOUN
ejpam-5794	34	1	[	[	X
ejpam-5794	34	2	11	11	NUM
ejpam-5794	34	3	]	]	PUNCT
ejpam-5794	34	4	coined	coin	VERB
ejpam-5794	34	5	the	the	DET
ejpam-5794	34	6	concept	concept	NOUN
ejpam-5794	34	7	of	of	ADP
ejpam-5794	34	8	rectangular	rectangular	ADJ
ejpam-5794	34	9	(	(	PUNCT
ejpam-5794	34	10	generalized	generalized	ADJ
ejpam-5794	34	11	)	)	PUNCT
ejpam-5794	34	12	mss	mss	NOUN
ejpam-5794	34	13	as	as	SCONJ
ejpam-5794	34	14	follows	follow	VERB
ejpam-5794	34	15	:	:	PUNCT
ejpam-5794	34	16	definition	definition	NOUN
ejpam-5794	34	17	4	4	NUM
ejpam-5794	34	18	.	.	PUNCT
ejpam-5794	34	19	consider	consider	VERB
ejpam-5794	34	20	a	a	DET
ejpam-5794	34	21	non	non	ADJ
ejpam-5794	34	22	-	-	ADJ
ejpam-5794	34	23	empty	empty	ADJ
ejpam-5794	34	24	set	set	ADJ
ejpam-5794	34	25	ℵ	ℵ	NOUN
ejpam-5794	34	26	and	and	CCONJ
ejpam-5794	34	27	the	the	DET
ejpam-5794	34	28	mapping	mapping	NOUN
ejpam-5794	34	29	∆	∆	PROPN
ejpam-5794	34	30	:	:	PUNCT
ejpam-5794	35	1	ℵ×ℵ	ℵ×ℵ	PUNCT
ejpam-5794	35	2	→	→	X
ejpam-5794	35	3	[	[	X
ejpam-5794	35	4	0,+∞	0,+∞	NUM
ejpam-5794	35	5	)	)	PUNCT
ejpam-5794	35	6	satisfies	satisfy	VERB
ejpam-5794	35	7	the	the	DET
ejpam-5794	35	8	following	follow	VERB
ejpam-5794	35	9	conditions	condition	NOUN
ejpam-5794	35	10	:	:	PUNCT
ejpam-5794	35	11	(	(	PUNCT
ejpam-5794	35	12	r1	r1	NOUN
ejpam-5794	35	13	)	)	PUNCT
ejpam-5794	35	14	∆(µ	∆(µ	NOUN
ejpam-5794	35	15	,	,	PUNCT
ejpam-5794	35	16	κ	κ	NOUN
ejpam-5794	35	17	)	)	PUNCT
ejpam-5794	35	18	=	=	SYM
ejpam-5794	35	19	0	0	PUNCT
ejpam-5794	36	1	if	if	SCONJ
ejpam-5794	36	2	and	and	CCONJ
ejpam-5794	36	3	only	only	ADV
ejpam-5794	36	4	if	if	SCONJ
ejpam-5794	36	5	µ	µ	X
ejpam-5794	36	6	=	=	SYM
ejpam-5794	36	7	κ	κ	NOUN
ejpam-5794	36	8	;	;	PUNCT
ejpam-5794	36	9	u.	u.	PROPN
ejpam-5794	36	10	ishtiaq	ishtiaq	PROPN
ejpam-5794	36	11	et	et	PROPN
ejpam-5794	36	12	al	al	PROPN
ejpam-5794	36	13	.	.	PUNCT
ejpam-5794	36	14	/	/	SYM
ejpam-5794	36	15	eur	eur	PROPN
ejpam-5794	36	16	.	.	PUNCT
ejpam-5794	37	1	j.	j.	PROPN
ejpam-5794	37	2	pure	pure	PROPN
ejpam-5794	37	3	appl	appl	PROPN
ejpam-5794	37	4	.	.	PROPN
ejpam-5794	37	5	math	math	PROPN
ejpam-5794	37	6	,	,	PUNCT
ejpam-5794	37	7	18	18	NUM
ejpam-5794	37	8	(	(	PUNCT
ejpam-5794	37	9	1	1	NUM
ejpam-5794	37	10	)	)	PUNCT
ejpam-5794	37	11	(	(	PUNCT
ejpam-5794	37	12	2025	2025	NUM
ejpam-5794	37	13	)	)	PUNCT
ejpam-5794	37	14	,	,	PUNCT
ejpam-5794	37	15	5794	5794	NUM
ejpam-5794	37	16	3	3	NUM
ejpam-5794	37	17	of	of	ADP
ejpam-5794	37	18	20	20	NUM
ejpam-5794	37	19	(	(	PUNCT
ejpam-5794	37	20	r2	r2	PROPN
ejpam-5794	37	21	)	)	PUNCT
ejpam-5794	38	1	∆(µ	∆(µ	NOUN
ejpam-5794	38	2	,	,	PUNCT
ejpam-5794	38	3	κ	κ	NOUN
ejpam-5794	38	4	)	)	PUNCT
ejpam-5794	38	5	=	=	SYM
ejpam-5794	38	6	∆(κ	∆(κ	NOUN
ejpam-5794	38	7	,	,	PUNCT
ejpam-5794	38	8	µ	µ	NOUN
ejpam-5794	38	9	)	)	PUNCT
ejpam-5794	38	10	,	,	PUNCT
ejpam-5794	38	11	for	for	ADP
ejpam-5794	38	12	all	all	DET
ejpam-5794	38	13	µ	µ	NOUN
ejpam-5794	38	14	,	,	PUNCT
ejpam-5794	38	15	κ	κ	PROPN
ejpam-5794	38	16	∈	∈	PROPN
ejpam-5794	38	17	ℵ	ℵ	AUX
ejpam-5794	38	18	;	;	PUNCT
ejpam-5794	38	19	(	(	PUNCT
ejpam-5794	38	20	r3	r3	NOUN
ejpam-5794	38	21	)	)	PUNCT
ejpam-5794	39	1	∆(µ	∆(µ	NOUN
ejpam-5794	39	2	,	,	PUNCT
ejpam-5794	39	3	κ	κ	NOUN
ejpam-5794	39	4	)	)	PUNCT
ejpam-5794	39	5	≤	≤	NOUN
ejpam-5794	40	1	∆(µ	∆(µ	NOUN
ejpam-5794	40	2	,	,	PUNCT
ejpam-5794	40	3	ϑ	ϑ	NOUN
ejpam-5794	40	4	)	)	PUNCT
ejpam-5794	40	5	+	+	CCONJ
ejpam-5794	40	6	∆(ϑ	∆(ϑ	NOUN
ejpam-5794	40	7	,	,	PUNCT
ejpam-5794	40	8	y	y	NOUN
ejpam-5794	40	9	)	)	PUNCT
ejpam-5794	40	10	+	+	CCONJ
ejpam-5794	41	1	∆(y	∆(y	NOUN
ejpam-5794	41	2	,	,	PUNCT
ejpam-5794	41	3	κ	κ	NOUN
ejpam-5794	41	4	)	)	PUNCT
ejpam-5794	41	5	;	;	PUNCT
ejpam-5794	41	6	for	for	ADP
ejpam-5794	41	7	all	all	DET
ejpam-5794	41	8	µ	µ	NOUN
ejpam-5794	41	9	,	,	PUNCT
ejpam-5794	41	10	κ	κ	PROPN
ejpam-5794	41	11	∈	∈	PROPN
ejpam-5794	41	12	ℵ	ℵ	NOUN
ejpam-5794	41	13	and	and	CCONJ
ejpam-5794	41	14	all	all	DET
ejpam-5794	41	15	distinct	distinct	ADJ
ejpam-5794	41	16	points	point	NOUN
ejpam-5794	41	17	ϑ	ϑ	NOUN
ejpam-5794	41	18	,	,	PUNCT
ejpam-5794	41	19	y	y	PROPN
ejpam-5794	41	20	∈	∈	PROPN
ejpam-5794	41	21	ℵ.	ℵ.	PROPN
ejpam-5794	42	1	then	then	ADV
ejpam-5794	42	2	the	the	DET
ejpam-5794	42	3	pair	pair	NOUN
ejpam-5794	42	4	(	(	PUNCT
ejpam-5794	42	5	∆,ℵ	∆,ℵ	CCONJ
ejpam-5794	42	6	)	)	PUNCT
ejpam-5794	42	7	is	be	AUX
ejpam-5794	42	8	called	call	VERB
ejpam-5794	42	9	a	a	DET
ejpam-5794	42	10	rectangular	rectangular	ADJ
ejpam-5794	42	11	ms	ms	NOUN
ejpam-5794	42	12	.	.	PROPN
ejpam-5794	42	13	in	in	ADP
ejpam-5794	42	14	2021	2021	NUM
ejpam-5794	42	15	,	,	PUNCT
ejpam-5794	42	16	alamgir	alamgir	PROPN
ejpam-5794	42	17	et	et	PROPN
ejpam-5794	42	18	al	al	PROPN
ejpam-5794	42	19	.	.	PUNCT
ejpam-5794	43	1	[	[	X
ejpam-5794	43	2	5	5	NUM
ejpam-5794	43	3	]	]	PUNCT
ejpam-5794	43	4	coined	coin	VERB
ejpam-5794	43	5	the	the	DET
ejpam-5794	43	6	concept	concept	NOUN
ejpam-5794	43	7	of	of	ADP
ejpam-5794	43	8	controlled	control	VERB
ejpam-5794	43	9	rectangular	rectangular	ADJ
ejpam-5794	43	10	ms	ms	NOUN
ejpam-5794	43	11	and	and	CCONJ
ejpam-5794	43	12	proved	prove	VERB
ejpam-5794	43	13	some	some	DET
ejpam-5794	43	14	fixed	fix	VERB
ejpam-5794	43	15	point	point	NOUN
ejpam-5794	43	16	results	result	NOUN
ejpam-5794	43	17	for	for	ADP
ejpam-5794	43	18	contraction	contraction	NOUN
ejpam-5794	43	19	mappings	mapping	NOUN
ejpam-5794	43	20	.	.	PUNCT
ejpam-5794	44	1	definition	definition	NOUN
ejpam-5794	44	2	5	5	NUM
ejpam-5794	44	3	.	.	PUNCT
ejpam-5794	44	4	consider	consider	VERB
ejpam-5794	44	5	a	a	DET
ejpam-5794	44	6	nonempty	nonempty	ADJ
ejpam-5794	44	7	set	set	VERB
ejpam-5794	44	8	ℵ	ℵ	NOUN
ejpam-5794	44	9	and	and	CCONJ
ejpam-5794	44	10	the	the	DET
ejpam-5794	44	11	function	function	NOUN
ejpam-5794	44	12	α	α	NOUN
ejpam-5794	44	13	:	:	PUNCT
ejpam-5794	44	14	ℵ	ℵ	PROPN
ejpam-5794	44	15	×	×	NOUN
ejpam-5794	44	16	ℵ	ℵ	X
ejpam-5794	44	17	→	→	SYM
ejpam-5794	44	18	[	[	X
ejpam-5794	44	19	0,+∞	0,+∞	NUM
ejpam-5794	44	20	)	)	PUNCT
ejpam-5794	44	21	.	.	PUNCT
ejpam-5794	45	1	then	then	ADV
ejpam-5794	45	2	a	a	DET
ejpam-5794	45	3	function	function	NOUN
ejpam-5794	45	4	∆	∆	PROPN
ejpam-5794	45	5	:	:	PUNCT
ejpam-5794	45	6	ℵ	ℵ	X
ejpam-5794	45	7	×	×	NOUN
ejpam-5794	45	8	ℵ	ℵ	X
ejpam-5794	45	9	→	→	SYM
ejpam-5794	45	10	[	[	X
ejpam-5794	45	11	0,+∞	0,+∞	NUM
ejpam-5794	45	12	)	)	PUNCT
ejpam-5794	45	13	is	be	AUX
ejpam-5794	45	14	said	say	VERB
ejpam-5794	45	15	to	to	PART
ejpam-5794	45	16	be	be	AUX
ejpam-5794	45	17	a	a	DET
ejpam-5794	45	18	controlled	control	VERB
ejpam-5794	45	19	rectangular	rectangular	ADJ
ejpam-5794	45	20	ms	ms	NOUN
ejpam-5794	45	21	if	if	SCONJ
ejpam-5794	45	22	the	the	DET
ejpam-5794	45	23	following	follow	VERB
ejpam-5794	45	24	axioms	axiom	NOUN
ejpam-5794	45	25	hold	hold	VERB
ejpam-5794	45	26	:	:	PUNCT
ejpam-5794	45	27	(	(	PUNCT
ejpam-5794	45	28	cr1	cr1	NOUN
ejpam-5794	45	29	)	)	PUNCT
ejpam-5794	45	30	∆(µ	∆(µ	NOUN
ejpam-5794	45	31	,	,	PUNCT
ejpam-5794	45	32	κ	κ	NOUN
ejpam-5794	45	33	)	)	PUNCT
ejpam-5794	45	34	=	=	SYM
ejpam-5794	45	35	0	0	NUM
ejpam-5794	45	36	for	for	ADP
ejpam-5794	45	37	all	all	PRON
ejpam-5794	45	38	ξ	ξ	X
ejpam-5794	45	39	>	>	PUNCT
ejpam-5794	45	40	0	0	PUNCT
ejpam-5794	46	1	if	if	SCONJ
ejpam-5794	46	2	and	and	CCONJ
ejpam-5794	46	3	only	only	ADV
ejpam-5794	46	4	if	if	SCONJ
ejpam-5794	46	5	µ	µ	X
ejpam-5794	46	6	=	=	SYM
ejpam-5794	46	7	κ	κ	NOUN
ejpam-5794	46	8	;	;	PUNCT
ejpam-5794	46	9	(	(	PUNCT
ejpam-5794	46	10	cr2	cr2	NOUN
ejpam-5794	46	11	)	)	PUNCT
ejpam-5794	46	12	∆(µ	∆(µ	PROPN
ejpam-5794	46	13	,	,	PUNCT
ejpam-5794	46	14	κ	κ	NOUN
ejpam-5794	46	15	)	)	PUNCT
ejpam-5794	46	16	=	=	SYM
ejpam-5794	46	17	∆(κ	∆(κ	NOUN
ejpam-5794	46	18	,	,	PUNCT
ejpam-5794	46	19	µ	µ	NOUN
ejpam-5794	46	20	)	)	PUNCT
ejpam-5794	46	21	for	for	ADP
ejpam-5794	46	22	all	all	PRON
ejpam-5794	46	23	ξ	ξ	X
ejpam-5794	46	24	>	>	X
ejpam-5794	46	25	0	0	NUM
ejpam-5794	46	26	;	;	PUNCT
ejpam-5794	46	27	(	(	PUNCT
ejpam-5794	46	28	cr3	cr3	NOUN
ejpam-5794	46	29	)	)	PUNCT
ejpam-5794	46	30	∆(µ	∆(µ	NOUN
ejpam-5794	46	31	,	,	PUNCT
ejpam-5794	46	32	κ	κ	NOUN
ejpam-5794	46	33	)	)	PUNCT
ejpam-5794	46	34	≤	≤	NOUN
ejpam-5794	46	35	α(µ	α(µ	ADV
ejpam-5794	46	36	,	,	PUNCT
ejpam-5794	46	37	ϑ)∆(µ	ϑ)∆(µ	PROPN
ejpam-5794	46	38	,	,	PUNCT
ejpam-5794	46	39	ϑ	ϑ	NOUN
ejpam-5794	46	40	)	)	PUNCT
ejpam-5794	46	41	+	+	CCONJ
ejpam-5794	46	42	α(ϑ	α(ϑ	PROPN
ejpam-5794	46	43	,	,	PUNCT
ejpam-5794	46	44	y)∆(ϑ	y)∆(ϑ	PROPN
ejpam-5794	46	45	,	,	PUNCT
ejpam-5794	46	46	y	y	PROPN
ejpam-5794	46	47	)	)	PUNCT
ejpam-5794	46	48	+	+	CCONJ
ejpam-5794	47	1	α(y	α(y	NOUN
ejpam-5794	47	2	,	,	PUNCT
ejpam-5794	47	3	κ)∆(y	κ)∆(y	PROPN
ejpam-5794	47	4	,	,	PUNCT
ejpam-5794	47	5	κ	κ	NOUN
ejpam-5794	47	6	)	)	PUNCT
ejpam-5794	47	7	,	,	PUNCT
ejpam-5794	47	8	for	for	ADP
ejpam-5794	47	9	all	all	DET
ejpam-5794	47	10	µ	µ	NOUN
ejpam-5794	47	11	,	,	PUNCT
ejpam-5794	47	12	κ	κ	PROPN
ejpam-5794	47	13	∈	∈	PROPN
ejpam-5794	47	14	ℵ	ℵ	NOUN
ejpam-5794	47	15	and	and	CCONJ
ejpam-5794	47	16	all	all	DET
ejpam-5794	47	17	distinct	distinct	ADJ
ejpam-5794	47	18	points	point	NOUN
ejpam-5794	47	19	ϑ	ϑ	NOUN
ejpam-5794	47	20	,	,	PUNCT
ejpam-5794	47	21	y	y	PROPN
ejpam-5794	47	22	∈	∈	PROPN
ejpam-5794	47	23	ℵ.	ℵ.	PROPN
ejpam-5794	48	1	then	then	ADV
ejpam-5794	48	2	the	the	DET
ejpam-5794	48	3	pair	pair	NOUN
ejpam-5794	48	4	(	(	PUNCT
ejpam-5794	48	5	∆,ℵ	∆,ℵ	CCONJ
ejpam-5794	48	6	)	)	PUNCT
ejpam-5794	48	7	is	be	AUX
ejpam-5794	48	8	called	call	VERB
ejpam-5794	48	9	a	a	DET
ejpam-5794	48	10	controlled	control	VERB
ejpam-5794	48	11	rectangular	rectangular	ADJ
ejpam-5794	48	12	ms	ms	NOUN
ejpam-5794	48	13	.	.	PROPN
ejpam-5794	49	1	we	we	PRON
ejpam-5794	49	2	refer	refer	VERB
ejpam-5794	49	3	[	[	X
ejpam-5794	49	4	1	1	NUM
ejpam-5794	49	5	,	,	PUNCT
ejpam-5794	49	6	2	2	NUM
ejpam-5794	49	7	,	,	PUNCT
ejpam-5794	49	8	9	9	NUM
ejpam-5794	49	9	,	,	PUNCT
ejpam-5794	49	10	15	15	NUM
ejpam-5794	49	11	,	,	PUNCT
ejpam-5794	49	12	24–27	24–27	NUM
ejpam-5794	49	13	,	,	PUNCT
ejpam-5794	49	14	29	29	NUM
ejpam-5794	49	15	]	]	PUNCT
ejpam-5794	49	16	for	for	ADP
ejpam-5794	49	17	more	more	ADJ
ejpam-5794	49	18	detail	detail	NOUN
ejpam-5794	49	19	.	.	PUNCT
ejpam-5794	50	1	aydi	aydi	VERB
ejpam-5794	50	2	et	et	PROPN
ejpam-5794	50	3	.	.	PUNCT
ejpam-5794	51	1	al	al	PROPN
ejpam-5794	51	2	.	.	PUNCT
ejpam-5794	52	1	[	[	X
ejpam-5794	52	2	6	6	NUM
ejpam-5794	52	3	]	]	PUNCT
ejpam-5794	52	4	proved	prove	VERB
ejpam-5794	52	5	a	a	DET
ejpam-5794	52	6	fixed	fix	VERB
ejpam-5794	52	7	point	point	NOUN
ejpam-5794	52	8	theorem	theorem	NOUN
ejpam-5794	52	9	for	for	ADP
ejpam-5794	52	10	set	set	NOUN
ejpam-5794	52	11	-	-	PUNCT
ejpam-5794	52	12	valued	value	VERB
ejpam-5794	52	13	quasi	quasi	NOUN
ejpam-5794	52	14	-	-	NOUN
ejpam-5794	52	15	contractions	contraction	NOUN
ejpam-5794	52	16	in	in	ADP
ejpam-5794	52	17	b−metric	b−metric	ADJ
ejpam-5794	52	18	spaces	space	NOUN
ejpam-5794	52	19	.	.	PUNCT
ejpam-5794	53	1	karapinar	karapinar	VERB
ejpam-5794	53	2	et	et	PROPN
ejpam-5794	53	3	.	.	PUNCT
ejpam-5794	54	1	al	al	PROPN
ejpam-5794	54	2	.	.	PUNCT
ejpam-5794	55	1	[	[	X
ejpam-5794	55	2	16–18	16–18	NUM
ejpam-5794	55	3	]	]	PUNCT
ejpam-5794	55	4	proved	prove	VERB
ejpam-5794	55	5	several	several	ADJ
ejpam-5794	55	6	interesting	interesting	ADJ
ejpam-5794	55	7	fixed	fix	VERB
ejpam-5794	55	8	point	point	NOUN
ejpam-5794	55	9	theorems	theorem	NOUN
ejpam-5794	55	10	under	under	ADP
ejpam-5794	55	11	nonlinear	nonlinear	ADJ
ejpam-5794	55	12	contractive	contractive	ADJ
ejpam-5794	55	13	conditions	condition	NOUN
ejpam-5794	55	14	in	in	ADP
ejpam-5794	55	15	partially	partially	ADV
ejpam-5794	55	16	ordered	order	VERB
ejpam-5794	55	17	metric	metric	ADJ
ejpam-5794	55	18	spaces	space	NOUN
ejpam-5794	55	19	.	.	PUNCT
ejpam-5794	56	1	souayah	souayah	NOUN
ejpam-5794	56	2	and	and	CCONJ
ejpam-5794	56	3	mrad	mrad	NOUN
ejpam-5794	57	1	[	[	X
ejpam-5794	57	2	28	28	NUM
ejpam-5794	57	3	]	]	PUNCT
ejpam-5794	57	4	proved	prove	VERB
ejpam-5794	57	5	some	some	DET
ejpam-5794	57	6	fixed	fix	VERB
ejpam-5794	57	7	point	point	NOUN
ejpam-5794	57	8	results	result	NOUN
ejpam-5794	57	9	for	for	ADP
ejpam-5794	57	10	contraction	contraction	NOUN
ejpam-5794	57	11	mappings	mapping	NOUN
ejpam-5794	57	12	in	in	ADP
ejpam-5794	57	13	the	the	DET
ejpam-5794	57	14	context	context	NOUN
ejpam-5794	57	15	of	of	ADP
ejpam-5794	57	16	controlled	control	VERB
ejpam-5794	57	17	partial	partial	ADJ
ejpam-5794	57	18	metric	metric	ADJ
ejpam-5794	57	19	type	type	NOUN
ejpam-5794	57	20	spaces	space	NOUN
ejpam-5794	57	21	.	.	PUNCT
ejpam-5794	58	1	debnath	debnath	PROPN
ejpam-5794	58	2	and	and	CCONJ
ejpam-5794	58	3	sen	sen	PROPN
ejpam-5794	58	4	[	[	X
ejpam-5794	58	5	14	14	NUM
ejpam-5794	58	6	]	]	PUNCT
ejpam-5794	58	7	proved	prove	VERB
ejpam-5794	58	8	various	various	ADJ
ejpam-5794	58	9	fixed	fix	VERB
ejpam-5794	58	10	point	point	NOUN
ejpam-5794	58	11	results	result	NOUN
ejpam-5794	58	12	of	of	ADP
ejpam-5794	58	13	interpolative	interpolative	ADJ
ejpam-5794	58	14	ćirić-reich	ćirić-reich	NOUN
ejpam-5794	58	15	–	–	PUNCT
ejpam-5794	58	16	rus	rus	NOUN
ejpam-5794	58	17	-	-	PUNCT
ejpam-5794	58	18	type	type	NOUN
ejpam-5794	58	19	contractions	contraction	NOUN
ejpam-5794	58	20	in	in	ADP
ejpam-5794	58	21	b−metric	b−metric	ADJ
ejpam-5794	58	22	spaces	space	NOUN
ejpam-5794	58	23	.	.	PUNCT
ejpam-5794	59	1	roy	roy	PROPN
ejpam-5794	59	2	et	et	PROPN
ejpam-5794	59	3	.	.	PUNCT
ejpam-5794	60	1	al	al	PROPN
ejpam-5794	60	2	.	.	PUNCT
ejpam-5794	61	1	[	[	X
ejpam-5794	61	2	23	23	NUM
ejpam-5794	61	3	]	]	PUNCT
ejpam-5794	61	4	provided	provide	VERB
ejpam-5794	61	5	an	an	DET
ejpam-5794	61	6	extended	extended	ADJ
ejpam-5794	61	7	-metric	-metric	ADJ
ejpam-5794	61	8	-	-	PUNCT
ejpam-5794	61	9	type	type	NOUN
ejpam-5794	61	10	space	space	NOUN
ejpam-5794	61	11	and	and	CCONJ
ejpam-5794	61	12	related	relate	VERB
ejpam-5794	61	13	fixed	fix	VERB
ejpam-5794	61	14	point	point	NOUN
ejpam-5794	61	15	theorems	theorem	NOUN
ejpam-5794	61	16	with	with	ADP
ejpam-5794	61	17	an	an	DET
ejpam-5794	61	18	application	application	NOUN
ejpam-5794	61	19	to	to	ADP
ejpam-5794	61	20	nonlinear	nonlinear	ADJ
ejpam-5794	61	21	integral	integral	ADJ
ejpam-5794	61	22	equations	equation	NOUN
ejpam-5794	61	23	.	.	PUNCT
ejpam-5794	62	1	rossafi	rossafi	NOUN
ejpam-5794	62	2	and	and	CCONJ
ejpam-5794	62	3	kari	kari	X
ejpam-5794	63	1	[	[	X
ejpam-5794	63	2	22	22	NUM
ejpam-5794	63	3	]	]	PUNCT
ejpam-5794	63	4	gave	give	VERB
ejpam-5794	63	5	some	some	DET
ejpam-5794	63	6	fixed	fix	VERB
ejpam-5794	63	7	point	point	NOUN
ejpam-5794	63	8	results	result	NOUN
ejpam-5794	63	9	in	in	ADP
ejpam-5794	63	10	the	the	DET
ejpam-5794	63	11	sense	sense	NOUN
ejpam-5794	63	12	of	of	ADP
ejpam-5794	63	13	controlled	control	VERB
ejpam-5794	63	14	rectangular	rectangular	ADJ
ejpam-5794	63	15	metric	metric	ADJ
ejpam-5794	63	16	spaces	space	NOUN
ejpam-5794	63	17	.	.	PUNCT
ejpam-5794	64	1	budhia	budhia	VERB
ejpam-5794	64	2	et	et	PROPN
ejpam-5794	64	3	.	.	PUNCT
ejpam-5794	65	1	al	al	PROPN
ejpam-5794	65	2	.	.	PUNCT
ejpam-5794	66	1	[	[	X
ejpam-5794	66	2	12	12	NUM
ejpam-5794	66	3	]	]	PUNCT
ejpam-5794	66	4	provided	provide	VERB
ejpam-5794	66	5	some	some	DET
ejpam-5794	66	6	new	new	ADJ
ejpam-5794	66	7	fixed	fix	VERB
ejpam-5794	66	8	point	point	NOUN
ejpam-5794	66	9	results	result	NOUN
ejpam-5794	66	10	in	in	ADP
ejpam-5794	66	11	rectangular	rectangular	ADJ
ejpam-5794	66	12	metric	metric	ADJ
ejpam-5794	66	13	spaces	space	NOUN
ejpam-5794	66	14	with	with	ADP
ejpam-5794	66	15	an	an	DET
ejpam-5794	66	16	application	application	NOUN
ejpam-5794	66	17	to	to	ADP
ejpam-5794	66	18	fractional	fractional	ADJ
ejpam-5794	66	19	-	-	PUNCT
ejpam-5794	66	20	order	order	NOUN
ejpam-5794	66	21	functional	functional	ADJ
ejpam-5794	66	22	differential	differential	ADJ
ejpam-5794	66	23	equations	equation	NOUN
ejpam-5794	66	24	.	.	PUNCT
ejpam-5794	67	1	aydi	aydi	VERB
ejpam-5794	67	2	et	et	PROPN
ejpam-5794	67	3	.	.	PUNCT
ejpam-5794	68	1	al	al	PROPN
ejpam-5794	68	2	.	.	PUNCT
ejpam-5794	69	1	[	[	X
ejpam-5794	69	2	7	7	X
ejpam-5794	69	3	]	]	PUNCT
ejpam-5794	69	4	presented	present	VERB
ejpam-5794	69	5	a	a	DET
ejpam-5794	69	6	common	common	ADJ
ejpam-5794	69	7	jungck	jungck	NOUN
ejpam-5794	69	8	type	type	NOUN
ejpam-5794	69	9	fixed	fix	VERB
ejpam-5794	69	10	point	point	NOUN
ejpam-5794	69	11	result	result	NOUN
ejpam-5794	69	12	in	in	ADP
ejpam-5794	69	13	extended	extended	ADJ
ejpam-5794	69	14	rectangular	rectangular	ADJ
ejpam-5794	69	15	b−metric	b−metric	ADJ
ejpam-5794	69	16	spaces	space	NOUN
ejpam-5794	69	17	.	.	PUNCT
ejpam-5794	70	1	aydi	aydi	VERB
ejpam-5794	70	2	et	et	PROPN
ejpam-5794	70	3	.	.	PUNCT
ejpam-5794	71	1	al	al	PROPN
ejpam-5794	71	2	.	.	PUNCT
ejpam-5794	72	1	[	[	X
ejpam-5794	72	2	8	8	NUM
ejpam-5794	72	3	]	]	PUNCT
ejpam-5794	72	4	gave	give	VERB
ejpam-5794	72	5	fixed	fix	VERB
ejpam-5794	72	6	-	-	PUNCT
ejpam-5794	72	7	discs	disc	NOUN
ejpam-5794	72	8	in	in	ADP
ejpam-5794	72	9	rectangular	rectangular	ADJ
ejpam-5794	72	10	metric	metric	ADJ
ejpam-5794	72	11	spaces	space	NOUN
ejpam-5794	72	12	.	.	PUNCT
ejpam-5794	73	1	kari	kari	X
ejpam-5794	73	2	et	et	PROPN
ejpam-5794	73	3	.	.	PUNCT
ejpam-5794	74	1	al	al	PROPN
ejpam-5794	74	2	.	.	PUNCT
ejpam-5794	75	1	[	[	X
ejpam-5794	75	2	19	19	NUM
ejpam-5794	75	3	]	]	PUNCT
ejpam-5794	75	4	established	establish	VERB
ejpam-5794	75	5	contraction	contraction	NOUN
ejpam-5794	75	6	mapping	mapping	NOUN
ejpam-5794	75	7	on	on	ADP
ejpam-5794	75	8	complete	complete	ADJ
ejpam-5794	75	9	rectangular	rectangular	ADJ
ejpam-5794	75	10	metric	metric	ADJ
ejpam-5794	75	11	spaces	space	NOUN
ejpam-5794	75	12	.	.	PUNCT
ejpam-5794	76	1	in	in	ADP
ejpam-5794	76	2	this	this	DET
ejpam-5794	76	3	manuscript	manuscript	NOUN
ejpam-5794	76	4	,	,	PUNCT
ejpam-5794	76	5	we	we	PRON
ejpam-5794	76	6	introduce	introduce	VERB
ejpam-5794	76	7	the	the	DET
ejpam-5794	76	8	notions	notion	NOUN
ejpam-5794	76	9	of	of	ADP
ejpam-5794	76	10	rectangular	rectangular	ADJ
ejpam-5794	76	11	modular	modular	ADJ
ejpam-5794	76	12	metric	metric	ADJ
ejpam-5794	76	13	space	space	NOUN
ejpam-5794	76	14	(	(	PUNCT
ejpam-5794	76	15	rmms	rmms	NOUN
ejpam-5794	76	16	)	)	PUNCT
ejpam-5794	76	17	and	and	CCONJ
ejpam-5794	76	18	controlled	control	VERB
ejpam-5794	76	19	rectangular	rectangular	ADJ
ejpam-5794	76	20	modular	modular	ADJ
ejpam-5794	76	21	metric	metric	ADJ
ejpam-5794	76	22	space	space	NOUN
ejpam-5794	76	23	(	(	PUNCT
ejpam-5794	76	24	crmms	crmms	PROPN
ejpam-5794	76	25	)	)	PUNCT
ejpam-5794	76	26	.	.	PUNCT
ejpam-5794	77	1	we	we	PRON
ejpam-5794	77	2	generalize	generalize	VERB
ejpam-5794	77	3	and	and	CCONJ
ejpam-5794	77	4	prove	prove	VERB
ejpam-5794	77	5	the	the	DET
ejpam-5794	77	6	well	well	ADV
ejpam-5794	77	7	-	-	PUNCT
ejpam-5794	77	8	known	know	VERB
ejpam-5794	77	9	banach	banach	NOUN
ejpam-5794	77	10	fixed	fix	VERB
ejpam-5794	77	11	point	point	NOUN
ejpam-5794	77	12	theorem	theorem	VERB
ejpam-5794	77	13	in	in	ADP
ejpam-5794	77	14	the	the	DET
ejpam-5794	77	15	sense	sense	NOUN
ejpam-5794	77	16	of	of	ADP
ejpam-5794	77	17	crmms	crmms	NOUN
ejpam-5794	77	18	.	.	PUNCT
ejpam-5794	78	1	we	we	PRON
ejpam-5794	78	2	also	also	ADV
ejpam-5794	78	3	give	give	VERB
ejpam-5794	78	4	some	some	DET
ejpam-5794	78	5	non	non	ADJ
ejpam-5794	78	6	-	-	ADJ
ejpam-5794	78	7	trivial	trivial	ADJ
ejpam-5794	78	8	examples	example	NOUN
ejpam-5794	78	9	to	to	PART
ejpam-5794	78	10	ensure	ensure	VERB
ejpam-5794	78	11	the	the	DET
ejpam-5794	78	12	validity	validity	NOUN
ejpam-5794	78	13	of	of	ADP
ejpam-5794	78	14	provided	provide	VERB
ejpam-5794	78	15	fixed	fix	VERB
ejpam-5794	78	16	point	point	NOUN
ejpam-5794	78	17	results	result	NOUN
ejpam-5794	78	18	.	.	PUNCT
ejpam-5794	79	1	at	at	ADP
ejpam-5794	79	2	the	the	DET
ejpam-5794	79	3	end	end	NOUN
ejpam-5794	79	4	,	,	PUNCT
ejpam-5794	79	5	we	we	PRON
ejpam-5794	79	6	use	use	VERB
ejpam-5794	79	7	a	a	DET
ejpam-5794	79	8	fixed	fix	VERB
ejpam-5794	79	9	point	point	NOUN
ejpam-5794	79	10	technique	technique	NOUN
ejpam-5794	79	11	to	to	PART
ejpam-5794	79	12	ensure	ensure	VERB
ejpam-5794	79	13	the	the	DET
ejpam-5794	79	14	existence	existence	NOUN
ejpam-5794	79	15	and	and	CCONJ
ejpam-5794	79	16	uniqueness	uniqueness	NOUN
ejpam-5794	79	17	of	of	ADP
ejpam-5794	79	18	non	non	ADJ
ejpam-5794	79	19	-	-	ADJ
ejpam-5794	79	20	linear	linear	ADJ
ejpam-5794	79	21	fractional	fractional	ADJ
ejpam-5794	79	22	differential	differential	NOUN
ejpam-5794	79	23	equations	equation	NOUN
ejpam-5794	79	24	.	.	PUNCT
ejpam-5794	80	1	from	from	ADP
ejpam-5794	80	2	now	now	ADV
ejpam-5794	80	3	to	to	ADP
ejpam-5794	80	4	onward	onward	NOUN
ejpam-5794	80	5	,	,	PUNCT
ejpam-5794	80	6	we	we	PRON
ejpam-5794	80	7	use	use	VERB
ejpam-5794	80	8	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	80	9	,	,	PUNCT
ejpam-5794	80	10	κ	κ	NOUN
ejpam-5794	80	11	)	)	PUNCT
ejpam-5794	80	12	=	=	SYM
ejpam-5794	81	1	∆(µ	∆(µ	NOUN
ejpam-5794	81	2	,	,	PUNCT
ejpam-5794	81	3	κ	κ	NOUN
ejpam-5794	81	4	,	,	PUNCT
ejpam-5794	81	5	ξ	ξ	NOUN
ejpam-5794	81	6	)	)	PUNCT
ejpam-5794	81	7	,	,	PUNCT
ejpam-5794	81	8	for	for	ADP
ejpam-5794	81	9	all	all	DET
ejpam-5794	81	10	µ	µ	NOUN
ejpam-5794	81	11	,	,	PUNCT
ejpam-5794	81	12	κ	κ	PROPN
ejpam-5794	81	13	∈	∈	PROPN
ejpam-5794	81	14	ℵ	ℵ	NOUN
ejpam-5794	81	15	which	which	PRON
ejpam-5794	81	16	denotes	denote	VERB
ejpam-5794	81	17	the	the	DET
ejpam-5794	81	18	map	map	NOUN
ejpam-5794	81	19	∆ξ	∆ξ	NOUN
ejpam-5794	81	20	:	:	PUNCT
ejpam-5794	81	21	ℵ	ℵ	PROPN
ejpam-5794	81	22	×	×	NOUN
ejpam-5794	81	23	ℵ	ℵ	X
ejpam-5794	81	24	×	×	NOUN
ejpam-5794	81	25	(	(	PUNCT
ejpam-5794	81	26	0,+∞	0,+∞	NUM
ejpam-5794	81	27	)	)	PUNCT
ejpam-5794	81	28	→	→	PUNCT
ejpam-5794	82	1	[	[	X
ejpam-5794	82	2	0,+∞	0,+∞	NUM
ejpam-5794	82	3	)	)	PUNCT
ejpam-5794	82	4	,	,	PUNCT
ejpam-5794	82	5	where	where	SCONJ
ejpam-5794	82	6	ξ	ξ	PROPN
ejpam-5794	82	7	∈	∈	PROPN
ejpam-5794	82	8	(	(	PUNCT
ejpam-5794	82	9	0,+∞	0,+∞	NUM
ejpam-5794	82	10	)	)	PUNCT
ejpam-5794	82	11	.	.	PUNCT
ejpam-5794	83	1	u.	u.	PROPN
ejpam-5794	83	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	83	3	et	et	PROPN
ejpam-5794	83	4	al	al	PROPN
ejpam-5794	83	5	.	.	PUNCT
ejpam-5794	83	6	/	/	SYM
ejpam-5794	83	7	eur	eur	PROPN
ejpam-5794	83	8	.	.	PUNCT
ejpam-5794	84	1	j.	j.	PROPN
ejpam-5794	84	2	pure	pure	PROPN
ejpam-5794	84	3	appl	appl	PROPN
ejpam-5794	84	4	.	.	PROPN
ejpam-5794	84	5	math	math	PROPN
ejpam-5794	84	6	,	,	PUNCT
ejpam-5794	84	7	18	18	NUM
ejpam-5794	84	8	(	(	PUNCT
ejpam-5794	84	9	1	1	NUM
ejpam-5794	84	10	)	)	PUNCT
ejpam-5794	84	11	(	(	PUNCT
ejpam-5794	84	12	2025	2025	NUM
ejpam-5794	84	13	)	)	PUNCT
ejpam-5794	84	14	,	,	PUNCT
ejpam-5794	84	15	5794	5794	NUM
ejpam-5794	84	16	4	4	NUM
ejpam-5794	84	17	of	of	ADP
ejpam-5794	84	18	20	20	NUM
ejpam-5794	84	19	2	2	NUM
ejpam-5794	84	20	.	.	PUNCT
ejpam-5794	84	21	main	main	ADJ
ejpam-5794	84	22	results	result	NOUN
ejpam-5794	84	23	in	in	ADP
ejpam-5794	84	24	this	this	DET
ejpam-5794	84	25	section	section	NOUN
ejpam-5794	84	26	,	,	PUNCT
ejpam-5794	84	27	we	we	PRON
ejpam-5794	84	28	will	will	AUX
ejpam-5794	84	29	introduce	introduce	VERB
ejpam-5794	84	30	the	the	DET
ejpam-5794	84	31	concepts	concept	NOUN
ejpam-5794	84	32	of	of	ADP
ejpam-5794	84	33	rmms	rmms	ADJ
ejpam-5794	84	34	and	and	CCONJ
ejpam-5794	84	35	crmms	crmms	NOUN
ejpam-5794	84	36	and	and	CCONJ
ejpam-5794	84	37	develop	develop	VERB
ejpam-5794	84	38	some	some	DET
ejpam-5794	84	39	fixed	fix	VERB
ejpam-5794	84	40	-	-	PUNCT
ejpam-5794	84	41	point	point	NOUN
ejpam-5794	84	42	results	result	NOUN
ejpam-5794	84	43	.	.	PUNCT
ejpam-5794	85	1	definition	definition	NOUN
ejpam-5794	85	2	6	6	NUM
ejpam-5794	85	3	.	.	PUNCT
ejpam-5794	85	4	consider	consider	VERB
ejpam-5794	85	5	a	a	DET
ejpam-5794	85	6	non	non	ADJ
ejpam-5794	85	7	-	-	ADJ
ejpam-5794	85	8	empty	empty	ADJ
ejpam-5794	85	9	set	set	ADJ
ejpam-5794	85	10	ℵ	ℵ	NOUN
ejpam-5794	85	11	and	and	CCONJ
ejpam-5794	85	12	the	the	DET
ejpam-5794	85	13	mapping	mapping	NOUN
ejpam-5794	85	14	∆ξ	∆ξ	NOUN
ejpam-5794	85	15	:	:	PUNCT
ejpam-5794	85	16	ℵ	ℵ	PROPN
ejpam-5794	85	17	×	×	NOUN
ejpam-5794	85	18	ℵ	ℵ	X
ejpam-5794	85	19	×	×	NOUN
ejpam-5794	85	20	(	(	PUNCT
ejpam-5794	85	21	0,+∞	0,+∞	NUM
ejpam-5794	85	22	)	)	PUNCT
ejpam-5794	85	23	→	→	PUNCT
ejpam-5794	86	1	[	[	X
ejpam-5794	86	2	0,+∞	0,+∞	NUM
ejpam-5794	86	3	)	)	PUNCT
ejpam-5794	86	4	,	,	PUNCT
ejpam-5794	86	5	which	which	PRON
ejpam-5794	86	6	satisfies	satisfy	VERB
ejpam-5794	86	7	the	the	DET
ejpam-5794	86	8	following	follow	VERB
ejpam-5794	86	9	axioms	axiom	NOUN
ejpam-5794	86	10	:	:	PUNCT
ejpam-5794	86	11	(	(	PUNCT
ejpam-5794	86	12	rm1	rm1	X
ejpam-5794	86	13	)	)	PUNCT
ejpam-5794	86	14	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	86	15	,	,	PUNCT
ejpam-5794	86	16	κ	κ	NOUN
ejpam-5794	86	17	)	)	PUNCT
ejpam-5794	86	18	=	=	SYM
ejpam-5794	86	19	0	0	PUNCT
ejpam-5794	87	1	if	if	SCONJ
ejpam-5794	87	2	and	and	CCONJ
ejpam-5794	87	3	only	only	ADV
ejpam-5794	87	4	if	if	SCONJ
ejpam-5794	87	5	µ	µ	X
ejpam-5794	87	6	=	=	SYM
ejpam-5794	87	7	κ	κ	NOUN
ejpam-5794	87	8	;	;	PUNCT
ejpam-5794	87	9	(	(	PUNCT
ejpam-5794	87	10	rm2	rm2	PROPN
ejpam-5794	87	11	)	)	PUNCT
ejpam-5794	87	12	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	87	13	,	,	PUNCT
ejpam-5794	87	14	κ	κ	NOUN
ejpam-5794	87	15	)	)	PUNCT
ejpam-5794	87	16	=	=	SYM
ejpam-5794	87	17	∆ξ(κ	∆ξ(κ	PROPN
ejpam-5794	87	18	,	,	PUNCT
ejpam-5794	87	19	µ	µ	NOUN
ejpam-5794	87	20	)	)	PUNCT
ejpam-5794	87	21	;	;	PUNCT
ejpam-5794	87	22	(	(	PUNCT
ejpam-5794	87	23	rm3	rm3	NOUN
ejpam-5794	87	24	)	)	PUNCT
ejpam-5794	87	25	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	87	26	,	,	PUNCT
ejpam-5794	87	27	κ	κ	NOUN
ejpam-5794	87	28	)	)	PUNCT
ejpam-5794	87	29	≤	≤	NOUN
ejpam-5794	87	30	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	87	31	,	,	PUNCT
ejpam-5794	87	32	ϑ	ϑ	NOUN
ejpam-5794	87	33	)	)	PUNCT
ejpam-5794	87	34	+	+	CCONJ
ejpam-5794	87	35	∆ξ(ϑ	∆ξ(ϑ	PROPN
ejpam-5794	87	36	,	,	PUNCT
ejpam-5794	87	37	y	y	NOUN
ejpam-5794	87	38	)	)	PUNCT
ejpam-5794	87	39	+	+	CCONJ
ejpam-5794	87	40	∆ξ(y	∆ξ(y	NOUN
ejpam-5794	87	41	,	,	PUNCT
ejpam-5794	87	42	κ	κ	NOUN
ejpam-5794	87	43	)	)	PUNCT
ejpam-5794	87	44	;	;	PUNCT
ejpam-5794	87	45	for	for	ADP
ejpam-5794	87	46	all	all	DET
ejpam-5794	87	47	ξ	ξ	PROPN
ejpam-5794	87	48	>	>	SYM
ejpam-5794	87	49	0	0	NUM
ejpam-5794	87	50	,	,	PUNCT
ejpam-5794	87	51	µ	µ	NOUN
ejpam-5794	87	52	,	,	PUNCT
ejpam-5794	87	53	κ	κ	PROPN
ejpam-5794	87	54	∈	∈	PROPN
ejpam-5794	87	55	ℵ	ℵ	NOUN
ejpam-5794	87	56	and	and	CCONJ
ejpam-5794	87	57	all	all	DET
ejpam-5794	87	58	distinct	distinct	ADJ
ejpam-5794	87	59	points	point	NOUN
ejpam-5794	87	60	ϑ	ϑ	NOUN
ejpam-5794	87	61	,	,	PUNCT
ejpam-5794	87	62	y	y	PROPN
ejpam-5794	87	63	∈	∈	PROPN
ejpam-5794	87	64	ℵ.	ℵ.	PROPN
ejpam-5794	88	1	then	then	ADV
ejpam-5794	88	2	the	the	DET
ejpam-5794	88	3	pair	pair	NOUN
ejpam-5794	88	4	(	(	PUNCT
ejpam-5794	88	5	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	88	6	,	,	PUNCT
ejpam-5794	88	7	ξ	ξ	X
ejpam-5794	88	8	)	)	PUNCT
ejpam-5794	88	9	is	be	AUX
ejpam-5794	88	10	called	call	VERB
ejpam-5794	88	11	rmms	rmms	ADJ
ejpam-5794	88	12	.	.	PUNCT
ejpam-5794	89	1	definition	definition	NOUN
ejpam-5794	89	2	7	7	NUM
ejpam-5794	89	3	.	.	PUNCT
ejpam-5794	89	4	consider	consider	VERB
ejpam-5794	89	5	a	a	DET
ejpam-5794	89	6	non	non	ADJ
ejpam-5794	89	7	-	-	ADJ
ejpam-5794	89	8	empty	empty	ADJ
ejpam-5794	89	9	set	set	ADJ
ejpam-5794	89	10	ℵ	ℵ	NOUN
ejpam-5794	89	11	and	and	CCONJ
ejpam-5794	89	12	α	α	NOUN
ejpam-5794	89	13	:	:	PUNCT
ejpam-5794	89	14	ℵ	ℵ	PROPN
ejpam-5794	89	15	×	×	NOUN
ejpam-5794	89	16	ℵ	ℵ	X
ejpam-5794	89	17	→	→	SYM
ejpam-5794	89	18	[	[	X
ejpam-5794	89	19	0,+∞	0,+∞	NUM
ejpam-5794	89	20	)	)	PUNCT
ejpam-5794	89	21	.	.	PUNCT
ejpam-5794	90	1	then	then	ADV
ejpam-5794	90	2	a	a	DET
ejpam-5794	90	3	function	function	NOUN
ejpam-5794	90	4	∆ξ	∆ξ	NOUN
ejpam-5794	90	5	:	:	PUNCT
ejpam-5794	90	6	ℵ×	ℵ×	ADP
ejpam-5794	90	7	ℵ×	ℵ×	PROPN
ejpam-5794	90	8	(	(	PUNCT
ejpam-5794	90	9	0,+∞	0,+∞	NUM
ejpam-5794	90	10	)	)	PUNCT
ejpam-5794	90	11	→	→	PUNCT
ejpam-5794	91	1	[	[	X
ejpam-5794	91	2	0,+∞	0,+∞	NUM
ejpam-5794	91	3	)	)	PUNCT
ejpam-5794	91	4	is	be	AUX
ejpam-5794	91	5	said	say	VERB
ejpam-5794	91	6	to	to	PART
ejpam-5794	91	7	be	be	AUX
ejpam-5794	91	8	controlled	control	VERB
ejpam-5794	91	9	rectangular	rectangular	ADJ
ejpam-5794	91	10	modular	modular	ADJ
ejpam-5794	91	11	metric	metric	NOUN
ejpam-5794	91	12	if	if	SCONJ
ejpam-5794	91	13	for	for	ADP
ejpam-5794	91	14	all	all	DET
ejpam-5794	91	15	ξ	ξ	X
ejpam-5794	91	16	>	>	SYM
ejpam-5794	91	17	0	0	NUM
ejpam-5794	91	18	,	,	PUNCT
ejpam-5794	91	19	µ	µ	NOUN
ejpam-5794	91	20	,	,	PUNCT
ejpam-5794	91	21	κ	κ	PROPN
ejpam-5794	91	22	∈	∈	PROPN
ejpam-5794	91	23	ℵ	ℵ	NOUN
ejpam-5794	91	24	and	and	CCONJ
ejpam-5794	91	25	distinct	distinct	ADJ
ejpam-5794	91	26	ϑ	ϑ	NOUN
ejpam-5794	91	27	,	,	PUNCT
ejpam-5794	91	28	y	y	PROPN
ejpam-5794	91	29	∈	∈	PROPN
ejpam-5794	91	30	ℵ	ℵ	ADP
ejpam-5794	91	31	the	the	DET
ejpam-5794	91	32	following	following	ADJ
ejpam-5794	91	33	axioms	axiom	NOUN
ejpam-5794	91	34	are	be	AUX
ejpam-5794	91	35	satisfied	satisfied	ADJ
ejpam-5794	91	36	:	:	PUNCT
ejpam-5794	91	37	(	(	PUNCT
ejpam-5794	91	38	cm1	cm1	NOUN
ejpam-5794	91	39	)	)	PUNCT
ejpam-5794	91	40	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	91	41	,	,	PUNCT
ejpam-5794	91	42	κ	κ	NOUN
ejpam-5794	91	43	)	)	PUNCT
ejpam-5794	91	44	=	=	SYM
ejpam-5794	91	45	0	0	PUNCT
ejpam-5794	92	1	if	if	SCONJ
ejpam-5794	92	2	and	and	CCONJ
ejpam-5794	92	3	only	only	ADV
ejpam-5794	92	4	if	if	SCONJ
ejpam-5794	92	5	µ	µ	X
ejpam-5794	92	6	=	=	SYM
ejpam-5794	92	7	κ	κ	NOUN
ejpam-5794	92	8	;	;	PUNCT
ejpam-5794	92	9	(	(	PUNCT
ejpam-5794	92	10	cm2	cm2	NOUN
ejpam-5794	92	11	)	)	PUNCT
ejpam-5794	92	12	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	92	13	,	,	PUNCT
ejpam-5794	92	14	κ	κ	NOUN
ejpam-5794	92	15	)	)	PUNCT
ejpam-5794	92	16	=	=	SYM
ejpam-5794	92	17	∆ξ(κ	∆ξ(κ	PROPN
ejpam-5794	92	18	,	,	PUNCT
ejpam-5794	92	19	µ	µ	NOUN
ejpam-5794	92	20	)	)	PUNCT
ejpam-5794	92	21	for	for	ADP
ejpam-5794	92	22	all	all	DET
ejpam-5794	92	23	µ	µ	NOUN
ejpam-5794	92	24	,	,	PUNCT
ejpam-5794	92	25	κ	κ	PROPN
ejpam-5794	92	26	∈	∈	PROPN
ejpam-5794	92	27	ℵ	ℵ	NOUN
ejpam-5794	92	28	;	;	PUNCT
ejpam-5794	92	29	(	(	PUNCT
ejpam-5794	92	30	cm3	cm3	NOUN
ejpam-5794	92	31	)	)	PUNCT
ejpam-5794	92	32	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	92	33	,	,	PUNCT
ejpam-5794	92	34	κ	κ	NOUN
ejpam-5794	92	35	)	)	PUNCT
ejpam-5794	92	36	≤	≤	NOUN
ejpam-5794	92	37	α(µ	α(µ	ADV
ejpam-5794	92	38	,	,	PUNCT
ejpam-5794	92	39	ϑ)∆ξ(µ	ϑ)∆ξ(µ	PROPN
ejpam-5794	92	40	,	,	PUNCT
ejpam-5794	92	41	ϑ	ϑ	NOUN
ejpam-5794	92	42	)	)	PUNCT
ejpam-5794	92	43	+	+	CCONJ
ejpam-5794	92	44	α(ϑ	α(ϑ	PROPN
ejpam-5794	92	45	,	,	PUNCT
ejpam-5794	92	46	y)∆ξ(ϑ	y)∆ξ(ϑ	PROPN
ejpam-5794	92	47	,	,	PUNCT
ejpam-5794	92	48	y	y	PROPN
ejpam-5794	92	49	)	)	PUNCT
ejpam-5794	92	50	+	+	CCONJ
ejpam-5794	92	51	α(y	α(y	NOUN
ejpam-5794	92	52	,	,	PUNCT
ejpam-5794	92	53	κ)∆ξ(y	κ)∆ξ(y	PROPN
ejpam-5794	92	54	,	,	PUNCT
ejpam-5794	92	55	κ	κ	NOUN
ejpam-5794	92	56	)	)	PUNCT
ejpam-5794	92	57	.	.	PUNCT
ejpam-5794	93	1	then	then	ADV
ejpam-5794	93	2	the	the	DET
ejpam-5794	93	3	pair	pair	NOUN
ejpam-5794	93	4	(	(	PUNCT
ejpam-5794	93	5	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	93	6	)	)	PUNCT
ejpam-5794	93	7	is	be	AUX
ejpam-5794	93	8	called	call	VERB
ejpam-5794	93	9	crmms	crmms	PROPN
ejpam-5794	93	10	.	.	PUNCT
ejpam-5794	94	1	example	example	NOUN
ejpam-5794	95	1	1	1	NUM
ejpam-5794	95	2	.	.	PUNCT
ejpam-5794	96	1	let	let	VERB
ejpam-5794	96	2	ℵ	ℵ	NOUN
ejpam-5794	96	3	=	=	SYM
ejpam-5794	96	4	n	n	PRON
ejpam-5794	96	5	define	define	VERB
ejpam-5794	96	6	∆ξ	∆ξ	NOUN
ejpam-5794	96	7	:	:	PUNCT
ejpam-5794	96	8	ℵ	ℵ	PROPN
ejpam-5794	96	9	×	×	NOUN
ejpam-5794	96	10	ℵ	ℵ	X
ejpam-5794	96	11	×	×	NOUN
ejpam-5794	96	12	(	(	PUNCT
ejpam-5794	96	13	0,+∞	0,+∞	NUM
ejpam-5794	96	14	)	)	PUNCT
ejpam-5794	96	15	→	→	PUNCT
ejpam-5794	97	1	[	[	X
ejpam-5794	97	2	0,+∞	0,+∞	NUM
ejpam-5794	97	3	)	)	PUNCT
ejpam-5794	97	4	,	,	PUNCT
ejpam-5794	97	5	by	by	ADP
ejpam-5794	97	6	∆(µ	∆(µ	NOUN
ejpam-5794	97	7	,	,	PUNCT
ejpam-5794	97	8	κ	κ	NOUN
ejpam-5794	97	9	,	,	PUNCT
ejpam-5794	97	10	ξ	ξ	NOUN
ejpam-5794	97	11	)	)	PUNCT
ejpam-5794	97	12	=	=	SYM
ejpam-5794	97	13			NOUN
ejpam-5794	97	14	0	0	NUM
ejpam-5794	97	15	,	,	PUNCT
ejpam-5794	97	16	if	if	SCONJ
ejpam-5794	97	17	µ	µ	X
ejpam-5794	97	18	=	=	SYM
ejpam-5794	97	19	κ	κ	NOUN
ejpam-5794	97	20	;	;	PUNCT
ejpam-5794	97	21	4η	4η	PROPN
ejpam-5794	97	22	ξ	ξ	X
ejpam-5794	97	23	,	,	PUNCT
ejpam-5794	97	24	if	if	SCONJ
ejpam-5794	97	25	µ	µ	NUM
ejpam-5794	97	26	,	,	PUNCT
ejpam-5794	97	27	κ	κ	PROPN
ejpam-5794	97	28	∈	∈	PROPN
ejpam-5794	97	29	{	{	PUNCT
ejpam-5794	97	30	1	1	NUM
ejpam-5794	97	31	,	,	PUNCT
ejpam-5794	97	32	2	2	NUM
ejpam-5794	97	33	and	and	CCONJ
ejpam-5794	97	34	µ	µ	PRON
ejpam-5794	97	35	̸=	̸=	PROPN
ejpam-5794	97	36	κ	κ	NUM
ejpam-5794	97	37	;	;	PUNCT
ejpam-5794	97	38	η	η	PROPN
ejpam-5794	97	39	ξ	ξ	PROPN
ejpam-5794	97	40	,	,	PUNCT
ejpam-5794	97	41	if	if	SCONJ
ejpam-5794	97	42	µ	µ	NOUN
ejpam-5794	97	43	or	or	CCONJ
ejpam-5794	97	44	κ	κ	NOUN
ejpam-5794	97	45	/∈	/∈	PUNCT
ejpam-5794	97	46	{	{	PUNCT
ejpam-5794	97	47	1	1	NUM
ejpam-5794	97	48	,	,	PUNCT
ejpam-5794	97	49	2	2	NUM
ejpam-5794	97	50	,	,	PUNCT
ejpam-5794	97	51	·	·	PUNCT
ejpam-5794	97	52	·	·	PUNCT
ejpam-5794	97	53	·	·	PUNCT
ejpam-5794	97	54	,	,	PUNCT
ejpam-5794	97	55	10	10	NUM
ejpam-5794	97	56	}	}	PUNCT
ejpam-5794	97	57	and	and	CCONJ
ejpam-5794	97	58	µ	µ	DET
ejpam-5794	97	59	̸=	̸=	PROPN
ejpam-5794	97	60	κ	κ	NOUN
ejpam-5794	97	61	;	;	PUNCT
ejpam-5794	97	62	where	where	SCONJ
ejpam-5794	97	63	η	η	PROPN
ejpam-5794	97	64	>	>	X
ejpam-5794	97	65	0	0	NUM
ejpam-5794	97	66	is	be	AUX
ejpam-5794	97	67	a	a	DET
ejpam-5794	97	68	constant	constant	ADJ
ejpam-5794	97	69	.	.	PUNCT
ejpam-5794	98	1	then	then	ADV
ejpam-5794	98	2	(	(	PUNCT
ejpam-5794	98	3	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	98	4	)	)	PUNCT
ejpam-5794	98	5	is	be	AUX
ejpam-5794	98	6	a	a	DET
ejpam-5794	98	7	crmms	crmms	NOUN
ejpam-5794	98	8	with	with	ADP
ejpam-5794	98	9	controlled	control	VERB
ejpam-5794	98	10	function	function	NOUN
ejpam-5794	98	11	α	α	NOUN
ejpam-5794	98	12	=	=	SYM
ejpam-5794	98	13	(	(	PUNCT
ejpam-5794	98	14	µ	µ	NOUN
ejpam-5794	98	15	,	,	PUNCT
ejpam-5794	98	16	κ	κ	NOUN
ejpam-5794	98	17	)	)	PUNCT
ejpam-5794	98	18	=	=	SYM
ejpam-5794	98	19	{	{	PUNCT
ejpam-5794	98	20	1	1	NUM
ejpam-5794	98	21	if	if	SCONJ
ejpam-5794	98	22	µ	µ	DET
ejpam-5794	98	23	̸=	̸=	PROPN
ejpam-5794	98	24	κ	κ	NOUN
ejpam-5794	98	25	;	;	PUNCT
ejpam-5794	98	26	1	1	NUM
ejpam-5794	98	27	+	+	NUM
ejpam-5794	98	28	µ+	µ+	X
ejpam-5794	98	29	κ	κ	X
ejpam-5794	98	30	if	if	SCONJ
ejpam-5794	98	31	µ	µ	X
ejpam-5794	98	32	=	=	SYM
ejpam-5794	98	33	κ	κ	NOUN
ejpam-5794	98	34	;	;	PUNCT
ejpam-5794	98	35	but	but	CCONJ
ejpam-5794	98	36	not	not	PART
ejpam-5794	98	37	rmms	rmms	ADJ
ejpam-5794	98	38	.	.	PUNCT
ejpam-5794	99	1	let	let	VERB
ejpam-5794	99	2	µ	µ	X
ejpam-5794	99	3	=	=	SYM
ejpam-5794	99	4	1	1	NUM
ejpam-5794	99	5	,	,	PUNCT
ejpam-5794	99	6	κ	κ	X
ejpam-5794	99	7	=	=	SYM
ejpam-5794	99	8	2	2	NUM
ejpam-5794	99	9	,	,	PUNCT
ejpam-5794	99	10	ϑ	ϑ	X
ejpam-5794	99	11	=	=	SYM
ejpam-5794	99	12	3	3	NUM
ejpam-5794	99	13	and	and	CCONJ
ejpam-5794	99	14	y	y	NOUN
ejpam-5794	99	15	=	=	SYM
ejpam-5794	99	16	4	4	NUM
ejpam-5794	99	17	,	,	PUNCT
ejpam-5794	99	18	then	then	ADV
ejpam-5794	99	19	from	from	ADP
ejpam-5794	99	20	triangular	triangular	NOUN
ejpam-5794	99	21	inequality	inequality	NOUN
ejpam-5794	99	22	(	(	PUNCT
ejpam-5794	99	23	rm3	rm3	NOUN
ejpam-5794	99	24	)	)	PUNCT
ejpam-5794	99	25	,	,	PUNCT
ejpam-5794	99	26	we	we	PRON
ejpam-5794	99	27	have	have	VERB
ejpam-5794	99	28	∆(µ	∆(µ	NOUN
ejpam-5794	99	29	,	,	PUNCT
ejpam-5794	99	30	κ	κ	NOUN
ejpam-5794	99	31	,	,	PUNCT
ejpam-5794	99	32	ξ	ξ	NOUN
ejpam-5794	99	33	)	)	PUNCT
ejpam-5794	99	34	≤	≤	NOUN
ejpam-5794	100	1	∆(µ	∆(µ	NOUN
ejpam-5794	100	2	,	,	PUNCT
ejpam-5794	100	3	ϑ	ϑ	X
ejpam-5794	100	4	,	,	PUNCT
ejpam-5794	100	5	ξ	ξ	NOUN
ejpam-5794	100	6	)	)	PUNCT
ejpam-5794	100	7	+	+	NUM
ejpam-5794	100	8	∆(ϑ	∆(ϑ	NOUN
ejpam-5794	100	9	,	,	PUNCT
ejpam-5794	100	10	y	y	PROPN
ejpam-5794	100	11	,	,	PUNCT
ejpam-5794	100	12	ξ	ξ	PROPN
ejpam-5794	100	13	)	)	PUNCT
ejpam-5794	100	14	+	+	CCONJ
ejpam-5794	100	15	∆(y	∆(y	NOUN
ejpam-5794	100	16	,	,	PUNCT
ejpam-5794	100	17	κ	κ	NOUN
ejpam-5794	100	18	,	,	PUNCT
ejpam-5794	100	19	ξ	ξ	NOUN
ejpam-5794	100	20	)	)	PUNCT
ejpam-5794	100	21	,	,	PUNCT
ejpam-5794	100	22	u.	u.	PROPN
ejpam-5794	100	23	ishtiaq	ishtiaq	PROPN
ejpam-5794	100	24	et	et	PROPN
ejpam-5794	100	25	al	al	PROPN
ejpam-5794	100	26	.	.	PUNCT
ejpam-5794	100	27	/	/	SYM
ejpam-5794	100	28	eur	eur	PROPN
ejpam-5794	100	29	.	.	PUNCT
ejpam-5794	101	1	j.	j.	PROPN
ejpam-5794	101	2	pure	pure	PROPN
ejpam-5794	101	3	appl	appl	PROPN
ejpam-5794	101	4	.	.	PROPN
ejpam-5794	101	5	math	math	PROPN
ejpam-5794	101	6	,	,	PUNCT
ejpam-5794	101	7	18	18	NUM
ejpam-5794	101	8	(	(	PUNCT
ejpam-5794	101	9	1	1	NUM
ejpam-5794	101	10	)	)	PUNCT
ejpam-5794	101	11	(	(	PUNCT
ejpam-5794	101	12	2025	2025	NUM
ejpam-5794	101	13	)	)	PUNCT
ejpam-5794	101	14	,	,	PUNCT
ejpam-5794	101	15	5794	5794	NUM
ejpam-5794	101	16	5	5	NUM
ejpam-5794	101	17	of	of	ADP
ejpam-5794	101	18	20	20	NUM
ejpam-5794	101	19	∆(1	∆(1	NOUN
ejpam-5794	101	20	,	,	PUNCT
ejpam-5794	101	21	2	2	NUM
ejpam-5794	101	22	,	,	PUNCT
ejpam-5794	101	23	ξ	ξ	NOUN
ejpam-5794	101	24	)	)	PUNCT
ejpam-5794	101	25	≤	≤	NOUN
ejpam-5794	101	26	∆(1	∆(1	NOUN
ejpam-5794	101	27	,	,	PUNCT
ejpam-5794	101	28	3	3	NUM
ejpam-5794	101	29	,	,	PUNCT
ejpam-5794	101	30	ξ	ξ	NOUN
ejpam-5794	101	31	)	)	PUNCT
ejpam-5794	101	32	+	+	NUM
ejpam-5794	101	33	∆(3	∆(3	NOUN
ejpam-5794	101	34	,	,	PUNCT
ejpam-5794	101	35	4	4	NUM
ejpam-5794	101	36	,	,	PUNCT
ejpam-5794	101	37	ξ	ξ	NOUN
ejpam-5794	101	38	)	)	PUNCT
ejpam-5794	101	39	+	+	CCONJ
ejpam-5794	101	40	∆(4	∆(4	NUM
ejpam-5794	101	41	,	,	PUNCT
ejpam-5794	101	42	2	2	NUM
ejpam-5794	101	43	,	,	PUNCT
ejpam-5794	101	44	ξ	ξ	NOUN
ejpam-5794	101	45	)	)	PUNCT
ejpam-5794	101	46	.	.	PUNCT
ejpam-5794	102	1	that	that	PRON
ejpam-5794	102	2	is	be	AUX
ejpam-5794	102	3	,	,	PUNCT
ejpam-5794	102	4	4η	4η	PROPN
ejpam-5794	102	5	ξ	ξ	PROPN
ejpam-5794	102	6	≤	≤	PROPN
ejpam-5794	102	7	η	η	X
ejpam-5794	102	8	ξ	ξ	PROPN
ejpam-5794	102	9	+	+	PROPN
ejpam-5794	102	10	η	η	PROPN
ejpam-5794	102	11	ξ	ξ	PROPN
ejpam-5794	102	12	+	+	PROPN
ejpam-5794	102	13	η	η	X
ejpam-5794	102	14	ξ	ξ	X
ejpam-5794	102	15	≤	≤	ADV
ejpam-5794	102	16	3η	3η	NUM
ejpam-5794	102	17	ξ	ξ	PROPN
ejpam-5794	102	18	after	after	ADP
ejpam-5794	102	19	simplification	simplification	NOUN
ejpam-5794	102	20	,	,	PUNCT
ejpam-5794	102	21	we	we	PRON
ejpam-5794	102	22	have	have	VERB
ejpam-5794	102	23	4	4	NUM
ejpam-5794	102	24	≤	≤	NUM
ejpam-5794	102	25	3	3	NUM
ejpam-5794	102	26	,	,	PUNCT
ejpam-5794	102	27	which	which	PRON
ejpam-5794	102	28	is	be	AUX
ejpam-5794	102	29	contradiction	contradiction	NOUN
ejpam-5794	102	30	.	.	PUNCT
ejpam-5794	103	1	hence	hence	ADV
ejpam-5794	103	2	,	,	PUNCT
ejpam-5794	103	3	crmms	crmms	PROPN
ejpam-5794	103	4	need	need	VERB
ejpam-5794	103	5	not	not	PART
ejpam-5794	103	6	to	to	PART
ejpam-5794	103	7	be	be	AUX
ejpam-5794	103	8	rmms	rmms	ADJ
ejpam-5794	103	9	.	.	PUNCT
ejpam-5794	104	1	also	also	ADV
ejpam-5794	104	2	observe	observe	VERB
ejpam-5794	104	3	that	that	SCONJ
ejpam-5794	104	4	it	it	PRON
ejpam-5794	104	5	is	be	AUX
ejpam-5794	104	6	not	not	PART
ejpam-5794	104	7	modular	modular	ADJ
ejpam-5794	104	8	b−ms	b−ms	NOUN
ejpam-5794	104	9	and	and	CCONJ
ejpam-5794	104	10	rectangular	rectangular	ADJ
ejpam-5794	104	11	b−ms	b−ms	NOUN
ejpam-5794	104	12	.	.	PUNCT
ejpam-5794	104	13	example	example	NOUN
ejpam-5794	105	1	2	2	NUM
ejpam-5794	105	2	.	.	PUNCT
ejpam-5794	105	3	let	let	VERB
ejpam-5794	105	4	ℵ	ℵ	NOUN
ejpam-5794	105	5	=	=	SYM
ejpam-5794	105	6	n	n	PRON
ejpam-5794	105	7	define	define	VERB
ejpam-5794	105	8	∆ξ	∆ξ	NOUN
ejpam-5794	105	9	:	:	PUNCT
ejpam-5794	105	10	ℵ	ℵ	PROPN
ejpam-5794	105	11	×	×	NOUN
ejpam-5794	105	12	ℵ	ℵ	X
ejpam-5794	105	13	×	×	NOUN
ejpam-5794	105	14	(	(	PUNCT
ejpam-5794	105	15	0,+∞	0,+∞	NUM
ejpam-5794	105	16	)	)	PUNCT
ejpam-5794	105	17	→	→	PUNCT
ejpam-5794	106	1	[	[	X
ejpam-5794	106	2	0,+∞	0,+∞	NUM
ejpam-5794	106	3	)	)	PUNCT
ejpam-5794	106	4	by	by	ADP
ejpam-5794	106	5	∆(µ	∆(µ	NOUN
ejpam-5794	106	6	,	,	PUNCT
ejpam-5794	106	7	κ	κ	NOUN
ejpam-5794	106	8	,	,	PUNCT
ejpam-5794	106	9	ξ	ξ	NOUN
ejpam-5794	106	10	)	)	PUNCT
ejpam-5794	106	11	=	=	PUNCT
ejpam-5794	107	1			PROPN
ejpam-5794	107	2	0	0	NUM
ejpam-5794	107	3	,	,	PUNCT
ejpam-5794	107	4	if	if	SCONJ
ejpam-5794	107	5	µ	µ	X
ejpam-5794	107	6	=	=	SYM
ejpam-5794	107	7	κ	κ	NOUN
ejpam-5794	107	8	;	;	PUNCT
ejpam-5794	107	9	10ηξ	10ηξ	NOUN
ejpam-5794	107	10	,	,	PUNCT
ejpam-5794	107	11	if	if	SCONJ
ejpam-5794	107	12	µ	µ	NUM
ejpam-5794	107	13	,	,	PUNCT
ejpam-5794	107	14	κ	κ	PROPN
ejpam-5794	107	15	∈	∈	PROPN
ejpam-5794	107	16	{	{	PUNCT
ejpam-5794	107	17	1	1	NUM
ejpam-5794	107	18	,	,	PUNCT
ejpam-5794	107	19	2	2	NUM
ejpam-5794	107	20	,	,	PUNCT
ejpam-5794	107	21	·	·	PUNCT
ejpam-5794	107	22	·	·	PUNCT
ejpam-5794	107	23	·	·	PUNCT
ejpam-5794	107	24	,	,	PUNCT
ejpam-5794	107	25	10	10	NUM
ejpam-5794	107	26	}	}	PUNCT
ejpam-5794	107	27	and	and	CCONJ
ejpam-5794	107	28	µ	µ	DET
ejpam-5794	107	29	̸=	̸=	PROPN
ejpam-5794	107	30	κ	κ	NOUN
ejpam-5794	107	31	;	;	PUNCT
ejpam-5794	107	32	2ηξ	2ηξ	NOUN
ejpam-5794	107	33	3	3	NUM
ejpam-5794	107	34	,	,	PUNCT
ejpam-5794	107	35	if	if	SCONJ
ejpam-5794	107	36	µ	µ	NOUN
ejpam-5794	107	37	or	or	CCONJ
ejpam-5794	107	38	κ	κ	NOUN
ejpam-5794	107	39	/∈	/∈	PUNCT
ejpam-5794	107	40	{	{	PUNCT
ejpam-5794	107	41	1	1	NUM
ejpam-5794	107	42	,	,	PUNCT
ejpam-5794	107	43	2	2	NUM
ejpam-5794	107	44	,	,	PUNCT
ejpam-5794	107	45	·	·	PUNCT
ejpam-5794	107	46	·	·	PUNCT
ejpam-5794	107	47	·	·	PUNCT
ejpam-5794	107	48	,	,	PUNCT
ejpam-5794	107	49	10	10	NUM
ejpam-5794	107	50	}	}	PUNCT
ejpam-5794	107	51	and	and	CCONJ
ejpam-5794	107	52	µ	µ	DET
ejpam-5794	107	53	̸=	̸=	PROPN
ejpam-5794	107	54	κ	κ	NOUN
ejpam-5794	107	55	;	;	PUNCT
ejpam-5794	107	56	where	where	SCONJ
ejpam-5794	107	57	η	η	PROPN
ejpam-5794	107	58	>	>	X
ejpam-5794	107	59	0	0	NUM
ejpam-5794	107	60	is	be	AUX
ejpam-5794	107	61	a	a	DET
ejpam-5794	107	62	constant	constant	ADJ
ejpam-5794	107	63	.	.	PUNCT
ejpam-5794	108	1	then	then	ADV
ejpam-5794	108	2	(	(	PUNCT
ejpam-5794	108	3	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	108	4	)	)	PUNCT
ejpam-5794	108	5	is	be	AUX
ejpam-5794	108	6	a	a	DET
ejpam-5794	108	7	crmms	crmms	NOUN
ejpam-5794	108	8	with	with	ADP
ejpam-5794	108	9	control	control	NOUN
ejpam-5794	108	10	function	function	NOUN
ejpam-5794	108	11	α	α	PROPN
ejpam-5794	108	12	=	=	SYM
ejpam-5794	108	13	(	(	PUNCT
ejpam-5794	108	14	µ	µ	NOUN
ejpam-5794	108	15	,	,	PUNCT
ejpam-5794	108	16	κ	κ	NOUN
ejpam-5794	108	17	)	)	PUNCT
ejpam-5794	108	18	=	=	SYM
ejpam-5794	108	19	{	{	PUNCT
ejpam-5794	108	20	3	3	NUM
ejpam-5794	108	21	if	if	SCONJ
ejpam-5794	108	22	µ	µ	DET
ejpam-5794	108	23	̸=	̸=	PROPN
ejpam-5794	108	24	κ	κ	NOUN
ejpam-5794	108	25	;	;	PUNCT
ejpam-5794	108	26	2(µ+	2(µ+	NUM
ejpam-5794	108	27	κ	κ	X
ejpam-5794	108	28	)	)	PUNCT
ejpam-5794	108	29	if	if	SCONJ
ejpam-5794	108	30	µ	µ	X
ejpam-5794	108	31	=	=	SYM
ejpam-5794	108	32	κ	κ	NOUN
ejpam-5794	108	33	;	;	PUNCT
ejpam-5794	108	34	but	but	CCONJ
ejpam-5794	108	35	not	not	PART
ejpam-5794	108	36	rmms	rmms	ADJ
ejpam-5794	108	37	.	.	PUNCT
ejpam-5794	109	1	let	let	VERB
ejpam-5794	109	2	µ	µ	X
ejpam-5794	109	3	=	=	SYM
ejpam-5794	109	4	5	5	NUM
ejpam-5794	109	5	,	,	PUNCT
ejpam-5794	109	6	κ	κ	X
ejpam-5794	109	7	=	=	SYM
ejpam-5794	109	8	8	8	NUM
ejpam-5794	109	9	,	,	PUNCT
ejpam-5794	109	10	ϑ	ϑ	X
ejpam-5794	109	11	=	=	SYM
ejpam-5794	109	12	11	11	NUM
ejpam-5794	109	13	and	and	CCONJ
ejpam-5794	109	14	y	y	NOUN
ejpam-5794	109	15	=	=	SYM
ejpam-5794	109	16	12	12	NUM
ejpam-5794	109	17	,	,	PUNCT
ejpam-5794	109	18	then	then	ADV
ejpam-5794	109	19	from	from	ADP
ejpam-5794	109	20	triangular	triangular	NOUN
ejpam-5794	109	21	inequality	inequality	NOUN
ejpam-5794	109	22	(	(	PUNCT
ejpam-5794	109	23	rm3	rm3	NOUN
ejpam-5794	109	24	)	)	PUNCT
ejpam-5794	109	25	,	,	PUNCT
ejpam-5794	109	26	we	we	PRON
ejpam-5794	109	27	have	have	VERB
ejpam-5794	109	28	∆(µ	∆(µ	NOUN
ejpam-5794	109	29	,	,	PUNCT
ejpam-5794	109	30	κ	κ	NOUN
ejpam-5794	109	31	,	,	PUNCT
ejpam-5794	109	32	ξ	ξ	NOUN
ejpam-5794	109	33	)	)	PUNCT
ejpam-5794	109	34	≤	≤	NOUN
ejpam-5794	110	1	∆(µ	∆(µ	NOUN
ejpam-5794	110	2	,	,	PUNCT
ejpam-5794	110	3	ϑ	ϑ	X
ejpam-5794	110	4	,	,	PUNCT
ejpam-5794	110	5	ξ	ξ	NOUN
ejpam-5794	110	6	)	)	PUNCT
ejpam-5794	110	7	+	+	NUM
ejpam-5794	110	8	∆(ϑ	∆(ϑ	NOUN
ejpam-5794	110	9	,	,	PUNCT
ejpam-5794	110	10	y	y	PROPN
ejpam-5794	110	11	,	,	PUNCT
ejpam-5794	110	12	ξ	ξ	PROPN
ejpam-5794	110	13	)	)	PUNCT
ejpam-5794	110	14	+	+	CCONJ
ejpam-5794	110	15	∆(y	∆(y	NOUN
ejpam-5794	110	16	,	,	PUNCT
ejpam-5794	110	17	κ	κ	NOUN
ejpam-5794	110	18	,	,	PUNCT
ejpam-5794	110	19	ξ	ξ	NOUN
ejpam-5794	110	20	)	)	PUNCT
ejpam-5794	110	21	,	,	PUNCT
ejpam-5794	110	22	∆(5	∆(5	NOUN
ejpam-5794	110	23	,	,	PUNCT
ejpam-5794	110	24	8	8	NUM
ejpam-5794	110	25	,	,	PUNCT
ejpam-5794	110	26	ξ	ξ	NOUN
ejpam-5794	110	27	)	)	PUNCT
ejpam-5794	110	28	≤	≤	NOUN
ejpam-5794	110	29	∆(5	∆(5	NOUN
ejpam-5794	110	30	,	,	PUNCT
ejpam-5794	110	31	11	11	NUM
ejpam-5794	110	32	,	,	PUNCT
ejpam-5794	110	33	ξ	ξ	NOUN
ejpam-5794	110	34	)	)	PUNCT
ejpam-5794	111	1	+	+	CCONJ
ejpam-5794	111	2	∆(11	∆(11	PROPN
ejpam-5794	111	3	,	,	PUNCT
ejpam-5794	111	4	12	12	NUM
ejpam-5794	111	5	,	,	PUNCT
ejpam-5794	111	6	ξ	ξ	NOUN
ejpam-5794	111	7	)	)	PUNCT
ejpam-5794	111	8	+	+	X
ejpam-5794	111	9	∆(12	∆(12	NOUN
ejpam-5794	111	10	,	,	PUNCT
ejpam-5794	111	11	8	8	NUM
ejpam-5794	111	12	,	,	PUNCT
ejpam-5794	111	13	ξ	ξ	NOUN
ejpam-5794	111	14	)	)	PUNCT
ejpam-5794	111	15	.	.	PUNCT
ejpam-5794	112	1	that	that	PRON
ejpam-5794	112	2	is	be	AUX
ejpam-5794	112	3	,	,	PUNCT
ejpam-5794	112	4	(	(	PUNCT
ejpam-5794	112	5	10η)ξ	10η)ξ	NUM
ejpam-5794	112	6	≤	≤	NOUN
ejpam-5794	112	7	(	(	PUNCT
ejpam-5794	112	8	2η	2η	NUM
ejpam-5794	112	9	)	)	PUNCT
ejpam-5794	113	1	ξ	ξ	PROPN
ejpam-5794	113	2	3	3	NUM
ejpam-5794	113	3	+	+	CCONJ
ejpam-5794	113	4	(	(	PUNCT
ejpam-5794	113	5	2η	2η	NUM
ejpam-5794	113	6	)	)	PUNCT
ejpam-5794	114	1	ξ	ξ	PROPN
ejpam-5794	114	2	3	3	NUM
ejpam-5794	114	3	+	+	CCONJ
ejpam-5794	114	4	(	(	PUNCT
ejpam-5794	114	5	2η	2η	NUM
ejpam-5794	114	6	)	)	PUNCT
ejpam-5794	114	7	ξ	ξ	PROPN
ejpam-5794	114	8	3	3	NUM
ejpam-5794	114	9	.	.	PUNCT
ejpam-5794	115	1	that	that	PRON
ejpam-5794	115	2	is	be	AUX
ejpam-5794	115	3	,	,	PUNCT
ejpam-5794	115	4	10	10	NUM
ejpam-5794	115	5	≤	≤	NUM
ejpam-5794	115	6	6	6	NUM
ejpam-5794	115	7	,	,	PUNCT
ejpam-5794	115	8	which	which	PRON
ejpam-5794	115	9	is	be	AUX
ejpam-5794	115	10	a	a	DET
ejpam-5794	115	11	contradiction	contradiction	NOUN
ejpam-5794	115	12	.	.	PUNCT
ejpam-5794	116	1	hence	hence	ADV
ejpam-5794	116	2	,	,	PUNCT
ejpam-5794	116	3	crmms	crmms	PROPN
ejpam-5794	116	4	does	do	AUX
ejpam-5794	116	5	not	not	PART
ejpam-5794	116	6	need	need	VERB
ejpam-5794	116	7	to	to	PART
ejpam-5794	116	8	be	be	AUX
ejpam-5794	116	9	rmms	rmms	ADJ
ejpam-5794	116	10	.	.	PUNCT
ejpam-5794	117	1	also	also	ADV
ejpam-5794	117	2	,	,	PUNCT
ejpam-5794	117	3	observe	observe	VERB
ejpam-5794	117	4	that	that	SCONJ
ejpam-5794	117	5	it	it	PRON
ejpam-5794	117	6	is	be	AUX
ejpam-5794	117	7	not	not	PART
ejpam-5794	117	8	modular	modular	ADJ
ejpam-5794	117	9	b−ms	b−ms	NOUN
ejpam-5794	117	10	and	and	CCONJ
ejpam-5794	117	11	rectangular	rectangular	ADJ
ejpam-5794	117	12	b−ms	b−ms	NOUN
ejpam-5794	117	13	.	.	PUNCT
ejpam-5794	118	1	remark	remark	PROPN
ejpam-5794	118	2	1	1	NUM
ejpam-5794	118	3	.	.	PUNCT
ejpam-5794	119	1	a	a	X
ejpam-5794	119	2	)	)	PUNCT
ejpam-5794	119	3	every	every	PRON
ejpam-5794	119	4	rectangular	rectangular	ADJ
ejpam-5794	119	5	ms	ms	NOUN
ejpam-5794	119	6	and	and	CCONJ
ejpam-5794	119	7	control	control	PROPN
ejpam-5794	119	8	ms	ms	PROPN
ejpam-5794	119	9	is	be	AUX
ejpam-5794	119	10	a	a	DET
ejpam-5794	119	11	crmms	crmms	NOUN
ejpam-5794	119	12	.	.	PUNCT
ejpam-5794	120	1	u.	u.	PROPN
ejpam-5794	120	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	120	3	et	et	PROPN
ejpam-5794	120	4	al	al	PROPN
ejpam-5794	120	5	.	.	PUNCT
ejpam-5794	120	6	/	/	SYM
ejpam-5794	120	7	eur	eur	PROPN
ejpam-5794	120	8	.	.	PUNCT
ejpam-5794	121	1	j.	j.	PROPN
ejpam-5794	121	2	pure	pure	PROPN
ejpam-5794	121	3	appl	appl	PROPN
ejpam-5794	121	4	.	.	PROPN
ejpam-5794	121	5	math	math	PROPN
ejpam-5794	121	6	,	,	PUNCT
ejpam-5794	121	7	18	18	NUM
ejpam-5794	121	8	(	(	PUNCT
ejpam-5794	121	9	1	1	NUM
ejpam-5794	121	10	)	)	PUNCT
ejpam-5794	121	11	(	(	PUNCT
ejpam-5794	121	12	2025	2025	NUM
ejpam-5794	121	13	)	)	PUNCT
ejpam-5794	121	14	,	,	PUNCT
ejpam-5794	121	15	5794	5794	NUM
ejpam-5794	121	16	6	6	NUM
ejpam-5794	121	17	of	of	ADP
ejpam-5794	121	18	20	20	NUM
ejpam-5794	121	19	b	b	NOUN
ejpam-5794	121	20	)	)	PUNCT
ejpam-5794	121	21	every	every	DET
ejpam-5794	121	22	crmms	crmms	NOUN
ejpam-5794	121	23	need	need	AUX
ejpam-5794	121	24	not	not	PART
ejpam-5794	121	25	be	be	AUX
ejpam-5794	121	26	rmms	rmms	ADJ
ejpam-5794	121	27	,	,	PUNCT
ejpam-5794	121	28	but	but	CCONJ
ejpam-5794	121	29	the	the	DET
ejpam-5794	121	30	converse	converse	NOUN
ejpam-5794	121	31	is	be	AUX
ejpam-5794	121	32	true	true	ADJ
ejpam-5794	121	33	,	,	PUNCT
ejpam-5794	121	34	as	as	SCONJ
ejpam-5794	121	35	shown	show	VERB
ejpam-5794	121	36	in	in	ADP
ejpam-5794	121	37	the	the	DET
ejpam-5794	121	38	above	above	ADJ
ejpam-5794	121	39	examples	example	NOUN
ejpam-5794	121	40	.	.	PUNCT
ejpam-5794	122	1	in	in	ADP
ejpam-5794	122	2	terms	term	NOUN
ejpam-5794	122	3	of	of	ADP
ejpam-5794	122	4	crmms	crmms	NOUN
ejpam-5794	122	5	,	,	PUNCT
ejpam-5794	122	6	the	the	DET
ejpam-5794	122	7	concepts	concept	NOUN
ejpam-5794	122	8	of	of	ADP
ejpam-5794	122	9	convergence	convergence	NOUN
ejpam-5794	122	10	,	,	PUNCT
ejpam-5794	122	11	cauchy	cauchy	NOUN
ejpam-5794	122	12	,	,	PUNCT
ejpam-5794	122	13	and	and	CCONJ
ejpam-5794	122	14	completeness	completeness	NOUN
ejpam-5794	122	15	can	can	AUX
ejpam-5794	122	16	be	be	AUX
ejpam-5794	122	17	easily	easily	ADV
ejpam-5794	122	18	generalized	generalize	VERB
ejpam-5794	122	19	.	.	PUNCT
ejpam-5794	123	1	definition	definition	NOUN
ejpam-5794	123	2	8	8	NUM
ejpam-5794	123	3	.	.	PUNCT
ejpam-5794	124	1	assume	assume	VERB
ejpam-5794	124	2	(	(	PUNCT
ejpam-5794	124	3	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	124	4	)	)	PUNCT
ejpam-5794	124	5	be	be	AUX
ejpam-5794	124	6	a	a	DET
ejpam-5794	124	7	crmms	crmms	NOUN
ejpam-5794	124	8	.	.	PUNCT
ejpam-5794	125	1	then	then	ADV
ejpam-5794	125	2	a	a	X
ejpam-5794	125	3	)	)	PUNCT
ejpam-5794	125	4	a	a	DET
ejpam-5794	125	5	sequence	sequence	NOUN
ejpam-5794	125	6	(	(	PUNCT
ejpam-5794	125	7	ϑn	ϑn	NOUN
ejpam-5794	125	8	)	)	PUNCT
ejpam-5794	125	9	in	in	ADP
ejpam-5794	125	10	ℵ	ℵ	NOUN
ejpam-5794	125	11	is	be	AUX
ejpam-5794	125	12	said	say	VERB
ejpam-5794	125	13	to	to	PART
ejpam-5794	125	14	be	be	AUX
ejpam-5794	125	15	convergent	convergent	ADJ
ejpam-5794	125	16	to	to	ADP
ejpam-5794	125	17	ϑ	ϑ	PROPN
ejpam-5794	125	18	∈	∈	NOUN
ejpam-5794	125	19	ℵ	ℵ	NOUN
ejpam-5794	125	20	if	if	SCONJ
ejpam-5794	125	21	lim	lim	PROPN
ejpam-5794	125	22	n−→+∞	n−→+∞	PROPN
ejpam-5794	125	23	∆ξ(ϑn	∆ξ(ϑn	PROPN
ejpam-5794	125	24	,	,	PUNCT
ejpam-5794	125	25	ϑ	ϑ	X
ejpam-5794	125	26	)	)	PUNCT
ejpam-5794	125	27	=	=	SYM
ejpam-5794	126	1	0	0	NUM
ejpam-5794	126	2	b	b	X
ejpam-5794	126	3	)	)	PUNCT
ejpam-5794	126	4	a	a	DET
ejpam-5794	126	5	sequence	sequence	NOUN
ejpam-5794	126	6	(	(	PUNCT
ejpam-5794	126	7	ϑn	ϑn	NOUN
ejpam-5794	126	8	)	)	PUNCT
ejpam-5794	126	9	in	in	ADP
ejpam-5794	126	10	ℵ	ℵ	PROPN
ejpam-5794	126	11	is	be	AUX
ejpam-5794	126	12	called	call	VERB
ejpam-5794	126	13	cauchy	cauchy	ADJ
ejpam-5794	126	14	sequence	sequence	NOUN
ejpam-5794	126	15	if	if	SCONJ
ejpam-5794	126	16	lim	lim	PROPN
ejpam-5794	126	17	n	n	CCONJ
ejpam-5794	126	18	,	,	PUNCT
ejpam-5794	126	19	m−→+∞	m−→+∞	PROPN
ejpam-5794	126	20	∆ξ(ϑn	∆ξ(ϑn	PROPN
ejpam-5794	126	21	,	,	PUNCT
ejpam-5794	126	22	ϑm	ϑm	PROPN
ejpam-5794	126	23	)	)	PUNCT
ejpam-5794	126	24	=	=	SYM
ejpam-5794	127	1	0	0	NUM
ejpam-5794	127	2	c	c	X
ejpam-5794	127	3	)	)	PUNCT
ejpam-5794	127	4	the	the	DET
ejpam-5794	127	5	pair	pair	NOUN
ejpam-5794	127	6	(	(	PUNCT
ejpam-5794	127	7	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	127	8	)	)	PUNCT
ejpam-5794	127	9	is	be	AUX
ejpam-5794	127	10	said	say	VERB
ejpam-5794	127	11	to	to	PART
ejpam-5794	127	12	be	be	AUX
ejpam-5794	127	13	a	a	DET
ejpam-5794	127	14	complete	complete	ADJ
ejpam-5794	127	15	crmms	crmms	NOUN
ejpam-5794	128	1	if	if	SCONJ
ejpam-5794	128	2	every	every	DET
ejpam-5794	128	3	cauchy	cauchy	ADJ
ejpam-5794	128	4	sequence	sequence	NOUN
ejpam-5794	128	5	in	in	ADP
ejpam-5794	128	6	ℵ	ℵ	ADJ
ejpam-5794	128	7	converges	converge	NOUN
ejpam-5794	128	8	in	in	ADP
ejpam-5794	128	9	ℵ.	ℵ.	PROPN
ejpam-5794	128	10	definition	definition	NOUN
ejpam-5794	128	11	9	9	NUM
ejpam-5794	128	12	.	.	PUNCT
ejpam-5794	128	13	assume	assume	VERB
ejpam-5794	128	14	(	(	PUNCT
ejpam-5794	128	15	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	128	16	)	)	PUNCT
ejpam-5794	128	17	be	be	VERB
ejpam-5794	128	18	crmms	crmms	ADJ
ejpam-5794	128	19	,	,	PUNCT
ejpam-5794	128	20	let	let	VERB
ejpam-5794	128	21	ϑ	ϑ	X
ejpam-5794	128	22	∈	∈	NOUN
ejpam-5794	128	23	ℵ	ℵ	NOUN
ejpam-5794	128	24	and	and	CCONJ
ejpam-5794	128	25	r	r	NOUN
ejpam-5794	128	26	>	>	X
ejpam-5794	128	27	0	0	NUM
ejpam-5794	128	28	.	.	PUNCT
ejpam-5794	129	1	then	then	ADV
ejpam-5794	129	2	,	,	PUNCT
ejpam-5794	129	3	i	i	PROPN
ejpam-5794	129	4	)	)	PUNCT
ejpam-5794	129	5	the	the	DET
ejpam-5794	129	6	open	open	ADJ
ejpam-5794	129	7	ball	ball	NOUN
ejpam-5794	129	8	denoted	denote	VERB
ejpam-5794	129	9	and	and	CCONJ
ejpam-5794	129	10	defined	define	VERB
ejpam-5794	129	11	by	by	ADP
ejpam-5794	129	12	b(ϑ	b(ϑ	PROPN
ejpam-5794	129	13	,	,	PUNCT
ejpam-5794	129	14	r	r	NOUN
ejpam-5794	129	15	)	)	PUNCT
ejpam-5794	129	16	=	=	SYM
ejpam-5794	129	17	{	{	PUNCT
ejpam-5794	129	18	ϑ0	ϑ0	NOUN
ejpam-5794	129	19	∈	∈	PROPN
ejpam-5794	129	20	ℵ,∆ξ(ϑ	ℵ,∆ξ(ϑ	NOUN
ejpam-5794	129	21	,	,	PUNCT
ejpam-5794	129	22	ϑ0	ϑ0	NOUN
ejpam-5794	129	23	)	)	PUNCT
ejpam-5794	129	24	<	<	X
ejpam-5794	129	25	r	r	X
ejpam-5794	129	26	}	}	PUNCT
ejpam-5794	129	27	,	,	PUNCT
ejpam-5794	129	28	ii	ii	PROPN
ejpam-5794	129	29	)	)	PUNCT
ejpam-5794	129	30	the	the	DET
ejpam-5794	129	31	mapping	mapping	NOUN
ejpam-5794	129	32	g	g	NOUN
ejpam-5794	129	33	:	:	PUNCT
ejpam-5794	129	34	ℵ	ℵ	PROPN
ejpam-5794	129	35	→	→	SYM
ejpam-5794	129	36	ℵ	ℵ	NOUN
ejpam-5794	129	37	is	be	AUX
ejpam-5794	129	38	said	say	VERB
ejpam-5794	129	39	to	to	PART
ejpam-5794	129	40	be	be	AUX
ejpam-5794	129	41	continuous	continuous	ADJ
ejpam-5794	129	42	at	at	ADP
ejpam-5794	129	43	ϑ	ϑ	PROPN
ejpam-5794	129	44	∈	∈	NOUN
ejpam-5794	129	45	ℵ	ℵ	NOUN
ejpam-5794	129	46	if	if	SCONJ
ejpam-5794	129	47	for	for	ADP
ejpam-5794	129	48	every	every	DET
ejpam-5794	129	49	γ	γ	X
ejpam-5794	129	50	>	>	X
ejpam-5794	129	51	0	0	PUNCT
ejpam-5794	129	52	and	and	CCONJ
ejpam-5794	129	53	δ	δ	PROPN
ejpam-5794	129	54	>	>	X
ejpam-5794	129	55	0	0	NUM
ejpam-5794	130	1	such	such	ADJ
ejpam-5794	130	2	that	that	SCONJ
ejpam-5794	130	3	g(b(ϑ	g(b(ϑ	PROPN
ejpam-5794	130	4	,	,	PUNCT
ejpam-5794	130	5	δ	δ	PROPN
ejpam-5794	130	6	)	)	PUNCT
ejpam-5794	130	7	)	)	PUNCT
ejpam-5794	130	8	⊆	⊆	NUM
ejpam-5794	130	9	b(g(ϑ	b(g(ϑ	NOUN
ejpam-5794	130	10	,	,	PUNCT
ejpam-5794	130	11	γ	γ	NOUN
ejpam-5794	130	12	)	)	PUNCT
ejpam-5794	130	13	)	)	PUNCT
ejpam-5794	130	14	.	.	PUNCT
ejpam-5794	131	1	if	if	SCONJ
ejpam-5794	131	2	g	g	PROPN
ejpam-5794	131	3	is	be	AUX
ejpam-5794	131	4	continuous	continuous	ADJ
ejpam-5794	131	5	at	at	ADP
ejpam-5794	131	6	ϑ	ϑ	NOUN
ejpam-5794	131	7	,	,	PUNCT
ejpam-5794	131	8	then	then	ADV
ejpam-5794	131	9	for	for	ADP
ejpam-5794	131	10	any	any	DET
ejpam-5794	131	11	sequence	sequence	NOUN
ejpam-5794	131	12	(	(	PUNCT
ejpam-5794	131	13	ϑn	ϑn	NOUN
ejpam-5794	131	14	)	)	PUNCT
ejpam-5794	131	15	converges	converge	NOUN
ejpam-5794	131	16	to	to	ADP
ejpam-5794	131	17	ϑ	ϑ	PRON
ejpam-5794	131	18	,	,	PUNCT
ejpam-5794	131	19	we	we	PRON
ejpam-5794	131	20	have	have	VERB
ejpam-5794	131	21	lim	lim	PROPN
ejpam-5794	131	22	n−→+∞	n−→+∞	PROPN
ejpam-5794	131	23	g(ϑn	g(ϑn	PROPN
ejpam-5794	131	24	)	)	PUNCT
ejpam-5794	131	25	=	=	SYM
ejpam-5794	131	26	g(ϑ	g(ϑ	PROPN
ejpam-5794	131	27	)	)	PUNCT
ejpam-5794	131	28	.	.	PUNCT
ejpam-5794	132	1	lemma	lemma	PROPN
ejpam-5794	132	2	1	1	NUM
ejpam-5794	132	3	.	.	PUNCT
ejpam-5794	132	4	assume(∆ξ,ℵ	assume(∆ξ,ℵ	PROPN
ejpam-5794	132	5	)	)	PUNCT
ejpam-5794	132	6	be	be	AUX
ejpam-5794	132	7	a	a	DET
ejpam-5794	132	8	crmms	crmms	NOUN
ejpam-5794	132	9	and	and	CCONJ
ejpam-5794	132	10	(	(	PUNCT
ejpam-5794	132	11	ϑn	ϑn	NOUN
ejpam-5794	132	12	)	)	PUNCT
ejpam-5794	132	13	be	be	AUX
ejpam-5794	132	14	a	a	DET
ejpam-5794	132	15	cauchy	cauchy	ADJ
ejpam-5794	132	16	sequence	sequence	NOUN
ejpam-5794	132	17	in	in	ADP
ejpam-5794	132	18	ℵ	ℵ	NOUN
ejpam-5794	132	19	and	and	CCONJ
ejpam-5794	132	20	(	(	PUNCT
ejpam-5794	132	21	ϑn	ϑn	NOUN
ejpam-5794	132	22	)	)	PUNCT
ejpam-5794	132	23	̸=	̸=	PROPN
ejpam-5794	132	24	(	(	PUNCT
ejpam-5794	132	25	ϑm	ϑm	PROPN
ejpam-5794	132	26	)	)	PUNCT
ejpam-5794	132	27	whenever	whenever	SCONJ
ejpam-5794	132	28	n	n	PRON
ejpam-5794	132	29	̸=	̸=	PROPN
ejpam-5794	132	30	m.	m.	NOUN
ejpam-5794	132	31	if	if	SCONJ
ejpam-5794	132	32	lim	lim	PROPN
ejpam-5794	132	33	n	n	CCONJ
ejpam-5794	132	34	,	,	PUNCT
ejpam-5794	132	35	m−→+∞	m−→+∞	PROPN
ejpam-5794	132	36	∆ξ(ϑn	∆ξ(ϑn	PROPN
ejpam-5794	132	37	,	,	PUNCT
ejpam-5794	132	38	ϑm	ϑm	PROPN
ejpam-5794	132	39	)	)	PUNCT
ejpam-5794	132	40	<	<	X
ejpam-5794	133	1	+	+	ADJ
ejpam-5794	133	2	∞	∞	PROPN
ejpam-5794	133	3	for	for	ADP
ejpam-5794	133	4	all	all	DET
ejpam-5794	133	5	(	(	PUNCT
ejpam-5794	133	6	ϑn	ϑn	NOUN
ejpam-5794	133	7	)	)	PUNCT
ejpam-5794	133	8	,	,	PUNCT
ejpam-5794	133	9	(	(	PUNCT
ejpam-5794	133	10	ϑm	ϑm	NOUN
ejpam-5794	133	11	)	)	PUNCT
ejpam-5794	133	12	∈	∈	PROPN
ejpam-5794	133	13	ℵ	ℵ	NOUN
ejpam-5794	133	14	,	,	PUNCT
ejpam-5794	133	15	then	then	ADV
ejpam-5794	133	16	(	(	PUNCT
ejpam-5794	133	17	ϑn	ϑn	NOUN
ejpam-5794	133	18	)	)	PUNCT
ejpam-5794	133	19	has	have	VERB
ejpam-5794	133	20	a	a	DET
ejpam-5794	133	21	unique	unique	ADJ
ejpam-5794	133	22	fixed	fix	VERB
ejpam-5794	133	23	point	point	NOUN
ejpam-5794	133	24	.	.	PUNCT
ejpam-5794	134	1	u.	u.	PROPN
ejpam-5794	134	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	134	3	et	et	PROPN
ejpam-5794	134	4	al	al	PROPN
ejpam-5794	134	5	.	.	PUNCT
ejpam-5794	134	6	/	/	SYM
ejpam-5794	134	7	eur	eur	PROPN
ejpam-5794	134	8	.	.	PUNCT
ejpam-5794	135	1	j.	j.	PROPN
ejpam-5794	135	2	pure	pure	PROPN
ejpam-5794	135	3	appl	appl	PROPN
ejpam-5794	135	4	.	.	PROPN
ejpam-5794	135	5	math	math	PROPN
ejpam-5794	135	6	,	,	PUNCT
ejpam-5794	135	7	18	18	NUM
ejpam-5794	135	8	(	(	PUNCT
ejpam-5794	135	9	1	1	NUM
ejpam-5794	135	10	)	)	PUNCT
ejpam-5794	135	11	(	(	PUNCT
ejpam-5794	135	12	2025	2025	NUM
ejpam-5794	135	13	)	)	PUNCT
ejpam-5794	135	14	,	,	PUNCT
ejpam-5794	135	15	5794	5794	NUM
ejpam-5794	135	16	7	7	NUM
ejpam-5794	135	17	of	of	ADP
ejpam-5794	135	18	20	20	NUM
ejpam-5794	135	19	proof	proof	NOUN
ejpam-5794	135	20	.	.	PUNCT
ejpam-5794	136	1	assume	assume	VERB
ejpam-5794	136	2	s	s	PROPN
ejpam-5794	136	3	,	,	PUNCT
ejpam-5794	136	4	t	t	PROPN
ejpam-5794	136	5	are	be	AUX
ejpam-5794	136	6	two	two	NUM
ejpam-5794	136	7	fixed	fix	VERB
ejpam-5794	136	8	point	point	NOUN
ejpam-5794	136	9	of	of	ADP
ejpam-5794	136	10	the	the	DET
ejpam-5794	136	11	sequence	sequence	NOUN
ejpam-5794	136	12	(	(	PUNCT
ejpam-5794	136	13	ϑn	ϑn	NOUN
ejpam-5794	136	14	)	)	PUNCT
ejpam-5794	136	15	in	in	ADP
ejpam-5794	136	16	ℵ.	ℵ.	PROPN
ejpam-5794	137	1	then	then	ADV
ejpam-5794	137	2	lim	lim	PROPN
ejpam-5794	137	3	n−→+∞	n−→+∞	PROPN
ejpam-5794	137	4	g(ϑn	g(ϑn	PROPN
ejpam-5794	137	5	)	)	PUNCT
ejpam-5794	137	6	=	=	PUNCT
ejpam-5794	138	1	s.	s.	PROPN
ejpam-5794	138	2	and	and	CCONJ
ejpam-5794	138	3	lim	lim	PROPN
ejpam-5794	138	4	n−→+∞	n−→+∞	PROPN
ejpam-5794	138	5	g(ϑn	g(ϑn	PROPN
ejpam-5794	138	6	)	)	PUNCT
ejpam-5794	138	7	=	=	PUNCT
ejpam-5794	139	1	t.	t.	NOUN
ejpam-5794	139	2	here	here	ADV
ejpam-5794	139	3	(	(	PUNCT
ejpam-5794	139	4	ϑn	ϑn	NOUN
ejpam-5794	139	5	)	)	PUNCT
ejpam-5794	139	6	is	be	AUX
ejpam-5794	139	7	a	a	DET
ejpam-5794	139	8	cauchy	cauchy	ADJ
ejpam-5794	139	9	sequence	sequence	NOUN
ejpam-5794	139	10	.	.	PUNCT
ejpam-5794	140	1	then	then	ADV
ejpam-5794	140	2	from	from	ADP
ejpam-5794	140	3	the	the	DET
ejpam-5794	140	4	triangular	triangular	NOUN
ejpam-5794	140	5	inequality	inequality	NOUN
ejpam-5794	140	6	(	(	PUNCT
ejpam-5794	140	7	cm3	cm3	NOUN
ejpam-5794	140	8	)	)	PUNCT
ejpam-5794	140	9	of	of	ADP
ejpam-5794	140	10	definition	definition	NOUN
ejpam-5794	140	11	(	(	PUNCT
ejpam-5794	140	12	7	7	NUM
ejpam-5794	140	13	)	)	PUNCT
ejpam-5794	140	14	,	,	PUNCT
ejpam-5794	140	15	we	we	PRON
ejpam-5794	140	16	have	have	VERB
ejpam-5794	140	17	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	140	18	,	,	PUNCT
ejpam-5794	140	19	κ	κ	NOUN
ejpam-5794	140	20	)	)	PUNCT
ejpam-5794	140	21	≤	≤	NOUN
ejpam-5794	140	22	α(µ	α(µ	ADV
ejpam-5794	140	23	,	,	PUNCT
ejpam-5794	140	24	ϑn)∆ξ(µ	ϑn)∆ξ(µ	PROPN
ejpam-5794	140	25	,	,	PUNCT
ejpam-5794	140	26	ϑn)+α(ϑn	ϑn)+α(ϑn	PROPN
ejpam-5794	140	27	,	,	PUNCT
ejpam-5794	140	28	ϑm)∆ξ(ϑn	ϑm)∆ξ(ϑn	NUM
ejpam-5794	140	29	,	,	PUNCT
ejpam-5794	140	30	ϑm)+α(ϑm	ϑm)+α(ϑm	PROPN
ejpam-5794	140	31	,	,	PUNCT
ejpam-5794	140	32	κ)∆ξ(ϑm	κ)∆ξ(ϑm	ADJ
ejpam-5794	140	33	,	,	PUNCT
ejpam-5794	140	34	κ	κ	NOUN
ejpam-5794	140	35	)	)	PUNCT
ejpam-5794	140	36	→	→	SYM
ejpam-5794	140	37	0	0	NUM
ejpam-5794	140	38	as	as	ADP
ejpam-5794	140	39	n	n	X
ejpam-5794	140	40	,	,	PUNCT
ejpam-5794	140	41	r	r	NOUN
ejpam-5794	140	42	→	→	SYM
ejpam-5794	140	43	+	+	ADJ
ejpam-5794	140	44	∞.	∞.	PROPN
ejpam-5794	140	45	(	(	PUNCT
ejpam-5794	140	46	2.1	2.1	NUM
ejpam-5794	140	47	)	)	PUNCT
ejpam-5794	140	48	this	this	PRON
ejpam-5794	140	49	implies	imply	VERB
ejpam-5794	140	50	that	that	SCONJ
ejpam-5794	140	51	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	140	52	,	,	PUNCT
ejpam-5794	140	53	κ	κ	NOUN
ejpam-5794	140	54	)	)	PUNCT
ejpam-5794	140	55	=	=	SYM
ejpam-5794	141	1	0	0	X
ejpam-5794	141	2	.	.	PUNCT
ejpam-5794	142	1	hence	hence	ADV
ejpam-5794	142	2	(	(	PUNCT
ejpam-5794	142	3	ϑn	ϑn	NOUN
ejpam-5794	142	4	)	)	PUNCT
ejpam-5794	142	5	has	have	VERB
ejpam-5794	142	6	a	a	DET
ejpam-5794	142	7	unique	unique	ADJ
ejpam-5794	142	8	fixed	fix	VERB
ejpam-5794	142	9	point	point	NOUN
ejpam-5794	142	10	in	in	ADP
ejpam-5794	142	11	ℵ.	ℵ.	PROPN
ejpam-5794	142	12	definition	definition	NOUN
ejpam-5794	142	13	10	10	NUM
ejpam-5794	142	14	.	.	PUNCT
ejpam-5794	143	1	suppose	suppose	VERB
ejpam-5794	143	2	(	(	PUNCT
ejpam-5794	143	3	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	143	4	)	)	PUNCT
ejpam-5794	143	5	be	be	AUX
ejpam-5794	143	6	a	a	DET
ejpam-5794	143	7	crmms	crmms	NOUN
ejpam-5794	143	8	.	.	PUNCT
ejpam-5794	144	1	then	then	ADV
ejpam-5794	144	2	the	the	DET
ejpam-5794	144	3	mapping	mapping	NOUN
ejpam-5794	144	4	i	i	NOUN
ejpam-5794	144	5	)	)	PUNCT
ejpam-5794	144	6	g	g	NOUN
ejpam-5794	144	7	:	:	PUNCT
ejpam-5794	144	8	ℵ	ℵ	PROPN
ejpam-5794	144	9	→	→	SYM
ejpam-5794	144	10	ℵ	ℵ	PRON
ejpam-5794	144	11	defined	define	VERB
ejpam-5794	144	12	by	by	ADP
ejpam-5794	144	13	ω(ϑ	ω(ϑ	PROPN
ejpam-5794	144	14	,	,	PUNCT
ejpam-5794	144	15	n	n	CCONJ
ejpam-5794	144	16	)	)	PUNCT
ejpam-5794	144	17	=	=	SYM
ejpam-5794	144	18	{	{	PUNCT
ejpam-5794	144	19	ϑ	ϑ	NOUN
ejpam-5794	144	20	,	,	PUNCT
ejpam-5794	144	21	gϑ	gϑ	INTJ
ejpam-5794	144	22	,	,	PUNCT
ejpam-5794	144	23	g2ϑ	g2ϑ	PROPN
ejpam-5794	144	24	,	,	PUNCT
ejpam-5794	144	25	·	·	PUNCT
ejpam-5794	144	26	·	·	PUNCT
ejpam-5794	144	27	·	·	PUNCT
ejpam-5794	144	28	gnϑ	gnϑ	ADJ
ejpam-5794	144	29	}	}	PUNCT
ejpam-5794	144	30	,	,	PUNCT
ejpam-5794	144	31	ω(ϑ,+∞	ω(ϑ,+∞	NUM
ejpam-5794	144	32	)	)	PUNCT
ejpam-5794	144	33	=	=	PUNCT
ejpam-5794	144	34	{	{	PUNCT
ejpam-5794	144	35	ϑ	ϑ	NOUN
ejpam-5794	144	36	,	,	PUNCT
ejpam-5794	144	37	gϑ	gϑ	INTJ
ejpam-5794	144	38	,	,	PUNCT
ejpam-5794	144	39	g2ϑ	g2ϑ	PROPN
ejpam-5794	144	40	,	,	PUNCT
ejpam-5794	144	41	·	·	PUNCT
ejpam-5794	144	42	·	·	PUNCT
ejpam-5794	144	43	·	·	PUNCT
ejpam-5794	144	44	gnϑ	gnϑ	INTJ
ejpam-5794	144	45	·	·	PUNCT
ejpam-5794	144	46	·	·	PUNCT
ejpam-5794	144	47	·	·	PUNCT
ejpam-5794	144	48	}	}	PUNCT
ejpam-5794	144	49	,	,	PUNCT
ejpam-5794	144	50	where	where	SCONJ
ejpam-5794	144	51	ϑ	ϑ	X
ejpam-5794	144	52	∈	∈	PROPN
ejpam-5794	144	53	ℵ	ℵ	NOUN
ejpam-5794	144	54	and	and	CCONJ
ejpam-5794	144	55	n	n	PRON
ejpam-5794	144	56	∈	∈	PROPN
ejpam-5794	144	57	n.	n.	NOUN
ejpam-5794	144	58	here	here	ADV
ejpam-5794	144	59	,	,	PUNCT
ejpam-5794	144	60	ω(ϑ,+∞	ω(ϑ,+∞	PROPN
ejpam-5794	144	61	)	)	PUNCT
ejpam-5794	144	62	is	be	AUX
ejpam-5794	144	63	known	know	VERB
ejpam-5794	144	64	as	as	ADP
ejpam-5794	144	65	orbit	orbit	NOUN
ejpam-5794	144	66	of	of	ADP
ejpam-5794	144	67	g.	g.	PROPN
ejpam-5794	144	68	ii	ii	PROPN
ejpam-5794	144	69	)	)	PUNCT
ejpam-5794	145	1	g	g	NOUN
ejpam-5794	145	2	:	:	PUNCT
ejpam-5794	145	3	ℵ	ℵ	PROPN
ejpam-5794	145	4	→	→	SYM
ejpam-5794	145	5	ℵ	ℵ	NOUN
ejpam-5794	145	6	is	be	AUX
ejpam-5794	145	7	known	know	VERB
ejpam-5794	145	8	as	as	ADP
ejpam-5794	145	9	g−orbitally	g−orbitally	ADV
ejpam-5794	145	10	continuous	continuous	ADJ
ejpam-5794	145	11	,	,	PUNCT
ejpam-5794	145	12	if	if	SCONJ
ejpam-5794	145	13	lim	lim	PROPN
ejpam-5794	145	14	k−→+∞	k−→+∞	PROPN
ejpam-5794	145	15	gnkϑ	gnkϑ	PROPN
ejpam-5794	145	16	=	=	PRON
ejpam-5794	145	17	ϑ	ϑ	PROPN
ejpam-5794	145	18	implies	imply	VERB
ejpam-5794	145	19	lim	lim	PROPN
ejpam-5794	145	20	k−→+∞	k−→+∞	PROPN
ejpam-5794	145	21	g	g	PROPN
ejpam-5794	145	22	(	(	PUNCT
ejpam-5794	145	23	gnkϑ	gnkϑ	NOUN
ejpam-5794	145	24	)	)	PUNCT
ejpam-5794	146	1	=	=	PUNCT
ejpam-5794	146	2	gϑ	gϑ	PROPN
ejpam-5794	146	3	for	for	ADP
ejpam-5794	146	4	ϑ	ϑ	PROPN
ejpam-5794	146	5	∈	∈	PROPN
ejpam-5794	146	6	ℵ.	ℵ.	NOUN
ejpam-5794	146	7	theorem	theorem	VERB
ejpam-5794	146	8	2	2	X
ejpam-5794	146	9	.	.	PUNCT
ejpam-5794	146	10	suppose	suppose	VERB
ejpam-5794	146	11	g	g	NOUN
ejpam-5794	146	12	:	:	PUNCT
ejpam-5794	146	13	ℵ	ℵ	PROPN
ejpam-5794	146	14	→	→	SYM
ejpam-5794	146	15	ℵ	ℵ	NOUN
ejpam-5794	146	16	is	be	AUX
ejpam-5794	146	17	a	a	DET
ejpam-5794	146	18	mapping	mapping	NOUN
ejpam-5794	146	19	in	in	ADP
ejpam-5794	146	20	a	a	DET
ejpam-5794	146	21	crmms	crmms	NOUN
ejpam-5794	146	22	(	(	PUNCT
ejpam-5794	146	23	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	146	24	)	)	PUNCT
ejpam-5794	146	25	.	.	PUNCT
ejpam-5794	147	1	assume	assume	VERB
ejpam-5794	147	2	that	that	SCONJ
ejpam-5794	147	3	the	the	DET
ejpam-5794	147	4	following	follow	VERB
ejpam-5794	147	5	conditions	condition	NOUN
ejpam-5794	147	6	hold	hold	VERB
ejpam-5794	147	7	:	:	PUNCT
ejpam-5794	147	8	a	a	X
ejpam-5794	147	9	)	)	PUNCT
ejpam-5794	147	10	for	for	ADP
ejpam-5794	147	11	all	all	DET
ejpam-5794	147	12	µ	µ	NOUN
ejpam-5794	147	13	,	,	PUNCT
ejpam-5794	147	14	κ	κ	PROPN
ejpam-5794	147	15	∈	∈	PROPN
ejpam-5794	147	16	ℵ	ℵ	NOUN
ejpam-5794	147	17	,	,	PUNCT
ejpam-5794	147	18	∆ξ(gµ	∆ξ(gµ	NOUN
ejpam-5794	147	19	,	,	PUNCT
ejpam-5794	147	20	gκ	gκ	NOUN
ejpam-5794	147	21	)	)	PUNCT
ejpam-5794	147	22	≤	≤	NOUN
ejpam-5794	147	23	λ∆ξ(µ	λ∆ξ(µ	NOUN
ejpam-5794	147	24	,	,	PUNCT
ejpam-5794	147	25	κ	κ	NOUN
ejpam-5794	147	26	)	)	PUNCT
ejpam-5794	147	27	,	,	PUNCT
ejpam-5794	147	28	b	b	X
ejpam-5794	147	29	)	)	PUNCT
ejpam-5794	147	30	sup	sup	NOUN
ejpam-5794	147	31	q≥1	q≥1	PROPN
ejpam-5794	147	32	lim	lim	PROPN
ejpam-5794	148	1	i−→+∞	i−→+∞	PROPN
ejpam-5794	148	2	α(µi	α(µi	PROPN
ejpam-5794	148	3	,	,	PUNCT
ejpam-5794	148	4	µq	µq	PROPN
ejpam-5794	148	5	)	)	PUNCT
ejpam-5794	148	6	(	(	PUNCT
ejpam-5794	148	7	α(µi,µ(i+1	α(µi,µ(i+1	NUM
ejpam-5794	148	8	)	)	PUNCT
ejpam-5794	148	9	)	)	PUNCT
ejpam-5794	148	10	α(µ(i−1),µi	α(µ(i−1),µi	NUM
ejpam-5794	148	11	)	)	PUNCT
ejpam-5794	148	12	)	)	PUNCT
ejpam-5794	149	1	λ	λ	X
ejpam-5794	149	2	<	<	X
ejpam-5794	149	3	1	1	NUM
ejpam-5794	149	4	for	for	ADP
ejpam-5794	149	5	any	any	DET
ejpam-5794	149	6	µi	µi	PROPN
ejpam-5794	149	7	∈	∈	PROPN
ejpam-5794	149	8	ℵ	ℵ	NOUN
ejpam-5794	149	9	,	,	PUNCT
ejpam-5794	149	10	c	c	NOUN
ejpam-5794	149	11	)	)	PUNCT
ejpam-5794	149	12	(	(	PUNCT
ejpam-5794	149	13	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	149	14	)	)	PUNCT
ejpam-5794	149	15	is	be	AUX
ejpam-5794	149	16	g	g	NOUN
ejpam-5794	149	17	is	be	AUX
ejpam-5794	149	18	orbitally	orbitally	ADV
ejpam-5794	149	19	complete	complete	ADJ
ejpam-5794	149	20	,	,	PUNCT
ejpam-5794	149	21	d	d	NOUN
ejpam-5794	149	22	)	)	PUNCT
ejpam-5794	149	23	g	g	NOUN
ejpam-5794	149	24	is	be	AUX
ejpam-5794	149	25	orbitally	orbitally	ADV
ejpam-5794	149	26	continuous	continuous	ADJ
ejpam-5794	149	27	,	,	PUNCT
ejpam-5794	150	1	u.	u.	PROPN
ejpam-5794	150	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	150	3	et	et	PROPN
ejpam-5794	150	4	al	al	PROPN
ejpam-5794	150	5	.	.	PUNCT
ejpam-5794	150	6	/	/	SYM
ejpam-5794	150	7	eur	eur	PROPN
ejpam-5794	150	8	.	.	PUNCT
ejpam-5794	151	1	j.	j.	PROPN
ejpam-5794	151	2	pure	pure	PROPN
ejpam-5794	151	3	appl	appl	PROPN
ejpam-5794	151	4	.	.	PROPN
ejpam-5794	151	5	math	math	PROPN
ejpam-5794	151	6	,	,	PUNCT
ejpam-5794	151	7	18	18	NUM
ejpam-5794	151	8	(	(	PUNCT
ejpam-5794	151	9	1	1	NUM
ejpam-5794	151	10	)	)	PUNCT
ejpam-5794	151	11	(	(	PUNCT
ejpam-5794	151	12	2025	2025	NUM
ejpam-5794	151	13	)	)	PUNCT
ejpam-5794	151	14	,	,	PUNCT
ejpam-5794	151	15	5794	5794	NUM
ejpam-5794	151	16	8	8	NUM
ejpam-5794	151	17	of	of	ADP
ejpam-5794	151	18	20	20	NUM
ejpam-5794	151	19	e	e	NOUN
ejpam-5794	151	20	)	)	PUNCT
ejpam-5794	151	21	for	for	ADP
ejpam-5794	151	22	each	each	DET
ejpam-5794	151	23	µ	µ	PRON
ejpam-5794	151	24	∈	∈	PROPN
ejpam-5794	151	25	ℵ	ℵ	NOUN
ejpam-5794	151	26	lim	lim	PROPN
ejpam-5794	151	27	n→+∞	n→+∞	PROPN
ejpam-5794	151	28	α(µn	α(µn	PROPN
ejpam-5794	151	29	,	,	PUNCT
ejpam-5794	151	30	µ	µ	NOUN
ejpam-5794	151	31	)	)	PUNCT
ejpam-5794	151	32	and	and	CCONJ
ejpam-5794	151	33	lim	lim	PROPN
ejpam-5794	151	34	n→+∞	n→+∞	PROPN
ejpam-5794	151	35	α(µ	α(µ	ADV
ejpam-5794	151	36	,	,	PUNCT
ejpam-5794	151	37	µn	µn	NOUN
ejpam-5794	151	38	)	)	PUNCT
ejpam-5794	151	39	exist	exist	VERB
ejpam-5794	151	40	and	and	CCONJ
ejpam-5794	151	41	finite	finite	PROPN
ejpam-5794	151	42	.	.	PUNCT
ejpam-5794	152	1	then	then	ADV
ejpam-5794	152	2	g	g	PROPN
ejpam-5794	152	3	has	have	VERB
ejpam-5794	152	4	a	a	DET
ejpam-5794	152	5	unique	unique	ADJ
ejpam-5794	152	6	fixed	fix	VERB
ejpam-5794	152	7	point	point	NOUN
ejpam-5794	152	8	.	.	PUNCT
ejpam-5794	153	1	proof	proof	NOUN
ejpam-5794	153	2	.	.	PUNCT
ejpam-5794	154	1	suppose	suppose	VERB
ejpam-5794	154	2	µ0	µ0	NOUN
ejpam-5794	154	3	be	be	VERB
ejpam-5794	154	4	any	any	DET
ejpam-5794	154	5	point	point	NOUN
ejpam-5794	154	6	in	in	ADP
ejpam-5794	154	7	ℵ.	ℵ.	PROPN
ejpam-5794	154	8	we	we	PRON
ejpam-5794	154	9	describe	describe	VERB
ejpam-5794	154	10	the	the	DET
ejpam-5794	154	11	iterative	iterative	NOUN
ejpam-5794	154	12	sequence	sequence	NOUN
ejpam-5794	154	13	(	(	PUNCT
ejpam-5794	154	14	µn	µn	NOUN
ejpam-5794	154	15	)	)	PUNCT
ejpam-5794	154	16	over	over	ADP
ejpam-5794	154	17	µ0	µ0	NOUN
ejpam-5794	154	18	as	as	SCONJ
ejpam-5794	154	19	follows	follow	VERB
ejpam-5794	154	20	g(µ0	g(µ0	NOUN
ejpam-5794	154	21	)	)	PUNCT
ejpam-5794	154	22	=	=	SYM
ejpam-5794	154	23	µ1	µ1	PROPN
ejpam-5794	154	24	,	,	PUNCT
ejpam-5794	154	25	g(µ1	g(µ1	NOUN
ejpam-5794	154	26	)	)	PUNCT
ejpam-5794	155	1	=	=	SYM
ejpam-5794	155	2	µ2	µ2	ADJ
ejpam-5794	155	3	,	,	PUNCT
ejpam-5794	155	4	g(µ2	g(µ2	NOUN
ejpam-5794	155	5	)	)	PUNCT
ejpam-5794	155	6	=	=	SYM
ejpam-5794	155	7	µ3	µ3	NOUN
ejpam-5794	155	8	·	·	PUNCT
ejpam-5794	155	9	·	·	PUNCT
ejpam-5794	155	10	·	·	PUNCT
ejpam-5794	155	11	gn(µ0	gn(µ0	X
ejpam-5794	155	12	)	)	PUNCT
ejpam-5794	155	13	=	=	SYM
ejpam-5794	155	14	µn	µn	NOUN
ejpam-5794	155	15	,	,	PUNCT
ejpam-5794	155	16	then	then	ADV
ejpam-5794	155	17	,	,	PUNCT
ejpam-5794	155	18	we	we	PRON
ejpam-5794	155	19	obtain	obtain	VERB
ejpam-5794	155	20	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	155	21	,	,	PUNCT
ejpam-5794	155	22	µ2	µ2	PROPN
ejpam-5794	155	23	)	)	PUNCT
ejpam-5794	155	24	=	=	PUNCT
ejpam-5794	155	25	∆ξ(g(µ0	∆ξ(g(µ0	PROPN
ejpam-5794	155	26	)	)	PUNCT
ejpam-5794	155	27	,	,	PUNCT
ejpam-5794	155	28	g	g	PROPN
ejpam-5794	155	29	2(µ0	2(µ0	NUM
ejpam-5794	155	30	)	)	PUNCT
ejpam-5794	155	31	)	)	PUNCT
ejpam-5794	156	1	≤	≤	NUM
ejpam-5794	156	2	λ∆ξ(µ0	λ∆ξ(µ0	NOUN
ejpam-5794	156	3	,	,	PUNCT
ejpam-5794	156	4	g(µ0	g(µ0	NOUN
ejpam-5794	156	5	)	)	PUNCT
ejpam-5794	156	6	)	)	PUNCT
ejpam-5794	157	1	=	=	SYM
ejpam-5794	157	2	λ∆ξ(µ0	λ∆ξ(µ0	NOUN
ejpam-5794	157	3	,	,	PUNCT
ejpam-5794	157	4	µ1	µ1	NOUN
ejpam-5794	157	5	)	)	PUNCT
ejpam-5794	157	6	recursively	recursively	NOUN
ejpam-5794	157	7	,	,	PUNCT
ejpam-5794	157	8	we	we	PRON
ejpam-5794	157	9	get	get	VERB
ejpam-5794	157	10	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	157	11	,	,	PUNCT
ejpam-5794	157	12	µ(n+1	µ(n+1	NUM
ejpam-5794	157	13	)	)	PUNCT
ejpam-5794	157	14	)	)	PUNCT
ejpam-5794	157	15	≤	≤	PROPN
ejpam-5794	157	16	∆ξ(g	∆ξ(g	PROPN
ejpam-5794	157	17	n(µ0	n(µ0	NOUN
ejpam-5794	157	18	)	)	PUNCT
ejpam-5794	157	19	,	,	PUNCT
ejpam-5794	157	20	g	g	PROPN
ejpam-5794	157	21	(	(	PUNCT
ejpam-5794	157	22	n+1)(µ0	n+1)(µ0	NOUN
ejpam-5794	157	23	)	)	PUNCT
ejpam-5794	157	24	)	)	PUNCT
ejpam-5794	157	25	≤	≤	NUM
ejpam-5794	158	1	λ∆ξ(g	λ∆ξ(g	X
ejpam-5794	158	2	(	(	PUNCT
ejpam-5794	158	3	n−1)(µ0	n−1)(µ0	PROPN
ejpam-5794	158	4	)	)	PUNCT
ejpam-5794	158	5	,	,	PUNCT
ejpam-5794	158	6	g	g	PROPN
ejpam-5794	158	7	n(µ0	n(µ0	NOUN
ejpam-5794	158	8	)	)	PUNCT
ejpam-5794	158	9	)	)	PUNCT
ejpam-5794	158	10	...	...	PUNCT
ejpam-5794	159	1	≤	≤	NUM
ejpam-5794	159	2	λn∆ξ(µ0	λn∆ξ(µ0	NOUN
ejpam-5794	159	3	,	,	PUNCT
ejpam-5794	159	4	µ1	µ1	NOUN
ejpam-5794	159	5	)	)	PUNCT
ejpam-5794	159	6	taking	take	VERB
ejpam-5794	159	7	lim	lim	PROPN
ejpam-5794	159	8	n→+∞	n→+∞	PROPN
ejpam-5794	159	9	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	159	10	,	,	PUNCT
ejpam-5794	159	11	µ(n+1	µ(n+1	NUM
ejpam-5794	159	12	)	)	PUNCT
ejpam-5794	159	13	)	)	PUNCT
ejpam-5794	160	1	=	=	PUNCT
ejpam-5794	160	2	0	0	X
ejpam-5794	160	3	.	.	PUNCT
ejpam-5794	161	1	similarly	similarly	ADV
ejpam-5794	161	2	,	,	PUNCT
ejpam-5794	161	3	lim	lim	PROPN
ejpam-5794	161	4	n→+∞	n→+∞	PROPN
ejpam-5794	161	5	∆ξ(µ(n+1	∆ξ(µ(n+1	PROPN
ejpam-5794	161	6	)	)	PUNCT
ejpam-5794	161	7	,	,	PUNCT
ejpam-5794	161	8	µ(n+2	µ(n+2	PUNCT
ejpam-5794	161	9	)	)	PUNCT
ejpam-5794	161	10	)	)	PUNCT
ejpam-5794	162	1	=	=	PUNCT
ejpam-5794	162	2	0	0	X
ejpam-5794	162	3	.	.	PUNCT
ejpam-5794	163	1	now	now	ADV
ejpam-5794	163	2	,	,	PUNCT
ejpam-5794	163	3	we	we	PRON
ejpam-5794	163	4	examine	examine	VERB
ejpam-5794	163	5	that	that	SCONJ
ejpam-5794	163	6	(	(	PUNCT
ejpam-5794	163	7	µn	µn	NOUN
ejpam-5794	163	8	)	)	PUNCT
ejpam-5794	163	9	is	be	AUX
ejpam-5794	163	10	a	a	DET
ejpam-5794	163	11	cauchy	cauchy	ADJ
ejpam-5794	163	12	sequence	sequence	NOUN
ejpam-5794	163	13	.	.	PUNCT
ejpam-5794	164	1	here	here	ADV
ejpam-5794	164	2	,	,	PUNCT
ejpam-5794	164	3	we	we	PRON
ejpam-5794	164	4	make	make	VERB
ejpam-5794	164	5	the	the	DET
ejpam-5794	164	6	following	follow	VERB
ejpam-5794	164	7	cases	case	NOUN
ejpam-5794	164	8	:	:	PUNCT
ejpam-5794	164	9	case	case	NOUN
ejpam-5794	164	10	1	1	NUM
ejpam-5794	164	11	:	:	PUNCT
ejpam-5794	164	12	suppose	suppose	VERB
ejpam-5794	164	13	p	p	PRON
ejpam-5794	164	14	be	be	AUX
ejpam-5794	164	15	an	an	DET
ejpam-5794	164	16	odd	odd	ADJ
ejpam-5794	164	17	number	number	NOUN
ejpam-5794	164	18	,	,	PUNCT
ejpam-5794	164	19	then	then	ADV
ejpam-5794	164	20	p	p	NOUN
ejpam-5794	164	21	=	=	SYM
ejpam-5794	164	22	2n+	2n+	NUM
ejpam-5794	164	23	1	1	NUM
ejpam-5794	164	24	and	and	CCONJ
ejpam-5794	164	25	r	r	NOUN
ejpam-5794	164	26	≥	≥	NUM
ejpam-5794	164	27	1	1	NUM
ejpam-5794	164	28	,	,	PUNCT
ejpam-5794	164	29	we	we	PRON
ejpam-5794	164	30	have	have	AUX
ejpam-5794	164	31	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	164	32	,	,	PUNCT
ejpam-5794	164	33	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	164	34	)	)	PUNCT
ejpam-5794	164	35	)	)	PUNCT
ejpam-5794	165	1	≤	≤	NUM
ejpam-5794	166	1	ξ	ξ	PRON
ejpam-5794	166	2	3	3	NUM
ejpam-5794	166	3	α(µn	α(µn	NUM
ejpam-5794	166	4	,	,	PUNCT
ejpam-5794	166	5	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	166	6	,	,	PUNCT
ejpam-5794	166	7	µ(n+1	µ(n+1	NUM
ejpam-5794	166	8	)	)	PUNCT
ejpam-5794	166	9	)	)	PUNCT
ejpam-5794	167	1	+	+	CCONJ
ejpam-5794	168	1	ξ	ξ	SYM
ejpam-5794	168	2	3	3	NUM
ejpam-5794	168	3	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	168	4	)	)	PUNCT
ejpam-5794	168	5	,	,	PUNCT
ejpam-5794	168	6	µ(n+2))∆ξ(µ(n+1	µ(n+2))∆ξ(µ(n+1	PROPN
ejpam-5794	168	7	)	)	PUNCT
ejpam-5794	168	8	,	,	PUNCT
ejpam-5794	168	9	µ(n+2	µ(n+2	PUNCT
ejpam-5794	168	10	)	)	PUNCT
ejpam-5794	168	11	)	)	PUNCT
ejpam-5794	169	1	+	+	CCONJ
ejpam-5794	170	1	ξ	ξ	SYM
ejpam-5794	170	2	3	3	NUM
ejpam-5794	170	3	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	170	4	)	)	PUNCT
ejpam-5794	170	5	,	,	PUNCT
ejpam-5794	170	6	µ(n+2r+1))∆ξ(µ(n+2	µ(n+2r+1))∆ξ(µ(n+2	NOUN
ejpam-5794	170	7	)	)	PUNCT
ejpam-5794	170	8	,	,	PUNCT
ejpam-5794	170	9	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	170	10	)	)	PUNCT
ejpam-5794	170	11	)	)	PUNCT
ejpam-5794	170	12	,	,	PUNCT
ejpam-5794	170	13	=	=	SYM
ejpam-5794	170	14	ξ	ξ	SYM
ejpam-5794	170	15	3	3	NUM
ejpam-5794	170	16	[	[	X
ejpam-5794	170	17	λnα(µn	λnα(µn	X
ejpam-5794	170	18	,	,	PUNCT
ejpam-5794	170	19	µ(n+1	µ(n+1	NUM
ejpam-5794	170	20	)	)	PUNCT
ejpam-5794	170	21	)	)	PUNCT
ejpam-5794	171	1	+	+	CCONJ
ejpam-5794	171	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	171	3	)	)	PUNCT
ejpam-5794	171	4	,	,	PUNCT
ejpam-5794	171	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	171	6	,	,	PUNCT
ejpam-5794	171	7	µ1	µ1	PROPN
ejpam-5794	171	8	)	)	PUNCT
ejpam-5794	171	9	+	+	NUM
ejpam-5794	171	10	ξ	ξ	SYM
ejpam-5794	171	11	3	3	NUM
ejpam-5794	171	12	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	171	13	)	)	PUNCT
ejpam-5794	171	14	,	,	PUNCT
ejpam-5794	171	15	µ(n+2r+1))∆ξ(µ(n+2	µ(n+2r+1))∆ξ(µ(n+2	NOUN
ejpam-5794	171	16	)	)	PUNCT
ejpam-5794	171	17	,	,	PUNCT
ejpam-5794	171	18	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	171	19	)	)	PUNCT
ejpam-5794	171	20	)	)	PUNCT
ejpam-5794	171	21	,	,	PUNCT
ejpam-5794	171	22	≤	≤	NUM
ejpam-5794	171	23	ξ	ξ	SYM
ejpam-5794	171	24	3	3	NUM
ejpam-5794	171	25	[	[	X
ejpam-5794	171	26	λnα(µn	λnα(µn	X
ejpam-5794	171	27	,	,	PUNCT
ejpam-5794	171	28	µ(n+1	µ(n+1	NUM
ejpam-5794	171	29	)	)	PUNCT
ejpam-5794	171	30	)	)	PUNCT
ejpam-5794	172	1	+	+	CCONJ
ejpam-5794	172	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	172	3	)	)	PUNCT
ejpam-5794	172	4	,	,	PUNCT
ejpam-5794	172	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	172	6	,	,	PUNCT
ejpam-5794	172	7	µ1	µ1	PROPN
ejpam-5794	172	8	)	)	PUNCT
ejpam-5794	172	9	+	+	NUM
ejpam-5794	172	10	ξ	ξ	SYM
ejpam-5794	172	11	3	3	NUM
ejpam-5794	172	12	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	172	13	)	)	PUNCT
ejpam-5794	172	14	,	,	PUNCT
ejpam-5794	172	15	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	172	16	)	)	PUNCT
ejpam-5794	172	17	)	)	PUNCT
ejpam-5794	173	1	[	[	PUNCT
ejpam-5794	173	2	ξ	ξ	X
ejpam-5794	173	3	3	3	NUM
ejpam-5794	173	4	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	173	5	)	)	PUNCT
ejpam-5794	173	6	,	,	PUNCT
ejpam-5794	173	7	µ(n+3))∆ξ(µ(n+2	µ(n+3))∆ξ(µ(n+2	NUM
ejpam-5794	173	8	)	)	PUNCT
ejpam-5794	173	9	,	,	PUNCT
ejpam-5794	173	10	µ(n+3	µ(n+3	PROPN
ejpam-5794	173	11	)	)	PUNCT
ejpam-5794	173	12	)	)	PUNCT
ejpam-5794	174	1	+	+	CCONJ
ejpam-5794	174	2	ξ	ξ	SYM
ejpam-5794	174	3	3	3	NUM
ejpam-5794	174	4	α(µ(n+3	α(µ(n+3	NOUN
ejpam-5794	174	5	)	)	PUNCT
ejpam-5794	174	6	,	,	PUNCT
ejpam-5794	174	7	µ(n+4))∆ξ(µ(n+3	µ(n+4))∆ξ(µ(n+3	NOUN
ejpam-5794	174	8	)	)	PUNCT
ejpam-5794	174	9	,	,	PUNCT
ejpam-5794	174	10	µ(n+4	µ(n+4	NUM
ejpam-5794	174	11	)	)	PUNCT
ejpam-5794	174	12	)	)	PUNCT
ejpam-5794	175	1	+	+	CCONJ
ejpam-5794	176	1	ξ	ξ	SYM
ejpam-5794	176	2	3	3	NUM
ejpam-5794	176	3	α(µ(n+4	α(µ(n+4	NOUN
ejpam-5794	176	4	)	)	PUNCT
ejpam-5794	176	5	,	,	PUNCT
ejpam-5794	176	6	µ(n+2r+1))∆ξ(µ(n+4	µ(n+2r+1))∆ξ(µ(n+4	NOUN
ejpam-5794	176	7	)	)	PUNCT
ejpam-5794	176	8	,	,	PUNCT
ejpam-5794	176	9	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	176	10	)	)	PUNCT
ejpam-5794	176	11	)	)	PUNCT
ejpam-5794	176	12	]	]	PUNCT
ejpam-5794	176	13	,	,	PUNCT
ejpam-5794	176	14	=	=	SYM
ejpam-5794	176	15	ξ	ξ	SYM
ejpam-5794	176	16	3	3	NUM
ejpam-5794	176	17	[	[	X
ejpam-5794	176	18	λnα(µn	λnα(µn	X
ejpam-5794	176	19	,	,	PUNCT
ejpam-5794	176	20	µ(n+1	µ(n+1	NUM
ejpam-5794	176	21	)	)	PUNCT
ejpam-5794	176	22	)	)	PUNCT
ejpam-5794	177	1	+	+	CCONJ
ejpam-5794	177	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	177	3	)	)	PUNCT
ejpam-5794	177	4	,	,	PUNCT
ejpam-5794	177	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	177	6	,	,	PUNCT
ejpam-5794	177	7	µ1	µ1	PROPN
ejpam-5794	177	8	)	)	PUNCT
ejpam-5794	178	1	+	+	NOUN
ejpam-5794	179	1	ξ2	ξ2	NOUN
ejpam-5794	179	2	32	32	NUM
ejpam-5794	179	3	[	[	SYM
ejpam-5794	179	4	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	179	5	)	)	PUNCT
ejpam-5794	179	6	,	,	PUNCT
ejpam-5794	179	7	µ(n+2r+1))α(µ(n+2	µ(n+2r+1))α(µ(n+2	VERB
ejpam-5794	179	8	)	)	PUNCT
ejpam-5794	179	9	,	,	PUNCT
ejpam-5794	179	10	µ(n+3))λ	µ(n+3))λ	PROPN
ejpam-5794	179	11	(	(	PUNCT
ejpam-5794	179	12	n+2	n+2	NOUN
ejpam-5794	179	13	)	)	PUNCT
ejpam-5794	179	14	+	+	NOUN
ejpam-5794	179	15	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	179	16	)	)	PUNCT
ejpam-5794	179	17	,	,	PUNCT
ejpam-5794	179	18	µ(n+2r+1))α(µ(n+3	µ(n+2r+1))α(µ(n+3	PROPN
ejpam-5794	179	19	)	)	PUNCT
ejpam-5794	179	20	,	,	PUNCT
ejpam-5794	179	21	µ(n+4))λ	µ(n+4))λ	X
ejpam-5794	179	22	(	(	PUNCT
ejpam-5794	179	23	n+3)]∆ξ(µ0	n+3)]∆ξ(µ0	NUM
ejpam-5794	179	24	,	,	PUNCT
ejpam-5794	179	25	µ1	µ1	PROPN
ejpam-5794	179	26	)	)	PUNCT
ejpam-5794	179	27	+	+	CCONJ
ejpam-5794	179	28	ξ2	ξ2	ADJ
ejpam-5794	179	29	32	32	NUM
ejpam-5794	179	30	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	179	31	)	)	PUNCT
ejpam-5794	179	32	,	,	PUNCT
ejpam-5794	179	33	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	179	34	)	)	PUNCT
ejpam-5794	179	35	,	,	PUNCT
ejpam-5794	179	36	µ(n+2r+1))∆ξ(µ(n+4	µ(n+2r+1))∆ξ(µ(n+4	NOUN
ejpam-5794	179	37	)	)	PUNCT
ejpam-5794	179	38	,	,	PUNCT
ejpam-5794	179	39	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	179	40	)	)	PUNCT
ejpam-5794	179	41	)	)	PUNCT
ejpam-5794	179	42	,	,	PUNCT
ejpam-5794	179	43	u.	u.	PROPN
ejpam-5794	179	44	ishtiaq	ishtiaq	PROPN
ejpam-5794	179	45	et	et	PROPN
ejpam-5794	179	46	al	al	PROPN
ejpam-5794	179	47	.	.	PUNCT
ejpam-5794	179	48	/	/	SYM
ejpam-5794	179	49	eur	eur	PROPN
ejpam-5794	179	50	.	.	PUNCT
ejpam-5794	180	1	j.	j.	PROPN
ejpam-5794	180	2	pure	pure	PROPN
ejpam-5794	180	3	appl	appl	PROPN
ejpam-5794	180	4	.	.	PROPN
ejpam-5794	180	5	math	math	PROPN
ejpam-5794	180	6	,	,	PUNCT
ejpam-5794	180	7	18	18	NUM
ejpam-5794	180	8	(	(	PUNCT
ejpam-5794	180	9	1	1	NUM
ejpam-5794	180	10	)	)	PUNCT
ejpam-5794	180	11	(	(	PUNCT
ejpam-5794	180	12	2025	2025	NUM
ejpam-5794	180	13	)	)	PUNCT
ejpam-5794	180	14	,	,	PUNCT
ejpam-5794	180	15	5794	5794	NUM
ejpam-5794	180	16	9	9	NUM
ejpam-5794	180	17	of	of	ADP
ejpam-5794	180	18	20	20	NUM
ejpam-5794	180	19	≤	≤	NOUN
ejpam-5794	180	20	ξ	ξ	SYM
ejpam-5794	180	21	3	3	NUM
ejpam-5794	180	22	[	[	X
ejpam-5794	180	23	λnα(µn	λnα(µn	X
ejpam-5794	180	24	,	,	PUNCT
ejpam-5794	180	25	µ(n+1	µ(n+1	NUM
ejpam-5794	180	26	)	)	PUNCT
ejpam-5794	180	27	)	)	PUNCT
ejpam-5794	181	1	+	+	CCONJ
ejpam-5794	181	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	181	3	)	)	PUNCT
ejpam-5794	181	4	,	,	PUNCT
ejpam-5794	181	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	181	6	,	,	PUNCT
ejpam-5794	181	7	µ1	µ1	PROPN
ejpam-5794	181	8	)	)	PUNCT
ejpam-5794	182	1	+	+	NOUN
ejpam-5794	183	1	ξ2	ξ2	NOUN
ejpam-5794	183	2	32	32	NUM
ejpam-5794	183	3	[	[	SYM
ejpam-5794	183	4	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	183	5	)	)	PUNCT
ejpam-5794	183	6	,	,	PUNCT
ejpam-5794	183	7	µ(n+2r+1))α(µ(n+2	µ(n+2r+1))α(µ(n+2	VERB
ejpam-5794	183	8	)	)	PUNCT
ejpam-5794	183	9	,	,	PUNCT
ejpam-5794	183	10	µ(n+3))λ	µ(n+3))λ	PROPN
ejpam-5794	183	11	(	(	PUNCT
ejpam-5794	183	12	n+2	n+2	NOUN
ejpam-5794	183	13	)	)	PUNCT
ejpam-5794	183	14	+	+	NOUN
ejpam-5794	183	15	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	183	16	)	)	PUNCT
ejpam-5794	183	17	,	,	PUNCT
ejpam-5794	183	18	µ(n+2r+1))α(µ(n+3	µ(n+2r+1))α(µ(n+3	PROPN
ejpam-5794	183	19	)	)	PUNCT
ejpam-5794	183	20	,	,	PUNCT
ejpam-5794	183	21	µ(n+4))λ	µ(n+4))λ	X
ejpam-5794	183	22	(	(	PUNCT
ejpam-5794	183	23	n+3)]∆ξ(µ0	n+3)]∆ξ(µ0	NUM
ejpam-5794	183	24	,	,	PUNCT
ejpam-5794	183	25	µ1	µ1	PROPN
ejpam-5794	183	26	)	)	PUNCT
ejpam-5794	183	27	+	+	CCONJ
ejpam-5794	183	28	ξ2	ξ2	ADJ
ejpam-5794	183	29	32	32	NUM
ejpam-5794	183	30	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	183	31	)	)	PUNCT
ejpam-5794	183	32	,	,	PUNCT
ejpam-5794	183	33	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	183	34	)	)	PUNCT
ejpam-5794	183	35	,	,	PUNCT
ejpam-5794	183	36	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	183	37	)	)	PUNCT
ejpam-5794	183	38	)	)	PUNCT
ejpam-5794	184	1	[	[	PUNCT
ejpam-5794	184	2	ξ	ξ	X
ejpam-5794	184	3	3	3	NUM
ejpam-5794	184	4	α(µ(n+4	α(µ(n+4	NOUN
ejpam-5794	184	5	)	)	PUNCT
ejpam-5794	184	6	,	,	PUNCT
ejpam-5794	184	7	µ(n+5))∆ξ(µ(n+4	µ(n+5))∆ξ(µ(n+4	NOUN
ejpam-5794	184	8	)	)	PUNCT
ejpam-5794	184	9	,	,	PUNCT
ejpam-5794	184	10	µ(n+5	µ(n+5	NUM
ejpam-5794	184	11	)	)	PUNCT
ejpam-5794	184	12	)	)	PUNCT
ejpam-5794	185	1	+	+	CCONJ
ejpam-5794	186	1	ξ	ξ	SYM
ejpam-5794	186	2	3	3	NUM
ejpam-5794	186	3	α(µ(n+5	α(µ(n+5	NOUN
ejpam-5794	186	4	)	)	PUNCT
ejpam-5794	186	5	,	,	PUNCT
ejpam-5794	186	6	µ(n+6))∆ξ(µ(n+5	µ(n+6))∆ξ(µ(n+5	NOUN
ejpam-5794	186	7	)	)	PUNCT
ejpam-5794	186	8	,	,	PUNCT
ejpam-5794	186	9	µ(n+6	µ(n+6	NUM
ejpam-5794	186	10	)	)	PUNCT
ejpam-5794	186	11	)	)	PUNCT
ejpam-5794	187	1	+	+	CCONJ
ejpam-5794	187	2	ξ	ξ	SYM
ejpam-5794	187	3	3	3	NUM
ejpam-5794	187	4	α(µ(n+6	α(µ(n+6	NOUN
ejpam-5794	187	5	)	)	PUNCT
ejpam-5794	187	6	,	,	PUNCT
ejpam-5794	187	7	µ(n+2r+1))∆ξ(µ(n+6	µ(n+2r+1))∆ξ(µ(n+6	NOUN
ejpam-5794	187	8	)	)	PUNCT
ejpam-5794	187	9	,	,	PUNCT
ejpam-5794	187	10	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	187	11	)	)	PUNCT
ejpam-5794	187	12	)	)	PUNCT
ejpam-5794	187	13	]	]	PUNCT
ejpam-5794	187	14	,	,	PUNCT
ejpam-5794	187	15	≤	≤	NUM
ejpam-5794	187	16	ξ	ξ	SYM
ejpam-5794	187	17	3	3	NUM
ejpam-5794	187	18	[	[	X
ejpam-5794	187	19	λnα(µn	λnα(µn	X
ejpam-5794	187	20	,	,	PUNCT
ejpam-5794	187	21	µ(n+1	µ(n+1	NUM
ejpam-5794	187	22	)	)	PUNCT
ejpam-5794	187	23	)	)	PUNCT
ejpam-5794	188	1	+	+	CCONJ
ejpam-5794	188	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	188	3	)	)	PUNCT
ejpam-5794	188	4	,	,	PUNCT
ejpam-5794	188	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	188	6	,	,	PUNCT
ejpam-5794	188	7	µ1	µ1	PROPN
ejpam-5794	188	8	)	)	PUNCT
ejpam-5794	189	1	+	+	NOUN
ejpam-5794	190	1	ξ2	ξ2	NOUN
ejpam-5794	190	2	32	32	NUM
ejpam-5794	190	3	[	[	SYM
ejpam-5794	190	4	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	190	5	)	)	PUNCT
ejpam-5794	190	6	,	,	PUNCT
ejpam-5794	190	7	µ(n+2r+1))α(µ(n+2	µ(n+2r+1))α(µ(n+2	VERB
ejpam-5794	190	8	)	)	PUNCT
ejpam-5794	190	9	,	,	PUNCT
ejpam-5794	190	10	µ(n+3))λ	µ(n+3))λ	PROPN
ejpam-5794	190	11	(	(	PUNCT
ejpam-5794	190	12	n+2	n+2	NOUN
ejpam-5794	190	13	)	)	PUNCT
ejpam-5794	190	14	+	+	NOUN
ejpam-5794	190	15	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	190	16	)	)	PUNCT
ejpam-5794	190	17	,	,	PUNCT
ejpam-5794	190	18	µ(n+2r+1))α(µ(n+3	µ(n+2r+1))α(µ(n+3	PROPN
ejpam-5794	190	19	)	)	PUNCT
ejpam-5794	190	20	,	,	PUNCT
ejpam-5794	190	21	µ(n+4))λ	µ(n+4))λ	X
ejpam-5794	190	22	(	(	PUNCT
ejpam-5794	190	23	n+3)]∆ξ(µ0	n+3)]∆ξ(µ0	NUM
ejpam-5794	190	24	,	,	PUNCT
ejpam-5794	190	25	µ1	µ1	PROPN
ejpam-5794	190	26	)	)	PUNCT
ejpam-5794	190	27	+	+	CCONJ
ejpam-5794	190	28	ξ2	ξ2	ADJ
ejpam-5794	190	29	32	32	NUM
ejpam-5794	190	30	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	190	31	)	)	PUNCT
ejpam-5794	190	32	,	,	PUNCT
ejpam-5794	190	33	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	190	34	)	)	PUNCT
ejpam-5794	190	35	,	,	PUNCT
ejpam-5794	190	36	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	190	37	)	)	PUNCT
ejpam-5794	190	38	)	)	PUNCT
ejpam-5794	191	1	[	[	PUNCT
ejpam-5794	191	2	ξ	ξ	SYM
ejpam-5794	191	3	3	3	NUM
ejpam-5794	191	4	λ(n+4)α(µ(n+4	λ(n+4)α(µ(n+4	NOUN
ejpam-5794	191	5	)	)	PUNCT
ejpam-5794	191	6	,	,	PUNCT
ejpam-5794	191	7	µ(n+5	µ(n+5	NUM
ejpam-5794	191	8	)	)	PUNCT
ejpam-5794	191	9	)	)	PUNCT
ejpam-5794	192	1	+	+	CCONJ
ejpam-5794	193	1	ξ	ξ	SYM
ejpam-5794	193	2	3	3	NUM
ejpam-5794	193	3	λ	λ	X
ejpam-5794	193	4	(	(	PUNCT
ejpam-5794	193	5	n+5	n+5	NOUN
ejpam-5794	193	6	)	)	PUNCT
ejpam-5794	193	7	α(µ(n+5	α(µ(n+5	NOUN
ejpam-5794	193	8	)	)	PUNCT
ejpam-5794	193	9	,	,	PUNCT
ejpam-5794	193	10	µ(n+6))]∆ξ(µ	µ(n+6))]∆ξ(µ	ADP
ejpam-5794	193	11	o	o	NOUN
ejpam-5794	193	12	,	,	PUNCT
ejpam-5794	193	13	µ1	µ1	PROPN
ejpam-5794	193	14	)	)	PUNCT
ejpam-5794	193	15	+	+	NUM
ejpam-5794	193	16	ξ	ξ	SYM
ejpam-5794	193	17	3	3	NUM
ejpam-5794	193	18	α(µ(n+6	α(µ(n+6	NOUN
ejpam-5794	193	19	)	)	PUNCT
ejpam-5794	193	20	,	,	PUNCT
ejpam-5794	193	21	µ(n+2r+1))∆ξ(µ(n+6	µ(n+2r+1))∆ξ(µ(n+6	NOUN
ejpam-5794	193	22	)	)	PUNCT
ejpam-5794	193	23	,	,	PUNCT
ejpam-5794	193	24	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	193	25	)	)	PUNCT
ejpam-5794	193	26	)	)	PUNCT
ejpam-5794	193	27	,	,	PUNCT
ejpam-5794	193	28	≤	≤	NUM
ejpam-5794	193	29	ξ	ξ	SYM
ejpam-5794	193	30	3	3	NUM
ejpam-5794	193	31	[	[	X
ejpam-5794	193	32	λnα(µn	λnα(µn	X
ejpam-5794	193	33	,	,	PUNCT
ejpam-5794	193	34	µ(n+1	µ(n+1	NUM
ejpam-5794	193	35	)	)	PUNCT
ejpam-5794	193	36	)	)	PUNCT
ejpam-5794	193	37	+	+	CCONJ
ejpam-5794	193	38	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	193	39	)	)	PUNCT
ejpam-5794	193	40	,	,	PUNCT
ejpam-5794	193	41	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	193	42	,	,	PUNCT
ejpam-5794	193	43	µ1	µ1	PROPN
ejpam-5794	193	44	)	)	PUNCT
ejpam-5794	193	45	+	+	NOUN
ejpam-5794	194	1	ξ2	ξ2	NOUN
ejpam-5794	194	2	32	32	NUM
ejpam-5794	195	1	[	[	X
ejpam-5794	195	2	λ(n+2)α(µ(n+2	λ(n+2)α(µ(n+2	NOUN
ejpam-5794	195	3	)	)	PUNCT
ejpam-5794	195	4	,	,	PUNCT
ejpam-5794	195	5	µ(n+2r+1))α(µ(n+2	µ(n+2r+1))α(µ(n+2	VERB
ejpam-5794	195	6	)	)	PUNCT
ejpam-5794	195	7	,	,	PUNCT
ejpam-5794	195	8	µ(n+3	µ(n+3	NUM
ejpam-5794	195	9	)	)	PUNCT
ejpam-5794	195	10	)	)	PUNCT
ejpam-5794	196	1	+	+	ADV
ejpam-5794	196	2	λ(n+3)α(µ(n+2	λ(n+3)α(µ(n+2	NOUN
ejpam-5794	196	3	)	)	PUNCT
ejpam-5794	196	4	,	,	PUNCT
ejpam-5794	196	5	µ(n+2r+1))α(µ(n+3	µ(n+2r+1))α(µ(n+3	PROPN
ejpam-5794	196	6	)	)	PUNCT
ejpam-5794	196	7	,	,	PUNCT
ejpam-5794	196	8	µ(n+4))]∆ξ(µ0	µ(n+4))]∆ξ(µ0	NOUN
ejpam-5794	196	9	,	,	PUNCT
ejpam-5794	196	10	µ1	µ1	PROPN
ejpam-5794	196	11	)	)	PUNCT
ejpam-5794	196	12	+	+	NOUN
ejpam-5794	196	13	ξ3	ξ3	NOUN
ejpam-5794	196	14	33	33	NUM
ejpam-5794	196	15	[	[	X
ejpam-5794	196	16	λ(n+4)α(µ(n+2	λ(n+4)α(µ(n+2	NOUN
ejpam-5794	196	17	)	)	PUNCT
ejpam-5794	196	18	,	,	PUNCT
ejpam-5794	196	19	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	196	20	)	)	PUNCT
ejpam-5794	196	21	,	,	PUNCT
ejpam-5794	196	22	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	196	23	)	)	PUNCT
ejpam-5794	196	24	,	,	PUNCT
ejpam-5794	196	25	µ(n+5	µ(n+5	NUM
ejpam-5794	196	26	)	)	PUNCT
ejpam-5794	196	27	)	)	PUNCT
ejpam-5794	197	1	+	+	VERB
ejpam-5794	197	2	λ(n+5)α(µ(n+2	λ(n+5)α(µ(n+2	ADJ
ejpam-5794	197	3	)	)	PUNCT
ejpam-5794	197	4	,	,	PUNCT
ejpam-5794	197	5	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	X
ejpam-5794	197	6	)	)	PUNCT
ejpam-5794	197	7	,	,	PUNCT
ejpam-5794	197	8	µ(n+2r+1))α(µ(n+5	µ(n+2r+1))α(µ(n+5	PROPN
ejpam-5794	197	9	)	)	PUNCT
ejpam-5794	197	10	,	,	PUNCT
ejpam-5794	197	11	µ(n+6	µ(n+6	NUM
ejpam-5794	197	12	)	)	PUNCT
ejpam-5794	197	13	)	)	PUNCT
ejpam-5794	197	14	]	]	PUNCT
ejpam-5794	198	1	∆ξ(µ0	∆ξ(µ0	NOUN
ejpam-5794	198	2	,	,	PUNCT
ejpam-5794	198	3	µ1	µ1	PROPN
ejpam-5794	198	4	)	)	PUNCT
ejpam-5794	198	5	...	...	PUNCT
ejpam-5794	199	1	+	+	CCONJ
ejpam-5794	199	2	ξm	ξm	PROPN
ejpam-5794	199	3	3	3	NUM
ejpam-5794	199	4	m	m	NOUN
ejpam-5794	199	5	[	[	X
ejpam-5794	199	6	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	199	7	)	)	PUNCT
ejpam-5794	199	8	,	,	PUNCT
ejpam-5794	199	9	µ(n+2r+1))α(µ(n+4	µ(n+2r+1))α(µ(n+4	PROPN
ejpam-5794	199	10	)	)	PUNCT
ejpam-5794	199	11	,	,	PUNCT
ejpam-5794	199	12	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	199	13	)	)	PUNCT
ejpam-5794	199	14	)	)	PUNCT
ejpam-5794	199	15	.	.	PUNCT
ejpam-5794	199	16	.	.	PUNCT
ejpam-5794	199	17	.	.	PUNCT
ejpam-5794	200	1	α(µ(n+2r−2	α(µ(n+2r−2	NOUN
ejpam-5794	200	2	)	)	PUNCT
ejpam-5794	200	3	,	,	PUNCT
ejpam-5794	200	4	µ(n+2r−1))λ	µ(n+2r−1))λ	PROPN
ejpam-5794	200	5	(	(	PUNCT
ejpam-5794	200	6	n+2r−2	n+2r−2	NOUN
ejpam-5794	200	7	)	)	PUNCT
ejpam-5794	200	8	+	+	NOUN
ejpam-5794	200	9	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	200	10	)	)	PUNCT
ejpam-5794	200	11	,	,	PUNCT
ejpam-5794	200	12	µ(n+2r−1	µ(n+2r−1	PROPN
ejpam-5794	200	13	)	)	PUNCT
ejpam-5794	200	14	)	)	PUNCT
ejpam-5794	200	15	·	·	PUNCT
ejpam-5794	200	16	·	·	PUNCT
ejpam-5794	201	1	·	·	PUNCT
ejpam-5794	201	2	α(µ(n+2r−1	α(µ(n+2r−1	NOUN
ejpam-5794	201	3	)	)	PUNCT
ejpam-5794	201	4	,	,	PUNCT
ejpam-5794	201	5	µ(n+2r))λ	µ(n+2r))λ	PROPN
ejpam-5794	201	6	(	(	PUNCT
ejpam-5794	201	7	n+2r−1	n+2r−1	PROPN
ejpam-5794	201	8	)	)	PUNCT
ejpam-5794	201	9	+	+	NOUN
ejpam-5794	201	10	α(µ(n+2	α(µ(n+2	NUM
ejpam-5794	201	11	)	)	PUNCT
ejpam-5794	201	12	,	,	PUNCT
ejpam-5794	201	13	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	201	14	)	)	PUNCT
ejpam-5794	201	15	)	)	PUNCT
ejpam-5794	201	16	.	.	PUNCT
ejpam-5794	201	17	.	.	PUNCT
ejpam-5794	201	18	.	.	PUNCT
ejpam-5794	202	1	α(µ(n+2r	α(µ(n+2r	NUM
ejpam-5794	202	2	)	)	PUNCT
ejpam-5794	202	3	,	,	PUNCT
ejpam-5794	202	4	µ(n+2r+1))λ	µ(n+2r+1))λ	PROPN
ejpam-5794	202	5	(	(	PUNCT
ejpam-5794	202	6	n+2r)]∆ξ(µ0	n+2r)]∆ξ(µ0	PROPN
ejpam-5794	202	7	,	,	PUNCT
ejpam-5794	202	8	µ1	µ1	PROPN
ejpam-5794	202	9	)	)	PUNCT
ejpam-5794	202	10	.	.	PUNCT
ejpam-5794	203	1	from	from	ADP
ejpam-5794	203	2	the	the	DET
ejpam-5794	203	3	above	above	ADJ
ejpam-5794	203	4	inequality	inequality	NOUN
ejpam-5794	203	5	,	,	PUNCT
ejpam-5794	203	6	we	we	PRON
ejpam-5794	203	7	get	get	VERB
ejpam-5794	203	8	lim	lim	PROPN
ejpam-5794	203	9	n→+∞	n→+∞	PROPN
ejpam-5794	203	10	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	203	11	,	,	PUNCT
ejpam-5794	203	12	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	203	13	)	)	PUNCT
ejpam-5794	203	14	)	)	PUNCT
ejpam-5794	204	1	=	=	PUNCT
ejpam-5794	204	2	0	0	X
ejpam-5794	204	3	.	.	PUNCT
ejpam-5794	205	1	u.	u.	PROPN
ejpam-5794	205	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	205	3	et	et	PROPN
ejpam-5794	205	4	al	al	PROPN
ejpam-5794	205	5	.	.	PUNCT
ejpam-5794	205	6	/	/	SYM
ejpam-5794	205	7	eur	eur	PROPN
ejpam-5794	205	8	.	.	PUNCT
ejpam-5794	206	1	j.	j.	PROPN
ejpam-5794	206	2	pure	pure	PROPN
ejpam-5794	206	3	appl	appl	PROPN
ejpam-5794	206	4	.	.	PROPN
ejpam-5794	206	5	math	math	PROPN
ejpam-5794	206	6	,	,	PUNCT
ejpam-5794	206	7	18	18	NUM
ejpam-5794	206	8	(	(	PUNCT
ejpam-5794	206	9	1	1	NUM
ejpam-5794	206	10	)	)	PUNCT
ejpam-5794	206	11	(	(	PUNCT
ejpam-5794	206	12	2025	2025	NUM
ejpam-5794	206	13	)	)	PUNCT
ejpam-5794	206	14	,	,	PUNCT
ejpam-5794	206	15	5794	5794	NUM
ejpam-5794	206	16	10	10	NUM
ejpam-5794	206	17	of	of	ADP
ejpam-5794	206	18	20	20	NUM
ejpam-5794	206	19	case	case	NOUN
ejpam-5794	206	20	:	:	PUNCT
ejpam-5794	206	21	2	2	NUM
ejpam-5794	206	22	let	let	VERB
ejpam-5794	206	23	p	p	PRON
ejpam-5794	206	24	be	be	AUX
ejpam-5794	206	25	an	an	DET
ejpam-5794	206	26	even	even	ADJ
ejpam-5794	206	27	number	number	NOUN
ejpam-5794	206	28	then	then	ADV
ejpam-5794	206	29	p	p	NOUN
ejpam-5794	206	30	=	=	PROPN
ejpam-5794	206	31	2n	2n	NUM
ejpam-5794	206	32	and	and	CCONJ
ejpam-5794	206	33	r	r	NOUN
ejpam-5794	206	34	≥	≥	NUM
ejpam-5794	206	35	1	1	NUM
ejpam-5794	206	36	,	,	PUNCT
ejpam-5794	206	37	then	then	ADV
ejpam-5794	206	38	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	206	39	,	,	PUNCT
ejpam-5794	206	40	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	206	41	)	)	PUNCT
ejpam-5794	206	42	)	)	PUNCT
ejpam-5794	207	1	≤	≤	NUM
ejpam-5794	207	2	ξ	ξ	X
ejpam-5794	207	3	3	3	NUM
ejpam-5794	207	4	[	[	X
ejpam-5794	207	5	α(µn	α(µn	NUM
ejpam-5794	207	6	,	,	PUNCT
ejpam-5794	207	7	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	207	8	,	,	PUNCT
ejpam-5794	207	9	µ(n+1	µ(n+1	NUM
ejpam-5794	207	10	)	)	PUNCT
ejpam-5794	207	11	)	)	PUNCT
ejpam-5794	208	1	+	+	CCONJ
ejpam-5794	209	1	ξ	ξ	SYM
ejpam-5794	209	2	3	3	NUM
ejpam-5794	209	3	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	209	4	)	)	PUNCT
ejpam-5794	209	5	,	,	PUNCT
ejpam-5794	209	6	µ(n+2))∆ξ(µ(n+1	µ(n+2))∆ξ(µ(n+1	PROPN
ejpam-5794	209	7	)	)	PUNCT
ejpam-5794	209	8	,	,	PUNCT
ejpam-5794	209	9	µ(n+2	µ(n+2	PUNCT
ejpam-5794	209	10	)	)	PUNCT
ejpam-5794	209	11	)	)	PUNCT
ejpam-5794	210	1	+	+	CCONJ
ejpam-5794	211	1	ξ	ξ	SYM
ejpam-5794	211	2	3	3	NUM
ejpam-5794	211	3	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	211	4	)	)	PUNCT
ejpam-5794	211	5	,	,	PUNCT
ejpam-5794	211	6	µ(n+2r))∆ξ(µ(n+2	µ(n+2r))∆ξ(µ(n+2	PROPN
ejpam-5794	211	7	)	)	PUNCT
ejpam-5794	211	8	,	,	PUNCT
ejpam-5794	211	9	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	211	10	)	)	PUNCT
ejpam-5794	211	11	)	)	PUNCT
ejpam-5794	211	12	]	]	PUNCT
ejpam-5794	211	13	=	=	PUNCT
ejpam-5794	211	14	ξ	ξ	SYM
ejpam-5794	211	15	3	3	NUM
ejpam-5794	211	16	[	[	X
ejpam-5794	211	17	λnα(µn	λnα(µn	X
ejpam-5794	211	18	,	,	PUNCT
ejpam-5794	211	19	µ(n+1	µ(n+1	NUM
ejpam-5794	211	20	)	)	PUNCT
ejpam-5794	211	21	)	)	PUNCT
ejpam-5794	212	1	+	+	CCONJ
ejpam-5794	212	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	212	3	)	)	PUNCT
ejpam-5794	212	4	,	,	PUNCT
ejpam-5794	212	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	212	6	,	,	PUNCT
ejpam-5794	212	7	µ1	µ1	PROPN
ejpam-5794	212	8	)	)	PUNCT
ejpam-5794	212	9	+	+	NUM
ejpam-5794	212	10	ξ	ξ	SYM
ejpam-5794	212	11	3	3	NUM
ejpam-5794	212	12	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	212	13	)	)	PUNCT
ejpam-5794	212	14	,	,	PUNCT
ejpam-5794	212	15	µ(n+2r))∆ξ(µ(n+2	µ(n+2r))∆ξ(µ(n+2	PROPN
ejpam-5794	212	16	)	)	PUNCT
ejpam-5794	212	17	,	,	PUNCT
ejpam-5794	212	18	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	212	19	)	)	PUNCT
ejpam-5794	212	20	)	)	PUNCT
ejpam-5794	212	21	,	,	PUNCT
ejpam-5794	212	22	≤	≤	NUM
ejpam-5794	212	23	ξ	ξ	SYM
ejpam-5794	212	24	3	3	NUM
ejpam-5794	212	25	[	[	X
ejpam-5794	212	26	λnα(µn	λnα(µn	X
ejpam-5794	212	27	,	,	PUNCT
ejpam-5794	212	28	µ(n+1	µ(n+1	NUM
ejpam-5794	212	29	)	)	PUNCT
ejpam-5794	212	30	)	)	PUNCT
ejpam-5794	213	1	+	+	CCONJ
ejpam-5794	213	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	213	3	)	)	PUNCT
ejpam-5794	213	4	,	,	PUNCT
ejpam-5794	213	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	213	6	,	,	PUNCT
ejpam-5794	213	7	µ1	µ1	PROPN
ejpam-5794	213	8	)	)	PUNCT
ejpam-5794	213	9	+	+	NUM
ejpam-5794	213	10	ξ	ξ	SYM
ejpam-5794	213	11	3	3	NUM
ejpam-5794	213	12	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	213	13	)	)	PUNCT
ejpam-5794	213	14	,	,	PUNCT
ejpam-5794	213	15	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	213	16	)	)	PUNCT
ejpam-5794	213	17	)	)	PUNCT
ejpam-5794	214	1	[	[	PUNCT
ejpam-5794	214	2	ξ	ξ	X
ejpam-5794	214	3	3	3	NUM
ejpam-5794	214	4	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	214	5	)	)	PUNCT
ejpam-5794	214	6	,	,	PUNCT
ejpam-5794	214	7	µ(n+3))∆ξ(µ(n+2	µ(n+3))∆ξ(µ(n+2	NUM
ejpam-5794	214	8	)	)	PUNCT
ejpam-5794	214	9	,	,	PUNCT
ejpam-5794	214	10	µ(n+3	µ(n+3	PROPN
ejpam-5794	214	11	)	)	PUNCT
ejpam-5794	214	12	)	)	PUNCT
ejpam-5794	215	1	+	+	CCONJ
ejpam-5794	215	2	ξ	ξ	SYM
ejpam-5794	215	3	3	3	NUM
ejpam-5794	215	4	α(µ(n+3	α(µ(n+3	NOUN
ejpam-5794	215	5	)	)	PUNCT
ejpam-5794	215	6	,	,	PUNCT
ejpam-5794	215	7	µ(n+4))∆ξ(µ(n+3	µ(n+4))∆ξ(µ(n+3	NOUN
ejpam-5794	215	8	)	)	PUNCT
ejpam-5794	215	9	,	,	PUNCT
ejpam-5794	215	10	µ(n+4	µ(n+4	NUM
ejpam-5794	215	11	)	)	PUNCT
ejpam-5794	215	12	)	)	PUNCT
ejpam-5794	216	1	+	+	CCONJ
ejpam-5794	217	1	ξ	ξ	SYM
ejpam-5794	217	2	3	3	NUM
ejpam-5794	217	3	α(µ(n+4	α(µ(n+4	NOUN
ejpam-5794	217	4	)	)	PUNCT
ejpam-5794	217	5	,	,	PUNCT
ejpam-5794	217	6	µ(n+2r))∆ξ(µ(n+4	µ(n+2r))∆ξ(µ(n+4	NOUN
ejpam-5794	217	7	)	)	PUNCT
ejpam-5794	217	8	,	,	PUNCT
ejpam-5794	217	9	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	217	10	)	)	PUNCT
ejpam-5794	217	11	)	)	PUNCT
ejpam-5794	218	1	]	]	PUNCT
ejpam-5794	218	2	,	,	PUNCT
ejpam-5794	218	3	≤	≤	NUM
ejpam-5794	218	4	ξ	ξ	SYM
ejpam-5794	218	5	3	3	NUM
ejpam-5794	218	6	[	[	X
ejpam-5794	218	7	λnα(µn	λnα(µn	X
ejpam-5794	218	8	,	,	PUNCT
ejpam-5794	218	9	µ(n+1	µ(n+1	NUM
ejpam-5794	218	10	)	)	PUNCT
ejpam-5794	218	11	)	)	PUNCT
ejpam-5794	219	1	+	+	CCONJ
ejpam-5794	219	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	219	3	)	)	PUNCT
ejpam-5794	219	4	,	,	PUNCT
ejpam-5794	219	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	219	6	,	,	PUNCT
ejpam-5794	219	7	µ1	µ1	PROPN
ejpam-5794	219	8	)	)	PUNCT
ejpam-5794	219	9	+	+	NOUN
ejpam-5794	220	1	ξ2	ξ2	NOUN
ejpam-5794	220	2	32	32	NUM
ejpam-5794	221	1	[	[	X
ejpam-5794	221	2	λ(n+2)α(µ(n+2	λ(n+2)α(µ(n+2	NOUN
ejpam-5794	221	3	)	)	PUNCT
ejpam-5794	221	4	,	,	PUNCT
ejpam-5794	221	5	µ(n+2r))α(µ(n+2	µ(n+2r))α(µ(n+2	NOUN
ejpam-5794	221	6	)	)	PUNCT
ejpam-5794	221	7	,	,	PUNCT
ejpam-5794	221	8	µ(n+3	µ(n+3	NUM
ejpam-5794	221	9	)	)	PUNCT
ejpam-5794	221	10	)	)	PUNCT
ejpam-5794	222	1	+	+	ADV
ejpam-5794	222	2	λ(n+3)α(µ(n+2	λ(n+3)α(µ(n+2	NOUN
ejpam-5794	222	3	)	)	PUNCT
ejpam-5794	222	4	,	,	PUNCT
ejpam-5794	222	5	µ(n+2r))α(µ(n+3	µ(n+2r))α(µ(n+3	NOUN
ejpam-5794	222	6	)	)	PUNCT
ejpam-5794	222	7	,	,	PUNCT
ejpam-5794	222	8	µ(n+4))]∆ξ(µ0	µ(n+4))]∆ξ(µ0	X
ejpam-5794	222	9	,	,	PUNCT
ejpam-5794	222	10	µ1	µ1	PROPN
ejpam-5794	222	11	)	)	PUNCT
ejpam-5794	222	12	+	+	CCONJ
ejpam-5794	222	13	ξ2	ξ2	ADJ
ejpam-5794	222	14	32	32	NUM
ejpam-5794	222	15	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	222	16	)	)	PUNCT
ejpam-5794	222	17	,	,	PUNCT
ejpam-5794	222	18	µ(n+2r))α(µ(n+4	µ(n+2r))α(µ(n+4	NOUN
ejpam-5794	222	19	)	)	PUNCT
ejpam-5794	222	20	,	,	PUNCT
ejpam-5794	222	21	µ(n+2r))∆ξ(µ(n+4	µ(n+2r))∆ξ(µ(n+4	NOUN
ejpam-5794	222	22	)	)	PUNCT
ejpam-5794	222	23	,	,	PUNCT
ejpam-5794	222	24	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	222	25	)	)	PUNCT
ejpam-5794	222	26	)	)	PUNCT
ejpam-5794	222	27	,	,	PUNCT
ejpam-5794	222	28	≤	≤	NUM
ejpam-5794	222	29	ξ	ξ	SYM
ejpam-5794	222	30	3	3	NUM
ejpam-5794	222	31	[	[	X
ejpam-5794	222	32	λnα(µn	λnα(µn	X
ejpam-5794	222	33	,	,	PUNCT
ejpam-5794	222	34	µ(n+1	µ(n+1	NUM
ejpam-5794	222	35	)	)	PUNCT
ejpam-5794	222	36	)	)	PUNCT
ejpam-5794	223	1	+	+	CCONJ
ejpam-5794	223	2	λ(n+1)α(µ(n+1	λ(n+1)α(µ(n+1	ADJ
ejpam-5794	223	3	)	)	PUNCT
ejpam-5794	223	4	,	,	PUNCT
ejpam-5794	223	5	µ(n+2))]∆ξ(µ0	µ(n+2))]∆ξ(µ0	NOUN
ejpam-5794	223	6	,	,	PUNCT
ejpam-5794	223	7	µ1	µ1	PROPN
ejpam-5794	223	8	)	)	PUNCT
ejpam-5794	223	9	+	+	NOUN
ejpam-5794	224	1	ξ2	ξ2	NOUN
ejpam-5794	224	2	32	32	NUM
ejpam-5794	225	1	[	[	X
ejpam-5794	225	2	λ(n+2)α(µ(n+2	λ(n+2)α(µ(n+2	NOUN
ejpam-5794	225	3	)	)	PUNCT
ejpam-5794	225	4	,	,	PUNCT
ejpam-5794	225	5	µ(n+2r))α(µ(n+2	µ(n+2r))α(µ(n+2	NOUN
ejpam-5794	225	6	)	)	PUNCT
ejpam-5794	225	7	,	,	PUNCT
ejpam-5794	225	8	µ(n+3	µ(n+3	NUM
ejpam-5794	225	9	)	)	PUNCT
ejpam-5794	225	10	)	)	PUNCT
ejpam-5794	226	1	+	+	ADV
ejpam-5794	226	2	λ(n+3)α(µ(n+2	λ(n+3)α(µ(n+2	NOUN
ejpam-5794	226	3	)	)	PUNCT
ejpam-5794	226	4	,	,	PUNCT
ejpam-5794	226	5	µ(n+2r))α(µ(n+3	µ(n+2r))α(µ(n+3	NOUN
ejpam-5794	226	6	)	)	PUNCT
ejpam-5794	226	7	,	,	PUNCT
ejpam-5794	226	8	µ(n+4))]∆ξ(µ0	µ(n+4))]∆ξ(µ0	X
ejpam-5794	226	9	,	,	PUNCT
ejpam-5794	226	10	µ1	µ1	PROPN
ejpam-5794	226	11	)	)	PUNCT
ejpam-5794	226	12	...	...	PUNCT
ejpam-5794	227	1	+	+	CCONJ
ejpam-5794	227	2	ξ(m−1	ξ(m−1	NOUN
ejpam-5794	227	3	)	)	PUNCT
ejpam-5794	227	4	3(m−1	3(m−1	NUM
ejpam-5794	227	5	)	)	PUNCT
ejpam-5794	228	1	[	[	X
ejpam-5794	228	2	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	228	3	)	)	PUNCT
ejpam-5794	228	4	,	,	PUNCT
ejpam-5794	228	5	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	228	6	)	)	PUNCT
ejpam-5794	228	7	)	)	PUNCT
ejpam-5794	228	8	·	·	PUNCT
ejpam-5794	228	9	·	·	PUNCT
ejpam-5794	228	10	·	·	PUNCT
ejpam-5794	228	11	α(µ(n+2−4	α(µ(n+2−4	NUM
ejpam-5794	228	12	)	)	PUNCT
ejpam-5794	228	13	,	,	PUNCT
ejpam-5794	228	14	µ(n+2r−3))λ	µ(n+2r−3))λ	PROPN
ejpam-5794	228	15	(	(	PUNCT
ejpam-5794	228	16	n+2r−4	n+2r−4	NOUN
ejpam-5794	228	17	)	)	PUNCT
ejpam-5794	228	18	+	+	NOUN
ejpam-5794	228	19	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	228	20	)	)	PUNCT
ejpam-5794	228	21	,	,	PUNCT
ejpam-5794	228	22	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	228	23	)	)	PUNCT
ejpam-5794	228	24	)	)	PUNCT
ejpam-5794	228	25	·	·	PUNCT
ejpam-5794	228	26	·	·	PUNCT
ejpam-5794	228	27	·	·	PUNCT
ejpam-5794	228	28	α(µ(n+2−3	α(µ(n+2−3	NUM
ejpam-5794	228	29	)	)	PUNCT
ejpam-5794	228	30	,	,	PUNCT
ejpam-5794	228	31	µ(n+2r−2))λ	µ(n+2r−2))λ	X
ejpam-5794	228	32	(	(	PUNCT
ejpam-5794	228	33	n+2r−3	n+2r−3	NOUN
ejpam-5794	228	34	)	)	PUNCT
ejpam-5794	228	35	+	+	NOUN
ejpam-5794	228	36	α(µ(n+2	α(µ(n+2	NOUN
ejpam-5794	228	37	)	)	PUNCT
ejpam-5794	228	38	,	,	PUNCT
ejpam-5794	228	39	µ(n+2r	µ(n+2r	NOUN
ejpam-5794	228	40	)	)	PUNCT
ejpam-5794	228	41	)	)	PUNCT
ejpam-5794	228	42	·	·	PUNCT
ejpam-5794	229	1	·	·	PUNCT
ejpam-5794	229	2	·	·	PUNCT
ejpam-5794	229	3	α(µ(n+2r−2	α(µ(n+2r−2	NOUN
ejpam-5794	229	4	)	)	PUNCT
ejpam-5794	229	5	,	,	PUNCT
ejpam-5794	229	6	µ(n+2r))λ	µ(n+2r))λ	PROPN
ejpam-5794	229	7	(	(	PUNCT
ejpam-5794	229	8	n+2r−2)]∆ξ(µ0	n+2r−2)]∆ξ(µ0	NOUN
ejpam-5794	229	9	,	,	PUNCT
ejpam-5794	229	10	µ1	µ1	PROPN
ejpam-5794	229	11	)	)	PUNCT
ejpam-5794	229	12	.	.	PUNCT
ejpam-5794	230	1	from	from	ADP
ejpam-5794	230	2	the	the	DET
ejpam-5794	230	3	above	above	ADJ
ejpam-5794	230	4	inequality	inequality	NOUN
ejpam-5794	230	5	,	,	PUNCT
ejpam-5794	230	6	we	we	PRON
ejpam-5794	230	7	get	get	VERB
ejpam-5794	230	8	lim	lim	PROPN
ejpam-5794	230	9	n→+∞	n→+∞	PROPN
ejpam-5794	230	10	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	230	11	,	,	PUNCT
ejpam-5794	230	12	µ(n+2r+1	µ(n+2r+1	PROPN
ejpam-5794	230	13	)	)	PUNCT
ejpam-5794	230	14	)	)	PUNCT
ejpam-5794	231	1	=	=	PUNCT
ejpam-5794	231	2	0	0	X
ejpam-5794	231	3	.	.	PUNCT
ejpam-5794	232	1	hence	hence	ADV
ejpam-5794	232	2	,	,	PUNCT
ejpam-5794	232	3	both	both	DET
ejpam-5794	232	4	cases	case	NOUN
ejpam-5794	232	5	show	show	VERB
ejpam-5794	232	6	that	that	SCONJ
ejpam-5794	232	7	{	{	PUNCT
ejpam-5794	232	8	µn	µn	NOUN
ejpam-5794	232	9	}	}	PUNCT
ejpam-5794	232	10	is	be	AUX
ejpam-5794	232	11	a	a	DET
ejpam-5794	232	12	cauchy	cauchy	ADJ
ejpam-5794	232	13	sequence	sequence	NOUN
ejpam-5794	232	14	.	.	PUNCT
ejpam-5794	233	1	as	as	SCONJ
ejpam-5794	233	2	ℵ	ℵ	NOUN
ejpam-5794	233	3	is	be	AUX
ejpam-5794	233	4	g−orbitally	g−orbitally	ADV
ejpam-5794	233	5	complete	complete	ADJ
ejpam-5794	233	6	,	,	PUNCT
ejpam-5794	233	7	so	so	SCONJ
ejpam-5794	233	8	there	there	PRON
ejpam-5794	233	9	exist	exist	VERB
ejpam-5794	233	10	µ	µ	PRON
ejpam-5794	233	11	∈	∈	NOUN
ejpam-5794	233	12	ℵ	ℵ	NOUN
ejpam-5794	233	13	such	such	ADJ
ejpam-5794	233	14	that	that	SCONJ
ejpam-5794	233	15	lim	lim	PROPN
ejpam-5794	233	16	n→+∞	n→+∞	VERB
ejpam-5794	233	17	µn	µn	PROPN
ejpam-5794	233	18	=	=	PUNCT
ejpam-5794	233	19	µ.	µ.	NOUN
ejpam-5794	233	20	now	now	ADV
ejpam-5794	233	21	we	we	PRON
ejpam-5794	233	22	show	show	VERB
ejpam-5794	233	23	that	that	SCONJ
ejpam-5794	233	24	µ	µ	NOUN
ejpam-5794	233	25	is	be	AUX
ejpam-5794	233	26	a	a	DET
ejpam-5794	233	27	fixed	fix	VERB
ejpam-5794	233	28	point	point	NOUN
ejpam-5794	233	29	of	of	ADP
ejpam-5794	233	30	g.	g.	PROPN
ejpam-5794	233	31	as	as	SCONJ
ejpam-5794	233	32	ℵ	ℵ	NOUN
ejpam-5794	233	33	is	be	AUX
ejpam-5794	233	34	g−orbitally	g−orbitally	ADV
ejpam-5794	233	35	continuous	continuous	ADJ
ejpam-5794	233	36	,	,	PUNCT
ejpam-5794	233	37	we	we	PRON
ejpam-5794	233	38	get	get	VERB
ejpam-5794	233	39	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	233	40	,	,	PUNCT
ejpam-5794	233	41	gµ	gµ	NOUN
ejpam-5794	233	42	)	)	PUNCT
ejpam-5794	233	43	≤	≤	NOUN
ejpam-5794	234	1	ξ	ξ	PRON
ejpam-5794	234	2	3	3	NUM
ejpam-5794	234	3	α(µ	α(µ	ADV
ejpam-5794	234	4	,	,	PUNCT
ejpam-5794	234	5	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	234	6	,	,	PUNCT
ejpam-5794	234	7	µn)+	µn)+	NOUN
ejpam-5794	234	8	ξ	ξ	PROPN
ejpam-5794	234	9	3	3	NUM
ejpam-5794	234	10	α(µ	α(µ	ADV
ejpam-5794	234	11	,	,	PUNCT
ejpam-5794	234	12	µ(n+1))∆ξ(µ	µ(n+1))∆ξ(µ	NOUN
ejpam-5794	234	13	,	,	PUNCT
ejpam-5794	234	14	µ(n+1))+	µ(n+1))+	VERB
ejpam-5794	234	15	ξ	ξ	SYM
ejpam-5794	234	16	3	3	NUM
ejpam-5794	234	17	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	234	18	)	)	PUNCT
ejpam-5794	234	19	,	,	PUNCT
ejpam-5794	234	20	gµ)∆ξ(µ(n+1	gµ)∆ξ(µ(n+1	PROPN
ejpam-5794	234	21	)	)	PUNCT
ejpam-5794	234	22	,	,	PUNCT
ejpam-5794	234	23	gµ	gµ	NOUN
ejpam-5794	234	24	)	)	PUNCT
ejpam-5794	234	25	.	.	PUNCT
ejpam-5794	235	1	u.	u.	PROPN
ejpam-5794	235	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	235	3	et	et	PROPN
ejpam-5794	235	4	al	al	PROPN
ejpam-5794	235	5	.	.	PUNCT
ejpam-5794	235	6	/	/	SYM
ejpam-5794	235	7	eur	eur	PROPN
ejpam-5794	235	8	.	.	PUNCT
ejpam-5794	236	1	j.	j.	PROPN
ejpam-5794	236	2	pure	pure	PROPN
ejpam-5794	236	3	appl	appl	PROPN
ejpam-5794	236	4	.	.	PROPN
ejpam-5794	236	5	math	math	PROPN
ejpam-5794	236	6	,	,	PUNCT
ejpam-5794	236	7	18	18	NUM
ejpam-5794	236	8	(	(	PUNCT
ejpam-5794	236	9	1	1	NUM
ejpam-5794	236	10	)	)	PUNCT
ejpam-5794	236	11	(	(	PUNCT
ejpam-5794	236	12	2025	2025	NUM
ejpam-5794	236	13	)	)	PUNCT
ejpam-5794	236	14	,	,	PUNCT
ejpam-5794	236	15	5794	5794	NUM
ejpam-5794	236	16	11	11	NUM
ejpam-5794	236	17	of	of	ADP
ejpam-5794	236	18	20	20	NUM
ejpam-5794	236	19	since	since	SCONJ
ejpam-5794	236	20	for	for	ADP
ejpam-5794	236	21	each	each	DET
ejpam-5794	236	22	µ	µ	PRON
ejpam-5794	236	23	∈	∈	NOUN
ejpam-5794	236	24	ℵ	ℵ	NOUN
ejpam-5794	236	25	,	,	PUNCT
ejpam-5794	237	1	lim	lim	PROPN
ejpam-5794	237	2	n→+∞	n→+∞	VERB
ejpam-5794	237	3	α(µn	α(µn	NUM
ejpam-5794	237	4	,	,	PUNCT
ejpam-5794	237	5	µ	µ	NOUN
ejpam-5794	237	6	)	)	PUNCT
ejpam-5794	237	7	and	and	CCONJ
ejpam-5794	237	8	lim	lim	PROPN
ejpam-5794	237	9	n→+∞	n→+∞	PROPN
ejpam-5794	237	10	α(µ	α(µ	ADV
ejpam-5794	237	11	,	,	PUNCT
ejpam-5794	237	12	µn	µn	NOUN
ejpam-5794	237	13	)	)	PUNCT
ejpam-5794	237	14	exist	exist	VERB
ejpam-5794	237	15	and	and	CCONJ
ejpam-5794	237	16	finite	finite	ADJ
ejpam-5794	237	17	,	,	PUNCT
ejpam-5794	237	18	so	so	ADV
ejpam-5794	237	19	by	by	ADP
ejpam-5794	237	20	taking	take	VERB
ejpam-5794	237	21	limit	limit	NOUN
ejpam-5794	237	22	and	and	CCONJ
ejpam-5794	237	23	utilizing	utilize	VERB
ejpam-5794	237	24	lim	lim	PROPN
ejpam-5794	237	25	n→+∞	n→+∞	PROPN
ejpam-5794	237	26	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	237	27	,	,	PUNCT
ejpam-5794	237	28	µ(n+1	µ(n+1	NUM
ejpam-5794	237	29	)	)	PUNCT
ejpam-5794	237	30	)	)	PUNCT
ejpam-5794	238	1	=	=	PUNCT
ejpam-5794	239	1	0	0	X
ejpam-5794	239	2	.	.	PUNCT
ejpam-5794	240	1	we	we	PRON
ejpam-5794	240	2	get	get	VERB
ejpam-5794	240	3	lim	lim	PROPN
ejpam-5794	240	4	n−→+∞	n−→+∞	PROPN
ejpam-5794	240	5	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	240	6	,	,	PUNCT
ejpam-5794	240	7	gµ	gµ	NOUN
ejpam-5794	240	8	)	)	PUNCT
ejpam-5794	240	9	=	=	SYM
ejpam-5794	241	1	0	0	X
ejpam-5794	241	2	.	.	PUNCT
ejpam-5794	242	1	that	that	PRON
ejpam-5794	242	2	is	be	AUX
ejpam-5794	242	3	,	,	PUNCT
ejpam-5794	242	4	gµ	gµ	NOUN
ejpam-5794	242	5	=	=	PUNCT
ejpam-5794	242	6	µ.	µ.	NOUN
ejpam-5794	242	7	hence	hence	ADV
ejpam-5794	242	8	µ	µ	X
ejpam-5794	242	9	is	be	AUX
ejpam-5794	242	10	a	a	DET
ejpam-5794	242	11	fixed	fix	VERB
ejpam-5794	242	12	point	point	NOUN
ejpam-5794	242	13	of	of	ADP
ejpam-5794	242	14	g.	g.	PROPN
ejpam-5794	242	15	in	in	ADP
ejpam-5794	242	16	view	view	NOUN
ejpam-5794	242	17	of	of	ADP
ejpam-5794	242	18	lemma	lemma	PROPN
ejpam-5794	242	19	(	(	PUNCT
ejpam-5794	242	20	2	2	NUM
ejpam-5794	242	21	)	)	PUNCT
ejpam-5794	242	22	,	,	PUNCT
ejpam-5794	242	23	µ	µ	X
ejpam-5794	242	24	is	be	AUX
ejpam-5794	242	25	unique	unique	ADJ
ejpam-5794	242	26	fixed	fix	VERB
ejpam-5794	242	27	point	point	NOUN
ejpam-5794	242	28	of	of	ADP
ejpam-5794	242	29	g.	g.	PROPN
ejpam-5794	242	30	corollary	corollary	NOUN
ejpam-5794	242	31	1	1	PROPN
ejpam-5794	242	32	.	.	PUNCT
ejpam-5794	243	1	suppose	suppose	VERB
ejpam-5794	243	2	g	g	NOUN
ejpam-5794	243	3	:	:	PUNCT
ejpam-5794	243	4	ℵ	ℵ	PROPN
ejpam-5794	243	5	→	→	SYM
ejpam-5794	243	6	ℵ	ℵ	ADJ
ejpam-5794	243	7	be	be	VERB
ejpam-5794	243	8	a	a	DET
ejpam-5794	243	9	mapping	mapping	NOUN
ejpam-5794	243	10	on	on	ADP
ejpam-5794	243	11	a	a	DET
ejpam-5794	243	12	complete	complete	ADJ
ejpam-5794	243	13	crmms	crmms	NOUN
ejpam-5794	243	14	(	(	PUNCT
ejpam-5794	243	15	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	243	16	)	)	PUNCT
ejpam-5794	243	17	.	.	PUNCT
ejpam-5794	244	1	assume	assume	VERB
ejpam-5794	244	2	that	that	SCONJ
ejpam-5794	244	3	the	the	DET
ejpam-5794	244	4	following	follow	VERB
ejpam-5794	244	5	conditions	condition	NOUN
ejpam-5794	244	6	hold	hold	VERB
ejpam-5794	244	7	:	:	PUNCT
ejpam-5794	244	8	a	a	X
ejpam-5794	244	9	)	)	PUNCT
ejpam-5794	244	10	for	for	ADP
ejpam-5794	244	11	all	all	DET
ejpam-5794	244	12	µ	µ	NOUN
ejpam-5794	244	13	,	,	PUNCT
ejpam-5794	244	14	κ	κ	PROPN
ejpam-5794	244	15	∈	∈	PROPN
ejpam-5794	244	16	ℵ	ℵ	NOUN
ejpam-5794	244	17	we	we	PRON
ejpam-5794	244	18	have	have	VERB
ejpam-5794	244	19	∆ξ(gµ	∆ξ(gµ	NOUN
ejpam-5794	244	20	,	,	PUNCT
ejpam-5794	244	21	gκ	gκ	NOUN
ejpam-5794	244	22	)	)	PUNCT
ejpam-5794	244	23	≤	≤	NOUN
ejpam-5794	244	24	λ∆ξ(µ	λ∆ξ(µ	NOUN
ejpam-5794	244	25	,	,	PUNCT
ejpam-5794	244	26	κ	κ	NOUN
ejpam-5794	244	27	)	)	PUNCT
ejpam-5794	244	28	,	,	PUNCT
ejpam-5794	244	29	λ	λ	PROPN
ejpam-5794	244	30	∈	∈	PROPN
ejpam-5794	245	1	[	[	X
ejpam-5794	245	2	0	0	NUM
ejpam-5794	245	3	,	,	PUNCT
ejpam-5794	245	4	1	1	NUM
ejpam-5794	245	5	)	)	PUNCT
ejpam-5794	245	6	,	,	PUNCT
ejpam-5794	245	7	b	b	X
ejpam-5794	245	8	)	)	PUNCT
ejpam-5794	245	9	sup(q≥1	sup(q≥1	NOUN
ejpam-5794	245	10	)	)	PUNCT
ejpam-5794	245	11	lim	lim	PROPN
ejpam-5794	245	12	n−→+∞	n−→+∞	PROPN
ejpam-5794	245	13	α(µi	α(µi	PROPN
ejpam-5794	245	14	,	,	PUNCT
ejpam-5794	245	15	µq	µq	PROPN
ejpam-5794	245	16	)	)	PUNCT
ejpam-5794	245	17	(	(	PUNCT
ejpam-5794	245	18	α(µ(i+1),µ(i+2	α(µ(i+1),µ(i+2	PROPN
ejpam-5794	245	19	)	)	PUNCT
ejpam-5794	245	20	)	)	PUNCT
ejpam-5794	245	21	α(µ(i−1),µi	α(µ(i−1),µi	NUM
ejpam-5794	245	22	)	)	PUNCT
ejpam-5794	245	23	)	)	PUNCT
ejpam-5794	246	1	λ	λ	X
ejpam-5794	246	2	<	<	X
ejpam-5794	246	3	1	1	NUM
ejpam-5794	246	4	,	,	PUNCT
ejpam-5794	246	5	for	for	SCONJ
ejpam-5794	246	6	any	any	DET
ejpam-5794	246	7	µi	µi	PROPN
ejpam-5794	246	8	∈	∈	PROPN
ejpam-5794	246	9	ℵ	ℵ	NOUN
ejpam-5794	246	10	,	,	PUNCT
ejpam-5794	246	11	c	c	NOUN
ejpam-5794	246	12	)	)	PUNCT
ejpam-5794	246	13	g	g	NOUN
ejpam-5794	246	14	is	be	AUX
ejpam-5794	246	15	continuous	continuous	ADJ
ejpam-5794	246	16	.	.	PUNCT
ejpam-5794	247	1	then	then	ADV
ejpam-5794	247	2	g	g	PROPN
ejpam-5794	247	3	has	have	VERB
ejpam-5794	247	4	a	a	DET
ejpam-5794	247	5	unique	unique	ADJ
ejpam-5794	247	6	fixed	fix	VERB
ejpam-5794	247	7	point	point	NOUN
ejpam-5794	247	8	.	.	PUNCT
ejpam-5794	248	1	example	example	NOUN
ejpam-5794	249	1	3	3	X
ejpam-5794	249	2	.	.	PUNCT
ejpam-5794	249	3	suppose	suppose	VERB
ejpam-5794	249	4	ℵ	ℵ	PROPN
ejpam-5794	249	5	=	=	SYM
ejpam-5794	249	6	r	r	NOUN
ejpam-5794	249	7	and	and	CCONJ
ejpam-5794	249	8	a	a	DET
ejpam-5794	249	9	mapping	mapping	NOUN
ejpam-5794	249	10	∆ξ	∆ξ	NOUN
ejpam-5794	249	11	:	:	PUNCT
ejpam-5794	249	12	ℵ	ℵ	PROPN
ejpam-5794	249	13	×	×	NOUN
ejpam-5794	249	14	ℵ	ℵ	X
ejpam-5794	249	15	×	×	NOUN
ejpam-5794	249	16	(	(	PUNCT
ejpam-5794	249	17	0,+∞	0,+∞	NUM
ejpam-5794	249	18	)	)	PUNCT
ejpam-5794	249	19	−→	−→	NOUN
ejpam-5794	249	20	ℵ	ℵ	ADP
ejpam-5794	249	21	define	define	NOUN
ejpam-5794	249	22	by	by	ADP
ejpam-5794	249	23	∆(µ	∆(µ	NOUN
ejpam-5794	249	24	,	,	PUNCT
ejpam-5794	249	25	κ	κ	NOUN
ejpam-5794	249	26	,	,	PUNCT
ejpam-5794	249	27	ξ	ξ	NOUN
ejpam-5794	249	28	)	)	PUNCT
ejpam-5794	249	29	=	=	PUNCT
ejpam-5794	249	30	|µ−	|µ−	VERB
ejpam-5794	249	31	κ|	κ|	PROPN
ejpam-5794	249	32	ξ	ξ	PROPN
ejpam-5794	249	33	+	+	CCONJ
ejpam-5794	249	34	|µ−	|µ−	ADJ
ejpam-5794	249	35	κ|	κ|	PROPN
ejpam-5794	249	36	then	then	ADV
ejpam-5794	249	37	(	(	PUNCT
ejpam-5794	249	38	∆ξ,ℵ	∆ξ,ℵ	NOUN
ejpam-5794	249	39	)	)	PUNCT
ejpam-5794	249	40	is	be	AUX
ejpam-5794	249	41	a	a	DET
ejpam-5794	249	42	complete	complete	ADJ
ejpam-5794	249	43	crmms	crmms	NOUN
ejpam-5794	249	44	with	with	ADP
ejpam-5794	249	45	controlled	control	VERB
ejpam-5794	249	46	function	function	NOUN
ejpam-5794	249	47	α	α	NOUN
ejpam-5794	249	48	=	=	SYM
ejpam-5794	249	49	(	(	PUNCT
ejpam-5794	249	50	µ	µ	NOUN
ejpam-5794	249	51	,	,	PUNCT
ejpam-5794	249	52	κ	κ	NOUN
ejpam-5794	249	53	)	)	PUNCT
ejpam-5794	249	54	=	=	SYM
ejpam-5794	249	55	{	{	PUNCT
ejpam-5794	249	56	1	1	NUM
ejpam-5794	249	57	if	if	SCONJ
ejpam-5794	249	58	µ	µ	DET
ejpam-5794	249	59	̸=	̸=	PROPN
ejpam-5794	249	60	κ	κ	NOUN
ejpam-5794	249	61	;	;	PUNCT
ejpam-5794	249	62	1	1	NUM
ejpam-5794	249	63	+	+	NUM
ejpam-5794	249	64	µ+	µ+	X
ejpam-5794	249	65	κ	κ	X
ejpam-5794	249	66	if	if	SCONJ
ejpam-5794	249	67	µ	µ	X
ejpam-5794	249	68	=	=	SYM
ejpam-5794	249	69	κ	κ	NOUN
ejpam-5794	249	70	;	;	PUNCT
ejpam-5794	249	71	but	but	CCONJ
ejpam-5794	249	72	not	not	PART
ejpam-5794	249	73	rmms	rmms	ADJ
ejpam-5794	249	74	.	.	PUNCT
ejpam-5794	250	1	define	define	VERB
ejpam-5794	250	2	a	a	DET
ejpam-5794	250	3	mapping	mapping	NOUN
ejpam-5794	250	4	g	g	NOUN
ejpam-5794	250	5	:	:	PUNCT
ejpam-5794	250	6	ℵ	ℵ	DET
ejpam-5794	250	7	−→	−→	NOUN
ejpam-5794	250	8	ℵ	ℵ	NOUN
ejpam-5794	250	9	by	by	ADP
ejpam-5794	250	10	g(µ	g(µ	PROPN
ejpam-5794	250	11	)	)	PUNCT
ejpam-5794	250	12	=	=	SYM
ejpam-5794	250	13	µ	µ	X
ejpam-5794	250	14	5	5	NUM
ejpam-5794	250	15	+	+	CCONJ
ejpam-5794	250	16	7	7	NUM
ejpam-5794	250	17	now	now	ADV
ejpam-5794	250	18	,	,	PUNCT
ejpam-5794	250	19	we	we	PRON
ejpam-5794	250	20	examine	examine	VERB
ejpam-5794	250	21	the	the	DET
ejpam-5794	250	22	contraction	contraction	NOUN
ejpam-5794	250	23	condition	condition	NOUN
ejpam-5794	250	24	.	.	PUNCT
ejpam-5794	251	1	let	let	VERB
ejpam-5794	251	2	3	3	NUM
ejpam-5794	251	3	4	4	NUM
ejpam-5794	251	4	≤	≤	NUM
ejpam-5794	252	1	λ	λ	X
ejpam-5794	252	2	<	<	X
ejpam-5794	252	3	1	1	NUM
ejpam-5794	252	4	,	,	PUNCT
ejpam-5794	252	5	then	then	ADV
ejpam-5794	252	6	∆(gµ	∆(gµ	NOUN
ejpam-5794	252	7	,	,	PUNCT
ejpam-5794	252	8	gκ	gκ	NOUN
ejpam-5794	252	9	,	,	PUNCT
ejpam-5794	252	10	ξ	ξ	X
ejpam-5794	252	11	)	)	PUNCT
ejpam-5794	252	12	=	=	SYM
ejpam-5794	252	13	|gµ−	|gµ−	PROPN
ejpam-5794	252	14	gκ|	gκ|	PROPN
ejpam-5794	252	15	ξ	ξ	PROPN
ejpam-5794	252	16	+	+	NUM
ejpam-5794	252	17	|gµ−	|gµ−	NUM
ejpam-5794	252	18	gκ|	gκ|	NOUN
ejpam-5794	252	19	=	=	SYM
ejpam-5794	252	20	|µ5	|µ5	NOUN
ejpam-5794	252	21	−	−	NOUN
ejpam-5794	252	22	κ	κ	NOUN
ejpam-5794	252	23	5	5	NUM
ejpam-5794	252	24	|	|	NOUN
ejpam-5794	252	25	ξ	ξ	X
ejpam-5794	253	1	+	+	NUM
ejpam-5794	253	2	|µ5	|µ5	NOUN
ejpam-5794	253	3	−	−	NOUN
ejpam-5794	253	4	κ	κ	NOUN
ejpam-5794	253	5	5	5	NUM
ejpam-5794	253	6	|	|	ADV
ejpam-5794	253	7	=	=	PUNCT
ejpam-5794	253	8	|µ−	|µ−	ADJ
ejpam-5794	253	9	κ|	κ|	NOUN
ejpam-5794	253	10	5ξ	5ξ	NOUN
ejpam-5794	253	11	+	+	CCONJ
ejpam-5794	253	12	|µ−	|µ−	ADJ
ejpam-5794	253	13	κ|	κ|	ADJ
ejpam-5794	253	14	≤	≤	NOUN
ejpam-5794	253	15	λ	λ	NOUN
ejpam-5794	253	16	|µ−	|µ−	ADJ
ejpam-5794	253	17	κ|	κ|	PROPN
ejpam-5794	253	18	ξ	ξ	PROPN
ejpam-5794	253	19	+	+	CCONJ
ejpam-5794	253	20	|µ−	|µ−	ADJ
ejpam-5794	253	21	κ|	κ|	NOUN
ejpam-5794	253	22	=	=	SYM
ejpam-5794	253	23	λ∆(µ	λ∆(µ	NOUN
ejpam-5794	253	24	,	,	PUNCT
ejpam-5794	253	25	κ	κ	NOUN
ejpam-5794	253	26	,	,	PUNCT
ejpam-5794	253	27	ξ	ξ	NOUN
ejpam-5794	253	28	)	)	PUNCT
ejpam-5794	253	29	.	.	PUNCT
ejpam-5794	254	1	observe	observe	VERB
ejpam-5794	254	2	that	that	SCONJ
ejpam-5794	254	3	all	all	DET
ejpam-5794	254	4	circumstances	circumstance	NOUN
ejpam-5794	254	5	of	of	ADP
ejpam-5794	254	6	corollary	corollary	ADJ
ejpam-5794	254	7	1	1	NUM
ejpam-5794	254	8	are	be	AUX
ejpam-5794	254	9	fulfilled	fulfil	VERB
ejpam-5794	254	10	and	and	CCONJ
ejpam-5794	254	11	35	35	NUM
ejpam-5794	254	12	4	4	NUM
ejpam-5794	254	13	is	be	AUX
ejpam-5794	254	14	a	a	DET
ejpam-5794	254	15	unique	unique	ADJ
ejpam-5794	254	16	fixed	fix	VERB
ejpam-5794	254	17	point	point	NOUN
ejpam-5794	254	18	of	of	ADP
ejpam-5794	254	19	g.	g.	PROPN
ejpam-5794	254	20	see	see	VERB
ejpam-5794	254	21	figures	figure	NOUN
ejpam-5794	254	22	1	1	NUM
ejpam-5794	254	23	,	,	PUNCT
ejpam-5794	254	24	2	2	NUM
ejpam-5794	254	25	and	and	CCONJ
ejpam-5794	254	26	3	3	NUM
ejpam-5794	254	27	for	for	ADP
ejpam-5794	254	28	more	more	ADJ
ejpam-5794	254	29	details	detail	NOUN
ejpam-5794	254	30	.	.	PUNCT
ejpam-5794	255	1	u.	u.	PROPN
ejpam-5794	255	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	255	3	et	et	PROPN
ejpam-5794	255	4	al	al	PROPN
ejpam-5794	255	5	.	.	PUNCT
ejpam-5794	255	6	/	/	SYM
ejpam-5794	255	7	eur	eur	PROPN
ejpam-5794	255	8	.	.	PUNCT
ejpam-5794	256	1	j.	j.	PROPN
ejpam-5794	256	2	pure	pure	PROPN
ejpam-5794	256	3	appl	appl	PROPN
ejpam-5794	256	4	.	.	PROPN
ejpam-5794	256	5	math	math	PROPN
ejpam-5794	256	6	,	,	PUNCT
ejpam-5794	256	7	18	18	NUM
ejpam-5794	256	8	(	(	PUNCT
ejpam-5794	256	9	1	1	NUM
ejpam-5794	256	10	)	)	PUNCT
ejpam-5794	256	11	(	(	PUNCT
ejpam-5794	256	12	2025	2025	NUM
ejpam-5794	256	13	)	)	PUNCT
ejpam-5794	256	14	,	,	PUNCT
ejpam-5794	256	15	5794	5794	NUM
ejpam-5794	256	16	12	12	NUM
ejpam-5794	256	17	of	of	ADP
ejpam-5794	256	18	20	20	NUM
ejpam-5794	256	19	figure	figure	NOUN
ejpam-5794	256	20	1	1	NUM
ejpam-5794	256	21	:	:	PUNCT
ejpam-5794	256	22	first	first	ADJ
ejpam-5794	256	23	view	view	NOUN
ejpam-5794	256	24	of	of	ADP
ejpam-5794	256	25	contraction	contraction	NOUN
ejpam-5794	256	26	mapping	mapping	NOUN
ejpam-5794	256	27	∆(gµ	∆(gµ	NOUN
ejpam-5794	256	28	,	,	PUNCT
ejpam-5794	256	29	gκ	gκ	NOUN
ejpam-5794	256	30	,	,	PUNCT
ejpam-5794	256	31	ξ	ξ	NOUN
ejpam-5794	256	32	)	)	PUNCT
ejpam-5794	256	33	≤	≤	NUM
ejpam-5794	256	34	λ∆(µ	λ∆(µ	NOUN
ejpam-5794	256	35	,	,	PUNCT
ejpam-5794	256	36	κ	κ	NOUN
ejpam-5794	256	37	,	,	PUNCT
ejpam-5794	256	38	ξ	ξ	NOUN
ejpam-5794	256	39	)	)	PUNCT
ejpam-5794	256	40	when	when	SCONJ
ejpam-5794	256	41	ξ	ξ	X
ejpam-5794	256	42	=	=	SYM
ejpam-5794	256	43	1	1	NUM
ejpam-5794	256	44	and	and	CCONJ
ejpam-5794	256	45	3	3	NUM
ejpam-5794	256	46	4	4	NUM
ejpam-5794	256	47	≤	≤	NUM
ejpam-5794	256	48	λ	λ	X
ejpam-5794	256	49	<	<	X
ejpam-5794	256	50	1	1	NUM
ejpam-5794	256	51	.	.	PUNCT
ejpam-5794	256	52	table	table	NOUN
ejpam-5794	256	53	1	1	NUM
ejpam-5794	256	54	:	:	PUNCT
ejpam-5794	256	55	the	the	DET
ejpam-5794	256	56	matrix	matrix	NOUN
ejpam-5794	256	57	of	of	ADP
ejpam-5794	256	58	values	value	NOUN
ejpam-5794	256	59	of	of	ADP
ejpam-5794	256	60	λ∆(µ	λ∆(µ	NOUN
ejpam-5794	256	61	,	,	PUNCT
ejpam-5794	256	62	κ	κ	NOUN
ejpam-5794	256	63	,	,	PUNCT
ejpam-5794	256	64	ξ	ξ	NOUN
ejpam-5794	256	65	)	)	PUNCT
ejpam-5794	256	66	0	0	NUM
ejpam-5794	257	1	0.4500	0.4500	NUM
ejpam-5794	257	2	0.6000	0.6000	NUM
ejpam-5794	257	3	0.6750	0.6750	NUM
ejpam-5794	257	4	0.7200	0.7200	NUM
ejpam-5794	257	5	0.7500	0.7500	NUM
ejpam-5794	257	6	0.7714	0.7714	NUM
ejpam-5794	257	7	0.7875	0.7875	NUM
ejpam-5794	257	8	0.8000	0.8000	NUM
ejpam-5794	257	9	0.8100	0.8100	NUM
ejpam-5794	257	10	0.8181	0.8181	NUM
ejpam-5794	257	11	0.4500	0.4500	NUM
ejpam-5794	257	12	0	0	NUM
ejpam-5794	257	13	0.4500	0.4500	NUM
ejpam-5794	257	14	0.6000	0.6000	NUM
ejpam-5794	257	15	0.6750	0.6750	NUM
ejpam-5794	257	16	0.7200	0.7200	NUM
ejpam-5794	257	17	0.7500	0.7500	NUM
ejpam-5794	257	18	0.7714	0.7714	NUM
ejpam-5794	257	19	0.7875	0.7875	NUM
ejpam-5794	257	20	0.8000	0.8000	NUM
ejpam-5794	257	21	0.8100	0.8100	NUM
ejpam-5794	257	22	0.6000	0.6000	NUM
ejpam-5794	257	23	0.4500	0.4500	NUM
ejpam-5794	257	24	0	0	NUM
ejpam-5794	257	25	0.4500	0.4500	NUM
ejpam-5794	257	26	0.6000	0.6000	NUM
ejpam-5794	257	27	0.6750	0.6750	NUM
ejpam-5794	257	28	0.7200	0.7200	NUM
ejpam-5794	257	29	0.7500	0.7500	NUM
ejpam-5794	257	30	0.7714	0.7714	NUM
ejpam-5794	257	31	0.7875	0.7875	NUM
ejpam-5794	257	32	0.8000	0.8000	NUM
ejpam-5794	257	33	0.6750	0.6750	NUM
ejpam-5794	257	34	0.6000	0.6000	NUM
ejpam-5794	257	35	0.4500	0.4500	NUM
ejpam-5794	257	36	0	0	NUM
ejpam-5794	257	37	0.4500	0.4500	NUM
ejpam-5794	257	38	0.6000	0.6000	NUM
ejpam-5794	257	39	0.6750	0.6750	NUM
ejpam-5794	257	40	0.7200	0.7200	NUM
ejpam-5794	257	41	0.7500	0.7500	NUM
ejpam-5794	257	42	0.7714	0.7714	NUM
ejpam-5794	257	43	0.7875	0.7875	NUM
ejpam-5794	257	44	0.7200	0.7200	NUM
ejpam-5794	257	45	0.6750	0.6750	NUM
ejpam-5794	257	46	0.6000	0.6000	NUM
ejpam-5794	257	47	0.4500	0.4500	NUM
ejpam-5794	257	48	0	0	NUM
ejpam-5794	257	49	0.4500	0.4500	NUM
ejpam-5794	257	50	0.6000	0.6000	NUM
ejpam-5794	257	51	0.6750	0.6750	NUM
ejpam-5794	257	52	0.7200	0.7200	NUM
ejpam-5794	257	53	0.7500	0.7500	NUM
ejpam-5794	257	54	0.7714	0.7714	NUM
ejpam-5794	257	55	0.7500	0.7500	NUM
ejpam-5794	257	56	0.7200	0.7200	NUM
ejpam-5794	257	57	0.6750	0.6750	NUM
ejpam-5794	257	58	0.6000	0.6000	NUM
ejpam-5794	257	59	0.4500	0.4500	NUM
ejpam-5794	257	60	0	0	NUM
ejpam-5794	257	61	0.4500	0.4500	NUM
ejpam-5794	257	62	0.6000	0.6000	NUM
ejpam-5794	257	63	0.6750	0.6750	NUM
ejpam-5794	257	64	0.7200	0.7200	NUM
ejpam-5794	257	65	0.7500	0.7500	NUM
ejpam-5794	257	66	0.7714	0.7714	NUM
ejpam-5794	257	67	0.7500	0.7500	NUM
ejpam-5794	257	68	0.7200	0.7200	NUM
ejpam-5794	257	69	0.6750	0.6750	NUM
ejpam-5794	257	70	0.6000	0.6000	NUM
ejpam-5794	257	71	0.4500	0.4500	NUM
ejpam-5794	257	72	0	0	NUM
ejpam-5794	257	73	0.4500	0.4500	NUM
ejpam-5794	257	74	0.6000	0.6000	NUM
ejpam-5794	257	75	0.6750	0.6750	NUM
ejpam-5794	257	76	0.7200	0.7200	NUM
ejpam-5794	257	77	0.7875	0.7875	NUM
ejpam-5794	257	78	0.7714	0.7714	NUM
ejpam-5794	257	79	0.7500	0.7500	NUM
ejpam-5794	257	80	0.7200	0.7200	NUM
ejpam-5794	257	81	0.6750	0.6750	NUM
ejpam-5794	257	82	0.6000	0.6000	NUM
ejpam-5794	257	83	0.4500	0.4500	NUM
ejpam-5794	257	84	0	0	NUM
ejpam-5794	257	85	0.4500	0.4500	NUM
ejpam-5794	257	86	0.6000	0.6000	NUM
ejpam-5794	257	87	0.6750	0.6750	NUM
ejpam-5794	257	88	0.8000	0.8000	NUM
ejpam-5794	258	1	0.7875	0.7875	NUM
ejpam-5794	258	2	0.7714	0.7714	NUM
ejpam-5794	258	3	0.7500	0.7500	NUM
ejpam-5794	258	4	0.7200	0.7200	NUM
ejpam-5794	258	5	0.6750	0.6750	NUM
ejpam-5794	258	6	0.6000	0.6000	NUM
ejpam-5794	258	7	0.4500	0.4500	NUM
ejpam-5794	258	8	0	0	NUM
ejpam-5794	258	9	0.4500	0.4500	NUM
ejpam-5794	258	10	0.6000	0.6000	NUM
ejpam-5794	258	11	0.8100	0.8100	NUM
ejpam-5794	258	12	0.8000	0.8000	NUM
ejpam-5794	258	13	0.7875	0.7875	NUM
ejpam-5794	258	14	0.7714	0.7714	NUM
ejpam-5794	258	15	0.7500	0.7500	NUM
ejpam-5794	258	16	0.7200	0.7200	NUM
ejpam-5794	258	17	0.6750	0.6750	NUM
ejpam-5794	258	18	0.6000	0.6000	NUM
ejpam-5794	258	19	0.4500	0.4500	NUM
ejpam-5794	258	20	0	0	NUM
ejpam-5794	258	21	0.4500	0.4500	NUM
ejpam-5794	258	22	0.8181	0.8181	NUM
ejpam-5794	258	23	0.8100	0.8100	NUM
ejpam-5794	258	24	0.8000	0.8000	NUM
ejpam-5794	258	25	0.7875	0.7875	NUM
ejpam-5794	258	26	0.7714	0.7714	NUM
ejpam-5794	258	27	0.7500	0.7500	NUM
ejpam-5794	258	28	0.7200	0.7200	NUM
ejpam-5794	258	29	0.6750	0.6750	NUM
ejpam-5794	258	30	0.6000	0.6000	NUM
ejpam-5794	258	31	0.4500	0.4500	NUM
ejpam-5794	258	32	0	0	NUM
ejpam-5794	258	33	theorem	theorem	NOUN
ejpam-5794	258	34	3	3	X
ejpam-5794	258	35	.	.	PUNCT
ejpam-5794	259	1	suppose	suppose	VERB
ejpam-5794	259	2	g	g	NOUN
ejpam-5794	259	3	:	:	PUNCT
ejpam-5794	259	4	ℵ	ℵ	PROPN
ejpam-5794	259	5	→	→	SYM
ejpam-5794	259	6	ℵ	ℵ	ADJ
ejpam-5794	259	7	be	be	VERB
ejpam-5794	259	8	a	a	DET
ejpam-5794	259	9	mapping	mapping	NOUN
ejpam-5794	259	10	on	on	ADP
ejpam-5794	259	11	a	a	DET
ejpam-5794	259	12	crmms	crmms	NOUN
ejpam-5794	259	13	(	(	PUNCT
ejpam-5794	259	14	∆ξ,ℵ	∆ξ,ℵ	PROPN
ejpam-5794	259	15	)	)	PUNCT
ejpam-5794	259	16	.	.	PUNCT
ejpam-5794	260	1	assume	assume	VERB
ejpam-5794	260	2	that	that	SCONJ
ejpam-5794	260	3	the	the	DET
ejpam-5794	260	4	following	follow	VERB
ejpam-5794	260	5	conditions	condition	NOUN
ejpam-5794	260	6	hold	hold	VERB
ejpam-5794	260	7	:	:	PUNCT
ejpam-5794	260	8	a	a	X
ejpam-5794	260	9	)	)	PUNCT
ejpam-5794	260	10	for	for	ADP
ejpam-5794	260	11	all	all	DET
ejpam-5794	260	12	µ	µ	NOUN
ejpam-5794	260	13	,	,	PUNCT
ejpam-5794	260	14	κ	κ	PROPN
ejpam-5794	260	15	∈	∈	PROPN
ejpam-5794	260	16	ℵ	ℵ	NOUN
ejpam-5794	260	17	,	,	PUNCT
ejpam-5794	260	18	∆ξ(gµ	∆ξ(gµ	NOUN
ejpam-5794	260	19	,	,	PUNCT
ejpam-5794	260	20	gκ	gκ	NOUN
ejpam-5794	260	21	)	)	PUNCT
ejpam-5794	260	22	≤	≤	NOUN
ejpam-5794	261	1	λ[∆ξ(µ	λ[∆ξ(µ	PROPN
ejpam-5794	261	2	,	,	PUNCT
ejpam-5794	261	3	gµ	gµ	PROPN
ejpam-5794	261	4	)	)	PUNCT
ejpam-5794	261	5	+	+	CCONJ
ejpam-5794	261	6	∆ξ(κ	∆ξ(κ	NOUN
ejpam-5794	261	7	,	,	PUNCT
ejpam-5794	261	8	gκ	gκ	NOUN
ejpam-5794	261	9	)	)	PUNCT
ejpam-5794	261	10	]	]	PUNCT
ejpam-5794	261	11	,	,	PUNCT
ejpam-5794	261	12	λ	λ	PROPN
ejpam-5794	261	13	∈	∈	PROPN
ejpam-5794	261	14	[	[	PUNCT
ejpam-5794	261	15	0	0	NUM
ejpam-5794	261	16	,	,	PUNCT
ejpam-5794	261	17	1	1	NUM
ejpam-5794	261	18	2	2	NUM
ejpam-5794	261	19	)	)	PUNCT
ejpam-5794	261	20	(	(	PUNCT
ejpam-5794	261	21	a	a	X
ejpam-5794	261	22	)	)	PUNCT
ejpam-5794	261	23	b	b	NOUN
ejpam-5794	261	24	)	)	PUNCT
ejpam-5794	261	25	sup(q≥1	sup(q≥1	NOUN
ejpam-5794	261	26	)	)	PUNCT
ejpam-5794	261	27	lim	lim	PROPN
ejpam-5794	262	1	i−→+∞	i−→+∞	PROPN
ejpam-5794	262	2	α(µi	α(µi	PROPN
ejpam-5794	262	3	,	,	PUNCT
ejpam-5794	262	4	µq	µq	PROPN
ejpam-5794	262	5	)	)	PUNCT
ejpam-5794	262	6	(	(	PUNCT
ejpam-5794	262	7	α(µ(i),µ(i+1	α(µ(i),µ(i+1	PROPN
ejpam-5794	262	8	)	)	PUNCT
ejpam-5794	262	9	)	)	PUNCT
ejpam-5794	263	1	α(µ(i−1),µi	α(µ(i−1),µi	NUM
ejpam-5794	263	2	)	)	PUNCT
ejpam-5794	263	3	)	)	PUNCT
ejpam-5794	264	1	λ	λ	X
ejpam-5794	264	2	<	<	X
ejpam-5794	264	3	1	1	NUM
ejpam-5794	264	4	,	,	PUNCT
ejpam-5794	264	5	for	for	ADP
ejpam-5794	264	6	any	any	DET
ejpam-5794	264	7	µi	µi	PROPN
ejpam-5794	264	8	∈	∈	PROPN
ejpam-5794	264	9	ℵ	ℵ	NOUN
ejpam-5794	264	10	,	,	PUNCT
ejpam-5794	264	11	where	where	SCONJ
ejpam-5794	264	12	λ	λ	PROPN
ejpam-5794	264	13	̸=	̸=	PROPN
ejpam-5794	264	14	1	1	NUM
ejpam-5794	264	15	α(µ1,µ2	α(µ1,µ2	NOUN
ejpam-5794	264	16	)	)	PUNCT
ejpam-5794	264	17	for	for	ADP
ejpam-5794	264	18	each	each	DET
ejpam-5794	264	19	µ1	µ1	PROPN
ejpam-5794	264	20	,	,	PUNCT
ejpam-5794	264	21	µ2	µ2	PROPN
ejpam-5794	264	22	∈	∈	PROPN
ejpam-5794	264	23	ℵ	ℵ	NOUN
ejpam-5794	264	24	,	,	PUNCT
ejpam-5794	264	25	c	c	NOUN
ejpam-5794	264	26	)	)	PUNCT
ejpam-5794	264	27	for	for	ADP
ejpam-5794	264	28	each	each	DET
ejpam-5794	264	29	µ	µ	PRON
ejpam-5794	264	30	∈	∈	PROPN
ejpam-5794	264	31	ℵ	ℵ	NOUN
ejpam-5794	264	32	lim	lim	PROPN
ejpam-5794	264	33	n−→+∞	n−→+∞	PROPN
ejpam-5794	264	34	α(µn	α(µn	PROPN
ejpam-5794	264	35	,	,	PUNCT
ejpam-5794	264	36	µ(n+1	µ(n+1	NUM
ejpam-5794	264	37	)	)	PUNCT
ejpam-5794	264	38	)	)	PUNCT
ejpam-5794	265	1	≤	≤	NUM
ejpam-5794	265	2	1	1	NUM
ejpam-5794	265	3	,	,	PUNCT
ejpam-5794	265	4	lim	lim	PROPN
ejpam-5794	265	5	n−→+∞	n−→+∞	PROPN
ejpam-5794	266	1	α(µ	α(µ	ADV
ejpam-5794	266	2	,	,	PUNCT
ejpam-5794	266	3	µn	µn	PROPN
ejpam-5794	266	4	)	)	PUNCT
ejpam-5794	266	5	and	and	CCONJ
ejpam-5794	266	6	lim	lim	PROPN
ejpam-5794	266	7	n−→+∞	n−→+∞	PROPN
ejpam-5794	266	8	α(µn	α(µn	PROPN
ejpam-5794	266	9	,	,	PUNCT
ejpam-5794	266	10	µ	µ	NOUN
ejpam-5794	266	11	)	)	PUNCT
ejpam-5794	266	12	exist	exist	VERB
ejpam-5794	266	13	and	and	CCONJ
ejpam-5794	266	14	finite	finite	PROPN
ejpam-5794	266	15	.	.	PUNCT
ejpam-5794	267	1	u.	u.	PROPN
ejpam-5794	267	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	267	3	et	et	PROPN
ejpam-5794	267	4	al	al	PROPN
ejpam-5794	267	5	.	.	PUNCT
ejpam-5794	267	6	/	/	SYM
ejpam-5794	267	7	eur	eur	PROPN
ejpam-5794	267	8	.	.	PUNCT
ejpam-5794	268	1	j.	j.	PROPN
ejpam-5794	268	2	pure	pure	PROPN
ejpam-5794	268	3	appl	appl	PROPN
ejpam-5794	268	4	.	.	PROPN
ejpam-5794	268	5	math	math	PROPN
ejpam-5794	268	6	,	,	PUNCT
ejpam-5794	268	7	18	18	NUM
ejpam-5794	268	8	(	(	PUNCT
ejpam-5794	268	9	1	1	NUM
ejpam-5794	268	10	)	)	PUNCT
ejpam-5794	268	11	(	(	PUNCT
ejpam-5794	268	12	2025	2025	NUM
ejpam-5794	268	13	)	)	PUNCT
ejpam-5794	268	14	,	,	PUNCT
ejpam-5794	268	15	5794	5794	NUM
ejpam-5794	268	16	13	13	NUM
ejpam-5794	268	17	of	of	ADP
ejpam-5794	268	18	20	20	NUM
ejpam-5794	268	19	figure	figure	NOUN
ejpam-5794	268	20	2	2	NUM
ejpam-5794	268	21	:	:	PUNCT
ejpam-5794	268	22	second	second	ADJ
ejpam-5794	268	23	view	view	NOUN
ejpam-5794	268	24	of	of	ADP
ejpam-5794	268	25	contraction	contraction	NOUN
ejpam-5794	268	26	mapping	mapping	NOUN
ejpam-5794	268	27	∆(gµ	∆(gµ	NOUN
ejpam-5794	268	28	,	,	PUNCT
ejpam-5794	268	29	gκ	gκ	NOUN
ejpam-5794	268	30	,	,	PUNCT
ejpam-5794	268	31	ξ	ξ	NOUN
ejpam-5794	268	32	)	)	PUNCT
ejpam-5794	268	33	≤	≤	NUM
ejpam-5794	268	34	λ∆(µ	λ∆(µ	NOUN
ejpam-5794	268	35	,	,	PUNCT
ejpam-5794	268	36	κ	κ	NOUN
ejpam-5794	268	37	,	,	PUNCT
ejpam-5794	268	38	ξ	ξ	NOUN
ejpam-5794	268	39	)	)	PUNCT
ejpam-5794	268	40	when	when	SCONJ
ejpam-5794	268	41	ξ	ξ	X
ejpam-5794	268	42	=	=	SYM
ejpam-5794	268	43	1	1	NUM
ejpam-5794	268	44	and	and	CCONJ
ejpam-5794	268	45	3	3	NUM
ejpam-5794	268	46	4	4	NUM
ejpam-5794	268	47	≤	≤	NUM
ejpam-5794	268	48	λ	λ	X
ejpam-5794	268	49	<	<	X
ejpam-5794	268	50	1	1	NUM
ejpam-5794	268	51	.	.	PUNCT
ejpam-5794	268	52	table	table	NOUN
ejpam-5794	268	53	2	2	NUM
ejpam-5794	268	54	:	:	PUNCT
ejpam-5794	268	55	the	the	DET
ejpam-5794	268	56	matrix	matrix	NOUN
ejpam-5794	268	57	of	of	ADP
ejpam-5794	268	58	values	value	NOUN
ejpam-5794	268	59	of	of	ADP
ejpam-5794	268	60	∆(gµ	∆(gµ	NOUN
ejpam-5794	268	61	,	,	PUNCT
ejpam-5794	268	62	gκ	gκ	NOUN
ejpam-5794	268	63	,	,	PUNCT
ejpam-5794	268	64	ξ	ξ	PROPN
ejpam-5794	268	65	)	)	PUNCT
ejpam-5794	268	66	0	0	NUM
ejpam-5794	269	1	0.1666	0.1666	NUM
ejpam-5794	269	2	0.2857	0.2857	NUM
ejpam-5794	269	3	0.3750	0.3750	NUM
ejpam-5794	269	4	0.4444	0.4444	NUM
ejpam-5794	269	5	0.5000	0.5000	NUM
ejpam-5794	269	6	0.5454	0.5454	NUM
ejpam-5794	269	7	0.5833	0.5833	NUM
ejpam-5794	269	8	0.6153	0.6153	NUM
ejpam-5794	269	9	0.6428	0.6428	NUM
ejpam-5794	269	10	0.6666	0.6666	NUM
ejpam-5794	269	11	0.1666	0.1666	NUM
ejpam-5794	269	12	0	0	PUNCT
ejpam-5794	270	1	0.1666	0.1666	NUM
ejpam-5794	270	2	0.2857	0.2857	NUM
ejpam-5794	270	3	0.3750	0.3750	NUM
ejpam-5794	270	4	0.4444	0.4444	NUM
ejpam-5794	270	5	0.5000	0.5000	NUM
ejpam-5794	270	6	0.5454	0.5454	NUM
ejpam-5794	270	7	0.5833	0.5833	NUM
ejpam-5794	270	8	0.6153	0.6153	NUM
ejpam-5794	270	9	0.6428	0.6428	NUM
ejpam-5794	270	10	0.2857	0.2857	NUM
ejpam-5794	270	11	0.1666	0.1666	NUM
ejpam-5794	270	12	0	0	PUNCT
ejpam-5794	270	13	0.1666	0.1666	NUM
ejpam-5794	270	14	0.2857	0.2857	NUM
ejpam-5794	270	15	0.3750	0.3750	NUM
ejpam-5794	270	16	0.4444	0.4444	NUM
ejpam-5794	270	17	0.5000	0.5000	NUM
ejpam-5794	270	18	0.5454	0.5454	NUM
ejpam-5794	270	19	0.5833	0.5833	NUM
ejpam-5794	270	20	0.6153	0.6153	NUM
ejpam-5794	270	21	0.3750	0.3750	NUM
ejpam-5794	270	22	0.2857	0.2857	NUM
ejpam-5794	270	23	0.1666	0.1666	NUM
ejpam-5794	270	24	0	0	PUNCT
ejpam-5794	271	1	0.1666	0.1666	NUM
ejpam-5794	271	2	0.2857	0.2857	NUM
ejpam-5794	271	3	0.3750	0.3750	NUM
ejpam-5794	271	4	0.4444	0.4444	NUM
ejpam-5794	271	5	0.5000	0.5000	NUM
ejpam-5794	271	6	0.5454	0.5454	NUM
ejpam-5794	271	7	0.5833	0.5833	NUM
ejpam-5794	271	8	0.4444	0.4444	NUM
ejpam-5794	271	9	0.3750	0.3750	NUM
ejpam-5794	271	10	0.2857	0.2857	NUM
ejpam-5794	271	11	0.1666	0.1666	NUM
ejpam-5794	271	12	0	0	PUNCT
ejpam-5794	272	1	0.1666	0.1666	NUM
ejpam-5794	272	2	0.2857	0.2857	NUM
ejpam-5794	272	3	0.3750	0.3750	NUM
ejpam-5794	272	4	0.4444	0.4444	NUM
ejpam-5794	272	5	0.5000	0.5000	NUM
ejpam-5794	272	6	0.5454	0.5454	NUM
ejpam-5794	272	7	0.5000	0.5000	NUM
ejpam-5794	272	8	0.4444	0.4444	NUM
ejpam-5794	272	9	0.3750	0.3750	NUM
ejpam-5794	272	10	0.2857	0.2857	NUM
ejpam-5794	272	11	0.1666	0.1666	NUM
ejpam-5794	272	12	0	0	PUNCT
ejpam-5794	273	1	0.1666	0.1666	NUM
ejpam-5794	273	2	0.2857	0.2857	NUM
ejpam-5794	273	3	0.3750	0.3750	NUM
ejpam-5794	273	4	0.4444	0.4444	NUM
ejpam-5794	273	5	0.5000	0.5000	NUM
ejpam-5794	273	6	0.5454	0.5454	NUM
ejpam-5794	273	7	0.5000	0.5000	NUM
ejpam-5794	273	8	0.4444	0.4444	NUM
ejpam-5794	273	9	0.3750	0.3750	NUM
ejpam-5794	273	10	0.2857	0.2857	NUM
ejpam-5794	273	11	0.1666	0.1666	NUM
ejpam-5794	273	12	0	0	PUNCT
ejpam-5794	274	1	0.1666	0.1666	NUM
ejpam-5794	274	2	0.2857	0.2857	NUM
ejpam-5794	274	3	0.3750	0.3750	NUM
ejpam-5794	274	4	0.4444	0.4444	NUM
ejpam-5794	274	5	0.5833	0.5833	NUM
ejpam-5794	274	6	0.5454	0.5454	NUM
ejpam-5794	274	7	0.5000	0.5000	NUM
ejpam-5794	274	8	0.4444	0.4444	NUM
ejpam-5794	274	9	0.3750	0.3750	NUM
ejpam-5794	274	10	0.2857	0.2857	NUM
ejpam-5794	274	11	0.1666	0.1666	NUM
ejpam-5794	274	12	0	0	PUNCT
ejpam-5794	275	1	0.1666	0.1666	NUM
ejpam-5794	275	2	0.2857	0.2857	NUM
ejpam-5794	275	3	0.3750	0.3750	NUM
ejpam-5794	275	4	0.6153	0.6153	NUM
ejpam-5794	275	5	0.5833	0.5833	NUM
ejpam-5794	275	6	0.5454	0.5454	NUM
ejpam-5794	275	7	0.5000	0.5000	NUM
ejpam-5794	275	8	0.4444	0.4444	NUM
ejpam-5794	275	9	0.3750	0.3750	NUM
ejpam-5794	275	10	0.2857	0.2857	NUM
ejpam-5794	275	11	0.1666	0.1666	NUM
ejpam-5794	275	12	0	0	PUNCT
ejpam-5794	276	1	0.1666	0.1666	NUM
ejpam-5794	276	2	0.2857	0.2857	NUM
ejpam-5794	276	3	0.6428	0.6428	NUM
ejpam-5794	276	4	0.6153	0.6153	NUM
ejpam-5794	276	5	0.5833	0.5833	NUM
ejpam-5794	276	6	0.5454	0.5454	NUM
ejpam-5794	276	7	0.5000	0.5000	NUM
ejpam-5794	276	8	0.4444	0.4444	NUM
ejpam-5794	276	9	0.3750	0.3750	NUM
ejpam-5794	276	10	0.2857	0.2857	NUM
ejpam-5794	276	11	0.1666	0.1666	NUM
ejpam-5794	276	12	0	0	PUNCT
ejpam-5794	276	13	0.1666	0.1666	NUM
ejpam-5794	276	14	0.6666	0.6666	NUM
ejpam-5794	276	15	0.6428	0.6428	NUM
ejpam-5794	276	16	0.6153	0.6153	NUM
ejpam-5794	276	17	0.5833	0.5833	NUM
ejpam-5794	276	18	0.5454	0.5454	NUM
ejpam-5794	276	19	0.5000	0.5000	NUM
ejpam-5794	276	20	0.4444	0.4444	NUM
ejpam-5794	276	21	0.3750	0.3750	NUM
ejpam-5794	276	22	0.2857	0.2857	NUM
ejpam-5794	276	23	0.1666	0.1666	NUM
ejpam-5794	276	24	0	0	PUNCT
ejpam-5794	277	1	then	then	ADV
ejpam-5794	277	2	g	g	PROPN
ejpam-5794	277	3	has	have	VERB
ejpam-5794	277	4	a	a	DET
ejpam-5794	277	5	unique	unique	ADJ
ejpam-5794	277	6	fixed	fix	VERB
ejpam-5794	277	7	point	point	NOUN
ejpam-5794	277	8	in	in	ADP
ejpam-5794	277	9	ℵ.	ℵ.	PROPN
ejpam-5794	277	10	proof	proof	PROPN
ejpam-5794	277	11	.	.	PUNCT
ejpam-5794	278	1	suppose	suppose	VERB
ejpam-5794	278	2	µ0	µ0	NOUN
ejpam-5794	278	3	be	be	VERB
ejpam-5794	278	4	any	any	DET
ejpam-5794	278	5	point	point	NOUN
ejpam-5794	278	6	in	in	ADP
ejpam-5794	278	7	ℵ.	ℵ.	PROPN
ejpam-5794	278	8	we	we	PRON
ejpam-5794	278	9	describe	describe	VERB
ejpam-5794	278	10	the	the	DET
ejpam-5794	278	11	iterative	iterative	NOUN
ejpam-5794	278	12	sequence	sequence	NOUN
ejpam-5794	278	13	(	(	PUNCT
ejpam-5794	278	14	µn	µn	NOUN
ejpam-5794	278	15	)	)	PUNCT
ejpam-5794	278	16	over	over	ADP
ejpam-5794	278	17	µ0	µ0	PROPN
ejpam-5794	278	18	,	,	PUNCT
ejpam-5794	278	19	g(µ0	g(µ0	NOUN
ejpam-5794	278	20	)	)	PUNCT
ejpam-5794	278	21	=	=	SYM
ejpam-5794	278	22	µ1	µ1	PROPN
ejpam-5794	278	23	,	,	PUNCT
ejpam-5794	278	24	g(µ1	g(µ1	NOUN
ejpam-5794	278	25	)	)	PUNCT
ejpam-5794	279	1	=	=	SYM
ejpam-5794	279	2	µ2	µ2	ADJ
ejpam-5794	279	3	,	,	PUNCT
ejpam-5794	279	4	g(µ2	g(µ2	NOUN
ejpam-5794	279	5	)	)	PUNCT
ejpam-5794	279	6	=	=	SYM
ejpam-5794	279	7	µ3	µ3	NOUN
ejpam-5794	279	8	·	·	PUNCT
ejpam-5794	279	9	·	·	PUNCT
ejpam-5794	279	10	·	·	PUNCT
ejpam-5794	279	11	gn(µ0	gn(µ0	X
ejpam-5794	279	12	)	)	PUNCT
ejpam-5794	279	13	=	=	SYM
ejpam-5794	279	14	µn	µn	PROPN
ejpam-5794	279	15	,	,	PUNCT
ejpam-5794	279	16	then	then	ADV
ejpam-5794	279	17	from	from	ADP
ejpam-5794	279	18	(	(	PUNCT
ejpam-5794	279	19	a	a	X
ejpam-5794	279	20	)	)	PUNCT
ejpam-5794	279	21	,	,	PUNCT
ejpam-5794	279	22	we	we	PRON
ejpam-5794	279	23	obtain	obtain	VERB
ejpam-5794	279	24	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	279	25	,	,	PUNCT
ejpam-5794	279	26	µ2	µ2	PROPN
ejpam-5794	279	27	)	)	PUNCT
ejpam-5794	279	28	=	=	PUNCT
ejpam-5794	280	1	∆ξ(gµ0	∆ξ(gµ0	PROPN
ejpam-5794	280	2	,	,	PUNCT
ejpam-5794	280	3	gµ1	gµ1	NOUN
ejpam-5794	280	4	)	)	PUNCT
ejpam-5794	280	5	,	,	PUNCT
ejpam-5794	280	6	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	280	7	,	,	PUNCT
ejpam-5794	280	8	µ2	µ2	NOUN
ejpam-5794	280	9	)	)	PUNCT
ejpam-5794	280	10	≤	≤	NOUN
ejpam-5794	280	11	λ[∆ξ(µ0	λ[∆ξ(µ0	NOUN
ejpam-5794	280	12	,	,	PUNCT
ejpam-5794	280	13	gµ0	gµ0	NOUN
ejpam-5794	280	14	)	)	PUNCT
ejpam-5794	280	15	+	+	CCONJ
ejpam-5794	280	16	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	280	17	,	,	PUNCT
ejpam-5794	280	18	gµ1	gµ1	NOUN
ejpam-5794	280	19	)	)	PUNCT
ejpam-5794	280	20	]	]	PUNCT
ejpam-5794	281	1	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	281	2	,	,	PUNCT
ejpam-5794	281	3	µ2	µ2	PROPN
ejpam-5794	281	4	)	)	PUNCT
ejpam-5794	281	5	=	=	SYM
ejpam-5794	282	1	λ[∆ξ(µ0	λ[∆ξ(µ0	NOUN
ejpam-5794	282	2	,	,	PUNCT
ejpam-5794	282	3	gµ0	gµ0	NOUN
ejpam-5794	282	4	)	)	PUNCT
ejpam-5794	282	5	+	+	CCONJ
ejpam-5794	282	6	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	282	7	,	,	PUNCT
ejpam-5794	282	8	µ2	µ2	PROPN
ejpam-5794	282	9	)	)	PUNCT
ejpam-5794	282	10	]	]	PUNCT
ejpam-5794	283	1	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	283	2	,	,	PUNCT
ejpam-5794	283	3	µ2)−	µ2)−	VERB
ejpam-5794	283	4	λ∆ξ(µ1	λ∆ξ(µ1	NOUN
ejpam-5794	283	5	,	,	PUNCT
ejpam-5794	283	6	µ2	µ2	PROPN
ejpam-5794	283	7	)	)	PUNCT
ejpam-5794	283	8	=	=	SYM
ejpam-5794	284	1	λ∆ξ(µ0	λ∆ξ(µ0	NOUN
ejpam-5794	284	2	,	,	PUNCT
ejpam-5794	284	3	µ1	µ1	PROPN
ejpam-5794	284	4	)	)	PUNCT
ejpam-5794	284	5	,	,	PUNCT
ejpam-5794	284	6	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	284	7	,	,	PUNCT
ejpam-5794	284	8	µ2	µ2	NOUN
ejpam-5794	284	9	)	)	PUNCT
ejpam-5794	284	10	≤	≤	PUNCT
ejpam-5794	285	1	λ	λ	PROPN
ejpam-5794	285	2	1−	1−	NUM
ejpam-5794	285	3	λ	λ	SYM
ejpam-5794	285	4	∆ξ(µ0	∆ξ(µ0	NOUN
ejpam-5794	285	5	,	,	PUNCT
ejpam-5794	285	6	µ1	µ1	PROPN
ejpam-5794	285	7	)	)	PUNCT
ejpam-5794	285	8	.	.	PUNCT
ejpam-5794	286	1	u.	u.	PROPN
ejpam-5794	286	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	286	3	et	et	PROPN
ejpam-5794	286	4	al	al	PROPN
ejpam-5794	286	5	.	.	PUNCT
ejpam-5794	286	6	/	/	SYM
ejpam-5794	286	7	eur	eur	PROPN
ejpam-5794	286	8	.	.	PUNCT
ejpam-5794	287	1	j.	j.	PROPN
ejpam-5794	287	2	pure	pure	PROPN
ejpam-5794	287	3	appl	appl	PROPN
ejpam-5794	287	4	.	.	PROPN
ejpam-5794	287	5	math	math	PROPN
ejpam-5794	287	6	,	,	PUNCT
ejpam-5794	287	7	18	18	NUM
ejpam-5794	287	8	(	(	PUNCT
ejpam-5794	287	9	1	1	NUM
ejpam-5794	287	10	)	)	PUNCT
ejpam-5794	287	11	(	(	PUNCT
ejpam-5794	287	12	2025	2025	NUM
ejpam-5794	287	13	)	)	PUNCT
ejpam-5794	287	14	,	,	PUNCT
ejpam-5794	287	15	5794	5794	NUM
ejpam-5794	287	16	14	14	NUM
ejpam-5794	287	17	of	of	ADP
ejpam-5794	287	18	20	20	NUM
ejpam-5794	287	19	figure	figure	NOUN
ejpam-5794	287	20	3	3	NUM
ejpam-5794	287	21	:	:	PUNCT
ejpam-5794	287	22	graph	graph	NOUN
ejpam-5794	287	23	of	of	ADP
ejpam-5794	287	24	g(µ	g(µ	PROPN
ejpam-5794	287	25	)	)	PUNCT
ejpam-5794	287	26	=	=	PUNCT
ejpam-5794	288	1	µ.	µ.	NOUN
ejpam-5794	288	2	it	it	PRON
ejpam-5794	288	3	is	be	AUX
ejpam-5794	288	4	easy	easy	ADJ
ejpam-5794	288	5	to	to	PART
ejpam-5794	288	6	see	see	VERB
ejpam-5794	288	7	that	that	PRON
ejpam-5794	288	8	shows	show	VERB
ejpam-5794	288	9	that	that	SCONJ
ejpam-5794	288	10	35	35	NUM
ejpam-5794	288	11	4	4	NUM
ejpam-5794	288	12	is	be	AUX
ejpam-5794	288	13	a	a	DET
ejpam-5794	288	14	unique	unique	ADJ
ejpam-5794	288	15	fixed	fix	VERB
ejpam-5794	288	16	point	point	NOUN
ejpam-5794	288	17	.	.	PUNCT
ejpam-5794	289	1	let	let	VERB
ejpam-5794	289	2	,	,	PUNCT
ejpam-5794	289	3	λ	λ	PROPN
ejpam-5794	289	4	(	(	PUNCT
ejpam-5794	289	5	1−λ	1−λ	NUM
ejpam-5794	289	6	)	)	PUNCT
ejpam-5794	289	7	=	=	SYM
ejpam-5794	290	1	α	α	X
ejpam-5794	290	2	<	<	X
ejpam-5794	290	3	1	1	NUM
ejpam-5794	290	4	,	,	PUNCT
ejpam-5794	290	5	as	as	ADP
ejpam-5794	290	6	λ	λ	PROPN
ejpam-5794	290	7	≤	≤	NUM
ejpam-5794	290	8	1	1	NUM
ejpam-5794	290	9	2	2	NUM
ejpam-5794	290	10	.	.	PUNCT
ejpam-5794	291	1	then	then	ADV
ejpam-5794	291	2	by	by	ADP
ejpam-5794	291	3	continuously	continuously	ADV
ejpam-5794	291	4	applying	apply	VERB
ejpam-5794	291	5	(	(	PUNCT
ejpam-5794	291	6	a	a	X
ejpam-5794	291	7	)	)	PUNCT
ejpam-5794	291	8	,	,	PUNCT
ejpam-5794	291	9	we	we	PRON
ejpam-5794	291	10	obtain	obtain	VERB
ejpam-5794	291	11	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	291	12	,	,	PUNCT
ejpam-5794	291	13	µ(n+1	µ(n+1	NUM
ejpam-5794	291	14	)	)	PUNCT
ejpam-5794	291	15	)	)	PUNCT
ejpam-5794	292	1	≤	≤	NOUN
ejpam-5794	293	1	αn∆ξ(µ0	αn∆ξ(µ0	ADJ
ejpam-5794	293	2	,	,	PUNCT
ejpam-5794	293	3	µ1	µ1	PROPN
ejpam-5794	293	4	)	)	PUNCT
ejpam-5794	293	5	.	.	PUNCT
ejpam-5794	294	1	taking	take	VERB
ejpam-5794	294	2	limit	limit	NOUN
ejpam-5794	294	3	on	on	ADP
ejpam-5794	294	4	both	both	DET
ejpam-5794	294	5	sides	side	NOUN
ejpam-5794	294	6	,	,	PUNCT
ejpam-5794	294	7	we	we	PRON
ejpam-5794	294	8	get	get	VERB
ejpam-5794	294	9	lim	lim	PROPN
ejpam-5794	294	10	n−→+∞	n−→+∞	PROPN
ejpam-5794	294	11	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	294	12	,	,	PUNCT
ejpam-5794	294	13	µ(n+1	µ(n+1	NUM
ejpam-5794	294	14	)	)	PUNCT
ejpam-5794	294	15	)	)	PUNCT
ejpam-5794	295	1	=	=	PUNCT
ejpam-5794	295	2	0	0	X
ejpam-5794	295	3	.	.	PUNCT
ejpam-5794	296	1	(	(	PUNCT
ejpam-5794	296	2	b	b	X
ejpam-5794	296	3	)	)	PUNCT
ejpam-5794	296	4	now	now	ADV
ejpam-5794	296	5	again	again	ADV
ejpam-5794	296	6	from	from	ADP
ejpam-5794	296	7	(	(	PUNCT
ejpam-5794	296	8	a	a	X
ejpam-5794	296	9	)	)	PUNCT
ejpam-5794	296	10	,	,	PUNCT
ejpam-5794	296	11	we	we	PRON
ejpam-5794	296	12	have	have	VERB
ejpam-5794	296	13	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	296	14	,	,	PUNCT
ejpam-5794	296	15	µ(n+2	µ(n+2	PUNCT
ejpam-5794	296	16	)	)	PUNCT
ejpam-5794	296	17	)	)	PUNCT
ejpam-5794	297	1	=	=	SYM
ejpam-5794	297	2	∆ξ(gµ(n−1	∆ξ(gµ(n−1	ADJ
ejpam-5794	297	3	)	)	PUNCT
ejpam-5794	297	4	,	,	PUNCT
ejpam-5794	297	5	gµ(n+1	gµ(n+1	PROPN
ejpam-5794	297	6	)	)	PUNCT
ejpam-5794	297	7	)	)	PUNCT
ejpam-5794	297	8	,	,	PUNCT
ejpam-5794	297	9	∆ξ(µ1	∆ξ(µ1	NOUN
ejpam-5794	297	10	,	,	PUNCT
ejpam-5794	297	11	µ2	µ2	NOUN
ejpam-5794	297	12	)	)	PUNCT
ejpam-5794	297	13	≤	≤	NUM
ejpam-5794	297	14	λ[∆ξ(µ(n−1	λ[∆ξ(µ(n−1	PROPN
ejpam-5794	297	15	)	)	PUNCT
ejpam-5794	297	16	,	,	PUNCT
ejpam-5794	297	17	gµ(n−1	gµ(n−1	PROPN
ejpam-5794	297	18	)	)	PUNCT
ejpam-5794	297	19	)	)	PUNCT
ejpam-5794	298	1	+	+	CCONJ
ejpam-5794	298	2	∆ξ(µ(n+1	∆ξ(µ(n+1	NOUN
ejpam-5794	298	3	)	)	PUNCT
ejpam-5794	298	4	,	,	PUNCT
ejpam-5794	298	5	gµ(n+1	gµ(n+1	PROPN
ejpam-5794	298	6	)	)	PUNCT
ejpam-5794	298	7	)	)	PUNCT
ejpam-5794	298	8	]	]	PUNCT
ejpam-5794	298	9	,	,	PUNCT
ejpam-5794	298	10	≤	≤	PROPN
ejpam-5794	298	11	λ[∆ξ(µ(n−1	λ[∆ξ(µ(n−1	PROPN
ejpam-5794	298	12	)	)	PUNCT
ejpam-5794	298	13	,	,	PUNCT
ejpam-5794	298	14	µn	µn	PROPN
ejpam-5794	298	15	)	)	PUNCT
ejpam-5794	298	16	+	+	CCONJ
ejpam-5794	298	17	∆ξ(µ(n+1	∆ξ(µ(n+1	NOUN
ejpam-5794	298	18	)	)	PUNCT
ejpam-5794	298	19	,	,	PUNCT
ejpam-5794	298	20	µ(n+2	µ(n+2	PRON
ejpam-5794	298	21	)	)	PUNCT
ejpam-5794	298	22	)	)	PUNCT
ejpam-5794	298	23	]	]	PUNCT
ejpam-5794	298	24	again	again	ADV
ejpam-5794	298	25	,	,	PUNCT
ejpam-5794	298	26	applying	apply	VERB
ejpam-5794	298	27	limit	limit	NOUN
ejpam-5794	298	28	on	on	ADP
ejpam-5794	298	29	the	the	DET
ejpam-5794	298	30	both	both	DET
ejpam-5794	298	31	sides	side	NOUN
ejpam-5794	298	32	,	,	PUNCT
ejpam-5794	298	33	we	we	PRON
ejpam-5794	298	34	get	get	VERB
ejpam-5794	298	35	lim	lim	PROPN
ejpam-5794	298	36	n−→+∞	n−→+∞	PROPN
ejpam-5794	298	37	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	298	38	,	,	PUNCT
ejpam-5794	298	39	µ(n+1	µ(n+1	NUM
ejpam-5794	298	40	)	)	PUNCT
ejpam-5794	298	41	)	)	PUNCT
ejpam-5794	299	1	=	=	PUNCT
ejpam-5794	299	2	0	0	X
ejpam-5794	299	3	.	.	PUNCT
ejpam-5794	300	1	(	(	PUNCT
ejpam-5794	300	2	c	c	X
ejpam-5794	300	3	)	)	PUNCT
ejpam-5794	300	4	now	now	ADV
ejpam-5794	300	5	we	we	PRON
ejpam-5794	300	6	prove	prove	VERB
ejpam-5794	300	7	that	that	SCONJ
ejpam-5794	300	8	the	the	DET
ejpam-5794	300	9	sequence	sequence	NOUN
ejpam-5794	300	10	{	{	PUNCT
ejpam-5794	300	11	µn	µn	PROPN
ejpam-5794	300	12	}	}	PUNCT
ejpam-5794	300	13	is	be	AUX
ejpam-5794	300	14	a	a	DET
ejpam-5794	300	15	cauchy	cauchy	ADJ
ejpam-5794	300	16	sequence	sequence	NOUN
ejpam-5794	300	17	.	.	PUNCT
ejpam-5794	301	1	using	use	VERB
ejpam-5794	301	2	equations	equation	NOUN
ejpam-5794	301	3	(	(	PUNCT
ejpam-5794	301	4	b	b	NOUN
ejpam-5794	301	5	)	)	PUNCT
ejpam-5794	301	6	and	and	CCONJ
ejpam-5794	301	7	(	(	PUNCT
ejpam-5794	301	8	c	c	NOUN
ejpam-5794	301	9	)	)	PUNCT
ejpam-5794	301	10	,	,	PUNCT
ejpam-5794	301	11	repeat	repeat	VERB
ejpam-5794	301	12	the	the	DET
ejpam-5794	301	13	method	method	NOUN
ejpam-5794	301	14	as	as	ADP
ejpam-5794	301	15	in	in	ADP
ejpam-5794	301	16	theorem	theorem	NOUN
ejpam-5794	301	17	(	(	PUNCT
ejpam-5794	301	18	0.2.6	0.2.6	NUM
ejpam-5794	301	19	)	)	PUNCT
ejpam-5794	301	20	,	,	PUNCT
ejpam-5794	301	21	we	we	PRON
ejpam-5794	301	22	examine	examine	VERB
ejpam-5794	301	23	that	that	SCONJ
ejpam-5794	301	24	{	{	PUNCT
ejpam-5794	301	25	µn	µn	NOUN
ejpam-5794	301	26	}	}	PUNCT
ejpam-5794	301	27	is	be	AUX
ejpam-5794	301	28	a	a	DET
ejpam-5794	301	29	cauchy	cauchy	ADJ
ejpam-5794	301	30	sequence	sequence	NOUN
ejpam-5794	301	31	.	.	PUNCT
ejpam-5794	302	1	as	as	SCONJ
ejpam-5794	302	2	ℵ	ℵ	NOUN
ejpam-5794	302	3	is	be	AUX
ejpam-5794	302	4	complete	complete	ADJ
ejpam-5794	302	5	,	,	PUNCT
ejpam-5794	302	6	so	so	SCONJ
ejpam-5794	302	7	there	there	PRON
ejpam-5794	302	8	exist	exist	VERB
ejpam-5794	302	9	µ	µ	PRON
ejpam-5794	302	10	∈	∈	NOUN
ejpam-5794	302	11	ℵ	ℵ	NOUN
ejpam-5794	302	12	such	such	ADJ
ejpam-5794	302	13	that	that	SCONJ
ejpam-5794	302	14	lim	lim	PROPN
ejpam-5794	302	15	n−→+∞	n−→+∞	PROPN
ejpam-5794	302	16	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	302	17	,	,	PUNCT
ejpam-5794	302	18	µ	µ	NOUN
ejpam-5794	302	19	)	)	PUNCT
ejpam-5794	302	20	=	=	SYM
ejpam-5794	303	1	0	0	X
ejpam-5794	303	2	.	.	PUNCT
ejpam-5794	304	1	(	(	PUNCT
ejpam-5794	304	2	d	d	X
ejpam-5794	304	3	)	)	PUNCT
ejpam-5794	304	4	now	now	ADV
ejpam-5794	304	5	we	we	PRON
ejpam-5794	304	6	examine	examine	VERB
ejpam-5794	304	7	that	that	SCONJ
ejpam-5794	304	8	µ	µ	NOUN
ejpam-5794	304	9	is	be	AUX
ejpam-5794	304	10	a	a	DET
ejpam-5794	304	11	fixed	fix	VERB
ejpam-5794	304	12	point	point	NOUN
ejpam-5794	304	13	of	of	ADP
ejpam-5794	304	14	g	g	PROPN
ejpam-5794	304	15	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	304	16	,	,	PUNCT
ejpam-5794	304	17	gµ	gµ	NOUN
ejpam-5794	304	18	)	)	PUNCT
ejpam-5794	304	19	≤	≤	NOUN
ejpam-5794	305	1	ξ	ξ	SYM
ejpam-5794	305	2	3	3	NUM
ejpam-5794	305	3	[	[	X
ejpam-5794	305	4	α(µ	α(µ	ADP
ejpam-5794	305	5	,	,	PUNCT
ejpam-5794	305	6	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	305	7	,	,	PUNCT
ejpam-5794	305	8	µn	µn	NOUN
ejpam-5794	305	9	)	)	PUNCT
ejpam-5794	305	10	+	+	CCONJ
ejpam-5794	305	11	α(µn	α(µn	NUM
ejpam-5794	305	12	,	,	PUNCT
ejpam-5794	305	13	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	305	14	,	,	PUNCT
ejpam-5794	305	15	µ(n+1	µ(n+1	NUM
ejpam-5794	305	16	)	)	PUNCT
ejpam-5794	305	17	)	)	PUNCT
ejpam-5794	306	1	u.	u.	PROPN
ejpam-5794	306	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	306	3	et	et	PROPN
ejpam-5794	306	4	al	al	PROPN
ejpam-5794	306	5	.	.	PUNCT
ejpam-5794	306	6	/	/	SYM
ejpam-5794	306	7	eur	eur	PROPN
ejpam-5794	306	8	.	.	PUNCT
ejpam-5794	307	1	j.	j.	PROPN
ejpam-5794	307	2	pure	pure	PROPN
ejpam-5794	307	3	appl	appl	PROPN
ejpam-5794	307	4	.	.	PROPN
ejpam-5794	307	5	math	math	PROPN
ejpam-5794	307	6	,	,	PUNCT
ejpam-5794	307	7	18	18	NUM
ejpam-5794	307	8	(	(	PUNCT
ejpam-5794	307	9	1	1	NUM
ejpam-5794	307	10	)	)	PUNCT
ejpam-5794	307	11	(	(	PUNCT
ejpam-5794	307	12	2025	2025	NUM
ejpam-5794	307	13	)	)	PUNCT
ejpam-5794	307	14	,	,	PUNCT
ejpam-5794	307	15	5794	5794	NUM
ejpam-5794	307	16	15	15	NUM
ejpam-5794	307	17	of	of	ADP
ejpam-5794	307	18	20	20	NUM
ejpam-5794	307	19	+	+	NOUN
ejpam-5794	307	20	α(µ(n+1	α(µ(n+1	NOUN
ejpam-5794	307	21	)	)	PUNCT
ejpam-5794	307	22	,	,	PUNCT
ejpam-5794	307	23	gµ)∆ξ(µ(n+1	gµ)∆ξ(µ(n+1	PROPN
ejpam-5794	307	24	)	)	PUNCT
ejpam-5794	307	25	,	,	PUNCT
ejpam-5794	307	26	gµ	gµ	PROPN
ejpam-5794	307	27	)	)	PUNCT
ejpam-5794	307	28	]	]	PUNCT
ejpam-5794	308	1	≤	≤	NUM
ejpam-5794	308	2	ξ	ξ	SYM
ejpam-5794	308	3	3	3	NUM
ejpam-5794	308	4	[	[	X
ejpam-5794	308	5	α(µ	α(µ	ADP
ejpam-5794	308	6	,	,	PUNCT
ejpam-5794	308	7	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	308	8	,	,	PUNCT
ejpam-5794	308	9	µn	µn	NOUN
ejpam-5794	308	10	)	)	PUNCT
ejpam-5794	308	11	+	+	CCONJ
ejpam-5794	308	12	α(µn	α(µn	NUM
ejpam-5794	308	13	,	,	PUNCT
ejpam-5794	308	14	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	308	15	,	,	PUNCT
ejpam-5794	308	16	µ(n+1	µ(n+1	NUM
ejpam-5794	308	17	)	)	PUNCT
ejpam-5794	308	18	)	)	PUNCT
ejpam-5794	309	1	+	+	NOUN
ejpam-5794	309	2	α(µ(n+1	α(µ(n+1	NOUN
ejpam-5794	309	3	)	)	PUNCT
ejpam-5794	309	4	,	,	PUNCT
ejpam-5794	309	5	gµ)∆ξ(gµn	gµ)∆ξ(gµn	PROPN
ejpam-5794	309	6	,	,	PUNCT
ejpam-5794	309	7	gµ	gµ	PROPN
ejpam-5794	309	8	)	)	PUNCT
ejpam-5794	309	9	]	]	PUNCT
ejpam-5794	309	10	,	,	PUNCT
ejpam-5794	309	11	≤	≤	NUM
ejpam-5794	309	12	ξ	ξ	SYM
ejpam-5794	309	13	3	3	NUM
ejpam-5794	310	1	[	[	X
ejpam-5794	310	2	α(µ	α(µ	ADP
ejpam-5794	310	3	,	,	PUNCT
ejpam-5794	310	4	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	310	5	,	,	PUNCT
ejpam-5794	310	6	µn	µn	NOUN
ejpam-5794	310	7	)	)	PUNCT
ejpam-5794	310	8	+	+	CCONJ
ejpam-5794	310	9	α(µn	α(µn	NUM
ejpam-5794	310	10	,	,	PUNCT
ejpam-5794	310	11	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	310	12	,	,	PUNCT
ejpam-5794	310	13	µ(n+1	µ(n+1	NUM
ejpam-5794	310	14	)	)	PUNCT
ejpam-5794	310	15	)	)	PUNCT
ejpam-5794	311	1	+	+	NOUN
ejpam-5794	311	2	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	311	3	)	)	PUNCT
ejpam-5794	311	4	,	,	PUNCT
ejpam-5794	311	5	gµ)λ(∆ξ(µn	gµ)λ(∆ξ(µn	NOUN
ejpam-5794	311	6	,	,	PUNCT
ejpam-5794	311	7	gµn	gµn	PROPN
ejpam-5794	311	8	)	)	PUNCT
ejpam-5794	312	1	+	+	CCONJ
ejpam-5794	312	2	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	312	3	,	,	PUNCT
ejpam-5794	312	4	gµ	gµ	NOUN
ejpam-5794	312	5	)	)	PUNCT
ejpam-5794	312	6	)	)	PUNCT
ejpam-5794	312	7	]	]	PUNCT
ejpam-5794	313	1	≤	≤	NUM
ejpam-5794	313	2	ξ	ξ	SYM
ejpam-5794	313	3	3	3	NUM
ejpam-5794	313	4	[	[	X
ejpam-5794	313	5	α(µ	α(µ	ADP
ejpam-5794	313	6	,	,	PUNCT
ejpam-5794	313	7	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	313	8	,	,	PUNCT
ejpam-5794	313	9	µn	µn	NOUN
ejpam-5794	313	10	)	)	PUNCT
ejpam-5794	313	11	]	]	PUNCT
ejpam-5794	314	1	+	+	PUNCT
ejpam-5794	314	2	ξ	ξ	SYM
ejpam-5794	314	3	3	3	NUM
ejpam-5794	314	4	[	[	X
ejpam-5794	314	5	α(µn	α(µn	NUM
ejpam-5794	314	6	,	,	PUNCT
ejpam-5794	314	7	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	314	8	,	,	PUNCT
ejpam-5794	314	9	µ(n+1	µ(n+1	NUM
ejpam-5794	314	10	)	)	PUNCT
ejpam-5794	314	11	)	)	PUNCT
ejpam-5794	314	12	]	]	PUNCT
ejpam-5794	315	1	+	+	PUNCT
ejpam-5794	315	2	ξ	ξ	SYM
ejpam-5794	315	3	3	3	NUM
ejpam-5794	315	4	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	315	5	)	)	PUNCT
ejpam-5794	315	6	,	,	PUNCT
ejpam-5794	315	7	gµ)λ∆ξ(µn	gµ)λ∆ξ(µn	NOUN
ejpam-5794	315	8	,	,	PUNCT
ejpam-5794	315	9	gµn	gµn	PROPN
ejpam-5794	315	10	)	)	PUNCT
ejpam-5794	316	1	+	+	CCONJ
ejpam-5794	316	2	ξ	ξ	SYM
ejpam-5794	316	3	3	3	NUM
ejpam-5794	316	4	λα(µ(n+1	λα(µ(n+1	NOUN
ejpam-5794	316	5	)	)	PUNCT
ejpam-5794	316	6	,	,	PUNCT
ejpam-5794	316	7	gµ)∆ξ(µ	gµ)∆ξ(µ	NOUN
ejpam-5794	316	8	,	,	PUNCT
ejpam-5794	316	9	gµ	gµ	NOUN
ejpam-5794	316	10	)	)	PUNCT
ejpam-5794	316	11	,	,	PUNCT
ejpam-5794	316	12	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	316	13	,	,	PUNCT
ejpam-5794	316	14	gµ)−	gµ)−	VERB
ejpam-5794	316	15	ξ	ξ	X
ejpam-5794	316	16	3	3	NUM
ejpam-5794	316	17	λα(µ(n+1	λα(µ(n+1	NOUN
ejpam-5794	316	18	)	)	PUNCT
ejpam-5794	316	19	,	,	PUNCT
ejpam-5794	316	20	gµ)∆ξ(µ	gµ)∆ξ(µ	NOUN
ejpam-5794	316	21	,	,	PUNCT
ejpam-5794	316	22	gµ	gµ	NOUN
ejpam-5794	316	23	)	)	PUNCT
ejpam-5794	316	24	≤	≤	NOUN
ejpam-5794	317	1	ξ	ξ	SYM
ejpam-5794	317	2	3	3	NUM
ejpam-5794	317	3	[	[	X
ejpam-5794	317	4	α(µ	α(µ	ADP
ejpam-5794	317	5	,	,	PUNCT
ejpam-5794	317	6	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	317	7	,	,	PUNCT
ejpam-5794	317	8	µn	µn	NOUN
ejpam-5794	317	9	)	)	PUNCT
ejpam-5794	317	10	]	]	PUNCT
ejpam-5794	318	1	+	+	PUNCT
ejpam-5794	318	2	ξ	ξ	SYM
ejpam-5794	318	3	3	3	NUM
ejpam-5794	318	4	[	[	X
ejpam-5794	318	5	α(µn	α(µn	NUM
ejpam-5794	318	6	,	,	PUNCT
ejpam-5794	318	7	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	318	8	,	,	PUNCT
ejpam-5794	318	9	µ(n+1	µ(n+1	NUM
ejpam-5794	318	10	)	)	PUNCT
ejpam-5794	318	11	)	)	PUNCT
ejpam-5794	318	12	]	]	PUNCT
ejpam-5794	319	1	+	+	PUNCT
ejpam-5794	319	2	ξ	ξ	SYM
ejpam-5794	319	3	3	3	NUM
ejpam-5794	319	4	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	319	5	)	)	PUNCT
ejpam-5794	319	6	,	,	PUNCT
ejpam-5794	319	7	gµ)λ∆ξ(µn	gµ)λ∆ξ(µn	NOUN
ejpam-5794	319	8	,	,	PUNCT
ejpam-5794	319	9	gµn	gµn	PROPN
ejpam-5794	319	10	)	)	PUNCT
ejpam-5794	319	11	,	,	PUNCT
ejpam-5794	319	12	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	319	13	,	,	PUNCT
ejpam-5794	319	14	gµ)(1−	gµ)(1−	PROPN
ejpam-5794	319	15	ξ	ξ	PROPN
ejpam-5794	319	16	3	3	NUM
ejpam-5794	319	17	λα(µ(n+1	λα(µ(n+1	NOUN
ejpam-5794	319	18	)	)	PUNCT
ejpam-5794	319	19	,	,	PUNCT
ejpam-5794	319	20	gµ	gµ	NOUN
ejpam-5794	319	21	)	)	PUNCT
ejpam-5794	319	22	)	)	PUNCT
ejpam-5794	320	1	≤	≤	NUM
ejpam-5794	321	1	ξ	ξ	X
ejpam-5794	321	2	3	3	NUM
ejpam-5794	322	1	[	[	X
ejpam-5794	322	2	α(µ	α(µ	ADP
ejpam-5794	322	3	,	,	PUNCT
ejpam-5794	322	4	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	322	5	,	,	PUNCT
ejpam-5794	322	6	µn	µn	NOUN
ejpam-5794	322	7	)	)	PUNCT
ejpam-5794	322	8	]	]	PUNCT
ejpam-5794	323	1	+	+	PUNCT
ejpam-5794	323	2	ξ	ξ	SYM
ejpam-5794	323	3	3	3	NUM
ejpam-5794	323	4	[	[	X
ejpam-5794	323	5	α(µn	α(µn	NUM
ejpam-5794	323	6	,	,	PUNCT
ejpam-5794	323	7	µ(n+1))∆ξ(µn	µ(n+1))∆ξ(µn	PROPN
ejpam-5794	323	8	,	,	PUNCT
ejpam-5794	323	9	µ(n+1	µ(n+1	NUM
ejpam-5794	323	10	)	)	PUNCT
ejpam-5794	323	11	)	)	PUNCT
ejpam-5794	323	12	]	]	PUNCT
ejpam-5794	324	1	+	+	PUNCT
ejpam-5794	324	2	ξ	ξ	SYM
ejpam-5794	324	3	3	3	NUM
ejpam-5794	324	4	α(µ(n+1	α(µ(n+1	NUM
ejpam-5794	324	5	)	)	PUNCT
ejpam-5794	324	6	,	,	PUNCT
ejpam-5794	324	7	gµ)λ∆ξ(µn	gµ)λ∆ξ(µn	NOUN
ejpam-5794	324	8	,	,	PUNCT
ejpam-5794	324	9	gµn	gµn	PROPN
ejpam-5794	324	10	)	)	PUNCT
ejpam-5794	324	11	,	,	PUNCT
ejpam-5794	324	12	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	324	13	,	,	PUNCT
ejpam-5794	324	14	gµ	gµ	NOUN
ejpam-5794	324	15	)	)	PUNCT
ejpam-5794	324	16	≤	≤	NOUN
ejpam-5794	324	17	(	(	PUNCT
ejpam-5794	324	18	ξ3	ξ3	NOUN
ejpam-5794	324	19	[	[	X
ejpam-5794	324	20	α(µ	α(µ	PROPN
ejpam-5794	324	21	,	,	PUNCT
ejpam-5794	324	22	µn)∆ξ(µ	µn)∆ξ(µ	X
ejpam-5794	324	23	,	,	PUNCT
ejpam-5794	324	24	µn	µn	NOUN
ejpam-5794	324	25	)	)	PUNCT
ejpam-5794	324	26	]	]	PUNCT
ejpam-5794	324	27	)	)	PUNCT
ejpam-5794	324	28	(	(	PUNCT
ejpam-5794	324	29	1−	1−	NUM
ejpam-5794	324	30	ξ	ξ	PROPN
ejpam-5794	324	31	3λα(µ(n+1	3λα(µ(n+1	PROPN
ejpam-5794	324	32	)	)	PUNCT
ejpam-5794	324	33	,	,	PUNCT
ejpam-5794	324	34	gµ	gµ	NOUN
ejpam-5794	324	35	)	)	PUNCT
ejpam-5794	324	36	)	)	PUNCT
ejpam-5794	325	1	e	e	X
ejpam-5794	325	2	(	(	PUNCT
ejpam-5794	325	3	1	1	NUM
ejpam-5794	325	4	)	)	PUNCT
ejpam-5794	325	5	+	+	CCONJ
ejpam-5794	325	6	(	(	PUNCT
ejpam-5794	325	7	ξ3	ξ3	NOUN
ejpam-5794	325	8	[	[	X
ejpam-5794	325	9	α(µn	α(µn	NUM
ejpam-5794	325	10	,	,	PUNCT
ejpam-5794	325	11	µ(n+1	µ(n+1	NUM
ejpam-5794	325	12	)	)	PUNCT
ejpam-5794	325	13	)	)	PUNCT
ejpam-5794	326	1	+	+	PUNCT
ejpam-5794	326	2	λα(µ(n+1	λα(µ(n+1	NOUN
ejpam-5794	326	3	)	)	PUNCT
ejpam-5794	326	4	,	,	PUNCT
ejpam-5794	326	5	gµ	gµ	NOUN
ejpam-5794	326	6	)	)	PUNCT
ejpam-5794	326	7	]	]	PUNCT
ejpam-5794	326	8	)	)	PUNCT
ejpam-5794	326	9	(	(	PUNCT
ejpam-5794	326	10	1−	1−	NUM
ejpam-5794	326	11	ξ	ξ	PROPN
ejpam-5794	326	12	3λα(µ(n+1	3λα(µ(n+1	PROPN
ejpam-5794	326	13	)	)	PUNCT
ejpam-5794	326	14	,	,	PUNCT
ejpam-5794	326	15	gµ	gµ	NOUN
ejpam-5794	326	16	)	)	PUNCT
ejpam-5794	326	17	)	)	PUNCT
ejpam-5794	326	18	for	for	ADP
ejpam-5794	326	19	each	each	DET
ejpam-5794	326	20	µ	µ	PRON
ejpam-5794	326	21	∈	∈	NOUN
ejpam-5794	326	22	ℵ	ℵ	NOUN
ejpam-5794	326	23	,	,	PUNCT
ejpam-5794	326	24	lim	lim	PROPN
ejpam-5794	326	25	n−→+∞	n−→+∞	PROPN
ejpam-5794	326	26	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	326	27	,	,	PUNCT
ejpam-5794	326	28	µ(n+1	µ(n+1	NUM
ejpam-5794	326	29	)	)	PUNCT
ejpam-5794	326	30	)	)	PUNCT
ejpam-5794	326	31	≤	≤	NUM
ejpam-5794	326	32	1	1	NUM
ejpam-5794	326	33	,	,	PUNCT
ejpam-5794	326	34	lim	lim	PROPN
ejpam-5794	326	35	n−→+∞	n−→+∞	PROPN
ejpam-5794	326	36	∆ξ(µn	∆ξ(µn	PROPN
ejpam-5794	326	37	,	,	PUNCT
ejpam-5794	326	38	µ),and	µ),and	PROPN
ejpam-5794	326	39	lim	lim	PROPN
ejpam-5794	326	40	n−→+∞	n−→+∞	PROPN
ejpam-5794	326	41	∆ξ(µ	∆ξ(µ	PROPN
ejpam-5794	326	42	,	,	PUNCT
ejpam-5794	326	43	µn	µn	NOUN
ejpam-5794	326	44	)	)	PUNCT
ejpam-5794	326	45	exist	exist	VERB
ejpam-5794	326	46	and	and	CCONJ
ejpam-5794	326	47	finite	finite	PROPN
ejpam-5794	326	48	.	.	PUNCT
ejpam-5794	327	1	therefore	therefore	ADV
ejpam-5794	327	2	,	,	PUNCT
ejpam-5794	327	3	by	by	ADP
ejpam-5794	327	4	taking	take	VERB
ejpam-5794	327	5	lim	lim	PROPN
ejpam-5794	327	6	n−→+∞	n−→+∞	PROPN
ejpam-5794	327	7	in	in	ADP
ejpam-5794	327	8	(	(	PUNCT
ejpam-5794	327	9	e	e	NOUN
ejpam-5794	327	10	)	)	PUNCT
ejpam-5794	327	11	and	and	CCONJ
ejpam-5794	327	12	using	use	VERB
ejpam-5794	327	13	(	(	PUNCT
ejpam-5794	327	14	b	b	NOUN
ejpam-5794	327	15	)	)	PUNCT
ejpam-5794	327	16	and	and	CCONJ
ejpam-5794	327	17	(	(	PUNCT
ejpam-5794	327	18	c	c	NOUN
ejpam-5794	327	19	)	)	PUNCT
ejpam-5794	327	20	,	,	PUNCT
ejpam-5794	327	21	we	we	PRON
ejpam-5794	327	22	obtain	obtain	VERB
ejpam-5794	327	23	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	327	24	,	,	PUNCT
ejpam-5794	327	25	gµ	gµ	NOUN
ejpam-5794	327	26	)	)	PUNCT
ejpam-5794	327	27	=	=	SYM
ejpam-5794	328	1	0	0	X
ejpam-5794	328	2	.	.	PUNCT
ejpam-5794	329	1	(	(	PUNCT
ejpam-5794	329	2	f	f	X
ejpam-5794	329	3	)	)	PUNCT
ejpam-5794	329	4	this	this	PRON
ejpam-5794	329	5	shows	show	VERB
ejpam-5794	329	6	that	that	SCONJ
ejpam-5794	329	7	µ	µ	NOUN
ejpam-5794	329	8	=	=	SYM
ejpam-5794	329	9	gµ.	gµ.	NOUN
ejpam-5794	329	10	for	for	ADP
ejpam-5794	329	11	uniqueness	uniqueness	NOUN
ejpam-5794	329	12	,	,	PUNCT
ejpam-5794	329	13	consider	consider	VERB
ejpam-5794	329	14	µ	µ	PRON
ejpam-5794	329	15	̸=	̸=	PROPN
ejpam-5794	329	16	κ	κ	NOUN
ejpam-5794	329	17	with	with	ADP
ejpam-5794	329	18	κ	κ	PROPN
ejpam-5794	329	19	be	be	AUX
ejpam-5794	329	20	another	another	DET
ejpam-5794	329	21	fixed	fix	VERB
ejpam-5794	329	22	point	point	NOUN
ejpam-5794	329	23	of	of	ADP
ejpam-5794	329	24	g	g	PROPN
ejpam-5794	329	25	then	then	ADV
ejpam-5794	329	26	from	from	ADP
ejpam-5794	329	27	(	(	PUNCT
ejpam-5794	329	28	a	a	X
ejpam-5794	329	29	)	)	PUNCT
ejpam-5794	329	30	,	,	PUNCT
ejpam-5794	329	31	we	we	PRON
ejpam-5794	329	32	obtain	obtain	VERB
ejpam-5794	329	33	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	329	34	,	,	PUNCT
ejpam-5794	329	35	κ	κ	NOUN
ejpam-5794	329	36	)	)	PUNCT
ejpam-5794	329	37	=	=	SYM
ejpam-5794	329	38	∆ξ(gµ	∆ξ(gµ	NOUN
ejpam-5794	329	39	,	,	PUNCT
ejpam-5794	329	40	gκ	gκ	NOUN
ejpam-5794	329	41	)	)	PUNCT
ejpam-5794	329	42	,	,	PUNCT
ejpam-5794	329	43	≤	≤	PROPN
ejpam-5794	329	44	λ[∆ξ(µ	λ[∆ξ(µ	PROPN
ejpam-5794	329	45	,	,	PUNCT
ejpam-5794	329	46	gµ	gµ	PROPN
ejpam-5794	329	47	)	)	PUNCT
ejpam-5794	329	48	+	+	CCONJ
ejpam-5794	330	1	∆ξ(κ	∆ξ(κ	NOUN
ejpam-5794	330	2	,	,	PUNCT
ejpam-5794	330	3	gκ	gκ	NOUN
ejpam-5794	330	4	)	)	PUNCT
ejpam-5794	330	5	]	]	PUNCT
ejpam-5794	330	6	≤	≤	NUM
ejpam-5794	330	7	λ[∆ξ(µ	λ[∆ξ(µ	PROPN
ejpam-5794	330	8	,	,	PUNCT
ejpam-5794	330	9	µ	µ	NOUN
ejpam-5794	330	10	)	)	PUNCT
ejpam-5794	330	11	+	+	CCONJ
ejpam-5794	330	12	∆ξ(κ	∆ξ(κ	NOUN
ejpam-5794	330	13	,	,	PUNCT
ejpam-5794	330	14	κ	κ	NOUN
ejpam-5794	330	15	)	)	PUNCT
ejpam-5794	330	16	]	]	PUNCT
ejpam-5794	331	1	we	we	PRON
ejpam-5794	331	2	get	get	VERB
ejpam-5794	331	3	,	,	PUNCT
ejpam-5794	331	4	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	331	5	,	,	PUNCT
ejpam-5794	331	6	κ	κ	NOUN
ejpam-5794	331	7	)	)	PUNCT
ejpam-5794	331	8	=	=	SYM
ejpam-5794	331	9	0	0	NUM
ejpam-5794	331	10	,	,	PUNCT
ejpam-5794	331	11	where	where	SCONJ
ejpam-5794	331	12	∆ξ(µ	∆ξ(µ	NOUN
ejpam-5794	331	13	,	,	PUNCT
ejpam-5794	331	14	µ	µ	NOUN
ejpam-5794	331	15	)	)	PUNCT
ejpam-5794	331	16	=	=	SYM
ejpam-5794	331	17	0	0	NUM
ejpam-5794	331	18	and	and	CCONJ
ejpam-5794	331	19	∆ξ(κ	∆ξ(κ	NOUN
ejpam-5794	331	20	,	,	PUNCT
ejpam-5794	331	21	κ	κ	NOUN
ejpam-5794	331	22	)	)	PUNCT
ejpam-5794	331	23	=	=	SYM
ejpam-5794	332	1	0	0	X
ejpam-5794	332	2	.	.	PUNCT
ejpam-5794	333	1	hence	hence	ADV
ejpam-5794	333	2	∆ξ(µ	∆ξ(µ	NUM
ejpam-5794	333	3	,	,	PUNCT
ejpam-5794	333	4	κ	κ	NOUN
ejpam-5794	333	5	)	)	PUNCT
ejpam-5794	333	6	=	=	SYM
ejpam-5794	333	7	0	0	NUM
ejpam-5794	333	8	,	,	PUNCT
ejpam-5794	333	9	this	this	PRON
ejpam-5794	333	10	implies	imply	VERB
ejpam-5794	333	11	that	that	SCONJ
ejpam-5794	333	12	µ	µ	X
ejpam-5794	333	13	=	=	SYM
ejpam-5794	333	14	κ	κ	NOUN
ejpam-5794	333	15	.	.	NOUN
ejpam-5794	333	16	hence	hence	ADV
ejpam-5794	333	17	µ	µ	X
ejpam-5794	333	18	is	be	AUX
ejpam-5794	333	19	a	a	DET
ejpam-5794	333	20	unique	unique	ADJ
ejpam-5794	333	21	fixed	fix	VERB
ejpam-5794	333	22	point	point	NOUN
ejpam-5794	333	23	of	of	ADP
ejpam-5794	333	24	g.	g.	PROPN
ejpam-5794	333	25	u.	u.	PROPN
ejpam-5794	333	26	ishtiaq	ishtiaq	PROPN
ejpam-5794	334	1	et	et	PROPN
ejpam-5794	334	2	al	al	PROPN
ejpam-5794	334	3	.	.	PUNCT
ejpam-5794	334	4	/	/	SYM
ejpam-5794	334	5	eur	eur	PROPN
ejpam-5794	334	6	.	.	PUNCT
ejpam-5794	335	1	j.	j.	PROPN
ejpam-5794	335	2	pure	pure	PROPN
ejpam-5794	335	3	appl	appl	PROPN
ejpam-5794	335	4	.	.	PROPN
ejpam-5794	335	5	math	math	PROPN
ejpam-5794	335	6	,	,	PUNCT
ejpam-5794	335	7	18	18	NUM
ejpam-5794	335	8	(	(	PUNCT
ejpam-5794	335	9	1	1	NUM
ejpam-5794	335	10	)	)	PUNCT
ejpam-5794	335	11	(	(	PUNCT
ejpam-5794	335	12	2025	2025	NUM
ejpam-5794	335	13	)	)	PUNCT
ejpam-5794	335	14	,	,	PUNCT
ejpam-5794	335	15	5794	5794	NUM
ejpam-5794	335	16	16	16	NUM
ejpam-5794	335	17	of	of	ADP
ejpam-5794	335	18	20	20	NUM
ejpam-5794	335	19	3	3	NUM
ejpam-5794	335	20	.	.	PUNCT
ejpam-5794	335	21	application	application	NOUN
ejpam-5794	335	22	fractional	fractional	ADJ
ejpam-5794	335	23	calculus	calculus	NOUN
ejpam-5794	335	24	in	in	ADP
ejpam-5794	335	25	this	this	DET
ejpam-5794	335	26	section	section	NOUN
ejpam-5794	335	27	,	,	PUNCT
ejpam-5794	335	28	we	we	PRON
ejpam-5794	335	29	use	use	VERB
ejpam-5794	335	30	corollary	corollary	ADJ
ejpam-5794	335	31	1	1	NUM
ejpam-5794	335	32	to	to	PART
ejpam-5794	335	33	find	find	VERB
ejpam-5794	335	34	the	the	DET
ejpam-5794	335	35	existence	existence	NOUN
ejpam-5794	335	36	and	and	CCONJ
ejpam-5794	335	37	uniqueness	uniqueness	NOUN
ejpam-5794	335	38	of	of	ADP
ejpam-5794	335	39	a	a	DET
ejpam-5794	335	40	solution	solution	NOUN
ejpam-5794	335	41	of	of	ADP
ejpam-5794	335	42	nonlinear	nonlinear	ADJ
ejpam-5794	335	43	fractional	fractional	ADJ
ejpam-5794	335	44	differential	differential	ADJ
ejpam-5794	335	45	equations	equation	NOUN
ejpam-5794	335	46	given	give	VERB
ejpam-5794	335	47	by	by	ADP
ejpam-5794	335	48	dα	dα	PROPN
ejpam-5794	335	49	c	c	PROPN
ejpam-5794	335	50	µ(l	µ(l	PROPN
ejpam-5794	335	51	)	)	PUNCT
ejpam-5794	335	52	=	=	SYM
ejpam-5794	335	53	f(l	f(l	PROPN
ejpam-5794	335	54	,	,	PUNCT
ejpam-5794	335	55	µ(l	µ(l	PROPN
ejpam-5794	335	56	)	)	PUNCT
ejpam-5794	335	57	)	)	PUNCT
ejpam-5794	336	1	(	(	PUNCT
ejpam-5794	336	2	l	l	NOUN
ejpam-5794	336	3	∈	∈	PROPN
ejpam-5794	336	4	(	(	PUNCT
ejpam-5794	336	5	0	0	NUM
ejpam-5794	336	6	,	,	PUNCT
ejpam-5794	336	7	1	1	NUM
ejpam-5794	336	8	)	)	PUNCT
ejpam-5794	336	9	,	,	PUNCT
ejpam-5794	336	10	α	α	PROPN
ejpam-5794	336	11	∈	∈	PROPN
ejpam-5794	336	12	(	(	PUNCT
ejpam-5794	336	13	1	1	NUM
ejpam-5794	336	14	,	,	PUNCT
ejpam-5794	336	15	2	2	NUM
ejpam-5794	336	16	]	]	NUM
ejpam-5794	336	17	)	)	PUNCT
ejpam-5794	336	18	,	,	PUNCT
ejpam-5794	336	19	with	with	ADP
ejpam-5794	336	20	boundary	boundary	ADJ
ejpam-5794	336	21	conditions	condition	NOUN
ejpam-5794	336	22	µ(0	µ(0	NOUN
ejpam-5794	336	23	)	)	PUNCT
ejpam-5794	336	24	=	=	SYM
ejpam-5794	336	25	0	0	NUM
ejpam-5794	336	26	,	,	PUNCT
ejpam-5794	336	27	µ′(0	µ′(0	X
ejpam-5794	336	28	)	)	PUNCT
ejpam-5794	336	29	=	=	SYM
ejpam-5794	336	30	iµ(l)l	iµ(l)l	PROPN
ejpam-5794	336	31	∈	∈	PROPN
ejpam-5794	336	32	(	(	PUNCT
ejpam-5794	336	33	0	0	NUM
ejpam-5794	336	34	,	,	PUNCT
ejpam-5794	336	35	1),where	1),where	NUM
ejpam-5794	336	36	dα	dα	VERB
ejpam-5794	336	37	c	c	PROPN
ejpam-5794	336	38	means	mean	VERB
ejpam-5794	336	39	caputo	caputo	PROPN
ejpam-5794	336	40	fractional	fractional	PROPN
ejpam-5794	336	41	derivative	derivative	NOUN
ejpam-5794	336	42	of	of	ADP
ejpam-5794	336	43	order	order	NOUN
ejpam-5794	336	44	α	α	NOUN
ejpam-5794	336	45	,	,	PUNCT
ejpam-5794	336	46	defined	define	VERB
ejpam-5794	336	47	by	by	ADP
ejpam-5794	336	48	dα	dα	PROPN
ejpam-5794	336	49	c	c	PROPN
ejpam-5794	336	50	f(l	f(l	PROPN
ejpam-5794	336	51	)	)	PUNCT
ejpam-5794	336	52	=	=	SYM
ejpam-5794	336	53	1	1	NUM
ejpam-5794	336	54	(	(	PUNCT
ejpam-5794	336	55	γ(n−	γ(n−	PROPN
ejpam-5794	336	56	α	α	NOUN
ejpam-5794	336	57	)	)	PUNCT
ejpam-5794	336	58	)	)	PUNCT
ejpam-5794	337	1	l∫	l∫	NUM
ejpam-5794	337	2	0	0	PUNCT
ejpam-5794	338	1	(	(	PUNCT
ejpam-5794	338	2	l	l	NOUN
ejpam-5794	338	3	−	−	PROPN
ejpam-5794	338	4	ω̄)(n−α−1)fn(ω̄)∆ω	ω̄)(n−α−1)fn(ω̄)∆ω	NUM
ejpam-5794	338	5	(	(	PUNCT
ejpam-5794	338	6	n−	n−	NOUN
ejpam-5794	338	7	1	1	NUM
ejpam-5794	338	8	<	<	X
ejpam-5794	338	9	α	α	X
ejpam-5794	338	10	<	<	X
ejpam-5794	338	11	n	n	CCONJ
ejpam-5794	338	12	,	,	PUNCT
ejpam-5794	338	13	n	n	NOUN
ejpam-5794	338	14	=	=	PUNCT
ejpam-5794	339	1	[	[	X
ejpam-5794	339	2	α	α	X
ejpam-5794	339	3	]	]	X
ejpam-5794	339	4	+	+	NOUN
ejpam-5794	339	5	1	1	X
ejpam-5794	339	6	)	)	PUNCT
ejpam-5794	339	7	and	and	CCONJ
ejpam-5794	339	8	f	f	NOUN
ejpam-5794	339	9	:	:	PUNCT
ejpam-5794	340	1	[	[	X
ejpam-5794	340	2	0	0	NUM
ejpam-5794	340	3	,	,	PUNCT
ejpam-5794	340	4	1]×	1]×	NUM
ejpam-5794	340	5	r	r	NOUN
ejpam-5794	340	6	−→	−→	NOUN
ejpam-5794	340	7	r+	r+	NOUN
ejpam-5794	340	8	is	be	AUX
ejpam-5794	340	9	a	a	DET
ejpam-5794	340	10	continuous	continuous	ADJ
ejpam-5794	340	11	function	function	NOUN
ejpam-5794	340	12	.	.	PUNCT
ejpam-5794	341	1	we	we	PRON
ejpam-5794	341	2	assume	assume	VERB
ejpam-5794	341	3	ℵ	ℵ	DET
ejpam-5794	341	4	=	=	SYM
ejpam-5794	341	5	c([0	c([0	NOUN
ejpam-5794	341	6	,	,	PUNCT
ejpam-5794	341	7	1],r	1],r	NUM
ejpam-5794	341	8	)	)	PUNCT
ejpam-5794	341	9	from[0	from[0	NOUN
ejpam-5794	341	10	,	,	PUNCT
ejpam-5794	341	11	1	1	NUM
ejpam-5794	341	12	]	]	PUNCT
ejpam-5794	341	13	into	into	ADP
ejpam-5794	341	14	r	r	NOUN
ejpam-5794	341	15	with	with	ADP
ejpam-5794	341	16	supremum	supremum	ADJ
ejpam-5794	341	17	|µ|	|µ|	PROPN
ejpam-5794	341	18	=	=	NOUN
ejpam-5794	341	19	sup	sup	NOUN
ejpam-5794	341	20	l∈[0,1	l∈[0,1	NOUN
ejpam-5794	341	21	]	]	PUNCT
ejpam-5794	341	22	|µ(l)|.the	|µ(l)|.the	DET
ejpam-5794	341	23	riemann	riemann	PROPN
ejpam-5794	341	24	-	-	PUNCT
ejpam-5794	341	25	liouville	liouville	VERB
ejpam-5794	341	26	fractional	fractional	ADJ
ejpam-5794	341	27	integral	integral	ADJ
ejpam-5794	341	28	of	of	ADP
ejpam-5794	341	29	order	order	NOUN
ejpam-5794	341	30	α	α	NOUN
ejpam-5794	341	31	is	be	AUX
ejpam-5794	341	32	given	give	VERB
ejpam-5794	341	33	by	by	ADP
ejpam-5794	341	34	iαf(l	iαf(l	PROPN
ejpam-5794	341	35	)	)	PUNCT
ejpam-5794	341	36	=	=	SYM
ejpam-5794	341	37	1	1	NUM
ejpam-5794	341	38	γ(α	γ(α	NOUN
ejpam-5794	341	39	)	)	PUNCT
ejpam-5794	341	40	l∫	l∫	NUM
ejpam-5794	341	41	0	0	PUNCT
ejpam-5794	341	42	(	(	PUNCT
ejpam-5794	341	43	l	l	NOUN
ejpam-5794	341	44	−	−	PROPN
ejpam-5794	341	45	ω)(α−1)f(ω)∆ω	ω)(α−1)f(ω)∆ω	PROPN
ejpam-5794	341	46	.	.	PUNCT
ejpam-5794	342	1	(	(	PUNCT
ejpam-5794	342	2	α	α	X
ejpam-5794	342	3	>	>	X
ejpam-5794	342	4	0	0	NUM
ejpam-5794	342	5	)	)	PUNCT
ejpam-5794	342	6	initially	initially	ADV
ejpam-5794	342	7	,	,	PUNCT
ejpam-5794	342	8	we	we	PRON
ejpam-5794	342	9	give	give	VERB
ejpam-5794	342	10	reasonable	reasonable	ADJ
ejpam-5794	342	11	form	form	NOUN
ejpam-5794	342	12	of	of	ADP
ejpam-5794	342	13	a	a	DET
ejpam-5794	342	14	nonlinear	nonlinear	ADJ
ejpam-5794	342	15	fractional	fractional	ADJ
ejpam-5794	342	16	differential	differential	ADJ
ejpam-5794	342	17	equation	equation	NOUN
ejpam-5794	342	18	and	and	CCONJ
ejpam-5794	342	19	then	then	ADV
ejpam-5794	342	20	inquest	inquest	VERB
ejpam-5794	342	21	the	the	DET
ejpam-5794	342	22	existence	existence	NOUN
ejpam-5794	342	23	of	of	ADP
ejpam-5794	342	24	a	a	DET
ejpam-5794	342	25	solution	solution	NOUN
ejpam-5794	342	26	.	.	PUNCT
ejpam-5794	343	1	now	now	ADV
ejpam-5794	343	2	,	,	PUNCT
ejpam-5794	343	3	we	we	PRON
ejpam-5794	343	4	assume	assume	VERB
ejpam-5794	343	5	the	the	DET
ejpam-5794	343	6	fractional	fractional	ADJ
ejpam-5794	343	7	differential	differential	ADJ
ejpam-5794	343	8	equation	equation	NOUN
ejpam-5794	343	9	given	give	VERB
ejpam-5794	343	10	by	by	ADP
ejpam-5794	343	11	dα	dα	PROPN
ejpam-5794	343	12	c	c	PROPN
ejpam-5794	343	13	µ(l	µ(l	PROPN
ejpam-5794	343	14	)	)	PUNCT
ejpam-5794	343	15	=	=	SYM
ejpam-5794	343	16	f(l	f(l	PROPN
ejpam-5794	343	17	,	,	PUNCT
ejpam-5794	343	18	µ(l	µ(l	PROPN
ejpam-5794	343	19	)	)	PUNCT
ejpam-5794	343	20	)	)	PUNCT
ejpam-5794	344	1	(	(	PUNCT
ejpam-5794	344	2	l	l	NOUN
ejpam-5794	344	3	∈	∈	PROPN
ejpam-5794	344	4	(	(	PUNCT
ejpam-5794	344	5	0	0	NUM
ejpam-5794	344	6	,	,	PUNCT
ejpam-5794	344	7	1	1	NUM
ejpam-5794	344	8	)	)	PUNCT
ejpam-5794	344	9	,	,	PUNCT
ejpam-5794	344	10	α	α	PROPN
ejpam-5794	344	11	∈	∈	PROPN
ejpam-5794	344	12	(	(	PUNCT
ejpam-5794	344	13	1	1	NUM
ejpam-5794	344	14	,	,	PUNCT
ejpam-5794	344	15	2	2	NUM
ejpam-5794	344	16	]	]	NUM
ejpam-5794	344	17	)	)	PUNCT
ejpam-5794	344	18	,	,	PUNCT
ejpam-5794	344	19	(	(	PUNCT
ejpam-5794	344	20	3.1	3.1	NUM
ejpam-5794	344	21	)	)	PUNCT
ejpam-5794	344	22	with	with	ADP
ejpam-5794	344	23	the	the	DET
ejpam-5794	344	24	boundary	boundary	ADJ
ejpam-5794	344	25	conditions	condition	NOUN
ejpam-5794	344	26	µ(0	µ(0	NOUN
ejpam-5794	344	27	)	)	PUNCT
ejpam-5794	344	28	=	=	SYM
ejpam-5794	344	29	0	0	NUM
ejpam-5794	344	30	,	,	PUNCT
ejpam-5794	344	31	µ′(0	µ′(0	X
ejpam-5794	344	32	)	)	PUNCT
ejpam-5794	344	33	=	=	SYM
ejpam-5794	344	34	iµ(l)(l	iµ(l)(l	NOUN
ejpam-5794	344	35	∈	∈	NOUN
ejpam-5794	344	36	(	(	PUNCT
ejpam-5794	344	37	0	0	NUM
ejpam-5794	344	38	,	,	PUNCT
ejpam-5794	344	39	1	1	NUM
ejpam-5794	344	40	)	)	PUNCT
ejpam-5794	344	41	)	)	PUNCT
ejpam-5794	344	42	,	,	PUNCT
ejpam-5794	344	43	where	where	SCONJ
ejpam-5794	344	44	i	i	PRON
ejpam-5794	344	45	f	f	X
ejpam-5794	344	46	:	:	PUNCT
ejpam-5794	345	1	[	[	X
ejpam-5794	345	2	0	0	NUM
ejpam-5794	345	3	,	,	PUNCT
ejpam-5794	345	4	1]×r	1]×r	NUM
ejpam-5794	345	5	−→	−→	NOUN
ejpam-5794	345	6	r+	r+	NOUN
ejpam-5794	345	7	is	be	AUX
ejpam-5794	345	8	a	a	DET
ejpam-5794	345	9	continuous	continuous	ADJ
ejpam-5794	345	10	function	function	NOUN
ejpam-5794	345	11	,	,	PUNCT
ejpam-5794	345	12	ii	ii	PROPN
ejpam-5794	345	13	µ(l	µ(l	PROPN
ejpam-5794	345	14	)	)	PUNCT
ejpam-5794	345	15	:	:	PUNCT
ejpam-5794	346	1	[	[	X
ejpam-5794	346	2	0	0	NUM
ejpam-5794	346	3	,	,	PUNCT
ejpam-5794	346	4	1	1	NUM
ejpam-5794	346	5	]	]	X
ejpam-5794	346	6	−→	−→	NOUN
ejpam-5794	346	7	r	r	NOUN
ejpam-5794	346	8	is	be	AUX
ejpam-5794	346	9	continuous	continuous	ADJ
ejpam-5794	346	10	,	,	PUNCT
ejpam-5794	346	11	meet	meet	VERB
ejpam-5794	346	12	the	the	DET
ejpam-5794	346	13	below	below	ADJ
ejpam-5794	346	14	conditions	condition	NOUN
ejpam-5794	347	1	|f(l	|f(l	PROPN
ejpam-5794	347	2	,	,	PUNCT
ejpam-5794	347	3	µ)−	µ)−	PROPN
ejpam-5794	347	4	f(l	f(l	NOUN
ejpam-5794	347	5	,	,	PUNCT
ejpam-5794	347	6	κ)|	κ)|	NOUN
ejpam-5794	347	7	≤	≤	NOUN
ejpam-5794	347	8	l|µ−	l|µ−	ADP
ejpam-5794	347	9	κ|	κ|	PROPN
ejpam-5794	347	10	,	,	PUNCT
ejpam-5794	347	11	for	for	ADP
ejpam-5794	347	12	all	all	DET
ejpam-5794	347	13	l	l	NOUN
ejpam-5794	347	14	∈	∈	PROPN
ejpam-5794	348	1	[	[	X
ejpam-5794	348	2	0	0	NUM
ejpam-5794	348	3	,	,	PUNCT
ejpam-5794	348	4	1	1	NUM
ejpam-5794	348	5	]	]	PUNCT
ejpam-5794	348	6	,	,	PUNCT
ejpam-5794	348	7	l	l	NOUN
ejpam-5794	348	8	is	be	AUX
ejpam-5794	348	9	a	a	DET
ejpam-5794	348	10	constant	constant	ADJ
ejpam-5794	348	11	with	with	ADP
ejpam-5794	348	12	lπ	lπ	PROPN
ejpam-5794	348	13	<	<	X
ejpam-5794	348	14	1	1	NUM
ejpam-5794	348	15	,	,	PUNCT
ejpam-5794	348	16	where	where	SCONJ
ejpam-5794	348	17	π	π	NOUN
ejpam-5794	348	18	=	=	SYM
ejpam-5794	348	19	1	1	NUM
ejpam-5794	348	20	γ(α+	γ(α+	DET
ejpam-5794	348	21	1	1	NUM
ejpam-5794	348	22	)	)	PUNCT
ejpam-5794	348	23	+	+	CCONJ
ejpam-5794	348	24	2κ(α+1)γ(α	2κ(α+1)γ(α	NUM
ejpam-5794	348	25	)	)	PUNCT
ejpam-5794	348	26	(	(	PUNCT
ejpam-5794	348	27	2−	2−	NUM
ejpam-5794	348	28	κ2)γ(α+	κ2)γ(α+	NUM
ejpam-5794	348	29	1	1	NUM
ejpam-5794	348	30	)	)	PUNCT
ejpam-5794	348	31	.	.	PUNCT
ejpam-5794	349	1	u.	u.	PROPN
ejpam-5794	349	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	349	3	et	et	PROPN
ejpam-5794	349	4	al	al	PROPN
ejpam-5794	349	5	.	.	PUNCT
ejpam-5794	349	6	/	/	SYM
ejpam-5794	349	7	eur	eur	PROPN
ejpam-5794	349	8	.	.	PUNCT
ejpam-5794	350	1	j.	j.	PROPN
ejpam-5794	350	2	pure	pure	PROPN
ejpam-5794	350	3	appl	appl	PROPN
ejpam-5794	350	4	.	.	PROPN
ejpam-5794	350	5	math	math	PROPN
ejpam-5794	350	6	,	,	PUNCT
ejpam-5794	350	7	18	18	NUM
ejpam-5794	350	8	(	(	PUNCT
ejpam-5794	350	9	1	1	NUM
ejpam-5794	350	10	)	)	PUNCT
ejpam-5794	350	11	(	(	PUNCT
ejpam-5794	350	12	2025	2025	NUM
ejpam-5794	350	13	)	)	PUNCT
ejpam-5794	350	14	,	,	PUNCT
ejpam-5794	350	15	5794	5794	NUM
ejpam-5794	350	16	17	17	NUM
ejpam-5794	350	17	of	of	ADP
ejpam-5794	350	18	20	20	NUM
ejpam-5794	350	19	then	then	ADV
ejpam-5794	350	20	the	the	DET
ejpam-5794	350	21	equation	equation	NOUN
ejpam-5794	350	22	(	(	PUNCT
ejpam-5794	350	23	3.1	3.1	NUM
ejpam-5794	350	24	)	)	PUNCT
ejpam-5794	350	25	has	have	VERB
ejpam-5794	350	26	a	a	DET
ejpam-5794	350	27	unique	unique	ADJ
ejpam-5794	350	28	solution	solution	NOUN
ejpam-5794	350	29	.	.	PUNCT
ejpam-5794	351	1	proof	proof	NOUN
ejpam-5794	351	2	.	.	PUNCT
ejpam-5794	352	1	we	we	PRON
ejpam-5794	352	2	define	define	VERB
ejpam-5794	352	3	a	a	DET
ejpam-5794	352	4	crmms	crmms	NOUN
ejpam-5794	352	5	by	by	ADP
ejpam-5794	352	6	∆(µ	∆(µ	NOUN
ejpam-5794	352	7	,	,	PUNCT
ejpam-5794	352	8	κ	κ	NOUN
ejpam-5794	352	9	,	,	PUNCT
ejpam-5794	352	10	ξ	ξ	X
ejpam-5794	352	11	)	)	PUNCT
ejpam-5794	352	12	=	=	SYM
ejpam-5794	352	13	|µ(l)−	|µ(l)−	PROPN
ejpam-5794	352	14	κ(l)|	κ(l)|	X
ejpam-5794	352	15	(	(	PUNCT
ejpam-5794	352	16	ξ	ξ	PROPN
ejpam-5794	352	17	+	+	NUM
ejpam-5794	352	18	|µ(l)−	|µ(l)−	PROPN
ejpam-5794	352	19	κ(l)|	κ(l)|	NOUN
ejpam-5794	352	20	)	)	PUNCT
ejpam-5794	352	21	for	for	ADP
ejpam-5794	352	22	all	all	DET
ejpam-5794	352	23	µ	µ	NOUN
ejpam-5794	352	24	,	,	PUNCT
ejpam-5794	352	25	κ	κ	PROPN
ejpam-5794	352	26	∈	∈	PROPN
ejpam-5794	352	27	ℵ	ℵ	NOUN
ejpam-5794	352	28	,	,	PUNCT
ejpam-5794	352	29	we	we	PRON
ejpam-5794	352	30	consider	consider	VERB
ejpam-5794	352	31	|µ−	|µ−	ADJ
ejpam-5794	352	32	κ|	κ|	NOUN
ejpam-5794	352	33	=	=	SYM
ejpam-5794	352	34	sup	sup	NOUN
ejpam-5794	352	35	(	(	PUNCT
ejpam-5794	352	36	l∈[0,1	l∈[0,1	NOUN
ejpam-5794	352	37	]	]	PUNCT
ejpam-5794	352	38	)	)	PUNCT
ejpam-5794	352	39	|µ(l)−	|µ(l)−	PROPN
ejpam-5794	352	40	κ(l)|	κ(l)|	PROPN
ejpam-5794	352	41	.	.	PUNCT
ejpam-5794	353	1	we	we	PRON
ejpam-5794	353	2	define	define	VERB
ejpam-5794	353	3	a	a	DET
ejpam-5794	353	4	mapping	mapping	NOUN
ejpam-5794	353	5	ψ	ψ	X
ejpam-5794	353	6	:	:	PUNCT
ejpam-5794	353	7	ℵ	ℵ	X
ejpam-5794	353	8	→	→	SYM
ejpam-5794	353	9	ℵ	ℵ	NOUN
ejpam-5794	353	10	by	by	ADP
ejpam-5794	353	11	µ(l	µ(l	PROPN
ejpam-5794	353	12	)	)	PUNCT
ejpam-5794	353	13	=	=	SYM
ejpam-5794	353	14	1	1	NUM
ejpam-5794	353	15	γ(α	γ(α	NOUN
ejpam-5794	353	16	)	)	PUNCT
ejpam-5794	353	17	l∫	l∫	NUM
ejpam-5794	353	18	0	0	NUM
ejpam-5794	353	19	(	(	PUNCT
ejpam-5794	353	20	l−ω)(α−1)f(ω	l−ω)(α−1)f(ω	NOUN
ejpam-5794	353	21	,	,	PUNCT
ejpam-5794	353	22	µ(ω))∆ω+	µ(ω))∆ω+	ADJ
ejpam-5794	353	23	2l	2l	NUM
ejpam-5794	353	24	(	(	PUNCT
ejpam-5794	353	25	2−	2−	NUM
ejpam-5794	353	26	κ2)γ(α	κ2)γ(α	X
ejpam-5794	353	27	)	)	PUNCT
ejpam-5794	353	28	κ∫	κ∫	PROPN
ejpam-5794	353	29	0	0	NUM
ejpam-5794	354	1			PROPN
ejpam-5794	354	2	ω∫	ω∫	NOUN
ejpam-5794	354	3	0	0	NUM
ejpam-5794	354	4	(	(	PUNCT
ejpam-5794	354	5	ω	ω	NUM
ejpam-5794	354	6	−m)(α−1)f(m,µ(m))∆m	−m)(α−1)f(m,µ(m))∆m	NOUN
ejpam-5794	354	7	)	)	PUNCT
ejpam-5794	355	1	∆ω	∆ω	PROPN
ejpam-5794	356	1	(	(	PUNCT
ejpam-5794	356	2	3.2	3.2	NUM
ejpam-5794	356	3	)	)	PUNCT
ejpam-5794	356	4	for	for	ADP
ejpam-5794	356	5	all	all	DET
ejpam-5794	356	6	l	l	NOUN
ejpam-5794	356	7	∈	∈	PROPN
ejpam-5794	357	1	[	[	X
ejpam-5794	357	2	0	0	NUM
ejpam-5794	357	3	,	,	PUNCT
ejpam-5794	357	4	1	1	NUM
ejpam-5794	357	5	]	]	PUNCT
ejpam-5794	357	6	.	.	PUNCT
ejpam-5794	358	1	an	an	DET
ejpam-5794	358	2	equation	equation	NOUN
ejpam-5794	358	3	(	(	PUNCT
ejpam-5794	358	4	3.1	3.1	NUM
ejpam-5794	358	5	)	)	PUNCT
ejpam-5794	358	6	has	have	VERB
ejpam-5794	358	7	a	a	DET
ejpam-5794	358	8	solution	solution	NOUN
ejpam-5794	358	9	,	,	PUNCT
ejpam-5794	358	10	for	for	ADP
ejpam-5794	358	11	a	a	DET
ejpam-5794	358	12	function	function	NOUN
ejpam-5794	358	13	µ	µ	PRON
ejpam-5794	358	14	∈	∈	PROPN
ejpam-5794	358	15	ℵ	ℵ	ADP
ejpam-5794	358	16	iff	iff	PROPN
ejpam-5794	358	17	µ(l	µ(l	PROPN
ejpam-5794	358	18	)	)	PUNCT
ejpam-5794	358	19	=	=	SYM
ejpam-5794	358	20	ψµ(l	ψµ(l	NUM
ejpam-5794	358	21	)	)	PUNCT
ejpam-5794	358	22	for	for	ADP
ejpam-5794	358	23	all	all	DET
ejpam-5794	358	24	l	l	NOUN
ejpam-5794	358	25	∈	∈	PROPN
ejpam-5794	359	1	[	[	X
ejpam-5794	359	2	0	0	NUM
ejpam-5794	359	3	,	,	PUNCT
ejpam-5794	359	4	1	1	NUM
ejpam-5794	359	5	]	]	PUNCT
ejpam-5794	359	6	.	.	PUNCT
ejpam-5794	360	1	for	for	ADP
ejpam-5794	360	2	all	all	DET
ejpam-5794	360	3	l	l	NOUN
ejpam-5794	360	4	∈	∈	PROPN
ejpam-5794	360	5	[	[	X
ejpam-5794	360	6	0	0	NUM
ejpam-5794	360	7	,	,	PUNCT
ejpam-5794	360	8	1	1	NUM
ejpam-5794	360	9	]	]	PUNCT
ejpam-5794	360	10	,	,	PUNCT
ejpam-5794	360	11	we	we	PRON
ejpam-5794	360	12	have	have	VERB
ejpam-5794	360	13	∆(ψµ	∆(ψµ	PROPN
ejpam-5794	360	14	,	,	PUNCT
ejpam-5794	360	15	ψκ	ψκ	PROPN
ejpam-5794	360	16	,	,	PUNCT
ejpam-5794	360	17	ξ	ξ	X
ejpam-5794	360	18	)	)	PUNCT
ejpam-5794	360	19	=	=	SYM
ejpam-5794	360	20	|ψµ(l)−	|ψµ(l)−	PROPN
ejpam-5794	360	21	ψκ(l)|	ψκ(l)|	PUNCT
ejpam-5794	360	22	(	(	PUNCT
ejpam-5794	360	23	ξ	ξ	X
ejpam-5794	360	24	+	+	NUM
ejpam-5794	360	25	|ψµ(l)−	|ψµ(l)−	PROPN
ejpam-5794	360	26	ψκ(l)|	ψκ(l)|	PROPN
ejpam-5794	360	27	)	)	PUNCT
ejpam-5794	360	28	.	.	PUNCT
ejpam-5794	361	1	(	(	PUNCT
ejpam-5794	361	2	3.3	3.3	NUM
ejpam-5794	361	3	)	)	PUNCT
ejpam-5794	361	4	now	now	ADV
ejpam-5794	361	5	,	,	PUNCT
ejpam-5794	361	6	|ψµ(l)−	|ψµ(l)−	PROPN
ejpam-5794	361	7	ψκ(l)|	ψκ(l)|	PUNCT
ejpam-5794	361	8	=	=	SYM
ejpam-5794	361	9	1	1	NUM
ejpam-5794	361	10	γ(α	γ(α	NOUN
ejpam-5794	361	11	)	)	PUNCT
ejpam-5794	361	12	l∫	l∫	NUM
ejpam-5794	361	13	0	0	PUNCT
ejpam-5794	362	1	(	(	PUNCT
ejpam-5794	362	2	l	l	NOUN
ejpam-5794	362	3	−	−	PROPN
ejpam-5794	362	4	ω)(α−1)f(ω	ω)(α−1)f(ω	NUM
ejpam-5794	362	5	,	,	PUNCT
ejpam-5794	362	6	µ(ω))∆ω	µ(ω))∆ω	NOUN
ejpam-5794	363	1	+	+	CCONJ
ejpam-5794	363	2	2l	2l	NUM
ejpam-5794	363	3	(	(	PUNCT
ejpam-5794	363	4	2−	2−	NUM
ejpam-5794	363	5	κ2)γ(α	κ2)γ(α	X
ejpam-5794	363	6	)	)	PUNCT
ejpam-5794	363	7	κ∫	κ∫	PROPN
ejpam-5794	363	8	0	0	NUM
ejpam-5794	364	1			PROPN
ejpam-5794	364	2	ω∫	ω∫	NOUN
ejpam-5794	364	3	0	0	NUM
ejpam-5794	364	4	(	(	PUNCT
ejpam-5794	364	5	ω	ω	NUM
ejpam-5794	364	6	−m)(α−1)f(m,µ(m))∆m	−m)(α−1)f(m,µ(m))∆m	NOUN
ejpam-5794	364	7	)	)	PUNCT
ejpam-5794	365	1	∆ω	∆ω	PUNCT
ejpam-5794	366	1	−	−	NOUN
ejpam-5794	366	2	1	1	NUM
ejpam-5794	366	3	γ(α	γ(α	NOUN
ejpam-5794	366	4	)	)	PUNCT
ejpam-5794	366	5	l∫	l∫	NUM
ejpam-5794	366	6	0	0	PUNCT
ejpam-5794	366	7	(	(	PUNCT
ejpam-5794	366	8	l	l	NOUN
ejpam-5794	366	9	−	−	PROPN
ejpam-5794	366	10	ω)(α−1)f(ω	ω)(α−1)f(ω	NUM
ejpam-5794	366	11	,	,	PUNCT
ejpam-5794	366	12	κ(ω))∆ω	κ(ω))∆ω	PROPN
ejpam-5794	366	13	+	+	CCONJ
ejpam-5794	366	14	2l	2l	NUM
ejpam-5794	366	15	(	(	PUNCT
ejpam-5794	366	16	2−	2−	NUM
ejpam-5794	366	17	κ2)γ(α	κ2)γ(α	X
ejpam-5794	366	18	)	)	PUNCT
ejpam-5794	366	19	κ∫	κ∫	PROPN
ejpam-5794	366	20	0	0	NUM
ejpam-5794	367	1			PROPN
ejpam-5794	367	2	ω∫	ω∫	NOUN
ejpam-5794	367	3	0	0	NUM
ejpam-5794	367	4	(	(	PUNCT
ejpam-5794	367	5	ω	ω	PROPN
ejpam-5794	367	6	−m)(α−1)f(m	−m)(α−1)f(m	PROPN
ejpam-5794	367	7	,	,	PUNCT
ejpam-5794	367	8	κ(m))∆m	κ(m))∆m	NOUN
ejpam-5794	367	9	)	)	PUNCT
ejpam-5794	368	1	∆ω	∆ω	PUNCT
ejpam-5794	369	1	≤	≤	ADV
ejpam-5794	369	2	1	1	NUM
ejpam-5794	369	3	γ(α	γ(α	NOUN
ejpam-5794	369	4	)	)	PUNCT
ejpam-5794	369	5	l∫	l∫	NUM
ejpam-5794	369	6	0	0	PUNCT
ejpam-5794	369	7	(	(	PUNCT
ejpam-5794	369	8	l	l	NOUN
ejpam-5794	369	9	−	−	PROPN
ejpam-5794	369	10	ω)(α−1	ω)(α−1	PROPN
ejpam-5794	369	11	)	)	PUNCT
ejpam-5794	369	12	|f(ω	|f(ω	NOUN
ejpam-5794	369	13	,	,	PUNCT
ejpam-5794	369	14	µ(ω))−	µ(ω))−	ADJ
ejpam-5794	369	15	f(ω	f(ω	PROPN
ejpam-5794	369	16	,	,	PUNCT
ejpam-5794	369	17	κ(ω))|∆ω	κ(ω))|∆ω	PROPN
ejpam-5794	369	18	+	+	CCONJ
ejpam-5794	369	19	2l	2l	NUM
ejpam-5794	369	20	(	(	PUNCT
ejpam-5794	369	21	2−	2−	NUM
ejpam-5794	369	22	κ2)γ(α	κ2)γ(α	X
ejpam-5794	369	23	)	)	PUNCT
ejpam-5794	369	24	κ∫	κ∫	PROPN
ejpam-5794	369	25	0	0	NUM
ejpam-5794	370	1			PROPN
ejpam-5794	370	2	ω∫	ω∫	NOUN
ejpam-5794	370	3	0	0	NUM
ejpam-5794	370	4	(	(	PUNCT
ejpam-5794	370	5	ω	ω	NOUN
ejpam-5794	370	6	−m)(α−1	−m)(α−1	NOUN
ejpam-5794	370	7	)	)	PUNCT
ejpam-5794	370	8	|f(ω	|f(ω	NOUN
ejpam-5794	370	9	,	,	PUNCT
ejpam-5794	370	10	µ(m))−	µ(m))−	PROPN
ejpam-5794	370	11	f(ω	f(ω	PROPN
ejpam-5794	370	12	,	,	PUNCT
ejpam-5794	370	13	κ(m))|∆m	κ(m))|∆m	PROPN
ejpam-5794	370	14			PROPN
ejpam-5794	370	15	≤	≤	NOUN
ejpam-5794	370	16	l	l	NOUN
ejpam-5794	370	17	|µ−	|µ−	ADJ
ejpam-5794	370	18	κ|	κ|	PROPN
ejpam-5794	370	19	γ(α	γ(α	NOUN
ejpam-5794	370	20	)	)	PUNCT
ejpam-5794	371	1	l∫	l∫	NUM
ejpam-5794	371	2	0	0	PUNCT
ejpam-5794	372	1	(	(	PUNCT
ejpam-5794	372	2	l	l	NOUN
ejpam-5794	372	3	−	−	PROPN
ejpam-5794	372	4	ω)(α−1)∆ω	ω)(α−1)∆ω	PROPN
ejpam-5794	372	5	+	+	CCONJ
ejpam-5794	372	6	2l	2l	NUM
ejpam-5794	372	7	|µ−	|µ−	ADJ
ejpam-5794	372	8	κ|	κ|	PROPN
ejpam-5794	372	9	γ(α	γ(α	NOUN
ejpam-5794	372	10	)	)	PUNCT
ejpam-5794	373	1	κ∫	κ∫	PROPN
ejpam-5794	373	2	0	0	NUM
ejpam-5794	374	1			PROPN
ejpam-5794	374	2	ω∫	ω∫	NOUN
ejpam-5794	374	3	0	0	NUM
ejpam-5794	375	1	(	(	PUNCT
ejpam-5794	375	2	ω	ω	NOUN
ejpam-5794	375	3	−m)(α−1)∆m	−m)(α−1)∆m	PROPN
ejpam-5794	376	1	∆ω	∆ω	X
ejpam-5794	377	1	u.	u.	NOUN
ejpam-5794	377	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	377	3	et	et	PROPN
ejpam-5794	377	4	al	al	PROPN
ejpam-5794	377	5	.	.	PUNCT
ejpam-5794	377	6	/	/	SYM
ejpam-5794	377	7	eur	eur	PROPN
ejpam-5794	377	8	.	.	PUNCT
ejpam-5794	378	1	j.	j.	PROPN
ejpam-5794	378	2	pure	pure	PROPN
ejpam-5794	378	3	appl	appl	PROPN
ejpam-5794	378	4	.	.	PROPN
ejpam-5794	378	5	math	math	PROPN
ejpam-5794	378	6	,	,	PUNCT
ejpam-5794	378	7	18	18	NUM
ejpam-5794	378	8	(	(	PUNCT
ejpam-5794	378	9	1	1	NUM
ejpam-5794	378	10	)	)	PUNCT
ejpam-5794	378	11	(	(	PUNCT
ejpam-5794	378	12	2025	2025	NUM
ejpam-5794	378	13	)	)	PUNCT
ejpam-5794	378	14	,	,	PUNCT
ejpam-5794	378	15	5794	5794	NUM
ejpam-5794	378	16	18	18	NUM
ejpam-5794	378	17	of	of	ADP
ejpam-5794	378	18	20	20	NUM
ejpam-5794	378	19	≤	≤	NUM
ejpam-5794	378	20	l	l	NOUN
ejpam-5794	378	21	|µ−	|µ−	ADJ
ejpam-5794	378	22	κ|	κ|	PROPN
ejpam-5794	378	23	γ(α+	γ(α+	DET
ejpam-5794	378	24	1	1	NUM
ejpam-5794	378	25	)	)	PUNCT
ejpam-5794	378	26	+	+	CCONJ
ejpam-5794	378	27	2κα+1l	2κα+1l	NUM
ejpam-5794	378	28	|µ−	|µ−	ADJ
ejpam-5794	378	29	κ|γ(α	κ|γ(α	NOUN
ejpam-5794	378	30	)	)	PUNCT
ejpam-5794	378	31	(	(	PUNCT
ejpam-5794	378	32	2−	2−	NUM
ejpam-5794	378	33	κ2	κ2	NOUN
ejpam-5794	378	34	)	)	PUNCT
ejpam-5794	378	35	γ(α+	γ(α+	PRON
ejpam-5794	378	36	2	2	NUM
ejpam-5794	378	37	)	)	PUNCT
ejpam-5794	378	38	≤	≤	NUM
ejpam-5794	378	39	l	l	NOUN
ejpam-5794	378	40	|µ−	|µ−	ADJ
ejpam-5794	378	41	κ|	κ|	NOUN
ejpam-5794	378	42	(	(	PUNCT
ejpam-5794	378	43	1	1	NUM
ejpam-5794	378	44	γ(α+	γ(α+	PRON
ejpam-5794	378	45	1	1	NUM
ejpam-5794	378	46	)	)	PUNCT
ejpam-5794	378	47	+	+	NUM
ejpam-5794	378	48	2κα+1γ(α	2κα+1γ(α	NUM
ejpam-5794	378	49	)	)	PUNCT
ejpam-5794	378	50	(	(	PUNCT
ejpam-5794	378	51	2−	2−	NUM
ejpam-5794	378	52	κ2	κ2	NOUN
ejpam-5794	378	53	)	)	PUNCT
ejpam-5794	378	54	γ(α+	γ(α+	DET
ejpam-5794	378	55	2	2	NUM
ejpam-5794	378	56	)	)	PUNCT
ejpam-5794	378	57	)	)	PUNCT
ejpam-5794	379	1	=	=	SYM
ejpam-5794	379	2	lπ|µ−	lπ|µ−	PUNCT
ejpam-5794	379	3	κ|	κ|	PROPN
ejpam-5794	379	4	.	.	PROPN
ejpam-5794	380	1	from	from	ADP
ejpam-5794	380	2	the	the	DET
ejpam-5794	380	3	fact	fact	NOUN
ejpam-5794	380	4	lπ	lπ	X
ejpam-5794	380	5	<	<	X
ejpam-5794	380	6	1	1	NUM
ejpam-5794	380	7	,	,	PUNCT
ejpam-5794	380	8	34	34	NUM
ejpam-5794	380	9	≤	≤	NUM
ejpam-5794	380	10	λ	λ	X
ejpam-5794	380	11	<	<	X
ejpam-5794	380	12	1	1	NUM
ejpam-5794	380	13	,	,	PUNCT
ejpam-5794	380	14	and	and	CCONJ
ejpam-5794	380	15	(	(	PUNCT
ejpam-5794	380	16	3.3	3.3	NUM
ejpam-5794	380	17	)	)	PUNCT
ejpam-5794	380	18	,	,	PUNCT
ejpam-5794	380	19	we	we	PRON
ejpam-5794	380	20	get	get	VERB
ejpam-5794	380	21	∆(ψµ	∆(ψµ	ADP
ejpam-5794	380	22	,	,	PUNCT
ejpam-5794	380	23	ψκ	ψκ	PROPN
ejpam-5794	380	24	,	,	PUNCT
ejpam-5794	380	25	ξ	ξ	X
ejpam-5794	380	26	)	)	PUNCT
ejpam-5794	380	27	=	=	SYM
ejpam-5794	380	28	|ψµ(l)−	|ψµ(l)−	PROPN
ejpam-5794	380	29	ψκ(l)|	ψκ(l)|	PUNCT
ejpam-5794	380	30	(	(	PUNCT
ejpam-5794	380	31	ξ	ξ	X
ejpam-5794	380	32	+	+	NUM
ejpam-5794	380	33	|ψµ(l)−	|ψµ(l)−	PROPN
ejpam-5794	380	34	ψκ(l)|	ψκ(l)|	PRON
ejpam-5794	380	35	)	)	PUNCT
ejpam-5794	380	36	≤	≤	NOUN
ejpam-5794	380	37	lπ|µ−	lπ|µ−	PUNCT
ejpam-5794	381	1	κ|	κ|	PROPN
ejpam-5794	381	2	(	(	PUNCT
ejpam-5794	381	3	ξ	ξ	X
ejpam-5794	381	4	+	+	CCONJ
ejpam-5794	381	5	lπ|µ−	lπ|µ−	PROPN
ejpam-5794	381	6	κ|	κ|	PROPN
ejpam-5794	381	7	)	)	PUNCT
ejpam-5794	381	8	≤	≤	NOUN
ejpam-5794	382	1	λ|µ−	λ|µ−	CCONJ
ejpam-5794	382	2	κ|	κ|	PROPN
ejpam-5794	382	3	(	(	PUNCT
ejpam-5794	382	4	ξ	ξ	X
ejpam-5794	382	5	+	+	CCONJ
ejpam-5794	382	6	|µ−	|µ−	ADJ
ejpam-5794	382	7	κ|	κ|	NOUN
ejpam-5794	382	8	)	)	PUNCT
ejpam-5794	382	9	=	=	SYM
ejpam-5794	382	10	λ∆(µ	λ∆(µ	NOUN
ejpam-5794	382	11	,	,	PUNCT
ejpam-5794	382	12	κ	κ	NOUN
ejpam-5794	382	13	,	,	PUNCT
ejpam-5794	382	14	ξ	ξ	NOUN
ejpam-5794	382	15	)	)	PUNCT
ejpam-5794	382	16	.	.	PUNCT
ejpam-5794	383	1	observe	observe	VERB
ejpam-5794	383	2	that	that	SCONJ
ejpam-5794	383	3	all	all	DET
ejpam-5794	383	4	conditions	condition	NOUN
ejpam-5794	383	5	of	of	ADP
ejpam-5794	383	6	corollary	corollary	ADJ
ejpam-5794	383	7	1	1	NUM
ejpam-5794	383	8	are	be	AUX
ejpam-5794	383	9	fulfilled	fulfil	VERB
ejpam-5794	383	10	.	.	PUNCT
ejpam-5794	384	1	this	this	PRON
ejpam-5794	384	2	implies	imply	VERB
ejpam-5794	384	3	that	that	SCONJ
ejpam-5794	384	4	µ(l	µ(l	PROPN
ejpam-5794	384	5	)	)	PUNCT
ejpam-5794	384	6	is	be	AUX
ejpam-5794	384	7	a	a	DET
ejpam-5794	384	8	unique	unique	ADJ
ejpam-5794	384	9	fixed	fix	VERB
ejpam-5794	384	10	point	point	NOUN
ejpam-5794	384	11	of	of	ADP
ejpam-5794	384	12	ψ	ψ	X
ejpam-5794	384	13	.	.	PUNCT
ejpam-5794	385	1	open	open	ADJ
ejpam-5794	385	2	problem	problem	NOUN
ejpam-5794	385	3	3.1	3.1	NUM
ejpam-5794	385	4	introduce	introduce	NOUN
ejpam-5794	385	5	a	a	DET
ejpam-5794	385	6	new	new	ADJ
ejpam-5794	385	7	notion	notion	NOUN
ejpam-5794	385	8	to	to	PART
ejpam-5794	385	9	combine	combine	VERB
ejpam-5794	385	10	the	the	DET
ejpam-5794	385	11	structure	structure	NOUN
ejpam-5794	385	12	of	of	ADP
ejpam-5794	385	13	fuzzy	fuzzy	ADJ
ejpam-5794	385	14	sets	set	NOUN
ejpam-5794	385	15	and	and	CCONJ
ejpam-5794	385	16	crmms	crmms	NOUN
ejpam-5794	385	17	and	and	CCONJ
ejpam-5794	385	18	then	then	ADV
ejpam-5794	385	19	prove	prove	VERB
ejpam-5794	385	20	theorem	theorem	ADJ
ejpam-5794	385	21	(	(	PUNCT
ejpam-5794	385	22	2	2	NUM
ejpam-5794	385	23	)	)	PUNCT
ejpam-5794	385	24	and	and	CCONJ
ejpam-5794	385	25	theorem	theorem	VERB
ejpam-5794	385	26	(	(	PUNCT
ejpam-5794	385	27	3	3	NUM
ejpam-5794	385	28	)	)	PUNCT
ejpam-5794	385	29	in	in	ADP
ejpam-5794	385	30	the	the	DET
ejpam-5794	385	31	context	context	NOUN
ejpam-5794	385	32	of	of	ADP
ejpam-5794	385	33	fuzzy	fuzzy	ADJ
ejpam-5794	385	34	crmms	crmms	NOUN
ejpam-5794	385	35	.	.	PUNCT
ejpam-5794	386	1	4	4	X
ejpam-5794	386	2	.	.	X
ejpam-5794	386	3	conclusion	conclusion	NOUN
ejpam-5794	386	4	in	in	ADP
ejpam-5794	386	5	this	this	DET
ejpam-5794	386	6	manuscript	manuscript	NOUN
ejpam-5794	386	7	,	,	PUNCT
ejpam-5794	386	8	we	we	PRON
ejpam-5794	386	9	established	establish	VERB
ejpam-5794	386	10	the	the	DET
ejpam-5794	386	11	notions	notion	NOUN
ejpam-5794	386	12	of	of	ADP
ejpam-5794	386	13	rectangular	rectangular	ADJ
ejpam-5794	386	14	modular	modular	ADJ
ejpam-5794	386	15	metric	metric	ADJ
ejpam-5794	386	16	space	space	NOUN
ejpam-5794	386	17	and	and	CCONJ
ejpam-5794	386	18	controlled	control	VERB
ejpam-5794	386	19	rectangular	rectangular	ADJ
ejpam-5794	386	20	modular	modular	ADJ
ejpam-5794	386	21	metric	metric	ADJ
ejpam-5794	386	22	space	space	NOUN
ejpam-5794	386	23	and	and	CCONJ
ejpam-5794	386	24	proved	prove	VERB
ejpam-5794	386	25	several	several	ADJ
ejpam-5794	386	26	fixed	fix	VERB
ejpam-5794	386	27	point	point	NOUN
ejpam-5794	386	28	results	result	NOUN
ejpam-5794	386	29	.	.	PUNCT
ejpam-5794	387	1	also	also	ADV
ejpam-5794	387	2	,	,	PUNCT
ejpam-5794	387	3	we	we	PRON
ejpam-5794	387	4	provide	provide	VERB
ejpam-5794	387	5	some	some	DET
ejpam-5794	387	6	non	non	ADJ
ejpam-5794	387	7	-	-	ADJ
ejpam-5794	387	8	trivial	trivial	ADJ
ejpam-5794	387	9	examples	example	NOUN
ejpam-5794	387	10	with	with	ADP
ejpam-5794	387	11	some	some	DET
ejpam-5794	387	12	graphical	graphical	ADJ
ejpam-5794	387	13	views	view	NOUN
ejpam-5794	387	14	and	and	CCONJ
ejpam-5794	387	15	an	an	DET
ejpam-5794	387	16	application	application	NOUN
ejpam-5794	387	17	to	to	ADP
ejpam-5794	387	18	fractional	fractional	ADJ
ejpam-5794	387	19	calculus	calculus	NOUN
ejpam-5794	387	20	.	.	PUNCT
ejpam-5794	388	1	these	these	DET
ejpam-5794	388	2	results	result	NOUN
ejpam-5794	388	3	are	be	AUX
ejpam-5794	388	4	in	in	ADP
ejpam-5794	388	5	more	more	ADV
ejpam-5794	388	6	generalized	generalized	ADJ
ejpam-5794	388	7	form	form	NOUN
ejpam-5794	388	8	in	in	ADP
ejpam-5794	388	9	the	the	DET
ejpam-5794	388	10	existing	exist	VERB
ejpam-5794	388	11	literature	literature	NOUN
ejpam-5794	388	12	.	.	PUNCT
ejpam-5794	389	1	this	this	DET
ejpam-5794	389	2	work	work	NOUN
ejpam-5794	389	3	can	can	AUX
ejpam-5794	389	4	easily	easily	ADV
ejpam-5794	389	5	be	be	AUX
ejpam-5794	389	6	extended	extend	VERB
ejpam-5794	389	7	in	in	ADP
ejpam-5794	389	8	the	the	DET
ejpam-5794	389	9	combined	combined	ADJ
ejpam-5794	389	10	structure	structure	NOUN
ejpam-5794	389	11	of	of	ADP
ejpam-5794	389	12	fuzzy	fuzzy	ADJ
ejpam-5794	389	13	sets	set	NOUN
ejpam-5794	389	14	and	and	CCONJ
ejpam-5794	389	15	controlled	control	VERB
ejpam-5794	389	16	rectangular	rectangular	ADJ
ejpam-5794	389	17	modular	modular	ADJ
ejpam-5794	389	18	metric	metric	ADJ
ejpam-5794	389	19	space	space	NOUN
ejpam-5794	389	20	.	.	PUNCT
ejpam-5794	390	1	references	reference	NOUN
ejpam-5794	390	2	[	[	X
ejpam-5794	390	3	1	1	NUM
ejpam-5794	390	4	]	]	PUNCT
ejpam-5794	390	5	m.	m.	NOUN
ejpam-5794	390	6	abbas	abbas	PROPN
ejpam-5794	390	7	,	,	PUNCT
ejpam-5794	390	8	f.	f.	PROPN
ejpam-5794	390	9	lael	lael	PROPN
ejpam-5794	390	10	,	,	PUNCT
ejpam-5794	390	11	and	and	CCONJ
ejpam-5794	390	12	n.	n.	PROPN
ejpam-5794	390	13	saleem	saleem	PROPN
ejpam-5794	390	14	.	.	PUNCT
ejpam-5794	391	1	fuzzy	fuzzy	ADJ
ejpam-5794	391	2	b	b	X
ejpam-5794	391	3	-	-	PUNCT
ejpam-5794	391	4	metric	metric	ADJ
ejpam-5794	391	5	spaces	space	NOUN
ejpam-5794	391	6	:	:	PUNCT
ejpam-5794	391	7	fixed	fix	VERB
ejpam-5794	391	8	point	point	NOUN
ejpam-5794	391	9	results	result	VERB
ejpam-5794	391	10	for	for	ADP
ejpam-5794	391	11	ψ	ψ	NOUN
ejpam-5794	391	12	-	-	NOUN
ejpam-5794	391	13	contraction	contraction	NOUN
ejpam-5794	391	14	correspondences	correspondence	NOUN
ejpam-5794	391	15	and	and	CCONJ
ejpam-5794	391	16	their	their	PRON
ejpam-5794	391	17	application	application	NOUN
ejpam-5794	391	18	.	.	PUNCT
ejpam-5794	392	1	axioms	axiom	NOUN
ejpam-5794	392	2	,	,	PUNCT
ejpam-5794	392	3	9(2):36	9(2):36	NOUN
ejpam-5794	392	4	,	,	PUNCT
ejpam-5794	392	5	2020	2020	NUM
ejpam-5794	392	6	.	.	PUNCT
ejpam-5794	393	1	[	[	X
ejpam-5794	393	2	2	2	NUM
ejpam-5794	393	3	]	]	PUNCT
ejpam-5794	393	4	m.	m.	NOUN
ejpam-5794	393	5	abbas	abbas	PROPN
ejpam-5794	393	6	,	,	PUNCT
ejpam-5794	393	7	n.	n.	PROPN
ejpam-5794	393	8	saleem	saleem	PROPN
ejpam-5794	393	9	,	,	PUNCT
ejpam-5794	393	10	and	and	CCONJ
ejpam-5794	393	11	m.	m.	PROPN
ejpam-5794	393	12	de	de	PROPN
ejpam-5794	393	13	la	la	PROPN
ejpam-5794	393	14	sen	sen	PROPN
ejpam-5794	393	15	.	.	PROPN
ejpam-5794	393	16	optimal	optimal	ADJ
ejpam-5794	393	17	coincidence	coincidence	NOUN
ejpam-5794	393	18	point	point	NOUN
ejpam-5794	393	19	results	result	NOUN
ejpam-5794	393	20	in	in	ADP
ejpam-5794	393	21	partially	partially	ADV
ejpam-5794	393	22	ordered	order	VERB
ejpam-5794	393	23	non	non	ADJ
ejpam-5794	393	24	-	-	ADJ
ejpam-5794	393	25	archimedean	archimedean	ADJ
ejpam-5794	393	26	fuzzy	fuzzy	ADJ
ejpam-5794	393	27	metric	metric	ADJ
ejpam-5794	393	28	spaces	space	NOUN
ejpam-5794	393	29	.	.	PUNCT
ejpam-5794	394	1	fixed	fix	VERB
ejpam-5794	394	2	point	point	NOUN
ejpam-5794	394	3	theory	theory	NOUN
ejpam-5794	394	4	and	and	CCONJ
ejpam-5794	394	5	applications	application	NOUN
ejpam-5794	394	6	,	,	PUNCT
ejpam-5794	394	7	2016(1):1–18	2016(1):1–18	NUM
ejpam-5794	394	8	,	,	PUNCT
ejpam-5794	394	9	2016	2016	NUM
ejpam-5794	394	10	.	.	PUNCT
ejpam-5794	395	1	[	[	X
ejpam-5794	395	2	3	3	NUM
ejpam-5794	395	3	]	]	PUNCT
ejpam-5794	395	4	a.	a.	NOUN
ejpam-5794	395	5	a.	a.	PROPN
ejpam-5794	395	6	abdou	abdou	PROPN
ejpam-5794	395	7	.	.	PUNCT
ejpam-5794	396	1	some	some	DET
ejpam-5794	396	2	fixed	fix	VERB
ejpam-5794	396	3	point	point	NOUN
ejpam-5794	396	4	theorems	theorem	NOUN
ejpam-5794	396	5	in	in	ADP
ejpam-5794	396	6	modular	modular	ADJ
ejpam-5794	396	7	metric	metric	ADJ
ejpam-5794	396	8	spaces	space	NOUN
ejpam-5794	396	9	.	.	PUNCT
ejpam-5794	397	1	j.	j.	PROPN
ejpam-5794	397	2	nonlinear	nonlinear	PROPN
ejpam-5794	397	3	sci	sci	PROPN
ejpam-5794	397	4	.	.	PUNCT
ejpam-5794	397	5	appl	appl	PROPN
ejpam-5794	397	6	,	,	PUNCT
ejpam-5794	397	7	9(6):4381–4387	9(6):4381–4387	NOUN
ejpam-5794	397	8	,	,	PUNCT
ejpam-5794	397	9	2016	2016	NUM
ejpam-5794	397	10	.	.	PUNCT
ejpam-5794	398	1	[	[	X
ejpam-5794	398	2	4	4	NUM
ejpam-5794	398	3	]	]	PUNCT
ejpam-5794	398	4	a.	a.	NOUN
ejpam-5794	398	5	a.	a.	PROPN
ejpam-5794	398	6	n.	n.	PROPN
ejpam-5794	398	7	abdou	abdou	PROPN
ejpam-5794	398	8	.	.	PUNCT
ejpam-5794	399	1	fixed	fix	VERB
ejpam-5794	399	2	points	point	NOUN
ejpam-5794	399	3	of	of	ADP
ejpam-5794	399	4	kannan	kannan	PROPN
ejpam-5794	399	5	maps	map	NOUN
ejpam-5794	399	6	in	in	ADP
ejpam-5794	399	7	modular	modular	ADJ
ejpam-5794	399	8	metric	metric	ADJ
ejpam-5794	399	9	spaces	space	NOUN
ejpam-5794	399	10	.	.	PUNCT
ejpam-5794	400	1	aims	aim	VERB
ejpam-5794	400	2	mathematics	mathematic	NOUN
ejpam-5794	400	3	,	,	PUNCT
ejpam-5794	400	4	5:6395–6403	5:6395–6403	NUM
ejpam-5794	400	5	,	,	PUNCT
ejpam-5794	400	6	2020	2020	NUM
ejpam-5794	400	7	.	.	PUNCT
ejpam-5794	401	1	u.	u.	PROPN
ejpam-5794	401	2	ishtiaq	ishtiaq	PROPN
ejpam-5794	401	3	et	et	PROPN
ejpam-5794	401	4	al	al	PROPN
ejpam-5794	401	5	.	.	PUNCT
ejpam-5794	401	6	/	/	SYM
ejpam-5794	401	7	eur	eur	PROPN
ejpam-5794	401	8	.	.	PUNCT
ejpam-5794	402	1	j.	j.	PROPN
ejpam-5794	402	2	pure	pure	PROPN
ejpam-5794	402	3	appl	appl	PROPN
ejpam-5794	402	4	.	.	PROPN
ejpam-5794	402	5	math	math	PROPN
ejpam-5794	402	6	,	,	PUNCT
ejpam-5794	402	7	18	18	NUM
ejpam-5794	402	8	(	(	PUNCT
ejpam-5794	402	9	1	1	NUM
ejpam-5794	402	10	)	)	PUNCT
ejpam-5794	402	11	(	(	PUNCT
ejpam-5794	402	12	2025	2025	NUM
ejpam-5794	402	13	)	)	PUNCT
ejpam-5794	402	14	,	,	PUNCT
ejpam-5794	402	15	5794	5794	NUM
ejpam-5794	402	16	19	19	NUM
ejpam-5794	402	17	of	of	ADP
ejpam-5794	402	18	20	20	NUM
ejpam-5794	402	19	[	[	SYM
ejpam-5794	402	20	5	5	NUM
ejpam-5794	402	21	]	]	X
ejpam-5794	402	22	n.	n.	PROPN
ejpam-5794	402	23	alamgir	alamgir	PROPN
ejpam-5794	402	24	,	,	PUNCT
ejpam-5794	402	25	q.	q.	PROPN
ejpam-5794	402	26	kiran	kiran	PROPN
ejpam-5794	402	27	,	,	PUNCT
ejpam-5794	402	28	h.	h.	PROPN
ejpam-5794	402	29	aydi	aydi	PROPN
ejpam-5794	402	30	,	,	PUNCT
ejpam-5794	402	31	and	and	CCONJ
ejpam-5794	402	32	y.	y.	PROPN
ejpam-5794	402	33	u.	u.	PROPN
ejpam-5794	402	34	gaba	gaba	PROPN
ejpam-5794	402	35	.	.	PUNCT
ejpam-5794	403	1	on	on	ADP
ejpam-5794	403	2	controlled	control	VERB
ejpam-5794	403	3	rectangular	rectangular	ADJ
ejpam-5794	403	4	metric	metric	ADJ
ejpam-5794	403	5	spaces	space	NOUN
ejpam-5794	403	6	and	and	CCONJ
ejpam-5794	403	7	an	an	DET
ejpam-5794	403	8	application	application	NOUN
ejpam-5794	403	9	.	.	PUNCT
ejpam-5794	404	1	journal	journal	NOUN
ejpam-5794	404	2	of	of	ADP
ejpam-5794	404	3	function	function	NOUN
ejpam-5794	404	4	spaces	space	NOUN
ejpam-5794	404	5	,	,	PUNCT
ejpam-5794	404	6	2021:1–9	2021:1–9	NUM
ejpam-5794	404	7	,	,	PUNCT
ejpam-5794	404	8	2021	2021	NUM
ejpam-5794	404	9	.	.	PUNCT
ejpam-5794	405	1	[	[	X
ejpam-5794	405	2	6	6	NUM
ejpam-5794	405	3	]	]	X
ejpam-5794	405	4	h.	h.	PROPN
ejpam-5794	405	5	aydi	aydi	PROPN
ejpam-5794	405	6	,	,	PUNCT
ejpam-5794	405	7	monica	monica	PROPN
ejpam-5794	405	8	-	-	PUNCT
ejpam-5794	405	9	f.	f.	PROPN
ejpam-5794	405	10	bota	bota	PROPN
ejpam-5794	405	11	,	,	PUNCT
ejpam-5794	405	12	e.	e.	PROPN
ejpam-5794	405	13	karapinar	karapinar	PROPN
ejpam-5794	405	14	,	,	PUNCT
ejpam-5794	405	15	and	and	CCONJ
ejpam-5794	405	16	s.	s.	PROPN
ejpam-5794	405	17	mitrovic	mitrovic	PROPN
ejpam-5794	405	18	.	.	PUNCT
ejpam-5794	406	1	a	a	DET
ejpam-5794	406	2	fixed	fix	VERB
ejpam-5794	406	3	point	point	NOUN
ejpam-5794	406	4	theorem	theorem	NOUN
ejpam-5794	406	5	for	for	ADP
ejpam-5794	406	6	set	set	NOUN
ejpam-5794	406	7	-	-	PUNCT
ejpam-5794	406	8	valued	value	VERB
ejpam-5794	406	9	quasi	quasi	NOUN
ejpam-5794	406	10	-	-	NOUN
ejpam-5794	406	11	contractions	contraction	NOUN
ejpam-5794	406	12	in	in	ADP
ejpam-5794	406	13	b	b	NOUN
ejpam-5794	406	14	-	-	ADJ
ejpam-5794	406	15	metric	metric	ADJ
ejpam-5794	406	16	spaces	space	NOUN
ejpam-5794	406	17	.	.	PUNCT
ejpam-5794	407	1	fixed	fix	VERB
ejpam-5794	407	2	point	point	NOUN
ejpam-5794	407	3	theory	theory	NOUN
ejpam-5794	407	4	and	and	CCONJ
ejpam-5794	407	5	applications	application	NOUN
ejpam-5794	407	6	,	,	PUNCT
ejpam-5794	407	7	88	88	NUM
ejpam-5794	407	8	,	,	PUNCT
ejpam-5794	407	9	2012	2012	NUM
ejpam-5794	407	10	.	.	PUNCT
ejpam-5794	408	1	[	[	X
ejpam-5794	408	2	7	7	X
ejpam-5794	408	3	]	]	X
ejpam-5794	408	4	h.	h.	PROPN
ejpam-5794	408	5	aydi	aydi	PROPN
ejpam-5794	408	6	,	,	PUNCT
ejpam-5794	408	7	z.	z.	PROPN
ejpam-5794	408	8	d.	d.	PROPN
ejpam-5794	408	9	mitrovic	mitrovic	PROPN
ejpam-5794	408	10	,	,	PUNCT
ejpam-5794	408	11	s.	s.	PROPN
ejpam-5794	408	12	radenovic	radenovic	PROPN
ejpam-5794	408	13	,	,	PUNCT
ejpam-5794	408	14	and	and	CCONJ
ejpam-5794	408	15	m.	m.	PROPN
ejpam-5794	408	16	de	de	PROPN
ejpam-5794	408	17	la	la	PROPN
ejpam-5794	408	18	sen	sen	PROPN
ejpam-5794	408	19	.	.	PROPN
ejpam-5794	408	20	on	on	ADP
ejpam-5794	408	21	a	a	DET
ejpam-5794	408	22	common	common	ADJ
ejpam-5794	408	23	jungck	jungck	NOUN
ejpam-5794	408	24	type	type	NOUN
ejpam-5794	408	25	fixed	fix	VERB
ejpam-5794	408	26	point	point	NOUN
ejpam-5794	408	27	result	result	NOUN
ejpam-5794	408	28	in	in	ADP
ejpam-5794	408	29	extended	extended	ADJ
ejpam-5794	408	30	rectangular	rectangular	ADJ
ejpam-5794	408	31	b	b	X
ejpam-5794	408	32	-	-	ADJ
ejpam-5794	408	33	metric	metric	ADJ
ejpam-5794	408	34	spaces	space	NOUN
ejpam-5794	408	35	.	.	PUNCT
ejpam-5794	409	1	axioms	axiom	NOUN
ejpam-5794	409	2	,	,	PUNCT
ejpam-5794	409	3	9(1):4	9(1):4	NOUN
ejpam-5794	409	4	,	,	PUNCT
ejpam-5794	409	5	2020	2020	NUM
ejpam-5794	409	6	.	.	PUNCT
ejpam-5794	410	1	[	[	X
ejpam-5794	410	2	8	8	NUM
ejpam-5794	410	3	]	]	X
ejpam-5794	410	4	h.	h.	PROPN
ejpam-5794	410	5	aydi	aydi	PROPN
ejpam-5794	410	6	,	,	PUNCT
ejpam-5794	410	7	n.	n.	PROPN
ejpam-5794	410	8	taş	taş	NOUN
ejpam-5794	410	9	,	,	PUNCT
ejpam-5794	410	10	n.	n.	PROPN
ejpam-5794	410	11	y.	y.	PROPN
ejpam-5794	410	12	özgür	özgür	PROPN
ejpam-5794	410	13	,	,	PUNCT
ejpam-5794	410	14	and	and	CCONJ
ejpam-5794	410	15	n.	n.	PROPN
ejpam-5794	410	16	mlaiki	mlaiki	PROPN
ejpam-5794	410	17	.	.	PUNCT
ejpam-5794	411	1	fixed	fix	VERB
ejpam-5794	411	2	-	-	PUNCT
ejpam-5794	411	3	discs	disc	NOUN
ejpam-5794	411	4	in	in	ADP
ejpam-5794	411	5	rectangular	rectangular	ADJ
ejpam-5794	411	6	metric	metric	ADJ
ejpam-5794	411	7	spaces	space	NOUN
ejpam-5794	411	8	.	.	PUNCT
ejpam-5794	412	1	symmetry	symmetry	NOUN
ejpam-5794	412	2	,	,	PUNCT
ejpam-5794	412	3	11(2):294	11(2):294	NUM
ejpam-5794	412	4	,	,	PUNCT
ejpam-5794	412	5	2019	2019	NUM
ejpam-5794	412	6	.	.	PUNCT
ejpam-5794	413	1	[	[	X
ejpam-5794	413	2	9	9	NUM
ejpam-5794	413	3	]	]	X
ejpam-5794	413	4	d.	d.	PROPN
ejpam-5794	413	5	baleanu	baleanu	PROPN
ejpam-5794	413	6	,	,	PUNCT
ejpam-5794	413	7	s.	s.	PROPN
ejpam-5794	413	8	rezapour	rezapour	PROPN
ejpam-5794	413	9	,	,	PUNCT
ejpam-5794	413	10	and	and	CCONJ
ejpam-5794	413	11	h.	h.	PROPN
ejpam-5794	413	12	mohammadi	mohammadi	NOUN
ejpam-5794	413	13	.	.	PUNCT
ejpam-5794	414	1	some	some	DET
ejpam-5794	414	2	existence	existence	NOUN
ejpam-5794	414	3	results	result	VERB
ejpam-5794	414	4	on	on	ADP
ejpam-5794	414	5	nonlinear	nonlinear	ADJ
ejpam-5794	414	6	fractional	fractional	ADJ
ejpam-5794	414	7	differential	differential	ADJ
ejpam-5794	414	8	equations	equation	NOUN
ejpam-5794	414	9	.	.	PUNCT
ejpam-5794	415	1	philosophical	philosophical	ADJ
ejpam-5794	415	2	transactions	transaction	NOUN
ejpam-5794	415	3	of	of	ADP
ejpam-5794	415	4	the	the	DET
ejpam-5794	415	5	royal	royal	PROPN
ejpam-5794	415	6	mathematical	mathematical	ADJ
ejpam-5794	415	7	society	society	NOUN
ejpam-5794	415	8	a	a	PRON
ejpam-5794	415	9	,	,	PUNCT
ejpam-5794	415	10	371:1–7	371:1–7	NUM
ejpam-5794	415	11	,	,	PUNCT
ejpam-5794	415	12	2013	2013	NUM
ejpam-5794	415	13	.	.	PUNCT
ejpam-5794	416	1	[	[	X
ejpam-5794	416	2	10	10	NUM
ejpam-5794	416	3	]	]	X
ejpam-5794	416	4	s.	s.	PROPN
ejpam-5794	416	5	banach	banach	PROPN
ejpam-5794	416	6	.	.	PUNCT
ejpam-5794	417	1	on	on	ADP
ejpam-5794	417	2	operations	operation	NOUN
ejpam-5794	417	3	in	in	ADP
ejpam-5794	417	4	abstract	abstract	ADJ
ejpam-5794	417	5	sets	set	NOUN
ejpam-5794	417	6	and	and	CCONJ
ejpam-5794	417	7	their	their	PRON
ejpam-5794	417	8	application	application	NOUN
ejpam-5794	417	9	to	to	ADP
ejpam-5794	417	10	integral	integral	ADJ
ejpam-5794	417	11	equations	equation	NOUN
ejpam-5794	417	12	.	.	PUNCT
ejpam-5794	418	1	fundamenta	fundamenta	PROPN
ejpam-5794	418	2	mathematicae	mathematicae	PROPN
ejpam-5794	418	3	,	,	PUNCT
ejpam-5794	418	4	3(1):133–181	3(1):133–181	NUM
ejpam-5794	418	5	,	,	PUNCT
ejpam-5794	418	6	1922	1922	NUM
ejpam-5794	418	7	.	.	PUNCT
ejpam-5794	419	1	[	[	X
ejpam-5794	419	2	11	11	NUM
ejpam-5794	419	3	]	]	PUNCT
ejpam-5794	419	4	a.	a.	NOUN
ejpam-5794	419	5	branciari	branciari	PROPN
ejpam-5794	419	6	.	.	PUNCT
ejpam-5794	420	1	a	a	DET
ejpam-5794	420	2	fixed	fix	VERB
ejpam-5794	420	3	point	point	NOUN
ejpam-5794	420	4	theorem	theorem	NOUN
ejpam-5794	420	5	of	of	ADP
ejpam-5794	420	6	banach	banach	NOUN
ejpam-5794	420	7	-	-	PUNCT
ejpam-5794	420	8	caccioppoli	caccioppoli	NOUN
ejpam-5794	420	9	type	type	NOUN
ejpam-5794	420	10	on	on	ADP
ejpam-5794	420	11	a	a	DET
ejpam-5794	420	12	class	class	NOUN
ejpam-5794	420	13	of	of	ADP
ejpam-5794	420	14	generalized	generalized	ADJ
ejpam-5794	420	15	mss	mss	PROPN
ejpam-5794	420	16	.	.	PUNCT
ejpam-5794	421	1	publicationes	publicatione	NOUN
ejpam-5794	421	2	mathematicae	mathematicae	PROPN
ejpam-5794	421	3	debrecen	debrecen	PROPN
ejpam-5794	421	4	,	,	PUNCT
ejpam-5794	421	5	57:31–37	57:31–37	PROPN
ejpam-5794	421	6	,	,	PUNCT
ejpam-5794	421	7	2000	2000	NUM
ejpam-5794	421	8	.	.	PUNCT
ejpam-5794	422	1	[	[	X
ejpam-5794	422	2	12	12	NUM
ejpam-5794	422	3	]	]	X
ejpam-5794	422	4	l.	l.	PROPN
ejpam-5794	422	5	budhia	budhia	PROPN
ejpam-5794	422	6	,	,	PUNCT
ejpam-5794	422	7	h.	h.	PROPN
ejpam-5794	422	8	aydi	aydi	PROPN
ejpam-5794	422	9	,	,	PUNCT
ejpam-5794	422	10	a.	a.	NOUN
ejpam-5794	422	11	h.	h.	PROPN
ejpam-5794	422	12	ansari	ansari	PROPN
ejpam-5794	422	13	,	,	PUNCT
ejpam-5794	422	14	and	and	CCONJ
ejpam-5794	422	15	d.	d.	PROPN
ejpam-5794	422	16	gopal	gopal	PROPN
ejpam-5794	422	17	.	.	PUNCT
ejpam-5794	423	1	some	some	DET
ejpam-5794	423	2	new	new	ADJ
ejpam-5794	423	3	fixed	fix	VERB
ejpam-5794	423	4	point	point	NOUN
ejpam-5794	423	5	results	result	NOUN
ejpam-5794	423	6	in	in	ADP
ejpam-5794	423	7	rectangular	rectangular	ADJ
ejpam-5794	423	8	metric	metric	ADJ
ejpam-5794	423	9	spaces	space	NOUN
ejpam-5794	423	10	with	with	ADP
ejpam-5794	423	11	an	an	DET
ejpam-5794	423	12	application	application	NOUN
ejpam-5794	423	13	to	to	ADP
ejpam-5794	423	14	fractional	fractional	ADJ
ejpam-5794	423	15	-	-	PUNCT
ejpam-5794	423	16	order	order	NOUN
ejpam-5794	423	17	functional	functional	ADJ
ejpam-5794	423	18	differential	differential	ADJ
ejpam-5794	423	19	equations	equation	NOUN
ejpam-5794	423	20	.	.	PUNCT
ejpam-5794	424	1	nonlinear	nonlinear	ADJ
ejpam-5794	424	2	analysis	analysis	NOUN
ejpam-5794	424	3	:	:	PUNCT
ejpam-5794	424	4	modelling	modelling	NOUN
ejpam-5794	424	5	and	and	CCONJ
ejpam-5794	424	6	control	control	NOUN
ejpam-5794	424	7	,	,	PUNCT
ejpam-5794	424	8	25:580–597	25:580–597	NUM
ejpam-5794	424	9	,	,	PUNCT
ejpam-5794	424	10	2020	2020	NUM
ejpam-5794	424	11	.	.	PUNCT
ejpam-5794	425	1	[	[	X
ejpam-5794	425	2	13	13	NUM
ejpam-5794	425	3	]	]	X
ejpam-5794	425	4	v.	v.	PROPN
ejpam-5794	425	5	v.	v.	ADP
ejpam-5794	425	6	chistyakov	chistyakov	PROPN
ejpam-5794	425	7	.	.	PUNCT
ejpam-5794	426	1	modular	modular	ADJ
ejpam-5794	426	2	metric	metric	ADJ
ejpam-5794	426	3	spaces	space	NOUN
ejpam-5794	426	4	,	,	PUNCT
ejpam-5794	426	5	i	i	PRON
ejpam-5794	426	6	:	:	PUNCT
ejpam-5794	426	7	basic	basic	ADJ
ejpam-5794	426	8	concepts	concept	NOUN
ejpam-5794	426	9	.	.	PUNCT
ejpam-5794	427	1	nonlinear	nonlinear	ADJ
ejpam-5794	427	2	analysis	analysis	NOUN
ejpam-5794	427	3	:	:	PUNCT
ejpam-5794	427	4	theory	theory	NOUN
ejpam-5794	427	5	,	,	PUNCT
ejpam-5794	427	6	methods	method	NOUN
ejpam-5794	427	7	&	&	CCONJ
ejpam-5794	427	8	applications	application	NOUN
ejpam-5794	427	9	,	,	PUNCT
ejpam-5794	427	10	72(1):1–14	72(1):1–14	NOUN
ejpam-5794	427	11	,	,	PUNCT
ejpam-5794	427	12	2010	2010	NUM
ejpam-5794	427	13	.	.	PUNCT
ejpam-5794	428	1	[	[	X
ejpam-5794	428	2	14	14	NUM
ejpam-5794	428	3	]	]	PUNCT
ejpam-5794	428	4	p.	p.	NOUN
ejpam-5794	428	5	debnath	debnath	NOUN
ejpam-5794	428	6	and	and	CCONJ
ejpam-5794	428	7	m.	m.	PROPN
ejpam-5794	428	8	de	de	PROPN
ejpam-5794	428	9	la	la	PROPN
ejpam-5794	428	10	sen	sen	PROPN
ejpam-5794	428	11	.	.	PROPN
ejpam-5794	428	12	fixed	fix	VERB
ejpam-5794	428	13	-	-	PUNCT
ejpam-5794	428	14	points	point	NOUN
ejpam-5794	428	15	of	of	ADP
ejpam-5794	428	16	interpolative	interpolative	ADJ
ejpam-5794	428	17	čirić-reich	čirić-reich	X
ejpam-5794	428	18	–	–	PUNCT
ejpam-5794	428	19	rus	rus	NOUN
ejpam-5794	428	20	-	-	PUNCT
ejpam-5794	428	21	type	type	NOUN
ejpam-5794	428	22	contractions	contraction	NOUN
ejpam-5794	428	23	in	in	ADP
ejpam-5794	428	24	b	b	NOUN
ejpam-5794	428	25	-	-	ADJ
ejpam-5794	428	26	metric	metric	ADJ
ejpam-5794	428	27	spaces	space	NOUN
ejpam-5794	428	28	.	.	PUNCT
ejpam-5794	429	1	symmetry	symmetry	NOUN
ejpam-5794	429	2	,	,	PUNCT
ejpam-5794	429	3	12(1):12	12(1):12	NUM
ejpam-5794	429	4	,	,	PUNCT
ejpam-5794	429	5	2020	2020	NUM
ejpam-5794	429	6	.	.	PUNCT
ejpam-5794	430	1	[	[	X
ejpam-5794	430	2	15	15	NUM
ejpam-5794	430	3	]	]	X
ejpam-5794	430	4	s.	s.	PROPN
ejpam-5794	430	5	furqan	furqan	PROPN
ejpam-5794	430	6	,	,	PUNCT
ejpam-5794	430	7	h.	h.	PROPN
ejpam-5794	430	8	isik	isik	PROPN
ejpam-5794	430	9	,	,	PUNCT
ejpam-5794	430	10	and	and	CCONJ
ejpam-5794	430	11	n.	n.	PROPN
ejpam-5794	430	12	saleem	saleem	PROPN
ejpam-5794	430	13	.	.	PUNCT
ejpam-5794	431	1	fuzzy	fuzzy	ADJ
ejpam-5794	431	2	triple	triple	PROPN
ejpam-5794	431	3	controlled	control	VERB
ejpam-5794	431	4	mss	mss	NOUN
ejpam-5794	431	5	and	and	CCONJ
ejpam-5794	431	6	related	relate	VERB
ejpam-5794	431	7	fixed	fix	VERB
ejpam-5794	431	8	point	point	NOUN
ejpam-5794	431	9	results	result	NOUN
ejpam-5794	431	10	.	.	PUNCT
ejpam-5794	432	1	journal	journal	NOUN
ejpam-5794	432	2	of	of	ADP
ejpam-5794	432	3	function	function	NOUN
ejpam-5794	432	4	spaces	space	NOUN
ejpam-5794	432	5	,	,	PUNCT
ejpam-5794	432	6	2021:1–8	2021:1–8	PROPN
ejpam-5794	432	7	,	,	PUNCT
ejpam-5794	432	8	2021	2021	NUM
ejpam-5794	432	9	.	.	PUNCT
ejpam-5794	433	1	[	[	X
ejpam-5794	433	2	16	16	NUM
ejpam-5794	433	3	]	]	X
ejpam-5794	433	4	e.	e.	PROPN
ejpam-5794	433	5	karapinar	karapinar	PROPN
ejpam-5794	433	6	.	.	PUNCT
ejpam-5794	434	1	generalizations	generalization	NOUN
ejpam-5794	434	2	of	of	ADP
ejpam-5794	434	3	caristi	caristi	PROPN
ejpam-5794	434	4	kirk	kirk	PROPN
ejpam-5794	434	5	’s	’s	PROPN
ejpam-5794	434	6	theorem	theorem	NOUN
ejpam-5794	434	7	on	on	ADP
ejpam-5794	434	8	partial	partial	ADJ
ejpam-5794	434	9	metric	metric	ADJ
ejpam-5794	434	10	spaces	space	NOUN
ejpam-5794	434	11	.	.	PUNCT
ejpam-5794	435	1	fixed	fix	VERB
ejpam-5794	435	2	point	point	NOUN
ejpam-5794	435	3	theory	theory	NOUN
ejpam-5794	435	4	and	and	CCONJ
ejpam-5794	435	5	applications	application	NOUN
ejpam-5794	435	6	,	,	PUNCT
ejpam-5794	435	7	4	4	NUM
ejpam-5794	435	8	,	,	PUNCT
ejpam-5794	435	9	2011	2011	NUM
ejpam-5794	435	10	.	.	PUNCT
ejpam-5794	436	1	[	[	X
ejpam-5794	436	2	17	17	NUM
ejpam-5794	436	3	]	]	X
ejpam-5794	436	4	e.	e.	PROPN
ejpam-5794	436	5	karapinar	karapinar	PROPN
ejpam-5794	436	6	and	and	CCONJ
ejpam-5794	436	7	inci	inci	PROPN
ejpam-5794	436	8	m.	m.	NOUN
ejpam-5794	436	9	erhan	erhan	PROPN
ejpam-5794	436	10	.	.	PUNCT
ejpam-5794	437	1	fixed	fix	VERB
ejpam-5794	437	2	point	point	NOUN
ejpam-5794	437	3	theorems	theorem	NOUN
ejpam-5794	437	4	for	for	ADP
ejpam-5794	437	5	operators	operator	NOUN
ejpam-5794	437	6	on	on	ADP
ejpam-5794	437	7	partial	partial	ADJ
ejpam-5794	437	8	metric	metric	ADJ
ejpam-5794	437	9	spaces	space	NOUN
ejpam-5794	437	10	.	.	PUNCT
ejpam-5794	438	1	applied	apply	VERB
ejpam-5794	438	2	mathematics	mathematics	NOUN
ejpam-5794	438	3	letters	letter	NOUN
ejpam-5794	438	4	,	,	PUNCT
ejpam-5794	438	5	24:1894–1899	24:1894–1899	NUM
ejpam-5794	438	6	,	,	PUNCT
ejpam-5794	438	7	2011	2011	NUM
ejpam-5794	438	8	.	.	PUNCT
ejpam-5794	439	1	[	[	X
ejpam-5794	439	2	18	18	NUM
ejpam-5794	439	3	]	]	X
ejpam-5794	439	4	e.	e.	PROPN
ejpam-5794	439	5	karapinar	karapinar	PROPN
ejpam-5794	439	6	,	,	PUNCT
ejpam-5794	439	7	w.	w.	PROPN
ejpam-5794	439	8	shatanawi	shatanawi	PROPN
ejpam-5794	439	9	,	,	PUNCT
ejpam-5794	439	10	and	and	CCONJ
ejpam-5794	439	11	z.	z.	PROPN
ejpam-5794	439	12	mustafa	mustafa	PROPN
ejpam-5794	439	13	.	.	PROPN
ejpam-5794	440	1	quadruple	quadruple	PROPN
ejpam-5794	440	2	fixed	fix	VERB
ejpam-5794	440	3	point	point	NOUN
ejpam-5794	440	4	theorems	theorem	NOUN
ejpam-5794	440	5	under	under	ADP
ejpam-5794	440	6	nonlinear	nonlinear	ADJ
ejpam-5794	440	7	contractive	contractive	ADJ
ejpam-5794	440	8	conditions	condition	NOUN
ejpam-5794	440	9	in	in	ADP
ejpam-5794	440	10	partially	partially	ADV
ejpam-5794	440	11	ordered	order	VERB
ejpam-5794	440	12	metric	metric	ADJ
ejpam-5794	440	13	spaces	space	NOUN
ejpam-5794	440	14	.	.	PUNCT
ejpam-5794	441	1	journal	journal	NOUN
ejpam-5794	441	2	of	of	ADP
ejpam-5794	441	3	applied	apply	VERB
ejpam-5794	441	4	mathematics	mathematic	NOUN
ejpam-5794	441	5	,	,	PUNCT
ejpam-5794	441	6	2012	2012	NUM
ejpam-5794	441	7	:	:	PUNCT
ejpam-5794	441	8	article	article	NOUN
ejpam-5794	441	9	i	i	PROPN
ejpam-5794	441	10	d	d	PROPN
ejpam-5794	441	11	951912	951912	NUM
ejpam-5794	441	12	,	,	PUNCT
ejpam-5794	441	13	17	17	NUM
ejpam-5794	441	14	pages	page	NOUN
ejpam-5794	441	15	,	,	PUNCT
ejpam-5794	441	16	2012	2012	NUM
ejpam-5794	441	17	.	.	PUNCT
ejpam-5794	442	1	[	[	X
ejpam-5794	442	2	19	19	NUM
ejpam-5794	442	3	]	]	PUNCT
ejpam-5794	442	4	a.	a.	NOUN
ejpam-5794	442	5	k.	k.	PROPN
ejpam-5794	442	6	kari	kari	PROPN
ejpam-5794	442	7	,	,	PUNCT
ejpam-5794	442	8	m.	m.	NOUN
ejpam-5794	442	9	rossafi	rossafi	PROPN
ejpam-5794	442	10	,	,	PUNCT
ejpam-5794	442	11	el	el	PROPN
ejpam-5794	442	12	.	.	PROPN
ejpam-5794	442	13	m.	m.	PROPN
ejpam-5794	442	14	marhrani	marhrani	PROPN
ejpam-5794	442	15	,	,	PUNCT
ejpam-5794	442	16	and	and	CCONJ
ejpam-5794	442	17	m.	m.	NOUN
ejpam-5794	442	18	aamri	aamri	PROPN
ejpam-5794	442	19	.	.	PUNCT
ejpam-5794	443	1	contraction	contraction	NOUN
ejpam-5794	443	2	on	on	ADP
ejpam-5794	443	3	complete	complete	ADJ
ejpam-5794	443	4	rectangular	rectangular	ADJ
ejpam-5794	443	5	metric	metric	ADJ
ejpam-5794	443	6	spaces	space	NOUN
ejpam-5794	443	7	.	.	PUNCT
ejpam-5794	444	1	international	international	ADJ
ejpam-5794	444	2	journal	journal	PROPN
ejpam-5794	444	3	of	of	ADP
ejpam-5794	444	4	mathematics	mathematics	PROPN
ejpam-5794	444	5	and	and	CCONJ
ejpam-5794	444	6	mathematical	mathematical	ADJ
ejpam-5794	444	7	sciences	science	NOUN
ejpam-5794	444	8	,	,	PUNCT
ejpam-5794	444	9	2020	2020	NUM
ejpam-5794	444	10	:	:	PUNCT
ejpam-5794	444	11	article	article	NOUN
ejpam-5794	444	12	i	i	PROPN
ejpam-5794	444	13	d	d	PROPN
ejpam-5794	444	14	5689458	5689458	NUM
ejpam-5794	444	15	,	,	PUNCT
ejpam-5794	444	16	9	9	NUM
ejpam-5794	444	17	pages	page	NOUN
ejpam-5794	444	18	,	,	PUNCT
ejpam-5794	444	19	2020	2020	NUM
ejpam-5794	444	20	.	.	PUNCT
ejpam-5794	445	1	[	[	X
ejpam-5794	445	2	20	20	NUM
ejpam-5794	445	3	]	]	X
ejpam-5794	445	4	d.	d.	PROPN
ejpam-5794	445	5	kinderlehrer	kinderlehrer	PROPN
ejpam-5794	445	6	and	and	CCONJ
ejpam-5794	445	7	g.	g.	PROPN
ejpam-5794	445	8	stampacchia	stampacchia	PROPN
ejpam-5794	445	9	.	.	PUNCT
ejpam-5794	446	1	an	an	DET
ejpam-5794	446	2	introduction	introduction	NOUN
ejpam-5794	446	3	to	to	ADP
ejpam-5794	446	4	variational	variational	ADJ
ejpam-5794	446	5	inequalities	inequality	NOUN
ejpam-5794	446	6	and	and	CCONJ
ejpam-5794	446	7	their	their	PRON
ejpam-5794	446	8	applications	application	NOUN
ejpam-5794	446	9	.	.	PUNCT
ejpam-5794	447	1	society	society	NOUN
ejpam-5794	447	2	for	for	ADP
ejpam-5794	447	3	industrial	industrial	ADJ
ejpam-5794	447	4	and	and	CCONJ
ejpam-5794	447	5	applied	applied	ADJ
ejpam-5794	447	6	mathematics	mathematic	NOUN
ejpam-5794	447	7	,	,	PUNCT
ejpam-5794	447	8	2000	2000	NUM
ejpam-5794	447	9	.	.	PUNCT
ejpam-5794	448	1	[	[	X
ejpam-5794	448	2	21	21	NUM
ejpam-5794	448	3	]	]	X
ejpam-5794	448	4	n.	n.	PROPN
ejpam-5794	448	5	mlaiki	mlaiki	PROPN
ejpam-5794	448	6	,	,	PUNCT
ejpam-5794	448	7	h.	h.	PROPN
ejpam-5794	448	8	aydi	aydi	PROPN
ejpam-5794	448	9	,	,	PUNCT
ejpam-5794	448	10	n.	n.	NOUN
ejpam-5794	448	11	souayah	souayah	NOUN
ejpam-5794	448	12	,	,	PUNCT
ejpam-5794	448	13	and	and	CCONJ
ejpam-5794	448	14	t.	t.	PROPN
ejpam-5794	448	15	abdeljawad	abdeljawad	NOUN
ejpam-5794	448	16	.	.	PUNCT
ejpam-5794	449	1	controlled	control	VERB
ejpam-5794	449	2	metric	metric	ADJ
ejpam-5794	449	3	type	type	NOUN
ejpam-5794	449	4	spaces	space	NOUN
ejpam-5794	449	5	and	and	CCONJ
ejpam-5794	449	6	the	the	DET
ejpam-5794	449	7	related	related	ADJ
ejpam-5794	449	8	contraction	contraction	NOUN
ejpam-5794	449	9	principle	principle	NOUN
ejpam-5794	449	10	.	.	PUNCT
ejpam-5794	450	1	mathematics	mathematic	NOUN
ejpam-5794	450	2	,	,	PUNCT
ejpam-5794	450	3	6:1–7	6:1–7	NOUN
ejpam-5794	450	4	,	,	PUNCT
ejpam-5794	450	5	2018	2018	NUM
ejpam-5794	450	6	.	.	PUNCT
ejpam-5794	451	1	[	[	X
ejpam-5794	451	2	22	22	NUM
ejpam-5794	451	3	]	]	PUNCT
ejpam-5794	451	4	m.	m.	NOUN
ejpam-5794	451	5	rossafi	rossafi	NOUN
ejpam-5794	451	6	and	and	CCONJ
ejpam-5794	451	7	a.	a.	PROPN
ejpam-5794	451	8	k.	k.	PROPN
ejpam-5794	451	9	kari	kari	PROPN
ejpam-5794	451	10	.	.	PUNCT
ejpam-5794	452	1	fixed	fix	VERB
ejpam-5794	452	2	point	point	NOUN
ejpam-5794	452	3	theorems	theorem	NOUN
ejpam-5794	452	4	in	in	ADP
ejpam-5794	452	5	controlled	control	VERB
ejpam-5794	452	6	rectangular	rectangular	ADJ
ejpam-5794	452	7	metric	metric	ADJ
ejpam-5794	452	8	spaces	space	NOUN
ejpam-5794	452	9	.	.	PUNCT
ejpam-5794	453	1	arxiv	arxiv	PROPN
ejpam-5794	453	2	preprint	preprint	PROPN
ejpam-5794	453	3	arxiv:2201.05691	arxiv:2201.05691	PROPN
ejpam-5794	453	4	,	,	PUNCT
ejpam-5794	453	5	2022	2022	NUM
ejpam-5794	453	6	.	.	PUNCT
ejpam-5794	454	1	[	[	X
ejpam-5794	454	2	23	23	NUM
ejpam-5794	454	3	]	]	PUNCT
ejpam-5794	454	4	k.	k.	PROPN
ejpam-5794	454	5	roy	roy	PROPN
ejpam-5794	454	6	,	,	PUNCT
ejpam-5794	454	7	s.	s.	PROPN
ejpam-5794	454	8	panja	panja	PROPN
ejpam-5794	454	9	,	,	PUNCT
ejpam-5794	454	10	m.	m.	NOUN
ejpam-5794	454	11	saha	saha	PROPN
ejpam-5794	454	12	,	,	PUNCT
ejpam-5794	454	13	and	and	CCONJ
ejpam-5794	454	14	v.	v.	ADP
ejpam-5794	454	15	parvaneh	parvaneh	NOUN
ejpam-5794	454	16	.	.	PUNCT
ejpam-5794	455	1	an	an	DET
ejpam-5794	455	2	extended	extend	VERB
ejpam-5794	455	3	-metric	-metric	ADJ
ejpam-5794	455	4	-	-	PUNCT
ejpam-5794	455	5	type	type	NOUN
ejpam-5794	455	6	space	space	NOUN
ejpam-5794	455	7	and	and	CCONJ
ejpam-5794	455	8	related	relate	VERB
ejpam-5794	455	9	fixed	fix	VERB
ejpam-5794	455	10	point	point	NOUN
ejpam-5794	455	11	theorems	theorem	NOUN
ejpam-5794	455	12	with	with	ADP
ejpam-5794	455	13	an	an	DET
ejpam-5794	455	14	application	application	NOUN
ejpam-5794	455	15	to	to	ADP
ejpam-5794	455	16	nonlinear	nonlinear	ADJ
ejpam-5794	455	17	integral	integral	ADJ
ejpam-5794	455	18	equations	equation	NOUN
ejpam-5794	455	19	.	.	PUNCT
ejpam-5794	456	1	adu	adu	PROPN
ejpam-5794	456	2	.	.	PUNCT
ejpam-5794	457	1	ishtiaq	ishtiaq	PROPN
ejpam-5794	457	2	et	et	PROPN
ejpam-5794	457	3	al	al	PROPN
ejpam-5794	457	4	.	.	PUNCT
ejpam-5794	457	5	/	/	SYM
ejpam-5794	457	6	eur	eur	PROPN
ejpam-5794	457	7	.	.	PUNCT
ejpam-5794	458	1	j.	j.	PROPN
ejpam-5794	458	2	pure	pure	PROPN
ejpam-5794	458	3	appl	appl	PROPN
ejpam-5794	458	4	.	.	PROPN
ejpam-5794	458	5	math	math	PROPN
ejpam-5794	458	6	,	,	PUNCT
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ejpam-5794	458	8	(	(	PUNCT
ejpam-5794	458	9	1	1	NUM
ejpam-5794	458	10	)	)	PUNCT
ejpam-5794	458	11	(	(	PUNCT
ejpam-5794	458	12	2025	2025	NUM
ejpam-5794	458	13	)	)	PUNCT
ejpam-5794	458	14	,	,	PUNCT
ejpam-5794	458	15	5794	5794	NUM
ejpam-5794	458	16	20	20	NUM
ejpam-5794	458	17	of	of	ADP
ejpam-5794	458	18	20	20	NUM
ejpam-5794	458	19	vances	vance	NOUN
ejpam-5794	458	20	in	in	ADP
ejpam-5794	458	21	mathematical	mathematical	ADJ
ejpam-5794	458	22	physics	physics	NOUN
ejpam-5794	458	23	,	,	PUNCT
ejpam-5794	458	24	2020	2020	NUM
ejpam-5794	458	25	:	:	PUNCT
ejpam-5794	458	26	article	article	NOUN
ejpam-5794	458	27	i	i	PROPN
ejpam-5794	458	28	d	d	PROPN
ejpam-5794	458	29	8868043	8868043	NUM
ejpam-5794	458	30	,	,	PUNCT
ejpam-5794	458	31	7	7	NUM
ejpam-5794	458	32	pages	page	NOUN
ejpam-5794	458	33	,	,	PUNCT
ejpam-5794	458	34	2020	2020	NUM
ejpam-5794	458	35	.	.	PUNCT
ejpam-5794	459	1	[	[	X
ejpam-5794	459	2	24	24	NUM
ejpam-5794	459	3	]	]	X
ejpam-5794	459	4	n.	n.	PROPN
ejpam-5794	459	5	saleem	saleem	PROPN
ejpam-5794	459	6	,	,	PUNCT
ejpam-5794	459	7	m.	m.	NOUN
ejpam-5794	459	8	abbas	abbas	PROPN
ejpam-5794	459	9	,	,	PUNCT
ejpam-5794	459	10	and	and	CCONJ
ejpam-5794	459	11	z.	z.	PROPN
ejpam-5794	459	12	raza	raza	PROPN
ejpam-5794	459	13	.	.	PUNCT
ejpam-5794	460	1	optimal	optimal	ADJ
ejpam-5794	460	2	coincidence	coincidence	NOUN
ejpam-5794	460	3	best	good	ADJ
ejpam-5794	460	4	approximation	approximation	NOUN
ejpam-5794	460	5	solution	solution	NOUN
ejpam-5794	460	6	in	in	ADP
ejpam-5794	460	7	non	non	ADJ
ejpam-5794	460	8	-	-	ADJ
ejpam-5794	460	9	archimedean	archimedean	ADJ
ejpam-5794	460	10	fuzzy	fuzzy	ADJ
ejpam-5794	460	11	metric	metric	ADJ
ejpam-5794	460	12	spaces	space	NOUN
ejpam-5794	460	13	.	.	PUNCT
ejpam-5794	461	1	iranian	iranian	ADJ
ejpam-5794	461	2	journal	journal	PROPN
ejpam-5794	461	3	of	of	ADP
ejpam-5794	461	4	fuzzy	fuzzy	ADJ
ejpam-5794	461	5	systems	system	NOUN
ejpam-5794	461	6	,	,	PUNCT
ejpam-5794	461	7	13(3):113	13(3):113	NUM
ejpam-5794	461	8	–	–	PUNCT
ejpam-5794	461	9	124	124	NUM
ejpam-5794	461	10	,	,	PUNCT
ejpam-5794	461	11	2016	2016	NUM
ejpam-5794	461	12	.	.	PUNCT
ejpam-5794	462	1	[	[	X
ejpam-5794	462	2	25	25	NUM
ejpam-5794	462	3	]	]	X
ejpam-5794	462	4	n.	n.	PROPN
ejpam-5794	462	5	saleem	saleem	PROPN
ejpam-5794	462	6	,	,	PUNCT
ejpam-5794	462	7	b.	b.	PROPN
ejpam-5794	462	8	ali	ali	PROPN
ejpam-5794	462	9	,	,	PUNCT
ejpam-5794	462	10	m.	m.	NOUN
ejpam-5794	462	11	abbas	abbas	PROPN
ejpam-5794	462	12	,	,	PUNCT
ejpam-5794	462	13	and	and	CCONJ
ejpam-5794	462	14	z.	z.	PROPN
ejpam-5794	462	15	raza	raza	PROPN
ejpam-5794	462	16	.	.	PUNCT
ejpam-5794	463	1	fixed	fix	VERB
ejpam-5794	463	2	points	point	NOUN
ejpam-5794	463	3	of	of	ADP
ejpam-5794	463	4	suzuki	suzuki	NOUN
ejpam-5794	463	5	type	type	NOUN
ejpam-5794	463	6	generalized	generalize	VERB
ejpam-5794	463	7	multivalued	multivalue	VERB
ejpam-5794	463	8	mappings	mapping	NOUN
ejpam-5794	463	9	in	in	ADP
ejpam-5794	463	10	fuzzy	fuzzy	ADJ
ejpam-5794	463	11	metric	metric	ADJ
ejpam-5794	463	12	spaces	space	NOUN
ejpam-5794	463	13	with	with	ADP
ejpam-5794	463	14	applications	application	NOUN
ejpam-5794	463	15	.	.	PUNCT
ejpam-5794	464	1	fixed	fix	VERB
ejpam-5794	464	2	point	point	NOUN
ejpam-5794	464	3	theory	theory	NOUN
ejpam-5794	464	4	and	and	CCONJ
ejpam-5794	464	5	applications	application	NOUN
ejpam-5794	464	6	,	,	PUNCT
ejpam-5794	464	7	2015(1):1–18	2015(1):1–18	NUM
ejpam-5794	464	8	,	,	PUNCT
ejpam-5794	464	9	2015	2015	NUM
ejpam-5794	464	10	.	.	PUNCT
ejpam-5794	465	1	[	[	X
ejpam-5794	465	2	26	26	NUM
ejpam-5794	465	3	]	]	X
ejpam-5794	465	4	n.	n.	PROPN
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ejpam-5794	465	6	,	,	PUNCT
ejpam-5794	465	7	h.	h.	PROPN
ejpam-5794	465	8	isik	isik	PROPN
ejpam-5794	465	9	,	,	PUNCT
ejpam-5794	465	10	s.	s.	PROPN
ejpam-5794	465	11	furqan	furqan	PROPN
ejpam-5794	465	12	,	,	PUNCT
ejpam-5794	465	13	and	and	CCONJ
ejpam-5794	465	14	c.	c.	PROPN
ejpam-5794	465	15	park	park	PROPN
ejpam-5794	465	16	.	.	PUNCT
ejpam-5794	466	1	fuzzy	fuzzy	ADJ
ejpam-5794	466	2	double	double	ADJ
ejpam-5794	466	3	controlled	control	VERB
ejpam-5794	466	4	metric	metric	ADJ
ejpam-5794	466	5	spaces	space	NOUN
ejpam-5794	466	6	and	and	CCONJ
ejpam-5794	466	7	related	related	ADJ
ejpam-5794	466	8	results	result	NOUN
ejpam-5794	466	9	.	.	PUNCT
ejpam-5794	467	1	journal	journal	NOUN
ejpam-5794	467	2	of	of	ADP
ejpam-5794	467	3	intelligent	intelligent	ADJ
ejpam-5794	467	4	&	&	CCONJ
ejpam-5794	467	5	fuzzy	fuzzy	ADJ
ejpam-5794	467	6	systems	system	NOUN
ejpam-5794	467	7	,	,	PUNCT
ejpam-5794	467	8	40:9977–9985	40:9977–9985	NOUN
ejpam-5794	467	9	,	,	PUNCT
ejpam-5794	467	10	2021	2021	NUM
ejpam-5794	467	11	.	.	PUNCT
ejpam-5794	468	1	[	[	X
ejpam-5794	468	2	27	27	NUM
ejpam-5794	468	3	]	]	X
ejpam-5794	468	4	n.	n.	PROPN
ejpam-5794	468	5	saleem	saleem	PROPN
ejpam-5794	468	6	,	,	PUNCT
ejpam-5794	468	7	j.	j.	PROPN
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ejpam-5794	468	9	,	,	PUNCT
ejpam-5794	468	10	w.	w.	PROPN
ejpam-5794	468	11	u.	u.	PROPN
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ejpam-5794	468	13	,	,	PUNCT
ejpam-5794	468	14	and	and	CCONJ
ejpam-5794	468	15	s.	s.	PROPN
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ejpam-5794	468	17	.	.	PUNCT
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ejpam-5794	469	2	point	point	NOUN
ejpam-5794	469	3	results	result	NOUN
ejpam-5794	469	4	for	for	ADP
ejpam-5794	469	5	multivalued	multivalued	ADJ
ejpam-5794	469	6	suzuki	suzuki	NOUN
ejpam-5794	469	7	type	type	NOUN
ejpam-5794	469	8	mappings	mapping	NOUN
ejpam-5794	469	9	using	use	VERB
ejpam-5794	469	10	θ	θ	NOUN
ejpam-5794	469	11	-	-	NOUN
ejpam-5794	469	12	contraction	contraction	NOUN
ejpam-5794	469	13	in	in	ADP
ejpam-5794	469	14	b	b	NOUN
ejpam-5794	469	15	-	-	ADJ
ejpam-5794	469	16	metric	metric	ADJ
ejpam-5794	469	17	spaces	space	NOUN
ejpam-5794	469	18	.	.	PUNCT
ejpam-5794	470	1	mathematics	mathematic	NOUN
ejpam-5794	470	2	,	,	PUNCT
ejpam-5794	470	3	7(11):1017	7(11):1017	NUM
ejpam-5794	470	4	,	,	PUNCT
ejpam-5794	470	5	2019	2019	NUM
ejpam-5794	470	6	.	.	PUNCT
ejpam-5794	471	1	[	[	X
ejpam-5794	471	2	28	28	NUM
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ejpam-5794	471	4	n.	n.	NOUN
ejpam-5794	471	5	souayah	souayah	NOUN
ejpam-5794	471	6	and	and	CCONJ
ejpam-5794	471	7	m.	m.	NOUN
ejpam-5794	471	8	mrad	mrad	PROPN
ejpam-5794	471	9	.	.	PUNCT
ejpam-5794	472	1	on	on	ADP
ejpam-5794	472	2	fixed	fix	VERB
ejpam-5794	472	3	-	-	PUNCT
ejpam-5794	472	4	point	point	NOUN
ejpam-5794	472	5	results	result	NOUN
ejpam-5794	472	6	in	in	ADP
ejpam-5794	472	7	controlled	control	VERB
ejpam-5794	472	8	partial	partial	ADJ
ejpam-5794	472	9	metric	metric	ADJ
ejpam-5794	472	10	type	type	NOUN
ejpam-5794	472	11	spaces	space	NOUN
ejpam-5794	472	12	with	with	ADP
ejpam-5794	472	13	a	a	DET
ejpam-5794	472	14	graph	graph	NOUN
ejpam-5794	472	15	.	.	PUNCT
ejpam-5794	473	1	mathematics	mathematic	NOUN
ejpam-5794	473	2	,	,	PUNCT
ejpam-5794	473	3	8:33	8:33	NUM
ejpam-5794	473	4	,	,	PUNCT
ejpam-5794	473	5	2020	2020	NUM
ejpam-5794	473	6	.	.	PUNCT
ejpam-5794	474	1	[	[	X
ejpam-5794	474	2	29	29	NUM
ejpam-5794	474	3	]	]	X
ejpam-5794	474	4	w.	w.	NOUN
ejpam-5794	474	5	sudsutad	sudsutad	PROPN
ejpam-5794	474	6	and	and	CCONJ
ejpam-5794	474	7	j.	j.	PROPN
ejpam-5794	474	8	tariboon	tariboon	PROPN
ejpam-5794	474	9	.	.	PUNCT
ejpam-5794	475	1	boundary	boundary	ADJ
ejpam-5794	475	2	value	value	NOUN
ejpam-5794	475	3	problems	problem	NOUN
ejpam-5794	475	4	for	for	ADP
ejpam-5794	475	5	fractional	fractional	ADJ
ejpam-5794	475	6	differential	differential	ADJ
ejpam-5794	475	7	equations	equation	NOUN
ejpam-5794	475	8	with	with	ADP
ejpam-5794	475	9	three	three	NUM
ejpam-5794	475	10	-	-	PUNCT
ejpam-5794	475	11	point	point	NOUN
ejpam-5794	475	12	fractional	fractional	ADJ
ejpam-5794	475	13	integral	integral	ADJ
ejpam-5794	475	14	boundary	boundary	ADJ
ejpam-5794	475	15	conditions	condition	NOUN
ejpam-5794	475	16	.	.	PUNCT
ejpam-5794	476	1	advances	advance	NOUN
ejpam-5794	476	2	in	in	ADP
ejpam-5794	476	3	difference	difference	NOUN
ejpam-5794	476	4	equations	equation	NOUN
ejpam-5794	476	5	,	,	PUNCT
ejpam-5794	476	6	93:1–10	93:1–10	NUM
ejpam-5794	476	7	,	,	PUNCT
ejpam-5794	476	8	2012	2012	NUM
ejpam-5794	476	9	.	.	PUNCT