id	sid	tid	token	lemma	pos
ejpam-5958	1	1	european	european	PROPN
ejpam-5958	1	2	journal	journal	PROPN
ejpam-5958	1	3	of	of	ADP
ejpam-5958	1	4	pure	pure	ADJ
ejpam-5958	1	5	and	and	CCONJ
ejpam-5958	1	6	applied	applied	ADJ
ejpam-5958	1	7	mathematics	mathematic	NOUN
ejpam-5958	1	8	2025	2025	NUM
ejpam-5958	1	9	,	,	PUNCT
ejpam-5958	1	10	vol	vol	NOUN
ejpam-5958	1	11	.	.	PROPN
ejpam-5958	1	12	18	18	NUM
ejpam-5958	1	13	,	,	PUNCT
ejpam-5958	1	14	issue	issue	NOUN
ejpam-5958	1	15	2	2	NUM
ejpam-5958	1	16	,	,	PUNCT
ejpam-5958	1	17	article	article	NOUN
ejpam-5958	1	18	number	number	NOUN
ejpam-5958	1	19	5958	5958	NUM
ejpam-5958	1	20	issn	issn	VERB
ejpam-5958	1	21	1307	1307	NUM
ejpam-5958	1	22	-	-	SYM
ejpam-5958	1	23	5543	5543	NUM
ejpam-5958	1	24	–	–	PUNCT
ejpam-5958	1	25	ejpam.com	ejpam.com	X
ejpam-5958	1	26	published	publish	VERB
ejpam-5958	1	27	by	by	ADP
ejpam-5958	1	28	new	new	PROPN
ejpam-5958	1	29	york	york	PROPN
ejpam-5958	1	30	business	business	PROPN
ejpam-5958	1	31	global	global	ADJ
ejpam-5958	1	32	fixed	fix	VERB
ejpam-5958	1	33	points	point	NOUN
ejpam-5958	1	34	for	for	ADP
ejpam-5958	1	35	generalized	generalized	ADJ
ejpam-5958	1	36	contractions	contraction	NOUN
ejpam-5958	1	37	in	in	ADP
ejpam-5958	1	38	b	b	NOUN
ejpam-5958	1	39	-	-	PUNCT
ejpam-5958	1	40	gauge	gauge	NOUN
ejpam-5958	1	41	spaces	space	NOUN
ejpam-5958	1	42	and	and	CCONJ
ejpam-5958	1	43	applications	application	NOUN
ejpam-5958	1	44	khadidja	khadidja	PROPN
ejpam-5958	1	45	nisse1	nisse1	PROPN
ejpam-5958	1	46	,	,	PUNCT
ejpam-5958	1	47	haitham	haitham	PROPN
ejpam-5958	1	48	qawaqneh2,∗	qawaqneh2,∗	PROPN
ejpam-5958	1	49	,	,	PUNCT
ejpam-5958	1	50	gawhara	gawhara	PROPN
ejpam-5958	1	51	al	al	PROPN
ejpam-5958	1	52	-	-	PUNCT
ejpam-5958	1	53	musannef3	musannef3	PROPN
ejpam-5958	1	54	,	,	PUNCT
ejpam-5958	1	55	habes	habe	VERB
ejpam-5958	1	56	alsamir4	alsamir4	NOUN
ejpam-5958	1	57	,	,	PUNCT
ejpam-5958	1	58	said	say	VERB
ejpam-5958	1	59	beloul5	beloul5	NOUN
ejpam-5958	1	60	1	1	NUM
ejpam-5958	1	61	laboratory	laboratory	NOUN
ejpam-5958	1	62	of	of	ADP
ejpam-5958	1	63	operators	operator	NOUN
ejpam-5958	1	64	theory	theory	NOUN
ejpam-5958	1	65	and	and	CCONJ
ejpam-5958	1	66	pdes	pde	NOUN
ejpam-5958	1	67	:	:	PUNCT
ejpam-5958	1	68	foundations	foundation	NOUN
ejpam-5958	1	69	and	and	CCONJ
ejpam-5958	1	70	applications	application	NOUN
ejpam-5958	1	71	,	,	PUNCT
ejpam-5958	1	72	department	department	NOUN
ejpam-5958	1	73	of	of	ADP
ejpam-5958	1	74	mathematics	mathematic	NOUN
ejpam-5958	1	75	,	,	PUNCT
ejpam-5958	1	76	faculty	faculty	NOUN
ejpam-5958	1	77	of	of	ADP
ejpam-5958	1	78	exact	exact	ADJ
ejpam-5958	1	79	sciences	science	NOUN
ejpam-5958	1	80	,	,	PUNCT
ejpam-5958	1	81	university	university	NOUN
ejpam-5958	1	82	of	of	ADP
ejpam-5958	1	83	el	el	PROPN
ejpam-5958	1	84	oued	oued	PROPN
ejpam-5958	1	85	,	,	PUNCT
ejpam-5958	1	86	p.o.box	p.o.box	PROPN
ejpam-5958	1	87	789	789	NUM
ejpam-5958	1	88	,	,	PUNCT
ejpam-5958	1	89	el	el	PROPN
ejpam-5958	1	90	oued	oued	PROPN
ejpam-5958	1	91	39000	39000	NUM
ejpam-5958	1	92	,	,	PUNCT
ejpam-5958	1	93	algeria	algeria	PROPN
ejpam-5958	1	94	2	2	NUM
ejpam-5958	1	95	al	al	PROPN
ejpam-5958	1	96	-	-	PUNCT
ejpam-5958	1	97	zaytoonah	zaytoonah	PROPN
ejpam-5958	1	98	university	university	PROPN
ejpam-5958	1	99	of	of	ADP
ejpam-5958	1	100	jordan	jordan	PROPN
ejpam-5958	1	101	,	,	PUNCT
ejpam-5958	1	102	amman	amman	PROPN
ejpam-5958	1	103	11733	11733	NUM
ejpam-5958	1	104	,	,	PUNCT
ejpam-5958	1	105	jordan	jordan	PROPN
ejpam-5958	1	106	3	3	NUM
ejpam-5958	1	107	faculty	faculty	NOUN
ejpam-5958	1	108	of	of	ADP
ejpam-5958	1	109	business	business	NOUN
ejpam-5958	1	110	studies	study	NOUN
ejpam-5958	1	111	,	,	PUNCT
ejpam-5958	1	112	arab	arab	ADJ
ejpam-5958	1	113	open	open	PROPN
ejpam-5958	1	114	university	university	PROPN
ejpam-5958	1	115	,	,	PUNCT
ejpam-5958	1	116	jeddah	jeddah	PROPN
ejpam-5958	1	117	,	,	PUNCT
ejpam-5958	1	118	saudi	saudi	PROPN
ejpam-5958	1	119	arabia	arabia	PROPN
ejpam-5958	1	120	4	4	NUM
ejpam-5958	1	121	finance	finance	NOUN
ejpam-5958	1	122	and	and	CCONJ
ejpam-5958	1	123	banking	banking	NOUN
ejpam-5958	1	124	department	department	NOUN
ejpam-5958	1	125	,	,	PUNCT
ejpam-5958	1	126	business	business	NOUN
ejpam-5958	1	127	administration	administration	PROPN
ejpam-5958	1	128	college	college	PROPN
ejpam-5958	1	129	,	,	PUNCT
ejpam-5958	1	130	dar	dar	PROPN
ejpam-5958	1	131	aluloom	aluloom	NOUN
ejpam-5958	1	132	university	university	PROPN
ejpam-5958	1	133	,	,	PUNCT
ejpam-5958	1	134	riyadh	riyadh	PROPN
ejpam-5958	1	135	,	,	PUNCT
ejpam-5958	1	136	saudi	saudi	PROPN
ejpam-5958	1	137	arabia	arabia	PROPN
ejpam-5958	1	138	5	5	NUM
ejpam-5958	1	139	laboratory	laboratory	NOUN
ejpam-5958	1	140	of	of	ADP
ejpam-5958	1	141	operators	operator	NOUN
ejpam-5958	1	142	theory	theory	NOUN
ejpam-5958	1	143	and	and	CCONJ
ejpam-5958	1	144	pde	pde	PROPN
ejpam-5958	1	145	labthop	labthop	PROPN
ejpam-5958	1	146	,	,	PUNCT
ejpam-5958	1	147	department	department	NOUN
ejpam-5958	1	148	of	of	ADP
ejpam-5958	1	149	mathematics	mathematic	NOUN
ejpam-5958	1	150	,	,	PUNCT
ejpam-5958	1	151	faculty	faculty	NOUN
ejpam-5958	1	152	of	of	ADP
ejpam-5958	1	153	exact	exact	ADJ
ejpam-5958	1	154	sciences	science	NOUN
ejpam-5958	1	155	,	,	PUNCT
ejpam-5958	1	156	university	university	NOUN
ejpam-5958	1	157	of	of	ADP
ejpam-5958	1	158	el	el	PROPN
ejpam-5958	1	159	oued	oued	PROPN
ejpam-5958	1	160	,	,	PUNCT
ejpam-5958	1	161	p.o.box	p.o.box	PROPN
ejpam-5958	1	162	789	789	NUM
ejpam-5958	1	163	,	,	PUNCT
ejpam-5958	1	164	el	el	PROPN
ejpam-5958	1	165	oued	oued	PROPN
ejpam-5958	1	166	39000	39000	NUM
ejpam-5958	1	167	,	,	PUNCT
ejpam-5958	1	168	algeria	algeria	PROPN
ejpam-5958	1	169	.	.	PUNCT
ejpam-5958	2	1	abstract	abstract	ADJ
ejpam-5958	2	2	.	.	PUNCT
ejpam-5958	3	1	in	in	ADP
ejpam-5958	3	2	this	this	DET
ejpam-5958	3	3	work	work	NOUN
ejpam-5958	3	4	,	,	PUNCT
ejpam-5958	3	5	we	we	PRON
ejpam-5958	3	6	extend	extend	VERB
ejpam-5958	3	7	and	and	CCONJ
ejpam-5958	3	8	generalize	generalize	VERB
ejpam-5958	3	9	,	,	PUNCT
ejpam-5958	3	10	the	the	DET
ejpam-5958	3	11	concept	concept	NOUN
ejpam-5958	3	12	of	of	ADP
ejpam-5958	3	13	α	α	PROPN
ejpam-5958	3	14	-	-	PUNCT
ejpam-5958	3	15	ψ	ψ	NOUN
ejpam-5958	3	16	contraction	contraction	NOUN
ejpam-5958	3	17	mappings	mapping	NOUN
ejpam-5958	3	18	in	in	ADP
ejpam-5958	3	19	the	the	DET
ejpam-5958	3	20	setting	setting	NOUN
ejpam-5958	3	21	of	of	ADP
ejpam-5958	3	22	b	b	NOUN
ejpam-5958	3	23	-	-	PUNCT
ejpam-5958	3	24	gauge	gauge	NOUN
ejpam-5958	3	25	spaces	space	NOUN
ejpam-5958	3	26	,	,	PUNCT
ejpam-5958	3	27	where	where	SCONJ
ejpam-5958	3	28	a	a	DET
ejpam-5958	3	29	new	new	ADJ
ejpam-5958	3	30	aspect	aspect	NOUN
ejpam-5958	3	31	of	of	ADP
ejpam-5958	3	32	extension	extension	NOUN
ejpam-5958	3	33	has	have	AUX
ejpam-5958	3	34	been	be	AUX
ejpam-5958	3	35	added	add	VERB
ejpam-5958	3	36	.	.	PUNCT
ejpam-5958	4	1	subsequently	subsequently	ADV
ejpam-5958	4	2	,	,	PUNCT
ejpam-5958	4	3	we	we	PRON
ejpam-5958	4	4	give	give	VERB
ejpam-5958	4	5	some	some	DET
ejpam-5958	4	6	related	relate	VERB
ejpam-5958	4	7	fixed	fix	VERB
ejpam-5958	4	8	point	point	NOUN
ejpam-5958	4	9	results	result	NOUN
ejpam-5958	4	10	that	that	PRON
ejpam-5958	4	11	generalize	generalize	VERB
ejpam-5958	4	12	many	many	ADJ
ejpam-5958	4	13	existing	exist	VERB
ejpam-5958	4	14	ones	one	NOUN
ejpam-5958	4	15	in	in	ADP
ejpam-5958	4	16	the	the	DET
ejpam-5958	4	17	literature	literature	NOUN
ejpam-5958	4	18	on	on	ADP
ejpam-5958	4	19	this	this	DET
ejpam-5958	4	20	topic	topic	NOUN
ejpam-5958	4	21	.	.	PUNCT
ejpam-5958	5	1	some	some	PRON
ejpam-5958	5	2	of	of	ADP
ejpam-5958	5	3	their	their	PRON
ejpam-5958	5	4	applications	application	NOUN
ejpam-5958	5	5	to	to	PART
ejpam-5958	5	6	nonlinear	nonlinear	VERB
ejpam-5958	5	7	integral	integral	ADJ
ejpam-5958	5	8	equations	equation	NOUN
ejpam-5958	5	9	on	on	ADP
ejpam-5958	5	10	unbounded	unbounded	ADJ
ejpam-5958	5	11	domains	domain	NOUN
ejpam-5958	5	12	,	,	PUNCT
ejpam-5958	5	13	including	include	VERB
ejpam-5958	5	14	fractional	fractional	ADJ
ejpam-5958	5	15	differential	differential	ADJ
ejpam-5958	5	16	equations	equation	NOUN
ejpam-5958	5	17	with	with	ADP
ejpam-5958	5	18	maxima	maxima	PROPN
ejpam-5958	5	19	,	,	PUNCT
ejpam-5958	5	20	are	be	AUX
ejpam-5958	5	21	also	also	ADV
ejpam-5958	5	22	presented	present	VERB
ejpam-5958	5	23	.	.	PUNCT
ejpam-5958	6	1	2020	2020	NUM
ejpam-5958	6	2	mathematics	mathematics	PROPN
ejpam-5958	6	3	subject	subject	NOUN
ejpam-5958	6	4	classifications	classification	NOUN
ejpam-5958	6	5	:	:	PUNCT
ejpam-5958	6	6	47h10	47h10	NUM
ejpam-5958	6	7	,	,	PUNCT
ejpam-5958	6	8	54h25	54h25	NUM
ejpam-5958	6	9	key	key	ADJ
ejpam-5958	6	10	words	word	NOUN
ejpam-5958	6	11	and	and	CCONJ
ejpam-5958	6	12	phrases	phrase	NOUN
ejpam-5958	6	13	:	:	PUNCT
ejpam-5958	6	14	α	α	NUM
ejpam-5958	6	15	-	-	PUNCT
ejpam-5958	6	16	ψ	ψ	NOUN
ejpam-5958	6	17	contraction	contraction	NOUN
ejpam-5958	6	18	,	,	PUNCT
ejpam-5958	6	19	fixed	fix	VERB
ejpam-5958	6	20	point	point	NOUN
ejpam-5958	6	21	theorem	theorem	VERB
ejpam-5958	6	22	,	,	PUNCT
ejpam-5958	6	23	b	b	X
ejpam-5958	6	24	-	-	PUNCT
ejpam-5958	6	25	gauge	gauge	NOUN
ejpam-5958	6	26	spaces	space	NOUN
ejpam-5958	6	27	1	1	NUM
ejpam-5958	6	28	.	.	PUNCT
ejpam-5958	6	29	introduction	introduction	NOUN
ejpam-5958	6	30	banach	banach	NOUN
ejpam-5958	6	31	’s	’s	PART
ejpam-5958	6	32	contraction	contraction	NOUN
ejpam-5958	6	33	principle	principle	NOUN
ejpam-5958	6	34	,	,	PUNCT
ejpam-5958	6	35	is	be	AUX
ejpam-5958	6	36	one	one	NUM
ejpam-5958	6	37	of	of	ADP
ejpam-5958	6	38	the	the	DET
ejpam-5958	6	39	most	most	ADV
ejpam-5958	6	40	important	important	ADJ
ejpam-5958	6	41	and	and	CCONJ
ejpam-5958	6	42	significant	significant	ADJ
ejpam-5958	6	43	results	result	NOUN
ejpam-5958	6	44	in	in	ADP
ejpam-5958	6	45	the	the	DET
ejpam-5958	6	46	fixed	fix	VERB
ejpam-5958	6	47	point	point	NOUN
ejpam-5958	6	48	theory	theory	NOUN
ejpam-5958	6	49	.	.	PUNCT
ejpam-5958	7	1	due	due	ADP
ejpam-5958	7	2	to	to	ADP
ejpam-5958	7	3	its	its	PRON
ejpam-5958	7	4	effective	effective	ADJ
ejpam-5958	7	5	applications	application	NOUN
ejpam-5958	7	6	in	in	ADP
ejpam-5958	7	7	various	various	ADJ
ejpam-5958	7	8	areas	area	NOUN
ejpam-5958	7	9	of	of	ADP
ejpam-5958	7	10	pure	pure	ADJ
ejpam-5958	7	11	and	and	CCONJ
ejpam-5958	7	12	applied	applied	ADJ
ejpam-5958	7	13	mathematics	mathematic	NOUN
ejpam-5958	7	14	,	,	PUNCT
ejpam-5958	7	15	it	it	PRON
ejpam-5958	7	16	has	have	AUX
ejpam-5958	7	17	attracted	attract	VERB
ejpam-5958	7	18	a	a	DET
ejpam-5958	7	19	wide	wide	ADJ
ejpam-5958	7	20	research	research	NOUN
ejpam-5958	7	21	interest	interest	NOUN
ejpam-5958	7	22	in	in	ADP
ejpam-5958	7	23	this	this	DET
ejpam-5958	7	24	theory	theory	NOUN
ejpam-5958	7	25	.	.	PUNCT
ejpam-5958	8	1	indeed	indeed	ADV
ejpam-5958	8	2	,	,	PUNCT
ejpam-5958	8	3	the	the	DET
ejpam-5958	8	4	related	related	ADJ
ejpam-5958	8	5	existing	exist	VERB
ejpam-5958	8	6	literature	literature	NOUN
ejpam-5958	8	7	is	be	AUX
ejpam-5958	8	8	fulled	full	VERB
ejpam-5958	8	9	with	with	ADP
ejpam-5958	8	10	different	different	ADJ
ejpam-5958	8	11	results	result	NOUN
ejpam-5958	8	12	extending	extend	VERB
ejpam-5958	8	13	banach	banach	NOUN
ejpam-5958	8	14	’s	’s	PART
ejpam-5958	8	15	principle	principle	NOUN
ejpam-5958	8	16	in	in	ADP
ejpam-5958	8	17	two	two	NUM
ejpam-5958	8	18	main	main	ADJ
ejpam-5958	8	19	directions	direction	NOUN
ejpam-5958	8	20	:	:	PUNCT
ejpam-5958	8	21	in	in	ADP
ejpam-5958	8	22	the	the	DET
ejpam-5958	8	23	sense	sense	NOUN
ejpam-5958	8	24	of	of	ADP
ejpam-5958	8	25	the	the	DET
ejpam-5958	8	26	contraction	contraction	NOUN
ejpam-5958	8	27	mappings	mapping	NOUN
ejpam-5958	8	28	or	or	CCONJ
ejpam-5958	8	29	(	(	PUNCT
ejpam-5958	8	30	and	and	CCONJ
ejpam-5958	8	31	)	)	PUNCT
ejpam-5958	8	32	in	in	ADP
ejpam-5958	8	33	the	the	DET
ejpam-5958	8	34	frame	frame	NOUN
ejpam-5958	8	35	of	of	ADP
ejpam-5958	8	36	generalized	generalized	ADJ
ejpam-5958	8	37	spaces	space	NOUN
ejpam-5958	8	38	.	.	PUNCT
ejpam-5958	9	1	the	the	DET
ejpam-5958	9	2	metric	metric	ADJ
ejpam-5958	9	3	space	space	NOUN
ejpam-5958	9	4	has	have	AUX
ejpam-5958	9	5	been	be	AUX
ejpam-5958	9	6	generalized	generalize	VERB
ejpam-5958	9	7	in	in	ADP
ejpam-5958	9	8	many	many	ADJ
ejpam-5958	9	9	different	different	ADJ
ejpam-5958	9	10	directions	direction	NOUN
ejpam-5958	9	11	.	.	PUNCT
ejpam-5958	10	1	one	one	NUM
ejpam-5958	10	2	of	of	ADP
ejpam-5958	10	3	the	the	DET
ejpam-5958	10	4	most	most	ADV
ejpam-5958	10	5	main	main	ADJ
ejpam-5958	10	6	generalizations	generalization	NOUN
ejpam-5958	10	7	directly	directly	ADV
ejpam-5958	10	8	related	relate	VERB
ejpam-5958	10	9	to	to	ADP
ejpam-5958	10	10	this	this	DET
ejpam-5958	10	11	work	work	NOUN
ejpam-5958	10	12	,	,	PUNCT
ejpam-5958	10	13	is	be	AUX
ejpam-5958	10	14	the	the	DET
ejpam-5958	10	15	gauge	gauge	ADJ
ejpam-5958	10	16	space	space	NOUN
ejpam-5958	10	17	∗corresponding	∗corresponde	VERB
ejpam-5958	10	18	author	author	NOUN
ejpam-5958	10	19	.	.	PUNCT
ejpam-5958	11	1	doi	doi	NOUN
ejpam-5958	11	2	:	:	PUNCT
ejpam-5958	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5958	https://doi.org/10.29020/nybg.ejpam.v18i2.5958	ADP
ejpam-5958	11	4	email	email	NOUN
ejpam-5958	11	5	addresses	address	NOUN
ejpam-5958	11	6	:	:	PUNCT
ejpam-5958	11	7	nisse-khadidja@univ-eloued.dz	nisse-khadidja@univ-eloued.dz	NOUN
ejpam-5958	11	8	(	(	PUNCT
ejpam-5958	11	9	k.	k.	NOUN
ejpam-5958	11	10	nisse	nisse	PROPN
ejpam-5958	11	11	)	)	PUNCT
ejpam-5958	11	12	,	,	PUNCT
ejpam-5958	11	13	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-5958	11	14	(	(	PUNCT
ejpam-5958	11	15	h.	h.	PROPN
ejpam-5958	11	16	qawaqneh	qawaqneh	PROPN
ejpam-5958	11	17	)	)	PUNCT
ejpam-5958	11	18	,	,	PUNCT
ejpam-5958	11	19	g.almusannef@arabou.edu.sa	g.almusannef@arabou.edu.sa	PROPN
ejpam-5958	11	20	(	(	PUNCT
ejpam-5958	11	21	j.m	j.m	PROPN
ejpam-5958	11	22	.	.	PROPN
ejpam-5958	11	23	al	al	PROPN
ejpam-5958	11	24	-	-	PUNCT
ejpam-5958	11	25	musannef	musannef	NOUN
ejpam-5958	11	26	)	)	PUNCT
ejpam-5958	11	27	,	,	PUNCT
ejpam-5958	11	28	habes@dau.edu.sa	habes@dau.edu.sa	PROPN
ejpam-5958	11	29	(	(	PUNCT
ejpam-5958	11	30	h.	h.	PROPN
ejpam-5958	11	31	alsamir	alsamir	PROPN
ejpam-5958	11	32	)	)	PUNCT
ejpam-5958	11	33	,	,	PUNCT
ejpam-5958	11	34	beloulsaid@gmail.com	beloulsaid@gmail.com	X
ejpam-5958	11	35	(	(	PUNCT
ejpam-5958	11	36	s.	s.	PROPN
ejpam-5958	11	37	beloul	beloul	PROPN
ejpam-5958	11	38	)	)	PUNCT
ejpam-5958	11	39	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5958	12	1	1	1	NUM
ejpam-5958	12	2	copyright	copyright	NOUN
ejpam-5958	12	3	:	:	PUNCT
ejpam-5958	12	4	©	©	PROPN
ejpam-5958	12	5	2025	2025	NUM
ejpam-5958	12	6	the	the	DET
ejpam-5958	12	7	author(s	author(s	NOUN
ejpam-5958	12	8	)	)	PUNCT
ejpam-5958	12	9	.	.	PUNCT
ejpam-5958	13	1	(	(	PUNCT
ejpam-5958	13	2	cc	cc	NOUN
ejpam-5958	13	3	by	by	ADP
ejpam-5958	13	4	-	-	PUNCT
ejpam-5958	13	5	nc	nc	PROPN
ejpam-5958	13	6	4.0	4.0	NUM
ejpam-5958	13	7	)	)	PUNCT
ejpam-5958	13	8	k.	k.	PROPN
ejpam-5958	13	9	nisse	nisse	PROPN
ejpam-5958	13	10	et	et	PROPN
ejpam-5958	13	11	al	al	PROPN
ejpam-5958	13	12	.	.	PUNCT
ejpam-5958	13	13	/	/	SYM
ejpam-5958	13	14	eur	eur	PROPN
ejpam-5958	13	15	.	.	PUNCT
ejpam-5958	14	1	j.	j.	PROPN
ejpam-5958	14	2	pure	pure	PROPN
ejpam-5958	14	3	appl	appl	PROPN
ejpam-5958	14	4	.	.	PROPN
ejpam-5958	14	5	math	math	PROPN
ejpam-5958	14	6	,	,	PUNCT
ejpam-5958	14	7	18	18	NUM
ejpam-5958	14	8	(	(	PUNCT
ejpam-5958	14	9	2	2	NUM
ejpam-5958	14	10	)	)	PUNCT
ejpam-5958	14	11	(	(	PUNCT
ejpam-5958	14	12	2025	2025	NUM
ejpam-5958	14	13	)	)	PUNCT
ejpam-5958	14	14	,	,	PUNCT
ejpam-5958	14	15	5958	5958	NUM
ejpam-5958	14	16	2	2	NUM
ejpam-5958	14	17	of	of	ADP
ejpam-5958	14	18	22	22	NUM
ejpam-5958	14	19	which	which	PRON
ejpam-5958	14	20	come	come	VERB
ejpam-5958	14	21	back	back	ADV
ejpam-5958	14	22	to	to	ADP
ejpam-5958	14	23	dugundji	dugundji	NOUN
ejpam-5958	14	24	[	[	X
ejpam-5958	14	25	1	1	NUM
ejpam-5958	14	26	]	]	PUNCT
ejpam-5958	14	27	.	.	PUNCT
ejpam-5958	15	1	briefly	briefly	NOUN
ejpam-5958	15	2	,	,	PUNCT
ejpam-5958	15	3	a	a	DET
ejpam-5958	15	4	gauge	gauge	ADJ
ejpam-5958	15	5	space	space	NOUN
ejpam-5958	15	6	is	be	AUX
ejpam-5958	15	7	a	a	DET
ejpam-5958	15	8	topological	topological	ADJ
ejpam-5958	15	9	space	space	NOUN
ejpam-5958	15	10	whose	whose	DET
ejpam-5958	15	11	topology	topology	NOUN
ejpam-5958	15	12	is	be	AUX
ejpam-5958	15	13	generated	generate	VERB
ejpam-5958	15	14	by	by	ADP
ejpam-5958	15	15	a	a	DET
ejpam-5958	15	16	separating	separate	VERB
ejpam-5958	15	17	family	family	NOUN
ejpam-5958	15	18	of	of	ADP
ejpam-5958	15	19	pseudo	pseudo	NOUN
ejpam-5958	15	20	-	-	NOUN
ejpam-5958	15	21	metrics	metric	NOUN
ejpam-5958	15	22	.	.	PUNCT
ejpam-5958	16	1	it	it	PRON
ejpam-5958	16	2	is	be	AUX
ejpam-5958	16	3	distinguished	distinguish	VERB
ejpam-5958	16	4	from	from	ADP
ejpam-5958	16	5	the	the	DET
ejpam-5958	16	6	metric	metric	ADJ
ejpam-5958	16	7	space	space	NOUN
ejpam-5958	16	8	by	by	ADP
ejpam-5958	16	9	the	the	DET
ejpam-5958	16	10	fact	fact	NOUN
ejpam-5958	16	11	that	that	SCONJ
ejpam-5958	16	12	the	the	DET
ejpam-5958	16	13	distance	distance	NOUN
ejpam-5958	16	14	between	between	ADP
ejpam-5958	16	15	two	two	NUM
ejpam-5958	16	16	distinct	distinct	ADJ
ejpam-5958	16	17	points	point	NOUN
ejpam-5958	16	18	may	may	AUX
ejpam-5958	16	19	be	be	AUX
ejpam-5958	16	20	zero	zero	NUM
ejpam-5958	16	21	.	.	PUNCT
ejpam-5958	17	1	for	for	ADP
ejpam-5958	17	2	more	more	ADJ
ejpam-5958	17	3	details	detail	NOUN
ejpam-5958	17	4	on	on	ADP
ejpam-5958	17	5	the	the	DET
ejpam-5958	17	6	gauge	gauge	ADJ
ejpam-5958	17	7	spaces	space	NOUN
ejpam-5958	17	8	and	and	CCONJ
ejpam-5958	17	9	related	relate	VERB
ejpam-5958	17	10	fixed	fix	VERB
ejpam-5958	17	11	point	point	NOUN
ejpam-5958	17	12	results	result	NOUN
ejpam-5958	17	13	,	,	PUNCT
ejpam-5958	17	14	we	we	PRON
ejpam-5958	17	15	refer	refer	VERB
ejpam-5958	17	16	to	to	ADP
ejpam-5958	17	17	[	[	X
ejpam-5958	17	18	1–5	1–5	X
ejpam-5958	17	19	]	]	X
ejpam-5958	17	20	.	.	PUNCT
ejpam-5958	18	1	an	an	DET
ejpam-5958	18	2	other	other	ADJ
ejpam-5958	18	3	generalization	generalization	NOUN
ejpam-5958	18	4	of	of	ADP
ejpam-5958	18	5	the	the	DET
ejpam-5958	18	6	metric	metric	ADJ
ejpam-5958	18	7	space	space	NOUN
ejpam-5958	18	8	which	which	PRON
ejpam-5958	18	9	relaxes	relax	VERB
ejpam-5958	18	10	the	the	DET
ejpam-5958	18	11	triangular	triangular	NOUN
ejpam-5958	18	12	inequality	inequality	NOUN
ejpam-5958	18	13	’s	’s	PART
ejpam-5958	18	14	axiom	axiom	NOUN
ejpam-5958	18	15	,	,	PUNCT
ejpam-5958	18	16	is	be	AUX
ejpam-5958	18	17	known	know	VERB
ejpam-5958	18	18	in	in	ADP
ejpam-5958	18	19	the	the	DET
ejpam-5958	18	20	fixed	fix	VERB
ejpam-5958	18	21	point	point	NOUN
ejpam-5958	18	22	theory	theory	NOUN
ejpam-5958	18	23	as	as	ADP
ejpam-5958	18	24	b	b	NOUN
ejpam-5958	18	25	-	-	PUNCT
ejpam-5958	18	26	metric	metric	ADJ
ejpam-5958	18	27	space	space	NOUN
ejpam-5958	18	28	.	.	PUNCT
ejpam-5958	19	1	to	to	PART
ejpam-5958	19	2	be	be	AUX
ejpam-5958	19	3	more	more	ADV
ejpam-5958	19	4	precise	precise	ADJ
ejpam-5958	19	5	,	,	PUNCT
ejpam-5958	19	6	we	we	PRON
ejpam-5958	19	7	state	state	VERB
ejpam-5958	19	8	the	the	DET
ejpam-5958	19	9	following	follow	VERB
ejpam-5958	19	10	definition	definition	NOUN
ejpam-5958	19	11	.	.	PUNCT
ejpam-5958	20	1	definition	definition	NOUN
ejpam-5958	20	2	1.1	1.1	NUM
ejpam-5958	20	3	.	.	PUNCT
ejpam-5958	21	1	[	[	X
ejpam-5958	21	2	6	6	NUM
ejpam-5958	21	3	]	]	PUNCT
ejpam-5958	21	4	let	let	VERB
ejpam-5958	21	5	x	x	PRON
ejpam-5958	21	6	be	be	AUX
ejpam-5958	21	7	a	a	DET
ejpam-5958	21	8	nonempty	nonempty	ADV
ejpam-5958	21	9	set	set	VERB
ejpam-5958	21	10	and	and	CCONJ
ejpam-5958	21	11	let	let	VERB
ejpam-5958	21	12	s	s	PRON
ejpam-5958	21	13	≥	≥	X
ejpam-5958	21	14	1	1	NUM
ejpam-5958	21	15	be	be	AUX
ejpam-5958	21	16	a	a	DET
ejpam-5958	21	17	given	give	VERB
ejpam-5958	21	18	real	real	ADJ
ejpam-5958	21	19	number	number	NOUN
ejpam-5958	21	20	.	.	PUNCT
ejpam-5958	22	1	a	a	DET
ejpam-5958	22	2	mapping	mapping	NOUN
ejpam-5958	22	3	d	d	NOUN
ejpam-5958	22	4	:	:	PUNCT
ejpam-5958	22	5	x	x	SYM
ejpam-5958	22	6	×x	×x	VERB
ejpam-5958	22	7	−→	−→	ADJ
ejpam-5958	22	8	r+	r+	NOUN
ejpam-5958	22	9	is	be	AUX
ejpam-5958	22	10	said	say	VERB
ejpam-5958	22	11	to	to	PART
ejpam-5958	22	12	be	be	AUX
ejpam-5958	22	13	a	a	DET
ejpam-5958	22	14	b	b	NOUN
ejpam-5958	22	15	-	-	ADJ
ejpam-5958	22	16	metric	metric	ADJ
ejpam-5958	22	17	,	,	PUNCT
ejpam-5958	22	18	if	if	SCONJ
ejpam-5958	22	19	for	for	ADP
ejpam-5958	22	20	all	all	DET
ejpam-5958	22	21	u	u	NOUN
ejpam-5958	22	22	,	,	PUNCT
ejpam-5958	22	23	v	v	NOUN
ejpam-5958	22	24	,	,	PUNCT
ejpam-5958	22	25	w	w	PROPN
ejpam-5958	22	26	∈	∈	PROPN
ejpam-5958	22	27	x	x	SYM
ejpam-5958	22	28	,	,	PUNCT
ejpam-5958	22	29	the	the	DET
ejpam-5958	22	30	following	follow	VERB
ejpam-5958	22	31	conditions	condition	NOUN
ejpam-5958	22	32	hold	hold	VERB
ejpam-5958	22	33	true	true	ADJ
ejpam-5958	22	34	(	(	PUNCT
ejpam-5958	22	35	b1	b1	NOUN
ejpam-5958	22	36	)	)	PUNCT
ejpam-5958	22	37	d(u	d(u	PROPN
ejpam-5958	22	38	,	,	PUNCT
ejpam-5958	22	39	v	v	NOUN
ejpam-5958	22	40	)	)	PUNCT
ejpam-5958	22	41	=	=	SYM
ejpam-5958	22	42	0	0	PUNCT
ejpam-5958	23	1	if	if	SCONJ
ejpam-5958	23	2	and	and	CCONJ
ejpam-5958	23	3	only	only	ADV
ejpam-5958	23	4	if	if	SCONJ
ejpam-5958	23	5	u	u	PROPN
ejpam-5958	23	6	=	=	SYM
ejpam-5958	23	7	v	v	NOUN
ejpam-5958	23	8	;	;	PUNCT
ejpam-5958	23	9	(	(	PUNCT
ejpam-5958	23	10	b2	b2	NOUN
ejpam-5958	23	11	)	)	PUNCT
ejpam-5958	23	12	d(u	d(u	PROPN
ejpam-5958	23	13	,	,	PUNCT
ejpam-5958	23	14	v	v	NOUN
ejpam-5958	23	15	)	)	PUNCT
ejpam-5958	23	16	=	=	SYM
ejpam-5958	24	1	d(v	d(v	PROPN
ejpam-5958	24	2	,	,	PUNCT
ejpam-5958	24	3	u	u	NOUN
ejpam-5958	24	4	)	)	PUNCT
ejpam-5958	24	5	;	;	PUNCT
ejpam-5958	24	6	(	(	PUNCT
ejpam-5958	24	7	b3	b3	PROPN
ejpam-5958	24	8	)	)	PUNCT
ejpam-5958	24	9	d(u	d(u	PROPN
ejpam-5958	24	10	,	,	PUNCT
ejpam-5958	24	11	w	w	NOUN
ejpam-5958	24	12	)	)	PUNCT
ejpam-5958	24	13	≤	≤	NOUN
ejpam-5958	24	14	s	s	PART
ejpam-5958	25	1	[	[	X
ejpam-5958	25	2	d(u	d(u	PROPN
ejpam-5958	25	3	,	,	PUNCT
ejpam-5958	25	4	v	v	NOUN
ejpam-5958	25	5	)	)	PUNCT
ejpam-5958	25	6	+	+	X
ejpam-5958	25	7	d(v	d(v	ADJ
ejpam-5958	25	8	,	,	PUNCT
ejpam-5958	25	9	w	w	NOUN
ejpam-5958	25	10	)	)	PUNCT
ejpam-5958	25	11	]	]	PUNCT
ejpam-5958	25	12	.	.	PUNCT
ejpam-5958	26	1	in	in	ADP
ejpam-5958	26	2	this	this	DET
ejpam-5958	26	3	case	case	NOUN
ejpam-5958	26	4	,	,	PUNCT
ejpam-5958	26	5	(	(	PUNCT
ejpam-5958	26	6	x	x	NOUN
ejpam-5958	26	7	,	,	PUNCT
ejpam-5958	26	8	d	d	NOUN
ejpam-5958	26	9	)	)	PUNCT
ejpam-5958	26	10	is	be	AUX
ejpam-5958	26	11	called	call	VERB
ejpam-5958	26	12	a	a	DET
ejpam-5958	26	13	b	b	NOUN
ejpam-5958	26	14	-	-	PUNCT
ejpam-5958	26	15	metric	metric	ADJ
ejpam-5958	26	16	space	space	NOUN
ejpam-5958	26	17	with	with	ADP
ejpam-5958	26	18	constant	constant	ADJ
ejpam-5958	26	19	s.	s.	PROPN
ejpam-5958	26	20	it	it	PRON
ejpam-5958	26	21	should	should	AUX
ejpam-5958	26	22	be	be	AUX
ejpam-5958	26	23	noted	note	VERB
ejpam-5958	26	24	that	that	SCONJ
ejpam-5958	26	25	this	this	DET
ejpam-5958	26	26	structure	structure	NOUN
ejpam-5958	26	27	is	be	AUX
ejpam-5958	26	28	found	find	VERB
ejpam-5958	26	29	in	in	ADP
ejpam-5958	26	30	the	the	DET
ejpam-5958	26	31	literature	literature	NOUN
ejpam-5958	26	32	under	under	ADP
ejpam-5958	26	33	other	other	ADJ
ejpam-5958	26	34	names	name	NOUN
ejpam-5958	26	35	such	such	ADJ
ejpam-5958	26	36	as	as	ADP
ejpam-5958	26	37	quasi	quasi	ADJ
ejpam-5958	26	38	-	-	ADJ
ejpam-5958	26	39	metric	metric	ADJ
ejpam-5958	26	40	space	space	NOUN
ejpam-5958	27	1	[	[	X
ejpam-5958	27	2	7	7	X
ejpam-5958	27	3	]	]	PUNCT
ejpam-5958	27	4	and	and	CCONJ
ejpam-5958	27	5	metric	metric	ADJ
ejpam-5958	27	6	type	type	NOUN
ejpam-5958	27	7	space	space	NOUN
ejpam-5958	27	8	[	[	X
ejpam-5958	27	9	8	8	NUM
ejpam-5958	27	10	]	]	PUNCT
ejpam-5958	27	11	.	.	PUNCT
ejpam-5958	28	1	for	for	ADP
ejpam-5958	28	2	more	more	ADJ
ejpam-5958	28	3	information	information	NOUN
ejpam-5958	28	4	on	on	ADP
ejpam-5958	28	5	the	the	DET
ejpam-5958	28	6	concept	concept	NOUN
ejpam-5958	28	7	and	and	CCONJ
ejpam-5958	28	8	origins	origin	NOUN
ejpam-5958	28	9	of	of	ADP
ejpam-5958	28	10	b	b	NOUN
ejpam-5958	28	11	-	-	PUNCT
ejpam-5958	28	12	metric	metric	ADJ
ejpam-5958	28	13	spaces	space	NOUN
ejpam-5958	28	14	,	,	PUNCT
ejpam-5958	28	15	we	we	PRON
ejpam-5958	28	16	reefer	reefer	VERB
ejpam-5958	28	17	to	to	ADP
ejpam-5958	28	18	the	the	DET
ejpam-5958	28	19	recent	recent	ADJ
ejpam-5958	28	20	survey	survey	NOUN
ejpam-5958	28	21	[	[	X
ejpam-5958	28	22	9	9	NUM
ejpam-5958	28	23	]	]	PUNCT
ejpam-5958	28	24	.	.	PUNCT
ejpam-5958	29	1	recently	recently	ADV
ejpam-5958	29	2	,	,	PUNCT
ejpam-5958	29	3	ali	ali	PROPN
ejpam-5958	29	4	et	et	PROPN
ejpam-5958	29	5	al	al	PROPN
ejpam-5958	29	6	.	.	PUNCT
ejpam-5958	30	1	[	[	X
ejpam-5958	30	2	10	10	NUM
ejpam-5958	30	3	]	]	SYM
ejpam-5958	30	4	extended	extended	ADJ
ejpam-5958	30	5	gauge	gauge	NOUN
ejpam-5958	30	6	spaces	space	NOUN
ejpam-5958	30	7	in	in	ADP
ejpam-5958	30	8	the	the	DET
ejpam-5958	30	9	setting	setting	NOUN
ejpam-5958	30	10	of	of	ADP
ejpam-5958	30	11	b	b	NOUN
ejpam-5958	30	12	-	-	PUNCT
ejpam-5958	30	13	pseudo	pseudo	NOUN
ejpam-5958	30	14	metrics	metric	NOUN
ejpam-5958	30	15	and	and	CCONJ
ejpam-5958	30	16	introduced	introduce	VERB
ejpam-5958	30	17	the	the	DET
ejpam-5958	30	18	so	so	ADV
ejpam-5958	30	19	called	call	VERB
ejpam-5958	30	20	b	b	NUM
ejpam-5958	30	21	-	-	PUNCT
ejpam-5958	30	22	gauge	gauge	NOUN
ejpam-5958	30	23	spaces	space	NOUN
ejpam-5958	30	24	and	and	CCONJ
ejpam-5958	30	25	proved	prove	VERB
ejpam-5958	30	26	some	some	DET
ejpam-5958	30	27	fixed	fix	VERB
ejpam-5958	30	28	point	point	NOUN
ejpam-5958	30	29	results	result	NOUN
ejpam-5958	30	30	for	for	ADP
ejpam-5958	30	31	multi	multi	ADJ
ejpam-5958	30	32	-	-	ADJ
ejpam-5958	30	33	valued	value	VERB
ejpam-5958	30	34	mappings	mapping	NOUN
ejpam-5958	30	35	in	in	ADP
ejpam-5958	30	36	this	this	DET
ejpam-5958	30	37	new	new	ADJ
ejpam-5958	30	38	space	space	NOUN
ejpam-5958	30	39	.	.	PUNCT
ejpam-5958	31	1	further	further	ADJ
ejpam-5958	31	2	generalizations	generalization	NOUN
ejpam-5958	31	3	of	of	ADP
ejpam-5958	31	4	the	the	DET
ejpam-5958	31	5	metric	metric	ADJ
ejpam-5958	31	6	structure	structure	NOUN
ejpam-5958	31	7	,	,	PUNCT
ejpam-5958	31	8	such	such	ADJ
ejpam-5958	31	9	as	as	ADP
ejpam-5958	31	10	generalized	generalize	VERB
ejpam-5958	31	11	metric	metric	ADJ
ejpam-5958	31	12	space	space	NOUN
ejpam-5958	31	13	(	(	PUNCT
ejpam-5958	31	14	known	know	VERB
ejpam-5958	31	15	as	as	ADP
ejpam-5958	31	16	branciari	branciari	ADJ
ejpam-5958	31	17	metric	metric	ADJ
ejpam-5958	31	18	space	space	NOUN
ejpam-5958	31	19	)	)	PUNCT
ejpam-5958	31	20	,	,	PUNCT
ejpam-5958	31	21	rectangular	rectangular	ADJ
ejpam-5958	31	22	b	b	X
ejpam-5958	31	23	-	-	ADJ
ejpam-5958	31	24	metric	metric	ADJ
ejpam-5958	31	25	space	space	NOUN
ejpam-5958	31	26	(	(	PUNCT
ejpam-5958	31	27	known	know	VERB
ejpam-5958	31	28	as	as	ADP
ejpam-5958	31	29	branciari	branciari	NOUN
ejpam-5958	31	30	b	b	X
ejpam-5958	31	31	-	-	PUNCT
ejpam-5958	31	32	metric	metric	ADJ
ejpam-5958	31	33	space	space	NOUN
ejpam-5958	31	34	)	)	PUNCT
ejpam-5958	31	35	and	and	CCONJ
ejpam-5958	31	36	extended	extend	VERB
ejpam-5958	31	37	b	b	X
ejpam-5958	31	38	-	-	PUNCT
ejpam-5958	31	39	metric	metric	ADJ
ejpam-5958	31	40	space	space	NOUN
ejpam-5958	31	41	and	and	CCONJ
ejpam-5958	31	42	other	other	ADJ
ejpam-5958	31	43	generalized	generalized	ADJ
ejpam-5958	31	44	metric	metric	ADJ
ejpam-5958	31	45	spaces	space	NOUN
ejpam-5958	31	46	can	can	AUX
ejpam-5958	31	47	be	be	AUX
ejpam-5958	31	48	found	find	VERB
ejpam-5958	31	49	in	in	ADP
ejpam-5958	31	50	[	[	X
ejpam-5958	31	51	11–26	11–26	NUM
ejpam-5958	31	52	]	]	PUNCT
ejpam-5958	31	53	.	.	PUNCT
ejpam-5958	32	1	the	the	DET
ejpam-5958	32	2	following	follow	VERB
ejpam-5958	32	3	generalized	generalized	ADJ
ejpam-5958	32	4	contraction	contraction	NOUN
ejpam-5958	32	5	condition	condition	NOUN
ejpam-5958	32	6	called	call	VERB
ejpam-5958	32	7	an	an	DET
ejpam-5958	32	8	α	α	PROPN
ejpam-5958	32	9	-	-	PUNCT
ejpam-5958	32	10	ψ	ψ	NOUN
ejpam-5958	32	11	contraction	contraction	NOUN
ejpam-5958	32	12	in	in	ADP
ejpam-5958	32	13	a	a	DET
ejpam-5958	32	14	metric	metric	ADJ
ejpam-5958	32	15	space	space	NOUN
ejpam-5958	32	16	(	(	PUNCT
ejpam-5958	32	17	x	x	X
ejpam-5958	32	18	,	,	PUNCT
ejpam-5958	32	19	d	d	NOUN
ejpam-5958	32	20	)	)	PUNCT
ejpam-5958	32	21	is	be	AUX
ejpam-5958	32	22	introduced	introduce	VERB
ejpam-5958	32	23	and	and	CCONJ
ejpam-5958	32	24	fixed	fix	VERB
ejpam-5958	32	25	point	point	NOUN
ejpam-5958	32	26	results	result	NOUN
ejpam-5958	32	27	for	for	ADP
ejpam-5958	32	28	such	such	ADJ
ejpam-5958	32	29	type	type	NOUN
ejpam-5958	32	30	of	of	ADP
ejpam-5958	32	31	contractions	contraction	NOUN
ejpam-5958	32	32	are	be	AUX
ejpam-5958	32	33	established	establish	VERB
ejpam-5958	32	34	by	by	ADP
ejpam-5958	32	35	samet	samet	PROPN
ejpam-5958	32	36	et	et	PROPN
ejpam-5958	32	37	al	al	PROPN
ejpam-5958	32	38	.	.	PUNCT
ejpam-5958	33	1	[	[	X
ejpam-5958	33	2	27	27	NUM
ejpam-5958	33	3	]	]	SYM
ejpam-5958	33	4	α(x	α(x	NOUN
ejpam-5958	33	5	,	,	PUNCT
ejpam-5958	33	6	y)d(fx	y)d(fx	PROPN
ejpam-5958	33	7	,	,	PUNCT
ejpam-5958	33	8	fy	fy	NOUN
ejpam-5958	33	9	)	)	PUNCT
ejpam-5958	33	10	≤	≤	NOUN
ejpam-5958	33	11	ψ(d(x	ψ(d(x	NOUN
ejpam-5958	33	12	,	,	PUNCT
ejpam-5958	33	13	y	y	NOUN
ejpam-5958	33	14	)	)	PUNCT
ejpam-5958	33	15	)	)	PUNCT
ejpam-5958	33	16	,	,	PUNCT
ejpam-5958	33	17	∀x	∀x	X
ejpam-5958	33	18	,	,	PUNCT
ejpam-5958	33	19	y	y	PROPN
ejpam-5958	33	20	∈	∈	PROPN
ejpam-5958	33	21	x	x	NOUN
ejpam-5958	33	22	,	,	PUNCT
ejpam-5958	33	23	where	where	SCONJ
ejpam-5958	33	24	α	α	NOUN
ejpam-5958	33	25	and	and	CCONJ
ejpam-5958	33	26	ψ	ψ	NOUN
ejpam-5958	33	27	are	be	AUX
ejpam-5958	33	28	auxiliary	auxiliary	ADJ
ejpam-5958	33	29	functions	function	NOUN
ejpam-5958	33	30	satisfying	satisfy	VERB
ejpam-5958	33	31	some	some	DET
ejpam-5958	33	32	conditions	condition	NOUN
ejpam-5958	33	33	.	.	PUNCT
ejpam-5958	34	1	many	many	ADJ
ejpam-5958	34	2	other	other	ADJ
ejpam-5958	34	3	results	result	NOUN
ejpam-5958	34	4	in	in	ADP
ejpam-5958	34	5	this	this	DET
ejpam-5958	34	6	direction	direction	NOUN
ejpam-5958	34	7	have	have	AUX
ejpam-5958	34	8	been	be	AUX
ejpam-5958	34	9	obtained	obtain	VERB
ejpam-5958	34	10	later	later	ADV
ejpam-5958	34	11	in	in	ADP
ejpam-5958	34	12	the	the	DET
ejpam-5958	34	13	setting	setting	NOUN
ejpam-5958	34	14	of	of	ADP
ejpam-5958	34	15	b	b	NOUN
ejpam-5958	34	16	-	-	PUNCT
ejpam-5958	34	17	metric	metric	ADJ
ejpam-5958	34	18	spaces	space	NOUN
ejpam-5958	34	19	and	and	CCONJ
ejpam-5958	34	20	gauge	gauge	NOUN
ejpam-5958	34	21	spaces	space	NOUN
ejpam-5958	34	22	with	with	ADP
ejpam-5958	34	23	applications	application	NOUN
ejpam-5958	34	24	,	,	PUNCT
ejpam-5958	34	25	see	see	VERB
ejpam-5958	35	1	e.g.	e.g.	ADV
ejpam-5958	35	2	[	[	X
ejpam-5958	35	3	5	5	NUM
ejpam-5958	35	4	,	,	PUNCT
ejpam-5958	35	5	28–35	28–35	NUM
ejpam-5958	35	6	]	]	PUNCT
ejpam-5958	35	7	and	and	CCONJ
ejpam-5958	35	8	the	the	DET
ejpam-5958	35	9	references	reference	NOUN
ejpam-5958	35	10	therein	therein	ADV
ejpam-5958	35	11	.	.	PUNCT
ejpam-5958	36	1	while	while	SCONJ
ejpam-5958	36	2	so	so	ADV
ejpam-5958	36	3	far	far	ADV
ejpam-5958	36	4	in	in	ADP
ejpam-5958	36	5	the	the	DET
ejpam-5958	36	6	existing	exist	VERB
ejpam-5958	36	7	literature	literature	NOUN
ejpam-5958	36	8	,	,	PUNCT
ejpam-5958	36	9	there	there	PRON
ejpam-5958	36	10	are	be	VERB
ejpam-5958	36	11	not	not	PART
ejpam-5958	36	12	enough	enough	ADJ
ejpam-5958	36	13	contributions	contribution	NOUN
ejpam-5958	36	14	on	on	ADP
ejpam-5958	36	15	this	this	PRON
ejpam-5958	36	16	or	or	CCONJ
ejpam-5958	36	17	even	even	ADV
ejpam-5958	36	18	other	other	ADJ
ejpam-5958	36	19	trends	trend	NOUN
ejpam-5958	36	20	in	in	ADP
ejpam-5958	36	21	the	the	DET
ejpam-5958	36	22	frame	frame	NOUN
ejpam-5958	36	23	of	of	ADP
ejpam-5958	36	24	b	b	NOUN
ejpam-5958	36	25	-	-	PUNCT
ejpam-5958	36	26	gauge	gauge	NOUN
ejpam-5958	36	27	spaces	space	NOUN
ejpam-5958	36	28	,	,	PUNCT
ejpam-5958	36	29	expect	expect	VERB
ejpam-5958	36	30	in	in	ADP
ejpam-5958	36	31	a	a	DET
ejpam-5958	36	32	few	few	ADJ
ejpam-5958	36	33	papers	paper	NOUN
ejpam-5958	36	34	such	such	ADJ
ejpam-5958	36	35	as	as	ADP
ejpam-5958	36	36	[	[	X
ejpam-5958	36	37	36–38	36–38	NUM
ejpam-5958	36	38	]	]	PUNCT
ejpam-5958	36	39	.	.	PUNCT
ejpam-5958	37	1	motivated	motivate	VERB
ejpam-5958	37	2	by	by	ADP
ejpam-5958	37	3	the	the	DET
ejpam-5958	37	4	last	last	ADJ
ejpam-5958	37	5	observation	observation	NOUN
ejpam-5958	37	6	and	and	CCONJ
ejpam-5958	37	7	inspired	inspire	VERB
ejpam-5958	37	8	by	by	ADP
ejpam-5958	37	9	[	[	X
ejpam-5958	37	10	27	27	NUM
ejpam-5958	37	11	,	,	PUNCT
ejpam-5958	37	12	33	33	NUM
ejpam-5958	37	13	,	,	PUNCT
ejpam-5958	37	14	39	39	NUM
ejpam-5958	37	15	]	]	PUNCT
ejpam-5958	37	16	,	,	PUNCT
ejpam-5958	37	17	we	we	PRON
ejpam-5958	37	18	aim	aim	VERB
ejpam-5958	37	19	through	through	ADP
ejpam-5958	37	20	this	this	DET
ejpam-5958	37	21	work	work	NOUN
ejpam-5958	37	22	to	to	PART
ejpam-5958	37	23	extend	extend	VERB
ejpam-5958	37	24	and	and	CCONJ
ejpam-5958	37	25	generalize	generalize	VERB
ejpam-5958	37	26	the	the	DET
ejpam-5958	37	27	concept	concept	NOUN
ejpam-5958	37	28	of	of	ADP
ejpam-5958	37	29	α	α	PROPN
ejpam-5958	37	30	-	-	PUNCT
ejpam-5958	37	31	ψ	ψ	NOUN
ejpam-5958	37	32	contraction	contraction	NOUN
ejpam-5958	37	33	mappings	mapping	NOUN
ejpam-5958	37	34	in	in	ADP
ejpam-5958	37	35	the	the	DET
ejpam-5958	37	36	setting	setting	NOUN
ejpam-5958	37	37	of	of	ADP
ejpam-5958	37	38	b	b	NOUN
ejpam-5958	37	39	-	-	PUNCT
ejpam-5958	37	40	gauge	gauge	NOUN
ejpam-5958	37	41	spaces	space	NOUN
ejpam-5958	37	42	,	,	PUNCT
ejpam-5958	37	43	where	where	SCONJ
ejpam-5958	37	44	a	a	DET
ejpam-5958	37	45	new	new	ADJ
ejpam-5958	37	46	aspect	aspect	NOUN
ejpam-5958	37	47	of	of	ADP
ejpam-5958	37	48	extension	extension	NOUN
ejpam-5958	37	49	has	have	AUX
ejpam-5958	37	50	been	be	AUX
ejpam-5958	37	51	added	add	VERB
ejpam-5958	37	52	.	.	PUNCT
ejpam-5958	38	1	subsequently	subsequently	ADV
ejpam-5958	38	2	,	,	PUNCT
ejpam-5958	38	3	we	we	PRON
ejpam-5958	38	4	give	give	VERB
ejpam-5958	38	5	some	some	DET
ejpam-5958	38	6	related	relate	VERB
ejpam-5958	38	7	fixed	fix	VERB
ejpam-5958	38	8	point	point	NOUN
ejpam-5958	38	9	results	result	NOUN
ejpam-5958	38	10	that	that	PRON
ejpam-5958	38	11	generalize	generalize	VERB
ejpam-5958	38	12	many	many	ADJ
ejpam-5958	38	13	existing	exist	VERB
ejpam-5958	38	14	ones	one	NOUN
ejpam-5958	38	15	in	in	ADP
ejpam-5958	38	16	the	the	DET
ejpam-5958	38	17	literature	literature	NOUN
ejpam-5958	38	18	on	on	ADP
ejpam-5958	38	19	this	this	DET
ejpam-5958	38	20	topic	topic	NOUN
ejpam-5958	38	21	.	.	PUNCT
ejpam-5958	39	1	some	some	PRON
ejpam-5958	39	2	of	of	ADP
ejpam-5958	39	3	their	their	PRON
ejpam-5958	39	4	applications	application	NOUN
ejpam-5958	39	5	to	to	PART
ejpam-5958	39	6	nonlinear	nonlinear	VERB
ejpam-5958	39	7	integral	integral	ADJ
ejpam-5958	39	8	equations	equation	NOUN
ejpam-5958	39	9	on	on	ADP
ejpam-5958	39	10	unbounded	unbounded	ADJ
ejpam-5958	39	11	domains	domain	NOUN
ejpam-5958	39	12	,	,	PUNCT
ejpam-5958	39	13	including	include	VERB
ejpam-5958	39	14	fractional	fractional	ADJ
ejpam-5958	39	15	differential	differential	ADJ
ejpam-5958	39	16	equations	equation	NOUN
ejpam-5958	39	17	with	with	ADP
ejpam-5958	39	18	maxima	maxima	PROPN
ejpam-5958	39	19	,	,	PUNCT
ejpam-5958	39	20	are	be	AUX
ejpam-5958	39	21	also	also	ADV
ejpam-5958	39	22	presented	present	VERB
ejpam-5958	39	23	.	.	PUNCT
ejpam-5958	40	1	k.	k.	PROPN
ejpam-5958	40	2	nisse	nisse	PROPN
ejpam-5958	40	3	et	et	PROPN
ejpam-5958	40	4	al	al	PROPN
ejpam-5958	40	5	.	.	PUNCT
ejpam-5958	40	6	/	/	SYM
ejpam-5958	40	7	eur	eur	PROPN
ejpam-5958	40	8	.	.	PUNCT
ejpam-5958	41	1	j.	j.	PROPN
ejpam-5958	41	2	pure	pure	PROPN
ejpam-5958	41	3	appl	appl	PROPN
ejpam-5958	41	4	.	.	PROPN
ejpam-5958	41	5	math	math	PROPN
ejpam-5958	41	6	,	,	PUNCT
ejpam-5958	41	7	18	18	NUM
ejpam-5958	41	8	(	(	PUNCT
ejpam-5958	41	9	2	2	NUM
ejpam-5958	41	10	)	)	PUNCT
ejpam-5958	41	11	(	(	PUNCT
ejpam-5958	41	12	2025	2025	NUM
ejpam-5958	41	13	)	)	PUNCT
ejpam-5958	41	14	,	,	PUNCT
ejpam-5958	41	15	5958	5958	NUM
ejpam-5958	41	16	3	3	NUM
ejpam-5958	41	17	of	of	ADP
ejpam-5958	41	18	22	22	NUM
ejpam-5958	41	19	2	2	NUM
ejpam-5958	41	20	.	.	PUNCT
ejpam-5958	41	21	preliminaries	preliminary	NOUN
ejpam-5958	41	22	we	we	PRON
ejpam-5958	41	23	start	start	VERB
ejpam-5958	41	24	by	by	ADP
ejpam-5958	41	25	recollecting	recollect	VERB
ejpam-5958	41	26	some	some	DET
ejpam-5958	41	27	definitions	definition	NOUN
ejpam-5958	41	28	from	from	ADP
ejpam-5958	41	29	[	[	X
ejpam-5958	41	30	10	10	NUM
ejpam-5958	41	31	]	]	PUNCT
ejpam-5958	41	32	to	to	PART
ejpam-5958	41	33	define	define	VERB
ejpam-5958	41	34	b	b	NUM
ejpam-5958	41	35	-	-	PUNCT
ejpam-5958	41	36	gauge	gauge	NOUN
ejpam-5958	41	37	spaces	space	NOUN
ejpam-5958	41	38	introduced	introduce	VERB
ejpam-5958	41	39	therein	therein	ADV
ejpam-5958	41	40	.	.	PUNCT
ejpam-5958	42	1	definition	definition	NOUN
ejpam-5958	42	2	2.1	2.1	NUM
ejpam-5958	42	3	.	.	PUNCT
ejpam-5958	43	1	[	[	X
ejpam-5958	43	2	10	10	NUM
ejpam-5958	43	3	]	]	PUNCT
ejpam-5958	43	4	let	let	VERB
ejpam-5958	43	5	e	e	PRON
ejpam-5958	43	6	be	be	AUX
ejpam-5958	43	7	a	a	DET
ejpam-5958	43	8	non	non	ADJ
ejpam-5958	43	9	-	-	ADJ
ejpam-5958	43	10	empty	empty	ADJ
ejpam-5958	43	11	set	set	NOUN
ejpam-5958	43	12	and	and	CCONJ
ejpam-5958	43	13	let	let	VERB
ejpam-5958	43	14	s	s	PRON
ejpam-5958	43	15	≥	≥	X
ejpam-5958	43	16	1	1	NUM
ejpam-5958	43	17	be	be	AUX
ejpam-5958	43	18	a	a	DET
ejpam-5958	43	19	given	give	VERB
ejpam-5958	43	20	real	real	ADJ
ejpam-5958	43	21	number	number	NOUN
ejpam-5958	43	22	.	.	PUNCT
ejpam-5958	44	1	a	a	DET
ejpam-5958	44	2	mapping	mapping	NOUN
ejpam-5958	44	3	d	d	NOUN
ejpam-5958	44	4	:	:	PUNCT
ejpam-5958	44	5	e	e	X
ejpam-5958	44	6	×	×	NOUN
ejpam-5958	44	7	e	e	ADP
ejpam-5958	44	8	−→	−→	NOUN
ejpam-5958	44	9	r+	r+	NOUN
ejpam-5958	44	10	is	be	AUX
ejpam-5958	44	11	said	say	VERB
ejpam-5958	44	12	to	to	PART
ejpam-5958	44	13	be	be	AUX
ejpam-5958	44	14	a	a	DET
ejpam-5958	44	15	b	b	NOUN
ejpam-5958	44	16	-	-	PUNCT
ejpam-5958	44	17	pseudo	pseudo	NOUN
ejpam-5958	44	18	metric	metric	NOUN
ejpam-5958	44	19	on	on	ADP
ejpam-5958	44	20	e	e	NOUN
ejpam-5958	44	21	,	,	PUNCT
ejpam-5958	44	22	if	if	SCONJ
ejpam-5958	44	23	for	for	ADP
ejpam-5958	44	24	all	all	DET
ejpam-5958	44	25	u	u	NOUN
ejpam-5958	44	26	,	,	PUNCT
ejpam-5958	44	27	v	v	NOUN
ejpam-5958	44	28	,	,	PUNCT
ejpam-5958	44	29	w	w	PROPN
ejpam-5958	44	30	∈	∈	PROPN
ejpam-5958	44	31	e	e	NOUN
ejpam-5958	44	32	,	,	PUNCT
ejpam-5958	44	33	the	the	DET
ejpam-5958	44	34	following	follow	VERB
ejpam-5958	44	35	conditions	condition	NOUN
ejpam-5958	44	36	hold	hold	VERB
ejpam-5958	44	37	true	true	ADJ
ejpam-5958	44	38	1	1	NUM
ejpam-5958	44	39	.	.	PUNCT
ejpam-5958	45	1	d(u	d(u	PROPN
ejpam-5958	45	2	,	,	PUNCT
ejpam-5958	45	3	u	u	NOUN
ejpam-5958	45	4	)	)	PUNCT
ejpam-5958	45	5	=	=	SYM
ejpam-5958	45	6	0	0	NUM
ejpam-5958	45	7	;	;	PUNCT
ejpam-5958	45	8	2	2	NUM
ejpam-5958	45	9	.	.	X
ejpam-5958	46	1	d(u	d(u	PROPN
ejpam-5958	46	2	,	,	PUNCT
ejpam-5958	46	3	v	v	NOUN
ejpam-5958	46	4	)	)	PUNCT
ejpam-5958	46	5	=	=	SYM
ejpam-5958	47	1	d(v	d(v	PROPN
ejpam-5958	47	2	,	,	PUNCT
ejpam-5958	47	3	u	u	NOUN
ejpam-5958	47	4	)	)	PUNCT
ejpam-5958	47	5	;	;	PUNCT
ejpam-5958	48	1	3	3	X
ejpam-5958	48	2	.	.	X
ejpam-5958	49	1	d(u	d(u	PROPN
ejpam-5958	49	2	,	,	PUNCT
ejpam-5958	49	3	w	w	NOUN
ejpam-5958	49	4	)	)	PUNCT
ejpam-5958	49	5	≤	≤	NOUN
ejpam-5958	49	6	s	s	PART
ejpam-5958	50	1	[	[	X
ejpam-5958	50	2	d(u	d(u	PROPN
ejpam-5958	50	3	,	,	PUNCT
ejpam-5958	50	4	v	v	NOUN
ejpam-5958	50	5	)	)	PUNCT
ejpam-5958	50	6	+	+	X
ejpam-5958	50	7	d(v	d(v	ADJ
ejpam-5958	50	8	,	,	PUNCT
ejpam-5958	50	9	w	w	NOUN
ejpam-5958	50	10	)	)	PUNCT
ejpam-5958	50	11	]	]	PUNCT
ejpam-5958	50	12	.	.	PUNCT
ejpam-5958	51	1	the	the	DET
ejpam-5958	51	2	d	d	NOUN
ejpam-5958	51	3	-	-	PUNCT
ejpam-5958	51	4	ball	ball	NOUN
ejpam-5958	51	5	of	of	ADP
ejpam-5958	51	6	radius	radius	NOUN
ejpam-5958	51	7	ϵ	ϵ	PROPN
ejpam-5958	51	8	>	>	X
ejpam-5958	51	9	0	0	NUM
ejpam-5958	51	10	centred	centre	VERB
ejpam-5958	51	11	at	at	ADP
ejpam-5958	51	12	u	u	NOUN
ejpam-5958	51	13	∈	∈	PROPN
ejpam-5958	51	14	e	e	NOUN
ejpam-5958	51	15	is	be	AUX
ejpam-5958	51	16	the	the	DET
ejpam-5958	51	17	set	set	NOUN
ejpam-5958	51	18	:	:	PUNCT
ejpam-5958	51	19	b(u	b(u	PROPN
ejpam-5958	51	20	,	,	PUNCT
ejpam-5958	51	21	d	d	X
ejpam-5958	51	22	,	,	PUNCT
ejpam-5958	51	23	ϵ	ϵ	NOUN
ejpam-5958	51	24	)	)	PUNCT
ejpam-5958	51	25	=	=	SYM
ejpam-5958	51	26	{	{	PUNCT
ejpam-5958	51	27	v	v	NUM
ejpam-5958	51	28	∈	∈	NOUN
ejpam-5958	51	29	e	e	NOUN
ejpam-5958	51	30	:	:	PUNCT
ejpam-5958	51	31	d(u	d(u	PROPN
ejpam-5958	51	32	,	,	PUNCT
ejpam-5958	51	33	v	v	NOUN
ejpam-5958	51	34	)	)	PUNCT
ejpam-5958	51	35	<	<	X
ejpam-5958	51	36	ϵ	ϵ	X
ejpam-5958	51	37	}	}	PUNCT
ejpam-5958	51	38	.	.	PUNCT
ejpam-5958	52	1	definition	definition	NOUN
ejpam-5958	52	2	2.2	2.2	NUM
ejpam-5958	52	3	.	.	PUNCT
ejpam-5958	53	1	[	[	X
ejpam-5958	53	2	10	10	NUM
ejpam-5958	53	3	]	]	X
ejpam-5958	53	4	a	a	DET
ejpam-5958	53	5	family	family	NOUN
ejpam-5958	53	6	d	d	NOUN
ejpam-5958	53	7	=	=	PRON
ejpam-5958	53	8	{	{	PUNCT
ejpam-5958	53	9	dν}ν∈n	dν}ν∈n	X
ejpam-5958	53	10	of	of	ADP
ejpam-5958	53	11	b	b	NOUN
ejpam-5958	53	12	-	-	PUNCT
ejpam-5958	53	13	pseudo	pseudo	NOUN
ejpam-5958	53	14	metrics	metric	NOUN
ejpam-5958	53	15	on	on	ADP
ejpam-5958	53	16	e	e	NOUN
ejpam-5958	53	17	is	be	AUX
ejpam-5958	53	18	said	say	VERB
ejpam-5958	53	19	to	to	PART
ejpam-5958	53	20	be	be	AUX
ejpam-5958	53	21	separating	separate	VERB
ejpam-5958	53	22	if	if	SCONJ
ejpam-5958	53	23	for	for	ADP
ejpam-5958	53	24	every	every	DET
ejpam-5958	53	25	two	two	NUM
ejpam-5958	53	26	distinct	distinct	ADJ
ejpam-5958	53	27	points	point	NOUN
ejpam-5958	53	28	u	u	NOUN
ejpam-5958	53	29	and	and	CCONJ
ejpam-5958	53	30	v	v	NOUN
ejpam-5958	53	31	,	,	PUNCT
ejpam-5958	53	32	there	there	PRON
ejpam-5958	53	33	exists	exist	VERB
ejpam-5958	53	34	dν	dν	VERB
ejpam-5958	53	35	∈	∈	PROPN
ejpam-5958	54	1	d	d	ADP
ejpam-5958	54	2	such	such	ADJ
ejpam-5958	54	3	that	that	SCONJ
ejpam-5958	54	4	dν(u	dν(u	NOUN
ejpam-5958	54	5	,	,	PUNCT
ejpam-5958	54	6	v	v	NOUN
ejpam-5958	54	7	)	)	PUNCT
ejpam-5958	54	8	̸=	̸=	PROPN
ejpam-5958	54	9	0	0	NUM
ejpam-5958	54	10	.	.	PUNCT
ejpam-5958	55	1	definition	definition	NOUN
ejpam-5958	55	2	2.3	2.3	NUM
ejpam-5958	55	3	.	.	PUNCT
ejpam-5958	56	1	[	[	X
ejpam-5958	56	2	10	10	NUM
ejpam-5958	56	3	]	]	PUNCT
ejpam-5958	56	4	let	let	VERB
ejpam-5958	56	5	e	e	PRON
ejpam-5958	56	6	be	be	AUX
ejpam-5958	56	7	a	a	DET
ejpam-5958	56	8	nonempty	nonempty	ADV
ejpam-5958	56	9	set	set	VERB
ejpam-5958	56	10	and	and	CCONJ
ejpam-5958	56	11	d	d	NOUN
ejpam-5958	56	12	=	=	PRON
ejpam-5958	56	13	{	{	PUNCT
ejpam-5958	56	14	dν}ν∈n	dν}ν∈n	VERB
ejpam-5958	56	15	a	a	DET
ejpam-5958	56	16	family	family	NOUN
ejpam-5958	56	17	of	of	ADP
ejpam-5958	56	18	b	b	NOUN
ejpam-5958	56	19	-	-	PUNCT
ejpam-5958	56	20	pseudo	pseudo	NOUN
ejpam-5958	56	21	metrics	metric	NOUN
ejpam-5958	56	22	on	on	ADP
ejpam-5958	56	23	e.	e.	PROPN
ejpam-5958	56	24	the	the	DET
ejpam-5958	56	25	topology	topology	NOUN
ejpam-5958	56	26	generated	generate	VERB
ejpam-5958	56	27	by	by	ADP
ejpam-5958	56	28	the	the	DET
ejpam-5958	56	29	family	family	NOUN
ejpam-5958	56	30	d	d	PROPN
ejpam-5958	56	31	and	and	CCONJ
ejpam-5958	56	32	denoted	denote	VERB
ejpam-5958	56	33	by	by	ADP
ejpam-5958	56	34	t	t	PROPN
ejpam-5958	56	35	(	(	PUNCT
ejpam-5958	56	36	d	d	PROPN
ejpam-5958	56	37	)	)	PUNCT
ejpam-5958	56	38	,	,	PUNCT
ejpam-5958	56	39	is	be	AUX
ejpam-5958	56	40	the	the	DET
ejpam-5958	56	41	topology	topology	NOUN
ejpam-5958	56	42	whose	whose	DET
ejpam-5958	56	43	subbase	subbase	NOUN
ejpam-5958	56	44	b(t	b(t	PROPN
ejpam-5958	56	45	)	)	PUNCT
ejpam-5958	56	46	is	be	AUX
ejpam-5958	56	47	the	the	DET
ejpam-5958	56	48	family	family	NOUN
ejpam-5958	56	49	of	of	ADP
ejpam-5958	56	50	all	all	DET
ejpam-5958	56	51	balls	ball	NOUN
ejpam-5958	56	52	dν(u	dν(u	X
ejpam-5958	56	53	,	,	PUNCT
ejpam-5958	56	54	ϵ	ϵ	NOUN
ejpam-5958	56	55	)	)	PUNCT
ejpam-5958	56	56	,	,	PUNCT
ejpam-5958	56	57	namely	namely	ADV
ejpam-5958	56	58	:	:	PUNCT
ejpam-5958	56	59	b(t	b(t	NOUN
ejpam-5958	56	60	)	)	PUNCT
ejpam-5958	57	1	=	=	PRON
ejpam-5958	57	2	{	{	PUNCT
ejpam-5958	57	3	dν(u	dν(u	NOUN
ejpam-5958	57	4	,	,	PUNCT
ejpam-5958	57	5	ϵ	ϵ	NOUN
ejpam-5958	57	6	)	)	PUNCT
ejpam-5958	57	7	:	:	PUNCT
ejpam-5958	57	8	u	u	NOUN
ejpam-5958	57	9	∈	∈	PROPN
ejpam-5958	57	10	e	e	NOUN
ejpam-5958	57	11	,	,	PUNCT
ejpam-5958	57	12	ϵ	ϵ	X
ejpam-5958	57	13	>	>	X
ejpam-5958	57	14	0	0	PROPN
ejpam-5958	57	15	,	,	PUNCT
ejpam-5958	57	16	ν	ν	X
ejpam-5958	57	17	∈	∈	PROPN
ejpam-5958	57	18	n	n	CCONJ
ejpam-5958	57	19	}	}	PUNCT
ejpam-5958	57	20	.	.	PUNCT
ejpam-5958	58	1	the	the	DET
ejpam-5958	58	2	pair	pair	NOUN
ejpam-5958	58	3	(	(	PUNCT
ejpam-5958	58	4	e	e	NOUN
ejpam-5958	58	5	,	,	PUNCT
ejpam-5958	58	6	b(t	b(t	NOUN
ejpam-5958	58	7	)	)	PUNCT
ejpam-5958	58	8	)	)	PUNCT
ejpam-5958	58	9	is	be	AUX
ejpam-5958	58	10	called	call	VERB
ejpam-5958	58	11	a	a	DET
ejpam-5958	58	12	b	b	NUM
ejpam-5958	58	13	-	-	PUNCT
ejpam-5958	58	14	gauge	gauge	NOUN
ejpam-5958	58	15	space	space	NOUN
ejpam-5958	58	16	and	and	CCONJ
ejpam-5958	58	17	is	be	AUX
ejpam-5958	58	18	hausdorff	hausdorff	NOUN
ejpam-5958	58	19	if	if	SCONJ
ejpam-5958	58	20	d	d	PROPN
ejpam-5958	58	21	is	be	AUX
ejpam-5958	58	22	separating	separate	VERB
ejpam-5958	58	23	.	.	PUNCT
ejpam-5958	59	1	the	the	DET
ejpam-5958	59	2	notions	notion	NOUN
ejpam-5958	59	3	of	of	ADP
ejpam-5958	59	4	convergent	convergent	NOUN
ejpam-5958	59	5	sequences	sequence	NOUN
ejpam-5958	59	6	,	,	PUNCT
ejpam-5958	59	7	cauchy	cauchy	NOUN
ejpam-5958	59	8	sequences	sequence	NOUN
ejpam-5958	59	9	and	and	CCONJ
ejpam-5958	59	10	completeness	completeness	NOUN
ejpam-5958	59	11	in	in	ADP
ejpam-5958	59	12	b	b	NOUN
ejpam-5958	59	13	-	-	PUNCT
ejpam-5958	59	14	gauge	gauge	NOUN
ejpam-5958	59	15	spaces	space	NOUN
ejpam-5958	59	16	,	,	PUNCT
ejpam-5958	59	17	are	be	AUX
ejpam-5958	59	18	similar	similar	ADJ
ejpam-5958	59	19	to	to	ADP
ejpam-5958	59	20	those	those	PRON
ejpam-5958	59	21	in	in	ADP
ejpam-5958	59	22	metric	metric	ADJ
ejpam-5958	59	23	spaces	space	NOUN
ejpam-5958	59	24	.	.	PUNCT
ejpam-5958	60	1	for	for	ADP
ejpam-5958	60	2	more	more	ADJ
ejpam-5958	60	3	details	detail	NOUN
ejpam-5958	60	4	on	on	ADP
ejpam-5958	60	5	these	these	DET
ejpam-5958	60	6	notions	notion	NOUN
ejpam-5958	60	7	and	and	CCONJ
ejpam-5958	60	8	further	further	ADJ
ejpam-5958	60	9	properties	property	NOUN
ejpam-5958	60	10	and	and	CCONJ
ejpam-5958	60	11	examples	example	NOUN
ejpam-5958	60	12	on	on	ADP
ejpam-5958	60	13	b	b	NOUN
ejpam-5958	60	14	-	-	PUNCT
ejpam-5958	60	15	gauge	gauge	NOUN
ejpam-5958	60	16	spaces	space	NOUN
ejpam-5958	60	17	,	,	PUNCT
ejpam-5958	60	18	we	we	PRON
ejpam-5958	60	19	refer	refer	VERB
ejpam-5958	60	20	to	to	ADP
ejpam-5958	60	21	[	[	X
ejpam-5958	60	22	10	10	NUM
ejpam-5958	60	23	]	]	PUNCT
ejpam-5958	60	24	.	.	PUNCT
ejpam-5958	61	1	in	in	ADP
ejpam-5958	61	2	the	the	DET
ejpam-5958	61	3	aim	aim	NOUN
ejpam-5958	61	4	of	of	ADP
ejpam-5958	61	5	generalizing	generalize	VERB
ejpam-5958	61	6	the	the	DET
ejpam-5958	61	7	contraction	contraction	NOUN
ejpam-5958	61	8	conditions	condition	NOUN
ejpam-5958	61	9	,	,	PUNCT
ejpam-5958	61	10	various	various	ADJ
ejpam-5958	61	11	families	family	NOUN
ejpam-5958	61	12	of	of	ADP
ejpam-5958	61	13	auxiliary	auxiliary	ADJ
ejpam-5958	61	14	functions	function	NOUN
ejpam-5958	61	15	are	be	AUX
ejpam-5958	61	16	introduced	introduce	VERB
ejpam-5958	61	17	in	in	ADP
ejpam-5958	61	18	the	the	DET
ejpam-5958	61	19	existing	exist	VERB
ejpam-5958	61	20	literature	literature	NOUN
ejpam-5958	61	21	.	.	PUNCT
ejpam-5958	62	1	in	in	ADP
ejpam-5958	62	2	this	this	DET
ejpam-5958	62	3	regard	regard	NOUN
ejpam-5958	62	4	,	,	PUNCT
ejpam-5958	62	5	we	we	PRON
ejpam-5958	62	6	introduce	introduce	VERB
ejpam-5958	62	7	now	now	ADV
ejpam-5958	62	8	one	one	NUM
ejpam-5958	62	9	of	of	ADP
ejpam-5958	62	10	such	such	ADJ
ejpam-5958	62	11	families	family	NOUN
ejpam-5958	62	12	.	.	PUNCT
ejpam-5958	63	1	for	for	ADP
ejpam-5958	63	2	s	s	PRON
ejpam-5958	63	3	≥	≥	NOUN
ejpam-5958	63	4	1	1	NUM
ejpam-5958	63	5	,	,	PUNCT
ejpam-5958	63	6	let	let	VERB
ejpam-5958	63	7	ψs	ψs	PART
ejpam-5958	63	8	be	be	AUX
ejpam-5958	63	9	the	the	DET
ejpam-5958	63	10	family	family	NOUN
ejpam-5958	63	11	of	of	ADP
ejpam-5958	63	12	functions	function	NOUN
ejpam-5958	63	13	ψ	ψ	NOUN
ejpam-5958	63	14	:	:	PUNCT
ejpam-5958	63	15	r+	r+	NOUN
ejpam-5958	63	16	−→	−→	ADJ
ejpam-5958	63	17	r+	r+	PUNCT
ejpam-5958	63	18	satisfying	satisfy	VERB
ejpam-5958	63	19	the	the	DET
ejpam-5958	63	20	following	follow	VERB
ejpam-5958	63	21	conditions	condition	NOUN
ejpam-5958	63	22	,	,	PUNCT
ejpam-5958	63	23	where	where	SCONJ
ejpam-5958	63	24	ψi	ψi	ADP
ejpam-5958	63	25	denotes	denote	VERB
ejpam-5958	63	26	the	the	DET
ejpam-5958	63	27	ith	ith	PROPN
ejpam-5958	63	28	iteration	iteration	NOUN
ejpam-5958	63	29	of	of	ADP
ejpam-5958	63	30	ψ	ψ	PROPN
ejpam-5958	63	31	.	.	PUNCT
ejpam-5958	64	1	(	(	PUNCT
ejpam-5958	64	2	ψs	ψs	NOUN
ejpam-5958	64	3	1	1	NUM
ejpam-5958	64	4	)	)	PUNCT
ejpam-5958	64	5	:	:	PUNCT
ejpam-5958	64	6	ψ	ψ	NOUN
ejpam-5958	64	7	is	be	AUX
ejpam-5958	64	8	non	non	ADJ
ejpam-5958	64	9	-	-	ADJ
ejpam-5958	64	10	decreasing	decrease	VERB
ejpam-5958	64	11	;	;	PUNCT
ejpam-5958	64	12	(	(	PUNCT
ejpam-5958	64	13	ψs	ψs	NOUN
ejpam-5958	64	14	2	2	NUM
ejpam-5958	64	15	)	)	PUNCT
ejpam-5958	64	16	:	:	PUNCT
ejpam-5958	64	17	ψ(st	ψ(st	X
ejpam-5958	64	18	)	)	PUNCT
ejpam-5958	64	19	=	=	SYM
ejpam-5958	64	20	sψ(t	sψ(t	PROPN
ejpam-5958	64	21	)	)	PUNCT
ejpam-5958	64	22	,	,	PUNCT
ejpam-5958	64	23	∀	∀	X
ejpam-5958	64	24	t	t	X
ejpam-5958	64	25	>	>	X
ejpam-5958	64	26	0	0	NUM
ejpam-5958	64	27	;	;	PUNCT
ejpam-5958	64	28	(	(	PUNCT
ejpam-5958	64	29	ψs	ψs	NOUN
ejpam-5958	64	30	3	3	NUM
ejpam-5958	64	31	)	)	PUNCT
ejpam-5958	64	32	:	:	PUNCT
ejpam-5958	65	1	∞∑	∞∑	NUM
ejpam-5958	65	2	i=1	i=1	PROPN
ejpam-5958	65	3	siψi(t	siψi(t	NOUN
ejpam-5958	65	4	)	)	PUNCT
ejpam-5958	65	5	<	<	X
ejpam-5958	66	1	+	+	X
ejpam-5958	66	2	∞	∞	PROPN
ejpam-5958	66	3	for	for	ADP
ejpam-5958	66	4	each	each	DET
ejpam-5958	66	5	t	t	PROPN
ejpam-5958	66	6	>	>	X
ejpam-5958	66	7	0	0	NUM
ejpam-5958	66	8	;	;	PUNCT
ejpam-5958	66	9	(	(	PUNCT
ejpam-5958	66	10	ψs	ψs	ADP
ejpam-5958	66	11	4	4	NUM
ejpam-5958	66	12	)	)	PUNCT
ejpam-5958	66	13	:	:	PUNCT
ejpam-5958	66	14	ψ(t1	ψ(t1	X
ejpam-5958	66	15	)	)	PUNCT
ejpam-5958	67	1	+	+	CCONJ
ejpam-5958	67	2	ψ(t2	ψ(t2	NOUN
ejpam-5958	67	3	)	)	PUNCT
ejpam-5958	67	4	≤	≤	NOUN
ejpam-5958	67	5	ψ(t1	ψ(t1	VERB
ejpam-5958	67	6	+	+	CCONJ
ejpam-5958	68	1	t2	t2	NOUN
ejpam-5958	69	1	)	)	PUNCT
ejpam-5958	69	2	,	,	PUNCT
ejpam-5958	69	3	∀	∀	X
ejpam-5958	69	4	t1	t1	NOUN
ejpam-5958	69	5	,	,	PUNCT
ejpam-5958	69	6	t2	t2	NOUN
ejpam-5958	69	7	>	>	X
ejpam-5958	69	8	0	0	X
ejpam-5958	69	9	.	.	PUNCT
ejpam-5958	70	1	k.	k.	PROPN
ejpam-5958	70	2	nisse	nisse	PROPN
ejpam-5958	70	3	et	et	PROPN
ejpam-5958	70	4	al	al	PROPN
ejpam-5958	70	5	.	.	PUNCT
ejpam-5958	70	6	/	/	SYM
ejpam-5958	70	7	eur	eur	PROPN
ejpam-5958	70	8	.	.	PUNCT
ejpam-5958	71	1	j.	j.	PROPN
ejpam-5958	71	2	pure	pure	PROPN
ejpam-5958	71	3	appl	appl	PROPN
ejpam-5958	71	4	.	.	PROPN
ejpam-5958	71	5	math	math	PROPN
ejpam-5958	71	6	,	,	PUNCT
ejpam-5958	71	7	18	18	NUM
ejpam-5958	71	8	(	(	PUNCT
ejpam-5958	71	9	2	2	NUM
ejpam-5958	71	10	)	)	PUNCT
ejpam-5958	71	11	(	(	PUNCT
ejpam-5958	71	12	2025	2025	NUM
ejpam-5958	71	13	)	)	PUNCT
ejpam-5958	71	14	,	,	PUNCT
ejpam-5958	71	15	5958	5958	NUM
ejpam-5958	71	16	4	4	NUM
ejpam-5958	71	17	of	of	ADP
ejpam-5958	71	18	22	22	NUM
ejpam-5958	71	19	example	example	NOUN
ejpam-5958	71	20	1	1	NUM
ejpam-5958	71	21	.	.	PUNCT
ejpam-5958	72	1	(	(	PUNCT
ejpam-5958	72	2	i	i	NOUN
ejpam-5958	72	3	)	)	PUNCT
ejpam-5958	72	4	let	let	VERB
ejpam-5958	72	5	ψ	ψ	NOUN
ejpam-5958	72	6	:	:	PUNCT
ejpam-5958	72	7	r+	r+	NOUN
ejpam-5958	72	8	−→	−→	ADJ
ejpam-5958	72	9	r+	r+	PUNCT
ejpam-5958	72	10	be	be	AUX
ejpam-5958	72	11	the	the	DET
ejpam-5958	72	12	function	function	NOUN
ejpam-5958	72	13	defined	define	VERB
ejpam-5958	72	14	by	by	ADP
ejpam-5958	72	15	:	:	PUNCT
ejpam-5958	72	16	ψ(t	ψ(t	PROPN
ejpam-5958	72	17	)	)	PUNCT
ejpam-5958	72	18	=	=	PUNCT
ejpam-5958	73	1	c	c	NOUN
ejpam-5958	73	2	t.	t.	NOUN
ejpam-5958	73	3	then	then	ADV
ejpam-5958	73	4	,	,	PUNCT
ejpam-5958	73	5	ψ	ψ	PROPN
ejpam-5958	73	6	∈	∈	PROPN
ejpam-5958	73	7	ψs	ψs	NOUN
ejpam-5958	73	8	,	,	PUNCT
ejpam-5958	73	9	for	for	ADP
ejpam-5958	73	10	all	all	DET
ejpam-5958	73	11	s	s	PART
ejpam-5958	73	12	≥	≥	NOUN
ejpam-5958	73	13	1	1	NUM
ejpam-5958	73	14	such	such	ADJ
ejpam-5958	73	15	that	that	DET
ejpam-5958	73	16	sc	sc	PROPN
ejpam-5958	73	17	<	<	X
ejpam-5958	73	18	1	1	NUM
ejpam-5958	73	19	.	.	PUNCT
ejpam-5958	73	20	(	(	PUNCT
ejpam-5958	73	21	ii	ii	NOUN
ejpam-5958	73	22	)	)	PUNCT
ejpam-5958	73	23	let	let	VERB
ejpam-5958	73	24	ψ	ψ	NOUN
ejpam-5958	73	25	:	:	PUNCT
ejpam-5958	73	26	r+	r+	NOUN
ejpam-5958	73	27	−→	−→	ADJ
ejpam-5958	73	28	r+	r+	PUNCT
ejpam-5958	73	29	be	be	AUX
ejpam-5958	73	30	the	the	DET
ejpam-5958	73	31	function	function	NOUN
ejpam-5958	73	32	defined	define	VERB
ejpam-5958	73	33	by	by	ADP
ejpam-5958	73	34	:	:	PUNCT
ejpam-5958	73	35	ψ(t	ψ(t	PROPN
ejpam-5958	73	36	)	)	PUNCT
ejpam-5958	74	1	=	=	PRON
ejpam-5958	74	2	{	{	PUNCT
ejpam-5958	74	3	t2	t2	NOUN
ejpam-5958	74	4	2	2	NUM
ejpam-5958	74	5	:	:	SYM
ejpam-5958	74	6	0	0	NUM
ejpam-5958	74	7	≤	≤	NUM
ejpam-5958	74	8	t	t	X
ejpam-5958	74	9	<	<	X
ejpam-5958	74	10	1	1	NUM
ejpam-5958	74	11	t	t	NOUN
ejpam-5958	74	12	2	2	NUM
ejpam-5958	74	13	:	:	PUNCT
ejpam-5958	74	14	t	t	PROPN
ejpam-5958	74	15	≥	≥	NUM
ejpam-5958	74	16	1	1	NUM
ejpam-5958	74	17	then	then	ADV
ejpam-5958	74	18	ψ	ψ	ADP
ejpam-5958	74	19	∈	∈	PROPN
ejpam-5958	74	20	ψ1	ψ1	NOUN
ejpam-5958	74	21	.	.	PUNCT
ejpam-5958	75	1	lemma	lemma	PROPN
ejpam-5958	75	2	2.4	2.4	NUM
ejpam-5958	75	3	.	.	PUNCT
ejpam-5958	76	1	for	for	ADP
ejpam-5958	76	2	every	every	DET
ejpam-5958	76	3	ψ	ψ	PROPN
ejpam-5958	76	4	∈	∈	PROPN
ejpam-5958	76	5	ψs	ψs	NOUN
ejpam-5958	76	6	,	,	PUNCT
ejpam-5958	76	7	the	the	DET
ejpam-5958	76	8	following	follow	VERB
ejpam-5958	76	9	properties	property	NOUN
ejpam-5958	76	10	are	be	AUX
ejpam-5958	76	11	satisfied	satisfied	ADJ
ejpam-5958	76	12	:	:	PUNCT
ejpam-5958	76	13	(	(	PUNCT
ejpam-5958	76	14	i	i	NOUN
ejpam-5958	76	15	)	)	PUNCT
ejpam-5958	76	16	ψ(t	ψ(t	PROPN
ejpam-5958	76	17	)	)	PUNCT
ejpam-5958	76	18	≤	≤	NUM
ejpam-5958	76	19	ψ(st	ψ(st	NOUN
ejpam-5958	76	20	)	)	PUNCT
ejpam-5958	76	21	<	<	X
ejpam-5958	76	22	t	t	PROPN
ejpam-5958	76	23	,	,	PUNCT
ejpam-5958	76	24	∀t	∀t	PROPN
ejpam-5958	76	25	>	>	X
ejpam-5958	76	26	0	0	NUM
ejpam-5958	76	27	;	;	PUNCT
ejpam-5958	76	28	(	(	PUNCT
ejpam-5958	76	29	ii	ii	NOUN
ejpam-5958	76	30	)	)	PUNCT
ejpam-5958	76	31	lim	lim	PROPN
ejpam-5958	76	32	t→0	t→0	PROPN
ejpam-5958	76	33	+	+	CCONJ
ejpam-5958	76	34	ψ(t	ψ(t	PROPN
ejpam-5958	76	35	)	)	PUNCT
ejpam-5958	77	1	=	=	SYM
ejpam-5958	77	2	0	0	X
ejpam-5958	77	3	.	.	PUNCT
ejpam-5958	78	1	proof	proof	NOUN
ejpam-5958	78	2	.	.	PUNCT
ejpam-5958	79	1	we	we	PRON
ejpam-5958	79	2	begin	begin	VERB
ejpam-5958	79	3	by	by	ADP
ejpam-5958	79	4	demonstrating	demonstrate	VERB
ejpam-5958	79	5	the	the	DET
ejpam-5958	79	6	following	follow	VERB
ejpam-5958	79	7	statement	statement	NOUN
ejpam-5958	79	8	:	:	PUNCT
ejpam-5958	79	9	ψ(st	ψ(st	X
ejpam-5958	79	10	)	)	PUNCT
ejpam-5958	79	11	<	<	X
ejpam-5958	79	12	t	t	PROPN
ejpam-5958	79	13	,	,	PUNCT
ejpam-5958	79	14	∀t	∀t	PROPN
ejpam-5958	79	15	>	>	X
ejpam-5958	79	16	0	0	NUM
ejpam-5958	79	17	.	.	PUNCT
ejpam-5958	80	1	(	(	PUNCT
ejpam-5958	80	2	2.1	2.1	NUM
ejpam-5958	80	3	)	)	PUNCT
ejpam-5958	80	4	to	to	ADP
ejpam-5958	80	5	this	this	DET
ejpam-5958	80	6	end	end	NOUN
ejpam-5958	80	7	,	,	PUNCT
ejpam-5958	80	8	we	we	PRON
ejpam-5958	80	9	proceed	proceed	VERB
ejpam-5958	80	10	by	by	ADP
ejpam-5958	80	11	contradiction	contradiction	NOUN
ejpam-5958	80	12	.	.	PUNCT
ejpam-5958	81	1	let	let	VERB
ejpam-5958	81	2	us	we	PRON
ejpam-5958	81	3	suppose	suppose	VERB
ejpam-5958	81	4	that	that	SCONJ
ejpam-5958	81	5	ψ(st0	ψ(st0	PROPN
ejpam-5958	81	6	)	)	PUNCT
ejpam-5958	81	7	≥	≥	NOUN
ejpam-5958	81	8	t0	t0	NOUN
ejpam-5958	81	9	for	for	ADP
ejpam-5958	81	10	some	some	DET
ejpam-5958	81	11	t0	t0	PROPN
ejpam-5958	81	12	>	>	X
ejpam-5958	81	13	0	0	X
ejpam-5958	81	14	.	.	PUNCT
ejpam-5958	82	1	from	from	ADP
ejpam-5958	82	2	(	(	PUNCT
ejpam-5958	82	3	ψs	ψs	NOUN
ejpam-5958	82	4	1	1	NUM
ejpam-5958	82	5	)	)	PUNCT
ejpam-5958	82	6	and	and	CCONJ
ejpam-5958	82	7	(	(	PUNCT
ejpam-5958	82	8	ψs	ψs	NOUN
ejpam-5958	82	9	2	2	NUM
ejpam-5958	82	10	)	)	PUNCT
ejpam-5958	82	11	,	,	PUNCT
ejpam-5958	82	12	we	we	PRON
ejpam-5958	82	13	get	get	VERB
ejpam-5958	82	14	:	:	PUNCT
ejpam-5958	82	15	s2ψ2(t0	s2ψ2(t0	ADJ
ejpam-5958	82	16	)	)	PUNCT
ejpam-5958	82	17	=	=	SYM
ejpam-5958	82	18	sψ(ψ(st0	sψ(ψ(st0	PROPN
ejpam-5958	82	19	)	)	PUNCT
ejpam-5958	82	20	)	)	PUNCT
ejpam-5958	82	21	≥	≥	NOUN
ejpam-5958	82	22	sψ(t0	sψ(t0	NOUN
ejpam-5958	82	23	)	)	PUNCT
ejpam-5958	82	24	=	=	SYM
ejpam-5958	83	1	ψ(st0	ψ(st0	ADJ
ejpam-5958	83	2	)	)	PUNCT
ejpam-5958	83	3	≥	≥	PROPN
ejpam-5958	83	4	t0	t0	NOUN
ejpam-5958	83	5	.	.	PUNCT
ejpam-5958	84	1	similarly	similarly	ADV
ejpam-5958	84	2	it	it	PRON
ejpam-5958	84	3	can	can	AUX
ejpam-5958	84	4	be	be	AUX
ejpam-5958	84	5	easily	easily	ADV
ejpam-5958	84	6	deduced	deduce	VERB
ejpam-5958	84	7	by	by	ADP
ejpam-5958	84	8	induction	induction	NOUN
ejpam-5958	84	9	that	that	SCONJ
ejpam-5958	84	10	:	:	PUNCT
ejpam-5958	84	11	∀i	∀i	NOUN
ejpam-5958	84	12	≥	≥	NOUN
ejpam-5958	84	13	1	1	NUM
ejpam-5958	84	14	:	:	PUNCT
ejpam-5958	84	15	siψi(t0	siψi(t0	ADJ
ejpam-5958	84	16	)	)	PUNCT
ejpam-5958	84	17	≥	≥	NOUN
ejpam-5958	84	18	t0	t0	NOUN
ejpam-5958	84	19	.	.	PUNCT
ejpam-5958	85	1	consequently	consequently	ADV
ejpam-5958	85	2	:	:	PUNCT
ejpam-5958	85	3	lim	lim	PROPN
ejpam-5958	85	4	i→∞	i→∞	NUM
ejpam-5958	85	5	siψi(t0	siψi(t0	NOUN
ejpam-5958	85	6	)	)	PUNCT
ejpam-5958	85	7	≥	≥	NOUN
ejpam-5958	85	8	t0	t0	X
ejpam-5958	85	9	>	>	X
ejpam-5958	85	10	0	0	PROPN
ejpam-5958	85	11	,	,	PUNCT
ejpam-5958	85	12	which	which	PRON
ejpam-5958	85	13	is	be	AUX
ejpam-5958	85	14	a	a	DET
ejpam-5958	85	15	contradiction	contradiction	NOUN
ejpam-5958	85	16	with	with	ADP
ejpam-5958	85	17	(	(	PUNCT
ejpam-5958	85	18	ψs	ψs	NOUN
ejpam-5958	85	19	3	3	NUM
ejpam-5958	85	20	)	)	PUNCT
ejpam-5958	85	21	.	.	PUNCT
ejpam-5958	86	1	hence	hence	ADV
ejpam-5958	86	2	,	,	PUNCT
ejpam-5958	86	3	(	(	PUNCT
ejpam-5958	86	4	2.1	2.1	NUM
ejpam-5958	86	5	)	)	PUNCT
ejpam-5958	86	6	is	be	AUX
ejpam-5958	86	7	proved	prove	VERB
ejpam-5958	86	8	.	.	PUNCT
ejpam-5958	87	1	the	the	DET
ejpam-5958	87	2	first	first	ADJ
ejpam-5958	87	3	inequality	inequality	NOUN
ejpam-5958	87	4	in	in	ADP
ejpam-5958	87	5	the	the	DET
ejpam-5958	87	6	statement	statement	NOUN
ejpam-5958	87	7	(	(	PUNCT
ejpam-5958	87	8	1	1	X
ejpam-5958	87	9	)	)	PUNCT
ejpam-5958	87	10	follows	follow	VERB
ejpam-5958	87	11	directly	directly	ADV
ejpam-5958	87	12	from	from	ADP
ejpam-5958	87	13	(	(	PUNCT
ejpam-5958	87	14	ψs	ψs	NOUN
ejpam-5958	87	15	1	1	NUM
ejpam-5958	87	16	)	)	PUNCT
ejpam-5958	87	17	(	(	PUNCT
ejpam-5958	87	18	recall	recall	VERB
ejpam-5958	87	19	that	that	PRON
ejpam-5958	87	20	s	s	VERB
ejpam-5958	87	21	≥	≥	NOUN
ejpam-5958	87	22	1	1	NUM
ejpam-5958	87	23	)	)	PUNCT
ejpam-5958	87	24	.	.	PUNCT
ejpam-5958	88	1	note	note	VERB
ejpam-5958	88	2	that	that	SCONJ
ejpam-5958	88	3	from	from	ADP
ejpam-5958	88	4	(	(	PUNCT
ejpam-5958	88	5	1	1	NUM
ejpam-5958	88	6	)	)	PUNCT
ejpam-5958	88	7	,	,	PUNCT
ejpam-5958	88	8	we	we	PRON
ejpam-5958	88	9	have	have	VERB
ejpam-5958	88	10	:	:	PUNCT
ejpam-5958	88	11	0	0	NUM
ejpam-5958	88	12	≤	≤	NUM
ejpam-5958	88	13	lim	lim	PROPN
ejpam-5958	88	14	t→0	t→0	AUX
ejpam-5958	88	15	+	+	CCONJ
ejpam-5958	88	16	ψ(t	ψ(t	PROPN
ejpam-5958	88	17	)	)	PUNCT
ejpam-5958	88	18	≤	≤	NOUN
ejpam-5958	89	1	lim	lim	PROPN
ejpam-5958	89	2	t→0	t→0	PROPN
ejpam-5958	89	3	+	+	PROPN
ejpam-5958	89	4	t	t	X
ejpam-5958	89	5	=	=	SYM
ejpam-5958	89	6	0	0	NUM
ejpam-5958	89	7	.	.	PUNCT
ejpam-5958	90	1	hence	hence	ADV
ejpam-5958	90	2	,	,	PUNCT
ejpam-5958	90	3	(	(	PUNCT
ejpam-5958	90	4	2	2	X
ejpam-5958	90	5	)	)	PUNCT
ejpam-5958	90	6	is	be	AUX
ejpam-5958	90	7	proved	prove	VERB
ejpam-5958	90	8	.	.	PUNCT
ejpam-5958	91	1	remark	remark	VERB
ejpam-5958	91	2	2.5	2.5	NUM
ejpam-5958	91	3	.	.	PUNCT
ejpam-5958	92	1	note	note	VERB
ejpam-5958	92	2	that	that	SCONJ
ejpam-5958	92	3	if	if	SCONJ
ejpam-5958	92	4	ψ	ψ	NOUN
ejpam-5958	92	5	is	be	AUX
ejpam-5958	92	6	a	a	DET
ejpam-5958	92	7	function	function	NOUN
ejpam-5958	92	8	satisfying	satisfy	VERB
ejpam-5958	92	9	(	(	PUNCT
ejpam-5958	92	10	ψs	ψs	NOUN
ejpam-5958	92	11	1	1	NUM
ejpam-5958	92	12	)	)	PUNCT
ejpam-5958	92	13	,	,	PUNCT
ejpam-5958	92	14	(	(	PUNCT
ejpam-5958	92	15	ψ	ψ	X
ejpam-5958	92	16	s	s	NOUN
ejpam-5958	92	17	2	2	NUM
ejpam-5958	92	18	)	)	PUNCT
ejpam-5958	92	19	and	and	CCONJ
ejpam-5958	92	20	(	(	PUNCT
ejpam-5958	92	21	ψs	ψs	NOUN
ejpam-5958	92	22	4	4	NUM
ejpam-5958	92	23	)	)	PUNCT
ejpam-5958	92	24	such	such	ADJ
ejpam-5958	92	25	that	that	DET
ejpam-5958	92	26	ψ(st	ψ(st	NOUN
ejpam-5958	92	27	)	)	PUNCT
ejpam-5958	92	28	<	<	X
ejpam-5958	92	29	t	t	PROPN
ejpam-5958	92	30	,	,	PUNCT
ejpam-5958	92	31	then	then	ADV
ejpam-5958	92	32	to	to	PART
ejpam-5958	92	33	conclude	conclude	VERB
ejpam-5958	92	34	that	that	PRON
ejpam-5958	92	35	ψ	ψ	ADP
ejpam-5958	92	36	∈	∈	PROPN
ejpam-5958	92	37	ψs	ψs	NOUN
ejpam-5958	92	38	,	,	PUNCT
ejpam-5958	92	39	it	it	PRON
ejpam-5958	92	40	is	be	AUX
ejpam-5958	92	41	sufficient	sufficient	ADJ
ejpam-5958	92	42	to	to	PART
ejpam-5958	92	43	show	show	VERB
ejpam-5958	92	44	that	that	SCONJ
ejpam-5958	92	45	ψ(s	ψ(s	PROPN
ejpam-5958	92	46	.	.	PUNCT
ejpam-5958	92	47	)	)	PUNCT
ejpam-5958	92	48	.	.	PUNCT
ejpam-5958	93	1	is	be	AUX
ejpam-5958	93	2	non	non	ADJ
ejpam-5958	93	3	-	-	ADJ
ejpam-5958	93	4	decreasing	decrease	VERB
ejpam-5958	93	5	.	.	PUNCT
ejpam-5958	94	1	indeed	indeed	ADV
ejpam-5958	94	2	,	,	PUNCT
ejpam-5958	94	3	we	we	PRON
ejpam-5958	94	4	have	have	VERB
ejpam-5958	94	5	:	:	PUNCT
ejpam-5958	94	6	si+1ψi+1(t	si+1ψi+1(t	X
ejpam-5958	94	7	)	)	PUNCT
ejpam-5958	94	8	siψi(t	siψi(t	NOUN
ejpam-5958	94	9	)	)	PUNCT
ejpam-5958	94	10	=	=	SYM
ejpam-5958	94	11	sψi+1(t	sψi+1(t	PROPN
ejpam-5958	94	12	)	)	PUNCT
ejpam-5958	94	13	ψi(t	ψi(t	PUNCT
ejpam-5958	94	14	)	)	PUNCT
ejpam-5958	95	1	=	=	SYM
ejpam-5958	95	2	ψ	ψ	X
ejpam-5958	95	3	(	(	PUNCT
ejpam-5958	95	4	sψi(t	sψi(t	PROPN
ejpam-5958	95	5	)	)	PUNCT
ejpam-5958	95	6	)	)	PUNCT
ejpam-5958	95	7	ψi(t	ψi(t	VERB
ejpam-5958	95	8	)	)	PUNCT
ejpam-5958	95	9	.	.	PUNCT
ejpam-5958	96	1	k.	k.	PROPN
ejpam-5958	96	2	nisse	nisse	PROPN
ejpam-5958	96	3	et	et	PROPN
ejpam-5958	96	4	al	al	PROPN
ejpam-5958	96	5	.	.	PUNCT
ejpam-5958	96	6	/	/	SYM
ejpam-5958	96	7	eur	eur	PROPN
ejpam-5958	96	8	.	.	PUNCT
ejpam-5958	97	1	j.	j.	PROPN
ejpam-5958	97	2	pure	pure	PROPN
ejpam-5958	97	3	appl	appl	PROPN
ejpam-5958	97	4	.	.	PROPN
ejpam-5958	97	5	math	math	PROPN
ejpam-5958	97	6	,	,	PUNCT
ejpam-5958	97	7	18	18	NUM
ejpam-5958	97	8	(	(	PUNCT
ejpam-5958	97	9	2	2	NUM
ejpam-5958	97	10	)	)	PUNCT
ejpam-5958	97	11	(	(	PUNCT
ejpam-5958	97	12	2025	2025	NUM
ejpam-5958	97	13	)	)	PUNCT
ejpam-5958	97	14	,	,	PUNCT
ejpam-5958	97	15	5958	5958	NUM
ejpam-5958	97	16	5	5	NUM
ejpam-5958	97	17	of	of	ADP
ejpam-5958	97	18	22	22	NUM
ejpam-5958	97	19	on	on	ADP
ejpam-5958	97	20	the	the	DET
ejpam-5958	97	21	other	other	ADJ
ejpam-5958	97	22	hand	hand	NOUN
ejpam-5958	97	23	,	,	PUNCT
ejpam-5958	97	24	from	from	ADP
ejpam-5958	97	25	the	the	DET
ejpam-5958	97	26	statement	statement	NOUN
ejpam-5958	97	27	(	(	PUNCT
ejpam-5958	97	28	1	1	NUM
ejpam-5958	97	29	)	)	PUNCT
ejpam-5958	97	30	in	in	ADP
ejpam-5958	97	31	lemma	lemma	PROPN
ejpam-5958	97	32	2.4	2.4	NUM
ejpam-5958	97	33	,	,	PUNCT
ejpam-5958	97	34	we	we	PRON
ejpam-5958	97	35	deduce	deduce	VERB
ejpam-5958	97	36	by	by	ADP
ejpam-5958	97	37	induction	induction	NOUN
ejpam-5958	97	38	that	that	SCONJ
ejpam-5958	97	39	:	:	PUNCT
ejpam-5958	97	40	∀i	∀i	NOUN
ejpam-5958	97	41	≥	≥	NOUN
ejpam-5958	97	42	1	1	NUM
ejpam-5958	97	43	:	:	PUNCT
ejpam-5958	97	44	ψi(t	ψi(t	NOUN
ejpam-5958	97	45	)	)	PUNCT
ejpam-5958	97	46	<	<	X
ejpam-5958	97	47	t.	t.	PROPN
ejpam-5958	97	48	hence	hence	ADV
ejpam-5958	97	49	,	,	PUNCT
ejpam-5958	97	50	from	from	ADP
ejpam-5958	97	51	the	the	DET
ejpam-5958	97	52	fact	fact	NOUN
ejpam-5958	97	53	that	that	SCONJ
ejpam-5958	97	54	ψ(s	ψ(s	PROPN
ejpam-5958	97	55	.	.	PUNCT
ejpam-5958	97	56	)	)	PUNCT
ejpam-5958	97	57	.	.	PUNCT
ejpam-5958	98	1	is	be	AUX
ejpam-5958	98	2	non	non	ADJ
ejpam-5958	98	3	-	-	ADJ
ejpam-5958	98	4	decreasing	decrease	VERB
ejpam-5958	98	5	,	,	PUNCT
ejpam-5958	98	6	we	we	PRON
ejpam-5958	98	7	obtain	obtain	VERB
ejpam-5958	98	8	:	:	PUNCT
ejpam-5958	98	9	si+1ψi+1(t	si+1ψi+1(t	X
ejpam-5958	98	10	)	)	PUNCT
ejpam-5958	98	11	siψi(t	siψi(t	NOUN
ejpam-5958	98	12	)	)	PUNCT
ejpam-5958	98	13	≤	≤	NOUN
ejpam-5958	98	14	ψ(st	ψ(st	NOUN
ejpam-5958	98	15	)	)	PUNCT
ejpam-5958	99	1	t	t	PROPN
ejpam-5958	99	2	<	<	X
ejpam-5958	99	3	t	t	X
ejpam-5958	99	4	t	t	NOUN
ejpam-5958	99	5	=	=	SYM
ejpam-5958	99	6	1	1	NUM
ejpam-5958	99	7	,	,	PUNCT
ejpam-5958	99	8	which	which	PRON
ejpam-5958	99	9	is	be	AUX
ejpam-5958	99	10	a	a	DET
ejpam-5958	99	11	sufficient	sufficient	ADJ
ejpam-5958	99	12	condition	condition	NOUN
ejpam-5958	99	13	leading	lead	VERB
ejpam-5958	99	14	to	to	ADP
ejpam-5958	99	15	(	(	PUNCT
ejpam-5958	99	16	ψs	ψs	NOUN
ejpam-5958	99	17	3	3	NUM
ejpam-5958	99	18	)	)	PUNCT
ejpam-5958	99	19	.	.	PUNCT
ejpam-5958	100	1	for	for	ADP
ejpam-5958	100	2	a	a	DET
ejpam-5958	100	3	mapping	mapping	NOUN
ejpam-5958	100	4	α	α	NOUN
ejpam-5958	100	5	:	:	PUNCT
ejpam-5958	100	6	e	e	X
ejpam-5958	100	7	×	×	NOUN
ejpam-5958	100	8	e	e	ADP
ejpam-5958	100	9	−→	−→	NOUN
ejpam-5958	100	10	r+	r+	NOUN
ejpam-5958	100	11	and	and	CCONJ
ejpam-5958	100	12	a	a	DET
ejpam-5958	100	13	non	non	ADJ
ejpam-5958	100	14	-	-	ADJ
ejpam-5958	100	15	decreasing	decrease	VERB
ejpam-5958	100	16	function	function	NOUN
ejpam-5958	100	17	ψ	ψ	NOUN
ejpam-5958	100	18	:	:	PUNCT
ejpam-5958	100	19	r+	r+	NOUN
ejpam-5958	100	20	−→	−→	ADJ
ejpam-5958	100	21	r+	r+	NOUN
ejpam-5958	100	22	,	,	PUNCT
ejpam-5958	100	23	such	such	ADJ
ejpam-5958	100	24	that	that	SCONJ
ejpam-5958	100	25	∞∑	∞∑	NUM
ejpam-5958	100	26	i=1	i=1	PRON
ejpam-5958	100	27	ψi(t	ψi(t	NOUN
ejpam-5958	100	28	)	)	PUNCT
ejpam-5958	100	29	<	<	X
ejpam-5958	101	1	+	+	ADJ
ejpam-5958	101	2	∞	∞	NUM
ejpam-5958	101	3	for	for	ADP
ejpam-5958	101	4	all	all	DET
ejpam-5958	101	5	t	t	PROPN
ejpam-5958	101	6	>	>	X
ejpam-5958	101	7	0	0	PROPN
ejpam-5958	101	8	,	,	PUNCT
ejpam-5958	101	9	the	the	DET
ejpam-5958	101	10	concepts	concept	NOUN
ejpam-5958	101	11	of	of	ADP
ejpam-5958	101	12	α	α	NOUN
ejpam-5958	101	13	-	-	PUNCT
ejpam-5958	101	14	admissible	admissible	ADJ
ejpam-5958	101	15	mappings	mapping	NOUN
ejpam-5958	101	16	and	and	CCONJ
ejpam-5958	101	17	α	α	NOUN
ejpam-5958	101	18	-	-	PUNCT
ejpam-5958	101	19	ψ	ψ	NOUN
ejpam-5958	101	20	contraction	contraction	NOUN
ejpam-5958	101	21	mappings	mapping	NOUN
ejpam-5958	101	22	in	in	ADP
ejpam-5958	101	23	a	a	DET
ejpam-5958	101	24	metric	metric	ADJ
ejpam-5958	101	25	space	space	NOUN
ejpam-5958	101	26	(	(	PUNCT
ejpam-5958	101	27	e	e	NOUN
ejpam-5958	101	28	,	,	PUNCT
ejpam-5958	101	29	d	d	PROPN
ejpam-5958	101	30	)	)	PUNCT
ejpam-5958	101	31	,	,	PUNCT
ejpam-5958	101	32	were	be	AUX
ejpam-5958	101	33	introduced	introduce	VERB
ejpam-5958	101	34	for	for	ADP
ejpam-5958	101	35	the	the	DET
ejpam-5958	101	36	first	first	ADJ
ejpam-5958	101	37	time	time	NOUN
ejpam-5958	101	38	by	by	ADP
ejpam-5958	101	39	samet	samet	PROPN
ejpam-5958	101	40	et	et	PROPN
ejpam-5958	101	41	al	al	PROPN
ejpam-5958	101	42	.	.	PUNCT
ejpam-5958	102	1	[	[	X
ejpam-5958	102	2	27	27	NUM
ejpam-5958	102	3	]	]	PUNCT
ejpam-5958	102	4	.	.	PUNCT
ejpam-5958	103	1	definition	definition	NOUN
ejpam-5958	103	2	2.6	2.6	NUM
ejpam-5958	103	3	.	.	PUNCT
ejpam-5958	104	1	a	a	DET
ejpam-5958	104	2	map	map	NOUN
ejpam-5958	104	3	f	f	X
ejpam-5958	104	4	:	:	PUNCT
ejpam-5958	104	5	e	e	X
ejpam-5958	104	6	−→	−→	NOUN
ejpam-5958	104	7	e	e	NOUN
ejpam-5958	104	8	is	be	AUX
ejpam-5958	104	9	said	say	VERB
ejpam-5958	104	10	to	to	PART
ejpam-5958	104	11	be	be	AUX
ejpam-5958	104	12	•	•	ADV
ejpam-5958	104	13	α	α	PRON
ejpam-5958	104	14	-	-	ADJ
ejpam-5958	104	15	admissible	admissible	ADJ
ejpam-5958	104	16	,	,	PUNCT
ejpam-5958	104	17	if	if	SCONJ
ejpam-5958	104	18	for	for	ADP
ejpam-5958	104	19	all	all	DET
ejpam-5958	104	20	x	x	NOUN
ejpam-5958	104	21	,	,	PUNCT
ejpam-5958	104	22	y	y	PROPN
ejpam-5958	104	23	∈	∈	PROPN
ejpam-5958	104	24	e	e	PROPN
ejpam-5958	104	25	:	:	PUNCT
ejpam-5958	104	26	α(x	α(x	PROPN
ejpam-5958	104	27	,	,	PUNCT
ejpam-5958	104	28	y	y	PROPN
ejpam-5958	104	29	)	)	PUNCT
ejpam-5958	104	30	≥	≥	NOUN
ejpam-5958	104	31	1	1	NUM
ejpam-5958	104	32	implies	imply	VERB
ejpam-5958	104	33	α(fx	α(fx	PROPN
ejpam-5958	104	34	,	,	PUNCT
ejpam-5958	104	35	fy	fy	PROPN
ejpam-5958	104	36	)	)	PUNCT
ejpam-5958	104	37	≥	≥	NOUN
ejpam-5958	104	38	1	1	NUM
ejpam-5958	104	39	•	•	NUM
ejpam-5958	104	40	α	α	NUM
ejpam-5958	104	41	-	-	PUNCT
ejpam-5958	104	42	ψ	ψ	NOUN
ejpam-5958	104	43	contraction	contraction	NOUN
ejpam-5958	104	44	mapping	mapping	NOUN
ejpam-5958	104	45	,	,	PUNCT
ejpam-5958	104	46	if	if	SCONJ
ejpam-5958	104	47	α(x	α(x	PROPN
ejpam-5958	104	48	,	,	PUNCT
ejpam-5958	104	49	y)d(fx	y)d(fx	PROPN
ejpam-5958	104	50	,	,	PUNCT
ejpam-5958	104	51	fy	fy	NOUN
ejpam-5958	104	52	)	)	PUNCT
ejpam-5958	104	53	≤	≤	NOUN
ejpam-5958	105	1	ψ(d(x	ψ(d(x	NOUN
ejpam-5958	105	2	,	,	PUNCT
ejpam-5958	105	3	y	y	NOUN
ejpam-5958	105	4	)	)	PUNCT
ejpam-5958	105	5	)	)	PUNCT
ejpam-5958	105	6	,	,	PUNCT
ejpam-5958	105	7	∀x	∀x	X
ejpam-5958	105	8	,	,	PUNCT
ejpam-5958	105	9	y	y	PROPN
ejpam-5958	105	10	∈	∈	PROPN
ejpam-5958	105	11	e.	e.	PROPN
ejpam-5958	105	12	later	later	ADV
ejpam-5958	105	13	,	,	PUNCT
ejpam-5958	105	14	other	other	ADJ
ejpam-5958	105	15	contraction	contraction	NOUN
ejpam-5958	105	16	conditions	condition	NOUN
ejpam-5958	105	17	of	of	ADP
ejpam-5958	105	18	such	such	ADJ
ejpam-5958	105	19	type	type	NOUN
ejpam-5958	105	20	have	have	AUX
ejpam-5958	105	21	been	be	AUX
ejpam-5958	105	22	considered	consider	VERB
ejpam-5958	105	23	by	by	ADP
ejpam-5958	105	24	many	many	ADJ
ejpam-5958	105	25	authors	author	NOUN
ejpam-5958	105	26	to	to	PART
ejpam-5958	105	27	extend	extend	VERB
ejpam-5958	105	28	the	the	DET
ejpam-5958	105	29	banach	banach	NOUN
ejpam-5958	105	30	’s	’s	PART
ejpam-5958	105	31	principle	principle	NOUN
ejpam-5958	105	32	.	.	PUNCT
ejpam-5958	106	1	in	in	ADP
ejpam-5958	106	2	these	these	DET
ejpam-5958	106	3	results	result	NOUN
ejpam-5958	106	4	,	,	PUNCT
ejpam-5958	106	5	the	the	DET
ejpam-5958	106	6	following	follow	VERB
ejpam-5958	106	7	condition	condition	NOUN
ejpam-5958	106	8	for	for	ADP
ejpam-5958	106	9	α	α	NOUN
ejpam-5958	106	10	-	-	PUNCT
ejpam-5958	106	11	admissible	admissible	ADJ
ejpam-5958	106	12	mappings	mapping	NOUN
ejpam-5958	106	13	f	f	NOUN
ejpam-5958	106	14	,	,	PUNCT
ejpam-5958	106	15	is	be	AUX
ejpam-5958	106	16	often	often	ADV
ejpam-5958	106	17	imposed	impose	VERB
ejpam-5958	106	18	∃x0	∃x0	PROPN
ejpam-5958	106	19	∈	∈	PROPN
ejpam-5958	106	20	e	e	NOUN
ejpam-5958	106	21	,	,	PUNCT
ejpam-5958	106	22	such	such	ADJ
ejpam-5958	106	23	that	that	DET
ejpam-5958	106	24	α(x0	α(x0	ADJ
ejpam-5958	106	25	,	,	PUNCT
ejpam-5958	106	26	fx0	fx0	PROPN
ejpam-5958	106	27	)	)	PUNCT
ejpam-5958	106	28	≥	≥	NOUN
ejpam-5958	106	29	1	1	NUM
ejpam-5958	106	30	.	.	PUNCT
ejpam-5958	107	1	(	(	PUNCT
ejpam-5958	107	2	2.2	2.2	NUM
ejpam-5958	107	3	)	)	PUNCT
ejpam-5958	107	4	in	in	ADP
ejpam-5958	107	5	[	[	X
ejpam-5958	107	6	33	33	NUM
ejpam-5958	107	7	]	]	PUNCT
ejpam-5958	107	8	,	,	PUNCT
ejpam-5958	107	9	the	the	DET
ejpam-5958	107	10	authors	author	NOUN
ejpam-5958	107	11	introduced	introduce	VERB
ejpam-5958	107	12	the	the	DET
ejpam-5958	107	13	following	following	ADJ
ejpam-5958	107	14	relaxed	relaxed	ADJ
ejpam-5958	107	15	condition	condition	NOUN
ejpam-5958	107	16	∃n	∃n	PROPN
ejpam-5958	107	17	∈	∈	PROPN
ejpam-5958	107	18	n∗	n∗	PROPN
ejpam-5958	107	19	,	,	PUNCT
ejpam-5958	107	20	∃	∃	PROPN
ejpam-5958	107	21	(	(	PUNCT
ejpam-5958	107	22	xp)np=0	xp)np=0	PROPN
ejpam-5958	107	23	⊂	⊂	PROPN
ejpam-5958	108	1	e	e	X
ejpam-5958	108	2	,	,	PUNCT
ejpam-5958	108	3	with	with	ADP
ejpam-5958	108	4	xn	xn	PROPN
ejpam-5958	108	5	=	=	SYM
ejpam-5958	108	6	fx0	fx0	PROPN
ejpam-5958	108	7	,	,	PUNCT
ejpam-5958	108	8	such	such	ADJ
ejpam-5958	108	9	that	that	PRON
ejpam-5958	108	10	α(xp−1	α(xp−1	PROPN
ejpam-5958	108	11	,	,	PUNCT
ejpam-5958	108	12	xp	xp	PROPN
ejpam-5958	108	13	)	)	PUNCT
ejpam-5958	108	14	≥	≥	NOUN
ejpam-5958	108	15	1	1	NUM
ejpam-5958	108	16	,	,	PUNCT
ejpam-5958	108	17	∀p	∀p	NOUN
ejpam-5958	108	18	=	=	SYM
ejpam-5958	108	19	1	1	NUM
ejpam-5958	108	20	,	,	PUNCT
ejpam-5958	108	21	..	..	PUNCT
ejpam-5958	108	22	,	,	PUNCT
ejpam-5958	108	23	n.	n.	PROPN
ejpam-5958	108	24	(	(	PUNCT
ejpam-5958	108	25	2.3	2.3	NUM
ejpam-5958	108	26	)	)	PUNCT
ejpam-5958	108	27	where	where	SCONJ
ejpam-5958	108	28	n∗	n∗	PROPN
ejpam-5958	108	29	=	=	SYM
ejpam-5958	108	30	n\{0	n\{0	PROPN
ejpam-5958	108	31	}	}	PUNCT
ejpam-5958	108	32	.	.	PUNCT
ejpam-5958	109	1	for	for	ADP
ejpam-5958	109	2	α	α	NOUN
ejpam-5958	109	3	-	-	PUNCT
ejpam-5958	109	4	admissible	admissible	ADJ
ejpam-5958	109	5	mapping	mapping	NOUN
ejpam-5958	109	6	f	f	NOUN
ejpam-5958	109	7	,	,	PUNCT
ejpam-5958	109	8	it	it	PRON
ejpam-5958	109	9	is	be	AUX
ejpam-5958	109	10	clear	clear	ADJ
ejpam-5958	109	11	that	that	SCONJ
ejpam-5958	109	12	if	if	SCONJ
ejpam-5958	109	13	(	(	PUNCT
ejpam-5958	109	14	2.2	2.2	NUM
ejpam-5958	109	15	)	)	PUNCT
ejpam-5958	109	16	is	be	AUX
ejpam-5958	109	17	satisfied	satisfied	ADJ
ejpam-5958	109	18	,	,	PUNCT
ejpam-5958	109	19	then	then	ADV
ejpam-5958	109	20	(	(	PUNCT
ejpam-5958	109	21	2.3	2.3	NUM
ejpam-5958	109	22	)	)	PUNCT
ejpam-5958	109	23	is	be	AUX
ejpam-5958	109	24	satisfied	satisfied	ADJ
ejpam-5958	109	25	too	too	ADV
ejpam-5958	109	26	with	with	ADP
ejpam-5958	109	27	n	n	NOUN
ejpam-5958	109	28	=	=	SYM
ejpam-5958	109	29	1	1	NUM
ejpam-5958	109	30	.	.	PUNCT
ejpam-5958	110	1	but	but	CCONJ
ejpam-5958	110	2	the	the	DET
ejpam-5958	110	3	following	follow	VERB
ejpam-5958	110	4	simple	simple	ADJ
ejpam-5958	110	5	example	example	NOUN
ejpam-5958	110	6	illustrates	illustrate	VERB
ejpam-5958	110	7	that	that	SCONJ
ejpam-5958	110	8	the	the	DET
ejpam-5958	110	9	converse	converse	NOUN
ejpam-5958	110	10	is	be	AUX
ejpam-5958	110	11	not	not	PART
ejpam-5958	110	12	necessarily	necessarily	ADV
ejpam-5958	110	13	true	true	ADJ
ejpam-5958	110	14	.	.	PUNCT
ejpam-5958	111	1	example	example	NOUN
ejpam-5958	112	1	2	2	NUM
ejpam-5958	112	2	.	.	PUNCT
ejpam-5958	112	3	let	let	VERB
ejpam-5958	112	4	x	x	PUNCT
ejpam-5958	112	5	=	=	PUNCT
ejpam-5958	112	6	{	{	PUNCT
ejpam-5958	112	7	0	0	NUM
ejpam-5958	112	8	,	,	PUNCT
ejpam-5958	112	9	1	1	NUM
ejpam-5958	112	10	,	,	PUNCT
ejpam-5958	112	11	2	2	NUM
ejpam-5958	112	12	,	,	PUNCT
ejpam-5958	112	13	3	3	NUM
ejpam-5958	112	14	}	}	PUNCT
ejpam-5958	112	15	,	,	PUNCT
ejpam-5958	112	16	f	f	X
ejpam-5958	112	17	:	:	PUNCT
ejpam-5958	112	18	x	x	PUNCT
ejpam-5958	112	19	−→	−→	NOUN
ejpam-5958	112	20	x	x	SYM
ejpam-5958	112	21	0	0	NUM
ejpam-5958	112	22	7→	7→	NUM
ejpam-5958	112	23	1	1	NUM
ejpam-5958	112	24	1	1	NUM
ejpam-5958	112	25	7→	7→	NUM
ejpam-5958	112	26	0	0	NUM
ejpam-5958	112	27	2	2	NUM
ejpam-5958	112	28	7→	7→	NUM
ejpam-5958	112	29	3	3	NUM
ejpam-5958	112	30	3	3	NUM
ejpam-5958	112	31	7→	7→	NUM
ejpam-5958	112	32	2	2	NUM
ejpam-5958	112	33	α	α	NOUN
ejpam-5958	112	34	:	:	PUNCT
ejpam-5958	112	35	x	x	X
ejpam-5958	112	36	×x	×x	VERB
ejpam-5958	112	37	−→	−→	NOUN
ejpam-5958	112	38	{	{	PUNCT
ejpam-5958	112	39	0	0	NUM
ejpam-5958	112	40	,	,	PUNCT
ejpam-5958	112	41	1	1	NUM
ejpam-5958	112	42	}	}	PUNCT
ejpam-5958	112	43	and	and	CCONJ
ejpam-5958	112	44	α(x	α(x	PROPN
ejpam-5958	112	45	,	,	PUNCT
ejpam-5958	112	46	y	y	PROPN
ejpam-5958	112	47	)	)	PUNCT
ejpam-5958	112	48	=	=	PRON
ejpam-5958	112	49	{	{	PUNCT
ejpam-5958	112	50	0	0	NUM
ejpam-5958	112	51	:	:	PUNCT
ejpam-5958	112	52	(	(	PUNCT
ejpam-5958	112	53	x	x	X
ejpam-5958	112	54	,	,	PUNCT
ejpam-5958	112	55	y	y	NOUN
ejpam-5958	112	56	)	)	PUNCT
ejpam-5958	112	57	∈	∈	NOUN
ejpam-5958	112	58	{	{	PUNCT
ejpam-5958	112	59	(	(	PUNCT
ejpam-5958	112	60	0	0	NUM
ejpam-5958	112	61	,	,	PUNCT
ejpam-5958	112	62	1	1	NUM
ejpam-5958	112	63	)	)	PUNCT
ejpam-5958	112	64	,	,	PUNCT
ejpam-5958	112	65	(	(	PUNCT
ejpam-5958	112	66	1	1	NUM
ejpam-5958	112	67	,	,	PUNCT
ejpam-5958	112	68	0	0	NUM
ejpam-5958	112	69	)	)	PUNCT
ejpam-5958	112	70	,	,	PUNCT
ejpam-5958	112	71	(	(	PUNCT
ejpam-5958	112	72	2	2	NUM
ejpam-5958	112	73	,	,	PUNCT
ejpam-5958	112	74	3	3	NUM
ejpam-5958	112	75	)	)	PUNCT
ejpam-5958	112	76	,	,	PUNCT
ejpam-5958	112	77	(	(	PUNCT
ejpam-5958	112	78	3	3	NUM
ejpam-5958	112	79	,	,	PUNCT
ejpam-5958	112	80	2	2	NUM
ejpam-5958	112	81	)	)	PUNCT
ejpam-5958	112	82	}	}	PUNCT
ejpam-5958	112	83	1	1	NUM
ejpam-5958	112	84	:	:	PUNCT
ejpam-5958	112	85	otherwise	otherwise	ADV
ejpam-5958	112	86	.	.	PUNCT
ejpam-5958	113	1	it	it	PRON
ejpam-5958	113	2	can	can	AUX
ejpam-5958	113	3	be	be	AUX
ejpam-5958	113	4	easily	easily	ADV
ejpam-5958	113	5	seen	see	VERB
ejpam-5958	113	6	that	that	SCONJ
ejpam-5958	113	7	f	f	PROPN
ejpam-5958	113	8	is	be	AUX
ejpam-5958	113	9	α	α	NOUN
ejpam-5958	113	10	-	-	ADJ
ejpam-5958	113	11	admissible	admissible	ADJ
ejpam-5958	113	12	and	and	CCONJ
ejpam-5958	113	13	(	(	PUNCT
ejpam-5958	113	14	2.2	2.2	NUM
ejpam-5958	113	15	)	)	PUNCT
ejpam-5958	113	16	is	be	AUX
ejpam-5958	113	17	not	not	PART
ejpam-5958	113	18	satisfied	satisfied	ADJ
ejpam-5958	113	19	.	.	PUNCT
ejpam-5958	114	1	whereas	whereas	SCONJ
ejpam-5958	114	2	,	,	PUNCT
ejpam-5958	114	3	there	there	PRON
ejpam-5958	114	4	exist	exist	VERB
ejpam-5958	114	5	x0	x0	PROPN
ejpam-5958	114	6	=	=	SYM
ejpam-5958	114	7	2	2	NUM
ejpam-5958	114	8	,	,	PUNCT
ejpam-5958	114	9	x1	x1	NOUN
ejpam-5958	114	10	=	=	SYM
ejpam-5958	114	11	1	1	NUM
ejpam-5958	114	12	and	and	CCONJ
ejpam-5958	114	13	x2	x2	NOUN
ejpam-5958	114	14	=	=	PUNCT
ejpam-5958	114	15	fx0	fx0	PROPN
ejpam-5958	114	16	=	=	SYM
ejpam-5958	114	17	3	3	NUM
ejpam-5958	114	18	,	,	PUNCT
ejpam-5958	114	19	such	such	ADJ
ejpam-5958	114	20	that	that	DET
ejpam-5958	114	21	α(x0	α(x0	NOUN
ejpam-5958	114	22	,	,	PUNCT
ejpam-5958	114	23	x1	x1	PROPN
ejpam-5958	114	24	)	)	PUNCT
ejpam-5958	115	1	=	=	SYM
ejpam-5958	115	2	α(x1	α(x1	ADJ
ejpam-5958	115	3	,	,	PUNCT
ejpam-5958	115	4	x2	x2	PROPN
ejpam-5958	115	5	)	)	PUNCT
ejpam-5958	115	6	=	=	SYM
ejpam-5958	115	7	1	1	NUM
ejpam-5958	115	8	≥	≥	NOUN
ejpam-5958	115	9	1	1	NUM
ejpam-5958	115	10	.	.	PUNCT
ejpam-5958	116	1	that	that	ADV
ejpam-5958	116	2	is	is	ADV
ejpam-5958	116	3	(	(	PUNCT
ejpam-5958	116	4	2.3	2.3	NUM
ejpam-5958	116	5	)	)	PUNCT
ejpam-5958	116	6	is	be	AUX
ejpam-5958	116	7	satisfied	satisfied	ADJ
ejpam-5958	116	8	with	with	ADP
ejpam-5958	116	9	n	n	NOUN
ejpam-5958	116	10	=	=	SYM
ejpam-5958	116	11	2	2	NUM
ejpam-5958	117	1	.	.	PUNCT
ejpam-5958	117	2	k.	k.	PROPN
ejpam-5958	117	3	nisse	nisse	PROPN
ejpam-5958	117	4	et	et	PROPN
ejpam-5958	117	5	al	al	PROPN
ejpam-5958	117	6	.	.	PUNCT
ejpam-5958	117	7	/	/	SYM
ejpam-5958	117	8	eur	eur	PROPN
ejpam-5958	117	9	.	.	PUNCT
ejpam-5958	118	1	j.	j.	PROPN
ejpam-5958	118	2	pure	pure	PROPN
ejpam-5958	118	3	appl	appl	PROPN
ejpam-5958	118	4	.	.	PROPN
ejpam-5958	118	5	math	math	PROPN
ejpam-5958	118	6	,	,	PUNCT
ejpam-5958	118	7	18	18	NUM
ejpam-5958	118	8	(	(	PUNCT
ejpam-5958	118	9	2	2	NUM
ejpam-5958	118	10	)	)	PUNCT
ejpam-5958	118	11	(	(	PUNCT
ejpam-5958	118	12	2025	2025	NUM
ejpam-5958	118	13	)	)	PUNCT
ejpam-5958	118	14	,	,	PUNCT
ejpam-5958	118	15	5958	5958	NUM
ejpam-5958	118	16	6	6	NUM
ejpam-5958	118	17	of	of	ADP
ejpam-5958	118	18	22	22	NUM
ejpam-5958	118	19	3	3	NUM
ejpam-5958	118	20	.	.	PUNCT
ejpam-5958	118	21	main	main	ADJ
ejpam-5958	118	22	results	result	NOUN
ejpam-5958	118	23	throughout	throughout	ADP
ejpam-5958	118	24	the	the	DET
ejpam-5958	118	25	sequel	sequel	NOUN
ejpam-5958	118	26	,	,	PUNCT
ejpam-5958	118	27	e	e	X
ejpam-5958	118	28	is	be	AUX
ejpam-5958	118	29	a	a	DET
ejpam-5958	118	30	non	non	ADJ
ejpam-5958	118	31	-	-	ADJ
ejpam-5958	118	32	empty	empty	ADJ
ejpam-5958	118	33	set	set	NOUN
ejpam-5958	118	34	endowed	endow	VERB
ejpam-5958	118	35	with	with	ADP
ejpam-5958	118	36	a	a	DET
ejpam-5958	118	37	separating	separate	VERB
ejpam-5958	118	38	complete	complete	ADJ
ejpam-5958	118	39	b	b	NOUN
ejpam-5958	118	40	-	-	PUNCT
ejpam-5958	118	41	gauge	gauge	NOUN
ejpam-5958	118	42	structure	structure	NOUN
ejpam-5958	118	43	d	d	NOUN
ejpam-5958	118	44	=	=	PRON
ejpam-5958	118	45	{	{	PUNCT
ejpam-5958	118	46	dν}ν∈n	dν}ν∈n	INTJ
ejpam-5958	118	47	,	,	PUNCT
ejpam-5958	118	48	where	where	SCONJ
ejpam-5958	118	49	n	n	PRON
ejpam-5958	118	50	is	be	AUX
ejpam-5958	118	51	an	an	DET
ejpam-5958	118	52	index	index	NOUN
ejpam-5958	118	53	set	set	NOUN
ejpam-5958	118	54	.	.	PUNCT
ejpam-5958	119	1	inspired	inspire	VERB
ejpam-5958	119	2	by	by	ADP
ejpam-5958	119	3	[	[	X
ejpam-5958	119	4	27	27	NUM
ejpam-5958	119	5	,	,	PUNCT
ejpam-5958	119	6	39	39	NUM
ejpam-5958	119	7	]	]	PUNCT
ejpam-5958	119	8	,	,	PUNCT
ejpam-5958	119	9	we	we	PRON
ejpam-5958	119	10	give	give	VERB
ejpam-5958	119	11	in	in	ADP
ejpam-5958	119	12	what	what	PRON
ejpam-5958	119	13	follows	follow	VERB
ejpam-5958	119	14	generalized	generalized	ADJ
ejpam-5958	119	15	concepts	concept	NOUN
ejpam-5958	119	16	of	of	ADP
ejpam-5958	119	17	α	α	NOUN
ejpam-5958	119	18	-	-	NOUN
ejpam-5958	119	19	admissibility	admissibility	NOUN
ejpam-5958	119	20	and	and	CCONJ
ejpam-5958	119	21	α	α	PROPN
ejpam-5958	119	22	-	-	PUNCT
ejpam-5958	119	23	ψ	ψ	NOUN
ejpam-5958	119	24	contractivity	contractivity	NOUN
ejpam-5958	119	25	in	in	ADP
ejpam-5958	119	26	the	the	DET
ejpam-5958	119	27	setting	setting	NOUN
ejpam-5958	119	28	of	of	ADP
ejpam-5958	119	29	b	b	NOUN
ejpam-5958	119	30	-	-	PUNCT
ejpam-5958	119	31	gauge	gauge	NOUN
ejpam-5958	119	32	spaces	space	NOUN
ejpam-5958	119	33	.	.	PUNCT
ejpam-5958	120	1	to	to	ADP
ejpam-5958	120	2	this	this	DET
ejpam-5958	120	3	end	end	NOUN
ejpam-5958	120	4	,	,	PUNCT
ejpam-5958	120	5	we	we	PRON
ejpam-5958	120	6	start	start	VERB
ejpam-5958	120	7	by	by	ADP
ejpam-5958	120	8	introducing	introduce	VERB
ejpam-5958	120	9	the	the	DET
ejpam-5958	120	10	following	follow	VERB
ejpam-5958	120	11	auxiliary	auxiliary	ADJ
ejpam-5958	120	12	family	family	NOUN
ejpam-5958	120	13	and	and	CCONJ
ejpam-5958	120	14	mapping	mapping	NOUN
ejpam-5958	120	15	.	.	PUNCT
ejpam-5958	121	1	we	we	PRON
ejpam-5958	121	2	denote	denote	VERB
ejpam-5958	121	3	by	by	ADP
ejpam-5958	121	4	αααν	αααν	NOUN
ejpam-5958	121	5	,	,	PUNCT
ejpam-5958	121	6	the	the	DET
ejpam-5958	121	7	following	follow	VERB
ejpam-5958	121	8	family	family	NOUN
ejpam-5958	121	9	:	:	PUNCT
ejpam-5958	121	10	αααν	αααν	NOUN
ejpam-5958	121	11	=	=	SYM
ejpam-5958	121	12	{	{	PUNCT
ejpam-5958	121	13	αν	αν	X
ejpam-5958	121	14	:	:	PUNCT
ejpam-5958	121	15	e×e	e×e	ADJ
ejpam-5958	121	16	−→	−→	ADJ
ejpam-5958	121	17	r+}ν∈n	r+}ν∈n	NOUN
ejpam-5958	121	18	.	.	PUNCT
ejpam-5958	122	1	w	w	X
ejpam-5958	122	2	:	:	PUNCT
ejpam-5958	122	3	n	n	CCONJ
ejpam-5958	123	1	−→	−→	NOUN
ejpam-5958	123	2	n	n	VERB
ejpam-5958	123	3	is	be	AUX
ejpam-5958	123	4	a	a	DET
ejpam-5958	123	5	mapping	mapping	NOUN
ejpam-5958	123	6	from	from	ADP
ejpam-5958	123	7	the	the	DET
ejpam-5958	123	8	index	index	NOUN
ejpam-5958	123	9	set	set	VERB
ejpam-5958	123	10	n	n	X
ejpam-5958	123	11	into	into	ADP
ejpam-5958	123	12	itself	itself	PRON
ejpam-5958	123	13	,	,	PUNCT
ejpam-5958	123	14	such	such	ADJ
ejpam-5958	123	15	that	that	SCONJ
ejpam-5958	123	16	:	:	PUNCT
ejpam-5958	123	17	∀ν	∀ν	PROPN
ejpam-5958	123	18	∈	∈	PROPN
ejpam-5958	123	19	n	n	PRON
ejpam-5958	123	20	,	,	PUNCT
ejpam-5958	123	21	∀u	∀u	NOUN
ejpam-5958	123	22	,	,	PUNCT
ejpam-5958	123	23	v	v	NOUN
ejpam-5958	123	24	∈	∈	NOUN
ejpam-5958	123	25	e	e	NOUN
ejpam-5958	123	26	:	:	PUNCT
ejpam-5958	123	27	dν(u	dν(u	NOUN
ejpam-5958	123	28	,	,	PUNCT
ejpam-5958	123	29	v	v	NOUN
ejpam-5958	123	30	)	)	PUNCT
ejpam-5958	123	31	≤	≤	NOUN
ejpam-5958	123	32	dw(ν)(u	dw(ν)(u	NOUN
ejpam-5958	123	33	,	,	PUNCT
ejpam-5958	123	34	v	v	NOUN
ejpam-5958	123	35	)	)	PUNCT
ejpam-5958	123	36	.	.	PUNCT
ejpam-5958	124	1	(	(	PUNCT
ejpam-5958	124	2	3.1	3.1	NUM
ejpam-5958	124	3	)	)	PUNCT
ejpam-5958	124	4	definition	definition	NOUN
ejpam-5958	124	5	3.1	3.1	NUM
ejpam-5958	124	6	.	.	PUNCT
ejpam-5958	125	1	a	a	DET
ejpam-5958	125	2	mapping	mapping	NOUN
ejpam-5958	125	3	f	f	NOUN
ejpam-5958	125	4	:	:	PUNCT
ejpam-5958	125	5	e	e	X
ejpam-5958	125	6	−→	−→	NOUN
ejpam-5958	125	7	e	e	NOUN
ejpam-5958	125	8	is	be	AUX
ejpam-5958	125	9	said	say	VERB
ejpam-5958	125	10	to	to	PART
ejpam-5958	125	11	be	be	AUX
ejpam-5958	125	12	αααν	αααν	NOUN
ejpam-5958	125	13	-	-	PUNCT
ejpam-5958	125	14	admissible	admissible	ADJ
ejpam-5958	125	15	,	,	PUNCT
ejpam-5958	125	16	if	if	SCONJ
ejpam-5958	125	17	∀ν	∀ν	PROPN
ejpam-5958	125	18	∈	∈	PROPN
ejpam-5958	125	19	n	n	PRON
ejpam-5958	125	20	,	,	PUNCT
ejpam-5958	125	21	∀u	∀u	NOUN
ejpam-5958	125	22	,	,	PUNCT
ejpam-5958	125	23	v	v	NOUN
ejpam-5958	125	24	∈	∈	NOUN
ejpam-5958	125	25	e	e	NOUN
ejpam-5958	125	26	:	:	PUNCT
ejpam-5958	125	27	αν(u	αν(u	NUM
ejpam-5958	125	28	,	,	PUNCT
ejpam-5958	125	29	v	v	NOUN
ejpam-5958	125	30	)	)	PUNCT
ejpam-5958	125	31	≥	≥	NOUN
ejpam-5958	125	32	1	1	NUM
ejpam-5958	125	33	implies	imply	VERB
ejpam-5958	125	34	αν(fu	αν(fu	PROPN
ejpam-5958	125	35	,	,	PUNCT
ejpam-5958	125	36	fv	fv	X
ejpam-5958	125	37	)	)	PUNCT
ejpam-5958	125	38	≥	≥	NOUN
ejpam-5958	125	39	1	1	NUM
ejpam-5958	125	40	.	.	PUNCT
ejpam-5958	126	1	definition	definition	NOUN
ejpam-5958	126	2	3.2	3.2	NUM
ejpam-5958	126	3	.	.	PUNCT
ejpam-5958	127	1	let	let	VERB
ejpam-5958	127	2	f	f	NOUN
ejpam-5958	127	3	:	:	PUNCT
ejpam-5958	127	4	e	e	AUX
ejpam-5958	127	5	−→	−→	NOUN
ejpam-5958	127	6	e	e	AUX
ejpam-5958	127	7	be	be	AUX
ejpam-5958	127	8	a	a	DET
ejpam-5958	127	9	given	give	VERB
ejpam-5958	127	10	mapping	mapping	NOUN
ejpam-5958	127	11	and	and	CCONJ
ejpam-5958	127	12	{	{	PUNCT
ejpam-5958	127	13	ψν}ν∈n	ψν}ν∈n	X
ejpam-5958	127	14	⊂	⊂	X
ejpam-5958	127	15	ψs	ψs	PROPN
ejpam-5958	127	16	.	.	PROPN
ejpam-5958	127	17	f	f	PROPN
ejpam-5958	127	18	is	be	AUX
ejpam-5958	127	19	said	say	VERB
ejpam-5958	127	20	to	to	PART
ejpam-5958	127	21	be	be	AUX
ejpam-5958	127	22	a	a	DET
ejpam-5958	127	23	generalized	generalized	ADJ
ejpam-5958	127	24	(	(	PUNCT
ejpam-5958	127	25	αααν	αααν	NOUN
ejpam-5958	127	26	,	,	PUNCT
ejpam-5958	127	27	ψ	ψ	X
ejpam-5958	127	28	s	s	SYM
ejpam-5958	127	29	,	,	PUNCT
ejpam-5958	127	30	w	w	NOUN
ejpam-5958	127	31	)	)	PUNCT
ejpam-5958	127	32	contraction	contraction	NOUN
ejpam-5958	127	33	if	if	SCONJ
ejpam-5958	127	34	αν(u	αν(u	NUM
ejpam-5958	127	35	,	,	PUNCT
ejpam-5958	127	36	v	v	NOUN
ejpam-5958	127	37	)	)	PUNCT
ejpam-5958	127	38	dν(fu	dν(fu	PROPN
ejpam-5958	127	39	,	,	PUNCT
ejpam-5958	127	40	fv	fv	NOUN
ejpam-5958	127	41	)	)	PUNCT
ejpam-5958	127	42	≤	≤	NOUN
ejpam-5958	127	43	ψν	ψν	PROPN
ejpam-5958	127	44	(	(	PUNCT
ejpam-5958	127	45	dw(ν)(u	dw(ν)(u	PROPN
ejpam-5958	127	46	,	,	PUNCT
ejpam-5958	127	47	v	v	NOUN
ejpam-5958	127	48	)	)	PUNCT
ejpam-5958	127	49	)	)	PUNCT
ejpam-5958	127	50	,	,	PUNCT
ejpam-5958	127	51	∀u	∀u	NOUN
ejpam-5958	127	52	,	,	PUNCT
ejpam-5958	127	53	v	v	NOUN
ejpam-5958	127	54	∈	∈	NOUN
ejpam-5958	127	55	e	e	NOUN
ejpam-5958	127	56	,	,	PUNCT
ejpam-5958	127	57	∀ν	∀ν	PROPN
ejpam-5958	127	58	∈	∈	PROPN
ejpam-5958	127	59	n	n	X
ejpam-5958	127	60	.	.	PUNCT
ejpam-5958	128	1	(	(	PUNCT
ejpam-5958	128	2	3.2	3.2	NUM
ejpam-5958	128	3	)	)	PUNCT
ejpam-5958	128	4	remark	remark	NOUN
ejpam-5958	128	5	3.3	3.3	NUM
ejpam-5958	128	6	.	.	PUNCT
ejpam-5958	129	1	it	it	PRON
ejpam-5958	129	2	should	should	AUX
ejpam-5958	129	3	be	be	AUX
ejpam-5958	129	4	noted	note	VERB
ejpam-5958	129	5	that	that	SCONJ
ejpam-5958	129	6	many	many	ADJ
ejpam-5958	129	7	α	α	NOUN
ejpam-5958	129	8	-	-	PUNCT
ejpam-5958	129	9	ψ	ψ	NOUN
ejpam-5958	129	10	contractive	contractive	ADJ
ejpam-5958	129	11	type	type	NOUN
ejpam-5958	129	12	mappings	mapping	NOUN
ejpam-5958	129	13	in	in	ADP
ejpam-5958	129	14	the	the	DET
ejpam-5958	129	15	literature	literature	NOUN
ejpam-5958	129	16	are	be	AUX
ejpam-5958	129	17	generalized	generalize	VERB
ejpam-5958	129	18	by	by	ADP
ejpam-5958	129	19	that	that	PRON
ejpam-5958	129	20	given	give	VERB
ejpam-5958	129	21	in	in	ADP
ejpam-5958	129	22	(	(	PUNCT
ejpam-5958	129	23	3.2	3.2	NUM
ejpam-5958	129	24	)	)	PUNCT
ejpam-5958	129	25	in	in	ADP
ejpam-5958	129	26	two	two	NUM
ejpam-5958	129	27	distinct	distinct	ADJ
ejpam-5958	129	28	aspects	aspect	NOUN
ejpam-5958	129	29	.	.	PUNCT
ejpam-5958	130	1	the	the	DET
ejpam-5958	130	2	introduction	introduction	NOUN
ejpam-5958	130	3	of	of	ADP
ejpam-5958	130	4	a	a	DET
ejpam-5958	130	5	family	family	NOUN
ejpam-5958	130	6	of	of	ADP
ejpam-5958	130	7	mappings	mapping	NOUN
ejpam-5958	130	8	αααν	αααν	NOUN
ejpam-5958	130	9	=	=	PUNCT
ejpam-5958	130	10	{	{	PUNCT
ejpam-5958	130	11	αν}ν∈n	αν}ν∈n	NOUN
ejpam-5958	130	12	instead	instead	ADV
ejpam-5958	130	13	of	of	ADP
ejpam-5958	130	14	only	only	ADV
ejpam-5958	130	15	one	one	NUM
ejpam-5958	130	16	mapping	mapping	NOUN
ejpam-5958	130	17	α	α	NOUN
ejpam-5958	130	18	is	be	AUX
ejpam-5958	130	19	the	the	DET
ejpam-5958	130	20	clear	clear	ADJ
ejpam-5958	130	21	first	first	ADJ
ejpam-5958	130	22	aspect	aspect	NOUN
ejpam-5958	130	23	of	of	ADP
ejpam-5958	130	24	generalization	generalization	NOUN
ejpam-5958	130	25	.	.	PUNCT
ejpam-5958	131	1	while	while	SCONJ
ejpam-5958	131	2	the	the	DET
ejpam-5958	131	3	introduction	introduction	NOUN
ejpam-5958	131	4	of	of	ADP
ejpam-5958	131	5	the	the	DET
ejpam-5958	131	6	mapping	mapping	NOUN
ejpam-5958	131	7	w	w	NOUN
ejpam-5958	131	8	is	be	AUX
ejpam-5958	131	9	the	the	DET
ejpam-5958	131	10	second	second	ADJ
ejpam-5958	131	11	one	one	NUM
ejpam-5958	131	12	.	.	PUNCT
ejpam-5958	132	1	indeed	indeed	ADV
ejpam-5958	132	2	,	,	PUNCT
ejpam-5958	132	3	since	since	SCONJ
ejpam-5958	132	4	some	some	DET
ejpam-5958	132	5	α	α	NOUN
ejpam-5958	132	6	-	-	PUNCT
ejpam-5958	132	7	ψ	ψ	NOUN
ejpam-5958	132	8	contraction	contraction	NOUN
ejpam-5958	132	9	conditions	condition	NOUN
ejpam-5958	132	10	introduced	introduce	VERB
ejpam-5958	132	11	in	in	ADP
ejpam-5958	132	12	similar	similar	ADJ
ejpam-5958	132	13	studies	study	NOUN
ejpam-5958	132	14	in	in	ADP
ejpam-5958	132	15	this	this	DET
ejpam-5958	132	16	direction	direction	NOUN
ejpam-5958	132	17	correspond	correspond	VERB
ejpam-5958	132	18	to	to	ADP
ejpam-5958	132	19	w	w	NOUN
ejpam-5958	132	20	=	=	PUNCT
ejpam-5958	132	21	in	in	ADP
ejpam-5958	132	22	[	[	X
ejpam-5958	132	23	4	4	NUM
ejpam-5958	132	24	,	,	PUNCT
ejpam-5958	132	25	10	10	NUM
ejpam-5958	132	26	,	,	PUNCT
ejpam-5958	132	27	33	33	NUM
ejpam-5958	132	28	,	,	PUNCT
ejpam-5958	132	29	36	36	NUM
ejpam-5958	132	30	]	]	PUNCT
ejpam-5958	132	31	,	,	PUNCT
ejpam-5958	132	32	then	then	ADV
ejpam-5958	132	33	in	in	ADP
ejpam-5958	132	34	view	view	NOUN
ejpam-5958	132	35	of	of	ADP
ejpam-5958	132	36	(	(	PUNCT
ejpam-5958	132	37	3.1	3.1	NUM
ejpam-5958	132	38	)	)	PUNCT
ejpam-5958	132	39	,	,	PUNCT
ejpam-5958	132	40	our	our	PRON
ejpam-5958	132	41	contraction	contraction	NOUN
ejpam-5958	132	42	condition	condition	NOUN
ejpam-5958	132	43	(	(	PUNCT
ejpam-5958	132	44	3.2	3.2	NUM
ejpam-5958	132	45	)	)	PUNCT
ejpam-5958	132	46	is	be	AUX
ejpam-5958	132	47	weaker	weak	ADJ
ejpam-5958	132	48	than	than	ADP
ejpam-5958	132	49	those	those	PRON
ejpam-5958	132	50	mentioned	mention	VERB
ejpam-5958	132	51	above	above	ADV
ejpam-5958	132	52	.	.	PUNCT
ejpam-5958	133	1	example	example	NOUN
ejpam-5958	134	1	3	3	X
ejpam-5958	134	2	.	.	PUNCT
ejpam-5958	135	1	let	let	VERB
ejpam-5958	135	2	x	x	PRON
ejpam-5958	135	3	be	be	AUX
ejpam-5958	135	4	the	the	DET
ejpam-5958	135	5	space	space	NOUN
ejpam-5958	135	6	of	of	ADP
ejpam-5958	135	7	all	all	DET
ejpam-5958	135	8	real	real	ADJ
ejpam-5958	135	9	sequences	sequence	NOUN
ejpam-5958	135	10	:	:	PUNCT
ejpam-5958	135	11	x	x	SYM
ejpam-5958	135	12	=	=	PRON
ejpam-5958	135	13	{	{	PUNCT
ejpam-5958	135	14	u	u	NOUN
ejpam-5958	135	15	=	=	PUNCT
ejpam-5958	135	16	(	(	PUNCT
ejpam-5958	135	17	u1	u1	PROPN
ejpam-5958	135	18	,	,	PUNCT
ejpam-5958	135	19	u2	u2	PROPN
ejpam-5958	135	20	,	,	PUNCT
ejpam-5958	135	21	...	...	PUNCT
ejpam-5958	135	22	,	,	PUNCT
ejpam-5958	135	23	un	un	PROPN
ejpam-5958	135	24	,	,	PUNCT
ejpam-5958	135	25	...	...	PUNCT
ejpam-5958	135	26	)	)	PUNCT
ejpam-5958	135	27	:	:	PUNCT
ejpam-5958	135	28	un	un	PROPN
ejpam-5958	135	29	∈	∈	PROPN
ejpam-5958	135	30	r	r	PROPN
ejpam-5958	135	31	,	,	PUNCT
ejpam-5958	135	32	n	n	PRON
ejpam-5958	135	33	∈	∈	PROPN
ejpam-5958	135	34	n∗	n∗	PROPN
ejpam-5958	135	35	}	}	PUNCT
ejpam-5958	135	36	.	.	PUNCT
ejpam-5958	136	1	for	for	ADP
ejpam-5958	136	2	each	each	DET
ejpam-5958	136	3	n	n	PRON
ejpam-5958	136	4	∈	∈	PROPN
ejpam-5958	136	5	n∗	n∗	NOUN
ejpam-5958	136	6	,	,	PUNCT
ejpam-5958	136	7	let	let	VERB
ejpam-5958	136	8	πn	πn	INTJ
ejpam-5958	136	9	:	:	PUNCT
ejpam-5958	136	10	x	x	PUNCT
ejpam-5958	136	11	−→	−→	NOUN
ejpam-5958	136	12	r	r	NOUN
ejpam-5958	136	13	be	be	VERB
ejpam-5958	136	14	the	the	DET
ejpam-5958	136	15	mapping	mapping	NOUN
ejpam-5958	136	16	defined	define	VERB
ejpam-5958	136	17	by	by	ADP
ejpam-5958	136	18	πn(u	πn(u	NOUN
ejpam-5958	136	19	)	)	PUNCT
ejpam-5958	136	20	=	=	SYM
ejpam-5958	137	1	un	un	AUX
ejpam-5958	137	2	.	.	PROPN
ejpam-5958	137	3	let	let	VERB
ejpam-5958	137	4	{	{	PUNCT
ejpam-5958	137	5	dn}n∈n∗	dn}n∈n∗	PROPN
ejpam-5958	137	6	be	be	AUX
ejpam-5958	137	7	the	the	DET
ejpam-5958	137	8	family	family	NOUN
ejpam-5958	137	9	of	of	ADP
ejpam-5958	137	10	b	b	NOUN
ejpam-5958	137	11	-	-	PUNCT
ejpam-5958	137	12	pseudo	pseudo	NOUN
ejpam-5958	137	13	-	-	PUNCT
ejpam-5958	137	14	metrics	metric	NOUN
ejpam-5958	137	15	with	with	ADP
ejpam-5958	137	16	constant	constant	ADJ
ejpam-5958	137	17	s	s	X
ejpam-5958	137	18	=	=	SYM
ejpam-5958	137	19	2	2	NUM
ejpam-5958	137	20	defined	define	VERB
ejpam-5958	137	21	on	on	ADP
ejpam-5958	137	22	x	x	PUNCT
ejpam-5958	137	23	by	by	ADP
ejpam-5958	137	24	dn(u	dn(u	NUM
ejpam-5958	137	25	,	,	PUNCT
ejpam-5958	137	26	v	v	NOUN
ejpam-5958	137	27	)	)	PUNCT
ejpam-5958	137	28	=	=	SYM
ejpam-5958	138	1	|πn(u)−	|πn(u)−	NOUN
ejpam-5958	138	2	πn(v)|2	πn(v)|2	ADV
ejpam-5958	138	3	let	let	VERB
ejpam-5958	138	4	w	w	X
ejpam-5958	138	5	:	:	PUNCT
ejpam-5958	138	6	n∗	n∗	PROPN
ejpam-5958	138	7	−→	−→	NOUN
ejpam-5958	138	8	n∗	n∗	NOUN
ejpam-5958	138	9	be	be	VERB
ejpam-5958	138	10	the	the	DET
ejpam-5958	138	11	mapping	mapping	NOUN
ejpam-5958	138	12	defined	define	VERB
ejpam-5958	138	13	by	by	ADP
ejpam-5958	138	14	w(n	w(n	PROPN
ejpam-5958	138	15	)	)	PUNCT
ejpam-5958	138	16	=	=	PUNCT
ejpam-5958	138	17	n+	n+	PUNCT
ejpam-5958	138	18	1	1	X
ejpam-5958	138	19	.	.	X
ejpam-5958	138	20	consider	consider	VERB
ejpam-5958	139	1	the	the	DET
ejpam-5958	139	2	map	map	NOUN
ejpam-5958	139	3	f	f	X
ejpam-5958	139	4	:	:	PUNCT
ejpam-5958	139	5	x	x	PUNCT
ejpam-5958	139	6	−→	−→	NOUN
ejpam-5958	139	7	x	x	PUNCT
ejpam-5958	139	8	defined	define	VERB
ejpam-5958	139	9	as	as	SCONJ
ejpam-5958	139	10	follows	follow	VERB
ejpam-5958	139	11	:	:	PUNCT
ejpam-5958	139	12	fu	fu	NOUN
ejpam-5958	139	13	=	=	PUNCT
ejpam-5958	139	14			PUNCT
ejpam-5958	139	15	(	(	PUNCT
ejpam-5958	139	16	(	(	PUNCT
ejpam-5958	139	17	1−	1−	NUM
ejpam-5958	139	18	1	1	NUM
ejpam-5958	139	19	2)(2−	2)(2−	NUM
ejpam-5958	139	20	u2	u2	PROPN
ejpam-5958	139	21	)	)	PUNCT
ejpam-5958	139	22	,	,	PUNCT
ejpam-5958	139	23	(	(	PUNCT
ejpam-5958	139	24	1−	1−	NUM
ejpam-5958	139	25	2	2	NUM
ejpam-5958	139	26	3)(2−	3)(2−	NUM
ejpam-5958	139	27	u3	u3	NOUN
ejpam-5958	139	28	)	)	PUNCT
ejpam-5958	139	29	,	,	PUNCT
ejpam-5958	139	30	...	...	PUNCT
ejpam-5958	139	31	,	,	PUNCT
ejpam-5958	139	32	(	(	PUNCT
ejpam-5958	139	33	1−	1−	NUM
ejpam-5958	139	34	n	n	NUM
ejpam-5958	139	35	n+1)(2−	n+1)(2−	NOUN
ejpam-5958	139	36	un+1	un+1	NOUN
ejpam-5958	139	37	)	)	PUNCT
ejpam-5958	139	38	,	,	PUNCT
ejpam-5958	139	39	...	...	PUNCT
ejpam-5958	139	40	)	)	PUNCT
ejpam-5958	139	41	,	,	PUNCT
ejpam-5958	139	42	∃n	∃n	PROPN
ejpam-5958	139	43	∈	∈	PROPN
ejpam-5958	139	44	n∗	n∗	PROPN
ejpam-5958	139	45	:	:	PUNCT
ejpam-5958	139	46	un	un	PROPN
ejpam-5958	139	47	≤	≤	PROPN
ejpam-5958	139	48	2	2	NUM
ejpam-5958	139	49	;	;	PUNCT
ejpam-5958	139	50	(	(	PUNCT
ejpam-5958	139	51	2u2	2u2	NUM
ejpam-5958	139	52	−	−	NOUN
ejpam-5958	139	53	2	2	NUM
ejpam-5958	139	54	,	,	PUNCT
ejpam-5958	139	55	2u3	2u3	NUM
ejpam-5958	139	56	−	−	PROPN
ejpam-5958	139	57	2	2	NUM
ejpam-5958	139	58	,	,	PUNCT
ejpam-5958	139	59	...	...	PUNCT
ejpam-5958	139	60	,	,	PUNCT
ejpam-5958	139	61	2un+1	2un+1	ADJ
ejpam-5958	139	62	−	−	PROPN
ejpam-5958	139	63	2	2	NUM
ejpam-5958	139	64	,	,	PUNCT
ejpam-5958	139	65	...	...	PUNCT
ejpam-5958	139	66	)	)	PUNCT
ejpam-5958	139	67	,	,	PUNCT
ejpam-5958	139	68	otherwise	otherwise	ADV
ejpam-5958	139	69	.	.	PUNCT
ejpam-5958	140	1	k.	k.	PROPN
ejpam-5958	140	2	nisse	nisse	PROPN
ejpam-5958	140	3	et	et	PROPN
ejpam-5958	140	4	al	al	PROPN
ejpam-5958	140	5	.	.	PUNCT
ejpam-5958	140	6	/	/	SYM
ejpam-5958	140	7	eur	eur	PROPN
ejpam-5958	140	8	.	.	PUNCT
ejpam-5958	141	1	j.	j.	PROPN
ejpam-5958	141	2	pure	pure	PROPN
ejpam-5958	141	3	appl	appl	PROPN
ejpam-5958	141	4	.	.	PROPN
ejpam-5958	141	5	math	math	PROPN
ejpam-5958	141	6	,	,	PUNCT
ejpam-5958	141	7	18	18	NUM
ejpam-5958	141	8	(	(	PUNCT
ejpam-5958	141	9	2	2	NUM
ejpam-5958	141	10	)	)	PUNCT
ejpam-5958	141	11	(	(	PUNCT
ejpam-5958	141	12	2025	2025	NUM
ejpam-5958	141	13	)	)	PUNCT
ejpam-5958	141	14	,	,	PUNCT
ejpam-5958	141	15	5958	5958	NUM
ejpam-5958	141	16	7	7	NUM
ejpam-5958	141	17	of	of	ADP
ejpam-5958	141	18	22	22	NUM
ejpam-5958	141	19	let	let	VERB
ejpam-5958	141	20	αααn	αααn	NOUN
ejpam-5958	141	21	=	=	PUNCT
ejpam-5958	141	22	{	{	PUNCT
ejpam-5958	141	23	α	α	NOUN
ejpam-5958	141	24	}	}	PUNCT
ejpam-5958	141	25	,	,	PUNCT
ejpam-5958	141	26	where	where	SCONJ
ejpam-5958	141	27	α	α	NOUN
ejpam-5958	141	28	:	:	PUNCT
ejpam-5958	141	29	x	x	X
ejpam-5958	141	30	×x	×x	VERB
ejpam-5958	141	31	−→	−→	ADJ
ejpam-5958	141	32	r+	r+	NOUN
ejpam-5958	141	33	is	be	AUX
ejpam-5958	141	34	the	the	DET
ejpam-5958	141	35	function	function	NOUN
ejpam-5958	141	36	given	give	VERB
ejpam-5958	141	37	by	by	ADP
ejpam-5958	141	38	:	:	PUNCT
ejpam-5958	141	39	α(u	α(u	NOUN
ejpam-5958	141	40	,	,	PUNCT
ejpam-5958	141	41	v	v	NOUN
ejpam-5958	141	42	)	)	PUNCT
ejpam-5958	141	43	=	=	NOUN
ejpam-5958	141	44	{	{	PUNCT
ejpam-5958	141	45	1	1	NUM
ejpam-5958	141	46	:	:	PUNCT
ejpam-5958	141	47	un	un	PROPN
ejpam-5958	141	48	,	,	PUNCT
ejpam-5958	141	49	vn	vn	VERB
ejpam-5958	141	50	≤	≤	ADV
ejpam-5958	141	51	2	2	NUM
ejpam-5958	141	52	for	for	ADP
ejpam-5958	141	53	some	some	DET
ejpam-5958	141	54	n	n	PRON
ejpam-5958	141	55	∈	∈	NOUN
ejpam-5958	141	56	n∗	n∗	NOUN
ejpam-5958	141	57	0	0	NUM
ejpam-5958	141	58	:	:	PUNCT
ejpam-5958	141	59	otherwise	otherwise	ADV
ejpam-5958	141	60	now	now	ADV
ejpam-5958	141	61	,	,	PUNCT
ejpam-5958	141	62	let	let	VERB
ejpam-5958	141	63	ψ2	ψ2	NOUN
ejpam-5958	141	64	be	be	AUX
ejpam-5958	141	65	the	the	DET
ejpam-5958	141	66	family	family	NOUN
ejpam-5958	141	67	of	of	ADP
ejpam-5958	141	68	the	the	DET
ejpam-5958	141	69	functions	function	NOUN
ejpam-5958	141	70	ψn	ψn	VERB
ejpam-5958	141	71	defined	define	VERB
ejpam-5958	141	72	for	for	ADP
ejpam-5958	141	73	each	each	DET
ejpam-5958	141	74	n	n	PRON
ejpam-5958	141	75	∈	∈	PROPN
ejpam-5958	141	76	n∗	n∗	NOUN
ejpam-5958	141	77	by	by	ADP
ejpam-5958	141	78	:	:	PUNCT
ejpam-5958	141	79	ψn(t	ψn(t	NUM
ejpam-5958	141	80	)	)	PUNCT
ejpam-5958	142	1	=	=	SYM
ejpam-5958	142	2	1	1	NUM
ejpam-5958	142	3	(	(	PUNCT
ejpam-5958	142	4	n+	n+	NUM
ejpam-5958	142	5	1)2	1)2	NUM
ejpam-5958	142	6	t	t	NOUN
ejpam-5958	142	7	let	let	VERB
ejpam-5958	142	8	u	u	NOUN
ejpam-5958	142	9	,	,	PUNCT
ejpam-5958	142	10	v	v	PROPN
ejpam-5958	142	11	∈	∈	PROPN
ejpam-5958	142	12	x	x	NOUN
ejpam-5958	142	13	,	,	PUNCT
ejpam-5958	142	14	we	we	PRON
ejpam-5958	142	15	distinguish	distinguish	VERB
ejpam-5958	142	16	two	two	NUM
ejpam-5958	142	17	cases	case	NOUN
ejpam-5958	142	18	:	:	PUNCT
ejpam-5958	142	19	case	case	NOUN
ejpam-5958	142	20	1	1	NUM
ejpam-5958	142	21	:	:	PUNCT
ejpam-5958	142	22	there	there	PRON
ejpam-5958	142	23	exists	exist	VERB
ejpam-5958	142	24	n	n	PRON
ejpam-5958	142	25	∈	∈	PROPN
ejpam-5958	142	26	n∗	n∗	NOUN
ejpam-5958	142	27	such	such	ADJ
ejpam-5958	142	28	that	that	DET
ejpam-5958	142	29	un	un	PROPN
ejpam-5958	142	30	,	,	PUNCT
ejpam-5958	142	31	vn	vn	VERB
ejpam-5958	142	32	≤	≤	ADV
ejpam-5958	142	33	2	2	NUM
ejpam-5958	142	34	.	.	PUNCT
ejpam-5958	143	1	then	then	ADV
ejpam-5958	143	2	:	:	PUNCT
ejpam-5958	143	3	α(u	α(u	NOUN
ejpam-5958	143	4	,	,	PUNCT
ejpam-5958	143	5	v)dn(fu	v)dn(fu	NOUN
ejpam-5958	143	6	,	,	PUNCT
ejpam-5958	143	7	fv	fv	NOUN
ejpam-5958	143	8	)	)	PUNCT
ejpam-5958	143	9	=	=	PUNCT
ejpam-5958	143	10	dn(fu	dn(fu	PROPN
ejpam-5958	143	11	,	,	PUNCT
ejpam-5958	143	12	fv	fv	X
ejpam-5958	143	13	)	)	PUNCT
ejpam-5958	143	14	=	=	SYM
ejpam-5958	143	15	∣∣∣(1−	∣∣∣(1−	PROPN
ejpam-5958	143	16	n	n	PRON
ejpam-5958	143	17	n+1)(2−	n+1)(2−	NOUN
ejpam-5958	143	18	un+1)−	un+1)−	ADJ
ejpam-5958	143	19	(	(	PUNCT
ejpam-5958	143	20	1−	1−	NUM
ejpam-5958	143	21	n	n	NUM
ejpam-5958	143	22	n+1)(2−	n+1)(2−	PROPN
ejpam-5958	143	23	vn+1	vn+1	PROPN
ejpam-5958	143	24	)	)	PUNCT
ejpam-5958	143	25	∣∣∣2	∣∣∣2	NOUN
ejpam-5958	143	26	=	=	PRON
ejpam-5958	143	27	(	(	PUNCT
ejpam-5958	143	28	1−	1−	NUM
ejpam-5958	143	29	n	n	SYM
ejpam-5958	143	30	n+1	n+1	NOUN
ejpam-5958	143	31	)	)	PUNCT
ejpam-5958	143	32	2	2	NUM
ejpam-5958	143	33	|un+1	|un+1	NOUN
ejpam-5958	143	34	−	−	NOUN
ejpam-5958	144	1	vn+1|2	vn+1|2	NOUN
ejpam-5958	144	2	=	=	NOUN
ejpam-5958	144	3	1	1	NUM
ejpam-5958	144	4	(	(	PUNCT
ejpam-5958	144	5	n+1)2	n+1)2	ADJ
ejpam-5958	144	6	|un+1	|un+1	NOUN
ejpam-5958	145	1	−	−	PROPN
ejpam-5958	146	1	vn+1|2	vn+1|2	PROPN
ejpam-5958	146	2	=	=	PUNCT
ejpam-5958	146	3	ψn	ψn	PROPN
ejpam-5958	146	4	(	(	PUNCT
ejpam-5958	146	5	dn+1(u	dn+1(u	PROPN
ejpam-5958	146	6	,	,	PUNCT
ejpam-5958	146	7	v	v	NOUN
ejpam-5958	146	8	)	)	PUNCT
ejpam-5958	146	9	)	)	PUNCT
ejpam-5958	147	1	=	=	PRON
ejpam-5958	147	2	ψn	ψn	X
ejpam-5958	147	3	(	(	PUNCT
ejpam-5958	147	4	dw(n)(u	dw(n)(u	PROPN
ejpam-5958	147	5	,	,	PUNCT
ejpam-5958	147	6	v	v	NOUN
ejpam-5958	147	7	)	)	PUNCT
ejpam-5958	147	8	)	)	PUNCT
ejpam-5958	147	9	case	case	NOUN
ejpam-5958	147	10	2	2	NUM
ejpam-5958	147	11	:	:	PUNCT
ejpam-5958	147	12	for	for	ADP
ejpam-5958	147	13	every	every	DET
ejpam-5958	147	14	n	n	PRON
ejpam-5958	147	15	∈	∈	PROPN
ejpam-5958	147	16	n∗	n∗	PROPN
ejpam-5958	147	17	:	:	PUNCT
ejpam-5958	147	18	un	un	PROPN
ejpam-5958	147	19	>	>	X
ejpam-5958	147	20	2	2	NUM
ejpam-5958	147	21	or	or	CCONJ
ejpam-5958	147	22	vn	vn	X
ejpam-5958	147	23	>	>	X
ejpam-5958	148	1	2	2	X
ejpam-5958	148	2	.	.	PUNCT
ejpam-5958	148	3	since	since	SCONJ
ejpam-5958	148	4	α(u	α(u	NOUN
ejpam-5958	148	5	,	,	PUNCT
ejpam-5958	148	6	v	v	NOUN
ejpam-5958	148	7	)	)	PUNCT
ejpam-5958	148	8	=	=	SYM
ejpam-5958	148	9	0	0	NUM
ejpam-5958	148	10	,	,	PUNCT
ejpam-5958	148	11	clearly	clearly	ADV
ejpam-5958	148	12	we	we	PRON
ejpam-5958	148	13	have	have	VERB
ejpam-5958	148	14	:	:	PUNCT
ejpam-5958	148	15	α(u	α(u	NOUN
ejpam-5958	148	16	,	,	PUNCT
ejpam-5958	148	17	v)dn(fu	v)dn(fu	NOUN
ejpam-5958	148	18	,	,	PUNCT
ejpam-5958	148	19	fv	fv	X
ejpam-5958	148	20	)	)	PUNCT
ejpam-5958	148	21	=	=	SYM
ejpam-5958	148	22	0	0	X
ejpam-5958	148	23	≤	≤	NUM
ejpam-5958	148	24	ψn	ψn	X
ejpam-5958	148	25	(	(	PUNCT
ejpam-5958	148	26	dw(n)(u	dw(n)(u	PROPN
ejpam-5958	148	27	,	,	PUNCT
ejpam-5958	148	28	v	v	NOUN
ejpam-5958	148	29	)	)	PUNCT
ejpam-5958	148	30	)	)	PUNCT
ejpam-5958	149	1	consequently	consequently	ADV
ejpam-5958	149	2	,	,	PUNCT
ejpam-5958	149	3	f	f	PROPN
ejpam-5958	149	4	is	be	AUX
ejpam-5958	149	5	a	a	DET
ejpam-5958	149	6	generalized	generalized	ADJ
ejpam-5958	149	7	(	(	PUNCT
ejpam-5958	149	8	αααn	αααn	NOUN
ejpam-5958	149	9	,	,	PUNCT
ejpam-5958	149	10	ψ	ψ	NOUN
ejpam-5958	149	11	2,w	2,w	NUM
ejpam-5958	149	12	)	)	PUNCT
ejpam-5958	149	13	contraction	contraction	NOUN
ejpam-5958	149	14	.	.	PUNCT
ejpam-5958	150	1	we	we	PRON
ejpam-5958	150	2	state	state	VERB
ejpam-5958	150	3	now	now	ADV
ejpam-5958	150	4	our	our	PRON
ejpam-5958	150	5	first	first	ADJ
ejpam-5958	150	6	main	main	ADJ
ejpam-5958	150	7	result	result	NOUN
ejpam-5958	150	8	.	.	PUNCT
ejpam-5958	151	1	theorem	theorem	NOUN
ejpam-5958	151	2	1	1	NUM
ejpam-5958	151	3	.	.	PUNCT
ejpam-5958	152	1	let	let	VERB
ejpam-5958	152	2	f	f	NOUN
ejpam-5958	152	3	:	:	PUNCT
ejpam-5958	152	4	e	e	AUX
ejpam-5958	152	5	−→	−→	NOUN
ejpam-5958	152	6	e	e	AUX
ejpam-5958	152	7	be	be	AUX
ejpam-5958	152	8	a	a	DET
ejpam-5958	152	9	a	a	DET
ejpam-5958	152	10	generalized	generalized	ADJ
ejpam-5958	152	11	(	(	PUNCT
ejpam-5958	152	12	αααν	αααν	NOUN
ejpam-5958	152	13	,	,	PUNCT
ejpam-5958	152	14	ψ	ψ	X
ejpam-5958	152	15	s	s	SYM
ejpam-5958	152	16	,	,	PUNCT
ejpam-5958	152	17	w	w	NOUN
ejpam-5958	152	18	)	)	PUNCT
ejpam-5958	152	19	contraction	contraction	NOUN
ejpam-5958	152	20	.	.	PUNCT
ejpam-5958	153	1	suppose	suppose	VERB
ejpam-5958	153	2	that	that	SCONJ
ejpam-5958	153	3	the	the	DET
ejpam-5958	153	4	following	follow	VERB
ejpam-5958	153	5	conditions	condition	NOUN
ejpam-5958	153	6	hold	hold	VERB
ejpam-5958	153	7	:	:	PUNCT
ejpam-5958	153	8	(	(	PUNCT
ejpam-5958	153	9	c1	c1	NOUN
ejpam-5958	153	10	)	)	PUNCT
ejpam-5958	153	11	f	f	PROPN
ejpam-5958	153	12	is	be	AUX
ejpam-5958	153	13	αααν	αααν	NOUN
ejpam-5958	153	14	-	-	PUNCT
ejpam-5958	153	15	admissible	admissible	ADJ
ejpam-5958	153	16	.	.	PUNCT
ejpam-5958	154	1	(	(	PUNCT
ejpam-5958	154	2	c2	c2	PROPN
ejpam-5958	154	3	)	)	PUNCT
ejpam-5958	155	1	∃x0	∃x0	PROPN
ejpam-5958	155	2	∈	∈	PROPN
ejpam-5958	155	3	e	e	NOUN
ejpam-5958	155	4	,	,	PUNCT
ejpam-5958	155	5	n	n	PROPN
ejpam-5958	155	6	∈	∈	PROPN
ejpam-5958	155	7	n∗	n∗	NOUN
ejpam-5958	155	8	and	and	CCONJ
ejpam-5958	155	9	(	(	PUNCT
ejpam-5958	155	10	ap0	ap0	PROPN
ejpam-5958	155	11	)	)	PUNCT
ejpam-5958	156	1	n	n	CCONJ
ejpam-5958	157	1	p=0	p=0	PROPN
ejpam-5958	157	2	⊂	⊂	PUNCT
ejpam-5958	157	3	e	e	X
ejpam-5958	157	4	,	,	PUNCT
ejpam-5958	157	5	with	with	ADP
ejpam-5958	157	6	a00	a00	NOUN
ejpam-5958	157	7	=	=	SYM
ejpam-5958	157	8	x0	x0	PROPN
ejpam-5958	157	9	and	and	CCONJ
ejpam-5958	157	10	an0	an0	PROPN
ejpam-5958	157	11	=	=	SYM
ejpam-5958	157	12	fx0	fx0	PROPN
ejpam-5958	157	13	,	,	PUNCT
ejpam-5958	157	14	such	such	ADJ
ejpam-5958	157	15	that	that	SCONJ
ejpam-5958	157	16	:	:	PUNCT
ejpam-5958	157	17	(	(	PUNCT
ejpam-5958	157	18	i	i	NOUN
ejpam-5958	157	19	)	)	PUNCT
ejpam-5958	157	20	αν(a	αν(a	PROPN
ejpam-5958	157	21	p−1	p−1	PROPN
ejpam-5958	157	22	0	0	NUM
ejpam-5958	157	23	,	,	PUNCT
ejpam-5958	157	24	ap0	ap0	PROPN
ejpam-5958	157	25	)	)	PUNCT
ejpam-5958	157	26	≥	≥	NOUN
ejpam-5958	157	27	1	1	NUM
ejpam-5958	157	28	,	,	PUNCT
ejpam-5958	157	29	∀p	∀p	NOUN
ejpam-5958	157	30	=	=	SYM
ejpam-5958	157	31	1	1	NUM
ejpam-5958	157	32	,	,	PUNCT
ejpam-5958	157	33	..	..	PUNCT
ejpam-5958	157	34	,	,	PUNCT
ejpam-5958	157	35	n	n	CCONJ
ejpam-5958	157	36	,	,	PUNCT
ejpam-5958	157	37	∀ν	∀ν	PROPN
ejpam-5958	157	38	∈	∈	PROPN
ejpam-5958	157	39	n	n	NOUN
ejpam-5958	157	40	;	;	PUNCT
ejpam-5958	157	41	(	(	PUNCT
ejpam-5958	157	42	ii	ii	NOUN
ejpam-5958	157	43	)	)	PUNCT
ejpam-5958	157	44	n∑	n∑	NOUN
ejpam-5958	158	1	p=1	p=1	PROPN
ejpam-5958	158	2	spdwi(ν)(a	spdwi(ν)(a	NOUN
ejpam-5958	158	3	p−1	p−1	PROPN
ejpam-5958	158	4	0	0	NUM
ejpam-5958	158	5	,	,	PUNCT
ejpam-5958	158	6	ap0	ap0	PROPN
ejpam-5958	158	7	)	)	PUNCT
ejpam-5958	158	8	≤ms	≤m	NOUN
ejpam-5958	158	9	,	,	PUNCT
ejpam-5958	158	10	ν(x	ν(x	PROPN
ejpam-5958	158	11	0	0	NUM
ejpam-5958	158	12	)	)	PUNCT
ejpam-5958	158	13	<	<	X
ejpam-5958	159	1	+	+	PROPN
ejpam-5958	159	2	∞	∞	NOUN
ejpam-5958	159	3	,	,	PUNCT
ejpam-5958	159	4	∀i	∀i	NOUN
ejpam-5958	159	5	∈	∈	NOUN
ejpam-5958	159	6	n	n	CCONJ
ejpam-5958	159	7	,	,	PUNCT
ejpam-5958	159	8	∀ν	∀ν	PROPN
ejpam-5958	159	9	∈	∈	PROPN
ejpam-5958	159	10	n	n	X
ejpam-5958	159	11	.	.	PUNCT
ejpam-5958	160	1	(	(	PUNCT
ejpam-5958	160	2	c3	c3	NOUN
ejpam-5958	160	3	)	)	PUNCT
ejpam-5958	160	4	∀ν	∀ν	PROPN
ejpam-5958	160	5	∈	∈	PROPN
ejpam-5958	160	6	n	n	NOUN
ejpam-5958	160	7	,	,	PUNCT
ejpam-5958	160	8	∃ψ̃ν	∃ψ̃ν	PUNCT
ejpam-5958	160	9	∈	∈	PROPN
ejpam-5958	161	1	ψs	ψs	ADP
ejpam-5958	161	2	:	:	PUNCT
ejpam-5958	161	3	ψwi(ν	ψwi(ν	PROPN
ejpam-5958	161	4	)	)	PUNCT
ejpam-5958	161	5	≤	≤	NUM
ejpam-5958	161	6	ψ̃ν	ψ̃ν	PRON
ejpam-5958	161	7	,	,	PUNCT
ejpam-5958	161	8	∀i	∀i	X
ejpam-5958	161	9	∈	∈	NOUN
ejpam-5958	161	10	n	n	CCONJ
ejpam-5958	161	11	(	(	PUNCT
ejpam-5958	161	12	c4	c4	NOUN
ejpam-5958	161	13	)	)	PUNCT
ejpam-5958	161	14	(	(	PUNCT
ejpam-5958	161	15	i	i	NOUN
ejpam-5958	161	16	)	)	PUNCT
ejpam-5958	161	17	f	f	PROPN
ejpam-5958	161	18	is	be	AUX
ejpam-5958	161	19	continuous	continuous	ADJ
ejpam-5958	161	20	or	or	CCONJ
ejpam-5958	162	1	k.	k.	PROPN
ejpam-5958	162	2	nisse	nisse	PROPN
ejpam-5958	162	3	et	et	PROPN
ejpam-5958	162	4	al	al	PROPN
ejpam-5958	162	5	.	.	PUNCT
ejpam-5958	162	6	/	/	SYM
ejpam-5958	162	7	eur	eur	PROPN
ejpam-5958	162	8	.	.	PUNCT
ejpam-5958	163	1	j.	j.	PROPN
ejpam-5958	163	2	pure	pure	PROPN
ejpam-5958	163	3	appl	appl	PROPN
ejpam-5958	163	4	.	.	PROPN
ejpam-5958	163	5	math	math	PROPN
ejpam-5958	163	6	,	,	PUNCT
ejpam-5958	163	7	18	18	NUM
ejpam-5958	163	8	(	(	PUNCT
ejpam-5958	163	9	2	2	NUM
ejpam-5958	163	10	)	)	PUNCT
ejpam-5958	163	11	(	(	PUNCT
ejpam-5958	163	12	2025	2025	NUM
ejpam-5958	163	13	)	)	PUNCT
ejpam-5958	163	14	,	,	PUNCT
ejpam-5958	163	15	5958	5958	NUM
ejpam-5958	163	16	8	8	NUM
ejpam-5958	163	17	of	of	ADP
ejpam-5958	163	18	22	22	NUM
ejpam-5958	163	19	(	(	PUNCT
ejpam-5958	163	20	ii	ii	NOUN
ejpam-5958	163	21	)	)	PUNCT
ejpam-5958	163	22	for	for	ADP
ejpam-5958	163	23	every	every	DET
ejpam-5958	163	24	sequence	sequence	NOUN
ejpam-5958	163	25	{	{	PUNCT
ejpam-5958	163	26	uk	uk	PROPN
ejpam-5958	163	27	}	}	PUNCT
ejpam-5958	163	28	k∈n	k∈n	PROPN
ejpam-5958	163	29	of	of	ADP
ejpam-5958	163	30	e	e	PROPN
ejpam-5958	163	31	,	,	PUNCT
ejpam-5958	163	32	such	such	ADJ
ejpam-5958	163	33	that	that	SCONJ
ejpam-5958	163	34	for	for	ADP
ejpam-5958	163	35	all	all	DET
ejpam-5958	163	36	k	k	PROPN
ejpam-5958	163	37	∈	∈	PROPN
ejpam-5958	163	38	n	n	PRON
ejpam-5958	163	39	and	and	CCONJ
ejpam-5958	163	40	the	the	DET
ejpam-5958	163	41	same	same	ADJ
ejpam-5958	163	42	positive	positive	ADJ
ejpam-5958	163	43	integer	integer	NOUN
ejpam-5958	163	44	n	n	CCONJ
ejpam-5958	163	45	given	give	VERB
ejpam-5958	163	46	in	in	ADP
ejpam-5958	163	47	(	(	PUNCT
ejpam-5958	163	48	c2	c2	PROPN
ejpam-5958	163	49	):	):	PUNCT
ejpam-5958	163	50	∃	∃	PROPN
ejpam-5958	163	51	(	(	PUNCT
ejpam-5958	163	52	apk	apk	PROPN
ejpam-5958	163	53	)	)	PUNCT
ejpam-5958	163	54	n	n	CCONJ
ejpam-5958	164	1	p=0	p=0	PROPN
ejpam-5958	164	2	⊂	⊂	PUNCT
ejpam-5958	164	3	e	e	PROPN
ejpam-5958	164	4	,	,	PUNCT
ejpam-5958	164	5	s.t	s.t	PROPN
ejpam-5958	164	6	.	.	PUNCT
ejpam-5958	164	7	a0k	a0k	ADP
ejpam-5958	164	8	=	=	SYM
ejpam-5958	164	9	uk	uk	PROPN
ejpam-5958	164	10	,	,	PUNCT
ejpam-5958	164	11	ank	ank	PROPN
ejpam-5958	164	12	=	=	PROPN
ejpam-5958	164	13	uk+1	uk+1	X
ejpam-5958	164	14	and	and	CCONJ
ejpam-5958	164	15	αν(a	αν(a	NUM
ejpam-5958	164	16	p−1	p−1	PROPN
ejpam-5958	164	17	k	k	PROPN
ejpam-5958	164	18	,	,	PUNCT
ejpam-5958	164	19	apk	apk	PROPN
ejpam-5958	164	20	)	)	PUNCT
ejpam-5958	164	21	≥	≥	NOUN
ejpam-5958	164	22	1	1	NUM
ejpam-5958	164	23	,	,	PUNCT
ejpam-5958	164	24	∀p	∀p	NOUN
ejpam-5958	164	25	=	=	SYM
ejpam-5958	164	26	1	1	NUM
ejpam-5958	164	27	,	,	PUNCT
ejpam-5958	164	28	n,∀ν	n,∀ν	NOUN
ejpam-5958	164	29	∈	∈	PROPN
ejpam-5958	164	30	n	n	NOUN
ejpam-5958	164	31	,	,	PUNCT
ejpam-5958	164	32	(	(	PUNCT
ejpam-5958	164	33	3.3	3.3	NUM
ejpam-5958	164	34	)	)	PUNCT
ejpam-5958	164	35	if	if	SCONJ
ejpam-5958	164	36	uk	uk	PROPN
ejpam-5958	164	37	−−−→	−−−→	VERB
ejpam-5958	164	38	k→∞	k→∞	PROPN
ejpam-5958	164	39	u	u	NOUN
ejpam-5958	164	40	,	,	PUNCT
ejpam-5958	164	41	then	then	ADV
ejpam-5958	164	42	there	there	PRON
ejpam-5958	164	43	exists	exist	VERB
ejpam-5958	164	44	a	a	DET
ejpam-5958	164	45	sub	sub	NOUN
ejpam-5958	164	46	-	-	NOUN
ejpam-5958	164	47	sequence	sequence	ADJ
ejpam-5958	164	48	{	{	PUNCT
ejpam-5958	164	49	ukl	ukl	NOUN
ejpam-5958	164	50	}	}	PUNCT
ejpam-5958	164	51	l∈n	l∈n	ADV
ejpam-5958	164	52	of	of	ADP
ejpam-5958	164	53	{	{	PUNCT
ejpam-5958	164	54	uk	uk	PROPN
ejpam-5958	164	55	}	}	PUNCT
ejpam-5958	164	56	k∈n	k∈n	PROPN
ejpam-5958	164	57	and	and	CCONJ
ejpam-5958	164	58	l0	l0	PROPN
ejpam-5958	164	59	∈	∈	PROPN
ejpam-5958	164	60	n	n	PRON
ejpam-5958	164	61	such	such	ADJ
ejpam-5958	164	62	that	that	SCONJ
ejpam-5958	164	63	αν(u	αν(u	NUM
ejpam-5958	164	64	kl	kl	NOUN
ejpam-5958	164	65	,	,	PUNCT
ejpam-5958	164	66	u	u	PROPN
ejpam-5958	164	67	)	)	PUNCT
ejpam-5958	164	68	≥	≥	NOUN
ejpam-5958	164	69	1	1	NUM
ejpam-5958	164	70	for	for	ADP
ejpam-5958	164	71	all	all	DET
ejpam-5958	164	72	l	l	PROPN
ejpam-5958	164	73	≥	≥	NUM
ejpam-5958	164	74	l0	l0	NOUN
ejpam-5958	164	75	.	.	PUNCT
ejpam-5958	165	1	then	then	ADV
ejpam-5958	165	2	,	,	PUNCT
ejpam-5958	165	3	f	f	PROPN
ejpam-5958	165	4	has	have	VERB
ejpam-5958	165	5	a	a	DET
ejpam-5958	165	6	fixed	fix	VERB
ejpam-5958	165	7	point	point	NOUN
ejpam-5958	165	8	.	.	PUNCT
ejpam-5958	166	1	proof	proof	NOUN
ejpam-5958	166	2	.	.	PUNCT
ejpam-5958	167	1	note	note	VERB
ejpam-5958	167	2	first	first	ADV
ejpam-5958	167	3	that	that	SCONJ
ejpam-5958	167	4	according	accord	VERB
ejpam-5958	167	5	to	to	ADP
ejpam-5958	167	6	(	(	PUNCT
ejpam-5958	167	7	c2(i	c2(i	NOUN
ejpam-5958	167	8	)	)	PUNCT
ejpam-5958	167	9	)	)	PUNCT
ejpam-5958	167	10	and	and	CCONJ
ejpam-5958	167	11	(	(	PUNCT
ejpam-5958	167	12	c1	c1	PROPN
ejpam-5958	167	13	)	)	PUNCT
ejpam-5958	167	14	,	,	PUNCT
ejpam-5958	167	15	we	we	PRON
ejpam-5958	167	16	deduce	deduce	VERB
ejpam-5958	167	17	by	by	ADP
ejpam-5958	167	18	induction	induction	NOUN
ejpam-5958	167	19	that	that	SCONJ
ejpam-5958	167	20	∀p	∀p	AUX
ejpam-5958	167	21	=	=	SYM
ejpam-5958	167	22	1	1	NUM
ejpam-5958	167	23	,	,	PUNCT
ejpam-5958	167	24	...	...	PUNCT
ejpam-5958	167	25	,	,	PUNCT
ejpam-5958	167	26	n	n	CCONJ
ejpam-5958	167	27	,	,	PUNCT
ejpam-5958	167	28	∀k	∀k	NOUN
ejpam-5958	167	29	∈	∈	PROPN
ejpam-5958	167	30	n	n	CCONJ
ejpam-5958	167	31	,	,	PUNCT
ejpam-5958	167	32	∀ν	∀ν	PROPN
ejpam-5958	167	33	∈	∈	PROPN
ejpam-5958	167	34	n	n	PRON
ejpam-5958	167	35	:	:	PUNCT
ejpam-5958	167	36	αν(f	αν(f	NUM
ejpam-5958	167	37	kap−1	kap−1	NOUN
ejpam-5958	167	38	0	0	NUM
ejpam-5958	167	39	,	,	PUNCT
ejpam-5958	167	40	f	f	PROPN
ejpam-5958	167	41	kap0	kap0	PROPN
ejpam-5958	167	42	)	)	PUNCT
ejpam-5958	167	43	≥	≥	PROPN
ejpam-5958	167	44	1	1	NUM
ejpam-5958	167	45	.	.	PUNCT
ejpam-5958	168	1	consequently	consequently	ADV
ejpam-5958	168	2	,	,	PUNCT
ejpam-5958	168	3	using	use	VERB
ejpam-5958	168	4	(	(	PUNCT
ejpam-5958	168	5	3.2	3.2	NUM
ejpam-5958	168	6	)	)	PUNCT
ejpam-5958	168	7	,	,	PUNCT
ejpam-5958	168	8	the	the	DET
ejpam-5958	168	9	following	follow	VERB
ejpam-5958	168	10	inequalities	inequality	NOUN
ejpam-5958	168	11	hold	hold	VERB
ejpam-5958	168	12	true	true	ADJ
ejpam-5958	168	13	:	:	PUNCT
ejpam-5958	168	14	dν	dν	PROPN
ejpam-5958	168	15	(	(	PUNCT
ejpam-5958	168	16	f	f	X
ejpam-5958	168	17	kap−1	kap−1	PROPN
ejpam-5958	168	18	0	0	NUM
ejpam-5958	168	19	,	,	PUNCT
ejpam-5958	168	20	f	f	PROPN
ejpam-5958	168	21	kap0	kap0	PROPN
ejpam-5958	168	22	)	)	PUNCT
ejpam-5958	168	23	≤	≤	NOUN
ejpam-5958	168	24	αν(f	αν(f	NUM
ejpam-5958	168	25	k−1ap−1	k−1ap−1	ADJ
ejpam-5958	168	26	0	0	NUM
ejpam-5958	168	27	,	,	PUNCT
ejpam-5958	168	28	f	f	PROPN
ejpam-5958	168	29	k−1ap0)dν	k−1ap0)dν	PROPN
ejpam-5958	168	30	(	(	PUNCT
ejpam-5958	168	31	f	f	PROPN
ejpam-5958	168	32	kap−1	kap−1	PROPN
ejpam-5958	168	33	0	0	NUM
ejpam-5958	168	34	,	,	PUNCT
ejpam-5958	168	35	f	f	PROPN
ejpam-5958	168	36	kap0	kap0	PROPN
ejpam-5958	168	37	)	)	PUNCT
ejpam-5958	168	38	≤	≤	PROPN
ejpam-5958	169	1	ψν	ψν	INTJ
ejpam-5958	169	2	(	(	PUNCT
ejpam-5958	169	3	dw(ν	dw(ν	X
ejpam-5958	169	4	)	)	PUNCT
ejpam-5958	169	5	(	(	PUNCT
ejpam-5958	169	6	f	f	PROPN
ejpam-5958	169	7	k−1ap−1	k−1ap−1	PROPN
ejpam-5958	169	8	0	0	NUM
ejpam-5958	169	9	,	,	PUNCT
ejpam-5958	169	10	f	f	PROPN
ejpam-5958	169	11	k−1ap0	k−1ap0	PROPN
ejpam-5958	169	12	)	)	PUNCT
ejpam-5958	169	13	)	)	PUNCT
ejpam-5958	169	14	,	,	PUNCT
ejpam-5958	169	15	for	for	ADP
ejpam-5958	169	16	all	all	DET
ejpam-5958	169	17	ν	ν	PRON
ejpam-5958	169	18	∈	∈	PROPN
ejpam-5958	169	19	n	n	NOUN
ejpam-5958	169	20	,	,	PUNCT
ejpam-5958	169	21	k	k	PROPN
ejpam-5958	169	22	∈	∈	PROPN
ejpam-5958	169	23	n	n	PROPN
ejpam-5958	169	24	and	and	CCONJ
ejpam-5958	169	25	p	p	NOUN
ejpam-5958	169	26	=	=	NOUN
ejpam-5958	169	27	1	1	NUM
ejpam-5958	169	28	,	,	PUNCT
ejpam-5958	169	29	...	...	PUNCT
ejpam-5958	169	30	,	,	PUNCT
ejpam-5958	169	31	n	n	X
ejpam-5958	169	32	.	.	PUNCT
ejpam-5958	170	1	now	now	ADV
ejpam-5958	170	2	,	,	PUNCT
ejpam-5958	170	3	since	since	SCONJ
ejpam-5958	170	4	ψν	ψν	PROPN
ejpam-5958	170	5	is	be	AUX
ejpam-5958	170	6	non	non	ADJ
ejpam-5958	170	7	-	-	ADJ
ejpam-5958	170	8	decreasing	decrease	VERB
ejpam-5958	170	9	for	for	ADP
ejpam-5958	170	10	each	each	DET
ejpam-5958	170	11	ν	ν	NOUN
ejpam-5958	170	12	∈	∈	PROPN
ejpam-5958	170	13	n	n	NOUN
ejpam-5958	170	14	,	,	PUNCT
ejpam-5958	170	15	repeated	repeat	VERB
ejpam-5958	170	16	application	application	NOUN
ejpam-5958	170	17	of	of	ADP
ejpam-5958	170	18	the	the	DET
ejpam-5958	170	19	previous	previous	ADJ
ejpam-5958	170	20	inequalities	inequality	NOUN
ejpam-5958	170	21	yield	yield	NOUN
ejpam-5958	170	22	:	:	PUNCT
ejpam-5958	170	23	dν(f	dν(f	NUM
ejpam-5958	170	24	kap−1	kap−1	PROPN
ejpam-5958	170	25	0	0	NUM
ejpam-5958	170	26	,	,	PUNCT
ejpam-5958	170	27	f	f	PROPN
ejpam-5958	170	28	kap0	kap0	PROPN
ejpam-5958	170	29	)	)	PUNCT
ejpam-5958	170	30	≤	≤	PROPN
ejpam-5958	171	1	ψν	ψν	INTJ
ejpam-5958	171	2	(	(	PUNCT
ejpam-5958	171	3	ψw(ν	ψw(ν	NOUN
ejpam-5958	171	4	)	)	PUNCT
ejpam-5958	171	5	(	(	PUNCT
ejpam-5958	171	6	...	...	PUNCT
ejpam-5958	171	7	ψwk−1(ν	ψwk−1(ν	X
ejpam-5958	171	8	)	)	PUNCT
ejpam-5958	171	9	(	(	PUNCT
ejpam-5958	171	10	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	171	11	p−1	p−1	PROPN
ejpam-5958	171	12	0	0	NUM
ejpam-5958	171	13	,	,	PUNCT
ejpam-5958	171	14	ap0	ap0	PROPN
ejpam-5958	171	15	)	)	PUNCT
ejpam-5958	171	16	)	)	PUNCT
ejpam-5958	171	17	...	...	PUNCT
ejpam-5958	171	18	)	)	PUNCT
ejpam-5958	171	19	)	)	PUNCT
ejpam-5958	171	20	,	,	PUNCT
ejpam-5958	171	21	for	for	ADP
ejpam-5958	171	22	all	all	DET
ejpam-5958	171	23	k	k	PROPN
ejpam-5958	171	24	∈	∈	PROPN
ejpam-5958	171	25	n	n	CCONJ
ejpam-5958	171	26	,	,	PUNCT
ejpam-5958	171	27	ν	ν	PROPN
ejpam-5958	171	28	∈	∈	PROPN
ejpam-5958	171	29	n	n	NOUN
ejpam-5958	171	30	and	and	CCONJ
ejpam-5958	171	31	every	every	DET
ejpam-5958	171	32	p	p	X
ejpam-5958	171	33	=	=	NOUN
ejpam-5958	171	34	1	1	NUM
ejpam-5958	171	35	,	,	PUNCT
ejpam-5958	171	36	...	...	PUNCT
ejpam-5958	171	37	,	,	PUNCT
ejpam-5958	171	38	n	n	X
ejpam-5958	171	39	.	.	PUNCT
ejpam-5958	172	1	hence	hence	ADV
ejpam-5958	172	2	,	,	PUNCT
ejpam-5958	172	3	by	by	ADP
ejpam-5958	172	4	means	mean	NOUN
ejpam-5958	172	5	of	of	ADP
ejpam-5958	172	6	(	(	PUNCT
ejpam-5958	172	7	c3	c3	PROPN
ejpam-5958	172	8	)	)	PUNCT
ejpam-5958	172	9	,	,	PUNCT
ejpam-5958	172	10	we	we	PRON
ejpam-5958	172	11	obtain	obtain	VERB
ejpam-5958	172	12	:	:	PUNCT
ejpam-5958	172	13	dν(f	dν(f	NUM
ejpam-5958	172	14	kap−1	kap−1	PROPN
ejpam-5958	172	15	0	0	NUM
ejpam-5958	172	16	,	,	PUNCT
ejpam-5958	172	17	f	f	PROPN
ejpam-5958	172	18	kap0	kap0	PROPN
ejpam-5958	172	19	)	)	PUNCT
ejpam-5958	172	20	≤	≤	NOUN
ejpam-5958	173	1	ψ̃ν	ψ̃ν	X
ejpam-5958	173	2	k	k	X
ejpam-5958	173	3	(	(	PUNCT
ejpam-5958	173	4	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	173	5	p−1	p−1	PROPN
ejpam-5958	173	6	0	0	NUM
ejpam-5958	173	7	,	,	PUNCT
ejpam-5958	173	8	ap0	ap0	PROPN
ejpam-5958	173	9	)	)	PUNCT
ejpam-5958	173	10	)	)	PUNCT
ejpam-5958	173	11	.	.	PUNCT
ejpam-5958	174	1	(	(	PUNCT
ejpam-5958	174	2	3.4	3.4	NUM
ejpam-5958	174	3	)	)	PUNCT
ejpam-5958	174	4	let	let	VERB
ejpam-5958	174	5	now	now	ADV
ejpam-5958	174	6	x0	x0	PROPN
ejpam-5958	174	7	be	be	AUX
ejpam-5958	174	8	the	the	DET
ejpam-5958	174	9	element	element	NOUN
ejpam-5958	174	10	introduced	introduce	VERB
ejpam-5958	174	11	in	in	ADP
ejpam-5958	174	12	(	(	PUNCT
ejpam-5958	174	13	c2(i	c2(i	NOUN
ejpam-5958	174	14	)	)	PUNCT
ejpam-5958	174	15	)	)	PUNCT
ejpam-5958	174	16	and	and	CCONJ
ejpam-5958	174	17	let	let	VERB
ejpam-5958	174	18	{	{	PUNCT
ejpam-5958	174	19	xk	xk	PROPN
ejpam-5958	174	20	}	}	PUNCT
ejpam-5958	174	21	k∈n	k∈n	AUX
ejpam-5958	174	22	be	be	AUX
ejpam-5958	174	23	the	the	DET
ejpam-5958	174	24	sequence	sequence	NOUN
ejpam-5958	174	25	in	in	ADP
ejpam-5958	174	26	e	e	NOUN
ejpam-5958	174	27	defined	define	VERB
ejpam-5958	174	28	by	by	ADP
ejpam-5958	174	29	xk+1	xk+1	PROPN
ejpam-5958	174	30	=	=	SYM
ejpam-5958	174	31	fxk	fxk	PROPN
ejpam-5958	174	32	.	.	PUNCT
ejpam-5958	174	33	assume	assume	VERB
ejpam-5958	174	34	that	that	SCONJ
ejpam-5958	174	35	xk+1	xk+1	PROPN
ejpam-5958	174	36	̸=	̸=	PROPN
ejpam-5958	174	37	xk	xk	PROPN
ejpam-5958	174	38	for	for	ADP
ejpam-5958	174	39	all	all	DET
ejpam-5958	174	40	k	k	PROPN
ejpam-5958	174	41	∈	∈	PROPN
ejpam-5958	174	42	n	n	CCONJ
ejpam-5958	174	43	,	,	PUNCT
ejpam-5958	174	44	since	since	SCONJ
ejpam-5958	174	45	otherwise	otherwise	ADV
ejpam-5958	174	46	the	the	DET
ejpam-5958	174	47	result	result	NOUN
ejpam-5958	174	48	is	be	AUX
ejpam-5958	174	49	clear	clear	ADJ
ejpam-5958	174	50	.	.	PUNCT
ejpam-5958	175	1	recall	recall	VERB
ejpam-5958	175	2	that	that	DET
ejpam-5958	175	3	a00	a00	NOUN
ejpam-5958	175	4	=	=	SYM
ejpam-5958	175	5	x0	x0	PROPN
ejpam-5958	175	6	and	and	CCONJ
ejpam-5958	175	7	an0	an0	PROPN
ejpam-5958	175	8	=	=	SYM
ejpam-5958	175	9	fx0	fx0	PROPN
ejpam-5958	175	10	,	,	PUNCT
ejpam-5958	175	11	then	then	ADV
ejpam-5958	175	12	for	for	ADP
ejpam-5958	175	13	all	all	DET
ejpam-5958	175	14	k	k	PROPN
ejpam-5958	175	15	∈	∈	PROPN
ejpam-5958	175	16	n	n	CCONJ
ejpam-5958	175	17	,	,	PUNCT
ejpam-5958	175	18	we	we	PRON
ejpam-5958	175	19	have	have	VERB
ejpam-5958	175	20	:	:	PUNCT
ejpam-5958	175	21	dν(f	dν(f	NUM
ejpam-5958	175	22	kx0	kx0	PROPN
ejpam-5958	175	23	,	,	PUNCT
ejpam-5958	175	24	f	f	PROPN
ejpam-5958	175	25	k+1x0	k+1x0	PROPN
ejpam-5958	175	26	)	)	PUNCT
ejpam-5958	175	27	≤	≤	PUNCT
ejpam-5958	176	1	sdν(f	sdν(f	PROPN
ejpam-5958	176	2	ka00	ka00	PROPN
ejpam-5958	176	3	,	,	PUNCT
ejpam-5958	176	4	f	f	PROPN
ejpam-5958	176	5	ka10	ka10	PROPN
ejpam-5958	176	6	)	)	PUNCT
ejpam-5958	176	7	+	+	NUM
ejpam-5958	176	8	s2dν(f	s2dν(f	PROPN
ejpam-5958	176	9	ka10	ka10	PROPN
ejpam-5958	176	10	,	,	PUNCT
ejpam-5958	176	11	f	f	PROPN
ejpam-5958	176	12	ka20	ka20	PROPN
ejpam-5958	176	13	)	)	PUNCT
ejpam-5958	176	14	+	+	CCONJ
ejpam-5958	176	15	...	...	PUNCT
ejpam-5958	176	16	+	+	CCONJ
ejpam-5958	176	17	sndν(f	sndν(f	NOUN
ejpam-5958	176	18	kan−1	kan−1	PROPN
ejpam-5958	176	19	0	0	NUM
ejpam-5958	176	20	,	,	PUNCT
ejpam-5958	176	21	f	f	PROPN
ejpam-5958	176	22	kan0	kan0	PROPN
ejpam-5958	176	23	)	)	PUNCT
ejpam-5958	176	24	.	.	PUNCT
ejpam-5958	177	1	k.	k.	PROPN
ejpam-5958	177	2	nisse	nisse	PROPN
ejpam-5958	177	3	et	et	PROPN
ejpam-5958	177	4	al	al	PROPN
ejpam-5958	177	5	.	.	PUNCT
ejpam-5958	177	6	/	/	SYM
ejpam-5958	177	7	eur	eur	PROPN
ejpam-5958	177	8	.	.	PUNCT
ejpam-5958	178	1	j.	j.	PROPN
ejpam-5958	178	2	pure	pure	PROPN
ejpam-5958	178	3	appl	appl	PROPN
ejpam-5958	178	4	.	.	PROPN
ejpam-5958	178	5	math	math	PROPN
ejpam-5958	178	6	,	,	PUNCT
ejpam-5958	178	7	18	18	NUM
ejpam-5958	178	8	(	(	PUNCT
ejpam-5958	178	9	2	2	NUM
ejpam-5958	178	10	)	)	PUNCT
ejpam-5958	178	11	(	(	PUNCT
ejpam-5958	178	12	2025	2025	NUM
ejpam-5958	178	13	)	)	PUNCT
ejpam-5958	178	14	,	,	PUNCT
ejpam-5958	178	15	5958	5958	NUM
ejpam-5958	178	16	9	9	NUM
ejpam-5958	178	17	of	of	ADP
ejpam-5958	178	18	22	22	NUM
ejpam-5958	178	19	hence	hence	ADV
ejpam-5958	178	20	,	,	PUNCT
ejpam-5958	178	21	using	use	VERB
ejpam-5958	178	22	(	(	PUNCT
ejpam-5958	178	23	3.4	3.4	NUM
ejpam-5958	178	24	)	)	PUNCT
ejpam-5958	178	25	together	together	ADV
ejpam-5958	178	26	with	with	ADP
ejpam-5958	178	27	(	(	PUNCT
ejpam-5958	178	28	ψs	ψs	NOUN
ejpam-5958	178	29	1	1	NUM
ejpam-5958	178	30	)	)	PUNCT
ejpam-5958	178	31	,	,	PUNCT
ejpam-5958	178	32	(	(	PUNCT
ejpam-5958	178	33	ψ	ψ	X
ejpam-5958	178	34	s	s	NOUN
ejpam-5958	178	35	2	2	NUM
ejpam-5958	178	36	)	)	PUNCT
ejpam-5958	178	37	and	and	CCONJ
ejpam-5958	178	38	(	(	PUNCT
ejpam-5958	178	39	ψs	ψs	NOUN
ejpam-5958	178	40	4	4	NUM
ejpam-5958	178	41	)	)	PUNCT
ejpam-5958	178	42	,	,	PUNCT
ejpam-5958	178	43	we	we	PRON
ejpam-5958	178	44	obtain	obtain	VERB
ejpam-5958	178	45	:	:	PUNCT
ejpam-5958	178	46	dν(f	dν(f	NUM
ejpam-5958	178	47	kx0	kx0	PROPN
ejpam-5958	178	48	,	,	PUNCT
ejpam-5958	178	49	f	f	PROPN
ejpam-5958	178	50	k+1x0	k+1x0	PROPN
ejpam-5958	178	51	)	)	PUNCT
ejpam-5958	178	52	≤	≤	PUNCT
ejpam-5958	179	1	sψ̃ν	sψ̃ν	X
ejpam-5958	179	2	k	k	NOUN
ejpam-5958	179	3	(	(	PUNCT
ejpam-5958	179	4	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	179	5	0	0	NUM
ejpam-5958	179	6	0	0	NUM
ejpam-5958	179	7	,	,	PUNCT
ejpam-5958	179	8	a	a	DET
ejpam-5958	179	9	1	1	NUM
ejpam-5958	179	10	0	0	NUM
ejpam-5958	179	11	)	)	PUNCT
ejpam-5958	179	12	)	)	PUNCT
ejpam-5958	180	1	+	+	CCONJ
ejpam-5958	180	2	s2	s2	VERB
ejpam-5958	180	3	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	180	4	k	k	X
ejpam-5958	180	5	(	(	PUNCT
ejpam-5958	180	6	dwk(ν)(a	dwk(ν)(a	NUM
ejpam-5958	180	7	1	1	NUM
ejpam-5958	180	8	0	0	NUM
ejpam-5958	180	9	,	,	PUNCT
ejpam-5958	180	10	a	a	DET
ejpam-5958	180	11	2	2	NUM
ejpam-5958	180	12	0	0	NUM
ejpam-5958	180	13	)	)	PUNCT
ejpam-5958	180	14	)	)	PUNCT
ejpam-5958	181	1	+	+	CCONJ
ejpam-5958	181	2	...	...	PUNCT
ejpam-5958	181	3	+	+	CCONJ
ejpam-5958	181	4	sn	sn	INTJ
ejpam-5958	181	5	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	181	6	k	k	X
ejpam-5958	181	7	(	(	PUNCT
ejpam-5958	181	8	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	181	9	n−1	n−1	PROPN
ejpam-5958	181	10	0	0	NUM
ejpam-5958	181	11	,	,	PUNCT
ejpam-5958	181	12	an0	an0	PROPN
ejpam-5958	181	13	)	)	PUNCT
ejpam-5958	181	14	)	)	PUNCT
ejpam-5958	182	1	=	=	PUNCT
ejpam-5958	183	1	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	183	2	k	k	X
ejpam-5958	183	3	(	(	PUNCT
ejpam-5958	183	4	sdwk(ν)(a	sdwk(ν)(a	PROPN
ejpam-5958	183	5	0	0	NUM
ejpam-5958	183	6	0	0	NUM
ejpam-5958	183	7	,	,	PUNCT
ejpam-5958	183	8	a	a	DET
ejpam-5958	183	9	1	1	NUM
ejpam-5958	183	10	0	0	NUM
ejpam-5958	183	11	)	)	PUNCT
ejpam-5958	183	12	)	)	PUNCT
ejpam-5958	184	1	+	+	CCONJ
ejpam-5958	185	1	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	185	2	k	k	X
ejpam-5958	186	1	(	(	PUNCT
ejpam-5958	186	2	s2dwk(ν)(a	s2dwk(ν)(a	NOUN
ejpam-5958	186	3	1	1	NUM
ejpam-5958	186	4	0	0	NUM
ejpam-5958	186	5	,	,	PUNCT
ejpam-5958	186	6	a	a	DET
ejpam-5958	186	7	2	2	NUM
ejpam-5958	186	8	0	0	NUM
ejpam-5958	186	9	)	)	PUNCT
ejpam-5958	186	10	)	)	PUNCT
ejpam-5958	187	1	+	+	CCONJ
ejpam-5958	187	2	...	...	PUNCT
ejpam-5958	188	1	+	+	CCONJ
ejpam-5958	189	1	ψ̃ν	ψ̃ν	VERB
ejpam-5958	189	2	k	k	X
ejpam-5958	190	1	(	(	PUNCT
ejpam-5958	190	2	sndwk(ν)(a	sndwk(ν)(a	NOUN
ejpam-5958	190	3	n−1	n−1	PROPN
ejpam-5958	190	4	0	0	NUM
ejpam-5958	190	5	,	,	PUNCT
ejpam-5958	190	6	an0	an0	PROPN
ejpam-5958	190	7	)	)	PUNCT
ejpam-5958	190	8	)	)	PUNCT
ejpam-5958	191	1	=	=	PUNCT
ejpam-5958	191	2	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	192	1	(	(	PUNCT
ejpam-5958	192	2	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	192	3	k−1	k−1	PROPN
ejpam-5958	192	4	(	(	PUNCT
ejpam-5958	192	5	sdwk(ν)(a	sdwk(ν)(a	PROPN
ejpam-5958	192	6	0	0	NUM
ejpam-5958	192	7	0	0	NUM
ejpam-5958	192	8	,	,	PUNCT
ejpam-5958	192	9	a	a	DET
ejpam-5958	192	10	1	1	NUM
ejpam-5958	192	11	0	0	NUM
ejpam-5958	192	12	)	)	PUNCT
ejpam-5958	192	13	)	)	PUNCT
ejpam-5958	192	14	)	)	PUNCT
ejpam-5958	193	1	+	+	CCONJ
ejpam-5958	193	2	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	193	3	(	(	PUNCT
ejpam-5958	193	4	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	193	5	k−1	k−1	PROPN
ejpam-5958	193	6	(	(	PUNCT
ejpam-5958	193	7	s2dwk(ν)(a	s2dwk(ν)(a	NOUN
ejpam-5958	193	8	1	1	NUM
ejpam-5958	193	9	0	0	NUM
ejpam-5958	193	10	,	,	PUNCT
ejpam-5958	193	11	a	a	DET
ejpam-5958	193	12	2	2	NUM
ejpam-5958	193	13	0	0	NUM
ejpam-5958	193	14	)	)	PUNCT
ejpam-5958	193	15	)	)	PUNCT
ejpam-5958	193	16	)	)	PUNCT
ejpam-5958	194	1	+	+	CCONJ
ejpam-5958	194	2	...	...	PUNCT
ejpam-5958	195	1	+	+	CCONJ
ejpam-5958	195	2	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	195	3	(	(	PUNCT
ejpam-5958	195	4	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	195	5	k−1	k−1	PROPN
ejpam-5958	195	6	(	(	PUNCT
ejpam-5958	195	7	sndwk(ν)(a	sndwk(ν)(a	PROPN
ejpam-5958	195	8	n−1	n−1	PROPN
ejpam-5958	195	9	0	0	NUM
ejpam-5958	195	10	,	,	PUNCT
ejpam-5958	195	11	an0	an0	PROPN
ejpam-5958	195	12	)	)	PUNCT
ejpam-5958	195	13	)	)	PUNCT
ejpam-5958	195	14	)	)	PUNCT
ejpam-5958	195	15	≤	≤	NUM
ejpam-5958	196	1	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	196	2	(	(	PUNCT
ejpam-5958	196	3	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	196	4	k−1	k−1	PROPN
ejpam-5958	196	5	(	(	PUNCT
ejpam-5958	196	6	s	s	X
ejpam-5958	196	7	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	196	8	0	0	NUM
ejpam-5958	196	9	0	0	NUM
ejpam-5958	196	10	,	,	PUNCT
ejpam-5958	196	11	a	a	DET
ejpam-5958	196	12	1	1	NUM
ejpam-5958	196	13	0	0	NUM
ejpam-5958	196	14	)	)	PUNCT
ejpam-5958	196	15	)	)	PUNCT
ejpam-5958	197	1	+	+	CCONJ
ejpam-5958	197	2	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	197	3	k−1	k−1	PROPN
ejpam-5958	197	4	(	(	PUNCT
ejpam-5958	197	5	s2	s2	PROPN
ejpam-5958	197	6	dwk(ν)(a	dwk(ν)(a	NUM
ejpam-5958	197	7	1	1	NUM
ejpam-5958	197	8	0	0	NUM
ejpam-5958	197	9	,	,	PUNCT
ejpam-5958	197	10	a	a	DET
ejpam-5958	197	11	2	2	NUM
ejpam-5958	197	12	0	0	NUM
ejpam-5958	197	13	)	)	PUNCT
ejpam-5958	197	14	)	)	PUNCT
ejpam-5958	198	1	+	+	CCONJ
ejpam-5958	198	2	...	...	PUNCT
ejpam-5958	199	1	+	+	ADJ
ejpam-5958	199	2	ψ̃ν	ψ̃ν	PROPN
ejpam-5958	199	3	k−1	k−1	PROPN
ejpam-5958	199	4	(	(	PUNCT
ejpam-5958	199	5	sn	sn	X
ejpam-5958	199	6	dwk(ν)(a	dwk(ν)(a	NUM
ejpam-5958	199	7	n−1	n−1	PROPN
ejpam-5958	199	8	0	0	NUM
ejpam-5958	199	9	,	,	PUNCT
ejpam-5958	199	10	an0	an0	PROPN
ejpam-5958	199	11	)	)	PUNCT
ejpam-5958	199	12	)	)	PUNCT
ejpam-5958	199	13	)	)	PUNCT
ejpam-5958	199	14	=	=	PUNCT
ejpam-5958	200	1	ψ̃ν	ψ̃ν	X
ejpam-5958	200	2	(	(	PUNCT
ejpam-5958	200	3	s	s	X
ejpam-5958	200	4	ψ̃ν	ψ̃ν	X
ejpam-5958	200	5	k−1	k−1	PROPN
ejpam-5958	200	6	(	(	PUNCT
ejpam-5958	200	7	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	200	8	0	0	NUM
ejpam-5958	200	9	0	0	NUM
ejpam-5958	200	10	,	,	PUNCT
ejpam-5958	200	11	a	a	DET
ejpam-5958	200	12	1	1	NUM
ejpam-5958	200	13	0	0	NUM
ejpam-5958	200	14	)	)	PUNCT
ejpam-5958	200	15	)	)	PUNCT
ejpam-5958	201	1	+	+	CCONJ
ejpam-5958	201	2	s2	s2	VERB
ejpam-5958	201	3	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	201	4	k−1	k−1	PROPN
ejpam-5958	201	5	(	(	PUNCT
ejpam-5958	201	6	dwk(ν)(a	dwk(ν)(a	NUM
ejpam-5958	201	7	1	1	NUM
ejpam-5958	201	8	0	0	NUM
ejpam-5958	201	9	,	,	PUNCT
ejpam-5958	201	10	a	a	DET
ejpam-5958	201	11	2	2	NUM
ejpam-5958	201	12	0	0	NUM
ejpam-5958	201	13	)	)	PUNCT
ejpam-5958	201	14	)	)	PUNCT
ejpam-5958	202	1	+	+	CCONJ
ejpam-5958	202	2	...	...	PUNCT
ejpam-5958	203	1	+	+	ADV
ejpam-5958	203	2	sn	sn	INTJ
ejpam-5958	203	3	ψ̃ν	ψ̃ν	X
ejpam-5958	203	4	k−1	k−1	PROPN
ejpam-5958	203	5	(	(	PUNCT
ejpam-5958	203	6	dwk(ν)(a	dwk(ν)(a	NUM
ejpam-5958	203	7	n−1	n−1	PROPN
ejpam-5958	203	8	0	0	NUM
ejpam-5958	203	9	,	,	PUNCT
ejpam-5958	203	10	an0	an0	PROPN
ejpam-5958	203	11	)	)	PUNCT
ejpam-5958	203	12	)	)	PUNCT
ejpam-5958	203	13	)	)	PUNCT
ejpam-5958	203	14	.	.	PUNCT
ejpam-5958	204	1	since	since	SCONJ
ejpam-5958	204	2	ψν	ψν	PROPN
ejpam-5958	204	3	is	be	AUX
ejpam-5958	204	4	non	non	ADJ
ejpam-5958	204	5	-	-	ADJ
ejpam-5958	204	6	decreasing	decrease	VERB
ejpam-5958	204	7	,	,	PUNCT
ejpam-5958	204	8	repeated	repeat	VERB
ejpam-5958	204	9	application	application	NOUN
ejpam-5958	204	10	of	of	ADP
ejpam-5958	204	11	the	the	DET
ejpam-5958	204	12	above	above	ADJ
ejpam-5958	204	13	inequalities	inequality	NOUN
ejpam-5958	204	14	yields	yield	NOUN
ejpam-5958	204	15	:	:	PUNCT
ejpam-5958	204	16	dν(f	dν(f	NUM
ejpam-5958	204	17	kx0	kx0	PROPN
ejpam-5958	204	18	,	,	PUNCT
ejpam-5958	204	19	f	f	PROPN
ejpam-5958	204	20	k+1x0	k+1x0	PROPN
ejpam-5958	204	21	)	)	PUNCT
ejpam-5958	204	22	≤	≤	PUNCT
ejpam-5958	205	1	ψ̃ν	ψ̃ν	X
ejpam-5958	205	2	k	k	PROPN
ejpam-5958	206	1			PROPN
ejpam-5958	206	2	n∑	n∑	PROPN
ejpam-5958	206	3	p=1	p=1	X
ejpam-5958	206	4	sp	sp	ADP
ejpam-5958	206	5	dwk(ν)(a	dwk(ν)(a	X
ejpam-5958	206	6	p−1	p−1	PROPN
ejpam-5958	206	7	0	0	NUM
ejpam-5958	206	8	,	,	PUNCT
ejpam-5958	206	9	ap0	ap0	PROPN
ejpam-5958	206	10	)	)	PUNCT
ejpam-5958	206	11			PROPN
ejpam-5958	206	12	.	.	PUNCT
ejpam-5958	207	1	consequently	consequently	ADV
ejpam-5958	207	2	,	,	PUNCT
ejpam-5958	207	3	it	it	PRON
ejpam-5958	207	4	follows	follow	VERB
ejpam-5958	207	5	from	from	ADP
ejpam-5958	207	6	(	(	PUNCT
ejpam-5958	207	7	c2(ii	c2(ii	NUM
ejpam-5958	207	8	)	)	PUNCT
ejpam-5958	207	9	):	):	PUNCT
ejpam-5958	207	10	dν(f	dν(f	NUM
ejpam-5958	207	11	kx0	kx0	PROPN
ejpam-5958	207	12	,	,	PUNCT
ejpam-5958	207	13	f	f	PROPN
ejpam-5958	207	14	k+1x0	k+1x0	PROPN
ejpam-5958	207	15	)	)	PUNCT
ejpam-5958	207	16	≤	≤	PUNCT
ejpam-5958	208	1	ψ̃ν	ψ̃ν	X
ejpam-5958	208	2	k	k	PROPN
ejpam-5958	209	1	(	(	PUNCT
ejpam-5958	209	2	ms	ms	PROPN
ejpam-5958	209	3	,	,	PUNCT
ejpam-5958	209	4	ν	ν	X
ejpam-5958	209	5	(	(	PUNCT
ejpam-5958	209	6	x0	x0	PROPN
ejpam-5958	209	7	)	)	PUNCT
ejpam-5958	209	8	)	)	PUNCT
ejpam-5958	209	9	.	.	PUNCT
ejpam-5958	210	1	(	(	PUNCT
ejpam-5958	210	2	3.5	3.5	X
ejpam-5958	210	3	)	)	PUNCT
ejpam-5958	210	4	we	we	PRON
ejpam-5958	210	5	are	be	AUX
ejpam-5958	210	6	now	now	ADV
ejpam-5958	210	7	ready	ready	ADJ
ejpam-5958	210	8	to	to	PART
ejpam-5958	210	9	prove	prove	VERB
ejpam-5958	210	10	that	that	SCONJ
ejpam-5958	210	11	{	{	PUNCT
ejpam-5958	210	12	xk	xk	PROPN
ejpam-5958	210	13	}	}	PUNCT
ejpam-5958	210	14	k∈n	k∈n	PROPN
ejpam-5958	210	15	is	be	AUX
ejpam-5958	210	16	a	a	DET
ejpam-5958	210	17	cauchy	cauchy	ADJ
ejpam-5958	210	18	sequence	sequence	NOUN
ejpam-5958	210	19	.	.	PUNCT
ejpam-5958	211	1	indeed	indeed	ADV
ejpam-5958	211	2	,	,	PUNCT
ejpam-5958	211	3	let	let	VERB
ejpam-5958	211	4	k	k	PROPN
ejpam-5958	211	5	∈	∈	PROPN
ejpam-5958	211	6	n	n	PROPN
ejpam-5958	211	7	and	and	CCONJ
ejpam-5958	211	8	m	m	PROPN
ejpam-5958	211	9	∈	∈	PROPN
ejpam-5958	211	10	n∗.	n∗.	NOUN
ejpam-5958	211	11	we	we	PRON
ejpam-5958	211	12	have	have	VERB
ejpam-5958	211	13	:	:	PUNCT
ejpam-5958	211	14	dν(f	dν(f	NUM
ejpam-5958	211	15	kx0	kx0	PROPN
ejpam-5958	211	16	,	,	PUNCT
ejpam-5958	211	17	f	f	PROPN
ejpam-5958	211	18	k+mx0	k+mx0	PROPN
ejpam-5958	211	19	)	)	PUNCT
ejpam-5958	211	20	≤	≤	NUM
ejpam-5958	211	21	sdν	sdν	NOUN
ejpam-5958	211	22	(	(	PUNCT
ejpam-5958	211	23	f	f	PROPN
ejpam-5958	211	24	kx0	kx0	PROPN
ejpam-5958	211	25	,	,	PUNCT
ejpam-5958	211	26	f	f	PROPN
ejpam-5958	211	27	k+1x0	k+1x0	PROPN
ejpam-5958	211	28	)	)	PUNCT
ejpam-5958	212	1	+	+	CCONJ
ejpam-5958	212	2	s2	s2	NOUN
ejpam-5958	212	3	dν	dν	VERB
ejpam-5958	212	4	(	(	PUNCT
ejpam-5958	212	5	f	f	PROPN
ejpam-5958	212	6	k+1x0	k+1x0	PROPN
ejpam-5958	212	7	,	,	PUNCT
ejpam-5958	212	8	f	f	PROPN
ejpam-5958	212	9	k+2x0	k+2x0	PROPN
ejpam-5958	212	10	)	)	PUNCT
ejpam-5958	213	1	+	+	CCONJ
ejpam-5958	213	2	...	...	PUNCT
ejpam-5958	214	1	+	+	CCONJ
ejpam-5958	214	2	sm−1	sm−1	NOUN
ejpam-5958	214	3	dν	dν	VERB
ejpam-5958	214	4	(	(	PUNCT
ejpam-5958	214	5	f	f	PROPN
ejpam-5958	214	6	k+m−2x0	k+m−2x0	PROPN
ejpam-5958	214	7	,	,	PUNCT
ejpam-5958	214	8	f	f	PROPN
ejpam-5958	214	9	k+m−1x0	k+m−1x0	PROPN
ejpam-5958	214	10	)	)	PUNCT
ejpam-5958	215	1	+	+	CCONJ
ejpam-5958	215	2	sm	sm	INTJ
ejpam-5958	215	3	dν	dν	VERB
ejpam-5958	215	4	(	(	PUNCT
ejpam-5958	215	5	f	f	PROPN
ejpam-5958	215	6	k+m−1x0	k+m−1x0	PROPN
ejpam-5958	215	7	,	,	PUNCT
ejpam-5958	215	8	f	f	PROPN
ejpam-5958	215	9	k+mx0	k+mx0	PROPN
ejpam-5958	215	10	)	)	PUNCT
ejpam-5958	215	11	.	.	PUNCT
ejpam-5958	216	1	k.	k.	PROPN
ejpam-5958	216	2	nisse	nisse	PROPN
ejpam-5958	216	3	et	et	PROPN
ejpam-5958	216	4	al	al	PROPN
ejpam-5958	216	5	.	.	PUNCT
ejpam-5958	216	6	/	/	SYM
ejpam-5958	216	7	eur	eur	PROPN
ejpam-5958	216	8	.	.	PUNCT
ejpam-5958	217	1	j.	j.	PROPN
ejpam-5958	217	2	pure	pure	PROPN
ejpam-5958	217	3	appl	appl	PROPN
ejpam-5958	217	4	.	.	PROPN
ejpam-5958	217	5	math	math	PROPN
ejpam-5958	217	6	,	,	PUNCT
ejpam-5958	217	7	18	18	NUM
ejpam-5958	217	8	(	(	PUNCT
ejpam-5958	217	9	2	2	NUM
ejpam-5958	217	10	)	)	PUNCT
ejpam-5958	217	11	(	(	PUNCT
ejpam-5958	217	12	2025	2025	NUM
ejpam-5958	217	13	)	)	PUNCT
ejpam-5958	217	14	,	,	PUNCT
ejpam-5958	217	15	5958	5958	NUM
ejpam-5958	217	16	10	10	NUM
ejpam-5958	217	17	of	of	ADP
ejpam-5958	217	18	22	22	NUM
ejpam-5958	217	19	it	it	PRON
ejpam-5958	217	20	follows	follow	VERB
ejpam-5958	217	21	so	so	ADV
ejpam-5958	217	22	from	from	ADP
ejpam-5958	217	23	(	(	PUNCT
ejpam-5958	217	24	3.5	3.5	NUM
ejpam-5958	217	25	)	)	PUNCT
ejpam-5958	217	26	,	,	PUNCT
ejpam-5958	217	27	that	that	SCONJ
ejpam-5958	217	28	dν(f	dν(f	ADP
ejpam-5958	217	29	kx0	kx0	PROPN
ejpam-5958	217	30	,	,	PUNCT
ejpam-5958	217	31	f	f	PROPN
ejpam-5958	217	32	k+mx0	k+mx0	PROPN
ejpam-5958	217	33	)	)	PUNCT
ejpam-5958	217	34	≤	≤	NOUN
ejpam-5958	218	1	sψ̃ν	sψ̃ν	X
ejpam-5958	218	2	k	k	NOUN
ejpam-5958	219	1	(	(	PUNCT
ejpam-5958	219	2	ms	ms	PROPN
ejpam-5958	219	3	,	,	PUNCT
ejpam-5958	219	4	ν(x	ν(x	PROPN
ejpam-5958	219	5	0	0	NUM
ejpam-5958	219	6	)	)	PUNCT
ejpam-5958	219	7	)	)	PUNCT
ejpam-5958	220	1	+	+	CCONJ
ejpam-5958	221	1	s2ψ̃ν	s2ψ̃ν	INTJ
ejpam-5958	221	2	k+1	k+1	X
ejpam-5958	221	3	(	(	PUNCT
ejpam-5958	221	4	ms	ms	PROPN
ejpam-5958	221	5	,	,	PUNCT
ejpam-5958	221	6	ν(x	ν(x	PROPN
ejpam-5958	221	7	0	0	NUM
ejpam-5958	221	8	)	)	PUNCT
ejpam-5958	221	9	)	)	PUNCT
ejpam-5958	222	1	+	+	CCONJ
ejpam-5958	222	2	...	...	PUNCT
ejpam-5958	223	1	+	+	CCONJ
ejpam-5958	223	2	smψ̃ν	smψ̃ν	ADJ
ejpam-5958	223	3	k+m−1	k+m−1	PROPN
ejpam-5958	223	4	(	(	PUNCT
ejpam-5958	223	5	ms	ms	PROPN
ejpam-5958	223	6	,	,	PUNCT
ejpam-5958	223	7	ν(x	ν(x	PROPN
ejpam-5958	223	8	0	0	NUM
ejpam-5958	223	9	)	)	PUNCT
ejpam-5958	223	10	)	)	PUNCT
ejpam-5958	224	1	=	=	SYM
ejpam-5958	224	2	1	1	NUM
ejpam-5958	224	3	sk−1	sk−1	PROPN
ejpam-5958	224	4	[	[	PUNCT
ejpam-5958	224	5	skψ̃ν	skψ̃ν	PROPN
ejpam-5958	224	6	i	i	PRON
ejpam-5958	224	7	(	(	PUNCT
ejpam-5958	224	8	ms	ms	PROPN
ejpam-5958	224	9	,	,	PUNCT
ejpam-5958	224	10	ν(x	ν(x	PROPN
ejpam-5958	224	11	0	0	NUM
ejpam-5958	224	12	)	)	PUNCT
ejpam-5958	224	13	)	)	PUNCT
ejpam-5958	225	1	+	+	CCONJ
ejpam-5958	225	2	sk+1ψ̃ν	sk+1ψ̃ν	PUNCT
ejpam-5958	225	3	i	i	PRON
ejpam-5958	225	4	(	(	PUNCT
ejpam-5958	225	5	ms	ms	PROPN
ejpam-5958	225	6	,	,	PUNCT
ejpam-5958	225	7	ν(x	ν(x	PROPN
ejpam-5958	225	8	0	0	NUM
ejpam-5958	225	9	)	)	PUNCT
ejpam-5958	225	10	)	)	PUNCT
ejpam-5958	226	1	+	+	CCONJ
ejpam-5958	226	2	...	...	PUNCT
ejpam-5958	227	1	+	+	CCONJ
ejpam-5958	228	1	sk+m−1ψ̃ν	sk+m−1ψ̃ν	INTJ
ejpam-5958	228	2	i	i	PRON
ejpam-5958	228	3	(	(	PUNCT
ejpam-5958	228	4	ms	ms	PROPN
ejpam-5958	228	5	,	,	PUNCT
ejpam-5958	228	6	ν(x	ν(x	PROPN
ejpam-5958	228	7	0	0	NUM
ejpam-5958	228	8	)	)	PUNCT
ejpam-5958	228	9	)	)	PUNCT
ejpam-5958	228	10	]	]	PUNCT
ejpam-5958	229	1	≤	≤	NUM
ejpam-5958	229	2	1	1	NUM
ejpam-5958	229	3	sk−1	sk−1	PROPN
ejpam-5958	229	4	∞∑	∞∑	NUM
ejpam-5958	229	5	i	i	PROPN
ejpam-5958	229	6	=	=	NOUN
ejpam-5958	229	7	k	k	X
ejpam-5958	229	8	si	si	X
ejpam-5958	229	9	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	229	10	i	i	INTJ
ejpam-5958	229	11	(	(	PUNCT
ejpam-5958	229	12	ms	ms	PROPN
ejpam-5958	229	13	,	,	PUNCT
ejpam-5958	229	14	ν(x	ν(x	PROPN
ejpam-5958	229	15	0	0	NUM
ejpam-5958	229	16	)	)	PUNCT
ejpam-5958	229	17	)	)	PUNCT
ejpam-5958	229	18	.	.	PUNCT
ejpam-5958	230	1	(	(	PUNCT
ejpam-5958	230	2	3.6	3.6	NUM
ejpam-5958	230	3	)	)	PUNCT
ejpam-5958	230	4	since	since	SCONJ
ejpam-5958	230	5	in	in	ADP
ejpam-5958	230	6	view	view	NOUN
ejpam-5958	230	7	of	of	ADP
ejpam-5958	230	8	(	(	PUNCT
ejpam-5958	230	9	ψs	ψs	NOUN
ejpam-5958	230	10	3	3	NUM
ejpam-5958	230	11	)	)	PUNCT
ejpam-5958	230	12	together	together	ADV
ejpam-5958	230	13	with	with	ADP
ejpam-5958	230	14	the	the	DET
ejpam-5958	230	15	second	second	ADJ
ejpam-5958	230	16	statement	statement	NOUN
ejpam-5958	230	17	of	of	ADP
ejpam-5958	230	18	lemma	lemma	PROPN
ejpam-5958	230	19	2.4	2.4	NUM
ejpam-5958	230	20	,	,	PUNCT
ejpam-5958	230	21	we	we	PRON
ejpam-5958	230	22	have	have	VERB
ejpam-5958	230	23	:	:	PUNCT
ejpam-5958	230	24	lim	lim	PROPN
ejpam-5958	230	25	k→∞	k→∞	NOUN
ejpam-5958	231	1	∞∑	∞∑	PROPN
ejpam-5958	231	2	i	i	PROPN
ejpam-5958	231	3	=	=	NOUN
ejpam-5958	231	4	k	k	X
ejpam-5958	231	5	si	si	X
ejpam-5958	232	1	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	232	2	i	i	INTJ
ejpam-5958	232	3	(	(	PUNCT
ejpam-5958	232	4	ms	ms	PROPN
ejpam-5958	232	5	,	,	PUNCT
ejpam-5958	232	6	ν(x	ν(x	PROPN
ejpam-5958	232	7	0	0	NUM
ejpam-5958	232	8	)	)	PUNCT
ejpam-5958	232	9	)	)	PUNCT
ejpam-5958	233	1	=	=	PUNCT
ejpam-5958	233	2	0	0	NUM
ejpam-5958	233	3	,	,	PUNCT
ejpam-5958	233	4	then	then	ADV
ejpam-5958	233	5	we	we	PRON
ejpam-5958	233	6	deduce	deduce	VERB
ejpam-5958	233	7	from	from	ADP
ejpam-5958	233	8	(	(	PUNCT
ejpam-5958	233	9	3.6	3.6	NUM
ejpam-5958	233	10	)	)	PUNCT
ejpam-5958	233	11	that	that	SCONJ
ejpam-5958	233	12	{	{	PUNCT
ejpam-5958	233	13	f	f	X
ejpam-5958	233	14	kx0	kx0	PROPN
ejpam-5958	233	15	=	=	SYM
ejpam-5958	233	16	xk	xk	PROPN
ejpam-5958	233	17	}	}	PUNCT
ejpam-5958	233	18	k∈n	k∈n	PROPN
ejpam-5958	233	19	is	be	AUX
ejpam-5958	233	20	a	a	DET
ejpam-5958	233	21	cauchy	cauchy	ADJ
ejpam-5958	233	22	sequence	sequence	NOUN
ejpam-5958	233	23	in	in	ADP
ejpam-5958	233	24	the	the	DET
ejpam-5958	233	25	complete	complete	ADJ
ejpam-5958	233	26	b	b	NOUN
ejpam-5958	233	27	-	-	PUNCT
ejpam-5958	233	28	gauge	gauge	NOUN
ejpam-5958	233	29	space	space	NOUN
ejpam-5958	233	30	e	e	NOUN
ejpam-5958	233	31	and	and	CCONJ
ejpam-5958	233	32	so	so	ADV
ejpam-5958	233	33	convergent	convergent	ADJ
ejpam-5958	233	34	to	to	ADP
ejpam-5958	233	35	some	some	DET
ejpam-5958	233	36	x∗	x∗	PROPN
ejpam-5958	233	37	∈	∈	PROPN
ejpam-5958	233	38	e.	e.	PROPN
ejpam-5958	233	39	that	that	ADV
ejpam-5958	233	40	is	be	AUX
ejpam-5958	233	41	,	,	PUNCT
ejpam-5958	233	42	for	for	ADP
ejpam-5958	233	43	all	all	PRON
ejpam-5958	233	44	ν	ν	PRON
ejpam-5958	233	45	∈	∈	NOUN
ejpam-5958	233	46	n	n	NOUN
ejpam-5958	233	47	:	:	PUNCT
ejpam-5958	233	48	lim	lim	PROPN
ejpam-5958	233	49	k→∞	k→∞	PROPN
ejpam-5958	233	50	dν(x	dν(x	X
ejpam-5958	234	1	k	k	X
ejpam-5958	234	2	,	,	PUNCT
ejpam-5958	234	3	x∗	x∗	PROPN
ejpam-5958	234	4	)	)	PUNCT
ejpam-5958	234	5	=	=	SYM
ejpam-5958	235	1	0	0	X
ejpam-5958	235	2	.	.	PUNCT
ejpam-5958	236	1	on	on	ADP
ejpam-5958	236	2	the	the	DET
ejpam-5958	236	3	other	other	ADJ
ejpam-5958	236	4	hand	hand	NOUN
ejpam-5958	236	5	,	,	PUNCT
ejpam-5958	236	6	the	the	DET
ejpam-5958	236	7	continuity	continuity	NOUN
ejpam-5958	236	8	of	of	ADP
ejpam-5958	236	9	f	f	PROPN
ejpam-5958	236	10	guaranteed	guarantee	VERB
ejpam-5958	236	11	by	by	ADP
ejpam-5958	236	12	(	(	PUNCT
ejpam-5958	236	13	c4(i	c4(i	PROPN
ejpam-5958	236	14	)	)	PUNCT
ejpam-5958	236	15	)	)	PUNCT
ejpam-5958	236	16	,	,	PUNCT
ejpam-5958	236	17	implies	imply	VERB
ejpam-5958	236	18	that	that	SCONJ
ejpam-5958	236	19	for	for	ADP
ejpam-5958	236	20	all	all	PRON
ejpam-5958	236	21	ν	ν	PRON
ejpam-5958	236	22	∈	∈	NOUN
ejpam-5958	236	23	n	n	NOUN
ejpam-5958	236	24	:	:	PUNCT
ejpam-5958	236	25	lim	lim	PROPN
ejpam-5958	236	26	k→∞	k→∞	PROPN
ejpam-5958	236	27	dν(x	dν(x	X
ejpam-5958	236	28	k	k	PROPN
ejpam-5958	236	29	,	,	PUNCT
ejpam-5958	236	30	fx∗	fx∗	ADJ
ejpam-5958	236	31	)	)	PUNCT
ejpam-5958	237	1	=	=	PUNCT
ejpam-5958	238	1	dν(fx	dν(fx	PROPN
ejpam-5958	238	2	k−1	k−1	PROPN
ejpam-5958	238	3	,	,	PUNCT
ejpam-5958	238	4	fx∗	fx∗	ADJ
ejpam-5958	238	5	)	)	PUNCT
ejpam-5958	238	6	=	=	SYM
ejpam-5958	238	7	0	0	X
ejpam-5958	238	8	.	.	PUNCT
ejpam-5958	239	1	thus	thus	ADV
ejpam-5958	239	2	,	,	PUNCT
ejpam-5958	239	3	for	for	ADP
ejpam-5958	239	4	all	all	PRON
ejpam-5958	239	5	ν	ν	PRON
ejpam-5958	239	6	∈	∈	PROPN
ejpam-5958	239	7	n	n	CCONJ
ejpam-5958	239	8	:	:	PUNCT
ejpam-5958	239	9	dν(x	dν(x	NUM
ejpam-5958	239	10	∗	∗	NOUN
ejpam-5958	239	11	,	,	PUNCT
ejpam-5958	239	12	fx∗	fx∗	NUM
ejpam-5958	239	13	)	)	PUNCT
ejpam-5958	239	14	≤	≤	PROPN
ejpam-5958	239	15	s	s	PART
ejpam-5958	239	16	(	(	PUNCT
ejpam-5958	239	17	dν(x	dν(x	NUM
ejpam-5958	239	18	∗	∗	NOUN
ejpam-5958	239	19	,	,	PUNCT
ejpam-5958	239	20	xk	xk	PROPN
ejpam-5958	239	21	)	)	PUNCT
ejpam-5958	239	22	+	+	CCONJ
ejpam-5958	239	23	dν(x	dν(x	NUM
ejpam-5958	239	24	k	k	NOUN
ejpam-5958	239	25	,	,	PUNCT
ejpam-5958	239	26	fx∗	fx∗	PROPN
ejpam-5958	239	27	)	)	PUNCT
ejpam-5958	239	28	)	)	PUNCT
ejpam-5958	240	1	−−−→	−−−→	VERB
ejpam-5958	240	2	k→∞	k→∞	NOUN
ejpam-5958	240	3	0	0	NUM
ejpam-5958	240	4	.	.	PUNCT
ejpam-5958	241	1	since	since	SCONJ
ejpam-5958	241	2	the	the	DET
ejpam-5958	241	3	b	b	NOUN
ejpam-5958	241	4	-	-	PUNCT
ejpam-5958	241	5	gauge	gauge	NOUN
ejpam-5958	241	6	structure	structure	NOUN
ejpam-5958	241	7	is	be	AUX
ejpam-5958	241	8	separating	separate	VERB
ejpam-5958	241	9	,	,	PUNCT
ejpam-5958	241	10	we	we	PRON
ejpam-5958	241	11	conclude	conclude	VERB
ejpam-5958	241	12	that	that	DET
ejpam-5958	241	13	x∗	x∗	PROPN
ejpam-5958	242	1	=	=	PUNCT
ejpam-5958	242	2	fx∗.	fx∗.	ADV
ejpam-5958	242	3	suppose	suppose	VERB
ejpam-5958	242	4	now	now	ADV
ejpam-5958	242	5	that	that	SCONJ
ejpam-5958	242	6	(	(	PUNCT
ejpam-5958	242	7	c4(ii	c4(ii	NUM
ejpam-5958	242	8	)	)	PUNCT
ejpam-5958	242	9	)	)	PUNCT
ejpam-5958	242	10	is	be	AUX
ejpam-5958	242	11	satisfied	satisfied	ADJ
ejpam-5958	242	12	.	.	PUNCT
ejpam-5958	243	1	note	note	VERB
ejpam-5958	243	2	first	first	ADV
ejpam-5958	243	3	that	that	SCONJ
ejpam-5958	243	4	(	(	PUNCT
ejpam-5958	243	5	c2(i	c2(i	NOUN
ejpam-5958	243	6	)	)	PUNCT
ejpam-5958	243	7	)	)	PUNCT
ejpam-5958	243	8	means	mean	VERB
ejpam-5958	243	9	that	that	SCONJ
ejpam-5958	243	10	(	(	PUNCT
ejpam-5958	243	11	3.3	3.3	NUM
ejpam-5958	243	12	)	)	PUNCT
ejpam-5958	243	13	is	be	AUX
ejpam-5958	243	14	satisfied	satisfied	ADJ
ejpam-5958	243	15	for	for	ADP
ejpam-5958	243	16	k	k	PROPN
ejpam-5958	243	17	=	=	SYM
ejpam-5958	243	18	0	0	PROPN
ejpam-5958	243	19	.	.	PUNCT
ejpam-5958	244	1	since	since	SCONJ
ejpam-5958	244	2	f	f	PROPN
ejpam-5958	244	3	is	be	AUX
ejpam-5958	244	4	αααν	αααν	NOUN
ejpam-5958	244	5	-	-	PUNCT
ejpam-5958	244	6	admissible	admissible	ADJ
ejpam-5958	244	7	,	,	PUNCT
ejpam-5958	244	8	it	it	PRON
ejpam-5958	244	9	follows	follow	VERB
ejpam-5958	244	10	by	by	ADP
ejpam-5958	244	11	induction	induction	NOUN
ejpam-5958	244	12	that	that	SCONJ
ejpam-5958	244	13	(	(	PUNCT
ejpam-5958	244	14	3.3	3.3	NUM
ejpam-5958	244	15	)	)	PUNCT
ejpam-5958	244	16	is	be	AUX
ejpam-5958	244	17	satisfied	satisfied	ADJ
ejpam-5958	244	18	for	for	ADP
ejpam-5958	244	19	each	each	DET
ejpam-5958	244	20	k	k	PROPN
ejpam-5958	244	21	≥	≥	NUM
ejpam-5958	244	22	1	1	NUM
ejpam-5958	244	23	with	with	ADP
ejpam-5958	244	24	apk	apk	PROPN
ejpam-5958	244	25	=	=	SYM
ejpam-5958	244	26	fapk−1	fapk−1	PROPN
ejpam-5958	244	27	,	,	PUNCT
ejpam-5958	244	28	for	for	ADP
ejpam-5958	244	29	all	all	DET
ejpam-5958	244	30	p	p	NOUN
ejpam-5958	244	31	=	=	NOUN
ejpam-5958	244	32	0	0	NUM
ejpam-5958	244	33	,	,	PUNCT
ejpam-5958	244	34	...	...	PUNCT
ejpam-5958	244	35	,	,	PUNCT
ejpam-5958	244	36	n	n	PROPN
ejpam-5958	244	37	.	.	PUNCT
ejpam-5958	245	1	thus	thus	ADV
ejpam-5958	245	2	,	,	PUNCT
ejpam-5958	245	3	according	accord	VERB
ejpam-5958	245	4	to	to	ADP
ejpam-5958	245	5	(	(	PUNCT
ejpam-5958	245	6	c4(ii	c4(ii	PROPN
ejpam-5958	245	7	)	)	PUNCT
ejpam-5958	245	8	)	)	PUNCT
ejpam-5958	245	9	,	,	PUNCT
ejpam-5958	245	10	there	there	PRON
ejpam-5958	245	11	exists	exist	VERB
ejpam-5958	245	12	a	a	DET
ejpam-5958	245	13	sub	sub	NOUN
ejpam-5958	245	14	-	-	NOUN
ejpam-5958	245	15	sequence	sequence	NOUN
ejpam-5958	245	16	{	{	PUNCT
ejpam-5958	245	17	xkl	xkl	PROPN
ejpam-5958	245	18	}	}	PUNCT
ejpam-5958	245	19	l∈n	l∈n	ADJ
ejpam-5958	245	20	and	and	CCONJ
ejpam-5958	245	21	some	some	DET
ejpam-5958	245	22	l0	l0	NOUN
ejpam-5958	245	23	such	such	ADJ
ejpam-5958	245	24	that	that	PRON
ejpam-5958	245	25	for	for	ADP
ejpam-5958	245	26	all	all	DET
ejpam-5958	245	27	l	l	NOUN
ejpam-5958	245	28	≥	≥	NOUN
ejpam-5958	245	29	l0	l0	NOUN
ejpam-5958	245	30	and	and	CCONJ
ejpam-5958	245	31	ν	ν	NOUN
ejpam-5958	245	32	∈	∈	PROPN
ejpam-5958	245	33	n	n	X
ejpam-5958	245	34	,	,	PUNCT
ejpam-5958	245	35	we	we	PRON
ejpam-5958	245	36	have	have	VERB
ejpam-5958	245	37	αν(x	αν(x	NUM
ejpam-5958	245	38	kl	kl	X
ejpam-5958	245	39	,	,	PUNCT
ejpam-5958	245	40	x∗	x∗	PROPN
ejpam-5958	245	41	)	)	PUNCT
ejpam-5958	245	42	≥	≥	NOUN
ejpam-5958	245	43	1	1	NUM
ejpam-5958	245	44	.	.	PUNCT
ejpam-5958	246	1	hence	hence	ADV
ejpam-5958	246	2	,	,	PUNCT
ejpam-5958	246	3	applying	apply	VERB
ejpam-5958	246	4	(	(	PUNCT
ejpam-5958	246	5	3.2	3.2	NUM
ejpam-5958	246	6	)	)	PUNCT
ejpam-5958	246	7	,	,	PUNCT
ejpam-5958	246	8	we	we	PRON
ejpam-5958	246	9	obtain	obtain	VERB
ejpam-5958	246	10	:	:	PUNCT
ejpam-5958	246	11	dν(fx	dν(fx	PROPN
ejpam-5958	246	12	kl	kl	PROPN
ejpam-5958	246	13	,	,	PUNCT
ejpam-5958	246	14	fx∗	fx∗	PROPN
ejpam-5958	246	15	)	)	PUNCT
ejpam-5958	246	16	≤	≤	NOUN
ejpam-5958	246	17	αν(x	αν(x	NUM
ejpam-5958	246	18	kl	kl	NOUN
ejpam-5958	246	19	,	,	PUNCT
ejpam-5958	246	20	x∗	x∗	PROPN
ejpam-5958	246	21	)	)	PUNCT
ejpam-5958	247	1	dν(fx	dν(fx	NOUN
ejpam-5958	247	2	kl	kl	NOUN
ejpam-5958	247	3	,	,	PUNCT
ejpam-5958	247	4	fx∗	fx∗	PROPN
ejpam-5958	247	5	)	)	PUNCT
ejpam-5958	247	6	≤	≤	NOUN
ejpam-5958	247	7	ψν	ψν	NOUN
ejpam-5958	247	8	(	(	PUNCT
ejpam-5958	247	9	dw(ν)(x	dw(ν)(x	NOUN
ejpam-5958	247	10	kl	kl	PROPN
ejpam-5958	247	11	,	,	PUNCT
ejpam-5958	247	12	x∗	x∗	PROPN
ejpam-5958	247	13	)	)	PUNCT
ejpam-5958	247	14	)	)	PUNCT
ejpam-5958	247	15	.	.	PUNCT
ejpam-5958	248	1	now	now	ADV
ejpam-5958	248	2	,	,	PUNCT
ejpam-5958	248	3	letting	let	VERB
ejpam-5958	248	4	l	l	NOUN
ejpam-5958	248	5	−→	−→	NOUN
ejpam-5958	248	6	∞	∞	NUM
ejpam-5958	248	7	in	in	ADP
ejpam-5958	248	8	the	the	DET
ejpam-5958	248	9	right	right	ADJ
ejpam-5958	248	10	hand	hand	NOUN
ejpam-5958	248	11	side	side	NOUN
ejpam-5958	248	12	of	of	ADP
ejpam-5958	248	13	the	the	DET
ejpam-5958	248	14	above	above	ADJ
ejpam-5958	248	15	inequality	inequality	NOUN
ejpam-5958	248	16	taking	take	VERB
ejpam-5958	248	17	into	into	ADP
ejpam-5958	248	18	account	account	NOUN
ejpam-5958	248	19	the	the	DET
ejpam-5958	248	20	second	second	ADJ
ejpam-5958	248	21	statement	statement	NOUN
ejpam-5958	248	22	of	of	ADP
ejpam-5958	248	23	lemma	lemma	PROPN
ejpam-5958	248	24	2.4	2.4	NUM
ejpam-5958	248	25	,	,	PUNCT
ejpam-5958	248	26	we	we	PRON
ejpam-5958	248	27	deduce	deduce	VERB
ejpam-5958	248	28	:	:	PUNCT
ejpam-5958	248	29	lim	lim	PROPN
ejpam-5958	248	30	l→∞	l→∞	NUM
ejpam-5958	249	1	dν(fx	dν(fx	PROPN
ejpam-5958	249	2	kl	kl	PROPN
ejpam-5958	249	3	,	,	PUNCT
ejpam-5958	249	4	fx∗	fx∗	X
ejpam-5958	249	5	)	)	PUNCT
ejpam-5958	250	1	=	=	SYM
ejpam-5958	250	2	0	0	NUM
ejpam-5958	250	3	,	,	PUNCT
ejpam-5958	250	4	∀ν	∀ν	PROPN
ejpam-5958	250	5	∈	∈	PROPN
ejpam-5958	250	6	n	n	X
ejpam-5958	250	7	.	.	PUNCT
ejpam-5958	251	1	k.	k.	PROPN
ejpam-5958	251	2	nisse	nisse	PROPN
ejpam-5958	251	3	et	et	PROPN
ejpam-5958	251	4	al	al	PROPN
ejpam-5958	251	5	.	.	PUNCT
ejpam-5958	251	6	/	/	SYM
ejpam-5958	251	7	eur	eur	PROPN
ejpam-5958	251	8	.	.	PUNCT
ejpam-5958	252	1	j.	j.	PROPN
ejpam-5958	252	2	pure	pure	PROPN
ejpam-5958	252	3	appl	appl	PROPN
ejpam-5958	252	4	.	.	PROPN
ejpam-5958	252	5	math	math	PROPN
ejpam-5958	252	6	,	,	PUNCT
ejpam-5958	252	7	18	18	NUM
ejpam-5958	252	8	(	(	PUNCT
ejpam-5958	252	9	2	2	NUM
ejpam-5958	252	10	)	)	PUNCT
ejpam-5958	252	11	(	(	PUNCT
ejpam-5958	252	12	2025	2025	NUM
ejpam-5958	252	13	)	)	PUNCT
ejpam-5958	252	14	,	,	PUNCT
ejpam-5958	252	15	5958	5958	NUM
ejpam-5958	252	16	11	11	NUM
ejpam-5958	252	17	of	of	ADP
ejpam-5958	252	18	22	22	NUM
ejpam-5958	252	19	that	that	PRON
ejpam-5958	252	20	is	be	AUX
ejpam-5958	252	21	lim	lim	PROPN
ejpam-5958	252	22	l→∞	l→∞	NUM
ejpam-5958	253	1	fxkl	fxkl	ADJ
ejpam-5958	253	2	=	=	SYM
ejpam-5958	253	3	fx∗.	fx∗.	PROPN
ejpam-5958	253	4	noting	note	VERB
ejpam-5958	253	5	that	that	SCONJ
ejpam-5958	253	6	lim	lim	PROPN
ejpam-5958	253	7	l→∞	l→∞	NUM
ejpam-5958	253	8	xkl+1	xkl+1	PROPN
ejpam-5958	254	1	=	=	PROPN
ejpam-5958	254	2	lim	lim	PROPN
ejpam-5958	254	3	l→∞	l→∞	NUM
ejpam-5958	254	4	fxkl	fxkl	PROPN
ejpam-5958	254	5	,	,	PUNCT
ejpam-5958	254	6	we	we	PRON
ejpam-5958	254	7	deduce	deduce	VERB
ejpam-5958	254	8	that	that	DET
ejpam-5958	254	9	x∗	x∗	PROPN
ejpam-5958	255	1	=	=	PUNCT
ejpam-5958	255	2	fx∗.	fx∗.	ADJ
ejpam-5958	255	3	the	the	DET
ejpam-5958	255	4	proof	proof	NOUN
ejpam-5958	255	5	is	be	AUX
ejpam-5958	255	6	complete	complete	ADJ
ejpam-5958	255	7	.	.	PUNCT
ejpam-5958	256	1	remark	remark	PROPN
ejpam-5958	256	2	3.4	3.4	NUM
ejpam-5958	256	3	.	.	PUNCT
ejpam-5958	257	1	condition	condition	NOUN
ejpam-5958	257	2	(	(	PUNCT
ejpam-5958	257	3	c2(i	c2(i	NOUN
ejpam-5958	257	4	)	)	PUNCT
ejpam-5958	257	5	)	)	PUNCT
ejpam-5958	257	6	is	be	AUX
ejpam-5958	257	7	an	an	DET
ejpam-5958	257	8	extension	extension	NOUN
ejpam-5958	257	9	of	of	ADP
ejpam-5958	257	10	(	(	PUNCT
ejpam-5958	257	11	2.3	2.3	NUM
ejpam-5958	257	12	)	)	PUNCT
ejpam-5958	257	13	in	in	ADP
ejpam-5958	257	14	the	the	DET
ejpam-5958	257	15	setting	setting	NOUN
ejpam-5958	257	16	of	of	ADP
ejpam-5958	257	17	b	b	NOUN
ejpam-5958	257	18	-	-	PUNCT
ejpam-5958	257	19	gauge	gauge	NOUN
ejpam-5958	257	20	spaces	space	NOUN
ejpam-5958	257	21	.	.	PUNCT
ejpam-5958	258	1	thus	thus	ADV
ejpam-5958	258	2	,	,	PUNCT
ejpam-5958	258	3	according	accord	VERB
ejpam-5958	258	4	to	to	ADP
ejpam-5958	258	5	example	example	NOUN
ejpam-5958	258	6	2	2	NUM
ejpam-5958	258	7	,	,	PUNCT
ejpam-5958	258	8	this	this	DET
ejpam-5958	258	9	condition	condition	NOUN
ejpam-5958	258	10	is	be	AUX
ejpam-5958	258	11	weaker	weak	ADJ
ejpam-5958	258	12	than	than	ADP
ejpam-5958	258	13	the	the	DET
ejpam-5958	258	14	condition	condition	NOUN
ejpam-5958	258	15	(	(	PUNCT
ejpam-5958	258	16	2.2	2.2	NUM
ejpam-5958	258	17	)	)	PUNCT
ejpam-5958	258	18	,	,	PUNCT
ejpam-5958	258	19	frequently	frequently	ADV
ejpam-5958	258	20	imposed	impose	VERB
ejpam-5958	258	21	in	in	ADP
ejpam-5958	258	22	the	the	DET
ejpam-5958	258	23	existing	exist	VERB
ejpam-5958	258	24	literature	literature	NOUN
ejpam-5958	258	25	on	on	ADP
ejpam-5958	258	26	this	this	DET
ejpam-5958	258	27	topic	topic	NOUN
ejpam-5958	258	28	,	,	PUNCT
ejpam-5958	258	29	like	like	ADP
ejpam-5958	258	30	in	in	ADP
ejpam-5958	258	31	[	[	X
ejpam-5958	258	32	37	37	NUM
ejpam-5958	258	33	,	,	PUNCT
ejpam-5958	258	34	38	38	NUM
ejpam-5958	258	35	,	,	PUNCT
ejpam-5958	258	36	40	40	NUM
ejpam-5958	258	37	]	]	PUNCT
ejpam-5958	258	38	.	.	PUNCT
ejpam-5958	259	1	sufficient	sufficient	ADJ
ejpam-5958	259	2	conditions	condition	NOUN
ejpam-5958	259	3	guaranteeing	guarantee	VERB
ejpam-5958	259	4	the	the	DET
ejpam-5958	259	5	uniqueness	uniqueness	NOUN
ejpam-5958	259	6	of	of	ADP
ejpam-5958	259	7	the	the	DET
ejpam-5958	259	8	fixed	fix	VERB
ejpam-5958	259	9	point	point	NOUN
ejpam-5958	259	10	is	be	AUX
ejpam-5958	259	11	given	give	VERB
ejpam-5958	259	12	in	in	ADP
ejpam-5958	259	13	the	the	DET
ejpam-5958	259	14	following	follow	VERB
ejpam-5958	259	15	theorem	theorem	NOUN
ejpam-5958	259	16	.	.	PUNCT
ejpam-5958	259	17	theorem	theorem	NOUN
ejpam-5958	259	18	2	2	NUM
ejpam-5958	259	19	.	.	PUNCT
ejpam-5958	260	1	let	let	AUX
ejpam-5958	260	2	f	f	NOUN
ejpam-5958	260	3	:	:	PUNCT
ejpam-5958	260	4	e	e	AUX
ejpam-5958	260	5	−→	−→	NOUN
ejpam-5958	260	6	e	e	AUX
ejpam-5958	260	7	be	be	AUX
ejpam-5958	260	8	a	a	DET
ejpam-5958	260	9	generalized	generalized	ADJ
ejpam-5958	260	10	(	(	PUNCT
ejpam-5958	260	11	αααν	αααν	NOUN
ejpam-5958	260	12	,	,	PUNCT
ejpam-5958	260	13	ψ	ψ	X
ejpam-5958	260	14	s	s	SYM
ejpam-5958	260	15	,	,	PUNCT
ejpam-5958	260	16	w	w	NOUN
ejpam-5958	260	17	)	)	PUNCT
ejpam-5958	260	18	contraction	contraction	NOUN
ejpam-5958	260	19	satisfying	satisfy	VERB
ejpam-5958	260	20	conditions	condition	NOUN
ejpam-5958	260	21	(	(	PUNCT
ejpam-5958	260	22	c1	c1	NOUN
ejpam-5958	260	23	)	)	PUNCT
ejpam-5958	260	24	,	,	PUNCT
ejpam-5958	260	25	(	(	PUNCT
ejpam-5958	260	26	c3	c3	PROPN
ejpam-5958	260	27	)	)	PUNCT
ejpam-5958	260	28	and	and	CCONJ
ejpam-5958	260	29	(	(	PUNCT
ejpam-5958	260	30	c4	c4	NOUN
ejpam-5958	260	31	)	)	PUNCT
ejpam-5958	260	32	in	in	ADP
ejpam-5958	260	33	theorem	theorem	NOUN
ejpam-5958	260	34	1	1	X
ejpam-5958	260	35	.	.	PUNCT
ejpam-5958	260	36	suppose	suppose	VERB
ejpam-5958	260	37	that	that	SCONJ
ejpam-5958	260	38	the	the	DET
ejpam-5958	260	39	following	follow	VERB
ejpam-5958	260	40	condition	condition	NOUN
ejpam-5958	260	41	holds	hold	VERB
ejpam-5958	260	42	˜(c2	˜(c2	NOUN
ejpam-5958	260	43	)	)	PUNCT
ejpam-5958	260	44	∀x	∀x	NUM
ejpam-5958	260	45	,	,	PUNCT
ejpam-5958	260	46	y	y	PROPN
ejpam-5958	260	47	∈	∈	PROPN
ejpam-5958	260	48	e	e	X
ejpam-5958	260	49	with	with	ADP
ejpam-5958	260	50	x	x	PROPN
ejpam-5958	260	51	̸=	̸=	PROPN
ejpam-5958	260	52	y	y	NUM
ejpam-5958	260	53	,	,	PUNCT
ejpam-5958	260	54	there	there	PRON
ejpam-5958	260	55	exists	exist	VERB
ejpam-5958	260	56	n	n	NOUN
ejpam-5958	260	57	=	=	SYM
ejpam-5958	260	58	n(x	n(x	PROPN
ejpam-5958	260	59	,	,	PUNCT
ejpam-5958	260	60	y	y	NOUN
ejpam-5958	260	61	)	)	PUNCT
ejpam-5958	260	62	∈	∈	PROPN
ejpam-5958	260	63	n∗	n∗	PROPN
ejpam-5958	260	64	and	and	CCONJ
ejpam-5958	260	65	(	(	PUNCT
ejpam-5958	260	66	apx	apx	PROPN
ejpam-5958	260	67	,	,	PUNCT
ejpam-5958	260	68	y)np=0	y)np=0	PUNCT
ejpam-5958	261	1	⊂	⊂	PUNCT
ejpam-5958	261	2	e	e	X
ejpam-5958	261	3	such	such	ADJ
ejpam-5958	261	4	that	that	PRON
ejpam-5958	261	5	:	:	PUNCT
ejpam-5958	261	6	(	(	PUNCT
ejpam-5958	261	7	i	i	NOUN
ejpam-5958	261	8	)	)	PUNCT
ejpam-5958	261	9	a0x	a0x	PROPN
ejpam-5958	261	10	,	,	PUNCT
ejpam-5958	261	11	y	y	PROPN
ejpam-5958	261	12	=	=	SYM
ejpam-5958	261	13	x	x	PROPN
ejpam-5958	261	14	,	,	PUNCT
ejpam-5958	261	15	anx	anx	ADJ
ejpam-5958	261	16	,	,	PUNCT
ejpam-5958	261	17	y	y	PROPN
ejpam-5958	261	18	=	=	SYM
ejpam-5958	261	19	y	y	PROPN
ejpam-5958	261	20	,	,	PUNCT
ejpam-5958	261	21	and	and	CCONJ
ejpam-5958	261	22	αν(a	αν(a	NUM
ejpam-5958	261	23	p−1	p−1	PROPN
ejpam-5958	261	24	x	x	PROPN
ejpam-5958	261	25	,	,	PUNCT
ejpam-5958	261	26	y	y	PROPN
ejpam-5958	261	27	,	,	PUNCT
ejpam-5958	261	28	a	a	DET
ejpam-5958	261	29	p	p	X
ejpam-5958	261	30	x	x	PROPN
ejpam-5958	261	31	,	,	PUNCT
ejpam-5958	261	32	y	y	PROPN
ejpam-5958	261	33	)	)	PUNCT
ejpam-5958	261	34	≥	≥	NOUN
ejpam-5958	261	35	1	1	NUM
ejpam-5958	261	36	,	,	PUNCT
ejpam-5958	261	37	∀p	∀p	NOUN
ejpam-5958	261	38	=	=	SYM
ejpam-5958	261	39	1	1	NUM
ejpam-5958	261	40	,	,	PUNCT
ejpam-5958	261	41	...	...	PUNCT
ejpam-5958	261	42	,	,	PUNCT
ejpam-5958	261	43	n,∀ν	n,∀ν	PRON
ejpam-5958	261	44	∈	∈	PROPN
ejpam-5958	261	45	n	n	NOUN
ejpam-5958	261	46	;	;	PUNCT
ejpam-5958	261	47	(	(	PUNCT
ejpam-5958	261	48	ii	ii	NOUN
ejpam-5958	261	49	)	)	PUNCT
ejpam-5958	261	50	n∑	n∑	NOUN
ejpam-5958	262	1	p=1	p=1	PROPN
ejpam-5958	262	2	spdwi(ν)(a	spdwi(ν)(a	NOUN
ejpam-5958	262	3	p−1	p−1	PROPN
ejpam-5958	262	4	x	x	PROPN
ejpam-5958	262	5	,	,	PUNCT
ejpam-5958	262	6	y	y	PROPN
ejpam-5958	262	7	,	,	PUNCT
ejpam-5958	262	8	a	a	DET
ejpam-5958	262	9	p	p	X
ejpam-5958	262	10	x	x	PROPN
ejpam-5958	262	11	,	,	PUNCT
ejpam-5958	262	12	y	y	NOUN
ejpam-5958	262	13	)	)	PUNCT
ejpam-5958	262	14	≤ms	≤m	NOUN
ejpam-5958	262	15	,	,	PUNCT
ejpam-5958	262	16	ν(x	ν(x	PROPN
ejpam-5958	262	17	,	,	PUNCT
ejpam-5958	262	18	y	y	NOUN
ejpam-5958	262	19	)	)	PUNCT
ejpam-5958	262	20	<	<	X
ejpam-5958	263	1	+	+	PROPN
ejpam-5958	263	2	∞	∞	NOUN
ejpam-5958	263	3	,	,	PUNCT
ejpam-5958	263	4	∀i	∀i	NOUN
ejpam-5958	263	5	∈	∈	NOUN
ejpam-5958	263	6	n	n	CCONJ
ejpam-5958	263	7	,	,	PUNCT
ejpam-5958	263	8	∀ν	∀ν	PROPN
ejpam-5958	263	9	∈	∈	PROPN
ejpam-5958	263	10	n	n	ADV
ejpam-5958	263	11	.	.	PUNCT
ejpam-5958	264	1	then	then	ADV
ejpam-5958	264	2	f	f	PROPN
ejpam-5958	264	3	has	have	VERB
ejpam-5958	264	4	a	a	DET
ejpam-5958	264	5	unique	unique	ADJ
ejpam-5958	264	6	fixed	fix	VERB
ejpam-5958	264	7	point	point	NOUN
ejpam-5958	264	8	.	.	PUNCT
ejpam-5958	265	1	proof	proof	NOUN
ejpam-5958	265	2	.	.	PUNCT
ejpam-5958	266	1	the	the	DET
ejpam-5958	266	2	existence	existence	NOUN
ejpam-5958	266	3	of	of	ADP
ejpam-5958	266	4	a	a	DET
ejpam-5958	266	5	fixed	fix	VERB
ejpam-5958	266	6	point	point	NOUN
ejpam-5958	266	7	for	for	ADP
ejpam-5958	266	8	f	f	PROPN
ejpam-5958	266	9	results	result	NOUN
ejpam-5958	266	10	from	from	ADP
ejpam-5958	266	11	theorem	theorem	ADJ
ejpam-5958	266	12	1	1	NUM
ejpam-5958	266	13	.	.	PUNCT
ejpam-5958	266	14	indeed	indeed	ADV
ejpam-5958	266	15	,	,	PUNCT
ejpam-5958	266	16	let	let	VERB
ejpam-5958	266	17	x0	x0	PROPN
ejpam-5958	266	18	be	be	AUX
ejpam-5958	266	19	an	an	DET
ejpam-5958	266	20	arbitrary	arbitrary	ADJ
ejpam-5958	266	21	element	element	NOUN
ejpam-5958	266	22	in	in	ADP
ejpam-5958	266	23	e.	e.	PROPN
ejpam-5958	266	24	•	•	PROPN
ejpam-5958	266	25	if	if	SCONJ
ejpam-5958	266	26	x0	x0	PROPN
ejpam-5958	266	27	=	=	SYM
ejpam-5958	266	28	fx0	fx0	PROPN
ejpam-5958	266	29	,	,	PUNCT
ejpam-5958	266	30	then	then	ADV
ejpam-5958	266	31	x0	x0	PROPN
ejpam-5958	266	32	is	be	AUX
ejpam-5958	266	33	a	a	DET
ejpam-5958	266	34	fixed	fix	VERB
ejpam-5958	266	35	point	point	NOUN
ejpam-5958	266	36	.	.	PUNCT
ejpam-5958	267	1	•	•	INTJ
ejpam-5958	267	2	if	if	SCONJ
ejpam-5958	267	3	x0	x0	PROPN
ejpam-5958	267	4	̸=	̸=	PROPN
ejpam-5958	267	5	fx0	fx0	ADV
ejpam-5958	267	6	,	,	PUNCT
ejpam-5958	267	7	then	then	ADV
ejpam-5958	267	8	with	with	ADP
ejpam-5958	267	9	x	x	PROPN
ejpam-5958	267	10	=	=	SYM
ejpam-5958	267	11	x0	x0	PROPN
ejpam-5958	267	12	and	and	CCONJ
ejpam-5958	267	13	y	y	PROPN
ejpam-5958	267	14	=	=	PUNCT
ejpam-5958	267	15	fx0	fx0	PROPN
ejpam-5958	267	16	condition	condition	NOUN
ejpam-5958	267	17	˜(c2	˜(c2	NOUN
ejpam-5958	267	18	)	)	PUNCT
ejpam-5958	267	19	reduces	reduce	VERB
ejpam-5958	267	20	to	to	ADP
ejpam-5958	267	21	condition	condition	NOUN
ejpam-5958	267	22	(	(	PUNCT
ejpam-5958	267	23	c2	c2	PROPN
ejpam-5958	267	24	)	)	PUNCT
ejpam-5958	267	25	in	in	ADP
ejpam-5958	267	26	theorem	theorem	NOUN
ejpam-5958	267	27	1	1	NUM
ejpam-5958	267	28	,	,	PUNCT
ejpam-5958	267	29	from	from	ADP
ejpam-5958	267	30	which	which	PRON
ejpam-5958	267	31	follows	follow	VERB
ejpam-5958	267	32	that	that	SCONJ
ejpam-5958	267	33	f	f	PROPN
ejpam-5958	267	34	has	have	VERB
ejpam-5958	267	35	a	a	DET
ejpam-5958	267	36	fixed	fix	VERB
ejpam-5958	267	37	point	point	NOUN
ejpam-5958	267	38	.	.	PUNCT
ejpam-5958	268	1	suppose	suppose	VERB
ejpam-5958	268	2	now	now	ADV
ejpam-5958	268	3	that	that	SCONJ
ejpam-5958	268	4	x	x	X
ejpam-5958	268	5	,	,	PUNCT
ejpam-5958	268	6	y	y	PROPN
ejpam-5958	268	7	are	be	AUX
ejpam-5958	268	8	two	two	NUM
ejpam-5958	268	9	fixed	fix	VERB
ejpam-5958	268	10	points	point	NOUN
ejpam-5958	268	11	of	of	ADP
ejpam-5958	268	12	f	f	PROPN
ejpam-5958	268	13	such	such	ADJ
ejpam-5958	268	14	that	that	SCONJ
ejpam-5958	268	15	x	x	X
ejpam-5958	268	16	̸=	̸=	PROPN
ejpam-5958	268	17	y.	y.	NOUN
ejpam-5958	268	18	by	by	ADP
ejpam-5958	268	19	means	mean	NOUN
ejpam-5958	268	20	of	of	ADP
ejpam-5958	268	21	(	(	PUNCT
ejpam-5958	268	22	c1	c1	PROPN
ejpam-5958	268	23	)	)	PUNCT
ejpam-5958	268	24	,	,	PUNCT
ejpam-5958	268	25	˜(c2	˜(c2	PROPN
ejpam-5958	268	26	)	)	PUNCT
ejpam-5958	268	27	,	,	PUNCT
ejpam-5958	268	28	(	(	PUNCT
ejpam-5958	268	29	c3	c3	PROPN
ejpam-5958	268	30	)	)	PUNCT
ejpam-5958	268	31	and	and	CCONJ
ejpam-5958	268	32	in	in	ADP
ejpam-5958	268	33	a	a	DET
ejpam-5958	268	34	similar	similar	ADJ
ejpam-5958	268	35	way	way	NOUN
ejpam-5958	268	36	as	as	SCONJ
ejpam-5958	268	37	that	that	PRON
ejpam-5958	268	38	used	use	VERB
ejpam-5958	268	39	to	to	PART
ejpam-5958	268	40	get	get	VERB
ejpam-5958	268	41	(	(	PUNCT
ejpam-5958	268	42	3.5	3.5	NUM
ejpam-5958	268	43	)	)	PUNCT
ejpam-5958	268	44	,	,	PUNCT
ejpam-5958	268	45	we	we	PRON
ejpam-5958	268	46	have	have	VERB
ejpam-5958	268	47	also	also	ADV
ejpam-5958	268	48	the	the	DET
ejpam-5958	268	49	following	follow	VERB
ejpam-5958	268	50	inequality	inequality	NOUN
ejpam-5958	268	51	:	:	PUNCT
ejpam-5958	268	52	dν(f	dν(f	NUM
ejpam-5958	268	53	kx	kx	PROPN
ejpam-5958	268	54	,	,	PUNCT
ejpam-5958	268	55	f	f	PROPN
ejpam-5958	268	56	ky	ky	PROPN
ejpam-5958	268	57	)	)	PUNCT
ejpam-5958	268	58	≤	≤	PUNCT
ejpam-5958	269	1	ψ̃ν	ψ̃ν	X
ejpam-5958	269	2	k	k	X
ejpam-5958	270	1	(	(	PUNCT
ejpam-5958	270	2	ms	ms	PROPN
ejpam-5958	270	3	,	,	PUNCT
ejpam-5958	270	4	ν	ν	X
ejpam-5958	270	5	(	(	PUNCT
ejpam-5958	270	6	x	x	NOUN
ejpam-5958	270	7	,	,	PUNCT
ejpam-5958	270	8	y	y	NOUN
ejpam-5958	270	9	)	)	PUNCT
ejpam-5958	270	10	)	)	PUNCT
ejpam-5958	270	11	,	,	PUNCT
ejpam-5958	270	12	for	for	ADP
ejpam-5958	270	13	all	all	DET
ejpam-5958	270	14	k	k	PROPN
ejpam-5958	270	15	∈	∈	PROPN
ejpam-5958	270	16	n	n	ADV
ejpam-5958	270	17	and	and	CCONJ
ejpam-5958	270	18	all	all	PRON
ejpam-5958	270	19	ν	ν	X
ejpam-5958	270	20	∈	∈	PROPN
ejpam-5958	270	21	n	n	NOUN
ejpam-5958	270	22	.	.	PUNCT
ejpam-5958	271	1	hence	hence	ADV
ejpam-5958	271	2	dν(x	dν(x	NUM
ejpam-5958	271	3	,	,	PUNCT
ejpam-5958	271	4	y	y	NOUN
ejpam-5958	271	5	)	)	PUNCT
ejpam-5958	271	6	=	=	PROPN
ejpam-5958	271	7	dν(f	dν(f	NUM
ejpam-5958	271	8	kx	kx	PROPN
ejpam-5958	271	9	,	,	PUNCT
ejpam-5958	271	10	f	f	PROPN
ejpam-5958	271	11	ky	ky	PROPN
ejpam-5958	271	12	)	)	PUNCT
ejpam-5958	271	13	≤	≤	PUNCT
ejpam-5958	272	1	ψ̃ν	ψ̃ν	X
ejpam-5958	272	2	k	k	X
ejpam-5958	273	1	(	(	PUNCT
ejpam-5958	273	2	ms	ms	PROPN
ejpam-5958	273	3	,	,	PUNCT
ejpam-5958	273	4	ν	ν	X
ejpam-5958	273	5	(	(	PUNCT
ejpam-5958	273	6	x	x	NOUN
ejpam-5958	273	7	,	,	PUNCT
ejpam-5958	273	8	y	y	NOUN
ejpam-5958	273	9	)	)	PUNCT
ejpam-5958	273	10	)	)	PUNCT
ejpam-5958	273	11	,	,	PUNCT
ejpam-5958	273	12	(	(	PUNCT
ejpam-5958	273	13	3.7	3.7	NUM
ejpam-5958	273	14	)	)	PUNCT
ejpam-5958	273	15	for	for	ADP
ejpam-5958	273	16	all	all	DET
ejpam-5958	273	17	k	k	PROPN
ejpam-5958	273	18	∈	∈	PROPN
ejpam-5958	273	19	n	n	ADV
ejpam-5958	273	20	and	and	CCONJ
ejpam-5958	273	21	all	all	PRON
ejpam-5958	273	22	ν	ν	X
ejpam-5958	273	23	∈	∈	PROPN
ejpam-5958	273	24	n	n	NOUN
ejpam-5958	273	25	.	.	PUNCT
ejpam-5958	274	1	noting	note	VERB
ejpam-5958	274	2	that	that	SCONJ
ejpam-5958	274	3	ψ̃ν	ψ̃ν	PUNCT
ejpam-5958	274	4	k	k	X
ejpam-5958	274	5	(	(	PUNCT
ejpam-5958	274	6	ms	ms	PROPN
ejpam-5958	274	7	,	,	PUNCT
ejpam-5958	274	8	ν	ν	X
ejpam-5958	274	9	(	(	PUNCT
ejpam-5958	274	10	x	x	NOUN
ejpam-5958	274	11	,	,	PUNCT
ejpam-5958	274	12	y	y	NOUN
ejpam-5958	274	13	)	)	PUNCT
ejpam-5958	274	14	)	)	PUNCT
ejpam-5958	274	15	≤	≤	NUM
ejpam-5958	274	16	sk	sk	VERB
ejpam-5958	274	17	ψ̃ν	ψ̃ν	PROPN
ejpam-5958	274	18	k	k	PROPN
ejpam-5958	274	19	(	(	PUNCT
ejpam-5958	274	20	ms	ms	PROPN
ejpam-5958	274	21	,	,	PUNCT
ejpam-5958	274	22	ν	ν	X
ejpam-5958	274	23	(	(	PUNCT
ejpam-5958	274	24	x	x	NOUN
ejpam-5958	274	25	,	,	PUNCT
ejpam-5958	274	26	y	y	NOUN
ejpam-5958	274	27	)	)	PUNCT
ejpam-5958	274	28	)	)	PUNCT
ejpam-5958	275	1	,	,	PUNCT
ejpam-5958	275	2	k.	k.	PROPN
ejpam-5958	275	3	nisse	nisse	PROPN
ejpam-5958	275	4	et	et	PROPN
ejpam-5958	275	5	al	al	PROPN
ejpam-5958	275	6	.	.	PUNCT
ejpam-5958	275	7	/	/	SYM
ejpam-5958	275	8	eur	eur	PROPN
ejpam-5958	275	9	.	.	PUNCT
ejpam-5958	276	1	j.	j.	PROPN
ejpam-5958	276	2	pure	pure	PROPN
ejpam-5958	276	3	appl	appl	PROPN
ejpam-5958	276	4	.	.	PROPN
ejpam-5958	276	5	math	math	PROPN
ejpam-5958	276	6	,	,	PUNCT
ejpam-5958	276	7	18	18	NUM
ejpam-5958	276	8	(	(	PUNCT
ejpam-5958	276	9	2	2	NUM
ejpam-5958	276	10	)	)	PUNCT
ejpam-5958	276	11	(	(	PUNCT
ejpam-5958	276	12	2025	2025	NUM
ejpam-5958	276	13	)	)	PUNCT
ejpam-5958	276	14	,	,	PUNCT
ejpam-5958	276	15	5958	5958	NUM
ejpam-5958	276	16	12	12	NUM
ejpam-5958	276	17	of	of	ADP
ejpam-5958	276	18	22	22	NUM
ejpam-5958	276	19	and	and	CCONJ
ejpam-5958	276	20	by	by	ADP
ejpam-5958	276	21	letting	let	VERB
ejpam-5958	276	22	k	k	PRON
ejpam-5958	276	23	−→	−→	ADJ
ejpam-5958	276	24	∞	∞	NUM
ejpam-5958	276	25	in	in	ADP
ejpam-5958	276	26	(	(	PUNCT
ejpam-5958	276	27	3.7	3.7	NUM
ejpam-5958	276	28	)	)	PUNCT
ejpam-5958	276	29	taking	take	VERB
ejpam-5958	276	30	into	into	ADP
ejpam-5958	276	31	account	account	NOUN
ejpam-5958	276	32	(	(	PUNCT
ejpam-5958	276	33	ψs	ψs	NOUN
ejpam-5958	276	34	3	3	NUM
ejpam-5958	276	35	)	)	PUNCT
ejpam-5958	276	36	,	,	PUNCT
ejpam-5958	276	37	we	we	PRON
ejpam-5958	276	38	deduce	deduce	VERB
ejpam-5958	276	39	:	:	PUNCT
ejpam-5958	276	40	dν(x	dν(x	NUM
ejpam-5958	276	41	,	,	PUNCT
ejpam-5958	276	42	y	y	NOUN
ejpam-5958	276	43	)	)	PUNCT
ejpam-5958	276	44	=	=	SYM
ejpam-5958	276	45	0	0	NUM
ejpam-5958	276	46	,	,	PUNCT
ejpam-5958	276	47	∀ν	∀ν	PROPN
ejpam-5958	276	48	∈	∈	PROPN
ejpam-5958	276	49	n	n	PRON
ejpam-5958	276	50	,	,	PUNCT
ejpam-5958	276	51	which	which	PRON
ejpam-5958	276	52	is	be	AUX
ejpam-5958	276	53	a	a	DET
ejpam-5958	276	54	contradiction	contradiction	NOUN
ejpam-5958	276	55	with	with	ADP
ejpam-5958	276	56	x	x	PROPN
ejpam-5958	276	57	̸=	̸=	PROPN
ejpam-5958	276	58	y	y	NUM
ejpam-5958	276	59	,	,	PUNCT
ejpam-5958	276	60	since	since	SCONJ
ejpam-5958	276	61	d	d	PROPN
ejpam-5958	276	62	is	be	AUX
ejpam-5958	276	63	separating	separate	VERB
ejpam-5958	276	64	.	.	PUNCT
ejpam-5958	277	1	the	the	DET
ejpam-5958	277	2	proof	proof	NOUN
ejpam-5958	277	3	is	be	AUX
ejpam-5958	277	4	complete	complete	ADJ
ejpam-5958	277	5	.	.	PUNCT
ejpam-5958	277	6	example	example	NOUN
ejpam-5958	278	1	4	4	X
ejpam-5958	278	2	.	.	PUNCT
ejpam-5958	278	3	let	let	VERB
ejpam-5958	278	4	x	x	PUNCT
ejpam-5958	278	5	=	=	PUNCT
ejpam-5958	278	6	r	r	NOUN
ejpam-5958	278	7	be	be	VERB
ejpam-5958	278	8	the	the	DET
ejpam-5958	278	9	complete	complete	ADJ
ejpam-5958	278	10	b	b	NUM
ejpam-5958	278	11	-	-	PUNCT
ejpam-5958	278	12	gauge	gauge	NOUN
ejpam-5958	278	13	space	space	NOUN
ejpam-5958	278	14	with	with	ADP
ejpam-5958	278	15	constant	constant	ADJ
ejpam-5958	278	16	s	s	X
ejpam-5958	278	17	=	=	SYM
ejpam-5958	278	18	2	2	NUM
ejpam-5958	278	19	,	,	PUNCT
ejpam-5958	278	20	endowed	endow	VERB
ejpam-5958	278	21	with	with	ADP
ejpam-5958	278	22	the	the	DET
ejpam-5958	278	23	separated	separated	ADJ
ejpam-5958	278	24	family	family	NOUN
ejpam-5958	278	25	of	of	ADP
ejpam-5958	278	26	b	b	NOUN
ejpam-5958	278	27	-	-	PUNCT
ejpam-5958	278	28	pseudo	pseudo	NOUN
ejpam-5958	278	29	-	-	PUNCT
ejpam-5958	278	30	metrics	metric	NOUN
ejpam-5958	278	31	d	d	NOUN
ejpam-5958	278	32	=	=	SYM
ejpam-5958	278	33	{	{	PUNCT
ejpam-5958	278	34	dn	dn	PROPN
ejpam-5958	278	35	,	,	PUNCT
ejpam-5958	278	36	n	n	PRON
ejpam-5958	278	37	≥	≥	NOUN
ejpam-5958	278	38	1	1	NUM
ejpam-5958	278	39	}	}	PUNCT
ejpam-5958	278	40	defined	define	VERB
ejpam-5958	278	41	by	by	ADP
ejpam-5958	278	42	:	:	PUNCT
ejpam-5958	278	43	dn(x	dn(x	X
ejpam-5958	278	44	,	,	PUNCT
ejpam-5958	278	45	y	y	NOUN
ejpam-5958	278	46	)	)	PUNCT
ejpam-5958	278	47	=	=	SYM
ejpam-5958	279	1	n(|x|	n(|x|	PROPN
ejpam-5958	280	1	−	−	NOUN
ejpam-5958	280	2	|y|)2	|y|)2	NOUN
ejpam-5958	280	3	.	.	PUNCT
ejpam-5958	281	1	let	let	VERB
ejpam-5958	281	2	fx	fx	NOUN
ejpam-5958	281	3	=	=	PUNCT
ejpam-5958	281	4	x	x	SYM
ejpam-5958	281	5	2	2	NUM
ejpam-5958	281	6	,	,	PUNCT
ejpam-5958	281	7	ψn(t	ψn(t	PUNCT
ejpam-5958	281	8	)	)	PUNCT
ejpam-5958	281	9	=	=	PUNCT
ejpam-5958	281	10	1	1	NUM
ejpam-5958	281	11	n+1	n+1	PROPN
ejpam-5958	281	12	t	t	PROPN
ejpam-5958	281	13	and	and	CCONJ
ejpam-5958	281	14	w(n	w(n	NUM
ejpam-5958	281	15	)	)	PUNCT
ejpam-5958	281	16	=	=	PUNCT
ejpam-5958	282	1	(	(	PUNCT
ejpam-5958	282	2	n+	n+	NUM
ejpam-5958	282	3	1)3	1)3	PROPN
ejpam-5958	282	4	for	for	ADP
ejpam-5958	282	5	all	all	DET
ejpam-5958	282	6	n	n	PRON
ejpam-5958	282	7	≥	≥	NOUN
ejpam-5958	282	8	1	1	NUM
ejpam-5958	282	9	.	.	X
ejpam-5958	283	1	αn(x	αn(x	NUM
ejpam-5958	283	2	,	,	PUNCT
ejpam-5958	283	3	y	y	NOUN
ejpam-5958	283	4	)	)	PUNCT
ejpam-5958	283	5	=	=	SYM
ejpam-5958	283	6	{	{	PUNCT
ejpam-5958	283	7	n	n	CCONJ
ejpam-5958	283	8	,	,	PUNCT
ejpam-5958	283	9	x	x	PROPN
ejpam-5958	283	10	̸=	̸=	PROPN
ejpam-5958	283	11	y	y	PROPN
ejpam-5958	283	12	0	0	NUM
ejpam-5958	283	13	,	,	PUNCT
ejpam-5958	283	14	otherwise	otherwise	ADV
ejpam-5958	283	15	.	.	PUNCT
ejpam-5958	284	1	for	for	ADP
ejpam-5958	284	2	x	x	X
ejpam-5958	284	3	,	,	PUNCT
ejpam-5958	284	4	y	y	PROPN
ejpam-5958	284	5	∈	∈	PROPN
ejpam-5958	284	6	r	r	NOUN
ejpam-5958	284	7	with	with	ADP
ejpam-5958	284	8	x	x	PUNCT
ejpam-5958	284	9	̸=	̸=	PROPN
ejpam-5958	284	10	y	y	NOUN
ejpam-5958	284	11	we	we	PRON
ejpam-5958	284	12	have	have	VERB
ejpam-5958	284	13	:	:	PUNCT
ejpam-5958	284	14	αn(x	αn(x	NUM
ejpam-5958	284	15	,	,	PUNCT
ejpam-5958	284	16	y)dn(fx	y)dn(fx	NUM
ejpam-5958	284	17	,	,	PUNCT
ejpam-5958	284	18	fy	fy	NOUN
ejpam-5958	284	19	)	)	PUNCT
ejpam-5958	284	20	=	=	SYM
ejpam-5958	284	21	n2	n2	NOUN
ejpam-5958	284	22	4	4	NUM
ejpam-5958	284	23	(	(	PUNCT
ejpam-5958	284	24	|x|	|x|	PROPN
ejpam-5958	284	25	−	−	PROPN
ejpam-5958	284	26	|y|)2	|y|)2	PROPN
ejpam-5958	284	27	and	and	CCONJ
ejpam-5958	284	28	ψn(d(n+1)3(x	ψn(d(n+1)3(x	PROPN
ejpam-5958	284	29	,	,	PUNCT
ejpam-5958	284	30	y	y	NOUN
ejpam-5958	284	31	)	)	PUNCT
ejpam-5958	284	32	)	)	PUNCT
ejpam-5958	285	1	=	=	PUNCT
ejpam-5958	285	2	(	(	PUNCT
ejpam-5958	285	3	n+	n+	NUM
ejpam-5958	285	4	1)2(|x|	1)2(|x|	NUM
ejpam-5958	286	1	−	−	PROPN
ejpam-5958	286	2	|y|)2	|y|)2	PROPN
ejpam-5958	286	3	then	then	ADV
ejpam-5958	286	4	,	,	PUNCT
ejpam-5958	286	5	for	for	ADP
ejpam-5958	286	6	x	x	SYM
ejpam-5958	286	7	̸=	̸=	PROPN
ejpam-5958	286	8	y	y	PROPN
ejpam-5958	286	9	and	and	CCONJ
ejpam-5958	286	10	n	n	PRON
ejpam-5958	286	11	≥	≥	NOUN
ejpam-5958	286	12	1	1	NUM
ejpam-5958	286	13	we	we	PRON
ejpam-5958	286	14	have	have	VERB
ejpam-5958	286	15	:	:	PUNCT
ejpam-5958	286	16	αn(x	αn(x	NUM
ejpam-5958	286	17	,	,	PUNCT
ejpam-5958	286	18	y)dn(fx	y)dn(fx	NUM
ejpam-5958	286	19	,	,	PUNCT
ejpam-5958	286	20	fy	fy	NOUN
ejpam-5958	286	21	)	)	PUNCT
ejpam-5958	286	22	≤	≤	PROPN
ejpam-5958	286	23	ψn(dw(n)(x	ψn(dw(n)(x	PROPN
ejpam-5958	286	24	,	,	PUNCT
ejpam-5958	286	25	y	y	PROPN
ejpam-5958	286	26	)	)	PUNCT
ejpam-5958	286	27	)	)	PUNCT
ejpam-5958	287	1	=	=	PUNCT
ejpam-5958	288	1	(	(	PUNCT
ejpam-5958	288	2	n+	n+	NUM
ejpam-5958	288	3	1)2(|x|	1)2(|x|	NUM
ejpam-5958	288	4	−	−	PROPN
ejpam-5958	288	5	|y|)2	|y|)2	PROPN
ejpam-5958	288	6	hence	hence	ADV
ejpam-5958	288	7	,	,	PUNCT
ejpam-5958	288	8	f	f	PROPN
ejpam-5958	288	9	is	be	AUX
ejpam-5958	288	10	a	a	DET
ejpam-5958	288	11	generalized	generalized	ADJ
ejpam-5958	288	12	(	(	PUNCT
ejpam-5958	288	13	αααn	αααn	NOUN
ejpam-5958	288	14	,	,	PUNCT
ejpam-5958	288	15	ψ	ψ	NOUN
ejpam-5958	288	16	2,w	2,w	NUM
ejpam-5958	288	17	)	)	PUNCT
ejpam-5958	288	18	contraction	contraction	NOUN
ejpam-5958	288	19	.	.	PUNCT
ejpam-5958	289	1	let	let	VERB
ejpam-5958	289	2	us	we	PRON
ejpam-5958	289	3	now	now	ADV
ejpam-5958	289	4	show	show	VERB
ejpam-5958	289	5	that	that	SCONJ
ejpam-5958	289	6	f	f	PROPN
ejpam-5958	289	7	verifies	verify	VERB
ejpam-5958	289	8	the	the	DET
ejpam-5958	289	9	other	other	ADJ
ejpam-5958	289	10	conditions	condition	NOUN
ejpam-5958	289	11	of	of	ADP
ejpam-5958	289	12	theorem	theorem	NOUN
ejpam-5958	289	13	2	2	NUM
ejpam-5958	289	14	.	.	PUNCT
ejpam-5958	289	15	indeed	indeed	ADV
ejpam-5958	289	16	,	,	PUNCT
ejpam-5958	289	17	for	for	ADP
ejpam-5958	289	18	(	(	PUNCT
ejpam-5958	289	19	c1	c1	PROPN
ejpam-5958	289	20	)	)	PUNCT
ejpam-5958	289	21	we	we	PRON
ejpam-5958	289	22	have	have	AUX
ejpam-5958	289	23	,	,	PUNCT
ejpam-5958	289	24	for	for	ADP
ejpam-5958	289	25	all	all	DET
ejpam-5958	289	26	n	n	PRON
ejpam-5958	289	27	≥	≥	NOUN
ejpam-5958	289	28	1	1	NUM
ejpam-5958	289	29	αn(x	αn(x	NUM
ejpam-5958	289	30	,	,	PUNCT
ejpam-5958	289	31	y	y	PROPN
ejpam-5958	289	32	)	)	PUNCT
ejpam-5958	289	33	≥	≥	NOUN
ejpam-5958	289	34	1	1	NUM
ejpam-5958	289	35	⇒	⇒	NOUN
ejpam-5958	289	36	αn(fx	αn(fx	PROPN
ejpam-5958	289	37	,	,	PUNCT
ejpam-5958	289	38	fy	fy	PROPN
ejpam-5958	289	39	)	)	PUNCT
ejpam-5958	289	40	=	=	SYM
ejpam-5958	289	41	n	n	X
ejpam-5958	289	42	≥	≥	NOUN
ejpam-5958	289	43	1	1	NUM
ejpam-5958	289	44	,	,	PUNCT
ejpam-5958	289	45	then	then	ADV
ejpam-5958	289	46	,	,	PUNCT
ejpam-5958	289	47	f	f	PROPN
ejpam-5958	289	48	is	be	AUX
ejpam-5958	289	49	αααn	αααn	NOUN
ejpam-5958	289	50	-	-	PUNCT
ejpam-5958	289	51	admissible	admissible	ADJ
ejpam-5958	289	52	.	.	PUNCT
ejpam-5958	290	1	it	it	PRON
ejpam-5958	290	2	can	can	AUX
ejpam-5958	290	3	be	be	AUX
ejpam-5958	290	4	easily	easily	ADV
ejpam-5958	290	5	seen	see	VERB
ejpam-5958	290	6	that	that	SCONJ
ejpam-5958	290	7	(	(	PUNCT
ejpam-5958	290	8	c3	c3	NOUN
ejpam-5958	290	9	)	)	PUNCT
ejpam-5958	290	10	is	be	AUX
ejpam-5958	290	11	satisfied	satisfied	ADJ
ejpam-5958	290	12	with	with	ADP
ejpam-5958	290	13	ψ̃n	ψ̃n	PROPN
ejpam-5958	290	14	=	=	SYM
ejpam-5958	290	15	ψn	ψn	PROPN
ejpam-5958	290	16	,	,	PUNCT
ejpam-5958	290	17	for	for	ADP
ejpam-5958	290	18	all	all	DET
ejpam-5958	290	19	n	n	PRON
ejpam-5958	290	20	≥	≥	NOUN
ejpam-5958	290	21	1	1	NUM
ejpam-5958	290	22	.	.	PUNCT
ejpam-5958	291	1	let	let	VERB
ejpam-5958	291	2	x	x	PRON
ejpam-5958	291	3	,	,	PUNCT
ejpam-5958	291	4	y	y	PROPN
ejpam-5958	291	5	∈	∈	PROPN
ejpam-5958	291	6	r	r	NOUN
ejpam-5958	291	7	such	such	ADJ
ejpam-5958	291	8	that	that	SCONJ
ejpam-5958	291	9	x	x	SYM
ejpam-5958	291	10	̸=	̸=	PROPN
ejpam-5958	291	11	y.	y.	NOUN
ejpam-5958	291	12	then	then	ADV
ejpam-5958	291	13	,	,	PUNCT
ejpam-5958	291	14	there	there	PRON
ejpam-5958	291	15	exists	exist	VERB
ejpam-5958	291	16	z	z	NOUN
ejpam-5958	291	17	∈	∈	PROPN
ejpam-5958	291	18	r	r	NOUN
ejpam-5958	292	1	such	such	ADJ
ejpam-5958	292	2	that	that	SCONJ
ejpam-5958	292	3	x	x	X
ejpam-5958	292	4	̸=	̸=	PROPN
ejpam-5958	292	5	z	z	PROPN
ejpam-5958	292	6	and	and	CCONJ
ejpam-5958	292	7	y	y	PROPN
ejpam-5958	292	8	̸=	̸=	PROPN
ejpam-5958	292	9	z.	z.	PROPN
ejpam-5958	292	10	hence	hence	ADV
ejpam-5958	292	11	,	,	PUNCT
ejpam-5958	292	12	for	for	ADP
ejpam-5958	292	13	all	all	DET
ejpam-5958	292	14	n	n	PRON
ejpam-5958	292	15	≥	≥	NOUN
ejpam-5958	292	16	1	1	NUM
ejpam-5958	292	17	,	,	PUNCT
ejpam-5958	292	18	we	we	PRON
ejpam-5958	292	19	have	have	VERB
ejpam-5958	292	20	αn(x	αn(x	NUM
ejpam-5958	292	21	,	,	PUNCT
ejpam-5958	292	22	z	z	NOUN
ejpam-5958	292	23	)	)	PUNCT
ejpam-5958	292	24	=	=	SYM
ejpam-5958	292	25	n	n	X
ejpam-5958	292	26	≥	≥	NOUN
ejpam-5958	292	27	1	1	NUM
ejpam-5958	292	28	and	and	CCONJ
ejpam-5958	292	29	αn(x	αn(x	NUM
ejpam-5958	292	30	,	,	PUNCT
ejpam-5958	292	31	z	z	NOUN
ejpam-5958	292	32	)	)	PUNCT
ejpam-5958	292	33	=	=	SYM
ejpam-5958	292	34	n	n	X
ejpam-5958	292	35	≥	≥	NOUN
ejpam-5958	292	36	1	1	NUM
ejpam-5958	292	37	.	.	PUNCT
ejpam-5958	292	38	then	then	ADV
ejpam-5958	292	39	˜(c2)-(i	˜(c2)-(i	NUM
ejpam-5958	292	40	)	)	PUNCT
ejpam-5958	292	41	holds	hold	VERB
ejpam-5958	292	42	with	with	ADP
ejpam-5958	292	43	n	n	NOUN
ejpam-5958	292	44	=	=	SYM
ejpam-5958	292	45	1	1	NUM
ejpam-5958	292	46	and	and	CCONJ
ejpam-5958	292	47	˜(c2)-(ii	˜(c2)-(ii	NOUN
ejpam-5958	292	48	)	)	PUNCT
ejpam-5958	292	49	follows	follow	VERB
ejpam-5958	292	50	immediately	immediately	ADV
ejpam-5958	292	51	from	from	ADP
ejpam-5958	292	52	the	the	DET
ejpam-5958	292	53	fact	fact	NOUN
ejpam-5958	292	54	that	that	SCONJ
ejpam-5958	292	55	ψi	ψi	ADP
ejpam-5958	292	56	n	n	ADV
ejpam-5958	292	57	≤	≤	X
ejpam-5958	292	58	ψn	ψn	X
ejpam-5958	292	59	for	for	ADP
ejpam-5958	292	60	all	all	PRON
ejpam-5958	292	61	i	i	PRON
ejpam-5958	292	62	∈	∈	PROPN
ejpam-5958	293	1	n.	n.	NOUN
ejpam-5958	294	1	it	it	PRON
ejpam-5958	294	2	is	be	AUX
ejpam-5958	294	3	not	not	PART
ejpam-5958	294	4	hard	hard	ADJ
ejpam-5958	294	5	to	to	PART
ejpam-5958	294	6	see	see	VERB
ejpam-5958	294	7	that	that	SCONJ
ejpam-5958	294	8	f	f	PROPN
ejpam-5958	294	9	is	be	AUX
ejpam-5958	294	10	continuous	continuous	ADJ
ejpam-5958	294	11	and	and	CCONJ
ejpam-5958	294	12	so	so	ADV
ejpam-5958	294	13	(	(	PUNCT
ejpam-5958	294	14	c4	c4	NOUN
ejpam-5958	294	15	)	)	PUNCT
ejpam-5958	294	16	is	be	AUX
ejpam-5958	294	17	satisfied	satisfied	ADJ
ejpam-5958	294	18	.	.	PUNCT
ejpam-5958	295	1	thus	thus	ADV
ejpam-5958	295	2	,	,	PUNCT
ejpam-5958	295	3	all	all	DET
ejpam-5958	295	4	conditions	condition	NOUN
ejpam-5958	295	5	of	of	ADP
ejpam-5958	295	6	theorem	theorem	ADJ
ejpam-5958	295	7	2	2	NUM
ejpam-5958	295	8	are	be	AUX
ejpam-5958	295	9	fulfilled	fulfil	VERB
ejpam-5958	295	10	and	and	CCONJ
ejpam-5958	295	11	consequently	consequently	ADV
ejpam-5958	295	12	f	f	X
ejpam-5958	295	13	has	have	VERB
ejpam-5958	295	14	a	a	DET
ejpam-5958	295	15	unique	unique	ADJ
ejpam-5958	295	16	fixed	fix	VERB
ejpam-5958	295	17	point	point	NOUN
ejpam-5958	295	18	,	,	PUNCT
ejpam-5958	295	19	which	which	PRON
ejpam-5958	295	20	is	be	AUX
ejpam-5958	295	21	0	0	NUM
ejpam-5958	295	22	.	.	PUNCT
ejpam-5958	296	1	let	let	VERB
ejpam-5958	296	2	us	we	PRON
ejpam-5958	296	3	state	state	VERB
ejpam-5958	296	4	the	the	DET
ejpam-5958	296	5	following	follow	VERB
ejpam-5958	296	6	conditions	condition	NOUN
ejpam-5958	296	7	(	(	PUNCT
ejpam-5958	296	8	pc2	pc2	NOUN
ejpam-5958	296	9	)	)	PUNCT
ejpam-5958	296	10	there	there	PRON
ejpam-5958	296	11	exists	exist	VERB
ejpam-5958	296	12	x0	x0	PROPN
ejpam-5958	296	13	∈	∈	PROPN
ejpam-5958	296	14	e	e	NOUN
ejpam-5958	296	15	such	such	ADJ
ejpam-5958	296	16	that	that	SCONJ
ejpam-5958	296	17	αν(x	αν(x	NUM
ejpam-5958	296	18	0	0	NUM
ejpam-5958	296	19	,	,	PUNCT
ejpam-5958	296	20	fx0	fx0	PROPN
ejpam-5958	296	21	)	)	PUNCT
ejpam-5958	296	22	≥	≥	NOUN
ejpam-5958	296	23	1	1	NUM
ejpam-5958	296	24	,	,	PUNCT
ejpam-5958	296	25	∀ν	∀ν	PROPN
ejpam-5958	296	26	∈	∈	PROPN
ejpam-5958	296	27	n	n	ADV
ejpam-5958	296	28	and	and	CCONJ
ejpam-5958	296	29	furthermore	furthermore	ADV
ejpam-5958	296	30	:	:	PUNCT
ejpam-5958	296	31	dwi(ν)(x	dwi(ν)(x	PROPN
ejpam-5958	296	32	0	0	NUM
ejpam-5958	296	33	,	,	PUNCT
ejpam-5958	296	34	fx0	fx0	NOUN
ejpam-5958	296	35	)	)	PUNCT
ejpam-5958	296	36	<	<	X
ejpam-5958	297	1	+	+	PROPN
ejpam-5958	297	2	∞	∞	NOUN
ejpam-5958	297	3	,	,	PUNCT
ejpam-5958	297	4	∀i	∀i	NOUN
ejpam-5958	297	5	∈	∈	NOUN
ejpam-5958	297	6	n	n	CCONJ
ejpam-5958	297	7	,	,	PUNCT
ejpam-5958	297	8	∀ν	∀ν	PROPN
ejpam-5958	297	9	∈	∈	PROPN
ejpam-5958	297	10	n	n	NOUN
ejpam-5958	297	11	;	;	PUNCT
ejpam-5958	297	12	(	(	PUNCT
ejpam-5958	297	13	p̃c2	p̃c2	PROPN
ejpam-5958	297	14	)	)	PUNCT
ejpam-5958	297	15	∀x	∀x	NUM
ejpam-5958	297	16	,	,	PUNCT
ejpam-5958	297	17	y	y	PROPN
ejpam-5958	297	18	∈	∈	PROPN
ejpam-5958	297	19	e	e	X
ejpam-5958	297	20	with	with	ADP
ejpam-5958	297	21	x	x	PROPN
ejpam-5958	297	22	̸=	̸=	PROPN
ejpam-5958	297	23	y	y	NUM
ejpam-5958	297	24	,	,	PUNCT
ejpam-5958	297	25	there	there	PRON
ejpam-5958	297	26	exists	exist	VERB
ejpam-5958	297	27	z	z	NOUN
ejpam-5958	297	28	∈	∈	PROPN
ejpam-5958	297	29	e	e	NOUN
ejpam-5958	297	30	such	such	ADJ
ejpam-5958	297	31	that	that	SCONJ
ejpam-5958	297	32	αν(x	αν(x	NUM
ejpam-5958	297	33	,	,	PUNCT
ejpam-5958	297	34	z	z	NOUN
ejpam-5958	297	35	)	)	PUNCT
ejpam-5958	297	36	≥	≥	NOUN
ejpam-5958	297	37	1	1	NUM
ejpam-5958	297	38	,	,	PUNCT
ejpam-5958	297	39	and	and	CCONJ
ejpam-5958	297	40	αν(y	αν(y	NUM
ejpam-5958	297	41	,	,	PUNCT
ejpam-5958	297	42	z	z	NOUN
ejpam-5958	297	43	)	)	PUNCT
ejpam-5958	297	44	≥	≥	NOUN
ejpam-5958	297	45	1	1	NUM
ejpam-5958	297	46	,	,	PUNCT
ejpam-5958	297	47	∀ν	∀ν	PROPN
ejpam-5958	297	48	∈	∈	PROPN
ejpam-5958	297	49	n	n	NOUN
ejpam-5958	297	50	;	;	PUNCT
ejpam-5958	297	51	(	(	PUNCT
ejpam-5958	297	52	pc4	pc4	NOUN
ejpam-5958	297	53	)	)	PUNCT
ejpam-5958	297	54	(	(	PUNCT
ejpam-5958	297	55	i	i	NOUN
ejpam-5958	297	56	)	)	PUNCT
ejpam-5958	298	1	f	f	PROPN
ejpam-5958	298	2	is	be	AUX
ejpam-5958	298	3	continuous	continuous	ADJ
ejpam-5958	298	4	,	,	PUNCT
ejpam-5958	298	5	or	or	CCONJ
ejpam-5958	298	6	k.	k.	PROPN
ejpam-5958	298	7	nisse	nisse	PROPN
ejpam-5958	298	8	et	et	PROPN
ejpam-5958	298	9	al	al	PROPN
ejpam-5958	298	10	.	.	PUNCT
ejpam-5958	298	11	/	/	SYM
ejpam-5958	298	12	eur	eur	PROPN
ejpam-5958	298	13	.	.	PUNCT
ejpam-5958	299	1	j.	j.	PROPN
ejpam-5958	299	2	pure	pure	PROPN
ejpam-5958	299	3	appl	appl	PROPN
ejpam-5958	299	4	.	.	PROPN
ejpam-5958	299	5	math	math	PROPN
ejpam-5958	299	6	,	,	PUNCT
ejpam-5958	299	7	18	18	NUM
ejpam-5958	299	8	(	(	PUNCT
ejpam-5958	299	9	2	2	NUM
ejpam-5958	299	10	)	)	PUNCT
ejpam-5958	299	11	(	(	PUNCT
ejpam-5958	299	12	2025	2025	NUM
ejpam-5958	299	13	)	)	PUNCT
ejpam-5958	299	14	,	,	PUNCT
ejpam-5958	299	15	5958	5958	NUM
ejpam-5958	299	16	13	13	NUM
ejpam-5958	299	17	of	of	ADP
ejpam-5958	299	18	22	22	NUM
ejpam-5958	299	19	(	(	PUNCT
ejpam-5958	299	20	ii	ii	NOUN
ejpam-5958	299	21	)	)	PUNCT
ejpam-5958	299	22	for	for	ADP
ejpam-5958	299	23	every	every	DET
ejpam-5958	299	24	sequence	sequence	NOUN
ejpam-5958	299	25	{	{	PUNCT
ejpam-5958	299	26	uk	uk	PROPN
ejpam-5958	299	27	}	}	PUNCT
ejpam-5958	299	28	k∈n	k∈n	PROPN
ejpam-5958	299	29	of	of	ADP
ejpam-5958	299	30	e	e	PROPN
ejpam-5958	299	31	,	,	PUNCT
ejpam-5958	299	32	such	such	ADJ
ejpam-5958	299	33	that	that	SCONJ
ejpam-5958	299	34	αν(u	αν(u	NUM
ejpam-5958	299	35	k−1	k−1	PROPN
ejpam-5958	299	36	,	,	PUNCT
ejpam-5958	299	37	uk	uk	PROPN
ejpam-5958	299	38	)	)	PUNCT
ejpam-5958	299	39	≥	≥	NOUN
ejpam-5958	299	40	1	1	NUM
ejpam-5958	299	41	,	,	PUNCT
ejpam-5958	299	42	∀ν	∀ν	PROPN
ejpam-5958	299	43	∈	∈	PROPN
ejpam-5958	299	44	n	n	CCONJ
ejpam-5958	299	45	,	,	PUNCT
ejpam-5958	299	46	if	if	SCONJ
ejpam-5958	299	47	uk	uk	PROPN
ejpam-5958	299	48	−−−→	−−−→	VERB
ejpam-5958	299	49	k→∞	k→∞	PROPN
ejpam-5958	299	50	u	u	NOUN
ejpam-5958	299	51	,	,	PUNCT
ejpam-5958	299	52	then	then	ADV
ejpam-5958	299	53	there	there	PRON
ejpam-5958	299	54	exists	exist	VERB
ejpam-5958	299	55	a	a	DET
ejpam-5958	299	56	sub	sub	NOUN
ejpam-5958	299	57	-	-	NOUN
ejpam-5958	299	58	sequence	sequence	ADJ
ejpam-5958	299	59	{	{	PUNCT
ejpam-5958	299	60	ukl	ukl	NOUN
ejpam-5958	299	61	}	}	PUNCT
ejpam-5958	299	62	l∈n	l∈n	ADV
ejpam-5958	299	63	of	of	ADP
ejpam-5958	299	64	{	{	PUNCT
ejpam-5958	299	65	uk	uk	PROPN
ejpam-5958	299	66	}	}	PUNCT
ejpam-5958	299	67	k∈n	k∈n	PROPN
ejpam-5958	299	68	and	and	CCONJ
ejpam-5958	299	69	l0	l0	PROPN
ejpam-5958	299	70	∈	∈	PROPN
ejpam-5958	299	71	n	n	PRON
ejpam-5958	299	72	such	such	ADJ
ejpam-5958	299	73	that	that	SCONJ
ejpam-5958	299	74	αν(u	αν(u	NUM
ejpam-5958	299	75	kl	kl	NOUN
ejpam-5958	299	76	,	,	PUNCT
ejpam-5958	299	77	u	u	PROPN
ejpam-5958	299	78	)	)	PUNCT
ejpam-5958	299	79	≥	≥	NOUN
ejpam-5958	299	80	1	1	NUM
ejpam-5958	299	81	for	for	ADP
ejpam-5958	299	82	all	all	DET
ejpam-5958	299	83	l	l	PROPN
ejpam-5958	299	84	≥	≥	NUM
ejpam-5958	299	85	l0	l0	NOUN
ejpam-5958	299	86	.	.	PUNCT
ejpam-5958	300	1	as	as	ADP
ejpam-5958	300	2	spacial	spacial	ADJ
ejpam-5958	300	3	cases	case	NOUN
ejpam-5958	300	4	of	of	ADP
ejpam-5958	300	5	(	(	PUNCT
ejpam-5958	300	6	c2	c2	PROPN
ejpam-5958	300	7	)	)	PUNCT
ejpam-5958	300	8	,	,	PUNCT
ejpam-5958	300	9	(	(	PUNCT
ejpam-5958	300	10	c̃2	c̃2	NOUN
ejpam-5958	300	11	)	)	PUNCT
ejpam-5958	300	12	and	and	CCONJ
ejpam-5958	300	13	(	(	PUNCT
ejpam-5958	300	14	c4	c4	NOUN
ejpam-5958	300	15	)	)	PUNCT
ejpam-5958	300	16	respectively	respectively	ADV
ejpam-5958	300	17	.	.	PUNCT
ejpam-5958	301	1	the	the	DET
ejpam-5958	301	2	following	follow	VERB
ejpam-5958	301	3	corollaries	corollary	NOUN
ejpam-5958	301	4	follow	follow	VERB
ejpam-5958	301	5	immediately	immediately	ADV
ejpam-5958	301	6	from	from	ADP
ejpam-5958	301	7	theorem	theorem	ADJ
ejpam-5958	301	8	1	1	NUM
ejpam-5958	301	9	and	and	CCONJ
ejpam-5958	301	10	theorem	theorem	VERB
ejpam-5958	301	11	2	2	NUM
ejpam-5958	301	12	.	.	PUNCT
ejpam-5958	301	13	corollary	corollary	ADJ
ejpam-5958	301	14	3.5	3.5	NUM
ejpam-5958	301	15	.	.	PUNCT
ejpam-5958	302	1	let	let	VERB
ejpam-5958	302	2	f	f	NOUN
ejpam-5958	302	3	:	:	PUNCT
ejpam-5958	302	4	e	e	AUX
ejpam-5958	302	5	−→	−→	NOUN
ejpam-5958	302	6	e	e	AUX
ejpam-5958	302	7	be	be	AUX
ejpam-5958	302	8	a	a	DET
ejpam-5958	302	9	generalized	generalized	ADJ
ejpam-5958	302	10	(	(	PUNCT
ejpam-5958	302	11	αααν	αααν	NOUN
ejpam-5958	302	12	,	,	PUNCT
ejpam-5958	302	13	ψ	ψ	X
ejpam-5958	302	14	s	s	SYM
ejpam-5958	302	15	,	,	PUNCT
ejpam-5958	302	16	w	w	NOUN
ejpam-5958	302	17	)	)	PUNCT
ejpam-5958	302	18	contraction	contraction	NOUN
ejpam-5958	302	19	.	.	PUNCT
ejpam-5958	303	1	suppose	suppose	VERB
ejpam-5958	303	2	that	that	SCONJ
ejpam-5958	303	3	in	in	ADP
ejpam-5958	303	4	addition	addition	NOUN
ejpam-5958	303	5	of	of	ADP
ejpam-5958	303	6	conditions	condition	NOUN
ejpam-5958	303	7	(	(	PUNCT
ejpam-5958	303	8	c1	c1	NOUN
ejpam-5958	303	9	)	)	PUNCT
ejpam-5958	303	10	,	,	PUNCT
ejpam-5958	303	11	(	(	PUNCT
ejpam-5958	303	12	c3	c3	PROPN
ejpam-5958	303	13	)	)	PUNCT
ejpam-5958	303	14	and	and	CCONJ
ejpam-5958	303	15	(	(	PUNCT
ejpam-5958	303	16	c4	c4	NOUN
ejpam-5958	303	17	)	)	PUNCT
ejpam-5958	303	18	of	of	ADP
ejpam-5958	303	19	theorem	theorem	NOUN
ejpam-5958	303	20	1	1	NUM
ejpam-5958	303	21	,	,	PUNCT
ejpam-5958	303	22	(	(	PUNCT
ejpam-5958	303	23	pc2	pc2	NOUN
ejpam-5958	303	24	)	)	PUNCT
ejpam-5958	303	25	holds	hold	VERB
ejpam-5958	303	26	true	true	ADJ
ejpam-5958	303	27	.	.	PUNCT
ejpam-5958	304	1	then	then	ADV
ejpam-5958	304	2	,	,	PUNCT
ejpam-5958	304	3	f	f	PROPN
ejpam-5958	304	4	has	have	VERB
ejpam-5958	304	5	a	a	DET
ejpam-5958	304	6	fixed	fix	VERB
ejpam-5958	304	7	point	point	NOUN
ejpam-5958	304	8	.	.	PUNCT
ejpam-5958	305	1	corollary	corollary	ADJ
ejpam-5958	305	2	3.6	3.6	NUM
ejpam-5958	305	3	.	.	PUNCT
ejpam-5958	306	1	let	let	VERB
ejpam-5958	306	2	f	f	NOUN
ejpam-5958	306	3	:	:	PUNCT
ejpam-5958	306	4	e	e	AUX
ejpam-5958	306	5	−→	−→	NOUN
ejpam-5958	306	6	e	e	AUX
ejpam-5958	306	7	be	be	AUX
ejpam-5958	306	8	a	a	DET
ejpam-5958	306	9	generalized	generalized	ADJ
ejpam-5958	306	10	(	(	PUNCT
ejpam-5958	306	11	αααν	αααν	NOUN
ejpam-5958	306	12	,	,	PUNCT
ejpam-5958	306	13	ψ	ψ	X
ejpam-5958	306	14	s	s	SYM
ejpam-5958	306	15	,	,	PUNCT
ejpam-5958	306	16	w	w	NOUN
ejpam-5958	306	17	)	)	PUNCT
ejpam-5958	306	18	contraction	contraction	NOUN
ejpam-5958	306	19	.	.	PUNCT
ejpam-5958	307	1	suppose	suppose	VERB
ejpam-5958	307	2	that	that	SCONJ
ejpam-5958	307	3	in	in	ADP
ejpam-5958	307	4	addition	addition	NOUN
ejpam-5958	307	5	of	of	ADP
ejpam-5958	307	6	conditions	condition	NOUN
ejpam-5958	307	7	(	(	PUNCT
ejpam-5958	307	8	c1	c1	NOUN
ejpam-5958	307	9	)	)	PUNCT
ejpam-5958	307	10	and	and	CCONJ
ejpam-5958	307	11	(	(	PUNCT
ejpam-5958	307	12	c3	c3	PROPN
ejpam-5958	307	13	)	)	PUNCT
ejpam-5958	307	14	of	of	ADP
ejpam-5958	307	15	theorem	theorem	ADJ
ejpam-5958	307	16	1	1	NUM
ejpam-5958	307	17	,	,	PUNCT
ejpam-5958	307	18	conditions	condition	NOUN
ejpam-5958	307	19	(	(	PUNCT
ejpam-5958	307	20	p̃c2	p̃c2	PROPN
ejpam-5958	307	21	)	)	PUNCT
ejpam-5958	307	22	and	and	CCONJ
ejpam-5958	307	23	(	(	PUNCT
ejpam-5958	307	24	pc4	pc4	NOUN
ejpam-5958	307	25	)	)	PUNCT
ejpam-5958	307	26	hold	hold	VERB
ejpam-5958	307	27	.	.	PUNCT
ejpam-5958	308	1	then	then	ADV
ejpam-5958	308	2	,	,	PUNCT
ejpam-5958	308	3	f	f	PROPN
ejpam-5958	308	4	has	have	VERB
ejpam-5958	308	5	a	a	DET
ejpam-5958	308	6	unique	unique	ADJ
ejpam-5958	308	7	fixed	fix	VERB
ejpam-5958	308	8	point	point	NOUN
ejpam-5958	308	9	.	.	PUNCT
ejpam-5958	309	1	4	4	X
ejpam-5958	309	2	.	.	X
ejpam-5958	309	3	application	application	NOUN
ejpam-5958	309	4	in	in	ADP
ejpam-5958	309	5	this	this	DET
ejpam-5958	309	6	section	section	NOUN
ejpam-5958	309	7	,	,	PUNCT
ejpam-5958	309	8	we	we	PRON
ejpam-5958	309	9	focus	focus	VERB
ejpam-5958	309	10	on	on	ADP
ejpam-5958	309	11	the	the	DET
ejpam-5958	309	12	existence	existence	NOUN
ejpam-5958	309	13	of	of	ADP
ejpam-5958	309	14	solutions	solution	NOUN
ejpam-5958	309	15	of	of	ADP
ejpam-5958	309	16	some	some	DET
ejpam-5958	309	17	nonlinear	nonlinear	ADJ
ejpam-5958	309	18	integral	integral	ADJ
ejpam-5958	309	19	equations	equation	NOUN
ejpam-5958	309	20	as	as	ADP
ejpam-5958	309	21	an	an	DET
ejpam-5958	309	22	application	application	NOUN
ejpam-5958	309	23	to	to	ADP
ejpam-5958	309	24	the	the	DET
ejpam-5958	309	25	results	result	NOUN
ejpam-5958	309	26	proved	prove	VERB
ejpam-5958	309	27	in	in	ADP
ejpam-5958	309	28	the	the	DET
ejpam-5958	309	29	previous	previous	ADJ
ejpam-5958	309	30	section	section	NOUN
ejpam-5958	309	31	.	.	PUNCT
ejpam-5958	310	1	let	let	VERB
ejpam-5958	310	2	us	we	PRON
ejpam-5958	310	3	consider	consider	VERB
ejpam-5958	310	4	the	the	DET
ejpam-5958	310	5	following	follow	VERB
ejpam-5958	310	6	integral	integral	ADJ
ejpam-5958	310	7	equation	equation	NOUN
ejpam-5958	310	8	:	:	PUNCT
ejpam-5958	310	9	x(t	x(t	PROPN
ejpam-5958	310	10	)	)	PUNCT
ejpam-5958	310	11	=	=	PUNCT
ejpam-5958	311	1			NUM
ejpam-5958	311	2	φ(0	φ(0	ADJ
ejpam-5958	311	3	)	)	PUNCT
ejpam-5958	312	1	+	+	NUM
ejpam-5958	312	2	∫	∫	PROPN
ejpam-5958	312	3	t	t	PROPN
ejpam-5958	312	4	0	0	NUM
ejpam-5958	312	5	g(t	g(t	PROPN
ejpam-5958	312	6	,	,	PUNCT
ejpam-5958	312	7	τ)f(τ	τ)f(τ	NUM
ejpam-5958	312	8	,	,	PUNCT
ejpam-5958	312	9	x(τ	x(τ	PROPN
ejpam-5958	312	10	)	)	PUNCT
ejpam-5958	312	11	,	,	PUNCT
ejpam-5958	312	12	gx(τ))dτ	gx(τ))dτ	PROPN
ejpam-5958	312	13	,	,	PUNCT
ejpam-5958	312	14	t	t	PROPN
ejpam-5958	312	15	>	>	X
ejpam-5958	312	16	0	0	NUM
ejpam-5958	312	17	φ(t	φ(t	PROPN
ejpam-5958	312	18	)	)	PUNCT
ejpam-5958	312	19	,	,	PUNCT
ejpam-5958	312	20	t	t	VERB
ejpam-5958	312	21	≤	≤	NUM
ejpam-5958	312	22	0	0	NUM
ejpam-5958	312	23	,	,	PUNCT
ejpam-5958	312	24	(	(	PUNCT
ejpam-5958	312	25	4.1	4.1	NUM
ejpam-5958	312	26	)	)	PUNCT
ejpam-5958	312	27	where	where	SCONJ
ejpam-5958	312	28	g	g	NOUN
ejpam-5958	312	29	:	:	PUNCT
ejpam-5958	312	30	r2	r2	PROPN
ejpam-5958	312	31	+	+	CCONJ
ejpam-5958	312	32	−→	−→	ADJ
ejpam-5958	312	33	r+	r+	NOUN
ejpam-5958	312	34	,	,	PUNCT
ejpam-5958	312	35	f	f	X
ejpam-5958	312	36	:	:	PUNCT
ejpam-5958	312	37	r+	r+	NOUN
ejpam-5958	312	38	×	×	NOUN
ejpam-5958	312	39	r2	r2	PROPN
ejpam-5958	312	40	−→	−→	NOUN
ejpam-5958	312	41	r	r	PROPN
ejpam-5958	312	42	,	,	PUNCT
ejpam-5958	312	43	φ	φ	X
ejpam-5958	312	44	:	:	PUNCT
ejpam-5958	312	45	]	]	PUNCT
ejpam-5958	313	1	−∞	−∞	NOUN
ejpam-5958	313	2	,	,	PUNCT
ejpam-5958	313	3	0	0	NUM
ejpam-5958	313	4	]	]	X
ejpam-5958	313	5	−→	−→	NOUN
ejpam-5958	313	6	r	r	NOUN
ejpam-5958	313	7	are	be	AUX
ejpam-5958	313	8	nonlinear	nonlinear	ADJ
ejpam-5958	313	9	continuous	continuous	ADJ
ejpam-5958	313	10	functions	function	NOUN
ejpam-5958	313	11	and	and	CCONJ
ejpam-5958	313	12	g	g	NOUN
ejpam-5958	313	13	:	:	PUNCT
ejpam-5958	313	14	c(r	c(r	NOUN
ejpam-5958	313	15	)	)	PUNCT
ejpam-5958	313	16	−→	−→	NOUN
ejpam-5958	313	17	c(r	c(r	NOUN
ejpam-5958	313	18	)	)	PUNCT
ejpam-5958	313	19	where	where	SCONJ
ejpam-5958	313	20	c(r	c(r	NOUN
ejpam-5958	313	21	)	)	PUNCT
ejpam-5958	313	22	denotes	denote	VERB
ejpam-5958	313	23	the	the	DET
ejpam-5958	313	24	set	set	NOUN
ejpam-5958	313	25	of	of	ADP
ejpam-5958	313	26	all	all	DET
ejpam-5958	313	27	real	real	ADJ
ejpam-5958	313	28	continuous	continuous	ADJ
ejpam-5958	313	29	functions	function	NOUN
ejpam-5958	313	30	on	on	ADP
ejpam-5958	313	31	r	r	NOUN
ejpam-5958	313	32	and	and	CCONJ
ejpam-5958	313	33	gx	gx	PROPN
ejpam-5958	313	34	is	be	AUX
ejpam-5958	313	35	a	a	DET
ejpam-5958	313	36	delay	delay	NOUN
ejpam-5958	313	37	function	function	NOUN
ejpam-5958	313	38	.	.	PUNCT
ejpam-5958	314	1	let	let	VERB
ejpam-5958	314	2	e	e	NOUN
ejpam-5958	314	3	=	=	SYM
ejpam-5958	314	4	c(r	c(r	NOUN
ejpam-5958	314	5	)	)	PUNCT
ejpam-5958	314	6	be	be	VERB
ejpam-5958	314	7	the	the	DET
ejpam-5958	314	8	complete	complete	ADJ
ejpam-5958	314	9	b	b	NUM
ejpam-5958	314	10	-	-	PUNCT
ejpam-5958	314	11	gauge	gauge	NOUN
ejpam-5958	314	12	space	space	NOUN
ejpam-5958	314	13	with	with	ADP
ejpam-5958	314	14	constant	constant	ADJ
ejpam-5958	314	15	s	s	X
ejpam-5958	314	16	=	=	SYM
ejpam-5958	314	17	2	2	NUM
ejpam-5958	314	18	,	,	PUNCT
ejpam-5958	314	19	endowed	endow	VERB
ejpam-5958	314	20	with	with	ADP
ejpam-5958	314	21	the	the	DET
ejpam-5958	314	22	separated	separated	ADJ
ejpam-5958	314	23	family	family	NOUN
ejpam-5958	314	24	of	of	ADP
ejpam-5958	314	25	b	b	NOUN
ejpam-5958	314	26	-	-	PUNCT
ejpam-5958	314	27	pseudo	pseudo	NOUN
ejpam-5958	314	28	-	-	PUNCT
ejpam-5958	314	29	metrics	metric	NOUN
ejpam-5958	314	30	{	{	PUNCT
ejpam-5958	314	31	dk}k∈k	dk}k∈k	NUM
ejpam-5958	314	32	defined	define	VERB
ejpam-5958	314	33	by	by	ADP
ejpam-5958	314	34	:	:	PUNCT
ejpam-5958	314	35	dk	dk	PROPN
ejpam-5958	314	36	(	(	PUNCT
ejpam-5958	314	37	x	x	PROPN
ejpam-5958	314	38	,	,	PUNCT
ejpam-5958	314	39	y	y	NOUN
ejpam-5958	314	40	)	)	PUNCT
ejpam-5958	314	41	=	=	SYM
ejpam-5958	314	42	sup	sup	NOUN
ejpam-5958	314	43	t∈k	t∈k	NOUN
ejpam-5958	314	44	{	{	PUNCT
ejpam-5958	314	45	e−λt	e−λt	NOUN
ejpam-5958	314	46	|x(t)−	|x(t)−	NOUN
ejpam-5958	314	47	y(t)|2	y(t)|2	PROPN
ejpam-5958	314	48	}	}	PUNCT
ejpam-5958	314	49	,	,	PUNCT
ejpam-5958	314	50	where	where	SCONJ
ejpam-5958	314	51	λ	λ	PROPN
ejpam-5958	314	52	is	be	AUX
ejpam-5958	314	53	a	a	DET
ejpam-5958	314	54	positive	positive	ADJ
ejpam-5958	314	55	real	real	ADJ
ejpam-5958	314	56	number	number	NOUN
ejpam-5958	314	57	to	to	PART
ejpam-5958	314	58	be	be	AUX
ejpam-5958	314	59	specified	specify	VERB
ejpam-5958	314	60	later	later	ADV
ejpam-5958	314	61	and	and	CCONJ
ejpam-5958	314	62	k	k	PROPN
ejpam-5958	314	63	is	be	AUX
ejpam-5958	314	64	the	the	DET
ejpam-5958	314	65	set	set	NOUN
ejpam-5958	314	66	of	of	ADP
ejpam-5958	314	67	all	all	DET
ejpam-5958	314	68	compact	compact	ADJ
ejpam-5958	314	69	sub	sub	NOUN
ejpam-5958	314	70	-	-	NOUN
ejpam-5958	314	71	sets	set	NOUN
ejpam-5958	314	72	of	of	ADP
ejpam-5958	314	73	r.	r.	PROPN
ejpam-5958	314	74	note	note	VERB
ejpam-5958	314	75	that	that	SCONJ
ejpam-5958	314	76	,	,	PUNCT
ejpam-5958	314	77	for	for	SCONJ
ejpam-5958	314	78	dk	dk	PROPN
ejpam-5958	314	79	defined	define	VERB
ejpam-5958	314	80	above	above	ADV
ejpam-5958	314	81	,	,	PUNCT
ejpam-5958	314	82	conditions	condition	NOUN
ejpam-5958	314	83	1	1	NUM
ejpam-5958	314	84	.	.	PUNCT
ejpam-5958	314	85	and	and	CCONJ
ejpam-5958	314	86	2	2	NUM
ejpam-5958	314	87	.	.	NOUN
ejpam-5958	314	88	of	of	ADP
ejpam-5958	314	89	definition	definition	NOUN
ejpam-5958	314	90	2.1	2.1	NUM
ejpam-5958	314	91	are	be	AUX
ejpam-5958	314	92	clearly	clearly	ADV
ejpam-5958	314	93	satisfied	satisfied	ADJ
ejpam-5958	314	94	.	.	PUNCT
ejpam-5958	315	1	moreover	moreover	ADV
ejpam-5958	315	2	,	,	PUNCT
ejpam-5958	315	3	for	for	ADP
ejpam-5958	315	4	all	all	DET
ejpam-5958	315	5	x	x	NOUN
ejpam-5958	315	6	,	,	PUNCT
ejpam-5958	315	7	y	y	PROPN
ejpam-5958	315	8	,	,	PUNCT
ejpam-5958	315	9	z	z	NOUN
ejpam-5958	315	10	∈	∈	PROPN
ejpam-5958	315	11	e	e	NOUN
ejpam-5958	315	12	and	and	CCONJ
ejpam-5958	315	13	for	for	ADP
ejpam-5958	315	14	every	every	DET
ejpam-5958	315	15	t	t	NOUN
ejpam-5958	315	16	∈	∈	PROPN
ejpam-5958	315	17	k	k	PROPN
ejpam-5958	315	18	∈	∈	PROPN
ejpam-5958	315	19	k	k	NOUN
ejpam-5958	315	20	,	,	PUNCT
ejpam-5958	315	21	by	by	ADP
ejpam-5958	315	22	means	mean	NOUN
ejpam-5958	315	23	of	of	ADP
ejpam-5958	315	24	young	young	PROPN
ejpam-5958	315	25	’s	’s	PART
ejpam-5958	315	26	inequality	inequality	NOUN
ejpam-5958	315	27	,	,	PUNCT
ejpam-5958	315	28	we	we	PRON
ejpam-5958	315	29	get	get	VERB
ejpam-5958	315	30	:	:	PUNCT
ejpam-5958	315	31	|x(t)−	|x(t)−	X
ejpam-5958	315	32	y(t)|2	y(t)|2	PROPN
ejpam-5958	315	33	≤	≤	PROPN
ejpam-5958	315	34	(	(	PUNCT
ejpam-5958	315	35	|x(t)−	|x(t)−	PROPN
ejpam-5958	315	36	z(t)|+	z(t)|+	PROPN
ejpam-5958	316	1	|z(t)−	|z(t)−	PROPN
ejpam-5958	316	2	y(t)|)2	y(t)|)2	NOUN
ejpam-5958	316	3	≤	≤	ADV
ejpam-5958	316	4	2	2	NUM
ejpam-5958	316	5	(	(	PUNCT
ejpam-5958	316	6	|x(t)−	|x(t)−	X
ejpam-5958	316	7	z(t)|2	z(t)|2	PROPN
ejpam-5958	316	8	+	+	CCONJ
ejpam-5958	316	9	|z(t)−	|z(t)−	PROPN
ejpam-5958	316	10	y(t)|2	y(t)|2	PROPN
ejpam-5958	316	11	)	)	PUNCT
ejpam-5958	317	1	k.	k.	PROPN
ejpam-5958	317	2	nisse	nisse	PROPN
ejpam-5958	317	3	et	et	PROPN
ejpam-5958	317	4	al	al	PROPN
ejpam-5958	317	5	.	.	PUNCT
ejpam-5958	317	6	/	/	SYM
ejpam-5958	317	7	eur	eur	PROPN
ejpam-5958	317	8	.	.	PUNCT
ejpam-5958	318	1	j.	j.	PROPN
ejpam-5958	318	2	pure	pure	PROPN
ejpam-5958	318	3	appl	appl	PROPN
ejpam-5958	318	4	.	.	PROPN
ejpam-5958	318	5	math	math	PROPN
ejpam-5958	318	6	,	,	PUNCT
ejpam-5958	318	7	18	18	NUM
ejpam-5958	318	8	(	(	PUNCT
ejpam-5958	318	9	2	2	NUM
ejpam-5958	318	10	)	)	PUNCT
ejpam-5958	318	11	(	(	PUNCT
ejpam-5958	318	12	2025	2025	NUM
ejpam-5958	318	13	)	)	PUNCT
ejpam-5958	318	14	,	,	PUNCT
ejpam-5958	318	15	5958	5958	NUM
ejpam-5958	318	16	14	14	NUM
ejpam-5958	318	17	of	of	ADP
ejpam-5958	318	18	22	22	NUM
ejpam-5958	318	19	consequently	consequently	ADV
ejpam-5958	318	20	:	:	PUNCT
ejpam-5958	318	21	e−λt|x(t)−	e−λt|x(t)−	PROPN
ejpam-5958	318	22	y(t)|2	y(t)|2	PROPN
ejpam-5958	318	23	≤	≤	ADV
ejpam-5958	318	24	2	2	NUM
ejpam-5958	318	25	(	(	PUNCT
ejpam-5958	318	26	dk	dk	X
ejpam-5958	318	27	(	(	PUNCT
ejpam-5958	318	28	x	x	X
ejpam-5958	318	29	,	,	PUNCT
ejpam-5958	318	30	z	z	NOUN
ejpam-5958	318	31	)	)	PUNCT
ejpam-5958	319	1	+	+	CCONJ
ejpam-5958	319	2	dk	dk	PROPN
ejpam-5958	319	3	(	(	PUNCT
ejpam-5958	319	4	z	z	PROPN
ejpam-5958	319	5	,	,	PUNCT
ejpam-5958	319	6	y	y	NOUN
ejpam-5958	319	7	)	)	PUNCT
ejpam-5958	319	8	)	)	PUNCT
ejpam-5958	319	9	thus	thus	ADV
ejpam-5958	319	10	,	,	PUNCT
ejpam-5958	319	11	taking	take	VERB
ejpam-5958	319	12	the	the	DET
ejpam-5958	319	13	supremum	supremum	NOUN
ejpam-5958	319	14	over	over	ADP
ejpam-5958	319	15	k	k	PROPN
ejpam-5958	319	16	on	on	ADP
ejpam-5958	319	17	the	the	DET
ejpam-5958	319	18	left	left	ADJ
ejpam-5958	319	19	-	-	PUNCT
ejpam-5958	319	20	hand	hand	NOUN
ejpam-5958	319	21	side	side	NOUN
ejpam-5958	319	22	of	of	ADP
ejpam-5958	319	23	the	the	DET
ejpam-5958	319	24	above	above	ADJ
ejpam-5958	319	25	inequality	inequality	NOUN
ejpam-5958	319	26	,	,	PUNCT
ejpam-5958	319	27	we	we	PRON
ejpam-5958	319	28	obtain	obtain	VERB
ejpam-5958	319	29	condition	condition	NOUN
ejpam-5958	319	30	3	3	NUM
ejpam-5958	319	31	.	.	PUNCT
ejpam-5958	319	32	of	of	ADP
ejpam-5958	319	33	definition	definition	NOUN
ejpam-5958	319	34	2.1	2.1	NUM
ejpam-5958	319	35	.	.	PUNCT
ejpam-5958	320	1	let	let	VERB
ejpam-5958	320	2	w	w	X
ejpam-5958	320	3	:	:	PUNCT
ejpam-5958	320	4	k	k	X
ejpam-5958	320	5	−→	−→	NOUN
ejpam-5958	320	6	k	k	PROPN
ejpam-5958	320	7	be	be	VERB
ejpam-5958	320	8	the	the	DET
ejpam-5958	320	9	mapping	mapping	NOUN
ejpam-5958	320	10	defined	define	VERB
ejpam-5958	320	11	by	by	ADP
ejpam-5958	320	12	:	:	PUNCT
ejpam-5958	320	13	w(k	w(k	PROPN
ejpam-5958	320	14	)	)	PUNCT
ejpam-5958	320	15	=	=	PUNCT
ejpam-5958	321	1			PUNCT
ejpam-5958	321	2	k	k	NOUN
ejpam-5958	321	3	,	,	PUNCT
ejpam-5958	321	4	if	if	SCONJ
ejpam-5958	321	5	k	k	PROPN
ejpam-5958	321	6	⊂	⊂	PROPN
ejpam-5958	321	7	r−	r−	PROPN
ejpam-5958	321	8	=]	=]	PROPN
ejpam-5958	321	9	−∞	−∞	PROPN
ejpam-5958	321	10	,	,	PUNCT
ejpam-5958	321	11	0	0	NUM
ejpam-5958	321	12	]	]	PUNCT
ejpam-5958	321	13	,	,	PUNCT
ejpam-5958	321	14	[	[	X
ejpam-5958	321	15	0	0	NUM
ejpam-5958	321	16	,	,	PUNCT
ejpam-5958	321	17	k∗	k∗	PROPN
ejpam-5958	321	18	]	]	PUNCT
ejpam-5958	321	19	,	,	PUNCT
ejpam-5958	321	20	otherwise	otherwise	ADV
ejpam-5958	321	21	,	,	PUNCT
ejpam-5958	321	22	(	(	PUNCT
ejpam-5958	321	23	4.2	4.2	NUM
ejpam-5958	321	24	)	)	PUNCT
ejpam-5958	321	25	where	where	SCONJ
ejpam-5958	321	26	k∗	k∗	NOUN
ejpam-5958	321	27	=	=	PUNCT
ejpam-5958	321	28	supk	supk	PROPN
ejpam-5958	321	29	.	.	PUNCT
ejpam-5958	322	1	let	let	VERB
ejpam-5958	322	2	us	we	PRON
ejpam-5958	322	3	now	now	ADV
ejpam-5958	322	4	consider	consider	VERB
ejpam-5958	322	5	the	the	DET
ejpam-5958	322	6	following	follow	VERB
ejpam-5958	322	7	assumptions	assumption	NOUN
ejpam-5958	322	8	:	:	PUNCT
ejpam-5958	322	9	(	(	PUNCT
ejpam-5958	322	10	b1	b1	NOUN
ejpam-5958	322	11	)	)	PUNCT
ejpam-5958	322	12	f	f	PROPN
ejpam-5958	322	13	is	be	AUX
ejpam-5958	322	14	a	a	DET
ejpam-5958	322	15	positive	positive	ADJ
ejpam-5958	322	16	function	function	NOUN
ejpam-5958	322	17	,	,	PUNCT
ejpam-5958	322	18	non	non	ADJ
ejpam-5958	322	19	-	-	ADJ
ejpam-5958	322	20	decreasing	decrease	VERB
ejpam-5958	322	21	with	with	ADP
ejpam-5958	322	22	respect	respect	NOUN
ejpam-5958	322	23	to	to	ADP
ejpam-5958	322	24	the	the	DET
ejpam-5958	322	25	second	second	ADJ
ejpam-5958	322	26	and	and	CCONJ
ejpam-5958	322	27	third	third	ADJ
ejpam-5958	322	28	arguments	argument	NOUN
ejpam-5958	322	29	,	,	PUNCT
ejpam-5958	322	30	and	and	CCONJ
ejpam-5958	322	31	for	for	ADP
ejpam-5958	322	32	some	some	DET
ejpam-5958	322	33	real	real	ADV
ejpam-5958	322	34	valued	value	VERB
ejpam-5958	322	35	function	function	NOUN
ejpam-5958	322	36	w	w	ADP
ejpam-5958	322	37	defined	define	VERB
ejpam-5958	322	38	on	on	ADP
ejpam-5958	322	39	r+	r+	X
ejpam-5958	322	40	,	,	PUNCT
ejpam-5958	322	41	the	the	DET
ejpam-5958	322	42	following	follow	VERB
ejpam-5958	322	43	inequality	inequality	NOUN
ejpam-5958	322	44	holds	hold	VERB
ejpam-5958	322	45	:	:	PUNCT
ejpam-5958	322	46	|f	|f	PROPN
ejpam-5958	322	47	(	(	PUNCT
ejpam-5958	322	48	t	t	PROPN
ejpam-5958	322	49	,	,	PUNCT
ejpam-5958	322	50	x(t	x(t	PROPN
ejpam-5958	322	51	)	)	PUNCT
ejpam-5958	322	52	,	,	PUNCT
ejpam-5958	322	53	gx(t))−	gx(t))−	ADP
ejpam-5958	322	54	f	f	PROPN
ejpam-5958	322	55	(	(	PUNCT
ejpam-5958	322	56	t	t	PROPN
ejpam-5958	322	57	,	,	PUNCT
ejpam-5958	322	58	y(t	y(t	PROPN
ejpam-5958	322	59	)	)	PUNCT
ejpam-5958	322	60	,	,	PUNCT
ejpam-5958	322	61	gy(t))|	gy(t))|	VERB
ejpam-5958	322	62	≤	≤	ADV
ejpam-5958	322	63	√	√	NUM
ejpam-5958	322	64	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	322	65	,	,	PUNCT
ejpam-5958	322	66	y	y	NOUN
ejpam-5958	322	67	)	)	PUNCT
ejpam-5958	322	68	eλtw	eλtw	NOUN
ejpam-5958	322	69	(	(	PUNCT
ejpam-5958	322	70	t	t	NOUN
ejpam-5958	322	71	)	)	PUNCT
ejpam-5958	322	72	,	,	PUNCT
ejpam-5958	322	73	(	(	PUNCT
ejpam-5958	322	74	4.3	4.3	NUM
ejpam-5958	322	75	)	)	PUNCT
ejpam-5958	322	76	for	for	ADP
ejpam-5958	322	77	all	all	DET
ejpam-5958	322	78	x	x	NOUN
ejpam-5958	322	79	,	,	PUNCT
ejpam-5958	322	80	y	y	PROPN
ejpam-5958	322	81	∈	∈	PROPN
ejpam-5958	322	82	e	e	PROPN
ejpam-5958	322	83	,	,	PUNCT
ejpam-5958	322	84	t	t	PROPN
ejpam-5958	322	85	∈	∈	PROPN
ejpam-5958	322	86	k+	k+	NOUN
ejpam-5958	322	87	and	and	CCONJ
ejpam-5958	322	88	λ	λ	X
ejpam-5958	322	89	≥	≥	NOUN
ejpam-5958	322	90	0	0	NUM
ejpam-5958	322	91	.	.	PUNCT
ejpam-5958	323	1	(	(	PUNCT
ejpam-5958	323	2	b2	b2	NOUN
ejpam-5958	323	3	)	)	PUNCT
ejpam-5958	323	4	there	there	PRON
ejpam-5958	323	5	exist	exist	VERB
ejpam-5958	323	6	p	p	PRON
ejpam-5958	323	7	,	,	PUNCT
ejpam-5958	323	8	q	q	X
ejpam-5958	323	9	>	>	X
ejpam-5958	323	10	1	1	NUM
ejpam-5958	323	11	with	with	ADP
ejpam-5958	323	12	1	1	NUM
ejpam-5958	323	13	p	p	NOUN
ejpam-5958	323	14	+	+	NOUN
ejpam-5958	323	15	1	1	NUM
ejpam-5958	323	16	q	q	NOUN
ejpam-5958	323	17	=	=	SYM
ejpam-5958	323	18	1	1	NUM
ejpam-5958	323	19	,	,	PUNCT
ejpam-5958	323	20	µ	µ	X
ejpam-5958	323	21	>	>	X
ejpam-5958	323	22	1	1	NUM
ejpam-5958	323	23	such	such	ADJ
ejpam-5958	323	24	that	that	PRON
ejpam-5958	323	25	for	for	ADP
ejpam-5958	323	26	all	all	DET
ejpam-5958	323	27	λ	λ	PROPN
ejpam-5958	323	28	≥	≥	NOUN
ejpam-5958	323	29	0	0	NUM
ejpam-5958	323	30	,	,	PUNCT
ejpam-5958	323	31	the	the	DET
ejpam-5958	323	32	following	follow	VERB
ejpam-5958	323	33	hold	hold	NOUN
ejpam-5958	323	34	:	:	PUNCT
ejpam-5958	323	35	(	(	PUNCT
ejpam-5958	323	36	i	i	NOUN
ejpam-5958	323	37	)	)	PUNCT
ejpam-5958	323	38	rµ(λ	rµ(λ	NUM
ejpam-5958	323	39	)	)	PUNCT
ejpam-5958	323	40	:	:	PUNCT
ejpam-5958	324	1	=	=	PUNCT
ejpam-5958	324	2	∫	∫	PROPN
ejpam-5958	325	1	+	+	NUM
ejpam-5958	325	2	∞	∞	NOUN
ejpam-5958	325	3	0	0	PUNCT
ejpam-5958	325	4	e	e	NOUN
ejpam-5958	325	5	−pλτ	−pλτ	ADP
ejpam-5958	325	6	µ	µ	PROPN
ejpam-5958	325	7	w	w	NOUN
ejpam-5958	325	8	p	p	NOUN
ejpam-5958	325	9	2	2	NUM
ejpam-5958	325	10	(	(	PUNCT
ejpam-5958	325	11	τ	τ	NOUN
ejpam-5958	325	12	)	)	PUNCT
ejpam-5958	325	13	dτ	dτ	NOUN
ejpam-5958	325	14	<	<	X
ejpam-5958	325	15	∞	∞	PROPN
ejpam-5958	325	16	;	;	PUNCT
ejpam-5958	325	17	(	(	PUNCT
ejpam-5958	325	18	ii	ii	NOUN
ejpam-5958	325	19	)	)	PUNCT
ejpam-5958	325	20	∀t	∀t	PROPN
ejpam-5958	325	21	>	>	X
ejpam-5958	325	22	0	0	NUM
ejpam-5958	325	23	,	,	PUNCT
ejpam-5958	325	24	sµ,t(λ	sµ,t(λ	PROPN
ejpam-5958	325	25	)	)	PUNCT
ejpam-5958	325	26	:	:	PUNCT
ejpam-5958	326	1	=	=	SYM
ejpam-5958	326	2	∫	∫	PROPN
ejpam-5958	326	3	t	t	PROPN
ejpam-5958	326	4	0	0	NUM
ejpam-5958	326	5	gq(t	gq(t	X
ejpam-5958	326	6	,	,	PUNCT
ejpam-5958	326	7	τ)e	τ)e	PUNCT
ejpam-5958	326	8	−λq	−λq	NOUN
ejpam-5958	326	9	2	2	NUM
ejpam-5958	326	10	[	[	PUNCT
ejpam-5958	326	11	t−	t−	PROPN
ejpam-5958	326	12	(	(	PUNCT
ejpam-5958	326	13	µ+2	µ+2	PROPN
ejpam-5958	326	14	µ	µ	X
ejpam-5958	326	15	)	)	PUNCT
ejpam-5958	326	16	τ	τ	PROPN
ejpam-5958	326	17	]	]	X
ejpam-5958	326	18	dτ	dτ	X
ejpam-5958	326	19	<	<	X
ejpam-5958	326	20	∞	∞	PROPN
ejpam-5958	326	21	;	;	PUNCT
ejpam-5958	326	22	(	(	PUNCT
ejpam-5958	326	23	iii	iii	X
ejpam-5958	326	24	)	)	PUNCT
ejpam-5958	326	25	rµ(λ)sµ,t(λ	rµ(λ)sµ,t(λ	PROPN
ejpam-5958	326	26	)	)	PUNCT
ejpam-5958	326	27	−−−→	−−−→	PROPN
ejpam-5958	326	28	λ→∞	λ→∞	NUM
ejpam-5958	326	29	0	0	NUM
ejpam-5958	326	30	,	,	PUNCT
ejpam-5958	326	31	∀t	∀t	PROPN
ejpam-5958	326	32	>	>	X
ejpam-5958	326	33	0	0	NUM
ejpam-5958	326	34	.	.	PUNCT
ejpam-5958	326	35	(	(	PUNCT
ejpam-5958	326	36	b3	b3	PROPN
ejpam-5958	326	37	)	)	PUNCT
ejpam-5958	326	38	for	for	ADP
ejpam-5958	326	39	every	every	DET
ejpam-5958	326	40	x	x	PROPN
ejpam-5958	326	41	,	,	PUNCT
ejpam-5958	326	42	y	y	PROPN
ejpam-5958	326	43	∈	∈	PROPN
ejpam-5958	326	44	e	e	NOUN
ejpam-5958	326	45	such	such	ADJ
ejpam-5958	326	46	that	that	SCONJ
ejpam-5958	326	47	x(t	x(t	PROPN
ejpam-5958	326	48	)	)	PUNCT
ejpam-5958	326	49	=	=	SYM
ejpam-5958	326	50	y(t	y(t	PROPN
ejpam-5958	326	51	)	)	PUNCT
ejpam-5958	326	52	for	for	ADP
ejpam-5958	326	53	t	t	PROPN
ejpam-5958	326	54	≤	≤	NUM
ejpam-5958	326	55	0	0	NUM
ejpam-5958	326	56	,	,	PUNCT
ejpam-5958	326	57	if	if	SCONJ
ejpam-5958	326	58	x(t	x(t	NOUN
ejpam-5958	326	59	)	)	PUNCT
ejpam-5958	326	60	≤	≤	NUM
ejpam-5958	326	61	y(t	y(t	NUM
ejpam-5958	326	62	)	)	PUNCT
ejpam-5958	326	63	for	for	ADP
ejpam-5958	326	64	t	t	PROPN
ejpam-5958	326	65	>	>	X
ejpam-5958	326	66	0	0	NUM
ejpam-5958	326	67	,	,	PUNCT
ejpam-5958	326	68	then	then	ADV
ejpam-5958	326	69	gx(t	gx(t	NOUN
ejpam-5958	326	70	)	)	PUNCT
ejpam-5958	326	71	≤	≤	NOUN
ejpam-5958	326	72	gy(t	gy(t	PUNCT
ejpam-5958	326	73	)	)	PUNCT
ejpam-5958	326	74	.	.	PUNCT
ejpam-5958	327	1	theorem	theorem	NOUN
ejpam-5958	327	2	3	3	NUM
ejpam-5958	327	3	.	.	PUNCT
ejpam-5958	328	1	under	under	ADP
ejpam-5958	328	2	assumptions	assumption	NOUN
ejpam-5958	328	3	(	(	PUNCT
ejpam-5958	328	4	b1)-(b3	b1)-(b3	PROPN
ejpam-5958	328	5	)	)	PUNCT
ejpam-5958	328	6	,	,	PUNCT
ejpam-5958	328	7	the	the	DET
ejpam-5958	328	8	problem	problem	NOUN
ejpam-5958	328	9	(	(	PUNCT
ejpam-5958	328	10	4.1	4.1	NUM
ejpam-5958	328	11	)	)	PUNCT
ejpam-5958	328	12	has	have	VERB
ejpam-5958	328	13	at	at	ADP
ejpam-5958	328	14	last	last	ADJ
ejpam-5958	328	15	one	one	NUM
ejpam-5958	328	16	global	global	ADJ
ejpam-5958	328	17	solution	solution	NOUN
ejpam-5958	328	18	in	in	ADP
ejpam-5958	328	19	e.	e.	PROPN
ejpam-5958	328	20	proof	proof	PROPN
ejpam-5958	328	21	.	.	PUNCT
ejpam-5958	329	1	let	let	VERB
ejpam-5958	329	2	f	f	NOUN
ejpam-5958	329	3	:	:	PUNCT
ejpam-5958	330	1	e	e	X
ejpam-5958	330	2	−→	−→	NOUN
ejpam-5958	330	3	e	e	NOUN
ejpam-5958	330	4	be	be	VERB
ejpam-5958	330	5	the	the	DET
ejpam-5958	330	6	mapping	mapping	NOUN
ejpam-5958	330	7	defined	define	VERB
ejpam-5958	330	8	by	by	ADP
ejpam-5958	330	9	:	:	PUNCT
ejpam-5958	330	10	fx(t	fx(t	NUM
ejpam-5958	330	11	)	)	PUNCT
ejpam-5958	331	1	=	=	PUNCT
ejpam-5958	332	1			NUM
ejpam-5958	332	2	φ(0	φ(0	ADJ
ejpam-5958	332	3	)	)	PUNCT
ejpam-5958	333	1	+	+	NUM
ejpam-5958	333	2	∫	∫	PROPN
ejpam-5958	333	3	t	t	PROPN
ejpam-5958	333	4	0	0	NUM
ejpam-5958	333	5	g(t	g(t	PROPN
ejpam-5958	333	6	,	,	PUNCT
ejpam-5958	333	7	τ)f(τ	τ)f(τ	NUM
ejpam-5958	333	8	,	,	PUNCT
ejpam-5958	333	9	x(τ	x(τ	PROPN
ejpam-5958	333	10	)	)	PUNCT
ejpam-5958	333	11	,	,	PUNCT
ejpam-5958	333	12	gx(τ))dτ	gx(τ))dτ	PROPN
ejpam-5958	333	13	,	,	PUNCT
ejpam-5958	333	14	t	t	PROPN
ejpam-5958	333	15	>	>	X
ejpam-5958	333	16	0	0	NUM
ejpam-5958	333	17	φ(t	φ(t	PROPN
ejpam-5958	333	18	)	)	PUNCT
ejpam-5958	333	19	,	,	PUNCT
ejpam-5958	333	20	t	t	VERB
ejpam-5958	333	21	≤	≤	NUM
ejpam-5958	333	22	0	0	NUM
ejpam-5958	333	23	.	.	PUNCT
ejpam-5958	334	1	(	(	PUNCT
ejpam-5958	334	2	4.4	4.4	NUM
ejpam-5958	334	3	)	)	PUNCT
ejpam-5958	334	4	k.	k.	PROPN
ejpam-5958	334	5	nisse	nisse	PROPN
ejpam-5958	334	6	et	et	PROPN
ejpam-5958	334	7	al	al	PROPN
ejpam-5958	334	8	.	.	PUNCT
ejpam-5958	334	9	/	/	SYM
ejpam-5958	334	10	eur	eur	PROPN
ejpam-5958	334	11	.	.	PUNCT
ejpam-5958	335	1	j.	j.	PROPN
ejpam-5958	335	2	pure	pure	PROPN
ejpam-5958	335	3	appl	appl	PROPN
ejpam-5958	335	4	.	.	PROPN
ejpam-5958	335	5	math	math	PROPN
ejpam-5958	335	6	,	,	PUNCT
ejpam-5958	335	7	18	18	NUM
ejpam-5958	335	8	(	(	PUNCT
ejpam-5958	335	9	2	2	NUM
ejpam-5958	335	10	)	)	PUNCT
ejpam-5958	335	11	(	(	PUNCT
ejpam-5958	335	12	2025	2025	NUM
ejpam-5958	335	13	)	)	PUNCT
ejpam-5958	335	14	,	,	PUNCT
ejpam-5958	335	15	5958	5958	NUM
ejpam-5958	335	16	15	15	NUM
ejpam-5958	335	17	of	of	ADP
ejpam-5958	335	18	22	22	NUM
ejpam-5958	335	19	the	the	DET
ejpam-5958	335	20	solutions	solution	NOUN
ejpam-5958	335	21	of	of	ADP
ejpam-5958	335	22	(	(	PUNCT
ejpam-5958	335	23	4.1	4.1	NUM
ejpam-5958	335	24	)	)	PUNCT
ejpam-5958	335	25	are	be	AUX
ejpam-5958	335	26	the	the	DET
ejpam-5958	335	27	fixed	fix	VERB
ejpam-5958	335	28	points	point	NOUN
ejpam-5958	335	29	of	of	ADP
ejpam-5958	335	30	f	f	PROPN
ejpam-5958	335	31	.	.	PUNCT
ejpam-5958	336	1	let	let	VERB
ejpam-5958	336	2	α	α	NOUN
ejpam-5958	336	3	:	:	PUNCT
ejpam-5958	336	4	e×e	e×e	ADJ
ejpam-5958	336	5	−→	−→	NOUN
ejpam-5958	336	6	r+	r+	NOUN
ejpam-5958	336	7	be	be	AUX
ejpam-5958	336	8	the	the	DET
ejpam-5958	336	9	function	function	NOUN
ejpam-5958	336	10	defined	define	VERB
ejpam-5958	336	11	by	by	ADP
ejpam-5958	336	12	:	:	PUNCT
ejpam-5958	336	13	α(x	α(x	PROPN
ejpam-5958	336	14	,	,	PUNCT
ejpam-5958	336	15	y	y	PROPN
ejpam-5958	336	16	)	)	PUNCT
ejpam-5958	337	1	=	=	PUNCT
ejpam-5958	337	2			NOUN
ejpam-5958	337	3	1	1	NUM
ejpam-5958	337	4	:	:	PUNCT
ejpam-5958	337	5	x(t	x(t	PROPN
ejpam-5958	337	6	)	)	PUNCT
ejpam-5958	337	7	≤	≤	NUM
ejpam-5958	337	8	y(t	y(t	NUM
ejpam-5958	337	9	)	)	PUNCT
ejpam-5958	337	10	:	:	PUNCT
ejpam-5958	338	1	∀t	∀t	PROPN
ejpam-5958	338	2	>	>	X
ejpam-5958	338	3	0	0	PUNCT
ejpam-5958	338	4	and	and	CCONJ
ejpam-5958	338	5	x(t	x(t	PROPN
ejpam-5958	338	6	)	)	PUNCT
ejpam-5958	338	7	=	=	SYM
ejpam-5958	338	8	y(t	y(t	X
ejpam-5958	338	9	)	)	PUNCT
ejpam-5958	338	10	=	=	SYM
ejpam-5958	338	11	φ(t	φ(t	PROPN
ejpam-5958	338	12	)	)	PUNCT
ejpam-5958	338	13	:	:	PUNCT
ejpam-5958	339	1	t	t	VERB
ejpam-5958	339	2	≤	≤	NUM
ejpam-5958	339	3	0	0	NUM
ejpam-5958	339	4	0	0	NUM
ejpam-5958	339	5	:	:	PUNCT
ejpam-5958	339	6	otherwise	otherwise	ADV
ejpam-5958	339	7	.	.	PUNCT
ejpam-5958	340	1	let	let	VERB
ejpam-5958	340	2	us	we	PRON
ejpam-5958	340	3	check	check	VERB
ejpam-5958	340	4	the	the	DET
ejpam-5958	340	5	generalized	generalized	ADJ
ejpam-5958	340	6	(	(	PUNCT
ejpam-5958	340	7	αααν	αααν	NOUN
ejpam-5958	340	8	,	,	PUNCT
ejpam-5958	340	9	ψ	ψ	X
ejpam-5958	340	10	s	s	SYM
ejpam-5958	340	11	,	,	PUNCT
ejpam-5958	340	12	w	w	NOUN
ejpam-5958	340	13	)	)	PUNCT
ejpam-5958	340	14	contraction	contraction	NOUN
ejpam-5958	340	15	condition	condition	NOUN
ejpam-5958	340	16	(	(	PUNCT
ejpam-5958	340	17	3.2	3.2	NUM
ejpam-5958	340	18	)	)	PUNCT
ejpam-5958	340	19	,	,	PUNCT
ejpam-5958	340	20	where	where	SCONJ
ejpam-5958	340	21	{	{	PUNCT
ejpam-5958	340	22	αk}k∈k	αk}k∈k	X
ejpam-5958	340	23	=	=	SYM
ejpam-5958	340	24	{	{	PUNCT
ejpam-5958	340	25	α	α	NOUN
ejpam-5958	340	26	}	}	PUNCT
ejpam-5958	340	27	and	and	CCONJ
ejpam-5958	340	28	{	{	PUNCT
ejpam-5958	340	29	ψk}k∈k	ψk}k∈k	NOUN
ejpam-5958	340	30	is	be	AUX
ejpam-5958	340	31	the	the	DET
ejpam-5958	340	32	family	family	NOUN
ejpam-5958	340	33	of	of	ADP
ejpam-5958	340	34	functions	function	NOUN
ejpam-5958	340	35	ψk	ψk	VERB
ejpam-5958	340	36	defined	define	VERB
ejpam-5958	340	37	by	by	ADP
ejpam-5958	340	38	(	(	PUNCT
ejpam-5958	340	39	4.8	4.8	NUM
ejpam-5958	340	40	)	)	PUNCT
ejpam-5958	340	41	.	.	PUNCT
ejpam-5958	341	1	the	the	DET
ejpam-5958	341	2	following	following	ADJ
ejpam-5958	341	3	obvious	obvious	ADJ
ejpam-5958	341	4	fact	fact	NOUN
ejpam-5958	341	5	is	be	AUX
ejpam-5958	341	6	necessary	necessary	ADJ
ejpam-5958	341	7	for	for	ADP
ejpam-5958	341	8	the	the	DET
ejpam-5958	341	9	final	final	ADJ
ejpam-5958	341	10	conclusion	conclusion	NOUN
ejpam-5958	341	11	.	.	PUNCT
ejpam-5958	342	1	∀x	∀x	NUM
ejpam-5958	342	2	,	,	PUNCT
ejpam-5958	342	3	y	y	PROPN
ejpam-5958	342	4	∈	∈	PROPN
ejpam-5958	342	5	e	e	PROPN
ejpam-5958	342	6	s.t	s.t	PROPN
ejpam-5958	342	7	.	.	PROPN
ejpam-5958	342	8	α(x	α(x	PROPN
ejpam-5958	342	9	,	,	PUNCT
ejpam-5958	342	10	y	y	PROPN
ejpam-5958	342	11	)	)	PUNCT
ejpam-5958	342	12	=	=	SYM
ejpam-5958	342	13	0	0	NUM
ejpam-5958	342	14	,	,	PUNCT
ejpam-5958	342	15	α(x	α(x	NOUN
ejpam-5958	342	16	,	,	PUNCT
ejpam-5958	342	17	y	y	NOUN
ejpam-5958	342	18	)	)	PUNCT
ejpam-5958	342	19	dk(fx	dk(fx	PROPN
ejpam-5958	342	20	,	,	PUNCT
ejpam-5958	342	21	fy	fy	PROPN
ejpam-5958	342	22	)	)	PUNCT
ejpam-5958	342	23	=	=	SYM
ejpam-5958	342	24	0	0	NUM
ejpam-5958	342	25	,	,	PUNCT
ejpam-5958	342	26	∀k	∀k	NOUN
ejpam-5958	342	27	∈	∈	PROPN
ejpam-5958	342	28	k	k	X
ejpam-5958	342	29	(	(	PUNCT
ejpam-5958	342	30	4.5	4.5	NUM
ejpam-5958	342	31	)	)	PUNCT
ejpam-5958	342	32	let	let	VERB
ejpam-5958	342	33	now	now	ADV
ejpam-5958	342	34	x	x	NOUN
ejpam-5958	342	35	,	,	PUNCT
ejpam-5958	342	36	y	y	PROPN
ejpam-5958	342	37	∈	∈	PROPN
ejpam-5958	342	38	e	e	NOUN
ejpam-5958	342	39	such	such	ADJ
ejpam-5958	342	40	that	that	DET
ejpam-5958	342	41	α(x	α(x	NOUN
ejpam-5958	342	42	,	,	PUNCT
ejpam-5958	342	43	y	y	PROPN
ejpam-5958	342	44	)	)	PUNCT
ejpam-5958	342	45	=	=	SYM
ejpam-5958	343	1	1	1	X
ejpam-5958	343	2	.	.	X
ejpam-5958	343	3	for	for	ADP
ejpam-5958	343	4	k	k	PROPN
ejpam-5958	343	5	∈	∈	PROPN
ejpam-5958	343	6	k	k	PROPN
ejpam-5958	343	7	and	and	CCONJ
ejpam-5958	343	8	t	t	PROPN
ejpam-5958	343	9	∈	∈	PROPN
ejpam-5958	344	1	k	k	INTJ
ejpam-5958	344	2	such	such	ADJ
ejpam-5958	344	3	that	that	SCONJ
ejpam-5958	344	4	t	t	PROPN
ejpam-5958	344	5	≤	≤	NOUN
ejpam-5958	344	6	0	0	NUM
ejpam-5958	344	7	.	.	PUNCT
ejpam-5958	345	1	we	we	PRON
ejpam-5958	345	2	have	have	VERB
ejpam-5958	345	3	:	:	PUNCT
ejpam-5958	345	4	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	345	5	fy(t)|	fy(t)|	NOUN
ejpam-5958	345	6	=	=	SYM
ejpam-5958	345	7	|φ(t)−	|φ(t)−	X
ejpam-5958	345	8	φ(t)|	φ(t)|	NOUN
ejpam-5958	345	9	=	=	NOUN
ejpam-5958	345	10	0	0	X
ejpam-5958	345	11	.	.	PUNCT
ejpam-5958	346	1	hence	hence	ADV
ejpam-5958	346	2	,	,	PUNCT
ejpam-5958	346	3	for	for	ADP
ejpam-5958	346	4	all	all	DET
ejpam-5958	346	5	t	t	NOUN
ejpam-5958	346	6	∈	∈	PROPN
ejpam-5958	346	7	k	k	PRON
ejpam-5958	346	8	such	such	ADJ
ejpam-5958	346	9	that	that	SCONJ
ejpam-5958	346	10	t	t	PROPN
ejpam-5958	346	11	≤	≤	NOUN
ejpam-5958	346	12	0	0	NUM
ejpam-5958	347	1	we	we	PRON
ejpam-5958	347	2	have	have	VERB
ejpam-5958	347	3	e−λt	e−λt	NOUN
ejpam-5958	347	4	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	347	5	fy(t)|2	fy(t)|2	VERB
ejpam-5958	347	6	=	=	SYM
ejpam-5958	347	7	0	0	X
ejpam-5958	347	8	.	.	PUNCT
ejpam-5958	348	1	(	(	PUNCT
ejpam-5958	348	2	4.6	4.6	NUM
ejpam-5958	348	3	)	)	PUNCT
ejpam-5958	348	4	now	now	ADV
ejpam-5958	348	5	,	,	PUNCT
ejpam-5958	348	6	for	for	ADP
ejpam-5958	348	7	t	t	PROPN
ejpam-5958	348	8	∈	∈	PROPN
ejpam-5958	349	1	k	k	PRON
ejpam-5958	349	2	such	such	ADJ
ejpam-5958	349	3	that	that	SCONJ
ejpam-5958	349	4	t	t	PROPN
ejpam-5958	349	5	>	>	X
ejpam-5958	349	6	0	0	NUM
ejpam-5958	349	7	,	,	PUNCT
ejpam-5958	349	8	using	use	VERB
ejpam-5958	349	9	(	(	PUNCT
ejpam-5958	349	10	b1	b1	NOUN
ejpam-5958	349	11	)	)	PUNCT
ejpam-5958	349	12	we	we	PRON
ejpam-5958	349	13	obtain	obtain	VERB
ejpam-5958	349	14	:	:	PUNCT
ejpam-5958	349	15	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	349	16	fy(t)|	fy(t)|	ADJ
ejpam-5958	349	17	≤	≤	NUM
ejpam-5958	349	18	∫	∫	PROPN
ejpam-5958	349	19	t	t	PROPN
ejpam-5958	349	20	0	0	NUM
ejpam-5958	349	21	g(t	g(t	PROPN
ejpam-5958	349	22	,	,	PUNCT
ejpam-5958	349	23	τ	τ	PROPN
ejpam-5958	349	24	)	)	PUNCT
ejpam-5958	349	25	|f	|f	PROPN
ejpam-5958	349	26	(	(	PUNCT
ejpam-5958	349	27	τ	τ	PROPN
ejpam-5958	349	28	,	,	PUNCT
ejpam-5958	349	29	x(τ	x(τ	PROPN
ejpam-5958	349	30	)	)	PUNCT
ejpam-5958	349	31	,	,	PUNCT
ejpam-5958	349	32	gx(τ))−	gx(τ))−	NUM
ejpam-5958	349	33	f	f	X
ejpam-5958	349	34	(	(	PUNCT
ejpam-5958	349	35	τ	τ	PROPN
ejpam-5958	349	36	,	,	PUNCT
ejpam-5958	349	37	y(τ	y(τ	PROPN
ejpam-5958	349	38	)	)	PUNCT
ejpam-5958	349	39	,	,	PUNCT
ejpam-5958	349	40	gy(τ))|	gy(τ))|	PROPN
ejpam-5958	349	41	dτ	dτ	X
ejpam-5958	349	42	≤	≤	NUM
ejpam-5958	349	43	√	√	PROPN
ejpam-5958	349	44	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	349	45	,	,	PUNCT
ejpam-5958	349	46	y	y	PROPN
ejpam-5958	349	47	)	)	PUNCT
ejpam-5958	349	48	∫	∫	PROPN
ejpam-5958	350	1	t	t	PROPN
ejpam-5958	350	2	0	0	NUM
ejpam-5958	350	3	g(t	g(t	PROPN
ejpam-5958	350	4	,	,	PUNCT
ejpam-5958	350	5	τ	τ	X
ejpam-5958	350	6	)	)	PUNCT
ejpam-5958	350	7	√	√	NOUN
ejpam-5958	350	8	eλτw	eλτw	NOUN
ejpam-5958	350	9	(	(	PUNCT
ejpam-5958	350	10	τ	τ	NOUN
ejpam-5958	350	11	)	)	PUNCT
ejpam-5958	350	12	dτ	dτ	PROPN
ejpam-5958	350	13	.	.	PROPN
ejpam-5958	350	14	.	.	PUNCT
ejpam-5958	351	1	now	now	ADV
ejpam-5958	351	2	,	,	PUNCT
ejpam-5958	351	3	multiplying	multiply	VERB
ejpam-5958	351	4	the	the	DET
ejpam-5958	351	5	above	above	ADJ
ejpam-5958	351	6	inequality	inequality	NOUN
ejpam-5958	351	7	by	by	ADP
ejpam-5958	351	8	e−	e−	PROPN
ejpam-5958	351	9	λt	λt	ADP
ejpam-5958	351	10	2	2	NUM
ejpam-5958	351	11	,	,	PUNCT
ejpam-5958	351	12	we	we	PRON
ejpam-5958	351	13	get	get	VERB
ejpam-5958	351	14	:	:	PUNCT
ejpam-5958	351	15	e−	e−	PROPN
ejpam-5958	351	16	λt	λt	ADP
ejpam-5958	351	17	2	2	NUM
ejpam-5958	351	18	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	351	19	fy(t)|	fy(t)|	ADJ
ejpam-5958	351	20	≤	≤	NUM
ejpam-5958	351	21	√	√	NUM
ejpam-5958	351	22	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	351	23	,	,	PUNCT
ejpam-5958	351	24	y	y	PROPN
ejpam-5958	351	25	)	)	PUNCT
ejpam-5958	352	1	[	[	X
ejpam-5958	352	2	∫	∫	X
ejpam-5958	352	3	t	t	X
ejpam-5958	352	4	0	0	NUM
ejpam-5958	353	1	e−	e−	X
ejpam-5958	353	2	λt	λt	ADP
ejpam-5958	353	3	2	2	NUM
ejpam-5958	353	4	g(t	g(t	PROPN
ejpam-5958	353	5	,	,	PUNCT
ejpam-5958	353	6	τ	τ	X
ejpam-5958	353	7	)	)	PUNCT
ejpam-5958	353	8	e	e	NOUN
ejpam-5958	353	9	λτ	λτ	ADP
ejpam-5958	353	10	2	2	NUM
ejpam-5958	353	11	√	√	PROPN
ejpam-5958	353	12	w	w	PROPN
ejpam-5958	353	13	(	(	PUNCT
ejpam-5958	353	14	τ	τ	NOUN
ejpam-5958	353	15	)	)	PUNCT
ejpam-5958	353	16	dτ	dτ	NOUN
ejpam-5958	353	17	]	]	X
ejpam-5958	353	18	=	=	PUNCT
ejpam-5958	353	19	√	√	NUM
ejpam-5958	353	20	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	353	21	,	,	PUNCT
ejpam-5958	353	22	y	y	PROPN
ejpam-5958	353	23	)	)	PUNCT
ejpam-5958	354	1	[	[	X
ejpam-5958	354	2	∫	∫	X
ejpam-5958	354	3	t	t	X
ejpam-5958	354	4	0	0	NUM
ejpam-5958	355	1	e−	e−	X
ejpam-5958	355	2	λt	λt	ADP
ejpam-5958	355	3	2	2	NUM
ejpam-5958	355	4	g(t	g(t	PROPN
ejpam-5958	355	5	,	,	PUNCT
ejpam-5958	355	6	τ	τ	X
ejpam-5958	355	7	)	)	PUNCT
ejpam-5958	355	8	e	e	PROPN
ejpam-5958	355	9	λ(µ+2)τ	λ(µ+2)τ	NOUN
ejpam-5958	355	10	2µ	2µ	NUM
ejpam-5958	355	11	e	e	X
ejpam-5958	355	12	−λτ	−λτ	X
ejpam-5958	355	13	µ	µ	PROPN
ejpam-5958	355	14	√	√	PROPN
ejpam-5958	355	15	w	w	PROPN
ejpam-5958	355	16	(	(	PUNCT
ejpam-5958	355	17	τ	τ	PROPN
ejpam-5958	355	18	)	)	PUNCT
ejpam-5958	355	19	dτ	dτ	NOUN
ejpam-5958	355	20	,	,	PUNCT
ejpam-5958	355	21	]	]	X
ejpam-5958	355	22	2	2	NUM
ejpam-5958	355	23	,	,	PUNCT
ejpam-5958	355	24	where	where	SCONJ
ejpam-5958	355	25	µ	µ	NOUN
ejpam-5958	355	26	is	be	AUX
ejpam-5958	355	27	the	the	DET
ejpam-5958	355	28	constant	constant	ADJ
ejpam-5958	355	29	introduced	introduce	VERB
ejpam-5958	355	30	in	in	ADP
ejpam-5958	355	31	(	(	PUNCT
ejpam-5958	355	32	b2	b2	NOUN
ejpam-5958	355	33	)	)	PUNCT
ejpam-5958	355	34	.	.	PUNCT
ejpam-5958	356	1	in	in	ADP
ejpam-5958	356	2	view	view	NOUN
ejpam-5958	356	3	of	of	ADP
ejpam-5958	356	4	(	(	PUNCT
ejpam-5958	356	5	b2(i).(ii	b2(i).(ii	NOUN
ejpam-5958	356	6	)	)	PUNCT
ejpam-5958	356	7	)	)	PUNCT
ejpam-5958	356	8	,	,	PUNCT
ejpam-5958	356	9	hölder	hölder	PROPN
ejpam-5958	356	10	’s	’s	PART
ejpam-5958	356	11	inequality	inequality	NOUN
ejpam-5958	356	12	gives	give	VERB
ejpam-5958	356	13	:	:	PUNCT
ejpam-5958	356	14	e−	e−	PROPN
ejpam-5958	356	15	λt	λt	ADP
ejpam-5958	356	16	2	2	NUM
ejpam-5958	356	17	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	356	18	fy(t)|	fy(t)|	ADJ
ejpam-5958	356	19	≤	≤	NUM
ejpam-5958	356	20	√	√	NUM
ejpam-5958	356	21	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	356	22	,	,	PUNCT
ejpam-5958	356	23	y	y	PROPN
ejpam-5958	356	24	)	)	PUNCT
ejpam-5958	356	25	(	(	PUNCT
ejpam-5958	356	26	∫	∫	PROPN
ejpam-5958	356	27	t	t	PROPN
ejpam-5958	356	28	0	0	NUM
ejpam-5958	356	29	e	e	NOUN
ejpam-5958	356	30	−pλτ	−pλτ	ADP
ejpam-5958	356	31	µ	µ	PROPN
ejpam-5958	356	32	w	w	NOUN
ejpam-5958	356	33	p	p	NOUN
ejpam-5958	356	34	2	2	NUM
ejpam-5958	356	35	(	(	PUNCT
ejpam-5958	356	36	τ	τ	NOUN
ejpam-5958	356	37	)	)	PUNCT
ejpam-5958	356	38	dτ	dτ	NOUN
ejpam-5958	356	39	)	)	PUNCT
ejpam-5958	356	40	1	1	NUM
ejpam-5958	357	1	p	p	NOUN
ejpam-5958	357	2	×	×	NOUN
ejpam-5958	357	3	(	(	PUNCT
ejpam-5958	357	4	∫	∫	PROPN
ejpam-5958	357	5	t	t	PROPN
ejpam-5958	357	6	0	0	NUM
ejpam-5958	357	7	gq(t	gq(t	X
ejpam-5958	357	8	,	,	PUNCT
ejpam-5958	357	9	τ	τ	X
ejpam-5958	357	10	)	)	PUNCT
ejpam-5958	357	11	e	e	NOUN
ejpam-5958	357	12	−λq	−λq	NOUN
ejpam-5958	357	13	2	2	NUM
ejpam-5958	357	14	[	[	PUNCT
ejpam-5958	357	15	t−	t−	PROPN
ejpam-5958	357	16	(	(	PUNCT
ejpam-5958	357	17	µ+2	µ+2	PROPN
ejpam-5958	357	18	µ	µ	X
ejpam-5958	357	19	)	)	PUNCT
ejpam-5958	357	20	τ	τ	PROPN
ejpam-5958	357	21	]	]	X
ejpam-5958	357	22	dτ	dτ	NOUN
ejpam-5958	357	23	)	)	PUNCT
ejpam-5958	357	24	1	1	NUM
ejpam-5958	357	25	q	q	NOUN
ejpam-5958	357	26	=	=	NOUN
ejpam-5958	357	27	√	√	NUM
ejpam-5958	357	28	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	357	29	,	,	PUNCT
ejpam-5958	357	30	y)r	y)r	X
ejpam-5958	357	31	1	1	NUM
ejpam-5958	357	32	p	p	X
ejpam-5958	357	33	µ	µ	X
ejpam-5958	357	34	(	(	PUNCT
ejpam-5958	357	35	λ)s	λ)s	X
ejpam-5958	357	36	1	1	NUM
ejpam-5958	357	37	q	q	NOUN
ejpam-5958	357	38	µ,t(λ	µ,t(λ	NOUN
ejpam-5958	357	39	)	)	PUNCT
ejpam-5958	357	40	.	.	PUNCT
ejpam-5958	358	1	in	in	ADP
ejpam-5958	358	2	conclusion	conclusion	NOUN
ejpam-5958	358	3	,	,	PUNCT
ejpam-5958	358	4	for	for	ADP
ejpam-5958	358	5	all	all	DET
ejpam-5958	358	6	t	t	NOUN
ejpam-5958	358	7	∈	∈	PROPN
ejpam-5958	358	8	k	k	PRON
ejpam-5958	358	9	such	such	ADJ
ejpam-5958	358	10	that	that	SCONJ
ejpam-5958	358	11	t	t	PROPN
ejpam-5958	358	12	>	>	X
ejpam-5958	358	13	0	0	NUM
ejpam-5958	359	1	we	we	PRON
ejpam-5958	359	2	have	have	VERB
ejpam-5958	359	3	:	:	PUNCT
ejpam-5958	359	4	e−λt	e−λt	PROPN
ejpam-5958	359	5	|fx(t)−	|fx(t)−	PROPN
ejpam-5958	359	6	fy(t)|2	fy(t)|2	VERB
ejpam-5958	359	7	≤	≤	ADJ
ejpam-5958	359	8	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	359	9	,	,	PUNCT
ejpam-5958	359	10	y	y	NOUN
ejpam-5958	359	11	)	)	PUNCT
ejpam-5958	359	12	r	r	NOUN
ejpam-5958	359	13	2	2	NUM
ejpam-5958	359	14	p	p	NOUN
ejpam-5958	359	15	µ	µ	X
ejpam-5958	359	16	(	(	PUNCT
ejpam-5958	359	17	λ	λ	NOUN
ejpam-5958	359	18	)	)	PUNCT
ejpam-5958	359	19	s	s	PART
ejpam-5958	359	20	2	2	NUM
ejpam-5958	359	21	q	q	NOUN
ejpam-5958	359	22	µ,t(λ	µ,t(λ	NOUN
ejpam-5958	359	23	)	)	PUNCT
ejpam-5958	359	24	.	.	PUNCT
ejpam-5958	360	1	(	(	PUNCT
ejpam-5958	360	2	4.7	4.7	NUM
ejpam-5958	360	3	)	)	PUNCT
ejpam-5958	360	4	k.	k.	PROPN
ejpam-5958	360	5	nisse	nisse	PROPN
ejpam-5958	360	6	et	et	PROPN
ejpam-5958	360	7	al	al	PROPN
ejpam-5958	360	8	.	.	PUNCT
ejpam-5958	360	9	/	/	SYM
ejpam-5958	360	10	eur	eur	PROPN
ejpam-5958	360	11	.	.	PUNCT
ejpam-5958	361	1	j.	j.	PROPN
ejpam-5958	361	2	pure	pure	PROPN
ejpam-5958	361	3	appl	appl	PROPN
ejpam-5958	361	4	.	.	PROPN
ejpam-5958	361	5	math	math	PROPN
ejpam-5958	361	6	,	,	PUNCT
ejpam-5958	361	7	18	18	NUM
ejpam-5958	361	8	(	(	PUNCT
ejpam-5958	361	9	2	2	NUM
ejpam-5958	361	10	)	)	PUNCT
ejpam-5958	361	11	(	(	PUNCT
ejpam-5958	361	12	2025	2025	NUM
ejpam-5958	361	13	)	)	PUNCT
ejpam-5958	361	14	,	,	PUNCT
ejpam-5958	361	15	5958	5958	NUM
ejpam-5958	361	16	16	16	NUM
ejpam-5958	361	17	of	of	ADP
ejpam-5958	361	18	22	22	NUM
ejpam-5958	361	19	let	let	VERB
ejpam-5958	361	20	us	we	PRON
ejpam-5958	361	21	now	now	ADV
ejpam-5958	361	22	define	define	VERB
ejpam-5958	361	23	the	the	DET
ejpam-5958	361	24	function	function	NOUN
ejpam-5958	361	25	ψk	ψk	NOUN
ejpam-5958	361	26	:	:	PUNCT
ejpam-5958	361	27	r+	r+	NOUN
ejpam-5958	361	28	−→	−→	ADJ
ejpam-5958	361	29	r+	r+	NOUN
ejpam-5958	361	30	as	as	SCONJ
ejpam-5958	361	31	follows	follow	VERB
ejpam-5958	361	32	:	:	PUNCT
ejpam-5958	361	33	ψk(t	ψk(t	X
ejpam-5958	361	34	)	)	PUNCT
ejpam-5958	361	35	=	=	PUNCT
ejpam-5958	362	1			PUNCT
ejpam-5958	362	2	r	r	NOUN
ejpam-5958	362	3	2	2	NUM
ejpam-5958	362	4	p	p	NOUN
ejpam-5958	362	5	µ	µ	X
ejpam-5958	362	6	(	(	PUNCT
ejpam-5958	362	7	λ	λ	NOUN
ejpam-5958	362	8	)	)	PUNCT
ejpam-5958	362	9	s	s	PART
ejpam-5958	362	10	2	2	NUM
ejpam-5958	362	11	q	q	NOUN
ejpam-5958	362	12	µ,k∗(λ	µ,k∗(λ	NOUN
ejpam-5958	362	13	)	)	PUNCT
ejpam-5958	362	14	t	t	PROPN
ejpam-5958	362	15	,	,	PUNCT
ejpam-5958	362	16	k∗	k∗	VERB
ejpam-5958	362	17	>	>	X
ejpam-5958	362	18	0	0	NUM
ejpam-5958	362	19	0	0	NUM
ejpam-5958	362	20	,	,	PUNCT
ejpam-5958	362	21	k∗	k∗	VERB
ejpam-5958	362	22	≤	≤	NUM
ejpam-5958	362	23	0	0	NUM
ejpam-5958	362	24	,	,	PUNCT
ejpam-5958	362	25	(	(	PUNCT
ejpam-5958	362	26	4.8	4.8	NUM
ejpam-5958	362	27	)	)	PUNCT
ejpam-5958	362	28	where	where	SCONJ
ejpam-5958	362	29	,	,	PUNCT
ejpam-5958	362	30	thanks	thank	NOUN
ejpam-5958	362	31	to	to	ADP
ejpam-5958	362	32	(	(	PUNCT
ejpam-5958	362	33	b2(iii	b2(iii	X
ejpam-5958	362	34	)	)	PUNCT
ejpam-5958	362	35	)	)	PUNCT
ejpam-5958	363	1	λ	λ	NOUN
ejpam-5958	363	2	is	be	AUX
ejpam-5958	363	3	fixed	fix	VERB
ejpam-5958	363	4	such	such	ADJ
ejpam-5958	363	5	that	that	SCONJ
ejpam-5958	363	6	2r	2r	NUM
ejpam-5958	363	7	2	2	NUM
ejpam-5958	363	8	p	p	X
ejpam-5958	363	9	µ	µ	X
ejpam-5958	363	10	(	(	PUNCT
ejpam-5958	363	11	λ	λ	NOUN
ejpam-5958	363	12	)	)	PUNCT
ejpam-5958	363	13	s	s	PART
ejpam-5958	363	14	2	2	NUM
ejpam-5958	363	15	q	q	NOUN
ejpam-5958	363	16	µ,k∗(λ	µ,k∗(λ	NOUN
ejpam-5958	363	17	)	)	PUNCT
ejpam-5958	363	18	<	<	X
ejpam-5958	363	19	1	1	X
ejpam-5958	363	20	.	.	PUNCT
ejpam-5958	363	21	(	(	PUNCT
ejpam-5958	363	22	4.9	4.9	NUM
ejpam-5958	363	23	)	)	PUNCT
ejpam-5958	363	24	it	it	PRON
ejpam-5958	363	25	is	be	AUX
ejpam-5958	363	26	clear	clear	ADJ
ejpam-5958	363	27	that	that	SCONJ
ejpam-5958	363	28	ψk	ψk	DET
ejpam-5958	363	29	satisfies	satisfie	NOUN
ejpam-5958	363	30	(	(	PUNCT
ejpam-5958	363	31	ψs	ψs	NOUN
ejpam-5958	363	32	1	1	NUM
ejpam-5958	363	33	)	)	PUNCT
ejpam-5958	363	34	,	,	PUNCT
ejpam-5958	363	35	(	(	PUNCT
ejpam-5958	363	36	ψ	ψ	X
ejpam-5958	363	37	s	s	NOUN
ejpam-5958	363	38	2	2	NUM
ejpam-5958	363	39	)	)	PUNCT
ejpam-5958	363	40	and	and	CCONJ
ejpam-5958	363	41	(	(	PUNCT
ejpam-5958	363	42	ψs	ψs	NOUN
ejpam-5958	363	43	4	4	NUM
ejpam-5958	363	44	)	)	PUNCT
ejpam-5958	363	45	.	.	PUNCT
ejpam-5958	364	1	furthermore	furthermore	ADV
ejpam-5958	364	2	,	,	PUNCT
ejpam-5958	364	3	ψk(s	ψk(s	NUM
ejpam-5958	364	4	.	.	PUNCT
ejpam-5958	364	5	)	)	PUNCT
ejpam-5958	364	6	.	.	PUNCT
ejpam-5958	365	1	is	be	AUX
ejpam-5958	365	2	constant	constant	ADJ
ejpam-5958	365	3	,	,	PUNCT
ejpam-5958	365	4	thus	thus	ADV
ejpam-5958	365	5	non	non	ADJ
ejpam-5958	365	6	-	-	ADJ
ejpam-5958	365	7	decreasing	decrease	VERB
ejpam-5958	365	8	and	and	CCONJ
ejpam-5958	365	9	in	in	ADP
ejpam-5958	365	10	view	view	NOUN
ejpam-5958	365	11	of	of	ADP
ejpam-5958	365	12	(	(	PUNCT
ejpam-5958	365	13	4.9	4.9	NUM
ejpam-5958	365	14	)	)	PUNCT
ejpam-5958	365	15	,	,	PUNCT
ejpam-5958	365	16	it	it	PRON
ejpam-5958	365	17	satisfies	satisfy	VERB
ejpam-5958	365	18	also	also	ADV
ejpam-5958	365	19	ψk(2	ψk(2	PROPN
ejpam-5958	365	20	t	t	PROPN
ejpam-5958	365	21	)	)	PUNCT
ejpam-5958	365	22	<	<	X
ejpam-5958	365	23	t.	t.	X
ejpam-5958	365	24	consequently	consequently	ADV
ejpam-5958	365	25	,	,	PUNCT
ejpam-5958	365	26	according	accord	VERB
ejpam-5958	365	27	to	to	PART
ejpam-5958	365	28	remark	remark	NOUN
ejpam-5958	365	29	2.5	2.5	NUM
ejpam-5958	365	30	,	,	PUNCT
ejpam-5958	365	31	ψk	ψk	PRON
ejpam-5958	365	32	∈	∈	PROPN
ejpam-5958	365	33	ψs	ψs	NOUN
ejpam-5958	365	34	.	.	NOUN
ejpam-5958	366	1	combining	combine	VERB
ejpam-5958	366	2	(	(	PUNCT
ejpam-5958	366	3	4.6	4.6	NUM
ejpam-5958	366	4	)	)	PUNCT
ejpam-5958	366	5	and	and	CCONJ
ejpam-5958	366	6	(	(	PUNCT
ejpam-5958	366	7	4.7	4.7	NUM
ejpam-5958	366	8	)	)	PUNCT
ejpam-5958	366	9	taking	take	VERB
ejpam-5958	366	10	into	into	ADP
ejpam-5958	366	11	account	account	NOUN
ejpam-5958	366	12	(	(	PUNCT
ejpam-5958	366	13	4.8	4.8	NUM
ejpam-5958	366	14	)	)	PUNCT
ejpam-5958	366	15	,	,	PUNCT
ejpam-5958	366	16	leads	lead	VERB
ejpam-5958	366	17	to	to	ADP
ejpam-5958	366	18	∀x	∀x	NUM
ejpam-5958	366	19	,	,	PUNCT
ejpam-5958	366	20	y	y	PROPN
ejpam-5958	366	21	∈	∈	PROPN
ejpam-5958	366	22	e	e	PROPN
ejpam-5958	366	23	s.t	s.t	PROPN
ejpam-5958	366	24	.	.	PROPN
ejpam-5958	366	25	α(x	α(x	PROPN
ejpam-5958	366	26	,	,	PUNCT
ejpam-5958	366	27	y	y	PROPN
ejpam-5958	366	28	)	)	PUNCT
ejpam-5958	366	29	=	=	SYM
ejpam-5958	366	30	1	1	NUM
ejpam-5958	366	31	,	,	PUNCT
ejpam-5958	366	32	α(x	α(x	NOUN
ejpam-5958	366	33	,	,	PUNCT
ejpam-5958	366	34	y	y	NOUN
ejpam-5958	366	35	)	)	PUNCT
ejpam-5958	366	36	dk(fx	dk(fx	PROPN
ejpam-5958	366	37	,	,	PUNCT
ejpam-5958	366	38	fy	fy	PROPN
ejpam-5958	366	39	)	)	PUNCT
ejpam-5958	366	40	≤	≤	NOUN
ejpam-5958	366	41	ψk	ψk	PROPN
ejpam-5958	366	42	(	(	PUNCT
ejpam-5958	366	43	dw(k)(x	dw(k)(x	PROPN
ejpam-5958	366	44	,	,	PUNCT
ejpam-5958	366	45	y	y	PROPN
ejpam-5958	366	46	)	)	PUNCT
ejpam-5958	366	47	)	)	PUNCT
ejpam-5958	366	48	,	,	PUNCT
ejpam-5958	367	1	∀k	∀k	X
ejpam-5958	367	2	∈	∈	PROPN
ejpam-5958	367	3	k.	k.	PROPN
ejpam-5958	367	4	(	(	PUNCT
ejpam-5958	367	5	4.10	4.10	NUM
ejpam-5958	367	6	)	)	PUNCT
ejpam-5958	367	7	now	now	ADV
ejpam-5958	367	8	,	,	PUNCT
ejpam-5958	367	9	(	(	PUNCT
ejpam-5958	367	10	3.2	3.2	NUM
ejpam-5958	367	11	)	)	PUNCT
ejpam-5958	367	12	follows	follow	VERB
ejpam-5958	367	13	immediately	immediately	ADV
ejpam-5958	367	14	from	from	ADP
ejpam-5958	367	15	(	(	PUNCT
ejpam-5958	367	16	4.5	4.5	NUM
ejpam-5958	367	17	)	)	PUNCT
ejpam-5958	367	18	and	and	CCONJ
ejpam-5958	367	19	(	(	PUNCT
ejpam-5958	367	20	4.10	4.10	NUM
ejpam-5958	367	21	)	)	PUNCT
ejpam-5958	367	22	.	.	PUNCT
ejpam-5958	368	1	in	in	ADP
ejpam-5958	368	2	other	other	ADJ
ejpam-5958	368	3	means	mean	NOUN
ejpam-5958	368	4	,	,	PUNCT
ejpam-5958	368	5	f	f	PROPN
ejpam-5958	368	6	is	be	AUX
ejpam-5958	368	7	a	a	DET
ejpam-5958	368	8	generalized	generalized	ADJ
ejpam-5958	368	9	(	(	PUNCT
ejpam-5958	368	10	αααν	αααν	NOUN
ejpam-5958	368	11	,	,	PUNCT
ejpam-5958	368	12	ψ	ψ	X
ejpam-5958	368	13	s	s	SYM
ejpam-5958	368	14	,	,	PUNCT
ejpam-5958	368	15	w	w	NOUN
ejpam-5958	368	16	)	)	PUNCT
ejpam-5958	368	17	contraction	contraction	NOUN
ejpam-5958	368	18	.	.	PUNCT
ejpam-5958	369	1	condition	condition	NOUN
ejpam-5958	369	2	(	(	PUNCT
ejpam-5958	369	3	i	i	NOUN
ejpam-5958	369	4	):	):	PUNCT
ejpam-5958	369	5	let	let	VERB
ejpam-5958	369	6	(	(	PUNCT
ejpam-5958	369	7	x	x	NOUN
ejpam-5958	369	8	,	,	PUNCT
ejpam-5958	369	9	y	y	NOUN
ejpam-5958	369	10	)	)	PUNCT
ejpam-5958	369	11	∈	∈	PROPN
ejpam-5958	370	1	e	e	X
ejpam-5958	370	2	×	×	NOUN
ejpam-5958	370	3	e	e	ADP
ejpam-5958	370	4	such	such	ADJ
ejpam-5958	370	5	that	that	DET
ejpam-5958	370	6	α(x	α(x	PROPN
ejpam-5958	370	7	,	,	PUNCT
ejpam-5958	370	8	y	y	PROPN
ejpam-5958	370	9	)	)	PUNCT
ejpam-5958	370	10	≥	≥	NOUN
ejpam-5958	370	11	1	1	NUM
ejpam-5958	370	12	.	.	PUNCT
ejpam-5958	370	13	then	then	ADV
ejpam-5958	370	14	for	for	ADP
ejpam-5958	370	15	t	t	PROPN
ejpam-5958	370	16	>	>	X
ejpam-5958	370	17	0	0	PROPN
ejpam-5958	370	18	,	,	PUNCT
ejpam-5958	370	19	we	we	PRON
ejpam-5958	370	20	have	have	VERB
ejpam-5958	370	21	x(t	x(t	NOUN
ejpam-5958	370	22	)	)	PUNCT
ejpam-5958	370	23	≤	≤	NUM
ejpam-5958	370	24	y(t	y(t	NUM
ejpam-5958	370	25	)	)	PUNCT
ejpam-5958	370	26	,	,	PUNCT
ejpam-5958	370	27	which	which	PRON
ejpam-5958	370	28	implies	imply	VERB
ejpam-5958	370	29	according	accord	VERB
ejpam-5958	370	30	to	to	ADP
ejpam-5958	370	31	(	(	PUNCT
ejpam-5958	370	32	b3	b3	PROPN
ejpam-5958	370	33	)	)	PUNCT
ejpam-5958	370	34	that	that	SCONJ
ejpam-5958	370	35	gx(t	gx(t	NOUN
ejpam-5958	370	36	)	)	PUNCT
ejpam-5958	370	37	≤	≤	NOUN
ejpam-5958	370	38	gy(t	gy(t	PUNCT
ejpam-5958	370	39	)	)	PUNCT
ejpam-5958	370	40	.	.	PUNCT
ejpam-5958	371	1	the	the	DET
ejpam-5958	371	2	following	follow	VERB
ejpam-5958	371	3	inequality	inequality	NOUN
ejpam-5958	371	4	follows	follow	VERB
ejpam-5958	371	5	so	so	ADV
ejpam-5958	371	6	for	for	ADP
ejpam-5958	371	7	t	t	PROPN
ejpam-5958	371	8	>	>	X
ejpam-5958	371	9	0	0	PROPN
ejpam-5958	371	10	,	,	PUNCT
ejpam-5958	371	11	from	from	ADP
ejpam-5958	371	12	the	the	DET
ejpam-5958	371	13	fact	fact	NOUN
ejpam-5958	371	14	that	that	SCONJ
ejpam-5958	371	15	f	f	PROPN
ejpam-5958	371	16	is	be	AUX
ejpam-5958	371	17	non	non	ADJ
ejpam-5958	371	18	-	-	ADJ
ejpam-5958	371	19	decreasing	decrease	VERB
ejpam-5958	371	20	with	with	ADP
ejpam-5958	371	21	respect	respect	NOUN
ejpam-5958	371	22	to	to	ADP
ejpam-5958	371	23	the	the	DET
ejpam-5958	371	24	second	second	ADJ
ejpam-5958	371	25	and	and	CCONJ
ejpam-5958	371	26	third	third	ADJ
ejpam-5958	371	27	arguments∫	arguments∫	NOUN
ejpam-5958	371	28	t	t	X
ejpam-5958	371	29	0	0	NUM
ejpam-5958	371	30	g(t	g(t	PROPN
ejpam-5958	371	31	,	,	PUNCT
ejpam-5958	371	32	τ)f(τ	τ)f(τ	NUM
ejpam-5958	371	33	,	,	PUNCT
ejpam-5958	371	34	x(τ	x(τ	PROPN
ejpam-5958	371	35	)	)	PUNCT
ejpam-5958	371	36	,	,	PUNCT
ejpam-5958	371	37	gx(τ))dτ	gx(τ))dτ	PROPN
ejpam-5958	371	38	≤	≤	NUM
ejpam-5958	372	1	∫	∫	PROPN
ejpam-5958	372	2	t	t	PROPN
ejpam-5958	372	3	0	0	NUM
ejpam-5958	372	4	g(t	g(t	PROPN
ejpam-5958	372	5	,	,	PUNCT
ejpam-5958	372	6	τ)f(τ	τ)f(τ	NOUN
ejpam-5958	372	7	,	,	PUNCT
ejpam-5958	372	8	y(τ	y(τ	PROPN
ejpam-5958	372	9	)	)	PUNCT
ejpam-5958	372	10	,	,	PUNCT
ejpam-5958	372	11	gy(τ))dτ	gy(τ))dτ	NOUN
ejpam-5958	372	12	,	,	PUNCT
ejpam-5958	372	13	which	which	PRON
ejpam-5958	372	14	clearly	clearly	ADV
ejpam-5958	372	15	leads	lead	VERB
ejpam-5958	372	16	to	to	ADP
ejpam-5958	372	17	fx(t	fx(t	NOUN
ejpam-5958	372	18	)	)	PUNCT
ejpam-5958	372	19	≤	≤	NOUN
ejpam-5958	372	20	fy(t	fy(t	NOUN
ejpam-5958	372	21	)	)	PUNCT
ejpam-5958	372	22	for	for	ADP
ejpam-5958	372	23	t	t	PROPN
ejpam-5958	372	24	>	>	X
ejpam-5958	372	25	0	0	X
ejpam-5958	372	26	.	.	PUNCT
ejpam-5958	373	1	on	on	ADP
ejpam-5958	373	2	the	the	DET
ejpam-5958	373	3	other	other	ADJ
ejpam-5958	373	4	hand	hand	NOUN
ejpam-5958	373	5	,	,	PUNCT
ejpam-5958	373	6	from	from	ADP
ejpam-5958	373	7	(	(	PUNCT
ejpam-5958	373	8	4.4	4.4	NUM
ejpam-5958	373	9	)	)	PUNCT
ejpam-5958	373	10	,	,	PUNCT
ejpam-5958	373	11	we	we	PRON
ejpam-5958	373	12	have	have	VERB
ejpam-5958	373	13	fx(t	fx(t	NOUN
ejpam-5958	373	14	)	)	PUNCT
ejpam-5958	373	15	=	=	SYM
ejpam-5958	373	16	fy(t	fy(t	X
ejpam-5958	373	17	)	)	PUNCT
ejpam-5958	373	18	=	=	SYM
ejpam-5958	373	19	φ(t	φ(t	PROPN
ejpam-5958	373	20	)	)	PUNCT
ejpam-5958	373	21	for	for	ADP
ejpam-5958	373	22	t	t	NOUN
ejpam-5958	373	23	≤	≤	NUM
ejpam-5958	373	24	0	0	NUM
ejpam-5958	373	25	.	.	PUNCT
ejpam-5958	374	1	that	that	PRON
ejpam-5958	374	2	is	be	AUX
ejpam-5958	374	3	α(fx	α(fx	PROPN
ejpam-5958	374	4	,	,	PUNCT
ejpam-5958	374	5	fy	fy	PROPN
ejpam-5958	374	6	)	)	PUNCT
ejpam-5958	374	7	≥	≥	NOUN
ejpam-5958	374	8	1	1	NUM
ejpam-5958	374	9	,	,	PUNCT
ejpam-5958	374	10	and	and	CCONJ
ejpam-5958	374	11	consequently	consequently	ADV
ejpam-5958	374	12	(	(	PUNCT
ejpam-5958	374	13	c1	c1	NOUN
ejpam-5958	374	14	)	)	PUNCT
ejpam-5958	374	15	is	be	AUX
ejpam-5958	374	16	satisfied	satisfied	ADJ
ejpam-5958	374	17	.	.	PUNCT
ejpam-5958	375	1	condition	condition	NOUN
ejpam-5958	375	2	(	(	PUNCT
ejpam-5958	375	3	ii	ii	NOUN
ejpam-5958	375	4	):	):	PUNCT
ejpam-5958	375	5	let	let	VERB
ejpam-5958	375	6	x0	x0	PROPN
ejpam-5958	375	7	∈	∈	PROPN
ejpam-5958	375	8	e	e	X
ejpam-5958	375	9	be	be	VERB
ejpam-5958	375	10	the	the	DET
ejpam-5958	375	11	function	function	NOUN
ejpam-5958	375	12	defined	define	VERB
ejpam-5958	375	13	by	by	ADP
ejpam-5958	375	14	:	:	PUNCT
ejpam-5958	375	15	x0(t	x0(t	NUM
ejpam-5958	375	16	)	)	PUNCT
ejpam-5958	375	17	=	=	PUNCT
ejpam-5958	376	1			PRON
ejpam-5958	376	2	φ(0	φ(0	ADJ
ejpam-5958	376	3	)	)	PUNCT
ejpam-5958	376	4	,	,	PUNCT
ejpam-5958	376	5	if	if	SCONJ
ejpam-5958	376	6	t	t	PROPN
ejpam-5958	376	7	>	>	X
ejpam-5958	376	8	0	0	NUM
ejpam-5958	376	9	φ(t	φ(t	PROPN
ejpam-5958	376	10	)	)	PUNCT
ejpam-5958	376	11	,	,	PUNCT
ejpam-5958	376	12	if	if	SCONJ
ejpam-5958	376	13	t	t	NOUN
ejpam-5958	376	14	≤	≤	NOUN
ejpam-5958	376	15	0	0	NUM
ejpam-5958	376	16	.	.	PUNCT
ejpam-5958	377	1	since	since	SCONJ
ejpam-5958	377	2	f	f	PROPN
ejpam-5958	377	3	is	be	AUX
ejpam-5958	377	4	positive	positive	ADJ
ejpam-5958	377	5	,	,	PUNCT
ejpam-5958	377	6	then	then	ADV
ejpam-5958	377	7	:	:	PUNCT
ejpam-5958	377	8	∫	∫	PROPN
ejpam-5958	377	9	t	t	PROPN
ejpam-5958	377	10	0	0	NUM
ejpam-5958	377	11	g(t	g(t	PROPN
ejpam-5958	377	12	,	,	PUNCT
ejpam-5958	377	13	τ)f(τ	τ)f(τ	NUM
ejpam-5958	377	14	,	,	PUNCT
ejpam-5958	377	15	x0(τ	x0(τ	X
ejpam-5958	377	16	)	)	PUNCT
ejpam-5958	377	17	,	,	PUNCT
ejpam-5958	377	18	gx0(τ))dτ	gx0(τ))dτ	VERB
ejpam-5958	377	19	≥	≥	NOUN
ejpam-5958	377	20	0	0	NUM
ejpam-5958	377	21	.	.	PUNCT
ejpam-5958	378	1	hence	hence	ADV
ejpam-5958	378	2	,	,	PUNCT
ejpam-5958	378	3	for	for	ADP
ejpam-5958	378	4	t	t	PROPN
ejpam-5958	378	5	>	>	X
ejpam-5958	378	6	0	0	PROPN
ejpam-5958	378	7	,	,	PUNCT
ejpam-5958	378	8	we	we	PRON
ejpam-5958	378	9	have	have	VERB
ejpam-5958	378	10	:	:	PUNCT
ejpam-5958	378	11	x0(t	x0(t	NUM
ejpam-5958	378	12	)	)	PUNCT
ejpam-5958	378	13	=	=	SYM
ejpam-5958	378	14	φ(0	φ(0	ADJ
ejpam-5958	378	15	)	)	PUNCT
ejpam-5958	378	16	≤	≤	PUNCT
ejpam-5958	378	17	φ(0	φ(0	PROPN
ejpam-5958	378	18	)	)	PUNCT
ejpam-5958	379	1	+	+	NUM
ejpam-5958	379	2	∫	∫	PROPN
ejpam-5958	379	3	t	t	PROPN
ejpam-5958	379	4	0	0	NUM
ejpam-5958	379	5	g(t	g(t	PROPN
ejpam-5958	379	6	,	,	PUNCT
ejpam-5958	379	7	τ)f(τ	τ)f(τ	NUM
ejpam-5958	379	8	,	,	PUNCT
ejpam-5958	379	9	x0(τ	x0(τ	X
ejpam-5958	379	10	)	)	PUNCT
ejpam-5958	379	11	,	,	PUNCT
ejpam-5958	379	12	gx0(τ))dτ	gx0(τ))dτ	NOUN
ejpam-5958	379	13	=	=	SYM
ejpam-5958	379	14	fx0(t	fx0(t	PROPN
ejpam-5958	379	15	)	)	PUNCT
ejpam-5958	379	16	,	,	PUNCT
ejpam-5958	379	17	k.	k.	PROPN
ejpam-5958	379	18	nisse	nisse	PROPN
ejpam-5958	379	19	et	et	PROPN
ejpam-5958	379	20	al	al	PROPN
ejpam-5958	379	21	.	.	PUNCT
ejpam-5958	379	22	/	/	SYM
ejpam-5958	379	23	eur	eur	PROPN
ejpam-5958	379	24	.	.	PUNCT
ejpam-5958	380	1	j.	j.	PROPN
ejpam-5958	380	2	pure	pure	PROPN
ejpam-5958	380	3	appl	appl	PROPN
ejpam-5958	380	4	.	.	PROPN
ejpam-5958	380	5	math	math	PROPN
ejpam-5958	380	6	,	,	PUNCT
ejpam-5958	380	7	18	18	NUM
ejpam-5958	380	8	(	(	PUNCT
ejpam-5958	380	9	2	2	NUM
ejpam-5958	380	10	)	)	PUNCT
ejpam-5958	380	11	(	(	PUNCT
ejpam-5958	380	12	2025	2025	NUM
ejpam-5958	380	13	)	)	PUNCT
ejpam-5958	380	14	,	,	PUNCT
ejpam-5958	380	15	5958	5958	NUM
ejpam-5958	380	16	17	17	NUM
ejpam-5958	380	17	of	of	ADP
ejpam-5958	380	18	22	22	NUM
ejpam-5958	380	19	and	and	CCONJ
ejpam-5958	380	20	for	for	ADP
ejpam-5958	380	21	t	t	PROPN
ejpam-5958	380	22	≤	≤	NUM
ejpam-5958	380	23	0	0	NUM
ejpam-5958	380	24	,	,	PUNCT
ejpam-5958	380	25	fx0(t	fx0(t	NUM
ejpam-5958	380	26	)	)	PUNCT
ejpam-5958	380	27	=	=	SYM
ejpam-5958	380	28	φ(t	φ(t	PROPN
ejpam-5958	380	29	)	)	PUNCT
ejpam-5958	380	30	=	=	PUNCT
ejpam-5958	380	31	x0(t	x0(t	PROPN
ejpam-5958	380	32	)	)	PUNCT
ejpam-5958	380	33	.	.	PUNCT
ejpam-5958	381	1	that	that	PRON
ejpam-5958	381	2	is	be	AUX
ejpam-5958	381	3	α(x0	α(x0	ADJ
ejpam-5958	381	4	,	,	PUNCT
ejpam-5958	381	5	fx0	fx0	PROPN
ejpam-5958	381	6	)	)	PUNCT
ejpam-5958	381	7	≥	≥	NOUN
ejpam-5958	382	1	1	1	NUM
ejpam-5958	382	2	.	.	PUNCT
ejpam-5958	383	1	furthermore	furthermore	ADV
ejpam-5958	383	2	,	,	PUNCT
ejpam-5958	383	3	we	we	PRON
ejpam-5958	383	4	have	have	VERB
ejpam-5958	383	5	:	:	PUNCT
ejpam-5958	383	6	dwi(k)(x	dwi(k)(x	NOUN
ejpam-5958	383	7	0	0	NUM
ejpam-5958	383	8	,	,	PUNCT
ejpam-5958	383	9	fx0	fx0	NOUN
ejpam-5958	383	10	)	)	PUNCT
ejpam-5958	383	11	=	=	SYM
ejpam-5958	383	12	dw(k)(x	dw(k)(x	NOUN
ejpam-5958	383	13	0	0	NUM
ejpam-5958	383	14	,	,	PUNCT
ejpam-5958	383	15	fx0	fx0	NOUN
ejpam-5958	383	16	)	)	PUNCT
ejpam-5958	383	17	=	=	SYM
ejpam-5958	383	18	sup	sup	NOUN
ejpam-5958	383	19	t∈[0,k∗	t∈[0,k∗	PROPN
ejpam-5958	383	20	]	]	X
ejpam-5958	383	21	e−λt	e−λt	NOUN
ejpam-5958	383	22	∣∣x0(t)−	∣∣x0(t)−	PROPN
ejpam-5958	383	23	fx0(t	fx0(t	PROPN
ejpam-5958	383	24	)	)	PUNCT
ejpam-5958	383	25	∣∣2	∣∣2	PROPN
ejpam-5958	383	26	<	<	X
ejpam-5958	383	27	∞	∞	PROPN
ejpam-5958	383	28	,	,	PUNCT
ejpam-5958	383	29	for	for	ADP
ejpam-5958	383	30	all	all	PRON
ejpam-5958	383	31	i	i	PRON
ejpam-5958	383	32	∈	∈	PROPN
ejpam-5958	383	33	n.	n.	NOUN
ejpam-5958	383	34	consequently	consequently	ADV
ejpam-5958	383	35	(	(	PUNCT
ejpam-5958	383	36	pc2	pc2	NOUN
ejpam-5958	383	37	)	)	PUNCT
ejpam-5958	383	38	is	be	AUX
ejpam-5958	383	39	satisfied	satisfied	ADJ
ejpam-5958	383	40	.	.	PUNCT
ejpam-5958	384	1	note	note	VERB
ejpam-5958	384	2	also	also	ADV
ejpam-5958	384	3	that	that	SCONJ
ejpam-5958	384	4	:	:	PUNCT
ejpam-5958	384	5	∀k	∀k	X
ejpam-5958	384	6	∈	∈	PROPN
ejpam-5958	384	7	k	k	PROPN
ejpam-5958	384	8	,	,	PUNCT
ejpam-5958	384	9	∀t	∀t	PROPN
ejpam-5958	384	10	>	>	X
ejpam-5958	384	11	0	0	NUM
ejpam-5958	384	12	:	:	PUNCT
ejpam-5958	384	13	ψk(t	ψk(t	X
ejpam-5958	384	14	)	)	PUNCT
ejpam-5958	384	15	=	=	SYM
ejpam-5958	384	16	ψwi(k)(t	ψwi(k)(t	NUM
ejpam-5958	384	17	)	)	PUNCT
ejpam-5958	384	18	,	,	PUNCT
ejpam-5958	384	19	for	for	ADP
ejpam-5958	384	20	all	all	PRON
ejpam-5958	384	21	i	i	PRON
ejpam-5958	384	22	∈	∈	PROPN
ejpam-5958	384	23	n∗	n∗	PROPN
ejpam-5958	384	24	,	,	PUNCT
ejpam-5958	384	25	and	and	CCONJ
ejpam-5958	384	26	so	so	ADV
ejpam-5958	384	27	(	(	PUNCT
ejpam-5958	384	28	c3	c3	NOUN
ejpam-5958	384	29	)	)	PUNCT
ejpam-5958	384	30	is	be	AUX
ejpam-5958	384	31	satisfied	satisfied	ADJ
ejpam-5958	384	32	with	with	ADP
ejpam-5958	384	33	ψ̃k	ψ̃k	ADJ
ejpam-5958	384	34	=	=	SYM
ejpam-5958	384	35	ψk	ψk	NOUN
ejpam-5958	384	36	.	.	PUNCT
ejpam-5958	385	1	let	let	VERB
ejpam-5958	385	2	{	{	PUNCT
ejpam-5958	385	3	xn}n∈n	xn}n∈n	PART
ejpam-5958	385	4	be	be	AUX
ejpam-5958	385	5	a	a	DET
ejpam-5958	385	6	sequence	sequence	NOUN
ejpam-5958	385	7	of	of	ADP
ejpam-5958	385	8	e	e	NOUN
ejpam-5958	385	9	such	such	ADJ
ejpam-5958	385	10	that	that	SCONJ
ejpam-5958	385	11	:	:	PUNCT
ejpam-5958	385	12	α(xn	α(xn	NOUN
ejpam-5958	385	13	,	,	PUNCT
ejpam-5958	385	14	xn+1	xn+1	NUM
ejpam-5958	385	15	)	)	PUNCT
ejpam-5958	385	16	≥	≥	NOUN
ejpam-5958	385	17	1	1	NUM
ejpam-5958	385	18	,	,	PUNCT
ejpam-5958	385	19	∀n	∀n	SYM
ejpam-5958	385	20	∈	∈	PROPN
ejpam-5958	385	21	n.	n.	NOUN
ejpam-5958	385	22	that	that	PRON
ejpam-5958	385	23	is	be	AUX
ejpam-5958	385	24	:	:	PUNCT
ejpam-5958	385	25	xn(t	xn(t	X
ejpam-5958	385	26	)	)	PUNCT
ejpam-5958	385	27	≤	≤	NUM
ejpam-5958	385	28	xn+1(t	xn+1(t	PROPN
ejpam-5958	385	29	)	)	PUNCT
ejpam-5958	385	30	,	,	PUNCT
ejpam-5958	385	31	for	for	ADP
ejpam-5958	385	32	all	all	DET
ejpam-5958	385	33	t	t	NOUN
ejpam-5958	385	34	>	>	X
ejpam-5958	385	35	0	0	PUNCT
ejpam-5958	385	36	and	and	CCONJ
ejpam-5958	385	37	xn(t	xn(t	NUM
ejpam-5958	385	38	)	)	PUNCT
ejpam-5958	385	39	=	=	SYM
ejpam-5958	386	1	xn+1(t	xn+1(t	PROPN
ejpam-5958	386	2	)	)	PUNCT
ejpam-5958	386	3	=	=	SYM
ejpam-5958	386	4	φ(t	φ(t	PROPN
ejpam-5958	386	5	)	)	PUNCT
ejpam-5958	386	6	for	for	ADP
ejpam-5958	386	7	all	all	DET
ejpam-5958	386	8	t	t	NOUN
ejpam-5958	386	9	≤	≤	NUM
ejpam-5958	386	10	0	0	NUM
ejpam-5958	386	11	.	.	PUNCT
ejpam-5958	387	1	(	(	PUNCT
ejpam-5958	387	2	4.11	4.11	NUM
ejpam-5958	387	3	)	)	PUNCT
ejpam-5958	387	4	suppose	suppose	VERB
ejpam-5958	387	5	now	now	ADV
ejpam-5958	387	6	that	that	SCONJ
ejpam-5958	387	7	{	{	PUNCT
ejpam-5958	387	8	xn}n∈n	xn}n∈n	PUNCT
ejpam-5958	387	9	converges	converge	VERB
ejpam-5958	387	10	to	to	ADP
ejpam-5958	387	11	some	some	DET
ejpam-5958	387	12	x	x	SYM
ejpam-5958	387	13	∈	∈	PROPN
ejpam-5958	387	14	e	e	NOUN
ejpam-5958	387	15	,	,	PUNCT
ejpam-5958	387	16	that	that	PRON
ejpam-5958	387	17	is	be	AUX
ejpam-5958	387	18	:	:	PUNCT
ejpam-5958	387	19	∀k	∀k	NOUN
ejpam-5958	387	20	∈	∈	PROPN
ejpam-5958	387	21	k	k	NOUN
ejpam-5958	387	22	,	,	PUNCT
ejpam-5958	387	23	sup	sup	NOUN
ejpam-5958	387	24	t∈k	t∈k	NOUN
ejpam-5958	387	25	{	{	PUNCT
ejpam-5958	387	26	e−λt	e−λt	NOUN
ejpam-5958	387	27	|xn(t)−	|xn(t)−	PROPN
ejpam-5958	387	28	x(t)|2	x(t)|2	PROPN
ejpam-5958	387	29	−−−→	−−−→	VERB
ejpam-5958	387	30	n→∞	n→∞	NUM
ejpam-5958	387	31	0	0	NUM
ejpam-5958	387	32	,	,	PUNCT
ejpam-5958	387	33	}	}	PUNCT
ejpam-5958	387	34	,	,	PUNCT
ejpam-5958	387	35	which	which	PRON
ejpam-5958	387	36	implies	imply	VERB
ejpam-5958	387	37	that	that	SCONJ
ejpam-5958	387	38	∀t	∀t	PROPN
ejpam-5958	387	39	∈	∈	PROPN
ejpam-5958	387	40	r	r	NOUN
ejpam-5958	387	41	,	,	PUNCT
ejpam-5958	387	42	{	{	PUNCT
ejpam-5958	387	43	xn(t)}n∈n	xn(t)}n∈n	X
ejpam-5958	387	44	converges	converge	VERB
ejpam-5958	387	45	to	to	ADP
ejpam-5958	387	46	x(t	x(t	PROPN
ejpam-5958	387	47	)	)	PUNCT
ejpam-5958	387	48	in	in	ADP
ejpam-5958	387	49	r.	r.	PROPN
ejpam-5958	387	50	hence	hence	ADV
ejpam-5958	387	51	,	,	PUNCT
ejpam-5958	387	52	according	accord	VERB
ejpam-5958	387	53	to	to	ADP
ejpam-5958	387	54	(	(	PUNCT
ejpam-5958	387	55	4.11	4.11	NUM
ejpam-5958	387	56	)	)	PUNCT
ejpam-5958	387	57	,	,	PUNCT
ejpam-5958	387	58	{	{	PUNCT
ejpam-5958	387	59	xn(t)}n∈n	xn(t)}n∈n	NOUN
ejpam-5958	387	60	is	be	AUX
ejpam-5958	387	61	a	a	DET
ejpam-5958	387	62	non	non	ADJ
ejpam-5958	387	63	-	-	ADJ
ejpam-5958	387	64	decreasing	decrease	VERB
ejpam-5958	387	65	real	real	ADJ
ejpam-5958	387	66	sequence	sequence	NOUN
ejpam-5958	387	67	for	for	ADP
ejpam-5958	387	68	t	t	PROPN
ejpam-5958	387	69	>	>	X
ejpam-5958	387	70	0	0	PUNCT
ejpam-5958	388	1	and	and	CCONJ
ejpam-5958	388	2	therefore	therefore	ADV
ejpam-5958	388	3	for	for	ADP
ejpam-5958	388	4	all	all	PRON
ejpam-5958	388	5	n	n	PRON
ejpam-5958	388	6	∈	∈	NOUN
ejpam-5958	388	7	n	n	CCONJ
ejpam-5958	388	8	:	:	PUNCT
ejpam-5958	388	9	xn(t	xn(t	NUM
ejpam-5958	388	10	)	)	PUNCT
ejpam-5958	388	11	≤	≤	NUM
ejpam-5958	388	12	x(t	x(t	PROPN
ejpam-5958	388	13	)	)	PUNCT
ejpam-5958	388	14	,	,	PUNCT
ejpam-5958	388	15	∀t	∀t	PROPN
ejpam-5958	388	16	>	>	X
ejpam-5958	388	17	0	0	NUM
ejpam-5958	388	18	and	and	CCONJ
ejpam-5958	388	19	xn(t	xn(t	NUM
ejpam-5958	388	20	)	)	PUNCT
ejpam-5958	388	21	=	=	SYM
ejpam-5958	388	22	x(t	x(t	PROPN
ejpam-5958	388	23	)	)	PUNCT
ejpam-5958	388	24	=	=	SYM
ejpam-5958	388	25	φ(t	φ(t	PROPN
ejpam-5958	388	26	)	)	PUNCT
ejpam-5958	388	27	,	,	PUNCT
ejpam-5958	388	28	∀t	∀t	PROPN
ejpam-5958	388	29	≤	≤	ADV
ejpam-5958	388	30	0	0	NUM
ejpam-5958	388	31	.	.	PUNCT
ejpam-5958	389	1	this	this	PRON
ejpam-5958	389	2	means	mean	VERB
ejpam-5958	389	3	that	that	SCONJ
ejpam-5958	389	4	α(xn	α(xn	NOUN
ejpam-5958	389	5	,	,	PUNCT
ejpam-5958	389	6	x	x	X
ejpam-5958	389	7	)	)	PUNCT
ejpam-5958	389	8	≥	≥	NOUN
ejpam-5958	389	9	1	1	NUM
ejpam-5958	389	10	for	for	ADP
ejpam-5958	389	11	all	all	PRON
ejpam-5958	389	12	n	n	PRON
ejpam-5958	389	13	∈	∈	NOUN
ejpam-5958	389	14	n	n	NOUN
ejpam-5958	389	15	and	and	CCONJ
ejpam-5958	389	16	consequently	consequently	ADV
ejpam-5958	389	17	(	(	PUNCT
ejpam-5958	389	18	pc4	pc4	NOUN
ejpam-5958	389	19	)	)	PUNCT
ejpam-5958	389	20	is	be	AUX
ejpam-5958	389	21	satisfied	satisfied	ADJ
ejpam-5958	389	22	.	.	PUNCT
ejpam-5958	390	1	then	then	ADV
ejpam-5958	390	2	,	,	PUNCT
ejpam-5958	390	3	all	all	DET
ejpam-5958	390	4	conditions	condition	NOUN
ejpam-5958	390	5	of	of	ADP
ejpam-5958	390	6	corollary	corollary	ADJ
ejpam-5958	390	7	3.6	3.6	NUM
ejpam-5958	390	8	are	be	AUX
ejpam-5958	390	9	fulfilled	fulfil	VERB
ejpam-5958	390	10	and	and	CCONJ
ejpam-5958	390	11	the	the	DET
ejpam-5958	390	12	proof	proof	NOUN
ejpam-5958	390	13	is	be	AUX
ejpam-5958	390	14	complete	complete	ADJ
ejpam-5958	390	15	.	.	PUNCT
ejpam-5958	391	1	the	the	DET
ejpam-5958	391	2	following	follow	VERB
ejpam-5958	391	3	corollary	corollary	NOUN
ejpam-5958	391	4	illustrates	illustrate	VERB
ejpam-5958	391	5	the	the	DET
ejpam-5958	391	6	efficiency	efficiency	NOUN
ejpam-5958	391	7	of	of	ADP
ejpam-5958	391	8	theorem	theorem	NOUN
ejpam-5958	391	9	3	3	NUM
ejpam-5958	391	10	in	in	ADP
ejpam-5958	391	11	the	the	DET
ejpam-5958	391	12	study	study	NOUN
ejpam-5958	391	13	of	of	ADP
ejpam-5958	391	14	some	some	DET
ejpam-5958	391	15	fractional	fractional	ADJ
ejpam-5958	391	16	differential	differential	ADJ
ejpam-5958	391	17	equations	equation	NOUN
ejpam-5958	391	18	with	with	ADP
ejpam-5958	391	19	”	"	PUNCT
ejpam-5958	391	20	maxima	maxima	NOUN
ejpam-5958	391	21	”	"	PUNCT
ejpam-5958	391	22	,	,	PUNCT
ejpam-5958	391	23	namely:cdδx(t	namely:cdδx(t	PROPN
ejpam-5958	391	24	)	)	PUNCT
ejpam-5958	392	1	=	=	SYM
ejpam-5958	392	2	f	f	PROPN
ejpam-5958	392	3	(	(	PUNCT
ejpam-5958	392	4	t	t	PROPN
ejpam-5958	392	5	,	,	PUNCT
ejpam-5958	392	6	x(t	x(t	PROPN
ejpam-5958	392	7	)	)	PUNCT
ejpam-5958	392	8	,	,	PUNCT
ejpam-5958	392	9	max	max	PROPN
ejpam-5958	392	10	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	392	11	)	)	PUNCT
ejpam-5958	392	12	,	,	PUNCT
ejpam-5958	392	13	b(t	b(t	PROPN
ejpam-5958	392	14	)	)	PUNCT
ejpam-5958	392	15	]	]	PUNCT
ejpam-5958	392	16	x	x	X
ejpam-5958	392	17	(	(	PUNCT
ejpam-5958	392	18	σ	σ	NOUN
ejpam-5958	392	19	)	)	PUNCT
ejpam-5958	392	20	)	)	PUNCT
ejpam-5958	392	21	,	,	PUNCT
ejpam-5958	392	22	t	t	X
ejpam-5958	392	23	>	>	X
ejpam-5958	392	24	0	0	PUNCT
ejpam-5958	393	1	x(t	x(t	PROPN
ejpam-5958	393	2	)	)	PUNCT
ejpam-5958	393	3	=	=	SYM
ejpam-5958	393	4	φ(t	φ(t	PROPN
ejpam-5958	393	5	)	)	PUNCT
ejpam-5958	393	6	,	,	PUNCT
ejpam-5958	393	7	t	t	VERB
ejpam-5958	393	8	≤	≤	NUM
ejpam-5958	393	9	0	0	NUM
ejpam-5958	393	10	,	,	PUNCT
ejpam-5958	393	11	(	(	PUNCT
ejpam-5958	393	12	4.12	4.12	NUM
ejpam-5958	393	13	)	)	PUNCT
ejpam-5958	393	14	where	where	SCONJ
ejpam-5958	393	15	cdδ	cdδ	NOUN
ejpam-5958	393	16	denotes	denote	VERB
ejpam-5958	393	17	the	the	DET
ejpam-5958	393	18	caputo	caputo	PROPN
ejpam-5958	393	19	fractional	fractional	PROPN
ejpam-5958	393	20	derivative	derivative	ADJ
ejpam-5958	393	21	operator	operator	NOUN
ejpam-5958	393	22	of	of	ADP
ejpam-5958	393	23	order	order	NOUN
ejpam-5958	393	24	δ	δ	X
ejpam-5958	393	25	∈	∈	PROPN
ejpam-5958	393	26	]	]	X
ejpam-5958	393	27	0	0	NUM
ejpam-5958	393	28	,	,	PUNCT
ejpam-5958	393	29	1	1	NUM
ejpam-5958	393	30	[	[	X
ejpam-5958	393	31	,	,	PUNCT
ejpam-5958	393	32	a	a	DET
ejpam-5958	393	33	,	,	PUNCT
ejpam-5958	393	34	b	b	NOUN
ejpam-5958	393	35	,	,	PUNCT
ejpam-5958	393	36	are	be	AUX
ejpam-5958	393	37	real	real	ADJ
ejpam-5958	393	38	continuous	continuous	ADJ
ejpam-5958	393	39	functions	function	NOUN
ejpam-5958	393	40	defined	define	VERB
ejpam-5958	393	41	on	on	ADP
ejpam-5958	393	42	r+	r+	NOUN
ejpam-5958	393	43	such	such	ADJ
ejpam-5958	393	44	that	that	SCONJ
ejpam-5958	393	45	a(t	a(t	NOUN
ejpam-5958	393	46	)	)	PUNCT
ejpam-5958	393	47	≤	≤	NUM
ejpam-5958	393	48	b(t	b(t	NOUN
ejpam-5958	393	49	)	)	PUNCT
ejpam-5958	393	50	≤	≤	NOUN
ejpam-5958	393	51	t	t	NOUN
ejpam-5958	393	52	,	,	PUNCT
ejpam-5958	393	53	f	f	PROPN
ejpam-5958	393	54	:	:	PUNCT
ejpam-5958	393	55	r+	r+	NOUN
ejpam-5958	393	56	×	×	NOUN
ejpam-5958	393	57	r2	r2	NOUN
ejpam-5958	393	58	−→	−→	NOUN
ejpam-5958	393	59	r	r	NOUN
ejpam-5958	393	60	is	be	AUX
ejpam-5958	393	61	a	a	DET
ejpam-5958	393	62	nonlinear	nonlinear	ADJ
ejpam-5958	393	63	continuous	continuous	ADJ
ejpam-5958	393	64	function	function	NOUN
ejpam-5958	393	65	and	and	CCONJ
ejpam-5958	393	66	φ	φ	NOUN
ejpam-5958	393	67	:	:	PUNCT
ejpam-5958	393	68	]	]	X
ejpam-5958	393	69	−∞	−∞	NOUN
ejpam-5958	393	70	,	,	PUNCT
ejpam-5958	393	71	0	0	NUM
ejpam-5958	393	72	]	]	X
ejpam-5958	393	73	−→	−→	NOUN
ejpam-5958	393	74	r	r	NOUN
ejpam-5958	393	75	is	be	AUX
ejpam-5958	393	76	a	a	DET
ejpam-5958	393	77	continuous	continuous	ADJ
ejpam-5958	393	78	function	function	NOUN
ejpam-5958	393	79	.	.	PUNCT
ejpam-5958	394	1	corollary	corollary	ADJ
ejpam-5958	394	2	4.1	4.1	NUM
ejpam-5958	394	3	.	.	PUNCT
ejpam-5958	395	1	assume	assume	VERB
ejpam-5958	395	2	that	that	SCONJ
ejpam-5958	395	3	the	the	DET
ejpam-5958	395	4	following	follow	VERB
ejpam-5958	395	5	conditions	condition	NOUN
ejpam-5958	395	6	hold	hold	VERB
ejpam-5958	395	7	:	:	PUNCT
ejpam-5958	396	1	k.	k.	PROPN
ejpam-5958	396	2	nisse	nisse	PROPN
ejpam-5958	396	3	et	et	PROPN
ejpam-5958	396	4	al	al	PROPN
ejpam-5958	396	5	.	.	PUNCT
ejpam-5958	396	6	/	/	SYM
ejpam-5958	396	7	eur	eur	PROPN
ejpam-5958	396	8	.	.	PUNCT
ejpam-5958	397	1	j.	j.	PROPN
ejpam-5958	397	2	pure	pure	PROPN
ejpam-5958	397	3	appl	appl	PROPN
ejpam-5958	397	4	.	.	PROPN
ejpam-5958	397	5	math	math	PROPN
ejpam-5958	397	6	,	,	PUNCT
ejpam-5958	397	7	18	18	NUM
ejpam-5958	397	8	(	(	PUNCT
ejpam-5958	397	9	2	2	NUM
ejpam-5958	397	10	)	)	PUNCT
ejpam-5958	397	11	(	(	PUNCT
ejpam-5958	397	12	2025	2025	NUM
ejpam-5958	397	13	)	)	PUNCT
ejpam-5958	397	14	,	,	PUNCT
ejpam-5958	397	15	5958	5958	NUM
ejpam-5958	397	16	18	18	NUM
ejpam-5958	397	17	of	of	ADP
ejpam-5958	397	18	22	22	NUM
ejpam-5958	397	19	(	(	PUNCT
ejpam-5958	397	20	h1	h1	PROPN
ejpam-5958	397	21	)	)	PUNCT
ejpam-5958	397	22	f	f	PROPN
ejpam-5958	397	23	is	be	AUX
ejpam-5958	397	24	a	a	DET
ejpam-5958	397	25	positive	positive	ADJ
ejpam-5958	397	26	function	function	NOUN
ejpam-5958	397	27	and	and	CCONJ
ejpam-5958	397	28	non	non	ADJ
ejpam-5958	397	29	-	-	ADJ
ejpam-5958	397	30	decreasing	decrease	VERB
ejpam-5958	397	31	with	with	ADP
ejpam-5958	397	32	respect	respect	NOUN
ejpam-5958	397	33	to	to	ADP
ejpam-5958	397	34	the	the	DET
ejpam-5958	397	35	second	second	ADJ
ejpam-5958	397	36	and	and	CCONJ
ejpam-5958	397	37	third	third	ADJ
ejpam-5958	397	38	arguments	argument	NOUN
ejpam-5958	397	39	,	,	PUNCT
ejpam-5958	397	40	such	such	ADJ
ejpam-5958	397	41	that	that	SCONJ
ejpam-5958	397	42	(	(	PUNCT
ejpam-5958	397	43	i	i	NOUN
ejpam-5958	397	44	)	)	PUNCT
ejpam-5958	397	45	|f	|f	PROPN
ejpam-5958	397	46	(	(	PUNCT
ejpam-5958	397	47	t	t	PROPN
ejpam-5958	397	48	,	,	PUNCT
ejpam-5958	397	49	ξ1	ξ1	NOUN
ejpam-5958	397	50	,	,	PUNCT
ejpam-5958	397	51	η1)−	η1)−	PROPN
ejpam-5958	397	52	f	f	X
ejpam-5958	397	53	(	(	PUNCT
ejpam-5958	397	54	t	t	PROPN
ejpam-5958	397	55	,	,	PUNCT
ejpam-5958	397	56	ξ2	ξ2	NOUN
ejpam-5958	397	57	,	,	PUNCT
ejpam-5958	397	58	η2)|	η2)|	PROPN
ejpam-5958	397	59	≤	≤	NUM
ejpam-5958	397	60	√	√	ADP
ejpam-5958	397	61	υ	υ	PROPN
ejpam-5958	397	62	(	(	PUNCT
ejpam-5958	397	63	t	t	PROPN
ejpam-5958	397	64	,	,	PUNCT
ejpam-5958	397	65	|ξ1	|ξ1	NOUN
ejpam-5958	397	66	−	−	NUM
ejpam-5958	397	67	ξ2|2	ξ2|2	NUM
ejpam-5958	397	68	,	,	PUNCT
ejpam-5958	397	69	|η1	|η1	VERB
ejpam-5958	397	70	−	−	PROPN
ejpam-5958	397	71	η2|2	η2|2	PROPN
ejpam-5958	397	72	)	)	PUNCT
ejpam-5958	397	73	,	,	PUNCT
ejpam-5958	397	74	whenever	whenever	SCONJ
ejpam-5958	397	75	the	the	DET
ejpam-5958	397	76	left	left	ADJ
ejpam-5958	397	77	hand	hand	NOUN
ejpam-5958	397	78	side	side	NOUN
ejpam-5958	397	79	is	be	AUX
ejpam-5958	397	80	defined	define	VERB
ejpam-5958	397	81	;	;	PUNCT
ejpam-5958	397	82	(	(	PUNCT
ejpam-5958	397	83	ii	ii	NOUN
ejpam-5958	397	84	)	)	PUNCT
ejpam-5958	397	85	υ	υ	NOUN
ejpam-5958	397	86	:	:	PUNCT
ejpam-5958	397	87	r3	r3	NOUN
ejpam-5958	397	88	+	+	CCONJ
ejpam-5958	397	89	−→	−→	ADJ
ejpam-5958	397	90	r+	r+	NOUN
ejpam-5958	397	91	is	be	AUX
ejpam-5958	397	92	a	a	DET
ejpam-5958	397	93	non	non	ADJ
ejpam-5958	397	94	-	-	ADJ
ejpam-5958	397	95	decreasing	decrease	VERB
ejpam-5958	397	96	function	function	NOUN
ejpam-5958	397	97	with	with	ADP
ejpam-5958	397	98	respect	respect	NOUN
ejpam-5958	397	99	to	to	ADP
ejpam-5958	397	100	the	the	DET
ejpam-5958	397	101	second	second	ADJ
ejpam-5958	397	102	and	and	CCONJ
ejpam-5958	397	103	third	third	ADJ
ejpam-5958	397	104	arguments	argument	NOUN
ejpam-5958	397	105	;	;	PUNCT
ejpam-5958	397	106	(	(	PUNCT
ejpam-5958	397	107	iii	iii	X
ejpam-5958	397	108	)	)	PUNCT
ejpam-5958	397	109	there	there	PRON
ejpam-5958	397	110	exists	exist	VERB
ejpam-5958	397	111	a	a	DET
ejpam-5958	397	112	real	real	ADV
ejpam-5958	397	113	valued	value	VERB
ejpam-5958	397	114	function	function	NOUN
ejpam-5958	397	115	w	w	ADP
ejpam-5958	397	116	defined	define	VERB
ejpam-5958	397	117	on	on	ADP
ejpam-5958	397	118	r+	r+	NOUN
ejpam-5958	397	119	,	,	PUNCT
ejpam-5958	397	120	such	such	ADJ
ejpam-5958	397	121	that	that	SCONJ
ejpam-5958	397	122	:	:	PUNCT
ejpam-5958	397	123	∀z	∀z	X
ejpam-5958	397	124	≥	≥	NOUN
ejpam-5958	397	125	0	0	NUM
ejpam-5958	397	126	:	:	PUNCT
ejpam-5958	397	127	υ	υ	X
ejpam-5958	397	128	(	(	PUNCT
ejpam-5958	397	129	.	.	PUNCT
ejpam-5958	397	130	,	,	PUNCT
ejpam-5958	397	131	z	z	X
ejpam-5958	397	132	,	,	PUNCT
ejpam-5958	397	133	z	z	NOUN
ejpam-5958	397	134	)	)	PUNCT
ejpam-5958	397	135	≤	≤	NOUN
ejpam-5958	397	136	zw	zw	PROPN
ejpam-5958	397	137	(	(	PUNCT
ejpam-5958	397	138	.	.	PUNCT
ejpam-5958	397	139	)	)	PUNCT
ejpam-5958	397	140	.	.	PUNCT
ejpam-5958	398	1	(	(	PUNCT
ejpam-5958	398	2	h2	h2	NOUN
ejpam-5958	398	3	)	)	PUNCT
ejpam-5958	398	4	there	there	PRON
ejpam-5958	398	5	exists	exist	VERB
ejpam-5958	398	6	µ	µ	X
ejpam-5958	398	7	>	>	X
ejpam-5958	398	8	1	1	NUM
ejpam-5958	398	9	such	such	ADJ
ejpam-5958	398	10	that	that	PRON
ejpam-5958	398	11	:	:	PUNCT
ejpam-5958	398	12	(	(	PUNCT
ejpam-5958	398	13	i	i	NOUN
ejpam-5958	398	14	)	)	PUNCT
ejpam-5958	398	15	rµ(λ	rµ(λ	NUM
ejpam-5958	398	16	)	)	PUNCT
ejpam-5958	398	17	:	:	PUNCT
ejpam-5958	399	1	=	=	PUNCT
ejpam-5958	399	2	∫	∫	PROPN
ejpam-5958	400	1	+	+	NUM
ejpam-5958	400	2	∞	∞	PROPN
ejpam-5958	400	3	0	0	PUNCT
ejpam-5958	400	4	e	e	X
ejpam-5958	400	5	−	−	PROPN
ejpam-5958	400	6	(	(	PUNCT
ejpam-5958	400	7	1+δ)λτ	1+δ)λτ	PROPN
ejpam-5958	400	8	δµ	δµ	PROPN
ejpam-5958	400	9	w	w	PROPN
ejpam-5958	400	10	1+δ	1+δ	NUM
ejpam-5958	400	11	2δ	2δ	NUM
ejpam-5958	400	12	(	(	PUNCT
ejpam-5958	400	13	τ	τ	NOUN
ejpam-5958	400	14	)	)	PUNCT
ejpam-5958	400	15	dτ	dτ	NOUN
ejpam-5958	400	16	<	<	X
ejpam-5958	400	17	∞	∞	PROPN
ejpam-5958	400	18	,	,	PUNCT
ejpam-5958	400	19	for	for	ADP
ejpam-5958	400	20	all	all	DET
ejpam-5958	400	21	λ	λ	PROPN
ejpam-5958	400	22	>	>	X
ejpam-5958	400	23	0	0	NUM
ejpam-5958	400	24	.	.	PUNCT
ejpam-5958	400	25	(	(	PUNCT
ejpam-5958	400	26	ii	ii	NOUN
ejpam-5958	400	27	)	)	PUNCT
ejpam-5958	400	28	rµ(λ	rµ(λ	NOUN
ejpam-5958	400	29	)	)	PUNCT
ejpam-5958	400	30	−−−→	−−−→	NOUN
ejpam-5958	400	31	λ→∞	λ→∞	NUM
ejpam-5958	400	32	0	0	NUM
ejpam-5958	400	33	,	,	PUNCT
ejpam-5958	400	34	∀t	∀t	PROPN
ejpam-5958	400	35	>	>	X
ejpam-5958	400	36	0	0	NUM
ejpam-5958	400	37	.	.	PUNCT
ejpam-5958	401	1	then	then	ADV
ejpam-5958	401	2	(	(	PUNCT
ejpam-5958	401	3	4.12	4.12	NUM
ejpam-5958	401	4	)	)	PUNCT
ejpam-5958	401	5	has	have	VERB
ejpam-5958	401	6	at	at	ADV
ejpam-5958	401	7	least	least	ADJ
ejpam-5958	401	8	one	one	NUM
ejpam-5958	401	9	global	global	ADJ
ejpam-5958	401	10	solution	solution	NOUN
ejpam-5958	401	11	in	in	ADP
ejpam-5958	401	12	e.	e.	PROPN
ejpam-5958	401	13	proof	proof	PROPN
ejpam-5958	401	14	.	.	PUNCT
ejpam-5958	402	1	using	use	VERB
ejpam-5958	402	2	the	the	DET
ejpam-5958	402	3	properties	property	NOUN
ejpam-5958	402	4	of	of	ADP
ejpam-5958	402	5	fractional	fractional	ADJ
ejpam-5958	402	6	integral	integral	ADJ
ejpam-5958	402	7	and	and	CCONJ
ejpam-5958	402	8	derivative	derivative	ADJ
ejpam-5958	402	9	operators	operator	NOUN
ejpam-5958	402	10	,	,	PUNCT
ejpam-5958	402	11	problem	problem	NOUN
ejpam-5958	402	12	(	(	PUNCT
ejpam-5958	402	13	4.12	4.12	NUM
ejpam-5958	402	14	)	)	PUNCT
ejpam-5958	402	15	is	be	AUX
ejpam-5958	402	16	transformed	transform	VERB
ejpam-5958	402	17	into	into	ADP
ejpam-5958	402	18	the	the	DET
ejpam-5958	402	19	following	follow	VERB
ejpam-5958	402	20	integral	integral	ADJ
ejpam-5958	402	21	equation	equation	NOUN
ejpam-5958	402	22	,	,	PUNCT
ejpam-5958	402	23	see	see	VERB
ejpam-5958	402	24	,	,	PUNCT
ejpam-5958	403	1	e.g.	e.g.	ADV
ejpam-5958	403	2	[	[	X
ejpam-5958	403	3	28	28	NUM
ejpam-5958	403	4	,	,	PUNCT
ejpam-5958	403	5	31	31	NUM
ejpam-5958	403	6	,	,	PUNCT
ejpam-5958	403	7	34	34	NUM
ejpam-5958	403	8	,	,	PUNCT
ejpam-5958	403	9	41–43	41–43	NUM
ejpam-5958	403	10	]	]	PUNCT
ejpam-5958	403	11	.	.	PUNCT
ejpam-5958	404	1	x(t	x(t	PROPN
ejpam-5958	404	2	)	)	PUNCT
ejpam-5958	405	1	=	=	PUNCT
ejpam-5958	405	2			PRON
ejpam-5958	405	3	φ(0	φ(0	ADJ
ejpam-5958	405	4	)	)	PUNCT
ejpam-5958	406	1	+	+	NUM
ejpam-5958	406	2	∫	∫	PROPN
ejpam-5958	406	3	t	t	PROPN
ejpam-5958	406	4	0	0	NUM
ejpam-5958	406	5	(	(	PUNCT
ejpam-5958	406	6	t−	t−	PROPN
ejpam-5958	406	7	τ)δ−1	τ)δ−1	NOUN
ejpam-5958	406	8	γ(δ	γ(δ	PROPN
ejpam-5958	406	9	)	)	PUNCT
ejpam-5958	406	10	f	f	PROPN
ejpam-5958	406	11	(	(	PUNCT
ejpam-5958	406	12	τ	τ	PROPN
ejpam-5958	406	13	,	,	PUNCT
ejpam-5958	406	14	x(τ	x(τ	PROPN
ejpam-5958	406	15	)	)	PUNCT
ejpam-5958	406	16	,	,	PUNCT
ejpam-5958	406	17	max	max	PROPN
ejpam-5958	406	18	σ∈[a(τ	σ∈[a(τ	PROPN
ejpam-5958	406	19	)	)	PUNCT
ejpam-5958	406	20	,	,	PUNCT
ejpam-5958	406	21	b(τ	b(τ	PROPN
ejpam-5958	406	22	)	)	PUNCT
ejpam-5958	406	23	]	]	PUNCT
ejpam-5958	406	24	x	x	X
ejpam-5958	406	25	(	(	PUNCT
ejpam-5958	406	26	σ	σ	NOUN
ejpam-5958	406	27	)	)	PUNCT
ejpam-5958	406	28	)	)	PUNCT
ejpam-5958	406	29	dτ	dτ	PROPN
ejpam-5958	406	30	,	,	PUNCT
ejpam-5958	406	31	t	t	PROPN
ejpam-5958	406	32	>	>	X
ejpam-5958	406	33	0	0	NUM
ejpam-5958	406	34	φ(t	φ(t	PROPN
ejpam-5958	406	35	)	)	PUNCT
ejpam-5958	406	36	,	,	PUNCT
ejpam-5958	406	37	t	t	VERB
ejpam-5958	406	38	≤	≤	NUM
ejpam-5958	406	39	0	0	NUM
ejpam-5958	406	40	,	,	PUNCT
ejpam-5958	406	41	(	(	PUNCT
ejpam-5958	406	42	4.13	4.13	NUM
ejpam-5958	406	43	)	)	PUNCT
ejpam-5958	406	44	which	which	PRON
ejpam-5958	406	45	is	be	AUX
ejpam-5958	406	46	identified	identify	VERB
ejpam-5958	406	47	to	to	ADP
ejpam-5958	406	48	(	(	PUNCT
ejpam-5958	406	49	4.1	4.1	NUM
ejpam-5958	406	50	)	)	PUNCT
ejpam-5958	406	51	,	,	PUNCT
ejpam-5958	406	52	with	with	ADP
ejpam-5958	406	53	g(t	g(t	PROPN
ejpam-5958	406	54	,	,	PUNCT
ejpam-5958	406	55	τ	τ	X
ejpam-5958	406	56	)	)	PUNCT
ejpam-5958	406	57	=	=	SYM
ejpam-5958	407	1	(	(	PUNCT
ejpam-5958	407	2	t−	t−	PROPN
ejpam-5958	407	3	τ)δ−1	τ)δ−1	NOUN
ejpam-5958	407	4	γ(δ	γ(δ	PROPN
ejpam-5958	407	5	)	)	PUNCT
ejpam-5958	407	6	and	and	CCONJ
ejpam-5958	407	7	gx(t	gx(t	NOUN
ejpam-5958	407	8	)	)	PUNCT
ejpam-5958	408	1	=	=	SYM
ejpam-5958	408	2	max	max	PROPN
ejpam-5958	408	3	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	408	4	)	)	PUNCT
ejpam-5958	408	5	,	,	PUNCT
ejpam-5958	408	6	b(t	b(t	PROPN
ejpam-5958	408	7	)	)	PUNCT
ejpam-5958	408	8	]	]	PUNCT
ejpam-5958	409	1	x	x	X
ejpam-5958	409	2	(	(	PUNCT
ejpam-5958	409	3	σ	σ	NOUN
ejpam-5958	409	4	)	)	PUNCT
ejpam-5958	409	5	.	.	PUNCT
ejpam-5958	410	1	therefore	therefore	ADV
ejpam-5958	410	2	,	,	PUNCT
ejpam-5958	410	3	it	it	PRON
ejpam-5958	410	4	is	be	AUX
ejpam-5958	410	5	sufficient	sufficient	ADJ
ejpam-5958	410	6	to	to	PART
ejpam-5958	410	7	show	show	VERB
ejpam-5958	410	8	that	that	SCONJ
ejpam-5958	410	9	conditions	condition	NOUN
ejpam-5958	410	10	(	(	PUNCT
ejpam-5958	410	11	b1)-(b3	b1)-(b3	PROPN
ejpam-5958	410	12	)	)	PUNCT
ejpam-5958	410	13	are	be	AUX
ejpam-5958	410	14	fulfilled	fulfil	VERB
ejpam-5958	410	15	,	,	PUNCT
ejpam-5958	410	16	to	to	PART
ejpam-5958	410	17	deduce	deduce	VERB
ejpam-5958	410	18	then	then	ADV
ejpam-5958	410	19	the	the	DET
ejpam-5958	410	20	result	result	NOUN
ejpam-5958	410	21	from	from	ADP
ejpam-5958	410	22	theorem	theorem	ADJ
ejpam-5958	410	23	3	3	X
ejpam-5958	410	24	.	.	PUNCT
ejpam-5958	411	1	let	let	VERB
ejpam-5958	411	2	x	x	PRON
ejpam-5958	411	3	,	,	PUNCT
ejpam-5958	411	4	y	y	PROPN
ejpam-5958	411	5	∈	∈	PROPN
ejpam-5958	411	6	e	e	PROPN
ejpam-5958	411	7	,	,	PUNCT
ejpam-5958	411	8	k	k	PROPN
ejpam-5958	411	9	∈	∈	PROPN
ejpam-5958	411	10	k	k	PROPN
ejpam-5958	411	11	and	and	CCONJ
ejpam-5958	411	12	t	t	PROPN
ejpam-5958	411	13	∈	∈	PROPN
ejpam-5958	412	1	k	k	PRON
ejpam-5958	412	2	such	such	ADJ
ejpam-5958	412	3	that	that	SCONJ
ejpam-5958	412	4	t	t	PROPN
ejpam-5958	412	5	>	>	X
ejpam-5958	412	6	0	0	X
ejpam-5958	412	7	.	.	PUNCT
ejpam-5958	413	1	using	use	VERB
ejpam-5958	413	2	(	(	PUNCT
ejpam-5958	413	3	h1(i	h1(i	NOUN
ejpam-5958	413	4	)	)	PUNCT
ejpam-5958	413	5	,	,	PUNCT
ejpam-5958	413	6	(	(	PUNCT
ejpam-5958	413	7	ii	ii	NOUN
ejpam-5958	413	8	)	)	PUNCT
ejpam-5958	413	9	)	)	PUNCT
ejpam-5958	414	1	we	we	PRON
ejpam-5958	414	2	obtain:∣∣∣∣f(t	obtain:∣∣∣∣f(t	VERB
ejpam-5958	414	3	,	,	PUNCT
ejpam-5958	414	4	x(t	x(t	PROPN
ejpam-5958	414	5	)	)	PUNCT
ejpam-5958	414	6	,	,	PUNCT
ejpam-5958	414	7	max	max	PROPN
ejpam-5958	414	8	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	414	9	)	)	PUNCT
ejpam-5958	414	10	,	,	PUNCT
ejpam-5958	414	11	b(t	b(t	PROPN
ejpam-5958	414	12	)	)	PUNCT
ejpam-5958	414	13	]	]	PUNCT
ejpam-5958	415	1	x	x	X
ejpam-5958	415	2	(	(	PUNCT
ejpam-5958	415	3	σ))−	σ))−	ADJ
ejpam-5958	415	4	f(t	f(t	NOUN
ejpam-5958	415	5	,	,	PUNCT
ejpam-5958	415	6	y(t	y(t	PROPN
ejpam-5958	415	7	)	)	PUNCT
ejpam-5958	415	8	,	,	PUNCT
ejpam-5958	415	9	max	max	PROPN
ejpam-5958	415	10	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	415	11	)	)	PUNCT
ejpam-5958	415	12	,	,	PUNCT
ejpam-5958	415	13	b(t	b(t	PROPN
ejpam-5958	415	14	)	)	PUNCT
ejpam-5958	415	15	]	]	PUNCT
ejpam-5958	416	1	y	y	PROPN
ejpam-5958	416	2	(	(	PUNCT
ejpam-5958	416	3	σ	σ	PROPN
ejpam-5958	416	4	)	)	PUNCT
ejpam-5958	416	5	)	)	PUNCT
ejpam-5958	416	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5958	416	7	≤	≤	NOUN
ejpam-5958	416	8	√√√√υ	√√√√υ	PROPN
ejpam-5958	416	9	(	(	PUNCT
ejpam-5958	416	10	t	t	PROPN
ejpam-5958	416	11	,	,	PUNCT
ejpam-5958	416	12	|x(t)−	|x(t)−	PROPN
ejpam-5958	416	13	y(t)|2	y(t)|2	PROPN
ejpam-5958	416	14	,	,	PUNCT
ejpam-5958	416	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5958	416	16	max	max	PROPN
ejpam-5958	416	17	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	416	18	)	)	PUNCT
ejpam-5958	416	19	,	,	PUNCT
ejpam-5958	416	20	b(t	b(t	PROPN
ejpam-5958	416	21	)	)	PUNCT
ejpam-5958	416	22	]	]	PUNCT
ejpam-5958	416	23	x	x	X
ejpam-5958	416	24	(	(	PUNCT
ejpam-5958	416	25	σ)−	σ)−	PROPN
ejpam-5958	416	26	max	max	PROPN
ejpam-5958	416	27	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	416	28	)	)	PUNCT
ejpam-5958	416	29	,	,	PUNCT
ejpam-5958	416	30	b(t	b(t	PROPN
ejpam-5958	416	31	)	)	PUNCT
ejpam-5958	416	32	]	]	PUNCT
ejpam-5958	417	1	y	y	PROPN
ejpam-5958	417	2	(	(	PUNCT
ejpam-5958	417	3	σ	σ	PROPN
ejpam-5958	417	4	)	)	PUNCT
ejpam-5958	417	5	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-5958	417	6	)	)	PUNCT
ejpam-5958	417	7	≤	≤	PROPN
ejpam-5958	417	8	k.	k.	PROPN
ejpam-5958	417	9	nisse	nisse	PROPN
ejpam-5958	417	10	et	et	PROPN
ejpam-5958	417	11	al	al	PROPN
ejpam-5958	417	12	.	.	PUNCT
ejpam-5958	417	13	/	/	SYM
ejpam-5958	417	14	eur	eur	PROPN
ejpam-5958	417	15	.	.	PUNCT
ejpam-5958	418	1	j.	j.	PROPN
ejpam-5958	418	2	pure	pure	PROPN
ejpam-5958	418	3	appl	appl	PROPN
ejpam-5958	418	4	.	.	PROPN
ejpam-5958	418	5	math	math	PROPN
ejpam-5958	418	6	,	,	PUNCT
ejpam-5958	418	7	18	18	NUM
ejpam-5958	418	8	(	(	PUNCT
ejpam-5958	418	9	2	2	NUM
ejpam-5958	418	10	)	)	PUNCT
ejpam-5958	418	11	(	(	PUNCT
ejpam-5958	418	12	2025	2025	NUM
ejpam-5958	418	13	)	)	PUNCT
ejpam-5958	418	14	,	,	PUNCT
ejpam-5958	418	15	5958	5958	NUM
ejpam-5958	418	16	19	19	NUM
ejpam-5958	418	17	of	of	ADP
ejpam-5958	418	18	22√	22√	NUM
ejpam-5958	418	19	υ	υ	NOUN
ejpam-5958	418	20	(	(	PUNCT
ejpam-5958	418	21	t	t	PROPN
ejpam-5958	418	22	,	,	PUNCT
ejpam-5958	418	23	|x(t)−	|x(t)−	PROPN
ejpam-5958	418	24	y(t)|2	y(t)|2	PROPN
ejpam-5958	418	25	,	,	PUNCT
ejpam-5958	418	26	max	max	PROPN
ejpam-5958	418	27	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	418	28	)	)	PUNCT
ejpam-5958	418	29	,	,	PUNCT
ejpam-5958	418	30	b(t	b(t	PROPN
ejpam-5958	418	31	)	)	PUNCT
ejpam-5958	418	32	]	]	PUNCT
ejpam-5958	418	33	|x	|x	X
ejpam-5958	418	34	(	(	PUNCT
ejpam-5958	418	35	σ)−	σ)−	PROPN
ejpam-5958	418	36	y	y	PROPN
ejpam-5958	418	37	(	(	PUNCT
ejpam-5958	418	38	σ)|2	σ)|2	NOUN
ejpam-5958	418	39	)	)	PUNCT
ejpam-5958	418	40	≤	≤	PUNCT
ejpam-5958	419	1	√	√	VERB
ejpam-5958	419	2	υ	υ	PROPN
ejpam-5958	419	3	(	(	PUNCT
ejpam-5958	419	4	t	t	PROPN
ejpam-5958	419	5	,	,	PUNCT
ejpam-5958	419	6	eλtdw(k)(x	eλtdw(k)(x	PROPN
ejpam-5958	419	7	,	,	PUNCT
ejpam-5958	419	8	y	y	PROPN
ejpam-5958	419	9	)	)	PUNCT
ejpam-5958	419	10	,	,	PUNCT
ejpam-5958	419	11	eλtdw(k)(x	eλtdw(k)(x	PROPN
ejpam-5958	419	12	,	,	PUNCT
ejpam-5958	419	13	y	y	PROPN
ejpam-5958	419	14	)	)	PUNCT
ejpam-5958	419	15	)	)	PUNCT
ejpam-5958	419	16	,	,	PUNCT
ejpam-5958	419	17	which	which	PRON
ejpam-5958	419	18	yields	yield	VERB
ejpam-5958	419	19	to	to	PART
ejpam-5958	419	20	(	(	PUNCT
ejpam-5958	419	21	4.3	4.3	NUM
ejpam-5958	419	22	)	)	PUNCT
ejpam-5958	419	23	thanks	thank	NOUN
ejpam-5958	419	24	to	to	ADP
ejpam-5958	419	25	(	(	PUNCT
ejpam-5958	419	26	h1(iii	h1(iii	NOUN
ejpam-5958	419	27	)	)	PUNCT
ejpam-5958	419	28	)	)	PUNCT
ejpam-5958	419	29	.	.	PUNCT
ejpam-5958	420	1	consequently	consequently	ADV
ejpam-5958	420	2	,	,	PUNCT
ejpam-5958	420	3	(	(	PUNCT
ejpam-5958	420	4	b1	b1	NOUN
ejpam-5958	420	5	)	)	PUNCT
ejpam-5958	420	6	is	be	AUX
ejpam-5958	420	7	fulfilled	fulfil	VERB
ejpam-5958	420	8	.	.	PUNCT
ejpam-5958	421	1	(	(	PUNCT
ejpam-5958	421	2	h2(i	h2(i	NOUN
ejpam-5958	421	3	)	)	PUNCT
ejpam-5958	421	4	)	)	PUNCT
ejpam-5958	422	1	implies	imply	VERB
ejpam-5958	422	2	(	(	PUNCT
ejpam-5958	422	3	b2(i	b2(i	NOUN
ejpam-5958	422	4	)	)	PUNCT
ejpam-5958	422	5	)	)	PUNCT
ejpam-5958	422	6	with	with	ADP
ejpam-5958	422	7	p	p	NOUN
ejpam-5958	422	8	=	=	SYM
ejpam-5958	422	9	1	1	NUM
ejpam-5958	422	10	+	+	SYM
ejpam-5958	422	11	1	1	NUM
ejpam-5958	422	12	δ	δ	NOUN
ejpam-5958	422	13	.	.	PUNCT
ejpam-5958	423	1	let	let	VERB
ejpam-5958	423	2	us	we	PRON
ejpam-5958	423	3	now	now	ADV
ejpam-5958	423	4	check	check	VERB
ejpam-5958	423	5	(	(	PUNCT
ejpam-5958	423	6	b2(ii	b2(ii	PROPN
ejpam-5958	423	7	)	)	PUNCT
ejpam-5958	423	8	)	)	PUNCT
ejpam-5958	424	1	where	where	SCONJ
ejpam-5958	424	2	q	q	NOUN
ejpam-5958	424	3	=	=	NOUN
ejpam-5958	424	4	1	1	NUM
ejpam-5958	424	5	+	+	NUM
ejpam-5958	424	6	δ	δ	PROPN
ejpam-5958	424	7	.	.	PUNCT
ejpam-5958	425	1	we	we	PRON
ejpam-5958	425	2	have	have	VERB
ejpam-5958	425	3	:	:	PUNCT
ejpam-5958	425	4	sµ,t(λ	sµ,t(λ	NUM
ejpam-5958	425	5	)	)	PUNCT
ejpam-5958	425	6	=	=	NOUN
ejpam-5958	425	7	1	1	NUM
ejpam-5958	425	8	γq(δ	γq(δ	NUM
ejpam-5958	425	9	)	)	PUNCT
ejpam-5958	425	10	∫	∫	PROPN
ejpam-5958	425	11	t	t	PROPN
ejpam-5958	425	12	0	0	NUM
ejpam-5958	425	13	(	(	PUNCT
ejpam-5958	425	14	t−	t−	PROPN
ejpam-5958	425	15	τ)q(δ−1)e	τ)q(δ−1)e	NOUN
ejpam-5958	425	16	−λq	−λq	NOUN
ejpam-5958	425	17	2	2	NUM
ejpam-5958	425	18	[	[	PUNCT
ejpam-5958	425	19	t−	t−	PROPN
ejpam-5958	425	20	(	(	PUNCT
ejpam-5958	425	21	µ+2	µ+2	PROPN
ejpam-5958	425	22	µ	µ	X
ejpam-5958	425	23	)	)	PUNCT
ejpam-5958	425	24	τ	τ	PROPN
ejpam-5958	425	25	]	]	PUNCT
ejpam-5958	425	26	dτ	dτ	X
ejpam-5958	425	27	≤	≤	ADV
ejpam-5958	425	28	1	1	NUM
ejpam-5958	425	29	γq(δ	γq(δ	NUM
ejpam-5958	425	30	)	)	PUNCT
ejpam-5958	426	1	∫	∫	PROPN
ejpam-5958	426	2	t	t	PROPN
ejpam-5958	426	3	0	0	NUM
ejpam-5958	426	4	(	(	PUNCT
ejpam-5958	426	5	t−	t−	PROPN
ejpam-5958	426	6	τ)q(δ−1)e	τ)q(δ−1)e	NOUN
ejpam-5958	426	7	−λq	−λq	NOUN
ejpam-5958	426	8	2	2	NUM
ejpam-5958	426	9	(	(	PUNCT
ejpam-5958	426	10	µ+2	µ+2	PROPN
ejpam-5958	426	11	µ	µ	X
ejpam-5958	426	12	)	)	PUNCT
ejpam-5958	426	13	(	(	PUNCT
ejpam-5958	426	14	t−τ	t−τ	NOUN
ejpam-5958	426	15	)	)	PUNCT
ejpam-5958	426	16	dτ	dτ	NOUN
ejpam-5958	426	17	.	.	NOUN
ejpam-5958	426	18	performing	perform	VERB
ejpam-5958	426	19	the	the	DET
ejpam-5958	426	20	change	change	NOUN
ejpam-5958	426	21	of	of	ADP
ejpam-5958	426	22	variable	variable	NOUN
ejpam-5958	426	23	x	x	PUNCT
ejpam-5958	427	1	=	=	SYM
ejpam-5958	427	2	λq	λq	ADJ
ejpam-5958	427	3	2	2	NUM
ejpam-5958	427	4	(	(	PUNCT
ejpam-5958	427	5	µ+2	µ+2	PROPN
ejpam-5958	427	6	µ	µ	X
ejpam-5958	427	7	)	)	PUNCT
ejpam-5958	427	8	(	(	PUNCT
ejpam-5958	427	9	t−	t−	PROPN
ejpam-5958	427	10	τ	τ	PROPN
ejpam-5958	427	11	)	)	PUNCT
ejpam-5958	427	12	,	,	PUNCT
ejpam-5958	427	13	we	we	PRON
ejpam-5958	427	14	get	get	VERB
ejpam-5958	427	15	:	:	PUNCT
ejpam-5958	427	16	sµ,t(λ	sµ,t(λ	NOUN
ejpam-5958	427	17	)	)	PUNCT
ejpam-5958	427	18	≤	≤	NUM
ejpam-5958	427	19	1	1	NUM
ejpam-5958	427	20	γq(δ	γq(δ	NUM
ejpam-5958	427	21	)	)	PUNCT
ejpam-5958	427	22	∫	∫	PROPN
ejpam-5958	428	1	∞	∞	PROPN
ejpam-5958	428	2	0	0	NUM
ejpam-5958	428	3	(	(	PUNCT
ejpam-5958	428	4	2µ	2µ	NUM
ejpam-5958	428	5	λq(µ+	λq(µ+	PROPN
ejpam-5958	428	6	2	2	NUM
ejpam-5958	428	7	)	)	PUNCT
ejpam-5958	428	8	)	)	PUNCT
ejpam-5958	428	9	q(δ−1	q(δ−1	PROPN
ejpam-5958	428	10	)	)	PUNCT
ejpam-5958	428	11	xq(δ−1)e−x	xq(δ−1)e−x	PROPN
ejpam-5958	428	12	dx	dx	PROPN
ejpam-5958	428	13	=	=	PUNCT
ejpam-5958	428	14	1	1	NUM
ejpam-5958	428	15	γ1+δ(δ	γ1+δ(δ	NUM
ejpam-5958	428	16	)	)	PUNCT
ejpam-5958	428	17	(	(	PUNCT
ejpam-5958	428	18	2µ	2µ	NUM
ejpam-5958	428	19	λq(µ+2	λq(µ+2	NOUN
ejpam-5958	428	20	)	)	PUNCT
ejpam-5958	428	21	)	)	PUNCT
ejpam-5958	428	22	δ2	δ2	VERB
ejpam-5958	428	23	γ(δ2	γ(δ2	NOUN
ejpam-5958	428	24	)	)	PUNCT
ejpam-5958	428	25	.	.	PUNCT
ejpam-5958	429	1	consequently	consequently	ADV
ejpam-5958	429	2	,	,	PUNCT
ejpam-5958	429	3	(	(	PUNCT
ejpam-5958	429	4	b2(ii	b2(ii	PROPN
ejpam-5958	429	5	)	)	PUNCT
ejpam-5958	429	6	)	)	PUNCT
ejpam-5958	429	7	is	be	AUX
ejpam-5958	429	8	satisfied	satisfied	ADJ
ejpam-5958	429	9	and	and	CCONJ
ejpam-5958	429	10	furthermore	furthermore	ADV
ejpam-5958	429	11	sµ,t(λ	sµ,t(λ	NOUN
ejpam-5958	429	12	)	)	PUNCT
ejpam-5958	429	13	−−−→	−−−→	NOUN
ejpam-5958	429	14	λ→∞	λ→∞	NUM
ejpam-5958	429	15	0	0	NUM
ejpam-5958	429	16	,	,	PUNCT
ejpam-5958	429	17	∀t	∀t	PROPN
ejpam-5958	429	18	>	>	X
ejpam-5958	429	19	0	0	NUM
ejpam-5958	429	20	.	.	PUNCT
ejpam-5958	430	1	the	the	DET
ejpam-5958	430	2	last	last	ADJ
ejpam-5958	430	3	fact	fact	NOUN
ejpam-5958	430	4	,	,	PUNCT
ejpam-5958	430	5	combined	combine	VERB
ejpam-5958	430	6	with	with	ADP
ejpam-5958	430	7	(	(	PUNCT
ejpam-5958	430	8	h2(ii	h2(ii	NOUN
ejpam-5958	430	9	)	)	PUNCT
ejpam-5958	430	10	)	)	PUNCT
ejpam-5958	430	11	implies	imply	VERB
ejpam-5958	430	12	(	(	PUNCT
ejpam-5958	430	13	b2(iii	b2(iii	NOUN
ejpam-5958	430	14	)	)	PUNCT
ejpam-5958	430	15	)	)	PUNCT
ejpam-5958	430	16	.	.	PUNCT
ejpam-5958	431	1	let	let	VERB
ejpam-5958	431	2	x	x	PRON
ejpam-5958	431	3	,	,	PUNCT
ejpam-5958	431	4	y	y	PROPN
ejpam-5958	431	5	∈	∈	PROPN
ejpam-5958	431	6	e	e	NOUN
ejpam-5958	431	7	,	,	PUNCT
ejpam-5958	431	8	such	such	ADJ
ejpam-5958	431	9	that	that	SCONJ
ejpam-5958	431	10	x(t	x(t	PROPN
ejpam-5958	431	11	)	)	PUNCT
ejpam-5958	431	12	=	=	SYM
ejpam-5958	431	13	y(t	y(t	PROPN
ejpam-5958	431	14	)	)	PUNCT
ejpam-5958	431	15	for	for	ADP
ejpam-5958	431	16	t	t	NOUN
ejpam-5958	431	17	≤	≤	NOUN
ejpam-5958	431	18	0	0	NUM
ejpam-5958	431	19	.	.	PUNCT
ejpam-5958	432	1	if	if	SCONJ
ejpam-5958	432	2	x(t	x(t	PROPN
ejpam-5958	432	3	)	)	PUNCT
ejpam-5958	432	4	≤	≤	NUM
ejpam-5958	432	5	y(t	y(t	NUM
ejpam-5958	432	6	)	)	PUNCT
ejpam-5958	432	7	for	for	ADP
ejpam-5958	432	8	t	t	PROPN
ejpam-5958	432	9	>	>	X
ejpam-5958	432	10	0	0	PROPN
ejpam-5958	432	11	,	,	PUNCT
ejpam-5958	432	12	then	then	ADV
ejpam-5958	432	13	we	we	PRON
ejpam-5958	432	14	have	have	VERB
ejpam-5958	432	15	:	:	PUNCT
ejpam-5958	432	16	{	{	PUNCT
ejpam-5958	432	17	x(σ	x(σ	NOUN
ejpam-5958	432	18	)	)	PUNCT
ejpam-5958	432	19	≤	≤	NUM
ejpam-5958	432	20	y(σ	y(σ	PROPN
ejpam-5958	432	21	)	)	PUNCT
ejpam-5958	432	22	,	,	PUNCT
ejpam-5958	432	23	σ	σ	PROPN
ejpam-5958	432	24	∈	∈	PROPN
ejpam-5958	433	1	[	[	X
ejpam-5958	433	2	a(t	a(t	NOUN
ejpam-5958	433	3	)	)	PUNCT
ejpam-5958	433	4	,	,	PUNCT
ejpam-5958	433	5	b(t)]+	b(t)]+	PROPN
ejpam-5958	433	6	x(σ	x(σ	NOUN
ejpam-5958	433	7	)	)	PUNCT
ejpam-5958	433	8	=	=	SYM
ejpam-5958	434	1	y(σ	y(σ	PROPN
ejpam-5958	434	2	)	)	PUNCT
ejpam-5958	434	3	,	,	PUNCT
ejpam-5958	434	4	σ	σ	PROPN
ejpam-5958	434	5	∈	∈	PROPN
ejpam-5958	435	1	[	[	X
ejpam-5958	435	2	a(t	a(t	NOUN
ejpam-5958	435	3	)	)	PUNCT
ejpam-5958	435	4	,	,	PUNCT
ejpam-5958	435	5	b(t)]−	b(t)]−	ADV
ejpam-5958	435	6	,	,	PUNCT
ejpam-5958	435	7	where	where	SCONJ
ejpam-5958	435	8	[	[	X
ejpam-5958	435	9	a(t	a(t	NOUN
ejpam-5958	435	10	)	)	PUNCT
ejpam-5958	435	11	,	,	PUNCT
ejpam-5958	435	12	b(t)]+	b(t)]+	PROPN
ejpam-5958	435	13	=	=	SYM
ejpam-5958	436	1	[	[	X
ejpam-5958	436	2	a(t	a(t	NOUN
ejpam-5958	436	3	)	)	PUNCT
ejpam-5958	436	4	,	,	PUNCT
ejpam-5958	436	5	b(t	b(t	PROPN
ejpam-5958	436	6	)	)	PUNCT
ejpam-5958	436	7	]	]	PUNCT
ejpam-5958	436	8	∩	∩	NOUN
ejpam-5958	436	9	r+	r+	NOUN
ejpam-5958	436	10	and	and	CCONJ
ejpam-5958	436	11	[	[	X
ejpam-5958	436	12	a(t	a(t	NOUN
ejpam-5958	436	13	)	)	PUNCT
ejpam-5958	436	14	,	,	PUNCT
ejpam-5958	436	15	b(t)]−	b(t)]−	NOUN
ejpam-5958	436	16	=	=	PUNCT
ejpam-5958	437	1	[	[	X
ejpam-5958	437	2	a(t	a(t	NOUN
ejpam-5958	437	3	)	)	PUNCT
ejpam-5958	437	4	,	,	PUNCT
ejpam-5958	437	5	b(t	b(t	PROPN
ejpam-5958	437	6	)	)	PUNCT
ejpam-5958	437	7	]	]	PUNCT
ejpam-5958	438	1	∩	∩	PROPN
ejpam-5958	438	2	r−.	r−.	PROPN
ejpam-5958	438	3	then	then	ADV
ejpam-5958	438	4			PROPN
ejpam-5958	438	5	sup	sup	NOUN
ejpam-5958	438	6	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	438	7	)	)	PUNCT
ejpam-5958	438	8	,	,	PUNCT
ejpam-5958	438	9	b(t)]+	b(t)]+	PROPN
ejpam-5958	438	10	x	x	SYM
ejpam-5958	438	11	(	(	PUNCT
ejpam-5958	438	12	σ	σ	NOUN
ejpam-5958	438	13	)	)	PUNCT
ejpam-5958	438	14	≤	≤	NUM
ejpam-5958	438	15	sup	sup	NUM
ejpam-5958	438	16	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	438	17	)	)	PUNCT
ejpam-5958	438	18	,	,	PUNCT
ejpam-5958	438	19	b(t)]+	b(t)]+	PROPN
ejpam-5958	438	20	y	y	PROPN
ejpam-5958	438	21	(	(	PUNCT
ejpam-5958	438	22	σ	σ	PROPN
ejpam-5958	438	23	)	)	PUNCT
ejpam-5958	438	24	max	max	PROPN
ejpam-5958	438	25	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	438	26	)	)	PUNCT
ejpam-5958	438	27	,	,	PUNCT
ejpam-5958	438	28	b(t)]−	b(t)]−	NOUN
ejpam-5958	438	29	x	x	X
ejpam-5958	438	30	(	(	PUNCT
ejpam-5958	438	31	σ	σ	NOUN
ejpam-5958	438	32	)	)	PUNCT
ejpam-5958	438	33	=	=	PROPN
ejpam-5958	438	34	max	max	PROPN
ejpam-5958	438	35	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	438	36	)	)	PUNCT
ejpam-5958	438	37	,	,	PUNCT
ejpam-5958	438	38	b(t)]−	b(t)]−	PROPN
ejpam-5958	438	39	y	y	PROPN
ejpam-5958	438	40	(	(	PUNCT
ejpam-5958	438	41	σ	σ	PROPN
ejpam-5958	438	42	)	)	PUNCT
ejpam-5958	438	43	.	.	PUNCT
ejpam-5958	439	1	consequently	consequently	ADV
ejpam-5958	439	2	max	max	PROPN
ejpam-5958	439	3	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	439	4	)	)	PUNCT
ejpam-5958	439	5	,	,	PUNCT
ejpam-5958	439	6	b(t	b(t	PROPN
ejpam-5958	439	7	)	)	PUNCT
ejpam-5958	439	8	]	]	PUNCT
ejpam-5958	440	1	x	x	X
ejpam-5958	440	2	(	(	PUNCT
ejpam-5958	440	3	σ	σ	NOUN
ejpam-5958	440	4	)	)	PUNCT
ejpam-5958	440	5	≤	≤	NUM
ejpam-5958	440	6	max	max	PROPN
ejpam-5958	440	7	σ∈[a(t	σ∈[a(t	PROPN
ejpam-5958	440	8	)	)	PUNCT
ejpam-5958	440	9	,	,	PUNCT
ejpam-5958	440	10	b(t	b(t	PROPN
ejpam-5958	440	11	)	)	PUNCT
ejpam-5958	440	12	]	]	PUNCT
ejpam-5958	441	1	y	y	PROPN
ejpam-5958	441	2	(	(	PUNCT
ejpam-5958	441	3	σ	σ	PROPN
ejpam-5958	441	4	)	)	PUNCT
ejpam-5958	441	5	,	,	PUNCT
ejpam-5958	441	6	that	that	ADV
ejpam-5958	441	7	is	is	ADV
ejpam-5958	441	8	(	(	PUNCT
ejpam-5958	441	9	b3	b3	PROPN
ejpam-5958	441	10	)	)	PUNCT
ejpam-5958	441	11	is	be	AUX
ejpam-5958	441	12	satisfied	satisfied	ADJ
ejpam-5958	441	13	.	.	PUNCT
ejpam-5958	442	1	then	then	ADV
ejpam-5958	442	2	all	all	DET
ejpam-5958	442	3	conditions	condition	NOUN
ejpam-5958	442	4	of	of	ADP
ejpam-5958	442	5	theorem	theorem	NOUN
ejpam-5958	442	6	3	3	NUM
ejpam-5958	442	7	are	be	AUX
ejpam-5958	442	8	fulfilled	fulfil	VERB
ejpam-5958	442	9	and	and	CCONJ
ejpam-5958	442	10	the	the	DET
ejpam-5958	442	11	proof	proof	NOUN
ejpam-5958	442	12	is	be	AUX
ejpam-5958	442	13	complete	complete	ADJ
ejpam-5958	442	14	.	.	PUNCT
ejpam-5958	443	1	5	5	X
ejpam-5958	443	2	.	.	X
ejpam-5958	443	3	conclusion	conclusion	NOUN
ejpam-5958	443	4	in	in	ADP
ejpam-5958	443	5	this	this	DET
ejpam-5958	443	6	work	work	NOUN
ejpam-5958	443	7	,	,	PUNCT
ejpam-5958	443	8	we	we	PRON
ejpam-5958	443	9	have	have	AUX
ejpam-5958	443	10	introduced	introduce	VERB
ejpam-5958	443	11	a	a	DET
ejpam-5958	443	12	new	new	ADJ
ejpam-5958	443	13	concept	concept	NOUN
ejpam-5958	443	14	in	in	ADP
ejpam-5958	443	15	b	b	NOUN
ejpam-5958	443	16	-	-	PUNCT
ejpam-5958	443	17	gauge	gauge	NOUN
ejpam-5958	443	18	metric	metric	ADJ
ejpam-5958	443	19	spaces	space	NOUN
ejpam-5958	443	20	called	call	VERB
ejpam-5958	443	21	generalized	generalized	ADJ
ejpam-5958	443	22	(	(	PUNCT
ejpam-5958	443	23	αααν	αααν	NOUN
ejpam-5958	443	24	,	,	PUNCT
ejpam-5958	443	25	ψ	ψ	X
ejpam-5958	443	26	s	s	SYM
ejpam-5958	443	27	,	,	PUNCT
ejpam-5958	443	28	w	w	NOUN
ejpam-5958	443	29	)	)	PUNCT
ejpam-5958	443	30	contraction	contraction	NOUN
ejpam-5958	443	31	,	,	PUNCT
ejpam-5958	443	32	which	which	PRON
ejpam-5958	443	33	extended	extend	VERB
ejpam-5958	443	34	α	α	NUM
ejpam-5958	443	35	-	-	PUNCT
ejpam-5958	443	36	ψ	ψ	NOUN
ejpam-5958	443	37	contraction	contraction	NOUN
ejpam-5958	443	38	in	in	ADP
ejpam-5958	443	39	ordinary	ordinary	ADJ
ejpam-5958	443	40	metric	metric	ADJ
ejpam-5958	443	41	spaces	space	NOUN
ejpam-5958	443	42	.	.	PUNCT
ejpam-5958	444	1	some	some	DET
ejpam-5958	444	2	related	related	ADJ
ejpam-5958	444	3	fixed	fix	VERB
ejpam-5958	444	4	point	point	NOUN
ejpam-5958	444	5	results	result	NOUN
ejpam-5958	444	6	were	be	AUX
ejpam-5958	444	7	given	give	VERB
ejpam-5958	444	8	using	use	VERB
ejpam-5958	444	9	such	such	ADJ
ejpam-5958	444	10	concept	concept	NOUN
ejpam-5958	444	11	,	,	PUNCT
ejpam-5958	444	12	where	where	SCONJ
ejpam-5958	444	13	weaker	weak	ADJ
ejpam-5958	444	14	conditions	condition	NOUN
ejpam-5958	444	15	have	have	AUX
ejpam-5958	444	16	been	be	AUX
ejpam-5958	444	17	applied	apply	VERB
ejpam-5958	444	18	in	in	ADP
ejpam-5958	444	19	comparison	comparison	NOUN
ejpam-5958	444	20	with	with	ADP
ejpam-5958	444	21	existing	exist	VERB
ejpam-5958	444	22	results	result	NOUN
ejpam-5958	444	23	.	.	PUNCT
ejpam-5958	445	1	moreover	moreover	ADV
ejpam-5958	445	2	,	,	PUNCT
ejpam-5958	445	3	applications	application	NOUN
ejpam-5958	445	4	to	to	PART
ejpam-5958	445	5	delay	delay	VERB
ejpam-5958	445	6	integral	integral	ADJ
ejpam-5958	445	7	equations	equation	NOUN
ejpam-5958	445	8	on	on	ADP
ejpam-5958	445	9	unbounded	unbounded	ADJ
ejpam-5958	445	10	domain	domain	NOUN
ejpam-5958	445	11	,	,	PUNCT
ejpam-5958	445	12	including	include	VERB
ejpam-5958	445	13	fractional	fractional	ADJ
ejpam-5958	445	14	differential	differential	ADJ
ejpam-5958	445	15	equations	equation	NOUN
ejpam-5958	445	16	with	with	ADP
ejpam-5958	445	17	maxima	maxima	NOUN
ejpam-5958	445	18	are	be	AUX
ejpam-5958	445	19	provided	provide	VERB
ejpam-5958	445	20	.	.	PUNCT
ejpam-5958	446	1	k.	k.	PROPN
ejpam-5958	446	2	nisse	nisse	PROPN
ejpam-5958	446	3	et	et	PROPN
ejpam-5958	446	4	al	al	PROPN
ejpam-5958	446	5	.	.	PUNCT
ejpam-5958	446	6	/	/	SYM
ejpam-5958	446	7	eur	eur	PROPN
ejpam-5958	446	8	.	.	PUNCT
ejpam-5958	447	1	j.	j.	PROPN
ejpam-5958	447	2	pure	pure	PROPN
ejpam-5958	447	3	appl	appl	PROPN
ejpam-5958	447	4	.	.	PROPN
ejpam-5958	447	5	math	math	PROPN
ejpam-5958	447	6	,	,	PUNCT
ejpam-5958	447	7	18	18	NUM
ejpam-5958	447	8	(	(	PUNCT
ejpam-5958	447	9	2	2	NUM
ejpam-5958	447	10	)	)	PUNCT
ejpam-5958	447	11	(	(	PUNCT
ejpam-5958	447	12	2025	2025	NUM
ejpam-5958	447	13	)	)	PUNCT
ejpam-5958	447	14	,	,	PUNCT
ejpam-5958	447	15	5958	5958	NUM
ejpam-5958	447	16	20	20	NUM
ejpam-5958	447	17	of	of	ADP
ejpam-5958	447	18	22	22	NUM
ejpam-5958	447	19	acknowledgements	acknowledgement	NOUN
ejpam-5958	447	20	we	we	PRON
ejpam-5958	447	21	extend	extend	VERB
ejpam-5958	447	22	their	their	PRON
ejpam-5958	447	23	appreciation	appreciation	NOUN
ejpam-5958	447	24	to	to	ADP
ejpam-5958	447	25	al	al	PROPN
ejpam-5958	447	26	-	-	PROPN
ejpam-5958	447	27	zaytoonah	zaytoonah	PROPN
ejpam-5958	447	28	university	university	PROPN
ejpam-5958	447	29	of	of	ADP
ejpam-5958	447	30	jordan(zuj	jordan(zuj	PROPN
ejpam-5958	447	31	)	)	PUNCT
ejpam-5958	447	32	and	and	CCONJ
ejpam-5958	447	33	to	to	ADP
ejpam-5958	447	34	the	the	DET
ejpam-5958	447	35	arab	arab	PROPN
ejpam-5958	447	36	open	open	PROPN
ejpam-5958	447	37	university	university	PROPN
ejpam-5958	447	38	,	,	PUNCT
ejpam-5958	447	39	jeddah	jeddah	PROPN
ejpam-5958	447	40	,	,	PUNCT
ejpam-5958	447	41	saudi	saudi	PROPN
ejpam-5958	447	42	arabia	arabia	PROPN
ejpam-5958	447	43	for	for	ADP
ejpam-5958	447	44	funding	fund	VERB
ejpam-5958	447	45	this	this	DET
ejpam-5958	447	46	work	work	NOUN
ejpam-5958	447	47	.	.	PUNCT
ejpam-5958	448	1	references	reference	NOUN
ejpam-5958	448	2	[	[	X
ejpam-5958	448	3	1	1	X
ejpam-5958	448	4	]	]	PUNCT
ejpam-5958	448	5	j.	j.	PROPN
ejpam-5958	448	6	dugundji	dugundji	PROPN
ejpam-5958	448	7	.	.	PUNCT
ejpam-5958	449	1	topology	topology	PROPN
ejpam-5958	449	2	.	.	PUNCT
ejpam-5958	450	1	allyn	allyn	PROPN
ejpam-5958	450	2	and	and	CCONJ
ejpam-5958	450	3	bacon	bacon	PROPN
ejpam-5958	450	4	,	,	PUNCT
ejpam-5958	450	5	boston	boston	PROPN
ejpam-5958	450	6	,	,	PUNCT
ejpam-5958	450	7	1966	1966	NUM
ejpam-5958	450	8	.	.	PUNCT
ejpam-5958	451	1	[	[	X
ejpam-5958	451	2	2	2	NUM
ejpam-5958	451	3	]	]	PUNCT
ejpam-5958	451	4	a.	a.	NOUN
ejpam-5958	451	5	chiş	chiş	PROPN
ejpam-5958	451	6	and	and	CCONJ
ejpam-5958	451	7	r.	r.	PROPN
ejpam-5958	451	8	precup	precup	PROPN
ejpam-5958	451	9	.	.	PUNCT
ejpam-5958	452	1	continuation	continuation	NOUN
ejpam-5958	452	2	theory	theory	NOUN
ejpam-5958	452	3	for	for	ADP
ejpam-5958	452	4	general	general	ADJ
ejpam-5958	452	5	contractions	contraction	NOUN
ejpam-5958	452	6	in	in	ADP
ejpam-5958	452	7	gauge	gauge	ADJ
ejpam-5958	452	8	spaces	space	NOUN
ejpam-5958	452	9	.	.	PUNCT
ejpam-5958	453	1	fixed	fix	VERB
ejpam-5958	453	2	point	point	NOUN
ejpam-5958	453	3	theory	theory	NOUN
ejpam-5958	453	4	and	and	CCONJ
ejpam-5958	453	5	applications	application	NOUN
ejpam-5958	453	6	,	,	PUNCT
ejpam-5958	453	7	2004:173–185	2004:173–185	ADP
ejpam-5958	453	8	,	,	PUNCT
ejpam-5958	453	9	2004	2004	NUM
ejpam-5958	453	10	.	.	PUNCT
ejpam-5958	454	1	[	[	X
ejpam-5958	454	2	3	3	NUM
ejpam-5958	454	3	]	]	X
ejpam-5958	454	4	m.	m.	NOUN
ejpam-5958	454	5	frigon	frigon	PROPN
ejpam-5958	454	6	.	.	PUNCT
ejpam-5958	455	1	fixed	fix	VERB
ejpam-5958	455	2	point	point	NOUN
ejpam-5958	455	3	results	result	NOUN
ejpam-5958	455	4	for	for	ADP
ejpam-5958	455	5	generalized	generalized	ADJ
ejpam-5958	455	6	contractions	contraction	NOUN
ejpam-5958	455	7	in	in	ADP
ejpam-5958	455	8	gauge	gauge	ADJ
ejpam-5958	455	9	spaces	space	NOUN
ejpam-5958	455	10	and	and	CCONJ
ejpam-5958	455	11	applications	application	NOUN
ejpam-5958	455	12	.	.	PUNCT
ejpam-5958	456	1	proceedings	proceeding	NOUN
ejpam-5958	456	2	of	of	ADP
ejpam-5958	456	3	the	the	DET
ejpam-5958	456	4	american	american	PROPN
ejpam-5958	456	5	mathematical	mathematical	PROPN
ejpam-5958	456	6	society	society	NOUN
ejpam-5958	456	7	,	,	PUNCT
ejpam-5958	456	8	128(10):2957–2965	128(10):2957–2965	NUM
ejpam-5958	456	9	,	,	PUNCT
ejpam-5958	456	10	2000	2000	NUM
ejpam-5958	456	11	.	.	PUNCT
ejpam-5958	457	1	[	[	X
ejpam-5958	457	2	4	4	X
ejpam-5958	457	3	]	]	X
ejpam-5958	457	4	h.	h.	PROPN
ejpam-5958	457	5	işık	işık	PROPN
ejpam-5958	457	6	and	and	CCONJ
ejpam-5958	457	7	c.	c.	PROPN
ejpam-5958	457	8	ionescu	ionescu	PROPN
ejpam-5958	457	9	.	.	PUNCT
ejpam-5958	458	1	new	new	ADJ
ejpam-5958	458	2	type	type	NOUN
ejpam-5958	458	3	of	of	ADP
ejpam-5958	458	4	multivalued	multivalued	ADJ
ejpam-5958	458	5	contractions	contraction	NOUN
ejpam-5958	458	6	with	with	ADP
ejpam-5958	458	7	related	related	ADJ
ejpam-5958	458	8	results	result	NOUN
ejpam-5958	458	9	and	and	CCONJ
ejpam-5958	458	10	applications	application	NOUN
ejpam-5958	458	11	.	.	PUNCT
ejpam-5958	459	1	fixed	fix	VERB
ejpam-5958	459	2	point	point	NOUN
ejpam-5958	459	3	theory	theory	NOUN
ejpam-5958	459	4	and	and	CCONJ
ejpam-5958	459	5	applications	application	NOUN
ejpam-5958	459	6	,	,	PUNCT
ejpam-5958	459	7	2011:98	2011:98	NUM
ejpam-5958	459	8	,	,	PUNCT
ejpam-5958	459	9	2011	2011	NUM
ejpam-5958	459	10	.	.	PUNCT
ejpam-5958	460	1	[	[	X
ejpam-5958	460	2	5	5	NUM
ejpam-5958	460	3	]	]	PUNCT
ejpam-5958	460	4	m.	m.	NOUN
ejpam-5958	460	5	cherichi	cherichi	PROPN
ejpam-5958	460	6	,	,	PUNCT
ejpam-5958	460	7	b.	b.	PROPN
ejpam-5958	460	8	samet	samet	PROPN
ejpam-5958	460	9	,	,	PUNCT
ejpam-5958	460	10	and	and	CCONJ
ejpam-5958	460	11	c.	c.	PROPN
ejpam-5958	460	12	vetro	vetro	PROPN
ejpam-5958	460	13	.	.	PUNCT
ejpam-5958	460	14	solvability	solvability	NOUN
ejpam-5958	460	15	of	of	ADP
ejpam-5958	460	16	integrodifferential	integrodifferential	ADJ
ejpam-5958	460	17	problem	problem	NOUN
ejpam-5958	460	18	via	via	ADP
ejpam-5958	460	19	fixed	fix	VERB
ejpam-5958	460	20	point	point	NOUN
ejpam-5958	460	21	theory	theory	NOUN
ejpam-5958	460	22	in	in	ADP
ejpam-5958	460	23	b	b	NOUN
ejpam-5958	460	24	-	-	ADJ
ejpam-5958	460	25	metric	metric	ADJ
ejpam-5958	460	26	spaces	space	NOUN
ejpam-5958	460	27	.	.	PUNCT
ejpam-5958	461	1	journal	journal	NOUN
ejpam-5958	461	2	of	of	ADP
ejpam-5958	461	3	function	function	NOUN
ejpam-5958	461	4	spaces	space	NOUN
ejpam-5958	461	5	and	and	CCONJ
ejpam-5958	461	6	applications	application	NOUN
ejpam-5958	461	7	,	,	PUNCT
ejpam-5958	461	8	2013:219839	2013:219839	NUM
ejpam-5958	461	9	,	,	PUNCT
ejpam-5958	461	10	2013	2013	NUM
ejpam-5958	461	11	.	.	PUNCT
ejpam-5958	462	1	[	[	X
ejpam-5958	462	2	6	6	NUM
ejpam-5958	462	3	]	]	PUNCT
ejpam-5958	462	4	s.	s.	PROPN
ejpam-5958	462	5	czerwik	czerwik	PROPN
ejpam-5958	462	6	.	.	PUNCT
ejpam-5958	463	1	contraction	contraction	NOUN
ejpam-5958	463	2	mappings	mapping	NOUN
ejpam-5958	463	3	in	in	ADP
ejpam-5958	463	4	b	b	NOUN
ejpam-5958	463	5	-	-	ADJ
ejpam-5958	463	6	metric	metric	ADJ
ejpam-5958	463	7	spaces	space	NOUN
ejpam-5958	463	8	.	.	PUNCT
ejpam-5958	464	1	acta	acta	PROPN
ejpam-5958	464	2	mathematica	mathematica	PROPN
ejpam-5958	464	3	et	et	PROPN
ejpam-5958	464	4	informatica	informatica	PROPN
ejpam-5958	464	5	universitatis	universitatis	PROPN
ejpam-5958	464	6	ostraviensis	ostraviensis	PROPN
ejpam-5958	464	7	,	,	PUNCT
ejpam-5958	464	8	1:5–11	1:5–11	NUM
ejpam-5958	464	9	,	,	PUNCT
ejpam-5958	464	10	1993	1993	NUM
ejpam-5958	464	11	.	.	PUNCT
ejpam-5958	465	1	[	[	X
ejpam-5958	465	2	7	7	X
ejpam-5958	465	3	]	]	X
ejpam-5958	465	4	d.	d.	PROPN
ejpam-5958	465	5	mitrea	mitrea	PROPN
ejpam-5958	465	6	,	,	PUNCT
ejpam-5958	465	7	i.	i.	PROPN
ejpam-5958	465	8	mitrea	mitrea	PROPN
ejpam-5958	465	9	,	,	PUNCT
ejpam-5958	465	10	m.	m.	NOUN
ejpam-5958	465	11	mitrea	mitrea	PROPN
ejpam-5958	465	12	,	,	PUNCT
ejpam-5958	465	13	and	and	CCONJ
ejpam-5958	465	14	s.	s.	PROPN
ejpam-5958	465	15	monniaux	monniaux	PROPN
ejpam-5958	465	16	.	.	PUNCT
ejpam-5958	466	1	groupoid	groupoid	PROPN
ejpam-5958	466	2	metrization	metrization	PROPN
ejpam-5958	466	3	theory	theory	NOUN
ejpam-5958	466	4	with	with	ADP
ejpam-5958	466	5	applications	application	NOUN
ejpam-5958	466	6	to	to	ADP
ejpam-5958	466	7	analysis	analysis	NOUN
ejpam-5958	466	8	on	on	ADP
ejpam-5958	466	9	quasi	quasi	ADJ
ejpam-5958	466	10	-	-	ADJ
ejpam-5958	466	11	metric	metric	ADJ
ejpam-5958	466	12	spaces	space	NOUN
ejpam-5958	466	13	and	and	CCONJ
ejpam-5958	466	14	functional	functional	ADJ
ejpam-5958	466	15	analysis	analysis	NOUN
ejpam-5958	466	16	.	.	PUNCT
ejpam-5958	467	1	birkhäuser	birkhäuser	NOUN
ejpam-5958	467	2	,	,	PUNCT
ejpam-5958	467	3	new	new	PROPN
ejpam-5958	467	4	york	york	PROPN
ejpam-5958	467	5	,	,	PUNCT
ejpam-5958	467	6	2013	2013	NUM
ejpam-5958	467	7	.	.	PUNCT
ejpam-5958	468	1	[	[	X
ejpam-5958	468	2	8	8	NUM
ejpam-5958	468	3	]	]	PUNCT
ejpam-5958	468	4	m.	m.	NOUN
ejpam-5958	468	5	a.	a.	NOUN
ejpam-5958	468	6	khamsi	khamsi	PROPN
ejpam-5958	468	7	and	and	CCONJ
ejpam-5958	468	8	n.	n.	PROPN
ejpam-5958	468	9	hussain	hussain	PROPN
ejpam-5958	468	10	.	.	PUNCT
ejpam-5958	469	1	kkm	kkm	PROPN
ejpam-5958	469	2	mappings	mapping	NOUN
ejpam-5958	469	3	in	in	ADP
ejpam-5958	469	4	metric	metric	ADJ
ejpam-5958	469	5	type	type	NOUN
ejpam-5958	469	6	spaces	space	NOUN
ejpam-5958	469	7	.	.	PUNCT
ejpam-5958	470	1	nonlinear	nonlinear	ADJ
ejpam-5958	470	2	analysis	analysis	NOUN
ejpam-5958	470	3	:	:	PUNCT
ejpam-5958	470	4	theory	theory	NOUN
ejpam-5958	470	5	,	,	PUNCT
ejpam-5958	470	6	methods	method	NOUN
ejpam-5958	470	7	&	&	CCONJ
ejpam-5958	470	8	applications	application	NOUN
ejpam-5958	470	9	,	,	PUNCT
ejpam-5958	470	10	73(9):3123–3129	73(9):3123–3129	NUM
ejpam-5958	470	11	,	,	PUNCT
ejpam-5958	470	12	2010	2010	NUM
ejpam-5958	470	13	.	.	PUNCT
ejpam-5958	471	1	[	[	X
ejpam-5958	471	2	9	9	NUM
ejpam-5958	471	3	]	]	PUNCT
ejpam-5958	471	4	v.	v.	ADP
ejpam-5958	471	5	berinde	berinde	NOUN
ejpam-5958	471	6	and	and	CCONJ
ejpam-5958	471	7	m.	m.	NOUN
ejpam-5958	471	8	păcurar	păcurar	NOUN
ejpam-5958	471	9	.	.	PUNCT
ejpam-5958	472	1	the	the	DET
ejpam-5958	472	2	early	early	ADJ
ejpam-5958	472	3	developments	development	NOUN
ejpam-5958	472	4	in	in	ADP
ejpam-5958	472	5	fixed	fix	VERB
ejpam-5958	472	6	point	point	NOUN
ejpam-5958	472	7	theory	theory	NOUN
ejpam-5958	472	8	on	on	ADP
ejpam-5958	472	9	b	b	X
ejpam-5958	472	10	-	-	PUNCT
ejpam-5958	472	11	metric	metric	ADJ
ejpam-5958	472	12	spaces	space	NOUN
ejpam-5958	472	13	:	:	PUNCT
ejpam-5958	472	14	a	a	DET
ejpam-5958	472	15	brief	brief	ADJ
ejpam-5958	472	16	survey	survey	NOUN
ejpam-5958	472	17	and	and	CCONJ
ejpam-5958	472	18	some	some	DET
ejpam-5958	472	19	important	important	ADJ
ejpam-5958	472	20	related	related	ADJ
ejpam-5958	472	21	aspects	aspect	NOUN
ejpam-5958	472	22	.	.	PUNCT
ejpam-5958	473	1	carpathian	carpathian	ADJ
ejpam-5958	473	2	journal	journal	PROPN
ejpam-5958	473	3	of	of	ADP
ejpam-5958	473	4	mathematics	mathematics	PROPN
ejpam-5958	473	5	,	,	PUNCT
ejpam-5958	473	6	38(3):523–538	38(3):523–538	PROPN
ejpam-5958	473	7	,	,	PUNCT
ejpam-5958	473	8	2022	2022	NUM
ejpam-5958	473	9	.	.	PUNCT
ejpam-5958	474	1	[	[	X
ejpam-5958	474	2	10	10	NUM
ejpam-5958	474	3	]	]	PUNCT
ejpam-5958	474	4	m.	m.	PROPN
ejpam-5958	474	5	u.	u.	PROPN
ejpam-5958	474	6	ali	ali	PROPN
ejpam-5958	474	7	,	,	PUNCT
ejpam-5958	474	8	t.	t.	PROPN
ejpam-5958	474	9	kamran	kamran	PROPN
ejpam-5958	474	10	,	,	PUNCT
ejpam-5958	474	11	and	and	CCONJ
ejpam-5958	474	12	m.	m.	NOUN
ejpam-5958	474	13	postolache	postolache	PROPN
ejpam-5958	474	14	.	.	PUNCT
ejpam-5958	475	1	fixed	fix	VERB
ejpam-5958	475	2	point	point	NOUN
ejpam-5958	475	3	theorems	theorem	NOUN
ejpam-5958	475	4	for	for	ADP
ejpam-5958	475	5	multivalued	multivalued	ADJ
ejpam-5958	475	6	g	g	NOUN
ejpam-5958	475	7	-	-	PUNCT
ejpam-5958	475	8	contractions	contraction	NOUN
ejpam-5958	475	9	in	in	ADP
ejpam-5958	475	10	hausdorff	hausdorff	PROPN
ejpam-5958	475	11	b	b	NOUN
ejpam-5958	475	12	-	-	PUNCT
ejpam-5958	475	13	gauge	gauge	NOUN
ejpam-5958	475	14	space	space	NOUN
ejpam-5958	475	15	.	.	PUNCT
ejpam-5958	476	1	journal	journal	PROPN
ejpam-5958	476	2	of	of	ADP
ejpam-5958	476	3	nonlinear	nonlinear	PROPN
ejpam-5958	476	4	sciences	sciences	PROPN
ejpam-5958	476	5	and	and	CCONJ
ejpam-5958	476	6	applications	application	NOUN
ejpam-5958	476	7	,	,	PUNCT
ejpam-5958	476	8	8(5):847–855	8(5):847–855	NUM
ejpam-5958	476	9	,	,	PUNCT
ejpam-5958	476	10	2015	2015	NUM
ejpam-5958	476	11	.	.	PUNCT
ejpam-5958	477	1	[	[	X
ejpam-5958	477	2	11	11	NUM
ejpam-5958	477	3	]	]	X
ejpam-5958	477	4	h.	h.	PROPN
ejpam-5958	477	5	alsamir	alsamir	PROPN
ejpam-5958	477	6	,	,	PUNCT
ejpam-5958	477	7	h.	h.	PROPN
ejpam-5958	477	8	qawaqneh	qawaqneh	PROPN
ejpam-5958	477	9	,	,	PUNCT
ejpam-5958	477	10	g.	g.	PROPN
ejpam-5958	477	11	al	al	PROPN
ejpam-5958	477	12	-	-	PUNCT
ejpam-5958	477	13	musannef	musannef	PROPN
ejpam-5958	477	14	,	,	PUNCT
ejpam-5958	477	15	and	and	CCONJ
ejpam-5958	477	16	r.	r.	PROPN
ejpam-5958	477	17	khalil	khalil	PROPN
ejpam-5958	477	18	.	.	PUNCT
ejpam-5958	478	1	common	common	ADJ
ejpam-5958	478	2	fixed	fix	VERB
ejpam-5958	478	3	point	point	NOUN
ejpam-5958	478	4	of	of	ADP
ejpam-5958	478	5	generalized	generalized	ADJ
ejpam-5958	478	6	berinde	berinde	NOUN
ejpam-5958	478	7	type	type	NOUN
ejpam-5958	478	8	contraction	contraction	NOUN
ejpam-5958	478	9	and	and	CCONJ
ejpam-5958	478	10	an	an	DET
ejpam-5958	478	11	application	application	NOUN
ejpam-5958	478	12	.	.	PUNCT
ejpam-5958	479	1	european	european	ADJ
ejpam-5958	479	2	journal	journal	PROPN
ejpam-5958	479	3	of	of	ADP
ejpam-5958	479	4	pure	pure	ADJ
ejpam-5958	479	5	and	and	CCONJ
ejpam-5958	479	6	applied	applied	ADJ
ejpam-5958	479	7	mathematics	mathematic	NOUN
ejpam-5958	479	8	,	,	PUNCT
ejpam-5958	479	9	17(4):2492–2504	17(4):2492–2504	NUM
ejpam-5958	479	10	,	,	PUNCT
ejpam-5958	479	11	2024	2024	NUM
ejpam-5958	479	12	.	.	PUNCT
ejpam-5958	480	1	[	[	X
ejpam-5958	480	2	12	12	NUM
ejpam-5958	480	3	]	]	PUNCT
ejpam-5958	480	4	h.	h.	PROPN
ejpam-5958	480	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	480	6	,	,	PUNCT
ejpam-5958	480	7	j.	j.	PROPN
ejpam-5958	480	8	manafian	manafian	PROPN
ejpam-5958	480	9	,	,	PUNCT
ejpam-5958	480	10	m.	m.	NOUN
ejpam-5958	480	11	alharthi	alharthi	PROPN
ejpam-5958	480	12	,	,	PUNCT
ejpam-5958	480	13	and	and	CCONJ
ejpam-5958	480	14	y.	y.	PROPN
ejpam-5958	480	15	alrashed	alrashe	VERB
ejpam-5958	480	16	.	.	PUNCT
ejpam-5958	481	1	stability	stability	NOUN
ejpam-5958	481	2	analysis	analysis	NOUN
ejpam-5958	481	3	,	,	PUNCT
ejpam-5958	481	4	modulation	modulation	NOUN
ejpam-5958	481	5	instability	instability	NOUN
ejpam-5958	481	6	,	,	PUNCT
ejpam-5958	481	7	and	and	CCONJ
ejpam-5958	481	8	beta	beta	NOUN
ejpam-5958	481	9	-	-	PUNCT
ejpam-5958	481	10	time	time	NOUN
ejpam-5958	481	11	fractional	fractional	ADJ
ejpam-5958	481	12	exact	exact	ADJ
ejpam-5958	481	13	soliton	soliton	NOUN
ejpam-5958	481	14	solutions	solution	NOUN
ejpam-5958	481	15	to	to	ADP
ejpam-5958	481	16	the	the	DET
ejpam-5958	481	17	van	van	PROPN
ejpam-5958	481	18	der	der	NOUN
ejpam-5958	481	19	waals	waal	NOUN
ejpam-5958	481	20	equation	equation	NOUN
ejpam-5958	481	21	.	.	PUNCT
ejpam-5958	482	1	mathematics	mathematic	NOUN
ejpam-5958	482	2	,	,	PUNCT
ejpam-5958	482	3	12(14):2257	12(14):2257	NUM
ejpam-5958	482	4	,	,	PUNCT
ejpam-5958	482	5	2024	2024	NUM
ejpam-5958	482	6	.	.	PUNCT
ejpam-5958	483	1	[	[	X
ejpam-5958	483	2	13	13	NUM
ejpam-5958	483	3	]	]	PUNCT
ejpam-5958	483	4	a.	a.	NOUN
ejpam-5958	483	5	branciari	branciari	PROPN
ejpam-5958	483	6	.	.	PUNCT
ejpam-5958	484	1	a	a	DET
ejpam-5958	484	2	fixed	fix	VERB
ejpam-5958	484	3	point	point	NOUN
ejpam-5958	484	4	theorem	theorem	NOUN
ejpam-5958	484	5	of	of	ADP
ejpam-5958	484	6	banach	banach	NOUN
ejpam-5958	484	7	-	-	PUNCT
ejpam-5958	484	8	caccioppoli	caccioppoli	NOUN
ejpam-5958	484	9	type	type	NOUN
ejpam-5958	484	10	on	on	ADP
ejpam-5958	484	11	a	a	DET
ejpam-5958	484	12	class	class	NOUN
ejpam-5958	484	13	of	of	ADP
ejpam-5958	484	14	generalized	generalized	ADJ
ejpam-5958	484	15	metric	metric	ADJ
ejpam-5958	484	16	spaces	space	NOUN
ejpam-5958	484	17	.	.	PUNCT
ejpam-5958	485	1	publicationes	publicatione	NOUN
ejpam-5958	485	2	mathematicae	mathematicae	PROPN
ejpam-5958	485	3	debrecen	debrecen	PROPN
ejpam-5958	485	4	,	,	PUNCT
ejpam-5958	485	5	57(1	57(1	PROPN
ejpam-5958	485	6	-	-	PUNCT
ejpam-5958	485	7	2):31–37	2):31–37	NUM
ejpam-5958	485	8	,	,	PUNCT
ejpam-5958	485	9	2000	2000	NUM
ejpam-5958	485	10	.	.	PUNCT
ejpam-5958	486	1	[	[	X
ejpam-5958	486	2	14	14	NUM
ejpam-5958	486	3	]	]	X
ejpam-5958	486	4	h.	h.	PROPN
ejpam-5958	486	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	486	6	,	,	PUNCT
ejpam-5958	486	7	h.	h.	PROPN
ejpam-5958	486	8	a.	a.	PROPN
ejpam-5958	486	9	hammad	hammad	PROPN
ejpam-5958	486	10	,	,	PUNCT
ejpam-5958	486	11	and	and	CCONJ
ejpam-5958	486	12	h.	h.	PROPN
ejpam-5958	486	13	aydi	aydi	VERB
ejpam-5958	486	14	.	.	PUNCT
ejpam-5958	487	1	exploring	explore	VERB
ejpam-5958	487	2	new	new	ADJ
ejpam-5958	487	3	geometric	geometric	ADJ
ejpam-5958	487	4	contraction	contraction	NOUN
ejpam-5958	487	5	mappings	mapping	NOUN
ejpam-5958	487	6	and	and	CCONJ
ejpam-5958	487	7	their	their	PRON
ejpam-5958	487	8	applications	application	NOUN
ejpam-5958	487	9	in	in	ADP
ejpam-5958	487	10	fractional	fractional	ADJ
ejpam-5958	487	11	metric	metric	ADJ
ejpam-5958	487	12	spaces	space	NOUN
ejpam-5958	487	13	.	.	PUNCT
ejpam-5958	488	1	aims	aim	VERB
ejpam-5958	488	2	mathematics	mathematic	NOUN
ejpam-5958	488	3	,	,	PUNCT
ejpam-5958	488	4	9(1):521–541	9(1):521–541	NUM
ejpam-5958	488	5	,	,	PUNCT
ejpam-5958	488	6	2024	2024	NUM
ejpam-5958	488	7	.	.	PUNCT
ejpam-5958	489	1	[	[	X
ejpam-5958	489	2	15	15	NUM
ejpam-5958	489	3	]	]	PUNCT
ejpam-5958	489	4	k.	k.	PROPN
ejpam-5958	489	5	h.	h.	PROPN
ejpam-5958	489	6	alam	alam	PROPN
ejpam-5958	489	7	,	,	PUNCT
ejpam-5958	489	8	y.	y.	PROPN
ejpam-5958	489	9	rohen	rohen	PROPN
ejpam-5958	489	10	,	,	PUNCT
ejpam-5958	489	11	i.	i.	PROPN
ejpam-5958	489	12	a.	a.	PROPN
ejpam-5958	489	13	kallel	kallel	PROPN
ejpam-5958	489	14	,	,	PUNCT
ejpam-5958	489	15	and	and	CCONJ
ejpam-5958	489	16	j.	j.	PROPN
ejpam-5958	489	17	ahmad	ahmad	PROPN
ejpam-5958	489	18	.	.	PUNCT
ejpam-5958	490	1	solution	solution	NOUN
ejpam-5958	490	2	of	of	ADP
ejpam-5958	490	3	an	an	DET
ejpam-5958	490	4	algebraic	algebraic	ADJ
ejpam-5958	490	5	linear	linear	NOUN
ejpam-5958	490	6	k.	k.	PROPN
ejpam-5958	490	7	nisse	nisse	PROPN
ejpam-5958	490	8	et	et	PROPN
ejpam-5958	490	9	al	al	PROPN
ejpam-5958	490	10	.	.	PUNCT
ejpam-5958	490	11	/	/	SYM
ejpam-5958	490	12	eur	eur	PROPN
ejpam-5958	490	13	.	.	PUNCT
ejpam-5958	491	1	j.	j.	PROPN
ejpam-5958	491	2	pure	pure	PROPN
ejpam-5958	491	3	appl	appl	PROPN
ejpam-5958	491	4	.	.	PROPN
ejpam-5958	491	5	math	math	PROPN
ejpam-5958	491	6	,	,	PUNCT
ejpam-5958	491	7	18	18	NUM
ejpam-5958	491	8	(	(	PUNCT
ejpam-5958	491	9	2	2	NUM
ejpam-5958	491	10	)	)	PUNCT
ejpam-5958	491	11	(	(	PUNCT
ejpam-5958	491	12	2025	2025	NUM
ejpam-5958	491	13	)	)	PUNCT
ejpam-5958	491	14	,	,	PUNCT
ejpam-5958	491	15	5958	5958	NUM
ejpam-5958	491	16	21	21	NUM
ejpam-5958	491	17	of	of	ADP
ejpam-5958	491	18	22	22	NUM
ejpam-5958	491	19	system	system	NOUN
ejpam-5958	491	20	of	of	ADP
ejpam-5958	491	21	equations	equation	NOUN
ejpam-5958	491	22	using	use	VERB
ejpam-5958	491	23	fixed	fix	VERB
ejpam-5958	491	24	point	point	NOUN
ejpam-5958	491	25	results	result	NOUN
ejpam-5958	491	26	in	in	ADP
ejpam-5958	491	27	c∗-algebra	c∗-algebra	PROPN
ejpam-5958	491	28	valued	value	VERB
ejpam-5958	491	29	extended	extend	VERB
ejpam-5958	491	30	branciari	branciari	PROPN
ejpam-5958	491	31	sb	sb	NOUN
ejpam-5958	491	32	-	-	ADJ
ejpam-5958	491	33	metric	metric	ADJ
ejpam-5958	491	34	spaces	space	NOUN
ejpam-5958	491	35	.	.	PUNCT
ejpam-5958	492	1	international	international	ADJ
ejpam-5958	492	2	journal	journal	NOUN
ejpam-5958	492	3	of	of	ADP
ejpam-5958	492	4	analysis	analysis	NOUN
ejpam-5958	492	5	and	and	CCONJ
ejpam-5958	492	6	applications	application	NOUN
ejpam-5958	492	7	,	,	PUNCT
ejpam-5958	492	8	22(139	22(139	NOUN
ejpam-5958	492	9	)	)	PUNCT
ejpam-5958	492	10	,	,	PUNCT
ejpam-5958	492	11	2024	2024	NUM
ejpam-5958	492	12	.	.	PUNCT
ejpam-5958	493	1	[	[	X
ejpam-5958	493	2	16	16	NUM
ejpam-5958	493	3	]	]	X
ejpam-5958	493	4	h.	h.	PROPN
ejpam-5958	493	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	493	6	,	,	PUNCT
ejpam-5958	493	7	m.	m.	PROPN
ejpam-5958	493	8	s.	s.	PROPN
ejpam-5958	493	9	m.	m.	PROPN
ejpam-5958	493	10	noorani	noorani	PROPN
ejpam-5958	493	11	,	,	PUNCT
ejpam-5958	493	12	and	and	CCONJ
ejpam-5958	493	13	w.	w.	PROPN
ejpam-5958	493	14	shatanawi	shatanawi	PROPN
ejpam-5958	493	15	.	.	PUNCT
ejpam-5958	494	1	fixed	fix	VERB
ejpam-5958	494	2	point	point	NOUN
ejpam-5958	494	3	theorems	theorem	NOUN
ejpam-5958	494	4	for	for	ADP
ejpam-5958	494	5	(	(	PUNCT
ejpam-5958	494	6	α	α	X
ejpam-5958	494	7	,	,	PUNCT
ejpam-5958	494	8	k	k	NOUN
ejpam-5958	494	9	,	,	PUNCT
ejpam-5958	494	10	θ)-contractive	θ)-contractive	PUNCT
ejpam-5958	494	11	multi	multi	ADJ
ejpam-5958	494	12	-	-	ADJ
ejpam-5958	494	13	valued	value	VERB
ejpam-5958	494	14	mapping	mapping	NOUN
ejpam-5958	494	15	in	in	ADP
ejpam-5958	494	16	b	b	NOUN
ejpam-5958	494	17	-	-	PUNCT
ejpam-5958	494	18	metric	metric	ADJ
ejpam-5958	494	19	space	space	NOUN
ejpam-5958	494	20	and	and	CCONJ
ejpam-5958	494	21	applications	application	NOUN
ejpam-5958	494	22	.	.	PUNCT
ejpam-5958	495	1	international	international	ADJ
ejpam-5958	495	2	journal	journal	PROPN
ejpam-5958	495	3	of	of	ADP
ejpam-5958	495	4	mathematics	mathematic	NOUN
ejpam-5958	495	5	and	and	CCONJ
ejpam-5958	495	6	computer	computer	NOUN
ejpam-5958	495	7	science	science	NOUN
ejpam-5958	495	8	,	,	PUNCT
ejpam-5958	495	9	14(1):263–283	14(1):263–283	NUM
ejpam-5958	495	10	,	,	PUNCT
ejpam-5958	495	11	2019	2019	NUM
ejpam-5958	495	12	.	.	PUNCT
ejpam-5958	496	1	[	[	X
ejpam-5958	496	2	17	17	NUM
ejpam-5958	496	3	]	]	X
ejpam-5958	496	4	h.	h.	PROPN
ejpam-5958	496	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	496	6	,	,	PUNCT
ejpam-5958	496	7	m.	m.	PROPN
ejpam-5958	496	8	s.	s.	PROPN
ejpam-5958	496	9	noorani	noorani	PROPN
ejpam-5958	496	10	,	,	PUNCT
ejpam-5958	496	11	and	and	CCONJ
ejpam-5958	496	12	w.	w.	PROPN
ejpam-5958	496	13	shatanawi	shatanawi	PROPN
ejpam-5958	496	14	.	.	PUNCT
ejpam-5958	497	1	fixed	fix	VERB
ejpam-5958	497	2	point	point	NOUN
ejpam-5958	497	3	results	result	NOUN
ejpam-5958	497	4	for	for	ADP
ejpam-5958	497	5	geraghty	geraghty	PROPN
ejpam-5958	497	6	type	type	NOUN
ejpam-5958	497	7	generalized	generalize	VERB
ejpam-5958	497	8	f	f	NOUN
ejpam-5958	497	9	-	-	PUNCT
ejpam-5958	497	10	contraction	contraction	NOUN
ejpam-5958	497	11	for	for	ADP
ejpam-5958	497	12	weak	weak	ADJ
ejpam-5958	497	13	admissible	admissible	ADJ
ejpam-5958	497	14	mappings	mapping	NOUN
ejpam-5958	497	15	in	in	ADP
ejpam-5958	497	16	metric	metric	ADJ
ejpam-5958	497	17	-	-	PUNCT
ejpam-5958	497	18	like	like	ADJ
ejpam-5958	497	19	spaces	space	NOUN
ejpam-5958	497	20	.	.	PUNCT
ejpam-5958	498	1	european	european	ADJ
ejpam-5958	498	2	journal	journal	PROPN
ejpam-5958	498	3	of	of	ADP
ejpam-5958	498	4	pure	pure	ADJ
ejpam-5958	498	5	and	and	CCONJ
ejpam-5958	498	6	applied	applied	ADJ
ejpam-5958	498	7	mathematics	mathematic	NOUN
ejpam-5958	498	8	,	,	PUNCT
ejpam-5958	498	9	11(3):702–716	11(3):702–716	PROPN
ejpam-5958	498	10	,	,	PUNCT
ejpam-5958	498	11	2018	2018	NUM
ejpam-5958	498	12	.	.	PUNCT
ejpam-5958	499	1	[	[	X
ejpam-5958	499	2	18	18	NUM
ejpam-5958	499	3	]	]	X
ejpam-5958	499	4	h.	h.	PROPN
ejpam-5958	499	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	499	6	,	,	PUNCT
ejpam-5958	499	7	m.	m.	PROPN
ejpam-5958	499	8	s.	s.	PROPN
ejpam-5958	499	9	m.	m.	PROPN
ejpam-5958	499	10	noorani	noorani	PROPN
ejpam-5958	499	11	,	,	PUNCT
ejpam-5958	499	12	and	and	CCONJ
ejpam-5958	499	13	h.	h.	PROPN
ejpam-5958	499	14	aydi	aydi	VERB
ejpam-5958	499	15	.	.	PUNCT
ejpam-5958	500	1	some	some	DET
ejpam-5958	500	2	new	new	ADJ
ejpam-5958	500	3	characterizations	characterization	NOUN
ejpam-5958	500	4	and	and	CCONJ
ejpam-5958	500	5	results	result	NOUN
ejpam-5958	500	6	for	for	ADP
ejpam-5958	500	7	fuzzy	fuzzy	ADJ
ejpam-5958	500	8	contractions	contraction	NOUN
ejpam-5958	500	9	in	in	ADP
ejpam-5958	500	10	fuzzy	fuzzy	ADJ
ejpam-5958	500	11	b	b	X
ejpam-5958	500	12	-	-	PUNCT
ejpam-5958	500	13	metric	metric	ADJ
ejpam-5958	500	14	spaces	space	NOUN
ejpam-5958	500	15	and	and	CCONJ
ejpam-5958	500	16	applications	application	NOUN
ejpam-5958	500	17	.	.	PUNCT
ejpam-5958	501	1	aims	aim	VERB
ejpam-5958	501	2	mathematics	mathematics	PROPN
ejpam-5958	501	3	,	,	PUNCT
ejpam-5958	501	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-5958	501	5	,	,	PUNCT
ejpam-5958	501	6	2023	2023	NUM
ejpam-5958	501	7	.	.	PUNCT
ejpam-5958	502	1	[	[	X
ejpam-5958	502	2	19	19	NUM
ejpam-5958	502	3	]	]	PUNCT
ejpam-5958	502	4	m.	m.	NOUN
ejpam-5958	502	5	nazam	nazam	PROPN
ejpam-5958	502	6	,	,	PUNCT
ejpam-5958	502	7	h.	h.	PROPN
ejpam-5958	502	8	aydi	aydi	PROPN
ejpam-5958	502	9	,	,	PUNCT
ejpam-5958	502	10	m.	m.	NOUN
ejpam-5958	502	11	s.	s.	PROPN
ejpam-5958	502	12	m.	m.	PROPN
ejpam-5958	502	13	noorani	noorani	PROPN
ejpam-5958	502	14	,	,	PUNCT
ejpam-5958	502	15	and	and	CCONJ
ejpam-5958	502	16	h.	h.	PROPN
ejpam-5958	502	17	qawaqneh	qawaqneh	PROPN
ejpam-5958	502	18	.	.	PUNCT
ejpam-5958	503	1	existence	existence	NOUN
ejpam-5958	503	2	of	of	ADP
ejpam-5958	503	3	fixed	fix	VERB
ejpam-5958	503	4	points	point	NOUN
ejpam-5958	503	5	of	of	ADP
ejpam-5958	503	6	four	four	NUM
ejpam-5958	503	7	maps	map	NOUN
ejpam-5958	503	8	for	for	ADP
ejpam-5958	503	9	a	a	DET
ejpam-5958	503	10	new	new	ADJ
ejpam-5958	503	11	generalized	generalized	ADJ
ejpam-5958	503	12	f	f	NOUN
ejpam-5958	503	13	-	-	PUNCT
ejpam-5958	503	14	contraction	contraction	NOUN
ejpam-5958	503	15	and	and	CCONJ
ejpam-5958	503	16	an	an	DET
ejpam-5958	503	17	application	application	NOUN
ejpam-5958	503	18	.	.	PUNCT
ejpam-5958	504	1	journal	journal	NOUN
ejpam-5958	504	2	of	of	ADP
ejpam-5958	504	3	function	function	NOUN
ejpam-5958	504	4	spaces	space	NOUN
ejpam-5958	504	5	,	,	PUNCT
ejpam-5958	504	6	2019:5980312	2019:5980312	NUM
ejpam-5958	504	7	,	,	PUNCT
ejpam-5958	504	8	2019	2019	NUM
ejpam-5958	504	9	.	.	PUNCT
ejpam-5958	505	1	[	[	X
ejpam-5958	505	2	20	20	NUM
ejpam-5958	505	3	]	]	PUNCT
ejpam-5958	505	4	h.	h.	PROPN
ejpam-5958	505	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	505	6	.	.	PUNCT
ejpam-5958	506	1	new	new	ADJ
ejpam-5958	506	2	functions	function	NOUN
ejpam-5958	506	3	for	for	ADP
ejpam-5958	506	4	fixed	fix	VERB
ejpam-5958	506	5	point	point	NOUN
ejpam-5958	506	6	results	result	NOUN
ejpam-5958	506	7	in	in	ADP
ejpam-5958	506	8	metric	metric	ADJ
ejpam-5958	506	9	spaces	space	NOUN
ejpam-5958	506	10	with	with	ADP
ejpam-5958	506	11	some	some	DET
ejpam-5958	506	12	applications	application	NOUN
ejpam-5958	506	13	.	.	PUNCT
ejpam-5958	507	1	indian	indian	ADJ
ejpam-5958	507	2	journal	journal	PROPN
ejpam-5958	507	3	of	of	ADP
ejpam-5958	507	4	mathematics	mathematic	NOUN
ejpam-5958	507	5	,	,	PUNCT
ejpam-5958	507	6	66(1):55–84	66(1):55–84	NOUN
ejpam-5958	507	7	,	,	PUNCT
ejpam-5958	507	8	2024	2024	NUM
ejpam-5958	507	9	.	.	PUNCT
ejpam-5958	508	1	[	[	X
ejpam-5958	508	2	21	21	NUM
ejpam-5958	508	3	]	]	X
ejpam-5958	508	4	h.	h.	PROPN
ejpam-5958	508	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	508	6	.	.	PUNCT
ejpam-5958	509	1	new	new	ADJ
ejpam-5958	509	2	contraction	contraction	NOUN
ejpam-5958	509	3	embedded	embed	VERB
ejpam-5958	509	4	with	with	ADP
ejpam-5958	509	5	simulation	simulation	NOUN
ejpam-5958	509	6	function	function	NOUN
ejpam-5958	509	7	and	and	CCONJ
ejpam-5958	509	8	cyclic	cyclic	ADJ
ejpam-5958	509	9	(	(	PUNCT
ejpam-5958	509	10	α	α	NOUN
ejpam-5958	509	11	,	,	PUNCT
ejpam-5958	509	12	β)admissible	β)admissible	ADJ
ejpam-5958	509	13	in	in	ADP
ejpam-5958	509	14	metric	metric	ADJ
ejpam-5958	509	15	-	-	PUNCT
ejpam-5958	509	16	like	like	ADJ
ejpam-5958	509	17	spaces	space	NOUN
ejpam-5958	509	18	.	.	PUNCT
ejpam-5958	510	1	international	international	ADJ
ejpam-5958	510	2	journal	journal	PROPN
ejpam-5958	510	3	of	of	ADP
ejpam-5958	510	4	mathematics	mathematic	NOUN
ejpam-5958	510	5	and	and	CCONJ
ejpam-5958	510	6	computer	computer	NOUN
ejpam-5958	510	7	science	science	NOUN
ejpam-5958	510	8	,	,	PUNCT
ejpam-5958	510	9	15(1):1029–1044	15(1):1029–1044	PROPN
ejpam-5958	510	10	,	,	PUNCT
ejpam-5958	510	11	2020	2020	NUM
ejpam-5958	510	12	.	.	PUNCT
ejpam-5958	511	1	[	[	X
ejpam-5958	511	2	22	22	NUM
ejpam-5958	511	3	]	]	PUNCT
ejpam-5958	511	4	h.	h.	PROPN
ejpam-5958	511	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	511	6	.	.	PUNCT
ejpam-5958	512	1	fractional	fractional	ADJ
ejpam-5958	512	2	analytic	analytic	ADJ
ejpam-5958	512	3	solutions	solution	NOUN
ejpam-5958	512	4	and	and	CCONJ
ejpam-5958	512	5	fixed	fix	VERB
ejpam-5958	512	6	point	point	NOUN
ejpam-5958	512	7	results	result	NOUN
ejpam-5958	512	8	with	with	ADP
ejpam-5958	512	9	some	some	DET
ejpam-5958	512	10	applications	application	NOUN
ejpam-5958	512	11	.	.	PUNCT
ejpam-5958	513	1	advances	advance	NOUN
ejpam-5958	513	2	in	in	ADP
ejpam-5958	513	3	fixed	fix	VERB
ejpam-5958	513	4	point	point	NOUN
ejpam-5958	513	5	theory	theory	NOUN
ejpam-5958	513	6	,	,	PUNCT
ejpam-5958	513	7	14(1):1–18	14(1):1–18	NUM
ejpam-5958	513	8	,	,	PUNCT
ejpam-5958	513	9	2024	2024	NUM
ejpam-5958	513	10	.	.	PUNCT
ejpam-5958	514	1	[	[	X
ejpam-5958	514	2	23	23	NUM
ejpam-5958	514	3	]	]	X
ejpam-5958	514	4	r.	r.	PROPN
ejpam-5958	514	5	george	george	PROPN
ejpam-5958	514	6	,	,	PUNCT
ejpam-5958	514	7	s.	s.	PROPN
ejpam-5958	514	8	radenović	radenović	PROPN
ejpam-5958	514	9	,	,	PUNCT
ejpam-5958	514	10	k.	k.	PROPN
ejpam-5958	515	1	p.	p.	PROPN
ejpam-5958	515	2	reshma	reshma	PROPN
ejpam-5958	515	3	,	,	PUNCT
ejpam-5958	515	4	and	and	CCONJ
ejpam-5958	515	5	s.	s.	PROPN
ejpam-5958	515	6	shukla	shukla	PROPN
ejpam-5958	515	7	.	.	PUNCT
ejpam-5958	516	1	rectangular	rectangular	ADJ
ejpam-5958	516	2	b	b	X
ejpam-5958	516	3	-	-	ADJ
ejpam-5958	516	4	metric	metric	ADJ
ejpam-5958	516	5	spaces	space	NOUN
ejpam-5958	516	6	and	and	CCONJ
ejpam-5958	516	7	contraction	contraction	NOUN
ejpam-5958	516	8	principle	principle	NOUN
ejpam-5958	516	9	.	.	PUNCT
ejpam-5958	517	1	journal	journal	PROPN
ejpam-5958	517	2	of	of	ADP
ejpam-5958	517	3	nonlinear	nonlinear	PROPN
ejpam-5958	517	4	sciences	sciences	PROPN
ejpam-5958	517	5	and	and	CCONJ
ejpam-5958	517	6	applications	application	NOUN
ejpam-5958	517	7	,	,	PUNCT
ejpam-5958	517	8	8(6):1005	8(6):1005	NUM
ejpam-5958	517	9	–	–	PUNCT
ejpam-5958	517	10	1013	1013	NUM
ejpam-5958	517	11	,	,	PUNCT
ejpam-5958	517	12	2015	2015	NUM
ejpam-5958	517	13	.	.	PUNCT
ejpam-5958	518	1	[	[	X
ejpam-5958	518	2	24	24	NUM
ejpam-5958	518	3	]	]	X
ejpam-5958	518	4	h.	h.	PROPN
ejpam-5958	518	5	alsamir	alsamir	PROPN
ejpam-5958	518	6	,	,	PUNCT
ejpam-5958	518	7	h.	h.	PROPN
ejpam-5958	518	8	aydi	aydi	PROPN
ejpam-5958	518	9	,	,	PUNCT
ejpam-5958	518	10	m.	m.	NOUN
ejpam-5958	518	11	s.	s.	PROPN
ejpam-5958	518	12	m.	m.	PROPN
ejpam-5958	518	13	noorani	noorani	PROPN
ejpam-5958	518	14	,	,	PUNCT
ejpam-5958	518	15	w.	w.	PROPN
ejpam-5958	518	16	shatanawi	shatanawi	PROPN
ejpam-5958	518	17	,	,	PUNCT
ejpam-5958	518	18	h.	h.	PROPN
ejpam-5958	518	19	akhadkulov	akhadkulov	PROPN
ejpam-5958	518	20	,	,	PUNCT
ejpam-5958	518	21	h.	h.	PROPN
ejpam-5958	518	22	qawaqneh	qawaqneh	PROPN
ejpam-5958	518	23	,	,	PUNCT
ejpam-5958	518	24	and	and	CCONJ
ejpam-5958	518	25	k.	k.	PROPN
ejpam-5958	518	26	alanazi	alanazi	PROPN
ejpam-5958	518	27	.	.	PUNCT
ejpam-5958	519	1	fixed	fix	VERB
ejpam-5958	519	2	point	point	NOUN
ejpam-5958	519	3	results	result	NOUN
ejpam-5958	519	4	in	in	ADP
ejpam-5958	519	5	metric	metric	ADJ
ejpam-5958	519	6	-	-	PUNCT
ejpam-5958	519	7	like	like	ADJ
ejpam-5958	519	8	spaces	space	NOUN
ejpam-5958	519	9	via	via	ADP
ejpam-5958	519	10	σ	σ	PROPN
ejpam-5958	519	11	-	-	PUNCT
ejpam-5958	519	12	simulation	simulation	NOUN
ejpam-5958	519	13	functions	function	NOUN
ejpam-5958	519	14	.	.	PUNCT
ejpam-5958	520	1	european	european	ADJ
ejpam-5958	520	2	journal	journal	PROPN
ejpam-5958	520	3	of	of	ADP
ejpam-5958	520	4	pure	pure	ADJ
ejpam-5958	520	5	and	and	CCONJ
ejpam-5958	520	6	applied	applied	ADJ
ejpam-5958	520	7	mathematics	mathematic	NOUN
ejpam-5958	520	8	,	,	PUNCT
ejpam-5958	520	9	12(1):88–100	12(1):88–100	NUM
ejpam-5958	520	10	,	,	PUNCT
ejpam-5958	520	11	2019	2019	NUM
ejpam-5958	520	12	.	.	PUNCT
ejpam-5958	521	1	[	[	X
ejpam-5958	521	2	25	25	NUM
ejpam-5958	521	3	]	]	PUNCT
ejpam-5958	521	4	t.	t.	PROPN
ejpam-5958	521	5	kamran	kamran	PROPN
ejpam-5958	521	6	,	,	PUNCT
ejpam-5958	521	7	m.	m.	NOUN
ejpam-5958	521	8	samreen	samreen	PROPN
ejpam-5958	521	9	,	,	PUNCT
ejpam-5958	521	10	and	and	CCONJ
ejpam-5958	521	11	o.	o.	PROPN
ejpam-5958	521	12	u.	u.	PROPN
ejpam-5958	521	13	ain	ain	PROPN
ejpam-5958	521	14	.	.	PUNCT
ejpam-5958	522	1	generalization	generalization	NOUN
ejpam-5958	522	2	of	of	ADP
ejpam-5958	522	3	metric	metric	ADJ
ejpam-5958	522	4	space	space	NOUN
ejpam-5958	522	5	and	and	CCONJ
ejpam-5958	522	6	some	some	DET
ejpam-5958	522	7	fixed	fix	VERB
ejpam-5958	522	8	point	point	NOUN
ejpam-5958	522	9	theorems	theorem	NOUN
ejpam-5958	522	10	.	.	PUNCT
ejpam-5958	523	1	mathematics	mathematic	NOUN
ejpam-5958	523	2	,	,	PUNCT
ejpam-5958	523	3	5(2):19	5(2):19	NUM
ejpam-5958	523	4	,	,	PUNCT
ejpam-5958	523	5	2017	2017	NUM
ejpam-5958	523	6	.	.	PUNCT
ejpam-5958	524	1	[	[	X
ejpam-5958	524	2	26	26	NUM
ejpam-5958	524	3	]	]	X
ejpam-5958	524	4	h.	h.	PROPN
ejpam-5958	524	5	qawaqneh	qawaqneh	PROPN
ejpam-5958	524	6	,	,	PUNCT
ejpam-5958	524	7	m.	m.	PROPN
ejpam-5958	524	8	s.	s.	PROPN
ejpam-5958	524	9	m.	m.	PROPN
ejpam-5958	524	10	noorani	noorani	PROPN
ejpam-5958	524	11	,	,	PUNCT
ejpam-5958	524	12	h.	h.	PROPN
ejpam-5958	524	13	aydi	aydi	PROPN
ejpam-5958	524	14	,	,	PUNCT
ejpam-5958	524	15	a.	a.	NOUN
ejpam-5958	524	16	zraiqat	zraiqat	PROPN
ejpam-5958	524	17	,	,	PUNCT
ejpam-5958	524	18	and	and	CCONJ
ejpam-5958	524	19	a.	a.	NOUN
ejpam-5958	524	20	h.	h.	PROPN
ejpam-5958	524	21	ansari	ansari	PROPN
ejpam-5958	524	22	.	.	PUNCT
ejpam-5958	525	1	on	on	ADP
ejpam-5958	525	2	fixed	fix	VERB
ejpam-5958	525	3	point	point	NOUN
ejpam-5958	525	4	results	result	NOUN
ejpam-5958	525	5	in	in	ADP
ejpam-5958	525	6	partial	partial	ADJ
ejpam-5958	525	7	b	b	NOUN
ejpam-5958	525	8	-	-	PUNCT
ejpam-5958	525	9	metric	metric	ADJ
ejpam-5958	525	10	spaces	space	NOUN
ejpam-5958	525	11	.	.	PUNCT
ejpam-5958	526	1	journal	journal	NOUN
ejpam-5958	526	2	of	of	ADP
ejpam-5958	526	3	function	function	NOUN
ejpam-5958	526	4	spaces	space	NOUN
ejpam-5958	526	5	,	,	PUNCT
ejpam-5958	526	6	2021:6680594	2021:6680594	NUM
ejpam-5958	526	7	,	,	PUNCT
ejpam-5958	526	8	2021	2021	NUM
ejpam-5958	526	9	.	.	PUNCT
ejpam-5958	527	1	[	[	X
ejpam-5958	527	2	27	27	NUM
ejpam-5958	527	3	]	]	X
ejpam-5958	527	4	b.	b.	PROPN
ejpam-5958	527	5	samet	samet	PROPN
ejpam-5958	527	6	,	,	PUNCT
ejpam-5958	527	7	c.	c.	PROPN
ejpam-5958	527	8	vetro	vetro	PROPN
ejpam-5958	527	9	,	,	PUNCT
ejpam-5958	527	10	and	and	CCONJ
ejpam-5958	527	11	p.	p.	PROPN
ejpam-5958	527	12	vetro	vetro	PROPN
ejpam-5958	527	13	.	.	PUNCT
ejpam-5958	528	1	fixed	fix	VERB
ejpam-5958	528	2	point	point	NOUN
ejpam-5958	528	3	theorems	theorem	NOUN
ejpam-5958	528	4	for	for	ADP
ejpam-5958	528	5	α	α	NOUN
ejpam-5958	528	6	-	-	PUNCT
ejpam-5958	528	7	ψ	ψ	NOUN
ejpam-5958	528	8	-	-	ADJ
ejpam-5958	528	9	contractive	contractive	ADJ
ejpam-5958	528	10	type	type	NOUN
ejpam-5958	528	11	mappings	mapping	NOUN
ejpam-5958	528	12	.	.	PUNCT
ejpam-5958	529	1	nonlinear	nonlinear	ADJ
ejpam-5958	529	2	analysis	analysis	NOUN
ejpam-5958	529	3	:	:	PUNCT
ejpam-5958	529	4	theory	theory	NOUN
ejpam-5958	529	5	,	,	PUNCT
ejpam-5958	529	6	methods	method	NOUN
ejpam-5958	529	7	&	&	CCONJ
ejpam-5958	529	8	applications	application	NOUN
ejpam-5958	529	9	,	,	PUNCT
ejpam-5958	529	10	75(4):2154–2165	75(4):2154–2165	NOUN
ejpam-5958	529	11	,	,	PUNCT
ejpam-5958	529	12	2012	2012	NUM
ejpam-5958	529	13	.	.	PUNCT
ejpam-5958	530	1	[	[	X
ejpam-5958	530	2	28	28	NUM
ejpam-5958	530	3	]	]	X
ejpam-5958	530	4	m.	m.	NOUN
ejpam-5958	530	5	elbes	elbes	PROPN
ejpam-5958	530	6	,	,	PUNCT
ejpam-5958	530	7	t.	t.	PROPN
ejpam-5958	530	8	kanan	kanan	PROPN
ejpam-5958	530	9	,	,	PUNCT
ejpam-5958	530	10	m.	m.	NOUN
ejpam-5958	530	11	alia	alia	PROPN
ejpam-5958	530	12	,	,	PUNCT
ejpam-5958	530	13	and	and	CCONJ
ejpam-5958	530	14	m.	m.	NOUN
ejpam-5958	530	15	ziad	ziad	PROPN
ejpam-5958	530	16	.	.	PUNCT
ejpam-5958	531	1	covid-19	covid-19	PROPN
ejpam-5958	531	2	detection	detection	NOUN
ejpam-5958	531	3	platform	platform	NOUN
ejpam-5958	531	4	from	from	ADP
ejpam-5958	531	5	x	x	ADJ
ejpam-5958	531	6	-	-	NOUN
ejpam-5958	531	7	ray	ray	NOUN
ejpam-5958	531	8	images	image	NOUN
ejpam-5958	531	9	using	use	VERB
ejpam-5958	531	10	deep	deep	ADJ
ejpam-5958	531	11	learning	learning	NOUN
ejpam-5958	531	12	.	.	PUNCT
ejpam-5958	532	1	international	international	ADJ
ejpam-5958	532	2	journal	journal	NOUN
ejpam-5958	532	3	of	of	ADP
ejpam-5958	532	4	advances	advance	NOUN
ejpam-5958	532	5	in	in	ADP
ejpam-5958	532	6	soft	soft	ADJ
ejpam-5958	532	7	computing	computing	NOUN
ejpam-5958	532	8	and	and	CCONJ
ejpam-5958	532	9	its	its	PRON
ejpam-5958	532	10	applications	application	NOUN
ejpam-5958	532	11	,	,	PUNCT
ejpam-5958	532	12	14(1):1–14	14(1):1–14	NUM
ejpam-5958	532	13	,	,	PUNCT
ejpam-5958	532	14	2022	2022	NUM
ejpam-5958	532	15	.	.	PUNCT
ejpam-5958	533	1	[	[	X
ejpam-5958	533	2	29	29	NUM
ejpam-5958	533	3	]	]	X
ejpam-5958	533	4	h.	h.	PROPN
ejpam-5958	533	5	afshari	afshari	PROPN
ejpam-5958	533	6	,	,	PUNCT
ejpam-5958	533	7	h.	h.	PROPN
ejpam-5958	533	8	aydi	aydi	PROPN
ejpam-5958	533	9	,	,	PUNCT
ejpam-5958	533	10	and	and	CCONJ
ejpam-5958	533	11	e.	e.	PROPN
ejpam-5958	533	12	karapınar	karapınar	PROPN
ejpam-5958	533	13	.	.	PUNCT
ejpam-5958	534	1	on	on	ADP
ejpam-5958	534	2	generalized	generalized	ADJ
ejpam-5958	534	3	α	α	PROPN
ejpam-5958	534	4	-	-	PUNCT
ejpam-5958	534	5	ψ	ψ	NOUN
ejpam-5958	534	6	-	-	ADJ
ejpam-5958	534	7	geraghty	geraghty	ADJ
ejpam-5958	534	8	contractions	contraction	NOUN
ejpam-5958	534	9	on	on	ADP
ejpam-5958	534	10	b	b	X
ejpam-5958	534	11	-	-	PUNCT
ejpam-5958	534	12	metric	metric	ADJ
ejpam-5958	534	13	spaces	space	NOUN
ejpam-5958	534	14	.	.	PUNCT
ejpam-5958	535	1	georgian	georgian	PROPN
ejpam-5958	535	2	mathematical	mathematical	PROPN
ejpam-5958	535	3	journal	journal	PROPN
ejpam-5958	535	4	,	,	PUNCT
ejpam-5958	535	5	27(1):9–21	27(1):9–21	NUM
ejpam-5958	535	6	,	,	PUNCT
ejpam-5958	535	7	2020	2020	NUM
ejpam-5958	535	8	.	.	PUNCT
ejpam-5958	536	1	[	[	X
ejpam-5958	536	2	30	30	NUM
ejpam-5958	536	3	]	]	X
ejpam-5958	536	4	b.	b.	PROPN
ejpam-5958	536	5	alqahtani	alqahtani	PROPN
ejpam-5958	536	6	,	,	PUNCT
ejpam-5958	536	7	e.	e.	PROPN
ejpam-5958	536	8	karapınar	karapınar	PROPN
ejpam-5958	536	9	,	,	PUNCT
ejpam-5958	536	10	and	and	CCONJ
ejpam-5958	536	11	a.	a.	NOUN
ejpam-5958	536	12	öztürk	öztürk	PROPN
ejpam-5958	536	13	.	.	PUNCT
ejpam-5958	537	1	on	on	ADP
ejpam-5958	537	2	(	(	PUNCT
ejpam-5958	537	3	α	α	NOUN
ejpam-5958	537	4	-	-	PUNCT
ejpam-5958	537	5	ψ)-k	ψ)-k	NOUN
ejpam-5958	537	6	-	-	PUNCT
ejpam-5958	537	7	contractions	contraction	NOUN
ejpam-5958	537	8	in	in	ADP
ejpam-5958	537	9	the	the	DET
ejpam-5958	537	10	extended	extended	ADJ
ejpam-5958	537	11	b	b	X
ejpam-5958	537	12	-	-	PUNCT
ejpam-5958	537	13	metric	metric	ADJ
ejpam-5958	537	14	space	space	NOUN
ejpam-5958	537	15	.	.	PUNCT
ejpam-5958	538	1	filomat	filomat	PROPN
ejpam-5958	538	2	,	,	PUNCT
ejpam-5958	538	3	32(15):5337–5345	32(15):5337–5345	NUM
ejpam-5958	538	4	,	,	PUNCT
ejpam-5958	538	5	2018	2018	NUM
ejpam-5958	538	6	.	.	PUNCT
ejpam-5958	539	1	[	[	X
ejpam-5958	539	2	31	31	NUM
ejpam-5958	539	3	]	]	PUNCT
ejpam-5958	539	4	i.	i.	PROPN
ejpam-5958	539	5	m.	m.	PROPN
ejpam-5958	539	6	batiha	batiha	PROPN
ejpam-5958	539	7	,	,	PUNCT
ejpam-5958	539	8	s.	s.	PROPN
ejpam-5958	539	9	a.	a.	PROPN
ejpam-5958	539	10	njadat	njadat	PROPN
ejpam-5958	539	11	,	,	PUNCT
ejpam-5958	539	12	r.	r.	PROPN
ejpam-5958	539	13	m.	m.	PROPN
ejpam-5958	539	14	batyha	batyha	PROPN
ejpam-5958	539	15	,	,	PUNCT
ejpam-5958	539	16	a.	a.	NOUN
ejpam-5958	539	17	zraiqat	zraiqat	PROPN
ejpam-5958	539	18	,	,	PUNCT
ejpam-5958	539	19	a.	a.	NOUN
ejpam-5958	539	20	dababneh	dababneh	PROPN
ejpam-5958	539	21	,	,	PUNCT
ejpam-5958	539	22	and	and	CCONJ
ejpam-5958	539	23	s.	s.	PROPN
ejpam-5958	539	24	momani	momani	PROPN
ejpam-5958	539	25	.	.	PUNCT
ejpam-5958	540	1	k.	k.	PROPN
ejpam-5958	540	2	nisse	nisse	PROPN
ejpam-5958	540	3	et	et	PROPN
ejpam-5958	540	4	al	al	PROPN
ejpam-5958	540	5	.	.	PUNCT
ejpam-5958	540	6	/	/	SYM
ejpam-5958	540	7	eur	eur	PROPN
ejpam-5958	540	8	.	.	PUNCT
ejpam-5958	541	1	j.	j.	PROPN
ejpam-5958	541	2	pure	pure	PROPN
ejpam-5958	541	3	appl	appl	PROPN
ejpam-5958	541	4	.	.	PROPN
ejpam-5958	541	5	math	math	PROPN
ejpam-5958	541	6	,	,	PUNCT
ejpam-5958	541	7	18	18	NUM
ejpam-5958	541	8	(	(	PUNCT
ejpam-5958	541	9	2	2	NUM
ejpam-5958	541	10	)	)	PUNCT
ejpam-5958	541	11	(	(	PUNCT
ejpam-5958	541	12	2025	2025	NUM
ejpam-5958	541	13	)	)	PUNCT
ejpam-5958	541	14	,	,	PUNCT
ejpam-5958	541	15	5958	5958	NUM
ejpam-5958	541	16	22	22	NUM
ejpam-5958	541	17	of	of	ADP
ejpam-5958	541	18	22	22	NUM
ejpam-5958	541	19	design	design	NOUN
ejpam-5958	541	20	fractional	fractional	ADJ
ejpam-5958	541	21	-	-	PUNCT
ejpam-5958	541	22	order	order	NOUN
ejpam-5958	541	23	pid	pid	NOUN
ejpam-5958	541	24	controllers	controller	NOUN
ejpam-5958	541	25	for	for	ADP
ejpam-5958	541	26	single	single	ADJ
ejpam-5958	541	27	-	-	PUNCT
ejpam-5958	541	28	joint	joint	ADJ
ejpam-5958	541	29	robot	robot	NOUN
ejpam-5958	541	30	arm	arm	NOUN
ejpam-5958	541	31	model	model	NOUN
ejpam-5958	541	32	.	.	PUNCT
ejpam-5958	542	1	international	international	ADJ
ejpam-5958	542	2	journal	journal	NOUN
ejpam-5958	542	3	of	of	ADP
ejpam-5958	542	4	advances	advance	NOUN
ejpam-5958	542	5	in	in	ADP
ejpam-5958	542	6	soft	soft	ADJ
ejpam-5958	542	7	computing	computing	NOUN
ejpam-5958	542	8	and	and	CCONJ
ejpam-5958	542	9	its	its	PRON
ejpam-5958	542	10	applications	application	NOUN
ejpam-5958	542	11	,	,	PUNCT
ejpam-5958	542	12	14(2):96–114	14(2):96–114	NUM
ejpam-5958	542	13	,	,	PUNCT
ejpam-5958	542	14	2022	2022	NUM
ejpam-5958	542	15	.	.	PUNCT
ejpam-5958	543	1	[	[	X
ejpam-5958	543	2	32	32	NUM
ejpam-5958	543	3	]	]	PUNCT
ejpam-5958	543	4	e.	e.	PROPN
ejpam-5958	543	5	karapınar	karapınar	PROPN
ejpam-5958	543	6	.	.	PUNCT
ejpam-5958	544	1	a	a	DET
ejpam-5958	544	2	short	short	ADJ
ejpam-5958	544	3	survey	survey	NOUN
ejpam-5958	544	4	on	on	ADP
ejpam-5958	544	5	the	the	DET
ejpam-5958	544	6	recent	recent	ADJ
ejpam-5958	544	7	fixed	fix	VERB
ejpam-5958	544	8	point	point	NOUN
ejpam-5958	544	9	results	result	NOUN
ejpam-5958	544	10	on	on	ADP
ejpam-5958	544	11	b	b	NOUN
ejpam-5958	544	12	-	-	PUNCT
ejpam-5958	544	13	metric	metric	ADJ
ejpam-5958	544	14	spaces	space	NOUN
ejpam-5958	544	15	.	.	PUNCT
ejpam-5958	545	1	constructive	constructive	ADJ
ejpam-5958	545	2	mathematical	mathematical	ADJ
ejpam-5958	545	3	analysis	analysis	NOUN
ejpam-5958	545	4	,	,	PUNCT
ejpam-5958	545	5	1(1):15–44	1(1):15–44	NUM
ejpam-5958	545	6	,	,	PUNCT
ejpam-5958	545	7	2018	2018	NUM
ejpam-5958	545	8	.	.	PUNCT
ejpam-5958	546	1	[	[	X
ejpam-5958	546	2	33	33	NUM
ejpam-5958	546	3	]	]	PUNCT
ejpam-5958	546	4	m.	m.	NOUN
ejpam-5958	546	5	jleli	jleli	PROPN
ejpam-5958	546	6	,	,	PUNCT
ejpam-5958	546	7	e.	e.	PROPN
ejpam-5958	546	8	karapınar	karapınar	PROPN
ejpam-5958	546	9	,	,	PUNCT
ejpam-5958	546	10	and	and	CCONJ
ejpam-5958	546	11	b.	b.	PROPN
ejpam-5958	546	12	samet	samet	PROPN
ejpam-5958	546	13	.	.	PUNCT
ejpam-5958	547	1	fixed	fix	VERB
ejpam-5958	547	2	point	point	NOUN
ejpam-5958	547	3	results	result	NOUN
ejpam-5958	547	4	for	for	ADP
ejpam-5958	547	5	α	α	NOUN
ejpam-5958	547	6	-	-	PUNCT
ejpam-5958	547	7	ψλ	ψλ	NOUN
ejpam-5958	547	8	-	-	PUNCT
ejpam-5958	547	9	contractions	contraction	NOUN
ejpam-5958	547	10	on	on	ADP
ejpam-5958	547	11	gauge	gauge	ADJ
ejpam-5958	547	12	spaces	space	NOUN
ejpam-5958	547	13	and	and	CCONJ
ejpam-5958	547	14	applications	application	NOUN
ejpam-5958	547	15	.	.	PUNCT
ejpam-5958	548	1	abstract	abstract	ADJ
ejpam-5958	548	2	and	and	CCONJ
ejpam-5958	548	3	applied	apply	VERB
ejpam-5958	548	4	analysis	analysis	NOUN
ejpam-5958	548	5	,	,	PUNCT
ejpam-5958	548	6	2013:730825	2013:730825	NUM
ejpam-5958	548	7	,	,	PUNCT
ejpam-5958	548	8	2013	2013	NUM
ejpam-5958	548	9	.	.	PUNCT
ejpam-5958	549	1	[	[	X
ejpam-5958	549	2	34	34	NUM
ejpam-5958	549	3	]	]	PUNCT
ejpam-5958	549	4	t.	t.	PROPN
ejpam-5958	549	5	kanan	kanan	PROPN
ejpam-5958	549	6	,	,	PUNCT
ejpam-5958	549	7	m.	m.	NOUN
ejpam-5958	549	8	elbes	elbes	PROPN
ejpam-5958	549	9	,	,	PUNCT
ejpam-5958	549	10	k.	k.	PROPN
ejpam-5958	549	11	abu	abu	PROPN
ejpam-5958	549	12	maria	maria	PROPN
ejpam-5958	549	13	,	,	PUNCT
ejpam-5958	549	14	and	and	CCONJ
ejpam-5958	549	15	m.	m.	NOUN
ejpam-5958	549	16	alia	alia	PROPN
ejpam-5958	549	17	.	.	PUNCT
ejpam-5958	550	1	exploring	explore	VERB
ejpam-5958	550	2	the	the	DET
ejpam-5958	550	3	potential	potential	NOUN
ejpam-5958	550	4	of	of	ADP
ejpam-5958	550	5	iotbased	iotbase	VERB
ejpam-5958	550	6	learning	learn	VERB
ejpam-5958	550	7	environments	environment	NOUN
ejpam-5958	550	8	in	in	ADP
ejpam-5958	550	9	education	education	NOUN
ejpam-5958	550	10	.	.	PUNCT
ejpam-5958	551	1	international	international	ADJ
ejpam-5958	551	2	journal	journal	NOUN
ejpam-5958	551	3	of	of	ADP
ejpam-5958	551	4	advances	advance	NOUN
ejpam-5958	551	5	in	in	ADP
ejpam-5958	551	6	soft	soft	ADJ
ejpam-5958	551	7	computing	computing	NOUN
ejpam-5958	551	8	and	and	CCONJ
ejpam-5958	551	9	its	its	PRON
ejpam-5958	551	10	applications	application	NOUN
ejpam-5958	551	11	,	,	PUNCT
ejpam-5958	551	12	15(2):1–17	15(2):1–17	NUM
ejpam-5958	551	13	,	,	PUNCT
ejpam-5958	551	14	2023	2023	NUM
ejpam-5958	551	15	.	.	PUNCT
ejpam-5958	552	1	[	[	X
ejpam-5958	552	2	35	35	NUM
ejpam-5958	552	3	]	]	X
ejpam-5958	552	4	b.	b.	PROPN
ejpam-5958	552	5	n.	n.	PROPN
ejpam-5958	552	6	abagarol	abagarol	PROPN
ejpam-5958	552	7	,	,	PUNCT
ejpam-5958	552	8	k.	k.	PROPN
ejpam-5958	552	9	k.	k.	PROPN
ejpam-5958	552	10	tola	tola	PROPN
ejpam-5958	552	11	,	,	PUNCT
ejpam-5958	552	12	and	and	CCONJ
ejpam-5958	552	13	m.	m.	NOUN
ejpam-5958	552	14	a.	a.	NOUN
ejpam-5958	552	15	mamud	mamud	PROPN
ejpam-5958	552	16	.	.	PUNCT
ejpam-5958	553	1	fixed	fix	VERB
ejpam-5958	553	2	point	point	NOUN
ejpam-5958	553	3	theorems	theorem	NOUN
ejpam-5958	553	4	for	for	ADP
ejpam-5958	553	5	generalized	generalized	ADJ
ejpam-5958	553	6	(	(	PUNCT
ejpam-5958	553	7	α	α	NOUN
ejpam-5958	553	8	-	-	PUNCT
ejpam-5958	553	9	ψ)-contraction	ψ)-contraction	NOUN
ejpam-5958	553	10	mappings	mapping	NOUN
ejpam-5958	553	11	in	in	ADP
ejpam-5958	553	12	rectangular	rectangular	ADJ
ejpam-5958	553	13	quasi	quasi	X
ejpam-5958	553	14	b	b	NOUN
ejpam-5958	553	15	-	-	ADJ
ejpam-5958	553	16	metric	metric	ADJ
ejpam-5958	553	17	spaces	space	NOUN
ejpam-5958	553	18	.	.	PUNCT
ejpam-5958	554	1	fixed	fix	VERB
ejpam-5958	554	2	point	point	NOUN
ejpam-5958	554	3	theory	theory	NOUN
ejpam-5958	554	4	and	and	CCONJ
ejpam-5958	554	5	algorithms	algorithm	NOUN
ejpam-5958	554	6	for	for	ADP
ejpam-5958	554	7	sciences	science	NOUN
ejpam-5958	554	8	and	and	CCONJ
ejpam-5958	554	9	engineering	engineering	NOUN
ejpam-5958	554	10	,	,	PUNCT
ejpam-5958	554	11	2022(13	2022(13	NUM
ejpam-5958	554	12	)	)	PUNCT
ejpam-5958	554	13	,	,	PUNCT
ejpam-5958	554	14	2022	2022	NUM
ejpam-5958	554	15	.	.	PUNCT
ejpam-5958	555	1	[	[	X
ejpam-5958	555	2	36	36	NUM
ejpam-5958	555	3	]	]	PUNCT
ejpam-5958	555	4	m.	m.	PROPN
ejpam-5958	555	5	u.	u.	PROPN
ejpam-5958	555	6	ali	ali	PROPN
ejpam-5958	555	7	and	and	CCONJ
ejpam-5958	555	8	f.	f.	PROPN
ejpam-5958	555	9	u.	u.	PROPN
ejpam-5958	555	10	din	din	PROPN
ejpam-5958	555	11	.	.	PROPN
ejpam-5958	555	12	discussion	discussion	NOUN
ejpam-5958	555	13	on	on	ADP
ejpam-5958	555	14	α	α	NOUN
ejpam-5958	555	15	-	-	PUNCT
ejpam-5958	555	16	contractions	contraction	NOUN
ejpam-5958	555	17	and	and	CCONJ
ejpam-5958	555	18	related	relate	VERB
ejpam-5958	555	19	fixed	fix	VERB
ejpam-5958	555	20	point	point	NOUN
ejpam-5958	555	21	theorems	theorem	NOUN
ejpam-5958	555	22	in	in	ADP
ejpam-5958	555	23	hausdorff	hausdorff	PROPN
ejpam-5958	555	24	b	b	NOUN
ejpam-5958	555	25	-	-	PUNCT
ejpam-5958	555	26	gauge	gauge	NOUN
ejpam-5958	555	27	spaces	space	NOUN
ejpam-5958	555	28	.	.	PUNCT
ejpam-5958	556	1	jordan	jordan	PROPN
ejpam-5958	556	2	journal	journal	PROPN
ejpam-5958	556	3	of	of	ADP
ejpam-5958	556	4	mathematics	mathematics	PROPN
ejpam-5958	556	5	and	and	CCONJ
ejpam-5958	556	6	statistics	statistic	NOUN
ejpam-5958	556	7	,	,	PUNCT
ejpam-5958	556	8	10(3):247–263	10(3):247–263	NUM
ejpam-5958	556	9	,	,	PUNCT
ejpam-5958	556	10	2017	2017	NUM
ejpam-5958	556	11	.	.	PUNCT
ejpam-5958	557	1	[	[	X
ejpam-5958	557	2	37	37	NUM
ejpam-5958	557	3	]	]	X
ejpam-5958	557	4	n.	n.	NOUN
ejpam-5958	557	5	zikria	zikria	PROPN
ejpam-5958	557	6	,	,	PUNCT
ejpam-5958	557	7	a.	a.	NOUN
ejpam-5958	557	8	mukheimer	mukheimer	PROPN
ejpam-5958	557	9	,	,	PUNCT
ejpam-5958	557	10	m.	m.	NOUN
ejpam-5958	557	11	samreen	samreen	PROPN
ejpam-5958	557	12	,	,	PUNCT
ejpam-5958	557	13	t.	t.	PROPN
ejpam-5958	557	14	kamran	kamran	PROPN
ejpam-5958	557	15	,	,	PUNCT
ejpam-5958	557	16	h.	h.	PROPN
ejpam-5958	557	17	aydi	aydi	PROPN
ejpam-5958	557	18	,	,	PUNCT
ejpam-5958	557	19	and	and	CCONJ
ejpam-5958	557	20	k.	k.	PROPN
ejpam-5958	557	21	abodayeh	abodayeh	PROPN
ejpam-5958	557	22	.	.	PUNCT
ejpam-5958	558	1	periodic	periodic	ADJ
ejpam-5958	558	2	and	and	CCONJ
ejpam-5958	558	3	fixed	fix	VERB
ejpam-5958	558	4	points	point	NOUN
ejpam-5958	558	5	for	for	ADP
ejpam-5958	558	6	f	f	NOUN
ejpam-5958	558	7	-	-	PUNCT
ejpam-5958	558	8	type	type	NOUN
ejpam-5958	558	9	contractions	contraction	NOUN
ejpam-5958	558	10	in	in	ADP
ejpam-5958	558	11	b	b	NOUN
ejpam-5958	558	12	-	-	PUNCT
ejpam-5958	558	13	gauge	gauge	NOUN
ejpam-5958	558	14	spaces	space	NOUN
ejpam-5958	558	15	.	.	PUNCT
ejpam-5958	559	1	aims	aim	VERB
ejpam-5958	559	2	mathematics	mathematic	NOUN
ejpam-5958	559	3	,	,	PUNCT
ejpam-5958	559	4	7(10):18393–18415	7(10):18393–18415	NUM
ejpam-5958	559	5	,	,	PUNCT
ejpam-5958	559	6	2022	2022	NUM
ejpam-5958	559	7	.	.	PUNCT
ejpam-5958	560	1	[	[	X
ejpam-5958	560	2	38	38	NUM
ejpam-5958	560	3	]	]	PUNCT
ejpam-5958	560	4	n.	n.	NOUN
ejpam-5958	560	5	zikria	zikria	PROPN
ejpam-5958	560	6	,	,	PUNCT
ejpam-5958	560	7	m.	m.	NOUN
ejpam-5958	560	8	samreen	samreen	PROPN
ejpam-5958	560	9	,	,	PUNCT
ejpam-5958	560	10	t.	t.	PROPN
ejpam-5958	560	11	kamran	kamran	PROPN
ejpam-5958	560	12	,	,	PUNCT
ejpam-5958	560	13	and	and	CCONJ
ejpam-5958	560	14	s.	s.	PROPN
ejpam-5958	560	15	s.	s.	PROPN
ejpam-5958	560	16	yeılkaya	yeılkaya	PROPN
ejpam-5958	560	17	.	.	PUNCT
ejpam-5958	561	1	periodic	periodic	ADJ
ejpam-5958	561	2	and	and	CCONJ
ejpam-5958	561	3	fixed	fix	VERB
ejpam-5958	561	4	points	point	NOUN
ejpam-5958	561	5	for	for	ADP
ejpam-5958	561	6	caristi	caristi	NOUN
ejpam-5958	561	7	-	-	PUNCT
ejpam-5958	561	8	type	type	NOUN
ejpam-5958	561	9	g	g	NOUN
ejpam-5958	561	10	-	-	PUNCT
ejpam-5958	561	11	contractions	contraction	NOUN
ejpam-5958	561	12	in	in	ADP
ejpam-5958	561	13	extended	extended	ADJ
ejpam-5958	561	14	b	b	NUM
ejpam-5958	561	15	-	-	PUNCT
ejpam-5958	561	16	gauge	gauge	NOUN
ejpam-5958	561	17	spaces	space	NOUN
ejpam-5958	561	18	.	.	PUNCT
ejpam-5958	562	1	journal	journal	NOUN
ejpam-5958	562	2	of	of	ADP
ejpam-5958	562	3	function	function	NOUN
ejpam-5958	562	4	spaces	space	NOUN
ejpam-5958	562	5	,	,	PUNCT
ejpam-5958	562	6	2021:5592343	2021:5592343	NUM
ejpam-5958	562	7	,	,	PUNCT
ejpam-5958	562	8	2021	2021	NUM
ejpam-5958	562	9	.	.	PUNCT
ejpam-5958	563	1	[	[	X
ejpam-5958	563	2	39	39	NUM
ejpam-5958	563	3	]	]	PUNCT
ejpam-5958	563	4	v.	v.	PROPN
ejpam-5958	563	5	g.	g.	PROPN
ejpam-5958	563	6	angelov	angelov	PROPN
ejpam-5958	563	7	.	.	PUNCT
ejpam-5958	564	1	fixed	fix	VERB
ejpam-5958	564	2	points	point	NOUN
ejpam-5958	564	3	results	result	NOUN
ejpam-5958	564	4	for	for	ADP
ejpam-5958	564	5	α	α	NOUN
ejpam-5958	564	6	-	-	PUNCT
ejpam-5958	564	7	ψλ	ψλ	NOUN
ejpam-5958	564	8	-	-	PUNCT
ejpam-5958	564	9	contractions	contraction	NOUN
ejpam-5958	564	10	on	on	ADP
ejpam-5958	564	11	gauge	gauge	ADJ
ejpam-5958	564	12	spaces	space	NOUN
ejpam-5958	564	13	in	in	ADP
ejpam-5958	564	14	uniform	uniform	ADJ
ejpam-5958	564	15	spaces	space	NOUN
ejpam-5958	564	16	and	and	CCONJ
ejpam-5958	564	17	applications	application	NOUN
ejpam-5958	564	18	.	.	PUNCT
ejpam-5958	565	1	cluj	cluj	PROPN
ejpam-5958	565	2	university	university	PROPN
ejpam-5958	565	3	press	press	NOUN
ejpam-5958	565	4	,	,	PUNCT
ejpam-5958	565	5	cluj	cluj	PROPN
ejpam-5958	565	6	-	-	PUNCT
ejpam-5958	565	7	napoca	napoca	NOUN
ejpam-5958	565	8	,	,	PUNCT
ejpam-5958	565	9	2009	2009	NUM
ejpam-5958	565	10	.	.	PUNCT
ejpam-5958	566	1	[	[	X
ejpam-5958	566	2	40	40	NUM
ejpam-5958	566	3	]	]	X
ejpam-5958	566	4	n.	n.	NOUN
ejpam-5958	566	5	zikria	zikria	PROPN
ejpam-5958	566	6	,	,	PUNCT
ejpam-5958	566	7	m.	m.	NOUN
ejpam-5958	566	8	samreen	samreen	PROPN
ejpam-5958	566	9	,	,	PUNCT
ejpam-5958	566	10	e.	e.	PROPN
ejpam-5958	566	11	savaş	savaş	PROPN
ejpam-5958	566	12	,	,	PUNCT
ejpam-5958	566	13	m.	m.	NOUN
ejpam-5958	566	14	de	de	PROPN
ejpam-5958	566	15	la	la	X
ejpam-5958	566	16	sen	sen	PROPN
ejpam-5958	566	17	,	,	PUNCT
ejpam-5958	566	18	and	and	CCONJ
ejpam-5958	566	19	t.	t.	PROPN
ejpam-5958	566	20	kamran	kamran	PROPN
ejpam-5958	566	21	.	.	PUNCT
ejpam-5958	567	1	periodic	periodic	ADJ
ejpam-5958	567	2	and	and	CCONJ
ejpam-5958	567	3	fixed	fix	VERB
ejpam-5958	567	4	points	point	NOUN
ejpam-5958	567	5	for	for	ADP
ejpam-5958	567	6	mappings	mapping	NOUN
ejpam-5958	567	7	in	in	ADP
ejpam-5958	567	8	extended	extended	ADJ
ejpam-5958	567	9	b	b	NUM
ejpam-5958	567	10	-	-	PUNCT
ejpam-5958	567	11	gauge	gauge	NOUN
ejpam-5958	567	12	spaces	space	NOUN
ejpam-5958	567	13	equipped	equip	VERB
ejpam-5958	567	14	with	with	ADP
ejpam-5958	567	15	a	a	DET
ejpam-5958	567	16	graph	graph	NOUN
ejpam-5958	567	17	.	.	PUNCT
ejpam-5958	567	18	demonstratio	demonstratio	PROPN
ejpam-5958	567	19	mathematica	mathematica	PROPN
ejpam-5958	567	20	,	,	PUNCT
ejpam-5958	567	21	57(1):20240016	57(1):20240016	NUM
ejpam-5958	567	22	,	,	PUNCT
ejpam-5958	567	23	2024	2024	NUM
ejpam-5958	567	24	.	.	PUNCT
ejpam-5958	568	1	[	[	X
ejpam-5958	568	2	41	41	NUM
ejpam-5958	568	3	]	]	PUNCT
ejpam-5958	568	4	a.	a.	NOUN
ejpam-5958	568	5	a.	a.	NOUN
ejpam-5958	568	6	kilbas	kilbas	PROPN
ejpam-5958	568	7	,	,	PUNCT
ejpam-5958	568	8	h.	h.	PROPN
ejpam-5958	568	9	m.	m.	PROPN
ejpam-5958	568	10	srivastava	srivastava	PROPN
ejpam-5958	568	11	,	,	PUNCT
ejpam-5958	568	12	and	and	CCONJ
ejpam-5958	568	13	j.	j.	PROPN
ejpam-5958	568	14	j.	j.	PROPN
ejpam-5958	568	15	trujillo	trujillo	PROPN
ejpam-5958	568	16	.	.	PUNCT
ejpam-5958	568	17	theory	theory	NOUN
ejpam-5958	568	18	and	and	CCONJ
ejpam-5958	568	19	applications	application	NOUN
ejpam-5958	568	20	of	of	ADP
ejpam-5958	568	21	fractional	fractional	ADJ
ejpam-5958	568	22	differential	differential	ADJ
ejpam-5958	568	23	equations	equation	NOUN
ejpam-5958	568	24	.	.	PUNCT
ejpam-5958	569	1	elsevier	elsevier	PROPN
ejpam-5958	569	2	,	,	PUNCT
ejpam-5958	569	3	new	new	PROPN
ejpam-5958	569	4	york	york	PROPN
ejpam-5958	569	5	,	,	PUNCT
ejpam-5958	569	6	2006	2006	NUM
ejpam-5958	569	7	.	.	PUNCT
ejpam-5958	570	1	[	[	X
ejpam-5958	570	2	42	42	NUM
ejpam-5958	570	3	]	]	PUNCT
ejpam-5958	570	4	k.	k.	PROPN
ejpam-5958	570	5	diethelm	diethelm	PROPN
ejpam-5958	570	6	.	.	PUNCT
ejpam-5958	571	1	the	the	DET
ejpam-5958	571	2	analysis	analysis	NOUN
ejpam-5958	571	3	of	of	ADP
ejpam-5958	571	4	fractional	fractional	ADJ
ejpam-5958	571	5	differential	differential	ADJ
ejpam-5958	571	6	equations	equation	NOUN
ejpam-5958	571	7	.	.	PUNCT
ejpam-5958	572	1	springer	springer	NOUN
ejpam-5958	572	2	,	,	PUNCT
ejpam-5958	572	3	berlin	berlin	PROPN
ejpam-5958	572	4	,	,	PUNCT
ejpam-5958	572	5	2004	2004	NUM
ejpam-5958	572	6	.	.	PUNCT
ejpam-5958	573	1	[	[	X
ejpam-5958	573	2	43	43	NUM
ejpam-5958	573	3	]	]	PUNCT
ejpam-5958	573	4	k.	k.	PROPN
ejpam-5958	573	5	nisse	nisse	PROPN
ejpam-5958	573	6	and	and	CCONJ
ejpam-5958	573	7	l.	l.	PROPN
ejpam-5958	573	8	nisse	nisse	PROPN
ejpam-5958	573	9	.	.	PUNCT
ejpam-5958	574	1	an	an	DET
ejpam-5958	574	2	iterative	iterative	NOUN
ejpam-5958	574	3	method	method	NOUN
ejpam-5958	574	4	for	for	ADP
ejpam-5958	574	5	solving	solve	VERB
ejpam-5958	574	6	a	a	DET
ejpam-5958	574	7	class	class	NOUN
ejpam-5958	574	8	of	of	ADP
ejpam-5958	574	9	fractional	fractional	ADJ
ejpam-5958	574	10	functional	functional	ADJ
ejpam-5958	574	11	differential	differential	ADJ
ejpam-5958	574	12	equations	equation	NOUN
ejpam-5958	574	13	with	with	ADP
ejpam-5958	574	14	maxima	maxima	PROPN
ejpam-5958	574	15	.	.	PUNCT
ejpam-5958	575	1	mathematics	mathematic	NOUN
ejpam-5958	575	2	,	,	PUNCT
ejpam-5958	575	3	6(2):27	6(2):27	NUM
ejpam-5958	575	4	,	,	PUNCT
ejpam-5958	575	5	2018	2018	NUM
ejpam-5958	575	6	.	.	PUNCT