id	sid	tid	token	lemma	pos
ejpam-5466	1	1	european	european	PROPN
ejpam-5466	1	2	journal	journal	PROPN
ejpam-5466	1	3	of	of	ADP
ejpam-5466	1	4	pure	pure	ADJ
ejpam-5466	1	5	and	and	CCONJ
ejpam-5466	1	6	applied	apply	VERB
ejpam-5466	1	7	mathematics	mathematic	NOUN
ejpam-5466	1	8	vol	vol	NOUN
ejpam-5466	1	9	.	.	PROPN
ejpam-5466	2	1	17	17	NUM
ejpam-5466	2	2	,	,	PUNCT
ejpam-5466	2	3	no	no	INTJ
ejpam-5466	2	4	.	.	NOUN
ejpam-5466	2	5	4	4	NUM
ejpam-5466	2	6	,	,	PUNCT
ejpam-5466	2	7	2024	2024	NUM
ejpam-5466	2	8	,	,	PUNCT
ejpam-5466	2	9	3093	3093	NUM
ejpam-5466	2	10	-	-	SYM
ejpam-5466	2	11	3108	3108	NUM
ejpam-5466	2	12	issn	issn	PROPN
ejpam-5466	2	13	1307	1307	NUM
ejpam-5466	2	14	-	-	SYM
ejpam-5466	2	15	5543	5543	NUM
ejpam-5466	2	16	–	–	PUNCT
ejpam-5466	2	17	ejpam.com	ejpam.com	X
ejpam-5466	2	18	published	publish	VERB
ejpam-5466	2	19	by	by	ADP
ejpam-5466	2	20	new	new	PROPN
ejpam-5466	2	21	york	york	PROPN
ejpam-5466	2	22	business	business	PROPN
ejpam-5466	2	23	global	global	ADJ
ejpam-5466	2	24	multivalued	multivalue	VERB
ejpam-5466	2	25	almost	almost	ADV
ejpam-5466	2	26	js	js	ADJ
ejpam-5466	2	27	-	-	PUNCT
ejpam-5466	2	28	contractions	contraction	NOUN
ejpam-5466	2	29	,	,	PUNCT
ejpam-5466	2	30	related	relate	VERB
ejpam-5466	2	31	fixed	fix	VERB
ejpam-5466	2	32	point	point	NOUN
ejpam-5466	2	33	results	result	NOUN
ejpam-5466	2	34	in	in	ADP
ejpam-5466	2	35	complete	complete	ADJ
ejpam-5466	2	36	b	b	X
ejpam-5466	2	37	-	-	ADJ
ejpam-5466	2	38	metric	metric	ADJ
ejpam-5466	2	39	spaces	space	NOUN
ejpam-5466	2	40	and	and	CCONJ
ejpam-5466	2	41	applications	application	NOUN
ejpam-5466	2	42	maroua	maroua	ADJ
ejpam-5466	2	43	meneceur1	meneceur1	PROPN
ejpam-5466	2	44	,	,	PUNCT
ejpam-5466	2	45	haitham	haitham	PROPN
ejpam-5466	2	46	qawaqneh2,∗	qawaqneh2,∗	PROPN
ejpam-5466	2	47	,	,	PUNCT
ejpam-5466	2	48	habes	habe	VERB
ejpam-5466	2	49	alsamir3	alsamir3	PROPN
ejpam-5466	2	50	,	,	PUNCT
ejpam-5466	2	51	gawhara	gawhara	PROPN
ejpam-5466	2	52	al	al	PROPN
ejpam-5466	2	53	-	-	PUNCT
ejpam-5466	2	54	musannef4	musannef4	PROPN
ejpam-5466	2	55	1	1	NUM
ejpam-5466	2	56	department	department	NOUN
ejpam-5466	2	57	of	of	ADP
ejpam-5466	2	58	mathematics	mathematic	NOUN
ejpam-5466	2	59	,	,	PUNCT
ejpam-5466	2	60	exact	exact	ADJ
ejpam-5466	2	61	sciences	science	NOUN
ejpam-5466	2	62	faculty	faculty	NOUN
ejpam-5466	2	63	,	,	PUNCT
ejpam-5466	2	64	university	university	NOUN
ejpam-5466	2	65	of	of	ADP
ejpam-5466	2	66	el	el	PROPN
ejpam-5466	2	67	oued	oued	PROPN
ejpam-5466	2	68	,	,	PUNCT
ejpam-5466	2	69	p.o.box	p.o.box	PROPN
ejpam-5466	2	70	789	789	NUM
ejpam-5466	2	71	,	,	PUNCT
ejpam-5466	2	72	el	el	PROPN
ejpam-5466	2	73	oued	oued	PROPN
ejpam-5466	2	74	39000	39000	NUM
ejpam-5466	2	75	,	,	PUNCT
ejpam-5466	2	76	algeria	algeria	PROPN
ejpam-5466	2	77	2	2	NUM
ejpam-5466	2	78	department	department	NOUN
ejpam-5466	2	79	of	of	ADP
ejpam-5466	2	80	mathematics	mathematic	NOUN
ejpam-5466	2	81	,	,	PUNCT
ejpam-5466	2	82	faculty	faculty	NOUN
ejpam-5466	2	83	of	of	ADP
ejpam-5466	2	84	science	science	NOUN
ejpam-5466	2	85	and	and	CCONJ
ejpam-5466	2	86	information	information	NOUN
ejpam-5466	2	87	technology	technology	NOUN
ejpam-5466	2	88	,	,	PUNCT
ejpam-5466	2	89	al	al	PROPN
ejpam-5466	2	90	-	-	PROPN
ejpam-5466	2	91	zaytoonah	zaytoonah	PROPN
ejpam-5466	2	92	university	university	PROPN
ejpam-5466	2	93	of	of	ADP
ejpam-5466	2	94	jordan	jordan	PROPN
ejpam-5466	2	95	,	,	PUNCT
ejpam-5466	2	96	amman	amman	PROPN
ejpam-5466	2	97	11733	11733	NUM
ejpam-5466	2	98	,	,	PUNCT
ejpam-5466	2	99	jordan	jordan	PROPN
ejpam-5466	2	100	3	3	NUM
ejpam-5466	2	101	finance	finance	NOUN
ejpam-5466	2	102	and	and	CCONJ
ejpam-5466	2	103	banking	banking	NOUN
ejpam-5466	2	104	department	department	NOUN
ejpam-5466	2	105	,	,	PUNCT
ejpam-5466	2	106	business	business	NOUN
ejpam-5466	2	107	administration	administration	PROPN
ejpam-5466	2	108	college	college	PROPN
ejpam-5466	2	109	,	,	PUNCT
ejpam-5466	2	110	dar	dar	PROPN
ejpam-5466	2	111	aluloom	aluloom	NOUN
ejpam-5466	2	112	university	university	PROPN
ejpam-5466	2	113	,	,	PUNCT
ejpam-5466	2	114	riyadh	riyadh	PROPN
ejpam-5466	2	115	,	,	PUNCT
ejpam-5466	2	116	saudi	saudi	PROPN
ejpam-5466	2	117	arabia	arabia	PROPN
ejpam-5466	2	118	3	3	NUM
ejpam-5466	2	119	faculty	faculty	NOUN
ejpam-5466	2	120	of	of	ADP
ejpam-5466	2	121	business	business	NOUN
ejpam-5466	2	122	studies	study	NOUN
ejpam-5466	2	123	,	,	PUNCT
ejpam-5466	2	124	arab	arab	ADJ
ejpam-5466	2	125	open	open	PROPN
ejpam-5466	2	126	university	university	PROPN
ejpam-5466	2	127	,	,	PUNCT
ejpam-5466	2	128	jeddah	jeddah	PROPN
ejpam-5466	2	129	,	,	PUNCT
ejpam-5466	2	130	saudi	saudi	PROPN
ejpam-5466	2	131	arabia	arabia	PROPN
ejpam-5466	2	132	abstract	abstract	NOUN
ejpam-5466	2	133	.	.	PUNCT
ejpam-5466	3	1	in	in	ADP
ejpam-5466	3	2	this	this	DET
ejpam-5466	3	3	paper	paper	NOUN
ejpam-5466	3	4	,	,	PUNCT
ejpam-5466	3	5	we	we	PRON
ejpam-5466	3	6	introduce	introduce	VERB
ejpam-5466	3	7	a	a	DET
ejpam-5466	3	8	new	new	ADJ
ejpam-5466	3	9	class	class	NOUN
ejpam-5466	3	10	of	of	ADP
ejpam-5466	3	11	multivalued	multivalue	VERB
ejpam-5466	3	12	contractions	contraction	NOUN
ejpam-5466	3	13	and	and	CCONJ
ejpam-5466	3	14	prove	prove	VERB
ejpam-5466	3	15	the	the	DET
ejpam-5466	3	16	existence	existence	NOUN
ejpam-5466	3	17	of	of	ADP
ejpam-5466	3	18	a	a	DET
ejpam-5466	3	19	fixed	fix	VERB
ejpam-5466	3	20	point	point	NOUN
ejpam-5466	3	21	for	for	ADP
ejpam-5466	3	22	such	such	ADJ
ejpam-5466	3	23	contractions	contraction	NOUN
ejpam-5466	3	24	.	.	PUNCT
ejpam-5466	4	1	some	some	DET
ejpam-5466	4	2	consequences	consequence	NOUN
ejpam-5466	4	3	are	be	AUX
ejpam-5466	4	4	presented	present	VERB
ejpam-5466	4	5	in	in	ADP
ejpam-5466	4	6	b	b	ADJ
ejpam-5466	4	7	-	-	PUNCT
ejpam-5466	4	8	metric	metric	ADJ
ejpam-5466	4	9	spaces	space	NOUN
ejpam-5466	4	10	endowed	endow	VERB
ejpam-5466	4	11	with	with	ADP
ejpam-5466	4	12	partial	partial	ADJ
ejpam-5466	4	13	order	order	NOUN
ejpam-5466	4	14	or	or	CCONJ
ejpam-5466	4	15	with	with	ADP
ejpam-5466	4	16	graph	graph	NOUN
ejpam-5466	4	17	.	.	PUNCT
ejpam-5466	5	1	to	to	PART
ejpam-5466	5	2	illustrate	illustrate	VERB
ejpam-5466	5	3	the	the	DET
ejpam-5466	5	4	applicability	applicability	NOUN
ejpam-5466	5	5	of	of	ADP
ejpam-5466	5	6	our	our	PRON
ejpam-5466	5	7	results	result	NOUN
ejpam-5466	5	8	,	,	PUNCT
ejpam-5466	5	9	we	we	PRON
ejpam-5466	5	10	offer	offer	VERB
ejpam-5466	5	11	an	an	DET
ejpam-5466	5	12	example	example	NOUN
ejpam-5466	5	13	and	and	CCONJ
ejpam-5466	5	14	an	an	DET
ejpam-5466	5	15	application	application	NOUN
ejpam-5466	5	16	to	to	ADP
ejpam-5466	5	17	the	the	DET
ejpam-5466	5	18	existence	existence	NOUN
ejpam-5466	5	19	of	of	ADP
ejpam-5466	5	20	solutions	solution	NOUN
ejpam-5466	5	21	of	of	ADP
ejpam-5466	5	22	an	an	DET
ejpam-5466	5	23	integral	integral	ADJ
ejpam-5466	5	24	inclusions	inclusion	NOUN
ejpam-5466	5	25	.	.	PUNCT
ejpam-5466	6	1	2020	2020	NUM
ejpam-5466	6	2	mathematics	mathematic	NOUN
ejpam-5466	6	3	subject	subject	NOUN
ejpam-5466	6	4	classifications	classification	NOUN
ejpam-5466	6	5	:	:	PUNCT
ejpam-5466	6	6	47h10	47h10	NUM
ejpam-5466	6	7	,	,	PUNCT
ejpam-5466	6	8	54h25	54h25	NUM
ejpam-5466	6	9	key	key	ADJ
ejpam-5466	6	10	words	word	NOUN
ejpam-5466	6	11	and	and	CCONJ
ejpam-5466	6	12	phrases	phrase	NOUN
ejpam-5466	6	13	:	:	PUNCT
ejpam-5466	6	14	ϑ-contraction	ϑ-contraction	NOUN
ejpam-5466	6	15	,	,	PUNCT
ejpam-5466	6	16	fixed	fix	VERB
ejpam-5466	6	17	point	point	NOUN
ejpam-5466	6	18	,	,	PUNCT
ejpam-5466	6	19	αs	αs	ADJ
ejpam-5466	6	20	-	-	ADJ
ejpam-5466	6	21	admissible	admissible	ADJ
ejpam-5466	6	22	,	,	PUNCT
ejpam-5466	6	23	volterra	volterra	NOUN
ejpam-5466	6	24	integral	integral	ADJ
ejpam-5466	6	25	inclusions	inclusion	NOUN
ejpam-5466	6	26	.	.	PUNCT
ejpam-5466	7	1	1	1	X
ejpam-5466	7	2	.	.	X
ejpam-5466	7	3	introduction	introduction	NOUN
ejpam-5466	7	4	and	and	CCONJ
ejpam-5466	7	5	preliminaries	preliminary	NOUN
ejpam-5466	7	6	one	one	NUM
ejpam-5466	7	7	of	of	ADP
ejpam-5466	7	8	the	the	DET
ejpam-5466	7	9	key	key	ADJ
ejpam-5466	7	10	generalizations	generalization	NOUN
ejpam-5466	7	11	for	for	ADP
ejpam-5466	7	12	metric	metric	ADJ
ejpam-5466	7	13	spaces	space	NOUN
ejpam-5466	7	14	is	be	AUX
ejpam-5466	7	15	the	the	DET
ejpam-5466	7	16	idea	idea	NOUN
ejpam-5466	7	17	of	of	ADP
ejpam-5466	7	18	a	a	DET
ejpam-5466	7	19	b	b	NOUN
ejpam-5466	7	20	-	-	PUNCT
ejpam-5466	7	21	metric	metric	ADJ
ejpam-5466	7	22	space	space	NOUN
ejpam-5466	7	23	.	.	PUNCT
ejpam-5466	8	1	bakhtin	bakhtin	NOUN
ejpam-5466	9	1	[	[	X
ejpam-5466	9	2	4	4	X
ejpam-5466	9	3	]	]	PUNCT
ejpam-5466	9	4	first	first	ADV
ejpam-5466	9	5	proposed	propose	VERB
ejpam-5466	9	6	the	the	DET
ejpam-5466	9	7	idea	idea	NOUN
ejpam-5466	9	8	of	of	ADP
ejpam-5466	9	9	building	build	VERB
ejpam-5466	9	10	such	such	ADJ
ejpam-5466	9	11	spaces	space	NOUN
ejpam-5466	9	12	,	,	PUNCT
ejpam-5466	9	13	and	and	CCONJ
ejpam-5466	9	14	czerwik[6	czerwik[6	NUM
ejpam-5466	9	15	]	]	PUNCT
ejpam-5466	9	16	refined	refine	VERB
ejpam-5466	9	17	it	it	PRON
ejpam-5466	9	18	.	.	PUNCT
ejpam-5466	10	1	several	several	ADJ
ejpam-5466	10	2	fixedpoint	fixedpoint	NOUN
ejpam-5466	10	3	results	result	NOUN
ejpam-5466	10	4	were	be	AUX
ejpam-5466	10	5	provided	provide	VERB
ejpam-5466	10	6	in	in	ADP
ejpam-5466	10	7	this	this	DET
ejpam-5466	10	8	way	way	NOUN
ejpam-5466	10	9	for	for	ADP
ejpam-5466	10	10	single	single	ADJ
ejpam-5466	10	11	or	or	CCONJ
ejpam-5466	10	12	set	set	VERB
ejpam-5466	10	13	valued	value	VERB
ejpam-5466	10	14	mappings	mapping	NOUN
ejpam-5466	10	15	,	,	PUNCT
ejpam-5466	10	16	for	for	ADP
ejpam-5466	10	17	instance	instance	NOUN
ejpam-5466	10	18	,	,	PUNCT
ejpam-5466	10	19	see[7	see[7	PROPN
ejpam-5466	10	20	,	,	PUNCT
ejpam-5466	10	21	13	13	NUM
ejpam-5466	10	22	,	,	PUNCT
ejpam-5466	10	23	23	23	NUM
ejpam-5466	10	24	,	,	PUNCT
ejpam-5466	10	25	24	24	NUM
ejpam-5466	10	26	,	,	PUNCT
ejpam-5466	10	27	26	26	NUM
ejpam-5466	10	28	]	]	PUNCT
ejpam-5466	10	29	.	.	PUNCT
ejpam-5466	11	1	one	one	NUM
ejpam-5466	11	2	of	of	ADP
ejpam-5466	11	3	the	the	DET
ejpam-5466	11	4	key	key	ADJ
ejpam-5466	11	5	generalizations	generalization	NOUN
ejpam-5466	11	6	for	for	ADP
ejpam-5466	11	7	metric	metric	ADJ
ejpam-5466	11	8	spaces	space	NOUN
ejpam-5466	11	9	is	be	AUX
ejpam-5466	11	10	the	the	DET
ejpam-5466	11	11	idea	idea	NOUN
ejpam-5466	11	12	of	of	ADP
ejpam-5466	11	13	a	a	DET
ejpam-5466	11	14	b	b	NOUN
ejpam-5466	11	15	-	-	PUNCT
ejpam-5466	11	16	metric	metric	ADJ
ejpam-5466	11	17	space	space	NOUN
ejpam-5466	11	18	.	.	PUNCT
ejpam-5466	12	1	bakhtin	bakhtin	NOUN
ejpam-5466	13	1	[	[	X
ejpam-5466	13	2	4	4	X
ejpam-5466	13	3	]	]	PUNCT
ejpam-5466	13	4	first	first	ADV
ejpam-5466	13	5	proposed	propose	VERB
ejpam-5466	13	6	the	the	DET
ejpam-5466	13	7	idea	idea	NOUN
ejpam-5466	13	8	of	of	ADP
ejpam-5466	13	9	building	build	VERB
ejpam-5466	13	10	such	such	ADJ
ejpam-5466	13	11	spaces	space	NOUN
ejpam-5466	13	12	,	,	PUNCT
ejpam-5466	13	13	and	and	CCONJ
ejpam-5466	13	14	czerwik	czerwik	PROPN
ejpam-5466	13	15	citesc1	citesc1	PROPN
ejpam-5466	13	16	refined	refine	VERB
ejpam-5466	13	17	it	it	PRON
ejpam-5466	13	18	.	.	PUNCT
ejpam-5466	14	1	several	several	ADJ
ejpam-5466	14	2	fixed	fix	VERB
ejpam-5466	14	3	-	-	PUNCT
ejpam-5466	14	4	point	point	NOUN
ejpam-5466	14	5	results	result	NOUN
ejpam-5466	14	6	were	be	AUX
ejpam-5466	14	7	provided	provide	VERB
ejpam-5466	14	8	in	in	ADP
ejpam-5466	14	9	this	this	DET
ejpam-5466	14	10	way	way	NOUN
ejpam-5466	14	11	for	for	ADP
ejpam-5466	14	12	single	single	ADJ
ejpam-5466	14	13	or	or	CCONJ
ejpam-5466	14	14	set	set	VERB
ejpam-5466	14	15	valued	value	VERB
ejpam-5466	14	16	mappings	mapping	NOUN
ejpam-5466	14	17	,	,	PUNCT
ejpam-5466	14	18	for	for	ADP
ejpam-5466	14	19	instance	instance	NOUN
ejpam-5466	14	20	,	,	PUNCT
ejpam-5466	14	21	see	see	VERB
ejpam-5466	14	22	[	[	X
ejpam-5466	14	23	7	7	NUM
ejpam-5466	14	24	,	,	PUNCT
ejpam-5466	14	25	13	13	NUM
ejpam-5466	14	26	,	,	PUNCT
ejpam-5466	14	27	23	23	NUM
ejpam-5466	14	28	,	,	PUNCT
ejpam-5466	14	29	24	24	NUM
ejpam-5466	14	30	,	,	PUNCT
ejpam-5466	14	31	26	26	NUM
ejpam-5466	14	32	]	]	PUNCT
ejpam-5466	14	33	.	.	PUNCT
ejpam-5466	15	1	however	however	ADV
ejpam-5466	15	2	,	,	PUNCT
ejpam-5466	15	3	samet	samet	PROPN
ejpam-5466	15	4	et	et	PROPN
ejpam-5466	15	5	al	al	PROPN
ejpam-5466	15	6	.	.	PUNCT
ejpam-5466	16	1	[	[	X
ejpam-5466	16	2	27	27	NUM
ejpam-5466	16	3	]	]	PUNCT
ejpam-5466	16	4	presented	present	VERB
ejpam-5466	16	5	the	the	DET
ejpam-5466	16	6	idea	idea	NOUN
ejpam-5466	16	7	of	of	ADP
ejpam-5466	16	8	α	α	NOUN
ejpam-5466	16	9	-	-	ADJ
ejpam-5466	16	10	admissible	admissible	ADJ
ejpam-5466	16	11	,	,	PUNCT
ejpam-5466	16	12	and	and	CCONJ
ejpam-5466	16	13	they	they	PRON
ejpam-5466	16	14	established	establish	VERB
ejpam-5466	16	15	some	some	DET
ejpam-5466	16	16	results	result	NOUN
ejpam-5466	16	17	.	.	PUNCT
ejpam-5466	17	1	some	some	DET
ejpam-5466	17	2	results	result	NOUN
ejpam-5466	17	3	were	be	AUX
ejpam-5466	17	4	reached	reach	VERB
ejpam-5466	17	5	by	by	ADP
ejpam-5466	17	6	using	use	VERB
ejpam-5466	17	7	this	this	DET
ejpam-5466	17	8	notion	notion	NOUN
ejpam-5466	17	9	in	in	ADP
ejpam-5466	17	10	conjunction	conjunction	NOUN
ejpam-5466	17	11	with	with	ADP
ejpam-5466	17	12	non	non	ADJ
ejpam-5466	17	13	-	-	ADJ
ejpam-5466	17	14	linear	linear	ADJ
ejpam-5466	17	15	contractions	contraction	NOUN
ejpam-5466	17	16	;	;	PUNCT
ejpam-5466	17	17	see	see	VERB
ejpam-5466	17	18	[	[	X
ejpam-5466	17	19	11	11	NUM
ejpam-5466	17	20	,	,	PUNCT
ejpam-5466	17	21	12	12	NUM
ejpam-5466	17	22	,	,	PUNCT
ejpam-5466	17	23	18	18	NUM
ejpam-5466	17	24	,	,	PUNCT
ejpam-5466	17	25	23	23	NUM
ejpam-5466	17	26	]	]	PUNCT
ejpam-5466	17	27	.	.	PUNCT
ejpam-5466	18	1	this	this	DET
ejpam-5466	18	2	∗corresponding	∗corresponde	VERB
ejpam-5466	18	3	author	author	NOUN
ejpam-5466	18	4	.	.	PUNCT
ejpam-5466	19	1	doi	doi	NOUN
ejpam-5466	19	2	:	:	PUNCT
ejpam-5466	19	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5466	https://doi.org/10.29020/nybg.ejpam.v17i4.5466	PROPN
ejpam-5466	19	4	email	email	NOUN
ejpam-5466	19	5	addresses	address	NOUN
ejpam-5466	19	6	:	:	PUNCT
ejpam-5466	19	7	chaimanoor9@gmail.com	chaimanoor9@gmail.com	X
ejpam-5466	19	8	(	(	PUNCT
ejpam-5466	19	9	m.	m.	NOUN
ejpam-5466	19	10	meneceur	meneceur	PROPN
ejpam-5466	19	11	)	)	PUNCT
ejpam-5466	19	12	,	,	PUNCT
ejpam-5466	19	13	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-5466	19	14	(	(	PUNCT
ejpam-5466	19	15	h.	h.	PROPN
ejpam-5466	19	16	qawaqneh	qawaqneh	PROPN
ejpam-5466	19	17	)	)	PUNCT
ejpam-5466	19	18	,	,	PUNCT
ejpam-5466	19	19	habes@dau.edu.sa	habes@dau.edu.sa	PROPN
ejpam-5466	19	20	(	(	PUNCT
ejpam-5466	19	21	h.	h.	PROPN
ejpam-5466	19	22	alsamir	alsamir	PROPN
ejpam-5466	19	23	)	)	PUNCT
ejpam-5466	19	24	,	,	PUNCT
ejpam-5466	19	25	g.almusannef@arabou.edu.sa	g.almusannef@arabou.edu.sa	PROPN
ejpam-5466	19	26	(	(	PUNCT
ejpam-5466	19	27	j.m	j.m	PROPN
ejpam-5466	19	28	.	.	PROPN
ejpam-5466	19	29	al	al	PROPN
ejpam-5466	19	30	-	-	PUNCT
ejpam-5466	19	31	musannef	musannef	PROPN
ejpam-5466	19	32	)	)	PUNCT
ejpam-5466	19	33	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5466	19	34	3093	3093	NUM
ejpam-5466	20	1	copyright	copyright	NOUN
ejpam-5466	20	2	:	:	PUNCT
ejpam-5466	20	3	©	©	PROPN
ejpam-5466	20	4	2024	2024	NUM
ejpam-5466	20	5	the	the	DET
ejpam-5466	20	6	author(s	author(s	NOUN
ejpam-5466	20	7	)	)	PUNCT
ejpam-5466	20	8	.	.	PUNCT
ejpam-5466	21	1	(	(	PUNCT
ejpam-5466	21	2	cc	cc	NOUN
ejpam-5466	21	3	by	by	ADP
ejpam-5466	21	4	-	-	PUNCT
ejpam-5466	21	5	nc	nc	PROPN
ejpam-5466	21	6	4.0	4.0	NUM
ejpam-5466	21	7	)	)	PUNCT
ejpam-5466	21	8	h.	h.	PROPN
ejpam-5466	21	9	qawaqneh	qawaqneh	PROPN
ejpam-5466	21	10	et	et	PROPN
ejpam-5466	21	11	al	al	PROPN
ejpam-5466	21	12	.	.	PUNCT
ejpam-5466	21	13	/	/	SYM
ejpam-5466	21	14	eur	eur	PROPN
ejpam-5466	21	15	.	.	PUNCT
ejpam-5466	22	1	j.	j.	PROPN
ejpam-5466	22	2	pure	pure	PROPN
ejpam-5466	22	3	appl	appl	PROPN
ejpam-5466	22	4	.	.	PROPN
ejpam-5466	22	5	math	math	PROPN
ejpam-5466	22	6	,	,	PUNCT
ejpam-5466	22	7	17	17	NUM
ejpam-5466	22	8	(	(	PUNCT
ejpam-5466	22	9	4	4	NUM
ejpam-5466	22	10	)	)	PUNCT
ejpam-5466	22	11	(	(	PUNCT
ejpam-5466	22	12	2024	2024	NUM
ejpam-5466	22	13	)	)	PUNCT
ejpam-5466	22	14	,	,	PUNCT
ejpam-5466	22	15	3093	3093	NUM
ejpam-5466	22	16	-	-	SYM
ejpam-5466	22	17	3108	3108	NUM
ejpam-5466	22	18	3094	3094	NUM
ejpam-5466	22	19	idea	idea	NOUN
ejpam-5466	22	20	was	be	AUX
ejpam-5466	22	21	later	later	ADV
ejpam-5466	22	22	extended	extend	VERB
ejpam-5466	22	23	to	to	ADP
ejpam-5466	22	24	αs	αs	ADJ
ejpam-5466	22	25	-	-	NOUN
ejpam-5466	22	26	admissible	admissible	ADJ
ejpam-5466	22	27	in	in	ADP
ejpam-5466	22	28	the	the	DET
ejpam-5466	22	29	setting	setting	NOUN
ejpam-5466	22	30	of	of	ADP
ejpam-5466	22	31	b	b	NOUN
ejpam-5466	22	32	-	-	PUNCT
ejpam-5466	22	33	metric	metric	ADJ
ejpam-5466	22	34	spaces	space	NOUN
ejpam-5466	22	35	by	by	ADP
ejpam-5466	22	36	ali	ali	PROPN
ejpam-5466	22	37	et	et	PROPN
ejpam-5466	22	38	al	al	PROPN
ejpam-5466	22	39	.	.	PUNCT
ejpam-5466	23	1	[	[	X
ejpam-5466	23	2	14	14	NUM
ejpam-5466	23	3	]	]	PUNCT
ejpam-5466	23	4	.	.	PUNCT
ejpam-5466	24	1	jleli	jleli	PROPN
ejpam-5466	24	2	and	and	CCONJ
ejpam-5466	24	3	samet	samet	VERB
ejpam-5466	25	1	[	[	X
ejpam-5466	25	2	10	10	NUM
ejpam-5466	25	3	]	]	PUNCT
ejpam-5466	25	4	established	establish	VERB
ejpam-5466	25	5	a	a	DET
ejpam-5466	25	6	novel	novel	ADJ
ejpam-5466	25	7	idea	idea	NOUN
ejpam-5466	25	8	known	know	VERB
ejpam-5466	25	9	as	as	ADP
ejpam-5466	25	10	the	the	DET
ejpam-5466	25	11	ϑ-contraction	ϑ-contraction	NOUN
ejpam-5466	25	12	and	and	CCONJ
ejpam-5466	25	13	proved	prove	VERB
ejpam-5466	25	14	the	the	DET
ejpam-5466	25	15	existence	existence	NOUN
ejpam-5466	25	16	of	of	ADP
ejpam-5466	25	17	fixed	fix	VERB
ejpam-5466	25	18	points	point	NOUN
ejpam-5466	25	19	.	.	PUNCT
ejpam-5466	26	1	here	here	ADV
ejpam-5466	26	2	,	,	PUNCT
ejpam-5466	26	3	it	it	PRON
ejpam-5466	26	4	is	be	AUX
ejpam-5466	26	5	important	important	ADJ
ejpam-5466	26	6	to	to	PART
ejpam-5466	26	7	note	note	VERB
ejpam-5466	26	8	that	that	SCONJ
ejpam-5466	26	9	a	a	DET
ejpam-5466	26	10	contraction	contraction	NOUN
ejpam-5466	26	11	in	in	ADP
ejpam-5466	26	12	in	in	ADP
ejpam-5466	26	13	the	the	DET
ejpam-5466	26	14	sense	sense	NOUN
ejpam-5466	26	15	of	of	ADP
ejpam-5466	26	16	banach	banach	NOUN
ejpam-5466	26	17	,	,	PUNCT
ejpam-5466	26	18	is	be	AUX
ejpam-5466	26	19	a	a	DET
ejpam-5466	26	20	particular	particular	ADJ
ejpam-5466	26	21	case	case	NOUN
ejpam-5466	26	22	of	of	ADP
ejpam-5466	26	23	ϑ-contraction	ϑ-contraction	NOUN
ejpam-5466	26	24	,	,	PUNCT
ejpam-5466	26	25	while	while	SCONJ
ejpam-5466	26	26	there	there	PRON
ejpam-5466	26	27	are	be	VERB
ejpam-5466	26	28	some	some	DET
ejpam-5466	26	29	ϑ-contractions	ϑ-contraction	NOUN
ejpam-5466	26	30	which	which	PRON
ejpam-5466	26	31	do	do	AUX
ejpam-5466	26	32	not	not	PART
ejpam-5466	26	33	satisfy	satisfy	VERB
ejpam-5466	26	34	banach	banach	ADV
ejpam-5466	26	35	contractive	contractive	ADJ
ejpam-5466	26	36	condition	condition	NOUN
ejpam-5466	26	37	.	.	PUNCT
ejpam-5466	27	1	subsequently	subsequently	ADV
ejpam-5466	27	2	,	,	PUNCT
ejpam-5466	27	3	several	several	ADJ
ejpam-5466	27	4	authors	author	NOUN
ejpam-5466	27	5	studied	study	VERB
ejpam-5466	27	6	different	different	ADJ
ejpam-5466	27	7	variations	variation	NOUN
ejpam-5466	27	8	of	of	ADP
ejpam-5466	27	9	ϑ-contractions	ϑ-contraction	NOUN
ejpam-5466	27	10	and	and	CCONJ
ejpam-5466	27	11	other	other	ADJ
ejpam-5466	27	12	different	different	ADJ
ejpam-5466	27	13	contractions	contraction	NOUN
ejpam-5466	27	14	in	in	ADP
ejpam-5466	27	15	single	single	ADJ
ejpam-5466	27	16	and	and	CCONJ
ejpam-5466	27	17	set	set	VERB
ejpam-5466	27	18	valued	value	VERB
ejpam-5466	27	19	cases	case	NOUN
ejpam-5466	27	20	,	,	PUNCT
ejpam-5466	27	21	for	for	ADP
ejpam-5466	27	22	example	example	NOUN
ejpam-5466	27	23	,	,	PUNCT
ejpam-5466	27	24	see	see	VERB
ejpam-5466	27	25	[	[	X
ejpam-5466	27	26	2	2	NUM
ejpam-5466	27	27	,	,	PUNCT
ejpam-5466	27	28	3	3	NUM
ejpam-5466	27	29	,	,	PUNCT
ejpam-5466	27	30	15–17	15–17	NUM
ejpam-5466	27	31	,	,	PUNCT
ejpam-5466	27	32	19–22	19–22	NUM
ejpam-5466	27	33	,	,	PUNCT
ejpam-5466	27	34	25	25	NUM
ejpam-5466	27	35	,	,	PUNCT
ejpam-5466	27	36	28	28	NUM
ejpam-5466	27	37	]	]	PUNCT
ejpam-5466	27	38	in	in	ADP
ejpam-5466	27	39	this	this	DET
ejpam-5466	27	40	work	work	NOUN
ejpam-5466	27	41	,	,	PUNCT
ejpam-5466	27	42	we	we	PRON
ejpam-5466	27	43	prove	prove	VERB
ejpam-5466	27	44	the	the	DET
ejpam-5466	27	45	existence	existence	NOUN
ejpam-5466	27	46	of	of	ADP
ejpam-5466	27	47	a	a	DET
ejpam-5466	27	48	fixed	fix	VERB
ejpam-5466	27	49	point	point	NOUN
ejpam-5466	27	50	for	for	ADP
ejpam-5466	27	51	such	such	DET
ejpam-5466	27	52	a	a	DET
ejpam-5466	27	53	novel	novel	ADJ
ejpam-5466	27	54	contraction	contraction	NOUN
ejpam-5466	27	55	type	type	NOUN
ejpam-5466	27	56	in	in	ADP
ejpam-5466	27	57	complete	complete	ADJ
ejpam-5466	27	58	b	b	X
ejpam-5466	27	59	-	-	ADJ
ejpam-5466	27	60	metric	metric	ADJ
ejpam-5466	27	61	spaces	space	NOUN
ejpam-5466	27	62	spaces	space	VERB
ejpam-5466	27	63	by	by	ADP
ejpam-5466	27	64	combining	combine	VERB
ejpam-5466	27	65	the	the	DET
ejpam-5466	27	66	notion	notion	NOUN
ejpam-5466	27	67	of	of	ADP
ejpam-5466	27	68	αs	αs	ADJ
ejpam-5466	27	69	-	-	ADJ
ejpam-5466	27	70	admissible	admissible	ADJ
ejpam-5466	27	71	mapping	mapping	NOUN
ejpam-5466	27	72	with	with	ADP
ejpam-5466	27	73	ϑ-contraction	ϑ-contraction	NOUN
ejpam-5466	27	74	in	in	ADP
ejpam-5466	27	75	the	the	DET
ejpam-5466	27	76	case	case	NOUN
ejpam-5466	27	77	of	of	ADP
ejpam-5466	27	78	multivalued	multivalue	VERB
ejpam-5466	27	79	mappings	mapping	NOUN
ejpam-5466	27	80	.	.	PUNCT
ejpam-5466	28	1	in	in	ADP
ejpam-5466	28	2	this	this	DET
ejpam-5466	28	3	work	work	NOUN
ejpam-5466	28	4	,	,	PUNCT
ejpam-5466	28	5	we	we	PRON
ejpam-5466	28	6	prove	prove	VERB
ejpam-5466	28	7	the	the	DET
ejpam-5466	28	8	existence	existence	NOUN
ejpam-5466	28	9	of	of	ADP
ejpam-5466	28	10	a	a	DET
ejpam-5466	28	11	fixed	fix	VERB
ejpam-5466	28	12	point	point	NOUN
ejpam-5466	28	13	for	for	ADP
ejpam-5466	28	14	such	such	DET
ejpam-5466	28	15	a	a	DET
ejpam-5466	28	16	novel	novel	ADJ
ejpam-5466	28	17	contraction	contraction	NOUN
ejpam-5466	28	18	type	type	NOUN
ejpam-5466	28	19	in	in	ADP
ejpam-5466	28	20	complete	complete	ADJ
ejpam-5466	28	21	b	b	X
ejpam-5466	28	22	-	-	ADJ
ejpam-5466	28	23	metric	metric	ADJ
ejpam-5466	28	24	spaces	space	NOUN
ejpam-5466	28	25	by	by	ADP
ejpam-5466	28	26	combining	combine	VERB
ejpam-5466	28	27	the	the	DET
ejpam-5466	28	28	notion	notion	NOUN
ejpam-5466	28	29	of	of	ADP
ejpam-5466	28	30	αs	αs	ADJ
ejpam-5466	28	31	-	-	ADJ
ejpam-5466	28	32	admissible	admissible	ADJ
ejpam-5466	28	33	mapping	mapping	NOUN
ejpam-5466	28	34	with	with	ADP
ejpam-5466	28	35	ϑcontraction	ϑcontraction	NOUN
ejpam-5466	28	36	in	in	ADP
ejpam-5466	28	37	the	the	DET
ejpam-5466	28	38	case	case	NOUN
ejpam-5466	28	39	of	of	ADP
ejpam-5466	28	40	multivalued	multivalue	VERB
ejpam-5466	28	41	mappings	mapping	NOUN
ejpam-5466	28	42	.	.	PUNCT
ejpam-5466	29	1	using	use	VERB
ejpam-5466	29	2	our	our	PRON
ejpam-5466	29	3	major	major	ADJ
ejpam-5466	29	4	findings	finding	NOUN
ejpam-5466	29	5	,	,	PUNCT
ejpam-5466	29	6	we	we	PRON
ejpam-5466	29	7	also	also	ADV
ejpam-5466	29	8	infer	infer	VERB
ejpam-5466	29	9	the	the	DET
ejpam-5466	29	10	existence	existence	NOUN
ejpam-5466	29	11	of	of	ADP
ejpam-5466	29	12	fixed	fix	VERB
ejpam-5466	29	13	points	point	NOUN
ejpam-5466	29	14	in	in	ADP
ejpam-5466	29	15	partially	partially	ADV
ejpam-5466	29	16	ordered	order	VERB
ejpam-5466	29	17	metric	metric	ADJ
ejpam-5466	29	18	spaces	space	NOUN
ejpam-5466	29	19	.	.	PUNCT
ejpam-5466	30	1	lastly	lastly	ADV
ejpam-5466	30	2	,	,	PUNCT
ejpam-5466	30	3	to	to	PART
ejpam-5466	30	4	demonstrate	demonstrate	VERB
ejpam-5466	30	5	the	the	DET
ejpam-5466	30	6	applicability	applicability	NOUN
ejpam-5466	30	7	of	of	ADP
ejpam-5466	30	8	our	our	PRON
ejpam-5466	30	9	results	result	NOUN
ejpam-5466	30	10	,	,	PUNCT
ejpam-5466	30	11	we	we	PRON
ejpam-5466	30	12	offer	offer	VERB
ejpam-5466	30	13	an	an	DET
ejpam-5466	30	14	example	example	NOUN
ejpam-5466	30	15	and	and	CCONJ
ejpam-5466	30	16	an	an	DET
ejpam-5466	30	17	application	application	NOUN
ejpam-5466	30	18	pertaining	pertain	VERB
ejpam-5466	30	19	to	to	ADP
ejpam-5466	30	20	an	an	DET
ejpam-5466	30	21	existence	existence	NOUN
ejpam-5466	30	22	problem	problem	NOUN
ejpam-5466	30	23	of	of	ADP
ejpam-5466	30	24	solutions	solution	NOUN
ejpam-5466	30	25	for	for	ADP
ejpam-5466	30	26	a	a	DET
ejpam-5466	30	27	volterra	volterra	NOUN
ejpam-5466	30	28	integral	integral	ADJ
ejpam-5466	30	29	inclusion	inclusion	NOUN
ejpam-5466	30	30	and	and	CCONJ
ejpam-5466	30	31	for	for	ADP
ejpam-5466	30	32	applications	application	NOUN
ejpam-5466	30	33	in	in	ADP
ejpam-5466	30	34	factional	factional	ADJ
ejpam-5466	30	35	equtions	eqution	NOUN
ejpam-5466	30	36	,	,	PUNCT
ejpam-5466	30	37	see	see	VERB
ejpam-5466	30	38	[	[	X
ejpam-5466	30	39	1	1	NUM
ejpam-5466	30	40	,	,	PUNCT
ejpam-5466	30	41	8	8	NUM
ejpam-5466	30	42	]	]	PUNCT
ejpam-5466	30	43	definition	definition	NOUN
ejpam-5466	30	44	1	1	NUM
ejpam-5466	30	45	.	.	PUNCT
ejpam-5466	31	1	[	[	X
ejpam-5466	31	2	14	14	NUM
ejpam-5466	31	3	]	]	PUNCT
ejpam-5466	31	4	let	let	VERB
ejpam-5466	31	5	x	x	PRON
ejpam-5466	31	6	be	be	AUX
ejpam-5466	31	7	a	a	DET
ejpam-5466	31	8	non	non	ADJ
ejpam-5466	31	9	-	-	ADJ
ejpam-5466	31	10	empty	empty	ADJ
ejpam-5466	31	11	set	set	NOUN
ejpam-5466	31	12	and	and	CCONJ
ejpam-5466	31	13	s	s	AUX
ejpam-5466	31	14	be	be	AUX
ejpam-5466	31	15	a	a	DET
ejpam-5466	31	16	real	real	ADJ
ejpam-5466	31	17	number	number	NOUN
ejpam-5466	31	18	with	with	ADP
ejpam-5466	31	19	s	s	PRON
ejpam-5466	31	20	≥	≥	NOUN
ejpam-5466	31	21	1	1	NUM
ejpam-5466	31	22	.	.	PUNCT
ejpam-5466	32	1	a	a	DET
ejpam-5466	32	2	function	function	NOUN
ejpam-5466	32	3	d	d	NOUN
ejpam-5466	32	4	:	:	PUNCT
ejpam-5466	32	5	x	x	SYM
ejpam-5466	32	6	×	×	NOUN
ejpam-5466	32	7	x	x	INTJ
ejpam-5466	32	8	→	→	X
ejpam-5466	32	9	[	[	X
ejpam-5466	32	10	0,∞	0,∞	NUM
ejpam-5466	32	11	)	)	PUNCT
ejpam-5466	32	12	is	be	AUX
ejpam-5466	32	13	a	a	DET
ejpam-5466	32	14	b	b	NOUN
ejpam-5466	32	15	-	-	ADJ
ejpam-5466	32	16	metric	metric	ADJ
ejpam-5466	32	17	on	on	ADP
ejpam-5466	32	18	x	x	SYM
ejpam-5466	32	19	if	if	SCONJ
ejpam-5466	32	20	for	for	ADP
ejpam-5466	32	21	all	all	PRON
ejpam-5466	32	22	ν	ν	PROPN
ejpam-5466	32	23	,	,	PUNCT
ejpam-5466	32	24	µ	µ	NOUN
ejpam-5466	32	25	,	,	PUNCT
ejpam-5466	32	26	η	η	PROPN
ejpam-5466	32	27	∈	∈	PROPN
ejpam-5466	32	28	x	x	PRON
ejpam-5466	32	29	,	,	PUNCT
ejpam-5466	32	30	it	it	PRON
ejpam-5466	32	31	satisfies	satisfy	VERB
ejpam-5466	32	32	the	the	DET
ejpam-5466	32	33	following	follow	VERB
ejpam-5466	32	34	conditions	condition	NOUN
ejpam-5466	32	35	:	:	PUNCT
ejpam-5466	32	36	(	(	PUNCT
ejpam-5466	32	37	b1	b1	NOUN
ejpam-5466	32	38	)	)	PUNCT
ejpam-5466	32	39	d(ν	d(ν	PROPN
ejpam-5466	32	40	,	,	PUNCT
ejpam-5466	32	41	µ	µ	NOUN
ejpam-5466	32	42	)	)	PUNCT
ejpam-5466	32	43	=	=	SYM
ejpam-5466	32	44	0	0	NUM
ejpam-5466	33	1	iff	iff	PROPN
ejpam-5466	33	2	ν	ν	PROPN
ejpam-5466	33	3	=	=	SYM
ejpam-5466	33	4	µ	µ	PROPN
ejpam-5466	33	5	,	,	PUNCT
ejpam-5466	33	6	(	(	PUNCT
ejpam-5466	33	7	b2	b2	NOUN
ejpam-5466	33	8	)	)	PUNCT
ejpam-5466	33	9	d(ν	d(ν	PROPN
ejpam-5466	33	10	,	,	PUNCT
ejpam-5466	33	11	µ	µ	NOUN
ejpam-5466	33	12	)	)	PUNCT
ejpam-5466	33	13	=	=	SYM
ejpam-5466	33	14	d(µ	d(µ	PROPN
ejpam-5466	33	15	,	,	PUNCT
ejpam-5466	33	16	ν	ν	NOUN
ejpam-5466	33	17	)	)	PUNCT
ejpam-5466	33	18	,	,	PUNCT
ejpam-5466	33	19	(	(	PUNCT
ejpam-5466	33	20	b3	b3	NOUN
ejpam-5466	33	21	)	)	PUNCT
ejpam-5466	33	22	d(ν	d(ν	PROPN
ejpam-5466	33	23	,	,	PUNCT
ejpam-5466	33	24	η	η	NOUN
ejpam-5466	33	25	)	)	PUNCT
ejpam-5466	33	26	≤	≤	NUM
ejpam-5466	33	27	s[d(ν	s[d(ν	NOUN
ejpam-5466	33	28	,	,	PUNCT
ejpam-5466	33	29	µ	µ	NOUN
ejpam-5466	33	30	)	)	PUNCT
ejpam-5466	33	31	+	+	CCONJ
ejpam-5466	33	32	d(µ	d(µ	PROPN
ejpam-5466	33	33	,	,	PUNCT
ejpam-5466	33	34	η	η	PROPN
ejpam-5466	33	35	)	)	PUNCT
ejpam-5466	33	36	]	]	PUNCT
ejpam-5466	33	37	.	.	PUNCT
ejpam-5466	34	1	a	a	DET
ejpam-5466	34	2	triplet	triplet	NOUN
ejpam-5466	34	3	(	(	PUNCT
ejpam-5466	34	4	x	x	NOUN
ejpam-5466	34	5	,	,	PUNCT
ejpam-5466	34	6	d	d	X
ejpam-5466	34	7	,	,	PUNCT
ejpam-5466	34	8	s	s	PART
ejpam-5466	34	9	)	)	PUNCT
ejpam-5466	34	10	is	be	AUX
ejpam-5466	34	11	called	call	VERB
ejpam-5466	34	12	a	a	DET
ejpam-5466	34	13	b	b	NOUN
ejpam-5466	34	14	-	-	PUNCT
ejpam-5466	34	15	metric	metric	ADJ
ejpam-5466	34	16	space	space	NOUN
ejpam-5466	34	17	.	.	PUNCT
ejpam-5466	35	1	every	every	DET
ejpam-5466	35	2	metric	metric	ADJ
ejpam-5466	35	3	space	space	NOUN
ejpam-5466	35	4	is	be	AUX
ejpam-5466	35	5	a	a	DET
ejpam-5466	35	6	b	b	NOUN
ejpam-5466	35	7	-	-	PUNCT
ejpam-5466	35	8	metric	metric	ADJ
ejpam-5466	35	9	space	space	NOUN
ejpam-5466	35	10	with	with	ADP
ejpam-5466	35	11	s	s	NOUN
ejpam-5466	35	12	=	=	SYM
ejpam-5466	35	13	1	1	X
ejpam-5466	35	14	.	.	PUNCT
ejpam-5466	35	15	denote	denote	VERB
ejpam-5466	35	16	the	the	DET
ejpam-5466	35	17	family	family	NOUN
ejpam-5466	35	18	of	of	ADP
ejpam-5466	35	19	non	non	ADJ
ejpam-5466	35	20	-	-	ADJ
ejpam-5466	35	21	empty	empty	ADJ
ejpam-5466	35	22	,	,	PUNCT
ejpam-5466	35	23	closed	closed	ADJ
ejpam-5466	35	24	and	and	CCONJ
ejpam-5466	35	25	bounded	bound	VERB
ejpam-5466	35	26	subsets	subset	NOUN
ejpam-5466	35	27	of	of	ADP
ejpam-5466	35	28	x	x	PUNCT
ejpam-5466	35	29	by	by	ADP
ejpam-5466	35	30	cb(x	cb(x	NOUN
ejpam-5466	35	31	)	)	PUNCT
ejpam-5466	35	32	.	.	PUNCT
ejpam-5466	36	1	for	for	ADP
ejpam-5466	36	2	a	a	DET
ejpam-5466	36	3	,	,	PUNCT
ejpam-5466	36	4	b	b	PROPN
ejpam-5466	36	5	∈	∈	PROPN
ejpam-5466	36	6	cb(x	cb(x	NUM
ejpam-5466	36	7	)	)	PUNCT
ejpam-5466	36	8	,	,	PUNCT
ejpam-5466	36	9	define	define	VERB
ejpam-5466	36	10	h	h	NOUN
ejpam-5466	36	11	:	:	PUNCT
ejpam-5466	36	12	cb(x)×	cb(x)×	PROPN
ejpam-5466	36	13	cb(x	cb(x	X
ejpam-5466	36	14	)	)	PUNCT
ejpam-5466	36	15	→	→	PUNCT
ejpam-5466	37	1	[	[	X
ejpam-5466	37	2	0,+∞	0,+∞	NUM
ejpam-5466	37	3	)	)	PUNCT
ejpam-5466	37	4	by	by	ADP
ejpam-5466	37	5	h(a	h(a	PROPN
ejpam-5466	37	6	,	,	PUNCT
ejpam-5466	37	7	b	b	NOUN
ejpam-5466	37	8	)	)	PUNCT
ejpam-5466	37	9	=	=	SYM
ejpam-5466	37	10	max	max	PROPN
ejpam-5466	37	11	{	{	PUNCT
ejpam-5466	37	12	sup	sup	PROPN
ejpam-5466	37	13	a∈a	a∈a	PRON
ejpam-5466	37	14	d(a	d(a	PROPN
ejpam-5466	37	15	,	,	PUNCT
ejpam-5466	37	16	b	b	NOUN
ejpam-5466	37	17	)	)	PUNCT
ejpam-5466	37	18	,	,	PUNCT
ejpam-5466	37	19	sup	sup	NOUN
ejpam-5466	37	20	b∈b	b∈b	NOUN
ejpam-5466	37	21	d(b	d(b	PROPN
ejpam-5466	37	22	,	,	PUNCT
ejpam-5466	37	23	a	a	PRON
ejpam-5466	37	24	)	)	PUNCT
ejpam-5466	37	25	}	}	PUNCT
ejpam-5466	37	26	where	where	SCONJ
ejpam-5466	37	27	d(a	d(a	PROPN
ejpam-5466	37	28	,	,	PUNCT
ejpam-5466	37	29	b	b	NOUN
ejpam-5466	37	30	)	)	PUNCT
ejpam-5466	37	31	=	=	SYM
ejpam-5466	37	32	inf	inf	NOUN
ejpam-5466	37	33	{	{	PUNCT
ejpam-5466	37	34	d(b	d(b	PROPN
ejpam-5466	37	35	,	,	PUNCT
ejpam-5466	37	36	ν	ν	NOUN
ejpam-5466	37	37	)	)	PUNCT
ejpam-5466	37	38	:	:	PUNCT
ejpam-5466	38	1	ν	ν	X
ejpam-5466	38	2	∈	∈	PROPN
ejpam-5466	38	3	b	b	NOUN
ejpam-5466	38	4	}	}	PUNCT
ejpam-5466	38	5	.	.	PUNCT
ejpam-5466	39	1	such	such	DET
ejpam-5466	39	2	a	a	DET
ejpam-5466	39	3	function	function	NOUN
ejpam-5466	39	4	h	h	NOUN
ejpam-5466	39	5	is	be	AUX
ejpam-5466	39	6	called	call	VERB
ejpam-5466	39	7	the	the	DET
ejpam-5466	39	8	pompeiu	pompeiu	NOUN
ejpam-5466	39	9	-	-	PUNCT
ejpam-5466	39	10	hausdorff	hausdorff	NOUN
ejpam-5466	39	11	metric	metric	NOUN
ejpam-5466	39	12	induced	induce	VERB
ejpam-5466	39	13	by	by	ADP
ejpam-5466	39	14	d	d	PROPN
ejpam-5466	39	15	,	,	PUNCT
ejpam-5466	39	16	for	for	ADP
ejpam-5466	39	17	more	more	ADJ
ejpam-5466	39	18	details	detail	NOUN
ejpam-5466	39	19	,	,	PUNCT
ejpam-5466	39	20	see	see	VERB
ejpam-5466	39	21	[	[	X
ejpam-5466	39	22	5	5	NUM
ejpam-5466	39	23	]	]	PUNCT
ejpam-5466	39	24	.	.	PUNCT
ejpam-5466	40	1	also	also	ADV
ejpam-5466	40	2	,	,	PUNCT
ejpam-5466	40	3	denote	denote	VERB
ejpam-5466	40	4	the	the	DET
ejpam-5466	40	5	family	family	NOUN
ejpam-5466	40	6	of	of	ADP
ejpam-5466	40	7	non	non	ADJ
ejpam-5466	40	8	-	-	ADJ
ejpam-5466	40	9	empty	empty	ADJ
ejpam-5466	40	10	and	and	CCONJ
ejpam-5466	40	11	closed	closed	ADJ
ejpam-5466	40	12	subsets	subset	NOUN
ejpam-5466	40	13	of	of	ADP
ejpam-5466	40	14	x	x	PUNCT
ejpam-5466	40	15	by	by	ADP
ejpam-5466	40	16	cl(x	cl(x	NOUN
ejpam-5466	40	17	)	)	PUNCT
ejpam-5466	40	18	.	.	PUNCT
ejpam-5466	41	1	lemma	lemma	PROPN
ejpam-5466	41	2	1	1	NUM
ejpam-5466	41	3	.	.	PUNCT
ejpam-5466	42	1	[	[	X
ejpam-5466	42	2	14	14	NUM
ejpam-5466	42	3	]	]	X
ejpam-5466	42	4	let	let	AUX
ejpam-5466	42	5	(	(	PUNCT
ejpam-5466	42	6	x	x	NOUN
ejpam-5466	42	7	,	,	PUNCT
ejpam-5466	42	8	d	d	X
ejpam-5466	42	9	,	,	PUNCT
ejpam-5466	42	10	s	s	PART
ejpam-5466	42	11	)	)	PUNCT
ejpam-5466	42	12	be	be	AUX
ejpam-5466	42	13	a	a	DET
ejpam-5466	42	14	b	b	NOUN
ejpam-5466	42	15	-	-	PUNCT
ejpam-5466	42	16	metric	metric	ADJ
ejpam-5466	42	17	space	space	NOUN
ejpam-5466	42	18	.	.	PUNCT
ejpam-5466	43	1	the	the	DET
ejpam-5466	43	2	following	follow	VERB
ejpam-5466	43	3	properties	property	NOUN
ejpam-5466	43	4	are	be	AUX
ejpam-5466	43	5	satisfied	satisfied	ADJ
ejpam-5466	43	6	:	:	PUNCT
ejpam-5466	43	7	1	1	X
ejpam-5466	43	8	)	)	PUNCT
ejpam-5466	43	9	d(ν	d(ν	PROPN
ejpam-5466	43	10	,	,	PUNCT
ejpam-5466	43	11	b	b	NOUN
ejpam-5466	43	12	)	)	PUNCT
ejpam-5466	43	13	≤	≤	NOUN
ejpam-5466	43	14	d(ν	d(ν	PROPN
ejpam-5466	43	15	,	,	PUNCT
ejpam-5466	43	16	b	b	NOUN
ejpam-5466	43	17	)	)	PUNCT
ejpam-5466	43	18	for	for	ADP
ejpam-5466	43	19	all	all	PRON
ejpam-5466	43	20	ν	ν	NOUN
ejpam-5466	43	21	∈	∈	PROPN
ejpam-5466	43	22	x	x	X
ejpam-5466	43	23	,	,	PUNCT
ejpam-5466	43	24	b	b	PROPN
ejpam-5466	43	25	∈	∈	PROPN
ejpam-5466	43	26	b	b	PROPN
ejpam-5466	43	27	and	and	CCONJ
ejpam-5466	43	28	b	b	X
ejpam-5466	43	29	∈	∈	NOUN
ejpam-5466	43	30	cb(x	cb(x	NUM
ejpam-5466	43	31	)	)	PUNCT
ejpam-5466	43	32	.	.	PUNCT
ejpam-5466	44	1	2	2	X
ejpam-5466	44	2	)	)	PUNCT
ejpam-5466	44	3	d(ν	d(ν	PROPN
ejpam-5466	44	4	,	,	PUNCT
ejpam-5466	44	5	b	b	NOUN
ejpam-5466	44	6	)	)	PUNCT
ejpam-5466	44	7	≤	≤	PROPN
ejpam-5466	44	8	h(a	h(a	PROPN
ejpam-5466	44	9	,	,	PUNCT
ejpam-5466	44	10	b	b	NOUN
ejpam-5466	44	11	)	)	PUNCT
ejpam-5466	44	12	for	for	ADP
ejpam-5466	44	13	all	all	PRON
ejpam-5466	44	14	ν	ν	X
ejpam-5466	44	15	∈	∈	NOUN
ejpam-5466	44	16	x	x	X
ejpam-5466	44	17	and	and	CCONJ
ejpam-5466	44	18	a	a	DET
ejpam-5466	44	19	,	,	PUNCT
ejpam-5466	44	20	b	b	X
ejpam-5466	44	21	∈	∈	PROPN
ejpam-5466	44	22	cb(x	cb(x	NUM
ejpam-5466	44	23	)	)	PUNCT
ejpam-5466	44	24	.	.	PUNCT
ejpam-5466	45	1	3	3	X
ejpam-5466	45	2	)	)	PUNCT
ejpam-5466	45	3	d(ν	d(ν	PROPN
ejpam-5466	45	4	,	,	PUNCT
ejpam-5466	45	5	a	a	PRON
ejpam-5466	45	6	)	)	PUNCT
ejpam-5466	45	7	≤	≤	PROPN
ejpam-5466	45	8	s(d(ν	s(d(ν	PROPN
ejpam-5466	45	9	,	,	PUNCT
ejpam-5466	45	10	µ	µ	NOUN
ejpam-5466	45	11	)	)	PUNCT
ejpam-5466	45	12	+	+	X
ejpam-5466	45	13	d(µ,b	d(µ,b	NOUN
ejpam-5466	45	14	)	)	PUNCT
ejpam-5466	45	15	)	)	PUNCT
ejpam-5466	45	16	for	for	ADP
ejpam-5466	45	17	all	all	DET
ejpam-5466	45	18	ν	ν	NOUN
ejpam-5466	45	19	,	,	PUNCT
ejpam-5466	45	20	µ	µ	X
ejpam-5466	45	21	∈	∈	NOUN
ejpam-5466	45	22	x	x	X
ejpam-5466	45	23	and	and	CCONJ
ejpam-5466	45	24	a	a	DET
ejpam-5466	45	25	,	,	PUNCT
ejpam-5466	45	26	b	b	X
ejpam-5466	45	27	∈	∈	PROPN
ejpam-5466	45	28	cb(x	cb(x	NUM
ejpam-5466	45	29	)	)	PUNCT
ejpam-5466	45	30	.	.	PUNCT
ejpam-5466	46	1	lemma	lemma	PROPN
ejpam-5466	46	2	2	2	NUM
ejpam-5466	46	3	.	.	PUNCT
ejpam-5466	47	1	[	[	X
ejpam-5466	47	2	6	6	NUM
ejpam-5466	47	3	]	]	PUNCT
ejpam-5466	47	4	let	let	VERB
ejpam-5466	47	5	(	(	PUNCT
ejpam-5466	47	6	x	x	NOUN
ejpam-5466	47	7	,	,	PUNCT
ejpam-5466	47	8	d	d	X
ejpam-5466	47	9	,	,	PUNCT
ejpam-5466	47	10	s	s	PART
ejpam-5466	47	11	)	)	PUNCT
ejpam-5466	47	12	be	be	AUX
ejpam-5466	47	13	a	a	DET
ejpam-5466	47	14	b	b	NOUN
ejpam-5466	47	15	-	-	PUNCT
ejpam-5466	47	16	metric	metric	ADJ
ejpam-5466	47	17	space	space	NOUN
ejpam-5466	47	18	and	and	CCONJ
ejpam-5466	47	19	a	a	DET
ejpam-5466	47	20	,	,	PUNCT
ejpam-5466	47	21	b	b	PROPN
ejpam-5466	47	22	∈	∈	NOUN
ejpam-5466	47	23	cl(x	cl(x	NOUN
ejpam-5466	47	24	)	)	PUNCT
ejpam-5466	47	25	with	with	ADP
ejpam-5466	47	26	h(a	h(a	PROPN
ejpam-5466	47	27	,	,	PUNCT
ejpam-5466	47	28	b	b	NOUN
ejpam-5466	47	29	)	)	PUNCT
ejpam-5466	47	30	>	>	X
ejpam-5466	48	1	0	0	X
ejpam-5466	48	2	.	.	PUNCT
ejpam-5466	49	1	then	then	ADV
ejpam-5466	49	2	,	,	PUNCT
ejpam-5466	49	3	for	for	ADP
ejpam-5466	49	4	each	each	DET
ejpam-5466	49	5	b	b	PROPN
ejpam-5466	49	6	∈	∈	PROPN
ejpam-5466	49	7	b	b	NOUN
ejpam-5466	49	8	,	,	PUNCT
ejpam-5466	49	9	there	there	PRON
ejpam-5466	49	10	exists	exist	VERB
ejpam-5466	49	11	a	a	DET
ejpam-5466	49	12	=	=	PUNCT
ejpam-5466	49	13	a(b	a(b	ADJ
ejpam-5466	49	14	)	)	PUNCT
ejpam-5466	49	15	∈	∈	PROPN
ejpam-5466	49	16	a	a	DET
ejpam-5466	49	17	such	such	ADJ
ejpam-5466	49	18	that	that	SCONJ
ejpam-5466	49	19	d(a	d(a	PROPN
ejpam-5466	49	20	,	,	PUNCT
ejpam-5466	49	21	b	b	NOUN
ejpam-5466	49	22	)	)	PUNCT
ejpam-5466	49	23	≤	≤	NOUN
ejpam-5466	49	24	sh(a	sh(a	NUM
ejpam-5466	49	25	,	,	PUNCT
ejpam-5466	49	26	b	b	NOUN
ejpam-5466	49	27	)	)	PUNCT
ejpam-5466	49	28	.	.	PUNCT
ejpam-5466	50	1	h.	h.	PROPN
ejpam-5466	50	2	qawaqneh	qawaqneh	PROPN
ejpam-5466	50	3	et	et	PROPN
ejpam-5466	50	4	al	al	PROPN
ejpam-5466	50	5	.	.	PUNCT
ejpam-5466	50	6	/	/	SYM
ejpam-5466	50	7	eur	eur	PROPN
ejpam-5466	50	8	.	.	PUNCT
ejpam-5466	51	1	j.	j.	PROPN
ejpam-5466	51	2	pure	pure	PROPN
ejpam-5466	51	3	appl	appl	PROPN
ejpam-5466	51	4	.	.	PROPN
ejpam-5466	51	5	math	math	PROPN
ejpam-5466	51	6	,	,	PUNCT
ejpam-5466	51	7	17	17	NUM
ejpam-5466	51	8	(	(	PUNCT
ejpam-5466	51	9	4	4	NUM
ejpam-5466	51	10	)	)	PUNCT
ejpam-5466	51	11	(	(	PUNCT
ejpam-5466	51	12	2024	2024	NUM
ejpam-5466	51	13	)	)	PUNCT
ejpam-5466	51	14	,	,	PUNCT
ejpam-5466	51	15	3093	3093	NUM
ejpam-5466	51	16	-	-	SYM
ejpam-5466	51	17	3108	3108	NUM
ejpam-5466	51	18	3095	3095	NUM
ejpam-5466	51	19	definition	definition	NOUN
ejpam-5466	51	20	2	2	NUM
ejpam-5466	51	21	.	.	PUNCT
ejpam-5466	52	1	[	[	X
ejpam-5466	52	2	26	26	NUM
ejpam-5466	52	3	]	]	PUNCT
ejpam-5466	52	4	consider	consider	VERB
ejpam-5466	52	5	a	a	DET
ejpam-5466	52	6	non	non	ADJ
ejpam-5466	52	7	-	-	ADJ
ejpam-5466	52	8	empty	empty	ADJ
ejpam-5466	52	9	set	set	NOUN
ejpam-5466	52	10	x	x	PUNCT
ejpam-5466	52	11	and	and	CCONJ
ejpam-5466	52	12	two	two	NUM
ejpam-5466	52	13	mappings	mapping	NOUN
ejpam-5466	52	14	t	t	NOUN
ejpam-5466	52	15	:	:	PUNCT
ejpam-5466	52	16	x	x	X
ejpam-5466	52	17	→	→	SYM
ejpam-5466	52	18	x	x	X
ejpam-5466	52	19	and	and	CCONJ
ejpam-5466	52	20	α	α	NOUN
ejpam-5466	52	21	:	:	PUNCT
ejpam-5466	52	22	x	x	PROPN
ejpam-5466	52	23	×x	×x	X
ejpam-5466	52	24	→	→	PUNCT
ejpam-5466	52	25	[	[	X
ejpam-5466	52	26	0,+∞	0,+∞	NUM
ejpam-5466	52	27	)	)	PUNCT
ejpam-5466	52	28	.	.	PUNCT
ejpam-5466	53	1	for	for	ADP
ejpam-5466	53	2	a	a	DET
ejpam-5466	53	3	given	give	VERB
ejpam-5466	53	4	real	real	ADJ
ejpam-5466	53	5	number	number	NOUN
ejpam-5466	53	6	s	s	PART
ejpam-5466	53	7	≥	≥	NOUN
ejpam-5466	53	8	1	1	NUM
ejpam-5466	53	9	,	,	PUNCT
ejpam-5466	53	10	t	t	PROPN
ejpam-5466	53	11	is	be	AUX
ejpam-5466	53	12	weak	weak	ADJ
ejpam-5466	53	13	α	α	PRON
ejpam-5466	53	14	-	-	ADJ
ejpam-5466	53	15	admissible	admissible	ADJ
ejpam-5466	53	16	of	of	ADP
ejpam-5466	53	17	type	type	NOUN
ejpam-5466	53	18	s	s	X
ejpam-5466	53	19	if	if	SCONJ
ejpam-5466	53	20	for	for	ADP
ejpam-5466	53	21	ν	ν	NOUN
ejpam-5466	53	22	∈	∈	PROPN
ejpam-5466	53	23	x	x	X
ejpam-5466	53	24	and	and	CCONJ
ejpam-5466	53	25	α(ν	α(ν	PROPN
ejpam-5466	53	26	,	,	PUNCT
ejpam-5466	53	27	t	t	NOUN
ejpam-5466	53	28	ν	ν	PROPN
ejpam-5466	53	29	)	)	PUNCT
ejpam-5466	53	30	≥	≥	NUM
ejpam-5466	53	31	s	s	X
ejpam-5466	53	32	,	,	PUNCT
ejpam-5466	53	33	we	we	PRON
ejpam-5466	53	34	have	have	VERB
ejpam-5466	53	35	α(t	α(t	PROPN
ejpam-5466	53	36	ν	ν	PROPN
ejpam-5466	53	37	,	,	PUNCT
ejpam-5466	53	38	t	t	PROPN
ejpam-5466	53	39	t	t	PROPN
ejpam-5466	53	40	ν	ν	PROPN
ejpam-5466	53	41	)	)	PUNCT
ejpam-5466	53	42	≥	≥	PROPN
ejpam-5466	53	43	s.	s.	PROPN
ejpam-5466	53	44	definition	definition	NOUN
ejpam-5466	53	45	3	3	NUM
ejpam-5466	53	46	.	.	PUNCT
ejpam-5466	54	1	[	[	X
ejpam-5466	54	2	14	14	NUM
ejpam-5466	54	3	]	]	X
ejpam-5466	54	4	let	let	AUX
ejpam-5466	54	5	(	(	PUNCT
ejpam-5466	54	6	x	x	NOUN
ejpam-5466	54	7	,	,	PUNCT
ejpam-5466	54	8	d	d	X
ejpam-5466	54	9	,	,	PUNCT
ejpam-5466	54	10	s	s	PART
ejpam-5466	54	11	)	)	PUNCT
ejpam-5466	54	12	be	be	AUX
ejpam-5466	54	13	a	a	DET
ejpam-5466	54	14	b	b	NOUN
ejpam-5466	54	15	-	-	PUNCT
ejpam-5466	54	16	metric	metric	ADJ
ejpam-5466	54	17	space	space	NOUN
ejpam-5466	54	18	.	.	PUNCT
ejpam-5466	55	1	for	for	ADP
ejpam-5466	55	2	a	a	DET
ejpam-5466	55	3	given	give	VERB
ejpam-5466	55	4	function	function	NOUN
ejpam-5466	55	5	α	α	NOUN
ejpam-5466	55	6	:	:	PUNCT
ejpam-5466	55	7	x	x	PROPN
ejpam-5466	55	8	×x	×x	X
ejpam-5466	55	9	→	→	PUNCT
ejpam-5466	55	10	[	[	X
ejpam-5466	55	11	0,+∞	0,+∞	NUM
ejpam-5466	55	12	)	)	PUNCT
ejpam-5466	55	13	,	,	PUNCT
ejpam-5466	55	14	a	a	DET
ejpam-5466	55	15	multivalued	multivalue	VERB
ejpam-5466	55	16	mapping	mapping	NOUN
ejpam-5466	55	17	t	t	NOUN
ejpam-5466	55	18	:	:	PUNCT
ejpam-5466	55	19	x	x	X
ejpam-5466	55	20	→	→	SYM
ejpam-5466	55	21	cl(x	cl(x	X
ejpam-5466	55	22	)	)	PUNCT
ejpam-5466	55	23	is	be	AUX
ejpam-5466	55	24	(	(	PUNCT
ejpam-5466	55	25	1	1	NUM
ejpam-5466	55	26	)	)	PUNCT
ejpam-5466	55	27	αs	αs	ADJ
ejpam-5466	55	28	-	-	ADJ
ejpam-5466	55	29	admissible	admissible	ADJ
ejpam-5466	55	30	,	,	PUNCT
ejpam-5466	55	31	if	if	SCONJ
ejpam-5466	55	32	for	for	ADP
ejpam-5466	55	33	each	each	DET
ejpam-5466	55	34	ν	ν	NOUN
ejpam-5466	55	35	∈	∈	PROPN
ejpam-5466	55	36	x	x	X
ejpam-5466	55	37	and	and	CCONJ
ejpam-5466	55	38	µ	µ	PROPN
ejpam-5466	55	39	∈	∈	NOUN
ejpam-5466	55	40	t	t	NOUN
ejpam-5466	55	41	ν	ν	NOUN
ejpam-5466	55	42	with	with	ADP
ejpam-5466	55	43	α(ν	α(ν	PROPN
ejpam-5466	55	44	,	,	PUNCT
ejpam-5466	55	45	µ	µ	NOUN
ejpam-5466	55	46	)	)	PUNCT
ejpam-5466	55	47	≥	≥	NOUN
ejpam-5466	55	48	s2	s2	PROPN
ejpam-5466	55	49	,	,	PUNCT
ejpam-5466	55	50	we	we	PRON
ejpam-5466	55	51	have	have	VERB
ejpam-5466	55	52	α(µ	α(µ	ADV
ejpam-5466	55	53	,	,	PUNCT
ejpam-5466	55	54	η	η	PROPN
ejpam-5466	55	55	)	)	PUNCT
ejpam-5466	55	56	≥	≥	NOUN
ejpam-5466	55	57	s2	s2	NOUN
ejpam-5466	55	58	for	for	ADP
ejpam-5466	55	59	each	each	DET
ejpam-5466	55	60	η	η	PROPN
ejpam-5466	55	61	∈	∈	PROPN
ejpam-5466	55	62	t	t	PROPN
ejpam-5466	55	63	µ.	µ.	NOUN
ejpam-5466	55	64	(	(	PUNCT
ejpam-5466	55	65	2	2	NUM
ejpam-5466	55	66	)	)	PUNCT
ejpam-5466	55	67	α∗	α∗	NOUN
ejpam-5466	55	68	s	s	VERB
ejpam-5466	55	69	-admissible	-admissible	ADJ
ejpam-5466	55	70	,	,	PUNCT
ejpam-5466	55	71	if	if	SCONJ
ejpam-5466	55	72	for	for	ADP
ejpam-5466	55	73	ν	ν	NOUN
ejpam-5466	55	74	,	,	PUNCT
ejpam-5466	55	75	µ	µ	X
ejpam-5466	55	76	∈	∈	NOUN
ejpam-5466	55	77	x	x	PUNCT
ejpam-5466	55	78	with	with	ADP
ejpam-5466	55	79	α(ν	α(ν	PROPN
ejpam-5466	55	80	,	,	PUNCT
ejpam-5466	55	81	µ	µ	NOUN
ejpam-5466	55	82	)	)	PUNCT
ejpam-5466	55	83	≥	≥	NOUN
ejpam-5466	55	84	s2	s2	NOUN
ejpam-5466	55	85	we	we	PRON
ejpam-5466	55	86	have	have	VERB
ejpam-5466	55	87	α∗(t	α∗(t	NOUN
ejpam-5466	55	88	ν	ν	PROPN
ejpam-5466	55	89	,	,	PUNCT
ejpam-5466	55	90	t	t	PROPN
ejpam-5466	55	91	µ	µ	NUM
ejpam-5466	55	92	)	)	PUNCT
ejpam-5466	55	93	≥	≥	NUM
ejpam-5466	55	94	s2	s2	PROPN
ejpam-5466	55	95	,	,	PUNCT
ejpam-5466	55	96	where	where	SCONJ
ejpam-5466	55	97	α∗(t	α∗(t	PROPN
ejpam-5466	55	98	ν	ν	PROPN
ejpam-5466	55	99	,	,	PUNCT
ejpam-5466	55	100	t	t	PROPN
ejpam-5466	55	101	µ	µ	NUM
ejpam-5466	55	102	)	)	PUNCT
ejpam-5466	55	103	=	=	SYM
ejpam-5466	55	104	inf	inf	NOUN
ejpam-5466	55	105	{	{	PUNCT
ejpam-5466	55	106	α(a	α(a	PROPN
ejpam-5466	55	107	,	,	PUNCT
ejpam-5466	55	108	b	b	NOUN
ejpam-5466	55	109	)	)	PUNCT
ejpam-5466	55	110	:	:	PUNCT
ejpam-5466	55	111	a	a	DET
ejpam-5466	55	112	∈	∈	PROPN
ejpam-5466	55	113	t	t	NOUN
ejpam-5466	55	114	ν	ν	PROPN
ejpam-5466	55	115	,	,	PUNCT
ejpam-5466	55	116	b	b	PROPN
ejpam-5466	55	117	∈	∈	PROPN
ejpam-5466	55	118	t	t	PROPN
ejpam-5466	55	119	µ	µ	X
ejpam-5466	55	120	}	}	PUNCT
ejpam-5466	55	121	.	.	PUNCT
ejpam-5466	56	1	definition	definition	NOUN
ejpam-5466	56	2	4	4	NUM
ejpam-5466	56	3	.	.	PUNCT
ejpam-5466	57	1	[	[	X
ejpam-5466	57	2	9	9	NUM
ejpam-5466	57	3	,	,	PUNCT
ejpam-5466	57	4	18	18	NUM
ejpam-5466	57	5	]	]	PUNCT
ejpam-5466	57	6	let	let	VERB
ejpam-5466	57	7	(	(	PUNCT
ejpam-5466	57	8	x	x	NOUN
ejpam-5466	57	9	,	,	PUNCT
ejpam-5466	57	10	d	d	NOUN
ejpam-5466	57	11	)	)	PUNCT
ejpam-5466	57	12	be	be	AUX
ejpam-5466	57	13	a	a	DET
ejpam-5466	57	14	metric	metric	ADJ
ejpam-5466	57	15	space	space	NOUN
ejpam-5466	57	16	,	,	PUNCT
ejpam-5466	57	17	and	and	CCONJ
ejpam-5466	57	18	t	t	X
ejpam-5466	57	19	:	:	PUNCT
ejpam-5466	58	1	x	x	X
ejpam-5466	58	2	→	→	SYM
ejpam-5466	58	3	cl(x	cl(x	X
ejpam-5466	58	4	)	)	PUNCT
ejpam-5466	58	5	and	and	CCONJ
ejpam-5466	58	6	α	α	NOUN
ejpam-5466	58	7	:	:	PUNCT
ejpam-5466	59	1	x×x	x×x	PROPN
ejpam-5466	59	2	→	→	PUNCT
ejpam-5466	59	3	[	[	X
ejpam-5466	59	4	0,+∞	0,+∞	NUM
ejpam-5466	59	5	)	)	PUNCT
ejpam-5466	59	6	be	be	AUX
ejpam-5466	59	7	given	give	VERB
ejpam-5466	59	8	maps	map	NOUN
ejpam-5466	59	9	.	.	PUNCT
ejpam-5466	60	1	then	then	ADV
ejpam-5466	60	2	t	t	PROPN
ejpam-5466	60	3	is	be	AUX
ejpam-5466	60	4	called	call	VERB
ejpam-5466	60	5	an	an	DET
ejpam-5466	60	6	αs	αs	ADJ
ejpam-5466	60	7	-	-	PUNCT
ejpam-5466	60	8	lower	low	ADJ
ejpam-5466	60	9	semi	semi	ADJ
ejpam-5466	60	10	-	-	ADJ
ejpam-5466	60	11	continuous	continuous	ADJ
ejpam-5466	60	12	if	if	SCONJ
ejpam-5466	60	13	for	for	SCONJ
ejpam-5466	60	14	ν	ν	NOUN
ejpam-5466	60	15	∈	∈	PROPN
ejpam-5466	60	16	x	x	X
ejpam-5466	60	17	and	and	CCONJ
ejpam-5466	60	18	a	a	DET
ejpam-5466	60	19	sequence	sequence	NOUN
ejpam-5466	60	20	{	{	PUNCT
ejpam-5466	60	21	νn	νn	VERB
ejpam-5466	60	22	}	}	PUNCT
ejpam-5466	60	23	in	in	ADP
ejpam-5466	60	24	x	x	PUNCT
ejpam-5466	60	25	with	with	ADP
ejpam-5466	60	26	limn→∞	limn→∞	PROPN
ejpam-5466	60	27	d(νn	d(νn	NOUN
ejpam-5466	60	28	,	,	PUNCT
ejpam-5466	60	29	ν	ν	NOUN
ejpam-5466	60	30	)	)	PUNCT
ejpam-5466	60	31	=	=	SYM
ejpam-5466	60	32	0	0	NUM
ejpam-5466	60	33	and	and	CCONJ
ejpam-5466	60	34	α(νn	α(νn	NUM
ejpam-5466	60	35	,	,	PUNCT
ejpam-5466	60	36	νn+1	νn+1	NUM
ejpam-5466	60	37	)	)	PUNCT
ejpam-5466	60	38	≥	≥	NOUN
ejpam-5466	60	39	s2	s2	VERB
ejpam-5466	60	40	for	for	ADP
ejpam-5466	60	41	all	all	PRON
ejpam-5466	60	42	n	n	PRON
ejpam-5466	60	43	∈	∈	PROPN
ejpam-5466	60	44	n	n	CCONJ
ejpam-5466	60	45	,	,	PUNCT
ejpam-5466	60	46	implies	imply	VERB
ejpam-5466	60	47	lim	lim	PROPN
ejpam-5466	60	48	inf	inf	PROPN
ejpam-5466	60	49	n→∞	n→∞	X
ejpam-5466	60	50	d(νn	d(νn	NOUN
ejpam-5466	60	51	,	,	PUNCT
ejpam-5466	60	52	t	t	NOUN
ejpam-5466	60	53	νn	νn	NOUN
ejpam-5466	60	54	)	)	PUNCT
ejpam-5466	60	55	≥	≥	NOUN
ejpam-5466	60	56	d(ν	d(ν	PROPN
ejpam-5466	60	57	,	,	PUNCT
ejpam-5466	60	58	t	t	NOUN
ejpam-5466	60	59	ν	ν	PROPN
ejpam-5466	60	60	)	)	PUNCT
ejpam-5466	60	61	.	.	PUNCT
ejpam-5466	61	1	definition	definition	NOUN
ejpam-5466	61	2	5	5	NUM
ejpam-5466	61	3	.	.	PUNCT
ejpam-5466	62	1	[	[	X
ejpam-5466	62	2	10	10	NUM
ejpam-5466	62	3	]	]	PUNCT
ejpam-5466	62	4	let	let	VERB
ejpam-5466	62	5	θs	θs	PRON
ejpam-5466	62	6	be	be	AUX
ejpam-5466	62	7	the	the	DET
ejpam-5466	62	8	set	set	NOUN
ejpam-5466	62	9	of	of	ADP
ejpam-5466	62	10	all	all	DET
ejpam-5466	62	11	functions	function	NOUN
ejpam-5466	62	12	ϑ	ϑ	X
ejpam-5466	62	13	:	:	PUNCT
ejpam-5466	62	14	(	(	PUNCT
ejpam-5466	62	15	0,+∞	0,+∞	NUM
ejpam-5466	62	16	)	)	PUNCT
ejpam-5466	62	17	→	→	SYM
ejpam-5466	62	18	(	(	PUNCT
ejpam-5466	62	19	1,+∞	1,+∞	NUM
ejpam-5466	62	20	)	)	PUNCT
ejpam-5466	62	21	such	such	ADJ
ejpam-5466	62	22	that	that	SCONJ
ejpam-5466	62	23	(	(	PUNCT
ejpam-5466	62	24	ϑ1	ϑ1	NOUN
ejpam-5466	62	25	)	)	PUNCT
ejpam-5466	62	26	ϑ	ϑ	PROPN
ejpam-5466	62	27	is	be	AUX
ejpam-5466	62	28	a	a	DET
ejpam-5466	62	29	strictly	strictly	ADV
ejpam-5466	62	30	increasing	increase	VERB
ejpam-5466	62	31	function	function	NOUN
ejpam-5466	62	32	;	;	PUNCT
ejpam-5466	62	33	(	(	PUNCT
ejpam-5466	62	34	ϑ2	ϑ2	PROPN
ejpam-5466	62	35	)	)	PUNCT
ejpam-5466	62	36	for	for	ADP
ejpam-5466	62	37	each	each	DET
ejpam-5466	62	38	sequence	sequence	NOUN
ejpam-5466	62	39	{	{	PUNCT
ejpam-5466	62	40	ωn	ωn	NOUN
ejpam-5466	62	41	}	}	PUNCT
ejpam-5466	62	42	of	of	ADP
ejpam-5466	62	43	positive	positive	ADJ
ejpam-5466	62	44	real	real	ADJ
ejpam-5466	62	45	numbers	number	NOUN
ejpam-5466	62	46	limn→∞	limn→∞	VERB
ejpam-5466	62	47	ϑ(ωn	ϑ(ωn	NOUN
ejpam-5466	62	48	)	)	PUNCT
ejpam-5466	62	49	=	=	SYM
ejpam-5466	62	50	1	1	NUM
ejpam-5466	62	51	iff	iff	NOUN
ejpam-5466	62	52	limn→∞	limn→∞	PROPN
ejpam-5466	62	53	ωn	ωn	ADP
ejpam-5466	62	54	=	=	SYM
ejpam-5466	62	55	0	0	NUM
ejpam-5466	62	56	;	;	PUNCT
ejpam-5466	62	57	(	(	PUNCT
ejpam-5466	62	58	ϑ3	ϑ3	NOUN
ejpam-5466	62	59	)	)	PUNCT
ejpam-5466	62	60	there	there	PRON
ejpam-5466	62	61	exist	exist	VERB
ejpam-5466	62	62	ρ	ρ	PROPN
ejpam-5466	62	63	∈	∈	PROPN
ejpam-5466	62	64	(	(	PUNCT
ejpam-5466	62	65	0	0	NUM
ejpam-5466	62	66	,	,	PUNCT
ejpam-5466	62	67	1	1	NUM
ejpam-5466	62	68	)	)	PUNCT
ejpam-5466	62	69	and	and	CCONJ
ejpam-5466	62	70	χ	χ	PRON
ejpam-5466	62	71	∈	∈	PROPN
ejpam-5466	62	72	(	(	PUNCT
ejpam-5466	62	73	0,+∞	0,+∞	NUM
ejpam-5466	62	74	]	]	X
ejpam-5466	62	75	such	such	ADJ
ejpam-5466	62	76	that	that	DET
ejpam-5466	62	77	limω→0	limω→0	NOUN
ejpam-5466	62	78	+	+	CCONJ
ejpam-5466	62	79	ϑ(ω)−1	ϑ(ω)−1	NOUN
ejpam-5466	62	80	ωρ	ωρ	NOUN
ejpam-5466	62	81	=	=	SYM
ejpam-5466	62	82	χ	χ	NOUN
ejpam-5466	62	83	;	;	PUNCT
ejpam-5466	62	84	(	(	PUNCT
ejpam-5466	62	85	ϑ4	ϑ4	NOUN
ejpam-5466	62	86	)	)	PUNCT
ejpam-5466	62	87	for	for	ADP
ejpam-5466	62	88	each	each	DET
ejpam-5466	62	89	sequence	sequence	NOUN
ejpam-5466	62	90	{	{	PUNCT
ejpam-5466	62	91	ωn	ωn	VERB
ejpam-5466	62	92	}	}	PUNCT
ejpam-5466	62	93	in	in	ADP
ejpam-5466	62	94	r+	r+	NOUN
ejpam-5466	62	95	such	such	ADJ
ejpam-5466	62	96	that	that	PRON
ejpam-5466	62	97	ϑ(sωn	ϑ(sωn	NOUN
ejpam-5466	62	98	)	)	PUNCT
ejpam-5466	62	99	≤	≤	NOUN
ejpam-5466	62	100	[	[	PUNCT
ejpam-5466	62	101	ϑ(ωn−1	ϑ(ωn−1	PROPN
ejpam-5466	62	102	)	)	PUNCT
ejpam-5466	62	103	]	]	PUNCT
ejpam-5466	63	1	ρ	ρ	X
ejpam-5466	63	2	,	,	PUNCT
ejpam-5466	63	3	where	where	SCONJ
ejpam-5466	63	4	ρ	ρ	PROPN
ejpam-5466	63	5	∈	∈	PROPN
ejpam-5466	63	6	(	(	PUNCT
ejpam-5466	63	7	0	0	NUM
ejpam-5466	63	8	,	,	PUNCT
ejpam-5466	63	9	1	1	NUM
ejpam-5466	63	10	)	)	PUNCT
ejpam-5466	63	11	,	,	PUNCT
ejpam-5466	63	12	then	then	ADV
ejpam-5466	63	13	ϑ(snωn	ϑ(snωn	NOUN
ejpam-5466	63	14	)	)	PUNCT
ejpam-5466	63	15	≤	≤	NOUN
ejpam-5466	63	16	[	[	PUNCT
ejpam-5466	63	17	ϑ(sn−1ωn	ϑ(sn−1ωn	NOUN
ejpam-5466	63	18	)	)	PUNCT
ejpam-5466	63	19	]	]	PUNCT
ejpam-5466	63	20	ρ	ρ	X
ejpam-5466	63	21	.	.	PUNCT
ejpam-5466	63	22	example	example	NOUN
ejpam-5466	64	1	1	1	NUM
ejpam-5466	64	2	.	.	PUNCT
ejpam-5466	65	1	the	the	DET
ejpam-5466	65	2	following	follow	VERB
ejpam-5466	65	3	functions	function	NOUN
ejpam-5466	65	4	ϑi	ϑi	PRON
ejpam-5466	65	5	:	:	PUNCT
ejpam-5466	65	6	(	(	PUNCT
ejpam-5466	65	7	0,+∞	0,+∞	NUM
ejpam-5466	65	8	)	)	PUNCT
ejpam-5466	65	9	→	→	SYM
ejpam-5466	65	10	(	(	PUNCT
ejpam-5466	65	11	1,+∞	1,+∞	NUM
ejpam-5466	65	12	)	)	PUNCT
ejpam-5466	65	13	for	for	ADP
ejpam-5466	65	14	i	i	PROPN
ejpam-5466	65	15	∈	∈	PROPN
ejpam-5466	65	16	{	{	PUNCT
ejpam-5466	65	17	1	1	NUM
ejpam-5466	65	18	,	,	PUNCT
ejpam-5466	65	19	2	2	NUM
ejpam-5466	65	20	,	,	PUNCT
ejpam-5466	65	21	3	3	NUM
ejpam-5466	65	22	,	,	PUNCT
ejpam-5466	65	23	4	4	NUM
ejpam-5466	65	24	}	}	PUNCT
ejpam-5466	65	25	,	,	PUNCT
ejpam-5466	65	26	are	be	AUX
ejpam-5466	65	27	the	the	DET
ejpam-5466	65	28	elements	element	NOUN
ejpam-5466	65	29	of	of	ADP
ejpam-5466	65	30	θs	θs	PROPN
ejpam-5466	65	31	.	.	PUNCT
ejpam-5466	66	1	(	(	PUNCT
ejpam-5466	66	2	i	i	NOUN
ejpam-5466	66	3	)	)	PUNCT
ejpam-5466	66	4	ϑ1(ω	ϑ1(ω	PROPN
ejpam-5466	66	5	)	)	PUNCT
ejpam-5466	66	6	=	=	PUNCT
ejpam-5466	66	7	eω	eω	PROPN
ejpam-5466	66	8	;	;	PUNCT
ejpam-5466	66	9	(	(	PUNCT
ejpam-5466	66	10	ii	ii	NOUN
ejpam-5466	66	11	)	)	PUNCT
ejpam-5466	66	12	ϑ2(ω	ϑ2(ω	NOUN
ejpam-5466	66	13	)	)	PUNCT
ejpam-5466	66	14	=	=	SYM
ejpam-5466	66	15	eωe	eωe	PROPN
ejpam-5466	66	16	ω	ω	PROPN
ejpam-5466	66	17	;	;	PUNCT
ejpam-5466	66	18	(	(	PUNCT
ejpam-5466	66	19	iii	iii	X
ejpam-5466	66	20	)	)	PUNCT
ejpam-5466	66	21	ϑ3(ω	ϑ3(ω	NOUN
ejpam-5466	66	22	)	)	PUNCT
ejpam-5466	66	23	=	=	SYM
ejpam-5466	66	24	e	e	NOUN
ejpam-5466	66	25	√	√	NUM
ejpam-5466	66	26	ω	ω	NUM
ejpam-5466	66	27	;	;	PUNCT
ejpam-5466	66	28	(	(	PUNCT
ejpam-5466	66	29	iv	iv	X
ejpam-5466	66	30	)	)	PUNCT
ejpam-5466	66	31	ϑ4(ω	ϑ4(ω	PROPN
ejpam-5466	66	32	)	)	PUNCT
ejpam-5466	66	33	=	=	PUNCT
ejpam-5466	67	1	e	e	X
ejpam-5466	67	2	√	√	ADJ
ejpam-5466	67	3	ωeω	ωeω	PRON
ejpam-5466	67	4	.	.	PUNCT
ejpam-5466	68	1	2	2	X
ejpam-5466	68	2	.	.	X
ejpam-5466	68	3	main	main	ADJ
ejpam-5466	68	4	results	result	NOUN
ejpam-5466	68	5	we	we	PRON
ejpam-5466	68	6	begin	begin	VERB
ejpam-5466	68	7	this	this	DET
ejpam-5466	68	8	section	section	NOUN
ejpam-5466	68	9	with	with	ADP
ejpam-5466	68	10	the	the	DET
ejpam-5466	68	11	following	follow	VERB
ejpam-5466	68	12	definition	definition	NOUN
ejpam-5466	68	13	.	.	PUNCT
ejpam-5466	69	1	h.	h.	PROPN
ejpam-5466	69	2	qawaqneh	qawaqneh	PROPN
ejpam-5466	69	3	et	et	PROPN
ejpam-5466	69	4	al	al	PROPN
ejpam-5466	69	5	.	.	PUNCT
ejpam-5466	69	6	/	/	SYM
ejpam-5466	69	7	eur	eur	PROPN
ejpam-5466	69	8	.	.	PUNCT
ejpam-5466	70	1	j.	j.	PROPN
ejpam-5466	70	2	pure	pure	PROPN
ejpam-5466	70	3	appl	appl	PROPN
ejpam-5466	70	4	.	.	PROPN
ejpam-5466	70	5	math	math	PROPN
ejpam-5466	70	6	,	,	PUNCT
ejpam-5466	70	7	17	17	NUM
ejpam-5466	70	8	(	(	PUNCT
ejpam-5466	70	9	4	4	NUM
ejpam-5466	70	10	)	)	PUNCT
ejpam-5466	70	11	(	(	PUNCT
ejpam-5466	70	12	2024	2024	NUM
ejpam-5466	70	13	)	)	PUNCT
ejpam-5466	70	14	,	,	PUNCT
ejpam-5466	70	15	3093	3093	NUM
ejpam-5466	70	16	-	-	SYM
ejpam-5466	70	17	3108	3108	NUM
ejpam-5466	70	18	3096	3096	NUM
ejpam-5466	70	19	definition	definition	NOUN
ejpam-5466	70	20	6	6	NUM
ejpam-5466	70	21	.	.	PUNCT
ejpam-5466	71	1	let	let	VERB
ejpam-5466	71	2	(	(	PUNCT
ejpam-5466	71	3	x	x	NOUN
ejpam-5466	71	4	,	,	PUNCT
ejpam-5466	71	5	d	d	X
ejpam-5466	71	6	,	,	PUNCT
ejpam-5466	71	7	s	s	PART
ejpam-5466	71	8	)	)	PUNCT
ejpam-5466	71	9	be	be	AUX
ejpam-5466	71	10	a	a	DET
ejpam-5466	71	11	b	b	NOUN
ejpam-5466	71	12	-	-	PUNCT
ejpam-5466	71	13	metric	metric	ADJ
ejpam-5466	71	14	space	space	NOUN
ejpam-5466	71	15	and	and	CCONJ
ejpam-5466	71	16	α	α	NOUN
ejpam-5466	71	17	:	:	PUNCT
ejpam-5466	72	1	x×x	x×x	PROPN
ejpam-5466	72	2	→	→	PUNCT
ejpam-5466	72	3	[	[	X
ejpam-5466	72	4	0,+∞	0,+∞	NUM
ejpam-5466	72	5	)	)	PUNCT
ejpam-5466	72	6	be	be	AUX
ejpam-5466	72	7	given	give	VERB
ejpam-5466	72	8	.	.	PUNCT
ejpam-5466	73	1	a	a	DET
ejpam-5466	73	2	map	map	NOUN
ejpam-5466	73	3	t	t	NOUN
ejpam-5466	73	4	:	:	PUNCT
ejpam-5466	73	5	x	x	SYM
ejpam-5466	73	6	→	→	SYM
ejpam-5466	73	7	cl(x	cl(x	X
ejpam-5466	73	8	)	)	PUNCT
ejpam-5466	73	9	is	be	AUX
ejpam-5466	73	10	called	call	VERB
ejpam-5466	73	11	multivalued	multivalued	ADJ
ejpam-5466	73	12	almost	almost	ADV
ejpam-5466	73	13	(	(	PUNCT
ejpam-5466	73	14	αs	αs	INTJ
ejpam-5466	73	15	,	,	PUNCT
ejpam-5466	73	16	ϑ	ϑ	NOUN
ejpam-5466	73	17	,	,	PUNCT
ejpam-5466	73	18	κ)-contraction	κ)-contraction	NOUN
ejpam-5466	73	19	of	of	ADP
ejpam-5466	73	20	hardy	hardy	ADJ
ejpam-5466	73	21	-	-	PUNCT
ejpam-5466	73	22	rogers	rogers	NOUN
ejpam-5466	73	23	type	type	NOUN
ejpam-5466	73	24	if	if	SCONJ
ejpam-5466	73	25	there	there	PRON
ejpam-5466	73	26	exist	exist	VERB
ejpam-5466	73	27	ϑ	ϑ	PRON
ejpam-5466	73	28	∈	∈	PROPN
ejpam-5466	73	29	θs	θ	NOUN
ejpam-5466	73	30	,	,	PUNCT
ejpam-5466	73	31	l	l	PROPN
ejpam-5466	73	32	≥	≥	NOUN
ejpam-5466	73	33	0	0	NUM
ejpam-5466	73	34	and	and	CCONJ
ejpam-5466	73	35	κ	κ	X
ejpam-5466	73	36	:	:	PUNCT
ejpam-5466	73	37	(	(	PUNCT
ejpam-5466	73	38	0,+∞	0,+∞	NUM
ejpam-5466	73	39	)	)	PUNCT
ejpam-5466	73	40	→	→	PUNCT
ejpam-5466	74	1	[	[	X
ejpam-5466	74	2	0	0	NUM
ejpam-5466	74	3	,	,	PUNCT
ejpam-5466	74	4	1	1	NUM
ejpam-5466	74	5	)	)	PUNCT
ejpam-5466	74	6	satisfies	satisfie	NOUN
ejpam-5466	74	7	limω→z+	limω→z+	DET
ejpam-5466	74	8	supκ(ω	supκ(ω	NOUN
ejpam-5466	74	9	)	)	PUNCT
ejpam-5466	74	10	<	<	X
ejpam-5466	74	11	1	1	NUM
ejpam-5466	74	12	for	for	ADP
ejpam-5466	74	13	all	all	DET
ejpam-5466	74	14	z	z	NOUN
ejpam-5466	74	15	∈	∈	PROPN
ejpam-5466	74	16	(	(	PUNCT
ejpam-5466	74	17	0,+∞	0,+∞	NUM
ejpam-5466	74	18	)	)	PUNCT
ejpam-5466	74	19	and	and	CCONJ
ejpam-5466	74	20	non	non	ADJ
ejpam-5466	74	21	-	-	ADJ
ejpam-5466	74	22	negative	negative	ADJ
ejpam-5466	74	23	real	real	ADJ
ejpam-5466	74	24	numbers	number	NOUN
ejpam-5466	74	25	a1	a1	PROPN
ejpam-5466	74	26	,	,	PUNCT
ejpam-5466	74	27	a2	a2	PROPN
ejpam-5466	74	28	,	,	PUNCT
ejpam-5466	74	29	a3	a3	NOUN
ejpam-5466	74	30	,	,	PUNCT
ejpam-5466	74	31	a4	a4	PROPN
ejpam-5466	74	32	,	,	PUNCT
ejpam-5466	74	33	a5	a5	VERB
ejpam-5466	74	34	with	with	ADP
ejpam-5466	74	35	a1	a1	NOUN
ejpam-5466	74	36	+	+	CCONJ
ejpam-5466	74	37	a2	a2	PROPN
ejpam-5466	74	38	+	+	CCONJ
ejpam-5466	74	39	a3	a3	NOUN
ejpam-5466	74	40	+	+	CCONJ
ejpam-5466	74	41	2sa4	2sa4	NUM
ejpam-5466	74	42	=	=	SYM
ejpam-5466	74	43	1	1	NUM
ejpam-5466	74	44	,	,	PUNCT
ejpam-5466	74	45	and	and	CCONJ
ejpam-5466	74	46	a3	a3	VERB
ejpam-5466	74	47	̸=	̸=	PROPN
ejpam-5466	74	48	1	1	NUM
ejpam-5466	74	49	such	such	ADJ
ejpam-5466	74	50	that	that	SCONJ
ejpam-5466	74	51	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	74	52	ν	ν	PROPN
ejpam-5466	74	53	,	,	PUNCT
ejpam-5466	74	54	t	t	PROPN
ejpam-5466	74	55	µ	µ	NUM
ejpam-5466	74	56	)	)	PUNCT
ejpam-5466	74	57	)	)	PUNCT
ejpam-5466	74	58	≤	≤	NOUN
ejpam-5466	74	59	[	[	PUNCT
ejpam-5466	74	60	ϑ(ns(ν	ϑ(ns(ν	PROPN
ejpam-5466	74	61	,	,	PUNCT
ejpam-5466	74	62	µ	µ	NOUN
ejpam-5466	74	63	)	)	PUNCT
ejpam-5466	74	64	)	)	PUNCT
ejpam-5466	74	65	]	]	SYM
ejpam-5466	74	66	κ(d(ν,µ	κ(d(ν,µ	X
ejpam-5466	74	67	)	)	PUNCT
ejpam-5466	75	1	+	+	CCONJ
ejpam-5466	75	2	lmin{d(ν	lmin{d(ν	PROPN
ejpam-5466	75	3	,	,	PUNCT
ejpam-5466	75	4	t	t	PROPN
ejpam-5466	75	5	µ	µ	NUM
ejpam-5466	75	6	)	)	PUNCT
ejpam-5466	75	7	,	,	PUNCT
ejpam-5466	75	8	d(µ	d(µ	PROPN
ejpam-5466	75	9	,	,	PUNCT
ejpam-5466	75	10	t	t	NOUN
ejpam-5466	75	11	ν	ν	PROPN
ejpam-5466	75	12	)	)	PUNCT
ejpam-5466	75	13	}	}	PUNCT
ejpam-5466	75	14	,	,	PUNCT
ejpam-5466	75	15	(	(	PUNCT
ejpam-5466	75	16	2.1	2.1	NUM
ejpam-5466	75	17	)	)	PUNCT
ejpam-5466	75	18	for	for	ADP
ejpam-5466	75	19	all	all	DET
ejpam-5466	75	20	ν	ν	NOUN
ejpam-5466	75	21	,	,	PUNCT
ejpam-5466	75	22	µ	µ	X
ejpam-5466	75	23	∈	∈	NOUN
ejpam-5466	75	24	x	x	PUNCT
ejpam-5466	75	25	with	with	ADP
ejpam-5466	75	26	α(ν	α(ν	PROPN
ejpam-5466	75	27	,	,	PUNCT
ejpam-5466	75	28	µ	µ	NOUN
ejpam-5466	75	29	)	)	PUNCT
ejpam-5466	75	30	≥	≥	NOUN
ejpam-5466	75	31	s2	s2	NOUN
ejpam-5466	75	32	and	and	CCONJ
ejpam-5466	75	33	h(t	h(t	PROPN
ejpam-5466	75	34	ν	ν	PROPN
ejpam-5466	75	35	,	,	PUNCT
ejpam-5466	75	36	t	t	PROPN
ejpam-5466	75	37	µ	µ	NUM
ejpam-5466	75	38	)	)	PUNCT
ejpam-5466	75	39	>	>	X
ejpam-5466	75	40	0	0	NUM
ejpam-5466	75	41	where	where	SCONJ
ejpam-5466	75	42	ns(ν	ns(ν	NUM
ejpam-5466	75	43	,	,	PUNCT
ejpam-5466	75	44	µ	µ	NOUN
ejpam-5466	75	45	)	)	PUNCT
ejpam-5466	75	46	=	=	SYM
ejpam-5466	75	47	a1d(ν	a1d(ν	PROPN
ejpam-5466	75	48	,	,	PUNCT
ejpam-5466	75	49	µ	µ	NOUN
ejpam-5466	75	50	)	)	PUNCT
ejpam-5466	75	51	+	+	SYM
ejpam-5466	75	52	a2d(ν	a2d(ν	PROPN
ejpam-5466	75	53	,	,	PUNCT
ejpam-5466	75	54	t	t	NOUN
ejpam-5466	75	55	ν	ν	PROPN
ejpam-5466	75	56	)	)	PUNCT
ejpam-5466	76	1	+	+	CCONJ
ejpam-5466	76	2	a3d(µ	a3d(µ	PROPN
ejpam-5466	76	3	,	,	PUNCT
ejpam-5466	76	4	t	t	PROPN
ejpam-5466	76	5	µ	µ	NUM
ejpam-5466	76	6	)	)	PUNCT
ejpam-5466	76	7	+	+	CCONJ
ejpam-5466	77	1	a4d(ν	a4d(ν	PROPN
ejpam-5466	77	2	,	,	PUNCT
ejpam-5466	77	3	t	t	PROPN
ejpam-5466	77	4	µ	µ	NUM
ejpam-5466	77	5	)	)	PUNCT
ejpam-5466	77	6	+	+	CCONJ
ejpam-5466	77	7	a5d(µ	a5d(µ	PROPN
ejpam-5466	77	8	,	,	PUNCT
ejpam-5466	77	9	t	t	NOUN
ejpam-5466	77	10	ν	ν	NOUN
ejpam-5466	77	11	)	)	PUNCT
ejpam-5466	77	12	.	.	PUNCT
ejpam-5466	78	1	if	if	SCONJ
ejpam-5466	78	2	α(ν	α(ν	PROPN
ejpam-5466	78	3	,	,	PUNCT
ejpam-5466	78	4	µ	µ	NOUN
ejpam-5466	78	5	)	)	PUNCT
ejpam-5466	78	6	=	=	SYM
ejpam-5466	78	7	s2	s2	PROPN
ejpam-5466	78	8	,	,	PUNCT
ejpam-5466	78	9	t	t	PROPN
ejpam-5466	78	10	is	be	AUX
ejpam-5466	78	11	said	say	VERB
ejpam-5466	78	12	to	to	PART
ejpam-5466	78	13	be	be	AUX
ejpam-5466	78	14	an	an	DET
ejpam-5466	78	15	almost	almost	ADV
ejpam-5466	78	16	(	(	PUNCT
ejpam-5466	78	17	ϑ	ϑ	X
ejpam-5466	78	18	,	,	PUNCT
ejpam-5466	78	19	κ)-contraction	κ)-contraction	NOUN
ejpam-5466	78	20	of	of	ADP
ejpam-5466	78	21	hardy	hardy	ADJ
ejpam-5466	78	22	-	-	PUNCT
ejpam-5466	78	23	rogers	rogers	NOUN
ejpam-5466	78	24	type	type	NOUN
ejpam-5466	78	25	.	.	PUNCT
ejpam-5466	79	1	theorem	theorem	NOUN
ejpam-5466	79	2	1	1	NUM
ejpam-5466	79	3	.	.	PUNCT
ejpam-5466	80	1	let	let	AUX
ejpam-5466	80	2	(	(	PUNCT
ejpam-5466	80	3	x	x	NOUN
ejpam-5466	80	4	,	,	PUNCT
ejpam-5466	80	5	d	d	X
ejpam-5466	80	6	,	,	PUNCT
ejpam-5466	80	7	s	s	PART
ejpam-5466	80	8	)	)	PUNCT
ejpam-5466	80	9	be	be	AUX
ejpam-5466	80	10	a	a	DET
ejpam-5466	80	11	complete	complete	ADJ
ejpam-5466	80	12	b	b	X
ejpam-5466	80	13	-	-	PUNCT
ejpam-5466	80	14	metric	metric	ADJ
ejpam-5466	80	15	space	space	NOUN
ejpam-5466	80	16	and	and	CCONJ
ejpam-5466	80	17	t	t	NOUN
ejpam-5466	80	18	:	:	PUNCT
ejpam-5466	80	19	x	x	X
ejpam-5466	80	20	→	→	X
ejpam-5466	80	21	cb(x	cb(x	NUM
ejpam-5466	80	22	)	)	PUNCT
ejpam-5466	80	23	be	be	AUX
ejpam-5466	80	24	a	a	DET
ejpam-5466	80	25	multivalued	multivalued	ADJ
ejpam-5466	80	26	almost	almost	ADV
ejpam-5466	80	27	(	(	PUNCT
ejpam-5466	80	28	αs	αs	INTJ
ejpam-5466	80	29	,	,	PUNCT
ejpam-5466	80	30	ϑ	ϑ	NOUN
ejpam-5466	80	31	,	,	PUNCT
ejpam-5466	80	32	κ)-contraction	κ)-contraction	NOUN
ejpam-5466	80	33	of	of	ADP
ejpam-5466	80	34	hardy	hardy	ADJ
ejpam-5466	80	35	-	-	PUNCT
ejpam-5466	80	36	rogers	rogers	NOUN
ejpam-5466	80	37	type	type	NOUN
ejpam-5466	80	38	.	.	PUNCT
ejpam-5466	81	1	assume	assume	VERB
ejpam-5466	81	2	that	that	SCONJ
ejpam-5466	81	3	the	the	DET
ejpam-5466	81	4	following	follow	VERB
ejpam-5466	81	5	conditions	condition	NOUN
ejpam-5466	81	6	are	be	AUX
ejpam-5466	81	7	satisfied	satisfied	ADJ
ejpam-5466	81	8	:	:	PUNCT
ejpam-5466	81	9	(	(	PUNCT
ejpam-5466	81	10	i	i	NOUN
ejpam-5466	81	11	)	)	PUNCT
ejpam-5466	81	12	t	t	PROPN
ejpam-5466	81	13	is	be	AUX
ejpam-5466	81	14	αs	αs	ADJ
ejpam-5466	81	15	-	-	ADJ
ejpam-5466	81	16	admissible	admissible	ADJ
ejpam-5466	81	17	;	;	PUNCT
ejpam-5466	81	18	(	(	PUNCT
ejpam-5466	81	19	ii	ii	NOUN
ejpam-5466	81	20	)	)	PUNCT
ejpam-5466	81	21	there	there	PRON
ejpam-5466	81	22	exist	exist	VERB
ejpam-5466	81	23	ν0	ν0	PROPN
ejpam-5466	81	24	∈	∈	PROPN
ejpam-5466	81	25	x	x	X
ejpam-5466	81	26	and	and	CCONJ
ejpam-5466	81	27	ν1	ν1	PROPN
ejpam-5466	81	28	∈	∈	PROPN
ejpam-5466	81	29	t	t	NOUN
ejpam-5466	81	30	ν0	ν0	PROPN
ejpam-5466	81	31	such	such	ADJ
ejpam-5466	81	32	that	that	DET
ejpam-5466	81	33	α(ν0	α(ν0	PROPN
ejpam-5466	81	34	,	,	PUNCT
ejpam-5466	81	35	ν1	ν1	PROPN
ejpam-5466	81	36	)	)	PUNCT
ejpam-5466	81	37	≥	≥	NOUN
ejpam-5466	81	38	s2	s2	PROPN
ejpam-5466	81	39	;	;	PUNCT
ejpam-5466	81	40	(	(	PUNCT
ejpam-5466	81	41	iii	iii	X
ejpam-5466	81	42	)	)	PUNCT
ejpam-5466	81	43	t	t	PROPN
ejpam-5466	81	44	is	be	AUX
ejpam-5466	81	45	αs	αs	ADJ
ejpam-5466	81	46	-	-	PUNCT
ejpam-5466	81	47	lower	low	ADJ
ejpam-5466	81	48	semi	semi	ADJ
ejpam-5466	81	49	-	-	ADJ
ejpam-5466	81	50	continuous	continuous	ADJ
ejpam-5466	81	51	,	,	PUNCT
ejpam-5466	81	52	or	or	CCONJ
ejpam-5466	81	53	x	x	NOUN
ejpam-5466	81	54	is	be	AUX
ejpam-5466	81	55	αs	αs	ADJ
ejpam-5466	81	56	-	-	ADJ
ejpam-5466	81	57	regular	regular	ADJ
ejpam-5466	81	58	,	,	PUNCT
ejpam-5466	81	59	that	that	ADV
ejpam-5466	81	60	is	is	ADV
ejpam-5466	81	61	,	,	PUNCT
ejpam-5466	81	62	for	for	SCONJ
ejpam-5466	81	63	every	every	DET
ejpam-5466	81	64	sequence	sequence	NOUN
ejpam-5466	81	65	{	{	PUNCT
ejpam-5466	81	66	νn	νn	VERB
ejpam-5466	81	67	}	}	PUNCT
ejpam-5466	81	68	in	in	ADP
ejpam-5466	81	69	x	x	X
ejpam-5466	81	70	such	such	ADJ
ejpam-5466	81	71	that	that	SCONJ
ejpam-5466	81	72	νn	νn	ADV
ejpam-5466	81	73	→	→	SYM
ejpam-5466	81	74	ν∗	ν∗	VERB
ejpam-5466	81	75	∈	∈	PROPN
ejpam-5466	81	76	x	x	X
ejpam-5466	81	77	and	and	CCONJ
ejpam-5466	81	78	α	α	PROPN
ejpam-5466	81	79	(	(	PUNCT
ejpam-5466	81	80	νn	νn	ADJ
ejpam-5466	81	81	,	,	PUNCT
ejpam-5466	81	82	νn+1	νn+1	NUM
ejpam-5466	81	83	)	)	PUNCT
ejpam-5466	81	84	≥	≥	NOUN
ejpam-5466	81	85	s2	s2	VERB
ejpam-5466	81	86	for	for	ADP
ejpam-5466	81	87	all	all	PRON
ejpam-5466	81	88	n	n	PRON
ejpam-5466	81	89	∈	∈	PROPN
ejpam-5466	81	90	n	n	CCONJ
ejpam-5466	81	91	,	,	PUNCT
ejpam-5466	81	92	then	then	ADV
ejpam-5466	81	93	α	α	X
ejpam-5466	81	94	(	(	PUNCT
ejpam-5466	81	95	νn	νn	PROPN
ejpam-5466	81	96	,	,	PUNCT
ejpam-5466	81	97	ν	ν	NOUN
ejpam-5466	81	98	∗	∗	NOUN
ejpam-5466	81	99	)	)	PUNCT
ejpam-5466	81	100	≥	≥	NUM
ejpam-5466	81	101	s2	s2	PROPN
ejpam-5466	81	102	,	,	PUNCT
ejpam-5466	81	103	for	for	ADP
ejpam-5466	81	104	all	all	DET
ejpam-5466	81	105	n	n	PRON
ejpam-5466	81	106	∈	∈	PROPN
ejpam-5466	81	107	n.	n.	NOUN
ejpam-5466	81	108	then	then	ADV
ejpam-5466	81	109	t	t	PROPN
ejpam-5466	81	110	has	have	VERB
ejpam-5466	81	111	a	a	DET
ejpam-5466	81	112	fixed	fix	VERB
ejpam-5466	81	113	point	point	NOUN
ejpam-5466	81	114	.	.	PUNCT
ejpam-5466	82	1	proof	proof	NOUN
ejpam-5466	82	2	.	.	PUNCT
ejpam-5466	83	1	from	from	ADP
ejpam-5466	83	2	the	the	DET
ejpam-5466	83	3	hypothesis	hypothesis	NOUN
ejpam-5466	83	4	(	(	PUNCT
ejpam-5466	83	5	2	2	NUM
ejpam-5466	83	6	)	)	PUNCT
ejpam-5466	83	7	,	,	PUNCT
ejpam-5466	83	8	there	there	PRON
ejpam-5466	83	9	exist	exist	VERB
ejpam-5466	83	10	ν0	ν0	PROPN
ejpam-5466	83	11	∈	∈	PROPN
ejpam-5466	83	12	x	x	X
ejpam-5466	83	13	and	and	CCONJ
ejpam-5466	83	14	ν1	ν1	PROPN
ejpam-5466	83	15	∈	∈	PROPN
ejpam-5466	83	16	t	t	NOUN
ejpam-5466	83	17	ν0	ν0	PROPN
ejpam-5466	83	18	such	such	ADJ
ejpam-5466	83	19	that	that	DET
ejpam-5466	83	20	α(ν0	α(ν0	PROPN
ejpam-5466	83	21	,	,	PUNCT
ejpam-5466	83	22	ν1	ν1	PROPN
ejpam-5466	83	23	)	)	PUNCT
ejpam-5466	83	24	≥	≥	NOUN
ejpam-5466	83	25	s2	s2	PROPN
ejpam-5466	83	26	.	.	PUNCT
ejpam-5466	84	1	if	if	SCONJ
ejpam-5466	84	2	ν0	ν0	PROPN
ejpam-5466	84	3	=	=	SYM
ejpam-5466	84	4	ν1	ν1	NOUN
ejpam-5466	84	5	or	or	CCONJ
ejpam-5466	84	6	ν1	ν1	NOUN
ejpam-5466	84	7	∈	∈	PROPN
ejpam-5466	84	8	t	t	PROPN
ejpam-5466	84	9	ν1	ν1	NOUN
ejpam-5466	84	10	,	,	PUNCT
ejpam-5466	84	11	then	then	ADV
ejpam-5466	84	12	ν1	ν1	NOUN
ejpam-5466	84	13	is	be	AUX
ejpam-5466	84	14	a	a	DET
ejpam-5466	84	15	fixed	fix	VERB
ejpam-5466	84	16	point	point	NOUN
ejpam-5466	84	17	of	of	ADP
ejpam-5466	84	18	t	t	PROPN
ejpam-5466	84	19	and	and	CCONJ
ejpam-5466	84	20	the	the	DET
ejpam-5466	84	21	proof	proof	NOUN
ejpam-5466	84	22	is	be	AUX
ejpam-5466	84	23	completed	complete	VERB
ejpam-5466	84	24	.	.	PUNCT
ejpam-5466	85	1	assume	assume	VERB
ejpam-5466	85	2	that	that	SCONJ
ejpam-5466	85	3	ν0	ν0	PROPN
ejpam-5466	85	4	̸=	̸=	PROPN
ejpam-5466	85	5	ν1	ν1	NOUN
ejpam-5466	85	6	and	and	CCONJ
ejpam-5466	85	7	ν1	ν1	NOUN
ejpam-5466	85	8	/∈	/∈	PUNCT
ejpam-5466	85	9	t	t	PROPN
ejpam-5466	85	10	ν1	ν1	NOUN
ejpam-5466	85	11	,	,	PUNCT
ejpam-5466	85	12	then	then	ADV
ejpam-5466	85	13	h(t	h(t	PROPN
ejpam-5466	85	14	ν0	ν0	PROPN
ejpam-5466	85	15	,	,	PUNCT
ejpam-5466	85	16	t	t	PROPN
ejpam-5466	85	17	ν1	ν1	PROPN
ejpam-5466	85	18	)	)	PUNCT
ejpam-5466	85	19	≥	≥	PROPN
ejpam-5466	85	20	d(ν1	d(ν1	PROPN
ejpam-5466	85	21	,	,	PUNCT
ejpam-5466	85	22	t	t	PROPN
ejpam-5466	85	23	ν1	ν1	PROPN
ejpam-5466	85	24	)	)	PUNCT
ejpam-5466	85	25	>	>	X
ejpam-5466	86	1	0	0	X
ejpam-5466	86	2	.	.	PUNCT
ejpam-5466	87	1	from	from	ADP
ejpam-5466	87	2	lemma	lemma	PROPN
ejpam-5466	87	3	2	2	NUM
ejpam-5466	87	4	,	,	PUNCT
ejpam-5466	87	5	there	there	PRON
ejpam-5466	87	6	exists	exist	VERB
ejpam-5466	87	7	ν2	ν2	PROPN
ejpam-5466	87	8	∈	∈	PROPN
ejpam-5466	87	9	t	t	NOUN
ejpam-5466	87	10	ν1	ν1	NOUN
ejpam-5466	87	11	such	such	ADJ
ejpam-5466	87	12	that	that	DET
ejpam-5466	87	13	d(ν1	d(ν1	NOUN
ejpam-5466	87	14	,	,	PUNCT
ejpam-5466	87	15	ν2	ν2	NOUN
ejpam-5466	87	16	)	)	PUNCT
ejpam-5466	87	17	≤	≤	NUM
ejpam-5466	87	18	sh(t	sh(t	PUNCT
ejpam-5466	87	19	ν0	ν0	PROPN
ejpam-5466	87	20	,	,	PUNCT
ejpam-5466	87	21	t	t	PROPN
ejpam-5466	87	22	ν1	ν1	PROPN
ejpam-5466	87	23	)	)	PUNCT
ejpam-5466	87	24	≤	≤	NUM
ejpam-5466	87	25	s2h(t	s2h(t	PROPN
ejpam-5466	87	26	ν0	ν0	PROPN
ejpam-5466	87	27	,	,	PUNCT
ejpam-5466	87	28	t	t	PROPN
ejpam-5466	87	29	ν1	ν1	PROPN
ejpam-5466	87	30	)	)	PUNCT
ejpam-5466	87	31	,	,	PUNCT
ejpam-5466	87	32	which	which	PRON
ejpam-5466	87	33	implies	imply	VERB
ejpam-5466	87	34	sd(ν1	sd(ν1	PROPN
ejpam-5466	87	35	,	,	PUNCT
ejpam-5466	87	36	ν2	ν2	NOUN
ejpam-5466	87	37	)	)	PUNCT
ejpam-5466	87	38	≤	≤	NUM
ejpam-5466	87	39	s3h(t	s3h(t	PROPN
ejpam-5466	87	40	ν0	ν0	PROPN
ejpam-5466	87	41	,	,	PUNCT
ejpam-5466	87	42	t	t	PROPN
ejpam-5466	87	43	ν1	ν1	PROPN
ejpam-5466	87	44	)	)	PUNCT
ejpam-5466	87	45	.	.	PUNCT
ejpam-5466	88	1	since	since	SCONJ
ejpam-5466	88	2	ϑ	ϑ	PROPN
ejpam-5466	88	3	is	be	AUX
ejpam-5466	88	4	strictly	strictly	ADV
ejpam-5466	88	5	increasing	increase	VERB
ejpam-5466	88	6	,	,	PUNCT
ejpam-5466	88	7	we	we	PRON
ejpam-5466	88	8	get	get	VERB
ejpam-5466	88	9	ϑ(sd(ν1	ϑ(sd(ν1	NOUN
ejpam-5466	88	10	,	,	PUNCT
ejpam-5466	88	11	ν2	ν2	NOUN
ejpam-5466	88	12	)	)	PUNCT
ejpam-5466	88	13	)	)	PUNCT
ejpam-5466	89	1	≤	≤	PROPN
ejpam-5466	89	2	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	89	3	ν0	ν0	PROPN
ejpam-5466	89	4	,	,	PUNCT
ejpam-5466	89	5	t	t	PROPN
ejpam-5466	89	6	ν1	ν1	PROPN
ejpam-5466	89	7	)	)	PUNCT
ejpam-5466	89	8	)	)	PUNCT
ejpam-5466	89	9	.	.	PUNCT
ejpam-5466	90	1	then	then	ADV
ejpam-5466	90	2	by	by	ADP
ejpam-5466	90	3	using	use	VERB
ejpam-5466	90	4	(	(	PUNCT
ejpam-5466	90	5	2.1	2.1	NUM
ejpam-5466	90	6	)	)	PUNCT
ejpam-5466	90	7	we	we	PRON
ejpam-5466	90	8	get	get	VERB
ejpam-5466	90	9	ϑ(sd(ν1	ϑ(sd(ν1	NOUN
ejpam-5466	90	10	,	,	PUNCT
ejpam-5466	90	11	ν2	ν2	NOUN
ejpam-5466	90	12	)	)	PUNCT
ejpam-5466	90	13	)	)	PUNCT
ejpam-5466	91	1	≤	≤	PROPN
ejpam-5466	91	2	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	91	3	ν0	ν0	PROPN
ejpam-5466	91	4	,	,	PUNCT
ejpam-5466	91	5	t	t	PROPN
ejpam-5466	91	6	ν1	ν1	PROPN
ejpam-5466	91	7	)	)	PUNCT
ejpam-5466	91	8	)	)	PUNCT
ejpam-5466	91	9	≤	≤	NOUN
ejpam-5466	91	10	[	[	PUNCT
ejpam-5466	91	11	ϑ(ns(ν0	ϑ(ns(ν0	NOUN
ejpam-5466	91	12	,	,	PUNCT
ejpam-5466	91	13	ν1	ν1	NOUN
ejpam-5466	91	14	)	)	PUNCT
ejpam-5466	91	15	)	)	PUNCT
ejpam-5466	92	1	]	]	PUNCT
ejpam-5466	92	2	κ(d(ν0,ν1	κ(d(ν0,ν1	PROPN
ejpam-5466	92	3	)	)	PUNCT
ejpam-5466	92	4	)	)	PUNCT
ejpam-5466	93	1	+	+	CCONJ
ejpam-5466	93	2	lmin{d(ν0	lmin{d(ν0	PROPN
ejpam-5466	93	3	,	,	PUNCT
ejpam-5466	93	4	t	t	PROPN
ejpam-5466	93	5	ν1	ν1	PROPN
ejpam-5466	93	6	)	)	PUNCT
ejpam-5466	93	7	,	,	PUNCT
ejpam-5466	93	8	d(ν1	d(ν1	NOUN
ejpam-5466	93	9	,	,	PUNCT
ejpam-5466	93	10	t	t	NOUN
ejpam-5466	93	11	ν0	ν0	PROPN
ejpam-5466	93	12	)	)	PUNCT
ejpam-5466	93	13	}	}	PUNCT
ejpam-5466	93	14	h.	h.	PROPN
ejpam-5466	93	15	qawaqneh	qawaqneh	PROPN
ejpam-5466	93	16	et	et	PROPN
ejpam-5466	93	17	al	al	PROPN
ejpam-5466	93	18	.	.	PUNCT
ejpam-5466	93	19	/	/	SYM
ejpam-5466	93	20	eur	eur	PROPN
ejpam-5466	93	21	.	.	PUNCT
ejpam-5466	94	1	j.	j.	PROPN
ejpam-5466	94	2	pure	pure	PROPN
ejpam-5466	94	3	appl	appl	PROPN
ejpam-5466	94	4	.	.	PROPN
ejpam-5466	94	5	math	math	PROPN
ejpam-5466	94	6	,	,	PUNCT
ejpam-5466	94	7	17	17	NUM
ejpam-5466	94	8	(	(	PUNCT
ejpam-5466	94	9	4	4	NUM
ejpam-5466	94	10	)	)	PUNCT
ejpam-5466	94	11	(	(	PUNCT
ejpam-5466	94	12	2024	2024	NUM
ejpam-5466	94	13	)	)	PUNCT
ejpam-5466	94	14	,	,	PUNCT
ejpam-5466	94	15	3093	3093	NUM
ejpam-5466	94	16	-	-	SYM
ejpam-5466	94	17	3108	3108	NUM
ejpam-5466	94	18	3097	3097	NUM
ejpam-5466	94	19	<	<	X
ejpam-5466	95	1	[	[	X
ejpam-5466	95	2	ϑ(ns(ν0	ϑ(ns(ν0	ADJ
ejpam-5466	95	3	,	,	PUNCT
ejpam-5466	95	4	ν1	ν1	NOUN
ejpam-5466	95	5	)	)	PUNCT
ejpam-5466	95	6	)	)	PUNCT
ejpam-5466	95	7	]	]	PUNCT
ejpam-5466	96	1	κ(d(ν0,ν1	κ(d(ν0,ν1	PROPN
ejpam-5466	96	2	)	)	PUNCT
ejpam-5466	96	3	)	)	PUNCT
ejpam-5466	96	4	<	<	X
ejpam-5466	96	5	ϑ(ns(ν0	ϑ(ns(ν0	PROPN
ejpam-5466	96	6	,	,	PUNCT
ejpam-5466	96	7	ν1	ν1	NOUN
ejpam-5466	96	8	)	)	PUNCT
ejpam-5466	96	9	)	)	PUNCT
ejpam-5466	96	10	,	,	PUNCT
ejpam-5466	96	11	which	which	PRON
ejpam-5466	96	12	gives	give	VERB
ejpam-5466	96	13	ϑ(sd(ν1	ϑ(sd(ν1	NOUN
ejpam-5466	96	14	,	,	PUNCT
ejpam-5466	96	15	ν2	ν2	NOUN
ejpam-5466	96	16	)	)	PUNCT
ejpam-5466	96	17	)	)	PUNCT
ejpam-5466	96	18	<	<	X
ejpam-5466	96	19	ϑ(ns(ν0	ϑ(ns(ν0	PROPN
ejpam-5466	96	20	,	,	PUNCT
ejpam-5466	96	21	ν1	ν1	NOUN
ejpam-5466	96	22	)	)	PUNCT
ejpam-5466	96	23	)	)	PUNCT
ejpam-5466	96	24	.	.	PUNCT
ejpam-5466	97	1	since	since	SCONJ
ejpam-5466	97	2	ϑ	ϑ	PROPN
ejpam-5466	97	3	is	be	AUX
ejpam-5466	97	4	increasing	increase	VERB
ejpam-5466	97	5	,	,	PUNCT
ejpam-5466	97	6	we	we	PRON
ejpam-5466	97	7	get	get	VERB
ejpam-5466	97	8	sd(ν1	sd(ν1	NOUN
ejpam-5466	97	9	,	,	PUNCT
ejpam-5466	97	10	ν2	ν2	NOUN
ejpam-5466	97	11	)	)	PUNCT
ejpam-5466	97	12	<	<	X
ejpam-5466	97	13	ns(ν0	ns(ν0	PROPN
ejpam-5466	97	14	,	,	PUNCT
ejpam-5466	97	15	ν1	ν1	PROPN
ejpam-5466	97	16	)	)	PUNCT
ejpam-5466	97	17	,	,	PUNCT
ejpam-5466	97	18	where	where	SCONJ
ejpam-5466	97	19	ns(ν0	ns(ν0	PROPN
ejpam-5466	97	20	,	,	PUNCT
ejpam-5466	97	21	ν1	ν1	NOUN
ejpam-5466	97	22	)	)	PUNCT
ejpam-5466	97	23	=	=	PUNCT
ejpam-5466	98	1	a1d(ν0	a1d(ν0	PROPN
ejpam-5466	98	2	,	,	PUNCT
ejpam-5466	98	3	ν1	ν1	NOUN
ejpam-5466	98	4	)	)	PUNCT
ejpam-5466	98	5	+	+	SYM
ejpam-5466	98	6	a2d(ν0	a2d(ν0	PROPN
ejpam-5466	98	7	,	,	PUNCT
ejpam-5466	98	8	t	t	NOUN
ejpam-5466	98	9	ν0	ν0	PROPN
ejpam-5466	98	10	)	)	PUNCT
ejpam-5466	99	1	+	+	CCONJ
ejpam-5466	99	2	a3d(ν1	a3d(ν1	PROPN
ejpam-5466	99	3	,	,	PUNCT
ejpam-5466	99	4	t	t	PROPN
ejpam-5466	99	5	ν1	ν1	NOUN
ejpam-5466	99	6	)	)	PUNCT
ejpam-5466	100	1	+	+	CCONJ
ejpam-5466	100	2	a4d(ν0	a4d(ν0	PROPN
ejpam-5466	100	3	,	,	PUNCT
ejpam-5466	100	4	t	t	PROPN
ejpam-5466	100	5	ν1	ν1	PROPN
ejpam-5466	100	6	)	)	PUNCT
ejpam-5466	101	1	+	+	CCONJ
ejpam-5466	101	2	a5d(ν1	a5d(ν1	PROPN
ejpam-5466	101	3	,	,	PUNCT
ejpam-5466	101	4	t	t	NOUN
ejpam-5466	101	5	ν0	ν0	PROPN
ejpam-5466	101	6	)	)	PUNCT
ejpam-5466	101	7	≤	≤	PUNCT
ejpam-5466	102	1	a1d(ν0	a1d(ν0	PROPN
ejpam-5466	102	2	,	,	PUNCT
ejpam-5466	102	3	ν1	ν1	NOUN
ejpam-5466	102	4	)	)	PUNCT
ejpam-5466	102	5	+	+	SYM
ejpam-5466	102	6	a2d(ν0	a2d(ν0	PROPN
ejpam-5466	102	7	,	,	PUNCT
ejpam-5466	102	8	ν1	ν1	NOUN
ejpam-5466	102	9	)	)	PUNCT
ejpam-5466	102	10	+	+	CCONJ
ejpam-5466	102	11	a3d(ν1	a3d(ν1	PROPN
ejpam-5466	102	12	,	,	PUNCT
ejpam-5466	102	13	ν2	ν2	NOUN
ejpam-5466	102	14	)	)	PUNCT
ejpam-5466	102	15	+	+	CCONJ
ejpam-5466	102	16	a4d(ν0	a4d(ν0	PROPN
ejpam-5466	102	17	,	,	PUNCT
ejpam-5466	102	18	ν2	ν2	NOUN
ejpam-5466	102	19	)	)	PUNCT
ejpam-5466	102	20	≤	≤	NOUN
ejpam-5466	102	21	a1d(ν0	a1d(ν0	PROPN
ejpam-5466	102	22	,	,	PUNCT
ejpam-5466	102	23	ν1	ν1	NOUN
ejpam-5466	102	24	)	)	PUNCT
ejpam-5466	102	25	+	+	SYM
ejpam-5466	102	26	a2d(ν0	a2d(ν0	PROPN
ejpam-5466	102	27	,	,	PUNCT
ejpam-5466	102	28	ν1	ν1	NOUN
ejpam-5466	102	29	)	)	PUNCT
ejpam-5466	102	30	+	+	CCONJ
ejpam-5466	102	31	a3d(ν1	a3d(ν1	PROPN
ejpam-5466	102	32	,	,	PUNCT
ejpam-5466	102	33	ν2	ν2	NOUN
ejpam-5466	102	34	)	)	PUNCT
ejpam-5466	102	35	+	+	SYM
ejpam-5466	102	36	sa4(d(ν0	sa4(d(ν0	PROPN
ejpam-5466	102	37	,	,	PUNCT
ejpam-5466	102	38	ν1	ν1	NOUN
ejpam-5466	102	39	)	)	PUNCT
ejpam-5466	102	40	+	+	NUM
ejpam-5466	102	41	d(ν1	d(ν1	NOUN
ejpam-5466	102	42	,	,	PUNCT
ejpam-5466	102	43	ν2	ν2	NOUN
ejpam-5466	102	44	)	)	PUNCT
ejpam-5466	102	45	)	)	PUNCT
ejpam-5466	102	46	≤	≤	NOUN
ejpam-5466	102	47	(	(	PUNCT
ejpam-5466	102	48	a1	a1	NOUN
ejpam-5466	102	49	+	+	CCONJ
ejpam-5466	102	50	a2	a2	PROPN
ejpam-5466	102	51	+	+	CCONJ
ejpam-5466	102	52	sa4)d(ν0	sa4)d(ν0	PROPN
ejpam-5466	102	53	,	,	PUNCT
ejpam-5466	102	54	ν1	ν1	NOUN
ejpam-5466	102	55	)	)	PUNCT
ejpam-5466	102	56	+	+	CCONJ
ejpam-5466	102	57	(	(	PUNCT
ejpam-5466	102	58	a3	a3	NOUN
ejpam-5466	102	59	+	+	CCONJ
ejpam-5466	102	60	sa4)d(ν1	sa4)d(ν1	NOUN
ejpam-5466	102	61	,	,	PUNCT
ejpam-5466	102	62	ν2	ν2	NOUN
ejpam-5466	102	63	)	)	PUNCT
ejpam-5466	102	64	,	,	PUNCT
ejpam-5466	102	65	which	which	PRON
ejpam-5466	102	66	implies	imply	VERB
ejpam-5466	102	67	that	that	PRON
ejpam-5466	102	68	d(ν1	d(ν1	NOUN
ejpam-5466	102	69	,	,	PUNCT
ejpam-5466	102	70	ν2	ν2	NOUN
ejpam-5466	102	71	)	)	PUNCT
ejpam-5466	102	72	≤	≤	NOUN
ejpam-5466	102	73	sd(ν1	sd(ν1	NOUN
ejpam-5466	102	74	,	,	PUNCT
ejpam-5466	102	75	ν2	ν2	NOUN
ejpam-5466	102	76	)	)	PUNCT
ejpam-5466	102	77	≤	≤	NOUN
ejpam-5466	102	78	(	(	PUNCT
ejpam-5466	102	79	a1	a1	NOUN
ejpam-5466	102	80	+	+	CCONJ
ejpam-5466	102	81	a2	a2	PROPN
ejpam-5466	102	82	+	+	CCONJ
ejpam-5466	102	83	sa4)d(ν0	sa4)d(ν0	PROPN
ejpam-5466	102	84	,	,	PUNCT
ejpam-5466	102	85	ν1	ν1	NOUN
ejpam-5466	102	86	)	)	PUNCT
ejpam-5466	102	87	+	+	CCONJ
ejpam-5466	102	88	(	(	PUNCT
ejpam-5466	102	89	a3	a3	NOUN
ejpam-5466	102	90	+	+	CCONJ
ejpam-5466	102	91	sa4)d(ν1	sa4)d(ν1	NOUN
ejpam-5466	102	92	,	,	PUNCT
ejpam-5466	102	93	ν2	ν2	NOUN
ejpam-5466	102	94	)	)	PUNCT
ejpam-5466	102	95	.	.	PUNCT
ejpam-5466	103	1	then	then	ADV
ejpam-5466	103	2	,	,	PUNCT
ejpam-5466	103	3	d(ν1	d(ν1	NOUN
ejpam-5466	103	4	,	,	PUNCT
ejpam-5466	103	5	ν2	ν2	NOUN
ejpam-5466	103	6	)	)	PUNCT
ejpam-5466	103	7	≤	≤	NOUN
ejpam-5466	103	8	a1	a1	NOUN
ejpam-5466	103	9	+	+	CCONJ
ejpam-5466	103	10	a2	a2	PROPN
ejpam-5466	103	11	+	+	CCONJ
ejpam-5466	103	12	sa4	sa4	NOUN
ejpam-5466	103	13	1−	1−	NUM
ejpam-5466	103	14	a3	a3	NOUN
ejpam-5466	103	15	−	−	PROPN
ejpam-5466	103	16	sa4	sa4	PROPN
ejpam-5466	103	17	d(ν0	d(ν0	PROPN
ejpam-5466	103	18	,	,	PUNCT
ejpam-5466	103	19	ν1	ν1	NOUN
ejpam-5466	103	20	)	)	PUNCT
ejpam-5466	103	21	.	.	PUNCT
ejpam-5466	104	1	since	since	SCONJ
ejpam-5466	104	2	a1	a1	NOUN
ejpam-5466	104	3	+	+	CCONJ
ejpam-5466	104	4	a2	a2	PROPN
ejpam-5466	104	5	+	+	CCONJ
ejpam-5466	104	6	a3	a3	NOUN
ejpam-5466	104	7	+	+	CCONJ
ejpam-5466	104	8	2sa4	2sa4	NUM
ejpam-5466	104	9	=	=	SYM
ejpam-5466	104	10	1	1	NUM
ejpam-5466	104	11	,	,	PUNCT
ejpam-5466	104	12	we	we	PRON
ejpam-5466	104	13	get	get	VERB
ejpam-5466	104	14	d(ν1	d(ν1	NOUN
ejpam-5466	104	15	,	,	PUNCT
ejpam-5466	104	16	ν2	ν2	NOUN
ejpam-5466	104	17	)	)	PUNCT
ejpam-5466	104	18	<	<	X
ejpam-5466	104	19	d(ν0	d(ν0	PROPN
ejpam-5466	104	20	,	,	PUNCT
ejpam-5466	104	21	ν1	ν1	NOUN
ejpam-5466	104	22	)	)	PUNCT
ejpam-5466	104	23	.	.	PUNCT
ejpam-5466	105	1	thus	thus	ADV
ejpam-5466	105	2	,	,	PUNCT
ejpam-5466	105	3	sd(ν1	sd(ν1	PROPN
ejpam-5466	105	4	,	,	PUNCT
ejpam-5466	105	5	ν2	ν2	NOUN
ejpam-5466	105	6	)	)	PUNCT
ejpam-5466	105	7	<	<	X
ejpam-5466	105	8	(	(	PUNCT
ejpam-5466	105	9	a1	a1	NOUN
ejpam-5466	105	10	+	+	CCONJ
ejpam-5466	105	11	a2	a2	PROPN
ejpam-5466	105	12	+	+	CCONJ
ejpam-5466	105	13	sa4)d(ν0	sa4)d(ν0	PROPN
ejpam-5466	105	14	,	,	PUNCT
ejpam-5466	105	15	ν1	ν1	NOUN
ejpam-5466	105	16	)	)	PUNCT
ejpam-5466	105	17	+	+	CCONJ
ejpam-5466	105	18	(	(	PUNCT
ejpam-5466	105	19	a3	a3	NOUN
ejpam-5466	105	20	+	+	CCONJ
ejpam-5466	105	21	sa4)d(ν0	sa4)d(ν0	PROPN
ejpam-5466	105	22	,	,	PUNCT
ejpam-5466	105	23	ν1	ν1	NOUN
ejpam-5466	105	24	)	)	PUNCT
ejpam-5466	105	25	=	=	SYM
ejpam-5466	105	26	d(ν0	d(ν0	PROPN
ejpam-5466	105	27	,	,	PUNCT
ejpam-5466	105	28	ν1	ν1	NOUN
ejpam-5466	105	29	)	)	PUNCT
ejpam-5466	105	30	,	,	PUNCT
ejpam-5466	105	31	and	and	CCONJ
ejpam-5466	105	32	so	so	ADV
ejpam-5466	105	33	ϑ(sd(ν1	ϑ(sd(ν1	ADJ
ejpam-5466	105	34	,	,	PUNCT
ejpam-5466	105	35	ν2	ν2	NOUN
ejpam-5466	105	36	)	)	PUNCT
ejpam-5466	105	37	)	)	PUNCT
ejpam-5466	105	38	≤	≤	NOUN
ejpam-5466	105	39	[	[	PUNCT
ejpam-5466	105	40	ϑ(d(ν0	ϑ(d(ν0	PROPN
ejpam-5466	105	41	,	,	PUNCT
ejpam-5466	105	42	ν1	ν1	NOUN
ejpam-5466	105	43	)	)	PUNCT
ejpam-5466	105	44	)	)	PUNCT
ejpam-5466	106	1	]	]	PUNCT
ejpam-5466	106	2	κ(d(ν0,ν1	κ(d(ν0,ν1	PROPN
ejpam-5466	106	3	)	)	PUNCT
ejpam-5466	106	4	)	)	PUNCT
ejpam-5466	106	5	.	.	PUNCT
ejpam-5466	107	1	assume	assume	VERB
ejpam-5466	107	2	that	that	SCONJ
ejpam-5466	107	3	ν1	ν1	NOUN
ejpam-5466	107	4	̸=	̸=	PROPN
ejpam-5466	107	5	ν2	ν2	NOUN
ejpam-5466	107	6	,	,	PUNCT
ejpam-5466	107	7	then	then	ADV
ejpam-5466	107	8	ν2	ν2	PROPN
ejpam-5466	107	9	/∈	/∈	PROPN
ejpam-5466	107	10	t	t	PROPN
ejpam-5466	107	11	ν2	ν2	NOUN
ejpam-5466	107	12	and	and	CCONJ
ejpam-5466	107	13	d(ν2	d(ν2	NOUN
ejpam-5466	107	14	,	,	PUNCT
ejpam-5466	107	15	t	t	PROPN
ejpam-5466	107	16	ν2	ν2	PROPN
ejpam-5466	107	17	)	)	PUNCT
ejpam-5466	107	18	>	>	X
ejpam-5466	107	19	0	0	PUNCT
ejpam-5466	108	1	so	so	ADV
ejpam-5466	108	2	h(t	h(t	PROPN
ejpam-5466	108	3	ν1	ν1	PROPN
ejpam-5466	108	4	,	,	PUNCT
ejpam-5466	108	5	t	t	NOUN
ejpam-5466	108	6	ν2	ν2	PROPN
ejpam-5466	108	7	)	)	PUNCT
ejpam-5466	108	8	>	>	X
ejpam-5466	108	9	0	0	X
ejpam-5466	108	10	.	.	PUNCT
ejpam-5466	108	11	from	from	ADP
ejpam-5466	108	12	lemma	lemma	PROPN
ejpam-5466	108	13	2	2	NUM
ejpam-5466	108	14	,	,	PUNCT
ejpam-5466	108	15	there	there	PRON
ejpam-5466	108	16	exists	exist	VERB
ejpam-5466	108	17	ν3	ν3	PROPN
ejpam-5466	108	18	∈	∈	PROPN
ejpam-5466	108	19	t	t	NOUN
ejpam-5466	108	20	ν2	ν2	NOUN
ejpam-5466	108	21	such	such	DET
ejpam-5466	108	22	that	that	DET
ejpam-5466	108	23	ϑ(sd(ν2	ϑ(sd(ν2	ADJ
ejpam-5466	108	24	,	,	PUNCT
ejpam-5466	108	25	ν3	ν3	NOUN
ejpam-5466	108	26	)	)	PUNCT
ejpam-5466	108	27	)	)	PUNCT
ejpam-5466	109	1	≤	≤	PROPN
ejpam-5466	109	2	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	109	3	ν1	ν1	NOUN
ejpam-5466	109	4	,	,	PUNCT
ejpam-5466	109	5	t	t	NOUN
ejpam-5466	109	6	ν2	ν2	PROPN
ejpam-5466	109	7	)	)	PUNCT
ejpam-5466	109	8	)	)	PUNCT
ejpam-5466	109	9	≤	≤	NOUN
ejpam-5466	109	10	[	[	PUNCT
ejpam-5466	109	11	ϑ(ns(ν1	ϑ(ns(ν1	NOUN
ejpam-5466	109	12	,	,	PUNCT
ejpam-5466	109	13	ν2	ν2	NOUN
ejpam-5466	109	14	)	)	PUNCT
ejpam-5466	109	15	)	)	PUNCT
ejpam-5466	110	1	]	]	PUNCT
ejpam-5466	110	2	κ(d(ν1,ν2	κ(d(ν1,ν2	NUM
ejpam-5466	110	3	)	)	PUNCT
ejpam-5466	110	4	)	)	PUNCT
ejpam-5466	111	1	+	+	CCONJ
ejpam-5466	111	2	lmin{d(ν1	lmin{d(ν1	PROPN
ejpam-5466	111	3	,	,	PUNCT
ejpam-5466	111	4	t	t	NOUN
ejpam-5466	111	5	ν2	ν2	PROPN
ejpam-5466	111	6	)	)	PUNCT
ejpam-5466	111	7	,	,	PUNCT
ejpam-5466	111	8	d(ν2	d(ν2	NOUN
ejpam-5466	111	9	,	,	PUNCT
ejpam-5466	111	10	t	t	PROPN
ejpam-5466	111	11	ν1	ν1	PROPN
ejpam-5466	111	12	)	)	PUNCT
ejpam-5466	111	13	}	}	PUNCT
ejpam-5466	111	14	<	<	X
ejpam-5466	112	1	[	[	X
ejpam-5466	112	2	ϑ(ns(ν1	ϑ(ns(ν1	NOUN
ejpam-5466	112	3	,	,	PUNCT
ejpam-5466	112	4	ν2	ν2	NOUN
ejpam-5466	112	5	)	)	PUNCT
ejpam-5466	112	6	)	)	PUNCT
ejpam-5466	112	7	]	]	PUNCT
ejpam-5466	113	1	κ(d(ν1,ν2	κ(d(ν1,ν2	PROPN
ejpam-5466	113	2	)	)	PUNCT
ejpam-5466	113	3	)	)	PUNCT
ejpam-5466	114	1	<	<	X
ejpam-5466	114	2	ϑ(ns(ν1	ϑ(ns(ν1	NOUN
ejpam-5466	114	3	,	,	PUNCT
ejpam-5466	114	4	ν2	ν2	NOUN
ejpam-5466	114	5	)	)	PUNCT
ejpam-5466	114	6	)	)	PUNCT
ejpam-5466	114	7	.	.	PUNCT
ejpam-5466	115	1	then	then	ADV
ejpam-5466	115	2	,	,	PUNCT
ejpam-5466	115	3	ϑ(sd(ν2	ϑ(sd(ν2	ADJ
ejpam-5466	115	4	,	,	PUNCT
ejpam-5466	115	5	ν3	ν3	NOUN
ejpam-5466	115	6	)	)	PUNCT
ejpam-5466	115	7	)	)	PUNCT
ejpam-5466	116	1	≤	≤	NUM
ejpam-5466	116	2	ϑ(ns(ν1	ϑ(ns(ν1	NOUN
ejpam-5466	116	3	,	,	PUNCT
ejpam-5466	116	4	ν2	ν2	NOUN
ejpam-5466	116	5	)	)	PUNCT
ejpam-5466	116	6	)	)	PUNCT
ejpam-5466	116	7	,	,	PUNCT
ejpam-5466	116	8	h.	h.	PROPN
ejpam-5466	116	9	qawaqneh	qawaqneh	PROPN
ejpam-5466	116	10	et	et	PROPN
ejpam-5466	116	11	al	al	PROPN
ejpam-5466	116	12	.	.	PUNCT
ejpam-5466	116	13	/	/	SYM
ejpam-5466	116	14	eur	eur	PROPN
ejpam-5466	116	15	.	.	PUNCT
ejpam-5466	117	1	j.	j.	PROPN
ejpam-5466	117	2	pure	pure	PROPN
ejpam-5466	117	3	appl	appl	PROPN
ejpam-5466	117	4	.	.	PROPN
ejpam-5466	117	5	math	math	PROPN
ejpam-5466	117	6	,	,	PUNCT
ejpam-5466	117	7	17	17	NUM
ejpam-5466	117	8	(	(	PUNCT
ejpam-5466	117	9	4	4	NUM
ejpam-5466	117	10	)	)	PUNCT
ejpam-5466	117	11	(	(	PUNCT
ejpam-5466	117	12	2024	2024	NUM
ejpam-5466	117	13	)	)	PUNCT
ejpam-5466	117	14	,	,	PUNCT
ejpam-5466	117	15	3093	3093	NUM
ejpam-5466	117	16	-	-	SYM
ejpam-5466	117	17	3108	3108	NUM
ejpam-5466	117	18	3098	3098	NUM
ejpam-5466	117	19	which	which	PRON
ejpam-5466	117	20	gives	give	VERB
ejpam-5466	117	21	sd(ν2	sd(ν2	NOUN
ejpam-5466	117	22	,	,	PUNCT
ejpam-5466	117	23	ν3	ν3	NOUN
ejpam-5466	117	24	)	)	PUNCT
ejpam-5466	117	25	<	<	X
ejpam-5466	117	26	ns(ν1	ns(ν1	NOUN
ejpam-5466	117	27	,	,	PUNCT
ejpam-5466	117	28	ν2	ν2	NOUN
ejpam-5466	117	29	)	)	PUNCT
ejpam-5466	117	30	,	,	PUNCT
ejpam-5466	117	31	where	where	SCONJ
ejpam-5466	117	32	ns(ν1	ns(ν1	NOUN
ejpam-5466	117	33	,	,	PUNCT
ejpam-5466	117	34	ν2	ν2	NOUN
ejpam-5466	117	35	)	)	PUNCT
ejpam-5466	117	36	=	=	SYM
ejpam-5466	118	1	a1d(ν1	a1d(ν1	NOUN
ejpam-5466	118	2	,	,	PUNCT
ejpam-5466	118	3	ν2	ν2	NOUN
ejpam-5466	118	4	)	)	PUNCT
ejpam-5466	118	5	+	+	CCONJ
ejpam-5466	118	6	a2d(ν1	a2d(ν1	PROPN
ejpam-5466	118	7	,	,	PUNCT
ejpam-5466	118	8	t	t	NOUN
ejpam-5466	118	9	ν1	ν1	NOUN
ejpam-5466	118	10	)	)	PUNCT
ejpam-5466	119	1	+	+	CCONJ
ejpam-5466	119	2	a3d(ν2	a3d(ν2	PROPN
ejpam-5466	119	3	,	,	PUNCT
ejpam-5466	119	4	t	t	NOUN
ejpam-5466	119	5	ν2	ν2	PROPN
ejpam-5466	119	6	)	)	PUNCT
ejpam-5466	120	1	+	+	CCONJ
ejpam-5466	120	2	a4d(ν1	a4d(ν1	PROPN
ejpam-5466	120	3	,	,	PUNCT
ejpam-5466	120	4	t	t	NOUN
ejpam-5466	120	5	ν2	ν2	PROPN
ejpam-5466	120	6	)	)	PUNCT
ejpam-5466	121	1	+	+	CCONJ
ejpam-5466	121	2	a5d(ν2	a5d(ν2	PROPN
ejpam-5466	121	3	,	,	PUNCT
ejpam-5466	121	4	t	t	PROPN
ejpam-5466	121	5	ν1	ν1	NOUN
ejpam-5466	121	6	)	)	PUNCT
ejpam-5466	121	7	.	.	PUNCT
ejpam-5466	122	1	≤	≤	PROPN
ejpam-5466	122	2	a1d(ν1	a1d(ν1	NOUN
ejpam-5466	122	3	,	,	PUNCT
ejpam-5466	122	4	ν2	ν2	NOUN
ejpam-5466	122	5	)	)	PUNCT
ejpam-5466	122	6	+	+	CCONJ
ejpam-5466	122	7	a2d(ν1	a2d(ν1	PROPN
ejpam-5466	122	8	,	,	PUNCT
ejpam-5466	122	9	ν2	ν2	NOUN
ejpam-5466	122	10	)	)	PUNCT
ejpam-5466	122	11	+	+	CCONJ
ejpam-5466	122	12	a3d(ν2	a3d(ν2	PROPN
ejpam-5466	122	13	,	,	PUNCT
ejpam-5466	122	14	ν3	ν3	NOUN
ejpam-5466	122	15	)	)	PUNCT
ejpam-5466	122	16	+	+	CCONJ
ejpam-5466	122	17	sa4(d(ν1	sa4(d(ν1	NOUN
ejpam-5466	122	18	,	,	PUNCT
ejpam-5466	122	19	ν2	ν2	NOUN
ejpam-5466	122	20	)	)	PUNCT
ejpam-5466	122	21	+	+	NUM
ejpam-5466	122	22	d(ν2	d(ν2	NOUN
ejpam-5466	122	23	,	,	PUNCT
ejpam-5466	122	24	ν3	ν3	NOUN
ejpam-5466	122	25	)	)	PUNCT
ejpam-5466	122	26	)	)	PUNCT
ejpam-5466	122	27	≤	≤	NOUN
ejpam-5466	122	28	(	(	PUNCT
ejpam-5466	122	29	a1	a1	NOUN
ejpam-5466	122	30	+	+	CCONJ
ejpam-5466	122	31	a2	a2	PROPN
ejpam-5466	122	32	+	+	CCONJ
ejpam-5466	122	33	sa4)d(ν1	sa4)d(ν1	NOUN
ejpam-5466	122	34	,	,	PUNCT
ejpam-5466	122	35	ν2	ν2	NOUN
ejpam-5466	122	36	)	)	PUNCT
ejpam-5466	122	37	+	+	CCONJ
ejpam-5466	122	38	(	(	PUNCT
ejpam-5466	122	39	a3	a3	NOUN
ejpam-5466	122	40	+	+	CCONJ
ejpam-5466	122	41	sa4)d(ν2	sa4)d(ν2	PROPN
ejpam-5466	122	42	,	,	PUNCT
ejpam-5466	122	43	ν3	ν3	NOUN
ejpam-5466	122	44	)	)	PUNCT
ejpam-5466	122	45	.	.	PUNCT
ejpam-5466	123	1	hence	hence	ADV
ejpam-5466	123	2	,	,	PUNCT
ejpam-5466	123	3	d(ν2	d(ν2	NOUN
ejpam-5466	123	4	,	,	PUNCT
ejpam-5466	123	5	ν3	ν3	NOUN
ejpam-5466	123	6	)	)	PUNCT
ejpam-5466	123	7	≤	≤	NUM
ejpam-5466	123	8	sd(ν2	sd(ν2	NOUN
ejpam-5466	123	9	,	,	PUNCT
ejpam-5466	123	10	ν3	ν3	NOUN
ejpam-5466	123	11	)	)	PUNCT
ejpam-5466	123	12	≤	≤	NOUN
ejpam-5466	123	13	(	(	PUNCT
ejpam-5466	123	14	a1	a1	NOUN
ejpam-5466	123	15	+	+	CCONJ
ejpam-5466	123	16	a2	a2	PROPN
ejpam-5466	123	17	+	+	CCONJ
ejpam-5466	123	18	sa4)d(ν1	sa4)d(ν1	NOUN
ejpam-5466	123	19	,	,	PUNCT
ejpam-5466	123	20	ν2	ν2	NOUN
ejpam-5466	123	21	)	)	PUNCT
ejpam-5466	123	22	+	+	CCONJ
ejpam-5466	123	23	(	(	PUNCT
ejpam-5466	123	24	a3	a3	NOUN
ejpam-5466	123	25	+	+	CCONJ
ejpam-5466	123	26	sa4)d(ν2	sa4)d(ν2	PROPN
ejpam-5466	123	27	,	,	PUNCT
ejpam-5466	123	28	ν3	ν3	NOUN
ejpam-5466	123	29	)	)	PUNCT
ejpam-5466	123	30	,	,	PUNCT
ejpam-5466	123	31	and	and	CCONJ
ejpam-5466	123	32	so	so	ADV
ejpam-5466	123	33	d(ν2	d(ν2	NOUN
ejpam-5466	123	34	,	,	PUNCT
ejpam-5466	123	35	ν3	ν3	NOUN
ejpam-5466	123	36	)	)	PUNCT
ejpam-5466	123	37	≤	≤	NOUN
ejpam-5466	123	38	a1	a1	NOUN
ejpam-5466	123	39	+	+	CCONJ
ejpam-5466	123	40	a2	a2	PROPN
ejpam-5466	123	41	+	+	CCONJ
ejpam-5466	123	42	sa4	sa4	NOUN
ejpam-5466	123	43	1−	1−	NUM
ejpam-5466	123	44	a3	a3	NOUN
ejpam-5466	123	45	−	−	PROPN
ejpam-5466	123	46	sa4	sa4	PROPN
ejpam-5466	123	47	d(ν1	d(ν1	NOUN
ejpam-5466	123	48	,	,	PUNCT
ejpam-5466	123	49	ν2	ν2	NOUN
ejpam-5466	123	50	)	)	PUNCT
ejpam-5466	123	51	.	.	PUNCT
ejpam-5466	124	1	since	since	SCONJ
ejpam-5466	124	2	a1	a1	NOUN
ejpam-5466	124	3	+	+	CCONJ
ejpam-5466	124	4	a2	a2	PROPN
ejpam-5466	124	5	+	+	CCONJ
ejpam-5466	124	6	a3	a3	NOUN
ejpam-5466	124	7	+	+	CCONJ
ejpam-5466	124	8	2sa4	2sa4	NUM
ejpam-5466	124	9	=	=	SYM
ejpam-5466	124	10	1	1	NUM
ejpam-5466	124	11	,	,	PUNCT
ejpam-5466	124	12	we	we	PRON
ejpam-5466	124	13	get	get	VERB
ejpam-5466	124	14	d(ν2	d(ν2	NOUN
ejpam-5466	124	15	,	,	PUNCT
ejpam-5466	124	16	ν3	ν3	NOUN
ejpam-5466	124	17	)	)	PUNCT
ejpam-5466	124	18	<	<	X
ejpam-5466	124	19	d(ν1	d(ν1	NOUN
ejpam-5466	124	20	,	,	PUNCT
ejpam-5466	124	21	ν2	ν2	NOUN
ejpam-5466	124	22	)	)	PUNCT
ejpam-5466	124	23	.	.	PUNCT
ejpam-5466	125	1	then	then	ADV
ejpam-5466	125	2	,	,	PUNCT
ejpam-5466	125	3	we	we	PRON
ejpam-5466	125	4	infer	infer	VERB
ejpam-5466	125	5	that	that	DET
ejpam-5466	125	6	ϑ(sd(ν2	ϑ(sd(ν2	ADJ
ejpam-5466	125	7	,	,	PUNCT
ejpam-5466	125	8	ν3	ν3	NOUN
ejpam-5466	125	9	)	)	PUNCT
ejpam-5466	125	10	≤	≤	NOUN
ejpam-5466	125	11	[	[	PUNCT
ejpam-5466	125	12	ϑ(d(ν1	ϑ(d(ν1	NOUN
ejpam-5466	125	13	,	,	PUNCT
ejpam-5466	125	14	ν2	ν2	NOUN
ejpam-5466	125	15	)	)	PUNCT
ejpam-5466	125	16	)	)	PUNCT
ejpam-5466	126	1	]	]	PUNCT
ejpam-5466	126	2	κ(d(ν1,ν2	κ(d(ν1,ν2	NUM
ejpam-5466	126	3	)	)	PUNCT
ejpam-5466	126	4	)	)	PUNCT
ejpam-5466	126	5	.	.	PUNCT
ejpam-5466	127	1	by	by	ADP
ejpam-5466	127	2	continuing	continue	VERB
ejpam-5466	127	3	in	in	ADP
ejpam-5466	127	4	this	this	DET
ejpam-5466	127	5	manner	manner	NOUN
ejpam-5466	127	6	,	,	PUNCT
ejpam-5466	127	7	we	we	PRON
ejpam-5466	127	8	construct	construct	VERB
ejpam-5466	127	9	a	a	DET
ejpam-5466	127	10	sequence	sequence	NOUN
ejpam-5466	127	11	{	{	PUNCT
ejpam-5466	127	12	νn	νn	PRON
ejpam-5466	127	13	}	}	PUNCT
ejpam-5466	127	14	in	in	ADP
ejpam-5466	127	15	x	x	NOUN
ejpam-5466	127	16	,	,	PUNCT
ejpam-5466	127	17	if	if	SCONJ
ejpam-5466	127	18	there	there	PRON
ejpam-5466	127	19	exists	exist	VERB
ejpam-5466	127	20	n0	n0	ADJ
ejpam-5466	127	21	such	such	ADJ
ejpam-5466	127	22	that	that	DET
ejpam-5466	127	23	νn0	νn0	NOUN
ejpam-5466	127	24	=	=	PUNCT
ejpam-5466	127	25	νn0	νn0	NOUN
ejpam-5466	127	26	+	+	PROPN
ejpam-5466	127	27	1	1	NUM
ejpam-5466	127	28	,	,	PUNCT
ejpam-5466	127	29	or	or	CCONJ
ejpam-5466	127	30	νn0	νn0	NOUN
ejpam-5466	127	31	+	+	NOUN
ejpam-5466	127	32	1	1	NUM
ejpam-5466	127	33	∈	∈	NOUN
ejpam-5466	127	34	t	t	NOUN
ejpam-5466	127	35	νn0	νn0	NOUN
ejpam-5466	127	36	+	+	PROPN
ejpam-5466	127	37	1	1	NUM
ejpam-5466	127	38	then	then	ADV
ejpam-5466	127	39	νn0	νn0	NOUN
ejpam-5466	127	40	+	+	NOUN
ejpam-5466	127	41	1	1	NUM
ejpam-5466	127	42	is	be	AUX
ejpam-5466	127	43	fixed	fix	VERB
ejpam-5466	127	44	point	point	NOUN
ejpam-5466	127	45	.	.	PUNCT
ejpam-5466	128	1	if	if	SCONJ
ejpam-5466	128	2	νn	νn	AUX
ejpam-5466	128	3	̸=	̸=	PROPN
ejpam-5466	128	4	νn+1	νn+1	NUM
ejpam-5466	128	5	and	and	CCONJ
ejpam-5466	128	6	νn+1	νn+1	NUM
ejpam-5466	128	7	/∈	/∈	PUNCT
ejpam-5466	129	1	t	t	PROPN
ejpam-5466	129	2	νn+1	νn+1	PROPN
ejpam-5466	129	3	,	,	PUNCT
ejpam-5466	129	4	then	then	ADV
ejpam-5466	129	5	h(t	h(t	PROPN
ejpam-5466	129	6	νn	νn	PROPN
ejpam-5466	129	7	,	,	PUNCT
ejpam-5466	129	8	t	t	PROPN
ejpam-5466	129	9	νn+1	νn+1	NUM
ejpam-5466	129	10	)	)	PUNCT
ejpam-5466	129	11	>	>	X
ejpam-5466	130	1	0	0	X
ejpam-5466	130	2	.	.	PUNCT
ejpam-5466	131	1	from	from	ADP
ejpam-5466	131	2	lemma	lemma	PROPN
ejpam-5466	131	3	2	2	NUM
ejpam-5466	131	4	,	,	PUNCT
ejpam-5466	131	5	there	there	PRON
ejpam-5466	131	6	exists	exist	VERB
ejpam-5466	131	7	νn+1	νn+1	NUM
ejpam-5466	131	8	∈	∈	NOUN
ejpam-5466	131	9	t	t	NOUN
ejpam-5466	131	10	νn	νn	PRON
ejpam-5466	131	11	such	such	ADJ
ejpam-5466	131	12	that	that	SCONJ
ejpam-5466	131	13	θ(sd(νn	θ(sd(νn	ADJ
ejpam-5466	131	14	,	,	PUNCT
ejpam-5466	131	15	νn+1	νn+1	NUM
ejpam-5466	131	16	)	)	PUNCT
ejpam-5466	131	17	)	)	PUNCT
ejpam-5466	131	18	≤	≤	NOUN
ejpam-5466	132	1	[	[	PUNCT
ejpam-5466	132	2	θ(d(νn−1	θ(d(νn−1	NOUN
ejpam-5466	132	3	,	,	PUNCT
ejpam-5466	132	4	νn	νn	NOUN
ejpam-5466	132	5	)	)	PUNCT
ejpam-5466	132	6	)	)	PUNCT
ejpam-5466	133	1	]	]	PUNCT
ejpam-5466	133	2	κ(d(νn−1,νn	κ(d(νn−1,νn	NOUN
ejpam-5466	133	3	)	)	PUNCT
ejpam-5466	133	4	)	)	PUNCT
ejpam-5466	133	5	,	,	PUNCT
ejpam-5466	133	6	for	for	ADP
ejpam-5466	133	7	all	all	DET
ejpam-5466	133	8	n	n	PRON
ejpam-5466	133	9	∈	∈	PROPN
ejpam-5466	133	10	n.	n.	NOUN
ejpam-5466	133	11	(	(	PUNCT
ejpam-5466	133	12	2.2	2.2	NUM
ejpam-5466	133	13	)	)	PUNCT
ejpam-5466	133	14	it	it	PRON
ejpam-5466	133	15	follows	follow	VERB
ejpam-5466	133	16	by	by	ADP
ejpam-5466	133	17	(	(	PUNCT
ejpam-5466	133	18	2.2	2.2	NUM
ejpam-5466	133	19	)	)	PUNCT
ejpam-5466	133	20	and	and	CCONJ
ejpam-5466	133	21	(	(	PUNCT
ejpam-5466	133	22	ϑ4	ϑ4	PROPN
ejpam-5466	133	23	)	)	PUNCT
ejpam-5466	133	24	that	that	SCONJ
ejpam-5466	133	25	θ(snd(νn	θ(snd(νn	NOUN
ejpam-5466	133	26	,	,	PUNCT
ejpam-5466	133	27	νn+1	νn+1	NUM
ejpam-5466	133	28	)	)	PUNCT
ejpam-5466	133	29	)	)	PUNCT
ejpam-5466	134	1	≤	≤	NOUN
ejpam-5466	134	2	[	[	PUNCT
ejpam-5466	134	3	θ(sn−1d(νn−1	θ(sn−1d(νn−1	ADJ
ejpam-5466	134	4	,	,	PUNCT
ejpam-5466	134	5	νn	νn	NOUN
ejpam-5466	134	6	)	)	PUNCT
ejpam-5466	134	7	)	)	PUNCT
ejpam-5466	134	8	]	]	PUNCT
ejpam-5466	134	9	κ(d(νn−1,νn	κ(d(νn−1,νn	NOUN
ejpam-5466	134	10	)	)	PUNCT
ejpam-5466	134	11	)	)	PUNCT
ejpam-5466	134	12	,	,	PUNCT
ejpam-5466	134	13	for	for	ADP
ejpam-5466	134	14	all	all	DET
ejpam-5466	134	15	n	n	PRON
ejpam-5466	134	16	∈	∈	PROPN
ejpam-5466	134	17	n.	n.	NOUN
ejpam-5466	134	18	(	(	PUNCT
ejpam-5466	134	19	2.3	2.3	NUM
ejpam-5466	134	20	)	)	PUNCT
ejpam-5466	134	21	since	since	SCONJ
ejpam-5466	134	22	ϑ	ϑ	PROPN
ejpam-5466	134	23	is	be	AUX
ejpam-5466	134	24	increasing	increase	VERB
ejpam-5466	134	25	,	,	PUNCT
ejpam-5466	134	26	then	then	ADV
ejpam-5466	134	27	the	the	DET
ejpam-5466	134	28	sequence	sequence	NOUN
ejpam-5466	134	29	{	{	PUNCT
ejpam-5466	134	30	d(νn	d(νn	NUM
ejpam-5466	134	31	,	,	PUNCT
ejpam-5466	134	32	νn+1	νn+1	NUM
ejpam-5466	134	33	)	)	PUNCT
ejpam-5466	134	34	}	}	PUNCT
ejpam-5466	134	35	is	be	AUX
ejpam-5466	134	36	decreasing	decrease	VERB
ejpam-5466	134	37	and	and	CCONJ
ejpam-5466	134	38	so	so	ADV
ejpam-5466	134	39	convergent	convergent	ADJ
ejpam-5466	134	40	.	.	PUNCT
ejpam-5466	135	1	by	by	ADP
ejpam-5466	135	2	the	the	DET
ejpam-5466	135	3	property	property	NOUN
ejpam-5466	135	4	of	of	ADP
ejpam-5466	135	5	κ	κ	NOUN
ejpam-5466	135	6	,	,	PUNCT
ejpam-5466	135	7	there	there	PRON
ejpam-5466	135	8	exist	exist	VERB
ejpam-5466	135	9	δ	δ	PROPN
ejpam-5466	135	10	∈	∈	PROPN
ejpam-5466	135	11	(	(	PUNCT
ejpam-5466	135	12	0	0	NUM
ejpam-5466	135	13	,	,	PUNCT
ejpam-5466	135	14	1	1	NUM
ejpam-5466	135	15	)	)	PUNCT
ejpam-5466	135	16	and	and	CCONJ
ejpam-5466	135	17	n0	n0	NUM
ejpam-5466	135	18	∈	∈	PROPN
ejpam-5466	135	19	n	n	PRON
ejpam-5466	135	20	such	such	ADJ
ejpam-5466	135	21	that	that	SCONJ
ejpam-5466	135	22	κ(d(νn	κ(d(νn	NOUN
ejpam-5466	135	23	,	,	PUNCT
ejpam-5466	135	24	νn+1	νn+1	NUM
ejpam-5466	135	25	)	)	PUNCT
ejpam-5466	135	26	)	)	PUNCT
ejpam-5466	136	1	<	<	X
ejpam-5466	136	2	δ	δ	PROPN
ejpam-5466	136	3	,	,	PUNCT
ejpam-5466	136	4	for	for	ADP
ejpam-5466	136	5	all	all	DET
ejpam-5466	136	6	n	n	PRON
ejpam-5466	136	7	≥	≥	NOUN
ejpam-5466	136	8	n0	n0	NUM
ejpam-5466	136	9	.	.	PUNCT
ejpam-5466	137	1	thus	thus	ADV
ejpam-5466	137	2	,	,	PUNCT
ejpam-5466	137	3	from	from	ADP
ejpam-5466	137	4	(	(	PUNCT
ejpam-5466	137	5	2.3	2.3	NUM
ejpam-5466	137	6	)	)	PUNCT
ejpam-5466	137	7	,	,	PUNCT
ejpam-5466	137	8	we	we	PRON
ejpam-5466	137	9	deduce	deduce	VERB
ejpam-5466	137	10	1	1	NUM
ejpam-5466	137	11	<	<	X
ejpam-5466	137	12	ϑ(snd(νn	ϑ(snd(νn	NOUN
ejpam-5466	137	13	,	,	PUNCT
ejpam-5466	137	14	νn+1	νn+1	NUM
ejpam-5466	137	15	)	)	PUNCT
ejpam-5466	137	16	)	)	PUNCT
ejpam-5466	137	17	≤	≤	NOUN
ejpam-5466	137	18	[	[	PUNCT
ejpam-5466	137	19	ϑ(sn−1d(νn−1	ϑ(sn−1d(νn−1	ADJ
ejpam-5466	137	20	,	,	PUNCT
ejpam-5466	137	21	νn	νn	NOUN
ejpam-5466	137	22	)	)	PUNCT
ejpam-5466	137	23	)	)	PUNCT
ejpam-5466	137	24	]	]	PUNCT
ejpam-5466	137	25	κ(d(νn−1,νn	κ(d(νn−1,νn	NOUN
ejpam-5466	137	26	)	)	PUNCT
ejpam-5466	137	27	≤	≤	PROPN
ejpam-5466	137	28	[	[	PUNCT
ejpam-5466	137	29	ϑ(sn−2d(νn−2	ϑ(sn−2d(νn−2	NOUN
ejpam-5466	137	30	,	,	PUNCT
ejpam-5466	137	31	νn−1	νn−1	PROPN
ejpam-5466	137	32	)	)	PUNCT
ejpam-5466	137	33	)	)	PUNCT
ejpam-5466	137	34	]	]	PUNCT
ejpam-5466	137	35	κ(d(νn−2,νn−1)κ(d(νn−1,νn	κ(d(νn−2,νn−1)κ(d(νn−1,νn	NOUN
ejpam-5466	137	36	)	)	PUNCT
ejpam-5466	137	37	...	...	PUNCT
ejpam-5466	138	1	≤	≤	NUM
ejpam-5466	138	2	[	[	PUNCT
ejpam-5466	138	3	ϑ(d(ν0	ϑ(d(ν0	PROPN
ejpam-5466	138	4	,	,	PUNCT
ejpam-5466	138	5	ν1	ν1	NOUN
ejpam-5466	138	6	)	)	PUNCT
ejpam-5466	138	7	)	)	PUNCT
ejpam-5466	139	1	]	]	PUNCT
ejpam-5466	139	2	δn−n0	δn−n0	NOUN
ejpam-5466	139	3	,	,	PUNCT
ejpam-5466	139	4	(	(	PUNCT
ejpam-5466	139	5	2.4	2.4	NUM
ejpam-5466	139	6	)	)	PUNCT
ejpam-5466	139	7	h.	h.	PROPN
ejpam-5466	139	8	qawaqneh	qawaqneh	PROPN
ejpam-5466	139	9	et	et	PROPN
ejpam-5466	139	10	al	al	PROPN
ejpam-5466	139	11	.	.	PUNCT
ejpam-5466	139	12	/	/	SYM
ejpam-5466	139	13	eur	eur	PROPN
ejpam-5466	139	14	.	.	PUNCT
ejpam-5466	140	1	j.	j.	PROPN
ejpam-5466	140	2	pure	pure	PROPN
ejpam-5466	140	3	appl	appl	PROPN
ejpam-5466	140	4	.	.	PROPN
ejpam-5466	140	5	math	math	PROPN
ejpam-5466	140	6	,	,	PUNCT
ejpam-5466	140	7	17	17	NUM
ejpam-5466	140	8	(	(	PUNCT
ejpam-5466	140	9	4	4	NUM
ejpam-5466	140	10	)	)	PUNCT
ejpam-5466	140	11	(	(	PUNCT
ejpam-5466	140	12	2024	2024	NUM
ejpam-5466	140	13	)	)	PUNCT
ejpam-5466	140	14	,	,	PUNCT
ejpam-5466	140	15	3093	3093	NUM
ejpam-5466	140	16	-	-	SYM
ejpam-5466	140	17	3108	3108	NUM
ejpam-5466	140	18	3099	3099	NUM
ejpam-5466	140	19	for	for	ADP
ejpam-5466	140	20	all	all	DET
ejpam-5466	140	21	n	n	PRON
ejpam-5466	140	22	≥	≥	NOUN
ejpam-5466	140	23	n0	n0	NUM
ejpam-5466	140	24	.	.	PUNCT
ejpam-5466	141	1	on	on	ADP
ejpam-5466	141	2	taking	take	VERB
ejpam-5466	141	3	the	the	DET
ejpam-5466	141	4	limit	limit	NOUN
ejpam-5466	141	5	as	as	ADP
ejpam-5466	141	6	n→	n→	PROPN
ejpam-5466	141	7	∞	∞	PROPN
ejpam-5466	141	8	,	,	PUNCT
ejpam-5466	141	9	we	we	PRON
ejpam-5466	141	10	get	get	VERB
ejpam-5466	141	11	lim	lim	PROPN
ejpam-5466	141	12	n→∞	n→∞	NUM
ejpam-5466	141	13	ϑ(snd(νn	ϑ(snd(νn	PROPN
ejpam-5466	141	14	,	,	PUNCT
ejpam-5466	141	15	νn+1	νn+1	NOUN
ejpam-5466	141	16	)	)	PUNCT
ejpam-5466	141	17	)	)	PUNCT
ejpam-5466	142	1	=	=	SYM
ejpam-5466	142	2	1	1	NUM
ejpam-5466	142	3	,	,	PUNCT
ejpam-5466	142	4	and	and	CCONJ
ejpam-5466	142	5	from	from	ADP
ejpam-5466	142	6	(	(	PUNCT
ejpam-5466	142	7	ϑ2	ϑ2	PROPN
ejpam-5466	142	8	)	)	PUNCT
ejpam-5466	142	9	,	,	PUNCT
ejpam-5466	142	10	lim	lim	PROPN
ejpam-5466	142	11	n→∞	n→∞	NUM
ejpam-5466	142	12	snd(νn	snd(νn	PROPN
ejpam-5466	142	13	,	,	PUNCT
ejpam-5466	142	14	νn+1	νn+1	NUM
ejpam-5466	142	15	)	)	PUNCT
ejpam-5466	142	16	=	=	SYM
ejpam-5466	143	1	0	0	X
ejpam-5466	143	2	.	.	PUNCT
ejpam-5466	144	1	now	now	ADV
ejpam-5466	144	2	,	,	PUNCT
ejpam-5466	144	3	we	we	PRON
ejpam-5466	144	4	prove	prove	VERB
ejpam-5466	144	5	{	{	PUNCT
ejpam-5466	144	6	νn	νn	AUX
ejpam-5466	144	7	}	}	PUNCT
ejpam-5466	144	8	is	be	AUX
ejpam-5466	144	9	a	a	DET
ejpam-5466	144	10	cauchy	cauchy	ADJ
ejpam-5466	144	11	sequence	sequence	NOUN
ejpam-5466	144	12	,	,	PUNCT
ejpam-5466	144	13	by	by	ADP
ejpam-5466	144	14	(	(	PUNCT
ejpam-5466	144	15	ϑ3	ϑ3	PROPN
ejpam-5466	144	16	)	)	PUNCT
ejpam-5466	144	17	there	there	PRON
ejpam-5466	144	18	exist	exist	VERB
ejpam-5466	144	19	ρ	ρ	PROPN
ejpam-5466	144	20	∈	∈	PROPN
ejpam-5466	144	21	(	(	PUNCT
ejpam-5466	144	22	0	0	NUM
ejpam-5466	144	23	,	,	PUNCT
ejpam-5466	144	24	1	1	NUM
ejpam-5466	144	25	)	)	PUNCT
ejpam-5466	144	26	and	and	CCONJ
ejpam-5466	144	27	χ	χ	PRON
ejpam-5466	144	28	∈	∈	PROPN
ejpam-5466	144	29	(	(	PUNCT
ejpam-5466	144	30	0,+∞	0,+∞	NUM
ejpam-5466	144	31	]	]	X
ejpam-5466	144	32	such	such	ADJ
ejpam-5466	144	33	that	that	SCONJ
ejpam-5466	144	34	lim	lim	PROPN
ejpam-5466	144	35	n→∞	n→∞	PRON
ejpam-5466	144	36	ϑ(snd(νn	ϑ(snd(νn	PROPN
ejpam-5466	144	37	,	,	PUNCT
ejpam-5466	144	38	νn+1))−	νn+1))−	ADJ
ejpam-5466	144	39	1	1	NUM
ejpam-5466	144	40	(	(	PUNCT
ejpam-5466	144	41	snd(νn	snd(νn	NOUN
ejpam-5466	144	42	,	,	PUNCT
ejpam-5466	144	43	νn+1))ρ	νn+1))ρ	NOUN
ejpam-5466	145	1	=	=	SYM
ejpam-5466	145	2	χ	χ	X
ejpam-5466	145	3	.	.	PUNCT
ejpam-5466	146	1	take	take	VERB
ejpam-5466	146	2	δ	δ	PROPN
ejpam-5466	146	3	∈	∈	PROPN
ejpam-5466	146	4	(	(	PUNCT
ejpam-5466	146	5	0	0	NUM
ejpam-5466	146	6	,	,	PUNCT
ejpam-5466	146	7	χ	χ	NOUN
ejpam-5466	146	8	)	)	PUNCT
ejpam-5466	146	9	.	.	PUNCT
ejpam-5466	147	1	by	by	ADP
ejpam-5466	147	2	the	the	DET
ejpam-5466	147	3	definition	definition	NOUN
ejpam-5466	147	4	of	of	ADP
ejpam-5466	147	5	limit	limit	NOUN
ejpam-5466	147	6	,	,	PUNCT
ejpam-5466	147	7	there	there	PRON
ejpam-5466	147	8	exists	exist	VERB
ejpam-5466	147	9	n1	n1	PROPN
ejpam-5466	147	10	∈	∈	PROPN
ejpam-5466	147	11	n	n	PRON
ejpam-5466	147	12	such	such	ADJ
ejpam-5466	147	13	that	that	SCONJ
ejpam-5466	147	14	(	(	PUNCT
ejpam-5466	147	15	snd(νn	snd(νn	NOUN
ejpam-5466	147	16	,	,	PUNCT
ejpam-5466	147	17	νn+1	νn+1	NUM
ejpam-5466	147	18	)	)	PUNCT
ejpam-5466	147	19	)	)	PUNCT
ejpam-5466	148	1	ρ	ρ	PROPN
ejpam-5466	148	2	≤	≤	PROPN
ejpam-5466	148	3	δ−1[θ(snd(νn	δ−1[θ(snd(νn	NOUN
ejpam-5466	148	4	,	,	PUNCT
ejpam-5466	148	5	νn+1))−	νn+1))−	ADJ
ejpam-5466	148	6	1	1	NUM
ejpam-5466	148	7	]	]	PUNCT
ejpam-5466	148	8	,	,	PUNCT
ejpam-5466	148	9	for	for	ADP
ejpam-5466	148	10	all	all	DET
ejpam-5466	148	11	n	n	PRON
ejpam-5466	148	12	≥	≥	NOUN
ejpam-5466	148	13	n1	n1	NOUN
ejpam-5466	148	14	.	.	PUNCT
ejpam-5466	149	1	using	use	VERB
ejpam-5466	149	2	(	(	PUNCT
ejpam-5466	149	3	2.4	2.4	NUM
ejpam-5466	149	4	)	)	PUNCT
ejpam-5466	149	5	and	and	CCONJ
ejpam-5466	149	6	the	the	DET
ejpam-5466	149	7	above	above	ADJ
ejpam-5466	149	8	inequality	inequality	NOUN
ejpam-5466	149	9	,	,	PUNCT
ejpam-5466	149	10	we	we	PRON
ejpam-5466	149	11	deduce	deduce	VERB
ejpam-5466	149	12	n(snd(νn	n(snd(νn	ADJ
ejpam-5466	149	13	,	,	PUNCT
ejpam-5466	149	14	νn+1	νn+1	NUM
ejpam-5466	149	15	)	)	PUNCT
ejpam-5466	149	16	)	)	PUNCT
ejpam-5466	150	1	ρ	ρ	PROPN
ejpam-5466	150	2	≤	≤	NUM
ejpam-5466	150	3	δ−1n([ϑ(d(ν0	δ−1n([ϑ(d(ν0	PROPN
ejpam-5466	150	4	,	,	PUNCT
ejpam-5466	150	5	ν1	ν1	NOUN
ejpam-5466	150	6	)	)	PUNCT
ejpam-5466	150	7	)	)	PUNCT
ejpam-5466	150	8	]	]	PUNCT
ejpam-5466	150	9	δn−n0	δn−n0	NOUN
ejpam-5466	150	10	−	−	NOUN
ejpam-5466	150	11	1	1	NUM
ejpam-5466	150	12	)	)	PUNCT
ejpam-5466	150	13	,	,	PUNCT
ejpam-5466	150	14	for	for	ADP
ejpam-5466	150	15	all	all	DET
ejpam-5466	150	16	n	n	PRON
ejpam-5466	150	17	≥	≥	NOUN
ejpam-5466	150	18	n1	n1	NOUN
ejpam-5466	150	19	.	.	PUNCT
ejpam-5466	151	1	this	this	PRON
ejpam-5466	151	2	implies	imply	VERB
ejpam-5466	151	3	that	that	SCONJ
ejpam-5466	151	4	lim	lim	PROPN
ejpam-5466	151	5	n→∞	n→∞	NUM
ejpam-5466	151	6	n(snd(νn	n(snd(νn	PROPN
ejpam-5466	151	7	,	,	PUNCT
ejpam-5466	151	8	νn+1	νn+1	NUM
ejpam-5466	151	9	)	)	PUNCT
ejpam-5466	151	10	)	)	PUNCT
ejpam-5466	152	1	ρ	ρ	PROPN
ejpam-5466	152	2	=	=	SYM
ejpam-5466	152	3	0	0	PROPN
ejpam-5466	152	4	.	.	PUNCT
ejpam-5466	153	1	thence	thence	NOUN
ejpam-5466	154	1	,	,	PUNCT
ejpam-5466	154	2	there	there	PRON
ejpam-5466	154	3	exists	exist	VERB
ejpam-5466	154	4	n2	n2	PROPN
ejpam-5466	154	5	∈	∈	PROPN
ejpam-5466	154	6	n	n	CCONJ
ejpam-5466	154	7	such	such	ADJ
ejpam-5466	155	1	that	that	SCONJ
ejpam-5466	155	2	snd(νn	snd(νn	NOUN
ejpam-5466	155	3	,	,	PUNCT
ejpam-5466	155	4	νn+1	νn+1	NUM
ejpam-5466	155	5	)	)	PUNCT
ejpam-5466	155	6	≤	≤	NOUN
ejpam-5466	155	7	1	1	NUM
ejpam-5466	155	8	n	n	NUM
ejpam-5466	155	9	1	1	NUM
ejpam-5466	155	10	ρ	ρ	NOUN
ejpam-5466	155	11	,	,	PUNCT
ejpam-5466	155	12	for	for	ADP
ejpam-5466	155	13	all	all	DET
ejpam-5466	155	14	n	n	PRON
ejpam-5466	155	15	≥	≥	NOUN
ejpam-5466	155	16	n2	n2	NOUN
ejpam-5466	155	17	.	.	PUNCT
ejpam-5466	155	18	(	(	PUNCT
ejpam-5466	155	19	2.5	2.5	NUM
ejpam-5466	155	20	)	)	PUNCT
ejpam-5466	155	21	let	let	VERB
ejpam-5466	155	22	m	m	PRON
ejpam-5466	155	23	>	>	X
ejpam-5466	155	24	n	n	CCONJ
ejpam-5466	155	25	≥	≥	NOUN
ejpam-5466	155	26	max{n0	max{n0	PROPN
ejpam-5466	155	27	,	,	PUNCT
ejpam-5466	155	28	n1	n1	NOUN
ejpam-5466	155	29	,	,	PUNCT
ejpam-5466	155	30	n2	n2	ADJ
ejpam-5466	155	31	}	}	PUNCT
ejpam-5466	155	32	.	.	PUNCT
ejpam-5466	156	1	then	then	ADV
ejpam-5466	156	2	,	,	PUNCT
ejpam-5466	156	3	using	use	VERB
ejpam-5466	156	4	the	the	DET
ejpam-5466	156	5	triangular	triangular	NOUN
ejpam-5466	156	6	inequality	inequality	NOUN
ejpam-5466	156	7	and	and	CCONJ
ejpam-5466	156	8	(	(	PUNCT
ejpam-5466	156	9	2.5	2.5	NUM
ejpam-5466	156	10	)	)	PUNCT
ejpam-5466	156	11	,	,	PUNCT
ejpam-5466	156	12	we	we	PRON
ejpam-5466	156	13	have	have	VERB
ejpam-5466	156	14	d(νn	d(νn	NOUN
ejpam-5466	156	15	,	,	PUNCT
ejpam-5466	156	16	νm	νm	NOUN
ejpam-5466	156	17	)	)	PUNCT
ejpam-5466	156	18	≤	≤	NOUN
ejpam-5466	156	19	m−1∑	m−1∑	NUM
ejpam-5466	156	20	j	j	NOUN
ejpam-5466	156	21	=	=	PROPN
ejpam-5466	156	22	n	n	PROPN
ejpam-5466	156	23	d(νj	d(νj	PROPN
ejpam-5466	156	24	,	,	PUNCT
ejpam-5466	156	25	νj+1	νj+1	NUM
ejpam-5466	156	26	)	)	PUNCT
ejpam-5466	156	27	≤	≤	NOUN
ejpam-5466	156	28	m−1∑	m−1∑	NUM
ejpam-5466	156	29	j	j	NOUN
ejpam-5466	156	30	=	=	NOUN
ejpam-5466	156	31	n	n	X
ejpam-5466	156	32	snd(νj	snd(νj	X
ejpam-5466	156	33	,	,	PUNCT
ejpam-5466	156	34	νj+1	νj+1	X
ejpam-5466	156	35	)	)	PUNCT
ejpam-5466	156	36	≤	≤	NOUN
ejpam-5466	156	37	m−1∑	m−1∑	NUM
ejpam-5466	156	38	j	j	NOUN
ejpam-5466	156	39	=	=	PROPN
ejpam-5466	156	40	n	n	PROPN
ejpam-5466	156	41	1	1	NUM
ejpam-5466	156	42	j	j	NOUN
ejpam-5466	156	43	1	1	NUM
ejpam-5466	156	44	p	p	NOUN
ejpam-5466	156	45	≤	≤	NOUN
ejpam-5466	156	46	∞∑	∞∑	NUM
ejpam-5466	156	47	j	j	PROPN
ejpam-5466	156	48	=	=	NOUN
ejpam-5466	156	49	n	n	PROPN
ejpam-5466	156	50	1	1	NUM
ejpam-5466	156	51	j	j	NOUN
ejpam-5466	156	52	1	1	NUM
ejpam-5466	156	53	p	p	NOUN
ejpam-5466	156	54	<	<	X
ejpam-5466	156	55	∞	∞	PROPN
ejpam-5466	156	56	,	,	PUNCT
ejpam-5466	156	57	and	and	CCONJ
ejpam-5466	156	58	so	so	ADV
ejpam-5466	156	59	{	{	PUNCT
ejpam-5466	156	60	νn	νn	AUX
ejpam-5466	156	61	}	}	PUNCT
ejpam-5466	156	62	is	be	AUX
ejpam-5466	156	63	a	a	DET
ejpam-5466	156	64	cauchy	cauchy	ADJ
ejpam-5466	156	65	sequence	sequence	NOUN
ejpam-5466	156	66	.	.	PUNCT
ejpam-5466	157	1	since	since	SCONJ
ejpam-5466	157	2	(	(	PUNCT
ejpam-5466	157	3	x	x	X
ejpam-5466	157	4	,	,	PUNCT
ejpam-5466	157	5	d	d	X
ejpam-5466	157	6	,	,	PUNCT
ejpam-5466	157	7	s	s	PART
ejpam-5466	157	8	)	)	PUNCT
ejpam-5466	157	9	is	be	AUX
ejpam-5466	157	10	complete	complete	ADJ
ejpam-5466	157	11	,	,	PUNCT
ejpam-5466	157	12	so	so	CCONJ
ejpam-5466	157	13	{	{	PUNCT
ejpam-5466	157	14	νn	νn	AUX
ejpam-5466	157	15	}	}	PUNCT
ejpam-5466	157	16	converges	converge	NOUN
ejpam-5466	157	17	to	to	ADP
ejpam-5466	157	18	some	some	DET
ejpam-5466	157	19	ν∗	ν∗	NOUN
ejpam-5466	157	20	∈	∈	PROPN
ejpam-5466	157	21	x.	x.	NOUN
ejpam-5466	158	1	if	if	SCONJ
ejpam-5466	158	2	t	t	PROPN
ejpam-5466	158	3	is	be	AUX
ejpam-5466	158	4	αs	αs	ADJ
ejpam-5466	158	5	-	-	PUNCT
ejpam-5466	158	6	lower	low	ADJ
ejpam-5466	158	7	semi	semi	ADJ
ejpam-5466	158	8	-	-	ADJ
ejpam-5466	158	9	continuous	continuous	ADJ
ejpam-5466	158	10	,	,	PUNCT
ejpam-5466	158	11	then	then	ADV
ejpam-5466	158	12	for	for	ADP
ejpam-5466	158	13	all	all	DET
ejpam-5466	158	14	n	n	DET
ejpam-5466	158	15	∈	∈	PROPN
ejpam-5466	158	16	n	n	CCONJ
ejpam-5466	158	17	,	,	PUNCT
ejpam-5466	158	18	we	we	PRON
ejpam-5466	158	19	have	have	VERB
ejpam-5466	158	20	d(νn	d(νn	NOUN
ejpam-5466	158	21	,	,	PUNCT
ejpam-5466	158	22	t	t	NOUN
ejpam-5466	158	23	νn	νn	NOUN
ejpam-5466	158	24	)	)	PUNCT
ejpam-5466	158	25	≤	≤	NOUN
ejpam-5466	158	26	d(νn	d(νn	NOUN
ejpam-5466	158	27	,	,	PUNCT
ejpam-5466	158	28	νn+1	νn+1	NUM
ejpam-5466	158	29	)	)	PUNCT
ejpam-5466	158	30	.	.	PUNCT
ejpam-5466	159	1	passing	pass	VERB
ejpam-5466	159	2	to	to	ADP
ejpam-5466	159	3	the	the	DET
ejpam-5466	159	4	limit	limit	NOUN
ejpam-5466	159	5	,	,	PUNCT
ejpam-5466	159	6	we	we	PRON
ejpam-5466	159	7	get	get	VERB
ejpam-5466	159	8	lim	lim	PROPN
ejpam-5466	159	9	n→∞	n→∞	X
ejpam-5466	159	10	d(νn	d(νn	NUM
ejpam-5466	159	11	,	,	PUNCT
ejpam-5466	159	12	t	t	NOUN
ejpam-5466	159	13	νn	νn	NOUN
ejpam-5466	159	14	)	)	PUNCT
ejpam-5466	159	15	=	=	SYM
ejpam-5466	160	1	0	0	X
ejpam-5466	160	2	.	.	PUNCT
ejpam-5466	160	3	then	then	ADV
ejpam-5466	160	4	taken	take	VERB
ejpam-5466	160	5	in	in	ADP
ejpam-5466	160	6	the	the	DET
ejpam-5466	160	7	account	account	NOUN
ejpam-5466	160	8	t	t	NOUN
ejpam-5466	160	9	is	be	AUX
ejpam-5466	160	10	αs	αs	ADJ
ejpam-5466	160	11	-	-	PUNCT
ejpam-5466	160	12	lower	low	ADJ
ejpam-5466	160	13	semi	semi	ADJ
ejpam-5466	160	14	-	-	ADJ
ejpam-5466	160	15	continuous	continuous	ADJ
ejpam-5466	160	16	,	,	PUNCT
ejpam-5466	160	17	we	we	PRON
ejpam-5466	160	18	obtain	obtain	VERB
ejpam-5466	160	19	0	0	NUM
ejpam-5466	160	20	<	<	X
ejpam-5466	160	21	d(ν∗	d(ν∗	X
ejpam-5466	160	22	,	,	PUNCT
ejpam-5466	160	23	t	t	PROPN
ejpam-5466	160	24	ν∗	ν∗	PROPN
ejpam-5466	160	25	)	)	PUNCT
ejpam-5466	160	26	≤	≤	PROPN
ejpam-5466	160	27	lim	lim	PROPN
ejpam-5466	160	28	inf	inf	PROPN
ejpam-5466	160	29	n→∞	n→∞	X
ejpam-5466	160	30	d(νn	d(νn	NUM
ejpam-5466	160	31	,	,	PUNCT
ejpam-5466	160	32	t	t	NOUN
ejpam-5466	160	33	νn	νn	NOUN
ejpam-5466	160	34	)	)	PUNCT
ejpam-5466	160	35	=	=	SYM
ejpam-5466	160	36	0	0	NUM
ejpam-5466	160	37	,	,	PUNCT
ejpam-5466	160	38	h.	h.	PROPN
ejpam-5466	160	39	qawaqneh	qawaqneh	PROPN
ejpam-5466	160	40	et	et	PROPN
ejpam-5466	160	41	al	al	PROPN
ejpam-5466	160	42	.	.	PUNCT
ejpam-5466	160	43	/	/	SYM
ejpam-5466	160	44	eur	eur	PROPN
ejpam-5466	160	45	.	.	PUNCT
ejpam-5466	161	1	j.	j.	PROPN
ejpam-5466	161	2	pure	pure	PROPN
ejpam-5466	161	3	appl	appl	PROPN
ejpam-5466	161	4	.	.	PROPN
ejpam-5466	161	5	math	math	PROPN
ejpam-5466	161	6	,	,	PUNCT
ejpam-5466	161	7	17	17	NUM
ejpam-5466	161	8	(	(	PUNCT
ejpam-5466	161	9	4	4	NUM
ejpam-5466	161	10	)	)	PUNCT
ejpam-5466	161	11	(	(	PUNCT
ejpam-5466	161	12	2024	2024	NUM
ejpam-5466	161	13	)	)	PUNCT
ejpam-5466	161	14	,	,	PUNCT
ejpam-5466	161	15	3093	3093	NUM
ejpam-5466	161	16	-	-	SYM
ejpam-5466	161	17	3108	3108	NUM
ejpam-5466	161	18	3100	3100	NUM
ejpam-5466	161	19	which	which	PRON
ejpam-5466	161	20	gives	give	VERB
ejpam-5466	161	21	d(ν∗	d(ν∗	PROPN
ejpam-5466	161	22	,	,	PUNCT
ejpam-5466	161	23	t	t	PROPN
ejpam-5466	161	24	ν∗	ν∗	PROPN
ejpam-5466	161	25	)	)	PUNCT
ejpam-5466	162	1	=	=	SYM
ejpam-5466	162	2	0	0	X
ejpam-5466	162	3	.	.	PUNCT
ejpam-5466	163	1	hence	hence	ADV
ejpam-5466	163	2	,	,	PUNCT
ejpam-5466	163	3	ν∗	ν∗	PROPN
ejpam-5466	163	4	is	be	AUX
ejpam-5466	163	5	a	a	DET
ejpam-5466	163	6	fixed	fix	VERB
ejpam-5466	163	7	point	point	NOUN
ejpam-5466	163	8	of	of	ADP
ejpam-5466	163	9	t	t	PROPN
ejpam-5466	163	10	.	.	PUNCT
ejpam-5466	164	1	if	if	SCONJ
ejpam-5466	164	2	x	x	PRON
ejpam-5466	164	3	is	be	AUX
ejpam-5466	164	4	αs	αs	ADJ
ejpam-5466	164	5	-	-	ADJ
ejpam-5466	164	6	regular	regular	ADJ
ejpam-5466	164	7	,	,	PUNCT
ejpam-5466	164	8	so	so	SCONJ
ejpam-5466	164	9	for	for	SCONJ
ejpam-5466	164	10	every	every	DET
ejpam-5466	164	11	sequence	sequence	NOUN
ejpam-5466	164	12	{	{	PUNCT
ejpam-5466	164	13	νn	νn	AUX
ejpam-5466	164	14	}	}	PUNCT
ejpam-5466	164	15	converges	converge	NOUN
ejpam-5466	164	16	to	to	PART
ejpam-5466	164	17	ν∗	ν∗	VERB
ejpam-5466	164	18	with	with	ADP
ejpam-5466	164	19	α(νn	α(νn	NUM
ejpam-5466	164	20	,	,	PUNCT
ejpam-5466	164	21	νn+1	νn+1	NUM
ejpam-5466	164	22	)	)	PUNCT
ejpam-5466	164	23	≥	≥	NOUN
ejpam-5466	164	24	s2	s2	PROPN
ejpam-5466	164	25	,	,	PUNCT
ejpam-5466	164	26	then	then	ADV
ejpam-5466	164	27	α(νn	α(νn	NUM
ejpam-5466	164	28	,	,	PUNCT
ejpam-5466	164	29	ν	ν	NOUN
ejpam-5466	164	30	∗	∗	NOUN
ejpam-5466	164	31	)	)	PUNCT
ejpam-5466	164	32	≥	≥	NOUN
ejpam-5466	164	33	s2	s2	NOUN
ejpam-5466	164	34	so	so	ADV
ejpam-5466	164	35	d(νn+1	d(νn+1	PROPN
ejpam-5466	164	36	,	,	PUNCT
ejpam-5466	164	37	t	t	PROPN
ejpam-5466	164	38	ν∗	ν∗	PROPN
ejpam-5466	164	39	)	)	PUNCT
ejpam-5466	164	40	>	>	X
ejpam-5466	164	41	0	0	NUM
ejpam-5466	164	42	,	,	PUNCT
ejpam-5466	164	43	which	which	PRON
ejpam-5466	164	44	implies	imply	VERB
ejpam-5466	164	45	h(t	h(t	PROPN
ejpam-5466	164	46	νn	νn	PROPN
ejpam-5466	164	47	,	,	PUNCT
ejpam-5466	164	48	t	t	PROPN
ejpam-5466	164	49	ν∗	ν∗	PROPN
ejpam-5466	164	50	)	)	PUNCT
ejpam-5466	164	51	>	>	X
ejpam-5466	164	52	0	0	NUM
ejpam-5466	164	53	,	,	PUNCT
ejpam-5466	164	54	then	then	ADV
ejpam-5466	164	55	by	by	ADP
ejpam-5466	164	56	(	(	PUNCT
ejpam-5466	164	57	2.1	2.1	NUM
ejpam-5466	164	58	)	)	PUNCT
ejpam-5466	164	59	,	,	PUNCT
ejpam-5466	164	60	we	we	PRON
ejpam-5466	164	61	get	get	VERB
ejpam-5466	164	62	1	1	NUM
ejpam-5466	164	63	<	<	X
ejpam-5466	164	64	ϑ(sd(νn+1	ϑ(sd(νn+1	NOUN
ejpam-5466	164	65	,	,	PUNCT
ejpam-5466	164	66	t	t	PROPN
ejpam-5466	164	67	ν∗	ν∗	PROPN
ejpam-5466	164	68	)	)	PUNCT
ejpam-5466	164	69	)	)	PUNCT
ejpam-5466	164	70	≤	≤	PROPN
ejpam-5466	165	1	ϑ(s3h(t	ϑ(s3h(t	VERB
ejpam-5466	165	2	νn	νn	PROPN
ejpam-5466	165	3	,	,	PUNCT
ejpam-5466	165	4	t	t	PROPN
ejpam-5466	165	5	ν∗	ν∗	PROPN
ejpam-5466	165	6	)	)	PUNCT
ejpam-5466	165	7	≤	≤	NOUN
ejpam-5466	166	1	[	[	X
ejpam-5466	166	2	ϑ(ns(d(ν0	ϑ(ns(d(ν0	PROPN
ejpam-5466	166	3	,	,	PUNCT
ejpam-5466	166	4	ν1	ν1	NOUN
ejpam-5466	166	5	)	)	PUNCT
ejpam-5466	166	6	)	)	PUNCT
ejpam-5466	166	7	)	)	PUNCT
ejpam-5466	166	8	]	]	PUNCT
ejpam-5466	167	1	δn−n0	δn−n0	X
ejpam-5466	167	2	<	<	X
ejpam-5466	167	3	[	[	X
ejpam-5466	167	4	ϑ(d(ν0	ϑ(d(ν0	PROPN
ejpam-5466	167	5	,	,	PUNCT
ejpam-5466	167	6	ν1	ν1	NOUN
ejpam-5466	167	7	)	)	PUNCT
ejpam-5466	167	8	)	)	PUNCT
ejpam-5466	167	9	]	]	PUNCT
ejpam-5466	168	1	δn−n0	δn−n0	NOUN
ejpam-5466	168	2	.	.	PUNCT
ejpam-5466	169	1	passing	pass	VERB
ejpam-5466	169	2	to	to	ADP
ejpam-5466	169	3	the	the	DET
ejpam-5466	169	4	limit	limit	NOUN
ejpam-5466	169	5	,	,	PUNCT
ejpam-5466	169	6	we	we	PRON
ejpam-5466	169	7	have	have	VERB
ejpam-5466	169	8	lim	lim	PROPN
ejpam-5466	169	9	n→∞	n→∞	NUM
ejpam-5466	169	10	ϑ(d(νn+1	ϑ(d(νn+1	PROPN
ejpam-5466	169	11	,	,	PUNCT
ejpam-5466	169	12	t	t	PROPN
ejpam-5466	169	13	ν∗	ν∗	PROPN
ejpam-5466	169	14	)	)	PUNCT
ejpam-5466	169	15	)	)	PUNCT
ejpam-5466	170	1	=	=	SYM
ejpam-5466	170	2	1	1	NUM
ejpam-5466	170	3	,	,	PUNCT
ejpam-5466	170	4	then	then	ADV
ejpam-5466	170	5	(	(	PUNCT
ejpam-5466	170	6	ϑ2	ϑ2	NOUN
ejpam-5466	170	7	)	)	PUNCT
ejpam-5466	170	8	gives	give	VERB
ejpam-5466	170	9	lim	lim	PROPN
ejpam-5466	170	10	n→∞	n→∞	X
ejpam-5466	170	11	d(νn+1	d(νn+1	PROPN
ejpam-5466	170	12	,	,	PUNCT
ejpam-5466	170	13	t	t	PROPN
ejpam-5466	170	14	ν∗	ν∗	PROPN
ejpam-5466	170	15	)	)	PUNCT
ejpam-5466	171	1	=	=	SYM
ejpam-5466	171	2	0	0	NUM
ejpam-5466	171	3	,	,	PUNCT
ejpam-5466	171	4	which	which	PRON
ejpam-5466	171	5	implies	imply	VERB
ejpam-5466	171	6	d(ν∗	d(ν∗	PROPN
ejpam-5466	171	7	,	,	PUNCT
ejpam-5466	171	8	t	t	PROPN
ejpam-5466	171	9	ν∗	ν∗	PROPN
ejpam-5466	171	10	)	)	PUNCT
ejpam-5466	172	1	=	=	SYM
ejpam-5466	172	2	0	0	X
ejpam-5466	172	3	.	.	PUNCT
ejpam-5466	173	1	hence	hence	ADV
ejpam-5466	173	2	ν∗	ν∗	PROPN
ejpam-5466	173	3	is	be	AUX
ejpam-5466	173	4	a	a	DET
ejpam-5466	173	5	fixed	fix	VERB
ejpam-5466	173	6	point	point	NOUN
ejpam-5466	173	7	of	of	ADP
ejpam-5466	173	8	t	t	PROPN
ejpam-5466	173	9	.	.	PUNCT
ejpam-5466	174	1	since	since	SCONJ
ejpam-5466	174	2	each	each	DET
ejpam-5466	174	3	α∗	α∗	NOUN
ejpam-5466	174	4	s	s	PART
ejpam-5466	174	5	-	-	PUNCT
ejpam-5466	174	6	admissible	admissible	ADJ
ejpam-5466	174	7	mapping	mapping	NOUN
ejpam-5466	174	8	is	be	AUX
ejpam-5466	174	9	also	also	ADV
ejpam-5466	174	10	αs	αs	ADJ
ejpam-5466	174	11	-	-	ADJ
ejpam-5466	174	12	admissible	admissible	ADJ
ejpam-5466	174	13	,	,	PUNCT
ejpam-5466	174	14	we	we	PRON
ejpam-5466	174	15	obtain	obtain	VERB
ejpam-5466	174	16	the	the	DET
ejpam-5466	174	17	following	follow	VERB
ejpam-5466	174	18	result	result	NOUN
ejpam-5466	174	19	.	.	PUNCT
ejpam-5466	175	1	corollary	corollary	ADJ
ejpam-5466	175	2	1	1	NUM
ejpam-5466	175	3	.	.	PUNCT
ejpam-5466	176	1	let	let	AUX
ejpam-5466	176	2	(	(	PUNCT
ejpam-5466	176	3	x	x	NOUN
ejpam-5466	176	4	,	,	PUNCT
ejpam-5466	176	5	d	d	X
ejpam-5466	176	6	,	,	PUNCT
ejpam-5466	176	7	s	s	PART
ejpam-5466	176	8	)	)	PUNCT
ejpam-5466	176	9	be	be	AUX
ejpam-5466	176	10	a	a	DET
ejpam-5466	176	11	complete	complete	ADJ
ejpam-5466	176	12	b	b	X
ejpam-5466	176	13	-	-	PUNCT
ejpam-5466	176	14	metric	metric	ADJ
ejpam-5466	176	15	space	space	NOUN
ejpam-5466	176	16	and	and	CCONJ
ejpam-5466	176	17	t	t	NOUN
ejpam-5466	176	18	:	:	PUNCT
ejpam-5466	176	19	x	x	X
ejpam-5466	176	20	→	→	X
ejpam-5466	176	21	cb(x	cb(x	NUM
ejpam-5466	176	22	)	)	PUNCT
ejpam-5466	176	23	be	be	AUX
ejpam-5466	176	24	a	a	DET
ejpam-5466	176	25	multivalued	multivalued	ADJ
ejpam-5466	176	26	almost	almost	ADV
ejpam-5466	176	27	(	(	PUNCT
ejpam-5466	176	28	αs	αs	INTJ
ejpam-5466	176	29	,	,	PUNCT
ejpam-5466	176	30	ϑ	ϑ	NOUN
ejpam-5466	176	31	,	,	PUNCT
ejpam-5466	176	32	κ)-contraction	κ)-contraction	NOUN
ejpam-5466	176	33	of	of	ADP
ejpam-5466	176	34	hardy	hardy	ADJ
ejpam-5466	176	35	-	-	PUNCT
ejpam-5466	176	36	rogers	rogers	NOUN
ejpam-5466	176	37	type	type	NOUN
ejpam-5466	176	38	.	.	PUNCT
ejpam-5466	177	1	assume	assume	VERB
ejpam-5466	177	2	that	that	SCONJ
ejpam-5466	177	3	the	the	DET
ejpam-5466	177	4	following	follow	VERB
ejpam-5466	177	5	conditions	condition	NOUN
ejpam-5466	177	6	are	be	AUX
ejpam-5466	177	7	satisfied	satisfied	ADJ
ejpam-5466	177	8	:	:	PUNCT
ejpam-5466	177	9	(	(	PUNCT
ejpam-5466	177	10	i	i	NOUN
ejpam-5466	177	11	)	)	PUNCT
ejpam-5466	177	12	t	t	PROPN
ejpam-5466	177	13	is	be	AUX
ejpam-5466	177	14	an	an	DET
ejpam-5466	177	15	α∗	α∗	NOUN
ejpam-5466	177	16	s	s	NOUN
ejpam-5466	177	17	-	-	PUNCT
ejpam-5466	177	18	admissible	admissible	ADJ
ejpam-5466	177	19	;	;	PUNCT
ejpam-5466	177	20	(	(	PUNCT
ejpam-5466	177	21	ii	ii	NOUN
ejpam-5466	177	22	)	)	PUNCT
ejpam-5466	177	23	there	there	PRON
ejpam-5466	177	24	exist	exist	VERB
ejpam-5466	177	25	ν0	ν0	PROPN
ejpam-5466	177	26	∈	∈	PROPN
ejpam-5466	177	27	x	x	X
ejpam-5466	177	28	and	and	CCONJ
ejpam-5466	177	29	ν1	ν1	PROPN
ejpam-5466	177	30	∈	∈	PROPN
ejpam-5466	177	31	t	t	NOUN
ejpam-5466	177	32	ν0	ν0	PROPN
ejpam-5466	177	33	such	such	ADJ
ejpam-5466	177	34	that	that	DET
ejpam-5466	177	35	α(ν0	α(ν0	PROPN
ejpam-5466	177	36	,	,	PUNCT
ejpam-5466	177	37	ν1	ν1	PROPN
ejpam-5466	177	38	)	)	PUNCT
ejpam-5466	177	39	≥	≥	NOUN
ejpam-5466	177	40	s2	s2	PROPN
ejpam-5466	177	41	;	;	PUNCT
ejpam-5466	177	42	(	(	PUNCT
ejpam-5466	177	43	iii	iii	X
ejpam-5466	177	44	)	)	PUNCT
ejpam-5466	177	45	t	t	PROPN
ejpam-5466	177	46	is	be	AUX
ejpam-5466	177	47	αs	αs	ADJ
ejpam-5466	177	48	-	-	PUNCT
ejpam-5466	177	49	lower	low	ADJ
ejpam-5466	177	50	semi	semi	ADJ
ejpam-5466	177	51	-	-	ADJ
ejpam-5466	177	52	continuous	continuous	ADJ
ejpam-5466	177	53	,	,	PUNCT
ejpam-5466	177	54	or	or	CCONJ
ejpam-5466	177	55	for	for	ADP
ejpam-5466	177	56	every	every	DET
ejpam-5466	177	57	sequence	sequence	NOUN
ejpam-5466	177	58	{	{	PUNCT
ejpam-5466	177	59	νn	νn	PRON
ejpam-5466	177	60	}	}	PUNCT
ejpam-5466	177	61	⊂	⊂	NOUN
ejpam-5466	177	62	x	x	PRON
ejpam-5466	177	63	converges	converge	VERB
ejpam-5466	177	64	to	to	ADP
ejpam-5466	177	65	some	some	DET
ejpam-5466	177	66	ν∗	ν∗	NOUN
ejpam-5466	177	67	in	in	ADP
ejpam-5466	177	68	x	x	X
ejpam-5466	177	69	and	and	CCONJ
ejpam-5466	177	70	α∗(νn	α∗(νn	NOUN
ejpam-5466	177	71	,	,	PUNCT
ejpam-5466	177	72	νn+1	νn+1	NUM
ejpam-5466	177	73	)	)	PUNCT
ejpam-5466	177	74	≥	≥	NOUN
ejpam-5466	177	75	s2	s2	PROPN
ejpam-5466	177	76	,	,	PUNCT
ejpam-5466	177	77	for	for	ADP
ejpam-5466	177	78	all	all	DET
ejpam-5466	177	79	n	n	PRON
ejpam-5466	177	80	∈	∈	PROPN
ejpam-5466	177	81	n.	n.	NOUN
ejpam-5466	177	82	then	then	ADV
ejpam-5466	177	83	α∗(νn	α∗(νn	NOUN
ejpam-5466	177	84	,	,	PUNCT
ejpam-5466	177	85	ν	ν	X
ejpam-5466	177	86	∗	∗	NOUN
ejpam-5466	177	87	)	)	PUNCT
ejpam-5466	177	88	≥	≥	NUM
ejpam-5466	177	89	s2	s2	PROPN
ejpam-5466	177	90	,	,	PUNCT
ejpam-5466	177	91	for	for	ADP
ejpam-5466	177	92	all	all	DET
ejpam-5466	177	93	n	n	PRON
ejpam-5466	177	94	∈	∈	PROPN
ejpam-5466	177	95	n.	n.	NOUN
ejpam-5466	177	96	then	then	ADV
ejpam-5466	177	97	t	t	PROPN
ejpam-5466	177	98	has	have	VERB
ejpam-5466	177	99	a	a	DET
ejpam-5466	177	100	fixed	fix	VERB
ejpam-5466	177	101	point	point	NOUN
ejpam-5466	177	102	.	.	PUNCT
ejpam-5466	178	1	corollary	corollary	ADJ
ejpam-5466	178	2	2	2	NUM
ejpam-5466	178	3	.	.	PUNCT
ejpam-5466	179	1	let	let	VERB
ejpam-5466	179	2	(	(	PUNCT
ejpam-5466	179	3	x	x	NOUN
ejpam-5466	179	4	,	,	PUNCT
ejpam-5466	179	5	d	d	X
ejpam-5466	179	6	,	,	PUNCT
ejpam-5466	179	7	s	s	PART
ejpam-5466	179	8	)	)	PUNCT
ejpam-5466	179	9	be	be	AUX
ejpam-5466	179	10	a	a	DET
ejpam-5466	179	11	complete	complete	ADJ
ejpam-5466	179	12	b	b	NOUN
ejpam-5466	179	13	-	-	PUNCT
ejpam-5466	179	14	metric	metric	ADJ
ejpam-5466	179	15	space	space	NOUN
ejpam-5466	179	16	,	,	PUNCT
ejpam-5466	179	17	α	α	NOUN
ejpam-5466	179	18	:	:	PUNCT
ejpam-5466	179	19	x×x	x×x	PROPN
ejpam-5466	179	20	→	→	PUNCT
ejpam-5466	180	1	[	[	X
ejpam-5466	180	2	0,+∞	0,+∞	NUM
ejpam-5466	180	3	)	)	PUNCT
ejpam-5466	180	4	be	be	AUX
ejpam-5466	180	5	a	a	DET
ejpam-5466	180	6	function	function	NOUN
ejpam-5466	180	7	and	and	CCONJ
ejpam-5466	180	8	t	t	NOUN
ejpam-5466	180	9	:	:	PUNCT
ejpam-5466	180	10	x	x	X
ejpam-5466	180	11	→	→	X
ejpam-5466	180	12	cb(x	cb(x	NUM
ejpam-5466	180	13	)	)	PUNCT
ejpam-5466	180	14	be	be	AUX
ejpam-5466	180	15	a	a	DET
ejpam-5466	180	16	multivalued	multivalue	VERB
ejpam-5466	180	17	mapping	mapping	NOUN
ejpam-5466	180	18	.	.	PUNCT
ejpam-5466	181	1	assume	assume	VERB
ejpam-5466	181	2	that	that	SCONJ
ejpam-5466	181	3	the	the	DET
ejpam-5466	181	4	following	follow	VERB
ejpam-5466	181	5	conditions	condition	NOUN
ejpam-5466	181	6	are	be	AUX
ejpam-5466	181	7	satisfied	satisfied	ADJ
ejpam-5466	181	8	:	:	PUNCT
ejpam-5466	181	9	(	(	PUNCT
ejpam-5466	181	10	i	i	NOUN
ejpam-5466	181	11	)	)	PUNCT
ejpam-5466	181	12	t	t	PROPN
ejpam-5466	181	13	is	be	AUX
ejpam-5466	181	14	an	an	DET
ejpam-5466	181	15	αs	αs	ADJ
ejpam-5466	181	16	-	-	ADJ
ejpam-5466	181	17	admissible	admissible	ADJ
ejpam-5466	181	18	;	;	PUNCT
ejpam-5466	181	19	(	(	PUNCT
ejpam-5466	181	20	ii	ii	NOUN
ejpam-5466	181	21	)	)	PUNCT
ejpam-5466	181	22	there	there	PRON
ejpam-5466	181	23	exist	exist	VERB
ejpam-5466	181	24	ν0	ν0	PROPN
ejpam-5466	181	25	∈	∈	PROPN
ejpam-5466	181	26	x	x	X
ejpam-5466	181	27	and	and	CCONJ
ejpam-5466	181	28	ν1	ν1	PROPN
ejpam-5466	181	29	∈	∈	PROPN
ejpam-5466	181	30	t	t	NOUN
ejpam-5466	181	31	ν0	ν0	PROPN
ejpam-5466	181	32	such	such	ADJ
ejpam-5466	181	33	that	that	SCONJ
ejpam-5466	181	34	α	α	PROPN
ejpam-5466	181	35	(	(	PUNCT
ejpam-5466	181	36	ν0	ν0	PROPN
ejpam-5466	181	37	,	,	PUNCT
ejpam-5466	181	38	ν1	ν1	PROPN
ejpam-5466	181	39	)	)	PUNCT
ejpam-5466	181	40	≥	≥	NOUN
ejpam-5466	181	41	s2	s2	PROPN
ejpam-5466	181	42	;	;	PUNCT
ejpam-5466	181	43	(	(	PUNCT
ejpam-5466	181	44	iii	iii	X
ejpam-5466	181	45	)	)	PUNCT
ejpam-5466	181	46	t	t	PROPN
ejpam-5466	181	47	is	be	AUX
ejpam-5466	181	48	αs	αs	ADJ
ejpam-5466	181	49	-	-	PUNCT
ejpam-5466	181	50	lower	low	ADJ
ejpam-5466	181	51	semi	semi	ADJ
ejpam-5466	181	52	-	-	ADJ
ejpam-5466	181	53	continuous	continuous	ADJ
ejpam-5466	181	54	,	,	PUNCT
ejpam-5466	181	55	or	or	CCONJ
ejpam-5466	181	56	x	x	NOUN
ejpam-5466	181	57	is	be	AUX
ejpam-5466	181	58	αs	αs	ADJ
ejpam-5466	181	59	-	-	ADJ
ejpam-5466	181	60	regular	regular	ADJ
ejpam-5466	181	61	;	;	PUNCT
ejpam-5466	181	62	(	(	PUNCT
ejpam-5466	181	63	iv	iv	X
ejpam-5466	181	64	)	)	PUNCT
ejpam-5466	181	65	there	there	PRON
ejpam-5466	181	66	exist	exist	VERB
ejpam-5466	181	67	ϑ	ϑ	PRON
ejpam-5466	181	68	∈	∈	PROPN
ejpam-5466	181	69	θs	θ	NOUN
ejpam-5466	181	70	,	,	PUNCT
ejpam-5466	181	71	l	l	PROPN
ejpam-5466	181	72	≥	≥	NOUN
ejpam-5466	181	73	0	0	NUM
ejpam-5466	181	74	and	and	CCONJ
ejpam-5466	181	75	κ	κ	X
ejpam-5466	181	76	:	:	PUNCT
ejpam-5466	181	77	(	(	PUNCT
ejpam-5466	181	78	0,+∞	0,+∞	NUM
ejpam-5466	181	79	)	)	PUNCT
ejpam-5466	181	80	→	→	PUNCT
ejpam-5466	182	1	[	[	X
ejpam-5466	182	2	0	0	NUM
ejpam-5466	182	3	,	,	PUNCT
ejpam-5466	182	4	1	1	NUM
ejpam-5466	182	5	)	)	PUNCT
ejpam-5466	182	6	satisfies	satisfie	NOUN
ejpam-5466	182	7	limω→z+	limω→z+	DET
ejpam-5466	182	8	supκ(ω	supκ(ω	NOUN
ejpam-5466	182	9	)	)	PUNCT
ejpam-5466	182	10	<	<	X
ejpam-5466	182	11	1	1	NUM
ejpam-5466	182	12	for	for	ADP
ejpam-5466	182	13	all	all	DET
ejpam-5466	182	14	z	z	NOUN
ejpam-5466	182	15	∈	∈	PROPN
ejpam-5466	182	16	(	(	PUNCT
ejpam-5466	182	17	0,+∞	0,+∞	NUM
ejpam-5466	182	18	)	)	PUNCT
ejpam-5466	182	19	and	and	CCONJ
ejpam-5466	182	20	nonnegative	nonnegative	VERB
ejpam-5466	182	21	real	real	ADJ
ejpam-5466	182	22	numbers	number	NOUN
ejpam-5466	182	23	a1	a1	PROPN
ejpam-5466	182	24	,	,	PUNCT
ejpam-5466	182	25	a2	a2	PROPN
ejpam-5466	182	26	,	,	PUNCT
ejpam-5466	182	27	a3	a3	NOUN
ejpam-5466	182	28	,	,	PUNCT
ejpam-5466	182	29	a4	a4	PROPN
ejpam-5466	182	30	,	,	PUNCT
ejpam-5466	182	31	a5	a5	VERB
ejpam-5466	182	32	with	with	ADP
ejpam-5466	182	33	a1	a1	NOUN
ejpam-5466	182	34	+	+	CCONJ
ejpam-5466	182	35	a2	a2	PROPN
ejpam-5466	182	36	+	+	CCONJ
ejpam-5466	182	37	a3	a3	NOUN
ejpam-5466	182	38	+	+	CCONJ
ejpam-5466	182	39	2sa4	2sa4	NUM
ejpam-5466	182	40	=	=	SYM
ejpam-5466	182	41	1	1	NUM
ejpam-5466	182	42	,	,	PUNCT
ejpam-5466	182	43	and	and	CCONJ
ejpam-5466	182	44	a3	a3	VERB
ejpam-5466	182	45	̸=	̸=	PROPN
ejpam-5466	182	46	1	1	NUM
ejpam-5466	182	47	such	such	ADJ
ejpam-5466	182	48	that	that	SCONJ
ejpam-5466	182	49	ϑ(s3α(ν	ϑ(s3α(ν	PROPN
ejpam-5466	182	50	,	,	PUNCT
ejpam-5466	182	51	µ)h(t	µ)h(t	VERB
ejpam-5466	182	52	ν	ν	PROPN
ejpam-5466	182	53	,	,	PUNCT
ejpam-5466	182	54	t	t	PROPN
ejpam-5466	182	55	µ	µ	NUM
ejpam-5466	182	56	)	)	PUNCT
ejpam-5466	182	57	)	)	PUNCT
ejpam-5466	182	58	≤	≤	NOUN
ejpam-5466	182	59	[	[	PUNCT
ejpam-5466	182	60	ϑ(ns(ν	ϑ(ns(ν	PROPN
ejpam-5466	182	61	,	,	PUNCT
ejpam-5466	182	62	µ	µ	NOUN
ejpam-5466	182	63	)	)	PUNCT
ejpam-5466	182	64	)	)	PUNCT
ejpam-5466	182	65	)	)	PUNCT
ejpam-5466	182	66	)	)	PUNCT
ejpam-5466	182	67	]	]	PUNCT
ejpam-5466	182	68	κ(d(ν,µ	κ(d(ν,µ	X
ejpam-5466	182	69	)	)	PUNCT
ejpam-5466	183	1	+	+	CCONJ
ejpam-5466	183	2	lmin{d(ν	lmin{d(ν	PROPN
ejpam-5466	183	3	,	,	PUNCT
ejpam-5466	183	4	t	t	PROPN
ejpam-5466	183	5	µ	µ	NUM
ejpam-5466	183	6	)	)	PUNCT
ejpam-5466	183	7	,	,	PUNCT
ejpam-5466	183	8	d(µ	d(µ	PROPN
ejpam-5466	183	9	,	,	PUNCT
ejpam-5466	183	10	t	t	NOUN
ejpam-5466	183	11	ν	ν	PROPN
ejpam-5466	183	12	)	)	PUNCT
ejpam-5466	183	13	}	}	PUNCT
ejpam-5466	183	14	,	,	PUNCT
ejpam-5466	183	15	for	for	ADP
ejpam-5466	183	16	all	all	DET
ejpam-5466	183	17	ν	ν	NOUN
ejpam-5466	183	18	,	,	PUNCT
ejpam-5466	183	19	µ	µ	X
ejpam-5466	183	20	∈	∈	NOUN
ejpam-5466	183	21	x	x	PUNCT
ejpam-5466	183	22	with	with	ADP
ejpam-5466	183	23	h(t	h(t	PROPN
ejpam-5466	183	24	ν	ν	PROPN
ejpam-5466	183	25	,	,	PUNCT
ejpam-5466	183	26	t	t	PROPN
ejpam-5466	183	27	µ	µ	NUM
ejpam-5466	183	28	)	)	PUNCT
ejpam-5466	183	29	>	>	X
ejpam-5466	183	30	0	0	NUM
ejpam-5466	183	31	,	,	PUNCT
ejpam-5466	183	32	where	where	SCONJ
ejpam-5466	183	33	ns(ν	ns(ν	NUM
ejpam-5466	183	34	,	,	PUNCT
ejpam-5466	183	35	µ	µ	NOUN
ejpam-5466	183	36	)	)	PUNCT
ejpam-5466	183	37	=	=	SYM
ejpam-5466	183	38	a1d(ν	a1d(ν	PROPN
ejpam-5466	183	39	,	,	PUNCT
ejpam-5466	183	40	µ	µ	NOUN
ejpam-5466	183	41	)	)	PUNCT
ejpam-5466	183	42	+	+	SYM
ejpam-5466	183	43	a2d(ν	a2d(ν	PROPN
ejpam-5466	183	44	,	,	PUNCT
ejpam-5466	183	45	t	t	NOUN
ejpam-5466	183	46	ν	ν	PROPN
ejpam-5466	183	47	)	)	PUNCT
ejpam-5466	184	1	+	+	CCONJ
ejpam-5466	184	2	a3d(µ	a3d(µ	PROPN
ejpam-5466	184	3	,	,	PUNCT
ejpam-5466	184	4	t	t	PROPN
ejpam-5466	184	5	µ	µ	NUM
ejpam-5466	184	6	)	)	PUNCT
ejpam-5466	184	7	+	+	CCONJ
ejpam-5466	185	1	a4d(ν	a4d(ν	PROPN
ejpam-5466	185	2	,	,	PUNCT
ejpam-5466	185	3	t	t	PROPN
ejpam-5466	185	4	µ	µ	NUM
ejpam-5466	185	5	)	)	PUNCT
ejpam-5466	185	6	+	+	CCONJ
ejpam-5466	185	7	a5d(µ	a5d(µ	PROPN
ejpam-5466	185	8	,	,	PUNCT
ejpam-5466	185	9	t	t	NOUN
ejpam-5466	185	10	ν	ν	NOUN
ejpam-5466	185	11	)	)	PUNCT
ejpam-5466	185	12	.	.	PUNCT
ejpam-5466	186	1	h.	h.	PROPN
ejpam-5466	186	2	qawaqneh	qawaqneh	PROPN
ejpam-5466	186	3	et	et	PROPN
ejpam-5466	186	4	al	al	PROPN
ejpam-5466	186	5	.	.	PUNCT
ejpam-5466	186	6	/	/	SYM
ejpam-5466	186	7	eur	eur	PROPN
ejpam-5466	186	8	.	.	PUNCT
ejpam-5466	187	1	j.	j.	PROPN
ejpam-5466	187	2	pure	pure	PROPN
ejpam-5466	187	3	appl	appl	PROPN
ejpam-5466	187	4	.	.	PROPN
ejpam-5466	187	5	math	math	PROPN
ejpam-5466	187	6	,	,	PUNCT
ejpam-5466	187	7	17	17	NUM
ejpam-5466	187	8	(	(	PUNCT
ejpam-5466	187	9	4	4	NUM
ejpam-5466	187	10	)	)	PUNCT
ejpam-5466	187	11	(	(	PUNCT
ejpam-5466	187	12	2024	2024	NUM
ejpam-5466	187	13	)	)	PUNCT
ejpam-5466	187	14	,	,	PUNCT
ejpam-5466	187	15	3093	3093	NUM
ejpam-5466	187	16	-	-	SYM
ejpam-5466	187	17	3108	3108	NUM
ejpam-5466	187	18	3101	3101	NUM
ejpam-5466	187	19	then	then	ADV
ejpam-5466	187	20	t	t	PROPN
ejpam-5466	187	21	has	have	VERB
ejpam-5466	187	22	a	a	DET
ejpam-5466	187	23	fixed	fix	VERB
ejpam-5466	187	24	point	point	NOUN
ejpam-5466	187	25	.	.	PUNCT
ejpam-5466	188	1	proof	proof	NOUN
ejpam-5466	188	2	.	.	PUNCT
ejpam-5466	189	1	for	for	ADP
ejpam-5466	189	2	all	all	DET
ejpam-5466	189	3	ν	ν	NOUN
ejpam-5466	189	4	,	,	PUNCT
ejpam-5466	189	5	µ	µ	X
ejpam-5466	189	6	∈	∈	X
ejpam-5466	189	7	x	x	X
ejpam-5466	189	8	,	,	PUNCT
ejpam-5466	189	9	we	we	PRON
ejpam-5466	189	10	have	have	VERB
ejpam-5466	189	11	h(t	h(t	PROPN
ejpam-5466	189	12	ν	ν	PROPN
ejpam-5466	189	13	,	,	PUNCT
ejpam-5466	189	14	t	t	PROPN
ejpam-5466	189	15	µ	µ	NOUN
ejpam-5466	189	16	)	)	PUNCT
ejpam-5466	189	17	≤	≤	NOUN
ejpam-5466	189	18	α(ν	α(ν	PROPN
ejpam-5466	189	19	,	,	PUNCT
ejpam-5466	189	20	µ)h(t	µ)h(t	VERB
ejpam-5466	189	21	ν	ν	PROPN
ejpam-5466	189	22	,	,	PUNCT
ejpam-5466	189	23	t	t	PROPN
ejpam-5466	189	24	µ	µ	NUM
ejpam-5466	189	25	)	)	PUNCT
ejpam-5466	189	26	,	,	PUNCT
ejpam-5466	189	27	since	since	SCONJ
ejpam-5466	189	28	ϑ	ϑ	NOUN
ejpam-5466	189	29	is	be	AUX
ejpam-5466	189	30	increasing	increase	VERB
ejpam-5466	189	31	function	function	NOUN
ejpam-5466	189	32	,	,	PUNCT
ejpam-5466	189	33	we	we	PRON
ejpam-5466	189	34	get	get	VERB
ejpam-5466	189	35	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	189	36	ν	ν	PROPN
ejpam-5466	189	37	,	,	PUNCT
ejpam-5466	189	38	t	t	PROPN
ejpam-5466	189	39	µ	µ	NUM
ejpam-5466	189	40	)	)	PUNCT
ejpam-5466	189	41	)	)	PUNCT
ejpam-5466	190	1	≤	≤	PROPN
ejpam-5466	190	2	ϑ(s3α(ν	ϑ(s3α(ν	PROPN
ejpam-5466	190	3	,	,	PUNCT
ejpam-5466	190	4	µ)h(t	µ)h(t	VERB
ejpam-5466	190	5	ν	ν	PROPN
ejpam-5466	190	6	,	,	PUNCT
ejpam-5466	190	7	t	t	PROPN
ejpam-5466	190	8	µ	µ	NUM
ejpam-5466	190	9	)	)	PUNCT
ejpam-5466	190	10	)	)	PUNCT
ejpam-5466	190	11	≤	≤	NOUN
ejpam-5466	190	12	[	[	PUNCT
ejpam-5466	190	13	ϑ(ns(ν	ϑ(ns(ν	PROPN
ejpam-5466	190	14	,	,	PUNCT
ejpam-5466	190	15	µ	µ	NOUN
ejpam-5466	190	16	)	)	PUNCT
ejpam-5466	190	17	)	)	PUNCT
ejpam-5466	190	18	)	)	PUNCT
ejpam-5466	190	19	)	)	PUNCT
ejpam-5466	190	20	]	]	PUNCT
ejpam-5466	190	21	κ(d(ν,µ	κ(d(ν,µ	X
ejpam-5466	190	22	)	)	PUNCT
ejpam-5466	191	1	+	+	CCONJ
ejpam-5466	191	2	lmin{d(ν	lmin{d(ν	PROPN
ejpam-5466	191	3	,	,	PUNCT
ejpam-5466	191	4	t	t	PROPN
ejpam-5466	191	5	µ	µ	NUM
ejpam-5466	191	6	)	)	PUNCT
ejpam-5466	191	7	,	,	PUNCT
ejpam-5466	191	8	d(µ	d(µ	PROPN
ejpam-5466	191	9	,	,	PUNCT
ejpam-5466	191	10	t	t	NOUN
ejpam-5466	191	11	ν	ν	PROPN
ejpam-5466	191	12	)	)	PUNCT
ejpam-5466	191	13	}	}	PUNCT
ejpam-5466	191	14	.	.	PUNCT
ejpam-5466	192	1	so	so	ADV
ejpam-5466	192	2	this	this	DET
ejpam-5466	192	3	result	result	NOUN
ejpam-5466	192	4	is	be	AUX
ejpam-5466	192	5	a	a	DET
ejpam-5466	192	6	consequence	consequence	NOUN
ejpam-5466	192	7	of	of	ADP
ejpam-5466	192	8	theorem	theorem	ADJ
ejpam-5466	192	9	1	1	NUM
ejpam-5466	192	10	.	.	PUNCT
ejpam-5466	192	11	corollary	corollary	ADJ
ejpam-5466	192	12	3	3	X
ejpam-5466	192	13	.	.	PUNCT
ejpam-5466	193	1	let	let	VERB
ejpam-5466	193	2	(	(	PUNCT
ejpam-5466	193	3	x	x	NOUN
ejpam-5466	193	4	,	,	PUNCT
ejpam-5466	193	5	d	d	X
ejpam-5466	193	6	,	,	PUNCT
ejpam-5466	193	7	s	s	PART
ejpam-5466	193	8	)	)	PUNCT
ejpam-5466	193	9	be	be	AUX
ejpam-5466	193	10	a	a	DET
ejpam-5466	193	11	complete	complete	ADJ
ejpam-5466	193	12	b	b	NOUN
ejpam-5466	193	13	-	-	PUNCT
ejpam-5466	193	14	metric	metric	ADJ
ejpam-5466	193	15	space	space	NOUN
ejpam-5466	193	16	,	,	PUNCT
ejpam-5466	193	17	α	α	NOUN
ejpam-5466	193	18	:	:	PUNCT
ejpam-5466	193	19	x×x	x×x	PROPN
ejpam-5466	193	20	→	→	PUNCT
ejpam-5466	194	1	[	[	X
ejpam-5466	194	2	0,+∞	0,+∞	NUM
ejpam-5466	194	3	)	)	PUNCT
ejpam-5466	194	4	be	be	AUX
ejpam-5466	194	5	a	a	DET
ejpam-5466	194	6	function	function	NOUN
ejpam-5466	194	7	and	and	CCONJ
ejpam-5466	194	8	t	t	NOUN
ejpam-5466	194	9	:	:	PUNCT
ejpam-5466	194	10	x	x	X
ejpam-5466	194	11	→	→	X
ejpam-5466	194	12	cb(x	cb(x	NUM
ejpam-5466	194	13	)	)	PUNCT
ejpam-5466	194	14	be	be	AUX
ejpam-5466	194	15	a	a	DET
ejpam-5466	194	16	multivalued	multivalue	VERB
ejpam-5466	194	17	mapping	mapping	NOUN
ejpam-5466	194	18	.	.	PUNCT
ejpam-5466	195	1	assume	assume	VERB
ejpam-5466	195	2	that	that	SCONJ
ejpam-5466	195	3	the	the	DET
ejpam-5466	195	4	following	follow	VERB
ejpam-5466	195	5	conditions	condition	NOUN
ejpam-5466	195	6	hold	hold	VERB
ejpam-5466	195	7	:	:	PUNCT
ejpam-5466	195	8	(	(	PUNCT
ejpam-5466	195	9	i	i	NOUN
ejpam-5466	195	10	)	)	PUNCT
ejpam-5466	195	11	t	t	PROPN
ejpam-5466	195	12	is	be	AUX
ejpam-5466	195	13	almost	almost	ADV
ejpam-5466	195	14	(	(	PUNCT
ejpam-5466	195	15	ϑ	ϑ	X
ejpam-5466	195	16	,	,	PUNCT
ejpam-5466	195	17	κ)-contraction	κ)-contraction	NOUN
ejpam-5466	195	18	of	of	ADP
ejpam-5466	195	19	hardy	hardy	ADJ
ejpam-5466	195	20	rogers	roger	NOUN
ejpam-5466	195	21	type	type	NOUN
ejpam-5466	195	22	.	.	PUNCT
ejpam-5466	196	1	(	(	PUNCT
ejpam-5466	196	2	i	i	NOUN
ejpam-5466	196	3	)	)	PUNCT
ejpam-5466	196	4	t	t	PROPN
ejpam-5466	196	5	is	be	AUX
ejpam-5466	196	6	lower	low	ADJ
ejpam-5466	196	7	semi	semi	ADV
ejpam-5466	196	8	continuous	continuous	ADJ
ejpam-5466	196	9	.	.	PUNCT
ejpam-5466	197	1	then	then	ADV
ejpam-5466	197	2	t	t	PROPN
ejpam-5466	197	3	has	have	VERB
ejpam-5466	197	4	a	a	DET
ejpam-5466	197	5	fixed	fix	VERB
ejpam-5466	197	6	point	point	NOUN
ejpam-5466	197	7	.	.	PUNCT
ejpam-5466	198	1	proof	proof	NOUN
ejpam-5466	198	2	.	.	PUNCT
ejpam-5466	199	1	it	it	PRON
ejpam-5466	199	2	suffices	suffice	VERB
ejpam-5466	199	3	to	to	PART
ejpam-5466	199	4	take	take	VERB
ejpam-5466	199	5	α(ν	α(ν	PROPN
ejpam-5466	199	6	,	,	PUNCT
ejpam-5466	199	7	µ	µ	NOUN
ejpam-5466	199	8	)	)	PUNCT
ejpam-5466	199	9	=	=	SYM
ejpam-5466	199	10	s2	s2	NOUN
ejpam-5466	199	11	for	for	ADP
ejpam-5466	199	12	all	all	DET
ejpam-5466	199	13	ν	ν	NOUN
ejpam-5466	199	14	,	,	PUNCT
ejpam-5466	199	15	µ	µ	X
ejpam-5466	199	16	∈	∈	NOUN
ejpam-5466	199	17	x	x	PUNCT
ejpam-5466	199	18	in	in	ADP
ejpam-5466	199	19	theorem1	theorem1	PROPN
ejpam-5466	199	20	.	.	PUNCT
ejpam-5466	199	21	example	example	NOUN
ejpam-5466	200	1	2	2	NUM
ejpam-5466	200	2	.	.	PUNCT
ejpam-5466	200	3	let	let	VERB
ejpam-5466	200	4	x	x	PUNCT
ejpam-5466	200	5	=	=	PUNCT
ejpam-5466	201	1	[	[	X
ejpam-5466	201	2	0	0	NUM
ejpam-5466	201	3	,	,	PUNCT
ejpam-5466	201	4	2	2	NUM
ejpam-5466	201	5	]	]	PUNCT
ejpam-5466	201	6	be	be	AUX
ejpam-5466	201	7	a	a	DET
ejpam-5466	201	8	set	set	NOUN
ejpam-5466	201	9	endowed	endow	VERB
ejpam-5466	201	10	with	with	ADP
ejpam-5466	201	11	a	a	DET
ejpam-5466	201	12	b	b	NOUN
ejpam-5466	201	13	-	-	PUNCT
ejpam-5466	201	14	metric	metric	ADJ
ejpam-5466	201	15	d(ν1	d(ν1	NOUN
ejpam-5466	201	16	,	,	PUNCT
ejpam-5466	201	17	ν2	ν2	NOUN
ejpam-5466	201	18	)	)	PUNCT
ejpam-5466	201	19	=	=	SYM
ejpam-5466	202	1	|ν1−ν2|2	|ν1−ν2|2	PROPN
ejpam-5466	202	2	.	.	PUNCT
ejpam-5466	203	1	define	define	VERB
ejpam-5466	203	2	t	t	NOUN
ejpam-5466	203	3	:	:	PUNCT
ejpam-5466	203	4	x	x	SYM
ejpam-5466	203	5	→	→	X
ejpam-5466	203	6	cb(x	cb(x	NUM
ejpam-5466	203	7	)	)	PUNCT
ejpam-5466	203	8	and	and	CCONJ
ejpam-5466	203	9	α	α	NOUN
ejpam-5466	203	10	:	:	PUNCT
ejpam-5466	204	1	x×x	x×x	PROPN
ejpam-5466	204	2	→	→	PUNCT
ejpam-5466	204	3	[	[	X
ejpam-5466	204	4	0,∞	0,∞	NOUN
ejpam-5466	204	5	)	)	PUNCT
ejpam-5466	204	6	by	by	ADP
ejpam-5466	204	7	t	t	NOUN
ejpam-5466	204	8	ν	ν	X
ejpam-5466	204	9	=	=	PUNCT
ejpam-5466	204	10	{	{	PUNCT
ejpam-5466	205	1	[	[	X
ejpam-5466	205	2	0	0	NUM
ejpam-5466	205	3	,	,	PUNCT
ejpam-5466	205	4	ν4	ν4	PROPN
ejpam-5466	205	5	]	]	PUNCT
ejpam-5466	205	6	,	,	PUNCT
ejpam-5466	205	7	ν	ν	PROPN
ejpam-5466	205	8	∈	∈	PROPN
ejpam-5466	206	1	[	[	X
ejpam-5466	206	2	0	0	NUM
ejpam-5466	206	3	,	,	PUNCT
ejpam-5466	206	4	2	2	NUM
ejpam-5466	206	5	)	)	PUNCT
ejpam-5466	206	6	{	{	PUNCT
ejpam-5466	206	7	2	2	NUM
ejpam-5466	206	8	}	}	PUNCT
ejpam-5466	206	9	,	,	PUNCT
ejpam-5466	206	10	ν	ν	X
ejpam-5466	206	11	=	=	SYM
ejpam-5466	206	12	2	2	NUM
ejpam-5466	206	13	and	and	CCONJ
ejpam-5466	206	14	α(ν	α(ν	PROPN
ejpam-5466	206	15	,	,	PUNCT
ejpam-5466	206	16	µ	µ	NOUN
ejpam-5466	206	17	)	)	PUNCT
ejpam-5466	207	1	=	=	NOUN
ejpam-5466	207	2	{	{	PUNCT
ejpam-5466	207	3	4	4	NUM
ejpam-5466	207	4	,	,	PUNCT
ejpam-5466	207	5	(	(	PUNCT
ejpam-5466	207	6	ν	ν	X
ejpam-5466	207	7	,	,	PUNCT
ejpam-5466	207	8	µ	µ	NOUN
ejpam-5466	207	9	)	)	PUNCT
ejpam-5466	207	10	∈	∈	PROPN
ejpam-5466	208	1	[	[	X
ejpam-5466	208	2	0	0	NUM
ejpam-5466	208	3	,	,	PUNCT
ejpam-5466	208	4	2	2	NUM
ejpam-5466	208	5	)	)	PUNCT
ejpam-5466	208	6	0	0	NUM
ejpam-5466	208	7	,	,	PUNCT
ejpam-5466	208	8	otherwise	otherwise	ADV
ejpam-5466	208	9	.	.	PUNCT
ejpam-5466	209	1	taking	take	VERB
ejpam-5466	209	2	ϑ(ω	ϑ(ω	ADV
ejpam-5466	209	3	)	)	PUNCT
ejpam-5466	209	4	=	=	SYM
ejpam-5466	209	5	eω	eω	PROPN
ejpam-5466	209	6	,	,	PUNCT
ejpam-5466	209	7	κ	κ	PROPN
ejpam-5466	209	8	=	=	SYM
ejpam-5466	209	9	3/4	3/4	NUM
ejpam-5466	209	10	,	,	PUNCT
ejpam-5466	209	11	s	s	PART
ejpam-5466	209	12	=	=	SYM
ejpam-5466	209	13	2	2	NUM
ejpam-5466	209	14	,	,	PUNCT
ejpam-5466	209	15	a1	a1	NOUN
ejpam-5466	209	16	=	=	NOUN
ejpam-5466	209	17	4	4	NUM
ejpam-5466	209	18	5	5	NUM
ejpam-5466	209	19	,	,	PUNCT
ejpam-5466	209	20	a2	a2	NOUN
ejpam-5466	209	21	=	=	SYM
ejpam-5466	209	22	a4	a4	PROPN
ejpam-5466	209	23	=	=	SYM
ejpam-5466	209	24	a5	a5	NOUN
ejpam-5466	209	25	=	=	SYM
ejpam-5466	209	26	0	0	NUM
ejpam-5466	209	27	and	and	CCONJ
ejpam-5466	209	28	a3	a3	NOUN
ejpam-5466	209	29	=	=	SYM
ejpam-5466	209	30	1/8	1/8	NUM
ejpam-5466	209	31	.	.	PUNCT
ejpam-5466	210	1	for	for	ADP
ejpam-5466	210	2	all	all	DET
ejpam-5466	210	3	ν	ν	PROPN
ejpam-5466	210	4	,	,	PUNCT
ejpam-5466	210	5	µ	µ	X
ejpam-5466	210	6	∈	∈	NOUN
ejpam-5466	210	7	(	(	PUNCT
ejpam-5466	210	8	0	0	NUM
ejpam-5466	210	9	,	,	PUNCT
ejpam-5466	210	10	2	2	NUM
ejpam-5466	210	11	)	)	PUNCT
ejpam-5466	210	12	,	,	PUNCT
ejpam-5466	210	13	we	we	PRON
ejpam-5466	210	14	have	have	VERB
ejpam-5466	210	15	α(ν	α(ν	PROPN
ejpam-5466	210	16	,	,	PUNCT
ejpam-5466	210	17	µ	µ	NOUN
ejpam-5466	210	18	)	)	PUNCT
ejpam-5466	210	19	=	=	SYM
ejpam-5466	210	20	4	4	NUM
ejpam-5466	210	21	,	,	PUNCT
ejpam-5466	210	22	h(t	h(t	PROPN
ejpam-5466	210	23	ν	ν	PROPN
ejpam-5466	210	24	,	,	PUNCT
ejpam-5466	210	25	t	t	PROPN
ejpam-5466	210	26	µ	µ	NUM
ejpam-5466	210	27	)	)	PUNCT
ejpam-5466	210	28	>	>	X
ejpam-5466	210	29	|ν−µ	|ν−µ	PROPN
ejpam-5466	210	30	4	4	NUM
ejpam-5466	210	31	|2	|2	NUM
ejpam-5466	210	32	>	>	X
ejpam-5466	210	33	0	0	PUNCT
ejpam-5466	210	34	and	and	CCONJ
ejpam-5466	210	35	d(ν	d(ν	PROPN
ejpam-5466	210	36	,	,	PUNCT
ejpam-5466	210	37	µ	µ	NOUN
ejpam-5466	210	38	)	)	PUNCT
ejpam-5466	210	39	=	=	SYM
ejpam-5466	210	40	|ν	|ν	NOUN
ejpam-5466	210	41	−	−	NOUN
ejpam-5466	210	42	µ|2	µ|2	PROPN
ejpam-5466	210	43	.	.	PROPN
ejpam-5466	211	1	then	then	ADV
ejpam-5466	211	2	8h(t	8h(t	NUM
ejpam-5466	211	3	ν	ν	NOUN
ejpam-5466	211	4	,	,	PUNCT
ejpam-5466	211	5	t	t	PROPN
ejpam-5466	211	6	µ	µ	NUM
ejpam-5466	211	7	)	)	PUNCT
ejpam-5466	211	8	=	=	SYM
ejpam-5466	211	9	1	1	NUM
ejpam-5466	211	10	2	2	NUM
ejpam-5466	211	11	|ν	|ν	NOUN
ejpam-5466	211	12	−	−	NOUN
ejpam-5466	211	13	µ|2	µ|2	NOUN
ejpam-5466	211	14	≤	≤	ADJ
ejpam-5466	211	15	3	3	NUM
ejpam-5466	211	16	4	4	NUM
ejpam-5466	211	17	|ν	|ν	NOUN
ejpam-5466	211	18	−	−	NOUN
ejpam-5466	211	19	µ|2	µ|2	NOUN
ejpam-5466	211	20	≤	≤	ADV
ejpam-5466	211	21	3	3	NUM
ejpam-5466	211	22	4	4	NUM
ejpam-5466	211	23	ns(ν	ns(ν	NUM
ejpam-5466	211	24	,	,	PUNCT
ejpam-5466	211	25	µ	µ	NOUN
ejpam-5466	211	26	)	)	PUNCT
ejpam-5466	211	27	,	,	PUNCT
ejpam-5466	211	28	which	which	PRON
ejpam-5466	211	29	implies	imply	VERB
ejpam-5466	211	30	that	that	SCONJ
ejpam-5466	211	31	e8h(t	e8h(t	PROPN
ejpam-5466	211	32	ν	ν	PROPN
ejpam-5466	211	33	,	,	PUNCT
ejpam-5466	211	34	t	t	PROPN
ejpam-5466	211	35	µ	µ	NOUN
ejpam-5466	211	36	)	)	PUNCT
ejpam-5466	211	37	≤	≤	NUM
ejpam-5466	211	38	e	e	X
ejpam-5466	211	39	9	9	NUM
ejpam-5466	211	40	16	16	NUM
ejpam-5466	211	41	d(ν,µ	d(ν,µ	NUM
ejpam-5466	211	42	)	)	PUNCT
ejpam-5466	211	43	≤	≤	NUM
ejpam-5466	211	44	e	e	NOUN
ejpam-5466	211	45	9	9	NUM
ejpam-5466	211	46	16	16	NUM
ejpam-5466	211	47	ns(ν,µ	ns(ν,µ	NOUN
ejpam-5466	211	48	)	)	PUNCT
ejpam-5466	211	49	.	.	PUNCT
ejpam-5466	212	1	t	t	PROPN
ejpam-5466	212	2	is	be	AUX
ejpam-5466	212	3	α	α	PRON
ejpam-5466	212	4	-	-	ADJ
ejpam-5466	212	5	continuous	continuous	ADJ
ejpam-5466	212	6	,	,	PUNCT
ejpam-5466	212	7	since	since	SCONJ
ejpam-5466	212	8	if	if	SCONJ
ejpam-5466	212	9	(	(	PUNCT
ejpam-5466	212	10	νn	νn	X
ejpam-5466	212	11	)	)	PUNCT
ejpam-5466	212	12	is	be	AUX
ejpam-5466	212	13	a	a	DET
ejpam-5466	212	14	sequence	sequence	NOUN
ejpam-5466	212	15	in	in	ADP
ejpam-5466	212	16	x	x	PUNCT
ejpam-5466	212	17	converges	converge	NOUN
ejpam-5466	212	18	to	to	PART
ejpam-5466	212	19	ν∗	ν∗	VERB
ejpam-5466	212	20	with	with	ADP
ejpam-5466	212	21	α(νn	α(νn	NUM
ejpam-5466	212	22	,	,	PUNCT
ejpam-5466	212	23	νn+1	νn+1	NUM
ejpam-5466	212	24	)	)	PUNCT
ejpam-5466	212	25	≥	≥	NOUN
ejpam-5466	212	26	4	4	NUM
ejpam-5466	212	27	,	,	PUNCT
ejpam-5466	212	28	then	then	ADV
ejpam-5466	212	29	(	(	PUNCT
ejpam-5466	212	30	νn	νn	X
ejpam-5466	212	31	)	)	PUNCT
ejpam-5466	212	32	⊂	⊂	PUNCT
ejpam-5466	213	1	[	[	X
ejpam-5466	213	2	0	0	NUM
ejpam-5466	213	3	,	,	PUNCT
ejpam-5466	213	4	2	2	NUM
ejpam-5466	213	5	)	)	PUNCT
ejpam-5466	213	6	which	which	PRON
ejpam-5466	213	7	implies	imply	VERB
ejpam-5466	213	8	tνn	tνn	PROPN
ejpam-5466	214	1	=	=	PUNCT
ejpam-5466	215	1	[	[	X
ejpam-5466	215	2	0	0	NUM
ejpam-5466	215	3	,	,	PUNCT
ejpam-5466	215	4	νn4	νn4	PROPN
ejpam-5466	215	5	]	]	PUNCT
ejpam-5466	215	6	and	and	CCONJ
ejpam-5466	215	7	lim	lim	PROPN
ejpam-5466	215	8	n→∞	n→∞	PRON
ejpam-5466	216	1	t	t	NOUN
ejpam-5466	216	2	νn	νn	NOUN
ejpam-5466	216	3	=	=	PUNCT
ejpam-5466	217	1	[	[	X
ejpam-5466	217	2	0	0	NUM
ejpam-5466	217	3	,	,	PUNCT
ejpam-5466	217	4	ν	ν	X
ejpam-5466	217	5	4	4	NUM
ejpam-5466	217	6	]	]	PUNCT
ejpam-5466	217	7	=	=	SYM
ejpam-5466	217	8	t	t	PROPN
ejpam-5466	217	9	ν∗.	ν∗.	NOUN
ejpam-5466	217	10	consequently	consequently	ADV
ejpam-5466	217	11	,	,	PUNCT
ejpam-5466	217	12	all	all	DET
ejpam-5466	217	13	conditions	condition	NOUN
ejpam-5466	217	14	of	of	ADP
ejpam-5466	217	15	theorem	theorem	NOUN
ejpam-5466	217	16	1	1	NUM
ejpam-5466	217	17	are	be	AUX
ejpam-5466	217	18	satisfied	satisfied	ADJ
ejpam-5466	217	19	.	.	PUNCT
ejpam-5466	218	1	then	then	ADV
ejpam-5466	218	2	t	t	PROPN
ejpam-5466	218	3	has	have	VERB
ejpam-5466	218	4	a	a	DET
ejpam-5466	218	5	fixed	fix	VERB
ejpam-5466	218	6	point	point	NOUN
ejpam-5466	218	7	which	which	PRON
ejpam-5466	218	8	is	be	AUX
ejpam-5466	218	9	2	2	NUM
ejpam-5466	218	10	.	.	PUNCT
ejpam-5466	218	11	h.	h.	PROPN
ejpam-5466	218	12	qawaqneh	qawaqneh	PROPN
ejpam-5466	218	13	et	et	PROPN
ejpam-5466	218	14	al	al	PROPN
ejpam-5466	218	15	.	.	PUNCT
ejpam-5466	218	16	/	/	SYM
ejpam-5466	218	17	eur	eur	PROPN
ejpam-5466	218	18	.	.	PUNCT
ejpam-5466	219	1	j.	j.	PROPN
ejpam-5466	219	2	pure	pure	PROPN
ejpam-5466	219	3	appl	appl	PROPN
ejpam-5466	219	4	.	.	PROPN
ejpam-5466	219	5	math	math	PROPN
ejpam-5466	219	6	,	,	PUNCT
ejpam-5466	219	7	17	17	NUM
ejpam-5466	219	8	(	(	PUNCT
ejpam-5466	219	9	4	4	NUM
ejpam-5466	219	10	)	)	PUNCT
ejpam-5466	219	11	(	(	PUNCT
ejpam-5466	219	12	2024	2024	NUM
ejpam-5466	219	13	)	)	PUNCT
ejpam-5466	219	14	,	,	PUNCT
ejpam-5466	219	15	3093	3093	NUM
ejpam-5466	219	16	-	-	SYM
ejpam-5466	219	17	3108	3108	NUM
ejpam-5466	219	18	3102	3102	NUM
ejpam-5466	219	19	now	now	ADV
ejpam-5466	219	20	,	,	PUNCT
ejpam-5466	219	21	we	we	PRON
ejpam-5466	219	22	give	give	VERB
ejpam-5466	219	23	some	some	DET
ejpam-5466	219	24	consequences	consequence	NOUN
ejpam-5466	219	25	concerning	concern	VERB
ejpam-5466	219	26	,	,	PUNCT
ejpam-5466	219	27	two	two	NUM
ejpam-5466	219	28	existence	existence	NOUN
ejpam-5466	219	29	theorems	theorem	NOUN
ejpam-5466	219	30	of	of	ADP
ejpam-5466	219	31	fixed	fix	VERB
ejpam-5466	219	32	point	point	NOUN
ejpam-5466	219	33	in	in	ADP
ejpam-5466	219	34	metric	metric	ADJ
ejpam-5466	219	35	space	space	NOUN
ejpam-5466	219	36	endowed	endow	VERB
ejpam-5466	219	37	with	with	ADP
ejpam-5466	219	38	a	a	DET
ejpam-5466	219	39	graph	graph	NOUN
ejpam-5466	219	40	and	and	CCONJ
ejpam-5466	219	41	other	other	ADJ
ejpam-5466	219	42	in	in	ADP
ejpam-5466	219	43	partially	partially	ADV
ejpam-5466	219	44	order	order	VERB
ejpam-5466	219	45	metric	metric	ADJ
ejpam-5466	219	46	spaces	space	NOUN
ejpam-5466	219	47	.	.	PUNCT
ejpam-5466	220	1	theorem	theorem	NOUN
ejpam-5466	220	2	2	2	NUM
ejpam-5466	220	3	.	.	X
ejpam-5466	221	1	let	let	AUX
ejpam-5466	221	2	(	(	PUNCT
ejpam-5466	221	3	x,⪯	x,⪯	VERB
ejpam-5466	221	4	,	,	PUNCT
ejpam-5466	221	5	d	d	NOUN
ejpam-5466	221	6	)	)	PUNCT
ejpam-5466	221	7	be	be	AUX
ejpam-5466	221	8	a	a	DET
ejpam-5466	221	9	complete	complete	ADJ
ejpam-5466	221	10	ordered	order	VERB
ejpam-5466	221	11	b	b	X
ejpam-5466	221	12	-	-	PUNCT
ejpam-5466	221	13	metric	metric	ADJ
ejpam-5466	221	14	space	space	NOUN
ejpam-5466	221	15	and	and	CCONJ
ejpam-5466	221	16	t	t	NOUN
ejpam-5466	221	17	:	:	PUNCT
ejpam-5466	221	18	x	x	X
ejpam-5466	221	19	→	→	X
ejpam-5466	221	20	cb(x	cb(x	NUM
ejpam-5466	221	21	)	)	PUNCT
ejpam-5466	221	22	be	be	AUX
ejpam-5466	221	23	a	a	DET
ejpam-5466	221	24	multivalued	multivalue	VERB
ejpam-5466	221	25	mapping	mapping	NOUN
ejpam-5466	221	26	.	.	PUNCT
ejpam-5466	222	1	assume	assume	VERB
ejpam-5466	222	2	that	that	SCONJ
ejpam-5466	222	3	the	the	DET
ejpam-5466	222	4	following	follow	VERB
ejpam-5466	222	5	assertions	assertion	NOUN
ejpam-5466	222	6	hold	hold	VERB
ejpam-5466	222	7	.	.	PUNCT
ejpam-5466	223	1	(	(	PUNCT
ejpam-5466	223	2	i	i	NOUN
ejpam-5466	223	3	)	)	PUNCT
ejpam-5466	223	4	for	for	ADP
ejpam-5466	223	5	each	each	DET
ejpam-5466	223	6	ν	ν	NOUN
ejpam-5466	223	7	∈	∈	PROPN
ejpam-5466	223	8	x	x	X
ejpam-5466	223	9	and	and	CCONJ
ejpam-5466	223	10	µ	µ	PROPN
ejpam-5466	223	11	∈	∈	NOUN
ejpam-5466	223	12	t	t	NOUN
ejpam-5466	223	13	ν	ν	NOUN
ejpam-5466	223	14	with	with	ADP
ejpam-5466	223	15	ν	ν	PROPN
ejpam-5466	223	16	⪯	⪯	PROPN
ejpam-5466	223	17	µ	µ	NUM
ejpam-5466	223	18	,	,	PUNCT
ejpam-5466	223	19	we	we	PRON
ejpam-5466	223	20	have	have	VERB
ejpam-5466	223	21	µ	µ	PRON
ejpam-5466	223	22	⪯	⪯	PROPN
ejpam-5466	223	23	η	η	PROPN
ejpam-5466	223	24	for	for	ADP
ejpam-5466	223	25	all	all	DET
ejpam-5466	223	26	ν3	ν3	PROPN
ejpam-5466	223	27	∈	∈	PROPN
ejpam-5466	223	28	t	t	NOUN
ejpam-5466	223	29	µ.	µ.	NOUN
ejpam-5466	223	30	(	(	PUNCT
ejpam-5466	223	31	ii	ii	NOUN
ejpam-5466	223	32	)	)	PUNCT
ejpam-5466	223	33	there	there	PRON
ejpam-5466	223	34	exist	exist	VERB
ejpam-5466	223	35	ν0	ν0	PROPN
ejpam-5466	223	36	∈	∈	PROPN
ejpam-5466	223	37	x	x	X
ejpam-5466	223	38	and	and	CCONJ
ejpam-5466	223	39	ν0	ν0	PROPN
ejpam-5466	223	40	∈	∈	PROPN
ejpam-5466	223	41	t	t	NOUN
ejpam-5466	223	42	ν0	ν0	PROPN
ejpam-5466	223	43	such	such	ADJ
ejpam-5466	223	44	that	that	SCONJ
ejpam-5466	223	45	ν0	ν0	PROPN
ejpam-5466	223	46	⪯	⪯	NOUN
ejpam-5466	223	47	ν1	ν1	NOUN
ejpam-5466	223	48	;	;	PUNCT
ejpam-5466	223	49	(	(	PUNCT
ejpam-5466	223	50	iii	iii	NOUN
ejpam-5466	223	51	)	)	PUNCT
ejpam-5466	223	52	for	for	ADP
ejpam-5466	223	53	ν∗	ν∗	ADJ
ejpam-5466	223	54	∈	∈	PROPN
ejpam-5466	223	55	x	x	X
ejpam-5466	223	56	and	and	CCONJ
ejpam-5466	223	57	a	a	DET
ejpam-5466	223	58	sequence	sequence	NOUN
ejpam-5466	223	59	{	{	PUNCT
ejpam-5466	223	60	νn	νn	VERB
ejpam-5466	223	61	}	}	PUNCT
ejpam-5466	223	62	in	in	ADP
ejpam-5466	223	63	x	x	PUNCT
ejpam-5466	223	64	with	with	ADP
ejpam-5466	223	65	limn→∞	limn→∞	NOUN
ejpam-5466	223	66	d(νn	d(νn	NOUN
ejpam-5466	223	67	,	,	PUNCT
ejpam-5466	223	68	ν	ν	NOUN
ejpam-5466	223	69	∗	∗	NOUN
ejpam-5466	223	70	)	)	PUNCT
ejpam-5466	224	1	=	=	SYM
ejpam-5466	224	2	0	0	PUNCT
ejpam-5466	224	3	and	and	CCONJ
ejpam-5466	224	4	νn	νn	AUX
ejpam-5466	224	5	⪯	⪯	NOUN
ejpam-5466	224	6	νn+1	νn+1	VERB
ejpam-5466	224	7	for	for	ADP
ejpam-5466	224	8	all	all	PRON
ejpam-5466	224	9	n	n	PRON
ejpam-5466	224	10	∈	∈	PROPN
ejpam-5466	224	11	n	n	CCONJ
ejpam-5466	224	12	,	,	PUNCT
ejpam-5466	224	13	implies	imply	VERB
ejpam-5466	224	14	lim	lim	PROPN
ejpam-5466	224	15	inf	inf	PROPN
ejpam-5466	224	16	n→∞	n→∞	X
ejpam-5466	224	17	d(νn	d(νn	NOUN
ejpam-5466	224	18	,	,	PUNCT
ejpam-5466	225	1	t	t	PROPN
ejpam-5466	225	2	νn	νn	PROPN
ejpam-5466	225	3	)	)	PUNCT
ejpam-5466	225	4	≥	≥	NOUN
ejpam-5466	225	5	d(ν∗	d(ν∗	PROPN
ejpam-5466	225	6	,	,	PUNCT
ejpam-5466	225	7	t	t	PROPN
ejpam-5466	225	8	ν∗	ν∗	PROPN
ejpam-5466	225	9	)	)	PUNCT
ejpam-5466	225	10	or	or	CCONJ
ejpam-5466	225	11	,	,	PUNCT
ejpam-5466	225	12	for	for	ADP
ejpam-5466	225	13	every	every	DET
ejpam-5466	225	14	sequence	sequence	NOUN
ejpam-5466	225	15	{	{	PUNCT
ejpam-5466	225	16	νn	νn	VERB
ejpam-5466	225	17	}	}	PUNCT
ejpam-5466	225	18	in	in	ADP
ejpam-5466	225	19	x	x	X
ejpam-5466	225	20	such	such	ADJ
ejpam-5466	225	21	that	that	SCONJ
ejpam-5466	225	22	νn	νn	ADV
ejpam-5466	225	23	→	→	SYM
ejpam-5466	225	24	ν∗	ν∗	VERB
ejpam-5466	225	25	∈	∈	PROPN
ejpam-5466	225	26	x	x	X
ejpam-5466	225	27	and	and	CCONJ
ejpam-5466	225	28	νn	νn	AUX
ejpam-5466	225	29	⪯	⪯	NOUN
ejpam-5466	225	30	νn+1	νn+1	VERB
ejpam-5466	225	31	for	for	ADP
ejpam-5466	225	32	all	all	DET
ejpam-5466	225	33	n	n	DET
ejpam-5466	225	34	∈	∈	PROPN
ejpam-5466	225	35	n	n	CCONJ
ejpam-5466	225	36	,	,	PUNCT
ejpam-5466	225	37	we	we	PRON
ejpam-5466	225	38	have	have	VERB
ejpam-5466	225	39	νn	νn	AUX
ejpam-5466	225	40	⪯	⪯	NOUN
ejpam-5466	225	41	ν∗	ν∗	VERB
ejpam-5466	225	42	for	for	ADP
ejpam-5466	225	43	all	all	DET
ejpam-5466	225	44	n	n	PRON
ejpam-5466	225	45	∈	∈	PROPN
ejpam-5466	225	46	n.	n.	NOUN
ejpam-5466	225	47	(	(	PUNCT
ejpam-5466	225	48	iv	iv	X
ejpam-5466	225	49	)	)	PUNCT
ejpam-5466	225	50	there	there	PRON
ejpam-5466	225	51	exist	exist	VERB
ejpam-5466	225	52	ϑ	ϑ	PRON
ejpam-5466	225	53	∈	∈	PROPN
ejpam-5466	225	54	θs	θ	NOUN
ejpam-5466	225	55	,	,	PUNCT
ejpam-5466	225	56	l	l	PROPN
ejpam-5466	225	57	≥	≥	NOUN
ejpam-5466	225	58	0	0	NUM
ejpam-5466	225	59	and	and	CCONJ
ejpam-5466	225	60	κ	κ	X
ejpam-5466	225	61	:	:	PUNCT
ejpam-5466	225	62	(	(	PUNCT
ejpam-5466	225	63	0,∞	0,∞	NOUN
ejpam-5466	225	64	)	)	PUNCT
ejpam-5466	225	65	→	→	PUNCT
ejpam-5466	226	1	[	[	X
ejpam-5466	226	2	0	0	NUM
ejpam-5466	226	3	,	,	PUNCT
ejpam-5466	226	4	1	1	NUM
ejpam-5466	226	5	)	)	PUNCT
ejpam-5466	226	6	satisfies	satisfie	NOUN
ejpam-5466	226	7	lim	lim	PROPN
ejpam-5466	226	8	ω→z+	ω→z+	PROPN
ejpam-5466	226	9	supκ(ω	supκ(ω	PROPN
ejpam-5466	226	10	)	)	PUNCT
ejpam-5466	226	11	<	<	X
ejpam-5466	226	12	1	1	NUM
ejpam-5466	226	13	for	for	ADP
ejpam-5466	226	14	all	all	DET
ejpam-5466	226	15	z	z	NOUN
ejpam-5466	226	16	∈	∈	PROPN
ejpam-5466	226	17	(	(	PUNCT
ejpam-5466	226	18	0,∞	0,∞	NOUN
ejpam-5466	226	19	)	)	PUNCT
ejpam-5466	226	20	such	such	ADJ
ejpam-5466	226	21	that	that	SCONJ
ejpam-5466	226	22	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	226	23	ν	ν	PROPN
ejpam-5466	226	24	,	,	PUNCT
ejpam-5466	226	25	t	t	PROPN
ejpam-5466	226	26	µ	µ	NUM
ejpam-5466	226	27	)	)	PUNCT
ejpam-5466	226	28	)	)	PUNCT
ejpam-5466	226	29	≤	≤	NOUN
ejpam-5466	226	30	[	[	PUNCT
ejpam-5466	226	31	ϑ(ns(ν	ϑ(ns(ν	PROPN
ejpam-5466	226	32	,	,	PUNCT
ejpam-5466	226	33	µ	µ	NOUN
ejpam-5466	226	34	)	)	PUNCT
ejpam-5466	226	35	)	)	PUNCT
ejpam-5466	226	36	]	]	SYM
ejpam-5466	226	37	κ(d(ν,µ	κ(d(ν,µ	NUM
ejpam-5466	226	38	)	)	PUNCT
ejpam-5466	226	39	)	)	PUNCT
ejpam-5466	227	1	+	+	CCONJ
ejpam-5466	227	2	lmin{d(ν	lmin{d(ν	PROPN
ejpam-5466	227	3	,	,	PUNCT
ejpam-5466	227	4	t	t	PROPN
ejpam-5466	227	5	µ	µ	NUM
ejpam-5466	227	6	)	)	PUNCT
ejpam-5466	227	7	,	,	PUNCT
ejpam-5466	227	8	d(µ	d(µ	PROPN
ejpam-5466	227	9	,	,	PUNCT
ejpam-5466	227	10	t	t	NOUN
ejpam-5466	227	11	ν	ν	PROPN
ejpam-5466	227	12	)	)	PUNCT
ejpam-5466	227	13	}	}	PUNCT
ejpam-5466	227	14	,	,	PUNCT
ejpam-5466	227	15	where	where	SCONJ
ejpam-5466	227	16	ns(ν	ns(ν	NUM
ejpam-5466	227	17	,	,	PUNCT
ejpam-5466	227	18	µ	µ	NOUN
ejpam-5466	227	19	)	)	PUNCT
ejpam-5466	227	20	=	=	SYM
ejpam-5466	227	21	a1d(ν	a1d(ν	PROPN
ejpam-5466	227	22	,	,	PUNCT
ejpam-5466	227	23	µ	µ	NOUN
ejpam-5466	227	24	)	)	PUNCT
ejpam-5466	227	25	+	+	SYM
ejpam-5466	227	26	a2d(ν	a2d(ν	PROPN
ejpam-5466	227	27	,	,	PUNCT
ejpam-5466	227	28	t	t	NOUN
ejpam-5466	227	29	ν	ν	PROPN
ejpam-5466	227	30	)	)	PUNCT
ejpam-5466	227	31	+	+	CCONJ
ejpam-5466	227	32	a3⌈(µ	a3⌈(µ	PROPN
ejpam-5466	227	33	,	,	PUNCT
ejpam-5466	227	34	t	t	PROPN
ejpam-5466	227	35	µ	µ	NUM
ejpam-5466	227	36	)	)	PUNCT
ejpam-5466	227	37	+	+	CCONJ
ejpam-5466	228	1	a4d(ν	a4d(ν	PROPN
ejpam-5466	228	2	,	,	PUNCT
ejpam-5466	228	3	t	t	PROPN
ejpam-5466	228	4	µ	µ	NUM
ejpam-5466	228	5	)	)	PUNCT
ejpam-5466	228	6	+	+	CCONJ
ejpam-5466	228	7	a5d(µ	a5d(µ	PROPN
ejpam-5466	228	8	,	,	PUNCT
ejpam-5466	228	9	t	t	NOUN
ejpam-5466	228	10	ν	ν	NOUN
ejpam-5466	228	11	)	)	PUNCT
ejpam-5466	228	12	.	.	PUNCT
ejpam-5466	229	1	then	then	ADV
ejpam-5466	229	2	t	t	PROPN
ejpam-5466	229	3	has	have	VERB
ejpam-5466	229	4	a	a	DET
ejpam-5466	229	5	fixed	fix	VERB
ejpam-5466	229	6	point	point	NOUN
ejpam-5466	229	7	.	.	PUNCT
ejpam-5466	230	1	proof	proof	NOUN
ejpam-5466	230	2	.	.	PUNCT
ejpam-5466	231	1	define	define	VERB
ejpam-5466	231	2	α	α	NOUN
ejpam-5466	231	3	:	:	PUNCT
ejpam-5466	231	4	x×x	x×x	PROPN
ejpam-5466	231	5	→	→	PUNCT
ejpam-5466	232	1	[	[	X
ejpam-5466	232	2	0,+∞	0,+∞	NUM
ejpam-5466	232	3	)	)	PUNCT
ejpam-5466	232	4	,	,	PUNCT
ejpam-5466	232	5	α	α	PROPN
ejpam-5466	232	6	(	(	PUNCT
ejpam-5466	232	7	ν	ν	PROPN
ejpam-5466	232	8	,	,	PUNCT
ejpam-5466	232	9	µ	µ	NOUN
ejpam-5466	232	10	)	)	PUNCT
ejpam-5466	232	11	=	=	SYM
ejpam-5466	232	12	{	{	PUNCT
ejpam-5466	232	13	s2	s2	PROPN
ejpam-5466	232	14	,	,	PUNCT
ejpam-5466	232	15	if	if	SCONJ
ejpam-5466	232	16	ν	ν	PROPN
ejpam-5466	232	17	⪯	⪯	NOUN
ejpam-5466	232	18	µ	µ	NUM
ejpam-5466	232	19	,	,	PUNCT
ejpam-5466	232	20	0	0	NUM
ejpam-5466	232	21	,	,	PUNCT
ejpam-5466	232	22	otherwise	otherwise	ADV
ejpam-5466	232	23	.	.	PUNCT
ejpam-5466	233	1	the	the	DET
ejpam-5466	233	2	rest	rest	NOUN
ejpam-5466	233	3	of	of	ADP
ejpam-5466	233	4	proof	proof	NOUN
ejpam-5466	233	5	is	be	AUX
ejpam-5466	233	6	like	like	ADP
ejpam-5466	233	7	the	the	DET
ejpam-5466	233	8	proof	proof	NOUN
ejpam-5466	233	9	of	of	ADP
ejpam-5466	233	10	theorem	theorem	NOUN
ejpam-5466	233	11	1	1	NUM
ejpam-5466	233	12	.	.	PUNCT
ejpam-5466	234	1	nextly	nextly	ADV
ejpam-5466	234	2	,	,	PUNCT
ejpam-5466	234	3	we	we	PRON
ejpam-5466	234	4	present	present	VERB
ejpam-5466	234	5	an	an	DET
ejpam-5466	234	6	existence	existence	NOUN
ejpam-5466	234	7	theorem	theorem	NOUN
ejpam-5466	234	8	of	of	ADP
ejpam-5466	234	9	a	a	DET
ejpam-5466	234	10	fixed	fix	VERB
ejpam-5466	234	11	point	point	NOUN
ejpam-5466	234	12	for	for	ADP
ejpam-5466	234	13	multivalued	multivalued	ADJ
ejpam-5466	234	14	ϑ-contractions	ϑ-contraction	NOUN
ejpam-5466	234	15	in	in	ADP
ejpam-5466	234	16	a	a	DET
ejpam-5466	234	17	b	b	NOUN
ejpam-5466	234	18	-	-	PUNCT
ejpam-5466	234	19	metric	metric	ADJ
ejpam-5466	234	20	space	space	NOUN
ejpam-5466	234	21	x	x	NOUN
ejpam-5466	234	22	,	,	PUNCT
ejpam-5466	234	23	endowed	endow	VERB
ejpam-5466	234	24	with	with	ADP
ejpam-5466	234	25	a	a	DET
ejpam-5466	234	26	graph	graph	NOUN
ejpam-5466	234	27	,	,	PUNCT
ejpam-5466	234	28	into	into	ADP
ejpam-5466	234	29	the	the	DET
ejpam-5466	234	30	space	space	NOUN
ejpam-5466	234	31	of	of	ADP
ejpam-5466	234	32	nonempty	nonempty	ADV
ejpam-5466	234	33	closed	close	VERB
ejpam-5466	234	34	and	and	CCONJ
ejpam-5466	234	35	bounded	bound	VERB
ejpam-5466	234	36	subsets	subset	NOUN
ejpam-5466	234	37	of	of	ADP
ejpam-5466	234	38	the	the	DET
ejpam-5466	234	39	metric	metric	ADJ
ejpam-5466	234	40	space	space	NOUN
ejpam-5466	234	41	.	.	PUNCT
ejpam-5466	235	1	consider	consider	VERB
ejpam-5466	235	2	a	a	DET
ejpam-5466	235	3	graph	graph	NOUN
ejpam-5466	235	4	g̃	g̃	PROPN
ejpam-5466	235	5	such	such	ADJ
ejpam-5466	235	6	that	that	SCONJ
ejpam-5466	235	7	the	the	DET
ejpam-5466	235	8	set	set	NOUN
ejpam-5466	235	9	v	v	NOUN
ejpam-5466	235	10	(	(	PUNCT
ejpam-5466	235	11	g̃	g̃	PROPN
ejpam-5466	235	12	)	)	PUNCT
ejpam-5466	235	13	of	of	ADP
ejpam-5466	235	14	its	its	PRON
ejpam-5466	235	15	vertices	vertex	NOUN
ejpam-5466	235	16	coincides	coincide	VERB
ejpam-5466	235	17	with	with	ADP
ejpam-5466	235	18	x	x	PUNCT
ejpam-5466	235	19	and	and	CCONJ
ejpam-5466	235	20	the	the	DET
ejpam-5466	235	21	set	set	NOUN
ejpam-5466	235	22	e	e	NOUN
ejpam-5466	235	23	(	(	PUNCT
ejpam-5466	235	24	g̃	g̃	PROPN
ejpam-5466	235	25	)	)	PUNCT
ejpam-5466	235	26	of	of	ADP
ejpam-5466	235	27	its	its	PRON
ejpam-5466	235	28	edges	edge	NOUN
ejpam-5466	235	29	contains	contain	VERB
ejpam-5466	235	30	all	all	DET
ejpam-5466	235	31	loops	loop	NOUN
ejpam-5466	235	32	;	;	PUNCT
ejpam-5466	235	33	that	that	PRON
ejpam-5466	235	34	is	is	ADV
ejpam-5466	235	35	,	,	PUNCT
ejpam-5466	235	36	e	e	X
ejpam-5466	235	37	(	(	PUNCT
ejpam-5466	235	38	g̃	g̃	PROPN
ejpam-5466	235	39	)	)	PUNCT
ejpam-5466	235	40	⊇	⊇	NOUN
ejpam-5466	235	41	∆	∆	PROPN
ejpam-5466	235	42	,	,	PUNCT
ejpam-5466	235	43	where	where	SCONJ
ejpam-5466	235	44	∆̃	∆̃	PRON
ejpam-5466	235	45	=	=	SYM
ejpam-5466	235	46	{	{	PUNCT
ejpam-5466	235	47	(	(	PUNCT
ejpam-5466	235	48	ν	ν	NOUN
ejpam-5466	235	49	,	,	PUNCT
ejpam-5466	235	50	ν	ν	NOUN
ejpam-5466	235	51	)	)	PUNCT
ejpam-5466	235	52	,	,	PUNCT
ejpam-5466	235	53	ν	ν	PROPN
ejpam-5466	235	54	∈	∈	NOUN
ejpam-5466	235	55	x	x	X
ejpam-5466	235	56	}	}	PUNCT
ejpam-5466	235	57	.	.	PUNCT
ejpam-5466	236	1	we	we	PRON
ejpam-5466	236	2	assume	assume	VERB
ejpam-5466	236	3	g̃	g̃	PROPN
ejpam-5466	236	4	has	have	VERB
ejpam-5466	236	5	no	no	DET
ejpam-5466	236	6	parallel	parallel	ADJ
ejpam-5466	236	7	edges	edge	NOUN
ejpam-5466	236	8	,	,	PUNCT
ejpam-5466	236	9	so	so	SCONJ
ejpam-5466	236	10	we	we	PRON
ejpam-5466	236	11	can	can	AUX
ejpam-5466	236	12	identify	identify	VERB
ejpam-5466	236	13	g̃	g̃	PROPN
ejpam-5466	236	14	with	with	ADP
ejpam-5466	236	15	the	the	DET
ejpam-5466	236	16	pair	pair	NOUN
ejpam-5466	236	17	(	(	PUNCT
ejpam-5466	236	18	v	v	NOUN
ejpam-5466	236	19	(	(	PUNCT
ejpam-5466	236	20	g̃	g̃	PROPN
ejpam-5466	236	21	)	)	PUNCT
ejpam-5466	236	22	,	,	PUNCT
ejpam-5466	236	23	e	e	X
ejpam-5466	236	24	(	(	PUNCT
ejpam-5466	236	25	g̃	g̃	PROPN
ejpam-5466	236	26	)	)	PUNCT
ejpam-5466	236	27	)	)	PUNCT
ejpam-5466	236	28	.	.	PUNCT
ejpam-5466	237	1	we	we	PRON
ejpam-5466	237	2	define	define	VERB
ejpam-5466	237	3	the	the	DET
ejpam-5466	237	4	function	function	NOUN
ejpam-5466	237	5	α	α	NOUN
ejpam-5466	237	6	:	:	PUNCT
ejpam-5466	237	7	x×x	x×x	PROPN
ejpam-5466	237	8	→	→	PUNCT
ejpam-5466	237	9	[	[	X
ejpam-5466	237	10	0,+∞	0,+∞	NUM
ejpam-5466	237	11	)	)	PUNCT
ejpam-5466	237	12	,	,	PUNCT
ejpam-5466	237	13	α	α	PROPN
ejpam-5466	237	14	(	(	PUNCT
ejpam-5466	237	15	ν	ν	PROPN
ejpam-5466	237	16	,	,	PUNCT
ejpam-5466	237	17	µ	µ	NOUN
ejpam-5466	237	18	)	)	PUNCT
ejpam-5466	237	19	=	=	SYM
ejpam-5466	237	20	{	{	PUNCT
ejpam-5466	237	21	s2	s2	PROPN
ejpam-5466	237	22	,	,	PUNCT
ejpam-5466	237	23	if	if	SCONJ
ejpam-5466	237	24	(	(	PUNCT
ejpam-5466	237	25	ν	ν	NOUN
ejpam-5466	237	26	,	,	PUNCT
ejpam-5466	237	27	µ	µ	NOUN
ejpam-5466	237	28	)	)	PUNCT
ejpam-5466	237	29	∈	∈	PROPN
ejpam-5466	237	30	e	e	X
ejpam-5466	237	31	(	(	PUNCT
ejpam-5466	237	32	g̃	g̃	PROPN
ejpam-5466	237	33	)	)	PUNCT
ejpam-5466	237	34	,	,	PUNCT
ejpam-5466	237	35	0	0	NUM
ejpam-5466	237	36	,	,	PUNCT
ejpam-5466	237	37	otherwise	otherwise	ADV
ejpam-5466	237	38	.	.	PUNCT
ejpam-5466	238	1	h.	h.	PROPN
ejpam-5466	238	2	qawaqneh	qawaqneh	PROPN
ejpam-5466	238	3	et	et	PROPN
ejpam-5466	238	4	al	al	PROPN
ejpam-5466	238	5	.	.	PUNCT
ejpam-5466	238	6	/	/	SYM
ejpam-5466	238	7	eur	eur	PROPN
ejpam-5466	238	8	.	.	PUNCT
ejpam-5466	239	1	j.	j.	PROPN
ejpam-5466	239	2	pure	pure	PROPN
ejpam-5466	239	3	appl	appl	PROPN
ejpam-5466	239	4	.	.	PROPN
ejpam-5466	239	5	math	math	PROPN
ejpam-5466	239	6	,	,	PUNCT
ejpam-5466	239	7	17	17	NUM
ejpam-5466	239	8	(	(	PUNCT
ejpam-5466	239	9	4	4	NUM
ejpam-5466	239	10	)	)	PUNCT
ejpam-5466	239	11	(	(	PUNCT
ejpam-5466	239	12	2024	2024	NUM
ejpam-5466	239	13	)	)	PUNCT
ejpam-5466	239	14	,	,	PUNCT
ejpam-5466	239	15	3093	3093	NUM
ejpam-5466	239	16	-	-	SYM
ejpam-5466	239	17	3108	3108	NUM
ejpam-5466	239	18	3103	3103	NUM
ejpam-5466	239	19	theorem	theorem	NOUN
ejpam-5466	239	20	3	3	X
ejpam-5466	239	21	.	.	PUNCT
ejpam-5466	240	1	let	let	AUX
ejpam-5466	240	2	(	(	PUNCT
ejpam-5466	240	3	x	x	NOUN
ejpam-5466	240	4	,	,	PUNCT
ejpam-5466	240	5	d	d	X
ejpam-5466	240	6	,	,	PUNCT
ejpam-5466	240	7	s	s	PART
ejpam-5466	240	8	)	)	PUNCT
ejpam-5466	240	9	be	be	AUX
ejpam-5466	240	10	a	a	DET
ejpam-5466	240	11	complete	complete	ADJ
ejpam-5466	240	12	b	b	X
ejpam-5466	240	13	-	-	PUNCT
ejpam-5466	240	14	metric	metric	ADJ
ejpam-5466	240	15	space	space	NOUN
ejpam-5466	240	16	endowed	endow	VERB
ejpam-5466	240	17	with	with	ADP
ejpam-5466	240	18	a	a	DET
ejpam-5466	240	19	graph	graph	NOUN
ejpam-5466	240	20	g̃	g̃	PROPN
ejpam-5466	240	21	and	and	CCONJ
ejpam-5466	240	22	t	t	NOUN
ejpam-5466	240	23	:	:	PUNCT
ejpam-5466	240	24	x	x	X
ejpam-5466	240	25	→	→	X
ejpam-5466	240	26	cb(x	cb(x	NUM
ejpam-5466	240	27	)	)	PUNCT
ejpam-5466	240	28	be	be	AUX
ejpam-5466	240	29	a	a	DET
ejpam-5466	240	30	multivalued	multivalue	VERB
ejpam-5466	240	31	mapping	mapping	NOUN
ejpam-5466	240	32	.	.	PUNCT
ejpam-5466	241	1	assume	assume	VERB
ejpam-5466	241	2	that	that	SCONJ
ejpam-5466	241	3	the	the	DET
ejpam-5466	241	4	following	follow	VERB
ejpam-5466	241	5	conditions	condition	NOUN
ejpam-5466	241	6	hold	hold	VERB
ejpam-5466	241	7	:	:	PUNCT
ejpam-5466	241	8	(	(	PUNCT
ejpam-5466	241	9	i	i	NOUN
ejpam-5466	241	10	)	)	PUNCT
ejpam-5466	241	11	for	for	ADP
ejpam-5466	241	12	each	each	DET
ejpam-5466	241	13	ν	ν	NOUN
ejpam-5466	241	14	∈	∈	PROPN
ejpam-5466	241	15	x	x	X
ejpam-5466	241	16	and	and	CCONJ
ejpam-5466	241	17	µ	µ	PROPN
ejpam-5466	241	18	∈	∈	NOUN
ejpam-5466	241	19	t	t	NOUN
ejpam-5466	241	20	ν	ν	NOUN
ejpam-5466	241	21	with	with	ADP
ejpam-5466	241	22	(	(	PUNCT
ejpam-5466	241	23	ν	ν	PROPN
ejpam-5466	241	24	,	,	PUNCT
ejpam-5466	241	25	µ	µ	NOUN
ejpam-5466	241	26	)	)	PUNCT
ejpam-5466	241	27	∈	∈	PROPN
ejpam-5466	241	28	e(g̃	e(g̃	PROPN
ejpam-5466	241	29	)	)	PUNCT
ejpam-5466	241	30	,	,	PUNCT
ejpam-5466	241	31	we	we	PRON
ejpam-5466	241	32	have	have	VERB
ejpam-5466	241	33	(	(	PUNCT
ejpam-5466	241	34	µ	µ	X
ejpam-5466	241	35	,	,	PUNCT
ejpam-5466	241	36	η	η	NOUN
ejpam-5466	241	37	)	)	PUNCT
ejpam-5466	241	38	∈	∈	PROPN
ejpam-5466	241	39	e(g̃	e(g̃	PROPN
ejpam-5466	241	40	)	)	PUNCT
ejpam-5466	241	41	for	for	ADP
ejpam-5466	241	42	all	all	DET
ejpam-5466	241	43	η	η	PROPN
ejpam-5466	241	44	∈	∈	PROPN
ejpam-5466	241	45	tµ	tµ	PRON
ejpam-5466	241	46	;	;	PUNCT
ejpam-5466	241	47	(	(	PUNCT
ejpam-5466	241	48	ii	ii	NOUN
ejpam-5466	241	49	)	)	PUNCT
ejpam-5466	241	50	there	there	PRON
ejpam-5466	241	51	exist	exist	VERB
ejpam-5466	241	52	ν0	ν0	PROPN
ejpam-5466	241	53	∈	∈	PROPN
ejpam-5466	241	54	x	x	X
ejpam-5466	241	55	and	and	CCONJ
ejpam-5466	241	56	ν1	ν1	PROPN
ejpam-5466	241	57	∈	∈	PROPN
ejpam-5466	241	58	t	t	NOUN
ejpam-5466	241	59	ν0	ν0	PROPN
ejpam-5466	241	60	such	such	ADJ
ejpam-5466	241	61	that	that	SCONJ
ejpam-5466	241	62	(	(	PUNCT
ejpam-5466	241	63	ν0	ν0	PROPN
ejpam-5466	241	64	,	,	PUNCT
ejpam-5466	241	65	ν1	ν1	NOUN
ejpam-5466	241	66	)	)	PUNCT
ejpam-5466	241	67	∈	∈	PROPN
ejpam-5466	241	68	e(g̃	e(g̃	PROPN
ejpam-5466	241	69	)	)	PUNCT
ejpam-5466	241	70	;	;	PUNCT
ejpam-5466	241	71	(	(	PUNCT
ejpam-5466	241	72	iii	iii	X
ejpam-5466	241	73	)	)	PUNCT
ejpam-5466	241	74	for	for	ADP
ejpam-5466	241	75	every	every	DET
ejpam-5466	241	76	sequence	sequence	NOUN
ejpam-5466	241	77	{	{	PUNCT
ejpam-5466	241	78	νn	νn	VERB
ejpam-5466	241	79	}	}	PUNCT
ejpam-5466	241	80	in	in	ADP
ejpam-5466	241	81	x	x	X
ejpam-5466	241	82	such	such	ADJ
ejpam-5466	241	83	that	that	SCONJ
ejpam-5466	241	84	νn	νn	ADV
ejpam-5466	241	85	→	→	SYM
ejpam-5466	241	86	ν∗	ν∗	VERB
ejpam-5466	241	87	∈	∈	PROPN
ejpam-5466	241	88	x	x	X
ejpam-5466	241	89	and	and	CCONJ
ejpam-5466	241	90	(	(	PUNCT
ejpam-5466	241	91	xn	xn	PROPN
ejpam-5466	241	92	,	,	PUNCT
ejpam-5466	241	93	xn+1	xn+1	NUM
ejpam-5466	241	94	)	)	PUNCT
ejpam-5466	241	95	∈	∈	PROPN
ejpam-5466	241	96	e(g̃	e(g̃	PROPN
ejpam-5466	241	97	)	)	PUNCT
ejpam-5466	241	98	for	for	ADP
ejpam-5466	241	99	all	all	DET
ejpam-5466	241	100	n	n	PRON
ejpam-5466	241	101	∈	∈	PROPN
ejpam-5466	241	102	n	n	CCONJ
ejpam-5466	241	103	,	,	PUNCT
ejpam-5466	241	104	we	we	PRON
ejpam-5466	241	105	have	have	AUX
ejpam-5466	241	106	(	(	PUNCT
ejpam-5466	241	107	νn	νn	VERB
ejpam-5466	241	108	,	,	PUNCT
ejpam-5466	241	109	ν	ν	NOUN
ejpam-5466	241	110	∗	∗	NOUN
ejpam-5466	241	111	)	)	PUNCT
ejpam-5466	241	112	∈	∈	PROPN
ejpam-5466	241	113	e(g̃	e(g̃	PROPN
ejpam-5466	241	114	)	)	PUNCT
ejpam-5466	241	115	for	for	ADP
ejpam-5466	241	116	all	all	PRON
ejpam-5466	241	117	n	n	PRON
ejpam-5466	241	118	∈	∈	PROPN
ejpam-5466	241	119	n	n	CCONJ
ejpam-5466	241	120	;	;	PUNCT
ejpam-5466	241	121	(	(	PUNCT
ejpam-5466	241	122	iv	iv	X
ejpam-5466	241	123	)	)	PUNCT
ejpam-5466	241	124	there	there	PRON
ejpam-5466	241	125	exist	exist	VERB
ejpam-5466	241	126	ϑ	ϑ	PRON
ejpam-5466	241	127	∈	∈	X
ejpam-5466	241	128	θs	θ	NOUN
ejpam-5466	241	129	and	and	CCONJ
ejpam-5466	241	130	κ	κ	X
ejpam-5466	241	131	:	:	PUNCT
ejpam-5466	241	132	(	(	PUNCT
ejpam-5466	241	133	0,∞	0,∞	NOUN
ejpam-5466	241	134	)	)	PUNCT
ejpam-5466	241	135	→	→	PUNCT
ejpam-5466	242	1	[	[	X
ejpam-5466	242	2	0	0	NUM
ejpam-5466	242	3	,	,	PUNCT
ejpam-5466	242	4	1	1	NUM
ejpam-5466	242	5	)	)	PUNCT
ejpam-5466	242	6	satisfies	satisfie	NOUN
ejpam-5466	242	7	lim	lim	PROPN
ejpam-5466	242	8	ω→z+	ω→z+	PROPN
ejpam-5466	242	9	supκ(ω	supκ(ω	PROPN
ejpam-5466	242	10	)	)	PUNCT
ejpam-5466	242	11	<	<	X
ejpam-5466	242	12	1	1	NUM
ejpam-5466	242	13	such	such	ADJ
ejpam-5466	242	14	that	that	SCONJ
ejpam-5466	242	15	ϑ(s3h(t	ϑ(s3h(t	PROPN
ejpam-5466	242	16	ν	ν	PROPN
ejpam-5466	242	17	,	,	PUNCT
ejpam-5466	242	18	t	t	PROPN
ejpam-5466	242	19	µ	µ	NUM
ejpam-5466	242	20	)	)	PUNCT
ejpam-5466	242	21	)	)	PUNCT
ejpam-5466	242	22	≤	≤	NOUN
ejpam-5466	242	23	[	[	PUNCT
ejpam-5466	242	24	ϑ(ns(ν	ϑ(ns(ν	PROPN
ejpam-5466	242	25	,	,	PUNCT
ejpam-5466	242	26	µ	µ	NOUN
ejpam-5466	242	27	)	)	PUNCT
ejpam-5466	242	28	)	)	PUNCT
ejpam-5466	242	29	]	]	SYM
ejpam-5466	242	30	κ(d(ν,µ	κ(d(ν,µ	NUM
ejpam-5466	242	31	)	)	PUNCT
ejpam-5466	242	32	)	)	PUNCT
ejpam-5466	243	1	+	+	CCONJ
ejpam-5466	243	2	lmin{d(ν	lmin{d(ν	PROPN
ejpam-5466	243	3	,	,	PUNCT
ejpam-5466	243	4	t	t	PROPN
ejpam-5466	243	5	µ	µ	NUM
ejpam-5466	243	6	)	)	PUNCT
ejpam-5466	243	7	,	,	PUNCT
ejpam-5466	243	8	d(µ	d(µ	PROPN
ejpam-5466	243	9	,	,	PUNCT
ejpam-5466	243	10	t	t	NOUN
ejpam-5466	243	11	ν	ν	PROPN
ejpam-5466	243	12	)	)	PUNCT
ejpam-5466	243	13	}	}	PUNCT
ejpam-5466	243	14	,	,	PUNCT
ejpam-5466	243	15	(	(	PUNCT
ejpam-5466	243	16	2.6	2.6	NUM
ejpam-5466	243	17	)	)	PUNCT
ejpam-5466	244	1	where	where	SCONJ
ejpam-5466	244	2	ns(ν	ns(ν	NUM
ejpam-5466	244	3	,	,	PUNCT
ejpam-5466	244	4	µ	µ	NOUN
ejpam-5466	244	5	)	)	PUNCT
ejpam-5466	244	6	=	=	SYM
ejpam-5466	244	7	a1d(ν	a1d(ν	PROPN
ejpam-5466	244	8	,	,	PUNCT
ejpam-5466	244	9	µ	µ	NOUN
ejpam-5466	244	10	)	)	PUNCT
ejpam-5466	244	11	+	+	SYM
ejpam-5466	244	12	a2d(ν	a2d(ν	PROPN
ejpam-5466	244	13	,	,	PUNCT
ejpam-5466	244	14	tµ	tµ	PRON
ejpam-5466	244	15	)	)	PUNCT
ejpam-5466	245	1	+	+	CCONJ
ejpam-5466	245	2	a3d(µ	a3d(µ	PROPN
ejpam-5466	245	3	,	,	PUNCT
ejpam-5466	245	4	t	t	PROPN
ejpam-5466	245	5	µ	µ	NUM
ejpam-5466	245	6	)	)	PUNCT
ejpam-5466	245	7	+	+	CCONJ
ejpam-5466	246	1	a4d(ν	a4d(ν	PROPN
ejpam-5466	246	2	,	,	PUNCT
ejpam-5466	246	3	t	t	PROPN
ejpam-5466	246	4	µ	µ	NUM
ejpam-5466	246	5	)	)	PUNCT
ejpam-5466	246	6	+	+	CCONJ
ejpam-5466	246	7	a5d(µ	a5d(µ	PROPN
ejpam-5466	246	8	,	,	PUNCT
ejpam-5466	246	9	t	t	NOUN
ejpam-5466	246	10	ν	ν	NOUN
ejpam-5466	246	11	)	)	PUNCT
ejpam-5466	246	12	.	.	PUNCT
ejpam-5466	247	1	then	then	ADV
ejpam-5466	247	2	t	t	PROPN
ejpam-5466	247	3	has	have	VERB
ejpam-5466	247	4	a	a	DET
ejpam-5466	247	5	fixed	fix	VERB
ejpam-5466	247	6	point	point	NOUN
ejpam-5466	247	7	.	.	PUNCT
ejpam-5466	248	1	proof	proof	NOUN
ejpam-5466	248	2	.	.	PUNCT
ejpam-5466	249	1	it	it	PRON
ejpam-5466	249	2	suffices	suffice	VERB
ejpam-5466	249	3	to	to	PART
ejpam-5466	249	4	consider	consider	VERB
ejpam-5466	249	5	α	α	NOUN
ejpam-5466	249	6	:	:	PUNCT
ejpam-5466	249	7	x×x	x×x	PROPN
ejpam-5466	249	8	→	→	PUNCT
ejpam-5466	250	1	[	[	X
ejpam-5466	250	2	0,+∞	0,+∞	NUM
ejpam-5466	250	3	)	)	PUNCT
ejpam-5466	250	4	,	,	PUNCT
ejpam-5466	250	5	α	α	PROPN
ejpam-5466	250	6	(	(	PUNCT
ejpam-5466	250	7	ν	ν	PROPN
ejpam-5466	250	8	,	,	PUNCT
ejpam-5466	250	9	µ	µ	NOUN
ejpam-5466	250	10	)	)	PUNCT
ejpam-5466	250	11	=	=	SYM
ejpam-5466	250	12	{	{	PUNCT
ejpam-5466	250	13	s2	s2	PROPN
ejpam-5466	250	14	,	,	PUNCT
ejpam-5466	250	15	if	if	SCONJ
ejpam-5466	250	16	(	(	PUNCT
ejpam-5466	250	17	ν	ν	NOUN
ejpam-5466	250	18	,	,	PUNCT
ejpam-5466	250	19	µ	µ	NOUN
ejpam-5466	250	20	)	)	PUNCT
ejpam-5466	250	21	∈	∈	PROPN
ejpam-5466	250	22	e	e	X
ejpam-5466	250	23	(	(	PUNCT
ejpam-5466	250	24	g̃	g̃	PROPN
ejpam-5466	250	25	)	)	PUNCT
ejpam-5466	250	26	,	,	PUNCT
ejpam-5466	250	27	0	0	NUM
ejpam-5466	250	28	,	,	PUNCT
ejpam-5466	250	29	otherwise	otherwise	ADV
ejpam-5466	250	30	.	.	PUNCT
ejpam-5466	250	31	.	.	PUNCT
ejpam-5466	251	1	3	3	X
ejpam-5466	251	2	.	.	X
ejpam-5466	251	3	application	application	NOUN
ejpam-5466	251	4	in	in	ADP
ejpam-5466	251	5	this	this	DET
ejpam-5466	251	6	section	section	NOUN
ejpam-5466	251	7	,	,	PUNCT
ejpam-5466	251	8	we	we	PRON
ejpam-5466	251	9	apply	apply	VERB
ejpam-5466	251	10	our	our	PRON
ejpam-5466	251	11	obtained	obtain	VERB
ejpam-5466	251	12	results	result	NOUN
ejpam-5466	251	13	to	to	PART
ejpam-5466	251	14	prove	prove	VERB
ejpam-5466	251	15	existence	existence	NOUN
ejpam-5466	251	16	theorem	theorem	NOUN
ejpam-5466	251	17	of	of	ADP
ejpam-5466	251	18	solution	solution	NOUN
ejpam-5466	251	19	for	for	ADP
ejpam-5466	251	20	an	an	DET
ejpam-5466	251	21	integral	integral	ADJ
ejpam-5466	251	22	inclusion	inclusion	NOUN
ejpam-5466	251	23	of	of	ADP
ejpam-5466	251	24	volterra	volterra	NOUN
ejpam-5466	251	25	-	-	PUNCT
ejpam-5466	251	26	type	type	NOUN
ejpam-5466	251	27	.	.	PUNCT
ejpam-5466	252	1	for	for	ADP
ejpam-5466	252	2	this	this	DET
ejpam-5466	252	3	purpose	purpose	NOUN
ejpam-5466	252	4	,	,	PUNCT
ejpam-5466	252	5	let	let	VERB
ejpam-5466	252	6	x	x	PRON
ejpam-5466	252	7	:	:	PUNCT
ejpam-5466	252	8	=	=	SYM
ejpam-5466	252	9	c([a	c([a	PROPN
ejpam-5466	252	10	,	,	PUNCT
ejpam-5466	252	11	b],r	b],r	NOUN
ejpam-5466	252	12	)	)	PUNCT
ejpam-5466	252	13	be	be	VERB
ejpam-5466	252	14	the	the	DET
ejpam-5466	252	15	space	space	NOUN
ejpam-5466	252	16	of	of	ADP
ejpam-5466	252	17	all	all	DET
ejpam-5466	252	18	continuous	continuous	ADJ
ejpam-5466	252	19	real	real	ADJ
ejpam-5466	252	20	valued	value	VERB
ejpam-5466	252	21	functions	function	NOUN
ejpam-5466	252	22	on	on	ADP
ejpam-5466	252	23	[	[	X
ejpam-5466	252	24	a	a	X
ejpam-5466	252	25	,	,	PUNCT
ejpam-5466	252	26	b	b	NOUN
ejpam-5466	252	27	]	]	PUNCT
ejpam-5466	252	28	.	.	PUNCT
ejpam-5466	253	1	note	note	VERB
ejpam-5466	253	2	that	that	SCONJ
ejpam-5466	253	3	x	x	PRON
ejpam-5466	253	4	is	be	AUX
ejpam-5466	253	5	b	b	NOUN
ejpam-5466	253	6	-	-	PUNCT
ejpam-5466	253	7	complete	complete	ADJ
ejpam-5466	253	8	b	b	X
ejpam-5466	253	9	-	-	PUNCT
ejpam-5466	253	10	metric	metric	ADJ
ejpam-5466	253	11	space	space	NOUN
ejpam-5466	253	12	by	by	ADP
ejpam-5466	253	13	considering	consider	VERB
ejpam-5466	253	14	d(ν	d(ν	PROPN
ejpam-5466	253	15	,	,	PUNCT
ejpam-5466	253	16	µ	µ	NOUN
ejpam-5466	253	17	)	)	PUNCT
ejpam-5466	253	18	=	=	SYM
ejpam-5466	253	19	sup	sup	NOUN
ejpam-5466	253	20	ω∈[a	ω∈[a	NOUN
ejpam-5466	253	21	,	,	PUNCT
ejpam-5466	253	22	b	b	X
ejpam-5466	253	23	]	]	PUNCT
ejpam-5466	253	24	|ν(ω)−µ(ω)|2	|ν(ω)−µ(ω)|2	PROPN
ejpam-5466	253	25	with	with	ADP
ejpam-5466	253	26	s	s	NOUN
ejpam-5466	253	27	=	=	SYM
ejpam-5466	253	28	2	2	NUM
ejpam-5466	253	29	and	and	CCONJ
ejpam-5466	253	30	define	define	VERB
ejpam-5466	253	31	α	α	NOUN
ejpam-5466	253	32	:	:	PUNCT
ejpam-5466	253	33	x×x	x×x	PROPN
ejpam-5466	253	34	→	→	NOUN
ejpam-5466	253	35	r+	r+	NOUN
ejpam-5466	253	36	by	by	ADP
ejpam-5466	253	37	α(ν	α(ν	PROPN
ejpam-5466	253	38	,	,	PUNCT
ejpam-5466	253	39	µ	µ	NOUN
ejpam-5466	253	40	)	)	PUNCT
ejpam-5466	253	41	=	=	SYM
ejpam-5466	253	42	4	4	NUM
ejpam-5466	253	43	,	,	PUNCT
ejpam-5466	253	44	for	for	ADP
ejpam-5466	253	45	all	all	DET
ejpam-5466	253	46	ν	ν	NOUN
ejpam-5466	253	47	,	,	PUNCT
ejpam-5466	253	48	µ	µ	X
ejpam-5466	253	49	∈	∈	NOUN
ejpam-5466	253	50	x.	x.	NOUN
ejpam-5466	253	51	consider	consider	VERB
ejpam-5466	253	52	now	now	ADV
ejpam-5466	253	53	the	the	DET
ejpam-5466	253	54	following	follow	VERB
ejpam-5466	253	55	problem	problem	NOUN
ejpam-5466	253	56	ν(t	ν(t	NOUN
ejpam-5466	253	57	)	)	PUNCT
ejpam-5466	253	58	∈	∈	PROPN
ejpam-5466	253	59	p(ω	p(ω	PROPN
ejpam-5466	253	60	)	)	PUNCT
ejpam-5466	254	1	+	+	NUM
ejpam-5466	254	2	∫	∫	PROPN
ejpam-5466	254	3	ω	ω	NUM
ejpam-5466	254	4	a	a	DET
ejpam-5466	254	5	f(ω	f(ω	PROPN
ejpam-5466	254	6	,	,	PUNCT
ejpam-5466	254	7	τ	τ	PROPN
ejpam-5466	254	8	,	,	PUNCT
ejpam-5466	254	9	ν(τ))dτ	ν(τ))dτ	PROPN
ejpam-5466	254	10	,	,	PUNCT
ejpam-5466	254	11	ω	ω	PROPN
ejpam-5466	254	12	∈	∈	PROPN
ejpam-5466	254	13	j	j	PROPN
ejpam-5466	254	14	=	=	PUNCT
ejpam-5466	255	1	[	[	X
ejpam-5466	255	2	a	a	X
ejpam-5466	255	3	,	,	PUNCT
ejpam-5466	255	4	b	b	NOUN
ejpam-5466	255	5	]	]	X
ejpam-5466	255	6	.	.	PUNCT
ejpam-5466	256	1	(	(	PUNCT
ejpam-5466	256	2	3.1	3.1	NUM
ejpam-5466	256	3	)	)	PUNCT
ejpam-5466	256	4	where	where	SCONJ
ejpam-5466	256	5	p	p	PROPN
ejpam-5466	256	6	∈	∈	PROPN
ejpam-5466	256	7	x	x	X
ejpam-5466	256	8	and	and	CCONJ
ejpam-5466	256	9	f	f	X
ejpam-5466	256	10	:	:	PUNCT
ejpam-5466	256	11	j	j	PROPN
ejpam-5466	256	12	×	×	NOUN
ejpam-5466	256	13	j	j	PROPN
ejpam-5466	256	14	×	×	NOUN
ejpam-5466	256	15	r	r	NOUN
ejpam-5466	256	16	→	→	SYM
ejpam-5466	256	17	k(r	k(r	NOUN
ejpam-5466	256	18	)	)	PUNCT
ejpam-5466	256	19	.	.	PUNCT
ejpam-5466	256	20	consider	consider	VERB
ejpam-5466	256	21	the	the	DET
ejpam-5466	256	22	set	set	NOUN
ejpam-5466	256	23	-	-	PUNCT
ejpam-5466	256	24	valued	value	VERB
ejpam-5466	256	25	operator	operator	NOUN
ejpam-5466	256	26	t	t	NOUN
ejpam-5466	256	27	:	:	PUNCT
ejpam-5466	256	28	x	x	X
ejpam-5466	256	29	→	→	SYM
ejpam-5466	256	30	cl(x	cl(x	NOUN
ejpam-5466	256	31	)	)	PUNCT
ejpam-5466	256	32	as	as	SCONJ
ejpam-5466	256	33	follows	follow	VERB
ejpam-5466	256	34	t	t	PROPN
ejpam-5466	256	35	ν(ω	ν(ω	NOUN
ejpam-5466	256	36	)	)	PUNCT
ejpam-5466	257	1	=	=	SYM
ejpam-5466	257	2	{	{	PUNCT
ejpam-5466	257	3	µ	µ	X
ejpam-5466	257	4	∈	∈	NOUN
ejpam-5466	257	5	x	x	X
ejpam-5466	257	6	:	:	PUNCT
ejpam-5466	257	7	µ	µ	X
ejpam-5466	257	8	∈	∈	PROPN
ejpam-5466	257	9	p(ω	p(ω	PROPN
ejpam-5466	257	10	)	)	PUNCT
ejpam-5466	258	1	+	+	NUM
ejpam-5466	258	2	∫	∫	PROPN
ejpam-5466	258	3	ω	ω	NUM
ejpam-5466	258	4	a	a	DET
ejpam-5466	258	5	f(ω	f(ω	PROPN
ejpam-5466	258	6	,	,	PUNCT
ejpam-5466	258	7	τ	τ	PROPN
ejpam-5466	258	8	,	,	PUNCT
ejpam-5466	258	9	ν(τ))dτ	ν(τ))dτ	PROPN
ejpam-5466	258	10	,	,	PUNCT
ejpam-5466	258	11	ω	ω	PROPN
ejpam-5466	258	12	∈	∈	PROPN
ejpam-5466	258	13	j	j	PROPN
ejpam-5466	258	14	}	}	PUNCT
ejpam-5466	258	15	.	.	PUNCT
ejpam-5466	259	1	we	we	PRON
ejpam-5466	259	2	consider	consider	VERB
ejpam-5466	259	3	the	the	DET
ejpam-5466	259	4	following	follow	VERB
ejpam-5466	259	5	hypotheses	hypothesis	NOUN
ejpam-5466	259	6	:	:	PUNCT
ejpam-5466	259	7	h.	h.	PROPN
ejpam-5466	259	8	qawaqneh	qawaqneh	PROPN
ejpam-5466	259	9	et	et	PROPN
ejpam-5466	259	10	al	al	PROPN
ejpam-5466	259	11	.	.	PUNCT
ejpam-5466	259	12	/	/	SYM
ejpam-5466	259	13	eur	eur	PROPN
ejpam-5466	259	14	.	.	PUNCT
ejpam-5466	260	1	j.	j.	PROPN
ejpam-5466	260	2	pure	pure	PROPN
ejpam-5466	260	3	appl	appl	PROPN
ejpam-5466	260	4	.	.	PROPN
ejpam-5466	260	5	math	math	PROPN
ejpam-5466	260	6	,	,	PUNCT
ejpam-5466	260	7	17	17	NUM
ejpam-5466	260	8	(	(	PUNCT
ejpam-5466	260	9	4	4	NUM
ejpam-5466	260	10	)	)	PUNCT
ejpam-5466	260	11	(	(	PUNCT
ejpam-5466	260	12	2024	2024	NUM
ejpam-5466	260	13	)	)	PUNCT
ejpam-5466	260	14	,	,	PUNCT
ejpam-5466	260	15	3093	3093	NUM
ejpam-5466	260	16	-	-	SYM
ejpam-5466	260	17	3108	3108	NUM
ejpam-5466	260	18	3104	3104	NUM
ejpam-5466	260	19	(	(	PUNCT
ejpam-5466	260	20	a1	a1	PROPN
ejpam-5466	260	21	)	)	PUNCT
ejpam-5466	260	22	:	:	PUNCT
ejpam-5466	260	23	for	for	ADP
ejpam-5466	260	24	each	each	DET
ejpam-5466	260	25	ν	ν	NOUN
ejpam-5466	260	26	∈	∈	PROPN
ejpam-5466	260	27	x	x	NOUN
ejpam-5466	260	28	,	,	PUNCT
ejpam-5466	260	29	the	the	DET
ejpam-5466	260	30	multivalued	multivalue	VERB
ejpam-5466	260	31	operator	operator	NOUN
ejpam-5466	260	32	fν	fν	NOUN
ejpam-5466	260	33	:	:	PUNCT
ejpam-5466	260	34	(	(	PUNCT
ejpam-5466	260	35	ω	ω	PROPN
ejpam-5466	260	36	,	,	PUNCT
ejpam-5466	260	37	τ	τ	PROPN
ejpam-5466	260	38	)	)	PUNCT
ejpam-5466	260	39	7→	7→	PROPN
ejpam-5466	260	40	f(ω	f(ω	PROPN
ejpam-5466	260	41	,	,	PUNCT
ejpam-5466	260	42	τ	τ	PROPN
ejpam-5466	260	43	,	,	PUNCT
ejpam-5466	260	44	ν(τ	ν(τ	PROPN
ejpam-5466	260	45	)	)	PUNCT
ejpam-5466	260	46	)	)	PUNCT
ejpam-5466	260	47	,	,	PUNCT
ejpam-5466	260	48	is	be	AUX
ejpam-5466	260	49	lower	low	ADJ
ejpam-5466	260	50	semi	semi	ADV
ejpam-5466	260	51	continuous	continuous	ADJ
ejpam-5466	260	52	.	.	PUNCT
ejpam-5466	261	1	(	(	PUNCT
ejpam-5466	261	2	a2	a2	PROPN
ejpam-5466	261	3	)	)	PUNCT
ejpam-5466	261	4	:	:	PUNCT
ejpam-5466	261	5	there	there	PRON
ejpam-5466	261	6	exists	exist	VERB
ejpam-5466	261	7	a	a	DET
ejpam-5466	261	8	continuous	continuous	ADJ
ejpam-5466	261	9	function	function	NOUN
ejpam-5466	261	10	ξ	ξ	PROPN
ejpam-5466	261	11	:	:	PUNCT
ejpam-5466	261	12	j	j	PROPN
ejpam-5466	261	13	×	×	PROPN
ejpam-5466	261	14	j	j	PROPN
ejpam-5466	261	15	→	→	PUNCT
ejpam-5466	262	1	[	[	X
ejpam-5466	262	2	0,+∞	0,+∞	NUM
ejpam-5466	262	3	)	)	PUNCT
ejpam-5466	262	4	such	such	ADJ
ejpam-5466	262	5	that	that	SCONJ
ejpam-5466	262	6	|qν(ω	|qν(ω	PROPN
ejpam-5466	262	7	,	,	PUNCT
ejpam-5466	262	8	τ)−	τ)−	PROPN
ejpam-5466	262	9	qµ(ω	qµ(ω	X
ejpam-5466	262	10	,	,	PUNCT
ejpam-5466	262	11	τ)|	τ)|	ADJ
ejpam-5466	262	12	≤	≤	NUM
ejpam-5466	262	13	ξ(ω	ξ(ω	NOUN
ejpam-5466	262	14	,	,	PUNCT
ejpam-5466	262	15	τ)|ν(τ)−	τ)|ν(τ)−	NOUN
ejpam-5466	262	16	µ(τ)|	µ(τ)|	PRON
ejpam-5466	262	17	.	.	PUNCT
ejpam-5466	263	1	for	for	ADP
ejpam-5466	263	2	all	all	DET
ejpam-5466	263	3	ν	ν	PROPN
ejpam-5466	263	4	,	,	PUNCT
ejpam-5466	263	5	µ	µ	X
ejpam-5466	263	6	∈	∈	X
ejpam-5466	263	7	x	x	NOUN
ejpam-5466	263	8	,	,	PUNCT
ejpam-5466	263	9	all	all	PRON
ejpam-5466	263	10	qν	qν	ADP
ejpam-5466	263	11	∈	∈	NOUN
ejpam-5466	263	12	fν	fν	NOUN
ejpam-5466	263	13	,	,	PUNCT
ejpam-5466	263	14	qµ	qµ	ADP
ejpam-5466	263	15	∈	∈	PROPN
ejpam-5466	263	16	fµ	fµ	NOUN
ejpam-5466	263	17	and	and	CCONJ
ejpam-5466	263	18	for	for	ADP
ejpam-5466	263	19	each	each	DET
ejpam-5466	263	20	(	(	PUNCT
ejpam-5466	263	21	ω	ω	PROPN
ejpam-5466	263	22	,	,	PUNCT
ejpam-5466	263	23	τ	τ	X
ejpam-5466	263	24	)	)	PUNCT
ejpam-5466	263	25	∈	∈	PROPN
ejpam-5466	264	1	j	j	PROPN
ejpam-5466	264	2	×	×	PROPN
ejpam-5466	264	3	j	j	PROPN
ejpam-5466	264	4	.	.	PUNCT
ejpam-5466	265	1	(	(	PUNCT
ejpam-5466	265	2	a3	a3	PROPN
ejpam-5466	265	3	)	)	PUNCT
ejpam-5466	265	4	:	:	PUNCT
ejpam-5466	265	5	there	there	PRON
ejpam-5466	265	6	exists	exist	VERB
ejpam-5466	265	7	γ	γ	PROPN
ejpam-5466	265	8	>	>	X
ejpam-5466	265	9	0	0	NUM
ejpam-5466	265	10	such	such	ADJ
ejpam-5466	265	11	that	that	DET
ejpam-5466	265	12	sup	sup	NOUN
ejpam-5466	265	13	ω∈j	ω∈j	NUM
ejpam-5466	265	14	∫	∫	PROPN
ejpam-5466	265	15	ω	ω	NUM
ejpam-5466	265	16	a	a	DET
ejpam-5466	265	17	|ξ(ω	|ξ(ω	NOUN
ejpam-5466	265	18	,	,	PUNCT
ejpam-5466	265	19	τ)|dτ	τ)|dτ	NOUN
ejpam-5466	265	20	≤	≤	NUM
ejpam-5466	265	21	(	(	PUNCT
ejpam-5466	265	22	e−γ	e−γ	NOUN
ejpam-5466	265	23	8	8	NUM
ejpam-5466	265	24	)	)	PUNCT
ejpam-5466	265	25	1	1	NUM
ejpam-5466	265	26	2	2	NUM
ejpam-5466	265	27	.	.	PUNCT
ejpam-5466	266	1	theorem	theorem	VERB
ejpam-5466	266	2	4	4	NUM
ejpam-5466	266	3	.	.	PUNCT
ejpam-5466	267	1	the	the	DET
ejpam-5466	267	2	integral	integral	ADJ
ejpam-5466	267	3	inclusion	inclusion	NOUN
ejpam-5466	267	4	(	(	PUNCT
ejpam-5466	267	5	3.1	3.1	NUM
ejpam-5466	267	6	)	)	PUNCT
ejpam-5466	267	7	has	have	VERB
ejpam-5466	267	8	a	a	DET
ejpam-5466	267	9	solution	solution	NOUN
ejpam-5466	267	10	in	in	ADP
ejpam-5466	267	11	x	x	PUNCT
ejpam-5466	267	12	provided	provide	VERB
ejpam-5466	267	13	the	the	DET
ejpam-5466	267	14	assumptions	assumption	NOUN
ejpam-5466	267	15	(	(	PUNCT
ejpam-5466	267	16	a1)−	a1)−	PROPN
ejpam-5466	267	17	(	(	PUNCT
ejpam-5466	267	18	a3	a3	NOUN
ejpam-5466	267	19	)	)	PUNCT
ejpam-5466	267	20	hold	hold	VERB
ejpam-5466	267	21	.	.	PUNCT
ejpam-5466	268	1	proof	proof	NOUN
ejpam-5466	268	2	.	.	PUNCT
ejpam-5466	269	1	the	the	DET
ejpam-5466	269	2	set	set	NOUN
ejpam-5466	269	3	-	-	PUNCT
ejpam-5466	269	4	valued	value	VERB
ejpam-5466	269	5	operator	operator	NOUN
ejpam-5466	269	6	fν(ω	fν(ω	PUNCT
ejpam-5466	269	7	,	,	PUNCT
ejpam-5466	269	8	τ	τ	X
ejpam-5466	269	9	)	)	PUNCT
ejpam-5466	269	10	:	:	PUNCT
ejpam-5466	270	1	j	j	PROPN
ejpam-5466	270	2	×	×	PROPN
ejpam-5466	270	3	j	j	PROPN
ejpam-5466	270	4	→	→	PUNCT
ejpam-5466	270	5	k(r	k(r	PROPN
ejpam-5466	270	6	)	)	PUNCT
ejpam-5466	270	7	is	be	AUX
ejpam-5466	270	8	lower	low	ADJ
ejpam-5466	270	9	semi	semi	ADV
ejpam-5466	270	10	continuous	continuous	ADJ
ejpam-5466	270	11	,	,	PUNCT
ejpam-5466	270	12	then	then	ADV
ejpam-5466	270	13	from	from	ADP
ejpam-5466	270	14	michael	michael	PROPN
ejpam-5466	270	15	’s	’s	PART
ejpam-5466	270	16	selection	selection	NOUN
ejpam-5466	270	17	theorem	theorem	VERB
ejpam-5466	270	18	,	,	PUNCT
ejpam-5466	270	19	for	for	ADP
ejpam-5466	270	20	ν	ν	DET
ejpam-5466	270	21	∈	∈	PROPN
ejpam-5466	270	22	x	x	SYM
ejpam-5466	270	23	there	there	PRON
ejpam-5466	270	24	exists	exist	VERB
ejpam-5466	270	25	a	a	DET
ejpam-5466	270	26	continuous	continuous	ADJ
ejpam-5466	270	27	function	function	NOUN
ejpam-5466	270	28	qν	qν	ADP
ejpam-5466	270	29	:	:	PUNCT
ejpam-5466	270	30	j	j	PROPN
ejpam-5466	270	31	×	×	PROPN
ejpam-5466	270	32	j	j	PROPN
ejpam-5466	270	33	→	→	PUNCT
ejpam-5466	270	34	r	r	NOUN
ejpam-5466	270	35	such	such	ADJ
ejpam-5466	270	36	that	that	PRON
ejpam-5466	270	37	qν(ω	qν(ω	NUM
ejpam-5466	270	38	,	,	PUNCT
ejpam-5466	270	39	τ	τ	X
ejpam-5466	270	40	)	)	PUNCT
ejpam-5466	270	41	∈	∈	PROPN
ejpam-5466	270	42	fν(ω	fν(ω	PUNCT
ejpam-5466	270	43	,	,	PUNCT
ejpam-5466	270	44	τ	τ	X
ejpam-5466	270	45	)	)	PUNCT
ejpam-5466	270	46	for	for	ADP
ejpam-5466	270	47	all	all	DET
ejpam-5466	270	48	ω	ω	PROPN
ejpam-5466	270	49	,	,	PUNCT
ejpam-5466	270	50	τ	τ	PROPN
ejpam-5466	270	51	∈	∈	PROPN
ejpam-5466	270	52	j	j	PROPN
ejpam-5466	270	53	.	.	PUNCT
ejpam-5466	271	1	it	it	PRON
ejpam-5466	271	2	follows	follow	VERB
ejpam-5466	271	3	that	that	SCONJ
ejpam-5466	271	4	p(ω	p(ω	PROPN
ejpam-5466	271	5	)	)	PUNCT
ejpam-5466	272	1	+	+	NUM
ejpam-5466	272	2	∫	∫	PROPN
ejpam-5466	272	3	ω	ω	NUM
ejpam-5466	272	4	a	a	DET
ejpam-5466	272	5	qν(ω	qν(ω	NOUN
ejpam-5466	272	6	,	,	PUNCT
ejpam-5466	272	7	τ)ds	τ)ds	PROPN
ejpam-5466	272	8	∈	∈	PROPN
ejpam-5466	272	9	t	t	NOUN
ejpam-5466	272	10	ν	ν	NOUN
ejpam-5466	272	11	,	,	PUNCT
ejpam-5466	272	12	so	so	SCONJ
ejpam-5466	272	13	t	t	PROPN
ejpam-5466	272	14	ν	ν	NOUN
ejpam-5466	272	15	is	be	AUX
ejpam-5466	272	16	non	non	ADJ
ejpam-5466	272	17	-	-	ADJ
ejpam-5466	272	18	empty	empty	ADJ
ejpam-5466	272	19	for	for	ADP
ejpam-5466	272	20	all	all	PRON
ejpam-5466	272	21	ν	ν	NOUN
ejpam-5466	272	22	∈	∈	NOUN
ejpam-5466	272	23	x̃.	x̃.	ADV
ejpam-5466	272	24	since	since	SCONJ
ejpam-5466	272	25	p	p	NOUN
ejpam-5466	272	26	and	and	CCONJ
ejpam-5466	272	27	qν	qν	PROPN
ejpam-5466	272	28	are	be	AUX
ejpam-5466	272	29	continuous	continuous	ADJ
ejpam-5466	272	30	on	on	ADP
ejpam-5466	272	31	j	j	PROPN
ejpam-5466	272	32	,	,	PUNCT
ejpam-5466	272	33	resp	resp	PROPN
ejpam-5466	272	34	.	.	PUNCT
ejpam-5466	273	1	j	j	PROPN
ejpam-5466	273	2	2	2	NUM
ejpam-5466	273	3	,	,	PUNCT
ejpam-5466	273	4	their	their	PRON
ejpam-5466	273	5	ranges	range	NOUN
ejpam-5466	273	6	are	be	AUX
ejpam-5466	273	7	bounded	bound	VERB
ejpam-5466	273	8	and	and	CCONJ
ejpam-5466	273	9	closed	close	VERB
ejpam-5466	273	10	and	and	CCONJ
ejpam-5466	273	11	hence	hence	ADV
ejpam-5466	273	12	t	t	PROPN
ejpam-5466	273	13	ν	ν	PROPN
ejpam-5466	273	14	is	be	AUX
ejpam-5466	273	15	bounded	bound	VERB
ejpam-5466	273	16	,	,	PUNCT
ejpam-5466	273	17	i.e.	i.e.	X
ejpam-5466	273	18	,	,	PUNCT
ejpam-5466	273	19	t	t	X
ejpam-5466	273	20	:	:	PUNCT
ejpam-5466	274	1	x	x	X
ejpam-5466	274	2	→	→	SYM
ejpam-5466	274	3	k(x	k(x	PROPN
ejpam-5466	274	4	)	)	PUNCT
ejpam-5466	274	5	.	.	PUNCT
ejpam-5466	275	1	let	let	VERB
ejpam-5466	275	2	ν	ν	NOUN
ejpam-5466	275	3	,	,	PUNCT
ejpam-5466	275	4	µ	µ	X
ejpam-5466	275	5	∈	∈	NOUN
ejpam-5466	275	6	x	x	PUNCT
ejpam-5466	275	7	and	and	CCONJ
ejpam-5466	275	8	let	let	VERB
ejpam-5466	275	9	ϑ	ϑ	X
ejpam-5466	275	10	∈	∈	PROPN
ejpam-5466	275	11	t	t	PROPN
ejpam-5466	275	12	ν	ν	PROPN
ejpam-5466	275	13	.	.	PUNCT
ejpam-5466	276	1	then	then	ADV
ejpam-5466	276	2	ϑ(ω	ϑ(ω	ADV
ejpam-5466	276	3	)	)	PUNCT
ejpam-5466	276	4	∈	∈	PROPN
ejpam-5466	276	5	p(ω	p(ω	PROPN
ejpam-5466	276	6	)	)	PUNCT
ejpam-5466	277	1	+	+	NUM
ejpam-5466	277	2	∫	∫	PROPN
ejpam-5466	277	3	ω	ω	NUM
ejpam-5466	277	4	a	a	DET
ejpam-5466	277	5	f(ω	f(ω	PROPN
ejpam-5466	277	6	,	,	PUNCT
ejpam-5466	277	7	τ	τ	PROPN
ejpam-5466	277	8	,	,	PUNCT
ejpam-5466	277	9	ν(τ))dτ	ν(τ))dτ	PROPN
ejpam-5466	277	10	,	,	PUNCT
ejpam-5466	277	11	ω	ω	PROPN
ejpam-5466	277	12	∈	∈	PROPN
ejpam-5466	277	13	j	j	PROPN
ejpam-5466	277	14	.	.	PUNCT
ejpam-5466	278	1	it	it	PRON
ejpam-5466	278	2	follows	follow	VERB
ejpam-5466	278	3	that	that	SCONJ
ejpam-5466	278	4	there	there	PRON
ejpam-5466	278	5	exists	exist	VERB
ejpam-5466	278	6	qν	qν	ADP
ejpam-5466	278	7	∈	∈	PROPN
ejpam-5466	278	8	f(ω	f(ω	PROPN
ejpam-5466	278	9	,	,	PUNCT
ejpam-5466	278	10	τ	τ	PROPN
ejpam-5466	278	11	)	)	PUNCT
ejpam-5466	278	12	such	such	ADJ
ejpam-5466	278	13	that	that	SCONJ
ejpam-5466	278	14	ϑ(ω	ϑ(ω	ADV
ejpam-5466	278	15	)	)	PUNCT
ejpam-5466	278	16	=	=	SYM
ejpam-5466	278	17	p(ω	p(ω	PROPN
ejpam-5466	278	18	)	)	PUNCT
ejpam-5466	279	1	+	+	NUM
ejpam-5466	279	2	∫	∫	PROPN
ejpam-5466	279	3	ω	ω	NUM
ejpam-5466	279	4	a	a	DET
ejpam-5466	279	5	qν(ω	qν(ω	NOUN
ejpam-5466	279	6	,	,	PUNCT
ejpam-5466	279	7	τ)dτ	τ)dτ	PROPN
ejpam-5466	279	8	,	,	PUNCT
ejpam-5466	279	9	(	(	PUNCT
ejpam-5466	279	10	ω	ω	PROPN
ejpam-5466	279	11	,	,	PUNCT
ejpam-5466	279	12	τ	τ	X
ejpam-5466	279	13	)	)	PUNCT
ejpam-5466	279	14	∈	∈	PROPN
ejpam-5466	280	1	j	j	PROPN
ejpam-5466	280	2	×	×	PROPN
ejpam-5466	280	3	j	j	PROPN
ejpam-5466	280	4	,	,	PUNCT
ejpam-5466	280	5	from	from	ADP
ejpam-5466	280	6	(	(	PUNCT
ejpam-5466	280	7	a2	a2	PROPN
ejpam-5466	280	8	)	)	PUNCT
ejpam-5466	280	9	,	,	PUNCT
ejpam-5466	280	10	there	there	PRON
ejpam-5466	280	11	exists	exist	VERB
ejpam-5466	280	12	ς(ω	ς(ω	PROPN
ejpam-5466	280	13	,	,	PUNCT
ejpam-5466	280	14	τ	τ	NOUN
ejpam-5466	280	15	)	)	PUNCT
ejpam-5466	280	16	∈	∈	PROPN
ejpam-5466	280	17	fµ(ω	fµ(ω	PROPN
ejpam-5466	280	18	,	,	PUNCT
ejpam-5466	280	19	τ	τ	PROPN
ejpam-5466	280	20	)	)	PUNCT
ejpam-5466	281	1	such	such	ADJ
ejpam-5466	281	2	that	that	SCONJ
ejpam-5466	281	3	|qν(ω	|qν(ω	PROPN
ejpam-5466	281	4	,	,	PUNCT
ejpam-5466	281	5	τ)−	τ)−	PROPN
ejpam-5466	281	6	ς(ω	ς(ω	PROPN
ejpam-5466	281	7	,	,	PUNCT
ejpam-5466	281	8	τ)|	τ)|	ADJ
ejpam-5466	281	9	≤	≤	NUM
ejpam-5466	281	10	ξ(ω	ξ(ω	NOUN
ejpam-5466	281	11	,	,	PUNCT
ejpam-5466	281	12	τ	τ	X
ejpam-5466	281	13	)	)	PUNCT
ejpam-5466	281	14	·	·	PUNCT
ejpam-5466	281	15	|ν(τ)−	|ν(τ)−	NUM
ejpam-5466	281	16	µ(τ)|2	µ(τ)|2	PROPN
ejpam-5466	281	17	,	,	PUNCT
ejpam-5466	281	18	for	for	ADP
ejpam-5466	281	19	all	all	DET
ejpam-5466	281	20	(	(	PUNCT
ejpam-5466	281	21	ω	ω	PROPN
ejpam-5466	281	22	,	,	PUNCT
ejpam-5466	281	23	τ	τ	X
ejpam-5466	281	24	)	)	PUNCT
ejpam-5466	281	25	∈	∈	PROPN
ejpam-5466	281	26	j	j	PROPN
ejpam-5466	281	27	×	×	PROPN
ejpam-5466	281	28	j	j	PROPN
ejpam-5466	281	29	.	.	PUNCT
ejpam-5466	282	1	let	let	VERB
ejpam-5466	282	2	p	p	PRON
ejpam-5466	282	3	be	be	AUX
ejpam-5466	282	4	a	a	DET
ejpam-5466	282	5	multi	multi	NOUN
ejpam-5466	282	6	valued	value	VERB
ejpam-5466	282	7	operator	operator	NOUN
ejpam-5466	282	8	defined	define	VERB
ejpam-5466	282	9	by	by	ADP
ejpam-5466	282	10	p(ω	p(ω	PROPN
ejpam-5466	282	11	,	,	PUNCT
ejpam-5466	282	12	τ	τ	PROPN
ejpam-5466	282	13	)	)	PUNCT
ejpam-5466	282	14	=	=	SYM
ejpam-5466	282	15	fµ(ω	fµ(ω	PROPN
ejpam-5466	282	16	,	,	PUNCT
ejpam-5466	282	17	τ	τ	NOUN
ejpam-5466	282	18	)	)	PUNCT
ejpam-5466	282	19	∩	∩	NOUN
ejpam-5466	282	20	{	{	PUNCT
ejpam-5466	282	21	z	z	NOUN
ejpam-5466	282	22	∈	∈	NOUN
ejpam-5466	282	23	r	r	NOUN
ejpam-5466	282	24	:	:	PUNCT
ejpam-5466	282	25	|qν(ω	|qν(ω	NOUN
ejpam-5466	282	26	,	,	PUNCT
ejpam-5466	282	27	τ)−	τ)−	PROPN
ejpam-5466	282	28	z|	z|	PROPN
ejpam-5466	282	29	≤	≤	NOUN
ejpam-5466	282	30	ξ(ω	ξ(ω	NOUN
ejpam-5466	282	31	,	,	PUNCT
ejpam-5466	282	32	τ	τ	X
ejpam-5466	282	33	)	)	PUNCT
ejpam-5466	282	34	·	·	PUNCT
ejpam-5466	282	35	|ν(τ)−	|ν(τ)−	NOUN
ejpam-5466	283	1	µ(τ)|	µ(τ)|	PRON
ejpam-5466	283	2	}	}	PUNCT
ejpam-5466	283	3	,	,	PUNCT
ejpam-5466	283	4	for	for	ADP
ejpam-5466	283	5	all	all	DET
ejpam-5466	283	6	(	(	PUNCT
ejpam-5466	283	7	ω	ω	PROPN
ejpam-5466	283	8	,	,	PUNCT
ejpam-5466	283	9	τ	τ	X
ejpam-5466	283	10	)	)	PUNCT
ejpam-5466	283	11	∈	∈	PROPN
ejpam-5466	284	1	j	j	PROPN
ejpam-5466	284	2	×	×	PROPN
ejpam-5466	284	3	j	j	PROPN
ejpam-5466	284	4	.	.	PUNCT
ejpam-5466	285	1	since	since	SCONJ
ejpam-5466	285	2	,	,	PUNCT
ejpam-5466	285	3	by	by	ADP
ejpam-5466	285	4	(	(	PUNCT
ejpam-5466	285	5	a1	a1	NOUN
ejpam-5466	285	6	)	)	PUNCT
ejpam-5466	285	7	,	,	PUNCT
ejpam-5466	285	8	p	p	NOUN
ejpam-5466	285	9	is	be	AUX
ejpam-5466	285	10	lower	low	ADJ
ejpam-5466	285	11	semi	semi	ADJ
ejpam-5466	285	12	-	-	ADJ
ejpam-5466	285	13	continuous	continuous	ADJ
ejpam-5466	285	14	,	,	PUNCT
ejpam-5466	285	15	there	there	PRON
ejpam-5466	285	16	exists	exist	VERB
ejpam-5466	285	17	a	a	DET
ejpam-5466	285	18	continuous	continuous	ADJ
ejpam-5466	285	19	function	function	NOUN
ejpam-5466	285	20	qµ(ω	qµ(ω	NOUN
ejpam-5466	285	21	,	,	PUNCT
ejpam-5466	285	22	τ	τ	X
ejpam-5466	285	23	)	)	PUNCT
ejpam-5466	285	24	∈	∈	PROPN
ejpam-5466	285	25	p(ω	p(ω	PROPN
ejpam-5466	285	26	,	,	PUNCT
ejpam-5466	285	27	τ	τ	PROPN
ejpam-5466	285	28	)	)	PUNCT
ejpam-5466	285	29	.	.	PUNCT
ejpam-5466	286	1	then	then	ADV
ejpam-5466	286	2	we	we	PRON
ejpam-5466	286	3	have	have	VERB
ejpam-5466	286	4	ζ(ω	ζ(ω	PROPN
ejpam-5466	286	5	)	)	PUNCT
ejpam-5466	286	6	=	=	SYM
ejpam-5466	286	7	p(ω	p(ω	PROPN
ejpam-5466	286	8	)	)	PUNCT
ejpam-5466	287	1	+	+	NUM
ejpam-5466	287	2	∫	∫	PROPN
ejpam-5466	287	3	ω	ω	NUM
ejpam-5466	287	4	a	a	DET
ejpam-5466	287	5	qµ(ω	qµ(ω	NOUN
ejpam-5466	287	6	,	,	PUNCT
ejpam-5466	287	7	τ)dτ	τ)dτ	PROPN
ejpam-5466	287	8	∈	∈	PROPN
ejpam-5466	287	9	p(ω	p(ω	PROPN
ejpam-5466	287	10	)	)	PUNCT
ejpam-5466	288	1	+	+	NUM
ejpam-5466	288	2	∫	∫	PROPN
ejpam-5466	288	3	ω	ω	NUM
ejpam-5466	288	4	a	a	DET
ejpam-5466	288	5	f(ω	f(ω	PROPN
ejpam-5466	288	6	,	,	PUNCT
ejpam-5466	288	7	τ	τ	PROPN
ejpam-5466	288	8	,	,	PUNCT
ejpam-5466	288	9	µ(τ))dτ	µ(τ))dτ	PROPN
ejpam-5466	288	10	,	,	PUNCT
ejpam-5466	289	1	ω	ω	PROPN
ejpam-5466	289	2	∈	∈	PROPN
ejpam-5466	289	3	j	j	PROPN
ejpam-5466	289	4	h.	h.	PROPN
ejpam-5466	289	5	qawaqneh	qawaqneh	PROPN
ejpam-5466	289	6	et	et	PROPN
ejpam-5466	289	7	al	al	PROPN
ejpam-5466	289	8	.	.	PUNCT
ejpam-5466	289	9	/	/	SYM
ejpam-5466	289	10	eur	eur	PROPN
ejpam-5466	289	11	.	.	PUNCT
ejpam-5466	290	1	j.	j.	PROPN
ejpam-5466	290	2	pure	pure	PROPN
ejpam-5466	290	3	appl	appl	PROPN
ejpam-5466	290	4	.	.	PROPN
ejpam-5466	290	5	math	math	PROPN
ejpam-5466	290	6	,	,	PUNCT
ejpam-5466	290	7	17	17	NUM
ejpam-5466	290	8	(	(	PUNCT
ejpam-5466	290	9	4	4	NUM
ejpam-5466	290	10	)	)	PUNCT
ejpam-5466	290	11	(	(	PUNCT
ejpam-5466	290	12	2024	2024	NUM
ejpam-5466	290	13	)	)	PUNCT
ejpam-5466	290	14	,	,	PUNCT
ejpam-5466	290	15	3093	3093	NUM
ejpam-5466	290	16	-	-	SYM
ejpam-5466	290	17	3108	3108	NUM
ejpam-5466	290	18	3105	3105	NUM
ejpam-5466	290	19	and	and	CCONJ
ejpam-5466	290	20	d(ϑ	d(ϑ	PROPN
ejpam-5466	290	21	,	,	PUNCT
ejpam-5466	290	22	t	t	NOUN
ejpam-5466	290	23	µ	µ	NOUN
ejpam-5466	290	24	)	)	PUNCT
ejpam-5466	290	25	≤	≤	NOUN
ejpam-5466	290	26	|ϑ(ω	|ϑ(ω	PROPN
ejpam-5466	290	27	,	,	PUNCT
ejpam-5466	290	28	τ)−	τ)−	PROPN
ejpam-5466	290	29	ζ(ω	ζ(ω	PROPN
ejpam-5466	290	30	,	,	PUNCT
ejpam-5466	290	31	τ)|2	τ)|2	PUNCT
ejpam-5466	290	32	≤	≤	NUM
ejpam-5466	290	33	(	(	PUNCT
ejpam-5466	290	34	∫	∫	PROPN
ejpam-5466	290	35	ω	ω	PROPN
ejpam-5466	290	36	a	a	DET
ejpam-5466	290	37	|qν(ω	|qν(ω	PROPN
ejpam-5466	290	38	,	,	PUNCT
ejpam-5466	290	39	τ)−	τ)−	PROPN
ejpam-5466	290	40	qµ(ω	qµ(ω	X
ejpam-5466	290	41	,	,	PUNCT
ejpam-5466	290	42	τ)|dτ	τ)|dτ	NOUN
ejpam-5466	290	43	)	)	PUNCT
ejpam-5466	290	44	2	2	NUM
ejpam-5466	290	45	≤	≤	NOUN
ejpam-5466	290	46	(	(	PUNCT
ejpam-5466	290	47	∫	∫	PROPN
ejpam-5466	290	48	ω	ω	NUM
ejpam-5466	290	49	a	a	DET
ejpam-5466	290	50	ξ(ω	ξ(ω	NOUN
ejpam-5466	290	51	,	,	PUNCT
ejpam-5466	290	52	τ)|ν(τ)−	τ)|ν(τ)−	ADJ
ejpam-5466	290	53	µ(τ)|dτ	µ(τ)|dτ	X
ejpam-5466	290	54	)	)	PUNCT
ejpam-5466	290	55	2	2	NUM
ejpam-5466	290	56	≤	≤	NOUN
ejpam-5466	290	57	sup	sup	NOUN
ejpam-5466	290	58	τ∈[a	τ∈[a	NOUN
ejpam-5466	290	59	,	,	PUNCT
ejpam-5466	290	60	b	b	NOUN
ejpam-5466	290	61	]	]	PUNCT
ejpam-5466	290	62	|ν(τ)−	|ν(τ)−	NOUN
ejpam-5466	290	63	µ(τ)|2	µ(τ)|2	PROPN
ejpam-5466	290	64	(	(	PUNCT
ejpam-5466	290	65	∫	∫	PROPN
ejpam-5466	290	66	ω	ω	NUM
ejpam-5466	290	67	a	a	DET
ejpam-5466	290	68	ξ(ω	ξ(ω	NOUN
ejpam-5466	290	69	,	,	PUNCT
ejpam-5466	290	70	τ)dτ	τ)dτ	NOUN
ejpam-5466	290	71	)	)	PUNCT
ejpam-5466	290	72	2	2	NUM
ejpam-5466	290	73	=	=	SYM
ejpam-5466	290	74	d(ν	d(ν	PROPN
ejpam-5466	290	75	,	,	PUNCT
ejpam-5466	290	76	µ	µ	NOUN
ejpam-5466	290	77	)	)	PUNCT
ejpam-5466	290	78	(	(	PUNCT
ejpam-5466	290	79	∫	∫	PROPN
ejpam-5466	290	80	ω	ω	NUM
ejpam-5466	290	81	a	a	DET
ejpam-5466	290	82	ξ(ω	ξ(ω	NOUN
ejpam-5466	290	83	,	,	PUNCT
ejpam-5466	290	84	τ)dτ)2	τ)dτ)2	VERB
ejpam-5466	290	85	≤	≤	ADJ
ejpam-5466	290	86	e−γ	e−γ	NOUN
ejpam-5466	290	87	8	8	NUM
ejpam-5466	290	88	d(ν	d(ν	PROPN
ejpam-5466	290	89	,	,	PUNCT
ejpam-5466	290	90	µ	µ	NOUN
ejpam-5466	290	91	)	)	PUNCT
ejpam-5466	290	92	.	.	PUNCT
ejpam-5466	291	1	consequently	consequently	ADV
ejpam-5466	291	2	,	,	PUNCT
ejpam-5466	291	3	we	we	PRON
ejpam-5466	291	4	have	have	VERB
ejpam-5466	291	5	8d(ϑ	8d(ϑ	NUM
ejpam-5466	291	6	,	,	PUNCT
ejpam-5466	291	7	t	t	PROPN
ejpam-5466	291	8	µ	µ	NOUN
ejpam-5466	291	9	)	)	PUNCT
ejpam-5466	292	1	≤	≤	NUM
ejpam-5466	292	2	e−γd(ν	e−γd(ν	PROPN
ejpam-5466	292	3	,	,	PUNCT
ejpam-5466	292	4	µ	µ	NOUN
ejpam-5466	292	5	)	)	PUNCT
ejpam-5466	292	6	,	,	PUNCT
ejpam-5466	292	7	interchanging	interchange	VERB
ejpam-5466	292	8	the	the	DET
ejpam-5466	292	9	role	role	NOUN
ejpam-5466	292	10	of	of	ADP
ejpam-5466	292	11	ν	ν	NOUN
ejpam-5466	292	12	and	and	CCONJ
ejpam-5466	292	13	µ	µ	NOUN
ejpam-5466	292	14	,	,	PUNCT
ejpam-5466	292	15	we	we	PRON
ejpam-5466	292	16	get	get	VERB
ejpam-5466	292	17	8h(t	8h(t	NUM
ejpam-5466	292	18	ν	ν	NOUN
ejpam-5466	292	19	,	,	PUNCT
ejpam-5466	292	20	t	t	PROPN
ejpam-5466	292	21	µ	µ	NOUN
ejpam-5466	292	22	)	)	PUNCT
ejpam-5466	292	23	≤	≤	NOUN
ejpam-5466	292	24	e−τd(ν	e−τd(ν	PROPN
ejpam-5466	292	25	,	,	PUNCT
ejpam-5466	292	26	µ	µ	NOUN
ejpam-5466	292	27	)	)	PUNCT
ejpam-5466	292	28	.	.	PUNCT
ejpam-5466	293	1	taking	take	VERB
ejpam-5466	293	2	exponents	exponent	NOUN
ejpam-5466	293	3	we	we	PRON
ejpam-5466	293	4	get	get	VERB
ejpam-5466	293	5	e(8h(t	e(8h(t	PROPN
ejpam-5466	293	6	ν	ν	PROPN
ejpam-5466	293	7	,	,	PUNCT
ejpam-5466	293	8	t	t	PROPN
ejpam-5466	293	9	µ	µ	NOUN
ejpam-5466	293	10	)	)	PUNCT
ejpam-5466	293	11	≤	≤	NOUN
ejpam-5466	293	12	[	[	PUNCT
ejpam-5466	293	13	ed(ν,µ	ed(ν,µ	PROPN
ejpam-5466	293	14	)	)	PUNCT
ejpam-5466	293	15	]	]	PUNCT
ejpam-5466	293	16	e−γ	e−γ	NOUN
ejpam-5466	293	17	then	then	ADV
ejpam-5466	293	18	,	,	PUNCT
ejpam-5466	293	19	the	the	DET
ejpam-5466	293	20	mapping	mapping	NOUN
ejpam-5466	293	21	t	t	NOUN
ejpam-5466	293	22	satisfies	satisfy	VERB
ejpam-5466	293	23	all	all	DET
ejpam-5466	293	24	the	the	DET
ejpam-5466	293	25	conditions	condition	NOUN
ejpam-5466	293	26	of	of	ADP
ejpam-5466	293	27	corollary	corollary	ADJ
ejpam-5466	293	28	3	3	NUM
ejpam-5466	293	29	with	with	ADP
ejpam-5466	293	30	ϑ(ω	ϑ(ω	ADV
ejpam-5466	293	31	)	)	PUNCT
ejpam-5466	293	32	=	=	SYM
ejpam-5466	293	33	eω	eω	PROPN
ejpam-5466	293	34	,	,	PUNCT
ejpam-5466	293	35	a1	a1	NOUN
ejpam-5466	293	36	=	=	SYM
ejpam-5466	293	37	1	1	NUM
ejpam-5466	293	38	,	,	PUNCT
ejpam-5466	293	39	ai	ai	VERB
ejpam-5466	293	40	=	=	ADJ
ejpam-5466	293	41	l	l	NOUN
ejpam-5466	293	42	=	=	SYM
ejpam-5466	293	43	0	0	NUM
ejpam-5466	293	44	,	,	PUNCT
ejpam-5466	293	45	i	i	PRON
ejpam-5466	293	46	=	=	NOUN
ejpam-5466	293	47	2	2	NUM
ejpam-5466	293	48	,	,	PUNCT
ejpam-5466	293	49	3	3	NUM
ejpam-5466	293	50	,	,	PUNCT
ejpam-5466	293	51	4	4	NUM
ejpam-5466	293	52	,	,	PUNCT
ejpam-5466	293	53	5	5	NUM
ejpam-5466	293	54	and	and	CCONJ
ejpam-5466	293	55	κ	κ	NOUN
ejpam-5466	293	56	=	=	PUNCT
ejpam-5466	293	57	e−γ	e−γ	NOUN
ejpam-5466	293	58	.	.	PUNCT
ejpam-5466	294	1	so	so	ADV
ejpam-5466	294	2	,	,	PUNCT
ejpam-5466	294	3	t	t	PROPN
ejpam-5466	294	4	has	have	VERB
ejpam-5466	294	5	a	a	DET
ejpam-5466	294	6	fixed	fix	VERB
ejpam-5466	294	7	point	point	NOUN
ejpam-5466	294	8	,	,	PUNCT
ejpam-5466	294	9	which	which	PRON
ejpam-5466	294	10	implies	imply	VERB
ejpam-5466	294	11	that	that	SCONJ
ejpam-5466	294	12	the	the	DET
ejpam-5466	294	13	integral	integral	ADJ
ejpam-5466	294	14	inclusion	inclusion	NOUN
ejpam-5466	294	15	(	(	PUNCT
ejpam-5466	294	16	3.1	3.1	NUM
ejpam-5466	294	17	)	)	PUNCT
ejpam-5466	294	18	has	have	VERB
ejpam-5466	294	19	a	a	DET
ejpam-5466	294	20	solution	solution	NOUN
ejpam-5466	294	21	in	in	ADP
ejpam-5466	294	22	x.	x.	NOUN
ejpam-5466	294	23	4	4	NUM
ejpam-5466	294	24	.	.	PUNCT
ejpam-5466	294	25	conclusion	conclusion	NOUN
ejpam-5466	294	26	in	in	ADP
ejpam-5466	294	27	presented	present	VERB
ejpam-5466	294	28	paper	paper	NOUN
ejpam-5466	294	29	we	we	PRON
ejpam-5466	294	30	have	have	AUX
ejpam-5466	294	31	introduced	introduce	VERB
ejpam-5466	294	32	a	a	DET
ejpam-5466	294	33	new	new	ADJ
ejpam-5466	294	34	class	class	NOUN
ejpam-5466	294	35	of	of	ADP
ejpam-5466	294	36	multivalued	multivalued	ADJ
ejpam-5466	294	37	contractions	contraction	NOUN
ejpam-5466	294	38	,	,	PUNCT
ejpam-5466	294	39	by	by	ADP
ejpam-5466	294	40	combining	combine	VERB
ejpam-5466	294	41	some	some	DET
ejpam-5466	294	42	concepts	concept	NOUN
ejpam-5466	294	43	,	,	PUNCT
ejpam-5466	294	44	as	as	SCONJ
ejpam-5466	294	45	generalized	generalized	ADJ
ejpam-5466	294	46	berinde	berinde	NOUN
ejpam-5466	294	47	type	type	NOUN
ejpam-5466	294	48	contractive	contractive	ADJ
ejpam-5466	294	49	conditions	condition	NOUN
ejpam-5466	294	50	and	and	CCONJ
ejpam-5466	294	51	αs	αs	ADJ
ejpam-5466	294	52	-	-	ADJ
ejpam-5466	294	53	admissible	admissible	ADJ
ejpam-5466	294	54	mappings	mapping	NOUN
ejpam-5466	294	55	due	due	ADP
ejpam-5466	294	56	to	to	ADP
ejpam-5466	294	57	[	[	X
ejpam-5466	294	58	14	14	NUM
ejpam-5466	294	59	]	]	PUNCT
ejpam-5466	294	60	with	with	ADP
ejpam-5466	294	61	jscontractions	jscontraction	NOUN
ejpam-5466	294	62	type	type	NOUN
ejpam-5466	294	63	due	due	ADP
ejpam-5466	294	64	to	to	ADP
ejpam-5466	294	65	[	[	X
ejpam-5466	294	66	10	10	NUM
ejpam-5466	294	67	]	]	PUNCT
ejpam-5466	294	68	also	also	ADV
ejpam-5466	294	69	we	we	PRON
ejpam-5466	294	70	have	have	AUX
ejpam-5466	294	71	proved	prove	VERB
ejpam-5466	294	72	the	the	DET
ejpam-5466	294	73	existence	existence	NOUN
ejpam-5466	294	74	of	of	ADP
ejpam-5466	294	75	a	a	DET
ejpam-5466	294	76	fixed	fix	VERB
ejpam-5466	294	77	point	point	NOUN
ejpam-5466	294	78	for	for	ADP
ejpam-5466	294	79	such	such	ADJ
ejpam-5466	294	80	novel	novel	ADJ
ejpam-5466	294	81	contractions	contraction	NOUN
ejpam-5466	294	82	under	under	ADP
ejpam-5466	294	83	some	some	DET
ejpam-5466	294	84	conditions	condition	NOUN
ejpam-5466	294	85	.	.	PUNCT
ejpam-5466	295	1	an	an	DET
ejpam-5466	295	2	example	example	NOUN
ejpam-5466	295	3	is	be	AUX
ejpam-5466	295	4	given	give	VERB
ejpam-5466	295	5	to	to	PART
ejpam-5466	295	6	support	support	VERB
ejpam-5466	295	7	the	the	DET
ejpam-5466	295	8	validity	validity	NOUN
ejpam-5466	295	9	of	of	ADP
ejpam-5466	295	10	our	our	PRON
ejpam-5466	295	11	results	result	NOUN
ejpam-5466	295	12	and	and	CCONJ
ejpam-5466	295	13	an	an	DET
ejpam-5466	295	14	application	application	NOUN
ejpam-5466	295	15	to	to	ADP
ejpam-5466	295	16	the	the	DET
ejpam-5466	295	17	existence	existence	NOUN
ejpam-5466	295	18	of	of	ADP
ejpam-5466	295	19	solutions	solution	NOUN
ejpam-5466	295	20	for	for	ADP
ejpam-5466	295	21	integral	integral	ADJ
ejpam-5466	295	22	inclusions	inclusion	NOUN
ejpam-5466	295	23	.	.	PUNCT
ejpam-5466	296	1	acknowledgements	acknowledgement	NOUN
ejpam-5466	296	2	we	we	PRON
ejpam-5466	296	3	extend	extend	VERB
ejpam-5466	296	4	their	their	PRON
ejpam-5466	296	5	appreciation	appreciation	NOUN
ejpam-5466	296	6	to	to	ADP
ejpam-5466	296	7	al	al	PROPN
ejpam-5466	296	8	-	-	PROPN
ejpam-5466	296	9	zaytoonah	zaytoonah	PROPN
ejpam-5466	296	10	university	university	PROPN
ejpam-5466	296	11	of	of	ADP
ejpam-5466	296	12	jordan	jordan	PROPN
ejpam-5466	296	13	(	(	PUNCT
ejpam-5466	296	14	zuj	zuj	PROPN
ejpam-5466	296	15	)	)	PUNCT
ejpam-5466	296	16	and	and	CCONJ
ejpam-5466	296	17	to	to	ADP
ejpam-5466	296	18	the	the	DET
ejpam-5466	296	19	deanship	deanship	NOUN
ejpam-5466	296	20	of	of	ADP
ejpam-5466	296	21	post	post	NOUN
ejpam-5466	296	22	graduate	graduate	ADJ
ejpam-5466	296	23	and	and	CCONJ
ejpam-5466	296	24	scientific	scientific	ADJ
ejpam-5466	296	25	research	research	NOUN
ejpam-5466	296	26	at	at	ADP
ejpam-5466	296	27	dar	dar	PROPN
ejpam-5466	296	28	al	al	PROPN
ejpam-5466	296	29	uloom	uloom	PROPN
ejpam-5466	296	30	university	university	PROPN
ejpam-5466	296	31	for	for	ADP
ejpam-5466	296	32	funding	fund	VERB
ejpam-5466	296	33	this	this	DET
ejpam-5466	296	34	work	work	NOUN
ejpam-5466	296	35	.	.	PUNCT
ejpam-5466	297	1	references	reference	NOUN
ejpam-5466	297	2	3106	3106	NUM
ejpam-5466	297	3	references	reference	NOUN
ejpam-5466	297	4	[	[	X
ejpam-5466	297	5	1	1	X
ejpam-5466	297	6	]	]	X
ejpam-5466	297	7	i	i	PRON
ejpam-5466	297	8	m	m	AUX
ejpam-5466	297	9	batiha	batiha	VERB
ejpam-5466	297	10	;	;	PUNCT
ejpam-5466	297	11	j	j	PROPN
ejpam-5466	297	12	oudetallah	oudetallah	PROPN
ejpam-5466	297	13	;	;	PUNCT
ejpam-5466	297	14	a	a	DET
ejpam-5466	297	15	ouannas	ouanna	NOUN
ejpam-5466	297	16	;	;	PUNCT
ejpam-5466	297	17	a	a	DET
ejpam-5466	297	18	a	a	DET
ejpam-5466	297	19	al	al	PROPN
ejpam-5466	297	20	-	-	PUNCT
ejpam-5466	297	21	nana	nana	PROPN
ejpam-5466	297	22	and	and	CCONJ
ejpam-5466	297	23	i	i	PRON
ejpam-5466	298	1	h	h	NOUN
ejpam-5466	298	2	jebril	jebril	VERB
ejpam-5466	298	3	.	.	PUNCT
ejpam-5466	299	1	tuning	tune	VERB
ejpam-5466	299	2	the	the	DET
ejpam-5466	299	3	fractional	fractional	ADJ
ejpam-5466	299	4	-	-	PUNCT
ejpam-5466	299	5	order	order	NOUN
ejpam-5466	299	6	pid	pid	NOUN
ejpam-5466	299	7	-	-	NOUN
ejpam-5466	299	8	controller	controller	NOUN
ejpam-5466	299	9	for	for	ADP
ejpam-5466	299	10	blood	blood	NOUN
ejpam-5466	299	11	glucose	glucose	NOUN
ejpam-5466	299	12	level	level	NOUN
ejpam-5466	299	13	of	of	ADP
ejpam-5466	299	14	diabetic	diabetic	ADJ
ejpam-5466	299	15	patients	patient	NOUN
ejpam-5466	299	16	.	.	PUNCT
ejpam-5466	300	1	international	international	ADJ
ejpam-5466	300	2	journal	journal	NOUN
ejpam-5466	300	3	of	of	ADP
ejpam-5466	300	4	advances	advance	NOUN
ejpam-5466	300	5	in	in	ADP
ejpam-5466	300	6	soft	soft	ADJ
ejpam-5466	300	7	computing	computing	NOUN
ejpam-5466	300	8	and	and	CCONJ
ejpam-5466	300	9	its	its	PRON
ejpam-5466	300	10	applications	application	NOUN
ejpam-5466	300	11	,	,	PUNCT
ejpam-5466	300	12	13(2):1–10	13(2):1–10	NOUN
ejpam-5466	300	13	,	,	PUNCT
ejpam-5466	300	14	2021	2021	NUM
ejpam-5466	300	15	.	.	PUNCT
ejpam-5466	301	1	[	[	X
ejpam-5466	301	2	2	2	NUM
ejpam-5466	301	3	]	]	X
ejpam-5466	301	4	h	h	NOUN
ejpam-5466	301	5	qawaqneh	qawaqneh	NOUN
ejpam-5466	301	6	;	;	PUNCT
ejpam-5466	301	7	j	j	PROPN
ejpam-5466	301	8	manafian	manafian	NOUN
ejpam-5466	301	9	;	;	PUNCT
ejpam-5466	302	1	m	m	VERB
ejpam-5466	302	2	alharthi	alharthi	PROPN
ejpam-5466	302	3	and	and	CCONJ
ejpam-5466	302	4	y	y	PROPN
ejpam-5466	302	5	alrashed	alrashe	VERB
ejpam-5466	302	6	.	.	PUNCT
ejpam-5466	303	1	stability	stability	NOUN
ejpam-5466	303	2	analysis	analysis	NOUN
ejpam-5466	303	3	,	,	PUNCT
ejpam-5466	303	4	modulation	modulation	NOUN
ejpam-5466	303	5	instability	instability	NOUN
ejpam-5466	303	6	,	,	PUNCT
ejpam-5466	303	7	and	and	CCONJ
ejpam-5466	303	8	beta	beta	NOUN
ejpam-5466	303	9	-	-	PUNCT
ejpam-5466	303	10	time	time	NOUN
ejpam-5466	303	11	fractional	fractional	ADJ
ejpam-5466	303	12	exact	exact	ADJ
ejpam-5466	303	13	soliton	soliton	NOUN
ejpam-5466	303	14	solutions	solution	NOUN
ejpam-5466	303	15	to	to	ADP
ejpam-5466	303	16	the	the	DET
ejpam-5466	303	17	van	van	PROPN
ejpam-5466	303	18	der	der	NOUN
ejpam-5466	303	19	waals	waal	NOUN
ejpam-5466	303	20	equation	equation	NOUN
ejpam-5466	303	21	.	.	PUNCT
ejpam-5466	304	1	mathematics	mathematic	NOUN
ejpam-5466	304	2	,	,	PUNCT
ejpam-5466	304	3	12(14:2257	12(14:2257	NUM
ejpam-5466	304	4	)	)	PUNCT
ejpam-5466	304	5	,	,	PUNCT
ejpam-5466	304	6	2024	2024	NUM
ejpam-5466	304	7	.	.	PUNCT
ejpam-5466	305	1	[	[	X
ejpam-5466	305	2	3	3	NUM
ejpam-5466	305	3	]	]	X
ejpam-5466	305	4	s	s	X
ejpam-5466	305	5	mahideb	mahideb	NOUN
ejpam-5466	305	6	;	;	PUNCT
ejpam-5466	305	7	a	a	DET
ejpam-5466	305	8	ali	ali	PROPN
ejpam-5466	305	9	and	and	CCONJ
ejpam-5466	305	10	s	s	VERB
ejpam-5466	305	11	beloul	beloul	PRON
ejpam-5466	305	12	.	.	PUNCT
ejpam-5466	306	1	on	on	ADP
ejpam-5466	306	2	generalized	generalized	ADJ
ejpam-5466	306	3	almost	almost	ADV
ejpam-5466	306	4	θ	θ	NOUN
ejpam-5466	306	5	-	-	NOUN
ejpam-5466	306	6	contractions	contraction	NOUN
ejpam-5466	306	7	with	with	ADP
ejpam-5466	306	8	an	an	DET
ejpam-5466	306	9	application	application	NOUN
ejpam-5466	306	10	to	to	ADP
ejpam-5466	306	11	fractional	fractional	ADJ
ejpam-5466	306	12	differential	differential	ADJ
ejpam-5466	306	13	equations	equation	NOUN
ejpam-5466	306	14	.	.	PUNCT
ejpam-5466	307	1	u.p.b	u.p.b	PROPN
ejpam-5466	307	2	.	.	PUNCT
ejpam-5466	308	1	sci	sci	PROPN
ejpam-5466	308	2	.	.	PUNCT
ejpam-5466	308	3	bull	bull	PROPN
ejpam-5466	308	4	.	.	PUNCT
ejpam-5466	308	5	,	,	PUNCT
ejpam-5466	308	6	series	series	PROPN
ejpam-5466	308	7	a	a	PRON
ejpam-5466	308	8	,	,	PUNCT
ejpam-5466	308	9	83(3):35–44	83(3):35–44	NUM
ejpam-5466	308	10	,	,	PUNCT
ejpam-5466	308	11	2021	2021	NUM
ejpam-5466	308	12	.	.	PUNCT
ejpam-5466	309	1	[	[	X
ejpam-5466	309	2	4	4	X
ejpam-5466	309	3	]	]	X
ejpam-5466	309	4	i	i	PRON
ejpam-5466	309	5	a	a	DET
ejpam-5466	309	6	bakhtin	bakhtin	NOUN
ejpam-5466	309	7	.	.	PUNCT
ejpam-5466	310	1	the	the	DET
ejpam-5466	310	2	contraction	contraction	NOUN
ejpam-5466	310	3	mapping	map	VERB
ejpam-5466	310	4	principle	principle	NOUN
ejpam-5466	310	5	in	in	ADP
ejpam-5466	310	6	almost	almost	ADV
ejpam-5466	310	7	metric	metric	ADJ
ejpam-5466	310	8	spaces	space	NOUN
ejpam-5466	310	9	.	.	PUNCT
ejpam-5466	311	1	j.	j.	PROPN
ejpam-5466	311	2	funct	funct	PROPN
ejpam-5466	311	3	.	.	PUNCT
ejpam-5466	312	1	anal	anal	PROPN
ejpam-5466	312	2	.	.	PROPN
ejpam-5466	312	3	,	,	PUNCT
ejpam-5466	312	4	30:26–37	30:26–37	PROPN
ejpam-5466	312	5	,	,	PUNCT
ejpam-5466	312	6	1989	1989	NUM
ejpam-5466	312	7	.	.	PUNCT
ejpam-5466	313	1	[	[	X
ejpam-5466	313	2	5	5	NUM
ejpam-5466	313	3	]	]	SYM
ejpam-5466	313	4	v	v	NOUN
ejpam-5466	313	5	berinde	berinde	NOUN
ejpam-5466	313	6	and	and	CCONJ
ejpam-5466	313	7	m	m	NOUN
ejpam-5466	313	8	pacurar	pacurar	NOUN
ejpam-5466	313	9	.	.	PUNCT
ejpam-5466	314	1	the	the	DET
ejpam-5466	314	2	role	role	NOUN
ejpam-5466	314	3	of	of	ADP
ejpam-5466	314	4	the	the	DET
ejpam-5466	314	5	pompeiu	pompeiu	NOUN
ejpam-5466	314	6	-	-	PUNCT
ejpam-5466	314	7	hausdorff	hausdorff	NOUN
ejpam-5466	314	8	metric	metric	NOUN
ejpam-5466	314	9	in	in	ADP
ejpam-5466	314	10	fixed	fix	VERB
ejpam-5466	314	11	point	point	NOUN
ejpam-5466	314	12	theory	theory	NOUN
ejpam-5466	314	13	.	.	PUNCT
ejpam-5466	315	1	creat	creat	PROPN
ejpam-5466	315	2	.	.	PUNCT
ejpam-5466	315	3	math	math	PROPN
ejpam-5466	315	4	.	.	PUNCT
ejpam-5466	316	1	inform	inform	NOUN
ejpam-5466	316	2	.	.	PUNCT
ejpam-5466	316	3	,	,	PUNCT
ejpam-5466	316	4	22:35–42	22:35–42	NUM
ejpam-5466	316	5	,	,	PUNCT
ejpam-5466	316	6	2013	2013	NUM
ejpam-5466	316	7	.	.	PUNCT
ejpam-5466	317	1	[	[	X
ejpam-5466	317	2	6	6	NUM
ejpam-5466	317	3	]	]	PUNCT
ejpam-5466	317	4	s	s	PART
ejpam-5466	317	5	czerwik	czerwik	PROPN
ejpam-5466	317	6	.	.	PUNCT
ejpam-5466	318	1	contraction	contraction	NOUN
ejpam-5466	318	2	mappings	mapping	NOUN
ejpam-5466	318	3	in	in	ADP
ejpam-5466	318	4	b	b	NOUN
ejpam-5466	318	5	-	-	ADJ
ejpam-5466	318	6	metric	metric	ADJ
ejpam-5466	318	7	spaces	space	NOUN
ejpam-5466	318	8	.	.	PUNCT
ejpam-5466	319	1	acta	acta	PROPN
ejpam-5466	319	2	math	math	PROPN
ejpam-5466	319	3	.	.	PUNCT
ejpam-5466	320	1	inform	inform	NOUN
ejpam-5466	320	2	.	.	PUNCT
ejpam-5466	321	1	univ	univ	PROPN
ejpam-5466	321	2	.	.	PUNCT
ejpam-5466	321	3	ostrav	ostrav	PROPN
ejpam-5466	321	4	.	.	PUNCT
ejpam-5466	321	5	,	,	PUNCT
ejpam-5466	321	6	1:5–11	1:5–11	NUM
ejpam-5466	321	7	,	,	PUNCT
ejpam-5466	321	8	1995	1995	NUM
ejpam-5466	321	9	.	.	PUNCT
ejpam-5466	322	1	[	[	X
ejpam-5466	322	2	7	7	NUM
ejpam-5466	322	3	]	]	X
ejpam-5466	322	4	s	s	PART
ejpam-5466	322	5	czerwik	czerwik	PROPN
ejpam-5466	322	6	.	.	PUNCT
ejpam-5466	323	1	nonlinear	nonlinear	ADJ
ejpam-5466	323	2	set	set	NOUN
ejpam-5466	323	3	-	-	PUNCT
ejpam-5466	323	4	valued	value	VERB
ejpam-5466	323	5	contraction	contraction	NOUN
ejpam-5466	323	6	mappings	mapping	NOUN
ejpam-5466	323	7	in	in	ADP
ejpam-5466	323	8	b	b	NOUN
ejpam-5466	323	9	-	-	ADJ
ejpam-5466	323	10	metric	metric	ADJ
ejpam-5466	323	11	spaces	space	NOUN
ejpam-5466	323	12	.	.	PUNCT
ejpam-5466	324	1	atti	atti	PROPN
ejpam-5466	324	2	semin	semin	PROPN
ejpam-5466	324	3	.	.	PUNCT
ejpam-5466	325	1	international	international	ADJ
ejpam-5466	325	2	journal	journal	PROPN
ejpam-5466	325	3	of	of	ADP
ejpam-5466	325	4	advances	advance	NOUN
ejpam-5466	325	5	in	in	ADP
ejpam-5466	325	6	soft	soft	ADJ
ejpam-5466	325	7	computing	computing	NOUN
ejpam-5466	325	8	and	and	CCONJ
ejpam-5466	325	9	its	its	PRON
ejpam-5466	325	10	applications	application	NOUN
ejpam-5466	325	11	,	,	PUNCT
ejpam-5466	325	12	46(2):263	46(2):263	NUM
ejpam-5466	325	13	–	–	PUNCT
ejpam-5466	325	14	276	276	NUM
ejpam-5466	325	15	,	,	PUNCT
ejpam-5466	325	16	1998	1998	NUM
ejpam-5466	325	17	.	.	PUNCT
ejpam-5466	326	1	[	[	X
ejpam-5466	326	2	8	8	NUM
ejpam-5466	326	3	]	]	X
ejpam-5466	326	4	i	i	PRON
ejpam-5466	326	5	m	m	AUX
ejpam-5466	326	6	batiha	batiha	VERB
ejpam-5466	326	7	;	;	PUNCT
ejpam-5466	326	8	s	s	VERB
ejpam-5466	326	9	a	a	DET
ejpam-5466	326	10	njadat	njadat	NOUN
ejpam-5466	326	11	;	;	PUNCT
ejpam-5466	326	12	r	r	NOUN
ejpam-5466	326	13	m	m	PROPN
ejpam-5466	326	14	batyha	batyha	NOUN
ejpam-5466	326	15	;	;	PUNCT
ejpam-5466	326	16	a	a	DET
ejpam-5466	326	17	zraiqat	zraiqat	NOUN
ejpam-5466	326	18	;	;	PUNCT
ejpam-5466	326	19	a	a	DET
ejpam-5466	326	20	dababneh	dababneh	NOUN
ejpam-5466	326	21	and	and	CCONJ
ejpam-5466	326	22	sh	sh	PROPN
ejpam-5466	326	23	momani	momani	PROPN
ejpam-5466	326	24	.	.	PUNCT
ejpam-5466	327	1	design	design	NOUN
ejpam-5466	327	2	fractional	fractional	ADJ
ejpam-5466	327	3	-	-	PUNCT
ejpam-5466	327	4	order	order	NOUN
ejpam-5466	327	5	pid	pid	NOUN
ejpam-5466	327	6	controllers	controller	NOUN
ejpam-5466	327	7	for	for	ADP
ejpam-5466	327	8	single	single	ADJ
ejpam-5466	327	9	-	-	PUNCT
ejpam-5466	327	10	joint	joint	ADJ
ejpam-5466	327	11	robot	robot	NOUN
ejpam-5466	327	12	arm	arm	NOUN
ejpam-5466	327	13	model	model	NOUN
ejpam-5466	327	14	.	.	PUNCT
ejpam-5466	328	1	international	international	ADJ
ejpam-5466	328	2	journal	journal	NOUN
ejpam-5466	328	3	of	of	ADP
ejpam-5466	328	4	advances	advance	NOUN
ejpam-5466	328	5	in	in	ADP
ejpam-5466	328	6	soft	soft	ADJ
ejpam-5466	328	7	computing	computing	NOUN
ejpam-5466	328	8	and	and	CCONJ
ejpam-5466	328	9	its	its	PRON
ejpam-5466	328	10	applications	application	NOUN
ejpam-5466	328	11	,	,	PUNCT
ejpam-5466	328	12	14(2):96–114	14(2):96–114	NUM
ejpam-5466	328	13	,	,	PUNCT
ejpam-5466	328	14	2022	2022	NUM
ejpam-5466	328	15	.	.	PUNCT
ejpam-5466	329	1	[	[	X
ejpam-5466	329	2	9	9	NUM
ejpam-5466	329	3	]	]	X
ejpam-5466	329	4	i	i	PRON
ejpam-5466	329	5	iqbal	iqbal	VERB
ejpam-5466	329	6	and	and	CCONJ
ejpam-5466	329	7	n	n	PRON
ejpam-5466	329	8	hussain	hussain	PROPN
ejpam-5466	329	9	.	.	PUNCT
ejpam-5466	330	1	fixed	fix	VERB
ejpam-5466	330	2	point	point	NOUN
ejpam-5466	330	3	results	result	NOUN
ejpam-5466	330	4	for	for	ADP
ejpam-5466	330	5	generalized	generalized	ADJ
ejpam-5466	330	6	multivalued	multivalue	VERB
ejpam-5466	330	7	nonlinear	nonlinear	ADJ
ejpam-5466	330	8	f	f	NOUN
ejpam-5466	330	9	-	-	PUNCT
ejpam-5466	330	10	contractions	contraction	NOUN
ejpam-5466	330	11	.	.	PUNCT
ejpam-5466	331	1	j.	j.	PROPN
ejpam-5466	331	2	nonlinear	nonlinear	PROPN
ejpam-5466	331	3	sci	sci	PROPN
ejpam-5466	331	4	.	.	PUNCT
ejpam-5466	331	5	appl	appl	PROPN
ejpam-5466	331	6	.	.	PROPN
ejpam-5466	331	7	,	,	PUNCT
ejpam-5466	331	8	9:5870–5893	9:5870–5893	NUM
ejpam-5466	331	9	,	,	PUNCT
ejpam-5466	331	10	2016	2016	NUM
ejpam-5466	331	11	.	.	PUNCT
ejpam-5466	332	1	[	[	X
ejpam-5466	332	2	10	10	NUM
ejpam-5466	332	3	]	]	X
ejpam-5466	332	4	m	m	VERB
ejpam-5466	332	5	jleli	jleli	ADJ
ejpam-5466	332	6	and	and	CCONJ
ejpam-5466	332	7	b	b	X
ejpam-5466	332	8	samet	samet	NOUN
ejpam-5466	332	9	.	.	PUNCT
ejpam-5466	333	1	a	a	DET
ejpam-5466	333	2	new	new	ADJ
ejpam-5466	333	3	generalization	generalization	NOUN
ejpam-5466	333	4	of	of	ADP
ejpam-5466	333	5	the	the	DET
ejpam-5466	333	6	banach	banach	NOUN
ejpam-5466	333	7	contraction	contraction	NOUN
ejpam-5466	333	8	principle	principle	NOUN
ejpam-5466	333	9	.	.	PUNCT
ejpam-5466	334	1	j.	j.	PROPN
ejpam-5466	334	2	inequal	inequal	PROPN
ejpam-5466	334	3	.	.	PUNCT
ejpam-5466	335	1	appl	appl	PROPN
ejpam-5466	335	2	.	.	PROPN
ejpam-5466	335	3	,	,	PUNCT
ejpam-5466	335	4	2014(38	2014(38	NUM
ejpam-5466	335	5	)	)	PUNCT
ejpam-5466	335	6	,	,	PUNCT
ejpam-5466	335	7	2014	2014	NUM
ejpam-5466	335	8	.	.	PUNCT
ejpam-5466	336	1	[	[	X
ejpam-5466	336	2	11	11	NUM
ejpam-5466	336	3	]	]	X
ejpam-5466	336	4	h	h	NOUN
ejpam-5466	336	5	işık	işık	PROPN
ejpam-5466	336	6	and	and	CCONJ
ejpam-5466	336	7	c	c	PROPN
ejpam-5466	336	8	ionescu	ionescu	NOUN
ejpam-5466	336	9	.	.	PUNCT
ejpam-5466	337	1	new	new	ADJ
ejpam-5466	337	2	type	type	NOUN
ejpam-5466	337	3	of	of	ADP
ejpam-5466	337	4	multivalued	multivalued	ADJ
ejpam-5466	337	5	contractions	contraction	NOUN
ejpam-5466	337	6	with	with	ADP
ejpam-5466	337	7	related	related	ADJ
ejpam-5466	337	8	results	result	NOUN
ejpam-5466	337	9	and	and	CCONJ
ejpam-5466	337	10	applications	application	NOUN
ejpam-5466	337	11	.	.	PUNCT
ejpam-5466	338	1	u.p.b	u.p.b	PROPN
ejpam-5466	338	2	.	.	PUNCT
ejpam-5466	339	1	sci	sci	PROPN
ejpam-5466	339	2	.	.	PUNCT
ejpam-5466	339	3	bull	bull	PROPN
ejpam-5466	339	4	.	.	PUNCT
ejpam-5466	339	5	,	,	PUNCT
ejpam-5466	339	6	series	series	PROPN
ejpam-5466	339	7	a	a	PRON
ejpam-5466	339	8	,	,	PUNCT
ejpam-5466	339	9	80(2):13–22	80(2):13–22	NUM
ejpam-5466	339	10	,	,	PUNCT
ejpam-5466	339	11	2018	2018	NUM
ejpam-5466	339	12	.	.	PUNCT
ejpam-5466	340	1	[	[	X
ejpam-5466	340	2	12	12	NUM
ejpam-5466	340	3	]	]	X
ejpam-5466	340	4	h	h	NOUN
ejpam-5466	340	5	kaddouri	kaddouri	PROPN
ejpam-5466	340	6	;	;	PUNCT
ejpam-5466	340	7	h	h	PROPN
ejpam-5466	340	8	işık	işık	PROPN
ejpam-5466	340	9	and	and	CCONJ
ejpam-5466	340	10	s	s	VERB
ejpam-5466	340	11	beloul	beloul	PRON
ejpam-5466	340	12	.	.	PUNCT
ejpam-5466	341	1	on	on	ADP
ejpam-5466	341	2	new	new	ADJ
ejpam-5466	341	3	extensions	extension	NOUN
ejpam-5466	341	4	of	of	ADP
ejpam-5466	341	5	f	f	NOUN
ejpam-5466	341	6	-	-	PUNCT
ejpam-5466	341	7	contraction	contraction	NOUN
ejpam-5466	341	8	with	with	ADP
ejpam-5466	341	9	an	an	DET
ejpam-5466	341	10	application	application	NOUN
ejpam-5466	341	11	to	to	ADP
ejpam-5466	341	12	integral	integral	ADJ
ejpam-5466	341	13	inclusions	inclusion	NOUN
ejpam-5466	341	14	.	.	PUNCT
ejpam-5466	342	1	u.p.b	u.p.b	PROPN
ejpam-5466	342	2	.	.	PUNCT
ejpam-5466	343	1	sci	sci	PROPN
ejpam-5466	343	2	.	.	PUNCT
ejpam-5466	343	3	bull	bull	PROPN
ejpam-5466	343	4	.	.	PUNCT
ejpam-5466	343	5	,	,	PUNCT
ejpam-5466	343	6	series	series	PROPN
ejpam-5466	343	7	a	a	PRON
ejpam-5466	343	8	,	,	PUNCT
ejpam-5466	343	9	38(3):31–42	38(3):31–42	NUM
ejpam-5466	343	10	,	,	PUNCT
ejpam-5466	343	11	2019	2019	NUM
ejpam-5466	343	12	.	.	PUNCT
ejpam-5466	344	1	[	[	X
ejpam-5466	344	2	13	13	NUM
ejpam-5466	344	3	]	]	SYM
ejpam-5466	344	4	h	h	NOUN
ejpam-5466	344	5	kaddouri	kaddouri	PROPN
ejpam-5466	344	6	and	and	CCONJ
ejpam-5466	344	7	s	s	VERB
ejpam-5466	344	8	beloul	beloul	PRON
ejpam-5466	344	9	.	.	PUNCT
ejpam-5466	345	1	fixed	fix	VERB
ejpam-5466	345	2	point	point	NOUN
ejpam-5466	345	3	theorems	theorem	NOUN
ejpam-5466	345	4	for	for	ADP
ejpam-5466	345	5	multivalued	multivalued	ADJ
ejpam-5466	345	6	wordowski	wordowski	ADJ
ejpam-5466	345	7	type	type	NOUN
ejpam-5466	345	8	contractions	contraction	NOUN
ejpam-5466	345	9	in	in	ADP
ejpam-5466	345	10	b	b	NOUN
ejpam-5466	345	11	-	-	ADJ
ejpam-5466	345	12	metric	metric	ADJ
ejpam-5466	345	13	spaces	space	NOUN
ejpam-5466	345	14	with	with	ADP
ejpam-5466	345	15	an	an	DET
ejpam-5466	345	16	application	application	NOUN
ejpam-5466	345	17	to	to	ADP
ejpam-5466	345	18	integral	integral	ADJ
ejpam-5466	345	19	inclusions	inclusion	NOUN
ejpam-5466	345	20	.	.	PUNCT
ejpam-5466	346	1	twms	twms	PROPN
ejpam-5466	346	2	j.	j.	PROPN
ejpam-5466	346	3	app	app	PROPN
ejpam-5466	346	4	.	.	PROPN
ejpam-5466	347	1	and	and	CCONJ
ejpam-5466	347	2	eng	eng	PROPN
ejpam-5466	347	3	.	.	PROPN
ejpam-5466	347	4	math	math	PROPN
ejpam-5466	347	5	.	.	PUNCT
ejpam-5466	347	6	,	,	PUNCT
ejpam-5466	347	7	11(4):1061–1071	11(4):1061–1071	NUM
ejpam-5466	347	8	,	,	PUNCT
ejpam-5466	347	9	2021	2021	NUM
ejpam-5466	347	10	.	.	PUNCT
ejpam-5466	348	1	references	reference	NOUN
ejpam-5466	348	2	3107	3107	NUM
ejpam-5466	349	1	[	[	X
ejpam-5466	349	2	14	14	NUM
ejpam-5466	349	3	]	]	X
ejpam-5466	349	4	m	m	VERB
ejpam-5466	349	5	u	u	NOUN
ejpam-5466	349	6	ali	ali	PROPN
ejpam-5466	349	7	;	;	PUNCT
ejpam-5466	349	8	t	t	PROPN
ejpam-5466	349	9	kamran	kamran	PROPN
ejpam-5466	349	10	and	and	CCONJ
ejpam-5466	349	11	m	m	PROPN
ejpam-5466	349	12	postolache	postolache	NOUN
ejpam-5466	349	13	.	.	PUNCT
ejpam-5466	350	1	solution	solution	NOUN
ejpam-5466	350	2	of	of	ADP
ejpam-5466	350	3	volterra	volterra	PROPN
ejpam-5466	350	4	integral	integral	ADJ
ejpam-5466	350	5	inclusion	inclusion	NOUN
ejpam-5466	350	6	in	in	ADP
ejpam-5466	350	7	bmetric	bmetric	ADJ
ejpam-5466	350	8	spaces	space	NOUN
ejpam-5466	350	9	via	via	ADP
ejpam-5466	350	10	new	new	ADJ
ejpam-5466	350	11	fixed	fix	VERB
ejpam-5466	350	12	point	point	NOUN
ejpam-5466	350	13	theorem	theorem	VERB
ejpam-5466	350	14	.	.	PUNCT
ejpam-5466	351	1	nonlinear	nonlinear	ADJ
ejpam-5466	351	2	anal	anal	PROPN
ejpam-5466	351	3	.	.	PUNCT
ejpam-5466	352	1	model	model	PROPN
ejpam-5466	352	2	.	.	PUNCT
ejpam-5466	353	1	control	control	NOUN
ejpam-5466	353	2	,	,	PUNCT
ejpam-5466	353	3	22(1):17	22(1):17	NUM
ejpam-5466	353	4	–	–	PUNCT
ejpam-5466	353	5	30	30	NUM
ejpam-5466	353	6	,	,	PUNCT
ejpam-5466	353	7	2017	2017	NUM
ejpam-5466	353	8	.	.	PUNCT
ejpam-5466	354	1	[	[	X
ejpam-5466	354	2	15	15	NUM
ejpam-5466	354	3	]	]	X
ejpam-5466	354	4	a	a	DET
ejpam-5466	354	5	ali	ali	PROPN
ejpam-5466	354	6	;	;	PUNCT
ejpam-5466	354	7	s	s	X
ejpam-5466	354	8	mahideb	mahideb	ADV
ejpam-5466	354	9	and	and	CCONJ
ejpam-5466	354	10	s	s	VERB
ejpam-5466	354	11	beloul	beloul	PRON
ejpam-5466	354	12	.	.	PUNCT
ejpam-5466	355	1	fixed	fix	VERB
ejpam-5466	355	2	point	point	NOUN
ejpam-5466	355	3	theorem	theorem	NOUN
ejpam-5466	355	4	for	for	ADP
ejpam-5466	355	5	multi	multi	ADJ
ejpam-5466	355	6	-	-	ADJ
ejpam-5466	355	7	valued	value	VERB
ejpam-5466	355	8	θδ	θδ	NOUN
ejpam-5466	355	9	-	-	PUNCT
ejpam-5466	355	10	contractions	contraction	NOUN
ejpam-5466	355	11	via	via	ADP
ejpam-5466	355	12	subsequential	subsequential	ADJ
ejpam-5466	355	13	continuity	continuity	NOUN
ejpam-5466	355	14	.	.	PUNCT
ejpam-5466	356	1	commun	commun	PROPN
ejpam-5466	356	2	.	.	PUNCT
ejpam-5466	357	1	fac	fac	PROPN
ejpam-5466	357	2	.	.	PUNCT
ejpam-5466	357	3	sci	sci	PROPN
ejpam-5466	357	4	.	.	PROPN
ejpam-5466	357	5	univ	univ	PROPN
ejpam-5466	357	6	.	.	PUNCT
ejpam-5466	358	1	ank	ank	PROPN
ejpam-5466	358	2	.	.	PROPN
ejpam-5466	358	3	ser	ser	PROPN
ejpam-5466	358	4	.	.	PUNCT
ejpam-5466	359	1	a1	a1	PROPN
ejpam-5466	359	2	.	.	PROPN
ejpam-5466	359	3	math	math	NOUN
ejpam-5466	359	4	.	.	PUNCT
ejpam-5466	360	1	stat	stat	PROPN
ejpam-5466	360	2	.	.	PUNCT
ejpam-5466	360	3	,	,	PUNCT
ejpam-5466	361	1	69(2):1473–1483	69(2):1473–1483	NUM
ejpam-5466	361	2	,	,	PUNCT
ejpam-5466	361	3	2020	2020	NUM
ejpam-5466	361	4	.	.	PUNCT
ejpam-5466	362	1	[	[	X
ejpam-5466	362	2	16	16	NUM
ejpam-5466	362	3	]	]	PUNCT
ejpam-5466	362	4	a	a	DET
ejpam-5466	362	5	ali	ali	PROPN
ejpam-5466	362	6	;	;	PUNCT
ejpam-5466	362	7	s	s	X
ejpam-5466	362	8	mahideb	mahideb	ADV
ejpam-5466	362	9	and	and	CCONJ
ejpam-5466	362	10	s	s	VERB
ejpam-5466	362	11	beloul	beloul	PRON
ejpam-5466	362	12	.	.	PUNCT
ejpam-5466	363	1	on	on	ADP
ejpam-5466	363	2	multivalued	multivalued	ADJ
ejpam-5466	363	3	fixed	fix	VERB
ejpam-5466	363	4	point	point	NOUN
ejpam-5466	363	5	for	for	ADP
ejpam-5466	363	6	(	(	PUNCT
ejpam-5466	363	7	α∗	α∗	NOUN
ejpam-5466	363	8	,	,	PUNCT
ejpam-5466	363	9	η∗	η∗	NOUN
ejpam-5466	363	10	,	,	PUNCT
ejpam-5466	363	11	θ	θ	NOUN
ejpam-5466	363	12	)	)	PUNCT
ejpam-5466	363	13	contractions	contraction	NOUN
ejpam-5466	363	14	with	with	ADP
ejpam-5466	363	15	an	an	DET
ejpam-5466	363	16	application	application	NOUN
ejpam-5466	363	17	.	.	PUNCT
ejpam-5466	364	1	j.	j.	PROPN
ejpam-5466	364	2	appl	appl	PROPN
ejpam-5466	364	3	.	.	PUNCT
ejpam-5466	365	1	pure	pure	ADJ
ejpam-5466	365	2	math	math	NOUN
ejpam-5466	365	3	,	,	PUNCT
ejpam-5466	365	4	3(3	3(3	NUM
ejpam-5466	365	5	-	-	SYM
ejpam-5466	365	6	5):215–229	5):215–229	NUM
ejpam-5466	365	7	,	,	PUNCT
ejpam-5466	365	8	2021	2021	NUM
ejpam-5466	365	9	.	.	PUNCT
ejpam-5466	366	1	[	[	X
ejpam-5466	366	2	17	17	NUM
ejpam-5466	366	3	]	]	X
ejpam-5466	366	4	m	m	VERB
ejpam-5466	366	5	meneceur	meneceur	NOUN
ejpam-5466	366	6	and	and	CCONJ
ejpam-5466	366	7	s	s	VERB
ejpam-5466	366	8	beloul	beloul	PRON
ejpam-5466	366	9	.	.	PUNCT
ejpam-5466	367	1	on	on	ADP
ejpam-5466	367	2	multivalued	multivalued	ADJ
ejpam-5466	367	3	theta	theta	NOUN
ejpam-5466	367	4	-	-	PUNCT
ejpam-5466	367	5	contractions	contraction	NOUN
ejpam-5466	367	6	of	of	ADP
ejpam-5466	367	7	berinde	berinde	NOUN
ejpam-5466	367	8	type	type	NOUN
ejpam-5466	367	9	with	with	ADP
ejpam-5466	367	10	an	an	DET
ejpam-5466	367	11	application	application	NOUN
ejpam-5466	367	12	to	to	ADP
ejpam-5466	367	13	fractional	fractional	ADJ
ejpam-5466	367	14	differential	differential	ADJ
ejpam-5466	367	15	inclusions	inclusion	NOUN
ejpam-5466	367	16	.	.	PUNCT
ejpam-5466	368	1	facta	facta	PROPN
ejpam-5466	368	2	univ	univ	PROPN
ejpam-5466	368	3	.	.	PUNCT
ejpam-5466	369	1	ser	ser	PROPN
ejpam-5466	369	2	.	.	PROPN
ejpam-5466	369	3	math	math	PROPN
ejpam-5466	369	4	.	.	PUNCT
ejpam-5466	370	1	inform	inform	NOUN
ejpam-5466	370	2	.	.	PUNCT
ejpam-5466	370	3	,	,	PUNCT
ejpam-5466	371	1	36(5):1047–1063	36(5):1047–1063	NUM
ejpam-5466	371	2	,	,	PUNCT
ejpam-5466	371	3	2021	2021	NUM
ejpam-5466	371	4	.	.	PUNCT
ejpam-5466	372	1	[	[	X
ejpam-5466	372	2	18	18	NUM
ejpam-5466	372	3	]	]	X
ejpam-5466	372	4	m	m	VERB
ejpam-5466	372	5	nazam	nazam	ADJ
ejpam-5466	372	6	;	;	PUNCT
ejpam-5466	372	7	a	a	DET
ejpam-5466	372	8	muhammad	muhammad	NOUN
ejpam-5466	372	9	and	and	CCONJ
ejpam-5466	372	10	m	m	PROPN
ejpam-5466	372	11	postolache	postolache	NOUN
ejpam-5466	372	12	.	.	PUNCT
ejpam-5466	373	1	coincidence	coincidence	NOUN
ejpam-5466	373	2	and	and	CCONJ
ejpam-5466	373	3	common	common	ADJ
ejpam-5466	373	4	fixed	fix	VERB
ejpam-5466	373	5	point	point	NOUN
ejpam-5466	373	6	theorems	theorem	NOUN
ejpam-5466	373	7	for	for	ADP
ejpam-5466	373	8	four	four	NUM
ejpam-5466	373	9	mappings	mapping	NOUN
ejpam-5466	373	10	satisfying	satisfy	VERB
ejpam-5466	373	11	(	(	PUNCT
ejpam-5466	373	12	αs	αs	ADJ
ejpam-5466	373	13	,	,	PUNCT
ejpam-5466	373	14	f)-contraction	f)-contraction	PROPN
ejpam-5466	373	15	.	.	PUNCT
ejpam-5466	374	1	nonlinear	nonlinear	ADJ
ejpam-5466	374	2	anal	anal	PROPN
ejpam-5466	374	3	.	.	PUNCT
ejpam-5466	375	1	model	model	PROPN
ejpam-5466	375	2	.	.	PUNCT
ejpam-5466	376	1	control	control	NOUN
ejpam-5466	376	2	,	,	PUNCT
ejpam-5466	376	3	23(4):664–690	23(4):664–690	NOUN
ejpam-5466	376	4	,	,	PUNCT
ejpam-5466	376	5	2018	2018	NUM
ejpam-5466	376	6	.	.	PUNCT
ejpam-5466	377	1	[	[	X
ejpam-5466	377	2	19	19	NUM
ejpam-5466	377	3	]	]	X
ejpam-5466	377	4	h	h	NOUN
ejpam-5466	377	5	qawagneh	qawagneh	PROPN
ejpam-5466	377	6	;	;	PUNCT
ejpam-5466	377	7	m	m	PROPN
ejpam-5466	377	8	s	s	VERB
ejpam-5466	377	9	m	m	NOUN
ejpam-5466	377	10	noorani	noorani	ADJ
ejpam-5466	377	11	and	and	CCONJ
ejpam-5466	377	12	w	w	PROPN
ejpam-5466	377	13	shatanawi	shatanawi	PROPN
ejpam-5466	377	14	.	.	PUNCT
ejpam-5466	378	1	fixed	fix	VERB
ejpam-5466	378	2	point	point	NOUN
ejpam-5466	378	3	theorems	theorem	NOUN
ejpam-5466	378	4	for	for	ADP
ejpam-5466	378	5	(	(	PUNCT
ejpam-5466	378	6	α	α	X
ejpam-5466	378	7	,	,	PUNCT
ejpam-5466	378	8	k	k	PROPN
ejpam-5466	378	9	,	,	PUNCT
ejpam-5466	378	10	θ)contractive	θ)contractive	ADJ
ejpam-5466	378	11	multi	multi	ADJ
ejpam-5466	378	12	-	-	ADJ
ejpam-5466	378	13	valued	value	VERB
ejpam-5466	378	14	mapping	mapping	NOUN
ejpam-5466	378	15	in	in	ADP
ejpam-5466	378	16	b	b	NOUN
ejpam-5466	378	17	-	-	PUNCT
ejpam-5466	378	18	metric	metric	ADJ
ejpam-5466	378	19	space	space	NOUN
ejpam-5466	378	20	and	and	CCONJ
ejpam-5466	378	21	applications	application	NOUN
ejpam-5466	378	22	.	.	PUNCT
ejpam-5466	379	1	international	international	ADJ
ejpam-5466	379	2	journal	journal	PROPN
ejpam-5466	379	3	of	of	ADP
ejpam-5466	379	4	mathematics	mathematic	NOUN
ejpam-5466	379	5	and	and	CCONJ
ejpam-5466	379	6	computer	computer	NOUN
ejpam-5466	379	7	science	science	NOUN
ejpam-5466	379	8	,	,	PUNCT
ejpam-5466	379	9	14(1):263–283	14(1):263–283	NUM
ejpam-5466	379	10	,	,	PUNCT
ejpam-5466	379	11	2019	2019	NUM
ejpam-5466	379	12	.	.	PUNCT
ejpam-5466	380	1	[	[	X
ejpam-5466	380	2	20	20	NUM
ejpam-5466	380	3	]	]	X
ejpam-5466	380	4	h	h	NOUN
ejpam-5466	380	5	qawaqneh	qawaqneh	PROPN
ejpam-5466	380	6	.	.	PUNCT
ejpam-5466	381	1	new	new	ADJ
ejpam-5466	381	2	contraction	contraction	NOUN
ejpam-5466	381	3	embedded	embed	VERB
ejpam-5466	381	4	with	with	ADP
ejpam-5466	381	5	simulation	simulation	NOUN
ejpam-5466	381	6	function	function	NOUN
ejpam-5466	381	7	and	and	CCONJ
ejpam-5466	381	8	cyclic	cyclic	ADJ
ejpam-5466	381	9	(	(	PUNCT
ejpam-5466	381	10	α	α	NOUN
ejpam-5466	381	11	,	,	PUNCT
ejpam-5466	381	12	β)−admissible	β)−admissible	ADJ
ejpam-5466	381	13	in	in	ADP
ejpam-5466	381	14	metric	metric	ADJ
ejpam-5466	381	15	-	-	PUNCT
ejpam-5466	381	16	like	like	ADJ
ejpam-5466	381	17	spaces	space	NOUN
ejpam-5466	381	18	.	.	PUNCT
ejpam-5466	382	1	international	international	ADJ
ejpam-5466	382	2	journal	journal	PROPN
ejpam-5466	382	3	of	of	ADP
ejpam-5466	382	4	mathematics	mathematic	NOUN
ejpam-5466	382	5	and	and	CCONJ
ejpam-5466	382	6	computer	computer	NOUN
ejpam-5466	382	7	science	science	NOUN
ejpam-5466	382	8	,	,	PUNCT
ejpam-5466	382	9	15(1):1029–1044	15(1):1029–1044	PROPN
ejpam-5466	382	10	,	,	PUNCT
ejpam-5466	382	11	2020	2020	NUM
ejpam-5466	382	12	.	.	PUNCT
ejpam-5466	383	1	[	[	X
ejpam-5466	383	2	21	21	NUM
ejpam-5466	383	3	]	]	X
ejpam-5466	383	4	h	h	NOUN
ejpam-5466	383	5	qawaqneh	qawaqneh	PROPN
ejpam-5466	383	6	.	.	PUNCT
ejpam-5466	384	1	fractional	fractional	ADJ
ejpam-5466	384	2	analytic	analytic	ADJ
ejpam-5466	384	3	solutions	solution	NOUN
ejpam-5466	384	4	and	and	CCONJ
ejpam-5466	384	5	fixed	fix	VERB
ejpam-5466	384	6	point	point	NOUN
ejpam-5466	384	7	results	result	NOUN
ejpam-5466	384	8	with	with	ADP
ejpam-5466	384	9	some	some	DET
ejpam-5466	384	10	applications	application	NOUN
ejpam-5466	384	11	.	.	PUNCT
ejpam-5466	385	1	adv	adv	PROPN
ejpam-5466	385	2	.	.	PUNCT
ejpam-5466	385	3	fixed	fix	VERB
ejpam-5466	385	4	point	point	NOUN
ejpam-5466	385	5	theory	theory	NOUN
ejpam-5466	385	6	,	,	PUNCT
ejpam-5466	385	7	14(1	14(1	NUM
ejpam-5466	385	8	)	)	PUNCT
ejpam-5466	385	9	,	,	PUNCT
ejpam-5466	385	10	2024	2024	NUM
ejpam-5466	385	11	.	.	PUNCT
ejpam-5466	386	1	[	[	X
ejpam-5466	386	2	22	22	NUM
ejpam-5466	386	3	]	]	X
ejpam-5466	386	4	h	h	NOUN
ejpam-5466	386	5	alsamir	alsamir	NOUN
ejpam-5466	386	6	;	;	PUNCT
ejpam-5466	386	7	h	h	NOUN
ejpam-5466	386	8	aydi	aydi	VERB
ejpam-5466	386	9	;	;	PUNCT
ejpam-5466	387	1	m	m	PROPN
ejpam-5466	387	2	s	s	PART
ejpam-5466	387	3	m	m	VERB
ejpam-5466	387	4	noorani	noorani	ADJ
ejpam-5466	387	5	;	;	PUNCT
ejpam-5466	387	6	w	w	NOUN
ejpam-5466	387	7	shatanawi	shatanawi	ADJ
ejpam-5466	387	8	;	;	PUNCT
ejpam-5466	387	9	h	h	NOUN
ejpam-5466	387	10	akhadkulov	akhadkulov	NOUN
ejpam-5466	387	11	;	;	PUNCT
ejpam-5466	387	12	h	h	NOUN
ejpam-5466	387	13	qawaqneh	qawaqneh	PROPN
ejpam-5466	387	14	and	and	CCONJ
ejpam-5466	387	15	k	k	PROPN
ejpam-5466	387	16	alanazi	alanazi	PROPN
ejpam-5466	387	17	.	.	PUNCT
ejpam-5466	388	1	fixed	fix	VERB
ejpam-5466	388	2	point	point	NOUN
ejpam-5466	388	3	results	result	NOUN
ejpam-5466	388	4	in	in	ADP
ejpam-5466	388	5	metric	metric	ADJ
ejpam-5466	388	6	-	-	PUNCT
ejpam-5466	388	7	like	like	ADJ
ejpam-5466	388	8	spaces	space	NOUN
ejpam-5466	388	9	via	via	ADP
ejpam-5466	388	10	σ	σ	PROPN
ejpam-5466	388	11	-	-	PUNCT
ejpam-5466	388	12	simulation	simulation	NOUN
ejpam-5466	388	13	functions	function	NOUN
ejpam-5466	388	14	.	.	PUNCT
ejpam-5466	389	1	european	european	ADJ
ejpam-5466	389	2	journal	journal	PROPN
ejpam-5466	389	3	of	of	ADP
ejpam-5466	389	4	pure	pure	ADJ
ejpam-5466	389	5	and	and	CCONJ
ejpam-5466	389	6	applied	applied	ADJ
ejpam-5466	389	7	mathematics	mathematic	NOUN
ejpam-5466	389	8	,	,	PUNCT
ejpam-5466	389	9	12(1):88–100	12(1):88–100	NUM
ejpam-5466	389	10	,	,	PUNCT
ejpam-5466	389	11	2019	2019	NUM
ejpam-5466	389	12	.	.	PUNCT
ejpam-5466	390	1	[	[	X
ejpam-5466	390	2	23	23	NUM
ejpam-5466	390	3	]	]	X
ejpam-5466	390	4	h	h	PROPN
ejpam-5466	390	5	asl	asl	PROPN
ejpam-5466	390	6	;	;	PUNCT
ejpam-5466	390	7	j	j	PROPN
ejpam-5466	390	8	rezapour	rezapour	PROPN
ejpam-5466	390	9	and	and	CCONJ
ejpam-5466	390	10	s	s	VERB
ejpam-5466	390	11	shahzad	shahzad	PROPN
ejpam-5466	390	12	.	.	PUNCT
ejpam-5466	391	1	on	on	ADP
ejpam-5466	391	2	fixed	fix	VERB
ejpam-5466	391	3	points	point	NOUN
ejpam-5466	391	4	of	of	ADP
ejpam-5466	391	5	α−ψ	α−ψ	NOUN
ejpam-5466	391	6	-	-	PUNCT
ejpam-5466	391	7	contractive	contractive	ADJ
ejpam-5466	391	8	multifunctions	multifunction	NOUN
ejpam-5466	391	9	.	.	PUNCT
ejpam-5466	392	1	fixed	fix	VERB
ejpam-5466	392	2	point	point	NOUN
ejpam-5466	392	3	theory	theory	NOUN
ejpam-5466	392	4	appl	appl	PROPN
ejpam-5466	392	5	.	.	PROPN
ejpam-5466	392	6	,	,	PUNCT
ejpam-5466	392	7	(	(	PUNCT
ejpam-5466	392	8	i	i	NOUN
ejpam-5466	392	9	d	d	PROPN
ejpam-5466	392	10	212	212	NUM
ejpam-5466	392	11	)	)	PUNCT
ejpam-5466	392	12	,	,	PUNCT
ejpam-5466	392	13	2012	2012	NUM
ejpam-5466	392	14	.	.	PUNCT
ejpam-5466	393	1	[	[	X
ejpam-5466	393	2	24	24	NUM
ejpam-5466	393	3	]	]	X
ejpam-5466	393	4	m	m	NOUN
ejpam-5466	393	5	cosentino	cosentino	NOUN
ejpam-5466	393	6	;	;	PUNCT
ejpam-5466	393	7	m	m	VERB
ejpam-5466	393	8	jleli	jleli	ADJ
ejpam-5466	393	9	;	;	PUNCT
ejpam-5466	393	10	b	b	X
ejpam-5466	393	11	samet	samet	NOUN
ejpam-5466	393	12	and	and	CCONJ
ejpam-5466	393	13	c	c	PROPN
ejpam-5466	393	14	vetro	vetro	X
ejpam-5466	393	15	.	.	PUNCT
ejpam-5466	394	1	solvability	solvability	NOUN
ejpam-5466	394	2	of	of	ADP
ejpam-5466	394	3	integrodifferential	integrodifferential	ADJ
ejpam-5466	394	4	problem	problem	NOUN
ejpam-5466	394	5	via	via	ADP
ejpam-5466	394	6	fixed	fix	VERB
ejpam-5466	394	7	point	point	NOUN
ejpam-5466	394	8	theory	theory	NOUN
ejpam-5466	394	9	in	in	ADP
ejpam-5466	394	10	b	b	NOUN
ejpam-5466	394	11	-	-	ADJ
ejpam-5466	394	12	metric	metric	ADJ
ejpam-5466	394	13	spaces	space	NOUN
ejpam-5466	394	14	.	.	PUNCT
ejpam-5466	395	1	fixed	fix	VERB
ejpam-5466	395	2	point	point	NOUN
ejpam-5466	395	3	theory	theory	NOUN
ejpam-5466	395	4	appl	appl	PROPN
ejpam-5466	395	5	.	.	PROPN
ejpam-5466	395	6	,	,	PUNCT
ejpam-5466	395	7	2015(70	2015(70	NUM
ejpam-5466	395	8	)	)	PUNCT
ejpam-5466	395	9	,	,	PUNCT
ejpam-5466	395	10	2015	2015	NUM
ejpam-5466	395	11	.	.	PUNCT
ejpam-5466	396	1	[	[	X
ejpam-5466	396	2	25	25	NUM
ejpam-5466	396	3	]	]	X
ejpam-5466	396	4	h	h	NOUN
ejpam-5466	396	5	qawagneh	qawagneh	PROPN
ejpam-5466	396	6	;	;	PUNCT
ejpam-5466	396	7	m	m	PROPN
ejpam-5466	396	8	s	s	PART
ejpam-5466	396	9	m	m	VERB
ejpam-5466	396	10	noorani	noorani	ADJ
ejpam-5466	396	11	;	;	PUNCT
ejpam-5466	396	12	w	w	NOUN
ejpam-5466	396	13	shatanawi	shatanawi	ADJ
ejpam-5466	396	14	and	and	CCONJ
ejpam-5466	396	15	h	h	PROPN
ejpam-5466	396	16	alsamir	alsamir	NOUN
ejpam-5466	396	17	.	.	PUNCT
ejpam-5466	397	1	fixed	fix	VERB
ejpam-5466	397	2	points	point	NOUN
ejpam-5466	397	3	for	for	ADP
ejpam-5466	397	4	triangular	triangular	NOUN
ejpam-5466	397	5	α−	α−	ADP
ejpam-5466	397	6	admissible	admissible	ADJ
ejpam-5466	397	7	geraghty	geraghty	PROPN
ejpam-5466	397	8	contractiontype	contractiontype	PROPN
ejpam-5466	397	9	mappings	mapping	NOUN
ejpam-5466	397	10	in	in	ADP
ejpam-5466	397	11	partial	partial	ADJ
ejpam-5466	397	12	bmetric	bmetric	ADJ
ejpam-5466	397	13	spaces	space	NOUN
ejpam-5466	397	14	.	.	PUNCT
ejpam-5466	398	1	international	international	ADJ
ejpam-5466	398	2	journal	journal	NOUN
ejpam-5466	398	3	of	of	ADP
ejpam-5466	398	4	analysis	analysis	NOUN
ejpam-5466	398	5	and	and	CCONJ
ejpam-5466	398	6	applications	application	NOUN
ejpam-5466	398	7	,	,	PUNCT
ejpam-5466	398	8	17(2):208–225	17(2):208–225	PROPN
ejpam-5466	398	9	,	,	PUNCT
ejpam-5466	398	10	2019	2019	NUM
ejpam-5466	398	11	.	.	PUNCT
ejpam-5466	399	1	[	[	X
ejpam-5466	399	2	26	26	NUM
ejpam-5466	399	3	]	]	X
ejpam-5466	399	4	w	w	PROPN
ejpam-5466	399	5	sintunavarat	sintunavarat	PROPN
ejpam-5466	399	6	.	.	PUNCT
ejpam-5466	400	1	nonlinear	nonlinear	ADJ
ejpam-5466	400	2	integral	integral	ADJ
ejpam-5466	400	3	equations	equation	NOUN
ejpam-5466	400	4	with	with	ADP
ejpam-5466	400	5	new	new	ADJ
ejpam-5466	400	6	admissibility	admissibility	NOUN
ejpam-5466	400	7	types	type	NOUN
ejpam-5466	400	8	in	in	ADP
ejpam-5466	400	9	b	b	NOUN
ejpam-5466	400	10	-	-	ADJ
ejpam-5466	400	11	metric	metric	ADJ
ejpam-5466	400	12	spaces	space	NOUN
ejpam-5466	400	13	.	.	PUNCT
ejpam-5466	401	1	j.	j.	PROPN
ejpam-5466	401	2	fixed	fix	VERB
ejpam-5466	401	3	point	point	PROPN
ejpam-5466	401	4	theory	theory	NOUN
ejpam-5466	401	5	appl	appl	PROPN
ejpam-5466	401	6	.	.	PROPN
ejpam-5466	401	7	,	,	PUNCT
ejpam-5466	401	8	18:397–416	18:397–416	NUM
ejpam-5466	401	9	,	,	PUNCT
ejpam-5466	401	10	2016	2016	NUM
ejpam-5466	401	11	.	.	PUNCT
ejpam-5466	402	1	references	reference	NOUN
ejpam-5466	402	2	3108	3108	NUM
ejpam-5466	403	1	[	[	X
ejpam-5466	403	2	27	27	NUM
ejpam-5466	403	3	]	]	SYM
ejpam-5466	403	4	b	b	X
ejpam-5466	403	5	samet	samet	NOUN
ejpam-5466	403	6	;	;	PUNCT
ejpam-5466	403	7	c	c	X
ejpam-5466	403	8	vetro	vetro	VERB
ejpam-5466	403	9	and	and	CCONJ
ejpam-5466	403	10	p	p	NOUN
ejpam-5466	403	11	vetro	vetro	NOUN
ejpam-5466	403	12	.	.	PUNCT
ejpam-5466	404	1	fixed	fix	VERB
ejpam-5466	404	2	point	point	NOUN
ejpam-5466	404	3	theorems	theorem	NOUN
ejpam-5466	404	4	for	for	ADP
ejpam-5466	404	5	α	α	PRON
ejpam-5466	404	6	−	−	NOUN
ejpam-5466	404	7	ψ	ψ	SYM
ejpam-5466	404	8	-contractive	-contractive	ADJ
ejpam-5466	404	9	type	type	NOUN
ejpam-5466	404	10	mappings	mapping	NOUN
ejpam-5466	404	11	.	.	PUNCT
ejpam-5466	405	1	nonlinear	nonlinear	ADJ
ejpam-5466	405	2	analysis	analysis	NOUN
ejpam-5466	405	3	,	,	PUNCT
ejpam-5466	405	4	7(4):2154–2165	7(4):2154–2165	NUM
ejpam-5466	405	5	,	,	PUNCT
ejpam-5466	405	6	2012	2012	NUM
ejpam-5466	405	7	.	.	PUNCT
ejpam-5466	406	1	[	[	X
ejpam-5466	406	2	28	28	NUM
ejpam-5466	406	3	]	]	X
ejpam-5466	406	4	h	h	NOUN
ejpam-5466	406	5	qawaqneh	qawaqneh	NOUN
ejpam-5466	406	6	;	;	PUNCT
ejpam-5466	406	7	m	m	PROPN
ejpam-5466	406	8	s	s	PART
ejpam-5466	406	9	m	m	VERB
ejpam-5466	406	10	noorani	noorani	ADJ
ejpam-5466	406	11	;	;	PUNCT
ejpam-5466	406	12	h	h	NOUN
ejpam-5466	406	13	aydi	aydi	VERB
ejpam-5466	406	14	;	;	PUNCT
ejpam-5466	406	15	a	a	DET
ejpam-5466	406	16	zraiqat	zraiqat	NOUN
ejpam-5466	406	17	and	and	CCONJ
ejpam-5466	406	18	a	a	DET
ejpam-5466	406	19	h	h	NOUN
ejpam-5466	406	20	ansari	ansari	ADJ
ejpam-5466	406	21	.	.	PUNCT
ejpam-5466	407	1	on	on	ADP
ejpam-5466	407	2	fixed	fix	VERB
ejpam-5466	407	3	pointresults	pointresult	NOUN
ejpam-5466	407	4	in	in	ADP
ejpam-5466	407	5	partial	partial	ADJ
ejpam-5466	407	6	b	b	NOUN
ejpam-5466	407	7	-	-	PUNCT
ejpam-5466	407	8	metric	metric	ADJ
ejpam-5466	407	9	spaces	space	NOUN
ejpam-5466	407	10	.	.	PUNCT
ejpam-5466	408	1	journal	journal	NOUN
ejpam-5466	408	2	of	of	ADP
ejpam-5466	408	3	function	function	NOUN
ejpam-5466	408	4	spaces	space	NOUN
ejpam-5466	408	5	,	,	PUNCT
ejpam-5466	408	6	2021	2021	NUM
ejpam-5466	408	7	,	,	PUNCT
ejpam-5466	408	8	2021	2021	NUM
ejpam-5466	408	9	.	.	PUNCT