id	sid	tid	token	lemma	pos
ejpam-6113	1	1	european	european	PROPN
ejpam-6113	1	2	journal	journal	PROPN
ejpam-6113	1	3	of	of	ADP
ejpam-6113	1	4	pure	pure	ADJ
ejpam-6113	1	5	and	and	CCONJ
ejpam-6113	1	6	applied	applied	ADJ
ejpam-6113	1	7	mathematics	mathematic	NOUN
ejpam-6113	1	8	2025	2025	NUM
ejpam-6113	1	9	,	,	PUNCT
ejpam-6113	1	10	vol	vol	NOUN
ejpam-6113	1	11	.	.	PROPN
ejpam-6113	1	12	18	18	NUM
ejpam-6113	1	13	,	,	PUNCT
ejpam-6113	1	14	issue	issue	NOUN
ejpam-6113	1	15	3	3	NUM
ejpam-6113	1	16	,	,	PUNCT
ejpam-6113	1	17	article	article	NOUN
ejpam-6113	1	18	number	number	NOUN
ejpam-6113	1	19	6113	6113	NUM
ejpam-6113	1	20	issn	issn	PROPN
ejpam-6113	1	21	1307	1307	NUM
ejpam-6113	1	22	-	-	SYM
ejpam-6113	1	23	5543	5543	NUM
ejpam-6113	1	24	–	–	PUNCT
ejpam-6113	1	25	ejpam.com	ejpam.com	X
ejpam-6113	1	26	published	publish	VERB
ejpam-6113	1	27	by	by	ADP
ejpam-6113	1	28	new	new	PROPN
ejpam-6113	1	29	york	york	PROPN
ejpam-6113	1	30	business	business	PROPN
ejpam-6113	1	31	global	global	ADJ
ejpam-6113	1	32	interpolative	interpolative	ADJ
ejpam-6113	1	33	contractions	contraction	NOUN
ejpam-6113	1	34	for	for	ADP
ejpam-6113	1	35	b	b	NOUN
ejpam-6113	1	36	-	-	PUNCT
ejpam-6113	1	37	metric	metric	ADJ
ejpam-6113	1	38	spaces	space	NOUN
ejpam-6113	1	39	and	and	CCONJ
ejpam-6113	1	40	their	their	PRON
ejpam-6113	1	41	applications	application	NOUN
ejpam-6113	1	42	dasari	dasari	PROPN
ejpam-6113	1	43	ratna	ratna	PROPN
ejpam-6113	1	44	babu1	babu1	PROPN
ejpam-6113	1	45	,	,	PUNCT
ejpam-6113	1	46	naga	naga	NOUN
ejpam-6113	1	47	koteswara	koteswara	PROPN
ejpam-6113	1	48	rao	rao	PROPN
ejpam-6113	1	49	koduru2,∗	koduru2,∗	PROPN
ejpam-6113	1	50	1	1	NUM
ejpam-6113	1	51	department	department	NOUN
ejpam-6113	1	52	of	of	ADP
ejpam-6113	1	53	mathematics	mathematics	PROPN
ejpam-6113	1	54	,	,	PUNCT
ejpam-6113	1	55	pscmr	pscmr	ADJ
ejpam-6113	1	56	college	college	NOUN
ejpam-6113	1	57	of	of	ADP
ejpam-6113	1	58	engineering	engineering	NOUN
ejpam-6113	1	59	and	and	CCONJ
ejpam-6113	1	60	technology	technology	NOUN
ejpam-6113	1	61	,	,	PUNCT
ejpam-6113	1	62	vijayawada	vijayawada	PROPN
ejpam-6113	1	63	,	,	PUNCT
ejpam-6113	1	64	andhra	andhra	PROPN
ejpam-6113	1	65	pradesh	pradesh	PROPN
ejpam-6113	1	66	,	,	PUNCT
ejpam-6113	1	67	india	india	PROPN
ejpam-6113	1	68	2	2	NUM
ejpam-6113	1	69	department	department	NOUN
ejpam-6113	1	70	of	of	ADP
ejpam-6113	1	71	mathematics	mathematics	PROPN
ejpam-6113	1	72	,	,	PUNCT
ejpam-6113	1	73	andhra	andhra	PROPN
ejpam-6113	1	74	loyola	loyola	PROPN
ejpam-6113	1	75	college	college	PROPN
ejpam-6113	1	76	,	,	PUNCT
ejpam-6113	1	77	vijayawada	vijayawada	PROPN
ejpam-6113	1	78	,	,	PUNCT
ejpam-6113	1	79	andhra	andhra	PROPN
ejpam-6113	1	80	pradesh	pradesh	PROPN
ejpam-6113	1	81	,	,	PUNCT
ejpam-6113	1	82	india	india	PROPN
ejpam-6113	1	83	abstract	abstract	NOUN
ejpam-6113	1	84	.	.	PUNCT
ejpam-6113	2	1	in	in	ADP
ejpam-6113	2	2	this	this	DET
ejpam-6113	2	3	research	research	NOUN
ejpam-6113	2	4	,	,	PUNCT
ejpam-6113	2	5	we	we	PRON
ejpam-6113	2	6	introduce	introduce	VERB
ejpam-6113	2	7	the	the	DET
ejpam-6113	2	8	interpolative	interpolative	ADJ
ejpam-6113	2	9	contractions	contraction	NOUN
ejpam-6113	2	10	for	for	ADP
ejpam-6113	2	11	a	a	DET
ejpam-6113	2	12	pair	pair	NOUN
ejpam-6113	2	13	of	of	ADP
ejpam-6113	2	14	maps	map	NOUN
ejpam-6113	2	15	in	in	ADP
ejpam-6113	2	16	bmetric	bmetric	ADJ
ejpam-6113	2	17	spaces	space	NOUN
ejpam-6113	2	18	and	and	CCONJ
ejpam-6113	2	19	we	we	PRON
ejpam-6113	2	20	utilize	utilize	VERB
ejpam-6113	2	21	the	the	DET
ejpam-6113	2	22	idea	idea	NOUN
ejpam-6113	2	23	of	of	ADP
ejpam-6113	2	24	interpolation	interpolation	NOUN
ejpam-6113	2	25	in	in	ADP
ejpam-6113	2	26	complete	complete	ADJ
ejpam-6113	2	27	b	b	X
ejpam-6113	2	28	-	-	ADJ
ejpam-6113	2	29	metric	metric	ADJ
ejpam-6113	2	30	spaces	space	NOUN
ejpam-6113	2	31	to	to	PART
ejpam-6113	2	32	prove	prove	VERB
ejpam-6113	2	33	the	the	DET
ejpam-6113	2	34	associated	associated	ADJ
ejpam-6113	2	35	common	common	ADJ
ejpam-6113	2	36	fixed	fix	VERB
ejpam-6113	2	37	point	point	NOUN
ejpam-6113	2	38	theorems	theorem	NOUN
ejpam-6113	2	39	.	.	PUNCT
ejpam-6113	3	1	our	our	PRON
ejpam-6113	3	2	findings	finding	NOUN
ejpam-6113	3	3	generalize	generalize	VERB
ejpam-6113	3	4	and	and	CCONJ
ejpam-6113	3	5	expand	expand	VERB
ejpam-6113	3	6	the	the	DET
ejpam-6113	3	7	findings	finding	NOUN
ejpam-6113	3	8	of	of	ADP
ejpam-6113	3	9	edraoui	edraoui	NOUN
ejpam-6113	3	10	et	et	PROPN
ejpam-6113	3	11	al	al	PROPN
ejpam-6113	3	12	.	.	PUNCT
ejpam-6113	4	1	[	[	X
ejpam-6113	4	2	7	7	X
ejpam-6113	4	3	]	]	PUNCT
ejpam-6113	4	4	and	and	CCONJ
ejpam-6113	4	5	karapınar	karapınar	NOUN
ejpam-6113	5	1	[	[	X
ejpam-6113	5	2	10	10	NUM
ejpam-6113	5	3	]	]	PUNCT
ejpam-6113	5	4	from	from	ADP
ejpam-6113	5	5	the	the	DET
ejpam-6113	5	6	metric	metric	ADJ
ejpam-6113	5	7	space	space	NOUN
ejpam-6113	5	8	setting	set	VERB
ejpam-6113	5	9	to	to	ADP
ejpam-6113	5	10	b	b	NOUN
ejpam-6113	5	11	-	-	PUNCT
ejpam-6113	5	12	metric	metric	ADJ
ejpam-6113	5	13	spaces	space	NOUN
ejpam-6113	5	14	.	.	PUNCT
ejpam-6113	6	1	we	we	PRON
ejpam-6113	6	2	provide	provide	VERB
ejpam-6113	6	3	instances	instance	NOUN
ejpam-6113	6	4	to	to	PART
ejpam-6113	6	5	support	support	VERB
ejpam-6113	6	6	our	our	PRON
ejpam-6113	6	7	conclusions	conclusion	NOUN
ejpam-6113	6	8	.	.	PUNCT
ejpam-6113	7	1	we	we	PRON
ejpam-6113	7	2	offer	offer	VERB
ejpam-6113	7	3	implementations	implementation	NOUN
ejpam-6113	7	4	to	to	PART
ejpam-6113	7	5	solve	solve	VERB
ejpam-6113	7	6	fredholm	fredholm	NOUN
ejpam-6113	7	7	-	-	PUNCT
ejpam-6113	7	8	type	type	NOUN
ejpam-6113	7	9	nonlinear	nonlinear	ADJ
ejpam-6113	7	10	integral	integral	ADJ
ejpam-6113	7	11	equations	equation	NOUN
ejpam-6113	7	12	and	and	CCONJ
ejpam-6113	7	13	functional	functional	ADJ
ejpam-6113	7	14	equations	equation	NOUN
ejpam-6113	7	15	that	that	PRON
ejpam-6113	7	16	emerge	emerge	VERB
ejpam-6113	7	17	in	in	ADP
ejpam-6113	7	18	dynamic	dynamic	ADJ
ejpam-6113	7	19	programming	programming	NOUN
ejpam-6113	7	20	in	in	ADP
ejpam-6113	7	21	order	order	NOUN
ejpam-6113	7	22	to	to	PART
ejpam-6113	7	23	illustrate	illustrate	VERB
ejpam-6113	7	24	the	the	DET
ejpam-6113	7	25	importance	importance	NOUN
ejpam-6113	7	26	of	of	ADP
ejpam-6113	7	27	our	our	PRON
ejpam-6113	7	28	theoretical	theoretical	ADJ
ejpam-6113	7	29	findings	finding	NOUN
ejpam-6113	7	30	.	.	PUNCT
ejpam-6113	8	1	2020	2020	NUM
ejpam-6113	8	2	mathematics	mathematic	NOUN
ejpam-6113	8	3	subject	subject	NOUN
ejpam-6113	8	4	classifications	classification	NOUN
ejpam-6113	8	5	:	:	PUNCT
ejpam-6113	8	6	47h10	47h10	NUM
ejpam-6113	8	7	,	,	PUNCT
ejpam-6113	8	8	54h25	54h25	NUM
ejpam-6113	8	9	key	key	ADJ
ejpam-6113	8	10	words	word	NOUN
ejpam-6113	8	11	and	and	CCONJ
ejpam-6113	8	12	phrases	phrase	NOUN
ejpam-6113	8	13	:	:	PUNCT
ejpam-6113	8	14	common	common	ADJ
ejpam-6113	8	15	fixed	fix	VERB
ejpam-6113	8	16	points	point	NOUN
ejpam-6113	8	17	,	,	PUNCT
ejpam-6113	8	18	b	b	X
ejpam-6113	8	19	-	-	PUNCT
ejpam-6113	8	20	metric	metric	ADJ
ejpam-6113	8	21	space	space	NOUN
ejpam-6113	8	22	,	,	PUNCT
ejpam-6113	8	23	integral	integral	ADJ
ejpam-6113	8	24	equation	equation	NOUN
ejpam-6113	8	25	,	,	PUNCT
ejpam-6113	8	26	functional	functional	ADJ
ejpam-6113	8	27	equation	equation	NOUN
ejpam-6113	8	28	1	1	NUM
ejpam-6113	8	29	.	.	PUNCT
ejpam-6113	8	30	introduction	introduction	NOUN
ejpam-6113	8	31	the	the	DET
ejpam-6113	8	32	successive	successive	ADJ
ejpam-6113	8	33	approximation	approximation	NOUN
ejpam-6113	8	34	methods	method	NOUN
ejpam-6113	8	35	that	that	PRON
ejpam-6113	8	36	were	be	AUX
ejpam-6113	8	37	first	first	ADV
ejpam-6113	8	38	developed	develop	VERB
ejpam-6113	8	39	by	by	ADP
ejpam-6113	8	40	a	a	DET
ejpam-6113	8	41	number	number	NOUN
ejpam-6113	8	42	of	of	ADP
ejpam-6113	8	43	prior	prior	ADJ
ejpam-6113	8	44	mathematicians	mathematician	NOUN
ejpam-6113	8	45	,	,	PUNCT
ejpam-6113	8	46	including	include	VERB
ejpam-6113	8	47	well	well	ADV
ejpam-6113	8	48	-	-	PUNCT
ejpam-6113	8	49	known	know	VERB
ejpam-6113	8	50	figures	figure	NOUN
ejpam-6113	8	51	like	like	ADP
ejpam-6113	8	52	cauchy	cauchy	PROPN
ejpam-6113	8	53	,	,	PUNCT
ejpam-6113	8	54	liouville	liouville	PROPN
ejpam-6113	8	55	,	,	PUNCT
ejpam-6113	8	56	picard	picard	NOUN
ejpam-6113	8	57	,	,	PUNCT
ejpam-6113	8	58	lipschitz	lipschitz	NOUN
ejpam-6113	8	59	,	,	PUNCT
ejpam-6113	8	60	and	and	CCONJ
ejpam-6113	8	61	others	other	NOUN
ejpam-6113	8	62	,	,	PUNCT
ejpam-6113	8	63	are	be	AUX
ejpam-6113	8	64	successfully	successfully	ADV
ejpam-6113	8	65	encapsulated	encapsulate	VERB
ejpam-6113	8	66	and	and	CCONJ
ejpam-6113	8	67	reinterpreted	reinterpret	VERB
ejpam-6113	8	68	by	by	ADP
ejpam-6113	8	69	the	the	DET
ejpam-6113	8	70	banach	banach	NOUN
ejpam-6113	8	71	contraction	contraction	NOUN
ejpam-6113	8	72	principle	principle	NOUN
ejpam-6113	8	73	.	.	PUNCT
ejpam-6113	9	1	czerwik	czerwik	PROPN
ejpam-6113	10	1	[	[	X
ejpam-6113	10	2	5	5	NUM
ejpam-6113	10	3	]	]	PUNCT
ejpam-6113	10	4	developed	develop	VERB
ejpam-6113	10	5	the	the	DET
ejpam-6113	10	6	idea	idea	NOUN
ejpam-6113	10	7	of	of	ADP
ejpam-6113	10	8	b	b	NOUN
ejpam-6113	10	9	-	-	PUNCT
ejpam-6113	10	10	metric	metric	ADJ
ejpam-6113	10	11	space	space	NOUN
ejpam-6113	10	12	,	,	PUNCT
ejpam-6113	10	13	often	often	ADV
ejpam-6113	10	14	known	know	VERB
ejpam-6113	10	15	as	as	ADP
ejpam-6113	10	16	metric	metric	ADJ
ejpam-6113	10	17	type	type	NOUN
ejpam-6113	10	18	space	space	NOUN
ejpam-6113	10	19	,	,	PUNCT
ejpam-6113	10	20	as	as	ADP
ejpam-6113	10	21	a	a	DET
ejpam-6113	10	22	generalization	generalization	NOUN
ejpam-6113	10	23	of	of	ADP
ejpam-6113	10	24	metric	metric	ADJ
ejpam-6113	10	25	space	space	NOUN
ejpam-6113	10	26	..	..	PUNCT
ejpam-6113	10	27	regarding	regard	VERB
ejpam-6113	10	28	the	the	DET
ejpam-6113	10	29	hardy	hardy	ADJ
ejpam-6113	10	30	-	-	PUNCT
ejpam-6113	10	31	rogers	rogers	NOUN
ejpam-6113	10	32	fixed	fix	VERB
ejpam-6113	10	33	point	point	NOUN
ejpam-6113	10	34	theorem	theorem	VERB
ejpam-6113	10	35	’s	’s	PART
ejpam-6113	10	36	generalization	generalization	NOUN
ejpam-6113	10	37	to	to	ADP
ejpam-6113	10	38	the	the	DET
ejpam-6113	10	39	interpolative	interpolative	ADJ
ejpam-6113	10	40	hardy	hardy	ADJ
ejpam-6113	10	41	-	-	PUNCT
ejpam-6113	10	42	rogers	rogers	NOUN
ejpam-6113	10	43	type	type	NOUN
ejpam-6113	10	44	contractive	contractive	ADJ
ejpam-6113	10	45	mapping	mapping	NOUN
ejpam-6113	10	46	.	.	PUNCT
ejpam-6113	11	1	interestingly	interestingly	ADV
ejpam-6113	11	2	,	,	PUNCT
ejpam-6113	11	3	this	this	DET
ejpam-6113	11	4	new	new	ADJ
ejpam-6113	11	5	kind	kind	NOUN
ejpam-6113	11	6	of	of	ADP
ejpam-6113	11	7	mapping	mapping	NOUN
ejpam-6113	11	8	was	be	AUX
ejpam-6113	11	9	first	first	ADV
ejpam-6113	11	10	developed	develop	VERB
ejpam-6113	11	11	by	by	ADP
ejpam-6113	11	12	karapınar	karapınar	PROPN
ejpam-6113	11	13	,	,	PUNCT
ejpam-6113	11	14	who	who	PRON
ejpam-6113	11	15	integrated	integrate	VERB
ejpam-6113	11	16	the	the	DET
ejpam-6113	11	17	interpolation	interpolation	NOUN
ejpam-6113	11	18	notion	notion	NOUN
ejpam-6113	11	19	into	into	ADP
ejpam-6113	11	20	the	the	DET
ejpam-6113	11	21	hardy	hardy	ADJ
ejpam-6113	11	22	-	-	PUNCT
ejpam-6113	11	23	rogers	rogers	NOUN
ejpam-6113	11	24	framework	framework	NOUN
ejpam-6113	11	25	.	.	PUNCT
ejpam-6113	12	1	this	this	DET
ejpam-6113	12	2	method	method	NOUN
ejpam-6113	12	3	probably	probably	ADV
ejpam-6113	12	4	broadens	broaden	VERB
ejpam-6113	12	5	the	the	DET
ejpam-6113	12	6	original	original	ADJ
ejpam-6113	12	7	theorem	theorem	NOUN
ejpam-6113	12	8	’s	’s	PART
ejpam-6113	12	9	usefulness	usefulness	NOUN
ejpam-6113	12	10	by	by	ADP
ejpam-6113	12	11	generating	generate	VERB
ejpam-6113	12	12	intermediate	intermediate	ADJ
ejpam-6113	12	13	points	point	NOUN
ejpam-6113	12	14	between	between	ADP
ejpam-6113	12	15	known	know	VERB
ejpam-6113	12	16	data	data	NOUN
ejpam-6113	12	17	points	point	NOUN
ejpam-6113	12	18	.	.	PUNCT
ejpam-6113	13	1	it	it	PRON
ejpam-6113	13	2	is	be	AUX
ejpam-6113	13	3	true	true	ADJ
ejpam-6113	13	4	that	that	SCONJ
ejpam-6113	13	5	interpolation	interpolation	NOUN
ejpam-6113	13	6	is	be	AUX
ejpam-6113	13	7	frequently	frequently	ADV
ejpam-6113	13	8	used	use	VERB
ejpam-6113	13	9	in	in	ADP
ejpam-6113	13	10	mathematical	mathematical	ADJ
ejpam-6113	13	11	study	study	NOUN
ejpam-6113	13	12	to	to	PART
ejpam-6113	13	13	generalize	generalize	VERB
ejpam-6113	13	14	different	different	ADJ
ejpam-6113	13	15	types	type	NOUN
ejpam-6113	13	16	of	of	ADP
ejpam-6113	13	17	contractions	contraction	NOUN
ejpam-6113	13	18	.	.	PUNCT
ejpam-6113	14	1	researchers	researcher	NOUN
ejpam-6113	14	2	can	can	AUX
ejpam-6113	14	3	broaden	broaden	VERB
ejpam-6113	14	4	the	the	DET
ejpam-6113	14	5	application	application	NOUN
ejpam-6113	14	6	of	of	ADP
ejpam-6113	14	7	current	current	ADJ
ejpam-6113	14	8	theorems	theorem	NOUN
ejpam-6113	14	9	and	and	CCONJ
ejpam-6113	14	10	offer	offer	VERB
ejpam-6113	14	11	a	a	DET
ejpam-6113	14	12	more	more	ADV
ejpam-6113	14	13	adaptable	adaptable	ADJ
ejpam-6113	14	14	framework	framework	NOUN
ejpam-6113	14	15	for	for	ADP
ejpam-6113	14	16	examining	examine	VERB
ejpam-6113	14	17	fixed	fix	VERB
ejpam-6113	14	18	points	point	NOUN
ejpam-6113	14	19	in	in	ADP
ejpam-6113	14	20	metric	metric	ADJ
ejpam-6113	14	21	spaces	space	NOUN
ejpam-6113	14	22	∗corresponding	∗corresponde	VERB
ejpam-6113	14	23	author	author	NOUN
ejpam-6113	14	24	.	.	PUNCT
ejpam-6113	15	1	doi	doi	NOUN
ejpam-6113	15	2	:	:	PUNCT
ejpam-6113	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6113	https://doi.org/10.29020/nybg.ejpam.v18i3.6113	ADJ
ejpam-6113	15	4	email	email	NOUN
ejpam-6113	15	5	addresses	address	NOUN
ejpam-6113	15	6	:	:	PUNCT
ejpam-6113	15	7	ratnababud@gmail.com	ratnababud@gmail.com	X
ejpam-6113	15	8	(	(	PUNCT
ejpam-6113	15	9	d.	d.	PROPN
ejpam-6113	15	10	r.	r.	PROPN
ejpam-6113	15	11	babu	babu	PROPN
ejpam-6113	15	12	)	)	PUNCT
ejpam-6113	15	13	,	,	PUNCT
ejpam-6113	15	14	nagakoteswararao.k@gmail.com	nagakoteswararao.k@gmail.com	X
ejpam-6113	15	15	(	(	PUNCT
ejpam-6113	15	16	k.	k.	PROPN
ejpam-6113	15	17	n.	n.	PROPN
ejpam-6113	15	18	k.	k.	PROPN
ejpam-6113	15	19	rao	rao	PROPN
ejpam-6113	15	20	)	)	PUNCT
ejpam-6113	15	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6113	16	1	1	1	NUM
ejpam-6113	16	2	copyright	copyright	NOUN
ejpam-6113	16	3	:	:	PUNCT
ejpam-6113	16	4	©	©	PROPN
ejpam-6113	16	5	2025	2025	NUM
ejpam-6113	16	6	the	the	DET
ejpam-6113	16	7	author(s	author(s	NOUN
ejpam-6113	16	8	)	)	PUNCT
ejpam-6113	16	9	.	.	PUNCT
ejpam-6113	17	1	(	(	PUNCT
ejpam-6113	17	2	cc	cc	NOUN
ejpam-6113	17	3	by	by	ADP
ejpam-6113	17	4	-	-	PUNCT
ejpam-6113	17	5	nc	nc	PROPN
ejpam-6113	17	6	4.0	4.0	NUM
ejpam-6113	17	7	)	)	PUNCT
ejpam-6113	17	8	d.	d.	PROPN
ejpam-6113	17	9	r.	r.	PROPN
ejpam-6113	17	10	babu	babu	PROPN
ejpam-6113	17	11	,	,	PUNCT
ejpam-6113	17	12	k.	k.	PROPN
ejpam-6113	17	13	n.	n.	PROPN
ejpam-6113	17	14	k.	k.	PROPN
ejpam-6113	18	1	rao	rao	PROPN
ejpam-6113	18	2	/	/	SYM
ejpam-6113	18	3	eur	eur	PROPN
ejpam-6113	18	4	.	.	PUNCT
ejpam-6113	19	1	j.	j.	PROPN
ejpam-6113	19	2	pure	pure	PROPN
ejpam-6113	19	3	appl	appl	PROPN
ejpam-6113	19	4	.	.	PROPN
ejpam-6113	19	5	math	math	PROPN
ejpam-6113	19	6	,	,	PUNCT
ejpam-6113	19	7	18	18	NUM
ejpam-6113	19	8	(	(	PUNCT
ejpam-6113	19	9	3	3	NUM
ejpam-6113	19	10	)	)	PUNCT
ejpam-6113	19	11	(	(	PUNCT
ejpam-6113	19	12	2025	2025	NUM
ejpam-6113	19	13	)	)	PUNCT
ejpam-6113	19	14	,	,	PUNCT
ejpam-6113	19	15	6113	6113	NUM
ejpam-6113	19	16	2	2	NUM
ejpam-6113	19	17	of	of	ADP
ejpam-6113	19	18	14	14	NUM
ejpam-6113	19	19	by	by	ADP
ejpam-6113	19	20	including	include	VERB
ejpam-6113	19	21	interpolation	interpolation	NOUN
ejpam-6113	19	22	techniques	technique	NOUN
ejpam-6113	19	23	into	into	ADP
ejpam-6113	19	24	contraction	contraction	NOUN
ejpam-6113	19	25	mappings	mapping	NOUN
ejpam-6113	19	26	.	.	PUNCT
ejpam-6113	20	1	it	it	PRON
ejpam-6113	20	2	appears	appear	VERB
ejpam-6113	20	3	that	that	SCONJ
ejpam-6113	20	4	the	the	DET
ejpam-6113	20	5	interpolative	interpolative	ADJ
ejpam-6113	20	6	approach	approach	NOUN
ejpam-6113	20	7	has	have	AUX
ejpam-6113	20	8	been	be	AUX
ejpam-6113	20	9	used	use	VERB
ejpam-6113	20	10	to	to	PART
ejpam-6113	20	11	generalize	generalize	VERB
ejpam-6113	20	12	various	various	ADJ
ejpam-6113	20	13	contraction	contraction	NOUN
ejpam-6113	20	14	types	type	NOUN
ejpam-6113	20	15	and	and	CCONJ
ejpam-6113	20	16	in	in	ADP
ejpam-6113	20	17	other	other	ADJ
ejpam-6113	20	18	studies	study	NOUN
ejpam-6113	20	19	.	.	PUNCT
ejpam-6113	21	1	this	this	PRON
ejpam-6113	21	2	illustrates	illustrate	VERB
ejpam-6113	21	3	the	the	DET
ejpam-6113	21	4	interpolation	interpolation	NOUN
ejpam-6113	21	5	approach	approach	NOUN
ejpam-6113	21	6	’s	’s	PART
ejpam-6113	21	7	adaptability	adaptability	NOUN
ejpam-6113	21	8	and	and	CCONJ
ejpam-6113	21	9	efficiency	efficiency	NOUN
ejpam-6113	21	10	in	in	ADP
ejpam-6113	21	11	extending	extend	VERB
ejpam-6113	21	12	the	the	DET
ejpam-6113	21	13	notion	notion	NOUN
ejpam-6113	21	14	of	of	ADP
ejpam-6113	21	15	fixed	fix	VERB
ejpam-6113	21	16	points	point	NOUN
ejpam-6113	21	17	and	and	CCONJ
ejpam-6113	21	18	offering	offer	VERB
ejpam-6113	21	19	fresh	fresh	ADJ
ejpam-6113	21	20	perspectives	perspective	NOUN
ejpam-6113	21	21	on	on	ADP
ejpam-6113	21	22	the	the	DET
ejpam-6113	21	23	existence	existence	NOUN
ejpam-6113	21	24	and	and	CCONJ
ejpam-6113	21	25	uniqueness	uniqueness	NOUN
ejpam-6113	21	26	of	of	ADP
ejpam-6113	21	27	solutions	solution	NOUN
ejpam-6113	21	28	.	.	PUNCT
ejpam-6113	22	1	i	i	PRON
ejpam-6113	22	2	suggest	suggest	AUX
ejpam-6113	22	3	consulting	consult	VERB
ejpam-6113	22	4	the	the	DET
ejpam-6113	22	5	relevant	relevant	ADJ
ejpam-6113	22	6	paper	paper	NOUN
ejpam-6113	22	7	[	[	X
ejpam-6113	22	8	6	6	NUM
ejpam-6113	22	9	,	,	PUNCT
ejpam-6113	22	10	8–16	8–16	PROPN
ejpam-6113	22	11	,	,	PUNCT
ejpam-6113	22	12	18	18	NUM
ejpam-6113	22	13	]	]	PUNCT
ejpam-6113	22	14	and	and	CCONJ
ejpam-6113	22	15	looking	look	VERB
ejpam-6113	22	16	into	into	ADP
ejpam-6113	22	17	similar	similar	ADJ
ejpam-6113	22	18	research	research	NOUN
ejpam-6113	22	19	in	in	ADP
ejpam-6113	22	20	the	the	DET
ejpam-6113	22	21	subject	subject	NOUN
ejpam-6113	22	22	to	to	PART
ejpam-6113	22	23	learn	learn	VERB
ejpam-6113	22	24	more	more	ADJ
ejpam-6113	22	25	about	about	ADP
ejpam-6113	22	26	the	the	DET
ejpam-6113	22	27	particulars	particular	NOUN
ejpam-6113	22	28	and	and	CCONJ
ejpam-6113	22	29	ramifications	ramification	NOUN
ejpam-6113	22	30	of	of	ADP
ejpam-6113	22	31	karapınar	karapınar	NOUN
ejpam-6113	22	32	’s	’s	PART
ejpam-6113	22	33	work	work	NOUN
ejpam-6113	22	34	as	as	ADV
ejpam-6113	22	35	well	well	ADV
ejpam-6113	22	36	as	as	ADP
ejpam-6113	22	37	the	the	DET
ejpam-6113	22	38	generalization	generalization	NOUN
ejpam-6113	22	39	of	of	ADP
ejpam-6113	22	40	other	other	ADJ
ejpam-6113	22	41	contraction	contraction	NOUN
ejpam-6113	22	42	forms	form	NOUN
ejpam-6113	22	43	utilizing	utilize	VERB
ejpam-6113	22	44	the	the	DET
ejpam-6113	22	45	interpolative	interpolative	ADJ
ejpam-6113	22	46	method	method	NOUN
ejpam-6113	22	47	.	.	PUNCT
ejpam-6113	23	1	these	these	DET
ejpam-6113	23	2	resources	resource	NOUN
ejpam-6113	23	3	ought	ought	AUX
ejpam-6113	23	4	to	to	PART
ejpam-6113	23	5	offer	offer	VERB
ejpam-6113	23	6	a	a	DET
ejpam-6113	23	7	more	more	ADV
ejpam-6113	23	8	thorough	thorough	ADJ
ejpam-6113	23	9	comprehension	comprehension	NOUN
ejpam-6113	23	10	of	of	ADP
ejpam-6113	23	11	the	the	DET
ejpam-6113	23	12	interpolative	interpolative	ADJ
ejpam-6113	23	13	contractive	contractive	ADJ
ejpam-6113	23	14	mapping	mapping	NOUN
ejpam-6113	23	15	of	of	ADP
ejpam-6113	23	16	the	the	DET
ejpam-6113	23	17	hardy	hardy	ADJ
ejpam-6113	23	18	-	-	PUNCT
ejpam-6113	23	19	rogers	rogers	NOUN
ejpam-6113	23	20	type	type	NOUN
ejpam-6113	23	21	and	and	CCONJ
ejpam-6113	23	22	its	its	PRON
ejpam-6113	23	23	uses	use	NOUN
ejpam-6113	23	24	in	in	ADP
ejpam-6113	23	25	fixed	fix	VERB
ejpam-6113	23	26	point	point	NOUN
ejpam-6113	23	27	theory	theory	NOUN
ejpam-6113	23	28	.	.	PUNCT
ejpam-6113	24	1	in	in	ADP
ejpam-6113	24	2	2018	2018	NUM
ejpam-6113	24	3	,	,	PUNCT
ejpam-6113	24	4	e.	e.	PROPN
ejpam-6113	24	5	karapınar	karapınar	PROPN
ejpam-6113	25	1	[	[	X
ejpam-6113	25	2	10	10	NUM
ejpam-6113	25	3	]	]	PUNCT
ejpam-6113	25	4	introduced	introduce	VERB
ejpam-6113	25	5	the	the	DET
ejpam-6113	25	6	notion	notion	NOUN
ejpam-6113	25	7	of	of	ADP
ejpam-6113	25	8	interpolative	interpolative	ADJ
ejpam-6113	25	9	kannan	kannan	PROPN
ejpam-6113	25	10	type	type	NOUN
ejpam-6113	25	11	contraction	contraction	NOUN
ejpam-6113	25	12	and	and	CCONJ
ejpam-6113	25	13	established	establish	VERB
ejpam-6113	25	14	corresponding	corresponding	ADJ
ejpam-6113	25	15	fixed	fix	VERB
ejpam-6113	25	16	point	point	NOUN
ejpam-6113	25	17	theorem	theorem	VERB
ejpam-6113	25	18	in	in	ADP
ejpam-6113	25	19	complete	complete	ADJ
ejpam-6113	25	20	metric	metric	ADJ
ejpam-6113	25	21	spaces	space	NOUN
ejpam-6113	25	22	.	.	PUNCT
ejpam-6113	26	1	definition	definition	NOUN
ejpam-6113	26	2	1	1	NUM
ejpam-6113	26	3	.	.	PUNCT
ejpam-6113	27	1	[	[	X
ejpam-6113	27	2	10	10	NUM
ejpam-6113	27	3	]	]	X
ejpam-6113	27	4	let	let	VERB
ejpam-6113	27	5	(	(	PUNCT
ejpam-6113	27	6	e	e	NOUN
ejpam-6113	27	7	,	,	PUNCT
ejpam-6113	27	8	d	d	NOUN
ejpam-6113	27	9	)	)	PUNCT
ejpam-6113	27	10	be	be	AUX
ejpam-6113	27	11	a	a	DET
ejpam-6113	27	12	metric	metric	ADJ
ejpam-6113	27	13	space	space	NOUN
ejpam-6113	27	14	.	.	PUNCT
ejpam-6113	28	1	a	a	DET
ejpam-6113	28	2	mappings	mapping	NOUN
ejpam-6113	28	3	t	t	NOUN
ejpam-6113	28	4	:	:	PUNCT
ejpam-6113	28	5	e	e	X
ejpam-6113	28	6	→	→	PUNCT
ejpam-6113	28	7	e	e	X
ejpam-6113	28	8	is	be	AUX
ejpam-6113	28	9	said	say	VERB
ejpam-6113	28	10	to	to	PART
ejpam-6113	28	11	be	be	AUX
ejpam-6113	28	12	interpolative	interpolative	ADJ
ejpam-6113	28	13	kannan	kannan	PROPN
ejpam-6113	28	14	type	type	NOUN
ejpam-6113	28	15	contraction	contraction	NOUN
ejpam-6113	28	16	if	if	SCONJ
ejpam-6113	28	17	there	there	PRON
ejpam-6113	28	18	exist	exist	VERB
ejpam-6113	28	19	a	a	DET
ejpam-6113	28	20	constant	constant	ADJ
ejpam-6113	28	21	λ	λ	X
ejpam-6113	28	22	∈	∈	PROPN
ejpam-6113	29	1	[	[	X
ejpam-6113	29	2	0	0	NUM
ejpam-6113	29	3	,	,	PUNCT
ejpam-6113	29	4	1	1	NUM
ejpam-6113	29	5	)	)	PUNCT
ejpam-6113	29	6	and	and	CCONJ
ejpam-6113	29	7	α	α	PRON
ejpam-6113	29	8	∈	∈	PROPN
ejpam-6113	29	9	(	(	PUNCT
ejpam-6113	29	10	0	0	NUM
ejpam-6113	29	11	,	,	PUNCT
ejpam-6113	29	12	1	1	NUM
ejpam-6113	29	13	)	)	PUNCT
ejpam-6113	29	14	such	such	ADJ
ejpam-6113	30	1	that	that	SCONJ
ejpam-6113	30	2	d(ta	d(ta	PROPN
ejpam-6113	30	3	,	,	PUNCT
ejpam-6113	30	4	tb	tb	NOUN
ejpam-6113	30	5	)	)	PUNCT
ejpam-6113	30	6	≤	≤	NOUN
ejpam-6113	30	7	λ[d(ta	λ[d(ta	PROPN
ejpam-6113	30	8	,	,	PUNCT
ejpam-6113	30	9	a)]α[d(tb	a)]α[d(tb	PROPN
ejpam-6113	30	10	,	,	PUNCT
ejpam-6113	30	11	b)]1−α	b)]1−α	X
ejpam-6113	30	12	for	for	ADP
ejpam-6113	30	13	all	all	DET
ejpam-6113	30	14	a	a	DET
ejpam-6113	30	15	,	,	PUNCT
ejpam-6113	30	16	b	b	X
ejpam-6113	30	17	∈	∈	PROPN
ejpam-6113	30	18	x	x	PUNCT
ejpam-6113	30	19	such	such	ADJ
ejpam-6113	30	20	that	that	PRON
ejpam-6113	30	21	ta	ta	AUX
ejpam-6113	30	22	̸=	̸=	PROPN
ejpam-6113	30	23	a.	a.	NOUN
ejpam-6113	30	24	theorem	theorem	NOUN
ejpam-6113	30	25	1	1	NUM
ejpam-6113	30	26	.	.	PUNCT
ejpam-6113	31	1	[	[	X
ejpam-6113	31	2	10	10	NUM
ejpam-6113	31	3	]	]	PUNCT
ejpam-6113	31	4	suppose	suppose	VERB
ejpam-6113	31	5	that	that	SCONJ
ejpam-6113	31	6	(	(	PUNCT
ejpam-6113	31	7	e	e	NOUN
ejpam-6113	31	8	,	,	PUNCT
ejpam-6113	31	9	d	d	NOUN
ejpam-6113	31	10	)	)	PUNCT
ejpam-6113	31	11	be	be	AUX
ejpam-6113	31	12	a	a	DET
ejpam-6113	31	13	complete	complete	ADJ
ejpam-6113	31	14	metric	metric	ADJ
ejpam-6113	31	15	space	space	NOUN
ejpam-6113	31	16	,	,	PUNCT
ejpam-6113	31	17	and	and	CCONJ
ejpam-6113	31	18	t	t	PROPN
ejpam-6113	31	19	is	be	AUX
ejpam-6113	31	20	a	a	DET
ejpam-6113	31	21	interpolative	interpolative	ADJ
ejpam-6113	31	22	kannan	kannan	PROPN
ejpam-6113	31	23	type	type	NOUN
ejpam-6113	31	24	contraction	contraction	NOUN
ejpam-6113	31	25	.	.	PUNCT
ejpam-6113	32	1	then	then	ADV
ejpam-6113	32	2	,	,	PUNCT
ejpam-6113	32	3	t	t	PROPN
ejpam-6113	32	4	has	have	VERB
ejpam-6113	32	5	a	a	DET
ejpam-6113	32	6	unique	unique	ADJ
ejpam-6113	32	7	common	common	ADJ
ejpam-6113	32	8	fixed	fix	VERB
ejpam-6113	32	9	point	point	NOUN
ejpam-6113	32	10	.	.	PUNCT
ejpam-6113	33	1	definition	definition	NOUN
ejpam-6113	33	2	2	2	NUM
ejpam-6113	33	3	.	.	PUNCT
ejpam-6113	34	1	[	[	X
ejpam-6113	34	2	16	16	NUM
ejpam-6113	34	3	]	]	X
ejpam-6113	34	4	let	let	VERB
ejpam-6113	34	5	(	(	PUNCT
ejpam-6113	34	6	e	e	NOUN
ejpam-6113	34	7	,	,	PUNCT
ejpam-6113	34	8	d	d	NOUN
ejpam-6113	34	9	)	)	PUNCT
ejpam-6113	34	10	be	be	AUX
ejpam-6113	34	11	a	a	DET
ejpam-6113	34	12	metric	metric	ADJ
ejpam-6113	34	13	space	space	NOUN
ejpam-6113	34	14	.	.	PUNCT
ejpam-6113	35	1	a	a	DET
ejpam-6113	35	2	mapping	mapping	NOUN
ejpam-6113	35	3	t	t	NOUN
ejpam-6113	35	4	:	:	PUNCT
ejpam-6113	35	5	e	e	X
ejpam-6113	35	6	→	→	PUNCT
ejpam-6113	35	7	e	e	X
ejpam-6113	35	8	is	be	AUX
ejpam-6113	35	9	said	say	VERB
ejpam-6113	35	10	to	to	PART
ejpam-6113	35	11	be	be	AUX
ejpam-6113	35	12	interpolative	interpolative	ADJ
ejpam-6113	35	13	hardy	hardy	ADJ
ejpam-6113	35	14	-	-	PUNCT
ejpam-6113	35	15	rogers	rogers	NOUN
ejpam-6113	35	16	contraction	contraction	NOUN
ejpam-6113	35	17	if	if	SCONJ
ejpam-6113	35	18	there	there	PRON
ejpam-6113	35	19	exist	exist	VERB
ejpam-6113	35	20	a	a	DET
ejpam-6113	35	21	constant	constant	ADJ
ejpam-6113	35	22	k	k	PROPN
ejpam-6113	35	23	∈	∈	PROPN
ejpam-6113	36	1	[	[	X
ejpam-6113	36	2	0	0	NUM
ejpam-6113	36	3	,	,	PUNCT
ejpam-6113	36	4	1	1	NUM
ejpam-6113	36	5	)	)	PUNCT
ejpam-6113	36	6	and	and	CCONJ
ejpam-6113	36	7	α	α	NOUN
ejpam-6113	36	8	,	,	PUNCT
ejpam-6113	36	9	β	β	X
ejpam-6113	36	10	,	,	PUNCT
ejpam-6113	36	11	γ	γ	PROPN
ejpam-6113	36	12	∈	∈	PROPN
ejpam-6113	36	13	(	(	PUNCT
ejpam-6113	36	14	0	0	NUM
ejpam-6113	36	15	,	,	PUNCT
ejpam-6113	36	16	1	1	NUM
ejpam-6113	36	17	)	)	PUNCT
ejpam-6113	36	18	with	with	ADP
ejpam-6113	36	19	α+	α+	PRON
ejpam-6113	36	20	β	β	NOUN
ejpam-6113	36	21	+	+	X
ejpam-6113	36	22	γ	γ	X
ejpam-6113	36	23	<	<	X
ejpam-6113	36	24	1	1	NUM
ejpam-6113	36	25	,	,	PUNCT
ejpam-6113	37	1	such	such	ADJ
ejpam-6113	37	2	that	that	SCONJ
ejpam-6113	37	3	d(ta	d(ta	PROPN
ejpam-6113	37	4	,	,	PUNCT
ejpam-6113	37	5	tb	tb	NOUN
ejpam-6113	37	6	)	)	PUNCT
ejpam-6113	37	7	≤	≤	NOUN
ejpam-6113	37	8	k[d(a	k[d(a	PROPN
ejpam-6113	37	9	,	,	PUNCT
ejpam-6113	37	10	b)β][d(ta	b)β][d(ta	PROPN
ejpam-6113	37	11	,	,	PUNCT
ejpam-6113	37	12	a)]γ	a)]γ	NOUN
ejpam-6113	37	13	[	[	X
ejpam-6113	37	14	d(tb	d(tb	NOUN
ejpam-6113	37	15	,	,	PUNCT
ejpam-6113	37	16	b)]α	b)]α	PROPN
ejpam-6113	37	17	[	[	PUNCT
ejpam-6113	37	18	d(ta	d(ta	PROPN
ejpam-6113	37	19	,	,	PUNCT
ejpam-6113	37	20	b	b	NOUN
ejpam-6113	37	21	)	)	PUNCT
ejpam-6113	37	22	+	+	CCONJ
ejpam-6113	37	23	d(a	d(a	PROPN
ejpam-6113	37	24	,	,	PUNCT
ejpam-6113	37	25	t	t	PROPN
ejpam-6113	37	26	b	b	NUM
ejpam-6113	37	27	)	)	PUNCT
ejpam-6113	37	28	2	2	NUM
ejpam-6113	37	29	]	]	SYM
ejpam-6113	37	30	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	37	31	for	for	ADP
ejpam-6113	37	32	all	all	DET
ejpam-6113	37	33	a	a	DET
ejpam-6113	37	34	,	,	PUNCT
ejpam-6113	37	35	b	b	X
ejpam-6113	37	36	∈	∈	PROPN
ejpam-6113	37	37	x	x	PUNCT
ejpam-6113	37	38	such	such	ADJ
ejpam-6113	37	39	that	that	PRON
ejpam-6113	37	40	ta	ta	AUX
ejpam-6113	37	41	̸=	̸=	PROPN
ejpam-6113	37	42	a.	a.	NOUN
ejpam-6113	37	43	theorem	theorem	NOUN
ejpam-6113	37	44	2	2	NUM
ejpam-6113	37	45	.	.	PUNCT
ejpam-6113	38	1	[	[	X
ejpam-6113	38	2	16	16	NUM
ejpam-6113	38	3	]	]	PUNCT
ejpam-6113	38	4	suppose	suppose	VERB
ejpam-6113	38	5	that	that	SCONJ
ejpam-6113	38	6	(	(	PUNCT
ejpam-6113	38	7	e	e	NOUN
ejpam-6113	38	8	,	,	PUNCT
ejpam-6113	38	9	d	d	NOUN
ejpam-6113	38	10	)	)	PUNCT
ejpam-6113	38	11	be	be	AUX
ejpam-6113	38	12	a	a	DET
ejpam-6113	38	13	complete	complete	ADJ
ejpam-6113	38	14	metric	metric	ADJ
ejpam-6113	38	15	space	space	NOUN
ejpam-6113	38	16	,	,	PUNCT
ejpam-6113	38	17	and	and	CCONJ
ejpam-6113	38	18	t	t	PROPN
ejpam-6113	38	19	is	be	AUX
ejpam-6113	38	20	a	a	DET
ejpam-6113	38	21	interpolative	interpolative	ADJ
ejpam-6113	38	22	hardy	hardy	ADJ
ejpam-6113	38	23	-	-	PUNCT
ejpam-6113	38	24	rogers	rogers	NOUN
ejpam-6113	38	25	pair	pair	NOUN
ejpam-6113	38	26	.	.	PUNCT
ejpam-6113	39	1	then	then	ADV
ejpam-6113	39	2	,	,	PUNCT
ejpam-6113	39	3	t	t	PROPN
ejpam-6113	39	4	has	have	VERB
ejpam-6113	39	5	a	a	DET
ejpam-6113	39	6	unique	unique	ADJ
ejpam-6113	39	7	common	common	ADJ
ejpam-6113	39	8	fixed	fix	VERB
ejpam-6113	39	9	point	point	NOUN
ejpam-6113	39	10	.	.	PUNCT
ejpam-6113	40	1	recently	recently	ADV
ejpam-6113	40	2	,	,	PUNCT
ejpam-6113	40	3	mohamed	mohamed	PROPN
ejpam-6113	40	4	edraoui	edraoui	PROPN
ejpam-6113	40	5	[	[	X
ejpam-6113	40	6	7	7	X
ejpam-6113	40	7	]	]	PUNCT
ejpam-6113	40	8	proved	prove	VERB
ejpam-6113	40	9	the	the	DET
ejpam-6113	40	10	following	follow	VERB
ejpam-6113	40	11	theorem	theorem	NOUN
ejpam-6113	40	12	using	use	VERB
ejpam-6113	40	13	interpolative	interpolative	ADJ
ejpam-6113	40	14	hardy	hardy	ADJ
ejpam-6113	40	15	-	-	PUNCT
ejpam-6113	40	16	rogers	rogers	NOUN
ejpam-6113	40	17	pair	pair	NOUN
ejpam-6113	40	18	contraction	contraction	NOUN
ejpam-6113	40	19	in	in	ADP
ejpam-6113	40	20	complete	complete	ADJ
ejpam-6113	40	21	metric	metric	ADJ
ejpam-6113	40	22	spaces	space	NOUN
ejpam-6113	40	23	.	.	PUNCT
ejpam-6113	41	1	definition	definition	NOUN
ejpam-6113	41	2	3	3	NUM
ejpam-6113	41	3	.	.	PUNCT
ejpam-6113	42	1	[	[	X
ejpam-6113	42	2	7	7	X
ejpam-6113	42	3	]	]	X
ejpam-6113	42	4	let	let	VERB
ejpam-6113	42	5	(	(	PUNCT
ejpam-6113	42	6	e	e	NOUN
ejpam-6113	42	7	,	,	PUNCT
ejpam-6113	42	8	d	d	NOUN
ejpam-6113	42	9	)	)	PUNCT
ejpam-6113	42	10	be	be	AUX
ejpam-6113	42	11	a	a	DET
ejpam-6113	42	12	metric	metric	ADJ
ejpam-6113	42	13	space	space	NOUN
ejpam-6113	42	14	.	.	PUNCT
ejpam-6113	43	1	a	a	DET
ejpam-6113	43	2	pair	pair	NOUN
ejpam-6113	43	3	of	of	ADP
ejpam-6113	43	4	mappings	mapping	NOUN
ejpam-6113	43	5	t	t	PROPN
ejpam-6113	43	6	,	,	PUNCT
ejpam-6113	43	7	s	s	PART
ejpam-6113	43	8	:	:	PUNCT
ejpam-6113	43	9	e	e	X
ejpam-6113	43	10	→	→	SYM
ejpam-6113	43	11	e	e	X
ejpam-6113	43	12	is	be	AUX
ejpam-6113	43	13	said	say	VERB
ejpam-6113	43	14	to	to	PART
ejpam-6113	43	15	be	be	AUX
ejpam-6113	43	16	interpolative	interpolative	ADJ
ejpam-6113	43	17	hardy	hardy	ADJ
ejpam-6113	43	18	-	-	PUNCT
ejpam-6113	43	19	rogers	rogers	NOUN
ejpam-6113	43	20	pair	pair	NOUN
ejpam-6113	43	21	contraction	contraction	NOUN
ejpam-6113	43	22	if	if	SCONJ
ejpam-6113	43	23	there	there	PRON
ejpam-6113	43	24	exist	exist	VERB
ejpam-6113	43	25	k	k	PROPN
ejpam-6113	43	26	∈	∈	PROPN
ejpam-6113	44	1	[	[	X
ejpam-6113	44	2	0	0	NUM
ejpam-6113	44	3	,	,	PUNCT
ejpam-6113	44	4	1	1	NUM
ejpam-6113	44	5	)	)	PUNCT
ejpam-6113	44	6	and	and	CCONJ
ejpam-6113	44	7	α	α	NOUN
ejpam-6113	44	8	,	,	PUNCT
ejpam-6113	44	9	β	β	X
ejpam-6113	44	10	,	,	PUNCT
ejpam-6113	44	11	γ	γ	PROPN
ejpam-6113	44	12	∈	∈	PROPN
ejpam-6113	44	13	(	(	PUNCT
ejpam-6113	44	14	0	0	NUM
ejpam-6113	44	15	,	,	PUNCT
ejpam-6113	44	16	1	1	NUM
ejpam-6113	44	17	)	)	PUNCT
ejpam-6113	44	18	with	with	ADP
ejpam-6113	44	19	α+	α+	PRON
ejpam-6113	44	20	β	β	NOUN
ejpam-6113	44	21	+	+	X
ejpam-6113	44	22	γ	γ	X
ejpam-6113	44	23	<	<	X
ejpam-6113	44	24	1	1	NUM
ejpam-6113	44	25	,	,	PUNCT
ejpam-6113	44	26	such	such	ADJ
ejpam-6113	44	27	that	that	SCONJ
ejpam-6113	44	28	d(ta	d(ta	PROPN
ejpam-6113	44	29	,	,	PUNCT
ejpam-6113	44	30	sb	sb	NOUN
ejpam-6113	44	31	)	)	PUNCT
ejpam-6113	44	32	≤	≤	PUNCT
ejpam-6113	44	33	k[d(a	k[d(a	PROPN
ejpam-6113	44	34	,	,	PUNCT
ejpam-6113	44	35	b)β][d(ta	b)β][d(ta	PROPN
ejpam-6113	44	36	,	,	PUNCT
ejpam-6113	44	37	a)]γ	a)]γ	NOUN
ejpam-6113	44	38	[	[	X
ejpam-6113	44	39	d(sb	d(sb	PROPN
ejpam-6113	44	40	,	,	PUNCT
ejpam-6113	44	41	b)]α	b)]α	PROPN
ejpam-6113	44	42	[	[	PUNCT
ejpam-6113	44	43	d(ta	d(ta	PROPN
ejpam-6113	44	44	,	,	PUNCT
ejpam-6113	44	45	b	b	NOUN
ejpam-6113	44	46	)	)	PUNCT
ejpam-6113	44	47	+	+	CCONJ
ejpam-6113	44	48	d(a	d(a	PROPN
ejpam-6113	44	49	,	,	PUNCT
ejpam-6113	44	50	sb	sb	NOUN
ejpam-6113	44	51	)	)	PUNCT
ejpam-6113	44	52	2	2	NUM
ejpam-6113	44	53	]	]	SYM
ejpam-6113	44	54	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	44	55	for	for	ADP
ejpam-6113	44	56	all	all	DET
ejpam-6113	44	57	a	a	PRON
ejpam-6113	44	58	,	,	PUNCT
ejpam-6113	44	59	b	b	X
ejpam-6113	44	60	∈	∈	PROPN
ejpam-6113	44	61	x	x	PUNCT
ejpam-6113	44	62	such	such	ADJ
ejpam-6113	44	63	that	that	PRON
ejpam-6113	44	64	ta	ta	ADP
ejpam-6113	44	65	̸=	̸=	PROPN
ejpam-6113	44	66	a	a	PRON
ejpam-6113	44	67	whenever	whenever	SCONJ
ejpam-6113	44	68	sb	sb	PROPN
ejpam-6113	44	69	̸=	̸=	PROPN
ejpam-6113	44	70	b.	b.	PROPN
ejpam-6113	44	71	theorem	theorem	VERB
ejpam-6113	44	72	3	3	NUM
ejpam-6113	44	73	.	.	PUNCT
ejpam-6113	45	1	[	[	X
ejpam-6113	45	2	7	7	X
ejpam-6113	45	3	]	]	PUNCT
ejpam-6113	45	4	suppose	suppose	VERB
ejpam-6113	45	5	that	that	SCONJ
ejpam-6113	45	6	(	(	PUNCT
ejpam-6113	45	7	e	e	NOUN
ejpam-6113	45	8	,	,	PUNCT
ejpam-6113	45	9	d	d	NOUN
ejpam-6113	45	10	)	)	PUNCT
ejpam-6113	45	11	be	be	AUX
ejpam-6113	45	12	a	a	DET
ejpam-6113	45	13	complete	complete	ADJ
ejpam-6113	45	14	metric	metric	ADJ
ejpam-6113	45	15	space	space	NOUN
ejpam-6113	45	16	,	,	PUNCT
ejpam-6113	45	17	and	and	CCONJ
ejpam-6113	45	18	(	(	PUNCT
ejpam-6113	45	19	t	t	PROPN
ejpam-6113	45	20	,	,	PUNCT
ejpam-6113	45	21	s	s	PART
ejpam-6113	45	22	)	)	PUNCT
ejpam-6113	45	23	is	be	AUX
ejpam-6113	45	24	a	a	DET
ejpam-6113	45	25	interpolative	interpolative	ADJ
ejpam-6113	45	26	hardy	hardy	ADJ
ejpam-6113	45	27	-	-	PUNCT
ejpam-6113	45	28	rogers	rogers	NOUN
ejpam-6113	45	29	pair	pair	NOUN
ejpam-6113	45	30	contraction	contraction	NOUN
ejpam-6113	45	31	.	.	PUNCT
ejpam-6113	46	1	then	then	ADV
ejpam-6113	46	2	,	,	PUNCT
ejpam-6113	46	3	s	s	X
ejpam-6113	46	4	and	and	CCONJ
ejpam-6113	46	5	t	t	PROPN
ejpam-6113	46	6	have	have	VERB
ejpam-6113	46	7	a	a	DET
ejpam-6113	46	8	unique	unique	ADJ
ejpam-6113	46	9	common	common	ADJ
ejpam-6113	46	10	fixed	fix	VERB
ejpam-6113	46	11	point	point	NOUN
ejpam-6113	46	12	.	.	PUNCT
ejpam-6113	47	1	d.	d.	PROPN
ejpam-6113	47	2	r.	r.	PROPN
ejpam-6113	47	3	babu	babu	PROPN
ejpam-6113	47	4	,	,	PUNCT
ejpam-6113	47	5	k.	k.	PROPN
ejpam-6113	47	6	n.	n.	PROPN
ejpam-6113	47	7	k.	k.	PROPN
ejpam-6113	48	1	rao	rao	PROPN
ejpam-6113	48	2	/	/	SYM
ejpam-6113	48	3	eur	eur	PROPN
ejpam-6113	48	4	.	.	PUNCT
ejpam-6113	49	1	j.	j.	PROPN
ejpam-6113	49	2	pure	pure	PROPN
ejpam-6113	49	3	appl	appl	PROPN
ejpam-6113	49	4	.	.	PROPN
ejpam-6113	49	5	math	math	PROPN
ejpam-6113	49	6	,	,	PUNCT
ejpam-6113	49	7	18	18	NUM
ejpam-6113	49	8	(	(	PUNCT
ejpam-6113	49	9	3	3	NUM
ejpam-6113	49	10	)	)	PUNCT
ejpam-6113	49	11	(	(	PUNCT
ejpam-6113	49	12	2025	2025	NUM
ejpam-6113	49	13	)	)	PUNCT
ejpam-6113	49	14	,	,	PUNCT
ejpam-6113	49	15	6113	6113	NUM
ejpam-6113	49	16	3	3	NUM
ejpam-6113	49	17	of	of	ADP
ejpam-6113	49	18	14	14	NUM
ejpam-6113	49	19	2	2	NUM
ejpam-6113	49	20	.	.	PUNCT
ejpam-6113	49	21	main	main	ADJ
ejpam-6113	49	22	results	result	NOUN
ejpam-6113	49	23	in	in	ADP
ejpam-6113	49	24	the	the	DET
ejpam-6113	49	25	following	following	NOUN
ejpam-6113	49	26	,	,	PUNCT
ejpam-6113	49	27	we	we	PRON
ejpam-6113	49	28	introduce	introduce	VERB
ejpam-6113	49	29	interpolative	interpolative	ADJ
ejpam-6113	49	30	contraction	contraction	NOUN
ejpam-6113	49	31	maps	map	NOUN
ejpam-6113	49	32	in	in	ADP
ejpam-6113	49	33	b	b	NOUN
ejpam-6113	49	34	-	-	PUNCT
ejpam-6113	49	35	metric	metric	ADJ
ejpam-6113	49	36	spaces	space	NOUN
ejpam-6113	49	37	.	.	PUNCT
ejpam-6113	50	1	the	the	DET
ejpam-6113	50	2	definition	definition	NOUN
ejpam-6113	50	3	of	of	ADP
ejpam-6113	50	4	hardy	hardy	ADJ
ejpam-6113	50	5	-	-	PUNCT
ejpam-6113	50	6	rogers	rogers	NOUN
ejpam-6113	50	7	-	-	PUNCT
ejpam-6113	50	8	type	type	NOUN
ejpam-6113	50	9	contraction	contraction	NOUN
ejpam-6113	50	10	has	have	AUX
ejpam-6113	50	11	been	be	AUX
ejpam-6113	50	12	generalized	generalize	VERB
ejpam-6113	50	13	by	by	ADP
ejpam-6113	50	14	adding	add	VERB
ejpam-6113	50	15	the	the	DET
ejpam-6113	50	16	notion	notion	NOUN
ejpam-6113	50	17	of	of	ADP
ejpam-6113	50	18	interpolation	interpolation	NOUN
ejpam-6113	50	19	.	.	PUNCT
ejpam-6113	51	1	the	the	DET
ejpam-6113	51	2	goal	goal	NOUN
ejpam-6113	51	3	is	be	AUX
ejpam-6113	51	4	to	to	PART
ejpam-6113	51	5	find	find	VERB
ejpam-6113	51	6	new	new	ADJ
ejpam-6113	51	7	qualities	quality	NOUN
ejpam-6113	51	8	and	and	CCONJ
ejpam-6113	51	9	broaden	broaden	VERB
ejpam-6113	51	10	the	the	DET
ejpam-6113	51	11	definition	definition	NOUN
ejpam-6113	51	12	of	of	ADP
ejpam-6113	51	13	a	a	DET
ejpam-6113	51	14	hardy	hardy	ADJ
ejpam-6113	51	15	-	-	PUNCT
ejpam-6113	51	16	rogers	rogers	NOUN
ejpam-6113	51	17	-	-	PUNCT
ejpam-6113	51	18	type	type	NOUN
ejpam-6113	51	19	contraction	contraction	NOUN
ejpam-6113	51	20	by	by	ADP
ejpam-6113	51	21	interpolation	interpolation	NOUN
ejpam-6113	51	22	.	.	PUNCT
ejpam-6113	52	1	definition	definition	NOUN
ejpam-6113	52	2	4	4	NUM
ejpam-6113	52	3	.	.	PUNCT
ejpam-6113	53	1	let	let	VERB
ejpam-6113	53	2	(	(	PUNCT
ejpam-6113	53	3	e	e	NOUN
ejpam-6113	53	4	,	,	PUNCT
ejpam-6113	53	5	d	d	PROPN
ejpam-6113	53	6	,	,	PUNCT
ejpam-6113	53	7	s	s	PART
ejpam-6113	53	8	)	)	PUNCT
ejpam-6113	53	9	be	be	AUX
ejpam-6113	53	10	a	a	DET
ejpam-6113	53	11	b	b	NOUN
ejpam-6113	53	12	-	-	PUNCT
ejpam-6113	53	13	metric	metric	ADJ
ejpam-6113	53	14	space	space	NOUN
ejpam-6113	53	15	.	.	PUNCT
ejpam-6113	54	1	a	a	DET
ejpam-6113	54	2	pair	pair	NOUN
ejpam-6113	54	3	of	of	ADP
ejpam-6113	54	4	mappings	mapping	NOUN
ejpam-6113	54	5	t	t	PROPN
ejpam-6113	54	6	,	,	PUNCT
ejpam-6113	54	7	s	s	PART
ejpam-6113	54	8	:	:	PUNCT
ejpam-6113	54	9	x	x	SYM
ejpam-6113	54	10	→	→	PUNCT
ejpam-6113	54	11	x	x	X
ejpam-6113	54	12	is	be	AUX
ejpam-6113	54	13	said	say	VERB
ejpam-6113	54	14	to	to	PART
ejpam-6113	54	15	be	be	AUX
ejpam-6113	54	16	interpolative	interpolative	ADJ
ejpam-6113	54	17	hardy	hardy	ADJ
ejpam-6113	54	18	-	-	PUNCT
ejpam-6113	54	19	rogers	rogers	NOUN
ejpam-6113	54	20	-	-	PUNCT
ejpam-6113	54	21	type	type	NOUN
ejpam-6113	54	22	contraction	contraction	NOUN
ejpam-6113	54	23	if	if	SCONJ
ejpam-6113	54	24	there	there	PRON
ejpam-6113	54	25	exist	exist	VERB
ejpam-6113	54	26	λ	λ	PROPN
ejpam-6113	54	27	∈	∈	PROPN
ejpam-6113	55	1	[	[	X
ejpam-6113	55	2	0	0	NUM
ejpam-6113	55	3	,	,	PUNCT
ejpam-6113	55	4	1	1	NUM
ejpam-6113	55	5	)	)	PUNCT
ejpam-6113	55	6	and	and	CCONJ
ejpam-6113	55	7	α	α	NOUN
ejpam-6113	55	8	,	,	PUNCT
ejpam-6113	55	9	β	β	X
ejpam-6113	55	10	,	,	PUNCT
ejpam-6113	55	11	γ	γ	PROPN
ejpam-6113	55	12	∈	∈	PROPN
ejpam-6113	55	13	(	(	PUNCT
ejpam-6113	55	14	0	0	NUM
ejpam-6113	55	15	,	,	PUNCT
ejpam-6113	55	16	1	1	NUM
ejpam-6113	55	17	)	)	PUNCT
ejpam-6113	55	18	with	with	ADP
ejpam-6113	55	19	α+	α+	PRON
ejpam-6113	55	20	β	β	NOUN
ejpam-6113	55	21	+	+	X
ejpam-6113	55	22	γ	γ	X
ejpam-6113	55	23	<	<	X
ejpam-6113	55	24	1	1	NUM
ejpam-6113	55	25	,	,	PUNCT
ejpam-6113	55	26	such	such	ADJ
ejpam-6113	55	27	that	that	SCONJ
ejpam-6113	55	28	d(ta	d(ta	PROPN
ejpam-6113	55	29	,	,	PUNCT
ejpam-6113	55	30	sb	sb	NOUN
ejpam-6113	55	31	)	)	PUNCT
ejpam-6113	55	32	≤	≤	PUNCT
ejpam-6113	56	1	λ[d(a	λ[d(a	X
ejpam-6113	56	2	,	,	PUNCT
ejpam-6113	56	3	b)β][d(ta	b)β][d(ta	PROPN
ejpam-6113	56	4	,	,	PUNCT
ejpam-6113	56	5	a)]γ	a)]γ	NOUN
ejpam-6113	56	6	[	[	X
ejpam-6113	56	7	d(sb	d(sb	PROPN
ejpam-6113	56	8	,	,	PUNCT
ejpam-6113	56	9	b)]α	b)]α	PROPN
ejpam-6113	56	10	[	[	PUNCT
ejpam-6113	56	11	d(ta	d(ta	PROPN
ejpam-6113	56	12	,	,	PUNCT
ejpam-6113	56	13	b	b	NOUN
ejpam-6113	56	14	)	)	PUNCT
ejpam-6113	56	15	+	+	CCONJ
ejpam-6113	56	16	d(a	d(a	PROPN
ejpam-6113	56	17	,	,	PUNCT
ejpam-6113	56	18	sb	sb	X
ejpam-6113	56	19	)	)	PUNCT
ejpam-6113	56	20	2s	2s	X
ejpam-6113	57	1	]	]	X
ejpam-6113	57	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	57	3	(	(	PUNCT
ejpam-6113	57	4	2.1	2.1	NUM
ejpam-6113	57	5	)	)	PUNCT
ejpam-6113	57	6	for	for	ADP
ejpam-6113	57	7	all	all	DET
ejpam-6113	57	8	a	a	PRON
ejpam-6113	57	9	,	,	PUNCT
ejpam-6113	57	10	b	b	X
ejpam-6113	57	11	∈	∈	PROPN
ejpam-6113	57	12	x	x	PUNCT
ejpam-6113	57	13	such	such	ADJ
ejpam-6113	57	14	that	that	PRON
ejpam-6113	57	15	ta	ta	ADP
ejpam-6113	57	16	̸=	̸=	PROPN
ejpam-6113	57	17	a	a	PRON
ejpam-6113	57	18	whenever	whenever	SCONJ
ejpam-6113	57	19	sb	sb	PROPN
ejpam-6113	57	20	̸=	̸=	PROPN
ejpam-6113	57	21	b.	b.	PROPN
ejpam-6113	57	22	proposition	proposition	NOUN
ejpam-6113	57	23	1	1	NUM
ejpam-6113	57	24	.	.	PUNCT
ejpam-6113	58	1	allow	allow	VERB
ejpam-6113	58	2	(	(	PUNCT
ejpam-6113	58	3	e	e	NOUN
ejpam-6113	58	4	,	,	PUNCT
ejpam-6113	58	5	d	d	NOUN
ejpam-6113	58	6	,	,	PUNCT
ejpam-6113	58	7	s	s	PART
ejpam-6113	58	8	)	)	PUNCT
ejpam-6113	58	9	to	to	PART
ejpam-6113	58	10	be	be	AUX
ejpam-6113	58	11	a	a	DET
ejpam-6113	58	12	b	b	NOUN
ejpam-6113	58	13	-	-	PUNCT
ejpam-6113	58	14	metric	metric	ADJ
ejpam-6113	58	15	space	space	NOUN
ejpam-6113	58	16	with	with	ADP
ejpam-6113	58	17	two	two	NUM
ejpam-6113	58	18	self	self	NOUN
ejpam-6113	58	19	-	-	PUNCT
ejpam-6113	58	20	maps	map	NOUN
ejpam-6113	58	21	t	t	PROPN
ejpam-6113	58	22	,	,	PUNCT
ejpam-6113	58	23	s	s	PART
ejpam-6113	58	24	:	:	PUNCT
ejpam-6113	58	25	e	e	X
ejpam-6113	58	26	→	→	SYM
ejpam-6113	58	27	e	e	PROPN
ejpam-6113	58	28	and	and	CCONJ
ejpam-6113	58	29	a	a	DET
ejpam-6113	58	30	coefficient	coefficient	NOUN
ejpam-6113	58	31	s	s	VERB
ejpam-6113	58	32	≥	≥	NOUN
ejpam-6113	58	33	1	1	NUM
ejpam-6113	58	34	.	.	PUNCT
ejpam-6113	59	1	the	the	DET
ejpam-6113	59	2	pair	pair	NOUN
ejpam-6113	59	3	(	(	PUNCT
ejpam-6113	59	4	t	t	PROPN
ejpam-6113	59	5	,	,	PUNCT
ejpam-6113	59	6	s	s	PART
ejpam-6113	59	7	)	)	PUNCT
ejpam-6113	59	8	is	be	AUX
ejpam-6113	59	9	assumed	assume	VERB
ejpam-6113	59	10	to	to	PART
ejpam-6113	59	11	be	be	AUX
ejpam-6113	59	12	an	an	DET
ejpam-6113	59	13	interpolative	interpolative	ADJ
ejpam-6113	59	14	hardy	hardy	ADJ
ejpam-6113	59	15	-	-	PUNCT
ejpam-6113	59	16	rogerstype	rogerstype	NOUN
ejpam-6113	59	17	contraction	contraction	NOUN
ejpam-6113	59	18	.	.	PUNCT
ejpam-6113	60	1	in	in	ADP
ejpam-6113	60	2	the	the	DET
ejpam-6113	60	3	event	event	NOUN
ejpam-6113	60	4	that	that	PRON
ejpam-6113	60	5	a	a	DET
ejpam-6113	60	6	′	′	NOUN
ejpam-6113	60	7	is	be	AUX
ejpam-6113	60	8	a	a	DET
ejpam-6113	60	9	fixed	fix	VERB
ejpam-6113	60	10	point	point	NOUN
ejpam-6113	60	11	of	of	ADP
ejpam-6113	60	12	s	s	PROPN
ejpam-6113	60	13	,	,	PUNCT
ejpam-6113	60	14	then	then	ADV
ejpam-6113	60	15	a	a	DET
ejpam-6113	60	16	′	′	NOUN
ejpam-6113	60	17	is	be	AUX
ejpam-6113	60	18	a	a	DET
ejpam-6113	60	19	fixed	fix	VERB
ejpam-6113	60	20	point	point	NOUN
ejpam-6113	60	21	of	of	ADP
ejpam-6113	60	22	t	t	PROPN
ejpam-6113	60	23	because	because	SCONJ
ejpam-6113	60	24	of	of	ADP
ejpam-6113	60	25	this	this	PRON
ejpam-6113	60	26	.	.	PUNCT
ejpam-6113	61	1	additionally	additionally	ADV
ejpam-6113	61	2	,	,	PUNCT
ejpam-6113	61	3	in	in	ADP
ejpam-6113	61	4	this	this	DET
ejpam-6113	61	5	instance	instance	NOUN
ejpam-6113	61	6	,	,	PUNCT
ejpam-6113	61	7	a	a	DET
ejpam-6113	61	8	′	′	NOUN
ejpam-6113	61	9	is	be	AUX
ejpam-6113	61	10	unique	unique	ADJ
ejpam-6113	61	11	.	.	PUNCT
ejpam-6113	62	1	theorem	theorem	ADJ
ejpam-6113	62	2	4	4	NUM
ejpam-6113	62	3	.	.	PUNCT
ejpam-6113	62	4	suppose	suppose	VERB
ejpam-6113	62	5	that	that	SCONJ
ejpam-6113	62	6	(	(	PUNCT
ejpam-6113	62	7	e	e	NOUN
ejpam-6113	62	8	,	,	PUNCT
ejpam-6113	62	9	d	d	PROPN
ejpam-6113	62	10	,	,	PUNCT
ejpam-6113	62	11	s	s	PART
ejpam-6113	62	12	)	)	PUNCT
ejpam-6113	62	13	be	be	AUX
ejpam-6113	62	14	a	a	DET
ejpam-6113	62	15	complete	complete	ADJ
ejpam-6113	62	16	b	b	NOUN
ejpam-6113	62	17	-	-	PUNCT
ejpam-6113	62	18	metric	metric	ADJ
ejpam-6113	62	19	space	space	NOUN
ejpam-6113	62	20	,	,	PUNCT
ejpam-6113	62	21	and	and	CCONJ
ejpam-6113	62	22	(	(	PUNCT
ejpam-6113	62	23	t	t	PROPN
ejpam-6113	62	24	,	,	PUNCT
ejpam-6113	62	25	s	s	PART
ejpam-6113	62	26	)	)	PUNCT
ejpam-6113	62	27	is	be	AUX
ejpam-6113	62	28	an	an	DET
ejpam-6113	62	29	interpolative	interpolative	ADJ
ejpam-6113	62	30	hardy	hardy	ADJ
ejpam-6113	62	31	-	-	PUNCT
ejpam-6113	62	32	rogers	rogers	NOUN
ejpam-6113	62	33	-	-	PUNCT
ejpam-6113	62	34	type	type	NOUN
ejpam-6113	62	35	contraction	contraction	NOUN
ejpam-6113	62	36	.	.	PUNCT
ejpam-6113	63	1	both	both	DET
ejpam-6113	63	2	s	s	PROPN
ejpam-6113	63	3	and	and	CCONJ
ejpam-6113	63	4	t	t	PROPN
ejpam-6113	63	5	have	have	VERB
ejpam-6113	63	6	a	a	DET
ejpam-6113	63	7	unique	unique	ADJ
ejpam-6113	63	8	common	common	ADJ
ejpam-6113	63	9	fixed	fix	VERB
ejpam-6113	63	10	point	point	NOUN
ejpam-6113	63	11	if	if	SCONJ
ejpam-6113	63	12	either	either	CCONJ
ejpam-6113	63	13	t	t	NOUN
ejpam-6113	63	14	or	or	CCONJ
ejpam-6113	63	15	s	s	NOUN
ejpam-6113	63	16	is	be	AUX
ejpam-6113	63	17	b	b	NOUN
ejpam-6113	63	18	-	-	PUNCT
ejpam-6113	63	19	continuous	continuous	ADJ
ejpam-6113	63	20	.	.	PUNCT
ejpam-6113	64	1	proof	proof	NOUN
ejpam-6113	64	2	.	.	PUNCT
ejpam-6113	65	1	let	let	VERB
ejpam-6113	65	2	a0	a0	PROPN
ejpam-6113	65	3	∈	∈	PROPN
ejpam-6113	65	4	e	e	PRON
ejpam-6113	65	5	be	be	AUX
ejpam-6113	65	6	an	an	DET
ejpam-6113	65	7	arbitrary	arbitrary	ADJ
ejpam-6113	65	8	point	point	NOUN
ejpam-6113	65	9	.	.	PUNCT
ejpam-6113	66	1	consider	consider	VERB
ejpam-6113	66	2	{	{	PUNCT
ejpam-6113	66	3	an	an	X
ejpam-6113	66	4	}	}	PUNCT
ejpam-6113	66	5	,	,	PUNCT
ejpam-6113	66	6	given	give	VERB
ejpam-6113	66	7	as	as	ADP
ejpam-6113	66	8	a2n+1	a2n+1	NOUN
ejpam-6113	66	9	=	=	SYM
ejpam-6113	66	10	ta2n	ta2n	PROPN
ejpam-6113	66	11	and	and	CCONJ
ejpam-6113	66	12	a2n+2	a2n+2	PRON
ejpam-6113	66	13	=	=	PUNCT
ejpam-6113	66	14	sa2n+1	sa2n+1	VERB
ejpam-6113	66	15	for	for	SCONJ
ejpam-6113	66	16	each	each	DET
ejpam-6113	66	17	positive	positive	ADJ
ejpam-6113	66	18	integer	integer	NOUN
ejpam-6113	66	19	n.	n.	NOUN
ejpam-6113	66	20	take	take	VERB
ejpam-6113	66	21	a	a	DET
ejpam-6113	66	22	=	=	PUNCT
ejpam-6113	66	23	a2n	a2n	PROPN
ejpam-6113	66	24	and	and	CCONJ
ejpam-6113	66	25	b	b	X
ejpam-6113	66	26	=	=	PUNCT
ejpam-6113	66	27	a2n+1	a2n+1	PROPN
ejpam-6113	66	28	in	in	ADP
ejpam-6113	66	29	(	(	PUNCT
ejpam-6113	66	30	2.1	2.1	NUM
ejpam-6113	66	31	)	)	PUNCT
ejpam-6113	66	32	,	,	PUNCT
ejpam-6113	66	33	we	we	PRON
ejpam-6113	66	34	get	get	VERB
ejpam-6113	66	35	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	66	36	,	,	PUNCT
ejpam-6113	66	37	a2n+2	a2n+2	PRON
ejpam-6113	66	38	)	)	PUNCT
ejpam-6113	66	39	=	=	SYM
ejpam-6113	67	1	d(ta2n	d(ta2n	X
ejpam-6113	67	2	,	,	PUNCT
ejpam-6113	67	3	sa2n+1	sa2n+1	NOUN
ejpam-6113	67	4	)	)	PUNCT
ejpam-6113	67	5	≤	≤	PROPN
ejpam-6113	67	6	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	67	7	,	,	PUNCT
ejpam-6113	67	8	a2n+1	a2n+1	NOUN
ejpam-6113	67	9	)	)	PUNCT
ejpam-6113	67	10	β][d(ta2n	β][d(ta2n	NOUN
ejpam-6113	67	11	,	,	PUNCT
ejpam-6113	67	12	a2n	a2n	ADV
ejpam-6113	67	13	)	)	PUNCT
ejpam-6113	67	14	]	]	PUNCT
ejpam-6113	68	1	γ	γ	X
ejpam-6113	68	2	[	[	X
ejpam-6113	68	3	d(sa2n+1	d(sa2n+1	ADJ
ejpam-6113	68	4	,	,	PUNCT
ejpam-6113	68	5	a2n+1	a2n+1	NOUN
ejpam-6113	68	6	)	)	PUNCT
ejpam-6113	68	7	]	]	PUNCT
ejpam-6113	69	1	α	α	PRON
ejpam-6113	69	2	[	[	PUNCT
ejpam-6113	69	3	12sd(ta2n	12sd(ta2n	NUM
ejpam-6113	69	4	,	,	PUNCT
ejpam-6113	69	5	a2n+1	a2n+1	NOUN
ejpam-6113	69	6	)	)	PUNCT
ejpam-6113	69	7	+	+	CCONJ
ejpam-6113	69	8	d(a2n	d(a2n	ADJ
ejpam-6113	69	9	,	,	PUNCT
ejpam-6113	69	10	sa2n+1	sa2n+1	NOUN
ejpam-6113	69	11	)	)	PUNCT
ejpam-6113	69	12	]	]	PUNCT
ejpam-6113	70	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	70	2	=	=	SYM
ejpam-6113	70	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	70	4	,	,	PUNCT
ejpam-6113	70	5	a2n+1	a2n+1	ADJ
ejpam-6113	70	6	)	)	PUNCT
ejpam-6113	70	7	β][d(a2n+1	β][d(a2n+1	NOUN
ejpam-6113	70	8	,	,	PUNCT
ejpam-6113	70	9	a2n	a2n	NOUN
ejpam-6113	70	10	)	)	PUNCT
ejpam-6113	70	11	]	]	PUNCT
ejpam-6113	71	1	γ	γ	X
ejpam-6113	71	2	[	[	X
ejpam-6113	71	3	d(a2n+2	d(a2n+2	X
ejpam-6113	71	4	,	,	PUNCT
ejpam-6113	71	5	a2n+1	a2n+1	NOUN
ejpam-6113	71	6	)	)	PUNCT
ejpam-6113	71	7	]	]	PUNCT
ejpam-6113	72	1	α	α	PRON
ejpam-6113	72	2	[	[	PUNCT
ejpam-6113	72	3	12sd(a2n+1	12sd(a2n+1	NUM
ejpam-6113	72	4	,	,	PUNCT
ejpam-6113	72	5	a2n+1	a2n+1	NOUN
ejpam-6113	72	6	)	)	PUNCT
ejpam-6113	72	7	+	+	SYM
ejpam-6113	72	8	d(a2n	d(a2n	ADJ
ejpam-6113	72	9	,	,	PUNCT
ejpam-6113	72	10	a2n+2	a2n+2	ADJ
ejpam-6113	72	11	)	)	PUNCT
ejpam-6113	72	12	]	]	PUNCT
ejpam-6113	73	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	73	2	then	then	ADV
ejpam-6113	73	3	[	[	X
ejpam-6113	73	4	d(a2n+1	d(a2n+1	X
ejpam-6113	73	5	,	,	PUNCT
ejpam-6113	73	6	a2n+2	a2n+2	PRON
ejpam-6113	73	7	)	)	PUNCT
ejpam-6113	73	8	]	]	PUNCT
ejpam-6113	74	1	1−α	1−α	NUM
ejpam-6113	74	2	≤	≤	NUM
ejpam-6113	74	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	74	4	,	,	PUNCT
ejpam-6113	74	5	a2n+1	a2n+1	PROPN
ejpam-6113	74	6	)	)	PUNCT
ejpam-6113	74	7	]	]	PUNCT
ejpam-6113	74	8	β+γ	β+γ	PUNCT
ejpam-6113	75	1	[	[	PUNCT
ejpam-6113	75	2	12sd(a2n	12sd(a2n	NUM
ejpam-6113	75	3	,	,	PUNCT
ejpam-6113	75	4	a2n+2	a2n+2	PRON
ejpam-6113	75	5	)	)	PUNCT
ejpam-6113	75	6	]	]	PUNCT
ejpam-6113	76	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	76	2	≤	≤	PROPN
ejpam-6113	76	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	76	4	,	,	PUNCT
ejpam-6113	76	5	a2n+1	a2n+1	PROPN
ejpam-6113	76	6	)	)	PUNCT
ejpam-6113	76	7	]	]	PUNCT
ejpam-6113	76	8	β+γ	β+γ	PUNCT
ejpam-6113	77	1	[	[	X
ejpam-6113	77	2	12	12	NUM
ejpam-6113	77	3	[	[	X
ejpam-6113	77	4	d(a2n	d(a2n	ADJ
ejpam-6113	77	5	,	,	PUNCT
ejpam-6113	77	6	a2n+1	a2n+1	ADJ
ejpam-6113	77	7	)	)	PUNCT
ejpam-6113	77	8	+	+	SYM
ejpam-6113	77	9	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	77	10	,	,	PUNCT
ejpam-6113	77	11	a2n+2	a2n+2	PRON
ejpam-6113	77	12	)	)	PUNCT
ejpam-6113	77	13	]	]	X
ejpam-6113	77	14	]	]	X
ejpam-6113	77	15	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	77	16	(	(	PUNCT
ejpam-6113	77	17	2.2	2.2	NUM
ejpam-6113	77	18	)	)	PUNCT
ejpam-6113	77	19	suppose	suppose	VERB
ejpam-6113	77	20	that	that	SCONJ
ejpam-6113	77	21	d(a2n	d(a2n	ADP
ejpam-6113	77	22	,	,	PUNCT
ejpam-6113	77	23	a2n+1	a2n+1	NOUN
ejpam-6113	77	24	)	)	PUNCT
ejpam-6113	77	25	<	<	X
ejpam-6113	77	26	d(a2n+1	d(a2n+1	PROPN
ejpam-6113	77	27	,	,	PUNCT
ejpam-6113	77	28	a2n+2	a2n+2	PRON
ejpam-6113	77	29	)	)	PUNCT
ejpam-6113	77	30	.	.	PUNCT
ejpam-6113	78	1	therefore	therefore	ADV
ejpam-6113	78	2	,	,	PUNCT
ejpam-6113	78	3	the	the	DET
ejpam-6113	78	4	inequality	inequality	NOUN
ejpam-6113	78	5	(	(	PUNCT
ejpam-6113	78	6	2.2	2.2	NUM
ejpam-6113	78	7	)	)	PUNCT
ejpam-6113	78	8	produces	produce	VERB
ejpam-6113	78	9	that	that	SCONJ
ejpam-6113	79	1	[	[	X
ejpam-6113	79	2	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	79	3	,	,	PUNCT
ejpam-6113	79	4	a2n+2	a2n+2	PRON
ejpam-6113	79	5	)	)	PUNCT
ejpam-6113	79	6	]	]	PUNCT
ejpam-6113	80	1	1−α	1−α	NUM
ejpam-6113	80	2	≤	≤	NUM
ejpam-6113	80	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	80	4	,	,	PUNCT
ejpam-6113	80	5	a2n+1	a2n+1	PROPN
ejpam-6113	80	6	)	)	PUNCT
ejpam-6113	80	7	]	]	PUNCT
ejpam-6113	80	8	β+γ	β+γ	PUNCT
ejpam-6113	81	1	[	[	X
ejpam-6113	81	2	d(a2n+1	d(a2n+1	X
ejpam-6113	81	3	,	,	PUNCT
ejpam-6113	81	4	a2n+2	a2n+2	PRON
ejpam-6113	81	5	)	)	PUNCT
ejpam-6113	81	6	]	]	PUNCT
ejpam-6113	81	7	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	81	8	implies	imply	VERB
ejpam-6113	81	9	that	that	SCONJ
ejpam-6113	81	10	[	[	X
ejpam-6113	81	11	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	81	12	,	,	PUNCT
ejpam-6113	81	13	a2n+2	a2n+2	PRON
ejpam-6113	81	14	)	)	PUNCT
ejpam-6113	81	15	]	]	PUNCT
ejpam-6113	81	16	β+γ	β+γ	PUNCT
ejpam-6113	81	17	≤	≤	NUM
ejpam-6113	81	18	λ[d(a2n	λ[d(a2n	NOUN
ejpam-6113	81	19	,	,	PUNCT
ejpam-6113	81	20	a2n+1	a2n+1	PROPN
ejpam-6113	81	21	)	)	PUNCT
ejpam-6113	81	22	]	]	PUNCT
ejpam-6113	81	23	β+γ	β+γ	PUNCT
ejpam-6113	81	24	d.	d.	PROPN
ejpam-6113	81	25	r.	r.	PROPN
ejpam-6113	81	26	babu	babu	PROPN
ejpam-6113	81	27	,	,	PUNCT
ejpam-6113	81	28	k.	k.	PROPN
ejpam-6113	81	29	n.	n.	PROPN
ejpam-6113	81	30	k.	k.	PROPN
ejpam-6113	82	1	rao	rao	PROPN
ejpam-6113	82	2	/	/	SYM
ejpam-6113	82	3	eur	eur	PROPN
ejpam-6113	82	4	.	.	PUNCT
ejpam-6113	83	1	j.	j.	PROPN
ejpam-6113	83	2	pure	pure	PROPN
ejpam-6113	83	3	appl	appl	PROPN
ejpam-6113	83	4	.	.	PROPN
ejpam-6113	83	5	math	math	PROPN
ejpam-6113	83	6	,	,	PUNCT
ejpam-6113	83	7	18	18	NUM
ejpam-6113	83	8	(	(	PUNCT
ejpam-6113	83	9	3	3	NUM
ejpam-6113	83	10	)	)	PUNCT
ejpam-6113	83	11	(	(	PUNCT
ejpam-6113	83	12	2025	2025	NUM
ejpam-6113	83	13	)	)	PUNCT
ejpam-6113	83	14	,	,	PUNCT
ejpam-6113	83	15	6113	6113	NUM
ejpam-6113	83	16	4	4	NUM
ejpam-6113	83	17	of	of	ADP
ejpam-6113	83	18	14	14	NUM
ejpam-6113	83	19	which	which	PRON
ejpam-6113	83	20	implies	imply	VERB
ejpam-6113	83	21	that	that	SCONJ
ejpam-6113	83	22	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	83	23	,	,	PUNCT
ejpam-6113	83	24	a2n+2	a2n+2	PRON
ejpam-6113	83	25	)	)	PUNCT
ejpam-6113	83	26	≤	≤	NUM
ejpam-6113	83	27	λ	λ	NOUN
ejpam-6113	83	28	1	1	NUM
ejpam-6113	83	29	β+γ	β+γ	PUNCT
ejpam-6113	83	30	d(a2n	d(a2n	ADJ
ejpam-6113	83	31	,	,	PUNCT
ejpam-6113	83	32	a2n+1	a2n+1	NOUN
ejpam-6113	83	33	)	)	PUNCT
ejpam-6113	83	34	<	<	X
ejpam-6113	83	35	d(a2n	d(a2n	PROPN
ejpam-6113	83	36	,	,	PUNCT
ejpam-6113	83	37	a2n+1	a2n+1	NOUN
ejpam-6113	83	38	)	)	PUNCT
ejpam-6113	83	39	,	,	PUNCT
ejpam-6113	83	40	which	which	PRON
ejpam-6113	83	41	is	be	AUX
ejpam-6113	83	42	a	a	DET
ejpam-6113	83	43	contradiction	contradiction	NOUN
ejpam-6113	83	44	.	.	PUNCT
ejpam-6113	84	1	thus	thus	ADV
ejpam-6113	84	2	,	,	PUNCT
ejpam-6113	84	3	we	we	PRON
ejpam-6113	84	4	have	have	VERB
ejpam-6113	84	5	d(a2n+1	d(a2n+1	NUM
ejpam-6113	84	6	,	,	PUNCT
ejpam-6113	84	7	a2n+2	a2n+2	PRON
ejpam-6113	84	8	)	)	PUNCT
ejpam-6113	84	9	≤	≤	NUM
ejpam-6113	84	10	d(a2n	d(a2n	ADJ
ejpam-6113	84	11	,	,	PUNCT
ejpam-6113	84	12	a2n+1	a2n+1	NOUN
ejpam-6113	84	13	)	)	PUNCT
ejpam-6113	84	14	.	.	PUNCT
ejpam-6113	85	1	from	from	ADP
ejpam-6113	85	2	(	(	PUNCT
ejpam-6113	85	3	2.2	2.2	NUM
ejpam-6113	85	4	)	)	PUNCT
ejpam-6113	85	5	,	,	PUNCT
ejpam-6113	85	6	we	we	PRON
ejpam-6113	85	7	have	have	VERB
ejpam-6113	85	8	[	[	X
ejpam-6113	85	9	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	85	10	,	,	PUNCT
ejpam-6113	85	11	a2n+2	a2n+2	PRON
ejpam-6113	85	12	)	)	PUNCT
ejpam-6113	85	13	]	]	PUNCT
ejpam-6113	86	1	1−α	1−α	NUM
ejpam-6113	86	2	≤	≤	NUM
ejpam-6113	86	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	86	4	,	,	PUNCT
ejpam-6113	86	5	a2n+1	a2n+1	PROPN
ejpam-6113	86	6	)	)	PUNCT
ejpam-6113	86	7	]	]	PUNCT
ejpam-6113	86	8	β+γ	β+γ	PUNCT
ejpam-6113	87	1	[	[	X
ejpam-6113	87	2	d(a2n	d(a2n	ADJ
ejpam-6113	87	3	,	,	PUNCT
ejpam-6113	87	4	a2n+1	a2n+1	NOUN
ejpam-6113	87	5	)	)	PUNCT
ejpam-6113	87	6	]	]	PUNCT
ejpam-6113	87	7	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	87	8	=	=	SYM
ejpam-6113	87	9	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	87	10	,	,	PUNCT
ejpam-6113	87	11	a2n+1	a2n+1	PROPN
ejpam-6113	87	12	)	)	PUNCT
ejpam-6113	87	13	]	]	PUNCT
ejpam-6113	87	14	1−α	1−α	NUM
ejpam-6113	87	15	which	which	PRON
ejpam-6113	87	16	implies	imply	VERB
ejpam-6113	87	17	that	that	SCONJ
ejpam-6113	87	18	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	87	19	,	,	PUNCT
ejpam-6113	87	20	a2n+2	a2n+2	PRON
ejpam-6113	87	21	)	)	PUNCT
ejpam-6113	87	22	≤	≤	NUM
ejpam-6113	87	23	λ	λ	PROPN
ejpam-6113	87	24	1	1	NUM
ejpam-6113	87	25	1−αd(a2n	1−αd(a2n	NUM
ejpam-6113	87	26	,	,	PUNCT
ejpam-6113	87	27	a2n+1	a2n+1	NOUN
ejpam-6113	87	28	)	)	PUNCT
ejpam-6113	87	29	=	=	SYM
ejpam-6113	87	30	κd(a2n	κd(a2n	PROPN
ejpam-6113	87	31	,	,	PUNCT
ejpam-6113	87	32	a2n+1	a2n+1	NOUN
ejpam-6113	87	33	)	)	PUNCT
ejpam-6113	87	34	...	...	PUNCT
ejpam-6113	88	1	=	=	SYM
ejpam-6113	88	2	κ2n+1d(a0	κ2n+1d(a0	NOUN
ejpam-6113	88	3	,	,	PUNCT
ejpam-6113	88	4	a1	a1	NOUN
ejpam-6113	88	5	)	)	PUNCT
ejpam-6113	88	6	.	.	PUNCT
ejpam-6113	89	1	(	(	PUNCT
ejpam-6113	89	2	2.3	2.3	NUM
ejpam-6113	89	3	)	)	PUNCT
ejpam-6113	89	4	therefore	therefore	ADV
ejpam-6113	89	5	,	,	PUNCT
ejpam-6113	89	6	d(a2n+1	d(a2n+1	PROPN
ejpam-6113	89	7	,	,	PUNCT
ejpam-6113	89	8	a2n+2	a2n+2	PRON
ejpam-6113	89	9	)	)	PUNCT
ejpam-6113	89	10	≤	≤	PROPN
ejpam-6113	89	11	κ2n+1d(a0	κ2n+1d(a0	PROPN
ejpam-6113	89	12	,	,	PUNCT
ejpam-6113	89	13	a1	a1	NOUN
ejpam-6113	89	14	)	)	PUNCT
ejpam-6113	89	15	.	.	PUNCT
ejpam-6113	90	1	now	now	ADV
ejpam-6113	90	2	,	,	PUNCT
ejpam-6113	90	3	take	take	VERB
ejpam-6113	90	4	a	a	DET
ejpam-6113	90	5	=	=	PUNCT
ejpam-6113	90	6	a2n	a2n	PROPN
ejpam-6113	90	7	and	and	CCONJ
ejpam-6113	90	8	b	b	X
ejpam-6113	90	9	=	=	X
ejpam-6113	90	10	a2n−1	a2n−1	PROPN
ejpam-6113	90	11	in	in	ADP
ejpam-6113	90	12	(	(	PUNCT
ejpam-6113	90	13	2.1	2.1	NUM
ejpam-6113	90	14	)	)	PUNCT
ejpam-6113	90	15	,	,	PUNCT
ejpam-6113	90	16	we	we	PRON
ejpam-6113	90	17	get	get	VERB
ejpam-6113	90	18	d(a2n+1	d(a2n+1	ADJ
ejpam-6113	90	19	,	,	PUNCT
ejpam-6113	90	20	a2n	a2n	ADV
ejpam-6113	90	21	)	)	PUNCT
ejpam-6113	90	22	=	=	SYM
ejpam-6113	90	23	d(ta2n	d(ta2n	NOUN
ejpam-6113	90	24	,	,	PUNCT
ejpam-6113	90	25	sa2n−1	sa2n−1	NUM
ejpam-6113	90	26	)	)	PUNCT
ejpam-6113	90	27	≤	≤	NUM
ejpam-6113	90	28	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	90	29	,	,	PUNCT
ejpam-6113	90	30	a2n−1	a2n−1	ADJ
ejpam-6113	90	31	)	)	PUNCT
ejpam-6113	90	32	β][d(ta2n	β][d(ta2n	NOUN
ejpam-6113	90	33	,	,	PUNCT
ejpam-6113	90	34	a2n	a2n	ADV
ejpam-6113	90	35	)	)	PUNCT
ejpam-6113	90	36	]	]	PUNCT
ejpam-6113	91	1	γ	γ	X
ejpam-6113	91	2	[	[	X
ejpam-6113	91	3	d(sa2n−1	d(sa2n−1	PROPN
ejpam-6113	91	4	,	,	PUNCT
ejpam-6113	91	5	a2n−1	a2n−1	PROPN
ejpam-6113	91	6	)	)	PUNCT
ejpam-6113	91	7	]	]	PUNCT
ejpam-6113	92	1	α	α	PROPN
ejpam-6113	92	2	[	[	PUNCT
ejpam-6113	92	3	12sd(ta2n	12sd(ta2n	X
ejpam-6113	92	4	,	,	PUNCT
ejpam-6113	92	5	a2n−1	a2n−1	ADJ
ejpam-6113	92	6	)	)	PUNCT
ejpam-6113	92	7	+	+	X
ejpam-6113	92	8	d(a2n	d(a2n	ADJ
ejpam-6113	92	9	,	,	PUNCT
ejpam-6113	92	10	sa2n−1	sa2n−1	NUM
ejpam-6113	92	11	)	)	PUNCT
ejpam-6113	92	12	]	]	PUNCT
ejpam-6113	93	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	93	2	=	=	SYM
ejpam-6113	93	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	93	4	,	,	PUNCT
ejpam-6113	93	5	a2n−1	a2n−1	ADJ
ejpam-6113	93	6	)	)	PUNCT
ejpam-6113	93	7	β][d(a2n+1	β][d(a2n+1	NOUN
ejpam-6113	93	8	,	,	PUNCT
ejpam-6113	93	9	a2n	a2n	NOUN
ejpam-6113	93	10	)	)	PUNCT
ejpam-6113	93	11	]	]	PUNCT
ejpam-6113	94	1	γ	γ	X
ejpam-6113	94	2	[	[	X
ejpam-6113	94	3	d(a2n	d(a2n	ADJ
ejpam-6113	94	4	,	,	PUNCT
ejpam-6113	94	5	a2n−1	a2n−1	ADJ
ejpam-6113	94	6	)	)	PUNCT
ejpam-6113	94	7	]	]	PUNCT
ejpam-6113	95	1	α	α	PROPN
ejpam-6113	95	2	[	[	PUNCT
ejpam-6113	95	3	12sd(a2n+1	12sd(a2n+1	NUM
ejpam-6113	95	4	,	,	PUNCT
ejpam-6113	95	5	a2n−1	a2n−1	ADJ
ejpam-6113	95	6	)	)	PUNCT
ejpam-6113	95	7	+	+	X
ejpam-6113	95	8	d(a2n	d(a2n	ADJ
ejpam-6113	95	9	,	,	PUNCT
ejpam-6113	95	10	a2n	a2n	NOUN
ejpam-6113	95	11	)	)	PUNCT
ejpam-6113	95	12	]	]	PUNCT
ejpam-6113	96	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	96	2	then	then	ADV
ejpam-6113	97	1	[	[	X
ejpam-6113	97	2	d(a2n+1	d(a2n+1	ADV
ejpam-6113	97	3	,	,	PUNCT
ejpam-6113	97	4	a2n	a2n	NOUN
ejpam-6113	97	5	)	)	PUNCT
ejpam-6113	97	6	]	]	PUNCT
ejpam-6113	98	1	1−γ	1−γ	NUM
ejpam-6113	98	2	≤	≤	NUM
ejpam-6113	98	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	98	4	,	,	PUNCT
ejpam-6113	98	5	a2n−1	a2n−1	PROPN
ejpam-6113	98	6	)	)	PUNCT
ejpam-6113	98	7	]	]	PUNCT
ejpam-6113	99	1	β+α	β+α	PUNCT
ejpam-6113	99	2	[	[	PUNCT
ejpam-6113	99	3	12sd(a2n+1	12sd(a2n+1	NUM
ejpam-6113	99	4	,	,	PUNCT
ejpam-6113	99	5	a2n−1	a2n−1	PROPN
ejpam-6113	99	6	)	)	PUNCT
ejpam-6113	99	7	]	]	PUNCT
ejpam-6113	100	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	100	2	≤	≤	PROPN
ejpam-6113	100	3	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	100	4	,	,	PUNCT
ejpam-6113	100	5	a2n−1	a2n−1	PROPN
ejpam-6113	100	6	)	)	PUNCT
ejpam-6113	100	7	]	]	PUNCT
ejpam-6113	100	8	β+α[12(d(a2n−1	β+α[12(d(a2n−1	PROPN
ejpam-6113	100	9	,	,	PUNCT
ejpam-6113	100	10	a2n	a2n	ADV
ejpam-6113	100	11	)	)	PUNCT
ejpam-6113	100	12	+	+	CCONJ
ejpam-6113	100	13	d(a2n	d(a2n	ADJ
ejpam-6113	100	14	,	,	PUNCT
ejpam-6113	100	15	a2n+1	a2n+1	NOUN
ejpam-6113	100	16	)	)	PUNCT
ejpam-6113	100	17	)	)	PUNCT
ejpam-6113	100	18	]	]	PUNCT
ejpam-6113	101	1	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	101	2	(	(	PUNCT
ejpam-6113	101	3	2.4	2.4	NUM
ejpam-6113	101	4	)	)	PUNCT
ejpam-6113	101	5	suppose	suppose	VERB
ejpam-6113	101	6	that	that	SCONJ
ejpam-6113	101	7	d(a2n−1	d(a2n−1	PROPN
ejpam-6113	101	8	,	,	PUNCT
ejpam-6113	101	9	a2n	a2n	ADV
ejpam-6113	101	10	)	)	PUNCT
ejpam-6113	101	11	<	<	X
ejpam-6113	101	12	d(a2n	d(a2n	PROPN
ejpam-6113	101	13	,	,	PUNCT
ejpam-6113	101	14	a2n+1	a2n+1	NOUN
ejpam-6113	101	15	)	)	PUNCT
ejpam-6113	101	16	.	.	PUNCT
ejpam-6113	102	1	thus	thus	ADV
ejpam-6113	102	2	,	,	PUNCT
ejpam-6113	102	3	the	the	DET
ejpam-6113	102	4	inequality	inequality	NOUN
ejpam-6113	102	5	(	(	PUNCT
ejpam-6113	102	6	2.4	2.4	NUM
ejpam-6113	102	7	)	)	PUNCT
ejpam-6113	102	8	produces	produce	VERB
ejpam-6113	102	9	that	that	SCONJ
ejpam-6113	103	1	[	[	X
ejpam-6113	103	2	d(a2n+1	d(a2n+1	ADV
ejpam-6113	103	3	,	,	PUNCT
ejpam-6113	103	4	a2n	a2n	NOUN
ejpam-6113	103	5	)	)	PUNCT
ejpam-6113	103	6	]	]	PUNCT
ejpam-6113	103	7	1−γ	1−γ	NUM
ejpam-6113	103	8	≤	≤	NUM
ejpam-6113	103	9	λ[d(a2n	λ[d(a2n	PROPN
ejpam-6113	103	10	,	,	PUNCT
ejpam-6113	103	11	a2n−1	a2n−1	PROPN
ejpam-6113	103	12	)	)	PUNCT
ejpam-6113	103	13	]	]	PUNCT
ejpam-6113	104	1	β+α[d(a2n+1	β+α[d(a2n+1	NOUN
ejpam-6113	104	2	,	,	PUNCT
ejpam-6113	104	3	a2n	a2n	ADV
ejpam-6113	104	4	)	)	PUNCT
ejpam-6113	104	5	]	]	PUNCT
ejpam-6113	104	6	1−α−β−γ	1−α−β−γ	PROPN
ejpam-6113	104	7	implies	imply	VERB
ejpam-6113	104	8	that	that	SCONJ
ejpam-6113	104	9	[	[	X
ejpam-6113	104	10	d(a2n	d(a2n	ADJ
ejpam-6113	104	11	,	,	PUNCT
ejpam-6113	104	12	a2n+1	a2n+1	NOUN
ejpam-6113	104	13	)	)	PUNCT
ejpam-6113	104	14	]	]	PUNCT
ejpam-6113	105	1	β+α	β+α	PUNCT
ejpam-6113	105	2	≤	≤	X
ejpam-6113	105	3	λ[d(a2n−1	λ[d(a2n−1	PROPN
ejpam-6113	105	4	,	,	PUNCT
ejpam-6113	105	5	a2n	a2n	NOUN
ejpam-6113	105	6	)	)	PUNCT
ejpam-6113	105	7	]	]	PUNCT
ejpam-6113	105	8	β+α	β+α	NUM
ejpam-6113	105	9	which	which	PRON
ejpam-6113	105	10	implies	imply	VERB
ejpam-6113	105	11	that	that	SCONJ
ejpam-6113	105	12	d(a2n	d(a2n	ADJ
ejpam-6113	105	13	,	,	PUNCT
ejpam-6113	105	14	a2n+1	a2n+1	NOUN
ejpam-6113	105	15	)	)	PUNCT
ejpam-6113	105	16	≤	≤	NUM
ejpam-6113	105	17	λ	λ	NOUN
ejpam-6113	105	18	1	1	NUM
ejpam-6113	105	19	β+αd(a2n−1	β+αd(a2n−1	ADJ
ejpam-6113	105	20	,	,	PUNCT
ejpam-6113	105	21	a2n	a2n	ADV
ejpam-6113	105	22	)	)	PUNCT
ejpam-6113	105	23	<	<	X
ejpam-6113	105	24	d(a2n−1	d(a2n−1	PROPN
ejpam-6113	105	25	,	,	PUNCT
ejpam-6113	105	26	a2n	a2n	NOUN
ejpam-6113	105	27	)	)	PUNCT
ejpam-6113	105	28	,	,	PUNCT
ejpam-6113	105	29	which	which	PRON
ejpam-6113	105	30	is	be	AUX
ejpam-6113	105	31	a	a	DET
ejpam-6113	105	32	contradiction	contradiction	NOUN
ejpam-6113	105	33	.	.	PUNCT
ejpam-6113	106	1	thus	thus	ADV
ejpam-6113	106	2	,	,	PUNCT
ejpam-6113	106	3	we	we	PRON
ejpam-6113	106	4	have	have	VERB
ejpam-6113	106	5	d(a2n	d(a2n	ADJ
ejpam-6113	106	6	,	,	PUNCT
ejpam-6113	106	7	a2n+1	a2n+1	NOUN
ejpam-6113	106	8	)	)	PUNCT
ejpam-6113	106	9	≤	≤	NOUN
ejpam-6113	106	10	d(a2n−1	d(a2n−1	PROPN
ejpam-6113	106	11	,	,	PUNCT
ejpam-6113	106	12	a2n	a2n	NOUN
ejpam-6113	106	13	)	)	PUNCT
ejpam-6113	106	14	.	.	PUNCT
ejpam-6113	107	1	from	from	ADP
ejpam-6113	107	2	(	(	PUNCT
ejpam-6113	107	3	2.4	2.4	NUM
ejpam-6113	107	4	)	)	PUNCT
ejpam-6113	107	5	,	,	PUNCT
ejpam-6113	107	6	we	we	PRON
ejpam-6113	107	7	have	have	VERB
ejpam-6113	107	8	[	[	X
ejpam-6113	107	9	d(a2n	d(a2n	ADJ
ejpam-6113	107	10	,	,	PUNCT
ejpam-6113	107	11	a2n+1	a2n+1	NOUN
ejpam-6113	107	12	)	)	PUNCT
ejpam-6113	107	13	]	]	PUNCT
ejpam-6113	108	1	1−γ	1−γ	X
ejpam-6113	108	2	≤	≤	X
ejpam-6113	108	3	λ[d(a2n−1	λ[d(a2n−1	PROPN
ejpam-6113	108	4	,	,	PUNCT
ejpam-6113	108	5	a2n	a2n	NOUN
ejpam-6113	108	6	)	)	PUNCT
ejpam-6113	108	7	]	]	PUNCT
ejpam-6113	109	1	β+α[d(a2n−1	β+α[d(a2n−1	PUNCT
ejpam-6113	109	2	,	,	PUNCT
ejpam-6113	109	3	a2n	a2n	NOUN
ejpam-6113	109	4	)	)	PUNCT
ejpam-6113	109	5	]	]	PUNCT
ejpam-6113	110	1	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	110	2	=	=	SYM
ejpam-6113	110	3	λ[d(a2n−1	λ[d(a2n−1	PROPN
ejpam-6113	110	4	,	,	PUNCT
ejpam-6113	110	5	a2n	a2n	NOUN
ejpam-6113	110	6	)	)	PUNCT
ejpam-6113	110	7	]	]	PUNCT
ejpam-6113	110	8	1−γ	1−γ	PROPN
ejpam-6113	110	9	d.	d.	PROPN
ejpam-6113	110	10	r.	r.	PROPN
ejpam-6113	110	11	babu	babu	PROPN
ejpam-6113	110	12	,	,	PUNCT
ejpam-6113	110	13	k.	k.	PROPN
ejpam-6113	110	14	n.	n.	PROPN
ejpam-6113	110	15	k.	k.	PROPN
ejpam-6113	111	1	rao	rao	PROPN
ejpam-6113	111	2	/	/	SYM
ejpam-6113	111	3	eur	eur	PROPN
ejpam-6113	111	4	.	.	PUNCT
ejpam-6113	112	1	j.	j.	PROPN
ejpam-6113	112	2	pure	pure	PROPN
ejpam-6113	112	3	appl	appl	PROPN
ejpam-6113	112	4	.	.	PROPN
ejpam-6113	112	5	math	math	PROPN
ejpam-6113	112	6	,	,	PUNCT
ejpam-6113	112	7	18	18	NUM
ejpam-6113	112	8	(	(	PUNCT
ejpam-6113	112	9	3	3	NUM
ejpam-6113	112	10	)	)	PUNCT
ejpam-6113	112	11	(	(	PUNCT
ejpam-6113	112	12	2025	2025	NUM
ejpam-6113	112	13	)	)	PUNCT
ejpam-6113	112	14	,	,	PUNCT
ejpam-6113	112	15	6113	6113	NUM
ejpam-6113	112	16	5	5	NUM
ejpam-6113	112	17	of	of	ADP
ejpam-6113	112	18	14	14	NUM
ejpam-6113	112	19	which	which	PRON
ejpam-6113	112	20	implies	imply	VERB
ejpam-6113	112	21	that	that	SCONJ
ejpam-6113	112	22	d(a2n	d(a2n	ADJ
ejpam-6113	112	23	,	,	PUNCT
ejpam-6113	112	24	a2n+1	a2n+1	NOUN
ejpam-6113	112	25	)	)	PUNCT
ejpam-6113	112	26	≤	≤	NUM
ejpam-6113	112	27	λ	λ	NOUN
ejpam-6113	112	28	1	1	NUM
ejpam-6113	112	29	1−γ	1−γ	NUM
ejpam-6113	112	30	d(a2n−1	d(a2n−1	PROPN
ejpam-6113	112	31	,	,	PUNCT
ejpam-6113	112	32	a2n	a2n	ADV
ejpam-6113	112	33	)	)	PUNCT
ejpam-6113	112	34	=	=	SYM
ejpam-6113	112	35	ιd(a2n−1	ιd(a2n−1	VERB
ejpam-6113	112	36	,	,	PUNCT
ejpam-6113	112	37	a2n	a2n	ADV
ejpam-6113	112	38	)	)	PUNCT
ejpam-6113	112	39	...	...	PUNCT
ejpam-6113	113	1	=	=	SYM
ejpam-6113	113	2	ι2nd(a0	ι2nd(a0	PROPN
ejpam-6113	113	3	,	,	PUNCT
ejpam-6113	113	4	a1	a1	NOUN
ejpam-6113	113	5	)	)	PUNCT
ejpam-6113	113	6	.	.	PUNCT
ejpam-6113	114	1	(	(	PUNCT
ejpam-6113	114	2	2.5	2.5	NUM
ejpam-6113	114	3	)	)	PUNCT
ejpam-6113	114	4	therefore	therefore	ADV
ejpam-6113	114	5	,	,	PUNCT
ejpam-6113	114	6	d(a2n	d(a2n	ADJ
ejpam-6113	114	7	,	,	PUNCT
ejpam-6113	114	8	a2n+1	a2n+1	NOUN
ejpam-6113	114	9	)	)	PUNCT
ejpam-6113	114	10	≤	≤	NOUN
ejpam-6113	114	11	ι2nd(a0	ι2nd(a0	NUM
ejpam-6113	114	12	,	,	PUNCT
ejpam-6113	114	13	a1	a1	PROPN
ejpam-6113	114	14	)	)	PUNCT
ejpam-6113	114	15	.	.	PUNCT
ejpam-6113	115	1	it	it	PRON
ejpam-6113	115	2	follows	follow	VERB
ejpam-6113	115	3	from	from	ADP
ejpam-6113	115	4	(	(	PUNCT
ejpam-6113	115	5	2.3	2.3	NUM
ejpam-6113	115	6	)	)	PUNCT
ejpam-6113	115	7	and	and	CCONJ
ejpam-6113	115	8	(	(	PUNCT
ejpam-6113	115	9	2.5	2.5	NUM
ejpam-6113	115	10	)	)	PUNCT
ejpam-6113	115	11	,	,	PUNCT
ejpam-6113	115	12	we	we	PRON
ejpam-6113	115	13	deduce	deduce	VERB
ejpam-6113	115	14	that	that	SCONJ
ejpam-6113	115	15	d(an	d(an	NOUN
ejpam-6113	115	16	,	,	PUNCT
ejpam-6113	115	17	an+1	an+1	NOUN
ejpam-6113	115	18	)	)	PUNCT
ejpam-6113	115	19	≤	≤	NOUN
ejpam-6113	116	1	knd(a0	knd(a0	PROPN
ejpam-6113	116	2	,	,	PUNCT
ejpam-6113	116	3	a1	a1	PROPN
ejpam-6113	116	4	)	)	PUNCT
ejpam-6113	116	5	for	for	ADP
ejpam-6113	116	6	all	all	DET
ejpam-6113	116	7	n	n	PRON
ejpam-6113	116	8	∈	∈	NOUN
ejpam-6113	116	9	n	n	NOUN
ejpam-6113	116	10	where	where	SCONJ
ejpam-6113	116	11	k	k	PROPN
ejpam-6113	116	12	=	=	SYM
ejpam-6113	116	13	min{κ	min{κ	PROPN
ejpam-6113	116	14	,	,	PUNCT
ejpam-6113	116	15	ι	ι	X
ejpam-6113	116	16	}	}	PUNCT
ejpam-6113	116	17	<	<	X
ejpam-6113	116	18	1	1	NUM
ejpam-6113	116	19	.	.	PUNCT
ejpam-6113	116	20	for	for	ADP
ejpam-6113	116	21	m	m	PROPN
ejpam-6113	116	22	>	>	X
ejpam-6113	116	23	0	0	NUM
ejpam-6113	116	24	.	.	PUNCT
ejpam-6113	117	1	by	by	ADP
ejpam-6113	117	2	employing	employ	VERB
ejpam-6113	117	3	the	the	DET
ejpam-6113	117	4	b	b	NOUN
ejpam-6113	117	5	-	-	PUNCT
ejpam-6113	117	6	triangular	triangular	NOUN
ejpam-6113	117	7	inequality	inequality	NOUN
ejpam-6113	117	8	,	,	PUNCT
ejpam-6113	117	9	we	we	PRON
ejpam-6113	117	10	arrive	arrive	VERB
ejpam-6113	117	11	at	at	ADP
ejpam-6113	117	12	d(an	d(an	PROPN
ejpam-6113	117	13	,	,	PUNCT
ejpam-6113	117	14	an+m	an+m	NOUN
ejpam-6113	117	15	)	)	PUNCT
ejpam-6113	117	16	≤	≤	PROPN
ejpam-6113	117	17	sd(an	sd(an	PROPN
ejpam-6113	117	18	,	,	PUNCT
ejpam-6113	117	19	an+1	an+1	NOUN
ejpam-6113	117	20	)	)	PUNCT
ejpam-6113	118	1	+	+	CCONJ
ejpam-6113	118	2	s2d(an+1	s2d(an+1	NOUN
ejpam-6113	118	3	,	,	PUNCT
ejpam-6113	118	4	an+2	an+2	ADV
ejpam-6113	118	5	)	)	PUNCT
ejpam-6113	119	1	+	+	CCONJ
ejpam-6113	119	2	.	.	PUNCT
ejpam-6113	119	3	.	.	PUNCT
ejpam-6113	120	1	.+	.+	NOUN
ejpam-6113	120	2	smd(an+m−1	smd(an+m−1	PROPN
ejpam-6113	120	3	,	,	PUNCT
ejpam-6113	120	4	an+m	an+m	PROPN
ejpam-6113	120	5	)	)	PUNCT
ejpam-6113	120	6	≤	≤	NOUN
ejpam-6113	120	7	sknd(a0	sknd(a0	NOUN
ejpam-6113	120	8	,	,	PUNCT
ejpam-6113	120	9	a1	a1	NOUN
ejpam-6113	120	10	)	)	PUNCT
ejpam-6113	120	11	+	+	CCONJ
ejpam-6113	120	12	s2kn+1d(a0	s2kn+1d(a0	ADJ
ejpam-6113	120	13	,	,	PUNCT
ejpam-6113	120	14	a1	a1	NOUN
ejpam-6113	120	15	)	)	PUNCT
ejpam-6113	120	16	+	+	CCONJ
ejpam-6113	120	17	.	.	PUNCT
ejpam-6113	120	18	.	.	PUNCT
ejpam-6113	121	1	.+	.+	NOUN
ejpam-6113	121	2	smkn+m−1d(a0	smkn+m−1d(a0	X
ejpam-6113	121	3	,	,	PUNCT
ejpam-6113	121	4	a1	a1	NOUN
ejpam-6113	121	5	)	)	PUNCT
ejpam-6113	121	6	=	=	PUNCT
ejpam-6113	121	7	skn[1	skn[1	PROPN
ejpam-6113	121	8	+	+	CCONJ
ejpam-6113	121	9	sk	sk	X
ejpam-6113	121	10	+	+	X
ejpam-6113	121	11	s2k2	s2k2	X
ejpam-6113	121	12	+	+	PUNCT
ejpam-6113	121	13	.	.	PUNCT
ejpam-6113	121	14	.	.	PUNCT
ejpam-6113	122	1	.+	.+	NOUN
ejpam-6113	122	2	sm−1km−1]d(a0	sm−1km−1]d(a0	NOUN
ejpam-6113	122	3	,	,	PUNCT
ejpam-6113	122	4	a1	a1	NOUN
ejpam-6113	122	5	)	)	PUNCT
ejpam-6113	122	6	≤	≤	NOUN
ejpam-6113	122	7	skn[1	skn[1	PROPN
ejpam-6113	122	8	+	+	CCONJ
ejpam-6113	122	9	sk	sk	X
ejpam-6113	122	10	+	+	CCONJ
ejpam-6113	122	11	(	(	PUNCT
ejpam-6113	122	12	sk)2	sk)2	VERB
ejpam-6113	122	13	+	+	PUNCT
ejpam-6113	122	14	.	.	PUNCT
ejpam-6113	122	15	.	.	PUNCT
ejpam-6113	123	1	.+	.+	NOUN
ejpam-6113	123	2	(	(	PUNCT
ejpam-6113	123	3	sk)m−1	sk)m−1	X
ejpam-6113	123	4	+	+	X
ejpam-6113	123	5	.	.	PUNCT
ejpam-6113	123	6	.	.	PUNCT
ejpam-6113	124	1	.]d(a0	.]d(a0	PROPN
ejpam-6113	124	2	,	,	PUNCT
ejpam-6113	124	3	a1	a1	PROPN
ejpam-6113	124	4	)	)	PUNCT
ejpam-6113	124	5	=	=	SYM
ejpam-6113	124	6	skn	skn	PROPN
ejpam-6113	124	7	1−skd(a0	1−skd(a0	NUM
ejpam-6113	124	8	,	,	PUNCT
ejpam-6113	124	9	a1	a1	NOUN
ejpam-6113	124	10	)	)	PUNCT
ejpam-6113	124	11	→	→	SYM
ejpam-6113	124	12	0	0	NUM
ejpam-6113	124	13	as	as	ADP
ejpam-6113	124	14	n	n	PROPN
ejpam-6113	124	15	→	→	SYM
ejpam-6113	124	16	∞.	∞.	PROPN
ejpam-6113	124	17	therefore	therefore	ADV
ejpam-6113	124	18	,	,	PUNCT
ejpam-6113	124	19	{	{	PUNCT
ejpam-6113	124	20	an	an	PRON
ejpam-6113	124	21	}	}	PUNCT
ejpam-6113	124	22	is	be	AUX
ejpam-6113	124	23	a	a	DET
ejpam-6113	124	24	b	b	PROPN
ejpam-6113	124	25	-	-	PUNCT
ejpam-6113	124	26	cauchy	cauchy	ADJ
ejpam-6113	124	27	sequence	sequence	NOUN
ejpam-6113	124	28	in	in	ADP
ejpam-6113	124	29	(	(	PUNCT
ejpam-6113	124	30	e	e	NOUN
ejpam-6113	124	31	,	,	PUNCT
ejpam-6113	124	32	d	d	NOUN
ejpam-6113	124	33	,	,	PUNCT
ejpam-6113	124	34	s	s	PART
ejpam-6113	124	35	)	)	PUNCT
ejpam-6113	124	36	and	and	CCONJ
ejpam-6113	124	37	by	by	ADP
ejpam-6113	124	38	completeness	completeness	NOUN
ejpam-6113	124	39	,	,	PUNCT
ejpam-6113	124	40	there	there	PRON
ejpam-6113	124	41	exists	exist	VERB
ejpam-6113	124	42	a	a	DET
ejpam-6113	124	43	′	′	NUM
ejpam-6113	124	44	such	such	ADJ
ejpam-6113	124	45	that	that	SCONJ
ejpam-6113	124	46	lim	lim	PROPN
ejpam-6113	124	47	n→∞	n→∞	PRON
ejpam-6113	124	48	an	an	DET
ejpam-6113	124	49	=	=	NOUN
ejpam-6113	124	50	a	a	DET
ejpam-6113	124	51	′	′	NOUN
ejpam-6113	124	52	.	.	PUNCT
ejpam-6113	125	1	hence	hence	ADV
ejpam-6113	125	2	,	,	PUNCT
ejpam-6113	125	3	a	a	DET
ejpam-6113	125	4	′	′	NOUN
ejpam-6113	125	5	=	=	PUNCT
ejpam-6113	125	6	lim	lim	PROPN
ejpam-6113	125	7	n→∞	n→∞	X
ejpam-6113	125	8	a2n+1	a2n+1	PROPN
ejpam-6113	125	9	=	=	SYM
ejpam-6113	125	10	lim	lim	PROPN
ejpam-6113	125	11	n→∞	n→∞	X
ejpam-6113	125	12	ta2n	ta2n	NUM
ejpam-6113	125	13	,	,	PUNCT
ejpam-6113	125	14	and	and	CCONJ
ejpam-6113	125	15	a	a	DET
ejpam-6113	125	16	′	′	NOUN
ejpam-6113	125	17	=	=	SYM
ejpam-6113	125	18	lim	lim	PROPN
ejpam-6113	125	19	n→∞	n→∞	X
ejpam-6113	126	1	a2n+2	a2n+2	PUNCT
ejpam-6113	126	2	=	=	SYM
ejpam-6113	126	3	lim	lim	PROPN
ejpam-6113	126	4	n→∞	n→∞	NUM
ejpam-6113	126	5	sa2n+1	sa2n+1	VERB
ejpam-6113	126	6	so	so	SCONJ
ejpam-6113	126	7	that	that	SCONJ
ejpam-6113	126	8	a	a	DET
ejpam-6113	126	9	′	′	NOUN
ejpam-6113	126	10	=	=	PUNCT
ejpam-6113	126	11	lim	lim	PROPN
ejpam-6113	126	12	n→∞	n→∞	X
ejpam-6113	127	1	ta2n	ta2n	PROPN
ejpam-6113	127	2	=	=	SYM
ejpam-6113	127	3	lim	lim	PROPN
ejpam-6113	127	4	n→∞	n→∞	NUM
ejpam-6113	127	5	sa2n+1	sa2n+1	NOUN
ejpam-6113	127	6	.	.	PUNCT
ejpam-6113	128	1	we	we	PRON
ejpam-6113	128	2	assume	assume	VERB
ejpam-6113	128	3	that	that	SCONJ
ejpam-6113	128	4	t	t	PROPN
ejpam-6113	128	5	is	be	AUX
ejpam-6113	128	6	b	b	NOUN
ejpam-6113	128	7	-	-	PUNCT
ejpam-6113	128	8	continuous	continuous	ADJ
ejpam-6113	128	9	.	.	PUNCT
ejpam-6113	129	1	since	since	SCONJ
ejpam-6113	129	2	a2n	a2n	PROPN
ejpam-6113	129	3	→	→	SYM
ejpam-6113	129	4	a	a	DET
ejpam-6113	129	5	′	′	NOUN
ejpam-6113	129	6	as	as	ADP
ejpam-6113	129	7	n	n	PROPN
ejpam-6113	129	8	→	→	SYM
ejpam-6113	129	9	∞	∞	PROPN
ejpam-6113	129	10	,	,	PUNCT
ejpam-6113	129	11	we	we	PRON
ejpam-6113	129	12	have	have	VERB
ejpam-6113	129	13	ta2n	ta2n	NUM
ejpam-6113	129	14	→	→	SYM
ejpam-6113	129	15	ta	ta	PART
ejpam-6113	129	16	′	′	NOUN
ejpam-6113	129	17	as	as	ADP
ejpam-6113	129	18	n	n	PROPN
ejpam-6113	129	19	→	→	SYM
ejpam-6113	129	20	∞.	∞.	PROPN
ejpam-6113	129	21	now	now	ADV
ejpam-6113	129	22	,	,	PUNCT
ejpam-6113	129	23	0	0	NUM
ejpam-6113	129	24	≤	≤	NUM
ejpam-6113	129	25	d(a	d(a	PROPN
ejpam-6113	129	26	′	′	NOUN
ejpam-6113	129	27	,	,	PUNCT
ejpam-6113	129	28	ta	ta	ADP
ejpam-6113	129	29	′	′	NUM
ejpam-6113	129	30	)	)	PUNCT
ejpam-6113	130	1	≤	≤	NOUN
ejpam-6113	131	1	s[d(a	s[d(a	PROPN
ejpam-6113	131	2	′	′	NOUN
ejpam-6113	131	3	,	,	PUNCT
ejpam-6113	131	4	ta2n	ta2n	NUM
ejpam-6113	131	5	)	)	PUNCT
ejpam-6113	131	6	+	+	NUM
ejpam-6113	131	7	d(ta2n	d(ta2n	NOUN
ejpam-6113	131	8	,	,	PUNCT
ejpam-6113	131	9	ta	ta	ADP
ejpam-6113	131	10	′	′	NUM
ejpam-6113	131	11	)	)	PUNCT
ejpam-6113	131	12	]	]	PUNCT
ejpam-6113	132	1	→	→	SYM
ejpam-6113	132	2	0	0	PUNCT
ejpam-6113	132	3	as	as	ADP
ejpam-6113	132	4	n	n	NOUN
ejpam-6113	132	5	→	→	SYM
ejpam-6113	132	6	∞.	∞.	PROPN
ejpam-6113	132	7	a	a	DET
ejpam-6113	132	8	′	′	NUM
ejpam-6113	132	9	is	be	AUX
ejpam-6113	132	10	a	a	DET
ejpam-6113	132	11	fixed	fix	VERB
ejpam-6113	132	12	point	point	NOUN
ejpam-6113	132	13	of	of	ADP
ejpam-6113	132	14	t	t	PROPN
ejpam-6113	132	15	as	as	ADP
ejpam-6113	132	16	a	a	DET
ejpam-6113	132	17	result	result	NOUN
ejpam-6113	132	18	.	.	PUNCT
ejpam-6113	133	1	according	accord	VERB
ejpam-6113	133	2	to	to	ADP
ejpam-6113	133	3	proposition	proposition	NOUN
ejpam-6113	133	4	1	1	NUM
ejpam-6113	133	5	,	,	PUNCT
ejpam-6113	133	6	a	a	DET
ejpam-6113	133	7	′	′	NOUN
ejpam-6113	133	8	is	be	AUX
ejpam-6113	133	9	a	a	DET
ejpam-6113	133	10	unique	unique	ADJ
ejpam-6113	133	11	common	common	ADJ
ejpam-6113	133	12	fixed	fix	VERB
ejpam-6113	133	13	point	point	NOUN
ejpam-6113	133	14	of	of	ADP
ejpam-6113	133	15	t	t	PROPN
ejpam-6113	133	16	and	and	CCONJ
ejpam-6113	133	17	s.	s.	PROPN
ejpam-6113	133	18	an	an	DET
ejpam-6113	133	19	example	example	NOUN
ejpam-6113	133	20	supporting	support	VERB
ejpam-6113	133	21	theorem	theorem	NOUN
ejpam-6113	133	22	4	4	NUM
ejpam-6113	133	23	is	be	AUX
ejpam-6113	133	24	shown	show	VERB
ejpam-6113	133	25	below	below	ADP
ejpam-6113	133	26	.	.	PUNCT
ejpam-6113	133	27	example	example	NOUN
ejpam-6113	134	1	1	1	NUM
ejpam-6113	134	2	.	.	PUNCT
ejpam-6113	134	3	let	let	VERB
ejpam-6113	134	4	e	e	NOUN
ejpam-6113	134	5	=	=	PUNCT
ejpam-6113	135	1	[	[	X
ejpam-6113	135	2	0	0	NUM
ejpam-6113	135	3	,	,	PUNCT
ejpam-6113	135	4	1	1	NUM
ejpam-6113	135	5	]	]	PUNCT
ejpam-6113	135	6	.	.	PUNCT
ejpam-6113	136	1	we	we	PRON
ejpam-6113	136	2	define	define	VERB
ejpam-6113	136	3	d	d	X
ejpam-6113	136	4	:	:	PUNCT
ejpam-6113	136	5	e	e	X
ejpam-6113	136	6	×	×	NOUN
ejpam-6113	136	7	e	e	X
ejpam-6113	136	8	→	→	PUNCT
ejpam-6113	136	9	r+	r+	NOUN
ejpam-6113	136	10	by	by	ADP
ejpam-6113	136	11	d(a	d(a	PROPN
ejpam-6113	136	12	,	,	PUNCT
ejpam-6113	136	13	b	b	NOUN
ejpam-6113	136	14	)	)	PUNCT
ejpam-6113	136	15	=	=	SYM
ejpam-6113	136	16			X
ejpam-6113	136	17	0	0	NUM
ejpam-6113	136	18	,	,	PUNCT
ejpam-6113	136	19	if	if	SCONJ
ejpam-6113	136	20	a	a	DET
ejpam-6113	136	21	=	=	SYM
ejpam-6113	136	22	b	b	NOUN
ejpam-6113	136	23	,	,	PUNCT
ejpam-6113	136	24	11	11	NUM
ejpam-6113	136	25	15	15	NUM
ejpam-6113	136	26	,	,	PUNCT
ejpam-6113	136	27	if	if	SCONJ
ejpam-6113	136	28	a	a	PRON
ejpam-6113	136	29	,	,	PUNCT
ejpam-6113	136	30	b	b	X
ejpam-6113	136	31	∈	∈	PROPN
ejpam-6113	137	1	[	[	X
ejpam-6113	137	2	0	0	NUM
ejpam-6113	137	3	,	,	PUNCT
ejpam-6113	137	4	23	23	NUM
ejpam-6113	137	5	]	]	PUNCT
ejpam-6113	137	6	,	,	PUNCT
ejpam-6113	137	7	23	23	NUM
ejpam-6113	137	8	25	25	NUM
ejpam-6113	137	9	+	+	CCONJ
ejpam-6113	137	10	a+b	a+b	NUM
ejpam-6113	137	11	26	26	NUM
ejpam-6113	137	12	,	,	PUNCT
ejpam-6113	137	13	if	if	SCONJ
ejpam-6113	137	14	a	a	PRON
ejpam-6113	137	15	,	,	PUNCT
ejpam-6113	137	16	b	b	X
ejpam-6113	137	17	∈	∈	PROPN
ejpam-6113	137	18	(	(	PUNCT
ejpam-6113	137	19	23	23	NUM
ejpam-6113	137	20	,	,	PUNCT
ejpam-6113	137	21	1	1	NUM
ejpam-6113	137	22	]	]	PUNCT
ejpam-6113	137	23	,	,	PUNCT
ejpam-6113	137	24	121	121	NUM
ejpam-6113	137	25	250	250	NUM
ejpam-6113	137	26	,	,	PUNCT
ejpam-6113	137	27	otherwise	otherwise	ADV
ejpam-6113	137	28	.	.	PUNCT
ejpam-6113	138	1	when	when	SCONJ
ejpam-6113	138	2	(	(	PUNCT
ejpam-6113	138	3	e	e	NOUN
ejpam-6113	138	4	,	,	PUNCT
ejpam-6113	138	5	d	d	PROPN
ejpam-6113	138	6	,	,	PUNCT
ejpam-6113	138	7	s	s	PART
ejpam-6113	138	8	)	)	PUNCT
ejpam-6113	138	9	has	have	VERB
ejpam-6113	138	10	the	the	DET
ejpam-6113	138	11	coefficient	coefficient	NOUN
ejpam-6113	138	12	s	s	X
ejpam-6113	138	13	=	=	NOUN
ejpam-6113	138	14	51	51	NUM
ejpam-6113	138	15	49	49	NUM
ejpam-6113	138	16	,	,	PUNCT
ejpam-6113	138	17	it	it	PRON
ejpam-6113	138	18	is	be	AUX
ejpam-6113	138	19	evident	evident	ADJ
ejpam-6113	138	20	that	that	SCONJ
ejpam-6113	138	21	it	it	PRON
ejpam-6113	138	22	is	be	AUX
ejpam-6113	138	23	a	a	DET
ejpam-6113	138	24	complete	complete	ADJ
ejpam-6113	138	25	b	b	NOUN
ejpam-6113	138	26	-	-	PUNCT
ejpam-6113	138	27	metric	metric	ADJ
ejpam-6113	138	28	space	space	NOUN
ejpam-6113	138	29	.	.	PUNCT
ejpam-6113	139	1	here	here	ADV
ejpam-6113	139	2	we	we	PRON
ejpam-6113	139	3	observe	observe	VERB
ejpam-6113	139	4	that	that	SCONJ
ejpam-6113	139	5	when	when	SCONJ
ejpam-6113	139	6	a	a	DET
ejpam-6113	139	7	=	=	SYM
ejpam-6113	139	8	9	9	NUM
ejpam-6113	139	9	10	10	NUM
ejpam-6113	139	10	,	,	PUNCT
ejpam-6113	139	11	b	b	X
ejpam-6113	139	12	=	=	SYM
ejpam-6113	139	13	1	1	NUM
ejpam-6113	139	14	and	and	CCONJ
ejpam-6113	139	15	c	c	NOUN
ejpam-6113	139	16	∈	∈	PROPN
ejpam-6113	139	17	(	(	PUNCT
ejpam-6113	139	18	0	0	NUM
ejpam-6113	139	19	,	,	PUNCT
ejpam-6113	139	20	23	23	NUM
ejpam-6113	139	21	]	]	PUNCT
ejpam-6113	139	22	,	,	PUNCT
ejpam-6113	139	23	we	we	PRON
ejpam-6113	139	24	have	have	VERB
ejpam-6113	139	25	d(a	d(a	PROPN
ejpam-6113	139	26	,	,	PUNCT
ejpam-6113	139	27	b	b	NOUN
ejpam-6113	139	28	)	)	PUNCT
ejpam-6113	139	29	=	=	SYM
ejpam-6113	140	1	23	23	NUM
ejpam-6113	140	2	25	25	NUM
ejpam-6113	140	3	+	+	CCONJ
ejpam-6113	140	4	a+b	a+b	NUM
ejpam-6113	140	5	26	26	NUM
ejpam-6113	140	6	=	=	SYM
ejpam-6113	140	7	1291	1291	NUM
ejpam-6113	140	8	1300	1300	NUM
ejpam-6113	141	1	̸=	̸=	PROPN
ejpam-6113	141	2	121	121	NUM
ejpam-6113	141	3	125	125	NUM
ejpam-6113	141	4	=	=	SYM
ejpam-6113	141	5	121	121	NUM
ejpam-6113	141	6	250	250	NUM
ejpam-6113	141	7	+	+	CCONJ
ejpam-6113	141	8	121	121	NUM
ejpam-6113	141	9	250	250	NUM
ejpam-6113	141	10	=	=	SYM
ejpam-6113	141	11	d(a	d(a	PROPN
ejpam-6113	141	12	,	,	PUNCT
ejpam-6113	141	13	c	c	NOUN
ejpam-6113	141	14	)	)	PUNCT
ejpam-6113	141	15	+	+	CCONJ
ejpam-6113	142	1	d(c	d(c	PROPN
ejpam-6113	142	2	,	,	PUNCT
ejpam-6113	142	3	b	b	NOUN
ejpam-6113	142	4	)	)	PUNCT
ejpam-6113	142	5	so	so	SCONJ
ejpam-6113	142	6	that	that	SCONJ
ejpam-6113	142	7	d	d	NOUN
ejpam-6113	142	8	is	be	AUX
ejpam-6113	142	9	not	not	PART
ejpam-6113	142	10	a	a	DET
ejpam-6113	142	11	metric	metric	NOUN
ejpam-6113	142	12	.	.	PUNCT
ejpam-6113	143	1	we	we	PRON
ejpam-6113	143	2	specify	specify	VERB
ejpam-6113	143	3	t	t	PROPN
ejpam-6113	143	4	,	,	PUNCT
ejpam-6113	143	5	s	s	PART
ejpam-6113	143	6	:	:	PUNCT
ejpam-6113	143	7	e	e	X
ejpam-6113	143	8	→	→	SYM
ejpam-6113	143	9	e	e	X
ejpam-6113	143	10	by	by	ADP
ejpam-6113	143	11	t	t	PROPN
ejpam-6113	143	12	(	(	PUNCT
ejpam-6113	143	13	a	a	X
ejpam-6113	143	14	)	)	PUNCT
ejpam-6113	143	15	=	=	NOUN
ejpam-6113	143	16	{	{	PUNCT
ejpam-6113	143	17	a	a	X
ejpam-6113	143	18	,	,	PUNCT
ejpam-6113	143	19	if	if	SCONJ
ejpam-6113	143	20	a	a	DET
ejpam-6113	143	21	∈	∈	NOUN
ejpam-6113	144	1	[	[	X
ejpam-6113	144	2	0	0	NUM
ejpam-6113	144	3	,	,	PUNCT
ejpam-6113	144	4	23	23	NUM
ejpam-6113	144	5	)	)	PUNCT
ejpam-6113	144	6	,	,	PUNCT
ejpam-6113	144	7	4	4	NUM
ejpam-6113	144	8	3	3	NUM
ejpam-6113	144	9	−	−	NOUN
ejpam-6113	144	10	a	a	PRON
ejpam-6113	144	11	,	,	PUNCT
ejpam-6113	144	12	if	if	SCONJ
ejpam-6113	144	13	a	a	DET
ejpam-6113	144	14	∈	∈	NOUN
ejpam-6113	144	15	[	[	X
ejpam-6113	144	16	23	23	NUM
ejpam-6113	144	17	,	,	PUNCT
ejpam-6113	144	18	1	1	NUM
ejpam-6113	144	19	]	]	PUNCT
ejpam-6113	144	20	and	and	CCONJ
ejpam-6113	144	21	s(a	s(a	PROPN
ejpam-6113	144	22	)	)	PUNCT
ejpam-6113	144	23	=	=	PRON
ejpam-6113	144	24	{	{	PUNCT
ejpam-6113	144	25	a2	a2	PROPN
ejpam-6113	144	26	+	+	PROPN
ejpam-6113	144	27	3	3	NUM
ejpam-6113	144	28	4	4	NUM
ejpam-6113	144	29	,	,	PUNCT
ejpam-6113	145	1	if	if	SCONJ
ejpam-6113	145	2	a	a	DET
ejpam-6113	145	3	∈	∈	NOUN
ejpam-6113	146	1	[	[	X
ejpam-6113	146	2	0	0	NUM
ejpam-6113	146	3	,	,	PUNCT
ejpam-6113	146	4	23	23	NUM
ejpam-6113	146	5	)	)	PUNCT
ejpam-6113	146	6	,	,	PUNCT
ejpam-6113	146	7	1−	1−	NUM
ejpam-6113	146	8	a	a	DET
ejpam-6113	146	9	2	2	NUM
ejpam-6113	146	10	,	,	PUNCT
ejpam-6113	146	11	if	if	SCONJ
ejpam-6113	146	12	a	a	DET
ejpam-6113	146	13	∈	∈	NOUN
ejpam-6113	147	1	[	[	X
ejpam-6113	147	2	23	23	NUM
ejpam-6113	147	3	,	,	PUNCT
ejpam-6113	147	4	1	1	NUM
ejpam-6113	147	5	]	]	PUNCT
ejpam-6113	147	6	.	.	PUNCT
ejpam-6113	148	1	d.	d.	PROPN
ejpam-6113	148	2	r.	r.	PROPN
ejpam-6113	148	3	babu	babu	PROPN
ejpam-6113	148	4	,	,	PUNCT
ejpam-6113	148	5	k.	k.	PROPN
ejpam-6113	148	6	n.	n.	PROPN
ejpam-6113	148	7	k.	k.	PROPN
ejpam-6113	149	1	rao	rao	PROPN
ejpam-6113	149	2	/	/	SYM
ejpam-6113	149	3	eur	eur	PROPN
ejpam-6113	149	4	.	.	PUNCT
ejpam-6113	150	1	j.	j.	PROPN
ejpam-6113	150	2	pure	pure	PROPN
ejpam-6113	150	3	appl	appl	PROPN
ejpam-6113	150	4	.	.	PROPN
ejpam-6113	150	5	math	math	PROPN
ejpam-6113	150	6	,	,	PUNCT
ejpam-6113	150	7	18	18	NUM
ejpam-6113	150	8	(	(	PUNCT
ejpam-6113	150	9	3	3	NUM
ejpam-6113	150	10	)	)	PUNCT
ejpam-6113	150	11	(	(	PUNCT
ejpam-6113	150	12	2025	2025	NUM
ejpam-6113	150	13	)	)	PUNCT
ejpam-6113	150	14	,	,	PUNCT
ejpam-6113	150	15	6113	6113	NUM
ejpam-6113	150	16	6	6	NUM
ejpam-6113	150	17	of	of	ADP
ejpam-6113	150	18	14	14	NUM
ejpam-6113	150	19	clearly	clearly	ADV
ejpam-6113	150	20	,	,	PUNCT
ejpam-6113	150	21	t	t	PROPN
ejpam-6113	150	22	is	be	AUX
ejpam-6113	150	23	b	b	NOUN
ejpam-6113	150	24	-	-	PUNCT
ejpam-6113	150	25	continuous	continuous	ADJ
ejpam-6113	150	26	.	.	PUNCT
ejpam-6113	151	1	we	we	PRON
ejpam-6113	151	2	take	take	VERB
ejpam-6113	151	3	λ	λ	X
ejpam-6113	151	4	=	=	NOUN
ejpam-6113	151	5	99	99	NUM
ejpam-6113	151	6	100	100	NUM
ejpam-6113	151	7	,	,	PUNCT
ejpam-6113	151	8	α	α	X
ejpam-6113	151	9	=	=	X
ejpam-6113	151	10	β	β	X
ejpam-6113	151	11	=	=	PUNCT
ejpam-6113	151	12	γ	γ	X
ejpam-6113	151	13	=	=	SYM
ejpam-6113	151	14	1	1	NUM
ejpam-6113	151	15	20	20	NUM
ejpam-6113	151	16	.	.	PUNCT
ejpam-6113	152	1	then	then	ADV
ejpam-6113	152	2	clearly	clearly	ADV
ejpam-6113	152	3	α+	α+	X
ejpam-6113	152	4	β	β	X
ejpam-6113	152	5	+	+	X
ejpam-6113	152	6	γ	γ	X
ejpam-6113	152	7	<	<	X
ejpam-6113	152	8	1	1	NUM
ejpam-6113	152	9	.	.	PUNCT
ejpam-6113	153	1	keeping	keep	VERB
ejpam-6113	153	2	generality	generality	NOUN
ejpam-6113	153	3	intact	intact	ADJ
ejpam-6113	153	4	,	,	PUNCT
ejpam-6113	153	5	we	we	PRON
ejpam-6113	153	6	suppose	suppose	VERB
ejpam-6113	153	7	that	that	SCONJ
ejpam-6113	153	8	a	a	DET
ejpam-6113	153	9	≥	≥	NOUN
ejpam-6113	153	10	b.	b.	PROPN
ejpam-6113	153	11	case(i	case(i	PROPN
ejpam-6113	153	12	):	):	PUNCT
ejpam-6113	153	13	a	a	PRON
ejpam-6113	153	14	,	,	PUNCT
ejpam-6113	153	15	b	b	X
ejpam-6113	153	16	∈	∈	PROPN
ejpam-6113	154	1	[	[	X
ejpam-6113	154	2	0	0	NUM
ejpam-6113	154	3	,	,	PUNCT
ejpam-6113	154	4	23	23	NUM
ejpam-6113	154	5	)	)	PUNCT
ejpam-6113	154	6	.	.	PUNCT
ejpam-6113	155	1	d(ta	d(ta	PROPN
ejpam-6113	155	2	,	,	PUNCT
ejpam-6113	155	3	sb	sb	X
ejpam-6113	155	4	)	)	PUNCT
ejpam-6113	155	5	=	=	SYM
ejpam-6113	155	6	121	121	NUM
ejpam-6113	155	7	250	250	NUM
ejpam-6113	155	8	≤	≤	NUM
ejpam-6113	155	9	99	99	NUM
ejpam-6113	155	10	100	100	NUM
ejpam-6113	155	11	[	[	PUNCT
ejpam-6113	155	12	11	11	NUM
ejpam-6113	155	13	15	15	NUM
ejpam-6113	155	14	]	]	SYM
ejpam-6113	155	15	1	1	NUM
ejpam-6113	155	16	20	20	NUM
ejpam-6113	155	17	[	[	PUNCT
ejpam-6113	155	18	11	11	NUM
ejpam-6113	155	19	15	15	NUM
ejpam-6113	155	20	]	]	SYM
ejpam-6113	155	21	1	1	NUM
ejpam-6113	155	22	20	20	NUM
ejpam-6113	155	23	[	[	PUNCT
ejpam-6113	155	24	121	121	NUM
ejpam-6113	155	25	250	250	NUM
ejpam-6113	155	26	]	]	SYM
ejpam-6113	155	27	1	1	NUM
ejpam-6113	155	28	20	20	NUM
ejpam-6113	155	29	[	[	PUNCT
ejpam-6113	155	30	223685	223685	NUM
ejpam-6113	155	31	382500	382500	NUM
ejpam-6113	155	32	]	]	PUNCT
ejpam-6113	155	33	17	17	NUM
ejpam-6113	155	34	20	20	NUM
ejpam-6113	155	35	=	=	SYM
ejpam-6113	155	36	λ	λ	X
ejpam-6113	156	1	[	[	X
ejpam-6113	156	2	d(a	d(a	PROPN
ejpam-6113	156	3	,	,	PUNCT
ejpam-6113	156	4	b)]β	b)]β	PROPN
ejpam-6113	157	1	[	[	X
ejpam-6113	157	2	d(a	d(a	PROPN
ejpam-6113	157	3	,	,	PUNCT
ejpam-6113	157	4	ta)]γ	ta)]γ	NOUN
ejpam-6113	157	5	[	[	X
ejpam-6113	157	6	d(b	d(b	PROPN
ejpam-6113	157	7	,	,	PUNCT
ejpam-6113	157	8	sb)]α	sb)]α	PROPN
ejpam-6113	157	9	[	[	PUNCT
ejpam-6113	157	10	d(b	d(b	PROPN
ejpam-6113	157	11	,	,	PUNCT
ejpam-6113	157	12	ta)+d(a	ta)+d(a	PROPN
ejpam-6113	157	13	,	,	PUNCT
ejpam-6113	157	14	sb	sb	X
ejpam-6113	157	15	)	)	PUNCT
ejpam-6113	157	16	2s	2s	X
ejpam-6113	158	1	]	]	X
ejpam-6113	158	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	158	3	case(ii	case(ii	PROPN
ejpam-6113	158	4	):	):	PUNCT
ejpam-6113	158	5	a	a	PRON
ejpam-6113	158	6	,	,	PUNCT
ejpam-6113	158	7	b	b	X
ejpam-6113	158	8	∈	∈	PROPN
ejpam-6113	158	9	(	(	PUNCT
ejpam-6113	158	10	23	23	NUM
ejpam-6113	158	11	,	,	PUNCT
ejpam-6113	158	12	1	1	NUM
ejpam-6113	158	13	]	]	PUNCT
ejpam-6113	158	14	.	.	PUNCT
ejpam-6113	159	1	d(ta	d(ta	PROPN
ejpam-6113	159	2	,	,	PUNCT
ejpam-6113	159	3	sb	sb	X
ejpam-6113	159	4	)	)	PUNCT
ejpam-6113	159	5	=	=	SYM
ejpam-6113	159	6	11	11	NUM
ejpam-6113	159	7	15	15	NUM
ejpam-6113	159	8	≤	≤	NUM
ejpam-6113	159	9	99	99	NUM
ejpam-6113	159	10	100	100	NUM
ejpam-6113	159	11	[	[	PUNCT
ejpam-6113	159	12	23	23	NUM
ejpam-6113	159	13	25	25	NUM
ejpam-6113	159	14	+	+	CCONJ
ejpam-6113	159	15	a+b	a+b	NUM
ejpam-6113	159	16	26	26	NUM
ejpam-6113	159	17	]	]	SYM
ejpam-6113	159	18	1	1	NUM
ejpam-6113	159	19	20	20	NUM
ejpam-6113	159	20	[	[	PUNCT
ejpam-6113	159	21	121	121	NUM
ejpam-6113	159	22	250	250	NUM
ejpam-6113	159	23	]	]	SYM
ejpam-6113	159	24	1	1	NUM
ejpam-6113	159	25	20	20	NUM
ejpam-6113	159	26	[	[	PUNCT
ejpam-6113	159	27	121	121	NUM
ejpam-6113	159	28	250	250	NUM
ejpam-6113	159	29	]	]	SYM
ejpam-6113	159	30	1	1	NUM
ejpam-6113	159	31	20	20	NUM
ejpam-6113	159	32	[	[	PUNCT
ejpam-6113	159	33	223685	223685	NUM
ejpam-6113	159	34	382500	382500	NUM
ejpam-6113	159	35	]	]	PUNCT
ejpam-6113	159	36	17	17	NUM
ejpam-6113	159	37	20	20	NUM
ejpam-6113	159	38	=	=	SYM
ejpam-6113	159	39	λ	λ	X
ejpam-6113	160	1	[	[	X
ejpam-6113	160	2	d(a	d(a	PROPN
ejpam-6113	160	3	,	,	PUNCT
ejpam-6113	160	4	b)]β	b)]β	PROPN
ejpam-6113	161	1	[	[	X
ejpam-6113	161	2	d(a	d(a	PROPN
ejpam-6113	161	3	,	,	PUNCT
ejpam-6113	161	4	ta)]γ	ta)]γ	NOUN
ejpam-6113	161	5	[	[	X
ejpam-6113	161	6	d(b	d(b	PROPN
ejpam-6113	161	7	,	,	PUNCT
ejpam-6113	161	8	sb)]α	sb)]α	PROPN
ejpam-6113	161	9	[	[	PUNCT
ejpam-6113	161	10	d(b	d(b	PROPN
ejpam-6113	161	11	,	,	PUNCT
ejpam-6113	161	12	ta)+d(a	ta)+d(a	PROPN
ejpam-6113	161	13	,	,	PUNCT
ejpam-6113	161	14	sb	sb	X
ejpam-6113	161	15	)	)	PUNCT
ejpam-6113	161	16	2s	2s	NOUN
ejpam-6113	162	1	]	]	X
ejpam-6113	162	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	162	3	case(iii	case(iii	PROPN
ejpam-6113	162	4	):	):	PUNCT
ejpam-6113	162	5	a	a	DET
ejpam-6113	162	6	∈	∈	NOUN
ejpam-6113	162	7	(	(	PUNCT
ejpam-6113	162	8	23	23	NUM
ejpam-6113	162	9	,	,	PUNCT
ejpam-6113	162	10	1	1	NUM
ejpam-6113	162	11	]	]	PUNCT
ejpam-6113	162	12	,	,	PUNCT
ejpam-6113	162	13	b	b	X
ejpam-6113	162	14	∈	∈	PROPN
ejpam-6113	163	1	[	[	X
ejpam-6113	163	2	0	0	NUM
ejpam-6113	163	3	,	,	PUNCT
ejpam-6113	163	4	23	23	NUM
ejpam-6113	163	5	)	)	PUNCT
ejpam-6113	163	6	.	.	PUNCT
ejpam-6113	164	1	d(ta	d(ta	PROPN
ejpam-6113	164	2	,	,	PUNCT
ejpam-6113	164	3	sb	sb	X
ejpam-6113	164	4	)	)	PUNCT
ejpam-6113	164	5	=	=	SYM
ejpam-6113	164	6	121	121	NUM
ejpam-6113	164	7	250	250	NUM
ejpam-6113	164	8	≤	≤	NUM
ejpam-6113	164	9	99	99	NUM
ejpam-6113	164	10	100	100	NUM
ejpam-6113	164	11	[	[	PUNCT
ejpam-6113	164	12	121	121	NUM
ejpam-6113	164	13	250	250	NUM
ejpam-6113	164	14	]	]	SYM
ejpam-6113	164	15	1	1	NUM
ejpam-6113	164	16	20	20	NUM
ejpam-6113	164	17	[	[	PUNCT
ejpam-6113	164	18	121	121	NUM
ejpam-6113	164	19	250	250	NUM
ejpam-6113	164	20	]	]	SYM
ejpam-6113	164	21	1	1	NUM
ejpam-6113	164	22	20	20	NUM
ejpam-6113	164	23	[	[	PUNCT
ejpam-6113	164	24	121	121	NUM
ejpam-6113	164	25	250	250	NUM
ejpam-6113	164	26	]	]	SYM
ejpam-6113	164	27	1	1	NUM
ejpam-6113	164	28	20	20	NUM
ejpam-6113	164	29	[	[	PUNCT
ejpam-6113	164	30	3038	3038	NUM
ejpam-6113	164	31	3825	3825	NUM
ejpam-6113	164	32	]	]	PUNCT
ejpam-6113	164	33	17	17	NUM
ejpam-6113	164	34	20	20	NUM
ejpam-6113	164	35	=	=	SYM
ejpam-6113	164	36	λ	λ	X
ejpam-6113	165	1	[	[	X
ejpam-6113	165	2	d(a	d(a	PROPN
ejpam-6113	165	3	,	,	PUNCT
ejpam-6113	165	4	b)]β	b)]β	PROPN
ejpam-6113	166	1	[	[	X
ejpam-6113	166	2	d(a	d(a	PROPN
ejpam-6113	166	3	,	,	PUNCT
ejpam-6113	166	4	ta)]γ	ta)]γ	NOUN
ejpam-6113	166	5	[	[	X
ejpam-6113	166	6	d(b	d(b	PROPN
ejpam-6113	166	7	,	,	PUNCT
ejpam-6113	166	8	sb)]α	sb)]α	PROPN
ejpam-6113	166	9	[	[	PUNCT
ejpam-6113	166	10	d(b	d(b	PROPN
ejpam-6113	166	11	,	,	PUNCT
ejpam-6113	166	12	ta)+d(a	ta)+d(a	PROPN
ejpam-6113	166	13	,	,	PUNCT
ejpam-6113	166	14	sb	sb	X
ejpam-6113	166	15	)	)	PUNCT
ejpam-6113	166	16	2s	2s	NOUN
ejpam-6113	167	1	]	]	X
ejpam-6113	167	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	167	3	from	from	ADP
ejpam-6113	167	4	all	all	DET
ejpam-6113	167	5	above	above	ADP
ejpam-6113	167	6	cases	case	NOUN
ejpam-6113	167	7	we	we	PRON
ejpam-6113	167	8	conclude	conclude	VERB
ejpam-6113	167	9	that	that	PRON
ejpam-6113	167	10	(	(	PUNCT
ejpam-6113	167	11	t	t	PROPN
ejpam-6113	167	12	,	,	PUNCT
ejpam-6113	167	13	s	s	PART
ejpam-6113	167	14	)	)	PUNCT
ejpam-6113	167	15	is	be	AUX
ejpam-6113	167	16	a	a	DET
ejpam-6113	167	17	pair	pair	NOUN
ejpam-6113	167	18	of	of	ADP
ejpam-6113	167	19	interpolative	interpolative	ADJ
ejpam-6113	167	20	hardy	hardy	ADJ
ejpam-6113	167	21	-	-	PUNCT
ejpam-6113	167	22	rogers	rogers	NOUN
ejpam-6113	167	23	contraction	contraction	NOUN
ejpam-6113	167	24	maps	map	NOUN
ejpam-6113	167	25	.	.	PUNCT
ejpam-6113	168	1	as	as	ADP
ejpam-6113	168	2	a	a	DET
ejpam-6113	168	3	result	result	NOUN
ejpam-6113	168	4	,	,	PUNCT
ejpam-6113	168	5	t	t	PROPN
ejpam-6113	168	6	and	and	CCONJ
ejpam-6113	168	7	s	s	VERB
ejpam-6113	168	8	satisfy	satisfy	NOUN
ejpam-6113	168	9	every	every	DET
ejpam-6113	168	10	hypothesis	hypothesis	NOUN
ejpam-6113	168	11	of	of	ADP
ejpam-6113	168	12	theorem	theorem	ADJ
ejpam-6113	168	13	4	4	NUM
ejpam-6113	168	14	,	,	PUNCT
ejpam-6113	168	15	and	and	CCONJ
ejpam-6113	168	16	2	2	NUM
ejpam-6113	168	17	3	3	NUM
ejpam-6113	168	18	is	be	AUX
ejpam-6113	168	19	the	the	DET
ejpam-6113	168	20	only	only	ADJ
ejpam-6113	168	21	joint	joint	ADJ
ejpam-6113	168	22	fixed	fix	VERB
ejpam-6113	168	23	point	point	NOUN
ejpam-6113	168	24	.	.	PUNCT
ejpam-6113	169	1	remark	remark	PROPN
ejpam-6113	169	2	1	1	NUM
ejpam-6113	169	3	.	.	PUNCT
ejpam-6113	169	4	theorem	theorem	VERB
ejpam-6113	169	5	4	4	NUM
ejpam-6113	169	6	and	and	CCONJ
ejpam-6113	169	7	example	example	NOUN
ejpam-6113	169	8	1	1	NUM
ejpam-6113	169	9	extend	extend	VERB
ejpam-6113	169	10	and	and	CCONJ
ejpam-6113	169	11	generalize	generalize	VERB
ejpam-6113	169	12	theorem	theorem	VERB
ejpam-6113	169	13	3	3	NUM
ejpam-6113	169	14	to	to	ADP
ejpam-6113	169	15	b	b	NOUN
ejpam-6113	169	16	-	-	PUNCT
ejpam-6113	169	17	metric	metric	ADJ
ejpam-6113	169	18	spaces	space	NOUN
ejpam-6113	169	19	.	.	PUNCT
ejpam-6113	170	1	theorem	theorem	ADJ
ejpam-6113	170	2	5	5	NUM
ejpam-6113	170	3	.	.	PUNCT
ejpam-6113	170	4	suppose	suppose	VERB
ejpam-6113	170	5	that	that	SCONJ
ejpam-6113	170	6	(	(	PUNCT
ejpam-6113	170	7	e	e	NOUN
ejpam-6113	170	8	,	,	PUNCT
ejpam-6113	170	9	d	d	PROPN
ejpam-6113	170	10	,	,	PUNCT
ejpam-6113	170	11	s	s	PART
ejpam-6113	170	12	)	)	PUNCT
ejpam-6113	170	13	be	be	AUX
ejpam-6113	170	14	a	a	DET
ejpam-6113	170	15	complete	complete	ADJ
ejpam-6113	170	16	b	b	NOUN
ejpam-6113	170	17	-	-	PUNCT
ejpam-6113	170	18	metric	metric	ADJ
ejpam-6113	170	19	space	space	NOUN
ejpam-6113	170	20	,	,	PUNCT
ejpam-6113	170	21	and	and	CCONJ
ejpam-6113	170	22	the	the	DET
ejpam-6113	170	23	maps	map	NOUN
ejpam-6113	170	24	t	t	PROPN
ejpam-6113	170	25	,	,	PUNCT
ejpam-6113	170	26	s	s	AUX
ejpam-6113	170	27	satisfy	satisfy	VERB
ejpam-6113	170	28	the	the	DET
ejpam-6113	170	29	following	follow	VERB
ejpam-6113	170	30	condition	condition	NOUN
ejpam-6113	170	31	:	:	PUNCT
ejpam-6113	170	32	there	there	PRON
ejpam-6113	170	33	exist	exist	VERB
ejpam-6113	170	34	a	a	DET
ejpam-6113	170	35	constant	constant	ADJ
ejpam-6113	170	36	λ	λ	X
ejpam-6113	170	37	∈	∈	PROPN
ejpam-6113	171	1	[	[	X
ejpam-6113	171	2	0	0	NUM
ejpam-6113	171	3	,	,	PUNCT
ejpam-6113	171	4	1	1	NUM
ejpam-6113	171	5	)	)	PUNCT
ejpam-6113	171	6	and	and	CCONJ
ejpam-6113	171	7	α	α	PRON
ejpam-6113	171	8	∈	∈	PROPN
ejpam-6113	171	9	(	(	PUNCT
ejpam-6113	171	10	0	0	NUM
ejpam-6113	171	11	,	,	PUNCT
ejpam-6113	171	12	1	1	NUM
ejpam-6113	171	13	)	)	PUNCT
ejpam-6113	171	14	such	such	ADJ
ejpam-6113	172	1	that	that	SCONJ
ejpam-6113	172	2	d(ta	d(ta	PROPN
ejpam-6113	172	3	,	,	PUNCT
ejpam-6113	172	4	sb	sb	NOUN
ejpam-6113	172	5	)	)	PUNCT
ejpam-6113	172	6	≤	≤	PUNCT
ejpam-6113	172	7	λ[d(ta	λ[d(ta	PROPN
ejpam-6113	172	8	,	,	PUNCT
ejpam-6113	172	9	a)]α[d(sb	a)]α[d(sb	PROPN
ejpam-6113	172	10	,	,	PUNCT
ejpam-6113	172	11	b)]1−α	b)]1−α	X
ejpam-6113	172	12	∀	∀	X
ejpam-6113	172	13	a	a	PRON
ejpam-6113	172	14	,	,	PUNCT
ejpam-6113	172	15	b	b	X
ejpam-6113	172	16	∈	∈	PROPN
ejpam-6113	172	17	x	x	PUNCT
ejpam-6113	173	1	such	such	ADJ
ejpam-6113	173	2	that	that	PRON
ejpam-6113	173	3	ta	ta	ADP
ejpam-6113	173	4	̸=	̸=	PROPN
ejpam-6113	173	5	a	a	DET
ejpam-6113	173	6	whenever	whenever	SCONJ
ejpam-6113	173	7	sa	sa	PROPN
ejpam-6113	173	8	̸=	̸=	PROPN
ejpam-6113	173	9	a.	a.	NOUN
ejpam-6113	173	10	both	both	PRON
ejpam-6113	173	11	s	s	PROPN
ejpam-6113	173	12	and	and	CCONJ
ejpam-6113	173	13	t	t	PROPN
ejpam-6113	173	14	have	have	VERB
ejpam-6113	173	15	a	a	DET
ejpam-6113	173	16	unique	unique	ADJ
ejpam-6113	173	17	common	common	ADJ
ejpam-6113	173	18	fixed	fix	VERB
ejpam-6113	173	19	point	point	NOUN
ejpam-6113	173	20	if	if	SCONJ
ejpam-6113	173	21	either	either	CCONJ
ejpam-6113	173	22	t	t	NOUN
ejpam-6113	173	23	or	or	CCONJ
ejpam-6113	173	24	s	s	NOUN
ejpam-6113	173	25	is	be	AUX
ejpam-6113	173	26	b	b	NOUN
ejpam-6113	173	27	-	-	PUNCT
ejpam-6113	173	28	continuous	continuous	ADJ
ejpam-6113	173	29	.	.	PUNCT
ejpam-6113	174	1	proof	proof	NOUN
ejpam-6113	174	2	.	.	PUNCT
ejpam-6113	175	1	since	since	SCONJ
ejpam-6113	175	2	the	the	DET
ejpam-6113	175	3	proof	proof	NOUN
ejpam-6113	175	4	resembles	resemble	VERB
ejpam-6113	175	5	theorem	theorem	NOUN
ejpam-6113	175	6	4	4	NUM
ejpam-6113	175	7	,	,	PUNCT
ejpam-6113	175	8	we	we	PRON
ejpam-6113	175	9	left	leave	VERB
ejpam-6113	175	10	it	it	PRON
ejpam-6113	175	11	out	out	ADP
ejpam-6113	175	12	.	.	PUNCT
ejpam-6113	176	1	example	example	NOUN
ejpam-6113	177	1	2	2	NUM
ejpam-6113	177	2	.	.	PUNCT
ejpam-6113	177	3	let	let	VERB
ejpam-6113	177	4	e	e	NOUN
ejpam-6113	177	5	=	=	PUNCT
ejpam-6113	177	6	r+	r+	X
ejpam-6113	177	7	.	.	PUNCT
ejpam-6113	178	1	we	we	PRON
ejpam-6113	178	2	define	define	VERB
ejpam-6113	178	3	d	d	X
ejpam-6113	178	4	:	:	PUNCT
ejpam-6113	178	5	e	e	X
ejpam-6113	178	6	×	×	NOUN
ejpam-6113	178	7	e	e	X
ejpam-6113	178	8	→	→	PUNCT
ejpam-6113	178	9	r+	r+	NOUN
ejpam-6113	178	10	by	by	ADP
ejpam-6113	178	11	d(a	d(a	PROPN
ejpam-6113	178	12	,	,	PUNCT
ejpam-6113	178	13	b	b	NOUN
ejpam-6113	178	14	)	)	PUNCT
ejpam-6113	178	15	=	=	SYM
ejpam-6113	178	16			X
ejpam-6113	178	17	0	0	NUM
ejpam-6113	178	18	,	,	PUNCT
ejpam-6113	178	19	if	if	SCONJ
ejpam-6113	178	20	a	a	DET
ejpam-6113	178	21	=	=	SYM
ejpam-6113	178	22	b	b	NOUN
ejpam-6113	178	23	,	,	PUNCT
ejpam-6113	178	24	4	4	NUM
ejpam-6113	178	25	,	,	PUNCT
ejpam-6113	178	26	if	if	SCONJ
ejpam-6113	178	27	a	a	PRON
ejpam-6113	178	28	,	,	PUNCT
ejpam-6113	178	29	b	b	X
ejpam-6113	178	30	∈	∈	PROPN
ejpam-6113	179	1	[	[	X
ejpam-6113	179	2	0	0	NUM
ejpam-6113	179	3	,	,	PUNCT
ejpam-6113	179	4	1	1	NUM
ejpam-6113	179	5	]	]	PUNCT
ejpam-6113	179	6	,	,	PUNCT
ejpam-6113	179	7	5	5	NUM
ejpam-6113	179	8	+	+	SYM
ejpam-6113	179	9	1	1	NUM
ejpam-6113	179	10	a+b	a+b	NUM
ejpam-6113	179	11	,	,	PUNCT
ejpam-6113	179	12	if	if	SCONJ
ejpam-6113	179	13	a	a	PRON
ejpam-6113	179	14	,	,	PUNCT
ejpam-6113	179	15	b	b	X
ejpam-6113	179	16	∈	∈	PROPN
ejpam-6113	179	17	(	(	PUNCT
ejpam-6113	179	18	1,∞	1,∞	NUM
ejpam-6113	179	19	)	)	PUNCT
ejpam-6113	179	20	,	,	PUNCT
ejpam-6113	179	21	27	27	NUM
ejpam-6113	179	22	10	10	NUM
ejpam-6113	179	23	,	,	PUNCT
ejpam-6113	179	24	otherwise	otherwise	ADV
ejpam-6113	179	25	.	.	PUNCT
ejpam-6113	180	1	d.	d.	PROPN
ejpam-6113	180	2	r.	r.	PROPN
ejpam-6113	180	3	babu	babu	PROPN
ejpam-6113	180	4	,	,	PUNCT
ejpam-6113	180	5	k.	k.	PROPN
ejpam-6113	180	6	n.	n.	PROPN
ejpam-6113	180	7	k.	k.	PROPN
ejpam-6113	181	1	rao	rao	PROPN
ejpam-6113	181	2	/	/	SYM
ejpam-6113	181	3	eur	eur	PROPN
ejpam-6113	181	4	.	.	PUNCT
ejpam-6113	182	1	j.	j.	PROPN
ejpam-6113	182	2	pure	pure	PROPN
ejpam-6113	182	3	appl	appl	PROPN
ejpam-6113	182	4	.	.	PROPN
ejpam-6113	182	5	math	math	PROPN
ejpam-6113	182	6	,	,	PUNCT
ejpam-6113	182	7	18	18	NUM
ejpam-6113	182	8	(	(	PUNCT
ejpam-6113	182	9	3	3	NUM
ejpam-6113	182	10	)	)	PUNCT
ejpam-6113	182	11	(	(	PUNCT
ejpam-6113	182	12	2025	2025	NUM
ejpam-6113	182	13	)	)	PUNCT
ejpam-6113	182	14	,	,	PUNCT
ejpam-6113	182	15	6113	6113	NUM
ejpam-6113	182	16	7	7	NUM
ejpam-6113	182	17	of	of	ADP
ejpam-6113	182	18	14	14	NUM
ejpam-6113	182	19	when	when	SCONJ
ejpam-6113	182	20	(	(	PUNCT
ejpam-6113	182	21	e	e	NOUN
ejpam-6113	182	22	,	,	PUNCT
ejpam-6113	182	23	d	d	PROPN
ejpam-6113	182	24	,	,	PUNCT
ejpam-6113	182	25	s	s	PART
ejpam-6113	182	26	)	)	PUNCT
ejpam-6113	182	27	has	have	VERB
ejpam-6113	182	28	the	the	DET
ejpam-6113	182	29	coefficient	coefficient	NOUN
ejpam-6113	182	30	s	s	PART
ejpam-6113	182	31	=	=	NOUN
ejpam-6113	182	32	489	489	NUM
ejpam-6113	182	33	480	480	NUM
ejpam-6113	182	34	,	,	PUNCT
ejpam-6113	182	35	it	it	PRON
ejpam-6113	182	36	is	be	AUX
ejpam-6113	182	37	evident	evident	ADJ
ejpam-6113	182	38	that	that	SCONJ
ejpam-6113	182	39	it	it	PRON
ejpam-6113	182	40	is	be	AUX
ejpam-6113	182	41	a	a	DET
ejpam-6113	182	42	complete	complete	ADJ
ejpam-6113	182	43	b	b	NOUN
ejpam-6113	182	44	-	-	PUNCT
ejpam-6113	182	45	metric	metric	ADJ
ejpam-6113	182	46	space	space	NOUN
ejpam-6113	182	47	.	.	PUNCT
ejpam-6113	183	1	here	here	ADV
ejpam-6113	183	2	we	we	PRON
ejpam-6113	183	3	observe	observe	VERB
ejpam-6113	183	4	that	that	SCONJ
ejpam-6113	183	5	when	when	SCONJ
ejpam-6113	183	6	a	a	DET
ejpam-6113	183	7	=	=	SYM
ejpam-6113	183	8	11	11	NUM
ejpam-6113	183	9	10	10	NUM
ejpam-6113	183	10	,	,	PUNCT
ejpam-6113	183	11	b	b	X
ejpam-6113	183	12	=	=	SYM
ejpam-6113	183	13	12	12	NUM
ejpam-6113	183	14	10	10	NUM
ejpam-6113	183	15	and	and	CCONJ
ejpam-6113	183	16	c	c	NOUN
ejpam-6113	183	17	∈	∈	PROPN
ejpam-6113	183	18	(	(	PUNCT
ejpam-6113	183	19	0	0	NUM
ejpam-6113	183	20	,	,	PUNCT
ejpam-6113	183	21	1	1	NUM
ejpam-6113	183	22	]	]	PUNCT
ejpam-6113	183	23	,	,	PUNCT
ejpam-6113	183	24	we	we	PRON
ejpam-6113	183	25	have	have	VERB
ejpam-6113	183	26	d(a	d(a	PROPN
ejpam-6113	183	27	,	,	PUNCT
ejpam-6113	183	28	b	b	NOUN
ejpam-6113	183	29	)	)	PUNCT
ejpam-6113	183	30	=	=	SYM
ejpam-6113	184	1	5	5	NUM
ejpam-6113	184	2	+	+	CCONJ
ejpam-6113	184	3	1	1	NUM
ejpam-6113	184	4	a+b	a+b	NUM
ejpam-6113	184	5	=	=	SYM
ejpam-6113	184	6	125	125	NUM
ejpam-6113	184	7	23	23	NUM
ejpam-6113	184	8	̸=	̸=	NOUN
ejpam-6113	184	9	27	27	NUM
ejpam-6113	184	10	5	5	NUM
ejpam-6113	184	11	=	=	SYM
ejpam-6113	184	12	27	27	NUM
ejpam-6113	184	13	10	10	NUM
ejpam-6113	184	14	+	+	CCONJ
ejpam-6113	184	15	27	27	NUM
ejpam-6113	184	16	10	10	NUM
ejpam-6113	184	17	=	=	SYM
ejpam-6113	184	18	d(a	d(a	PROPN
ejpam-6113	184	19	,	,	PUNCT
ejpam-6113	184	20	c	c	NOUN
ejpam-6113	184	21	)	)	PUNCT
ejpam-6113	184	22	+	+	CCONJ
ejpam-6113	184	23	d(c	d(c	PROPN
ejpam-6113	184	24	,	,	PUNCT
ejpam-6113	184	25	b	b	NOUN
ejpam-6113	184	26	)	)	PUNCT
ejpam-6113	184	27	so	so	SCONJ
ejpam-6113	184	28	that	that	SCONJ
ejpam-6113	184	29	d	d	NOUN
ejpam-6113	184	30	is	be	AUX
ejpam-6113	184	31	not	not	PART
ejpam-6113	184	32	a	a	DET
ejpam-6113	184	33	metric	metric	NOUN
ejpam-6113	184	34	.	.	PUNCT
ejpam-6113	185	1	we	we	PRON
ejpam-6113	185	2	define	define	VERB
ejpam-6113	185	3	t	t	PROPN
ejpam-6113	185	4	,	,	PUNCT
ejpam-6113	185	5	s	s	PART
ejpam-6113	185	6	:	:	PUNCT
ejpam-6113	185	7	e	e	X
ejpam-6113	185	8	→	→	SYM
ejpam-6113	185	9	e	e	X
ejpam-6113	185	10	by	by	ADP
ejpam-6113	185	11	t	t	PROPN
ejpam-6113	185	12	(	(	PUNCT
ejpam-6113	185	13	a	a	X
ejpam-6113	185	14	)	)	PUNCT
ejpam-6113	185	15	=	=	PRON
ejpam-6113	185	16	{	{	PUNCT
ejpam-6113	185	17	log(1	log(1	NOUN
ejpam-6113	185	18	+	+	CCONJ
ejpam-6113	185	19	a	a	X
ejpam-6113	185	20	)	)	PUNCT
ejpam-6113	185	21	,	,	PUNCT
ejpam-6113	185	22	if	if	SCONJ
ejpam-6113	185	23	a	a	DET
ejpam-6113	185	24	∈	∈	NOUN
ejpam-6113	186	1	[	[	X
ejpam-6113	186	2	0	0	NUM
ejpam-6113	186	3	,	,	PUNCT
ejpam-6113	186	4	1	1	NUM
ejpam-6113	186	5	)	)	PUNCT
ejpam-6113	186	6	,	,	PUNCT
ejpam-6113	186	7	2	2	NUM
ejpam-6113	186	8	a2	a2	NOUN
ejpam-6113	186	9	+	+	NOUN
ejpam-6113	186	10	1	1	NUM
ejpam-6113	186	11	,	,	PUNCT
ejpam-6113	186	12	if	if	SCONJ
ejpam-6113	186	13	a	a	DET
ejpam-6113	186	14	∈	∈	PROPN
ejpam-6113	187	1	[	[	X
ejpam-6113	187	2	1,∞	1,∞	NUM
ejpam-6113	187	3	)	)	PUNCT
ejpam-6113	187	4	and	and	CCONJ
ejpam-6113	187	5	s(a	s(a	NOUN
ejpam-6113	187	6	)	)	PUNCT
ejpam-6113	188	1	=	=	PRON
ejpam-6113	188	2	{	{	PUNCT
ejpam-6113	188	3	exp	exp	NOUN
ejpam-6113	188	4	a	a	NOUN
ejpam-6113	188	5	,	,	PUNCT
ejpam-6113	188	6	if	if	SCONJ
ejpam-6113	188	7	a	a	DET
ejpam-6113	188	8	∈	∈	NOUN
ejpam-6113	189	1	[	[	X
ejpam-6113	189	2	0	0	NUM
ejpam-6113	189	3	,	,	PUNCT
ejpam-6113	189	4	1	1	NUM
ejpam-6113	189	5	)	)	PUNCT
ejpam-6113	189	6	,	,	PUNCT
ejpam-6113	189	7	1+a	1+a	NUM
ejpam-6113	189	8	2	2	NUM
ejpam-6113	189	9	,	,	PUNCT
ejpam-6113	189	10	if	if	SCONJ
ejpam-6113	189	11	a	a	DET
ejpam-6113	189	12	∈	∈	NOUN
ejpam-6113	189	13	[	[	X
ejpam-6113	189	14	1,∞	1,∞	NUM
ejpam-6113	189	15	)	)	PUNCT
ejpam-6113	189	16	.	.	PUNCT
ejpam-6113	190	1	clearly	clearly	ADV
ejpam-6113	190	2	,	,	PUNCT
ejpam-6113	190	3	t	t	PROPN
ejpam-6113	190	4	is	be	AUX
ejpam-6113	190	5	b	b	NOUN
ejpam-6113	190	6	-	-	PUNCT
ejpam-6113	190	7	continuous	continuous	ADJ
ejpam-6113	190	8	.	.	PUNCT
ejpam-6113	191	1	we	we	PRON
ejpam-6113	191	2	take	take	VERB
ejpam-6113	191	3	λ	λ	X
ejpam-6113	191	4	=	=	NOUN
ejpam-6113	191	5	99	99	NUM
ejpam-6113	191	6	100	100	NUM
ejpam-6113	191	7	,	,	PUNCT
ejpam-6113	191	8	α	α	NOUN
ejpam-6113	191	9	=	=	NOUN
ejpam-6113	191	10	4	4	NUM
ejpam-6113	191	11	5	5	NUM
ejpam-6113	191	12	.	.	PUNCT
ejpam-6113	192	1	assuming	assume	VERB
ejpam-6113	192	2	a	a	DET
ejpam-6113	192	3	≥	≥	NOUN
ejpam-6113	192	4	b	b	NOUN
ejpam-6113	192	5	,	,	PUNCT
ejpam-6113	192	6	we	we	PRON
ejpam-6113	192	7	maintain	maintain	VERB
ejpam-6113	192	8	generality	generality	NOUN
ejpam-6113	192	9	.	.	PUNCT
ejpam-6113	193	1	case(i	case(i	NOUN
ejpam-6113	193	2	):	):	PUNCT
ejpam-6113	193	3	a	a	PRON
ejpam-6113	193	4	,	,	PUNCT
ejpam-6113	193	5	b	b	X
ejpam-6113	193	6	∈	∈	PROPN
ejpam-6113	194	1	[	[	X
ejpam-6113	194	2	0	0	NUM
ejpam-6113	194	3	,	,	PUNCT
ejpam-6113	194	4	1	1	NUM
ejpam-6113	194	5	)	)	PUNCT
ejpam-6113	194	6	.	.	PUNCT
ejpam-6113	195	1	d(ta	d(ta	PROPN
ejpam-6113	195	2	,	,	PUNCT
ejpam-6113	195	3	sb	sb	X
ejpam-6113	195	4	)	)	PUNCT
ejpam-6113	195	5	=	=	SYM
ejpam-6113	195	6	27	27	NUM
ejpam-6113	195	7	10	10	NUM
ejpam-6113	195	8	≤	≤	NUM
ejpam-6113	195	9	99	99	NUM
ejpam-6113	195	10	100	100	NUM
ejpam-6113	195	11	[	[	X
ejpam-6113	195	12	4	4	NUM
ejpam-6113	195	13	]	]	SYM
ejpam-6113	195	14	4	4	NUM
ejpam-6113	195	15	5	5	NUM
ejpam-6113	195	16	[	[	PUNCT
ejpam-6113	195	17	27	27	NUM
ejpam-6113	195	18	10	10	NUM
ejpam-6113	195	19	]	]	SYM
ejpam-6113	195	20	1	1	NUM
ejpam-6113	195	21	5	5	NUM
ejpam-6113	195	22	=	=	SYM
ejpam-6113	195	23	λ	λ	X
ejpam-6113	196	1	[	[	X
ejpam-6113	196	2	d(a	d(a	PROPN
ejpam-6113	196	3	,	,	PUNCT
ejpam-6113	196	4	ta)]α	ta)]α	NOUN
ejpam-6113	197	1	[	[	X
ejpam-6113	197	2	d(b	d(b	PROPN
ejpam-6113	197	3	,	,	PUNCT
ejpam-6113	197	4	sb)]1−α	sb)]1−α	X
ejpam-6113	198	1	case(ii	case(ii	ADJ
ejpam-6113	198	2	):	):	PUNCT
ejpam-6113	198	3	a	a	PRON
ejpam-6113	198	4	,	,	PUNCT
ejpam-6113	198	5	b	b	X
ejpam-6113	198	6	∈	∈	PROPN
ejpam-6113	198	7	(	(	PUNCT
ejpam-6113	198	8	1,∞	1,∞	NUM
ejpam-6113	198	9	)	)	PUNCT
ejpam-6113	198	10	.	.	PUNCT
ejpam-6113	199	1	d(ta	d(ta	PROPN
ejpam-6113	199	2	,	,	PUNCT
ejpam-6113	199	3	sb	sb	X
ejpam-6113	199	4	)	)	PUNCT
ejpam-6113	199	5	=	=	SYM
ejpam-6113	199	6	27	27	NUM
ejpam-6113	199	7	10	10	NUM
ejpam-6113	199	8	≤	≤	NUM
ejpam-6113	199	9	99	99	NUM
ejpam-6113	199	10	100	100	NUM
ejpam-6113	199	11	[	[	X
ejpam-6113	199	12	4	4	NUM
ejpam-6113	199	13	]	]	SYM
ejpam-6113	199	14	4	4	NUM
ejpam-6113	199	15	5	5	NUM
ejpam-6113	199	16	[	[	PUNCT
ejpam-6113	199	17	27	27	NUM
ejpam-6113	199	18	10	10	NUM
ejpam-6113	199	19	]	]	SYM
ejpam-6113	199	20	1	1	NUM
ejpam-6113	199	21	5	5	NUM
ejpam-6113	199	22	=	=	SYM
ejpam-6113	199	23	λ	λ	X
ejpam-6113	200	1	[	[	X
ejpam-6113	200	2	d(a	d(a	PROPN
ejpam-6113	200	3	,	,	PUNCT
ejpam-6113	200	4	ta)]α	ta)]α	NOUN
ejpam-6113	201	1	[	[	X
ejpam-6113	201	2	d(b	d(b	PROPN
ejpam-6113	201	3	,	,	PUNCT
ejpam-6113	201	4	sb)]1−α	sb)]1−α	X
ejpam-6113	201	5	case(iii	case(iii	PROPN
ejpam-6113	201	6	):	):	PUNCT
ejpam-6113	201	7	a	a	DET
ejpam-6113	201	8	∈	∈	NOUN
ejpam-6113	201	9	(	(	PUNCT
ejpam-6113	201	10	1,∞	1,∞	NUM
ejpam-6113	201	11	)	)	PUNCT
ejpam-6113	201	12	,	,	PUNCT
ejpam-6113	201	13	b	b	X
ejpam-6113	201	14	∈	∈	PROPN
ejpam-6113	202	1	[	[	X
ejpam-6113	202	2	0	0	NUM
ejpam-6113	202	3	,	,	PUNCT
ejpam-6113	202	4	1	1	NUM
ejpam-6113	202	5	)	)	PUNCT
ejpam-6113	202	6	.	.	PUNCT
ejpam-6113	203	1	d(ta	d(ta	PROPN
ejpam-6113	203	2	,	,	PUNCT
ejpam-6113	203	3	sb	sb	X
ejpam-6113	203	4	)	)	PUNCT
ejpam-6113	203	5	=	=	SYM
ejpam-6113	203	6	27	27	NUM
ejpam-6113	203	7	10	10	NUM
ejpam-6113	203	8	≤	≤	NUM
ejpam-6113	203	9	99	99	NUM
ejpam-6113	203	10	100	100	NUM
ejpam-6113	203	11	[	[	X
ejpam-6113	203	12	4	4	NUM
ejpam-6113	203	13	]	]	SYM
ejpam-6113	203	14	4	4	NUM
ejpam-6113	203	15	5	5	NUM
ejpam-6113	203	16	[	[	PUNCT
ejpam-6113	203	17	27	27	NUM
ejpam-6113	203	18	10	10	NUM
ejpam-6113	203	19	]	]	SYM
ejpam-6113	203	20	1	1	NUM
ejpam-6113	203	21	5	5	NUM
ejpam-6113	203	22	=	=	SYM
ejpam-6113	203	23	λ	λ	X
ejpam-6113	204	1	[	[	X
ejpam-6113	204	2	d(a	d(a	PROPN
ejpam-6113	204	3	,	,	PUNCT
ejpam-6113	204	4	ta)]α	ta)]α	NOUN
ejpam-6113	205	1	[	[	X
ejpam-6113	205	2	d(b	d(b	X
ejpam-6113	205	3	,	,	PUNCT
ejpam-6113	205	4	sb)]1−α	sb)]1−α	VERB
ejpam-6113	205	5	from	from	ADP
ejpam-6113	205	6	all	all	DET
ejpam-6113	205	7	above	above	ADP
ejpam-6113	205	8	cases	case	NOUN
ejpam-6113	205	9	we	we	PRON
ejpam-6113	205	10	conclude	conclude	VERB
ejpam-6113	205	11	that	that	PRON
ejpam-6113	205	12	(	(	PUNCT
ejpam-6113	205	13	t	t	PROPN
ejpam-6113	205	14	,	,	PUNCT
ejpam-6113	205	15	s	s	PART
ejpam-6113	205	16	)	)	PUNCT
ejpam-6113	205	17	is	be	AUX
ejpam-6113	205	18	an	an	DET
ejpam-6113	205	19	interpolative	interpolative	ADJ
ejpam-6113	205	20	kannan	kannan	NOUN
ejpam-6113	205	21	-	-	PUNCT
ejpam-6113	205	22	type	type	NOUN
ejpam-6113	205	23	contraction	contraction	NOUN
ejpam-6113	205	24	maps	map	NOUN
ejpam-6113	205	25	.	.	PUNCT
ejpam-6113	206	1	thus	thus	ADV
ejpam-6113	206	2	,	,	PUNCT
ejpam-6113	206	3	1	1	NUM
ejpam-6113	206	4	is	be	AUX
ejpam-6113	206	5	the	the	DET
ejpam-6113	206	6	only	only	ADJ
ejpam-6113	206	7	common	common	ADJ
ejpam-6113	206	8	fixed	fix	VERB
ejpam-6113	206	9	point	point	NOUN
ejpam-6113	206	10	,	,	PUNCT
ejpam-6113	206	11	and	and	CCONJ
ejpam-6113	206	12	t	t	PROPN
ejpam-6113	206	13	and	and	CCONJ
ejpam-6113	206	14	s	s	AUX
ejpam-6113	206	15	satisfy	satisfy	NOUN
ejpam-6113	206	16	every	every	DET
ejpam-6113	206	17	hypothesis	hypothesis	NOUN
ejpam-6113	206	18	of	of	ADP
ejpam-6113	206	19	theorem	theorem	ADJ
ejpam-6113	206	20	5	5	NUM
ejpam-6113	206	21	.	.	PUNCT
ejpam-6113	206	22	corollary	corollary	ADJ
ejpam-6113	206	23	1	1	PROPN
ejpam-6113	206	24	.	.	PUNCT
ejpam-6113	206	25	suppose	suppose	VERB
ejpam-6113	206	26	that	that	SCONJ
ejpam-6113	206	27	(	(	PUNCT
ejpam-6113	206	28	e	e	NOUN
ejpam-6113	206	29	,	,	PUNCT
ejpam-6113	206	30	d	d	PROPN
ejpam-6113	206	31	,	,	PUNCT
ejpam-6113	206	32	s	s	PART
ejpam-6113	206	33	)	)	PUNCT
ejpam-6113	206	34	be	be	AUX
ejpam-6113	206	35	a	a	DET
ejpam-6113	206	36	complete	complete	ADJ
ejpam-6113	206	37	b	b	NOUN
ejpam-6113	206	38	-	-	PUNCT
ejpam-6113	206	39	metric	metric	ADJ
ejpam-6113	206	40	space	space	NOUN
ejpam-6113	206	41	,	,	PUNCT
ejpam-6113	206	42	and	and	CCONJ
ejpam-6113	206	43	the	the	DET
ejpam-6113	206	44	map	map	NOUN
ejpam-6113	206	45	t	t	NOUN
ejpam-6113	206	46	satisfies	satisfy	VERB
ejpam-6113	206	47	the	the	DET
ejpam-6113	206	48	following	follow	VERB
ejpam-6113	206	49	condition	condition	NOUN
ejpam-6113	206	50	:	:	PUNCT
ejpam-6113	206	51	there	there	PRON
ejpam-6113	206	52	exist	exist	VERB
ejpam-6113	206	53	a	a	DET
ejpam-6113	206	54	constant	constant	ADJ
ejpam-6113	206	55	λ	λ	X
ejpam-6113	206	56	∈	∈	PROPN
ejpam-6113	207	1	[	[	X
ejpam-6113	207	2	0	0	NUM
ejpam-6113	207	3	,	,	PUNCT
ejpam-6113	207	4	1	1	NUM
ejpam-6113	207	5	)	)	PUNCT
ejpam-6113	207	6	and	and	CCONJ
ejpam-6113	207	7	α	α	NOUN
ejpam-6113	207	8	,	,	PUNCT
ejpam-6113	207	9	β	β	X
ejpam-6113	207	10	,	,	PUNCT
ejpam-6113	207	11	γ	γ	PROPN
ejpam-6113	207	12	∈	∈	PROPN
ejpam-6113	207	13	(	(	PUNCT
ejpam-6113	207	14	0	0	NUM
ejpam-6113	207	15	,	,	PUNCT
ejpam-6113	207	16	1	1	NUM
ejpam-6113	207	17	)	)	PUNCT
ejpam-6113	207	18	with	with	ADP
ejpam-6113	207	19	α+β+γ	α+β+γ	NUM
ejpam-6113	207	20	<	<	X
ejpam-6113	207	21	1	1	NUM
ejpam-6113	207	22	,	,	PUNCT
ejpam-6113	207	23	such	such	ADJ
ejpam-6113	207	24	that	that	SCONJ
ejpam-6113	207	25	d(ta	d(ta	PROPN
ejpam-6113	207	26	,	,	PUNCT
ejpam-6113	207	27	tb	tb	NOUN
ejpam-6113	207	28	)	)	PUNCT
ejpam-6113	207	29	≤	≤	NOUN
ejpam-6113	208	1	λ[d(a	λ[d(a	X
ejpam-6113	208	2	,	,	PUNCT
ejpam-6113	208	3	b)β][d(ta	b)β][d(ta	PROPN
ejpam-6113	208	4	,	,	PUNCT
ejpam-6113	208	5	a)]γ	a)]γ	NOUN
ejpam-6113	208	6	[	[	X
ejpam-6113	208	7	d(tb	d(tb	NOUN
ejpam-6113	208	8	,	,	PUNCT
ejpam-6113	208	9	b)]α	b)]α	PROPN
ejpam-6113	208	10	[	[	PUNCT
ejpam-6113	208	11	d(ta	d(ta	PROPN
ejpam-6113	208	12	,	,	PUNCT
ejpam-6113	208	13	b	b	NOUN
ejpam-6113	208	14	)	)	PUNCT
ejpam-6113	209	1	+	+	CCONJ
ejpam-6113	209	2	d(a	d(a	PROPN
ejpam-6113	209	3	,	,	PUNCT
ejpam-6113	209	4	tb	tb	NOUN
ejpam-6113	209	5	)	)	PUNCT
ejpam-6113	209	6	2s	2s	NOUN
ejpam-6113	210	1	]	]	X
ejpam-6113	210	2	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	210	3	for	for	ADP
ejpam-6113	210	4	all	all	DET
ejpam-6113	210	5	a	a	PRON
ejpam-6113	210	6	,	,	PUNCT
ejpam-6113	210	7	b	b	X
ejpam-6113	210	8	∈	∈	PROPN
ejpam-6113	210	9	x	x	PUNCT
ejpam-6113	210	10	such	such	ADJ
ejpam-6113	210	11	that	that	PRON
ejpam-6113	210	12	ta	ta	PROPN
ejpam-6113	210	13	̸=	̸=	PROPN
ejpam-6113	210	14	a.	a.	NOUN
ejpam-6113	210	15	then	then	ADV
ejpam-6113	210	16	t	t	PROPN
ejpam-6113	210	17	has	have	VERB
ejpam-6113	210	18	a	a	DET
ejpam-6113	210	19	unique	unique	ADJ
ejpam-6113	210	20	fixed	fix	VERB
ejpam-6113	210	21	point	point	NOUN
ejpam-6113	210	22	in	in	ADP
ejpam-6113	210	23	e.	e.	PROPN
ejpam-6113	210	24	remark	remark	PROPN
ejpam-6113	210	25	2	2	NUM
ejpam-6113	210	26	.	.	PUNCT
ejpam-6113	210	27	corollary	corollary	ADJ
ejpam-6113	210	28	1	1	NUM
ejpam-6113	210	29	extend	extend	NOUN
ejpam-6113	210	30	and	and	CCONJ
ejpam-6113	210	31	generalize	generalize	VERB
ejpam-6113	210	32	theorem	theorem	VERB
ejpam-6113	210	33	2	2	NUM
ejpam-6113	210	34	to	to	ADP
ejpam-6113	210	35	b	b	NOUN
ejpam-6113	210	36	-	-	PUNCT
ejpam-6113	210	37	metric	metric	ADJ
ejpam-6113	210	38	spaces	space	NOUN
ejpam-6113	210	39	.	.	PUNCT
ejpam-6113	211	1	corollary	corollary	ADJ
ejpam-6113	211	2	2	2	NUM
ejpam-6113	211	3	.	.	PUNCT
ejpam-6113	211	4	suppose	suppose	VERB
ejpam-6113	211	5	that	that	SCONJ
ejpam-6113	211	6	(	(	PUNCT
ejpam-6113	211	7	e	e	NOUN
ejpam-6113	211	8	,	,	PUNCT
ejpam-6113	211	9	d	d	PROPN
ejpam-6113	211	10	,	,	PUNCT
ejpam-6113	211	11	s	s	PART
ejpam-6113	211	12	)	)	PUNCT
ejpam-6113	211	13	be	be	AUX
ejpam-6113	211	14	a	a	DET
ejpam-6113	211	15	complete	complete	ADJ
ejpam-6113	211	16	b	b	NOUN
ejpam-6113	211	17	-	-	PUNCT
ejpam-6113	211	18	metric	metric	ADJ
ejpam-6113	211	19	space	space	NOUN
ejpam-6113	211	20	,	,	PUNCT
ejpam-6113	211	21	and	and	CCONJ
ejpam-6113	211	22	the	the	DET
ejpam-6113	211	23	map	map	NOUN
ejpam-6113	211	24	t	t	NOUN
ejpam-6113	211	25	satisfies	satisfy	VERB
ejpam-6113	211	26	the	the	DET
ejpam-6113	211	27	following	follow	VERB
ejpam-6113	211	28	condition	condition	NOUN
ejpam-6113	211	29	:	:	PUNCT
ejpam-6113	211	30	there	there	PRON
ejpam-6113	211	31	exist	exist	VERB
ejpam-6113	211	32	a	a	DET
ejpam-6113	211	33	constant	constant	ADJ
ejpam-6113	211	34	λ	λ	X
ejpam-6113	211	35	∈	∈	PROPN
ejpam-6113	212	1	[	[	X
ejpam-6113	212	2	0	0	NUM
ejpam-6113	212	3	,	,	PUNCT
ejpam-6113	212	4	1	1	NUM
ejpam-6113	212	5	)	)	PUNCT
ejpam-6113	212	6	and	and	CCONJ
ejpam-6113	212	7	α	α	PRON
ejpam-6113	212	8	∈	∈	PROPN
ejpam-6113	212	9	(	(	PUNCT
ejpam-6113	212	10	0	0	NUM
ejpam-6113	212	11	,	,	PUNCT
ejpam-6113	212	12	1	1	NUM
ejpam-6113	212	13	)	)	PUNCT
ejpam-6113	212	14	such	such	ADJ
ejpam-6113	213	1	that	that	SCONJ
ejpam-6113	213	2	d(ta	d(ta	PROPN
ejpam-6113	213	3	,	,	PUNCT
ejpam-6113	213	4	tb	tb	NOUN
ejpam-6113	213	5	)	)	PUNCT
ejpam-6113	213	6	≤	≤	NOUN
ejpam-6113	213	7	λ[d(ta	λ[d(ta	PROPN
ejpam-6113	213	8	,	,	PUNCT
ejpam-6113	213	9	a)]γ	a)]γ	NOUN
ejpam-6113	213	10	[	[	X
ejpam-6113	213	11	d(tb	d(tb	NOUN
ejpam-6113	213	12	,	,	PUNCT
ejpam-6113	213	13	b)]1−α	b)]1−α	X
ejpam-6113	213	14	for	for	ADP
ejpam-6113	213	15	all	all	DET
ejpam-6113	213	16	a	a	DET
ejpam-6113	213	17	,	,	PUNCT
ejpam-6113	213	18	b	b	X
ejpam-6113	213	19	∈	∈	PROPN
ejpam-6113	213	20	x	x	PUNCT
ejpam-6113	213	21	such	such	ADJ
ejpam-6113	213	22	that	that	PRON
ejpam-6113	213	23	ta	ta	PROPN
ejpam-6113	213	24	̸=	̸=	PROPN
ejpam-6113	213	25	a.	a.	NOUN
ejpam-6113	213	26	then	then	ADV
ejpam-6113	213	27	t	t	PROPN
ejpam-6113	213	28	has	have	VERB
ejpam-6113	213	29	a	a	DET
ejpam-6113	213	30	unique	unique	ADJ
ejpam-6113	213	31	fixed	fix	VERB
ejpam-6113	213	32	point	point	NOUN
ejpam-6113	213	33	in	in	ADP
ejpam-6113	213	34	e.	e.	PROPN
ejpam-6113	213	35	remark	remark	PROPN
ejpam-6113	213	36	3	3	NUM
ejpam-6113	213	37	.	.	PUNCT
ejpam-6113	213	38	corollary	corollary	ADJ
ejpam-6113	213	39	2	2	NUM
ejpam-6113	213	40	extend	extend	NOUN
ejpam-6113	213	41	and	and	CCONJ
ejpam-6113	213	42	generalize	generalize	VERB
ejpam-6113	213	43	theorem	theorem	VERB
ejpam-6113	213	44	1	1	NUM
ejpam-6113	213	45	to	to	ADP
ejpam-6113	213	46	b	b	NOUN
ejpam-6113	213	47	-	-	PUNCT
ejpam-6113	213	48	metric	metric	ADJ
ejpam-6113	213	49	spaces	space	NOUN
ejpam-6113	213	50	.	.	PUNCT
ejpam-6113	214	1	d.	d.	PROPN
ejpam-6113	214	2	r.	r.	PROPN
ejpam-6113	214	3	babu	babu	PROPN
ejpam-6113	214	4	,	,	PUNCT
ejpam-6113	214	5	k.	k.	PROPN
ejpam-6113	214	6	n.	n.	PROPN
ejpam-6113	214	7	k.	k.	PROPN
ejpam-6113	215	1	rao	rao	PROPN
ejpam-6113	215	2	/	/	SYM
ejpam-6113	215	3	eur	eur	PROPN
ejpam-6113	215	4	.	.	PUNCT
ejpam-6113	216	1	j.	j.	PROPN
ejpam-6113	216	2	pure	pure	PROPN
ejpam-6113	216	3	appl	appl	PROPN
ejpam-6113	216	4	.	.	PROPN
ejpam-6113	216	5	math	math	PROPN
ejpam-6113	216	6	,	,	PUNCT
ejpam-6113	216	7	18	18	NUM
ejpam-6113	216	8	(	(	PUNCT
ejpam-6113	216	9	3	3	NUM
ejpam-6113	216	10	)	)	PUNCT
ejpam-6113	216	11	(	(	PUNCT
ejpam-6113	216	12	2025	2025	NUM
ejpam-6113	216	13	)	)	PUNCT
ejpam-6113	216	14	,	,	PUNCT
ejpam-6113	216	15	6113	6113	NUM
ejpam-6113	216	16	8	8	NUM
ejpam-6113	216	17	of	of	ADP
ejpam-6113	216	18	14	14	NUM
ejpam-6113	216	19	3	3	NUM
ejpam-6113	216	20	.	.	PUNCT
ejpam-6113	217	1	nonlinear	nonlinear	ADJ
ejpam-6113	217	2	integral	integral	ADJ
ejpam-6113	217	3	equations	equation	NOUN
ejpam-6113	217	4	:	:	PUNCT
ejpam-6113	217	5	an	an	DET
ejpam-6113	217	6	approach	approach	NOUN
ejpam-6113	217	7	the	the	DET
ejpam-6113	217	8	primary	primary	ADJ
ejpam-6113	217	9	objective	objective	NOUN
ejpam-6113	217	10	of	of	ADP
ejpam-6113	217	11	this	this	DET
ejpam-6113	217	12	section	section	NOUN
ejpam-6113	217	13	is	be	AUX
ejpam-6113	217	14	to	to	PART
ejpam-6113	217	15	determine	determine	VERB
ejpam-6113	217	16	the	the	DET
ejpam-6113	217	17	solution	solution	NOUN
ejpam-6113	217	18	to	to	ADP
ejpam-6113	217	19	an	an	DET
ejpam-6113	217	20	integral	integral	ADJ
ejpam-6113	217	21	problem	problem	NOUN
ejpam-6113	217	22	.	.	PUNCT
ejpam-6113	218	1	if	if	SCONJ
ejpam-6113	218	2	[	[	X
ejpam-6113	218	3	a	a	X
ejpam-6113	218	4	,	,	PUNCT
ejpam-6113	218	5	b	b	X
ejpam-6113	218	6	]	]	X
ejpam-6113	218	7	is	be	AUX
ejpam-6113	218	8	a	a	DET
ejpam-6113	218	9	closed	closed	ADJ
ejpam-6113	218	10	and	and	CCONJ
ejpam-6113	218	11	bounded	bound	VERB
ejpam-6113	218	12	integral	integral	ADJ
ejpam-6113	218	13	in	in	ADP
ejpam-6113	218	14	r	r	NOUN
ejpam-6113	218	15	,	,	PUNCT
ejpam-6113	218	16	then	then	ADV
ejpam-6113	218	17	ω	ω	NUM
ejpam-6113	218	18	=	=	SYM
ejpam-6113	218	19	c[a	c[a	PROPN
ejpam-6113	218	20	,	,	PUNCT
ejpam-6113	218	21	b	b	AUX
ejpam-6113	218	22	]	]	X
ejpam-6113	218	23	is	be	AUX
ejpam-6113	218	24	a	a	DET
ejpam-6113	218	25	set	set	NOUN
ejpam-6113	218	26	of	of	ADP
ejpam-6113	218	27	real	real	ADV
ejpam-6113	218	28	valued	value	VERB
ejpam-6113	218	29	continuous	continuous	ADJ
ejpam-6113	218	30	functions	function	NOUN
ejpam-6113	218	31	on	on	ADP
ejpam-6113	218	32	[	[	X
ejpam-6113	218	33	a	a	DET
ejpam-6113	218	34	,	,	PUNCT
ejpam-6113	218	35	b].d	b].d	NUM
ejpam-6113	218	36	:	:	PUNCT
ejpam-6113	218	37	ω	ω	NUM
ejpam-6113	218	38	×	×	PROPN
ejpam-6113	218	39	ω	ω	PROPN
ejpam-6113	218	40	→	→	PUNCT
ejpam-6113	218	41	r+	r+	PRON
ejpam-6113	218	42	is	be	AUX
ejpam-6113	218	43	what	what	PRON
ejpam-6113	218	44	we	we	PRON
ejpam-6113	218	45	define	define	VERB
ejpam-6113	218	46	.	.	PUNCT
ejpam-6113	219	1	for	for	ADP
ejpam-6113	219	2	every	every	DET
ejpam-6113	219	3	ξ	ξ	PROPN
ejpam-6113	219	4	,	,	PUNCT
ejpam-6113	219	5	η	η	PROPN
ejpam-6113	219	6	∈	∈	PROPN
ejpam-6113	219	7	ω	ω	PROPN
ejpam-6113	219	8	,	,	PUNCT
ejpam-6113	219	9	d(ξ	d(ξ	PROPN
ejpam-6113	219	10	,	,	PUNCT
ejpam-6113	219	11	η	η	NOUN
ejpam-6113	219	12	)	)	PUNCT
ejpam-6113	219	13	=	=	SYM
ejpam-6113	219	14	max	max	PROPN
ejpam-6113	219	15	t∈[a	t∈[a	NOUN
ejpam-6113	219	16	,	,	PUNCT
ejpam-6113	219	17	b	b	NOUN
ejpam-6113	219	18	]	]	PUNCT
ejpam-6113	219	19	|ξ(t)−	|ξ(t)−	PROPN
ejpam-6113	219	20	η(t)|p	η(t)|p	PROPN
ejpam-6113	219	21	,	,	PUNCT
ejpam-6113	219	22	where	where	SCONJ
ejpam-6113	219	23	p	p	NOUN
ejpam-6113	219	24	>	>	X
ejpam-6113	219	25	1	1	NUM
ejpam-6113	219	26	is	be	AUX
ejpam-6113	219	27	a	a	DET
ejpam-6113	219	28	real	real	ADJ
ejpam-6113	219	29	number	number	NOUN
ejpam-6113	219	30	.	.	PUNCT
ejpam-6113	220	1	therefore	therefore	ADV
ejpam-6113	220	2	(	(	PUNCT
ejpam-6113	220	3	ω	ω	NOUN
ejpam-6113	220	4	,	,	PUNCT
ejpam-6113	220	5	d	d	NOUN
ejpam-6113	220	6	)	)	PUNCT
ejpam-6113	220	7	is	be	AUX
ejpam-6113	220	8	a	a	DET
ejpam-6113	220	9	complete	complete	ADJ
ejpam-6113	220	10	b	b	X
ejpam-6113	220	11	-	-	PUNCT
ejpam-6113	220	12	metric	metric	ADJ
ejpam-6113	220	13	space	space	NOUN
ejpam-6113	220	14	with	with	ADP
ejpam-6113	220	15	s	s	NOUN
ejpam-6113	220	16	=	=	NOUN
ejpam-6113	220	17	2p−1	2p−1	NUM
ejpam-6113	220	18	.	.	PUNCT
ejpam-6113	221	1	several	several	ADJ
ejpam-6113	221	2	authors	author	NOUN
ejpam-6113	221	3	have	have	AUX
ejpam-6113	221	4	studied	study	VERB
ejpam-6113	221	5	the	the	DET
ejpam-6113	221	6	unique	unique	ADJ
ejpam-6113	221	7	solution	solution	NOUN
ejpam-6113	221	8	of	of	ADP
ejpam-6113	221	9	a	a	DET
ejpam-6113	221	10	system	system	NOUN
ejpam-6113	221	11	of	of	ADP
ejpam-6113	221	12	nonlinear	nonlinear	ADJ
ejpam-6113	221	13	integral	integral	ADJ
ejpam-6113	221	14	equations	equation	NOUN
ejpam-6113	222	1	[	[	X
ejpam-6113	222	2	1–3	1–3	NOUN
ejpam-6113	222	3	,	,	PUNCT
ejpam-6113	222	4	17	17	NUM
ejpam-6113	222	5	]	]	PUNCT
ejpam-6113	222	6	.	.	PUNCT
ejpam-6113	223	1	we	we	PRON
ejpam-6113	223	2	demonstrate	demonstrate	VERB
ejpam-6113	223	3	the	the	DET
ejpam-6113	223	4	existence	existence	NOUN
ejpam-6113	223	5	of	of	ADP
ejpam-6113	223	6	a	a	DET
ejpam-6113	223	7	single	single	ADJ
ejpam-6113	223	8	common	common	ADJ
ejpam-6113	223	9	solution	solution	NOUN
ejpam-6113	223	10	for	for	ADP
ejpam-6113	223	11	a	a	DET
ejpam-6113	223	12	system	system	NOUN
ejpam-6113	223	13	of	of	ADP
ejpam-6113	223	14	two	two	NUM
ejpam-6113	223	15	nonlinear	nonlinear	ADJ
ejpam-6113	223	16	integral	integral	ADJ
ejpam-6113	223	17	equations	equation	NOUN
ejpam-6113	223	18	of	of	ADP
ejpam-6113	223	19	fredholm	fredholm	NOUN
ejpam-6113	223	20	type	type	NOUN
ejpam-6113	223	21	,	,	PUNCT
ejpam-6113	223	22	which	which	PRON
ejpam-6113	223	23	is	be	AUX
ejpam-6113	223	24	defined	define	VERB
ejpam-6113	223	25	by	by	ADP
ejpam-6113	223	26			NUM
ejpam-6113	223	27	ξ(t	ξ(t	NOUN
ejpam-6113	223	28	)	)	PUNCT
ejpam-6113	223	29	=	=	SYM
ejpam-6113	223	30	f(t	f(t	NOUN
ejpam-6113	223	31	)	)	PUNCT
ejpam-6113	224	1	+	+	NUM
ejpam-6113	224	2	µ	µ	PROPN
ejpam-6113	224	3	b∫	b∫	NOUN
ejpam-6113	224	4	a	a	PRON
ejpam-6113	224	5	d1(t	d1(t	PROPN
ejpam-6113	224	6	,	,	PUNCT
ejpam-6113	224	7	r	r	NOUN
ejpam-6113	224	8	,	,	PUNCT
ejpam-6113	224	9	ξ(r))dr	ξ(r))dr	NOUN
ejpam-6113	224	10	,	,	PUNCT
ejpam-6113	224	11	ζ(t	ζ(t	PROPN
ejpam-6113	224	12	)	)	PUNCT
ejpam-6113	224	13	=	=	SYM
ejpam-6113	224	14	f(t	f(t	NOUN
ejpam-6113	224	15	)	)	PUNCT
ejpam-6113	225	1	+	+	NUM
ejpam-6113	225	2	µ	µ	PROPN
ejpam-6113	225	3	b∫	b∫	NOUN
ejpam-6113	225	4	a	a	DET
ejpam-6113	225	5	d2(t	d2(t	PROPN
ejpam-6113	225	6	,	,	PUNCT
ejpam-6113	225	7	r	r	NOUN
ejpam-6113	225	8	,	,	PUNCT
ejpam-6113	225	9	ζ(r))dr	ζ(r))dr	NOUN
ejpam-6113	225	10	(	(	PUNCT
ejpam-6113	225	11	3.1	3.1	NUM
ejpam-6113	225	12	)	)	PUNCT
ejpam-6113	225	13	where	where	SCONJ
ejpam-6113	225	14	ξ	ξ	PROPN
ejpam-6113	225	15	∈	∈	PROPN
ejpam-6113	225	16	c[a	c[a	NOUN
ejpam-6113	225	17	,	,	PUNCT
ejpam-6113	225	18	b	b	NOUN
ejpam-6113	225	19	]	]	X
ejpam-6113	225	20	,	,	PUNCT
ejpam-6113	225	21	µ	µ	PROPN
ejpam-6113	225	22	∈	∈	PROPN
ejpam-6113	225	23	r	r	PROPN
ejpam-6113	225	24	,	,	PUNCT
ejpam-6113	225	25	t	t	PROPN
ejpam-6113	225	26	,	,	PUNCT
ejpam-6113	225	27	r	r	NOUN
ejpam-6113	225	28	∈	∈	PROPN
ejpam-6113	226	1	[	[	X
ejpam-6113	226	2	a	a	X
ejpam-6113	226	3	,	,	PUNCT
ejpam-6113	226	4	b],d1,d2	b],d1,d2	NOUN
ejpam-6113	226	5	:	:	PUNCT
ejpam-6113	227	1	[	[	X
ejpam-6113	227	2	a	a	X
ejpam-6113	227	3	,	,	PUNCT
ejpam-6113	227	4	b	b	NOUN
ejpam-6113	227	5	]	]	X
ejpam-6113	227	6	×	×	NOUN
ejpam-6113	227	7	[	[	X
ejpam-6113	227	8	a	a	X
ejpam-6113	227	9	,	,	PUNCT
ejpam-6113	227	10	b	b	NOUN
ejpam-6113	227	11	]	]	X
ejpam-6113	227	12	×	×	NOUN
ejpam-6113	227	13	r	r	NOUN
ejpam-6113	227	14	→	→	SYM
ejpam-6113	227	15	r	r	NOUN
ejpam-6113	227	16	and	and	CCONJ
ejpam-6113	227	17	f	f	NOUN
ejpam-6113	227	18	:	:	PUNCT
ejpam-6113	228	1	[	[	X
ejpam-6113	228	2	a	a	X
ejpam-6113	228	3	,	,	PUNCT
ejpam-6113	228	4	b	b	NOUN
ejpam-6113	228	5	]	]	X
ejpam-6113	228	6	→	→	PUNCT
ejpam-6113	228	7	r	r	NOUN
ejpam-6113	228	8	are	be	AUX
ejpam-6113	228	9	continuous	continuous	ADJ
ejpam-6113	228	10	functions	function	NOUN
ejpam-6113	228	11	.	.	PUNCT
ejpam-6113	229	1	consider	consider	VERB
ejpam-6113	229	2	two	two	NUM
ejpam-6113	229	3	mappings	mapping	NOUN
ejpam-6113	229	4	f1,f2	f1,f2	PROPN
ejpam-6113	229	5	:	:	PUNCT
ejpam-6113	230	1	ω	ω	X
ejpam-6113	230	2	→	→	SYM
ejpam-6113	230	3	ω	ω	PROPN
ejpam-6113	230	4	that	that	PRON
ejpam-6113	230	5	are	be	AUX
ejpam-6113	230	6	specified	specify	VERB
ejpam-6113	230	7	by	by	PROPN
ejpam-6113	230	8	f1(ξ(t	f1(ξ(t	NOUN
ejpam-6113	230	9	)	)	PUNCT
ejpam-6113	230	10	)	)	PUNCT
ejpam-6113	231	1	=	=	SYM
ejpam-6113	231	2	f(t	f(t	NOUN
ejpam-6113	231	3	)	)	PUNCT
ejpam-6113	232	1	+	+	NUM
ejpam-6113	232	2	µ	µ	PROPN
ejpam-6113	232	3	b∫	b∫	NOUN
ejpam-6113	232	4	a	a	PRON
ejpam-6113	232	5	d1(t	d1(t	PROPN
ejpam-6113	232	6	,	,	PUNCT
ejpam-6113	232	7	r	r	NOUN
ejpam-6113	232	8	,	,	PUNCT
ejpam-6113	232	9	ξ(r))dr	ξ(r))dr	NOUN
ejpam-6113	232	10	,	,	PUNCT
ejpam-6113	232	11	f2(ξ(t	f2(ξ(t	NUM
ejpam-6113	232	12	)	)	PUNCT
ejpam-6113	232	13	)	)	PUNCT
ejpam-6113	233	1	=	=	SYM
ejpam-6113	233	2	f(t	f(t	NOUN
ejpam-6113	233	3	)	)	PUNCT
ejpam-6113	234	1	+	+	NUM
ejpam-6113	234	2	µ	µ	PROPN
ejpam-6113	234	3	b∫	b∫	NOUN
ejpam-6113	234	4	a	a	DET
ejpam-6113	234	5	d2(t	d2(t	PROPN
ejpam-6113	234	6	,	,	PUNCT
ejpam-6113	234	7	r	r	NOUN
ejpam-6113	234	8	,	,	PUNCT
ejpam-6113	234	9	ξ(r))dr	ξ(r))dr	NOUN
ejpam-6113	234	10	(	(	PUNCT
ejpam-6113	234	11	3.2	3.2	NUM
ejpam-6113	234	12	)	)	PUNCT
ejpam-6113	234	13	make	make	VERB
ejpam-6113	234	14	the	the	DET
ejpam-6113	234	15	following	follow	VERB
ejpam-6113	234	16	assumptions	assumption	NOUN
ejpam-6113	234	17	:	:	PUNCT
ejpam-6113	234	18	(	(	PUNCT
ejpam-6113	234	19	i	i	NOUN
ejpam-6113	234	20	)	)	PUNCT
ejpam-6113	234	21	there	there	PRON
ejpam-6113	234	22	exists	exist	VERB
ejpam-6113	234	23	a	a	DET
ejpam-6113	234	24	continuous	continuous	ADJ
ejpam-6113	234	25	function	function	NOUN
ejpam-6113	234	26	γ	γ	NOUN
ejpam-6113	234	27	:	:	PUNCT
ejpam-6113	235	1	[	[	X
ejpam-6113	235	2	a	a	DET
ejpam-6113	235	3	,	,	PUNCT
ejpam-6113	235	4	b]×	b]×	NOUN
ejpam-6113	235	5	[	[	X
ejpam-6113	235	6	a	a	X
ejpam-6113	235	7	,	,	PUNCT
ejpam-6113	235	8	b	b	NOUN
ejpam-6113	235	9	]	]	X
ejpam-6113	235	10	→	→	SYM
ejpam-6113	235	11	r+	r+	NOUN
ejpam-6113	235	12	,	,	PUNCT
ejpam-6113	235	13	such	such	ADJ
ejpam-6113	235	14	that	that	DET
ejpam-6113	235	15	max	max	PROPN
ejpam-6113	235	16	r∈[a	r∈[a	NOUN
ejpam-6113	235	17	,	,	PUNCT
ejpam-6113	235	18	b	b	X
ejpam-6113	235	19	]	]	X
ejpam-6113	235	20	b∫	b∫	NOUN
ejpam-6113	235	21	a	a	DET
ejpam-6113	235	22	γ(t	γ(t	NOUN
ejpam-6113	235	23	,	,	PUNCT
ejpam-6113	235	24	r)dr	r)dr	PROPN
ejpam-6113	235	25	≤	≤	NOUN
ejpam-6113	235	26	1	1	NUM
ejpam-6113	235	27	;	;	PUNCT
ejpam-6113	235	28	(	(	PUNCT
ejpam-6113	235	29	ii	ii	NOUN
ejpam-6113	235	30	)	)	PUNCT
ejpam-6113	235	31	there	there	PRON
ejpam-6113	235	32	exists	exist	VERB
ejpam-6113	235	33	a	a	DET
ejpam-6113	235	34	constant	constant	ADJ
ejpam-6113	235	35	k	k	PROPN
ejpam-6113	235	36	∈	∈	PROPN
ejpam-6113	235	37	(	(	PUNCT
ejpam-6113	235	38	0	0	NUM
ejpam-6113	235	39	,	,	PUNCT
ejpam-6113	235	40	1	1	NUM
ejpam-6113	235	41	)	)	PUNCT
ejpam-6113	235	42	such	such	ADJ
ejpam-6113	235	43	that	that	PRON
ejpam-6113	235	44	for	for	ADP
ejpam-6113	235	45	all	all	DET
ejpam-6113	235	46	t	t	PROPN
ejpam-6113	235	47	,	,	PUNCT
ejpam-6113	235	48	r	r	NOUN
ejpam-6113	235	49	∈	∈	PROPN
ejpam-6113	236	1	[	[	X
ejpam-6113	236	2	a	a	X
ejpam-6113	236	3	,	,	PUNCT
ejpam-6113	236	4	b	b	NOUN
ejpam-6113	236	5	]	]	X
ejpam-6113	236	6	,	,	PUNCT
ejpam-6113	236	7	ξ	ξ	PROPN
ejpam-6113	236	8	,	,	PUNCT
ejpam-6113	236	9	ζ	ζ	NOUN
ejpam-6113	236	10	∈	∈	PROPN
ejpam-6113	236	11	r	r	NOUN
ejpam-6113	236	12	,	,	PUNCT
ejpam-6113	236	13	and	and	CCONJ
ejpam-6113	236	14	α	α	NOUN
ejpam-6113	236	15	,	,	PUNCT
ejpam-6113	236	16	β	β	X
ejpam-6113	236	17	,	,	PUNCT
ejpam-6113	236	18	γ	γ	PROPN
ejpam-6113	236	19	∈	∈	PROPN
ejpam-6113	236	20	(	(	PUNCT
ejpam-6113	236	21	0	0	NUM
ejpam-6113	236	22	,	,	PUNCT
ejpam-6113	236	23	1	1	NUM
ejpam-6113	236	24	)	)	PUNCT
ejpam-6113	236	25	with	with	ADP
ejpam-6113	236	26	α+	α+	PRON
ejpam-6113	236	27	β	β	NOUN
ejpam-6113	236	28	+	+	X
ejpam-6113	236	29	γ	γ	X
ejpam-6113	236	30	<	<	X
ejpam-6113	236	31	1	1	NUM
ejpam-6113	236	32	,	,	PUNCT
ejpam-6113	236	33	the	the	DET
ejpam-6113	236	34	following	follow	VERB
ejpam-6113	236	35	condition	condition	NOUN
ejpam-6113	236	36	is	be	AUX
ejpam-6113	236	37	satisfied	satisfied	ADJ
ejpam-6113	236	38	:	:	PUNCT
ejpam-6113	236	39	|d1(t	|d1(t	NUM
ejpam-6113	236	40	,	,	PUNCT
ejpam-6113	236	41	r	r	NOUN
ejpam-6113	236	42	,	,	PUNCT
ejpam-6113	236	43	ξ1(r))−d2(t	ξ1(r))−d2(t	NOUN
ejpam-6113	236	44	,	,	PUNCT
ejpam-6113	236	45	r	r	NOUN
ejpam-6113	236	46	,	,	PUNCT
ejpam-6113	237	1	ξ2(r)|p	ξ2(r)|p	X
ejpam-6113	237	2	≤	≤	ADV
ejpam-6113	237	3	k	k	X
ejpam-6113	237	4	(	(	PUNCT
ejpam-6113	237	5	b−a)p−126p−6γ(t	b−a)p−126p−6γ(t	NOUN
ejpam-6113	237	6	,	,	PUNCT
ejpam-6113	237	7	r)∆(ξ1	r)∆(ξ1	ADJ
ejpam-6113	237	8	,	,	PUNCT
ejpam-6113	237	9	ξ2	ξ2	NOUN
ejpam-6113	237	10	)	)	PUNCT
ejpam-6113	237	11	,	,	PUNCT
ejpam-6113	237	12	where	where	SCONJ
ejpam-6113	237	13	∆(ξ1	∆(ξ1	NUM
ejpam-6113	237	14	,	,	PUNCT
ejpam-6113	237	15	ξ2	ξ2	NOUN
ejpam-6113	237	16	)	)	PUNCT
ejpam-6113	237	17	=	=	PUNCT
ejpam-6113	238	1	[	[	X
ejpam-6113	238	2	|ξ1(r)−	|ξ1(r)−	X
ejpam-6113	238	3	ξ2(r)|p]β	ξ2(r)|p]β	NUM
ejpam-6113	239	1	[	[	X
ejpam-6113	239	2	|ξ1(r)−f1ξ1(r)|p]γ	|ξ1(r)−f1ξ1(r)|p]γ	ADP
ejpam-6113	239	3	[	[	X
ejpam-6113	239	4	|ξ1(r)−f1ξ1(r)|p]α	|ξ1(r)−f1ξ1(r)|p]α	ADJ
ejpam-6113	239	5	[	[	PUNCT
ejpam-6113	239	6	|ξ1(r)−f2ξ2(r)|p+|ξ2(r)−f1ξ1(r)|p	|ξ1(r)−f2ξ2(r)|p+|ξ2(r)−f1ξ1(r)|p	ADJ
ejpam-6113	239	7	2p	2p	NOUN
ejpam-6113	239	8	]	]	SYM
ejpam-6113	239	9	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	239	10	(	(	PUNCT
ejpam-6113	239	11	iii	iii	NOUN
ejpam-6113	239	12	)	)	PUNCT
ejpam-6113	239	13	|µ|	|µ|	PROPN
ejpam-6113	239	14	≤	≤	NUM
ejpam-6113	239	15	1	1	NUM
ejpam-6113	239	16	.	.	PUNCT
ejpam-6113	239	17	theorem	theorem	VERB
ejpam-6113	239	18	6	6	NUM
ejpam-6113	239	19	.	.	PUNCT
ejpam-6113	240	1	the	the	DET
ejpam-6113	240	2	requirements	requirement	NOUN
ejpam-6113	240	3	(	(	PUNCT
ejpam-6113	240	4	i	i	NOUN
ejpam-6113	240	5	)	)	PUNCT
ejpam-6113	240	6	−	−	PROPN
ejpam-6113	240	7	(	(	PUNCT
ejpam-6113	240	8	iii	iii	NOUN
ejpam-6113	240	9	)	)	PUNCT
ejpam-6113	240	10	hold	hold	VERB
ejpam-6113	240	11	if	if	SCONJ
ejpam-6113	240	12	(	(	PUNCT
ejpam-6113	240	13	3.2	3.2	NUM
ejpam-6113	240	14	)	)	PUNCT
ejpam-6113	240	15	is	be	AUX
ejpam-6113	240	16	used	use	VERB
ejpam-6113	240	17	to	to	PART
ejpam-6113	240	18	define	define	VERB
ejpam-6113	240	19	f1,f2	f1,f2	PROPN
ejpam-6113	240	20	:	:	PUNCT
ejpam-6113	241	1	ω	ω	PROPN
ejpam-6113	241	2	→	→	SYM
ejpam-6113	241	3	ω	ω	PROPN
ejpam-6113	241	4	.	.	PUNCT
ejpam-6113	242	1	next	next	ADV
ejpam-6113	242	2	,	,	PUNCT
ejpam-6113	242	3	there	there	PRON
ejpam-6113	242	4	is	be	VERB
ejpam-6113	242	5	a	a	DET
ejpam-6113	242	6	unique	unique	ADJ
ejpam-6113	242	7	common	common	ADJ
ejpam-6113	242	8	solution	solution	NOUN
ejpam-6113	242	9	in	in	ADP
ejpam-6113	242	10	ω	ω	PROPN
ejpam-6113	242	11	for	for	ADP
ejpam-6113	242	12	the	the	DET
ejpam-6113	242	13	system	system	NOUN
ejpam-6113	242	14	of	of	ADP
ejpam-6113	242	15	nonlinear	nonlinear	ADJ
ejpam-6113	242	16	integral	integral	ADJ
ejpam-6113	242	17	equations	equation	NOUN
ejpam-6113	242	18	(	(	PUNCT
ejpam-6113	242	19	3.1	3.1	NUM
ejpam-6113	242	20	)	)	PUNCT
ejpam-6113	242	21	.	.	PUNCT
ejpam-6113	243	1	d.	d.	PROPN
ejpam-6113	243	2	r.	r.	PROPN
ejpam-6113	243	3	babu	babu	PROPN
ejpam-6113	243	4	,	,	PUNCT
ejpam-6113	243	5	k.	k.	PROPN
ejpam-6113	243	6	n.	n.	PROPN
ejpam-6113	243	7	k.	k.	PROPN
ejpam-6113	244	1	rao	rao	PROPN
ejpam-6113	244	2	/	/	SYM
ejpam-6113	244	3	eur	eur	PROPN
ejpam-6113	244	4	.	.	PUNCT
ejpam-6113	245	1	j.	j.	PROPN
ejpam-6113	245	2	pure	pure	PROPN
ejpam-6113	245	3	appl	appl	PROPN
ejpam-6113	245	4	.	.	PROPN
ejpam-6113	245	5	math	math	PROPN
ejpam-6113	245	6	,	,	PUNCT
ejpam-6113	245	7	18	18	NUM
ejpam-6113	245	8	(	(	PUNCT
ejpam-6113	245	9	3	3	NUM
ejpam-6113	245	10	)	)	PUNCT
ejpam-6113	245	11	(	(	PUNCT
ejpam-6113	245	12	2025	2025	NUM
ejpam-6113	245	13	)	)	PUNCT
ejpam-6113	245	14	,	,	PUNCT
ejpam-6113	245	15	6113	6113	NUM
ejpam-6113	245	16	9	9	NUM
ejpam-6113	245	17	of	of	ADP
ejpam-6113	245	18	14	14	NUM
ejpam-6113	245	19	proof	proof	NOUN
ejpam-6113	245	20	.	.	PUNCT
ejpam-6113	246	1	let	let	VERB
ejpam-6113	246	2	ξ	ξ	X
ejpam-6113	246	3	,	,	PUNCT
ejpam-6113	246	4	η	η	PROPN
ejpam-6113	246	5	∈	∈	PROPN
ejpam-6113	246	6	ω	ω	PROPN
ejpam-6113	246	7	and	and	CCONJ
ejpam-6113	246	8	let	let	VERB
ejpam-6113	246	9	q	q	NOUN
ejpam-6113	246	10	∈	∈	NOUN
ejpam-6113	246	11	r	r	NOUN
ejpam-6113	246	12	such	such	ADJ
ejpam-6113	246	13	that	that	SCONJ
ejpam-6113	246	14	1	1	NUM
ejpam-6113	246	15	p	p	NOUN
ejpam-6113	246	16	+	+	NOUN
ejpam-6113	246	17	1	1	NUM
ejpam-6113	246	18	q	q	NOUN
ejpam-6113	246	19	=	=	NOUN
ejpam-6113	246	20	1	1	NUM
ejpam-6113	246	21	using	use	VERB
ejpam-6113	246	22	hölder	hölder	NOUN
ejpam-6113	246	23	’s	’s	PART
ejpam-6113	246	24	inequality	inequality	NOUN
ejpam-6113	246	25	and	and	CCONJ
ejpam-6113	246	26	from	from	ADP
ejpam-6113	246	27	the	the	DET
ejpam-6113	246	28	conditions	condition	NOUN
ejpam-6113	246	29	(	(	PUNCT
ejpam-6113	246	30	i)−	i)−	PROPN
ejpam-6113	246	31	(	(	PUNCT
ejpam-6113	246	32	iii	iii	NOUN
ejpam-6113	246	33	)	)	PUNCT
ejpam-6113	246	34	,	,	PUNCT
ejpam-6113	246	35	for	for	ADP
ejpam-6113	246	36	all	all	DET
ejpam-6113	246	37	t	t	PROPN
ejpam-6113	246	38	,	,	PUNCT
ejpam-6113	246	39	we	we	PRON
ejpam-6113	246	40	have	have	VERB
ejpam-6113	246	41	d(f1ξ1,f2ξ2	d(f1ξ1,f2ξ2	ADJ
ejpam-6113	246	42	)	)	PUNCT
ejpam-6113	246	43	=	=	SYM
ejpam-6113	246	44	max	max	PROPN
ejpam-6113	246	45	t∈[a	t∈[a	NOUN
ejpam-6113	246	46	,	,	PUNCT
ejpam-6113	246	47	b	b	NOUN
ejpam-6113	246	48	]	]	X
ejpam-6113	246	49	|f1ξ1(t)−f2ξ2(t)|p	|f1ξ1(t)−f2ξ2(t)|p	PROPN
ejpam-6113	246	50	=	=	SYM
ejpam-6113	246	51	|µ|p	|µ|p	PROPN
ejpam-6113	246	52	max	max	PROPN
ejpam-6113	246	53	t∈[a	t∈[a	NOUN
ejpam-6113	246	54	,	,	PUNCT
ejpam-6113	246	55	b	b	NOUN
ejpam-6113	246	56	]	]	X
ejpam-6113	246	57	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6113	246	58	b∫a	b∫a	PROPN
ejpam-6113	246	59	d1(t	d1(t	PROPN
ejpam-6113	246	60	,	,	PUNCT
ejpam-6113	246	61	r	r	NOUN
ejpam-6113	246	62	,	,	PUNCT
ejpam-6113	246	63	ξ1(r)−	ξ1(r)−	NOUN
ejpam-6113	246	64	b∫	b∫	NOUN
ejpam-6113	246	65	a	a	DET
ejpam-6113	246	66	d2(t	d2(t	PROPN
ejpam-6113	246	67	,	,	PUNCT
ejpam-6113	246	68	r	r	NOUN
ejpam-6113	246	69	,	,	PUNCT
ejpam-6113	246	70	ξ2(r)dr	ξ2(r)dr	NOUN
ejpam-6113	246	71	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6113	247	1	p	p	X
ejpam-6113	247	2	=	=	PUNCT
ejpam-6113	247	3	|µ|p	|µ|p	PROPN
ejpam-6113	247	4	max	max	PROPN
ejpam-6113	247	5	t∈[a	t∈[a	NOUN
ejpam-6113	247	6	,	,	PUNCT
ejpam-6113	247	7	b	b	NOUN
ejpam-6113	247	8	]	]	X
ejpam-6113	247	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6113	247	10	b∫a	b∫a	PROPN
ejpam-6113	247	11	(	(	PUNCT
ejpam-6113	247	12	d1(t	d1(t	PROPN
ejpam-6113	247	13	,	,	PUNCT
ejpam-6113	247	14	r	r	NOUN
ejpam-6113	247	15	,	,	PUNCT
ejpam-6113	247	16	ξ1(r)−d2(t	ξ1(r)−d2(t	PROPN
ejpam-6113	247	17	,	,	PUNCT
ejpam-6113	247	18	r	r	NOUN
ejpam-6113	247	19	,	,	PUNCT
ejpam-6113	247	20	ξ2(r))dr	ξ2(r))dr	NOUN
ejpam-6113	248	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6113	248	2	p	p	NOUN
ejpam-6113	248	3	≤	≤	PUNCT
ejpam-6113	248	4	|µ|p	|µ|p	PROPN
ejpam-6113	248	5	max	max	PROPN
ejpam-6113	248	6	t∈[a	t∈[a	NOUN
ejpam-6113	248	7	,	,	PUNCT
ejpam-6113	248	8	b	b	NOUN
ejpam-6113	248	9	]	]	X
ejpam-6113	248	10	(	(	PUNCT
ejpam-6113	248	11	b∫	b∫	NOUN
ejpam-6113	248	12	a	a	DET
ejpam-6113	248	13	1pdr	1pdr	NUM
ejpam-6113	248	14	)	)	PUNCT
ejpam-6113	248	15	1	1	NUM
ejpam-6113	248	16	q	q	NOUN
ejpam-6113	248	17	(	(	PUNCT
ejpam-6113	248	18	b∫	b∫	PROPN
ejpam-6113	248	19	a	a	DET
ejpam-6113	248	20	|(d1(t	|(d1(t	PROPN
ejpam-6113	248	21	,	,	PUNCT
ejpam-6113	248	22	r	r	NOUN
ejpam-6113	248	23	,	,	PUNCT
ejpam-6113	248	24	ξ1(r)−d2(t	ξ1(r)−d2(t	PROPN
ejpam-6113	248	25	,	,	PUNCT
ejpam-6113	248	26	r	r	NOUN
ejpam-6113	248	27	,	,	PUNCT
ejpam-6113	248	28	ξ2(r))|p	ξ2(r))|p	NUM
ejpam-6113	248	29	dr	dr	PROPN
ejpam-6113	248	30	)	)	PUNCT
ejpam-6113	248	31	1	1	NUM
ejpam-6113	248	32	p	p	NOUN
ejpam-6113	248	33	p	p	PROPN
ejpam-6113	248	34	≤	≤	NOUN
ejpam-6113	248	35	(	(	PUNCT
ejpam-6113	248	36	b−	b−	NOUN
ejpam-6113	248	37	a	a	NOUN
ejpam-6113	248	38	)	)	PUNCT
ejpam-6113	248	39	p	p	X
ejpam-6113	248	40	q	q	PROPN
ejpam-6113	248	41	max	max	PROPN
ejpam-6113	248	42	t∈[a	t∈[a	NOUN
ejpam-6113	248	43	,	,	PUNCT
ejpam-6113	248	44	b	b	NOUN
ejpam-6113	248	45	]	]	X
ejpam-6113	248	46	(	(	PUNCT
ejpam-6113	248	47	b∫	b∫	NOUN
ejpam-6113	248	48	a	a	PRON
ejpam-6113	248	49	|(d1(t	|(d1(t	PROPN
ejpam-6113	248	50	,	,	PUNCT
ejpam-6113	248	51	r	r	NOUN
ejpam-6113	248	52	,	,	PUNCT
ejpam-6113	248	53	ξ1(r)−d2(t	ξ1(r)−d2(t	PROPN
ejpam-6113	248	54	,	,	PUNCT
ejpam-6113	248	55	r	r	NOUN
ejpam-6113	248	56	,	,	PUNCT
ejpam-6113	248	57	ξ2(r))|p	ξ2(r))|p	NUM
ejpam-6113	248	58	dr	dr	PROPN
ejpam-6113	248	59	)	)	PUNCT
ejpam-6113	248	60	=	=	PUNCT
ejpam-6113	249	1	(	(	PUNCT
ejpam-6113	249	2	b−	b−	PROPN
ejpam-6113	249	3	a)p−1	a)p−1	PROPN
ejpam-6113	249	4	max	max	PROPN
ejpam-6113	249	5	t∈[a	t∈[a	PROPN
ejpam-6113	249	6	,	,	PUNCT
ejpam-6113	249	7	b	b	NOUN
ejpam-6113	249	8	]	]	X
ejpam-6113	249	9	(	(	PUNCT
ejpam-6113	249	10	b∫	b∫	NOUN
ejpam-6113	249	11	a	a	DET
ejpam-6113	249	12	|(d1(t	|(d1(t	PROPN
ejpam-6113	249	13	,	,	PUNCT
ejpam-6113	249	14	r	r	NOUN
ejpam-6113	249	15	,	,	PUNCT
ejpam-6113	249	16	ξ1(r)−d2(t	ξ1(r)−d2(t	PROPN
ejpam-6113	249	17	,	,	PUNCT
ejpam-6113	249	18	r	r	NOUN
ejpam-6113	249	19	,	,	PUNCT
ejpam-6113	249	20	ξ2(r))|p	ξ2(r))|p	NUM
ejpam-6113	249	21	dr	dr	PROPN
ejpam-6113	249	22	)	)	PUNCT
ejpam-6113	249	23	≤	≤	NOUN
ejpam-6113	249	24	(	(	PUNCT
ejpam-6113	249	25	b−	b−	PROPN
ejpam-6113	249	26	a)p−1	a)p−1	PROPN
ejpam-6113	249	27	max	max	PROPN
ejpam-6113	249	28	t∈[a	t∈[a	PROPN
ejpam-6113	249	29	,	,	PUNCT
ejpam-6113	249	30	b	b	X
ejpam-6113	249	31	]	]	X
ejpam-6113	249	32	b∫	b∫	PROPN
ejpam-6113	249	33	a	a	X
ejpam-6113	249	34	k	k	PROPN
ejpam-6113	249	35	(	(	PUNCT
ejpam-6113	249	36	b−a)p−126p−6γ(t	b−a)p−126p−6γ(t	NOUN
ejpam-6113	249	37	,	,	PUNCT
ejpam-6113	249	38	r)∆(ξ1	r)∆(ξ1	ADJ
ejpam-6113	249	39	,	,	PUNCT
ejpam-6113	249	40	ξ2	ξ2	NOUN
ejpam-6113	249	41	)	)	PUNCT
ejpam-6113	249	42	which	which	PRON
ejpam-6113	249	43	implies	imply	VERB
ejpam-6113	249	44	that	that	SCONJ
ejpam-6113	249	45	d(f1ξ1,f2ξ2	d(f1ξ1,f2ξ2	ADJ
ejpam-6113	249	46	)	)	PUNCT
ejpam-6113	249	47	≤	≤	PUNCT
ejpam-6113	249	48	k	k	PROPN
ejpam-6113	249	49	s6	s6	PROPN
ejpam-6113	250	1	[	[	X
ejpam-6113	250	2	|ξ1(r)−	|ξ1(r)−	X
ejpam-6113	251	1	ξ2(r)|p]β	ξ2(r)|p]β	NUM
ejpam-6113	251	2	[	[	X
ejpam-6113	251	3	|ξ1(r)−f1ξ1(r)|p]γ	|ξ1(r)−f1ξ1(r)|p]γ	ADP
ejpam-6113	251	4	[	[	X
ejpam-6113	251	5	|ξ1(r)−f1ξ1(r)|p]α	|ξ1(r)−f1ξ1(r)|p]α	ADJ
ejpam-6113	251	6	[	[	PUNCT
ejpam-6113	251	7	|ξ1(r)−f2ξ2(r)|p+|ξ2(r)−f1ξ1(r)|p	|ξ1(r)−f2ξ2(r)|p+|ξ2(r)−f1ξ1(r)|p	ADJ
ejpam-6113	251	8	2p	2p	NOUN
ejpam-6113	251	9	]	]	PUNCT
ejpam-6113	251	10	1−α−β−γ	1−α−β−γ	NUM
ejpam-6113	251	11	=	=	SYM
ejpam-6113	251	12	λ∆(ξ1	λ∆(ξ1	PROPN
ejpam-6113	251	13	,	,	PUNCT
ejpam-6113	251	14	ξ2	ξ2	NOUN
ejpam-6113	251	15	)	)	PUNCT
ejpam-6113	251	16	where	where	SCONJ
ejpam-6113	251	17	λ	λ	X
ejpam-6113	251	18	=	=	SYM
ejpam-6113	251	19	k	k	PROPN
ejpam-6113	251	20	s2	s2	PROPN
ejpam-6113	251	21	∈	∈	PROPN
ejpam-6113	251	22	(	(	PUNCT
ejpam-6113	251	23	0	0	NUM
ejpam-6113	251	24	,	,	PUNCT
ejpam-6113	251	25	1	1	NUM
ejpam-6113	251	26	)	)	PUNCT
ejpam-6113	251	27	.	.	PUNCT
ejpam-6113	252	1	as	as	ADP
ejpam-6113	252	2	a	a	DET
ejpam-6113	252	3	result	result	NOUN
ejpam-6113	252	4	,	,	PUNCT
ejpam-6113	252	5	f1,f2	f1,f2	PROPN
ejpam-6113	252	6	have	have	VERB
ejpam-6113	252	7	a	a	DET
ejpam-6113	252	8	unique	unique	ADJ
ejpam-6113	252	9	common	common	ADJ
ejpam-6113	252	10	solution	solution	NOUN
ejpam-6113	252	11	of	of	ADP
ejpam-6113	252	12	the	the	DET
ejpam-6113	252	13	system	system	NOUN
ejpam-6113	252	14	of	of	ADP
ejpam-6113	252	15	nonlinear	nonlinear	ADJ
ejpam-6113	252	16	integral	integral	ADJ
ejpam-6113	252	17	equations	equation	NOUN
ejpam-6113	252	18	specified	specify	VERB
ejpam-6113	252	19	in	in	ADP
ejpam-6113	252	20	(	(	PUNCT
ejpam-6113	252	21	3.1	3.1	NUM
ejpam-6113	252	22	)	)	PUNCT
ejpam-6113	252	23	,	,	PUNCT
ejpam-6113	252	24	since	since	SCONJ
ejpam-6113	252	25	all	all	DET
ejpam-6113	252	26	the	the	DET
ejpam-6113	252	27	requirements	requirement	NOUN
ejpam-6113	252	28	of	of	ADP
ejpam-6113	252	29	theorem	theorem	ADJ
ejpam-6113	252	30	4	4	NUM
ejpam-6113	252	31	are	be	AUX
ejpam-6113	252	32	satisfied	satisfied	ADJ
ejpam-6113	252	33	.	.	PUNCT
ejpam-6113	253	1	4	4	X
ejpam-6113	253	2	.	.	X
ejpam-6113	253	3	application	application	NOUN
ejpam-6113	253	4	to	to	ADP
ejpam-6113	253	5	dynamic	dynamic	ADJ
ejpam-6113	253	6	programming	programming	NOUN
ejpam-6113	253	7	the	the	DET
ejpam-6113	253	8	decision	decision	NOUN
ejpam-6113	253	9	space	space	NOUN
ejpam-6113	253	10	is	be	AUX
ejpam-6113	253	11	d	d	PROPN
ejpam-6113	253	12	⊆	⊆	NUM
ejpam-6113	253	13	x1	x1	NUM
ejpam-6113	253	14	,	,	PUNCT
ejpam-6113	253	15	and	and	CCONJ
ejpam-6113	253	16	the	the	DET
ejpam-6113	253	17	state	state	NOUN
ejpam-6113	253	18	space	space	NOUN
ejpam-6113	253	19	is	be	AUX
ejpam-6113	253	20	s	s	VERB
ejpam-6113	253	21	⊆	⊆	NUM
ejpam-6113	253	22	x2	x2	NOUN
ejpam-6113	253	23	.	.	PUNCT
ejpam-6113	254	1	x1	x1	PROPN
ejpam-6113	254	2	and	and	CCONJ
ejpam-6113	254	3	x2	x2	PROPN
ejpam-6113	254	4	are	be	AUX
ejpam-6113	254	5	assumed	assume	VERB
ejpam-6113	254	6	to	to	PART
ejpam-6113	254	7	be	be	AUX
ejpam-6113	254	8	two	two	NUM
ejpam-6113	254	9	banach	banach	NOUN
ejpam-6113	254	10	spaces	space	NOUN
ejpam-6113	254	11	in	in	ADP
ejpam-6113	254	12	this	this	DET
ejpam-6113	254	13	section	section	NOUN
ejpam-6113	254	14	.	.	PUNCT
ejpam-6113	255	1	all	all	DET
ejpam-6113	255	2	bounded	bound	VERB
ejpam-6113	255	3	real	real	ADJ
ejpam-6113	255	4	valued	value	VERB
ejpam-6113	255	5	functions	function	NOUN
ejpam-6113	255	6	on	on	ADP
ejpam-6113	255	7	s	s	NOUN
ejpam-6113	255	8	have	have	VERB
ejpam-6113	255	9	a	a	DET
ejpam-6113	255	10	banach	banach	NOUN
ejpam-6113	255	11	space	space	NOUN
ejpam-6113	255	12	called	call	VERB
ejpam-6113	255	13	ω(s	ω(s	PROPN
ejpam-6113	255	14	)	)	PUNCT
ejpam-6113	255	15	,	,	PUNCT
ejpam-6113	255	16	whose	whose	DET
ejpam-6113	255	17	b	b	NOUN
ejpam-6113	255	18	-	-	ADJ
ejpam-6113	255	19	metric	metric	ADJ
ejpam-6113	255	20	is	be	AUX
ejpam-6113	255	21	defined	define	VERB
ejpam-6113	255	22	as	as	ADP
ejpam-6113	255	23	follows	follow	VERB
ejpam-6113	255	24	:	:	PUNCT
ejpam-6113	255	25	d(ξ	d(ξ	PROPN
ejpam-6113	255	26	,	,	PUNCT
ejpam-6113	255	27	ζ	ζ	NOUN
ejpam-6113	255	28	)	)	PUNCT
ejpam-6113	255	29	=	=	SYM
ejpam-6113	255	30	sup	sup	NOUN
ejpam-6113	255	31	t∈s	t∈s	NOUN
ejpam-6113	255	32	|	|	NOUN
ejpam-6113	255	33	ξ(t	ξ(t	NOUN
ejpam-6113	255	34	)	)	PUNCT
ejpam-6113	255	35	−	−	ADP
ejpam-6113	255	36	ζ(t	ζ(t	PROPN
ejpam-6113	255	37	)	)	PUNCT
ejpam-6113	255	38	|p	|p	PROPN
ejpam-6113	255	39	,	,	PUNCT
ejpam-6113	255	40	∀	∀	X
ejpam-6113	255	41	ξ	ξ	NOUN
ejpam-6113	255	42	,	,	PUNCT
ejpam-6113	255	43	ζ	ζ	NOUN
ejpam-6113	255	44	∈	∈	NOUN
ejpam-6113	255	45	ω(s	ω(s	NOUN
ejpam-6113	255	46	)	)	PUNCT
ejpam-6113	255	47	with	with	ADP
ejpam-6113	255	48	coefficient	coefficient	NOUN
ejpam-6113	255	49	s	s	PART
ejpam-6113	255	50	=	=	X
ejpam-6113	255	51	2p−1	2p−1	PROPN
ejpam-6113	255	52	and	and	CCONJ
ejpam-6113	255	53	the	the	DET
ejpam-6113	255	54	norm	norm	NOUN
ejpam-6113	255	55	is	be	AUX
ejpam-6113	255	56	defined	define	VERB
ejpam-6113	255	57	as	as	ADP
ejpam-6113	255	58	∥f∥	∥f∥	PROPN
ejpam-6113	255	59	=	=	SYM
ejpam-6113	255	60	sup{|	sup{|	NOUN
ejpam-6113	255	61	f(t	f(t	PROPN
ejpam-6113	255	62	)	)	PUNCT
ejpam-6113	256	1	|	|	ADV
ejpam-6113	256	2	:	:	PUNCT
ejpam-6113	256	3	t	t	PROPN
ejpam-6113	256	4	∈	∈	PROPN
ejpam-6113	256	5	s	s	PART
ejpam-6113	256	6	}	}	PUNCT
ejpam-6113	256	7	,	,	PUNCT
ejpam-6113	256	8	where	where	SCONJ
ejpam-6113	256	9	f	f	PROPN
ejpam-6113	256	10	∈	∈	PROPN
ejpam-6113	256	11	ω(s	ω(s	PROPN
ejpam-6113	256	12	)	)	PUNCT
ejpam-6113	256	13	.	.	PUNCT
ejpam-6113	257	1	ω(s	ω(s	NOUN
ejpam-6113	257	2	,	,	PUNCT
ejpam-6113	257	3	d	d	X
ejpam-6113	257	4	)	)	PUNCT
ejpam-6113	257	5	is	be	AUX
ejpam-6113	257	6	obviously	obviously	ADV
ejpam-6113	257	7	a	a	DET
ejpam-6113	257	8	complete	complete	ADJ
ejpam-6113	257	9	b	b	X
ejpam-6113	257	10	-	-	PUNCT
ejpam-6113	257	11	metric	metric	ADJ
ejpam-6113	257	12	space	space	NOUN
ejpam-6113	257	13	.	.	PUNCT
ejpam-6113	258	1	according	accord	VERB
ejpam-6113	258	2	to	to	ADP
ejpam-6113	258	3	bellman	bellman	PROPN
ejpam-6113	258	4	et	et	PROPN
ejpam-6113	258	5	al	al	PROPN
ejpam-6113	258	6	.	.	PUNCT
ejpam-6113	259	1	[	[	X
ejpam-6113	259	2	4	4	NUM
ejpam-6113	259	3	]	]	PUNCT
ejpam-6113	259	4	,	,	PUNCT
ejpam-6113	259	5	the	the	DET
ejpam-6113	259	6	functional	functional	ADJ
ejpam-6113	259	7	equation	equation	NOUN
ejpam-6113	259	8	in	in	ADP
ejpam-6113	259	9	dynamic	dynamic	ADJ
ejpam-6113	259	10	programming	programming	NOUN
ejpam-6113	259	11	has	have	VERB
ejpam-6113	259	12	the	the	DET
ejpam-6113	259	13	following	following	ADJ
ejpam-6113	259	14	basic	basic	ADJ
ejpam-6113	259	15	form	form	NOUN
ejpam-6113	259	16	:	:	PUNCT
ejpam-6113	259	17	f(ξ	f(ξ	X
ejpam-6113	259	18	)	)	PUNCT
ejpam-6113	259	19	=	=	SYM
ejpam-6113	260	1	h	h	NOUN
ejpam-6113	260	2	ζ∈d̃	ζ∈d̃	NOUN
ejpam-6113	260	3	(	(	PUNCT
ejpam-6113	260	4	ξ	ξ	X
ejpam-6113	260	5	,	,	PUNCT
ejpam-6113	260	6	ζ	ζ	NOUN
ejpam-6113	260	7	,	,	PUNCT
ejpam-6113	260	8	f(t	f(t	PROPN
ejpam-6113	260	9	(	(	PUNCT
ejpam-6113	260	10	ξ	ξ	PROPN
ejpam-6113	260	11	,	,	PUNCT
ejpam-6113	260	12	ζ	ζ	NOUN
ejpam-6113	260	13	)	)	PUNCT
ejpam-6113	260	14	)	)	PUNCT
ejpam-6113	260	15	)	)	PUNCT
ejpam-6113	260	16	,	,	PUNCT
ejpam-6113	260	17	ξ	ξ	PROPN
ejpam-6113	260	18	∈	∈	PROPN
ejpam-6113	260	19	s	s	NOUN
ejpam-6113	260	20	,	,	PUNCT
ejpam-6113	260	21	where	where	SCONJ
ejpam-6113	260	22	t	t	PROPN
ejpam-6113	260	23	indicates	indicate	VERB
ejpam-6113	260	24	the	the	DET
ejpam-6113	260	25	process	process	NOUN
ejpam-6113	260	26	transformation	transformation	NOUN
ejpam-6113	260	27	,	,	PUNCT
ejpam-6113	260	28	f(ξ	f(ξ	PROPN
ejpam-6113	260	29	)	)	PUNCT
ejpam-6113	260	30	indicates	indicate	VERB
ejpam-6113	260	31	the	the	DET
ejpam-6113	260	32	optimal	optimal	ADJ
ejpam-6113	260	33	return	return	NOUN
ejpam-6113	260	34	function	function	NOUN
ejpam-6113	260	35	with	with	ADP
ejpam-6113	260	36	the	the	DET
ejpam-6113	260	37	initial	initial	ADJ
ejpam-6113	260	38	state	state	NOUN
ejpam-6113	260	39	ξ	ξ	PROPN
ejpam-6113	260	40	,	,	PUNCT
ejpam-6113	260	41	and	and	CCONJ
ejpam-6113	260	42	opt	opt	NOUN
ejpam-6113	260	43	stands	stand	VERB
ejpam-6113	260	44	for	for	ADP
ejpam-6113	260	45	sup	sup	NOUN
ejpam-6113	260	46	or	or	CCONJ
ejpam-6113	260	47	d.	d.	PROPN
ejpam-6113	260	48	r.	r.	PROPN
ejpam-6113	260	49	babu	babu	PROPN
ejpam-6113	260	50	,	,	PUNCT
ejpam-6113	260	51	k.	k.	PROPN
ejpam-6113	260	52	n.	n.	PROPN
ejpam-6113	260	53	k.	k.	PROPN
ejpam-6113	261	1	rao	rao	PROPN
ejpam-6113	261	2	/	/	SYM
ejpam-6113	261	3	eur	eur	PROPN
ejpam-6113	261	4	.	.	PUNCT
ejpam-6113	262	1	j.	j.	PROPN
ejpam-6113	262	2	pure	pure	PROPN
ejpam-6113	262	3	appl	appl	PROPN
ejpam-6113	262	4	.	.	PROPN
ejpam-6113	262	5	math	math	PROPN
ejpam-6113	262	6	,	,	PUNCT
ejpam-6113	262	7	18	18	NUM
ejpam-6113	262	8	(	(	PUNCT
ejpam-6113	262	9	3	3	NUM
ejpam-6113	262	10	)	)	PUNCT
ejpam-6113	262	11	(	(	PUNCT
ejpam-6113	262	12	2025	2025	NUM
ejpam-6113	262	13	)	)	PUNCT
ejpam-6113	262	14	,	,	PUNCT
ejpam-6113	262	15	6113	6113	NUM
ejpam-6113	262	16	10	10	NUM
ejpam-6113	262	17	of	of	ADP
ejpam-6113	262	18	14	14	NUM
ejpam-6113	262	19	inf	inf	NOUN
ejpam-6113	262	20	.	.	PUNCT
ejpam-6113	263	1	the	the	DET
ejpam-6113	263	2	state	state	NOUN
ejpam-6113	263	3	and	and	CCONJ
ejpam-6113	263	4	decision	decision	NOUN
ejpam-6113	263	5	vectors	vector	NOUN
ejpam-6113	263	6	are	be	AUX
ejpam-6113	263	7	denoted	denote	VERB
ejpam-6113	263	8	by	by	ADP
ejpam-6113	263	9	ξ	ξ	PROPN
ejpam-6113	263	10	and	and	CCONJ
ejpam-6113	263	11	ζ	ζ	NOUN
ejpam-6113	263	12	,	,	PUNCT
ejpam-6113	263	13	respectively	respectively	ADV
ejpam-6113	263	14	.	.	PUNCT
ejpam-6113	264	1	we	we	PRON
ejpam-6113	264	2	look	look	VERB
ejpam-6113	264	3	at	at	ADP
ejpam-6113	264	4	the	the	DET
ejpam-6113	264	5	functional	functional	ADJ
ejpam-6113	264	6	equation	equation	NOUN
ejpam-6113	264	7	system	system	PUNCT
ejpam-6113	264	8	f1(νs	f1(νs	PROPN
ejpam-6113	264	9	)	)	PUNCT
ejpam-6113	264	10	=	=	VERB
ejpam-6113	264	11	opt	opt	ADJ
ejpam-6113	264	12	νd∈d̃	νd∈d̃	PROPN
ejpam-6113	264	13	(	(	PUNCT
ejpam-6113	264	14	η1(νs	η1(νs	PROPN
ejpam-6113	264	15	,	,	PUNCT
ejpam-6113	264	16	νd	νd	PROPN
ejpam-6113	264	17	)	)	PUNCT
ejpam-6113	264	18	+	+	X
ejpam-6113	265	1	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	265	2	,	,	PUNCT
ejpam-6113	265	3	νd	νd	NOUN
ejpam-6113	265	4	,	,	PUNCT
ejpam-6113	265	5	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	265	6	,	,	PUNCT
ejpam-6113	265	7	νd))))∀νs	νd))))∀νs	ADP
ejpam-6113	265	8	∈	∈	PROPN
ejpam-6113	265	9	s	s	NOUN
ejpam-6113	265	10	,	,	PUNCT
ejpam-6113	265	11	f2(νs	f2(νs	PROPN
ejpam-6113	265	12	)	)	PUNCT
ejpam-6113	265	13	=	=	VERB
ejpam-6113	265	14	opt	opt	ADJ
ejpam-6113	265	15	νd∈d̃	νd∈d̃	PROPN
ejpam-6113	265	16	(	(	PUNCT
ejpam-6113	265	17	η2(νs	η2(νs	PROPN
ejpam-6113	265	18	,	,	PUNCT
ejpam-6113	265	19	νd	νd	PROPN
ejpam-6113	265	20	)	)	PUNCT
ejpam-6113	265	21	+	+	NUM
ejpam-6113	265	22	ξ2(νs	ξ2(νs	NUM
ejpam-6113	265	23	,	,	PUNCT
ejpam-6113	265	24	νd	νd	NOUN
ejpam-6113	265	25	,	,	PUNCT
ejpam-6113	265	26	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	265	27	,	,	PUNCT
ejpam-6113	265	28	νd))))∀νs	νd))))∀νs	ADP
ejpam-6113	265	29	∈	∈	PROPN
ejpam-6113	265	30	s	s	PART
ejpam-6113	265	31	(	(	PUNCT
ejpam-6113	265	32	4.1	4.1	NUM
ejpam-6113	265	33	)	)	PUNCT
ejpam-6113	265	34	where	where	SCONJ
ejpam-6113	265	35	the	the	DET
ejpam-6113	265	36	state	state	NOUN
ejpam-6113	265	37	vector	vector	NOUN
ejpam-6113	265	38	is	be	AUX
ejpam-6113	265	39	νs	νs	PRON
ejpam-6113	265	40	,	,	PUNCT
ejpam-6113	265	41	the	the	DET
ejpam-6113	265	42	decision	decision	NOUN
ejpam-6113	265	43	vector	vector	NOUN
ejpam-6113	265	44	is	be	AUX
ejpam-6113	265	45	νd	νd	NOUN
ejpam-6113	265	46	,	,	PUNCT
ejpam-6113	265	47	the	the	DET
ejpam-6113	265	48	process	process	NOUN
ejpam-6113	265	49	transformations	transformation	NOUN
ejpam-6113	265	50	are	be	AUX
ejpam-6113	265	51	represented	represent	VERB
ejpam-6113	265	52	by	by	ADP
ejpam-6113	265	53	ρ1	ρ1	NOUN
ejpam-6113	265	54	,	,	PUNCT
ejpam-6113	265	55	ρ2	ρ2	NOUN
ejpam-6113	265	56	,	,	PUNCT
ejpam-6113	265	57	and	and	CCONJ
ejpam-6113	265	58	the	the	DET
ejpam-6113	265	59	optimal	optimal	ADJ
ejpam-6113	265	60	return	return	NOUN
ejpam-6113	265	61	functions	function	NOUN
ejpam-6113	265	62	with	with	ADP
ejpam-6113	265	63	initial	initial	ADJ
ejpam-6113	265	64	state	state	NOUN
ejpam-6113	265	65	νs	νs	NOUN
ejpam-6113	265	66	are	be	AUX
ejpam-6113	265	67	indicated	indicate	VERB
ejpam-6113	265	68	by	by	ADP
ejpam-6113	265	69	f1(νs	f1(νs	PROPN
ejpam-6113	265	70	)	)	PUNCT
ejpam-6113	265	71	,	,	PUNCT
ejpam-6113	265	72	f2(νs	f2(νs	PROPN
ejpam-6113	265	73	)	)	PUNCT
ejpam-6113	265	74	.	.	PUNCT
ejpam-6113	266	1	let	let	VERB
ejpam-6113	267	1	f1,f2	f1,f2	PROPN
ejpam-6113	267	2	:	:	PUNCT
ejpam-6113	267	3	ω(s	ω(s	NUM
ejpam-6113	267	4	)	)	PUNCT
ejpam-6113	267	5	→	→	SYM
ejpam-6113	267	6	ω(s	ω(s	NUM
ejpam-6113	267	7	)	)	PUNCT
ejpam-6113	267	8	be	be	VERB
ejpam-6113	267	9	two	two	NUM
ejpam-6113	267	10	mappings	mapping	NOUN
ejpam-6113	267	11	defined	define	VERB
ejpam-6113	267	12	by;	by;	X
ejpam-6113	267	13	f1f1(νs	f1f1(νs	PROPN
ejpam-6113	267	14	)	)	PUNCT
ejpam-6113	268	1	=	=	PUNCT
ejpam-6113	268	2	opt	opt	ADJ
ejpam-6113	268	3	νd∈d̃	νd∈d̃	PROPN
ejpam-6113	268	4	(	(	PUNCT
ejpam-6113	268	5	η1(νs	η1(νs	PROPN
ejpam-6113	268	6	,	,	PUNCT
ejpam-6113	268	7	νd	νd	PROPN
ejpam-6113	268	8	)	)	PUNCT
ejpam-6113	268	9	+	+	X
ejpam-6113	268	10	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	268	11	,	,	PUNCT
ejpam-6113	268	12	νd	νd	NOUN
ejpam-6113	268	13	,	,	PUNCT
ejpam-6113	268	14	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	268	15	,	,	PUNCT
ejpam-6113	268	16	νd))))∀νs	νd))))∀νs	ADP
ejpam-6113	268	17	∈	∈	PROPN
ejpam-6113	268	18	s	s	NOUN
ejpam-6113	268	19	,	,	PUNCT
ejpam-6113	268	20	f2f2(νs	f2f2(νs	PROPN
ejpam-6113	268	21	)	)	PUNCT
ejpam-6113	268	22	=	=	PUNCT
ejpam-6113	268	23	opt	opt	ADJ
ejpam-6113	268	24	νd∈d̃	νd∈d̃	PROPN
ejpam-6113	268	25	(	(	PUNCT
ejpam-6113	268	26	η2(νs	η2(νs	PROPN
ejpam-6113	268	27	,	,	PUNCT
ejpam-6113	268	28	νd	νd	PROPN
ejpam-6113	268	29	)	)	PUNCT
ejpam-6113	268	30	+	+	NUM
ejpam-6113	268	31	ξ2(νs	ξ2(νs	NUM
ejpam-6113	268	32	,	,	PUNCT
ejpam-6113	268	33	νd	νd	NOUN
ejpam-6113	268	34	,	,	PUNCT
ejpam-6113	268	35	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	268	36	,	,	PUNCT
ejpam-6113	268	37	νd))))∀νs	νd))))∀νs	ADP
ejpam-6113	268	38	∈	∈	PROPN
ejpam-6113	268	39	s	s	PART
ejpam-6113	268	40	(	(	PUNCT
ejpam-6113	268	41	4.2	4.2	NUM
ejpam-6113	268	42	)	)	PUNCT
ejpam-6113	268	43	assume	assume	VERB
ejpam-6113	268	44	the	the	DET
ejpam-6113	268	45	following	follow	VERB
ejpam-6113	268	46	:	:	PUNCT
ejpam-6113	268	47	(	(	PUNCT
ejpam-6113	268	48	da	da	NOUN
ejpam-6113	268	49	)	)	PUNCT
ejpam-6113	268	50	for	for	ADP
ejpam-6113	268	51	all	all	PRON
ejpam-6113	268	52	(	(	PUNCT
ejpam-6113	268	53	νs	νs	NOUN
ejpam-6113	268	54	,	,	PUNCT
ejpam-6113	268	55	νd	νd	PROPN
ejpam-6113	268	56	,	,	PUNCT
ejpam-6113	268	57	f1	f1	NOUN
ejpam-6113	268	58	,	,	PUNCT
ejpam-6113	268	59	f2	f2	PROPN
ejpam-6113	268	60	)	)	PUNCT
ejpam-6113	268	61	∈	∈	PROPN
ejpam-6113	268	62	s×d×ω(s)×ω(s)×ω(s)×ω(s	s×d×ω(s)×ω(s)×ω(s)×ω(s	PROPN
ejpam-6113	268	63	)	)	PUNCT
ejpam-6113	268	64	and	and	CCONJ
ejpam-6113	268	65	there	there	PRON
ejpam-6113	268	66	exist	exist	VERB
ejpam-6113	268	67	0	0	NUM
ejpam-6113	268	68	<	<	X
ejpam-6113	268	69	h	h	X
ejpam-6113	268	70	<	<	X
ejpam-6113	268	71	1	1	NUM
ejpam-6113	268	72	and	and	CCONJ
ejpam-6113	268	73	0	0	NUM
ejpam-6113	268	74	<	<	X
ejpam-6113	268	75	α	α	X
ejpam-6113	268	76	<	<	X
ejpam-6113	268	77	1	1	NUM
ejpam-6113	268	78	,	,	PUNCT
ejpam-6113	268	79	such	such	ADJ
ejpam-6113	268	80	that	that	PRON
ejpam-6113	268	81	;	;	PUNCT
ejpam-6113	268	82	|	|	ADV
ejpam-6113	268	83	ξ1(νs	ξ1(νs	NUM
ejpam-6113	268	84	,	,	PUNCT
ejpam-6113	268	85	νd	νd	NOUN
ejpam-6113	268	86	,	,	PUNCT
ejpam-6113	268	87	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	268	88	,	,	PUNCT
ejpam-6113	268	89	νd)))−	νd)))−	PROPN
ejpam-6113	268	90	ξ2(νs	ξ2(νs	NUM
ejpam-6113	268	91	,	,	PUNCT
ejpam-6113	268	92	νd	νd	NOUN
ejpam-6113	268	93	,	,	PUNCT
ejpam-6113	268	94	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	268	95	,	,	PUNCT
ejpam-6113	268	96	νd	νd	NOUN
ejpam-6113	268	97	)	)	PUNCT
ejpam-6113	268	98	)	)	PUNCT
ejpam-6113	268	99	)	)	PUNCT
ejpam-6113	269	1	|	|	ADV
ejpam-6113	269	2	+	+	CCONJ
ejpam-6113	269	3	|	|	ADV
ejpam-6113	269	4	η1(νs	η1(νs	PROPN
ejpam-6113	269	5	,	,	PUNCT
ejpam-6113	269	6	νd)−	νd)−	NOUN
ejpam-6113	269	7	η2(νs	η2(νs	PROPN
ejpam-6113	269	8	,	,	PUNCT
ejpam-6113	269	9	νd	νd	PROPN
ejpam-6113	269	10	)	)	PUNCT
ejpam-6113	269	11	|	|	ADV
ejpam-6113	269	12	≤	≤	NOUN
ejpam-6113	269	13	[	[	PUNCT
ejpam-6113	269	14	h	h	NOUN
ejpam-6113	269	15	24p−4m(f1	24p−4m(f1	NOUN
ejpam-6113	269	16	,	,	PUNCT
ejpam-6113	269	17	f2	f2	PROPN
ejpam-6113	269	18	)	)	PUNCT
ejpam-6113	269	19	]	]	PUNCT
ejpam-6113	270	1	1	1	NUM
ejpam-6113	270	2	p	p	NOUN
ejpam-6113	270	3	where	where	SCONJ
ejpam-6113	270	4	m(f1	m(f1	NOUN
ejpam-6113	270	5	,	,	PUNCT
ejpam-6113	270	6	f2	f2	PROPN
ejpam-6113	270	7	)	)	PUNCT
ejpam-6113	270	8	=	=	PUNCT
ejpam-6113	271	1	[	[	X
ejpam-6113	271	2	|f1	|f1	NOUN
ejpam-6113	271	3	−f1f1|p]α	−f1f1|p]α	NOUN
ejpam-6113	271	4	[	[	X
ejpam-6113	271	5	|f2	|f2	ADP
ejpam-6113	271	6	−f2f2|p]1−α	−f2f2|p]1−α	PROPN
ejpam-6113	271	7	(	(	PUNCT
ejpam-6113	271	8	db	db	PROPN
ejpam-6113	271	9	)	)	PUNCT
ejpam-6113	271	10	ρi	ρi	PROPN
ejpam-6113	271	11	,	,	PUNCT
ejpam-6113	271	12	ξi	ξi	PROPN
ejpam-6113	271	13	are	be	AUX
ejpam-6113	271	14	bounded	bound	VERB
ejpam-6113	271	15	i	i	PRON
ejpam-6113	271	16	=	=	NOUN
ejpam-6113	271	17	1	1	NUM
ejpam-6113	271	18	,	,	PUNCT
ejpam-6113	271	19	2	2	NUM
ejpam-6113	271	20	.	.	X
ejpam-6113	271	21	theorem	theorem	ADJ
ejpam-6113	271	22	7	7	PROPN
ejpam-6113	271	23	.	.	PUNCT
ejpam-6113	271	24	assume	assume	VERB
ejpam-6113	271	25	f1,f2	f1,f2	PROPN
ejpam-6113	271	26	:	:	PUNCT
ejpam-6113	271	27	ω(s	ω(s	NUM
ejpam-6113	271	28	)	)	PUNCT
ejpam-6113	271	29	→	→	SYM
ejpam-6113	271	30	ω(s	ω(s	NUM
ejpam-6113	271	31	)	)	PUNCT
ejpam-6113	271	32	be	be	AUX
ejpam-6113	271	33	defined	define	VERB
ejpam-6113	271	34	by	by	ADP
ejpam-6113	271	35	(	(	PUNCT
ejpam-6113	271	36	4.2	4.2	NUM
ejpam-6113	271	37	)	)	PUNCT
ejpam-6113	271	38	for	for	ADP
ejpam-6113	271	39	which	which	PRON
ejpam-6113	271	40	the	the	DET
ejpam-6113	271	41	conditions	condition	NOUN
ejpam-6113	271	42	da	da	VERB
ejpam-6113	271	43	and	and	CCONJ
ejpam-6113	271	44	db	db	PROPN
ejpam-6113	271	45	are	be	AUX
ejpam-6113	271	46	satisfied	satisfied	ADJ
ejpam-6113	271	47	.	.	PUNCT
ejpam-6113	272	1	then	then	ADV
ejpam-6113	272	2	,	,	PUNCT
ejpam-6113	272	3	there	there	PRON
ejpam-6113	272	4	is	be	VERB
ejpam-6113	272	5	a	a	DET
ejpam-6113	272	6	unique	unique	ADJ
ejpam-6113	272	7	bounded	bounded	ADJ
ejpam-6113	272	8	common	common	ADJ
ejpam-6113	272	9	solution	solution	NOUN
ejpam-6113	272	10	in	in	ADP
ejpam-6113	272	11	ω(s	ω(s	PROPN
ejpam-6113	272	12	)	)	PUNCT
ejpam-6113	272	13	for	for	ADP
ejpam-6113	272	14	the	the	DET
ejpam-6113	272	15	system	system	NOUN
ejpam-6113	272	16	of	of	ADP
ejpam-6113	272	17	functional	functional	ADJ
ejpam-6113	272	18	equations	equation	NOUN
ejpam-6113	272	19	provided	provide	VERB
ejpam-6113	272	20	by	by	ADP
ejpam-6113	272	21	(	(	PUNCT
ejpam-6113	272	22	4.1	4.1	NUM
ejpam-6113	272	23	)	)	PUNCT
ejpam-6113	272	24	.	.	PUNCT
ejpam-6113	273	1	proof	proof	NOUN
ejpam-6113	273	2	.	.	PUNCT
ejpam-6113	274	1	let	let	VERB
ejpam-6113	274	2	νs	νs	PRON
ejpam-6113	274	3	∈	∈	PROPN
ejpam-6113	274	4	s	s	PROPN
ejpam-6113	274	5	,	,	PUNCT
ejpam-6113	274	6	f1	f1	NOUN
ejpam-6113	274	7	,	,	PUNCT
ejpam-6113	274	8	f2	f2	NOUN
ejpam-6113	274	9	∈	∈	PROPN
ejpam-6113	274	10	ω(s	ω(s	NOUN
ejpam-6113	274	11	)	)	PUNCT
ejpam-6113	274	12	and	and	CCONJ
ejpam-6113	274	13	ϵ	ϵ	X
ejpam-6113	274	14	>	>	X
ejpam-6113	274	15	0	0	X
ejpam-6113	274	16	.	.	PUNCT
ejpam-6113	275	1	as	as	ADP
ejpam-6113	275	2	ρi	ρi	PROPN
ejpam-6113	275	3	,	,	PUNCT
ejpam-6113	275	4	ξi	ξi	PROPN
ejpam-6113	275	5	are	be	AUX
ejpam-6113	275	6	bounded	bound	VERB
ejpam-6113	275	7	for	for	ADP
ejpam-6113	275	8	i	i	PROPN
ejpam-6113	275	9	=	=	NOUN
ejpam-6113	275	10	1	1	NUM
ejpam-6113	275	11	,	,	PUNCT
ejpam-6113	275	12	2	2	NUM
ejpam-6113	275	13	∃	∃	PROPN
ejpam-6113	275	14	l	l	PROPN
ejpam-6113	275	15	≥	≥	PROPN
ejpam-6113	275	16	0	0	NUM
ejpam-6113	275	17	∋	∋	NOUN
ejpam-6113	275	18	sup{||ρ1(νs	sup{||ρ1(ν	NOUN
ejpam-6113	275	19	,	,	PUNCT
ejpam-6113	275	20	νd)||	νd)||	NOUN
ejpam-6113	275	21	,	,	PUNCT
ejpam-6113	275	22	||ρ2(νs	||ρ2(νs	PROPN
ejpam-6113	275	23	,	,	PUNCT
ejpam-6113	275	24	νd)||	νd)||	NOUN
ejpam-6113	275	25	,	,	PUNCT
ejpam-6113	275	26	||ξ2(νs	||ξ2(νs	NOUN
ejpam-6113	275	27	,	,	PUNCT
ejpam-6113	275	28	νd	νd	PROPN
ejpam-6113	275	29	,	,	PUNCT
ejpam-6113	275	30	t)||	t)||	NOUN
ejpam-6113	275	31	:	:	PUNCT
ejpam-6113	275	32	(	(	PUNCT
ejpam-6113	276	1	νs	νs	NOUN
ejpam-6113	276	2	,	,	PUNCT
ejpam-6113	276	3	νd	νd	PROPN
ejpam-6113	276	4	,	,	PUNCT
ejpam-6113	276	5	t	t	PROPN
ejpam-6113	276	6	)	)	PUNCT
ejpam-6113	276	7	∈	∈	PROPN
ejpam-6113	276	8	s	s	PART
ejpam-6113	276	9	×	×	NOUN
ejpam-6113	276	10	d	d	X
ejpam-6113	276	11	×	×	NOUN
ejpam-6113	276	12	r	r	NOUN
ejpam-6113	276	13	}	}	PUNCT
ejpam-6113	276	14	≤	≤	PROPN
ejpam-6113	276	15	l.	l.	NOUN
ejpam-6113	276	16	(	(	PUNCT
ejpam-6113	276	17	4.3	4.3	NUM
ejpam-6113	276	18	)	)	PUNCT
ejpam-6113	276	19	from	from	ADP
ejpam-6113	276	20	the	the	DET
ejpam-6113	276	21	inequalities	inequality	NOUN
ejpam-6113	276	22	(	(	PUNCT
ejpam-6113	276	23	4.2	4.2	NUM
ejpam-6113	276	24	)	)	PUNCT
ejpam-6113	276	25	and	and	CCONJ
ejpam-6113	276	26	(	(	PUNCT
ejpam-6113	276	27	4.3	4.3	NUM
ejpam-6113	276	28	)	)	PUNCT
ejpam-6113	276	29	,	,	PUNCT
ejpam-6113	276	30	we	we	PRON
ejpam-6113	276	31	conclude	conclude	VERB
ejpam-6113	276	32	that	that	SCONJ
ejpam-6113	276	33	f1,f2	f1,f2	PROPN
ejpam-6113	276	34	are	be	AUX
ejpam-6113	276	35	self	self	NOUN
ejpam-6113	276	36	mappings	mapping	NOUN
ejpam-6113	276	37	of	of	ADP
ejpam-6113	276	38	ω(s	ω(s	PROPN
ejpam-6113	276	39	)	)	PUNCT
ejpam-6113	276	40	first	first	ADV
ejpam-6113	276	41	assume	assume	VERB
ejpam-6113	276	42	that	that	SCONJ
ejpam-6113	276	43	opt	opt	VERB
ejpam-6113	276	44	νs∈d̃	νs∈d̃	ADJ
ejpam-6113	276	45	=	=	SYM
ejpam-6113	276	46	inf	inf	NOUN
ejpam-6113	276	47	νd∈d	νd∈d	NOUN
ejpam-6113	276	48	.	.	PUNCT
ejpam-6113	277	1	the	the	DET
ejpam-6113	277	2	inequality	inequality	NOUN
ejpam-6113	277	3	(	(	PUNCT
ejpam-6113	277	4	4.2	4.2	NUM
ejpam-6113	277	5	)	)	PUNCT
ejpam-6113	277	6	allows	allow	VERB
ejpam-6113	277	7	us	we	PRON
ejpam-6113	277	8	to	to	PART
ejpam-6113	277	9	determine	determine	VERB
ejpam-6113	277	10	νd	νd	NOUN
ejpam-6113	277	11	∈	∈	PROPN
ejpam-6113	277	12	d	d	NOUN
ejpam-6113	277	13	and	and	CCONJ
ejpam-6113	277	14	(	(	PUNCT
ejpam-6113	277	15	νs	νs	NOUN
ejpam-6113	277	16	,	,	PUNCT
ejpam-6113	277	17	f	f	PROPN
ejpam-6113	277	18	,	,	PUNCT
ejpam-6113	277	19	g	g	NOUN
ejpam-6113	277	20	)	)	PUNCT
ejpam-6113	277	21	∈	∈	PROPN
ejpam-6113	277	22	s	s	PART
ejpam-6113	277	23	×ω(s)×ω(s	×ω(s)×ω(s	PROPN
ejpam-6113	277	24	)	)	PUNCT
ejpam-6113	277	25	such	such	ADJ
ejpam-6113	277	26	that	that	SCONJ
ejpam-6113	277	27	f1f1(νs	f1f1(νs	NOUN
ejpam-6113	277	28	)	)	PUNCT
ejpam-6113	277	29	>	>	X
ejpam-6113	278	1	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	278	2	,	,	PUNCT
ejpam-6113	278	3	νd	νd	NOUN
ejpam-6113	278	4	,	,	PUNCT
ejpam-6113	278	5	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	278	6	,	,	PUNCT
ejpam-6113	278	7	νd	νd	NOUN
ejpam-6113	278	8	)	)	PUNCT
ejpam-6113	278	9	)	)	PUNCT
ejpam-6113	278	10	)	)	PUNCT
ejpam-6113	279	1	+	+	PUNCT
ejpam-6113	280	1	η1(νs	η1(νs	PROPN
ejpam-6113	280	2	,	,	PUNCT
ejpam-6113	280	3	νd)−	νd)−	X
ejpam-6113	280	4	ϵ	ϵ	X
ejpam-6113	280	5	(	(	PUNCT
ejpam-6113	280	6	4.4	4.4	NUM
ejpam-6113	280	7	)	)	PUNCT
ejpam-6113	280	8	f1f2(νs	f1f2(νs	PROPN
ejpam-6113	280	9	)	)	PUNCT
ejpam-6113	280	10	>	>	X
ejpam-6113	281	1	ξ2(νs	ξ2(νs	NUM
ejpam-6113	281	2	,	,	PUNCT
ejpam-6113	281	3	νd	νd	NOUN
ejpam-6113	281	4	,	,	PUNCT
ejpam-6113	281	5	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	281	6	,	,	PUNCT
ejpam-6113	281	7	νd	νd	NOUN
ejpam-6113	281	8	)	)	PUNCT
ejpam-6113	281	9	)	)	PUNCT
ejpam-6113	281	10	)	)	PUNCT
ejpam-6113	282	1	+	+	CCONJ
ejpam-6113	282	2	η2(νs	η2(ν	NOUN
ejpam-6113	282	3	,	,	PUNCT
ejpam-6113	282	4	νd)−	νd)−	X
ejpam-6113	282	5	ϵ	ϵ	X
ejpam-6113	282	6	(	(	PUNCT
ejpam-6113	282	7	4.5	4.5	NUM
ejpam-6113	282	8	)	)	PUNCT
ejpam-6113	282	9	d.	d.	PROPN
ejpam-6113	282	10	r.	r.	PROPN
ejpam-6113	282	11	babu	babu	PROPN
ejpam-6113	282	12	,	,	PUNCT
ejpam-6113	282	13	k.	k.	PROPN
ejpam-6113	282	14	n.	n.	PROPN
ejpam-6113	282	15	k.	k.	PROPN
ejpam-6113	282	16	rao	rao	PROPN
ejpam-6113	282	17	/	/	SYM
ejpam-6113	282	18	eur	eur	PROPN
ejpam-6113	282	19	.	.	PUNCT
ejpam-6113	283	1	j.	j.	PROPN
ejpam-6113	283	2	pure	pure	PROPN
ejpam-6113	283	3	appl	appl	PROPN
ejpam-6113	283	4	.	.	PROPN
ejpam-6113	283	5	math	math	PROPN
ejpam-6113	283	6	,	,	PUNCT
ejpam-6113	283	7	18	18	NUM
ejpam-6113	283	8	(	(	PUNCT
ejpam-6113	283	9	3	3	NUM
ejpam-6113	283	10	)	)	PUNCT
ejpam-6113	283	11	(	(	PUNCT
ejpam-6113	283	12	2025	2025	NUM
ejpam-6113	283	13	)	)	PUNCT
ejpam-6113	283	14	,	,	PUNCT
ejpam-6113	283	15	6113	6113	NUM
ejpam-6113	283	16	11	11	NUM
ejpam-6113	283	17	of	of	ADP
ejpam-6113	283	18	14	14	NUM
ejpam-6113	283	19	f1f1(νs	f1f1(νs	NOUN
ejpam-6113	283	20	)	)	PUNCT
ejpam-6113	283	21	≤	≤	NOUN
ejpam-6113	284	1	ξ1(νs	ξ1(νs	NUM
ejpam-6113	284	2	,	,	PUNCT
ejpam-6113	284	3	νd	νd	NOUN
ejpam-6113	284	4	,	,	PUNCT
ejpam-6113	284	5	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	284	6	,	,	PUNCT
ejpam-6113	284	7	νd	νd	NOUN
ejpam-6113	284	8	)	)	PUNCT
ejpam-6113	284	9	)	)	PUNCT
ejpam-6113	284	10	)	)	PUNCT
ejpam-6113	285	1	+	+	PUNCT
ejpam-6113	285	2	η1(νs	η1(νs	PROPN
ejpam-6113	285	3	,	,	PUNCT
ejpam-6113	285	4	νd	νd	PROPN
ejpam-6113	285	5	)	)	PUNCT
ejpam-6113	285	6	(	(	PUNCT
ejpam-6113	285	7	4.6	4.6	NUM
ejpam-6113	285	8	)	)	PUNCT
ejpam-6113	285	9	f1f2(νs	f1f2(νs	PROPN
ejpam-6113	285	10	)	)	PUNCT
ejpam-6113	285	11	≤	≤	NOUN
ejpam-6113	285	12	ξ2(νs	ξ2(νs	NUM
ejpam-6113	285	13	,	,	PUNCT
ejpam-6113	285	14	νd	νd	NOUN
ejpam-6113	285	15	,	,	PUNCT
ejpam-6113	285	16	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	285	17	,	,	PUNCT
ejpam-6113	285	18	νd	νd	NOUN
ejpam-6113	285	19	)	)	PUNCT
ejpam-6113	285	20	)	)	PUNCT
ejpam-6113	285	21	)	)	PUNCT
ejpam-6113	286	1	+	+	CCONJ
ejpam-6113	286	2	η2(νs	η2(νs	PROPN
ejpam-6113	286	3	,	,	PUNCT
ejpam-6113	286	4	νd	νd	PROPN
ejpam-6113	286	5	)	)	PUNCT
ejpam-6113	286	6	(	(	PUNCT
ejpam-6113	286	7	4.7	4.7	NUM
ejpam-6113	286	8	)	)	PUNCT
ejpam-6113	286	9	by	by	ADP
ejpam-6113	286	10	using	use	VERB
ejpam-6113	286	11	the	the	DET
ejpam-6113	286	12	inequalities	inequality	NOUN
ejpam-6113	286	13	(	(	PUNCT
ejpam-6113	286	14	4.4	4.4	NUM
ejpam-6113	286	15	)	)	PUNCT
ejpam-6113	286	16	and	and	CCONJ
ejpam-6113	286	17	(	(	PUNCT
ejpam-6113	286	18	4.7	4.7	NUM
ejpam-6113	286	19	)	)	PUNCT
ejpam-6113	286	20	,	,	PUNCT
ejpam-6113	286	21	we	we	PRON
ejpam-6113	286	22	get	get	VERB
ejpam-6113	286	23	that	that	NUM
ejpam-6113	286	24	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	286	25	)	)	PUNCT
ejpam-6113	286	26	>	>	X
ejpam-6113	287	1	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	287	2	,	,	PUNCT
ejpam-6113	287	3	νd	νd	NOUN
ejpam-6113	287	4	,	,	PUNCT
ejpam-6113	287	5	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	287	6	,	,	PUNCT
ejpam-6113	287	7	νd)))−	νd)))−	PROPN
ejpam-6113	287	8	ξ2(νs	ξ2(νs	NUM
ejpam-6113	287	9	,	,	PUNCT
ejpam-6113	287	10	νd	νd	NOUN
ejpam-6113	287	11	,	,	PUNCT
ejpam-6113	287	12	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	287	13	,	,	PUNCT
ejpam-6113	287	14	νd	νd	NOUN
ejpam-6113	287	15	)	)	PUNCT
ejpam-6113	287	16	)	)	PUNCT
ejpam-6113	287	17	)	)	PUNCT
ejpam-6113	288	1	+	+	PUNCT
ejpam-6113	288	2	η1(νs	η1(νs	PROPN
ejpam-6113	288	3	,	,	PUNCT
ejpam-6113	288	4	νd)−	νd)−	NOUN
ejpam-6113	288	5	η2(νs	η2(νs	PROPN
ejpam-6113	288	6	,	,	PUNCT
ejpam-6113	288	7	νd)−	νd)−	X
ejpam-6113	288	8	ϵ	ϵ	DET
ejpam-6113	288	9	≥	≥	NOUN
ejpam-6113	288	10	−{|	−{|	X
ejpam-6113	288	11	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	288	12	,	,	PUNCT
ejpam-6113	288	13	νd	νd	NOUN
ejpam-6113	288	14	,	,	PUNCT
ejpam-6113	288	15	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	288	16	,	,	PUNCT
ejpam-6113	288	17	νd)))−	νd)))−	PROPN
ejpam-6113	288	18	ξ2(νs	ξ2(νs	NUM
ejpam-6113	288	19	,	,	PUNCT
ejpam-6113	288	20	νd	νd	NOUN
ejpam-6113	288	21	,	,	PUNCT
ejpam-6113	288	22	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	288	23	,	,	PUNCT
ejpam-6113	288	24	νd	νd	NOUN
ejpam-6113	288	25	)	)	PUNCT
ejpam-6113	288	26	)	)	PUNCT
ejpam-6113	288	27	)	)	PUNCT
ejpam-6113	289	1	|	|	ADV
ejpam-6113	289	2	+	+	CCONJ
ejpam-6113	289	3	|	|	ADV
ejpam-6113	289	4	η1(νs	η1(νs	PROPN
ejpam-6113	289	5	,	,	PUNCT
ejpam-6113	289	6	νd)−	νd)−	NOUN
ejpam-6113	289	7	η2(νs	η2(νs	PROPN
ejpam-6113	289	8	,	,	PUNCT
ejpam-6113	289	9	νd	νd	PROPN
ejpam-6113	289	10	)	)	PUNCT
ejpam-6113	289	11	|	|	ADV
ejpam-6113	290	1	+	+	ADP
ejpam-6113	290	2	ϵ	ϵ	X
ejpam-6113	290	3	}	}	PUNCT
ejpam-6113	290	4	(	(	PUNCT
ejpam-6113	290	5	4.8	4.8	NUM
ejpam-6113	290	6	)	)	PUNCT
ejpam-6113	290	7	also	also	ADV
ejpam-6113	290	8	,	,	PUNCT
ejpam-6113	290	9	from	from	ADP
ejpam-6113	290	10	(	(	PUNCT
ejpam-6113	290	11	4.5	4.5	NUM
ejpam-6113	290	12	)	)	PUNCT
ejpam-6113	290	13	and	and	CCONJ
ejpam-6113	290	14	(	(	PUNCT
ejpam-6113	290	15	4.6	4.6	NUM
ejpam-6113	290	16	)	)	PUNCT
ejpam-6113	290	17	,	,	PUNCT
ejpam-6113	290	18	we	we	PRON
ejpam-6113	290	19	have	have	NUM
ejpam-6113	290	20	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(νs	PROPN
ejpam-6113	290	21	)	)	PUNCT
ejpam-6113	290	22	≤	≤	NOUN
ejpam-6113	290	23	ξ1(νs	ξ1(νs	NUM
ejpam-6113	290	24	,	,	PUNCT
ejpam-6113	290	25	νd	νd	NOUN
ejpam-6113	290	26	,	,	PUNCT
ejpam-6113	290	27	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	290	28	,	,	PUNCT
ejpam-6113	290	29	νd)))−	νd)))−	PROPN
ejpam-6113	290	30	ξ2(νs	ξ2(νs	NUM
ejpam-6113	290	31	,	,	PUNCT
ejpam-6113	290	32	νd	νd	NOUN
ejpam-6113	290	33	,	,	PUNCT
ejpam-6113	290	34	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	290	35	,	,	PUNCT
ejpam-6113	290	36	νd	νd	NOUN
ejpam-6113	290	37	)	)	PUNCT
ejpam-6113	290	38	)	)	PUNCT
ejpam-6113	290	39	)	)	PUNCT
ejpam-6113	291	1	+	+	PUNCT
ejpam-6113	291	2	η1(νs	η1(νs	PROPN
ejpam-6113	291	3	,	,	PUNCT
ejpam-6113	291	4	νd)−	νd)−	X
ejpam-6113	291	5	η2(νs	η2(νs	PROPN
ejpam-6113	291	6	,	,	PUNCT
ejpam-6113	291	7	νd	νd	PROPN
ejpam-6113	291	8	)	)	PUNCT
ejpam-6113	291	9	+	+	NUM
ejpam-6113	291	10	ϵ	ϵ	ADP
ejpam-6113	291	11	≤|	≤|	NOUN
ejpam-6113	291	12	ξ1(νs	ξ1(ν	NOUN
ejpam-6113	291	13	,	,	PUNCT
ejpam-6113	291	14	νd	νd	NOUN
ejpam-6113	291	15	,	,	PUNCT
ejpam-6113	291	16	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	291	17	,	,	PUNCT
ejpam-6113	291	18	νd)))−	νd)))−	PROPN
ejpam-6113	291	19	ξ2(νs	ξ2(νs	NUM
ejpam-6113	291	20	,	,	PUNCT
ejpam-6113	291	21	νd	νd	NOUN
ejpam-6113	291	22	,	,	PUNCT
ejpam-6113	291	23	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	291	24	,	,	PUNCT
ejpam-6113	291	25	νd	νd	NOUN
ejpam-6113	291	26	)	)	PUNCT
ejpam-6113	291	27	)	)	PUNCT
ejpam-6113	291	28	)	)	PUNCT
ejpam-6113	292	1	|	|	ADV
ejpam-6113	292	2	+	+	CCONJ
ejpam-6113	292	3	|	|	ADV
ejpam-6113	292	4	η1(νs	η1(νs	PROPN
ejpam-6113	292	5	,	,	PUNCT
ejpam-6113	292	6	νd)−	νd)−	NOUN
ejpam-6113	292	7	η2(νs	η2(νs	PROPN
ejpam-6113	292	8	,	,	PUNCT
ejpam-6113	292	9	νd	νd	PROPN
ejpam-6113	292	10	)	)	PUNCT
ejpam-6113	292	11	|	|	NOUN
ejpam-6113	292	12	+	+	ADP
ejpam-6113	292	13	ϵ	ϵ	X
ejpam-6113	292	14	(	(	PUNCT
ejpam-6113	292	15	4.9	4.9	NUM
ejpam-6113	292	16	)	)	PUNCT
ejpam-6113	292	17	by	by	ADP
ejpam-6113	292	18	using	use	VERB
ejpam-6113	292	19	(	(	PUNCT
ejpam-6113	292	20	4.8	4.8	NUM
ejpam-6113	292	21	)	)	PUNCT
ejpam-6113	292	22	and	and	CCONJ
ejpam-6113	292	23	(	(	PUNCT
ejpam-6113	292	24	4.9	4.9	NUM
ejpam-6113	292	25	)	)	PUNCT
ejpam-6113	292	26	,	,	PUNCT
ejpam-6113	292	27	we	we	PRON
ejpam-6113	292	28	get	get	VERB
ejpam-6113	292	29	that	that	PRON
ejpam-6113	292	30	|	|	NOUN
ejpam-6113	292	31	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	292	32	)	)	PUNCT
ejpam-6113	293	1	|	|	ADV
ejpam-6113	293	2	<	<	X
ejpam-6113	293	3	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	293	4	,	,	PUNCT
ejpam-6113	293	5	νd	νd	NOUN
ejpam-6113	293	6	,	,	PUNCT
ejpam-6113	293	7	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	293	8	,	,	PUNCT
ejpam-6113	293	9	νd)))−	νd)))−	PROPN
ejpam-6113	293	10	ξ2(νs	ξ2(νs	NUM
ejpam-6113	293	11	,	,	PUNCT
ejpam-6113	293	12	νd	νd	NOUN
ejpam-6113	293	13	,	,	PUNCT
ejpam-6113	293	14	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	293	15	,	,	PUNCT
ejpam-6113	293	16	νd	νd	NOUN
ejpam-6113	293	17	)	)	PUNCT
ejpam-6113	293	18	)	)	PUNCT
ejpam-6113	293	19	)	)	PUNCT
ejpam-6113	294	1	+	+	PUNCT
ejpam-6113	294	2	η1(νs	η1(νs	PROPN
ejpam-6113	294	3	,	,	PUNCT
ejpam-6113	294	4	νd)−	νd)−	X
ejpam-6113	294	5	η2(νs	η2(νs	PROPN
ejpam-6113	294	6	,	,	PUNCT
ejpam-6113	294	7	νd	νd	PROPN
ejpam-6113	294	8	)	)	PUNCT
ejpam-6113	294	9	+	+	CCONJ
ejpam-6113	294	10	ϵ	ϵ	X
ejpam-6113	294	11	≤	≤	NUM
ejpam-6113	294	12	ξ1(νs	ξ1(νs	NUM
ejpam-6113	294	13	,	,	PUNCT
ejpam-6113	294	14	νd	νd	NOUN
ejpam-6113	294	15	,	,	PUNCT
ejpam-6113	294	16	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	294	17	,	,	PUNCT
ejpam-6113	294	18	νd)))−	νd)))−	PROPN
ejpam-6113	294	19	ξ2(νs	ξ2(νs	NUM
ejpam-6113	294	20	,	,	PUNCT
ejpam-6113	294	21	νd	νd	NOUN
ejpam-6113	294	22	,	,	PUNCT
ejpam-6113	294	23	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	294	24	,	,	PUNCT
ejpam-6113	294	25	νd	νd	NOUN
ejpam-6113	294	26	)	)	PUNCT
ejpam-6113	294	27	)	)	PUNCT
ejpam-6113	294	28	)	)	PUNCT
ejpam-6113	295	1	+	+	PUNCT
ejpam-6113	295	2	η1(νs	η1(νs	PROPN
ejpam-6113	295	3	,	,	PUNCT
ejpam-6113	295	4	νd)−	νd)−	X
ejpam-6113	295	5	η2(νs	η2(νs	PROPN
ejpam-6113	295	6	,	,	PUNCT
ejpam-6113	295	7	νd	νd	PROPN
ejpam-6113	295	8	)	)	PUNCT
ejpam-6113	295	9	+	+	CCONJ
ejpam-6113	295	10	ϵ	ϵ	ADP
ejpam-6113	295	11	now	now	ADV
ejpam-6113	295	12	,	,	PUNCT
ejpam-6113	295	13	we	we	PRON
ejpam-6113	295	14	support	support	VERB
ejpam-6113	295	15	that	that	PRON
ejpam-6113	295	16	opt	opt	VERB
ejpam-6113	295	17	νd∈d̃	νd∈d̃	ADV
ejpam-6113	295	18	=	=	SYM
ejpam-6113	295	19	sup	sup	NOUN
ejpam-6113	295	20	νd∈d	νd∈d	ADV
ejpam-6113	295	21	.	.	PUNCT
ejpam-6113	296	1	from	from	ADP
ejpam-6113	296	2	(	(	PUNCT
ejpam-6113	296	3	4.2	4.2	NUM
ejpam-6113	296	4	)	)	PUNCT
ejpam-6113	296	5	,	,	PUNCT
ejpam-6113	296	6	we	we	PRON
ejpam-6113	296	7	can	can	AUX
ejpam-6113	296	8	determine	determine	VERB
ejpam-6113	296	9	νd	νd	NOUN
ejpam-6113	296	10	∈	∈	PROPN
ejpam-6113	296	11	d	d	NOUN
ejpam-6113	296	12	and	and	CCONJ
ejpam-6113	296	13	(	(	PUNCT
ejpam-6113	296	14	νs	νs	NOUN
ejpam-6113	296	15	,	,	PUNCT
ejpam-6113	296	16	f	f	PROPN
ejpam-6113	296	17	,	,	PUNCT
ejpam-6113	296	18	g	g	NOUN
ejpam-6113	296	19	)	)	PUNCT
ejpam-6113	296	20	∈	∈	PROPN
ejpam-6113	296	21	s	s	PART
ejpam-6113	296	22	×	×	NOUN
ejpam-6113	296	23	ω(s)×	ω(s)×	PROPN
ejpam-6113	296	24	ω(s	ω(s	NOUN
ejpam-6113	296	25	)	)	PUNCT
ejpam-6113	296	26	such	such	ADJ
ejpam-6113	296	27	that	that	SCONJ
ejpam-6113	296	28	f1f1(νs	f1f1(νs	NOUN
ejpam-6113	296	29	)	)	PUNCT
ejpam-6113	296	30	<	<	X
ejpam-6113	297	1	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	297	2	,	,	PUNCT
ejpam-6113	297	3	νd	νd	NOUN
ejpam-6113	297	4	,	,	PUNCT
ejpam-6113	297	5	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	297	6	,	,	PUNCT
ejpam-6113	297	7	νd	νd	NOUN
ejpam-6113	297	8	)	)	PUNCT
ejpam-6113	297	9	)	)	PUNCT
ejpam-6113	297	10	)	)	PUNCT
ejpam-6113	298	1	+	+	PUNCT
ejpam-6113	298	2	η1(νs	η1(νs	PROPN
ejpam-6113	298	3	,	,	PUNCT
ejpam-6113	298	4	νd	νd	NOUN
ejpam-6113	298	5	)	)	PUNCT
ejpam-6113	299	1	+	+	CCONJ
ejpam-6113	299	2	ϵ	ϵ	X
ejpam-6113	299	3	(	(	PUNCT
ejpam-6113	299	4	4.10	4.10	NUM
ejpam-6113	299	5	)	)	PUNCT
ejpam-6113	299	6	f1f2(νs	f1f2(ν	NOUN
ejpam-6113	299	7	)	)	PUNCT
ejpam-6113	299	8	<	<	X
ejpam-6113	299	9	ξ2(νs	ξ2(νs	NUM
ejpam-6113	299	10	,	,	PUNCT
ejpam-6113	299	11	νd	νd	NOUN
ejpam-6113	299	12	,	,	PUNCT
ejpam-6113	299	13	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	299	14	,	,	PUNCT
ejpam-6113	299	15	νd	νd	NOUN
ejpam-6113	299	16	)	)	PUNCT
ejpam-6113	299	17	)	)	PUNCT
ejpam-6113	299	18	)	)	PUNCT
ejpam-6113	300	1	+	+	CCONJ
ejpam-6113	300	2	η2(νs	η2(νs	PROPN
ejpam-6113	300	3	,	,	PUNCT
ejpam-6113	300	4	νd	νd	PROPN
ejpam-6113	300	5	)	)	PUNCT
ejpam-6113	300	6	+	+	CCONJ
ejpam-6113	300	7	ϵ	ϵ	X
ejpam-6113	300	8	(	(	PUNCT
ejpam-6113	300	9	4.11	4.11	NUM
ejpam-6113	300	10	)	)	PUNCT
ejpam-6113	300	11	f1f1(νs	f1f1(νs	NOUN
ejpam-6113	300	12	)	)	PUNCT
ejpam-6113	300	13	<	<	X
ejpam-6113	301	1	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	301	2	,	,	PUNCT
ejpam-6113	301	3	νd	νd	NOUN
ejpam-6113	301	4	,	,	PUNCT
ejpam-6113	301	5	f1(ρ1(νs	f1(ρ1(νs	PROPN
ejpam-6113	301	6	,	,	PUNCT
ejpam-6113	301	7	νd	νd	NOUN
ejpam-6113	301	8	)	)	PUNCT
ejpam-6113	301	9	)	)	PUNCT
ejpam-6113	301	10	)	)	PUNCT
ejpam-6113	302	1	+	+	PUNCT
ejpam-6113	302	2	η1(νs	η1(νs	PROPN
ejpam-6113	302	3	,	,	PUNCT
ejpam-6113	302	4	νd	νd	PROPN
ejpam-6113	302	5	)	)	PUNCT
ejpam-6113	302	6	(	(	PUNCT
ejpam-6113	302	7	4.12	4.12	NUM
ejpam-6113	302	8	)	)	PUNCT
ejpam-6113	302	9	f1f2(νs	f1f2(νs	PROPN
ejpam-6113	302	10	)	)	PUNCT
ejpam-6113	302	11	<	<	X
ejpam-6113	302	12	ξ2(νs	ξ2(νs	NUM
ejpam-6113	302	13	,	,	PUNCT
ejpam-6113	302	14	νd	νd	NOUN
ejpam-6113	302	15	,	,	PUNCT
ejpam-6113	302	16	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	302	17	,	,	PUNCT
ejpam-6113	302	18	νd	νd	NOUN
ejpam-6113	302	19	)	)	PUNCT
ejpam-6113	302	20	)	)	PUNCT
ejpam-6113	302	21	)	)	PUNCT
ejpam-6113	303	1	+	+	CCONJ
ejpam-6113	303	2	η2(νs	η2(νs	PROPN
ejpam-6113	303	3	,	,	PUNCT
ejpam-6113	303	4	νd	νd	PROPN
ejpam-6113	303	5	)	)	PUNCT
ejpam-6113	303	6	(	(	PUNCT
ejpam-6113	303	7	4.13	4.13	NUM
ejpam-6113	303	8	)	)	PUNCT
ejpam-6113	303	9	using	use	VERB
ejpam-6113	303	10	the	the	DET
ejpam-6113	303	11	inequalities	inequality	NOUN
ejpam-6113	303	12	(	(	PUNCT
ejpam-6113	303	13	4.10	4.10	NUM
ejpam-6113	303	14	)	)	PUNCT
ejpam-6113	303	15	and	and	CCONJ
ejpam-6113	303	16	(	(	PUNCT
ejpam-6113	303	17	4.13	4.13	NUM
ejpam-6113	303	18	)	)	PUNCT
ejpam-6113	303	19	,	,	PUNCT
ejpam-6113	303	20	we	we	PRON
ejpam-6113	303	21	have	have	NUM
ejpam-6113	303	22	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(νs	PROPN
ejpam-6113	303	23	)	)	PUNCT
ejpam-6113	303	24	<	<	X
ejpam-6113	303	25	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	303	26	,	,	PUNCT
ejpam-6113	303	27	νd	νd	NOUN
ejpam-6113	303	28	,	,	PUNCT
ejpam-6113	303	29	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	303	30	,	,	PUNCT
ejpam-6113	303	31	νd)))−	νd)))−	PROPN
ejpam-6113	303	32	ξ2(νs	ξ2(νs	NUM
ejpam-6113	303	33	,	,	PUNCT
ejpam-6113	303	34	νd	νd	NOUN
ejpam-6113	303	35	,	,	PUNCT
ejpam-6113	303	36	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	303	37	,	,	PUNCT
ejpam-6113	303	38	νd	νd	NOUN
ejpam-6113	303	39	)	)	PUNCT
ejpam-6113	303	40	)	)	PUNCT
ejpam-6113	303	41	)	)	PUNCT
ejpam-6113	304	1	+	+	PUNCT
ejpam-6113	304	2	η1(νs	η1(νs	PROPN
ejpam-6113	304	3	,	,	PUNCT
ejpam-6113	304	4	νd)−	νd)−	X
ejpam-6113	304	5	η2(νs	η2(νs	PROPN
ejpam-6113	304	6	,	,	PUNCT
ejpam-6113	304	7	νd	νd	PROPN
ejpam-6113	304	8	)	)	PUNCT
ejpam-6113	304	9	+	+	NUM
ejpam-6113	304	10	ϵ	ϵ	ADP
ejpam-6113	304	11	≤|	≤|	NOUN
ejpam-6113	304	12	ξ1(νs	ξ1(ν	NOUN
ejpam-6113	304	13	,	,	PUNCT
ejpam-6113	304	14	νd	νd	NOUN
ejpam-6113	304	15	,	,	PUNCT
ejpam-6113	304	16	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	304	17	,	,	PUNCT
ejpam-6113	304	18	νd)))−	νd)))−	PROPN
ejpam-6113	304	19	ξ2(νs	ξ2(νs	NUM
ejpam-6113	304	20	,	,	PUNCT
ejpam-6113	304	21	νd	νd	NOUN
ejpam-6113	304	22	,	,	PUNCT
ejpam-6113	304	23	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	304	24	,	,	PUNCT
ejpam-6113	304	25	νd	νd	NOUN
ejpam-6113	304	26	)	)	PUNCT
ejpam-6113	304	27	)	)	PUNCT
ejpam-6113	304	28	)	)	PUNCT
ejpam-6113	305	1	|	|	ADV
ejpam-6113	305	2	+	+	CCONJ
ejpam-6113	305	3	|	|	ADV
ejpam-6113	305	4	η1(νs	η1(νs	PROPN
ejpam-6113	305	5	,	,	PUNCT
ejpam-6113	305	6	νd)−	νd)−	NOUN
ejpam-6113	305	7	η2(νs	η2(νs	PROPN
ejpam-6113	305	8	,	,	PUNCT
ejpam-6113	305	9	νd	νd	PROPN
ejpam-6113	305	10	)	)	PUNCT
ejpam-6113	305	11	|	|	NOUN
ejpam-6113	305	12	+	+	SYM
ejpam-6113	305	13	ϵ	ϵ	X
ejpam-6113	305	14	(	(	PUNCT
ejpam-6113	305	15	4.14	4.14	NUM
ejpam-6113	305	16	)	)	PUNCT
ejpam-6113	305	17	also	also	ADV
ejpam-6113	305	18	,	,	PUNCT
ejpam-6113	305	19	from	from	ADP
ejpam-6113	305	20	the	the	DET
ejpam-6113	305	21	inequalities	inequality	NOUN
ejpam-6113	305	22	(	(	PUNCT
ejpam-6113	305	23	4.11	4.11	NUM
ejpam-6113	305	24	)	)	PUNCT
ejpam-6113	305	25	and	and	CCONJ
ejpam-6113	305	26	(	(	PUNCT
ejpam-6113	305	27	4.12	4.12	NUM
ejpam-6113	305	28	)	)	PUNCT
ejpam-6113	305	29	,	,	PUNCT
ejpam-6113	305	30	we	we	PRON
ejpam-6113	305	31	get	get	VERB
ejpam-6113	305	32	that	that	NUM
ejpam-6113	305	33	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	305	34	)	)	PUNCT
ejpam-6113	305	35	≥	≥	NOUN
ejpam-6113	306	1	ξ1(νs	ξ1(νs	NUM
ejpam-6113	306	2	,	,	PUNCT
ejpam-6113	306	3	νd	νd	NOUN
ejpam-6113	306	4	,	,	PUNCT
ejpam-6113	306	5	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	306	6	,	,	PUNCT
ejpam-6113	306	7	νd)))−	νd)))−	PROPN
ejpam-6113	306	8	ξ2(νs	ξ2(νs	NUM
ejpam-6113	306	9	,	,	PUNCT
ejpam-6113	306	10	νd	νd	NOUN
ejpam-6113	306	11	,	,	PUNCT
ejpam-6113	306	12	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	306	13	,	,	PUNCT
ejpam-6113	306	14	νd	νd	NOUN
ejpam-6113	306	15	)	)	PUNCT
ejpam-6113	306	16	)	)	PUNCT
ejpam-6113	306	17	)	)	PUNCT
ejpam-6113	307	1	+	+	PUNCT
ejpam-6113	307	2	η1(νs	η1(νs	PROPN
ejpam-6113	307	3	,	,	PUNCT
ejpam-6113	307	4	νd)−	νd)−	NOUN
ejpam-6113	307	5	η2(νs	η2(νs	PROPN
ejpam-6113	307	6	,	,	PUNCT
ejpam-6113	307	7	νd)−	νd)−	X
ejpam-6113	307	8	ϵ	ϵ	DET
ejpam-6113	307	9	≥	≥	NOUN
ejpam-6113	307	10	−{|	−{|	X
ejpam-6113	307	11	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	307	12	,	,	PUNCT
ejpam-6113	307	13	νd	νd	NOUN
ejpam-6113	307	14	,	,	PUNCT
ejpam-6113	307	15	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	307	16	,	,	PUNCT
ejpam-6113	307	17	νd)))−	νd)))−	PROPN
ejpam-6113	307	18	ξ2(νs	ξ2(νs	NUM
ejpam-6113	307	19	,	,	PUNCT
ejpam-6113	307	20	νd	νd	NOUN
ejpam-6113	307	21	,	,	PUNCT
ejpam-6113	307	22	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	307	23	,	,	PUNCT
ejpam-6113	307	24	νd	νd	NOUN
ejpam-6113	307	25	)	)	PUNCT
ejpam-6113	307	26	)	)	PUNCT
ejpam-6113	307	27	)	)	PUNCT
ejpam-6113	308	1	|	|	ADV
ejpam-6113	308	2	+	+	CCONJ
ejpam-6113	308	3	|	|	ADV
ejpam-6113	308	4	η1(νs	η1(νs	PROPN
ejpam-6113	308	5	,	,	PUNCT
ejpam-6113	308	6	νd)−	νd)−	NOUN
ejpam-6113	308	7	η2(νs	η2(νs	PROPN
ejpam-6113	308	8	,	,	PUNCT
ejpam-6113	308	9	νd	νd	PROPN
ejpam-6113	308	10	)	)	PUNCT
ejpam-6113	308	11	+	+	CCONJ
ejpam-6113	308	12	ϵ	ϵ	X
ejpam-6113	308	13	}	}	PUNCT
ejpam-6113	308	14	(	(	PUNCT
ejpam-6113	308	15	4.15	4.15	NUM
ejpam-6113	308	16	)	)	PUNCT
ejpam-6113	308	17	d.	d.	PROPN
ejpam-6113	308	18	r.	r.	PROPN
ejpam-6113	308	19	babu	babu	PROPN
ejpam-6113	308	20	,	,	PUNCT
ejpam-6113	308	21	k.	k.	PROPN
ejpam-6113	308	22	n.	n.	PROPN
ejpam-6113	308	23	k.	k.	PROPN
ejpam-6113	309	1	rao	rao	PROPN
ejpam-6113	309	2	/	/	SYM
ejpam-6113	309	3	eur	eur	PROPN
ejpam-6113	309	4	.	.	PUNCT
ejpam-6113	310	1	j.	j.	PROPN
ejpam-6113	310	2	pure	pure	PROPN
ejpam-6113	310	3	appl	appl	PROPN
ejpam-6113	310	4	.	.	PROPN
ejpam-6113	310	5	math	math	PROPN
ejpam-6113	310	6	,	,	PUNCT
ejpam-6113	310	7	18	18	NUM
ejpam-6113	310	8	(	(	PUNCT
ejpam-6113	310	9	3	3	NUM
ejpam-6113	310	10	)	)	PUNCT
ejpam-6113	310	11	(	(	PUNCT
ejpam-6113	310	12	2025	2025	NUM
ejpam-6113	310	13	)	)	PUNCT
ejpam-6113	310	14	,	,	PUNCT
ejpam-6113	310	15	6113	6113	NUM
ejpam-6113	310	16	12	12	NUM
ejpam-6113	310	17	of	of	ADP
ejpam-6113	310	18	14	14	NUM
ejpam-6113	310	19	from	from	ADP
ejpam-6113	310	20	(	(	PUNCT
ejpam-6113	310	21	4.14	4.14	NUM
ejpam-6113	310	22	)	)	PUNCT
ejpam-6113	310	23	and	and	CCONJ
ejpam-6113	310	24	(	(	PUNCT
ejpam-6113	310	25	4.15	4.15	NUM
ejpam-6113	310	26	)	)	PUNCT
ejpam-6113	310	27	,	,	PUNCT
ejpam-6113	311	1	we	we	PRON
ejpam-6113	311	2	have	have	NUM
ejpam-6113	311	3	|	|	ADV
ejpam-6113	311	4	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	311	5	)	)	PUNCT
ejpam-6113	311	6	|	|	ADV
ejpam-6113	311	7	<	<	X
ejpam-6113	311	8	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	311	9	,	,	PUNCT
ejpam-6113	311	10	νd	νd	NOUN
ejpam-6113	311	11	,	,	PUNCT
ejpam-6113	311	12	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	311	13	,	,	PUNCT
ejpam-6113	311	14	νd)))−	νd)))−	PROPN
ejpam-6113	311	15	ξ2(νs	ξ2(νs	NUM
ejpam-6113	311	16	,	,	PUNCT
ejpam-6113	311	17	νd	νd	NOUN
ejpam-6113	311	18	,	,	PUNCT
ejpam-6113	311	19	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	311	20	,	,	PUNCT
ejpam-6113	311	21	νd	νd	NOUN
ejpam-6113	311	22	)	)	PUNCT
ejpam-6113	311	23	)	)	PUNCT
ejpam-6113	311	24	)	)	PUNCT
ejpam-6113	312	1	+	+	PUNCT
ejpam-6113	312	2	η1(νs	η1(νs	PROPN
ejpam-6113	312	3	,	,	PUNCT
ejpam-6113	312	4	νd)−	νd)−	NOUN
ejpam-6113	312	5	η2(νs	η2(νs	PROPN
ejpam-6113	312	6	,	,	PUNCT
ejpam-6113	312	7	νd)−	νd)−	X
ejpam-6113	312	8	ϵ	ϵ	X
ejpam-6113	312	9	≤|	≤|	NOUN
ejpam-6113	312	10	ξ1(νs	ξ1(ν	NOUN
ejpam-6113	312	11	,	,	PUNCT
ejpam-6113	312	12	νd	νd	NOUN
ejpam-6113	312	13	,	,	PUNCT
ejpam-6113	312	14	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	312	15	,	,	PUNCT
ejpam-6113	312	16	νd)))−	νd)))−	PROPN
ejpam-6113	312	17	ξ2(νs	ξ2(νs	NUM
ejpam-6113	312	18	,	,	PUNCT
ejpam-6113	312	19	νd	νd	NOUN
ejpam-6113	312	20	,	,	PUNCT
ejpam-6113	312	21	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	312	22	,	,	PUNCT
ejpam-6113	312	23	νd	νd	NOUN
ejpam-6113	312	24	)	)	PUNCT
ejpam-6113	312	25	)	)	PUNCT
ejpam-6113	312	26	)	)	PUNCT
ejpam-6113	313	1	|	|	ADV
ejpam-6113	313	2	+	+	CCONJ
ejpam-6113	313	3	|	|	ADV
ejpam-6113	313	4	η1(νs	η1(νs	PROPN
ejpam-6113	313	5	,	,	PUNCT
ejpam-6113	313	6	νd)−	νd)−	NOUN
ejpam-6113	313	7	η2(νs	η2(νs	PROPN
ejpam-6113	313	8	,	,	PUNCT
ejpam-6113	313	9	νd	νd	PROPN
ejpam-6113	313	10	)	)	PUNCT
ejpam-6113	313	11	+	+	CCONJ
ejpam-6113	313	12	ϵ	ϵ	X
ejpam-6113	313	13	(	(	PUNCT
ejpam-6113	313	14	4.16	4.16	NUM
ejpam-6113	313	15	)	)	PUNCT
ejpam-6113	313	16	on	on	ADP
ejpam-6113	313	17	taking	take	VERB
ejpam-6113	313	18	ϵ	ϵ	X
ejpam-6113	313	19	→	→	SYM
ejpam-6113	313	20	0	0	NUM
ejpam-6113	313	21	in	in	ADP
ejpam-6113	313	22	(	(	PUNCT
ejpam-6113	313	23	4.16	4.16	NUM
ejpam-6113	313	24	)	)	PUNCT
ejpam-6113	313	25	,	,	PUNCT
ejpam-6113	313	26	we	we	PRON
ejpam-6113	313	27	obtain	obtain	VERB
ejpam-6113	313	28	that	that	PRON
ejpam-6113	313	29	|	|	ADV
ejpam-6113	313	30	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	313	31	)	)	PUNCT
ejpam-6113	313	32	|≤|	|≤|	X
ejpam-6113	313	33	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	313	34	,	,	PUNCT
ejpam-6113	313	35	νd	νd	NOUN
ejpam-6113	313	36	,	,	PUNCT
ejpam-6113	313	37	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	313	38	,	,	PUNCT
ejpam-6113	313	39	νd)))−	νd)))−	PROPN
ejpam-6113	313	40	ξ2(νs	ξ2(νs	NUM
ejpam-6113	313	41	,	,	PUNCT
ejpam-6113	313	42	νd	νd	NOUN
ejpam-6113	313	43	,	,	PUNCT
ejpam-6113	313	44	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	313	45	,	,	PUNCT
ejpam-6113	313	46	νd	νd	NOUN
ejpam-6113	313	47	)	)	PUNCT
ejpam-6113	313	48	)	)	PUNCT
ejpam-6113	313	49	)	)	PUNCT
ejpam-6113	314	1	|	|	ADV
ejpam-6113	314	2	+	+	CCONJ
ejpam-6113	314	3	|	|	ADV
ejpam-6113	314	4	η1(νs	η1(νs	PROPN
ejpam-6113	314	5	,	,	PUNCT
ejpam-6113	314	6	νd)−	νd)−	NOUN
ejpam-6113	314	7	η2(νs	η2(νs	PROPN
ejpam-6113	314	8	,	,	PUNCT
ejpam-6113	314	9	νd	νd	PROPN
ejpam-6113	314	10	)	)	PUNCT
ejpam-6113	314	11	|	|	ADV
ejpam-6113	314	12	from	from	ADP
ejpam-6113	314	13	the	the	DET
ejpam-6113	314	14	condition	condition	NOUN
ejpam-6113	314	15	(	(	PUNCT
ejpam-6113	314	16	db	db	PROPN
ejpam-6113	314	17	)	)	PUNCT
ejpam-6113	314	18	,	,	PUNCT
ejpam-6113	314	19	we	we	PRON
ejpam-6113	314	20	have	have	VERB
ejpam-6113	314	21	|	|	ADV
ejpam-6113	314	22	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	314	23	)	)	PUNCT
ejpam-6113	314	24	|≤|	|≤|	X
ejpam-6113	314	25	ξ1(νs	ξ1(νs	PROPN
ejpam-6113	314	26	,	,	PUNCT
ejpam-6113	314	27	νd	νd	NOUN
ejpam-6113	314	28	,	,	PUNCT
ejpam-6113	314	29	f1(ρ1(νs	f1(ρ1(νs	ADP
ejpam-6113	314	30	,	,	PUNCT
ejpam-6113	314	31	νd)))−	νd)))−	PROPN
ejpam-6113	314	32	ξ2(νs	ξ2(νs	NUM
ejpam-6113	314	33	,	,	PUNCT
ejpam-6113	314	34	νd	νd	NOUN
ejpam-6113	314	35	,	,	PUNCT
ejpam-6113	314	36	f2(ρ2(νs	f2(ρ2(νs	ADJ
ejpam-6113	314	37	,	,	PUNCT
ejpam-6113	314	38	νd	νd	NOUN
ejpam-6113	314	39	)	)	PUNCT
ejpam-6113	314	40	)	)	PUNCT
ejpam-6113	314	41	)	)	PUNCT
ejpam-6113	315	1	|	|	ADV
ejpam-6113	315	2	+	+	CCONJ
ejpam-6113	315	3	|	|	ADV
ejpam-6113	315	4	η1(νs	η1(νs	PROPN
ejpam-6113	315	5	,	,	PUNCT
ejpam-6113	315	6	νd)−	νd)−	NOUN
ejpam-6113	315	7	η2(νs	η2(νs	PROPN
ejpam-6113	315	8	,	,	PUNCT
ejpam-6113	315	9	νd	νd	PROPN
ejpam-6113	315	10	)	)	PUNCT
ejpam-6113	315	11	|	|	ADV
ejpam-6113	315	12	≤	≤	NOUN
ejpam-6113	315	13	[	[	PUNCT
ejpam-6113	315	14	h	h	NOUN
ejpam-6113	315	15	24p−4m(f1	24p−4m(f1	NOUN
ejpam-6113	315	16	,	,	PUNCT
ejpam-6113	315	17	f2	f2	PROPN
ejpam-6113	315	18	)	)	PUNCT
ejpam-6113	315	19	]	]	PUNCT
ejpam-6113	315	20	1	1	NUM
ejpam-6113	315	21	p	p	NOUN
ejpam-6113	315	22	≤	≤	NOUN
ejpam-6113	315	23	[	[	PUNCT
ejpam-6113	315	24	sup	sup	NOUN
ejpam-6113	315	25	νs∈s	νs∈s	PROPN
ejpam-6113	315	26	(	(	PUNCT
ejpam-6113	315	27	h	h	NOUN
ejpam-6113	315	28	24p−4	24p−4	NUM
ejpam-6113	316	1	[	[	X
ejpam-6113	316	2	|f1	|f1	NOUN
ejpam-6113	316	3	−f1f1|p]α	−f1f1|p]α	NOUN
ejpam-6113	317	1	[	[	X
ejpam-6113	317	2	|f2	|f2	ADV
ejpam-6113	317	3	−f2f2|p]1−α	−f2f2|p]1−α	NOUN
ejpam-6113	317	4	]	]	PUNCT
ejpam-6113	317	5	1	1	NUM
ejpam-6113	317	6	p	p	NOUN
ejpam-6113	317	7	which	which	PRON
ejpam-6113	317	8	implies	imply	VERB
ejpam-6113	317	9	that	that	SCONJ
ejpam-6113	317	10	sup	sup	PROPN
ejpam-6113	317	11	νs∈s	νs∈s	PROPN
ejpam-6113	317	12	|	|	ADP
ejpam-6113	317	13	f1f1(νs)−f1f2(νs	f1f1(νs)−f1f2(ν	NOUN
ejpam-6113	317	14	)	)	PUNCT
ejpam-6113	317	15	|p	|p	VERB
ejpam-6113	317	16	≤	≤	ADJ
ejpam-6113	317	17	h	h	NOUN
ejpam-6113	317	18	24p−4	24p−4	NUM
ejpam-6113	317	19	sup	sup	NOUN
ejpam-6113	317	20	νs∈s	νs∈s	PROPN
ejpam-6113	318	1	[	[	X
ejpam-6113	318	2	|f1	|f1	NOUN
ejpam-6113	318	3	−f1f1|p]α	−f1f1|p]α	PROPN
ejpam-6113	319	1	[	[	X
ejpam-6113	319	2	|f2	|f2	ADV
ejpam-6113	319	3	−f2f2|p]1−α	−f2f2|p]1−α	PROPN
ejpam-6113	319	4	.	.	PUNCT
ejpam-6113	320	1	now	now	ADV
ejpam-6113	320	2	,	,	PUNCT
ejpam-6113	320	3	for	for	ADP
ejpam-6113	320	4	all	all	DET
ejpam-6113	320	5	f1	f1	NOUN
ejpam-6113	320	6	,	,	PUNCT
ejpam-6113	320	7	f2	f2	NOUN
ejpam-6113	320	8	∈	∈	PROPN
ejpam-6113	320	9	ω(s	ω(s	PROPN
ejpam-6113	320	10	)	)	PUNCT
ejpam-6113	320	11	,	,	PUNCT
ejpam-6113	320	12	we	we	PRON
ejpam-6113	320	13	have	have	VERB
ejpam-6113	320	14	d(f1f1,f1f2	d(f1f1,f1f2	NOUN
ejpam-6113	320	15	)	)	PUNCT
ejpam-6113	320	16	≤	≤	NUM
ejpam-6113	320	17	h	h	NOUN
ejpam-6113	320	18	24p−4	24p−4	NUM
ejpam-6113	320	19	[	[	X
ejpam-6113	320	20	d(f1,f1f1	d(f1,f1f1	NOUN
ejpam-6113	320	21	)	)	PUNCT
ejpam-6113	320	22	]	]	PUNCT
ejpam-6113	321	1	α	α	X
ejpam-6113	322	1	[	[	X
ejpam-6113	322	2	d(f2,f2f2	d(f2,f2f2	X
ejpam-6113	322	3	)	)	PUNCT
ejpam-6113	322	4	]	]	PUNCT
ejpam-6113	323	1	1−α	1−α	NUM
ejpam-6113	323	2	.	.	PUNCT
ejpam-6113	324	1	consequently	consequently	ADV
ejpam-6113	324	2	,	,	PUNCT
ejpam-6113	324	3	f1,f2	f1,f2	PROPN
ejpam-6113	324	4	have	have	VERB
ejpam-6113	324	5	a	a	DET
ejpam-6113	324	6	unique	unique	ADJ
ejpam-6113	324	7	bounded	bounded	ADJ
ejpam-6113	324	8	common	common	ADJ
ejpam-6113	324	9	solution	solution	NOUN
ejpam-6113	324	10	to	to	ADP
ejpam-6113	324	11	the	the	DET
ejpam-6113	324	12	system	system	NOUN
ejpam-6113	324	13	of	of	ADP
ejpam-6113	324	14	functional	functional	ADJ
ejpam-6113	324	15	equations	equation	NOUN
ejpam-6113	324	16	(	(	PUNCT
ejpam-6113	324	17	4.1	4.1	NUM
ejpam-6113	324	18	)	)	PUNCT
ejpam-6113	324	19	since	since	SCONJ
ejpam-6113	324	20	all	all	DET
ejpam-6113	324	21	the	the	DET
ejpam-6113	324	22	requirements	requirement	NOUN
ejpam-6113	324	23	of	of	ADP
ejpam-6113	324	24	theorem	theorem	NOUN
ejpam-6113	324	25	5	5	NUM
ejpam-6113	324	26	are	be	AUX
ejpam-6113	324	27	met	meet	VERB
ejpam-6113	324	28	.	.	PUNCT
ejpam-6113	325	1	5	5	X
ejpam-6113	325	2	.	.	X
ejpam-6113	325	3	conclusion	conclusion	NOUN
ejpam-6113	325	4	and	and	CCONJ
ejpam-6113	325	5	future	future	ADJ
ejpam-6113	325	6	work	work	NOUN
ejpam-6113	325	7	in	in	ADP
ejpam-6113	325	8	this	this	DET
ejpam-6113	325	9	paper	paper	NOUN
ejpam-6113	325	10	,	,	PUNCT
ejpam-6113	325	11	we	we	PRON
ejpam-6113	325	12	studied	study	VERB
ejpam-6113	325	13	fixed	fix	VERB
ejpam-6113	325	14	point	point	NOUN
ejpam-6113	325	15	results	result	NOUN
ejpam-6113	325	16	for	for	ADP
ejpam-6113	325	17	interpolative	interpolative	ADJ
ejpam-6113	325	18	contraction	contraction	NOUN
ejpam-6113	325	19	mappings	mapping	NOUN
ejpam-6113	325	20	in	in	ADP
ejpam-6113	325	21	b	b	NOUN
ejpam-6113	325	22	-	-	ADJ
ejpam-6113	325	23	metric	metric	ADJ
ejpam-6113	325	24	spaces	space	NOUN
ejpam-6113	325	25	.	.	PUNCT
ejpam-6113	326	1	using	use	VERB
ejpam-6113	326	2	similar	similar	ADJ
ejpam-6113	326	3	approaches	approach	NOUN
ejpam-6113	326	4	,	,	PUNCT
ejpam-6113	326	5	it	it	PRON
ejpam-6113	326	6	can	can	AUX
ejpam-6113	326	7	be	be	AUX
ejpam-6113	326	8	studied	study	VERB
ejpam-6113	326	9	new	new	ADJ
ejpam-6113	326	10	fixed	fix	VERB
ejpam-6113	326	11	point	point	NOUN
ejpam-6113	326	12	results	result	NOUN
ejpam-6113	326	13	on	on	ADP
ejpam-6113	326	14	metric	metric	ADJ
ejpam-6113	326	15	and	and	CCONJ
ejpam-6113	326	16	some	some	DET
ejpam-6113	326	17	generalized	generalized	ADJ
ejpam-6113	326	18	metric	metric	ADJ
ejpam-6113	326	19	spaces	space	NOUN
ejpam-6113	326	20	.	.	PUNCT
ejpam-6113	327	1	the	the	DET
ejpam-6113	327	2	investigation	investigation	NOUN
ejpam-6113	327	3	of	of	ADP
ejpam-6113	327	4	certain	certain	ADJ
ejpam-6113	327	5	circumstances	circumstance	NOUN
ejpam-6113	327	6	to	to	PART
ejpam-6113	327	7	exclude	exclude	VERB
ejpam-6113	327	8	the	the	DET
ejpam-6113	327	9	identity	identity	NOUN
ejpam-6113	327	10	map	map	NOUN
ejpam-6113	327	11	of	of	ADP
ejpam-6113	327	12	e	e	PROPN
ejpam-6113	327	13	from	from	ADP
ejpam-6113	327	14	theorem	theorem	ADJ
ejpam-6113	327	15	4	4	NUM
ejpam-6113	327	16	and	and	CCONJ
ejpam-6113	327	17	theorem	theorem	VERB
ejpam-6113	327	18	5	5	NUM
ejpam-6113	327	19	and	and	CCONJ
ejpam-6113	327	20	related	related	ADJ
ejpam-6113	327	21	results	result	NOUN
ejpam-6113	327	22	is	be	AUX
ejpam-6113	327	23	a	a	DET
ejpam-6113	327	24	worthwhile	worthwhile	ADJ
ejpam-6113	327	25	problem	problem	NOUN
ejpam-6113	327	26	for	for	ADP
ejpam-6113	327	27	future	future	ADJ
ejpam-6113	327	28	effort	effort	NOUN
ejpam-6113	327	29	.	.	PUNCT
ejpam-6113	328	1	acknowledgements	acknowledgement	NOUN
ejpam-6113	328	2	the	the	DET
ejpam-6113	328	3	authors	author	NOUN
ejpam-6113	328	4	are	be	AUX
ejpam-6113	328	5	sincerely	sincerely	ADV
ejpam-6113	328	6	thankful	thankful	ADJ
ejpam-6113	328	7	to	to	ADP
ejpam-6113	328	8	the	the	DET
ejpam-6113	328	9	anonymous	anonymous	ADJ
ejpam-6113	328	10	referee	referee	NOUN
ejpam-6113	328	11	for	for	ADP
ejpam-6113	328	12	the	the	DET
ejpam-6113	328	13	valuable	valuable	ADJ
ejpam-6113	328	14	suggestions	suggestion	NOUN
ejpam-6113	328	15	which	which	PRON
ejpam-6113	328	16	helped	help	VERB
ejpam-6113	328	17	us	we	PRON
ejpam-6113	328	18	to	to	PART
ejpam-6113	328	19	improve	improve	VERB
ejpam-6113	328	20	the	the	DET
ejpam-6113	328	21	quality	quality	NOUN
ejpam-6113	328	22	of	of	ADP
ejpam-6113	328	23	the	the	DET
ejpam-6113	328	24	paper	paper	NOUN
ejpam-6113	328	25	.	.	PUNCT
ejpam-6113	329	1	d.	d.	PROPN
ejpam-6113	329	2	r.	r.	PROPN
ejpam-6113	329	3	babu	babu	PROPN
ejpam-6113	329	4	,	,	PUNCT
ejpam-6113	329	5	k.	k.	PROPN
ejpam-6113	329	6	n.	n.	PROPN
ejpam-6113	329	7	k.	k.	PROPN
ejpam-6113	330	1	rao	rao	PROPN
ejpam-6113	330	2	/	/	SYM
ejpam-6113	330	3	eur	eur	PROPN
ejpam-6113	330	4	.	.	PUNCT
ejpam-6113	331	1	j.	j.	PROPN
ejpam-6113	331	2	pure	pure	PROPN
ejpam-6113	331	3	appl	appl	PROPN
ejpam-6113	331	4	.	.	PROPN
ejpam-6113	331	5	math	math	PROPN
ejpam-6113	331	6	,	,	PUNCT
ejpam-6113	331	7	18	18	NUM
ejpam-6113	331	8	(	(	PUNCT
ejpam-6113	331	9	3	3	NUM
ejpam-6113	331	10	)	)	PUNCT
ejpam-6113	331	11	(	(	PUNCT
ejpam-6113	331	12	2025	2025	NUM
ejpam-6113	331	13	)	)	PUNCT
ejpam-6113	331	14	,	,	PUNCT
ejpam-6113	331	15	6113	6113	NUM
ejpam-6113	331	16	13	13	NUM
ejpam-6113	331	17	of	of	ADP
ejpam-6113	331	18	14	14	NUM
ejpam-6113	331	19	references	reference	NOUN
ejpam-6113	331	20	[	[	X
ejpam-6113	331	21	1	1	NUM
ejpam-6113	331	22	]	]	PUNCT
ejpam-6113	331	23	d.	d.	PROPN
ejpam-6113	331	24	r.	r.	PROPN
ejpam-6113	331	25	babu	babu	PROPN
ejpam-6113	331	26	.	.	PUNCT
ejpam-6113	332	1	some	some	DET
ejpam-6113	332	2	best	good	ADJ
ejpam-6113	332	3	proximity	proximity	NOUN
ejpam-6113	332	4	theorems	theorem	NOUN
ejpam-6113	332	5	for	for	ADP
ejpam-6113	332	6	generalized	generalized	ADJ
ejpam-6113	332	7	proximal	proximal	ADJ
ejpam-6113	332	8	z	z	NOUN
ejpam-6113	332	9	-	-	PUNCT
ejpam-6113	332	10	contraction	contraction	NOUN
ejpam-6113	332	11	maps	map	NOUN
ejpam-6113	332	12	in	in	ADP
ejpam-6113	332	13	b	b	NOUN
ejpam-6113	332	14	-	-	ADJ
ejpam-6113	332	15	metric	metric	ADJ
ejpam-6113	332	16	spaces	space	NOUN
ejpam-6113	332	17	with	with	ADP
ejpam-6113	332	18	applications	application	NOUN
ejpam-6113	332	19	.	.	PUNCT
ejpam-6113	333	1	sahand	sahand	PROPN
ejpam-6113	333	2	commun	commun	PROPN
ejpam-6113	333	3	.	.	PUNCT
ejpam-6113	334	1	math	math	PROPN
ejpam-6113	334	2	.	.	PUNCT
ejpam-6113	335	1	anal	anal	PROPN
ejpam-6113	335	2	.	.	PROPN
ejpam-6113	335	3	,	,	PUNCT
ejpam-6113	335	4	22(2):201	22(2):201	NUM
ejpam-6113	335	5	–	–	PUNCT
ejpam-6113	335	6	222	222	NUM
ejpam-6113	335	7	,	,	PUNCT
ejpam-6113	335	8	2025	2025	NUM
ejpam-6113	335	9	.	.	PUNCT
ejpam-6113	336	1	[	[	X
ejpam-6113	336	2	2	2	NUM
ejpam-6113	336	3	]	]	X
ejpam-6113	336	4	d.	d.	PROPN
ejpam-6113	336	5	r.	r.	PROPN
ejpam-6113	336	6	babu	babu	PROPN
ejpam-6113	336	7	k.	k.	PROPN
ejpam-6113	336	8	b.	b.	PROPN
ejpam-6113	336	9	chander	chander	PROPN
ejpam-6113	336	10	n.	n.	PROPN
ejpam-6113	336	11	siva	siva	PROPN
ejpam-6113	336	12	prasad	prasad	PROPN
ejpam-6113	336	13	shaik	shaik	PROPN
ejpam-6113	336	14	asha	asha	PROPN
ejpam-6113	336	15	e.	e.	PROPN
ejpam-6113	336	16	sundesh	sundesh	PROPN
ejpam-6113	336	17	babu	babu	PROPN
ejpam-6113	336	18	and	and	CCONJ
ejpam-6113	336	19	t.	t.	PROPN
ejpam-6113	336	20	v.	v.	PROPN
ejpam-6113	336	21	p.	p.	PROPN
ejpam-6113	336	22	kumar	kumar	PROPN
ejpam-6113	336	23	.	.	PUNCT
ejpam-6113	337	1	some	some	DET
ejpam-6113	337	2	coupled	couple	VERB
ejpam-6113	337	3	fixed	fix	VERB
ejpam-6113	337	4	point	point	NOUN
ejpam-6113	337	5	theorems	theorem	NOUN
ejpam-6113	337	6	on	on	ADP
ejpam-6113	337	7	orthogonal	orthogonal	ADJ
ejpam-6113	337	8	b	b	NOUN
ejpam-6113	337	9	-	-	PUNCT
ejpam-6113	337	10	metric	metric	ADJ
ejpam-6113	337	11	spaces	space	NOUN
ejpam-6113	337	12	with	with	ADP
ejpam-6113	337	13	applications	application	NOUN
ejpam-6113	337	14	.	.	PUNCT
ejpam-6113	338	1	bull	bull	NOUN
ejpam-6113	338	2	.	.	PUNCT
ejpam-6113	339	1	math	math	NOUN
ejpam-6113	339	2	.	.	PUNCT
ejpam-6113	340	1	anal	anal	PROPN
ejpam-6113	340	2	.	.	PUNCT
ejpam-6113	340	3	appl	appl	PROPN
ejpam-6113	340	4	.	.	PROPN
ejpam-6113	340	5	,	,	PUNCT
ejpam-6113	340	6	16(3):45–61	16(3):45–61	NUM
ejpam-6113	340	7	,	,	PUNCT
ejpam-6113	340	8	2024	2024	NUM
ejpam-6113	340	9	.	.	PUNCT
ejpam-6113	341	1	[	[	X
ejpam-6113	341	2	3	3	X
ejpam-6113	341	3	]	]	X
ejpam-6113	341	4	d.	d.	PROPN
ejpam-6113	341	5	r.	r.	PROPN
ejpam-6113	341	6	babu	babu	PROPN
ejpam-6113	341	7	n.	n.	PROPN
ejpam-6113	341	8	siva	siva	PROPN
ejpam-6113	341	9	prasad	prasad	PROPN
ejpam-6113	341	10	v.	v.	ADP
ejpam-6113	341	11	a.	a.	PROPN
ejpam-6113	341	12	babu	babu	PROPN
ejpam-6113	341	13	and	and	CCONJ
ejpam-6113	341	14	k.	k.	PROPN
ejpam-6113	341	15	b.	b.	PROPN
ejpam-6113	341	16	chander	chander	PROPN
ejpam-6113	341	17	.	.	PUNCT
ejpam-6113	342	1	some	some	DET
ejpam-6113	342	2	common	common	ADJ
ejpam-6113	342	3	fixed	fix	VERB
ejpam-6113	342	4	point	point	NOUN
ejpam-6113	342	5	theorems	theorem	NOUN
ejpam-6113	342	6	in	in	ADP
ejpam-6113	342	7	b	b	NOUN
ejpam-6113	342	8	-	-	ADJ
ejpam-6113	342	9	metric	metric	ADJ
ejpam-6113	342	10	spaces	space	NOUN
ejpam-6113	342	11	via	via	ADP
ejpam-6113	342	12	f	f	NOUN
ejpam-6113	342	13	-	-	PUNCT
ejpam-6113	342	14	class	class	NOUN
ejpam-6113	342	15	function	function	NOUN
ejpam-6113	342	16	with	with	ADP
ejpam-6113	342	17	applications	application	NOUN
ejpam-6113	342	18	.	.	PUNCT
ejpam-6113	343	1	adv	adv	PROPN
ejpam-6113	343	2	.	.	PUNCT
ejpam-6113	343	3	fixed	fix	VERB
ejpam-6113	343	4	point	point	NOUN
ejpam-6113	343	5	theory	theory	NOUN
ejpam-6113	343	6	,	,	PUNCT
ejpam-6113	343	7	14	14	NUM
ejpam-6113	343	8	(	(	PUNCT
ejpam-6113	343	9	24):38	24):38	NUM
ejpam-6113	343	10	pages	page	NOUN
ejpam-6113	343	11	,	,	PUNCT
ejpam-6113	343	12	https://doi.org/10.28919/afpt/8515	https://doi.org/10.28919/afpt/8515	PROPN
ejpam-6113	343	13	,	,	PUNCT
ejpam-6113	343	14	2024	2024	NUM
ejpam-6113	343	15	.	.	PUNCT
ejpam-6113	344	1	[	[	X
ejpam-6113	344	2	4	4	X
ejpam-6113	344	3	]	]	PUNCT
ejpam-6113	344	4	r.	r.	PROPN
ejpam-6113	344	5	bellman	bellman	PROPN
ejpam-6113	344	6	and	and	CCONJ
ejpam-6113	344	7	e.	e.	PROPN
ejpam-6113	344	8	s.	s.	PROPN
ejpam-6113	344	9	lee	lee	PROPN
ejpam-6113	344	10	.	.	PUNCT
ejpam-6113	345	1	functional	functional	ADJ
ejpam-6113	345	2	equations	equation	NOUN
ejpam-6113	345	3	arising	arise	VERB
ejpam-6113	345	4	in	in	ADP
ejpam-6113	345	5	dynamic	dynamic	ADJ
ejpam-6113	345	6	programming	programming	NOUN
ejpam-6113	345	7	.	.	PUNCT
ejpam-6113	346	1	aequationes	aequatione	NOUN
ejpam-6113	346	2	math	math	PROPN
ejpam-6113	346	3	.	.	PUNCT
ejpam-6113	346	4	,	,	PUNCT
ejpam-6113	346	5	17:1–18	17:1–18	NUM
ejpam-6113	346	6	,	,	PUNCT
ejpam-6113	346	7	1978	1978	NUM
ejpam-6113	346	8	.	.	PUNCT
ejpam-6113	347	1	[	[	X
ejpam-6113	347	2	5	5	X
ejpam-6113	347	3	]	]	PUNCT
ejpam-6113	347	4	s.	s.	PROPN
ejpam-6113	347	5	czerwik	czerwik	PROPN
ejpam-6113	347	6	.	.	PUNCT
ejpam-6113	348	1	contraction	contraction	NOUN
ejpam-6113	348	2	mappings	mapping	NOUN
ejpam-6113	348	3	in	in	ADP
ejpam-6113	348	4	b	b	NOUN
ejpam-6113	348	5	-	-	ADJ
ejpam-6113	348	6	metric	metric	ADJ
ejpam-6113	348	7	spaces	space	NOUN
ejpam-6113	348	8	.	.	PUNCT
ejpam-6113	349	1	acta	acta	PROPN
ejpam-6113	349	2	math	math	PROPN
ejpam-6113	349	3	.	.	PUNCT
ejpam-6113	350	1	inform	inform	NOUN
ejpam-6113	350	2	.	.	PUNCT
ejpam-6113	351	1	univ	univ	PROPN
ejpam-6113	351	2	.	.	PUNCT
ejpam-6113	351	3	ostraviensis	ostraviensis	NOUN
ejpam-6113	351	4	,	,	PUNCT
ejpam-6113	351	5	1:5–11	1:5–11	NUM
ejpam-6113	351	6	,	,	PUNCT
ejpam-6113	351	7	1993	1993	NUM
ejpam-6113	351	8	.	.	PUNCT
ejpam-6113	352	1	[	[	X
ejpam-6113	352	2	6	6	NUM
ejpam-6113	352	3	]	]	PUNCT
ejpam-6113	352	4	d.	d.	PROPN
ejpam-6113	352	5	devi	devi	PROPN
ejpam-6113	352	6	and	and	CCONJ
ejpam-6113	352	7	d.	d.	PROPN
ejpam-6113	352	8	pradip	pradip	PROPN
ejpam-6113	352	9	.	.	PUNCT
ejpam-6113	353	1	fixed	fix	VERB
ejpam-6113	353	2	points	point	NOUN
ejpam-6113	353	3	of	of	ADP
ejpam-6113	353	4	two	two	NUM
ejpam-6113	353	5	interpolative	interpolative	ADJ
ejpam-6113	353	6	cyclic	cyclic	ADJ
ejpam-6113	353	7	contractions	contraction	NOUN
ejpam-6113	353	8	in	in	ADP
ejpam-6113	353	9	bmetric	bmetric	ADJ
ejpam-6113	353	10	spaces	space	NOUN
ejpam-6113	353	11	.	.	PUNCT
ejpam-6113	354	1	heliyon	heliyon	NOUN
ejpam-6113	354	2	,	,	PUNCT
ejpam-6113	354	3	11(1):7	11(1):7	NUM
ejpam-6113	354	4	pages	page	NOUN
ejpam-6113	354	5	,	,	PUNCT
ejpam-6113	354	6	https://doi.org/10.1016/j.heliyon.2025.e41667	https://doi.org/10.1016/j.heliyon.2025.e41667	NOUN
ejpam-6113	354	7	,	,	PUNCT
ejpam-6113	354	8	2025	2025	NUM
ejpam-6113	354	9	.	.	PUNCT
ejpam-6113	355	1	[	[	X
ejpam-6113	355	2	7	7	X
ejpam-6113	355	3	]	]	X
ejpam-6113	355	4	m.	m.	NOUN
ejpam-6113	355	5	edraoui	edraoui	NOUN
ejpam-6113	355	6	and	and	CCONJ
ejpam-6113	355	7	m.	m.	NOUN
ejpam-6113	355	8	aamri	aamri	PROPN
ejpam-6113	355	9	.	.	PUNCT
ejpam-6113	356	1	common	common	ADJ
ejpam-6113	356	2	fixed	fix	VERB
ejpam-6113	356	3	point	point	NOUN
ejpam-6113	356	4	of	of	ADP
ejpam-6113	356	5	interpolative	interpolative	ADJ
ejpam-6113	356	6	hardy	hardy	ADJ
ejpam-6113	356	7	-	-	PUNCT
ejpam-6113	356	8	rogers	rogers	NOUN
ejpam-6113	356	9	pair	pair	NOUN
ejpam-6113	356	10	contraction	contraction	NOUN
ejpam-6113	356	11	.	.	PUNCT
ejpam-6113	357	1	filomat	filomat	PROPN
ejpam-6113	357	2	,	,	PUNCT
ejpam-6113	357	3	38(17):6169–6175	38(17):6169–6175	NUM
ejpam-6113	357	4	,	,	PUNCT
ejpam-6113	357	5	https://doi.org/10.2298/fil2417169e	https://doi.org/10.2298/fil2417169e	PROPN
ejpam-6113	357	6	,	,	PUNCT
ejpam-6113	357	7	2024	2024	NUM
ejpam-6113	357	8	.	.	PUNCT
ejpam-6113	358	1	[	[	X
ejpam-6113	358	2	8	8	NUM
ejpam-6113	358	3	]	]	X
ejpam-6113	358	4	y.	y.	PROPN
ejpam-6113	358	5	u.	u.	PROPN
ejpam-6113	358	6	gaba	gaba	PROPN
ejpam-6113	358	7	and	and	CCONJ
ejpam-6113	358	8	e.	e.	PROPN
ejpam-6113	358	9	karapınar	karapınar	PROPN
ejpam-6113	358	10	.	.	PUNCT
ejpam-6113	359	1	a	a	DET
ejpam-6113	359	2	new	new	ADJ
ejpam-6113	359	3	approach	approach	NOUN
ejpam-6113	359	4	to	to	ADP
ejpam-6113	359	5	the	the	DET
ejpam-6113	359	6	interpolative	interpolative	ADJ
ejpam-6113	359	7	contractions	contraction	NOUN
ejpam-6113	359	8	.	.	PUNCT
ejpam-6113	360	1	axioms	axiom	NOUN
ejpam-6113	360	2	,	,	PUNCT
ejpam-6113	360	3	8(4):4	8(4):4	NOUN
ejpam-6113	360	4	pages	page	NOUN
ejpam-6113	360	5	,	,	PUNCT
ejpam-6113	360	6	https://doi.org/10.3390/axioms8040110	https://doi.org/10.3390/axioms8040110	NOUN
ejpam-6113	360	7	,	,	PUNCT
ejpam-6113	360	8	2019	2019	NUM
ejpam-6113	360	9	.	.	PUNCT
ejpam-6113	361	1	[	[	X
ejpam-6113	361	2	9	9	NUM
ejpam-6113	361	3	]	]	X
ejpam-6113	361	4	amine	amine	PROPN
ejpam-6113	361	5	el	el	PROPN
ejpam-6113	361	6	koufi	koufi	PROPN
ejpam-6113	361	7	m.	m.	NOUN
ejpam-6113	361	8	edraoui	edraoui	PROPN
ejpam-6113	361	9	and	and	CCONJ
ejpam-6113	361	10	s.	s.	PROPN
ejpam-6113	361	11	semami	semami	PROPN
ejpam-6113	361	12	.	.	PUNCT
ejpam-6113	362	1	fixed	fix	VERB
ejpam-6113	362	2	points	point	NOUN
ejpam-6113	362	3	results	result	NOUN
ejpam-6113	362	4	for	for	ADP
ejpam-6113	362	5	various	various	ADJ
ejpam-6113	362	6	types	type	NOUN
ejpam-6113	362	7	of	of	ADP
ejpam-6113	362	8	interpolative	interpolative	ADJ
ejpam-6113	362	9	cyclic	cyclic	ADJ
ejpam-6113	362	10	contraction	contraction	NOUN
ejpam-6113	362	11	.	.	PUNCT
ejpam-6113	363	1	appl	appl	PROPN
ejpam-6113	363	2	.	.	PUNCT
ejpam-6113	364	1	gen	gen	PROPN
ejpam-6113	364	2	.	.	PROPN
ejpam-6113	364	3	topol	topol	PROPN
ejpam-6113	364	4	.	.	PROPN
ejpam-6113	364	5	,	,	PUNCT
ejpam-6113	364	6	24(2):247–252	24(2):247–252	NUM
ejpam-6113	364	7	,	,	PUNCT
ejpam-6113	364	8	2023	2023	NUM
ejpam-6113	364	9	.	.	PUNCT
ejpam-6113	365	1	[	[	X
ejpam-6113	365	2	10	10	NUM
ejpam-6113	365	3	]	]	X
ejpam-6113	365	4	e.	e.	PROPN
ejpam-6113	365	5	karapınar	karapınar	PROPN
ejpam-6113	365	6	.	.	PUNCT
ejpam-6113	366	1	revisiting	revisit	VERB
ejpam-6113	366	2	the	the	DET
ejpam-6113	366	3	kannan	kannan	PROPN
ejpam-6113	366	4	type	type	NOUN
ejpam-6113	366	5	contractions	contraction	NOUN
ejpam-6113	366	6	via	via	ADP
ejpam-6113	366	7	interpolation	interpolation	NOUN
ejpam-6113	366	8	.	.	PUNCT
ejpam-6113	367	1	adv	adv	PROPN
ejpam-6113	367	2	.	.	PUNCT
ejpam-6113	367	3	theory	theory	PROPN
ejpam-6113	367	4	nonlinear	nonlinear	PROPN
ejpam-6113	367	5	anal	anal	PROPN
ejpam-6113	367	6	.	.	PUNCT
ejpam-6113	368	1	appl	appl	PROPN
ejpam-6113	368	2	.	.	PROPN
ejpam-6113	368	3	,	,	PUNCT
ejpam-6113	368	4	2(2):85–87	2(2):85–87	NUM
ejpam-6113	368	5	,	,	PUNCT
ejpam-6113	368	6	https://doi.org/10.31197/atnaa.431135	https://doi.org/10.31197/atnaa.431135	NOUN
ejpam-6113	368	7	,	,	PUNCT
ejpam-6113	368	8	2018	2018	NUM
ejpam-6113	368	9	.	.	PUNCT
ejpam-6113	369	1	[	[	X
ejpam-6113	369	2	11	11	NUM
ejpam-6113	369	3	]	]	PUNCT
ejpam-6113	369	4	e.	e.	PROPN
ejpam-6113	369	5	karapınar	karapınar	PROPN
ejpam-6113	369	6	.	.	PUNCT
ejpam-6113	370	1	interpolative	interpolative	PROPN
ejpam-6113	370	2	kannan	kannan	PROPN
ejpam-6113	370	3	-	-	PUNCT
ejpam-6113	370	4	meir	meir	PROPN
ejpam-6113	370	5	-	-	PUNCT
ejpam-6113	370	6	keeler	keeler	PROPN
ejpam-6113	370	7	type	type	NOUN
ejpam-6113	370	8	contraction	contraction	NOUN
ejpam-6113	370	9	.	.	PUNCT
ejpam-6113	371	1	adv	adv	PROPN
ejpam-6113	371	2	.	.	PUNCT
ejpam-6113	371	3	theory	theory	PROPN
ejpam-6113	371	4	nonlinear	nonlinear	PROPN
ejpam-6113	371	5	anal	anal	PROPN
ejpam-6113	371	6	.	.	PUNCT
ejpam-6113	372	1	appl	appl	PROPN
ejpam-6113	372	2	.	.	PROPN
ejpam-6113	372	3	,	,	PUNCT
ejpam-6113	372	4	5(4):611–614	5(4):611–614	NUM
ejpam-6113	372	5	,	,	PUNCT
ejpam-6113	372	6	https://doi.org/10.31197/atnaa.989389	https://doi.org/10.31197/atnaa.989389	NOUN
ejpam-6113	372	7	,	,	PUNCT
ejpam-6113	372	8	2021	2021	NUM
ejpam-6113	372	9	.	.	PUNCT
ejpam-6113	373	1	[	[	X
ejpam-6113	373	2	12	12	NUM
ejpam-6113	373	3	]	]	PUNCT
ejpam-6113	373	4	e.	e.	PROPN
ejpam-6113	373	5	karapınar	karapınar	PROPN
ejpam-6113	373	6	and	and	CCONJ
ejpam-6113	373	7	r.	r.	PROPN
ejpam-6113	373	8	p.	p.	PROPN
ejpam-6113	373	9	agarwal	agarwal	PROPN
ejpam-6113	373	10	.	.	PUNCT
ejpam-6113	374	1	interpolative	interpolative	ADJ
ejpam-6113	374	2	rus	rus	PROPN
ejpam-6113	374	3	-	-	PUNCT
ejpam-6113	374	4	reich	reich	NOUN
ejpam-6113	374	5	-	-	PUNCT
ejpam-6113	374	6	ćirić	ćirić	NOUN
ejpam-6113	374	7	type	type	NOUN
ejpam-6113	374	8	contractions	contraction	NOUN
ejpam-6113	374	9	via	via	ADP
ejpam-6113	374	10	simulation	simulation	NOUN
ejpam-6113	374	11	functions	function	NOUN
ejpam-6113	374	12	.	.	PUNCT
ejpam-6113	375	1	an	an	DET
ejpam-6113	375	2	.	.	PUNCT
ejpam-6113	375	3	st	st	PROPN
ejpam-6113	375	4	.	.	PROPN
ejpam-6113	375	5	univ	univ	PROPN
ejpam-6113	375	6	.	.	PUNCT
ejpam-6113	376	1	ovidius	ovidius	PROPN
ejpam-6113	376	2	constanta	constanta	PROPN
ejpam-6113	376	3	,	,	PUNCT
ejpam-6113	376	4	27(3):137–152	27(3):137–152	PROPN
ejpam-6113	376	5	,	,	PUNCT
ejpam-6113	376	6	2019	2019	NUM
ejpam-6113	376	7	.	.	PUNCT
ejpam-6113	377	1	[	[	X
ejpam-6113	377	2	13	13	NUM
ejpam-6113	377	3	]	]	PUNCT
ejpam-6113	377	4	e.	e.	PROPN
ejpam-6113	377	5	karapınar	karapınar	PROPN
ejpam-6113	377	6	a.	a.	PROPN
ejpam-6113	377	7	ali	ali	PROPN
ejpam-6113	377	8	a.	a.	PROPN
ejpam-6113	377	9	hussain	hussain	PROPN
ejpam-6113	377	10	and	and	CCONJ
ejpam-6113	377	11	h.	h.	PROPN
ejpam-6113	377	12	aydi	aydi	PROPN
ejpam-6113	377	13	.	.	PUNCT
ejpam-6113	378	1	on	on	ADP
ejpam-6113	378	2	interpolative	interpolative	ADJ
ejpam-6113	378	3	hardy	hardy	ADJ
ejpam-6113	378	4	-	-	PUNCT
ejpam-6113	378	5	rogers	rogers	NOUN
ejpam-6113	378	6	type	type	NOUN
ejpam-6113	378	7	multivalued	multivalue	VERB
ejpam-6113	378	8	contractions	contraction	NOUN
ejpam-6113	378	9	via	via	ADP
ejpam-6113	378	10	a	a	DET
ejpam-6113	378	11	simulation	simulation	NOUN
ejpam-6113	378	12	function	function	NOUN
ejpam-6113	378	13	.	.	PUNCT
ejpam-6113	379	1	filomat	filomat	PROPN
ejpam-6113	379	2	,	,	PUNCT
ejpam-6113	379	3	36(8):2847–2856	36(8):2847–2856	PROPN
ejpam-6113	379	4	,	,	PUNCT
ejpam-6113	379	5	https://doi.org/10.2298/fil2208847k	https://doi.org/10.2298/fil2208847k	PROPN
ejpam-6113	379	6	,	,	PUNCT
ejpam-6113	379	7	2022	2022	NUM
ejpam-6113	379	8	.	.	PUNCT
ejpam-6113	380	1	[	[	X
ejpam-6113	380	2	14	14	NUM
ejpam-6113	380	3	]	]	X
ejpam-6113	380	4	e.	e.	PROPN
ejpam-6113	380	5	karapınar	karapınar	PROPN
ejpam-6113	380	6	a.	a.	PROPN
ejpam-6113	380	7	fulga	fulga	NOUN
ejpam-6113	380	8	and	and	CCONJ
ejpam-6113	380	9	s.	s.	PROPN
ejpam-6113	380	10	s.	s.	PROPN
ejpam-6113	380	11	yesilkaya	yesilkaya	PROPN
ejpam-6113	380	12	.	.	PUNCT
ejpam-6113	381	1	new	new	ADJ
ejpam-6113	381	2	results	result	NOUN
ejpam-6113	381	3	on	on	ADP
ejpam-6113	381	4	perov	perov	NOUN
ejpam-6113	381	5	-	-	PUNCT
ejpam-6113	381	6	interpolative	interpolative	ADJ
ejpam-6113	381	7	contractions	contraction	NOUN
ejpam-6113	381	8	of	of	ADP
ejpam-6113	381	9	suzuki	suzuki	NOUN
ejpam-6113	381	10	type	type	NOUN
ejpam-6113	381	11	mappings	mapping	NOUN
ejpam-6113	381	12	.	.	PUNCT
ejpam-6113	382	1	j.	j.	PROPN
ejpam-6113	382	2	funct	funct	PROPN
ejpam-6113	382	3	.	.	PUNCT
ejpam-6113	383	1	spaces	space	NOUN
ejpam-6113	383	2	,	,	PUNCT
ejpam-6113	383	3	article	article	NOUN
ejpam-6113	383	4	i	i	PROPN
ejpam-6113	383	5	d	d	PROPN
ejpam-6113	383	6	9587604:7	9587604:7	NUM
ejpam-6113	383	7	pages	page	NOUN
ejpam-6113	383	8	,	,	PUNCT
ejpam-6113	383	9	https://doi.org/10.1155/2021/9587604	https://doi.org/10.1155/2021/9587604	PROPN
ejpam-6113	383	10	,	,	PUNCT
ejpam-6113	383	11	2021	2021	NUM
ejpam-6113	383	12	.	.	PUNCT
ejpam-6113	384	1	[	[	X
ejpam-6113	384	2	15	15	NUM
ejpam-6113	384	3	]	]	X
ejpam-6113	384	4	e.	e.	PROPN
ejpam-6113	384	5	karapınar	karapınar	PROPN
ejpam-6113	384	6	a.	a.	PROPN
ejpam-6113	384	7	fulga	fulga	NOUN
ejpam-6113	384	8	and	and	CCONJ
ejpam-6113	384	9	s.	s.	PROPN
ejpam-6113	384	10	s.	s.	PROPN
ejpam-6113	384	11	yesilkaya	yesilkaya	PROPN
ejpam-6113	384	12	.	.	PUNCT
ejpam-6113	385	1	interpolative	interpolative	PROPN
ejpam-6113	385	2	meir	meir	PROPN
ejpam-6113	385	3	–	–	PUNCT
ejpam-6113	385	4	keeler	keeler	NOUN
ejpam-6113	385	5	mappings	mapping	NOUN
ejpam-6113	385	6	in	in	ADP
ejpam-6113	385	7	modular	modular	ADJ
ejpam-6113	385	8	metric	metric	ADJ
ejpam-6113	385	9	spaces	space	NOUN
ejpam-6113	385	10	.	.	PUNCT
ejpam-6113	386	1	mathematics	mathematic	NOUN
ejpam-6113	386	2	,	,	PUNCT
ejpam-6113	386	3	10(16):13	10(16):13	NUM
ejpam-6113	386	4	pages	page	NOUN
ejpam-6113	386	5	,	,	PUNCT
ejpam-6113	386	6	https://doi.org/10.3390/math10162986	https://doi.org/10.3390/math10162986	PROPN
ejpam-6113	386	7	,	,	PUNCT
ejpam-6113	386	8	2022	2022	NUM
ejpam-6113	386	9	.	.	PUNCT
ejpam-6113	387	1	[	[	X
ejpam-6113	387	2	16	16	NUM
ejpam-6113	387	3	]	]	X
ejpam-6113	387	4	e.	e.	PROPN
ejpam-6113	387	5	karapınar	karapınar	PROPN
ejpam-6113	387	6	o.	o.	PROPN
ejpam-6113	387	7	alqahtani	alqahtani	PROPN
ejpam-6113	387	8	and	and	CCONJ
ejpam-6113	387	9	h.	h.	PROPN
ejpam-6113	387	10	aydi	aydi	VERB
ejpam-6113	387	11	.	.	PUNCT
ejpam-6113	388	1	on	on	ADP
ejpam-6113	388	2	interpolative	interpolative	ADJ
ejpam-6113	388	3	hardy	hardy	ADJ
ejpam-6113	388	4	-	-	PUNCT
ejpam-6113	388	5	rogers	rogers	NOUN
ejpam-6113	388	6	type	type	NOUN
ejpam-6113	388	7	contractions	contraction	NOUN
ejpam-6113	388	8	.	.	PUNCT
ejpam-6113	389	1	symmetry	symmetry	NOUN
ejpam-6113	389	2	,	,	PUNCT
ejpam-6113	389	3	11(8):7	11(8):7	PROPN
ejpam-6113	389	4	pages	page	NOUN
ejpam-6113	389	5	,	,	PUNCT
ejpam-6113	389	6	doi:10.3390	doi:10.3390	NOUN
ejpam-6113	389	7	/	/	SYM
ejpam-6113	389	8	sym11010008	sym11010008	NOUN
ejpam-6113	389	9	,	,	PUNCT
ejpam-6113	389	10	2018	2018	NUM
ejpam-6113	389	11	.	.	PUNCT
ejpam-6113	390	1	[	[	X
ejpam-6113	390	2	17	17	NUM
ejpam-6113	391	1	]	]	X
ejpam-6113	391	2	d.	d.	PROPN
ejpam-6113	391	3	r.	r.	PROPN
ejpam-6113	391	4	babu	babu	PROPN
ejpam-6113	391	5	k.	k.	PROPN
ejpam-6113	391	6	b.	b.	PROPN
ejpam-6113	391	7	chander	chander	PROPN
ejpam-6113	392	1	t.	t.	PROPN
ejpam-6113	393	1	v.	v.	PROPN
ejpam-6113	393	2	p.	p.	PROPN
ejpam-6113	393	3	kumar	kumar	PROPN
ejpam-6113	393	4	n.	n.	PROPN
ejpam-6113	393	5	siva	siva	PROPN
ejpam-6113	393	6	prasad	prasad	PROPN
ejpam-6113	393	7	and	and	CCONJ
ejpam-6113	393	8	k.	k.	PROPN
ejpam-6113	393	9	narayana	narayana	PROPN
ejpam-6113	393	10	.	.	PUNCT
ejpam-6113	394	1	fixed	fix	VERB
ejpam-6113	394	2	points	point	NOUN
ejpam-6113	394	3	of	of	ADP
ejpam-6113	394	4	cyclic	cyclic	ADJ
ejpam-6113	394	5	(	(	PUNCT
ejpam-6113	394	6	σ̈	σ̈	ADJ
ejpam-6113	394	7	,	,	PUNCT
ejpam-6113	394	8	λ̈)-admissible	λ̈)-admissible	ADJ
ejpam-6113	394	9	generalized	generalized	ADJ
ejpam-6113	394	10	contraction	contraction	NOUN
ejpam-6113	394	11	type	type	NOUN
ejpam-6113	394	12	maps	map	NOUN
ejpam-6113	394	13	in	in	ADP
ejpam-6113	394	14	b	b	NOUN
ejpam-6113	394	15	-	-	PUNCT
ejpam-6113	394	16	metric	metric	ADJ
ejpam-6113	394	17	spaces	space	NOUN
ejpam-6113	394	18	d.	d.	PROPN
ejpam-6113	394	19	r.	r.	PROPN
ejpam-6113	394	20	babu	babu	PROPN
ejpam-6113	394	21	,	,	PUNCT
ejpam-6113	394	22	k.	k.	PROPN
ejpam-6113	394	23	n.	n.	PROPN
ejpam-6113	394	24	k.	k.	PROPN
ejpam-6113	395	1	rao	rao	PROPN
ejpam-6113	395	2	/	/	SYM
ejpam-6113	395	3	eur	eur	PROPN
ejpam-6113	395	4	.	.	PUNCT
ejpam-6113	396	1	j.	j.	PROPN
ejpam-6113	396	2	pure	pure	PROPN
ejpam-6113	396	3	appl	appl	PROPN
ejpam-6113	396	4	.	.	PROPN
ejpam-6113	396	5	math	math	PROPN
ejpam-6113	396	6	,	,	PUNCT
ejpam-6113	396	7	18	18	NUM
ejpam-6113	396	8	(	(	PUNCT
ejpam-6113	396	9	3	3	NUM
ejpam-6113	396	10	)	)	PUNCT
ejpam-6113	396	11	(	(	PUNCT
ejpam-6113	396	12	2025	2025	NUM
ejpam-6113	396	13	)	)	PUNCT
ejpam-6113	396	14	,	,	PUNCT
ejpam-6113	396	15	6113	6113	NUM
ejpam-6113	396	16	14	14	NUM
ejpam-6113	396	17	of	of	ADP
ejpam-6113	396	18	14	14	NUM
ejpam-6113	396	19	with	with	ADP
ejpam-6113	396	20	applications	application	NOUN
ejpam-6113	396	21	.	.	PUNCT
ejpam-6113	397	1	appl	appl	PROPN
ejpam-6113	397	2	.	.	PROPN
ejpam-6113	397	3	math	math	NOUN
ejpam-6113	397	4	.	.	PUNCT
ejpam-6113	398	1	e	e	X
ejpam-6113	398	2	-	-	NOUN
ejpam-6113	398	3	notes	note	NOUN
ejpam-6113	398	4	,	,	PUNCT
ejpam-6113	398	5	24:379–398	24:379–398	PROPN
ejpam-6113	398	6	,	,	PUNCT
ejpam-6113	398	7	2024	2024	NUM
ejpam-6113	398	8	.	.	PUNCT
ejpam-6113	399	1	[	[	X
ejpam-6113	399	2	18	18	NUM
ejpam-6113	399	3	]	]	PUNCT
ejpam-6113	399	4	k.	k.	PROPN
ejpam-6113	399	5	roy	roy	PROPN
ejpam-6113	399	6	and	and	CCONJ
ejpam-6113	399	7	s.	s.	PROPN
ejpam-6113	399	8	panja	panja	PROPN
ejpam-6113	399	9	.	.	PUNCT
ejpam-6113	400	1	from	from	ADP
ejpam-6113	400	2	interpolative	interpolative	ADJ
ejpam-6113	400	3	contractive	contractive	ADJ
ejpam-6113	400	4	mappings	mapping	NOUN
ejpam-6113	400	5	to	to	ADP
ejpam-6113	400	6	generalized	generalize	VERB
ejpam-6113	400	7	ćirić-quasi	ćirić-quasi	NOUN
ejpam-6113	400	8	contraction	contraction	NOUN
ejpam-6113	400	9	mappings	mapping	NOUN
ejpam-6113	400	10	.	.	PUNCT
ejpam-6113	401	1	appl	appl	PROPN
ejpam-6113	401	2	.	.	PUNCT
ejpam-6113	402	1	gen	gen	PROPN
ejpam-6113	402	2	.	.	PROPN
ejpam-6113	402	3	topol	topol	PROPN
ejpam-6113	402	4	.	.	PROPN
ejpam-6113	402	5	,	,	PUNCT
ejpam-6113	403	1	22(1):109–120	22(1):109–120	NUM
ejpam-6113	403	2	,	,	PUNCT
ejpam-6113	403	3	https://doi.org/10.4995/agt.2021.14045	https://doi.org/10.4995/agt.2021.14045	PRON
ejpam-6113	403	4	,	,	PUNCT
ejpam-6113	403	5	2023	2023	NUM
ejpam-6113	403	6	.	.	PUNCT