id	sid	tid	token	lemma	pos
ejpam-6811	1	1	european	european	PROPN
ejpam-6811	1	2	journal	journal	PROPN
ejpam-6811	1	3	of	of	ADP
ejpam-6811	1	4	pure	pure	ADJ
ejpam-6811	1	5	and	and	CCONJ
ejpam-6811	1	6	applied	applied	ADJ
ejpam-6811	1	7	mathematics	mathematic	NOUN
ejpam-6811	1	8	2025	2025	NUM
ejpam-6811	1	9	,	,	PUNCT
ejpam-6811	1	10	vol	vol	NOUN
ejpam-6811	1	11	.	.	PROPN
ejpam-6811	1	12	18	18	NUM
ejpam-6811	1	13	,	,	PUNCT
ejpam-6811	1	14	issue	issue	NOUN
ejpam-6811	1	15	4	4	NUM
ejpam-6811	1	16	,	,	PUNCT
ejpam-6811	1	17	article	article	NOUN
ejpam-6811	1	18	number	number	NOUN
ejpam-6811	1	19	6811	6811	NUM
ejpam-6811	1	20	issn	issn	VERB
ejpam-6811	1	21	1307	1307	NUM
ejpam-6811	1	22	-	-	SYM
ejpam-6811	1	23	5543	5543	NUM
ejpam-6811	1	24	–	–	PUNCT
ejpam-6811	1	25	ejpam.com	ejpam.com	X
ejpam-6811	1	26	published	publish	VERB
ejpam-6811	1	27	by	by	ADP
ejpam-6811	1	28	new	new	PROPN
ejpam-6811	1	29	york	york	PROPN
ejpam-6811	1	30	business	business	PROPN
ejpam-6811	1	31	global	global	ADJ
ejpam-6811	1	32	solving	solve	VERB
ejpam-6811	1	33	fractional	fractional	ADJ
ejpam-6811	1	34	differential	differential	ADJ
ejpam-6811	1	35	equations	equation	NOUN
ejpam-6811	1	36	in	in	ADP
ejpam-6811	1	37	b	b	NOUN
ejpam-6811	1	38	-	-	PUNCT
ejpam-6811	1	39	metric	metric	ADJ
ejpam-6811	1	40	spaces	space	NOUN
ejpam-6811	1	41	tailored	tailor	VERB
ejpam-6811	1	42	with	with	ADP
ejpam-6811	1	43	a	a	DET
ejpam-6811	1	44	directed	direct	VERB
ejpam-6811	1	45	graph	graph	NOUN
ejpam-6811	1	46	dur	dur	PROPN
ejpam-6811	1	47	-	-	PUNCT
ejpam-6811	1	48	e	e	ADJ
ejpam-6811	1	49	-	-	ADJ
ejpam-6811	1	50	shehwar	shehwar	ADJ
ejpam-6811	1	51	sagheer1	sagheer1	NOUN
ejpam-6811	1	52	,	,	PUNCT
ejpam-6811	1	53	haitham	haitham	PROPN
ejpam-6811	1	54	qawaqneh2	qawaqneh2	PROPN
ejpam-6811	1	55	,	,	PUNCT
ejpam-6811	1	56	samina	samina	PROPN
ejpam-6811	1	57	batul1	batul1	PROPN
ejpam-6811	1	58	,	,	PUNCT
ejpam-6811	1	59	isma	isma	PROPN
ejpam-6811	1	60	urooj1	urooj1	PROPN
ejpam-6811	1	61	,	,	PUNCT
ejpam-6811	1	62	zainab	zainab	PROPN
ejpam-6811	1	63	rahman1	rahman1	PROPN
ejpam-6811	1	64	,	,	PUNCT
ejpam-6811	1	65	hassen	hassen	PROPN
ejpam-6811	1	66	aydi3,4,∗	aydi3,4,∗	NOUN
ejpam-6811	1	67	1	1	NUM
ejpam-6811	1	68	department	department	NOUN
ejpam-6811	1	69	of	of	ADP
ejpam-6811	1	70	mathematics	mathematic	NOUN
ejpam-6811	1	71	,	,	PUNCT
ejpam-6811	1	72	capital	capital	NOUN
ejpam-6811	1	73	university	university	PROPN
ejpam-6811	1	74	of	of	ADP
ejpam-6811	1	75	science	science	NOUN
ejpam-6811	1	76	and	and	CCONJ
ejpam-6811	1	77	technology	technology	NOUN
ejpam-6811	1	78	,	,	PUNCT
ejpam-6811	1	79	islamabad	islamabad	PROPN
ejpam-6811	1	80	,	,	PUNCT
ejpam-6811	1	81	pakistan	pakistan	PROPN
ejpam-6811	1	82	2	2	NUM
ejpam-6811	1	83	al	al	PROPN
ejpam-6811	1	84	-	-	PUNCT
ejpam-6811	1	85	zaytoonah	zaytoonah	PROPN
ejpam-6811	1	86	university	university	PROPN
ejpam-6811	1	87	of	of	ADP
ejpam-6811	1	88	jordan	jordan	PROPN
ejpam-6811	1	89	,	,	PUNCT
ejpam-6811	1	90	amman	amman	PROPN
ejpam-6811	1	91	11733	11733	NUM
ejpam-6811	1	92	,	,	PUNCT
ejpam-6811	1	93	jordan	jordan	PROPN
ejpam-6811	1	94	3	3	NUM
ejpam-6811	1	95	université	université	PROPN
ejpam-6811	1	96	de	de	X
ejpam-6811	1	97	sousse	sousse	PROPN
ejpam-6811	1	98	,	,	PUNCT
ejpam-6811	1	99	institut	institut	PROPN
ejpam-6811	1	100	supérieur	supérieur	PROPN
ejpam-6811	1	101	d’informatique	d’informatique	PROPN
ejpam-6811	1	102	et	et	PROPN
ejpam-6811	1	103	des	des	X
ejpam-6811	1	104	techniques	techniques	X
ejpam-6811	1	105	de	de	X
ejpam-6811	1	106	communication	communication	NOUN
ejpam-6811	1	107	,	,	PUNCT
ejpam-6811	1	108	h.	h.	PROPN
ejpam-6811	1	109	sousse	sousse	PROPN
ejpam-6811	1	110	4000	4000	NUM
ejpam-6811	1	111	,	,	PUNCT
ejpam-6811	1	112	tunisia	tunisia	PROPN
ejpam-6811	1	113	4	4	NUM
ejpam-6811	1	114	department	department	NOUN
ejpam-6811	1	115	of	of	ADP
ejpam-6811	1	116	mathematics	mathematic	NOUN
ejpam-6811	1	117	,	,	PUNCT
ejpam-6811	1	118	sefako	sefako	VERB
ejpam-6811	1	119	makgatho	makgatho	PROPN
ejpam-6811	1	120	health	health	PROPN
ejpam-6811	1	121	sciences	sciences	PROPN
ejpam-6811	1	122	university	university	PROPN
ejpam-6811	1	123	,	,	PUNCT
ejpam-6811	1	124	ga	ga	PROPN
ejpam-6811	1	125	-	-	NOUN
ejpam-6811	1	126	rankuwa	rankuwa	PROPN
ejpam-6811	1	127	,	,	PUNCT
ejpam-6811	1	128	south	south	PROPN
ejpam-6811	1	129	africa	africa	PROPN
ejpam-6811	1	130	abstract	abstract	PROPN
ejpam-6811	1	131	.	.	PUNCT
ejpam-6811	2	1	this	this	DET
ejpam-6811	2	2	study	study	NOUN
ejpam-6811	2	3	introduces	introduce	VERB
ejpam-6811	2	4	an	an	DET
ejpam-6811	2	5	extended	extended	ADJ
ejpam-6811	2	6	class	class	NOUN
ejpam-6811	2	7	of	of	ADP
ejpam-6811	2	8	contractions	contraction	NOUN
ejpam-6811	2	9	incorporating	incorporate	VERB
ejpam-6811	2	10	auxiliary	auxiliary	ADJ
ejpam-6811	2	11	functions	function	NOUN
ejpam-6811	2	12	.	.	PUNCT
ejpam-6811	3	1	we	we	PRON
ejpam-6811	3	2	examine	examine	VERB
ejpam-6811	3	3	the	the	DET
ejpam-6811	3	4	existence	existence	NOUN
ejpam-6811	3	5	of	of	ADP
ejpam-6811	3	6	solutions	solution	NOUN
ejpam-6811	3	7	for	for	ADP
ejpam-6811	3	8	caputo	caputo	PROPN
ejpam-6811	3	9	fractional	fractional	PROPN
ejpam-6811	3	10	differential	differential	ADJ
ejpam-6811	3	11	equations	equation	NOUN
ejpam-6811	3	12	with	with	ADP
ejpam-6811	3	13	integral	integral	ADJ
ejpam-6811	3	14	boundary	boundary	ADJ
ejpam-6811	3	15	conditions	condition	NOUN
ejpam-6811	3	16	within	within	ADP
ejpam-6811	3	17	the	the	DET
ejpam-6811	3	18	framework	framework	NOUN
ejpam-6811	3	19	of	of	ADP
ejpam-6811	3	20	b	b	NOUN
ejpam-6811	3	21	-	-	PUNCT
ejpam-6811	3	22	metric	metric	ADJ
ejpam-6811	3	23	spaces	space	NOUN
ejpam-6811	3	24	endowed	endow	VERB
ejpam-6811	3	25	with	with	ADP
ejpam-6811	3	26	a	a	DET
ejpam-6811	3	27	directed	direct	VERB
ejpam-6811	3	28	graph	graph	NOUN
ejpam-6811	3	29	.	.	PUNCT
ejpam-6811	4	1	the	the	DET
ejpam-6811	4	2	established	establish	VERB
ejpam-6811	4	3	findings	finding	NOUN
ejpam-6811	4	4	not	not	PART
ejpam-6811	4	5	only	only	ADV
ejpam-6811	4	6	generalize	generalize	VERB
ejpam-6811	4	7	but	but	CCONJ
ejpam-6811	4	8	also	also	ADV
ejpam-6811	4	9	unify	unify	VERB
ejpam-6811	4	10	a	a	DET
ejpam-6811	4	11	number	number	NOUN
ejpam-6811	4	12	of	of	ADP
ejpam-6811	4	13	significant	significant	ADJ
ejpam-6811	4	14	results	result	NOUN
ejpam-6811	4	15	in	in	ADP
ejpam-6811	4	16	the	the	DET
ejpam-6811	4	17	existing	exist	VERB
ejpam-6811	4	18	literature	literature	NOUN
ejpam-6811	4	19	,	,	PUNCT
ejpam-6811	4	20	as	as	SCONJ
ejpam-6811	4	21	demonstrated	demonstrate	VERB
ejpam-6811	4	22	by	by	ADP
ejpam-6811	4	23	supporting	support	VERB
ejpam-6811	4	24	theoretical	theoretical	ADJ
ejpam-6811	4	25	developments	development	NOUN
ejpam-6811	4	26	and	and	CCONJ
ejpam-6811	4	27	illustrative	illustrative	ADJ
ejpam-6811	4	28	examples	example	NOUN
ejpam-6811	4	29	.	.	PUNCT
ejpam-6811	5	1	2020	2020	NUM
ejpam-6811	5	2	mathematics	mathematic	NOUN
ejpam-6811	5	3	subject	subject	NOUN
ejpam-6811	5	4	classifications	classification	NOUN
ejpam-6811	5	5	:	:	PUNCT
ejpam-6811	5	6	34a08	34a08	NUM
ejpam-6811	5	7	,	,	PUNCT
ejpam-6811	5	8	47h10	47h10	NUM
ejpam-6811	5	9	,	,	PUNCT
ejpam-6811	5	10	54h25	54h25	NUM
ejpam-6811	5	11	key	key	ADJ
ejpam-6811	5	12	words	word	NOUN
ejpam-6811	5	13	and	and	CCONJ
ejpam-6811	5	14	phrases	phrase	NOUN
ejpam-6811	5	15	:	:	PUNCT
ejpam-6811	5	16	b	b	X
ejpam-6811	5	17	-	-	PUNCT
ejpam-6811	5	18	metric	metric	ADJ
ejpam-6811	5	19	space	space	NOUN
ejpam-6811	5	20	(	(	PUNCT
ejpam-6811	5	21	bms	bms	NOUN
ejpam-6811	5	22	)	)	PUNCT
ejpam-6811	5	23	,	,	PUNCT
ejpam-6811	5	24	fractional	fractional	ADJ
ejpam-6811	5	25	differential	differential	NOUN
ejpam-6811	5	26	equation	equation	NOUN
ejpam-6811	5	27	,	,	PUNCT
ejpam-6811	5	28	auxiliary	auxiliary	ADJ
ejpam-6811	5	29	function	function	NOUN
ejpam-6811	5	30	,	,	PUNCT
ejpam-6811	5	31	directed	direct	VERB
ejpam-6811	5	32	graph	graph	NOUN
ejpam-6811	5	33	(	(	PUNCT
ejpam-6811	5	34	dg	dg	PROPN
ejpam-6811	5	35	)	)	PUNCT
ejpam-6811	5	36	,	,	PUNCT
ejpam-6811	5	37	coincidence	coincidence	NOUN
ejpam-6811	5	38	point	point	NOUN
ejpam-6811	5	39	(	(	PUNCT
ejpam-6811	5	40	cp	cp	NOUN
ejpam-6811	5	41	)	)	PUNCT
ejpam-6811	5	42	,	,	PUNCT
ejpam-6811	5	43	caputo	caputo	PROPN
ejpam-6811	5	44	fractional	fractional	PROPN
ejpam-6811	5	45	differential	differential	NOUN
ejpam-6811	5	46	equation	equation	NOUN
ejpam-6811	5	47	(	(	PUNCT
ejpam-6811	5	48	cfde	cfde	NOUN
ejpam-6811	5	49	)	)	PUNCT
ejpam-6811	5	50	1	1	NUM
ejpam-6811	5	51	.	.	PUNCT
ejpam-6811	6	1	introduction	introduction	NOUN
ejpam-6811	6	2	and	and	CCONJ
ejpam-6811	6	3	preliminaries	preliminary	NOUN
ejpam-6811	6	4	fixed	fix	VERB
ejpam-6811	6	5	point	point	NOUN
ejpam-6811	6	6	theory	theory	NOUN
ejpam-6811	6	7	constitutes	constitute	VERB
ejpam-6811	6	8	a	a	DET
ejpam-6811	6	9	dynamic	dynamic	ADJ
ejpam-6811	6	10	and	and	CCONJ
ejpam-6811	6	11	significant	significant	ADJ
ejpam-6811	6	12	area	area	NOUN
ejpam-6811	6	13	of	of	ADP
ejpam-6811	6	14	mathematical	mathematical	ADJ
ejpam-6811	6	15	research	research	NOUN
ejpam-6811	6	16	,	,	PUNCT
ejpam-6811	6	17	with	with	ADP
ejpam-6811	6	18	its	its	PRON
ejpam-6811	6	19	principles	principle	NOUN
ejpam-6811	6	20	providing	provide	VERB
ejpam-6811	6	21	foundational	foundational	ADJ
ejpam-6811	6	22	tools	tool	NOUN
ejpam-6811	6	23	for	for	ADP
ejpam-6811	6	24	a	a	DET
ejpam-6811	6	25	wide	wide	ADJ
ejpam-6811	6	26	array	array	NOUN
ejpam-6811	6	27	of	of	ADP
ejpam-6811	6	28	scientific	scientific	ADJ
ejpam-6811	6	29	disciplines	discipline	NOUN
ejpam-6811	6	30	.	.	PUNCT
ejpam-6811	7	1	its	its	PRON
ejpam-6811	7	2	application	application	NOUN
ejpam-6811	7	3	to	to	ADP
ejpam-6811	7	4	fractional	fractional	ADJ
ejpam-6811	7	5	differential	differential	ADJ
ejpam-6811	7	6	equations	equation	NOUN
ejpam-6811	7	7	,	,	PUNCT
ejpam-6811	7	8	in	in	ADP
ejpam-6811	7	9	particular	particular	ADJ
ejpam-6811	7	10	,	,	PUNCT
ejpam-6811	7	11	has	have	AUX
ejpam-6811	7	12	been	be	AUX
ejpam-6811	7	13	instrumental	instrumental	ADJ
ejpam-6811	7	14	in	in	ADP
ejpam-6811	7	15	advancing	advance	VERB
ejpam-6811	7	16	analytical	analytical	ADJ
ejpam-6811	7	17	techniques	technique	NOUN
ejpam-6811	7	18	for	for	ADP
ejpam-6811	7	19	solving	solve	VERB
ejpam-6811	7	20	complex	complex	ADJ
ejpam-6811	7	21	nonlinear	nonlinear	ADJ
ejpam-6811	7	22	problems	problem	NOUN
ejpam-6811	7	23	.	.	PUNCT
ejpam-6811	8	1	the	the	DET
ejpam-6811	8	2	field	field	NOUN
ejpam-6811	8	3	has	have	AUX
ejpam-6811	8	4	evolved	evolve	VERB
ejpam-6811	8	5	considerably	considerably	ADV
ejpam-6811	8	6	[	[	X
ejpam-6811	8	7	1	1	NUM
ejpam-6811	8	8	,	,	PUNCT
ejpam-6811	8	9	2	2	NUM
ejpam-6811	8	10	]	]	PUNCT
ejpam-6811	8	11	since	since	SCONJ
ejpam-6811	8	12	banach	banach	NOUN
ejpam-6811	8	13	’s	’s	PART
ejpam-6811	8	14	seminal	seminal	ADJ
ejpam-6811	8	15	contraction	contraction	NOUN
ejpam-6811	8	16	principle	principle	NOUN
ejpam-6811	9	1	[	[	X
ejpam-6811	9	2	3	3	NUM
ejpam-6811	9	3	]	]	PUNCT
ejpam-6811	9	4	,	,	PUNCT
ejpam-6811	9	5	leading	lead	VERB
ejpam-6811	9	6	to	to	ADP
ejpam-6811	9	7	numerous	numerous	ADJ
ejpam-6811	9	8	extensions	extension	NOUN
ejpam-6811	9	9	in	in	ADP
ejpam-6811	9	10	generalized	generalized	ADJ
ejpam-6811	9	11	metric	metric	ADJ
ejpam-6811	9	12	spaces	space	NOUN
ejpam-6811	9	13	.	.	PUNCT
ejpam-6811	10	1	a	a	DET
ejpam-6811	10	2	prominent	prominent	ADJ
ejpam-6811	10	3	such	such	ADJ
ejpam-6811	10	4	generalization	generalization	NOUN
ejpam-6811	10	5	is	be	AUX
ejpam-6811	10	6	the	the	DET
ejpam-6811	10	7	b	b	NOUN
ejpam-6811	10	8	-	-	PUNCT
ejpam-6811	10	9	metric	metric	ADJ
ejpam-6811	10	10	space	space	NOUN
ejpam-6811	10	11	(	(	PUNCT
ejpam-6811	10	12	bms	bms	NOUN
ejpam-6811	10	13	)	)	PUNCT
ejpam-6811	10	14	,	,	PUNCT
ejpam-6811	10	15	introduced	introduce	VERB
ejpam-6811	10	16	independently	independently	ADV
ejpam-6811	10	17	by	by	ADP
ejpam-6811	10	18	czerwik	czerwik	PROPN
ejpam-6811	10	19	[	[	X
ejpam-6811	10	20	4	4	NUM
ejpam-6811	10	21	]	]	PUNCT
ejpam-6811	10	22	and	and	CCONJ
ejpam-6811	10	23	bakhtin	bakhtin	NOUN
ejpam-6811	10	24	[	[	X
ejpam-6811	10	25	5	5	NUM
ejpam-6811	10	26	]	]	PUNCT
ejpam-6811	10	27	,	,	PUNCT
ejpam-6811	10	28	which	which	PRON
ejpam-6811	10	29	∗corresponding	∗corresponde	VERB
ejpam-6811	10	30	author	author	NOUN
ejpam-6811	10	31	.	.	PUNCT
ejpam-6811	11	1	doi	doi	NOUN
ejpam-6811	11	2	:	:	PUNCT
ejpam-6811	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6811	https://doi.org/10.29020/nybg.ejpam.v18i4.6811	ADP
ejpam-6811	11	4	email	email	NOUN
ejpam-6811	11	5	addresses	address	NOUN
ejpam-6811	11	6	:	:	PUNCT
ejpam-6811	11	7	d.e.shehwar@cust.edu.pk	d.e.shehwar@cust.edu.pk	PROPN
ejpam-6811	11	8	(	(	PUNCT
ejpam-6811	11	9	d.	d.	PROPN
ejpam-6811	11	10	e.	e.	PROPN
ejpam-6811	11	11	shehwar	shehwar	PROPN
ejpam-6811	11	12	sagheer	sagheer	PROPN
ejpam-6811	11	13	)	)	PUNCT
ejpam-6811	11	14	,	,	PUNCT
ejpam-6811	11	15	h.alqawaqneh@zuj.edu.jo	h.alqawaqneh@zuj.edu.jo	PROPN
ejpam-6811	11	16	(	(	PUNCT
ejpam-6811	11	17	h.	h.	PROPN
ejpam-6811	11	18	qawaqneh	qawaqneh	PROPN
ejpam-6811	11	19	)	)	PUNCT
ejpam-6811	11	20	,	,	PUNCT
ejpam-6811	11	21	samina.batul@cust.edu.pk	samina.batul@cust.edu.pk	NOUN
ejpam-6811	11	22	(	(	PUNCT
ejpam-6811	11	23	s.	s.	PROPN
ejpam-6811	11	24	batul	batul	PROPN
ejpam-6811	11	25	)	)	PUNCT
ejpam-6811	11	26	,	,	PUNCT
ejpam-6811	11	27	mmt203011@cust.pk	mmt203011@cust.pk	PROPN
ejpam-6811	11	28	(	(	PUNCT
ejpam-6811	11	29	i.	i.	NOUN
ejpam-6811	11	30	urooj	urooj	PROPN
ejpam-6811	11	31	)	)	PUNCT
ejpam-6811	11	32	,	,	PUNCT
ejpam-6811	11	33	mmt193039@cust.pk	mmt193039@cust.pk	PROPN
ejpam-6811	11	34	(	(	PUNCT
ejpam-6811	11	35	z.	z.	PROPN
ejpam-6811	11	36	rahman	rahman	PROPN
ejpam-6811	11	37	)	)	PUNCT
ejpam-6811	11	38	,	,	PUNCT
ejpam-6811	11	39	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	INTJ
ejpam-6811	11	40	(	(	PUNCT
ejpam-6811	11	41	h.	h.	PROPN
ejpam-6811	11	42	aydi	aydi	ADJ
ejpam-6811	11	43	)	)	PUNCT
ejpam-6811	11	44	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6811	11	45	1	1	NUM
ejpam-6811	11	46	copyright	copyright	NOUN
ejpam-6811	11	47	:	:	PUNCT
ejpam-6811	12	1	©	©	PROPN
ejpam-6811	12	2	2025	2025	NUM
ejpam-6811	12	3	the	the	DET
ejpam-6811	12	4	author(s	author(s	NOUN
ejpam-6811	12	5	)	)	PUNCT
ejpam-6811	12	6	.	.	PUNCT
ejpam-6811	13	1	(	(	PUNCT
ejpam-6811	13	2	cc	cc	NOUN
ejpam-6811	13	3	by	by	ADP
ejpam-6811	13	4	-	-	PUNCT
ejpam-6811	13	5	nc	nc	PROPN
ejpam-6811	13	6	4.0	4.0	NUM
ejpam-6811	13	7	)	)	PUNCT
ejpam-6811	13	8	d.	d.	PROPN
ejpam-6811	13	9	e.	e.	PROPN
ejpam-6811	13	10	shehwar	shehwar	PROPN
ejpam-6811	13	11	sagheer	sagheer	PROPN
ejpam-6811	13	12	et	et	PROPN
ejpam-6811	13	13	al	al	PROPN
ejpam-6811	13	14	.	.	PUNCT
ejpam-6811	13	15	/	/	SYM
ejpam-6811	13	16	eur	eur	PROPN
ejpam-6811	13	17	.	.	PUNCT
ejpam-6811	14	1	j.	j.	PROPN
ejpam-6811	14	2	pure	pure	PROPN
ejpam-6811	14	3	appl	appl	PROPN
ejpam-6811	14	4	.	.	PROPN
ejpam-6811	14	5	math	math	PROPN
ejpam-6811	14	6	,	,	PUNCT
ejpam-6811	14	7	18	18	NUM
ejpam-6811	14	8	(	(	PUNCT
ejpam-6811	14	9	4	4	NUM
ejpam-6811	14	10	)	)	PUNCT
ejpam-6811	14	11	(	(	PUNCT
ejpam-6811	14	12	2025	2025	NUM
ejpam-6811	14	13	)	)	PUNCT
ejpam-6811	14	14	,	,	PUNCT
ejpam-6811	14	15	6811	6811	NUM
ejpam-6811	14	16	2	2	NUM
ejpam-6811	14	17	of	of	ADP
ejpam-6811	14	18	24	24	NUM
ejpam-6811	14	19	has	have	AUX
ejpam-6811	14	20	since	since	ADV
ejpam-6811	14	21	become	become	VERB
ejpam-6811	14	22	a	a	DET
ejpam-6811	14	23	fertile	fertile	ADJ
ejpam-6811	14	24	ground	ground	NOUN
ejpam-6811	14	25	for	for	ADP
ejpam-6811	14	26	research	research	NOUN
ejpam-6811	14	27	.	.	PUNCT
ejpam-6811	15	1	notable	notable	ADJ
ejpam-6811	15	2	contributions	contribution	NOUN
ejpam-6811	15	3	include	include	VERB
ejpam-6811	15	4	the	the	DET
ejpam-6811	15	5	work	work	NOUN
ejpam-6811	15	6	of	of	ADP
ejpam-6811	15	7	afshari	afshari	NOUN
ejpam-6811	15	8	et	et	PROPN
ejpam-6811	15	9	al	al	PROPN
ejpam-6811	15	10	.	.	PUNCT
ejpam-6811	16	1	[	[	X
ejpam-6811	16	2	6	6	NUM
ejpam-6811	16	3	]	]	PUNCT
ejpam-6811	16	4	and	and	CCONJ
ejpam-6811	16	5	aydi	aydi	VERB
ejpam-6811	16	6	et	et	PROPN
ejpam-6811	16	7	al	al	PROPN
ejpam-6811	16	8	.	.	PUNCT
ejpam-6811	17	1	[	[	X
ejpam-6811	17	2	7	7	X
ejpam-6811	17	3	]	]	PUNCT
ejpam-6811	17	4	on	on	ADP
ejpam-6811	17	5	multivalued	multivalued	ADJ
ejpam-6811	17	6	mappings	mapping	NOUN
ejpam-6811	17	7	,	,	PUNCT
ejpam-6811	17	8	among	among	ADP
ejpam-6811	17	9	other	other	ADJ
ejpam-6811	17	10	significant	significant	ADJ
ejpam-6811	17	11	developments	development	NOUN
ejpam-6811	17	12	[	[	X
ejpam-6811	17	13	8–16	8–16	PROPN
ejpam-6811	17	14	]	]	PUNCT
ejpam-6811	17	15	.	.	PUNCT
ejpam-6811	18	1	a	a	DET
ejpam-6811	18	2	pivotal	pivotal	ADJ
ejpam-6811	18	3	expansion	expansion	NOUN
ejpam-6811	18	4	of	of	ADP
ejpam-6811	18	5	this	this	DET
ejpam-6811	18	6	framework	framework	NOUN
ejpam-6811	18	7	occurred	occur	VERB
ejpam-6811	18	8	when	when	SCONJ
ejpam-6811	18	9	jachymski	jachymski	PROPN
ejpam-6811	18	10	[	[	X
ejpam-6811	18	11	jachymski	jachymski	X
ejpam-6811	18	12	]	]	PUNCT
ejpam-6811	18	13	incorporated	incorporate	VERB
ejpam-6811	18	14	the	the	DET
ejpam-6811	18	15	concept	concept	NOUN
ejpam-6811	18	16	of	of	ADP
ejpam-6811	18	17	directed	direct	VERB
ejpam-6811	18	18	graphs	graph	NOUN
ejpam-6811	18	19	into	into	ADP
ejpam-6811	18	20	metric	metric	ADJ
ejpam-6811	18	21	fixed	fix	VERB
ejpam-6811	18	22	point	point	NOUN
ejpam-6811	18	23	theory	theory	NOUN
ejpam-6811	18	24	,	,	PUNCT
ejpam-6811	18	25	inspiring	inspire	VERB
ejpam-6811	18	26	subsequent	subsequent	ADJ
ejpam-6811	18	27	research	research	NOUN
ejpam-6811	18	28	in	in	ADP
ejpam-6811	18	29	graph	graph	NOUN
ejpam-6811	18	30	-	-	PUNCT
ejpam-6811	18	31	based	base	VERB
ejpam-6811	18	32	frameworks	framework	NOUN
ejpam-6811	18	33	[	[	X
ejpam-6811	18	34	17–21	17–21	NUM
ejpam-6811	18	35	]	]	X
ejpam-6811	18	36	.	.	PUNCT
ejpam-6811	19	1	more	more	ADV
ejpam-6811	19	2	recently	recently	ADV
ejpam-6811	19	3	,	,	PUNCT
ejpam-6811	19	4	the	the	DET
ejpam-6811	19	5	integration	integration	NOUN
ejpam-6811	19	6	of	of	ADP
ejpam-6811	19	7	auxiliary	auxiliary	ADJ
ejpam-6811	19	8	functions	function	NOUN
ejpam-6811	19	9	has	have	AUX
ejpam-6811	19	10	further	far	ADV
ejpam-6811	19	11	enriched	enrich	VERB
ejpam-6811	19	12	the	the	DET
ejpam-6811	19	13	theory	theory	NOUN
ejpam-6811	19	14	.	.	PUNCT
ejpam-6811	20	1	karapinar	karapinar	VERB
ejpam-6811	20	2	et	et	PROPN
ejpam-6811	20	3	al	al	PROPN
ejpam-6811	20	4	.	.	PUNCT
ejpam-6811	21	1	[	[	X
ejpam-6811	21	2	22	22	NUM
ejpam-6811	21	3	]	]	PUNCT
ejpam-6811	21	4	demonstrated	demonstrate	VERB
ejpam-6811	21	5	their	their	PRON
ejpam-6811	21	6	efficacy	efficacy	NOUN
ejpam-6811	21	7	in	in	ADP
ejpam-6811	21	8	establishing	establish	VERB
ejpam-6811	21	9	existence	existence	NOUN
ejpam-6811	21	10	and	and	CCONJ
ejpam-6811	21	11	uniqueness	uniqueness	NOUN
ejpam-6811	21	12	results	result	NOUN
ejpam-6811	21	13	for	for	ADP
ejpam-6811	21	14	fractional	fractional	ADJ
ejpam-6811	21	15	differential	differential	ADJ
ejpam-6811	21	16	equations	equation	NOUN
ejpam-6811	21	17	,	,	PUNCT
ejpam-6811	21	18	an	an	DET
ejpam-6811	21	19	approach	approach	NOUN
ejpam-6811	21	20	extended	extend	VERB
ejpam-6811	21	21	by	by	ADP
ejpam-6811	21	22	wongsaijai	wongsaijai	PROPN
ejpam-6811	21	23	et	et	NOUN
ejpam-6811	21	24	al	al	PROPN
ejpam-6811	21	25	.	.	PUNCT
ejpam-6811	22	1	[	[	X
ejpam-6811	22	2	23	23	NUM
ejpam-6811	22	3	]	]	PUNCT
ejpam-6811	22	4	to	to	ADP
ejpam-6811	22	5	metric	metric	ADJ
ejpam-6811	22	6	spaces	space	NOUN
ejpam-6811	22	7	with	with	ADP
ejpam-6811	22	8	graphs	graph	NOUN
ejpam-6811	22	9	.	.	PUNCT
ejpam-6811	23	1	motivated	motivate	VERB
ejpam-6811	23	2	by	by	ADP
ejpam-6811	23	3	these	these	DET
ejpam-6811	23	4	advancements	advancement	NOUN
ejpam-6811	23	5	,	,	PUNCT
ejpam-6811	23	6	this	this	DET
ejpam-6811	23	7	research	research	NOUN
ejpam-6811	23	8	aims	aim	VERB
ejpam-6811	23	9	to	to	PART
ejpam-6811	23	10	develop	develop	VERB
ejpam-6811	23	11	a	a	DET
ejpam-6811	23	12	unified	unified	ADJ
ejpam-6811	23	13	approach	approach	NOUN
ejpam-6811	23	14	within	within	ADP
ejpam-6811	23	15	b	b	NOUN
ejpam-6811	23	16	-	-	ADJ
ejpam-6811	23	17	metric	metric	ADJ
ejpam-6811	23	18	spaces	space	NOUN
ejpam-6811	23	19	endowed	endow	VERB
ejpam-6811	23	20	with	with	ADP
ejpam-6811	23	21	a	a	DET
ejpam-6811	23	22	directed	direct	VERB
ejpam-6811	23	23	graph	graph	NOUN
ejpam-6811	23	24	.	.	PUNCT
ejpam-6811	24	1	the	the	DET
ejpam-6811	24	2	primary	primary	ADJ
ejpam-6811	24	3	contributions	contribution	NOUN
ejpam-6811	24	4	of	of	ADP
ejpam-6811	24	5	this	this	DET
ejpam-6811	24	6	work	work	NOUN
ejpam-6811	24	7	are	be	AUX
ejpam-6811	24	8	fourfold	fourfold	ADJ
ejpam-6811	24	9	:	:	PUNCT
ejpam-6811	24	10	(	(	PUNCT
ejpam-6811	24	11	i	i	NOUN
ejpam-6811	24	12	)	)	PUNCT
ejpam-6811	24	13	we	we	PRON
ejpam-6811	24	14	introduce	introduce	VERB
ejpam-6811	24	15	a	a	DET
ejpam-6811	24	16	broader	broad	ADJ
ejpam-6811	24	17	class	class	NOUN
ejpam-6811	24	18	of	of	ADP
ejpam-6811	24	19	contractions	contraction	NOUN
ejpam-6811	24	20	integrated	integrate	VERB
ejpam-6811	24	21	with	with	ADP
ejpam-6811	24	22	auxiliary	auxiliary	ADJ
ejpam-6811	24	23	functions	function	NOUN
ejpam-6811	24	24	,	,	PUNCT
ejpam-6811	24	25	extending	extend	VERB
ejpam-6811	24	26	the	the	DET
ejpam-6811	24	27	results	result	NOUN
ejpam-6811	24	28	of	of	ADP
ejpam-6811	24	29	the	the	DET
ejpam-6811	24	30	aforementioned	aforementioned	ADJ
ejpam-6811	24	31	studies	study	NOUN
ejpam-6811	24	32	to	to	ADP
ejpam-6811	24	33	the	the	DET
ejpam-6811	24	34	more	more	ADV
ejpam-6811	24	35	general	general	ADJ
ejpam-6811	24	36	setting	setting	NOUN
ejpam-6811	24	37	of	of	ADP
ejpam-6811	24	38	bmss	bmss	NOUN
ejpam-6811	24	39	.	.	PUNCT
ejpam-6811	25	1	previous	previous	ADJ
ejpam-6811	25	2	research	research	NOUN
ejpam-6811	25	3	has	have	AUX
ejpam-6811	25	4	established	establish	VERB
ejpam-6811	25	5	foundational	foundational	ADJ
ejpam-6811	25	6	results	result	NOUN
ejpam-6811	25	7	in	in	ADP
ejpam-6811	25	8	this	this	DET
ejpam-6811	25	9	area	area	NOUN
ejpam-6811	25	10	.	.	PUNCT
ejpam-6811	26	1	karapinar	karapinar	VERB
ejpam-6811	26	2	et	et	PROPN
ejpam-6811	26	3	al	al	PROPN
ejpam-6811	26	4	.	.	PUNCT
ejpam-6811	27	1	[	[	X
ejpam-6811	27	2	22	22	NUM
ejpam-6811	27	3	]	]	PUNCT
ejpam-6811	27	4	demonstrated	demonstrate	VERB
ejpam-6811	27	5	the	the	DET
ejpam-6811	27	6	existence	existence	NOUN
ejpam-6811	27	7	of	of	ADP
ejpam-6811	27	8	fixed	fix	VERB
ejpam-6811	27	9	points	point	NOUN
ejpam-6811	27	10	in	in	ADP
ejpam-6811	27	11	the	the	DET
ejpam-6811	27	12	context	context	NOUN
ejpam-6811	27	13	of	of	ADP
ejpam-6811	27	14	metric	metric	ADJ
ejpam-6811	27	15	spaces	space	NOUN
ejpam-6811	27	16	;	;	PUNCT
ejpam-6811	27	17	however	however	ADV
ejpam-6811	27	18	,	,	PUNCT
ejpam-6811	27	19	their	their	PRON
ejpam-6811	27	20	work	work	NOUN
ejpam-6811	27	21	did	do	AUX
ejpam-6811	27	22	not	not	PART
ejpam-6811	27	23	incorporate	incorporate	VERB
ejpam-6811	27	24	a	a	DET
ejpam-6811	27	25	directed	direct	VERB
ejpam-6811	27	26	graph	graph	NOUN
ejpam-6811	27	27	framework	framework	NOUN
ejpam-6811	27	28	.	.	PUNCT
ejpam-6811	28	1	similarly	similarly	ADV
ejpam-6811	28	2	,	,	PUNCT
ejpam-6811	28	3	wongsaijai	wongsaijai	INTJ
ejpam-6811	28	4	et	et	NOUN
ejpam-6811	28	5	al	al	PROPN
ejpam-6811	28	6	.	.	PUNCT
ejpam-6811	29	1	[	[	X
ejpam-6811	29	2	23	23	NUM
ejpam-6811	29	3	]	]	PUNCT
ejpam-6811	29	4	extended	extend	VERB
ejpam-6811	29	5	this	this	DET
ejpam-6811	29	6	line	line	NOUN
ejpam-6811	29	7	of	of	ADP
ejpam-6811	29	8	inquiry	inquiry	NOUN
ejpam-6811	29	9	by	by	ADP
ejpam-6811	29	10	considering	consider	VERB
ejpam-6811	29	11	a	a	DET
ejpam-6811	29	12	directed	direct	VERB
ejpam-6811	29	13	graph	graph	NOUN
ejpam-6811	29	14	,	,	PUNCT
ejpam-6811	29	15	but	but	CCONJ
ejpam-6811	29	16	their	their	PRON
ejpam-6811	29	17	analysis	analysis	NOUN
ejpam-6811	29	18	was	be	AUX
ejpam-6811	29	19	confined	confine	VERB
ejpam-6811	29	20	to	to	ADP
ejpam-6811	29	21	a	a	DET
ejpam-6811	29	22	context	context	NOUN
ejpam-6811	29	23	that	that	PRON
ejpam-6811	29	24	did	do	AUX
ejpam-6811	29	25	not	not	PART
ejpam-6811	29	26	address	address	VERB
ejpam-6811	29	27	the	the	DET
ejpam-6811	29	28	challenges	challenge	NOUN
ejpam-6811	29	29	posed	pose	VERB
ejpam-6811	29	30	by	by	ADP
ejpam-6811	29	31	the	the	DET
ejpam-6811	29	32	triangular	triangular	NOUN
ejpam-6811	29	33	inequality	inequality	NOUN
ejpam-6811	29	34	in	in	ADP
ejpam-6811	29	35	b	b	NOUN
ejpam-6811	29	36	-	-	ADJ
ejpam-6811	29	37	metric	metric	ADJ
ejpam-6811	29	38	spaces	space	NOUN
ejpam-6811	29	39	.	.	PUNCT
ejpam-6811	30	1	(	(	PUNCT
ejpam-6811	30	2	ii	ii	X
ejpam-6811	30	3	)	)	PUNCT
ejpam-6811	30	4	we	we	PRON
ejpam-6811	30	5	establish	establish	VERB
ejpam-6811	30	6	significant	significant	ADJ
ejpam-6811	30	7	theoretical	theoretical	ADJ
ejpam-6811	30	8	results	result	NOUN
ejpam-6811	30	9	,	,	PUNCT
ejpam-6811	30	10	including	include	VERB
ejpam-6811	30	11	theorems	theorem	NOUN
ejpam-6811	30	12	on	on	ADP
ejpam-6811	30	13	the	the	DET
ejpam-6811	30	14	existence	existence	NOUN
ejpam-6811	30	15	of	of	ADP
ejpam-6811	30	16	coincidence	coincidence	NOUN
ejpam-6811	30	17	points	point	NOUN
ejpam-6811	30	18	,	,	PUNCT
ejpam-6811	30	19	leveraging	leverage	VERB
ejpam-6811	30	20	the	the	DET
ejpam-6811	30	21	properties	property	NOUN
ejpam-6811	30	22	of	of	ADP
ejpam-6811	30	23	these	these	DET
ejpam-6811	30	24	auxiliary	auxiliary	ADJ
ejpam-6811	30	25	functions	function	NOUN
ejpam-6811	30	26	.	.	PUNCT
ejpam-6811	31	1	(	(	PUNCT
ejpam-6811	31	2	iii	iii	X
ejpam-6811	31	3	)	)	PUNCT
ejpam-6811	31	4	we	we	PRON
ejpam-6811	31	5	pioneer	pioneer	VERB
ejpam-6811	31	6	the	the	DET
ejpam-6811	31	7	analysis	analysis	NOUN
ejpam-6811	31	8	of	of	ADP
ejpam-6811	31	9	fixed	fix	VERB
ejpam-6811	31	10	points	point	NOUN
ejpam-6811	31	11	in	in	ADP
ejpam-6811	31	12	a	a	DET
ejpam-6811	31	13	context	context	NOUN
ejpam-6811	31	14	involving	involve	VERB
ejpam-6811	31	15	two	two	NUM
ejpam-6811	31	16	distinct	distinct	ADJ
ejpam-6811	31	17	metrics	metric	NOUN
ejpam-6811	31	18	on	on	ADP
ejpam-6811	31	19	a	a	DET
ejpam-6811	31	20	non	non	ADJ
ejpam-6811	31	21	-	-	ADJ
ejpam-6811	31	22	empty	empty	ADJ
ejpam-6811	31	23	set	set	NOUN
ejpam-6811	31	24	.	.	PUNCT
ejpam-6811	32	1	(	(	PUNCT
ejpam-6811	32	2	iv	iv	X
ejpam-6811	32	3	)	)	PUNCT
ejpam-6811	32	4	the	the	DET
ejpam-6811	32	5	proposed	propose	VERB
ejpam-6811	32	6	framework	framework	NOUN
ejpam-6811	32	7	is	be	AUX
ejpam-6811	32	8	not	not	PART
ejpam-6811	32	9	merely	merely	ADV
ejpam-6811	32	10	theoretical	theoretical	ADJ
ejpam-6811	32	11	;	;	PUNCT
ejpam-6811	32	12	it	it	PRON
ejpam-6811	32	13	provides	provide	VERB
ejpam-6811	32	14	an	an	DET
ejpam-6811	32	15	effective	effective	ADJ
ejpam-6811	32	16	method	method	NOUN
ejpam-6811	32	17	for	for	ADP
ejpam-6811	32	18	predicting	predict	VERB
ejpam-6811	32	19	solutions	solution	NOUN
ejpam-6811	32	20	to	to	ADP
ejpam-6811	32	21	fractional	fractional	ADJ
ejpam-6811	32	22	differential	differential	ADJ
ejpam-6811	32	23	equations	equation	NOUN
ejpam-6811	32	24	,	,	PUNCT
ejpam-6811	32	25	which	which	PRON
ejpam-6811	32	26	are	be	AUX
ejpam-6811	32	27	critical	critical	ADJ
ejpam-6811	32	28	in	in	ADP
ejpam-6811	32	29	modeling	model	VERB
ejpam-6811	32	30	phenomena	phenomenon	NOUN
ejpam-6811	32	31	across	across	ADP
ejpam-6811	32	32	physics	physics	NOUN
ejpam-6811	32	33	and	and	CCONJ
ejpam-6811	32	34	engineering	engineering	NOUN
ejpam-6811	32	35	[	[	X
ejpam-6811	32	36	24–26	24–26	NUM
ejpam-6811	32	37	]	]	PUNCT
ejpam-6811	32	38	.	.	PUNCT
ejpam-6811	33	1	a	a	DET
ejpam-6811	33	2	key	key	ADJ
ejpam-6811	33	3	advantage	advantage	NOUN
ejpam-6811	33	4	of	of	ADP
ejpam-6811	33	5	our	our	PRON
ejpam-6811	33	6	results	result	NOUN
ejpam-6811	33	7	is	be	AUX
ejpam-6811	33	8	their	their	PRON
ejpam-6811	33	9	capacity	capacity	NOUN
ejpam-6811	33	10	to	to	PART
ejpam-6811	33	11	yield	yield	VERB
ejpam-6811	33	12	precise	precise	ADJ
ejpam-6811	33	13	estimates	estimate	NOUN
ejpam-6811	33	14	for	for	ADP
ejpam-6811	33	15	solutions	solution	NOUN
ejpam-6811	33	16	,	,	PUNCT
ejpam-6811	33	17	enhancing	enhance	VERB
ejpam-6811	33	18	their	their	PRON
ejpam-6811	33	19	practical	practical	ADJ
ejpam-6811	33	20	utility	utility	NOUN
ejpam-6811	33	21	.	.	PUNCT
ejpam-6811	34	1	2	2	X
ejpam-6811	34	2	.	.	X
ejpam-6811	34	3	preliminaries	preliminary	NOUN
ejpam-6811	34	4	in	in	ADP
ejpam-6811	34	5	this	this	DET
ejpam-6811	34	6	work	work	NOUN
ejpam-6811	34	7	,	,	PUNCT
ejpam-6811	34	8	x	x	PRON
ejpam-6811	34	9	denotes	denote	VERB
ejpam-6811	34	10	a	a	DET
ejpam-6811	34	11	non	non	ADJ
ejpam-6811	34	12	-	-	ADJ
ejpam-6811	34	13	empty	empty	ADJ
ejpam-6811	34	14	set	set	NOUN
ejpam-6811	34	15	and	and	CCONJ
ejpam-6811	34	16	ḡ	ḡ	VERB
ejpam-6811	34	17	=	=	SYM
ejpam-6811	34	18	(	(	PUNCT
ejpam-6811	34	19	v	v	NOUN
ejpam-6811	34	20	(	(	PUNCT
ejpam-6811	34	21	ḡ	ḡ	VERB
ejpam-6811	34	22	)	)	PUNCT
ejpam-6811	34	23	,	,	PUNCT
ejpam-6811	34	24	e(ḡ	e(ḡ	PROPN
ejpam-6811	34	25	)	)	PUNCT
ejpam-6811	34	26	)	)	PUNCT
ejpam-6811	34	27	will	will	AUX
ejpam-6811	34	28	represent	represent	VERB
ejpam-6811	34	29	a	a	DET
ejpam-6811	34	30	directed	direct	VERB
ejpam-6811	34	31	graph	graph	NOUN
ejpam-6811	34	32	(	(	PUNCT
ejpam-6811	34	33	dg	dg	NOUN
ejpam-6811	34	34	)	)	PUNCT
ejpam-6811	34	35	.	.	PUNCT
ejpam-6811	35	1	let	let	VERB
ejpam-6811	35	2	us	we	PRON
ejpam-6811	35	3	examine	examine	VERB
ejpam-6811	35	4	some	some	DET
ejpam-6811	35	5	fundamental	fundamental	ADJ
ejpam-6811	35	6	principles	principle	NOUN
ejpam-6811	35	7	and	and	CCONJ
ejpam-6811	35	8	implications	implication	NOUN
ejpam-6811	35	9	that	that	PRON
ejpam-6811	35	10	will	will	AUX
ejpam-6811	35	11	serve	serve	VERB
ejpam-6811	35	12	as	as	ADP
ejpam-6811	35	13	the	the	DET
ejpam-6811	35	14	stage	stage	NOUN
ejpam-6811	35	15	for	for	ADP
ejpam-6811	35	16	our	our	PRON
ejpam-6811	35	17	primary	primary	ADJ
ejpam-6811	35	18	findings	finding	NOUN
ejpam-6811	35	19	.	.	PUNCT
ejpam-6811	36	1	definition	definition	NOUN
ejpam-6811	36	2	1	1	NUM
ejpam-6811	36	3	.	.	PUNCT
ejpam-6811	37	1	let	let	VERB
ejpam-6811	37	2	x	x	SYM
ejpam-6811	37	3	6=	6=	ADP
ejpam-6811	37	4	∅	∅	NOUN
ejpam-6811	37	5	and	and	CCONJ
ejpam-6811	37	6	b	b	NOUN
ejpam-6811	37	7	∈	∈	NOUN
ejpam-6811	37	8	r	r	NOUN
ejpam-6811	37	9	such	such	DET
ejpam-6811	37	10	that	that	DET
ejpam-6811	37	11	b	b	NOUN
ejpam-6811	37	12	≥	≥	NUM
ejpam-6811	37	13	1	1	NUM
ejpam-6811	37	14	.	.	PUNCT
ejpam-6811	38	1	a	a	DET
ejpam-6811	38	2	mapping	mapping	NOUN
ejpam-6811	38	3	db	db	X
ejpam-6811	38	4	:	:	PUNCT
ejpam-6811	38	5	x	x	PROPN
ejpam-6811	38	6	×x	×x	X
ejpam-6811	38	7	→	→	X
ejpam-6811	38	8	[	[	X
ejpam-6811	38	9	0,∞	0,∞	NOUN
ejpam-6811	38	10	)	)	PUNCT
ejpam-6811	38	11	satisfying	satisfy	VERB
ejpam-6811	38	12	the	the	DET
ejpam-6811	38	13	following	follow	VERB
ejpam-6811	38	14	axioms	axiom	NOUN
ejpam-6811	38	15	is	be	AUX
ejpam-6811	38	16	called	call	VERB
ejpam-6811	38	17	a	a	DET
ejpam-6811	38	18	b	b	NOUN
ejpam-6811	38	19	-	-	NOUN
ejpam-6811	38	20	metric	metric	ADJ
ejpam-6811	38	21	on	on	ADP
ejpam-6811	38	22	x	x	NOUN
ejpam-6811	38	23	:	:	PUNCT
ejpam-6811	38	24	d́b(1	d́b(1	NOUN
ejpam-6811	38	25	):	):	PUNCT
ejpam-6811	38	26	db(x	db(x	ADJ
ejpam-6811	38	27	,	,	PUNCT
ejpam-6811	38	28	y	y	NOUN
ejpam-6811	38	29	)	)	PUNCT
ejpam-6811	38	30	=	=	SYM
ejpam-6811	38	31	0	0	NUM
ejpam-6811	38	32	⇔	⇔	X
ejpam-6811	38	33	x	x	X
ejpam-6811	38	34	=	=	SYM
ejpam-6811	38	35	y	y	PROPN
ejpam-6811	38	36	;	;	PUNCT
ejpam-6811	38	37	d́b(2	d́b(2	PROPN
ejpam-6811	38	38	):	):	PUNCT
ejpam-6811	38	39	db(x	db(x	ADJ
ejpam-6811	38	40	,	,	PUNCT
ejpam-6811	38	41	y	y	NOUN
ejpam-6811	38	42	)	)	PUNCT
ejpam-6811	38	43	=	=	PUNCT
ejpam-6811	38	44	db(y	db(y	ADJ
ejpam-6811	38	45	,	,	PUNCT
ejpam-6811	38	46	x	x	X
ejpam-6811	38	47	)	)	PUNCT
ejpam-6811	38	48	;	;	PUNCT
ejpam-6811	38	49	d.	d.	PROPN
ejpam-6811	38	50	e.	e.	PROPN
ejpam-6811	38	51	shehwar	shehwar	PROPN
ejpam-6811	38	52	sagheer	sagheer	PROPN
ejpam-6811	38	53	et	et	PROPN
ejpam-6811	38	54	al	al	PROPN
ejpam-6811	38	55	.	.	PUNCT
ejpam-6811	38	56	/	/	SYM
ejpam-6811	38	57	eur	eur	PROPN
ejpam-6811	38	58	.	.	PUNCT
ejpam-6811	39	1	j.	j.	PROPN
ejpam-6811	39	2	pure	pure	PROPN
ejpam-6811	39	3	appl	appl	PROPN
ejpam-6811	39	4	.	.	PROPN
ejpam-6811	39	5	math	math	PROPN
ejpam-6811	39	6	,	,	PUNCT
ejpam-6811	39	7	18	18	NUM
ejpam-6811	39	8	(	(	PUNCT
ejpam-6811	39	9	4	4	NUM
ejpam-6811	39	10	)	)	PUNCT
ejpam-6811	39	11	(	(	PUNCT
ejpam-6811	39	12	2025	2025	NUM
ejpam-6811	39	13	)	)	PUNCT
ejpam-6811	39	14	,	,	PUNCT
ejpam-6811	39	15	6811	6811	NUM
ejpam-6811	39	16	3	3	NUM
ejpam-6811	39	17	of	of	ADP
ejpam-6811	39	18	24	24	NUM
ejpam-6811	39	19	d́b(3	d́b(3	NOUN
ejpam-6811	39	20	):	):	PUNCT
ejpam-6811	39	21	db(x	db(x	ADJ
ejpam-6811	39	22	,	,	PUNCT
ejpam-6811	39	23	y	y	NOUN
ejpam-6811	39	24	)	)	PUNCT
ejpam-6811	39	25	≤	≤	NOUN
ejpam-6811	39	26	b{db(x	b{db(x	PROPN
ejpam-6811	39	27	,	,	PUNCT
ejpam-6811	39	28	z	z	NOUN
ejpam-6811	39	29	)	)	PUNCT
ejpam-6811	39	30	+	+	CCONJ
ejpam-6811	39	31	db(z	db(z	PROPN
ejpam-6811	39	32	,	,	PUNCT
ejpam-6811	39	33	y	y	NOUN
ejpam-6811	39	34	)	)	PUNCT
ejpam-6811	39	35	}	}	PUNCT
ejpam-6811	39	36	,	,	PUNCT
ejpam-6811	39	37	for	for	ADP
ejpam-6811	39	38	all	all	DET
ejpam-6811	39	39	x	x	NOUN
ejpam-6811	39	40	,	,	PUNCT
ejpam-6811	39	41	y	y	PROPN
ejpam-6811	39	42	,	,	PUNCT
ejpam-6811	39	43	z	z	PROPN
ejpam-6811	39	44	∈	∈	PROPN
ejpam-6811	39	45	x.	x.	NOUN
ejpam-6811	40	1	the	the	DET
ejpam-6811	40	2	pair	pair	NOUN
ejpam-6811	40	3	(	(	PUNCT
ejpam-6811	40	4	x	x	NOUN
ejpam-6811	40	5	,	,	PUNCT
ejpam-6811	40	6	db	db	PROPN
ejpam-6811	40	7	)	)	PUNCT
ejpam-6811	40	8	is	be	AUX
ejpam-6811	40	9	said	say	VERB
ejpam-6811	40	10	to	to	PART
ejpam-6811	40	11	be	be	AUX
ejpam-6811	40	12	a	a	DET
ejpam-6811	40	13	bms	bms	PROPN
ejpam-6811	40	14	.	.	PUNCT
ejpam-6811	40	15	example	example	NOUN
ejpam-6811	41	1	1	1	NUM
ejpam-6811	41	2	.	.	PUNCT
ejpam-6811	42	1	[	[	X
ejpam-6811	42	2	27	27	NUM
ejpam-6811	42	3	]	]	PUNCT
ejpam-6811	42	4	let	let	VERB
ejpam-6811	42	5	x	x	SYM
ejpam-6811	42	6	=	=	PUNCT
ejpam-6811	42	7	lp(r	lp(r	X
ejpam-6811	42	8	)	)	PUNCT
ejpam-6811	42	9	(	(	PUNCT
ejpam-6811	42	10	with	with	ADP
ejpam-6811	42	11	p	p	PROPN
ejpam-6811	42	12	∈	∈	PROPN
ejpam-6811	42	13	(	(	PUNCT
ejpam-6811	42	14	0	0	NUM
ejpam-6811	42	15	,	,	PUNCT
ejpam-6811	42	16	1	1	NUM
ejpam-6811	42	17	)	)	PUNCT
ejpam-6811	42	18	)	)	PUNCT
ejpam-6811	42	19	be	be	AUX
ejpam-6811	42	20	the	the	DET
ejpam-6811	42	21	space	space	NOUN
ejpam-6811	42	22	of	of	ADP
ejpam-6811	42	23	all	all	DET
ejpam-6811	42	24	real	real	ADJ
ejpam-6811	42	25	sequences	sequence	NOUN
ejpam-6811	42	26	having	have	VERB
ejpam-6811	42	27	the	the	DET
ejpam-6811	42	28	property	property	NOUN
ejpam-6811	42	29	lp(r	lp(r	PUNCT
ejpam-6811	42	30	)	)	PUNCT
ejpam-6811	43	1	=	=	PRON
ejpam-6811	44	1	{	{	PUNCT
ejpam-6811	44	2	x	x	SYM
ejpam-6811	44	3	=	=	PUNCT
ejpam-6811	44	4	xk	xk	PROPN
ejpam-6811	44	5	⊂	⊂	PROPN
ejpam-6811	44	6	r	r	X
ejpam-6811	44	7	}	}	PUNCT
ejpam-6811	44	8	,	,	PUNCT
ejpam-6811	44	9	such	such	ADJ
ejpam-6811	44	10	that	that	DET
ejpam-6811	44	11	∑∞	∑∞	NOUN
ejpam-6811	44	12	k=1	k=1	X
ejpam-6811	45	1	|xk|p	|xk|p	X
ejpam-6811	45	2	<	<	X
ejpam-6811	45	3	∞	∞	NUM
ejpam-6811	45	4	and	and	CCONJ
ejpam-6811	45	5	define	define	VERB
ejpam-6811	45	6	a	a	DET
ejpam-6811	45	7	function	function	NOUN
ejpam-6811	45	8	db	db	NOUN
ejpam-6811	45	9	:	:	PUNCT
ejpam-6811	45	10	x	x	PROPN
ejpam-6811	45	11	×x	×x	ADP
ejpam-6811	45	12	→	→	SYM
ejpam-6811	45	13	r+	r+	NOUN
ejpam-6811	45	14	as	as	ADP
ejpam-6811	45	15	db(x	db(x	ADJ
ejpam-6811	45	16	,	,	PUNCT
ejpam-6811	45	17	y	y	NOUN
ejpam-6811	45	18	)	)	PUNCT
ejpam-6811	46	1	=	=	NOUN
ejpam-6811	47	1	(	(	PUNCT
ejpam-6811	47	2	∞∑	∞∑	NUM
ejpam-6811	47	3	k=1	k=1	X
ejpam-6811	47	4	|xk	|xk	ADP
ejpam-6811	47	5	−	−	NOUN
ejpam-6811	47	6	yk|p	yk|p	NOUN
ejpam-6811	47	7	)	)	PUNCT
ejpam-6811	47	8	1	1	NUM
ejpam-6811	47	9	/	/	SYM
ejpam-6811	47	10	p	p	NOUN
ejpam-6811	47	11	,	,	PUNCT
ejpam-6811	47	12	then	then	ADV
ejpam-6811	47	13	(	(	PUNCT
ejpam-6811	47	14	x	x	X
ejpam-6811	47	15	,	,	PUNCT
ejpam-6811	47	16	db	db	PROPN
ejpam-6811	47	17	)	)	PUNCT
ejpam-6811	47	18	is	be	AUX
ejpam-6811	47	19	a	a	DET
ejpam-6811	47	20	bms	bms	NOUN
ejpam-6811	47	21	with	with	ADP
ejpam-6811	47	22	b	b	NOUN
ejpam-6811	47	23	=	=	SYM
ejpam-6811	47	24	2	2	NUM
ejpam-6811	47	25	1	1	NUM
ejpam-6811	47	26	p	p	NOUN
ejpam-6811	47	27	.	.	PUNCT
ejpam-6811	48	1	encouraged	encourage	VERB
ejpam-6811	48	2	by	by	ADP
ejpam-6811	48	3	the	the	DET
ejpam-6811	48	4	ideas	idea	NOUN
ejpam-6811	48	5	of	of	ADP
ejpam-6811	48	6	charoensawan	charoensawan	NOUN
ejpam-6811	48	7	et	et	NOUN
ejpam-6811	48	8	al	al	PROPN
ejpam-6811	48	9	.	.	PUNCT
ejpam-6811	49	1	[	[	X
ejpam-6811	49	2	28	28	NUM
ejpam-6811	49	3	]	]	PUNCT
ejpam-6811	49	4	,	,	PUNCT
ejpam-6811	49	5	we	we	PRON
ejpam-6811	49	6	present	present	VERB
ejpam-6811	49	7	some	some	DET
ejpam-6811	49	8	key	key	ADJ
ejpam-6811	49	9	concepts	concept	NOUN
ejpam-6811	49	10	,	,	PUNCT
ejpam-6811	49	11	particularly	particularly	ADV
ejpam-6811	49	12	regarding	regard	VERB
ejpam-6811	49	13	common	common	ADJ
ejpam-6811	49	14	fixed	fix	VERB
ejpam-6811	49	15	points	point	NOUN
ejpam-6811	49	16	and	and	CCONJ
ejpam-6811	49	17	coincidence	coincidence	NOUN
ejpam-6811	49	18	points	point	NOUN
ejpam-6811	49	19	in	in	ADP
ejpam-6811	49	20	bmss	bmss	NOUN
ejpam-6811	49	21	endowed	endow	VERB
ejpam-6811	49	22	with	with	ADP
ejpam-6811	49	23	a	a	DET
ejpam-6811	49	24	dg	dg	NOUN
ejpam-6811	49	25	.	.	PUNCT
ejpam-6811	50	1	definition	definition	NOUN
ejpam-6811	50	2	2	2	NUM
ejpam-6811	50	3	.	.	PUNCT
ejpam-6811	51	1	let	let	VERB
ejpam-6811	51	2	(	(	PUNCT
ejpam-6811	51	3	x	x	NOUN
ejpam-6811	51	4	,	,	PUNCT
ejpam-6811	51	5	db	db	PROPN
ejpam-6811	51	6	)	)	PUNCT
ejpam-6811	51	7	be	be	AUX
ejpam-6811	51	8	a	a	DET
ejpam-6811	51	9	bms	bms	NOUN
ejpam-6811	51	10	and	and	CCONJ
ejpam-6811	51	11	db	db	PROPN
ejpam-6811	51	12	be	be	AUX
ejpam-6811	51	13	a	a	DET
ejpam-6811	51	14	continuous	continuous	ADJ
ejpam-6811	51	15	metric	metric	NOUN
ejpam-6811	51	16	.	.	PUNCT
ejpam-6811	52	1	let	let	VERB
ejpam-6811	52	2	∆	∆	PROPN
ejpam-6811	52	3	denote	denote	VERB
ejpam-6811	52	4	the	the	DET
ejpam-6811	52	5	diagonal	diagonal	NOUN
ejpam-6811	52	6	of	of	ADP
ejpam-6811	52	7	x	x	SYM
ejpam-6811	52	8	×	×	PROPN
ejpam-6811	52	9	x	x	NOUN
ejpam-6811	52	10	,	,	PUNCT
ejpam-6811	52	11	then	then	ADV
ejpam-6811	52	12	(	(	PUNCT
ejpam-6811	52	13	x	x	X
ejpam-6811	52	14	,	,	PUNCT
ejpam-6811	52	15	db	db	PROPN
ejpam-6811	52	16	)	)	PUNCT
ejpam-6811	52	17	is	be	AUX
ejpam-6811	52	18	considered	consider	VERB
ejpam-6811	52	19	to	to	PART
ejpam-6811	52	20	be	be	AUX
ejpam-6811	52	21	endowed	endow	VERB
ejpam-6811	52	22	with	with	ADP
ejpam-6811	52	23	a	a	DET
ejpam-6811	52	24	directed	direct	VERB
ejpam-6811	52	25	graph	graph	NOUN
ejpam-6811	52	26	ḡ	ḡ	VERB
ejpam-6811	52	27	=	=	SYM
ejpam-6811	52	28	(	(	PUNCT
ejpam-6811	52	29	v	v	NOUN
ejpam-6811	52	30	(	(	PUNCT
ejpam-6811	52	31	ḡ	ḡ	VERB
ejpam-6811	52	32	)	)	PUNCT
ejpam-6811	52	33	,	,	PUNCT
ejpam-6811	52	34	e(ḡ	e(ḡ	PROPN
ejpam-6811	52	35	)	)	PUNCT
ejpam-6811	52	36	)	)	PUNCT
ejpam-6811	53	1	if	if	SCONJ
ejpam-6811	53	2	v	v	X
ejpam-6811	53	3	(	(	PUNCT
ejpam-6811	53	4	ḡ	ḡ	VERB
ejpam-6811	53	5	)	)	PUNCT
ejpam-6811	53	6	is	be	AUX
ejpam-6811	53	7	the	the	DET
ejpam-6811	53	8	set	set	NOUN
ejpam-6811	53	9	of	of	ADP
ejpam-6811	53	10	all	all	DET
ejpam-6811	53	11	the	the	DET
ejpam-6811	53	12	elements	element	NOUN
ejpam-6811	53	13	of	of	ADP
ejpam-6811	53	14	x	x	NOUN
ejpam-6811	53	15	,	,	PUNCT
ejpam-6811	53	16	and	and	CCONJ
ejpam-6811	53	17	the	the	DET
ejpam-6811	53	18	set	set	NOUN
ejpam-6811	53	19	e(ḡ	e(ḡ	NOUN
ejpam-6811	53	20	)	)	PUNCT
ejpam-6811	53	21	contains	contain	VERB
ejpam-6811	53	22	all	all	DET
ejpam-6811	53	23	elements	element	NOUN
ejpam-6811	53	24	of	of	ADP
ejpam-6811	53	25	∆	∆	PROPN
ejpam-6811	53	26	,	,	PUNCT
ejpam-6811	53	27	excluding	exclude	VERB
ejpam-6811	53	28	parallel	parallel	ADJ
ejpam-6811	53	29	edges	edge	NOUN
ejpam-6811	53	30	.	.	PUNCT
ejpam-6811	54	1	definition	definition	NOUN
ejpam-6811	54	2	3	3	NUM
ejpam-6811	54	3	.	.	PUNCT
ejpam-6811	55	1	let	let	VERB
ejpam-6811	55	2	(	(	PUNCT
ejpam-6811	55	3	x	x	NOUN
ejpam-6811	55	4	,	,	PUNCT
ejpam-6811	55	5	db	db	PROPN
ejpam-6811	55	6	)	)	PUNCT
ejpam-6811	55	7	be	be	AUX
ejpam-6811	55	8	a	a	DET
ejpam-6811	55	9	bms	bms	NOUN
ejpam-6811	55	10	together	together	ADV
ejpam-6811	55	11	with	with	ADP
ejpam-6811	55	12	ḡ	ḡ	ADJ
ejpam-6811	55	13	=	=	SYM
ejpam-6811	55	14	(	(	PUNCT
ejpam-6811	55	15	v	v	NOUN
ejpam-6811	55	16	(	(	PUNCT
ejpam-6811	55	17	ḡ	ḡ	VERB
ejpam-6811	55	18	)	)	PUNCT
ejpam-6811	55	19	,	,	PUNCT
ejpam-6811	55	20	e(ḡ	e(ḡ	PROPN
ejpam-6811	55	21	)	)	PUNCT
ejpam-6811	55	22	)	)	PUNCT
ejpam-6811	55	23	,	,	PUNCT
ejpam-6811	55	24	and	and	CCONJ
ejpam-6811	55	25	db	db	PROPN
ejpam-6811	55	26	be	be	AUX
ejpam-6811	55	27	a	a	DET
ejpam-6811	55	28	continuous	continuous	ADJ
ejpam-6811	55	29	metric	metric	NOUN
ejpam-6811	55	30	,	,	PUNCT
ejpam-6811	55	31	then	then	ADV
ejpam-6811	55	32	for	for	ADP
ejpam-6811	55	33	t	t	PROPN
ejpam-6811	55	34	,	,	PUNCT
ejpam-6811	55	35	s	s	PART
ejpam-6811	55	36	:	:	PUNCT
ejpam-6811	55	37	x	x	SYM
ejpam-6811	55	38	→	→	SYM
ejpam-6811	55	39	x	x	SYM
ejpam-6811	55	40	,	,	PUNCT
ejpam-6811	55	41	c(t	c(t	PROPN
ejpam-6811	55	42	,	,	PUNCT
ejpam-6811	55	43	s	s	PART
ejpam-6811	55	44	)	)	PUNCT
ejpam-6811	55	45	=	=	SYM
ejpam-6811	55	46	{	{	PUNCT
ejpam-6811	55	47	x	x	PUNCT
ejpam-6811	55	48	∈	∈	PROPN
ejpam-6811	55	49	x	x	X
ejpam-6811	55	50	:	:	PUNCT
ejpam-6811	55	51	tx	tx	PROPN
ejpam-6811	55	52	=	=	SYM
ejpam-6811	55	53	sx	sx	PROPN
ejpam-6811	55	54	}	}	PUNCT
ejpam-6811	55	55	,	,	PUNCT
ejpam-6811	55	56	is	be	AUX
ejpam-6811	55	57	called	call	VERB
ejpam-6811	55	58	the	the	DET
ejpam-6811	55	59	set	set	NOUN
ejpam-6811	55	60	of	of	ADP
ejpam-6811	55	61	cps	cps	PROPN
ejpam-6811	55	62	of	of	ADP
ejpam-6811	55	63	t	t	PROPN
ejpam-6811	55	64	and	and	CCONJ
ejpam-6811	55	65	s.	s.	PROPN
ejpam-6811	55	66	we	we	PRON
ejpam-6811	55	67	also	also	ADV
ejpam-6811	55	68	have	have	VERB
ejpam-6811	55	69	cm(t	cm(t	NOUN
ejpam-6811	55	70	,	,	PUNCT
ejpam-6811	55	71	s	s	X
ejpam-6811	55	72	)	)	PUNCT
ejpam-6811	55	73	=	=	SYM
ejpam-6811	56	1	{	{	PUNCT
ejpam-6811	56	2	x	x	PUNCT
ejpam-6811	56	3	∈	∈	PROPN
ejpam-6811	56	4	x	x	X
ejpam-6811	56	5	:	:	PUNCT
ejpam-6811	56	6	tx	tx	PROPN
ejpam-6811	56	7	=	=	PUNCT
ejpam-6811	56	8	sx	sx	PROPN
ejpam-6811	56	9	=	=	PUNCT
ejpam-6811	56	10	x	x	NOUN
ejpam-6811	56	11	}	}	PUNCT
ejpam-6811	56	12	,	,	PUNCT
ejpam-6811	56	13	denoting	denote	VERB
ejpam-6811	56	14	the	the	DET
ejpam-6811	56	15	set	set	NOUN
ejpam-6811	56	16	of	of	ADP
ejpam-6811	56	17	common	common	ADJ
ejpam-6811	56	18	fixed	fix	VERB
ejpam-6811	56	19	points	point	NOUN
ejpam-6811	56	20	for	for	ADP
ejpam-6811	56	21	the	the	DET
ejpam-6811	56	22	two	two	NUM
ejpam-6811	56	23	mappings	mapping	NOUN
ejpam-6811	56	24	.	.	PUNCT
ejpam-6811	57	1	also	also	ADV
ejpam-6811	57	2	,	,	PUNCT
ejpam-6811	57	3	we	we	PRON
ejpam-6811	57	4	define	define	VERB
ejpam-6811	57	5	v	v	ADP
ejpam-6811	57	6	(	(	PUNCT
ejpam-6811	57	7	t	t	PROPN
ejpam-6811	57	8	,	,	PUNCT
ejpam-6811	57	9	s	s	PART
ejpam-6811	57	10	)	)	PUNCT
ejpam-6811	57	11	=	=	SYM
ejpam-6811	57	12	{	{	PUNCT
ejpam-6811	57	13	x	x	PUNCT
ejpam-6811	57	14	∈	∈	PROPN
ejpam-6811	57	15	x	x	X
ejpam-6811	57	16	:	:	PUNCT
ejpam-6811	57	17	(	(	PUNCT
ejpam-6811	57	18	tx	tx	INTJ
ejpam-6811	57	19	,	,	PUNCT
ejpam-6811	57	20	sx	sx	PROPN
ejpam-6811	57	21	)	)	PUNCT
ejpam-6811	57	22	∈	∈	PROPN
ejpam-6811	57	23	e(ḡ	e(ḡ	PROPN
ejpam-6811	57	24	)	)	PUNCT
ejpam-6811	57	25	}	}	PUNCT
ejpam-6811	57	26	.	.	PUNCT
ejpam-6811	58	1	remark	remark	NOUN
ejpam-6811	58	2	1	1	NUM
ejpam-6811	58	3	.	.	PUNCT
ejpam-6811	59	1	the	the	DET
ejpam-6811	59	2	set	set	NOUN
ejpam-6811	59	3	e(ḡ	e(ḡ	NOUN
ejpam-6811	59	4	)	)	PUNCT
ejpam-6811	59	5	possesses	possess	VERB
ejpam-6811	59	6	the	the	DET
ejpam-6811	59	7	transitive	transitive	ADJ
ejpam-6811	59	8	property	property	NOUN
ejpam-6811	59	9	if	if	SCONJ
ejpam-6811	59	10	(	(	PUNCT
ejpam-6811	59	11	x	x	NOUN
ejpam-6811	59	12	,	,	PUNCT
ejpam-6811	59	13	y	y	PROPN
ejpam-6811	59	14	)	)	PUNCT
ejpam-6811	59	15	,	,	PUNCT
ejpam-6811	59	16	(	(	PUNCT
ejpam-6811	59	17	y	y	NOUN
ejpam-6811	59	18	,	,	PUNCT
ejpam-6811	59	19	z	z	NOUN
ejpam-6811	59	20	)	)	PUNCT
ejpam-6811	59	21	∈	∈	PROPN
ejpam-6811	59	22	e(ḡ	e(ḡ	PROPN
ejpam-6811	59	23	)	)	PUNCT
ejpam-6811	59	24	,	,	PUNCT
ejpam-6811	59	25	then	then	ADV
ejpam-6811	59	26	(	(	PUNCT
ejpam-6811	59	27	x	x	X
ejpam-6811	59	28	,	,	PUNCT
ejpam-6811	59	29	z	z	NOUN
ejpam-6811	59	30	)	)	PUNCT
ejpam-6811	59	31	∈	∈	PROPN
ejpam-6811	59	32	e(ḡ	e(ḡ	PROPN
ejpam-6811	59	33	)	)	PUNCT
ejpam-6811	59	34	.	.	PUNCT
ejpam-6811	60	1	definition	definition	NOUN
ejpam-6811	60	2	4	4	NUM
ejpam-6811	60	3	.	.	PUNCT
ejpam-6811	61	1	let	let	VERB
ejpam-6811	61	2	(	(	PUNCT
ejpam-6811	61	3	x	x	NOUN
ejpam-6811	61	4	,	,	PUNCT
ejpam-6811	61	5	db	db	PROPN
ejpam-6811	61	6	)	)	PUNCT
ejpam-6811	61	7	be	be	AUX
ejpam-6811	61	8	a	a	DET
ejpam-6811	61	9	bms	bms	NOUN
ejpam-6811	61	10	together	together	ADV
ejpam-6811	61	11	with	with	ADP
ejpam-6811	61	12	a	a	DET
ejpam-6811	61	13	dg	dg	NOUN
ejpam-6811	61	14	,	,	PUNCT
ejpam-6811	61	15	where	where	SCONJ
ejpam-6811	61	16	db	db	PROPN
ejpam-6811	61	17	is	be	AUX
ejpam-6811	61	18	a	a	DET
ejpam-6811	61	19	continuous	continuous	ADJ
ejpam-6811	61	20	metric	metric	ADJ
ejpam-6811	61	21	functional	functional	NOUN
ejpam-6811	61	22	.	.	PUNCT
ejpam-6811	62	1	a	a	DET
ejpam-6811	62	2	self	self	NOUN
ejpam-6811	62	3	-	-	PUNCT
ejpam-6811	62	4	mapping	mapping	NOUN
ejpam-6811	62	5	t	t	NOUN
ejpam-6811	62	6	on	on	ADP
ejpam-6811	62	7	x	x	VERB
ejpam-6811	62	8	is	be	AUX
ejpam-6811	62	9	called	call	VERB
ejpam-6811	62	10	gb	gb	ADV
ejpam-6811	62	11	-	-	PUNCT
ejpam-6811	62	12	continuous	continuous	ADJ
ejpam-6811	62	13	at	at	ADP
ejpam-6811	62	14	x	x	X
ejpam-6811	62	15	∈	∈	PROPN
ejpam-6811	62	16	x	x	INTJ
ejpam-6811	62	17	if	if	SCONJ
ejpam-6811	62	18	for	for	ADP
ejpam-6811	62	19	any	any	DET
ejpam-6811	62	20	sequence	sequence	NOUN
ejpam-6811	62	21	{	{	PUNCT
ejpam-6811	62	22	xn	xn	NOUN
ejpam-6811	62	23	}	}	PUNCT
ejpam-6811	62	24	in	in	ADP
ejpam-6811	62	25	x	x	PUNCT
ejpam-6811	62	26	with	with	ADP
ejpam-6811	62	27	(	(	PUNCT
ejpam-6811	62	28	xn	xn	PROPN
ejpam-6811	62	29	,	,	PUNCT
ejpam-6811	62	30	xn+1	xn+1	NUM
ejpam-6811	62	31	)	)	PUNCT
ejpam-6811	62	32	∈	∈	PROPN
ejpam-6811	62	33	e(ḡ	e(ḡ	PROPN
ejpam-6811	62	34	)	)	PUNCT
ejpam-6811	62	35	,	,	PUNCT
ejpam-6811	62	36	we	we	PRON
ejpam-6811	62	37	have	have	VERB
ejpam-6811	62	38	if	if	SCONJ
ejpam-6811	62	39	xn	xn	PROPN
ejpam-6811	62	40	−→	−→	ADV
ejpam-6811	62	41	x	x	PUNCT
ejpam-6811	62	42	txn	txn	AUX
ejpam-6811	62	43	−→	−→	NOUN
ejpam-6811	62	44	tx	tx	VERB
ejpam-6811	62	45	∀	∀	X
ejpam-6811	62	46	n	n	ADP
ejpam-6811	62	47	∈	∈	PROPN
ejpam-6811	62	48	n	n	CCONJ
ejpam-6811	62	49	,	,	PUNCT
ejpam-6811	62	50	and	and	CCONJ
ejpam-6811	62	51	if	if	SCONJ
ejpam-6811	62	52	this	this	PRON
ejpam-6811	62	53	holds	hold	VERB
ejpam-6811	62	54	for	for	ADP
ejpam-6811	62	55	all	all	DET
ejpam-6811	62	56	x	x	SYM
ejpam-6811	62	57	∈	∈	NOUN
ejpam-6811	62	58	x	x	NOUN
ejpam-6811	62	59	,	,	PUNCT
ejpam-6811	62	60	then	then	ADV
ejpam-6811	62	61	t	t	PROPN
ejpam-6811	62	62	is	be	AUX
ejpam-6811	62	63	called	call	VERB
ejpam-6811	62	64	gb	gb	ADV
ejpam-6811	62	65	-	-	PUNCT
ejpam-6811	62	66	continuous	continuous	ADJ
ejpam-6811	62	67	.	.	PUNCT
ejpam-6811	63	1	d.	d.	PROPN
ejpam-6811	63	2	e.	e.	PROPN
ejpam-6811	63	3	shehwar	shehwar	PROPN
ejpam-6811	63	4	sagheer	sagheer	PROPN
ejpam-6811	63	5	et	et	PROPN
ejpam-6811	63	6	al	al	PROPN
ejpam-6811	63	7	.	.	PUNCT
ejpam-6811	63	8	/	/	SYM
ejpam-6811	63	9	eur	eur	PROPN
ejpam-6811	63	10	.	.	PUNCT
ejpam-6811	64	1	j.	j.	PROPN
ejpam-6811	64	2	pure	pure	PROPN
ejpam-6811	64	3	appl	appl	PROPN
ejpam-6811	64	4	.	.	PROPN
ejpam-6811	64	5	math	math	PROPN
ejpam-6811	64	6	,	,	PUNCT
ejpam-6811	64	7	18	18	NUM
ejpam-6811	64	8	(	(	PUNCT
ejpam-6811	64	9	4	4	NUM
ejpam-6811	64	10	)	)	PUNCT
ejpam-6811	64	11	(	(	PUNCT
ejpam-6811	64	12	2025	2025	NUM
ejpam-6811	64	13	)	)	PUNCT
ejpam-6811	64	14	,	,	PUNCT
ejpam-6811	64	15	6811	6811	NUM
ejpam-6811	64	16	4	4	NUM
ejpam-6811	64	17	of	of	ADP
ejpam-6811	64	18	24	24	NUM
ejpam-6811	64	19	remark	remark	NOUN
ejpam-6811	64	20	2	2	NUM
ejpam-6811	64	21	.	.	PUNCT
ejpam-6811	65	1	in	in	ADP
ejpam-6811	65	2	a	a	DET
ejpam-6811	65	3	bms	bms	NOUN
ejpam-6811	65	4	equipped	equip	VERB
ejpam-6811	65	5	with	with	ADP
ejpam-6811	65	6	ḡ	ḡ	ADJ
ejpam-6811	65	7	=	=	SYM
ejpam-6811	65	8	(	(	PUNCT
ejpam-6811	65	9	v	v	NOUN
ejpam-6811	65	10	(	(	PUNCT
ejpam-6811	65	11	ḡ	ḡ	VERB
ejpam-6811	65	12	)	)	PUNCT
ejpam-6811	65	13	,	,	PUNCT
ejpam-6811	65	14	e(ḡ	e(ḡ	PROPN
ejpam-6811	65	15	)	)	PUNCT
ejpam-6811	65	16	)	)	PUNCT
ejpam-6811	65	17	,	,	PUNCT
ejpam-6811	65	18	we	we	PRON
ejpam-6811	65	19	say	say	VERB
ejpam-6811	65	20	that	that	SCONJ
ejpam-6811	65	21	(	(	PUNCT
ejpam-6811	65	22	x	x	NOUN
ejpam-6811	65	23	,	,	PUNCT
ejpam-6811	65	24	db	db	PROPN
ejpam-6811	65	25	,	,	PUNCT
ejpam-6811	65	26	ḡ	ḡ	VERB
ejpam-6811	65	27	)	)	PUNCT
ejpam-6811	65	28	has	have	VERB
ejpam-6811	65	29	property	property	NOUN
ejpam-6811	65	30	a	a	DET
ejpam-6811	65	31	if	if	NOUN
ejpam-6811	65	32	for	for	ADP
ejpam-6811	65	33	any	any	DET
ejpam-6811	65	34	sequence	sequence	NOUN
ejpam-6811	65	35	{	{	PUNCT
ejpam-6811	65	36	xn	xn	NOUN
ejpam-6811	65	37	}	}	PUNCT
ejpam-6811	65	38	in	in	ADP
ejpam-6811	65	39	x	x	PUNCT
ejpam-6811	65	40	with	with	ADP
ejpam-6811	65	41	xn	xn	PROPN
ejpam-6811	65	42	→	→	SYM
ejpam-6811	65	43	x	x	SYM
ejpam-6811	65	44	∈	∈	NOUN
ejpam-6811	65	45	x	x	NOUN
ejpam-6811	65	46	,	,	PUNCT
ejpam-6811	65	47	we	we	PRON
ejpam-6811	65	48	have	have	VERB
ejpam-6811	65	49	(	(	PUNCT
ejpam-6811	65	50	xn	xn	PROPN
ejpam-6811	65	51	,	,	PUNCT
ejpam-6811	65	52	xn+1	xn+1	NUM
ejpam-6811	65	53	)	)	PUNCT
ejpam-6811	65	54	∈	∈	PROPN
ejpam-6811	65	55	e(ḡ	e(ḡ	PROPN
ejpam-6811	65	56	)	)	PUNCT
ejpam-6811	65	57	(	(	PUNCT
ejpam-6811	65	58	xn	xn	PROPN
ejpam-6811	65	59	,	,	PUNCT
ejpam-6811	65	60	x	x	X
ejpam-6811	65	61	)	)	PUNCT
ejpam-6811	65	62	∈	∈	PROPN
ejpam-6811	65	63	e(ḡ	e(ḡ	NOUN
ejpam-6811	65	64	)	)	PUNCT
ejpam-6811	65	65	∀	∀	PUNCT
ejpam-6811	65	66	n	n	PRON
ejpam-6811	65	67	∈	∈	PROPN
ejpam-6811	65	68	n.	n.	NOUN
ejpam-6811	65	69	(	(	PUNCT
ejpam-6811	65	70	1	1	NUM
ejpam-6811	65	71	)	)	PUNCT
ejpam-6811	65	72	definition	definition	NOUN
ejpam-6811	65	73	5	5	NUM
ejpam-6811	65	74	.	.	PUNCT
ejpam-6811	66	1	let	let	VERB
ejpam-6811	66	2	(	(	PUNCT
ejpam-6811	66	3	x	x	NOUN
ejpam-6811	66	4	,	,	PUNCT
ejpam-6811	66	5	db	db	PROPN
ejpam-6811	66	6	)	)	PUNCT
ejpam-6811	66	7	be	be	VERB
ejpam-6811	66	8	a	a	DET
ejpam-6811	66	9	bms	bms	NOUN
ejpam-6811	66	10	endowed	endow	VERB
ejpam-6811	66	11	with	with	ADP
ejpam-6811	66	12	a	a	DET
ejpam-6811	66	13	dg	dg	NOUN
ejpam-6811	66	14	where	where	SCONJ
ejpam-6811	66	15	db	db	PART
ejpam-6811	66	16	be	be	AUX
ejpam-6811	66	17	a	a	DET
ejpam-6811	66	18	continuous	continuous	ADJ
ejpam-6811	66	19	metric	metric	ADJ
ejpam-6811	66	20	functional	functional	NOUN
ejpam-6811	66	21	.	.	PUNCT
ejpam-6811	67	1	also	also	ADV
ejpam-6811	67	2	let	let	VERB
ejpam-6811	67	3	t	t	PROPN
ejpam-6811	67	4	,	,	PUNCT
ejpam-6811	67	5	s	s	PART
ejpam-6811	67	6	:	:	PUNCT
ejpam-6811	67	7	x	x	SYM
ejpam-6811	67	8	→	→	PUNCT
ejpam-6811	67	9	x	x	PUNCT
ejpam-6811	67	10	be	be	AUX
ejpam-6811	67	11	two	two	NUM
ejpam-6811	67	12	functions	function	NOUN
ejpam-6811	67	13	then	then	ADV
ejpam-6811	67	14	t	t	PROPN
ejpam-6811	67	15	is	be	AUX
ejpam-6811	67	16	called	call	VERB
ejpam-6811	67	17	s	s	NOUN
ejpam-6811	67	18	-	-	PUNCT
ejpam-6811	67	19	edge	edge	NOUN
ejpam-6811	67	20	preserving	preserve	VERB
ejpam-6811	67	21	with	with	ADP
ejpam-6811	67	22	respect	respect	NOUN
ejpam-6811	67	23	to	to	ADP
ejpam-6811	67	24	ḡ	ḡ	VERB
ejpam-6811	67	25	,	,	PUNCT
ejpam-6811	67	26	if	if	SCONJ
ejpam-6811	67	27	following	follow	VERB
ejpam-6811	67	28	condition	condition	NOUN
ejpam-6811	67	29	holds	hold	VERB
ejpam-6811	67	30	,	,	PUNCT
ejpam-6811	67	31	(	(	PUNCT
ejpam-6811	67	32	sx	sx	PROPN
ejpam-6811	67	33	,	,	PUNCT
ejpam-6811	67	34	sy	sy	PROPN
ejpam-6811	67	35	)	)	PUNCT
ejpam-6811	67	36	∈	∈	PROPN
ejpam-6811	67	37	e(ḡ	e(ḡ	NOUN
ejpam-6811	67	38	)	)	PUNCT
ejpam-6811	67	39	⇒	⇒	NOUN
ejpam-6811	67	40	(	(	PUNCT
ejpam-6811	67	41	tx	tx	PROPN
ejpam-6811	67	42	,	,	PUNCT
ejpam-6811	67	43	ty	ty	INTJ
ejpam-6811	67	44	)	)	PUNCT
ejpam-6811	67	45	∈	∈	PROPN
ejpam-6811	67	46	e(ḡ	e(ḡ	NOUN
ejpam-6811	67	47	)	)	PUNCT
ejpam-6811	67	48	∀	∀	X
ejpam-6811	68	1	x	x	SYM
ejpam-6811	68	2	∈	∈	NOUN
ejpam-6811	68	3	x.	x.	NOUN
ejpam-6811	68	4	agarwal	agarwal	PROPN
ejpam-6811	68	5	et	et	PROPN
ejpam-6811	68	6	al	al	PROPN
ejpam-6811	68	7	.	.	PUNCT
ejpam-6811	69	1	[	[	X
ejpam-6811	69	2	29	29	NUM
ejpam-6811	69	3	]	]	PUNCT
ejpam-6811	69	4	demonstrated	demonstrate	VERB
ejpam-6811	69	5	some	some	DET
ejpam-6811	69	6	excellent	excellent	ADJ
ejpam-6811	69	7	results	result	NOUN
ejpam-6811	69	8	for	for	ADP
ejpam-6811	69	9	local	local	ADJ
ejpam-6811	69	10	and	and	CCONJ
ejpam-6811	69	11	global	global	ADJ
ejpam-6811	69	12	fixed	fix	VERB
ejpam-6811	69	13	points	point	NOUN
ejpam-6811	69	14	.	.	PUNCT
ejpam-6811	70	1	they	they	PRON
ejpam-6811	70	2	used	use	VERB
ejpam-6811	70	3	generalized	generalized	ADJ
ejpam-6811	70	4	contractions	contraction	NOUN
ejpam-6811	70	5	in	in	ADP
ejpam-6811	70	6	the	the	DET
ejpam-6811	70	7	domain	domain	NOUN
ejpam-6811	70	8	of	of	ADP
ejpam-6811	70	9	metric	metric	ADJ
ejpam-6811	70	10	spaces	space	NOUN
ejpam-6811	70	11	having	have	VERB
ejpam-6811	70	12	two	two	NUM
ejpam-6811	70	13	distance	distance	NOUN
ejpam-6811	70	14	functions	function	NOUN
ejpam-6811	70	15	simultaneously	simultaneously	ADV
ejpam-6811	70	16	.	.	PUNCT
ejpam-6811	71	1	inspired	inspire	VERB
ejpam-6811	71	2	by	by	ADP
ejpam-6811	71	3	his	his	PRON
ejpam-6811	71	4	work	work	NOUN
ejpam-6811	71	5	,	,	PUNCT
ejpam-6811	71	6	we	we	PRON
ejpam-6811	71	7	present	present	VERB
ejpam-6811	71	8	the	the	DET
ejpam-6811	71	9	following	follow	VERB
ejpam-6811	71	10	ideas	idea	NOUN
ejpam-6811	71	11	,	,	PUNCT
ejpam-6811	71	12	which	which	PRON
ejpam-6811	71	13	are	be	AUX
ejpam-6811	71	14	going	go	VERB
ejpam-6811	71	15	to	to	PART
ejpam-6811	71	16	facilitate	facilitate	VERB
ejpam-6811	71	17	us	we	PRON
ejpam-6811	71	18	in	in	ADP
ejpam-6811	71	19	proving	prove	VERB
ejpam-6811	71	20	our	our	PRON
ejpam-6811	71	21	main	main	ADJ
ejpam-6811	71	22	results	result	NOUN
ejpam-6811	71	23	.	.	PUNCT
ejpam-6811	72	1	let	let	VERB
ejpam-6811	72	2	x	x	PRON
ejpam-6811	72	3	be	be	AUX
ejpam-6811	72	4	a	a	DET
ejpam-6811	72	5	non	non	ADJ
ejpam-6811	72	6	-	-	ADJ
ejpam-6811	72	7	empty	empty	ADJ
ejpam-6811	72	8	set	set	NOUN
ejpam-6811	72	9	and	and	CCONJ
ejpam-6811	72	10	we	we	PRON
ejpam-6811	72	11	define	define	VERB
ejpam-6811	72	12	db	db	PROPN
ejpam-6811	72	13	and	and	CCONJ
ejpam-6811	72	14	d′b	d′b	ADP
ejpam-6811	72	15	such	such	ADJ
ejpam-6811	72	16	that	that	PRON
ejpam-6811	72	17	(	(	PUNCT
ejpam-6811	72	18	x	x	NOUN
ejpam-6811	72	19	,	,	PUNCT
ejpam-6811	72	20	db	db	PROPN
ejpam-6811	72	21	)	)	PUNCT
ejpam-6811	72	22	and	and	CCONJ
ejpam-6811	72	23	(	(	PUNCT
ejpam-6811	72	24	x	x	NOUN
ejpam-6811	72	25	,	,	PUNCT
ejpam-6811	72	26	d′b	d′b	PROPN
ejpam-6811	72	27	)	)	PUNCT
ejpam-6811	72	28	both	both	PRON
ejpam-6811	72	29	are	be	AUX
ejpam-6811	72	30	bmss	bmss	ADJ
ejpam-6811	72	31	.	.	PUNCT
ejpam-6811	73	1	then	then	ADV
ejpam-6811	73	2	if	if	SCONJ
ejpam-6811	73	3	we	we	PRON
ejpam-6811	73	4	say	say	VERB
ejpam-6811	73	5	db	db	VERB
ejpam-6811	73	6	≤	≤	PROPN
ejpam-6811	73	7	d′b	d′b	PROPN
ejpam-6811	73	8	then	then	ADV
ejpam-6811	73	9	it	it	PRON
ejpam-6811	73	10	means	mean	VERB
ejpam-6811	73	11	db(x	db(x	ADJ
ejpam-6811	73	12	,	,	PUNCT
ejpam-6811	73	13	y	y	NOUN
ejpam-6811	73	14	)	)	PUNCT
ejpam-6811	73	15	≤	≤	PROPN
ejpam-6811	73	16	d′b(x	d′b(x	PROPN
ejpam-6811	73	17	,	,	PUNCT
ejpam-6811	73	18	y	y	NOUN
ejpam-6811	73	19	)	)	PUNCT
ejpam-6811	73	20	for	for	ADP
ejpam-6811	73	21	all	all	DET
ejpam-6811	73	22	x	x	NOUN
ejpam-6811	73	23	,	,	PUNCT
ejpam-6811	73	24	y	y	PROPN
ejpam-6811	73	25	∈	∈	PROPN
ejpam-6811	73	26	x.	x.	NOUN
ejpam-6811	74	1	if	if	SCONJ
ejpam-6811	74	2	there	there	PRON
ejpam-6811	74	3	are	be	VERB
ejpam-6811	74	4	two	two	NUM
ejpam-6811	74	5	functions	function	NOUN
ejpam-6811	74	6	t	t	NOUN
ejpam-6811	74	7	,	,	PUNCT
ejpam-6811	74	8	s	s	PART
ejpam-6811	74	9	:	:	PUNCT
ejpam-6811	74	10	x	x	SYM
ejpam-6811	74	11	→	→	PUNCT
ejpam-6811	74	12	x	x	SYM
ejpam-6811	74	13	then	then	ADV
ejpam-6811	74	14	t	t	PROPN
ejpam-6811	74	15	is	be	AUX
ejpam-6811	74	16	said	say	VERB
ejpam-6811	74	17	to	to	PART
ejpam-6811	74	18	be	be	AUX
ejpam-6811	74	19	s	s	NOUN
ejpam-6811	74	20	-	-	PUNCT
ejpam-6811	74	21	non	non	ADJ
ejpam-6811	74	22	-	-	ADJ
ejpam-6811	74	23	decreasing	decrease	VERB
ejpam-6811	74	24	if	if	SCONJ
ejpam-6811	74	25	sx	sx	PROPN
ejpam-6811	74	26	≤	≤	PUNCT
ejpam-6811	74	27	sy	sy	NOUN
ejpam-6811	74	28	tx	tx	PROPN
ejpam-6811	74	29	≤	≤	NUM
ejpam-6811	74	30	ty	ty	ADP
ejpam-6811	74	31	∀	∀	NOUN
ejpam-6811	74	32	x	x	NOUN
ejpam-6811	74	33	,	,	PUNCT
ejpam-6811	74	34	y	y	PROPN
ejpam-6811	74	35	∈	∈	PROPN
ejpam-6811	74	36	x	x	NOUN
ejpam-6811	74	37	,	,	PUNCT
ejpam-6811	74	38	and	and	CCONJ
ejpam-6811	74	39	if	if	SCONJ
ejpam-6811	74	40	s	s	X
ejpam-6811	74	41	is	be	AUX
ejpam-6811	74	42	an	an	DET
ejpam-6811	74	43	identity	identity	NOUN
ejpam-6811	74	44	map	map	NOUN
ejpam-6811	74	45	then	then	ADV
ejpam-6811	74	46	we	we	PRON
ejpam-6811	74	47	say	say	VERB
ejpam-6811	74	48	t	t	PROPN
ejpam-6811	74	49	is	be	AUX
ejpam-6811	74	50	called	call	VERB
ejpam-6811	74	51	a	a	DET
ejpam-6811	74	52	non	non	ADJ
ejpam-6811	74	53	-	-	ADJ
ejpam-6811	74	54	decreasing	decrease	VERB
ejpam-6811	74	55	map	map	NOUN
ejpam-6811	74	56	.	.	PUNCT
ejpam-6811	75	1	definition	definition	NOUN
ejpam-6811	75	2	6	6	NUM
ejpam-6811	75	3	.	.	PUNCT
ejpam-6811	76	1	let	let	VERB
ejpam-6811	76	2	(	(	PUNCT
ejpam-6811	76	3	x	x	NOUN
ejpam-6811	76	4	,	,	PUNCT
ejpam-6811	76	5	db	db	PROPN
ejpam-6811	76	6	)	)	PUNCT
ejpam-6811	76	7	be	be	VERB
ejpam-6811	76	8	a	a	DET
ejpam-6811	76	9	bms	bms	NOUN
ejpam-6811	76	10	endowed	endow	VERB
ejpam-6811	76	11	with	with	ADP
ejpam-6811	76	12	a	a	DET
ejpam-6811	76	13	directed	direct	VERB
ejpam-6811	76	14	graph	graph	NOUN
ejpam-6811	76	15	ḡ	ḡ	VERB
ejpam-6811	76	16	=	=	SYM
ejpam-6811	76	17	(	(	PUNCT
ejpam-6811	76	18	v	v	NOUN
ejpam-6811	76	19	(	(	PUNCT
ejpam-6811	76	20	ḡ	ḡ	VERB
ejpam-6811	76	21	)	)	PUNCT
ejpam-6811	76	22	,	,	PUNCT
ejpam-6811	76	23	e(ḡ	e(ḡ	PROPN
ejpam-6811	76	24	)	)	PUNCT
ejpam-6811	76	25	)	)	PUNCT
ejpam-6811	76	26	,	,	PUNCT
ejpam-6811	76	27	where	where	SCONJ
ejpam-6811	76	28	db	db	PROPN
ejpam-6811	76	29	is	be	AUX
ejpam-6811	76	30	a	a	DET
ejpam-6811	76	31	continuous	continuous	ADJ
ejpam-6811	76	32	metric.consider	metric.consider	NOUN
ejpam-6811	76	33	a	a	DET
ejpam-6811	76	34	sequence	sequence	NOUN
ejpam-6811	76	35	{	{	PUNCT
ejpam-6811	76	36	xn	xn	NOUN
ejpam-6811	76	37	}	}	PUNCT
ejpam-6811	76	38	be	be	AUX
ejpam-6811	76	39	a	a	DET
ejpam-6811	76	40	sequence	sequence	NOUN
ejpam-6811	76	41	in	in	ADP
ejpam-6811	76	42	(	(	PUNCT
ejpam-6811	76	43	x	x	NOUN
ejpam-6811	76	44	,	,	PUNCT
ejpam-6811	76	45	db	db	PROPN
ejpam-6811	76	46	)	)	PUNCT
ejpam-6811	76	47	.	.	PUNCT
ejpam-6811	77	1	the	the	DET
ejpam-6811	77	2	mappings	mapping	NOUN
ejpam-6811	77	3	t	t	PROPN
ejpam-6811	77	4	,	,	PUNCT
ejpam-6811	77	5	s	s	PART
ejpam-6811	77	6	:	:	PUNCT
ejpam-6811	77	7	x	x	SYM
ejpam-6811	77	8	→	→	SYM
ejpam-6811	77	9	x	x	X
ejpam-6811	77	10	are	be	AUX
ejpam-6811	77	11	db	db	PROPN
ejpam-6811	77	12	are	be	AUX
ejpam-6811	77	13	called	call	VERB
ejpam-6811	77	14	compatible	compatible	ADJ
ejpam-6811	77	15	,	,	PUNCT
ejpam-6811	77	16	if	if	SCONJ
ejpam-6811	77	17	we	we	PRON
ejpam-6811	77	18	have	have	VERB
ejpam-6811	77	19	lim	lim	PROPN
ejpam-6811	77	20	n→∞	n→∞	PRON
ejpam-6811	77	21	db(stxn	db(stxn	PROPN
ejpam-6811	77	22	,	,	PUNCT
ejpam-6811	77	23	tsxn	tsxn	NOUN
ejpam-6811	77	24	)	)	PUNCT
ejpam-6811	77	25	=	=	SYM
ejpam-6811	78	1	0	0	NUM
ejpam-6811	78	2	,	,	PUNCT
ejpam-6811	78	3	whenever	whenever	SCONJ
ejpam-6811	78	4	lim	lim	PROPN
ejpam-6811	78	5	n→∞	n→∞	PRON
ejpam-6811	78	6	txn	txn	X
ejpam-6811	78	7	=	=	SYM
ejpam-6811	78	8	lim	lim	PROPN
ejpam-6811	78	9	n→∞	n→∞	NUM
ejpam-6811	79	1	sxn	sxn	PROPN
ejpam-6811	79	2	.	.	PUNCT
ejpam-6811	80	1	definition	definition	NOUN
ejpam-6811	80	2	7	7	NUM
ejpam-6811	80	3	.	.	PUNCT
ejpam-6811	81	1	let	let	VERB
ejpam-6811	81	2	(	(	PUNCT
ejpam-6811	81	3	x	x	NOUN
ejpam-6811	81	4	,	,	PUNCT
ejpam-6811	81	5	db	db	PROPN
ejpam-6811	81	6	)	)	PUNCT
ejpam-6811	81	7	and	and	CCONJ
ejpam-6811	81	8	(	(	PUNCT
ejpam-6811	81	9	n	n	X
ejpam-6811	81	10	,	,	PUNCT
ejpam-6811	81	11	d′b	d′b	PROPN
ejpam-6811	81	12	)	)	PUNCT
ejpam-6811	81	13	be	be	AUX
ejpam-6811	81	14	two	two	NUM
ejpam-6811	81	15	bmss	bmss	NOUN
ejpam-6811	81	16	and	and	CCONJ
ejpam-6811	81	17	t	t	NOUN
ejpam-6811	81	18	:	:	PUNCT
ejpam-6811	81	19	x	x	X
ejpam-6811	81	20	→	→	SYM
ejpam-6811	81	21	n	n	NOUN
ejpam-6811	81	22	and	and	CCONJ
ejpam-6811	81	23	s	s	VERB
ejpam-6811	81	24	:	:	PUNCT
ejpam-6811	81	25	x	x	SYM
ejpam-6811	81	26	→	→	PUNCT
ejpam-6811	81	27	x	x	PUNCT
ejpam-6811	81	28	be	be	AUX
ejpam-6811	81	29	two	two	NUM
ejpam-6811	81	30	functions	function	NOUN
ejpam-6811	81	31	.	.	PUNCT
ejpam-6811	82	1	then	then	ADV
ejpam-6811	82	2	t	t	PROPN
ejpam-6811	82	3	is	be	AUX
ejpam-6811	82	4	s	s	NOUN
ejpam-6811	82	5	-	-	NOUN
ejpam-6811	82	6	cauchy	cauchy	ADJ
ejpam-6811	82	7	on	on	ADP
ejpam-6811	82	8	x	x	SYM
ejpam-6811	82	9	if	if	SCONJ
ejpam-6811	82	10	for	for	ADP
ejpam-6811	82	11	any	any	DET
ejpam-6811	82	12	sequence	sequence	NOUN
ejpam-6811	82	13	{	{	PUNCT
ejpam-6811	82	14	xn	xn	NOUN
ejpam-6811	82	15	}	}	PUNCT
ejpam-6811	82	16	in	in	ADP
ejpam-6811	82	17	x	x	X
ejpam-6811	82	18	the	the	DET
ejpam-6811	82	19	sequence	sequence	NOUN
ejpam-6811	82	20	{	{	PUNCT
ejpam-6811	82	21	sxn	sxn	NOUN
ejpam-6811	82	22	}	}	PUNCT
ejpam-6811	82	23	is	be	AUX
ejpam-6811	82	24	cauchy	cauchy	ADJ
ejpam-6811	82	25	in	in	ADP
ejpam-6811	82	26	x	x	PROPN
ejpam-6811	82	27	implies	imply	VERB
ejpam-6811	82	28	that	that	SCONJ
ejpam-6811	82	29	the	the	DET
ejpam-6811	82	30	sequence	sequence	NOUN
ejpam-6811	82	31	{	{	PUNCT
ejpam-6811	82	32	txn	txn	NOUN
ejpam-6811	82	33	}	}	PUNCT
ejpam-6811	82	34	is	be	AUX
ejpam-6811	82	35	cauchy	cauchy	ADJ
ejpam-6811	82	36	in	in	ADP
ejpam-6811	82	37	(	(	PUNCT
ejpam-6811	82	38	n	n	X
ejpam-6811	82	39	,	,	PUNCT
ejpam-6811	82	40	d′b	d′b	PROPN
ejpam-6811	82	41	)	)	PUNCT
ejpam-6811	82	42	.	.	PUNCT
ejpam-6811	83	1	the	the	DET
ejpam-6811	83	2	following	follow	VERB
ejpam-6811	83	3	definition	definition	NOUN
ejpam-6811	83	4	is	be	AUX
ejpam-6811	83	5	analogous	analogous	ADJ
ejpam-6811	83	6	to	to	ADP
ejpam-6811	83	7	those	those	PRON
ejpam-6811	83	8	given	give	VERB
ejpam-6811	83	9	in	in	ADP
ejpam-6811	83	10	[	[	NOUN
ejpam-6811	83	11	23	23	NUM
ejpam-6811	83	12	]	]	PUNCT
ejpam-6811	83	13	and	and	CCONJ
ejpam-6811	83	14	[	[	X
ejpam-6811	83	15	22	22	NUM
ejpam-6811	83	16	]	]	PUNCT
ejpam-6811	83	17	in	in	ADP
ejpam-6811	83	18	bms	bms	PROPN
ejpam-6811	83	19	.	.	PUNCT
ejpam-6811	84	1	definition	definition	NOUN
ejpam-6811	84	2	8	8	NUM
ejpam-6811	84	3	.	.	PUNCT
ejpam-6811	85	1	let	let	VERB
ejpam-6811	85	2	(	(	PUNCT
ejpam-6811	85	3	x	x	NOUN
ejpam-6811	85	4	,	,	PUNCT
ejpam-6811	85	5	db	db	PROPN
ejpam-6811	85	6	)	)	PUNCT
ejpam-6811	85	7	be	be	AUX
ejpam-6811	85	8	a	a	DET
ejpam-6811	85	9	bms	bms	NOUN
ejpam-6811	85	10	a	a	DET
ejpam-6811	85	11	function	function	NOUN
ejpam-6811	85	12	and	and	CCONJ
ejpam-6811	85	13	{	{	PUNCT
ejpam-6811	85	14	xn	xn	PUNCT
ejpam-6811	85	15	}	}	PUNCT
ejpam-6811	85	16	,	,	PUNCT
ejpam-6811	85	17	{	{	PUNCT
ejpam-6811	85	18	yn	yn	NOUN
ejpam-6811	85	19	}	}	PUNCT
ejpam-6811	85	20	be	be	VERB
ejpam-6811	85	21	two	two	NUM
ejpam-6811	85	22	sequences	sequence	NOUN
ejpam-6811	85	23	in	in	ADP
ejpam-6811	85	24	x	x	PUNCT
ejpam-6811	85	25	such	such	ADJ
ejpam-6811	85	26	that	that	SCONJ
ejpam-6811	85	27	the	the	DET
ejpam-6811	85	28	sequence	sequence	NOUN
ejpam-6811	85	29	{	{	PUNCT
ejpam-6811	85	30	db(xn	db(xn	PROPN
ejpam-6811	85	31	,	,	PUNCT
ejpam-6811	85	32	yn	yn	PROPN
ejpam-6811	85	33	)	)	PUNCT
ejpam-6811	85	34	}	}	PUNCT
ejpam-6811	85	35	is	be	AUX
ejpam-6811	85	36	decreasing	decrease	VERB
ejpam-6811	85	37	and	and	CCONJ
ejpam-6811	85	38	convergent	convergent	NOUN
ejpam-6811	85	39	.	.	PUNCT
ejpam-6811	86	1	a	a	DET
ejpam-6811	86	2	function	function	NOUN
ejpam-6811	86	3	ψ	ψ	NOUN
ejpam-6811	86	4	:	:	PUNCT
ejpam-6811	86	5	x×x	x×x	PROPN
ejpam-6811	86	6	→	→	SYM
ejpam-6811	87	1	[	[	X
ejpam-6811	87	2	0	0	NUM
ejpam-6811	87	3	,	,	PUNCT
ejpam-6811	87	4	1	1	NUM
ejpam-6811	87	5	]	]	PUNCT
ejpam-6811	87	6	satisfying	satisfy	VERB
ejpam-6811	87	7	the	the	DET
ejpam-6811	87	8	condition	condition	NOUN
ejpam-6811	87	9	,	,	PUNCT
ejpam-6811	87	10	if	if	SCONJ
ejpam-6811	87	11	lim	lim	PROPN
ejpam-6811	87	12	n→∞	n→∞	NUM
ejpam-6811	87	13	ψ(xn	ψ(xn	PROPN
ejpam-6811	87	14	,	,	PUNCT
ejpam-6811	87	15	yn	yn	NOUN
ejpam-6811	87	16	)	)	PUNCT
ejpam-6811	87	17	=	=	SYM
ejpam-6811	87	18	1	1	NUM
ejpam-6811	87	19	then	then	ADV
ejpam-6811	87	20	lim	lim	PROPN
ejpam-6811	87	21	n→∞	n→∞	NUM
ejpam-6811	87	22	db(xn	db(xn	PROPN
ejpam-6811	87	23	,	,	PUNCT
ejpam-6811	87	24	yn	yn	PROPN
ejpam-6811	87	25	)	)	PUNCT
ejpam-6811	87	26	=	=	SYM
ejpam-6811	87	27	0	0	NUM
ejpam-6811	87	28	,	,	PUNCT
ejpam-6811	87	29	is	be	AUX
ejpam-6811	87	30	called	call	VERB
ejpam-6811	87	31	an	an	DET
ejpam-6811	87	32	auxiliary	auxiliary	ADJ
ejpam-6811	87	33	function	function	NOUN
ejpam-6811	87	34	.	.	PUNCT
ejpam-6811	88	1	throughout	throughout	ADP
ejpam-6811	88	2	the	the	DET
ejpam-6811	88	3	article	article	NOUN
ejpam-6811	88	4	,	,	PUNCT
ejpam-6811	88	5	such	such	DET
ejpam-6811	88	6	a	a	DET
ejpam-6811	88	7	family	family	NOUN
ejpam-6811	88	8	of	of	ADP
ejpam-6811	88	9	functions	function	NOUN
ejpam-6811	88	10	will	will	AUX
ejpam-6811	88	11	be	be	AUX
ejpam-6811	88	12	represented	represent	VERB
ejpam-6811	88	13	by	by	ADP
ejpam-6811	88	14	ψ	ψ	X
ejpam-6811	88	15	=	=	NOUN
ejpam-6811	88	16	ψ(x	ψ(x	NOUN
ejpam-6811	88	17	)	)	PUNCT
ejpam-6811	88	18	.	.	PUNCT
ejpam-6811	89	1	moreover	moreover	ADV
ejpam-6811	89	2	,	,	PUNCT
ejpam-6811	89	3	let	let	VERB
ejpam-6811	89	4	the	the	DET
ejpam-6811	89	5	function	function	NOUN
ejpam-6811	89	6	φ	φ	NOUN
ejpam-6811	89	7	:	:	PUNCT
ejpam-6811	90	1	[	[	X
ejpam-6811	90	2	0,∞	0,∞	NUM
ejpam-6811	90	3	)	)	PUNCT
ejpam-6811	90	4	→	→	PUNCT
ejpam-6811	91	1	[	[	X
ejpam-6811	91	2	0,∞	0,∞	X
ejpam-6811	91	3	)	)	PUNCT
ejpam-6811	91	4	be	be	AUX
ejpam-6811	91	5	increasing	increase	VERB
ejpam-6811	91	6	and	and	CCONJ
ejpam-6811	91	7	continuous	continuous	ADJ
ejpam-6811	91	8	satisfying	satisfy	VERB
ejpam-6811	91	9	the	the	DET
ejpam-6811	91	10	property	property	NOUN
ejpam-6811	91	11	φ(x	φ(x	NOUN
ejpam-6811	91	12	)	)	PUNCT
ejpam-6811	92	1	=	=	SYM
ejpam-6811	92	2	0x	0x	NOUN
ejpam-6811	92	3	=	=	SYM
ejpam-6811	92	4	0	0	X
ejpam-6811	92	5	.	.	PUNCT
ejpam-6811	93	1	in	in	ADP
ejpam-6811	93	2	the	the	DET
ejpam-6811	93	3	upcoming	upcoming	ADJ
ejpam-6811	93	4	discussion	discussion	NOUN
ejpam-6811	93	5	,	,	PUNCT
ejpam-6811	93	6	denote	denote	VERB
ejpam-6811	93	7	the	the	DET
ejpam-6811	93	8	collection	collection	NOUN
ejpam-6811	93	9	of	of	ADP
ejpam-6811	93	10	all	all	DET
ejpam-6811	93	11	such	such	ADJ
ejpam-6811	93	12	functions	function	NOUN
ejpam-6811	93	13	by	by	ADP
ejpam-6811	93	14	φ	φ	PROPN
ejpam-6811	93	15	.	.	PUNCT
ejpam-6811	94	1	d.	d.	PROPN
ejpam-6811	94	2	e.	e.	PROPN
ejpam-6811	94	3	shehwar	shehwar	PROPN
ejpam-6811	94	4	sagheer	sagheer	PROPN
ejpam-6811	94	5	et	et	PROPN
ejpam-6811	94	6	al	al	PROPN
ejpam-6811	94	7	.	.	PUNCT
ejpam-6811	94	8	/	/	SYM
ejpam-6811	94	9	eur	eur	PROPN
ejpam-6811	94	10	.	.	PUNCT
ejpam-6811	95	1	j.	j.	PROPN
ejpam-6811	95	2	pure	pure	PROPN
ejpam-6811	95	3	appl	appl	PROPN
ejpam-6811	95	4	.	.	PROPN
ejpam-6811	95	5	math	math	PROPN
ejpam-6811	95	6	,	,	PUNCT
ejpam-6811	95	7	18	18	NUM
ejpam-6811	95	8	(	(	PUNCT
ejpam-6811	95	9	4	4	NUM
ejpam-6811	95	10	)	)	PUNCT
ejpam-6811	95	11	(	(	PUNCT
ejpam-6811	95	12	2025	2025	NUM
ejpam-6811	95	13	)	)	PUNCT
ejpam-6811	95	14	,	,	PUNCT
ejpam-6811	95	15	6811	6811	NUM
ejpam-6811	95	16	5	5	NUM
ejpam-6811	95	17	of	of	ADP
ejpam-6811	95	18	24	24	NUM
ejpam-6811	95	19	3	3	NUM
ejpam-6811	95	20	.	.	PUNCT
ejpam-6811	95	21	main	main	ADJ
ejpam-6811	95	22	results	result	NOUN
ejpam-6811	95	23	in	in	ADP
ejpam-6811	95	24	the	the	DET
ejpam-6811	95	25	following	follow	VERB
ejpam-6811	95	26	section	section	NOUN
ejpam-6811	95	27	,	,	PUNCT
ejpam-6811	95	28	we	we	PRON
ejpam-6811	95	29	derive	derive	VERB
ejpam-6811	95	30	several	several	ADJ
ejpam-6811	95	31	fixed	fix	VERB
ejpam-6811	95	32	point	point	NOUN
ejpam-6811	95	33	results	result	NOUN
ejpam-6811	95	34	in	in	ADP
ejpam-6811	95	35	the	the	DET
ejpam-6811	95	36	framework	framework	NOUN
ejpam-6811	95	37	of	of	ADP
ejpam-6811	95	38	bms	bms	PROPN
ejpam-6811	95	39	implementing	implement	VERB
ejpam-6811	95	40	rational	rational	ADJ
ejpam-6811	95	41	type	type	NOUN
ejpam-6811	95	42	contractions	contraction	NOUN
ejpam-6811	95	43	.	.	PUNCT
ejpam-6811	96	1	in	in	ADP
ejpam-6811	96	2	addition	addition	NOUN
ejpam-6811	96	3	,	,	PUNCT
ejpam-6811	96	4	an	an	DET
ejpam-6811	96	5	example	example	NOUN
ejpam-6811	96	6	and	and	CCONJ
ejpam-6811	96	7	an	an	DET
ejpam-6811	96	8	application	application	NOUN
ejpam-6811	96	9	are	be	AUX
ejpam-6811	96	10	provided	provide	VERB
ejpam-6811	96	11	to	to	PART
ejpam-6811	96	12	help	help	VERB
ejpam-6811	96	13	readers	reader	NOUN
ejpam-6811	96	14	understand	understand	VERB
ejpam-6811	96	15	our	our	PRON
ejpam-6811	96	16	conclusion	conclusion	NOUN
ejpam-6811	96	17	more	more	ADV
ejpam-6811	96	18	thoroughly	thoroughly	ADV
ejpam-6811	96	19	.	.	PUNCT
ejpam-6811	97	1	definition	definition	NOUN
ejpam-6811	97	2	9	9	NUM
ejpam-6811	97	3	.	.	PUNCT
ejpam-6811	98	1	let	let	VERB
ejpam-6811	98	2	(	(	PUNCT
ejpam-6811	98	3	x	x	NOUN
ejpam-6811	98	4	,	,	PUNCT
ejpam-6811	98	5	db	db	PROPN
ejpam-6811	98	6	)	)	PUNCT
ejpam-6811	98	7	be	be	AUX
ejpam-6811	98	8	a	a	DET
ejpam-6811	98	9	bms	bms	NOUN
ejpam-6811	98	10	together	together	ADV
ejpam-6811	98	11	with	with	ADP
ejpam-6811	98	12	a	a	DET
ejpam-6811	98	13	dg	dg	NOUN
ejpam-6811	98	14	,	,	PUNCT
ejpam-6811	98	15	ḡ	ḡ	VERB
ejpam-6811	98	16	=	=	SYM
ejpam-6811	98	17	(	(	PUNCT
ejpam-6811	98	18	v	v	NOUN
ejpam-6811	98	19	(	(	PUNCT
ejpam-6811	98	20	ḡ	ḡ	VERB
ejpam-6811	98	21	)	)	PUNCT
ejpam-6811	98	22	,	,	PUNCT
ejpam-6811	98	23	e(ḡ	e(ḡ	PROPN
ejpam-6811	98	24	)	)	PUNCT
ejpam-6811	98	25	)	)	PUNCT
ejpam-6811	98	26	and	and	CCONJ
ejpam-6811	98	27	let	let	VERB
ejpam-6811	98	28	t	t	PROPN
ejpam-6811	98	29	,	,	PUNCT
ejpam-6811	98	30	s	s	PART
ejpam-6811	98	31	:	:	PUNCT
ejpam-6811	98	32	x	x	SYM
ejpam-6811	98	33	→	→	PUNCT
ejpam-6811	98	34	x	x	PUNCT
ejpam-6811	98	35	be	be	AUX
ejpam-6811	98	36	two	two	NUM
ejpam-6811	98	37	functions	function	NOUN
ejpam-6811	98	38	,	,	PUNCT
ejpam-6811	98	39	where	where	SCONJ
ejpam-6811	98	40	t	t	PROPN
ejpam-6811	98	41	is	be	AUX
ejpam-6811	98	42	s	s	NOUN
ejpam-6811	98	43	-	-	PUNCT
ejpam-6811	98	44	edge	edge	NOUN
ejpam-6811	98	45	preserving	preserve	VERB
ejpam-6811	98	46	with	with	ADP
ejpam-6811	98	47	respect	respect	NOUN
ejpam-6811	98	48	to	to	ADP
ejpam-6811	98	49	ḡ	ḡ	VERB
ejpam-6811	98	50	,	,	PUNCT
ejpam-6811	98	51	then	then	ADV
ejpam-6811	98	52	(	(	PUNCT
ejpam-6811	98	53	t	t	PROPN
ejpam-6811	98	54	,	,	PUNCT
ejpam-6811	98	55	s	s	PART
ejpam-6811	98	56	)	)	PUNCT
ejpam-6811	98	57	is	be	AUX
ejpam-6811	98	58	called	call	VERB
ejpam-6811	98	59	a	a	DET
ejpam-6811	98	60	ψ	ψ	NOUN
ejpam-6811	98	61	−	−	PROPN
ejpam-6811	98	62	φ	φ	NUM
ejpam-6811	98	63	-	-	NOUN
ejpam-6811	98	64	contraction	contraction	NOUN
ejpam-6811	98	65	if	if	SCONJ
ejpam-6811	98	66	for	for	ADP
ejpam-6811	98	67	all	all	DET
ejpam-6811	98	68	x	x	NOUN
ejpam-6811	98	69	,	,	PUNCT
ejpam-6811	98	70	y	y	PROPN
ejpam-6811	98	71	∈	∈	PROPN
ejpam-6811	98	72	x	x	PUNCT
ejpam-6811	98	73	with	with	ADP
ejpam-6811	98	74	(	(	PUNCT
ejpam-6811	98	75	sx	sx	PROPN
ejpam-6811	98	76	,	,	PUNCT
ejpam-6811	98	77	sy	sy	NOUN
ejpam-6811	98	78	)	)	PUNCT
ejpam-6811	98	79	∈	∈	PROPN
ejpam-6811	98	80	e(ḡ	e(ḡ	PROPN
ejpam-6811	98	81	)	)	PUNCT
ejpam-6811	98	82	there	there	PRON
ejpam-6811	98	83	exist	exist	VERB
ejpam-6811	98	84	two	two	NUM
ejpam-6811	98	85	functions	function	NOUN
ejpam-6811	98	86	φ	φ	PROPN
ejpam-6811	98	87	∈	∈	PROPN
ejpam-6811	98	88	φ	φ	PROPN
ejpam-6811	98	89	and	and	CCONJ
ejpam-6811	98	90	ψ	ψ	X
ejpam-6811	98	91	∈	∈	PROPN
ejpam-6811	98	92	ψ	ψ	NOUN
ejpam-6811	98	93	,	,	PUNCT
ejpam-6811	98	94	such	such	ADJ
ejpam-6811	98	95	that	that	PRON
ejpam-6811	98	96	φ(db(tx	φ(db(tx	NOUN
ejpam-6811	98	97	,	,	PUNCT
ejpam-6811	98	98	ty	ty	NOUN
ejpam-6811	98	99	)	)	PUNCT
ejpam-6811	98	100	)	)	PUNCT
ejpam-6811	98	101	≤	≤	PROPN
ejpam-6811	98	102	ψ(sx	ψ(sx	PROPN
ejpam-6811	98	103	,	,	PUNCT
ejpam-6811	98	104	sy)φ(δ(m((sx	sy)φ(δ(m((sx	PROPN
ejpam-6811	98	105	,	,	PUNCT
ejpam-6811	98	106	sx	sx	PROPN
ejpam-6811	98	107	)	)	PUNCT
ejpam-6811	98	108	)	)	PUNCT
ejpam-6811	98	109	)	)	PUNCT
ejpam-6811	98	110	,	,	PUNCT
ejpam-6811	98	111	(	(	PUNCT
ejpam-6811	98	112	2	2	X
ejpam-6811	98	113	)	)	PUNCT
ejpam-6811	98	114	where	where	SCONJ
ejpam-6811	98	115	δ	δ	PROPN
ejpam-6811	98	116	≤	≤	NOUN
ejpam-6811	98	117	1	1	NUM
ejpam-6811	98	118	bν	bν	ADV
ejpam-6811	98	119	for	for	ADP
ejpam-6811	98	120	all	all	DET
ejpam-6811	98	121	ν	ν	NOUN
ejpam-6811	98	122	>	>	X
ejpam-6811	98	123	3	3	NUM
ejpam-6811	98	124	and	and	CCONJ
ejpam-6811	98	125	m	m	PRON
ejpam-6811	98	126	:	:	PUNCT
ejpam-6811	98	127	x	x	X
ejpam-6811	98	128	×x	×x	X
ejpam-6811	98	129	→	→	X
ejpam-6811	98	130	[	[	X
ejpam-6811	98	131	0,∞	0,∞	NOUN
ejpam-6811	98	132	)	)	PUNCT
ejpam-6811	98	133	for	for	ADP
ejpam-6811	98	134	any	any	DET
ejpam-6811	98	135	x	x	NOUN
ejpam-6811	98	136	,	,	PUNCT
ejpam-6811	98	137	y	y	PROPN
ejpam-6811	98	138	∈	∈	PROPN
ejpam-6811	98	139	x	x	PUNCT
ejpam-6811	98	140	is	be	AUX
ejpam-6811	98	141	given	give	VERB
ejpam-6811	98	142	as	as	ADP
ejpam-6811	98	143	:	:	PUNCT
ejpam-6811	98	144	m(sx	m(sx	NOUN
ejpam-6811	98	145	,	,	PUNCT
ejpam-6811	98	146	sy	sy	NOUN
ejpam-6811	98	147	)	)	PUNCT
ejpam-6811	99	1	=	=	NOUN
ejpam-6811	99	2	max	max	NOUN
ejpam-6811	99	3	{	{	PUNCT
ejpam-6811	99	4	db(sx	db(sx	PROPN
ejpam-6811	99	5	,	,	PUNCT
ejpam-6811	99	6	tx)db(ty	tx)db(ty	PROPN
ejpam-6811	99	7	,	,	PUNCT
ejpam-6811	99	8	sy	sy	NOUN
ejpam-6811	99	9	)	)	PUNCT
ejpam-6811	99	10	db(sx	db(sx	PROPN
ejpam-6811	99	11	,	,	PUNCT
ejpam-6811	99	12	sy	sy	NOUN
ejpam-6811	99	13	)	)	PUNCT
ejpam-6811	99	14	,	,	PUNCT
ejpam-6811	99	15	db(sx	db(sx	PROPN
ejpam-6811	99	16	,	,	PUNCT
ejpam-6811	99	17	sy	sy	NOUN
ejpam-6811	99	18	)	)	PUNCT
ejpam-6811	99	19	,	,	PUNCT
ejpam-6811	99	20	db(sx	db(sx	PROPN
ejpam-6811	99	21	,	,	PUNCT
ejpam-6811	99	22	tx	tx	PROPN
ejpam-6811	99	23	)	)	PUNCT
ejpam-6811	99	24	,	,	PUNCT
ejpam-6811	99	25	db(sy	db(sy	PROPN
ejpam-6811	99	26	,	,	PUNCT
ejpam-6811	99	27	ty	ty	NOUN
ejpam-6811	99	28	)	)	PUNCT
ejpam-6811	99	29	,	,	PUNCT
ejpam-6811	99	30	db(sx	db(sx	PROPN
ejpam-6811	99	31	,	,	PUNCT
ejpam-6811	99	32	ty	ty	INTJ
ejpam-6811	99	33	)	)	PUNCT
ejpam-6811	99	34	+	+	CCONJ
ejpam-6811	100	1	db(sy	db(sy	PROPN
ejpam-6811	100	2	,	,	PUNCT
ejpam-6811	100	3	tx	tx	PROPN
ejpam-6811	100	4	)	)	PUNCT
ejpam-6811	100	5	2b	2b	NOUN
ejpam-6811	100	6	}	}	PUNCT
ejpam-6811	100	7	.	.	PUNCT
ejpam-6811	101	1	(	(	PUNCT
ejpam-6811	101	2	3	3	X
ejpam-6811	101	3	)	)	PUNCT
ejpam-6811	101	4	lemma	lemma	PROPN
ejpam-6811	101	5	1	1	NUM
ejpam-6811	101	6	.	.	PUNCT
ejpam-6811	102	1	[	[	X
ejpam-6811	102	2	30	30	NUM
ejpam-6811	102	3	]	]	X
ejpam-6811	102	4	let	let	VERB
ejpam-6811	102	5	(	(	PUNCT
ejpam-6811	102	6	x	x	NOUN
ejpam-6811	102	7	,	,	PUNCT
ejpam-6811	102	8	db	db	PROPN
ejpam-6811	102	9	)	)	PUNCT
ejpam-6811	102	10	be	be	AUX
ejpam-6811	102	11	a	a	DET
ejpam-6811	102	12	bms	bms	NOUN
ejpam-6811	102	13	with	with	ADP
ejpam-6811	102	14	b	b	PROPN
ejpam-6811	102	15	≥	≥	NUM
ejpam-6811	102	16	1	1	NUM
ejpam-6811	102	17	,	,	PUNCT
ejpam-6811	102	18	and	and	CCONJ
ejpam-6811	102	19	the	the	DET
ejpam-6811	102	20	sequences	sequence	NOUN
ejpam-6811	102	21	{	{	PUNCT
ejpam-6811	102	22	xn	xn	NUM
ejpam-6811	102	23	}	}	PUNCT
ejpam-6811	102	24	,	,	PUNCT
ejpam-6811	102	25	{	{	PUNCT
ejpam-6811	102	26	yn	yn	NOUN
ejpam-6811	102	27	}	}	PUNCT
ejpam-6811	102	28	∈	∈	PROPN
ejpam-6811	102	29	x	x	PRON
ejpam-6811	102	30	converge	converge	VERB
ejpam-6811	102	31	respectively	respectively	ADV
ejpam-6811	102	32	to	to	ADP
ejpam-6811	102	33	a	a	PRON
ejpam-6811	102	34	and	and	CCONJ
ejpam-6811	102	35	b.	b.	PROPN
ejpam-6811	103	1	then	then	ADV
ejpam-6811	103	2	we	we	PRON
ejpam-6811	103	3	have	have	VERB
ejpam-6811	103	4	1	1	NUM
ejpam-6811	103	5	b2	b2	NOUN
ejpam-6811	103	6	db(a	db(a	NOUN
ejpam-6811	103	7	,	,	PUNCT
ejpam-6811	103	8	b	b	NOUN
ejpam-6811	103	9	)	)	PUNCT
ejpam-6811	103	10	≤	≤	NOUN
ejpam-6811	103	11	lim	lim	PROPN
ejpam-6811	103	12	inf	inf	PROPN
ejpam-6811	103	13	n→∞	n→∞	NUM
ejpam-6811	103	14	db(xn	db(xn	PROPN
ejpam-6811	103	15	,	,	PUNCT
ejpam-6811	103	16	yn	yn	PROPN
ejpam-6811	103	17	)	)	PUNCT
ejpam-6811	103	18	≤	≤	NOUN
ejpam-6811	104	1	lim	lim	PROPN
ejpam-6811	104	2	sup	sup	VERB
ejpam-6811	104	3	n→∞	n→∞	NUM
ejpam-6811	104	4	db(xn	db(xn	PROPN
ejpam-6811	104	5	,	,	PUNCT
ejpam-6811	104	6	yn	yn	PROPN
ejpam-6811	104	7	)	)	PUNCT
ejpam-6811	104	8	≤	≤	NOUN
ejpam-6811	104	9	bdb(a	bdb(a	PROPN
ejpam-6811	104	10	,	,	PUNCT
ejpam-6811	104	11	b	b	NOUN
ejpam-6811	104	12	)	)	PUNCT
ejpam-6811	104	13	.	.	PUNCT
ejpam-6811	105	1	in	in	ADP
ejpam-6811	105	2	particular	particular	ADJ
ejpam-6811	105	3	,	,	PUNCT
ejpam-6811	105	4	if	if	SCONJ
ejpam-6811	105	5	a	a	DET
ejpam-6811	105	6	=	=	SYM
ejpam-6811	105	7	b	b	NOUN
ejpam-6811	105	8	,	,	PUNCT
ejpam-6811	105	9	then	then	ADV
ejpam-6811	105	10	we	we	PRON
ejpam-6811	105	11	have	have	VERB
ejpam-6811	105	12	limn→∞	limn→∞	PROPN
ejpam-6811	105	13	db(xn	db(xn	PROPN
ejpam-6811	105	14	,	,	PUNCT
ejpam-6811	105	15	yn	yn	PROPN
ejpam-6811	105	16	)	)	PUNCT
ejpam-6811	105	17	=	=	SYM
ejpam-6811	106	1	0	0	X
ejpam-6811	106	2	.	.	PUNCT
ejpam-6811	107	1	moreover	moreover	ADV
ejpam-6811	107	2	,	,	PUNCT
ejpam-6811	107	3	for	for	ADP
ejpam-6811	107	4	each	each	DET
ejpam-6811	107	5	c	c	NOUN
ejpam-6811	107	6	∈	∈	PROPN
ejpam-6811	107	7	x	x	X
ejpam-6811	107	8	,	,	PUNCT
ejpam-6811	107	9	we	we	PRON
ejpam-6811	107	10	have	have	VERB
ejpam-6811	107	11	1	1	NUM
ejpam-6811	107	12	b	b	NOUN
ejpam-6811	107	13	db(a	db(a	NOUN
ejpam-6811	107	14	,	,	PUNCT
ejpam-6811	107	15	c	c	NOUN
ejpam-6811	107	16	)	)	PUNCT
ejpam-6811	107	17	≤	≤	NOUN
ejpam-6811	107	18	lim	lim	PROPN
ejpam-6811	107	19	inf	inf	PROPN
ejpam-6811	107	20	n→∞	n→∞	NUM
ejpam-6811	107	21	db(xn	db(xn	PROPN
ejpam-6811	107	22	,	,	PUNCT
ejpam-6811	107	23	c	c	NOUN
ejpam-6811	107	24	)	)	PUNCT
ejpam-6811	107	25	≤	≤	NOUN
ejpam-6811	107	26	lim	lim	PROPN
ejpam-6811	107	27	sup	sup	VERB
ejpam-6811	107	28	n→∞	n→∞	NUM
ejpam-6811	107	29	db(xn	db(xn	NOUN
ejpam-6811	107	30	,	,	PUNCT
ejpam-6811	107	31	c	c	NOUN
ejpam-6811	107	32	)	)	PUNCT
ejpam-6811	107	33	≤	≤	NOUN
ejpam-6811	107	34	bdb(a	bdb(a	PROPN
ejpam-6811	107	35	,	,	PUNCT
ejpam-6811	107	36	c	c	NOUN
ejpam-6811	107	37	)	)	PUNCT
ejpam-6811	107	38	.	.	PUNCT
ejpam-6811	108	1	lemma	lemma	PROPN
ejpam-6811	108	2	2	2	X
ejpam-6811	108	3	.	.	PUNCT
ejpam-6811	109	1	let	let	VERB
ejpam-6811	109	2	(	(	PUNCT
ejpam-6811	109	3	x	x	NOUN
ejpam-6811	109	4	,	,	PUNCT
ejpam-6811	109	5	db	db	PROPN
ejpam-6811	109	6	)	)	PUNCT
ejpam-6811	109	7	be	be	AUX
ejpam-6811	109	8	a	a	DET
ejpam-6811	109	9	complete	complete	ADJ
ejpam-6811	109	10	bms	bms	NOUN
ejpam-6811	109	11	equipped	equip	VERB
ejpam-6811	109	12	with	with	ADP
ejpam-6811	109	13	a	a	DET
ejpam-6811	109	14	dg	dg	NOUN
ejpam-6811	109	15	,	,	PUNCT
ejpam-6811	109	16	and	and	CCONJ
ejpam-6811	109	17	db	db	AUX
ejpam-6811	109	18	be	be	AUX
ejpam-6811	109	19	continuous	continuous	ADJ
ejpam-6811	109	20	metric	metric	NOUN
ejpam-6811	109	21	.	.	PUNCT
ejpam-6811	110	1	also	also	ADV
ejpam-6811	110	2	consider	consider	VERB
ejpam-6811	110	3	the	the	DET
ejpam-6811	110	4	pair	pair	NOUN
ejpam-6811	110	5	(	(	PUNCT
ejpam-6811	110	6	t	t	PROPN
ejpam-6811	110	7	,	,	PUNCT
ejpam-6811	110	8	s	s	PART
ejpam-6811	110	9	)	)	PUNCT
ejpam-6811	110	10	is	be	AUX
ejpam-6811	110	11	a	a	DET
ejpam-6811	110	12	ψ−φ	ψ−φ	NOUN
ejpam-6811	110	13	-	-	PUNCT
ejpam-6811	110	14	contraction	contraction	NOUN
ejpam-6811	110	15	satisfying	satisfy	VERB
ejpam-6811	110	16	the	the	DET
ejpam-6811	110	17	following	follow	VERB
ejpam-6811	110	18	axioms	axiom	NOUN
ejpam-6811	110	19	:	:	PUNCT
ejpam-6811	110	20	(	(	PUNCT
ejpam-6811	110	21	1	1	X
ejpam-6811	110	22	)	)	PUNCT
ejpam-6811	110	23	t	t	NOUN
ejpam-6811	110	24	(	(	PUNCT
ejpam-6811	110	25	x	x	NOUN
ejpam-6811	110	26	)	)	PUNCT
ejpam-6811	110	27	⊆	⊆	NUM
ejpam-6811	110	28	s(x	s(x	NOUN
ejpam-6811	110	29	)	)	PUNCT
ejpam-6811	110	30	;	;	PUNCT
ejpam-6811	110	31	(	(	PUNCT
ejpam-6811	110	32	2	2	X
ejpam-6811	110	33	)	)	PUNCT
ejpam-6811	110	34	e(ḡ	e(ḡ	PROPN
ejpam-6811	110	35	)	)	PUNCT
ejpam-6811	110	36	is	be	AUX
ejpam-6811	110	37	transitive	transitive	ADJ
ejpam-6811	110	38	;	;	PUNCT
ejpam-6811	110	39	(	(	PUNCT
ejpam-6811	110	40	3	3	X
ejpam-6811	110	41	)	)	PUNCT
ejpam-6811	110	42	lim	lim	PROPN
ejpam-6811	110	43	n→∞	n→∞	NUM
ejpam-6811	110	44	db(sxn	db(sxn	PROPN
ejpam-6811	110	45	,	,	PUNCT
ejpam-6811	110	46	sxn+1	sxn+1	X
ejpam-6811	110	47	)	)	PUNCT
ejpam-6811	110	48	=	=	SYM
ejpam-6811	110	49	0	0	NUM
ejpam-6811	110	50	,	,	PUNCT
ejpam-6811	110	51	then	then	ADV
ejpam-6811	110	52	{	{	PUNCT
ejpam-6811	110	53	sxn	sxn	NOUN
ejpam-6811	110	54	}	}	PUNCT
ejpam-6811	110	55	is	be	AUX
ejpam-6811	110	56	a	a	DET
ejpam-6811	110	57	cauchy	cauchy	ADJ
ejpam-6811	110	58	sequence	sequence	NOUN
ejpam-6811	110	59	in	in	ADP
ejpam-6811	110	60	(	(	PUNCT
ejpam-6811	110	61	x	x	NOUN
ejpam-6811	110	62	,	,	PUNCT
ejpam-6811	110	63	db	db	PROPN
ejpam-6811	110	64	)	)	PUNCT
ejpam-6811	110	65	.	.	PUNCT
ejpam-6811	111	1	proof	proof	NOUN
ejpam-6811	111	2	.	.	PUNCT
ejpam-6811	112	1	suppose	suppose	VERB
ejpam-6811	112	2	on	on	ADP
ejpam-6811	112	3	contrary	contrary	ADJ
ejpam-6811	112	4	that	that	SCONJ
ejpam-6811	112	5	{	{	PUNCT
ejpam-6811	112	6	sxn	sxn	NOUN
ejpam-6811	112	7	}	}	PUNCT
ejpam-6811	112	8	is	be	AUX
ejpam-6811	112	9	not	not	PART
ejpam-6811	112	10	cauchy	cauchy	ADJ
ejpam-6811	112	11	and	and	CCONJ
ejpam-6811	112	12	the	the	DET
ejpam-6811	112	13	sequences	sequence	NOUN
ejpam-6811	112	14	{	{	PUNCT
ejpam-6811	112	15	jn	jn	PROPN
ejpam-6811	112	16	}	}	PUNCT
ejpam-6811	112	17	,	,	PUNCT
ejpam-6811	112	18	{	{	PUNCT
ejpam-6811	112	19	kn	kn	NOUN
ejpam-6811	112	20	}	}	PUNCT
ejpam-6811	112	21	∈	∈	PROPN
ejpam-6811	112	22	n	n	NOUN
ejpam-6811	112	23	are	be	AUX
ejpam-6811	112	24	such	such	ADJ
ejpam-6811	112	25	that	that	SCONJ
ejpam-6811	112	26	jn	jn	PROPN
ejpam-6811	112	27	>	>	PROPN
ejpam-6811	112	28	kn	kn	PROPN
ejpam-6811	112	29	>	>	X
ejpam-6811	112	30	n	n	PROPN
ejpam-6811	112	31	,	,	PUNCT
ejpam-6811	112	32	db(sxjn	db(sxjn	PROPN
ejpam-6811	112	33	,	,	PUNCT
ejpam-6811	112	34	sxkn	sxkn	NOUN
ejpam-6811	112	35	)	)	PUNCT
ejpam-6811	112	36	≥	≥	X
ejpam-6811	112	37	ε	ε	PROPN
ejpam-6811	112	38	,	,	PUNCT
ejpam-6811	112	39	and	and	CCONJ
ejpam-6811	112	40	db(sxjn−1	db(sxjn−1	NUM
ejpam-6811	112	41	,	,	PUNCT
ejpam-6811	112	42	sxkn	sxkn	NOUN
ejpam-6811	112	43	)	)	PUNCT
ejpam-6811	112	44	<	<	X
ejpam-6811	112	45	ε	ε	PROPN
ejpam-6811	112	46	.	.	PUNCT
ejpam-6811	113	1	(	(	PUNCT
ejpam-6811	113	2	4	4	X
ejpam-6811	113	3	)	)	PUNCT
ejpam-6811	113	4	d.	d.	PROPN
ejpam-6811	113	5	e.	e.	PROPN
ejpam-6811	113	6	shehwar	shehwar	PROPN
ejpam-6811	113	7	sagheer	sagheer	PROPN
ejpam-6811	113	8	et	et	PROPN
ejpam-6811	113	9	al	al	PROPN
ejpam-6811	113	10	.	.	PUNCT
ejpam-6811	113	11	/	/	SYM
ejpam-6811	113	12	eur	eur	PROPN
ejpam-6811	113	13	.	.	PUNCT
ejpam-6811	114	1	j.	j.	PROPN
ejpam-6811	114	2	pure	pure	PROPN
ejpam-6811	114	3	appl	appl	PROPN
ejpam-6811	114	4	.	.	PROPN
ejpam-6811	114	5	math	math	PROPN
ejpam-6811	114	6	,	,	PUNCT
ejpam-6811	114	7	18	18	NUM
ejpam-6811	114	8	(	(	PUNCT
ejpam-6811	114	9	4	4	NUM
ejpam-6811	114	10	)	)	PUNCT
ejpam-6811	114	11	(	(	PUNCT
ejpam-6811	114	12	2025	2025	NUM
ejpam-6811	114	13	)	)	PUNCT
ejpam-6811	114	14	,	,	PUNCT
ejpam-6811	114	15	6811	6811	NUM
ejpam-6811	114	16	6	6	NUM
ejpam-6811	114	17	of	of	ADP
ejpam-6811	114	18	24	24	NUM
ejpam-6811	114	19	using	use	VERB
ejpam-6811	114	20	the	the	DET
ejpam-6811	114	21	triangular	triangular	NOUN
ejpam-6811	114	22	inequality	inequality	NOUN
ejpam-6811	114	23	,	,	PUNCT
ejpam-6811	114	24	ε	ε	PROPN
ejpam-6811	114	25	≤	≤	PROPN
ejpam-6811	114	26	db(xjn	db(xjn	NOUN
ejpam-6811	114	27	,	,	PUNCT
ejpam-6811	114	28	xkn	xkn	PROPN
ejpam-6811	114	29	)	)	PUNCT
ejpam-6811	114	30	≤	≤	NUM
ejpam-6811	114	31	b[db(xjn	b[db(xjn	PUNCT
ejpam-6811	114	32	,	,	PUNCT
ejpam-6811	114	33	xjn−1	xjn−1	PROPN
ejpam-6811	114	34	)	)	PUNCT
ejpam-6811	115	1	+	+	CCONJ
ejpam-6811	115	2	db(xjn−1	db(xjn−1	ADJ
ejpam-6811	115	3	,	,	PUNCT
ejpam-6811	115	4	xkn	xkn	PROPN
ejpam-6811	115	5	)	)	PUNCT
ejpam-6811	115	6	]	]	PUNCT
ejpam-6811	116	1	<	<	X
ejpam-6811	116	2	bdb(xjn	bdb(xjn	NOUN
ejpam-6811	116	3	,	,	PUNCT
ejpam-6811	116	4	xjn−1	xjn−1	PROPN
ejpam-6811	116	5	)	)	PUNCT
ejpam-6811	116	6	+	+	CCONJ
ejpam-6811	116	7	bε	bε	NOUN
ejpam-6811	116	8	.	.	PUNCT
ejpam-6811	116	9	by	by	ADP
ejpam-6811	116	10	letting	let	VERB
ejpam-6811	116	11	limit	limit	NOUN
ejpam-6811	116	12	n→	n→	PUNCT
ejpam-6811	116	13	∞	∞	PROPN
ejpam-6811	116	14	,	,	PUNCT
ejpam-6811	116	15	ε	ε	PROPN
ejpam-6811	116	16	≤	≤	PROPN
ejpam-6811	116	17	lim	lim	PROPN
ejpam-6811	116	18	inf	inf	PROPN
ejpam-6811	116	19	n→∞	n→∞	NUM
ejpam-6811	116	20	db(xjn	db(xjn	NOUN
ejpam-6811	116	21	,	,	PUNCT
ejpam-6811	116	22	xkn	xkn	PROPN
ejpam-6811	116	23	)	)	PUNCT
ejpam-6811	116	24	≤	≤	NOUN
ejpam-6811	117	1	lim	lim	PROPN
ejpam-6811	117	2	sup	sup	VERB
ejpam-6811	117	3	n→∞	n→∞	NUM
ejpam-6811	117	4	db(xjn	db(xjn	NOUN
ejpam-6811	117	5	,	,	PUNCT
ejpam-6811	117	6	xkn	xkn	PROPN
ejpam-6811	117	7	)	)	PUNCT
ejpam-6811	117	8	≤	≤	NUM
ejpam-6811	117	9	bε	bε	NOUN
ejpam-6811	117	10	.	.	PUNCT
ejpam-6811	118	1	(	(	PUNCT
ejpam-6811	118	2	5	5	NUM
ejpam-6811	118	3	)	)	PUNCT
ejpam-6811	118	4	also	also	ADV
ejpam-6811	118	5	,	,	PUNCT
ejpam-6811	118	6	one	one	PRON
ejpam-6811	118	7	can	can	AUX
ejpam-6811	118	8	easily	easily	ADV
ejpam-6811	118	9	get	get	VERB
ejpam-6811	118	10	ε	ε	PROPN
ejpam-6811	118	11	b	b	PROPN
ejpam-6811	118	12	≤	≤	PROPN
ejpam-6811	118	13	lim	lim	PROPN
ejpam-6811	118	14	inf	inf	PROPN
ejpam-6811	118	15	n→∞	n→∞	NUM
ejpam-6811	118	16	db(xjn	db(xjn	PROPN
ejpam-6811	118	17	,	,	PUNCT
ejpam-6811	118	18	xkn+1	xkn+1	PROPN
ejpam-6811	118	19	)	)	PUNCT
ejpam-6811	118	20	≤	≤	NOUN
ejpam-6811	118	21	lim	lim	PROPN
ejpam-6811	118	22	sup	sup	VERB
ejpam-6811	118	23	n→∞	n→∞	NUM
ejpam-6811	118	24	db(xjn	db(xjn	NOUN
ejpam-6811	118	25	,	,	PUNCT
ejpam-6811	118	26	xkn+1	xkn+1	PROPN
ejpam-6811	118	27	)	)	PUNCT
ejpam-6811	118	28	≤	≤	NOUN
ejpam-6811	118	29	b2ε	b2ε	NOUN
ejpam-6811	118	30	,	,	PUNCT
ejpam-6811	118	31	ε	ε	PROPN
ejpam-6811	118	32	b	b	PROPN
ejpam-6811	118	33	≤	≤	PROPN
ejpam-6811	118	34	lim	lim	PROPN
ejpam-6811	118	35	inf	inf	PROPN
ejpam-6811	118	36	n→∞	n→∞	NUM
ejpam-6811	118	37	db(xjn+1	db(xjn+1	PROPN
ejpam-6811	118	38	,	,	PUNCT
ejpam-6811	118	39	xkn	xkn	PROPN
ejpam-6811	118	40	)	)	PUNCT
ejpam-6811	118	41	≤	≤	NOUN
ejpam-6811	118	42	lim	lim	PROPN
ejpam-6811	118	43	sup	sup	VERB
ejpam-6811	118	44	n→∞	n→∞	NUM
ejpam-6811	118	45	db(xjn+1	db(xjn+1	PROPN
ejpam-6811	118	46	,	,	PUNCT
ejpam-6811	118	47	xkn	xkn	PROPN
ejpam-6811	118	48	)	)	PUNCT
ejpam-6811	118	49	≤	≤	NOUN
ejpam-6811	118	50	b2ε	b2ε	NOUN
ejpam-6811	118	51	,	,	PUNCT
ejpam-6811	118	52	ε	ε	PROPN
ejpam-6811	118	53	b2	b2	PROPN
ejpam-6811	118	54	≤	≤	PROPN
ejpam-6811	118	55	lim	lim	PROPN
ejpam-6811	118	56	inf	inf	PROPN
ejpam-6811	118	57	n→∞	n→∞	NUM
ejpam-6811	118	58	db(xjn+1	db(xjn+1	PROPN
ejpam-6811	118	59	,	,	PUNCT
ejpam-6811	118	60	xkn+1	xkn+1	PROPN
ejpam-6811	118	61	)	)	PUNCT
ejpam-6811	118	62	≤	≤	NOUN
ejpam-6811	118	63	lim	lim	PROPN
ejpam-6811	118	64	sup	sup	VERB
ejpam-6811	118	65	n→∞	n→∞	NUM
ejpam-6811	118	66	db(xjn+1	db(xjn+1	PROPN
ejpam-6811	118	67	,	,	PUNCT
ejpam-6811	118	68	xkn+1	xkn+1	PROPN
ejpam-6811	118	69	)	)	PUNCT
ejpam-6811	118	70	≤	≤	PUNCT
ejpam-6811	119	1	b3ε	b3ε	PROPN
ejpam-6811	119	2	.	.	PUNCT
ejpam-6811	120	1	now	now	ADV
ejpam-6811	120	2	,	,	PUNCT
ejpam-6811	120	3	as	as	SCONJ
ejpam-6811	120	4	t	t	PROPN
ejpam-6811	120	5	(	(	PUNCT
ejpam-6811	120	6	x	x	NOUN
ejpam-6811	120	7	)	)	PUNCT
ejpam-6811	120	8	⊆	⊆	NUM
ejpam-6811	120	9	s(x	s(x	NOUN
ejpam-6811	120	10	)	)	PUNCT
ejpam-6811	120	11	holds	hold	VERB
ejpam-6811	120	12	,	,	PUNCT
ejpam-6811	120	13	then	then	ADV
ejpam-6811	120	14	we	we	PRON
ejpam-6811	120	15	can	can	AUX
ejpam-6811	120	16	construct	construct	VERB
ejpam-6811	120	17	a	a	DET
ejpam-6811	120	18	sequence	sequence	NOUN
ejpam-6811	120	19	xn	xn	SYM
ejpam-6811	120	20	∈	∈	PROPN
ejpam-6811	120	21	x	x	PUNCT
ejpam-6811	120	22	such	such	ADJ
ejpam-6811	120	23	that	that	DET
ejpam-6811	120	24	sxn	sxn	NOUN
ejpam-6811	120	25	=	=	PROPN
ejpam-6811	120	26	txn−1	txn−1	PROPN
ejpam-6811	120	27	for	for	ADP
ejpam-6811	120	28	all	all	DET
ejpam-6811	120	29	n	n	PRON
ejpam-6811	120	30	∈	∈	NOUN
ejpam-6811	121	1	n	n	CCONJ
ejpam-6811	121	2	then	then	ADV
ejpam-6811	121	3	(	(	PUNCT
ejpam-6811	121	4	sx0	sx0	PROPN
ejpam-6811	121	5	,	,	PUNCT
ejpam-6811	121	6	tx0	tx0	NOUN
ejpam-6811	121	7	)	)	PUNCT
ejpam-6811	121	8	=	=	SYM
ejpam-6811	121	9	(	(	PUNCT
ejpam-6811	121	10	sx0	sx0	PROPN
ejpam-6811	121	11	,	,	PUNCT
ejpam-6811	121	12	sx1	sx1	NOUN
ejpam-6811	121	13	)	)	PUNCT
ejpam-6811	121	14	∈	∈	PROPN
ejpam-6811	121	15	e(ḡ	e(ḡ	NOUN
ejpam-6811	121	16	)	)	PUNCT
ejpam-6811	121	17	,	,	PUNCT
ejpam-6811	121	18	and	and	CCONJ
ejpam-6811	121	19	inductively	inductively	ADV
ejpam-6811	121	20	we	we	PRON
ejpam-6811	121	21	may	may	AUX
ejpam-6811	121	22	write	write	VERB
ejpam-6811	121	23	(	(	PUNCT
ejpam-6811	121	24	sxn−1	sxn−1	PROPN
ejpam-6811	121	25	,	,	PUNCT
ejpam-6811	121	26	sxn	sxn	NOUN
ejpam-6811	121	27	)	)	PUNCT
ejpam-6811	121	28	∈	∈	PROPN
ejpam-6811	121	29	e(ḡ	e(ḡ	PROPN
ejpam-6811	121	30	)	)	PUNCT
ejpam-6811	121	31	,	,	PUNCT
ejpam-6811	121	32	for	for	ADP
ejpam-6811	121	33	any	any	DET
ejpam-6811	121	34	n.	n.	NOUN
ejpam-6811	121	35	for	for	ADP
ejpam-6811	121	36	(	(	PUNCT
ejpam-6811	121	37	sxjn	sxjn	NOUN
ejpam-6811	121	38	,	,	PUNCT
ejpam-6811	121	39	sxkn	sxkn	NOUN
ejpam-6811	121	40	)	)	PUNCT
ejpam-6811	121	41	∈	∈	PROPN
ejpam-6811	121	42	e(ḡ	e(ḡ	PROPN
ejpam-6811	121	43	)	)	PUNCT
ejpam-6811	121	44	,	,	PUNCT
ejpam-6811	121	45	we	we	PRON
ejpam-6811	121	46	may	may	AUX
ejpam-6811	121	47	write	write	VERB
ejpam-6811	121	48	φ(db(sxjn+1	φ(db(sxjn+1	VERB
ejpam-6811	121	49	,	,	PUNCT
ejpam-6811	121	50	sxkn+1	sxkn+1	NOUN
ejpam-6811	121	51	)	)	PUNCT
ejpam-6811	121	52	)	)	PUNCT
ejpam-6811	122	1	=	=	NUM
ejpam-6811	122	2	φ(db(txjn	φ(db(txjn	NOUN
ejpam-6811	122	3	,	,	PUNCT
ejpam-6811	122	4	txkn	txkn	NOUN
ejpam-6811	122	5	)	)	PUNCT
ejpam-6811	122	6	)	)	PUNCT
ejpam-6811	122	7	≤	≤	NUM
ejpam-6811	122	8	ψ(db(sxjn	ψ(db(sxjn	NOUN
ejpam-6811	122	9	,	,	PUNCT
ejpam-6811	122	10	sxkn))φ(δ(m(sxjn	sxkn))φ(δ(m(sxjn	PROPN
ejpam-6811	122	11	,	,	PUNCT
ejpam-6811	122	12	sxkn	sxkn	NOUN
ejpam-6811	122	13	)	)	PUNCT
ejpam-6811	122	14	)	)	PUNCT
ejpam-6811	122	15	)	)	PUNCT
ejpam-6811	122	16	≤	≤	NOUN
ejpam-6811	122	17	φ(δ(m(sxjn	φ(δ(m(sxjn	NOUN
ejpam-6811	122	18	,	,	PUNCT
ejpam-6811	122	19	sxkn	sxkn	NOUN
ejpam-6811	122	20	)	)	PUNCT
ejpam-6811	122	21	)	)	PUNCT
ejpam-6811	122	22	)	)	PUNCT
ejpam-6811	122	23	,	,	PUNCT
ejpam-6811	122	24	(	(	PUNCT
ejpam-6811	122	25	6	6	X
ejpam-6811	122	26	)	)	PUNCT
ejpam-6811	122	27	where	where	SCONJ
ejpam-6811	122	28	m(sxjn	m(sxjn	NOUN
ejpam-6811	122	29	,	,	PUNCT
ejpam-6811	122	30	sxkn	sxkn	NOUN
ejpam-6811	122	31	)	)	PUNCT
ejpam-6811	122	32	=	=	SYM
ejpam-6811	122	33	max	max	PROPN
ejpam-6811	122	34	{	{	PUNCT
ejpam-6811	122	35	db(sxjn	db(sxjn	PROPN
ejpam-6811	122	36	,	,	PUNCT
ejpam-6811	122	37	txjn)db(txkn	txjn)db(txkn	NOUN
ejpam-6811	122	38	,	,	PUNCT
ejpam-6811	122	39	sxkn	sxkn	NOUN
ejpam-6811	122	40	)	)	PUNCT
ejpam-6811	122	41	db(sxjn	db(sxjn	NOUN
ejpam-6811	122	42	,	,	PUNCT
ejpam-6811	122	43	sxkn	sxkn	NOUN
ejpam-6811	122	44	)	)	PUNCT
ejpam-6811	122	45	,	,	PUNCT
ejpam-6811	122	46	db(sxjn	db(sxjn	PROPN
ejpam-6811	122	47	,	,	PUNCT
ejpam-6811	122	48	sxkn	sxkn	NOUN
ejpam-6811	122	49	)	)	PUNCT
ejpam-6811	122	50	,	,	PUNCT
ejpam-6811	122	51	db(sxjn	db(sxjn	PROPN
ejpam-6811	122	52	,	,	PUNCT
ejpam-6811	122	53	txjn	txjn	NOUN
ejpam-6811	122	54	)	)	PUNCT
ejpam-6811	122	55	,	,	PUNCT
ejpam-6811	122	56	db(sxkn	db(sxkn	NOUN
ejpam-6811	122	57	,	,	PUNCT
ejpam-6811	122	58	txkn	txkn	NOUN
ejpam-6811	122	59	)	)	PUNCT
ejpam-6811	122	60	,	,	PUNCT
ejpam-6811	122	61	db(sxjn	db(sxjn	NOUN
ejpam-6811	122	62	,	,	PUNCT
ejpam-6811	122	63	txkn	txkn	NOUN
ejpam-6811	122	64	)	)	PUNCT
ejpam-6811	123	1	+	+	NUM
ejpam-6811	123	2	db(sxkn	db(sxkn	NOUN
ejpam-6811	123	3	,	,	PUNCT
ejpam-6811	123	4	txjn	txjn	ADJ
ejpam-6811	123	5	)	)	PUNCT
ejpam-6811	123	6	2b	2b	NOUN
ejpam-6811	123	7	}	}	PUNCT
ejpam-6811	123	8	=	=	SYM
ejpam-6811	123	9	max	max	PROPN
ejpam-6811	123	10	{	{	PUNCT
ejpam-6811	123	11	db(sxjn	db(sxjn	PROPN
ejpam-6811	123	12	,	,	PUNCT
ejpam-6811	123	13	sxjn+1)db(sxkn+1	sxjn+1)db(sxkn+1	NOUN
ejpam-6811	123	14	,	,	PUNCT
ejpam-6811	123	15	sxkn	sxkn	NOUN
ejpam-6811	123	16	)	)	PUNCT
ejpam-6811	123	17	db(sxjn	db(sxjn	NOUN
ejpam-6811	123	18	,	,	PUNCT
ejpam-6811	123	19	sxkn	sxkn	NOUN
ejpam-6811	123	20	)	)	PUNCT
ejpam-6811	123	21	,	,	PUNCT
ejpam-6811	123	22	db(sxjn	db(sxjn	PROPN
ejpam-6811	123	23	,	,	PUNCT
ejpam-6811	123	24	sxkn	sxkn	NOUN
ejpam-6811	123	25	)	)	PUNCT
ejpam-6811	123	26	,	,	PUNCT
ejpam-6811	123	27	db(sxjn	db(sxjn	PROPN
ejpam-6811	123	28	,	,	PUNCT
ejpam-6811	123	29	sxjn+1	sxjn+1	PROPN
ejpam-6811	123	30	)	)	PUNCT
ejpam-6811	123	31	,	,	PUNCT
ejpam-6811	123	32	db(sxkn	db(sxkn	NOUN
ejpam-6811	123	33	,	,	PUNCT
ejpam-6811	123	34	sxkn+1	sxkn+1	PROPN
ejpam-6811	123	35	)	)	PUNCT
ejpam-6811	123	36	,	,	PUNCT
ejpam-6811	123	37	db(sxjn	db(sxjn	NOUN
ejpam-6811	123	38	,	,	PUNCT
ejpam-6811	123	39	sxkn+1	sxkn+1	PROPN
ejpam-6811	123	40	)	)	PUNCT
ejpam-6811	124	1	+	+	NUM
ejpam-6811	124	2	db(sxkn	db(sxkn	NOUN
ejpam-6811	124	3	,	,	PUNCT
ejpam-6811	124	4	sxjn+1	sxjn+1	NOUN
ejpam-6811	124	5	)	)	PUNCT
ejpam-6811	124	6	2b	2b	NOUN
ejpam-6811	124	7	}	}	PUNCT
ejpam-6811	124	8	.	.	PUNCT
ejpam-6811	125	1	≤	≤	NUM
ejpam-6811	125	2	max	max	PROPN
ejpam-6811	125	3	{	{	PUNCT
ejpam-6811	125	4	db(sxjn	db(sxjn	PROPN
ejpam-6811	125	5	,	,	PUNCT
ejpam-6811	125	6	sxjn+1)db(sxkn+1	sxjn+1)db(sxkn+1	NOUN
ejpam-6811	125	7	,	,	PUNCT
ejpam-6811	125	8	sxkn	sxkn	NOUN
ejpam-6811	125	9	)	)	PUNCT
ejpam-6811	125	10	db(sxjn	db(sxjn	NOUN
ejpam-6811	125	11	,	,	PUNCT
ejpam-6811	125	12	sxkn	sxkn	NOUN
ejpam-6811	125	13	)	)	PUNCT
ejpam-6811	125	14	,	,	PUNCT
ejpam-6811	125	15	db(sxjn	db(sxjn	PROPN
ejpam-6811	125	16	,	,	PUNCT
ejpam-6811	125	17	sxkn	sxkn	NOUN
ejpam-6811	125	18	)	)	PUNCT
ejpam-6811	125	19	,	,	PUNCT
ejpam-6811	125	20	db(sxjn	db(sxjn	PROPN
ejpam-6811	125	21	,	,	PUNCT
ejpam-6811	125	22	sxjn+1	sxjn+1	PROPN
ejpam-6811	125	23	)	)	PUNCT
ejpam-6811	125	24	,	,	PUNCT
ejpam-6811	125	25	db(sxkn	db(sxkn	NOUN
ejpam-6811	125	26	,	,	PUNCT
ejpam-6811	125	27	sxkn+1	sxkn+1	PROPN
ejpam-6811	125	28	)	)	PUNCT
ejpam-6811	125	29	,	,	PUNCT
ejpam-6811	125	30	db(sxjn	db(sxjn	PROPN
ejpam-6811	125	31	,	,	PUNCT
ejpam-6811	125	32	sxkn	sxkn	NOUN
ejpam-6811	125	33	)	)	PUNCT
ejpam-6811	126	1	+	+	NUM
ejpam-6811	126	2	db(sxkn	db(sxkn	NOUN
ejpam-6811	126	3	,	,	PUNCT
ejpam-6811	126	4	sxkn+1	sxkn+1	NOUN
ejpam-6811	126	5	)	)	PUNCT
ejpam-6811	127	1	+	+	NUM
ejpam-6811	127	2	db(sxkn	db(sxkn	NOUN
ejpam-6811	127	3	,	,	PUNCT
ejpam-6811	127	4	sxjn	sxjn	NOUN
ejpam-6811	127	5	)	)	PUNCT
ejpam-6811	128	1	+	+	NUM
ejpam-6811	128	2	db(sxjn	db(sxjn	PROPN
ejpam-6811	128	3	,	,	PUNCT
ejpam-6811	128	4	sxjn+1	sxjn+1	NOUN
ejpam-6811	128	5	)	)	PUNCT
ejpam-6811	128	6	2	2	NUM
ejpam-6811	128	7	}	}	PUNCT
ejpam-6811	128	8	.	.	PUNCT
ejpam-6811	129	1	after	after	ADP
ejpam-6811	129	2	doing	do	VERB
ejpam-6811	129	3	simple	simple	ADJ
ejpam-6811	129	4	calculations	calculation	NOUN
ejpam-6811	129	5	and	and	CCONJ
ejpam-6811	129	6	using	use	VERB
ejpam-6811	129	7	the	the	DET
ejpam-6811	129	8	assumption	assumption	NOUN
ejpam-6811	129	9	(	(	PUNCT
ejpam-6811	129	10	3	3	NUM
ejpam-6811	129	11	)	)	PUNCT
ejpam-6811	129	12	,	,	PUNCT
ejpam-6811	129	13	we	we	PRON
ejpam-6811	129	14	get	get	VERB
ejpam-6811	129	15	lim	lim	PROPN
ejpam-6811	129	16	sup	sup	PROPN
ejpam-6811	129	17	k→∞	k→∞	PROPN
ejpam-6811	129	18	m(sxkn	m(sxkn	NOUN
ejpam-6811	129	19	,	,	PUNCT
ejpam-6811	129	20	sxjn	sxjn	NOUN
ejpam-6811	129	21	)	)	PUNCT
ejpam-6811	129	22	≤	≤	NOUN
ejpam-6811	129	23	lim	lim	PROPN
ejpam-6811	129	24	sup	sup	PROPN
ejpam-6811	129	25	db(sxkn	db(sxkn	PROPN
ejpam-6811	129	26	,	,	PUNCT
ejpam-6811	129	27	sxjn	sxjn	NOUN
ejpam-6811	129	28	)	)	PUNCT
ejpam-6811	129	29	.	.	PUNCT
ejpam-6811	130	1	d.	d.	PROPN
ejpam-6811	130	2	e.	e.	PROPN
ejpam-6811	130	3	shehwar	shehwar	PROPN
ejpam-6811	130	4	sagheer	sagheer	PROPN
ejpam-6811	130	5	et	et	PROPN
ejpam-6811	130	6	al	al	PROPN
ejpam-6811	130	7	.	.	PUNCT
ejpam-6811	130	8	/	/	SYM
ejpam-6811	130	9	eur	eur	PROPN
ejpam-6811	130	10	.	.	PUNCT
ejpam-6811	131	1	j.	j.	PROPN
ejpam-6811	131	2	pure	pure	PROPN
ejpam-6811	131	3	appl	appl	PROPN
ejpam-6811	131	4	.	.	PROPN
ejpam-6811	131	5	math	math	PROPN
ejpam-6811	131	6	,	,	PUNCT
ejpam-6811	131	7	18	18	NUM
ejpam-6811	131	8	(	(	PUNCT
ejpam-6811	131	9	4	4	NUM
ejpam-6811	131	10	)	)	PUNCT
ejpam-6811	131	11	(	(	PUNCT
ejpam-6811	131	12	2025	2025	NUM
ejpam-6811	131	13	)	)	PUNCT
ejpam-6811	131	14	,	,	PUNCT
ejpam-6811	131	15	6811	6811	NUM
ejpam-6811	131	16	7	7	NUM
ejpam-6811	131	17	of	of	ADP
ejpam-6811	131	18	24	24	NUM
ejpam-6811	131	19	from	from	ADP
ejpam-6811	131	20	(	(	PUNCT
ejpam-6811	131	21	6	6	NUM
ejpam-6811	131	22	)	)	PUNCT
ejpam-6811	131	23	,	,	PUNCT
ejpam-6811	131	24	we	we	PRON
ejpam-6811	131	25	obtain	obtain	VERB
ejpam-6811	131	26	ε	ε	PROPN
ejpam-6811	131	27	b2	b2	NOUN
ejpam-6811	131	28	≤	≤	ADJ
ejpam-6811	131	29	lim	lim	PROPN
ejpam-6811	131	30	sup	sup	PROPN
ejpam-6811	131	31	k→∞	k→∞	PROPN
ejpam-6811	131	32	db(sxjn+1	db(sxjn+1	PROPN
ejpam-6811	131	33	,	,	PUNCT
ejpam-6811	131	34	sxkn+1	sxkn+1	NOUN
ejpam-6811	131	35	)	)	PUNCT
ejpam-6811	131	36	)	)	PUNCT
ejpam-6811	132	1	≤	≤	NOUN
ejpam-6811	132	2	lim	lim	PROPN
ejpam-6811	132	3	sup	sup	PROPN
ejpam-6811	132	4	k→∞	k→∞	NOUN
ejpam-6811	132	5	δ(db(sxkn	δ(db(sxkn	NOUN
ejpam-6811	132	6	,	,	PUNCT
ejpam-6811	132	7	sxjn	sxjn	NOUN
ejpam-6811	132	8	)	)	PUNCT
ejpam-6811	132	9	)	)	PUNCT
ejpam-6811	132	10	.	.	PUNCT
ejpam-6811	133	1	also	also	ADV
ejpam-6811	133	2	,	,	PUNCT
ejpam-6811	133	3	by	by	ADP
ejpam-6811	133	4	using	use	VERB
ejpam-6811	133	5	property	property	NOUN
ejpam-6811	133	6	of	of	ADP
ejpam-6811	133	7	φ	φ	PROPN
ejpam-6811	133	8	,	,	PUNCT
ejpam-6811	133	9	we	we	PRON
ejpam-6811	133	10	get	get	VERB
ejpam-6811	133	11	φ	φ	NUM
ejpam-6811	133	12	(	(	PUNCT
ejpam-6811	133	13	ε	ε	PROPN
ejpam-6811	133	14	b2	b2	PROPN
ejpam-6811	133	15	)	)	PUNCT
ejpam-6811	133	16	≤	≤	NOUN
ejpam-6811	134	1	lim	lim	PROPN
ejpam-6811	134	2	sup	sup	PROPN
ejpam-6811	134	3	k→∞	k→∞	ADV
ejpam-6811	134	4	φ(db(sxjn+1	φ(db(sxjn+1	NOUN
ejpam-6811	134	5	,	,	PUNCT
ejpam-6811	134	6	sxkn+1	sxkn+1	NOUN
ejpam-6811	134	7	)	)	PUNCT
ejpam-6811	134	8	)	)	PUNCT
ejpam-6811	135	1	≤	≤	NOUN
ejpam-6811	135	2	lim	lim	PROPN
ejpam-6811	135	3	sup	sup	PROPN
ejpam-6811	135	4	k→∞	k→∞	NOUN
ejpam-6811	135	5	φ(δ(db(sxkn	φ(δ(db(sxkn	ADJ
ejpam-6811	135	6	,	,	PUNCT
ejpam-6811	135	7	sxjn	sxjn	NOUN
ejpam-6811	135	8	)	)	PUNCT
ejpam-6811	135	9	)	)	PUNCT
ejpam-6811	135	10	)	)	PUNCT
ejpam-6811	135	11	.	.	PUNCT
ejpam-6811	136	1	now	now	ADV
ejpam-6811	136	2	,	,	PUNCT
ejpam-6811	136	3	by	by	ADP
ejpam-6811	136	4	the	the	DET
ejpam-6811	136	5	continuity	continuity	NOUN
ejpam-6811	136	6	of	of	ADP
ejpam-6811	136	7	φ	φ	PROPN
ejpam-6811	136	8	and	and	CCONJ
ejpam-6811	136	9	using	use	VERB
ejpam-6811	136	10	δ	δ	PROPN
ejpam-6811	136	11	≤	≤	ADV
ejpam-6811	136	12	1	1	NUM
ejpam-6811	136	13	bν	bν	ADJ
ejpam-6811	136	14	we	we	PRON
ejpam-6811	136	15	get	get	VERB
ejpam-6811	136	16	φ	φ	NUM
ejpam-6811	136	17	(	(	PUNCT
ejpam-6811	136	18	ε	ε	PROPN
ejpam-6811	136	19	b2	b2	PROPN
ejpam-6811	136	20	)	)	PUNCT
ejpam-6811	136	21	≤	≤	PROPN
ejpam-6811	137	1	φ	φ	PROPN
ejpam-6811	137	2	(	(	PUNCT
ejpam-6811	137	3	1	1	NUM
ejpam-6811	137	4	bν	bν	PROPN
ejpam-6811	137	5	(	(	PUNCT
ejpam-6811	137	6	bε	bε	NOUN
ejpam-6811	137	7	)	)	PUNCT
ejpam-6811	137	8	)	)	PUNCT
ejpam-6811	137	9	,	,	PUNCT
ejpam-6811	137	10	which	which	PRON
ejpam-6811	137	11	is	be	AUX
ejpam-6811	137	12	a	a	DET
ejpam-6811	137	13	contradiction	contradiction	NOUN
ejpam-6811	137	14	as	as	ADP
ejpam-6811	137	15	ν	ν	X
ejpam-6811	137	16	>	>	X
ejpam-6811	137	17	3	3	NUM
ejpam-6811	137	18	.	.	PUNCT
ejpam-6811	138	1	hence	hence	ADV
ejpam-6811	138	2	,	,	PUNCT
ejpam-6811	138	3	{	{	PUNCT
ejpam-6811	138	4	sxn	sxn	NOUN
ejpam-6811	138	5	}	}	PUNCT
ejpam-6811	138	6	is	be	AUX
ejpam-6811	138	7	a	a	DET
ejpam-6811	138	8	cauchy	cauchy	ADJ
ejpam-6811	138	9	sequence	sequence	NOUN
ejpam-6811	138	10	in	in	ADP
ejpam-6811	138	11	(	(	PUNCT
ejpam-6811	138	12	x	x	NOUN
ejpam-6811	138	13	,	,	PUNCT
ejpam-6811	138	14	db	db	PROPN
ejpam-6811	138	15	)	)	PUNCT
ejpam-6811	138	16	.	.	PUNCT
ejpam-6811	139	1	theorem	theorem	NOUN
ejpam-6811	139	2	1	1	X
ejpam-6811	139	3	.	.	PUNCT
ejpam-6811	140	1	let	let	VERB
ejpam-6811	140	2	(	(	PUNCT
ejpam-6811	140	3	x	x	NOUN
ejpam-6811	140	4	,	,	PUNCT
ejpam-6811	140	5	db	db	PROPN
ejpam-6811	140	6	)	)	PUNCT
ejpam-6811	140	7	be	be	AUX
ejpam-6811	140	8	a	a	DET
ejpam-6811	140	9	complete	complete	ADJ
ejpam-6811	140	10	bms	bms	NOUN
ejpam-6811	140	11	with	with	ADP
ejpam-6811	140	12	ḡ	ḡ	VERB
ejpam-6811	140	13	=	=	SYM
ejpam-6811	140	14	(	(	PUNCT
ejpam-6811	140	15	v	v	NOUN
ejpam-6811	140	16	(	(	PUNCT
ejpam-6811	140	17	ḡ	ḡ	VERB
ejpam-6811	140	18	)	)	PUNCT
ejpam-6811	140	19	,	,	PUNCT
ejpam-6811	140	20	e(ḡ	e(ḡ	PROPN
ejpam-6811	140	21	)	)	PUNCT
ejpam-6811	140	22	)	)	PUNCT
ejpam-6811	141	1	a	a	DET
ejpam-6811	141	2	dg	dg	NOUN
ejpam-6811	141	3	and	and	CCONJ
ejpam-6811	141	4	db	db	AUX
ejpam-6811	141	5	be	be	AUX
ejpam-6811	141	6	continuous	continuous	ADJ
ejpam-6811	141	7	.	.	PUNCT
ejpam-6811	142	1	let	let	VERB
ejpam-6811	142	2	d′b	d′b	PRON
ejpam-6811	142	3	be	be	AUX
ejpam-6811	142	4	another	another	DET
ejpam-6811	142	5	continuous	continuous	ADJ
ejpam-6811	142	6	function	function	NOUN
ejpam-6811	142	7	and	and	CCONJ
ejpam-6811	142	8	the	the	DET
ejpam-6811	142	9	pair	pair	NOUN
ejpam-6811	142	10	(	(	PUNCT
ejpam-6811	142	11	t	t	PROPN
ejpam-6811	142	12	,	,	PUNCT
ejpam-6811	142	13	s	s	AUX
ejpam-6811	142	14	)	)	PUNCT
ejpam-6811	142	15	be	be	AUX
ejpam-6811	142	16	an	an	DET
ejpam-6811	142	17	ψ	ψ	NOUN
ejpam-6811	142	18	−	−	NOUN
ejpam-6811	142	19	φcontraction	φcontraction	NOUN
ejpam-6811	142	20	with	with	ADP
ejpam-6811	142	21	respect	respect	NOUN
ejpam-6811	142	22	to	to	ADP
ejpam-6811	142	23	db	db	VERB
ejpam-6811	142	24	together	together	ADV
ejpam-6811	142	25	with	with	ADP
ejpam-6811	142	26	the	the	DET
ejpam-6811	142	27	following	following	NOUN
ejpam-6811	142	28	:	:	PUNCT
ejpam-6811	142	29	(	(	PUNCT
ejpam-6811	142	30	i	i	NOUN
ejpam-6811	142	31	)	)	PUNCT
ejpam-6811	142	32	s	s	VERB
ejpam-6811	142	33	:	:	PUNCT
ejpam-6811	142	34	(	(	PUNCT
ejpam-6811	142	35	x	x	NOUN
ejpam-6811	142	36	,	,	PUNCT
ejpam-6811	142	37	d′b	d′b	PROPN
ejpam-6811	142	38	)	)	PUNCT
ejpam-6811	142	39	→	→	SYM
ejpam-6811	142	40	(	(	PUNCT
ejpam-6811	142	41	x	x	NOUN
ejpam-6811	142	42	,	,	PUNCT
ejpam-6811	142	43	d′b	d′b	PROPN
ejpam-6811	142	44	)	)	PUNCT
ejpam-6811	142	45	is	be	AUX
ejpam-6811	142	46	continuous	continuous	ADJ
ejpam-6811	142	47	,	,	PUNCT
ejpam-6811	142	48	and	and	CCONJ
ejpam-6811	142	49	s(x	s(x	NOUN
ejpam-6811	142	50	)	)	PUNCT
ejpam-6811	143	1	is	be	AUX
ejpam-6811	143	2	closed	close	VERB
ejpam-6811	143	3	w.r.t	w.r.t	ADJ
ejpam-6811	143	4	d′b	d′b	PROPN
ejpam-6811	143	5	;	;	PUNCT
ejpam-6811	143	6	(	(	PUNCT
ejpam-6811	143	7	ii	ii	NOUN
ejpam-6811	143	8	)	)	PUNCT
ejpam-6811	143	9	t	t	PROPN
ejpam-6811	143	10	(	(	PUNCT
ejpam-6811	143	11	x	x	NOUN
ejpam-6811	143	12	)	)	PUNCT
ejpam-6811	143	13	⊆	⊆	NUM
ejpam-6811	143	14	s(x	s(x	NOUN
ejpam-6811	143	15	)	)	PUNCT
ejpam-6811	143	16	;	;	PUNCT
ejpam-6811	143	17	(	(	PUNCT
ejpam-6811	143	18	iii	iii	NOUN
ejpam-6811	143	19	)	)	PUNCT
ejpam-6811	143	20	e(ḡ	e(ḡ	PROPN
ejpam-6811	143	21	)	)	PUNCT
ejpam-6811	143	22	is	be	AUX
ejpam-6811	143	23	a	a	DET
ejpam-6811	143	24	transitive	transitive	ADJ
ejpam-6811	143	25	set	set	NOUN
ejpam-6811	143	26	;	;	PUNCT
ejpam-6811	143	27	(	(	PUNCT
ejpam-6811	143	28	iv	iv	X
ejpam-6811	143	29	)	)	PUNCT
ejpam-6811	143	30	if	if	SCONJ
ejpam-6811	143	31	db	db	PROPN
ejpam-6811	143	32	�	�	PROPN
ejpam-6811	143	33	d′b	d′b	PROPN
ejpam-6811	143	34	assume	assume	VERB
ejpam-6811	143	35	that	that	SCONJ
ejpam-6811	143	36	t	t	NOUN
ejpam-6811	143	37	:	:	PUNCT
ejpam-6811	143	38	(	(	PUNCT
ejpam-6811	143	39	x	x	NOUN
ejpam-6811	143	40	,	,	PUNCT
ejpam-6811	143	41	db	db	PROPN
ejpam-6811	143	42	)	)	PUNCT
ejpam-6811	143	43	→	→	SYM
ejpam-6811	143	44	(	(	PUNCT
ejpam-6811	143	45	x	x	NOUN
ejpam-6811	143	46	,	,	PUNCT
ejpam-6811	143	47	d′b	d′b	PROPN
ejpam-6811	143	48	)	)	PUNCT
ejpam-6811	143	49	is	be	AUX
ejpam-6811	143	50	s	s	NOUN
ejpam-6811	143	51	-	-	ADJ
ejpam-6811	143	52	cauchy	cauchy	ADJ
ejpam-6811	143	53	sequence	sequence	NOUN
ejpam-6811	143	54	on	on	ADP
ejpam-6811	143	55	x	x	ADP
ejpam-6811	143	56	;	;	PUNCT
ejpam-6811	143	57	(	(	PUNCT
ejpam-6811	143	58	v	v	NOUN
ejpam-6811	143	59	)	)	PUNCT
ejpam-6811	143	60	t	t	NOUN
ejpam-6811	143	61	:	:	PUNCT
ejpam-6811	143	62	(	(	PUNCT
ejpam-6811	143	63	x	x	NOUN
ejpam-6811	143	64	,	,	PUNCT
ejpam-6811	143	65	d′b	d′b	PROPN
ejpam-6811	143	66	)	)	PUNCT
ejpam-6811	143	67	→	→	SYM
ejpam-6811	143	68	(	(	PUNCT
ejpam-6811	143	69	x	x	NOUN
ejpam-6811	143	70	,	,	PUNCT
ejpam-6811	143	71	d′b	d′b	PROPN
ejpam-6811	143	72	)	)	PUNCT
ejpam-6811	143	73	is	be	AUX
ejpam-6811	143	74	ḡb	ḡb	NOUN
ejpam-6811	143	75	-	-	ADJ
ejpam-6811	143	76	continuous	continuous	ADJ
ejpam-6811	143	77	and	and	CCONJ
ejpam-6811	143	78	t	t	PROPN
ejpam-6811	143	79	,	,	PUNCT
ejpam-6811	143	80	s	s	VERB
ejpam-6811	143	81	are	be	AUX
ejpam-6811	143	82	d′b	d′b	NOUN
ejpam-6811	143	83	-	-	PUNCT
ejpam-6811	143	84	compatible	compatible	ADJ
ejpam-6811	143	85	,	,	PUNCT
ejpam-6811	143	86	then	then	ADV
ejpam-6811	143	87	v	v	X
ejpam-6811	143	88	(	(	PUNCT
ejpam-6811	143	89	t	t	PROPN
ejpam-6811	143	90	,	,	PUNCT
ejpam-6811	143	91	s	s	PROPN
ejpam-6811	143	92	)	)	PUNCT
ejpam-6811	143	93	6=	6=	ADP
ejpam-6811	143	94	⇔	⇔	PROPN
ejpam-6811	143	95	c(t	c(t	PROPN
ejpam-6811	143	96	,	,	PUNCT
ejpam-6811	143	97	s	s	NOUN
ejpam-6811	143	98	)	)	PUNCT
ejpam-6811	143	99	6=	6=	NUM
ejpam-6811	143	100	.	.	PUNCT
ejpam-6811	144	1	(	(	PUNCT
ejpam-6811	144	2	7	7	X
ejpam-6811	144	3	)	)	PUNCT
ejpam-6811	144	4	proof	proof	NOUN
ejpam-6811	144	5	.	.	PUNCT
ejpam-6811	145	1	if	if	SCONJ
ejpam-6811	145	2	c(t	c(t	PROPN
ejpam-6811	145	3	,	,	PUNCT
ejpam-6811	145	4	s	s	PROPN
ejpam-6811	145	5	)	)	PUNCT
ejpam-6811	145	6	6=	6=	PUNCT
ejpam-6811	145	7	then	then	ADV
ejpam-6811	145	8	let	let	VERB
ejpam-6811	145	9	x	x	X
ejpam-6811	145	10	∈	∈	PROPN
ejpam-6811	145	11	c(t	c(t	PROPN
ejpam-6811	145	12	,	,	PUNCT
ejpam-6811	145	13	s	s	NOUN
ejpam-6811	145	14	)	)	PUNCT
ejpam-6811	145	15	.	.	PUNCT
ejpam-6811	146	1	this	this	PRON
ejpam-6811	146	2	means	mean	VERB
ejpam-6811	146	3	tx	tx	PROPN
ejpam-6811	146	4	=	=	SYM
ejpam-6811	146	5	sx	sx	PROPN
ejpam-6811	146	6	.	.	PUNCT
ejpam-6811	147	1	then	then	ADV
ejpam-6811	147	2	(	(	PUNCT
ejpam-6811	147	3	tx	tx	PROPN
ejpam-6811	147	4	,	,	PUNCT
ejpam-6811	147	5	sx	sx	PROPN
ejpam-6811	147	6	)	)	PUNCT
ejpam-6811	147	7	=	=	SYM
ejpam-6811	147	8	(	(	PUNCT
ejpam-6811	147	9	sx	sx	PROPN
ejpam-6811	147	10	,	,	PUNCT
ejpam-6811	147	11	sx	sx	PROPN
ejpam-6811	147	12	)	)	PUNCT
ejpam-6811	147	13	∈	∈	PROPN
ejpam-6811	147	14	∆	∆	PROPN
ejpam-6811	147	15	⊂	⊂	X
ejpam-6811	147	16	e(ḡ	e(ḡ	PROPN
ejpam-6811	147	17	)	)	PUNCT
ejpam-6811	147	18	.	.	PUNCT
ejpam-6811	148	1	we	we	PRON
ejpam-6811	148	2	have	have	AUX
ejpam-6811	148	3	,	,	PUNCT
ejpam-6811	148	4	(	(	PUNCT
ejpam-6811	148	5	sx	sx	PROPN
ejpam-6811	148	6	,	,	PUNCT
ejpam-6811	148	7	sx	sx	PROPN
ejpam-6811	148	8	)	)	PUNCT
ejpam-6811	148	9	=	=	SYM
ejpam-6811	148	10	(	(	PUNCT
ejpam-6811	148	11	tx	tx	PROPN
ejpam-6811	148	12	,	,	PUNCT
ejpam-6811	148	13	sx	sx	PROPN
ejpam-6811	148	14	)	)	PUNCT
ejpam-6811	148	15	∈	∈	PROPN
ejpam-6811	148	16	e(ḡ	e(ḡ	NOUN
ejpam-6811	148	17	)	)	PUNCT
ejpam-6811	148	18	showing	show	VERB
ejpam-6811	148	19	that	that	SCONJ
ejpam-6811	148	20	x	x	X
ejpam-6811	148	21	∈	∈	NOUN
ejpam-6811	148	22	v	v	X
ejpam-6811	148	23	(	(	PUNCT
ejpam-6811	148	24	t	t	PROPN
ejpam-6811	148	25	,	,	PUNCT
ejpam-6811	148	26	s	s	PART
ejpam-6811	148	27	)	)	PUNCT
ejpam-6811	148	28	thus	thus	ADV
ejpam-6811	148	29	,	,	PUNCT
ejpam-6811	148	30	v	v	X
ejpam-6811	148	31	(	(	PUNCT
ejpam-6811	148	32	t	t	PROPN
ejpam-6811	148	33	,	,	PUNCT
ejpam-6811	148	34	s	s	PROPN
ejpam-6811	148	35	)	)	PUNCT
ejpam-6811	148	36	6=	6=	NUM
ejpam-6811	148	37	.	.	PUNCT
ejpam-6811	149	1	now	now	ADV
ejpam-6811	149	2	,	,	PUNCT
ejpam-6811	149	3	to	to	PART
ejpam-6811	149	4	verify	verify	VERB
ejpam-6811	149	5	other	other	ADJ
ejpam-6811	149	6	side	side	NOUN
ejpam-6811	149	7	,	,	PUNCT
ejpam-6811	149	8	suppose	suppose	VERB
ejpam-6811	149	9	that	that	SCONJ
ejpam-6811	149	10	v	v	X
ejpam-6811	149	11	(	(	PUNCT
ejpam-6811	149	12	t	t	PROPN
ejpam-6811	149	13	,	,	PUNCT
ejpam-6811	149	14	s	s	NOUN
ejpam-6811	149	15	)	)	PUNCT
ejpam-6811	149	16	6=	6=	NUM
ejpam-6811	149	17	and	and	CCONJ
ejpam-6811	149	18	x0	x0	PROPN
ejpam-6811	149	19	∈	∈	PROPN
ejpam-6811	149	20	x	x	PUNCT
ejpam-6811	149	21	with	with	ADP
ejpam-6811	149	22	(	(	PUNCT
ejpam-6811	149	23	sx0	sx0	PROPN
ejpam-6811	149	24	,	,	PUNCT
ejpam-6811	149	25	tx0	tx0	ADJ
ejpam-6811	149	26	)	)	PUNCT
ejpam-6811	149	27	∈	∈	PROPN
ejpam-6811	149	28	e(ḡ	e(ḡ	PROPN
ejpam-6811	149	29	)	)	PUNCT
ejpam-6811	149	30	.	.	PUNCT
ejpam-6811	150	1	now	now	ADV
ejpam-6811	150	2	,	,	PUNCT
ejpam-6811	150	3	as	as	ADP
ejpam-6811	150	4	(	(	PUNCT
ejpam-6811	150	5	2	2	X
ejpam-6811	150	6	)	)	PUNCT
ejpam-6811	150	7	holds	hold	VERB
ejpam-6811	150	8	then	then	ADV
ejpam-6811	150	9	we	we	PRON
ejpam-6811	150	10	can	can	AUX
ejpam-6811	150	11	construct	construct	VERB
ejpam-6811	150	12	a	a	DET
ejpam-6811	150	13	sequence	sequence	NOUN
ejpam-6811	150	14	xn	xn	SYM
ejpam-6811	150	15	∈	∈	PROPN
ejpam-6811	150	16	x	x	PUNCT
ejpam-6811	150	17	such	such	ADJ
ejpam-6811	150	18	that	that	DET
ejpam-6811	150	19	sxn	sxn	NOUN
ejpam-6811	150	20	=	=	PROPN
ejpam-6811	150	21	txn−1	txn−1	PROPN
ejpam-6811	150	22	for	for	ADP
ejpam-6811	150	23	all	all	PRON
ejpam-6811	150	24	n	n	PRON
ejpam-6811	150	25	∈	∈	PROPN
ejpam-6811	150	26	n.	n.	NOUN
ejpam-6811	150	27	note	note	VERB
ejpam-6811	150	28	that	that	SCONJ
ejpam-6811	150	29	if	if	SCONJ
ejpam-6811	150	30	sxn	sxn	NOUN
ejpam-6811	150	31	=	=	SYM
ejpam-6811	150	32	sxn−1	sxn−1	PROPN
ejpam-6811	150	33	for	for	ADP
ejpam-6811	150	34	some	some	DET
ejpam-6811	150	35	n	n	CCONJ
ejpam-6811	150	36	,	,	PUNCT
ejpam-6811	150	37	then	then	ADV
ejpam-6811	150	38	xn−1	xn−1	PROPN
ejpam-6811	150	39	∈	∈	PROPN
ejpam-6811	150	40	c(t	c(t	PROPN
ejpam-6811	150	41	,	,	PUNCT
ejpam-6811	150	42	s	s	NOUN
ejpam-6811	150	43	)	)	PUNCT
ejpam-6811	150	44	.	.	PUNCT
ejpam-6811	151	1	this	this	PRON
ejpam-6811	151	2	leads	lead	VERB
ejpam-6811	151	3	to	to	ADP
ejpam-6811	151	4	a	a	DET
ejpam-6811	151	5	trivial	trivial	ADJ
ejpam-6811	151	6	case	case	NOUN
ejpam-6811	151	7	so	so	ADV
ejpam-6811	151	8	suppose	suppose	VERB
ejpam-6811	151	9	that	that	SCONJ
ejpam-6811	151	10	sxn	sxn	NOUN
ejpam-6811	151	11	6=	6=	PUNCT
ejpam-6811	151	12	sxn−1	sxn−1	PROPN
ejpam-6811	151	13	for	for	ADP
ejpam-6811	151	14	every	every	DET
ejpam-6811	151	15	n	n	PRON
ejpam-6811	151	16	∈	∈	PROPN
ejpam-6811	151	17	n.	n.	NOUN
ejpam-6811	151	18	now	now	ADV
ejpam-6811	151	19	,	,	PUNCT
ejpam-6811	151	20	as	as	ADP
ejpam-6811	151	21	(	(	PUNCT
ejpam-6811	151	22	sx0	sx0	PROPN
ejpam-6811	151	23	,	,	PUNCT
ejpam-6811	151	24	tx0	tx0	NOUN
ejpam-6811	151	25	)	)	PUNCT
ejpam-6811	151	26	=	=	SYM
ejpam-6811	151	27	(	(	PUNCT
ejpam-6811	151	28	sx0	sx0	PROPN
ejpam-6811	151	29	,	,	PUNCT
ejpam-6811	151	30	sx1	sx1	NOUN
ejpam-6811	151	31	)	)	PUNCT
ejpam-6811	151	32	∈	∈	PROPN
ejpam-6811	151	33	e(ḡ	e(ḡ	NOUN
ejpam-6811	151	34	)	)	PUNCT
ejpam-6811	151	35	,	,	PUNCT
ejpam-6811	151	36	and	and	CCONJ
ejpam-6811	151	37	inductively	inductively	ADV
ejpam-6811	151	38	we	we	PRON
ejpam-6811	151	39	may	may	AUX
ejpam-6811	151	40	write	write	VERB
ejpam-6811	151	41	(	(	PUNCT
ejpam-6811	151	42	sxn−1	sxn−1	PROPN
ejpam-6811	151	43	,	,	PUNCT
ejpam-6811	151	44	sxn	sxn	NOUN
ejpam-6811	151	45	)	)	PUNCT
ejpam-6811	151	46	∈	∈	PROPN
ejpam-6811	151	47	e(ḡ	e(ḡ	PROPN
ejpam-6811	151	48	)	)	PUNCT
ejpam-6811	151	49	,	,	PUNCT
ejpam-6811	151	50	for	for	ADP
ejpam-6811	151	51	any	any	DET
ejpam-6811	151	52	n.	n.	NOUN
ejpam-6811	151	53	using	use	VERB
ejpam-6811	151	54	contraction	contraction	NOUN
ejpam-6811	151	55	conditions	condition	NOUN
ejpam-6811	151	56	,	,	PUNCT
ejpam-6811	151	57	φ(db(sxn+1	φ(db(sxn+1	NUM
ejpam-6811	151	58	,	,	PUNCT
ejpam-6811	151	59	sxn+2	sxn+2	NOUN
ejpam-6811	151	60	)	)	PUNCT
ejpam-6811	151	61	)	)	PUNCT
ejpam-6811	152	1	=	=	PUNCT
ejpam-6811	152	2	φ(db(txn	φ(db(txn	NOUN
ejpam-6811	152	3	,	,	PUNCT
ejpam-6811	152	4	txn+1	txn+1	NOUN
ejpam-6811	152	5	)	)	PUNCT
ejpam-6811	152	6	)	)	PUNCT
ejpam-6811	152	7	≤	≤	NUM
ejpam-6811	152	8	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	152	9	,	,	PUNCT
ejpam-6811	152	10	sxn+1))φ(δ(m(sxn	sxn+1))φ(δ(m(sxn	NOUN
ejpam-6811	152	11	,	,	PUNCT
ejpam-6811	152	12	sxn+1	sxn+1	NOUN
ejpam-6811	152	13	)	)	PUNCT
ejpam-6811	152	14	)	)	PUNCT
ejpam-6811	152	15	)	)	PUNCT
ejpam-6811	152	16	)	)	PUNCT
ejpam-6811	152	17	,	,	PUNCT
ejpam-6811	152	18	(	(	PUNCT
ejpam-6811	152	19	8)	8)	NUM
ejpam-6811	152	20	d.	d.	PROPN
ejpam-6811	152	21	e.	e.	PROPN
ejpam-6811	152	22	shehwar	shehwar	PROPN
ejpam-6811	152	23	sagheer	sagheer	PROPN
ejpam-6811	152	24	et	et	PROPN
ejpam-6811	152	25	al	al	PROPN
ejpam-6811	152	26	.	.	PUNCT
ejpam-6811	152	27	/	/	SYM
ejpam-6811	152	28	eur	eur	PROPN
ejpam-6811	152	29	.	.	PUNCT
ejpam-6811	153	1	j.	j.	PROPN
ejpam-6811	153	2	pure	pure	PROPN
ejpam-6811	153	3	appl	appl	PROPN
ejpam-6811	153	4	.	.	PROPN
ejpam-6811	153	5	math	math	PROPN
ejpam-6811	153	6	,	,	PUNCT
ejpam-6811	153	7	18	18	NUM
ejpam-6811	153	8	(	(	PUNCT
ejpam-6811	153	9	4	4	NUM
ejpam-6811	153	10	)	)	PUNCT
ejpam-6811	153	11	(	(	PUNCT
ejpam-6811	153	12	2025	2025	NUM
ejpam-6811	153	13	)	)	PUNCT
ejpam-6811	153	14	,	,	PUNCT
ejpam-6811	153	15	6811	6811	NUM
ejpam-6811	153	16	8	8	NUM
ejpam-6811	153	17	of	of	ADP
ejpam-6811	153	18	24	24	NUM
ejpam-6811	153	19	where	where	SCONJ
ejpam-6811	153	20	m(sxn	m(sxn	NOUN
ejpam-6811	153	21	,	,	PUNCT
ejpam-6811	153	22	sxn+1	sxn+1	NOUN
ejpam-6811	153	23	)	)	PUNCT
ejpam-6811	153	24	=	=	SYM
ejpam-6811	154	1	max	max	PROPN
ejpam-6811	154	2	{	{	PUNCT
ejpam-6811	154	3	db(sxn	db(sxn	PROPN
ejpam-6811	154	4	,	,	PUNCT
ejpam-6811	154	5	txn)db(txn+1	txn)db(txn+1	PROPN
ejpam-6811	154	6	,	,	PUNCT
ejpam-6811	154	7	sxn+1	sxn+1	NOUN
ejpam-6811	154	8	)	)	PUNCT
ejpam-6811	154	9	db(sxn	db(sxn	PROPN
ejpam-6811	154	10	,	,	PUNCT
ejpam-6811	154	11	sxn+1	sxn+1	NOUN
ejpam-6811	154	12	)	)	PUNCT
ejpam-6811	154	13	,	,	PUNCT
ejpam-6811	154	14	db(sxn	db(sxn	NOUN
ejpam-6811	154	15	,	,	PUNCT
ejpam-6811	154	16	sxn+1	sxn+1	PROPN
ejpam-6811	154	17	)	)	PUNCT
ejpam-6811	154	18	,	,	PUNCT
ejpam-6811	154	19	db(sxn	db(sxn	PROPN
ejpam-6811	154	20	,	,	PUNCT
ejpam-6811	154	21	txn	txn	NOUN
ejpam-6811	154	22	)	)	PUNCT
ejpam-6811	154	23	,	,	PUNCT
ejpam-6811	154	24	db(sxn+1	db(sxn+1	PROPN
ejpam-6811	154	25	,	,	PUNCT
ejpam-6811	154	26	txn+1	txn+1	NOUN
ejpam-6811	154	27	)	)	PUNCT
ejpam-6811	154	28	,	,	PUNCT
ejpam-6811	154	29	db(sxn	db(sxn	NOUN
ejpam-6811	154	30	,	,	PUNCT
ejpam-6811	154	31	txn+1	txn+1	NOUN
ejpam-6811	154	32	)	)	PUNCT
ejpam-6811	155	1	+	+	X
ejpam-6811	155	2	db(sxn+1	db(sxn+1	ADJ
ejpam-6811	155	3	,	,	PUNCT
ejpam-6811	155	4	txn	txn	NOUN
ejpam-6811	155	5	)	)	PUNCT
ejpam-6811	155	6	2b	2b	NOUN
ejpam-6811	155	7	}	}	PUNCT
ejpam-6811	155	8	.	.	PUNCT
ejpam-6811	156	1	=	=	SYM
ejpam-6811	156	2	max	max	PROPN
ejpam-6811	156	3	{	{	PUNCT
ejpam-6811	156	4	db(sxn	db(sxn	PROPN
ejpam-6811	156	5	,	,	PUNCT
ejpam-6811	156	6	sxn+1)db(sxn	sxn+1)db(sxn	NOUN
ejpam-6811	156	7	,	,	PUNCT
ejpam-6811	156	8	sxn+1	sxn+1	PROPN
ejpam-6811	156	9	)	)	PUNCT
ejpam-6811	156	10	,	,	PUNCT
ejpam-6811	156	11	db(sxn+1	db(sxn+1	PROPN
ejpam-6811	156	12	,	,	PUNCT
ejpam-6811	156	13	sxn+2	sxn+2	PROPN
ejpam-6811	156	14	)	)	PUNCT
ejpam-6811	156	15	,	,	PUNCT
ejpam-6811	156	16	db(sxn	db(sxn	PROPN
ejpam-6811	156	17	,	,	PUNCT
ejpam-6811	156	18	sxn+2	sxn+2	PRON
ejpam-6811	156	19	)	)	PUNCT
ejpam-6811	156	20	+	+	X
ejpam-6811	156	21	db(sxn+1	db(sxn+1	ADJ
ejpam-6811	156	22	,	,	PUNCT
ejpam-6811	156	23	sxn+1	sxn+1	X
ejpam-6811	156	24	)	)	PUNCT
ejpam-6811	156	25	2b	2b	NOUN
ejpam-6811	156	26	}	}	PUNCT
ejpam-6811	156	27	=	=	SYM
ejpam-6811	156	28	max	max	PROPN
ejpam-6811	156	29	{	{	PUNCT
ejpam-6811	156	30	db(sxn	db(sxn	PROPN
ejpam-6811	156	31	,	,	PUNCT
ejpam-6811	156	32	sxn+1	sxn+1	PROPN
ejpam-6811	156	33	)	)	PUNCT
ejpam-6811	156	34	,	,	PUNCT
ejpam-6811	156	35	db(sxn+1	db(sxn+1	PROPN
ejpam-6811	156	36	,	,	PUNCT
ejpam-6811	156	37	sxn+2	sxn+2	PROPN
ejpam-6811	156	38	)	)	PUNCT
ejpam-6811	156	39	,	,	PUNCT
ejpam-6811	156	40	db(sxn	db(sxn	PROPN
ejpam-6811	156	41	,	,	PUNCT
ejpam-6811	156	42	sxn+2	sxn+2	PART
ejpam-6811	156	43	)	)	PUNCT
ejpam-6811	156	44	2b	2b	NUM
ejpam-6811	156	45	}	}	PUNCT
ejpam-6811	156	46	≤	≤	ADJ
ejpam-6811	156	47	max{db(sxn	max{db(sxn	NOUN
ejpam-6811	156	48	,	,	PUNCT
ejpam-6811	156	49	sxn+1	sxn+1	NOUN
ejpam-6811	156	50	)	)	PUNCT
ejpam-6811	156	51	,	,	PUNCT
ejpam-6811	156	52	db(sxn+1	db(sxn+1	PROPN
ejpam-6811	156	53	,	,	PUNCT
ejpam-6811	156	54	sxn+2	sxn+2	PROPN
ejpam-6811	156	55	)	)	PUNCT
ejpam-6811	156	56	}	}	PUNCT
ejpam-6811	156	57	.	.	PUNCT
ejpam-6811	157	1	we	we	PRON
ejpam-6811	157	2	will	will	AUX
ejpam-6811	157	3	observe	observe	VERB
ejpam-6811	157	4	both	both	DET
ejpam-6811	157	5	possibilities	possibility	NOUN
ejpam-6811	157	6	separately	separately	ADV
ejpam-6811	157	7	,	,	PUNCT
ejpam-6811	157	8	if	if	SCONJ
ejpam-6811	157	9	m(sxn	m(sxn	NOUN
ejpam-6811	157	10	,	,	PUNCT
ejpam-6811	157	11	sxn+1	sxn+1	NOUN
ejpam-6811	157	12	)	)	PUNCT
ejpam-6811	157	13	=	=	SYM
ejpam-6811	158	1	db(sxn+1	db(sxn+1	X
ejpam-6811	158	2	,	,	PUNCT
ejpam-6811	158	3	sxn+2	sxn+2	PROPN
ejpam-6811	158	4	)	)	PUNCT
ejpam-6811	158	5	.	.	PUNCT
ejpam-6811	159	1	then	then	ADV
ejpam-6811	159	2	,	,	PUNCT
ejpam-6811	159	3	from	from	ADP
ejpam-6811	159	4	(	(	PUNCT
ejpam-6811	159	5	8)	8)	NUM
ejpam-6811	159	6	,	,	PUNCT
ejpam-6811	159	7	φ(db(sxn+1	φ(db(sxn+1	NUM
ejpam-6811	159	8	,	,	PUNCT
ejpam-6811	159	9	sxn+2	sxn+2	NOUN
ejpam-6811	159	10	)	)	PUNCT
ejpam-6811	159	11	)	)	PUNCT
ejpam-6811	159	12	≤	≤	NUM
ejpam-6811	159	13	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	159	14	,	,	PUNCT
ejpam-6811	159	15	sxn+1))φ(δ(db(sxn+1	sxn+1))φ(δ(db(sxn+1	NOUN
ejpam-6811	159	16	,	,	PUNCT
ejpam-6811	159	17	sxn+2	sxn+2	NOUN
ejpam-6811	159	18	)	)	PUNCT
ejpam-6811	159	19	)	)	PUNCT
ejpam-6811	159	20	)	)	PUNCT
ejpam-6811	159	21	≤	≤	NUM
ejpam-6811	159	22	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	159	23	,	,	PUNCT
ejpam-6811	159	24	sxn+1))φ(db(sxn+1	sxn+1))φ(db(sxn+1	PROPN
ejpam-6811	159	25	,	,	PUNCT
ejpam-6811	159	26	sxn+2	sxn+2	PROPN
ejpam-6811	159	27	)	)	PUNCT
ejpam-6811	159	28	)	)	PUNCT
ejpam-6811	159	29	≤	≤	PROPN
ejpam-6811	159	30	φ(db(sxn+1	φ(db(sxn+1	PROPN
ejpam-6811	159	31	,	,	PUNCT
ejpam-6811	159	32	sxn+2	sxn+2	NOUN
ejpam-6811	159	33	)	)	PUNCT
ejpam-6811	159	34	)	)	PUNCT
ejpam-6811	159	35	,	,	PUNCT
ejpam-6811	159	36	for	for	ADP
ejpam-6811	159	37	each	each	DET
ejpam-6811	159	38	n	n	PRON
ejpam-6811	159	39	≥	≥	NOUN
ejpam-6811	159	40	0	0	NUM
ejpam-6811	159	41	.	.	PUNCT
ejpam-6811	160	1	as	as	ADP
ejpam-6811	160	2	by	by	ADP
ejpam-6811	160	3	assumption	assumption	NOUN
ejpam-6811	160	4	sxn+1	sxn+1	NOUN
ejpam-6811	160	5	6=	6=	NUM
ejpam-6811	160	6	sxn+2	sxn+2	VERB
ejpam-6811	160	7	so	so	ADV
ejpam-6811	160	8	db(sxn+1	db(sxn+1	ADJ
ejpam-6811	160	9	,	,	PUNCT
ejpam-6811	160	10	sxn+2	sxn+2	PROPN
ejpam-6811	160	11	)	)	PUNCT
ejpam-6811	160	12	>	>	X
ejpam-6811	161	1	0	0	X
ejpam-6811	161	2	.	.	PUNCT
ejpam-6811	162	1	then	then	ADV
ejpam-6811	162	2	we	we	PRON
ejpam-6811	162	3	have	have	VERB
ejpam-6811	162	4	φ(db(sxn+1	φ(db(sxn+1	NUM
ejpam-6811	162	5	,	,	PUNCT
ejpam-6811	162	6	sxn+2	sxn+2	NOUN
ejpam-6811	162	7	)	)	PUNCT
ejpam-6811	162	8	)	)	PUNCT
ejpam-6811	163	1	>	>	X
ejpam-6811	163	2	0	0	X
ejpam-6811	163	3	.	.	X
ejpam-6811	164	1	showing	show	VERB
ejpam-6811	164	2	that	that	SCONJ
ejpam-6811	164	3	limn→∞	limn→∞	PROPN
ejpam-6811	164	4	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	164	5	,	,	PUNCT
ejpam-6811	164	6	sxn+1	sxn+1	NOUN
ejpam-6811	164	7	)	)	PUNCT
ejpam-6811	164	8	)	)	PUNCT
ejpam-6811	165	1	=	=	SYM
ejpam-6811	166	1	1	1	X
ejpam-6811	166	2	.	.	PUNCT
ejpam-6811	166	3	thus	thus	ADV
ejpam-6811	166	4	db(sxn	db(sxn	PROPN
ejpam-6811	166	5	,	,	PUNCT
ejpam-6811	166	6	sxn+1	sxn+1	NOUN
ejpam-6811	166	7	)	)	PUNCT
ejpam-6811	166	8	)	)	PUNCT
ejpam-6811	167	1	=	=	PUNCT
ejpam-6811	167	2	0	0	X
ejpam-6811	167	3	.	.	PUNCT
ejpam-6811	167	4	also	also	ADV
ejpam-6811	167	5	,	,	PUNCT
ejpam-6811	167	6	in	in	ADP
ejpam-6811	167	7	the	the	DET
ejpam-6811	167	8	same	same	ADJ
ejpam-6811	167	9	manner	manner	NOUN
ejpam-6811	167	10	we	we	PRON
ejpam-6811	167	11	get	get	VERB
ejpam-6811	167	12	φ(db(sxn+1	φ(db(sxn+1	NUM
ejpam-6811	167	13	,	,	PUNCT
ejpam-6811	167	14	sxn+2	sxn+2	NOUN
ejpam-6811	167	15	)	)	PUNCT
ejpam-6811	167	16	)	)	PUNCT
ejpam-6811	167	17	≤	≤	NUM
ejpam-6811	167	18	ψ(db(sxn	ψ(db(sxn	NOUN
ejpam-6811	167	19	,	,	PUNCT
ejpam-6811	167	20	sxn+1))φ(δ(db(sxn	sxn+1))φ(δ(db(sxn	NOUN
ejpam-6811	167	21	,	,	PUNCT
ejpam-6811	167	22	sxn+1	sxn+1	NOUN
ejpam-6811	167	23	)	)	PUNCT
ejpam-6811	167	24	)	)	PUNCT
ejpam-6811	167	25	)	)	PUNCT
ejpam-6811	167	26	≤	≤	NUM
ejpam-6811	167	27	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	167	28	,	,	PUNCT
ejpam-6811	167	29	sxn+1))φ(db(sxn	sxn+1))φ(db(sxn	PROPN
ejpam-6811	167	30	,	,	PUNCT
ejpam-6811	167	31	sxn+1	sxn+1	NOUN
ejpam-6811	167	32	)	)	PUNCT
ejpam-6811	167	33	)	)	PUNCT
ejpam-6811	167	34	,	,	PUNCT
ejpam-6811	167	35	(	(	PUNCT
ejpam-6811	167	36	9	9	X
ejpam-6811	167	37	)	)	PUNCT
ejpam-6811	167	38	showing	show	VERB
ejpam-6811	167	39	that	that	DET
ejpam-6811	167	40	db(sxn	db(sxn	NOUN
ejpam-6811	167	41	,	,	PUNCT
ejpam-6811	167	42	sxn+1	sxn+1	PROPN
ejpam-6811	167	43	)	)	PUNCT
ejpam-6811	167	44	is	be	AUX
ejpam-6811	167	45	a	a	DET
ejpam-6811	167	46	non	non	ADJ
ejpam-6811	167	47	-	-	ADJ
ejpam-6811	167	48	increasing	increasing	ADJ
ejpam-6811	167	49	sequence	sequence	NOUN
ejpam-6811	167	50	.	.	PUNCT
ejpam-6811	168	1	also	also	ADV
ejpam-6811	168	2	,	,	PUNCT
ejpam-6811	168	3	by	by	ADP
ejpam-6811	168	4	using	use	VERB
ejpam-6811	168	5	properties	property	NOUN
ejpam-6811	168	6	of	of	ADP
ejpam-6811	168	7	φ	φ	NUM
ejpam-6811	168	8	,	,	PUNCT
ejpam-6811	168	9	we	we	PRON
ejpam-6811	168	10	observe	observe	VERB
ejpam-6811	168	11	that	that	SCONJ
ejpam-6811	168	12	φ(db(sxn	φ(db(sxn	NOUN
ejpam-6811	168	13	,	,	PUNCT
ejpam-6811	168	14	sxn+1	sxn+1	NOUN
ejpam-6811	168	15	)	)	PUNCT
ejpam-6811	168	16	)	)	PUNCT
ejpam-6811	168	17	is	be	AUX
ejpam-6811	168	18	a	a	DET
ejpam-6811	168	19	non	non	ADJ
ejpam-6811	168	20	-	-	ADJ
ejpam-6811	168	21	increasing	increase	VERB
ejpam-6811	168	22	sequence	sequence	NOUN
ejpam-6811	168	23	and	and	CCONJ
ejpam-6811	168	24	it	it	PRON
ejpam-6811	168	25	is	be	AUX
ejpam-6811	168	26	also	also	ADV
ejpam-6811	168	27	bounded	bound	VERB
ejpam-6811	168	28	below	below	ADV
ejpam-6811	168	29	so	so	SCONJ
ejpam-6811	168	30	that	that	SCONJ
ejpam-6811	168	31	it	it	PRON
ejpam-6811	168	32	would	would	AUX
ejpam-6811	168	33	be	be	AUX
ejpam-6811	168	34	a	a	DET
ejpam-6811	168	35	convergent	convergent	NOUN
ejpam-6811	168	36	sequence	sequence	NOUN
ejpam-6811	168	37	.	.	PUNCT
ejpam-6811	169	1	eventually	eventually	ADV
ejpam-6811	169	2	,	,	PUNCT
ejpam-6811	169	3	there	there	PRON
ejpam-6811	169	4	exists	exist	VERB
ejpam-6811	169	5	c	c	PROPN
ejpam-6811	169	6	≥	≥	NUM
ejpam-6811	169	7	0	0	NUM
ejpam-6811	169	8	such	such	ADJ
ejpam-6811	169	9	that	that	PRON
ejpam-6811	169	10	(	(	PUNCT
ejpam-6811	169	11	db(sxn	db(sxn	NOUN
ejpam-6811	169	12	,	,	PUNCT
ejpam-6811	169	13	sxn+1	sxn+1	NOUN
ejpam-6811	169	14	)	)	PUNCT
ejpam-6811	169	15	)	)	PUNCT
ejpam-6811	170	1	=	=	SYM
ejpam-6811	170	2	c.	c.	PROPN
ejpam-6811	170	3	now	now	ADV
ejpam-6811	170	4	,	,	PUNCT
ejpam-6811	170	5	suppose	suppose	VERB
ejpam-6811	170	6	on	on	ADP
ejpam-6811	170	7	contrary	contrary	ADV
ejpam-6811	170	8	that	that	SCONJ
ejpam-6811	170	9	lim	lim	PROPN
ejpam-6811	170	10	n→∞	n→∞	NUM
ejpam-6811	170	11	db(sxn	db(sxn	PROPN
ejpam-6811	170	12	,	,	PUNCT
ejpam-6811	170	13	sxn+1	sxn+1	PROPN
ejpam-6811	170	14	)	)	PUNCT
ejpam-6811	170	15	>	>	X
ejpam-6811	171	1	0	0	X
ejpam-6811	171	2	.	.	PUNCT
ejpam-6811	172	1	also	also	ADV
ejpam-6811	172	2	,	,	PUNCT
ejpam-6811	172	3	lim	lim	PROPN
ejpam-6811	172	4	n→∞	n→∞	X
ejpam-6811	172	5	φ(db(sxn	φ(db(sxn	PROPN
ejpam-6811	172	6	,	,	PUNCT
ejpam-6811	172	7	sxn+1	sxn+1	NOUN
ejpam-6811	172	8	)	)	PUNCT
ejpam-6811	172	9	)	)	PUNCT
ejpam-6811	172	10	>	>	X
ejpam-6811	172	11	0	0	NUM
ejpam-6811	172	12	,	,	PUNCT
ejpam-6811	172	13	then	then	ADV
ejpam-6811	172	14	form	form	NOUN
ejpam-6811	172	15	(	(	PUNCT
ejpam-6811	172	16	9	9	NUM
ejpam-6811	172	17	)	)	PUNCT
ejpam-6811	172	18	,	,	PUNCT
ejpam-6811	172	19	we	we	PRON
ejpam-6811	172	20	have	have	VERB
ejpam-6811	172	21	1	1	NUM
ejpam-6811	172	22	=	=	SYM
ejpam-6811	172	23	lim	lim	PROPN
ejpam-6811	172	24	n→∞	n→∞	X
ejpam-6811	172	25	φ(db(sxn+1	φ(db(sxn+1	PROPN
ejpam-6811	172	26	,	,	PUNCT
ejpam-6811	172	27	sxn+2	sxn+2	NOUN
ejpam-6811	172	28	)	)	PUNCT
ejpam-6811	172	29	)	)	PUNCT
ejpam-6811	173	1	φ(db(sxn	φ(db(sxn	NOUN
ejpam-6811	173	2	,	,	PUNCT
ejpam-6811	173	3	sxn+1	sxn+1	NOUN
ejpam-6811	173	4	)	)	PUNCT
ejpam-6811	173	5	)	)	PUNCT
ejpam-6811	174	1	≤	≤	PROPN
ejpam-6811	174	2	lim	lim	PROPN
ejpam-6811	174	3	n→∞	n→∞	NUM
ejpam-6811	174	4	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	174	5	,	,	PUNCT
ejpam-6811	174	6	sxn+1	sxn+1	NOUN
ejpam-6811	174	7	)	)	PUNCT
ejpam-6811	174	8	)	)	PUNCT
ejpam-6811	174	9	≤	≤	NUM
ejpam-6811	174	10	1	1	NUM
ejpam-6811	174	11	.	.	PUNCT
ejpam-6811	175	1	therefore	therefore	ADV
ejpam-6811	175	2	,	,	PUNCT
ejpam-6811	175	3	lim	lim	PROPN
ejpam-6811	175	4	n→∞	n→∞	NUM
ejpam-6811	175	5	ψ(db(sxn	ψ(db(sxn	NUM
ejpam-6811	175	6	,	,	PUNCT
ejpam-6811	175	7	sxn+1	sxn+1	NOUN
ejpam-6811	175	8	)	)	PUNCT
ejpam-6811	175	9	)	)	PUNCT
ejpam-6811	175	10	=	=	SYM
ejpam-6811	175	11	1	1	NUM
ejpam-6811	175	12	producing	produce	VERB
ejpam-6811	175	13	lim	lim	PROPN
ejpam-6811	175	14	n→∞	n→∞	NUM
ejpam-6811	175	15	db(sxn	db(sxn	PROPN
ejpam-6811	175	16	,	,	PUNCT
ejpam-6811	175	17	sxn+1	sxn+1	X
ejpam-6811	175	18	)	)	PUNCT
ejpam-6811	175	19	=	=	SYM
ejpam-6811	175	20	0	0	NUM
ejpam-6811	175	21	,	,	PUNCT
ejpam-6811	175	22	i.e.	i.e.	X
ejpam-6811	175	23	,	,	PUNCT
ejpam-6811	175	24	c	c	NOUN
ejpam-6811	175	25	=	=	SYM
ejpam-6811	175	26	0	0	PROPN
ejpam-6811	175	27	,	,	PUNCT
ejpam-6811	175	28	which	which	PRON
ejpam-6811	175	29	is	be	AUX
ejpam-6811	175	30	a	a	DET
ejpam-6811	175	31	contradiction	contradiction	NOUN
ejpam-6811	175	32	.	.	PUNCT
ejpam-6811	176	1	so	so	ADV
ejpam-6811	176	2	we	we	PRON
ejpam-6811	176	3	get	get	VERB
ejpam-6811	176	4	lim	lim	PROPN
ejpam-6811	176	5	n→∞	n→∞	NUM
ejpam-6811	176	6	db(sxn	db(sxn	PROPN
ejpam-6811	176	7	,	,	PUNCT
ejpam-6811	176	8	sxn+1	sxn+1	X
ejpam-6811	176	9	)	)	PUNCT
ejpam-6811	176	10	=	=	SYM
ejpam-6811	177	1	0	0	X
ejpam-6811	177	2	.	.	PUNCT
ejpam-6811	177	3	d.	d.	PROPN
ejpam-6811	177	4	e.	e.	PROPN
ejpam-6811	177	5	shehwar	shehwar	PROPN
ejpam-6811	177	6	sagheer	sagheer	PROPN
ejpam-6811	177	7	et	et	PROPN
ejpam-6811	177	8	al	al	PROPN
ejpam-6811	177	9	.	.	PUNCT
ejpam-6811	177	10	/	/	SYM
ejpam-6811	177	11	eur	eur	PROPN
ejpam-6811	177	12	.	.	PUNCT
ejpam-6811	178	1	j.	j.	PROPN
ejpam-6811	178	2	pure	pure	PROPN
ejpam-6811	178	3	appl	appl	PROPN
ejpam-6811	178	4	.	.	PROPN
ejpam-6811	178	5	math	math	PROPN
ejpam-6811	178	6	,	,	PUNCT
ejpam-6811	178	7	18	18	NUM
ejpam-6811	178	8	(	(	PUNCT
ejpam-6811	178	9	4	4	NUM
ejpam-6811	178	10	)	)	PUNCT
ejpam-6811	178	11	(	(	PUNCT
ejpam-6811	178	12	2025	2025	NUM
ejpam-6811	178	13	)	)	PUNCT
ejpam-6811	178	14	,	,	PUNCT
ejpam-6811	178	15	6811	6811	NUM
ejpam-6811	178	16	9	9	NUM
ejpam-6811	178	17	of	of	ADP
ejpam-6811	178	18	24	24	NUM
ejpam-6811	178	19	lemma	lemma	PROPN
ejpam-6811	178	20	(	(	PUNCT
ejpam-6811	178	21	2	2	NUM
ejpam-6811	178	22	)	)	PUNCT
ejpam-6811	178	23	shows	show	VERB
ejpam-6811	178	24	that	that	SCONJ
ejpam-6811	178	25	{	{	PUNCT
ejpam-6811	178	26	sxn	sxn	NOUN
ejpam-6811	178	27	}	}	PUNCT
ejpam-6811	178	28	is	be	AUX
ejpam-6811	178	29	a	a	DET
ejpam-6811	178	30	cauchy	cauchy	ADJ
ejpam-6811	178	31	sequence	sequence	NOUN
ejpam-6811	178	32	in	in	ADP
ejpam-6811	178	33	(	(	PUNCT
ejpam-6811	178	34	x	x	NOUN
ejpam-6811	178	35	,	,	PUNCT
ejpam-6811	178	36	db	db	PROPN
ejpam-6811	178	37	)	)	PUNCT
ejpam-6811	178	38	.	.	PUNCT
ejpam-6811	179	1	finally	finally	ADV
ejpam-6811	179	2	,	,	PUNCT
ejpam-6811	179	3	to	to	PART
ejpam-6811	179	4	show	show	VERB
ejpam-6811	179	5	that	that	SCONJ
ejpam-6811	179	6	{	{	PUNCT
ejpam-6811	179	7	sxn	sxn	NOUN
ejpam-6811	179	8	}	}	PUNCT
ejpam-6811	179	9	is	be	AUX
ejpam-6811	179	10	a	a	DET
ejpam-6811	179	11	cauchy	cauchy	ADJ
ejpam-6811	179	12	sequence	sequence	NOUN
ejpam-6811	179	13	in	in	ADP
ejpam-6811	179	14	(	(	PUNCT
ejpam-6811	179	15	x	x	NOUN
ejpam-6811	179	16	,	,	PUNCT
ejpam-6811	179	17	d′b	d′b	PROPN
ejpam-6811	179	18	)	)	PUNCT
ejpam-6811	179	19	too	too	ADV
ejpam-6811	179	20	.	.	PUNCT
ejpam-6811	180	1	notice	notice	VERB
ejpam-6811	180	2	that	that	SCONJ
ejpam-6811	180	3	if	if	SCONJ
ejpam-6811	180	4	db	db	PROPN
ejpam-6811	180	5	≥	≥	NOUN
ejpam-6811	180	6	d′b	d′b	PROPN
ejpam-6811	180	7	,	,	PUNCT
ejpam-6811	180	8	proof	proof	NOUN
ejpam-6811	180	9	is	be	AUX
ejpam-6811	180	10	trivial	trivial	ADJ
ejpam-6811	180	11	.	.	PUNCT
ejpam-6811	181	1	so	so	ADV
ejpam-6811	181	2	take	take	VERB
ejpam-6811	181	3	db	db	PROPN
ejpam-6811	181	4	�	�	PROPN
ejpam-6811	181	5	d′b	d′b	PROPN
ejpam-6811	181	6	.	.	PUNCT
ejpam-6811	182	1	now	now	ADV
ejpam-6811	182	2	,	,	PUNCT
ejpam-6811	182	3	as	as	SCONJ
ejpam-6811	182	4	{	{	PUNCT
ejpam-6811	182	5	sxn	sxn	NOUN
ejpam-6811	182	6	}	}	PUNCT
ejpam-6811	182	7	is	be	AUX
ejpam-6811	182	8	a	a	DET
ejpam-6811	182	9	cauchy	cauchy	ADJ
ejpam-6811	182	10	sequence	sequence	NOUN
ejpam-6811	182	11	in	in	ADP
ejpam-6811	182	12	(	(	PUNCT
ejpam-6811	182	13	x	x	NOUN
ejpam-6811	182	14	,	,	PUNCT
ejpam-6811	182	15	db	db	PROPN
ejpam-6811	182	16	)	)	PUNCT
ejpam-6811	182	17	and	and	CCONJ
ejpam-6811	182	18	t	t	PROPN
ejpam-6811	182	19	is	be	AUX
ejpam-6811	182	20	s	s	NOUN
ejpam-6811	182	21	-	-	NOUN
ejpam-6811	182	22	cauchy	cauchy	ADJ
ejpam-6811	182	23	on	on	ADP
ejpam-6811	182	24	x	x	VERB
ejpam-6811	182	25	so	so	ADV
ejpam-6811	182	26	have	have	AUX
ejpam-6811	182	27	{	{	PUNCT
ejpam-6811	182	28	txn	txn	NOUN
ejpam-6811	182	29	}	}	PUNCT
ejpam-6811	182	30	is	be	AUX
ejpam-6811	182	31	a	a	DET
ejpam-6811	182	32	cauchy	cauchy	ADJ
ejpam-6811	182	33	sequence	sequence	NOUN
ejpam-6811	182	34	in	in	ADP
ejpam-6811	182	35	(	(	PUNCT
ejpam-6811	182	36	x	x	NOUN
ejpam-6811	182	37	,	,	PUNCT
ejpam-6811	182	38	d′b	d′b	PROPN
ejpam-6811	182	39	)	)	PUNCT
ejpam-6811	182	40	.	.	PUNCT
ejpam-6811	183	1	this	this	PRON
ejpam-6811	183	2	means	mean	VERB
ejpam-6811	183	3	their	their	PRON
ejpam-6811	183	4	exists	exist	NOUN
ejpam-6811	183	5	n0	n0	PROPN
ejpam-6811	183	6	∈	∈	PROPN
ejpam-6811	183	7	n	n	CCONJ
ejpam-6811	183	8	such	such	ADJ
ejpam-6811	183	9	that	that	DET
ejpam-6811	183	10	d′b(sxn+1	d′b(sxn+1	PROPN
ejpam-6811	183	11	,	,	PUNCT
ejpam-6811	183	12	sxm+1	sxm+1	NOUN
ejpam-6811	183	13	)	)	PUNCT
ejpam-6811	183	14	=	=	SYM
ejpam-6811	183	15	d′b(txn	d′b(txn	PROPN
ejpam-6811	183	16	,	,	PUNCT
ejpam-6811	183	17	txm	txm	PROPN
ejpam-6811	183	18	)	)	PUNCT
ejpam-6811	183	19	<	<	X
ejpam-6811	183	20	ε	ε	PROPN
ejpam-6811	183	21	∀m	∀m	PROPN
ejpam-6811	183	22	,	,	PUNCT
ejpam-6811	183	23	n	n	PRON
ejpam-6811	183	24	≥	≥	NOUN
ejpam-6811	183	25	n0	n0	NUM
ejpam-6811	183	26	.	.	PUNCT
ejpam-6811	184	1	showing	show	VERB
ejpam-6811	184	2	that	that	SCONJ
ejpam-6811	184	3	{	{	PUNCT
ejpam-6811	184	4	sxn	sxn	NOUN
ejpam-6811	184	5	}	}	PUNCT
ejpam-6811	184	6	is	be	AUX
ejpam-6811	184	7	a	a	DET
ejpam-6811	184	8	cauchy	cauchy	ADJ
ejpam-6811	184	9	sequence	sequence	NOUN
ejpam-6811	184	10	in	in	ADP
ejpam-6811	184	11	(	(	PUNCT
ejpam-6811	184	12	x	x	NOUN
ejpam-6811	184	13	,	,	PUNCT
ejpam-6811	184	14	d′b	d′b	PROPN
ejpam-6811	184	15	)	)	PUNCT
ejpam-6811	184	16	.	.	PUNCT
ejpam-6811	185	1	now	now	ADV
ejpam-6811	185	2	as	as	ADP
ejpam-6811	185	3	s(x	s(x	PROPN
ejpam-6811	185	4	)	)	PUNCT
ejpam-6811	185	5	is	be	AUX
ejpam-6811	185	6	closed	close	VERB
ejpam-6811	185	7	with	with	ADP
ejpam-6811	185	8	respect	respect	NOUN
ejpam-6811	185	9	to	to	ADP
ejpam-6811	185	10	d′b	d′b	PROPN
ejpam-6811	185	11	,	,	PUNCT
ejpam-6811	185	12	and	and	CCONJ
ejpam-6811	185	13	(	(	PUNCT
ejpam-6811	185	14	x	x	NOUN
ejpam-6811	185	15	,	,	PUNCT
ejpam-6811	185	16	d′b	d′b	PROPN
ejpam-6811	185	17	)	)	PUNCT
ejpam-6811	185	18	is	be	AUX
ejpam-6811	185	19	complete	complete	ADJ
ejpam-6811	185	20	,	,	PUNCT
ejpam-6811	185	21	so	so	SCONJ
ejpam-6811	185	22	there	there	PRON
ejpam-6811	185	23	exists	exist	VERB
ejpam-6811	185	24	x∗	x∗	PROPN
ejpam-6811	185	25	∈	∈	PROPN
ejpam-6811	185	26	s(x	s(x	PROPN
ejpam-6811	185	27	)	)	PUNCT
ejpam-6811	186	1	such	such	ADJ
ejpam-6811	186	2	that	that	SCONJ
ejpam-6811	186	3	lim	lim	PROPN
ejpam-6811	186	4	n→∞	n→∞	NUM
ejpam-6811	186	5	sxn	sxn	NOUN
ejpam-6811	187	1	=	=	PROPN
ejpam-6811	188	1	lim	lim	PROPN
ejpam-6811	188	2	n→∞	n→∞	X
ejpam-6811	189	1	txn	txn	NOUN
ejpam-6811	189	2	=	=	PUNCT
ejpam-6811	189	3	x∗.	x∗.	PROPN
ejpam-6811	189	4	(	(	PUNCT
ejpam-6811	189	5	10	10	NUM
ejpam-6811	189	6	)	)	PUNCT
ejpam-6811	189	7	also	also	ADV
ejpam-6811	189	8	,	,	PUNCT
ejpam-6811	189	9	t	t	PROPN
ejpam-6811	189	10	is	be	AUX
ejpam-6811	189	11	ǧb	ǧb	NOUN
ejpam-6811	189	12	-	-	PUNCT
ejpam-6811	189	13	continuous	continuous	ADJ
ejpam-6811	189	14	together	together	ADV
ejpam-6811	189	15	with	with	ADP
ejpam-6811	189	16	d′b	d′b	NOUN
ejpam-6811	189	17	-	-	PUNCT
ejpam-6811	189	18	compatibility	compatibility	NOUN
ejpam-6811	189	19	of	of	ADP
ejpam-6811	189	20	t	t	PROPN
ejpam-6811	189	21	and	and	CCONJ
ejpam-6811	189	22	s.	s.	PROPN
ejpam-6811	189	23	hence	hence	ADV
ejpam-6811	189	24	,	,	PUNCT
ejpam-6811	189	25	we	we	PRON
ejpam-6811	189	26	conclude	conclude	VERB
ejpam-6811	189	27	lim	lim	PROPN
ejpam-6811	189	28	n→∞	n→∞	NUM
ejpam-6811	189	29	d′b(tsxn	d′b(tsxn	PROPN
ejpam-6811	189	30	,	,	PUNCT
ejpam-6811	189	31	stxn	stxn	NOUN
ejpam-6811	189	32	)	)	PUNCT
ejpam-6811	189	33	=	=	SYM
ejpam-6811	190	1	0	0	X
ejpam-6811	190	2	.	.	PUNCT
ejpam-6811	191	1	(	(	PUNCT
ejpam-6811	191	2	11	11	NUM
ejpam-6811	191	3	)	)	PUNCT
ejpam-6811	191	4	now	now	ADV
ejpam-6811	191	5	,	,	PUNCT
ejpam-6811	191	6	consider	consider	VERB
ejpam-6811	191	7	d′b(sx	d′b(sx	NOUN
ejpam-6811	191	8	∗	∗	NOUN
ejpam-6811	191	9	,	,	PUNCT
ejpam-6811	191	10	tx∗	tx∗	NOUN
ejpam-6811	191	11	)	)	PUNCT
ejpam-6811	191	12	≤	≤	NUM
ejpam-6811	191	13	b{d′b(sx∗	b{d′b(sx∗	NOUN
ejpam-6811	191	14	,	,	PUNCT
ejpam-6811	191	15	stxn	stxn	NOUN
ejpam-6811	191	16	)	)	PUNCT
ejpam-6811	191	17	+	+	CCONJ
ejpam-6811	192	1	d′b(stxn	d′b(stxn	NOUN
ejpam-6811	192	2	,	,	PUNCT
ejpam-6811	192	3	tx	tx	PROPN
ejpam-6811	192	4	∗	∗	NOUN
ejpam-6811	192	5	)	)	PUNCT
ejpam-6811	192	6	}	}	PUNCT
ejpam-6811	192	7	≤	≤	NUM
ejpam-6811	192	8	bd′b(sx	bd′b(sx	PROPN
ejpam-6811	192	9	∗	∗	NOUN
ejpam-6811	192	10	,	,	PUNCT
ejpam-6811	192	11	stxn	stxn	NOUN
ejpam-6811	192	12	)	)	PUNCT
ejpam-6811	192	13	+	+	SYM
ejpam-6811	192	14	b2{d′b(stxn	b2{d′b(stxn	ADJ
ejpam-6811	192	15	,	,	PUNCT
ejpam-6811	192	16	tsxn	tsxn	NOUN
ejpam-6811	192	17	)	)	PUNCT
ejpam-6811	192	18	+	+	NUM
ejpam-6811	192	19	d′b(tsxn	d′b(tsxn	NOUN
ejpam-6811	192	20	,	,	PUNCT
ejpam-6811	192	21	tx	tx	PROPN
ejpam-6811	192	22	∗	∗	NOUN
ejpam-6811	192	23	)	)	PUNCT
ejpam-6811	192	24	}	}	PUNCT
ejpam-6811	192	25	.	.	PUNCT
ejpam-6811	193	1	taking	take	VERB
ejpam-6811	193	2	n→	n→	ADV
ejpam-6811	193	3	∞	∞	PROPN
ejpam-6811	193	4	and	and	CCONJ
ejpam-6811	193	5	by	by	ADP
ejpam-6811	193	6	(	(	PUNCT
ejpam-6811	193	7	10	10	NUM
ejpam-6811	193	8	)	)	PUNCT
ejpam-6811	193	9	,	,	PUNCT
ejpam-6811	193	10	we	we	PRON
ejpam-6811	193	11	get	get	VERB
ejpam-6811	193	12	d′b(sx	d′b(sx	NOUN
ejpam-6811	193	13	∗	∗	NOUN
ejpam-6811	193	14	,	,	PUNCT
ejpam-6811	193	15	tx∗	tx∗	NOUN
ejpam-6811	193	16	)	)	PUNCT
ejpam-6811	194	1	=	=	PUNCT
ejpam-6811	194	2	0	0	X
ejpam-6811	194	3	.	.	X
ejpam-6811	194	4	showing	show	VERB
ejpam-6811	194	5	that	that	SCONJ
ejpam-6811	194	6	sx∗	sx∗	PROPN
ejpam-6811	194	7	=	=	SYM
ejpam-6811	194	8	tx∗	tx∗	PROPN
ejpam-6811	194	9	,	,	PUNCT
ejpam-6811	194	10	thus	thus	ADV
ejpam-6811	194	11	x∗	x∗	PROPN
ejpam-6811	194	12	∈	∈	PROPN
ejpam-6811	194	13	c(t	c(t	PROPN
ejpam-6811	194	14	,	,	PUNCT
ejpam-6811	194	15	s	s	PART
ejpam-6811	194	16	)	)	PUNCT
ejpam-6811	194	17	⇒	⇒	PROPN
ejpam-6811	194	18	c(t	c(t	PROPN
ejpam-6811	194	19	,	,	PUNCT
ejpam-6811	194	20	s	s	PROPN
ejpam-6811	194	21	)	)	PUNCT
ejpam-6811	194	22	6=	6=	PUNCT
ejpam-6811	194	23	.	.	PUNCT
ejpam-6811	195	1	theorem	theorem	NOUN
ejpam-6811	195	2	2	2	NUM
ejpam-6811	195	3	.	.	X
ejpam-6811	196	1	let	let	VERB
ejpam-6811	196	2	(	(	PUNCT
ejpam-6811	196	3	x	x	NOUN
ejpam-6811	196	4	,	,	PUNCT
ejpam-6811	196	5	db	db	PROPN
ejpam-6811	196	6	)	)	PUNCT
ejpam-6811	196	7	be	be	AUX
ejpam-6811	196	8	a	a	DET
ejpam-6811	196	9	complete	complete	ADJ
ejpam-6811	196	10	bms	bms	NOUN
ejpam-6811	196	11	equipped	equip	VERB
ejpam-6811	196	12	with	with	ADP
ejpam-6811	196	13	a	a	DET
ejpam-6811	196	14	dg	dg	NOUN
ejpam-6811	196	15	and	and	CCONJ
ejpam-6811	196	16	a	a	DET
ejpam-6811	196	17	continuous	continuous	ADJ
ejpam-6811	196	18	metric	metric	ADJ
ejpam-6811	196	19	db	db	NOUN
ejpam-6811	196	20	,	,	PUNCT
ejpam-6811	196	21	let	let	VERB
ejpam-6811	196	22	d′b	d′b	PRON
ejpam-6811	196	23	be	be	AUX
ejpam-6811	196	24	another	another	DET
ejpam-6811	196	25	continuous	continuous	ADJ
ejpam-6811	196	26	metric	metric	NOUN
ejpam-6811	196	27	.	.	PUNCT
ejpam-6811	197	1	define	define	VERB
ejpam-6811	197	2	two	two	NUM
ejpam-6811	197	3	functions	function	NOUN
ejpam-6811	197	4	t	t	PROPN
ejpam-6811	197	5	,	,	PUNCT
ejpam-6811	197	6	s	s	PART
ejpam-6811	197	7	:	:	PUNCT
ejpam-6811	197	8	x	x	SYM
ejpam-6811	197	9	→	→	SYM
ejpam-6811	197	10	x	x	SYM
ejpam-6811	197	11	where	where	SCONJ
ejpam-6811	197	12	(	(	PUNCT
ejpam-6811	197	13	t	t	PROPN
ejpam-6811	197	14	,	,	PUNCT
ejpam-6811	197	15	s	s	PART
ejpam-6811	197	16	)	)	PUNCT
ejpam-6811	197	17	satisfies	satisfie	NOUN
ejpam-6811	197	18	ψ	ψ	X
ejpam-6811	197	19	−	−	PROPN
ejpam-6811	197	20	φ	φ	NUM
ejpam-6811	197	21	-	-	NOUN
ejpam-6811	197	22	contraction	contraction	NOUN
ejpam-6811	197	23	with	with	ADP
ejpam-6811	197	24	respect	respect	NOUN
ejpam-6811	197	25	to	to	ADP
ejpam-6811	197	26	db	db	PROPN
ejpam-6811	198	1	and	and	CCONJ
ejpam-6811	198	2	we	we	PRON
ejpam-6811	198	3	have	have	AUX
ejpam-6811	198	4	,	,	PUNCT
ejpam-6811	198	5	(	(	PUNCT
ejpam-6811	198	6	1	1	X
ejpam-6811	198	7	)	)	PUNCT
ejpam-6811	198	8	s	s	VERB
ejpam-6811	198	9	is	be	AUX
ejpam-6811	198	10	a	a	DET
ejpam-6811	198	11	continuous	continuous	ADJ
ejpam-6811	198	12	mapping	mapping	NOUN
ejpam-6811	198	13	and	and	CCONJ
ejpam-6811	198	14	s(x	s(x	NOUN
ejpam-6811	198	15	)	)	PUNCT
ejpam-6811	198	16	is	be	AUX
ejpam-6811	198	17	closed	close	VERB
ejpam-6811	198	18	;	;	PUNCT
ejpam-6811	198	19	(	(	PUNCT
ejpam-6811	198	20	2	2	X
ejpam-6811	198	21	)	)	PUNCT
ejpam-6811	198	22	t	t	NOUN
ejpam-6811	198	23	(	(	PUNCT
ejpam-6811	198	24	x	x	NOUN
ejpam-6811	198	25	)	)	PUNCT
ejpam-6811	198	26	⊆	⊆	NUM
ejpam-6811	198	27	s(x	s(x	NOUN
ejpam-6811	198	28	)	)	PUNCT
ejpam-6811	198	29	;	;	PUNCT
ejpam-6811	198	30	(	(	PUNCT
ejpam-6811	198	31	3	3	X
ejpam-6811	198	32	)	)	PUNCT
ejpam-6811	198	33	e(ḡ	e(ḡ	PROPN
ejpam-6811	198	34	)	)	PUNCT
ejpam-6811	198	35	is	be	AUX
ejpam-6811	198	36	a	a	DET
ejpam-6811	198	37	transitive	transitive	ADJ
ejpam-6811	198	38	set	set	NOUN
ejpam-6811	198	39	;	;	PUNCT
ejpam-6811	198	40	(	(	PUNCT
ejpam-6811	198	41	4	4	X
ejpam-6811	198	42	)	)	PUNCT
ejpam-6811	198	43	if	if	SCONJ
ejpam-6811	198	44	db	db	PROPN
ejpam-6811	198	45	�	�	PROPN
ejpam-6811	198	46	d′b	d′b	PROPN
ejpam-6811	198	47	with	with	ADP
ejpam-6811	198	48	t	t	PROPN
ejpam-6811	198	49	:	:	PUNCT
ejpam-6811	198	50	(	(	PUNCT
ejpam-6811	198	51	x	x	NOUN
ejpam-6811	198	52	,	,	PUNCT
ejpam-6811	198	53	db	db	PROPN
ejpam-6811	198	54	)	)	PUNCT
ejpam-6811	198	55	→	→	SYM
ejpam-6811	198	56	(	(	PUNCT
ejpam-6811	198	57	x	x	NOUN
ejpam-6811	198	58	,	,	PUNCT
ejpam-6811	198	59	d′b	d′b	PROPN
ejpam-6811	198	60	)	)	PUNCT
ejpam-6811	198	61	is	be	AUX
ejpam-6811	198	62	g	g	NOUN
ejpam-6811	198	63	-	-	PUNCT
ejpam-6811	198	64	cauchy	cauchy	ADJ
ejpam-6811	198	65	sequence	sequence	NOUN
ejpam-6811	198	66	on	on	ADP
ejpam-6811	198	67	x	x	ADP
ejpam-6811	198	68	;	;	PUNCT
ejpam-6811	198	69	(	(	PUNCT
ejpam-6811	198	70	5	5	NUM
ejpam-6811	198	71	)	)	PUNCT
ejpam-6811	198	72	(	(	PUNCT
ejpam-6811	198	73	x	x	NOUN
ejpam-6811	198	74	,	,	PUNCT
ejpam-6811	198	75	db	db	PROPN
ejpam-6811	198	76	,	,	PUNCT
ejpam-6811	198	77	ḡ	ḡ	VERB
ejpam-6811	198	78	)	)	PUNCT
ejpam-6811	198	79	have	have	VERB
ejpam-6811	198	80	property	property	NOUN
ejpam-6811	198	81	a	a	DET
ejpam-6811	198	82	(	(	PUNCT
ejpam-6811	198	83	1	1	NUM
ejpam-6811	198	84	)	)	PUNCT
ejpam-6811	198	85	.	.	PUNCT
ejpam-6811	199	1	as	as	ADP
ejpam-6811	199	2	a	a	DET
ejpam-6811	199	3	consequence	consequence	NOUN
ejpam-6811	199	4	,	,	PUNCT
ejpam-6811	199	5	v	v	X
ejpam-6811	199	6	(	(	PUNCT
ejpam-6811	199	7	t	t	PROPN
ejpam-6811	199	8	,	,	PUNCT
ejpam-6811	199	9	s	s	PROPN
ejpam-6811	199	10	)	)	PUNCT
ejpam-6811	199	11	6=	6=	ADP
ejpam-6811	199	12	⇔	⇔	PROPN
ejpam-6811	199	13	c(t	c(t	PROPN
ejpam-6811	199	14	,	,	PUNCT
ejpam-6811	199	15	s	s	NOUN
ejpam-6811	199	16	)	)	PUNCT
ejpam-6811	199	17	6=	6=	NUM
ejpam-6811	199	18	.	.	PUNCT
ejpam-6811	200	1	(	(	PUNCT
ejpam-6811	200	2	12	12	NUM
ejpam-6811	200	3	)	)	PUNCT
ejpam-6811	200	4	proof	proof	NOUN
ejpam-6811	200	5	.	.	PUNCT
ejpam-6811	201	1	we	we	PRON
ejpam-6811	201	2	can	can	AUX
ejpam-6811	201	3	observe	observe	VERB
ejpam-6811	201	4	that	that	SCONJ
ejpam-6811	201	5	all	all	DET
ejpam-6811	201	6	other	other	ADJ
ejpam-6811	201	7	conditions	condition	NOUN
ejpam-6811	201	8	of	of	ADP
ejpam-6811	201	9	this	this	DET
ejpam-6811	201	10	result	result	NOUN
ejpam-6811	201	11	coincide	coincide	NOUN
ejpam-6811	201	12	with	with	ADP
ejpam-6811	201	13	theorem	theorem	ADJ
ejpam-6811	201	14	1	1	NUM
ejpam-6811	201	15	,	,	PUNCT
ejpam-6811	201	16	so	so	SCONJ
ejpam-6811	201	17	it	it	PRON
ejpam-6811	201	18	is	be	AUX
ejpam-6811	201	19	sufficient	sufficient	ADJ
ejpam-6811	201	20	to	to	PART
ejpam-6811	201	21	check	check	VERB
ejpam-6811	201	22	that	that	SCONJ
ejpam-6811	201	23	even	even	ADV
ejpam-6811	201	24	with	with	ADP
ejpam-6811	201	25	assumption	assumption	NOUN
ejpam-6811	201	26	(	(	PUNCT
ejpam-6811	201	27	5	5	NUM
ejpam-6811	201	28	)	)	PUNCT
ejpam-6811	201	29	,	,	PUNCT
ejpam-6811	201	30	we	we	PRON
ejpam-6811	201	31	will	will	AUX
ejpam-6811	201	32	get	get	VERB
ejpam-6811	201	33	if	if	SCONJ
ejpam-6811	201	34	v	v	NOUN
ejpam-6811	201	35	(	(	PUNCT
ejpam-6811	201	36	t	t	PROPN
ejpam-6811	201	37	,	,	PUNCT
ejpam-6811	201	38	s	s	PROPN
ejpam-6811	201	39	)	)	PUNCT
ejpam-6811	201	40	6=	6=	PUNCT
ejpam-6811	201	41	then	then	ADV
ejpam-6811	201	42	c(t	c(t	PROPN
ejpam-6811	201	43	,	,	PUNCT
ejpam-6811	201	44	s	s	NOUN
ejpam-6811	201	45	)	)	PUNCT
ejpam-6811	201	46	6=	6=	PUNCT
ejpam-6811	201	47	.	.	PUNCT
ejpam-6811	202	1	d.	d.	PROPN
ejpam-6811	202	2	e.	e.	PROPN
ejpam-6811	202	3	shehwar	shehwar	PROPN
ejpam-6811	202	4	sagheer	sagheer	PROPN
ejpam-6811	202	5	et	et	PROPN
ejpam-6811	202	6	al	al	PROPN
ejpam-6811	202	7	.	.	PUNCT
ejpam-6811	202	8	/	/	SYM
ejpam-6811	202	9	eur	eur	PROPN
ejpam-6811	202	10	.	.	PUNCT
ejpam-6811	203	1	j.	j.	PROPN
ejpam-6811	203	2	pure	pure	PROPN
ejpam-6811	203	3	appl	appl	PROPN
ejpam-6811	203	4	.	.	PROPN
ejpam-6811	203	5	math	math	PROPN
ejpam-6811	203	6	,	,	PUNCT
ejpam-6811	203	7	18	18	NUM
ejpam-6811	203	8	(	(	PUNCT
ejpam-6811	203	9	4	4	NUM
ejpam-6811	203	10	)	)	PUNCT
ejpam-6811	203	11	(	(	PUNCT
ejpam-6811	203	12	2025	2025	NUM
ejpam-6811	203	13	)	)	PUNCT
ejpam-6811	203	14	,	,	PUNCT
ejpam-6811	203	15	6811	6811	NUM
ejpam-6811	203	16	10	10	NUM
ejpam-6811	203	17	of	of	ADP
ejpam-6811	203	18	24	24	NUM
ejpam-6811	203	19	as	as	ADP
ejpam-6811	203	20	{	{	PUNCT
ejpam-6811	203	21	sxn	sxn	NOUN
ejpam-6811	203	22	}	}	PUNCT
ejpam-6811	203	23	is	be	AUX
ejpam-6811	203	24	a	a	DET
ejpam-6811	203	25	cauchy	cauchy	ADJ
ejpam-6811	203	26	sequence	sequence	NOUN
ejpam-6811	203	27	and	and	CCONJ
ejpam-6811	203	28	s(x	s(x	NOUN
ejpam-6811	203	29	)	)	PUNCT
ejpam-6811	203	30	is	be	AUX
ejpam-6811	203	31	closed	close	VERB
ejpam-6811	203	32	in	in	ADP
ejpam-6811	203	33	x	x	NOUN
ejpam-6811	203	34	,	,	PUNCT
ejpam-6811	203	35	so	so	SCONJ
ejpam-6811	203	36	for	for	ADP
ejpam-6811	203	37	some	some	DET
ejpam-6811	203	38	x∗	x∗	PROPN
ejpam-6811	203	39	∈	∈	PROPN
ejpam-6811	203	40	x	x	INTJ
ejpam-6811	203	41	we	we	PRON
ejpam-6811	203	42	have	have	VERB
ejpam-6811	204	1	lim	lim	PROPN
ejpam-6811	204	2	n→∞	n→∞	NUM
ejpam-6811	204	3	sxn	sxn	NOUN
ejpam-6811	204	4	=	=	PUNCT
ejpam-6811	204	5	sx∗	sx∗	PROPN
ejpam-6811	204	6	=	=	PROPN
ejpam-6811	204	7	lim	lim	PROPN
ejpam-6811	204	8	n→∞	n→∞	NUM
ejpam-6811	204	9	txn	txn	NOUN
ejpam-6811	204	10	.	.	PUNCT
ejpam-6811	205	1	(	(	PUNCT
ejpam-6811	205	2	13	13	NUM
ejpam-6811	205	3	)	)	PUNCT
ejpam-6811	205	4	we	we	PRON
ejpam-6811	205	5	claim	claim	VERB
ejpam-6811	205	6	that	that	SCONJ
ejpam-6811	205	7	x∗	x∗	PROPN
ejpam-6811	205	8	∈	∈	PROPN
ejpam-6811	205	9	c(t	c(t	PROPN
ejpam-6811	205	10	,	,	PUNCT
ejpam-6811	205	11	s	s	PART
ejpam-6811	205	12	)	)	PUNCT
ejpam-6811	205	13	,	,	PUNCT
ejpam-6811	205	14	since	since	SCONJ
ejpam-6811	205	15	if	if	SCONJ
ejpam-6811	205	16	,	,	PUNCT
ejpam-6811	205	17	x∗	x∗	PROPN
ejpam-6811	205	18	is	be	AUX
ejpam-6811	205	19	not	not	PART
ejpam-6811	205	20	a	a	DET
ejpam-6811	205	21	coincident	coincident	ADJ
ejpam-6811	205	22	point	point	NOUN
ejpam-6811	205	23	of	of	ADP
ejpam-6811	205	24	t	t	PROPN
ejpam-6811	205	25	and	and	CCONJ
ejpam-6811	205	26	s	s	PROPN
ejpam-6811	205	27	,	,	PUNCT
ejpam-6811	205	28	then	then	ADV
ejpam-6811	205	29	tx∗	tx∗	PRON
ejpam-6811	205	30	6=	6=	PUNCT
ejpam-6811	206	1	sx∗.	sx∗.	PROPN
ejpam-6811	206	2	so	so	ADV
ejpam-6811	206	3	,	,	PUNCT
ejpam-6811	206	4	db(tx	db(tx	PROPN
ejpam-6811	206	5	∗	∗	NOUN
ejpam-6811	206	6	,	,	PUNCT
ejpam-6811	206	7	sx∗	sx∗	PROPN
ejpam-6811	206	8	)	)	PUNCT
ejpam-6811	206	9	>	>	X
ejpam-6811	206	10	0	0	X
ejpam-6811	206	11	.	.	PUNCT
ejpam-6811	207	1	(	(	PUNCT
ejpam-6811	207	2	14	14	NUM
ejpam-6811	207	3	)	)	PUNCT
ejpam-6811	207	4	then	then	ADV
ejpam-6811	207	5	(	(	PUNCT
ejpam-6811	207	6	sxn	sxn	INTJ
ejpam-6811	207	7	,	,	PUNCT
ejpam-6811	207	8	sx	sx	PROPN
ejpam-6811	207	9	∗	∗	NOUN
ejpam-6811	207	10	)	)	PUNCT
ejpam-6811	207	11	∈	∈	PROPN
ejpam-6811	207	12	e(ḡ	e(ḡ	PROPN
ejpam-6811	207	13	)	)	PUNCT
ejpam-6811	207	14	for	for	ADP
ejpam-6811	207	15	all	all	DET
ejpam-6811	207	16	n	n	NOUN
ejpam-6811	207	17	because	because	SCONJ
ejpam-6811	207	18	(	(	PUNCT
ejpam-6811	207	19	x	x	NOUN
ejpam-6811	207	20	,	,	PUNCT
ejpam-6811	207	21	db	db	PROPN
ejpam-6811	207	22	,	,	PUNCT
ejpam-6811	207	23	ḡ	ḡ	ADJ
ejpam-6811	207	24	)	)	PUNCT
ejpam-6811	207	25	attains	attain	VERB
ejpam-6811	207	26	the	the	DET
ejpam-6811	207	27	property	property	NOUN
ejpam-6811	207	28	a.	a.	NOUN
ejpam-6811	207	29	also	also	ADV
ejpam-6811	207	30	,	,	PUNCT
ejpam-6811	207	31	db(sx	db(sx	ADJ
ejpam-6811	207	32	∗	∗	NOUN
ejpam-6811	207	33	,	,	PUNCT
ejpam-6811	207	34	tx∗	tx∗	NOUN
ejpam-6811	207	35	)	)	PUNCT
ejpam-6811	207	36	≤	≤	PROPN
ejpam-6811	207	37	b{db(sx∗	b{db(sx∗	PROPN
ejpam-6811	207	38	,	,	PUNCT
ejpam-6811	207	39	txn(k	txn(k	PROPN
ejpam-6811	207	40	)	)	PUNCT
ejpam-6811	207	41	)	)	PUNCT
ejpam-6811	208	1	+	+	CCONJ
ejpam-6811	208	2	db(txn(k	db(txn(k	ADJ
ejpam-6811	208	3	)	)	PUNCT
ejpam-6811	208	4	,	,	PUNCT
ejpam-6811	208	5	tx	tx	PROPN
ejpam-6811	208	6	∗	∗	NOUN
ejpam-6811	208	7	)	)	PUNCT
ejpam-6811	208	8	}	}	PUNCT
ejpam-6811	208	9	,	,	PUNCT
ejpam-6811	208	10	or	or	CCONJ
ejpam-6811	208	11	db(sx	db(sx	PROPN
ejpam-6811	208	12	∗	∗	NOUN
ejpam-6811	208	13	,	,	PUNCT
ejpam-6811	208	14	tx∗)−	tx∗)−	NOUN
ejpam-6811	208	15	bdb(sx	bdb(sx	NOUN
ejpam-6811	208	16	∗	∗	NOUN
ejpam-6811	208	17	,	,	PUNCT
ejpam-6811	208	18	txn(k	txn(k	PROPN
ejpam-6811	208	19	)	)	PUNCT
ejpam-6811	208	20	)	)	PUNCT
ejpam-6811	208	21	≤	≤	NUM
ejpam-6811	209	1	bdb(txn(k	bdb(txn(k	NOUN
ejpam-6811	209	2	)	)	PUNCT
ejpam-6811	209	3	,	,	PUNCT
ejpam-6811	209	4	tx	tx	PROPN
ejpam-6811	209	5	∗	∗	NOUN
ejpam-6811	209	6	)	)	PUNCT
ejpam-6811	209	7	.	.	PUNCT
ejpam-6811	210	1	we	we	PRON
ejpam-6811	210	2	have	have	VERB
ejpam-6811	210	3	φ(db(sx	φ(db(sx	NOUN
ejpam-6811	210	4	∗	∗	NOUN
ejpam-6811	210	5	,	,	PUNCT
ejpam-6811	210	6	tx∗)−	tx∗)−	NOUN
ejpam-6811	210	7	bdb(sx	bdb(sx	NOUN
ejpam-6811	210	8	∗	∗	NOUN
ejpam-6811	210	9	,	,	PUNCT
ejpam-6811	210	10	txn(k	txn(k	PROPN
ejpam-6811	210	11	)	)	PUNCT
ejpam-6811	210	12	)	)	PUNCT
ejpam-6811	210	13	)	)	PUNCT
ejpam-6811	210	14	≤	≤	NUM
ejpam-6811	210	15	φ(bdb(txn(k	φ(bdb(txn(k	NUM
ejpam-6811	210	16	)	)	PUNCT
ejpam-6811	210	17	,	,	PUNCT
ejpam-6811	210	18	tx	tx	PROPN
ejpam-6811	210	19	∗	∗	NOUN
ejpam-6811	210	20	)	)	PUNCT
ejpam-6811	210	21	)	)	PUNCT
ejpam-6811	210	22	≤	≤	NUM
ejpam-6811	211	1	ψ(db(sxn(k	ψ(db(sxn(k	NUM
ejpam-6811	211	2	)	)	PUNCT
ejpam-6811	211	3	,	,	PUNCT
ejpam-6811	211	4	sx	sx	PROPN
ejpam-6811	211	5	∗))φ(δ(bm(sxn(k	∗))φ(δ(bm(sxn(k	PROPN
ejpam-6811	211	6	)	)	PUNCT
ejpam-6811	211	7	,	,	PUNCT
ejpam-6811	211	8	sx	sx	PROPN
ejpam-6811	211	9	∗	∗	NOUN
ejpam-6811	211	10	)	)	PUNCT
ejpam-6811	211	11	)	)	PUNCT
ejpam-6811	211	12	)	)	PUNCT
ejpam-6811	212	1	≤	≤	NUM
ejpam-6811	212	2	ψ(db(sxn(k	ψ(db(sxn(k	NUM
ejpam-6811	212	3	)	)	PUNCT
ejpam-6811	212	4	,	,	PUNCT
ejpam-6811	212	5	sx	sx	PROPN
ejpam-6811	212	6	∗))φ(m(sxn(k	∗))φ(m(sxn(k	PROPN
ejpam-6811	212	7	)	)	PUNCT
ejpam-6811	212	8	,	,	PUNCT
ejpam-6811	212	9	sx	sx	PROPN
ejpam-6811	212	10	∗	∗	NOUN
ejpam-6811	212	11	)	)	PUNCT
ejpam-6811	212	12	)	)	PUNCT
ejpam-6811	212	13	,	,	PUNCT
ejpam-6811	212	14	(	(	PUNCT
ejpam-6811	212	15	15	15	NUM
ejpam-6811	212	16	)	)	PUNCT
ejpam-6811	212	17	then	then	ADV
ejpam-6811	212	18	m((sxn(k	m((sxn(k	X
ejpam-6811	212	19	)	)	PUNCT
ejpam-6811	212	20	,	,	PUNCT
ejpam-6811	212	21	sx	sx	PROPN
ejpam-6811	212	22	∗	∗	NOUN
ejpam-6811	212	23	)	)	PUNCT
ejpam-6811	213	1	=	=	PRON
ejpam-6811	213	2	max	max	X
ejpam-6811	213	3	{	{	PUNCT
ejpam-6811	213	4	db(sxn(k	db(sxn(k	PROPN
ejpam-6811	213	5	)	)	PUNCT
ejpam-6811	213	6	,	,	PUNCT
ejpam-6811	213	7	txn(k))db(tx	txn(k))db(tx	DET
ejpam-6811	213	8	∗	∗	NOUN
ejpam-6811	213	9	,	,	PUNCT
ejpam-6811	213	10	sx∗	sx∗	NOUN
ejpam-6811	213	11	)	)	PUNCT
ejpam-6811	213	12	db(sxn(k	db(sxn(k	NOUN
ejpam-6811	213	13	)	)	PUNCT
ejpam-6811	213	14	,	,	PUNCT
ejpam-6811	213	15	sx∗	sx∗	PROPN
ejpam-6811	213	16	)	)	PUNCT
ejpam-6811	213	17	,	,	PUNCT
ejpam-6811	213	18	db(sxn(k	db(sxn(k	NOUN
ejpam-6811	213	19	)	)	PUNCT
ejpam-6811	213	20	,	,	PUNCT
ejpam-6811	213	21	sx	sx	PROPN
ejpam-6811	213	22	∗	∗	NOUN
ejpam-6811	213	23	)	)	PUNCT
ejpam-6811	213	24	,	,	PUNCT
ejpam-6811	213	25	db(sxn(k	db(sxn(k	NOUN
ejpam-6811	213	26	)	)	PUNCT
ejpam-6811	213	27	,	,	PUNCT
ejpam-6811	213	28	txn(k	txn(k	PROPN
ejpam-6811	213	29	)	)	PUNCT
ejpam-6811	213	30	)	)	PUNCT
ejpam-6811	213	31	,	,	PUNCT
ejpam-6811	213	32	db(sx	db(sx	VERB
ejpam-6811	213	33	∗	∗	NOUN
ejpam-6811	213	34	,	,	PUNCT
ejpam-6811	213	35	tx∗	tx∗	NOUN
ejpam-6811	213	36	)	)	PUNCT
ejpam-6811	213	37	,	,	PUNCT
ejpam-6811	213	38	db(sxn(k	db(sxn(k	NOUN
ejpam-6811	213	39	)	)	PUNCT
ejpam-6811	213	40	,	,	PUNCT
ejpam-6811	213	41	tx	tx	PROPN
ejpam-6811	213	42	∗	∗	NOUN
ejpam-6811	213	43	)	)	PUNCT
ejpam-6811	213	44	+	+	NUM
ejpam-6811	213	45	db(sx	db(sx	PROPN
ejpam-6811	213	46	∗	∗	NOUN
ejpam-6811	213	47	,	,	PUNCT
ejpam-6811	213	48	txn(k	txn(k	PROPN
ejpam-6811	213	49	)	)	PUNCT
ejpam-6811	213	50	)	)	PUNCT
ejpam-6811	213	51	2b	2b	NOUN
ejpam-6811	213	52	}	}	PUNCT
ejpam-6811	213	53	.	.	PUNCT
ejpam-6811	214	1	using	use	VERB
ejpam-6811	214	2	(	(	PUNCT
ejpam-6811	214	3	13	13	NUM
ejpam-6811	214	4	)	)	PUNCT
ejpam-6811	214	5	and	and	CCONJ
ejpam-6811	214	6	taking	take	VERB
ejpam-6811	214	7	limit	limit	NOUN
ejpam-6811	214	8	n→	n→	PUNCT
ejpam-6811	214	9	∞	∞	PROPN
ejpam-6811	214	10	,	,	PUNCT
ejpam-6811	214	11	we	we	PRON
ejpam-6811	214	12	will	will	AUX
ejpam-6811	214	13	get	get	VERB
ejpam-6811	214	14	lim	lim	PROPN
ejpam-6811	214	15	n→∞	n→∞	PRON
ejpam-6811	214	16	m((sxn(k	m((sxn(k	PRON
ejpam-6811	214	17	)	)	PUNCT
ejpam-6811	214	18	,	,	PUNCT
ejpam-6811	214	19	sx	sx	PROPN
ejpam-6811	214	20	∗	∗	NOUN
ejpam-6811	214	21	)	)	PUNCT
ejpam-6811	215	1	=	=	SYM
ejpam-6811	215	2	lim	lim	PROPN
ejpam-6811	215	3	n→∞	n→∞	NUM
ejpam-6811	215	4	db(sx	db(sx	PROPN
ejpam-6811	215	5	∗	∗	NOUN
ejpam-6811	215	6	,	,	PUNCT
ejpam-6811	215	7	tx∗	tx∗	NOUN
ejpam-6811	215	8	)	)	PUNCT
ejpam-6811	215	9	>	>	X
ejpam-6811	215	10	0	0	X
ejpam-6811	215	11	.	.	PUNCT
ejpam-6811	216	1	from	from	ADP
ejpam-6811	216	2	the	the	DET
ejpam-6811	216	3	condition	condition	NOUN
ejpam-6811	216	4	(	(	PUNCT
ejpam-6811	216	5	15	15	NUM
ejpam-6811	216	6	)	)	PUNCT
ejpam-6811	216	7	,	,	PUNCT
ejpam-6811	216	8	we	we	PRON
ejpam-6811	216	9	have	have	VERB
ejpam-6811	216	10	lim	lim	PROPN
ejpam-6811	216	11	n→∞	n→∞	X
ejpam-6811	216	12	ψ(db(sxn(k	ψ(db(sxn(k	NOUN
ejpam-6811	216	13	)	)	PUNCT
ejpam-6811	216	14	,	,	PUNCT
ejpam-6811	216	15	sx	sx	PROPN
ejpam-6811	216	16	∗	∗	NOUN
ejpam-6811	216	17	)	)	PUNCT
ejpam-6811	217	1	=	=	SYM
ejpam-6811	217	2	1	1	NUM
ejpam-6811	217	3	,	,	PUNCT
ejpam-6811	217	4	hence	hence	ADV
ejpam-6811	217	5	lim	lim	PROPN
ejpam-6811	217	6	n→∞	n→∞	NUM
ejpam-6811	217	7	db(sxn(k	db(sxn(k	PROPN
ejpam-6811	217	8	)	)	PUNCT
ejpam-6811	217	9	,	,	PUNCT
ejpam-6811	217	10	sx	sx	PROPN
ejpam-6811	217	11	∗	∗	NOUN
ejpam-6811	217	12	)	)	PUNCT
ejpam-6811	217	13	=	=	PUNCT
ejpam-6811	218	1	db(tx	db(tx	PROPN
ejpam-6811	218	2	∗	∗	NOUN
ejpam-6811	218	3	,	,	PUNCT
ejpam-6811	218	4	sx∗	sx∗	PROPN
ejpam-6811	218	5	)	)	PUNCT
ejpam-6811	219	1	=	=	SYM
ejpam-6811	219	2	0	0	X
ejpam-6811	219	3	.	.	PUNCT
ejpam-6811	220	1	it	it	PRON
ejpam-6811	220	2	is	be	AUX
ejpam-6811	220	3	a	a	DET
ejpam-6811	220	4	contradiction	contradiction	NOUN
ejpam-6811	220	5	to	to	ADP
ejpam-6811	220	6	(	(	PUNCT
ejpam-6811	220	7	14	14	NUM
ejpam-6811	220	8	)	)	PUNCT
ejpam-6811	220	9	.	.	PUNCT
ejpam-6811	221	1	hence	hence	ADV
ejpam-6811	221	2	,	,	PUNCT
ejpam-6811	221	3	x∗	x∗	PROPN
ejpam-6811	221	4	∈	∈	PROPN
ejpam-6811	221	5	c(t	c(t	PROPN
ejpam-6811	221	6	,	,	PUNCT
ejpam-6811	221	7	s	s	AUX
ejpam-6811	221	8	)	)	PUNCT
ejpam-6811	221	9	proving	prove	VERB
ejpam-6811	221	10	that	that	SCONJ
ejpam-6811	221	11	c(t	c(t	PROPN
ejpam-6811	221	12	,	,	PUNCT
ejpam-6811	221	13	s	s	NOUN
ejpam-6811	221	14	)	)	PUNCT
ejpam-6811	221	15	6=	6=	PUNCT
ejpam-6811	221	16	.	.	PUNCT
ejpam-6811	222	1	theorem	theorem	NOUN
ejpam-6811	222	2	3	3	X
ejpam-6811	222	3	.	.	PUNCT
ejpam-6811	223	1	if	if	SCONJ
ejpam-6811	223	2	all	all	DET
ejpam-6811	223	3	the	the	DET
ejpam-6811	223	4	conditions	condition	NOUN
ejpam-6811	223	5	of	of	ADP
ejpam-6811	223	6	theorem	theorem	NOUN
ejpam-6811	223	7	1	1	NUM
ejpam-6811	223	8	are	be	AUX
ejpam-6811	223	9	adopted	adopt	VERB
ejpam-6811	223	10	and	and	CCONJ
ejpam-6811	223	11	for	for	ADP
ejpam-6811	223	12	any	any	DET
ejpam-6811	223	13	x	x	NOUN
ejpam-6811	223	14	,	,	PUNCT
ejpam-6811	223	15	y	y	PROPN
ejpam-6811	223	16	∈	∈	PROPN
ejpam-6811	223	17	c(t	c(t	PROPN
ejpam-6811	223	18	,	,	PUNCT
ejpam-6811	223	19	s	s	PART
ejpam-6811	223	20	)	)	PUNCT
ejpam-6811	223	21	with	with	ADP
ejpam-6811	223	22	sx	sx	PROPN
ejpam-6811	223	23	6=	6=	PROPN
ejpam-6811	223	24	sy	sy	PROPN
ejpam-6811	223	25	,	,	PUNCT
ejpam-6811	223	26	and	and	CCONJ
ejpam-6811	223	27	it	it	PRON
ejpam-6811	223	28	is	be	AUX
ejpam-6811	223	29	true	true	ADJ
ejpam-6811	223	30	that	that	SCONJ
ejpam-6811	223	31	(	(	PUNCT
ejpam-6811	223	32	sx	sx	PROPN
ejpam-6811	223	33	,	,	PUNCT
ejpam-6811	223	34	sy	sy	PROPN
ejpam-6811	223	35	)	)	PUNCT
ejpam-6811	223	36	∈	∈	PROPN
ejpam-6811	223	37	e(ḡ	e(ḡ	PROPN
ejpam-6811	223	38	)	)	PUNCT
ejpam-6811	223	39	then	then	ADV
ejpam-6811	223	40	v	v	X
ejpam-6811	223	41	(	(	PUNCT
ejpam-6811	223	42	t	t	PROPN
ejpam-6811	223	43	,	,	PUNCT
ejpam-6811	223	44	s	s	PROPN
ejpam-6811	223	45	)	)	PUNCT
ejpam-6811	223	46	6=	6=	ADP
ejpam-6811	223	47	⇔	⇔	PROPN
ejpam-6811	223	48	cm(t	cm(t	PROPN
ejpam-6811	223	49	,	,	PUNCT
ejpam-6811	223	50	s	s	NOUN
ejpam-6811	223	51	)	)	PUNCT
ejpam-6811	223	52	6=	6=	PUNCT
ejpam-6811	223	53	.	.	PUNCT
ejpam-6811	224	1	proof	proof	NOUN
ejpam-6811	224	2	.	.	PUNCT
ejpam-6811	225	1	from	from	ADP
ejpam-6811	225	2	theorem	theorem	NOUN
ejpam-6811	225	3	1	1	NUM
ejpam-6811	225	4	,	,	PUNCT
ejpam-6811	225	5	there	there	PRON
ejpam-6811	225	6	exists	exist	VERB
ejpam-6811	225	7	x	x	X
ejpam-6811	225	8	∈	∈	PROPN
ejpam-6811	225	9	x	x	PUNCT
ejpam-6811	225	10	such	such	ADJ
ejpam-6811	225	11	that	that	DET
ejpam-6811	225	12	sx	sx	PROPN
ejpam-6811	225	13	=	=	SYM
ejpam-6811	225	14	tx	tx	PROPN
ejpam-6811	225	15	.	.	PUNCT
ejpam-6811	226	1	suppose	suppose	VERB
ejpam-6811	226	2	that	that	SCONJ
ejpam-6811	226	3	there	there	PRON
ejpam-6811	226	4	exists	exist	VERB
ejpam-6811	226	5	another	another	DET
ejpam-6811	226	6	element	element	NOUN
ejpam-6811	226	7	y	y	PROPN
ejpam-6811	226	8	∈	∈	PROPN
ejpam-6811	227	1	x	x	X
ejpam-6811	227	2	then	then	ADV
ejpam-6811	227	3	sy	sy	INTJ
ejpam-6811	227	4	=	=	SYM
ejpam-6811	227	5	ty	ty	INTJ
ejpam-6811	227	6	.	.	PUNCT
ejpam-6811	228	1	we	we	PRON
ejpam-6811	228	2	will	will	AUX
ejpam-6811	228	3	prove	prove	VERB
ejpam-6811	228	4	that	that	SCONJ
ejpam-6811	228	5	sx	sx	PROPN
ejpam-6811	228	6	=	=	SYM
ejpam-6811	228	7	sy	sy	PROPN
ejpam-6811	228	8	.	.	PROPN
ejpam-6811	228	9	on	on	ADP
ejpam-6811	228	10	the	the	DET
ejpam-6811	228	11	contrary	contrary	NOUN
ejpam-6811	228	12	,	,	PUNCT
ejpam-6811	228	13	suppose	suppose	VERB
ejpam-6811	228	14	it	it	PRON
ejpam-6811	228	15	is	be	AUX
ejpam-6811	228	16	not	not	PART
ejpam-6811	228	17	true	true	ADJ
ejpam-6811	228	18	then	then	ADV
ejpam-6811	228	19	by	by	ADP
ejpam-6811	228	20	assumption	assumption	NOUN
ejpam-6811	228	21	(	(	PUNCT
ejpam-6811	228	22	sx	sx	PROPN
ejpam-6811	228	23	,	,	PUNCT
ejpam-6811	228	24	sy	sy	PROPN
ejpam-6811	228	25	)	)	PUNCT
ejpam-6811	228	26	∈	∈	PROPN
ejpam-6811	228	27	e(ḡ	e(ḡ	PROPN
ejpam-6811	228	28	)	)	PUNCT
ejpam-6811	228	29	.	.	PUNCT
ejpam-6811	229	1	now	now	ADV
ejpam-6811	229	2	,	,	PUNCT
ejpam-6811	229	3	we	we	PRON
ejpam-6811	229	4	may	may	AUX
ejpam-6811	229	5	write	write	VERB
ejpam-6811	229	6	φ(db(ts	φ(db(t	NOUN
ejpam-6811	229	7	,	,	PUNCT
ejpam-6811	229	8	sy	sy	NOUN
ejpam-6811	229	9	)	)	PUNCT
ejpam-6811	229	10	)	)	PUNCT
ejpam-6811	230	1	≤	≤	NUM
ejpam-6811	230	2	ψ(db(sx	ψ(db(sx	NOUN
ejpam-6811	230	3	,	,	PUNCT
ejpam-6811	230	4	sy))φ(δ(m(sx	sy))φ(δ(m(sx	NOUN
ejpam-6811	230	5	,	,	PUNCT
ejpam-6811	230	6	sy	sy	NOUN
ejpam-6811	230	7	)	)	PUNCT
ejpam-6811	230	8	)	)	PUNCT
ejpam-6811	230	9	)	)	PUNCT
ejpam-6811	230	10	≤	≤	NUM
ejpam-6811	230	11	ψ(db(sx	ψ(db(sx	NOUN
ejpam-6811	230	12	,	,	PUNCT
ejpam-6811	230	13	sy))φ(m(sx	sy))φ(m(sx	NOUN
ejpam-6811	230	14	,	,	PUNCT
ejpam-6811	230	15	sy	sy	NOUN
ejpam-6811	230	16	)	)	PUNCT
ejpam-6811	230	17	)	)	PUNCT
ejpam-6811	230	18	≤	≤	NUM
ejpam-6811	230	19	φ(m(sx	φ(m(sx	NOUN
ejpam-6811	230	20	,	,	PUNCT
ejpam-6811	230	21	sy	sy	NOUN
ejpam-6811	230	22	)	)	PUNCT
ejpam-6811	230	23	)	)	PUNCT
ejpam-6811	231	1	=	=	SYM
ejpam-6811	231	2	φdb(tx	φdb(tx	NOUN
ejpam-6811	231	3	,	,	PUNCT
ejpam-6811	231	4	ty	ty	NOUN
ejpam-6811	231	5	)	)	PUNCT
ejpam-6811	231	6	)	)	PUNCT
ejpam-6811	231	7	.	.	PUNCT
ejpam-6811	232	1	d.	d.	PROPN
ejpam-6811	232	2	e.	e.	PROPN
ejpam-6811	232	3	shehwar	shehwar	PROPN
ejpam-6811	232	4	sagheer	sagheer	PROPN
ejpam-6811	232	5	et	et	PROPN
ejpam-6811	232	6	al	al	PROPN
ejpam-6811	232	7	.	.	PUNCT
ejpam-6811	232	8	/	/	SYM
ejpam-6811	232	9	eur	eur	PROPN
ejpam-6811	232	10	.	.	PUNCT
ejpam-6811	233	1	j.	j.	PROPN
ejpam-6811	233	2	pure	pure	PROPN
ejpam-6811	233	3	appl	appl	PROPN
ejpam-6811	233	4	.	.	PROPN
ejpam-6811	233	5	math	math	PROPN
ejpam-6811	233	6	,	,	PUNCT
ejpam-6811	233	7	18	18	NUM
ejpam-6811	233	8	(	(	PUNCT
ejpam-6811	233	9	4	4	NUM
ejpam-6811	233	10	)	)	PUNCT
ejpam-6811	233	11	(	(	PUNCT
ejpam-6811	233	12	2025	2025	NUM
ejpam-6811	233	13	)	)	PUNCT
ejpam-6811	233	14	,	,	PUNCT
ejpam-6811	233	15	6811	6811	NUM
ejpam-6811	233	16	11	11	NUM
ejpam-6811	233	17	of	of	ADP
ejpam-6811	233	18	24	24	NUM
ejpam-6811	233	19	thus	thus	ADV
ejpam-6811	233	20	,	,	PUNCT
ejpam-6811	233	21	ψ(sx	ψ(sx	PROPN
ejpam-6811	233	22	,	,	PUNCT
ejpam-6811	233	23	sy	sy	NOUN
ejpam-6811	233	24	)	)	PUNCT
ejpam-6811	233	25	=	=	SYM
ejpam-6811	233	26	1	1	NUM
ejpam-6811	233	27	,	,	PUNCT
ejpam-6811	233	28	hence	hence	ADV
ejpam-6811	233	29	sy	sy	PROPN
ejpam-6811	233	30	=	=	SYM
ejpam-6811	233	31	sx	sx	PROPN
ejpam-6811	233	32	.	.	PROPN
ejpam-6811	234	1	next	next	ADV
ejpam-6811	234	2	,	,	PUNCT
ejpam-6811	234	3	as	as	SCONJ
ejpam-6811	234	4	x	x	PRON
ejpam-6811	234	5	is	be	AUX
ejpam-6811	234	6	the	the	DET
ejpam-6811	234	7	coincidence	coincidence	NOUN
ejpam-6811	234	8	point	point	NOUN
ejpam-6811	234	9	so	so	ADV
ejpam-6811	234	10	xn	xn	PUNCT
ejpam-6811	235	1	=	=	PUNCT
ejpam-6811	235	2	x.	x.	NOUN
ejpam-6811	235	3	we	we	PRON
ejpam-6811	235	4	may	may	AUX
ejpam-6811	235	5	construct	construct	VERB
ejpam-6811	235	6	a	a	DET
ejpam-6811	235	7	sequence	sequence	NOUN
ejpam-6811	235	8	such	such	ADJ
ejpam-6811	235	9	that	that	PRON
ejpam-6811	235	10	txn−1	txn−1	PROPN
ejpam-6811	235	11	=	=	SYM
ejpam-6811	235	12	sxn	sxn	NOUN
ejpam-6811	235	13	=	=	PUNCT
ejpam-6811	235	14	sx	sx	PROPN
ejpam-6811	235	15	=	=	PUNCT
ejpam-6811	235	16	ts	ts	NOUN
ejpam-6811	235	17	for	for	ADP
ejpam-6811	235	18	every	every	DET
ejpam-6811	235	19	n	n	PRON
ejpam-6811	235	20	∈	∈	PROPN
ejpam-6811	235	21	n.	n.	NOUN
ejpam-6811	235	22	now	now	ADV
ejpam-6811	235	23	,	,	PUNCT
ejpam-6811	235	24	let	let	VERB
ejpam-6811	235	25	r	r	NOUN
ejpam-6811	235	26	=	=	PUNCT
ejpam-6811	235	27	sx	sx	PROPN
ejpam-6811	235	28	then	then	ADV
ejpam-6811	235	29	sr	sr	PROPN
ejpam-6811	235	30	=	=	SYM
ejpam-6811	235	31	ssx	ssx	PROPN
ejpam-6811	235	32	=	=	SYM
ejpam-6811	235	33	stx	stx	PROPN
ejpam-6811	235	34	.	.	PUNCT
ejpam-6811	236	1	then	then	ADV
ejpam-6811	236	2	,	,	PUNCT
ejpam-6811	236	3	lim	lim	PROPN
ejpam-6811	236	4	n→∞	n→∞	X
ejpam-6811	236	5	txn	txn	X
ejpam-6811	236	6	=	=	SYM
ejpam-6811	236	7	lim	lim	PROPN
ejpam-6811	236	8	n→∞	n→∞	NUM
ejpam-6811	237	1	sxn	sxn	NOUN
ejpam-6811	237	2	=	=	SYM
ejpam-6811	237	3	tx	tx	PROPN
ejpam-6811	237	4	,	,	PUNCT
ejpam-6811	237	5	in	in	ADP
ejpam-6811	237	6	(	(	PUNCT
ejpam-6811	237	7	x	x	NOUN
ejpam-6811	237	8	,	,	PUNCT
ejpam-6811	237	9	d′b	d′b	PROPN
ejpam-6811	237	10	)	)	PUNCT
ejpam-6811	237	11	.	.	PUNCT
ejpam-6811	238	1	also	also	ADV
ejpam-6811	238	2	,	,	PUNCT
ejpam-6811	238	3	lim	lim	PROPN
ejpam-6811	238	4	n→∞	n→∞	NUM
ejpam-6811	238	5	d′b(stxn	d′b(stxn	PROPN
ejpam-6811	238	6	,	,	PUNCT
ejpam-6811	238	7	tsxn	tsxn	NOUN
ejpam-6811	238	8	)	)	PUNCT
ejpam-6811	238	9	=	=	SYM
ejpam-6811	238	10	0	0	NUM
ejpam-6811	238	11	,	,	PUNCT
ejpam-6811	238	12	since	since	SCONJ
ejpam-6811	238	13	s	s	PRON
ejpam-6811	238	14	and	and	CCONJ
ejpam-6811	238	15	t	t	PROPN
ejpam-6811	238	16	are	be	AUX
ejpam-6811	238	17	compatible	compatible	ADJ
ejpam-6811	238	18	with	with	ADP
ejpam-6811	238	19	respect	respect	NOUN
ejpam-6811	238	20	to	to	ADP
ejpam-6811	238	21	d′b	d′b	PROPN
ejpam-6811	238	22	.	.	PUNCT
ejpam-6811	239	1	this	this	PRON
ejpam-6811	239	2	means	mean	VERB
ejpam-6811	239	3	stx	stx	NOUN
ejpam-6811	239	4	=	=	SYM
ejpam-6811	239	5	tsx	tsx	PROPN
ejpam-6811	239	6	,	,	PUNCT
ejpam-6811	239	7	so	so	ADV
ejpam-6811	239	8	sr	sr	PROPN
ejpam-6811	239	9	=	=	PROPN
ejpam-6811	239	10	stx	stx	NOUN
ejpam-6811	239	11	=	=	PUNCT
ejpam-6811	239	12	tsx	tsx	PROPN
ejpam-6811	239	13	=	=	PUNCT
ejpam-6811	239	14	tr	tr	VERB
ejpam-6811	239	15	,	,	PUNCT
ejpam-6811	239	16	showing	show	VERB
ejpam-6811	239	17	that	that	SCONJ
ejpam-6811	239	18	r	r	NOUN
ejpam-6811	239	19	∈	∈	PROPN
ejpam-6811	239	20	c(t	c(t	PROPN
ejpam-6811	239	21	,	,	PUNCT
ejpam-6811	239	22	s	s	NOUN
ejpam-6811	239	23	)	)	PUNCT
ejpam-6811	239	24	.	.	PUNCT
ejpam-6811	240	1	also	also	ADV
ejpam-6811	240	2	,	,	PUNCT
ejpam-6811	240	3	from	from	ADP
ejpam-6811	240	4	the	the	DET
ejpam-6811	240	5	above	above	ADJ
ejpam-6811	240	6	calculations	calculation	NOUN
ejpam-6811	240	7	sr	sr	NOUN
ejpam-6811	240	8	=	=	PUNCT
ejpam-6811	240	9	tr	tr	VERB
ejpam-6811	240	10	=	=	NOUN
ejpam-6811	240	11	sx	sx	NOUN
ejpam-6811	240	12	=	=	NOUN
ejpam-6811	240	13	r	r	NOUN
ejpam-6811	240	14	this	this	PRON
ejpam-6811	240	15	shows	show	VERB
ejpam-6811	240	16	r	r	NOUN
ejpam-6811	240	17	∈	∈	PROPN
ejpam-6811	240	18	cm(s	cm(s	NOUN
ejpam-6811	240	19	,	,	PUNCT
ejpam-6811	240	20	t	t	PROPN
ejpam-6811	240	21	)	)	PUNCT
ejpam-6811	240	22	.	.	PUNCT
ejpam-6811	241	1	4	4	X
ejpam-6811	241	2	.	.	NUM
ejpam-6811	241	3	consequences	consequence	NOUN
ejpam-6811	241	4	and	and	CCONJ
ejpam-6811	241	5	an	an	DET
ejpam-6811	241	6	application	application	NOUN
ejpam-6811	241	7	if	if	SCONJ
ejpam-6811	241	8	we	we	PRON
ejpam-6811	241	9	use	use	VERB
ejpam-6811	241	10	δ(m((sx	δ(m((sx	PROPN
ejpam-6811	241	11	,	,	PUNCT
ejpam-6811	241	12	sy	sy	NOUN
ejpam-6811	241	13	)	)	PUNCT
ejpam-6811	241	14	)	)	PUNCT
ejpam-6811	241	15	)	)	PUNCT
ejpam-6811	242	1	=	=	PUNCT
ejpam-6811	242	2	db(sx	db(sx	PROPN
ejpam-6811	242	3	,	,	PUNCT
ejpam-6811	242	4	sy	sy	NOUN
ejpam-6811	242	5	)	)	PUNCT
ejpam-6811	242	6	)	)	PUNCT
ejpam-6811	242	7	,	,	PUNCT
ejpam-6811	242	8	then	then	ADV
ejpam-6811	242	9	we	we	PRON
ejpam-6811	242	10	will	will	AUX
ejpam-6811	242	11	get	get	VERB
ejpam-6811	242	12	following	follow	VERB
ejpam-6811	242	13	result	result	NOUN
ejpam-6811	242	14	:	:	PUNCT
ejpam-6811	242	15	corollary	corollary	ADJ
ejpam-6811	242	16	1	1	X
ejpam-6811	242	17	.	.	PUNCT
ejpam-6811	243	1	let	let	VERB
ejpam-6811	243	2	(	(	PUNCT
ejpam-6811	243	3	x	x	NOUN
ejpam-6811	243	4	,	,	PUNCT
ejpam-6811	243	5	db	db	PROPN
ejpam-6811	243	6	)	)	PUNCT
ejpam-6811	243	7	be	be	AUX
ejpam-6811	243	8	a	a	DET
ejpam-6811	243	9	complete	complete	ADJ
ejpam-6811	243	10	bms	bms	NOUN
ejpam-6811	243	11	with	with	ADP
ejpam-6811	243	12	ḡ	ḡ	VERB
ejpam-6811	243	13	as	as	ADP
ejpam-6811	243	14	a	a	DET
ejpam-6811	243	15	dg	dg	NOUN
ejpam-6811	243	16	,	,	PUNCT
ejpam-6811	243	17	and	and	CCONJ
ejpam-6811	243	18	db	db	AUX
ejpam-6811	243	19	be	be	AUX
ejpam-6811	243	20	continuous	continuous	ADJ
ejpam-6811	243	21	.	.	PUNCT
ejpam-6811	244	1	let	let	VERB
ejpam-6811	244	2	d′b	d′b	PRON
ejpam-6811	244	3	be	be	AUX
ejpam-6811	244	4	another	another	DET
ejpam-6811	244	5	continuous	continuous	ADJ
ejpam-6811	244	6	function	function	NOUN
ejpam-6811	244	7	and	and	CCONJ
ejpam-6811	244	8	the	the	DET
ejpam-6811	244	9	functions	function	NOUN
ejpam-6811	244	10	(	(	PUNCT
ejpam-6811	244	11	t	t	PROPN
ejpam-6811	244	12	,	,	PUNCT
ejpam-6811	244	13	s	s	PART
ejpam-6811	244	14	)	)	PUNCT
ejpam-6811	244	15	satisfy	satisfy	VERB
ejpam-6811	244	16	an	an	DET
ejpam-6811	244	17	ψ	ψ	NOUN
ejpam-6811	244	18	−	−	PROPN
ejpam-6811	244	19	φ	φ	NUM
ejpam-6811	244	20	-	-	PUNCT
ejpam-6811	244	21	contraction	contraction	NOUN
ejpam-6811	244	22	w.r.t	w.r.t	NOUN
ejpam-6811	244	23	db	db	AUX
ejpam-6811	244	24	satisfying	satisfy	VERB
ejpam-6811	244	25	the	the	DET
ejpam-6811	244	26	axioms	axiom	NOUN
ejpam-6811	244	27	given	give	VERB
ejpam-6811	244	28	below	below	ADP
ejpam-6811	244	29	:	:	PUNCT
ejpam-6811	244	30	(	(	PUNCT
ejpam-6811	244	31	1	1	X
ejpam-6811	244	32	)	)	PUNCT
ejpam-6811	244	33	s	s	VERB
ejpam-6811	244	34	:	:	PUNCT
ejpam-6811	244	35	(	(	PUNCT
ejpam-6811	244	36	x	x	NOUN
ejpam-6811	244	37	,	,	PUNCT
ejpam-6811	244	38	d′b	d′b	PROPN
ejpam-6811	244	39	)	)	PUNCT
ejpam-6811	244	40	→	→	SYM
ejpam-6811	244	41	(	(	PUNCT
ejpam-6811	244	42	x	x	NOUN
ejpam-6811	244	43	,	,	PUNCT
ejpam-6811	244	44	d′b	d′b	PROPN
ejpam-6811	244	45	)	)	PUNCT
ejpam-6811	244	46	is	be	AUX
ejpam-6811	244	47	continuous	continuous	ADJ
ejpam-6811	244	48	with	with	ADP
ejpam-6811	244	49	s(x	s(x	NOUN
ejpam-6811	244	50	)	)	PUNCT
ejpam-6811	245	1	is	be	AUX
ejpam-6811	245	2	closed	close	VERB
ejpam-6811	245	3	w.r.t	w.r.t	ADJ
ejpam-6811	245	4	d′b	d′b	PROPN
ejpam-6811	245	5	;	;	PUNCT
ejpam-6811	245	6	(	(	PUNCT
ejpam-6811	245	7	2	2	X
ejpam-6811	245	8	)	)	PUNCT
ejpam-6811	245	9	t	t	NOUN
ejpam-6811	245	10	(	(	PUNCT
ejpam-6811	245	11	x	x	NOUN
ejpam-6811	245	12	)	)	PUNCT
ejpam-6811	245	13	⊆	⊆	NUM
ejpam-6811	245	14	s(x	s(x	NOUN
ejpam-6811	245	15	)	)	PUNCT
ejpam-6811	245	16	;	;	PUNCT
ejpam-6811	245	17	(	(	PUNCT
ejpam-6811	245	18	3	3	X
ejpam-6811	245	19	)	)	PUNCT
ejpam-6811	245	20	e(ḡ	e(ḡ	PROPN
ejpam-6811	245	21	)	)	PUNCT
ejpam-6811	245	22	is	be	AUX
ejpam-6811	245	23	a	a	DET
ejpam-6811	245	24	transitive	transitive	ADJ
ejpam-6811	245	25	set	set	NOUN
ejpam-6811	245	26	;	;	PUNCT
ejpam-6811	245	27	(	(	PUNCT
ejpam-6811	245	28	4	4	X
ejpam-6811	245	29	)	)	PUNCT
ejpam-6811	245	30	if	if	SCONJ
ejpam-6811	245	31	db	db	PROPN
ejpam-6811	245	32	�	�	PROPN
ejpam-6811	245	33	d′b	d′b	PROPN
ejpam-6811	245	34	,	,	PUNCT
ejpam-6811	245	35	assume	assume	VERB
ejpam-6811	245	36	that	that	SCONJ
ejpam-6811	245	37	t	t	NOUN
ejpam-6811	245	38	:	:	PUNCT
ejpam-6811	245	39	(	(	PUNCT
ejpam-6811	245	40	x	x	NOUN
ejpam-6811	245	41	,	,	PUNCT
ejpam-6811	245	42	db	db	PROPN
ejpam-6811	245	43	)	)	PUNCT
ejpam-6811	245	44	→	→	SYM
ejpam-6811	245	45	(	(	PUNCT
ejpam-6811	245	46	x	x	NOUN
ejpam-6811	245	47	,	,	PUNCT
ejpam-6811	245	48	d′b	d′b	PROPN
ejpam-6811	245	49	)	)	PUNCT
ejpam-6811	245	50	is	be	AUX
ejpam-6811	245	51	s	s	NOUN
ejpam-6811	245	52	-	-	ADJ
ejpam-6811	245	53	cauchy	cauchy	ADJ
ejpam-6811	245	54	sequence	sequence	NOUN
ejpam-6811	245	55	in	in	ADP
ejpam-6811	245	56	x	x	ADP
ejpam-6811	245	57	;	;	PUNCT
ejpam-6811	245	58	(	(	PUNCT
ejpam-6811	245	59	5	5	X
ejpam-6811	245	60	)	)	PUNCT
ejpam-6811	245	61	t	t	NOUN
ejpam-6811	245	62	:	:	PUNCT
ejpam-6811	245	63	(	(	PUNCT
ejpam-6811	245	64	x	x	NOUN
ejpam-6811	245	65	,	,	PUNCT
ejpam-6811	245	66	d′b	d′b	PROPN
ejpam-6811	245	67	)	)	PUNCT
ejpam-6811	245	68	→	→	SYM
ejpam-6811	245	69	(	(	PUNCT
ejpam-6811	245	70	x	x	NOUN
ejpam-6811	245	71	,	,	PUNCT
ejpam-6811	245	72	d′b	d′b	PROPN
ejpam-6811	245	73	)	)	PUNCT
ejpam-6811	245	74	is	be	AUX
ejpam-6811	245	75	ḡb	ḡb	NOUN
ejpam-6811	245	76	-	-	ADJ
ejpam-6811	245	77	continuous	continuous	ADJ
ejpam-6811	245	78	with	with	ADP
ejpam-6811	245	79	t	t	PROPN
ejpam-6811	245	80	and	and	CCONJ
ejpam-6811	245	81	s	s	AUX
ejpam-6811	245	82	also	also	ADV
ejpam-6811	245	83	being	be	AUX
ejpam-6811	245	84	d′b	d′b	NOUN
ejpam-6811	245	85	-	-	PUNCT
ejpam-6811	245	86	compatible	compatible	ADJ
ejpam-6811	245	87	;	;	PUNCT
ejpam-6811	245	88	(	(	PUNCT
ejpam-6811	245	89	6	6	X
ejpam-6811	245	90	)	)	PUNCT
ejpam-6811	245	91	there	there	PRON
ejpam-6811	245	92	exist	exist	VERB
ejpam-6811	245	93	two	two	NUM
ejpam-6811	245	94	functions	function	NOUN
ejpam-6811	245	95	φ	φ	PROPN
ejpam-6811	245	96	∈	∈	PROPN
ejpam-6811	245	97	φ	φ	PROPN
ejpam-6811	245	98	and	and	CCONJ
ejpam-6811	245	99	ψ	ψ	X
ejpam-6811	245	100	∈	∈	PROPN
ejpam-6811	245	101	ψ	ψ	ADP
ejpam-6811	245	102	such	such	ADJ
ejpam-6811	245	103	that	that	SCONJ
ejpam-6811	245	104	φ(db(ts	φ(db(t	NOUN
ejpam-6811	245	105	,	,	PUNCT
ejpam-6811	245	106	t	t	PROPN
ejpam-6811	245	107	t	t	PROPN
ejpam-6811	245	108	)	)	PUNCT
ejpam-6811	245	109	)	)	PUNCT
ejpam-6811	245	110	≤	≤	PROPN
ejpam-6811	246	1	ψ(sx	ψ(sx	PROPN
ejpam-6811	246	2	,	,	PUNCT
ejpam-6811	246	3	sy)φ(db(sx	sy)φ(db(sx	PROPN
ejpam-6811	246	4	,	,	PUNCT
ejpam-6811	246	5	sy	sy	NOUN
ejpam-6811	246	6	)	)	PUNCT
ejpam-6811	246	7	)	)	PUNCT
ejpam-6811	246	8	)	)	PUNCT
ejpam-6811	246	9	,	,	PUNCT
ejpam-6811	246	10	then	then	ADV
ejpam-6811	246	11	v	v	X
ejpam-6811	246	12	(	(	PUNCT
ejpam-6811	246	13	t	t	PROPN
ejpam-6811	246	14	,	,	PUNCT
ejpam-6811	246	15	s	s	NOUN
ejpam-6811	246	16	)	)	PUNCT
ejpam-6811	246	17	6=	6=	ADP
ejpam-6811	246	18	⇒	⇒	PROPN
ejpam-6811	246	19	c(t	c(t	PROPN
ejpam-6811	246	20	,	,	PUNCT
ejpam-6811	246	21	s	s	NOUN
ejpam-6811	246	22	)	)	PUNCT
ejpam-6811	246	23	6=	6=	NUM
ejpam-6811	246	24	.	.	PUNCT
ejpam-6811	247	1	(	(	PUNCT
ejpam-6811	247	2	16	16	NUM
ejpam-6811	247	3	)	)	PUNCT
ejpam-6811	247	4	example	example	NOUN
ejpam-6811	248	1	2	2	NUM
ejpam-6811	248	2	.	.	PUNCT
ejpam-6811	248	3	let	let	VERB
ejpam-6811	248	4	x	x	PUNCT
ejpam-6811	248	5	=	=	PUNCT
ejpam-6811	249	1	[	[	X
ejpam-6811	249	2	0,∞	0,∞	NUM
ejpam-6811	249	3	)	)	PUNCT
ejpam-6811	249	4	⊆	⊆	NUM
ejpam-6811	249	5	r	r	NOUN
ejpam-6811	249	6	and	and	CCONJ
ejpam-6811	249	7	define	define	VERB
ejpam-6811	249	8	db	db	PROPN
ejpam-6811	249	9	,	,	PUNCT
ejpam-6811	249	10	d′b	d′b	PROPN
ejpam-6811	249	11	:	:	PUNCT
ejpam-6811	249	12	x	x	X
ejpam-6811	249	13	×x	×x	X
ejpam-6811	249	14	→	→	NOUN
ejpam-6811	249	15	x	x	X
ejpam-6811	249	16	such	such	ADJ
ejpam-6811	249	17	that	that	DET
ejpam-6811	249	18	db(x	db(x	ADJ
ejpam-6811	249	19	,	,	PUNCT
ejpam-6811	249	20	y	y	NOUN
ejpam-6811	249	21	)	)	PUNCT
ejpam-6811	249	22	=	=	PUNCT
ejpam-6811	249	23	|x−	|x−	PROPN
ejpam-6811	249	24	y|2	y|2	PROPN
ejpam-6811	249	25	and	and	CCONJ
ejpam-6811	249	26	d′b(x	d′b(x	PROPN
ejpam-6811	249	27	,	,	PUNCT
ejpam-6811	249	28	y	y	NOUN
ejpam-6811	249	29	)	)	PUNCT
ejpam-6811	249	30	=	=	SYM
ejpam-6811	249	31	r|x−	r|x−	PROPN
ejpam-6811	249	32	y|2	y|2	PROPN
ejpam-6811	249	33	,	,	PUNCT
ejpam-6811	249	34	where	where	SCONJ
ejpam-6811	249	35	r	r	NOUN
ejpam-6811	249	36	>	>	X
ejpam-6811	249	37	1	1	NUM
ejpam-6811	249	38	is	be	AUX
ejpam-6811	249	39	any	any	DET
ejpam-6811	249	40	constant	constant	ADJ
ejpam-6811	249	41	.	.	PUNCT
ejpam-6811	250	1	it	it	PRON
ejpam-6811	250	2	is	be	AUX
ejpam-6811	250	3	easy	easy	ADJ
ejpam-6811	250	4	to	to	PART
ejpam-6811	250	5	check	check	VERB
ejpam-6811	250	6	that	that	PRON
ejpam-6811	250	7	db	db	PROPN
ejpam-6811	250	8	and	and	CCONJ
ejpam-6811	250	9	d′b	d′b	PROPN
ejpam-6811	250	10	are	be	AUX
ejpam-6811	250	11	b	b	PRON
ejpam-6811	250	12	metrics	metric	NOUN
ejpam-6811	250	13	on	on	ADP
ejpam-6811	250	14	x	x	NOUN
ejpam-6811	250	15	,	,	PUNCT
ejpam-6811	250	16	also	also	ADV
ejpam-6811	250	17	db	db	VERB
ejpam-6811	250	18	<	<	X
ejpam-6811	250	19	d′b	d′b	PROPN
ejpam-6811	250	20	.	.	PUNCT
ejpam-6811	251	1	now	now	ADV
ejpam-6811	251	2	suppose	suppose	VERB
ejpam-6811	251	3	that	that	SCONJ
ejpam-6811	251	4	e(ḡ	e(ḡ	PROPN
ejpam-6811	251	5	)	)	PUNCT
ejpam-6811	251	6	=	=	SYM
ejpam-6811	251	7	{	{	PUNCT
ejpam-6811	251	8	(	(	PUNCT
ejpam-6811	251	9	x	x	NOUN
ejpam-6811	251	10	,	,	PUNCT
ejpam-6811	251	11	y	y	PROPN
ejpam-6811	251	12	)	)	PUNCT
ejpam-6811	251	13	:	:	PUNCT
ejpam-6811	252	1	x	x	X
ejpam-6811	252	2	=	=	PUNCT
ejpam-6811	252	3	y	y	PROPN
ejpam-6811	252	4	or	or	CCONJ
ejpam-6811	252	5	x	x	NOUN
ejpam-6811	252	6	,	,	PUNCT
ejpam-6811	252	7	y	y	PROPN
ejpam-6811	252	8	∈	∈	PROPN
ejpam-6811	253	1	[	[	X
ejpam-6811	253	2	0	0	NUM
ejpam-6811	253	3	,	,	PUNCT
ejpam-6811	253	4	1	1	NUM
ejpam-6811	253	5	]	]	PUNCT
ejpam-6811	253	6	with	with	ADP
ejpam-6811	253	7	x	x	SYM
ejpam-6811	253	8	≤	≤	NUM
ejpam-6811	253	9	y	y	NOUN
ejpam-6811	253	10	}	}	PUNCT
ejpam-6811	253	11	.	.	PUNCT
ejpam-6811	254	1	d.	d.	PROPN
ejpam-6811	254	2	e.	e.	PROPN
ejpam-6811	254	3	shehwar	shehwar	PROPN
ejpam-6811	254	4	sagheer	sagheer	PROPN
ejpam-6811	254	5	et	et	PROPN
ejpam-6811	254	6	al	al	PROPN
ejpam-6811	254	7	.	.	PUNCT
ejpam-6811	254	8	/	/	SYM
ejpam-6811	254	9	eur	eur	PROPN
ejpam-6811	254	10	.	.	PUNCT
ejpam-6811	255	1	j.	j.	PROPN
ejpam-6811	255	2	pure	pure	PROPN
ejpam-6811	255	3	appl	appl	PROPN
ejpam-6811	255	4	.	.	PROPN
ejpam-6811	255	5	math	math	PROPN
ejpam-6811	255	6	,	,	PUNCT
ejpam-6811	255	7	18	18	NUM
ejpam-6811	255	8	(	(	PUNCT
ejpam-6811	255	9	4	4	NUM
ejpam-6811	255	10	)	)	PUNCT
ejpam-6811	255	11	(	(	PUNCT
ejpam-6811	255	12	2025	2025	NUM
ejpam-6811	255	13	)	)	PUNCT
ejpam-6811	255	14	,	,	PUNCT
ejpam-6811	255	15	6811	6811	NUM
ejpam-6811	255	16	12	12	NUM
ejpam-6811	255	17	of	of	ADP
ejpam-6811	255	18	24	24	NUM
ejpam-6811	255	19	and	and	CCONJ
ejpam-6811	255	20	,	,	PUNCT
ejpam-6811	255	21	define	define	VERB
ejpam-6811	255	22	two	two	NUM
ejpam-6811	255	23	continuous	continuous	ADJ
ejpam-6811	255	24	self	self	NOUN
ejpam-6811	255	25	mappings	mapping	NOUN
ejpam-6811	255	26	on	on	ADP
ejpam-6811	255	27	x	x	PUNCT
ejpam-6811	255	28	as	as	ADP
ejpam-6811	255	29	follow	follow	VERB
ejpam-6811	255	30	sx	sx	PROPN
ejpam-6811	255	31	=	=	SYM
ejpam-6811	255	32	x2	x2	PROPN
ejpam-6811	255	33	and	and	CCONJ
ejpam-6811	255	34	tx	tx	PROPN
ejpam-6811	255	35	=	=	SYM
ejpam-6811	255	36	ln	ln	ADJ
ejpam-6811	255	37	(	(	PUNCT
ejpam-6811	255	38	1	1	NUM
ejpam-6811	256	1	+	+	NUM
ejpam-6811	256	2	x2	x2	PROPN
ejpam-6811	256	3	4	4	NUM
ejpam-6811	256	4	)	)	PUNCT
ejpam-6811	256	5	for	for	ADP
ejpam-6811	256	6	all	all	PRON
ejpam-6811	257	1	x.	x.	NOUN
ejpam-6811	257	2	now	now	ADV
ejpam-6811	257	3	,	,	PUNCT
ejpam-6811	257	4	consider	consider	VERB
ejpam-6811	257	5	(	(	PUNCT
ejpam-6811	257	6	sx	sx	PROPN
ejpam-6811	257	7	,	,	PUNCT
ejpam-6811	257	8	sy	sy	PROPN
ejpam-6811	257	9	)	)	PUNCT
ejpam-6811	257	10	∈	∈	PROPN
ejpam-6811	257	11	e(ḡ	e(ḡ	PROPN
ejpam-6811	257	12	)	)	PUNCT
ejpam-6811	257	13	,	,	PUNCT
ejpam-6811	257	14	note	note	VERB
ejpam-6811	257	15	that	that	SCONJ
ejpam-6811	257	16	if	if	SCONJ
ejpam-6811	257	17	x	x	X
ejpam-6811	257	18	=	=	SYM
ejpam-6811	257	19	y	y	PROPN
ejpam-6811	257	20	then	then	ADV
ejpam-6811	257	21	(	(	PUNCT
ejpam-6811	257	22	tx	tx	PROPN
ejpam-6811	257	23	,	,	PUNCT
ejpam-6811	257	24	ty	ty	INTJ
ejpam-6811	257	25	)	)	PUNCT
ejpam-6811	257	26	∈	∈	PROPN
ejpam-6811	257	27	e(ḡ	e(ḡ	PROPN
ejpam-6811	257	28	)	)	PUNCT
ejpam-6811	257	29	.	.	PUNCT
ejpam-6811	258	1	also	also	ADV
ejpam-6811	258	2	,	,	PUNCT
ejpam-6811	258	3	if	if	SCONJ
ejpam-6811	258	4	(	(	PUNCT
ejpam-6811	258	5	sx	sx	INTJ
ejpam-6811	258	6	,	,	PUNCT
ejpam-6811	258	7	sy	sy	PROPN
ejpam-6811	258	8	)	)	PUNCT
ejpam-6811	258	9	∈	∈	PROPN
ejpam-6811	258	10	e(ḡ	e(ḡ	PROPN
ejpam-6811	258	11	)	)	PUNCT
ejpam-6811	258	12	and	and	CCONJ
ejpam-6811	258	13	sx	sx	PROPN
ejpam-6811	258	14	≤	≤	PROPN
ejpam-6811	258	15	sy	sy	INTJ
ejpam-6811	258	16	then	then	ADV
ejpam-6811	258	17	sx	sx	PROPN
ejpam-6811	258	18	=	=	SYM
ejpam-6811	258	19	x2	x2	PROPN
ejpam-6811	258	20	,	,	PUNCT
ejpam-6811	258	21	sy	sy	NOUN
ejpam-6811	258	22	=	=	PUNCT
ejpam-6811	258	23	y2	y2	PROPN
ejpam-6811	258	24	∈	∈	PROPN
ejpam-6811	259	1	[	[	X
ejpam-6811	259	2	0	0	NUM
ejpam-6811	259	3	,	,	PUNCT
ejpam-6811	259	4	1	1	NUM
ejpam-6811	259	5	]	]	PUNCT
ejpam-6811	259	6	and	and	CCONJ
ejpam-6811	259	7	x2	x2	PROPN
ejpam-6811	259	8	=	=	PUNCT
ejpam-6811	259	9	sx	sx	PROPN
ejpam-6811	259	10	≤	≤	PUNCT
ejpam-6811	259	11	sy	sy	NOUN
ejpam-6811	259	12	=	=	PUNCT
ejpam-6811	259	13	y2	y2	PROPN
ejpam-6811	259	14	.	.	PUNCT
ejpam-6811	260	1	therefore	therefore	ADV
ejpam-6811	260	2	,	,	PUNCT
ejpam-6811	260	3	we	we	PRON
ejpam-6811	260	4	have	have	VERB
ejpam-6811	260	5	tx	tx	NOUN
ejpam-6811	260	6	=	=	PUNCT
ejpam-6811	260	7	ln	ln	ADJ
ejpam-6811	260	8	(	(	PUNCT
ejpam-6811	260	9	1	1	NUM
ejpam-6811	261	1	+	+	NUM
ejpam-6811	261	2	x2	x2	PROPN
ejpam-6811	261	3	4	4	X
ejpam-6811	261	4	)	)	PUNCT
ejpam-6811	261	5	≤	≤	NOUN
ejpam-6811	262	1	ln	ln	ADV
ejpam-6811	262	2	(	(	PUNCT
ejpam-6811	262	3	1	1	NUM
ejpam-6811	262	4	+	+	CCONJ
ejpam-6811	262	5	y2	y2	NOUN
ejpam-6811	262	6	4	4	NUM
ejpam-6811	262	7	)	)	PUNCT
ejpam-6811	263	1	=	=	SYM
ejpam-6811	263	2	ty	ty	PROPN
ejpam-6811	263	3	,	,	PUNCT
ejpam-6811	263	4	showing	show	VERB
ejpam-6811	263	5	that	that	SCONJ
ejpam-6811	263	6	(	(	PUNCT
ejpam-6811	263	7	tx	tx	PROPN
ejpam-6811	263	8	,	,	PUNCT
ejpam-6811	263	9	ty	ty	INTJ
ejpam-6811	263	10	)	)	PUNCT
ejpam-6811	263	11	∈	∈	PROPN
ejpam-6811	263	12	e(ḡ	e(ḡ	PROPN
ejpam-6811	263	13	)	)	PUNCT
ejpam-6811	263	14	.	.	PUNCT
ejpam-6811	264	1	next	next	ADV
ejpam-6811	264	2	,	,	PUNCT
ejpam-6811	264	3	define	define	VERB
ejpam-6811	264	4	φ(x	φ(x	NOUN
ejpam-6811	264	5	)	)	PUNCT
ejpam-6811	264	6	=	=	SYM
ejpam-6811	265	1	x	x	SYM
ejpam-6811	265	2	4	4	NUM
ejpam-6811	265	3	and	and	CCONJ
ejpam-6811	265	4	ψ	ψ	X
ejpam-6811	265	5	:	:	PUNCT
ejpam-6811	265	6	x	x	PROPN
ejpam-6811	265	7	×x	×x	X
ejpam-6811	265	8	→	→	SYM
ejpam-6811	265	9	[	[	X
ejpam-6811	265	10	0	0	NUM
ejpam-6811	265	11	,	,	PUNCT
ejpam-6811	265	12	1	1	NUM
ejpam-6811	265	13	]	]	PUNCT
ejpam-6811	265	14	as	as	ADP
ejpam-6811	265	15	ψ(x	ψ(x	PROPN
ejpam-6811	265	16	,	,	PUNCT
ejpam-6811	265	17	y	y	NOUN
ejpam-6811	265	18	)	)	PUNCT
ejpam-6811	265	19	=	=	PUNCT
ejpam-6811	265	20			PUNCT
ejpam-6811	265	21	ln	ln	ADJ
ejpam-6811	265	22	(	(	PUNCT
ejpam-6811	265	23	2	2	NUM
ejpam-6811	265	24	+	+	NUM
ejpam-6811	265	25	√	√	NUM
ejpam-6811	265	26	|x−y|	|x−y|	ADP
ejpam-6811	265	27	2	2	NUM
ejpam-6811	265	28	)	)	PUNCT
ejpam-6811	265	29	√	√	NUM
ejpam-6811	265	30	|x−y|	|x−y|	NOUN
ejpam-6811	265	31	,	,	PUNCT
ejpam-6811	265	32	if	if	SCONJ
ejpam-6811	265	33	|x−	|x−	NOUN
ejpam-6811	265	34	y|	y|	VERB
ejpam-6811	265	35	>	>	X
ejpam-6811	265	36	1	1	NUM
ejpam-6811	265	37	0	0	NUM
ejpam-6811	265	38	,	,	PUNCT
ejpam-6811	265	39	if	if	SCONJ
ejpam-6811	265	40	|x−	|x−	PROPN
ejpam-6811	265	41	y|	y|	NOUN
ejpam-6811	265	42	∈	∈	PROPN
ejpam-6811	266	1	[	[	X
ejpam-6811	266	2	0	0	NUM
ejpam-6811	266	3	,	,	PUNCT
ejpam-6811	266	4	1	1	NUM
ejpam-6811	266	5	)	)	PUNCT
ejpam-6811	266	6	.	.	PUNCT
ejpam-6811	267	1	now	now	ADV
ejpam-6811	267	2	,	,	PUNCT
ejpam-6811	267	3	we	we	PRON
ejpam-6811	267	4	have	have	AUX
ejpam-6811	267	5	φ(db(tx	φ(db(tx	VERB
ejpam-6811	267	6	,	,	PUNCT
ejpam-6811	267	7	ty	ty	INTJ
ejpam-6811	267	8	)	)	PUNCT
ejpam-6811	267	9	=	=	PUNCT
ejpam-6811	268	1	|	|	ADV
ejpam-6811	268	2	ln(1	ln(1	PROPN
ejpam-6811	268	3	+	+	CCONJ
ejpam-6811	268	4	x2	x2	PROPN
ejpam-6811	268	5	4	4	NUM
ejpam-6811	268	6	)	)	PUNCT
ejpam-6811	268	7	−	−	PROPN
ejpam-6811	269	1	ln(1	ln(1	NOUN
ejpam-6811	269	2	+	+	CCONJ
ejpam-6811	269	3	y2	y2	PROPN
ejpam-6811	269	4	4	4	NUM
ejpam-6811	269	5	)	)	PUNCT
ejpam-6811	269	6	|	|	ADV
ejpam-6811	269	7	2	2	NUM
ejpam-6811	269	8	4	4	NUM
ejpam-6811	269	9	=	=	SYM
ejpam-6811	269	10	(	(	PUNCT
ejpam-6811	269	11	ln(1	ln(1	NOUN
ejpam-6811	269	12	+	+	CCONJ
ejpam-6811	269	13	y2	y2	PROPN
ejpam-6811	269	14	4	4	NUM
ejpam-6811	269	15	)	)	PUNCT
ejpam-6811	269	16	−	−	PROPN
ejpam-6811	270	1	ln(1	ln(1	NOUN
ejpam-6811	270	2	+	+	CCONJ
ejpam-6811	270	3	x2	x2	PROPN
ejpam-6811	270	4	4	4	NUM
ejpam-6811	270	5	)	)	PUNCT
ejpam-6811	270	6	)	)	PUNCT
ejpam-6811	270	7	2	2	NUM
ejpam-6811	270	8	4	4	NUM
ejpam-6811	270	9	=	=	SYM
ejpam-6811	270	10	ln	ln	NOUN
ejpam-6811	270	11	(	(	PUNCT
ejpam-6811	270	12	2	2	NUM
ejpam-6811	270	13	+	+	NUM
ejpam-6811	270	14	y2	y2	NOUN
ejpam-6811	270	15	2	2	NUM
ejpam-6811	270	16	1+x2	1+x2	NUM
ejpam-6811	270	17	4	4	NUM
ejpam-6811	270	18	)	)	PUNCT
ejpam-6811	270	19	4	4	NUM
ejpam-6811	270	20	=	=	SYM
ejpam-6811	270	21	ln	ln	NOUN
ejpam-6811	270	22	(	(	PUNCT
ejpam-6811	270	23	2	2	NUM
ejpam-6811	270	24	+	+	CCONJ
ejpam-6811	270	25	y2	y2	SYM
ejpam-6811	270	26	2	2	NUM
ejpam-6811	270	27	−x2	−x2	PROPN
ejpam-6811	270	28	2	2	NUM
ejpam-6811	270	29	1+x2	1+x2	NUM
ejpam-6811	270	30	4	4	NUM
ejpam-6811	270	31	)	)	PUNCT
ejpam-6811	270	32	4	4	NUM
ejpam-6811	270	33	≤	≤	NOUN
ejpam-6811	270	34	ln(2	ln(2	PROPN
ejpam-6811	270	35	+	+	CCONJ
ejpam-6811	270	36	∣∣y2	∣∣y2	NOUN
ejpam-6811	270	37	2	2	NUM
ejpam-6811	270	38	−	−	NOUN
ejpam-6811	270	39	x2	x2	NOUN
ejpam-6811	270	40	2	2	NUM
ejpam-6811	270	41	∣∣	∣∣	X
ejpam-6811	270	42	)	)	PUNCT
ejpam-6811	270	43	4	4	NUM
ejpam-6811	271	1	=	=	SYM
ejpam-6811	271	2	ln(2	ln(2	NOUN
ejpam-6811	271	3	+	+	CCONJ
ejpam-6811	271	4	1	1	NUM
ejpam-6811	271	5	2	2	NUM
ejpam-6811	271	6	∣∣y2	∣∣y2	NOUN
ejpam-6811	271	7	−	−	NOUN
ejpam-6811	271	8	x2	x2	PROPN
ejpam-6811	271	9	∣∣	∣∣	X
ejpam-6811	271	10	)	)	PUNCT
ejpam-6811	271	11	4	4	NUM
ejpam-6811	271	12	∣∣y2	∣∣y2	NOUN
ejpam-6811	272	1	−	−	PROPN
ejpam-6811	273	1	x2	x2	INTJ
ejpam-6811	273	2	∣∣∣∣y2	∣∣∣∣y2	PUNCT
ejpam-6811	274	1	−	−	PROPN
ejpam-6811	274	2	x2	x2	PROPN
ejpam-6811	274	3	∣∣	∣∣	X
ejpam-6811	274	4	≤	≤	X
ejpam-6811	275	1	ln(2	ln(2	NOUN
ejpam-6811	275	2	+	+	CCONJ
ejpam-6811	275	3	1	1	NUM
ejpam-6811	275	4	2	2	NUM
ejpam-6811	275	5	∣∣y2	∣∣y2	NOUN
ejpam-6811	275	6	−	−	PROPN
ejpam-6811	276	1	x2	x2	INTJ
ejpam-6811	276	2	∣∣)∣∣y2	∣∣)∣∣y2	NUM
ejpam-6811	276	3	−	−	PROPN
ejpam-6811	276	4	x2	x2	PROPN
ejpam-6811	276	5	∣∣	∣∣	NUM
ejpam-6811	276	6	∣∣y2	∣∣y2	ADV
ejpam-6811	276	7	−	−	PROPN
ejpam-6811	276	8	x2	x2	PROPN
ejpam-6811	276	9	∣∣2	∣∣2	PROPN
ejpam-6811	276	10	4	4	NUM
ejpam-6811	276	11	=	=	SYM
ejpam-6811	276	12	ψ(sx	ψ(sx	PROPN
ejpam-6811	276	13	,	,	PUNCT
ejpam-6811	276	14	sy)φ(db(sx	sy)φ(db(sx	PROPN
ejpam-6811	276	15	,	,	PUNCT
ejpam-6811	276	16	sy	sy	NOUN
ejpam-6811	276	17	)	)	PUNCT
ejpam-6811	276	18	,	,	PUNCT
ejpam-6811	276	19	showing	show	VERB
ejpam-6811	276	20	that	that	SCONJ
ejpam-6811	276	21	the	the	DET
ejpam-6811	276	22	contraction	contraction	NOUN
ejpam-6811	276	23	condition	condition	NOUN
ejpam-6811	276	24	holds	hold	VERB
ejpam-6811	276	25	.	.	PUNCT
ejpam-6811	277	1	now	now	ADV
ejpam-6811	277	2	,	,	PUNCT
ejpam-6811	277	3	as	as	ADP
ejpam-6811	277	4	db	db	PROPN
ejpam-6811	277	5	<	<	X
ejpam-6811	277	6	d′b	d′b	X
ejpam-6811	277	7	we	we	PRON
ejpam-6811	277	8	will	will	AUX
ejpam-6811	277	9	show	show	VERB
ejpam-6811	277	10	that	that	PRON
ejpam-6811	277	11	t	t	NOUN
ejpam-6811	277	12	:	:	PUNCT
ejpam-6811	277	13	(	(	PUNCT
ejpam-6811	277	14	x	x	NOUN
ejpam-6811	277	15	,	,	PUNCT
ejpam-6811	277	16	db	db	PROPN
ejpam-6811	277	17	)	)	PUNCT
ejpam-6811	277	18	→	→	SYM
ejpam-6811	277	19	(	(	PUNCT
ejpam-6811	277	20	x	x	NOUN
ejpam-6811	277	21	,	,	PUNCT
ejpam-6811	277	22	d′b	d′b	PROPN
ejpam-6811	277	23	)	)	PUNCT
ejpam-6811	277	24	is	be	AUX
ejpam-6811	277	25	s	s	NOUN
ejpam-6811	277	26	-	-	NOUN
ejpam-6811	277	27	cauchy	cauchy	NOUN
ejpam-6811	277	28	.	.	PUNCT
ejpam-6811	278	1	if	if	SCONJ
ejpam-6811	278	2	for	for	ADP
ejpam-6811	278	3	ε	ε	PROPN
ejpam-6811	278	4	>	>	X
ejpam-6811	278	5	0	0	PUNCT
ejpam-6811	279	1	the	the	DET
ejpam-6811	279	2	sequence	sequence	NOUN
ejpam-6811	279	3	{	{	PUNCT
ejpam-6811	279	4	xn	xn	NOUN
ejpam-6811	279	5	}	}	PUNCT
ejpam-6811	279	6	∈	∈	PROPN
ejpam-6811	279	7	x	x	PUNCT
ejpam-6811	279	8	with	with	ADP
ejpam-6811	279	9	{	{	PUNCT
ejpam-6811	279	10	sxn	sxn	NOUN
ejpam-6811	279	11	}	}	PUNCT
ejpam-6811	279	12	being	be	AUX
ejpam-6811	279	13	cauchy	cauchy	ADJ
ejpam-6811	279	14	in	in	ADP
ejpam-6811	279	15	(	(	PUNCT
ejpam-6811	279	16	x	x	NOUN
ejpam-6811	279	17	,	,	PUNCT
ejpam-6811	279	18	db	db	PROPN
ejpam-6811	279	19	)	)	PUNCT
ejpam-6811	279	20	there	there	PRON
ejpam-6811	279	21	exists	exist	VERB
ejpam-6811	279	22	n0	n0	PROPN
ejpam-6811	279	23	∈	∈	PROPN
ejpam-6811	279	24	n	n	PRON
ejpam-6811	279	25	such	such	ADJ
ejpam-6811	279	26	that	that	DET
ejpam-6811	279	27	db(sxn	db(sxn	NOUN
ejpam-6811	279	28	,	,	PUNCT
ejpam-6811	279	29	sxk	sxk	PROPN
ejpam-6811	279	30	)	)	PUNCT
ejpam-6811	279	31	<	<	X
ejpam-6811	279	32	ε	ε	PROPN
ejpam-6811	279	33	r	r	NOUN
ejpam-6811	279	34	∀	∀	X
ejpam-6811	279	35	n	n	CCONJ
ejpam-6811	279	36	,	,	PUNCT
ejpam-6811	279	37	k	k	PROPN
ejpam-6811	279	38	≥	≥	PROPN
ejpam-6811	279	39	n0	n0	NUM
ejpam-6811	279	40	.	.	PUNCT
ejpam-6811	280	1	d.	d.	PROPN
ejpam-6811	280	2	e.	e.	PROPN
ejpam-6811	280	3	shehwar	shehwar	PROPN
ejpam-6811	280	4	sagheer	sagheer	PROPN
ejpam-6811	280	5	et	et	PROPN
ejpam-6811	280	6	al	al	PROPN
ejpam-6811	280	7	.	.	PUNCT
ejpam-6811	280	8	/	/	SYM
ejpam-6811	280	9	eur	eur	PROPN
ejpam-6811	280	10	.	.	PUNCT
ejpam-6811	281	1	j.	j.	PROPN
ejpam-6811	281	2	pure	pure	PROPN
ejpam-6811	281	3	appl	appl	PROPN
ejpam-6811	281	4	.	.	PROPN
ejpam-6811	281	5	math	math	PROPN
ejpam-6811	281	6	,	,	PUNCT
ejpam-6811	281	7	18	18	NUM
ejpam-6811	281	8	(	(	PUNCT
ejpam-6811	281	9	4	4	NUM
ejpam-6811	281	10	)	)	PUNCT
ejpam-6811	281	11	(	(	PUNCT
ejpam-6811	281	12	2025	2025	NUM
ejpam-6811	281	13	)	)	PUNCT
ejpam-6811	281	14	,	,	PUNCT
ejpam-6811	281	15	6811	6811	NUM
ejpam-6811	281	16	13	13	NUM
ejpam-6811	281	17	of	of	ADP
ejpam-6811	281	18	24	24	NUM
ejpam-6811	281	19	therefore	therefore	ADV
ejpam-6811	281	20	,	,	PUNCT
ejpam-6811	281	21	d′b(txn	d′b(txn	PROPN
ejpam-6811	281	22	,	,	PUNCT
ejpam-6811	281	23	txk	txk	ADJ
ejpam-6811	281	24	)	)	PUNCT
ejpam-6811	281	25	=	=	SYM
ejpam-6811	282	1	r	r	NOUN
ejpam-6811	282	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6811	283	1	ln(1	ln(1	NOUN
ejpam-6811	284	1	+	+	CCONJ
ejpam-6811	285	1	(	(	PUNCT
ejpam-6811	285	2	xn	xn	X
ejpam-6811	285	3	)	)	PUNCT
ejpam-6811	285	4	2	2	NUM
ejpam-6811	285	5	4	4	NUM
ejpam-6811	285	6	)	)	PUNCT
ejpam-6811	285	7	−	−	PROPN
ejpam-6811	286	1	ln(1	ln(1	NOUN
ejpam-6811	286	2	+	+	CCONJ
ejpam-6811	286	3	(	(	PUNCT
ejpam-6811	286	4	xk	xk	NOUN
ejpam-6811	286	5	)	)	PUNCT
ejpam-6811	286	6	2	2	NUM
ejpam-6811	286	7	4	4	NUM
ejpam-6811	286	8	)	)	PUNCT
ejpam-6811	286	9	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-6811	286	10	=	=	SYM
ejpam-6811	286	11	r	r	NOUN
ejpam-6811	286	12	(	(	PUNCT
ejpam-6811	286	13	ln(1	ln(1	NOUN
ejpam-6811	286	14	+	+	CCONJ
ejpam-6811	286	15	(	(	PUNCT
ejpam-6811	286	16	xk	xk	NOUN
ejpam-6811	286	17	)	)	PUNCT
ejpam-6811	286	18	2	2	NUM
ejpam-6811	286	19	4	4	NUM
ejpam-6811	286	20	)	)	PUNCT
ejpam-6811	286	21	−	−	PROPN
ejpam-6811	287	1	ln(1	ln(1	NOUN
ejpam-6811	287	2	+	+	CCONJ
ejpam-6811	287	3	(	(	PUNCT
ejpam-6811	287	4	xn	xn	X
ejpam-6811	287	5	)	)	PUNCT
ejpam-6811	287	6	2	2	NUM
ejpam-6811	287	7	4	4	NUM
ejpam-6811	287	8	)	)	PUNCT
ejpam-6811	287	9	)	)	PUNCT
ejpam-6811	287	10	2	2	NUM
ejpam-6811	288	1	=	=	SYM
ejpam-6811	288	2	r	r	NOUN
ejpam-6811	288	3	ln	ln	NOUN
ejpam-6811	288	4	(	(	PUNCT
ejpam-6811	288	5	2	2	NUM
ejpam-6811	288	6	+	+	CCONJ
ejpam-6811	288	7	(	(	PUNCT
ejpam-6811	288	8	xk	xk	ADJ
ejpam-6811	288	9	)	)	PUNCT
ejpam-6811	288	10	2	2	NUM
ejpam-6811	288	11	2	2	NUM
ejpam-6811	288	12	1	1	NUM
ejpam-6811	288	13	+	+	CCONJ
ejpam-6811	288	14	(	(	PUNCT
ejpam-6811	288	15	xn)2	xn)2	PROPN
ejpam-6811	288	16	4	4	NUM
ejpam-6811	288	17	)	)	PUNCT
ejpam-6811	288	18	=	=	SYM
ejpam-6811	288	19	r	r	NOUN
ejpam-6811	288	20	ln	ln	NOUN
ejpam-6811	288	21	(	(	PUNCT
ejpam-6811	288	22	2	2	NUM
ejpam-6811	288	23	+	+	CCONJ
ejpam-6811	288	24	(	(	PUNCT
ejpam-6811	288	25	xk	xk	ADJ
ejpam-6811	288	26	)	)	PUNCT
ejpam-6811	288	27	2	2	NUM
ejpam-6811	288	28	2	2	NUM
ejpam-6811	288	29	−	−	NOUN
ejpam-6811	288	30	(	(	PUNCT
ejpam-6811	288	31	xn)2	xn)2	PROPN
ejpam-6811	288	32	2	2	NUM
ejpam-6811	288	33	1	1	NUM
ejpam-6811	288	34	+	+	CCONJ
ejpam-6811	288	35	(	(	PUNCT
ejpam-6811	288	36	xn)2	xn)2	PROPN
ejpam-6811	288	37	4	4	NUM
ejpam-6811	288	38	)	)	PUNCT
ejpam-6811	288	39	≤	≤	NOUN
ejpam-6811	289	1	r	r	NOUN
ejpam-6811	289	2	ln	ln	NOUN
ejpam-6811	289	3	(	(	PUNCT
ejpam-6811	289	4	2	2	NUM
ejpam-6811	289	5	+	+	NUM
ejpam-6811	289	6	∣∣∣∣(xk)22	∣∣∣∣(xk)22	NOUN
ejpam-6811	289	7	−	−	PROPN
ejpam-6811	289	8	(	(	PUNCT
ejpam-6811	289	9	xn	xn	PROPN
ejpam-6811	289	10	)	)	PUNCT
ejpam-6811	289	11	2	2	NUM
ejpam-6811	289	12	2	2	NUM
ejpam-6811	289	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6811	289	14	)	)	PUNCT
ejpam-6811	289	15	=	=	SYM
ejpam-6811	290	1	r	r	NOUN
ejpam-6811	290	2	ln(2	ln(2	NOUN
ejpam-6811	290	3	+	+	CCONJ
ejpam-6811	290	4	1	1	NUM
ejpam-6811	290	5	2	2	NUM
ejpam-6811	290	6	∣∣(xk)2	∣∣(xk)2	NOUN
ejpam-6811	290	7	−	−	PROPN
ejpam-6811	290	8	(	(	PUNCT
ejpam-6811	290	9	xn	xn	X
ejpam-6811	290	10	)	)	PUNCT
ejpam-6811	290	11	2	2	NUM
ejpam-6811	290	12	∣∣)∣∣(xk)2	∣∣)∣∣(xk)2	NUM
ejpam-6811	290	13	−	−	PROPN
ejpam-6811	290	14	(	(	PUNCT
ejpam-6811	290	15	xn)2	xn)2	PROPN
ejpam-6811	290	16	∣∣2	∣∣2	PROPN
ejpam-6811	290	17	∣∣(xk)2	∣∣(xk)2	NOUN
ejpam-6811	290	18	−	−	PROPN
ejpam-6811	290	19	(	(	PUNCT
ejpam-6811	290	20	xn	xn	X
ejpam-6811	290	21	)	)	PUNCT
ejpam-6811	290	22	2	2	NUM
ejpam-6811	290	23	∣∣2	∣∣2	PROPN
ejpam-6811	290	24	≤	≤	NOUN
ejpam-6811	290	25	r	r	NOUN
ejpam-6811	290	26	∣∣(xk)2	∣∣(xk)2	NOUN
ejpam-6811	290	27	−	−	PROPN
ejpam-6811	290	28	(	(	PUNCT
ejpam-6811	290	29	xn	xn	X
ejpam-6811	290	30	)	)	PUNCT
ejpam-6811	290	31	2	2	NUM
ejpam-6811	290	32	∣∣2	∣∣2	PROPN
ejpam-6811	290	33	=	=	PUNCT
ejpam-6811	290	34	rdb(sxn	rdb(sxn	NOUN
ejpam-6811	290	35	,	,	PUNCT
ejpam-6811	290	36	sxk	sxk	PROPN
ejpam-6811	290	37	)	)	PUNCT
ejpam-6811	290	38	<	<	X
ejpam-6811	290	39	r	r	NOUN
ejpam-6811	290	40	ε	ε	PROPN
ejpam-6811	290	41	r	r	NOUN
ejpam-6811	290	42	=	=	SYM
ejpam-6811	290	43	ε	ε	PROPN
ejpam-6811	290	44	,	,	PUNCT
ejpam-6811	290	45	showing	show	VERB
ejpam-6811	290	46	that	that	SCONJ
ejpam-6811	290	47	t	t	PROPN
ejpam-6811	290	48	is	be	AUX
ejpam-6811	290	49	s−cauchy	s−cauchy	NOUN
ejpam-6811	290	50	.	.	PUNCT
ejpam-6811	291	1	also	also	ADV
ejpam-6811	291	2	,	,	PUNCT
ejpam-6811	291	3	by	by	ADP
ejpam-6811	291	4	using	use	VERB
ejpam-6811	291	5	the	the	DET
ejpam-6811	291	6	fact	fact	NOUN
ejpam-6811	291	7	that	that	SCONJ
ejpam-6811	291	8	t	t	PROPN
ejpam-6811	291	9	and	and	CCONJ
ejpam-6811	291	10	s	s	VERB
ejpam-6811	291	11	are	be	AUX
ejpam-6811	291	12	db	db	ADJ
ejpam-6811	291	13	-	-	PUNCT
ejpam-6811	291	14	compatible	compatible	ADJ
ejpam-6811	291	15	,	,	PUNCT
ejpam-6811	291	16	we	we	PRON
ejpam-6811	291	17	may	may	AUX
ejpam-6811	291	18	write	write	VERB
ejpam-6811	291	19	lim	lim	PROPN
ejpam-6811	291	20	n→∞	n→∞	NUM
ejpam-6811	292	1	sxn	sxn	NOUN
ejpam-6811	292	2	=	=	PROPN
ejpam-6811	292	3	lim	lim	PROPN
ejpam-6811	292	4	n→∞	n→∞	X
ejpam-6811	293	1	txn	txn	NOUN
ejpam-6811	293	2	=	=	SYM
ejpam-6811	293	3	x	x	NOUN
ejpam-6811	293	4	,	,	PUNCT
ejpam-6811	293	5	then	then	ADV
ejpam-6811	293	6	ln(1	ln(1	PROPN
ejpam-6811	293	7	+	+	CCONJ
ejpam-6811	293	8	x	x	SYM
ejpam-6811	293	9	4	4	X
ejpam-6811	293	10	)	)	PUNCT
ejpam-6811	293	11	=	=	PUNCT
ejpam-6811	294	1	x	x	ADP
ejpam-6811	294	2	this	this	PRON
ejpam-6811	294	3	implies	imply	VERB
ejpam-6811	294	4	x	x	X
ejpam-6811	294	5	=	=	SYM
ejpam-6811	294	6	0	0	PROPN
ejpam-6811	294	7	.	.	PUNCT
ejpam-6811	295	1	and	and	CCONJ
ejpam-6811	295	2	letting	let	VERB
ejpam-6811	295	3	n→	n→	PUNCT
ejpam-6811	295	4	∞	∞	PROPN
ejpam-6811	295	5	we	we	PRON
ejpam-6811	295	6	have	have	VERB
ejpam-6811	295	7	d′b(stxn	d′b(stxn	NOUN
ejpam-6811	295	8	,	,	PUNCT
ejpam-6811	295	9	tsxn	tsxn	NOUN
ejpam-6811	295	10	)	)	PUNCT
ejpam-6811	296	1	=	=	SYM
ejpam-6811	296	2	r	r	NOUN
ejpam-6811	296	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6811	296	4	(	(	PUNCT
ejpam-6811	296	5	ln	ln	NOUN
ejpam-6811	296	6	(	(	PUNCT
ejpam-6811	296	7	1	1	NUM
ejpam-6811	296	8	+	+	CCONJ
ejpam-6811	296	9	(	(	PUNCT
ejpam-6811	296	10	xn	xn	X
ejpam-6811	296	11	)	)	PUNCT
ejpam-6811	296	12	2	2	NUM
ejpam-6811	296	13	4	4	NUM
ejpam-6811	296	14	)	)	PUNCT
ejpam-6811	296	15	)	)	PUNCT
ejpam-6811	296	16	2	2	NUM
ejpam-6811	296	17	−	−	NOUN
ejpam-6811	296	18	ln	ln	NOUN
ejpam-6811	296	19	(	(	PUNCT
ejpam-6811	296	20	1	1	NUM
ejpam-6811	296	21	+	+	CCONJ
ejpam-6811	296	22	(	(	PUNCT
ejpam-6811	296	23	xn	xn	X
ejpam-6811	296	24	)	)	PUNCT
ejpam-6811	296	25	4	4	NUM
ejpam-6811	296	26	4	4	NUM
ejpam-6811	296	27	)	)	PUNCT
ejpam-6811	296	28	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-6811	296	29	→	→	SYM
ejpam-6811	296	30	0	0	NUM
ejpam-6811	296	31	.	.	PUNCT
ejpam-6811	297	1	finally	finally	ADV
ejpam-6811	297	2	,	,	PUNCT
ejpam-6811	297	3	we	we	PRON
ejpam-6811	297	4	have	have	AUX
ejpam-6811	297	5	(	(	PUNCT
ejpam-6811	297	6	s0	s0	PROPN
ejpam-6811	297	7	,	,	PUNCT
ejpam-6811	297	8	t0	t0	PROPN
ejpam-6811	297	9	)	)	PUNCT
ejpam-6811	297	10	=	=	SYM
ejpam-6811	297	11	(	(	PUNCT
ejpam-6811	297	12	0	0	NUM
ejpam-6811	297	13	,	,	PUNCT
ejpam-6811	297	14	0	0	NUM
ejpam-6811	297	15	)	)	PUNCT
ejpam-6811	297	16	belongs	belong	VERB
ejpam-6811	297	17	to	to	PART
ejpam-6811	297	18	set	set	VERB
ejpam-6811	297	19	of	of	ADP
ejpam-6811	297	20	edges	edge	NOUN
ejpam-6811	297	21	,	,	PUNCT
ejpam-6811	297	22	that	that	ADV
ejpam-6811	297	23	is	is	ADV
ejpam-6811	297	24	,	,	PUNCT
ejpam-6811	297	25	v	v	X
ejpam-6811	297	26	(	(	PUNCT
ejpam-6811	297	27	t	t	PROPN
ejpam-6811	297	28	,	,	PUNCT
ejpam-6811	297	29	s	s	NOUN
ejpam-6811	297	30	)	)	PUNCT
ejpam-6811	297	31	6=	6=	ADP
ejpam-6811	297	32	⇒	⇒	PROPN
ejpam-6811	297	33	c(t	c(t	PROPN
ejpam-6811	297	34	,	,	PUNCT
ejpam-6811	297	35	s	s	NOUN
ejpam-6811	297	36	)	)	PUNCT
ejpam-6811	297	37	6=	6=	NUM
ejpam-6811	297	38	.	.	PUNCT
ejpam-6811	298	1	now	now	ADV
ejpam-6811	298	2	,	,	PUNCT
ejpam-6811	298	3	we	we	PRON
ejpam-6811	298	4	will	will	AUX
ejpam-6811	298	5	prove	prove	VERB
ejpam-6811	298	6	that	that	SCONJ
ejpam-6811	298	7	our	our	PRON
ejpam-6811	298	8	results	result	NOUN
ejpam-6811	298	9	can	can	AUX
ejpam-6811	298	10	be	be	AUX
ejpam-6811	298	11	used	use	VERB
ejpam-6811	298	12	to	to	PART
ejpam-6811	298	13	analyze	analyze	VERB
ejpam-6811	298	14	the	the	DET
ejpam-6811	298	15	existence	existence	NOUN
ejpam-6811	298	16	of	of	ADP
ejpam-6811	298	17	solutions	solution	NOUN
ejpam-6811	298	18	for	for	ADP
ejpam-6811	298	19	fractional	fractional	ADJ
ejpam-6811	298	20	boundary	boundary	ADJ
ejpam-6811	298	21	value	value	NOUN
ejpam-6811	298	22	problems	problem	NOUN
ejpam-6811	298	23	of	of	ADP
ejpam-6811	298	24	the	the	DET
ejpam-6811	298	25	caputo	caputo	PROPN
ejpam-6811	298	26	variety	variety	NOUN
ejpam-6811	298	27	with	with	ADP
ejpam-6811	298	28	fractional	fractional	ADJ
ejpam-6811	298	29	order	order	NOUN
ejpam-6811	298	30	γ	γ	NOUN
ejpam-6811	298	31	.	.	PUNCT
ejpam-6811	299	1	here	here	ADV
ejpam-6811	299	2	,	,	PUNCT
ejpam-6811	299	3	we	we	PRON
ejpam-6811	299	4	have	have	VERB
ejpam-6811	299	5	γ	γ	X
ejpam-6811	299	6	∈	∈	PROPN
ejpam-6811	299	7	(	(	PUNCT
ejpam-6811	299	8	n−	n−	NOUN
ejpam-6811	299	9	1	1	NUM
ejpam-6811	299	10	,	,	PUNCT
ejpam-6811	299	11	n	n	CCONJ
ejpam-6811	299	12	]	]	PUNCT
ejpam-6811	299	13	where	where	SCONJ
ejpam-6811	299	14	the	the	DET
ejpam-6811	299	15	integer	integer	NOUN
ejpam-6811	299	16	n	n	PRON
ejpam-6811	299	17	is	be	AUX
ejpam-6811	299	18	such	such	ADJ
ejpam-6811	299	19	that	that	SCONJ
ejpam-6811	299	20	n	n	CCONJ
ejpam-6811	299	21	≥	≥	NOUN
ejpam-6811	299	22	2	2	NUM
ejpam-6811	299	23	.	.	PUNCT
ejpam-6811	299	24	let	let	VERB
ejpam-6811	299	25	q(x	q(x	NOUN
ejpam-6811	299	26	)	)	PUNCT
ejpam-6811	299	27	be	be	AUX
ejpam-6811	299	28	a	a	DET
ejpam-6811	299	29	continuous	continuous	ADJ
ejpam-6811	299	30	function	function	NOUN
ejpam-6811	299	31	and	and	CCONJ
ejpam-6811	299	32	γ	γ	NOUN
ejpam-6811	299	33	be	be	AUX
ejpam-6811	299	34	a	a	DET
ejpam-6811	299	35	real	real	ADJ
ejpam-6811	299	36	number	number	NOUN
ejpam-6811	299	37	.	.	PUNCT
ejpam-6811	300	1	the	the	DET
ejpam-6811	300	2	γ	γ	PROPN
ejpam-6811	300	3	order	order	NOUN
ejpam-6811	300	4	caputo	caputo	PROPN
ejpam-6811	300	5	derivative	derivative	NOUN
ejpam-6811	300	6	is	be	AUX
ejpam-6811	300	7	as	as	SCONJ
ejpam-6811	300	8	follows	follow	VERB
ejpam-6811	300	9	cdγq	cdγq	NOUN
ejpam-6811	300	10	=	=	PUNCT
ejpam-6811	300	11	idγe−γddγeq	idγe−γddγeq	PROPN
ejpam-6811	300	12	.	.	PUNCT
ejpam-6811	301	1	d.	d.	PROPN
ejpam-6811	301	2	e.	e.	PROPN
ejpam-6811	301	3	shehwar	shehwar	PROPN
ejpam-6811	301	4	sagheer	sagheer	PROPN
ejpam-6811	301	5	et	et	PROPN
ejpam-6811	301	6	al	al	PROPN
ejpam-6811	301	7	.	.	PUNCT
ejpam-6811	301	8	/	/	SYM
ejpam-6811	301	9	eur	eur	PROPN
ejpam-6811	301	10	.	.	PUNCT
ejpam-6811	302	1	j.	j.	PROPN
ejpam-6811	302	2	pure	pure	PROPN
ejpam-6811	302	3	appl	appl	PROPN
ejpam-6811	302	4	.	.	PROPN
ejpam-6811	302	5	math	math	PROPN
ejpam-6811	302	6	,	,	PUNCT
ejpam-6811	302	7	18	18	NUM
ejpam-6811	302	8	(	(	PUNCT
ejpam-6811	302	9	4	4	NUM
ejpam-6811	302	10	)	)	PUNCT
ejpam-6811	302	11	(	(	PUNCT
ejpam-6811	302	12	2025	2025	NUM
ejpam-6811	302	13	)	)	PUNCT
ejpam-6811	302	14	,	,	PUNCT
ejpam-6811	302	15	6811	6811	NUM
ejpam-6811	302	16	14	14	NUM
ejpam-6811	302	17	of	of	ADP
ejpam-6811	302	18	24	24	NUM
ejpam-6811	302	19	here	here	ADV
ejpam-6811	302	20	,	,	PUNCT
ejpam-6811	302	21	iγ	iγ	NOUN
ejpam-6811	302	22	is	be	AUX
ejpam-6811	302	23	the	the	DET
ejpam-6811	302	24	riemann	riemann	PROPN
ejpam-6811	302	25	-	-	PUNCT
ejpam-6811	302	26	liouville	liouville	VERB
ejpam-6811	302	27	integral	integral	ADJ
ejpam-6811	302	28	operator	operator	NOUN
ejpam-6811	302	29	defined	define	VERB
ejpam-6811	302	30	below	below	ADP
ejpam-6811	302	31	iγq(x	iγq(x	PROPN
ejpam-6811	302	32	)	)	PUNCT
ejpam-6811	302	33	=	=	SYM
ejpam-6811	302	34	1	1	NUM
ejpam-6811	302	35	γ(γ	γ(γ	NOUN
ejpam-6811	302	36	)	)	PUNCT
ejpam-6811	302	37	∫	∫	PROPN
ejpam-6811	303	1	x	x	X
ejpam-6811	303	2	0	0	PUNCT
ejpam-6811	303	3	(	(	PUNCT
ejpam-6811	303	4	x−	x−	PROPN
ejpam-6811	303	5	ξ)γ−1	ξ)γ−1	PROPN
ejpam-6811	303	6	q(ξ	q(ξ	PROPN
ejpam-6811	303	7	)	)	PUNCT
ejpam-6811	304	1	dξ	dξ	PROPN
ejpam-6811	304	2	,	,	PUNCT
ejpam-6811	304	3	γ(γ	γ(γ	NOUN
ejpam-6811	304	4	)	)	PUNCT
ejpam-6811	304	5	=	=	SYM
ejpam-6811	305	1	∫	∫	PROPN
ejpam-6811	306	1	∞	∞	NOUN
ejpam-6811	306	2	0	0	NUM
ejpam-6811	307	1	xγ−1e−x	xγ−1e−x	PROPN
ejpam-6811	307	2	dx	dx	PROPN
ejpam-6811	307	3	.	.	PUNCT
ejpam-6811	308	1	i0	i0	PROPN
ejpam-6811	308	2	is	be	AUX
ejpam-6811	308	3	the	the	DET
ejpam-6811	308	4	identity	identity	NOUN
ejpam-6811	308	5	operator	operator	NOUN
ejpam-6811	308	6	.	.	PUNCT
ejpam-6811	309	1	we	we	PRON
ejpam-6811	309	2	will	will	AUX
ejpam-6811	309	3	consider	consider	VERB
ejpam-6811	309	4	a	a	DET
ejpam-6811	309	5	nonlinear	nonlinear	ADJ
ejpam-6811	309	6	cfde	cfde	NOUN
ejpam-6811	309	7	of	of	ADP
ejpam-6811	309	8	the	the	DET
ejpam-6811	309	9	form	form	NOUN
ejpam-6811	309	10	(	(	PUNCT
ejpam-6811	309	11	cdγy)(x	cdγy)(x	NOUN
ejpam-6811	309	12	)	)	PUNCT
ejpam-6811	310	1	=	=	SYM
ejpam-6811	310	2	υ	υ	PROPN
ejpam-6811	310	3	(	(	PUNCT
ejpam-6811	310	4	x	x	PROPN
ejpam-6811	310	5	,	,	PUNCT
ejpam-6811	310	6	y(x	y(x	PROPN
ejpam-6811	310	7	)	)	PUNCT
ejpam-6811	310	8	)	)	PUNCT
ejpam-6811	310	9	,	,	PUNCT
ejpam-6811	310	10	x	x	PUNCT
ejpam-6811	310	11	∈	∈	PROPN
ejpam-6811	311	1	[	[	X
ejpam-6811	311	2	0	0	NUM
ejpam-6811	311	3	,	,	PUNCT
ejpam-6811	311	4	1	1	NUM
ejpam-6811	311	5	]	]	PUNCT
ejpam-6811	311	6	and	and	CCONJ
ejpam-6811	311	7	γ	γ	X
ejpam-6811	311	8	∈	∈	PROPN
ejpam-6811	311	9	(	(	PUNCT
ejpam-6811	311	10	n−	n−	NOUN
ejpam-6811	311	11	1	1	NUM
ejpam-6811	311	12	,	,	PUNCT
ejpam-6811	311	13	n	n	CCONJ
ejpam-6811	311	14	]	]	X
ejpam-6811	311	15	(	(	PUNCT
ejpam-6811	311	16	17	17	NUM
ejpam-6811	311	17	)	)	PUNCT
ejpam-6811	311	18	along	along	ADP
ejpam-6811	311	19	with	with	ADP
ejpam-6811	311	20	y	y	PROPN
ejpam-6811	311	21	=	=	SYM
ejpam-6811	311	22	y′	y′	NOUN
ejpam-6811	311	23	=	=	SYM
ejpam-6811	311	24	·	·	PUNCT
ejpam-6811	311	25	·	·	PUNCT
ejpam-6811	311	26	·	·	PUNCT
ejpam-6811	311	27	=	=	PUNCT
ejpam-6811	311	28	y(n−2	y(n−2	PROPN
ejpam-6811	311	29	)	)	PUNCT
ejpam-6811	311	30	=	=	SYM
ejpam-6811	311	31	0	0	PUNCT
ejpam-6811	312	1	at	at	ADP
ejpam-6811	312	2	x	x	X
ejpam-6811	312	3	=	=	SYM
ejpam-6811	312	4	0	0	NUM
ejpam-6811	312	5	,	,	PUNCT
ejpam-6811	312	6	and	and	CCONJ
ejpam-6811	312	7	y	y	PROPN
ejpam-6811	312	8	=	=	SYM
ejpam-6811	312	9	∫	∫	PROPN
ejpam-6811	312	10	η	η	PROPN
ejpam-6811	312	11	0	0	PROPN
ejpam-6811	312	12	y(ξ	y(ξ	PROPN
ejpam-6811	312	13	)	)	PUNCT
ejpam-6811	312	14	dξ	dξ	VERB
ejpam-6811	312	15	at	at	ADP
ejpam-6811	312	16	x	x	X
ejpam-6811	313	1	=	=	SYM
ejpam-6811	313	2	1	1	NUM
ejpam-6811	313	3	,	,	PUNCT
ejpam-6811	313	4	(	(	PUNCT
ejpam-6811	313	5	18	18	NUM
ejpam-6811	313	6	)	)	PUNCT
ejpam-6811	314	1	where	where	SCONJ
ejpam-6811	314	2	υ	υ	NOUN
ejpam-6811	314	3	:	:	PUNCT
ejpam-6811	315	1	[	[	X
ejpam-6811	315	2	0	0	NUM
ejpam-6811	315	3	,	,	PUNCT
ejpam-6811	315	4	1]×	1]×	NUM
ejpam-6811	315	5	r	r	NOUN
ejpam-6811	315	6	→	→	SYM
ejpam-6811	315	7	r	r	NOUN
ejpam-6811	315	8	and	and	CCONJ
ejpam-6811	315	9	η	η	PROPN
ejpam-6811	315	10	∈	∈	PROPN
ejpam-6811	316	1	[	[	X
ejpam-6811	316	2	0	0	NUM
ejpam-6811	316	3	,	,	PUNCT
ejpam-6811	316	4	1	1	NUM
ejpam-6811	316	5	]	]	PUNCT
ejpam-6811	316	6	.	.	PUNCT
ejpam-6811	317	1	this	this	PRON
ejpam-6811	317	2	is	be	AUX
ejpam-6811	317	3	a	a	DET
ejpam-6811	317	4	specific	specific	ADJ
ejpam-6811	317	5	volterra	volterra	NOUN
ejpam-6811	317	6	integral	integral	ADJ
ejpam-6811	317	7	equation	equation	NOUN
ejpam-6811	317	8	and	and	CCONJ
ejpam-6811	317	9	the	the	DET
ejpam-6811	317	10	solution	solution	NOUN
ejpam-6811	317	11	y	y	PROPN
ejpam-6811	317	12	∈	∈	PROPN
ejpam-6811	317	13	c[0	c[0	PROPN
ejpam-6811	317	14	,	,	PUNCT
ejpam-6811	317	15	1	1	NUM
ejpam-6811	317	16	]	]	PUNCT
ejpam-6811	317	17	is	be	AUX
ejpam-6811	317	18	of	of	ADP
ejpam-6811	317	19	the	the	DET
ejpam-6811	317	20	form	form	NOUN
ejpam-6811	317	21	y(x	y(x	NOUN
ejpam-6811	317	22	)	)	PUNCT
ejpam-6811	317	23	=	=	SYM
ejpam-6811	317	24	a0	a0	NOUN
ejpam-6811	317	25	+	+	CCONJ
ejpam-6811	317	26	a1x+	a1x+	NOUN
ejpam-6811	317	27	a2x	a2x	ADP
ejpam-6811	317	28	2	2	NUM
ejpam-6811	317	29	+	+	CCONJ
ejpam-6811	317	30	·	·	PUNCT
ejpam-6811	317	31	·	·	PUNCT
ejpam-6811	317	32	·	·	PUNCT
ejpam-6811	318	1	+	+	NUM
ejpam-6811	318	2	an−1x	an−1x	PROPN
ejpam-6811	318	3	n−1	n−1	PROPN
ejpam-6811	318	4	+	+	CCONJ
ejpam-6811	318	5	1	1	NUM
ejpam-6811	318	6	γ(γ	γ(γ	NOUN
ejpam-6811	318	7	)	)	PUNCT
ejpam-6811	318	8	∫	∫	PROPN
ejpam-6811	319	1	x	x	X
ejpam-6811	319	2	0	0	PUNCT
ejpam-6811	319	3	(	(	PUNCT
ejpam-6811	319	4	x−	x−	PROPN
ejpam-6811	319	5	ξ)γ−1	ξ)γ−1	VERB
ejpam-6811	319	6	υ	υ	PROPN
ejpam-6811	319	7	(	(	PUNCT
ejpam-6811	319	8	ξ	ξ	PROPN
ejpam-6811	319	9	,	,	PUNCT
ejpam-6811	319	10	y(ξ	y(ξ	PROPN
ejpam-6811	319	11	)	)	PUNCT
ejpam-6811	319	12	)	)	PUNCT
ejpam-6811	320	1	dξ	dξ	PROPN
ejpam-6811	320	2	,	,	PUNCT
ejpam-6811	320	3	where	where	SCONJ
ejpam-6811	320	4	ai	ai	NOUN
ejpam-6811	320	5	are	be	AUX
ejpam-6811	320	6	real	real	ADJ
ejpam-6811	320	7	numbers	number	NOUN
ejpam-6811	320	8	.	.	PUNCT
ejpam-6811	321	1	the	the	DET
ejpam-6811	321	2	boundary	boundary	ADJ
ejpam-6811	321	3	conditions	condition	NOUN
ejpam-6811	321	4	given	give	VERB
ejpam-6811	321	5	in	in	ADP
ejpam-6811	321	6	(	(	PUNCT
ejpam-6811	321	7	4.3	4.3	NUM
ejpam-6811	321	8	)	)	PUNCT
ejpam-6811	321	9	mean	mean	PROPN
ejpam-6811	321	10	a0	a0	NOUN
ejpam-6811	321	11	=	=	SYM
ejpam-6811	321	12	a1	a1	PROPN
ejpam-6811	321	13	=	=	SYM
ejpam-6811	321	14	·	·	PUNCT
ejpam-6811	321	15	·	·	PUNCT
ejpam-6811	321	16	·	·	PUNCT
ejpam-6811	322	1	=	=	PUNCT
ejpam-6811	322	2	an−2	an−2	PROPN
ejpam-6811	322	3	=	=	SYM
ejpam-6811	322	4	0	0	NUM
ejpam-6811	322	5	y(x	y(x	PROPN
ejpam-6811	322	6	)	)	PUNCT
ejpam-6811	322	7	=	=	PUNCT
ejpam-6811	323	1	an−1x	an−1x	PROPN
ejpam-6811	323	2	n−1	n−1	PROPN
ejpam-6811	323	3	+	+	CCONJ
ejpam-6811	323	4	iγυ	iγυ	X
ejpam-6811	323	5	(	(	PUNCT
ejpam-6811	323	6	x	x	X
ejpam-6811	323	7	,	,	PUNCT
ejpam-6811	323	8	y(x	y(x	PROPN
ejpam-6811	323	9	)	)	PUNCT
ejpam-6811	323	10	)	)	PUNCT
ejpam-6811	323	11	and	and	CCONJ
ejpam-6811	323	12	y(1	y(1	PROPN
ejpam-6811	323	13	)	)	PUNCT
ejpam-6811	324	1	=	=	SYM
ejpam-6811	324	2	∫	∫	PROPN
ejpam-6811	324	3	η	η	PROPN
ejpam-6811	324	4	0	0	PROPN
ejpam-6811	324	5	y(ξ	y(ξ	PROPN
ejpam-6811	324	6	)	)	PUNCT
ejpam-6811	325	1	dξ	dξ	PROPN
ejpam-6811	326	1	=	=	PUNCT
ejpam-6811	326	2	an−1	an−1	PROPN
ejpam-6811	326	3	+	+	NUM
ejpam-6811	326	4	1	1	NUM
ejpam-6811	326	5	γ(γ	γ(γ	NOUN
ejpam-6811	326	6	)	)	PUNCT
ejpam-6811	326	7	∫	∫	PROPN
ejpam-6811	326	8	1	1	NUM
ejpam-6811	326	9	0	0	NUM
ejpam-6811	326	10	(	(	PUNCT
ejpam-6811	326	11	1−	1−	NUM
ejpam-6811	326	12	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	326	13	υ	υ	PROPN
ejpam-6811	326	14	(	(	PUNCT
ejpam-6811	326	15	ξ	ξ	PROPN
ejpam-6811	326	16	,	,	PUNCT
ejpam-6811	326	17	y(ξ	y(ξ	PROPN
ejpam-6811	326	18	)	)	PUNCT
ejpam-6811	326	19	)	)	PUNCT
ejpam-6811	327	1	dξ	dξ	PROPN
ejpam-6811	327	2	,	,	PUNCT
ejpam-6811	327	3	⇒	⇒	VERB
ejpam-6811	327	4	an−1	an−1	PROPN
ejpam-6811	327	5	=	=	SYM
ejpam-6811	327	6	∫	∫	PROPN
ejpam-6811	327	7	η	η	PROPN
ejpam-6811	327	8	0	0	PROPN
ejpam-6811	327	9	y(ξ	y(ξ	PROPN
ejpam-6811	327	10	)	)	PUNCT
ejpam-6811	328	1	dξ	dξ	ADP
ejpam-6811	328	2	−	−	NOUN
ejpam-6811	328	3	1	1	NUM
ejpam-6811	328	4	γ(γ	γ(γ	NOUN
ejpam-6811	328	5	)	)	PUNCT
ejpam-6811	328	6	∫	∫	PROPN
ejpam-6811	329	1	1	1	NUM
ejpam-6811	329	2	0	0	NUM
ejpam-6811	329	3	(	(	PUNCT
ejpam-6811	329	4	1−	1−	NUM
ejpam-6811	329	5	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	329	6	υ	υ	PROPN
ejpam-6811	329	7	(	(	PUNCT
ejpam-6811	329	8	ξ	ξ	PROPN
ejpam-6811	329	9	,	,	PUNCT
ejpam-6811	329	10	y(ξ	y(ξ	PROPN
ejpam-6811	329	11	)	)	PUNCT
ejpam-6811	329	12	)	)	PUNCT
ejpam-6811	329	13	dξ	dξ	PROPN
ejpam-6811	329	14	=	=	SYM
ejpam-6811	330	1	∫	∫	PROPN
ejpam-6811	330	2	η	η	PROPN
ejpam-6811	330	3	0	0	PROPN
ejpam-6811	330	4	(	(	PUNCT
ejpam-6811	330	5	an−1ξ	an−1ξ	PROPN
ejpam-6811	330	6	n−1	n−1	PROPN
ejpam-6811	330	7	+	+	CCONJ
ejpam-6811	330	8	1	1	NUM
ejpam-6811	330	9	γ(γ	γ(γ	NOUN
ejpam-6811	330	10	)	)	PUNCT
ejpam-6811	330	11	∫	∫	PROPN
ejpam-6811	331	1	ξ	ξ	X
ejpam-6811	331	2	0	0	PUNCT
ejpam-6811	331	3	(	(	PUNCT
ejpam-6811	331	4	ξ	ξ	X
ejpam-6811	331	5	−	−	PROPN
ejpam-6811	331	6	ϑ)γ−1	ϑ)γ−1	PROPN
ejpam-6811	331	7	υ	υ	X
ejpam-6811	331	8	(	(	PUNCT
ejpam-6811	331	9	ϑ	ϑ	X
ejpam-6811	331	10	,	,	PUNCT
ejpam-6811	331	11	y(ϑ	y(ϑ	PROPN
ejpam-6811	331	12	)	)	PUNCT
ejpam-6811	331	13	)	)	PUNCT
ejpam-6811	331	14	dϑ	dϑ	NOUN
ejpam-6811	331	15	)	)	PUNCT
ejpam-6811	332	1	dξ	dξ	ADP
ejpam-6811	332	2	−	−	NOUN
ejpam-6811	332	3	1	1	NUM
ejpam-6811	332	4	γ(γ	γ(γ	NOUN
ejpam-6811	332	5	)	)	PUNCT
ejpam-6811	332	6	∫	∫	PROPN
ejpam-6811	333	1	1	1	NUM
ejpam-6811	333	2	0	0	NUM
ejpam-6811	333	3	(	(	PUNCT
ejpam-6811	333	4	1−	1−	NUM
ejpam-6811	333	5	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	333	6	υ	υ	PROPN
ejpam-6811	333	7	(	(	PUNCT
ejpam-6811	333	8	ξ	ξ	PROPN
ejpam-6811	333	9	,	,	PUNCT
ejpam-6811	333	10	y(ξ	y(ξ	PROPN
ejpam-6811	333	11	)	)	PUNCT
ejpam-6811	333	12	)	)	PUNCT
ejpam-6811	334	1	dξ	dξ	PROPN
ejpam-6811	335	1	=	=	PUNCT
ejpam-6811	335	2	ηn	ηn	ADJ
ejpam-6811	335	3	n	n	CCONJ
ejpam-6811	335	4	an−1	an−1	PROPN
ejpam-6811	335	5	+	+	NUM
ejpam-6811	335	6	1	1	NUM
ejpam-6811	335	7	γ(γ	γ(γ	NOUN
ejpam-6811	335	8	)	)	PUNCT
ejpam-6811	335	9	∫	∫	PROPN
ejpam-6811	335	10	η	η	PROPN
ejpam-6811	335	11	0	0	PROPN
ejpam-6811	335	12	∫	∫	PROPN
ejpam-6811	335	13	ξ	ξ	X
ejpam-6811	335	14	0	0	PUNCT
ejpam-6811	335	15	(	(	PUNCT
ejpam-6811	335	16	ξ	ξ	X
ejpam-6811	335	17	−	−	PROPN
ejpam-6811	335	18	ϑ)γ−1	ϑ)γ−1	PROPN
ejpam-6811	335	19	υ	υ	X
ejpam-6811	335	20	(	(	PUNCT
ejpam-6811	335	21	ϑ	ϑ	X
ejpam-6811	335	22	,	,	PUNCT
ejpam-6811	335	23	y(ϑ	y(ϑ	PROPN
ejpam-6811	335	24	)	)	PUNCT
ejpam-6811	335	25	)	)	PUNCT
ejpam-6811	335	26	dϑdξ	dϑdξ	ADV
ejpam-6811	336	1	−	−	PROPN
ejpam-6811	336	2	1	1	NUM
ejpam-6811	336	3	γ(γ	γ(γ	NOUN
ejpam-6811	336	4	)	)	PUNCT
ejpam-6811	336	5	∫	∫	PROPN
ejpam-6811	337	1	1	1	NUM
ejpam-6811	337	2	0	0	NUM
ejpam-6811	337	3	(	(	PUNCT
ejpam-6811	337	4	1−	1−	NUM
ejpam-6811	337	5	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	337	6	υ	υ	PROPN
ejpam-6811	337	7	(	(	PUNCT
ejpam-6811	337	8	ξ	ξ	PROPN
ejpam-6811	337	9	,	,	PUNCT
ejpam-6811	337	10	y(ξ	y(ξ	PROPN
ejpam-6811	337	11	)	)	PUNCT
ejpam-6811	337	12	)	)	PUNCT
ejpam-6811	337	13	dξ	dξ	PROPN
ejpam-6811	337	14	=	=	SYM
ejpam-6811	338	1	n	n	PROPN
ejpam-6811	338	2	(	(	PUNCT
ejpam-6811	338	3	n−	n−	NOUN
ejpam-6811	338	4	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	338	5	)	)	PUNCT
ejpam-6811	338	6	∫	∫	PROPN
ejpam-6811	338	7	η	η	PROPN
ejpam-6811	338	8	0	0	PROPN
ejpam-6811	338	9	∫	∫	PROPN
ejpam-6811	338	10	ξ	ξ	X
ejpam-6811	338	11	0	0	PUNCT
ejpam-6811	338	12	(	(	PUNCT
ejpam-6811	338	13	ξ	ξ	X
ejpam-6811	338	14	−	−	PROPN
ejpam-6811	338	15	ϑ)γ−1	ϑ)γ−1	PROPN
ejpam-6811	338	16	υ	υ	X
ejpam-6811	338	17	(	(	PUNCT
ejpam-6811	338	18	ϑ	ϑ	X
ejpam-6811	338	19	,	,	PUNCT
ejpam-6811	338	20	y(ϑ	y(ϑ	PROPN
ejpam-6811	338	21	)	)	PUNCT
ejpam-6811	338	22	)	)	PUNCT
ejpam-6811	338	23	dϑdξ	dϑdξ	ADV
ejpam-6811	338	24	−	−	PROPN
ejpam-6811	339	1	n	n	CCONJ
ejpam-6811	339	2	(	(	PUNCT
ejpam-6811	339	3	n−	n−	NOUN
ejpam-6811	339	4	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	339	5	)	)	PUNCT
ejpam-6811	339	6	∫	∫	PROPN
ejpam-6811	339	7	1	1	NUM
ejpam-6811	339	8	0	0	NUM
ejpam-6811	339	9	(	(	PUNCT
ejpam-6811	339	10	1−	1−	NUM
ejpam-6811	339	11	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	339	12	υ	υ	PROPN
ejpam-6811	339	13	(	(	PUNCT
ejpam-6811	339	14	ξ	ξ	PROPN
ejpam-6811	339	15	,	,	PUNCT
ejpam-6811	339	16	y(ξ	y(ξ	PROPN
ejpam-6811	339	17	)	)	PUNCT
ejpam-6811	339	18	)	)	PUNCT
ejpam-6811	340	1	dξ	dξ	PROPN
ejpam-6811	340	2	.	.	PUNCT
ejpam-6811	341	1	substituting	substitute	VERB
ejpam-6811	341	2	this	this	DET
ejpam-6811	341	3	value	value	NOUN
ejpam-6811	341	4	in	in	ADP
ejpam-6811	341	5	y(x	y(x	NOUN
ejpam-6811	341	6	)	)	PUNCT
ejpam-6811	341	7	gives	give	VERB
ejpam-6811	341	8	the	the	DET
ejpam-6811	341	9	solution	solution	NOUN
ejpam-6811	341	10	of	of	ADP
ejpam-6811	341	11	the	the	DET
ejpam-6811	341	12	boundary	boundary	ADJ
ejpam-6811	341	13	value	value	NOUN
ejpam-6811	341	14	problem	problem	NOUN
ejpam-6811	341	15	given	give	VERB
ejpam-6811	341	16	above	above	ADV
ejpam-6811	341	17	to	to	PART
ejpam-6811	341	18	be	be	AUX
ejpam-6811	341	19	the	the	DET
ejpam-6811	341	20	same	same	ADJ
ejpam-6811	341	21	as	as	ADP
ejpam-6811	341	22	that	that	PRON
ejpam-6811	341	23	of	of	ADP
ejpam-6811	341	24	the	the	DET
ejpam-6811	341	25	volterra	volterra	NOUN
ejpam-6811	341	26	integral	integral	ADJ
ejpam-6811	341	27	equation	equation	NOUN
ejpam-6811	341	28	,	,	PUNCT
ejpam-6811	341	29	i.e.	i.e.	X
ejpam-6811	341	30	y(x	y(x	NOUN
ejpam-6811	341	31	)	)	PUNCT
ejpam-6811	342	1	=	=	SYM
ejpam-6811	342	2	nxn−1	nxn−1	PROPN
ejpam-6811	342	3	(	(	PUNCT
ejpam-6811	342	4	n−	n−	NOUN
ejpam-6811	342	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	342	6	)	)	PUNCT
ejpam-6811	342	7	∫	∫	PROPN
ejpam-6811	342	8	η	η	PROPN
ejpam-6811	342	9	0	0	PROPN
ejpam-6811	342	10	∫	∫	PROPN
ejpam-6811	342	11	ξ	ξ	X
ejpam-6811	342	12	0	0	PUNCT
ejpam-6811	342	13	(	(	PUNCT
ejpam-6811	342	14	ξ	ξ	X
ejpam-6811	342	15	−	−	PROPN
ejpam-6811	342	16	ϑ)γ−1	ϑ)γ−1	PROPN
ejpam-6811	342	17	υ	υ	X
ejpam-6811	342	18	(	(	PUNCT
ejpam-6811	342	19	ϑ	ϑ	X
ejpam-6811	342	20	,	,	PUNCT
ejpam-6811	342	21	y(ϑ	y(ϑ	PROPN
ejpam-6811	342	22	)	)	PUNCT
ejpam-6811	342	23	)	)	PUNCT
ejpam-6811	342	24	dϑdξ	dϑdξ	ADV
ejpam-6811	343	1	−	−	PROPN
ejpam-6811	343	2	nxn−1	nxn−1	PROPN
ejpam-6811	343	3	(	(	PUNCT
ejpam-6811	343	4	n−	n−	NOUN
ejpam-6811	343	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	343	6	)	)	PUNCT
ejpam-6811	343	7	∫	∫	PROPN
ejpam-6811	343	8	1	1	NUM
ejpam-6811	343	9	0	0	NUM
ejpam-6811	343	10	(	(	PUNCT
ejpam-6811	343	11	1−	1−	NUM
ejpam-6811	343	12	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	343	13	υ	υ	PROPN
ejpam-6811	343	14	(	(	PUNCT
ejpam-6811	343	15	ξ	ξ	PROPN
ejpam-6811	343	16	,	,	PUNCT
ejpam-6811	343	17	y(ξ	y(ξ	PROPN
ejpam-6811	343	18	)	)	PUNCT
ejpam-6811	343	19	)	)	PUNCT
ejpam-6811	343	20	dξ	dξ	VERB
ejpam-6811	344	1	+	+	CCONJ
ejpam-6811	344	2	1	1	NUM
ejpam-6811	344	3	γ(γ	γ(γ	NOUN
ejpam-6811	344	4	)	)	PUNCT
ejpam-6811	344	5	∫	∫	PROPN
ejpam-6811	344	6	x	x	X
ejpam-6811	344	7	0	0	PUNCT
ejpam-6811	344	8	(	(	PUNCT
ejpam-6811	344	9	x−	x−	PROPN
ejpam-6811	344	10	ξ)γ−1	ξ)γ−1	VERB
ejpam-6811	344	11	υ	υ	PROPN
ejpam-6811	344	12	(	(	PUNCT
ejpam-6811	344	13	ξ	ξ	PROPN
ejpam-6811	344	14	,	,	PUNCT
ejpam-6811	344	15	y(ξ	y(ξ	PROPN
ejpam-6811	344	16	)	)	PUNCT
ejpam-6811	344	17	)	)	PUNCT
ejpam-6811	345	1	dξ	dξ	PROPN
ejpam-6811	345	2	.	.	PUNCT
ejpam-6811	346	1	d.	d.	PROPN
ejpam-6811	346	2	e.	e.	PROPN
ejpam-6811	346	3	shehwar	shehwar	PROPN
ejpam-6811	346	4	sagheer	sagheer	PROPN
ejpam-6811	346	5	et	et	PROPN
ejpam-6811	346	6	al	al	PROPN
ejpam-6811	346	7	.	.	PUNCT
ejpam-6811	346	8	/	/	SYM
ejpam-6811	346	9	eur	eur	PROPN
ejpam-6811	346	10	.	.	PUNCT
ejpam-6811	347	1	j.	j.	PROPN
ejpam-6811	347	2	pure	pure	PROPN
ejpam-6811	347	3	appl	appl	PROPN
ejpam-6811	347	4	.	.	PROPN
ejpam-6811	347	5	math	math	PROPN
ejpam-6811	347	6	,	,	PUNCT
ejpam-6811	347	7	18	18	NUM
ejpam-6811	347	8	(	(	PUNCT
ejpam-6811	347	9	4	4	NUM
ejpam-6811	347	10	)	)	PUNCT
ejpam-6811	347	11	(	(	PUNCT
ejpam-6811	347	12	2025	2025	NUM
ejpam-6811	347	13	)	)	PUNCT
ejpam-6811	347	14	,	,	PUNCT
ejpam-6811	347	15	6811	6811	NUM
ejpam-6811	347	16	15	15	NUM
ejpam-6811	347	17	of	of	ADP
ejpam-6811	347	18	24	24	NUM
ejpam-6811	347	19	to	to	PART
ejpam-6811	347	20	transform	transform	VERB
ejpam-6811	347	21	this	this	PRON
ejpam-6811	347	22	into	into	ADP
ejpam-6811	347	23	a	a	DET
ejpam-6811	347	24	fixed	fix	VERB
ejpam-6811	347	25	point	point	NOUN
ejpam-6811	347	26	problem	problem	NOUN
ejpam-6811	347	27	,	,	PUNCT
ejpam-6811	347	28	construct	construct	VERB
ejpam-6811	347	29	t	t	PROPN
ejpam-6811	347	30	:	:	PUNCT
ejpam-6811	347	31	c[0	c[0	PROPN
ejpam-6811	347	32	,	,	PUNCT
ejpam-6811	347	33	1	1	NUM
ejpam-6811	347	34	]	]	PUNCT
ejpam-6811	347	35	→	→	X
ejpam-6811	347	36	c[0	c[0	PROPN
ejpam-6811	347	37	,	,	PUNCT
ejpam-6811	347	38	1	1	NUM
ejpam-6811	347	39	]	]	PUNCT
ejpam-6811	347	40	as	as	ADP
ejpam-6811	347	41	below	below	ADP
ejpam-6811	347	42	t	t	PROPN
ejpam-6811	347	43	(	(	PUNCT
ejpam-6811	347	44	y(x	y(x	PROPN
ejpam-6811	347	45	)	)	PUNCT
ejpam-6811	347	46	)	)	PUNCT
ejpam-6811	348	1	=	=	SYM
ejpam-6811	348	2	nxn−1	nxn−1	PROPN
ejpam-6811	348	3	(	(	PUNCT
ejpam-6811	348	4	n−	n−	NOUN
ejpam-6811	348	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	348	6	)	)	PUNCT
ejpam-6811	348	7	∫	∫	PROPN
ejpam-6811	348	8	η	η	PROPN
ejpam-6811	348	9	0	0	PROPN
ejpam-6811	348	10	∫	∫	PROPN
ejpam-6811	348	11	ξ	ξ	X
ejpam-6811	348	12	0	0	PUNCT
ejpam-6811	348	13	(	(	PUNCT
ejpam-6811	348	14	ξ	ξ	X
ejpam-6811	348	15	−	−	PROPN
ejpam-6811	348	16	ϑ)γ−1	ϑ)γ−1	PROPN
ejpam-6811	348	17	υ	υ	X
ejpam-6811	348	18	(	(	PUNCT
ejpam-6811	348	19	ϑ	ϑ	X
ejpam-6811	348	20	,	,	PUNCT
ejpam-6811	348	21	y(ϑ	y(ϑ	PROPN
ejpam-6811	348	22	)	)	PUNCT
ejpam-6811	348	23	)	)	PUNCT
ejpam-6811	348	24	dϑdξ	dϑdξ	ADV
ejpam-6811	349	1	−	−	PROPN
ejpam-6811	349	2	nxn−1	nxn−1	PROPN
ejpam-6811	349	3	(	(	PUNCT
ejpam-6811	349	4	n−	n−	NOUN
ejpam-6811	349	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	349	6	)	)	PUNCT
ejpam-6811	349	7	∫	∫	PROPN
ejpam-6811	349	8	1	1	NUM
ejpam-6811	349	9	0	0	NUM
ejpam-6811	349	10	(	(	PUNCT
ejpam-6811	349	11	1−	1−	NUM
ejpam-6811	349	12	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	349	13	υ	υ	PROPN
ejpam-6811	349	14	(	(	PUNCT
ejpam-6811	349	15	ξ	ξ	PROPN
ejpam-6811	349	16	,	,	PUNCT
ejpam-6811	349	17	y(ξ	y(ξ	PROPN
ejpam-6811	349	18	)	)	PUNCT
ejpam-6811	349	19	)	)	PUNCT
ejpam-6811	349	20	dξ	dξ	VERB
ejpam-6811	350	1	+	+	CCONJ
ejpam-6811	350	2	1	1	NUM
ejpam-6811	350	3	γ(γ	γ(γ	NOUN
ejpam-6811	350	4	)	)	PUNCT
ejpam-6811	350	5	∫	∫	PROPN
ejpam-6811	350	6	x	x	X
ejpam-6811	350	7	0	0	PUNCT
ejpam-6811	350	8	(	(	PUNCT
ejpam-6811	350	9	x−	x−	PROPN
ejpam-6811	350	10	ξ)γ−1	ξ)γ−1	VERB
ejpam-6811	350	11	υ	υ	PROPN
ejpam-6811	350	12	(	(	PUNCT
ejpam-6811	350	13	ξ	ξ	PROPN
ejpam-6811	350	14	,	,	PUNCT
ejpam-6811	350	15	y(ξ	y(ξ	PROPN
ejpam-6811	350	16	)	)	PUNCT
ejpam-6811	350	17	)	)	PUNCT
ejpam-6811	351	1	dξ	dξ	PROPN
ejpam-6811	351	2	.	.	PUNCT
ejpam-6811	352	1	the	the	DET
ejpam-6811	352	2	solution	solution	NOUN
ejpam-6811	352	3	of	of	ADP
ejpam-6811	352	4	the	the	DET
ejpam-6811	352	5	boundary	boundary	ADJ
ejpam-6811	352	6	value	value	NOUN
ejpam-6811	352	7	problem	problem	NOUN
ejpam-6811	352	8	described	describe	VERB
ejpam-6811	352	9	in	in	ADP
ejpam-6811	352	10	equations	equation	NOUN
ejpam-6811	352	11	(	(	PUNCT
ejpam-6811	352	12	4.2)-(4.3	4.2)-(4.3	NUM
ejpam-6811	352	13	)	)	PUNCT
ejpam-6811	352	14	is	be	AUX
ejpam-6811	352	15	given	give	VERB
ejpam-6811	352	16	by	by	ADP
ejpam-6811	352	17	ty	ty	NOUN
ejpam-6811	352	18	=	=	PUNCT
ejpam-6811	353	1	y.	y.	NOUN
ejpam-6811	353	2	we	we	PRON
ejpam-6811	353	3	will	will	AUX
ejpam-6811	353	4	now	now	ADV
ejpam-6811	353	5	show	show	VERB
ejpam-6811	353	6	that	that	SCONJ
ejpam-6811	353	7	a	a	DET
ejpam-6811	353	8	solution	solution	NOUN
ejpam-6811	353	9	for	for	ADP
ejpam-6811	353	10	this	this	DET
ejpam-6811	353	11	fixed	fix	VERB
ejpam-6811	353	12	point	point	NOUN
ejpam-6811	353	13	problem	problem	NOUN
ejpam-6811	353	14	exists	exist	VERB
ejpam-6811	353	15	by	by	ADP
ejpam-6811	353	16	considering	consider	VERB
ejpam-6811	353	17	(	(	PUNCT
ejpam-6811	353	18	c[0	c[0	PROPN
ejpam-6811	353	19	,	,	PUNCT
ejpam-6811	353	20	1	1	NUM
ejpam-6811	353	21	]	]	PUNCT
ejpam-6811	353	22	,	,	PUNCT
ejpam-6811	353	23	||	||	NOUN
ejpam-6811	353	24	·	·	PUNCT
ejpam-6811	354	1	||∗∞	||∗∞	NOUN
ejpam-6811	354	2	)	)	PUNCT
ejpam-6811	354	3	as	as	ADP
ejpam-6811	354	4	a	a	DET
ejpam-6811	354	5	base	base	NOUN
ejpam-6811	354	6	space	space	NOUN
ejpam-6811	354	7	with	with	ADP
ejpam-6811	354	8	a	a	DET
ejpam-6811	354	9	directed	direct	VERB
ejpam-6811	354	10	graph	graph	NOUN
ejpam-6811	354	11	ḡ.	ḡ.	PUNCT
ejpam-6811	354	12	we	we	PRON
ejpam-6811	354	13	define	define	VERB
ejpam-6811	354	14	the	the	DET
ejpam-6811	354	15	b	b	NOUN
ejpam-6811	354	16	-	-	ADJ
ejpam-6811	354	17	metric	metric	ADJ
ejpam-6811	354	18	||	||	NOUN
ejpam-6811	355	1	·	·	PUNCT
ejpam-6811	356	1	||∗∞	||∗∞	NOUN
ejpam-6811	356	2	as	as	SCONJ
ejpam-6811	356	3	||q	||q	ADJ
ejpam-6811	356	4	−r||∗∞	−r||∗∞	NOUN
ejpam-6811	356	5	=	=	PUNCT
ejpam-6811	356	6	sup	sup	NOUN
ejpam-6811	356	7	x∈[0,1	x∈[0,1	NOUN
ejpam-6811	356	8	]	]	PUNCT
ejpam-6811	356	9	∣∣q(x)−r(x	∣∣q(x)−r(x	ADV
ejpam-6811	356	10	)	)	PUNCT
ejpam-6811	356	11	∣∣2	∣∣2	PROPN
ejpam-6811	356	12	,	,	PUNCT
ejpam-6811	356	13	with	with	ADP
ejpam-6811	356	14	b	b	NOUN
ejpam-6811	356	15	=	=	SYM
ejpam-6811	356	16	2	2	NUM
ejpam-6811	356	17	.	.	PUNCT
ejpam-6811	357	1	the	the	DET
ejpam-6811	357	2	following	follow	VERB
ejpam-6811	357	3	conditions	condition	NOUN
ejpam-6811	357	4	are	be	AUX
ejpam-6811	357	5	also	also	ADV
ejpam-6811	357	6	important	important	ADJ
ejpam-6811	357	7	for	for	ADP
ejpam-6811	357	8	our	our	PRON
ejpam-6811	357	9	discussion	discussion	NOUN
ejpam-6811	357	10	.	.	PUNCT
ejpam-6811	358	1	i.	i.	PROPN
ejpam-6811	358	2	there	there	PRON
ejpam-6811	358	3	exists	exist	VERB
ejpam-6811	358	4	q0	q0	PROPN
ejpam-6811	358	5	∈	∈	PROPN
ejpam-6811	358	6	c[0	c[0	PROPN
ejpam-6811	358	7	,	,	PUNCT
ejpam-6811	358	8	1	1	NUM
ejpam-6811	358	9	]	]	PUNCT
ejpam-6811	358	10	such	such	ADJ
ejpam-6811	358	11	that	that	SCONJ
ejpam-6811	358	12	(	(	PUNCT
ejpam-6811	358	13	q0,tq0	q0,tq0	X
ejpam-6811	358	14	)	)	PUNCT
ejpam-6811	358	15	∈	∈	PROPN
ejpam-6811	358	16	e(ḡ	e(ḡ	PROPN
ejpam-6811	358	17	)	)	PUNCT
ejpam-6811	358	18	.	.	PUNCT
ejpam-6811	359	1	ii	ii	PROPN
ejpam-6811	359	2	.	.	PUNCT
ejpam-6811	360	1	t	t	PROPN
ejpam-6811	360	2	is	be	AUX
ejpam-6811	360	3	edge	edge	NOUN
ejpam-6811	360	4	preserving	preserve	VERB
ejpam-6811	360	5	on	on	ADP
ejpam-6811	360	6	c[0	c[0	PROPN
ejpam-6811	360	7	,	,	PUNCT
ejpam-6811	360	8	1	1	NUM
ejpam-6811	360	9	]	]	PUNCT
ejpam-6811	360	10	,	,	PUNCT
ejpam-6811	360	11	iii	iii	X
ejpam-6811	360	12	.	.	NOUN
ejpam-6811	361	1	for	for	ADP
ejpam-6811	361	2	a	a	DET
ejpam-6811	361	3	sequence	sequence	NOUN
ejpam-6811	361	4	{	{	PUNCT
ejpam-6811	361	5	qn	qn	NOUN
ejpam-6811	361	6	}	}	PUNCT
ejpam-6811	361	7	∈	∈	PROPN
ejpam-6811	361	8	c[0	c[0	PROPN
ejpam-6811	361	9	,	,	PUNCT
ejpam-6811	361	10	1	1	X
ejpam-6811	361	11	]	]	PUNCT
ejpam-6811	361	12	converging	converge	VERB
ejpam-6811	361	13	to	to	ADP
ejpam-6811	361	14	q	q	NOUN
ejpam-6811	361	15	with	with	ADP
ejpam-6811	361	16	(	(	PUNCT
ejpam-6811	361	17	qn	qn	INTJ
ejpam-6811	361	18	,	,	PUNCT
ejpam-6811	361	19	qn+1	qn+1	NUM
ejpam-6811	361	20	)	)	PUNCT
ejpam-6811	361	21	∈	∈	PROPN
ejpam-6811	361	22	e(ḡ	e(ḡ	NOUN
ejpam-6811	361	23	)	)	PUNCT
ejpam-6811	361	24	∀	∀	PUNCT
ejpam-6811	361	25	n	n	PRON
ejpam-6811	361	26	∈	∈	PROPN
ejpam-6811	361	27	n	n	CCONJ
ejpam-6811	361	28	,	,	PUNCT
ejpam-6811	361	29	we	we	PRON
ejpam-6811	361	30	must	must	AUX
ejpam-6811	361	31	have	have	AUX
ejpam-6811	361	32	(	(	PUNCT
ejpam-6811	361	33	qn	qn	INTJ
ejpam-6811	361	34	,	,	PUNCT
ejpam-6811	361	35	q	q	NOUN
ejpam-6811	361	36	)	)	PUNCT
ejpam-6811	361	37	is	be	AUX
ejpam-6811	361	38	an	an	DET
ejpam-6811	361	39	edge	edge	NOUN
ejpam-6811	361	40	for	for	ADP
ejpam-6811	361	41	each	each	DET
ejpam-6811	361	42	n	n	PRON
ejpam-6811	361	43	∈	∈	PROPN
ejpam-6811	361	44	n	n	CCONJ
ejpam-6811	361	45	,	,	PUNCT
ejpam-6811	361	46	iv	iv	X
ejpam-6811	361	47	.	.	PUNCT
ejpam-6811	362	1	set	set	NOUN
ejpam-6811	362	2	of	of	ADP
ejpam-6811	362	3	edges	edge	NOUN
ejpam-6811	362	4	is	be	AUX
ejpam-6811	362	5	transitive	transitive	ADJ
ejpam-6811	362	6	,	,	PUNCT
ejpam-6811	362	7	v.	v.	PROPN
ejpam-6811	362	8	∃	∃	PROPN
ejpam-6811	362	9	φ	φ	PROPN
ejpam-6811	362	10	∈	∈	PROPN
ejpam-6811	362	11	φ	φ	PROPN
ejpam-6811	362	12	with	with	ADP
ejpam-6811	362	13	φ(r	φ(r	NOUN
ejpam-6811	362	14	)	)	PUNCT
ejpam-6811	362	15	<	<	X
ejpam-6811	362	16	r	r	NOUN
ejpam-6811	362	17	,	,	PUNCT
ejpam-6811	362	18	∀	∀	NOUN
ejpam-6811	362	19	r	r	NOUN
ejpam-6811	362	20	∈	∈	PROPN
ejpam-6811	362	21	(	(	PUNCT
ejpam-6811	362	22	0	0	NUM
ejpam-6811	362	23	,	,	PUNCT
ejpam-6811	362	24	1	1	NUM
ejpam-6811	362	25	]	]	PUNCT
ejpam-6811	362	26	such	such	ADJ
ejpam-6811	362	27	that∣∣∣υ(x	that∣∣∣υ(x	ADJ
ejpam-6811	362	28	,	,	PUNCT
ejpam-6811	362	29	q(x	q(x	PROPN
ejpam-6811	362	30	)	)	PUNCT
ejpam-6811	362	31	)	)	PUNCT
ejpam-6811	363	1	−	−	NOUN
ejpam-6811	363	2	υ	υ	INTJ
ejpam-6811	363	3	(	(	PUNCT
ejpam-6811	363	4	x	x	NOUN
ejpam-6811	363	5	,	,	PUNCT
ejpam-6811	363	6	r(x	r(x	NOUN
ejpam-6811	363	7	)	)	PUNCT
ejpam-6811	363	8	)	)	PUNCT
ejpam-6811	364	1	∣∣∣	∣∣∣	NOUN
ejpam-6811	364	2	≤	≤	NUM
ejpam-6811	364	3	k1φ	k1φ	X
ejpam-6811	364	4	(	(	PUNCT
ejpam-6811	364	5	∣∣q(x)−r(x	∣∣q(x)−r(x	X
ejpam-6811	364	6	)	)	PUNCT
ejpam-6811	364	7	∣∣	∣∣	NUM
ejpam-6811	364	8	)	)	PUNCT
ejpam-6811	364	9	,	,	PUNCT
ejpam-6811	364	10	(	(	PUNCT
ejpam-6811	364	11	19	19	NUM
ejpam-6811	364	12	)	)	PUNCT
ejpam-6811	364	13	and	and	CCONJ
ejpam-6811	364	14	∣∣∣υ(x	∣∣∣υ(x	ADJ
ejpam-6811	364	15	,	,	PUNCT
ejpam-6811	364	16	q(x	q(x	NOUN
ejpam-6811	364	17	)	)	PUNCT
ejpam-6811	364	18	)	)	PUNCT
ejpam-6811	365	1	−	−	NOUN
ejpam-6811	365	2	υ	υ	INTJ
ejpam-6811	365	3	(	(	PUNCT
ejpam-6811	365	4	x	x	NOUN
ejpam-6811	365	5	,	,	PUNCT
ejpam-6811	365	6	r(x	r(x	NOUN
ejpam-6811	365	7	)	)	PUNCT
ejpam-6811	365	8	)	)	PUNCT
ejpam-6811	365	9	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	365	10	≤	≤	ADV
ejpam-6811	365	11	k2φ	k2φ	PROPN
ejpam-6811	365	12	(	(	PUNCT
ejpam-6811	365	13	∣∣q(x)−r(x	∣∣q(x)−r(x	ADV
ejpam-6811	365	14	)	)	PUNCT
ejpam-6811	365	15	∣∣2	∣∣2	NUM
ejpam-6811	365	16	)	)	PUNCT
ejpam-6811	365	17	,	,	PUNCT
ejpam-6811	365	18	(	(	PUNCT
ejpam-6811	365	19	20	20	NUM
ejpam-6811	365	20	)	)	PUNCT
ejpam-6811	365	21	where	where	SCONJ
ejpam-6811	365	22	k1	k1	NOUN
ejpam-6811	365	23	≤	≤	NUM
ejpam-6811	365	24	(	(	PUNCT
ejpam-6811	365	25	n−	n−	NOUN
ejpam-6811	365	26	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	365	27	+	+	CCONJ
ejpam-6811	365	28	2	2	X
ejpam-6811	365	29	)	)	PUNCT
ejpam-6811	365	30	nηγ+1	nηγ+1	NOUN
ejpam-6811	365	31	+	+	CCONJ
ejpam-6811	365	32	(	(	PUNCT
ejpam-6811	365	33	γ	γ	X
ejpam-6811	365	34	+	+	NOUN
ejpam-6811	365	35	1)(2n−	1)(2n−	NUM
ejpam-6811	365	36	ηn	ηn	ADJ
ejpam-6811	365	37	)	)	PUNCT
ejpam-6811	365	38	,	,	PUNCT
ejpam-6811	365	39	k2	k2	ADJ
ejpam-6811	365	40	≤	≤	NOUN
ejpam-6811	365	41	(	(	PUNCT
ejpam-6811	365	42	2γ	2γ	NOUN
ejpam-6811	365	43	−	−	PROPN
ejpam-6811	365	44	1)(n−	1)(n−	NUM
ejpam-6811	365	45	ηn)2γ(γ	ηn)2γ(γ	NOUN
ejpam-6811	366	1	+	+	X
ejpam-6811	366	2	1)γ(γ	1)γ(γ	NUM
ejpam-6811	366	3	+	+	CCONJ
ejpam-6811	366	4	2	2	NUM
ejpam-6811	366	5	)	)	PUNCT
ejpam-6811	366	6	γ(γ	γ(γ	PROPN
ejpam-6811	367	1	+	+	CCONJ
ejpam-6811	367	2	1	1	X
ejpam-6811	367	3	)	)	PUNCT
ejpam-6811	367	4	[	[	PUNCT
ejpam-6811	367	5	n2η2γ	n2η2γ	NUM
ejpam-6811	367	6	+	+	NUM
ejpam-6811	367	7	2γ	2γ	NOUN
ejpam-6811	367	8	[	[	PUNCT
ejpam-6811	367	9	n2	n2	NOUN
ejpam-6811	367	10	+	+	CCONJ
ejpam-6811	367	11	(	(	PUNCT
ejpam-6811	367	12	n−	n−	NOUN
ejpam-6811	367	13	ηn)2	ηn)2	PROPN
ejpam-6811	367	14	]	]	PUNCT
ejpam-6811	367	15	]	]	PUNCT
ejpam-6811	368	1	+	+	CCONJ
ejpam-6811	368	2	2(2γ	2(2γ	NUM
ejpam-6811	368	3	−	−	NOUN
ejpam-6811	368	4	1)n	1)n	X
ejpam-6811	368	5	[	[	PUNCT
ejpam-6811	368	6	nγ+2	nγ+2	X
ejpam-6811	368	7	+	+	CCONJ
ejpam-6811	368	8	ηγ+1(n−	ηγ+1(n−	VERB
ejpam-6811	368	9	ηn	ηn	PROPN
ejpam-6811	368	10	)	)	PUNCT
ejpam-6811	369	1	+	+	CCONJ
ejpam-6811	369	2	(	(	PUNCT
ejpam-6811	369	3	γ	γ	X
ejpam-6811	369	4	+	+	X
ejpam-6811	369	5	1)(n−	1)(n−	NUM
ejpam-6811	369	6	ηn	ηn	ADJ
ejpam-6811	369	7	)	)	PUNCT
ejpam-6811	369	8	]	]	PUNCT
ejpam-6811	369	9	,	,	PUNCT
ejpam-6811	369	10	and	and	CCONJ
ejpam-6811	369	11	k2	k2	PROPN
ejpam-6811	369	12	1	1	NUM
ejpam-6811	369	13	(	(	PUNCT
ejpam-6811	369	14	φ(||	φ(||	PROPN
ejpam-6811	369	15	q	q	ADJ
ejpam-6811	369	16	−r	−r	ADJ
ejpam-6811	369	17	||∞	||∞	PROPN
ejpam-6811	369	18	)	)	PUNCT
ejpam-6811	369	19	)	)	PUNCT
ejpam-6811	369	20	2	2	NUM
ejpam-6811	369	21	≤	≤	NOUN
ejpam-6811	369	22	k2	k2	NOUN
ejpam-6811	369	23	(	(	PUNCT
ejpam-6811	369	24	φ(||	φ(||	PROPN
ejpam-6811	369	25	q	q	PROPN
ejpam-6811	369	26	−r	−r	ADJ
ejpam-6811	369	27	||∗∞	||∗∞	NOUN
ejpam-6811	369	28	)	)	PUNCT
ejpam-6811	369	29	)	)	PUNCT
ejpam-6811	369	30	.	.	PUNCT
ejpam-6811	370	1	vi	vi	X
ejpam-6811	370	2	.	.	PUNCT
ejpam-6811	370	3	√∫	√∫	PROPN
ejpam-6811	370	4	η	η	PROPN
ejpam-6811	370	5	0	0	NUM
ejpam-6811	370	6	∫	∫	PROPN
ejpam-6811	370	7	ξ	ξ	PROPN
ejpam-6811	370	8	0	0	NUM
ejpam-6811	371	1	|	|	PROPN
ejpam-6811	371	2	ξ	ξ	PROPN
ejpam-6811	371	3	−	−	PROPN
ejpam-6811	371	4	ϑ	ϑ	PROPN
ejpam-6811	371	5	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	371	6	)	)	PUNCT
ejpam-6811	371	7	dϑdξ	dϑdξ	PROPN
ejpam-6811	371	8	√∫	√∫	PROPN
ejpam-6811	371	9	η	η	PROPN
ejpam-6811	371	10	0	0	NUM
ejpam-6811	371	11	∫	∫	PROPN
ejpam-6811	371	12	ξ	ξ	X
ejpam-6811	371	13	0	0	NUM
ejpam-6811	371	14	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	371	15	)	)	PUNCT
ejpam-6811	371	16	)	)	PUNCT
ejpam-6811	372	1	−	−	PROPN
ejpam-6811	372	2	υ	υ	PROPN
ejpam-6811	372	3	(	(	PUNCT
ejpam-6811	372	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	372	5	)	)	PUNCT
ejpam-6811	372	6	)	)	PUNCT
ejpam-6811	372	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	372	8	dϑdξ	dϑdξ	PROPN
ejpam-6811	372	9	≥	≥	PROPN
ejpam-6811	372	10	1	1	NUM
ejpam-6811	372	11	,	,	PUNCT
ejpam-6811	372	12	d.	d.	PROPN
ejpam-6811	372	13	e.	e.	PROPN
ejpam-6811	372	14	shehwar	shehwar	PROPN
ejpam-6811	372	15	sagheer	sagheer	PROPN
ejpam-6811	372	16	et	et	PROPN
ejpam-6811	372	17	al	al	PROPN
ejpam-6811	372	18	.	.	PUNCT
ejpam-6811	372	19	/	/	SYM
ejpam-6811	372	20	eur	eur	PROPN
ejpam-6811	372	21	.	.	PUNCT
ejpam-6811	373	1	j.	j.	PROPN
ejpam-6811	373	2	pure	pure	PROPN
ejpam-6811	373	3	appl	appl	PROPN
ejpam-6811	373	4	.	.	PROPN
ejpam-6811	373	5	math	math	PROPN
ejpam-6811	373	6	,	,	PUNCT
ejpam-6811	373	7	18	18	NUM
ejpam-6811	373	8	(	(	PUNCT
ejpam-6811	373	9	4	4	NUM
ejpam-6811	373	10	)	)	PUNCT
ejpam-6811	373	11	(	(	PUNCT
ejpam-6811	373	12	2025	2025	NUM
ejpam-6811	373	13	)	)	PUNCT
ejpam-6811	373	14	,	,	PUNCT
ejpam-6811	373	15	6811	6811	NUM
ejpam-6811	373	16	16	16	NUM
ejpam-6811	373	17	of	of	ADP
ejpam-6811	373	18	24√∫	24√∫	NUM
ejpam-6811	373	19	1	1	NUM
ejpam-6811	373	20	0	0	NUM
ejpam-6811	374	1	|	|	CCONJ
ejpam-6811	374	2	1−	1−	NUM
ejpam-6811	374	3	ξ	ξ	PROPN
ejpam-6811	374	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	374	5	)	)	PUNCT
ejpam-6811	374	6	dξ	dξ	PROPN
ejpam-6811	375	1	√∫	√∫	NOUN
ejpam-6811	375	2	1	1	NUM
ejpam-6811	375	3	0	0	NUM
ejpam-6811	375	4	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	375	5	,	,	PUNCT
ejpam-6811	375	6	q(ξ	q(ξ	PROPN
ejpam-6811	375	7	)	)	PUNCT
ejpam-6811	375	8	)	)	PUNCT
ejpam-6811	376	1	−	−	NOUN
ejpam-6811	376	2	υ	υ	NOUN
ejpam-6811	376	3	(	(	PUNCT
ejpam-6811	376	4	ξ	ξ	PROPN
ejpam-6811	376	5	,	,	PUNCT
ejpam-6811	376	6	r(ξ	r(ξ	NOUN
ejpam-6811	376	7	)	)	PUNCT
ejpam-6811	376	8	)	)	PUNCT
ejpam-6811	376	9	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	376	10	dξ	dξ	PROPN
ejpam-6811	376	11	≥	≥	PROPN
ejpam-6811	376	12	1	1	NUM
ejpam-6811	376	13	and	and	CCONJ
ejpam-6811	376	14	√∫	√∫	PROPN
ejpam-6811	376	15	x	x	SYM
ejpam-6811	376	16	0	0	NUM
ejpam-6811	377	1	|	|	ADV
ejpam-6811	377	2	x−	x−	PROPN
ejpam-6811	377	3	ξ	ξ	PROPN
ejpam-6811	377	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	377	5	)	)	PUNCT
ejpam-6811	377	6	dξ	dξ	PROPN
ejpam-6811	377	7	√∫	√∫	NOUN
ejpam-6811	377	8	x	x	SYM
ejpam-6811	377	9	0	0	NUM
ejpam-6811	377	10	∣∣∣υ(ξ	∣∣∣υ(ξ	PROPN
ejpam-6811	377	11	,	,	PUNCT
ejpam-6811	377	12	q(ξ	q(ξ	PROPN
ejpam-6811	377	13	)	)	PUNCT
ejpam-6811	377	14	)	)	PUNCT
ejpam-6811	378	1	−	−	NOUN
ejpam-6811	378	2	υ	υ	NOUN
ejpam-6811	378	3	(	(	PUNCT
ejpam-6811	378	4	ξ	ξ	PROPN
ejpam-6811	378	5	,	,	PUNCT
ejpam-6811	378	6	r(ξ	r(ξ	NOUN
ejpam-6811	378	7	)	)	PUNCT
ejpam-6811	378	8	)	)	PUNCT
ejpam-6811	378	9	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	378	10	dξ	dξ	PROPN
ejpam-6811	378	11	≥	≥	PROPN
ejpam-6811	378	12	1	1	NUM
ejpam-6811	378	13	.	.	PUNCT
ejpam-6811	379	1	using	use	VERB
ejpam-6811	379	2	these	these	DET
ejpam-6811	379	3	conditions	condition	NOUN
ejpam-6811	379	4	,	,	PUNCT
ejpam-6811	379	5	we	we	PRON
ejpam-6811	379	6	will	will	AUX
ejpam-6811	379	7	now	now	ADV
ejpam-6811	379	8	consider	consider	VERB
ejpam-6811	379	9	the	the	DET
ejpam-6811	379	10	following	follow	VERB
ejpam-6811	379	11	result	result	NOUN
ejpam-6811	379	12	.	.	PUNCT
ejpam-6811	380	1	theorem	theorem	ADJ
ejpam-6811	380	2	4	4	NUM
ejpam-6811	380	3	.	.	PUNCT
ejpam-6811	380	4	consider	consider	VERB
ejpam-6811	380	5	a	a	DET
ejpam-6811	380	6	complete	complete	ADJ
ejpam-6811	380	7	bms	bms	NOUN
ejpam-6811	380	8	(	(	PUNCT
ejpam-6811	380	9	x	x	NOUN
ejpam-6811	380	10	,	,	PUNCT
ejpam-6811	380	11	db	db	PROPN
ejpam-6811	380	12	)	)	PUNCT
ejpam-6811	380	13	accompanied	accompany	VERB
ejpam-6811	380	14	with	with	ADP
ejpam-6811	380	15	a	a	DET
ejpam-6811	380	16	directed	direct	VERB
ejpam-6811	380	17	graph	graph	NOUN
ejpam-6811	380	18	ḡ	ḡ	VERB
ejpam-6811	380	19	=(	=(	NOUN
ejpam-6811	380	20	v	v	NOUN
ejpam-6811	380	21	(	(	PUNCT
ejpam-6811	380	22	ḡ	ḡ	VERB
ejpam-6811	380	23	)	)	PUNCT
ejpam-6811	380	24	,	,	PUNCT
ejpam-6811	380	25	e(ḡ	e(ḡ	PROPN
ejpam-6811	380	26	)	)	PUNCT
ejpam-6811	380	27	)	)	PUNCT
ejpam-6811	380	28	and	and	CCONJ
ejpam-6811	380	29	conditions	condition	NOUN
ejpam-6811	381	1	i	i	PRON
ejpam-6811	381	2	to	to	ADP
ejpam-6811	381	3	vi	vi	PROPN
ejpam-6811	381	4	are	be	AUX
ejpam-6811	381	5	satisfied	satisfied	ADJ
ejpam-6811	381	6	.	.	PUNCT
ejpam-6811	382	1	then	then	ADV
ejpam-6811	382	2	the	the	DET
ejpam-6811	382	3	integral	integral	ADJ
ejpam-6811	382	4	operator	operator	NOUN
ejpam-6811	382	5	t	t	PROPN
ejpam-6811	382	6	defined	define	VERB
ejpam-6811	382	7	above	above	ADV
ejpam-6811	382	8	has	have	VERB
ejpam-6811	382	9	a	a	DET
ejpam-6811	382	10	fixed	fix	VERB
ejpam-6811	382	11	point	point	NOUN
ejpam-6811	382	12	q∗	q∗	NOUN
ejpam-6811	382	13	∈	∈	PROPN
ejpam-6811	382	14	c[0	c[0	PROPN
ejpam-6811	382	15	,	,	PUNCT
ejpam-6811	382	16	1	1	NUM
ejpam-6811	382	17	]	]	PUNCT
ejpam-6811	382	18	.	.	PUNCT
ejpam-6811	383	1	further	far	ADV
ejpam-6811	383	2	,	,	PUNCT
ejpam-6811	383	3	this	this	DET
ejpam-6811	383	4	fixed	fix	VERB
ejpam-6811	383	5	point	point	NOUN
ejpam-6811	383	6	is	be	AUX
ejpam-6811	383	7	a	a	DET
ejpam-6811	383	8	solution	solution	NOUN
ejpam-6811	383	9	for	for	ADP
ejpam-6811	383	10	the	the	DET
ejpam-6811	383	11	boundary	boundary	ADJ
ejpam-6811	383	12	value	value	NOUN
ejpam-6811	383	13	problem	problem	NOUN
ejpam-6811	383	14	given	give	VERB
ejpam-6811	383	15	in	in	ADP
ejpam-6811	383	16	(	(	PUNCT
ejpam-6811	383	17	4.2	4.2	NUM
ejpam-6811	383	18	)	)	PUNCT
ejpam-6811	383	19	(	(	PUNCT
ejpam-6811	383	20	4.3	4.3	NUM
ejpam-6811	383	21	)	)	PUNCT
ejpam-6811	383	22	.	.	PUNCT
ejpam-6811	384	1	proof	proof	NOUN
ejpam-6811	384	2	.	.	PUNCT
ejpam-6811	385	1	let	let	VERB
ejpam-6811	385	2	s	s	PRON
ejpam-6811	385	3	be	be	AUX
ejpam-6811	385	4	the	the	DET
ejpam-6811	385	5	identity	identity	NOUN
ejpam-6811	385	6	map	map	NOUN
ejpam-6811	385	7	defined	define	VERB
ejpam-6811	385	8	on	on	ADP
ejpam-6811	385	9	c[0	c[0	PROPN
ejpam-6811	385	10	,	,	PUNCT
ejpam-6811	385	11	1	1	NUM
ejpam-6811	385	12	]	]	PUNCT
ejpam-6811	385	13	.	.	PUNCT
ejpam-6811	386	1	from	from	ADP
ejpam-6811	386	2	iii	iii	PROPN
ejpam-6811	386	3	,	,	PUNCT
ejpam-6811	386	4	we	we	PRON
ejpam-6811	386	5	see	see	VERB
ejpam-6811	386	6	that	that	SCONJ
ejpam-6811	386	7	t	t	PROPN
ejpam-6811	386	8	is	be	AUX
ejpam-6811	386	9	s	s	NOUN
ejpam-6811	386	10	-	-	PUNCT
ejpam-6811	386	11	edge	edge	NOUN
ejpam-6811	386	12	preserving	preserve	VERB
ejpam-6811	386	13	with	with	ADP
ejpam-6811	386	14	respect	respect	NOUN
ejpam-6811	386	15	to	to	ADP
ejpam-6811	386	16	ḡ.	ḡ.	PROPN
ejpam-6811	386	17	from	from	ADP
ejpam-6811	386	18	iv	iv	NUM
ejpam-6811	386	19	,	,	PUNCT
ejpam-6811	386	20	we	we	PRON
ejpam-6811	386	21	have	have	VERB
ejpam-6811	386	22	(	(	PUNCT
ejpam-6811	386	23	c[0	c[0	PROPN
ejpam-6811	386	24	,	,	PUNCT
ejpam-6811	386	25	1	1	NUM
ejpam-6811	386	26	]	]	PUNCT
ejpam-6811	386	27	,	,	PUNCT
ejpam-6811	386	28	||	||	NOUN
ejpam-6811	386	29	·	·	PUNCT
ejpam-6811	387	1	||∞	||∞	NOUN
ejpam-6811	387	2	,	,	PUNCT
ejpam-6811	387	3	ḡ	ḡ	VERB
ejpam-6811	387	4	)	)	PUNCT
ejpam-6811	387	5	has	have	VERB
ejpam-6811	387	6	the	the	DET
ejpam-6811	387	7	property	property	NOUN
ejpam-6811	387	8	i.	i.	NOUN
ejpam-6811	387	9	finally	finally	ADV
ejpam-6811	387	10	,	,	PUNCT
ejpam-6811	387	11	v	v	PRON
ejpam-6811	387	12	shows	show	VERB
ejpam-6811	387	13	that	that	SCONJ
ejpam-6811	387	14	e(ḡ	e(ḡ	PROPN
ejpam-6811	387	15	)	)	PUNCT
ejpam-6811	387	16	has	have	VERB
ejpam-6811	387	17	the	the	DET
ejpam-6811	387	18	transitivity	transitivity	NOUN
ejpam-6811	387	19	property	property	NOUN
ejpam-6811	387	20	.	.	PUNCT
ejpam-6811	388	1	using	use	VERB
ejpam-6811	388	2	i	i	PRON
ejpam-6811	388	3	,	,	PUNCT
ejpam-6811	388	4	∀	∀	X
ejpam-6811	388	5	(	(	PUNCT
ejpam-6811	388	6	q	q	X
ejpam-6811	388	7	,	,	PUNCT
ejpam-6811	388	8	r	r	NOUN
ejpam-6811	388	9	)	)	PUNCT
ejpam-6811	388	10	∈	∈	PROPN
ejpam-6811	388	11	e(ḡ	e(ḡ	PROPN
ejpam-6811	388	12	)	)	PUNCT
ejpam-6811	388	13	,	,	PUNCT
ejpam-6811	388	14	consider∣∣∣t(q(x	consider∣∣∣t(q(x	PROPN
ejpam-6811	388	15	)	)	PUNCT
ejpam-6811	388	16	)	)	PUNCT
ejpam-6811	389	1	−	−	PROPN
ejpam-6811	389	2	t	t	PROPN
ejpam-6811	389	3	(	(	PUNCT
ejpam-6811	389	4	r(x	r(x	PROPN
ejpam-6811	389	5	)	)	PUNCT
ejpam-6811	389	6	)	)	PUNCT
ejpam-6811	389	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	389	8	=	=	SYM
ejpam-6811	390	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6811	390	2	nxn−1	nxn−1	PROPN
ejpam-6811	390	3	(	(	PUNCT
ejpam-6811	390	4	n−	n−	NOUN
ejpam-6811	390	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	390	6	)	)	PUNCT
ejpam-6811	390	7	∫	∫	PROPN
ejpam-6811	390	8	η	η	PROPN
ejpam-6811	390	9	0	0	PROPN
ejpam-6811	390	10	∫	∫	PROPN
ejpam-6811	390	11	ξ	ξ	X
ejpam-6811	390	12	0	0	PUNCT
ejpam-6811	390	13	(	(	PUNCT
ejpam-6811	390	14	ξ	ξ	X
ejpam-6811	390	15	−	−	PROPN
ejpam-6811	390	16	ϑ)γ−1	ϑ)γ−1	NOUN
ejpam-6811	390	17	(	(	PUNCT
ejpam-6811	390	18	υ	υ	NOUN
ejpam-6811	390	19	(	(	PUNCT
ejpam-6811	390	20	ϑ,q(ϑ	ϑ,q(ϑ	NOUN
ejpam-6811	390	21	)	)	PUNCT
ejpam-6811	390	22	)	)	PUNCT
ejpam-6811	391	1	−	−	NOUN
ejpam-6811	391	2	υ	υ	PROPN
ejpam-6811	391	3	(	(	PUNCT
ejpam-6811	391	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	391	5	)	)	PUNCT
ejpam-6811	391	6	)	)	PUNCT
ejpam-6811	391	7	)	)	PUNCT
ejpam-6811	391	8	dϑdξ	dϑdξ	ADV
ejpam-6811	392	1	−	−	PROPN
ejpam-6811	392	2	nxn−1	nxn−1	PROPN
ejpam-6811	392	3	(	(	PUNCT
ejpam-6811	392	4	n−	n−	NOUN
ejpam-6811	392	5	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	392	6	)	)	PUNCT
ejpam-6811	392	7	∫	∫	PROPN
ejpam-6811	392	8	1	1	NUM
ejpam-6811	392	9	0	0	NUM
ejpam-6811	392	10	(	(	PUNCT
ejpam-6811	392	11	1−	1−	NUM
ejpam-6811	392	12	ξ)γ−1	ξ)γ−1	NOUN
ejpam-6811	392	13	(	(	PUNCT
ejpam-6811	392	14	υ	υ	X
ejpam-6811	392	15	(	(	PUNCT
ejpam-6811	392	16	ϑ,q(ξ	ϑ,q(ξ	NUM
ejpam-6811	392	17	)	)	PUNCT
ejpam-6811	392	18	)	)	PUNCT
ejpam-6811	393	1	−	−	NOUN
ejpam-6811	393	2	υ	υ	NOUN
ejpam-6811	393	3	(	(	PUNCT
ejpam-6811	393	4	ϑ,r(ξ	ϑ,r(ξ	NOUN
ejpam-6811	393	5	)	)	PUNCT
ejpam-6811	393	6	)	)	PUNCT
ejpam-6811	393	7	)	)	PUNCT
ejpam-6811	393	8	dξ	dξ	PROPN
ejpam-6811	394	1	+	+	CCONJ
ejpam-6811	394	2	1	1	NUM
ejpam-6811	394	3	γ(γ	γ(γ	NOUN
ejpam-6811	394	4	)	)	PUNCT
ejpam-6811	394	5	∫	∫	PROPN
ejpam-6811	395	1	x	x	X
ejpam-6811	395	2	0	0	PUNCT
ejpam-6811	395	3	(	(	PUNCT
ejpam-6811	395	4	x−	x−	PROPN
ejpam-6811	395	5	ξ)γ−1	ξ)γ−1	PROPN
ejpam-6811	395	6	(	(	PUNCT
ejpam-6811	395	7	υ	υ	X
ejpam-6811	395	8	(	(	PUNCT
ejpam-6811	395	9	ξ	ξ	PROPN
ejpam-6811	395	10	,	,	PUNCT
ejpam-6811	395	11	q(ξ	q(ξ	ADJ
ejpam-6811	395	12	)	)	PUNCT
ejpam-6811	395	13	)	)	PUNCT
ejpam-6811	396	1	−	−	NOUN
ejpam-6811	396	2	υ	υ	NOUN
ejpam-6811	396	3	(	(	PUNCT
ejpam-6811	396	4	ξ	ξ	PROPN
ejpam-6811	396	5	,	,	PUNCT
ejpam-6811	396	6	r(ξ	r(ξ	NOUN
ejpam-6811	396	7	)	)	PUNCT
ejpam-6811	396	8	)	)	PUNCT
ejpam-6811	396	9	)	)	PUNCT
ejpam-6811	396	10	dξ	dξ	ADP
ejpam-6811	396	11	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6811	396	12	2	2	NUM
ejpam-6811	396	13	.	.	PUNCT
ejpam-6811	397	1	expanding	expand	VERB
ejpam-6811	397	2	the	the	DET
ejpam-6811	397	3	square	square	NOUN
ejpam-6811	397	4	on	on	ADP
ejpam-6811	397	5	the	the	DET
ejpam-6811	397	6	right	right	ADJ
ejpam-6811	397	7	hand	hand	NOUN
ejpam-6811	397	8	side	side	NOUN
ejpam-6811	397	9	and	and	CCONJ
ejpam-6811	397	10	further	further	ADJ
ejpam-6811	397	11	manipulation	manipulation	NOUN
ejpam-6811	397	12	gives∣∣∣t(q(x	gives∣∣∣t(q(x	NOUN
ejpam-6811	397	13	)	)	PUNCT
ejpam-6811	397	14	)	)	PUNCT
ejpam-6811	398	1	−	−	PROPN
ejpam-6811	398	2	t	t	PROPN
ejpam-6811	398	3	(	(	PUNCT
ejpam-6811	398	4	r(x	r(x	PROPN
ejpam-6811	398	5	)	)	PUNCT
ejpam-6811	398	6	)	)	PUNCT
ejpam-6811	398	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	398	8	≤	≤	PROPN
ejpam-6811	398	9	n2x2(n−1	n2x2(n−1	PROPN
ejpam-6811	398	10	)	)	PUNCT
ejpam-6811	398	11	(	(	PUNCT
ejpam-6811	398	12	n−	n−	NOUN
ejpam-6811	398	13	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	398	14	)	)	PUNCT
ejpam-6811	399	1	[	[	X
ejpam-6811	399	2	∫	∫	PROPN
ejpam-6811	399	3	η	η	PROPN
ejpam-6811	399	4	0	0	PROPN
ejpam-6811	399	5	∫	∫	PROPN
ejpam-6811	399	6	ξ	ξ	PROPN
ejpam-6811	399	7	0	0	NUM
ejpam-6811	400	1	|	|	PROPN
ejpam-6811	401	1	ξ	ξ	X
ejpam-6811	401	2	−	−	PROPN
ejpam-6811	401	3	ϑ	ϑ	X
ejpam-6811	401	4	|γ−1	|γ−1	NOUN
ejpam-6811	401	5	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	401	6	)	)	PUNCT
ejpam-6811	401	7	)	)	PUNCT
ejpam-6811	402	1	−	−	PROPN
ejpam-6811	402	2	υ	υ	PROPN
ejpam-6811	402	3	(	(	PUNCT
ejpam-6811	402	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	402	5	)	)	PUNCT
ejpam-6811	402	6	)	)	PUNCT
ejpam-6811	402	7	∣∣∣	∣∣∣	PROPN
ejpam-6811	402	8	dϑdξ]2	dϑdξ]2	PROPN
ejpam-6811	402	9	+	+	CCONJ
ejpam-6811	402	10	n2x2(n−1	n2x2(n−1	PROPN
ejpam-6811	402	11	)	)	PUNCT
ejpam-6811	402	12	(	(	PUNCT
ejpam-6811	402	13	n−	n−	NOUN
ejpam-6811	402	14	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	402	15	)	)	PUNCT
ejpam-6811	403	1	[	[	X
ejpam-6811	403	2	∫	∫	X
ejpam-6811	403	3	1	1	NUM
ejpam-6811	403	4	0	0	NUM
ejpam-6811	404	1	|	|	CCONJ
ejpam-6811	404	2	1−	1−	NUM
ejpam-6811	404	3	ξ	ξ	PROPN
ejpam-6811	404	4	|γ−1	|γ−1	ADJ
ejpam-6811	404	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	404	6	,	,	PUNCT
ejpam-6811	404	7	q(ξ	q(ξ	PROPN
ejpam-6811	404	8	)	)	PUNCT
ejpam-6811	404	9	)	)	PUNCT
ejpam-6811	405	1	−	−	NOUN
ejpam-6811	405	2	υ	υ	NOUN
ejpam-6811	405	3	(	(	PUNCT
ejpam-6811	405	4	ξ	ξ	PROPN
ejpam-6811	405	5	,	,	PUNCT
ejpam-6811	405	6	r(ξ	r(ξ	NOUN
ejpam-6811	405	7	)	)	PUNCT
ejpam-6811	405	8	)	)	PUNCT
ejpam-6811	405	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	406	1	dξ]2	dξ]2	PROPN
ejpam-6811	407	1	+	+	CCONJ
ejpam-6811	407	2	1	1	NUM
ejpam-6811	407	3	γ2(γ	γ2(γ	NOUN
ejpam-6811	407	4	)	)	PUNCT
ejpam-6811	408	1	[	[	X
ejpam-6811	408	2	∫	∫	X
ejpam-6811	408	3	x	x	SYM
ejpam-6811	408	4	0	0	NUM
ejpam-6811	409	1	|	|	ADV
ejpam-6811	409	2	x−	x−	PROPN
ejpam-6811	409	3	ξ	ξ	PROPN
ejpam-6811	409	4	|γ−1	|γ−1	ADJ
ejpam-6811	409	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	409	6	,	,	PUNCT
ejpam-6811	409	7	q(ξ	q(ξ	PROPN
ejpam-6811	409	8	)	)	PUNCT
ejpam-6811	409	9	)	)	PUNCT
ejpam-6811	410	1	−	−	NOUN
ejpam-6811	410	2	υ	υ	NOUN
ejpam-6811	410	3	(	(	PUNCT
ejpam-6811	410	4	ξ	ξ	PROPN
ejpam-6811	410	5	,	,	PUNCT
ejpam-6811	410	6	r(ξ	r(ξ	NOUN
ejpam-6811	410	7	)	)	PUNCT
ejpam-6811	410	8	)	)	PUNCT
ejpam-6811	410	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	411	1	dξ]2	dξ]2	PROPN
ejpam-6811	411	2	+	+	CCONJ
ejpam-6811	411	3	2n2x2(n−1	2n2x2(n−1	NUM
ejpam-6811	411	4	)	)	PUNCT
ejpam-6811	411	5	(	(	PUNCT
ejpam-6811	411	6	n−	n−	NOUN
ejpam-6811	411	7	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	411	8	)	)	PUNCT
ejpam-6811	412	1	[	[	X
ejpam-6811	412	2	∫	∫	PROPN
ejpam-6811	412	3	η	η	PROPN
ejpam-6811	412	4	0	0	PROPN
ejpam-6811	412	5	∫	∫	PROPN
ejpam-6811	412	6	ξ	ξ	PROPN
ejpam-6811	412	7	0	0	NUM
ejpam-6811	413	1	|	|	PROPN
ejpam-6811	414	1	ξ	ξ	X
ejpam-6811	414	2	−	−	PROPN
ejpam-6811	414	3	ϑ	ϑ	X
ejpam-6811	414	4	|γ−1	|γ−1	NOUN
ejpam-6811	414	5	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	414	6	)	)	PUNCT
ejpam-6811	414	7	)	)	PUNCT
ejpam-6811	415	1	−	−	PROPN
ejpam-6811	415	2	υ	υ	PROPN
ejpam-6811	415	3	(	(	PUNCT
ejpam-6811	415	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	415	5	)	)	PUNCT
ejpam-6811	415	6	)	)	PUNCT
ejpam-6811	415	7	∣∣∣	∣∣∣	ADP
ejpam-6811	415	8	dϑdξ][∫	dϑdξ][∫	NOUN
ejpam-6811	415	9	1	1	NUM
ejpam-6811	415	10	0	0	NUM
ejpam-6811	416	1	|	|	CCONJ
ejpam-6811	416	2	1−	1−	NUM
ejpam-6811	416	3	ξ	ξ	PROPN
ejpam-6811	416	4	|γ−1	|γ−1	ADJ
ejpam-6811	416	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	416	6	,	,	PUNCT
ejpam-6811	416	7	q(ξ	q(ξ	PROPN
ejpam-6811	416	8	)	)	PUNCT
ejpam-6811	416	9	)	)	PUNCT
ejpam-6811	417	1	−	−	NOUN
ejpam-6811	417	2	υ	υ	NOUN
ejpam-6811	417	3	(	(	PUNCT
ejpam-6811	417	4	ξ	ξ	PROPN
ejpam-6811	417	5	,	,	PUNCT
ejpam-6811	417	6	r(ξ	r(ξ	NOUN
ejpam-6811	417	7	)	)	PUNCT
ejpam-6811	417	8	)	)	PUNCT
ejpam-6811	417	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	418	1	dξ	dξ	PROPN
ejpam-6811	418	2	]	]	PUNCT
ejpam-6811	418	3	d.	d.	PROPN
ejpam-6811	418	4	e.	e.	PROPN
ejpam-6811	419	1	shehwar	shehwar	PROPN
ejpam-6811	419	2	sagheer	sagheer	PROPN
ejpam-6811	419	3	et	et	PROPN
ejpam-6811	419	4	al	al	PROPN
ejpam-6811	419	5	.	.	PUNCT
ejpam-6811	419	6	/	/	SYM
ejpam-6811	419	7	eur	eur	PROPN
ejpam-6811	419	8	.	.	PUNCT
ejpam-6811	420	1	j.	j.	PROPN
ejpam-6811	420	2	pure	pure	PROPN
ejpam-6811	420	3	appl	appl	PROPN
ejpam-6811	420	4	.	.	PROPN
ejpam-6811	420	5	math	math	PROPN
ejpam-6811	420	6	,	,	PUNCT
ejpam-6811	420	7	18	18	NUM
ejpam-6811	420	8	(	(	PUNCT
ejpam-6811	420	9	4	4	NUM
ejpam-6811	420	10	)	)	PUNCT
ejpam-6811	420	11	(	(	PUNCT
ejpam-6811	420	12	2025	2025	NUM
ejpam-6811	420	13	)	)	PUNCT
ejpam-6811	420	14	,	,	PUNCT
ejpam-6811	420	15	6811	6811	NUM
ejpam-6811	420	16	17	17	NUM
ejpam-6811	420	17	of	of	ADP
ejpam-6811	420	18	24	24	NUM
ejpam-6811	420	19	+	+	CCONJ
ejpam-6811	420	20	2nx(n−1	2nx(n−1	NUM
ejpam-6811	420	21	)	)	PUNCT
ejpam-6811	420	22	(	(	PUNCT
ejpam-6811	420	23	n−	n−	NOUN
ejpam-6811	420	24	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	420	25	)	)	PUNCT
ejpam-6811	421	1	[	[	X
ejpam-6811	421	2	∫	∫	PROPN
ejpam-6811	421	3	η	η	PROPN
ejpam-6811	421	4	0	0	PROPN
ejpam-6811	421	5	∫	∫	PROPN
ejpam-6811	421	6	ξ	ξ	PROPN
ejpam-6811	421	7	0	0	NUM
ejpam-6811	422	1	|	|	PROPN
ejpam-6811	423	1	ξ	ξ	X
ejpam-6811	423	2	−	−	PROPN
ejpam-6811	423	3	ϑ	ϑ	X
ejpam-6811	423	4	|γ−1	|γ−1	NOUN
ejpam-6811	423	5	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	423	6	)	)	PUNCT
ejpam-6811	423	7	)	)	PUNCT
ejpam-6811	424	1	−	−	PROPN
ejpam-6811	424	2	υ	υ	PROPN
ejpam-6811	424	3	(	(	PUNCT
ejpam-6811	424	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	424	5	)	)	PUNCT
ejpam-6811	424	6	)	)	PUNCT
ejpam-6811	424	7	∣∣∣	∣∣∣	ADP
ejpam-6811	424	8	dϑdξ][∫	dϑdξ][∫	NOUN
ejpam-6811	424	9	x	x	SYM
ejpam-6811	424	10	0	0	NUM
ejpam-6811	425	1	|	|	ADV
ejpam-6811	425	2	x−	x−	PROPN
ejpam-6811	425	3	ξ	ξ	PROPN
ejpam-6811	425	4	|γ−1	|γ−1	ADJ
ejpam-6811	425	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	425	6	,	,	PUNCT
ejpam-6811	425	7	q(ξ	q(ξ	PROPN
ejpam-6811	425	8	)	)	PUNCT
ejpam-6811	425	9	)	)	PUNCT
ejpam-6811	426	1	−	−	NOUN
ejpam-6811	426	2	υ	υ	NOUN
ejpam-6811	426	3	(	(	PUNCT
ejpam-6811	426	4	ξ	ξ	PROPN
ejpam-6811	426	5	,	,	PUNCT
ejpam-6811	426	6	r(ξ	r(ξ	NOUN
ejpam-6811	426	7	)	)	PUNCT
ejpam-6811	426	8	)	)	PUNCT
ejpam-6811	426	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	427	1	dξ	dξ	PROPN
ejpam-6811	427	2	]	]	PUNCT
ejpam-6811	427	3	+	+	CCONJ
ejpam-6811	427	4	2nx(n−1	2nx(n−1	NUM
ejpam-6811	427	5	)	)	PUNCT
ejpam-6811	427	6	(	(	PUNCT
ejpam-6811	427	7	n−	n−	NOUN
ejpam-6811	427	8	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	427	9	)	)	PUNCT
ejpam-6811	428	1	[	[	X
ejpam-6811	428	2	∫	∫	X
ejpam-6811	428	3	1	1	NUM
ejpam-6811	428	4	0	0	NUM
ejpam-6811	429	1	|	|	CCONJ
ejpam-6811	429	2	1−	1−	NUM
ejpam-6811	429	3	ξ	ξ	PROPN
ejpam-6811	429	4	|γ−1	|γ−1	ADJ
ejpam-6811	429	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	429	6	,	,	PUNCT
ejpam-6811	429	7	q(ξ	q(ξ	PROPN
ejpam-6811	429	8	)	)	PUNCT
ejpam-6811	429	9	)	)	PUNCT
ejpam-6811	430	1	−	−	NOUN
ejpam-6811	430	2	υ	υ	NOUN
ejpam-6811	430	3	(	(	PUNCT
ejpam-6811	430	4	ξ	ξ	PROPN
ejpam-6811	430	5	,	,	PUNCT
ejpam-6811	430	6	r(ξ	r(ξ	NOUN
ejpam-6811	430	7	)	)	PUNCT
ejpam-6811	430	8	)	)	PUNCT
ejpam-6811	431	1	∣∣∣	∣∣∣	ADP
ejpam-6811	431	2	dξ][∫	dξ][∫	PROPN
ejpam-6811	431	3	x	x	X
ejpam-6811	431	4	0	0	NUM
ejpam-6811	431	5	|	|	ADV
ejpam-6811	431	6	x−	x−	PROPN
ejpam-6811	431	7	ξ	ξ	PROPN
ejpam-6811	431	8	|γ−1	|γ−1	ADJ
ejpam-6811	431	9	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	431	10	,	,	PUNCT
ejpam-6811	431	11	q(ξ	q(ξ	PROPN
ejpam-6811	431	12	)	)	PUNCT
ejpam-6811	431	13	)	)	PUNCT
ejpam-6811	432	1	−	−	NOUN
ejpam-6811	432	2	υ	υ	NOUN
ejpam-6811	432	3	(	(	PUNCT
ejpam-6811	432	4	ξ	ξ	PROPN
ejpam-6811	432	5	,	,	PUNCT
ejpam-6811	432	6	r(ξ	r(ξ	NOUN
ejpam-6811	432	7	)	)	PUNCT
ejpam-6811	432	8	)	)	PUNCT
ejpam-6811	432	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	433	1	dξ	dξ	PROPN
ejpam-6811	433	2	]	]	PUNCT
ejpam-6811	433	3	.	.	PUNCT
ejpam-6811	434	1	the	the	DET
ejpam-6811	434	2	cauchy	cauchy	PROPN
ejpam-6811	434	3	-	-	PUNCT
ejpam-6811	434	4	schwarz	schwarz	PROPN
ejpam-6811	434	5	inequality	inequality	PROPN
ejpam-6811	434	6	states	state	VERB
ejpam-6811	434	7	∫	∫	PROPN
ejpam-6811	434	8	b	b	PROPN
ejpam-6811	434	9	a	a	PROPN
ejpam-6811	434	10	t	t	PROPN
ejpam-6811	434	11	(	(	PUNCT
ejpam-6811	434	12	x)s(x	x)s(x	PROPN
ejpam-6811	434	13	)	)	PUNCT
ejpam-6811	435	1	dx	dx	PROPN
ejpam-6811	435	2	≤	≤	PROPN
ejpam-6811	436	1	√∫	√∫	PROPN
ejpam-6811	436	2	b	b	PROPN
ejpam-6811	436	3	a	a	DET
ejpam-6811	436	4	t	t	NOUN
ejpam-6811	436	5	2(x	2(x	NUM
ejpam-6811	436	6	)	)	PUNCT
ejpam-6811	437	1	dx	dx	PROPN
ejpam-6811	437	2	√∫	√∫	PROPN
ejpam-6811	437	3	b	b	PROPN
ejpam-6811	437	4	a	a	DET
ejpam-6811	437	5	x2(x	x2(x	PROPN
ejpam-6811	437	6	)	)	PUNCT
ejpam-6811	437	7	dx	dx	PROPN
ejpam-6811	437	8	.	.	PUNCT
ejpam-6811	438	1	assuming	assume	VERB
ejpam-6811	438	2	that	that	SCONJ
ejpam-6811	438	3	the	the	DET
ejpam-6811	438	4	value	value	NOUN
ejpam-6811	438	5	on	on	ADP
ejpam-6811	438	6	the	the	DET
ejpam-6811	438	7	right	right	ADJ
ejpam-6811	438	8	hand	hand	NOUN
ejpam-6811	438	9	side	side	NOUN
ejpam-6811	438	10	is	be	AUX
ejpam-6811	438	11	not	not	PART
ejpam-6811	438	12	less	less	ADJ
ejpam-6811	438	13	than	than	ADP
ejpam-6811	438	14	1	1	NUM
ejpam-6811	438	15	and	and	CCONJ
ejpam-6811	438	16	squaring	square	VERB
ejpam-6811	438	17	both	both	DET
ejpam-6811	438	18	sides	side	NOUN
ejpam-6811	438	19	,	,	PUNCT
ejpam-6811	438	20	we	we	PRON
ejpam-6811	438	21	get	get	VERB
ejpam-6811	438	22	[	[	PUNCT
ejpam-6811	438	23	∫	∫	PROPN
ejpam-6811	438	24	b	b	PROPN
ejpam-6811	438	25	a	a	PROPN
ejpam-6811	438	26	t	t	PROPN
ejpam-6811	438	27	(	(	PUNCT
ejpam-6811	438	28	x)s(x	x)s(x	PROPN
ejpam-6811	438	29	)	)	PUNCT
ejpam-6811	438	30	dx	dx	PROPN
ejpam-6811	439	1	]	]	PUNCT
ejpam-6811	439	2	2	2	NUM
ejpam-6811	439	3	≤	≤	NUM
ejpam-6811	439	4	∫	∫	PROPN
ejpam-6811	439	5	b	b	PROPN
ejpam-6811	439	6	a	a	DET
ejpam-6811	439	7	t	t	NOUN
ejpam-6811	439	8	2(x	2(x	NUM
ejpam-6811	439	9	)	)	PUNCT
ejpam-6811	440	1	dx	dx	PROPN
ejpam-6811	440	2	∫	∫	PROPN
ejpam-6811	441	1	b	b	PROPN
ejpam-6811	441	2	a	a	DET
ejpam-6811	441	3	x2(x	x2(x	PROPN
ejpam-6811	441	4	)	)	PUNCT
ejpam-6811	441	5	dx	dx	PROPN
ejpam-6811	441	6	.	.	PUNCT
ejpam-6811	442	1	applying	apply	VERB
ejpam-6811	442	2	this	this	PRON
ejpam-6811	442	3	to	to	ADP
ejpam-6811	442	4	the	the	DET
ejpam-6811	442	5	first	first	ADJ
ejpam-6811	442	6	3	3	NUM
ejpam-6811	442	7	terms	term	NOUN
ejpam-6811	442	8	of	of	ADP
ejpam-6811	442	9	the	the	DET
ejpam-6811	442	10	right	right	ADJ
ejpam-6811	442	11	-	-	PUNCT
ejpam-6811	442	12	hand	hand	NOUN
ejpam-6811	442	13	side	side	NOUN
ejpam-6811	442	14	in	in	ADP
ejpam-6811	442	15	the	the	DET
ejpam-6811	442	16	contraction	contraction	NOUN
ejpam-6811	442	17	condition	condition	NOUN
ejpam-6811	442	18	above	above	ADV
ejpam-6811	442	19	,	,	PUNCT
ejpam-6811	442	20	we	we	PRON
ejpam-6811	442	21	get∣∣∣t(q(x	get∣∣∣t(q(x	PROPN
ejpam-6811	442	22	)	)	PUNCT
ejpam-6811	442	23	)	)	PUNCT
ejpam-6811	443	1	−	−	PROPN
ejpam-6811	443	2	t	t	PROPN
ejpam-6811	443	3	(	(	PUNCT
ejpam-6811	443	4	r(x	r(x	PROPN
ejpam-6811	443	5	)	)	PUNCT
ejpam-6811	443	6	)	)	PUNCT
ejpam-6811	443	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	443	8	≤	≤	PROPN
ejpam-6811	443	9	n2x2(n−1	n2x2(n−1	PROPN
ejpam-6811	443	10	)	)	PUNCT
ejpam-6811	443	11	(	(	PUNCT
ejpam-6811	443	12	n−	n−	PROPN
ejpam-6811	443	13	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	443	14	)	)	PUNCT
ejpam-6811	443	15	∫	∫	PROPN
ejpam-6811	443	16	η	η	PROPN
ejpam-6811	443	17	0	0	PROPN
ejpam-6811	443	18	∫	∫	PROPN
ejpam-6811	443	19	ξ	ξ	PROPN
ejpam-6811	443	20	0	0	NUM
ejpam-6811	444	1	|	|	PROPN
ejpam-6811	445	1	ξ	ξ	PROPN
ejpam-6811	445	2	−	−	PROPN
ejpam-6811	445	3	ϑ	ϑ	PROPN
ejpam-6811	445	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	445	5	)	)	PUNCT
ejpam-6811	445	6	dϑdξ	dϑdξ	PROPN
ejpam-6811	445	7	∫	∫	PROPN
ejpam-6811	445	8	η	η	PROPN
ejpam-6811	445	9	0	0	PROPN
ejpam-6811	445	10	∫	∫	PROPN
ejpam-6811	445	11	ξ	ξ	X
ejpam-6811	445	12	0	0	NUM
ejpam-6811	445	13	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	445	14	)	)	PUNCT
ejpam-6811	445	15	)	)	PUNCT
ejpam-6811	446	1	−	−	PROPN
ejpam-6811	446	2	υ	υ	PROPN
ejpam-6811	446	3	(	(	PUNCT
ejpam-6811	446	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	446	5	)	)	PUNCT
ejpam-6811	446	6	)	)	PUNCT
ejpam-6811	446	7	∣∣∣2dϑdξ	∣∣∣2dϑdξ	VERB
ejpam-6811	447	1	+	+	PUNCT
ejpam-6811	447	2	n2x2(n−1	n2x2(n−1	ADJ
ejpam-6811	447	3	)	)	PUNCT
ejpam-6811	447	4	(	(	PUNCT
ejpam-6811	447	5	n−	n−	PROPN
ejpam-6811	447	6	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	447	7	)	)	PUNCT
ejpam-6811	447	8	∫	∫	PROPN
ejpam-6811	448	1	1	1	NUM
ejpam-6811	448	2	0	0	NUM
ejpam-6811	449	1	|	|	CCONJ
ejpam-6811	449	2	1−	1−	NUM
ejpam-6811	449	3	ξ	ξ	PROPN
ejpam-6811	449	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	449	5	)	)	PUNCT
ejpam-6811	450	1	dξ	dξ	PROPN
ejpam-6811	450	2	∫	∫	PROPN
ejpam-6811	450	3	1	1	NUM
ejpam-6811	450	4	0	0	NUM
ejpam-6811	450	5	∣∣∣υ(ξ	∣∣∣υ(ξ	PROPN
ejpam-6811	450	6	,	,	PUNCT
ejpam-6811	450	7	q(ξ	q(ξ	PROPN
ejpam-6811	450	8	)	)	PUNCT
ejpam-6811	450	9	)	)	PUNCT
ejpam-6811	451	1	−	−	NOUN
ejpam-6811	451	2	υ	υ	NOUN
ejpam-6811	451	3	(	(	PUNCT
ejpam-6811	451	4	ξ	ξ	PROPN
ejpam-6811	451	5	,	,	PUNCT
ejpam-6811	451	6	r(ξ	r(ξ	NOUN
ejpam-6811	451	7	)	)	PUNCT
ejpam-6811	451	8	)	)	PUNCT
ejpam-6811	451	9	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	451	10	dξ	dξ	PROPN
ejpam-6811	452	1	+	+	PROPN
ejpam-6811	452	2	1	1	NUM
ejpam-6811	452	3	γ2(γ	γ2(γ	NOUN
ejpam-6811	452	4	)	)	PUNCT
ejpam-6811	452	5	∫	∫	PROPN
ejpam-6811	452	6	x	x	SYM
ejpam-6811	452	7	0	0	NUM
ejpam-6811	453	1	|	|	ADV
ejpam-6811	453	2	x−	x−	PROPN
ejpam-6811	453	3	ξ	ξ	PROPN
ejpam-6811	453	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	453	5	)	)	PUNCT
ejpam-6811	454	1	dξ	dξ	PROPN
ejpam-6811	454	2	∫	∫	PROPN
ejpam-6811	454	3	x	x	SYM
ejpam-6811	454	4	0	0	NUM
ejpam-6811	454	5	∣∣∣υ(ξ	∣∣∣υ(ξ	PROPN
ejpam-6811	454	6	,	,	PUNCT
ejpam-6811	454	7	q(ξ	q(ξ	PROPN
ejpam-6811	454	8	)	)	PUNCT
ejpam-6811	454	9	)	)	PUNCT
ejpam-6811	455	1	−	−	NOUN
ejpam-6811	455	2	υ	υ	NOUN
ejpam-6811	455	3	(	(	PUNCT
ejpam-6811	455	4	ξ	ξ	PROPN
ejpam-6811	455	5	,	,	PUNCT
ejpam-6811	455	6	r(ξ	r(ξ	NOUN
ejpam-6811	455	7	)	)	PUNCT
ejpam-6811	455	8	)	)	PUNCT
ejpam-6811	455	9	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	455	10	dξ	dξ	PROPN
ejpam-6811	455	11	+	+	CCONJ
ejpam-6811	455	12	2n2x2(n−1	2n2x2(n−1	NUM
ejpam-6811	455	13	)	)	PUNCT
ejpam-6811	455	14	(	(	PUNCT
ejpam-6811	455	15	n−	n−	NOUN
ejpam-6811	455	16	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	455	17	)	)	PUNCT
ejpam-6811	456	1	[	[	X
ejpam-6811	456	2	∫	∫	PROPN
ejpam-6811	456	3	η	η	PROPN
ejpam-6811	456	4	0	0	PROPN
ejpam-6811	456	5	∫	∫	PROPN
ejpam-6811	456	6	ξ	ξ	PROPN
ejpam-6811	456	7	0	0	NUM
ejpam-6811	457	1	|	|	PROPN
ejpam-6811	458	1	ξ	ξ	X
ejpam-6811	458	2	−	−	PROPN
ejpam-6811	458	3	ϑ	ϑ	X
ejpam-6811	458	4	|γ−1	|γ−1	NOUN
ejpam-6811	458	5	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	458	6	)	)	PUNCT
ejpam-6811	458	7	)	)	PUNCT
ejpam-6811	459	1	−	−	PROPN
ejpam-6811	459	2	υ	υ	PROPN
ejpam-6811	459	3	(	(	PUNCT
ejpam-6811	459	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	459	5	)	)	PUNCT
ejpam-6811	459	6	)	)	PUNCT
ejpam-6811	459	7	∣∣∣	∣∣∣	ADP
ejpam-6811	459	8	dϑdξ][∫	dϑdξ][∫	NOUN
ejpam-6811	459	9	1	1	NUM
ejpam-6811	459	10	0	0	NUM
ejpam-6811	460	1	|	|	CCONJ
ejpam-6811	460	2	1−	1−	NUM
ejpam-6811	460	3	ξ	ξ	PROPN
ejpam-6811	460	4	|γ−1	|γ−1	ADJ
ejpam-6811	460	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	460	6	,	,	PUNCT
ejpam-6811	460	7	q(ξ	q(ξ	PROPN
ejpam-6811	460	8	)	)	PUNCT
ejpam-6811	460	9	)	)	PUNCT
ejpam-6811	461	1	−	−	NOUN
ejpam-6811	461	2	υ	υ	NOUN
ejpam-6811	461	3	(	(	PUNCT
ejpam-6811	461	4	ξ	ξ	PROPN
ejpam-6811	461	5	,	,	PUNCT
ejpam-6811	461	6	r(ξ	r(ξ	NOUN
ejpam-6811	461	7	)	)	PUNCT
ejpam-6811	461	8	)	)	PUNCT
ejpam-6811	461	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	462	1	dξ	dξ	PROPN
ejpam-6811	462	2	]	]	PUNCT
ejpam-6811	462	3	+	+	CCONJ
ejpam-6811	462	4	2nx(n−1	2nx(n−1	NUM
ejpam-6811	462	5	)	)	PUNCT
ejpam-6811	462	6	(	(	PUNCT
ejpam-6811	462	7	n−	n−	NOUN
ejpam-6811	462	8	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	462	9	)	)	PUNCT
ejpam-6811	463	1	[	[	X
ejpam-6811	463	2	∫	∫	PROPN
ejpam-6811	463	3	η	η	PROPN
ejpam-6811	463	4	0	0	PROPN
ejpam-6811	463	5	∫	∫	PROPN
ejpam-6811	463	6	ξ	ξ	PROPN
ejpam-6811	463	7	0	0	NUM
ejpam-6811	464	1	|	|	PROPN
ejpam-6811	465	1	ξ	ξ	X
ejpam-6811	465	2	−	−	PROPN
ejpam-6811	465	3	ϑ	ϑ	X
ejpam-6811	465	4	|γ−1	|γ−1	NOUN
ejpam-6811	465	5	∣∣∣υ(ϑ,q(ϑ	∣∣∣υ(ϑ,q(ϑ	NOUN
ejpam-6811	465	6	)	)	PUNCT
ejpam-6811	465	7	)	)	PUNCT
ejpam-6811	466	1	−	−	PROPN
ejpam-6811	466	2	υ	υ	PROPN
ejpam-6811	466	3	(	(	PUNCT
ejpam-6811	466	4	ϑ,r(ϑ	ϑ,r(ϑ	NUM
ejpam-6811	466	5	)	)	PUNCT
ejpam-6811	466	6	)	)	PUNCT
ejpam-6811	466	7	∣∣∣	∣∣∣	ADP
ejpam-6811	466	8	dϑdξ][∫	dϑdξ][∫	NOUN
ejpam-6811	466	9	x	x	SYM
ejpam-6811	466	10	0	0	NUM
ejpam-6811	467	1	|	|	ADV
ejpam-6811	467	2	x−	x−	PROPN
ejpam-6811	467	3	ξ	ξ	PROPN
ejpam-6811	467	4	|γ−1	|γ−1	ADJ
ejpam-6811	467	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	467	6	,	,	PUNCT
ejpam-6811	467	7	q(ξ	q(ξ	PROPN
ejpam-6811	467	8	)	)	PUNCT
ejpam-6811	467	9	)	)	PUNCT
ejpam-6811	468	1	−	−	NOUN
ejpam-6811	468	2	υ	υ	NOUN
ejpam-6811	468	3	(	(	PUNCT
ejpam-6811	468	4	ξ	ξ	PROPN
ejpam-6811	468	5	,	,	PUNCT
ejpam-6811	468	6	r(ξ	r(ξ	NOUN
ejpam-6811	468	7	)	)	PUNCT
ejpam-6811	468	8	)	)	PUNCT
ejpam-6811	468	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	469	1	dξ	dξ	PROPN
ejpam-6811	469	2	]	]	PUNCT
ejpam-6811	469	3	+	+	CCONJ
ejpam-6811	469	4	2nx(n−1	2nx(n−1	NUM
ejpam-6811	469	5	)	)	PUNCT
ejpam-6811	469	6	(	(	PUNCT
ejpam-6811	469	7	n−	n−	NOUN
ejpam-6811	469	8	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	469	9	)	)	PUNCT
ejpam-6811	470	1	[	[	X
ejpam-6811	470	2	∫	∫	X
ejpam-6811	470	3	1	1	NUM
ejpam-6811	470	4	0	0	NUM
ejpam-6811	471	1	|	|	CCONJ
ejpam-6811	471	2	1−	1−	NUM
ejpam-6811	471	3	ξ	ξ	PROPN
ejpam-6811	471	4	|γ−1	|γ−1	ADJ
ejpam-6811	471	5	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	471	6	,	,	PUNCT
ejpam-6811	471	7	q(ξ	q(ξ	PROPN
ejpam-6811	471	8	)	)	PUNCT
ejpam-6811	471	9	)	)	PUNCT
ejpam-6811	472	1	−	−	NOUN
ejpam-6811	472	2	υ	υ	NOUN
ejpam-6811	472	3	(	(	PUNCT
ejpam-6811	472	4	ξ	ξ	PROPN
ejpam-6811	472	5	,	,	PUNCT
ejpam-6811	472	6	r(ξ	r(ξ	NOUN
ejpam-6811	472	7	)	)	PUNCT
ejpam-6811	472	8	)	)	PUNCT
ejpam-6811	473	1	∣∣∣	∣∣∣	ADP
ejpam-6811	473	2	dξ][∫	dξ][∫	PROPN
ejpam-6811	473	3	x	x	X
ejpam-6811	473	4	0	0	NUM
ejpam-6811	473	5	|	|	ADV
ejpam-6811	473	6	x−	x−	PROPN
ejpam-6811	473	7	ξ	ξ	PROPN
ejpam-6811	473	8	|γ−1	|γ−1	ADJ
ejpam-6811	473	9	∣∣∣υ(ξ	∣∣∣υ(ξ	NOUN
ejpam-6811	473	10	,	,	PUNCT
ejpam-6811	473	11	q(ξ	q(ξ	PROPN
ejpam-6811	473	12	)	)	PUNCT
ejpam-6811	473	13	)	)	PUNCT
ejpam-6811	474	1	−	−	NOUN
ejpam-6811	474	2	υ	υ	NOUN
ejpam-6811	474	3	(	(	PUNCT
ejpam-6811	474	4	ξ	ξ	PROPN
ejpam-6811	474	5	,	,	PUNCT
ejpam-6811	474	6	r(ξ	r(ξ	NOUN
ejpam-6811	474	7	)	)	PUNCT
ejpam-6811	474	8	)	)	PUNCT
ejpam-6811	474	9	∣∣∣	∣∣∣	NOUN
ejpam-6811	475	1	dξ	dξ	PROPN
ejpam-6811	475	2	]	]	PUNCT
ejpam-6811	475	3	.	.	PUNCT
ejpam-6811	476	1	d.	d.	PROPN
ejpam-6811	476	2	e.	e.	PROPN
ejpam-6811	476	3	shehwar	shehwar	PROPN
ejpam-6811	476	4	sagheer	sagheer	PROPN
ejpam-6811	476	5	et	et	PROPN
ejpam-6811	476	6	al	al	PROPN
ejpam-6811	476	7	.	.	PUNCT
ejpam-6811	476	8	/	/	SYM
ejpam-6811	476	9	eur	eur	PROPN
ejpam-6811	476	10	.	.	PUNCT
ejpam-6811	477	1	j.	j.	PROPN
ejpam-6811	477	2	pure	pure	PROPN
ejpam-6811	477	3	appl	appl	PROPN
ejpam-6811	477	4	.	.	PROPN
ejpam-6811	477	5	math	math	PROPN
ejpam-6811	477	6	,	,	PUNCT
ejpam-6811	477	7	18	18	NUM
ejpam-6811	477	8	(	(	PUNCT
ejpam-6811	477	9	4	4	NUM
ejpam-6811	477	10	)	)	PUNCT
ejpam-6811	477	11	(	(	PUNCT
ejpam-6811	477	12	2025	2025	NUM
ejpam-6811	477	13	)	)	PUNCT
ejpam-6811	477	14	,	,	PUNCT
ejpam-6811	477	15	6811	6811	NUM
ejpam-6811	477	16	18	18	NUM
ejpam-6811	477	17	of	of	ADP
ejpam-6811	477	18	24	24	NUM
ejpam-6811	477	19	using	use	VERB
ejpam-6811	477	20	(	(	PUNCT
ejpam-6811	477	21	4.4	4.4	NUM
ejpam-6811	477	22	)	)	PUNCT
ejpam-6811	477	23	and	and	CCONJ
ejpam-6811	477	24	(	(	PUNCT
ejpam-6811	477	25	4.5	4.5	NUM
ejpam-6811	477	26	)	)	PUNCT
ejpam-6811	478	1	,	,	PUNCT
ejpam-6811	478	2	we	we	PRON
ejpam-6811	478	3	get	get	VERB
ejpam-6811	478	4	∣∣∣t(q(x	∣∣∣t(q(x	PROPN
ejpam-6811	478	5	)	)	PUNCT
ejpam-6811	478	6	)	)	PUNCT
ejpam-6811	479	1	−	−	PROPN
ejpam-6811	479	2	t	t	PROPN
ejpam-6811	479	3	(	(	PUNCT
ejpam-6811	479	4	r(x	r(x	PROPN
ejpam-6811	479	5	)	)	PUNCT
ejpam-6811	479	6	)	)	PUNCT
ejpam-6811	479	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	479	8	≤	≤	PROPN
ejpam-6811	479	9	n2x2(n−1	n2x2(n−1	PROPN
ejpam-6811	479	10	)	)	PUNCT
ejpam-6811	479	11	(	(	PUNCT
ejpam-6811	479	12	n−	n−	PROPN
ejpam-6811	479	13	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	479	14	)	)	PUNCT
ejpam-6811	479	15	∫	∫	PROPN
ejpam-6811	479	16	η	η	PROPN
ejpam-6811	479	17	0	0	PROPN
ejpam-6811	479	18	∫	∫	PROPN
ejpam-6811	479	19	ξ	ξ	PROPN
ejpam-6811	479	20	0	0	NUM
ejpam-6811	480	1	|	|	PROPN
ejpam-6811	481	1	ξ	ξ	PROPN
ejpam-6811	481	2	−	−	PROPN
ejpam-6811	481	3	ϑ	ϑ	PROPN
ejpam-6811	481	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	481	5	)	)	PUNCT
ejpam-6811	481	6	dϑdξ	dϑdξ	PROPN
ejpam-6811	481	7	∫	∫	PROPN
ejpam-6811	481	8	η	η	PROPN
ejpam-6811	481	9	0	0	PROPN
ejpam-6811	481	10	∫	∫	PROPN
ejpam-6811	481	11	ξ	ξ	SYM
ejpam-6811	481	12	0	0	PUNCT
ejpam-6811	481	13	k2φ	k2φ	PROPN
ejpam-6811	481	14	(	(	PUNCT
ejpam-6811	481	15	|	|	ADV
ejpam-6811	481	16	q	q	PROPN
ejpam-6811	481	17	−r	−r	ADJ
ejpam-6811	481	18	|2	|2	NUM
ejpam-6811	481	19	)	)	PUNCT
ejpam-6811	481	20	dϑdξ	dϑdξ	NOUN
ejpam-6811	482	1	+	+	CCONJ
ejpam-6811	482	2	n2x2(n−1	n2x2(n−1	ADJ
ejpam-6811	482	3	)	)	PUNCT
ejpam-6811	482	4	(	(	PUNCT
ejpam-6811	482	5	n−	n−	PROPN
ejpam-6811	482	6	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	482	7	)	)	PUNCT
ejpam-6811	482	8	∫	∫	PROPN
ejpam-6811	483	1	1	1	NUM
ejpam-6811	483	2	0	0	NUM
ejpam-6811	484	1	|	|	CCONJ
ejpam-6811	484	2	1−	1−	NUM
ejpam-6811	484	3	ξ	ξ	PROPN
ejpam-6811	484	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	484	5	)	)	PUNCT
ejpam-6811	485	1	dξ	dξ	PROPN
ejpam-6811	485	2	∫	∫	PROPN
ejpam-6811	485	3	1	1	NUM
ejpam-6811	485	4	0	0	NUM
ejpam-6811	485	5	k2φ	k2φ	PROPN
ejpam-6811	485	6	(	(	PUNCT
ejpam-6811	485	7	|	|	ADV
ejpam-6811	485	8	q	q	PROPN
ejpam-6811	485	9	−r	−r	ADJ
ejpam-6811	485	10	|2	|2	NUM
ejpam-6811	485	11	)	)	PUNCT
ejpam-6811	486	1	dξ	dξ	PROPN
ejpam-6811	487	1	+	+	PUNCT
ejpam-6811	487	2	1	1	NUM
ejpam-6811	487	3	γ2(γ	γ2(γ	NOUN
ejpam-6811	487	4	)	)	PUNCT
ejpam-6811	487	5	∫	∫	PROPN
ejpam-6811	487	6	x	x	SYM
ejpam-6811	487	7	0	0	NUM
ejpam-6811	488	1	|	|	ADV
ejpam-6811	488	2	x−	x−	PROPN
ejpam-6811	488	3	ξ	ξ	PROPN
ejpam-6811	488	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	488	5	)	)	PUNCT
ejpam-6811	489	1	dξ	dξ	PROPN
ejpam-6811	489	2	∫	∫	PROPN
ejpam-6811	489	3	x	x	SYM
ejpam-6811	489	4	0	0	PROPN
ejpam-6811	489	5	k2φ	k2φ	PROPN
ejpam-6811	489	6	(	(	PUNCT
ejpam-6811	489	7	|	|	ADV
ejpam-6811	489	8	q	q	PROPN
ejpam-6811	489	9	−r	−r	ADJ
ejpam-6811	489	10	|2	|2	NUM
ejpam-6811	489	11	)	)	PUNCT
ejpam-6811	490	1	dξ	dξ	PROPN
ejpam-6811	491	1	+	+	CCONJ
ejpam-6811	491	2	2n2x2(n−1	2n2x2(n−1	NUM
ejpam-6811	491	3	)	)	PUNCT
ejpam-6811	491	4	(	(	PUNCT
ejpam-6811	491	5	n−	n−	NOUN
ejpam-6811	491	6	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	491	7	)	)	PUNCT
ejpam-6811	492	1	[	[	X
ejpam-6811	492	2	∫	∫	PROPN
ejpam-6811	492	3	η	η	PROPN
ejpam-6811	492	4	0	0	PROPN
ejpam-6811	492	5	∫	∫	PROPN
ejpam-6811	492	6	ξ	ξ	PROPN
ejpam-6811	492	7	0	0	NUM
ejpam-6811	493	1	|	|	PROPN
ejpam-6811	494	1	ξ	ξ	X
ejpam-6811	494	2	−	−	PROPN
ejpam-6811	494	3	ϑ	ϑ	X
ejpam-6811	494	4	|γ−1	|γ−1	ADJ
ejpam-6811	494	5	k1φ	k1φ	NOUN
ejpam-6811	494	6	(	(	PUNCT
ejpam-6811	494	7	|	|	ADV
ejpam-6811	494	8	q	q	PROPN
ejpam-6811	494	9	−r	−r	ADJ
ejpam-6811	494	10	|	|	NOUN
ejpam-6811	494	11	)	)	PUNCT
ejpam-6811	494	12	dϑdξ	dϑdξ	NOUN
ejpam-6811	494	13	]	]	PUNCT
ejpam-6811	495	1	[	[	X
ejpam-6811	495	2	∫	∫	X
ejpam-6811	495	3	1	1	NUM
ejpam-6811	495	4	0	0	NUM
ejpam-6811	496	1	|	|	CCONJ
ejpam-6811	496	2	1−	1−	NUM
ejpam-6811	496	3	ξ	ξ	PROPN
ejpam-6811	496	4	|γ−1	|γ−1	ADJ
ejpam-6811	496	5	k1φ	k1φ	NOUN
ejpam-6811	496	6	(	(	PUNCT
ejpam-6811	496	7	|	|	ADV
ejpam-6811	496	8	q	q	PROPN
ejpam-6811	496	9	−r	−r	PROPN
ejpam-6811	496	10	|	|	ADV
ejpam-6811	496	11	)	)	PUNCT
ejpam-6811	496	12	dξ	dξ	X
ejpam-6811	496	13	]	]	PUNCT
ejpam-6811	497	1	+	+	CCONJ
ejpam-6811	497	2	2nx(n−1	2nx(n−1	NUM
ejpam-6811	497	3	)	)	PUNCT
ejpam-6811	497	4	(	(	PUNCT
ejpam-6811	497	5	n−	n−	NOUN
ejpam-6811	497	6	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	497	7	)	)	PUNCT
ejpam-6811	498	1	[	[	X
ejpam-6811	498	2	∫	∫	PROPN
ejpam-6811	498	3	η	η	PROPN
ejpam-6811	498	4	0	0	PROPN
ejpam-6811	498	5	∫	∫	PROPN
ejpam-6811	498	6	ξ	ξ	PROPN
ejpam-6811	498	7	0	0	NUM
ejpam-6811	499	1	|	|	PROPN
ejpam-6811	500	1	ξ	ξ	X
ejpam-6811	500	2	−	−	PROPN
ejpam-6811	500	3	ϑ	ϑ	X
ejpam-6811	500	4	|γ−1	|γ−1	ADJ
ejpam-6811	500	5	k1φ	k1φ	NOUN
ejpam-6811	500	6	(	(	PUNCT
ejpam-6811	500	7	|	|	ADV
ejpam-6811	500	8	q	q	PROPN
ejpam-6811	500	9	−r	−r	ADJ
ejpam-6811	500	10	|	|	NOUN
ejpam-6811	500	11	)	)	PUNCT
ejpam-6811	500	12	dϑdξ	dϑdξ	NOUN
ejpam-6811	500	13	]	]	PUNCT
ejpam-6811	501	1	[	[	X
ejpam-6811	501	2	∫	∫	X
ejpam-6811	501	3	x	x	SYM
ejpam-6811	501	4	0	0	NUM
ejpam-6811	502	1	|	|	ADV
ejpam-6811	502	2	x−	x−	PROPN
ejpam-6811	502	3	ξ	ξ	PROPN
ejpam-6811	502	4	|γ−1	|γ−1	ADJ
ejpam-6811	502	5	k1φ	k1φ	NOUN
ejpam-6811	502	6	(	(	PUNCT
ejpam-6811	502	7	|	|	ADV
ejpam-6811	502	8	q	q	PROPN
ejpam-6811	502	9	−r	−r	PROPN
ejpam-6811	502	10	|	|	ADV
ejpam-6811	502	11	)	)	PUNCT
ejpam-6811	502	12	dξ	dξ	X
ejpam-6811	502	13	]	]	PUNCT
ejpam-6811	503	1	+	+	CCONJ
ejpam-6811	503	2	2nx(n−1	2nx(n−1	NUM
ejpam-6811	503	3	)	)	PUNCT
ejpam-6811	503	4	(	(	PUNCT
ejpam-6811	503	5	n−	n−	NOUN
ejpam-6811	503	6	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	503	7	)	)	PUNCT
ejpam-6811	504	1	[	[	X
ejpam-6811	504	2	∫	∫	X
ejpam-6811	504	3	1	1	NUM
ejpam-6811	504	4	0	0	NUM
ejpam-6811	505	1	|	|	CCONJ
ejpam-6811	505	2	1−	1−	NUM
ejpam-6811	505	3	ξ	ξ	PROPN
ejpam-6811	505	4	|γ−1	|γ−1	ADJ
ejpam-6811	505	5	k1φ	k1φ	NOUN
ejpam-6811	505	6	(	(	PUNCT
ejpam-6811	505	7	|	|	ADV
ejpam-6811	505	8	q	q	PROPN
ejpam-6811	505	9	−r	−r	PROPN
ejpam-6811	505	10	|	|	ADV
ejpam-6811	505	11	)	)	PUNCT
ejpam-6811	505	12	dξ	dξ	X
ejpam-6811	505	13	]	]	PUNCT
ejpam-6811	506	1	[	[	X
ejpam-6811	506	2	∫	∫	X
ejpam-6811	506	3	x	x	SYM
ejpam-6811	506	4	0	0	NUM
ejpam-6811	507	1	|	|	ADV
ejpam-6811	507	2	x−	x−	PROPN
ejpam-6811	507	3	ξ	ξ	PROPN
ejpam-6811	507	4	|γ−1	|γ−1	ADJ
ejpam-6811	507	5	k1φ	k1φ	NOUN
ejpam-6811	507	6	(	(	PUNCT
ejpam-6811	507	7	|	|	ADV
ejpam-6811	507	8	q	q	PROPN
ejpam-6811	507	9	−r	−r	PROPN
ejpam-6811	507	10	|	|	ADV
ejpam-6811	507	11	)	)	PUNCT
ejpam-6811	507	12	dξ	dξ	PROPN
ejpam-6811	507	13	]	]	PUNCT
ejpam-6811	507	14	.	.	PUNCT
ejpam-6811	508	1	since	since	SCONJ
ejpam-6811	508	2	x	x	PROPN
ejpam-6811	508	3	∈	∈	PROPN
ejpam-6811	508	4	[	[	X
ejpam-6811	508	5	0	0	NUM
ejpam-6811	508	6	,	,	PUNCT
ejpam-6811	508	7	1	1	NUM
ejpam-6811	508	8	]	]	PUNCT
ejpam-6811	508	9	,	,	PUNCT
ejpam-6811	508	10	we	we	PRON
ejpam-6811	508	11	have	have	VERB
ejpam-6811	508	12	∣∣∣t(q(x	∣∣∣t(q(x	PROPN
ejpam-6811	508	13	)	)	PUNCT
ejpam-6811	508	14	)	)	PUNCT
ejpam-6811	509	1	−	−	PROPN
ejpam-6811	509	2	t	t	PROPN
ejpam-6811	509	3	(	(	PUNCT
ejpam-6811	509	4	r(x	r(x	PROPN
ejpam-6811	509	5	)	)	PUNCT
ejpam-6811	509	6	)	)	PUNCT
ejpam-6811	509	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	510	1	≤	≤	NUM
ejpam-6811	510	2	∫	∫	PROPN
ejpam-6811	510	3	η	η	PROPN
ejpam-6811	510	4	0	0	PROPN
ejpam-6811	510	5	∫	∫	PROPN
ejpam-6811	510	6	ξ	ξ	PROPN
ejpam-6811	510	7	0	0	NUM
ejpam-6811	511	1	|	|	PROPN
ejpam-6811	512	1	ξ	ξ	PROPN
ejpam-6811	512	2	−	−	PROPN
ejpam-6811	512	3	ϑ	ϑ	PROPN
ejpam-6811	512	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	512	5	)	)	PUNCT
ejpam-6811	512	6	dϑdξ	dϑdξ	PROPN
ejpam-6811	512	7	∫	∫	PROPN
ejpam-6811	512	8	η	η	PROPN
ejpam-6811	512	9	0	0	PROPN
ejpam-6811	512	10	∫	∫	PROPN
ejpam-6811	512	11	ξ	ξ	SYM
ejpam-6811	512	12	0	0	PUNCT
ejpam-6811	512	13	k2φ	k2φ	PROPN
ejpam-6811	512	14	(	(	PUNCT
ejpam-6811	512	15	|	|	ADV
ejpam-6811	512	16	q	q	PROPN
ejpam-6811	512	17	−r	−r	ADJ
ejpam-6811	512	18	|2	|2	NUM
ejpam-6811	512	19	)	)	PUNCT
ejpam-6811	512	20	dϑdξ	dϑdξ	NOUN
ejpam-6811	513	1	+	+	CCONJ
ejpam-6811	513	2	n2	n2	ADJ
ejpam-6811	513	3	(	(	PUNCT
ejpam-6811	513	4	n−	n−	PROPN
ejpam-6811	513	5	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	513	6	)	)	PUNCT
ejpam-6811	513	7	∫	∫	PROPN
ejpam-6811	514	1	1	1	NUM
ejpam-6811	514	2	0	0	NUM
ejpam-6811	515	1	|	|	CCONJ
ejpam-6811	515	2	1−	1−	NUM
ejpam-6811	515	3	ξ	ξ	PROPN
ejpam-6811	515	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	515	5	)	)	PUNCT
ejpam-6811	516	1	dξ	dξ	PROPN
ejpam-6811	516	2	∫	∫	PROPN
ejpam-6811	516	3	1	1	NUM
ejpam-6811	516	4	0	0	NUM
ejpam-6811	516	5	k2φ	k2φ	PROPN
ejpam-6811	516	6	(	(	PUNCT
ejpam-6811	516	7	|	|	ADV
ejpam-6811	516	8	q	q	PROPN
ejpam-6811	516	9	−r	−r	ADJ
ejpam-6811	516	10	|2	|2	NUM
ejpam-6811	516	11	)	)	PUNCT
ejpam-6811	517	1	dξ	dξ	PROPN
ejpam-6811	518	1	+	+	PUNCT
ejpam-6811	518	2	1	1	NUM
ejpam-6811	518	3	γ2(γ	γ2(γ	NOUN
ejpam-6811	518	4	)	)	PUNCT
ejpam-6811	518	5	∫	∫	PROPN
ejpam-6811	518	6	x	x	SYM
ejpam-6811	518	7	0	0	NUM
ejpam-6811	519	1	|	|	ADV
ejpam-6811	519	2	x−	x−	PROPN
ejpam-6811	519	3	ξ	ξ	PROPN
ejpam-6811	519	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	519	5	)	)	PUNCT
ejpam-6811	520	1	dξ	dξ	PROPN
ejpam-6811	520	2	∫	∫	PROPN
ejpam-6811	520	3	x	x	SYM
ejpam-6811	520	4	0	0	PROPN
ejpam-6811	520	5	k2φ	k2φ	PROPN
ejpam-6811	520	6	(	(	PUNCT
ejpam-6811	520	7	|	|	ADV
ejpam-6811	520	8	q	q	PROPN
ejpam-6811	520	9	−r	−r	ADJ
ejpam-6811	520	10	|2	|2	NUM
ejpam-6811	520	11	)	)	PUNCT
ejpam-6811	521	1	dξ	dξ	PROPN
ejpam-6811	522	1	+	+	ADJ
ejpam-6811	522	2	2n2	2n2	NUM
ejpam-6811	522	3	(	(	PUNCT
ejpam-6811	522	4	n−	n−	NOUN
ejpam-6811	522	5	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	522	6	)	)	PUNCT
ejpam-6811	523	1	[	[	X
ejpam-6811	523	2	∫	∫	PROPN
ejpam-6811	523	3	η	η	PROPN
ejpam-6811	523	4	0	0	PROPN
ejpam-6811	523	5	∫	∫	PROPN
ejpam-6811	523	6	ξ	ξ	PROPN
ejpam-6811	523	7	0	0	NUM
ejpam-6811	524	1	|	|	PROPN
ejpam-6811	525	1	ξ	ξ	X
ejpam-6811	525	2	−	−	PROPN
ejpam-6811	525	3	ϑ	ϑ	X
ejpam-6811	525	4	|γ−1	|γ−1	ADJ
ejpam-6811	525	5	k1φ	k1φ	NOUN
ejpam-6811	525	6	(	(	PUNCT
ejpam-6811	525	7	|	|	ADV
ejpam-6811	525	8	q	q	PROPN
ejpam-6811	525	9	−r	−r	ADJ
ejpam-6811	525	10	|	|	NOUN
ejpam-6811	525	11	)	)	PUNCT
ejpam-6811	525	12	dϑdξ	dϑdξ	NOUN
ejpam-6811	525	13	]	]	PUNCT
ejpam-6811	526	1	[	[	X
ejpam-6811	526	2	∫	∫	X
ejpam-6811	526	3	1	1	NUM
ejpam-6811	526	4	0	0	NUM
ejpam-6811	527	1	|	|	CCONJ
ejpam-6811	527	2	1−	1−	NUM
ejpam-6811	527	3	ξ	ξ	PROPN
ejpam-6811	527	4	|γ−1	|γ−1	ADJ
ejpam-6811	527	5	k1φ	k1φ	NOUN
ejpam-6811	527	6	(	(	PUNCT
ejpam-6811	527	7	|	|	ADV
ejpam-6811	527	8	q	q	PROPN
ejpam-6811	527	9	−r	−r	PROPN
ejpam-6811	527	10	|	|	ADV
ejpam-6811	527	11	)	)	PUNCT
ejpam-6811	527	12	dξ	dξ	PROPN
ejpam-6811	527	13	]	]	PUNCT
ejpam-6811	528	1	+	+	CCONJ
ejpam-6811	528	2	2n	2n	NUM
ejpam-6811	528	3	(	(	PUNCT
ejpam-6811	528	4	n−	n−	NOUN
ejpam-6811	528	5	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	528	6	)	)	PUNCT
ejpam-6811	529	1	[	[	X
ejpam-6811	529	2	∫	∫	PROPN
ejpam-6811	529	3	η	η	PROPN
ejpam-6811	529	4	0	0	PROPN
ejpam-6811	529	5	∫	∫	PROPN
ejpam-6811	529	6	ξ	ξ	PROPN
ejpam-6811	529	7	0	0	NUM
ejpam-6811	530	1	|	|	PROPN
ejpam-6811	531	1	ξ	ξ	X
ejpam-6811	531	2	−	−	PROPN
ejpam-6811	531	3	ϑ	ϑ	X
ejpam-6811	531	4	|γ−1	|γ−1	ADJ
ejpam-6811	531	5	k1φ	k1φ	NOUN
ejpam-6811	531	6	(	(	PUNCT
ejpam-6811	531	7	|	|	ADV
ejpam-6811	531	8	q	q	PROPN
ejpam-6811	531	9	−r	−r	ADJ
ejpam-6811	531	10	|	|	NOUN
ejpam-6811	531	11	)	)	PUNCT
ejpam-6811	531	12	dϑdξ	dϑdξ	NOUN
ejpam-6811	531	13	]	]	PUNCT
ejpam-6811	532	1	[	[	X
ejpam-6811	532	2	∫	∫	X
ejpam-6811	532	3	x	x	SYM
ejpam-6811	532	4	0	0	NUM
ejpam-6811	533	1	|	|	ADV
ejpam-6811	533	2	x−	x−	PROPN
ejpam-6811	533	3	ξ	ξ	PROPN
ejpam-6811	533	4	|γ−1	|γ−1	ADJ
ejpam-6811	533	5	k1φ	k1φ	NOUN
ejpam-6811	533	6	(	(	PUNCT
ejpam-6811	533	7	|	|	ADV
ejpam-6811	533	8	q	q	PROPN
ejpam-6811	533	9	−r	−r	PROPN
ejpam-6811	533	10	|	|	ADV
ejpam-6811	533	11	)	)	PUNCT
ejpam-6811	533	12	dξ	dξ	PROPN
ejpam-6811	533	13	]	]	PUNCT
ejpam-6811	534	1	+	+	CCONJ
ejpam-6811	534	2	2n	2n	NUM
ejpam-6811	534	3	(	(	PUNCT
ejpam-6811	534	4	n−	n−	NOUN
ejpam-6811	534	5	ηn)γ2(γ	ηn)γ2(γ	NOUN
ejpam-6811	534	6	)	)	PUNCT
ejpam-6811	535	1	[	[	X
ejpam-6811	535	2	∫	∫	X
ejpam-6811	535	3	1	1	NUM
ejpam-6811	535	4	0	0	NUM
ejpam-6811	536	1	|	|	CCONJ
ejpam-6811	536	2	1−	1−	NUM
ejpam-6811	536	3	ξ	ξ	PROPN
ejpam-6811	536	4	|γ−1	|γ−1	ADJ
ejpam-6811	536	5	k1φ	k1φ	NOUN
ejpam-6811	536	6	(	(	PUNCT
ejpam-6811	536	7	|	|	ADV
ejpam-6811	536	8	q	q	PROPN
ejpam-6811	536	9	−r	−r	PROPN
ejpam-6811	536	10	|	|	ADV
ejpam-6811	536	11	)	)	PUNCT
ejpam-6811	536	12	dξ	dξ	X
ejpam-6811	536	13	]	]	PUNCT
ejpam-6811	537	1	[	[	X
ejpam-6811	537	2	∫	∫	X
ejpam-6811	537	3	x	x	SYM
ejpam-6811	537	4	0	0	NUM
ejpam-6811	538	1	|	|	ADV
ejpam-6811	538	2	x−	x−	PROPN
ejpam-6811	538	3	ξ	ξ	PROPN
ejpam-6811	538	4	|γ−1	|γ−1	ADJ
ejpam-6811	538	5	k1φ	k1φ	NOUN
ejpam-6811	538	6	(	(	PUNCT
ejpam-6811	538	7	|	|	ADV
ejpam-6811	538	8	q	q	PROPN
ejpam-6811	538	9	−r	−r	PROPN
ejpam-6811	538	10	|	|	ADV
ejpam-6811	538	11	)	)	PUNCT
ejpam-6811	538	12	dξ	dξ	PROPN
ejpam-6811	538	13	]	]	PUNCT
ejpam-6811	538	14	≤	≤	NUM
ejpam-6811	538	15	n2	n2	NOUN
ejpam-6811	538	16	(	(	PUNCT
ejpam-6811	538	17	n−	n−	NOUN
ejpam-6811	538	18	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	538	19	)	)	PUNCT
ejpam-6811	539	1	[	[	X
ejpam-6811	539	2	∫	∫	PROPN
ejpam-6811	539	3	η	η	PROPN
ejpam-6811	539	4	0	0	PROPN
ejpam-6811	539	5	∫	∫	PROPN
ejpam-6811	539	6	ξ	ξ	PROPN
ejpam-6811	539	7	0	0	NUM
ejpam-6811	540	1	|	|	PROPN
ejpam-6811	541	1	ξ	ξ	PROPN
ejpam-6811	541	2	−	−	PROPN
ejpam-6811	541	3	ϑ	ϑ	X
ejpam-6811	541	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	541	5	)	)	PUNCT
ejpam-6811	541	6	dϑdξ	dϑdξ	NOUN
ejpam-6811	542	1	+	+	CCONJ
ejpam-6811	542	2	∫	∫	PROPN
ejpam-6811	543	1	1	1	NUM
ejpam-6811	543	2	0	0	NUM
ejpam-6811	544	1	|	|	CCONJ
ejpam-6811	544	2	1−	1−	NUM
ejpam-6811	544	3	ξ	ξ	PROPN
ejpam-6811	544	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	544	5	)	)	PUNCT
ejpam-6811	545	1	dξ	dξ	PROPN
ejpam-6811	545	2	d.	d.	PROPN
ejpam-6811	545	3	e.	e.	PROPN
ejpam-6811	546	1	shehwar	shehwar	PROPN
ejpam-6811	546	2	sagheer	sagheer	PROPN
ejpam-6811	546	3	et	et	PROPN
ejpam-6811	546	4	al	al	PROPN
ejpam-6811	546	5	.	.	PUNCT
ejpam-6811	546	6	/	/	SYM
ejpam-6811	546	7	eur	eur	PROPN
ejpam-6811	546	8	.	.	PUNCT
ejpam-6811	547	1	j.	j.	PROPN
ejpam-6811	547	2	pure	pure	PROPN
ejpam-6811	547	3	appl	appl	PROPN
ejpam-6811	547	4	.	.	PROPN
ejpam-6811	547	5	math	math	PROPN
ejpam-6811	547	6	,	,	PUNCT
ejpam-6811	547	7	18	18	NUM
ejpam-6811	547	8	(	(	PUNCT
ejpam-6811	547	9	4	4	NUM
ejpam-6811	547	10	)	)	PUNCT
ejpam-6811	547	11	(	(	PUNCT
ejpam-6811	547	12	2025	2025	NUM
ejpam-6811	547	13	)	)	PUNCT
ejpam-6811	547	14	,	,	PUNCT
ejpam-6811	547	15	6811	6811	NUM
ejpam-6811	547	16	19	19	NUM
ejpam-6811	547	17	of	of	ADP
ejpam-6811	547	18	24	24	NUM
ejpam-6811	547	19	+	+	CCONJ
ejpam-6811	547	20	(	(	PUNCT
ejpam-6811	547	21	n−	n−	PROPN
ejpam-6811	547	22	ηn)2	ηn)2	PROPN
ejpam-6811	547	23	n2	n2	PROPN
ejpam-6811	547	24	∫	∫	PROPN
ejpam-6811	547	25	x	x	SYM
ejpam-6811	547	26	0	0	NUM
ejpam-6811	548	1	|	|	ADV
ejpam-6811	548	2	x−	x−	PROPN
ejpam-6811	548	3	ξ	ξ	PROPN
ejpam-6811	548	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	548	5	)	)	PUNCT
ejpam-6811	548	6	dξ	dξ	X
ejpam-6811	548	7	]	]	PUNCT
ejpam-6811	549	1	[	[	PUNCT
ejpam-6811	549	2	k2φ	k2φ	PROPN
ejpam-6811	549	3	(	(	PUNCT
ejpam-6811	549	4	||	||	PROPN
ejpam-6811	549	5	q	q	PROPN
ejpam-6811	549	6	−r	−r	PROPN
ejpam-6811	549	7	||∗∞	||∗∞	PROPN
ejpam-6811	549	8	)	)	PUNCT
ejpam-6811	549	9	]	]	PUNCT
ejpam-6811	550	1	+	+	CCONJ
ejpam-6811	550	2	2n2	2n2	NUM
ejpam-6811	550	3	(	(	PUNCT
ejpam-6811	550	4	n−	n−	NOUN
ejpam-6811	550	5	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	550	6	)	)	PUNCT
ejpam-6811	551	1	[	[	X
ejpam-6811	551	2	∫	∫	PROPN
ejpam-6811	551	3	η	η	PROPN
ejpam-6811	551	4	0	0	PROPN
ejpam-6811	551	5	∫	∫	PROPN
ejpam-6811	551	6	ξ	ξ	PROPN
ejpam-6811	551	7	0	0	NUM
ejpam-6811	552	1	|	|	PROPN
ejpam-6811	553	1	ξ	ξ	X
ejpam-6811	553	2	−	−	PROPN
ejpam-6811	553	3	ϑ	ϑ	X
ejpam-6811	553	4	|γ−1	|γ−1	ADJ
ejpam-6811	553	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	553	6	∫	∫	PROPN
ejpam-6811	554	1	1	1	NUM
ejpam-6811	554	2	0	0	NUM
ejpam-6811	555	1	|	|	CCONJ
ejpam-6811	555	2	1−	1−	NUM
ejpam-6811	555	3	ξ	ξ	PROPN
ejpam-6811	555	4	|γ−1	|γ−1	NOUN
ejpam-6811	555	5	dξ	dξ	PROPN
ejpam-6811	556	1	+	+	CCONJ
ejpam-6811	556	2	(	(	PUNCT
ejpam-6811	556	3	n−	n−	NOUN
ejpam-6811	556	4	ηn	ηn	ADJ
ejpam-6811	556	5	)	)	PUNCT
ejpam-6811	556	6	n	n	CCONJ
ejpam-6811	556	7	∫	∫	PROPN
ejpam-6811	556	8	η	η	PROPN
ejpam-6811	556	9	0	0	PROPN
ejpam-6811	556	10	∫	∫	PROPN
ejpam-6811	557	1	ξ	ξ	PROPN
ejpam-6811	557	2	0	0	NUM
ejpam-6811	558	1	|	|	PROPN
ejpam-6811	559	1	ξ	ξ	X
ejpam-6811	559	2	−	−	PROPN
ejpam-6811	559	3	ϑ	ϑ	X
ejpam-6811	559	4	|γ−1	|γ−1	ADJ
ejpam-6811	559	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	559	6	∫	∫	PROPN
ejpam-6811	560	1	x	x	SYM
ejpam-6811	560	2	0	0	NUM
ejpam-6811	561	1	|	|	ADV
ejpam-6811	561	2	x−	x−	PROPN
ejpam-6811	561	3	ξ	ξ	PROPN
ejpam-6811	561	4	|γ−1	|γ−1	PROPN
ejpam-6811	561	5	dξ	dξ	PROPN
ejpam-6811	562	1	+	+	CCONJ
ejpam-6811	562	2	(	(	PUNCT
ejpam-6811	562	3	n−	n−	NOUN
ejpam-6811	562	4	ηn	ηn	ADJ
ejpam-6811	562	5	)	)	PUNCT
ejpam-6811	562	6	n	n	CCONJ
ejpam-6811	562	7	∫	∫	NOUN
ejpam-6811	562	8	1	1	NUM
ejpam-6811	562	9	0	0	NUM
ejpam-6811	563	1	|	|	CCONJ
ejpam-6811	563	2	1−	1−	NUM
ejpam-6811	563	3	ξ	ξ	PROPN
ejpam-6811	563	4	|γ−1	|γ−1	PROPN
ejpam-6811	563	5	dξ	dξ	PROPN
ejpam-6811	563	6	∫	∫	PROPN
ejpam-6811	563	7	x	x	X
ejpam-6811	563	8	0	0	NUM
ejpam-6811	564	1	|	|	ADV
ejpam-6811	564	2	x−	x−	PROPN
ejpam-6811	564	3	ξ	ξ	PROPN
ejpam-6811	564	4	|γ−1	|γ−1	PROPN
ejpam-6811	564	5	dξ	dξ	X
ejpam-6811	564	6	]	]	X
ejpam-6811	564	7	[	[	PUNCT
ejpam-6811	564	8	k2	k2	X
ejpam-6811	564	9	1	1	NUM
ejpam-6811	564	10	(	(	PUNCT
ejpam-6811	564	11	φ	φ	PROPN
ejpam-6811	564	12	(	(	PUNCT
ejpam-6811	564	13	||	||	PROPN
ejpam-6811	564	14	q	q	PROPN
ejpam-6811	564	15	−r	−r	PROPN
ejpam-6811	564	16	||∞	||∞	PROPN
ejpam-6811	564	17	)	)	PUNCT
ejpam-6811	564	18	)	)	PUNCT
ejpam-6811	564	19	2	2	X
ejpam-6811	564	20	]	]	PUNCT
ejpam-6811	564	21	≤	≤	NOUN
ejpam-6811	564	22	2n2	2n2	NUM
ejpam-6811	564	23	(	(	PUNCT
ejpam-6811	564	24	n−	n−	PROPN
ejpam-6811	564	25	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	564	26	)	)	PUNCT
ejpam-6811	565	1	[	[	X
ejpam-6811	565	2	∫	∫	PROPN
ejpam-6811	565	3	η	η	PROPN
ejpam-6811	565	4	0	0	PROPN
ejpam-6811	565	5	∫	∫	PROPN
ejpam-6811	565	6	ξ	ξ	PROPN
ejpam-6811	565	7	0	0	NUM
ejpam-6811	566	1	|	|	PROPN
ejpam-6811	567	1	ξ	ξ	PROPN
ejpam-6811	567	2	−	−	PROPN
ejpam-6811	567	3	ϑ	ϑ	X
ejpam-6811	567	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	567	5	)	)	PUNCT
ejpam-6811	567	6	dϑdξ	dϑdξ	NOUN
ejpam-6811	568	1	+	+	CCONJ
ejpam-6811	568	2	∫	∫	PROPN
ejpam-6811	569	1	1	1	NUM
ejpam-6811	569	2	0	0	NUM
ejpam-6811	570	1	|	|	CCONJ
ejpam-6811	570	2	1−	1−	NUM
ejpam-6811	570	3	ξ	ξ	PROPN
ejpam-6811	570	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	570	5	)	)	PUNCT
ejpam-6811	570	6	dξ	dξ	PROPN
ejpam-6811	571	1	+	+	CCONJ
ejpam-6811	571	2	(	(	PUNCT
ejpam-6811	571	3	n−	n−	PROPN
ejpam-6811	571	4	ηn)2	ηn)2	PROPN
ejpam-6811	571	5	n2	n2	PROPN
ejpam-6811	571	6	∫	∫	PROPN
ejpam-6811	572	1	x	x	SYM
ejpam-6811	572	2	0	0	NUM
ejpam-6811	573	1	|	|	ADV
ejpam-6811	573	2	x−	x−	PROPN
ejpam-6811	573	3	ξ	ξ	PROPN
ejpam-6811	573	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	573	5	)	)	PUNCT
ejpam-6811	573	6	dξ	dξ	PROPN
ejpam-6811	574	1	+	+	CCONJ
ejpam-6811	574	2	∫	∫	PROPN
ejpam-6811	574	3	η	η	PROPN
ejpam-6811	574	4	0	0	PROPN
ejpam-6811	574	5	∫	∫	PROPN
ejpam-6811	575	1	ξ	ξ	PROPN
ejpam-6811	575	2	0	0	NUM
ejpam-6811	576	1	|	|	PROPN
ejpam-6811	577	1	ξ	ξ	X
ejpam-6811	577	2	−	−	PROPN
ejpam-6811	577	3	ϑ	ϑ	X
ejpam-6811	577	4	|γ−1	|γ−1	ADJ
ejpam-6811	577	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	577	6	∫	∫	PROPN
ejpam-6811	578	1	1	1	NUM
ejpam-6811	578	2	0	0	NUM
ejpam-6811	579	1	|	|	CCONJ
ejpam-6811	579	2	1−	1−	NUM
ejpam-6811	579	3	ξ	ξ	PROPN
ejpam-6811	579	4	|γ−1	|γ−1	NOUN
ejpam-6811	579	5	dξ	dξ	PROPN
ejpam-6811	580	1	+	+	CCONJ
ejpam-6811	580	2	(	(	PUNCT
ejpam-6811	580	3	n−	n−	NOUN
ejpam-6811	580	4	ηn	ηn	ADJ
ejpam-6811	580	5	)	)	PUNCT
ejpam-6811	580	6	n	n	CCONJ
ejpam-6811	580	7	∫	∫	PROPN
ejpam-6811	580	8	η	η	PROPN
ejpam-6811	580	9	0	0	PROPN
ejpam-6811	580	10	∫	∫	PROPN
ejpam-6811	581	1	ξ	ξ	PROPN
ejpam-6811	581	2	0	0	NUM
ejpam-6811	582	1	|	|	PROPN
ejpam-6811	583	1	ξ	ξ	X
ejpam-6811	583	2	−	−	PROPN
ejpam-6811	583	3	ϑ	ϑ	X
ejpam-6811	583	4	|γ−1	|γ−1	ADJ
ejpam-6811	583	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	583	6	∫	∫	PROPN
ejpam-6811	584	1	x	x	SYM
ejpam-6811	584	2	0	0	NUM
ejpam-6811	585	1	|	|	ADV
ejpam-6811	585	2	x−	x−	PROPN
ejpam-6811	585	3	ξ	ξ	PROPN
ejpam-6811	585	4	|γ−1	|γ−1	PROPN
ejpam-6811	585	5	dξ	dξ	PROPN
ejpam-6811	586	1	+	+	CCONJ
ejpam-6811	586	2	(	(	PUNCT
ejpam-6811	586	3	n−	n−	NOUN
ejpam-6811	586	4	ηn	ηn	ADJ
ejpam-6811	586	5	)	)	PUNCT
ejpam-6811	586	6	n	n	CCONJ
ejpam-6811	586	7	∫	∫	NOUN
ejpam-6811	586	8	1	1	NUM
ejpam-6811	586	9	0	0	NUM
ejpam-6811	587	1	|	|	CCONJ
ejpam-6811	587	2	1−	1−	NUM
ejpam-6811	587	3	ξ	ξ	PROPN
ejpam-6811	587	4	|γ−1	|γ−1	PROPN
ejpam-6811	587	5	dξ	dξ	PROPN
ejpam-6811	587	6	∫	∫	PROPN
ejpam-6811	587	7	x	x	X
ejpam-6811	587	8	0	0	NUM
ejpam-6811	588	1	|	|	ADV
ejpam-6811	588	2	x−	x−	PROPN
ejpam-6811	588	3	ξ	ξ	PROPN
ejpam-6811	588	4	|γ−1	|γ−1	PROPN
ejpam-6811	588	5	dξ	dξ	X
ejpam-6811	588	6	]	]	X
ejpam-6811	588	7	[	[	PUNCT
ejpam-6811	588	8	k2φ	k2φ	PROPN
ejpam-6811	588	9	(	(	PUNCT
ejpam-6811	588	10	||	||	PROPN
ejpam-6811	588	11	q	q	PROPN
ejpam-6811	588	12	−r	−r	PROPN
ejpam-6811	588	13	||∗∞	||∗∞	PROPN
ejpam-6811	588	14	)	)	PUNCT
ejpam-6811	588	15	]	]	PUNCT
ejpam-6811	588	16	.	.	PUNCT
ejpam-6811	589	1	let	let	VERB
ejpam-6811	589	2	c	c	NOUN
ejpam-6811	589	3	=	=	SYM
ejpam-6811	589	4	2n2	2n2	NUM
ejpam-6811	589	5	(	(	PUNCT
ejpam-6811	589	6	n−	n−	PROPN
ejpam-6811	589	7	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	589	8	)	)	PUNCT
ejpam-6811	589	9	sup	sup	NOUN
ejpam-6811	589	10	x∈(0,1	x∈(0,1	ADV
ejpam-6811	589	11	)	)	PUNCT
ejpam-6811	590	1	[	[	X
ejpam-6811	590	2	∫	∫	X
ejpam-6811	590	3	η	η	PROPN
ejpam-6811	590	4	0	0	PROPN
ejpam-6811	590	5	∫	∫	PROPN
ejpam-6811	590	6	ξ	ξ	PROPN
ejpam-6811	590	7	0	0	NUM
ejpam-6811	590	8	|	|	PROPN
ejpam-6811	590	9	ξ	ξ	PROPN
ejpam-6811	590	10	−	−	PROPN
ejpam-6811	590	11	ϑ	ϑ	X
ejpam-6811	590	12	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	590	13	)	)	PUNCT
ejpam-6811	590	14	dϑdξ	dϑdξ	NOUN
ejpam-6811	591	1	+	+	CCONJ
ejpam-6811	591	2	∫	∫	PROPN
ejpam-6811	592	1	1	1	NUM
ejpam-6811	592	2	0	0	NUM
ejpam-6811	593	1	|	|	CCONJ
ejpam-6811	593	2	1−	1−	NUM
ejpam-6811	593	3	ξ	ξ	PROPN
ejpam-6811	593	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	593	5	)	)	PUNCT
ejpam-6811	593	6	dξ	dξ	PROPN
ejpam-6811	594	1	+	+	CCONJ
ejpam-6811	594	2	(	(	PUNCT
ejpam-6811	594	3	n−	n−	PROPN
ejpam-6811	594	4	ηn)2	ηn)2	PROPN
ejpam-6811	594	5	n2	n2	PROPN
ejpam-6811	594	6	∫	∫	PROPN
ejpam-6811	595	1	x	x	SYM
ejpam-6811	595	2	0	0	NUM
ejpam-6811	596	1	|	|	ADV
ejpam-6811	596	2	x−	x−	PROPN
ejpam-6811	596	3	ξ	ξ	PROPN
ejpam-6811	596	4	|2(γ−1	|2(γ−1	NOUN
ejpam-6811	596	5	)	)	PUNCT
ejpam-6811	596	6	dξ	dξ	PROPN
ejpam-6811	597	1	+	+	CCONJ
ejpam-6811	597	2	∫	∫	PROPN
ejpam-6811	597	3	η	η	PROPN
ejpam-6811	597	4	0	0	PROPN
ejpam-6811	597	5	∫	∫	PROPN
ejpam-6811	598	1	ξ	ξ	PROPN
ejpam-6811	598	2	0	0	NUM
ejpam-6811	599	1	|	|	PROPN
ejpam-6811	600	1	ξ	ξ	X
ejpam-6811	600	2	−	−	PROPN
ejpam-6811	600	3	ϑ	ϑ	X
ejpam-6811	600	4	|γ−1	|γ−1	ADJ
ejpam-6811	600	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	600	6	∫	∫	PROPN
ejpam-6811	601	1	1	1	NUM
ejpam-6811	601	2	0	0	NUM
ejpam-6811	602	1	|	|	CCONJ
ejpam-6811	602	2	1−	1−	NUM
ejpam-6811	602	3	ξ	ξ	PROPN
ejpam-6811	602	4	|γ−1	|γ−1	NOUN
ejpam-6811	602	5	dξ	dξ	PROPN
ejpam-6811	603	1	+	+	CCONJ
ejpam-6811	603	2	(	(	PUNCT
ejpam-6811	603	3	n−	n−	NOUN
ejpam-6811	603	4	ηn	ηn	ADJ
ejpam-6811	603	5	)	)	PUNCT
ejpam-6811	603	6	n	n	CCONJ
ejpam-6811	603	7	∫	∫	PROPN
ejpam-6811	603	8	η	η	PROPN
ejpam-6811	603	9	0	0	PROPN
ejpam-6811	603	10	∫	∫	PROPN
ejpam-6811	604	1	ξ	ξ	PROPN
ejpam-6811	604	2	0	0	NUM
ejpam-6811	605	1	|	|	PROPN
ejpam-6811	606	1	ξ	ξ	X
ejpam-6811	606	2	−	−	PROPN
ejpam-6811	606	3	ϑ	ϑ	X
ejpam-6811	606	4	|γ−1	|γ−1	ADJ
ejpam-6811	606	5	dϑdξ	dϑdξ	ADJ
ejpam-6811	606	6	∫	∫	PROPN
ejpam-6811	607	1	x	x	SYM
ejpam-6811	607	2	0	0	NUM
ejpam-6811	608	1	|	|	ADV
ejpam-6811	608	2	x−	x−	PROPN
ejpam-6811	608	3	ξ	ξ	PROPN
ejpam-6811	608	4	|γ−1	|γ−1	PROPN
ejpam-6811	608	5	dξ	dξ	PROPN
ejpam-6811	609	1	+	+	CCONJ
ejpam-6811	609	2	(	(	PUNCT
ejpam-6811	609	3	n−	n−	NOUN
ejpam-6811	609	4	ηn	ηn	ADJ
ejpam-6811	609	5	)	)	PUNCT
ejpam-6811	609	6	n	n	CCONJ
ejpam-6811	609	7	∫	∫	NOUN
ejpam-6811	609	8	1	1	NUM
ejpam-6811	609	9	0	0	NUM
ejpam-6811	610	1	|	|	CCONJ
ejpam-6811	610	2	1−	1−	NUM
ejpam-6811	610	3	ξ	ξ	PROPN
ejpam-6811	610	4	|γ−1	|γ−1	PROPN
ejpam-6811	610	5	dξ	dξ	PROPN
ejpam-6811	610	6	∫	∫	PROPN
ejpam-6811	610	7	x	x	X
ejpam-6811	610	8	0	0	NUM
ejpam-6811	611	1	|	|	ADV
ejpam-6811	611	2	x−	x−	PROPN
ejpam-6811	611	3	ξ	ξ	PROPN
ejpam-6811	611	4	|γ−1	|γ−1	PROPN
ejpam-6811	611	5	dξ	dξ	X
ejpam-6811	611	6	]	]	PUNCT
ejpam-6811	611	7	.	.	PUNCT
ejpam-6811	612	1	further	further	ADJ
ejpam-6811	612	2	calculations	calculation	NOUN
ejpam-6811	612	3	give	give	VERB
ejpam-6811	612	4	c	c	NOUN
ejpam-6811	612	5	=	=	SYM
ejpam-6811	612	6	2n2	2n2	NUM
ejpam-6811	612	7	(	(	PUNCT
ejpam-6811	612	8	n−	n−	NOUN
ejpam-6811	612	9	ηn)2γ2(γ	ηn)2γ2(γ	NOUN
ejpam-6811	612	10	)	)	PUNCT
ejpam-6811	613	1	[	[	PUNCT
ejpam-6811	613	2	η2γ	η2γ	PROPN
ejpam-6811	613	3	2γ(2γ	2γ(2γ	NUM
ejpam-6811	613	4	−	−	NOUN
ejpam-6811	613	5	1	1	NUM
ejpam-6811	613	6	)	)	PUNCT
ejpam-6811	613	7	+	+	CCONJ
ejpam-6811	613	8	1	1	NUM
ejpam-6811	613	9	2γ	2γ	NOUN
ejpam-6811	613	10	−	−	PROPN
ejpam-6811	613	11	1	1	NUM
ejpam-6811	613	12	+	+	CCONJ
ejpam-6811	613	13	(	(	PUNCT
ejpam-6811	613	14	n−	n−	NOUN
ejpam-6811	613	15	ηn)2	ηn)2	VERB
ejpam-6811	613	16	n2(2γ	n2(2γ	NOUN
ejpam-6811	613	17	−	−	PROPN
ejpam-6811	613	18	1	1	NUM
ejpam-6811	613	19	)	)	PUNCT
ejpam-6811	614	1	+	+	CCONJ
ejpam-6811	614	2	nγ+1	nγ+1	NUM
ejpam-6811	614	3	γ2(γ	γ2(γ	NOUN
ejpam-6811	615	1	+	+	NOUN
ejpam-6811	615	2	1	1	NUM
ejpam-6811	615	3	)	)	PUNCT
ejpam-6811	615	4	+	+	X
ejpam-6811	615	5	ηγ+1(n−	ηγ+1(n−	ADJ
ejpam-6811	615	6	ηn	ηn	ADJ
ejpam-6811	615	7	)	)	PUNCT
ejpam-6811	615	8	nγ2(γ	nγ2(γ	PROPN
ejpam-6811	615	9	+	+	CCONJ
ejpam-6811	615	10	1	1	X
ejpam-6811	615	11	)	)	PUNCT
ejpam-6811	615	12	+	+	CCONJ
ejpam-6811	615	13	n−	n−	NOUN
ejpam-6811	615	14	ηn	ηn	VERB
ejpam-6811	615	15	nγ2	nγ2	NUM
ejpam-6811	615	16	]	]	PUNCT
ejpam-6811	615	17	.	.	PUNCT
ejpam-6811	616	1	we	we	PRON
ejpam-6811	616	2	see	see	VERB
ejpam-6811	616	3	that	that	SCONJ
ejpam-6811	616	4	k2	k2	ADJ
ejpam-6811	616	5	≤	≤	ADV
ejpam-6811	616	6	1	1	NUM
ejpam-6811	616	7	c	c	NOUN
ejpam-6811	616	8	.	.	PUNCT
ejpam-6811	617	1	this	this	PRON
ejpam-6811	617	2	gives	give	VERB
ejpam-6811	617	3	us	we	PRON
ejpam-6811	617	4	∣∣∣t(q(x	∣∣∣t(q(x	PROPN
ejpam-6811	617	5	)	)	PUNCT
ejpam-6811	617	6	)	)	PUNCT
ejpam-6811	618	1	−	−	PROPN
ejpam-6811	618	2	t	t	PROPN
ejpam-6811	618	3	(	(	PUNCT
ejpam-6811	618	4	r(x	r(x	PROPN
ejpam-6811	618	5	)	)	PUNCT
ejpam-6811	618	6	)	)	PUNCT
ejpam-6811	618	7	∣∣∣2	∣∣∣2	NOUN
ejpam-6811	618	8	≤	≤	PROPN
ejpam-6811	618	9	φ	φ	PROPN
ejpam-6811	618	10	(	(	PUNCT
ejpam-6811	618	11	||q	||q	ADJ
ejpam-6811	618	12	−r||∗∞	−r||∗∞	PROPN
ejpam-6811	618	13	)	)	PUNCT
ejpam-6811	619	1	d.	d.	PROPN
ejpam-6811	619	2	e.	e.	PROPN
ejpam-6811	619	3	shehwar	shehwar	PROPN
ejpam-6811	619	4	sagheer	sagheer	PROPN
ejpam-6811	619	5	et	et	PROPN
ejpam-6811	619	6	al	al	PROPN
ejpam-6811	619	7	.	.	PUNCT
ejpam-6811	619	8	/	/	SYM
ejpam-6811	619	9	eur	eur	PROPN
ejpam-6811	619	10	.	.	PUNCT
ejpam-6811	620	1	j.	j.	PROPN
ejpam-6811	620	2	pure	pure	PROPN
ejpam-6811	620	3	appl	appl	PROPN
ejpam-6811	620	4	.	.	PROPN
ejpam-6811	620	5	math	math	PROPN
ejpam-6811	620	6	,	,	PUNCT
ejpam-6811	620	7	18	18	NUM
ejpam-6811	620	8	(	(	PUNCT
ejpam-6811	620	9	4	4	NUM
ejpam-6811	620	10	)	)	PUNCT
ejpam-6811	620	11	(	(	PUNCT
ejpam-6811	620	12	2025	2025	NUM
ejpam-6811	620	13	)	)	PUNCT
ejpam-6811	620	14	,	,	PUNCT
ejpam-6811	620	15	6811	6811	NUM
ejpam-6811	620	16	20	20	NUM
ejpam-6811	620	17	of	of	ADP
ejpam-6811	620	18	24	24	NUM
ejpam-6811	620	19	=	=	SYM
ejpam-6811	620	20	φ	φ	PROPN
ejpam-6811	620	21	(	(	PUNCT
ejpam-6811	620	22	db(q	db(q	NOUN
ejpam-6811	620	23	,	,	PUNCT
ejpam-6811	620	24	r	r	NOUN
ejpam-6811	620	25	)	)	PUNCT
ejpam-6811	620	26	)	)	PUNCT
ejpam-6811	620	27	.	.	PUNCT
ejpam-6811	621	1	define	define	VERB
ejpam-6811	621	2	an	an	DET
ejpam-6811	621	3	auxiliary	auxiliary	ADJ
ejpam-6811	621	4	function	function	NOUN
ejpam-6811	621	5	ψ	ψ	NOUN
ejpam-6811	621	6	with	with	ADP
ejpam-6811	621	7	domain	domain	NOUN
ejpam-6811	621	8	in	in	ADP
ejpam-6811	621	9	c[0	c[0	PROPN
ejpam-6811	621	10	,	,	PUNCT
ejpam-6811	621	11	1]×	1]×	NUM
ejpam-6811	621	12	c[0	c[0	PROPN
ejpam-6811	621	13	,	,	PUNCT
ejpam-6811	621	14	1	1	NUM
ejpam-6811	621	15	]	]	PUNCT
ejpam-6811	621	16	and	and	CCONJ
ejpam-6811	621	17	range	range	VERB
ejpam-6811	621	18	in	in	ADP
ejpam-6811	621	19	[	[	X
ejpam-6811	621	20	0	0	NUM
ejpam-6811	621	21	,	,	PUNCT
ejpam-6811	621	22	1	1	NUM
ejpam-6811	621	23	]	]	PUNCT
ejpam-6811	621	24	by	by	ADP
ejpam-6811	621	25	ψ(q	ψ(q	NOUN
ejpam-6811	621	26	,	,	PUNCT
ejpam-6811	621	27	r	r	NOUN
ejpam-6811	621	28	)	)	PUNCT
ejpam-6811	621	29	=	=	SYM
ejpam-6811	622	1			PROPN
ejpam-6811	622	2	φ	φ	X
ejpam-6811	622	3	(	(	PUNCT
ejpam-6811	622	4	||q	||q	ADJ
ejpam-6811	622	5	−r||∗∞	−r||∗∞	NOUN
ejpam-6811	622	6	)	)	PUNCT
ejpam-6811	623	1	||q	||q	ADV
ejpam-6811	623	2	−r||∗∞	−r||∗∞	NOUN
ejpam-6811	623	3	,	,	PUNCT
ejpam-6811	623	4	if	if	SCONJ
ejpam-6811	623	5	q	q	X
ejpam-6811	623	6	6=	6=	NUM
ejpam-6811	623	7	r	r	NOUN
ejpam-6811	623	8	,	,	PUNCT
ejpam-6811	623	9	0	0	NUM
ejpam-6811	623	10	,	,	PUNCT
ejpam-6811	623	11	if	if	SCONJ
ejpam-6811	623	12	q	q	NOUN
ejpam-6811	623	13	=	=	PUNCT
ejpam-6811	623	14	r.	r.	NOUN
ejpam-6811	623	15	we	we	PRON
ejpam-6811	623	16	see	see	VERB
ejpam-6811	623	17	that	that	SCONJ
ejpam-6811	623	18	all	all	DET
ejpam-6811	623	19	conditions	condition	NOUN
ejpam-6811	623	20	of	of	ADP
ejpam-6811	623	21	theorem	theorem	ADJ
ejpam-6811	623	22	3.5	3.5	NUM
ejpam-6811	623	23	are	be	AUX
ejpam-6811	623	24	satisfied	satisfied	ADJ
ejpam-6811	623	25	,	,	PUNCT
ejpam-6811	623	26	and	and	CCONJ
ejpam-6811	623	27	so	so	ADV
ejpam-6811	623	28	there	there	PRON
ejpam-6811	623	29	must	must	AUX
ejpam-6811	623	30	be	be	AUX
ejpam-6811	623	31	a	a	DET
ejpam-6811	623	32	fixed	fix	VERB
ejpam-6811	623	33	point	point	NOUN
ejpam-6811	623	34	q∗	q∗	NOUN
ejpam-6811	623	35	of	of	ADP
ejpam-6811	623	36	t	t	PROPN
ejpam-6811	623	37	in	in	ADP
ejpam-6811	623	38	c[0	c[0	PROPN
ejpam-6811	623	39	,	,	PUNCT
ejpam-6811	623	40	1	1	NUM
ejpam-6811	623	41	]	]	PUNCT
ejpam-6811	623	42	.	.	PUNCT
ejpam-6811	624	1	we	we	PRON
ejpam-6811	624	2	now	now	ADV
ejpam-6811	624	3	consider	consider	VERB
ejpam-6811	624	4	the	the	DET
ejpam-6811	624	5	case	case	NOUN
ejpam-6811	624	6	where	where	SCONJ
ejpam-6811	624	7	n	n	PROPN
ejpam-6811	624	8	=	=	SYM
ejpam-6811	624	9	2	2	X
ejpam-6811	624	10	.	.	PUNCT
ejpam-6811	625	1	this	this	PRON
ejpam-6811	625	2	gives	give	VERB
ejpam-6811	625	3	k1	k1	NOUN
ejpam-6811	625	4	≤	≤	NUM
ejpam-6811	625	5	(	(	PUNCT
ejpam-6811	625	6	2−	2−	NUM
ejpam-6811	625	7	η2)γ(γ	η2)γ(γ	VERB
ejpam-6811	625	8	+	+	CCONJ
ejpam-6811	625	9	2	2	NUM
ejpam-6811	625	10	)	)	PUNCT
ejpam-6811	625	11	2ηγ+1	2ηγ+1	NUM
ejpam-6811	626	1	+	+	CCONJ
ejpam-6811	626	2	(	(	PUNCT
ejpam-6811	626	3	γ	γ	X
ejpam-6811	626	4	+	+	CCONJ
ejpam-6811	626	5	1)(4−	1)(4−	NUM
ejpam-6811	626	6	η2	η2	PROPN
ejpam-6811	626	7	)	)	PUNCT
ejpam-6811	626	8	.	.	PUNCT
ejpam-6811	627	1	since	since	SCONJ
ejpam-6811	627	2	η	η	PROPN
ejpam-6811	627	3	∈	∈	PROPN
ejpam-6811	627	4	[	[	X
ejpam-6811	627	5	0	0	NUM
ejpam-6811	627	6	,	,	PUNCT
ejpam-6811	627	7	1	1	NUM
ejpam-6811	627	8	]	]	PUNCT
ejpam-6811	627	9	,	,	PUNCT
ejpam-6811	627	10	putting	put	VERB
ejpam-6811	627	11	η	η	PROPN
ejpam-6811	627	12	=	=	SYM
ejpam-6811	627	13	1	1	NUM
ejpam-6811	627	14	gives	give	VERB
ejpam-6811	627	15	k1	k1	NOUN
ejpam-6811	627	16	≤	≤	NOUN
ejpam-6811	627	17	γ(γ	γ(γ	PROPN
ejpam-6811	628	1	+	+	CCONJ
ejpam-6811	628	2	2	2	X
ejpam-6811	628	3	)	)	PUNCT
ejpam-6811	628	4	5	5	NUM
ejpam-6811	628	5	+	+	SYM
ejpam-6811	628	6	3γ	3γ	NUM
ejpam-6811	628	7	.	.	PUNCT
ejpam-6811	629	1	similarly	similarly	ADV
ejpam-6811	629	2	,	,	PUNCT
ejpam-6811	629	3	we	we	PRON
ejpam-6811	629	4	get	get	VERB
ejpam-6811	629	5	k2	k2	ADJ
ejpam-6811	629	6	≤	≤	NOUN
ejpam-6811	629	7	(	(	PUNCT
ejpam-6811	629	8	2γ	2γ	NOUN
ejpam-6811	629	9	−	−	PROPN
ejpam-6811	629	10	1)γ(γ	1)γ(γ	NUM
ejpam-6811	629	11	+	+	CCONJ
ejpam-6811	629	12	1)γ(γ	1)γ(γ	NUM
ejpam-6811	629	13	+	+	CCONJ
ejpam-6811	629	14	2	2	NUM
ejpam-6811	629	15	)	)	SYM
ejpam-6811	629	16	2	2	NUM
ejpam-6811	629	17	[	[	PUNCT
ejpam-6811	629	18	γ(γ	γ(γ	PROPN
ejpam-6811	629	19	+	+	CCONJ
ejpam-6811	630	1	1)(5γ	1)(5γ	NUM
ejpam-6811	630	2	+	+	NOUN
ejpam-6811	630	3	2	2	NUM
ejpam-6811	630	4	)	)	PUNCT
ejpam-6811	630	5	+	+	NUM
ejpam-6811	630	6	2(2γ	2(2γ	NUM
ejpam-6811	630	7	−	−	NOUN
ejpam-6811	630	8	1)(γ	1)(γ	NUM
ejpam-6811	630	9	+	+	CCONJ
ejpam-6811	630	10	2	2	NUM
ejpam-6811	630	11	+	+	NUM
ejpam-6811	630	12	2γ+2	2γ+2	NUM
ejpam-6811	630	13	)	)	PUNCT
ejpam-6811	630	14	]	]	PUNCT
ejpam-6811	630	15	.	.	PUNCT
ejpam-6811	631	1	this	this	PRON
ejpam-6811	631	2	gives	give	VERB
ejpam-6811	631	3	the	the	DET
ejpam-6811	631	4	following	follow	VERB
ejpam-6811	631	5	corollary	corollary	NOUN
ejpam-6811	631	6	.	.	PUNCT
ejpam-6811	632	1	corollary	corollary	ADJ
ejpam-6811	632	2	2	2	NUM
ejpam-6811	632	3	.	.	PUNCT
ejpam-6811	633	1	let	let	VERB
ejpam-6811	633	2	(	(	PUNCT
ejpam-6811	633	3	c[0	c[0	PROPN
ejpam-6811	633	4	,	,	PUNCT
ejpam-6811	633	5	1	1	NUM
ejpam-6811	633	6	]	]	PUNCT
ejpam-6811	633	7	,	,	PUNCT
ejpam-6811	633	8	db	db	PROPN
ejpam-6811	633	9	)	)	PUNCT
ejpam-6811	633	10	be	be	AUX
ejpam-6811	633	11	a	a	DET
ejpam-6811	633	12	complete	complete	ADJ
ejpam-6811	633	13	bms	bms	NOUN
ejpam-6811	633	14	with	with	ADP
ejpam-6811	633	15	a	a	DET
ejpam-6811	633	16	dg	dg	NOUN
ejpam-6811	633	17	.	.	PUNCT
ejpam-6811	634	1	we	we	PRON
ejpam-6811	634	2	define	define	VERB
ejpam-6811	634	3	the	the	DET
ejpam-6811	634	4	transitive	transitive	ADJ
ejpam-6811	634	5	set	set	NOUN
ejpam-6811	634	6	of	of	ADP
ejpam-6811	634	7	edges	edge	NOUN
ejpam-6811	634	8	of	of	ADP
ejpam-6811	634	9	the	the	DET
ejpam-6811	634	10	graph	graph	NOUN
ejpam-6811	634	11	ḡ	ḡ	VERB
ejpam-6811	634	12	by	by	ADP
ejpam-6811	634	13	e(ḡ	e(ḡ	NOUN
ejpam-6811	634	14	)	)	PUNCT
ejpam-6811	634	15	=	=	PRON
ejpam-6811	634	16	{	{	PUNCT
ejpam-6811	634	17	(	(	PUNCT
ejpam-6811	634	18	q	q	NOUN
ejpam-6811	634	19	,	,	PUNCT
ejpam-6811	634	20	r	r	NOUN
ejpam-6811	634	21	)	)	PUNCT
ejpam-6811	634	22	:	:	PUNCT
ejpam-6811	634	23	ε	ε	PROPN
ejpam-6811	634	24	(	(	PUNCT
ejpam-6811	634	25	q(x),r(x	q(x),r(x	PROPN
ejpam-6811	634	26	)	)	PUNCT
ejpam-6811	634	27	)	)	PUNCT
ejpam-6811	634	28	≥	≥	NOUN
ejpam-6811	634	29	0	0	NUM
ejpam-6811	634	30	}	}	PUNCT
ejpam-6811	634	31	.	.	PUNCT
ejpam-6811	635	1	suppose	suppose	VERB
ejpam-6811	635	2	the	the	DET
ejpam-6811	635	3	following	follow	VERB
ejpam-6811	635	4	conditions	condition	NOUN
ejpam-6811	635	5	are	be	AUX
ejpam-6811	635	6	satisfied	satisfied	ADJ
ejpam-6811	635	7	for	for	ADP
ejpam-6811	635	8	all	all	DET
ejpam-6811	635	9	x	x	SYM
ejpam-6811	635	10	∈	∈	PROPN
ejpam-6811	636	1	[	[	X
ejpam-6811	636	2	0	0	NUM
ejpam-6811	636	3	,	,	PUNCT
ejpam-6811	636	4	1	1	NUM
ejpam-6811	636	5	]	]	PUNCT
ejpam-6811	636	6	.	.	PUNCT
ejpam-6811	637	1	i.	i.	PROPN
ejpam-6811	637	2	there	there	PRON
ejpam-6811	637	3	exist	exist	VERB
ejpam-6811	637	4	ε	ε	PROPN
ejpam-6811	637	5	:	:	PUNCT
ejpam-6811	638	1	r2	r2	PROPN
ejpam-6811	638	2	→	→	SYM
ejpam-6811	638	3	r	r	NOUN
ejpam-6811	638	4	and	and	CCONJ
ejpam-6811	638	5	φ	φ	NUM
ejpam-6811	638	6	∈	∈	PROPN
ejpam-6811	638	7	φ	φ	PROPN
ejpam-6811	638	8	with	with	ADP
ejpam-6811	638	9	φ(r	φ(r	NOUN
ejpam-6811	638	10	)	)	PUNCT
ejpam-6811	638	11	<	<	X
ejpam-6811	638	12	r	r	NOUN
ejpam-6811	638	13	∀	∀	NOUN
ejpam-6811	638	14	r	r	NOUN
ejpam-6811	638	15	∈	∈	PROPN
ejpam-6811	638	16	(	(	PUNCT
ejpam-6811	638	17	0	0	NUM
ejpam-6811	638	18	,	,	PUNCT
ejpam-6811	638	19	1	1	NUM
ejpam-6811	638	20	]	]	SYM
ejpam-6811	638	21	3	3	NUM
ejpam-6811	638	22	∀	∀	X
ejpam-6811	638	23	q	q	ADJ
ejpam-6811	638	24	,	,	PUNCT
ejpam-6811	638	25	r	r	NOUN
ejpam-6811	638	26	∈	∈	PROPN
ejpam-6811	638	27	c[0	c[0	PROPN
ejpam-6811	638	28	,	,	PUNCT
ejpam-6811	638	29	1	1	NUM
ejpam-6811	638	30	]	]	PUNCT
ejpam-6811	638	31	with	with	ADP
ejpam-6811	638	32	ε	ε	PROPN
ejpam-6811	638	33	(	(	PUNCT
ejpam-6811	638	34	q(ξ),r(ξ	q(ξ),r(ξ	NOUN
ejpam-6811	638	35	)	)	PUNCT
ejpam-6811	638	36	)	)	PUNCT
ejpam-6811	639	1	≥	≥	NOUN
ejpam-6811	639	2	0	0	NUM
ejpam-6811	639	3	∀	∀	PUNCT
ejpam-6811	639	4	ξ	ξ	X
ejpam-6811	639	5	∈	∈	PROPN
ejpam-6811	640	1	[	[	X
ejpam-6811	640	2	0	0	NUM
ejpam-6811	640	3	,	,	PUNCT
ejpam-6811	640	4	1	1	NUM
ejpam-6811	640	5	]	]	PUNCT
ejpam-6811	640	6	,	,	PUNCT
ejpam-6811	640	7	∣∣υ(x	∣∣υ(x	PROPN
ejpam-6811	640	8	,	,	PUNCT
ejpam-6811	640	9	q(x	q(x	PROPN
ejpam-6811	640	10	)	)	PUNCT
ejpam-6811	640	11	)	)	PUNCT
ejpam-6811	641	1	−	−	NOUN
ejpam-6811	641	2	υ	υ	INTJ
ejpam-6811	641	3	(	(	PUNCT
ejpam-6811	641	4	x	x	NOUN
ejpam-6811	641	5	,	,	PUNCT
ejpam-6811	641	6	r(x	r(x	NOUN
ejpam-6811	641	7	)	)	PUNCT
ejpam-6811	641	8	)	)	PUNCT
ejpam-6811	642	1	∣∣	∣∣	PROPN
ejpam-6811	642	2	≤	≤	NUM
ejpam-6811	642	3	k1φ	k1φ	X
ejpam-6811	642	4	(	(	PUNCT
ejpam-6811	642	5	|	|	ADV
ejpam-6811	642	6	q(x)−r(x	q(x)−r(x	X
ejpam-6811	642	7	)	)	PUNCT
ejpam-6811	642	8	|	|	ADV
ejpam-6811	642	9	)	)	PUNCT
ejpam-6811	642	10	≤	≤	NOUN
ejpam-6811	642	11	γ(γ	γ(γ	PROPN
ejpam-6811	642	12	+	+	CCONJ
ejpam-6811	642	13	2	2	X
ejpam-6811	642	14	)	)	PUNCT
ejpam-6811	642	15	5	5	NUM
ejpam-6811	642	16	+	+	SYM
ejpam-6811	642	17	3γ	3γ	NUM
ejpam-6811	642	18	φ	φ	NOUN
ejpam-6811	642	19	(	(	PUNCT
ejpam-6811	642	20	|	|	ADV
ejpam-6811	642	21	q(x)−r(x	q(x)−r(x	X
ejpam-6811	642	22	)	)	PUNCT
ejpam-6811	642	23	|	|	ADV
ejpam-6811	642	24	)	)	PUNCT
ejpam-6811	642	25	and∣∣υ(x	and∣∣υ(x	NOUN
ejpam-6811	642	26	,	,	PUNCT
ejpam-6811	642	27	q(x	q(x	PROPN
ejpam-6811	642	28	)	)	PUNCT
ejpam-6811	642	29	)	)	PUNCT
ejpam-6811	643	1	−	−	NOUN
ejpam-6811	644	1	υ	υ	INTJ
ejpam-6811	644	2	(	(	PUNCT
ejpam-6811	644	3	x	x	NOUN
ejpam-6811	644	4	,	,	PUNCT
ejpam-6811	644	5	r(x	r(x	NOUN
ejpam-6811	644	6	)	)	PUNCT
ejpam-6811	644	7	)	)	PUNCT
ejpam-6811	644	8	∣∣2	∣∣2	PROPN
ejpam-6811	644	9	≤	≤	NOUN
ejpam-6811	644	10	k2φ	k2φ	NOUN
ejpam-6811	644	11	(	(	PUNCT
ejpam-6811	644	12	|	|	ADV
ejpam-6811	644	13	q(x)−r(x	q(x)−r(x	X
ejpam-6811	644	14	)	)	PUNCT
ejpam-6811	644	15	|2	|2	NUM
ejpam-6811	644	16	)	)	PUNCT
ejpam-6811	644	17	≤	≤	NOUN
ejpam-6811	644	18	(	(	PUNCT
ejpam-6811	644	19	2γ	2γ	NOUN
ejpam-6811	644	20	−	−	PROPN
ejpam-6811	644	21	1)γ(γ	1)γ(γ	NUM
ejpam-6811	644	22	+	+	CCONJ
ejpam-6811	644	23	1)γ(γ	1)γ(γ	NUM
ejpam-6811	644	24	+	+	CCONJ
ejpam-6811	644	25	2	2	NUM
ejpam-6811	644	26	)	)	SYM
ejpam-6811	644	27	2	2	NUM
ejpam-6811	644	28	[	[	PUNCT
ejpam-6811	644	29	γ(γ	γ(γ	PROPN
ejpam-6811	644	30	+	+	CCONJ
ejpam-6811	645	1	1)(5γ	1)(5γ	NUM
ejpam-6811	645	2	+	+	NOUN
ejpam-6811	645	3	2	2	NUM
ejpam-6811	645	4	)	)	PUNCT
ejpam-6811	645	5	+	+	NUM
ejpam-6811	645	6	2(2γ	2(2γ	NUM
ejpam-6811	645	7	−	−	NOUN
ejpam-6811	645	8	1)(γ	1)(γ	NUM
ejpam-6811	645	9	+	+	CCONJ
ejpam-6811	645	10	2	2	NUM
ejpam-6811	645	11	+	+	NUM
ejpam-6811	645	12	2γ+2	2γ+2	NUM
ejpam-6811	645	13	)	)	PUNCT
ejpam-6811	645	14	]	]	PUNCT
ejpam-6811	645	15	φ	φ	X
ejpam-6811	645	16	(	(	PUNCT
ejpam-6811	645	17	|	|	NOUN
ejpam-6811	645	18	q(x)−r(x	q(x)−r(x	NOUN
ejpam-6811	645	19	)	)	PUNCT
ejpam-6811	645	20	|2	|2	NUM
ejpam-6811	645	21	)	)	PUNCT
ejpam-6811	645	22	.	.	PUNCT
ejpam-6811	646	1	ii	ii	X
ejpam-6811	646	2	.	.	PUNCT
ejpam-6811	647	1	there	there	PRON
ejpam-6811	647	2	exists	exist	VERB
ejpam-6811	647	3	q0	q0	PROPN
ejpam-6811	647	4	∈	∈	PROPN
ejpam-6811	647	5	c[0	c[0	PROPN
ejpam-6811	647	6	,	,	PUNCT
ejpam-6811	647	7	1	1	NUM
ejpam-6811	647	8	]	]	PUNCT
ejpam-6811	647	9	such	such	ADJ
ejpam-6811	647	10	that	that	DET
ejpam-6811	647	11	ε	ε	PROPN
ejpam-6811	647	12	(	(	PUNCT
ejpam-6811	647	13	q0(x),tq0(x	q0(x),tq0(x	NOUN
ejpam-6811	647	14	)	)	PUNCT
ejpam-6811	647	15	)	)	PUNCT
ejpam-6811	647	16	≥	≥	NOUN
ejpam-6811	647	17	0	0	NUM
ejpam-6811	647	18	.	.	PUNCT
ejpam-6811	648	1	d.	d.	PROPN
ejpam-6811	648	2	e.	e.	PROPN
ejpam-6811	648	3	shehwar	shehwar	PROPN
ejpam-6811	648	4	sagheer	sagheer	PROPN
ejpam-6811	648	5	et	et	PROPN
ejpam-6811	648	6	al	al	PROPN
ejpam-6811	648	7	.	.	PUNCT
ejpam-6811	648	8	/	/	SYM
ejpam-6811	648	9	eur	eur	PROPN
ejpam-6811	648	10	.	.	PUNCT
ejpam-6811	649	1	j.	j.	PROPN
ejpam-6811	649	2	pure	pure	PROPN
ejpam-6811	649	3	appl	appl	PROPN
ejpam-6811	649	4	.	.	PROPN
ejpam-6811	649	5	math	math	PROPN
ejpam-6811	649	6	,	,	PUNCT
ejpam-6811	649	7	18	18	NUM
ejpam-6811	649	8	(	(	PUNCT
ejpam-6811	649	9	4	4	NUM
ejpam-6811	649	10	)	)	PUNCT
ejpam-6811	649	11	(	(	PUNCT
ejpam-6811	649	12	2025	2025	NUM
ejpam-6811	649	13	)	)	PUNCT
ejpam-6811	649	14	,	,	PUNCT
ejpam-6811	649	15	6811	6811	NUM
ejpam-6811	649	16	21	21	NUM
ejpam-6811	649	17	of	of	ADP
ejpam-6811	649	18	24	24	NUM
ejpam-6811	649	19	iii	iii	NOUN
ejpam-6811	649	20	.	.	PUNCT
ejpam-6811	650	1	for	for	ADP
ejpam-6811	650	2	all	all	DET
ejpam-6811	650	3	q	q	NOUN
ejpam-6811	650	4	,	,	PUNCT
ejpam-6811	650	5	r	r	NOUN
ejpam-6811	650	6	∈	∈	PROPN
ejpam-6811	650	7	c[0	c[0	PROPN
ejpam-6811	650	8	,	,	PUNCT
ejpam-6811	650	9	1	1	NUM
ejpam-6811	650	10	]	]	PUNCT
ejpam-6811	650	11	,	,	PUNCT
ejpam-6811	650	12	we	we	PRON
ejpam-6811	650	13	have	have	VERB
ejpam-6811	650	14	ε	ε	PROPN
ejpam-6811	650	15	(	(	PUNCT
ejpam-6811	650	16	q(x),r(x	q(x),r(x	PROPN
ejpam-6811	650	17	)	)	PUNCT
ejpam-6811	650	18	)	)	PUNCT
ejpam-6811	650	19	≥	≥	NOUN
ejpam-6811	650	20	0ε	0ε	NOUN
ejpam-6811	650	21	(	(	PUNCT
ejpam-6811	650	22	tq(x),tr(x	tq(x),tr(x	NOUN
ejpam-6811	650	23	)	)	PUNCT
ejpam-6811	650	24	)	)	PUNCT
ejpam-6811	650	25	≥	≥	NOUN
ejpam-6811	650	26	0	0	NUM
ejpam-6811	650	27	.	.	NUM
ejpam-6811	651	1	iv	iv	X
ejpam-6811	651	2	.	.	PUNCT
ejpam-6811	652	1	let	let	VERB
ejpam-6811	652	2	the	the	DET
ejpam-6811	652	3	sequence	sequence	NOUN
ejpam-6811	652	4	{	{	PUNCT
ejpam-6811	652	5	qn	qn	NOUN
ejpam-6811	652	6	}	}	PUNCT
ejpam-6811	652	7	∈	∈	PROPN
ejpam-6811	652	8	c[0	c[0	PROPN
ejpam-6811	652	9	,	,	PUNCT
ejpam-6811	652	10	1	1	NUM
ejpam-6811	652	11	]	]	PUNCT
ejpam-6811	652	12	converge	converge	VERB
ejpam-6811	652	13	to	to	ADP
ejpam-6811	652	14	q	q	PROPN
ejpam-6811	652	15	∈	∈	PROPN
ejpam-6811	652	16	c[0	c[0	PROPN
ejpam-6811	652	17	,	,	PUNCT
ejpam-6811	652	18	1	1	NUM
ejpam-6811	652	19	]	]	PUNCT
ejpam-6811	652	20	with	with	ADP
ejpam-6811	652	21	ε	ε	PROPN
ejpam-6811	652	22	(	(	PUNCT
ejpam-6811	652	23	qn(x),qn+1(x	qn(x),qn+1(x	NOUN
ejpam-6811	652	24	)	)	PUNCT
ejpam-6811	652	25	)	)	PUNCT
ejpam-6811	653	1	≥	≥	NOUN
ejpam-6811	653	2	0	0	NUM
ejpam-6811	653	3	∀	∀	NOUN
ejpam-6811	653	4	n	n	PRON
ejpam-6811	653	5	∈	∈	NOUN
ejpam-6811	653	6	n	n	PART
ejpam-6811	653	7	⇒	⇒	NOUN
ejpam-6811	653	8	ε	ε	PROPN
ejpam-6811	653	9	(	(	PUNCT
ejpam-6811	653	10	qn(x),q(x	qn(x),q(x	NUM
ejpam-6811	653	11	)	)	PUNCT
ejpam-6811	653	12	)	)	PUNCT
ejpam-6811	654	1	≥	≥	NOUN
ejpam-6811	654	2	0	0	NUM
ejpam-6811	654	3	∀	∀	NOUN
ejpam-6811	654	4	n	n	PRON
ejpam-6811	654	5	∈	∈	PROPN
ejpam-6811	654	6	n.	n.	NOUN
ejpam-6811	654	7	v.	v.	PROPN
ejpam-6811	654	8	for	for	ADP
ejpam-6811	654	9	all	all	DET
ejpam-6811	654	10	q	q	ADJ
ejpam-6811	654	11	,	,	PUNCT
ejpam-6811	654	12	r	r	NOUN
ejpam-6811	654	13	,	,	PUNCT
ejpam-6811	654	14	w	w	PROPN
ejpam-6811	654	15	∈	∈	PROPN
ejpam-6811	654	16	c[0	c[0	PROPN
ejpam-6811	654	17	,	,	PUNCT
ejpam-6811	654	18	1	1	NUM
ejpam-6811	654	19	]	]	PUNCT
ejpam-6811	654	20	,	,	PUNCT
ejpam-6811	654	21	we	we	PRON
ejpam-6811	654	22	have	have	VERB
ejpam-6811	654	23	ε	ε	PROPN
ejpam-6811	654	24	(	(	PUNCT
ejpam-6811	654	25	q(x),r(x	q(x),r(x	PROPN
ejpam-6811	654	26	)	)	PUNCT
ejpam-6811	654	27	)	)	PUNCT
ejpam-6811	655	1	≥	≥	NOUN
ejpam-6811	655	2	0	0	NUM
ejpam-6811	655	3	and	and	CCONJ
ejpam-6811	655	4	ε	ε	PROPN
ejpam-6811	655	5	(	(	PUNCT
ejpam-6811	655	6	r(x),w(x	r(x),w(x	PROPN
ejpam-6811	655	7	)	)	PUNCT
ejpam-6811	655	8	)	)	PUNCT
ejpam-6811	656	1	≥	≥	NOUN
ejpam-6811	656	2	0	0	NUM
ejpam-6811	656	3	ε	ε	PROPN
ejpam-6811	656	4	(	(	PUNCT
ejpam-6811	656	5	q(x),w(x	q(x),w(x	PROPN
ejpam-6811	656	6	)	)	PUNCT
ejpam-6811	656	7	)	)	PUNCT
ejpam-6811	656	8	≥	≥	NOUN
ejpam-6811	656	9	0	0	NUM
ejpam-6811	656	10	.	.	PUNCT
ejpam-6811	657	1	then	then	ADV
ejpam-6811	657	2	the	the	DET
ejpam-6811	657	3	boundary	boundary	ADJ
ejpam-6811	657	4	value	value	NOUN
ejpam-6811	657	5	problem	problem	NOUN
ejpam-6811	657	6	(	(	PUNCT
ejpam-6811	657	7	cdγy)(x	cdγy)(x	NOUN
ejpam-6811	657	8	)	)	PUNCT
ejpam-6811	658	1	=	=	SYM
ejpam-6811	658	2	υ	υ	PROPN
ejpam-6811	658	3	(	(	PUNCT
ejpam-6811	658	4	x	x	PROPN
ejpam-6811	658	5	,	,	PUNCT
ejpam-6811	658	6	y(x	y(x	PROPN
ejpam-6811	658	7	)	)	PUNCT
ejpam-6811	658	8	)	)	PUNCT
ejpam-6811	658	9	,	,	PUNCT
ejpam-6811	658	10	x	x	PUNCT
ejpam-6811	658	11	∈	∈	PROPN
ejpam-6811	659	1	[	[	X
ejpam-6811	659	2	0	0	NUM
ejpam-6811	659	3	,	,	PUNCT
ejpam-6811	659	4	1	1	NUM
ejpam-6811	659	5	]	]	PUNCT
ejpam-6811	659	6	and	and	CCONJ
ejpam-6811	659	7	γ	γ	PROPN
ejpam-6811	659	8	∈	∈	PROPN
ejpam-6811	659	9	(	(	PUNCT
ejpam-6811	659	10	1	1	NUM
ejpam-6811	659	11	,	,	PUNCT
ejpam-6811	659	12	2	2	NUM
ejpam-6811	659	13	]	]	PUNCT
ejpam-6811	659	14	along	along	ADP
ejpam-6811	659	15	with	with	ADP
ejpam-6811	659	16	y(0	y(0	PROPN
ejpam-6811	659	17	)	)	PUNCT
ejpam-6811	659	18	=	=	SYM
ejpam-6811	659	19	0	0	NUM
ejpam-6811	659	20	and	and	CCONJ
ejpam-6811	659	21	y(1	y(1	PROPN
ejpam-6811	659	22	)	)	PUNCT
ejpam-6811	659	23	=	=	SYM
ejpam-6811	659	24	∫	∫	PROPN
ejpam-6811	659	25	η	η	PROPN
ejpam-6811	659	26	0	0	PROPN
ejpam-6811	659	27	y(ξ)dξ	y(ξ)dξ	PROPN
ejpam-6811	659	28	,	,	PUNCT
ejpam-6811	659	29	η	η	PROPN
ejpam-6811	659	30	∈	∈	PROPN
ejpam-6811	660	1	[	[	X
ejpam-6811	660	2	0	0	NUM
ejpam-6811	660	3	,	,	PUNCT
ejpam-6811	660	4	1	1	NUM
ejpam-6811	660	5	]	]	PUNCT
ejpam-6811	660	6	has	have	VERB
ejpam-6811	660	7	a	a	DET
ejpam-6811	660	8	solution	solution	NOUN
ejpam-6811	660	9	q∗	q∗	NOUN
ejpam-6811	660	10	∈	∈	PROPN
ejpam-6811	660	11	c[0	c[0	PROPN
ejpam-6811	660	12	,	,	PUNCT
ejpam-6811	660	13	1	1	NUM
ejpam-6811	660	14	]	]	PUNCT
ejpam-6811	660	15	.	.	PUNCT
ejpam-6811	661	1	next	next	ADV
ejpam-6811	661	2	,	,	PUNCT
ejpam-6811	661	3	we	we	PRON
ejpam-6811	661	4	take	take	VERB
ejpam-6811	661	5	the	the	DET
ejpam-6811	661	6	case	case	NOUN
ejpam-6811	661	7	when	when	SCONJ
ejpam-6811	661	8	e(ḡ	e(ḡ	PROPN
ejpam-6811	661	9	)	)	PUNCT
ejpam-6811	661	10	=	=	SYM
ejpam-6811	661	11	c[0	c[0	PROPN
ejpam-6811	661	12	,	,	PUNCT
ejpam-6811	661	13	1	1	NUM
ejpam-6811	661	14	]	]	X
ejpam-6811	661	15	×	×	PROPN
ejpam-6811	661	16	c[0	c[0	PROPN
ejpam-6811	661	17	,	,	PUNCT
ejpam-6811	661	18	1	1	NUM
ejpam-6811	661	19	]	]	PUNCT
ejpam-6811	661	20	.	.	PUNCT
ejpam-6811	662	1	here	here	ADV
ejpam-6811	662	2	,	,	PUNCT
ejpam-6811	662	3	the	the	DET
ejpam-6811	662	4	conditions	condition	NOUN
ejpam-6811	662	5	i	i	PRON
ejpam-6811	662	6	v	v	VERB
ejpam-6811	662	7	can	can	AUX
ejpam-6811	662	8	be	be	AUX
ejpam-6811	662	9	given	give	VERB
ejpam-6811	662	10	by	by	ADP
ejpam-6811	662	11	the	the	DET
ejpam-6811	662	12	following	follow	VERB
ejpam-6811	662	13	single	single	ADJ
ejpam-6811	662	14	condition	condition	NOUN
ejpam-6811	662	15	satisfied	satisfied	ADJ
ejpam-6811	662	16	for	for	ADP
ejpam-6811	662	17	all	all	DET
ejpam-6811	662	18	x	x	SYM
ejpam-6811	662	19	∈	∈	PROPN
ejpam-6811	663	1	[	[	X
ejpam-6811	663	2	0	0	NUM
ejpam-6811	663	3	,	,	PUNCT
ejpam-6811	663	4	1	1	NUM
ejpam-6811	663	5	]	]	PUNCT
ejpam-6811	663	6	.	.	PUNCT
ejpam-6811	663	7	∀	∀	PUNCT
ejpam-6811	664	1	q	q	X
ejpam-6811	664	2	,	,	PUNCT
ejpam-6811	664	3	r	r	NOUN
ejpam-6811	664	4	∈	∈	PROPN
ejpam-6811	664	5	c[0	c[0	PROPN
ejpam-6811	664	6	,	,	PUNCT
ejpam-6811	664	7	1	1	NUM
ejpam-6811	664	8	]	]	PUNCT
ejpam-6811	664	9	,	,	PUNCT
ejpam-6811	664	10	∃	∃	PROPN
ejpam-6811	664	11	φ	φ	PROPN
ejpam-6811	664	12	∈	∈	PROPN
ejpam-6811	664	13	φ	φ	PROPN
ejpam-6811	664	14	with	with	ADP
ejpam-6811	664	15	φ(r	φ(r	NOUN
ejpam-6811	664	16	)	)	PUNCT
ejpam-6811	664	17	<	<	X
ejpam-6811	664	18	r	r	NOUN
ejpam-6811	664	19	∀	∀	NOUN
ejpam-6811	664	20	r	r	NOUN
ejpam-6811	664	21	∈	∈	PROPN
ejpam-6811	664	22	(	(	PUNCT
ejpam-6811	664	23	0	0	NUM
ejpam-6811	664	24	,	,	PUNCT
ejpam-6811	664	25	1	1	NUM
ejpam-6811	664	26	]	]	PUNCT
ejpam-6811	664	27	,	,	PUNCT
ejpam-6811	664	28	3∣∣υ(x	3∣∣υ(x	NUM
ejpam-6811	664	29	,	,	PUNCT
ejpam-6811	664	30	q(x	q(x	NOUN
ejpam-6811	664	31	)	)	PUNCT
ejpam-6811	664	32	)	)	PUNCT
ejpam-6811	665	1	−	−	NOUN
ejpam-6811	665	2	υ	υ	INTJ
ejpam-6811	665	3	(	(	PUNCT
ejpam-6811	665	4	x	x	NOUN
ejpam-6811	665	5	,	,	PUNCT
ejpam-6811	665	6	r(x	r(x	NOUN
ejpam-6811	665	7	)	)	PUNCT
ejpam-6811	665	8	)	)	PUNCT
ejpam-6811	666	1	∣∣	∣∣	PROPN
ejpam-6811	666	2	≤	≤	NUM
ejpam-6811	666	3	k1φ	k1φ	X
ejpam-6811	666	4	(	(	PUNCT
ejpam-6811	666	5	|	|	ADV
ejpam-6811	666	6	q(x)−r(x	q(x)−r(x	X
ejpam-6811	666	7	)	)	PUNCT
ejpam-6811	666	8	|	|	ADV
ejpam-6811	666	9	)	)	PUNCT
ejpam-6811	666	10	,	,	PUNCT
ejpam-6811	666	11	∣∣υ(x	∣∣υ(x	PROPN
ejpam-6811	666	12	,	,	PUNCT
ejpam-6811	666	13	q(x	q(x	PROPN
ejpam-6811	666	14	)	)	PUNCT
ejpam-6811	666	15	)	)	PUNCT
ejpam-6811	667	1	−	−	NOUN
ejpam-6811	668	1	υ	υ	INTJ
ejpam-6811	668	2	(	(	PUNCT
ejpam-6811	668	3	x	x	NOUN
ejpam-6811	668	4	,	,	PUNCT
ejpam-6811	668	5	r(x	r(x	NOUN
ejpam-6811	668	6	)	)	PUNCT
ejpam-6811	668	7	)	)	PUNCT
ejpam-6811	668	8	∣∣2	∣∣2	PROPN
ejpam-6811	668	9	≤	≤	NOUN
ejpam-6811	668	10	k2φ	k2φ	NOUN
ejpam-6811	668	11	(	(	PUNCT
ejpam-6811	668	12	|	|	ADV
ejpam-6811	668	13	q(x)−r(x	q(x)−r(x	X
ejpam-6811	668	14	)	)	PUNCT
ejpam-6811	668	15	|2	|2	NUM
ejpam-6811	668	16	)	)	PUNCT
ejpam-6811	668	17	,	,	PUNCT
ejpam-6811	668	18	where	where	SCONJ
ejpam-6811	668	19	k1	k1	NOUN
ejpam-6811	668	20	≤	≤	NUM
ejpam-6811	668	21	(	(	PUNCT
ejpam-6811	668	22	n−	n−	NOUN
ejpam-6811	668	23	ηn)γ(γ	ηn)γ(γ	VERB
ejpam-6811	668	24	+	+	CCONJ
ejpam-6811	668	25	2	2	X
ejpam-6811	668	26	)	)	PUNCT
ejpam-6811	668	27	nηγ+1	nηγ+1	NOUN
ejpam-6811	669	1	+	+	CCONJ
ejpam-6811	669	2	(	(	PUNCT
ejpam-6811	669	3	γ	γ	X
ejpam-6811	669	4	+	+	NOUN
ejpam-6811	669	5	1)(2n−	1)(2n−	NUM
ejpam-6811	669	6	ηn	ηn	ADJ
ejpam-6811	669	7	)	)	PUNCT
ejpam-6811	669	8	,	,	PUNCT
ejpam-6811	669	9	and	and	CCONJ
ejpam-6811	669	10	k2	k2	ADJ
ejpam-6811	669	11	≤	≤	NOUN
ejpam-6811	669	12	(	(	PUNCT
ejpam-6811	669	13	2γ	2γ	NOUN
ejpam-6811	669	14	−	−	PROPN
ejpam-6811	669	15	1)(n−	1)(n−	NUM
ejpam-6811	669	16	ηn)2γ(γ	ηn)2γ(γ	NOUN
ejpam-6811	670	1	+	+	X
ejpam-6811	670	2	1)γ(γ	1)γ(γ	NUM
ejpam-6811	670	3	+	+	CCONJ
ejpam-6811	670	4	2	2	NUM
ejpam-6811	670	5	)	)	PUNCT
ejpam-6811	670	6	γ(γ	γ(γ	PROPN
ejpam-6811	671	1	+	+	CCONJ
ejpam-6811	671	2	1	1	X
ejpam-6811	671	3	)	)	PUNCT
ejpam-6811	671	4	[	[	PUNCT
ejpam-6811	671	5	n2η2γ	n2η2γ	NUM
ejpam-6811	671	6	+	+	NUM
ejpam-6811	671	7	2γ	2γ	NOUN
ejpam-6811	671	8	[	[	PUNCT
ejpam-6811	671	9	n2	n2	NOUN
ejpam-6811	671	10	+	+	CCONJ
ejpam-6811	671	11	(	(	PUNCT
ejpam-6811	671	12	n−	n−	NOUN
ejpam-6811	671	13	ηn)2	ηn)2	PROPN
ejpam-6811	671	14	]	]	PUNCT
ejpam-6811	671	15	]	]	PUNCT
ejpam-6811	672	1	+	+	CCONJ
ejpam-6811	672	2	2(2γ	2(2γ	NUM
ejpam-6811	672	3	−	−	NOUN
ejpam-6811	672	4	1)n	1)n	X
ejpam-6811	672	5	[	[	PUNCT
ejpam-6811	672	6	nγ+2	nγ+2	X
ejpam-6811	672	7	+	+	CCONJ
ejpam-6811	672	8	ηγ+1(n−	ηγ+1(n−	VERB
ejpam-6811	672	9	ηn	ηn	PROPN
ejpam-6811	672	10	)	)	PUNCT
ejpam-6811	673	1	+	+	CCONJ
ejpam-6811	673	2	(	(	PUNCT
ejpam-6811	673	3	γ	γ	X
ejpam-6811	673	4	+	+	X
ejpam-6811	673	5	1)(n−	1)(n−	NUM
ejpam-6811	673	6	ηn	ηn	ADJ
ejpam-6811	673	7	)	)	PUNCT
ejpam-6811	673	8	]	]	PUNCT
ejpam-6811	673	9	.	.	PUNCT
ejpam-6811	674	1	this	this	PRON
ejpam-6811	674	2	gives	give	VERB
ejpam-6811	674	3	the	the	DET
ejpam-6811	674	4	following	follow	VERB
ejpam-6811	674	5	corollary	corollary	NOUN
ejpam-6811	674	6	.	.	PUNCT
ejpam-6811	675	1	corollary	corollary	ADJ
ejpam-6811	675	2	3	3	NUM
ejpam-6811	675	3	.	.	PUNCT
ejpam-6811	676	1	let	let	VERB
ejpam-6811	676	2	(	(	PUNCT
ejpam-6811	676	3	x	x	NOUN
ejpam-6811	676	4	,	,	PUNCT
ejpam-6811	676	5	db	db	PROPN
ejpam-6811	676	6	)	)	PUNCT
ejpam-6811	676	7	be	be	AUX
ejpam-6811	676	8	a	a	DET
ejpam-6811	676	9	complete	complete	ADJ
ejpam-6811	676	10	bms	bms	NOUN
ejpam-6811	676	11	accompanied	accompany	VERB
ejpam-6811	676	12	with	with	ADP
ejpam-6811	676	13	a	a	DET
ejpam-6811	676	14	dg	dg	PROPN
ejpam-6811	676	15	,	,	PUNCT
ejpam-6811	676	16	ḡ	ḡ	VERB
ejpam-6811	676	17	=	=	SYM
ejpam-6811	676	18	(	(	PUNCT
ejpam-6811	676	19	v	v	NOUN
ejpam-6811	676	20	(	(	PUNCT
ejpam-6811	676	21	ḡ	ḡ	VERB
ejpam-6811	676	22	)	)	PUNCT
ejpam-6811	676	23	,	,	PUNCT
ejpam-6811	676	24	e(ḡ	e(ḡ	PROPN
ejpam-6811	676	25	)	)	PUNCT
ejpam-6811	676	26	)	)	PUNCT
ejpam-6811	676	27	with	with	ADP
ejpam-6811	676	28	e(ḡ	e(ḡ	PROPN
ejpam-6811	676	29	)	)	PUNCT
ejpam-6811	676	30	as	as	SCONJ
ejpam-6811	676	31	defined	define	VERB
ejpam-6811	676	32	above	above	ADV
ejpam-6811	676	33	.	.	PUNCT
ejpam-6811	677	1	then	then	ADV
ejpam-6811	677	2	the	the	DET
ejpam-6811	677	3	boundary	boundary	ADJ
ejpam-6811	677	4	value	value	NOUN
ejpam-6811	677	5	problem	problem	NOUN
ejpam-6811	677	6	given	give	VERB
ejpam-6811	677	7	by	by	ADP
ejpam-6811	677	8	(	(	PUNCT
ejpam-6811	677	9	4.2)-(4.3	4.2)-(4.3	NUM
ejpam-6811	677	10	)	)	PUNCT
ejpam-6811	677	11	has	have	VERB
ejpam-6811	677	12	a	a	DET
ejpam-6811	677	13	solution	solution	NOUN
ejpam-6811	677	14	q∗	q∗	NOUN
ejpam-6811	677	15	∈	∈	PROPN
ejpam-6811	677	16	c[0	c[0	PROPN
ejpam-6811	677	17	,	,	PUNCT
ejpam-6811	677	18	1	1	NUM
ejpam-6811	677	19	]	]	PUNCT
ejpam-6811	677	20	.	.	PUNCT
ejpam-6811	678	1	d.	d.	PROPN
ejpam-6811	678	2	e.	e.	PROPN
ejpam-6811	678	3	shehwar	shehwar	PROPN
ejpam-6811	678	4	sagheer	sagheer	PROPN
ejpam-6811	678	5	et	et	PROPN
ejpam-6811	678	6	al	al	PROPN
ejpam-6811	678	7	.	.	PUNCT
ejpam-6811	678	8	/	/	SYM
ejpam-6811	678	9	eur	eur	PROPN
ejpam-6811	678	10	.	.	PUNCT
ejpam-6811	679	1	j.	j.	PROPN
ejpam-6811	679	2	pure	pure	PROPN
ejpam-6811	679	3	appl	appl	PROPN
ejpam-6811	679	4	.	.	PROPN
ejpam-6811	679	5	math	math	PROPN
ejpam-6811	679	6	,	,	PUNCT
ejpam-6811	679	7	18	18	NUM
ejpam-6811	679	8	(	(	PUNCT
ejpam-6811	679	9	4	4	NUM
ejpam-6811	679	10	)	)	PUNCT
ejpam-6811	679	11	(	(	PUNCT
ejpam-6811	679	12	2025	2025	NUM
ejpam-6811	679	13	)	)	PUNCT
ejpam-6811	679	14	,	,	PUNCT
ejpam-6811	679	15	6811	6811	NUM
ejpam-6811	679	16	22	22	NUM
ejpam-6811	679	17	of	of	ADP
ejpam-6811	679	18	24	24	NUM
ejpam-6811	679	19	5	5	NUM
ejpam-6811	679	20	.	.	PUNCT
ejpam-6811	679	21	conclusion	conclusion	NOUN
ejpam-6811	679	22	this	this	DET
ejpam-6811	679	23	manuscript	manuscript	NOUN
ejpam-6811	679	24	presents	present	VERB
ejpam-6811	679	25	the	the	DET
ejpam-6811	679	26	following	follow	VERB
ejpam-6811	679	27	contributions	contribution	NOUN
ejpam-6811	679	28	:	:	PUNCT
ejpam-6811	679	29	•	•	NUM
ejpam-6811	679	30	we	we	PRON
ejpam-6811	679	31	introduce	introduce	VERB
ejpam-6811	679	32	ψ	ψ	X
ejpam-6811	679	33	−	−	PROPN
ejpam-6811	679	34	φ	φ	PROPN
ejpam-6811	679	35	contraction	contraction	NOUN
ejpam-6811	679	36	mappings	mapping	NOUN
ejpam-6811	679	37	in	in	ADP
ejpam-6811	679	38	the	the	DET
ejpam-6811	679	39	setting	setting	NOUN
ejpam-6811	679	40	of	of	ADP
ejpam-6811	679	41	bmss	bmss	NOUN
ejpam-6811	679	42	with	with	ADP
ejpam-6811	679	43	a	a	DET
ejpam-6811	679	44	directed	direct	VERB
ejpam-6811	679	45	graph	graph	NOUN
ejpam-6811	679	46	.	.	PUNCT
ejpam-6811	680	1	for	for	ADP
ejpam-6811	680	2	these	these	DET
ejpam-6811	680	3	mappings	mapping	NOUN
ejpam-6811	680	4	,	,	PUNCT
ejpam-6811	680	5	we	we	PRON
ejpam-6811	680	6	derive	derive	VERB
ejpam-6811	680	7	conditions	condition	NOUN
ejpam-6811	680	8	under	under	ADP
ejpam-6811	680	9	which	which	PRON
ejpam-6811	680	10	common	common	ADJ
ejpam-6811	680	11	fixed	fix	VERB
ejpam-6811	680	12	points	point	NOUN
ejpam-6811	680	13	exist	exist	VERB
ejpam-6811	680	14	and	and	CCONJ
ejpam-6811	680	15	we	we	PRON
ejpam-6811	680	16	present	present	VERB
ejpam-6811	680	17	supporting	support	VERB
ejpam-6811	680	18	examples	example	NOUN
ejpam-6811	680	19	.	.	PUNCT
ejpam-6811	681	1	we	we	PRON
ejpam-6811	681	2	also	also	ADV
ejpam-6811	681	3	investigate	investigate	VERB
ejpam-6811	681	4	generalized	generalized	ADJ
ejpam-6811	681	5	rational	rational	ADJ
ejpam-6811	681	6	contractions	contraction	NOUN
ejpam-6811	681	7	for	for	ADP
ejpam-6811	681	8	spaces	space	NOUN
ejpam-6811	681	9	with	with	ADP
ejpam-6811	681	10	two	two	NUM
ejpam-6811	681	11	metrics	metric	NOUN
ejpam-6811	681	12	.	.	PUNCT
ejpam-6811	682	1	•	•	INTJ
ejpam-6811	682	2	we	we	PRON
ejpam-6811	682	3	validate	validate	VERB
ejpam-6811	682	4	our	our	PRON
ejpam-6811	682	5	theoretical	theoretical	ADJ
ejpam-6811	682	6	results	result	NOUN
ejpam-6811	682	7	by	by	ADP
ejpam-6811	682	8	applying	apply	VERB
ejpam-6811	682	9	them	they	PRON
ejpam-6811	682	10	to	to	PART
ejpam-6811	682	11	prove	prove	VERB
ejpam-6811	682	12	the	the	DET
ejpam-6811	682	13	existence	existence	NOUN
ejpam-6811	682	14	of	of	ADP
ejpam-6811	682	15	a	a	DET
ejpam-6811	682	16	solution	solution	NOUN
ejpam-6811	682	17	for	for	ADP
ejpam-6811	682	18	a	a	DET
ejpam-6811	682	19	caputo	caputo	NOUN
ejpam-6811	682	20	-	-	PUNCT
ejpam-6811	682	21	type	type	NOUN
ejpam-6811	682	22	fractional	fractional	ADJ
ejpam-6811	682	23	boundary	boundary	ADJ
ejpam-6811	682	24	value	value	NOUN
ejpam-6811	682	25	problem	problem	NOUN
ejpam-6811	682	26	.	.	PUNCT
ejpam-6811	683	1	•	•	X
ejpam-6811	683	2	our	our	PRON
ejpam-6811	683	3	planned	plan	VERB
ejpam-6811	683	4	research	research	NOUN
ejpam-6811	683	5	includes	include	VERB
ejpam-6811	683	6	developing	develop	VERB
ejpam-6811	683	7	iterative	iterative	NOUN
ejpam-6811	683	8	solution	solution	NOUN
ejpam-6811	683	9	methods	method	NOUN
ejpam-6811	683	10	.	.	PUNCT
ejpam-6811	684	1	we	we	PRON
ejpam-6811	684	2	also	also	ADV
ejpam-6811	684	3	suggest	suggest	VERB
ejpam-6811	684	4	that	that	SCONJ
ejpam-6811	684	5	these	these	DET
ejpam-6811	684	6	results	result	NOUN
ejpam-6811	684	7	can	can	AUX
ejpam-6811	684	8	be	be	AUX
ejpam-6811	684	9	extended	extend	VERB
ejpam-6811	684	10	to	to	ADP
ejpam-6811	684	11	other	other	ADJ
ejpam-6811	684	12	fractional	fractional	ADJ
ejpam-6811	684	13	problems	problem	NOUN
ejpam-6811	684	14	and	and	CCONJ
ejpam-6811	684	15	to	to	ADP
ejpam-6811	684	16	the	the	DET
ejpam-6811	684	17	more	more	ADV
ejpam-6811	684	18	general	general	ADJ
ejpam-6811	684	19	framework	framework	NOUN
ejpam-6811	684	20	of	of	ADP
ejpam-6811	684	21	extendedbmss	extendedbmss	PROPN
ejpam-6811	684	22	.	.	PUNCT
ejpam-6811	685	1	acknowledgements	acknowledgement	NOUN
ejpam-6811	685	2	we	we	PRON
ejpam-6811	685	3	acknowledge	acknowledge	VERB
ejpam-6811	685	4	the	the	DET
ejpam-6811	685	5	support	support	NOUN
ejpam-6811	685	6	of	of	ADP
ejpam-6811	685	7	this	this	DET
ejpam-6811	685	8	research	research	NOUN
ejpam-6811	685	9	from	from	ADP
ejpam-6811	685	10	al	al	PROPN
ejpam-6811	685	11	-	-	PROPN
ejpam-6811	685	12	zaytoonah	zaytoonah	PROPN
ejpam-6811	685	13	university	university	PROPN
ejpam-6811	685	14	.	.	PUNCT
ejpam-6811	686	1	authors	author	NOUN
ejpam-6811	686	2	’	'	PUNCT
ejpam-6811	686	3	contributions	contribution	NOUN
ejpam-6811	686	4	all	all	DET
ejpam-6811	686	5	authors	author	NOUN
ejpam-6811	686	6	contribute	contribute	VERB
ejpam-6811	686	7	equally	equally	ADV
ejpam-6811	686	8	in	in	ADP
ejpam-6811	686	9	this	this	DET
ejpam-6811	686	10	paper	paper	NOUN
ejpam-6811	686	11	.	.	PUNCT
ejpam-6811	687	1	conflict	conflict	NOUN
ejpam-6811	687	2	of	of	ADP
ejpam-6811	687	3	interest	interest	NOUN
ejpam-6811	687	4	the	the	DET
ejpam-6811	687	5	authors	author	NOUN
ejpam-6811	687	6	declare	declare	VERB
ejpam-6811	687	7	that	that	SCONJ
ejpam-6811	687	8	they	they	PRON
ejpam-6811	687	9	have	have	VERB
ejpam-6811	687	10	no	no	DET
ejpam-6811	687	11	conflict	conflict	NOUN
ejpam-6811	687	12	of	of	ADP
ejpam-6811	687	13	interest	interest	NOUN
ejpam-6811	687	14	.	.	PUNCT
ejpam-6811	688	1	references	reference	NOUN
ejpam-6811	688	2	[	[	X
ejpam-6811	688	3	1	1	X
ejpam-6811	688	4	]	]	PUNCT
ejpam-6811	688	5	haitham	haitham	PROPN
ejpam-6811	688	6	qawaqneh	qawaqneh	PROPN
ejpam-6811	688	7	,	,	PUNCT
ejpam-6811	688	8	hasanen	hasanen	PROPN
ejpam-6811	688	9	a	a	DET
ejpam-6811	688	10	hammad	hammad	PROPN
ejpam-6811	688	11	,	,	PUNCT
ejpam-6811	688	12	and	and	CCONJ
ejpam-6811	688	13	hassen	hassen	PROPN
ejpam-6811	688	14	aydi	aydi	VERB
ejpam-6811	688	15	.	.	PUNCT
ejpam-6811	689	1	exploring	explore	VERB
ejpam-6811	689	2	new	new	ADJ
ejpam-6811	689	3	geometric	geometric	ADJ
ejpam-6811	689	4	contraction	contraction	NOUN
ejpam-6811	689	5	mappings	mapping	NOUN
ejpam-6811	689	6	and	and	CCONJ
ejpam-6811	689	7	their	their	PRON
ejpam-6811	689	8	applications	application	NOUN
ejpam-6811	689	9	in	in	ADP
ejpam-6811	689	10	fractional	fractional	ADJ
ejpam-6811	689	11	metric	metric	ADJ
ejpam-6811	689	12	spaces	space	NOUN
ejpam-6811	689	13	.	.	PUNCT
ejpam-6811	690	1	aims	aim	VERB
ejpam-6811	690	2	mathematics	mathematic	NOUN
ejpam-6811	690	3	,	,	PUNCT
ejpam-6811	690	4	9(1):521–541	9(1):521–541	NUM
ejpam-6811	690	5	,	,	PUNCT
ejpam-6811	690	6	2024	2024	NUM
ejpam-6811	690	7	.	.	PUNCT
ejpam-6811	691	1	[	[	X
ejpam-6811	691	2	2	2	X
ejpam-6811	691	3	]	]	X
ejpam-6811	691	4	muhammad	muhammad	PROPN
ejpam-6811	691	5	nazam	nazam	PROPN
ejpam-6811	691	6	,	,	PUNCT
ejpam-6811	691	7	hassen	hassen	PROPN
ejpam-6811	691	8	aydi	aydi	ADV
ejpam-6811	691	9	,	,	PUNCT
ejpam-6811	691	10	mohd	mohd	PROPN
ejpam-6811	691	11	salmi	salmi	PROPN
ejpam-6811	691	12	noorani	noorani	PROPN
ejpam-6811	691	13	,	,	PUNCT
ejpam-6811	691	14	and	and	CCONJ
ejpam-6811	691	15	haitham	haitham	PROPN
ejpam-6811	691	16	qawaqneh	qawaqneh	PROPN
ejpam-6811	691	17	.	.	PUNCT
ejpam-6811	692	1	existence	existence	NOUN
ejpam-6811	692	2	of	of	ADP
ejpam-6811	692	3	fixed	fix	VERB
ejpam-6811	692	4	points	point	NOUN
ejpam-6811	692	5	of	of	ADP
ejpam-6811	692	6	four	four	NUM
ejpam-6811	692	7	maps	map	NOUN
ejpam-6811	692	8	for	for	ADP
ejpam-6811	692	9	a	a	DET
ejpam-6811	692	10	new	new	ADJ
ejpam-6811	692	11	generalized	generalized	ADJ
ejpam-6811	692	12	f	f	NOUN
ejpam-6811	692	13	-	-	PUNCT
ejpam-6811	692	14	contraction	contraction	NOUN
ejpam-6811	692	15	and	and	CCONJ
ejpam-6811	692	16	an	an	DET
ejpam-6811	692	17	application	application	NOUN
ejpam-6811	692	18	.	.	PUNCT
ejpam-6811	693	1	journal	journal	NOUN
ejpam-6811	693	2	of	of	ADP
ejpam-6811	693	3	function	function	NOUN
ejpam-6811	693	4	spaces	space	NOUN
ejpam-6811	693	5	,	,	PUNCT
ejpam-6811	693	6	2019(1):5980312	2019(1):5980312	NUM
ejpam-6811	693	7	,	,	PUNCT
ejpam-6811	693	8	2019	2019	NUM
ejpam-6811	693	9	.	.	PUNCT
ejpam-6811	694	1	[	[	X
ejpam-6811	694	2	3	3	X
ejpam-6811	694	3	]	]	X
ejpam-6811	694	4	stefan	stefan	PROPN
ejpam-6811	694	5	banach	banach	PROPN
ejpam-6811	694	6	.	.	PUNCT
ejpam-6811	695	1	sur	sur	PROPN
ejpam-6811	695	2	les	les	PROPN
ejpam-6811	695	3	operations	operation	NOUN
ejpam-6811	695	4	dans	dan	NOUN
ejpam-6811	695	5	les	le	NOUN
ejpam-6811	695	6	ensembles	ensemble	NOUN
ejpam-6811	695	7	abstraits	abstrait	NOUN
ejpam-6811	695	8	et	et	PROPN
ejpam-6811	695	9	leur	leur	X
ejpam-6811	695	10	application	application	PROPN
ejpam-6811	695	11	aux	aux	PROPN
ejpam-6811	695	12	equations	equation	NOUN
ejpam-6811	695	13	integrales	integrale	NOUN
ejpam-6811	695	14	.	.	PUNCT
ejpam-6811	696	1	fundamenta	fundamenta	PROPN
ejpam-6811	696	2	mathematicae	mathematicae	PROPN
ejpam-6811	696	3	,	,	PUNCT
ejpam-6811	696	4	3(1):133–181	3(1):133–181	NUM
ejpam-6811	696	5	,	,	PUNCT
ejpam-6811	696	6	1922	1922	NUM
ejpam-6811	696	7	.	.	PUNCT
ejpam-6811	697	1	[	[	X
ejpam-6811	697	2	4	4	X
ejpam-6811	697	3	]	]	X
ejpam-6811	697	4	stefan	stefan	PROPN
ejpam-6811	697	5	czerwik	czerwik	PROPN
ejpam-6811	697	6	.	.	PUNCT
ejpam-6811	698	1	contraction	contraction	NOUN
ejpam-6811	698	2	mappings	mapping	NOUN
ejpam-6811	698	3	in	in	ADP
ejpam-6811	698	4	b	b	NOUN
ejpam-6811	698	5	-	-	ADJ
ejpam-6811	698	6	metric	metric	ADJ
ejpam-6811	698	7	spaces	space	NOUN
ejpam-6811	698	8	.	.	PUNCT
ejpam-6811	699	1	acta	acta	PROPN
ejpam-6811	699	2	mathematica	mathematica	PROPN
ejpam-6811	699	3	et	et	PROPN
ejpam-6811	699	4	informatica	informatica	PROPN
ejpam-6811	699	5	universitatis	universitatis	PROPN
ejpam-6811	699	6	ostraviensis	ostraviensis	PROPN
ejpam-6811	699	7	,	,	PUNCT
ejpam-6811	699	8	1(1):5–11	1(1):5–11	NUM
ejpam-6811	699	9	,	,	PUNCT
ejpam-6811	699	10	1993	1993	NUM
ejpam-6811	699	11	.	.	PUNCT
ejpam-6811	700	1	[	[	X
ejpam-6811	700	2	5	5	NUM
ejpam-6811	700	3	]	]	SYM
ejpam-6811	700	4	i.a	i.a	PROPN
ejpam-6811	700	5	.	.	PROPN
ejpam-6811	700	6	bakhtin	bakhtin	PROPN
ejpam-6811	700	7	.	.	PUNCT
ejpam-6811	701	1	the	the	DET
ejpam-6811	701	2	contraction	contraction	NOUN
ejpam-6811	701	3	mapping	map	VERB
ejpam-6811	701	4	principle	principle	NOUN
ejpam-6811	701	5	in	in	ADP
ejpam-6811	701	6	quasimetric	quasimetric	ADJ
ejpam-6811	701	7	spaces	space	NOUN
ejpam-6811	701	8	.	.	PUNCT
ejpam-6811	702	1	functional	functional	ADJ
ejpam-6811	702	2	analysis	analysis	NOUN
ejpam-6811	702	3	,	,	PUNCT
ejpam-6811	702	4	30:26–37	30:26–37	PROPN
ejpam-6811	702	5	,	,	PUNCT
ejpam-6811	702	6	1989	1989	NUM
ejpam-6811	702	7	.	.	PUNCT
ejpam-6811	703	1	[	[	X
ejpam-6811	703	2	6	6	NUM
ejpam-6811	703	3	]	]	X
ejpam-6811	703	4	hojjat	hojjat	NOUN
ejpam-6811	703	5	afshari	afshari	PROPN
ejpam-6811	703	6	,	,	PUNCT
ejpam-6811	703	7	hassen	hassen	PROPN
ejpam-6811	703	8	aydi	aydi	ADV
ejpam-6811	703	9	,	,	PUNCT
ejpam-6811	703	10	and	and	CCONJ
ejpam-6811	703	11	erdal	erdal	PROPN
ejpam-6811	703	12	karapinar	karapinar	PROPN
ejpam-6811	703	13	.	.	PUNCT
ejpam-6811	704	1	existence	existence	NOUN
ejpam-6811	704	2	of	of	ADP
ejpam-6811	704	3	fixed	fix	VERB
ejpam-6811	704	4	points	point	NOUN
ejpam-6811	704	5	of	of	ADP
ejpam-6811	704	6	setvalued	setvalue	VERB
ejpam-6811	704	7	mappings	mapping	NOUN
ejpam-6811	704	8	in	in	ADP
ejpam-6811	704	9	b	b	NOUN
ejpam-6811	704	10	-	-	ADJ
ejpam-6811	704	11	metric	metric	ADJ
ejpam-6811	704	12	spaces	space	NOUN
ejpam-6811	704	13	.	.	PUNCT
ejpam-6811	705	1	east	east	PROPN
ejpam-6811	705	2	asian	asian	PROPN
ejpam-6811	705	3	math	math	PROPN
ejpam-6811	705	4	.	.	PUNCT
ejpam-6811	706	1	j	j	PROPN
ejpam-6811	706	2	,	,	PUNCT
ejpam-6811	706	3	32(3):319–332	32(3):319–332	PROPN
ejpam-6811	706	4	,	,	PUNCT
ejpam-6811	706	5	2016	2016	NUM
ejpam-6811	706	6	.	.	PUNCT
ejpam-6811	707	1	d.	d.	PROPN
ejpam-6811	707	2	e.	e.	PROPN
ejpam-6811	707	3	shehwar	shehwar	PROPN
ejpam-6811	707	4	sagheer	sagheer	PROPN
ejpam-6811	707	5	et	et	PROPN
ejpam-6811	707	6	al	al	PROPN
ejpam-6811	707	7	.	.	PUNCT
ejpam-6811	707	8	/	/	SYM
ejpam-6811	707	9	eur	eur	PROPN
ejpam-6811	707	10	.	.	PUNCT
ejpam-6811	708	1	j.	j.	PROPN
ejpam-6811	708	2	pure	pure	PROPN
ejpam-6811	708	3	appl	appl	PROPN
ejpam-6811	708	4	.	.	PROPN
ejpam-6811	708	5	math	math	PROPN
ejpam-6811	708	6	,	,	PUNCT
ejpam-6811	708	7	18	18	NUM
ejpam-6811	708	8	(	(	PUNCT
ejpam-6811	708	9	4	4	NUM
ejpam-6811	708	10	)	)	PUNCT
ejpam-6811	708	11	(	(	PUNCT
ejpam-6811	708	12	2025	2025	NUM
ejpam-6811	708	13	)	)	PUNCT
ejpam-6811	708	14	,	,	PUNCT
ejpam-6811	708	15	6811	6811	NUM
ejpam-6811	708	16	23	23	NUM
ejpam-6811	708	17	of	of	ADP
ejpam-6811	708	18	24	24	NUM
ejpam-6811	708	19	[	[	X
ejpam-6811	708	20	7	7	NUM
ejpam-6811	708	21	]	]	X
ejpam-6811	708	22	hassen	hassen	PROPN
ejpam-6811	708	23	aydi	aydi	VERB
ejpam-6811	708	24	,	,	PUNCT
ejpam-6811	708	25	monica	monica	PROPN
ejpam-6811	708	26	-	-	PUNCT
ejpam-6811	708	27	felicia	felicia	PROPN
ejpam-6811	708	28	bota	bota	NOUN
ejpam-6811	708	29	,	,	PUNCT
ejpam-6811	708	30	erdal	erdal	PROPN
ejpam-6811	708	31	karapinar	karapinar	PROPN
ejpam-6811	708	32	,	,	PUNCT
ejpam-6811	708	33	and	and	CCONJ
ejpam-6811	708	34	slobodanka	slobodanka	NOUN
ejpam-6811	708	35	mitrović	mitrović	VERB
ejpam-6811	708	36	.	.	PUNCT
ejpam-6811	709	1	a	a	DET
ejpam-6811	709	2	fixed	fix	VERB
ejpam-6811	709	3	point	point	NOUN
ejpam-6811	709	4	theorem	theorem	NOUN
ejpam-6811	709	5	for	for	ADP
ejpam-6811	709	6	set	set	NOUN
ejpam-6811	709	7	-	-	PUNCT
ejpam-6811	709	8	valued	value	VERB
ejpam-6811	709	9	quasi	quasi	NOUN
ejpam-6811	709	10	-	-	NOUN
ejpam-6811	709	11	contractions	contraction	NOUN
ejpam-6811	709	12	in	in	ADP
ejpam-6811	709	13	b	b	NOUN
ejpam-6811	709	14	-	-	ADJ
ejpam-6811	709	15	metric	metric	ADJ
ejpam-6811	709	16	spaces	space	NOUN
ejpam-6811	709	17	.	.	PUNCT
ejpam-6811	710	1	fixed	fix	VERB
ejpam-6811	710	2	point	point	NOUN
ejpam-6811	710	3	theory	theory	NOUN
ejpam-6811	710	4	and	and	CCONJ
ejpam-6811	710	5	applications	application	NOUN
ejpam-6811	710	6	,	,	PUNCT
ejpam-6811	710	7	2012(1):88	2012(1):88	NUM
ejpam-6811	710	8	,	,	PUNCT
ejpam-6811	710	9	2012	2012	NUM
ejpam-6811	710	10	.	.	PUNCT
ejpam-6811	711	1	[	[	X
ejpam-6811	711	2	8	8	NUM
ejpam-6811	711	3	]	]	X
ejpam-6811	711	4	thounaojam	thounaojam	NOUN
ejpam-6811	711	5	stephen	stephen	PROPN
ejpam-6811	711	6	,	,	PUNCT
ejpam-6811	711	7	yumnam	yumnam	NOUN
ejpam-6811	711	8	rohen	rohen	NOUN
ejpam-6811	711	9	,	,	PUNCT
ejpam-6811	711	10	m	m	PROPN
ejpam-6811	711	11	kuber	kuber	PROPN
ejpam-6811	711	12	singh	singh	PROPN
ejpam-6811	711	13	,	,	PUNCT
ejpam-6811	711	14	and	and	CCONJ
ejpam-6811	711	15	konthoujam	konthoujam	PROPN
ejpam-6811	711	16	sangita	sangita	PROPN
ejpam-6811	711	17	devi	devi	PROPN
ejpam-6811	711	18	.	.	PUNCT
ejpam-6811	712	1	some	some	DET
ejpam-6811	712	2	rational	rational	ADJ
ejpam-6811	712	3	f	f	NOUN
ejpam-6811	712	4	-	-	PUNCT
ejpam-6811	712	5	contractions	contraction	NOUN
ejpam-6811	712	6	in	in	ADP
ejpam-6811	712	7	b	b	NOUN
ejpam-6811	712	8	-	-	ADJ
ejpam-6811	712	9	metric	metric	ADJ
ejpam-6811	712	10	spaces	space	NOUN
ejpam-6811	712	11	and	and	CCONJ
ejpam-6811	712	12	fixed	fix	VERB
ejpam-6811	712	13	points	point	NOUN
ejpam-6811	712	14	.	.	PUNCT
ejpam-6811	713	1	nonlinear	nonlinear	ADJ
ejpam-6811	713	2	functional	functional	ADJ
ejpam-6811	713	3	analysis	analysis	NOUN
ejpam-6811	713	4	and	and	CCONJ
ejpam-6811	713	5	applications	application	NOUN
ejpam-6811	713	6	,	,	PUNCT
ejpam-6811	713	7	pages	page	NOUN
ejpam-6811	713	8	309–322	309–322	NUM
ejpam-6811	713	9	,	,	PUNCT
ejpam-6811	713	10	2022	2022	NUM
ejpam-6811	713	11	.	.	PUNCT
ejpam-6811	714	1	[	[	X
ejpam-6811	714	2	9	9	NUM
ejpam-6811	714	3	]	]	X
ejpam-6811	714	4	mudasir	mudasir	PROPN
ejpam-6811	714	5	younis	younis	PROPN
ejpam-6811	714	6	,	,	PUNCT
ejpam-6811	714	7	deepak	deepak	PROPN
ejpam-6811	714	8	singh	singh	PROPN
ejpam-6811	714	9	,	,	PUNCT
ejpam-6811	714	10	ishak	ishak	PROPN
ejpam-6811	714	11	altun	altun	PROPN
ejpam-6811	714	12	,	,	PUNCT
ejpam-6811	714	13	and	and	CCONJ
ejpam-6811	714	14	varsha	varsha	PROPN
ejpam-6811	714	15	chauhan	chauhan	PROPN
ejpam-6811	714	16	.	.	PUNCT
ejpam-6811	714	17	graphical	graphical	ADJ
ejpam-6811	714	18	structure	structure	NOUN
ejpam-6811	714	19	of	of	ADP
ejpam-6811	714	20	extended	extended	ADJ
ejpam-6811	714	21	b	b	X
ejpam-6811	714	22	-	-	ADJ
ejpam-6811	714	23	metric	metric	ADJ
ejpam-6811	714	24	spaces	space	NOUN
ejpam-6811	714	25	:	:	PUNCT
ejpam-6811	714	26	an	an	DET
ejpam-6811	714	27	application	application	NOUN
ejpam-6811	714	28	to	to	ADP
ejpam-6811	714	29	the	the	DET
ejpam-6811	714	30	transverse	transverse	NOUN
ejpam-6811	714	31	oscillations	oscillation	NOUN
ejpam-6811	714	32	of	of	ADP
ejpam-6811	714	33	a	a	DET
ejpam-6811	714	34	homogeneous	homogeneous	ADJ
ejpam-6811	714	35	bar	bar	NOUN
ejpam-6811	714	36	.	.	PUNCT
ejpam-6811	715	1	international	international	ADJ
ejpam-6811	715	2	journal	journal	PROPN
ejpam-6811	715	3	of	of	ADP
ejpam-6811	715	4	nonlinear	nonlinear	PROPN
ejpam-6811	715	5	sciences	sciences	PROPN
ejpam-6811	715	6	and	and	CCONJ
ejpam-6811	715	7	numerical	numerical	PROPN
ejpam-6811	715	8	simulation	simulation	PROPN
ejpam-6811	715	9	,	,	PUNCT
ejpam-6811	715	10	23(7	23(7	PROPN
ejpam-6811	715	11	-	-	PUNCT
ejpam-6811	715	12	8):1239–1252	8):1239–1252	NOUN
ejpam-6811	715	13	,	,	PUNCT
ejpam-6811	715	14	2022	2022	NUM
ejpam-6811	715	15	.	.	PUNCT
ejpam-6811	716	1	[	[	X
ejpam-6811	716	2	10	10	NUM
ejpam-6811	716	3	]	]	X
ejpam-6811	716	4	haitham	haitham	PROPN
ejpam-6811	716	5	qawaqneh	qawaqneh	PROPN
ejpam-6811	716	6	,	,	PUNCT
ejpam-6811	716	7	mohd	mohd	PROPN
ejpam-6811	716	8	salmi	salmi	PROPN
ejpam-6811	716	9	md	md	PROPN
ejpam-6811	716	10	noorani	noorani	PROPN
ejpam-6811	716	11	,	,	PUNCT
ejpam-6811	716	12	hassen	hassen	PROPN
ejpam-6811	716	13	aydi	aydi	VERB
ejpam-6811	716	14	,	,	PUNCT
ejpam-6811	716	15	amjed	amjed	PROPN
ejpam-6811	716	16	zraiqat	zraiqat	PROPN
ejpam-6811	716	17	,	,	PUNCT
ejpam-6811	716	18	and	and	CCONJ
ejpam-6811	716	19	arslan	arslan	PROPN
ejpam-6811	716	20	hojat	hojat	PROPN
ejpam-6811	716	21	ansari	ansari	PROPN
ejpam-6811	716	22	.	.	PUNCT
ejpam-6811	717	1	on	on	ADP
ejpam-6811	717	2	fixed	fix	VERB
ejpam-6811	717	3	point	point	NOUN
ejpam-6811	717	4	results	result	NOUN
ejpam-6811	717	5	in	in	ADP
ejpam-6811	717	6	partial	partial	ADJ
ejpam-6811	717	7	b	b	NOUN
ejpam-6811	717	8	-	-	PUNCT
ejpam-6811	717	9	metric	metric	ADJ
ejpam-6811	717	10	spaces	space	NOUN
ejpam-6811	717	11	.	.	PUNCT
ejpam-6811	718	1	journal	journal	NOUN
ejpam-6811	718	2	of	of	ADP
ejpam-6811	718	3	function	function	NOUN
ejpam-6811	718	4	spaces	space	NOUN
ejpam-6811	718	5	,	,	PUNCT
ejpam-6811	718	6	2021(1):8769190	2021(1):8769190	NUM
ejpam-6811	718	7	,	,	PUNCT
ejpam-6811	718	8	2021	2021	NUM
ejpam-6811	718	9	.	.	PUNCT
ejpam-6811	719	1	[	[	X
ejpam-6811	719	2	11	11	NUM
ejpam-6811	719	3	]	]	PUNCT
ejpam-6811	719	4	haitham	haitham	PROPN
ejpam-6811	719	5	qawaqneh	qawaqneh	PROPN
ejpam-6811	719	6	,	,	PUNCT
ejpam-6811	719	7	mohd	mohd	PROPN
ejpam-6811	719	8	salmi	salmi	PROPN
ejpam-6811	719	9	md	md	PROPN
ejpam-6811	719	10	noorani	noorani	PROPN
ejpam-6811	719	11	,	,	PUNCT
ejpam-6811	719	12	and	and	CCONJ
ejpam-6811	719	13	hassen	hassen	PROPN
ejpam-6811	719	14	aydi	aydi	VERB
ejpam-6811	719	15	.	.	PUNCT
ejpam-6811	720	1	some	some	DET
ejpam-6811	720	2	new	new	ADJ
ejpam-6811	720	3	characterizations	characterization	NOUN
ejpam-6811	720	4	and	and	CCONJ
ejpam-6811	720	5	results	result	NOUN
ejpam-6811	720	6	for	for	ADP
ejpam-6811	720	7	fuzzy	fuzzy	ADJ
ejpam-6811	720	8	contractions	contraction	NOUN
ejpam-6811	720	9	in	in	ADP
ejpam-6811	720	10	fuzzy	fuzzy	ADJ
ejpam-6811	720	11	b	b	X
ejpam-6811	720	12	-	-	PUNCT
ejpam-6811	720	13	metric	metric	ADJ
ejpam-6811	720	14	spaces	space	NOUN
ejpam-6811	720	15	and	and	CCONJ
ejpam-6811	720	16	applications	application	NOUN
ejpam-6811	720	17	.	.	PUNCT
ejpam-6811	721	1	aims	aim	VERB
ejpam-6811	721	2	mathematics	mathematics	PROPN
ejpam-6811	721	3	,	,	PUNCT
ejpam-6811	721	4	8(3):6682–6696	8(3):6682–6696	NOUN
ejpam-6811	721	5	,	,	PUNCT
ejpam-6811	721	6	2023	2023	NUM
ejpam-6811	721	7	.	.	PUNCT
ejpam-6811	722	1	[	[	X
ejpam-6811	722	2	12	12	NUM
ejpam-6811	722	3	]	]	X
ejpam-6811	722	4	samina	samina	PROPN
ejpam-6811	722	5	batul	batul	PROPN
ejpam-6811	722	6	,	,	PUNCT
ejpam-6811	722	7	faisar	faisar	PROPN
ejpam-6811	722	8	mehmood	mehmood	PROPN
ejpam-6811	722	9	,	,	PUNCT
ejpam-6811	722	10	azhar	azhar	PROPN
ejpam-6811	722	11	hussain	hussain	PROPN
ejpam-6811	722	12	,	,	PUNCT
ejpam-6811	722	13	d	d	PROPN
ejpam-6811	722	14	sagheer	sagheer	NOUN
ejpam-6811	722	15	,	,	PUNCT
ejpam-6811	722	16	hassen	hassen	PROPN
ejpam-6811	722	17	aydi	aydi	ADV
ejpam-6811	722	18	,	,	PUNCT
ejpam-6811	722	19	and	and	CCONJ
ejpam-6811	722	20	aiman	aiman	PROPN
ejpam-6811	722	21	mukheimer	mukheimer	PROPN
ejpam-6811	722	22	.	.	PUNCT
ejpam-6811	723	1	multivalued	multivalue	VERB
ejpam-6811	723	2	contraction	contraction	NOUN
ejpam-6811	723	3	maps	map	NOUN
ejpam-6811	723	4	on	on	ADP
ejpam-6811	723	5	fuzzy	fuzzy	ADJ
ejpam-6811	723	6	b	b	X
ejpam-6811	723	7	-	-	PUNCT
ejpam-6811	723	8	metric	metric	ADJ
ejpam-6811	723	9	spaces	space	NOUN
ejpam-6811	723	10	and	and	CCONJ
ejpam-6811	723	11	an	an	DET
ejpam-6811	723	12	application	application	NOUN
ejpam-6811	723	13	.	.	PUNCT
ejpam-6811	724	1	aims	aim	VERB
ejpam-6811	724	2	math	math	NOUN
ejpam-6811	724	3	,	,	PUNCT
ejpam-6811	724	4	7(4):5925–5942	7(4):5925–5942	NUM
ejpam-6811	724	5	,	,	PUNCT
ejpam-6811	724	6	2022	2022	NUM
ejpam-6811	724	7	.	.	PUNCT
ejpam-6811	725	1	[	[	X
ejpam-6811	725	2	13	13	NUM
ejpam-6811	725	3	]	]	X
ejpam-6811	725	4	muhammad	muhammad	PROPN
ejpam-6811	725	5	anwar	anwar	PROPN
ejpam-6811	725	6	,	,	PUNCT
ejpam-6811	725	7	dur	dur	PROPN
ejpam-6811	725	8	-	-	PUNCT
ejpam-6811	725	9	e	e	ADJ
ejpam-6811	725	10	-	-	ADJ
ejpam-6811	725	11	shehwar	shehwar	ADJ
ejpam-6811	725	12	sagheer	sagheer	NOUN
ejpam-6811	725	13	,	,	PUNCT
ejpam-6811	725	14	and	and	CCONJ
ejpam-6811	725	15	rashid	rashid	PROPN
ejpam-6811	725	16	ali	ali	PROPN
ejpam-6811	725	17	.	.	PUNCT
ejpam-6811	726	1	fixed	fix	VERB
ejpam-6811	726	2	point	point	NOUN
ejpam-6811	726	3	theorems	theorem	NOUN
ejpam-6811	726	4	of	of	ADP
ejpam-6811	726	5	wardowski	wardowski	PROPN
ejpam-6811	726	6	type	type	NOUN
ejpam-6811	726	7	mappings	mapping	NOUN
ejpam-6811	726	8	in	in	ADP
ejpam-6811	726	9	sb	sb	NOUN
ejpam-6811	726	10	-	-	ADJ
ejpam-6811	726	11	metric	metric	ADJ
ejpam-6811	726	12	spaces	space	NOUN
ejpam-6811	726	13	.	.	PUNCT
ejpam-6811	727	1	thai	thai	PROPN
ejpam-6811	727	2	journal	journal	PROPN
ejpam-6811	727	3	of	of	ADP
ejpam-6811	727	4	mathematics	mathematic	NOUN
ejpam-6811	727	5	,	,	PUNCT
ejpam-6811	727	6	20(2):945–956	20(2):945–956	NUM
ejpam-6811	727	7	,	,	PUNCT
ejpam-6811	727	8	2022	2022	NUM
ejpam-6811	727	9	.	.	PUNCT
ejpam-6811	728	1	[	[	X
ejpam-6811	728	2	14	14	NUM
ejpam-6811	728	3	]	]	X
ejpam-6811	728	4	erdal	erdal	X
ejpam-6811	728	5	karapinar	karapinar	PROPN
ejpam-6811	728	6	and	and	CCONJ
ejpam-6811	728	7	cristian	cristian	PROPN
ejpam-6811	728	8	chifu	chifu	PROPN
ejpam-6811	728	9	.	.	PUNCT
ejpam-6811	729	1	results	result	NOUN
ejpam-6811	729	2	in	in	ADP
ejpam-6811	729	3	wt	wt	NOUN
ejpam-6811	729	4	-	-	PUNCT
ejpam-6811	729	5	distance	distance	NOUN
ejpam-6811	729	6	over	over	ADP
ejpam-6811	729	7	b	b	NOUN
ejpam-6811	729	8	-	-	PUNCT
ejpam-6811	729	9	metric	metric	ADJ
ejpam-6811	729	10	spaces	space	NOUN
ejpam-6811	729	11	.	.	PUNCT
ejpam-6811	730	1	mathematics	mathematic	NOUN
ejpam-6811	730	2	,	,	PUNCT
ejpam-6811	730	3	8(2):220	8(2):220	NUM
ejpam-6811	730	4	,	,	PUNCT
ejpam-6811	730	5	2020	2020	NUM
ejpam-6811	730	6	.	.	PUNCT
ejpam-6811	731	1	[	[	X
ejpam-6811	731	2	15	15	NUM
ejpam-6811	731	3	]	]	X
ejpam-6811	731	4	m.	m.	NOUN
ejpam-6811	731	5	elbes	elbes	PROPN
ejpam-6811	731	6	,	,	PUNCT
ejpam-6811	731	7	kanan	kanan	PROPN
ejpam-6811	731	8	t.	t.	PROPN
ejpam-6811	731	9	,	,	PUNCT
ejpam-6811	731	10	m.	m.	NOUN
ejpam-6811	731	11	alia	alia	PROPN
ejpam-6811	731	12	,	,	PUNCT
ejpam-6811	731	13	and	and	CCONJ
ejpam-6811	731	14	ziad	ziad	PROPN
ejpam-6811	731	15	m.	m.	NOUN
ejpam-6811	731	16	covd-19	covd-19	PROPN
ejpam-6811	731	17	detection	detection	NOUN
ejpam-6811	731	18	platform	platform	NOUN
ejpam-6811	731	19	from	from	ADP
ejpam-6811	731	20	x	x	ADJ
ejpam-6811	731	21	-	-	NOUN
ejpam-6811	731	22	ray	ray	NOUN
ejpam-6811	731	23	images	image	NOUN
ejpam-6811	731	24	using	use	VERB
ejpam-6811	731	25	deep	deep	ADJ
ejpam-6811	731	26	learning	learning	NOUN
ejpam-6811	731	27	.	.	PUNCT
ejpam-6811	732	1	international	international	ADJ
ejpam-6811	732	2	journal	journal	NOUN
ejpam-6811	732	3	of	of	ADP
ejpam-6811	732	4	advances	advance	NOUN
ejpam-6811	732	5	in	in	ADP
ejpam-6811	732	6	soft	soft	ADJ
ejpam-6811	732	7	computing	computing	NOUN
ejpam-6811	732	8	and	and	CCONJ
ejpam-6811	732	9	its	its	PRON
ejpam-6811	732	10	applications	application	NOUN
ejpam-6811	732	11	,	,	PUNCT
ejpam-6811	732	12	14(1	14(1	NUM
ejpam-6811	732	13	)	)	PUNCT
ejpam-6811	732	14	,	,	PUNCT
ejpam-6811	732	15	2022	2022	NUM
ejpam-6811	732	16	.	.	PUNCT
ejpam-6811	733	1	[	[	X
ejpam-6811	733	2	16	16	NUM
ejpam-6811	733	3	]	]	X
ejpam-6811	733	4	haitham	haitham	PROPN
ejpam-6811	733	5	qawaqneh	qawaqneh	PROPN
ejpam-6811	733	6	.	.	PUNCT
ejpam-6811	734	1	new	new	ADJ
ejpam-6811	734	2	functions	function	NOUN
ejpam-6811	734	3	for	for	ADP
ejpam-6811	734	4	fixed	fix	VERB
ejpam-6811	734	5	point	point	NOUN
ejpam-6811	734	6	results	result	NOUN
ejpam-6811	734	7	in	in	ADP
ejpam-6811	734	8	metric	metric	ADJ
ejpam-6811	734	9	spaces	space	NOUN
ejpam-6811	734	10	with	with	ADP
ejpam-6811	734	11	some	some	DET
ejpam-6811	734	12	applications	application	NOUN
ejpam-6811	734	13	.	.	PUNCT
ejpam-6811	735	1	indian	indian	ADJ
ejpam-6811	735	2	journal	journal	PROPN
ejpam-6811	735	3	of	of	ADP
ejpam-6811	735	4	mathematics	mathematic	NOUN
ejpam-6811	735	5	,	,	PUNCT
ejpam-6811	735	6	66(1):55–84	66(1):55–84	NOUN
ejpam-6811	735	7	,	,	PUNCT
ejpam-6811	735	8	2024	2024	NUM
ejpam-6811	735	9	.	.	PUNCT
ejpam-6811	736	1	[	[	X
ejpam-6811	736	2	17	17	NUM
ejpam-6811	736	3	]	]	X
ejpam-6811	736	4	monther	monther	PROPN
ejpam-6811	736	5	rashed	rashed	PROPN
ejpam-6811	736	6	alfuraidan	alfuraidan	PROPN
ejpam-6811	736	7	.	.	PUNCT
ejpam-6811	737	1	the	the	DET
ejpam-6811	737	2	contraction	contraction	NOUN
ejpam-6811	737	3	principle	principle	NOUN
ejpam-6811	737	4	for	for	ADP
ejpam-6811	737	5	multivalued	multivalued	ADJ
ejpam-6811	737	6	mappings	mapping	NOUN
ejpam-6811	737	7	on	on	ADP
ejpam-6811	737	8	a	a	DET
ejpam-6811	737	9	modular	modular	ADJ
ejpam-6811	737	10	metric	metric	ADJ
ejpam-6811	737	11	space	space	NOUN
ejpam-6811	737	12	with	with	ADP
ejpam-6811	737	13	a	a	DET
ejpam-6811	737	14	graph	graph	NOUN
ejpam-6811	737	15	.	.	PUNCT
ejpam-6811	738	1	canadian	canadian	ADJ
ejpam-6811	738	2	mathematical	mathematical	ADJ
ejpam-6811	738	3	bulletin	bulletin	NOUN
ejpam-6811	738	4	,	,	PUNCT
ejpam-6811	738	5	59(1):3–12	59(1):3–12	NUM
ejpam-6811	738	6	,	,	PUNCT
ejpam-6811	738	7	2016	2016	NUM
ejpam-6811	738	8	.	.	PUNCT
ejpam-6811	739	1	[	[	X
ejpam-6811	739	2	18	18	NUM
ejpam-6811	739	3	]	]	PUNCT
ejpam-6811	739	4	ismat	ismat	NOUN
ejpam-6811	739	5	beg	beg	PROPN
ejpam-6811	739	6	,	,	PUNCT
ejpam-6811	739	7	asma	asma	PROPN
ejpam-6811	739	8	rashid	rashid	PROPN
ejpam-6811	739	9	butt	butt	PROPN
ejpam-6811	739	10	,	,	PUNCT
ejpam-6811	739	11	and	and	CCONJ
ejpam-6811	739	12	slobodan	slobodan	PROPN
ejpam-6811	739	13	radojevic	radojevic	PROPN
ejpam-6811	739	14	.	.	PUNCT
ejpam-6811	740	1	the	the	DET
ejpam-6811	740	2	contraction	contraction	NOUN
ejpam-6811	740	3	principle	principle	NOUN
ejpam-6811	740	4	for	for	ADP
ejpam-6811	740	5	set	set	VERB
ejpam-6811	740	6	valued	value	VERB
ejpam-6811	740	7	mappings	mapping	NOUN
ejpam-6811	740	8	on	on	ADP
ejpam-6811	740	9	a	a	DET
ejpam-6811	740	10	metric	metric	ADJ
ejpam-6811	740	11	space	space	NOUN
ejpam-6811	740	12	with	with	ADP
ejpam-6811	740	13	a	a	DET
ejpam-6811	740	14	graph	graph	NOUN
ejpam-6811	740	15	.	.	PUNCT
ejpam-6811	741	1	computers	computer	NOUN
ejpam-6811	741	2	&	&	CCONJ
ejpam-6811	741	3	mathematics	mathematics	PROPN
ejpam-6811	741	4	with	with	ADP
ejpam-6811	741	5	applications	application	NOUN
ejpam-6811	741	6	,	,	PUNCT
ejpam-6811	741	7	60(5):1214–1219	60(5):1214–1219	NOUN
ejpam-6811	741	8	,	,	PUNCT
ejpam-6811	741	9	2010	2010	NUM
ejpam-6811	741	10	.	.	PUNCT
ejpam-6811	742	1	[	[	X
ejpam-6811	742	2	19	19	NUM
ejpam-6811	742	3	]	]	X
ejpam-6811	742	4	florin	florin	PROPN
ejpam-6811	742	5	bojor	bojor	PROPN
ejpam-6811	742	6	.	.	PUNCT
ejpam-6811	743	1	fixed	fix	VERB
ejpam-6811	743	2	point	point	NOUN
ejpam-6811	743	3	theorems	theorem	NOUN
ejpam-6811	743	4	for	for	ADP
ejpam-6811	743	5	reich	reich	NOUN
ejpam-6811	743	6	type	type	NOUN
ejpam-6811	743	7	contractions	contraction	NOUN
ejpam-6811	743	8	on	on	ADP
ejpam-6811	743	9	metric	metric	ADJ
ejpam-6811	743	10	spaces	space	NOUN
ejpam-6811	743	11	with	with	ADP
ejpam-6811	743	12	a	a	DET
ejpam-6811	743	13	graph	graph	NOUN
ejpam-6811	743	14	.	.	PUNCT
ejpam-6811	744	1	nonlinear	nonlinear	ADJ
ejpam-6811	744	2	analysis	analysis	NOUN
ejpam-6811	744	3	:	:	PUNCT
ejpam-6811	744	4	theory	theory	NOUN
ejpam-6811	744	5	,	,	PUNCT
ejpam-6811	744	6	methods	method	NOUN
ejpam-6811	744	7	&	&	CCONJ
ejpam-6811	744	8	applications	application	NOUN
ejpam-6811	744	9	,	,	PUNCT
ejpam-6811	744	10	75(9):3895–3901	75(9):3895–3901	NUM
ejpam-6811	744	11	,	,	PUNCT
ejpam-6811	744	12	2012	2012	NUM
ejpam-6811	744	13	.	.	PUNCT
ejpam-6811	745	1	[	[	X
ejpam-6811	745	2	20	20	NUM
ejpam-6811	745	3	]	]	PUNCT
ejpam-6811	745	4	mudasir	mudasir	PROPN
ejpam-6811	745	5	younis	younis	PROPN
ejpam-6811	745	6	and	and	CCONJ
ejpam-6811	745	7	dhirendra	dhirendra	PROPN
ejpam-6811	745	8	bahuguna	bahuguna	PROPN
ejpam-6811	745	9	.	.	PUNCT
ejpam-6811	746	1	a	a	DET
ejpam-6811	746	2	unique	unique	ADJ
ejpam-6811	746	3	approach	approach	NOUN
ejpam-6811	746	4	to	to	ADP
ejpam-6811	746	5	graph	graph	NOUN
ejpam-6811	746	6	-	-	PUNCT
ejpam-6811	746	7	based	base	VERB
ejpam-6811	746	8	metric	metric	ADJ
ejpam-6811	746	9	spaces	space	NOUN
ejpam-6811	746	10	with	with	ADP
ejpam-6811	746	11	an	an	DET
ejpam-6811	746	12	application	application	NOUN
ejpam-6811	746	13	to	to	ADP
ejpam-6811	746	14	rocket	rocket	NOUN
ejpam-6811	746	15	ascension	ascension	NOUN
ejpam-6811	746	16	.	.	PUNCT
ejpam-6811	747	1	computational	computational	ADJ
ejpam-6811	747	2	and	and	CCONJ
ejpam-6811	747	3	applied	applied	ADJ
ejpam-6811	747	4	mathematics	mathematic	NOUN
ejpam-6811	747	5	,	,	PUNCT
ejpam-6811	747	6	42(1):44	42(1):44	NUM
ejpam-6811	747	7	,	,	PUNCT
ejpam-6811	747	8	2023	2023	NUM
ejpam-6811	747	9	.	.	PUNCT
ejpam-6811	748	1	[	[	X
ejpam-6811	748	2	21	21	NUM
ejpam-6811	748	3	]	]	X
ejpam-6811	748	4	haitham	haitham	PROPN
ejpam-6811	748	5	qawaqneh	qawaqneh	PROPN
ejpam-6811	748	6	,	,	PUNCT
ejpam-6811	748	7	mohd	mohd	PROPN
ejpam-6811	748	8	salmi	salmi	PROPN
ejpam-6811	748	9	noorani	noorani	PROPN
ejpam-6811	748	10	,	,	PUNCT
ejpam-6811	748	11	hassen	hassen	PROPN
ejpam-6811	748	12	aydi	aydi	ADV
ejpam-6811	748	13	,	,	PUNCT
ejpam-6811	748	14	and	and	CCONJ
ejpam-6811	748	15	wasfi	wasfi	ADV
ejpam-6811	748	16	shatanawi	shatanawi	ADJ
ejpam-6811	748	17	.	.	PUNCT
ejpam-6811	749	1	on	on	ADP
ejpam-6811	749	2	common	common	ADJ
ejpam-6811	749	3	fixed	fix	VERB
ejpam-6811	749	4	point	point	NOUN
ejpam-6811	749	5	results	result	NOUN
ejpam-6811	749	6	for	for	ADP
ejpam-6811	749	7	new	new	ADJ
ejpam-6811	749	8	contractions	contraction	NOUN
ejpam-6811	749	9	with	with	ADP
ejpam-6811	749	10	applications	application	NOUN
ejpam-6811	749	11	to	to	PART
ejpam-6811	749	12	graph	graph	VERB
ejpam-6811	749	13	and	and	CCONJ
ejpam-6811	749	14	integral	integral	ADJ
ejpam-6811	749	15	equations	equation	NOUN
ejpam-6811	749	16	.	.	PUNCT
ejpam-6811	750	1	mathematics	mathematic	NOUN
ejpam-6811	750	2	,	,	PUNCT
ejpam-6811	750	3	7(11):1082	7(11):1082	NOUN
ejpam-6811	750	4	,	,	PUNCT
ejpam-6811	750	5	2019	2019	NUM
ejpam-6811	750	6	.	.	PUNCT
ejpam-6811	751	1	d.	d.	PROPN
ejpam-6811	751	2	e.	e.	PROPN
ejpam-6811	751	3	shehwar	shehwar	PROPN
ejpam-6811	751	4	sagheer	sagheer	PROPN
ejpam-6811	751	5	et	et	PROPN
ejpam-6811	751	6	al	al	PROPN
ejpam-6811	751	7	.	.	PUNCT
ejpam-6811	751	8	/	/	SYM
ejpam-6811	751	9	eur	eur	PROPN
ejpam-6811	751	10	.	.	PUNCT
ejpam-6811	752	1	j.	j.	PROPN
ejpam-6811	752	2	pure	pure	PROPN
ejpam-6811	752	3	appl	appl	PROPN
ejpam-6811	752	4	.	.	PROPN
ejpam-6811	752	5	math	math	PROPN
ejpam-6811	752	6	,	,	PUNCT
ejpam-6811	752	7	18	18	NUM
ejpam-6811	752	8	(	(	PUNCT
ejpam-6811	752	9	4	4	NUM
ejpam-6811	752	10	)	)	PUNCT
ejpam-6811	752	11	(	(	PUNCT
ejpam-6811	752	12	2025	2025	NUM
ejpam-6811	752	13	)	)	PUNCT
ejpam-6811	752	14	,	,	PUNCT
ejpam-6811	752	15	6811	6811	NUM
ejpam-6811	752	16	24	24	NUM
ejpam-6811	752	17	of	of	ADP
ejpam-6811	752	18	24	24	NUM
ejpam-6811	752	19	[	[	SYM
ejpam-6811	752	20	22	22	NUM
ejpam-6811	752	21	]	]	PUNCT
ejpam-6811	752	22	erdal	erdal	PROPN
ejpam-6811	752	23	karapinar	karapinar	PROPN
ejpam-6811	752	24	,	,	PUNCT
ejpam-6811	752	25	thabet	thabet	ADJ
ejpam-6811	752	26	abdeljawad	abdeljawad	NOUN
ejpam-6811	752	27	,	,	PUNCT
ejpam-6811	752	28	and	and	CCONJ
ejpam-6811	752	29	fahd	fahd	PROPN
ejpam-6811	752	30	jarad	jarad	PROPN
ejpam-6811	752	31	.	.	PUNCT
ejpam-6811	753	1	applying	apply	VERB
ejpam-6811	753	2	new	new	ADJ
ejpam-6811	753	3	fixed	fix	VERB
ejpam-6811	753	4	point	point	NOUN
ejpam-6811	753	5	theorems	theorem	NOUN
ejpam-6811	753	6	on	on	ADP
ejpam-6811	753	7	fractional	fractional	ADJ
ejpam-6811	753	8	and	and	CCONJ
ejpam-6811	753	9	ordinary	ordinary	ADJ
ejpam-6811	753	10	differential	differential	ADJ
ejpam-6811	753	11	equations	equation	NOUN
ejpam-6811	753	12	.	.	PUNCT
ejpam-6811	754	1	advances	advance	NOUN
ejpam-6811	754	2	in	in	ADP
ejpam-6811	754	3	difference	difference	NOUN
ejpam-6811	754	4	equations	equation	NOUN
ejpam-6811	754	5	,	,	PUNCT
ejpam-6811	754	6	2019(1):1–25	2019(1):1–25	NUM
ejpam-6811	754	7	,	,	PUNCT
ejpam-6811	754	8	2019	2019	NUM
ejpam-6811	754	9	.	.	PUNCT
ejpam-6811	755	1	[	[	X
ejpam-6811	755	2	23	23	NUM
ejpam-6811	755	3	]	]	X
ejpam-6811	755	4	ben	ben	PROPN
ejpam-6811	755	5	wongsaijai	wongsaijai	PROPN
ejpam-6811	755	6	,	,	PUNCT
ejpam-6811	755	7	phakdi	phakdi	PROPN
ejpam-6811	755	8	charoensawan	charoensawan	PROPN
ejpam-6811	755	9	,	,	PUNCT
ejpam-6811	755	10	teeranush	teeranush	ADJ
ejpam-6811	755	11	suebcharoen	suebcharoen	NOUN
ejpam-6811	755	12	,	,	PUNCT
ejpam-6811	755	13	and	and	CCONJ
ejpam-6811	755	14	watchareepan	watchareepan	ADJ
ejpam-6811	755	15	atiponrat	atiponrat	NOUN
ejpam-6811	755	16	.	.	PUNCT
ejpam-6811	756	1	common	common	ADJ
ejpam-6811	756	2	fixed	fix	VERB
ejpam-6811	756	3	point	point	NOUN
ejpam-6811	756	4	theorems	theorem	NOUN
ejpam-6811	756	5	for	for	ADP
ejpam-6811	756	6	auxiliary	auxiliary	ADJ
ejpam-6811	756	7	functions	function	NOUN
ejpam-6811	756	8	with	with	ADP
ejpam-6811	756	9	applications	application	NOUN
ejpam-6811	756	10	in	in	ADP
ejpam-6811	756	11	fractional	fractional	ADJ
ejpam-6811	756	12	differential	differential	ADJ
ejpam-6811	756	13	equation	equation	NOUN
ejpam-6811	756	14	.	.	PUNCT
ejpam-6811	757	1	advances	advance	NOUN
ejpam-6811	757	2	in	in	ADP
ejpam-6811	757	3	difference	difference	NOUN
ejpam-6811	757	4	equations	equation	NOUN
ejpam-6811	757	5	,	,	PUNCT
ejpam-6811	757	6	2021(1):503	2021(1):503	NUM
ejpam-6811	757	7	,	,	PUNCT
ejpam-6811	757	8	2021	2021	NUM
ejpam-6811	757	9	.	.	PUNCT
ejpam-6811	758	1	[	[	X
ejpam-6811	758	2	24	24	NUM
ejpam-6811	758	3	]	]	X
ejpam-6811	758	4	rezan	rezan	NOUN
ejpam-6811	758	5	sevinik	sevinik	VERB
ejpam-6811	758	6	adiguzel	adiguzel	PROPN
ejpam-6811	758	7	,	,	PUNCT
ejpam-6811	758	8	umit	umit	VERB
ejpam-6811	758	9	aksoy	aksoy	PROPN
ejpam-6811	758	10	,	,	PUNCT
ejpam-6811	758	11	erdal	erdal	PROPN
ejpam-6811	758	12	karapinar	karapinar	PROPN
ejpam-6811	758	13	,	,	PUNCT
ejpam-6811	758	14	and	and	CCONJ
ejpam-6811	758	15	inci	inci	PROPN
ejpam-6811	758	16	m	m	VERB
ejpam-6811	758	17	erhan	erhan	ADP
ejpam-6811	758	18	.	.	PUNCT
ejpam-6811	759	1	on	on	ADP
ejpam-6811	759	2	the	the	DET
ejpam-6811	759	3	solution	solution	NOUN
ejpam-6811	759	4	of	of	ADP
ejpam-6811	759	5	a	a	DET
ejpam-6811	759	6	boundary	boundary	ADJ
ejpam-6811	759	7	value	value	NOUN
ejpam-6811	759	8	problem	problem	NOUN
ejpam-6811	759	9	associated	associate	VERB
ejpam-6811	759	10	with	with	ADP
ejpam-6811	759	11	a	a	DET
ejpam-6811	759	12	fractional	fractional	ADJ
ejpam-6811	759	13	differential	differential	NOUN
ejpam-6811	759	14	equation	equation	NOUN
ejpam-6811	759	15	.	.	PUNCT
ejpam-6811	760	1	mathematical	mathematical	ADJ
ejpam-6811	760	2	methods	method	NOUN
ejpam-6811	760	3	in	in	ADP
ejpam-6811	760	4	the	the	DET
ejpam-6811	760	5	applied	apply	VERB
ejpam-6811	760	6	sciences	science	NOUN
ejpam-6811	760	7	,	,	PUNCT
ejpam-6811	760	8	47(13):10928–10939	47(13):10928–10939	NUM
ejpam-6811	760	9	,	,	PUNCT
ejpam-6811	760	10	2024	2024	NUM
ejpam-6811	760	11	.	.	PUNCT
ejpam-6811	761	1	[	[	X
ejpam-6811	761	2	25	25	NUM
ejpam-6811	761	3	]	]	X
ejpam-6811	761	4	rezan	rezan	NOUN
ejpam-6811	761	5	sevinik	sevinik	VERB
ejpam-6811	761	6	adiguzel	adiguzel	PROPN
ejpam-6811	761	7	,	,	PUNCT
ejpam-6811	761	8	umit	umit	VERB
ejpam-6811	761	9	aksoy	aksoy	PROPN
ejpam-6811	761	10	,	,	PUNCT
ejpam-6811	761	11	erdal	erdal	PROPN
ejpam-6811	761	12	karapinar	karapinar	PROPN
ejpam-6811	761	13	,	,	PUNCT
ejpam-6811	761	14	and	and	CCONJ
ejpam-6811	761	15	inci	inci	PROPN
ejpam-6811	761	16	m	m	VERB
ejpam-6811	761	17	erhan	erhan	ADP
ejpam-6811	761	18	.	.	PUNCT
ejpam-6811	762	1	on	on	ADP
ejpam-6811	762	2	the	the	DET
ejpam-6811	762	3	solutions	solution	NOUN
ejpam-6811	762	4	of	of	ADP
ejpam-6811	762	5	fractional	fractional	ADJ
ejpam-6811	762	6	differential	differential	ADJ
ejpam-6811	762	7	equations	equation	NOUN
ejpam-6811	762	8	via	via	ADP
ejpam-6811	762	9	geraghty	geraghty	PROPN
ejpam-6811	762	10	type	type	NOUN
ejpam-6811	762	11	hybrid	hybrid	ADJ
ejpam-6811	762	12	contractions	contraction	NOUN
ejpam-6811	762	13	.	.	PUNCT
ejpam-6811	762	14	2021	2021	NUM
ejpam-6811	762	15	.	.	PUNCT
ejpam-6811	763	1	[	[	X
ejpam-6811	763	2	26	26	NUM
ejpam-6811	763	3	]	]	X
ejpam-6811	763	4	duha	duha	NOUN
ejpam-6811	763	5	abu	abu	PROPN
ejpam-6811	763	6	judeh	judeh	PROPN
ejpam-6811	763	7	and	and	CCONJ
ejpam-6811	763	8	m	m	PROPN
ejpam-6811	763	9	abu	abu	PROPN
ejpam-6811	763	10	hammad	hammad	PROPN
ejpam-6811	763	11	.	.	PUNCT
ejpam-6811	764	1	applications	application	NOUN
ejpam-6811	764	2	of	of	ADP
ejpam-6811	764	3	conformable	conformable	ADJ
ejpam-6811	764	4	fractional	fractional	ADJ
ejpam-6811	764	5	pareto	pareto	ADJ
ejpam-6811	764	6	probability	probability	NOUN
ejpam-6811	764	7	distribution	distribution	NOUN
ejpam-6811	764	8	.	.	PUNCT
ejpam-6811	765	1	int	int	NOUN
ejpam-6811	765	2	.	.	PUNCT
ejpam-6811	766	1	j.	j.	PROPN
ejpam-6811	766	2	advance	advance	VERB
ejpam-6811	766	3	soft	soft	ADJ
ejpam-6811	766	4	compu	compu	PROPN
ejpam-6811	766	5	.	.	PUNCT
ejpam-6811	767	1	appl	appl	PROPN
ejpam-6811	767	2	,	,	PUNCT
ejpam-6811	767	3	14(2):115–124	14(2):115–124	NUM
ejpam-6811	767	4	,	,	PUNCT
ejpam-6811	767	5	2022	2022	NUM
ejpam-6811	767	6	.	.	PUNCT
ejpam-6811	768	1	[	[	X
ejpam-6811	768	2	27	27	NUM
ejpam-6811	768	3	]	]	X
ejpam-6811	768	4	william	william	PROPN
ejpam-6811	768	5	kirk	kirk	PROPN
ejpam-6811	768	6	and	and	CCONJ
ejpam-6811	768	7	naseer	naseer	PROPN
ejpam-6811	768	8	shahzad	shahzad	PROPN
ejpam-6811	768	9	.	.	PUNCT
ejpam-6811	769	1	fixed	fix	VERB
ejpam-6811	769	2	point	point	NOUN
ejpam-6811	769	3	theory	theory	NOUN
ejpam-6811	769	4	in	in	ADP
ejpam-6811	769	5	distance	distance	NOUN
ejpam-6811	769	6	spaces	space	NOUN
ejpam-6811	769	7	,	,	PUNCT
ejpam-6811	769	8	volume	volume	NOUN
ejpam-6811	769	9	1	1	NUM
ejpam-6811	769	10	.	.	PUNCT
ejpam-6811	769	11	springer	springer	NOUN
ejpam-6811	769	12	,	,	PUNCT
ejpam-6811	769	13	2014	2014	NUM
ejpam-6811	769	14	.	.	PUNCT
ejpam-6811	770	1	[	[	X
ejpam-6811	770	2	28	28	NUM
ejpam-6811	770	3	]	]	X
ejpam-6811	770	4	p	p	X
ejpam-6811	770	5	charoensawan	charoensawan	NOUN
ejpam-6811	770	6	and	and	CCONJ
ejpam-6811	770	7	w	w	NOUN
ejpam-6811	770	8	atiponrat	atiponrat	NOUN
ejpam-6811	770	9	.	.	PUNCT
ejpam-6811	771	1	common	common	ADJ
ejpam-6811	771	2	fixed	fix	VERB
ejpam-6811	771	3	point	point	NOUN
ejpam-6811	771	4	and	and	CCONJ
ejpam-6811	771	5	coupled	couple	VERB
ejpam-6811	771	6	coincidence	coincidence	NOUN
ejpam-6811	771	7	point	point	NOUN
ejpam-6811	771	8	theorems	theorem	NOUN
ejpam-6811	771	9	for	for	ADP
ejpam-6811	771	10	geraghty	geraghty	PROPN
ejpam-6811	771	11	’s	’s	PART
ejpam-6811	771	12	type	type	NOUN
ejpam-6811	771	13	contraction	contraction	NOUN
ejpam-6811	771	14	mapping	mapping	NOUN
ejpam-6811	771	15	with	with	ADP
ejpam-6811	771	16	two	two	NUM
ejpam-6811	771	17	metrics	metric	NOUN
ejpam-6811	771	18	endowed	endow	VERB
ejpam-6811	771	19	with	with	ADP
ejpam-6811	771	20	a	a	DET
ejpam-6811	771	21	directed	direct	VERB
ejpam-6811	771	22	graph	graph	NOUN
ejpam-6811	771	23	.	.	PUNCT
ejpam-6811	772	1	journal	journal	NOUN
ejpam-6811	772	2	of	of	ADP
ejpam-6811	772	3	mathematics	mathematic	NOUN
ejpam-6811	772	4	,	,	PUNCT
ejpam-6811	772	5	2017(1):5746704	2017(1):5746704	X
ejpam-6811	772	6	,	,	PUNCT
ejpam-6811	772	7	2017	2017	NUM
ejpam-6811	772	8	.	.	PUNCT
ejpam-6811	773	1	[	[	X
ejpam-6811	773	2	29	29	NUM
ejpam-6811	773	3	]	]	X
ejpam-6811	773	4	ravi	ravi	NOUN
ejpam-6811	773	5	p	p	PROPN
ejpam-6811	773	6	agarwal	agarwal	PROPN
ejpam-6811	773	7	and	and	CCONJ
ejpam-6811	773	8	donal	donal	PROPN
ejpam-6811	773	9	o′regan	o′regan	NOUN
ejpam-6811	773	10	.	.	PUNCT
ejpam-6811	774	1	fixed	fix	VERB
ejpam-6811	774	2	point	point	NOUN
ejpam-6811	774	3	theory	theory	NOUN
ejpam-6811	774	4	for	for	ADP
ejpam-6811	774	5	generalized	generalized	ADJ
ejpam-6811	774	6	contractions	contraction	NOUN
ejpam-6811	774	7	on	on	ADP
ejpam-6811	774	8	spaces	space	NOUN
ejpam-6811	774	9	with	with	ADP
ejpam-6811	774	10	two	two	NUM
ejpam-6811	774	11	metrics	metric	NOUN
ejpam-6811	774	12	.	.	PUNCT
ejpam-6811	775	1	journal	journal	PROPN
ejpam-6811	775	2	of	of	ADP
ejpam-6811	775	3	mathematical	mathematical	ADJ
ejpam-6811	775	4	analysis	analysis	NOUN
ejpam-6811	775	5	and	and	CCONJ
ejpam-6811	775	6	applications	application	NOUN
ejpam-6811	775	7	,	,	PUNCT
ejpam-6811	775	8	248(2):402–414	248(2):402–414	NUM
ejpam-6811	775	9	,	,	PUNCT
ejpam-6811	775	10	2000	2000	NUM
ejpam-6811	775	11	.	.	PUNCT
ejpam-6811	776	1	[	[	X
ejpam-6811	776	2	30	30	NUM
ejpam-6811	776	3	]	]	X
ejpam-6811	776	4	asadollah	asadollah	PROPN
ejpam-6811	776	5	aghajani	aghajani	PROPN
ejpam-6811	776	6	,	,	PUNCT
ejpam-6811	776	7	mujahid	mujahid	NOUN
ejpam-6811	776	8	abbas	abbas	NOUN
ejpam-6811	776	9	,	,	PUNCT
ejpam-6811	776	10	and	and	CCONJ
ejpam-6811	776	11	jamal	jamal	PROPN
ejpam-6811	776	12	roshan	roshan	PROPN
ejpam-6811	776	13	.	.	PUNCT
ejpam-6811	776	14	common	common	ADJ
ejpam-6811	776	15	fixed	fix	VERB
ejpam-6811	776	16	point	point	NOUN
ejpam-6811	776	17	of	of	ADP
ejpam-6811	776	18	generalized	generalized	ADJ
ejpam-6811	776	19	weak	weak	ADJ
ejpam-6811	776	20	contractive	contractive	ADJ
ejpam-6811	776	21	mappings	mapping	NOUN
ejpam-6811	776	22	in	in	ADP
ejpam-6811	776	23	partially	partially	ADV
ejpam-6811	776	24	ordered	order	VERB
ejpam-6811	776	25	b	b	ADJ
ejpam-6811	776	26	-	-	ADJ
ejpam-6811	776	27	metric	metric	ADJ
ejpam-6811	776	28	spaces	space	NOUN
ejpam-6811	776	29	.	.	PUNCT
ejpam-6811	777	1	mathematica	mathematica	PROPN
ejpam-6811	777	2	slovaca	slovaca	PROPN
ejpam-6811	777	3	,	,	PUNCT
ejpam-6811	777	4	64(4):941–960	64(4):941–960	PROPN
ejpam-6811	777	5	,	,	PUNCT
ejpam-6811	777	6	2014	2014	NUM
ejpam-6811	777	7	.	.	PUNCT