id	sid	tid	token	lemma	pos
ejpam-5826	1	1	european	european	PROPN
ejpam-5826	1	2	journal	journal	PROPN
ejpam-5826	1	3	of	of	ADP
ejpam-5826	1	4	pure	pure	ADJ
ejpam-5826	1	5	and	and	CCONJ
ejpam-5826	1	6	applied	applied	ADJ
ejpam-5826	1	7	mathematics	mathematic	NOUN
ejpam-5826	1	8	2025	2025	NUM
ejpam-5826	1	9	,	,	PUNCT
ejpam-5826	1	10	vol	vol	NOUN
ejpam-5826	1	11	.	.	PROPN
ejpam-5826	1	12	18	18	NUM
ejpam-5826	1	13	,	,	PUNCT
ejpam-5826	1	14	issue	issue	NOUN
ejpam-5826	1	15	2	2	NUM
ejpam-5826	1	16	,	,	PUNCT
ejpam-5826	1	17	article	article	NOUN
ejpam-5826	1	18	number	number	NOUN
ejpam-5826	1	19	5826	5826	NUM
ejpam-5826	1	20	issn	issn	PROPN
ejpam-5826	1	21	1307	1307	NUM
ejpam-5826	1	22	-	-	SYM
ejpam-5826	1	23	5543	5543	NUM
ejpam-5826	1	24	–	–	PUNCT
ejpam-5826	1	25	ejpam.com	ejpam.com	X
ejpam-5826	1	26	published	publish	VERB
ejpam-5826	1	27	by	by	ADP
ejpam-5826	1	28	new	new	PROPN
ejpam-5826	1	29	york	york	PROPN
ejpam-5826	1	30	business	business	PROPN
ejpam-5826	1	31	global	global	ADJ
ejpam-5826	1	32	common	common	ADJ
ejpam-5826	1	33	fixed	fix	VERB
ejpam-5826	1	34	points	point	NOUN
ejpam-5826	1	35	of	of	ADP
ejpam-5826	1	36	asymptotically	asymptotically	ADV
ejpam-5826	1	37	regular	regular	ADJ
ejpam-5826	1	38	mappings	mapping	NOUN
ejpam-5826	1	39	in	in	ADP
ejpam-5826	1	40	convex	convex	ADJ
ejpam-5826	1	41	metric	metric	ADJ
ejpam-5826	1	42	spaces	space	NOUN
ejpam-5826	1	43	with	with	ADP
ejpam-5826	1	44	application	application	NOUN
ejpam-5826	1	45	abdul	abdul	PROPN
ejpam-5826	1	46	rahim	rahim	PROPN
ejpam-5826	1	47	khan1	khan1	PROPN
ejpam-5826	1	48	,	,	PUNCT
ejpam-5826	1	49	godwin	godwin	PROPN
ejpam-5826	1	50	chidi	chidi	PROPN
ejpam-5826	1	51	ugwunnadi2,3,∗	ugwunnadi2,3,∗	PROPN
ejpam-5826	1	52	,	,	PUNCT
ejpam-5826	1	53	maggie	maggie	NOUN
ejpam-5826	1	54	aphane3	aphane3	PROPN
ejpam-5826	1	55	,	,	PUNCT
ejpam-5826	1	56	faizan	faizan	PROPN
ejpam-5826	1	57	yousaf1	yousaf1	PROPN
ejpam-5826	1	58	,	,	PUNCT
ejpam-5826	1	59	amir	amir	PROPN
ejpam-5826	1	60	abbas1	abbas1	PROPN
ejpam-5826	1	61	1	1	NUM
ejpam-5826	1	62	department	department	NOUN
ejpam-5826	1	63	of	of	ADP
ejpam-5826	1	64	mathematics	mathematic	NOUN
ejpam-5826	1	65	and	and	CCONJ
ejpam-5826	1	66	statistics	statistic	NOUN
ejpam-5826	1	67	,	,	PUNCT
ejpam-5826	1	68	university	university	NOUN
ejpam-5826	1	69	of	of	ADP
ejpam-5826	1	70	southern	southern	PROPN
ejpam-5826	1	71	punjab	punjab	PROPN
ejpam-5826	1	72	,	,	PUNCT
ejpam-5826	1	73	multan	multan	PROPN
ejpam-5826	1	74	,	,	PUNCT
ejpam-5826	1	75	pakistan	pakistan	PROPN
ejpam-5826	1	76	2	2	NUM
ejpam-5826	1	77	department	department	NOUN
ejpam-5826	1	78	of	of	ADP
ejpam-5826	1	79	mathematics	mathematic	NOUN
ejpam-5826	1	80	,	,	PUNCT
ejpam-5826	1	81	faculty	faculty	NOUN
ejpam-5826	1	82	of	of	ADP
ejpam-5826	1	83	science	science	NOUN
ejpam-5826	1	84	and	and	CCONJ
ejpam-5826	1	85	engineering	engineering	NOUN
ejpam-5826	1	86	,	,	PUNCT
ejpam-5826	1	87	university	university	NOUN
ejpam-5826	1	88	of	of	ADP
ejpam-5826	1	89	eswatini	eswatini	PROPN
ejpam-5826	1	90	,	,	PUNCT
ejpam-5826	1	91	private	private	ADJ
ejpam-5826	1	92	bag	bag	NOUN
ejpam-5826	1	93	4	4	NUM
ejpam-5826	1	94	,	,	PUNCT
ejpam-5826	1	95	kwaluseni	kwaluseni	PROPN
ejpam-5826	1	96	m201	m201	PROPN
ejpam-5826	1	97	,	,	PUNCT
ejpam-5826	1	98	eswatini	eswatini	VERB
ejpam-5826	1	99	3	3	NUM
ejpam-5826	1	100	department	department	NOUN
ejpam-5826	1	101	of	of	ADP
ejpam-5826	1	102	mathematics	mathematic	NOUN
ejpam-5826	1	103	and	and	CCONJ
ejpam-5826	1	104	applied	apply	VERB
ejpam-5826	1	105	mathematics	mathematic	NOUN
ejpam-5826	1	106	,	,	PUNCT
ejpam-5826	1	107	sefako	sefako	VERB
ejpam-5826	1	108	makgatho	makgatho	PROPN
ejpam-5826	1	109	health	health	PROPN
ejpam-5826	1	110	sciences	sciences	PROPN
ejpam-5826	1	111	university	university	PROPN
ejpam-5826	1	112	,	,	PUNCT
ejpam-5826	1	113	medunsa	medunsa	PROPN
ejpam-5826	1	114	,	,	PUNCT
ejpam-5826	1	115	p.o	p.o	PROPN
ejpam-5826	1	116	.	.	PROPN
ejpam-5826	1	117	box	box	PROPN
ejpam-5826	1	118	94	94	PROPN
ejpam-5826	1	119	,	,	PUNCT
ejpam-5826	1	120	pretoria	pretoria	PROPN
ejpam-5826	1	121	0204	0204	NUM
ejpam-5826	1	122	,	,	PUNCT
ejpam-5826	1	123	south	south	PROPN
ejpam-5826	1	124	africa	africa	PROPN
ejpam-5826	1	125	abstract	abstract	PROPN
ejpam-5826	1	126	.	.	PUNCT
ejpam-5826	2	1	in	in	ADP
ejpam-5826	2	2	this	this	DET
ejpam-5826	2	3	paper	paper	NOUN
ejpam-5826	2	4	,	,	PUNCT
ejpam-5826	2	5	based	base	VERB
ejpam-5826	2	6	upon	upon	SCONJ
ejpam-5826	2	7	górnicki	górnicki	PROPN
ejpam-5826	2	8	’s	’s	PART
ejpam-5826	2	9	work	work	NOUN
ejpam-5826	2	10	on	on	ADP
ejpam-5826	2	11	fixed	fix	VERB
ejpam-5826	2	12	points	point	NOUN
ejpam-5826	2	13	of	of	ADP
ejpam-5826	2	14	a	a	DET
ejpam-5826	2	15	continuous	continuous	ADJ
ejpam-5826	2	16	asymptotically	asymptotically	ADV
ejpam-5826	2	17	regular	regular	ADJ
ejpam-5826	2	18	self	self	NOUN
ejpam-5826	2	19	-	-	PUNCT
ejpam-5826	2	20	mapping	mapping	NOUN
ejpam-5826	2	21	on	on	ADP
ejpam-5826	2	22	a	a	DET
ejpam-5826	2	23	metric	metric	ADJ
ejpam-5826	2	24	space	space	NOUN
ejpam-5826	2	25	,	,	PUNCT
ejpam-5826	2	26	we	we	PRON
ejpam-5826	2	27	establish	establish	VERB
ejpam-5826	2	28	common	common	ADJ
ejpam-5826	2	29	fixed	fix	VERB
ejpam-5826	2	30	point	point	NOUN
ejpam-5826	2	31	results	result	NOUN
ejpam-5826	2	32	for	for	ADP
ejpam-5826	2	33	similar	similar	ADJ
ejpam-5826	2	34	self	self	NOUN
ejpam-5826	2	35	-	-	PUNCT
ejpam-5826	2	36	mappings	mapping	NOUN
ejpam-5826	2	37	and	and	CCONJ
ejpam-5826	2	38	their	their	PRON
ejpam-5826	2	39	average	average	ADJ
ejpam-5826	2	40	mappings	mapping	NOUN
ejpam-5826	2	41	on	on	ADP
ejpam-5826	2	42	a	a	DET
ejpam-5826	2	43	convex	convex	ADJ
ejpam-5826	2	44	metric	metric	ADJ
ejpam-5826	2	45	space	space	NOUN
ejpam-5826	2	46	by	by	ADP
ejpam-5826	2	47	using	use	VERB
ejpam-5826	2	48	various	various	ADJ
ejpam-5826	2	49	types	type	NOUN
ejpam-5826	2	50	of	of	ADP
ejpam-5826	2	51	contractive	contractive	ADJ
ejpam-5826	2	52	conditions	condition	NOUN
ejpam-5826	2	53	.	.	PUNCT
ejpam-5826	3	1	the	the	DET
ejpam-5826	3	2	closedness	closedness	NOUN
ejpam-5826	3	3	and	and	CCONJ
ejpam-5826	3	4	convexity	convexity	NOUN
ejpam-5826	3	5	of	of	ADP
ejpam-5826	3	6	the	the	DET
ejpam-5826	3	7	set	set	NOUN
ejpam-5826	3	8	of	of	ADP
ejpam-5826	3	9	fixed	fix	VERB
ejpam-5826	3	10	points	point	NOUN
ejpam-5826	3	11	of	of	ADP
ejpam-5826	3	12	a	a	DET
ejpam-5826	3	13	nonselfmapping	nonselfmapping	NOUN
ejpam-5826	3	14	is	be	AUX
ejpam-5826	3	15	obtained	obtain	VERB
ejpam-5826	3	16	here	here	ADV
ejpam-5826	3	17	in	in	ADP
ejpam-5826	3	18	the	the	DET
ejpam-5826	3	19	context	context	NOUN
ejpam-5826	3	20	of	of	ADP
ejpam-5826	3	21	a	a	DET
ejpam-5826	3	22	uniformly	uniformly	ADV
ejpam-5826	3	23	convex	convex	ADJ
ejpam-5826	3	24	hyperbolic	hyperbolic	ADJ
ejpam-5826	3	25	space	space	NOUN
ejpam-5826	3	26	.	.	PUNCT
ejpam-5826	4	1	we	we	PRON
ejpam-5826	4	2	also	also	ADV
ejpam-5826	4	3	apply	apply	VERB
ejpam-5826	4	4	our	our	PRON
ejpam-5826	4	5	findings	finding	NOUN
ejpam-5826	4	6	to	to	PART
ejpam-5826	4	7	solve	solve	VERB
ejpam-5826	4	8	volterra	volterra	NOUN
ejpam-5826	4	9	type	type	VERB
ejpam-5826	4	10	integral	integral	ADJ
ejpam-5826	4	11	equations	equation	NOUN
ejpam-5826	4	12	,	,	PUNCT
ejpam-5826	4	13	demonstrating	demonstrate	VERB
ejpam-5826	4	14	practical	practical	ADJ
ejpam-5826	4	15	use	use	NOUN
ejpam-5826	4	16	of	of	ADP
ejpam-5826	4	17	our	our	PRON
ejpam-5826	4	18	work	work	NOUN
ejpam-5826	4	19	in	in	ADP
ejpam-5826	4	20	mathematical	mathematical	ADJ
ejpam-5826	4	21	analysis	analysis	NOUN
ejpam-5826	4	22	and	and	CCONJ
ejpam-5826	4	23	its	its	PRON
ejpam-5826	4	24	related	related	ADJ
ejpam-5826	4	25	fields	field	NOUN
ejpam-5826	4	26	.	.	PUNCT
ejpam-5826	5	1	2020	2020	NUM
ejpam-5826	5	2	mathematics	mathematic	NOUN
ejpam-5826	5	3	subject	subject	NOUN
ejpam-5826	5	4	classifications	classification	NOUN
ejpam-5826	5	5	:	:	PUNCT
ejpam-5826	5	6	47h05	47h05	NUM
ejpam-5826	5	7	,	,	PUNCT
ejpam-5826	5	8	47j20	47j20	NUM
ejpam-5826	5	9	,	,	PUNCT
ejpam-5826	5	10	47j25	47j25	NUM
ejpam-5826	5	11	,	,	PUNCT
ejpam-5826	5	12	65k15	65k15	NUM
ejpam-5826	5	13	key	key	ADJ
ejpam-5826	5	14	words	word	NOUN
ejpam-5826	5	15	and	and	CCONJ
ejpam-5826	5	16	phrases	phrase	NOUN
ejpam-5826	5	17	:	:	PUNCT
ejpam-5826	5	18	górnicki	górnicki	NOUN
ejpam-5826	5	19	type	type	NOUN
ejpam-5826	5	20	contraction	contraction	NOUN
ejpam-5826	5	21	mapping	mapping	NOUN
ejpam-5826	5	22	;	;	PUNCT
ejpam-5826	5	23	common	common	ADJ
ejpam-5826	5	24	fixed	fix	VERB
ejpam-5826	5	25	point	point	NOUN
ejpam-5826	5	26	;	;	PUNCT
ejpam-5826	5	27	convex	convex	VERB
ejpam-5826	5	28	metric	metric	ADJ
ejpam-5826	5	29	space	space	NOUN
ejpam-5826	5	30	,	,	PUNCT
ejpam-5826	5	31	uniformly	uniformly	ADV
ejpam-5826	5	32	convex	convex	VERB
ejpam-5826	5	33	hyperbolic	hyperbolic	ADJ
ejpam-5826	5	34	space	space	NOUN
ejpam-5826	5	35	;	;	PUNCT
ejpam-5826	5	36	asymptotically	asymptotically	ADV
ejpam-5826	5	37	regular	regular	ADJ
ejpam-5826	5	38	mapping	mapping	NOUN
ejpam-5826	5	39	;	;	PUNCT
ejpam-5826	5	40	nonlinear	nonlinear	ADJ
ejpam-5826	5	41	integral	integral	ADJ
ejpam-5826	5	42	equations	equation	NOUN
ejpam-5826	5	43	1	1	NUM
ejpam-5826	5	44	.	.	X
ejpam-5826	6	1	introduction	introduction	NOUN
ejpam-5826	6	2	fixed	fix	VERB
ejpam-5826	6	3	point	point	NOUN
ejpam-5826	6	4	theory	theory	NOUN
ejpam-5826	6	5	is	be	AUX
ejpam-5826	6	6	an	an	DET
ejpam-5826	6	7	integral	integral	ADJ
ejpam-5826	6	8	part	part	NOUN
ejpam-5826	6	9	of	of	ADP
ejpam-5826	6	10	modern	modern	ADJ
ejpam-5826	6	11	mathematics	mathematic	NOUN
ejpam-5826	6	12	,	,	PUNCT
ejpam-5826	6	13	offering	offer	VERB
ejpam-5826	6	14	essential	essential	ADJ
ejpam-5826	6	15	tools	tool	NOUN
ejpam-5826	6	16	and	and	CCONJ
ejpam-5826	6	17	techniques	technique	NOUN
ejpam-5826	6	18	for	for	ADP
ejpam-5826	6	19	resolving	resolve	VERB
ejpam-5826	6	20	various	various	ADJ
ejpam-5826	6	21	problems	problem	NOUN
ejpam-5826	6	22	in	in	ADP
ejpam-5826	6	23	nonlinear	nonlinear	ADJ
ejpam-5826	6	24	analysis	analysis	NOUN
ejpam-5826	6	25	,	,	PUNCT
ejpam-5826	6	26	optimization	optimization	NOUN
ejpam-5826	6	27	,	,	PUNCT
ejpam-5826	6	28	economics	economic	NOUN
ejpam-5826	6	29	,	,	PUNCT
ejpam-5826	6	30	and	and	CCONJ
ejpam-5826	6	31	engineering	engineering	NOUN
ejpam-5826	6	32	.	.	PUNCT
ejpam-5826	7	1	over	over	ADP
ejpam-5826	7	2	the	the	DET
ejpam-5826	7	3	past	past	ADJ
ejpam-5826	7	4	two	two	NUM
ejpam-5826	7	5	decades	decade	NOUN
ejpam-5826	7	6	,	,	PUNCT
ejpam-5826	7	7	the	the	DET
ejpam-5826	7	8	development	development	NOUN
ejpam-5826	7	9	of	of	ADP
ejpam-5826	7	10	this	this	DET
ejpam-5826	7	11	theory	theory	NOUN
ejpam-5826	7	12	in	in	ADP
ejpam-5826	7	13	metrictype	metrictype	NOUN
ejpam-5826	7	14	spaces	space	NOUN
ejpam-5826	7	15	has	have	AUX
ejpam-5826	7	16	garnered	garner	VERB
ejpam-5826	7	17	significant	significant	ADJ
ejpam-5826	7	18	attention	attention	NOUN
ejpam-5826	7	19	from	from	ADP
ejpam-5826	7	20	researchers	researcher	NOUN
ejpam-5826	7	21	,	,	PUNCT
ejpam-5826	7	22	especially	especially	ADV
ejpam-5826	7	23	its	its	PRON
ejpam-5826	7	24	usefulness	usefulness	NOUN
ejpam-5826	7	25	for	for	ADP
ejpam-5826	7	26	solving	solve	VERB
ejpam-5826	7	27	many	many	ADJ
ejpam-5826	7	28	existence	existence	NOUN
ejpam-5826	7	29	problems	problem	NOUN
ejpam-5826	7	30	in	in	ADP
ejpam-5826	7	31	nonlinear	nonlinear	ADJ
ejpam-5826	7	32	differential	differential	ADJ
ejpam-5826	7	33	and	and	CCONJ
ejpam-5826	7	34	integral	integral	ADJ
ejpam-5826	7	35	equations	equation	NOUN
ejpam-5826	7	36	with	with	ADP
ejpam-5826	7	37	applications	application	NOUN
ejpam-5826	7	38	in	in	ADP
ejpam-5826	7	39	engineering	engineering	NOUN
ejpam-5826	7	40	and	and	CCONJ
ejpam-5826	7	41	applied	apply	VERB
ejpam-5826	7	42	sciences	science	NOUN
ejpam-5826	7	43	[	[	X
ejpam-5826	7	44	1	1	NUM
ejpam-5826	7	45	]	]	PUNCT
ejpam-5826	7	46	.	.	PUNCT
ejpam-5826	8	1	the	the	DET
ejpam-5826	8	2	relevance	relevance	NOUN
ejpam-5826	8	3	and	and	CCONJ
ejpam-5826	8	4	applicability	applicability	NOUN
ejpam-5826	8	5	of	of	ADP
ejpam-5826	8	6	∗corresponding	∗corresponde	VERB
ejpam-5826	8	7	author	author	NOUN
ejpam-5826	8	8	.	.	PUNCT
ejpam-5826	9	1	doi	doi	NOUN
ejpam-5826	9	2	:	:	PUNCT
ejpam-5826	9	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5826	https://doi.org/10.29020/nybg.ejpam.v18i2.5826	PROPN
ejpam-5826	9	4	email	email	NOUN
ejpam-5826	9	5	addresses	address	NOUN
ejpam-5826	9	6	:	:	PUNCT
ejpam-5826	9	7	abdulrahimkhan@isp.edu.pk	abdulrahimkhan@isp.edu.pk	PROPN
ejpam-5826	9	8	(	(	PUNCT
ejpam-5826	9	9	a.	a.	PROPN
ejpam-5826	9	10	r.	r.	PROPN
ejpam-5826	9	11	khan	khan	PROPN
ejpam-5826	9	12	)	)	PUNCT
ejpam-5826	9	13	,	,	PUNCT
ejpam-5826	9	14	gcugwunnadi@uniswa.sz	gcugwunnadi@uniswa.sz	PROPN
ejpam-5826	9	15	(	(	PUNCT
ejpam-5826	9	16	g.	g.	PROPN
ejpam-5826	9	17	c.	c.	PROPN
ejpam-5826	9	18	ugwunnadi	ugwunnadi	PROPN
ejpam-5826	9	19	)	)	PUNCT
ejpam-5826	9	20	,	,	PUNCT
ejpam-5826	9	21	maggie.aphane@smu.ac.za	maggie.aphane@smu.ac.za	PROPN
ejpam-5826	9	22	(	(	PUNCT
ejpam-5826	9	23	m.	m.	NOUN
ejpam-5826	9	24	aphane	aphane	PROPN
ejpam-5826	9	25	)	)	PUNCT
ejpam-5826	9	26	,	,	PUNCT
ejpam-5826	9	27	faizanyousef967@gmil.com	faizanyousef967@gmil.com	PROPN
ejpam-5826	9	28	(	(	PUNCT
ejpam-5826	9	29	f.	f.	PROPN
ejpam-5826	9	30	yousaf	yousaf	PROPN
ejpam-5826	9	31	)	)	PUNCT
ejpam-5826	9	32	,	,	PUNCT
ejpam-5826	9	33	aamirbuzdar112@gmail.com	aamirbuzdar112@gmail.com	X
ejpam-5826	9	34	(	(	PUNCT
ejpam-5826	9	35	a.	a.	NOUN
ejpam-5826	9	36	abbas	abbas	PROPN
ejpam-5826	9	37	)	)	PUNCT
ejpam-5826	9	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5826	10	1	1	1	NUM
ejpam-5826	10	2	copyright	copyright	NOUN
ejpam-5826	10	3	:	:	PUNCT
ejpam-5826	10	4	©	©	PROPN
ejpam-5826	10	5	2025	2025	NUM
ejpam-5826	10	6	the	the	DET
ejpam-5826	10	7	author(s	author(s	NOUN
ejpam-5826	10	8	)	)	PUNCT
ejpam-5826	10	9	.	.	PUNCT
ejpam-5826	11	1	(	(	PUNCT
ejpam-5826	11	2	cc	cc	NOUN
ejpam-5826	11	3	by	by	ADP
ejpam-5826	11	4	-	-	PUNCT
ejpam-5826	11	5	nc	nc	PROPN
ejpam-5826	11	6	4.0	4.0	NUM
ejpam-5826	11	7	)	)	PUNCT
ejpam-5826	11	8	a.	a.	PROPN
ejpam-5826	11	9	r.	r.	PROPN
ejpam-5826	11	10	khan	khan	PROPN
ejpam-5826	11	11	et	et	PROPN
ejpam-5826	11	12	al	al	PROPN
ejpam-5826	11	13	.	.	PUNCT
ejpam-5826	11	14	/	/	SYM
ejpam-5826	11	15	eur	eur	PROPN
ejpam-5826	11	16	.	.	PUNCT
ejpam-5826	12	1	j.	j.	PROPN
ejpam-5826	12	2	pure	pure	PROPN
ejpam-5826	12	3	appl	appl	PROPN
ejpam-5826	12	4	.	.	PROPN
ejpam-5826	12	5	math	math	PROPN
ejpam-5826	12	6	,	,	PUNCT
ejpam-5826	12	7	18	18	NUM
ejpam-5826	12	8	(	(	PUNCT
ejpam-5826	12	9	2	2	NUM
ejpam-5826	12	10	)	)	PUNCT
ejpam-5826	12	11	(	(	PUNCT
ejpam-5826	12	12	2025	2025	NUM
ejpam-5826	12	13	)	)	PUNCT
ejpam-5826	12	14	,	,	PUNCT
ejpam-5826	12	15	5826	5826	NUM
ejpam-5826	12	16	2	2	NUM
ejpam-5826	12	17	of	of	ADP
ejpam-5826	12	18	23	23	NUM
ejpam-5826	12	19	fixed	fix	VERB
ejpam-5826	12	20	point	point	NOUN
ejpam-5826	12	21	theory	theory	NOUN
ejpam-5826	12	22	continues	continue	VERB
ejpam-5826	12	23	to	to	PART
ejpam-5826	12	24	expand	expand	VERB
ejpam-5826	12	25	as	as	ADP
ejpam-5826	12	26	new	new	ADJ
ejpam-5826	12	27	results	result	NOUN
ejpam-5826	12	28	and	and	CCONJ
ejpam-5826	12	29	methodologies	methodology	NOUN
ejpam-5826	12	30	emerge	emerge	VERB
ejpam-5826	12	31	.	.	PUNCT
ejpam-5826	13	1	recently	recently	ADV
ejpam-5826	13	2	,	,	PUNCT
ejpam-5826	13	3	górnicki	górnicki	PROPN
ejpam-5826	14	1	[	[	X
ejpam-5826	14	2	2	2	NUM
ejpam-5826	14	3	]	]	PUNCT
ejpam-5826	14	4	generalized	generalize	VERB
ejpam-5826	14	5	a	a	DET
ejpam-5826	14	6	well	well	ADV
ejpam-5826	14	7	-	-	PUNCT
ejpam-5826	14	8	known	know	VERB
ejpam-5826	14	9	result	result	NOUN
ejpam-5826	14	10	of	of	ADP
ejpam-5826	14	11	reich	reich	PROPN
ejpam-5826	15	1	[	[	X
ejpam-5826	15	2	3	3	NUM
ejpam-5826	15	3	]	]	PUNCT
ejpam-5826	15	4	related	relate	VERB
ejpam-5826	15	5	to	to	ADP
ejpam-5826	15	6	contractions	contraction	NOUN
ejpam-5826	15	7	on	on	ADP
ejpam-5826	15	8	a	a	DET
ejpam-5826	15	9	complete	complete	ADJ
ejpam-5826	15	10	metric	metric	ADJ
ejpam-5826	15	11	space	space	NOUN
ejpam-5826	15	12	.	.	PUNCT
ejpam-5826	16	1	this	this	DET
ejpam-5826	16	2	new	new	ADJ
ejpam-5826	16	3	result	result	NOUN
ejpam-5826	16	4	has	have	AUX
ejpam-5826	16	5	been	be	AUX
ejpam-5826	16	6	further	far	ADV
ejpam-5826	16	7	extended	extend	VERB
ejpam-5826	16	8	by	by	ADP
ejpam-5826	16	9	bisht	bisht	PROPN
ejpam-5826	17	1	[	[	X
ejpam-5826	17	2	4	4	NUM
ejpam-5826	17	3	]	]	PUNCT
ejpam-5826	17	4	,	,	PUNCT
ejpam-5826	17	5	karapinar	karapinar	VERB
ejpam-5826	17	6	et	et	PROPN
ejpam-5826	17	7	al	al	PROPN
ejpam-5826	17	8	.	.	PUNCT
ejpam-5826	18	1	[	[	X
ejpam-5826	18	2	5	5	NUM
ejpam-5826	18	3	]	]	PUNCT
ejpam-5826	18	4	,	,	PUNCT
ejpam-5826	18	5	and	and	CCONJ
ejpam-5826	18	6	panja	panja	INTJ
ejpam-5826	18	7	et	et	PROPN
ejpam-5826	18	8	al	al	PROPN
ejpam-5826	18	9	.	.	PUNCT
ejpam-5826	19	1	[	[	X
ejpam-5826	19	2	6	6	NUM
ejpam-5826	19	3	]	]	PUNCT
ejpam-5826	19	4	for	for	ADP
ejpam-5826	19	5	discontinuous	discontinuous	ADJ
ejpam-5826	19	6	mappings	mapping	NOUN
ejpam-5826	19	7	and	and	CCONJ
ejpam-5826	19	8	by	by	ADP
ejpam-5826	19	9	khan	khan	PROPN
ejpam-5826	19	10	and	and	CCONJ
ejpam-5826	19	11	oyetunbi	oyetunbi	NOUN
ejpam-5826	19	12	[	[	X
ejpam-5826	19	13	7	7	X
ejpam-5826	19	14	]	]	PUNCT
ejpam-5826	19	15	for	for	ADP
ejpam-5826	19	16	two	two	NUM
ejpam-5826	19	17	discontinuous	discontinuous	ADJ
ejpam-5826	19	18	mappings	mapping	NOUN
ejpam-5826	19	19	satisfying	satisfy	VERB
ejpam-5826	19	20	a	a	DET
ejpam-5826	19	21	lipschitz	lipschitz	NOUN
ejpam-5826	19	22	-	-	PUNCT
ejpam-5826	19	23	kannan	kannan	PROPN
ejpam-5826	19	24	type	type	NOUN
ejpam-5826	19	25	condition	condition	NOUN
ejpam-5826	19	26	considered	consider	VERB
ejpam-5826	19	27	in	in	ADP
ejpam-5826	19	28	[	[	X
ejpam-5826	19	29	8	8	NUM
ejpam-5826	19	30	]	]	PUNCT
ejpam-5826	19	31	.	.	PUNCT
ejpam-5826	20	1	these	these	DET
ejpam-5826	20	2	advancements	advancement	NOUN
ejpam-5826	20	3	highlight	highlight	VERB
ejpam-5826	20	4	the	the	DET
ejpam-5826	20	5	dynamic	dynamic	ADJ
ejpam-5826	20	6	nature	nature	NOUN
ejpam-5826	20	7	of	of	ADP
ejpam-5826	20	8	fixed	fix	VERB
ejpam-5826	20	9	point	point	NOUN
ejpam-5826	20	10	theory	theory	NOUN
ejpam-5826	20	11	.	.	PUNCT
ejpam-5826	21	1	applications	application	NOUN
ejpam-5826	21	2	of	of	ADP
ejpam-5826	21	3	fixed	fix	VERB
ejpam-5826	21	4	point	point	NOUN
ejpam-5826	21	5	theory	theory	NOUN
ejpam-5826	21	6	have	have	AUX
ejpam-5826	21	7	been	be	AUX
ejpam-5826	21	8	widely	widely	ADV
ejpam-5826	21	9	explored	explore	VERB
ejpam-5826	21	10	in	in	ADP
ejpam-5826	21	11	various	various	ADJ
ejpam-5826	21	12	settings	setting	NOUN
ejpam-5826	21	13	.	.	PUNCT
ejpam-5826	22	1	specifically	specifically	ADV
ejpam-5826	22	2	,	,	PUNCT
ejpam-5826	22	3	the	the	DET
ejpam-5826	22	4	theory	theory	NOUN
ejpam-5826	22	5	has	have	AUX
ejpam-5826	22	6	been	be	AUX
ejpam-5826	22	7	instrumental	instrumental	ADJ
ejpam-5826	22	8	in	in	ADP
ejpam-5826	22	9	developing	develop	VERB
ejpam-5826	22	10	iterative	iterative	NOUN
ejpam-5826	22	11	methods	method	NOUN
ejpam-5826	22	12	for	for	ADP
ejpam-5826	22	13	solving	solve	VERB
ejpam-5826	22	14	existence	existence	NOUN
ejpam-5826	22	15	and	and	CCONJ
ejpam-5826	22	16	uniqueness	uniqueness	NOUN
ejpam-5826	22	17	problems	problem	NOUN
ejpam-5826	22	18	in	in	ADP
ejpam-5826	22	19	differential	differential	ADJ
ejpam-5826	22	20	and	and	CCONJ
ejpam-5826	22	21	integral	integral	ADJ
ejpam-5826	22	22	equations	equation	NOUN
ejpam-5826	22	23	,	,	PUNCT
ejpam-5826	22	24	as	as	ADV
ejpam-5826	22	25	well	well	ADV
ejpam-5826	22	26	as	as	ADP
ejpam-5826	22	27	systems	system	NOUN
ejpam-5826	22	28	of	of	ADP
ejpam-5826	22	29	linear	linear	PROPN
ejpam-5826	22	30	equations	equation	NOUN
ejpam-5826	22	31	.	.	PUNCT
ejpam-5826	23	1	these	these	DET
ejpam-5826	23	2	applications	application	NOUN
ejpam-5826	23	3	demonstrate	demonstrate	VERB
ejpam-5826	23	4	the	the	DET
ejpam-5826	23	5	versatility	versatility	NOUN
ejpam-5826	23	6	of	of	ADP
ejpam-5826	23	7	fixed	fix	VERB
ejpam-5826	23	8	point	point	NOUN
ejpam-5826	23	9	theory	theory	NOUN
ejpam-5826	23	10	in	in	ADP
ejpam-5826	23	11	addressing	address	VERB
ejpam-5826	23	12	complex	complex	ADJ
ejpam-5826	23	13	mathematical	mathematical	ADJ
ejpam-5826	23	14	challenges	challenge	NOUN
ejpam-5826	23	15	.	.	PUNCT
ejpam-5826	24	1	the	the	DET
ejpam-5826	24	2	theory	theory	NOUN
ejpam-5826	24	3	’s	’	VERB
ejpam-5826	24	4	ability	ability	NOUN
ejpam-5826	24	5	to	to	PART
ejpam-5826	24	6	ensure	ensure	VERB
ejpam-5826	24	7	the	the	DET
ejpam-5826	24	8	existence	existence	NOUN
ejpam-5826	24	9	and	and	CCONJ
ejpam-5826	24	10	uniqueness	uniqueness	NOUN
ejpam-5826	24	11	of	of	ADP
ejpam-5826	24	12	solutions	solution	NOUN
ejpam-5826	24	13	makes	make	VERB
ejpam-5826	24	14	it	it	PRON
ejpam-5826	24	15	a	a	DET
ejpam-5826	24	16	valuable	valuable	ADJ
ejpam-5826	24	17	tool	tool	NOUN
ejpam-5826	24	18	for	for	ADP
ejpam-5826	24	19	tackling	tackle	VERB
ejpam-5826	24	20	a	a	DET
ejpam-5826	24	21	wide	wide	ADJ
ejpam-5826	24	22	range	range	NOUN
ejpam-5826	24	23	of	of	ADP
ejpam-5826	24	24	real	real	ADJ
ejpam-5826	24	25	-	-	PUNCT
ejpam-5826	24	26	world	world	NOUN
ejpam-5826	24	27	problems	problem	NOUN
ejpam-5826	24	28	in	in	ADP
ejpam-5826	24	29	mathematics	mathematic	NOUN
ejpam-5826	24	30	,	,	PUNCT
ejpam-5826	24	31	engineering	engineering	NOUN
ejpam-5826	24	32	and	and	CCONJ
ejpam-5826	24	33	applied	apply	VERB
ejpam-5826	24	34	sciences	science	NOUN
ejpam-5826	24	35	[	[	X
ejpam-5826	24	36	1	1	NUM
ejpam-5826	24	37	,	,	PUNCT
ejpam-5826	24	38	9	9	NUM
ejpam-5826	24	39	,	,	PUNCT
ejpam-5826	24	40	10	10	NUM
ejpam-5826	24	41	]	]	PUNCT
ejpam-5826	24	42	.	.	PUNCT
ejpam-5826	25	1	in	in	ADP
ejpam-5826	25	2	this	this	DET
ejpam-5826	25	3	paper	paper	NOUN
ejpam-5826	25	4	,	,	PUNCT
ejpam-5826	25	5	we	we	PRON
ejpam-5826	25	6	aim	aim	VERB
ejpam-5826	25	7	to	to	PART
ejpam-5826	25	8	contribute	contribute	VERB
ejpam-5826	25	9	to	to	ADP
ejpam-5826	25	10	this	this	DET
ejpam-5826	25	11	growing	grow	VERB
ejpam-5826	25	12	body	body	NOUN
ejpam-5826	25	13	of	of	ADP
ejpam-5826	25	14	knowledge	knowledge	NOUN
ejpam-5826	25	15	by	by	ADP
ejpam-5826	25	16	proving	prove	VERB
ejpam-5826	25	17	fixed	fix	VERB
ejpam-5826	25	18	point	point	NOUN
ejpam-5826	25	19	and	and	CCONJ
ejpam-5826	25	20	common	common	ADJ
ejpam-5826	25	21	fixed	fix	VERB
ejpam-5826	25	22	point	point	NOUN
ejpam-5826	25	23	results	result	NOUN
ejpam-5826	25	24	for	for	ADP
ejpam-5826	25	25	asymptotically	asymptotically	ADV
ejpam-5826	25	26	regular	regular	ADJ
ejpam-5826	25	27	mappings	mapping	NOUN
ejpam-5826	25	28	in	in	ADP
ejpam-5826	25	29	hyperbolic	hyperbolic	ADJ
ejpam-5826	25	30	spaces	space	NOUN
ejpam-5826	25	31	and	and	CCONJ
ejpam-5826	25	32	convex	convex	VERB
ejpam-5826	25	33	metric	metric	ADJ
ejpam-5826	25	34	spaces	space	NOUN
ejpam-5826	25	35	.	.	PUNCT
ejpam-5826	26	1	our	our	PRON
ejpam-5826	26	2	work	work	NOUN
ejpam-5826	26	3	is	be	AUX
ejpam-5826	26	4	built	build	VERB
ejpam-5826	26	5	on	on	ADP
ejpam-5826	26	6	a	a	DET
ejpam-5826	26	7	basic	basic	ADJ
ejpam-5826	26	8	concept	concept	NOUN
ejpam-5826	26	9	introduced	introduce	VERB
ejpam-5826	26	10	by	by	ADP
ejpam-5826	26	11	browder	browder	NOUN
ejpam-5826	26	12	and	and	CCONJ
ejpam-5826	26	13	petryshyn	petryshyn	NOUN
ejpam-5826	26	14	[	[	X
ejpam-5826	26	15	11	11	NUM
ejpam-5826	26	16	]	]	PUNCT
ejpam-5826	26	17	,	,	PUNCT
ejpam-5826	26	18	namely	namely	ADV
ejpam-5826	26	19	,	,	PUNCT
ejpam-5826	26	20	asymptotically	asymptotically	ADV
ejpam-5826	26	21	regular	regular	ADJ
ejpam-5826	26	22	mapping	mapping	NOUN
ejpam-5826	26	23	and	and	CCONJ
ejpam-5826	26	24	explores	explore	VERB
ejpam-5826	26	25	its	its	PRON
ejpam-5826	26	26	implications	implication	NOUN
ejpam-5826	26	27	in	in	ADP
ejpam-5826	26	28	more	more	ADJ
ejpam-5826	26	29	general	general	ADJ
ejpam-5826	26	30	spaces	space	NOUN
ejpam-5826	26	31	.	.	PUNCT
ejpam-5826	27	1	2	2	X
ejpam-5826	27	2	.	.	X
ejpam-5826	27	3	preliminaries	preliminary	NOUN
ejpam-5826	27	4	let	let	VERB
ejpam-5826	27	5	(	(	PUNCT
ejpam-5826	27	6	q	q	NOUN
ejpam-5826	27	7	,	,	PUNCT
ejpam-5826	27	8	d	d	X
ejpam-5826	27	9	)	)	PUNCT
ejpam-5826	27	10	be	be	AUX
ejpam-5826	27	11	a	a	DET
ejpam-5826	27	12	metric	metric	ADJ
ejpam-5826	27	13	space	space	NOUN
ejpam-5826	27	14	and	and	CCONJ
ejpam-5826	27	15	e	e	NOUN
ejpam-5826	27	16	:	:	PUNCT
ejpam-5826	27	17	q	q	X
ejpam-5826	27	18	→	→	X
ejpam-5826	27	19	q	q	AUX
ejpam-5826	27	20	be	be	AUX
ejpam-5826	27	21	a	a	DET
ejpam-5826	27	22	mapping	mapping	NOUN
ejpam-5826	27	23	.	.	PUNCT
ejpam-5826	28	1	a	a	DET
ejpam-5826	28	2	point	point	NOUN
ejpam-5826	28	3	q0	q0	PROPN
ejpam-5826	28	4	∈	∈	PROPN
ejpam-5826	28	5	q	q	NOUN
ejpam-5826	28	6	is	be	AUX
ejpam-5826	28	7	called	call	VERB
ejpam-5826	28	8	fixed	fix	VERB
ejpam-5826	28	9	point	point	NOUN
ejpam-5826	28	10	of	of	ADP
ejpam-5826	28	11	e	e	PROPN
ejpam-5826	28	12	if	if	SCONJ
ejpam-5826	28	13	eq0	eq0	VERB
ejpam-5826	28	14	=	=	PUNCT
ejpam-5826	28	15	q0	q0	PROPN
ejpam-5826	28	16	.	.	PUNCT
ejpam-5826	29	1	the	the	DET
ejpam-5826	29	2	set	set	NOUN
ejpam-5826	29	3	of	of	ADP
ejpam-5826	29	4	fixed	fix	VERB
ejpam-5826	29	5	points	point	NOUN
ejpam-5826	29	6	of	of	ADP
ejpam-5826	29	7	e	e	PROPN
ejpam-5826	29	8	is	be	AUX
ejpam-5826	29	9	denoted	denote	VERB
ejpam-5826	29	10	and	and	CCONJ
ejpam-5826	29	11	defined	define	VERB
ejpam-5826	29	12	as	as	ADP
ejpam-5826	29	13	fix(e	fix(e	PROPN
ejpam-5826	29	14	)	)	PUNCT
ejpam-5826	29	15	:	:	PUNCT
ejpam-5826	30	1	=	=	SYM
ejpam-5826	30	2	{	{	PUNCT
ejpam-5826	30	3	q0	q0	PROPN
ejpam-5826	30	4	∈	∈	PROPN
ejpam-5826	30	5	q	q	NOUN
ejpam-5826	30	6	:	:	PUNCT
ejpam-5826	30	7	eq0	eq0	X
ejpam-5826	30	8	=	=	SYM
ejpam-5826	30	9	q0	q0	PROPN
ejpam-5826	30	10	}	}	PUNCT
ejpam-5826	30	11	.	.	PUNCT
ejpam-5826	31	1	the	the	DET
ejpam-5826	31	2	concept	concept	NOUN
ejpam-5826	31	3	of	of	ADP
ejpam-5826	31	4	asymptotically	asymptotically	ADV
ejpam-5826	31	5	regular	regular	ADJ
ejpam-5826	31	6	mappings	mapping	NOUN
ejpam-5826	31	7	was	be	AUX
ejpam-5826	31	8	introduced	introduce	VERB
ejpam-5826	31	9	by	by	ADP
ejpam-5826	31	10	browder	browder	NOUN
ejpam-5826	31	11	and	and	CCONJ
ejpam-5826	31	12	petryshyn	petryshyn	NOUN
ejpam-5826	31	13	[	[	X
ejpam-5826	31	14	11	11	NUM
ejpam-5826	31	15	]	]	PUNCT
ejpam-5826	31	16	.	.	PUNCT
ejpam-5826	32	1	a	a	DET
ejpam-5826	32	2	mapping	mapping	NOUN
ejpam-5826	32	3	e	e	NOUN
ejpam-5826	32	4	:	:	PUNCT
ejpam-5826	32	5	q	q	X
ejpam-5826	32	6	→	→	PUNCT
ejpam-5826	32	7	q	q	X
ejpam-5826	32	8	is	be	AUX
ejpam-5826	32	9	called	call	VERB
ejpam-5826	32	10	asymptotically	asymptotically	ADV
ejpam-5826	32	11	regular	regular	ADJ
ejpam-5826	32	12	at	at	ADP
ejpam-5826	32	13	x0	x0	PROPN
ejpam-5826	32	14	∈	∈	PROPN
ejpam-5826	33	1	q	q	X
ejpam-5826	33	2	,	,	PUNCT
ejpam-5826	33	3	if	if	SCONJ
ejpam-5826	33	4	limn→∞	limn→∞	PRON
ejpam-5826	33	5	d(enx0	d(enx0	NOUN
ejpam-5826	33	6	,	,	PUNCT
ejpam-5826	33	7	e	e	X
ejpam-5826	33	8	n+1x0	n+1x0	PROPN
ejpam-5826	33	9	)	)	PUNCT
ejpam-5826	33	10	=	=	PUNCT
ejpam-5826	34	1	0	0	X
ejpam-5826	34	2	.	.	PUNCT
ejpam-5826	35	1	if	if	SCONJ
ejpam-5826	35	2	e	e	PROPN
ejpam-5826	35	3	is	be	AUX
ejpam-5826	35	4	asymptotically	asymptotically	ADV
ejpam-5826	35	5	regular	regular	ADJ
ejpam-5826	35	6	at	at	ADP
ejpam-5826	35	7	each	each	DET
ejpam-5826	35	8	point	point	NOUN
ejpam-5826	35	9	of	of	ADP
ejpam-5826	35	10	q	q	NOUN
ejpam-5826	35	11	,	,	PUNCT
ejpam-5826	35	12	then	then	ADV
ejpam-5826	35	13	e	e	NOUN
ejpam-5826	35	14	is	be	AUX
ejpam-5826	35	15	said	say	VERB
ejpam-5826	35	16	to	to	PART
ejpam-5826	35	17	be	be	AUX
ejpam-5826	35	18	asymptotically	asymptotically	ADV
ejpam-5826	35	19	regular	regular	ADJ
ejpam-5826	35	20	on	on	ADP
ejpam-5826	35	21	q.	q.	PROPN
ejpam-5826	35	22	e	e	PROPN
ejpam-5826	35	23	is	be	AUX
ejpam-5826	35	24	non	non	ADJ
ejpam-5826	35	25	-	-	ADJ
ejpam-5826	35	26	expansive	expansive	ADJ
ejpam-5826	35	27	if	if	SCONJ
ejpam-5826	35	28	d(ex	d(ex	NOUN
ejpam-5826	35	29	,	,	PUNCT
ejpam-5826	35	30	ey	ey	NOUN
ejpam-5826	35	31	)	)	PUNCT
ejpam-5826	35	32	≤	≤	NOUN
ejpam-5826	35	33	d(x	d(x	PROPN
ejpam-5826	35	34	,	,	PUNCT
ejpam-5826	35	35	y	y	NOUN
ejpam-5826	35	36	)	)	PUNCT
ejpam-5826	35	37	for	for	ADP
ejpam-5826	35	38	all	all	DET
ejpam-5826	35	39	x	x	NOUN
ejpam-5826	35	40	,	,	PUNCT
ejpam-5826	35	41	y	y	PROPN
ejpam-5826	35	42	∈	∈	PROPN
ejpam-5826	35	43	q.	q.	PROPN
ejpam-5826	35	44	consider	consider	VERB
ejpam-5826	35	45	q	q	NOUN
ejpam-5826	35	46	=	=	NOUN
ejpam-5826	35	47	r	r	NOUN
ejpam-5826	35	48	,	,	PUNCT
ejpam-5826	35	49	the	the	DET
ejpam-5826	35	50	set	set	NOUN
ejpam-5826	35	51	of	of	ADP
ejpam-5826	35	52	real	real	ADJ
ejpam-5826	35	53	numbers	number	NOUN
ejpam-5826	35	54	with	with	ADP
ejpam-5826	35	55	its	its	PRON
ejpam-5826	35	56	usual	usual	ADJ
ejpam-5826	35	57	metric	metric	ADJ
ejpam-5826	35	58	d(q	d(q	PROPN
ejpam-5826	35	59	,	,	PUNCT
ejpam-5826	35	60	p	p	NOUN
ejpam-5826	35	61	)	)	PUNCT
ejpam-5826	35	62	=	=	NOUN
ejpam-5826	35	63	|q	|q	NOUN
ejpam-5826	35	64	−	−	NOUN
ejpam-5826	35	65	p|	p|	NOUN
ejpam-5826	35	66	.	.	PUNCT
ejpam-5826	36	1	suppose	suppose	VERB
ejpam-5826	36	2	e	e	NOUN
ejpam-5826	36	3	:	:	PUNCT
ejpam-5826	36	4	q	q	X
ejpam-5826	36	5	→	→	PUNCT
ejpam-5826	36	6	q	q	X
ejpam-5826	36	7	is	be	AUX
ejpam-5826	36	8	given	give	VERB
ejpam-5826	36	9	by	by	ADP
ejpam-5826	36	10	eq	eq	NOUN
ejpam-5826	36	11	=	=	NOUN
ejpam-5826	36	12	q	q	PROPN
ejpam-5826	36	13	2	2	NUM
ejpam-5826	36	14	.	.	PUNCT
ejpam-5826	37	1	this	this	DET
ejpam-5826	37	2	function	function	NOUN
ejpam-5826	37	3	is	be	AUX
ejpam-5826	37	4	both	both	PRON
ejpam-5826	37	5	asymptotically	asymptotically	ADV
ejpam-5826	37	6	regular	regular	ADJ
ejpam-5826	37	7	and	and	CCONJ
ejpam-5826	37	8	non	non	ADJ
ejpam-5826	37	9	-	-	ADJ
ejpam-5826	37	10	expansive	expansive	ADJ
ejpam-5826	37	11	.	.	PUNCT
ejpam-5826	38	1	if	if	SCONJ
ejpam-5826	38	2	e	e	PROPN
ejpam-5826	38	3	is	be	AUX
ejpam-5826	38	4	a	a	DET
ejpam-5826	38	5	function	function	NOUN
ejpam-5826	38	6	on	on	ADP
ejpam-5826	38	7	a	a	DET
ejpam-5826	38	8	metric	metric	ADJ
ejpam-5826	38	9	space	space	NOUN
ejpam-5826	38	10	q	q	NOUN
ejpam-5826	38	11	into	into	ADP
ejpam-5826	38	12	itself	itself	PRON
ejpam-5826	38	13	,	,	PUNCT
ejpam-5826	38	14	then	then	ADV
ejpam-5826	38	15	the	the	DET
ejpam-5826	38	16	set	set	NOUN
ejpam-5826	38	17	o(e	o(e	PROPN
ejpam-5826	38	18	,	,	PUNCT
ejpam-5826	38	19	e	e	NOUN
ejpam-5826	38	20	)	)	PUNCT
ejpam-5826	38	21	:	:	PUNCT
ejpam-5826	38	22	=	=	SYM
ejpam-5826	38	23	{	{	PUNCT
ejpam-5826	38	24	ene	ene	NOUN
ejpam-5826	38	25	:	:	PUNCT
ejpam-5826	38	26	n	n	PROPN
ejpam-5826	38	27	=	=	SYM
ejpam-5826	38	28	0	0	NUM
ejpam-5826	38	29	,	,	PUNCT
ejpam-5826	38	30	1	1	NUM
ejpam-5826	38	31	,	,	PUNCT
ejpam-5826	38	32	2	2	NUM
ejpam-5826	38	33	,	,	PUNCT
ejpam-5826	38	34	3	3	NUM
ejpam-5826	38	35	,	,	PUNCT
ejpam-5826	38	36	·	·	PUNCT
ejpam-5826	38	37	·	·	PUNCT
ejpam-5826	38	38	·	·	PUNCT
ejpam-5826	38	39	}	}	PUNCT
ejpam-5826	38	40	is	be	AUX
ejpam-5826	38	41	called	call	VERB
ejpam-5826	38	42	the	the	DET
ejpam-5826	38	43	orbit	orbit	NOUN
ejpam-5826	38	44	of	of	ADP
ejpam-5826	38	45	e	e	PROPN
ejpam-5826	38	46	at	at	ADP
ejpam-5826	38	47	the	the	DET
ejpam-5826	38	48	point	point	NOUN
ejpam-5826	38	49	e	e	X
ejpam-5826	38	50	∈	∈	PROPN
ejpam-5826	38	51	q.	q.	NOUN
ejpam-5826	38	52	e	e	PROPN
ejpam-5826	38	53	is	be	AUX
ejpam-5826	38	54	called	call	VERB
ejpam-5826	38	55	orbitally	orbitally	ADV
ejpam-5826	38	56	continuous	continuous	ADJ
ejpam-5826	38	57	at	at	ADP
ejpam-5826	38	58	p	p	PROPN
ejpam-5826	38	59	∈	∈	PROPN
ejpam-5826	38	60	q	q	NOUN
ejpam-5826	38	61	if	if	SCONJ
ejpam-5826	38	62	for	for	ADP
ejpam-5826	38	63	any	any	DET
ejpam-5826	38	64	sequence	sequence	NOUN
ejpam-5826	38	65	{	{	PUNCT
ejpam-5826	38	66	qk	qk	NOUN
ejpam-5826	38	67	}	}	PUNCT
ejpam-5826	38	68	⊂	⊂	PROPN
ejpam-5826	38	69	o(e	o(e	PROPN
ejpam-5826	38	70	,	,	PUNCT
ejpam-5826	38	71	q	q	NOUN
ejpam-5826	38	72	)	)	PUNCT
ejpam-5826	38	73	for	for	ADP
ejpam-5826	38	74	some	some	DET
ejpam-5826	38	75	q	q	PROPN
ejpam-5826	38	76	∈	∈	PROPN
ejpam-5826	38	77	q	q	NOUN
ejpam-5826	38	78	,	,	PUNCT
ejpam-5826	38	79	limk→∞	limk→∞	ADV
ejpam-5826	38	80	qk	qk	ADP
ejpam-5826	38	81	=	=	SYM
ejpam-5826	38	82	p	p	NOUN
ejpam-5826	38	83	entails	entail	VERB
ejpam-5826	38	84	that	that	SCONJ
ejpam-5826	38	85	limk→∞eqk	limk→∞eqk	PRON
ejpam-5826	38	86	=	=	SYM
ejpam-5826	38	87	ep	ep	PROPN
ejpam-5826	38	88	.	.	PUNCT
ejpam-5826	39	1	we	we	PRON
ejpam-5826	39	2	say	say	VERB
ejpam-5826	39	3	that	that	SCONJ
ejpam-5826	39	4	e	e	NOUN
ejpam-5826	39	5	is	be	AUX
ejpam-5826	39	6	orbitally	orbitally	ADV
ejpam-5826	39	7	continuous	continuous	ADJ
ejpam-5826	39	8	on	on	ADP
ejpam-5826	39	9	q	q	NOUN
ejpam-5826	39	10	if	if	SCONJ
ejpam-5826	39	11	e	e	NOUN
ejpam-5826	39	12	is	be	AUX
ejpam-5826	39	13	orbitally	orbitally	ADV
ejpam-5826	39	14	continuous	continuous	ADJ
ejpam-5826	39	15	at	at	ADP
ejpam-5826	39	16	each	each	DET
ejpam-5826	39	17	point	point	NOUN
ejpam-5826	39	18	p	p	PROPN
ejpam-5826	39	19	∈	∈	PROPN
ejpam-5826	39	20	q.	q.	NOUN
ejpam-5826	39	21	clearly	clearly	ADV
ejpam-5826	39	22	,	,	PUNCT
ejpam-5826	39	23	continuity	continuity	NOUN
ejpam-5826	39	24	implies	imply	VERB
ejpam-5826	39	25	orbital	orbital	ADJ
ejpam-5826	39	26	continuity	continuity	NOUN
ejpam-5826	39	27	,	,	PUNCT
ejpam-5826	39	28	but	but	CCONJ
ejpam-5826	39	29	the	the	DET
ejpam-5826	39	30	converse	converse	NOUN
ejpam-5826	39	31	is	be	AUX
ejpam-5826	39	32	not	not	PART
ejpam-5826	39	33	true	true	ADJ
ejpam-5826	39	34	[	[	X
ejpam-5826	39	35	4	4	NUM
ejpam-5826	39	36	,	,	PUNCT
ejpam-5826	39	37	12	12	NUM
ejpam-5826	39	38	,	,	PUNCT
ejpam-5826	39	39	13	13	NUM
ejpam-5826	39	40	]	]	PUNCT
ejpam-5826	39	41	.	.	PUNCT
ejpam-5826	40	1	a	a	DET
ejpam-5826	40	2	self	self	NOUN
ejpam-5826	40	3	-	-	PUNCT
ejpam-5826	40	4	mapping	mapping	NOUN
ejpam-5826	40	5	e	e	NOUN
ejpam-5826	40	6	on	on	ADP
ejpam-5826	40	7	a	a	DET
ejpam-5826	40	8	metric	metric	ADJ
ejpam-5826	40	9	space	space	NOUN
ejpam-5826	40	10	q	q	NOUN
ejpam-5826	40	11	,	,	PUNCT
ejpam-5826	40	12	is	be	AUX
ejpam-5826	40	13	called	call	VERB
ejpam-5826	40	14	k	k	ADJ
ejpam-5826	40	15	-	-	ADJ
ejpam-5826	40	16	continuous	continuous	ADJ
ejpam-5826	40	17	,	,	PUNCT
ejpam-5826	40	18	k	k	PROPN
ejpam-5826	40	19	=	=	SYM
ejpam-5826	40	20	1	1	NUM
ejpam-5826	40	21	,	,	PUNCT
ejpam-5826	40	22	2	2	NUM
ejpam-5826	40	23	,	,	PUNCT
ejpam-5826	40	24	·	·	PUNCT
ejpam-5826	40	25	·	·	PUNCT
ejpam-5826	40	26	·	·	PUNCT
ejpam-5826	41	1	if	if	SCONJ
ejpam-5826	41	2	lim	lim	PROPN
ejpam-5826	41	3	n→∞	n→∞	PRON
ejpam-5826	41	4	ek−1qn	ek−1qn	NUM
ejpam-5826	41	5	=	=	SYM
ejpam-5826	41	6	z	z	NOUN
ejpam-5826	41	7	implies	imply	VERB
ejpam-5826	41	8	that	that	SCONJ
ejpam-5826	41	9	lim	lim	PROPN
ejpam-5826	41	10	n→∞	n→∞	PRON
ejpam-5826	41	11	ekqn	ekqn	PROPN
ejpam-5826	41	12	=	=	SYM
ejpam-5826	41	13	ez	ez	PROPN
ejpam-5826	41	14	.	.	PROPN
ejpam-5826	41	15	note	note	VERB
ejpam-5826	41	16	that	that	SCONJ
ejpam-5826	41	17	1	1	NUM
ejpam-5826	41	18	-	-	PUNCT
ejpam-5826	41	19	continuity	continuity	NOUN
ejpam-5826	41	20	is	be	AUX
ejpam-5826	41	21	equivalent	equivalent	ADJ
ejpam-5826	41	22	to	to	ADP
ejpam-5826	41	23	continuity	continuity	NOUN
ejpam-5826	41	24	,	,	PUNCT
ejpam-5826	41	25	and	and	CCONJ
ejpam-5826	41	26	for	for	ADP
ejpam-5826	41	27	any	any	DET
ejpam-5826	41	28	k	k	NOUN
ejpam-5826	41	29	=	=	SYM
ejpam-5826	41	30	1	1	NUM
ejpam-5826	41	31	,	,	PUNCT
ejpam-5826	41	32	2	2	NUM
ejpam-5826	41	33	,	,	PUNCT
ejpam-5826	41	34	...	...	PUNCT
ejpam-5826	41	35	,	,	PUNCT
ejpam-5826	41	36	k	k	X
ejpam-5826	41	37	-	-	PUNCT
ejpam-5826	41	38	continuity	continuity	NOUN
ejpam-5826	41	39	implies	imply	VERB
ejpam-5826	41	40	(	(	PUNCT
ejpam-5826	41	41	k	k	PROPN
ejpam-5826	41	42	+	+	NOUN
ejpam-5826	41	43	1)-continuity	1)-continuity	NUM
ejpam-5826	41	44	,	,	PUNCT
ejpam-5826	41	45	while	while	SCONJ
ejpam-5826	41	46	the	the	DET
ejpam-5826	41	47	converse	converse	NOUN
ejpam-5826	41	48	is	be	AUX
ejpam-5826	41	49	not	not	PART
ejpam-5826	41	50	true	true	ADJ
ejpam-5826	41	51	.	.	PUNCT
ejpam-5826	42	1	moreover	moreover	ADV
ejpam-5826	42	2	,	,	PUNCT
ejpam-5826	42	3	continuity	continuity	NOUN
ejpam-5826	42	4	of	of	ADP
ejpam-5826	42	5	e	e	PROPN
ejpam-5826	42	6	and	and	CCONJ
ejpam-5826	42	7	k	k	NOUN
ejpam-5826	42	8	-	-	NOUN
ejpam-5826	42	9	continuity	continuity	NOUN
ejpam-5826	42	10	of	of	ADP
ejpam-5826	42	11	e	e	NOUN
ejpam-5826	42	12	are	be	AUX
ejpam-5826	42	13	independent	independent	ADJ
ejpam-5826	42	14	conditions	condition	NOUN
ejpam-5826	42	15	when	when	SCONJ
ejpam-5826	42	16	k	k	PROPN
ejpam-5826	42	17	>	>	X
ejpam-5826	42	18	1([13	1([13	NUM
ejpam-5826	42	19	]	]	PUNCT
ejpam-5826	42	20	,	,	PUNCT
ejpam-5826	42	21	examples	example	NOUN
ejpam-5826	42	22	1.2	1.2	NUM
ejpam-5826	42	23	-	-	SYM
ejpam-5826	42	24	1.5	1.5	NUM
ejpam-5826	42	25	)	)	PUNCT
ejpam-5826	42	26	.	.	PUNCT
ejpam-5826	43	1	górnicki	górnicki	PROPN
ejpam-5826	44	1	[	[	X
ejpam-5826	44	2	2	2	X
ejpam-5826	44	3	]	]	PUNCT
ejpam-5826	44	4	has	have	AUX
ejpam-5826	44	5	obtained	obtain	VERB
ejpam-5826	44	6	the	the	DET
ejpam-5826	44	7	following	following	ADJ
ejpam-5826	44	8	result	result	NOUN
ejpam-5826	44	9	.	.	PUNCT
ejpam-5826	45	1	a.	a.	PROPN
ejpam-5826	45	2	r.	r.	PROPN
ejpam-5826	45	3	khan	khan	PROPN
ejpam-5826	45	4	et	et	PROPN
ejpam-5826	45	5	al	al	PROPN
ejpam-5826	45	6	.	.	PUNCT
ejpam-5826	45	7	/	/	SYM
ejpam-5826	45	8	eur	eur	PROPN
ejpam-5826	45	9	.	.	PUNCT
ejpam-5826	46	1	j.	j.	PROPN
ejpam-5826	46	2	pure	pure	PROPN
ejpam-5826	46	3	appl	appl	PROPN
ejpam-5826	46	4	.	.	PROPN
ejpam-5826	46	5	math	math	PROPN
ejpam-5826	46	6	,	,	PUNCT
ejpam-5826	46	7	18	18	NUM
ejpam-5826	46	8	(	(	PUNCT
ejpam-5826	46	9	2	2	NUM
ejpam-5826	46	10	)	)	PUNCT
ejpam-5826	46	11	(	(	PUNCT
ejpam-5826	46	12	2025	2025	NUM
ejpam-5826	46	13	)	)	PUNCT
ejpam-5826	46	14	,	,	PUNCT
ejpam-5826	46	15	5826	5826	NUM
ejpam-5826	46	16	3	3	NUM
ejpam-5826	46	17	of	of	ADP
ejpam-5826	46	18	23	23	NUM
ejpam-5826	46	19	theorem	theorem	NOUN
ejpam-5826	46	20	1	1	NUM
ejpam-5826	46	21	.	.	PUNCT
ejpam-5826	47	1	(	(	PUNCT
ejpam-5826	47	2	[	[	X
ejpam-5826	47	3	2	2	NUM
ejpam-5826	47	4	]	]	PUNCT
ejpam-5826	47	5	,	,	PUNCT
ejpam-5826	47	6	theorem	theorem	VERB
ejpam-5826	47	7	2.6	2.6	NUM
ejpam-5826	47	8	)	)	PUNCT
ejpam-5826	47	9	suppose	suppose	VERB
ejpam-5826	47	10	that	that	SCONJ
ejpam-5826	47	11	(	(	PUNCT
ejpam-5826	47	12	q	q	X
ejpam-5826	47	13	,	,	PUNCT
ejpam-5826	47	14	d	d	NOUN
ejpam-5826	47	15	)	)	PUNCT
ejpam-5826	47	16	is	be	AUX
ejpam-5826	47	17	a	a	DET
ejpam-5826	47	18	complete	complete	ADJ
ejpam-5826	47	19	metric	metric	ADJ
ejpam-5826	47	20	space	space	NOUN
ejpam-5826	47	21	and	and	CCONJ
ejpam-5826	47	22	e	e	NOUN
ejpam-5826	47	23	is	be	AUX
ejpam-5826	47	24	a	a	DET
ejpam-5826	47	25	continuous	continuous	ADJ
ejpam-5826	47	26	asymptotically	asymptotically	ADV
ejpam-5826	47	27	regular	regular	ADJ
ejpam-5826	47	28	self	self	NOUN
ejpam-5826	47	29	-	-	PUNCT
ejpam-5826	47	30	mapping	mapping	NOUN
ejpam-5826	47	31	on	on	ADP
ejpam-5826	47	32	q	q	VERB
ejpam-5826	47	33	satisfying	satisfy	VERB
ejpam-5826	47	34	the	the	DET
ejpam-5826	47	35	following	follow	VERB
ejpam-5826	47	36	condition	condition	NOUN
ejpam-5826	47	37	:	:	PUNCT
ejpam-5826	47	38	d(eq	d(eq	PROPN
ejpam-5826	47	39	,	,	PUNCT
ejpam-5826	47	40	ep	ep	NOUN
ejpam-5826	47	41	)	)	PUNCT
ejpam-5826	47	42	≤	≤	NOUN
ejpam-5826	47	43	µd(q	µd(q	NOUN
ejpam-5826	47	44	,	,	PUNCT
ejpam-5826	47	45	p	p	NOUN
ejpam-5826	47	46	)	)	PUNCT
ejpam-5826	47	47	+	+	CCONJ
ejpam-5826	47	48	ν{d(q	ν{d(q	PROPN
ejpam-5826	47	49	,	,	PUNCT
ejpam-5826	47	50	eq	eq	NOUN
ejpam-5826	47	51	)	)	PUNCT
ejpam-5826	48	1	+	+	CCONJ
ejpam-5826	48	2	d(p	d(p	PROPN
ejpam-5826	48	3	,	,	PUNCT
ejpam-5826	48	4	ep)},∀q	ep)},∀q	ADJ
ejpam-5826	48	5	,	,	PUNCT
ejpam-5826	48	6	p	p	NOUN
ejpam-5826	48	7	∈	∈	ADJ
ejpam-5826	48	8	q	q	X
ejpam-5826	48	9	(	(	PUNCT
ejpam-5826	48	10	1	1	NUM
ejpam-5826	48	11	)	)	PUNCT
ejpam-5826	48	12	where	where	SCONJ
ejpam-5826	48	13	0	0	NUM
ejpam-5826	48	14	≤	≤	X
ejpam-5826	48	15	µ	µ	X
ejpam-5826	48	16	<	<	X
ejpam-5826	48	17	1	1	NUM
ejpam-5826	48	18	,	,	PUNCT
ejpam-5826	48	19	0	0	NUM
ejpam-5826	48	20	≤	≤	NUM
ejpam-5826	48	21	ν	ν	ADP
ejpam-5826	48	22	<	<	X
ejpam-5826	48	23	∞.	∞.	PROPN
ejpam-5826	48	24	then	then	ADV
ejpam-5826	48	25	e	e	PROPN
ejpam-5826	48	26	has	have	VERB
ejpam-5826	48	27	a	a	DET
ejpam-5826	48	28	unique	unique	ADJ
ejpam-5826	48	29	fixed	fix	VERB
ejpam-5826	48	30	point	point	NOUN
ejpam-5826	48	31	x	x	X
ejpam-5826	48	32	∈	∈	PROPN
ejpam-5826	48	33	q	q	NOUN
ejpam-5826	48	34	and	and	CCONJ
ejpam-5826	48	35	enq	enq	PROPN
ejpam-5826	48	36	→	→	PUNCT
ejpam-5826	48	37	x	x	X
ejpam-5826	48	38	for	for	ADP
ejpam-5826	48	39	each	each	DET
ejpam-5826	48	40	q	q	PROPN
ejpam-5826	48	41	∈	∈	PROPN
ejpam-5826	48	42	q	q	X
ejpam-5826	48	43	.	.	PUNCT
ejpam-5826	49	1	khan	khan	PROPN
ejpam-5826	49	2	and	and	CCONJ
ejpam-5826	49	3	oyetunbi	oyetunbi	NOUN
ejpam-5826	49	4	[	[	X
ejpam-5826	49	5	7	7	X
ejpam-5826	49	6	]	]	PUNCT
ejpam-5826	49	7	have	have	AUX
ejpam-5826	49	8	obtained	obtain	VERB
ejpam-5826	49	9	the	the	DET
ejpam-5826	49	10	following	following	ADJ
ejpam-5826	49	11	generalization	generalization	NOUN
ejpam-5826	49	12	of	of	ADP
ejpam-5826	49	13	theorem	theorem	ADJ
ejpam-5826	49	14	1	1	NUM
ejpam-5826	49	15	.	.	PUNCT
ejpam-5826	49	16	theorem	theorem	NOUN
ejpam-5826	49	17	2	2	NUM
ejpam-5826	49	18	.	.	PUNCT
ejpam-5826	50	1	(	(	PUNCT
ejpam-5826	50	2	[	[	X
ejpam-5826	50	3	7],theorem	7],theorem	NUM
ejpam-5826	50	4	2.2	2.2	NUM
ejpam-5826	50	5	)	)	PUNCT
ejpam-5826	50	6	suppose	suppose	VERB
ejpam-5826	50	7	that	that	SCONJ
ejpam-5826	50	8	(	(	PUNCT
ejpam-5826	50	9	q	q	X
ejpam-5826	50	10	,	,	PUNCT
ejpam-5826	50	11	d	d	NOUN
ejpam-5826	50	12	)	)	PUNCT
ejpam-5826	50	13	is	be	AUX
ejpam-5826	50	14	a	a	DET
ejpam-5826	50	15	complete	complete	ADJ
ejpam-5826	50	16	metric	metric	ADJ
ejpam-5826	50	17	space	space	NOUN
ejpam-5826	50	18	,	,	PUNCT
ejpam-5826	50	19	e	e	PROPN
ejpam-5826	50	20	and	and	CCONJ
ejpam-5826	50	21	f	f	PROPN
ejpam-5826	50	22	are	be	AUX
ejpam-5826	50	23	asymptotically	asymptotically	ADV
ejpam-5826	50	24	regular	regular	ADJ
ejpam-5826	50	25	self	self	NOUN
ejpam-5826	50	26	-	-	PUNCT
ejpam-5826	50	27	mappings	mapping	NOUN
ejpam-5826	50	28	on	on	ADP
ejpam-5826	50	29	q	q	NOUN
ejpam-5826	50	30	satisfying	satisfy	VERB
ejpam-5826	50	31	the	the	DET
ejpam-5826	50	32	following	follow	VERB
ejpam-5826	50	33	condition	condition	NOUN
ejpam-5826	50	34	:	:	PUNCT
ejpam-5826	50	35	d(eq	d(eq	PROPN
ejpam-5826	50	36	,	,	PUNCT
ejpam-5826	50	37	fp	fp	ADJ
ejpam-5826	50	38	)	)	PUNCT
ejpam-5826	50	39	≤	≤	NOUN
ejpam-5826	50	40	µd(q	µd(q	NOUN
ejpam-5826	50	41	,	,	PUNCT
ejpam-5826	50	42	p	p	NOUN
ejpam-5826	50	43	)	)	PUNCT
ejpam-5826	51	1	+	+	CCONJ
ejpam-5826	51	2	ν{d(q	ν{d(q	PROPN
ejpam-5826	51	3	,	,	PUNCT
ejpam-5826	51	4	eq	eq	NOUN
ejpam-5826	51	5	)	)	PUNCT
ejpam-5826	51	6	+	+	CCONJ
ejpam-5826	51	7	d(p	d(p	PROPN
ejpam-5826	51	8	,	,	PUNCT
ejpam-5826	51	9	fp	fp	NOUN
ejpam-5826	51	10	)	)	PUNCT
ejpam-5826	51	11	}	}	PUNCT
ejpam-5826	51	12	,	,	PUNCT
ejpam-5826	51	13	∀q	∀q	PROPN
ejpam-5826	51	14	,	,	PUNCT
ejpam-5826	51	15	p	p	PROPN
ejpam-5826	51	16	∈	∈	PROPN
ejpam-5826	51	17	q	q	X
ejpam-5826	51	18	(	(	PUNCT
ejpam-5826	51	19	2	2	NUM
ejpam-5826	51	20	)	)	PUNCT
ejpam-5826	51	21	where	where	SCONJ
ejpam-5826	51	22	0	0	NUM
ejpam-5826	51	23	≤	≤	X
ejpam-5826	51	24	µ	µ	X
ejpam-5826	51	25	<	<	X
ejpam-5826	51	26	1	1	NUM
ejpam-5826	51	27	,	,	PUNCT
ejpam-5826	51	28	0	0	NUM
ejpam-5826	51	29	≤	≤	NUM
ejpam-5826	51	30	ν	ν	NOUN
ejpam-5826	51	31	<	<	X
ejpam-5826	51	32	∞.	∞.	PROPN
ejpam-5826	51	33	suppose	suppose	VERB
ejpam-5826	51	34	further	far	ADV
ejpam-5826	51	35	that	that	SCONJ
ejpam-5826	51	36	e	e	PROPN
ejpam-5826	51	37	and	and	CCONJ
ejpam-5826	51	38	f	f	PROPN
ejpam-5826	51	39	are	be	AUX
ejpam-5826	51	40	either	either	CCONJ
ejpam-5826	51	41	k	k	ADJ
ejpam-5826	51	42	-	-	ADJ
ejpam-5826	51	43	continuous	continuous	ADJ
ejpam-5826	51	44	for	for	ADP
ejpam-5826	51	45	some	some	DET
ejpam-5826	51	46	k	k	PROPN
ejpam-5826	51	47	≥	≥	NUM
ejpam-5826	51	48	1	1	NUM
ejpam-5826	51	49	or	or	CCONJ
ejpam-5826	51	50	orbitally	orbitally	ADV
ejpam-5826	51	51	continuous	continuous	ADJ
ejpam-5826	51	52	.	.	PUNCT
ejpam-5826	52	1	then	then	ADV
ejpam-5826	52	2	e	e	PROPN
ejpam-5826	52	3	and	and	CCONJ
ejpam-5826	52	4	f	f	PROPN
ejpam-5826	52	5	have	have	VERB
ejpam-5826	52	6	a	a	DET
ejpam-5826	52	7	unique	unique	ADJ
ejpam-5826	52	8	common	common	ADJ
ejpam-5826	52	9	fixed	fix	VERB
ejpam-5826	52	10	point	point	NOUN
ejpam-5826	52	11	b.	b.	PROPN
ejpam-5826	53	1	furthermore	furthermore	ADV
ejpam-5826	53	2	,	,	PUNCT
ejpam-5826	53	3	limn→∞enq	limn→∞enq	PROPN
ejpam-5826	53	4	=	=	SYM
ejpam-5826	53	5	b	b	X
ejpam-5826	53	6	=	=	PUNCT
ejpam-5826	53	7	limn→∞	limn→∞	PROPN
ejpam-5826	53	8	fnq	fnq	NOUN
ejpam-5826	53	9	for	for	ADP
ejpam-5826	53	10	any	any	DET
ejpam-5826	53	11	q	q	PROPN
ejpam-5826	53	12	∈	∈	PROPN
ejpam-5826	53	13	q.	q.	NOUN
ejpam-5826	53	14	here	here	ADV
ejpam-5826	53	15	is	be	AUX
ejpam-5826	53	16	a	a	DET
ejpam-5826	53	17	result	result	NOUN
ejpam-5826	53	18	of	of	ADP
ejpam-5826	53	19	khan	khan	PROPN
ejpam-5826	53	20	and	and	CCONJ
ejpam-5826	53	21	oyetunbi	oyetunbi	NOUN
ejpam-5826	53	22	[	[	X
ejpam-5826	53	23	7	7	X
ejpam-5826	53	24	]	]	PUNCT
ejpam-5826	53	25	without	without	ADP
ejpam-5826	53	26	asymptotically	asymptotically	ADV
ejpam-5826	53	27	regularity	regularity	NOUN
ejpam-5826	53	28	of	of	ADP
ejpam-5826	53	29	the	the	DET
ejpam-5826	53	30	mappings	mapping	NOUN
ejpam-5826	53	31	.	.	PUNCT
ejpam-5826	54	1	theorem	theorem	NOUN
ejpam-5826	54	2	3	3	NUM
ejpam-5826	54	3	.	.	PUNCT
ejpam-5826	55	1	[	[	X
ejpam-5826	55	2	7	7	NUM
ejpam-5826	55	3	,	,	PUNCT
ejpam-5826	55	4	theorem	theorem	VERB
ejpam-5826	55	5	2.6	2.6	NUM
ejpam-5826	55	6	]	]	PUNCT
ejpam-5826	55	7	suppose	suppose	VERB
ejpam-5826	55	8	that	that	SCONJ
ejpam-5826	55	9	(	(	PUNCT
ejpam-5826	55	10	q	q	X
ejpam-5826	55	11	,	,	PUNCT
ejpam-5826	55	12	d	d	NOUN
ejpam-5826	55	13	)	)	PUNCT
ejpam-5826	55	14	is	be	AUX
ejpam-5826	55	15	a	a	DET
ejpam-5826	55	16	complete	complete	ADJ
ejpam-5826	55	17	metric	metric	ADJ
ejpam-5826	55	18	space	space	NOUN
ejpam-5826	55	19	and	and	CCONJ
ejpam-5826	55	20	e	e	NOUN
ejpam-5826	55	21	,	,	PUNCT
ejpam-5826	55	22	f	f	X
ejpam-5826	55	23	:	:	PUNCT
ejpam-5826	55	24	q	q	X
ejpam-5826	55	25	→	→	X
ejpam-5826	55	26	q	q	X
ejpam-5826	55	27	are	be	AUX
ejpam-5826	55	28	continuous	continuous	ADJ
ejpam-5826	55	29	mappings	mapping	NOUN
ejpam-5826	55	30	satisfying	satisfy	VERB
ejpam-5826	55	31	(	(	PUNCT
ejpam-5826	55	32	2	2	NUM
ejpam-5826	55	33	)	)	PUNCT
ejpam-5826	55	34	.	.	PUNCT
ejpam-5826	56	1	suppose	suppose	VERB
ejpam-5826	56	2	that	that	SCONJ
ejpam-5826	56	3	e	e	PROPN
ejpam-5826	56	4	and	and	CCONJ
ejpam-5826	56	5	f	f	PROPN
ejpam-5826	56	6	have	have	VERB
ejpam-5826	56	7	a	a	DET
ejpam-5826	56	8	common	common	ADJ
ejpam-5826	56	9	approximate	approximate	ADJ
ejpam-5826	56	10	fixed	fix	VERB
ejpam-5826	56	11	point	point	NOUN
ejpam-5826	56	12	sequence	sequence	NOUN
ejpam-5826	56	13	(	(	PUNCT
ejpam-5826	56	14	i.e.	i.e.	X
ejpam-5826	56	15	there	there	PRON
ejpam-5826	56	16	exists	exist	VERB
ejpam-5826	56	17	a	a	DET
ejpam-5826	56	18	sequence	sequence	NOUN
ejpam-5826	56	19	{	{	PUNCT
ejpam-5826	56	20	qn	qn	NOUN
ejpam-5826	56	21	}	}	PUNCT
ejpam-5826	56	22	⊂	⊂	PROPN
ejpam-5826	56	23	q	q	NOUN
ejpam-5826	56	24	such	such	ADJ
ejpam-5826	56	25	that	that	SCONJ
ejpam-5826	56	26	d(qn	d(qn	PROPN
ejpam-5826	56	27	,	,	PUNCT
ejpam-5826	56	28	eqn	eqn	NOUN
ejpam-5826	56	29	)	)	PUNCT
ejpam-5826	56	30	→	→	SYM
ejpam-5826	56	31	0	0	NUM
ejpam-5826	56	32	and	and	CCONJ
ejpam-5826	56	33	d(qn	d(qn	PROPN
ejpam-5826	56	34	,	,	PUNCT
ejpam-5826	56	35	f	f	PROPN
ejpam-5826	56	36	qn	qn	PROPN
ejpam-5826	56	37	)	)	PUNCT
ejpam-5826	56	38	→	→	SYM
ejpam-5826	56	39	0	0	NUM
ejpam-5826	56	40	as	as	ADP
ejpam-5826	56	41	n	n	PROPN
ejpam-5826	56	42	→	→	SYM
ejpam-5826	56	43	∞	∞	NUM
ejpam-5826	56	44	)	)	PUNCT
ejpam-5826	56	45	.	.	PUNCT
ejpam-5826	57	1	then	then	ADV
ejpam-5826	57	2	e	e	PROPN
ejpam-5826	57	3	and	and	CCONJ
ejpam-5826	57	4	f	f	PROPN
ejpam-5826	57	5	have	have	VERB
ejpam-5826	57	6	a	a	DET
ejpam-5826	57	7	unique	unique	ADJ
ejpam-5826	57	8	common	common	ADJ
ejpam-5826	57	9	fixed	fix	VERB
ejpam-5826	57	10	point	point	NOUN
ejpam-5826	57	11	q.	q.	PROPN
ejpam-5826	57	12	in	in	ADP
ejpam-5826	57	13	particular	particular	ADJ
ejpam-5826	57	14	,	,	PUNCT
ejpam-5826	57	15	qn	qn	INTJ
ejpam-5826	57	16	→	→	SYM
ejpam-5826	57	17	q	q	X
ejpam-5826	57	18	,	,	PUNCT
ejpam-5826	57	19	as	as	ADP
ejpam-5826	57	20	n	n	PROPN
ejpam-5826	57	21	→	→	SYM
ejpam-5826	57	22	∞.	∞.	PROPN
ejpam-5826	57	23	lemma	lemma	PROPN
ejpam-5826	57	24	1	1	NUM
ejpam-5826	57	25	(	(	PUNCT
ejpam-5826	57	26	[	[	X
ejpam-5826	57	27	14],lemma	14],lemma	NUM
ejpam-5826	57	28	2.1	2.1	NUM
ejpam-5826	57	29	)	)	PUNCT
ejpam-5826	57	30	.	.	PUNCT
ejpam-5826	58	1	let	let	VERB
ejpam-5826	58	2	{	{	PUNCT
ejpam-5826	58	3	τn	τn	VERB
ejpam-5826	58	4	}	}	PUNCT
ejpam-5826	58	5	,	,	PUNCT
ejpam-5826	58	6	{	{	PUNCT
ejpam-5826	58	7	ϕn	ϕn	NOUN
ejpam-5826	58	8	}	}	PUNCT
ejpam-5826	58	9	and	and	CCONJ
ejpam-5826	58	10	{	{	PUNCT
ejpam-5826	58	11	χn	χn	ADV
ejpam-5826	58	12	}	}	PUNCT
ejpam-5826	58	13	be	be	AUX
ejpam-5826	58	14	three	three	NUM
ejpam-5826	58	15	real	real	ADJ
ejpam-5826	58	16	sequences	sequence	NOUN
ejpam-5826	58	17	with	with	ADP
ejpam-5826	58	18	τn	τn	ADP
ejpam-5826	58	19	≥	≥	NOUN
ejpam-5826	58	20	0	0	NUM
ejpam-5826	59	1	and	and	CCONJ
ejpam-5826	59	2	ϕn	ϕn	ADP
ejpam-5826	59	3	∈	∈	PROPN
ejpam-5826	59	4	(	(	PUNCT
ejpam-5826	59	5	0	0	NUM
ejpam-5826	59	6	,	,	PUNCT
ejpam-5826	59	7	1	1	NUM
ejpam-5826	59	8	)	)	PUNCT
ejpam-5826	59	9	.	.	PUNCT
ejpam-5826	59	10	suppose	suppose	VERB
ejpam-5826	59	11	that	that	SCONJ
ejpam-5826	59	12	(	(	PUNCT
ejpam-5826	59	13	i)τn+1	i)τn+1	ADJ
ejpam-5826	59	14	≤	≤	NOUN
ejpam-5826	59	15	(	(	PUNCT
ejpam-5826	59	16	1−	1−	NUM
ejpam-5826	59	17	ϕn)τn	ϕn)τn	PUNCT
ejpam-5826	60	1	+	+	CCONJ
ejpam-5826	60	2	ϕnχn	ϕnχn	PROPN
ejpam-5826	60	3	(	(	PUNCT
ejpam-5826	60	4	ii	ii	NOUN
ejpam-5826	60	5	)	)	PUNCT
ejpam-5826	60	6	∑∞	∑∞	NOUN
ejpam-5826	60	7	n=1	n=1	PUNCT
ejpam-5826	61	1	ϕn	ϕn	NOUN
ejpam-5826	61	2	=	=	SYM
ejpam-5826	61	3	∞	∞	PROPN
ejpam-5826	61	4	(	(	PUNCT
ejpam-5826	61	5	iii	iii	NOUN
ejpam-5826	61	6	)	)	PUNCT
ejpam-5826	61	7	lim	lim	NOUN
ejpam-5826	61	8	supn→∞χn	supn→∞χn	VERB
ejpam-5826	61	9	≤	≤	NUM
ejpam-5826	61	10	0	0	NUM
ejpam-5826	62	1	or	or	CCONJ
ejpam-5826	62	2	∑∞	∑∞	NOUN
ejpam-5826	62	3	n=1	n=1	PROPN
ejpam-5826	62	4	ϕnχn	ϕnχn	NOUN
ejpam-5826	62	5	is	be	AUX
ejpam-5826	62	6	convergent	convergent	ADJ
ejpam-5826	62	7	.	.	PUNCT
ejpam-5826	63	1	then	then	ADV
ejpam-5826	63	2	limn→∞	limn→∞	PROPN
ejpam-5826	63	3	τn	τn	ADP
ejpam-5826	63	4	=	=	SYM
ejpam-5826	63	5	0	0	PROPN
ejpam-5826	63	6	.	.	PUNCT
ejpam-5826	63	7	definition	definition	NOUN
ejpam-5826	63	8	1	1	NUM
ejpam-5826	63	9	.	.	PUNCT
ejpam-5826	64	1	[	[	X
ejpam-5826	64	2	14	14	NUM
ejpam-5826	64	3	]	]	PUNCT
ejpam-5826	64	4	let	let	VERB
ejpam-5826	64	5	r+	r+	NOUN
ejpam-5826	64	6	:	:	PUNCT
ejpam-5826	64	7	=	=	PUNCT
ejpam-5826	64	8	{	{	PUNCT
ejpam-5826	64	9	f	f	PROPN
ejpam-5826	64	10	∈	∈	PROPN
ejpam-5826	64	11	r	r	NOUN
ejpam-5826	65	1	|	|	NOUN
ejpam-5826	65	2	f	f	PROPN
ejpam-5826	65	3	≥	≥	NOUN
ejpam-5826	65	4	0	0	NUM
ejpam-5826	65	5	}	}	PUNCT
ejpam-5826	65	6	.	.	PUNCT
ejpam-5826	66	1	define	define	VERB
ejpam-5826	66	2	a	a	DET
ejpam-5826	66	3	function	function	NOUN
ejpam-5826	66	4	κ	κ	NOUN
ejpam-5826	66	5	:	:	PUNCT
ejpam-5826	66	6	r+	r+	X
ejpam-5826	66	7	→	→	PUNCT
ejpam-5826	66	8	[	[	X
ejpam-5826	66	9	0	0	NUM
ejpam-5826	66	10	,	,	PUNCT
ejpam-5826	66	11	1	1	NUM
ejpam-5826	66	12	]	]	PUNCT
ejpam-5826	66	13	satisfying	satisfy	VERB
ejpam-5826	66	14	the	the	DET
ejpam-5826	66	15	following	follow	VERB
ejpam-5826	66	16	properties	property	NOUN
ejpam-5826	66	17	:	:	PUNCT
ejpam-5826	66	18	(	(	PUNCT
ejpam-5826	66	19	i	i	NOUN
ejpam-5826	66	20	)	)	PUNCT
ejpam-5826	66	21	0	0	NUM
ejpam-5826	67	1	≤	≤	NUM
ejpam-5826	67	2	κ(f	κ(f	NOUN
ejpam-5826	67	3	)	)	PUNCT
ejpam-5826	68	1	<	<	X
ejpam-5826	68	2	1	1	NUM
ejpam-5826	68	3	for	for	ADP
ejpam-5826	68	4	all	all	DET
ejpam-5826	68	5	f	f	PROPN
ejpam-5826	68	6	>	>	X
ejpam-5826	68	7	0	0	NUM
ejpam-5826	68	8	.	.	PUNCT
ejpam-5826	68	9	(	(	PUNCT
ejpam-5826	68	10	ii	ii	NOUN
ejpam-5826	68	11	)	)	PUNCT
ejpam-5826	68	12	limn→∞	limn→∞	PROPN
ejpam-5826	68	13	κ(fn	κ(fn	PROPN
ejpam-5826	68	14	)	)	PUNCT
ejpam-5826	68	15	=	=	SYM
ejpam-5826	68	16	1	1	NUM
ejpam-5826	68	17	implies	imply	VERB
ejpam-5826	68	18	limn→∞	limn→∞	PROPN
ejpam-5826	68	19	fn	fn	NOUN
ejpam-5826	68	20	=	=	SYM
ejpam-5826	68	21	0	0	PROPN
ejpam-5826	68	22	.	.	PUNCT
ejpam-5826	69	1	the	the	DET
ejpam-5826	69	2	collection	collection	NOUN
ejpam-5826	69	3	of	of	ADP
ejpam-5826	69	4	all	all	DET
ejpam-5826	69	5	functions	function	NOUN
ejpam-5826	69	6	κ(f	κ(f	PROPN
ejpam-5826	69	7	)	)	PUNCT
ejpam-5826	69	8	is	be	AUX
ejpam-5826	69	9	denoted	denote	VERB
ejpam-5826	69	10	by	by	ADP
ejpam-5826	69	11	s.	s.	PROPN
ejpam-5826	69	12	kohlenbouch	kohlenbouch	PROPN
ejpam-5826	70	1	[	[	X
ejpam-5826	70	2	10	10	NUM
ejpam-5826	70	3	]	]	PUNCT
ejpam-5826	70	4	proposed	propose	VERB
ejpam-5826	70	5	the	the	DET
ejpam-5826	70	6	concept	concept	NOUN
ejpam-5826	70	7	of	of	ADP
ejpam-5826	70	8	a	a	DET
ejpam-5826	70	9	hyperbolic	hyperbolic	ADJ
ejpam-5826	70	10	metric	metric	ADJ
ejpam-5826	70	11	space	space	NOUN
ejpam-5826	70	12	as	as	SCONJ
ejpam-5826	70	13	follows	follow	VERB
ejpam-5826	70	14	.	.	PUNCT
ejpam-5826	71	1	a.	a.	PROPN
ejpam-5826	71	2	r.	r.	PROPN
ejpam-5826	71	3	khan	khan	PROPN
ejpam-5826	71	4	et	et	PROPN
ejpam-5826	71	5	al	al	PROPN
ejpam-5826	71	6	.	.	PUNCT
ejpam-5826	71	7	/	/	SYM
ejpam-5826	71	8	eur	eur	PROPN
ejpam-5826	71	9	.	.	PUNCT
ejpam-5826	72	1	j.	j.	PROPN
ejpam-5826	72	2	pure	pure	PROPN
ejpam-5826	72	3	appl	appl	PROPN
ejpam-5826	72	4	.	.	PROPN
ejpam-5826	72	5	math	math	PROPN
ejpam-5826	72	6	,	,	PUNCT
ejpam-5826	72	7	18	18	NUM
ejpam-5826	72	8	(	(	PUNCT
ejpam-5826	72	9	2	2	NUM
ejpam-5826	72	10	)	)	PUNCT
ejpam-5826	72	11	(	(	PUNCT
ejpam-5826	72	12	2025	2025	NUM
ejpam-5826	72	13	)	)	PUNCT
ejpam-5826	72	14	,	,	PUNCT
ejpam-5826	72	15	5826	5826	NUM
ejpam-5826	72	16	4	4	NUM
ejpam-5826	72	17	of	of	ADP
ejpam-5826	72	18	23	23	NUM
ejpam-5826	72	19	definition	definition	NOUN
ejpam-5826	72	20	2	2	NUM
ejpam-5826	72	21	.	.	PUNCT
ejpam-5826	73	1	a	a	DET
ejpam-5826	73	2	hyperbolic	hyperbolic	ADJ
ejpam-5826	73	3	space	space	NOUN
ejpam-5826	73	4	is	be	AUX
ejpam-5826	73	5	a	a	DET
ejpam-5826	73	6	triplet	triplet	NOUN
ejpam-5826	73	7	(	(	PUNCT
ejpam-5826	73	8	q	q	NOUN
ejpam-5826	73	9	,	,	PUNCT
ejpam-5826	73	10	d	d	PROPN
ejpam-5826	73	11	,	,	PUNCT
ejpam-5826	73	12	η	η	NOUN
ejpam-5826	73	13	)	)	PUNCT
ejpam-5826	73	14	where	where	SCONJ
ejpam-5826	73	15	(	(	PUNCT
ejpam-5826	73	16	q	q	X
ejpam-5826	73	17	,	,	PUNCT
ejpam-5826	73	18	d	d	NOUN
ejpam-5826	73	19	)	)	PUNCT
ejpam-5826	73	20	is	be	AUX
ejpam-5826	73	21	a	a	DET
ejpam-5826	73	22	metric	metric	ADJ
ejpam-5826	73	23	space	space	NOUN
ejpam-5826	73	24	and	and	CCONJ
ejpam-5826	73	25	η	η	PROPN
ejpam-5826	73	26	:	:	PUNCT
ejpam-5826	74	1	q×q×[0	q×q×[0	PROPN
ejpam-5826	74	2	,	,	PUNCT
ejpam-5826	74	3	1	1	NUM
ejpam-5826	74	4	]	]	PUNCT
ejpam-5826	74	5	→	→	PUNCT
ejpam-5826	74	6	q	q	X
ejpam-5826	74	7	satisfies	satisfy	VERB
ejpam-5826	74	8	the	the	DET
ejpam-5826	74	9	following	follow	VERB
ejpam-5826	74	10	conditions	condition	NOUN
ejpam-5826	74	11	,	,	PUNCT
ejpam-5826	74	12	for	for	ADP
ejpam-5826	74	13	all	all	DET
ejpam-5826	74	14	ω	ω	NUM
ejpam-5826	74	15	,	,	PUNCT
ejpam-5826	74	16	ξ	ξ	PROPN
ejpam-5826	74	17	,	,	PUNCT
ejpam-5826	74	18	κ	κ	NOUN
ejpam-5826	74	19	,	,	PUNCT
ejpam-5826	74	20	ι	ι	PROPN
ejpam-5826	74	21	∈	∈	PROPN
ejpam-5826	74	22	q	q	X
ejpam-5826	74	23	and	and	CCONJ
ejpam-5826	74	24	µ	µ	NOUN
ejpam-5826	74	25	,	,	PUNCT
ejpam-5826	74	26	x	x	SYM
ejpam-5826	74	27	∈	∈	PROPN
ejpam-5826	75	1	[	[	X
ejpam-5826	75	2	0	0	NUM
ejpam-5826	75	3	,	,	PUNCT
ejpam-5826	75	4	1	1	NUM
ejpam-5826	75	5	]	]	PUNCT
ejpam-5826	75	6	(	(	PUNCT
ejpam-5826	75	7	η1	η1	NOUN
ejpam-5826	75	8	)	)	PUNCT
ejpam-5826	75	9	:	:	PUNCT
ejpam-5826	76	1	d(ι	d(ι	VERB
ejpam-5826	76	2	,	,	PUNCT
ejpam-5826	76	3	η(ω	η(ω	NOUN
ejpam-5826	76	4	,	,	PUNCT
ejpam-5826	76	5	ξ	ξ	PROPN
ejpam-5826	76	6	,	,	PUNCT
ejpam-5826	76	7	µ	µ	NOUN
ejpam-5826	76	8	)	)	PUNCT
ejpam-5826	76	9	)	)	PUNCT
ejpam-5826	76	10	≤	≤	NOUN
ejpam-5826	76	11	(	(	PUNCT
ejpam-5826	76	12	1−	1−	NUM
ejpam-5826	76	13	µ)d(ι	µ)d(ι	NOUN
ejpam-5826	76	14	,	,	PUNCT
ejpam-5826	76	15	ω	ω	NOUN
ejpam-5826	76	16	)	)	PUNCT
ejpam-5826	76	17	+	+	NUM
ejpam-5826	76	18	µd(ι	µd(ι	NOUN
ejpam-5826	76	19	,	,	PUNCT
ejpam-5826	76	20	ξ	ξ	NOUN
ejpam-5826	76	21	)	)	PUNCT
ejpam-5826	76	22	,	,	PUNCT
ejpam-5826	76	23	(	(	PUNCT
ejpam-5826	76	24	η2	η2	X
ejpam-5826	76	25	)	)	PUNCT
ejpam-5826	76	26	:	:	PUNCT
ejpam-5826	76	27	d(η(ω	d(η(ω	PROPN
ejpam-5826	76	28	,	,	PUNCT
ejpam-5826	76	29	ξ	ξ	PROPN
ejpam-5826	76	30	,	,	PUNCT
ejpam-5826	76	31	µ	µ	NOUN
ejpam-5826	76	32	)	)	PUNCT
ejpam-5826	76	33	,	,	PUNCT
ejpam-5826	76	34	η(ω	η(ω	NOUN
ejpam-5826	76	35	,	,	PUNCT
ejpam-5826	76	36	ξ	ξ	PROPN
ejpam-5826	76	37	,	,	PUNCT
ejpam-5826	76	38	x	x	NOUN
ejpam-5826	76	39	)	)	PUNCT
ejpam-5826	76	40	)	)	PUNCT
ejpam-5826	77	1	=	=	SYM
ejpam-5826	77	2	|µ−	|µ−	ADJ
ejpam-5826	77	3	x|d(ω	x|d(ω	PROPN
ejpam-5826	77	4	,	,	PUNCT
ejpam-5826	77	5	ξ	ξ	NOUN
ejpam-5826	77	6	)	)	PUNCT
ejpam-5826	77	7	,	,	PUNCT
ejpam-5826	77	8	(	(	PUNCT
ejpam-5826	77	9	η3	η3	PROPN
ejpam-5826	77	10	)	)	PUNCT
ejpam-5826	77	11	:	:	PUNCT
ejpam-5826	77	12	η(ω	η(ω	NOUN
ejpam-5826	77	13	,	,	PUNCT
ejpam-5826	77	14	ξ	ξ	PROPN
ejpam-5826	77	15	,	,	PUNCT
ejpam-5826	77	16	µ	µ	NOUN
ejpam-5826	77	17	)	)	PUNCT
ejpam-5826	77	18	=	=	SYM
ejpam-5826	78	1	η(ξ	η(ξ	PROPN
ejpam-5826	78	2	,	,	PUNCT
ejpam-5826	78	3	ω	ω	PROPN
ejpam-5826	78	4	,	,	PUNCT
ejpam-5826	78	5	1−	1−	NUM
ejpam-5826	78	6	µ	µ	NUM
ejpam-5826	78	7	)	)	PUNCT
ejpam-5826	78	8	,	,	PUNCT
ejpam-5826	78	9	(	(	PUNCT
ejpam-5826	78	10	η4	η4	VERB
ejpam-5826	78	11	)	)	PUNCT
ejpam-5826	78	12	:	:	PUNCT
ejpam-5826	78	13	d(η(ω	d(η(ω	NOUN
ejpam-5826	78	14	,	,	PUNCT
ejpam-5826	78	15	ι	ι	PROPN
ejpam-5826	78	16	,	,	PUNCT
ejpam-5826	78	17	µ	µ	NOUN
ejpam-5826	78	18	)	)	PUNCT
ejpam-5826	78	19	,	,	PUNCT
ejpam-5826	78	20	η(ξ	η(ξ	PROPN
ejpam-5826	78	21	,	,	PUNCT
ejpam-5826	78	22	κ	κ	PROPN
ejpam-5826	78	23	,	,	PUNCT
ejpam-5826	78	24	µ	µ	NOUN
ejpam-5826	78	25	)	)	PUNCT
ejpam-5826	78	26	)	)	PUNCT
ejpam-5826	78	27	≤	≤	NOUN
ejpam-5826	78	28	(	(	PUNCT
ejpam-5826	78	29	1−	1−	NUM
ejpam-5826	78	30	µ)d(ω	µ)d(ω	PROPN
ejpam-5826	78	31	,	,	PUNCT
ejpam-5826	78	32	ξ	ξ	X
ejpam-5826	78	33	)	)	PUNCT
ejpam-5826	78	34	+	+	NUM
ejpam-5826	78	35	µd(ι	µd(ι	NOUN
ejpam-5826	78	36	,	,	PUNCT
ejpam-5826	78	37	κ	κ	NOUN
ejpam-5826	78	38	)	)	PUNCT
ejpam-5826	78	39	.	.	PUNCT
ejpam-5826	79	1	in	in	ADP
ejpam-5826	79	2	case	case	NOUN
ejpam-5826	79	3	only	only	ADV
ejpam-5826	79	4	(	(	PUNCT
ejpam-5826	79	5	η1	η1	NOUN
ejpam-5826	79	6	)	)	PUNCT
ejpam-5826	79	7	is	be	AUX
ejpam-5826	79	8	satisfied	satisfied	ADJ
ejpam-5826	79	9	,	,	PUNCT
ejpam-5826	79	10	then	then	ADV
ejpam-5826	79	11	the	the	DET
ejpam-5826	79	12	definition	definition	NOUN
ejpam-5826	79	13	2	2	NUM
ejpam-5826	79	14	of	of	ADP
ejpam-5826	79	15	hyperbolic	hyperbolic	ADJ
ejpam-5826	79	16	space	space	NOUN
ejpam-5826	79	17	coincides	coincide	VERB
ejpam-5826	79	18	with	with	ADP
ejpam-5826	79	19	the	the	DET
ejpam-5826	79	20	convex	convex	ADJ
ejpam-5826	79	21	metric	metric	ADJ
ejpam-5826	79	22	space	space	NOUN
ejpam-5826	79	23	introduced	introduce	VERB
ejpam-5826	79	24	by	by	ADP
ejpam-5826	79	25	takahashi	takahashi	PROPN
ejpam-5826	79	26	[	[	X
ejpam-5826	79	27	15	15	NUM
ejpam-5826	79	28	]	]	PUNCT
ejpam-5826	79	29	.	.	PUNCT
ejpam-5826	80	1	clearly	clearly	ADV
ejpam-5826	80	2	,	,	PUNCT
ejpam-5826	80	3	a	a	DET
ejpam-5826	80	4	hyperbolic	hyperbolic	ADJ
ejpam-5826	80	5	space	space	NOUN
ejpam-5826	80	6	is	be	AUX
ejpam-5826	80	7	a	a	DET
ejpam-5826	80	8	convex	convex	ADJ
ejpam-5826	80	9	metric	metric	ADJ
ejpam-5826	80	10	space	space	NOUN
ejpam-5826	80	11	.	.	PUNCT
ejpam-5826	81	1	in	in	ADP
ejpam-5826	81	2	the	the	DET
ejpam-5826	81	3	case	case	NOUN
ejpam-5826	81	4	of	of	ADP
ejpam-5826	81	5	a	a	DET
ejpam-5826	81	6	convex	convex	ADJ
ejpam-5826	81	7	metric	metric	ADJ
ejpam-5826	81	8	space	space	NOUN
ejpam-5826	81	9	,	,	PUNCT
ejpam-5826	81	10	we	we	PRON
ejpam-5826	81	11	shall	shall	AUX
ejpam-5826	81	12	replace	replace	VERB
ejpam-5826	81	13	η	η	PROPN
ejpam-5826	81	14	by	by	ADP
ejpam-5826	81	15	w	w	PROPN
ejpam-5826	81	16	(	(	PUNCT
ejpam-5826	81	17	a	a	DET
ejpam-5826	81	18	convex	convex	ADJ
ejpam-5826	81	19	structure	structure	NOUN
ejpam-5826	81	20	on	on	ADP
ejpam-5826	81	21	q	q	NOUN
ejpam-5826	81	22	)	)	PUNCT
ejpam-5826	81	23	and	and	CCONJ
ejpam-5826	81	24	denote	denote	VERB
ejpam-5826	81	25	it	it	PRON
ejpam-5826	81	26	by	by	ADP
ejpam-5826	81	27	(	(	PUNCT
ejpam-5826	81	28	q	q	ADJ
ejpam-5826	81	29	,	,	PUNCT
ejpam-5826	81	30	d	d	NOUN
ejpam-5826	81	31	,	,	PUNCT
ejpam-5826	81	32	w	w	NOUN
ejpam-5826	81	33	)	)	PUNCT
ejpam-5826	81	34	.	.	PUNCT
ejpam-5826	82	1	a	a	DET
ejpam-5826	82	2	nonempty	nonempty	NOUN
ejpam-5826	82	3	subset	subset	VERB
ejpam-5826	82	4	j	j	PROPN
ejpam-5826	82	5	of	of	ADP
ejpam-5826	82	6	a	a	DET
ejpam-5826	82	7	convex	convex	ADJ
ejpam-5826	82	8	metric	metric	ADJ
ejpam-5826	82	9	space	space	NOUN
ejpam-5826	82	10	q	q	NOUN
ejpam-5826	82	11	is	be	AUX
ejpam-5826	82	12	convex	convex	ADJ
ejpam-5826	82	13	if	if	SCONJ
ejpam-5826	82	14	w	w	PROPN
ejpam-5826	82	15	(	(	PUNCT
ejpam-5826	82	16	p	p	X
ejpam-5826	82	17	,	,	PUNCT
ejpam-5826	82	18	q	q	ADJ
ejpam-5826	82	19	,	,	PUNCT
ejpam-5826	82	20	λ	λ	NOUN
ejpam-5826	82	21	)	)	PUNCT
ejpam-5826	82	22	∈	∈	PROPN
ejpam-5826	82	23	j	j	PROPN
ejpam-5826	82	24	for	for	ADP
ejpam-5826	82	25	all	all	DET
ejpam-5826	82	26	p	p	NOUN
ejpam-5826	82	27	,	,	PUNCT
ejpam-5826	82	28	q	q	PROPN
ejpam-5826	82	29	∈	∈	PROPN
ejpam-5826	82	30	j	j	PROPN
ejpam-5826	82	31	and	and	CCONJ
ejpam-5826	82	32	λ	λ	PROPN
ejpam-5826	82	33	∈	∈	PROPN
ejpam-5826	83	1	[	[	X
ejpam-5826	83	2	0	0	NUM
ejpam-5826	83	3	,	,	PUNCT
ejpam-5826	83	4	1	1	NUM
ejpam-5826	83	5	]	]	PUNCT
ejpam-5826	83	6	.	.	PUNCT
ejpam-5826	84	1	in	in	ADP
ejpam-5826	84	2	the	the	DET
ejpam-5826	84	3	context	context	NOUN
ejpam-5826	84	4	of	of	ADP
ejpam-5826	84	5	a	a	DET
ejpam-5826	84	6	normed	normed	ADJ
ejpam-5826	84	7	space	space	NOUN
ejpam-5826	84	8	q	q	NOUN
ejpam-5826	84	9	,	,	PUNCT
ejpam-5826	84	10	the	the	DET
ejpam-5826	84	11	natural	natural	ADJ
ejpam-5826	84	12	convex	convex	NOUN
ejpam-5826	84	13	structure	structure	NOUN
ejpam-5826	84	14	on	on	ADP
ejpam-5826	84	15	q	q	PROPN
ejpam-5826	84	16	is	be	AUX
ejpam-5826	84	17	given	give	VERB
ejpam-5826	84	18	by	by	ADP
ejpam-5826	84	19	w	w	PROPN
ejpam-5826	84	20	(	(	PUNCT
ejpam-5826	84	21	p	p	X
ejpam-5826	84	22	,	,	PUNCT
ejpam-5826	84	23	q;λ	q;λ	PRON
ejpam-5826	84	24	)	)	PUNCT
ejpam-5826	85	1	=	=	SYM
ejpam-5826	85	2	λp+	λp+	NOUN
ejpam-5826	85	3	(	(	PUNCT
ejpam-5826	85	4	1−	1−	NUM
ejpam-5826	85	5	λ)q	λ)q	ADJ
ejpam-5826	85	6	,	,	PUNCT
ejpam-5826	85	7	p	p	X
ejpam-5826	85	8	,	,	PUNCT
ejpam-5826	85	9	q	q	PROPN
ejpam-5826	85	10	∈	∈	PROPN
ejpam-5826	85	11	q	q	NOUN
ejpam-5826	85	12	and	and	CCONJ
ejpam-5826	85	13	λ	λ	X
ejpam-5826	85	14	∈	∈	PROPN
ejpam-5826	86	1	[	[	X
ejpam-5826	86	2	0	0	NUM
ejpam-5826	86	3	,	,	PUNCT
ejpam-5826	86	4	1	1	NUM
ejpam-5826	86	5	]	]	PUNCT
ejpam-5826	86	6	.	.	PUNCT
ejpam-5826	87	1	if	if	SCONJ
ejpam-5826	87	2	j	j	PROPN
ejpam-5826	87	3	is	be	AUX
ejpam-5826	87	4	a	a	DET
ejpam-5826	87	5	convex	convex	NOUN
ejpam-5826	87	6	subset	subset	NOUN
ejpam-5826	87	7	of	of	ADP
ejpam-5826	87	8	a	a	DET
ejpam-5826	87	9	normed	normed	ADJ
ejpam-5826	87	10	space	space	NOUN
ejpam-5826	87	11	and	and	CCONJ
ejpam-5826	87	12	e	e	NOUN
ejpam-5826	87	13	:	:	PUNCT
ejpam-5826	87	14	j	j	PROPN
ejpam-5826	87	15	→	→	SYM
ejpam-5826	87	16	j	j	PROPN
ejpam-5826	87	17	,	,	PUNCT
ejpam-5826	87	18	then	then	ADV
ejpam-5826	87	19	the	the	DET
ejpam-5826	87	20	average	average	ADJ
ejpam-5826	87	21	mapping	mapping	NOUN
ejpam-5826	87	22	eµ	eµ	INTJ
ejpam-5826	87	23	:	:	PUNCT
ejpam-5826	87	24	j	j	PROPN
ejpam-5826	87	25	→	→	SYM
ejpam-5826	87	26	j	j	PROPN
ejpam-5826	87	27	is	be	AUX
ejpam-5826	87	28	given	give	VERB
ejpam-5826	87	29	by	by	ADP
ejpam-5826	87	30	eµp	eµp	NOUN
ejpam-5826	87	31	=	=	SYM
ejpam-5826	87	32	(	(	PUNCT
ejpam-5826	87	33	1−	1−	NUM
ejpam-5826	87	34	µ)p+	µ)p+	NUM
ejpam-5826	87	35	µep	µep	PROPN
ejpam-5826	87	36	,	,	PUNCT
ejpam-5826	87	37	where	where	SCONJ
ejpam-5826	87	38	µ	µ	X
ejpam-5826	87	39	∈	∈	X
ejpam-5826	87	40	(	(	PUNCT
ejpam-5826	87	41	0	0	NUM
ejpam-5826	87	42	,	,	PUNCT
ejpam-5826	87	43	1	1	NUM
ejpam-5826	87	44	]	]	PUNCT
ejpam-5826	87	45	.	.	PUNCT
ejpam-5826	88	1	a	a	DET
ejpam-5826	88	2	hyperbolic	hyperbolic	ADJ
ejpam-5826	88	3	space	space	NOUN
ejpam-5826	88	4	(	(	PUNCT
ejpam-5826	88	5	q	q	NOUN
ejpam-5826	88	6	,	,	PUNCT
ejpam-5826	88	7	d	d	PROPN
ejpam-5826	88	8	,	,	PUNCT
ejpam-5826	88	9	η	η	NOUN
ejpam-5826	88	10	)	)	PUNCT
ejpam-5826	88	11	is	be	AUX
ejpam-5826	88	12	said	say	VERB
ejpam-5826	88	13	to	to	PART
ejpam-5826	88	14	be	be	AUX
ejpam-5826	88	15	uniformly	uniformly	ADV
ejpam-5826	88	16	convex	convex	ADJ
ejpam-5826	88	17	if	if	SCONJ
ejpam-5826	88	18	for	for	ADP
ejpam-5826	88	19	all	all	DET
ejpam-5826	88	20	x	x	NOUN
ejpam-5826	88	21	,	,	PUNCT
ejpam-5826	88	22	y	y	PROPN
ejpam-5826	88	23	,	,	PUNCT
ejpam-5826	88	24	z	z	PROPN
ejpam-5826	88	25	∈	∈	PROPN
ejpam-5826	89	1	q	q	NOUN
ejpam-5826	89	2	,	,	PUNCT
ejpam-5826	89	3	r	r	NOUN
ejpam-5826	89	4	>	>	X
ejpam-5826	89	5	0	0	PUNCT
ejpam-5826	89	6	and	and	CCONJ
ejpam-5826	89	7	ε	ε	PROPN
ejpam-5826	89	8	∈	∈	PROPN
ejpam-5826	89	9	(	(	PUNCT
ejpam-5826	89	10	0	0	NUM
ejpam-5826	89	11	,	,	PUNCT
ejpam-5826	89	12	2	2	NUM
ejpam-5826	89	13	]	]	PUNCT
ejpam-5826	89	14	,	,	PUNCT
ejpam-5826	89	15	there	there	PRON
ejpam-5826	89	16	exists	exist	VERB
ejpam-5826	89	17	δ	δ	PROPN
ejpam-5826	89	18	∈	∈	PROPN
ejpam-5826	89	19	(	(	PUNCT
ejpam-5826	89	20	0	0	NUM
ejpam-5826	89	21	,	,	PUNCT
ejpam-5826	89	22	1	1	NUM
ejpam-5826	89	23	]	]	PUNCT
ejpam-5826	89	24	such	such	ADJ
ejpam-5826	89	25	that	that	SCONJ
ejpam-5826	89	26	d	d	PROPN
ejpam-5826	89	27	(	(	PUNCT
ejpam-5826	89	28	η	η	PROPN
ejpam-5826	89	29	(	(	PUNCT
ejpam-5826	89	30	x	x	PROPN
ejpam-5826	89	31	,	,	PUNCT
ejpam-5826	89	32	y	y	PROPN
ejpam-5826	89	33	,	,	PUNCT
ejpam-5826	89	34	1/2	1/2	NUM
ejpam-5826	89	35	)	)	PUNCT
ejpam-5826	89	36	,	,	PUNCT
ejpam-5826	89	37	z	z	X
ejpam-5826	89	38	)	)	PUNCT
ejpam-5826	89	39	≤	≤	NOUN
ejpam-5826	89	40	(	(	PUNCT
ejpam-5826	89	41	1	1	NUM
ejpam-5826	89	42	−	−	NOUN
ejpam-5826	89	43	δ)r	δ)r	NOUN
ejpam-5826	89	44	whenever	whenever	SCONJ
ejpam-5826	89	45	d(x	d(x	PROPN
ejpam-5826	89	46	,	,	PUNCT
ejpam-5826	89	47	z	z	NOUN
ejpam-5826	89	48	)	)	PUNCT
ejpam-5826	89	49	≤	≤	NOUN
ejpam-5826	89	50	r	r	NOUN
ejpam-5826	89	51	and	and	CCONJ
ejpam-5826	89	52	d(y	d(y	NOUN
ejpam-5826	89	53	,	,	PUNCT
ejpam-5826	89	54	z	z	NOUN
ejpam-5826	89	55	)	)	PUNCT
ejpam-5826	89	56	≤	≤	NOUN
ejpam-5826	89	57	r	r	NOUN
ejpam-5826	89	58	and	and	CCONJ
ejpam-5826	89	59	d(x	d(x	PROPN
ejpam-5826	89	60	,	,	PUNCT
ejpam-5826	89	61	y	y	PROPN
ejpam-5826	89	62	)	)	PUNCT
ejpam-5826	89	63	≥	≥	NOUN
ejpam-5826	89	64	εr	εr	VERB
ejpam-5826	89	65	.	.	PUNCT
ejpam-5826	90	1	a	a	DET
ejpam-5826	90	2	map	map	NOUN
ejpam-5826	90	3	h	h	NOUN
ejpam-5826	90	4	:	:	PUNCT
ejpam-5826	90	5	(	(	PUNCT
ejpam-5826	90	6	0,∞	0,∞	NUM
ejpam-5826	90	7	)	)	PUNCT
ejpam-5826	90	8	×	×	NOUN
ejpam-5826	90	9	(	(	PUNCT
ejpam-5826	90	10	0	0	NUM
ejpam-5826	90	11	,	,	PUNCT
ejpam-5826	90	12	2	2	NUM
ejpam-5826	90	13	]	]	PUNCT
ejpam-5826	90	14	→	→	X
ejpam-5826	90	15	(	(	PUNCT
ejpam-5826	90	16	0	0	NUM
ejpam-5826	90	17	,	,	PUNCT
ejpam-5826	90	18	1	1	NUM
ejpam-5826	90	19	]	]	PUNCT
ejpam-5826	90	20	which	which	PRON
ejpam-5826	90	21	provides	provide	VERB
ejpam-5826	90	22	in	in	ADP
ejpam-5826	90	23	the	the	DET
ejpam-5826	90	24	above	above	ADJ
ejpam-5826	90	25	definition	definition	NOUN
ejpam-5826	90	26	,	,	PUNCT
ejpam-5826	90	27	a	a	DET
ejpam-5826	90	28	δ	δ	NOUN
ejpam-5826	90	29	=	=	SYM
ejpam-5826	90	30	h(r	h(r	PROPN
ejpam-5826	90	31	,	,	PUNCT
ejpam-5826	90	32	ε	ε	PROPN
ejpam-5826	90	33	)	)	PUNCT
ejpam-5826	90	34	for	for	ADP
ejpam-5826	90	35	r	r	NOUN
ejpam-5826	90	36	>	>	X
ejpam-5826	90	37	0	0	PUNCT
ejpam-5826	90	38	and	and	CCONJ
ejpam-5826	90	39	for	for	ADP
ejpam-5826	90	40	a	a	DET
ejpam-5826	90	41	fixed	fix	VERB
ejpam-5826	90	42	ε	ε	PROPN
ejpam-5826	90	43	∈	∈	PROPN
ejpam-5826	90	44	(	(	PUNCT
ejpam-5826	90	45	0	0	NUM
ejpam-5826	90	46	,	,	PUNCT
ejpam-5826	90	47	2	2	NUM
ejpam-5826	90	48	]	]	PUNCT
ejpam-5826	90	49	,	,	PUNCT
ejpam-5826	90	50	is	be	AUX
ejpam-5826	90	51	called	call	VERB
ejpam-5826	90	52	modulus	modulus	NOUN
ejpam-5826	90	53	of	of	ADP
ejpam-5826	90	54	uniform	uniform	ADJ
ejpam-5826	90	55	convexity	convexity	NOUN
ejpam-5826	90	56	.	.	PUNCT
ejpam-5826	91	1	we	we	PRON
ejpam-5826	91	2	call	call	VERB
ejpam-5826	91	3	h	h	NOUN
ejpam-5826	91	4	monotone	monotone	NOUN
ejpam-5826	91	5	if	if	SCONJ
ejpam-5826	91	6	it	it	PRON
ejpam-5826	91	7	decreases	decrease	VERB
ejpam-5826	91	8	with	with	ADP
ejpam-5826	91	9	r	r	NOUN
ejpam-5826	91	10	(	(	PUNCT
ejpam-5826	91	11	for	for	ADP
ejpam-5826	91	12	a	a	DET
ejpam-5826	91	13	fixed	fix	VERB
ejpam-5826	91	14	ε	ε	PROPN
ejpam-5826	91	15	)	)	PUNCT
ejpam-5826	91	16	.	.	PUNCT
ejpam-5826	92	1	let	let	AUX
ejpam-5826	92	2	{	{	PUNCT
ejpam-5826	92	3	qn	qn	PART
ejpam-5826	92	4	}	}	PUNCT
ejpam-5826	92	5	be	be	AUX
ejpam-5826	92	6	a	a	DET
ejpam-5826	92	7	bounded	bounded	ADJ
ejpam-5826	92	8	sequence	sequence	NOUN
ejpam-5826	92	9	in	in	ADP
ejpam-5826	92	10	a	a	DET
ejpam-5826	92	11	hyperbolic	hyperbolic	ADJ
ejpam-5826	92	12	space	space	NOUN
ejpam-5826	92	13	q.	q.	NOUN
ejpam-5826	92	14	for	for	ADP
ejpam-5826	92	15	q	q	PROPN
ejpam-5826	92	16	∈	∈	PROPN
ejpam-5826	92	17	q	q	NOUN
ejpam-5826	92	18	,	,	PUNCT
ejpam-5826	92	19	we	we	PRON
ejpam-5826	92	20	define	define	VERB
ejpam-5826	92	21	a	a	DET
ejpam-5826	92	22	continuous	continuous	ADJ
ejpam-5826	92	23	functional	functional	ADJ
ejpam-5826	92	24	r	r	NOUN
ejpam-5826	92	25	(	(	PUNCT
ejpam-5826	92	26	.	.	NUM
ejpam-5826	92	27	,	,	PUNCT
ejpam-5826	92	28	{	{	PUNCT
ejpam-5826	92	29	qn	qn	NOUN
ejpam-5826	92	30	}	}	PUNCT
ejpam-5826	92	31	)	)	PUNCT
ejpam-5826	92	32	:	:	PUNCT
ejpam-5826	92	33	q	q	X
ejpam-5826	93	1	→	→	PUNCT
ejpam-5826	93	2	[	[	X
ejpam-5826	93	3	0,∞	0,∞	NOUN
ejpam-5826	93	4	)	)	PUNCT
ejpam-5826	93	5	by	by	ADP
ejpam-5826	93	6	r(q	r(q	PROPN
ejpam-5826	93	7	,	,	PUNCT
ejpam-5826	93	8	{	{	PUNCT
ejpam-5826	93	9	qn	qn	NOUN
ejpam-5826	93	10	}	}	PUNCT
ejpam-5826	93	11	)	)	PUNCT
ejpam-5826	94	1	=	=	SYM
ejpam-5826	94	2	lim	lim	PROPN
ejpam-5826	94	3	n→∞	n→∞	NUM
ejpam-5826	94	4	sup	sup	PROPN
ejpam-5826	94	5	d(qn	d(qn	PROPN
ejpam-5826	94	6	,	,	PUNCT
ejpam-5826	94	7	q	q	NOUN
ejpam-5826	94	8	)	)	PUNCT
ejpam-5826	94	9	.	.	PUNCT
ejpam-5826	95	1	the	the	DET
ejpam-5826	95	2	aymptotic	aymptotic	ADJ
ejpam-5826	95	3	radius	radius	NOUN
ejpam-5826	95	4	ρ	ρ	PROPN
ejpam-5826	95	5	=	=	SYM
ejpam-5826	95	6	r({qn	r({qn	PROPN
ejpam-5826	95	7	}	}	PUNCT
ejpam-5826	95	8	)	)	PUNCT
ejpam-5826	95	9	of	of	ADP
ejpam-5826	95	10	{	{	PUNCT
ejpam-5826	95	11	qn	qn	NOUN
ejpam-5826	95	12	}	}	PUNCT
ejpam-5826	95	13	is	be	AUX
ejpam-5826	95	14	given	give	VERB
ejpam-5826	95	15	by	by	ADP
ejpam-5826	95	16	ρ	ρ	PROPN
ejpam-5826	95	17	=	=	SYM
ejpam-5826	95	18	inf{r(q	inf{r(q	PROPN
ejpam-5826	95	19	,	,	PUNCT
ejpam-5826	95	20	{	{	PUNCT
ejpam-5826	95	21	qn	qn	NOUN
ejpam-5826	95	22	}	}	PUNCT
ejpam-5826	95	23	)	)	PUNCT
ejpam-5826	95	24	:	:	PUNCT
ejpam-5826	95	25	q	q	PUNCT
ejpam-5826	95	26	∈	∈	PROPN
ejpam-5826	95	27	q	q	X
ejpam-5826	95	28	}	}	PUNCT
ejpam-5826	95	29	.	.	PUNCT
ejpam-5826	96	1	the	the	DET
ejpam-5826	96	2	asymptotic	asymptotic	ADJ
ejpam-5826	96	3	center	center	NOUN
ejpam-5826	96	4	of	of	ADP
ejpam-5826	96	5	a	a	DET
ejpam-5826	96	6	bounded	bounded	ADJ
ejpam-5826	96	7	sequence	sequence	NOUN
ejpam-5826	96	8	{	{	PUNCT
ejpam-5826	96	9	qn	qn	NOUN
ejpam-5826	96	10	}	}	PUNCT
ejpam-5826	96	11	with	with	ADP
ejpam-5826	96	12	respect	respect	NOUN
ejpam-5826	96	13	to	to	ADP
ejpam-5826	96	14	a	a	DET
ejpam-5826	96	15	subset	subset	ADJ
ejpam-5826	96	16	u	u	NOUN
ejpam-5826	96	17	of	of	ADP
ejpam-5826	96	18	q	q	PROPN
ejpam-5826	96	19	is	be	AUX
ejpam-5826	96	20	defined	define	VERB
ejpam-5826	96	21	as	as	ADP
ejpam-5826	96	22	:	:	PUNCT
ejpam-5826	96	23	au	au	X
ejpam-5826	96	24	(	(	PUNCT
ejpam-5826	96	25	{	{	PUNCT
ejpam-5826	96	26	qn	qn	NOUN
ejpam-5826	96	27	}	}	PUNCT
ejpam-5826	96	28	)	)	PUNCT
ejpam-5826	97	1	=	=	PRON
ejpam-5826	97	2	{	{	PUNCT
ejpam-5826	97	3	q	q	NOUN
ejpam-5826	97	4	∈	∈	PROPN
ejpam-5826	97	5	q	q	NOUN
ejpam-5826	97	6	:	:	PUNCT
ejpam-5826	97	7	r(q	r(q	PROPN
ejpam-5826	97	8	,	,	PUNCT
ejpam-5826	97	9	{	{	PUNCT
ejpam-5826	97	10	qn	qn	NOUN
ejpam-5826	97	11	}	}	PUNCT
ejpam-5826	97	12	)	)	PUNCT
ejpam-5826	97	13	≤	≤	NUM
ejpam-5826	97	14	r(p	r(p	NOUN
ejpam-5826	97	15	,	,	PUNCT
ejpam-5826	97	16	{	{	PUNCT
ejpam-5826	97	17	qn	qn	NOUN
ejpam-5826	97	18	}	}	PUNCT
ejpam-5826	97	19	)	)	PUNCT
ejpam-5826	97	20	for	for	ADP
ejpam-5826	97	21	any	any	DET
ejpam-5826	97	22	p	p	PROPN
ejpam-5826	97	23	∈	∈	PROPN
ejpam-5826	97	24	u	u	NOUN
ejpam-5826	97	25	}	}	PUNCT
ejpam-5826	97	26	.	.	PUNCT
ejpam-5826	98	1	if	if	SCONJ
ejpam-5826	98	2	the	the	DET
ejpam-5826	98	3	asymptotic	asymptotic	ADJ
ejpam-5826	98	4	center	center	NOUN
ejpam-5826	98	5	is	be	AUX
ejpam-5826	98	6	taken	take	VERB
ejpam-5826	98	7	with	with	ADP
ejpam-5826	98	8	respect	respect	NOUN
ejpam-5826	98	9	to	to	ADP
ejpam-5826	98	10	q	q	NOUN
ejpam-5826	98	11	,	,	PUNCT
ejpam-5826	98	12	then	then	ADV
ejpam-5826	98	13	it	it	PRON
ejpam-5826	98	14	is	be	AUX
ejpam-5826	98	15	simply	simply	ADV
ejpam-5826	98	16	denoted	denote	VERB
ejpam-5826	98	17	by	by	ADP
ejpam-5826	98	18	a({qn	a({qn	PROPN
ejpam-5826	98	19	}	}	PUNCT
ejpam-5826	98	20	)	)	PUNCT
ejpam-5826	98	21	.	.	PUNCT
ejpam-5826	99	1	it	it	PRON
ejpam-5826	99	2	is	be	AUX
ejpam-5826	99	3	known	know	VERB
ejpam-5826	99	4	that	that	SCONJ
ejpam-5826	99	5	uniformly	uniformly	ADV
ejpam-5826	99	6	convex	convex	VERB
ejpam-5826	99	7	banach	banach	NOUN
ejpam-5826	99	8	spaces	space	NOUN
ejpam-5826	99	9	and	and	CCONJ
ejpam-5826	99	10	even	even	ADV
ejpam-5826	99	11	cat(0	cat(0	ADJ
ejpam-5826	99	12	)	)	PUNCT
ejpam-5826	99	13	spaces	space	NOUN
ejpam-5826	99	14	enjoy	enjoy	VERB
ejpam-5826	99	15	the	the	DET
ejpam-5826	99	16	property	property	NOUN
ejpam-5826	99	17	that	that	PRON
ejpam-5826	99	18	”	"	PUNCT
ejpam-5826	99	19	bounded	bound	VERB
ejpam-5826	99	20	sequences	sequence	NOUN
ejpam-5826	99	21	have	have	VERB
ejpam-5826	99	22	unique	unique	ADJ
ejpam-5826	99	23	asymptotic	asymptotic	ADJ
ejpam-5826	99	24	centers	center	NOUN
ejpam-5826	99	25	with	with	ADP
ejpam-5826	99	26	respect	respect	NOUN
ejpam-5826	99	27	to	to	ADP
ejpam-5826	99	28	closed	close	VERB
ejpam-5826	99	29	convex	convex	ADJ
ejpam-5826	99	30	subsets	subset	NOUN
ejpam-5826	99	31	”	"	PUNCT
ejpam-5826	99	32	.	.	PUNCT
ejpam-5826	100	1	the	the	DET
ejpam-5826	100	2	following	follow	VERB
ejpam-5826	100	3	lemma	lemma	PROPN
ejpam-5826	100	4	ensures	ensure	VERB
ejpam-5826	100	5	that	that	SCONJ
ejpam-5826	100	6	this	this	DET
ejpam-5826	100	7	property	property	NOUN
ejpam-5826	100	8	also	also	ADV
ejpam-5826	100	9	holds	hold	VERB
ejpam-5826	100	10	in	in	ADP
ejpam-5826	100	11	complete	complete	ADJ
ejpam-5826	100	12	uniformly	uniformly	ADV
ejpam-5826	100	13	convex	convex	ADJ
ejpam-5826	100	14	hyperbolic	hyperbolic	ADJ
ejpam-5826	100	15	spaces	space	NOUN
ejpam-5826	100	16	.	.	PUNCT
ejpam-5826	101	1	a.	a.	PROPN
ejpam-5826	101	2	r.	r.	PROPN
ejpam-5826	101	3	khan	khan	PROPN
ejpam-5826	101	4	et	et	PROPN
ejpam-5826	101	5	al	al	PROPN
ejpam-5826	101	6	.	.	PUNCT
ejpam-5826	101	7	/	/	SYM
ejpam-5826	101	8	eur	eur	PROPN
ejpam-5826	101	9	.	.	PUNCT
ejpam-5826	102	1	j.	j.	PROPN
ejpam-5826	102	2	pure	pure	PROPN
ejpam-5826	102	3	appl	appl	PROPN
ejpam-5826	102	4	.	.	PROPN
ejpam-5826	102	5	math	math	PROPN
ejpam-5826	102	6	,	,	PUNCT
ejpam-5826	102	7	18	18	NUM
ejpam-5826	102	8	(	(	PUNCT
ejpam-5826	102	9	2	2	NUM
ejpam-5826	102	10	)	)	PUNCT
ejpam-5826	102	11	(	(	PUNCT
ejpam-5826	102	12	2025	2025	NUM
ejpam-5826	102	13	)	)	PUNCT
ejpam-5826	102	14	,	,	PUNCT
ejpam-5826	102	15	5826	5826	NUM
ejpam-5826	102	16	5	5	NUM
ejpam-5826	102	17	of	of	ADP
ejpam-5826	102	18	23	23	NUM
ejpam-5826	102	19	lemma	lemma	PROPN
ejpam-5826	102	20	2	2	NUM
ejpam-5826	102	21	.	.	PUNCT
ejpam-5826	103	1	(	(	PUNCT
ejpam-5826	103	2	[	[	X
ejpam-5826	103	3	16	16	NUM
ejpam-5826	103	4	,	,	PUNCT
ejpam-5826	103	5	lemma	lemma	PROPN
ejpam-5826	103	6	2.2	2.2	NUM
ejpam-5826	103	7	]	]	PUNCT
ejpam-5826	103	8	)	)	PUNCT
ejpam-5826	103	9	.	.	PUNCT
ejpam-5826	104	1	let	let	AUX
ejpam-5826	104	2	(	(	PUNCT
ejpam-5826	104	3	q	q	ADJ
ejpam-5826	104	4	,	,	PUNCT
ejpam-5826	104	5	d	d	PROPN
ejpam-5826	104	6	,	,	PUNCT
ejpam-5826	104	7	η	η	NOUN
ejpam-5826	104	8	)	)	PUNCT
ejpam-5826	104	9	be	be	AUX
ejpam-5826	104	10	a	a	DET
ejpam-5826	104	11	complete	complete	ADJ
ejpam-5826	104	12	uniformly	uniformly	ADV
ejpam-5826	104	13	convex	convex	ADJ
ejpam-5826	104	14	hyperbolic	hyperbolic	ADJ
ejpam-5826	104	15	space	space	NOUN
ejpam-5826	104	16	with	with	ADP
ejpam-5826	104	17	monotone	monotone	ADJ
ejpam-5826	104	18	modulus	modulus	NOUN
ejpam-5826	104	19	of	of	ADP
ejpam-5826	104	20	uniform	uniform	ADJ
ejpam-5826	104	21	convexity	convexity	NOUN
ejpam-5826	104	22	.	.	PUNCT
ejpam-5826	105	1	then	then	ADV
ejpam-5826	105	2	every	every	DET
ejpam-5826	105	3	bounded	bounded	ADJ
ejpam-5826	105	4	sequence	sequence	NOUN
ejpam-5826	105	5	{	{	PUNCT
ejpam-5826	105	6	qn	qn	NOUN
ejpam-5826	105	7	}	}	PUNCT
ejpam-5826	105	8	in	in	ADP
ejpam-5826	105	9	q	q	PROPN
ejpam-5826	105	10	has	have	VERB
ejpam-5826	105	11	a	a	DET
ejpam-5826	105	12	unique	unique	ADJ
ejpam-5826	105	13	asymptotic	asymptotic	ADJ
ejpam-5826	105	14	center	center	NOUN
ejpam-5826	105	15	with	with	ADP
ejpam-5826	105	16	respect	respect	NOUN
ejpam-5826	105	17	to	to	ADP
ejpam-5826	105	18	any	any	DET
ejpam-5826	105	19	nonempty	nonempty	ADV
ejpam-5826	105	20	closed	close	VERB
ejpam-5826	105	21	convex	convex	NOUN
ejpam-5826	105	22	subset	subset	VERB
ejpam-5826	105	23	u	u	NOUN
ejpam-5826	105	24	of	of	ADP
ejpam-5826	105	25	q.	q.	PROPN
ejpam-5826	105	26	recall	recall	PROPN
ejpam-5826	105	27	that	that	SCONJ
ejpam-5826	105	28	a	a	DET
ejpam-5826	105	29	bounded	bounded	ADJ
ejpam-5826	105	30	sequence	sequence	NOUN
ejpam-5826	105	31	{	{	PUNCT
ejpam-5826	105	32	qn	qn	NOUN
ejpam-5826	105	33	}	}	PUNCT
ejpam-5826	105	34	in	in	ADP
ejpam-5826	105	35	q	q	PROPN
ejpam-5826	105	36	is	be	AUX
ejpam-5826	105	37	known	know	VERB
ejpam-5826	105	38	as	as	ADP
ejpam-5826	105	39	∆	∆	PROPN
ejpam-5826	105	40	−	−	PROPN
ejpam-5826	105	41	convergent	convergent	NOUN
ejpam-5826	105	42	to	to	ADP
ejpam-5826	105	43	q	q	PROPN
ejpam-5826	105	44	∈	∈	PROPN
ejpam-5826	105	45	q	q	NOUN
ejpam-5826	105	46	if	if	SCONJ
ejpam-5826	105	47	q	q	ADJ
ejpam-5826	105	48	is	be	AUX
ejpam-5826	105	49	the	the	DET
ejpam-5826	105	50	unique	unique	ADJ
ejpam-5826	105	51	asymptotic	asymptotic	ADJ
ejpam-5826	105	52	center	center	NOUN
ejpam-5826	105	53	of	of	ADP
ejpam-5826	105	54	{	{	PUNCT
ejpam-5826	105	55	un	un	PROPN
ejpam-5826	105	56	}	}	PUNCT
ejpam-5826	105	57	for	for	ADP
ejpam-5826	105	58	every	every	DET
ejpam-5826	105	59	subsequence	subsequence	NOUN
ejpam-5826	105	60	{	{	PUNCT
ejpam-5826	105	61	un}of	un}of	PROPN
ejpam-5826	105	62	{	{	PUNCT
ejpam-5826	105	63	qn	qn	NOUN
ejpam-5826	105	64	}	}	PUNCT
ejpam-5826	105	65	.	.	PUNCT
ejpam-5826	106	1	in	in	ADP
ejpam-5826	106	2	this	this	DET
ejpam-5826	106	3	case	case	NOUN
ejpam-5826	106	4	,	,	PUNCT
ejpam-5826	106	5	we	we	PRON
ejpam-5826	106	6	write	write	VERB
ejpam-5826	106	7	∆−	∆−	NOUN
ejpam-5826	106	8	lim	lim	PROPN
ejpam-5826	106	9	n→∞	n→∞	PRON
ejpam-5826	106	10	{	{	PUNCT
ejpam-5826	106	11	qn	qn	NOUN
ejpam-5826	106	12	}	}	PUNCT
ejpam-5826	106	13	=	=	PUNCT
ejpam-5826	106	14	q.	q.	NOUN
ejpam-5826	106	15	we	we	PRON
ejpam-5826	106	16	include	include	VERB
ejpam-5826	106	17	the	the	DET
ejpam-5826	106	18	following	follow	VERB
ejpam-5826	106	19	lemmas	lemma	NOUN
ejpam-5826	106	20	of	of	ADP
ejpam-5826	106	21	berinde	berinde	NOUN
ejpam-5826	106	22	and	and	CCONJ
ejpam-5826	106	23	pacurar	pacurar	NOUN
ejpam-5826	106	24	[	[	X
ejpam-5826	106	25	17	17	NUM
ejpam-5826	106	26	,	,	PUNCT
ejpam-5826	106	27	18	18	NUM
ejpam-5826	106	28	]	]	PUNCT
ejpam-5826	106	29	for	for	ADP
ejpam-5826	106	30	a	a	DET
ejpam-5826	106	31	ready	ready	ADJ
ejpam-5826	106	32	reference	reference	NOUN
ejpam-5826	106	33	.	.	PUNCT
ejpam-5826	107	1	lemma	lemma	PROPN
ejpam-5826	107	2	3	3	X
ejpam-5826	107	3	.	.	PUNCT
ejpam-5826	108	1	let	let	VERB
ejpam-5826	108	2	(	(	PUNCT
ejpam-5826	108	3	q	q	X
ejpam-5826	108	4	,	,	PUNCT
ejpam-5826	108	5	d	d	NOUN
ejpam-5826	108	6	,	,	PUNCT
ejpam-5826	108	7	w	w	NOUN
ejpam-5826	108	8	)	)	PUNCT
ejpam-5826	108	9	be	be	AUX
ejpam-5826	108	10	a	a	DET
ejpam-5826	108	11	convex	convex	ADJ
ejpam-5826	108	12	metric	metric	ADJ
ejpam-5826	108	13	space	space	NOUN
ejpam-5826	108	14	.	.	PUNCT
ejpam-5826	109	1	for	for	ADP
ejpam-5826	109	2	all	all	DET
ejpam-5826	109	3	x	x	NOUN
ejpam-5826	109	4	,	,	PUNCT
ejpam-5826	109	5	y	y	PROPN
ejpam-5826	109	6	∈	∈	PROPN
ejpam-5826	109	7	q	q	X
ejpam-5826	109	8	and	and	CCONJ
ejpam-5826	109	9	any	any	DET
ejpam-5826	109	10	λ	λ	X
ejpam-5826	109	11	∈	∈	PROPN
ejpam-5826	110	1	[	[	X
ejpam-5826	110	2	0	0	NUM
ejpam-5826	110	3	,	,	PUNCT
ejpam-5826	110	4	1	1	NUM
ejpam-5826	110	5	]	]	PUNCT
ejpam-5826	110	6	,	,	PUNCT
ejpam-5826	110	7	we	we	PRON
ejpam-5826	110	8	have	have	VERB
ejpam-5826	110	9	d(x	d(x	NOUN
ejpam-5826	110	10	,	,	PUNCT
ejpam-5826	110	11	y	y	NOUN
ejpam-5826	110	12	)	)	PUNCT
ejpam-5826	111	1	=	=	SYM
ejpam-5826	111	2	d(x	d(x	PROPN
ejpam-5826	111	3	,	,	PUNCT
ejpam-5826	111	4	w	w	PROPN
ejpam-5826	111	5	(	(	PUNCT
ejpam-5826	111	6	x	x	NOUN
ejpam-5826	111	7	,	,	PUNCT
ejpam-5826	111	8	y;λ	y;λ	PROPN
ejpam-5826	111	9	)	)	PUNCT
ejpam-5826	111	10	)	)	PUNCT
ejpam-5826	112	1	+	+	CCONJ
ejpam-5826	112	2	d(w	d(w	PROPN
ejpam-5826	112	3	(	(	PUNCT
ejpam-5826	112	4	x	x	NOUN
ejpam-5826	112	5	,	,	PUNCT
ejpam-5826	112	6	y;λ	y;λ	PROPN
ejpam-5826	112	7	)	)	PUNCT
ejpam-5826	112	8	,	,	PUNCT
ejpam-5826	112	9	y	y	PROPN
ejpam-5826	112	10	)	)	PUNCT
ejpam-5826	112	11	.	.	PUNCT
ejpam-5826	113	1	proof	proof	NOUN
ejpam-5826	113	2	.	.	PUNCT
ejpam-5826	114	1	by	by	ADP
ejpam-5826	114	2	the	the	DET
ejpam-5826	114	3	triangular	triangular	NOUN
ejpam-5826	114	4	inequality	inequality	NOUN
ejpam-5826	114	5	and	and	CCONJ
ejpam-5826	114	6	(	(	PUNCT
ejpam-5826	114	7	η1	η1	NOUN
ejpam-5826	114	8	)	)	PUNCT
ejpam-5826	114	9	,	,	PUNCT
ejpam-5826	114	10	we	we	PRON
ejpam-5826	114	11	get	get	VERB
ejpam-5826	114	12	d(x	d(x	NOUN
ejpam-5826	114	13	,	,	PUNCT
ejpam-5826	114	14	y	y	NOUN
ejpam-5826	114	15	)	)	PUNCT
ejpam-5826	114	16	≤	≤	NOUN
ejpam-5826	114	17	d(x	d(x	NOUN
ejpam-5826	114	18	,	,	PUNCT
ejpam-5826	114	19	w	w	NOUN
ejpam-5826	114	20	(	(	PUNCT
ejpam-5826	114	21	x	x	NOUN
ejpam-5826	114	22	,	,	PUNCT
ejpam-5826	114	23	y;λ	y;λ	PROPN
ejpam-5826	114	24	)	)	PUNCT
ejpam-5826	114	25	)	)	PUNCT
ejpam-5826	115	1	+	+	CCONJ
ejpam-5826	115	2	d(w	d(w	PROPN
ejpam-5826	115	3	(	(	PUNCT
ejpam-5826	115	4	x	x	NOUN
ejpam-5826	115	5	,	,	PUNCT
ejpam-5826	115	6	y;λ	y;λ	PROPN
ejpam-5826	115	7	)	)	PUNCT
ejpam-5826	115	8	,	,	PUNCT
ejpam-5826	115	9	y	y	NOUN
ejpam-5826	115	10	)	)	PUNCT
ejpam-5826	115	11	≤	≤	NOUN
ejpam-5826	115	12	λd(x	λd(x	PUNCT
ejpam-5826	115	13	,	,	PUNCT
ejpam-5826	115	14	x	x	X
ejpam-5826	115	15	)	)	PUNCT
ejpam-5826	115	16	+	+	CCONJ
ejpam-5826	115	17	(	(	PUNCT
ejpam-5826	115	18	1−	1−	NUM
ejpam-5826	115	19	λ)d(x	λ)d(x	NOUN
ejpam-5826	115	20	,	,	PUNCT
ejpam-5826	115	21	y	y	NOUN
ejpam-5826	115	22	)	)	PUNCT
ejpam-5826	115	23	+	+	CCONJ
ejpam-5826	115	24	λd(x	λd(x	NUM
ejpam-5826	115	25	,	,	PUNCT
ejpam-5826	115	26	y	y	NOUN
ejpam-5826	115	27	)	)	PUNCT
ejpam-5826	115	28	+	+	CCONJ
ejpam-5826	115	29	(	(	PUNCT
ejpam-5826	115	30	1−	1−	NUM
ejpam-5826	115	31	λ)d(y	λ)d(y	PROPN
ejpam-5826	115	32	,	,	PUNCT
ejpam-5826	115	33	y	y	NOUN
ejpam-5826	115	34	)	)	PUNCT
ejpam-5826	115	35	=	=	SYM
ejpam-5826	115	36	d(x	d(x	PROPN
ejpam-5826	115	37	,	,	PUNCT
ejpam-5826	115	38	y	y	PROPN
ejpam-5826	115	39	)	)	PUNCT
ejpam-5826	115	40	.	.	PUNCT
ejpam-5826	116	1	lemma	lemma	PROPN
ejpam-5826	116	2	4	4	X
ejpam-5826	116	3	.	.	PUNCT
ejpam-5826	117	1	let	let	VERB
ejpam-5826	117	2	(	(	PUNCT
ejpam-5826	117	3	q	q	X
ejpam-5826	117	4	,	,	PUNCT
ejpam-5826	117	5	d	d	NOUN
ejpam-5826	117	6	,	,	PUNCT
ejpam-5826	117	7	w	w	PROPN
ejpam-5826	117	8	)	)	PUNCT
ejpam-5826	117	9	be	be	AUX
ejpam-5826	117	10	a	a	DET
ejpam-5826	117	11	convex	convex	ADJ
ejpam-5826	117	12	metric	metric	ADJ
ejpam-5826	117	13	space	space	NOUN
ejpam-5826	117	14	.	.	PUNCT
ejpam-5826	118	1	for	for	ADP
ejpam-5826	118	2	all	all	DET
ejpam-5826	118	3	x	x	NOUN
ejpam-5826	118	4	,	,	PUNCT
ejpam-5826	118	5	y	y	PROPN
ejpam-5826	118	6	∈	∈	PROPN
ejpam-5826	118	7	q	q	X
ejpam-5826	118	8	and	and	CCONJ
ejpam-5826	118	9	any	any	DET
ejpam-5826	118	10	λ	λ	X
ejpam-5826	118	11	∈	∈	PROPN
ejpam-5826	119	1	[	[	X
ejpam-5826	119	2	0	0	NUM
ejpam-5826	119	3	,	,	PUNCT
ejpam-5826	119	4	1	1	NUM
ejpam-5826	119	5	]	]	PUNCT
ejpam-5826	119	6	,	,	PUNCT
ejpam-5826	119	7	we	we	PRON
ejpam-5826	119	8	have	have	VERB
ejpam-5826	119	9	d(x	d(x	NOUN
ejpam-5826	119	10	,	,	PUNCT
ejpam-5826	119	11	w	w	PROPN
ejpam-5826	119	12	(	(	PUNCT
ejpam-5826	119	13	x	x	NOUN
ejpam-5826	119	14	,	,	PUNCT
ejpam-5826	119	15	y;λ	y;λ	PROPN
ejpam-5826	119	16	)	)	PUNCT
ejpam-5826	119	17	)	)	PUNCT
ejpam-5826	120	1	=	=	PUNCT
ejpam-5826	120	2	(	(	PUNCT
ejpam-5826	120	3	1−	1−	NUM
ejpam-5826	120	4	λ)d(x	λ)d(x	NOUN
ejpam-5826	120	5	,	,	PUNCT
ejpam-5826	120	6	y	y	NOUN
ejpam-5826	120	7	)	)	PUNCT
ejpam-5826	120	8	and	and	CCONJ
ejpam-5826	120	9	d(w	d(w	PROPN
ejpam-5826	120	10	(	(	PUNCT
ejpam-5826	120	11	x	x	NOUN
ejpam-5826	120	12	,	,	PUNCT
ejpam-5826	120	13	y;λ	y;λ	PROPN
ejpam-5826	120	14	)	)	PUNCT
ejpam-5826	120	15	,	,	PUNCT
ejpam-5826	120	16	y	y	PROPN
ejpam-5826	120	17	)	)	PUNCT
ejpam-5826	120	18	=	=	SYM
ejpam-5826	121	1	λd(x	λd(x	X
ejpam-5826	121	2	,	,	PUNCT
ejpam-5826	121	3	y	y	NOUN
ejpam-5826	121	4	)	)	PUNCT
ejpam-5826	121	5	.	.	PUNCT
ejpam-5826	122	1	proof	proof	NOUN
ejpam-5826	122	2	.	.	PUNCT
ejpam-5826	123	1	by	by	ADP
ejpam-5826	123	2	(	(	PUNCT
ejpam-5826	123	3	η1	η1	NOUN
ejpam-5826	123	4	)	)	PUNCT
ejpam-5826	123	5	,	,	PUNCT
ejpam-5826	123	6	we	we	PRON
ejpam-5826	123	7	get	get	VERB
ejpam-5826	123	8	d(x	d(x	NOUN
ejpam-5826	123	9	,	,	PUNCT
ejpam-5826	123	10	w	w	NOUN
ejpam-5826	123	11	(	(	PUNCT
ejpam-5826	123	12	x	x	NOUN
ejpam-5826	123	13	,	,	PUNCT
ejpam-5826	123	14	y;λ	y;λ	PROPN
ejpam-5826	123	15	)	)	PUNCT
ejpam-5826	123	16	)	)	PUNCT
ejpam-5826	123	17	≤	≤	NOUN
ejpam-5826	123	18	(	(	PUNCT
ejpam-5826	123	19	1−	1−	NUM
ejpam-5826	123	20	λ)d(x	λ)d(x	NOUN
ejpam-5826	123	21	,	,	PUNCT
ejpam-5826	123	22	y	y	NOUN
ejpam-5826	123	23	)	)	PUNCT
ejpam-5826	123	24	,	,	PUNCT
ejpam-5826	123	25	and	and	CCONJ
ejpam-5826	123	26	d(w	d(w	PROPN
ejpam-5826	123	27	(	(	PUNCT
ejpam-5826	123	28	x	x	NOUN
ejpam-5826	123	29	,	,	PUNCT
ejpam-5826	123	30	y;λ	y;λ	PROPN
ejpam-5826	123	31	)	)	PUNCT
ejpam-5826	123	32	,	,	PUNCT
ejpam-5826	123	33	y	y	NOUN
ejpam-5826	123	34	)	)	PUNCT
ejpam-5826	123	35	≤	≤	NOUN
ejpam-5826	123	36	λd(x	λd(x	PUNCT
ejpam-5826	123	37	,	,	PUNCT
ejpam-5826	123	38	y	y	NOUN
ejpam-5826	123	39	)	)	PUNCT
ejpam-5826	123	40	.	.	PUNCT
ejpam-5826	124	1	if	if	SCONJ
ejpam-5826	124	2	we	we	PRON
ejpam-5826	124	3	had	have	VERB
ejpam-5826	124	4	strict	strict	ADJ
ejpam-5826	124	5	inequality	inequality	NOUN
ejpam-5826	124	6	in	in	ADP
ejpam-5826	124	7	either	either	PRON
ejpam-5826	124	8	of	of	ADP
ejpam-5826	124	9	the	the	DET
ejpam-5826	124	10	above	above	ADJ
ejpam-5826	124	11	two	two	NUM
ejpam-5826	124	12	inequalities	inequality	NOUN
ejpam-5826	124	13	,	,	PUNCT
ejpam-5826	124	14	then	then	ADV
ejpam-5826	124	15	,	,	PUNCT
ejpam-5826	124	16	by	by	ADP
ejpam-5826	124	17	lemma	lemma	PROPN
ejpam-5826	124	18	3	3	NUM
ejpam-5826	124	19	,	,	PUNCT
ejpam-5826	124	20	we	we	PRON
ejpam-5826	124	21	would	would	AUX
ejpam-5826	124	22	reach	reach	VERB
ejpam-5826	124	23	the	the	DET
ejpam-5826	124	24	contradiction	contradiction	NOUN
ejpam-5826	124	25	d(x	d(x	PROPN
ejpam-5826	124	26	,	,	PUNCT
ejpam-5826	124	27	y	y	NOUN
ejpam-5826	124	28	)	)	PUNCT
ejpam-5826	124	29	=	=	SYM
ejpam-5826	125	1	d(x	d(x	PROPN
ejpam-5826	125	2	,	,	PUNCT
ejpam-5826	125	3	w	w	PROPN
ejpam-5826	125	4	(	(	PUNCT
ejpam-5826	125	5	x	x	NOUN
ejpam-5826	125	6	,	,	PUNCT
ejpam-5826	125	7	y;λ	y;λ	PROPN
ejpam-5826	125	8	)	)	PUNCT
ejpam-5826	125	9	)	)	PUNCT
ejpam-5826	126	1	+	+	CCONJ
ejpam-5826	126	2	d(w	d(w	PROPN
ejpam-5826	126	3	(	(	PUNCT
ejpam-5826	126	4	x	x	NOUN
ejpam-5826	126	5	,	,	PUNCT
ejpam-5826	126	6	y;λ	y;λ	PROPN
ejpam-5826	126	7	)	)	PUNCT
ejpam-5826	126	8	,	,	PUNCT
ejpam-5826	126	9	y	y	PROPN
ejpam-5826	126	10	)	)	PUNCT
ejpam-5826	126	11	<	<	X
ejpam-5826	126	12	d(x	d(x	PROPN
ejpam-5826	126	13	,	,	PUNCT
ejpam-5826	126	14	y	y	PROPN
ejpam-5826	126	15	)	)	PUNCT
ejpam-5826	126	16	.	.	PUNCT
ejpam-5826	127	1	lemma	lemma	PROPN
ejpam-5826	127	2	5	5	X
ejpam-5826	127	3	.	.	PUNCT
ejpam-5826	128	1	let	let	VERB
ejpam-5826	128	2	(	(	PUNCT
ejpam-5826	128	3	q	q	X
ejpam-5826	128	4	,	,	PUNCT
ejpam-5826	128	5	d	d	NOUN
ejpam-5826	128	6	,	,	PUNCT
ejpam-5826	128	7	w	w	PROPN
ejpam-5826	128	8	)	)	PUNCT
ejpam-5826	128	9	be	be	AUX
ejpam-5826	128	10	a	a	DET
ejpam-5826	128	11	convex	convex	ADJ
ejpam-5826	128	12	metric	metric	ADJ
ejpam-5826	128	13	space	space	NOUN
ejpam-5826	128	14	and	and	CCONJ
ejpam-5826	128	15	e	e	NOUN
ejpam-5826	128	16	:	:	PUNCT
ejpam-5826	128	17	q	q	X
ejpam-5826	128	18	→	→	X
ejpam-5826	128	19	q	q	X
ejpam-5826	128	20	be	be	AUX
ejpam-5826	128	21	a	a	DET
ejpam-5826	128	22	mapping	mapping	NOUN
ejpam-5826	128	23	.	.	PUNCT
ejpam-5826	129	1	define	define	VERB
ejpam-5826	129	2	the	the	DET
ejpam-5826	129	3	mapping	mapping	NOUN
ejpam-5826	129	4	eλ	eλ	NOUN
ejpam-5826	129	5	:	:	PUNCT
ejpam-5826	129	6	q	q	X
ejpam-5826	129	7	→	→	PUNCT
ejpam-5826	129	8	q	q	X
ejpam-5826	129	9	by	by	ADP
ejpam-5826	129	10	eλx	eλx	NOUN
ejpam-5826	129	11	=	=	SYM
ejpam-5826	129	12	w	w	PROPN
ejpam-5826	129	13	(	(	PUNCT
ejpam-5826	129	14	x	x	NOUN
ejpam-5826	129	15	,	,	PUNCT
ejpam-5826	129	16	ex;λ	ex;λ	NOUN
ejpam-5826	129	17	)	)	PUNCT
ejpam-5826	129	18	,	,	PUNCT
ejpam-5826	129	19	x	x	PUNCT
ejpam-5826	129	20	∈	∈	PROPN
ejpam-5826	129	21	q.	q.	NOUN
ejpam-5826	129	22	then	then	ADV
ejpam-5826	129	23	for	for	ADP
ejpam-5826	129	24	any	any	DET
ejpam-5826	129	25	λ	λ	PROPN
ejpam-5826	129	26	∈	∈	PROPN
ejpam-5826	130	1	[	[	X
ejpam-5826	130	2	0	0	NUM
ejpam-5826	130	3	,	,	PUNCT
ejpam-5826	130	4	1	1	NUM
ejpam-5826	130	5	)	)	PUNCT
ejpam-5826	130	6	,	,	PUNCT
ejpam-5826	130	7	fix(e	fix(e	PROPN
ejpam-5826	130	8	)	)	PUNCT
ejpam-5826	130	9	=	=	NOUN
ejpam-5826	130	10	fix(eλ	fix(eλ	NOUN
ejpam-5826	130	11	)	)	PUNCT
ejpam-5826	130	12	.	.	PUNCT
ejpam-5826	131	1	a.	a.	PROPN
ejpam-5826	131	2	r.	r.	PROPN
ejpam-5826	131	3	khan	khan	PROPN
ejpam-5826	131	4	et	et	PROPN
ejpam-5826	131	5	al	al	PROPN
ejpam-5826	131	6	.	.	PUNCT
ejpam-5826	131	7	/	/	SYM
ejpam-5826	131	8	eur	eur	PROPN
ejpam-5826	131	9	.	.	PUNCT
ejpam-5826	132	1	j.	j.	PROPN
ejpam-5826	132	2	pure	pure	PROPN
ejpam-5826	132	3	appl	appl	PROPN
ejpam-5826	132	4	.	.	PROPN
ejpam-5826	132	5	math	math	PROPN
ejpam-5826	132	6	,	,	PUNCT
ejpam-5826	132	7	18	18	NUM
ejpam-5826	132	8	(	(	PUNCT
ejpam-5826	132	9	2	2	NUM
ejpam-5826	132	10	)	)	PUNCT
ejpam-5826	132	11	(	(	PUNCT
ejpam-5826	132	12	2025	2025	NUM
ejpam-5826	132	13	)	)	PUNCT
ejpam-5826	132	14	,	,	PUNCT
ejpam-5826	132	15	5826	5826	NUM
ejpam-5826	132	16	6	6	NUM
ejpam-5826	132	17	of	of	ADP
ejpam-5826	132	18	23	23	NUM
ejpam-5826	132	19	proof	proof	NOUN
ejpam-5826	132	20	.	.	PUNCT
ejpam-5826	133	1	for	for	ADP
ejpam-5826	133	2	λ	λ	PROPN
ejpam-5826	133	3	=	=	SYM
ejpam-5826	133	4	0	0	NUM
ejpam-5826	133	5	,	,	PUNCT
ejpam-5826	133	6	eλ	eλ	NOUN
ejpam-5826	133	7	=	=	SYM
ejpam-5826	133	8	e	e	PROPN
ejpam-5826	133	9	and	and	CCONJ
ejpam-5826	133	10	the	the	DET
ejpam-5826	133	11	assertion	assertion	NOUN
ejpam-5826	133	12	is	be	AUX
ejpam-5826	133	13	trivial	trivial	ADJ
ejpam-5826	133	14	.	.	PUNCT
ejpam-5826	134	1	assume	assume	VERB
ejpam-5826	134	2	λ	λ	X
ejpam-5826	134	3	∈	∈	PROPN
ejpam-5826	134	4	(	(	PUNCT
ejpam-5826	134	5	0	0	NUM
ejpam-5826	134	6	,	,	PUNCT
ejpam-5826	134	7	1	1	NUM
ejpam-5826	134	8	)	)	PUNCT
ejpam-5826	134	9	and	and	CCONJ
ejpam-5826	134	10	let	let	VERB
ejpam-5826	134	11	a	a	DET
ejpam-5826	134	12	∈	∈	PROPN
ejpam-5826	134	13	fix(e	fix(e	PROPN
ejpam-5826	134	14	)	)	PUNCT
ejpam-5826	134	15	.	.	PUNCT
ejpam-5826	135	1	this	this	PRON
ejpam-5826	135	2	means	mean	VERB
ejpam-5826	135	3	a	a	DET
ejpam-5826	135	4	=	=	SYM
ejpam-5826	135	5	ea	ea	NOUN
ejpam-5826	135	6	and	and	CCONJ
ejpam-5826	135	7	therefore	therefore	ADV
ejpam-5826	135	8	it	it	PRON
ejpam-5826	135	9	follows	follow	VERB
ejpam-5826	135	10	that	that	SCONJ
ejpam-5826	135	11	d(a	d(a	PROPN
ejpam-5826	135	12	,	,	PUNCT
ejpam-5826	135	13	eλa	eλa	ADJ
ejpam-5826	135	14	)	)	PUNCT
ejpam-5826	135	15	=	=	SYM
ejpam-5826	136	1	d(a	d(a	PROPN
ejpam-5826	136	2	,	,	PUNCT
ejpam-5826	136	3	w	w	PROPN
ejpam-5826	136	4	(	(	PUNCT
ejpam-5826	136	5	a	a	PRON
ejpam-5826	136	6	,	,	PUNCT
ejpam-5826	136	7	ea;λ	ea;λ	NUM
ejpam-5826	136	8	)	)	PUNCT
ejpam-5826	136	9	)	)	PUNCT
ejpam-5826	136	10	≤	≤	PUNCT
ejpam-5826	137	1	d(a	d(a	PROPN
ejpam-5826	137	2	,	,	PUNCT
ejpam-5826	137	3	a	a	NOUN
ejpam-5826	137	4	)	)	PUNCT
ejpam-5826	137	5	+	+	CCONJ
ejpam-5826	137	6	(	(	PUNCT
ejpam-5826	137	7	1−	1−	NUM
ejpam-5826	137	8	λ)d(a	λ)d(a	X
ejpam-5826	137	9	,	,	PUNCT
ejpam-5826	137	10	ea	ea	X
ejpam-5826	137	11	)	)	PUNCT
ejpam-5826	137	12	=	=	SYM
ejpam-5826	137	13	0	0	NUM
ejpam-5826	137	14	,	,	PUNCT
ejpam-5826	137	15	i.e.	i.e.	X
ejpam-5826	137	16	,	,	PUNCT
ejpam-5826	137	17	a	a	DET
ejpam-5826	137	18	∈	∈	PROPN
ejpam-5826	137	19	fix(eλ	fix(eλ	NOUN
ejpam-5826	137	20	)	)	PUNCT
ejpam-5826	137	21	.	.	PUNCT
ejpam-5826	138	1	conversely	conversely	ADV
ejpam-5826	138	2	,	,	PUNCT
ejpam-5826	138	3	assume	assume	VERB
ejpam-5826	138	4	that	that	SCONJ
ejpam-5826	138	5	a	a	DET
ejpam-5826	138	6	∈	∈	PROPN
ejpam-5826	138	7	fix(eλ	fix(eλ	NOUN
ejpam-5826	138	8	)	)	PUNCT
ejpam-5826	138	9	.	.	PUNCT
ejpam-5826	139	1	this	this	PRON
ejpam-5826	139	2	means	mean	VERB
ejpam-5826	139	3	that	that	SCONJ
ejpam-5826	139	4	d(a	d(a	PROPN
ejpam-5826	139	5	,	,	PUNCT
ejpam-5826	139	6	ea	ea	NUM
ejpam-5826	139	7	)	)	PUNCT
ejpam-5826	139	8	=	=	SYM
ejpam-5826	139	9	0	0	NUM
ejpam-5826	139	10	,	,	PUNCT
ejpam-5826	139	11	which	which	PRON
ejpam-5826	139	12	implies	imply	VERB
ejpam-5826	139	13	d(a	d(a	PROPN
ejpam-5826	139	14	,	,	PUNCT
ejpam-5826	139	15	w	w	PROPN
ejpam-5826	139	16	(	(	PUNCT
ejpam-5826	139	17	a	a	PRON
ejpam-5826	139	18	,	,	PUNCT
ejpam-5826	139	19	ea;λ	ea;λ	NUM
ejpam-5826	139	20	)	)	PUNCT
ejpam-5826	139	21	)	)	PUNCT
ejpam-5826	140	1	=	=	PUNCT
ejpam-5826	140	2	0	0	X
ejpam-5826	140	3	.	.	PUNCT
ejpam-5826	141	1	by	by	ADP
ejpam-5826	141	2	lemma	lemma	PROPN
ejpam-5826	141	3	4	4	NUM
ejpam-5826	141	4	,	,	PUNCT
ejpam-5826	141	5	d(a	d(a	PROPN
ejpam-5826	141	6	,	,	PUNCT
ejpam-5826	141	7	w	w	PROPN
ejpam-5826	141	8	(	(	PUNCT
ejpam-5826	141	9	a	a	PRON
ejpam-5826	141	10	,	,	PUNCT
ejpam-5826	141	11	ea;λ	ea;λ	NUM
ejpam-5826	141	12	)	)	PUNCT
ejpam-5826	141	13	)	)	PUNCT
ejpam-5826	142	1	=	=	PUNCT
ejpam-5826	142	2	(	(	PUNCT
ejpam-5826	142	3	1−	1−	NUM
ejpam-5826	142	4	λ)d(a	λ)d(a	X
ejpam-5826	142	5	,	,	PUNCT
ejpam-5826	142	6	ea	ea	X
ejpam-5826	142	7	)	)	PUNCT
ejpam-5826	142	8	,	,	PUNCT
ejpam-5826	142	9	so	so	CCONJ
ejpam-5826	142	10	it	it	PRON
ejpam-5826	142	11	follows	follow	VERB
ejpam-5826	142	12	that	that	SCONJ
ejpam-5826	142	13	(	(	PUNCT
ejpam-5826	142	14	1−	1−	NUM
ejpam-5826	142	15	λ).d(a	λ).d(a	PROPN
ejpam-5826	142	16	,	,	PUNCT
ejpam-5826	142	17	ea	ea	X
ejpam-5826	142	18	)	)	PUNCT
ejpam-5826	142	19	=	=	SYM
ejpam-5826	142	20	0	0	NUM
ejpam-5826	142	21	,	,	PUNCT
ejpam-5826	142	22	which	which	PRON
ejpam-5826	142	23	,	,	PUNCT
ejpam-5826	142	24	in	in	ADP
ejpam-5826	142	25	view	view	NOUN
ejpam-5826	142	26	of	of	ADP
ejpam-5826	142	27	the	the	DET
ejpam-5826	142	28	fact	fact	NOUN
ejpam-5826	142	29	that	that	SCONJ
ejpam-5826	142	30	(	(	PUNCT
ejpam-5826	142	31	1−	1−	NUM
ejpam-5826	142	32	λ	λ	NOUN
ejpam-5826	142	33	)	)	PUNCT
ejpam-5826	142	34	̸=	̸=	PROPN
ejpam-5826	142	35	0	0	NUM
ejpam-5826	142	36	,	,	PUNCT
ejpam-5826	142	37	implies	imply	VERB
ejpam-5826	142	38	d(a	d(a	PROPN
ejpam-5826	142	39	,	,	PUNCT
ejpam-5826	142	40	ea	ea	NUM
ejpam-5826	142	41	)	)	PUNCT
ejpam-5826	142	42	=	=	SYM
ejpam-5826	143	1	0	0	X
ejpam-5826	143	2	.	.	PUNCT
ejpam-5826	144	1	hence	hence	ADV
ejpam-5826	144	2	a	a	DET
ejpam-5826	144	3	∈	∈	PROPN
ejpam-5826	144	4	fix(e	fix(e	PROPN
ejpam-5826	144	5	)	)	PUNCT
ejpam-5826	144	6	.	.	PUNCT
ejpam-5826	145	1	3	3	X
ejpam-5826	145	2	.	.	X
ejpam-5826	145	3	common	common	ADJ
ejpam-5826	145	4	fixed	fix	VERB
ejpam-5826	145	5	points	point	NOUN
ejpam-5826	145	6	results	result	NOUN
ejpam-5826	145	7	following	follow	VERB
ejpam-5826	145	8	the	the	DET
ejpam-5826	145	9	notion	notion	NOUN
ejpam-5826	145	10	introduced	introduce	VERB
ejpam-5826	145	11	in	in	ADP
ejpam-5826	145	12	definition	definition	NOUN
ejpam-5826	145	13	1	1	NUM
ejpam-5826	145	14	by	by	ADP
ejpam-5826	145	15	huang	huang	PROPN
ejpam-5826	145	16	and	and	CCONJ
ejpam-5826	145	17	qian	qian	PROPN
ejpam-5826	146	1	[	[	X
ejpam-5826	146	2	14	14	NUM
ejpam-5826	146	3	]	]	PUNCT
ejpam-5826	146	4	,	,	PUNCT
ejpam-5826	146	5	we	we	PRON
ejpam-5826	146	6	extended	extend	VERB
ejpam-5826	146	7	theorem	theorem	VERB
ejpam-5826	146	8	3	3	NUM
ejpam-5826	146	9	by	by	ADP
ejpam-5826	146	10	replacing	replace	VERB
ejpam-5826	146	11	µ	µ	NOUN
ejpam-5826	146	12	with	with	ADP
ejpam-5826	146	13	a	a	DET
ejpam-5826	146	14	function	function	NOUN
ejpam-5826	146	15	κ	κ	ADP
ejpam-5826	146	16	∈	∈	PROPN
ejpam-5826	146	17	s	s	PART
ejpam-5826	146	18	and	and	CCONJ
ejpam-5826	146	19	weakening	weaken	VERB
ejpam-5826	146	20	the	the	DET
ejpam-5826	146	21	continuity	continuity	NOUN
ejpam-5826	146	22	hypothesis	hypothesis	NOUN
ejpam-5826	146	23	.	.	PUNCT
ejpam-5826	147	1	theorem	theorem	ADJ
ejpam-5826	147	2	4	4	NUM
ejpam-5826	147	3	.	.	PUNCT
ejpam-5826	147	4	suppose	suppose	VERB
ejpam-5826	147	5	that	that	SCONJ
ejpam-5826	147	6	(	(	PUNCT
ejpam-5826	147	7	q	q	X
ejpam-5826	147	8	,	,	PUNCT
ejpam-5826	147	9	d	d	NOUN
ejpam-5826	147	10	)	)	PUNCT
ejpam-5826	147	11	is	be	AUX
ejpam-5826	147	12	a	a	DET
ejpam-5826	147	13	complete	complete	ADJ
ejpam-5826	147	14	metric	metric	ADJ
ejpam-5826	147	15	space	space	NOUN
ejpam-5826	147	16	and	and	CCONJ
ejpam-5826	147	17	e	e	PROPN
ejpam-5826	147	18	and	and	CCONJ
ejpam-5826	147	19	f	f	PROPN
ejpam-5826	147	20	are	be	AUX
ejpam-5826	147	21	asymptotically	asymptotically	ADV
ejpam-5826	147	22	regular	regular	ADJ
ejpam-5826	147	23	self	self	NOUN
ejpam-5826	147	24	-	-	PUNCT
ejpam-5826	147	25	mappings	mapping	NOUN
ejpam-5826	147	26	on	on	ADP
ejpam-5826	147	27	q.	q.	PROPN
ejpam-5826	147	28	suppose	suppose	VERB
ejpam-5826	147	29	that	that	SCONJ
ejpam-5826	147	30	there	there	PRON
ejpam-5826	147	31	exist	exist	VERB
ejpam-5826	147	32	a	a	DET
ejpam-5826	147	33	function	function	NOUN
ejpam-5826	147	34	κ	κ	ADP
ejpam-5826	147	35	∈	∈	PROPN
ejpam-5826	147	36	s	s	X
ejpam-5826	147	37	and	and	CCONJ
ejpam-5826	147	38	a	a	DET
ejpam-5826	147	39	constant	constant	ADJ
ejpam-5826	147	40	k	k	PROPN
ejpam-5826	147	41	∈	∈	PROPN
ejpam-5826	148	1	[	[	X
ejpam-5826	148	2	0,+∞	0,+∞	NUM
ejpam-5826	148	3	)	)	PUNCT
ejpam-5826	148	4	satisfying	satisfy	VERB
ejpam-5826	148	5	the	the	DET
ejpam-5826	148	6	following	follow	VERB
ejpam-5826	148	7	condition	condition	NOUN
ejpam-5826	148	8	:	:	PUNCT
ejpam-5826	148	9	d(eq	d(eq	PROPN
ejpam-5826	148	10	,	,	PUNCT
ejpam-5826	148	11	fp	fp	ADJ
ejpam-5826	148	12	)	)	PUNCT
ejpam-5826	148	13	≤	≤	NOUN
ejpam-5826	148	14	κ(d(q	κ(d(q	PROPN
ejpam-5826	148	15	,	,	PUNCT
ejpam-5826	148	16	p))d(q	p))d(q	PROPN
ejpam-5826	148	17	,	,	PUNCT
ejpam-5826	148	18	p	p	NOUN
ejpam-5826	148	19	)	)	PUNCT
ejpam-5826	149	1	+	+	NOUN
ejpam-5826	149	2	k{d(q	k{d(q	ADJ
ejpam-5826	149	3	,	,	PUNCT
ejpam-5826	149	4	eq	eq	NOUN
ejpam-5826	149	5	)	)	PUNCT
ejpam-5826	149	6	+	+	CCONJ
ejpam-5826	149	7	d(p	d(p	PROPN
ejpam-5826	149	8	,	,	PUNCT
ejpam-5826	149	9	fp	fp	NOUN
ejpam-5826	149	10	)	)	PUNCT
ejpam-5826	149	11	}	}	PUNCT
ejpam-5826	149	12	(	(	PUNCT
ejpam-5826	149	13	3	3	X
ejpam-5826	149	14	)	)	PUNCT
ejpam-5826	149	15	for	for	ADP
ejpam-5826	149	16	all	all	DET
ejpam-5826	149	17	q	q	NOUN
ejpam-5826	149	18	,	,	PUNCT
ejpam-5826	149	19	p	p	PROPN
ejpam-5826	149	20	∈	∈	PROPN
ejpam-5826	149	21	q.	q.	PROPN
ejpam-5826	149	22	suppose	suppose	VERB
ejpam-5826	149	23	that	that	SCONJ
ejpam-5826	149	24	e	e	PROPN
ejpam-5826	149	25	and	and	CCONJ
ejpam-5826	149	26	f	f	PROPN
ejpam-5826	149	27	have	have	VERB
ejpam-5826	149	28	a	a	DET
ejpam-5826	149	29	common	common	ADJ
ejpam-5826	149	30	approximate	approximate	ADJ
ejpam-5826	149	31	fixed	fix	VERB
ejpam-5826	149	32	point	point	NOUN
ejpam-5826	149	33	sequence	sequence	NOUN
ejpam-5826	149	34	(	(	PUNCT
ejpam-5826	149	35	i.e.	i.e.	X
ejpam-5826	149	36	,	,	PUNCT
ejpam-5826	149	37	there	there	PRON
ejpam-5826	149	38	is	be	VERB
ejpam-5826	149	39	a	a	DET
ejpam-5826	149	40	sequence	sequence	NOUN
ejpam-5826	149	41	{	{	PUNCT
ejpam-5826	149	42	qh	qh	NOUN
ejpam-5826	149	43	}	}	PUNCT
ejpam-5826	149	44	⊂	⊂	PROPN
ejpam-5826	149	45	q	q	X
ejpam-5826	149	46	,	,	PUNCT
ejpam-5826	149	47	such	such	ADJ
ejpam-5826	149	48	that	that	SCONJ
ejpam-5826	149	49	d(qh	d(qh	NOUN
ejpam-5826	149	50	,	,	PUNCT
ejpam-5826	149	51	eqh	eqh	NOUN
ejpam-5826	149	52	)	)	PUNCT
ejpam-5826	149	53	→	→	SYM
ejpam-5826	149	54	0	0	NUM
ejpam-5826	149	55	and	and	CCONJ
ejpam-5826	149	56	d(qh	d(qh	NOUN
ejpam-5826	149	57	,	,	PUNCT
ejpam-5826	149	58	f	f	PROPN
ejpam-5826	149	59	qh	qh	PROPN
ejpam-5826	149	60	)	)	PUNCT
ejpam-5826	149	61	→	→	SYM
ejpam-5826	149	62	0	0	PUNCT
ejpam-5826	149	63	as	as	ADP
ejpam-5826	149	64	h	h	NOUN
ejpam-5826	149	65	→	→	SYM
ejpam-5826	149	66	∞	∞	NUM
ejpam-5826	149	67	)	)	PUNCT
ejpam-5826	149	68	.	.	PUNCT
ejpam-5826	150	1	then	then	ADV
ejpam-5826	150	2	e	e	PROPN
ejpam-5826	150	3	and	and	CCONJ
ejpam-5826	150	4	f	f	PROPN
ejpam-5826	150	5	have	have	VERB
ejpam-5826	150	6	a	a	DET
ejpam-5826	150	7	unique	unique	ADJ
ejpam-5826	150	8	common	common	ADJ
ejpam-5826	150	9	fixed	fix	VERB
ejpam-5826	150	10	point	point	NOUN
ejpam-5826	150	11	p	p	NOUN
ejpam-5826	150	12	provided	provide	VERB
ejpam-5826	150	13	e	e	NOUN
ejpam-5826	150	14	and	and	CCONJ
ejpam-5826	150	15	f	f	PROPN
ejpam-5826	150	16	are	be	AUX
ejpam-5826	150	17	either	either	CCONJ
ejpam-5826	150	18	k	k	ADJ
ejpam-5826	150	19	-	-	ADJ
ejpam-5826	150	20	continuous	continuous	ADJ
ejpam-5826	150	21	or	or	CCONJ
ejpam-5826	150	22	orbitally	orbitally	ADV
ejpam-5826	150	23	continuous	continuous	ADJ
ejpam-5826	150	24	.	.	PUNCT
ejpam-5826	151	1	in	in	ADP
ejpam-5826	151	2	particular	particular	ADJ
ejpam-5826	151	3	,	,	PUNCT
ejpam-5826	151	4	{	{	PUNCT
ejpam-5826	151	5	qh	qh	NOUN
ejpam-5826	151	6	}	}	PUNCT
ejpam-5826	151	7	→	→	SYM
ejpam-5826	151	8	p	p	NOUN
ejpam-5826	151	9	as	as	ADP
ejpam-5826	151	10	h	h	PROPN
ejpam-5826	151	11	→	→	SYM
ejpam-5826	151	12	∞.	∞.	PROPN
ejpam-5826	151	13	proof	proof	NOUN
ejpam-5826	151	14	.	.	PUNCT
ejpam-5826	152	1	take	take	VERB
ejpam-5826	152	2	q	q	PROPN
ejpam-5826	152	3	∈	∈	PROPN
ejpam-5826	152	4	q.	q.	NOUN
ejpam-5826	152	5	define	define	VERB
ejpam-5826	152	6	qh	qh	NOUN
ejpam-5826	152	7	=	=	NOUN
ejpam-5826	152	8	ehq	ehq	NOUN
ejpam-5826	152	9	and	and	CCONJ
ejpam-5826	152	10	ph	ph	NOUN
ejpam-5826	152	11	=	=	SYM
ejpam-5826	152	12	f	f	X
ejpam-5826	152	13	hq	hq	NOUN
ejpam-5826	152	14	for	for	ADP
ejpam-5826	152	15	all	all	DET
ejpam-5826	152	16	h	h	NOUN
ejpam-5826	152	17	∈	∈	PROPN
ejpam-5826	152	18	n.	n.	NOUN
ejpam-5826	152	19	by	by	ADP
ejpam-5826	152	20	(	(	PUNCT
ejpam-5826	152	21	3	3	NUM
ejpam-5826	152	22	)	)	PUNCT
ejpam-5826	152	23	,	,	PUNCT
ejpam-5826	152	24	we	we	PRON
ejpam-5826	152	25	have	have	VERB
ejpam-5826	152	26	d(eh+1q	d(eh+1q	NOUN
ejpam-5826	152	27	,	,	PUNCT
ejpam-5826	152	28	f	f	PROPN
ejpam-5826	152	29	h+1q	h+1q	PROPN
ejpam-5826	152	30	)	)	PUNCT
ejpam-5826	152	31	=	=	SYM
ejpam-5826	152	32	d(e(ehq	d(e(ehq	NOUN
ejpam-5826	152	33	)	)	PUNCT
ejpam-5826	152	34	,	,	PUNCT
ejpam-5826	152	35	f	f	PROPN
ejpam-5826	152	36	(	(	PUNCT
ejpam-5826	152	37	f	f	PROPN
ejpam-5826	152	38	hq	hq	PROPN
ejpam-5826	152	39	)	)	PUNCT
ejpam-5826	152	40	)	)	PUNCT
ejpam-5826	152	41	(	(	PUNCT
ejpam-5826	152	42	4	4	X
ejpam-5826	152	43	)	)	PUNCT
ejpam-5826	152	44	d(eh+1q	d(eh+1q	NOUN
ejpam-5826	152	45	,	,	PUNCT
ejpam-5826	152	46	f	f	PROPN
ejpam-5826	152	47	h+1q	h+1q	PROPN
ejpam-5826	152	48	)	)	PUNCT
ejpam-5826	152	49	≤	≤	NUM
ejpam-5826	152	50	κ(d(ehq	κ(d(ehq	NOUN
ejpam-5826	152	51	,	,	PUNCT
ejpam-5826	152	52	f	f	PROPN
ejpam-5826	152	53	hq))d(ehq	hq))d(ehq	PROPN
ejpam-5826	152	54	,	,	PUNCT
ejpam-5826	152	55	f	f	PROPN
ejpam-5826	152	56	hq	hq	NOUN
ejpam-5826	152	57	)	)	PUNCT
ejpam-5826	153	1	+	+	NOUN
ejpam-5826	153	2	k[d(ehq	k[d(ehq	PROPN
ejpam-5826	153	3	,	,	PUNCT
ejpam-5826	153	4	eh+1q	eh+1q	NOUN
ejpam-5826	153	5	)	)	PUNCT
ejpam-5826	154	1	+	+	CCONJ
ejpam-5826	154	2	d(f	d(f	NOUN
ejpam-5826	154	3	hq	hq	VERB
ejpam-5826	154	4	,	,	PUNCT
ejpam-5826	154	5	f	f	PROPN
ejpam-5826	154	6	h+1q	h+1q	PROPN
ejpam-5826	154	7	)	)	PUNCT
ejpam-5826	154	8	]	]	PUNCT
ejpam-5826	154	9	.	.	PUNCT
ejpam-5826	155	1	(	(	PUNCT
ejpam-5826	155	2	5	5	X
ejpam-5826	155	3	)	)	PUNCT
ejpam-5826	155	4	in	in	ADP
ejpam-5826	155	5	view	view	NOUN
ejpam-5826	155	6	of	of	ADP
ejpam-5826	155	7	the	the	DET
ejpam-5826	155	8	condition	condition	NOUN
ejpam-5826	155	9	,	,	PUNCT
ejpam-5826	155	10	0	0	NUM
ejpam-5826	155	11	≤	≤	NUM
ejpam-5826	155	12	κ(d(ehq	κ(d(ehq	NOUN
ejpam-5826	155	13	,	,	PUNCT
ejpam-5826	155	14	f	f	PROPN
ejpam-5826	155	15	hq	hq	PROPN
ejpam-5826	155	16	)	)	PUNCT
ejpam-5826	155	17	)	)	PUNCT
ejpam-5826	155	18	≤	≤	NUM
ejpam-5826	155	19	1	1	NUM
ejpam-5826	155	20	,	,	PUNCT
ejpam-5826	155	21	we	we	PRON
ejpam-5826	155	22	consider	consider	VERB
ejpam-5826	155	23	two	two	NUM
ejpam-5826	155	24	cases	case	NOUN
ejpam-5826	155	25	for	for	ADP
ejpam-5826	155	26	lim	lim	PROPN
ejpam-5826	155	27	suph→∞	suph→∞	PROPN
ejpam-5826	155	28	κ(d(ehq	κ(d(ehq	PROPN
ejpam-5826	155	29	)	)	PUNCT
ejpam-5826	155	30	,	,	PUNCT
ejpam-5826	155	31	f	f	PROPN
ejpam-5826	155	32	hq	hq	PROPN
ejpam-5826	155	33	)	)	PUNCT
ejpam-5826	155	34	.	.	PUNCT
ejpam-5826	156	1	case	case	NOUN
ejpam-5826	156	2	1	1	NUM
ejpam-5826	156	3	:	:	PUNCT
ejpam-5826	156	4	lim	lim	PROPN
ejpam-5826	156	5	sup	sup	PROPN
ejpam-5826	156	6	h→∞	h→∞	NUM
ejpam-5826	156	7	κ(d(ehq	κ(d(ehq	NOUN
ejpam-5826	156	8	,	,	PUNCT
ejpam-5826	156	9	f	f	PROPN
ejpam-5826	156	10	hq	hq	PROPN
ejpam-5826	156	11	)	)	PUNCT
ejpam-5826	156	12	)	)	PUNCT
ejpam-5826	157	1	=	=	SYM
ejpam-5826	157	2	1	1	X
ejpam-5826	157	3	.	.	PUNCT
ejpam-5826	157	4	a.	a.	PROPN
ejpam-5826	157	5	r.	r.	PROPN
ejpam-5826	157	6	khan	khan	PROPN
ejpam-5826	157	7	et	et	PROPN
ejpam-5826	157	8	al	al	PROPN
ejpam-5826	157	9	.	.	PUNCT
ejpam-5826	157	10	/	/	SYM
ejpam-5826	157	11	eur	eur	PROPN
ejpam-5826	157	12	.	.	PUNCT
ejpam-5826	158	1	j.	j.	PROPN
ejpam-5826	158	2	pure	pure	PROPN
ejpam-5826	158	3	appl	appl	PROPN
ejpam-5826	158	4	.	.	PROPN
ejpam-5826	158	5	math	math	PROPN
ejpam-5826	158	6	,	,	PUNCT
ejpam-5826	158	7	18	18	NUM
ejpam-5826	158	8	(	(	PUNCT
ejpam-5826	158	9	2	2	NUM
ejpam-5826	158	10	)	)	PUNCT
ejpam-5826	158	11	(	(	PUNCT
ejpam-5826	158	12	2025	2025	NUM
ejpam-5826	158	13	)	)	PUNCT
ejpam-5826	158	14	,	,	PUNCT
ejpam-5826	158	15	5826	5826	NUM
ejpam-5826	158	16	7	7	NUM
ejpam-5826	158	17	of	of	ADP
ejpam-5826	158	18	23	23	NUM
ejpam-5826	158	19	in	in	ADP
ejpam-5826	158	20	this	this	DET
ejpam-5826	158	21	case	case	NOUN
ejpam-5826	158	22	,	,	PUNCT
ejpam-5826	158	23	there	there	PRON
ejpam-5826	158	24	exists	exist	VERB
ejpam-5826	158	25	a	a	DET
ejpam-5826	158	26	subsequence	subsequence	NOUN
ejpam-5826	158	27	{	{	PUNCT
ejpam-5826	158	28	κ(d(ehkq	κ(d(ehkq	PROPN
ejpam-5826	158	29	,	,	PUNCT
ejpam-5826	158	30	f	f	PROPN
ejpam-5826	158	31	hkq	hkq	PROPN
ejpam-5826	158	32	)	)	PUNCT
ejpam-5826	158	33	)	)	PUNCT
ejpam-5826	158	34	}	}	PUNCT
ejpam-5826	158	35	of	of	ADP
ejpam-5826	158	36	{	{	PUNCT
ejpam-5826	158	37	κ(d(ehq	κ(d(ehq	PROPN
ejpam-5826	158	38	,	,	PUNCT
ejpam-5826	158	39	f	f	PROPN
ejpam-5826	158	40	hq	hq	PROPN
ejpam-5826	158	41	)	)	PUNCT
ejpam-5826	158	42	)	)	PUNCT
ejpam-5826	158	43	}	}	PUNCT
ejpam-5826	158	44	such	such	ADJ
ejpam-5826	158	45	that	that	SCONJ
ejpam-5826	158	46	lim	lim	PROPN
ejpam-5826	158	47	k→∞	k→∞	PROPN
ejpam-5826	158	48	κ(d(ehkq	κ(d(ehkq	PROPN
ejpam-5826	158	49	,	,	PUNCT
ejpam-5826	158	50	f	f	PROPN
ejpam-5826	158	51	hkq	hkq	PROPN
ejpam-5826	158	52	)	)	PUNCT
ejpam-5826	158	53	)	)	PUNCT
ejpam-5826	159	1	=	=	PUNCT
ejpam-5826	159	2	1	1	X
ejpam-5826	159	3	.	.	PUNCT
ejpam-5826	159	4	(	(	PUNCT
ejpam-5826	159	5	6	6	NUM
ejpam-5826	159	6	)	)	PUNCT
ejpam-5826	159	7	now	now	ADV
ejpam-5826	159	8	(	(	PUNCT
ejpam-5826	159	9	6	6	NUM
ejpam-5826	159	10	)	)	PUNCT
ejpam-5826	159	11	implies	imply	VERB
ejpam-5826	159	12	on	on	ADP
ejpam-5826	159	13	the	the	DET
ejpam-5826	159	14	basis	basis	NOUN
ejpam-5826	159	15	of	of	ADP
ejpam-5826	159	16	definition	definition	NOUN
ejpam-5826	159	17	1	1	NUM
ejpam-5826	159	18	,	,	PUNCT
ejpam-5826	159	19	lim	lim	PROPN
ejpam-5826	159	20	k→∞	k→∞	PROPN
ejpam-5826	159	21	d(ehkq	d(ehkq	PROPN
ejpam-5826	159	22	,	,	PUNCT
ejpam-5826	159	23	f	f	PROPN
ejpam-5826	159	24	hkq	hkq	NOUN
ejpam-5826	159	25	)	)	PUNCT
ejpam-5826	159	26	=	=	SYM
ejpam-5826	160	1	0	0	X
ejpam-5826	160	2	.	.	PUNCT
ejpam-5826	161	1	(	(	PUNCT
ejpam-5826	161	2	7	7	X
ejpam-5826	161	3	)	)	PUNCT
ejpam-5826	161	4	we	we	PRON
ejpam-5826	161	5	prove	prove	VERB
ejpam-5826	161	6	that	that	SCONJ
ejpam-5826	161	7	{	{	PUNCT
ejpam-5826	161	8	ehkq	ehkq	NOUN
ejpam-5826	161	9	}	}	PUNCT
ejpam-5826	161	10	is	be	AUX
ejpam-5826	161	11	a	a	DET
ejpam-5826	161	12	cauchy	cauchy	ADJ
ejpam-5826	161	13	sequence	sequence	NOUN
ejpam-5826	161	14	.	.	PUNCT
ejpam-5826	162	1	suppose	suppose	VERB
ejpam-5826	162	2	on	on	ADP
ejpam-5826	162	3	the	the	DET
ejpam-5826	162	4	contrary	contrary	NOUN
ejpam-5826	162	5	that	that	SCONJ
ejpam-5826	162	6	{	{	PUNCT
ejpam-5826	162	7	ehkq	ehkq	NOUN
ejpam-5826	162	8	}	}	PUNCT
ejpam-5826	162	9	is	be	AUX
ejpam-5826	162	10	not	not	PART
ejpam-5826	162	11	a	a	DET
ejpam-5826	162	12	cauchy	cauchy	ADJ
ejpam-5826	162	13	sequence	sequence	NOUN
ejpam-5826	162	14	.	.	PUNCT
ejpam-5826	163	1	then	then	ADV
ejpam-5826	163	2	there	there	PRON
ejpam-5826	163	3	exists	exist	VERB
ejpam-5826	163	4	ϵ0	ϵ0	ADJ
ejpam-5826	163	5	>	>	X
ejpam-5826	163	6	0	0	PUNCT
ejpam-5826	164	1	and	and	CCONJ
ejpam-5826	164	2	two	two	NUM
ejpam-5826	164	3	integer	integer	NOUN
ejpam-5826	164	4	sequences	sequence	NOUN
ejpam-5826	164	5	{	{	PUNCT
ejpam-5826	164	6	hk̃(i	hk̃(i	NOUN
ejpam-5826	164	7	)	)	PUNCT
ejpam-5826	164	8	}	}	PUNCT
ejpam-5826	164	9	,	,	PUNCT
ejpam-5826	164	10	{	{	PUNCT
ejpam-5826	164	11	hk(i	hk(i	NOUN
ejpam-5826	164	12	)	)	PUNCT
ejpam-5826	164	13	}	}	PUNCT
ejpam-5826	164	14	of	of	ADP
ejpam-5826	164	15	{	{	PUNCT
ejpam-5826	164	16	hk	hk	PROPN
ejpam-5826	164	17	}	}	PUNCT
ejpam-5826	164	18	with	with	ADP
ejpam-5826	164	19	hk̃(i	hk̃(i	NOUN
ejpam-5826	164	20	)	)	PUNCT
ejpam-5826	164	21	>	>	PUNCT
ejpam-5826	164	22	hk(i	hk(i	ADP
ejpam-5826	164	23	)	)	PUNCT
ejpam-5826	164	24	>	>	X
ejpam-5826	165	1	i	i	PRON
ejpam-5826	165	2	such	such	ADJ
ejpam-5826	165	3	that	that	SCONJ
ejpam-5826	165	4	d(e	d(e	PROPN
ejpam-5826	165	5	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	165	6	,	,	PUNCT
ejpam-5826	165	7	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	165	8	)	)	PUNCT
ejpam-5826	165	9	≥	≥	NOUN
ejpam-5826	165	10	ϵ0	ϵ0	ADJ
ejpam-5826	165	11	,	,	PUNCT
ejpam-5826	165	12	i	i	PRON
ejpam-5826	165	13	=	=	NOUN
ejpam-5826	165	14	1	1	NUM
ejpam-5826	165	15	,	,	PUNCT
ejpam-5826	165	16	2	2	NUM
ejpam-5826	165	17	,	,	PUNCT
ejpam-5826	165	18	3	3	NUM
ejpam-5826	165	19	,	,	PUNCT
ejpam-5826	165	20	·	·	PUNCT
ejpam-5826	165	21	·	·	PUNCT
ejpam-5826	165	22	·	·	PUNCT
ejpam-5826	165	23	(	(	PUNCT
ejpam-5826	165	24	8)	8)	NUM
ejpam-5826	165	25	consequently	consequently	ADV
ejpam-5826	165	26	,	,	PUNCT
ejpam-5826	165	27	we	we	PRON
ejpam-5826	165	28	have	have	AUX
ejpam-5826	165	29	ϵ0	ϵ0	VERB
ejpam-5826	165	30	≤	≤	NUM
ejpam-5826	165	31	d(e	d(e	PROPN
ejpam-5826	165	32	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	165	33	,	,	PUNCT
ejpam-5826	165	34	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	165	35	)	)	PUNCT
ejpam-5826	165	36	,	,	PUNCT
ejpam-5826	165	37	ϵ0	ϵ0	VERB
ejpam-5826	165	38	≤	≤	PUNCT
ejpam-5826	165	39	d(e	d(e	PROPN
ejpam-5826	165	40	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	165	41	,	,	PUNCT
ejpam-5826	165	42	ehk(i−1)q	ehk(i−1)q	NOUN
ejpam-5826	165	43	)	)	PUNCT
ejpam-5826	165	44	+	+	NUM
ejpam-5826	166	1	d(e	d(e	PROPN
ejpam-5826	166	2	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	166	3	,	,	PUNCT
ejpam-5826	166	4	ehk(i−1)q	ehk(i−1)q	NOUN
ejpam-5826	166	5	)	)	PUNCT
ejpam-5826	167	1	+	+	NUM
ejpam-5826	167	2	d(e	d(e	PROPN
ejpam-5826	167	3	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	167	4	,	,	PUNCT
ejpam-5826	167	5	ehk(i)q	ehk(i)q	NOUN
ejpam-5826	167	6	)	)	PUNCT
ejpam-5826	167	7	.	.	PUNCT
ejpam-5826	168	1	(	(	PUNCT
ejpam-5826	168	2	9	9	X
ejpam-5826	168	3	)	)	PUNCT
ejpam-5826	168	4	if	if	SCONJ
ejpam-5826	168	5	i	i	PRON
ejpam-5826	168	6	→	→	SYM
ejpam-5826	168	7	∞	∞	PROPN
ejpam-5826	168	8	in	in	ADP
ejpam-5826	168	9	(	(	PUNCT
ejpam-5826	168	10	9	9	NUM
ejpam-5826	168	11	)	)	PUNCT
ejpam-5826	168	12	,	,	PUNCT
ejpam-5826	168	13	then	then	ADV
ejpam-5826	168	14	by	by	ADP
ejpam-5826	168	15	asymptotic	asymptotic	ADJ
ejpam-5826	168	16	regularity	regularity	NOUN
ejpam-5826	168	17	of	of	ADP
ejpam-5826	168	18	e	e	NOUN
ejpam-5826	168	19	,	,	PUNCT
ejpam-5826	168	20	we	we	PRON
ejpam-5826	168	21	obtain	obtain	VERB
ejpam-5826	168	22	lim	lim	PROPN
ejpam-5826	168	23	inf	inf	PROPN
ejpam-5826	168	24	i→∞	i→∞	NOUN
ejpam-5826	168	25	d(e	d(e	PROPN
ejpam-5826	168	26	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	168	27	,	,	PUNCT
ejpam-5826	168	28	ehk(i−1)q	ehk(i−1)q	PROPN
ejpam-5826	168	29	)	)	PUNCT
ejpam-5826	168	30	≥	≥	NOUN
ejpam-5826	168	31	ϵ0	ϵ0	ADJ
ejpam-5826	168	32	.	.	PUNCT
ejpam-5826	169	1	(	(	PUNCT
ejpam-5826	169	2	10	10	NUM
ejpam-5826	169	3	)	)	PUNCT
ejpam-5826	169	4	now	now	ADV
ejpam-5826	169	5	by	by	ADP
ejpam-5826	169	6	(	(	PUNCT
ejpam-5826	169	7	3	3	NUM
ejpam-5826	169	8	)	)	PUNCT
ejpam-5826	169	9	,	,	PUNCT
ejpam-5826	169	10	we	we	PRON
ejpam-5826	169	11	have	have	VERB
ejpam-5826	169	12	d(e	d(e	PROPN
ejpam-5826	169	13	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	169	14	,	,	PUNCT
ejpam-5826	169	15	ehk(i)q	ehk(i)q	ADJ
ejpam-5826	169	16	)	)	PUNCT
ejpam-5826	169	17	≤	≤	PUNCT
ejpam-5826	169	18	d(e	d(e	PROPN
ejpam-5826	169	19	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	169	20	,	,	PUNCT
ejpam-5826	169	21	f	f	PROPN
ejpam-5826	169	22	hk(i)q	hk(i)q	PROPN
ejpam-5826	169	23	)	)	PUNCT
ejpam-5826	170	1	+	+	NUM
ejpam-5826	170	2	d(f	d(f	NOUN
ejpam-5826	170	3	hk(i)q	hk(i)q	NOUN
ejpam-5826	170	4	,	,	PUNCT
ejpam-5826	170	5	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	170	6	)	)	PUNCT
ejpam-5826	170	7	(	(	PUNCT
ejpam-5826	170	8	11	11	NUM
ejpam-5826	170	9	)	)	PUNCT
ejpam-5826	170	10	d(e	d(e	PROPN
ejpam-5826	170	11	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	170	12	,	,	PUNCT
ejpam-5826	170	13	ehk(i)q	ehk(i)q	NOUN
ejpam-5826	170	14	)	)	PUNCT
ejpam-5826	170	15	≤	≤	NOUN
ejpam-5826	170	16	κ(d(e	κ(d(e	PROPN
ejpam-5826	170	17	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	170	18	,	,	PUNCT
ejpam-5826	170	19	f	f	PROPN
ejpam-5826	170	20	hk(i−1)q))d(e	hk(i−1)q))d(e	PART
ejpam-5826	170	21	hk̃(i−1)q	hk̃(i−1)q	PROPN
ejpam-5826	170	22	,	,	PUNCT
ejpam-5826	170	23	f	f	PROPN
ejpam-5826	170	24	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	170	25	)	)	PUNCT
ejpam-5826	171	1	+	+	ADP
ejpam-5826	171	2	k[d(e	k[d(e	NOUN
ejpam-5826	171	3	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	171	4	,	,	PUNCT
ejpam-5826	171	5	f	f	PROPN
ejpam-5826	171	6	hk̃(i)q	hk̃(i)q	PROPN
ejpam-5826	171	7	)	)	PUNCT
ejpam-5826	172	1	+	+	NUM
ejpam-5826	172	2	d(f	d(f	VERB
ejpam-5826	172	3	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	172	4	,	,	PUNCT
ejpam-5826	172	5	f	f	PROPN
ejpam-5826	172	6	hk(i)q	hk(i)q	PROPN
ejpam-5826	172	7	)	)	PUNCT
ejpam-5826	172	8	]	]	PUNCT
ejpam-5826	173	1	+	+	PUNCT
ejpam-5826	173	2	d(f	d(f	NOUN
ejpam-5826	173	3	hk(i)q	hk(i)q	NOUN
ejpam-5826	173	4	,	,	PUNCT
ejpam-5826	173	5	ehk(i)q	ehk(i)q	NOUN
ejpam-5826	173	6	)	)	PUNCT
ejpam-5826	173	7	.	.	PUNCT
ejpam-5826	174	1	and	and	CCONJ
ejpam-5826	174	2	d(e	d(e	PROPN
ejpam-5826	174	3	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	174	4	,	,	PUNCT
ejpam-5826	174	5	ehk(i)q	ehk(i)q	NOUN
ejpam-5826	174	6	)	)	PUNCT
ejpam-5826	174	7	≤	≤	NOUN
ejpam-5826	174	8	κ(d(e	κ(d(e	PROPN
ejpam-5826	174	9	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	174	10	,	,	PUNCT
ejpam-5826	174	11	f	f	PROPN
ejpam-5826	174	12	hk(i−1)q))d(e	hk(i−1)q))d(e	PART
ejpam-5826	174	13	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	174	14	,	,	PUNCT
ejpam-5826	174	15	ehkĩq	ehkĩq	NUM
ejpam-5826	174	16	)	)	PUNCT
ejpam-5826	174	17	+	+	NOUN
ejpam-5826	174	18	d(e	d(e	PROPN
ejpam-5826	174	19	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	174	20	,	,	PUNCT
ejpam-5826	174	21	ehk(i−)q	ehk(i−)q	ADJ
ejpam-5826	174	22	)	)	PUNCT
ejpam-5826	175	1	+	+	PUNCT
ejpam-5826	176	1	d(ehk(i)q	d(ehk(i)q	PROPN
ejpam-5826	176	2	,	,	PUNCT
ejpam-5826	176	3	f	f	PROPN
ejpam-5826	176	4	hk(i)q)d(f	hk(i)q)d(f	X
ejpam-5826	176	5	hk(i)q	hk(i)q	PROPN
ejpam-5826	176	6	,	,	PUNCT
ejpam-5826	176	7	f	f	PROPN
ejpam-5826	176	8	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	176	9	)	)	PUNCT
ejpam-5826	177	1	+	+	ADP
ejpam-5826	177	2	k[d(e	k[d(e	PROPN
ejpam-5826	177	3	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	177	4	,	,	PUNCT
ejpam-5826	177	5	ehkĩq	ehkĩq	NUM
ejpam-5826	177	6	)	)	PUNCT
ejpam-5826	178	1	+	+	NUM
ejpam-5826	178	2	d(f	d(f	VERB
ejpam-5826	178	3	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	178	4	,	,	PUNCT
ejpam-5826	178	5	f	f	PROPN
ejpam-5826	178	6	hk(i)q	hk(i)q	PROPN
ejpam-5826	178	7	)	)	PUNCT
ejpam-5826	178	8	+	+	NOUN
ejpam-5826	178	9	d(f	d(f	NOUN
ejpam-5826	178	10	hk(i)q	hk(i)q	NOUN
ejpam-5826	178	11	,	,	PUNCT
ejpam-5826	178	12	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	178	13	)	)	PUNCT
ejpam-5826	178	14	]	]	PUNCT
ejpam-5826	178	15	.	.	PUNCT
ejpam-5826	179	1	(	(	PUNCT
ejpam-5826	179	2	12	12	X
ejpam-5826	179	3	)	)	PUNCT
ejpam-5826	179	4	dividing	divide	VERB
ejpam-5826	179	5	both	both	DET
ejpam-5826	179	6	sides	side	NOUN
ejpam-5826	179	7	of	of	ADP
ejpam-5826	179	8	the	the	DET
ejpam-5826	179	9	inequality	inequality	NOUN
ejpam-5826	179	10	(	(	PUNCT
ejpam-5826	179	11	12	12	NUM
ejpam-5826	179	12	)	)	PUNCT
ejpam-5826	179	13	by	by	ADP
ejpam-5826	179	14	d(e	d(e	PROPN
ejpam-5826	179	15	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	179	16	,	,	PUNCT
ejpam-5826	179	17	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	179	18	)	)	PUNCT
ejpam-5826	179	19	and	and	CCONJ
ejpam-5826	179	20	comparing	compare	VERB
ejpam-5826	179	21	the	the	DET
ejpam-5826	179	22	new	new	ADJ
ejpam-5826	179	23	inequality	inequality	NOUN
ejpam-5826	179	24	with	with	ADP
ejpam-5826	179	25	(	(	PUNCT
ejpam-5826	179	26	8)	8)	NUM
ejpam-5826	179	27	,	,	PUNCT
ejpam-5826	179	28	we	we	PRON
ejpam-5826	179	29	conclude	conclude	VERB
ejpam-5826	179	30	that	that	SCONJ
ejpam-5826	179	31	a.	a.	PROPN
ejpam-5826	179	32	r.	r.	PROPN
ejpam-5826	179	33	khan	khan	PROPN
ejpam-5826	179	34	et	et	PROPN
ejpam-5826	179	35	al	al	PROPN
ejpam-5826	179	36	.	.	PUNCT
ejpam-5826	179	37	/	/	SYM
ejpam-5826	179	38	eur	eur	PROPN
ejpam-5826	179	39	.	.	PUNCT
ejpam-5826	180	1	j.	j.	PROPN
ejpam-5826	180	2	pure	pure	PROPN
ejpam-5826	180	3	appl	appl	PROPN
ejpam-5826	180	4	.	.	PROPN
ejpam-5826	180	5	math	math	PROPN
ejpam-5826	180	6	,	,	PUNCT
ejpam-5826	180	7	18	18	NUM
ejpam-5826	180	8	(	(	PUNCT
ejpam-5826	180	9	2	2	NUM
ejpam-5826	180	10	)	)	PUNCT
ejpam-5826	180	11	(	(	PUNCT
ejpam-5826	180	12	2025	2025	NUM
ejpam-5826	180	13	)	)	PUNCT
ejpam-5826	180	14	,	,	PUNCT
ejpam-5826	180	15	5826	5826	NUM
ejpam-5826	180	16	8	8	NUM
ejpam-5826	180	17	of	of	ADP
ejpam-5826	180	18	23	23	NUM
ejpam-5826	180	19	1	1	NUM
ejpam-5826	180	20	≤	≤	NOUN
ejpam-5826	180	21	κ(d(e	κ(d(e	PROPN
ejpam-5826	180	22	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	180	23	,	,	PUNCT
ejpam-5826	180	24	f	f	PROPN
ejpam-5826	180	25	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	180	26	)	)	PUNCT
ejpam-5826	180	27	)	)	PUNCT
ejpam-5826	181	1	(	(	PUNCT
ejpam-5826	181	2	d(e	d(e	NOUN
ejpam-5826	181	3	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	181	4	,	,	PUNCT
ejpam-5826	181	5	ehk̃(i)q	ehk̃(i)q	PROPN
ejpam-5826	181	6	)	)	PUNCT
ejpam-5826	182	1	d(e	d(e	PROPN
ejpam-5826	182	2	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	182	3	,	,	PUNCT
ejpam-5826	182	4	ehk(i)q	ehk(i)q	NOUN
ejpam-5826	182	5	)	)	PUNCT
ejpam-5826	182	6	)	)	PUNCT
ejpam-5826	183	1	+1	+1	PROPN
ejpam-5826	183	2	+	+	PUNCT
ejpam-5826	183	3	d(ehk(i)q	d(ehk(i)q	PROPN
ejpam-5826	183	4	,	,	PUNCT
ejpam-5826	183	5	f	f	PROPN
ejpam-5826	183	6	hk(i)q	hk(i)q	PROPN
ejpam-5826	183	7	)	)	PUNCT
ejpam-5826	183	8	d(e	d(e	PROPN
ejpam-5826	183	9	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	183	10	,	,	PUNCT
ejpam-5826	183	11	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	183	12	)	)	PUNCT
ejpam-5826	184	1	+	+	NUM
ejpam-5826	184	2	d(f	d(f	NOUN
ejpam-5826	184	3	hk(i)q	hk(i)q	PROPN
ejpam-5826	184	4	,	,	PUNCT
ejpam-5826	184	5	f	f	PROPN
ejpam-5826	184	6	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	184	7	)	)	PUNCT
ejpam-5826	184	8	d(e	d(e	PROPN
ejpam-5826	184	9	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	184	10	,	,	PUNCT
ejpam-5826	184	11	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	184	12	)	)	PUNCT
ejpam-5826	185	1	+	+	PROPN
ejpam-5826	185	2	k	k	PROPN
ejpam-5826	185	3	d(e	d(e	PROPN
ejpam-5826	185	4	hk̃(i−1)q	hk̃(i−1)q	NOUN
ejpam-5826	185	5	,	,	PUNCT
ejpam-5826	185	6	f	f	PROPN
ejpam-5826	185	7	hk̃(i)q	hk̃(i)q	PROPN
ejpam-5826	185	8	)	)	PUNCT
ejpam-5826	185	9	+	+	NUM
ejpam-5826	185	10	d(f	d(f	VERB
ejpam-5826	185	11	hk(i−1)q	hk(i−1)q	NOUN
ejpam-5826	185	12	,	,	PUNCT
ejpam-5826	185	13	f	f	PROPN
ejpam-5826	185	14	hk(i)q	hk(i)q	PROPN
ejpam-5826	185	15	)	)	PUNCT
ejpam-5826	185	16	d(e	d(e	PROPN
ejpam-5826	185	17	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	185	18	,	,	PUNCT
ejpam-5826	185	19	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	185	20	)	)	PUNCT
ejpam-5826	185	21	+	+	NUM
ejpam-5826	185	22	d(f	d(f	NOUN
ejpam-5826	185	23	hk(i)q	hk(i)q	ADP
ejpam-5826	185	24	,	,	PUNCT
ejpam-5826	185	25	ehk(i)q	ehk(i)q	ADJ
ejpam-5826	185	26	)	)	PUNCT
ejpam-5826	185	27	d(e	d(e	PROPN
ejpam-5826	185	28	hk̃(i)q	hk̃(i)q	NOUN
ejpam-5826	185	29	,	,	PUNCT
ejpam-5826	185	30	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	185	31	)	)	PUNCT
ejpam-5826	185	32	.	.	PUNCT
ejpam-5826	186	1	(	(	PUNCT
ejpam-5826	186	2	13	13	X
ejpam-5826	186	3	)	)	PUNCT
ejpam-5826	186	4	let	let	VERB
ejpam-5826	186	5	i	i	PRON
ejpam-5826	186	6	→	→	SYM
ejpam-5826	186	7	∞	∞	PROPN
ejpam-5826	186	8	in	in	ADP
ejpam-5826	186	9	(	(	PUNCT
ejpam-5826	186	10	13	13	NUM
ejpam-5826	186	11	)	)	PUNCT
ejpam-5826	186	12	,	,	PUNCT
ejpam-5826	186	13	using	use	VERB
ejpam-5826	186	14	(	(	PUNCT
ejpam-5826	186	15	7	7	NUM
ejpam-5826	186	16	)	)	PUNCT
ejpam-5826	186	17	,	,	PUNCT
ejpam-5826	186	18	(	(	PUNCT
ejpam-5826	186	19	8)	8)	NUM
ejpam-5826	186	20	,	,	PUNCT
ejpam-5826	186	21	asymptotically	asymptotically	ADV
ejpam-5826	186	22	regularity	regularity	NOUN
ejpam-5826	186	23	of	of	ADP
ejpam-5826	186	24	e	e	PROPN
ejpam-5826	186	25	and	and	CCONJ
ejpam-5826	186	26	f	f	PROPN
ejpam-5826	186	27	and	and	CCONJ
ejpam-5826	186	28	the	the	DET
ejpam-5826	186	29	fact	fact	NOUN
ejpam-5826	186	30	0	0	NUM
ejpam-5826	186	31	≤	≤	NUM
ejpam-5826	186	32	κ	κ	NOUN
ejpam-5826	186	33	(	(	PUNCT
ejpam-5826	186	34	.	.	PUNCT
ejpam-5826	186	35	)	)	PUNCT
ejpam-5826	187	1	≤	≤	NOUN
ejpam-5826	187	2	1	1	NUM
ejpam-5826	187	3	,	,	PUNCT
ejpam-5826	187	4	we	we	PRON
ejpam-5826	187	5	deduce	deduce	VERB
ejpam-5826	187	6	that	that	SCONJ
ejpam-5826	187	7	lim	lim	PROPN
ejpam-5826	187	8	i→∞	i→∞	VERB
ejpam-5826	187	9	κ(d(e	κ(d(e	PROPN
ejpam-5826	187	10	hk̃(i)−1	hk̃(i)−1	PROPN
ejpam-5826	187	11	q	q	PROPN
ejpam-5826	187	12	,	,	PUNCT
ejpam-5826	187	13	f	f	PROPN
ejpam-5826	187	14	hk(i)−1q	hk(i)−1q	PROPN
ejpam-5826	187	15	)	)	PUNCT
ejpam-5826	187	16	)	)	PUNCT
ejpam-5826	188	1	=	=	PUNCT
ejpam-5826	188	2	1	1	X
ejpam-5826	188	3	.	.	X
ejpam-5826	188	4	using	use	VERB
ejpam-5826	188	5	definition	definition	NOUN
ejpam-5826	188	6	1	1	NUM
ejpam-5826	188	7	,	,	PUNCT
ejpam-5826	188	8	we	we	PRON
ejpam-5826	188	9	obtain	obtain	VERB
ejpam-5826	188	10	lim	lim	PROPN
ejpam-5826	188	11	i→∞	i→∞	PROPN
ejpam-5826	188	12	(	(	PUNCT
ejpam-5826	188	13	d(e	d(e	NOUN
ejpam-5826	188	14	hk̃(i)−1	hk̃(i)−1	VERB
ejpam-5826	188	15	q	q	PROPN
ejpam-5826	188	16	,	,	PUNCT
ejpam-5826	188	17	f	f	PROPN
ejpam-5826	188	18	hk(i)−1q	hk(i)−1q	PROPN
ejpam-5826	188	19	)	)	PUNCT
ejpam-5826	188	20	)	)	PUNCT
ejpam-5826	189	1	=	=	PUNCT
ejpam-5826	189	2	0	0	X
ejpam-5826	189	3	.	.	PUNCT
ejpam-5826	190	1	(	(	PUNCT
ejpam-5826	190	2	14	14	NUM
ejpam-5826	190	3	)	)	PUNCT
ejpam-5826	190	4	in	in	ADP
ejpam-5826	190	5	view	view	NOUN
ejpam-5826	190	6	of	of	ADP
ejpam-5826	190	7	d(e	d(e	PROPN
ejpam-5826	190	8	hk̃(i)−1	hk̃(i)−1	VERB
ejpam-5826	190	9	q	q	ADJ
ejpam-5826	190	10	,	,	PUNCT
ejpam-5826	190	11	ehk(i)−1q	ehk(i)−1q	NOUN
ejpam-5826	190	12	)	)	PUNCT
ejpam-5826	190	13	≤	≤	PUNCT
ejpam-5826	191	1	d(e	d(e	PROPN
ejpam-5826	191	2	hk̃(i)−1	hk̃(i)−1	VERB
ejpam-5826	191	3	q	q	PROPN
ejpam-5826	191	4	,	,	PUNCT
ejpam-5826	191	5	f	f	PROPN
ejpam-5826	191	6	hk(i)−1q	hk(i)−1q	PROPN
ejpam-5826	191	7	)	)	PUNCT
ejpam-5826	192	1	+	+	NUM
ejpam-5826	192	2	d(f	d(f	PROPN
ejpam-5826	192	3	hk(i)−1q	hk(i)−1q	PROPN
ejpam-5826	192	4	,	,	PUNCT
ejpam-5826	192	5	ehk(i)−1q	ehk(i)−1q	PROPN
ejpam-5826	192	6	)	)	PUNCT
ejpam-5826	192	7	,	,	PUNCT
ejpam-5826	192	8	a	a	DET
ejpam-5826	192	9	combination	combination	NOUN
ejpam-5826	192	10	of	of	ADP
ejpam-5826	192	11	(	(	PUNCT
ejpam-5826	192	12	7	7	NUM
ejpam-5826	192	13	)	)	PUNCT
ejpam-5826	192	14	and	and	CCONJ
ejpam-5826	192	15	(	(	PUNCT
ejpam-5826	192	16	14	14	NUM
ejpam-5826	192	17	)	)	PUNCT
ejpam-5826	192	18	,	,	PUNCT
ejpam-5826	192	19	gives	give	VERB
ejpam-5826	192	20	lim	lim	PROPN
ejpam-5826	192	21	i→∞	i→∞	NUM
ejpam-5826	192	22	d(e	d(e	PROPN
ejpam-5826	192	23	hk̃(i)−1	hk̃(i)−1	VERB
ejpam-5826	192	24	q	q	NOUN
ejpam-5826	192	25	,	,	PUNCT
ejpam-5826	192	26	f	f	PROPN
ejpam-5826	192	27	hk(i)−1q	hk(i)−1q	PROPN
ejpam-5826	192	28	)	)	PUNCT
ejpam-5826	193	1	=	=	PUNCT
ejpam-5826	194	1	0	0	X
ejpam-5826	194	2	.	.	PUNCT
ejpam-5826	195	1	it	it	PRON
ejpam-5826	195	2	contradicts	contradict	VERB
ejpam-5826	195	3	(	(	PUNCT
ejpam-5826	195	4	10	10	NUM
ejpam-5826	195	5	)	)	PUNCT
ejpam-5826	195	6	.	.	PUNCT
ejpam-5826	196	1	hence	hence	ADV
ejpam-5826	196	2	{	{	PUNCT
ejpam-5826	196	3	qhk	qhk	NOUN
ejpam-5826	196	4	}	}	PUNCT
ejpam-5826	196	5	=	=	SYM
ejpam-5826	196	6	{	{	PUNCT
ejpam-5826	196	7	ehkq	ehkq	NOUN
ejpam-5826	196	8	}	}	PUNCT
ejpam-5826	196	9	is	be	AUX
ejpam-5826	196	10	a	a	DET
ejpam-5826	196	11	cauchy	cauchy	ADJ
ejpam-5826	196	12	sequence	sequence	NOUN
ejpam-5826	196	13	.	.	PUNCT
ejpam-5826	197	1	since	since	SCONJ
ejpam-5826	197	2	q	q	PROPN
ejpam-5826	197	3	is	be	AUX
ejpam-5826	197	4	complete	complete	ADJ
ejpam-5826	197	5	,	,	PUNCT
ejpam-5826	197	6	{	{	PUNCT
ejpam-5826	197	7	qhk	qhk	NOUN
ejpam-5826	197	8	}	}	PUNCT
ejpam-5826	197	9	converges	converge	VERB
ejpam-5826	197	10	to	to	ADP
ejpam-5826	197	11	u	u	NOUN
ejpam-5826	197	12	in	in	ADP
ejpam-5826	197	13	q.	q.	NOUN
ejpam-5826	197	14	since	since	SCONJ
ejpam-5826	197	15	d(f	d(f	NOUN
ejpam-5826	197	16	hkq	hkq	NOUN
ejpam-5826	197	17	,	,	PUNCT
ejpam-5826	197	18	u	u	NOUN
ejpam-5826	197	19	)	)	PUNCT
ejpam-5826	197	20	≤	≤	NUM
ejpam-5826	197	21	d(ehkq	d(ehkq	NOUN
ejpam-5826	197	22	,	,	PUNCT
ejpam-5826	197	23	f	f	PROPN
ejpam-5826	197	24	hkq	hkq	PROPN
ejpam-5826	197	25	)	)	PUNCT
ejpam-5826	197	26	+	+	CCONJ
ejpam-5826	198	1	d(ehkq	d(ehkq	PROPN
ejpam-5826	198	2	,	,	PUNCT
ejpam-5826	198	3	u	u	NOUN
ejpam-5826	198	4	)	)	PUNCT
ejpam-5826	198	5	,	,	PUNCT
ejpam-5826	198	6	therefore	therefore	ADV
ejpam-5826	198	7	by	by	ADP
ejpam-5826	198	8	(	(	PUNCT
ejpam-5826	198	9	7	7	NUM
ejpam-5826	198	10	)	)	PUNCT
ejpam-5826	198	11	,	,	PUNCT
ejpam-5826	198	12	we	we	PRON
ejpam-5826	198	13	conclude	conclude	VERB
ejpam-5826	198	14	that	that	SCONJ
ejpam-5826	198	15	{	{	PUNCT
ejpam-5826	198	16	f	f	PROPN
ejpam-5826	198	17	hkq	hkq	PROPN
ejpam-5826	198	18	}	}	PUNCT
ejpam-5826	198	19	converges	converge	VERB
ejpam-5826	198	20	to	to	PART
ejpam-5826	198	21	u.	u.	VERB
ejpam-5826	198	22	suppose	suppose	VERB
ejpam-5826	198	23	that	that	SCONJ
ejpam-5826	198	24	e	e	PROPN
ejpam-5826	198	25	is	be	AUX
ejpam-5826	198	26	orbitally	orbitally	ADV
ejpam-5826	198	27	continuous	continuous	ADJ
ejpam-5826	198	28	.	.	PUNCT
ejpam-5826	199	1	let	let	VERB
ejpam-5826	199	2	{	{	PUNCT
ejpam-5826	199	3	eqh	eqh	NOUN
ejpam-5826	199	4	}	}	PUNCT
ejpam-5826	199	5	be	be	AUX
ejpam-5826	199	6	a	a	DET
ejpam-5826	199	7	sequence	sequence	NOUN
ejpam-5826	199	8	in	in	ADP
ejpam-5826	199	9	the	the	DET
ejpam-5826	199	10	orbit	orbit	NOUN
ejpam-5826	199	11	of	of	ADP
ejpam-5826	199	12	e	e	PROPN
ejpam-5826	199	13	at	at	ADP
ejpam-5826	199	14	the	the	DET
ejpam-5826	199	15	point	point	NOUN
ejpam-5826	199	16	q.	q.	NOUN
ejpam-5826	199	17	the	the	DET
ejpam-5826	199	18	orbital	orbital	ADJ
ejpam-5826	199	19	continuity	continuity	NOUN
ejpam-5826	199	20	of	of	ADP
ejpam-5826	199	21	e	e	PROPN
ejpam-5826	199	22	implies	imply	VERB
ejpam-5826	199	23	that	that	SCONJ
ejpam-5826	199	24	{	{	PUNCT
ejpam-5826	199	25	eqhk	eqhk	NOUN
ejpam-5826	199	26	}	}	PUNCT
ejpam-5826	199	27	converges	converge	VERB
ejpam-5826	199	28	to	to	ADP
ejpam-5826	199	29	eu	eu	PROPN
ejpam-5826	199	30	.	.	PUNCT
ejpam-5826	200	1	by	by	ADP
ejpam-5826	200	2	asymptotically	asymptotically	ADV
ejpam-5826	200	3	regularity	regularity	NOUN
ejpam-5826	200	4	of	of	ADP
ejpam-5826	200	5	e	e	NOUN
ejpam-5826	200	6	,	,	PUNCT
ejpam-5826	200	7	we	we	PRON
ejpam-5826	200	8	have	have	VERB
ejpam-5826	200	9	lim	lim	PROPN
ejpam-5826	200	10	k→∞	k→∞	PROPN
ejpam-5826	200	11	d(qhk+1	d(qhk+1	VERB
ejpam-5826	200	12	,	,	PUNCT
ejpam-5826	200	13	qhk	qhk	ADJ
ejpam-5826	200	14	)	)	PUNCT
ejpam-5826	201	1	=	=	PROPN
ejpam-5826	201	2	lim	lim	PROPN
ejpam-5826	201	3	k→∞	k→∞	PROPN
ejpam-5826	201	4	d(ehk+1q	d(ehk+1q	PROPN
ejpam-5826	201	5	,	,	PUNCT
ejpam-5826	201	6	ehkq	ehkq	NOUN
ejpam-5826	201	7	)	)	PUNCT
ejpam-5826	201	8	=	=	SYM
ejpam-5826	201	9	0	0	NUM
ejpam-5826	201	10	,	,	PUNCT
ejpam-5826	201	11	which	which	PRON
ejpam-5826	201	12	gives	give	VERB
ejpam-5826	201	13	lim	lim	PROPN
ejpam-5826	201	14	k→∞	k→∞	NOUN
ejpam-5826	201	15	d(qhk+1	d(qhk+1	VERB
ejpam-5826	201	16	,	,	PUNCT
ejpam-5826	201	17	qhk	qhk	ADJ
ejpam-5826	201	18	)	)	PUNCT
ejpam-5826	201	19	≤	≤	NOUN
ejpam-5826	202	1	lim	lim	PROPN
ejpam-5826	202	2	k→∞	k→∞	PROPN
ejpam-5826	202	3	(	(	PUNCT
ejpam-5826	202	4	d(qhk+1	d(qhk+1	NOUN
ejpam-5826	202	5	,	,	PUNCT
ejpam-5826	202	6	eqhk+1	eqhk+1	NOUN
ejpam-5826	202	7	)	)	PUNCT
ejpam-5826	203	1	+	+	CCONJ
ejpam-5826	203	2	d(eqhk+1	d(eqhk+1	NOUN
ejpam-5826	203	3	,	,	PUNCT
ejpam-5826	203	4	eqhk	eqhk	NOUN
ejpam-5826	203	5	)	)	PUNCT
ejpam-5826	204	1	+	+	NUM
ejpam-5826	204	2	d(eqhk	d(eqhk	NOUN
ejpam-5826	204	3	,	,	PUNCT
ejpam-5826	204	4	qhk	qhk	NOUN
ejpam-5826	204	5	)	)	PUNCT
ejpam-5826	204	6	)	)	PUNCT
ejpam-5826	204	7	.	.	PUNCT
ejpam-5826	205	1	a.	a.	PROPN
ejpam-5826	205	2	r.	r.	PROPN
ejpam-5826	205	3	khan	khan	PROPN
ejpam-5826	205	4	et	et	PROPN
ejpam-5826	205	5	al	al	PROPN
ejpam-5826	205	6	.	.	PUNCT
ejpam-5826	205	7	/	/	SYM
ejpam-5826	205	8	eur	eur	PROPN
ejpam-5826	205	9	.	.	PUNCT
ejpam-5826	206	1	j.	j.	PROPN
ejpam-5826	206	2	pure	pure	PROPN
ejpam-5826	206	3	appl	appl	PROPN
ejpam-5826	206	4	.	.	PROPN
ejpam-5826	206	5	math	math	PROPN
ejpam-5826	206	6	,	,	PUNCT
ejpam-5826	206	7	18	18	NUM
ejpam-5826	206	8	(	(	PUNCT
ejpam-5826	206	9	2	2	NUM
ejpam-5826	206	10	)	)	PUNCT
ejpam-5826	206	11	(	(	PUNCT
ejpam-5826	206	12	2025	2025	NUM
ejpam-5826	206	13	)	)	PUNCT
ejpam-5826	206	14	,	,	PUNCT
ejpam-5826	206	15	5826	5826	NUM
ejpam-5826	206	16	9	9	NUM
ejpam-5826	206	17	of	of	ADP
ejpam-5826	206	18	23	23	NUM
ejpam-5826	206	19	since	since	SCONJ
ejpam-5826	206	20	d(qhk+1	d(qhk+1	NOUN
ejpam-5826	206	21	,	,	PUNCT
ejpam-5826	206	22	eqhk+1	eqhk+1	NOUN
ejpam-5826	206	23	)	)	PUNCT
ejpam-5826	206	24	→	→	SYM
ejpam-5826	206	25	0	0	NUM
ejpam-5826	206	26	,	,	PUNCT
ejpam-5826	206	27	d(eqhk	d(eqhk	NOUN
ejpam-5826	206	28	,	,	PUNCT
ejpam-5826	206	29	qhk	qhk	NOUN
ejpam-5826	206	30	)	)	PUNCT
ejpam-5826	207	1	→	→	SYM
ejpam-5826	207	2	0	0	NUM
ejpam-5826	207	3	,	,	PUNCT
ejpam-5826	207	4	therefore	therefore	ADV
ejpam-5826	207	5	,	,	PUNCT
ejpam-5826	207	6	lim	lim	PROPN
ejpam-5826	207	7	k→∞	k→∞	PROPN
ejpam-5826	207	8	d(qhk+1	d(qhk+1	VERB
ejpam-5826	207	9	,	,	PUNCT
ejpam-5826	207	10	qhk	qhk	ADJ
ejpam-5826	207	11	)	)	PUNCT
ejpam-5826	208	1	=	=	PUNCT
ejpam-5826	208	2	0	0	X
ejpam-5826	208	3	.	.	PUNCT
ejpam-5826	209	1	hence	hence	ADV
ejpam-5826	209	2	lim	lim	PROPN
ejpam-5826	209	3	k→∞	k→∞	NOUN
ejpam-5826	209	4	eqhk	eqhk	PROPN
ejpam-5826	209	5	=	=	PROPN
ejpam-5826	209	6	lim	lim	PROPN
ejpam-5826	209	7	k→∞	k→∞	PROPN
ejpam-5826	209	8	qhk+1	qhk+1	PROPN
ejpam-5826	209	9	=	=	SYM
ejpam-5826	209	10	lim	lim	PROPN
ejpam-5826	209	11	k→∞	k→∞	NOUN
ejpam-5826	209	12	qhk	qhk	NOUN
ejpam-5826	209	13	=	=	SYM
ejpam-5826	209	14	u	u	PROPN
ejpam-5826	209	15	implies	imply	VERB
ejpam-5826	209	16	that	that	SCONJ
ejpam-5826	209	17	eu	eu	PROPN
ejpam-5826	209	18	=	=	SYM
ejpam-5826	209	19	u	u	PROPN
ejpam-5826	209	20	by	by	ADP
ejpam-5826	209	21	the	the	DET
ejpam-5826	209	22	uniqueness	uniqueness	NOUN
ejpam-5826	209	23	of	of	ADP
ejpam-5826	209	24	limit	limit	NOUN
ejpam-5826	209	25	.	.	PUNCT
ejpam-5826	210	1	now	now	ADV
ejpam-5826	210	2	suppose	suppose	VERB
ejpam-5826	210	3	that	that	SCONJ
ejpam-5826	210	4	e	e	PROPN
ejpam-5826	210	5	is	be	AUX
ejpam-5826	210	6	k	k	ADJ
ejpam-5826	210	7	-	-	ADJ
ejpam-5826	210	8	continuous	continuous	ADJ
ejpam-5826	210	9	.	.	PUNCT
ejpam-5826	211	1	in	in	ADP
ejpam-5826	211	2	view	view	NOUN
ejpam-5826	211	3	of	of	ADP
ejpam-5826	211	4	d(qhk+j	d(qhk+j	NOUN
ejpam-5826	211	5	,	,	PUNCT
ejpam-5826	211	6	qhk	qhk	ADJ
ejpam-5826	211	7	)	)	PUNCT
ejpam-5826	211	8	≤	≤	NOUN
ejpam-5826	211	9	d(qhk+j	d(qhk+j	NOUN
ejpam-5826	211	10	,	,	PUNCT
ejpam-5826	211	11	qhk+j−1	qhk+j−1	NOUN
ejpam-5826	211	12	)	)	PUNCT
ejpam-5826	212	1	+	+	CCONJ
ejpam-5826	212	2	·	·	PUNCT
ejpam-5826	212	3	·	·	PUNCT
ejpam-5826	212	4	·	·	PUNCT
ejpam-5826	212	5	+	+	CCONJ
ejpam-5826	212	6	d(qhk+1	d(qhk+1	NUM
ejpam-5826	212	7	,	,	PUNCT
ejpam-5826	212	8	qhk	qhk	ADJ
ejpam-5826	212	9	)	)	PUNCT
ejpam-5826	212	10	and	and	CCONJ
ejpam-5826	212	11	d(ehk+jqhk+j	d(ehk+jqhk+j	NOUN
ejpam-5826	212	12	,	,	PUNCT
ejpam-5826	212	13	ehkqhk	ehkqhk	ADV
ejpam-5826	212	14	)	)	PUNCT
ejpam-5826	212	15	=	=	SYM
ejpam-5826	212	16	d(ehk+jq	d(ehk+jq	PROPN
ejpam-5826	212	17	,	,	PUNCT
ejpam-5826	212	18	ehk+j−1q	ehk+j−1q	NUM
ejpam-5826	212	19	)	)	PUNCT
ejpam-5826	213	1	+	+	CCONJ
ejpam-5826	213	2	·	·	PUNCT
ejpam-5826	213	3	·	·	PUNCT
ejpam-5826	213	4	·	·	PUNCT
ejpam-5826	213	5	+	+	NUM
ejpam-5826	213	6	d(ehk+1q	d(ehk+1q	PROPN
ejpam-5826	213	7	,	,	PUNCT
ejpam-5826	213	8	ehkq	ehkq	NOUN
ejpam-5826	213	9	)	)	PUNCT
ejpam-5826	213	10	,	,	PUNCT
ejpam-5826	213	11	for	for	ADP
ejpam-5826	213	12	all	all	DET
ejpam-5826	213	13	j	j	NOUN
ejpam-5826	213	14	=	=	SYM
ejpam-5826	213	15	1	1	NUM
ejpam-5826	213	16	,	,	PUNCT
ejpam-5826	213	17	2	2	NUM
ejpam-5826	213	18	,	,	PUNCT
ejpam-5826	213	19	3	3	NUM
ejpam-5826	213	20	,	,	PUNCT
ejpam-5826	213	21	·	·	PUNCT
ejpam-5826	213	22	·	·	PUNCT
ejpam-5826	213	23	·	·	PUNCT
ejpam-5826	213	24	,	,	PUNCT
ejpam-5826	213	25	k	k	X
ejpam-5826	213	26	by	by	ADP
ejpam-5826	213	27	asymptotic	asymptotic	ADJ
ejpam-5826	213	28	regularity	regularity	NOUN
ejpam-5826	213	29	of	of	ADP
ejpam-5826	213	30	e	e	NOUN
ejpam-5826	213	31	,	,	PUNCT
ejpam-5826	213	32	we	we	PRON
ejpam-5826	213	33	get	get	VERB
ejpam-5826	213	34	lim	lim	PROPN
ejpam-5826	213	35	k→∞	k→∞	NOUN
ejpam-5826	213	36	qhk+j	qhk+j	PROPN
ejpam-5826	214	1	=	=	SYM
ejpam-5826	215	1	lim	lim	PROPN
ejpam-5826	215	2	k→∞	k→∞	PROPN
ejpam-5826	215	3	qhk	qhk	PROPN
ejpam-5826	215	4	=	=	SYM
ejpam-5826	215	5	u	u	PROPN
ejpam-5826	215	6	,	,	PUNCT
ejpam-5826	215	7	j	j	PROPN
ejpam-5826	215	8	=	=	SYM
ejpam-5826	215	9	1	1	NUM
ejpam-5826	215	10	,	,	PUNCT
ejpam-5826	215	11	2	2	NUM
ejpam-5826	215	12	,	,	PUNCT
ejpam-5826	215	13	3	3	NUM
ejpam-5826	215	14	,	,	PUNCT
ejpam-5826	215	15	·	·	PUNCT
ejpam-5826	215	16	·	·	PUNCT
ejpam-5826	215	17	·	·	PUNCT
ejpam-5826	215	18	,	,	PUNCT
ejpam-5826	215	19	k.	k.	PROPN
ejpam-5826	215	20	(	(	PUNCT
ejpam-5826	215	21	15	15	NUM
ejpam-5826	215	22	)	)	PUNCT
ejpam-5826	215	23	in	in	ADP
ejpam-5826	215	24	particular	particular	ADJ
ejpam-5826	215	25	,	,	PUNCT
ejpam-5826	215	26	lim	lim	PROPN
ejpam-5826	215	27	k→∞	k→∞	PROPN
ejpam-5826	215	28	ek−1qhk	ek−1qhk	PROPN
ejpam-5826	215	29	=	=	PROPN
ejpam-5826	215	30	lim	lim	PROPN
ejpam-5826	215	31	k→∞	k→∞	NOUN
ejpam-5826	215	32	qhk+j−1	qhk+j−1	X
ejpam-5826	215	33	=	=	PUNCT
ejpam-5826	215	34	u.	u.	NOUN
ejpam-5826	215	35	(	(	PUNCT
ejpam-5826	215	36	16	16	NUM
ejpam-5826	215	37	)	)	PUNCT
ejpam-5826	215	38	as	as	SCONJ
ejpam-5826	215	39	e	e	NOUN
ejpam-5826	215	40	is	be	AUX
ejpam-5826	215	41	k	k	ADJ
ejpam-5826	215	42	-	-	ADJ
ejpam-5826	215	43	continuous	continuous	ADJ
ejpam-5826	215	44	,	,	PUNCT
ejpam-5826	215	45	(	(	PUNCT
ejpam-5826	215	46	16	16	NUM
ejpam-5826	215	47	)	)	PUNCT
ejpam-5826	215	48	gives	give	VERB
ejpam-5826	215	49	lim	lim	PROPN
ejpam-5826	215	50	k→∞	k→∞	NOUN
ejpam-5826	215	51	ekqhk	ekqhk	PROPN
ejpam-5826	215	52	=	=	PROPN
ejpam-5826	215	53	eu	eu	PROPN
ejpam-5826	215	54	.	.	PUNCT
ejpam-5826	216	1	(	(	PUNCT
ejpam-5826	216	2	17	17	NUM
ejpam-5826	216	3	)	)	PUNCT
ejpam-5826	216	4	by	by	ADP
ejpam-5826	216	5	(	(	PUNCT
ejpam-5826	216	6	15	15	NUM
ejpam-5826	216	7	)	)	PUNCT
ejpam-5826	216	8	,	,	PUNCT
ejpam-5826	216	9	we	we	PRON
ejpam-5826	216	10	have	have	VERB
ejpam-5826	216	11	lim	lim	PROPN
ejpam-5826	216	12	k→∞	k→∞	NOUN
ejpam-5826	216	13	ekqhk	ekqhk	PROPN
ejpam-5826	217	1	=	=	PROPN
ejpam-5826	217	2	lim	lim	PROPN
ejpam-5826	217	3	k→∞	k→∞	NOUN
ejpam-5826	217	4	qhk+j	qhk+j	PROPN
ejpam-5826	217	5	=	=	PUNCT
ejpam-5826	217	6	u.	u.	NOUN
ejpam-5826	217	7	(	(	PUNCT
ejpam-5826	217	8	18	18	NUM
ejpam-5826	217	9	)	)	PUNCT
ejpam-5826	217	10	a	a	DET
ejpam-5826	217	11	combination	combination	NOUN
ejpam-5826	217	12	of	of	ADP
ejpam-5826	217	13	(	(	PUNCT
ejpam-5826	217	14	17	17	NUM
ejpam-5826	217	15	)	)	PUNCT
ejpam-5826	217	16	and	and	CCONJ
ejpam-5826	217	17	(	(	PUNCT
ejpam-5826	217	18	18	18	NUM
ejpam-5826	217	19	)	)	PUNCT
ejpam-5826	217	20	,	,	PUNCT
ejpam-5826	217	21	gives	give	VERB
ejpam-5826	217	22	eu	eu	PROPN
ejpam-5826	217	23	=	=	NOUN
ejpam-5826	217	24	u.	u.	PROPN
ejpam-5826	217	25	similarly	similarly	ADV
ejpam-5826	217	26	,	,	PUNCT
ejpam-5826	217	27	we	we	PRON
ejpam-5826	217	28	can	can	AUX
ejpam-5826	217	29	prove	prove	VERB
ejpam-5826	217	30	that	that	DET
ejpam-5826	217	31	fu	fu	NOUN
ejpam-5826	217	32	=	=	NOUN
ejpam-5826	217	33	u.	u.	NOUN
ejpam-5826	218	1	so	so	ADV
ejpam-5826	218	2	u	u	NOUN
ejpam-5826	218	3	is	be	AUX
ejpam-5826	218	4	a	a	DET
ejpam-5826	218	5	common	common	ADJ
ejpam-5826	218	6	fixed	fix	VERB
ejpam-5826	218	7	point	point	NOUN
ejpam-5826	218	8	of	of	ADP
ejpam-5826	218	9	e	e	PROPN
ejpam-5826	218	10	and	and	CCONJ
ejpam-5826	218	11	f	f	PROPN
ejpam-5826	218	12	.	.	PUNCT
ejpam-5826	219	1	next	next	ADV
ejpam-5826	219	2	,	,	PUNCT
ejpam-5826	219	3	assume	assume	VERB
ejpam-5826	219	4	that	that	SCONJ
ejpam-5826	219	5	v	v	NOUN
ejpam-5826	219	6	is	be	AUX
ejpam-5826	219	7	another	another	DET
ejpam-5826	219	8	common	common	ADJ
ejpam-5826	219	9	fixed	fix	VERB
ejpam-5826	219	10	point	point	NOUN
ejpam-5826	219	11	of	of	ADP
ejpam-5826	219	12	e	e	PROPN
ejpam-5826	219	13	and	and	CCONJ
ejpam-5826	219	14	f	f	PROPN
ejpam-5826	219	15	with	with	ADP
ejpam-5826	219	16	u	u	NOUN
ejpam-5826	219	17	̸=	̸=	PROPN
ejpam-5826	219	18	v.	v.	ADP
ejpam-5826	219	19	definition	definition	NOUN
ejpam-5826	219	20	1	1	NUM
ejpam-5826	219	21	(	(	PUNCT
ejpam-5826	219	22	i	i	NOUN
ejpam-5826	219	23	)	)	PUNCT
ejpam-5826	219	24	applied	apply	VERB
ejpam-5826	219	25	to	to	ADP
ejpam-5826	219	26	(	(	PUNCT
ejpam-5826	219	27	3	3	X
ejpam-5826	219	28	)	)	PUNCT
ejpam-5826	219	29	gives	give	VERB
ejpam-5826	219	30	d(u	d(u	PROPN
ejpam-5826	219	31	,	,	PUNCT
ejpam-5826	219	32	v	v	NOUN
ejpam-5826	219	33	)	)	PUNCT
ejpam-5826	219	34	=	=	SYM
ejpam-5826	219	35	d(eu	d(eu	NOUN
ejpam-5826	219	36	,	,	PUNCT
ejpam-5826	219	37	fv	fv	NOUN
ejpam-5826	219	38	)	)	PUNCT
ejpam-5826	219	39	≤	≤	NOUN
ejpam-5826	219	40	κ(d(u	κ(d(u	PROPN
ejpam-5826	219	41	,	,	PUNCT
ejpam-5826	219	42	v))d(u	v))d(u	PROPN
ejpam-5826	219	43	,	,	PUNCT
ejpam-5826	219	44	v	v	NOUN
ejpam-5826	219	45	)	)	PUNCT
ejpam-5826	220	1	+	+	NOUN
ejpam-5826	220	2	k[d(u	k[d(u	PROPN
ejpam-5826	220	3	,	,	PUNCT
ejpam-5826	220	4	eu	eu	NOUN
ejpam-5826	220	5	)	)	PUNCT
ejpam-5826	221	1	+	+	X
ejpam-5826	221	2	d(v	d(v	PROPN
ejpam-5826	221	3	,	,	PUNCT
ejpam-5826	221	4	fv	fv	NOUN
ejpam-5826	221	5	)	)	PUNCT
ejpam-5826	221	6	]	]	PUNCT
ejpam-5826	221	7	.	.	PUNCT
ejpam-5826	222	1	a.	a.	PROPN
ejpam-5826	222	2	r.	r.	PROPN
ejpam-5826	222	3	khan	khan	PROPN
ejpam-5826	222	4	et	et	PROPN
ejpam-5826	222	5	al	al	PROPN
ejpam-5826	222	6	.	.	PUNCT
ejpam-5826	222	7	/	/	SYM
ejpam-5826	222	8	eur	eur	PROPN
ejpam-5826	222	9	.	.	PUNCT
ejpam-5826	223	1	j.	j.	PROPN
ejpam-5826	223	2	pure	pure	PROPN
ejpam-5826	223	3	appl	appl	PROPN
ejpam-5826	223	4	.	.	PROPN
ejpam-5826	223	5	math	math	PROPN
ejpam-5826	223	6	,	,	PUNCT
ejpam-5826	223	7	18	18	NUM
ejpam-5826	223	8	(	(	PUNCT
ejpam-5826	223	9	2	2	NUM
ejpam-5826	223	10	)	)	PUNCT
ejpam-5826	223	11	(	(	PUNCT
ejpam-5826	223	12	2025	2025	NUM
ejpam-5826	223	13	)	)	PUNCT
ejpam-5826	223	14	,	,	PUNCT
ejpam-5826	223	15	5826	5826	NUM
ejpam-5826	223	16	10	10	NUM
ejpam-5826	223	17	of	of	ADP
ejpam-5826	223	18	23	23	NUM
ejpam-5826	223	19	d(u	d(u	PROPN
ejpam-5826	223	20	,	,	PUNCT
ejpam-5826	223	21	v	v	NOUN
ejpam-5826	223	22	)	)	PUNCT
ejpam-5826	223	23	≤	≤	NOUN
ejpam-5826	223	24	κ(d(u	κ(d(u	PROPN
ejpam-5826	223	25	,	,	PUNCT
ejpam-5826	223	26	v))d(u	v))d(u	PROPN
ejpam-5826	223	27	,	,	PUNCT
ejpam-5826	223	28	v	v	NOUN
ejpam-5826	223	29	)	)	PUNCT
ejpam-5826	223	30	.	.	PUNCT
ejpam-5826	224	1	d(u	d(u	PROPN
ejpam-5826	224	2	,	,	PUNCT
ejpam-5826	224	3	v	v	NOUN
ejpam-5826	224	4	)	)	PUNCT
ejpam-5826	224	5	<	<	X
ejpam-5826	224	6	d(u	d(u	PROPN
ejpam-5826	224	7	,	,	PUNCT
ejpam-5826	224	8	v	v	NOUN
ejpam-5826	224	9	)	)	PUNCT
ejpam-5826	224	10	,	,	PUNCT
ejpam-5826	224	11	which	which	PRON
ejpam-5826	224	12	is	be	AUX
ejpam-5826	224	13	a	a	DET
ejpam-5826	224	14	contradiction	contradiction	NOUN
ejpam-5826	224	15	.	.	PUNCT
ejpam-5826	225	1	therefore	therefore	ADV
ejpam-5826	225	2	common	common	ADJ
ejpam-5826	225	3	fixed	fix	VERB
ejpam-5826	225	4	point	point	NOUN
ejpam-5826	225	5	of	of	ADP
ejpam-5826	225	6	e	e	PROPN
ejpam-5826	225	7	and	and	CCONJ
ejpam-5826	225	8	f	f	PROPN
ejpam-5826	225	9	is	be	AUX
ejpam-5826	225	10	unique	unique	ADJ
ejpam-5826	225	11	.	.	PUNCT
ejpam-5826	226	1	case	case	NOUN
ejpam-5826	226	2	2	2	NUM
ejpam-5826	226	3	:	:	PUNCT
ejpam-5826	226	4	lim	lim	PROPN
ejpam-5826	226	5	sup	sup	PROPN
ejpam-5826	226	6	h→∞	h→∞	NUM
ejpam-5826	226	7	κ(d(ehq	κ(d(ehq	NOUN
ejpam-5826	226	8	,	,	PUNCT
ejpam-5826	226	9	f	f	PROPN
ejpam-5826	226	10	hq	hq	PROPN
ejpam-5826	226	11	)	)	PUNCT
ejpam-5826	226	12	)	)	PUNCT
ejpam-5826	227	1	<	<	X
ejpam-5826	227	2	1	1	X
ejpam-5826	227	3	.	.	PUNCT
ejpam-5826	227	4	in	in	ADP
ejpam-5826	227	5	this	this	DET
ejpam-5826	227	6	case	case	NOUN
ejpam-5826	227	7	,	,	PUNCT
ejpam-5826	227	8	there	there	PRON
ejpam-5826	227	9	exists	exist	VERB
ejpam-5826	227	10	σ	σ	PROPN
ejpam-5826	227	11	∈	∈	PROPN
ejpam-5826	227	12	(	(	PUNCT
ejpam-5826	227	13	0	0	NUM
ejpam-5826	227	14	,	,	PUNCT
ejpam-5826	227	15	1	1	NUM
ejpam-5826	227	16	)	)	PUNCT
ejpam-5826	227	17	such	such	ADJ
ejpam-5826	227	18	that	that	SCONJ
ejpam-5826	227	19	0	0	NUM
ejpam-5826	227	20	<	<	X
ejpam-5826	227	21	κ(d(ehq	κ(d(ehq	NOUN
ejpam-5826	227	22	,	,	PUNCT
ejpam-5826	227	23	f	f	PROPN
ejpam-5826	227	24	hq	hq	PROPN
ejpam-5826	227	25	)	)	PUNCT
ejpam-5826	227	26	)	)	PUNCT
ejpam-5826	228	1	<	<	X
ejpam-5826	228	2	σ	σ	PROPN
ejpam-5826	228	3	.	.	PUNCT
ejpam-5826	229	1	by	by	ADP
ejpam-5826	229	2	(	(	PUNCT
ejpam-5826	229	3	5	5	X
ejpam-5826	229	4	)	)	PUNCT
ejpam-5826	229	5	we	we	PRON
ejpam-5826	229	6	have	have	AUX
ejpam-5826	229	7	(	(	PUNCT
ejpam-5826	229	8	d(eh+1q	d(eh+1q	PROPN
ejpam-5826	229	9	,	,	PUNCT
ejpam-5826	229	10	f	f	PROPN
ejpam-5826	229	11	h+1q	h+1q	NOUN
ejpam-5826	229	12	)	)	PUNCT
ejpam-5826	229	13	)	)	PUNCT
ejpam-5826	229	14	≤	≤	NUM
ejpam-5826	229	15	σd(ehq	σd(ehq	NOUN
ejpam-5826	229	16	,	,	PUNCT
ejpam-5826	229	17	f	f	PROPN
ejpam-5826	229	18	hq	hq	NOUN
ejpam-5826	229	19	)	)	PUNCT
ejpam-5826	230	1	+	+	NOUN
ejpam-5826	230	2	k(d(ehq	k(d(ehq	NOUN
ejpam-5826	230	3	,	,	PUNCT
ejpam-5826	230	4	eh+1q	eh+1q	NOUN
ejpam-5826	230	5	)	)	PUNCT
ejpam-5826	230	6	+	+	CCONJ
ejpam-5826	230	7	d(f	d(f	NOUN
ejpam-5826	230	8	hq	hq	VERB
ejpam-5826	230	9	,	,	PUNCT
ejpam-5826	230	10	f	f	PROPN
ejpam-5826	230	11	h+1q	h+1q	PROPN
ejpam-5826	230	12	)	)	PUNCT
ejpam-5826	230	13	)	)	PUNCT
ejpam-5826	230	14	.	.	PUNCT
ejpam-5826	231	1	(	(	PUNCT
ejpam-5826	231	2	19	19	NUM
ejpam-5826	231	3	)	)	PUNCT
ejpam-5826	231	4	let	let	VERB
ejpam-5826	231	5	uh	uh	INTJ
ejpam-5826	231	6	=	=	SYM
ejpam-5826	231	7	d(ehq	d(ehq	PROPN
ejpam-5826	231	8	,	,	PUNCT
ejpam-5826	231	9	f	f	PROPN
ejpam-5826	231	10	hq	hq	PROPN
ejpam-5826	231	11	)	)	PUNCT
ejpam-5826	231	12	,	,	PUNCT
ejpam-5826	231	13	vh	vh	PROPN
ejpam-5826	231	14	=	=	SYM
ejpam-5826	231	15	1−	1−	NUM
ejpam-5826	231	16	σ	σ	NUM
ejpam-5826	231	17	,	,	PUNCT
ejpam-5826	231	18	wh	wh	NOUN
ejpam-5826	231	19	=	=	PUNCT
ejpam-5826	231	20	k(d(ehq	k(d(ehq	PROPN
ejpam-5826	231	21	,	,	PUNCT
ejpam-5826	231	22	eh+1q	eh+1q	NOUN
ejpam-5826	231	23	)	)	PUNCT
ejpam-5826	232	1	+	+	CCONJ
ejpam-5826	232	2	d(f	d(f	NOUN
ejpam-5826	232	3	hq	hq	VERB
ejpam-5826	232	4	,	,	PUNCT
ejpam-5826	232	5	f	f	PROPN
ejpam-5826	232	6	h+1q	h+1q	PROPN
ejpam-5826	232	7	)	)	PUNCT
ejpam-5826	232	8	)	)	PUNCT
ejpam-5826	233	1	1−	1−	NUM
ejpam-5826	233	2	σ	σ	NOUN
ejpam-5826	233	3	.	.	PUNCT
ejpam-5826	234	1	by	by	ADP
ejpam-5826	234	2	(	(	PUNCT
ejpam-5826	234	3	19	19	NUM
ejpam-5826	234	4	)	)	PUNCT
ejpam-5826	234	5	,	,	PUNCT
ejpam-5826	234	6	we	we	PRON
ejpam-5826	234	7	have	have	VERB
ejpam-5826	234	8	uh+1	uh+1	ADJ
ejpam-5826	234	9	≤	≤	NOUN
ejpam-5826	234	10	(	(	PUNCT
ejpam-5826	234	11	1−	1−	NUM
ejpam-5826	234	12	vh)uh	vh)uh	NUM
ejpam-5826	234	13	+	+	NUM
ejpam-5826	234	14	vhwh,∀h	vhwh,∀h	NOUN
ejpam-5826	234	15	∈	∈	PROPN
ejpam-5826	234	16	n.	n.	NOUN
ejpam-5826	234	17	since	since	SCONJ
ejpam-5826	234	18	e	e	PROPN
ejpam-5826	234	19	and	and	CCONJ
ejpam-5826	234	20	f	f	PROPN
ejpam-5826	234	21	are	be	AUX
ejpam-5826	234	22	asymptotically	asymptotically	ADV
ejpam-5826	234	23	regular	regular	ADJ
ejpam-5826	234	24	on	on	ADP
ejpam-5826	234	25	q	q	NOUN
ejpam-5826	234	26	,	,	PUNCT
ejpam-5826	234	27	we	we	PRON
ejpam-5826	234	28	conclude	conclude	VERB
ejpam-5826	234	29	lim	lim	PROPN
ejpam-5826	234	30	h→∞	h→∞	NUM
ejpam-5826	234	31	wh	wh	X
ejpam-5826	234	32	=	=	SYM
ejpam-5826	234	33	0	0	X
ejpam-5826	234	34	.	.	PUNCT
ejpam-5826	235	1	moreover	moreover	ADV
ejpam-5826	235	2	,	,	PUNCT
ejpam-5826	235	3	∞∑	∞∑	PROPN
ejpam-5826	235	4	h=1	h=1	X
ejpam-5826	235	5	vh	vh	NOUN
ejpam-5826	235	6	=	=	SYM
ejpam-5826	235	7	∞∑	∞∑	NUM
ejpam-5826	235	8	h=1	h=1	X
ejpam-5826	235	9	(	(	PUNCT
ejpam-5826	235	10	1−	1−	NUM
ejpam-5826	235	11	σ	σ	NUM
ejpam-5826	235	12	)	)	PUNCT
ejpam-5826	235	13	=	=	SYM
ejpam-5826	235	14	∞.	∞.	PROPN
ejpam-5826	235	15	by	by	ADP
ejpam-5826	235	16	lemma	lemma	PROPN
ejpam-5826	235	17	1	1	NUM
ejpam-5826	235	18	,	,	PUNCT
ejpam-5826	235	19	lim	lim	PROPN
ejpam-5826	235	20	h→∞	h→∞	NUM
ejpam-5826	235	21	(	(	PUNCT
ejpam-5826	235	22	ehq	ehq	NOUN
ejpam-5826	235	23	,	,	PUNCT
ejpam-5826	235	24	f	f	PROPN
ejpam-5826	235	25	hq	hq	NOUN
ejpam-5826	235	26	)	)	PUNCT
ejpam-5826	235	27	=	=	SYM
ejpam-5826	236	1	0	0	X
ejpam-5826	236	2	.	.	PUNCT
ejpam-5826	237	1	hence	hence	ADV
ejpam-5826	237	2	for	for	ADP
ejpam-5826	237	3	any	any	DET
ejpam-5826	237	4	subsequence	subsequence	NOUN
ejpam-5826	237	5	{	{	PUNCT
ejpam-5826	237	6	hk(i	hk(i	NOUN
ejpam-5826	237	7	)	)	PUNCT
ejpam-5826	237	8	}	}	PUNCT
ejpam-5826	237	9	of	of	ADP
ejpam-5826	237	10	{	{	PUNCT
ejpam-5826	237	11	hk	hk	PROPN
ejpam-5826	237	12	}	}	PUNCT
ejpam-5826	237	13	,	,	PUNCT
ejpam-5826	237	14	we	we	PRON
ejpam-5826	237	15	have	have	VERB
ejpam-5826	237	16	lim	lim	PROPN
ejpam-5826	237	17	i→∞	i→∞	PROPN
ejpam-5826	237	18	(	(	PUNCT
ejpam-5826	237	19	ehk(i)q	ehk(i)q	PROPN
ejpam-5826	237	20	,	,	PUNCT
ejpam-5826	237	21	f	f	PROPN
ejpam-5826	237	22	h(i)q	h(i)q	PROPN
ejpam-5826	237	23	)	)	PUNCT
ejpam-5826	237	24	=	=	SYM
ejpam-5826	238	1	0	0	X
ejpam-5826	238	2	.	.	PUNCT
ejpam-5826	239	1	thus	thus	ADV
ejpam-5826	239	2	(	(	PUNCT
ejpam-5826	239	3	7	7	X
ejpam-5826	239	4	)	)	PUNCT
ejpam-5826	239	5	holds	hold	VERB
ejpam-5826	239	6	.	.	PUNCT
ejpam-5826	240	1	the	the	DET
ejpam-5826	240	2	rest	rest	NOUN
ejpam-5826	240	3	of	of	ADP
ejpam-5826	240	4	proof	proof	NOUN
ejpam-5826	240	5	is	be	AUX
ejpam-5826	240	6	the	the	DET
ejpam-5826	240	7	same	same	ADJ
ejpam-5826	240	8	as	as	ADP
ejpam-5826	240	9	in	in	ADP
ejpam-5826	240	10	case	case	NOUN
ejpam-5826	240	11	i.	i.	NOUN
ejpam-5826	240	12	next	next	ADV
ejpam-5826	240	13	,	,	PUNCT
ejpam-5826	240	14	we	we	PRON
ejpam-5826	240	15	present	present	VERB
ejpam-5826	240	16	a	a	DET
ejpam-5826	240	17	numerical	numerical	ADJ
ejpam-5826	240	18	example	example	NOUN
ejpam-5826	240	19	to	to	PART
ejpam-5826	240	20	illustrate	illustrate	VERB
ejpam-5826	240	21	theorem	theorem	NOUN
ejpam-5826	240	22	4	4	NUM
ejpam-5826	240	23	.	.	NOUN
ejpam-5826	240	24	example	example	NOUN
ejpam-5826	241	1	1	1	NUM
ejpam-5826	241	2	.	.	X
ejpam-5826	241	3	consider	consider	VERB
ejpam-5826	241	4	q	q	NOUN
ejpam-5826	242	1	=	=	PUNCT
ejpam-5826	243	1	[	[	X
ejpam-5826	243	2	0	0	NUM
ejpam-5826	243	3	,	,	PUNCT
ejpam-5826	243	4	1	1	NUM
ejpam-5826	243	5	]	]	PUNCT
ejpam-5826	243	6	,	,	PUNCT
ejpam-5826	243	7	equipped	equip	VERB
ejpam-5826	243	8	with	with	ADP
ejpam-5826	243	9	the	the	DET
ejpam-5826	243	10	metric	metric	ADJ
ejpam-5826	243	11	d	d	NOUN
ejpam-5826	243	12	defined	define	VERB
ejpam-5826	243	13	by	by	ADP
ejpam-5826	243	14	d(q	d(q	PROPN
ejpam-5826	243	15	,	,	PUNCT
ejpam-5826	243	16	p	p	NOUN
ejpam-5826	243	17	)	)	PUNCT
ejpam-5826	243	18	=	=	NOUN
ejpam-5826	243	19	|q	|q	NOUN
ejpam-5826	243	20	−	−	NOUN
ejpam-5826	243	21	p|	p|	NOUN
ejpam-5826	243	22	.	.	PUNCT
ejpam-5826	244	1	define	define	VERB
ejpam-5826	244	2	self	self	NOUN
ejpam-5826	244	3	-	-	PUNCT
ejpam-5826	244	4	mappings	mapping	NOUN
ejpam-5826	244	5	on	on	ADP
ejpam-5826	244	6	q	q	NOUN
ejpam-5826	244	7	:	:	PUNCT
ejpam-5826	244	8	eq	eq	NOUN
ejpam-5826	244	9	=	=	PUNCT
ejpam-5826	244	10	q	q	PROPN
ejpam-5826	244	11	2	2	NUM
ejpam-5826	244	12	and	and	CCONJ
ejpam-5826	244	13	fq	fq	NOUN
ejpam-5826	244	14	=	=	PROPN
ejpam-5826	244	15	q	q	PROPN
ejpam-5826	244	16	3	3	NUM
ejpam-5826	244	17	for	for	ADP
ejpam-5826	244	18	all	all	DET
ejpam-5826	244	19	q	q	PROPN
ejpam-5826	244	20	∈	∈	PROPN
ejpam-5826	244	21	q.	q.	PROPN
ejpam-5826	244	22	a.	a.	PROPN
ejpam-5826	244	23	r.	r.	PROPN
ejpam-5826	244	24	khan	khan	PROPN
ejpam-5826	244	25	et	et	PROPN
ejpam-5826	244	26	al	al	PROPN
ejpam-5826	244	27	.	.	PUNCT
ejpam-5826	244	28	/	/	SYM
ejpam-5826	244	29	eur	eur	PROPN
ejpam-5826	244	30	.	.	PUNCT
ejpam-5826	245	1	j.	j.	PROPN
ejpam-5826	245	2	pure	pure	PROPN
ejpam-5826	245	3	appl	appl	PROPN
ejpam-5826	245	4	.	.	PROPN
ejpam-5826	245	5	math	math	PROPN
ejpam-5826	245	6	,	,	PUNCT
ejpam-5826	245	7	18	18	NUM
ejpam-5826	245	8	(	(	PUNCT
ejpam-5826	245	9	2	2	NUM
ejpam-5826	245	10	)	)	PUNCT
ejpam-5826	245	11	(	(	PUNCT
ejpam-5826	245	12	2025	2025	NUM
ejpam-5826	245	13	)	)	PUNCT
ejpam-5826	245	14	,	,	PUNCT
ejpam-5826	245	15	5826	5826	NUM
ejpam-5826	245	16	11	11	NUM
ejpam-5826	245	17	of	of	ADP
ejpam-5826	245	18	23	23	NUM
ejpam-5826	245	19	for	for	ADP
ejpam-5826	245	20	q	q	NOUN
ejpam-5826	245	21	=	=	SYM
ejpam-5826	245	22	1	1	NUM
ejpam-5826	245	23	2	2	NUM
ejpam-5826	245	24	∈	∈	NOUN
ejpam-5826	245	25	q	q	NOUN
ejpam-5826	245	26	,	,	PUNCT
ejpam-5826	246	1	lim	lim	PROPN
ejpam-5826	246	2	k→∞	k→∞	PROPN
ejpam-5826	246	3	d	d	PROPN
ejpam-5826	246	4	(	(	PUNCT
ejpam-5826	246	5	ek	ek	X
ejpam-5826	246	6	(	(	PUNCT
ejpam-5826	246	7	1	1	NUM
ejpam-5826	246	8	2	2	NUM
ejpam-5826	246	9	)	)	PUNCT
ejpam-5826	246	10	,	,	PUNCT
ejpam-5826	246	11	ek+1	ek+1	NOUN
ejpam-5826	246	12	(	(	PUNCT
ejpam-5826	246	13	1	1	NUM
ejpam-5826	246	14	2	2	NUM
ejpam-5826	246	15	)	)	PUNCT
ejpam-5826	246	16	)	)	PUNCT
ejpam-5826	247	1	=	=	SYM
ejpam-5826	247	2	lim	lim	PROPN
ejpam-5826	247	3	k→∞	k→∞	NOUN
ejpam-5826	247	4	∣∣∣	∣∣∣	NOUN
ejpam-5826	247	5	1	1	NUM
ejpam-5826	247	6	2k+1	2k+1	NUM
ejpam-5826	247	7	−	−	NOUN
ejpam-5826	247	8	1	1	NUM
ejpam-5826	247	9	2k+2	2k+2	NOUN
ejpam-5826	247	10	∣∣∣	∣∣∣	NOUN
ejpam-5826	247	11	=	=	SYM
ejpam-5826	247	12	0	0	NUM
ejpam-5826	247	13	implies	imply	VERB
ejpam-5826	247	14	that	that	SCONJ
ejpam-5826	247	15	e	e	NOUN
ejpam-5826	247	16	is	be	AUX
ejpam-5826	247	17	asymptotically	asymptotically	ADV
ejpam-5826	247	18	regular	regular	ADJ
ejpam-5826	247	19	.	.	PUNCT
ejpam-5826	248	1	similarly	similarly	ADV
ejpam-5826	248	2	,	,	PUNCT
ejpam-5826	248	3	it	it	PRON
ejpam-5826	248	4	can	can	AUX
ejpam-5826	248	5	be	be	AUX
ejpam-5826	248	6	demonstrated	demonstrate	VERB
ejpam-5826	248	7	that	that	SCONJ
ejpam-5826	248	8	f	f	PROPN
ejpam-5826	248	9	is	be	AUX
ejpam-5826	248	10	asymptotically	asymptotically	ADV
ejpam-5826	248	11	regular	regular	ADJ
ejpam-5826	248	12	.	.	PUNCT
ejpam-5826	249	1	furthermore	furthermore	ADV
ejpam-5826	249	2	,	,	PUNCT
ejpam-5826	249	3	the	the	DET
ejpam-5826	249	4	mappings	mapping	NOUN
ejpam-5826	249	5	e	e	NOUN
ejpam-5826	249	6	and	and	CCONJ
ejpam-5826	249	7	f	f	PROPN
ejpam-5826	249	8	are	be	AUX
ejpam-5826	249	9	orbitally	orbitally	ADV
ejpam-5826	249	10	continuous	continuous	ADJ
ejpam-5826	249	11	.	.	PUNCT
ejpam-5826	250	1	next	next	ADV
ejpam-5826	250	2	,	,	PUNCT
ejpam-5826	250	3	we	we	PRON
ejpam-5826	250	4	establish	establish	VERB
ejpam-5826	250	5	that	that	SCONJ
ejpam-5826	251	1	e	e	PROPN
ejpam-5826	251	2	and	and	CCONJ
ejpam-5826	251	3	f	f	PROPN
ejpam-5826	251	4	satisfy	satisfy	NOUN
ejpam-5826	251	5	condition	condition	NOUN
ejpam-5826	251	6	(	(	PUNCT
ejpam-5826	251	7	3	3	NUM
ejpam-5826	251	8	)	)	PUNCT
ejpam-5826	251	9	with	with	ADP
ejpam-5826	251	10	the	the	DET
ejpam-5826	251	11	parameter	parameter	NOUN
ejpam-5826	251	12	k	k	PROPN
ejpam-5826	251	13	=	=	SYM
ejpam-5826	251	14	1	1	X
ejpam-5826	251	15	.	.	PUNCT
ejpam-5826	251	16	now	now	ADV
ejpam-5826	251	17	define	define	VERB
ejpam-5826	251	18	κ	κ	NOUN
ejpam-5826	251	19	:	:	PUNCT
ejpam-5826	251	20	r+	r+	X
ejpam-5826	251	21	→	→	PUNCT
ejpam-5826	251	22	[	[	X
ejpam-5826	251	23	0	0	NUM
ejpam-5826	251	24	,	,	PUNCT
ejpam-5826	251	25	1	1	NUM
ejpam-5826	251	26	]	]	PUNCT
ejpam-5826	251	27	by	by	ADP
ejpam-5826	251	28	κ(t	κ(t	NOUN
ejpam-5826	251	29	)	)	PUNCT
ejpam-5826	252	1	=	=	PRON
ejpam-5826	252	2	{	{	PUNCT
ejpam-5826	252	3	1	1	NUM
ejpam-5826	252	4	2	2	NUM
ejpam-5826	252	5	+	+	CCONJ
ejpam-5826	252	6	1	1	NUM
ejpam-5826	252	7	2	2	NUM
ejpam-5826	252	8	t	t	NOUN
ejpam-5826	252	9	if	if	SCONJ
ejpam-5826	252	10	t	t	PROPN
ejpam-5826	252	11	∈	∈	PROPN
ejpam-5826	253	1	[	[	X
ejpam-5826	253	2	0	0	NUM
ejpam-5826	253	3	,	,	PUNCT
ejpam-5826	253	4	1	1	NUM
ejpam-5826	253	5	]	]	PUNCT
ejpam-5826	253	6	,	,	PUNCT
ejpam-5826	253	7	1	1	NUM
ejpam-5826	253	8	if	if	SCONJ
ejpam-5826	253	9	t	t	PROPN
ejpam-5826	253	10	∈	∈	PROPN
ejpam-5826	253	11	(	(	PUNCT
ejpam-5826	253	12	1,+∞	1,+∞	NUM
ejpam-5826	253	13	)	)	PUNCT
ejpam-5826	253	14	.	.	PUNCT
ejpam-5826	254	1	then	then	ADV
ejpam-5826	254	2	κ	κ	PROPN
ejpam-5826	254	3	∈	∈	PROPN
ejpam-5826	254	4	s	s	PROPN
ejpam-5826	254	5	,	,	PUNCT
ejpam-5826	254	6	for	for	ADP
ejpam-5826	254	7	any	any	DET
ejpam-5826	254	8	q	q	NOUN
ejpam-5826	254	9	,	,	PUNCT
ejpam-5826	254	10	p	p	PROPN
ejpam-5826	254	11	∈	∈	PROPN
ejpam-5826	254	12	q	q	X
ejpam-5826	254	13	,	,	PUNCT
ejpam-5826	254	14	since	since	SCONJ
ejpam-5826	254	15	|q	|q	NOUN
ejpam-5826	254	16	−	−	PROPN
ejpam-5826	254	17	p|	p|	NOUN
ejpam-5826	254	18	≤	≤	NUM
ejpam-5826	254	19	1	1	NUM
ejpam-5826	254	20	.	.	X
ejpam-5826	255	1	consider	consider	VERB
ejpam-5826	255	2	(	(	PUNCT
ejpam-5826	255	3	3	3	NUM
ejpam-5826	255	4	)	)	PUNCT
ejpam-5826	255	5	in	in	ADP
ejpam-5826	255	6	the	the	DET
ejpam-5826	255	7	form	form	NOUN
ejpam-5826	255	8	κ(d(q	κ(d(q	PROPN
ejpam-5826	255	9	,	,	PUNCT
ejpam-5826	255	10	p))d(q	p))d(q	PROPN
ejpam-5826	255	11	,	,	PUNCT
ejpam-5826	255	12	p	p	NOUN
ejpam-5826	255	13	)	)	PUNCT
ejpam-5826	256	1	+	+	CCONJ
ejpam-5826	256	2	d(q	d(q	PROPN
ejpam-5826	256	3	,	,	PUNCT
ejpam-5826	256	4	eq	eq	NOUN
ejpam-5826	256	5	)	)	PUNCT
ejpam-5826	256	6	+	+	CCONJ
ejpam-5826	256	7	d(p	d(p	PROPN
ejpam-5826	256	8	,	,	PUNCT
ejpam-5826	256	9	fp)−	fp)−	NOUN
ejpam-5826	256	10	d(eq	d(eq	PROPN
ejpam-5826	256	11	,	,	PUNCT
ejpam-5826	256	12	fp	fp	ADJ
ejpam-5826	256	13	)	)	PUNCT
ejpam-5826	256	14	=	=	SYM
ejpam-5826	256	15	1	1	NUM
ejpam-5826	256	16	2	2	NUM
ejpam-5826	256	17	(	(	PUNCT
ejpam-5826	256	18	1	1	NUM
ejpam-5826	256	19	+	+	CCONJ
ejpam-5826	256	20	|q	|q	NOUN
ejpam-5826	256	21	−	−	NOUN
ejpam-5826	256	22	p|)|q	p|)|q	VERB
ejpam-5826	256	23	−	−	PROPN
ejpam-5826	256	24	p|+	p|+	PROPN
ejpam-5826	256	25	∣∣∣q	∣∣∣q	NUM
ejpam-5826	256	26	−	−	NOUN
ejpam-5826	256	27	q	q	PROPN
ejpam-5826	256	28	2	2	PROPN
ejpam-5826	256	29	∣∣∣+	∣∣∣+	NUM
ejpam-5826	256	30	∣∣∣p−	∣∣∣p−	NOUN
ejpam-5826	256	31	p	p	X
ejpam-5826	256	32	3	3	NUM
ejpam-5826	256	33	∣∣∣−	∣∣∣−	PROPN
ejpam-5826	256	34	∣∣∣q	∣∣∣q	NUM
ejpam-5826	256	35	2	2	NUM
ejpam-5826	256	36	−	−	NOUN
ejpam-5826	257	1	p	p	NOUN
ejpam-5826	257	2	3	3	NUM
ejpam-5826	257	3	∣∣∣	∣∣∣	NOUN
ejpam-5826	257	4	=	=	SYM
ejpam-5826	257	5	1	1	NUM
ejpam-5826	257	6	2	2	NUM
ejpam-5826	257	7	(	(	PUNCT
ejpam-5826	257	8	1	1	NUM
ejpam-5826	257	9	+	+	CCONJ
ejpam-5826	257	10	|q	|q	NOUN
ejpam-5826	257	11	−	−	NOUN
ejpam-5826	257	12	p|)|q	p|)|q	VERB
ejpam-5826	258	1	−	−	PROPN
ejpam-5826	258	2	p|+	p|+	NOUN
ejpam-5826	258	3	q	q	NOUN
ejpam-5826	258	4	2	2	NUM
ejpam-5826	258	5	+	+	NUM
ejpam-5826	258	6	2p	2p	NUM
ejpam-5826	258	7	3	3	NUM
ejpam-5826	258	8	−	−	NOUN
ejpam-5826	258	9	∣∣∣q	∣∣∣q	NUM
ejpam-5826	258	10	2	2	NUM
ejpam-5826	258	11	−	−	NOUN
ejpam-5826	258	12	p	p	NOUN
ejpam-5826	258	13	3	3	NUM
ejpam-5826	258	14	∣∣∣.	∣∣∣.	NOUN
ejpam-5826	258	15	(	(	PUNCT
ejpam-5826	258	16	20	20	NUM
ejpam-5826	258	17	)	)	PUNCT
ejpam-5826	258	18	now	now	ADV
ejpam-5826	258	19	,	,	PUNCT
ejpam-5826	258	20	there	there	PRON
ejpam-5826	258	21	are	be	VERB
ejpam-5826	258	22	two	two	NUM
ejpam-5826	258	23	cases	case	NOUN
ejpam-5826	258	24	to	to	PART
ejpam-5826	258	25	consider	consider	VERB
ejpam-5826	258	26	for	for	ADP
ejpam-5826	258	27	(	(	PUNCT
ejpam-5826	258	28	20	20	NUM
ejpam-5826	258	29	):	):	PUNCT
ejpam-5826	258	30	case	case	NOUN
ejpam-5826	258	31	i.	i.	NOUN
ejpam-5826	258	32	if	if	SCONJ
ejpam-5826	258	33	q	q	PROPN
ejpam-5826	258	34	≥	≥	AUX
ejpam-5826	258	35	p	p	X
ejpam-5826	258	36	,	,	PUNCT
ejpam-5826	258	37	then	then	ADV
ejpam-5826	258	38	we	we	PRON
ejpam-5826	258	39	have	have	VERB
ejpam-5826	258	40	:	:	PUNCT
ejpam-5826	258	41	1	1	NUM
ejpam-5826	258	42	2	2	NUM
ejpam-5826	258	43	(	(	PUNCT
ejpam-5826	258	44	1	1	NUM
ejpam-5826	258	45	+	+	CCONJ
ejpam-5826	258	46	(	(	PUNCT
ejpam-5826	258	47	q	q	NOUN
ejpam-5826	258	48	−	−	PROPN
ejpam-5826	258	49	p))(q	p))(q	NOUN
ejpam-5826	258	50	−	−	PROPN
ejpam-5826	259	1	p	p	X
ejpam-5826	259	2	)	)	PUNCT
ejpam-5826	260	1	+	+	CCONJ
ejpam-5826	260	2	q	q	NOUN
ejpam-5826	260	3	2	2	NUM
ejpam-5826	260	4	+	+	NUM
ejpam-5826	260	5	2p	2p	NUM
ejpam-5826	260	6	3	3	NUM
ejpam-5826	260	7	−	−	NOUN
ejpam-5826	260	8	(	(	PUNCT
ejpam-5826	260	9	q	q	PROPN
ejpam-5826	260	10	2	2	NUM
ejpam-5826	260	11	−	−	NOUN
ejpam-5826	260	12	p	p	NOUN
ejpam-5826	260	13	3	3	NUM
ejpam-5826	260	14	)	)	PUNCT
ejpam-5826	260	15	=	=	SYM
ejpam-5826	260	16	1	1	NUM
ejpam-5826	260	17	2	2	NUM
ejpam-5826	260	18	(	(	PUNCT
ejpam-5826	260	19	q	q	NOUN
ejpam-5826	260	20	−	−	PROPN
ejpam-5826	260	21	p	p	NOUN
ejpam-5826	260	22	)	)	PUNCT
ejpam-5826	260	23	+	+	CCONJ
ejpam-5826	260	24	1	1	NUM
ejpam-5826	260	25	2	2	NUM
ejpam-5826	260	26	(	(	PUNCT
ejpam-5826	260	27	q	q	NOUN
ejpam-5826	260	28	−	−	PROPN
ejpam-5826	260	29	p)2	p)2	NOUN
ejpam-5826	260	30	+	+	CCONJ
ejpam-5826	260	31	q	q	NOUN
ejpam-5826	260	32	2	2	NUM
ejpam-5826	260	33	+	+	NUM
ejpam-5826	260	34	2p	2p	NUM
ejpam-5826	260	35	3	3	NUM
ejpam-5826	260	36	−	−	NOUN
ejpam-5826	260	37	q	q	NOUN
ejpam-5826	260	38	2	2	NUM
ejpam-5826	260	39	+	+	CCONJ
ejpam-5826	260	40	p	p	NOUN
ejpam-5826	260	41	3	3	NUM
ejpam-5826	260	42	=	=	SYM
ejpam-5826	260	43	1	1	NUM
ejpam-5826	260	44	2	2	NUM
ejpam-5826	260	45	(	(	PUNCT
ejpam-5826	260	46	q	q	PROPN
ejpam-5826	261	1	+	+	CCONJ
ejpam-5826	261	2	p	p	X
ejpam-5826	261	3	)	)	PUNCT
ejpam-5826	261	4	+	+	CCONJ
ejpam-5826	261	5	1	1	NUM
ejpam-5826	261	6	2	2	NUM
ejpam-5826	261	7	(	(	PUNCT
ejpam-5826	261	8	q	q	NOUN
ejpam-5826	261	9	−	−	PROPN
ejpam-5826	261	10	p)2	p)2	NOUN
ejpam-5826	261	11	≥	≥	NOUN
ejpam-5826	261	12	0	0	NUM
ejpam-5826	261	13	;	;	PUNCT
ejpam-5826	261	14	thus	thus	ADV
ejpam-5826	261	15	d(eq	d(eq	PROPN
ejpam-5826	261	16	,	,	PUNCT
ejpam-5826	261	17	fp	fp	ADJ
ejpam-5826	261	18	)	)	PUNCT
ejpam-5826	261	19	≤	≤	NOUN
ejpam-5826	261	20	κ(d(q	κ(d(q	PROPN
ejpam-5826	261	21	,	,	PUNCT
ejpam-5826	261	22	p))d(q	p))d(q	PROPN
ejpam-5826	261	23	,	,	PUNCT
ejpam-5826	261	24	p	p	NOUN
ejpam-5826	261	25	)	)	PUNCT
ejpam-5826	261	26	+	+	CCONJ
ejpam-5826	261	27	d(q	d(q	PROPN
ejpam-5826	261	28	,	,	PUNCT
ejpam-5826	261	29	eq	eq	NOUN
ejpam-5826	261	30	)	)	PUNCT
ejpam-5826	261	31	+	+	CCONJ
ejpam-5826	261	32	d(p	d(p	PROPN
ejpam-5826	261	33	,	,	PUNCT
ejpam-5826	261	34	fp	fp	NOUN
ejpam-5826	261	35	)	)	PUNCT
ejpam-5826	261	36	.	.	PUNCT
ejpam-5826	262	1	case	case	NOUN
ejpam-5826	262	2	ii	ii	X
ejpam-5826	262	3	.	.	PUNCT
ejpam-5826	263	1	if	if	SCONJ
ejpam-5826	263	2	q	q	X
ejpam-5826	263	3	<	<	X
ejpam-5826	263	4	p	p	X
ejpam-5826	263	5	,	,	PUNCT
ejpam-5826	263	6	then	then	ADV
ejpam-5826	263	7	we	we	PRON
ejpam-5826	263	8	have	have	VERB
ejpam-5826	263	9	:	:	PUNCT
ejpam-5826	263	10	1	1	NUM
ejpam-5826	263	11	2	2	NUM
ejpam-5826	263	12	(	(	PUNCT
ejpam-5826	263	13	1	1	NUM
ejpam-5826	263	14	+	+	CCONJ
ejpam-5826	263	15	(	(	PUNCT
ejpam-5826	263	16	p−	p−	NOUN
ejpam-5826	263	17	q))(p−	q))(p−	VERB
ejpam-5826	263	18	q	q	NOUN
ejpam-5826	263	19	)	)	PUNCT
ejpam-5826	263	20	+	+	CCONJ
ejpam-5826	263	21	q	q	NOUN
ejpam-5826	263	22	2	2	NUM
ejpam-5826	263	23	+	+	NUM
ejpam-5826	263	24	2p	2p	NUM
ejpam-5826	263	25	3	3	NUM
ejpam-5826	263	26	−	−	NOUN
ejpam-5826	263	27	∣∣∣q	∣∣∣q	NUM
ejpam-5826	263	28	2	2	NUM
ejpam-5826	263	29	−	−	NOUN
ejpam-5826	263	30	p	p	NOUN
ejpam-5826	263	31	3	3	NUM
ejpam-5826	263	32	∣∣∣	∣∣∣	NOUN
ejpam-5826	263	33	=	=	SYM
ejpam-5826	263	34	{	{	PUNCT
ejpam-5826	263	35	1	1	NUM
ejpam-5826	263	36	2(p−	2(p−	NUM
ejpam-5826	263	37	q	q	NOUN
ejpam-5826	263	38	)	)	PUNCT
ejpam-5826	264	1	+	+	CCONJ
ejpam-5826	264	2	1	1	NUM
ejpam-5826	264	3	2(p−	2(p−	NUM
ejpam-5826	264	4	q)2	q)2	NOUN
ejpam-5826	264	5	+	+	CCONJ
ejpam-5826	264	6	p	p	NOUN
ejpam-5826	264	7	if	if	SCONJ
ejpam-5826	264	8	q	q	PROPN
ejpam-5826	264	9	3	3	NUM
ejpam-5826	264	10	≥	≥	NOUN
ejpam-5826	264	11	p	p	NOUN
ejpam-5826	264	12	3	3	NUM
ejpam-5826	264	13	,	,	PUNCT
ejpam-5826	264	14	1	1	NUM
ejpam-5826	264	15	2(p−	2(p−	NUM
ejpam-5826	264	16	q	q	NOUN
ejpam-5826	264	17	)	)	PUNCT
ejpam-5826	264	18	+	+	CCONJ
ejpam-5826	264	19	1	1	NUM
ejpam-5826	264	20	2(p−	2(p−	NUM
ejpam-5826	264	21	q)2	q)2	NOUN
ejpam-5826	264	22	+	+	CCONJ
ejpam-5826	264	23	q	q	PROPN
ejpam-5826	265	1	+	+	CCONJ
ejpam-5826	265	2	p	p	X
ejpam-5826	265	3	3	3	NUM
ejpam-5826	265	4	if	if	SCONJ
ejpam-5826	265	5	q	q	PROPN
ejpam-5826	265	6	2	2	NUM
ejpam-5826	265	7	<	<	X
ejpam-5826	265	8	p	p	X
ejpam-5826	265	9	3	3	NUM
ejpam-5826	265	10	≥	≥	NOUN
ejpam-5826	265	11	0	0	NUM
ejpam-5826	265	12	;	;	PUNCT
ejpam-5826	265	13	hence	hence	ADV
ejpam-5826	265	14	d(eq	d(eq	PROPN
ejpam-5826	265	15	,	,	PUNCT
ejpam-5826	265	16	fp	fp	ADJ
ejpam-5826	265	17	)	)	PUNCT
ejpam-5826	265	18	≤	≤	NOUN
ejpam-5826	265	19	κ(d(q	κ(d(q	PROPN
ejpam-5826	265	20	,	,	PUNCT
ejpam-5826	265	21	p))d(q	p))d(q	PROPN
ejpam-5826	265	22	,	,	PUNCT
ejpam-5826	265	23	p	p	NOUN
ejpam-5826	265	24	)	)	PUNCT
ejpam-5826	266	1	+	+	CCONJ
ejpam-5826	266	2	d(q	d(q	PROPN
ejpam-5826	266	3	,	,	PUNCT
ejpam-5826	266	4	eq	eq	NOUN
ejpam-5826	266	5	)	)	PUNCT
ejpam-5826	266	6	+	+	CCONJ
ejpam-5826	266	7	d(p	d(p	PROPN
ejpam-5826	266	8	,	,	PUNCT
ejpam-5826	266	9	fp	fp	NOUN
ejpam-5826	266	10	)	)	PUNCT
ejpam-5826	266	11	.	.	PUNCT
ejpam-5826	267	1	therefore	therefore	ADV
ejpam-5826	267	2	e	e	PROPN
ejpam-5826	267	3	and	and	CCONJ
ejpam-5826	267	4	f	f	PROPN
ejpam-5826	267	5	satisfy	satisfy	NOUN
ejpam-5826	267	6	(	(	PUNCT
ejpam-5826	267	7	3	3	NUM
ejpam-5826	267	8	)	)	PUNCT
ejpam-5826	267	9	with	with	ADP
ejpam-5826	267	10	k	k	PROPN
ejpam-5826	267	11	=	=	SYM
ejpam-5826	267	12	1	1	X
ejpam-5826	267	13	.	.	PUNCT
ejpam-5826	268	1	next	next	ADV
ejpam-5826	268	2	,	,	PUNCT
ejpam-5826	268	3	we	we	PRON
ejpam-5826	268	4	show	show	VERB
ejpam-5826	268	5	that	that	SCONJ
ejpam-5826	268	6	e	e	PROPN
ejpam-5826	268	7	and	and	CCONJ
ejpam-5826	268	8	f	f	PROPN
ejpam-5826	268	9	have	have	VERB
ejpam-5826	268	10	a	a	DET
ejpam-5826	268	11	common	common	ADJ
ejpam-5826	268	12	approximate	approximate	ADJ
ejpam-5826	268	13	fixed	fix	VERB
ejpam-5826	268	14	point	point	NOUN
ejpam-5826	268	15	sequence	sequence	NOUN
ejpam-5826	268	16	.	.	PUNCT
ejpam-5826	269	1	consider	consider	VERB
ejpam-5826	269	2	the	the	DET
ejpam-5826	269	3	sequence	sequence	NOUN
ejpam-5826	269	4	{	{	PUNCT
ejpam-5826	269	5	qk	qk	NOUN
ejpam-5826	269	6	}	}	PUNCT
ejpam-5826	269	7	⊂	⊂	PROPN
ejpam-5826	269	8	q	q	X
ejpam-5826	269	9	where	where	SCONJ
ejpam-5826	269	10	qk	qk	NOUN
ejpam-5826	269	11	=	=	SYM
ejpam-5826	269	12	1	1	NUM
ejpam-5826	269	13	k	k	NOUN
ejpam-5826	269	14	.	.	PUNCT
ejpam-5826	270	1	d(qk	d(qk	NOUN
ejpam-5826	270	2	,	,	PUNCT
ejpam-5826	270	3	eqk	eqk	NOUN
ejpam-5826	270	4	)	)	PUNCT
ejpam-5826	270	5	=	=	SYM
ejpam-5826	270	6	∣∣∣∣1k	∣∣∣∣1k	NOUN
ejpam-5826	270	7	−	−	NUM
ejpam-5826	270	8	1	1	NUM
ejpam-5826	270	9	2k	2k	NOUN
ejpam-5826	270	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5826	270	11	=	=	SYM
ejpam-5826	270	12	1	1	NUM
ejpam-5826	270	13	2k	2k	NUM
ejpam-5826	270	14	→	→	SYM
ejpam-5826	270	15	0	0	PUNCT
ejpam-5826	270	16	as	as	ADP
ejpam-5826	270	17	k	k	PROPN
ejpam-5826	270	18	→	→	SYM
ejpam-5826	270	19	∞	∞	PROPN
ejpam-5826	270	20	,	,	PUNCT
ejpam-5826	270	21	a.	a.	PROPN
ejpam-5826	270	22	r.	r.	PROPN
ejpam-5826	270	23	khan	khan	PROPN
ejpam-5826	270	24	et	et	PROPN
ejpam-5826	270	25	al	al	PROPN
ejpam-5826	270	26	.	.	PUNCT
ejpam-5826	270	27	/	/	SYM
ejpam-5826	270	28	eur	eur	PROPN
ejpam-5826	270	29	.	.	PUNCT
ejpam-5826	271	1	j.	j.	PROPN
ejpam-5826	271	2	pure	pure	PROPN
ejpam-5826	271	3	appl	appl	PROPN
ejpam-5826	271	4	.	.	PROPN
ejpam-5826	271	5	math	math	PROPN
ejpam-5826	271	6	,	,	PUNCT
ejpam-5826	271	7	18	18	NUM
ejpam-5826	271	8	(	(	PUNCT
ejpam-5826	271	9	2	2	NUM
ejpam-5826	271	10	)	)	PUNCT
ejpam-5826	271	11	(	(	PUNCT
ejpam-5826	271	12	2025	2025	NUM
ejpam-5826	271	13	)	)	PUNCT
ejpam-5826	271	14	,	,	PUNCT
ejpam-5826	271	15	5826	5826	NUM
ejpam-5826	271	16	12	12	NUM
ejpam-5826	271	17	of	of	ADP
ejpam-5826	271	18	23	23	NUM
ejpam-5826	271	19	and	and	CCONJ
ejpam-5826	271	20	d(qk	d(qk	PROPN
ejpam-5826	271	21	,	,	PUNCT
ejpam-5826	271	22	f	f	PROPN
ejpam-5826	271	23	qk	qk	PROPN
ejpam-5826	271	24	)	)	PUNCT
ejpam-5826	271	25	=	=	SYM
ejpam-5826	271	26	∣∣∣∣1k	∣∣∣∣1k	NOUN
ejpam-5826	271	27	−	−	NOUN
ejpam-5826	271	28	1	1	NUM
ejpam-5826	271	29	3k	3k	NOUN
ejpam-5826	271	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5826	271	31	=	=	SYM
ejpam-5826	271	32	1	1	NUM
ejpam-5826	271	33	3k	3k	NUM
ejpam-5826	271	34	→	→	SYM
ejpam-5826	271	35	0	0	PUNCT
ejpam-5826	271	36	as	as	ADP
ejpam-5826	271	37	k	k	PROPN
ejpam-5826	271	38	→	→	SYM
ejpam-5826	271	39	∞.	∞.	PROPN
ejpam-5826	271	40	hence	hence	ADV
ejpam-5826	271	41	,	,	PUNCT
ejpam-5826	271	42	e	e	PROPN
ejpam-5826	271	43	and	and	CCONJ
ejpam-5826	271	44	f	f	PROPN
ejpam-5826	271	45	have	have	VERB
ejpam-5826	271	46	a	a	DET
ejpam-5826	271	47	common	common	ADJ
ejpam-5826	271	48	approximate	approximate	ADJ
ejpam-5826	271	49	fixed	fix	VERB
ejpam-5826	271	50	point	point	NOUN
ejpam-5826	271	51	sequence	sequence	NOUN
ejpam-5826	271	52	.	.	PUNCT
ejpam-5826	272	1	since	since	SCONJ
ejpam-5826	272	2	e	e	PROPN
ejpam-5826	272	3	and	and	CCONJ
ejpam-5826	272	4	f	f	PROPN
ejpam-5826	272	5	are	be	AUX
ejpam-5826	272	6	both	both	ADV
ejpam-5826	272	7	continuous	continuous	ADJ
ejpam-5826	272	8	(	(	PUNCT
ejpam-5826	272	9	and	and	CCONJ
ejpam-5826	272	10	thus	thus	ADV
ejpam-5826	272	11	k	k	ADJ
ejpam-5826	272	12	-	-	ADJ
ejpam-5826	272	13	continuous	continuous	ADJ
ejpam-5826	272	14	)	)	PUNCT
ejpam-5826	272	15	,	,	PUNCT
ejpam-5826	272	16	therefore	therefore	ADV
ejpam-5826	272	17	by	by	ADP
ejpam-5826	272	18	theorem	theorem	NOUN
ejpam-5826	272	19	4	4	NUM
ejpam-5826	272	20	,	,	PUNCT
ejpam-5826	272	21	they	they	PRON
ejpam-5826	272	22	have	have	VERB
ejpam-5826	272	23	a	a	DET
ejpam-5826	272	24	unique	unique	ADJ
ejpam-5826	272	25	common	common	ADJ
ejpam-5826	272	26	fixed	fix	VERB
ejpam-5826	272	27	point	point	NOUN
ejpam-5826	272	28	q	q	PROPN
ejpam-5826	273	1	=	=	NOUN
ejpam-5826	273	2	0	0	X
ejpam-5826	273	3	.	.	PUNCT
ejpam-5826	274	1	in	in	ADP
ejpam-5826	274	2	particular	particular	ADJ
ejpam-5826	274	3	,	,	PUNCT
ejpam-5826	274	4	{	{	PUNCT
ejpam-5826	274	5	qk	qk	INTJ
ejpam-5826	274	6	}	}	PUNCT
ejpam-5826	274	7	→	→	SYM
ejpam-5826	274	8	0	0	PUNCT
ejpam-5826	274	9	as	as	SCONJ
ejpam-5826	274	10	k	k	PROPN
ejpam-5826	274	11	→	→	SYM
ejpam-5826	274	12	∞.	∞.	PROPN
ejpam-5826	274	13	we	we	PRON
ejpam-5826	274	14	now	now	ADV
ejpam-5826	274	15	present	present	VERB
ejpam-5826	274	16	a	a	DET
ejpam-5826	274	17	partial	partial	ADJ
ejpam-5826	274	18	extension	extension	NOUN
ejpam-5826	274	19	of	of	ADP
ejpam-5826	274	20	theorem	theorem	NOUN
ejpam-5826	274	21	2	2	NUM
ejpam-5826	274	22	for	for	ADP
ejpam-5826	274	23	a	a	DET
ejpam-5826	274	24	function	function	NOUN
ejpam-5826	274	25	which	which	PRON
ejpam-5826	274	26	is	be	AUX
ejpam-5826	274	27	not	not	PART
ejpam-5826	274	28	asymptotically	asymptotically	ADV
ejpam-5826	274	29	regular	regular	ADJ
ejpam-5826	274	30	and	and	CCONJ
ejpam-5826	274	31	is	be	AUX
ejpam-5826	274	32	defined	define	VERB
ejpam-5826	274	33	on	on	ADP
ejpam-5826	274	34	a	a	DET
ejpam-5826	274	35	closed	closed	ADJ
ejpam-5826	274	36	and	and	CCONJ
ejpam-5826	274	37	convex	convex	NOUN
ejpam-5826	274	38	subset	subset	NOUN
ejpam-5826	274	39	of	of	ADP
ejpam-5826	274	40	a	a	DET
ejpam-5826	274	41	uniformly	uniformly	ADV
ejpam-5826	274	42	convex	convex	ADJ
ejpam-5826	274	43	hyperbolic	hyperbolic	ADJ
ejpam-5826	274	44	space	space	NOUN
ejpam-5826	274	45	.	.	PUNCT
ejpam-5826	275	1	theorem	theorem	NOUN
ejpam-5826	275	2	5	5	NUM
ejpam-5826	275	3	.	.	PUNCT
ejpam-5826	276	1	let	let	VERB
ejpam-5826	276	2	j	j	PROPN
ejpam-5826	276	3	be	be	AUX
ejpam-5826	276	4	a	a	DET
ejpam-5826	276	5	nonempty	nonempty	ADV
ejpam-5826	276	6	closed	close	VERB
ejpam-5826	276	7	and	and	CCONJ
ejpam-5826	276	8	convex	convex	NOUN
ejpam-5826	276	9	subset	subset	NOUN
ejpam-5826	276	10	of	of	ADP
ejpam-5826	276	11	complete	complete	ADJ
ejpam-5826	276	12	uniformly	uniformly	ADV
ejpam-5826	276	13	convex	convex	ADJ
ejpam-5826	276	14	hyperbolic	hyperbolic	ADJ
ejpam-5826	276	15	space	space	NOUN
ejpam-5826	276	16	q	q	NOUN
ejpam-5826	276	17	with	with	ADP
ejpam-5826	276	18	monotone	monotone	ADJ
ejpam-5826	276	19	modulus	modulus	NOUN
ejpam-5826	276	20	of	of	ADP
ejpam-5826	276	21	convexity	convexity	PROPN
ejpam-5826	276	22	η	η	PROPN
ejpam-5826	276	23	.	.	PROPN
ejpam-5826	277	1	let	let	VERB
ejpam-5826	277	2	e	e	NOUN
ejpam-5826	277	3	:	:	PUNCT
ejpam-5826	277	4	j	j	PROPN
ejpam-5826	277	5	→	→	PUNCT
ejpam-5826	277	6	q	q	AUX
ejpam-5826	277	7	be	be	AUX
ejpam-5826	277	8	a	a	DET
ejpam-5826	277	9	mapping	mapping	NOUN
ejpam-5826	277	10	satisfying	satisfy	VERB
ejpam-5826	277	11	d(eq	d(eq	PROPN
ejpam-5826	277	12	,	,	PUNCT
ejpam-5826	277	13	ep	ep	NOUN
ejpam-5826	277	14	)	)	PUNCT
ejpam-5826	277	15	≤	≤	NOUN
ejpam-5826	277	16	µd(q	µd(q	NOUN
ejpam-5826	277	17	,	,	PUNCT
ejpam-5826	277	18	p	p	NOUN
ejpam-5826	277	19	)	)	PUNCT
ejpam-5826	278	1	+	+	CCONJ
ejpam-5826	278	2	ν{d(q	ν{d(q	PROPN
ejpam-5826	278	3	,	,	PUNCT
ejpam-5826	278	4	eq	eq	NOUN
ejpam-5826	278	5	)	)	PUNCT
ejpam-5826	278	6	+	+	CCONJ
ejpam-5826	278	7	d(p	d(p	PROPN
ejpam-5826	278	8	,	,	PUNCT
ejpam-5826	278	9	ep	ep	PROPN
ejpam-5826	278	10	)	)	PUNCT
ejpam-5826	278	11	}	}	PUNCT
ejpam-5826	278	12	,	,	PUNCT
ejpam-5826	278	13	for	for	ADP
ejpam-5826	278	14	all	all	DET
ejpam-5826	278	15	q	q	NOUN
ejpam-5826	278	16	,	,	PUNCT
ejpam-5826	278	17	p	p	PROPN
ejpam-5826	278	18	∈	∈	PROPN
ejpam-5826	278	19	j	j	PROPN
ejpam-5826	278	20	,	,	PUNCT
ejpam-5826	278	21	(	(	PUNCT
ejpam-5826	278	22	21	21	NUM
ejpam-5826	278	23	)	)	PUNCT
ejpam-5826	278	24	where	where	SCONJ
ejpam-5826	278	25	0	0	NUM
ejpam-5826	278	26	≤	≤	X
ejpam-5826	278	27	µ	µ	X
ejpam-5826	278	28	<	<	X
ejpam-5826	278	29	1	1	NUM
ejpam-5826	278	30	,	,	PUNCT
ejpam-5826	278	31	0	0	NUM
ejpam-5826	278	32	≤	≤	NUM
ejpam-5826	279	1	ν	ν	ADP
ejpam-5826	279	2	<	<	X
ejpam-5826	279	3	∞	∞	PROPN
ejpam-5826	279	4	with	with	ADP
ejpam-5826	279	5	µ+2νblue<1	µ+2νblue<1	NOUN
ejpam-5826	279	6	.	.	PUNCT
ejpam-5826	280	1	let	let	AUX
ejpam-5826	280	2	{	{	PUNCT
ejpam-5826	280	3	qk	qk	PART
ejpam-5826	280	4	}	}	PUNCT
ejpam-5826	280	5	be	be	AUX
ejpam-5826	280	6	a	a	DET
ejpam-5826	280	7	bounded	bounded	ADJ
ejpam-5826	280	8	sequence	sequence	NOUN
ejpam-5826	280	9	in	in	ADP
ejpam-5826	280	10	j	j	PROPN
ejpam-5826	280	11	such	such	ADJ
ejpam-5826	280	12	that	that	SCONJ
ejpam-5826	280	13	limk→∞	limk→∞	PROPN
ejpam-5826	280	14	d(qk	d(qk	NOUN
ejpam-5826	280	15	,	,	PUNCT
ejpam-5826	280	16	eqk	eqk	NOUN
ejpam-5826	280	17	)	)	PUNCT
ejpam-5826	280	18	=	=	SYM
ejpam-5826	280	19	0	0	NUM
ejpam-5826	280	20	and	and	CCONJ
ejpam-5826	280	21	∆−	∆−	NOUN
ejpam-5826	280	22	limk→∞	limk→∞	ADV
ejpam-5826	280	23	qk	qk	ADP
ejpam-5826	280	24	=	=	NOUN
ejpam-5826	280	25	q∗.	q∗.	NOUN
ejpam-5826	280	26	then	then	ADV
ejpam-5826	280	27	e	e	PROPN
ejpam-5826	280	28	has	have	VERB
ejpam-5826	280	29	a	a	DET
ejpam-5826	280	30	unique	unique	ADJ
ejpam-5826	280	31	fixed	fix	VERB
ejpam-5826	280	32	point	point	NOUN
ejpam-5826	280	33	q∗.	q∗.	NOUN
ejpam-5826	280	34	proof	proof	NOUN
ejpam-5826	280	35	.	.	PUNCT
ejpam-5826	281	1	let	let	VERB
ejpam-5826	281	2	{	{	PUNCT
ejpam-5826	281	3	qk	qk	PART
ejpam-5826	281	4	}	}	PUNCT
ejpam-5826	281	5	be	be	AUX
ejpam-5826	281	6	any	any	DET
ejpam-5826	281	7	bounded	bounded	ADJ
ejpam-5826	281	8	sequence	sequence	NOUN
ejpam-5826	281	9	in	in	ADP
ejpam-5826	281	10	j	j	PROPN
ejpam-5826	281	11	.	.	PUNCT
ejpam-5826	282	1	since	since	SCONJ
ejpam-5826	282	2	j	j	PROPN
ejpam-5826	282	3	is	be	AUX
ejpam-5826	282	4	a	a	DET
ejpam-5826	282	5	subset	subset	NOUN
ejpam-5826	282	6	of	of	ADP
ejpam-5826	282	7	q	q	PRON
ejpam-5826	282	8	which	which	PRON
ejpam-5826	282	9	is	be	AUX
ejpam-5826	282	10	complete	complete	ADJ
ejpam-5826	282	11	convex	convex	ADJ
ejpam-5826	282	12	hyperbolic	hyperbolic	ADJ
ejpam-5826	282	13	space	space	NOUN
ejpam-5826	282	14	with	with	ADP
ejpam-5826	282	15	monotone	monotone	ADJ
ejpam-5826	282	16	uniform	uniform	ADJ
ejpam-5826	282	17	convexity	convexity	NOUN
ejpam-5826	282	18	,	,	PUNCT
ejpam-5826	282	19	therefore	therefore	ADV
ejpam-5826	282	20	by	by	ADP
ejpam-5826	282	21	lemma	lemma	PROPN
ejpam-5826	282	22	2	2	NUM
ejpam-5826	282	23	,	,	PUNCT
ejpam-5826	282	24	{	{	PUNCT
ejpam-5826	282	25	qk	qk	AUX
ejpam-5826	282	26	}	}	PUNCT
ejpam-5826	282	27	has	have	VERB
ejpam-5826	282	28	a	a	DET
ejpam-5826	282	29	unique	unique	ADJ
ejpam-5826	282	30	asymptotic	asymptotic	ADJ
ejpam-5826	282	31	center	center	NOUN
ejpam-5826	282	32	in	in	ADP
ejpam-5826	282	33	j	j	PROPN
ejpam-5826	282	34	.	.	PUNCT
ejpam-5826	283	1	but	but	CCONJ
ejpam-5826	283	2	∆−	∆−	NOUN
ejpam-5826	283	3	limk→∞	limk→∞	ADV
ejpam-5826	283	4	qk	qk	ADP
ejpam-5826	283	5	=	=	NOUN
ejpam-5826	283	6	q∗.	q∗.	NOUN
ejpam-5826	283	7	so	so	ADV
ejpam-5826	283	8	a({qk	a({qk	NOUN
ejpam-5826	283	9	}	}	PUNCT
ejpam-5826	283	10	)	)	PUNCT
ejpam-5826	284	1	=	=	SYM
ejpam-5826	284	2	q∗.	q∗.	NOUN
ejpam-5826	284	3	using	use	VERB
ejpam-5826	284	4	(	(	PUNCT
ejpam-5826	284	5	21	21	NUM
ejpam-5826	284	6	)	)	PUNCT
ejpam-5826	284	7	,	,	PUNCT
ejpam-5826	284	8	we	we	PRON
ejpam-5826	284	9	get	get	VERB
ejpam-5826	284	10	d(qk	d(qk	NOUN
ejpam-5826	284	11	,	,	PUNCT
ejpam-5826	284	12	eq∗	eq∗	NOUN
ejpam-5826	284	13	)	)	PUNCT
ejpam-5826	284	14	≤	≤	NUM
ejpam-5826	284	15	d(qk	d(qk	NOUN
ejpam-5826	284	16	,	,	PUNCT
ejpam-5826	284	17	eqk	eqk	NOUN
ejpam-5826	284	18	)	)	PUNCT
ejpam-5826	284	19	+	+	X
ejpam-5826	284	20	d(eqk	d(eqk	ADJ
ejpam-5826	284	21	,	,	PUNCT
ejpam-5826	284	22	eq∗	eq∗	NOUN
ejpam-5826	284	23	)	)	PUNCT
ejpam-5826	284	24	.	.	PUNCT
ejpam-5826	285	1	≤	≤	NUM
ejpam-5826	285	2	d(qk	d(qk	NOUN
ejpam-5826	285	3	,	,	PUNCT
ejpam-5826	285	4	eqk	eqk	NOUN
ejpam-5826	285	5	)	)	PUNCT
ejpam-5826	285	6	+	+	CCONJ
ejpam-5826	285	7	µd(qk	µd(qk	PROPN
ejpam-5826	285	8	,	,	PUNCT
ejpam-5826	285	9	q	q	NOUN
ejpam-5826	285	10	∗	∗	NOUN
ejpam-5826	285	11	)	)	PUNCT
ejpam-5826	285	12	+	+	CCONJ
ejpam-5826	285	13	ν[d(qk	ν[d(qk	NOUN
ejpam-5826	285	14	,	,	PUNCT
ejpam-5826	285	15	eqk	eqk	NOUN
ejpam-5826	285	16	)	)	PUNCT
ejpam-5826	285	17	+	+	SYM
ejpam-5826	285	18	d(q∗	d(q∗	ADV
ejpam-5826	285	19	,	,	PUNCT
ejpam-5826	285	20	eq∗	eq∗	NOUN
ejpam-5826	285	21	)	)	PUNCT
ejpam-5826	285	22	]	]	PUNCT
ejpam-5826	285	23	.	.	PUNCT
ejpam-5826	286	1	≤	≤	NUM
ejpam-5826	286	2	(	(	PUNCT
ejpam-5826	286	3	1	1	NUM
ejpam-5826	286	4	+	+	NUM
ejpam-5826	286	5	ν)d(qk	ν)d(qk	NOUN
ejpam-5826	286	6	,	,	PUNCT
ejpam-5826	286	7	eqk	eqk	NOUN
ejpam-5826	286	8	)	)	PUNCT
ejpam-5826	286	9	+	+	CCONJ
ejpam-5826	286	10	(	(	PUNCT
ejpam-5826	286	11	µ+	µ+	X
ejpam-5826	286	12	ν)d(qk	ν)d(qk	NOUN
ejpam-5826	286	13	,	,	PUNCT
ejpam-5826	286	14	q	q	NOUN
ejpam-5826	286	15	∗	∗	NOUN
ejpam-5826	286	16	)	)	PUNCT
ejpam-5826	287	1	+	+	CCONJ
ejpam-5826	287	2	νd(qk	νd(qk	PROPN
ejpam-5826	287	3	,	,	PUNCT
ejpam-5826	287	4	eq∗	eq∗	NOUN
ejpam-5826	287	5	)	)	PUNCT
ejpam-5826	287	6	.	.	PUNCT
ejpam-5826	288	1	thus	thus	ADV
ejpam-5826	288	2	d(qk	d(qk	PROPN
ejpam-5826	288	3	,	,	PUNCT
ejpam-5826	288	4	eq∗	eq∗	NOUN
ejpam-5826	288	5	)	)	PUNCT
ejpam-5826	288	6	≤	≤	NUM
ejpam-5826	288	7	1	1	NUM
ejpam-5826	288	8	+	+	CCONJ
ejpam-5826	288	9	ν	ν	NOUN
ejpam-5826	288	10	1−	1−	NUM
ejpam-5826	288	11	ν	ν	X
ejpam-5826	288	12	d(qk	d(qk	NOUN
ejpam-5826	288	13	,	,	PUNCT
ejpam-5826	288	14	eqk	eqk	NOUN
ejpam-5826	288	15	)	)	PUNCT
ejpam-5826	288	16	+	+	NUM
ejpam-5826	288	17	µ+	µ+	X
ejpam-5826	288	18	ν	ν	NOUN
ejpam-5826	288	19	1−	1−	NUM
ejpam-5826	288	20	ν	ν	X
ejpam-5826	288	21	d(qk	d(qk	PROPN
ejpam-5826	288	22	,	,	PUNCT
ejpam-5826	288	23	q	q	NOUN
ejpam-5826	288	24	∗	∗	NOUN
ejpam-5826	288	25	)	)	PUNCT
ejpam-5826	288	26	=	=	SYM
ejpam-5826	288	27	1	1	NUM
ejpam-5826	288	28	+	+	CCONJ
ejpam-5826	288	29	ν	ν	NOUN
ejpam-5826	288	30	1−	1−	NUM
ejpam-5826	288	31	ν	ν	X
ejpam-5826	288	32	d(qk	d(qk	NOUN
ejpam-5826	288	33	,	,	PUNCT
ejpam-5826	288	34	eqk	eqk	NOUN
ejpam-5826	288	35	)	)	PUNCT
ejpam-5826	288	36	+	+	CCONJ
ejpam-5826	288	37	µ+	µ+	PRON
ejpam-5826	288	38	2ν	2ν	NUM
ejpam-5826	288	39	−	−	NOUN
ejpam-5826	288	40	ν	ν	NOUN
ejpam-5826	288	41	1−	1−	NUM
ejpam-5826	288	42	ν	ν	X
ejpam-5826	288	43	d(qk	d(qk	PROPN
ejpam-5826	288	44	,	,	PUNCT
ejpam-5826	288	45	q	q	NOUN
ejpam-5826	288	46	∗	∗	NOUN
ejpam-5826	288	47	)	)	PUNCT
ejpam-5826	288	48	≤	≤	NUM
ejpam-5826	288	49	1	1	NUM
ejpam-5826	288	50	+	+	CCONJ
ejpam-5826	288	51	ν	ν	NOUN
ejpam-5826	288	52	1−	1−	NUM
ejpam-5826	288	53	ν	ν	X
ejpam-5826	288	54	d(qk	d(qk	NOUN
ejpam-5826	288	55	,	,	PUNCT
ejpam-5826	288	56	eqk	eqk	NOUN
ejpam-5826	288	57	)	)	PUNCT
ejpam-5826	288	58	+	+	CCONJ
ejpam-5826	288	59	d(qk	d(qk	NOUN
ejpam-5826	288	60	,	,	PUNCT
ejpam-5826	288	61	q	q	NOUN
ejpam-5826	288	62	∗	∗	NOUN
ejpam-5826	288	63	)	)	PUNCT
ejpam-5826	288	64	.	.	PUNCT
ejpam-5826	289	1	(	(	PUNCT
ejpam-5826	289	2	22	22	NUM
ejpam-5826	289	3	)	)	PUNCT
ejpam-5826	289	4	since	since	SCONJ
ejpam-5826	289	5	limk→∞	limk→∞	ADJ
ejpam-5826	289	6	d(qk	d(qk	NOUN
ejpam-5826	289	7	,	,	PUNCT
ejpam-5826	289	8	eqk	eqk	NOUN
ejpam-5826	289	9	)	)	PUNCT
ejpam-5826	289	10	=	=	SYM
ejpam-5826	289	11	0	0	NUM
ejpam-5826	289	12	,	,	PUNCT
ejpam-5826	289	13	taking	take	VERB
ejpam-5826	289	14	lim	lim	PROPN
ejpam-5826	289	15	sup	sup	NOUN
ejpam-5826	289	16	on	on	ADP
ejpam-5826	289	17	both	both	DET
ejpam-5826	289	18	sides	side	NOUN
ejpam-5826	289	19	of	of	ADP
ejpam-5826	289	20	inequality	inequality	NOUN
ejpam-5826	289	21	(	(	PUNCT
ejpam-5826	289	22	22	22	NUM
ejpam-5826	289	23	)	)	PUNCT
ejpam-5826	289	24	,	,	PUNCT
ejpam-5826	289	25	we	we	PRON
ejpam-5826	289	26	obtain	obtain	VERB
ejpam-5826	289	27	r(eq∗	r(eq∗	PROPN
ejpam-5826	289	28	,	,	PUNCT
ejpam-5826	289	29	qk	qk	NOUN
ejpam-5826	289	30	)	)	PUNCT
ejpam-5826	289	31	=	=	SYM
ejpam-5826	289	32	lim	lim	PROPN
ejpam-5826	289	33	sup	sup	PROPN
ejpam-5826	289	34	k→∞	k→∞	NUM
ejpam-5826	289	35	d(qk	d(qk	PROPN
ejpam-5826	289	36	,	,	PUNCT
ejpam-5826	289	37	eq∗	eq∗	NOUN
ejpam-5826	289	38	)	)	PUNCT
ejpam-5826	289	39	≤	≤	NOUN
ejpam-5826	289	40	lim	lim	PROPN
ejpam-5826	289	41	sup	sup	PROPN
ejpam-5826	289	42	k→∞	k→∞	PROPN
ejpam-5826	289	43	d(qk	d(qk	NOUN
ejpam-5826	289	44	,	,	PUNCT
ejpam-5826	289	45	q	q	NOUN
ejpam-5826	289	46	∗	∗	NOUN
ejpam-5826	289	47	)	)	PUNCT
ejpam-5826	289	48	=	=	SYM
ejpam-5826	289	49	r(q∗	r(q∗	NOUN
ejpam-5826	289	50	,	,	PUNCT
ejpam-5826	289	51	{	{	PUNCT
ejpam-5826	289	52	qk	qk	NOUN
ejpam-5826	289	53	}	}	PUNCT
ejpam-5826	289	54	)	)	PUNCT
ejpam-5826	289	55	.	.	PUNCT
ejpam-5826	290	1	we	we	PRON
ejpam-5826	290	2	know	know	VERB
ejpam-5826	290	3	that	that	DET
ejpam-5826	290	4	asymptotic	asymptotic	ADJ
ejpam-5826	290	5	center	center	NOUN
ejpam-5826	290	6	of	of	ADP
ejpam-5826	290	7	sequence	sequence	NOUN
ejpam-5826	290	8	{	{	PUNCT
ejpam-5826	290	9	qk	qk	AUX
ejpam-5826	290	10	}	}	PUNCT
ejpam-5826	290	11	is	be	AUX
ejpam-5826	290	12	unique	unique	ADJ
ejpam-5826	290	13	,	,	PUNCT
ejpam-5826	290	14	so	so	CCONJ
ejpam-5826	290	15	eq∗	eq∗	NOUN
ejpam-5826	290	16	=	=	SYM
ejpam-5826	290	17	q∗	q∗	NOUN
ejpam-5826	290	18	;	;	PUNCT
ejpam-5826	290	19	thus	thus	ADV
ejpam-5826	290	20	q∗	q∗	NOUN
ejpam-5826	290	21	∈	∈	PROPN
ejpam-5826	290	22	fix(e	fix(e	PROPN
ejpam-5826	290	23	)	)	PUNCT
ejpam-5826	290	24	.	.	PUNCT
ejpam-5826	291	1	the	the	DET
ejpam-5826	291	2	uniqueness	uniqueness	NOUN
ejpam-5826	291	3	of	of	ADP
ejpam-5826	291	4	fixed	fix	VERB
ejpam-5826	291	5	point	point	NOUN
ejpam-5826	291	6	follows	follow	VERB
ejpam-5826	291	7	by	by	ADP
ejpam-5826	291	8	(	(	PUNCT
ejpam-5826	291	9	21	21	NUM
ejpam-5826	291	10	)	)	PUNCT
ejpam-5826	291	11	.	.	PUNCT
ejpam-5826	292	1	a.	a.	PROPN
ejpam-5826	292	2	r.	r.	PROPN
ejpam-5826	292	3	khan	khan	PROPN
ejpam-5826	292	4	et	et	PROPN
ejpam-5826	292	5	al	al	PROPN
ejpam-5826	292	6	.	.	PUNCT
ejpam-5826	292	7	/	/	SYM
ejpam-5826	292	8	eur	eur	PROPN
ejpam-5826	292	9	.	.	PUNCT
ejpam-5826	293	1	j.	j.	PROPN
ejpam-5826	293	2	pure	pure	PROPN
ejpam-5826	293	3	appl	appl	PROPN
ejpam-5826	293	4	.	.	PROPN
ejpam-5826	293	5	math	math	PROPN
ejpam-5826	293	6	,	,	PUNCT
ejpam-5826	293	7	18	18	NUM
ejpam-5826	293	8	(	(	PUNCT
ejpam-5826	293	9	2	2	NUM
ejpam-5826	293	10	)	)	PUNCT
ejpam-5826	293	11	(	(	PUNCT
ejpam-5826	293	12	2025	2025	NUM
ejpam-5826	293	13	)	)	PUNCT
ejpam-5826	293	14	,	,	PUNCT
ejpam-5826	293	15	5826	5826	NUM
ejpam-5826	293	16	13	13	NUM
ejpam-5826	293	17	of	of	ADP
ejpam-5826	293	18	23	23	NUM
ejpam-5826	293	19	example	example	NOUN
ejpam-5826	293	20	2	2	NUM
ejpam-5826	293	21	.	.	PUNCT
ejpam-5826	294	1	let	let	VERB
ejpam-5826	294	2	q	q	NOUN
ejpam-5826	294	3	=	=	PUNCT
ejpam-5826	294	4	r2	r2	PROPN
ejpam-5826	294	5	and	and	CCONJ
ejpam-5826	294	6	d∗	d∗	NOUN
ejpam-5826	294	7	:	:	PUNCT
ejpam-5826	294	8	r2	r2	PROPN
ejpam-5826	294	9	×	×	PROPN
ejpam-5826	294	10	r2	r2	PROPN
ejpam-5826	294	11	→	→	PUNCT
ejpam-5826	294	12	[	[	X
ejpam-5826	294	13	0,∞	0,∞	X
ejpam-5826	294	14	)	)	PUNCT
ejpam-5826	294	15	be	be	AUX
ejpam-5826	294	16	defined	define	VERB
ejpam-5826	294	17	by	by	ADP
ejpam-5826	294	18	d∗(q̄	d∗(q̄	NOUN
ejpam-5826	294	19	,	,	PUNCT
ejpam-5826	294	20	p̄	p̄	NOUN
ejpam-5826	294	21	)	)	PUNCT
ejpam-5826	295	1	=	=	SYM
ejpam-5826	295	2	√	√	NUM
ejpam-5826	295	3	(	(	PUNCT
ejpam-5826	295	4	q1	q1	PROPN
ejpam-5826	295	5	−	−	PROPN
ejpam-5826	295	6	p1)2	p1)2	X
ejpam-5826	295	7	+	+	CCONJ
ejpam-5826	295	8	(	(	PUNCT
ejpam-5826	295	9	q21	q21	PROPN
ejpam-5826	295	10	−	−	PROPN
ejpam-5826	295	11	q2	q2	NOUN
ejpam-5826	295	12	−	−	PROPN
ejpam-5826	295	13	p21	p21	PROPN
ejpam-5826	295	14	+	+	CCONJ
ejpam-5826	295	15	p2)2	p2)2	ADP
ejpam-5826	295	16	,	,	PUNCT
ejpam-5826	295	17	(	(	PUNCT
ejpam-5826	295	18	23	23	NUM
ejpam-5826	295	19	)	)	PUNCT
ejpam-5826	295	20	where	where	SCONJ
ejpam-5826	295	21	q̄	q̄	ADJ
ejpam-5826	295	22	=	=	SYM
ejpam-5826	295	23	(	(	PUNCT
ejpam-5826	295	24	q1	q1	PROPN
ejpam-5826	295	25	,	,	PUNCT
ejpam-5826	295	26	q2	q2	NOUN
ejpam-5826	295	27	)	)	PUNCT
ejpam-5826	295	28	,	,	PUNCT
ejpam-5826	295	29	p̄	p̄	NOUN
ejpam-5826	295	30	=	=	SYM
ejpam-5826	295	31	(	(	PUNCT
ejpam-5826	295	32	p1	p1	PROPN
ejpam-5826	295	33	,	,	PUNCT
ejpam-5826	295	34	p2	p2	NOUN
ejpam-5826	295	35	)	)	PUNCT
ejpam-5826	295	36	∈	∈	NOUN
ejpam-5826	295	37	r2	r2	NOUN
ejpam-5826	295	38	.	.	PUNCT
ejpam-5826	296	1	then	then	ADV
ejpam-5826	296	2	(	(	PUNCT
ejpam-5826	296	3	r2	r2	PROPN
ejpam-5826	296	4	,	,	PUNCT
ejpam-5826	296	5	d∗	d∗	PROPN
ejpam-5826	296	6	)	)	PUNCT
ejpam-5826	296	7	is	be	AUX
ejpam-5826	296	8	not	not	PART
ejpam-5826	296	9	a	a	DET
ejpam-5826	296	10	metric	metric	ADJ
ejpam-5826	296	11	space	space	NOUN
ejpam-5826	296	12	in	in	ADP
ejpam-5826	296	13	the	the	DET
ejpam-5826	296	14	classical	classical	ADJ
ejpam-5826	296	15	sense	sense	NOUN
ejpam-5826	296	16	but	but	CCONJ
ejpam-5826	296	17	is	be	AUX
ejpam-5826	296	18	a	a	DET
ejpam-5826	296	19	hardamard	hardamard	NOUN
ejpam-5826	296	20	space	space	NOUN
ejpam-5826	296	21	(	(	PUNCT
ejpam-5826	296	22	see	see	VERB
ejpam-5826	296	23	[	[	X
ejpam-5826	296	24	19	19	NUM
ejpam-5826	296	25	]	]	NUM
ejpam-5826	296	26	)	)	PUNCT
ejpam-5826	296	27	.	.	PUNCT
ejpam-5826	297	1	hence	hence	ADV
ejpam-5826	297	2	(	(	PUNCT
ejpam-5826	297	3	r2	r2	PROPN
ejpam-5826	297	4	,	,	PUNCT
ejpam-5826	297	5	d∗	d∗	PROPN
ejpam-5826	297	6	)	)	PUNCT
ejpam-5826	297	7	is	be	AUX
ejpam-5826	297	8	a	a	DET
ejpam-5826	297	9	complete	complete	ADJ
ejpam-5826	297	10	uniformly	uniformly	ADV
ejpam-5826	297	11	convex	convex	ADJ
ejpam-5826	297	12	hyperbolic	hyperbolic	ADJ
ejpam-5826	297	13	space	space	NOUN
ejpam-5826	297	14	(	(	PUNCT
ejpam-5826	297	15	for	for	ADP
ejpam-5826	297	16	details	detail	NOUN
ejpam-5826	297	17	,	,	PUNCT
ejpam-5826	297	18	see	see	VERB
ejpam-5826	297	19	example	example	NOUN
ejpam-5826	297	20	2.1	2.1	NUM
ejpam-5826	297	21	in	in	ADP
ejpam-5826	297	22	[	[	X
ejpam-5826	297	23	20	20	NUM
ejpam-5826	297	24	]	]	NUM
ejpam-5826	297	25	)	)	PUNCT
ejpam-5826	297	26	.	.	PUNCT
ejpam-5826	298	1	let	let	VERB
ejpam-5826	298	2	j	j	NOUN
ejpam-5826	298	3	=	=	PUNCT
ejpam-5826	299	1	[	[	X
ejpam-5826	299	2	0	0	NUM
ejpam-5826	299	3	,	,	PUNCT
ejpam-5826	299	4	1]×	1]×	NUM
ejpam-5826	299	5	[	[	X
ejpam-5826	299	6	0	0	NUM
ejpam-5826	299	7	,	,	PUNCT
ejpam-5826	299	8	1	1	NUM
ejpam-5826	299	9	]	]	PUNCT
ejpam-5826	299	10	.	.	PUNCT
ejpam-5826	300	1	define	define	VERB
ejpam-5826	300	2	e	e	NOUN
ejpam-5826	300	3	:	:	PUNCT
ejpam-5826	300	4	j	j	PROPN
ejpam-5826	300	5	→	→	SYM
ejpam-5826	300	6	q	q	X
ejpam-5826	300	7	as	as	ADP
ejpam-5826	300	8	eq̄	eq̄	NOUN
ejpam-5826	300	9	=	=	SYM
ejpam-5826	300	10	(	(	PUNCT
ejpam-5826	300	11	q1	q1	PROPN
ejpam-5826	300	12	,	,	PUNCT
ejpam-5826	300	13	q	q	PROPN
ejpam-5826	300	14	2	2	NUM
ejpam-5826	300	15	1	1	NUM
ejpam-5826	300	16	+	+	NUM
ejpam-5826	300	17	q2	q2	NOUN
ejpam-5826	300	18	)	)	PUNCT
ejpam-5826	300	19	,	,	PUNCT
ejpam-5826	300	20	where	where	SCONJ
ejpam-5826	300	21	q̄	q̄	ADJ
ejpam-5826	300	22	=	=	SYM
ejpam-5826	300	23	(	(	PUNCT
ejpam-5826	300	24	q1	q1	PROPN
ejpam-5826	300	25	,	,	PUNCT
ejpam-5826	300	26	q2	q2	NOUN
ejpam-5826	300	27	)	)	PUNCT
ejpam-5826	300	28	.	.	PUNCT
ejpam-5826	301	1	for	for	ADP
ejpam-5826	301	2	any	any	DET
ejpam-5826	301	3	µ	µ	PROPN
ejpam-5826	301	4	∈	∈	NOUN
ejpam-5826	301	5	[	[	PUNCT
ejpam-5826	301	6	2	2	NUM
ejpam-5826	301	7	5	5	NUM
ejpam-5826	301	8	,	,	PUNCT
ejpam-5826	301	9	1	1	NUM
ejpam-5826	301	10	)	)	PUNCT
ejpam-5826	301	11	and	and	CCONJ
ejpam-5826	301	12	0	0	NUM
ejpam-5826	301	13	≤	≤	NUM
ejpam-5826	301	14	ν	ν	ADP
ejpam-5826	301	15	<	<	X
ejpam-5826	301	16	∞	∞	PROPN
ejpam-5826	301	17	with	with	ADP
ejpam-5826	301	18	µ	µ	PROPN
ejpam-5826	301	19	+	+	NUM
ejpam-5826	301	20	2ν	2ν	NOUN
ejpam-5826	301	21	<	<	X
ejpam-5826	301	22	1	1	NUM
ejpam-5826	301	23	,	,	PUNCT
ejpam-5826	301	24	we	we	PRON
ejpam-5826	301	25	need	need	VERB
ejpam-5826	301	26	to	to	PART
ejpam-5826	301	27	verify	verify	VERB
ejpam-5826	301	28	the	the	DET
ejpam-5826	301	29	following	following	NOUN
ejpam-5826	301	30	,	,	PUNCT
ejpam-5826	301	31	for	for	ADP
ejpam-5826	301	32	any	any	DET
ejpam-5826	301	33	q̄	q̄	NOUN
ejpam-5826	301	34	,	,	PUNCT
ejpam-5826	301	35	p̄	p̄	PROPN
ejpam-5826	301	36	∈	∈	PROPN
ejpam-5826	301	37	j	j	PROPN
ejpam-5826	301	38	,	,	PUNCT
ejpam-5826	301	39	γ	γ	X
ejpam-5826	301	40	:	:	PUNCT
ejpam-5826	301	41	=	=	SYM
ejpam-5826	301	42	µd∗(q̄	µd∗(q̄	NOUN
ejpam-5826	301	43	,	,	PUNCT
ejpam-5826	301	44	p̄	p̄	NOUN
ejpam-5826	301	45	)	)	PUNCT
ejpam-5826	301	46	+	+	CCONJ
ejpam-5826	301	47	ν[d∗(q̄	ν[d∗(q̄	ADJ
ejpam-5826	301	48	,	,	PUNCT
ejpam-5826	301	49	eq̄	eq̄	NOUN
ejpam-5826	301	50	)	)	PUNCT
ejpam-5826	302	1	+	+	CCONJ
ejpam-5826	302	2	d∗(p̄	d∗(p̄	NOUN
ejpam-5826	302	3	,	,	PUNCT
ejpam-5826	302	4	ep̄)]−	ep̄)]−	X
ejpam-5826	302	5	d∗(eq̄,ep̄	d∗(eq̄,ep̄	NOUN
ejpam-5826	302	6	)	)	PUNCT
ejpam-5826	302	7	≥	≥	NOUN
ejpam-5826	302	8	0	0	NUM
ejpam-5826	302	9	.	.	PUNCT
ejpam-5826	303	1	(	(	PUNCT
ejpam-5826	303	2	24	24	NUM
ejpam-5826	303	3	)	)	PUNCT
ejpam-5826	303	4	thus	thus	ADV
ejpam-5826	303	5	,	,	PUNCT
ejpam-5826	303	6	for	for	ADP
ejpam-5826	303	7	any	any	DET
ejpam-5826	303	8	q̄	q̄	NOUN
ejpam-5826	303	9	=	=	SYM
ejpam-5826	303	10	(	(	PUNCT
ejpam-5826	303	11	q1	q1	PROPN
ejpam-5826	303	12	,	,	PUNCT
ejpam-5826	303	13	q2	q2	NOUN
ejpam-5826	303	14	)	)	PUNCT
ejpam-5826	303	15	,	,	PUNCT
ejpam-5826	303	16	p̄	p̄	NOUN
ejpam-5826	303	17	=	=	SYM
ejpam-5826	303	18	(	(	PUNCT
ejpam-5826	303	19	p1	p1	PROPN
ejpam-5826	303	20	,	,	PUNCT
ejpam-5826	303	21	p2	p2	X
ejpam-5826	303	22	)	)	PUNCT
ejpam-5826	303	23	∈	∈	PROPN
ejpam-5826	303	24	j	j	PROPN
ejpam-5826	303	25	,	,	PUNCT
ejpam-5826	303	26	by	by	ADP
ejpam-5826	303	27	using	use	VERB
ejpam-5826	303	28	(	(	PUNCT
ejpam-5826	303	29	23	23	NUM
ejpam-5826	303	30	)	)	PUNCT
ejpam-5826	303	31	in	in	ADP
ejpam-5826	303	32	(	(	PUNCT
ejpam-5826	303	33	24	24	NUM
ejpam-5826	303	34	)	)	PUNCT
ejpam-5826	303	35	,	,	PUNCT
ejpam-5826	303	36	we	we	PRON
ejpam-5826	303	37	get	get	VERB
ejpam-5826	303	38	γ	γ	X
ejpam-5826	303	39	=	=	SYM
ejpam-5826	303	40	d∗((q1	d∗((q1	PROPN
ejpam-5826	303	41	,	,	PUNCT
ejpam-5826	303	42	q2	q2	NOUN
ejpam-5826	303	43	)	)	PUNCT
ejpam-5826	303	44	,	,	PUNCT
ejpam-5826	303	45	(	(	PUNCT
ejpam-5826	303	46	p1	p1	NOUN
ejpam-5826	303	47	,	,	PUNCT
ejpam-5826	303	48	p2	p2	NOUN
ejpam-5826	303	49	)	)	PUNCT
ejpam-5826	303	50	)	)	PUNCT
ejpam-5826	304	1	+	+	CCONJ
ejpam-5826	304	2	d∗((q1	d∗((q1	PROPN
ejpam-5826	304	3	,	,	PUNCT
ejpam-5826	304	4	q2	q2	NOUN
ejpam-5826	304	5	)	)	PUNCT
ejpam-5826	304	6	,	,	PUNCT
ejpam-5826	304	7	(	(	PUNCT
ejpam-5826	304	8	q1	q1	PROPN
ejpam-5826	304	9	,	,	PUNCT
ejpam-5826	304	10	q	q	PROPN
ejpam-5826	304	11	2	2	NUM
ejpam-5826	304	12	1	1	NUM
ejpam-5826	304	13	+	+	NUM
ejpam-5826	304	14	q2	q2	NOUN
ejpam-5826	304	15	)	)	PUNCT
ejpam-5826	304	16	)	)	PUNCT
ejpam-5826	305	1	+	+	CCONJ
ejpam-5826	305	2	d∗((p1	d∗((p1	NOUN
ejpam-5826	305	3	,	,	PUNCT
ejpam-5826	305	4	p2	p2	PROPN
ejpam-5826	305	5	)	)	PUNCT
ejpam-5826	305	6	,	,	PUNCT
ejpam-5826	305	7	(	(	PUNCT
ejpam-5826	305	8	p1	p1	NOUN
ejpam-5826	305	9	,	,	PUNCT
ejpam-5826	305	10	p	p	NOUN
ejpam-5826	305	11	2	2	NUM
ejpam-5826	305	12	1	1	NUM
ejpam-5826	305	13	+	+	NUM
ejpam-5826	305	14	p2	p2	NOUN
ejpam-5826	305	15	)	)	PUNCT
ejpam-5826	305	16	)	)	PUNCT
ejpam-5826	306	1	−d∗((q1	−d∗((q1	PROPN
ejpam-5826	306	2	,	,	PUNCT
ejpam-5826	306	3	q	q	NOUN
ejpam-5826	306	4	2	2	NUM
ejpam-5826	306	5	1	1	NUM
ejpam-5826	306	6	+	+	NUM
ejpam-5826	306	7	q2	q2	NOUN
ejpam-5826	306	8	)	)	PUNCT
ejpam-5826	306	9	,	,	PUNCT
ejpam-5826	306	10	(	(	PUNCT
ejpam-5826	306	11	p1	p1	NOUN
ejpam-5826	306	12	,	,	PUNCT
ejpam-5826	306	13	p	p	NOUN
ejpam-5826	306	14	2	2	NUM
ejpam-5826	306	15	1	1	NUM
ejpam-5826	306	16	+	+	NUM
ejpam-5826	306	17	p2	p2	NOUN
ejpam-5826	306	18	)	)	PUNCT
ejpam-5826	306	19	)	)	PUNCT
ejpam-5826	307	1	=	=	SYM
ejpam-5826	307	2	µ	µ	PRON
ejpam-5826	307	3	√	√	NUM
ejpam-5826	307	4	(	(	PUNCT
ejpam-5826	307	5	q1	q1	PROPN
ejpam-5826	307	6	−	−	PROPN
ejpam-5826	307	7	p1)2	p1)2	X
ejpam-5826	307	8	+	+	CCONJ
ejpam-5826	307	9	(	(	PUNCT
ejpam-5826	307	10	q21	q21	PROPN
ejpam-5826	307	11	−	−	PROPN
ejpam-5826	307	12	q1	q1	NOUN
ejpam-5826	307	13	−	−	NOUN
ejpam-5826	307	14	p22	p22	NOUN
ejpam-5826	307	15	+	+	CCONJ
ejpam-5826	307	16	p2)2	p2)2	ADP
ejpam-5826	307	17	+	+	NOUN
ejpam-5826	307	18	ν	ν	NOUN
ejpam-5826	307	19	(	(	PUNCT
ejpam-5826	307	20	√	√	NUM
ejpam-5826	307	21	(	(	PUNCT
ejpam-5826	307	22	q1	q1	NOUN
ejpam-5826	307	23	−	−	PROPN
ejpam-5826	307	24	q1)2	q1)2	SYM
ejpam-5826	308	1	+	+	CCONJ
ejpam-5826	308	2	(	(	PUNCT
ejpam-5826	308	3	q21	q21	PROPN
ejpam-5826	308	4	−	−	PROPN
ejpam-5826	308	5	q2	q2	NOUN
ejpam-5826	308	6	−	−	PROPN
ejpam-5826	308	7	q21	q21	PROPN
ejpam-5826	308	8	+	+	CCONJ
ejpam-5826	308	9	(	(	PUNCT
ejpam-5826	308	10	q21	q21	PROPN
ejpam-5826	308	11	+	+	NUM
ejpam-5826	308	12	q2))2	q2))2	NOUN
ejpam-5826	308	13	+	+	CCONJ
ejpam-5826	308	14	√	√	PROPN
ejpam-5826	308	15	(	(	PUNCT
ejpam-5826	308	16	p1	p1	PROPN
ejpam-5826	308	17	−	−	PROPN
ejpam-5826	309	1	p1)2	p1)2	X
ejpam-5826	310	1	+	+	CCONJ
ejpam-5826	310	2	(	(	PUNCT
ejpam-5826	310	3	p21	p21	NOUN
ejpam-5826	310	4	−	−	PROPN
ejpam-5826	310	5	p2	p2	PROPN
ejpam-5826	310	6	−	−	PROPN
ejpam-5826	310	7	p21	p21	NOUN
ejpam-5826	310	8	+	+	CCONJ
ejpam-5826	310	9	(	(	PUNCT
ejpam-5826	310	10	p21	p21	NOUN
ejpam-5826	310	11	+	+	CCONJ
ejpam-5826	310	12	p2))2	p2))2	NOUN
ejpam-5826	310	13	)	)	PUNCT
ejpam-5826	311	1	−	−	ADP
ejpam-5826	312	1	√	√	NUM
ejpam-5826	312	2	(	(	PUNCT
ejpam-5826	312	3	q1	q1	PROPN
ejpam-5826	312	4	−	−	PROPN
ejpam-5826	313	1	p1)2	p1)2	X
ejpam-5826	314	1	+	+	CCONJ
ejpam-5826	314	2	(	(	PUNCT
ejpam-5826	314	3	q21	q21	NOUN
ejpam-5826	314	4	−	−	PROPN
ejpam-5826	314	5	(	(	PUNCT
ejpam-5826	314	6	q21	q21	NOUN
ejpam-5826	314	7	+	+	CCONJ
ejpam-5826	314	8	q2)−	q2)−	ADJ
ejpam-5826	314	9	p21	p21	NOUN
ejpam-5826	314	10	+	+	CCONJ
ejpam-5826	314	11	(	(	PUNCT
ejpam-5826	314	12	p21	p21	NOUN
ejpam-5826	314	13	+	+	CCONJ
ejpam-5826	314	14	p2))2	p2))2	NOUN
ejpam-5826	314	15	=	=	SYM
ejpam-5826	314	16	µ	µ	SYM
ejpam-5826	314	17	√	√	NUM
ejpam-5826	314	18	(	(	PUNCT
ejpam-5826	314	19	q1	q1	PROPN
ejpam-5826	314	20	−	−	PROPN
ejpam-5826	314	21	p1)2	p1)2	X
ejpam-5826	314	22	+	+	CCONJ
ejpam-5826	314	23	(	(	PUNCT
ejpam-5826	314	24	(	(	PUNCT
ejpam-5826	314	25	q2	q2	NOUN
ejpam-5826	314	26	−	−	NOUN
ejpam-5826	314	27	p2	p2	PROPN
ejpam-5826	314	28	)	)	PUNCT
ejpam-5826	314	29	+	+	CCONJ
ejpam-5826	314	30	(	(	PUNCT
ejpam-5826	314	31	q21	q21	PROPN
ejpam-5826	314	32	−	−	PROPN
ejpam-5826	314	33	p21	p21	NOUN
ejpam-5826	314	34	)	)	PUNCT
ejpam-5826	314	35	)	)	PUNCT
ejpam-5826	314	36	2	2	NUM
ejpam-5826	315	1	+	+	NUM
ejpam-5826	315	2	ν(q21	ν(q21	NOUN
ejpam-5826	315	3	+	+	CCONJ
ejpam-5826	315	4	p21)−	p21)−	NOUN
ejpam-5826	315	5	√	√	PROPN
ejpam-5826	315	6	(	(	PUNCT
ejpam-5826	315	7	q1	q1	PROPN
ejpam-5826	315	8	−	−	PROPN
ejpam-5826	315	9	p1)2	p1)2	PROPN
ejpam-5826	315	10	+	+	CCONJ
ejpam-5826	315	11	(	(	PUNCT
ejpam-5826	315	12	q2	q2	NOUN
ejpam-5826	315	13	−	−	PROPN
ejpam-5826	315	14	p2)2	p2)2	ADP
ejpam-5826	315	15	≥	≥	NOUN
ejpam-5826	315	16	0	0	NUM
ejpam-5826	316	1	hence	hence	ADV
ejpam-5826	316	2	(	(	PUNCT
ejpam-5826	316	3	24	24	NUM
ejpam-5826	316	4	)	)	PUNCT
ejpam-5826	316	5	holds	hold	VERB
ejpam-5826	316	6	.	.	PUNCT
ejpam-5826	317	1	therefore	therefore	ADV
ejpam-5826	317	2	e	e	X
ejpam-5826	317	3	satisfies	satisfie	NOUN
ejpam-5826	317	4	(	(	PUNCT
ejpam-5826	317	5	21	21	NUM
ejpam-5826	317	6	)	)	PUNCT
ejpam-5826	317	7	with	with	ADP
ejpam-5826	317	8	µ	µ	PRON
ejpam-5826	317	9	∈	∈	NOUN
ejpam-5826	317	10	[	[	PUNCT
ejpam-5826	317	11	2	2	NUM
ejpam-5826	317	12	5	5	NUM
ejpam-5826	317	13	,	,	PUNCT
ejpam-5826	317	14	1	1	NUM
ejpam-5826	317	15	)	)	PUNCT
ejpam-5826	317	16	and	and	CCONJ
ejpam-5826	317	17	0	0	NUM
ejpam-5826	317	18	≤	≤	NUM
ejpam-5826	317	19	ν	ν	ADP
ejpam-5826	317	20	<	<	X
ejpam-5826	317	21	∞	∞	NUM
ejpam-5826	317	22	where	where	SCONJ
ejpam-5826	317	23	µ+	µ+	DET
ejpam-5826	317	24	2ν	2ν	NOUN
ejpam-5826	317	25	<	<	X
ejpam-5826	317	26	1	1	X
ejpam-5826	317	27	.	.	X
ejpam-5826	317	28	for	for	ADP
ejpam-5826	317	29	any	any	DET
ejpam-5826	317	30	qk	qk	NOUN
ejpam-5826	317	31	∈	∈	PROPN
ejpam-5826	317	32	j	j	PROPN
ejpam-5826	317	33	,	,	PUNCT
ejpam-5826	317	34	define	define	VERB
ejpam-5826	317	35	qk	qk	NOUN
ejpam-5826	317	36	=	=	PUNCT
ejpam-5826	317	37	(	(	PUNCT
ejpam-5826	317	38	1	1	NUM
ejpam-5826	317	39	k	k	NOUN
ejpam-5826	317	40	,	,	PUNCT
ejpam-5826	317	41	1	1	NUM
ejpam-5826	317	42	k	k	NOUN
ejpam-5826	317	43	)	)	PUNCT
ejpam-5826	317	44	.	.	PUNCT
ejpam-5826	318	1	then	then	ADV
ejpam-5826	318	2	eqk	eqk	NOUN
ejpam-5826	318	3	=	=	SYM
ejpam-5826	318	4	(	(	PUNCT
ejpam-5826	318	5	1	1	NUM
ejpam-5826	318	6	k	k	NOUN
ejpam-5826	318	7	,	,	PUNCT
ejpam-5826	318	8	1	1	NUM
ejpam-5826	318	9	k2	k2	NOUN
ejpam-5826	318	10	+	+	CCONJ
ejpam-5826	318	11	1	1	NUM
ejpam-5826	318	12	k	k	NOUN
ejpam-5826	318	13	)	)	PUNCT
ejpam-5826	318	14	,	,	PUNCT
ejpam-5826	318	15	so	so	SCONJ
ejpam-5826	318	16	from	from	ADP
ejpam-5826	318	17	(	(	PUNCT
ejpam-5826	318	18	23	23	NUM
ejpam-5826	318	19	)	)	PUNCT
ejpam-5826	318	20	,	,	PUNCT
ejpam-5826	318	21	we	we	PRON
ejpam-5826	318	22	get	get	VERB
ejpam-5826	318	23	that	that	SCONJ
ejpam-5826	318	24	d∗(qk	d∗(qk	NOUN
ejpam-5826	318	25	,	,	PUNCT
ejpam-5826	318	26	eqk	eqk	NOUN
ejpam-5826	318	27	)	)	PUNCT
ejpam-5826	318	28	=	=	SYM
ejpam-5826	318	29	d∗	d∗	PROPN
ejpam-5826	318	30	(	(	PUNCT
ejpam-5826	318	31	1	1	NUM
ejpam-5826	318	32	k	k	NOUN
ejpam-5826	318	33	,	,	PUNCT
ejpam-5826	318	34	1	1	NUM
ejpam-5826	318	35	k2	k2	NOUN
ejpam-5826	318	36	+	+	CCONJ
ejpam-5826	318	37	1	1	NUM
ejpam-5826	318	38	k	k	NOUN
ejpam-5826	318	39	)	)	PUNCT
ejpam-5826	318	40	=	=	PUNCT
ejpam-5826	319	1	√(1	√(1	NOUN
ejpam-5826	319	2	k	k	NOUN
ejpam-5826	319	3	−	−	PROPN
ejpam-5826	319	4	1	1	NUM
ejpam-5826	319	5	k	k	NOUN
ejpam-5826	319	6	)	)	PUNCT
ejpam-5826	319	7	2	2	NUM
ejpam-5826	320	1	+	+	CCONJ
ejpam-5826	320	2	(	(	PUNCT
ejpam-5826	320	3	1	1	NUM
ejpam-5826	320	4	k2	k2	NOUN
ejpam-5826	320	5	−	−	PROPN
ejpam-5826	320	6	1	1	NUM
ejpam-5826	320	7	k	k	NOUN
ejpam-5826	320	8	−	−	PROPN
ejpam-5826	320	9	1	1	NUM
ejpam-5826	320	10	k2	k2	NOUN
ejpam-5826	320	11	+	+	CCONJ
ejpam-5826	320	12	(	(	PUNCT
ejpam-5826	320	13	1	1	NUM
ejpam-5826	320	14	k2	k2	NOUN
ejpam-5826	320	15	+	+	CCONJ
ejpam-5826	320	16	1	1	NUM
ejpam-5826	320	17	k	k	NOUN
ejpam-5826	320	18	)	)	PUNCT
ejpam-5826	320	19	)	)	PUNCT
ejpam-5826	320	20	2	2	NUM
ejpam-5826	320	21	=	=	SYM
ejpam-5826	320	22	1	1	NUM
ejpam-5826	320	23	k2	k2	NOUN
ejpam-5826	320	24	.	.	PUNCT
ejpam-5826	321	1	it	it	PRON
ejpam-5826	321	2	follows	follow	VERB
ejpam-5826	321	3	that	that	SCONJ
ejpam-5826	321	4	d∗(qk	d∗(qk	NOUN
ejpam-5826	321	5	,	,	PUNCT
ejpam-5826	321	6	eqk	eqk	NOUN
ejpam-5826	321	7	)	)	PUNCT
ejpam-5826	321	8	→	→	SYM
ejpam-5826	321	9	0	0	PUNCT
ejpam-5826	321	10	as	as	ADP
ejpam-5826	321	11	k	k	PROPN
ejpam-5826	321	12	→	→	SYM
ejpam-5826	321	13	∞.	∞.	PROPN
ejpam-5826	321	14	all	all	DET
ejpam-5826	321	15	the	the	DET
ejpam-5826	321	16	assumptions	assumption	NOUN
ejpam-5826	321	17	of	of	ADP
ejpam-5826	321	18	theorem	theorem	ADJ
ejpam-5826	321	19	5	5	NUM
ejpam-5826	321	20	hold	hold	NOUN
ejpam-5826	321	21	and	and	CCONJ
ejpam-5826	321	22	hence	hence	ADV
ejpam-5826	321	23	,	,	PUNCT
ejpam-5826	321	24	the	the	DET
ejpam-5826	321	25	mapping	mapping	NOUN
ejpam-5826	321	26	e	e	NOUN
ejpam-5826	321	27	has	have	VERB
ejpam-5826	321	28	a	a	DET
ejpam-5826	321	29	unique	unique	ADJ
ejpam-5826	321	30	fixed	fix	VERB
ejpam-5826	321	31	point	point	NOUN
ejpam-5826	321	32	at	at	ADP
ejpam-5826	321	33	(	(	PUNCT
ejpam-5826	321	34	0	0	NUM
ejpam-5826	321	35	,	,	PUNCT
ejpam-5826	321	36	0	0	NUM
ejpam-5826	321	37	)	)	PUNCT
ejpam-5826	321	38	.	.	PUNCT
ejpam-5826	322	1	khan	khan	PROPN
ejpam-5826	323	1	[	[	X
ejpam-5826	323	2	21	21	NUM
ejpam-5826	323	3	]	]	PUNCT
ejpam-5826	323	4	has	have	AUX
ejpam-5826	323	5	studied	study	VERB
ejpam-5826	323	6	some	some	DET
ejpam-5826	323	7	properties	property	NOUN
ejpam-5826	323	8	of	of	ADP
ejpam-5826	323	9	the	the	DET
ejpam-5826	323	10	set	set	NOUN
ejpam-5826	323	11	of	of	ADP
ejpam-5826	323	12	fixed	fix	VERB
ejpam-5826	323	13	points	point	NOUN
ejpam-5826	323	14	of	of	ADP
ejpam-5826	323	15	a	a	DET
ejpam-5826	323	16	∗-nonexpansive	∗-nonexpansive	ADJ
ejpam-5826	323	17	mapping	mapping	NOUN
ejpam-5826	323	18	in	in	ADP
ejpam-5826	323	19	the	the	DET
ejpam-5826	323	20	context	context	NOUN
ejpam-5826	323	21	of	of	ADP
ejpam-5826	323	22	strictly	strictly	ADV
ejpam-5826	323	23	convex	convex	ADJ
ejpam-5826	323	24	banach	banach	NOUN
ejpam-5826	323	25	spaces	space	VERB
ejpam-5826	323	26	.	.	PUNCT
ejpam-5826	324	1	in	in	ADP
ejpam-5826	324	2	the	the	DET
ejpam-5826	324	3	following	follow	VERB
ejpam-5826	324	4	result	result	NOUN
ejpam-5826	324	5	,	,	PUNCT
ejpam-5826	324	6	we	we	PRON
ejpam-5826	324	7	establish	establish	VERB
ejpam-5826	324	8	the	the	DET
ejpam-5826	324	9	closedness	closedness	NOUN
ejpam-5826	324	10	and	and	CCONJ
ejpam-5826	324	11	convexity	convexity	NOUN
ejpam-5826	324	12	of	of	ADP
ejpam-5826	324	13	the	the	DET
ejpam-5826	324	14	set	set	NOUN
ejpam-5826	324	15	of	of	ADP
ejpam-5826	324	16	fixed	fix	VERB
ejpam-5826	324	17	points	point	NOUN
ejpam-5826	324	18	of	of	ADP
ejpam-5826	324	19	a	a	DET
ejpam-5826	324	20	contractive	contractive	ADJ
ejpam-5826	324	21	-	-	PUNCT
ejpam-5826	324	22	type	type	NOUN
ejpam-5826	324	23	mapping	mapping	NOUN
ejpam-5826	324	24	on	on	ADP
ejpam-5826	324	25	a	a	DET
ejpam-5826	324	26	convex	convex	ADJ
ejpam-5826	324	27	metric	metric	ADJ
ejpam-5826	324	28	space	space	NOUN
ejpam-5826	324	29	.	.	PUNCT
ejpam-5826	325	1	theorem	theorem	ADJ
ejpam-5826	325	2	6	6	NUM
ejpam-5826	325	3	.	.	PUNCT
ejpam-5826	326	1	let	let	VERB
ejpam-5826	326	2	j	j	PROPN
ejpam-5826	326	3	be	be	AUX
ejpam-5826	326	4	a	a	DET
ejpam-5826	326	5	closed	closed	ADJ
ejpam-5826	326	6	and	and	CCONJ
ejpam-5826	326	7	convex	convex	NOUN
ejpam-5826	326	8	subset	subset	NOUN
ejpam-5826	326	9	of	of	ADP
ejpam-5826	326	10	a	a	DET
ejpam-5826	326	11	convex	convex	ADJ
ejpam-5826	326	12	metric	metric	ADJ
ejpam-5826	326	13	space	space	NOUN
ejpam-5826	326	14	q	q	PROPN
ejpam-5826	326	15	and	and	CCONJ
ejpam-5826	326	16	e	e	NOUN
ejpam-5826	326	17	:	:	PUNCT
ejpam-5826	326	18	j	j	PROPN
ejpam-5826	326	19	→	→	PUNCT
ejpam-5826	326	20	q	q	AUX
ejpam-5826	326	21	be	be	AUX
ejpam-5826	326	22	a	a	DET
ejpam-5826	326	23	mapping	mapping	NOUN
ejpam-5826	326	24	satisfying	satisfy	VERB
ejpam-5826	326	25	(	(	PUNCT
ejpam-5826	326	26	21	21	NUM
ejpam-5826	326	27	)	)	PUNCT
ejpam-5826	326	28	.	.	PUNCT
ejpam-5826	327	1	then	then	ADV
ejpam-5826	327	2	fix(e	fix(e	PROPN
ejpam-5826	327	3	)	)	PUNCT
ejpam-5826	327	4	is	be	AUX
ejpam-5826	327	5	closed	close	VERB
ejpam-5826	327	6	and	and	CCONJ
ejpam-5826	327	7	convex	convex	PROPN
ejpam-5826	327	8	.	.	PUNCT
ejpam-5826	328	1	a.	a.	PROPN
ejpam-5826	328	2	r.	r.	PROPN
ejpam-5826	328	3	khan	khan	PROPN
ejpam-5826	328	4	et	et	PROPN
ejpam-5826	328	5	al	al	PROPN
ejpam-5826	328	6	.	.	PUNCT
ejpam-5826	328	7	/	/	SYM
ejpam-5826	328	8	eur	eur	PROPN
ejpam-5826	328	9	.	.	PUNCT
ejpam-5826	329	1	j.	j.	PROPN
ejpam-5826	329	2	pure	pure	PROPN
ejpam-5826	329	3	appl	appl	PROPN
ejpam-5826	329	4	.	.	PROPN
ejpam-5826	329	5	math	math	PROPN
ejpam-5826	329	6	,	,	PUNCT
ejpam-5826	329	7	18	18	NUM
ejpam-5826	329	8	(	(	PUNCT
ejpam-5826	329	9	2	2	NUM
ejpam-5826	329	10	)	)	PUNCT
ejpam-5826	329	11	(	(	PUNCT
ejpam-5826	329	12	2025	2025	NUM
ejpam-5826	329	13	)	)	PUNCT
ejpam-5826	329	14	,	,	PUNCT
ejpam-5826	329	15	5826	5826	NUM
ejpam-5826	329	16	14	14	NUM
ejpam-5826	329	17	of	of	ADP
ejpam-5826	329	18	23	23	NUM
ejpam-5826	329	19	proof	proof	NOUN
ejpam-5826	329	20	.	.	PUNCT
ejpam-5826	330	1	if	if	SCONJ
ejpam-5826	330	2	fix(e	fix(e	PROPN
ejpam-5826	330	3	)	)	PUNCT
ejpam-5826	330	4	=	=	NOUN
ejpam-5826	330	5	∅	∅	NOUN
ejpam-5826	330	6	,	,	PUNCT
ejpam-5826	330	7	then	then	ADV
ejpam-5826	330	8	nothing	nothing	PRON
ejpam-5826	330	9	to	to	PART
ejpam-5826	330	10	show	show	VERB
ejpam-5826	330	11	,	,	PUNCT
ejpam-5826	330	12	since	since	SCONJ
ejpam-5826	330	13	empty	empty	ADJ
ejpam-5826	330	14	set	set	NOUN
ejpam-5826	330	15	is	be	AUX
ejpam-5826	330	16	closed	close	VERB
ejpam-5826	330	17	and	and	CCONJ
ejpam-5826	330	18	convex	convex	NOUN
ejpam-5826	330	19	.	.	PUNCT
ejpam-5826	331	1	now	now	ADV
ejpam-5826	331	2	assume	assume	VERB
ejpam-5826	331	3	that	that	SCONJ
ejpam-5826	331	4	fix(e	fix(e	PROPN
ejpam-5826	331	5	)	)	PUNCT
ejpam-5826	331	6	̸=	̸=	PROPN
ejpam-5826	331	7	∅.	∅.	ADP
ejpam-5826	331	8	we	we	PRON
ejpam-5826	331	9	first	first	ADV
ejpam-5826	331	10	show	show	VERB
ejpam-5826	331	11	that	that	SCONJ
ejpam-5826	331	12	fix(e	fix(e	PROPN
ejpam-5826	331	13	)	)	PUNCT
ejpam-5826	331	14	is	be	AUX
ejpam-5826	331	15	closed	close	VERB
ejpam-5826	331	16	.	.	PUNCT
ejpam-5826	332	1	let	let	VERB
ejpam-5826	332	2	{	{	PUNCT
ejpam-5826	332	3	qk	qk	PART
ejpam-5826	332	4	}	}	PUNCT
ejpam-5826	332	5	be	be	AUX
ejpam-5826	332	6	a	a	DET
ejpam-5826	332	7	sequence	sequence	NOUN
ejpam-5826	332	8	in	in	ADP
ejpam-5826	332	9	fix(e	fix(e	PROPN
ejpam-5826	332	10	)	)	PUNCT
ejpam-5826	332	11	such	such	ADJ
ejpam-5826	332	12	that	that	SCONJ
ejpam-5826	332	13	{	{	PUNCT
ejpam-5826	332	14	qk	qk	PART
ejpam-5826	332	15	}	}	PUNCT
ejpam-5826	332	16	converges	converge	NOUN
ejpam-5826	332	17	to	to	ADP
ejpam-5826	332	18	a	a	DET
ejpam-5826	332	19	point	point	NOUN
ejpam-5826	332	20	u	u	NOUN
ejpam-5826	332	21	in	in	ADP
ejpam-5826	332	22	j	j	PROPN
ejpam-5826	332	23	.	.	PUNCT
ejpam-5826	333	1	we	we	PRON
ejpam-5826	333	2	show	show	VERB
ejpam-5826	333	3	that	that	SCONJ
ejpam-5826	333	4	u	u	PROPN
ejpam-5826	333	5	∈	∈	PROPN
ejpam-5826	333	6	fix(e	fix(e	PROPN
ejpam-5826	333	7	)	)	PUNCT
ejpam-5826	333	8	.	.	PUNCT
ejpam-5826	334	1	by	by	ADP
ejpam-5826	334	2	(	(	PUNCT
ejpam-5826	334	3	21	21	NUM
ejpam-5826	334	4	)	)	PUNCT
ejpam-5826	334	5	,	,	PUNCT
ejpam-5826	334	6	we	we	PRON
ejpam-5826	334	7	obtain	obtain	VERB
ejpam-5826	334	8	d(qk	d(qk	NOUN
ejpam-5826	334	9	,	,	PUNCT
ejpam-5826	334	10	eu	eu	PROPN
ejpam-5826	334	11	)	)	PUNCT
ejpam-5826	334	12	=	=	PUNCT
ejpam-5826	335	1	d(eqk	d(eqk	ADJ
ejpam-5826	335	2	,	,	PUNCT
ejpam-5826	335	3	eu	eu	NOUN
ejpam-5826	335	4	)	)	PUNCT
ejpam-5826	335	5	≤	≤	PUNCT
ejpam-5826	335	6	µd(qk	µd(qk	PROPN
ejpam-5826	335	7	,	,	PUNCT
ejpam-5826	335	8	u	u	NOUN
ejpam-5826	335	9	)	)	PUNCT
ejpam-5826	335	10	+	+	CCONJ
ejpam-5826	335	11	ν[d(qk	ν[d(qk	NOUN
ejpam-5826	335	12	,	,	PUNCT
ejpam-5826	335	13	eqk	eqk	NOUN
ejpam-5826	335	14	)	)	PUNCT
ejpam-5826	335	15	+	+	CCONJ
ejpam-5826	335	16	d(u	d(u	PROPN
ejpam-5826	335	17	,	,	PUNCT
ejpam-5826	335	18	eu	eu	PROPN
ejpam-5826	335	19	)	)	PUNCT
ejpam-5826	335	20	]	]	PUNCT
ejpam-5826	335	21	.	.	PUNCT
ejpam-5826	335	22	implies	imply	VERB
ejpam-5826	335	23	d(qk	d(qk	PROPN
ejpam-5826	335	24	,	,	PUNCT
ejpam-5826	335	25	eu	eu	PROPN
ejpam-5826	335	26	)	)	PUNCT
ejpam-5826	335	27	≤	≤	PUNCT
ejpam-5826	335	28	µd(qk	µd(qk	PROPN
ejpam-5826	335	29	,	,	PUNCT
ejpam-5826	335	30	u	u	NOUN
ejpam-5826	335	31	)	)	PUNCT
ejpam-5826	335	32	+	+	CCONJ
ejpam-5826	335	33	ν[d(u	ν[d(u	PROPN
ejpam-5826	335	34	,	,	PUNCT
ejpam-5826	335	35	qk	qk	NOUN
ejpam-5826	335	36	)	)	PUNCT
ejpam-5826	335	37	+	+	CCONJ
ejpam-5826	335	38	d(qk	d(qk	PROPN
ejpam-5826	335	39	,	,	PUNCT
ejpam-5826	335	40	eu	eu	PROPN
ejpam-5826	335	41	)	)	PUNCT
ejpam-5826	335	42	]	]	PUNCT
ejpam-5826	335	43	.	.	PUNCT
ejpam-5826	336	1	thus	thus	ADV
ejpam-5826	336	2	d(u	d(u	PROPN
ejpam-5826	336	3	,	,	PUNCT
ejpam-5826	336	4	eu	eu	NOUN
ejpam-5826	336	5	)	)	PUNCT
ejpam-5826	336	6	≤	≤	PUNCT
ejpam-5826	337	1	d(u	d(u	PROPN
ejpam-5826	337	2	,	,	PUNCT
ejpam-5826	337	3	qk	qk	NOUN
ejpam-5826	337	4	)	)	PUNCT
ejpam-5826	337	5	+	+	CCONJ
ejpam-5826	337	6	d(qk	d(qk	PROPN
ejpam-5826	337	7	,	,	PUNCT
ejpam-5826	337	8	eu	eu	PROPN
ejpam-5826	337	9	)	)	PUNCT
ejpam-5826	337	10	≤	≤	PUNCT
ejpam-5826	338	1	d(u	d(u	PROPN
ejpam-5826	338	2	,	,	PUNCT
ejpam-5826	338	3	qk	qk	NOUN
ejpam-5826	338	4	)	)	PUNCT
ejpam-5826	338	5	+	+	CCONJ
ejpam-5826	338	6	µd(qk	µd(qk	PROPN
ejpam-5826	338	7	,	,	PUNCT
ejpam-5826	338	8	u	u	NOUN
ejpam-5826	338	9	)	)	PUNCT
ejpam-5826	338	10	+	+	CCONJ
ejpam-5826	338	11	ν[d(qk	ν[d(qk	NOUN
ejpam-5826	338	12	,	,	PUNCT
ejpam-5826	338	13	eqk	eqk	NOUN
ejpam-5826	338	14	)	)	PUNCT
ejpam-5826	338	15	+	+	CCONJ
ejpam-5826	338	16	d(u	d(u	PROPN
ejpam-5826	338	17	,	,	PUNCT
ejpam-5826	338	18	eu	eu	PROPN
ejpam-5826	338	19	)	)	PUNCT
ejpam-5826	338	20	]	]	PUNCT
ejpam-5826	339	1	=	=	PUNCT
ejpam-5826	339	2	(	(	PUNCT
ejpam-5826	339	3	1	1	NUM
ejpam-5826	339	4	+	+	CCONJ
ejpam-5826	339	5	µ)d(qk	µ)d(qk	NUM
ejpam-5826	339	6	,	,	PUNCT
ejpam-5826	339	7	u	u	NOUN
ejpam-5826	339	8	)	)	PUNCT
ejpam-5826	339	9	+	+	CCONJ
ejpam-5826	339	10	νd(u	νd(u	NOUN
ejpam-5826	339	11	,	,	PUNCT
ejpam-5826	339	12	eu	eu	PROPN
ejpam-5826	339	13	)	)	PUNCT
ejpam-5826	339	14	;	;	PUNCT
ejpam-5826	339	15	hence	hence	ADV
ejpam-5826	339	16	d(u	d(u	PROPN
ejpam-5826	339	17	,	,	PUNCT
ejpam-5826	339	18	eu	eu	NOUN
ejpam-5826	339	19	)	)	PUNCT
ejpam-5826	339	20	≤	≤	NOUN
ejpam-5826	339	21	1	1	NUM
ejpam-5826	339	22	+	+	SYM
ejpam-5826	339	23	µ	µ	X
ejpam-5826	339	24	1−	1−	NUM
ejpam-5826	339	25	ν	ν	X
ejpam-5826	339	26	d(qk	d(qk	PROPN
ejpam-5826	339	27	,	,	PUNCT
ejpam-5826	339	28	u	u	NOUN
ejpam-5826	339	29	)	)	PUNCT
ejpam-5826	339	30	(	(	PUNCT
ejpam-5826	339	31	25	25	NUM
ejpam-5826	339	32	)	)	PUNCT
ejpam-5826	339	33	as	as	ADP
ejpam-5826	339	34	µ	µ	X
ejpam-5826	339	35	∈	∈	NOUN
ejpam-5826	339	36	[	[	X
ejpam-5826	339	37	0	0	NUM
ejpam-5826	339	38	,	,	PUNCT
ejpam-5826	339	39	1	1	NUM
ejpam-5826	339	40	)	)	PUNCT
ejpam-5826	339	41	and	and	CCONJ
ejpam-5826	339	42	µ	µ	PRON
ejpam-5826	339	43	+	+	NUM
ejpam-5826	339	44	2ν	2ν	NOUN
ejpam-5826	339	45	<	<	X
ejpam-5826	339	46	1	1	NUM
ejpam-5826	339	47	,	,	PUNCT
ejpam-5826	339	48	that	that	ADV
ejpam-5826	339	49	is	is	ADV
ejpam-5826	339	50	,	,	PUNCT
ejpam-5826	339	51	ν	ν	X
ejpam-5826	339	52	<	<	X
ejpam-5826	339	53	1	1	NUM
ejpam-5826	339	54	and	and	CCONJ
ejpam-5826	339	55	since	since	SCONJ
ejpam-5826	339	56	{	{	PUNCT
ejpam-5826	339	57	qk	qk	INTJ
ejpam-5826	339	58	}	}	PUNCT
ejpam-5826	339	59	→	→	SYM
ejpam-5826	339	60	u	u	NOUN
ejpam-5826	339	61	as	as	ADP
ejpam-5826	339	62	k	k	PROPN
ejpam-5826	339	63	→	→	SYM
ejpam-5826	339	64	∞	∞	PROPN
ejpam-5826	339	65	,	,	PUNCT
ejpam-5826	339	66	therefore	therefore	ADV
ejpam-5826	339	67	limk→∞	limk→∞	ADJ
ejpam-5826	339	68	d(qk	d(qk	PROPN
ejpam-5826	339	69	,	,	PUNCT
ejpam-5826	339	70	u	u	NOUN
ejpam-5826	339	71	)	)	PUNCT
ejpam-5826	339	72	=	=	SYM
ejpam-5826	339	73	0	0	X
ejpam-5826	339	74	.	.	PUNCT
ejpam-5826	339	75	from	from	ADP
ejpam-5826	339	76	(	(	PUNCT
ejpam-5826	339	77	25	25	NUM
ejpam-5826	339	78	)	)	PUNCT
ejpam-5826	339	79	,	,	PUNCT
ejpam-5826	339	80	we	we	PRON
ejpam-5826	339	81	get	get	VERB
ejpam-5826	339	82	u	u	PRON
ejpam-5826	339	83	∈	∈	PROPN
ejpam-5826	339	84	fix(e	fix(e	PROPN
ejpam-5826	339	85	)	)	PUNCT
ejpam-5826	339	86	as	as	SCONJ
ejpam-5826	339	87	desired	desire	VERB
ejpam-5826	339	88	.	.	PUNCT
ejpam-5826	340	1	next	next	ADV
ejpam-5826	340	2	,	,	PUNCT
ejpam-5826	340	3	we	we	PRON
ejpam-5826	340	4	show	show	VERB
ejpam-5826	340	5	that	that	SCONJ
ejpam-5826	340	6	fix(e	fix(e	PROPN
ejpam-5826	340	7	)	)	PUNCT
ejpam-5826	340	8	is	be	AUX
ejpam-5826	340	9	convex	convex	PROPN
ejpam-5826	340	10	.	.	PUNCT
ejpam-5826	341	1	let	let	VERB
ejpam-5826	341	2	q	q	X
ejpam-5826	341	3	,	,	PUNCT
ejpam-5826	341	4	p	p	PROPN
ejpam-5826	341	5	∈	∈	PROPN
ejpam-5826	341	6	fix(e	fix(e	PROPN
ejpam-5826	341	7	)	)	PUNCT
ejpam-5826	341	8	and	and	CCONJ
ejpam-5826	341	9	α	α	PRON
ejpam-5826	341	10	∈	∈	PROPN
ejpam-5826	342	1	[	[	X
ejpam-5826	342	2	0	0	NUM
ejpam-5826	342	3	,	,	PUNCT
ejpam-5826	342	4	1	1	NUM
ejpam-5826	342	5	]	]	PUNCT
ejpam-5826	342	6	.	.	PUNCT
ejpam-5826	343	1	for	for	ADP
ejpam-5826	343	2	any	any	DET
ejpam-5826	343	3	z	z	PROPN
ejpam-5826	343	4	∈	∈	PROPN
ejpam-5826	343	5	j	j	PROPN
ejpam-5826	343	6	,	,	PUNCT
ejpam-5826	343	7	assume	assume	VERB
ejpam-5826	343	8	that	that	SCONJ
ejpam-5826	343	9	z	z	NOUN
ejpam-5826	343	10	=	=	PUNCT
ejpam-5826	343	11	η(q	η(q	NOUN
ejpam-5826	343	12	,	,	PUNCT
ejpam-5826	343	13	p	p	X
ejpam-5826	343	14	,	,	PUNCT
ejpam-5826	343	15	α	α	NOUN
ejpam-5826	343	16	)	)	PUNCT
ejpam-5826	343	17	.	.	PUNCT
ejpam-5826	344	1	now	now	ADV
ejpam-5826	344	2	we	we	PRON
ejpam-5826	344	3	show	show	VERB
ejpam-5826	344	4	that	that	SCONJ
ejpam-5826	344	5	z	z	PROPN
ejpam-5826	344	6	∈	∈	PROPN
ejpam-5826	344	7	fix(e	fix(e	PROPN
ejpam-5826	344	8	)	)	PUNCT
ejpam-5826	344	9	,	,	PUNCT
ejpam-5826	344	10	that	that	ADV
ejpam-5826	344	11	is	be	AUX
ejpam-5826	344	12	,	,	PUNCT
ejpam-5826	344	13	z	z	PROPN
ejpam-5826	344	14	=	=	SYM
ejpam-5826	344	15	ez	ez	PROPN
ejpam-5826	344	16	or	or	CCONJ
ejpam-5826	344	17	e(η(q	e(η(q	PROPN
ejpam-5826	344	18	,	,	PUNCT
ejpam-5826	344	19	p	p	X
ejpam-5826	344	20	,	,	PUNCT
ejpam-5826	344	21	α	α	NOUN
ejpam-5826	344	22	)	)	PUNCT
ejpam-5826	344	23	)	)	PUNCT
ejpam-5826	345	1	=	=	SYM
ejpam-5826	345	2	η(q	η(q	NOUN
ejpam-5826	345	3	,	,	PUNCT
ejpam-5826	345	4	p	p	X
ejpam-5826	345	5	,	,	PUNCT
ejpam-5826	345	6	α	α	NOUN
ejpam-5826	345	7	)	)	PUNCT
ejpam-5826	345	8	.	.	PUNCT
ejpam-5826	346	1	thus	thus	ADV
ejpam-5826	346	2	d(q	d(q	PROPN
ejpam-5826	346	3	,	,	PUNCT
ejpam-5826	346	4	ez	ez	NOUN
ejpam-5826	346	5	)	)	PUNCT
ejpam-5826	346	6	=	=	SYM
ejpam-5826	346	7	d(eq	d(eq	PROPN
ejpam-5826	346	8	,	,	PUNCT
ejpam-5826	346	9	ez	ez	NOUN
ejpam-5826	346	10	)	)	PUNCT
ejpam-5826	346	11	≤	≤	NOUN
ejpam-5826	346	12	µd(q	µd(q	NOUN
ejpam-5826	346	13	,	,	PUNCT
ejpam-5826	346	14	z	z	NOUN
ejpam-5826	346	15	)	)	PUNCT
ejpam-5826	346	16	+	+	CCONJ
ejpam-5826	346	17	ν[d(q	ν[d(q	NOUN
ejpam-5826	346	18	,	,	PUNCT
ejpam-5826	346	19	eq	eq	NOUN
ejpam-5826	346	20	)	)	PUNCT
ejpam-5826	346	21	+	+	CCONJ
ejpam-5826	346	22	d(z	d(z	PROPN
ejpam-5826	346	23	,	,	PUNCT
ejpam-5826	346	24	ez	ez	PROPN
ejpam-5826	346	25	)	)	PUNCT
ejpam-5826	346	26	]	]	PUNCT
ejpam-5826	346	27	.	.	PUNCT
ejpam-5826	347	1	≤	≤	NOUN
ejpam-5826	347	2	µd(q	µd(q	NOUN
ejpam-5826	347	3	,	,	PUNCT
ejpam-5826	347	4	z	z	NOUN
ejpam-5826	347	5	)	)	PUNCT
ejpam-5826	348	1	+	+	CCONJ
ejpam-5826	348	2	ν[d(z	ν[d(z	NOUN
ejpam-5826	348	3	,	,	PUNCT
ejpam-5826	348	4	q	q	X
ejpam-5826	348	5	)	)	PUNCT
ejpam-5826	348	6	+	+	CCONJ
ejpam-5826	348	7	d(q	d(q	PROPN
ejpam-5826	348	8	,	,	PUNCT
ejpam-5826	348	9	ez	ez	NOUN
ejpam-5826	348	10	)	)	PUNCT
ejpam-5826	348	11	]	]	PUNCT
ejpam-5826	348	12	.	.	PUNCT
ejpam-5826	349	1	≤	≤	NUM
ejpam-5826	349	2	(	(	PUNCT
ejpam-5826	349	3	µ+	µ+	X
ejpam-5826	349	4	ν)d(q	ν)d(q	PROPN
ejpam-5826	349	5	,	,	PUNCT
ejpam-5826	349	6	z	z	NOUN
ejpam-5826	349	7	)	)	PUNCT
ejpam-5826	349	8	+	+	CCONJ
ejpam-5826	349	9	νd(q	νd(q	PROPN
ejpam-5826	349	10	,	,	PUNCT
ejpam-5826	349	11	ez	ez	NOUN
ejpam-5826	349	12	)	)	PUNCT
ejpam-5826	349	13	.	.	PUNCT
ejpam-5826	350	1	hence	hence	ADV
ejpam-5826	350	2	d(q	d(q	PROPN
ejpam-5826	350	3	,	,	PUNCT
ejpam-5826	350	4	ez	ez	NOUN
ejpam-5826	350	5	)	)	PUNCT
ejpam-5826	350	6	≤	≤	NOUN
ejpam-5826	350	7	(	(	PUNCT
ejpam-5826	350	8	µ+	µ+	X
ejpam-5826	350	9	ν	ν	NOUN
ejpam-5826	350	10	)	)	PUNCT
ejpam-5826	350	11	1−	1−	NUM
ejpam-5826	351	1	ν	ν	X
ejpam-5826	351	2	d(q	d(q	PROPN
ejpam-5826	351	3	,	,	PUNCT
ejpam-5826	351	4	z	z	NOUN
ejpam-5826	351	5	)	)	PUNCT
ejpam-5826	351	6	≤	≤	NOUN
ejpam-5826	351	7	d(q	d(q	PROPN
ejpam-5826	351	8	,	,	PUNCT
ejpam-5826	351	9	z	z	NOUN
ejpam-5826	351	10	)	)	PUNCT
ejpam-5826	351	11	.	.	PUNCT
ejpam-5826	352	1	(	(	PUNCT
ejpam-5826	352	2	26	26	NUM
ejpam-5826	352	3	)	)	PUNCT
ejpam-5826	352	4	similarly	similarly	ADV
ejpam-5826	352	5	,	,	PUNCT
ejpam-5826	352	6	d(p	d(p	PROPN
ejpam-5826	352	7	,	,	PUNCT
ejpam-5826	352	8	ez	ez	NOUN
ejpam-5826	352	9	)	)	PUNCT
ejpam-5826	352	10	≤	≤	NOUN
ejpam-5826	352	11	d(p	d(p	PROPN
ejpam-5826	352	12	,	,	PUNCT
ejpam-5826	352	13	z	z	NOUN
ejpam-5826	352	14	)	)	PUNCT
ejpam-5826	352	15	.	.	PUNCT
ejpam-5826	353	1	(	(	PUNCT
ejpam-5826	353	2	27	27	NUM
ejpam-5826	353	3	)	)	PUNCT
ejpam-5826	353	4	using	use	VERB
ejpam-5826	353	5	(	(	PUNCT
ejpam-5826	353	6	26	26	NUM
ejpam-5826	353	7	)	)	PUNCT
ejpam-5826	353	8	,	,	PUNCT
ejpam-5826	353	9	(	(	PUNCT
ejpam-5826	353	10	27	27	NUM
ejpam-5826	353	11	)	)	PUNCT
ejpam-5826	353	12	and	and	CCONJ
ejpam-5826	353	13	(	(	PUNCT
ejpam-5826	353	14	η1	η1	NOUN
ejpam-5826	353	15	)	)	PUNCT
ejpam-5826	353	16	,	,	PUNCT
ejpam-5826	353	17	we	we	PRON
ejpam-5826	353	18	get	get	VERB
ejpam-5826	353	19	d(q	d(q	VERB
ejpam-5826	353	20	,	,	PUNCT
ejpam-5826	353	21	p	p	NOUN
ejpam-5826	353	22	)	)	PUNCT
ejpam-5826	353	23	≤	≤	NOUN
ejpam-5826	353	24	d(q	d(q	PROPN
ejpam-5826	353	25	,	,	PUNCT
ejpam-5826	353	26	ez	ez	PROPN
ejpam-5826	353	27	)	)	PUNCT
ejpam-5826	354	1	+	+	CCONJ
ejpam-5826	354	2	d(ez	d(ez	PROPN
ejpam-5826	354	3	,	,	PUNCT
ejpam-5826	354	4	p	p	NOUN
ejpam-5826	354	5	)	)	PUNCT
ejpam-5826	354	6	.	.	PUNCT
ejpam-5826	355	1	≤	≤	PROPN
ejpam-5826	355	2	d(q	d(q	PROPN
ejpam-5826	355	3	,	,	PUNCT
ejpam-5826	355	4	z	z	NOUN
ejpam-5826	355	5	)	)	PUNCT
ejpam-5826	356	1	+	+	CCONJ
ejpam-5826	356	2	d(z	d(z	PROPN
ejpam-5826	356	3	,	,	PUNCT
ejpam-5826	356	4	p	p	NOUN
ejpam-5826	356	5	)	)	PUNCT
ejpam-5826	356	6	.	.	PUNCT
ejpam-5826	357	1	≤	≤	PROPN
ejpam-5826	357	2	d(q	d(q	PROPN
ejpam-5826	357	3	,	,	PUNCT
ejpam-5826	357	4	η(q	η(q	NOUN
ejpam-5826	357	5	,	,	PUNCT
ejpam-5826	357	6	p	p	X
ejpam-5826	357	7	,	,	PUNCT
ejpam-5826	357	8	α	α	NOUN
ejpam-5826	357	9	)	)	PUNCT
ejpam-5826	357	10	)	)	PUNCT
ejpam-5826	358	1	+	+	CCONJ
ejpam-5826	358	2	d(η(q	d(η(q	NOUN
ejpam-5826	358	3	,	,	PUNCT
ejpam-5826	358	4	p	p	X
ejpam-5826	358	5	,	,	PUNCT
ejpam-5826	358	6	α	α	NOUN
ejpam-5826	358	7	)	)	PUNCT
ejpam-5826	358	8	,	,	PUNCT
ejpam-5826	358	9	p	p	X
ejpam-5826	358	10	)	)	PUNCT
ejpam-5826	358	11	≤	≤	NOUN
ejpam-5826	358	12	(	(	PUNCT
ejpam-5826	358	13	1−	1−	NUM
ejpam-5826	358	14	α)d(q	α)d(q	NUM
ejpam-5826	358	15	,	,	PUNCT
ejpam-5826	358	16	q	q	NOUN
ejpam-5826	358	17	)	)	PUNCT
ejpam-5826	358	18	+	+	X
ejpam-5826	358	19	αd(q	αd(q	NUM
ejpam-5826	358	20	,	,	PUNCT
ejpam-5826	358	21	p	p	NOUN
ejpam-5826	358	22	)	)	PUNCT
ejpam-5826	359	1	+	+	CCONJ
ejpam-5826	359	2	(	(	PUNCT
ejpam-5826	359	3	1−	1−	NUM
ejpam-5826	359	4	α)d(q	α)d(q	NUM
ejpam-5826	359	5	,	,	PUNCT
ejpam-5826	359	6	p	p	NOUN
ejpam-5826	359	7	)	)	PUNCT
ejpam-5826	360	1	+	+	CCONJ
ejpam-5826	360	2	d(p	d(p	PROPN
ejpam-5826	360	3	,	,	PUNCT
ejpam-5826	360	4	p	p	NOUN
ejpam-5826	360	5	)	)	PUNCT
ejpam-5826	360	6	a.	a.	PROPN
ejpam-5826	360	7	r.	r.	PROPN
ejpam-5826	360	8	khan	khan	PROPN
ejpam-5826	360	9	et	et	PROPN
ejpam-5826	360	10	al	al	PROPN
ejpam-5826	360	11	.	.	PUNCT
ejpam-5826	360	12	/	/	SYM
ejpam-5826	360	13	eur	eur	PROPN
ejpam-5826	360	14	.	.	PUNCT
ejpam-5826	361	1	j.	j.	PROPN
ejpam-5826	361	2	pure	pure	PROPN
ejpam-5826	361	3	appl	appl	PROPN
ejpam-5826	361	4	.	.	PROPN
ejpam-5826	361	5	math	math	PROPN
ejpam-5826	361	6	,	,	PUNCT
ejpam-5826	361	7	18	18	NUM
ejpam-5826	361	8	(	(	PUNCT
ejpam-5826	361	9	2	2	NUM
ejpam-5826	361	10	)	)	PUNCT
ejpam-5826	361	11	(	(	PUNCT
ejpam-5826	361	12	2025	2025	NUM
ejpam-5826	361	13	)	)	PUNCT
ejpam-5826	361	14	,	,	PUNCT
ejpam-5826	361	15	5826	5826	NUM
ejpam-5826	361	16	15	15	NUM
ejpam-5826	361	17	of	of	ADP
ejpam-5826	361	18	23	23	NUM
ejpam-5826	361	19	=	=	SYM
ejpam-5826	361	20	d(p	d(p	PROPN
ejpam-5826	361	21	,	,	PUNCT
ejpam-5826	361	22	q	q	NOUN
ejpam-5826	361	23	)	)	PUNCT
ejpam-5826	361	24	thus	thus	ADV
ejpam-5826	361	25	,	,	PUNCT
ejpam-5826	361	26	we	we	PRON
ejpam-5826	361	27	conclude	conclude	VERB
ejpam-5826	361	28	by	by	ADP
ejpam-5826	361	29	(	(	PUNCT
ejpam-5826	361	30	26	26	NUM
ejpam-5826	361	31	)	)	PUNCT
ejpam-5826	361	32	)	)	PUNCT
ejpam-5826	361	33	and	and	CCONJ
ejpam-5826	361	34	(	(	PUNCT
ejpam-5826	361	35	27	27	NUM
ejpam-5826	361	36	)	)	PUNCT
ejpam-5826	362	1	that	that	PRON
ejpam-5826	362	2	d(q	d(q	PROPN
ejpam-5826	362	3	,	,	PUNCT
ejpam-5826	362	4	ez	ez	NOUN
ejpam-5826	362	5	)	)	PUNCT
ejpam-5826	362	6	=	=	SYM
ejpam-5826	363	1	d(q	d(q	PROPN
ejpam-5826	363	2	,	,	PUNCT
ejpam-5826	363	3	z	z	NOUN
ejpam-5826	363	4	)	)	PUNCT
ejpam-5826	363	5	and	and	CCONJ
ejpam-5826	363	6	d(p	d(p	PROPN
ejpam-5826	363	7	,	,	PUNCT
ejpam-5826	363	8	ez	ez	PROPN
ejpam-5826	363	9	)	)	PUNCT
ejpam-5826	363	10	=	=	SYM
ejpam-5826	363	11	d(p	d(p	PROPN
ejpam-5826	363	12	,	,	PUNCT
ejpam-5826	363	13	z	z	NOUN
ejpam-5826	363	14	)	)	PUNCT
ejpam-5826	364	1	because	because	SCONJ
ejpam-5826	364	2	if	if	SCONJ
ejpam-5826	364	3	d(q	d(q	PROPN
ejpam-5826	364	4	,	,	PUNCT
ejpam-5826	364	5	ez	ez	PROPN
ejpam-5826	364	6	)	)	PUNCT
ejpam-5826	364	7	<	<	X
ejpam-5826	364	8	d(q	d(q	PROPN
ejpam-5826	364	9	,	,	PUNCT
ejpam-5826	364	10	z	z	NOUN
ejpam-5826	364	11	)	)	PUNCT
ejpam-5826	364	12	or	or	CCONJ
ejpam-5826	364	13	d(p	d(p	PROPN
ejpam-5826	364	14	,	,	PUNCT
ejpam-5826	364	15	ez	ez	PROPN
ejpam-5826	364	16	)	)	PUNCT
ejpam-5826	364	17	<	<	X
ejpam-5826	364	18	d(p	d(p	PROPN
ejpam-5826	364	19	,	,	PUNCT
ejpam-5826	364	20	z	z	NOUN
ejpam-5826	364	21	)	)	PUNCT
ejpam-5826	364	22	,	,	PUNCT
ejpam-5826	364	23	then	then	ADV
ejpam-5826	364	24	we	we	PRON
ejpam-5826	364	25	will	will	AUX
ejpam-5826	364	26	obtain	obtain	VERB
ejpam-5826	364	27	a	a	DET
ejpam-5826	364	28	contradiction	contradiction	NOUN
ejpam-5826	364	29	d(p	d(p	PROPN
ejpam-5826	364	30	,	,	PUNCT
ejpam-5826	364	31	q	q	NOUN
ejpam-5826	364	32	)	)	PUNCT
ejpam-5826	364	33	<	<	X
ejpam-5826	364	34	d(p	d(p	PROPN
ejpam-5826	364	35	,	,	PUNCT
ejpam-5826	364	36	q	q	NOUN
ejpam-5826	364	37	)	)	PUNCT
ejpam-5826	364	38	.	.	PUNCT
ejpam-5826	365	1	hence	hence	ADV
ejpam-5826	365	2	ez	ez	X
ejpam-5826	365	3	=	=	PROPN
ejpam-5826	365	4	z	z	PROPN
ejpam-5826	365	5	,	,	PUNCT
ejpam-5826	365	6	that	that	ADV
ejpam-5826	365	7	is	is	ADV
ejpam-5826	365	8	,	,	PUNCT
ejpam-5826	365	9	eη((q	eη((q	PROPN
ejpam-5826	365	10	,	,	PUNCT
ejpam-5826	365	11	p	p	X
ejpam-5826	365	12	,	,	PUNCT
ejpam-5826	365	13	α	α	NOUN
ejpam-5826	365	14	)	)	PUNCT
ejpam-5826	365	15	)	)	PUNCT
ejpam-5826	366	1	=	=	SYM
ejpam-5826	366	2	η(q	η(q	NOUN
ejpam-5826	366	3	,	,	PUNCT
ejpam-5826	366	4	p	p	X
ejpam-5826	366	5	,	,	PUNCT
ejpam-5826	366	6	α	α	NOUN
ejpam-5826	366	7	)	)	PUNCT
ejpam-5826	366	8	for	for	ADP
ejpam-5826	366	9	all	all	DET
ejpam-5826	366	10	q	q	NOUN
ejpam-5826	366	11	,	,	PUNCT
ejpam-5826	366	12	p	p	PROPN
ejpam-5826	366	13	∈	∈	PROPN
ejpam-5826	366	14	fix(e	fix(e	PROPN
ejpam-5826	366	15	)	)	PUNCT
ejpam-5826	366	16	and	and	CCONJ
ejpam-5826	366	17	α	α	PRON
ejpam-5826	366	18	∈	∈	PROPN
ejpam-5826	367	1	[	[	X
ejpam-5826	367	2	0	0	NUM
ejpam-5826	367	3	,	,	PUNCT
ejpam-5826	367	4	1	1	NUM
ejpam-5826	367	5	]	]	PUNCT
ejpam-5826	367	6	.	.	PUNCT
ejpam-5826	368	1	therefore	therefore	ADV
ejpam-5826	368	2	fix(e	fix(e	PROPN
ejpam-5826	368	3	)	)	PUNCT
ejpam-5826	368	4	is	be	AUX
ejpam-5826	368	5	convex	convex	PROPN
ejpam-5826	368	6	.	.	PUNCT
ejpam-5826	369	1	based	base	VERB
ejpam-5826	369	2	on	on	ADP
ejpam-5826	369	3	lemma	lemma	PROPN
ejpam-5826	369	4	5	5	NUM
ejpam-5826	369	5	,	,	PUNCT
ejpam-5826	369	6	we	we	PRON
ejpam-5826	369	7	introduce	introduce	VERB
ejpam-5826	369	8	the	the	DET
ejpam-5826	369	9	contractive	contractive	ADJ
ejpam-5826	369	10	condition	condition	NOUN
ejpam-5826	369	11	for	for	ADP
ejpam-5826	369	12	self	self	NOUN
ejpam-5826	369	13	-	-	PUNCT
ejpam-5826	369	14	mappings	mapping	NOUN
ejpam-5826	369	15	tλ	tλ	NOUN
ejpam-5826	369	16	and	and	CCONJ
ejpam-5826	369	17	sλ	sλ	VERB
ejpam-5826	369	18	on	on	ADV
ejpam-5826	369	19	q	q	NOUN
ejpam-5826	369	20	as	as	SCONJ
ejpam-5826	369	21	follows	follow	VERB
ejpam-5826	369	22	:	:	PUNCT
ejpam-5826	369	23	d(tλx	d(tλx	X
ejpam-5826	369	24	,	,	PUNCT
ejpam-5826	369	25	sλy	sλy	NOUN
ejpam-5826	369	26	)	)	PUNCT
ejpam-5826	370	1	≤	≤	NOUN
ejpam-5826	370	2	m(d(x	m(d(x	PROPN
ejpam-5826	370	3	,	,	PUNCT
ejpam-5826	370	4	y	y	NOUN
ejpam-5826	370	5	)	)	PUNCT
ejpam-5826	370	6	)	)	PUNCT
ejpam-5826	371	1	+	+	VERB
ejpam-5826	371	2	k{d(x	k{d(x	PROPN
ejpam-5826	371	3	,	,	PUNCT
ejpam-5826	371	4	tλx	tλx	NOUN
ejpam-5826	371	5	)	)	PUNCT
ejpam-5826	372	1	+	+	CCONJ
ejpam-5826	372	2	d(y	d(y	NOUN
ejpam-5826	372	3	,	,	PUNCT
ejpam-5826	372	4	sλy	sλy	NOUN
ejpam-5826	372	5	)	)	PUNCT
ejpam-5826	372	6	}	}	PUNCT
ejpam-5826	372	7	(	(	PUNCT
ejpam-5826	372	8	28	28	NUM
ejpam-5826	372	9	)	)	PUNCT
ejpam-5826	373	1	where	where	SCONJ
ejpam-5826	373	2	0	0	NUM
ejpam-5826	373	3	≤	≤	NUM
ejpam-5826	373	4	m	m	VERB
ejpam-5826	373	5	<	<	X
ejpam-5826	373	6	1	1	NUM
ejpam-5826	373	7	,	,	PUNCT
ejpam-5826	373	8	1	1	NUM
ejpam-5826	373	9	<	<	X
ejpam-5826	373	10	k	k	X
ejpam-5826	373	11	<	<	X
ejpam-5826	373	12	∞	∞	PROPN
ejpam-5826	373	13	and	and	CCONJ
ejpam-5826	373	14	m	m	PROPN
ejpam-5826	373	15	+	+	NOUN
ejpam-5826	373	16	2k	2k	NUM
ejpam-5826	373	17	≤	≤	NUM
ejpam-5826	373	18	1	1	NUM
ejpam-5826	373	19	.	.	PUNCT
ejpam-5826	374	1	an	an	DET
ejpam-5826	374	2	extension	extension	NOUN
ejpam-5826	374	3	of	of	ADP
ejpam-5826	374	4	theorem	theorem	NOUN
ejpam-5826	374	5	2	2	NUM
ejpam-5826	374	6	,	,	PUNCT
ejpam-5826	374	7	is	be	AUX
ejpam-5826	374	8	obtained	obtain	VERB
ejpam-5826	374	9	by	by	ADP
ejpam-5826	374	10	replacing	replace	VERB
ejpam-5826	374	11	the	the	DET
ejpam-5826	374	12	maps	map	NOUN
ejpam-5826	374	13	e	e	NOUN
ejpam-5826	374	14	and	and	CCONJ
ejpam-5826	374	15	f	f	PROPN
ejpam-5826	374	16	on	on	ADP
ejpam-5826	374	17	a	a	DET
ejpam-5826	374	18	metric	metric	ADJ
ejpam-5826	374	19	space	space	NOUN
ejpam-5826	374	20	with	with	ADP
ejpam-5826	374	21	their	their	PRON
ejpam-5826	374	22	,	,	PUNCT
ejpam-5826	374	23	respective	respective	ADJ
ejpam-5826	374	24	,	,	PUNCT
ejpam-5826	374	25	average	average	ADJ
ejpam-5826	374	26	mappings	mapping	NOUN
ejpam-5826	374	27	,	,	PUNCT
ejpam-5826	374	28	in	in	ADP
ejpam-5826	374	29	the	the	DET
ejpam-5826	374	30	context	context	NOUN
ejpam-5826	374	31	of	of	ADP
ejpam-5826	374	32	a	a	DET
ejpam-5826	374	33	convex	convex	ADJ
ejpam-5826	374	34	metric	metric	ADJ
ejpam-5826	374	35	space	space	NOUN
ejpam-5826	374	36	,	,	PUNCT
ejpam-5826	374	37	as	as	SCONJ
ejpam-5826	374	38	follows	follow	VERB
ejpam-5826	374	39	.	.	PUNCT
ejpam-5826	375	1	theorem	theorem	ADJ
ejpam-5826	375	2	7	7	NUM
ejpam-5826	375	3	.	.	PUNCT
ejpam-5826	376	1	let	let	VERB
ejpam-5826	376	2	(	(	PUNCT
ejpam-5826	376	3	q	q	X
ejpam-5826	376	4	,	,	PUNCT
ejpam-5826	376	5	d	d	NOUN
ejpam-5826	376	6	,	,	PUNCT
ejpam-5826	376	7	w	w	PROPN
ejpam-5826	376	8	)	)	PUNCT
ejpam-5826	376	9	be	be	AUX
ejpam-5826	376	10	a	a	DET
ejpam-5826	376	11	complete	complete	ADJ
ejpam-5826	376	12	convex	convex	NOUN
ejpam-5826	376	13	metric	metric	ADJ
ejpam-5826	376	14	space	space	NOUN
ejpam-5826	376	15	.	.	PUNCT
ejpam-5826	377	1	assume	assume	VERB
ejpam-5826	377	2	that	that	SCONJ
ejpam-5826	377	3	tλ	tλ	NOUN
ejpam-5826	377	4	and	and	CCONJ
ejpam-5826	377	5	sλ	sλ	NOUN
ejpam-5826	377	6	are	be	AUX
ejpam-5826	377	7	asymptotically	asymptotically	ADV
ejpam-5826	377	8	regular	regular	ADJ
ejpam-5826	377	9	self	self	NOUN
ejpam-5826	377	10	-	-	PUNCT
ejpam-5826	377	11	mappings	mapping	NOUN
ejpam-5826	377	12	on	on	ADP
ejpam-5826	377	13	q	q	NOUN
ejpam-5826	377	14	satisfying	satisfying	ADJ
ejpam-5826	377	15	(	(	PUNCT
ejpam-5826	377	16	28	28	NUM
ejpam-5826	377	17	)	)	PUNCT
ejpam-5826	377	18	.	.	PUNCT
ejpam-5826	378	1	if	if	SCONJ
ejpam-5826	378	2	tλ	tλ	NOUN
ejpam-5826	378	3	and	and	CCONJ
ejpam-5826	378	4	sλ	sλ	NOUN
ejpam-5826	378	5	are	be	AUX
ejpam-5826	378	6	orbitally	orbitally	ADV
ejpam-5826	378	7	continuous	continuous	ADJ
ejpam-5826	378	8	or	or	CCONJ
ejpam-5826	378	9	k	k	NOUN
ejpam-5826	378	10	-	-	ADJ
ejpam-5826	378	11	continuous	continuous	ADJ
ejpam-5826	378	12	for	for	ADP
ejpam-5826	378	13	some	some	DET
ejpam-5826	378	14	k	k	PROPN
ejpam-5826	378	15	≥	≥	NUM
ejpam-5826	378	16	1	1	NUM
ejpam-5826	378	17	,	,	PUNCT
ejpam-5826	378	18	then	then	ADV
ejpam-5826	378	19	tλ	tλ	NOUN
ejpam-5826	378	20	and	and	CCONJ
ejpam-5826	378	21	sλ	sλ	AUX
ejpam-5826	378	22	have	have	VERB
ejpam-5826	378	23	a	a	DET
ejpam-5826	378	24	unique	unique	ADJ
ejpam-5826	378	25	common	common	ADJ
ejpam-5826	378	26	fixed	fix	VERB
ejpam-5826	378	27	point	point	NOUN
ejpam-5826	378	28	p.	p.	NOUN
ejpam-5826	378	29	furthermore	furthermore	ADV
ejpam-5826	378	30	,	,	PUNCT
ejpam-5826	378	31	limn→∞	limn→∞	PROPN
ejpam-5826	378	32	tn	tn	PROPN
ejpam-5826	378	33	λ	λ	PROPN
ejpam-5826	378	34	x	x	X
ejpam-5826	379	1	=	=	PUNCT
ejpam-5826	379	2	p	p	X
ejpam-5826	379	3	=	=	PUNCT
ejpam-5826	379	4	limn→∞	limn→∞	PROPN
ejpam-5826	379	5	sn	sn	PROPN
ejpam-5826	379	6	λx	λx	PROPN
ejpam-5826	379	7	for	for	ADP
ejpam-5826	379	8	any	any	DET
ejpam-5826	379	9	x	x	SYM
ejpam-5826	379	10	∈	∈	PROPN
ejpam-5826	379	11	q.	q.	NOUN
ejpam-5826	379	12	proof	proof	NOUN
ejpam-5826	379	13	.	.	PUNCT
ejpam-5826	380	1	step	step	NOUN
ejpam-5826	380	2	1	1	NUM
ejpam-5826	380	3	:	:	PUNCT
ejpam-5826	380	4	we	we	PRON
ejpam-5826	380	5	note	note	VERB
ejpam-5826	380	6	that	that	SCONJ
ejpam-5826	380	7	the	the	DET
ejpam-5826	380	8	picard	picard	NOUN
ejpam-5826	380	9	iterations	iteration	NOUN
ejpam-5826	380	10	of	of	ADP
ejpam-5826	380	11	tλ	tλ	ADP
ejpam-5826	380	12	and	and	CCONJ
ejpam-5826	380	13	sλ	sλ	VERB
ejpam-5826	380	14	form	form	VERB
ejpam-5826	380	15	the	the	DET
ejpam-5826	380	16	krasnoselskij	krasnoselskij	NOUN
ejpam-5826	380	17	iterative	iterative	NOUN
ejpam-5826	380	18	sequence	sequence	NOUN
ejpam-5826	380	19	{	{	PUNCT
ejpam-5826	380	20	xn}∞n=0	xn}∞n=0	NUM
ejpam-5826	380	21	defined	define	VERB
ejpam-5826	380	22	by	by	ADP
ejpam-5826	380	23	xn+1	xn+1	PROPN
ejpam-5826	380	24	=	=	SYM
ejpam-5826	380	25	tλxn	tλxn	PROPN
ejpam-5826	380	26	=	=	SYM
ejpam-5826	380	27	(	(	PUNCT
ejpam-5826	380	28	1−	1−	NUM
ejpam-5826	380	29	µ)xn	µ)xn	NOUN
ejpam-5826	380	30	+	+	CCONJ
ejpam-5826	380	31	µtλxn	µtλxn	NOUN
ejpam-5826	380	32	and	and	CCONJ
ejpam-5826	380	33	xn	xn	PUNCT
ejpam-5826	380	34	=	=	SYM
ejpam-5826	380	35	sλxn−1	sλxn−1	PROPN
ejpam-5826	380	36	n	n	NOUN
ejpam-5826	380	37	=	=	SYM
ejpam-5826	380	38	0	0	NUM
ejpam-5826	380	39	,	,	PUNCT
ejpam-5826	380	40	1	1	NUM
ejpam-5826	380	41	,	,	PUNCT
ejpam-5826	380	42	2	2	NUM
ejpam-5826	380	43	,	,	PUNCT
ejpam-5826	380	44	·	·	PUNCT
ejpam-5826	380	45	·	·	PUNCT
ejpam-5826	380	46	·	·	PUNCT
ejpam-5826	380	47	(	(	PUNCT
ejpam-5826	380	48	29	29	NUM
ejpam-5826	380	49	)	)	PUNCT
ejpam-5826	380	50	using	use	VERB
ejpam-5826	380	51	(	(	PUNCT
ejpam-5826	380	52	28	28	NUM
ejpam-5826	380	53	)	)	PUNCT
ejpam-5826	380	54	,	,	PUNCT
ejpam-5826	380	55	we	we	PRON
ejpam-5826	380	56	get	get	VERB
ejpam-5826	380	57	d(xn+1	d(xn+1	NOUN
ejpam-5826	380	58	,	,	PUNCT
ejpam-5826	380	59	xn	xn	NOUN
ejpam-5826	380	60	)	)	PUNCT
ejpam-5826	380	61	≤	≤	NUM
ejpam-5826	380	62	md(xn	md(xn	NOUN
ejpam-5826	380	63	,	,	PUNCT
ejpam-5826	380	64	xn−1	xn−1	PROPN
ejpam-5826	380	65	)	)	PUNCT
ejpam-5826	381	1	+	+	PROPN
ejpam-5826	381	2	k{d(xn	k{d(xn	X
ejpam-5826	381	3	,	,	PUNCT
ejpam-5826	381	4	xn+1	xn+1	NUM
ejpam-5826	381	5	)	)	PUNCT
ejpam-5826	381	6	+	+	CCONJ
ejpam-5826	381	7	d(xn−1	d(xn−1	NOUN
ejpam-5826	381	8	,	,	PUNCT
ejpam-5826	381	9	xn	xn	PROPN
ejpam-5826	381	10	)	)	PUNCT
ejpam-5826	381	11	}	}	PUNCT
ejpam-5826	381	12	;	;	PUNCT
ejpam-5826	381	13	thus	thus	ADV
ejpam-5826	381	14	d(xn+1	d(xn+1	PROPN
ejpam-5826	381	15	,	,	PUNCT
ejpam-5826	381	16	xn	xn	PROPN
ejpam-5826	381	17	)	)	PUNCT
ejpam-5826	381	18	≤	≤	NOUN
ejpam-5826	381	19	(	(	PUNCT
ejpam-5826	382	1	m	m	VERB
ejpam-5826	382	2	+	+	ADJ
ejpam-5826	382	3	k	k	X
ejpam-5826	382	4	)	)	PUNCT
ejpam-5826	382	5	1−k	1−k	NUM
ejpam-5826	383	1	d(xn	d(xn	ADJ
ejpam-5826	383	2	,	,	PUNCT
ejpam-5826	383	3	xn−1	xn−1	PROPN
ejpam-5826	383	4	)	)	PUNCT
ejpam-5826	383	5	d(xn+1	d(xn+1	PROPN
ejpam-5826	383	6	,	,	PUNCT
ejpam-5826	383	7	xn	xn	PROPN
ejpam-5826	383	8	)	)	PUNCT
ejpam-5826	383	9	≤	≤	NOUN
ejpam-5826	384	1	αd(xn	αd(xn	PROPN
ejpam-5826	384	2	,	,	PUNCT
ejpam-5826	384	3	xn−1	xn−1	PROPN
ejpam-5826	384	4	)	)	PUNCT
ejpam-5826	384	5	,	,	PUNCT
ejpam-5826	384	6	(	(	PUNCT
ejpam-5826	384	7	α	α	X
ejpam-5826	384	8	:	:	PUNCT
ejpam-5826	384	9	=	=	NOUN
ejpam-5826	384	10	m	m	VERB
ejpam-5826	384	11	+	+	PROPN
ejpam-5826	384	12	k	k	X
ejpam-5826	384	13	1−k	1−k	NUM
ejpam-5826	384	14	)	)	PUNCT
ejpam-5826	384	15	,	,	PUNCT
ejpam-5826	384	16	(	(	PUNCT
ejpam-5826	384	17	30	30	NUM
ejpam-5826	384	18	)	)	PUNCT
ejpam-5826	384	19	which	which	PRON
ejpam-5826	384	20	inductively	inductively	ADV
ejpam-5826	384	21	implies	imply	VERB
ejpam-5826	384	22	that	that	SCONJ
ejpam-5826	384	23	d(tn+1	d(tn+1	PROPN
ejpam-5826	384	24	λ	λ	PROPN
ejpam-5826	384	25	x	x	PROPN
ejpam-5826	384	26	,	,	PUNCT
ejpam-5826	384	27	sn	sn	PROPN
ejpam-5826	384	28	λx	λx	PROPN
ejpam-5826	384	29	)	)	PUNCT
ejpam-5826	384	30	=	=	SYM
ejpam-5826	385	1	d(xn+1	d(xn+1	PROPN
ejpam-5826	385	2	,	,	PUNCT
ejpam-5826	385	3	xn	xn	PROPN
ejpam-5826	385	4	)	)	PUNCT
ejpam-5826	385	5	≤	≤	NUM
ejpam-5826	385	6	αnd(x1	αnd(x1	NOUN
ejpam-5826	385	7	,	,	PUNCT
ejpam-5826	385	8	x0	x0	PROPN
ejpam-5826	385	9	)	)	PUNCT
ejpam-5826	385	10	.	.	PUNCT
ejpam-5826	386	1	(	(	PUNCT
ejpam-5826	386	2	31	31	NUM
ejpam-5826	386	3	)	)	PUNCT
ejpam-5826	386	4	this	this	PRON
ejpam-5826	386	5	implies	imply	VERB
ejpam-5826	386	6	d(tn+1	d(tn+1	PROPN
ejpam-5826	386	7	λ	λ	PROPN
ejpam-5826	386	8	x	x	PROPN
ejpam-5826	386	9	,	,	PUNCT
ejpam-5826	386	10	sn	sn	PROPN
ejpam-5826	386	11	λx	λx	PROPN
ejpam-5826	386	12	)	)	PUNCT
ejpam-5826	386	13	→	→	SYM
ejpam-5826	386	14	0	0	NUM
ejpam-5826	386	15	as	as	ADP
ejpam-5826	386	16	n	n	NOUN
ejpam-5826	386	17	→	→	SYM
ejpam-5826	386	18	∞.	∞.	PROPN
ejpam-5826	386	19	a.	a.	PROPN
ejpam-5826	386	20	r.	r.	PROPN
ejpam-5826	386	21	khan	khan	PROPN
ejpam-5826	386	22	et	et	PROPN
ejpam-5826	386	23	al	al	PROPN
ejpam-5826	386	24	.	.	PUNCT
ejpam-5826	386	25	/	/	SYM
ejpam-5826	386	26	eur	eur	PROPN
ejpam-5826	386	27	.	.	PUNCT
ejpam-5826	387	1	j.	j.	PROPN
ejpam-5826	387	2	pure	pure	PROPN
ejpam-5826	387	3	appl	appl	PROPN
ejpam-5826	387	4	.	.	PROPN
ejpam-5826	387	5	math	math	PROPN
ejpam-5826	387	6	,	,	PUNCT
ejpam-5826	387	7	18	18	NUM
ejpam-5826	387	8	(	(	PUNCT
ejpam-5826	387	9	2	2	NUM
ejpam-5826	387	10	)	)	PUNCT
ejpam-5826	387	11	(	(	PUNCT
ejpam-5826	387	12	2025	2025	NUM
ejpam-5826	387	13	)	)	PUNCT
ejpam-5826	387	14	,	,	PUNCT
ejpam-5826	387	15	5826	5826	NUM
ejpam-5826	387	16	16	16	NUM
ejpam-5826	387	17	of	of	ADP
ejpam-5826	387	18	23	23	NUM
ejpam-5826	387	19	step	step	NOUN
ejpam-5826	387	20	2	2	NUM
ejpam-5826	387	21	:	:	PUNCT
ejpam-5826	387	22	we	we	PRON
ejpam-5826	387	23	now	now	ADV
ejpam-5826	387	24	prove	prove	VERB
ejpam-5826	387	25	that	that	SCONJ
ejpam-5826	387	26	{	{	PUNCT
ejpam-5826	387	27	xn}∞n=0	xn}∞n=0	X
ejpam-5826	387	28	is	be	AUX
ejpam-5826	387	29	a	a	DET
ejpam-5826	387	30	cauchy	cauchy	ADJ
ejpam-5826	387	31	sequence	sequence	NOUN
ejpam-5826	387	32	.	.	PUNCT
ejpam-5826	388	1	suppose	suppose	VERB
ejpam-5826	388	2	on	on	ADP
ejpam-5826	388	3	contrary	contrary	ADJ
ejpam-5826	388	4	that	that	SCONJ
ejpam-5826	388	5	{	{	PUNCT
ejpam-5826	388	6	xn}∞n=0	xn}∞n=0	PRON
ejpam-5826	388	7	is	be	AUX
ejpam-5826	388	8	not	not	PART
ejpam-5826	388	9	a	a	DET
ejpam-5826	388	10	cauchy	cauchy	ADJ
ejpam-5826	388	11	sequence	sequence	NOUN
ejpam-5826	388	12	.	.	PUNCT
ejpam-5826	389	1	then	then	ADV
ejpam-5826	389	2	there	there	PRON
ejpam-5826	389	3	exisst	exisst	VERB
ejpam-5826	389	4	ϵ	ϵ	ADP
ejpam-5826	389	5	>	>	X
ejpam-5826	389	6	0	0	PUNCT
ejpam-5826	389	7	and	and	CCONJ
ejpam-5826	389	8	sequences	sequence	NOUN
ejpam-5826	389	9	of	of	ADP
ejpam-5826	389	10	numbers	number	NOUN
ejpam-5826	389	11	{	{	PUNCT
ejpam-5826	389	12	m(k	m(k	PROPN
ejpam-5826	389	13	)	)	PUNCT
ejpam-5826	389	14	}	}	PUNCT
ejpam-5826	389	15	and	and	CCONJ
ejpam-5826	389	16	{	{	PUNCT
ejpam-5826	389	17	n(k	n(k	PROPN
ejpam-5826	389	18	)	)	PUNCT
ejpam-5826	389	19	}	}	PUNCT
ejpam-5826	389	20	with	with	ADP
ejpam-5826	389	21	m(k	m(k	PROPN
ejpam-5826	389	22	)	)	PUNCT
ejpam-5826	389	23	>	>	X
ejpam-5826	390	1	n(k	n(k	PROPN
ejpam-5826	390	2	)	)	PUNCT
ejpam-5826	390	3	>	>	X
ejpam-5826	391	1	k	k	PROPN
ejpam-5826	391	2	for	for	ADP
ejpam-5826	391	3	k	k	PROPN
ejpam-5826	391	4	=	=	SYM
ejpam-5826	391	5	1	1	NUM
ejpam-5826	391	6	,	,	PUNCT
ejpam-5826	391	7	2	2	NUM
ejpam-5826	391	8	,	,	PUNCT
ejpam-5826	391	9	3	3	NUM
ejpam-5826	391	10	,	,	PUNCT
ejpam-5826	391	11	·	·	PUNCT
ejpam-5826	391	12	·	·	PUNCT
ejpam-5826	391	13	·	·	PUNCT
ejpam-5826	391	14	such	such	ADJ
ejpam-5826	391	15	that	that	SCONJ
ejpam-5826	391	16	d(t	d(t	PROPN
ejpam-5826	391	17	m(k	m(k	PROPN
ejpam-5826	391	18	)	)	PUNCT
ejpam-5826	391	19	λ	λ	PROPN
ejpam-5826	391	20	,	,	PUNCT
ejpam-5826	391	21	t	t	PROPN
ejpam-5826	391	22	n(k	n(k	PROPN
ejpam-5826	391	23	)	)	PUNCT
ejpam-5826	391	24	λ	λ	PROPN
ejpam-5826	391	25	)	)	PUNCT
ejpam-5826	391	26	≥	≥	PROPN
ejpam-5826	391	27	ϵ.	ϵ.	NOUN
ejpam-5826	391	28	(	(	PUNCT
ejpam-5826	391	29	32	32	NUM
ejpam-5826	391	30	)	)	PUNCT
ejpam-5826	391	31	assume	assume	VERB
ejpam-5826	391	32	that	that	SCONJ
ejpam-5826	391	33	m(k	m(k	PROPN
ejpam-5826	391	34	)	)	PUNCT
ejpam-5826	391	35	≥	≥	NOUN
ejpam-5826	391	36	n(k	n(k	PROPN
ejpam-5826	391	37	)	)	PUNCT
ejpam-5826	391	38	.	.	PUNCT
ejpam-5826	392	1	so	so	ADV
ejpam-5826	392	2	by	by	ADP
ejpam-5826	392	3	(	(	PUNCT
ejpam-5826	392	4	31	31	NUM
ejpam-5826	392	5	)	)	PUNCT
ejpam-5826	392	6	,	,	PUNCT
ejpam-5826	392	7	we	we	PRON
ejpam-5826	392	8	have	have	VERB
ejpam-5826	392	9	d(t	d(t	PROPN
ejpam-5826	392	10	m(k)−1	m(k)−1	PROPN
ejpam-5826	392	11	λ	λ	PROPN
ejpam-5826	392	12	x	x	PROPN
ejpam-5826	392	13	,	,	PUNCT
ejpam-5826	392	14	t	t	PROPN
ejpam-5826	392	15	n(k	n(k	PROPN
ejpam-5826	392	16	)	)	PUNCT
ejpam-5826	392	17	λ	λ	NOUN
ejpam-5826	392	18	x	x	NOUN
ejpam-5826	392	19	)	)	PUNCT
ejpam-5826	392	20	<	<	X
ejpam-5826	392	21	ϵ.	ϵ.	NOUN
ejpam-5826	393	1	hence	hence	ADV
ejpam-5826	393	2	ϵ	ϵ	X
ejpam-5826	393	3	≤	≤	PROPN
ejpam-5826	393	4	d(t	d(t	PROPN
ejpam-5826	393	5	m(k	m(k	PROPN
ejpam-5826	393	6	)	)	PUNCT
ejpam-5826	393	7	λ	λ	PROPN
ejpam-5826	393	8	x	x	PROPN
ejpam-5826	393	9	,	,	PUNCT
ejpam-5826	393	10	t	t	PROPN
ejpam-5826	393	11	n(k	n(k	PROPN
ejpam-5826	393	12	)	)	PUNCT
ejpam-5826	393	13	λ	λ	NOUN
ejpam-5826	393	14	x	x	SYM
ejpam-5826	393	15	)	)	PUNCT
ejpam-5826	393	16	≤	≤	PROPN
ejpam-5826	393	17	d(t	d(t	PROPN
ejpam-5826	393	18	n(k	n(k	PROPN
ejpam-5826	393	19	)	)	PUNCT
ejpam-5826	394	1	λ	λ	NOUN
ejpam-5826	394	2	x	x	PROPN
ejpam-5826	394	3	,	,	PUNCT
ejpam-5826	394	4	t	t	PROPN
ejpam-5826	394	5	n(k)−1	n(k)−1	PROPN
ejpam-5826	394	6	λ	λ	PROPN
ejpam-5826	394	7	x	x	NOUN
ejpam-5826	394	8	)	)	PUNCT
ejpam-5826	394	9	+	+	CCONJ
ejpam-5826	394	10	d(t	d(t	PROPN
ejpam-5826	394	11	m(k)−1	m(k)−1	PROPN
ejpam-5826	394	12	λ	λ	PROPN
ejpam-5826	394	13	x	x	PROPN
ejpam-5826	394	14	,	,	PUNCT
ejpam-5826	394	15	t	t	PROPN
ejpam-5826	394	16	n(k	n(k	PROPN
ejpam-5826	394	17	)	)	PUNCT
ejpam-5826	394	18	λ	λ	NOUN
ejpam-5826	394	19	x	x	NOUN
ejpam-5826	394	20	)	)	PUNCT
ejpam-5826	394	21	<	<	X
ejpam-5826	394	22	d(t	d(t	PROPN
ejpam-5826	394	23	m(k	m(k	PROPN
ejpam-5826	394	24	)	)	PUNCT
ejpam-5826	394	25	λ	λ	PROPN
ejpam-5826	394	26	x	x	PROPN
ejpam-5826	394	27	,	,	PUNCT
ejpam-5826	394	28	t	t	PROPN
ejpam-5826	394	29	m(k)−1	m(k)−1	PROPN
ejpam-5826	394	30	λ	λ	PROPN
ejpam-5826	394	31	x	x	NOUN
ejpam-5826	394	32	)	)	PUNCT
ejpam-5826	395	1	+	+	CCONJ
ejpam-5826	395	2	ϵ.	ϵ.	NOUN
ejpam-5826	395	3	(	(	PUNCT
ejpam-5826	395	4	33	33	NUM
ejpam-5826	395	5	)	)	PUNCT
ejpam-5826	395	6	letting	let	VERB
ejpam-5826	395	7	k	k	X
ejpam-5826	395	8	→	→	SYM
ejpam-5826	395	9	∞	∞	PROPN
ejpam-5826	395	10	and	and	CCONJ
ejpam-5826	395	11	using	use	VERB
ejpam-5826	395	12	asymptotically	asymptotically	ADV
ejpam-5826	395	13	regularity	regularity	NOUN
ejpam-5826	395	14	of	of	ADP
ejpam-5826	395	15	tλ	tλ	ADP
ejpam-5826	395	16	,	,	PUNCT
ejpam-5826	395	17	we	we	PRON
ejpam-5826	395	18	get	get	VERB
ejpam-5826	395	19	lim	lim	PROPN
ejpam-5826	395	20	k→∞	k→∞	PROPN
ejpam-5826	395	21	d(t	d(t	PROPN
ejpam-5826	395	22	m(k	m(k	PROPN
ejpam-5826	395	23	)	)	PUNCT
ejpam-5826	395	24	λ	λ	PROPN
ejpam-5826	395	25	x	x	PROPN
ejpam-5826	395	26	,	,	PUNCT
ejpam-5826	395	27	t	t	PROPN
ejpam-5826	395	28	n(k	n(k	PROPN
ejpam-5826	395	29	)	)	PUNCT
ejpam-5826	395	30	λ	λ	NOUN
ejpam-5826	395	31	x	x	NOUN
ejpam-5826	395	32	)	)	PUNCT
ejpam-5826	396	1	=	=	VERB
ejpam-5826	396	2	ϵ.	ϵ.	NOUN
ejpam-5826	396	3	now	now	ADV
ejpam-5826	396	4	the	the	DET
ejpam-5826	396	5	following	follow	VERB
ejpam-5826	396	6	inequality	inequality	NOUN
ejpam-5826	396	7	and	and	CCONJ
ejpam-5826	396	8	asymptotic	asymptotic	ADJ
ejpam-5826	396	9	regularity	regularity	NOUN
ejpam-5826	396	10	of	of	ADP
ejpam-5826	396	11	tλ	tλ	ADP
ejpam-5826	396	12	d(t	d(t	PROPN
ejpam-5826	396	13	m(k)−1	m(k)−1	PROPN
ejpam-5826	396	14	λ	λ	PROPN
ejpam-5826	396	15	x	x	PROPN
ejpam-5826	396	16	,	,	PUNCT
ejpam-5826	396	17	t	t	PROPN
ejpam-5826	396	18	n(k)−1	n(k)−1	PROPN
ejpam-5826	396	19	λ	λ	PROPN
ejpam-5826	396	20	x	x	NOUN
ejpam-5826	396	21	)	)	PUNCT
ejpam-5826	396	22	≤	≤	PROPN
ejpam-5826	396	23	d(t	d(t	PROPN
ejpam-5826	396	24	m(k)−1	m(k)−1	PROPN
ejpam-5826	396	25	λ	λ	PROPN
ejpam-5826	396	26	x	x	PROPN
ejpam-5826	396	27	,	,	PUNCT
ejpam-5826	396	28	t	t	PROPN
ejpam-5826	396	29	m(k	m(k	PROPN
ejpam-5826	396	30	)	)	PUNCT
ejpam-5826	396	31	λ	λ	NOUN
ejpam-5826	396	32	x	x	NOUN
ejpam-5826	396	33	)	)	PUNCT
ejpam-5826	396	34	+	+	CCONJ
ejpam-5826	396	35	d(t	d(t	PROPN
ejpam-5826	396	36	m(k	m(k	PROPN
ejpam-5826	396	37	)	)	PUNCT
ejpam-5826	396	38	λ	λ	PROPN
ejpam-5826	396	39	x	x	PROPN
ejpam-5826	396	40	,	,	PUNCT
ejpam-5826	396	41	t	t	PROPN
ejpam-5826	396	42	m(k	m(k	PROPN
ejpam-5826	396	43	)	)	PUNCT
ejpam-5826	396	44	λ	λ	NOUN
ejpam-5826	396	45	x	x	X
ejpam-5826	396	46	)	)	PUNCT
ejpam-5826	396	47	+	+	PROPN
ejpam-5826	396	48	d(t	d(t	PROPN
ejpam-5826	396	49	n(k	n(k	PROPN
ejpam-5826	396	50	)	)	PUNCT
ejpam-5826	396	51	λ	λ	NOUN
ejpam-5826	396	52	x	x	PROPN
ejpam-5826	396	53	,	,	PUNCT
ejpam-5826	396	54	t	t	PROPN
ejpam-5826	396	55	n(k)−1	n(k)−1	PROPN
ejpam-5826	396	56	λ	λ	PROPN
ejpam-5826	396	57	x	x	NOUN
ejpam-5826	396	58	)	)	PUNCT
ejpam-5826	396	59	imply	imply	ADP
ejpam-5826	396	60	lim	lim	PROPN
ejpam-5826	396	61	k→∞	k→∞	PROPN
ejpam-5826	396	62	d(t	d(t	PROPN
ejpam-5826	396	63	m(k)−1	m(k)−1	PROPN
ejpam-5826	396	64	λ	λ	PROPN
ejpam-5826	396	65	x	x	PROPN
ejpam-5826	396	66	,	,	PUNCT
ejpam-5826	396	67	t	t	PROPN
ejpam-5826	396	68	n(k)−1	n(k)−1	PROPN
ejpam-5826	396	69	λ	λ	PROPN
ejpam-5826	396	70	x	x	NOUN
ejpam-5826	396	71	)	)	PUNCT
ejpam-5826	396	72	=	=	VERB
ejpam-5826	397	1	ϵ.	ϵ.	NOUN
ejpam-5826	397	2	from	from	ADP
ejpam-5826	397	3	(	(	PUNCT
ejpam-5826	397	4	29	29	NUM
ejpam-5826	397	5	)	)	PUNCT
ejpam-5826	397	6	,	,	PUNCT
ejpam-5826	397	7	we	we	PRON
ejpam-5826	397	8	get	get	VERB
ejpam-5826	397	9	d(t	d(t	PROPN
ejpam-5826	397	10	m(k	m(k	PROPN
ejpam-5826	397	11	)	)	PUNCT
ejpam-5826	397	12	λ	λ	PROPN
ejpam-5826	397	13	x	x	PROPN
ejpam-5826	397	14	,	,	PUNCT
ejpam-5826	397	15	t	t	PROPN
ejpam-5826	397	16	n(k	n(k	PROPN
ejpam-5826	397	17	)	)	PUNCT
ejpam-5826	397	18	λ	λ	NOUN
ejpam-5826	397	19	x	x	NOUN
ejpam-5826	397	20	)	)	PUNCT
ejpam-5826	397	21	≤	≤	PROPN
ejpam-5826	397	22	d(t	d(t	PROPN
ejpam-5826	397	23	m(k	m(k	PROPN
ejpam-5826	397	24	)	)	PUNCT
ejpam-5826	397	25	λ	λ	NOUN
ejpam-5826	397	26	x	x	SYM
ejpam-5826	397	27	,	,	PUNCT
ejpam-5826	397	28	s	s	PART
ejpam-5826	397	29	n(k	n(k	PROPN
ejpam-5826	397	30	)	)	PUNCT
ejpam-5826	397	31	λ	λ	NOUN
ejpam-5826	397	32	x	x	NOUN
ejpam-5826	397	33	)	)	PUNCT
ejpam-5826	398	1	+	+	CCONJ
ejpam-5826	398	2	d(s	d(s	PROPN
ejpam-5826	398	3	n(k	n(k	PROPN
ejpam-5826	398	4	)	)	PUNCT
ejpam-5826	399	1	λ	λ	NOUN
ejpam-5826	399	2	x	x	PROPN
ejpam-5826	399	3	,	,	PUNCT
ejpam-5826	399	4	t	t	PROPN
ejpam-5826	399	5	n(k	n(k	PROPN
ejpam-5826	399	6	)	)	PUNCT
ejpam-5826	399	7	λ	λ	NOUN
ejpam-5826	399	8	x	x	NOUN
ejpam-5826	399	9	)	)	PUNCT
ejpam-5826	399	10	and	and	CCONJ
ejpam-5826	399	11	d(t	d(t	PROPN
ejpam-5826	399	12	m(k	m(k	PROPN
ejpam-5826	399	13	)	)	PUNCT
ejpam-5826	399	14	λ	λ	PROPN
ejpam-5826	399	15	x	x	PROPN
ejpam-5826	399	16	,	,	PUNCT
ejpam-5826	399	17	t	t	PROPN
ejpam-5826	399	18	n(k	n(k	PROPN
ejpam-5826	399	19	)	)	PUNCT
ejpam-5826	399	20	λ	λ	NOUN
ejpam-5826	399	21	x	x	NOUN
ejpam-5826	399	22	)	)	PUNCT
ejpam-5826	399	23	≤	≤	NOUN
ejpam-5826	399	24	d(s	d(s	PROPN
ejpam-5826	399	25	n(k	n(k	PROPN
ejpam-5826	399	26	)	)	PUNCT
ejpam-5826	400	1	λ	λ	NOUN
ejpam-5826	400	2	x	x	PROPN
ejpam-5826	400	3	,	,	PUNCT
ejpam-5826	400	4	t	t	PROPN
ejpam-5826	400	5	n(k	n(k	PROPN
ejpam-5826	400	6	)	)	PUNCT
ejpam-5826	400	7	λ	λ	NOUN
ejpam-5826	400	8	x	x	X
ejpam-5826	400	9	)	)	PUNCT
ejpam-5826	400	10	+	+	PRON
ejpam-5826	400	11	md(t	md(t	NOUN
ejpam-5826	400	12	m(k)−1	m(k)−1	NOUN
ejpam-5826	400	13	λ	λ	PROPN
ejpam-5826	400	14	x	x	PROPN
ejpam-5826	400	15	,	,	PUNCT
ejpam-5826	400	16	t	t	PROPN
ejpam-5826	400	17	n(k)−1	n(k)−1	PROPN
ejpam-5826	400	18	λ	λ	PROPN
ejpam-5826	400	19	x	x	X
ejpam-5826	400	20	)	)	PUNCT
ejpam-5826	401	1	+	+	ADP
ejpam-5826	401	2	k[d(t	k[d(t	X
ejpam-5826	401	3	m(k)−1	m(k)−1	NOUN
ejpam-5826	401	4	λ	λ	X
ejpam-5826	401	5	x	x	PROPN
ejpam-5826	401	6	,	,	PUNCT
ejpam-5826	401	7	t	t	PROPN
ejpam-5826	401	8	m(k	m(k	PROPN
ejpam-5826	401	9	)	)	PUNCT
ejpam-5826	401	10	λ	λ	NOUN
ejpam-5826	401	11	x	x	NOUN
ejpam-5826	401	12	)	)	PUNCT
ejpam-5826	401	13	+	+	CCONJ
ejpam-5826	401	14	d(s	d(s	PROPN
ejpam-5826	401	15	n(k)−1	n(k)−1	PROPN
ejpam-5826	401	16	λ	λ	PROPN
ejpam-5826	401	17	x	x	PROPN
ejpam-5826	401	18	,	,	PUNCT
ejpam-5826	401	19	s	s	PART
ejpam-5826	401	20	n(k	n(k	PROPN
ejpam-5826	401	21	)	)	PUNCT
ejpam-5826	401	22	λ	λ	NOUN
ejpam-5826	401	23	x	x	NOUN
ejpam-5826	401	24	)	)	PUNCT
ejpam-5826	401	25	]	]	PUNCT
ejpam-5826	402	1	+	+	NOUN
ejpam-5826	402	2	md(t	md(t	ADJ
ejpam-5826	402	3	n(k)−1	n(k)−1	PROPN
ejpam-5826	402	4	λ	λ	NOUN
ejpam-5826	402	5	x	x	NOUN
ejpam-5826	402	6	,	,	PUNCT
ejpam-5826	402	7	s	s	VERB
ejpam-5826	402	8	n(k)−1	n(k)−1	ADJ
ejpam-5826	402	9	λ	λ	NOUN
ejpam-5826	402	10	x	x	NOUN
ejpam-5826	402	11	)	)	PUNCT
ejpam-5826	402	12	.	.	PUNCT
ejpam-5826	403	1	letting	let	VERB
ejpam-5826	403	2	k	k	X
ejpam-5826	403	3	→	→	SYM
ejpam-5826	403	4	∞	∞	PROPN
ejpam-5826	403	5	,	,	PUNCT
ejpam-5826	403	6	it	it	PRON
ejpam-5826	403	7	follows	follow	VERB
ejpam-5826	403	8	by	by	ADP
ejpam-5826	403	9	(	(	PUNCT
ejpam-5826	403	10	30	30	NUM
ejpam-5826	403	11	)	)	PUNCT
ejpam-5826	403	12	(	(	PUNCT
ejpam-5826	403	13	32	32	NUM
ejpam-5826	403	14	)	)	PUNCT
ejpam-5826	403	15	and	and	CCONJ
ejpam-5826	403	16	(	(	PUNCT
ejpam-5826	403	17	33	33	NUM
ejpam-5826	403	18	)	)	PUNCT
ejpam-5826	403	19	that	that	PRON
ejpam-5826	403	20	ϵ	ϵ	PROPN
ejpam-5826	403	21	≤	≤	NOUN
ejpam-5826	403	22	mϵ.	mϵ.	VERB
ejpam-5826	403	23	this	this	PRON
ejpam-5826	403	24	is	be	AUX
ejpam-5826	403	25	a	a	DET
ejpam-5826	403	26	contradiction	contradiction	NOUN
ejpam-5826	403	27	.	.	PUNCT
ejpam-5826	404	1	therefore	therefore	ADV
ejpam-5826	404	2	{	{	PUNCT
ejpam-5826	404	3	xn	xn	X
ejpam-5826	404	4	}	}	PUNCT
ejpam-5826	404	5	is	be	AUX
ejpam-5826	404	6	a	a	DET
ejpam-5826	404	7	cauchy	cauchy	ADJ
ejpam-5826	404	8	sequence	sequence	NOUN
ejpam-5826	404	9	.	.	PUNCT
ejpam-5826	405	1	given	give	VERB
ejpam-5826	405	2	that	that	PRON
ejpam-5826	405	3	q	q	NOUN
ejpam-5826	405	4	is	be	AUX
ejpam-5826	405	5	complete	complete	ADJ
ejpam-5826	405	6	,	,	PUNCT
ejpam-5826	405	7	{	{	PUNCT
ejpam-5826	405	8	xn	xn	NOUN
ejpam-5826	405	9	}	}	PUNCT
ejpam-5826	405	10	converges	converge	NOUN
ejpam-5826	405	11	to	to	ADP
ejpam-5826	405	12	p	p	PROPN
ejpam-5826	405	13	∈	∈	PROPN
ejpam-5826	405	14	q.	q.	NOUN
ejpam-5826	405	15	moreover	moreover	ADV
ejpam-5826	405	16	,	,	PUNCT
ejpam-5826	405	17	d(sn	d(sn	PROPN
ejpam-5826	405	18	λx	λx	PROPN
ejpam-5826	405	19	,	,	PUNCT
ejpam-5826	405	20	p	p	X
ejpam-5826	405	21	)	)	PUNCT
ejpam-5826	405	22	≤	≤	PROPN
ejpam-5826	405	23	d(sn	d(sn	PROPN
ejpam-5826	405	24	λx	λx	PROPN
ejpam-5826	405	25	,	,	PUNCT
ejpam-5826	405	26	t	t	PROPN
ejpam-5826	405	27	n	n	CCONJ
ejpam-5826	405	28	λ	λ	X
ejpam-5826	405	29	x	x	NOUN
ejpam-5826	405	30	)	)	PUNCT
ejpam-5826	405	31	+	+	NUM
ejpam-5826	405	32	d(tn	d(tn	PROPN
ejpam-5826	405	33	λ	λ	NOUN
ejpam-5826	405	34	x	x	NOUN
ejpam-5826	405	35	,	,	PUNCT
ejpam-5826	405	36	p	p	NOUN
ejpam-5826	405	37	)	)	PUNCT
ejpam-5826	405	38	,	,	PUNCT
ejpam-5826	405	39	so	so	CCONJ
ejpam-5826	405	40	it	it	PRON
ejpam-5826	405	41	follows	follow	VERB
ejpam-5826	405	42	from	from	ADP
ejpam-5826	405	43	step	step	NOUN
ejpam-5826	405	44	1	1	NUM
ejpam-5826	405	45	that	that	PRON
ejpam-5826	405	46	tn	tn	PROPN
ejpam-5826	405	47	λ	λ	NOUN
ejpam-5826	405	48	x	x	PUNCT
ejpam-5826	405	49	and	and	CCONJ
ejpam-5826	405	50	sn	sn	PROPN
ejpam-5826	405	51	λx	λx	PROPN
ejpam-5826	405	52	converge	converge	VERB
ejpam-5826	405	53	to	to	ADP
ejpam-5826	405	54	p	p	PROPN
ejpam-5826	405	55	∈	∈	PROPN
ejpam-5826	405	56	q.	q.	PROPN
ejpam-5826	405	57	a.	a.	PROPN
ejpam-5826	405	58	r.	r.	PROPN
ejpam-5826	405	59	khan	khan	PROPN
ejpam-5826	405	60	et	et	PROPN
ejpam-5826	405	61	al	al	PROPN
ejpam-5826	405	62	.	.	PUNCT
ejpam-5826	405	63	/	/	SYM
ejpam-5826	405	64	eur	eur	PROPN
ejpam-5826	405	65	.	.	PUNCT
ejpam-5826	406	1	j.	j.	PROPN
ejpam-5826	406	2	pure	pure	PROPN
ejpam-5826	406	3	appl	appl	PROPN
ejpam-5826	406	4	.	.	PROPN
ejpam-5826	406	5	math	math	PROPN
ejpam-5826	406	6	,	,	PUNCT
ejpam-5826	406	7	18	18	NUM
ejpam-5826	406	8	(	(	PUNCT
ejpam-5826	406	9	2	2	NUM
ejpam-5826	406	10	)	)	PUNCT
ejpam-5826	406	11	(	(	PUNCT
ejpam-5826	406	12	2025	2025	NUM
ejpam-5826	406	13	)	)	PUNCT
ejpam-5826	406	14	,	,	PUNCT
ejpam-5826	406	15	5826	5826	NUM
ejpam-5826	406	16	17	17	NUM
ejpam-5826	406	17	of	of	ADP
ejpam-5826	406	18	23	23	NUM
ejpam-5826	406	19	step	step	NOUN
ejpam-5826	406	20	3	3	NUM
ejpam-5826	406	21	:	:	PUNCT
ejpam-5826	406	22	tλ	tλ	NOUN
ejpam-5826	406	23	and	and	CCONJ
ejpam-5826	406	24	sλ	sλ	AUX
ejpam-5826	406	25	have	have	VERB
ejpam-5826	406	26	a	a	DET
ejpam-5826	406	27	unique	unique	ADJ
ejpam-5826	406	28	common	common	ADJ
ejpam-5826	406	29	fixed	fix	VERB
ejpam-5826	406	30	point	point	NOUN
ejpam-5826	406	31	p.	p.	NOUN
ejpam-5826	406	32	let	let	VERB
ejpam-5826	406	33	tλ	tλ	PART
ejpam-5826	406	34	be	be	AUX
ejpam-5826	406	35	k	k	ADJ
ejpam-5826	406	36	-	-	ADJ
ejpam-5826	406	37	continuous	continuous	ADJ
ejpam-5826	406	38	.	.	PUNCT
ejpam-5826	407	1	since	since	SCONJ
ejpam-5826	407	2	limn→∞	limn→∞	PRON
ejpam-5826	407	3	tn−1	tn−1	PROPN
ejpam-5826	407	4	λ	λ	NOUN
ejpam-5826	407	5	x	x	PUNCT
ejpam-5826	407	6	=	=	PUNCT
ejpam-5826	407	7	p.	p.	NOUN
ejpam-5826	408	1	so	so	ADV
ejpam-5826	408	2	by	by	ADP
ejpam-5826	408	3	k	k	NOUN
ejpam-5826	408	4	-	-	NOUN
ejpam-5826	408	5	continuity	continuity	NOUN
ejpam-5826	408	6	of	of	ADP
ejpam-5826	408	7	tλ	tλ	ADP
ejpam-5826	408	8	,	,	PUNCT
ejpam-5826	408	9	limn→∞	limn→∞	PROPN
ejpam-5826	408	10	tn	tn	PROPN
ejpam-5826	408	11	λ	λ	PROPN
ejpam-5826	408	12	x	x	X
ejpam-5826	408	13	=	=	SYM
ejpam-5826	408	14	tλp	tλp	NOUN
ejpam-5826	408	15	.	.	PUNCT
ejpam-5826	409	1	by	by	ADP
ejpam-5826	409	2	uniqueness	uniqueness	NOUN
ejpam-5826	409	3	of	of	ADP
ejpam-5826	409	4	limit	limit	NOUN
ejpam-5826	409	5	,	,	PUNCT
ejpam-5826	409	6	tλp	tλp	X
ejpam-5826	409	7	=	=	SYM
ejpam-5826	409	8	p.	p.	NOUN
ejpam-5826	409	9	analogically	analogically	ADV
ejpam-5826	409	10	,	,	PUNCT
ejpam-5826	409	11	suppose	suppose	VERB
ejpam-5826	409	12	that	that	SCONJ
ejpam-5826	409	13	tλ	tλ	NOUN
ejpam-5826	409	14	is	be	AUX
ejpam-5826	409	15	orbital	orbital	ADJ
ejpam-5826	409	16	continuous	continuous	ADJ
ejpam-5826	409	17	.	.	PUNCT
ejpam-5826	410	1	since	since	SCONJ
ejpam-5826	410	2	limn→∞	limn→∞	PROPN
ejpam-5826	410	3	xn	xn	PUNCT
ejpam-5826	410	4	=	=	SYM
ejpam-5826	410	5	p	p	NOUN
ejpam-5826	410	6	,	,	PUNCT
ejpam-5826	410	7	orbital	orbital	ADJ
ejpam-5826	410	8	continuity	continuity	NOUN
ejpam-5826	410	9	of	of	ADP
ejpam-5826	410	10	tλ	tλ	ADP
ejpam-5826	410	11	implies	imply	VERB
ejpam-5826	410	12	that	that	SCONJ
ejpam-5826	410	13	lim	lim	PROPN
ejpam-5826	410	14	n→∞	n→∞	PRON
ejpam-5826	410	15	tλxn	tλxn	PROPN
ejpam-5826	410	16	=	=	SYM
ejpam-5826	410	17	tλp	tλp	PROPN
ejpam-5826	410	18	.	.	PUNCT
ejpam-5826	411	1	this	this	DET
ejpam-5826	411	2	yield	yield	NOUN
ejpam-5826	411	3	tλp	tλp	NOUN
ejpam-5826	411	4	=	=	PUNCT
ejpam-5826	412	1	p.	p.	NOUN
ejpam-5826	412	2	similarly	similarly	ADV
ejpam-5826	412	3	,	,	PUNCT
ejpam-5826	412	4	limn→∞	limn→∞	PROPN
ejpam-5826	412	5	sn	sn	X
ejpam-5826	412	6	λx	λx	PROPN
ejpam-5826	413	1	=	=	SYM
ejpam-5826	413	2	p	p	X
ejpam-5826	413	3	,	,	PUNCT
ejpam-5826	413	4	we	we	PRON
ejpam-5826	413	5	have	have	VERB
ejpam-5826	413	6	that	that	PRON
ejpam-5826	413	7	sp	sp	ADP
ejpam-5826	413	8	=	=	SYM
ejpam-5826	413	9	p.	p.	NOUN
ejpam-5826	414	1	hence	hence	ADV
ejpam-5826	414	2	p	p	PROPN
ejpam-5826	414	3	∈	∈	PROPN
ejpam-5826	414	4	fix(tλ	fix(tλ	NOUN
ejpam-5826	414	5	)	)	PUNCT
ejpam-5826	414	6	∩	∩	NOUN
ejpam-5826	414	7	fix(sλ	fix(sλ	NOUN
ejpam-5826	414	8	)	)	PUNCT
ejpam-5826	414	9	.	.	PUNCT
ejpam-5826	415	1	uniqueness	uniqueness	NOUN
ejpam-5826	415	2	:	:	PUNCT
ejpam-5826	415	3	assume	assume	VERB
ejpam-5826	415	4	that	that	SCONJ
ejpam-5826	415	5	p	p	X
ejpam-5826	415	6	,	,	PUNCT
ejpam-5826	415	7	q	q	PROPN
ejpam-5826	415	8	∈	∈	PROPN
ejpam-5826	415	9	fix(tλ	fix(tλ	NOUN
ejpam-5826	415	10	)	)	PUNCT
ejpam-5826	415	11	⋂	⋂	PROPN
ejpam-5826	415	12	fix(sλ	fix(sλ	NOUN
ejpam-5826	415	13	)	)	PUNCT
ejpam-5826	415	14	and	and	CCONJ
ejpam-5826	415	15	q1	q1	PROPN
ejpam-5826	415	16	̸=	̸=	PROPN
ejpam-5826	415	17	p.	p.	NOUN
ejpam-5826	415	18	let	let	VERB
ejpam-5826	415	19	x	x	PUNCT
ejpam-5826	415	20	=	=	PUNCT
ejpam-5826	415	21	p	p	PROPN
ejpam-5826	415	22	and	and	CCONJ
ejpam-5826	415	23	y	y	PROPN
ejpam-5826	415	24	=	=	PROPN
ejpam-5826	415	25	q1	q1	PROPN
ejpam-5826	415	26	.	.	PUNCT
ejpam-5826	416	1	then	then	ADV
ejpam-5826	416	2	(	(	PUNCT
ejpam-5826	416	3	28	28	NUM
ejpam-5826	416	4	)	)	PUNCT
ejpam-5826	416	5	becomes	become	VERB
ejpam-5826	416	6	d(p	d(p	PROPN
ejpam-5826	416	7	,	,	PUNCT
ejpam-5826	416	8	q1	q1	PROPN
ejpam-5826	416	9	)	)	PUNCT
ejpam-5826	416	10	≤	≤	NOUN
ejpam-5826	416	11	md(p	md(p	NUM
ejpam-5826	416	12	,	,	PUNCT
ejpam-5826	416	13	q1	q1	PROPN
ejpam-5826	416	14	)	)	PUNCT
ejpam-5826	416	15	.	.	PUNCT
ejpam-5826	417	1	it	it	PRON
ejpam-5826	417	2	is	be	AUX
ejpam-5826	417	3	a	a	DET
ejpam-5826	417	4	contradiction	contradiction	NOUN
ejpam-5826	417	5	.	.	PUNCT
ejpam-5826	418	1	hence	hence	ADV
ejpam-5826	418	2	p	p	PROPN
ejpam-5826	418	3	is	be	AUX
ejpam-5826	418	4	a	a	DET
ejpam-5826	418	5	unique	unique	ADJ
ejpam-5826	418	6	common	common	ADJ
ejpam-5826	418	7	fixed	fix	VERB
ejpam-5826	418	8	point	point	NOUN
ejpam-5826	418	9	of	of	ADP
ejpam-5826	418	10	tλ	tλ	NOUN
ejpam-5826	418	11	and	and	CCONJ
ejpam-5826	418	12	sλ	sλ	NOUN
ejpam-5826	418	13	.	.	PUNCT
ejpam-5826	419	1	in	in	ADP
ejpam-5826	419	2	the	the	DET
ejpam-5826	419	3	light	light	NOUN
ejpam-5826	419	4	of	of	ADP
ejpam-5826	419	5	lemma	lemma	PROPN
ejpam-5826	419	6	5	5	NUM
ejpam-5826	419	7	,	,	PUNCT
ejpam-5826	419	8	we	we	PRON
ejpam-5826	419	9	define	define	VERB
ejpam-5826	419	10	zemfirescue	zemfirescue	NOUN
ejpam-5826	419	11	mapping	mapping	NOUN
ejpam-5826	419	12	in	in	ADP
ejpam-5826	419	13	terms	term	NOUN
ejpam-5826	419	14	of	of	ADP
ejpam-5826	419	15	tλ	tλ	ADP
ejpam-5826	419	16	:	:	PUNCT
ejpam-5826	419	17	definition	definition	NOUN
ejpam-5826	419	18	3	3	NUM
ejpam-5826	419	19	.	.	PUNCT
ejpam-5826	420	1	let	let	AUX
ejpam-5826	420	2	(	(	PUNCT
ejpam-5826	420	3	q	q	X
ejpam-5826	420	4	,	,	PUNCT
ejpam-5826	420	5	d	d	NOUN
ejpam-5826	420	6	,	,	PUNCT
ejpam-5826	420	7	w	w	PROPN
ejpam-5826	420	8	)	)	PUNCT
ejpam-5826	420	9	be	be	AUX
ejpam-5826	420	10	a	a	DET
ejpam-5826	420	11	complete	complete	ADJ
ejpam-5826	420	12	convex	convex	NOUN
ejpam-5826	420	13	metric	metric	ADJ
ejpam-5826	420	14	space	space	NOUN
ejpam-5826	420	15	and	and	CCONJ
ejpam-5826	420	16	tλ	tλ	ADP
ejpam-5826	420	17	:	:	PUNCT
ejpam-5826	420	18	q	q	X
ejpam-5826	420	19	→	→	PUNCT
ejpam-5826	420	20	q	q	X
ejpam-5826	420	21	satisfies	satisfie	NOUN
ejpam-5826	420	22	the	the	DET
ejpam-5826	420	23	following	follow	VERB
ejpam-5826	420	24	conditions	condition	NOUN
ejpam-5826	420	25	.	.	PUNCT
ejpam-5826	421	1	(	(	PUNCT
ejpam-5826	421	2	i	i	NOUN
ejpam-5826	421	3	)	)	PUNCT
ejpam-5826	421	4	d(tλx	d(tλx	PROPN
ejpam-5826	421	5	,	,	PUNCT
ejpam-5826	421	6	tλy	tλy	NOUN
ejpam-5826	421	7	)	)	PUNCT
ejpam-5826	421	8	≤	≤	NOUN
ejpam-5826	421	9	ad(x	ad(x	PUNCT
ejpam-5826	421	10	,	,	PUNCT
ejpam-5826	421	11	y	y	PROPN
ejpam-5826	421	12	)	)	PUNCT
ejpam-5826	421	13	,	,	PUNCT
ejpam-5826	421	14	0	0	PUNCT
ejpam-5826	421	15	<	<	X
ejpam-5826	421	16	a	a	DET
ejpam-5826	421	17	<	<	X
ejpam-5826	421	18	1	1	NUM
ejpam-5826	421	19	,	,	PUNCT
ejpam-5826	421	20	(	(	PUNCT
ejpam-5826	421	21	ii	ii	NOUN
ejpam-5826	421	22	)	)	PUNCT
ejpam-5826	421	23	d(tλx	d(tλx	PROPN
ejpam-5826	421	24	,	,	PUNCT
ejpam-5826	421	25	tλy	tλy	NOUN
ejpam-5826	421	26	)	)	PUNCT
ejpam-5826	421	27	≤	≤	NUM
ejpam-5826	421	28	b	b	X
ejpam-5826	421	29	(	(	PUNCT
ejpam-5826	421	30	(	(	PUNCT
ejpam-5826	421	31	d(x	d(x	PROPN
ejpam-5826	421	32	,	,	PUNCT
ejpam-5826	421	33	tλx	tλx	NOUN
ejpam-5826	421	34	)	)	PUNCT
ejpam-5826	422	1	+	+	CCONJ
ejpam-5826	422	2	d(y	d(y	NOUN
ejpam-5826	422	3	,	,	PUNCT
ejpam-5826	422	4	tλy	tλy	NOUN
ejpam-5826	422	5	)	)	PUNCT
ejpam-5826	422	6	)	)	PUNCT
ejpam-5826	422	7	,	,	PUNCT
ejpam-5826	422	8	0	0	PUNCT
ejpam-5826	422	9	<	<	X
ejpam-5826	422	10	b	b	X
ejpam-5826	422	11	<	<	X
ejpam-5826	422	12	1	1	NUM
ejpam-5826	422	13	2	2	NUM
ejpam-5826	422	14	(	(	PUNCT
ejpam-5826	422	15	iii	iii	NOUN
ejpam-5826	422	16	)	)	PUNCT
ejpam-5826	422	17	d(tλx	d(tλx	PROPN
ejpam-5826	422	18	,	,	PUNCT
ejpam-5826	422	19	tλy	tλy	NOUN
ejpam-5826	422	20	)	)	PUNCT
ejpam-5826	422	21	≤	≤	NUM
ejpam-5826	423	1	c	c	NOUN
ejpam-5826	423	2	(	(	PUNCT
ejpam-5826	423	3	d(x	d(x	PROPN
ejpam-5826	423	4	,	,	PUNCT
ejpam-5826	423	5	tλy	tλy	NOUN
ejpam-5826	423	6	)	)	PUNCT
ejpam-5826	424	1	+	+	CCONJ
ejpam-5826	424	2	d(y	d(y	NOUN
ejpam-5826	424	3	,	,	PUNCT
ejpam-5826	424	4	tλx	tλx	NOUN
ejpam-5826	424	5	)	)	PUNCT
ejpam-5826	424	6	)	)	PUNCT
ejpam-5826	424	7	,	,	PUNCT
ejpam-5826	424	8	0	0	PUNCT
ejpam-5826	424	9	<	<	X
ejpam-5826	424	10	c	c	X
ejpam-5826	424	11	<	<	X
ejpam-5826	424	12	1	1	NUM
ejpam-5826	424	13	2	2	NUM
ejpam-5826	424	14	.	.	PUNCT
ejpam-5826	425	1	an	an	DET
ejpam-5826	425	2	analogue	analogue	NOUN
ejpam-5826	425	3	of	of	ADP
ejpam-5826	425	4	theorem	theorem	NOUN
ejpam-5826	425	5	1	1	NUM
ejpam-5826	425	6	by	by	ADP
ejpam-5826	425	7	zamfiresuc	zamfiresuc	PROPN
ejpam-5826	426	1	[	[	X
ejpam-5826	426	2	22	22	NUM
ejpam-5826	426	3	]	]	PUNCT
ejpam-5826	426	4	for	for	ADP
ejpam-5826	426	5	the	the	DET
ejpam-5826	426	6	mapping	mapping	NOUN
ejpam-5826	426	7	tλ	tλ	NOUN
ejpam-5826	426	8	is	be	AUX
ejpam-5826	426	9	presented	present	VERB
ejpam-5826	426	10	below	below	ADV
ejpam-5826	426	11	.	.	PUNCT
ejpam-5826	427	1	theorem	theorem	ADJ
ejpam-5826	427	2	8	8	NUM
ejpam-5826	427	3	.	.	PUNCT
ejpam-5826	428	1	let	let	VERB
ejpam-5826	428	2	(	(	PUNCT
ejpam-5826	428	3	q	q	X
ejpam-5826	428	4	,	,	PUNCT
ejpam-5826	428	5	d	d	NOUN
ejpam-5826	428	6	,	,	PUNCT
ejpam-5826	428	7	w	w	PROPN
ejpam-5826	428	8	)	)	PUNCT
ejpam-5826	428	9	be	be	AUX
ejpam-5826	428	10	a	a	DET
ejpam-5826	428	11	complete	complete	ADJ
ejpam-5826	428	12	convex	convex	NOUN
ejpam-5826	428	13	metric	metric	ADJ
ejpam-5826	428	14	space	space	NOUN
ejpam-5826	428	15	and	and	CCONJ
ejpam-5826	428	16	tλ	tλ	ADP
ejpam-5826	428	17	:	:	PUNCT
ejpam-5826	428	18	q	q	X
ejpam-5826	428	19	→	→	X
ejpam-5826	428	20	q	q	X
ejpam-5826	428	21	be	be	AUX
ejpam-5826	428	22	zamfirescue	zamfirescue	NOUN
ejpam-5826	428	23	asymptotically	asymptotically	ADV
ejpam-5826	428	24	regular	regular	ADJ
ejpam-5826	428	25	map	map	NOUN
ejpam-5826	428	26	.	.	PUNCT
ejpam-5826	429	1	then	then	ADV
ejpam-5826	429	2	,	,	PUNCT
ejpam-5826	429	3	(	(	PUNCT
ejpam-5826	429	4	i	i	NOUN
ejpam-5826	429	5	)	)	PUNCT
ejpam-5826	429	6	fix(tλ	fix(tλ	PROPN
ejpam-5826	429	7	)	)	PUNCT
ejpam-5826	429	8	=	=	PUNCT
ejpam-5826	430	1	{	{	PUNCT
ejpam-5826	430	2	p	p	X
ejpam-5826	430	3	}	}	PUNCT
ejpam-5826	430	4	,	,	PUNCT
ejpam-5826	430	5	and	and	CCONJ
ejpam-5826	430	6	(	(	PUNCT
ejpam-5826	430	7	ii	ii	NOUN
ejpam-5826	430	8	)	)	PUNCT
ejpam-5826	430	9	the	the	DET
ejpam-5826	430	10	sequence	sequence	NOUN
ejpam-5826	430	11	{	{	PUNCT
ejpam-5826	430	12	xn}∞n=0	xn}∞n=0	NUM
ejpam-5826	430	13	obtained	obtain	VERB
ejpam-5826	430	14	from	from	ADP
ejpam-5826	430	15	the	the	DET
ejpam-5826	430	16	iterative	iterative	NOUN
ejpam-5826	430	17	process	process	NOUN
ejpam-5826	430	18	xn+1	xn+1	PROPN
ejpam-5826	431	1	=	=	SYM
ejpam-5826	431	2	w	w	PROPN
ejpam-5826	431	3	(	(	PUNCT
ejpam-5826	431	4	xn	xn	PROPN
ejpam-5826	431	5	,	,	PUNCT
ejpam-5826	431	6	tλxn;λ	tλxn;λ	NOUN
ejpam-5826	431	7	)	)	PUNCT
ejpam-5826	431	8	,	,	PUNCT
ejpam-5826	431	9	n	n	PRON
ejpam-5826	431	10	≥	≥	NOUN
ejpam-5826	431	11	0	0	NUM
ejpam-5826	431	12	converges	converge	NOUN
ejpam-5826	431	13	to	to	ADP
ejpam-5826	431	14	p	p	PRON
ejpam-5826	431	15	,	,	PUNCT
ejpam-5826	431	16	for	for	ADP
ejpam-5826	431	17	x0	x0	PROPN
ejpam-5826	431	18	∈	∈	PROPN
ejpam-5826	431	19	q.	q.	NOUN
ejpam-5826	431	20	proof	proof	NOUN
ejpam-5826	431	21	.	.	PUNCT
ejpam-5826	432	1	we	we	PRON
ejpam-5826	432	2	note	note	VERB
ejpam-5826	432	3	that	that	SCONJ
ejpam-5826	432	4	the	the	DET
ejpam-5826	432	5	picard	picard	NOUN
ejpam-5826	432	6	iterations	iteration	NOUN
ejpam-5826	432	7	of	of	ADP
ejpam-5826	432	8	tλ	tλ	PART
ejpam-5826	432	9	actually	actually	ADV
ejpam-5826	432	10	form	form	VERB
ejpam-5826	432	11	the	the	DET
ejpam-5826	432	12	kranoselskij	kranoselskij	PROPN
ejpam-5826	432	13	iterative	iterative	NOUN
ejpam-5826	432	14	process	process	NOUN
ejpam-5826	432	15	{	{	PUNCT
ejpam-5826	432	16	xn}∞n=0	xn}∞n=0	X
ejpam-5826	432	17	.	.	PUNCT
ejpam-5826	433	1	now	now	ADV
ejpam-5826	433	2	,	,	PUNCT
ejpam-5826	433	3	choose	choose	VERB
ejpam-5826	433	4	x0	x0	PROPN
ejpam-5826	433	5	∈	∈	PROPN
ejpam-5826	433	6	q	q	X
ejpam-5826	433	7	arbitrarily	arbitrarily	ADV
ejpam-5826	433	8	and	and	CCONJ
ejpam-5826	433	9	fix	fix	VERB
ejpam-5826	433	10	integer	integer	NOUN
ejpam-5826	433	11	n	n	PRON
ejpam-5826	433	12	≥	≥	NOUN
ejpam-5826	433	13	0	0	NUM
ejpam-5826	433	14	.	.	PUNCT
ejpam-5826	434	1	consider	consider	VERB
ejpam-5826	434	2	x	x	X
ejpam-5826	434	3	=	=	SYM
ejpam-5826	434	4	tn	tn	PROPN
ejpam-5826	434	5	λ	λ	NOUN
ejpam-5826	434	6	x0	x0	PROPN
ejpam-5826	434	7	and	and	CCONJ
ejpam-5826	434	8	y	y	PROPN
ejpam-5826	434	9	=	=	SYM
ejpam-5826	434	10	tn+1	tn+1	PROPN
ejpam-5826	434	11	λ	λ	NOUN
ejpam-5826	434	12	x0	x0	PROPN
ejpam-5826	434	13	,	,	PUNCT
ejpam-5826	434	14	we	we	PRON
ejpam-5826	434	15	obtain	obtain	VERB
ejpam-5826	434	16	by	by	ADP
ejpam-5826	434	17	definition	definition	NOUN
ejpam-5826	434	18	3(i	3(i	NUM
ejpam-5826	434	19	)	)	PUNCT
ejpam-5826	434	20	,	,	PUNCT
ejpam-5826	434	21	with	with	ADP
ejpam-5826	434	22	δ	δ	PROPN
ejpam-5826	434	23	<	<	X
ejpam-5826	434	24	1	1	NUM
ejpam-5826	434	25	d(tn+1	d(tn+1	PROPN
ejpam-5826	434	26	λ	λ	NOUN
ejpam-5826	434	27	x0	x0	PROPN
ejpam-5826	434	28	,	,	PUNCT
ejpam-5826	434	29	t	t	PROPN
ejpam-5826	435	1	n+2	n+2	NUM
ejpam-5826	436	1	λ	λ	NOUN
ejpam-5826	436	2	x0	x0	PROPN
ejpam-5826	436	3	)	)	PUNCT
ejpam-5826	436	4	≤	≤	NUM
ejpam-5826	436	5	δd(tn	δd(tn	ADJ
ejpam-5826	436	6	λ	λ	X
ejpam-5826	436	7	x0	x0	PROPN
ejpam-5826	436	8	,	,	PUNCT
ejpam-5826	436	9	t	t	PROPN
ejpam-5826	436	10	n+1	n+1	PROPN
ejpam-5826	436	11	λ	λ	X
ejpam-5826	436	12	x0	x0	NUM
ejpam-5826	436	13	)	)	PUNCT
ejpam-5826	436	14	and	and	CCONJ
ejpam-5826	436	15	by	by	ADP
ejpam-5826	436	16	definition	definition	NOUN
ejpam-5826	436	17	3(ii	3(ii	NUM
ejpam-5826	436	18	)	)	PUNCT
ejpam-5826	436	19	d(tn+1	d(tn+1	PROPN
ejpam-5826	436	20	λ	λ	PROPN
ejpam-5826	436	21	x0	x0	PROPN
ejpam-5826	436	22	,	,	PUNCT
ejpam-5826	436	23	t	t	PROPN
ejpam-5826	436	24	n+2	n+2	NUM
ejpam-5826	436	25	λ	λ	NOUN
ejpam-5826	436	26	x0	x0	PROPN
ejpam-5826	436	27	)	)	PUNCT
ejpam-5826	436	28	≤	≤	NUM
ejpam-5826	436	29	b	b	X
ejpam-5826	436	30	(	(	PUNCT
ejpam-5826	436	31	d(tn	d(tn	PROPN
ejpam-5826	436	32	λ	λ	NOUN
ejpam-5826	436	33	x0	x0	PROPN
ejpam-5826	436	34	,	,	PUNCT
ejpam-5826	436	35	t	t	PROPN
ejpam-5826	436	36	n+1	n+1	PROPN
ejpam-5826	436	37	λ	λ	X
ejpam-5826	436	38	x0	x0	NUM
ejpam-5826	436	39	)	)	PUNCT
ejpam-5826	437	1	+	+	PUNCT
ejpam-5826	437	2	d(tn+1	d(tn+1	ADJ
ejpam-5826	437	3	λ	λ	PROPN
ejpam-5826	437	4	x0	x0	PROPN
ejpam-5826	437	5	,	,	PUNCT
ejpam-5826	437	6	t	t	PROPN
ejpam-5826	437	7	n+2	n+2	NUM
ejpam-5826	437	8	λ	λ	NOUN
ejpam-5826	437	9	x0	x0	PROPN
ejpam-5826	437	10	)	)	PUNCT
ejpam-5826	437	11	)	)	PUNCT
ejpam-5826	437	12	which	which	PRON
ejpam-5826	437	13	implies	imply	VERB
ejpam-5826	437	14	d(tn+1	d(tn+1	PROPN
ejpam-5826	437	15	λ	λ	PROPN
ejpam-5826	437	16	x0	x0	PROPN
ejpam-5826	437	17	,	,	PUNCT
ejpam-5826	437	18	t	t	PROPN
ejpam-5826	437	19	n+2	n+2	NUM
ejpam-5826	438	1	λ	λ	NOUN
ejpam-5826	438	2	x0	x0	PROPN
ejpam-5826	438	3	)	)	PUNCT
ejpam-5826	438	4	≤	≤	NUM
ejpam-5826	438	5	b	b	X
ejpam-5826	438	6	1−	1−	NUM
ejpam-5826	438	7	b	b	SYM
ejpam-5826	438	8	d(tn	d(tn	PROPN
ejpam-5826	438	9	λ	λ	NOUN
ejpam-5826	438	10	x0	x0	PROPN
ejpam-5826	438	11	,	,	PUNCT
ejpam-5826	438	12	t	t	PROPN
ejpam-5826	438	13	n+1	n+1	PROPN
ejpam-5826	438	14	λ	λ	PROPN
ejpam-5826	438	15	x0	x0	PROPN
ejpam-5826	438	16	)	)	PUNCT
ejpam-5826	438	17	.	.	PUNCT
ejpam-5826	439	1	a.	a.	PROPN
ejpam-5826	439	2	r.	r.	PROPN
ejpam-5826	439	3	khan	khan	PROPN
ejpam-5826	439	4	et	et	PROPN
ejpam-5826	439	5	al	al	PROPN
ejpam-5826	439	6	.	.	PUNCT
ejpam-5826	439	7	/	/	SYM
ejpam-5826	439	8	eur	eur	PROPN
ejpam-5826	439	9	.	.	PUNCT
ejpam-5826	440	1	j.	j.	PROPN
ejpam-5826	440	2	pure	pure	PROPN
ejpam-5826	440	3	appl	appl	PROPN
ejpam-5826	440	4	.	.	PROPN
ejpam-5826	440	5	math	math	PROPN
ejpam-5826	440	6	,	,	PUNCT
ejpam-5826	440	7	18	18	NUM
ejpam-5826	440	8	(	(	PUNCT
ejpam-5826	440	9	2	2	NUM
ejpam-5826	440	10	)	)	PUNCT
ejpam-5826	440	11	(	(	PUNCT
ejpam-5826	440	12	2025	2025	NUM
ejpam-5826	440	13	)	)	PUNCT
ejpam-5826	440	14	,	,	PUNCT
ejpam-5826	440	15	5826	5826	NUM
ejpam-5826	440	16	18	18	NUM
ejpam-5826	440	17	of	of	ADP
ejpam-5826	440	18	23	23	NUM
ejpam-5826	440	19	thus	thus	ADV
ejpam-5826	440	20	d(tn+1	d(tn+1	ADJ
ejpam-5826	440	21	λ	λ	PROPN
ejpam-5826	440	22	x0	x0	PROPN
ejpam-5826	440	23	,	,	PUNCT
ejpam-5826	440	24	t	t	PROPN
ejpam-5826	440	25	n+2	n+2	NUM
ejpam-5826	441	1	λ	λ	NOUN
ejpam-5826	441	2	x0	x0	PROPN
ejpam-5826	441	3	)	)	PUNCT
ejpam-5826	441	4	≤	≤	NUM
ejpam-5826	441	5	δd(tn	δd(tn	ADJ
ejpam-5826	441	6	λ	λ	X
ejpam-5826	441	7	x0	x0	PROPN
ejpam-5826	441	8	,	,	PUNCT
ejpam-5826	441	9	t	t	PROPN
ejpam-5826	441	10	n+1	n+1	PROPN
ejpam-5826	441	11	λ	λ	X
ejpam-5826	441	12	x0	x0	PROPN
ejpam-5826	441	13	)	)	PUNCT
ejpam-5826	441	14	where	where	SCONJ
ejpam-5826	441	15	δ	δ	NOUN
ejpam-5826	441	16	:	:	PUNCT
ejpam-5826	441	17	=	=	SYM
ejpam-5826	441	18	b	b	PROPN
ejpam-5826	441	19	1−	1−	NUM
ejpam-5826	441	20	b	b	PROPN
ejpam-5826	441	21	.	.	PUNCT
ejpam-5826	442	1	similarly	similarly	ADV
ejpam-5826	442	2	,	,	PUNCT
ejpam-5826	442	3	with	with	ADP
ejpam-5826	442	4	condition	condition	NOUN
ejpam-5826	442	5	(	(	PUNCT
ejpam-5826	442	6	iii	iii	NOUN
ejpam-5826	442	7	)	)	PUNCT
ejpam-5826	442	8	of	of	ADP
ejpam-5826	442	9	definition	definition	NOUN
ejpam-5826	442	10	3	3	NUM
ejpam-5826	442	11	,	,	PUNCT
ejpam-5826	442	12	we	we	PRON
ejpam-5826	442	13	obtain	obtain	VERB
ejpam-5826	442	14	d(tn+1	d(tn+1	PROPN
ejpam-5826	442	15	λ	λ	PROPN
ejpam-5826	442	16	x0	x0	PROPN
ejpam-5826	442	17	,	,	PUNCT
ejpam-5826	442	18	t	t	PROPN
ejpam-5826	442	19	n+2	n+2	NUM
ejpam-5826	443	1	λ	λ	NOUN
ejpam-5826	443	2	x0	x0	PROPN
ejpam-5826	443	3	)	)	PUNCT
ejpam-5826	444	1	≤	≤	NUM
ejpam-5826	444	2	c	c	NOUN
ejpam-5826	444	3	(	(	PUNCT
ejpam-5826	444	4	d(tn	d(tn	PROPN
ejpam-5826	444	5	λ	λ	NOUN
ejpam-5826	444	6	x0	x0	PROPN
ejpam-5826	444	7	,	,	PUNCT
ejpam-5826	444	8	t	t	PROPN
ejpam-5826	444	9	n+2	n+2	NUM
ejpam-5826	444	10	λ	λ	NOUN
ejpam-5826	444	11	x0	x0	PROPN
ejpam-5826	444	12	)	)	PUNCT
ejpam-5826	445	1	+	+	PUNCT
ejpam-5826	445	2	d(tn+1	d(tn+1	ADJ
ejpam-5826	445	3	λ	λ	PROPN
ejpam-5826	445	4	x0	x0	PROPN
ejpam-5826	445	5	,	,	PUNCT
ejpam-5826	445	6	t	t	PROPN
ejpam-5826	445	7	n+1	n+1	PROPN
ejpam-5826	445	8	λ	λ	X
ejpam-5826	445	9	x0	x0	PROPN
ejpam-5826	445	10	)	)	PUNCT
ejpam-5826	445	11	)	)	PUNCT
ejpam-5826	445	12	.	.	PUNCT
ejpam-5826	446	1	hence	hence	ADV
ejpam-5826	446	2	d(tn+1	d(tn+1	VERB
ejpam-5826	446	3	λ	λ	PROPN
ejpam-5826	446	4	x0	x0	PROPN
ejpam-5826	446	5	,	,	PUNCT
ejpam-5826	446	6	t	t	PROPN
ejpam-5826	447	1	n+2	n+2	NUM
ejpam-5826	447	2	λ	λ	NOUN
ejpam-5826	447	3	x0	x0	PROPN
ejpam-5826	447	4	)	)	PUNCT
ejpam-5826	447	5	≤	≤	NUM
ejpam-5826	447	6	δd(tn	δd(tn	ADJ
ejpam-5826	447	7	λ	λ	X
ejpam-5826	447	8	x0	x0	PROPN
ejpam-5826	447	9	,	,	PUNCT
ejpam-5826	447	10	t	t	PROPN
ejpam-5826	447	11	n+1	n+1	PROPN
ejpam-5826	447	12	λ	λ	PROPN
ejpam-5826	447	13	x0	x0	PROPN
ejpam-5826	447	14	)	)	PUNCT
ejpam-5826	447	15	.	.	PUNCT
ejpam-5826	448	1	this	this	DET
ejpam-5826	448	2	inequality	inequality	NOUN
ejpam-5826	448	3	is	be	AUX
ejpam-5826	448	4	true	true	ADJ
ejpam-5826	448	5	for	for	ADP
ejpam-5826	448	6	every	every	DET
ejpam-5826	448	7	n.	n.	NOUN
ejpam-5826	448	8	so	so	SCONJ
ejpam-5826	448	9	that	that	SCONJ
ejpam-5826	448	10	{	{	PUNCT
ejpam-5826	448	11	tn	tn	PROPN
ejpam-5826	448	12	λ	λ	PROPN
ejpam-5826	448	13	(	(	PUNCT
ejpam-5826	448	14	x0)}∞n=0	x0)}∞n=0	PROPN
ejpam-5826	448	15	is	be	AUX
ejpam-5826	448	16	a	a	DET
ejpam-5826	448	17	cauchy	cauchy	ADJ
ejpam-5826	448	18	sequence	sequence	NOUN
ejpam-5826	448	19	and	and	CCONJ
ejpam-5826	448	20	therefore	therefore	ADV
ejpam-5826	448	21	converges	converge	VERB
ejpam-5826	448	22	to	to	ADP
ejpam-5826	448	23	some	some	DET
ejpam-5826	448	24	point	point	NOUN
ejpam-5826	448	25	p	p	PROPN
ejpam-5826	448	26	∈	∈	PROPN
ejpam-5826	448	27	q.	q.	NOUN
ejpam-5826	448	28	(	(	PUNCT
ejpam-5826	448	29	i	i	NOUN
ejpam-5826	448	30	)	)	PUNCT
ejpam-5826	448	31	we	we	PRON
ejpam-5826	448	32	now	now	ADV
ejpam-5826	448	33	prove	prove	VERB
ejpam-5826	448	34	that	that	SCONJ
ejpam-5826	448	35	p	p	NOUN
ejpam-5826	448	36	is	be	AUX
ejpam-5826	448	37	a	a	DET
ejpam-5826	448	38	fixed	fix	VERB
ejpam-5826	448	39	point	point	NOUN
ejpam-5826	448	40	of	of	ADP
ejpam-5826	448	41	tλ	tλ	ADP
ejpam-5826	448	42	.	.	PUNCT
ejpam-5826	448	43	suppose	suppose	VERB
ejpam-5826	448	44	tλp	tλp	PROPN
ejpam-5826	448	45	̸=	̸=	PROPN
ejpam-5826	448	46	p.	p.	NOUN
ejpam-5826	448	47	we	we	PRON
ejpam-5826	448	48	consider	consider	VERB
ejpam-5826	448	49	the	the	DET
ejpam-5826	448	50	ball	ball	NOUN
ejpam-5826	448	51	b	b	PROPN
ejpam-5826	448	52	=	=	PRON
ejpam-5826	448	53	{	{	PUNCT
ejpam-5826	448	54	p	p	X
ejpam-5826	448	55	∈	∈	PROPN
ejpam-5826	448	56	q	q	NOUN
ejpam-5826	448	57	:	:	PUNCT
ejpam-5826	448	58	d(p	d(p	PROPN
ejpam-5826	448	59	,	,	PUNCT
ejpam-5826	448	60	x	x	NOUN
ejpam-5826	448	61	)	)	PUNCT
ejpam-5826	448	62	≤	≤	NUM
ejpam-5826	448	63	1	1	NUM
ejpam-5826	448	64	4	4	NUM
ejpam-5826	448	65	d(p	d(p	PROPN
ejpam-5826	448	66	,	,	PUNCT
ejpam-5826	448	67	tλp	tλp	NOUN
ejpam-5826	448	68	)	)	PUNCT
ejpam-5826	448	69	}	}	PUNCT
ejpam-5826	448	70	.	.	PUNCT
ejpam-5826	449	1	observe	observe	VERB
ejpam-5826	449	2	that	that	SCONJ
ejpam-5826	449	3	d(x	d(x	NOUN
ejpam-5826	449	4	,	,	PUNCT
ejpam-5826	449	5	tλp	tλp	PROPN
ejpam-5826	449	6	)	)	PUNCT
ejpam-5826	449	7	≥	≥	NOUN
ejpam-5826	449	8	3	3	NUM
ejpam-5826	449	9	4d(p	4d(p	NUM
ejpam-5826	449	10	,	,	PUNCT
ejpam-5826	449	11	tλp	tλp	PROPN
ejpam-5826	449	12	)	)	PUNCT
ejpam-5826	449	13	for	for	ADP
ejpam-5826	449	14	every	every	DET
ejpam-5826	449	15	point	point	NOUN
ejpam-5826	449	16	p	p	PROPN
ejpam-5826	449	17	∈	∈	PROPN
ejpam-5826	449	18	b.	b.	PROPN
ejpam-5826	450	1	so	so	ADV
ejpam-5826	450	2	there	there	PRON
ejpam-5826	450	3	exists	exist	VERB
ejpam-5826	450	4	a	a	DET
ejpam-5826	450	5	number	number	NOUN
ejpam-5826	450	6	n	n	ADP
ejpam-5826	450	7	such	such	ADJ
ejpam-5826	450	8	that	that	PRON
ejpam-5826	450	9	tn	tn	PROPN
ejpam-5826	450	10	λ	λ	PROPN
ejpam-5826	450	11	x0	x0	PROPN
ejpam-5826	450	12	∈	∈	PROPN
ejpam-5826	450	13	b	b	PROPN
ejpam-5826	450	14	for	for	ADP
ejpam-5826	450	15	each	each	DET
ejpam-5826	450	16	n	n	DET
ejpam-5826	450	17	≥	≥	NOUN
ejpam-5826	450	18	n	n	NOUN
ejpam-5826	450	19	.	.	PUNCT
ejpam-5826	451	1	now	now	ADV
ejpam-5826	451	2	taking	take	VERB
ejpam-5826	451	3	x	x	PUNCT
ejpam-5826	451	4	=	=	PUNCT
ejpam-5826	451	5	tn	tn	PROPN
ejpam-5826	451	6	λ	λ	PROPN
ejpam-5826	451	7	x0	x0	PROPN
ejpam-5826	451	8	and	and	CCONJ
ejpam-5826	451	9	y	y	PROPN
ejpam-5826	452	1	=	=	PUNCT
ejpam-5826	452	2	p.	p.	NOUN
ejpam-5826	452	3	we	we	PRON
ejpam-5826	452	4	must	must	AUX
ejpam-5826	452	5	have	have	VERB
ejpam-5826	452	6	one	one	NUM
ejpam-5826	452	7	of	of	ADP
ejpam-5826	452	8	the	the	DET
ejpam-5826	452	9	following	follow	VERB
ejpam-5826	452	10	situations	situation	NOUN
ejpam-5826	452	11	:	:	PUNCT
ejpam-5826	452	12	(	(	PUNCT
ejpam-5826	452	13	a	a	X
ejpam-5826	452	14	)	)	PUNCT
ejpam-5826	452	15	d(tn+1	d(tn+1	PROPN
ejpam-5826	452	16	λ	λ	PROPN
ejpam-5826	452	17	x0	x0	PROPN
ejpam-5826	452	18	,	,	PUNCT
ejpam-5826	452	19	tλp	tλp	ADJ
ejpam-5826	452	20	)	)	PUNCT
ejpam-5826	452	21	≤	≤	NUM
ejpam-5826	453	1	ad(tn	ad(tn	NOUN
ejpam-5826	454	1	λ	λ	PROPN
ejpam-5826	454	2	x0	x0	PROPN
ejpam-5826	454	3	,	,	PUNCT
ejpam-5826	454	4	p	p	X
ejpam-5826	454	5	)	)	PUNCT
ejpam-5826	454	6	,	,	PUNCT
ejpam-5826	454	7	which	which	PRON
ejpam-5826	454	8	sets	set	VERB
ejpam-5826	454	9	a	a	DET
ejpam-5826	454	10	contradiction	contradiction	NOUN
ejpam-5826	454	11	as	as	SCONJ
ejpam-5826	454	12	follows	follow	VERB
ejpam-5826	454	13	d(tn	d(tn	PROPN
ejpam-5826	454	14	λ	λ	NOUN
ejpam-5826	454	15	x0	x0	PROPN
ejpam-5826	454	16	,	,	PUNCT
ejpam-5826	454	17	p	p	NOUN
ejpam-5826	454	18	)	)	PUNCT
ejpam-5826	454	19	≤	≤	NUM
ejpam-5826	454	20	1	1	NUM
ejpam-5826	454	21	4	4	NUM
ejpam-5826	454	22	d(p	d(p	PROPN
ejpam-5826	454	23	,	,	PUNCT
ejpam-5826	454	24	tλp	tλp	NOUN
ejpam-5826	454	25	)	)	PUNCT
ejpam-5826	454	26	<	<	X
ejpam-5826	454	27	d(tn+1	d(tn+1	PROPN
ejpam-5826	454	28	λ	λ	X
ejpam-5826	454	29	x0	x0	PROPN
ejpam-5826	454	30	,	,	PUNCT
ejpam-5826	454	31	tλp	tλp	PROPN
ejpam-5826	454	32	)	)	PUNCT
ejpam-5826	454	33	,	,	PUNCT
ejpam-5826	454	34	(	(	PUNCT
ejpam-5826	454	35	b	b	X
ejpam-5826	454	36	)	)	PUNCT
ejpam-5826	454	37	d(tn	d(tn	PROPN
ejpam-5826	454	38	λ	λ	NOUN
ejpam-5826	454	39	x0	x0	PROPN
ejpam-5826	454	40	,	,	PUNCT
ejpam-5826	454	41	tλp	tλp	ADJ
ejpam-5826	454	42	)	)	PUNCT
ejpam-5826	454	43	≤	≤	NOUN
ejpam-5826	454	44	b	b	X
ejpam-5826	454	45	(	(	PUNCT
ejpam-5826	454	46	d(tn	d(tn	PROPN
ejpam-5826	454	47	λ	λ	NOUN
ejpam-5826	454	48	x0	x0	PROPN
ejpam-5826	454	49	,	,	PUNCT
ejpam-5826	454	50	t	t	PROPN
ejpam-5826	454	51	n+1	n+1	PROPN
ejpam-5826	454	52	λ	λ	X
ejpam-5826	454	53	x0	x0	PROPN
ejpam-5826	454	54	)	)	PUNCT
ejpam-5826	455	1	+	+	CCONJ
ejpam-5826	455	2	d(p	d(p	PROPN
ejpam-5826	455	3	,	,	PUNCT
ejpam-5826	455	4	tλp	tλp	NOUN
ejpam-5826	455	5	)	)	PUNCT
ejpam-5826	455	6	)	)	PUNCT
ejpam-5826	455	7	,	,	PUNCT
ejpam-5826	455	8	contradicting	contradict	VERB
ejpam-5826	455	9	b	b	X
ejpam-5826	455	10	(	(	PUNCT
ejpam-5826	455	11	d(tn	d(tn	PROPN
ejpam-5826	455	12	λ	λ	NOUN
ejpam-5826	455	13	x0	x0	PROPN
ejpam-5826	455	14	,	,	PUNCT
ejpam-5826	455	15	t	t	PROPN
ejpam-5826	455	16	n+1	n+1	PROPN
ejpam-5826	455	17	λ	λ	X
ejpam-5826	455	18	x0	x0	PROPN
ejpam-5826	455	19	)	)	PUNCT
ejpam-5826	456	1	+	+	CCONJ
ejpam-5826	456	2	d(p	d(p	PROPN
ejpam-5826	456	3	,	,	PUNCT
ejpam-5826	456	4	tλp	tλp	NOUN
ejpam-5826	456	5	)	)	PUNCT
ejpam-5826	456	6	)	)	PUNCT
ejpam-5826	456	7	<	<	X
ejpam-5826	457	1	1	1	NUM
ejpam-5826	457	2	2	2	NUM
ejpam-5826	457	3	(	(	PUNCT
ejpam-5826	457	4	d(tn	d(tn	PROPN
ejpam-5826	457	5	λ	λ	X
ejpam-5826	457	6	x	x	NOUN
ejpam-5826	457	7	,	,	PUNCT
ejpam-5826	457	8	p	p	NOUN
ejpam-5826	457	9	)	)	PUNCT
ejpam-5826	457	10	+	+	CCONJ
ejpam-5826	457	11	d(p	d(p	PROPN
ejpam-5826	457	12	,	,	PUNCT
ejpam-5826	457	13	tn+1	tn+1	NOUN
ejpam-5826	457	14	λ	λ	X
ejpam-5826	457	15	x0	x0	NUM
ejpam-5826	457	16	)	)	PUNCT
ejpam-5826	458	1	+	+	CCONJ
ejpam-5826	458	2	d(p	d(p	PROPN
ejpam-5826	458	3	,	,	PUNCT
ejpam-5826	458	4	tλp	tλp	NOUN
ejpam-5826	458	5	)	)	PUNCT
ejpam-5826	458	6	)	)	PUNCT
ejpam-5826	458	7	≤	≤	ADV
ejpam-5826	458	8	3	3	NUM
ejpam-5826	458	9	4	4	NUM
ejpam-5826	458	10	d(p	d(p	PROPN
ejpam-5826	458	11	,	,	PUNCT
ejpam-5826	458	12	tλp	tλp	NOUN
ejpam-5826	458	13	)	)	PUNCT
ejpam-5826	458	14	≤	≤	PUNCT
ejpam-5826	458	15	d(tn+1	d(tn+1	ADJ
ejpam-5826	458	16	λ	λ	X
ejpam-5826	458	17	x0	x0	PROPN
ejpam-5826	458	18	,	,	PUNCT
ejpam-5826	458	19	tλp	tλp	PROPN
ejpam-5826	458	20	)	)	PUNCT
ejpam-5826	458	21	(	(	PUNCT
ejpam-5826	458	22	c	c	X
ejpam-5826	458	23	)	)	PUNCT
ejpam-5826	458	24	d(tn+1	d(tn+1	PROPN
ejpam-5826	458	25	λ	λ	PROPN
ejpam-5826	458	26	x0	x0	PROPN
ejpam-5826	458	27	,	,	PUNCT
ejpam-5826	458	28	tλp	tλp	ADJ
ejpam-5826	458	29	)	)	PUNCT
ejpam-5826	458	30	≤	≤	NUM
ejpam-5826	458	31	c	c	NOUN
ejpam-5826	458	32	(	(	PUNCT
ejpam-5826	458	33	d(tn	d(tn	PROPN
ejpam-5826	458	34	λ	λ	NOUN
ejpam-5826	458	35	x0	x0	PROPN
ejpam-5826	458	36	,	,	PUNCT
ejpam-5826	458	37	tλ(p	tλ(p	NOUN
ejpam-5826	458	38	)	)	PUNCT
ejpam-5826	458	39	)	)	PUNCT
ejpam-5826	459	1	+	+	PUNCT
ejpam-5826	459	2	d(tn+1	d(tn+1	ADJ
ejpam-5826	459	3	λ	λ	NOUN
ejpam-5826	459	4	x0	x0	PROPN
ejpam-5826	459	5	,	,	PUNCT
ejpam-5826	459	6	p	p	NOUN
ejpam-5826	459	7	)	)	PUNCT
ejpam-5826	459	8	)	)	PUNCT
ejpam-5826	460	1	contradicting	contradict	VERB
ejpam-5826	460	2	c	c	NOUN
ejpam-5826	460	3	(	(	PUNCT
ejpam-5826	460	4	d(tn	d(tn	PROPN
ejpam-5826	460	5	λ	λ	NOUN
ejpam-5826	460	6	x0	x0	PROPN
ejpam-5826	460	7	,	,	PUNCT
ejpam-5826	460	8	tλ(p	tλ(p	NOUN
ejpam-5826	460	9	)	)	PUNCT
ejpam-5826	460	10	)	)	PUNCT
ejpam-5826	461	1	+	+	PUNCT
ejpam-5826	461	2	d(tn+1	d(tn+1	ADJ
ejpam-5826	461	3	λ	λ	NOUN
ejpam-5826	461	4	x0	x0	PROPN
ejpam-5826	461	5	,	,	PUNCT
ejpam-5826	461	6	p	p	NOUN
ejpam-5826	461	7	)	)	PUNCT
ejpam-5826	461	8	)	)	PUNCT
ejpam-5826	462	1	<	<	X
ejpam-5826	462	2	1	1	NUM
ejpam-5826	462	3	2	2	NUM
ejpam-5826	462	4	(	(	PUNCT
ejpam-5826	462	5	d(tn	d(tn	PROPN
ejpam-5826	462	6	λ	λ	NOUN
ejpam-5826	462	7	x0	x0	PROPN
ejpam-5826	462	8	,	,	PUNCT
ejpam-5826	462	9	p	p	X
ejpam-5826	462	10	)	)	PUNCT
ejpam-5826	463	1	+	+	CCONJ
ejpam-5826	463	2	d(p	d(p	PROPN
ejpam-5826	463	3	,	,	PUNCT
ejpam-5826	463	4	tλp	tλp	NOUN
ejpam-5826	463	5	)	)	PUNCT
ejpam-5826	463	6	+	+	SYM
ejpam-5826	463	7	d(tn+1	d(tn+1	ADJ
ejpam-5826	463	8	λ	λ	NOUN
ejpam-5826	463	9	x0	x0	PROPN
ejpam-5826	463	10	,	,	PUNCT
ejpam-5826	463	11	p	p	NOUN
ejpam-5826	463	12	)	)	PUNCT
ejpam-5826	463	13	)	)	PUNCT
ejpam-5826	463	14	≤	≤	ADV
ejpam-5826	463	15	3	3	NUM
ejpam-5826	463	16	4	4	NUM
ejpam-5826	463	17	d(p	d(p	PROPN
ejpam-5826	463	18	,	,	PUNCT
ejpam-5826	463	19	tλ	tλ	ADP
ejpam-5826	463	20	,	,	PUNCT
ejpam-5826	463	21	p	p	NOUN
ejpam-5826	463	22	)	)	PUNCT
ejpam-5826	463	23	≤	≤	NUM
ejpam-5826	464	1	d(tn+1	d(tn+1	ADJ
ejpam-5826	464	2	λ	λ	PROPN
ejpam-5826	464	3	x0	x0	PROPN
ejpam-5826	464	4	,	,	PUNCT
ejpam-5826	464	5	tλp	tλp	ADJ
ejpam-5826	464	6	)	)	PUNCT
ejpam-5826	464	7	thus	thus	ADV
ejpam-5826	464	8	tλp	tλp	X
ejpam-5826	465	1	=	=	PUNCT
ejpam-5826	465	2	p.	p.	NOUN
ejpam-5826	465	3	now	now	ADV
ejpam-5826	465	4	we	we	PRON
ejpam-5826	465	5	show	show	VERB
ejpam-5826	465	6	that	that	SCONJ
ejpam-5826	465	7	this	this	DET
ejpam-5826	465	8	fixed	fix	VERB
ejpam-5826	465	9	point	point	NOUN
ejpam-5826	465	10	p	p	NOUN
ejpam-5826	465	11	is	be	AUX
ejpam-5826	465	12	unique	unique	ADJ
ejpam-5826	465	13	.	.	PUNCT
ejpam-5826	466	1	suppose	suppose	VERB
ejpam-5826	466	2	that	that	SCONJ
ejpam-5826	466	3	this	this	PRON
ejpam-5826	466	4	is	be	AUX
ejpam-5826	466	5	not	not	PART
ejpam-5826	466	6	true	true	ADJ
ejpam-5826	466	7	.	.	PUNCT
ejpam-5826	467	1	let	let	VERB
ejpam-5826	467	2	tλp	tλp	NOUN
ejpam-5826	467	3	′	′	NOUN
ejpam-5826	468	1	=	=	PUNCT
ejpam-5826	469	1	p	p	NOUN
ejpam-5826	469	2	′	′	NOUN
ejpam-5826	469	3	for	for	ADP
ejpam-5826	469	4	some	some	DET
ejpam-5826	469	5	point	point	NOUN
ejpam-5826	469	6	p	p	NOUN
ejpam-5826	470	1	′	′	NUM
ejpam-5826	470	2	̸=	̸=	PROPN
ejpam-5826	470	3	p	p	PROPN
ejpam-5826	470	4	∈	∈	PROPN
ejpam-5826	470	5	q.	q.	NOUN
ejpam-5826	470	6	then	then	ADV
ejpam-5826	470	7	d(tλp	d(tλp	PROPN
ejpam-5826	470	8	,	,	PUNCT
ejpam-5826	470	9	tλp	tλp	NOUN
ejpam-5826	470	10	′	′	NUM
ejpam-5826	470	11	)	)	PUNCT
ejpam-5826	471	1	=	=	SYM
ejpam-5826	471	2	d(p	d(p	PROPN
ejpam-5826	471	3	,	,	PUNCT
ejpam-5826	471	4	p	p	NOUN
ejpam-5826	471	5	′	′	NOUN
ejpam-5826	471	6	)	)	PUNCT
ejpam-5826	471	7	a.	a.	PROPN
ejpam-5826	471	8	r.	r.	PROPN
ejpam-5826	471	9	khan	khan	PROPN
ejpam-5826	471	10	et	et	PROPN
ejpam-5826	471	11	al	al	PROPN
ejpam-5826	471	12	.	.	PUNCT
ejpam-5826	471	13	/	/	SYM
ejpam-5826	471	14	eur	eur	PROPN
ejpam-5826	471	15	.	.	PUNCT
ejpam-5826	472	1	j.	j.	PROPN
ejpam-5826	472	2	pure	pure	PROPN
ejpam-5826	472	3	appl	appl	PROPN
ejpam-5826	472	4	.	.	PROPN
ejpam-5826	472	5	math	math	PROPN
ejpam-5826	472	6	,	,	PUNCT
ejpam-5826	472	7	18	18	NUM
ejpam-5826	472	8	(	(	PUNCT
ejpam-5826	472	9	2	2	NUM
ejpam-5826	472	10	)	)	PUNCT
ejpam-5826	472	11	(	(	PUNCT
ejpam-5826	472	12	2025	2025	NUM
ejpam-5826	472	13	)	)	PUNCT
ejpam-5826	472	14	,	,	PUNCT
ejpam-5826	472	15	5826	5826	NUM
ejpam-5826	472	16	19	19	NUM
ejpam-5826	472	17	of	of	ADP
ejpam-5826	472	18	23	23	NUM
ejpam-5826	472	19	d(tλp	d(tλp	NOUN
ejpam-5826	472	20	,	,	PUNCT
ejpam-5826	472	21	tλp	tλp	NOUN
ejpam-5826	472	22	′	′	NUM
ejpam-5826	472	23	)	)	PUNCT
ejpam-5826	473	1	>	>	X
ejpam-5826	474	1	d(p	d(p	PROPN
ejpam-5826	474	2	,	,	PUNCT
ejpam-5826	474	3	tλp	tλp	NOUN
ejpam-5826	474	4	)	)	PUNCT
ejpam-5826	474	5	+	+	CCONJ
ejpam-5826	474	6	d(p	d(p	PROPN
ejpam-5826	474	7	′	′	NUM
ejpam-5826	474	8	,	,	PUNCT
ejpam-5826	474	9	tλp	tλp	INTJ
ejpam-5826	474	10	′	′	NUM
ejpam-5826	474	11	)	)	PUNCT
ejpam-5826	474	12	d(tλp	d(tλp	NOUN
ejpam-5826	474	13	,	,	PUNCT
ejpam-5826	474	14	tλp	tλp	NOUN
ejpam-5826	474	15	′	′	NUM
ejpam-5826	474	16	)	)	PUNCT
ejpam-5826	475	1	=	=	SYM
ejpam-5826	475	2	1	1	NUM
ejpam-5826	475	3	2	2	NUM
ejpam-5826	475	4	(	(	PUNCT
ejpam-5826	475	5	d(p	d(p	PROPN
ejpam-5826	475	6	,	,	PUNCT
ejpam-5826	475	7	tλp	tλp	NOUN
ejpam-5826	475	8	′	′	NUM
ejpam-5826	475	9	)	)	PUNCT
ejpam-5826	476	1	+	+	CCONJ
ejpam-5826	476	2	d(p	d(p	PROPN
ejpam-5826	476	3	′	′	NUM
ejpam-5826	476	4	,	,	PUNCT
ejpam-5826	476	5	tλ(p	tλ(p	NUM
ejpam-5826	476	6	)	)	PUNCT
ejpam-5826	476	7	)	)	PUNCT
ejpam-5826	476	8	)	)	PUNCT
ejpam-5826	477	1	so	so	SCONJ
ejpam-5826	477	2	that	that	SCONJ
ejpam-5826	477	3	none	none	NOUN
ejpam-5826	477	4	of	of	ADP
ejpam-5826	477	5	the	the	DET
ejpam-5826	477	6	three	three	NUM
ejpam-5826	477	7	conditions	condition	NOUN
ejpam-5826	477	8	of	of	ADP
ejpam-5826	477	9	zamfirescue	zamfirescue	NOUN
ejpam-5826	477	10	map	map	NOUN
ejpam-5826	477	11	is	be	AUX
ejpam-5826	477	12	satisfied	satisfied	ADJ
ejpam-5826	477	13	by	by	ADP
ejpam-5826	477	14	the	the	DET
ejpam-5826	477	15	points	point	NOUN
ejpam-5826	477	16	p	p	NOUN
ejpam-5826	477	17	and	and	CCONJ
ejpam-5826	477	18	p	p	NOUN
ejpam-5826	477	19	′	′	NOUN
ejpam-5826	477	20	.	.	PUNCT
ejpam-5826	478	1	this	this	PRON
ejpam-5826	478	2	is	be	AUX
ejpam-5826	478	3	a	a	DET
ejpam-5826	478	4	contradiction	contradiction	NOUN
ejpam-5826	478	5	.	.	PUNCT
ejpam-5826	479	1	hence	hence	ADV
ejpam-5826	479	2	tλ	tλ	AUX
ejpam-5826	479	3	has	have	VERB
ejpam-5826	479	4	a	a	DET
ejpam-5826	479	5	unique	unique	ADJ
ejpam-5826	479	6	fixed	fix	VERB
ejpam-5826	479	7	point	point	NOUN
ejpam-5826	479	8	.	.	PUNCT
ejpam-5826	480	1	(	(	PUNCT
ejpam-5826	480	2	ii	ii	NOUN
ejpam-5826	480	3	)	)	PUNCT
ejpam-5826	480	4	obvious	obvious	ADJ
ejpam-5826	480	5	.	.	PUNCT
ejpam-5826	481	1	it	it	PRON
ejpam-5826	481	2	is	be	AUX
ejpam-5826	481	3	natural	natural	ADJ
ejpam-5826	481	4	to	to	PART
ejpam-5826	481	5	ask	ask	VERB
ejpam-5826	481	6	,	,	PUNCT
ejpam-5826	481	7	when	when	SCONJ
ejpam-5826	481	8	the	the	DET
ejpam-5826	481	9	assumption	assumption	NOUN
ejpam-5826	481	10	that	that	PRON
ejpam-5826	481	11	tλ	tλ	NOUN
ejpam-5826	481	12	is	be	AUX
ejpam-5826	481	13	asymptotically	asymptotically	ADV
ejpam-5826	481	14	regular	regular	ADJ
ejpam-5826	481	15	in	in	ADP
ejpam-5826	481	16	theorem	theorem	NOUN
ejpam-5826	481	17	7	7	NUM
ejpam-5826	481	18	,	,	PUNCT
ejpam-5826	481	19	is	be	AUX
ejpam-5826	481	20	satisfied	satisfied	ADJ
ejpam-5826	481	21	.	.	PUNCT
ejpam-5826	482	1	for	for	ADP
ejpam-5826	482	2	an	an	DET
ejpam-5826	482	3	affirmative	affirmative	ADJ
ejpam-5826	482	4	answer	answer	NOUN
ejpam-5826	482	5	to	to	ADP
ejpam-5826	482	6	this	this	DET
ejpam-5826	482	7	question	question	NOUN
ejpam-5826	482	8	,	,	PUNCT
ejpam-5826	482	9	we	we	PRON
ejpam-5826	482	10	need	need	VERB
ejpam-5826	482	11	the	the	DET
ejpam-5826	482	12	following	follow	VERB
ejpam-5826	482	13	useful	useful	ADJ
ejpam-5826	482	14	result	result	NOUN
ejpam-5826	482	15	.	.	PUNCT
ejpam-5826	483	1	theorem	theorem	VERB
ejpam-5826	483	2	9	9	NUM
ejpam-5826	483	3	.	.	PUNCT
ejpam-5826	484	1	[	[	X
ejpam-5826	484	2	9	9	NUM
ejpam-5826	484	3	,	,	PUNCT
ejpam-5826	484	4	theorem	theorem	VERB
ejpam-5826	484	5	5.2.7	5.2.7	X
ejpam-5826	484	6	]	]	X
ejpam-5826	484	7	let	let	VERB
ejpam-5826	484	8	j	j	PROPN
ejpam-5826	484	9	be	be	AUX
ejpam-5826	484	10	a	a	DET
ejpam-5826	484	11	nonempty	nonempty	ADJ
ejpam-5826	484	12	convex	convex	NOUN
ejpam-5826	484	13	subset	subset	NOUN
ejpam-5826	484	14	of	of	ADP
ejpam-5826	484	15	a	a	DET
ejpam-5826	484	16	normed	normed	ADJ
ejpam-5826	484	17	space	space	NOUN
ejpam-5826	484	18	q	q	PROPN
ejpam-5826	484	19	and	and	CCONJ
ejpam-5826	484	20	t	t	PROPN
ejpam-5826	484	21	be	be	AUX
ejpam-5826	484	22	non	non	ADJ
ejpam-5826	484	23	-	-	ADJ
ejpam-5826	484	24	expansive	expansive	ADJ
ejpam-5826	484	25	map	map	NOUN
ejpam-5826	484	26	on	on	ADP
ejpam-5826	484	27	j	j	PROPN
ejpam-5826	484	28	.	.	PUNCT
ejpam-5826	485	1	if	if	SCONJ
ejpam-5826	485	2	for	for	ADP
ejpam-5826	485	3	x0	x0	PROPN
ejpam-5826	485	4	∈	∈	PROPN
ejpam-5826	485	5	j	j	PROPN
ejpam-5826	485	6	,	,	PUNCT
ejpam-5826	485	7	{	{	PUNCT
ejpam-5826	485	8	tn	tn	PROPN
ejpam-5826	485	9	λ	λ	PROPN
ejpam-5826	485	10	x0	x0	PROPN
ejpam-5826	485	11	}	}	PUNCT
ejpam-5826	485	12	is	be	AUX
ejpam-5826	485	13	bounded	bound	VERB
ejpam-5826	485	14	,	,	PUNCT
ejpam-5826	485	15	then	then	ADV
ejpam-5826	485	16	the	the	DET
ejpam-5826	485	17	average	average	ADJ
ejpam-5826	485	18	map	map	NOUN
ejpam-5826	485	19	tλ	tλ	NOUN
ejpam-5826	485	20	is	be	AUX
ejpam-5826	485	21	asymptotically	asymptotically	ADV
ejpam-5826	485	22	regular	regular	ADJ
ejpam-5826	485	23	at	at	ADP
ejpam-5826	485	24	x0	x0	PROPN
ejpam-5826	485	25	.	.	PUNCT
ejpam-5826	486	1	for	for	ADP
ejpam-5826	486	2	the	the	DET
ejpam-5826	486	3	existence	existence	NOUN
ejpam-5826	486	4	of	of	ADP
ejpam-5826	486	5	fixed	fix	VERB
ejpam-5826	486	6	points	point	NOUN
ejpam-5826	486	7	,	,	PUNCT
ejpam-5826	486	8	apart	apart	ADV
ejpam-5826	486	9	from	from	ADP
ejpam-5826	486	10	the	the	DET
ejpam-5826	486	11	other	other	ADJ
ejpam-5826	486	12	conditions	condition	NOUN
ejpam-5826	486	13	,	,	PUNCT
ejpam-5826	486	14	huang	huang	PROPN
ejpam-5826	486	15	and	and	CCONJ
ejpam-5826	486	16	qian	qian	PROPN
ejpam-5826	486	17	(	(	PUNCT
ejpam-5826	486	18	[	[	X
ejpam-5826	486	19	14	14	NUM
ejpam-5826	486	20	,	,	PUNCT
ejpam-5826	486	21	theorem	theorem	VERB
ejpam-5826	486	22	2.5	2.5	NUM
ejpam-5826	486	23	]	]	PUNCT
ejpam-5826	486	24	)	)	PUNCT
ejpam-5826	486	25	have	have	AUX
ejpam-5826	486	26	imposed	impose	VERB
ejpam-5826	486	27	continuity	continuity	NOUN
ejpam-5826	486	28	condition	condition	NOUN
ejpam-5826	486	29	on	on	ADP
ejpam-5826	486	30	the	the	DET
ejpam-5826	486	31	mappings	mapping	NOUN
ejpam-5826	486	32	already	already	ADV
ejpam-5826	486	33	satisfying	satisfy	VERB
ejpam-5826	486	34	contractive	contractive	ADJ
ejpam-5826	486	35	condition	condition	NOUN
ejpam-5826	486	36	similar	similar	ADJ
ejpam-5826	486	37	to	to	ADP
ejpam-5826	486	38	(	(	PUNCT
ejpam-5826	486	39	1	1	NUM
ejpam-5826	486	40	)	)	PUNCT
ejpam-5826	486	41	.	.	PUNCT
ejpam-5826	487	1	in	in	ADP
ejpam-5826	487	2	the	the	DET
ejpam-5826	487	3	result	result	NOUN
ejpam-5826	487	4	to	to	PART
ejpam-5826	487	5	follow	follow	VERB
ejpam-5826	487	6	,	,	PUNCT
ejpam-5826	487	7	we	we	PRON
ejpam-5826	487	8	employ	employ	VERB
ejpam-5826	487	9	weak	weak	ADJ
ejpam-5826	487	10	requirement	requirement	NOUN
ejpam-5826	487	11	of	of	ADP
ejpam-5826	487	12	nonexpansiveness	nonexpansiveness	NOUN
ejpam-5826	487	13	to	to	PART
ejpam-5826	487	14	get	get	VERB
ejpam-5826	487	15	nonexpansive	nonexpansive	ADJ
ejpam-5826	487	16	version	version	NOUN
ejpam-5826	487	17	of	of	ADP
ejpam-5826	487	18	górnicki	górnicki	PROPN
ejpam-5826	487	19	result	result	NOUN
ejpam-5826	487	20	for	for	ADP
ejpam-5826	487	21	the	the	DET
ejpam-5826	487	22	average	average	ADJ
ejpam-5826	487	23	mapping	mapping	NOUN
ejpam-5826	487	24	.	.	PUNCT
ejpam-5826	488	1	theorem	theorem	ADJ
ejpam-5826	488	2	10	10	NUM
ejpam-5826	488	3	.	.	PUNCT
ejpam-5826	489	1	let	let	VERB
ejpam-5826	489	2	j	j	PROPN
ejpam-5826	489	3	be	be	AUX
ejpam-5826	489	4	a	a	DET
ejpam-5826	489	5	nonempty	nonempty	ADJ
ejpam-5826	489	6	convex	convex	NOUN
ejpam-5826	489	7	subset	subset	NOUN
ejpam-5826	489	8	of	of	ADP
ejpam-5826	489	9	a	a	DET
ejpam-5826	489	10	normed	normed	ADJ
ejpam-5826	489	11	space	space	NOUN
ejpam-5826	489	12	q	q	PROPN
ejpam-5826	489	13	and	and	CCONJ
ejpam-5826	489	14	t	t	PROPN
ejpam-5826	489	15	:	:	PUNCT
ejpam-5826	489	16	j	j	PROPN
ejpam-5826	489	17	→	→	SYM
ejpam-5826	489	18	j	j	PROPN
ejpam-5826	489	19	be	be	AUX
ejpam-5826	489	20	non	non	ADJ
ejpam-5826	489	21	-	-	ADJ
ejpam-5826	489	22	expansive	expansive	ADJ
ejpam-5826	489	23	map	map	NOUN
ejpam-5826	489	24	satisfying	satisfying	ADJ
ejpam-5826	489	25	(	(	PUNCT
ejpam-5826	489	26	1	1	NUM
ejpam-5826	489	27	)	)	PUNCT
ejpam-5826	489	28	.	.	PUNCT
ejpam-5826	490	1	if	if	SCONJ
ejpam-5826	490	2	for	for	ADP
ejpam-5826	490	3	x0	x0	PROPN
ejpam-5826	490	4	∈	∈	PROPN
ejpam-5826	490	5	j	j	PROPN
ejpam-5826	490	6	,	,	PUNCT
ejpam-5826	490	7	{	{	PUNCT
ejpam-5826	490	8	tn	tn	PROPN
ejpam-5826	490	9	λ	λ	PROPN
ejpam-5826	490	10	x0	x0	PROPN
ejpam-5826	490	11	}	}	PUNCT
ejpam-5826	490	12	is	be	AUX
ejpam-5826	490	13	bounded	bound	VERB
ejpam-5826	490	14	,	,	PUNCT
ejpam-5826	490	15	then	then	ADV
ejpam-5826	490	16	tλ	tλ	PRON
ejpam-5826	490	17	has	have	VERB
ejpam-5826	490	18	a	a	DET
ejpam-5826	490	19	unique	unique	ADJ
ejpam-5826	490	20	fixed	fix	VERB
ejpam-5826	490	21	point	point	NOUN
ejpam-5826	490	22	p	p	PROPN
ejpam-5826	490	23	∈	∈	PROPN
ejpam-5826	490	24	q.	q.	NOUN
ejpam-5826	490	25	moreover	moreover	ADV
ejpam-5826	490	26	,	,	PUNCT
ejpam-5826	490	27	{	{	PUNCT
ejpam-5826	490	28	xn}∞n=0	xn}∞n=0	X
ejpam-5826	490	29	,	,	PUNCT
ejpam-5826	490	30	the	the	DET
ejpam-5826	490	31	krasnoselskij	krasnoselskij	NOUN
ejpam-5826	490	32	iterative	iterative	NOUN
ejpam-5826	490	33	sequence	sequence	NOUN
ejpam-5826	490	34	converges	converge	VERB
ejpam-5826	490	35	to	to	ADP
ejpam-5826	490	36	p.	p.	NOUN
ejpam-5826	490	37	proof	proof	NOUN
ejpam-5826	490	38	.	.	PUNCT
ejpam-5826	491	1	the	the	DET
ejpam-5826	491	2	map	map	NOUN
ejpam-5826	491	3	tλ	tλ	NOUN
ejpam-5826	491	4	is	be	AUX
ejpam-5826	491	5	asymptotically	asymptotically	ADV
ejpam-5826	491	6	regular	regular	ADJ
ejpam-5826	491	7	at	at	ADP
ejpam-5826	491	8	x0	x0	PROPN
ejpam-5826	491	9	by	by	ADP
ejpam-5826	491	10	theorem	theorem	NOUN
ejpam-5826	491	11	9	9	NUM
ejpam-5826	491	12	.	.	PUNCT
ejpam-5826	492	1	now	now	ADV
ejpam-5826	492	2	the	the	DET
ejpam-5826	492	3	rest	rest	NOUN
ejpam-5826	492	4	of	of	ADP
ejpam-5826	492	5	the	the	DET
ejpam-5826	492	6	proof	proof	NOUN
ejpam-5826	492	7	is	be	AUX
ejpam-5826	492	8	similar	similar	ADJ
ejpam-5826	492	9	to	to	ADP
ejpam-5826	492	10	that	that	PRON
ejpam-5826	492	11	of	of	ADP
ejpam-5826	492	12	theorem	theorem	NOUN
ejpam-5826	492	13	1	1	NUM
ejpam-5826	492	14	.	.	NOUN
ejpam-5826	492	15	remark	remark	NOUN
ejpam-5826	492	16	1	1	NUM
ejpam-5826	492	17	.	.	PUNCT
ejpam-5826	493	1	(	(	PUNCT
ejpam-5826	493	2	1	1	X
ejpam-5826	493	3	)	)	PUNCT
ejpam-5826	493	4	theorem	theorem	VERB
ejpam-5826	493	5	2.5	2.5	NUM
ejpam-5826	493	6	of	of	ADP
ejpam-5826	493	7	khan	khan	PROPN
ejpam-5826	493	8	and	and	CCONJ
ejpam-5826	493	9	oyetuabi	oyetuabi	NOUN
ejpam-5826	494	1	[	[	X
ejpam-5826	494	2	7	7	NUM
ejpam-5826	494	3	]	]	PUNCT
ejpam-5826	494	4	,	,	PUNCT
ejpam-5826	494	5	holds	hold	VERB
ejpam-5826	494	6	in	in	ADP
ejpam-5826	494	7	a	a	DET
ejpam-5826	494	8	convex	convex	ADJ
ejpam-5826	494	9	metric	metric	ADJ
ejpam-5826	494	10	space	space	NOUN
ejpam-5826	494	11	with	with	ADP
ejpam-5826	494	12	the	the	DET
ejpam-5826	494	13	same	same	ADJ
ejpam-5826	494	14	proof	proof	NOUN
ejpam-5826	494	15	.	.	PUNCT
ejpam-5826	495	1	(	(	PUNCT
ejpam-5826	495	2	2	2	X
ejpam-5826	495	3	)	)	PUNCT
ejpam-5826	495	4	theorem	theorem	NOUN
ejpam-5826	495	5	10	10	NUM
ejpam-5826	495	6	provides	provide	VERB
ejpam-5826	495	7	a	a	DET
ejpam-5826	495	8	non	non	ADJ
ejpam-5826	495	9	-	-	ADJ
ejpam-5826	495	10	expansive	expansive	ADJ
ejpam-5826	495	11	version	version	NOUN
ejpam-5826	495	12	of	of	ADP
ejpam-5826	495	13	theorem	theorem	NOUN
ejpam-5826	495	14	1	1	NUM
ejpam-5826	495	15	with	with	ADP
ejpam-5826	495	16	a	a	DET
ejpam-5826	495	17	very	very	ADV
ejpam-5826	495	18	simple	simple	ADJ
ejpam-5826	495	19	proof	proof	NOUN
ejpam-5826	495	20	.	.	PUNCT
ejpam-5826	496	1	4	4	X
ejpam-5826	496	2	.	.	X
ejpam-5826	496	3	application	application	NOUN
ejpam-5826	496	4	:	:	PUNCT
ejpam-5826	496	5	volterra	volterra	NOUN
ejpam-5826	496	6	-	-	PUNCT
ejpam-5826	496	7	type	type	NOUN
ejpam-5826	496	8	integral	integral	ADJ
ejpam-5826	496	9	equations	equation	NOUN
ejpam-5826	496	10	in	in	ADP
ejpam-5826	496	11	this	this	DET
ejpam-5826	496	12	section	section	NOUN
ejpam-5826	496	13	,	,	PUNCT
ejpam-5826	496	14	we	we	PRON
ejpam-5826	496	15	investigate	investigate	VERB
ejpam-5826	496	16	the	the	DET
ejpam-5826	496	17	existence	existence	NOUN
ejpam-5826	496	18	and	and	CCONJ
ejpam-5826	496	19	uniqueness	uniqueness	NOUN
ejpam-5826	496	20	of	of	ADP
ejpam-5826	496	21	the	the	DET
ejpam-5826	496	22	common	common	ADJ
ejpam-5826	496	23	solution	solution	NOUN
ejpam-5826	496	24	of	of	ADP
ejpam-5826	496	25	volterra	volterra	NOUN
ejpam-5826	496	26	-	-	PUNCT
ejpam-5826	496	27	type	type	NOUN
ejpam-5826	496	28	integral	integral	ADJ
ejpam-5826	496	29	equations	equation	NOUN
ejpam-5826	496	30	,	,	PUNCT
ejpam-5826	496	31	utilizing	utilize	VERB
ejpam-5826	496	32	the	the	DET
ejpam-5826	496	33	common	common	ADJ
ejpam-5826	496	34	fixed	fix	VERB
ejpam-5826	496	35	point	point	NOUN
ejpam-5826	496	36	result	result	NOUN
ejpam-5826	496	37	established	establish	VERB
ejpam-5826	496	38	in	in	ADP
ejpam-5826	496	39	theorem	theorem	ADJ
ejpam-5826	496	40	4	4	NUM
ejpam-5826	496	41	.	.	PUNCT
ejpam-5826	497	1	volterra	volterra	NOUN
ejpam-5826	497	2	-	-	PUNCT
ejpam-5826	497	3	type	type	NOUN
ejpam-5826	497	4	integral	integral	ADJ
ejpam-5826	497	5	equations	equation	NOUN
ejpam-5826	497	6	play	play	VERB
ejpam-5826	497	7	a	a	DET
ejpam-5826	497	8	significant	significant	ADJ
ejpam-5826	497	9	role	role	NOUN
ejpam-5826	497	10	in	in	ADP
ejpam-5826	497	11	various	various	ADJ
ejpam-5826	497	12	fields	field	NOUN
ejpam-5826	497	13	,	,	PUNCT
ejpam-5826	497	14	including	include	VERB
ejpam-5826	497	15	physics	physics	NOUN
ejpam-5826	497	16	,	,	PUNCT
ejpam-5826	497	17	biology	biology	NOUN
ejpam-5826	497	18	,	,	PUNCT
ejpam-5826	497	19	and	and	CCONJ
ejpam-5826	497	20	engineering	engineering	NOUN
ejpam-5826	497	21	,	,	PUNCT
ejpam-5826	497	22	in	in	ADP
ejpam-5826	497	23	view	view	NOUN
ejpam-5826	497	24	of	of	ADP
ejpam-5826	497	25	their	their	PRON
ejpam-5826	497	26	capability	capability	NOUN
ejpam-5826	497	27	to	to	PART
ejpam-5826	497	28	model	model	VERB
ejpam-5826	497	29	systems	system	NOUN
ejpam-5826	497	30	with	with	ADP
ejpam-5826	497	31	memory	memory	NOUN
ejpam-5826	497	32	effects	effect	NOUN
ejpam-5826	497	33	.	.	PUNCT
ejpam-5826	498	1	these	these	DET
ejpam-5826	498	2	equations	equation	NOUN
ejpam-5826	498	3	are	be	AUX
ejpam-5826	498	4	crucial	crucial	ADJ
ejpam-5826	498	5	for	for	ADP
ejpam-5826	498	6	capturing	capture	VERB
ejpam-5826	498	7	the	the	DET
ejpam-5826	498	8	dynamics	dynamic	NOUN
ejpam-5826	498	9	of	of	ADP
ejpam-5826	498	10	processes	process	NOUN
ejpam-5826	498	11	where	where	SCONJ
ejpam-5826	498	12	the	the	DET
ejpam-5826	498	13	future	future	ADJ
ejpam-5826	498	14	state	state	PROPN
ejpam-5826	498	15	a.	a.	PROPN
ejpam-5826	498	16	r.	r.	PROPN
ejpam-5826	498	17	khan	khan	PROPN
ejpam-5826	498	18	et	et	PROPN
ejpam-5826	498	19	al	al	PROPN
ejpam-5826	498	20	.	.	PUNCT
ejpam-5826	498	21	/	/	SYM
ejpam-5826	498	22	eur	eur	PROPN
ejpam-5826	498	23	.	.	PUNCT
ejpam-5826	499	1	j.	j.	PROPN
ejpam-5826	499	2	pure	pure	PROPN
ejpam-5826	499	3	appl	appl	PROPN
ejpam-5826	499	4	.	.	PROPN
ejpam-5826	499	5	math	math	PROPN
ejpam-5826	499	6	,	,	PUNCT
ejpam-5826	499	7	18	18	NUM
ejpam-5826	499	8	(	(	PUNCT
ejpam-5826	499	9	2	2	NUM
ejpam-5826	499	10	)	)	PUNCT
ejpam-5826	499	11	(	(	PUNCT
ejpam-5826	499	12	2025	2025	NUM
ejpam-5826	499	13	)	)	PUNCT
ejpam-5826	499	14	,	,	PUNCT
ejpam-5826	499	15	5826	5826	NUM
ejpam-5826	499	16	20	20	NUM
ejpam-5826	499	17	of	of	ADP
ejpam-5826	499	18	23	23	NUM
ejpam-5826	499	19	depends	depend	VERB
ejpam-5826	499	20	on	on	ADP
ejpam-5826	499	21	the	the	DET
ejpam-5826	499	22	entire	entire	ADJ
ejpam-5826	499	23	history	history	NOUN
ejpam-5826	499	24	of	of	ADP
ejpam-5826	499	25	the	the	DET
ejpam-5826	499	26	system	system	NOUN
ejpam-5826	499	27	,	,	PUNCT
ejpam-5826	499	28	such	such	ADJ
ejpam-5826	499	29	as	as	ADP
ejpam-5826	499	30	in	in	ADP
ejpam-5826	499	31	viscoelastic	viscoelastic	ADJ
ejpam-5826	499	32	materials	material	NOUN
ejpam-5826	499	33	,	,	PUNCT
ejpam-5826	499	34	population	population	NOUN
ejpam-5826	499	35	dynamics	dynamic	NOUN
ejpam-5826	499	36	,	,	PUNCT
ejpam-5826	499	37	and	and	CCONJ
ejpam-5826	499	38	heat	heat	NOUN
ejpam-5826	499	39	conduction	conduction	NOUN
ejpam-5826	499	40	.	.	PUNCT
ejpam-5826	500	1	the	the	DET
ejpam-5826	500	2	importance	importance	NOUN
ejpam-5826	500	3	of	of	ADP
ejpam-5826	500	4	volterra	volterra	NOUN
ejpam-5826	500	5	-	-	PUNCT
ejpam-5826	500	6	type	type	NOUN
ejpam-5826	500	7	integral	integral	ADJ
ejpam-5826	500	8	equations	equation	NOUN
ejpam-5826	500	9	lies	lie	VERB
ejpam-5826	500	10	in	in	ADP
ejpam-5826	500	11	their	their	PRON
ejpam-5826	500	12	ability	ability	NOUN
ejpam-5826	500	13	to	to	PART
ejpam-5826	500	14	provide	provide	VERB
ejpam-5826	500	15	insights	insight	NOUN
ejpam-5826	500	16	into	into	ADP
ejpam-5826	500	17	the	the	DET
ejpam-5826	500	18	existence	existence	NOUN
ejpam-5826	500	19	and	and	CCONJ
ejpam-5826	500	20	uniqueness	uniqueness	NOUN
ejpam-5826	500	21	of	of	ADP
ejpam-5826	500	22	solutions	solution	NOUN
ejpam-5826	500	23	to	to	ADP
ejpam-5826	500	24	complex	complex	ADJ
ejpam-5826	500	25	mathematical	mathematical	ADJ
ejpam-5826	500	26	problems	problem	NOUN
ejpam-5826	500	27	.	.	PUNCT
ejpam-5826	501	1	by	by	ADP
ejpam-5826	501	2	applying	apply	VERB
ejpam-5826	501	3	fixed	fix	VERB
ejpam-5826	501	4	point	point	NOUN
ejpam-5826	501	5	theorems	theorem	NOUN
ejpam-5826	501	6	,	,	PUNCT
ejpam-5826	501	7	researchers	researcher	NOUN
ejpam-5826	501	8	can	can	AUX
ejpam-5826	501	9	establish	establish	VERB
ejpam-5826	501	10	stability	stability	NOUN
ejpam-5826	501	11	and	and	CCONJ
ejpam-5826	501	12	convergence	convergence	NOUN
ejpam-5826	501	13	of	of	ADP
ejpam-5826	501	14	these	these	DET
ejpam-5826	501	15	solutions	solution	NOUN
ejpam-5826	501	16	;	;	PUNCT
ejpam-5826	501	17	thereby	thereby	ADV
ejpam-5826	501	18	addressing	address	VERB
ejpam-5826	501	19	fundamental	fundamental	ADJ
ejpam-5826	501	20	challenges	challenge	NOUN
ejpam-5826	501	21	in	in	ADP
ejpam-5826	501	22	both	both	CCONJ
ejpam-5826	501	23	theoretical	theoretical	ADJ
ejpam-5826	501	24	and	and	CCONJ
ejpam-5826	501	25	applied	applied	ADJ
ejpam-5826	501	26	mathematics	mathematic	NOUN
ejpam-5826	501	27	.	.	PUNCT
ejpam-5826	502	1	the	the	DET
ejpam-5826	502	2	reader	reader	NOUN
ejpam-5826	502	3	interested	interested	ADJ
ejpam-5826	502	4	in	in	ADP
ejpam-5826	502	5	this	this	DET
ejpam-5826	502	6	matter	matter	NOUN
ejpam-5826	502	7	,	,	PUNCT
ejpam-5826	502	8	is	be	AUX
ejpam-5826	502	9	referred	refer	VERB
ejpam-5826	502	10	to	to	ADP
ejpam-5826	502	11	the	the	DET
ejpam-5826	502	12	recent	recent	ADJ
ejpam-5826	502	13	literature	literature	NOUN
ejpam-5826	502	14	developed	develop	VERB
ejpam-5826	502	15	in	in	ADP
ejpam-5826	502	16	[	[	X
ejpam-5826	502	17	23–25	23–25	NUM
ejpam-5826	502	18	]	]	PUNCT
ejpam-5826	502	19	.	.	PUNCT
ejpam-5826	503	1	let	let	VERB
ejpam-5826	503	2	q	q	PRON
ejpam-5826	503	3	be	be	AUX
ejpam-5826	503	4	the	the	DET
ejpam-5826	503	5	space	space	NOUN
ejpam-5826	503	6	of	of	ADP
ejpam-5826	503	7	continuous	continuous	ADJ
ejpam-5826	503	8	functions	function	NOUN
ejpam-5826	503	9	on	on	ADP
ejpam-5826	503	10	[	[	X
ejpam-5826	503	11	0	0	NUM
ejpam-5826	503	12	,	,	PUNCT
ejpam-5826	503	13	t	t	X
ejpam-5826	503	14	]	]	PUNCT
ejpam-5826	503	15	equipped	equip	VERB
ejpam-5826	503	16	with	with	ADP
ejpam-5826	503	17	the	the	DET
ejpam-5826	503	18	supremum	supremum	ADJ
ejpam-5826	503	19	norm	norm	NOUN
ejpam-5826	503	20	.	.	PUNCT
ejpam-5826	504	1	that	that	PRON
ejpam-5826	504	2	is	be	AUX
ejpam-5826	504	3	,	,	PUNCT
ejpam-5826	504	4	q	q	X
ejpam-5826	504	5	:	:	PUNCT
ejpam-5826	504	6	=	=	SYM
ejpam-5826	504	7	{	{	PUNCT
ejpam-5826	504	8	u	u	NOUN
ejpam-5826	504	9	:	:	PUNCT
ejpam-5826	504	10	[	[	X
ejpam-5826	504	11	0	0	NUM
ejpam-5826	504	12	,	,	PUNCT
ejpam-5826	504	13	t	t	X
ejpam-5826	504	14	]	]	PUNCT
ejpam-5826	504	15	→	→	PUNCT
ejpam-5826	504	16	r	r	X
ejpam-5826	504	17	:	:	PUNCT
ejpam-5826	504	18	u	u	NOUN
ejpam-5826	504	19	is	be	AUX
ejpam-5826	504	20	continuous	continuous	ADJ
ejpam-5826	504	21	}	}	PUNCT
ejpam-5826	504	22	.	.	PUNCT
ejpam-5826	505	1	define	define	VERB
ejpam-5826	505	2	a	a	DET
ejpam-5826	505	3	metric	metric	ADJ
ejpam-5826	505	4	d	d	NOUN
ejpam-5826	505	5	:	:	PUNCT
ejpam-5826	505	6	q×q	q×q	NOUN
ejpam-5826	505	7	→	→	SYM
ejpam-5826	505	8	r+	r+	NOUN
ejpam-5826	505	9	by	by	ADP
ejpam-5826	505	10	d(u	d(u	PROPN
ejpam-5826	505	11	,	,	PUNCT
ejpam-5826	505	12	v	v	NOUN
ejpam-5826	505	13	)	)	PUNCT
ejpam-5826	505	14	=	=	PUNCT
ejpam-5826	506	1	||u−	||u−	NOUN
ejpam-5826	506	2	v||∞	v||∞	NOUN
ejpam-5826	506	3	=	=	PUNCT
ejpam-5826	506	4	sup	sup	NOUN
ejpam-5826	506	5	t∈[0,t	t∈[0,t	PROPN
ejpam-5826	506	6	]	]	PUNCT
ejpam-5826	506	7	|u(t)−	|u(t)−	X
ejpam-5826	506	8	v(t)|	v(t)|	PROPN
ejpam-5826	506	9	,	,	PUNCT
ejpam-5826	506	10	u	u	NOUN
ejpam-5826	506	11	,	,	PUNCT
ejpam-5826	506	12	v	v	PROPN
ejpam-5826	506	13	∈	∈	PROPN
ejpam-5826	506	14	q.	q.	NOUN
ejpam-5826	506	15	then	then	ADV
ejpam-5826	506	16	(	(	PUNCT
ejpam-5826	506	17	q	q	X
ejpam-5826	506	18	,	,	PUNCT
ejpam-5826	506	19	d	d	NOUN
ejpam-5826	506	20	)	)	PUNCT
ejpam-5826	506	21	is	be	AUX
ejpam-5826	506	22	a	a	DET
ejpam-5826	506	23	complete	complete	ADJ
ejpam-5826	506	24	metric	metric	ADJ
ejpam-5826	506	25	space	space	NOUN
ejpam-5826	506	26	.	.	PUNCT
ejpam-5826	507	1	we	we	PRON
ejpam-5826	507	2	consider	consider	VERB
ejpam-5826	507	3	the	the	DET
ejpam-5826	507	4	following	follow	VERB
ejpam-5826	507	5	volterra	volterra	NOUN
ejpam-5826	507	6	-	-	PUNCT
ejpam-5826	507	7	type	type	NOUN
ejpam-5826	507	8	integral	integral	ADJ
ejpam-5826	507	9	equations	equation	NOUN
ejpam-5826	507	10	formulated	formulate	VERB
ejpam-5826	507	11	as	as	ADP
ejpam-5826	507	12	a	a	DET
ejpam-5826	507	13	common	common	ADJ
ejpam-5826	507	14	fixed	fix	VERB
ejpam-5826	507	15	point	point	NOUN
ejpam-5826	507	16	problem	problem	NOUN
ejpam-5826	507	17	of	of	ADP
ejpam-5826	507	18	the	the	DET
ejpam-5826	507	19	following	follow	VERB
ejpam-5826	507	20	nonlinear	nonlinear	ADJ
ejpam-5826	507	21	mappings	mapping	NOUN
ejpam-5826	507	22	:	:	PUNCT
ejpam-5826	507	23	u(t	u(t	NOUN
ejpam-5826	507	24	)	)	PUNCT
ejpam-5826	507	25	=	=	SYM
ejpam-5826	508	1	∫	∫	PROPN
ejpam-5826	508	2	t	t	NOUN
ejpam-5826	508	3	0	0	NUM
ejpam-5826	509	1	k1(t	k1(t	PROPN
ejpam-5826	509	2	,	,	PUNCT
ejpam-5826	509	3	s	s	X
ejpam-5826	509	4	,	,	PUNCT
ejpam-5826	509	5	u(s))ds	u(s))ds	PROPN
ejpam-5826	509	6	(	(	PUNCT
ejpam-5826	509	7	34	34	NUM
ejpam-5826	509	8	)	)	PUNCT
ejpam-5826	509	9	v(t	v(t	NOUN
ejpam-5826	509	10	)	)	PUNCT
ejpam-5826	509	11	=	=	SYM
ejpam-5826	510	1	∫	∫	PROPN
ejpam-5826	510	2	t	t	NOUN
ejpam-5826	510	3	0	0	NUM
ejpam-5826	511	1	k2(t	k2(t	PROPN
ejpam-5826	511	2	,	,	PUNCT
ejpam-5826	511	3	s	s	PROPN
ejpam-5826	511	4	,	,	PUNCT
ejpam-5826	511	5	v(s))ds	v(s))ds	PROPN
ejpam-5826	511	6	(	(	PUNCT
ejpam-5826	511	7	35	35	NUM
ejpam-5826	511	8	)	)	PUNCT
ejpam-5826	511	9	for	for	ADP
ejpam-5826	511	10	all	all	DET
ejpam-5826	511	11	t	t	PROPN
ejpam-5826	511	12	,	,	PUNCT
ejpam-5826	511	13	s	s	PART
ejpam-5826	511	14	∈	∈	PROPN
ejpam-5826	512	1	[	[	X
ejpam-5826	512	2	0	0	NUM
ejpam-5826	512	3	,	,	PUNCT
ejpam-5826	512	4	t	t	X
ejpam-5826	512	5	]	]	PUNCT
ejpam-5826	512	6	,	,	PUNCT
ejpam-5826	512	7	where	where	SCONJ
ejpam-5826	512	8	the	the	DET
ejpam-5826	512	9	kernels	kernel	NOUN
ejpam-5826	512	10	k1(t	k1(t	PROPN
ejpam-5826	512	11	,	,	PUNCT
ejpam-5826	512	12	s	s	X
ejpam-5826	512	13	,	,	PUNCT
ejpam-5826	512	14	u(s	u(s	ADJ
ejpam-5826	512	15	)	)	PUNCT
ejpam-5826	512	16	)	)	PUNCT
ejpam-5826	512	17	and	and	CCONJ
ejpam-5826	512	18	k2(t	k2(t	PROPN
ejpam-5826	512	19	,	,	PUNCT
ejpam-5826	512	20	s	s	PROPN
ejpam-5826	512	21	,	,	PUNCT
ejpam-5826	512	22	v(s	v(s	PROPN
ejpam-5826	512	23	)	)	PUNCT
ejpam-5826	512	24	)	)	PUNCT
ejpam-5826	512	25	are	be	AUX
ejpam-5826	512	26	known	know	VERB
ejpam-5826	512	27	function	function	NOUN
ejpam-5826	512	28	.	.	PUNCT
ejpam-5826	513	1	we	we	PRON
ejpam-5826	513	2	will	will	AUX
ejpam-5826	513	3	find	find	VERB
ejpam-5826	513	4	the	the	DET
ejpam-5826	513	5	solution	solution	NOUN
ejpam-5826	513	6	of	of	ADP
ejpam-5826	513	7	(	(	PUNCT
ejpam-5826	513	8	34	34	NUM
ejpam-5826	513	9	)	)	PUNCT
ejpam-5826	513	10	and	and	CCONJ
ejpam-5826	513	11	(	(	PUNCT
ejpam-5826	513	12	35	35	NUM
ejpam-5826	513	13	)	)	PUNCT
ejpam-5826	513	14	.	.	PUNCT
ejpam-5826	514	1	now	now	ADV
ejpam-5826	514	2	,	,	PUNCT
ejpam-5826	514	3	we	we	PRON
ejpam-5826	514	4	prove	prove	VERB
ejpam-5826	514	5	the	the	DET
ejpam-5826	514	6	following	follow	VERB
ejpam-5826	514	7	theorem	theorem	NOUN
ejpam-5826	514	8	to	to	PART
ejpam-5826	514	9	ensure	ensure	VERB
ejpam-5826	514	10	the	the	DET
ejpam-5826	514	11	existence	existence	NOUN
ejpam-5826	514	12	of	of	ADP
ejpam-5826	514	13	common	common	ADJ
ejpam-5826	514	14	solution	solution	NOUN
ejpam-5826	514	15	of	of	ADP
ejpam-5826	514	16	the	the	DET
ejpam-5826	514	17	integral	integral	ADJ
ejpam-5826	514	18	equations	equation	NOUN
ejpam-5826	514	19	(	(	PUNCT
ejpam-5826	514	20	34	34	NUM
ejpam-5826	514	21	)	)	PUNCT
ejpam-5826	514	22	and	and	CCONJ
ejpam-5826	514	23	(	(	PUNCT
ejpam-5826	514	24	35	35	NUM
ejpam-5826	514	25	)	)	PUNCT
ejpam-5826	514	26	.	.	PUNCT
ejpam-5826	515	1	theorem	theorem	VERB
ejpam-5826	515	2	11	11	NUM
ejpam-5826	515	3	.	.	PUNCT
ejpam-5826	516	1	assume	assume	VERB
ejpam-5826	516	2	that	that	SCONJ
ejpam-5826	516	3	the	the	DET
ejpam-5826	516	4	following	follow	VERB
ejpam-5826	516	5	conditions	condition	NOUN
ejpam-5826	516	6	are	be	AUX
ejpam-5826	516	7	satisfied	satisfied	ADJ
ejpam-5826	516	8	:	:	PUNCT
ejpam-5826	516	9	(	(	PUNCT
ejpam-5826	516	10	a	a	X
ejpam-5826	516	11	)	)	PUNCT
ejpam-5826	516	12	k1,k2	k1,k2	PROPN
ejpam-5826	516	13	:	:	PUNCT
ejpam-5826	517	1	[	[	X
ejpam-5826	517	2	0	0	NUM
ejpam-5826	517	3	,	,	PUNCT
ejpam-5826	517	4	t	t	X
ejpam-5826	517	5	]	]	X
ejpam-5826	517	6	×	×	NOUN
ejpam-5826	518	1	[	[	X
ejpam-5826	518	2	0	0	NUM
ejpam-5826	518	3	,	,	PUNCT
ejpam-5826	518	4	t	t	X
ejpam-5826	518	5	]	]	PUNCT
ejpam-5826	518	6	×q	×q	ADJ
ejpam-5826	518	7	→	→	SYM
ejpam-5826	518	8	r+	r+	X
ejpam-5826	518	9	,	,	PUNCT
ejpam-5826	518	10	(	(	PUNCT
ejpam-5826	518	11	b	b	X
ejpam-5826	518	12	)	)	PUNCT
ejpam-5826	518	13	define	define	VERB
ejpam-5826	518	14	the	the	DET
ejpam-5826	518	15	mappings	mapping	NOUN
ejpam-5826	518	16	e	e	NOUN
ejpam-5826	518	17	and	and	CCONJ
ejpam-5826	518	18	f	f	PROPN
ejpam-5826	518	19	as	as	SCONJ
ejpam-5826	518	20	follows	follow	VERB
ejpam-5826	518	21	:	:	PUNCT
ejpam-5826	518	22	(	(	PUNCT
ejpam-5826	518	23	eu)(t	eu)(t	PROPN
ejpam-5826	518	24	)	)	PUNCT
ejpam-5826	519	1	=	=	SYM
ejpam-5826	520	1	∫	∫	PROPN
ejpam-5826	520	2	t	t	NOUN
ejpam-5826	520	3	0	0	NUM
ejpam-5826	521	1	k1(t	k1(t	PROPN
ejpam-5826	521	2	,	,	PUNCT
ejpam-5826	521	3	s	s	X
ejpam-5826	521	4	,	,	PUNCT
ejpam-5826	521	5	u(s))ds	u(s))ds	X
ejpam-5826	521	6	(	(	PUNCT
ejpam-5826	521	7	36	36	NUM
ejpam-5826	521	8	)	)	PUNCT
ejpam-5826	521	9	(	(	PUNCT
ejpam-5826	521	10	fv)(t	fv)(t	PROPN
ejpam-5826	521	11	)	)	PUNCT
ejpam-5826	521	12	=	=	SYM
ejpam-5826	522	1	∫	∫	PROPN
ejpam-5826	522	2	t	t	NOUN
ejpam-5826	522	3	0	0	NUM
ejpam-5826	523	1	k2(t	k2(t	PROPN
ejpam-5826	523	2	,	,	PUNCT
ejpam-5826	523	3	s	s	PROPN
ejpam-5826	523	4	,	,	PUNCT
ejpam-5826	523	5	v(s))ds	v(s))ds	PROPN
ejpam-5826	523	6	.	.	PUNCT
ejpam-5826	524	1	(	(	PUNCT
ejpam-5826	524	2	37	37	NUM
ejpam-5826	524	3	)	)	PUNCT
ejpam-5826	524	4	assume	assume	VERB
ejpam-5826	524	5	further	far	ADV
ejpam-5826	524	6	that	that	SCONJ
ejpam-5826	524	7	a.	a.	PROPN
ejpam-5826	524	8	r.	r.	PROPN
ejpam-5826	524	9	khan	khan	PROPN
ejpam-5826	524	10	et	et	PROPN
ejpam-5826	524	11	al	al	PROPN
ejpam-5826	524	12	.	.	PUNCT
ejpam-5826	524	13	/	/	SYM
ejpam-5826	524	14	eur	eur	PROPN
ejpam-5826	524	15	.	.	PUNCT
ejpam-5826	525	1	j.	j.	PROPN
ejpam-5826	525	2	pure	pure	PROPN
ejpam-5826	525	3	appl	appl	PROPN
ejpam-5826	525	4	.	.	PROPN
ejpam-5826	525	5	math	math	PROPN
ejpam-5826	525	6	,	,	PUNCT
ejpam-5826	525	7	18	18	NUM
ejpam-5826	525	8	(	(	PUNCT
ejpam-5826	525	9	2	2	NUM
ejpam-5826	525	10	)	)	PUNCT
ejpam-5826	525	11	(	(	PUNCT
ejpam-5826	525	12	2025	2025	NUM
ejpam-5826	525	13	)	)	PUNCT
ejpam-5826	525	14	,	,	PUNCT
ejpam-5826	525	15	5826	5826	NUM
ejpam-5826	525	16	21	21	NUM
ejpam-5826	525	17	of	of	ADP
ejpam-5826	525	18	23	23	NUM
ejpam-5826	525	19	(	(	PUNCT
ejpam-5826	525	20	i	i	NOUN
ejpam-5826	525	21	)	)	PUNCT
ejpam-5826	525	22	there	there	PRON
ejpam-5826	525	23	exists	exist	VERB
ejpam-5826	525	24	a	a	DET
ejpam-5826	525	25	continuous	continuous	ADJ
ejpam-5826	525	26	functions	function	NOUN
ejpam-5826	525	27	τ	τ	X
ejpam-5826	525	28	:	:	PUNCT
ejpam-5826	526	1	[	[	X
ejpam-5826	526	2	0	0	NUM
ejpam-5826	526	3	,	,	PUNCT
ejpam-5826	526	4	t	t	X
ejpam-5826	526	5	]	]	PUNCT
ejpam-5826	526	6	×	×	NOUN
ejpam-5826	527	1	[	[	X
ejpam-5826	527	2	0	0	NUM
ejpam-5826	527	3	,	,	PUNCT
ejpam-5826	527	4	t	t	X
ejpam-5826	527	5	]	]	PUNCT
ejpam-5826	527	6	→	→	SYM
ejpam-5826	527	7	r+	r+	NOUN
ejpam-5826	527	8	and	and	CCONJ
ejpam-5826	527	9	a	a	DET
ejpam-5826	527	10	continuous	continuous	ADJ
ejpam-5826	527	11	and	and	CCONJ
ejpam-5826	527	12	nondecreasing	nondecreasing	ADJ
ejpam-5826	527	13	function	function	NOUN
ejpam-5826	527	14	α	α	NOUN
ejpam-5826	527	15	:	:	PUNCT
ejpam-5826	527	16	r+	r+	NOUN
ejpam-5826	527	17	→	→	PUNCT
ejpam-5826	527	18	r+	r+	NOUN
ejpam-5826	527	19	such	such	ADJ
ejpam-5826	527	20	that	that	SCONJ
ejpam-5826	527	21	α(0	α(0	NOUN
ejpam-5826	527	22	)	)	PUNCT
ejpam-5826	527	23	=	=	SYM
ejpam-5826	527	24	0	0	NUM
ejpam-5826	527	25	and	and	CCONJ
ejpam-5826	527	26	α(t	α(t	PROPN
ejpam-5826	527	27	)	)	PUNCT
ejpam-5826	527	28	<	<	X
ejpam-5826	527	29	t	t	PROPN
ejpam-5826	527	30	for	for	ADP
ejpam-5826	527	31	t	t	PROPN
ejpam-5826	527	32	>	>	X
ejpam-5826	527	33	0	0	PUNCT
ejpam-5826	528	1	satisfying	satisfy	VERB
ejpam-5826	528	2	∣∣∣k1(t	∣∣∣k1(t	PROPN
ejpam-5826	528	3	,	,	PUNCT
ejpam-5826	528	4	s	s	PROPN
ejpam-5826	528	5	,	,	PUNCT
ejpam-5826	528	6	u(s))−k2(t	u(s))−k2(t	PROPN
ejpam-5826	528	7	,	,	PUNCT
ejpam-5826	528	8	s	s	NOUN
ejpam-5826	528	9	,	,	PUNCT
ejpam-5826	528	10	v(s	v(s	PROPN
ejpam-5826	528	11	)	)	PUNCT
ejpam-5826	528	12	)	)	PUNCT
ejpam-5826	528	13	∣∣∣	∣∣∣	ADP
ejpam-5826	528	14	≤	≤	PROPN
ejpam-5826	528	15	τ(t	τ(t	NOUN
ejpam-5826	528	16	,	,	PUNCT
ejpam-5826	528	17	s)α(|u−	s)α(|u−	NOUN
ejpam-5826	528	18	v|	v|	NOUN
ejpam-5826	528	19	)	)	PUNCT
ejpam-5826	528	20	for	for	ADP
ejpam-5826	528	21	t	t	PROPN
ejpam-5826	528	22	,	,	PUNCT
ejpam-5826	528	23	s	s	PART
ejpam-5826	528	24	∈	∈	PROPN
ejpam-5826	529	1	[	[	X
ejpam-5826	529	2	0	0	NUM
ejpam-5826	529	3	,	,	PUNCT
ejpam-5826	529	4	t	t	NOUN
ejpam-5826	529	5	]	]	PUNCT
ejpam-5826	529	6	and	and	CCONJ
ejpam-5826	529	7	u(s	u(s	NUM
ejpam-5826	529	8	)	)	PUNCT
ejpam-5826	529	9	,	,	PUNCT
ejpam-5826	529	10	v(s	v(s	X
ejpam-5826	529	11	)	)	PUNCT
ejpam-5826	529	12	∈	∈	PROPN
ejpam-5826	529	13	q.	q.	PROPN
ejpam-5826	529	14	(	(	PUNCT
ejpam-5826	529	15	ii	ii	NOUN
ejpam-5826	529	16	)	)	PUNCT
ejpam-5826	529	17	sup	sup	NOUN
ejpam-5826	529	18	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	529	19	]	]	PUNCT
ejpam-5826	530	1	∫	∫	PROPN
ejpam-5826	530	2	t	t	PROPN
ejpam-5826	530	3	0	0	PUNCT
ejpam-5826	530	4	τ(t	τ(t	PROPN
ejpam-5826	530	5	,	,	PUNCT
ejpam-5826	530	6	s)ds	s)ds	PROPN
ejpam-5826	530	7	≤	≤	PROPN
ejpam-5826	530	8	ω	ω	PROPN
ejpam-5826	530	9	,	,	PUNCT
ejpam-5826	530	10	for	for	ADP
ejpam-5826	530	11	some	some	DET
ejpam-5826	530	12	ω	ω	NUM
ejpam-5826	530	13	∈	∈	PROPN
ejpam-5826	530	14	(	(	PUNCT
ejpam-5826	530	15	0	0	NUM
ejpam-5826	530	16	,	,	PUNCT
ejpam-5826	530	17	1	1	NUM
ejpam-5826	530	18	)	)	PUNCT
ejpam-5826	530	19	.	.	PUNCT
ejpam-5826	531	1	then	then	ADV
ejpam-5826	531	2	e	e	PROPN
ejpam-5826	531	3	and	and	CCONJ
ejpam-5826	531	4	f	f	PROPN
ejpam-5826	531	5	have	have	VERB
ejpam-5826	531	6	a	a	DET
ejpam-5826	531	7	unique	unique	ADJ
ejpam-5826	531	8	common	common	ADJ
ejpam-5826	531	9	solution	solution	NOUN
ejpam-5826	531	10	.	.	PUNCT
ejpam-5826	532	1	proof	proof	NOUN
ejpam-5826	532	2	.	.	PUNCT
ejpam-5826	533	1	let	let	VERB
ejpam-5826	533	2	u	u	NOUN
ejpam-5826	533	3	,	,	PUNCT
ejpam-5826	533	4	v	v	PROPN
ejpam-5826	533	5	∈	∈	PROPN
ejpam-5826	533	6	q.	q.	NOUN
ejpam-5826	533	7	by	by	ADP
ejpam-5826	533	8	assumptions	assumption	NOUN
ejpam-5826	533	9	(	(	PUNCT
ejpam-5826	533	10	i	i	NOUN
ejpam-5826	533	11	)	)	PUNCT
ejpam-5826	533	12	and	and	CCONJ
ejpam-5826	533	13	(	(	PUNCT
ejpam-5826	533	14	ii	ii	NOUN
ejpam-5826	533	15	)	)	PUNCT
ejpam-5826	533	16	,	,	PUNCT
ejpam-5826	533	17	we	we	PRON
ejpam-5826	533	18	have	have	VERB
ejpam-5826	533	19	d(eu	d(eu	NOUN
ejpam-5826	533	20	,	,	PUNCT
ejpam-5826	533	21	fv	fv	NOUN
ejpam-5826	533	22	)	)	PUNCT
ejpam-5826	533	23	=	=	SYM
ejpam-5826	534	1	||eu−	||eu−	ADV
ejpam-5826	534	2	fv||∞	fv||∞	NOUN
ejpam-5826	534	3	=	=	SYM
ejpam-5826	534	4	sup	sup	PROPN
ejpam-5826	534	5	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	534	6	]	]	X
ejpam-5826	535	1	|(eu)(t)−	|(eu)(t)−	PROPN
ejpam-5826	535	2	(	(	PUNCT
ejpam-5826	535	3	fv)(t)|	fv)(t)|	PROPN
ejpam-5826	535	4	=	=	NOUN
ejpam-5826	535	5	sup	sup	NOUN
ejpam-5826	535	6	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	535	7	]	]	X
ejpam-5826	535	8	∣∣∣	∣∣∣	ADJ
ejpam-5826	535	9	∫	∫	PROPN
ejpam-5826	535	10	t	t	PROPN
ejpam-5826	535	11	0	0	NUM
ejpam-5826	535	12	k1(t	k1(t	PROPN
ejpam-5826	535	13	,	,	PUNCT
ejpam-5826	535	14	s	s	AUX
ejpam-5826	535	15	,	,	PUNCT
ejpam-5826	535	16	u(s))ds−	u(s))ds−	VERB
ejpam-5826	535	17	∫	∫	PROPN
ejpam-5826	535	18	t	t	PROPN
ejpam-5826	535	19	0	0	NUM
ejpam-5826	536	1	k2(t	k2(t	PROPN
ejpam-5826	536	2	,	,	PUNCT
ejpam-5826	536	3	s	s	PART
ejpam-5826	536	4	,	,	PUNCT
ejpam-5826	536	5	v(s))ds	v(s))ds	ADV
ejpam-5826	536	6	∣∣∣	∣∣∣	NOUN
ejpam-5826	537	1	=	=	PUNCT
ejpam-5826	537	2	sup	sup	NOUN
ejpam-5826	537	3	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	537	4	]	]	X
ejpam-5826	537	5	∣∣∣	∣∣∣	ADJ
ejpam-5826	537	6	∫	∫	PROPN
ejpam-5826	537	7	t	t	PROPN
ejpam-5826	537	8	0	0	NUM
ejpam-5826	538	1	(	(	PUNCT
ejpam-5826	538	2	k1(t	k1(t	PROPN
ejpam-5826	538	3	,	,	PUNCT
ejpam-5826	538	4	s	s	X
ejpam-5826	538	5	,	,	PUNCT
ejpam-5826	538	6	u(s))−k2(t	u(s))−k2(t	PROPN
ejpam-5826	538	7	,	,	PUNCT
ejpam-5826	538	8	s	s	NOUN
ejpam-5826	538	9	,	,	PUNCT
ejpam-5826	538	10	v(s	v(s	PROPN
ejpam-5826	538	11	)	)	PUNCT
ejpam-5826	538	12	)	)	PUNCT
ejpam-5826	538	13	)	)	PUNCT
ejpam-5826	539	1	ds	ds	PRON
ejpam-5826	539	2	∣∣∣	∣∣∣	ADJ
ejpam-5826	539	3	≤	≤	NUM
ejpam-5826	539	4	sup	sup	NOUN
ejpam-5826	539	5	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	539	6	]	]	PUNCT
ejpam-5826	539	7	∫	∫	PROPN
ejpam-5826	539	8	t	t	NOUN
ejpam-5826	539	9	0	0	X
ejpam-5826	539	10	∣∣∣k1(t	∣∣∣k1(t	PROPN
ejpam-5826	539	11	,	,	PUNCT
ejpam-5826	539	12	s	s	PROPN
ejpam-5826	539	13	,	,	PUNCT
ejpam-5826	539	14	u(s))−k2(t	u(s))−k2(t	PROPN
ejpam-5826	539	15	,	,	PUNCT
ejpam-5826	539	16	s	s	NOUN
ejpam-5826	539	17	,	,	PUNCT
ejpam-5826	539	18	v(s	v(s	PROPN
ejpam-5826	539	19	)	)	PUNCT
ejpam-5826	539	20	)	)	PUNCT
ejpam-5826	540	1	∣∣∣ds	∣∣∣ds	PART
ejpam-5826	541	1	≤	≤	ADJ
ejpam-5826	541	2	sup	sup	NOUN
ejpam-5826	541	3	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	541	4	]	]	PUNCT
ejpam-5826	542	1	∫	∫	PROPN
ejpam-5826	542	2	t	t	PROPN
ejpam-5826	542	3	0	0	NUM
ejpam-5826	542	4	τ(t	τ(t	PROPN
ejpam-5826	542	5	,	,	PUNCT
ejpam-5826	542	6	s)α(|u−	s)α(|u−	PROPN
ejpam-5826	542	7	v|)ds	v|)ds	NOUN
ejpam-5826	542	8	≤	≤	NUM
ejpam-5826	542	9	sup	sup	NOUN
ejpam-5826	542	10	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	542	11	]	]	PUNCT
ejpam-5826	543	1	∫	∫	PROPN
ejpam-5826	543	2	t	t	PROPN
ejpam-5826	543	3	0	0	NUM
ejpam-5826	543	4	τ(t	τ(t	PROPN
ejpam-5826	543	5	,	,	PUNCT
ejpam-5826	543	6	s)|u−	s)|u−	NOUN
ejpam-5826	543	7	v|ds	v|ds	SYM
ejpam-5826	543	8	≤	≤	X
ejpam-5826	543	9	||u−	||u−	NOUN
ejpam-5826	543	10	v||∞	v||∞	PROPN
ejpam-5826	543	11	sup	sup	NOUN
ejpam-5826	543	12	t∈[0,t	t∈[0,t	NOUN
ejpam-5826	543	13	]	]	PUNCT
ejpam-5826	543	14	∫	∫	PROPN
ejpam-5826	543	15	t	t	PROPN
ejpam-5826	543	16	0	0	PUNCT
ejpam-5826	543	17	τ(t	τ(t	PROPN
ejpam-5826	543	18	,	,	PUNCT
ejpam-5826	543	19	s)ds	s)ds	PROPN
ejpam-5826	543	20	≤	≤	PROPN
ejpam-5826	543	21	ω||u−	ω||u−	ADV
ejpam-5826	543	22	v||∞	v||∞	PROPN
ejpam-5826	543	23	=	=	SYM
ejpam-5826	543	24	ω	ω	PROPN
ejpam-5826	543	25	(	(	PUNCT
ejpam-5826	543	26	||u−	||u−	NOUN
ejpam-5826	543	27	v	v	NOUN
ejpam-5826	543	28	+	+	CCONJ
ejpam-5826	543	29	(	(	PUNCT
ejpam-5826	543	30	e(u)−	e(u)−	PROPN
ejpam-5826	543	31	u)−	u)−	PROPN
ejpam-5826	543	32	(	(	PUNCT
ejpam-5826	543	33	e(u)−	e(u)−	PROPN
ejpam-5826	543	34	u	u	PROPN
ejpam-5826	543	35	)	)	PUNCT
ejpam-5826	543	36	+	+	CCONJ
ejpam-5826	543	37	(	(	PUNCT
ejpam-5826	543	38	v	v	NOUN
ejpam-5826	543	39	−	−	PROPN
ejpam-5826	543	40	f	f	NOUN
ejpam-5826	543	41	(	(	PUNCT
ejpam-5826	543	42	v))−	v))−	X
ejpam-5826	543	43	(	(	PUNCT
ejpam-5826	543	44	v	v	NOUN
ejpam-5826	543	45	−	−	PROPN
ejpam-5826	543	46	f	f	PROPN
ejpam-5826	543	47	(	(	PUNCT
ejpam-5826	543	48	v))||∞	v))||∞	PROPN
ejpam-5826	543	49	)	)	PUNCT
ejpam-5826	544	1	≤	≤	PROPN
ejpam-5826	544	2	ω	ω	PROPN
ejpam-5826	544	3	(	(	PUNCT
ejpam-5826	544	4	2||u−	2||u−	NUM
ejpam-5826	544	5	v||∞|+	v||∞|+	PROPN
ejpam-5826	544	6	||u−	||u−	NOUN
ejpam-5826	544	7	e(u)||∞	e(u)||∞	PROPN
ejpam-5826	544	8	+	+	CCONJ
ejpam-5826	544	9	||v	||v	NOUN
ejpam-5826	544	10	−	−	NOUN
ejpam-5826	544	11	f	f	PROPN
ejpam-5826	544	12	(	(	PUNCT
ejpam-5826	544	13	v)||∞	v)||∞	X
ejpam-5826	544	14	+	+	CCONJ
ejpam-5826	545	1	||e(u)−	||e(u)−	NOUN
ejpam-5826	545	2	f	f	NOUN
ejpam-5826	545	3	(	(	PUNCT
ejpam-5826	545	4	v)||∞	v)||∞	PROPN
ejpam-5826	545	5	)	)	PUNCT
ejpam-5826	545	6	;	;	PUNCT
ejpam-5826	545	7	thus	thus	ADV
ejpam-5826	545	8	d(eu	d(eu	NOUN
ejpam-5826	545	9	,	,	PUNCT
ejpam-5826	545	10	fv	fv	NOUN
ejpam-5826	545	11	)	)	PUNCT
ejpam-5826	545	12	≤	≤	NOUN
ejpam-5826	545	13	2ω	2ω	PROPN
ejpam-5826	545	14	1−	1−	NUM
ejpam-5826	545	15	ω	ω	NUM
ejpam-5826	545	16	d(u	d(u	PROPN
ejpam-5826	545	17	,	,	PUNCT
ejpam-5826	545	18	v	v	NOUN
ejpam-5826	545	19	)	)	PUNCT
ejpam-5826	545	20	+	+	CCONJ
ejpam-5826	546	1	ω	ω	NUM
ejpam-5826	546	2	1−	1−	NUM
ejpam-5826	546	3	ω	ω	NUM
ejpam-5826	546	4	(	(	PUNCT
ejpam-5826	546	5	d(u	d(u	PROPN
ejpam-5826	546	6	,	,	PUNCT
ejpam-5826	546	7	eu	eu	PROPN
ejpam-5826	546	8	)	)	PUNCT
ejpam-5826	546	9	+	+	X
ejpam-5826	546	10	d(v	d(v	ADJ
ejpam-5826	546	11	,	,	PUNCT
ejpam-5826	546	12	fv	fv	NOUN
ejpam-5826	546	13	)	)	PUNCT
ejpam-5826	546	14	)	)	PUNCT
ejpam-5826	547	1	letting	let	VERB
ejpam-5826	547	2	κ(d(u	κ(d(u	PROPN
ejpam-5826	547	3	,	,	PUNCT
ejpam-5826	547	4	v	v	NOUN
ejpam-5826	547	5	)	)	PUNCT
ejpam-5826	547	6	)	)	PUNCT
ejpam-5826	548	1	:	:	PUNCT
ejpam-5826	548	2	=	=	SYM
ejpam-5826	548	3	2ω	2ω	NUM
ejpam-5826	548	4	1−ω	1−ω	NUM
ejpam-5826	548	5	,	,	PUNCT
ejpam-5826	548	6	it	it	PRON
ejpam-5826	548	7	follows	follow	VERB
ejpam-5826	548	8	that	that	SCONJ
ejpam-5826	548	9	the	the	DET
ejpam-5826	548	10	mappings	mapping	NOUN
ejpam-5826	548	11	e	e	NOUN
ejpam-5826	548	12	and	and	CCONJ
ejpam-5826	548	13	f	f	PROPN
ejpam-5826	548	14	satisfy	satisfy	NOUN
ejpam-5826	548	15	(	(	PUNCT
ejpam-5826	548	16	3	3	NUM
ejpam-5826	548	17	)	)	PUNCT
ejpam-5826	548	18	.	.	PUNCT
ejpam-5826	549	1	hence	hence	ADV
ejpam-5826	549	2	by	by	ADP
ejpam-5826	549	3	theorem	theorem	NOUN
ejpam-5826	549	4	4	4	NUM
ejpam-5826	549	5	,	,	PUNCT
ejpam-5826	549	6	there	there	PRON
ejpam-5826	549	7	exists	exist	VERB
ejpam-5826	549	8	a	a	DET
ejpam-5826	549	9	unique	unique	ADJ
ejpam-5826	549	10	common	common	ADJ
ejpam-5826	549	11	fixed	fix	VERB
ejpam-5826	549	12	point	point	NOUN
ejpam-5826	549	13	of	of	ADP
ejpam-5826	549	14	e	e	PROPN
ejpam-5826	549	15	and	and	CCONJ
ejpam-5826	549	16	f	f	PROPN
ejpam-5826	549	17	which	which	PRON
ejpam-5826	549	18	is	be	AUX
ejpam-5826	549	19	the	the	DET
ejpam-5826	549	20	common	common	ADJ
ejpam-5826	549	21	solution	solution	NOUN
ejpam-5826	549	22	of	of	ADP
ejpam-5826	549	23	the	the	DET
ejpam-5826	549	24	voterra	voterra	NOUN
ejpam-5826	549	25	-	-	PUNCT
ejpam-5826	549	26	type	type	NOUN
ejpam-5826	549	27	integral	integral	ADJ
ejpam-5826	549	28	equations	equation	NOUN
ejpam-5826	549	29	(	(	PUNCT
ejpam-5826	549	30	34	34	NUM
ejpam-5826	549	31	)	)	PUNCT
ejpam-5826	549	32	and	and	CCONJ
ejpam-5826	549	33	(	(	PUNCT
ejpam-5826	549	34	35	35	NUM
ejpam-5826	549	35	)	)	PUNCT
ejpam-5826	549	36	.	.	PUNCT
ejpam-5826	550	1	a.	a.	PROPN
ejpam-5826	550	2	r.	r.	PROPN
ejpam-5826	550	3	khan	khan	PROPN
ejpam-5826	550	4	et	et	PROPN
ejpam-5826	550	5	al	al	PROPN
ejpam-5826	550	6	.	.	PUNCT
ejpam-5826	550	7	/	/	SYM
ejpam-5826	550	8	eur	eur	PROPN
ejpam-5826	550	9	.	.	PUNCT
ejpam-5826	551	1	j.	j.	PROPN
ejpam-5826	551	2	pure	pure	PROPN
ejpam-5826	551	3	appl	appl	PROPN
ejpam-5826	551	4	.	.	PROPN
ejpam-5826	551	5	math	math	PROPN
ejpam-5826	551	6	,	,	PUNCT
ejpam-5826	551	7	18	18	NUM
ejpam-5826	551	8	(	(	PUNCT
ejpam-5826	551	9	2	2	NUM
ejpam-5826	551	10	)	)	PUNCT
ejpam-5826	551	11	(	(	PUNCT
ejpam-5826	551	12	2025	2025	NUM
ejpam-5826	551	13	)	)	PUNCT
ejpam-5826	551	14	,	,	PUNCT
ejpam-5826	551	15	5826	5826	NUM
ejpam-5826	551	16	22	22	NUM
ejpam-5826	551	17	of	of	ADP
ejpam-5826	551	18	23	23	NUM
ejpam-5826	551	19	5	5	NUM
ejpam-5826	551	20	.	.	PUNCT
ejpam-5826	552	1	conclusions	conclusion	NOUN
ejpam-5826	552	2	we	we	PRON
ejpam-5826	552	3	have	have	AUX
ejpam-5826	552	4	extended	extend	VERB
ejpam-5826	552	5	the	the	DET
ejpam-5826	552	6	existing	exist	VERB
ejpam-5826	552	7	body	body	NOUN
ejpam-5826	552	8	of	of	ADP
ejpam-5826	552	9	knowledge	knowledge	NOUN
ejpam-5826	552	10	on	on	ADP
ejpam-5826	552	11	fixed	fix	VERB
ejpam-5826	552	12	point	point	NOUN
ejpam-5826	552	13	theory	theory	NOUN
ejpam-5826	552	14	for	for	ADP
ejpam-5826	552	15	asymptotically	asymptotically	ADV
ejpam-5826	552	16	regular	regular	ADJ
ejpam-5826	552	17	mappings	mapping	NOUN
ejpam-5826	552	18	on	on	ADP
ejpam-5826	552	19	a	a	DET
ejpam-5826	552	20	metric	metric	ADJ
ejpam-5826	552	21	space	space	NOUN
ejpam-5826	552	22	by	by	ADP
ejpam-5826	552	23	proving	prove	VERB
ejpam-5826	552	24	new	new	ADJ
ejpam-5826	552	25	common	common	ADJ
ejpam-5826	552	26	fixed	fix	VERB
ejpam-5826	552	27	point	point	NOUN
ejpam-5826	552	28	results	result	NOUN
ejpam-5826	552	29	on	on	ADP
ejpam-5826	552	30	convex	convex	ADJ
ejpam-5826	552	31	metric	metric	ADJ
ejpam-5826	552	32	spaces	space	NOUN
ejpam-5826	552	33	.	.	PUNCT
ejpam-5826	553	1	our	our	PRON
ejpam-5826	553	2	work	work	NOUN
ejpam-5826	553	3	verifies	verifie	NOUN
ejpam-5826	553	4	that	that	SCONJ
ejpam-5826	553	5	under	under	ADP
ejpam-5826	553	6	certain	certain	ADJ
ejpam-5826	553	7	contractive	contractive	ADJ
ejpam-5826	553	8	conditions	condition	NOUN
ejpam-5826	553	9	,	,	PUNCT
ejpam-5826	553	10	asymptotically	asymptotically	ADV
ejpam-5826	553	11	regular	regular	ADJ
ejpam-5826	553	12	self	self	NOUN
ejpam-5826	553	13	-	-	PUNCT
ejpam-5826	553	14	mappings	mapping	NOUN
ejpam-5826	553	15	not	not	PART
ejpam-5826	553	16	only	only	ADV
ejpam-5826	553	17	possess	possess	VERB
ejpam-5826	553	18	unique	unique	ADJ
ejpam-5826	553	19	fixed	fix	VERB
ejpam-5826	553	20	points	point	NOUN
ejpam-5826	553	21	but	but	CCONJ
ejpam-5826	553	22	also	also	ADV
ejpam-5826	553	23	exhibit	exhibit	VERB
ejpam-5826	553	24	properties	property	NOUN
ejpam-5826	553	25	of	of	ADP
ejpam-5826	553	26	closedness	closedness	NOUN
ejpam-5826	553	27	and	and	CCONJ
ejpam-5826	553	28	convexity	convexity	NOUN
ejpam-5826	553	29	for	for	ADP
ejpam-5826	553	30	their	their	PRON
ejpam-5826	553	31	fixed	fix	VERB
ejpam-5826	553	32	point	point	NOUN
ejpam-5826	553	33	sets	set	NOUN
ejpam-5826	553	34	.	.	PUNCT
ejpam-5826	554	1	we	we	PRON
ejpam-5826	554	2	have	have	AUX
ejpam-5826	554	3	also	also	ADV
ejpam-5826	554	4	demonstrated	demonstrate	VERB
ejpam-5826	554	5	that	that	SCONJ
ejpam-5826	554	6	replacing	replace	VERB
ejpam-5826	554	7	standard	standard	ADJ
ejpam-5826	554	8	mappings	mapping	NOUN
ejpam-5826	554	9	with	with	ADP
ejpam-5826	554	10	their	their	PRON
ejpam-5826	554	11	average	average	ADJ
ejpam-5826	554	12	mappings	mapping	NOUN
ejpam-5826	554	13	in	in	ADP
ejpam-5826	554	14	a	a	DET
ejpam-5826	554	15	convex	convex	ADJ
ejpam-5826	554	16	metric	metric	ADJ
ejpam-5826	554	17	space	space	NOUN
ejpam-5826	554	18	context	context	NOUN
ejpam-5826	554	19	retains	retain	VERB
ejpam-5826	554	20	their	their	PRON
ejpam-5826	554	21	fixed	fix	VERB
ejpam-5826	554	22	point	point	NOUN
ejpam-5826	554	23	properties	property	NOUN
ejpam-5826	554	24	.	.	PUNCT
ejpam-5826	555	1	furthermore	furthermore	ADV
ejpam-5826	555	2	,	,	PUNCT
ejpam-5826	555	3	we	we	PRON
ejpam-5826	555	4	have	have	AUX
ejpam-5826	555	5	applied	apply	VERB
ejpam-5826	555	6	our	our	PRON
ejpam-5826	555	7	theoretical	theoretical	ADJ
ejpam-5826	555	8	findings	finding	NOUN
ejpam-5826	555	9	to	to	PART
ejpam-5826	555	10	solve	solve	VERB
ejpam-5826	555	11	integral	integral	ADJ
ejpam-5826	555	12	equations	equation	NOUN
ejpam-5826	555	13	,	,	PUNCT
ejpam-5826	555	14	showcasing	showcase	VERB
ejpam-5826	555	15	the	the	DET
ejpam-5826	555	16	practical	practical	ADJ
ejpam-5826	555	17	utility	utility	NOUN
ejpam-5826	555	18	of	of	ADP
ejpam-5826	555	19	our	our	PRON
ejpam-5826	555	20	theorems	theorem	NOUN
ejpam-5826	555	21	in	in	ADP
ejpam-5826	555	22	real	real	ADJ
ejpam-5826	555	23	-	-	PUNCT
ejpam-5826	555	24	world	world	NOUN
ejpam-5826	555	25	problems	problem	NOUN
ejpam-5826	555	26	.	.	PUNCT
ejpam-5826	556	1	these	these	DET
ejpam-5826	556	2	results	result	NOUN
ejpam-5826	556	3	are	be	AUX
ejpam-5826	556	4	pivotal	pivotal	ADJ
ejpam-5826	556	5	in	in	ADP
ejpam-5826	556	6	advancing	advance	VERB
ejpam-5826	556	7	the	the	DET
ejpam-5826	556	8	understanding	understanding	NOUN
ejpam-5826	556	9	of	of	ADP
ejpam-5826	556	10	fixed	fix	VERB
ejpam-5826	556	11	point	point	NOUN
ejpam-5826	556	12	theory	theory	NOUN
ejpam-5826	556	13	in	in	ADP
ejpam-5826	556	14	more	more	ADV
ejpam-5826	556	15	general	general	ADJ
ejpam-5826	556	16	and	and	CCONJ
ejpam-5826	556	17	complex	complex	ADJ
ejpam-5826	556	18	spaces	space	NOUN
ejpam-5826	556	19	,	,	PUNCT
ejpam-5826	556	20	offering	offer	VERB
ejpam-5826	556	21	new	new	ADJ
ejpam-5826	556	22	avenues	avenue	NOUN
ejpam-5826	556	23	for	for	ADP
ejpam-5826	556	24	future	future	ADJ
ejpam-5826	556	25	research	research	NOUN
ejpam-5826	556	26	and	and	CCONJ
ejpam-5826	556	27	applications	application	NOUN
ejpam-5826	556	28	in	in	ADP
ejpam-5826	556	29	various	various	ADJ
ejpam-5826	556	30	mathematical	mathematical	ADJ
ejpam-5826	556	31	and	and	CCONJ
ejpam-5826	556	32	practical	practical	ADJ
ejpam-5826	556	33	fields	field	NOUN
ejpam-5826	556	34	.	.	PUNCT
ejpam-5826	557	1	looking	look	VERB
ejpam-5826	557	2	ahead	ahead	ADV
ejpam-5826	557	3	,	,	PUNCT
ejpam-5826	557	4	several	several	ADJ
ejpam-5826	557	5	interesting	interesting	ADJ
ejpam-5826	557	6	directions	direction	NOUN
ejpam-5826	557	7	arise	arise	VERB
ejpam-5826	557	8	for	for	ADP
ejpam-5826	557	9	future	future	ADJ
ejpam-5826	557	10	exploration	exploration	NOUN
ejpam-5826	557	11	:	:	PUNCT
ejpam-5826	557	12	(	(	PUNCT
ejpam-5826	557	13	i	i	NOUN
ejpam-5826	557	14	)	)	PUNCT
ejpam-5826	557	15	establishing	establish	VERB
ejpam-5826	557	16	an	an	DET
ejpam-5826	557	17	analogue	analogue	NOUN
ejpam-5826	557	18	of	of	ADP
ejpam-5826	557	19	theorem	theorem	NOUN
ejpam-5826	557	20	5	5	NUM
ejpam-5826	557	21	in	in	ADP
ejpam-5826	557	22	a	a	DET
ejpam-5826	557	23	convex	convex	ADJ
ejpam-5826	557	24	metric	metric	ADJ
ejpam-5826	557	25	space	space	NOUN
ejpam-5826	557	26	.	.	PUNCT
ejpam-5826	558	1	(	(	PUNCT
ejpam-5826	558	2	ii	ii	NOUN
ejpam-5826	558	3	)	)	PUNCT
ejpam-5826	558	4	finding	find	VERB
ejpam-5826	558	5	an	an	DET
ejpam-5826	558	6	analogue	analogue	NOUN
ejpam-5826	558	7	of	of	ADP
ejpam-5826	558	8	theorem	theorem	NOUN
ejpam-5826	558	9	6	6	NUM
ejpam-5826	558	10	for	for	ADP
ejpam-5826	558	11	a	a	DET
ejpam-5826	558	12	quasi	quasi	ADJ
ejpam-5826	558	13	-	-	ADJ
ejpam-5826	558	14	nonexpansive	nonexpansive	ADJ
ejpam-5826	558	15	map	map	NOUN
ejpam-5826	558	16	.	.	PUNCT
ejpam-5826	559	1	(	(	PUNCT
ejpam-5826	559	2	iii	iii	X
ejpam-5826	559	3	)	)	PUNCT
ejpam-5826	559	4	addressing	address	VERB
ejpam-5826	559	5	the	the	DET
ejpam-5826	559	6	question	question	NOUN
ejpam-5826	559	7	posed	pose	VERB
ejpam-5826	559	8	before	before	ADP
ejpam-5826	559	9	theorem	theorem	NOUN
ejpam-5826	559	10	9	9	NUM
ejpam-5826	559	11	in	in	ADP
ejpam-5826	559	12	the	the	DET
ejpam-5826	559	13	context	context	NOUN
ejpam-5826	559	14	of	of	ADP
ejpam-5826	559	15	a	a	DET
ejpam-5826	559	16	convex	convex	ADJ
ejpam-5826	559	17	metric	metric	ADJ
ejpam-5826	559	18	space	space	NOUN
ejpam-5826	559	19	.	.	PUNCT
ejpam-5826	560	1	acknowledgements	acknowledgement	VERB
ejpam-5826	560	2	the	the	DET
ejpam-5826	560	3	authors	author	NOUN
ejpam-5826	560	4	g.	g.	PROPN
ejpam-5826	560	5	c.	c.	PROPN
ejpam-5826	560	6	ugwunnadi	ugwunnadi	PROPN
ejpam-5826	560	7	and	and	CCONJ
ejpam-5826	560	8	m.	m.	PROPN
ejpam-5826	560	9	aphane	aphane	PROPN
ejpam-5826	560	10	are	be	AUX
ejpam-5826	560	11	grateful	grateful	ADJ
ejpam-5826	560	12	to	to	ADP
ejpam-5826	560	13	department	department	NOUN
ejpam-5826	560	14	of	of	ADP
ejpam-5826	560	15	mathematics	mathematic	NOUN
ejpam-5826	560	16	and	and	CCONJ
ejpam-5826	560	17	applied	apply	VERB
ejpam-5826	560	18	mathematics	mathematic	NOUN
ejpam-5826	560	19	,	,	PUNCT
ejpam-5826	560	20	sefako	sefako	ADJ
ejpam-5826	560	21	makgato	makgato	ADJ
ejpam-5826	560	22	health	health	PROPN
ejpam-5826	560	23	science	science	PROPN
ejpam-5826	560	24	university	university	PROPN
ejpam-5826	560	25	,	,	PUNCT
ejpam-5826	560	26	pretoria	pretoria	PROPN
ejpam-5826	560	27	0204	0204	NUM
ejpam-5826	560	28	,	,	PUNCT
ejpam-5826	560	29	south	south	PROPN
ejpam-5826	560	30	africa	africa	PROPN
ejpam-5826	560	31	for	for	ADP
ejpam-5826	560	32	supporting	support	VERB
ejpam-5826	560	33	this	this	DET
ejpam-5826	560	34	research	research	NOUN
ejpam-5826	560	35	work	work	NOUN
ejpam-5826	560	36	.	.	PUNCT
ejpam-5826	561	1	references	reference	NOUN
ejpam-5826	561	2	[	[	X
ejpam-5826	561	3	1	1	NUM
ejpam-5826	561	4	]	]	PUNCT
ejpam-5826	561	5	n.	n.	PROPN
ejpam-5826	561	6	hussain	hussain	PROPN
ejpam-5826	561	7	,	,	PUNCT
ejpam-5826	561	8	s	s	PART
ejpam-5826	561	9	m	m	VERB
ejpam-5826	561	10	alsulami	alsulami	NOUN
ejpam-5826	561	11	,	,	PUNCT
ejpam-5826	561	12	and	and	CCONJ
ejpam-5826	561	13	h	h	NOUN
ejpam-5826	561	14	alamri	alamri	ADJ
ejpam-5826	561	15	.	.	PUNCT
ejpam-5826	562	1	solving	solve	VERB
ejpam-5826	562	2	fractional	fractional	ADJ
ejpam-5826	562	3	diffenerential	diffenerential	ADJ
ejpam-5826	562	4	equations	equation	NOUN
ejpam-5826	562	5	via	via	ADP
ejpam-5826	562	6	fixed	fix	VERB
ejpam-5826	562	7	points	point	NOUN
ejpam-5826	562	8	of	of	ADP
ejpam-5826	562	9	chatterjea	chatterjea	ADJ
ejpam-5826	562	10	maps	map	NOUN
ejpam-5826	562	11	.	.	PUNCT
ejpam-5826	563	1	computer	computer	NOUN
ejpam-5826	563	2	modeling	modeling	NOUN
ejpam-5826	563	3	engr	engr	NOUN
ejpam-5826	563	4	.	.	PUNCT
ejpam-5826	564	1	sc	sc	PROPN
ejpam-5826	564	2	.	.	PROPN
ejpam-5826	564	3	,	,	PUNCT
ejpam-5826	564	4	135:2617–2648	135:2617–2648	PROPN
ejpam-5826	564	5	,	,	PUNCT
ejpam-5826	564	6	2023	2023	NUM
ejpam-5826	564	7	.	.	PUNCT
ejpam-5826	565	1	[	[	X
ejpam-5826	565	2	2	2	NUM
ejpam-5826	565	3	]	]	X
ejpam-5826	565	4	j	j	PROPN
ejpam-5826	565	5	górnicki	górnicki	PROPN
ejpam-5826	565	6	.	.	PROPN
ejpam-5826	566	1	remarks	remark	NOUN
ejpam-5826	566	2	on	on	ADP
ejpam-5826	566	3	asymptotic	asymptotic	ADJ
ejpam-5826	566	4	regularity	regularity	NOUN
ejpam-5826	566	5	and	and	CCONJ
ejpam-5826	566	6	fixed	fix	VERB
ejpam-5826	566	7	points	point	NOUN
ejpam-5826	566	8	.	.	PUNCT
ejpam-5826	567	1	j.	j.	PROPN
ejpam-5826	567	2	fixed	fix	VERB
ejpam-5826	567	3	point	point	PROPN
ejpam-5826	567	4	theory	theory	NOUN
ejpam-5826	567	5	appl	appl	PROPN
ejpam-5826	567	6	.	.	PROPN
ejpam-5826	567	7	,	,	PUNCT
ejpam-5826	567	8	21:29	21:29	NUM
ejpam-5826	567	9	,	,	PUNCT
ejpam-5826	567	10	2019	2019	NUM
ejpam-5826	567	11	.	.	PUNCT
ejpam-5826	568	1	[	[	X
ejpam-5826	568	2	3	3	NUM
ejpam-5826	568	3	]	]	X
ejpam-5826	568	4	s	s	PART
ejpam-5826	568	5	reich	reich	PROPN
ejpam-5826	568	6	.	.	PUNCT
ejpam-5826	569	1	some	some	DET
ejpam-5826	569	2	remarks	remark	NOUN
ejpam-5826	569	3	concerning	concern	VERB
ejpam-5826	569	4	contration	contration	NOUN
ejpam-5826	569	5	mappings	mapping	NOUN
ejpam-5826	569	6	.	.	PUNCT
ejpam-5826	570	1	canada	canada	PROPN
ejpam-5826	570	2	.	.	PUNCT
ejpam-5826	571	1	math	math	PROPN
ejpam-5826	571	2	.	.	PUNCT
ejpam-5826	572	1	bull	bull	PROPN
ejpam-5826	572	2	.	.	PUNCT
ejpam-5826	572	3	,	,	PUNCT
ejpam-5826	572	4	14:121	14:121	NUM
ejpam-5826	572	5	–	–	PUNCT
ejpam-5826	572	6	165	165	NUM
ejpam-5826	572	7	,	,	PUNCT
ejpam-5826	572	8	1971	1971	NUM
ejpam-5826	572	9	.	.	PUNCT
ejpam-5826	573	1	[	[	X
ejpam-5826	573	2	4	4	NUM
ejpam-5826	573	3	]	]	X
ejpam-5826	573	4	r	r	NOUN
ejpam-5826	573	5	k	k	X
ejpam-5826	573	6	bisht	bisht	PROPN
ejpam-5826	573	7	.	.	PUNCT
ejpam-5826	574	1	a	a	DET
ejpam-5826	574	2	note	note	NOUN
ejpam-5826	574	3	on	on	ADP
ejpam-5826	574	4	fixed	fix	VERB
ejpam-5826	574	5	point	point	NOUN
ejpam-5826	574	6	theorem	theorem	NOUN
ejpam-5826	574	7	of	of	ADP
ejpam-5826	574	8	górnicki	górnicki	PROPN
ejpam-5826	574	9	.	.	PUNCT
ejpam-5826	575	1	j.	j.	PROPN
ejpam-5826	575	2	fixed	fix	VERB
ejpam-5826	575	3	point	point	PROPN
ejpam-5826	575	4	theory	theory	NOUN
ejpam-5826	575	5	appl	appl	PROPN
ejpam-5826	575	6	.	.	PROPN
ejpam-5826	575	7	,	,	PUNCT
ejpam-5826	575	8	21:54	21:54	NUM
ejpam-5826	575	9	,	,	PUNCT
ejpam-5826	575	10	2019	2019	NUM
ejpam-5826	575	11	.	.	PUNCT
ejpam-5826	576	1	[	[	X
ejpam-5826	576	2	5	5	NUM
ejpam-5826	576	3	]	]	PUNCT
ejpam-5826	576	4	e	e	X
ejpam-5826	576	5	karapınar	karapınar	NOUN
ejpam-5826	576	6	,	,	PUNCT
ejpam-5826	576	7	m	m	PROPN
ejpam-5826	576	8	de	de	X
ejpam-5826	576	9	la	la	X
ejpam-5826	576	10	sen	sen	PROPN
ejpam-5826	576	11	,	,	PUNCT
ejpam-5826	576	12	and	and	CCONJ
ejpam-5826	576	13	a	a	DET
ejpam-5826	576	14	fulga	fulga	NOUN
ejpam-5826	576	15	.	.	PUNCT
ejpam-5826	577	1	a	a	DET
ejpam-5826	577	2	note	note	NOUN
ejpam-5826	577	3	on	on	ADP
ejpam-5826	577	4	the	the	DET
ejpam-5826	577	5	górnicki	górnicki	NOUN
ejpam-5826	577	6	-	-	PUNCT
ejpam-5826	577	7	proinov	proinov	ADJ
ejpam-5826	577	8	type	type	NOUN
ejpam-5826	577	9	contraction	contraction	NOUN
ejpam-5826	577	10	.	.	PUNCT
ejpam-5826	578	1	j.	j.	PROPN
ejpam-5826	578	2	function	function	PROPN
ejpam-5826	578	3	spaces	space	NOUN
ejpam-5826	578	4	,	,	PUNCT
ejpam-5826	578	5	article	article	NOUN
ejpam-5826	578	6	i	i	PROPN
ejpam-5826	578	7	d	d	PROPN
ejpam-5826	578	8	6686644:8	6686644:8	NUM
ejpam-5826	578	9	pages	page	NOUN
ejpam-5826	578	10	,	,	PUNCT
ejpam-5826	578	11	2021	2021	NUM
ejpam-5826	578	12	.	.	PUNCT
ejpam-5826	579	1	[	[	X
ejpam-5826	579	2	6	6	NUM
ejpam-5826	579	3	]	]	X
ejpam-5826	579	4	s	s	VERB
ejpam-5826	579	5	panja	panja	PROPN
ejpam-5826	579	6	,	,	PUNCT
ejpam-5826	579	7	k	k	PROPN
ejpam-5826	579	8	roy	roy	PROPN
ejpam-5826	579	9	,	,	PUNCT
ejpam-5826	579	10	m	m	PROPN
ejpam-5826	579	11	saha	saha	NOUN
ejpam-5826	579	12	,	,	PUNCT
ejpam-5826	579	13	and	and	CCONJ
ejpam-5826	579	14	r	r	NOUN
ejpam-5826	579	15	k	k	X
ejpam-5826	579	16	bisht	bisht	ADV
ejpam-5826	579	17	.	.	PUNCT
ejpam-5826	580	1	some	some	DET
ejpam-5826	580	2	fixed	fix	VERB
ejpam-5826	580	3	point	point	NOUN
ejpam-5826	580	4	theorems	theorem	NOUN
ejpam-5826	580	5	via	via	ADP
ejpam-5826	580	6	asymptotic	asymptotic	ADJ
ejpam-5826	580	7	regularity	regularity	NOUN
ejpam-5826	580	8	.	.	PUNCT
ejpam-5826	581	1	filomat	filomat	NOUN
ejpam-5826	581	2	,	,	PUNCT
ejpam-5826	581	3	34(5):1621–1627	34(5):1621–1627	NUM
ejpam-5826	581	4	,	,	PUNCT
ejpam-5826	581	5	2020	2020	NUM
ejpam-5826	581	6	.	.	PUNCT
ejpam-5826	582	1	a.	a.	PROPN
ejpam-5826	582	2	r.	r.	PROPN
ejpam-5826	582	3	khan	khan	PROPN
ejpam-5826	582	4	et	et	PROPN
ejpam-5826	582	5	al	al	PROPN
ejpam-5826	582	6	.	.	PUNCT
ejpam-5826	582	7	/	/	SYM
ejpam-5826	582	8	eur	eur	PROPN
ejpam-5826	582	9	.	.	PUNCT
ejpam-5826	583	1	j.	j.	PROPN
ejpam-5826	583	2	pure	pure	PROPN
ejpam-5826	583	3	appl	appl	PROPN
ejpam-5826	583	4	.	.	PROPN
ejpam-5826	583	5	math	math	PROPN
ejpam-5826	583	6	,	,	PUNCT
ejpam-5826	583	7	18	18	NUM
ejpam-5826	583	8	(	(	PUNCT
ejpam-5826	583	9	2	2	NUM
ejpam-5826	583	10	)	)	PUNCT
ejpam-5826	583	11	(	(	PUNCT
ejpam-5826	583	12	2025	2025	NUM
ejpam-5826	583	13	)	)	PUNCT
ejpam-5826	583	14	,	,	PUNCT
ejpam-5826	583	15	5826	5826	NUM
ejpam-5826	583	16	23	23	NUM
ejpam-5826	583	17	of	of	ADP
ejpam-5826	583	18	23	23	NUM
ejpam-5826	584	1	[	[	X
ejpam-5826	584	2	7	7	NUM
ejpam-5826	584	3	]	]	SYM
ejpam-5826	584	4	a	a	DET
ejpam-5826	584	5	r	r	NOUN
ejpam-5826	584	6	khan	khan	PROPN
ejpam-5826	584	7	and	and	CCONJ
ejpam-5826	584	8	d	d	PROPN
ejpam-5826	584	9	m	m	NOUN
ejpam-5826	584	10	oyetundi	oyetundi	ADJ
ejpam-5826	584	11	.	.	PUNCT
ejpam-5826	585	1	on	on	ADP
ejpam-5826	585	2	some	some	DET
ejpam-5826	585	3	mappings	mapping	NOUN
ejpam-5826	585	4	with	with	ADP
ejpam-5826	585	5	a	a	DET
ejpam-5826	585	6	unique	unique	ADJ
ejpam-5826	585	7	common	common	ADJ
ejpam-5826	585	8	fixed	fix	VERB
ejpam-5826	585	9	point	point	NOUN
ejpam-5826	585	10	.	.	PUNCT
ejpam-5826	586	1	j.	j.	PROPN
ejpam-5826	586	2	fixed	fix	VERB
ejpam-5826	586	3	point	point	PROPN
ejpam-5826	586	4	theory	theory	NOUN
ejpam-5826	586	5	appl	appl	PROPN
ejpam-5826	586	6	.	.	PROPN
ejpam-5826	586	7	,	,	PUNCT
ejpam-5826	586	8	1:22–47	1:22–47	NUM
ejpam-5826	586	9	,	,	PUNCT
ejpam-5826	586	10	2020	2020	NUM
ejpam-5826	586	11	.	.	PUNCT
ejpam-5826	587	1	[	[	X
ejpam-5826	587	2	8	8	NUM
ejpam-5826	587	3	]	]	X
ejpam-5826	587	4	r	r	NOUN
ejpam-5826	587	5	kannan	kannan	PROPN
ejpam-5826	587	6	.	.	PUNCT
ejpam-5826	588	1	some	some	DET
ejpam-5826	588	2	results	result	NOUN
ejpam-5826	588	3	on	on	ADP
ejpam-5826	588	4	fixed	fix	VERB
ejpam-5826	588	5	points	point	NOUN
ejpam-5826	588	6	.	.	PUNCT
ejpam-5826	589	1	bull	bull	NOUN
ejpam-5826	589	2	.	.	PUNCT
ejpam-5826	590	1	calc	calc	PROPN
ejpam-5826	590	2	.	.	PUNCT
ejpam-5826	591	1	math	math	PROPN
ejpam-5826	591	2	.	.	PUNCT
ejpam-5826	592	1	soc	soc	PROPN
ejpam-5826	592	2	.	.	PUNCT
ejpam-5826	592	3	,	,	PUNCT
ejpam-5826	592	4	60:71–76	60:71–76	NUM
ejpam-5826	592	5	,	,	PUNCT
ejpam-5826	592	6	1968	1968	NUM
ejpam-5826	592	7	.	.	PUNCT
ejpam-5826	593	1	[	[	X
ejpam-5826	593	2	9	9	NUM
ejpam-5826	593	3	]	]	X
ejpam-5826	593	4	r	r	NOUN
ejpam-5826	593	5	p	p	PROPN
ejpam-5826	593	6	agarwal	agarwal	PROPN
ejpam-5826	593	7	,	,	PUNCT
ejpam-5826	593	8	b	b	PROPN
ejpam-5826	593	9	o’regan	o’regan	PROPN
ejpam-5826	593	10	,	,	PUNCT
ejpam-5826	593	11	and	and	CCONJ
ejpam-5826	593	12	d	d	NOUN
ejpam-5826	593	13	r	r	NOUN
ejpam-5826	593	14	sahu	sahu	PROPN
ejpam-5826	593	15	.	.	PUNCT
ejpam-5826	593	16	fixed	fix	VERB
ejpam-5826	593	17	point	point	NOUN
ejpam-5826	593	18	theory	theory	NOUN
ejpam-5826	593	19	for	for	ADP
ejpam-5826	593	20	lipschitzian	lipschitzian	ADJ
ejpam-5826	593	21	-	-	PUNCT
ejpam-5826	593	22	type	type	NOUN
ejpam-5826	593	23	mappings	mapping	NOUN
ejpam-5826	593	24	with	with	ADP
ejpam-5826	593	25	applications	application	NOUN
ejpam-5826	593	26	.	.	PUNCT
ejpam-5826	593	27	.	.	PUNCT
ejpam-5826	594	1	springer	springer	NOUN
ejpam-5826	594	2	,	,	PUNCT
ejpam-5826	594	3	new	new	PROPN
ejpam-5826	594	4	york	york	PROPN
ejpam-5826	594	5	,	,	PUNCT
ejpam-5826	594	6	ny	ny	PROPN
ejpam-5826	594	7	,	,	PUNCT
ejpam-5826	594	8	2009	2009	NUM
ejpam-5826	594	9	.	.	PUNCT
ejpam-5826	595	1	[	[	X
ejpam-5826	595	2	10	10	NUM
ejpam-5826	595	3	]	]	X
ejpam-5826	595	4	u	u	NOUN
ejpam-5826	595	5	kohlenbouch	kohlenbouch	NOUN
ejpam-5826	595	6	.	.	PUNCT
ejpam-5826	596	1	some	some	DET
ejpam-5826	596	2	logical	logical	ADJ
ejpam-5826	596	3	metatheorems	metatheorem	NOUN
ejpam-5826	596	4	with	with	ADP
ejpam-5826	596	5	applications	application	NOUN
ejpam-5826	596	6	in	in	ADP
ejpam-5826	596	7	functional	functional	ADJ
ejpam-5826	596	8	analysis	analysis	NOUN
ejpam-5826	596	9	.	.	PUNCT
ejpam-5826	597	1	trans	trans	PROPN
ejpam-5826	597	2	.	.	PUNCT
ejpam-5826	598	1	amer	amer	PROPN
ejpam-5826	598	2	.	.	PUNCT
ejpam-5826	598	3	math	math	PROPN
ejpam-5826	598	4	.	.	PUNCT
ejpam-5826	599	1	soc	soc	PROPN
ejpam-5826	599	2	.	.	PUNCT
ejpam-5826	599	3	,	,	PUNCT
ejpam-5826	599	4	357:89–128	357:89–128	NUM
ejpam-5826	599	5	,	,	PUNCT
ejpam-5826	599	6	2004	2004	NUM
ejpam-5826	599	7	.	.	PUNCT
ejpam-5826	600	1	[	[	X
ejpam-5826	600	2	11	11	NUM
ejpam-5826	600	3	]	]	X
ejpam-5826	600	4	f	f	PROPN
ejpam-5826	600	5	e	e	NOUN
ejpam-5826	600	6	browder	browder	NOUN
ejpam-5826	600	7	and	and	CCONJ
ejpam-5826	600	8	w	w	NOUN
ejpam-5826	600	9	v	v	NOUN
ejpam-5826	600	10	petryshyn	petryshyn	NOUN
ejpam-5826	600	11	.	.	PUNCT
ejpam-5826	601	1	the	the	DET
ejpam-5826	601	2	solution	solution	NOUN
ejpam-5826	601	3	by	by	ADP
ejpam-5826	601	4	iteration	iteration	NOUN
ejpam-5826	601	5	of	of	ADP
ejpam-5826	601	6	nonlinear	nonlinear	ADJ
ejpam-5826	601	7	functional	functional	ADJ
ejpam-5826	601	8	equations	equation	NOUN
ejpam-5826	601	9	in	in	ADP
ejpam-5826	601	10	banach	banach	NOUN
ejpam-5826	601	11	spaces	space	NOUN
ejpam-5826	601	12	.	.	PUNCT
ejpam-5826	602	1	bull	bull	NOUN
ejpam-5826	602	2	.	.	PUNCT
ejpam-5826	603	1	am	be	AUX
ejpam-5826	603	2	.	.	PUNCT
ejpam-5826	604	1	math	math	NOUN
ejpam-5826	604	2	.	.	PUNCT
ejpam-5826	605	1	soc	soc	PROPN
ejpam-5826	605	2	.	.	PUNCT
ejpam-5826	605	3	,	,	PUNCT
ejpam-5826	606	1	72:571–575	72:571–575	PROPN
ejpam-5826	606	2	,	,	PUNCT
ejpam-5826	606	3	1966	1966	NUM
ejpam-5826	606	4	.	.	PUNCT
ejpam-5826	607	1	[	[	X
ejpam-5826	607	2	12	12	NUM
ejpam-5826	607	3	]	]	PUNCT
ejpam-5826	607	4	l	l	NOUN
ejpam-5826	607	5	j	j	PROPN
ejpam-5826	607	6	ćirić.	ćirić.	PROPN
ejpam-5826	607	7	on	on	ADP
ejpam-5826	607	8	contraction	contraction	NOUN
ejpam-5826	607	9	type	type	NOUN
ejpam-5826	607	10	mappings	mapping	NOUN
ejpam-5826	607	11	.	.	PUNCT
ejpam-5826	608	1	math	math	NOUN
ejpam-5826	608	2	.	.	PUNCT
ejpam-5826	609	1	balk	balk	VERB
ejpam-5826	609	2	.	.	PUNCT
ejpam-5826	610	1	,	,	PUNCT
ejpam-5826	610	2	1:52–57	1:52–57	NUM
ejpam-5826	610	3	,	,	PUNCT
ejpam-5826	610	4	1971	1971	NUM
ejpam-5826	610	5	.	.	PUNCT
ejpam-5826	611	1	[	[	X
ejpam-5826	611	2	13	13	NUM
ejpam-5826	611	3	]	]	PUNCT
ejpam-5826	611	4	a	a	DET
ejpam-5826	611	5	pant	pant	NOUN
ejpam-5826	611	6	and	and	CCONJ
ejpam-5826	611	7	r	r	NOUN
ejpam-5826	611	8	p	p	NOUN
ejpam-5826	611	9	pant	pant	NOUN
ejpam-5826	611	10	.	.	PUNCT
ejpam-5826	612	1	fixed	fix	VERB
ejpam-5826	612	2	points	point	NOUN
ejpam-5826	612	3	and	and	CCONJ
ejpam-5826	612	4	continuity	continuity	NOUN
ejpam-5826	612	5	of	of	ADP
ejpam-5826	612	6	contractive	contractive	ADJ
ejpam-5826	612	7	maps	map	NOUN
ejpam-5826	612	8	.	.	PUNCT
ejpam-5826	613	1	filomat	filomat	NOUN
ejpam-5826	613	2	,	,	PUNCT
ejpam-5826	613	3	31:3501–3507	31:3501–3507	NUM
ejpam-5826	613	4	,	,	PUNCT
ejpam-5826	613	5	2017	2017	NUM
ejpam-5826	613	6	.	.	PUNCT
ejpam-5826	614	1	[	[	X
ejpam-5826	614	2	14	14	NUM
ejpam-5826	614	3	]	]	X
ejpam-5826	614	4	h	h	PROPN
ejpam-5826	614	5	huang	huang	PROPN
ejpam-5826	614	6	and	and	CCONJ
ejpam-5826	614	7	x	x	PROPN
ejpam-5826	614	8	qian	qian	PROPN
ejpam-5826	614	9	.	.	PUNCT
ejpam-5826	615	1	on	on	ADP
ejpam-5826	615	2	common	common	ADJ
ejpam-5826	615	3	fixed	fix	VERB
ejpam-5826	615	4	point	point	NOUN
ejpam-5826	615	5	of	of	ADP
ejpam-5826	615	6	nonlinear	nonlinear	ADJ
ejpam-5826	615	7	contractive	contractive	ADJ
ejpam-5826	615	8	mappings	mapping	NOUN
ejpam-5826	615	9	.	.	PUNCT
ejpam-5826	616	1	aims	aim	VERB
ejpam-5826	616	2	mathematics	mathematic	NOUN
ejpam-5826	616	3	,	,	PUNCT
ejpam-5826	616	4	1(1):607–621	1(1):607–621	NUM
ejpam-5826	616	5	,	,	PUNCT
ejpam-5826	616	6	2022	2022	NUM
ejpam-5826	616	7	.	.	PUNCT
ejpam-5826	617	1	[	[	X
ejpam-5826	617	2	15	15	NUM
ejpam-5826	617	3	]	]	X
ejpam-5826	617	4	w	w	PROPN
ejpam-5826	617	5	takahashi	takahashi	PROPN
ejpam-5826	617	6	.	.	PUNCT
ejpam-5826	618	1	a	a	DET
ejpam-5826	618	2	convexity	convexity	NOUN
ejpam-5826	618	3	in	in	ADP
ejpam-5826	618	4	metric	metric	ADJ
ejpam-5826	618	5	spaces	space	NOUN
ejpam-5826	618	6	and	and	CCONJ
ejpam-5826	618	7	nonexpansive	nonexpansive	ADJ
ejpam-5826	618	8	mappings	mapping	NOUN
ejpam-5826	618	9	.	.	PUNCT
ejpam-5826	619	1	kodai	kodai	PROPN
ejpam-5826	619	2	math	math	PROPN
ejpam-5826	619	3	sem	sem	PROPN
ejpam-5826	619	4	rep	rep	PROPN
ejpam-5826	619	5	.	.	PROPN
ejpam-5826	619	6	,	,	PUNCT
ejpam-5826	619	7	22:142–149	22:142–149	PROPN
ejpam-5826	619	8	,	,	PUNCT
ejpam-5826	619	9	1970	1970	NUM
ejpam-5826	619	10	.	.	PUNCT
ejpam-5826	620	1	[	[	X
ejpam-5826	620	2	16	16	NUM
ejpam-5826	620	3	]	]	PUNCT
ejpam-5826	620	4	a	a	DET
ejpam-5826	620	5	r	r	NOUN
ejpam-5826	620	6	khan	khan	PROPN
ejpam-5826	620	7	,	,	PUNCT
ejpam-5826	620	8	h	h	PROPN
ejpam-5826	620	9	fukhar	fukhar	VERB
ejpam-5826	620	10	ud	ud	INTJ
ejpam-5826	620	11	din	din	PROPN
ejpam-5826	620	12	,	,	PUNCT
ejpam-5826	620	13	and	and	CCONJ
ejpam-5826	620	14	m	m	VERB
ejpam-5826	620	15	a	a	DET
ejpam-5826	620	16	a.khan	a.khan	NOUN
ejpam-5826	620	17	.	.	PUNCT
ejpam-5826	621	1	an	an	DET
ejpam-5826	621	2	implicit	implicit	ADJ
ejpam-5826	621	3	algorithm	algorithm	NOUN
ejpam-5826	621	4	for	for	ADP
ejpam-5826	621	5	two	two	NUM
ejpam-5826	621	6	finite	finite	ADJ
ejpam-5826	621	7	families	family	NOUN
ejpam-5826	621	8	of	of	ADP
ejpam-5826	621	9	nonexpansive	nonexpansive	ADJ
ejpam-5826	621	10	type	type	NOUN
ejpam-5826	621	11	maps	map	NOUN
ejpam-5826	621	12	in	in	ADP
ejpam-5826	621	13	hyperblic	hyperblic	ADJ
ejpam-5826	621	14	spaces	space	NOUN
ejpam-5826	621	15	.	.	PUNCT
ejpam-5826	622	1	fixed	fix	VERB
ejpam-5826	622	2	point	point	NOUN
ejpam-5826	622	3	theory	theory	NOUN
ejpam-5826	622	4	appl	appl	PROPN
ejpam-5826	622	5	.	.	PROPN
ejpam-5826	622	6	,	,	PUNCT
ejpam-5826	622	7	2012:54	2012:54	NUM
ejpam-5826	622	8	,	,	PUNCT
ejpam-5826	622	9	2012	2012	NUM
ejpam-5826	622	10	.	.	PUNCT
ejpam-5826	623	1	[	[	X
ejpam-5826	623	2	17	17	NUM
ejpam-5826	623	3	]	]	SYM
ejpam-5826	623	4	v	v	NOUN
ejpam-5826	623	5	berinde	berinde	NOUN
ejpam-5826	623	6	and	and	CCONJ
ejpam-5826	623	7	m	m	NOUN
ejpam-5826	623	8	pacurar	pacurar	NOUN
ejpam-5826	623	9	.	.	PUNCT
ejpam-5826	624	1	existence	existence	NOUN
ejpam-5826	624	2	and	and	CCONJ
ejpam-5826	624	3	approximation	approximation	NOUN
ejpam-5826	624	4	of	of	ADP
ejpam-5826	624	5	fixed	fix	VERB
ejpam-5826	624	6	point	point	NOUN
ejpam-5826	624	7	of	of	ADP
ejpam-5826	624	8	enriched	enrich	VERB
ejpam-5826	624	9	contractions	contraction	NOUN
ejpam-5826	624	10	and	and	CCONJ
ejpam-5826	624	11	enriched	enriched	ADJ
ejpam-5826	624	12	f	f	PROPN
ejpam-5826	624	13	-contractions	-contraction	NOUN
ejpam-5826	624	14	.	.	PUNCT
ejpam-5826	624	15	.	.	PUNCT
ejpam-5826	625	1	symmetry	symmetry	PROPN
ejpam-5826	625	2	,	,	PUNCT
ejpam-5826	625	3	13:498	13:498	NUM
ejpam-5826	625	4	,	,	PUNCT
ejpam-5826	625	5	2021	2021	NUM
ejpam-5826	625	6	.	.	PUNCT
ejpam-5826	626	1	[	[	X
ejpam-5826	626	2	18	18	NUM
ejpam-5826	626	3	]	]	SYM
ejpam-5826	626	4	v	v	NOUN
ejpam-5826	626	5	berinde	berinde	NOUN
ejpam-5826	626	6	and	and	CCONJ
ejpam-5826	626	7	m	m	PROPN
ejpam-5826	626	8	pacurar	pacurar	NOUN
ejpam-5826	626	9	.	.	PUNCT
ejpam-5826	627	1	fixed	fix	VERB
ejpam-5826	627	2	point	point	NOUN
ejpam-5826	627	3	theorems	theorem	NOUN
ejpam-5826	627	4	for	for	ADP
ejpam-5826	627	5	enriched	enriched	ADJ
ejpam-5826	627	6	ciric	ciric	ADJ
ejpam-5826	627	7	-	-	PUNCT
ejpam-5826	627	8	reich	reich	NOUN
ejpam-5826	627	9	-	-	PUNCT
ejpam-5826	627	10	rus	rus	NOUN
ejpam-5826	627	11	contractions	contraction	NOUN
ejpam-5826	627	12	in	in	ADP
ejpam-5826	627	13	banach	banach	NOUN
ejpam-5826	627	14	spaces	space	NOUN
ejpam-5826	627	15	and	and	CCONJ
ejpam-5826	627	16	convex	convex	VERB
ejpam-5826	627	17	metric	metric	ADJ
ejpam-5826	627	18	spaces	space	NOUN
ejpam-5826	627	19	.	.	PUNCT
ejpam-5826	628	1	carpathian	carpathian	ADJ
ejpam-5826	628	2	j.math	j.math	NOUN
ejpam-5826	628	3	,	,	PUNCT
ejpam-5826	628	4	37:173–185	37:173–185	NUM
ejpam-5826	628	5	,	,	PUNCT
ejpam-5826	628	6	2021	2021	NUM
ejpam-5826	628	7	.	.	PUNCT
ejpam-5826	629	1	[	[	X
ejpam-5826	629	2	19	19	NUM
ejpam-5826	629	3	]	]	X
ejpam-5826	629	4	g	g	PROPN
ejpam-5826	629	5	z	z	NOUN
ejpam-5826	629	6	eskandani	eskandani	NOUN
ejpam-5826	629	7	and	and	CCONJ
ejpam-5826	629	8	m	m	AUX
ejpam-5826	629	9	raeisi	raeisi	VERB
ejpam-5826	629	10	.	.	PUNCT
ejpam-5826	630	1	three	three	NUM
ejpam-5826	630	2	convergence	convergence	NOUN
ejpam-5826	630	3	results	result	NOUN
ejpam-5826	630	4	for	for	ADP
ejpam-5826	630	5	inexact	inexact	ADJ
ejpam-5826	630	6	orbits	orbit	NOUN
ejpam-5826	630	7	of	of	ADP
ejpam-5826	630	8	nonexpansive	nonexpansive	ADJ
ejpam-5826	630	9	mappings	mapping	NOUN
ejpam-5826	630	10	.	.	PUNCT
ejpam-5826	631	1	j.	j.	PROPN
ejpam-5826	631	2	appl	appl	PROPN
ejpam-5826	631	3	.	.	PUNCT
ejpam-5826	632	1	numer	numer	PROPN
ejpam-5826	632	2	.	.	PROPN
ejpam-5826	633	1	optim	optim	PROPN
ejpam-5826	633	2	.	.	PROPN
ejpam-5826	633	3	,	,	PUNCT
ejpam-5826	633	4	1:157–165	1:157–165	NUM
ejpam-5826	633	5	,	,	PUNCT
ejpam-5826	633	6	2019	2019	NUM
ejpam-5826	633	7	.	.	PUNCT
ejpam-5826	634	1	[	[	X
ejpam-5826	634	2	20	20	NUM
ejpam-5826	634	3	]	]	X
ejpam-5826	634	4	m	m	VERB
ejpam-5826	634	5	a	a	DET
ejpam-5826	634	6	khamsi	khamsi	NOUN
ejpam-5826	634	7	and	and	CCONJ
ejpam-5826	634	8	a	a	DET
ejpam-5826	634	9	r	r	NOUN
ejpam-5826	634	10	khan	khan	PROPN
ejpam-5826	634	11	.	.	PUNCT
ejpam-5826	635	1	inequalities	inequality	NOUN
ejpam-5826	635	2	in	in	ADP
ejpam-5826	635	3	metric	metric	ADJ
ejpam-5826	635	4	spaces	space	NOUN
ejpam-5826	635	5	with	with	ADP
ejpam-5826	635	6	applications	application	NOUN
ejpam-5826	635	7	.	.	PUNCT
ejpam-5826	636	1	nonlinear	nonlinear	ADJ
ejpam-5826	636	2	analysis	analysis	NOUN
ejpam-5826	636	3	,	,	PUNCT
ejpam-5826	636	4	74:4036–4045	74:4036–4045	NUM
ejpam-5826	636	5	,	,	PUNCT
ejpam-5826	636	6	2011	2011	NUM
ejpam-5826	636	7	.	.	PUNCT
ejpam-5826	637	1	[	[	X
ejpam-5826	637	2	21	21	NUM
ejpam-5826	637	3	]	]	X
ejpam-5826	637	4	a	a	DET
ejpam-5826	637	5	r	r	NOUN
ejpam-5826	637	6	khan	khan	NOUN
ejpam-5826	637	7	.	.	PUNCT
ejpam-5826	638	1	properties	property	NOUN
ejpam-5826	638	2	of	of	ADP
ejpam-5826	638	3	fixed	fix	VERB
ejpam-5826	638	4	point	point	NOUN
ejpam-5826	638	5	set	set	NOUN
ejpam-5826	638	6	of	of	ADP
ejpam-5826	638	7	a	a	DET
ejpam-5826	638	8	multivaued	multivaued	ADJ
ejpam-5826	638	9	map	map	NOUN
ejpam-5826	638	10	.	.	PUNCT
ejpam-5826	639	1	j.	j.	PROPN
ejpam-5826	639	2	appl	appl	PROPN
ejpam-5826	639	3	.	.	PROPN
ejpam-5826	640	1	math	math	PROPN
ejpam-5826	640	2	.	.	PUNCT
ejpam-5826	640	3	stoch	stoch	PROPN
ejpam-5826	640	4	.	.	PUNCT
ejpam-5826	641	1	anal	anal	PROPN
ejpam-5826	641	2	.	.	PUNCT
ejpam-5826	641	3	,	,	PUNCT
ejpam-5826	641	4	3:323–331	3:323–331	NUM
ejpam-5826	641	5	,	,	PUNCT
ejpam-5826	641	6	2005	2005	NUM
ejpam-5826	641	7	.	.	PUNCT
ejpam-5826	642	1	[	[	X
ejpam-5826	642	2	22	22	NUM
ejpam-5826	642	3	]	]	PUNCT
ejpam-5826	642	4	t	t	PROPN
ejpam-5826	642	5	zamfirescu	zamfirescu	PROPN
ejpam-5826	642	6	.	.	PUNCT
ejpam-5826	643	1	fixed	fix	VERB
ejpam-5826	643	2	point	point	NOUN
ejpam-5826	643	3	theoerms	theoerm	NOUN
ejpam-5826	643	4	in	in	ADP
ejpam-5826	643	5	metric	metric	ADJ
ejpam-5826	643	6	spaces	space	NOUN
ejpam-5826	643	7	.	.	PUNCT
ejpam-5826	644	1	arch	arch	NOUN
ejpam-5826	644	2	.	.	PUNCT
ejpam-5826	645	1	math	math	NOUN
ejpam-5826	645	2	.	.	PUNCT
ejpam-5826	645	3	,	,	PUNCT
ejpam-5826	645	4	23:292–298	23:292–298	NUM
ejpam-5826	645	5	,	,	PUNCT
ejpam-5826	645	6	1972	1972	NUM
ejpam-5826	645	7	.	.	PUNCT
ejpam-5826	646	1	[	[	X
ejpam-5826	646	2	23	23	NUM
ejpam-5826	646	3	]	]	X
ejpam-5826	646	4	h	h	NOUN
ejpam-5826	646	5	brunner	brunner	PROPN
ejpam-5826	646	6	.	.	PUNCT
ejpam-5826	647	1	volterra	volterra	PROPN
ejpam-5826	647	2	integral	integral	ADJ
ejpam-5826	647	3	equations	equation	NOUN
ejpam-5826	647	4	:	:	PUNCT
ejpam-5826	647	5	an	an	DET
ejpam-5826	647	6	introduction	introduction	NOUN
ejpam-5826	647	7	to	to	ADP
ejpam-5826	647	8	theory	theory	NOUN
ejpam-5826	647	9	and	and	CCONJ
ejpam-5826	647	10	applications	application	NOUN
ejpam-5826	647	11	.	.	PUNCT
ejpam-5826	648	1	cambridge	cambridge	PROPN
ejpam-5826	648	2	university	university	PROPN
ejpam-5826	648	3	press	press	PROPN
ejpam-5826	648	4	,	,	PUNCT
ejpam-5826	648	5	cambridge	cambridge	PROPN
ejpam-5826	648	6	university	university	PROPN
ejpam-5826	648	7	,	,	PUNCT
ejpam-5826	648	8	2017	2017	NUM
ejpam-5826	648	9	.	.	PUNCT
ejpam-5826	649	1	[	[	X
ejpam-5826	649	2	24	24	NUM
ejpam-5826	649	3	]	]	PUNCT
ejpam-5826	649	4	a	a	DET
ejpam-5826	649	5	friedman	friedman	NOUN
ejpam-5826	649	6	.	.	PUNCT
ejpam-5826	650	1	on	on	ADP
ejpam-5826	650	2	integral	integral	ADJ
ejpam-5826	650	3	equations	equation	NOUN
ejpam-5826	650	4	of	of	ADP
ejpam-5826	650	5	volterra	volterra	PROPN
ejpam-5826	650	6	type	type	PROPN
ejpam-5826	650	7	.	.	PUNCT
ejpam-5826	651	1	journal	journal	PROPN
ejpam-5826	651	2	d’analyse	d’analyse	PROPN
ejpam-5826	651	3	mathématique	mathématique	PROPN
ejpam-5826	651	4	,	,	PUNCT
ejpam-5826	651	5	11:381–413	11:381–413	PROPN
ejpam-5826	651	6	,	,	PUNCT
ejpam-5826	651	7	1963	1963	NUM
ejpam-5826	651	8	.	.	PUNCT
ejpam-5826	652	1	[	[	X
ejpam-5826	652	2	25	25	NUM
ejpam-5826	652	3	]	]	PUNCT
ejpam-5826	652	4	a	a	DET
ejpam-5826	652	5	i	i	NOUN
ejpam-5826	652	6	kozhanov	kozhanov	PROPN
ejpam-5826	652	7	and	and	CCONJ
ejpam-5826	652	8	b	b	X
ejpam-5826	652	9	k	k	PROPN
ejpam-5826	652	10	barotov	barotov	PROPN
ejpam-5826	652	11	.	.	PUNCT
ejpam-5826	653	1	volterra	volterra	PROPN
ejpam-5826	653	2	type	type	PROPN
ejpam-5826	653	3	integro	integro	PROPN
ejpam-5826	653	4	-	-	PUNCT
ejpam-5826	653	5	differential	differential	NOUN
ejpam-5826	653	6	equations	equation	NOUN
ejpam-5826	653	7	with	with	ADP
ejpam-5826	653	8	degeneracy	degeneracy	PROPN
ejpam-5826	653	9	.	.	PUNCT
ejpam-5826	654	1	j.	j.	PROPN
ejpam-5826	654	2	mathematical	mathematical	PROPN
ejpam-5826	654	3	sci	sci	PROPN
ejpam-5826	654	4	.	.	PROPN
ejpam-5826	654	5	,	,	PUNCT
ejpam-5826	654	6	287:69–75	287:69–75	NUM
ejpam-5826	654	7	,	,	PUNCT
ejpam-5826	654	8	2025	2025	NUM
ejpam-5826	654	9	.	.	PUNCT