id	sid	tid	token	lemma	pos
ejpam-3298	1	1	common	common	ADJ
ejpam-3298	1	2	fixed	fix	VERB
ejpam-3298	1	3	point	point	NOUN
ejpam-3298	1	4	theorems	theorem	NOUN
ejpam-3298	1	5	in	in	ADP
ejpam-3298	1	6	metric	metric	ADJ
ejpam-3298	1	7	spaces	space	NOUN
ejpam-3298	1	8	with	with	ADP
ejpam-3298	1	9	applications	application	NOUN
ejpam-3298	1	10	european	european	PROPN
ejpam-3298	1	11	journal	journal	PROPN
ejpam-3298	1	12	of	of	ADP
ejpam-3298	1	13	pure	pure	ADJ
ejpam-3298	1	14	and	and	CCONJ
ejpam-3298	1	15	applied	apply	VERB
ejpam-3298	1	16	mathematics	mathematic	NOUN
ejpam-3298	1	17	vol	vol	NOUN
ejpam-3298	1	18	.	.	PUNCT
ejpam-3298	2	1	11	11	NUM
ejpam-3298	2	2	,	,	PUNCT
ejpam-3298	2	3	no	no	INTJ
ejpam-3298	2	4	.	.	NOUN
ejpam-3298	2	5	4	4	NUM
ejpam-3298	2	6	,	,	PUNCT
ejpam-3298	2	7	2018	2018	NUM
ejpam-3298	2	8	,	,	PUNCT
ejpam-3298	2	9	1177	1177	NUM
ejpam-3298	2	10	-	-	SYM
ejpam-3298	2	11	1190	1190	NUM
ejpam-3298	2	12	issn	issn	PROPN
ejpam-3298	2	13	1307	1307	NUM
ejpam-3298	2	14	-	-	SYM
ejpam-3298	2	15	5543	5543	NUM
ejpam-3298	2	16	–	–	PUNCT
ejpam-3298	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3298	2	18	published	publish	VERB
ejpam-3298	2	19	by	by	ADP
ejpam-3298	2	20	new	new	PROPN
ejpam-3298	2	21	york	york	PROPN
ejpam-3298	2	22	business	business	PROPN
ejpam-3298	2	23	global	global	ADJ
ejpam-3298	2	24	common	common	ADJ
ejpam-3298	2	25	fixed	fix	VERB
ejpam-3298	2	26	point	point	NOUN
ejpam-3298	2	27	theorems	theorem	NOUN
ejpam-3298	2	28	in	in	ADP
ejpam-3298	2	29	metric	metric	ADJ
ejpam-3298	2	30	spaces	space	NOUN
ejpam-3298	2	31	with	with	ADP
ejpam-3298	2	32	applications	application	NOUN
ejpam-3298	2	33	pushpendra	pushpendra	NOUN
ejpam-3298	2	34	semwal1,∗	semwal1,∗	NOUN
ejpam-3298	2	35	,	,	PUNCT
ejpam-3298	2	36	komal1	komal1	PROPN
ejpam-3298	2	37	1	1	NUM
ejpam-3298	2	38	department	department	NOUN
ejpam-3298	2	39	of	of	ADP
ejpam-3298	2	40	mathematics	mathematic	NOUN
ejpam-3298	2	41	,	,	PUNCT
ejpam-3298	2	42	sops	sop	NOUN
ejpam-3298	2	43	,	,	PUNCT
ejpam-3298	2	44	doon	doon	PROPN
ejpam-3298	2	45	university	university	PROPN
ejpam-3298	2	46	,	,	PUNCT
ejpam-3298	2	47	dehradun	dehradun	PROPN
ejpam-3298	2	48	,	,	PUNCT
ejpam-3298	2	49	india	india	PROPN
ejpam-3298	2	50	abstract	abstract	NOUN
ejpam-3298	2	51	.	.	PUNCT
ejpam-3298	3	1	in	in	ADP
ejpam-3298	3	2	this	this	DET
ejpam-3298	3	3	paper	paper	NOUN
ejpam-3298	3	4	,	,	PUNCT
ejpam-3298	3	5	we	we	PRON
ejpam-3298	3	6	investigate	investigate	VERB
ejpam-3298	3	7	the	the	DET
ejpam-3298	3	8	existence	existence	NOUN
ejpam-3298	3	9	and	and	CCONJ
ejpam-3298	3	10	uniqueness	uniqueness	NOUN
ejpam-3298	3	11	of	of	ADP
ejpam-3298	3	12	common	common	ADJ
ejpam-3298	3	13	fixed	fix	VERB
ejpam-3298	3	14	point	point	NOUN
ejpam-3298	3	15	theorems	theorem	NOUN
ejpam-3298	3	16	for	for	ADP
ejpam-3298	3	17	certain	certain	ADJ
ejpam-3298	3	18	contractive	contractive	ADJ
ejpam-3298	3	19	type	type	NOUN
ejpam-3298	3	20	of	of	ADP
ejpam-3298	3	21	mappings	mapping	NOUN
ejpam-3298	3	22	.	.	PUNCT
ejpam-3298	4	1	as	as	ADP
ejpam-3298	4	2	an	an	DET
ejpam-3298	4	3	application	application	NOUN
ejpam-3298	4	4	the	the	DET
ejpam-3298	4	5	existence	existence	NOUN
ejpam-3298	4	6	and	and	CCONJ
ejpam-3298	4	7	uniqueness	uniqueness	NOUN
ejpam-3298	4	8	of	of	ADP
ejpam-3298	4	9	common	common	ADJ
ejpam-3298	4	10	solutions	solution	NOUN
ejpam-3298	4	11	for	for	ADP
ejpam-3298	4	12	a	a	DET
ejpam-3298	4	13	system	system	NOUN
ejpam-3298	4	14	of	of	ADP
ejpam-3298	4	15	functional	functional	ADJ
ejpam-3298	4	16	equations	equation	NOUN
ejpam-3298	4	17	arising	arise	VERB
ejpam-3298	4	18	in	in	ADP
ejpam-3298	4	19	dynamic	dynamic	ADJ
ejpam-3298	4	20	programming	programming	NOUN
ejpam-3298	4	21	are	be	AUX
ejpam-3298	4	22	discuss	discus	VERB
ejpam-3298	4	23	by	by	ADP
ejpam-3298	4	24	using	use	VERB
ejpam-3298	4	25	the	the	DET
ejpam-3298	4	26	our	our	PRON
ejpam-3298	4	27	results	result	NOUN
ejpam-3298	4	28	.	.	PUNCT
ejpam-3298	5	1	2010	2010	NUM
ejpam-3298	5	2	mathematics	mathematic	NOUN
ejpam-3298	5	3	subject	subject	NOUN
ejpam-3298	5	4	classifications	classification	NOUN
ejpam-3298	5	5	:	:	PUNCT
ejpam-3298	5	6	49l20	49l20	NUM
ejpam-3298	5	7	,	,	PUNCT
ejpam-3298	5	8	49l99	49l99	NUM
ejpam-3298	5	9	,	,	PUNCT
ejpam-3298	5	10	54h25	54h25	NUM
ejpam-3298	5	11	,	,	PUNCT
ejpam-3298	5	12	90c39	90c39	NOUN
ejpam-3298	5	13	key	key	ADJ
ejpam-3298	5	14	words	word	NOUN
ejpam-3298	5	15	and	and	CCONJ
ejpam-3298	5	16	phrases	phrase	NOUN
ejpam-3298	5	17	:	:	PUNCT
ejpam-3298	5	18	common	common	ADJ
ejpam-3298	5	19	fixed	fix	VERB
ejpam-3298	5	20	point	point	NOUN
ejpam-3298	5	21	,	,	PUNCT
ejpam-3298	5	22	asymptotically	asymptotically	ADV
ejpam-3298	5	23	continuous	continuous	ADJ
ejpam-3298	5	24	,	,	PUNCT
ejpam-3298	5	25	weakly	weakly	ADV
ejpam-3298	5	26	compatible	compatible	ADJ
ejpam-3298	5	27	mapping	mapping	NOUN
ejpam-3298	5	28	.	.	PUNCT
ejpam-3298	6	1	1	1	X
ejpam-3298	6	2	.	.	X
ejpam-3298	6	3	introduction	introduction	NOUN
ejpam-3298	6	4	bellman	bellman	NOUN
ejpam-3298	6	5	and	and	CCONJ
ejpam-3298	6	6	lee	lee	PROPN
ejpam-3298	7	1	[	[	X
ejpam-3298	7	2	3	3	NUM
ejpam-3298	7	3	]	]	PUNCT
ejpam-3298	7	4	first	first	ADV
ejpam-3298	7	5	introduced	introduce	VERB
ejpam-3298	7	6	the	the	DET
ejpam-3298	7	7	basic	basic	ADJ
ejpam-3298	7	8	form	form	NOUN
ejpam-3298	7	9	of	of	ADP
ejpam-3298	7	10	the	the	DET
ejpam-3298	7	11	functional	functional	ADJ
ejpam-3298	7	12	equations	equation	NOUN
ejpam-3298	7	13	in	in	ADP
ejpam-3298	7	14	dynamic	dynamic	ADJ
ejpam-3298	7	15	programming	programming	NOUN
ejpam-3298	7	16	is	be	AUX
ejpam-3298	7	17	as	as	SCONJ
ejpam-3298	7	18	follows	follow	VERB
ejpam-3298	7	19	:	:	PUNCT
ejpam-3298	7	20	f(x	f(x	PROPN
ejpam-3298	7	21	)	)	PUNCT
ejpam-3298	8	1	=	=	SYM
ejpam-3298	8	2	opty∈dh(x	opty∈dh(x	PROPN
ejpam-3298	8	3	,	,	PUNCT
ejpam-3298	8	4	y	y	PROPN
ejpam-3298	8	5	,	,	PUNCT
ejpam-3298	8	6	f(t	f(t	PROPN
ejpam-3298	8	7	(	(	PUNCT
ejpam-3298	8	8	x	x	X
ejpam-3298	8	9	,	,	PUNCT
ejpam-3298	8	10	y)))∀x	y)))∀x	NOUN
ejpam-3298	8	11	∈	∈	NOUN
ejpam-3298	8	12	s	s	X
ejpam-3298	8	13	(	(	PUNCT
ejpam-3298	8	14	1	1	NUM
ejpam-3298	8	15	)	)	PUNCT
ejpam-3298	8	16	where	where	SCONJ
ejpam-3298	8	17	opt	opt	NOUN
ejpam-3298	8	18	represent	represent	VERB
ejpam-3298	8	19	sup	sup	NOUN
ejpam-3298	8	20	.	.	PUNCT
ejpam-3298	8	21	or	or	CCONJ
ejpam-3298	8	22	inf	inf	PROPN
ejpam-3298	8	23	.	.	PROPN
ejpam-3298	8	24	,	,	PUNCT
ejpam-3298	8	25	x	x	X
ejpam-3298	8	26	,	,	PUNCT
ejpam-3298	8	27	y	y	PROPN
ejpam-3298	8	28	denote	denote	VERB
ejpam-3298	8	29	the	the	DET
ejpam-3298	8	30	state	state	NOUN
ejpam-3298	8	31	and	and	CCONJ
ejpam-3298	8	32	decicion	decicion	NOUN
ejpam-3298	8	33	vectors	vector	NOUN
ejpam-3298	8	34	respectively	respectively	ADV
ejpam-3298	8	35	,	,	PUNCT
ejpam-3298	8	36	t	t	PROPN
ejpam-3298	8	37	stands	stand	VERB
ejpam-3298	8	38	for	for	ADP
ejpam-3298	8	39	the	the	DET
ejpam-3298	8	40	transformation	transformation	NOUN
ejpam-3298	8	41	of	of	ADP
ejpam-3298	8	42	the	the	DET
ejpam-3298	8	43	process	process	NOUN
ejpam-3298	8	44	and	and	CCONJ
ejpam-3298	8	45	f(x	f(x	NOUN
ejpam-3298	8	46	)	)	PUNCT
ejpam-3298	9	1	represents	represent	VERB
ejpam-3298	9	2	the	the	DET
ejpam-3298	9	3	optimal	optimal	ADJ
ejpam-3298	9	4	return	return	NOUN
ejpam-3298	9	5	function	function	NOUN
ejpam-3298	9	6	with	with	ADP
ejpam-3298	9	7	the	the	DET
ejpam-3298	9	8	initial	initial	ADJ
ejpam-3298	9	9	state	state	NOUN
ejpam-3298	9	10	x.afterwards	x.afterward	NOUN
ejpam-3298	9	11	,	,	PUNCT
ejpam-3298	9	12	the	the	DET
ejpam-3298	9	13	existence	existence	NOUN
ejpam-3298	9	14	and	and	CCONJ
ejpam-3298	9	15	uniqueness	uniqueness	NOUN
ejpam-3298	9	16	of	of	ADP
ejpam-3298	9	17	fixed	fix	VERB
ejpam-3298	9	18	point	point	NOUN
ejpam-3298	9	19	solutions	solution	NOUN
ejpam-3298	9	20	for	for	ADP
ejpam-3298	9	21	several	several	ADJ
ejpam-3298	9	22	classes	class	NOUN
ejpam-3298	9	23	of	of	ADP
ejpam-3298	9	24	contractive	contractive	ADJ
ejpam-3298	9	25	mappings	mapping	NOUN
ejpam-3298	9	26	and	and	CCONJ
ejpam-3298	9	27	functional	functional	ADJ
ejpam-3298	9	28	equations	equation	NOUN
ejpam-3298	9	29	studied	study	VERB
ejpam-3298	9	30	by	by	ADP
ejpam-3298	9	31	many	many	ADJ
ejpam-3298	9	32	investigators	investigator	NOUN
ejpam-3298	9	33	such	such	ADJ
ejpam-3298	9	34	as	as	ADP
ejpam-3298	9	35	bhakta	bhakta	NOUN
ejpam-3298	9	36	and	and	CCONJ
ejpam-3298	9	37	mitra	mitra	PROPN
ejpam-3298	10	1	[	[	X
ejpam-3298	10	2	5	5	NUM
ejpam-3298	10	3	]	]	PUNCT
ejpam-3298	10	4	,	,	PUNCT
ejpam-3298	10	5	liu	liu	PROPN
ejpam-3298	11	1	[	[	X
ejpam-3298	11	2	15	15	NUM
ejpam-3298	11	3	]	]	PUNCT
ejpam-3298	11	4	,	,	PUNCT
ejpam-3298	11	5	liu	liu	PROPN
ejpam-3298	11	6	and	and	CCONJ
ejpam-3298	11	7	ume	ume	ADJ
ejpam-3298	12	1	[	[	X
ejpam-3298	12	2	20	20	NUM
ejpam-3298	12	3	]	]	PUNCT
ejpam-3298	12	4	,	,	PUNCT
ejpam-3298	12	5	pathak	pathak	PROPN
ejpam-3298	12	6	and	and	CCONJ
ejpam-3298	12	7	fisher	fisher	PROPN
ejpam-3298	12	8	[	[	X
ejpam-3298	12	9	21	21	NUM
ejpam-3298	12	10	]	]	PUNCT
ejpam-3298	12	11	,	,	PUNCT
ejpam-3298	12	12	baskaran	baskaran	ADJ
ejpam-3298	12	13	and	and	CCONJ
ejpam-3298	12	14	subhramanyam	subhramanyam	VERB
ejpam-3298	13	1	[	[	X
ejpam-3298	13	2	1	1	X
ejpam-3298	13	3	]	]	PUNCT
ejpam-3298	13	4	and	and	CCONJ
ejpam-3298	13	5	others	other	NOUN
ejpam-3298	13	6	.	.	PUNCT
ejpam-3298	14	1	ray	ray	VERB
ejpam-3298	15	1	[	[	X
ejpam-3298	15	2	22	22	NUM
ejpam-3298	15	3	]	]	PUNCT
ejpam-3298	15	4	proved	prove	VERB
ejpam-3298	15	5	two	two	NUM
ejpam-3298	15	6	common	common	ADJ
ejpam-3298	15	7	fixed	fix	VERB
ejpam-3298	15	8	point	point	NOUN
ejpam-3298	15	9	theorems	theorem	NOUN
ejpam-3298	15	10	for	for	ADP
ejpam-3298	15	11	three	three	NUM
ejpam-3298	15	12	self	self	NOUN
ejpam-3298	15	13	mappings	mapping	NOUN
ejpam-3298	15	14	f	f	NOUN
ejpam-3298	15	15	,	,	PUNCT
ejpam-3298	15	16	g	g	PROPN
ejpam-3298	15	17	and	and	CCONJ
ejpam-3298	15	18	h	h	NOUN
ejpam-3298	15	19	in	in	ADP
ejpam-3298	15	20	the	the	DET
ejpam-3298	15	21	complete	complete	ADJ
ejpam-3298	15	22	metric	metric	ADJ
ejpam-3298	15	23	space	space	NOUN
ejpam-3298	15	24	using	use	VERB
ejpam-3298	15	25	the	the	DET
ejpam-3298	15	26	following	follow	VERB
ejpam-3298	15	27	contractive	contractive	ADJ
ejpam-3298	15	28	condition	condition	NOUN
ejpam-3298	15	29	:	:	PUNCT
ejpam-3298	16	1	d(fx	d(fx	NOUN
ejpam-3298	16	2	,	,	PUNCT
ejpam-3298	16	3	gy	gy	NOUN
ejpam-3298	16	4	)	)	PUNCT
ejpam-3298	16	5	≤	≤	NUM
ejpam-3298	16	6	d(hx	d(hx	PROPN
ejpam-3298	16	7	,	,	PUNCT
ejpam-3298	16	8	hy)−	hy)−	X
ejpam-3298	16	9	w(d(hx	w(d(hx	NOUN
ejpam-3298	16	10	,	,	PUNCT
ejpam-3298	16	11	hy)),∀x	hy)),∀x	PROPN
ejpam-3298	16	12	,	,	PUNCT
ejpam-3298	16	13	y	y	PROPN
ejpam-3298	16	14	∈	∈	PROPN
ejpam-3298	16	15	x	x	X
ejpam-3298	16	16	(	(	PUNCT
ejpam-3298	16	17	2	2	X
ejpam-3298	16	18	)	)	PUNCT
ejpam-3298	16	19	∗corresponding	∗corresponde	VERB
ejpam-3298	16	20	author	author	NOUN
ejpam-3298	16	21	.	.	PUNCT
ejpam-3298	17	1	doi	doi	NOUN
ejpam-3298	17	2	:	:	PUNCT
ejpam-3298	17	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3298	https://doi.org/10.29020/nybg.ejpam.v11i4.3298	NOUN
ejpam-3298	17	4	email	email	NOUN
ejpam-3298	17	5	addresses	address	NOUN
ejpam-3298	17	6	:	:	PUNCT
ejpam-3298	17	7	psrsdm@gmail.com	psrsdm@gmail.com	X
ejpam-3298	17	8	(	(	PUNCT
ejpam-3298	17	9	p.	p.	NOUN
ejpam-3298	17	10	semwal	semwal	NOUN
ejpam-3298	17	11	)	)	PUNCT
ejpam-3298	17	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3298	18	1	1177	1177	NUM
ejpam-3298	18	2	c	c	X
ejpam-3298	18	3	©	©	PROPN
ejpam-3298	18	4	2018	2018	NUM
ejpam-3298	18	5	ejpam	ejpam	VERB
ejpam-3298	18	6	all	all	DET
ejpam-3298	18	7	rights	right	NOUN
ejpam-3298	18	8	reserved	reserve	VERB
ejpam-3298	18	9	.	.	PUNCT
ejpam-3298	19	1	p.	p.	NOUN
ejpam-3298	19	2	semwal	semwal	NOUN
ejpam-3298	19	3	,	,	PUNCT
ejpam-3298	19	4	komal	komal	PROPN
ejpam-3298	19	5	/	/	SYM
ejpam-3298	19	6	eur	eur	PROPN
ejpam-3298	19	7	.	.	PUNCT
ejpam-3298	20	1	j.	j.	PROPN
ejpam-3298	20	2	pure	pure	PROPN
ejpam-3298	20	3	appl	appl	PROPN
ejpam-3298	20	4	.	.	PROPN
ejpam-3298	20	5	math	math	PROPN
ejpam-3298	20	6	,	,	PUNCT
ejpam-3298	20	7	11	11	NUM
ejpam-3298	20	8	(	(	PUNCT
ejpam-3298	20	9	4	4	NUM
ejpam-3298	20	10	)	)	PUNCT
ejpam-3298	20	11	(	(	PUNCT
ejpam-3298	20	12	2018	2018	NUM
ejpam-3298	20	13	)	)	PUNCT
ejpam-3298	20	14	,	,	PUNCT
ejpam-3298	20	15	1177	1177	NUM
ejpam-3298	20	16	-	-	SYM
ejpam-3298	20	17	1190	1190	NUM
ejpam-3298	20	18	1178	1178	NUM
ejpam-3298	20	19	further	far	ADV
ejpam-3298	20	20	liu[15	liu[15	NOUN
ejpam-3298	20	21	]	]	PUNCT
ejpam-3298	20	22	established	establish	VERB
ejpam-3298	20	23	common	common	ADJ
ejpam-3298	20	24	fixed	fix	VERB
ejpam-3298	20	25	point	point	NOUN
ejpam-3298	20	26	theorem	theorem	NOUN
ejpam-3298	20	27	and	and	CCONJ
ejpam-3298	20	28	introduced	introduce	VERB
ejpam-3298	20	29	a	a	DET
ejpam-3298	20	30	class	class	NOUN
ejpam-3298	20	31	of	of	ADP
ejpam-3298	20	32	mappings	mapping	NOUN
ejpam-3298	20	33	in	in	ADP
ejpam-3298	20	34	a	a	DET
ejpam-3298	20	35	complete	complete	ADJ
ejpam-3298	20	36	metric	metric	ADJ
ejpam-3298	20	37	space	space	NOUN
ejpam-3298	20	38	as	as	SCONJ
ejpam-3298	20	39	follows	follow	VERB
ejpam-3298	20	40	:	:	PUNCT
ejpam-3298	20	41	d(fx	d(fx	NOUN
ejpam-3298	20	42	,	,	PUNCT
ejpam-3298	20	43	gy	gy	NOUN
ejpam-3298	20	44	)	)	PUNCT
ejpam-3298	20	45	≤	≤	NUM
ejpam-3298	20	46	max{d(hx	max{d(hx	PROPN
ejpam-3298	20	47	,	,	PUNCT
ejpam-3298	20	48	hy	hy	NOUN
ejpam-3298	20	49	)	)	PUNCT
ejpam-3298	20	50	,	,	PUNCT
ejpam-3298	20	51	d(hx	d(hx	PROPN
ejpam-3298	20	52	,	,	PUNCT
ejpam-3298	20	53	fx	fx	NOUN
ejpam-3298	20	54	)	)	PUNCT
ejpam-3298	20	55	,	,	PUNCT
ejpam-3298	20	56	d(hy	d(hy	PROPN
ejpam-3298	20	57	,	,	PUNCT
ejpam-3298	20	58	gy	gy	NOUN
ejpam-3298	20	59	)	)	PUNCT
ejpam-3298	20	60	}	}	PUNCT
ejpam-3298	20	61	−	−	PROPN
ejpam-3298	20	62	w(max{d(hx	w(max{d(hx	PROPN
ejpam-3298	20	63	,	,	PUNCT
ejpam-3298	20	64	hy	hy	NOUN
ejpam-3298	20	65	)	)	PUNCT
ejpam-3298	20	66	,	,	PUNCT
ejpam-3298	20	67	d(hx	d(hx	PROPN
ejpam-3298	20	68	,	,	PUNCT
ejpam-3298	20	69	fx	fx	NOUN
ejpam-3298	20	70	)	)	PUNCT
ejpam-3298	20	71	,	,	PUNCT
ejpam-3298	20	72	d(hy	d(hy	PROPN
ejpam-3298	20	73	,	,	PUNCT
ejpam-3298	20	74	gy	gy	NOUN
ejpam-3298	20	75	)	)	PUNCT
ejpam-3298	20	76	}	}	PUNCT
ejpam-3298	20	77	)	)	PUNCT
ejpam-3298	20	78	.	.	PUNCT
ejpam-3298	21	1	(	(	PUNCT
ejpam-3298	21	2	3	3	X
ejpam-3298	21	3	)	)	PUNCT
ejpam-3298	21	4	recall	recall	NOUN
ejpam-3298	21	5	that	that	SCONJ
ejpam-3298	21	6	the	the	DET
ejpam-3298	21	7	notion	notion	NOUN
ejpam-3298	21	8	of	of	ADP
ejpam-3298	21	9	orbitally	orbitally	ADV
ejpam-3298	21	10	complete	complete	ADJ
ejpam-3298	21	11	metric	metric	ADJ
ejpam-3298	21	12	space	space	NOUN
ejpam-3298	21	13	and	and	CCONJ
ejpam-3298	21	14	orbitally	orbitally	ADV
ejpam-3298	21	15	continuous	continuous	ADJ
ejpam-3298	21	16	mapping	mapping	NOUN
ejpam-3298	21	17	were	be	AUX
ejpam-3298	21	18	introduced	introduce	VERB
ejpam-3298	21	19	by	by	ADP
ejpam-3298	21	20	ciric	ciric	ADJ
ejpam-3298	22	1	[	[	X
ejpam-3298	22	2	9	9	NUM
ejpam-3298	22	3	]	]	PUNCT
ejpam-3298	22	4	.	.	PUNCT
ejpam-3298	23	1	these	these	DET
ejpam-3298	23	2	definitions	definition	NOUN
ejpam-3298	23	3	were	be	AUX
ejpam-3298	23	4	extended	extend	VERB
ejpam-3298	23	5	to	to	ADP
ejpam-3298	23	6	the	the	DET
ejpam-3298	23	7	case	case	NOUN
ejpam-3298	23	8	of	of	ADP
ejpam-3298	23	9	two	two	NUM
ejpam-3298	23	10	or	or	CCONJ
ejpam-3298	23	11	three	three	NUM
ejpam-3298	23	12	mappings	mapping	NOUN
ejpam-3298	23	13	by	by	ADP
ejpam-3298	23	14	sastry	sastry	NOUN
ejpam-3298	23	15	et	et	PROPN
ejpam-3298	23	16	al.[12	al.[12	PROPN
ejpam-3298	23	17	]	]	PUNCT
ejpam-3298	23	18	.	.	PUNCT
ejpam-3298	24	1	some	some	DET
ejpam-3298	24	2	common	common	ADJ
ejpam-3298	24	3	fixed	fix	VERB
ejpam-3298	24	4	point	point	NOUN
ejpam-3298	24	5	results	result	NOUN
ejpam-3298	24	6	in	in	ADP
ejpam-3298	24	7	this	this	DET
ejpam-3298	24	8	situation	situation	NOUN
ejpam-3298	24	9	were	be	AUX
ejpam-3298	24	10	obtained	obtain	VERB
ejpam-3298	24	11	in	in	ADP
ejpam-3298	24	12	[	[	X
ejpam-3298	24	13	12	12	NUM
ejpam-3298	24	14	]	]	PUNCT
ejpam-3298	24	15	.	.	PUNCT
ejpam-3298	25	1	we	we	PRON
ejpam-3298	25	2	give	give	VERB
ejpam-3298	25	3	now	now	ADV
ejpam-3298	25	4	respective	respective	ADJ
ejpam-3298	25	5	definitions	definition	NOUN
ejpam-3298	25	6	for	for	ADP
ejpam-3298	25	7	pairs	pair	NOUN
ejpam-3298	25	8	of	of	ADP
ejpam-3298	25	9	mappings	mapping	NOUN
ejpam-3298	25	10	given	give	VERB
ejpam-3298	25	11	in	in	ADP
ejpam-3298	25	12	literature	literature	NOUN
ejpam-3298	25	13	.	.	PUNCT
ejpam-3298	26	1	2	2	X
ejpam-3298	26	2	.	.	X
ejpam-3298	26	3	priliminaries	priliminarie	NOUN
ejpam-3298	26	4	definition	definition	VERB
ejpam-3298	26	5	1	1	NUM
ejpam-3298	26	6	(	(	PUNCT
ejpam-3298	26	7	6	6	NUM
ejpam-3298	26	8	)	)	PUNCT
ejpam-3298	26	9	.	.	PUNCT
ejpam-3298	27	1	a	a	DET
ejpam-3298	27	2	self	self	NOUN
ejpam-3298	27	3	map	map	NOUN
ejpam-3298	27	4	f	f	PROPN
ejpam-3298	27	5	on	on	ADP
ejpam-3298	27	6	a	a	DET
ejpam-3298	27	7	metric	metric	ADJ
ejpam-3298	27	8	space	space	NOUN
ejpam-3298	27	9	(	(	PUNCT
ejpam-3298	27	10	x	x	X
ejpam-3298	27	11	,	,	PUNCT
ejpam-3298	27	12	d	d	NOUN
ejpam-3298	27	13	)	)	PUNCT
ejpam-3298	27	14	is	be	AUX
ejpam-3298	27	15	said	say	VERB
ejpam-3298	27	16	to	to	PART
ejpam-3298	27	17	be	be	AUX
ejpam-3298	27	18	asymptotically	asymptotically	ADV
ejpam-3298	27	19	regular	regular	ADJ
ejpam-3298	27	20	at	at	ADP
ejpam-3298	27	21	a	a	DET
ejpam-3298	27	22	point	point	NOUN
ejpam-3298	27	23	x	x	PUNCT
ejpam-3298	27	24	in	in	ADP
ejpam-3298	27	25	x	x	PRON
ejpam-3298	27	26	if	if	SCONJ
ejpam-3298	27	27	limn→∞d(fn(x	limn→∞d(fn(x	PROPN
ejpam-3298	27	28	)	)	PUNCT
ejpam-3298	27	29	,	,	PUNCT
ejpam-3298	27	30	fn+1(x	fn+1(x	NOUN
ejpam-3298	27	31	)	)	PUNCT
ejpam-3298	27	32	)	)	PUNCT
ejpam-3298	28	1	=	=	PUNCT
ejpam-3298	28	2	0	0	X
ejpam-3298	28	3	.	.	PUNCT
ejpam-3298	28	4	where	where	SCONJ
ejpam-3298	28	5	fn(x	fn(x	X
ejpam-3298	28	6	)	)	PUNCT
ejpam-3298	28	7	denotes	denote	VERB
ejpam-3298	28	8	the	the	DET
ejpam-3298	28	9	nth	nth	PROPN
ejpam-3298	28	10	iterate	iterate	NOUN
ejpam-3298	28	11	of	of	ADP
ejpam-3298	28	12	f	f	PROPN
ejpam-3298	28	13	at	at	ADP
ejpam-3298	28	14	x.	x.	NOUN
ejpam-3298	28	15	definition	definition	NOUN
ejpam-3298	28	16	2	2	NUM
ejpam-3298	28	17	(	(	PUNCT
ejpam-3298	28	18	6	6	NUM
ejpam-3298	28	19	)	)	PUNCT
ejpam-3298	28	20	.	.	PUNCT
ejpam-3298	29	1	let	let	VERB
ejpam-3298	29	2	f	f	PROPN
ejpam-3298	29	3	and	and	CCONJ
ejpam-3298	29	4	g	g	PROPN
ejpam-3298	29	5	be	be	VERB
ejpam-3298	29	6	two	two	NUM
ejpam-3298	29	7	self	self	NOUN
ejpam-3298	29	8	mappings	mapping	NOUN
ejpam-3298	29	9	of	of	ADP
ejpam-3298	29	10	x	x	X
ejpam-3298	29	11	and	and	CCONJ
ejpam-3298	29	12	{	{	PUNCT
ejpam-3298	29	13	xn	xn	NOUN
ejpam-3298	29	14	}	}	PUNCT
ejpam-3298	29	15	a	a	DET
ejpam-3298	29	16	sequence	sequence	NOUN
ejpam-3298	29	17	in	in	ADP
ejpam-3298	29	18	x	x	NOUN
ejpam-3298	29	19	,	,	PUNCT
ejpam-3298	29	20	then	then	ADV
ejpam-3298	29	21	{	{	PUNCT
ejpam-3298	29	22	xn	xn	X
ejpam-3298	29	23	}	}	PUNCT
ejpam-3298	29	24	is	be	AUX
ejpam-3298	29	25	said	say	VERB
ejpam-3298	29	26	to	to	PART
ejpam-3298	29	27	be	be	AUX
ejpam-3298	29	28	asymptotically	asymptotically	ADV
ejpam-3298	29	29	gregular	gregular	ADJ
ejpam-3298	29	30	with	with	ADP
ejpam-3298	29	31	respect	respect	NOUN
ejpam-3298	29	32	to	to	ADP
ejpam-3298	29	33	f	f	PROPN
ejpam-3298	29	34	if	if	SCONJ
ejpam-3298	29	35	limn→∞d(fxn	limn→∞d(fxn	PROPN
ejpam-3298	29	36	,	,	PUNCT
ejpam-3298	29	37	gxn	gxn	PROPN
ejpam-3298	29	38	)	)	PUNCT
ejpam-3298	29	39	=	=	SYM
ejpam-3298	30	1	0	0	X
ejpam-3298	30	2	.	.	PUNCT
ejpam-3298	31	1	definition	definition	NOUN
ejpam-3298	31	2	3	3	NUM
ejpam-3298	31	3	(	(	PUNCT
ejpam-3298	31	4	9	9	NUM
ejpam-3298	31	5	)	)	PUNCT
ejpam-3298	31	6	.	.	PUNCT
ejpam-3298	32	1	let	let	AUX
ejpam-3298	32	2	{	{	PUNCT
ejpam-3298	32	3	xn	xn	X
ejpam-3298	32	4	}	}	PUNCT
ejpam-3298	32	5	is	be	AUX
ejpam-3298	32	6	a	a	DET
ejpam-3298	32	7	sequence	sequence	NOUN
ejpam-3298	32	8	which	which	PRON
ejpam-3298	32	9	is	be	AUX
ejpam-3298	32	10	asymptotically	asymptotically	ADV
ejpam-3298	32	11	gregular	gregular	ADJ
ejpam-3298	32	12	with	with	ADP
ejpam-3298	32	13	respect	respect	NOUN
ejpam-3298	32	14	to	to	ADP
ejpam-3298	32	15	f	f	PROPN
ejpam-3298	32	16	,	,	PUNCT
ejpam-3298	32	17	then	then	ADV
ejpam-3298	32	18	o(f	o(f	PROPN
ejpam-3298	32	19	,	,	PUNCT
ejpam-3298	32	20	xn	xn	PROPN
ejpam-3298	32	21	)	)	PUNCT
ejpam-3298	33	1	=	=	PRON
ejpam-3298	33	2	{	{	PUNCT
ejpam-3298	33	3	fx1	fx1	PROPN
ejpam-3298	33	4	,	,	PUNCT
ejpam-3298	33	5	fx2	fx2	PROPN
ejpam-3298	33	6	,	,	PUNCT
ejpam-3298	33	7	fx3	fx3	NOUN
ejpam-3298	33	8	,	,	PUNCT
ejpam-3298	33	9	...	...	PUNCT
ejpam-3298	33	10	fxn	fxn	NOUN
ejpam-3298	33	11	,	,	PUNCT
ejpam-3298	33	12	...	...	PUNCT
ejpam-3298	33	13	}	}	PUNCT
ejpam-3298	33	14	is	be	AUX
ejpam-3298	33	15	called	call	VERB
ejpam-3298	33	16	asymptotic	asymptotic	ADJ
ejpam-3298	33	17	orbit	orbit	NOUN
ejpam-3298	33	18	of	of	ADP
ejpam-3298	33	19	f	f	PROPN
ejpam-3298	33	20	.	.	PUNCT
ejpam-3298	34	1	definition	definition	NOUN
ejpam-3298	34	2	4	4	NUM
ejpam-3298	34	3	(	(	PUNCT
ejpam-3298	34	4	12	12	NUM
ejpam-3298	34	5	)	)	PUNCT
ejpam-3298	34	6	.	.	PUNCT
ejpam-3298	35	1	x	x	PUNCT
ejpam-3298	35	2	is	be	AUX
ejpam-3298	35	3	said	say	VERB
ejpam-3298	35	4	to	to	PART
ejpam-3298	35	5	be	be	AUX
ejpam-3298	35	6	f	f	PRON
ejpam-3298	35	7	-asymptotically	-asymptotically	ADV
ejpam-3298	35	8	complete	complete	ADJ
ejpam-3298	35	9	if	if	SCONJ
ejpam-3298	35	10	every	every	DET
ejpam-3298	35	11	cauchy	cauchy	ADJ
ejpam-3298	35	12	sequence	sequence	NOUN
ejpam-3298	35	13	of	of	ADP
ejpam-3298	35	14	the	the	DET
ejpam-3298	35	15	form	form	NOUN
ejpam-3298	35	16	{	{	PUNCT
ejpam-3298	35	17	fxn	fxn	NOUN
ejpam-3298	35	18	}	}	PUNCT
ejpam-3298	35	19	converges	converge	NOUN
ejpam-3298	35	20	in	in	ADP
ejpam-3298	35	21	x.	x.	NOUN
ejpam-3298	35	22	definition	definition	NOUN
ejpam-3298	35	23	5	5	NUM
ejpam-3298	35	24	(	(	PUNCT
ejpam-3298	35	25	12	12	NUM
ejpam-3298	35	26	)	)	PUNCT
ejpam-3298	35	27	.	.	PUNCT
ejpam-3298	36	1	a	a	DET
ejpam-3298	36	2	self	self	NOUN
ejpam-3298	36	3	map	map	NOUN
ejpam-3298	36	4	f	f	PROPN
ejpam-3298	36	5	is	be	AUX
ejpam-3298	36	6	said	say	VERB
ejpam-3298	36	7	to	to	PART
ejpam-3298	36	8	be	be	AUX
ejpam-3298	36	9	asymptotically	asymptotically	ADV
ejpam-3298	36	10	continuous	continuous	ADJ
ejpam-3298	36	11	if	if	SCONJ
ejpam-3298	36	12	it	it	PRON
ejpam-3298	36	13	is	be	AUX
ejpam-3298	36	14	continuous	continuous	ADJ
ejpam-3298	36	15	on	on	ADP
ejpam-3298	36	16	closure	closure	NOUN
ejpam-3298	36	17	of	of	ADP
ejpam-3298	36	18	o(f	o(f	PROPN
ejpam-3298	36	19	,	,	PUNCT
ejpam-3298	36	20	xn	xn	PROPN
ejpam-3298	36	21	)	)	PUNCT
ejpam-3298	36	22	.	.	PUNCT
ejpam-3298	37	1	definition	definition	NOUN
ejpam-3298	37	2	6	6	NUM
ejpam-3298	37	3	.	.	PUNCT
ejpam-3298	37	4	two	two	NUM
ejpam-3298	37	5	self	self	NOUN
ejpam-3298	37	6	maps	map	NOUN
ejpam-3298	37	7	g	g	NOUN
ejpam-3298	37	8	and	and	CCONJ
ejpam-3298	37	9	h	h	NOUN
ejpam-3298	37	10	of	of	ADP
ejpam-3298	37	11	x	x	SYM
ejpam-3298	37	12	are	be	AUX
ejpam-3298	37	13	said	say	VERB
ejpam-3298	37	14	to	to	PART
ejpam-3298	37	15	be	be	AUX
ejpam-3298	37	16	weakly	weakly	ADV
ejpam-3298	37	17	commuting	commute	VERB
ejpam-3298	37	18	if	if	SCONJ
ejpam-3298	37	19	d(ghx	d(ghx	PROPN
ejpam-3298	37	20	,	,	PUNCT
ejpam-3298	37	21	hgx	hgx	NOUN
ejpam-3298	37	22	)	)	PUNCT
ejpam-3298	37	23	≤	≤	NOUN
ejpam-3298	37	24	d(gx	d(gx	PROPN
ejpam-3298	37	25	,	,	PUNCT
ejpam-3298	37	26	hx	hx	PROPN
ejpam-3298	37	27	)	)	PUNCT
ejpam-3298	37	28	∀x	∀x	VERB
ejpam-3298	37	29	∈	∈	NOUN
ejpam-3298	37	30	x	x	SYM
ejpam-3298	37	31	definition	definition	NOUN
ejpam-3298	37	32	7	7	NUM
ejpam-3298	37	33	(	(	PUNCT
ejpam-3298	37	34	12	12	NUM
ejpam-3298	37	35	)	)	PUNCT
ejpam-3298	37	36	.	.	PUNCT
ejpam-3298	38	1	let	let	VERB
ejpam-3298	38	2	f	f	X
ejpam-3298	38	3	,	,	PUNCT
ejpam-3298	38	4	g	g	PROPN
ejpam-3298	38	5	and	and	CCONJ
ejpam-3298	38	6	h	h	NOUN
ejpam-3298	38	7	be	be	VERB
ejpam-3298	38	8	three	three	NUM
ejpam-3298	38	9	self	self	NOUN
ejpam-3298	38	10	maps	map	NOUN
ejpam-3298	38	11	on	on	ADP
ejpam-3298	38	12	a	a	DET
ejpam-3298	38	13	metric	metric	ADJ
ejpam-3298	38	14	space	space	NOUN
ejpam-3298	38	15	x.	x.	NOUN
ejpam-3298	39	1	(	(	PUNCT
ejpam-3298	39	2	i	i	NOUN
ejpam-3298	39	3	)	)	PUNCT
ejpam-3298	39	4	if	if	SCONJ
ejpam-3298	39	5	for	for	ADP
ejpam-3298	39	6	a	a	DET
ejpam-3298	39	7	point	point	NOUN
ejpam-3298	39	8	x0	x0	PROPN
ejpam-3298	39	9	∈	∈	PROPN
ejpam-3298	39	10	x	x	PRON
ejpam-3298	39	11	,	,	PUNCT
ejpam-3298	39	12	there	there	PRON
ejpam-3298	39	13	exists	exist	VERB
ejpam-3298	39	14	a	a	DET
ejpam-3298	39	15	sequence	sequence	NOUN
ejpam-3298	39	16	{	{	PUNCT
ejpam-3298	39	17	xn	xn	NOUN
ejpam-3298	39	18	}	}	PUNCT
ejpam-3298	39	19	in	in	ADP
ejpam-3298	39	20	x	x	SYM
ejpam-3298	39	21	such	such	ADJ
ejpam-3298	39	22	that	that	DET
ejpam-3298	39	23	fx2n	fx2n	PROPN
ejpam-3298	39	24	=	=	SYM
ejpam-3298	39	25	hx2n+1	hx2n+1	PROPN
ejpam-3298	39	26	and	and	CCONJ
ejpam-3298	39	27	gx2n+1	gx2n+1	PROPN
ejpam-3298	39	28	=	=	SYM
ejpam-3298	39	29	hx2n+2	hx2n+2	PROPN
ejpam-3298	39	30	,	,	PUNCT
ejpam-3298	39	31	n	n	NOUN
ejpam-3298	39	32	=	=	SYM
ejpam-3298	39	33	0	0	NUM
ejpam-3298	39	34	,	,	PUNCT
ejpam-3298	39	35	1	1	NUM
ejpam-3298	39	36	,	,	PUNCT
ejpam-3298	39	37	2	2	NUM
ejpam-3298	39	38	....	....	PUNCT
ejpam-3298	39	39	then	then	ADV
ejpam-3298	39	40	the	the	DET
ejpam-3298	39	41	set	set	NOUN
ejpam-3298	39	42	o(x0	o(x0	PROPN
ejpam-3298	39	43	,	,	PUNCT
ejpam-3298	39	44	f	f	PROPN
ejpam-3298	39	45	,	,	PUNCT
ejpam-3298	39	46	g	g	PROPN
ejpam-3298	39	47	,	,	PUNCT
ejpam-3298	39	48	h	h	NOUN
ejpam-3298	39	49	)	)	PUNCT
ejpam-3298	39	50	=	=	SYM
ejpam-3298	39	51	{	{	PUNCT
ejpam-3298	39	52	txn|n	txn|n	NOUN
ejpam-3298	39	53	=	=	SYM
ejpam-3298	39	54	0	0	NUM
ejpam-3298	39	55	,	,	PUNCT
ejpam-3298	39	56	1	1	NUM
ejpam-3298	39	57	,	,	PUNCT
ejpam-3298	39	58	2	2	NUM
ejpam-3298	39	59	...	...	PUNCT
ejpam-3298	39	60	}	}	PUNCT
ejpam-3298	39	61	is	be	AUX
ejpam-3298	39	62	called	call	VERB
ejpam-3298	39	63	the	the	DET
ejpam-3298	39	64	orbit	orbit	NOUN
ejpam-3298	39	65	of	of	ADP
ejpam-3298	39	66	(	(	PUNCT
ejpam-3298	39	67	f	f	X
ejpam-3298	39	68	,	,	PUNCT
ejpam-3298	39	69	g	g	PROPN
ejpam-3298	39	70	,	,	PUNCT
ejpam-3298	39	71	h	h	NOUN
ejpam-3298	39	72	)	)	PUNCT
ejpam-3298	39	73	at	at	ADP
ejpam-3298	39	74	x0	x0	PROPN
ejpam-3298	39	75	.	.	PUNCT
ejpam-3298	40	1	(	(	PUNCT
ejpam-3298	40	2	ii	ii	NOUN
ejpam-3298	40	3	)	)	PUNCT
ejpam-3298	40	4	the	the	DET
ejpam-3298	40	5	space	space	NOUN
ejpam-3298	40	6	(	(	PUNCT
ejpam-3298	40	7	x	x	X
ejpam-3298	40	8	,	,	PUNCT
ejpam-3298	40	9	d	d	NOUN
ejpam-3298	40	10	)	)	PUNCT
ejpam-3298	40	11	is	be	AUX
ejpam-3298	40	12	said	say	VERB
ejpam-3298	40	13	to	to	PART
ejpam-3298	40	14	be	be	AUX
ejpam-3298	40	15	(	(	PUNCT
ejpam-3298	40	16	f	f	X
ejpam-3298	40	17	,	,	PUNCT
ejpam-3298	40	18	g	g	PROPN
ejpam-3298	40	19	,	,	PUNCT
ejpam-3298	40	20	h)−	h)−	PROPN
ejpam-3298	40	21	orbitally	orbitally	ADV
ejpam-3298	40	22	complete	complete	ADJ
ejpam-3298	40	23	if	if	SCONJ
ejpam-3298	40	24	every	every	DET
ejpam-3298	40	25	cauchy	cauchy	ADJ
ejpam-3298	40	26	sequence	sequence	NOUN
ejpam-3298	40	27	in	in	ADP
ejpam-3298	40	28	o(x0	o(x0	PROPN
ejpam-3298	40	29	,	,	PUNCT
ejpam-3298	40	30	f	f	PROPN
ejpam-3298	40	31	,	,	PUNCT
ejpam-3298	40	32	g	g	PROPN
ejpam-3298	40	33	,	,	PUNCT
ejpam-3298	40	34	h	h	NOUN
ejpam-3298	40	35	)	)	PUNCT
ejpam-3298	40	36	converges	converge	NOUN
ejpam-3298	40	37	in	in	ADP
ejpam-3298	40	38	x.	x.	PROPN
ejpam-3298	40	39	p.	p.	NOUN
ejpam-3298	40	40	semwal	semwal	NOUN
ejpam-3298	40	41	,	,	PUNCT
ejpam-3298	40	42	komal	komal	PROPN
ejpam-3298	40	43	/	/	SYM
ejpam-3298	40	44	eur	eur	PROPN
ejpam-3298	40	45	.	.	PUNCT
ejpam-3298	41	1	j.	j.	PROPN
ejpam-3298	41	2	pure	pure	PROPN
ejpam-3298	41	3	appl	appl	PROPN
ejpam-3298	41	4	.	.	PROPN
ejpam-3298	41	5	math	math	PROPN
ejpam-3298	41	6	,	,	PUNCT
ejpam-3298	41	7	11	11	NUM
ejpam-3298	41	8	(	(	PUNCT
ejpam-3298	41	9	4	4	NUM
ejpam-3298	41	10	)	)	PUNCT
ejpam-3298	41	11	(	(	PUNCT
ejpam-3298	41	12	2018	2018	NUM
ejpam-3298	41	13	)	)	PUNCT
ejpam-3298	41	14	,	,	PUNCT
ejpam-3298	41	15	1177	1177	NUM
ejpam-3298	41	16	-	-	SYM
ejpam-3298	41	17	1190	1190	NUM
ejpam-3298	41	18	1179	1179	NUM
ejpam-3298	41	19	(	(	PUNCT
ejpam-3298	41	20	iii	iii	NOUN
ejpam-3298	41	21	)	)	PUNCT
ejpam-3298	41	22	the	the	DET
ejpam-3298	41	23	map	map	NOUN
ejpam-3298	41	24	h	h	NOUN
ejpam-3298	41	25	is	be	AUX
ejpam-3298	41	26	said	say	VERB
ejpam-3298	41	27	to	to	PART
ejpam-3298	41	28	be	be	AUX
ejpam-3298	41	29	(	(	PUNCT
ejpam-3298	41	30	f	f	X
ejpam-3298	41	31	,	,	PUNCT
ejpam-3298	41	32	g	g	PROPN
ejpam-3298	41	33	,	,	PUNCT
ejpam-3298	41	34	h)orbitally	h)orbitally	ADV
ejpam-3298	41	35	continuous	continuous	ADJ
ejpam-3298	41	36	at	at	ADP
ejpam-3298	41	37	x0	x0	PROPN
ejpam-3298	41	38	if	if	SCONJ
ejpam-3298	41	39	it	it	PRON
ejpam-3298	41	40	is	be	AUX
ejpam-3298	41	41	continuous	continuous	ADJ
ejpam-3298	41	42	on	on	ADP
ejpam-3298	41	43	o(x0	o(x0	PROPN
ejpam-3298	41	44	,	,	PUNCT
ejpam-3298	41	45	f	f	PROPN
ejpam-3298	41	46	,	,	PUNCT
ejpam-3298	41	47	g	g	PROPN
ejpam-3298	41	48	,	,	PUNCT
ejpam-3298	41	49	h	h	NOUN
ejpam-3298	41	50	)	)	PUNCT
ejpam-3298	41	51	.	.	PUNCT
ejpam-3298	42	1	(	(	PUNCT
ejpam-3298	42	2	iv	iv	X
ejpam-3298	42	3	)	)	PUNCT
ejpam-3298	42	4	the	the	DET
ejpam-3298	42	5	pair	pair	NOUN
ejpam-3298	42	6	(	(	PUNCT
ejpam-3298	42	7	f	f	X
ejpam-3298	42	8	,	,	PUNCT
ejpam-3298	42	9	g	g	NOUN
ejpam-3298	42	10	)	)	PUNCT
ejpam-3298	42	11	is	be	AUX
ejpam-3298	42	12	said	say	VERB
ejpam-3298	42	13	to	to	PART
ejpam-3298	42	14	be	be	AUX
ejpam-3298	42	15	asymptotically	asymptotically	ADV
ejpam-3298	42	16	regular	regular	ADJ
ejpam-3298	42	17	w.r.to	w.r.to	NOUN
ejpam-3298	42	18	h	h	NOUN
ejpam-3298	42	19	at	at	ADP
ejpam-3298	42	20	x0	x0	PROPN
ejpam-3298	42	21	if	if	SCONJ
ejpam-3298	42	22	there	there	PRON
ejpam-3298	42	23	exists	exist	VERB
ejpam-3298	42	24	a	a	DET
ejpam-3298	42	25	sequence	sequence	NOUN
ejpam-3298	42	26	{	{	PUNCT
ejpam-3298	42	27	xn	xn	NOUN
ejpam-3298	42	28	}	}	PUNCT
ejpam-3298	42	29	in	in	ADP
ejpam-3298	42	30	x	x	SYM
ejpam-3298	42	31	such	such	ADJ
ejpam-3298	42	32	that	that	DET
ejpam-3298	42	33	fx2n	fx2n	PROPN
ejpam-3298	42	34	=	=	SYM
ejpam-3298	42	35	hx2n+1	hx2n+1	PROPN
ejpam-3298	42	36	,	,	PUNCT
ejpam-3298	42	37	gx2n+1	gx2n+1	PROPN
ejpam-3298	42	38	=	=	SYM
ejpam-3298	42	39	hx2n+2	hx2n+2	PROPN
ejpam-3298	42	40	;	;	PUNCT
ejpam-3298	42	41	n	n	PROPN
ejpam-3298	42	42	=	=	SYM
ejpam-3298	42	43	0	0	NUM
ejpam-3298	42	44	,	,	PUNCT
ejpam-3298	42	45	1	1	NUM
ejpam-3298	42	46	,	,	PUNCT
ejpam-3298	42	47	2	2	NUM
ejpam-3298	42	48	,	,	PUNCT
ejpam-3298	42	49	...	...	PUNCT
ejpam-3298	42	50	and	and	CCONJ
ejpam-3298	42	51	d(hxn	d(hxn	NOUN
ejpam-3298	42	52	,	,	PUNCT
ejpam-3298	42	53	hn+1)→	hn+1)→	NOUN
ejpam-3298	42	54	0	0	NUM
ejpam-3298	42	55	as	as	ADP
ejpam-3298	42	56	n→∞.	n→∞.	ADJ
ejpam-3298	42	57	throughout	throughout	ADP
ejpam-3298	42	58	in	in	ADP
ejpam-3298	42	59	this	this	DET
ejpam-3298	42	60	paper	paper	NOUN
ejpam-3298	42	61	,	,	PUNCT
ejpam-3298	42	62	we	we	PRON
ejpam-3298	42	63	assume	assume	VERB
ejpam-3298	42	64	that	that	SCONJ
ejpam-3298	42	65	r+	r+	PRON
ejpam-3298	42	66	=	=	PUNCT
ejpam-3298	43	1	[	[	X
ejpam-3298	43	2	0,+∞	0,+∞	NUM
ejpam-3298	43	3	)	)	PUNCT
ejpam-3298	43	4	,	,	PUNCT
ejpam-3298	43	5	r	r	NOUN
ejpam-3298	43	6	=	=	SYM
ejpam-3298	43	7	(	(	PUNCT
ejpam-3298	43	8	−∞,+∞	−∞,+∞	NUM
ejpam-3298	43	9	)	)	PUNCT
ejpam-3298	43	10	,	,	PUNCT
ejpam-3298	43	11	w	w	NOUN
ejpam-3298	43	12	and	and	CCONJ
ejpam-3298	43	13	n	n	CCONJ
ejpam-3298	43	14	denote	denote	VERB
ejpam-3298	43	15	the	the	DET
ejpam-3298	43	16	set	set	NOUN
ejpam-3298	43	17	of	of	ADP
ejpam-3298	43	18	all	all	DET
ejpam-3298	43	19	non	non	ADJ
ejpam-3298	43	20	-	-	ADJ
ejpam-3298	43	21	negative	negative	ADJ
ejpam-3298	43	22	and	and	CCONJ
ejpam-3298	43	23	positive	positive	ADJ
ejpam-3298	43	24	integers	integer	NOUN
ejpam-3298	43	25	respectively	respectively	ADV
ejpam-3298	43	26	.	.	PUNCT
ejpam-3298	44	1	w	w	NOUN
ejpam-3298	44	2	=	=	PRON
ejpam-3298	44	3	{	{	PUNCT
ejpam-3298	44	4	w	w	NOUN
ejpam-3298	44	5	:	:	PUNCT
ejpam-3298	44	6	w	w	X
ejpam-3298	44	7	:	:	PUNCT
ejpam-3298	44	8	r+	r+	NOUN
ejpam-3298	44	9	→	→	PUNCT
ejpam-3298	44	10	r+is	r+is	NOUN
ejpam-3298	44	11	continuous	continuous	ADJ
ejpam-3298	44	12	mappings	mapping	NOUN
ejpam-3298	44	13	with	with	ADP
ejpam-3298	44	14	0	0	NUM
ejpam-3298	44	15	<	<	X
ejpam-3298	44	16	w(t	w(t	PROPN
ejpam-3298	44	17	)	)	PUNCT
ejpam-3298	44	18	<	<	X
ejpam-3298	44	19	t	t	X
ejpam-3298	44	20	∀	∀	X
ejpam-3298	44	21	t	t	X
ejpam-3298	44	22	>	>	X
ejpam-3298	44	23	0	0	NUM
ejpam-3298	44	24	}	}	PUNCT
ejpam-3298	44	25	(	(	PUNCT
ejpam-3298	44	26	4	4	X
ejpam-3298	44	27	)	)	PUNCT
ejpam-3298	44	28	let	let	VERB
ejpam-3298	45	1	φ	φ	PROPN
ejpam-3298	45	2	=	=	SYM
ejpam-3298	45	3	{	{	PUNCT
ejpam-3298	45	4	φ	φ	NOUN
ejpam-3298	45	5	:	:	PUNCT
ejpam-3298	45	6	φ	φ	NUM
ejpam-3298	45	7	:	:	PUNCT
ejpam-3298	46	1	[	[	X
ejpam-3298	46	2	0,∞)→	0,∞)→	NOUN
ejpam-3298	46	3	[	[	X
ejpam-3298	46	4	0,∞	0,∞	NOUN
ejpam-3298	46	5	)	)	PUNCT
ejpam-3298	46	6	}	}	PUNCT
ejpam-3298	46	7	satisfying	satisfy	VERB
ejpam-3298	46	8	the	the	DET
ejpam-3298	46	9	following	follow	VERB
ejpam-3298	46	10	conditions	condition	NOUN
ejpam-3298	46	11	:	:	PUNCT
ejpam-3298	46	12	(	(	PUNCT
ejpam-3298	46	13	i	i	NOUN
ejpam-3298	46	14	)	)	PUNCT
ejpam-3298	46	15	φ	φ	PROPN
ejpam-3298	46	16	is	be	AUX
ejpam-3298	46	17	continuous	continuous	ADJ
ejpam-3298	46	18	and	and	CCONJ
ejpam-3298	46	19	non	non	ADJ
ejpam-3298	46	20	-	-	ADJ
ejpam-3298	46	21	decreasing	decrease	VERB
ejpam-3298	46	22	(	(	PUNCT
ejpam-3298	46	23	ii	ii	NOUN
ejpam-3298	46	24	)	)	PUNCT
ejpam-3298	46	25	φ(t	φ(t	PROPN
ejpam-3298	46	26	)	)	PUNCT
ejpam-3298	46	27	<	<	X
ejpam-3298	46	28	t	t	X
ejpam-3298	46	29	∀t	∀t	PROPN
ejpam-3298	46	30	∈	∈	PROPN
ejpam-3298	47	1	[	[	X
ejpam-3298	47	2	0,∞	0,∞	NUM
ejpam-3298	47	3	)	)	PUNCT
ejpam-3298	47	4	(	(	PUNCT
ejpam-3298	47	5	iii	iii	NOUN
ejpam-3298	47	6	)	)	PUNCT
ejpam-3298	47	7	limn→∞φ(tn	limn→∞φ(tn	NOUN
ejpam-3298	47	8	)	)	PUNCT
ejpam-3298	48	1	=	=	SYM
ejpam-3298	48	2	0	0	NUM
ejpam-3298	49	1	⇐	⇐	ADJ
ejpam-3298	49	2	⇒	⇒	NOUN
ejpam-3298	49	3	limn→∞tn	limn→∞tn	NOUN
ejpam-3298	49	4	=	=	SYM
ejpam-3298	49	5	0	0	X
ejpam-3298	49	6	.	.	PUNCT
ejpam-3298	50	1	let	let	VERB
ejpam-3298	50	2	ψ=	ψ=	NOUN
ejpam-3298	50	3	{	{	PUNCT
ejpam-3298	50	4	ψ	ψ	X
ejpam-3298	50	5	:	:	PUNCT
ejpam-3298	50	6	ψ	ψ	X
ejpam-3298	50	7	:	:	PUNCT
ejpam-3298	51	1	[	[	X
ejpam-3298	51	2	0,∞)→	0,∞)→	NOUN
ejpam-3298	51	3	[	[	X
ejpam-3298	51	4	0,∞	0,∞	NOUN
ejpam-3298	51	5	)	)	PUNCT
ejpam-3298	51	6	}	}	PUNCT
ejpam-3298	51	7	satisfying	satisfy	VERB
ejpam-3298	51	8	the	the	DET
ejpam-3298	51	9	following	follow	VERB
ejpam-3298	51	10	conditions	condition	NOUN
ejpam-3298	51	11	:	:	PUNCT
ejpam-3298	51	12	(	(	PUNCT
ejpam-3298	51	13	i	i	NOUN
ejpam-3298	51	14	)	)	PUNCT
ejpam-3298	51	15	ψ	ψ	NOUN
ejpam-3298	51	16	is	be	AUX
ejpam-3298	51	17	non	non	ADJ
ejpam-3298	51	18	-	-	ADJ
ejpam-3298	51	19	decreasing	decrease	VERB
ejpam-3298	51	20	(	(	PUNCT
ejpam-3298	51	21	ii	ii	NOUN
ejpam-3298	51	22	)	)	PUNCT
ejpam-3298	51	23	φ(t	φ(t	PROPN
ejpam-3298	51	24	)	)	PUNCT
ejpam-3298	51	25	<	<	X
ejpam-3298	51	26	ψ(t	ψ(t	PROPN
ejpam-3298	51	27	)	)	PUNCT
ejpam-3298	51	28	∀t	∀t	PROPN
ejpam-3298	51	29	>	>	X
ejpam-3298	51	30	0	0	PUNCT
ejpam-3298	52	1	(	(	PUNCT
ejpam-3298	52	2	iii)ψ(a+	iii)ψ(a+	NOUN
ejpam-3298	52	3	b	b	NOUN
ejpam-3298	52	4	)	)	PUNCT
ejpam-3298	52	5	≤	≤	NOUN
ejpam-3298	52	6	ψ(a	ψ(a	PROPN
ejpam-3298	52	7	)	)	PUNCT
ejpam-3298	52	8	+	+	NUM
ejpam-3298	52	9	ψ(b	ψ(b	NOUN
ejpam-3298	52	10	)	)	PUNCT
ejpam-3298	52	11	∀a	∀a	PROPN
ejpam-3298	52	12	,	,	PUNCT
ejpam-3298	52	13	b	b	X
ejpam-3298	52	14	∈	∈	PROPN
ejpam-3298	53	1	[	[	X
ejpam-3298	53	2	0,∞	0,∞	NUM
ejpam-3298	53	3	)	)	PUNCT
ejpam-3298	53	4	(	(	PUNCT
ejpam-3298	53	5	iv	iv	X
ejpam-3298	53	6	)	)	PUNCT
ejpam-3298	53	7	ψ(t	ψ(t	PROPN
ejpam-3298	53	8	)	)	PUNCT
ejpam-3298	53	9	<	<	X
ejpam-3298	53	10	t	t	X
ejpam-3298	53	11	∀t	∀t	PROPN
ejpam-3298	53	12	∈	∈	PROPN
ejpam-3298	54	1	[	[	X
ejpam-3298	54	2	0,∞	0,∞	NOUN
ejpam-3298	54	3	)	)	PUNCT
ejpam-3298	54	4	the	the	DET
ejpam-3298	54	5	aim	aim	NOUN
ejpam-3298	54	6	of	of	ADP
ejpam-3298	54	7	this	this	DET
ejpam-3298	54	8	paper	paper	NOUN
ejpam-3298	54	9	is	be	AUX
ejpam-3298	54	10	to	to	PART
ejpam-3298	54	11	provide	provide	VERB
ejpam-3298	54	12	the	the	DET
ejpam-3298	54	13	sufficient	sufficient	ADJ
ejpam-3298	54	14	conditions	condition	NOUN
ejpam-3298	54	15	for	for	ADP
ejpam-3298	54	16	the	the	DET
ejpam-3298	54	17	existence	existence	NOUN
ejpam-3298	54	18	and	and	CCONJ
ejpam-3298	54	19	uniqueness	uniqueness	NOUN
ejpam-3298	54	20	of	of	ADP
ejpam-3298	54	21	common	common	ADJ
ejpam-3298	54	22	fixed	fix	VERB
ejpam-3298	54	23	point	point	NOUN
ejpam-3298	54	24	for	for	ADP
ejpam-3298	54	25	the	the	DET
ejpam-3298	54	26	following	follow	VERB
ejpam-3298	54	27	type	type	NOUN
ejpam-3298	54	28	of	of	ADP
ejpam-3298	54	29	contractive	contractive	ADJ
ejpam-3298	54	30	mappings	mapping	NOUN
ejpam-3298	54	31	metric	metric	ADJ
ejpam-3298	54	32	space	space	NOUN
ejpam-3298	54	33	(	(	PUNCT
ejpam-3298	54	34	x	x	X
ejpam-3298	54	35	,	,	PUNCT
ejpam-3298	54	36	d	d	NOUN
ejpam-3298	54	37	)	)	PUNCT
ejpam-3298	54	38	.	.	PUNCT
ejpam-3298	55	1	ψ(d(fx	ψ(d(fx	NOUN
ejpam-3298	55	2	,	,	PUNCT
ejpam-3298	55	3	gy	gy	NOUN
ejpam-3298	55	4	)	)	PUNCT
ejpam-3298	55	5	)	)	PUNCT
ejpam-3298	55	6	≤	≤	NUM
ejpam-3298	55	7	max{φ(d(hx	max{φ(d(hx	X
ejpam-3298	55	8	,	,	PUNCT
ejpam-3298	55	9	hy	hy	NOUN
ejpam-3298	55	10	)	)	PUNCT
ejpam-3298	55	11	)	)	PUNCT
ejpam-3298	55	12	,	,	PUNCT
ejpam-3298	55	13	φ(d(hx	φ(d(hx	NOUN
ejpam-3298	55	14	,	,	PUNCT
ejpam-3298	55	15	fx	fx	PROPN
ejpam-3298	55	16	)	)	PUNCT
ejpam-3298	55	17	,	,	PUNCT
ejpam-3298	55	18	φ	φ	X
ejpam-3298	55	19	(	(	PUNCT
ejpam-3298	55	20	1	1	NUM
ejpam-3298	55	21	2	2	NUM
ejpam-3298	55	22	(	(	PUNCT
ejpam-3298	55	23	[	[	X
ejpam-3298	55	24	d(hx	d(hx	X
ejpam-3298	55	25	,	,	PUNCT
ejpam-3298	55	26	hy	hy	NOUN
ejpam-3298	55	27	)	)	PUNCT
ejpam-3298	55	28	+	+	NUM
ejpam-3298	55	29	d(fx	d(fx	PROPN
ejpam-3298	55	30	,	,	PUNCT
ejpam-3298	55	31	gy	gy	NOUN
ejpam-3298	55	32	)	)	PUNCT
ejpam-3298	55	33	]	]	PUNCT
ejpam-3298	55	34	)	)	PUNCT
ejpam-3298	55	35	)	)	PUNCT
ejpam-3298	55	36	)	)	PUNCT
ejpam-3298	55	37	,	,	PUNCT
ejpam-3298	55	38	φ(d(hy	φ(d(hy	NOUN
ejpam-3298	55	39	,	,	PUNCT
ejpam-3298	55	40	gy	gy	NOUN
ejpam-3298	55	41	)	)	PUNCT
ejpam-3298	55	42	)	)	PUNCT
ejpam-3298	55	43	}	}	PUNCT
ejpam-3298	55	44	−w(max{φ(d(hx	−w(max{φ(d(hx	PROPN
ejpam-3298	55	45	,	,	PUNCT
ejpam-3298	55	46	hy	hy	NOUN
ejpam-3298	55	47	)	)	PUNCT
ejpam-3298	55	48	)	)	PUNCT
ejpam-3298	55	49	,	,	PUNCT
ejpam-3298	55	50	φ(d(hx	φ(d(hx	NOUN
ejpam-3298	55	51	,	,	PUNCT
ejpam-3298	55	52	fx	fx	NOUN
ejpam-3298	55	53	)	)	PUNCT
ejpam-3298	55	54	)	)	PUNCT
ejpam-3298	55	55	,	,	PUNCT
ejpam-3298	55	56	φ(d(hy	φ(d(hy	NOUN
ejpam-3298	55	57	,	,	PUNCT
ejpam-3298	55	58	gy	gy	NOUN
ejpam-3298	55	59	)	)	PUNCT
ejpam-3298	55	60	)	)	PUNCT
ejpam-3298	55	61	,	,	PUNCT
ejpam-3298	55	62	φ	φ	X
ejpam-3298	55	63	(	(	PUNCT
ejpam-3298	55	64	1	1	NUM
ejpam-3298	55	65	2	2	NUM
ejpam-3298	55	66	(	(	PUNCT
ejpam-3298	55	67	[	[	X
ejpam-3298	55	68	d(hx	d(hx	X
ejpam-3298	55	69	,	,	PUNCT
ejpam-3298	55	70	hy	hy	NOUN
ejpam-3298	55	71	)	)	PUNCT
ejpam-3298	55	72	+	+	NUM
ejpam-3298	55	73	d(fx	d(fx	PROPN
ejpam-3298	55	74	,	,	PUNCT
ejpam-3298	55	75	gy	gy	NOUN
ejpam-3298	55	76	)	)	PUNCT
ejpam-3298	55	77	]	]	PUNCT
ejpam-3298	55	78	)	)	PUNCT
ejpam-3298	55	79	)	)	PUNCT
ejpam-3298	55	80	}	}	PUNCT
ejpam-3298	55	81	)	)	PUNCT
ejpam-3298	55	82	.	.	PUNCT
ejpam-3298	56	1	(	(	PUNCT
ejpam-3298	56	2	5	5	X
ejpam-3298	56	3	)	)	PUNCT
ejpam-3298	56	4	for	for	ADP
ejpam-3298	56	5	all	all	DET
ejpam-3298	56	6	x	x	NOUN
ejpam-3298	56	7	,	,	PUNCT
ejpam-3298	56	8	y	y	PROPN
ejpam-3298	56	9	∈	∈	PROPN
ejpam-3298	56	10	x.where	x.where	X
ejpam-3298	57	1	ψ	ψ	PROPN
ejpam-3298	57	2	and	and	CCONJ
ejpam-3298	57	3	φ	φ	PROPN
ejpam-3298	57	4	are	be	AUX
ejpam-3298	57	5	defined	define	VERB
ejpam-3298	57	6	above	above	ADP
ejpam-3298	57	7	.	.	PUNCT
ejpam-3298	58	1	as	as	ADP
ejpam-3298	58	2	an	an	DET
ejpam-3298	58	3	applications	application	NOUN
ejpam-3298	58	4	,	,	PUNCT
ejpam-3298	58	5	we	we	PRON
ejpam-3298	58	6	discuss	discuss	VERB
ejpam-3298	58	7	the	the	DET
ejpam-3298	58	8	existence	existence	NOUN
ejpam-3298	58	9	and	and	CCONJ
ejpam-3298	58	10	uniqueness	uniqueness	NOUN
ejpam-3298	58	11	of	of	ADP
ejpam-3298	58	12	common	common	ADJ
ejpam-3298	58	13	solutions	solution	NOUN
ejpam-3298	58	14	of	of	ADP
ejpam-3298	58	15	the	the	DET
ejpam-3298	58	16	following	follow	VERB
ejpam-3298	58	17	functional	functional	ADJ
ejpam-3298	58	18	equations	equation	NOUN
ejpam-3298	58	19	arising	arise	VERB
ejpam-3298	58	20	in	in	ADP
ejpam-3298	58	21	dynamic	dynamic	ADJ
ejpam-3298	58	22	programming	programming	NOUN
ejpam-3298	58	23	.	.	PUNCT
ejpam-3298	59	1	f(x	f(x	NOUN
ejpam-3298	59	2	)	)	PUNCT
ejpam-3298	60	1	=	=	SYM
ejpam-3298	60	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	60	3	,	,	PUNCT
ejpam-3298	60	4	y	y	NOUN
ejpam-3298	60	5	)	)	PUNCT
ejpam-3298	61	1	+	+	NOUN
ejpam-3298	61	2	h(x	h(x	PROPN
ejpam-3298	61	3	,	,	PUNCT
ejpam-3298	61	4	y	y	PROPN
ejpam-3298	61	5	,	,	PUNCT
ejpam-3298	61	6	f(t	f(t	PROPN
ejpam-3298	61	7	(	(	PUNCT
ejpam-3298	61	8	x	x	X
ejpam-3298	61	9	,	,	PUNCT
ejpam-3298	61	10	y)))}∀x	y)))}∀x	PROPN
ejpam-3298	61	11	∈	∈	PROPN
ejpam-3298	61	12	s	s	X
ejpam-3298	61	13	(	(	PUNCT
ejpam-3298	61	14	6	6	NUM
ejpam-3298	61	15	)	)	PUNCT
ejpam-3298	61	16	and	and	CCONJ
ejpam-3298	61	17	fi(x	fi(x	NUM
ejpam-3298	61	18	)	)	PUNCT
ejpam-3298	61	19	=	=	SYM
ejpam-3298	61	20	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	61	21	,	,	PUNCT
ejpam-3298	61	22	y	y	NOUN
ejpam-3298	61	23	)	)	PUNCT
ejpam-3298	61	24	+	+	NOUN
ejpam-3298	61	25	hi(x	hi(x	NOUN
ejpam-3298	61	26	,	,	PUNCT
ejpam-3298	61	27	y	y	PROPN
ejpam-3298	61	28	,	,	PUNCT
ejpam-3298	61	29	fi(t	fi(t	X
ejpam-3298	61	30	(	(	PUNCT
ejpam-3298	61	31	x	x	X
ejpam-3298	61	32	,	,	PUNCT
ejpam-3298	61	33	y)))}∀x	y)))}∀x	PROPN
ejpam-3298	61	34	∈	∈	PROPN
ejpam-3298	61	35	s&i	s&i	NOUN
ejpam-3298	61	36	∈	∈	PROPN
ejpam-3298	61	37	{	{	PUNCT
ejpam-3298	61	38	1	1	NUM
ejpam-3298	61	39	,	,	PUNCT
ejpam-3298	61	40	2	2	NUM
ejpam-3298	61	41	,	,	PUNCT
ejpam-3298	61	42	3	3	NUM
ejpam-3298	61	43	}	}	PUNCT
ejpam-3298	61	44	(	(	PUNCT
ejpam-3298	61	45	7	7	X
ejpam-3298	61	46	)	)	PUNCT
ejpam-3298	61	47	p.	p.	NOUN
ejpam-3298	61	48	semwal	semwal	NOUN
ejpam-3298	61	49	,	,	PUNCT
ejpam-3298	61	50	komal	komal	PROPN
ejpam-3298	61	51	/	/	SYM
ejpam-3298	61	52	eur	eur	PROPN
ejpam-3298	61	53	.	.	PUNCT
ejpam-3298	62	1	j.	j.	PROPN
ejpam-3298	62	2	pure	pure	PROPN
ejpam-3298	62	3	appl	appl	PROPN
ejpam-3298	62	4	.	.	PROPN
ejpam-3298	62	5	math	math	PROPN
ejpam-3298	62	6	,	,	PUNCT
ejpam-3298	62	7	11	11	NUM
ejpam-3298	62	8	(	(	PUNCT
ejpam-3298	62	9	4	4	NUM
ejpam-3298	62	10	)	)	PUNCT
ejpam-3298	62	11	(	(	PUNCT
ejpam-3298	62	12	2018	2018	NUM
ejpam-3298	62	13	)	)	PUNCT
ejpam-3298	62	14	,	,	PUNCT
ejpam-3298	62	15	1177	1177	NUM
ejpam-3298	62	16	-	-	SYM
ejpam-3298	62	17	1190	1190	NUM
ejpam-3298	62	18	1180	1180	NUM
ejpam-3298	62	19	3	3	NUM
ejpam-3298	62	20	.	.	PUNCT
ejpam-3298	62	21	main	main	ADJ
ejpam-3298	62	22	results	result	NOUN
ejpam-3298	62	23	theorem	theorem	VERB
ejpam-3298	62	24	1	1	NUM
ejpam-3298	62	25	.	.	PUNCT
ejpam-3298	63	1	let	let	VERB
ejpam-3298	63	2	f	f	X
ejpam-3298	63	3	,	,	PUNCT
ejpam-3298	63	4	g	g	PROPN
ejpam-3298	63	5	and	and	CCONJ
ejpam-3298	63	6	h	h	NOUN
ejpam-3298	63	7	be	be	VERB
ejpam-3298	63	8	three	three	NUM
ejpam-3298	63	9	self	self	NOUN
ejpam-3298	63	10	maps	map	NOUN
ejpam-3298	63	11	on	on	ADP
ejpam-3298	63	12	a	a	DET
ejpam-3298	63	13	metric	metric	ADJ
ejpam-3298	63	14	space	space	NOUN
ejpam-3298	63	15	x	x	X
ejpam-3298	63	16	satisfying	satisfy	VERB
ejpam-3298	63	17	:	:	PUNCT
ejpam-3298	63	18	(	(	PUNCT
ejpam-3298	63	19	i	i	NOUN
ejpam-3298	63	20	)	)	PUNCT
ejpam-3298	63	21	either	either	CCONJ
ejpam-3298	63	22	f	f	PROPN
ejpam-3298	63	23	commute	commute	NOUN
ejpam-3298	63	24	with	with	ADP
ejpam-3298	63	25	h	h	NOUN
ejpam-3298	63	26	or	or	CCONJ
ejpam-3298	63	27	g	g	PROPN
ejpam-3298	63	28	commute	commute	NOUN
ejpam-3298	63	29	with	with	ADP
ejpam-3298	63	30	h.	h.	PROPN
ejpam-3298	63	31	(	(	PUNCT
ejpam-3298	63	32	ii	ii	PROPN
ejpam-3298	63	33	)	)	PUNCT
ejpam-3298	63	34	there	there	PRON
ejpam-3298	63	35	exists	exist	VERB
ejpam-3298	63	36	w	w	NOUN
ejpam-3298	63	37	∈w	∈w	NOUN
ejpam-3298	63	38	such	such	ADJ
ejpam-3298	63	39	that	that	SCONJ
ejpam-3298	63	40	(	(	PUNCT
ejpam-3298	63	41	5	5	X
ejpam-3298	63	42	)	)	PUNCT
ejpam-3298	63	43	hold	hold	VERB
ejpam-3298	63	44	for	for	ADP
ejpam-3298	63	45	all	all	DET
ejpam-3298	63	46	x	x	NOUN
ejpam-3298	63	47	,	,	PUNCT
ejpam-3298	63	48	y	y	PROPN
ejpam-3298	63	49	∈	∈	PROPN
ejpam-3298	63	50	x.	x.	NOUN
ejpam-3298	63	51	(	(	PUNCT
ejpam-3298	63	52	iii	iii	NOUN
ejpam-3298	63	53	)	)	PUNCT
ejpam-3298	63	54	the	the	DET
ejpam-3298	63	55	pair	pair	NOUN
ejpam-3298	63	56	(	(	PUNCT
ejpam-3298	63	57	f	f	X
ejpam-3298	63	58	,	,	PUNCT
ejpam-3298	63	59	g	g	NOUN
ejpam-3298	63	60	)	)	PUNCT
ejpam-3298	63	61	is	be	AUX
ejpam-3298	63	62	asymptotically	asymptotically	ADV
ejpam-3298	63	63	regular	regular	ADJ
ejpam-3298	63	64	with	with	ADP
ejpam-3298	63	65	respect	respect	NOUN
ejpam-3298	63	66	to	to	ADP
ejpam-3298	63	67	h	h	NOUN
ejpam-3298	63	68	at	at	ADP
ejpam-3298	63	69	x0	x0	PROPN
ejpam-3298	63	70	.	.	PUNCT
ejpam-3298	64	1	(	(	PUNCT
ejpam-3298	64	2	iv)the	iv)the	DET
ejpam-3298	64	3	space	space	NOUN
ejpam-3298	64	4	x	x	X
ejpam-3298	64	5	is	be	AUX
ejpam-3298	64	6	(	(	PUNCT
ejpam-3298	64	7	f	f	X
ejpam-3298	64	8	,	,	PUNCT
ejpam-3298	64	9	g	g	PROPN
ejpam-3298	64	10	,	,	PUNCT
ejpam-3298	64	11	h)-orbitally	h)-orbitally	ADV
ejpam-3298	64	12	complete	complete	ADJ
ejpam-3298	64	13	at	at	ADP
ejpam-3298	64	14	x0	x0	PROPN
ejpam-3298	64	15	and	and	CCONJ
ejpam-3298	64	16	h	h	NOUN
ejpam-3298	64	17	is	be	AUX
ejpam-3298	64	18	orbitally	orbitally	ADV
ejpam-3298	64	19	continuous	continuous	ADJ
ejpam-3298	64	20	at	at	ADP
ejpam-3298	64	21	x0	x0	PROPN
ejpam-3298	64	22	.	.	PUNCT
ejpam-3298	65	1	then	then	ADV
ejpam-3298	65	2	f	f	X
ejpam-3298	65	3	,	,	PUNCT
ejpam-3298	65	4	g	g	PROPN
ejpam-3298	65	5	and	and	CCONJ
ejpam-3298	65	6	h	h	NOUN
ejpam-3298	65	7	have	have	VERB
ejpam-3298	65	8	a	a	DET
ejpam-3298	65	9	unique	unique	ADJ
ejpam-3298	65	10	common	common	ADJ
ejpam-3298	65	11	fixed	fix	VERB
ejpam-3298	65	12	point	point	NOUN
ejpam-3298	65	13	in	in	ADP
ejpam-3298	65	14	x.	x.	NOUN
ejpam-3298	65	15	proof	proof	NOUN
ejpam-3298	65	16	since	since	SCONJ
ejpam-3298	65	17	(	(	PUNCT
ejpam-3298	65	18	f	f	X
ejpam-3298	65	19	,	,	PUNCT
ejpam-3298	65	20	g	g	NOUN
ejpam-3298	65	21	)	)	PUNCT
ejpam-3298	65	22	is	be	AUX
ejpam-3298	65	23	asymptotically	asymptotically	ADV
ejpam-3298	65	24	respect	respect	NOUN
ejpam-3298	65	25	to	to	ADP
ejpam-3298	65	26	h	h	NOUN
ejpam-3298	65	27	at	at	ADP
ejpam-3298	65	28	x0	x0	PROPN
ejpam-3298	65	29	,	,	PUNCT
ejpam-3298	65	30	there	there	PRON
ejpam-3298	65	31	exists	exist	VERB
ejpam-3298	65	32	a	a	DET
ejpam-3298	65	33	sequence	sequence	NOUN
ejpam-3298	65	34	{	{	PUNCT
ejpam-3298	65	35	xn	xn	NOUN
ejpam-3298	65	36	}	}	PUNCT
ejpam-3298	65	37	in	in	ADP
ejpam-3298	65	38	x	x	SYM
ejpam-3298	65	39	such	such	ADJ
ejpam-3298	65	40	that	that	DET
ejpam-3298	65	41	fx2n	fx2n	PROPN
ejpam-3298	65	42	=	=	SYM
ejpam-3298	65	43	hx2n+1	hx2n+1	PROPN
ejpam-3298	65	44	and	and	CCONJ
ejpam-3298	65	45	gx2n+1	gx2n+1	PROPN
ejpam-3298	65	46	=	=	SYM
ejpam-3298	65	47	hx2n+2	hx2n+2	PROPN
ejpam-3298	65	48	,	,	PUNCT
ejpam-3298	65	49	n	n	NOUN
ejpam-3298	65	50	=	=	SYM
ejpam-3298	65	51	0	0	NUM
ejpam-3298	65	52	,	,	PUNCT
ejpam-3298	65	53	1	1	NUM
ejpam-3298	65	54	,	,	PUNCT
ejpam-3298	65	55	2	2	NUM
ejpam-3298	65	56	,	,	PUNCT
ejpam-3298	65	57	...	...	PUNCT
ejpam-3298	65	58	and	and	CCONJ
ejpam-3298	65	59	d(hxn	d(hxn	NOUN
ejpam-3298	65	60	,	,	PUNCT
ejpam-3298	65	61	hxn+1)→	hxn+1)→	PROPN
ejpam-3298	65	62	zero	zero	NUM
ejpam-3298	65	63	as	as	ADP
ejpam-3298	65	64	n→∞.	n→∞.	NUM
ejpam-3298	65	65	now	now	ADV
ejpam-3298	65	66	we	we	PRON
ejpam-3298	65	67	show	show	VERB
ejpam-3298	65	68	that	that	SCONJ
ejpam-3298	65	69	hxn	hxn	NOUN
ejpam-3298	65	70	is	be	AUX
ejpam-3298	65	71	cauchy.on	cauchy.on	NUM
ejpam-3298	65	72	contrary	contrary	ADJ
ejpam-3298	65	73	suppose	suppose	VERB
ejpam-3298	65	74	that	that	SCONJ
ejpam-3298	65	75	hxn	hxn	NOUN
ejpam-3298	65	76	is	be	AUX
ejpam-3298	65	77	not	not	PART
ejpam-3298	65	78	cauchy	cauchy	ADJ
ejpam-3298	65	79	,	,	PUNCT
ejpam-3298	65	80	then	then	ADV
ejpam-3298	65	81	there	there	PRON
ejpam-3298	65	82	exists	exist	VERB
ejpam-3298	65	83	an	an	DET
ejpam-3298	65	84	ε	ε	PROPN
ejpam-3298	65	85	>	>	X
ejpam-3298	65	86	0	0	PUNCT
ejpam-3298	66	1	and	and	CCONJ
ejpam-3298	66	2	positive	positive	ADJ
ejpam-3298	66	3	integers	integer	NOUN
ejpam-3298	66	4	mk	mk	PROPN
ejpam-3298	66	5	and	and	CCONJ
ejpam-3298	66	6	nk	nk	PROPN
ejpam-3298	66	7	with	with	ADP
ejpam-3298	66	8	mk	mk	PROPN
ejpam-3298	66	9	<	<	X
ejpam-3298	66	10	nk	nk	PROPN
ejpam-3298	66	11	such	such	ADJ
ejpam-3298	66	12	that	that	DET
ejpam-3298	66	13	d(hxmk	d(hxmk	NOUN
ejpam-3298	66	14	,	,	PUNCT
ejpam-3298	66	15	hxnk	hxnk	PROPN
ejpam-3298	66	16	)	)	PUNCT
ejpam-3298	66	17	≥	≥	PROPN
ejpam-3298	66	18	ε	ε	PROPN
ejpam-3298	66	19	and	and	CCONJ
ejpam-3298	66	20	d(hxmk	d(hxmk	NOUN
ejpam-3298	66	21	,	,	PUNCT
ejpam-3298	66	22	hxnk−1	hxnk−1	X
ejpam-3298	66	23	)	)	PUNCT
ejpam-3298	66	24	≤	≤	PUNCT
ejpam-3298	66	25	ε	ε	PROPN
ejpam-3298	66	26	for	for	ADP
ejpam-3298	66	27	all	all	DET
ejpam-3298	66	28	k	k	NOUN
ejpam-3298	66	29	=	=	SYM
ejpam-3298	66	30	0	0	NUM
ejpam-3298	66	31	,	,	PUNCT
ejpam-3298	66	32	1	1	NUM
ejpam-3298	66	33	,	,	PUNCT
ejpam-3298	66	34	2	2	NUM
ejpam-3298	66	35	,	,	PUNCT
ejpam-3298	66	36	....	....	PUNCT
ejpam-3298	66	37	since	since	SCONJ
ejpam-3298	66	38	d(hxmk	d(hxmk	NOUN
ejpam-3298	66	39	,	,	PUNCT
ejpam-3298	66	40	hxnk	hxnk	PROPN
ejpam-3298	66	41	)	)	PUNCT
ejpam-3298	66	42	≤	≤	NUM
ejpam-3298	66	43	d(hxmk	d(hxmk	NOUN
ejpam-3298	66	44	,	,	PUNCT
ejpam-3298	66	45	hxnk−1	hxnk−1	X
ejpam-3298	66	46	)	)	PUNCT
ejpam-3298	67	1	+	+	CCONJ
ejpam-3298	68	1	d(hxnk−1	d(hxnk−1	ADJ
ejpam-3298	68	2	,	,	PUNCT
ejpam-3298	68	3	hxnk	hxnk	NOUN
ejpam-3298	68	4	)	)	PUNCT
ejpam-3298	68	5	.then	.then	PUNCT
ejpam-3298	69	1	we	we	PRON
ejpam-3298	69	2	obtain	obtain	VERB
ejpam-3298	69	3	d(hxmk	d(hxmk	NOUN
ejpam-3298	69	4	,	,	PUNCT
ejpam-3298	69	5	hxnk	hxnk	PROPN
ejpam-3298	69	6	)	)	PUNCT
ejpam-3298	69	7	→	→	SYM
ejpam-3298	69	8	ε	ε	PROPN
ejpam-3298	69	9	as	as	SCONJ
ejpam-3298	69	10	k	k	PROPN
ejpam-3298	69	11	→∞.	→∞.	PROPN
ejpam-3298	69	12	now	now	ADV
ejpam-3298	69	13	there	there	PRON
ejpam-3298	69	14	are	be	VERB
ejpam-3298	69	15	four	four	NUM
ejpam-3298	69	16	cases	case	NOUN
ejpam-3298	69	17	:	:	PUNCT
ejpam-3298	69	18	(	(	PUNCT
ejpam-3298	69	19	i	i	NOUN
ejpam-3298	69	20	)	)	PUNCT
ejpam-3298	69	21	mk	mk	PROPN
ejpam-3298	69	22	is	be	AUX
ejpam-3298	69	23	even	even	ADV
ejpam-3298	69	24	and	and	CCONJ
ejpam-3298	69	25	nk	nk	PROPN
ejpam-3298	69	26	is	be	AUX
ejpam-3298	69	27	odd	odd	ADJ
ejpam-3298	69	28	(	(	PUNCT
ejpam-3298	69	29	ii	ii	NOUN
ejpam-3298	69	30	)	)	PUNCT
ejpam-3298	69	31	mk	mk	PROPN
ejpam-3298	69	32	is	be	AUX
ejpam-3298	69	33	even	even	ADV
ejpam-3298	69	34	and	and	CCONJ
ejpam-3298	69	35	nk	nk	PROPN
ejpam-3298	69	36	is	be	AUX
ejpam-3298	69	37	even	even	ADV
ejpam-3298	69	38	(	(	PUNCT
ejpam-3298	69	39	iii	iii	X
ejpam-3298	69	40	)	)	PUNCT
ejpam-3298	69	41	mk	mk	NOUN
ejpam-3298	69	42	is	be	AUX
ejpam-3298	69	43	odd	odd	ADJ
ejpam-3298	69	44	and	and	CCONJ
ejpam-3298	69	45	nk	nk	PROPN
ejpam-3298	69	46	is	be	AUX
ejpam-3298	69	47	even	even	ADV
ejpam-3298	69	48	(	(	PUNCT
ejpam-3298	69	49	iv	iv	X
ejpam-3298	69	50	)	)	PUNCT
ejpam-3298	69	51	mk	mk	NOUN
ejpam-3298	69	52	is	be	AUX
ejpam-3298	69	53	odd	odd	ADJ
ejpam-3298	69	54	and	and	CCONJ
ejpam-3298	69	55	nk	nk	PROPN
ejpam-3298	69	56	is	be	AUX
ejpam-3298	69	57	odd	odd	ADJ
ejpam-3298	69	58	.	.	PUNCT
ejpam-3298	70	1	suppose	suppose	VERB
ejpam-3298	70	2	mk	mk	PROPN
ejpam-3298	70	3	is	be	AUX
ejpam-3298	70	4	even	even	ADV
ejpam-3298	70	5	and	and	CCONJ
ejpam-3298	70	6	nk	nk	PROPN
ejpam-3298	70	7	is	be	AUX
ejpam-3298	70	8	odd	odd	ADJ
ejpam-3298	70	9	,	,	PUNCT
ejpam-3298	70	10	we	we	PRON
ejpam-3298	70	11	have	have	VERB
ejpam-3298	70	12	ψ(d(hxmk	ψ(d(hxmk	NOUN
ejpam-3298	70	13	,	,	PUNCT
ejpam-3298	70	14	hxnk	hxnk	NOUN
ejpam-3298	70	15	)	)	PUNCT
ejpam-3298	70	16	)	)	PUNCT
ejpam-3298	71	1	≤	≤	NUM
ejpam-3298	71	2	ψ(d(hxmk	ψ(d(hxmk	NOUN
ejpam-3298	71	3	,	,	PUNCT
ejpam-3298	71	4	hxmk+1	hxmk+1	NOUN
ejpam-3298	71	5	)	)	PUNCT
ejpam-3298	71	6	)	)	PUNCT
ejpam-3298	72	1	+	+	CCONJ
ejpam-3298	72	2	ψ(d(hxmk+1	ψ(d(hxmk+1	NOUN
ejpam-3298	72	3	,	,	PUNCT
ejpam-3298	72	4	hxnk+1	hxnk+1	NOUN
ejpam-3298	72	5	)	)	PUNCT
ejpam-3298	72	6	)	)	PUNCT
ejpam-3298	73	1	+	+	CCONJ
ejpam-3298	73	2	ψ(d(hxnk+1	ψ(d(hxnk+1	NOUN
ejpam-3298	73	3	,	,	PUNCT
ejpam-3298	73	4	hxnk	hxnk	NOUN
ejpam-3298	73	5	)	)	PUNCT
ejpam-3298	73	6	)	)	PUNCT
ejpam-3298	73	7	≤	≤	NUM
ejpam-3298	73	8	ψ(d(hxmk	ψ(d(hxmk	NOUN
ejpam-3298	73	9	,	,	PUNCT
ejpam-3298	73	10	hxmk+1	hxmk+1	NOUN
ejpam-3298	73	11	)	)	PUNCT
ejpam-3298	73	12	)	)	PUNCT
ejpam-3298	74	1	+	+	VERB
ejpam-3298	74	2	max{φ(d(hxmk	max{φ(d(hxmk	PROPN
ejpam-3298	74	3	,	,	PUNCT
ejpam-3298	74	4	hxk	hxk	PROPN
ejpam-3298	74	5	)	)	PUNCT
ejpam-3298	74	6	)	)	PUNCT
ejpam-3298	74	7	,	,	PUNCT
ejpam-3298	74	8	φ(d(fxmk	φ(d(fxmk	PROPN
ejpam-3298	74	9	,	,	PUNCT
ejpam-3298	74	10	hxmk	hxmk	PROPN
ejpam-3298	74	11	)	)	PUNCT
ejpam-3298	74	12	)	)	PUNCT
ejpam-3298	74	13	,	,	PUNCT
ejpam-3298	74	14	φ(d(gxnk	φ(d(gxnk	PROPN
ejpam-3298	74	15	,	,	PUNCT
ejpam-3298	74	16	hxnk	hxnk	PROPN
ejpam-3298	74	17	)	)	PUNCT
ejpam-3298	74	18	)	)	PUNCT
ejpam-3298	74	19	,	,	PUNCT
ejpam-3298	74	20	φ	φ	X
ejpam-3298	74	21	(	(	PUNCT
ejpam-3298	74	22	1	1	NUM
ejpam-3298	74	23	2	2	NUM
ejpam-3298	74	24	[	[	X
ejpam-3298	74	25	d(hxmk	d(hxmk	NOUN
ejpam-3298	74	26	,	,	PUNCT
ejpam-3298	74	27	hxnk	hxnk	PROPN
ejpam-3298	74	28	)	)	PUNCT
ejpam-3298	75	1	+	+	CCONJ
ejpam-3298	75	2	d(fxmk	d(fxmk	ADJ
ejpam-3298	75	3	,	,	PUNCT
ejpam-3298	75	4	gxnk	gxnk	NOUN
ejpam-3298	75	5	)	)	PUNCT
ejpam-3298	75	6	]	]	PUNCT
ejpam-3298	75	7	)	)	PUNCT
ejpam-3298	75	8	}	}	PUNCT
ejpam-3298	75	9	−	−	ADP
ejpam-3298	75	10	w(max{φ(d(hxmk	w(max{φ(d(hxmk	INTJ
ejpam-3298	75	11	,	,	PUNCT
ejpam-3298	75	12	hxk	hxk	PROPN
ejpam-3298	75	13	)	)	PUNCT
ejpam-3298	75	14	)	)	PUNCT
ejpam-3298	75	15	,	,	PUNCT
ejpam-3298	75	16	φ(d(fxmk	φ(d(fxmk	PROPN
ejpam-3298	75	17	,	,	PUNCT
ejpam-3298	75	18	hxmk	hxmk	PROPN
ejpam-3298	75	19	)	)	PUNCT
ejpam-3298	75	20	)	)	PUNCT
ejpam-3298	75	21	,	,	PUNCT
ejpam-3298	75	22	φ(d(gxnk	φ(d(gxnk	PROPN
ejpam-3298	75	23	,	,	PUNCT
ejpam-3298	75	24	hxnk	hxnk	PROPN
ejpam-3298	75	25	)	)	PUNCT
ejpam-3298	75	26	)	)	PUNCT
ejpam-3298	75	27	,	,	PUNCT
ejpam-3298	75	28	φ	φ	X
ejpam-3298	75	29	(	(	PUNCT
ejpam-3298	75	30	1	1	NUM
ejpam-3298	75	31	2	2	NUM
ejpam-3298	75	32	[	[	X
ejpam-3298	75	33	d(hxmk	d(hxmk	NOUN
ejpam-3298	75	34	,	,	PUNCT
ejpam-3298	75	35	hxnk	hxnk	PROPN
ejpam-3298	75	36	)	)	PUNCT
ejpam-3298	76	1	+	+	CCONJ
ejpam-3298	76	2	d(fxmk	d(fxmk	ADJ
ejpam-3298	76	3	,	,	PUNCT
ejpam-3298	76	4	gxnk	gxnk	NOUN
ejpam-3298	76	5	)	)	PUNCT
ejpam-3298	76	6	]	]	PUNCT
ejpam-3298	76	7	)	)	PUNCT
ejpam-3298	76	8	}	}	PUNCT
ejpam-3298	76	9	)	)	PUNCT
ejpam-3298	77	1	+	+	CCONJ
ejpam-3298	77	2	ψ(d(hxnk+1	ψ(d(hxnk+1	NOUN
ejpam-3298	77	3	,	,	PUNCT
ejpam-3298	77	4	hxnk	hxnk	NOUN
ejpam-3298	77	5	)	)	PUNCT
ejpam-3298	77	6	)	)	PUNCT
ejpam-3298	78	1	letting	let	VERB
ejpam-3298	78	2	k	k	PROPN
ejpam-3298	78	3	→∞	→∞	PROPN
ejpam-3298	78	4	,	,	PUNCT
ejpam-3298	78	5	we	we	PRON
ejpam-3298	78	6	obtain	obtain	VERB
ejpam-3298	78	7	ψ(ε	ψ(ε	PROPN
ejpam-3298	78	8	)	)	PUNCT
ejpam-3298	78	9	≤	≤	PROPN
ejpam-3298	78	10	φ(ε)−	φ(ε)−	PROPN
ejpam-3298	78	11	w(φ(ε	w(φ(ε	PROPN
ejpam-3298	78	12	)	)	PUNCT
ejpam-3298	78	13	)	)	PUNCT
ejpam-3298	79	1	<	<	X
ejpam-3298	79	2	φ(ε	φ(ε	PROPN
ejpam-3298	79	3	)	)	PUNCT
ejpam-3298	79	4	a	a	DET
ejpam-3298	79	5	contradiction.in	contradiction.in	X
ejpam-3298	79	6	the	the	DET
ejpam-3298	79	7	remaining	remain	VERB
ejpam-3298	79	8	cases	case	NOUN
ejpam-3298	79	9	we	we	PRON
ejpam-3298	79	10	have	have	VERB
ejpam-3298	79	11	a	a	DET
ejpam-3298	79	12	similar	similar	ADJ
ejpam-3298	79	13	situation.hence	situation.hence	NOUN
ejpam-3298	79	14	{	{	PUNCT
ejpam-3298	79	15	hxn	hxn	NOUN
ejpam-3298	79	16	}	}	PUNCT
ejpam-3298	79	17	is	be	AUX
ejpam-3298	79	18	cauchy.since	cauchy.since	NOUN
ejpam-3298	79	19	x	x	PUNCT
ejpam-3298	79	20	is	be	AUX
ejpam-3298	79	21	(	(	PUNCT
ejpam-3298	79	22	f	f	X
ejpam-3298	79	23	,	,	PUNCT
ejpam-3298	79	24	g	g	PROPN
ejpam-3298	79	25	,	,	PUNCT
ejpam-3298	79	26	h)orbitally	h)orbitally	ADV
ejpam-3298	79	27	complete	complete	ADJ
ejpam-3298	79	28	at	at	ADP
ejpam-3298	79	29	x0	x0	PROPN
ejpam-3298	79	30	,	,	PUNCT
ejpam-3298	79	31	it	it	PRON
ejpam-3298	79	32	follows	follow	VERB
ejpam-3298	79	33	that	that	SCONJ
ejpam-3298	79	34	there	there	PRON
ejpam-3298	79	35	exist	exist	VERB
ejpam-3298	79	36	z	z	NOUN
ejpam-3298	79	37	∈	∈	PROPN
ejpam-3298	79	38	x	x	SYM
ejpam-3298	79	39	s.t	s.t	PROPN
ejpam-3298	79	40	.	.	PROPN
ejpam-3298	79	41	hxn	hxn	NOUN
ejpam-3298	79	42	→	→	PUNCT
ejpam-3298	79	43	z	z	NOUN
ejpam-3298	79	44	as	as	ADP
ejpam-3298	79	45	n→∞.	n→∞.	ADJ
ejpam-3298	79	46	now	now	ADV
ejpam-3298	79	47	,	,	PUNCT
ejpam-3298	79	48	again	again	ADV
ejpam-3298	79	49	ψ(d(fx2n	ψ(d(fx2n	NOUN
ejpam-3298	79	50	,	,	PUNCT
ejpam-3298	79	51	gz	gz	NOUN
ejpam-3298	79	52	)	)	PUNCT
ejpam-3298	79	53	)	)	PUNCT
ejpam-3298	80	1	≤	≤	NOUN
ejpam-3298	80	2	max{φ(d(hx2n	max{φ(d(hx2n	NOUN
ejpam-3298	80	3	,	,	PUNCT
ejpam-3298	80	4	hz	hz	NOUN
ejpam-3298	80	5	)	)	PUNCT
ejpam-3298	80	6	)	)	PUNCT
ejpam-3298	80	7	,	,	PUNCT
ejpam-3298	80	8	φ(d(fx2n	φ(d(fx2n	ADV
ejpam-3298	80	9	,	,	PUNCT
ejpam-3298	80	10	hx2n	hx2n	PROPN
ejpam-3298	80	11	)	)	PUNCT
ejpam-3298	80	12	)	)	PUNCT
ejpam-3298	80	13	,	,	PUNCT
ejpam-3298	80	14	φ(d(gz	φ(d(gz	ADP
ejpam-3298	80	15	,	,	PUNCT
ejpam-3298	80	16	hz	hz	NOUN
ejpam-3298	80	17	)	)	PUNCT
ejpam-3298	80	18	)	)	PUNCT
ejpam-3298	80	19	,	,	PUNCT
ejpam-3298	80	20	φ	φ	X
ejpam-3298	80	21	(	(	PUNCT
ejpam-3298	80	22	1	1	NUM
ejpam-3298	80	23	2	2	NUM
ejpam-3298	80	24	[	[	X
ejpam-3298	80	25	d(hx2n	d(hx2n	NOUN
ejpam-3298	80	26	,	,	PUNCT
ejpam-3298	80	27	hz	hz	X
ejpam-3298	80	28	)	)	PUNCT
ejpam-3298	80	29	+	+	NUM
ejpam-3298	80	30	d(fx2n	d(fx2n	PROPN
ejpam-3298	80	31	,	,	PUNCT
ejpam-3298	80	32	gz	gz	NOUN
ejpam-3298	80	33	)	)	PUNCT
ejpam-3298	80	34	]	]	PUNCT
ejpam-3298	80	35	)	)	PUNCT
ejpam-3298	80	36	}	}	PUNCT
ejpam-3298	80	37	−	−	ADP
ejpam-3298	80	38	w((max{φ(d(hx2n	w((max{φ(d(hx2n	NOUN
ejpam-3298	80	39	,	,	PUNCT
ejpam-3298	80	40	hz	hz	NOUN
ejpam-3298	80	41	)	)	PUNCT
ejpam-3298	80	42	)	)	PUNCT
ejpam-3298	80	43	,	,	PUNCT
ejpam-3298	80	44	φ(d(fx2n	φ(d(fx2n	ADV
ejpam-3298	80	45	,	,	PUNCT
ejpam-3298	80	46	hx2n	hx2n	PROPN
ejpam-3298	80	47	)	)	PUNCT
ejpam-3298	80	48	)	)	PUNCT
ejpam-3298	80	49	,	,	PUNCT
ejpam-3298	80	50	φ(d(gz	φ(d(gz	ADP
ejpam-3298	80	51	,	,	PUNCT
ejpam-3298	80	52	hz	hz	NOUN
ejpam-3298	80	53	)	)	PUNCT
ejpam-3298	80	54	)	)	PUNCT
ejpam-3298	80	55	,	,	PUNCT
ejpam-3298	80	56	φ	φ	X
ejpam-3298	80	57	(	(	PUNCT
ejpam-3298	80	58	1	1	NUM
ejpam-3298	80	59	2	2	NUM
ejpam-3298	80	60	[	[	X
ejpam-3298	80	61	d(hx2n	d(hx2n	NOUN
ejpam-3298	80	62	,	,	PUNCT
ejpam-3298	80	63	hz	hz	X
ejpam-3298	80	64	)	)	PUNCT
ejpam-3298	80	65	+	+	NUM
ejpam-3298	80	66	d(fx2n	d(fx2n	PROPN
ejpam-3298	80	67	,	,	PUNCT
ejpam-3298	80	68	gz	gz	NOUN
ejpam-3298	80	69	)	)	PUNCT
ejpam-3298	80	70	]	]	PUNCT
ejpam-3298	80	71	)	)	PUNCT
ejpam-3298	80	72	}	}	PUNCT
ejpam-3298	80	73	)	)	PUNCT
ejpam-3298	80	74	)	)	PUNCT
ejpam-3298	80	75	and	and	CCONJ
ejpam-3298	80	76	ψ(d(fz	ψ(d(fz	NOUN
ejpam-3298	80	77	,	,	PUNCT
ejpam-3298	80	78	gx2n+1	gx2n+1	PROPN
ejpam-3298	80	79	)	)	PUNCT
ejpam-3298	80	80	)	)	PUNCT
ejpam-3298	80	81	≤	≤	NUM
ejpam-3298	80	82	max{φ(d(hz	max{φ(d(hz	NUM
ejpam-3298	80	83	,	,	PUNCT
ejpam-3298	80	84	hx2n+1	hx2n+1	PROPN
ejpam-3298	80	85	)	)	PUNCT
ejpam-3298	80	86	)	)	PUNCT
ejpam-3298	80	87	,	,	PUNCT
ejpam-3298	80	88	φ(d(fz	φ(d(fz	NOUN
ejpam-3298	80	89	,	,	PUNCT
ejpam-3298	80	90	hz	hz	NOUN
ejpam-3298	80	91	)	)	PUNCT
ejpam-3298	80	92	)	)	PUNCT
ejpam-3298	80	93	,	,	PUNCT
ejpam-3298	80	94	φ(d(gx2n+1	φ(d(gx2n+1	NOUN
ejpam-3298	80	95	,	,	PUNCT
ejpam-3298	80	96	hx2n+1	hx2n+1	PROPN
ejpam-3298	80	97	)	)	PUNCT
ejpam-3298	80	98	)	)	PUNCT
ejpam-3298	80	99	,	,	PUNCT
ejpam-3298	80	100	p.	p.	NOUN
ejpam-3298	80	101	semwal	semwal	NOUN
ejpam-3298	80	102	,	,	PUNCT
ejpam-3298	80	103	komal	komal	PROPN
ejpam-3298	80	104	/	/	SYM
ejpam-3298	80	105	eur	eur	PROPN
ejpam-3298	80	106	.	.	PUNCT
ejpam-3298	81	1	j.	j.	PROPN
ejpam-3298	81	2	pure	pure	PROPN
ejpam-3298	81	3	appl	appl	PROPN
ejpam-3298	81	4	.	.	PROPN
ejpam-3298	81	5	math	math	PROPN
ejpam-3298	81	6	,	,	PUNCT
ejpam-3298	81	7	11	11	NUM
ejpam-3298	81	8	(	(	PUNCT
ejpam-3298	81	9	4	4	NUM
ejpam-3298	81	10	)	)	PUNCT
ejpam-3298	81	11	(	(	PUNCT
ejpam-3298	81	12	2018	2018	NUM
ejpam-3298	81	13	)	)	PUNCT
ejpam-3298	81	14	,	,	PUNCT
ejpam-3298	81	15	1177	1177	NUM
ejpam-3298	81	16	-	-	SYM
ejpam-3298	81	17	1190	1190	NUM
ejpam-3298	81	18	1181	1181	NUM
ejpam-3298	81	19	φ	φ	PROPN
ejpam-3298	81	20	(	(	PUNCT
ejpam-3298	81	21	1	1	NUM
ejpam-3298	81	22	2	2	NUM
ejpam-3298	81	23	[	[	X
ejpam-3298	81	24	d(hz	d(hz	PROPN
ejpam-3298	81	25	,	,	PUNCT
ejpam-3298	81	26	hx2n+1	hx2n+1	PROPN
ejpam-3298	81	27	)	)	PUNCT
ejpam-3298	82	1	+	+	CCONJ
ejpam-3298	82	2	d(fz	d(fz	PROPN
ejpam-3298	82	3	,	,	PUNCT
ejpam-3298	82	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	82	5	)	)	PUNCT
ejpam-3298	82	6	]	]	PUNCT
ejpam-3298	82	7	)	)	PUNCT
ejpam-3298	82	8	}	}	PUNCT
ejpam-3298	82	9	−	−	PUNCT
ejpam-3298	82	10	w((max{φ(d(hz	w((max{φ(d(hz	ADJ
ejpam-3298	82	11	,	,	PUNCT
ejpam-3298	82	12	hx2n+1	hx2n+1	PROPN
ejpam-3298	82	13	)	)	PUNCT
ejpam-3298	82	14	)	)	PUNCT
ejpam-3298	82	15	,	,	PUNCT
ejpam-3298	82	16	φ(d(fz	φ(d(fz	NOUN
ejpam-3298	82	17	,	,	PUNCT
ejpam-3298	82	18	hz	hz	NOUN
ejpam-3298	82	19	)	)	PUNCT
ejpam-3298	82	20	)	)	PUNCT
ejpam-3298	82	21	,	,	PUNCT
ejpam-3298	82	22	−	−	PROPN
ejpam-3298	82	23	φ(d(gx2n+1	φ(d(gx2n+1	PROPN
ejpam-3298	82	24	,	,	PUNCT
ejpam-3298	82	25	hx2n+1	hx2n+1	PROPN
ejpam-3298	82	26	)	)	PUNCT
ejpam-3298	82	27	)	)	PUNCT
ejpam-3298	82	28	,	,	PUNCT
ejpam-3298	82	29	φ	φ	X
ejpam-3298	82	30	(	(	PUNCT
ejpam-3298	82	31	1	1	NUM
ejpam-3298	82	32	2	2	NUM
ejpam-3298	82	33	[	[	X
ejpam-3298	82	34	d(hz	d(hz	PROPN
ejpam-3298	82	35	,	,	PUNCT
ejpam-3298	82	36	hx2n+1	hx2n+1	PROPN
ejpam-3298	82	37	)	)	PUNCT
ejpam-3298	83	1	+	+	CCONJ
ejpam-3298	83	2	d(fz	d(fz	PROPN
ejpam-3298	83	3	,	,	PUNCT
ejpam-3298	83	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	83	5	)	)	PUNCT
ejpam-3298	83	6	]	]	PUNCT
ejpam-3298	83	7	)	)	PUNCT
ejpam-3298	83	8	}	}	PUNCT
ejpam-3298	83	9	)	)	PUNCT
ejpam-3298	83	10	)	)	PUNCT
ejpam-3298	84	1	taking	take	VERB
ejpam-3298	84	2	k	k	PROPN
ejpam-3298	84	3	→∞	→∞	PROPN
ejpam-3298	84	4	,	,	PUNCT
ejpam-3298	84	5	we	we	PRON
ejpam-3298	84	6	obtain	obtain	VERB
ejpam-3298	84	7	ψ(d(z	ψ(d(z	PROPN
ejpam-3298	84	8	,	,	PUNCT
ejpam-3298	84	9	gz	gz	NOUN
ejpam-3298	84	10	)	)	PUNCT
ejpam-3298	84	11	)	)	PUNCT
ejpam-3298	85	1	≤	≤	PUNCT
ejpam-3298	86	1	max{φ(d(z	max{φ(d(z	NOUN
ejpam-3298	86	2	,	,	PUNCT
ejpam-3298	86	3	hz	hz	NOUN
ejpam-3298	86	4	)	)	PUNCT
ejpam-3298	86	5	)	)	PUNCT
ejpam-3298	86	6	,	,	PUNCT
ejpam-3298	86	7	φ(d(z	φ(d(z	PROPN
ejpam-3298	86	8	,	,	PUNCT
ejpam-3298	86	9	z	z	NOUN
ejpam-3298	86	10	)	)	PUNCT
ejpam-3298	86	11	)	)	PUNCT
ejpam-3298	86	12	,	,	PUNCT
ejpam-3298	86	13	φ(gz	φ(gz	NOUN
ejpam-3298	86	14	,	,	PUNCT
ejpam-3298	86	15	hz	hz	NOUN
ejpam-3298	86	16	)	)	PUNCT
ejpam-3298	86	17	,	,	PUNCT
ejpam-3298	86	18	φ	φ	X
ejpam-3298	86	19	(	(	PUNCT
ejpam-3298	86	20	1	1	NUM
ejpam-3298	86	21	2	2	NUM
ejpam-3298	86	22	[	[	X
ejpam-3298	86	23	d(hz	d(hz	PROPN
ejpam-3298	86	24	,	,	PUNCT
ejpam-3298	86	25	z	z	NOUN
ejpam-3298	86	26	)	)	PUNCT
ejpam-3298	87	1	+	+	CCONJ
ejpam-3298	87	2	d(z	d(z	PROPN
ejpam-3298	87	3	,	,	PUNCT
ejpam-3298	87	4	gz	gz	NOUN
ejpam-3298	87	5	)	)	PUNCT
ejpam-3298	87	6	]	]	PUNCT
ejpam-3298	87	7	)	)	PUNCT
ejpam-3298	87	8	}	}	PUNCT
ejpam-3298	87	9	−	−	ADP
ejpam-3298	87	10	w((max{φ(d(z	w((max{φ(d(z	NOUN
ejpam-3298	87	11	,	,	PUNCT
ejpam-3298	87	12	hz	hz	PROPN
ejpam-3298	87	13	)	)	PUNCT
ejpam-3298	87	14	)	)	PUNCT
ejpam-3298	87	15	,	,	PUNCT
ejpam-3298	87	16	φ(d(z	φ(d(z	PROPN
ejpam-3298	87	17	,	,	PUNCT
ejpam-3298	87	18	z	z	NOUN
ejpam-3298	87	19	)	)	PUNCT
ejpam-3298	87	20	)	)	PUNCT
ejpam-3298	87	21	,	,	PUNCT
ejpam-3298	87	22	φ(d(gz	φ(d(gz	ADP
ejpam-3298	87	23	,	,	PUNCT
ejpam-3298	87	24	hz	hz	NOUN
ejpam-3298	87	25	)	)	PUNCT
ejpam-3298	87	26	)	)	PUNCT
ejpam-3298	87	27	,	,	PUNCT
ejpam-3298	87	28	φ	φ	X
ejpam-3298	87	29	(	(	PUNCT
ejpam-3298	87	30	1	1	NUM
ejpam-3298	87	31	2	2	NUM
ejpam-3298	87	32	[	[	X
ejpam-3298	87	33	d(hz	d(hz	PROPN
ejpam-3298	87	34	,	,	PUNCT
ejpam-3298	87	35	z	z	NOUN
ejpam-3298	87	36	)	)	PUNCT
ejpam-3298	87	37	+	+	CCONJ
ejpam-3298	87	38	d(z	d(z	PROPN
ejpam-3298	87	39	,	,	PUNCT
ejpam-3298	87	40	gz	gz	NOUN
ejpam-3298	87	41	)	)	PUNCT
ejpam-3298	87	42	]	]	PUNCT
ejpam-3298	87	43	)	)	PUNCT
ejpam-3298	87	44	}	}	PUNCT
ejpam-3298	87	45	)	)	PUNCT
ejpam-3298	87	46	)	)	PUNCT
ejpam-3298	87	47	(	(	PUNCT
ejpam-3298	87	48	8)	8)	NUM
ejpam-3298	87	49	and	and	CCONJ
ejpam-3298	87	50	ψ(d(fz	ψ(d(fz	NOUN
ejpam-3298	87	51	,	,	PUNCT
ejpam-3298	87	52	z	z	NOUN
ejpam-3298	87	53	)	)	PUNCT
ejpam-3298	87	54	)	)	PUNCT
ejpam-3298	88	1	≤	≤	PUNCT
ejpam-3298	89	1	max{φ(d(z	max{φ(d(z	NOUN
ejpam-3298	89	2	,	,	PUNCT
ejpam-3298	89	3	hz	hz	NOUN
ejpam-3298	89	4	)	)	PUNCT
ejpam-3298	89	5	)	)	PUNCT
ejpam-3298	89	6	,	,	PUNCT
ejpam-3298	89	7	φ(d(z	φ(d(z	PROPN
ejpam-3298	89	8	,	,	PUNCT
ejpam-3298	89	9	z	z	NOUN
ejpam-3298	89	10	)	)	PUNCT
ejpam-3298	89	11	)	)	PUNCT
ejpam-3298	89	12	,	,	PUNCT
ejpam-3298	89	13	φ(d(gz	φ(d(gz	ADP
ejpam-3298	89	14	,	,	PUNCT
ejpam-3298	89	15	hz	hz	NOUN
ejpam-3298	89	16	)	)	PUNCT
ejpam-3298	89	17	)	)	PUNCT
ejpam-3298	89	18	,	,	PUNCT
ejpam-3298	89	19	φ	φ	X
ejpam-3298	89	20	(	(	PUNCT
ejpam-3298	89	21	1	1	NUM
ejpam-3298	89	22	2	2	NUM
ejpam-3298	89	23	[	[	X
ejpam-3298	89	24	d(hz	d(hz	PROPN
ejpam-3298	89	25	,	,	PUNCT
ejpam-3298	89	26	z	z	NOUN
ejpam-3298	89	27	)	)	PUNCT
ejpam-3298	89	28	+	+	CCONJ
ejpam-3298	89	29	d(fz	d(fz	PROPN
ejpam-3298	89	30	,	,	PUNCT
ejpam-3298	89	31	z	z	NOUN
ejpam-3298	89	32	)	)	PUNCT
ejpam-3298	89	33	]	]	PUNCT
ejpam-3298	89	34	)	)	PUNCT
ejpam-3298	89	35	}	}	PUNCT
ejpam-3298	89	36	−	−	ADP
ejpam-3298	89	37	w((max{φ(d(z	w((max{φ(d(z	NOUN
ejpam-3298	89	38	,	,	PUNCT
ejpam-3298	89	39	hz	hz	PROPN
ejpam-3298	89	40	)	)	PUNCT
ejpam-3298	89	41	)	)	PUNCT
ejpam-3298	89	42	,	,	PUNCT
ejpam-3298	89	43	φ(d(z	φ(d(z	PROPN
ejpam-3298	89	44	,	,	PUNCT
ejpam-3298	89	45	z	z	NOUN
ejpam-3298	89	46	)	)	PUNCT
ejpam-3298	89	47	)	)	PUNCT
ejpam-3298	89	48	,	,	PUNCT
ejpam-3298	89	49	φ(d(gz	φ(d(gz	ADP
ejpam-3298	89	50	,	,	PUNCT
ejpam-3298	89	51	hz	hz	NOUN
ejpam-3298	89	52	)	)	PUNCT
ejpam-3298	89	53	)	)	PUNCT
ejpam-3298	89	54	,	,	PUNCT
ejpam-3298	89	55	φ	φ	X
ejpam-3298	89	56	(	(	PUNCT
ejpam-3298	89	57	1	1	NUM
ejpam-3298	89	58	2	2	NUM
ejpam-3298	89	59	[	[	X
ejpam-3298	89	60	d(hz	d(hz	PROPN
ejpam-3298	89	61	,	,	PUNCT
ejpam-3298	89	62	z	z	NOUN
ejpam-3298	89	63	)	)	PUNCT
ejpam-3298	89	64	+	+	CCONJ
ejpam-3298	89	65	d(fz	d(fz	PROPN
ejpam-3298	89	66	,	,	PUNCT
ejpam-3298	89	67	z	z	NOUN
ejpam-3298	89	68	)	)	PUNCT
ejpam-3298	89	69	]	]	PUNCT
ejpam-3298	89	70	)	)	PUNCT
ejpam-3298	89	71	}	}	PUNCT
ejpam-3298	89	72	)	)	PUNCT
ejpam-3298	89	73	)	)	PUNCT
ejpam-3298	89	74	(	(	PUNCT
ejpam-3298	89	75	9	9	X
ejpam-3298	89	76	)	)	PUNCT
ejpam-3298	89	77	since	since	SCONJ
ejpam-3298	89	78	h	h	NOUN
ejpam-3298	89	79	is	be	AUX
ejpam-3298	89	80	orbitally	orbitally	ADV
ejpam-3298	89	81	continuous	continuous	ADJ
ejpam-3298	89	82	at	at	ADP
ejpam-3298	89	83	x0	x0	PROPN
ejpam-3298	89	84	and	and	CCONJ
ejpam-3298	89	85	fh	fh	PROPN
ejpam-3298	89	86	=	=	PUNCT
ejpam-3298	90	1	hf	hf	INTJ
ejpam-3298	90	2	,	,	PUNCT
ejpam-3298	90	3	we	we	PRON
ejpam-3298	90	4	infer	infer	VERB
ejpam-3298	90	5	that	that	PRON
ejpam-3298	90	6	fhx2n	fhx2n	PUNCT
ejpam-3298	90	7	=	=	PUNCT
ejpam-3298	91	1	hf2n	hf2n	PROPN
ejpam-3298	91	2	→	→	SYM
ejpam-3298	91	3	tz	tz	NOUN
ejpam-3298	91	4	as	as	SCONJ
ejpam-3298	91	5	n→∞.similarly	n→∞.similarly	ADV
ejpam-3298	91	6	ghx2n+1	ghx2n+1	NOUN
ejpam-3298	91	7	=	=	SYM
ejpam-3298	91	8	hgx2n+1	hgx2n+1	PROPN
ejpam-3298	91	9	→	→	PUNCT
ejpam-3298	91	10	hz	hz	X
ejpam-3298	91	11	as	as	ADP
ejpam-3298	91	12	n→∞.	n→∞.	ADJ
ejpam-3298	91	13	again	again	ADV
ejpam-3298	91	14	,	,	PUNCT
ejpam-3298	91	15	ψ(d(fhx2n	ψ(d(fhx2n	NOUN
ejpam-3298	91	16	,	,	PUNCT
ejpam-3298	91	17	gx2n+1	gx2n+1	PROPN
ejpam-3298	91	18	)	)	PUNCT
ejpam-3298	91	19	)	)	PUNCT
ejpam-3298	91	20	≤	≤	NUM
ejpam-3298	91	21	max{φ(d(hhx2n	max{φ(d(hhx2n	PROPN
ejpam-3298	91	22	,	,	PUNCT
ejpam-3298	91	23	hx2n+1	hx2n+1	PROPN
ejpam-3298	91	24	)	)	PUNCT
ejpam-3298	91	25	)	)	PUNCT
ejpam-3298	91	26	,	,	PUNCT
ejpam-3298	91	27	φ(d(fhx2n	φ(d(fhx2n	ADV
ejpam-3298	91	28	,	,	PUNCT
ejpam-3298	91	29	hhx2n	hhx2n	PROPN
ejpam-3298	91	30	)	)	PUNCT
ejpam-3298	91	31	)	)	PUNCT
ejpam-3298	91	32	,	,	PUNCT
ejpam-3298	91	33	φ(d(gx2n+1	φ(d(gx2n+1	X
ejpam-3298	91	34	,	,	PUNCT
ejpam-3298	91	35	hx2n+1	hx2n+1	PROPN
ejpam-3298	91	36	)	)	PUNCT
ejpam-3298	91	37	)	)	PUNCT
ejpam-3298	91	38	,	,	PUNCT
ejpam-3298	91	39	φ	φ	X
ejpam-3298	91	40	(	(	PUNCT
ejpam-3298	91	41	1	1	NUM
ejpam-3298	91	42	2	2	NUM
ejpam-3298	91	43	[	[	PUNCT
ejpam-3298	91	44	d(hhx2n	d(hhx2n	NOUN
ejpam-3298	91	45	,	,	PUNCT
ejpam-3298	91	46	hx2n+1	hx2n+1	PROPN
ejpam-3298	91	47	)	)	PUNCT
ejpam-3298	92	1	+	+	NUM
ejpam-3298	92	2	d(fhx2n	d(fhx2n	NOUN
ejpam-3298	92	3	,	,	PUNCT
ejpam-3298	92	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	92	5	)	)	PUNCT
ejpam-3298	92	6	]	]	PUNCT
ejpam-3298	92	7	)	)	PUNCT
ejpam-3298	92	8	}	}	PUNCT
ejpam-3298	92	9	−	−	PROPN
ejpam-3298	92	10	w(max{φ(d(hhx2n	w(max{φ(d(hhx2n	PROPN
ejpam-3298	92	11	,	,	PUNCT
ejpam-3298	92	12	hx2n+1	hx2n+1	PROPN
ejpam-3298	92	13	)	)	PUNCT
ejpam-3298	92	14	)	)	PUNCT
ejpam-3298	92	15	,	,	PUNCT
ejpam-3298	92	16	φ(d(fhx2n	φ(d(fhx2n	ADV
ejpam-3298	92	17	,	,	PUNCT
ejpam-3298	92	18	hhx2n	hhx2n	PROPN
ejpam-3298	92	19	)	)	PUNCT
ejpam-3298	92	20	)	)	PUNCT
ejpam-3298	92	21	,	,	PUNCT
ejpam-3298	92	22	φ(d(gx2n+1	φ(d(gx2n+1	X
ejpam-3298	92	23	,	,	PUNCT
ejpam-3298	92	24	hx2n+1	hx2n+1	PROPN
ejpam-3298	92	25	)	)	PUNCT
ejpam-3298	92	26	)	)	PUNCT
ejpam-3298	92	27	,	,	PUNCT
ejpam-3298	92	28	φ	φ	X
ejpam-3298	92	29	(	(	PUNCT
ejpam-3298	92	30	1	1	NUM
ejpam-3298	92	31	2	2	NUM
ejpam-3298	92	32	[	[	PUNCT
ejpam-3298	92	33	d(hhx2n	d(hhx2n	NOUN
ejpam-3298	92	34	,	,	PUNCT
ejpam-3298	92	35	hx2n+1	hx2n+1	PROPN
ejpam-3298	92	36	)	)	PUNCT
ejpam-3298	93	1	+	+	NUM
ejpam-3298	93	2	d(fhx2n	d(fhx2n	NOUN
ejpam-3298	93	3	,	,	PUNCT
ejpam-3298	93	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	93	5	)	)	PUNCT
ejpam-3298	93	6	]	]	PUNCT
ejpam-3298	93	7	)	)	PUNCT
ejpam-3298	93	8	}	}	PUNCT
ejpam-3298	93	9	)	)	PUNCT
ejpam-3298	93	10	taking	take	VERB
ejpam-3298	93	11	k	k	PROPN
ejpam-3298	93	12	→∞	→∞	PROPN
ejpam-3298	93	13	,	,	PUNCT
ejpam-3298	93	14	we	we	PRON
ejpam-3298	93	15	obtain	obtain	VERB
ejpam-3298	93	16	ψ(d(hz	ψ(d(hz	SYM
ejpam-3298	93	17	,	,	PUNCT
ejpam-3298	93	18	z	z	NOUN
ejpam-3298	93	19	)	)	PUNCT
ejpam-3298	93	20	)	)	PUNCT
ejpam-3298	94	1	≤	≤	NOUN
ejpam-3298	94	2	max{φ(d(hz	max{φ(d(hz	NUM
ejpam-3298	94	3	,	,	PUNCT
ejpam-3298	94	4	z	z	NOUN
ejpam-3298	94	5	)	)	PUNCT
ejpam-3298	94	6	)	)	PUNCT
ejpam-3298	94	7	,	,	PUNCT
ejpam-3298	94	8	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	94	9	,	,	PUNCT
ejpam-3298	94	10	hz	hz	NOUN
ejpam-3298	94	11	)	)	PUNCT
ejpam-3298	94	12	)	)	PUNCT
ejpam-3298	94	13	,	,	PUNCT
ejpam-3298	94	14	φ(d(z	φ(d(z	PROPN
ejpam-3298	94	15	,	,	PUNCT
ejpam-3298	94	16	z	z	NOUN
ejpam-3298	94	17	)	)	PUNCT
ejpam-3298	94	18	)	)	PUNCT
ejpam-3298	94	19	,	,	PUNCT
ejpam-3298	94	20	φ	φ	X
ejpam-3298	94	21	(	(	PUNCT
ejpam-3298	94	22	1	1	NUM
ejpam-3298	94	23	2	2	NUM
ejpam-3298	94	24	[	[	X
ejpam-3298	94	25	d(hz	d(hz	PROPN
ejpam-3298	94	26	,	,	PUNCT
ejpam-3298	94	27	z	z	NOUN
ejpam-3298	94	28	)	)	PUNCT
ejpam-3298	94	29	+	+	CCONJ
ejpam-3298	94	30	d(hz	d(hz	PROPN
ejpam-3298	94	31	,	,	PUNCT
ejpam-3298	94	32	z	z	NOUN
ejpam-3298	94	33	)	)	PUNCT
ejpam-3298	94	34	]	]	PUNCT
ejpam-3298	94	35	)	)	PUNCT
ejpam-3298	94	36	}	}	PUNCT
ejpam-3298	94	37	−	−	ADP
ejpam-3298	94	38	w((max{φ(d(hz	w((max{φ(d(hz	ADJ
ejpam-3298	94	39	,	,	PUNCT
ejpam-3298	94	40	z	z	NOUN
ejpam-3298	94	41	)	)	PUNCT
ejpam-3298	94	42	)	)	PUNCT
ejpam-3298	94	43	,	,	PUNCT
ejpam-3298	94	44	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	94	45	,	,	PUNCT
ejpam-3298	94	46	hz	hz	NOUN
ejpam-3298	94	47	)	)	PUNCT
ejpam-3298	94	48	)	)	PUNCT
ejpam-3298	94	49	,	,	PUNCT
ejpam-3298	94	50	φ(d(z	φ(d(z	PROPN
ejpam-3298	94	51	,	,	PUNCT
ejpam-3298	94	52	z	z	NOUN
ejpam-3298	94	53	)	)	PUNCT
ejpam-3298	94	54	)	)	PUNCT
ejpam-3298	94	55	,	,	PUNCT
ejpam-3298	94	56	φ	φ	X
ejpam-3298	94	57	(	(	PUNCT
ejpam-3298	94	58	1	1	NUM
ejpam-3298	94	59	2	2	NUM
ejpam-3298	94	60	[	[	X
ejpam-3298	94	61	d(hz	d(hz	PROPN
ejpam-3298	94	62	,	,	PUNCT
ejpam-3298	94	63	z	z	NOUN
ejpam-3298	94	64	)	)	PUNCT
ejpam-3298	94	65	+	+	CCONJ
ejpam-3298	94	66	d(hz	d(hz	PROPN
ejpam-3298	94	67	,	,	PUNCT
ejpam-3298	94	68	z	z	NOUN
ejpam-3298	94	69	)	)	PUNCT
ejpam-3298	94	70	]	]	PUNCT
ejpam-3298	94	71	)	)	PUNCT
ejpam-3298	94	72	}	}	PUNCT
ejpam-3298	94	73	)	)	PUNCT
ejpam-3298	94	74	)	)	PUNCT
ejpam-3298	94	75	implies	imply	VERB
ejpam-3298	94	76	that	that	SCONJ
ejpam-3298	94	77	ψ(d(hz	ψ(d(hz	SYM
ejpam-3298	94	78	,	,	PUNCT
ejpam-3298	94	79	z	z	NOUN
ejpam-3298	94	80	)	)	PUNCT
ejpam-3298	94	81	)	)	PUNCT
ejpam-3298	94	82	≤	≤	PROPN
ejpam-3298	94	83	φ(d(z	φ(d(z	PROPN
ejpam-3298	94	84	,	,	PUNCT
ejpam-3298	94	85	hz))−	hz))−	NOUN
ejpam-3298	94	86	w(φ(d(z	w(φ(d(z	PROPN
ejpam-3298	94	87	,	,	PUNCT
ejpam-3298	94	88	hz	hz	NOUN
ejpam-3298	94	89	)	)	PUNCT
ejpam-3298	94	90	)	)	PUNCT
ejpam-3298	95	1	<	<	X
ejpam-3298	95	2	φ(d(z	φ(d(z	PROPN
ejpam-3298	95	3	,	,	PUNCT
ejpam-3298	95	4	hz	hz	NOUN
ejpam-3298	95	5	)	)	PUNCT
ejpam-3298	95	6	)	)	PUNCT
ejpam-3298	96	1	a	a	DET
ejpam-3298	96	2	contradiction.hence	contradiction.hence	NOUN
ejpam-3298	96	3	hz	hz	VERB
ejpam-3298	96	4	=	=	SYM
ejpam-3298	96	5	z.using	z.use	VERB
ejpam-3298	96	6	(	(	PUNCT
ejpam-3298	96	7	8)	8)	NUM
ejpam-3298	96	8	and	and	CCONJ
ejpam-3298	96	9	(	(	PUNCT
ejpam-3298	96	10	9	9	NUM
ejpam-3298	96	11	)	)	PUNCT
ejpam-3298	96	12	together	together	ADV
ejpam-3298	96	13	with	with	ADP
ejpam-3298	96	14	tz	tz	PROPN
ejpam-3298	96	15	=	=	SYM
ejpam-3298	96	16	z	z	PROPN
ejpam-3298	96	17	,	,	PUNCT
ejpam-3298	96	18	we	we	PRON
ejpam-3298	96	19	infer	infer	VERB
ejpam-3298	96	20	that	that	DET
ejpam-3298	96	21	fz	fz	VERB
ejpam-3298	97	1	=	=	NOUN
ejpam-3298	97	2	gz	gz	NOUN
ejpam-3298	97	3	=	=	NOUN
ejpam-3298	97	4	hz	hz	PROPN
ejpam-3298	97	5	=	=	PUNCT
ejpam-3298	97	6	z.further	z.further	NOUN
ejpam-3298	97	7	uniqueness	uniqueness	NOUN
ejpam-3298	97	8	of	of	ADP
ejpam-3298	97	9	common	common	ADJ
ejpam-3298	97	10	fixed	fix	VERB
ejpam-3298	97	11	point	point	NOUN
ejpam-3298	97	12	can	can	AUX
ejpam-3298	97	13	easily	easily	ADV
ejpam-3298	97	14	prove	prove	VERB
ejpam-3298	97	15	.	.	PUNCT
ejpam-3298	98	1	taking	take	VERB
ejpam-3298	98	2	ψ(t	ψ(t	PROPN
ejpam-3298	98	3	)	)	PUNCT
ejpam-3298	98	4	=	=	SYM
ejpam-3298	98	5	t	t	PROPN
ejpam-3298	98	6	and	and	CCONJ
ejpam-3298	98	7	φ(t	φ(t	PROPN
ejpam-3298	98	8	)	)	PUNCT
ejpam-3298	99	1	=	=	SYM
ejpam-3298	100	1	ht	ht	INTJ
ejpam-3298	100	2	where	where	SCONJ
ejpam-3298	100	3	<	<	X
ejpam-3298	100	4	h	h	X
ejpam-3298	100	5	<	<	X
ejpam-3298	100	6	1	1	NUM
ejpam-3298	100	7	,	,	PUNCT
ejpam-3298	100	8	we	we	PRON
ejpam-3298	100	9	state	state	VERB
ejpam-3298	100	10	the	the	DET
ejpam-3298	100	11	following	follow	VERB
ejpam-3298	100	12	p.	p.	PROPN
ejpam-3298	100	13	semwal	semwal	NOUN
ejpam-3298	100	14	,	,	PUNCT
ejpam-3298	100	15	komal	komal	PROPN
ejpam-3298	100	16	/	/	SYM
ejpam-3298	100	17	eur	eur	PROPN
ejpam-3298	100	18	.	.	PUNCT
ejpam-3298	101	1	j.	j.	PROPN
ejpam-3298	101	2	pure	pure	PROPN
ejpam-3298	101	3	appl	appl	PROPN
ejpam-3298	101	4	.	.	PROPN
ejpam-3298	101	5	math	math	PROPN
ejpam-3298	101	6	,	,	PUNCT
ejpam-3298	101	7	11	11	NUM
ejpam-3298	101	8	(	(	PUNCT
ejpam-3298	101	9	4	4	NUM
ejpam-3298	101	10	)	)	PUNCT
ejpam-3298	101	11	(	(	PUNCT
ejpam-3298	101	12	2018	2018	NUM
ejpam-3298	101	13	)	)	PUNCT
ejpam-3298	101	14	,	,	PUNCT
ejpam-3298	101	15	1177	1177	NUM
ejpam-3298	101	16	-	-	SYM
ejpam-3298	101	17	1190	1190	NUM
ejpam-3298	101	18	1182	1182	NUM
ejpam-3298	101	19	corollary	corollary	NOUN
ejpam-3298	101	20	1	1	NUM
ejpam-3298	101	21	.	.	PUNCT
ejpam-3298	102	1	let	let	VERB
ejpam-3298	102	2	a	a	DET
ejpam-3298	102	3	,	,	PUNCT
ejpam-3298	102	4	b	b	NOUN
ejpam-3298	102	5	and	and	CCONJ
ejpam-3298	102	6	t	t	PROPN
ejpam-3298	102	7	be	be	AUX
ejpam-3298	102	8	self	self	NOUN
ejpam-3298	102	9	maps	map	NOUN
ejpam-3298	102	10	on	on	ADP
ejpam-3298	102	11	a	a	DET
ejpam-3298	102	12	metric	metric	ADJ
ejpam-3298	102	13	space	space	NOUN
ejpam-3298	102	14	(	(	PUNCT
ejpam-3298	102	15	x	x	X
ejpam-3298	102	16	,	,	PUNCT
ejpam-3298	102	17	d	d	NOUN
ejpam-3298	102	18	)	)	PUNCT
ejpam-3298	102	19	such	such	ADJ
ejpam-3298	102	20	that	that	SCONJ
ejpam-3298	102	21	t	t	NOUN
ejpam-3298	102	22	commutes	commute	NOUN
ejpam-3298	102	23	with	with	ADP
ejpam-3298	102	24	both	both	CCONJ
ejpam-3298	102	25	a	a	PRON
ejpam-3298	102	26	and	and	CCONJ
ejpam-3298	102	27	b	b	NOUN
ejpam-3298	102	28	and	and	CCONJ
ejpam-3298	102	29	the	the	DET
ejpam-3298	102	30	pair	pair	NOUN
ejpam-3298	102	31	(	(	PUNCT
ejpam-3298	102	32	a	a	DET
ejpam-3298	102	33	,	,	PUNCT
ejpam-3298	102	34	b	b	NOUN
ejpam-3298	102	35	)	)	PUNCT
ejpam-3298	102	36	is	be	AUX
ejpam-3298	102	37	asymptotically	asymptotically	ADV
ejpam-3298	102	38	regular	regular	ADJ
ejpam-3298	102	39	w.r.to	w.r.to	NOUN
ejpam-3298	102	40	t	t	NOUN
ejpam-3298	102	41	at	at	ADP
ejpam-3298	102	42	x0	x0	PROPN
ejpam-3298	102	43	∈	∈	PROPN
ejpam-3298	103	1	x	x	X
ejpam-3298	103	2	,	,	PUNCT
ejpam-3298	103	3	x	x	PUNCT
ejpam-3298	103	4	is	be	AUX
ejpam-3298	103	5	orbitally	orbitally	ADV
ejpam-3298	103	6	complete	complete	ADJ
ejpam-3298	103	7	and	and	CCONJ
ejpam-3298	103	8	t	t	PROPN
ejpam-3298	103	9	is	be	AUX
ejpam-3298	103	10	orbitally	orbitally	ADV
ejpam-3298	103	11	continuous	continuous	ADJ
ejpam-3298	103	12	at	at	ADP
ejpam-3298	103	13	x0	x0	PROPN
ejpam-3298	103	14	and	and	CCONJ
ejpam-3298	103	15	d(ax	d(ax	PROPN
ejpam-3298	103	16	,	,	PUNCT
ejpam-3298	103	17	by	by	ADP
ejpam-3298	103	18	)	)	PUNCT
ejpam-3298	103	19	≤	≤	PROPN
ejpam-3298	103	20	φ{max{d(tx	φ{max{d(tx	PROPN
ejpam-3298	103	21	,	,	PUNCT
ejpam-3298	103	22	ty	ty	NOUN
ejpam-3298	103	23	)	)	PUNCT
ejpam-3298	103	24	,	,	PUNCT
ejpam-3298	103	25	d(ax	d(ax	PROPN
ejpam-3298	103	26	,	,	PUNCT
ejpam-3298	103	27	tx	tx	PROPN
ejpam-3298	103	28	)	)	PUNCT
ejpam-3298	103	29	)	)	PUNCT
ejpam-3298	103	30	,	,	PUNCT
ejpam-3298	103	31	d(by	d(by	PROPN
ejpam-3298	103	32	,	,	PUNCT
ejpam-3298	103	33	ty	ty	NOUN
ejpam-3298	103	34	)	)	PUNCT
ejpam-3298	103	35	,	,	PUNCT
ejpam-3298	103	36	1	1	NUM
ejpam-3298	103	37	2	2	NUM
ejpam-3298	103	38	[	[	X
ejpam-3298	103	39	d(tx	d(tx	ADJ
ejpam-3298	103	40	,	,	PUNCT
ejpam-3298	103	41	ty	ty	NOUN
ejpam-3298	103	42	)	)	PUNCT
ejpam-3298	103	43	+	+	CCONJ
ejpam-3298	103	44	d(ax	d(ax	PROPN
ejpam-3298	103	45	,	,	PUNCT
ejpam-3298	103	46	by	by	ADP
ejpam-3298	103	47	)	)	PUNCT
ejpam-3298	103	48	]	]	PUNCT
ejpam-3298	103	49	)	)	PUNCT
ejpam-3298	103	50	}	}	PUNCT
ejpam-3298	104	1	−	−	ADP
ejpam-3298	104	2	w((max{d(tx	w((max{d(tx	PROPN
ejpam-3298	104	3	,	,	PUNCT
ejpam-3298	104	4	ty	ty	NOUN
ejpam-3298	104	5	)	)	PUNCT
ejpam-3298	104	6	,	,	PUNCT
ejpam-3298	104	7	d(ax	d(ax	PROPN
ejpam-3298	104	8	,	,	PUNCT
ejpam-3298	104	9	tx	tx	PROPN
ejpam-3298	104	10	)	)	PUNCT
ejpam-3298	104	11	)	)	PUNCT
ejpam-3298	104	12	,	,	PUNCT
ejpam-3298	104	13	d(by	d(by	PROPN
ejpam-3298	104	14	,	,	PUNCT
ejpam-3298	104	15	ty	ty	NOUN
ejpam-3298	104	16	)	)	PUNCT
ejpam-3298	104	17	,	,	PUNCT
ejpam-3298	104	18	1	1	NUM
ejpam-3298	104	19	2	2	NUM
ejpam-3298	104	20	[	[	X
ejpam-3298	104	21	d(tx	d(tx	ADJ
ejpam-3298	104	22	,	,	PUNCT
ejpam-3298	104	23	ty	ty	NOUN
ejpam-3298	104	24	)	)	PUNCT
ejpam-3298	104	25	+	+	CCONJ
ejpam-3298	104	26	d(ax	d(ax	PROPN
ejpam-3298	104	27	,	,	PUNCT
ejpam-3298	104	28	by	by	ADP
ejpam-3298	104	29	)	)	PUNCT
ejpam-3298	104	30	]	]	PUNCT
ejpam-3298	104	31	)	)	PUNCT
ejpam-3298	104	32	}	}	PUNCT
ejpam-3298	104	33	)	)	PUNCT
ejpam-3298	104	34	)	)	PUNCT
ejpam-3298	104	35	for	for	ADP
ejpam-3298	104	36	all	all	DET
ejpam-3298	104	37	x	x	NOUN
ejpam-3298	104	38	,	,	PUNCT
ejpam-3298	104	39	y	y	PROPN
ejpam-3298	104	40	∈	∈	PROPN
ejpam-3298	104	41	x.	x.	NOUN
ejpam-3298	104	42	then	then	ADV
ejpam-3298	104	43	a	a	DET
ejpam-3298	104	44	,	,	PUNCT
ejpam-3298	104	45	b	b	PROPN
ejpam-3298	104	46	and	and	CCONJ
ejpam-3298	104	47	t	t	PROPN
ejpam-3298	104	48	have	have	AUX
ejpam-3298	104	49	unique	unique	ADJ
ejpam-3298	104	50	common	common	ADJ
ejpam-3298	104	51	fixed	fix	VERB
ejpam-3298	104	52	point	point	NOUN
ejpam-3298	104	53	in	in	ADP
ejpam-3298	104	54	x.	x.	PROPN
ejpam-3298	104	55	theorem	theorem	VERB
ejpam-3298	104	56	2	2	X
ejpam-3298	104	57	.	.	PUNCT
ejpam-3298	105	1	let	let	VERB
ejpam-3298	105	2	(	(	PUNCT
ejpam-3298	105	3	x	x	NOUN
ejpam-3298	105	4	,	,	PUNCT
ejpam-3298	105	5	d	d	NOUN
ejpam-3298	105	6	)	)	PUNCT
ejpam-3298	105	7	be	be	AUX
ejpam-3298	105	8	a	a	DET
ejpam-3298	105	9	metric	metric	ADJ
ejpam-3298	105	10	space	space	NOUN
ejpam-3298	105	11	and	and	CCONJ
ejpam-3298	105	12	f	f	PROPN
ejpam-3298	105	13	,	,	PUNCT
ejpam-3298	105	14	g	g	PROPN
ejpam-3298	105	15	and	and	CCONJ
ejpam-3298	105	16	h	h	PROPN
ejpam-3298	105	17	be	be	VERB
ejpam-3298	105	18	self	self	NOUN
ejpam-3298	105	19	mappings	mapping	NOUN
ejpam-3298	105	20	on	on	ADP
ejpam-3298	105	21	x	x	SYM
ejpam-3298	105	22	such	such	ADJ
ejpam-3298	105	23	that	that	SCONJ
ejpam-3298	105	24	f(x)∪	f(x)∪	PROPN
ejpam-3298	105	25	g(x	g(x	PROPN
ejpam-3298	105	26	)	)	PUNCT
ejpam-3298	106	1	⊆	⊆	NUM
ejpam-3298	106	2	h(x).if	h(x).if	NOUN
ejpam-3298	106	3	there	there	ADV
ejpam-3298	106	4	exists	exist	VERB
ejpam-3298	106	5	a	a	DET
ejpam-3298	106	6	w	w	NOUN
ejpam-3298	106	7	∈w	∈w	NOUN
ejpam-3298	106	8	satisfying	satisfy	VERB
ejpam-3298	106	9	(	(	PUNCT
ejpam-3298	106	10	5).then	5).then	NUM
ejpam-3298	106	11	the	the	DET
ejpam-3298	106	12	pair	pair	NOUN
ejpam-3298	106	13	(	(	PUNCT
ejpam-3298	106	14	f	f	X
ejpam-3298	106	15	,	,	PUNCT
ejpam-3298	106	16	h	h	NOUN
ejpam-3298	106	17	)	)	PUNCT
ejpam-3298	106	18	and	and	CCONJ
ejpam-3298	106	19	(	(	PUNCT
ejpam-3298	106	20	g	g	NOUN
ejpam-3298	106	21	,	,	PUNCT
ejpam-3298	106	22	h	h	NOUN
ejpam-3298	106	23	)	)	PUNCT
ejpam-3298	106	24	have	have	VERB
ejpam-3298	106	25	a	a	DET
ejpam-3298	106	26	coincidence	coincidence	NOUN
ejpam-3298	106	27	point	point	NOUN
ejpam-3298	106	28	in	in	ADP
ejpam-3298	106	29	x	x	PRON
ejpam-3298	106	30	,	,	PUNCT
ejpam-3298	106	31	provided	provide	VERB
ejpam-3298	106	32	that	that	SCONJ
ejpam-3298	106	33	(	(	PUNCT
ejpam-3298	106	34	i	i	NOUN
ejpam-3298	106	35	)	)	PUNCT
ejpam-3298	106	36	x	x	X
ejpam-3298	106	37	is	be	AUX
ejpam-3298	106	38	h	h	NOUN
ejpam-3298	106	39	-	-	PUNCT
ejpam-3298	106	40	asymptotically	asymptotically	ADV
ejpam-3298	106	41	complete	complete	ADJ
ejpam-3298	106	42	,	,	PUNCT
ejpam-3298	106	43	(	(	PUNCT
ejpam-3298	106	44	ii	ii	NOUN
ejpam-3298	106	45	)	)	PUNCT
ejpam-3298	106	46	h	h	NOUN
ejpam-3298	106	47	is	be	AUX
ejpam-3298	106	48	asymptotically	asymptotically	ADV
ejpam-3298	106	49	continuous	continuous	ADJ
ejpam-3298	106	50	and	and	CCONJ
ejpam-3298	106	51	(	(	PUNCT
ejpam-3298	106	52	iii	iii	NOUN
ejpam-3298	106	53	)	)	PUNCT
ejpam-3298	106	54	h	h	NOUN
ejpam-3298	106	55	is	be	AUX
ejpam-3298	106	56	weakly	weakly	ADJ
ejpam-3298	106	57	commute	commute	NOUN
ejpam-3298	106	58	with	with	ADP
ejpam-3298	106	59	f	f	PROPN
ejpam-3298	106	60	and	and	CCONJ
ejpam-3298	106	61	g.further	g.further	ADJ
ejpam-3298	106	62	f	f	PROPN
ejpam-3298	106	63	,	,	PUNCT
ejpam-3298	106	64	g	g	PROPN
ejpam-3298	106	65	and	and	CCONJ
ejpam-3298	106	66	h	h	NOUN
ejpam-3298	106	67	have	have	VERB
ejpam-3298	106	68	a	a	DET
ejpam-3298	106	69	unique	unique	ADJ
ejpam-3298	106	70	common	common	ADJ
ejpam-3298	106	71	fixed	fix	VERB
ejpam-3298	106	72	point	point	NOUN
ejpam-3298	106	73	in	in	ADP
ejpam-3298	106	74	x.	x.	NOUN
ejpam-3298	106	75	proof	proof	NOUN
ejpam-3298	106	76	let	let	VERB
ejpam-3298	106	77	x0	x0	PROPN
ejpam-3298	106	78	∈	∈	PROPN
ejpam-3298	106	79	x	x	PRON
ejpam-3298	106	80	be	be	AUX
ejpam-3298	106	81	any	any	DET
ejpam-3298	106	82	point	point	NOUN
ejpam-3298	106	83	in	in	ADP
ejpam-3298	106	84	x.	x.	NOUN
ejpam-3298	106	85	since	since	SCONJ
ejpam-3298	106	86	f(x)∪g(x	f(x)∪g(x	NUM
ejpam-3298	106	87	)	)	PUNCT
ejpam-3298	106	88	⊆	⊆	NUM
ejpam-3298	106	89	h(x).we	h(x).we	NOUN
ejpam-3298	106	90	choose	choose	VERB
ejpam-3298	106	91	sequence	sequence	NOUN
ejpam-3298	106	92	{	{	PUNCT
ejpam-3298	106	93	xn	xn	NOUN
ejpam-3298	106	94	}	}	PUNCT
ejpam-3298	106	95	∈	∈	PROPN
ejpam-3298	106	96	x	x	PUNCT
ejpam-3298	107	1	such	such	ADJ
ejpam-3298	107	2	that	that	DET
ejpam-3298	107	3	fx2n	fx2n	PROPN
ejpam-3298	107	4	=	=	SYM
ejpam-3298	107	5	hx2n+1	hx2n+1	PROPN
ejpam-3298	107	6	and	and	CCONJ
ejpam-3298	107	7	gx2n+1	gx2n+1	PROPN
ejpam-3298	107	8	=	=	SYM
ejpam-3298	107	9	hx2n+2	hx2n+2	PROPN
ejpam-3298	107	10	for	for	ADP
ejpam-3298	107	11	all	all	DET
ejpam-3298	107	12	n	n	PRON
ejpam-3298	107	13	∈	∈	PROPN
ejpam-3298	107	14	w.	w.	NOUN
ejpam-3298	107	15	by	by	ADP
ejpam-3298	107	16	(	(	PUNCT
ejpam-3298	107	17	5	5	NUM
ejpam-3298	107	18	)	)	PUNCT
ejpam-3298	107	19	,	,	PUNCT
ejpam-3298	107	20	we	we	PRON
ejpam-3298	107	21	conclude	conclude	VERB
ejpam-3298	107	22	that	that	PRON
ejpam-3298	107	23	ψ(d(hx2n+1	ψ(d(hx2n+1	NOUN
ejpam-3298	107	24	,	,	PUNCT
ejpam-3298	107	25	hx2n+2	hx2n+2	PROPN
ejpam-3298	107	26	)	)	PUNCT
ejpam-3298	107	27	)	)	PUNCT
ejpam-3298	108	1	=	=	PUNCT
ejpam-3298	108	2	ψ(d(fx2n	ψ(d(fx2n	PROPN
ejpam-3298	108	3	,	,	PUNCT
ejpam-3298	108	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	108	5	)	)	PUNCT
ejpam-3298	108	6	)	)	PUNCT
ejpam-3298	108	7	≤	≤	PROPN
ejpam-3298	109	1	max{φ(d(h2n	max{φ(d(h2n	PROPN
ejpam-3298	109	2	,	,	PUNCT
ejpam-3298	109	3	hx2n+1	hx2n+1	PROPN
ejpam-3298	109	4	)	)	PUNCT
ejpam-3298	109	5	)	)	PUNCT
ejpam-3298	109	6	,	,	PUNCT
ejpam-3298	109	7	φ(d(hx2n	φ(d(hx2n	ADP
ejpam-3298	109	8	,	,	PUNCT
ejpam-3298	109	9	fx2n	fx2n	PROPN
ejpam-3298	109	10	)	)	PUNCT
ejpam-3298	109	11	)	)	PUNCT
ejpam-3298	109	12	,	,	PUNCT
ejpam-3298	109	13	φ(d(hx2n+1	φ(d(hx2n+1	ADJ
ejpam-3298	109	14	,	,	PUNCT
ejpam-3298	109	15	gx2n+1	gx2n+1	PROPN
ejpam-3298	109	16	)	)	PUNCT
ejpam-3298	109	17	)	)	PUNCT
ejpam-3298	109	18	,	,	PUNCT
ejpam-3298	109	19	φ	φ	X
ejpam-3298	109	20	(	(	PUNCT
ejpam-3298	109	21	1	1	NUM
ejpam-3298	109	22	2	2	NUM
ejpam-3298	109	23	(	(	PUNCT
ejpam-3298	109	24	[	[	X
ejpam-3298	109	25	d(hx2n	d(hx2n	X
ejpam-3298	109	26	,	,	PUNCT
ejpam-3298	109	27	hx2n+1	hx2n+1	PROPN
ejpam-3298	109	28	)	)	PUNCT
ejpam-3298	110	1	+	+	NUM
ejpam-3298	110	2	d(fx2n	d(fx2n	PROPN
ejpam-3298	110	3	,	,	PUNCT
ejpam-3298	110	4	gx2n+1	gx2n+1	PROPN
ejpam-3298	110	5	)	)	PUNCT
ejpam-3298	110	6	]	]	PUNCT
ejpam-3298	110	7	)	)	PUNCT
ejpam-3298	110	8	)	)	PUNCT
ejpam-3298	110	9	}	}	PUNCT
ejpam-3298	111	1	−	−	PROPN
ejpam-3298	111	2	w(max{φ(d(h2n	w(max{φ(d(h2n	PROPN
ejpam-3298	111	3	,	,	PUNCT
ejpam-3298	111	4	hx2n+1	hx2n+1	PROPN
ejpam-3298	111	5	)	)	PUNCT
ejpam-3298	111	6	)	)	PUNCT
ejpam-3298	111	7	,	,	PUNCT
ejpam-3298	111	8	φ(d(hx2n	φ(d(hx2n	ADP
ejpam-3298	111	9	,	,	PUNCT
ejpam-3298	111	10	fx2n	fx2n	PROPN
ejpam-3298	111	11	)	)	PUNCT
ejpam-3298	111	12	)	)	PUNCT
ejpam-3298	111	13	,	,	PUNCT
ejpam-3298	111	14	φ(d(hx2n+1	φ(d(hx2n+1	ADJ
ejpam-3298	111	15	,	,	PUNCT
ejpam-3298	111	16	gx2n+1	gx2n+1	PROPN
ejpam-3298	111	17	)	)	PUNCT
ejpam-3298	111	18	)	)	PUNCT
ejpam-3298	111	19	,	,	PUNCT
ejpam-3298	111	20	φ	φ	X
ejpam-3298	111	21	(	(	PUNCT
ejpam-3298	111	22	1	1	NUM
ejpam-3298	111	23	2	2	NUM
ejpam-3298	111	24	(	(	PUNCT
ejpam-3298	111	25	[	[	X
ejpam-3298	111	26	d(hx2n	d(hx2n	X
ejpam-3298	111	27	,	,	PUNCT
ejpam-3298	111	28	hx2n+1	hx2n+1	PROPN
ejpam-3298	111	29	)	)	PUNCT
ejpam-3298	111	30	+	+	NUM
ejpam-3298	111	31	d(fx2n	d(fx2n	PROPN
ejpam-3298	111	32	,	,	PUNCT
ejpam-3298	111	33	gx2n+1	gx2n+1	PROPN
ejpam-3298	111	34	)	)	PUNCT
ejpam-3298	111	35	]	]	PUNCT
ejpam-3298	111	36	)	)	PUNCT
ejpam-3298	111	37	)	)	PUNCT
ejpam-3298	111	38	}	}	PUNCT
ejpam-3298	111	39	)	)	PUNCT
ejpam-3298	112	1	this	this	DET
ejpam-3298	112	2	yields	yield	NOUN
ejpam-3298	112	3	ψ(d2n+1	ψ(d2n+1	PROPN
ejpam-3298	112	4	)	)	PUNCT
ejpam-3298	112	5	≤	≤	NUM
ejpam-3298	112	6	max{φ(d2n	max{φ(d2n	NOUN
ejpam-3298	112	7	)	)	PUNCT
ejpam-3298	112	8	,	,	PUNCT
ejpam-3298	112	9	φ(d2n	φ(d2n	PROPN
ejpam-3298	112	10	)	)	PUNCT
ejpam-3298	112	11	,	,	PUNCT
ejpam-3298	112	12	φ(d2n+1	φ(d2n+1	NUM
ejpam-3298	112	13	)	)	PUNCT
ejpam-3298	112	14	,	,	PUNCT
ejpam-3298	112	15	φ	φ	X
ejpam-3298	112	16	(	(	PUNCT
ejpam-3298	112	17	1	1	NUM
ejpam-3298	112	18	2	2	NUM
ejpam-3298	112	19	(	(	PUNCT
ejpam-3298	112	20	d2n	d2n	PROPN
ejpam-3298	112	21	+	+	CCONJ
ejpam-3298	112	22	d2n+1	d2n+1	PROPN
ejpam-3298	112	23	)	)	PUNCT
ejpam-3298	112	24	)	)	PUNCT
ejpam-3298	112	25	}	}	PUNCT
ejpam-3298	112	26	−w(max{φ(d2n	−w(max{φ(d2n	NOUN
ejpam-3298	112	27	)	)	PUNCT
ejpam-3298	112	28	,	,	PUNCT
ejpam-3298	112	29	φ(d2n	φ(d2n	PROPN
ejpam-3298	112	30	)	)	PUNCT
ejpam-3298	112	31	,	,	PUNCT
ejpam-3298	112	32	φ(d2n+1	φ(d2n+1	NUM
ejpam-3298	112	33	)	)	PUNCT
ejpam-3298	112	34	,	,	PUNCT
ejpam-3298	112	35	φ	φ	X
ejpam-3298	112	36	(	(	PUNCT
ejpam-3298	112	37	1	1	NUM
ejpam-3298	112	38	2	2	NUM
ejpam-3298	112	39	(	(	PUNCT
ejpam-3298	112	40	d2n	d2n	PROPN
ejpam-3298	112	41	+	+	CCONJ
ejpam-3298	112	42	d2n+1	d2n+1	PROPN
ejpam-3298	112	43	)	)	PUNCT
ejpam-3298	112	44	)	)	PUNCT
ejpam-3298	112	45	}	}	PUNCT
ejpam-3298	112	46	)	)	PUNCT
ejpam-3298	112	47	.	.	PUNCT
ejpam-3298	113	1	suppose	suppose	VERB
ejpam-3298	113	2	d2n+1	d2n+1	VERB
ejpam-3298	113	3	>	>	X
ejpam-3298	113	4	d2n	d2n	PROPN
ejpam-3298	113	5	,	,	PUNCT
ejpam-3298	113	6	then	then	ADV
ejpam-3298	113	7	φ(d2n+1	φ(d2n+1	NUM
ejpam-3298	113	8	)	)	PUNCT
ejpam-3298	113	9	>	>	X
ejpam-3298	114	1	φ(d2n).using	φ(d2n).use	VERB
ejpam-3298	114	2	(	(	PUNCT
ejpam-3298	114	3	5	5	NUM
ejpam-3298	114	4	)	)	PUNCT
ejpam-3298	114	5	,	,	PUNCT
ejpam-3298	114	6	we	we	PRON
ejpam-3298	114	7	have	have	VERB
ejpam-3298	114	8	ψ(d2n+1	ψ(d2n+1	NOUN
ejpam-3298	114	9	)	)	PUNCT
ejpam-3298	114	10	≤	≤	NUM
ejpam-3298	114	11	φ(d2n+1)−	φ(d2n+1)−	PROPN
ejpam-3298	114	12	w(φ(d2n+1	w(φ(d2n+1	PROPN
ejpam-3298	114	13	)	)	PUNCT
ejpam-3298	114	14	)	)	PUNCT
ejpam-3298	115	1	<	<	X
ejpam-3298	115	2	φ(d2n+1	φ(d2n+1	X
ejpam-3298	115	3	)	)	PUNCT
ejpam-3298	115	4	a	a	PRON
ejpam-3298	115	5	contradiction.consequently	contradiction.consequently	ADV
ejpam-3298	115	6	,	,	PUNCT
ejpam-3298	115	7	we	we	PRON
ejpam-3298	115	8	have	have	AUX
ejpam-3298	115	9	d2n+1	d2n+1	VERB
ejpam-3298	115	10	≤	≤	NUM
ejpam-3298	115	11	d2n	d2n	NOUN
ejpam-3298	115	12	,	,	PUNCT
ejpam-3298	115	13	from	from	ADP
ejpam-3298	115	14	(	(	PUNCT
ejpam-3298	115	15	5	5	X
ejpam-3298	115	16	)	)	PUNCT
ejpam-3298	115	17	we	we	PRON
ejpam-3298	115	18	have	have	AUX
ejpam-3298	115	19	ψ(d2n+1	ψ(d2n+1	NOUN
ejpam-3298	115	20	)	)	PUNCT
ejpam-3298	115	21	≤	≤	NUM
ejpam-3298	115	22	φ(d2n)−	φ(d2n)−	PROPN
ejpam-3298	115	23	w(φ(d2n	w(φ(d2n	PROPN
ejpam-3298	115	24	)	)	PUNCT
ejpam-3298	115	25	)	)	PUNCT
ejpam-3298	116	1	<	<	X
ejpam-3298	116	2	φ(d2n	φ(d2n	PROPN
ejpam-3298	116	3	)	)	PUNCT
ejpam-3298	116	4	for	for	ADP
ejpam-3298	116	5	any	any	DET
ejpam-3298	116	6	n	n	PRON
ejpam-3298	116	7	∈	∈	PROPN
ejpam-3298	116	8	w.	w.	NOUN
ejpam-3298	116	9	similarly	similarly	ADV
ejpam-3298	116	10	,	,	PUNCT
ejpam-3298	116	11	we	we	PRON
ejpam-3298	116	12	have	have	VERB
ejpam-3298	116	13	ψ(d2n	ψ(d2n	NOUN
ejpam-3298	116	14	)	)	PUNCT
ejpam-3298	116	15	≤	≤	NOUN
ejpam-3298	116	16	φ(d2n−1	φ(d2n−1	PROPN
ejpam-3298	116	17	)	)	PUNCT
ejpam-3298	116	18	−	−	PROPN
ejpam-3298	116	19	w(φ(d2n−1	w(φ(d2n−1	PROPN
ejpam-3298	116	20	)	)	PUNCT
ejpam-3298	116	21	)	)	PUNCT
ejpam-3298	117	1	<	<	X
ejpam-3298	117	2	φ(d2n−1	φ(d2n−1	PROPN
ejpam-3298	117	3	)	)	PUNCT
ejpam-3298	117	4	for	for	ADP
ejpam-3298	117	5	all	all	DET
ejpam-3298	117	6	n	n	PRON
ejpam-3298	117	7	∈	∈	PROPN
ejpam-3298	117	8	n	n	DET
ejpam-3298	117	9	.it	.it	PUNCT
ejpam-3298	117	10	follows	follow	VERB
ejpam-3298	117	11	that	that	SCONJ
ejpam-3298	117	12	ψ(dn	ψ(dn	NOUN
ejpam-3298	117	13	)	)	PUNCT
ejpam-3298	117	14	≤	≤	NOUN
ejpam-3298	117	15	φ(dn−1)−	φ(dn−1)−	PROPN
ejpam-3298	117	16	w(φ(dn−1	w(φ(dn−1	NOUN
ejpam-3298	117	17	)	)	PUNCT
ejpam-3298	117	18	)	)	PUNCT
ejpam-3298	118	1	∀n	∀n	NUM
ejpam-3298	118	2	∈	∈	PROPN
ejpam-3298	118	3	n	n	CCONJ
ejpam-3298	118	4	(	(	PUNCT
ejpam-3298	118	5	10	10	NUM
ejpam-3298	118	6	)	)	PUNCT
ejpam-3298	118	7	p.	p.	NOUN
ejpam-3298	118	8	semwal	semwal	NOUN
ejpam-3298	118	9	,	,	PUNCT
ejpam-3298	118	10	komal	komal	PROPN
ejpam-3298	118	11	/	/	SYM
ejpam-3298	118	12	eur	eur	PROPN
ejpam-3298	118	13	.	.	PUNCT
ejpam-3298	119	1	j.	j.	PROPN
ejpam-3298	119	2	pure	pure	PROPN
ejpam-3298	119	3	appl	appl	PROPN
ejpam-3298	119	4	.	.	PROPN
ejpam-3298	119	5	math	math	PROPN
ejpam-3298	119	6	,	,	PUNCT
ejpam-3298	119	7	11	11	NUM
ejpam-3298	119	8	(	(	PUNCT
ejpam-3298	119	9	4	4	NUM
ejpam-3298	119	10	)	)	PUNCT
ejpam-3298	119	11	(	(	PUNCT
ejpam-3298	119	12	2018	2018	NUM
ejpam-3298	119	13	)	)	PUNCT
ejpam-3298	119	14	,	,	PUNCT
ejpam-3298	119	15	1177	1177	NUM
ejpam-3298	119	16	-	-	SYM
ejpam-3298	119	17	1190	1190	NUM
ejpam-3298	119	18	1183	1183	NUM
ejpam-3298	119	19	from	from	ADP
ejpam-3298	119	20	(	(	PUNCT
ejpam-3298	119	21	10	10	NUM
ejpam-3298	119	22	)	)	PUNCT
ejpam-3298	120	1	,	,	PUNCT
ejpam-3298	120	2	we	we	PRON
ejpam-3298	120	3	have	have	VERB
ejpam-3298	120	4	n∑	n∑	NOUN
ejpam-3298	120	5	i=0	i=0	ADJ
ejpam-3298	120	6	w(φ(di	w(φ(di	NOUN
ejpam-3298	120	7	)	)	PUNCT
ejpam-3298	120	8	)	)	PUNCT
ejpam-3298	120	9	≤	≤	NUM
ejpam-3298	120	10	φ(d0)−	φ(d0)−	PROPN
ejpam-3298	120	11	ψ(dn	ψ(dn	PROPN
ejpam-3298	120	12	)	)	PUNCT
ejpam-3298	120	13	<	<	X
ejpam-3298	120	14	φ(d0	φ(d0	PROPN
ejpam-3298	120	15	)	)	PUNCT
ejpam-3298	121	1	∀n	∀n	NUM
ejpam-3298	121	2	∈	∈	PROPN
ejpam-3298	121	3	n	n	CCONJ
ejpam-3298	121	4	thus	thus	ADV
ejpam-3298	121	5	the	the	DET
ejpam-3298	121	6	sequence	sequence	NOUN
ejpam-3298	121	7	{	{	PUNCT
ejpam-3298	121	8	dn	dn	VERB
ejpam-3298	121	9	}	}	PUNCT
ejpam-3298	121	10	is	be	AUX
ejpam-3298	121	11	decreasing	decrease	VERB
ejpam-3298	121	12	sequence	sequence	NOUN
ejpam-3298	121	13	whereas	whereas	SCONJ
ejpam-3298	121	14	the	the	DET
ejpam-3298	121	15	series	series	PROPN
ejpam-3298	121	16	∑∞	∑∞	PROPN
ejpam-3298	121	17	n=0w(φ(dn	n=0w(φ(dn	PROPN
ejpam-3298	121	18	)	)	PUNCT
ejpam-3298	121	19	)	)	PUNCT
ejpam-3298	121	20	and	and	CCONJ
ejpam-3298	121	21	{	{	PUNCT
ejpam-3298	121	22	φ(dn	φ(dn	NOUN
ejpam-3298	121	23	)	)	PUNCT
ejpam-3298	121	24	}	}	PUNCT
ejpam-3298	121	25	are	be	AUX
ejpam-3298	121	26	convergent.it	convergent.it	NOUN
ejpam-3298	121	27	is	be	AUX
ejpam-3298	121	28	clear	clear	ADJ
ejpam-3298	121	29	that	that	SCONJ
ejpam-3298	121	30	limn→∞w(φ(dn	limn→∞w(φ(dn	NOUN
ejpam-3298	121	31	)	)	PUNCT
ejpam-3298	121	32	)	)	PUNCT
ejpam-3298	122	1	=	=	PUNCT
ejpam-3298	122	2	0	0	X
ejpam-3298	122	3	.	.	PUNCT
ejpam-3298	123	1	since	since	SCONJ
ejpam-3298	123	2	sequence	sequence	NOUN
ejpam-3298	123	3	{	{	PUNCT
ejpam-3298	123	4	dn	dn	VERB
ejpam-3298	123	5	}	}	PUNCT
ejpam-3298	123	6	is	be	AUX
ejpam-3298	123	7	decreasing	decrease	VERB
ejpam-3298	123	8	so	so	ADV
ejpam-3298	123	9	there	there	PRON
ejpam-3298	123	10	exists	exist	VERB
ejpam-3298	123	11	p	p	PROPN
ejpam-3298	123	12	∈	∈	PROPN
ejpam-3298	123	13	r+	r+	NOUN
ejpam-3298	123	14	such	such	ADJ
ejpam-3298	123	15	that	that	SCONJ
ejpam-3298	123	16	limn→∞dn	limn→∞dn	PRON
ejpam-3298	123	17	=	=	PUNCT
ejpam-3298	124	1	p.	p.	NOUN
ejpam-3298	124	2	by	by	ADP
ejpam-3298	124	3	continuity	continuity	NOUN
ejpam-3298	124	4	of	of	ADP
ejpam-3298	124	5	φ	φ	PROPN
ejpam-3298	124	6	and	and	CCONJ
ejpam-3298	124	7	w	w	NOUN
ejpam-3298	124	8	we	we	PRON
ejpam-3298	124	9	have	have	VERB
ejpam-3298	124	10	limn→∞w(φ(dn	limn→∞w(φ(dn	NOUN
ejpam-3298	124	11	)	)	PUNCT
ejpam-3298	124	12	)	)	PUNCT
ejpam-3298	125	1	=	=	PUNCT
ejpam-3298	125	2	w(φ(p	w(φ(p	ADV
ejpam-3298	125	3	)	)	PUNCT
ejpam-3298	125	4	)	)	PUNCT
ejpam-3298	126	1	=	=	PUNCT
ejpam-3298	127	1	0.thus	0.thus	NUM
ejpam-3298	128	1	p	p	X
ejpam-3298	128	2	=	=	NOUN
ejpam-3298	128	3	0	0	X
ejpam-3298	128	4	.	.	PUNCT
ejpam-3298	128	5	therefore	therefore	ADV
ejpam-3298	128	6	limn→∞d(hxn	limn→∞d(hxn	PROPN
ejpam-3298	128	7	,	,	PUNCT
ejpam-3298	128	8	hxn+1	hxn+1	NOUN
ejpam-3298	128	9	)	)	PUNCT
ejpam-3298	128	10	=	=	SYM
ejpam-3298	128	11	0	0	NUM
ejpam-3298	128	12	implies	imply	VERB
ejpam-3298	128	13	that	that	SCONJ
ejpam-3298	128	14	limn→∞d(hx2n	limn→∞d(hx2n	PROPN
ejpam-3298	128	15	,	,	PUNCT
ejpam-3298	128	16	hx2n+1	hx2n+1	PROPN
ejpam-3298	128	17	)	)	PUNCT
ejpam-3298	128	18	=	=	SYM
ejpam-3298	128	19	0	0	NUM
ejpam-3298	128	20	means	mean	VERB
ejpam-3298	128	21	that	that	SCONJ
ejpam-3298	128	22	limn→∞d(hx2n	limn→∞d(hx2n	NOUN
ejpam-3298	128	23	,	,	PUNCT
ejpam-3298	128	24	fx2n	fx2n	PROPN
ejpam-3298	128	25	)	)	PUNCT
ejpam-3298	128	26	=	=	SYM
ejpam-3298	128	27	0	0	NUM
ejpam-3298	128	28	and	and	CCONJ
ejpam-3298	128	29	limn→∞d(hx2n+1	limn→∞d(hx2n+1	PROPN
ejpam-3298	128	30	,	,	PUNCT
ejpam-3298	128	31	gx2n+1	gx2n+1	PROPN
ejpam-3298	128	32	)	)	PUNCT
ejpam-3298	129	1	=	=	SYM
ejpam-3298	129	2	0	0	X
ejpam-3298	129	3	.	.	PUNCT
ejpam-3298	130	1	i.e.	i.e.	X
ejpam-3298	130	2	the	the	DET
ejpam-3298	130	3	sequence	sequence	NOUN
ejpam-3298	130	4	{	{	PUNCT
ejpam-3298	130	5	xn	xn	NOUN
ejpam-3298	130	6	}	}	PUNCT
ejpam-3298	130	7	is	be	AUX
ejpam-3298	130	8	asymptotically	asymptotically	ADV
ejpam-3298	130	9	h	h	NOUN
ejpam-3298	130	10	-	-	ADJ
ejpam-3298	130	11	regular	regular	ADJ
ejpam-3298	130	12	with	with	ADP
ejpam-3298	130	13	respect	respect	NOUN
ejpam-3298	130	14	to	to	ADP
ejpam-3298	130	15	f	f	PROPN
ejpam-3298	130	16	and	and	CCONJ
ejpam-3298	130	17	g.	g.	PROPN
ejpam-3298	130	18	next	next	ADV
ejpam-3298	130	19	we	we	PRON
ejpam-3298	130	20	show	show	VERB
ejpam-3298	130	21	that	that	SCONJ
ejpam-3298	130	22	{	{	PUNCT
ejpam-3298	130	23	hxn	hxn	NOUN
ejpam-3298	130	24	}	}	PUNCT
ejpam-3298	130	25	is	be	AUX
ejpam-3298	130	26	cauchy	cauchy	ADJ
ejpam-3298	130	27	sequence	sequence	NOUN
ejpam-3298	130	28	in	in	ADP
ejpam-3298	130	29	x.we	x.we	PROPN
ejpam-3298	130	30	need	need	NOUN
ejpam-3298	130	31	only	only	ADV
ejpam-3298	130	32	to	to	PART
ejpam-3298	130	33	show	show	VERB
ejpam-3298	130	34	that	that	SCONJ
ejpam-3298	130	35	{	{	PUNCT
ejpam-3298	130	36	hx2n	hx2n	PROPN
ejpam-3298	130	37	}	}	PUNCT
ejpam-3298	130	38	is	be	AUX
ejpam-3298	130	39	cauchy	cauchy	NOUN
ejpam-3298	130	40	sequence.on	sequence.on	X
ejpam-3298	130	41	contrary	contrary	ADV
ejpam-3298	130	42	suppose	suppose	VERB
ejpam-3298	130	43	{	{	PUNCT
ejpam-3298	130	44	hxn	hxn	NOUN
ejpam-3298	130	45	}	}	PUNCT
ejpam-3298	130	46	is	be	AUX
ejpam-3298	130	47	not	not	PART
ejpam-3298	130	48	cauchy.then	cauchy.then	NOUN
ejpam-3298	130	49	there	there	PRON
ejpam-3298	130	50	exists	exist	VERB
ejpam-3298	130	51	some	some	DET
ejpam-3298	130	52	ε	ε	PROPN
ejpam-3298	130	53	>	>	X
ejpam-3298	130	54	0	0	NUM
ejpam-3298	130	55	such	such	ADJ
ejpam-3298	130	56	that	that	PRON
ejpam-3298	130	57	for	for	ADP
ejpam-3298	130	58	any	any	DET
ejpam-3298	130	59	even	even	ADV
ejpam-3298	130	60	integers	integer	NOUN
ejpam-3298	130	61	2m(k	2m(k	NUM
ejpam-3298	130	62	)	)	PUNCT
ejpam-3298	130	63	and	and	CCONJ
ejpam-3298	130	64	2n(k	2n(k	NUM
ejpam-3298	130	65	)	)	PUNCT
ejpam-3298	130	66	with	with	ADP
ejpam-3298	130	67	2m(k	2m(k	PROPN
ejpam-3298	130	68	)	)	PUNCT
ejpam-3298	130	69	>	>	X
ejpam-3298	131	1	2n(k	2n(k	PROPN
ejpam-3298	131	2	)	)	PUNCT
ejpam-3298	132	1	>	>	X
ejpam-3298	132	2	2k	2k	PROPN
ejpam-3298	132	3	and	and	CCONJ
ejpam-3298	132	4	d(hx2m(k	d(hx2m(k	NOUN
ejpam-3298	132	5	)	)	PUNCT
ejpam-3298	132	6	,	,	PUNCT
ejpam-3298	132	7	h2n(k	h2n(k	PROPN
ejpam-3298	132	8	)	)	PUNCT
ejpam-3298	132	9	)	)	PUNCT
ejpam-3298	133	1	>	>	PUNCT
ejpam-3298	133	2	ε	ε	PROPN
ejpam-3298	133	3	.	.	PUNCT
ejpam-3298	133	4	further	far	ADV
ejpam-3298	133	5	,	,	PUNCT
ejpam-3298	133	6	let	let	VERB
ejpam-3298	133	7	2m(k	2m(k	NUM
ejpam-3298	133	8	)	)	PUNCT
ejpam-3298	133	9	denote	denote	VERB
ejpam-3298	133	10	the	the	DET
ejpam-3298	133	11	least	least	ADJ
ejpam-3298	133	12	even	even	ADV
ejpam-3298	133	13	positive	positive	ADJ
ejpam-3298	133	14	integer	integer	NOUN
ejpam-3298	133	15	exceeding	exceed	VERB
ejpam-3298	133	16	2n(k	2n(k	PROPN
ejpam-3298	133	17	)	)	PUNCT
ejpam-3298	133	18	which	which	PRON
ejpam-3298	133	19	satisfies	satisfy	VERB
ejpam-3298	133	20	that	that	DET
ejpam-3298	133	21	2m(k	2m(k	NOUN
ejpam-3298	133	22	)	)	PUNCT
ejpam-3298	133	23	>	>	X
ejpam-3298	134	1	2n(k	2n(k	PROPN
ejpam-3298	134	2	)	)	PUNCT
ejpam-3298	134	3	>	>	X
ejpam-3298	135	1	2k	2k	PROPN
ejpam-3298	135	2	d(hx2m(k)−2	d(hx2m(k)−2	PROPN
ejpam-3298	135	3	,	,	PUNCT
ejpam-3298	135	4	hx2n(k	hx2n(k	NUM
ejpam-3298	135	5	)	)	PUNCT
ejpam-3298	135	6	)	)	PUNCT
ejpam-3298	135	7	≤	≤	NUM
ejpam-3298	135	8	ε	ε	PROPN
ejpam-3298	135	9	and	and	CCONJ
ejpam-3298	135	10	d(hx2mk	d(hx2mk	AUX
ejpam-3298	135	11	,	,	PUNCT
ejpam-3298	135	12	hx2n(k	hx2n(k	NUM
ejpam-3298	135	13	)	)	PUNCT
ejpam-3298	135	14	)	)	PUNCT
ejpam-3298	135	15	>	>	PUNCT
ejpam-3298	136	1	ε	ε	PROPN
ejpam-3298	136	2	.	.	PUNCT
ejpam-3298	137	1	(	(	PUNCT
ejpam-3298	137	2	11	11	NUM
ejpam-3298	137	3	)	)	PUNCT
ejpam-3298	137	4	note	note	VERB
ejpam-3298	137	5	that	that	SCONJ
ejpam-3298	137	6	for	for	ADP
ejpam-3298	137	7	any	any	DET
ejpam-3298	137	8	k	k	PROPN
ejpam-3298	137	9	∈	∈	PROPN
ejpam-3298	137	10	n	n	PRON
ejpam-3298	137	11	d(hx2m(k	d(hx2m(k	NOUN
ejpam-3298	137	12	)	)	PUNCT
ejpam-3298	137	13	,	,	PUNCT
ejpam-3298	137	14	hx2n(k	hx2n(k	NUM
ejpam-3298	137	15	)	)	PUNCT
ejpam-3298	137	16	)	)	PUNCT
ejpam-3298	137	17	≤	≤	X
ejpam-3298	138	1	d2m(k)−1	d2m(k)−1	NOUN
ejpam-3298	138	2	+	+	CCONJ
ejpam-3298	138	3	d2m(k)−2	d2m(k)−2	NOUN
ejpam-3298	138	4	+	+	CCONJ
ejpam-3298	138	5	d(hx2m(k)−2	d(hx2m(k)−2	PROPN
ejpam-3298	138	6	,	,	PUNCT
ejpam-3298	138	7	hx2n(k	hx2n(k	NUM
ejpam-3298	138	8	)	)	PUNCT
ejpam-3298	138	9	)	)	PUNCT
ejpam-3298	138	10	.	.	PUNCT
ejpam-3298	139	1	|d(hx2m(k	|d(hx2m(k	PROPN
ejpam-3298	139	2	)	)	PUNCT
ejpam-3298	139	3	,	,	PUNCT
ejpam-3298	139	4	hx2n(k)+1)−	hx2n(k)+1)−	PROPN
ejpam-3298	139	5	d(hx2m(k	d(hx2m(k	PROPN
ejpam-3298	139	6	)	)	PUNCT
ejpam-3298	139	7	,	,	PUNCT
ejpam-3298	139	8	hx2n(k))|	hx2n(k))|	X
ejpam-3298	139	9	≤	≤	NUM
ejpam-3298	140	1	d2n(k	d2n(k	PROPN
ejpam-3298	140	2	)	)	PUNCT
ejpam-3298	140	3	.	.	PUNCT
ejpam-3298	141	1	|d(hx2m(k)+1	|d(hx2m(k)+1	PROPN
ejpam-3298	141	2	,	,	PUNCT
ejpam-3298	141	3	hx2n(k)+1)−	hx2n(k)+1)−	PROPN
ejpam-3298	141	4	d(hx2m(k	d(hx2m(k	PROPN
ejpam-3298	141	5	)	)	PUNCT
ejpam-3298	141	6	,	,	PUNCT
ejpam-3298	141	7	hx2n(k)+1)|	hx2n(k)+1)|	PROPN
ejpam-3298	141	8	≤	≤	PROPN
ejpam-3298	141	9	d2m(k	d2m(k	PROPN
ejpam-3298	141	10	)	)	PUNCT
ejpam-3298	141	11	.	.	PUNCT
ejpam-3298	142	1	|d(hx2m(k)+1	|d(hx2m(k)+1	NOUN
ejpam-3298	142	2	,	,	PUNCT
ejpam-3298	142	3	hx2n(k)+2)−	hx2n(k)+2)−	PROPN
ejpam-3298	142	4	d(hx2m(k)+1	d(hx2m(k)+1	PROPN
ejpam-3298	142	5	,	,	PUNCT
ejpam-3298	142	6	hx2n(k)+1)|	hx2n(k)+1)|	PROPN
ejpam-3298	142	7	≤	≤	ADJ
ejpam-3298	142	8	d2n(k)+1	d2n(k)+1	NOUN
ejpam-3298	142	9	.	.	PUNCT
ejpam-3298	143	1	from	from	ADP
ejpam-3298	143	2	above	above	ADP
ejpam-3298	143	3	inequalities	inequality	NOUN
ejpam-3298	143	4	,	,	PUNCT
ejpam-3298	143	5	we	we	PRON
ejpam-3298	143	6	infer	infer	VERB
ejpam-3298	143	7	that	that	SCONJ
ejpam-3298	143	8	ε	ε	PROPN
ejpam-3298	143	9	=	=	SYM
ejpam-3298	143	10	limn→∞d(hx2m(k	limn→∞d(hx2m(k	PROPN
ejpam-3298	143	11	)	)	PUNCT
ejpam-3298	143	12	,	,	PUNCT
ejpam-3298	143	13	hx2n(k	hx2n(k	NUM
ejpam-3298	143	14	)	)	PUNCT
ejpam-3298	143	15	)	)	PUNCT
ejpam-3298	144	1	=	=	PUNCT
ejpam-3298	144	2	limn→∞d(hx2m(k	limn→∞d(hx2m(k	PROPN
ejpam-3298	144	3	)	)	PUNCT
ejpam-3298	144	4	,	,	PUNCT
ejpam-3298	144	5	hx2n(k)+1	hx2n(k)+1	PROPN
ejpam-3298	144	6	)	)	PUNCT
ejpam-3298	144	7	=	=	SYM
ejpam-3298	144	8	limn→∞d(hx2m(k)+1	limn→∞d(hx2m(k)+1	NOUN
ejpam-3298	144	9	,	,	PUNCT
ejpam-3298	144	10	hx2n(k)+1	hx2n(k)+1	NOUN
ejpam-3298	144	11	)	)	PUNCT
ejpam-3298	144	12	=	=	SYM
ejpam-3298	144	13	limn→∞d(hx2m(k)+1	limn→∞d(hx2m(k)+1	NOUN
ejpam-3298	144	14	,	,	PUNCT
ejpam-3298	144	15	hx2n(k)+2	hx2n(k)+2	NOUN
ejpam-3298	144	16	)	)	PUNCT
ejpam-3298	144	17	.	.	PUNCT
ejpam-3298	145	1	p.	p.	NOUN
ejpam-3298	145	2	semwal	semwal	NOUN
ejpam-3298	145	3	,	,	PUNCT
ejpam-3298	145	4	komal	komal	PROPN
ejpam-3298	145	5	/	/	SYM
ejpam-3298	145	6	eur	eur	PROPN
ejpam-3298	145	7	.	.	PUNCT
ejpam-3298	146	1	j.	j.	PROPN
ejpam-3298	146	2	pure	pure	PROPN
ejpam-3298	146	3	appl	appl	PROPN
ejpam-3298	146	4	.	.	PROPN
ejpam-3298	146	5	math	math	PROPN
ejpam-3298	146	6	,	,	PUNCT
ejpam-3298	146	7	11	11	NUM
ejpam-3298	146	8	(	(	PUNCT
ejpam-3298	146	9	4	4	NUM
ejpam-3298	146	10	)	)	PUNCT
ejpam-3298	146	11	(	(	PUNCT
ejpam-3298	146	12	2018	2018	NUM
ejpam-3298	146	13	)	)	PUNCT
ejpam-3298	146	14	,	,	PUNCT
ejpam-3298	146	15	1177	1177	NUM
ejpam-3298	146	16	-	-	SYM
ejpam-3298	146	17	1190	1190	NUM
ejpam-3298	146	18	1184	1184	NUM
ejpam-3298	146	19	again	again	ADV
ejpam-3298	146	20	from	from	ADP
ejpam-3298	146	21	(	(	PUNCT
ejpam-3298	146	22	5	5	NUM
ejpam-3298	146	23	)	)	PUNCT
ejpam-3298	146	24	,	,	PUNCT
ejpam-3298	146	25	we	we	PRON
ejpam-3298	146	26	have	have	AUX
ejpam-3298	146	27	ψ(d(fx2m(k	ψ(d(fx2m(k	NOUN
ejpam-3298	146	28	)	)	PUNCT
ejpam-3298	146	29	,	,	PUNCT
ejpam-3298	146	30	gx2n(k)+1	gx2n(k)+1	NOUN
ejpam-3298	146	31	)	)	PUNCT
ejpam-3298	146	32	)	)	PUNCT
ejpam-3298	146	33	≤	≤	NUM
ejpam-3298	147	1	max{φ(d(hx2m(k	max{φ(d(hx2m(k	PROPN
ejpam-3298	147	2	)	)	PUNCT
ejpam-3298	147	3	,	,	PUNCT
ejpam-3298	147	4	hx2n(k)+1	hx2n(k)+1	PROPN
ejpam-3298	147	5	)	)	PUNCT
ejpam-3298	147	6	)	)	PUNCT
ejpam-3298	147	7	,	,	PUNCT
ejpam-3298	147	8	φ(d2m(k	φ(d2m(k	PROPN
ejpam-3298	147	9	)	)	PUNCT
ejpam-3298	147	10	)	)	PUNCT
ejpam-3298	147	11	,	,	PUNCT
ejpam-3298	147	12	φ(d2n(k)+1	φ(d2n(k)+1	NOUN
ejpam-3298	147	13	)	)	PUNCT
ejpam-3298	147	14	,	,	PUNCT
ejpam-3298	147	15	φ	φ	X
ejpam-3298	147	16	(	(	PUNCT
ejpam-3298	147	17	1	1	NUM
ejpam-3298	147	18	2	2	NUM
ejpam-3298	147	19	[	[	X
ejpam-3298	147	20	d(hx2m(k	d(hx2m(k	NOUN
ejpam-3298	147	21	)	)	PUNCT
ejpam-3298	147	22	,	,	PUNCT
ejpam-3298	147	23	hx2n(k)+1	hx2n(k)+1	PROPN
ejpam-3298	147	24	)	)	PUNCT
ejpam-3298	147	25	+	+	NOUN
ejpam-3298	147	26	d(fx2m(k	d(fx2m(k	NOUN
ejpam-3298	147	27	)	)	PUNCT
ejpam-3298	147	28	,	,	PUNCT
ejpam-3298	147	29	gx2n(k)+1	gx2n(k)+1	NOUN
ejpam-3298	147	30	)	)	PUNCT
ejpam-3298	147	31	]	]	PUNCT
ejpam-3298	147	32	)	)	PUNCT
ejpam-3298	147	33	}	}	PUNCT
ejpam-3298	147	34	−	−	ADP
ejpam-3298	147	35	w(max{φ(d(hx2m(k	w(max{φ(d(hx2m(k	NOUN
ejpam-3298	147	36	)	)	PUNCT
ejpam-3298	147	37	,	,	PUNCT
ejpam-3298	147	38	hx2n(k)+1	hx2n(k)+1	PROPN
ejpam-3298	147	39	)	)	PUNCT
ejpam-3298	147	40	)	)	PUNCT
ejpam-3298	147	41	,	,	PUNCT
ejpam-3298	147	42	φ(d2m(k	φ(d2m(k	PROPN
ejpam-3298	147	43	)	)	PUNCT
ejpam-3298	147	44	)	)	PUNCT
ejpam-3298	147	45	,	,	PUNCT
ejpam-3298	147	46	φ(d2n(k)+1	φ(d2n(k)+1	NOUN
ejpam-3298	147	47	)	)	PUNCT
ejpam-3298	147	48	,	,	PUNCT
ejpam-3298	147	49	φ	φ	X
ejpam-3298	147	50	(	(	PUNCT
ejpam-3298	147	51	1	1	NUM
ejpam-3298	147	52	2	2	NUM
ejpam-3298	147	53	[	[	X
ejpam-3298	147	54	d(hx2m(k	d(hx2m(k	NOUN
ejpam-3298	147	55	)	)	PUNCT
ejpam-3298	147	56	,	,	PUNCT
ejpam-3298	147	57	hx2n(k)+1	hx2n(k)+1	PROPN
ejpam-3298	147	58	)	)	PUNCT
ejpam-3298	147	59	+	+	NUM
ejpam-3298	147	60	d(fx2m(k	d(fx2m(k	NOUN
ejpam-3298	147	61	)	)	PUNCT
ejpam-3298	147	62	,	,	PUNCT
ejpam-3298	147	63	gx2n(k)+1	gx2n(k)+1	NOUN
ejpam-3298	147	64	)	)	PUNCT
ejpam-3298	147	65	]	]	PUNCT
ejpam-3298	147	66	)	)	PUNCT
ejpam-3298	147	67	}	}	PUNCT
ejpam-3298	147	68	)	)	PUNCT
ejpam-3298	147	69	taking	take	VERB
ejpam-3298	147	70	k	k	PROPN
ejpam-3298	147	71	→∞	→∞	PROPN
ejpam-3298	147	72	,	,	PUNCT
ejpam-3298	147	73	we	we	PRON
ejpam-3298	147	74	deduce	deduce	VERB
ejpam-3298	147	75	that	that	SCONJ
ejpam-3298	147	76	ψ(ε	ψ(ε	PROPN
ejpam-3298	147	77	)	)	PUNCT
ejpam-3298	147	78	≤	≤	PROPN
ejpam-3298	147	79	max{φ(ε	max{φ(ε	PROPN
ejpam-3298	147	80	)	)	PUNCT
ejpam-3298	147	81	,	,	PUNCT
ejpam-3298	147	82	φ(0	φ(0	ADJ
ejpam-3298	147	83	)	)	PUNCT
ejpam-3298	147	84	,	,	PUNCT
ejpam-3298	147	85	φ(0	φ(0	ADJ
ejpam-3298	147	86	)	)	PUNCT
ejpam-3298	147	87	,	,	PUNCT
ejpam-3298	147	88	φ	φ	X
ejpam-3298	147	89	(	(	PUNCT
ejpam-3298	147	90	1	1	NUM
ejpam-3298	147	91	2	2	NUM
ejpam-3298	148	1	[	[	X
ejpam-3298	148	2	ε+	ε+	X
ejpam-3298	148	3	ε	ε	PROPN
ejpam-3298	148	4	]	]	X
ejpam-3298	148	5	)	)	PUNCT
ejpam-3298	148	6	}	}	PUNCT
ejpam-3298	148	7	−	−	PROPN
ejpam-3298	148	8	w(max{φ(ε	w(max{φ(ε	PROPN
ejpam-3298	148	9	)	)	PUNCT
ejpam-3298	148	10	,	,	PUNCT
ejpam-3298	148	11	φ(0	φ(0	ADJ
ejpam-3298	148	12	)	)	PUNCT
ejpam-3298	148	13	,	,	PUNCT
ejpam-3298	148	14	φ(0	φ(0	ADJ
ejpam-3298	148	15	)	)	PUNCT
ejpam-3298	148	16	,	,	PUNCT
ejpam-3298	148	17	φ	φ	X
ejpam-3298	148	18	(	(	PUNCT
ejpam-3298	148	19	1	1	NUM
ejpam-3298	148	20	2	2	NUM
ejpam-3298	148	21	[	[	X
ejpam-3298	148	22	ε+	ε+	X
ejpam-3298	148	23	ε	ε	PROPN
ejpam-3298	148	24	]	]	X
ejpam-3298	148	25	)	)	PUNCT
ejpam-3298	148	26	}	}	PUNCT
ejpam-3298	148	27	)	)	PUNCT
ejpam-3298	148	28	ψ(ε	ψ(ε	PROPN
ejpam-3298	148	29	)	)	PUNCT
ejpam-3298	148	30	≤	≤	PROPN
ejpam-3298	148	31	φ(ε)−	φ(ε)−	PROPN
ejpam-3298	148	32	w(φ(ε	w(φ(ε	PROPN
ejpam-3298	148	33	)	)	PUNCT
ejpam-3298	148	34	)	)	PUNCT
ejpam-3298	149	1	<	<	X
ejpam-3298	149	2	φ(ε	φ(ε	PROPN
ejpam-3298	149	3	)	)	PUNCT
ejpam-3298	149	4	a	a	DET
ejpam-3298	149	5	contradiction	contradiction	NOUN
ejpam-3298	149	6	and	and	CCONJ
ejpam-3298	149	7	hence	hence	ADV
ejpam-3298	149	8	{	{	PUNCT
ejpam-3298	149	9	hxn	hxn	NOUN
ejpam-3298	149	10	}	}	PUNCT
ejpam-3298	149	11	is	be	AUX
ejpam-3298	149	12	cauchy	cauchy	ADJ
ejpam-3298	149	13	sequence.since	sequence.since	NOUN
ejpam-3298	149	14	x	x	PUNCT
ejpam-3298	149	15	is	be	AUX
ejpam-3298	149	16	asymptotically	asymptotically	ADV
ejpam-3298	149	17	h	h	ADJ
ejpam-3298	149	18	-	-	PUNCT
ejpam-3298	149	19	complete	complete	ADJ
ejpam-3298	149	20	implies	imply	VERB
ejpam-3298	149	21	that	that	SCONJ
ejpam-3298	149	22	the	the	DET
ejpam-3298	149	23	sequence	sequence	NOUN
ejpam-3298	149	24	{	{	PUNCT
ejpam-3298	149	25	hxn	hxn	NOUN
ejpam-3298	149	26	}	}	PUNCT
ejpam-3298	149	27	converges	converge	VERB
ejpam-3298	149	28	to	to	ADP
ejpam-3298	149	29	a	a	DET
ejpam-3298	149	30	point	point	NOUN
ejpam-3298	149	31	z	z	NOUN
ejpam-3298	149	32	∈	∈	NOUN
ejpam-3298	150	1	x.we	x.we	PRON
ejpam-3298	150	2	infer	infer	VERB
ejpam-3298	150	3	that	that	SCONJ
ejpam-3298	150	4	{	{	PUNCT
ejpam-3298	150	5	hx2n	hx2n	NOUN
ejpam-3298	150	6	}	}	PUNCT
ejpam-3298	150	7	and	and	CCONJ
ejpam-3298	150	8	{	{	PUNCT
ejpam-3298	150	9	hx2n+1	hx2n+1	NOUN
ejpam-3298	150	10	}	}	PUNCT
ejpam-3298	150	11	also	also	ADV
ejpam-3298	150	12	converges	converge	VERB
ejpam-3298	150	13	to	to	ADP
ejpam-3298	150	14	z.	z.	PROPN
ejpam-3298	150	15	h	h	PROPN
ejpam-3298	150	16	is	be	AUX
ejpam-3298	150	17	asymptotically	asymptotically	ADV
ejpam-3298	150	18	continuous	continuous	ADJ
ejpam-3298	150	19	implies	implie	NOUN
ejpam-3298	150	20	that	that	SCONJ
ejpam-3298	150	21	hhx2n	hhx2n	PROPN
ejpam-3298	150	22	→	→	SYM
ejpam-3298	150	23	hz	hz	PROPN
ejpam-3298	150	24	,	,	PUNCT
ejpam-3298	150	25	hhx2n+1	hhx2n+1	PROPN
ejpam-3298	150	26	→	→	SYM
ejpam-3298	150	27	hz	hz	PROPN
ejpam-3298	150	28	,	,	PUNCT
ejpam-3298	150	29	hfx2n	hfx2n	PROPN
ejpam-3298	150	30	→	→	SYM
ejpam-3298	150	31	hz	hz	PROPN
ejpam-3298	150	32	,	,	PUNCT
ejpam-3298	150	33	hgx2n+1	hgx2n+1	X
ejpam-3298	150	34	→	→	PUNCT
ejpam-3298	150	35	hz	hz	VERB
ejpam-3298	150	36	as	as	ADP
ejpam-3298	150	37	n→∞.	n→∞.	PROPN
ejpam-3298	150	38	now	now	ADV
ejpam-3298	150	39	using	use	VERB
ejpam-3298	150	40	weakly	weakly	ADJ
ejpam-3298	150	41	commutativity	commutativity	NOUN
ejpam-3298	150	42	and	and	CCONJ
ejpam-3298	150	43	sub	sub	VERB
ejpam-3298	150	44	additivity	additivity	NOUN
ejpam-3298	150	45	of	of	ADP
ejpam-3298	150	46	ψ	ψ	NOUN
ejpam-3298	150	47	,	,	PUNCT
ejpam-3298	150	48	we	we	PRON
ejpam-3298	150	49	have	have	VERB
ejpam-3298	150	50	ψ(d(fhx2n	ψ(d(fhx2n	NOUN
ejpam-3298	150	51	,	,	PUNCT
ejpam-3298	150	52	hz	hz	NOUN
ejpam-3298	150	53	)	)	PUNCT
ejpam-3298	150	54	)	)	PUNCT
ejpam-3298	150	55	≤	≤	NUM
ejpam-3298	150	56	ψ(d(fhx2n	ψ(d(fhx2n	NOUN
ejpam-3298	150	57	,	,	PUNCT
ejpam-3298	150	58	hfx2n	hfx2n	PROPN
ejpam-3298	150	59	)	)	PUNCT
ejpam-3298	150	60	)	)	PUNCT
ejpam-3298	151	1	+	+	CCONJ
ejpam-3298	151	2	ψ(d(hfx2n	ψ(d(hfx2n	NOUN
ejpam-3298	151	3	,	,	PUNCT
ejpam-3298	151	4	hz	hz	NOUN
ejpam-3298	151	5	)	)	PUNCT
ejpam-3298	151	6	)	)	PUNCT
ejpam-3298	151	7	≤	≤	NUM
ejpam-3298	152	1	ψ(d(fx2n	ψ(d(fx2n	PROPN
ejpam-3298	152	2	,	,	PUNCT
ejpam-3298	152	3	hx2n	hx2n	PROPN
ejpam-3298	152	4	)	)	PUNCT
ejpam-3298	152	5	)	)	PUNCT
ejpam-3298	153	1	+	+	CCONJ
ejpam-3298	153	2	ψ(d(hfx2n	ψ(d(hfx2n	NOUN
ejpam-3298	153	3	,	,	PUNCT
ejpam-3298	153	4	hz	hz	NOUN
ejpam-3298	153	5	)	)	PUNCT
ejpam-3298	153	6	)	)	PUNCT
ejpam-3298	153	7	taking	take	VERB
ejpam-3298	153	8	n→∞	n→∞	PRON
ejpam-3298	153	9	implies	imply	VERB
ejpam-3298	153	10	that	that	SCONJ
ejpam-3298	153	11	fhx2n	fhx2n	PROPN
ejpam-3298	153	12	→	→	SYM
ejpam-3298	153	13	hz	hz	PROPN
ejpam-3298	153	14	.	.	PROPN
ejpam-3298	153	15	similarly	similarly	ADV
ejpam-3298	153	16	ghx2n+1	ghx2n+1	VERB
ejpam-3298	153	17	→	→	SYM
ejpam-3298	153	18	hz	hz	PRON
ejpam-3298	153	19	.	.	PUNCT
ejpam-3298	153	20	suppose	suppose	VERB
ejpam-3298	153	21	d(hz	d(hz	PROPN
ejpam-3298	153	22	,	,	PUNCT
ejpam-3298	153	23	gz	gz	NOUN
ejpam-3298	153	24	)	)	PUNCT
ejpam-3298	153	25	>	>	X
ejpam-3298	154	1	0	0	X
ejpam-3298	154	2	.	.	PUNCT
ejpam-3298	155	1	then	then	ADV
ejpam-3298	155	2	ψ(d(hz	ψ(d(hz	SYM
ejpam-3298	155	3	,	,	PUNCT
ejpam-3298	155	4	gz	gz	NOUN
ejpam-3298	155	5	)	)	PUNCT
ejpam-3298	155	6	)	)	PUNCT
ejpam-3298	155	7	≤	≤	NUM
ejpam-3298	155	8	ψ(d(hz	ψ(d(hz	NOUN
ejpam-3298	155	9	,	,	PUNCT
ejpam-3298	155	10	fhx2n	fhx2n	NOUN
ejpam-3298	155	11	)	)	PUNCT
ejpam-3298	155	12	)	)	PUNCT
ejpam-3298	156	1	+	+	CCONJ
ejpam-3298	156	2	ψ(d(fhx2n	ψ(d(fhx2n	NOUN
ejpam-3298	156	3	,	,	PUNCT
ejpam-3298	156	4	gz	gz	NOUN
ejpam-3298	156	5	)	)	PUNCT
ejpam-3298	156	6	)	)	PUNCT
ejpam-3298	157	1	≤	≤	NUM
ejpam-3298	157	2	ψ(d(hz	ψ(d(hz	NOUN
ejpam-3298	157	3	,	,	PUNCT
ejpam-3298	157	4	fhx2n	fhx2n	NOUN
ejpam-3298	157	5	)	)	PUNCT
ejpam-3298	157	6	)	)	PUNCT
ejpam-3298	158	1	+	+	PUNCT
ejpam-3298	158	2	max{φ(d(hhx2n	max{φ(d(hhx2n	NOUN
ejpam-3298	158	3	,	,	PUNCT
ejpam-3298	158	4	hz	hz	NOUN
ejpam-3298	158	5	)	)	PUNCT
ejpam-3298	158	6	)	)	PUNCT
ejpam-3298	158	7	,	,	PUNCT
ejpam-3298	158	8	φ(d(hhx2n	φ(d(hhx2n	NOUN
ejpam-3298	158	9	,	,	PUNCT
ejpam-3298	158	10	fhx2n	fhx2n	NOUN
ejpam-3298	158	11	)	)	PUNCT
ejpam-3298	158	12	)	)	PUNCT
ejpam-3298	158	13	,	,	PUNCT
ejpam-3298	158	14	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	158	15	,	,	PUNCT
ejpam-3298	158	16	gz	gz	NOUN
ejpam-3298	158	17	)	)	PUNCT
ejpam-3298	158	18	)	)	PUNCT
ejpam-3298	158	19	,	,	PUNCT
ejpam-3298	158	20	φ	φ	X
ejpam-3298	158	21	(	(	PUNCT
ejpam-3298	158	22	1	1	NUM
ejpam-3298	158	23	2	2	NUM
ejpam-3298	158	24	[	[	PUNCT
ejpam-3298	158	25	d(hhx2n	d(hhx2n	NOUN
ejpam-3298	158	26	,	,	PUNCT
ejpam-3298	158	27	hz	hz	VERB
ejpam-3298	158	28	)	)	PUNCT
ejpam-3298	159	1	+	+	NUM
ejpam-3298	159	2	d(fh2n	d(fh2n	NOUN
ejpam-3298	159	3	,	,	PUNCT
ejpam-3298	159	4	gz	gz	NOUN
ejpam-3298	159	5	)	)	PUNCT
ejpam-3298	159	6	]	]	PUNCT
ejpam-3298	159	7	)	)	PUNCT
ejpam-3298	159	8	}	}	PUNCT
ejpam-3298	160	1	−	−	PROPN
ejpam-3298	160	2	w(max{φ(d(hhx2n	w(max{φ(d(hhx2n	PROPN
ejpam-3298	160	3	,	,	PUNCT
ejpam-3298	160	4	hz	hz	NOUN
ejpam-3298	160	5	)	)	PUNCT
ejpam-3298	160	6	)	)	PUNCT
ejpam-3298	160	7	,	,	PUNCT
ejpam-3298	160	8	φ(d(hhx2n	φ(d(hhx2n	NOUN
ejpam-3298	160	9	,	,	PUNCT
ejpam-3298	160	10	fhx2n	fhx2n	NOUN
ejpam-3298	160	11	)	)	PUNCT
ejpam-3298	160	12	)	)	PUNCT
ejpam-3298	160	13	,	,	PUNCT
ejpam-3298	160	14	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	160	15	,	,	PUNCT
ejpam-3298	160	16	gz	gz	NOUN
ejpam-3298	160	17	)	)	PUNCT
ejpam-3298	160	18	)	)	PUNCT
ejpam-3298	160	19	,	,	PUNCT
ejpam-3298	160	20	φ	φ	X
ejpam-3298	160	21	(	(	PUNCT
ejpam-3298	160	22	1	1	NUM
ejpam-3298	160	23	2	2	NUM
ejpam-3298	160	24	[	[	PUNCT
ejpam-3298	160	25	d(hhx2n	d(hhx2n	NOUN
ejpam-3298	160	26	,	,	PUNCT
ejpam-3298	160	27	hz	hz	VERB
ejpam-3298	160	28	)	)	PUNCT
ejpam-3298	160	29	+	+	NUM
ejpam-3298	160	30	d(fh2n	d(fh2n	NOUN
ejpam-3298	160	31	,	,	PUNCT
ejpam-3298	160	32	gz	gz	NOUN
ejpam-3298	160	33	)	)	PUNCT
ejpam-3298	160	34	]	]	PUNCT
ejpam-3298	160	35	)	)	PUNCT
ejpam-3298	160	36	}	}	PUNCT
ejpam-3298	160	37	)	)	PUNCT
ejpam-3298	161	1	taking	take	VERB
ejpam-3298	161	2	n→∞	n→∞	NUM
ejpam-3298	161	3	,	,	PUNCT
ejpam-3298	161	4	we	we	PRON
ejpam-3298	161	5	infer	infer	VERB
ejpam-3298	161	6	that	that	SCONJ
ejpam-3298	161	7	ψ(d(hz	ψ(d(hz	SYM
ejpam-3298	161	8	,	,	PUNCT
ejpam-3298	161	9	gz	gz	NOUN
ejpam-3298	161	10	)	)	PUNCT
ejpam-3298	161	11	)	)	PUNCT
ejpam-3298	161	12	≤	≤	NUM
ejpam-3298	161	13	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	161	14	,	,	PUNCT
ejpam-3298	161	15	gz	gz	NOUN
ejpam-3298	161	16	)	)	PUNCT
ejpam-3298	161	17	)	)	PUNCT
ejpam-3298	162	1	a	a	DET
ejpam-3298	162	2	contradiction.hence	contradiction.hence	NOUN
ejpam-3298	162	3	hz	hz	VERB
ejpam-3298	162	4	=	=	PUNCT
ejpam-3298	162	5	gz	gz	PROPN
ejpam-3298	162	6	.	.	PUNCT
ejpam-3298	163	1	similarly	similarly	ADV
ejpam-3298	163	2	we	we	PRON
ejpam-3298	163	3	can	can	AUX
ejpam-3298	163	4	easily	easily	ADV
ejpam-3298	163	5	prove	prove	VERB
ejpam-3298	163	6	that	that	SCONJ
ejpam-3298	163	7	hz	hz	VERB
ejpam-3298	163	8	=	=	SYM
ejpam-3298	163	9	fz.next	fz.next	NOUN
ejpam-3298	163	10	we	we	PRON
ejpam-3298	163	11	have	have	VERB
ejpam-3298	163	12	to	to	PART
ejpam-3298	163	13	show	show	VERB
ejpam-3298	163	14	that	that	SCONJ
ejpam-3298	163	15	z	z	NOUN
ejpam-3298	163	16	is	be	AUX
ejpam-3298	163	17	fixed	fix	VERB
ejpam-3298	163	18	point	point	NOUN
ejpam-3298	163	19	of	of	ADP
ejpam-3298	163	20	h.	h.	PROPN
ejpam-3298	163	21	suppose	suppose	VERB
ejpam-3298	163	22	that	that	SCONJ
ejpam-3298	163	23	d(hz	d(hz	PROPN
ejpam-3298	163	24	,	,	PUNCT
ejpam-3298	163	25	z	z	NOUN
ejpam-3298	163	26	)	)	PUNCT
ejpam-3298	163	27	>	>	X
ejpam-3298	164	1	0.from	0.from	NUM
ejpam-3298	164	2	(	(	PUNCT
ejpam-3298	164	3	5	5	NUM
ejpam-3298	164	4	)	)	PUNCT
ejpam-3298	164	5	,	,	PUNCT
ejpam-3298	164	6	we	we	PRON
ejpam-3298	164	7	have	have	VERB
ejpam-3298	164	8	ψ(d(fx2n	ψ(d(fx2n	NOUN
ejpam-3298	164	9	,	,	PUNCT
ejpam-3298	164	10	ghx2n	ghx2n	PROPN
ejpam-3298	164	11	)	)	PUNCT
ejpam-3298	164	12	)	)	PUNCT
ejpam-3298	165	1	≤	≤	NOUN
ejpam-3298	165	2	max{φ(d(hx2n	max{φ(d(hx2n	NOUN
ejpam-3298	165	3	,	,	PUNCT
ejpam-3298	165	4	hhx2n	hhx2n	PROPN
ejpam-3298	165	5	)	)	PUNCT
ejpam-3298	165	6	)	)	PUNCT
ejpam-3298	165	7	,	,	PUNCT
ejpam-3298	165	8	φ(d(hx2n	φ(d(hx2n	ADP
ejpam-3298	165	9	,	,	PUNCT
ejpam-3298	165	10	fx2n	fx2n	PROPN
ejpam-3298	165	11	)	)	PUNCT
ejpam-3298	165	12	)	)	PUNCT
ejpam-3298	165	13	,	,	PUNCT
ejpam-3298	165	14	φ(d(hhx2n	φ(d(hhx2n	NOUN
ejpam-3298	165	15	,	,	PUNCT
ejpam-3298	165	16	ghx2n	ghx2n	NOUN
ejpam-3298	165	17	)	)	PUNCT
ejpam-3298	165	18	)	)	PUNCT
ejpam-3298	165	19	,	,	PUNCT
ejpam-3298	165	20	p.	p.	NOUN
ejpam-3298	165	21	semwal	semwal	NOUN
ejpam-3298	165	22	,	,	PUNCT
ejpam-3298	165	23	komal	komal	PROPN
ejpam-3298	165	24	/	/	SYM
ejpam-3298	165	25	eur	eur	PROPN
ejpam-3298	165	26	.	.	PUNCT
ejpam-3298	166	1	j.	j.	PROPN
ejpam-3298	166	2	pure	pure	PROPN
ejpam-3298	166	3	appl	appl	PROPN
ejpam-3298	166	4	.	.	PROPN
ejpam-3298	166	5	math	math	PROPN
ejpam-3298	166	6	,	,	PUNCT
ejpam-3298	166	7	11	11	NUM
ejpam-3298	166	8	(	(	PUNCT
ejpam-3298	166	9	4	4	NUM
ejpam-3298	166	10	)	)	PUNCT
ejpam-3298	166	11	(	(	PUNCT
ejpam-3298	166	12	2018	2018	NUM
ejpam-3298	166	13	)	)	PUNCT
ejpam-3298	166	14	,	,	PUNCT
ejpam-3298	166	15	1177	1177	NUM
ejpam-3298	166	16	-	-	SYM
ejpam-3298	166	17	1190	1190	NUM
ejpam-3298	166	18	1185	1185	NUM
ejpam-3298	166	19	φ	φ	PROPN
ejpam-3298	166	20	(	(	PUNCT
ejpam-3298	166	21	1	1	NUM
ejpam-3298	166	22	2	2	NUM
ejpam-3298	166	23	[	[	X
ejpam-3298	166	24	d(hx2n	d(hx2n	NOUN
ejpam-3298	166	25	,	,	PUNCT
ejpam-3298	166	26	hhx2n	hhx2n	PUNCT
ejpam-3298	166	27	)	)	PUNCT
ejpam-3298	167	1	+	+	NUM
ejpam-3298	167	2	d(fx2n	d(fx2n	PROPN
ejpam-3298	167	3	,	,	PUNCT
ejpam-3298	167	4	ghx2n	ghx2n	PROPN
ejpam-3298	167	5	)	)	PUNCT
ejpam-3298	167	6	]	]	PUNCT
ejpam-3298	167	7	)	)	PUNCT
ejpam-3298	167	8	}	}	PUNCT
ejpam-3298	168	1	−	−	PROPN
ejpam-3298	168	2	w(max{φ(d(hx2n	w(max{φ(d(hx2n	PROPN
ejpam-3298	168	3	,	,	PUNCT
ejpam-3298	168	4	hhx2n	hhx2n	PROPN
ejpam-3298	168	5	)	)	PUNCT
ejpam-3298	168	6	)	)	PUNCT
ejpam-3298	168	7	,	,	PUNCT
ejpam-3298	168	8	φ(d(hx2n	φ(d(hx2n	ADP
ejpam-3298	168	9	,	,	PUNCT
ejpam-3298	168	10	fx2n	fx2n	PROPN
ejpam-3298	168	11	)	)	PUNCT
ejpam-3298	168	12	)	)	PUNCT
ejpam-3298	168	13	,	,	PUNCT
ejpam-3298	168	14	φ(d(hhx2n	φ(d(hhx2n	NOUN
ejpam-3298	168	15	,	,	PUNCT
ejpam-3298	168	16	ghx2n	ghx2n	PROPN
ejpam-3298	168	17	)	)	PUNCT
ejpam-3298	168	18	)	)	PUNCT
ejpam-3298	168	19	,	,	PUNCT
ejpam-3298	168	20	φ	φ	X
ejpam-3298	168	21	(	(	PUNCT
ejpam-3298	168	22	1	1	NUM
ejpam-3298	168	23	2	2	NUM
ejpam-3298	168	24	[	[	X
ejpam-3298	168	25	d(hx2n	d(hx2n	NOUN
ejpam-3298	168	26	,	,	PUNCT
ejpam-3298	168	27	hhx2n	hhx2n	PUNCT
ejpam-3298	168	28	)	)	PUNCT
ejpam-3298	168	29	+	+	NUM
ejpam-3298	168	30	d(fx2n	d(fx2n	PROPN
ejpam-3298	168	31	,	,	PUNCT
ejpam-3298	168	32	ghx2n	ghx2n	PROPN
ejpam-3298	168	33	)	)	PUNCT
ejpam-3298	168	34	]	]	PUNCT
ejpam-3298	168	35	)	)	PUNCT
ejpam-3298	168	36	}	}	PUNCT
ejpam-3298	168	37	)	)	PUNCT
ejpam-3298	168	38	taking	take	VERB
ejpam-3298	168	39	n→∞	n→∞	NUM
ejpam-3298	168	40	,	,	PUNCT
ejpam-3298	168	41	we	we	PRON
ejpam-3298	168	42	infer	infer	VERB
ejpam-3298	168	43	that	that	SCONJ
ejpam-3298	168	44	ψ(d(z	ψ(d(z	PROPN
ejpam-3298	168	45	,	,	PUNCT
ejpam-3298	168	46	hz	hz	PROPN
ejpam-3298	168	47	)	)	PUNCT
ejpam-3298	168	48	)	)	PUNCT
ejpam-3298	168	49	≤	≤	NUM
ejpam-3298	168	50	max{φ(d(z	max{φ(d(z	NOUN
ejpam-3298	168	51	,	,	PUNCT
ejpam-3298	168	52	hz	hz	NOUN
ejpam-3298	168	53	)	)	PUNCT
ejpam-3298	168	54	)	)	PUNCT
ejpam-3298	168	55	,	,	PUNCT
ejpam-3298	168	56	φ(0	φ(0	ADJ
ejpam-3298	168	57	)	)	PUNCT
ejpam-3298	168	58	,	,	PUNCT
ejpam-3298	168	59	φ(0	φ(0	ADJ
ejpam-3298	168	60	)	)	PUNCT
ejpam-3298	168	61	,	,	PUNCT
ejpam-3298	168	62	φ	φ	X
ejpam-3298	168	63	(	(	PUNCT
ejpam-3298	168	64	1	1	NUM
ejpam-3298	168	65	2	2	NUM
ejpam-3298	168	66	[	[	X
ejpam-3298	168	67	d(z	d(z	NOUN
ejpam-3298	168	68	,	,	PUNCT
ejpam-3298	168	69	hz	hz	VERB
ejpam-3298	168	70	)	)	PUNCT
ejpam-3298	169	1	+	+	NUM
ejpam-3298	169	2	d(z	d(z	PROPN
ejpam-3298	169	3	,	,	PUNCT
ejpam-3298	169	4	hz	hz	NOUN
ejpam-3298	169	5	)	)	PUNCT
ejpam-3298	169	6	]	]	PUNCT
ejpam-3298	169	7	)	)	PUNCT
ejpam-3298	169	8	}	}	PUNCT
ejpam-3298	170	1	−w(max{φ(d(z	−w(max{φ(d(z	NUM
ejpam-3298	170	2	,	,	PUNCT
ejpam-3298	170	3	hz	hz	NOUN
ejpam-3298	170	4	)	)	PUNCT
ejpam-3298	170	5	)	)	PUNCT
ejpam-3298	170	6	,	,	PUNCT
ejpam-3298	170	7	φ(0	φ(0	ADJ
ejpam-3298	170	8	)	)	PUNCT
ejpam-3298	170	9	,	,	PUNCT
ejpam-3298	170	10	φ(0	φ(0	ADJ
ejpam-3298	170	11	)	)	PUNCT
ejpam-3298	170	12	,	,	PUNCT
ejpam-3298	170	13	φ	φ	X
ejpam-3298	170	14	(	(	PUNCT
ejpam-3298	170	15	1	1	NUM
ejpam-3298	170	16	2	2	NUM
ejpam-3298	170	17	[	[	X
ejpam-3298	170	18	d(z	d(z	NOUN
ejpam-3298	170	19	,	,	PUNCT
ejpam-3298	170	20	hz	hz	VERB
ejpam-3298	170	21	)	)	PUNCT
ejpam-3298	171	1	+	+	NUM
ejpam-3298	171	2	d(z	d(z	PROPN
ejpam-3298	171	3	,	,	PUNCT
ejpam-3298	171	4	hz	hz	NOUN
ejpam-3298	171	5	)	)	PUNCT
ejpam-3298	171	6	]	]	PUNCT
ejpam-3298	171	7	)	)	PUNCT
ejpam-3298	171	8	}	}	PUNCT
ejpam-3298	171	9	)	)	PUNCT
ejpam-3298	171	10	implies	imply	VERB
ejpam-3298	171	11	that	that	SCONJ
ejpam-3298	171	12	ψ(d(z	ψ(d(z	PROPN
ejpam-3298	171	13	,	,	PUNCT
ejpam-3298	171	14	hz	hz	PROPN
ejpam-3298	171	15	)	)	PUNCT
ejpam-3298	171	16	)	)	PUNCT
ejpam-3298	171	17	≤	≤	PROPN
ejpam-3298	171	18	φ(d(z	φ(d(z	PROPN
ejpam-3298	171	19	,	,	PUNCT
ejpam-3298	171	20	hz))−	hz))−	NOUN
ejpam-3298	171	21	w(φ(d(z	w(φ(d(z	PROPN
ejpam-3298	171	22	,	,	PUNCT
ejpam-3298	171	23	hz	hz	NOUN
ejpam-3298	171	24	)	)	PUNCT
ejpam-3298	171	25	)	)	PUNCT
ejpam-3298	171	26	)	)	PUNCT
ejpam-3298	172	1	<	<	X
ejpam-3298	172	2	φ(d(z	φ(d(z	PROPN
ejpam-3298	172	3	,	,	PUNCT
ejpam-3298	172	4	hz	hz	NOUN
ejpam-3298	172	5	)	)	PUNCT
ejpam-3298	172	6	)	)	PUNCT
ejpam-3298	173	1	a	a	DET
ejpam-3298	173	2	contradiction.hence	contradiction.hence	NOUN
ejpam-3298	173	3	hz	hz	VERB
ejpam-3298	173	4	=	=	PUNCT
ejpam-3298	173	5	z.	z.	PROPN
ejpam-3298	173	6	therefore	therefore	ADV
ejpam-3298	173	7	fz	fz	X
ejpam-3298	173	8	=	=	NOUN
ejpam-3298	173	9	gz	gz	PROPN
ejpam-3298	174	1	=	=	NOUN
ejpam-3298	174	2	hz	hz	PROPN
ejpam-3298	174	3	=	=	PUNCT
ejpam-3298	174	4	z.	z.	X
ejpam-3298	174	5	i.e.	i.e.	X
ejpam-3298	174	6	z	z	PROPN
ejpam-3298	174	7	is	be	AUX
ejpam-3298	174	8	common	common	ADJ
ejpam-3298	174	9	fixed	fix	VERB
ejpam-3298	174	10	point	point	NOUN
ejpam-3298	174	11	of	of	ADP
ejpam-3298	174	12	f	f	PROPN
ejpam-3298	174	13	,	,	PUNCT
ejpam-3298	174	14	g	g	PROPN
ejpam-3298	174	15	and	and	CCONJ
ejpam-3298	174	16	h.	h.	PROPN
ejpam-3298	175	1	finally	finally	ADV
ejpam-3298	175	2	,	,	PUNCT
ejpam-3298	175	3	we	we	PRON
ejpam-3298	175	4	show	show	VERB
ejpam-3298	175	5	that	that	SCONJ
ejpam-3298	175	6	z	z	NOUN
ejpam-3298	175	7	is	be	AUX
ejpam-3298	175	8	unique	unique	ADJ
ejpam-3298	175	9	fixed	fix	VERB
ejpam-3298	175	10	point	point	NOUN
ejpam-3298	175	11	of	of	ADP
ejpam-3298	175	12	f	f	PROPN
ejpam-3298	175	13	,	,	PUNCT
ejpam-3298	175	14	g&h.suppose	g&h.suppose	VERB
ejpam-3298	175	15	z′	z′	NUM
ejpam-3298	175	16	be	be	AUX
ejpam-3298	175	17	another	another	DET
ejpam-3298	175	18	fixed	fix	VERB
ejpam-3298	175	19	point	point	NOUN
ejpam-3298	175	20	.	.	PUNCT
ejpam-3298	176	1	then	then	ADV
ejpam-3298	176	2	from	from	ADP
ejpam-3298	176	3	(	(	PUNCT
ejpam-3298	176	4	5	5	NUM
ejpam-3298	176	5	)	)	PUNCT
ejpam-3298	176	6	,	,	PUNCT
ejpam-3298	176	7	we	we	PRON
ejpam-3298	176	8	obtain	obtain	VERB
ejpam-3298	176	9	ψ(d(fz	ψ(d(fz	NOUN
ejpam-3298	176	10	,	,	PUNCT
ejpam-3298	176	11	gz′	gz′	NOUN
ejpam-3298	176	12	)	)	PUNCT
ejpam-3298	176	13	)	)	PUNCT
ejpam-3298	176	14	≤	≤	NUM
ejpam-3298	176	15	max{φ(d(hz	max{φ(d(hz	NUM
ejpam-3298	176	16	,	,	PUNCT
ejpam-3298	176	17	hz′	hz′	NUM
ejpam-3298	176	18	)	)	PUNCT
ejpam-3298	176	19	)	)	PUNCT
ejpam-3298	176	20	,	,	PUNCT
ejpam-3298	176	21	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	176	22	,	,	PUNCT
ejpam-3298	176	23	fz	fz	NOUN
ejpam-3298	176	24	)	)	PUNCT
ejpam-3298	176	25	)	)	PUNCT
ejpam-3298	176	26	,	,	PUNCT
ejpam-3298	176	27	φ(d(hz′	φ(d(hz′	X
ejpam-3298	176	28	,	,	PUNCT
ejpam-3298	176	29	gz′	gz′	NOUN
ejpam-3298	176	30	)	)	PUNCT
ejpam-3298	176	31	)	)	PUNCT
ejpam-3298	176	32	,	,	PUNCT
ejpam-3298	176	33	φ	φ	X
ejpam-3298	176	34	(	(	PUNCT
ejpam-3298	176	35	1	1	NUM
ejpam-3298	176	36	2	2	NUM
ejpam-3298	176	37	[	[	X
ejpam-3298	176	38	d(hz	d(hz	X
ejpam-3298	176	39	,	,	PUNCT
ejpam-3298	176	40	hz′	hz′	NUM
ejpam-3298	176	41	)	)	PUNCT
ejpam-3298	177	1	+	+	CCONJ
ejpam-3298	177	2	d(fz	d(fz	PROPN
ejpam-3298	177	3	,	,	PUNCT
ejpam-3298	177	4	gz′	gz′	NOUN
ejpam-3298	177	5	)	)	PUNCT
ejpam-3298	177	6	]	]	PUNCT
ejpam-3298	177	7	)	)	PUNCT
ejpam-3298	177	8	}	}	PUNCT
ejpam-3298	177	9	−w(max{φ(d(hz	−w(max{φ(d(hz	NUM
ejpam-3298	177	10	,	,	PUNCT
ejpam-3298	177	11	hz′	hz′	NUM
ejpam-3298	177	12	)	)	PUNCT
ejpam-3298	177	13	)	)	PUNCT
ejpam-3298	177	14	,	,	PUNCT
ejpam-3298	177	15	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	177	16	,	,	PUNCT
ejpam-3298	177	17	fz	fz	NOUN
ejpam-3298	177	18	)	)	PUNCT
ejpam-3298	177	19	)	)	PUNCT
ejpam-3298	177	20	,	,	PUNCT
ejpam-3298	177	21	φ(d(hz′	φ(d(hz′	X
ejpam-3298	177	22	,	,	PUNCT
ejpam-3298	177	23	gz′	gz′	NOUN
ejpam-3298	177	24	)	)	PUNCT
ejpam-3298	177	25	)	)	PUNCT
ejpam-3298	177	26	,	,	PUNCT
ejpam-3298	177	27	φ	φ	X
ejpam-3298	177	28	(	(	PUNCT
ejpam-3298	177	29	1	1	NUM
ejpam-3298	177	30	2	2	NUM
ejpam-3298	177	31	[	[	X
ejpam-3298	177	32	d(hz	d(hz	X
ejpam-3298	177	33	,	,	PUNCT
ejpam-3298	177	34	hz′	hz′	NUM
ejpam-3298	177	35	)	)	PUNCT
ejpam-3298	178	1	+	+	CCONJ
ejpam-3298	178	2	d(fz	d(fz	PROPN
ejpam-3298	178	3	,	,	PUNCT
ejpam-3298	178	4	gz′	gz′	NOUN
ejpam-3298	178	5	)	)	PUNCT
ejpam-3298	178	6	]	]	PUNCT
ejpam-3298	178	7	)	)	PUNCT
ejpam-3298	178	8	}	}	PUNCT
ejpam-3298	178	9	)	)	PUNCT
ejpam-3298	179	1	we	we	PRON
ejpam-3298	179	2	infer	infer	VERB
ejpam-3298	179	3	that	that	SCONJ
ejpam-3298	179	4	ψ(d(hz	ψ(d(hz	NOUN
ejpam-3298	179	5	,	,	PUNCT
ejpam-3298	179	6	hz′	hz′	NUM
ejpam-3298	179	7	)	)	PUNCT
ejpam-3298	179	8	)	)	PUNCT
ejpam-3298	179	9	≤	≤	NUM
ejpam-3298	179	10	φ(d(hz	φ(d(hz	NOUN
ejpam-3298	179	11	,	,	PUNCT
ejpam-3298	179	12	hz′))−	hz′))−	PROPN
ejpam-3298	179	13	w(φ(d(hz	w(φ(d(hz	PROPN
ejpam-3298	179	14	,	,	PUNCT
ejpam-3298	179	15	hz′	hz′	NUM
ejpam-3298	179	16	)	)	PUNCT
ejpam-3298	179	17	)	)	PUNCT
ejpam-3298	179	18	)	)	PUNCT
ejpam-3298	179	19	<	<	X
ejpam-3298	179	20	φ(d(hz	φ(d(hz	X
ejpam-3298	179	21	,	,	PUNCT
ejpam-3298	179	22	hz′	hz′	NUM
ejpam-3298	179	23	)	)	PUNCT
ejpam-3298	179	24	)	)	PUNCT
ejpam-3298	179	25	a	a	DET
ejpam-3298	179	26	contradiction	contradiction	NOUN
ejpam-3298	179	27	.	.	PUNCT
ejpam-3298	180	1	hence	hence	ADV
ejpam-3298	180	2	z	z	NOUN
ejpam-3298	180	3	=	=	PUNCT
ejpam-3298	180	4	z′.	z′.	PROPN
ejpam-3298	180	5	corollary	corollary	ADJ
ejpam-3298	180	6	2	2	NUM
ejpam-3298	180	7	.	.	PUNCT
ejpam-3298	181	1	let	let	VERB
ejpam-3298	181	2	(	(	PUNCT
ejpam-3298	181	3	x	x	NOUN
ejpam-3298	181	4	,	,	PUNCT
ejpam-3298	181	5	d	d	NOUN
ejpam-3298	181	6	)	)	PUNCT
ejpam-3298	181	7	be	be	AUX
ejpam-3298	181	8	a	a	DET
ejpam-3298	181	9	complete	complete	ADJ
ejpam-3298	181	10	metric	metric	ADJ
ejpam-3298	181	11	space	space	NOUN
ejpam-3298	181	12	and	and	CCONJ
ejpam-3298	181	13	f	f	PROPN
ejpam-3298	181	14	,	,	PUNCT
ejpam-3298	181	15	g	g	PROPN
ejpam-3298	181	16	and	and	CCONJ
ejpam-3298	181	17	h	h	PROPN
ejpam-3298	181	18	be	be	VERB
ejpam-3298	181	19	self	self	NOUN
ejpam-3298	181	20	mappings	mapping	NOUN
ejpam-3298	181	21	on	on	ADP
ejpam-3298	181	22	x	x	SYM
ejpam-3298	181	23	such	such	ADJ
ejpam-3298	181	24	that	that	SCONJ
ejpam-3298	181	25	f(x	f(x	PROPN
ejpam-3298	181	26	)	)	PUNCT
ejpam-3298	181	27	∪	∪	ADP
ejpam-3298	181	28	g(x	g(x	NOUN
ejpam-3298	181	29	)	)	PUNCT
ejpam-3298	181	30	⊆	⊆	NUM
ejpam-3298	181	31	h(x).if	h(x).if	NOUN
ejpam-3298	181	32	there	there	ADV
ejpam-3298	181	33	exists	exist	VERB
ejpam-3298	181	34	a	a	DET
ejpam-3298	181	35	w	w	PROPN
ejpam-3298	181	36	∈	∈	PROPN
ejpam-3298	181	37	w	w	NOUN
ejpam-3298	181	38	satisfying	satisfy	VERB
ejpam-3298	181	39	(	(	PUNCT
ejpam-3298	181	40	5).then	5).then	ADV
ejpam-3298	181	41	the	the	DET
ejpam-3298	181	42	pair	pair	NOUN
ejpam-3298	181	43	(	(	PUNCT
ejpam-3298	181	44	f	f	X
ejpam-3298	181	45	,	,	PUNCT
ejpam-3298	181	46	h	h	NOUN
ejpam-3298	181	47	)	)	PUNCT
ejpam-3298	181	48	and	and	CCONJ
ejpam-3298	181	49	(	(	PUNCT
ejpam-3298	181	50	g	g	NOUN
ejpam-3298	181	51	,	,	PUNCT
ejpam-3298	181	52	h	h	NOUN
ejpam-3298	181	53	)	)	PUNCT
ejpam-3298	181	54	have	have	VERB
ejpam-3298	181	55	a	a	DET
ejpam-3298	181	56	coincidence	coincidence	NOUN
ejpam-3298	181	57	point	point	NOUN
ejpam-3298	181	58	in	in	ADP
ejpam-3298	181	59	x	x	PRON
ejpam-3298	181	60	,	,	PUNCT
ejpam-3298	181	61	provided	provide	VERB
ejpam-3298	181	62	that	that	SCONJ
ejpam-3298	181	63	(	(	PUNCT
ejpam-3298	181	64	i	i	NOUN
ejpam-3298	181	65	)	)	PUNCT
ejpam-3298	181	66	h	h	PROPN
ejpam-3298	181	67	is	be	AUX
ejpam-3298	181	68	continuous	continuous	ADJ
ejpam-3298	181	69	and	and	CCONJ
ejpam-3298	181	70	(	(	PUNCT
ejpam-3298	181	71	iii	iii	NOUN
ejpam-3298	181	72	)	)	PUNCT
ejpam-3298	181	73	h	h	NOUN
ejpam-3298	181	74	commutes	commute	NOUN
ejpam-3298	181	75	with	with	ADP
ejpam-3298	181	76	both	both	CCONJ
ejpam-3298	181	77	f	f	PROPN
ejpam-3298	181	78	and	and	CCONJ
ejpam-3298	181	79	g.further	g.further	ADJ
ejpam-3298	181	80	f	f	PROPN
ejpam-3298	181	81	,	,	PUNCT
ejpam-3298	181	82	g	g	PROPN
ejpam-3298	181	83	and	and	CCONJ
ejpam-3298	181	84	h	h	NOUN
ejpam-3298	181	85	have	have	VERB
ejpam-3298	181	86	a	a	DET
ejpam-3298	181	87	unique	unique	ADJ
ejpam-3298	181	88	common	common	ADJ
ejpam-3298	181	89	fixed	fix	VERB
ejpam-3298	181	90	point	point	NOUN
ejpam-3298	181	91	in	in	ADP
ejpam-3298	181	92	x.	x.	NOUN
ejpam-3298	181	93	taking	take	VERB
ejpam-3298	181	94	ψ(t	ψ(t	PROPN
ejpam-3298	181	95	)	)	PUNCT
ejpam-3298	182	1	=	=	SYM
ejpam-3298	182	2	t	t	NOUN
ejpam-3298	182	3	=	=	PUNCT
ejpam-3298	182	4	φ(t),in	φ(t),in	NOUN
ejpam-3298	182	5	cor.2	cor.2	NOUN
ejpam-3298	182	6	we	we	PRON
ejpam-3298	182	7	obtain	obtain	VERB
ejpam-3298	182	8	the	the	DET
ejpam-3298	182	9	following	follow	VERB
ejpam-3298	182	10	p.	p.	NOUN
ejpam-3298	182	11	semwal	semwal	NOUN
ejpam-3298	182	12	,	,	PUNCT
ejpam-3298	182	13	komal	komal	PROPN
ejpam-3298	182	14	/	/	SYM
ejpam-3298	182	15	eur	eur	PROPN
ejpam-3298	182	16	.	.	PUNCT
ejpam-3298	183	1	j.	j.	PROPN
ejpam-3298	183	2	pure	pure	PROPN
ejpam-3298	183	3	appl	appl	PROPN
ejpam-3298	183	4	.	.	PROPN
ejpam-3298	183	5	math	math	PROPN
ejpam-3298	183	6	,	,	PUNCT
ejpam-3298	183	7	11	11	NUM
ejpam-3298	183	8	(	(	PUNCT
ejpam-3298	183	9	4	4	NUM
ejpam-3298	183	10	)	)	PUNCT
ejpam-3298	183	11	(	(	PUNCT
ejpam-3298	183	12	2018	2018	NUM
ejpam-3298	183	13	)	)	PUNCT
ejpam-3298	183	14	,	,	PUNCT
ejpam-3298	183	15	1177	1177	NUM
ejpam-3298	183	16	-	-	SYM
ejpam-3298	183	17	1190	1190	NUM
ejpam-3298	183	18	1186	1186	NUM
ejpam-3298	183	19	corollary	corollary	NOUN
ejpam-3298	183	20	3	3	X
ejpam-3298	183	21	.	.	PUNCT
ejpam-3298	184	1	let	let	AUX
ejpam-3298	184	2	(	(	PUNCT
ejpam-3298	184	3	x	x	NOUN
ejpam-3298	184	4	,	,	PUNCT
ejpam-3298	184	5	d	d	NOUN
ejpam-3298	184	6	)	)	PUNCT
ejpam-3298	184	7	be	be	AUX
ejpam-3298	184	8	a	a	DET
ejpam-3298	184	9	complete	complete	ADJ
ejpam-3298	184	10	metric	metric	ADJ
ejpam-3298	184	11	space.let	space.let	X
ejpam-3298	184	12	f	f	PROPN
ejpam-3298	184	13	,	,	PUNCT
ejpam-3298	184	14	g	g	PROPN
ejpam-3298	184	15	and	and	CCONJ
ejpam-3298	184	16	h	h	PROPN
ejpam-3298	184	17	be	be	VERB
ejpam-3298	184	18	self	self	NOUN
ejpam-3298	184	19	maps	map	NOUN
ejpam-3298	184	20	on	on	ADP
ejpam-3298	184	21	x	x	SYM
ejpam-3298	184	22	such	such	ADJ
ejpam-3298	184	23	that	that	SCONJ
ejpam-3298	184	24	f(x	f(x	PROPN
ejpam-3298	184	25	)	)	PUNCT
ejpam-3298	184	26	∪	∪	ADP
ejpam-3298	184	27	g(x	g(x	NOUN
ejpam-3298	184	28	)	)	PUNCT
ejpam-3298	184	29	⊆	⊆	NUM
ejpam-3298	184	30	h(x	h(x	PROPN
ejpam-3298	184	31	)	)	PUNCT
ejpam-3298	184	32	and	and	CCONJ
ejpam-3298	184	33	h	h	NOUN
ejpam-3298	184	34	is	be	AUX
ejpam-3298	184	35	continuous	continuous	ADJ
ejpam-3298	184	36	and	and	CCONJ
ejpam-3298	184	37	commute	commute	VERB
ejpam-3298	184	38	with	with	ADP
ejpam-3298	184	39	both	both	CCONJ
ejpam-3298	184	40	f	f	PROPN
ejpam-3298	184	41	and	and	CCONJ
ejpam-3298	184	42	g.	g.	PROPN
ejpam-3298	184	43	if	if	SCONJ
ejpam-3298	184	44	there	there	PRON
ejpam-3298	184	45	exists	exist	VERB
ejpam-3298	184	46	a	a	DET
ejpam-3298	184	47	w	w	NOUN
ejpam-3298	184	48	∈w	∈w	NOUN
ejpam-3298	184	49	satisfying	satisfy	VERB
ejpam-3298	184	50	the	the	DET
ejpam-3298	184	51	following	follow	VERB
ejpam-3298	184	52	condition	condition	NOUN
ejpam-3298	184	53	:	:	PUNCT
ejpam-3298	184	54	d(fx	d(fx	NOUN
ejpam-3298	184	55	,	,	PUNCT
ejpam-3298	184	56	gy	gy	NOUN
ejpam-3298	184	57	)	)	PUNCT
ejpam-3298	184	58	≤	≤	NUM
ejpam-3298	184	59	max{d(hx	max{d(hx	PROPN
ejpam-3298	184	60	,	,	PUNCT
ejpam-3298	184	61	hy	hy	NOUN
ejpam-3298	184	62	)	)	PUNCT
ejpam-3298	184	63	,	,	PUNCT
ejpam-3298	184	64	d(hx	d(hx	PROPN
ejpam-3298	184	65	,	,	PUNCT
ejpam-3298	184	66	fx	fx	NOUN
ejpam-3298	184	67	)	)	PUNCT
ejpam-3298	184	68	,	,	PUNCT
ejpam-3298	184	69	d(hy	d(hy	PROPN
ejpam-3298	184	70	,	,	PUNCT
ejpam-3298	184	71	gy	gy	NOUN
ejpam-3298	184	72	)	)	PUNCT
ejpam-3298	184	73	,	,	PUNCT
ejpam-3298	184	74	1	1	NUM
ejpam-3298	184	75	2	2	NUM
ejpam-3298	184	76	[	[	X
ejpam-3298	184	77	d(hx	d(hx	X
ejpam-3298	184	78	,	,	PUNCT
ejpam-3298	184	79	hy	hy	NOUN
ejpam-3298	184	80	)	)	PUNCT
ejpam-3298	185	1	+	+	NUM
ejpam-3298	185	2	d(fx	d(fx	PROPN
ejpam-3298	185	3	,	,	PUNCT
ejpam-3298	185	4	gy	gy	NOUN
ejpam-3298	185	5	)	)	PUNCT
ejpam-3298	185	6	]	]	PUNCT
ejpam-3298	185	7	}	}	PUNCT
ejpam-3298	185	8	−	−	PROPN
ejpam-3298	185	9	w(max{d(hx	w(max{d(hx	PROPN
ejpam-3298	185	10	,	,	PUNCT
ejpam-3298	185	11	hy	hy	NOUN
ejpam-3298	185	12	)	)	PUNCT
ejpam-3298	185	13	,	,	PUNCT
ejpam-3298	185	14	d(hx	d(hx	PROPN
ejpam-3298	185	15	,	,	PUNCT
ejpam-3298	185	16	fx	fx	NOUN
ejpam-3298	185	17	)	)	PUNCT
ejpam-3298	185	18	,	,	PUNCT
ejpam-3298	185	19	d(hy	d(hy	PROPN
ejpam-3298	185	20	,	,	PUNCT
ejpam-3298	185	21	gy	gy	NOUN
ejpam-3298	185	22	)	)	PUNCT
ejpam-3298	185	23	,	,	PUNCT
ejpam-3298	185	24	1	1	NUM
ejpam-3298	185	25	2	2	NUM
ejpam-3298	185	26	[	[	X
ejpam-3298	185	27	d(hx	d(hx	X
ejpam-3298	185	28	,	,	PUNCT
ejpam-3298	185	29	hy	hy	NOUN
ejpam-3298	185	30	)	)	PUNCT
ejpam-3298	186	1	+	+	NUM
ejpam-3298	186	2	d(fx	d(fx	PROPN
ejpam-3298	186	3	,	,	PUNCT
ejpam-3298	186	4	gy	gy	NOUN
ejpam-3298	186	5	)	)	PUNCT
ejpam-3298	186	6	]	]	PUNCT
ejpam-3298	186	7	}	}	PUNCT
ejpam-3298	186	8	)	)	PUNCT
ejpam-3298	186	9	for	for	ADP
ejpam-3298	186	10	all	all	DET
ejpam-3298	186	11	x	x	NOUN
ejpam-3298	186	12	,	,	PUNCT
ejpam-3298	186	13	y	y	PROPN
ejpam-3298	186	14	∈	∈	PROPN
ejpam-3298	186	15	x.	x.	NOUN
ejpam-3298	187	1	then	then	ADV
ejpam-3298	187	2	the	the	DET
ejpam-3298	187	3	pair	pair	NOUN
ejpam-3298	187	4	(	(	PUNCT
ejpam-3298	187	5	f	f	X
ejpam-3298	187	6	,	,	PUNCT
ejpam-3298	187	7	h	h	NOUN
ejpam-3298	187	8	)	)	PUNCT
ejpam-3298	187	9	and	and	CCONJ
ejpam-3298	187	10	(	(	PUNCT
ejpam-3298	187	11	g	g	NOUN
ejpam-3298	187	12	,	,	PUNCT
ejpam-3298	187	13	h	h	NOUN
ejpam-3298	187	14	)	)	PUNCT
ejpam-3298	187	15	have	have	VERB
ejpam-3298	187	16	coincidence	coincidence	NOUN
ejpam-3298	187	17	point	point	NOUN
ejpam-3298	187	18	,	,	PUNCT
ejpam-3298	187	19	further	further	ADJ
ejpam-3298	187	20	f	f	X
ejpam-3298	187	21	,	,	PUNCT
ejpam-3298	187	22	g	g	PROPN
ejpam-3298	187	23	and	and	CCONJ
ejpam-3298	187	24	h	h	NOUN
ejpam-3298	187	25	have	have	AUX
ejpam-3298	187	26	unique	unique	ADJ
ejpam-3298	187	27	common	common	ADJ
ejpam-3298	187	28	fixed	fix	VERB
ejpam-3298	187	29	point	point	NOUN
ejpam-3298	187	30	in	in	ADP
ejpam-3298	187	31	x.	x.	NOUN
ejpam-3298	187	32	taking	take	VERB
ejpam-3298	187	33	h	h	NOUN
ejpam-3298	187	34	=	=	PUNCT
ejpam-3298	188	1	i	i	PROPN
ejpam-3298	188	2	,	,	PUNCT
ejpam-3298	188	3	in	in	ADP
ejpam-3298	188	4	cor.3	cor.3	NUM
ejpam-3298	188	5	we	we	PRON
ejpam-3298	188	6	gain	gain	VERB
ejpam-3298	188	7	the	the	DET
ejpam-3298	188	8	following	follow	VERB
ejpam-3298	188	9	corollary	corollary	ADJ
ejpam-3298	188	10	4	4	NUM
ejpam-3298	188	11	.	.	PUNCT
ejpam-3298	189	1	let	let	AUX
ejpam-3298	189	2	(	(	PUNCT
ejpam-3298	189	3	x	x	NOUN
ejpam-3298	189	4	,	,	PUNCT
ejpam-3298	189	5	d	d	NOUN
ejpam-3298	189	6	)	)	PUNCT
ejpam-3298	189	7	be	be	AUX
ejpam-3298	189	8	a	a	DET
ejpam-3298	189	9	complete	complete	ADJ
ejpam-3298	189	10	metric	metric	ADJ
ejpam-3298	189	11	space.let	space.let	X
ejpam-3298	189	12	f	f	PROPN
ejpam-3298	189	13	and	and	CCONJ
ejpam-3298	189	14	g	g	PROPN
ejpam-3298	189	15	be	be	VERB
ejpam-3298	189	16	self	self	NOUN
ejpam-3298	189	17	maps	map	NOUN
ejpam-3298	189	18	on	on	ADP
ejpam-3298	189	19	x.	x.	NOUN
ejpam-3298	189	20	if	if	SCONJ
ejpam-3298	189	21	there	there	PRON
ejpam-3298	189	22	exists	exist	VERB
ejpam-3298	189	23	a	a	DET
ejpam-3298	189	24	w	w	NOUN
ejpam-3298	189	25	∈w	∈w	NOUN
ejpam-3298	189	26	satisfying	satisfy	VERB
ejpam-3298	189	27	the	the	DET
ejpam-3298	189	28	following	follow	VERB
ejpam-3298	189	29	condition	condition	NOUN
ejpam-3298	189	30	:	:	PUNCT
ejpam-3298	189	31	d(fx	d(fx	NOUN
ejpam-3298	189	32	,	,	PUNCT
ejpam-3298	189	33	gy	gy	NOUN
ejpam-3298	189	34	)	)	PUNCT
ejpam-3298	189	35	≤	≤	NOUN
ejpam-3298	190	1	max{d(x	max{d(x	PROPN
ejpam-3298	190	2	,	,	PUNCT
ejpam-3298	190	3	y	y	NOUN
ejpam-3298	190	4	)	)	PUNCT
ejpam-3298	190	5	,	,	PUNCT
ejpam-3298	190	6	d(x	d(x	PROPN
ejpam-3298	190	7	,	,	PUNCT
ejpam-3298	190	8	fx	fx	PROPN
ejpam-3298	190	9	)	)	PUNCT
ejpam-3298	190	10	,	,	PUNCT
ejpam-3298	190	11	d(y	d(y	PROPN
ejpam-3298	190	12	,	,	PUNCT
ejpam-3298	190	13	gy	gy	NOUN
ejpam-3298	190	14	)	)	PUNCT
ejpam-3298	190	15	,	,	PUNCT
ejpam-3298	190	16	1	1	NUM
ejpam-3298	190	17	2	2	NUM
ejpam-3298	191	1	[	[	X
ejpam-3298	191	2	d(x	d(x	PROPN
ejpam-3298	191	3	,	,	PUNCT
ejpam-3298	191	4	y	y	NOUN
ejpam-3298	191	5	)	)	PUNCT
ejpam-3298	191	6	+	+	CCONJ
ejpam-3298	191	7	d(fx	d(fx	NOUN
ejpam-3298	191	8	,	,	PUNCT
ejpam-3298	191	9	gy	gy	NOUN
ejpam-3298	191	10	)	)	PUNCT
ejpam-3298	191	11	]	]	PUNCT
ejpam-3298	191	12	}	}	PUNCT
ejpam-3298	191	13	−	−	ADP
ejpam-3298	191	14	w(max{d(x	w(max{d(x	PROPN
ejpam-3298	191	15	,	,	PUNCT
ejpam-3298	191	16	y	y	PROPN
ejpam-3298	191	17	)	)	PUNCT
ejpam-3298	191	18	,	,	PUNCT
ejpam-3298	191	19	d(x	d(x	PROPN
ejpam-3298	191	20	,	,	PUNCT
ejpam-3298	191	21	fx	fx	PROPN
ejpam-3298	191	22	)	)	PUNCT
ejpam-3298	191	23	,	,	PUNCT
ejpam-3298	191	24	d(y	d(y	PROPN
ejpam-3298	191	25	,	,	PUNCT
ejpam-3298	191	26	gy	gy	NOUN
ejpam-3298	191	27	)	)	PUNCT
ejpam-3298	191	28	,	,	PUNCT
ejpam-3298	191	29	1	1	NUM
ejpam-3298	191	30	2	2	NUM
ejpam-3298	192	1	[	[	X
ejpam-3298	192	2	d(x	d(x	PROPN
ejpam-3298	192	3	,	,	PUNCT
ejpam-3298	192	4	y	y	NOUN
ejpam-3298	192	5	)	)	PUNCT
ejpam-3298	192	6	+	+	CCONJ
ejpam-3298	192	7	d(fx	d(fx	NOUN
ejpam-3298	192	8	,	,	PUNCT
ejpam-3298	192	9	gy	gy	NOUN
ejpam-3298	192	10	)	)	PUNCT
ejpam-3298	192	11	]	]	PUNCT
ejpam-3298	192	12	}	}	PUNCT
ejpam-3298	192	13	)	)	PUNCT
ejpam-3298	192	14	for	for	ADP
ejpam-3298	192	15	all	all	DET
ejpam-3298	192	16	x	x	NOUN
ejpam-3298	192	17	,	,	PUNCT
ejpam-3298	192	18	y	y	PROPN
ejpam-3298	192	19	∈	∈	PROPN
ejpam-3298	192	20	x.	x.	NOUN
ejpam-3298	193	1	then	then	ADV
ejpam-3298	193	2	f	f	PROPN
ejpam-3298	193	3	and	and	CCONJ
ejpam-3298	193	4	g	g	PROPN
ejpam-3298	193	5	have	have	VERB
ejpam-3298	193	6	unique	unique	ADJ
ejpam-3298	193	7	common	common	ADJ
ejpam-3298	193	8	fixed	fix	VERB
ejpam-3298	193	9	point	point	NOUN
ejpam-3298	193	10	in	in	ADP
ejpam-3298	193	11	x.	x.	NOUN
ejpam-3298	193	12	4	4	NUM
ejpam-3298	193	13	.	.	PUNCT
ejpam-3298	194	1	an	an	DET
ejpam-3298	194	2	application	application	NOUN
ejpam-3298	194	3	throughout	throughout	ADP
ejpam-3298	194	4	in	in	ADP
ejpam-3298	194	5	this	this	DET
ejpam-3298	194	6	section	section	NOUN
ejpam-3298	194	7	,	,	PUNCT
ejpam-3298	194	8	let	let	VERB
ejpam-3298	194	9	x	x	PRON
ejpam-3298	194	10	and	and	CCONJ
ejpam-3298	194	11	y	y	PROPN
ejpam-3298	194	12	be	be	VERB
ejpam-3298	194	13	banach	banach	ADV
ejpam-3298	194	14	spaces	space	NOUN
ejpam-3298	194	15	s	s	NOUN
ejpam-3298	194	16	⊆	⊆	NUM
ejpam-3298	194	17	x	x	NOUN
ejpam-3298	194	18	be	be	AUX
ejpam-3298	194	19	the	the	DET
ejpam-3298	194	20	state	state	NOUN
ejpam-3298	194	21	space	space	NOUN
ejpam-3298	194	22	and	and	CCONJ
ejpam-3298	194	23	d	d	PROPN
ejpam-3298	194	24	⊆	⊆	NUM
ejpam-3298	194	25	y	y	PROPN
ejpam-3298	194	26	be	be	AUX
ejpam-3298	194	27	decision	decision	NOUN
ejpam-3298	194	28	space	space	NOUN
ejpam-3298	194	29	.	.	PUNCT
ejpam-3298	195	1	b(s	b(	NOUN
ejpam-3298	195	2	)	)	PUNCT
ejpam-3298	195	3	denotes	denote	VERB
ejpam-3298	195	4	the	the	DET
ejpam-3298	195	5	set	set	NOUN
ejpam-3298	195	6	of	of	ADP
ejpam-3298	195	7	all	all	DET
ejpam-3298	195	8	real	real	ADV
ejpam-3298	195	9	-	-	PUNCT
ejpam-3298	195	10	valued	value	VERB
ejpam-3298	195	11	bounded	bound	VERB
ejpam-3298	195	12	functions	function	NOUN
ejpam-3298	195	13	on	on	ADP
ejpam-3298	195	14	s.put	s.put	VERB
ejpam-3298	195	15	d(a	d(a	PROPN
ejpam-3298	195	16	,	,	PUNCT
ejpam-3298	195	17	b	b	NOUN
ejpam-3298	195	18	)	)	PUNCT
ejpam-3298	196	1	=	=	SYM
ejpam-3298	196	2	supx∈s	supx∈s	PROPN
ejpam-3298	196	3	|a(x)−	|a(x)−	PROPN
ejpam-3298	196	4	b(x)|,∀a	b(x)|,∀a	PROPN
ejpam-3298	196	5	,	,	PUNCT
ejpam-3298	196	6	b	b	X
ejpam-3298	196	7	∈	∈	PROPN
ejpam-3298	196	8	b(s).it	b(s).it	NOUN
ejpam-3298	196	9	is	be	AUX
ejpam-3298	196	10	obvious	obvious	ADJ
ejpam-3298	196	11	that	that	SCONJ
ejpam-3298	196	12	(	(	PUNCT
ejpam-3298	196	13	b(s	b(	NOUN
ejpam-3298	196	14	)	)	PUNCT
ejpam-3298	196	15	,	,	PUNCT
ejpam-3298	196	16	d	d	X
ejpam-3298	196	17	)	)	PUNCT
ejpam-3298	196	18	is	be	AUX
ejpam-3298	196	19	a	a	DET
ejpam-3298	196	20	complete	complete	ADJ
ejpam-3298	196	21	metric	metric	ADJ
ejpam-3298	196	22	space	space	NOUN
ejpam-3298	196	23	.	.	PUNCT
ejpam-3298	197	1	define	define	VERB
ejpam-3298	197	2	u	u	NOUN
ejpam-3298	197	3	:	:	PUNCT
ejpam-3298	198	1	s×d	s×d	PROPN
ejpam-3298	198	2	→	→	SYM
ejpam-3298	198	3	r	r	PROPN
ejpam-3298	198	4	,	,	PUNCT
ejpam-3298	198	5	t	t	NOUN
ejpam-3298	198	6	:	:	PUNCT
ejpam-3298	198	7	s×d	s×d	PROPN
ejpam-3298	198	8	→	→	SYM
ejpam-3298	198	9	s	s	VERB
ejpam-3298	198	10	andhi	andhi	NOUN
ejpam-3298	198	11	:	:	PUNCT
ejpam-3298	198	12	s×d×r→	s×d×r→	NOUN
ejpam-3298	198	13	r	r	NOUN
ejpam-3298	198	14	for	for	ADP
ejpam-3298	198	15	i	i	PRON
ejpam-3298	198	16	=	=	PUNCT
ejpam-3298	198	17	{	{	PUNCT
ejpam-3298	198	18	1	1	NUM
ejpam-3298	198	19	,	,	PUNCT
ejpam-3298	198	20	2	2	NUM
ejpam-3298	198	21	,	,	PUNCT
ejpam-3298	198	22	3	3	NUM
ejpam-3298	198	23	}	}	PUNCT
ejpam-3298	198	24	.	.	PUNCT
ejpam-3298	199	1	now	now	ADV
ejpam-3298	199	2	we	we	PRON
ejpam-3298	199	3	study	study	VERB
ejpam-3298	199	4	those	those	DET
ejpam-3298	199	5	conditions	condition	NOUN
ejpam-3298	199	6	which	which	PRON
ejpam-3298	199	7	guarantee	guarantee	VERB
ejpam-3298	199	8	the	the	DET
ejpam-3298	199	9	existence	existence	NOUN
ejpam-3298	199	10	and	and	CCONJ
ejpam-3298	199	11	uniqueness	uniqueness	NOUN
ejpam-3298	199	12	of	of	ADP
ejpam-3298	199	13	common	common	ADJ
ejpam-3298	199	14	solutions	solution	NOUN
ejpam-3298	199	15	of	of	ADP
ejpam-3298	199	16	functional	functional	ADJ
ejpam-3298	199	17	equations	equation	NOUN
ejpam-3298	199	18	(	(	PUNCT
ejpam-3298	199	19	7	7	NUM
ejpam-3298	199	20	)	)	PUNCT
ejpam-3298	199	21	.	.	PUNCT
ejpam-3298	200	1	theorem	theorem	NOUN
ejpam-3298	200	2	3	3	NUM
ejpam-3298	200	3	.	.	PUNCT
ejpam-3298	201	1	if	if	SCONJ
ejpam-3298	201	2	the	the	DET
ejpam-3298	201	3	following	follow	VERB
ejpam-3298	201	4	conditions	condition	NOUN
ejpam-3298	201	5	are	be	AUX
ejpam-3298	201	6	satisfied	satisfied	ADJ
ejpam-3298	201	7	(	(	PUNCT
ejpam-3298	201	8	c1	c1	NOUN
ejpam-3298	201	9	)	)	PUNCT
ejpam-3298	201	10	u	u	NOUN
ejpam-3298	201	11	and	and	CCONJ
ejpam-3298	201	12	hi	hi	INTJ
ejpam-3298	201	13	are	be	AUX
ejpam-3298	201	14	bounded	bound	VERB
ejpam-3298	201	15	for	for	ADP
ejpam-3298	201	16	i	i	PRON
ejpam-3298	201	17	=	=	PUNCT
ejpam-3298	201	18	{	{	PUNCT
ejpam-3298	201	19	1	1	NUM
ejpam-3298	201	20	,	,	PUNCT
ejpam-3298	201	21	2	2	NUM
ejpam-3298	201	22	,	,	PUNCT
ejpam-3298	201	23	3	3	NUM
ejpam-3298	201	24	}	}	PUNCT
ejpam-3298	201	25	(	(	PUNCT
ejpam-3298	201	26	c2	c2	PROPN
ejpam-3298	201	27	)	)	PUNCT
ejpam-3298	201	28	there	there	PRON
ejpam-3298	201	29	exist	exist	VERB
ejpam-3298	201	30	φ	φ	PROPN
ejpam-3298	201	31	∈	∈	PROPN
ejpam-3298	201	32	φ	φ	X
ejpam-3298	201	33	,	,	PUNCT
ejpam-3298	201	34	ψ	ψ	PROPN
ejpam-3298	201	35	∈	∈	PROPN
ejpam-3298	201	36	ψ	ψ	NOUN
ejpam-3298	201	37	and	and	CCONJ
ejpam-3298	201	38	w	w	PROPN
ejpam-3298	201	39	∈w	∈w	NOUN
ejpam-3298	201	40	satisfying	satisfy	VERB
ejpam-3298	201	41	ψ|h1(x	ψ|h1(x	PROPN
ejpam-3298	201	42	,	,	PUNCT
ejpam-3298	201	43	y	y	NOUN
ejpam-3298	201	44	,	,	PUNCT
ejpam-3298	201	45	a(t	a(t	NOUN
ejpam-3298	201	46	)	)	PUNCT
ejpam-3298	201	47	)	)	PUNCT
ejpam-3298	202	1	−	−	PROPN
ejpam-3298	202	2	h2(x	h2(x	PROPN
ejpam-3298	202	3	,	,	PUNCT
ejpam-3298	202	4	y	y	PROPN
ejpam-3298	202	5	,	,	PUNCT
ejpam-3298	202	6	b(t))|	b(t))|	VERB
ejpam-3298	202	7	≤	≤	NOUN
ejpam-3298	202	8	max{φ(d(ha	max{φ(d(ha	NOUN
ejpam-3298	202	9	,	,	PUNCT
ejpam-3298	202	10	hb	hb	PROPN
ejpam-3298	202	11	)	)	PUNCT
ejpam-3298	202	12	)	)	PUNCT
ejpam-3298	202	13	,	,	PUNCT
ejpam-3298	202	14	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	202	15	,	,	PUNCT
ejpam-3298	202	16	fa	fa	NOUN
ejpam-3298	202	17	)	)	PUNCT
ejpam-3298	202	18	)	)	PUNCT
ejpam-3298	202	19	,	,	PUNCT
ejpam-3298	202	20	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	202	21	,	,	PUNCT
ejpam-3298	202	22	gb	gb	NOUN
ejpam-3298	202	23	)	)	PUNCT
ejpam-3298	202	24	)	)	PUNCT
ejpam-3298	202	25	,	,	PUNCT
ejpam-3298	202	26	φ	φ	X
ejpam-3298	202	27	(	(	PUNCT
ejpam-3298	202	28	1	1	NUM
ejpam-3298	202	29	2	2	NUM
ejpam-3298	202	30	[	[	X
ejpam-3298	202	31	d(ha	d(ha	NOUN
ejpam-3298	202	32	,	,	PUNCT
ejpam-3298	202	33	hb	hb	PROPN
ejpam-3298	202	34	)	)	PUNCT
ejpam-3298	202	35	+	+	NUM
ejpam-3298	202	36	d(fa	d(fa	NOUN
ejpam-3298	202	37	,	,	PUNCT
ejpam-3298	202	38	gb	gb	NOUN
ejpam-3298	202	39	)	)	PUNCT
ejpam-3298	202	40	]	]	PUNCT
ejpam-3298	202	41	)	)	PUNCT
ejpam-3298	202	42	}	}	PUNCT
ejpam-3298	202	43	−	−	PROPN
ejpam-3298	202	44	w(max{φ(d(ha	w(max{φ(d(ha	NOUN
ejpam-3298	202	45	,	,	PUNCT
ejpam-3298	202	46	hb	hb	PROPN
ejpam-3298	202	47	)	)	PUNCT
ejpam-3298	202	48	)	)	PUNCT
ejpam-3298	202	49	,	,	PUNCT
ejpam-3298	202	50	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	202	51	,	,	PUNCT
ejpam-3298	202	52	fa	fa	NOUN
ejpam-3298	202	53	)	)	PUNCT
ejpam-3298	202	54	)	)	PUNCT
ejpam-3298	202	55	,	,	PUNCT
ejpam-3298	202	56	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	202	57	,	,	PUNCT
ejpam-3298	202	58	gb	gb	NOUN
ejpam-3298	202	59	)	)	PUNCT
ejpam-3298	202	60	)	)	PUNCT
ejpam-3298	202	61	,	,	PUNCT
ejpam-3298	202	62	φ	φ	X
ejpam-3298	202	63	(	(	PUNCT
ejpam-3298	202	64	1	1	NUM
ejpam-3298	202	65	2	2	NUM
ejpam-3298	202	66	[	[	X
ejpam-3298	202	67	d(ha	d(ha	NOUN
ejpam-3298	202	68	,	,	PUNCT
ejpam-3298	202	69	hb	hb	PROPN
ejpam-3298	202	70	)	)	PUNCT
ejpam-3298	202	71	+	+	NUM
ejpam-3298	202	72	d(fa	d(fa	NOUN
ejpam-3298	202	73	,	,	PUNCT
ejpam-3298	202	74	gb	gb	NOUN
ejpam-3298	202	75	)	)	PUNCT
ejpam-3298	202	76	]	]	PUNCT
ejpam-3298	202	77	)	)	PUNCT
ejpam-3298	202	78	}	}	PUNCT
ejpam-3298	202	79	)	)	PUNCT
ejpam-3298	203	1	p.	p.	NOUN
ejpam-3298	203	2	semwal	semwal	NOUN
ejpam-3298	203	3	,	,	PUNCT
ejpam-3298	203	4	komal	komal	PROPN
ejpam-3298	203	5	/	/	SYM
ejpam-3298	203	6	eur	eur	PROPN
ejpam-3298	203	7	.	.	PUNCT
ejpam-3298	204	1	j.	j.	PROPN
ejpam-3298	204	2	pure	pure	PROPN
ejpam-3298	204	3	appl	appl	PROPN
ejpam-3298	204	4	.	.	PROPN
ejpam-3298	204	5	math	math	PROPN
ejpam-3298	204	6	,	,	PUNCT
ejpam-3298	204	7	11	11	NUM
ejpam-3298	204	8	(	(	PUNCT
ejpam-3298	204	9	4	4	NUM
ejpam-3298	204	10	)	)	PUNCT
ejpam-3298	204	11	(	(	PUNCT
ejpam-3298	204	12	2018	2018	NUM
ejpam-3298	204	13	)	)	PUNCT
ejpam-3298	204	14	,	,	PUNCT
ejpam-3298	204	15	1177	1177	NUM
ejpam-3298	204	16	-	-	SYM
ejpam-3298	204	17	1190	1190	NUM
ejpam-3298	204	18	1187	1187	NUM
ejpam-3298	204	19	for	for	ADP
ejpam-3298	204	20	all	all	DET
ejpam-3298	204	21	(	(	PUNCT
ejpam-3298	204	22	x	x	NOUN
ejpam-3298	204	23	,	,	PUNCT
ejpam-3298	204	24	y	y	NOUN
ejpam-3298	204	25	)	)	PUNCT
ejpam-3298	204	26	∈	∈	PROPN
ejpam-3298	204	27	s	s	PART
ejpam-3298	204	28	×d	×d	NOUN
ejpam-3298	204	29	;	;	PUNCT
ejpam-3298	204	30	a	a	DET
ejpam-3298	204	31	,	,	PUNCT
ejpam-3298	204	32	b	b	PROPN
ejpam-3298	204	33	∈	∈	PROPN
ejpam-3298	204	34	b(s	b(	NOUN
ejpam-3298	204	35	)	)	PUNCT
ejpam-3298	204	36	and	and	CCONJ
ejpam-3298	204	37	t	t	NOUN
ejpam-3298	204	38	∈	∈	PROPN
ejpam-3298	204	39	s.where	s.where	SCONJ
ejpam-3298	204	40	f	f	PROPN
ejpam-3298	204	41	,	,	PUNCT
ejpam-3298	204	42	g	g	PROPN
ejpam-3298	204	43	and	and	CCONJ
ejpam-3298	204	44	h	h	NOUN
ejpam-3298	204	45	are	be	AUX
ejpam-3298	204	46	defined	define	VERB
ejpam-3298	204	47	as	as	SCONJ
ejpam-3298	204	48	follows	follow	VERB
ejpam-3298	204	49	:	:	PUNCT
ejpam-3298	204	50	for	for	ADP
ejpam-3298	204	51	all	all	PRON
ejpam-3298	204	52	x	x	SYM
ejpam-3298	204	53	∈	∈	PROPN
ejpam-3298	204	54	s	s	NOUN
ejpam-3298	204	55	,	,	PUNCT
ejpam-3298	204	56	ai	ai	VERB
ejpam-3298	204	57	∈	∈	PROPN
ejpam-3298	204	58	b(s	b(	NOUN
ejpam-3298	204	59	)	)	PUNCT
ejpam-3298	204	60	and	and	CCONJ
ejpam-3298	204	61	i	i	PRON
ejpam-3298	204	62	=	=	PUNCT
ejpam-3298	204	63	{	{	PUNCT
ejpam-3298	204	64	1	1	NUM
ejpam-3298	204	65	,	,	PUNCT
ejpam-3298	204	66	2	2	NUM
ejpam-3298	204	67	,	,	PUNCT
ejpam-3298	204	68	3	3	NUM
ejpam-3298	204	69	}	}	SYM
ejpam-3298	204	70	f(a1(x	f(a1(x	NOUN
ejpam-3298	204	71	)	)	PUNCT
ejpam-3298	204	72	)	)	PUNCT
ejpam-3298	205	1	=	=	SYM
ejpam-3298	205	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	205	3	,	,	PUNCT
ejpam-3298	205	4	y	y	NOUN
ejpam-3298	205	5	)	)	PUNCT
ejpam-3298	206	1	+	+	NOUN
ejpam-3298	206	2	h1(x	h1(x	PROPN
ejpam-3298	206	3	,	,	PUNCT
ejpam-3298	206	4	y	y	PROPN
ejpam-3298	206	5	,	,	PUNCT
ejpam-3298	206	6	a1(t	a1(t	PROPN
ejpam-3298	206	7	(	(	PUNCT
ejpam-3298	206	8	x	x	NOUN
ejpam-3298	206	9	,	,	PUNCT
ejpam-3298	206	10	y	y	NOUN
ejpam-3298	206	11	)	)	PUNCT
ejpam-3298	206	12	)	)	PUNCT
ejpam-3298	206	13	)	)	PUNCT
ejpam-3298	206	14	}	}	PUNCT
ejpam-3298	206	15	g(a2(x	g(a2(x	PROPN
ejpam-3298	206	16	)	)	PUNCT
ejpam-3298	206	17	)	)	PUNCT
ejpam-3298	207	1	=	=	SYM
ejpam-3298	207	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	207	3	,	,	PUNCT
ejpam-3298	207	4	y	y	NOUN
ejpam-3298	207	5	)	)	PUNCT
ejpam-3298	208	1	+	+	PROPN
ejpam-3298	208	2	h2(x	h2(x	PROPN
ejpam-3298	208	3	,	,	PUNCT
ejpam-3298	208	4	y	y	PROPN
ejpam-3298	208	5	,	,	PUNCT
ejpam-3298	208	6	a2(t	a2(t	PRON
ejpam-3298	208	7	(	(	PUNCT
ejpam-3298	208	8	x	x	NOUN
ejpam-3298	208	9	,	,	PUNCT
ejpam-3298	208	10	y	y	NOUN
ejpam-3298	208	11	)	)	PUNCT
ejpam-3298	208	12	)	)	PUNCT
ejpam-3298	208	13	)	)	PUNCT
ejpam-3298	208	14	}	}	PUNCT
ejpam-3298	208	15	h(a3(x	h(a3(x	NOUN
ejpam-3298	208	16	)	)	PUNCT
ejpam-3298	208	17	)	)	PUNCT
ejpam-3298	209	1	=	=	SYM
ejpam-3298	209	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	209	3	,	,	PUNCT
ejpam-3298	209	4	y	y	NOUN
ejpam-3298	209	5	)	)	PUNCT
ejpam-3298	209	6	+	+	PROPN
ejpam-3298	209	7	h3(x	h3(x	PROPN
ejpam-3298	209	8	,	,	PUNCT
ejpam-3298	209	9	y	y	PROPN
ejpam-3298	209	10	,	,	PUNCT
ejpam-3298	209	11	a3(t	a3(t	PROPN
ejpam-3298	209	12	(	(	PUNCT
ejpam-3298	209	13	x	x	PROPN
ejpam-3298	209	14	,	,	PUNCT
ejpam-3298	209	15	y	y	NOUN
ejpam-3298	209	16	)	)	PUNCT
ejpam-3298	209	17	)	)	PUNCT
ejpam-3298	209	18	)	)	PUNCT
ejpam-3298	209	19	}	}	PUNCT
ejpam-3298	209	20	(	(	PUNCT
ejpam-3298	209	21	c3	c3	NOUN
ejpam-3298	209	22	)	)	PUNCT
ejpam-3298	209	23	f(b(s	f(b(	NOUN
ejpam-3298	209	24	)	)	PUNCT
ejpam-3298	209	25	)	)	PUNCT
ejpam-3298	209	26	∪	∪	ADP
ejpam-3298	209	27	g(b(s	g(b(	NOUN
ejpam-3298	209	28	)	)	PUNCT
ejpam-3298	209	29	)	)	PUNCT
ejpam-3298	209	30	⊆	⊆	NUM
ejpam-3298	209	31	h(b(s	h(b(	NOUN
ejpam-3298	209	32	)	)	PUNCT
ejpam-3298	209	33	)	)	PUNCT
ejpam-3298	209	34	and	and	CCONJ
ejpam-3298	209	35	h	h	NOUN
ejpam-3298	209	36	is	be	AUX
ejpam-3298	209	37	asymptotically	asymptotically	ADV
ejpam-3298	209	38	continuous	continuous	ADJ
ejpam-3298	209	39	and	and	CCONJ
ejpam-3298	209	40	weakly	weakly	ADJ
ejpam-3298	209	41	commute	commute	NOUN
ejpam-3298	209	42	with	with	ADP
ejpam-3298	209	43	both	both	DET
ejpam-3298	209	44	f	f	PROPN
ejpam-3298	209	45	and	and	CCONJ
ejpam-3298	209	46	g.	g.	PROPN
ejpam-3298	209	47	then	then	ADV
ejpam-3298	209	48	the	the	DET
ejpam-3298	209	49	system	system	NOUN
ejpam-3298	209	50	of	of	ADP
ejpam-3298	209	51	functional	functional	ADJ
ejpam-3298	209	52	equations	equation	NOUN
ejpam-3298	209	53	possess	possess	VERB
ejpam-3298	209	54	a	a	DET
ejpam-3298	209	55	unique	unique	ADJ
ejpam-3298	209	56	common	common	ADJ
ejpam-3298	209	57	solution	solution	NOUN
ejpam-3298	209	58	in	in	ADP
ejpam-3298	209	59	b(s	b(	NOUN
ejpam-3298	209	60	)	)	PUNCT
ejpam-3298	209	61	.	.	PUNCT
ejpam-3298	210	1	proof	proof	NOUN
ejpam-3298	210	2	from	from	ADP
ejpam-3298	210	3	(	(	PUNCT
ejpam-3298	210	4	c1	c1	PROPN
ejpam-3298	210	5	)	)	PUNCT
ejpam-3298	210	6	and	and	CCONJ
ejpam-3298	210	7	(	(	PUNCT
ejpam-3298	210	8	c2	c2	PROPN
ejpam-3298	210	9	)	)	PUNCT
ejpam-3298	210	10	,	,	PUNCT
ejpam-3298	210	11	f	f	X
ejpam-3298	210	12	,	,	PUNCT
ejpam-3298	210	13	g	g	PROPN
ejpam-3298	210	14	and	and	CCONJ
ejpam-3298	210	15	h	h	PROPN
ejpam-3298	210	16	be	be	VERB
ejpam-3298	210	17	self	self	NOUN
ejpam-3298	210	18	maps	map	NOUN
ejpam-3298	210	19	on	on	ADP
ejpam-3298	210	20	b(s	b(	NOUN
ejpam-3298	210	21	)	)	PUNCT
ejpam-3298	210	22	.	.	PUNCT
ejpam-3298	211	1	let	let	VERB
ejpam-3298	211	2	a	a	PRON
ejpam-3298	211	3	,	,	PUNCT
ejpam-3298	211	4	b	b	PROPN
ejpam-3298	211	5	∈	∈	PROPN
ejpam-3298	211	6	b(s	b(	NOUN
ejpam-3298	211	7	)	)	PUNCT
ejpam-3298	211	8	and	and	CCONJ
ejpam-3298	211	9	x	x	PUNCT
ejpam-3298	211	10	∈	∈	NOUN
ejpam-3298	211	11	s.for	s.for	ADP
ejpam-3298	211	12	any	any	DET
ejpam-3298	211	13	ε	ε	PROPN
ejpam-3298	211	14	>	>	X
ejpam-3298	211	15	0	0	PUNCT
ejpam-3298	212	1	there	there	PRON
ejpam-3298	212	2	exist	exist	VERB
ejpam-3298	212	3	y	y	PROPN
ejpam-3298	212	4	,	,	PUNCT
ejpam-3298	212	5	z	z	NOUN
ejpam-3298	212	6	∈	∈	PROPN
ejpam-3298	212	7	d	d	ADP
ejpam-3298	212	8	satisfying	satisfy	VERB
ejpam-3298	212	9	f(a(x	f(a(x	NOUN
ejpam-3298	212	10	)	)	PUNCT
ejpam-3298	212	11	)	)	PUNCT
ejpam-3298	213	1	<	<	X
ejpam-3298	213	2	u(x	u(x	PROPN
ejpam-3298	213	3	,	,	PUNCT
ejpam-3298	213	4	y	y	NOUN
ejpam-3298	213	5	)	)	PUNCT
ejpam-3298	214	1	+	+	NOUN
ejpam-3298	214	2	h1(x	h1(x	PROPN
ejpam-3298	214	3	,	,	PUNCT
ejpam-3298	214	4	y	y	NOUN
ejpam-3298	214	5	,	,	PUNCT
ejpam-3298	214	6	a(t	a(t	PROPN
ejpam-3298	214	7	(	(	PUNCT
ejpam-3298	214	8	x	x	X
ejpam-3298	214	9	,	,	PUNCT
ejpam-3298	214	10	y	y	NOUN
ejpam-3298	214	11	)	)	PUNCT
ejpam-3298	214	12	)	)	PUNCT
ejpam-3298	214	13	)	)	PUNCT
ejpam-3298	215	1	+	+	CCONJ
ejpam-3298	215	2	ε	ε	PROPN
ejpam-3298	215	3	g(b(x	g(b(x	PROPN
ejpam-3298	215	4	)	)	PUNCT
ejpam-3298	215	5	)	)	PUNCT
ejpam-3298	216	1	<	<	X
ejpam-3298	216	2	u(x	u(x	PROPN
ejpam-3298	216	3	,	,	PUNCT
ejpam-3298	216	4	z	z	NOUN
ejpam-3298	216	5	)	)	PUNCT
ejpam-3298	217	1	+	+	PROPN
ejpam-3298	217	2	h2(x	h2(x	PROPN
ejpam-3298	217	3	,	,	PUNCT
ejpam-3298	217	4	z	z	PROPN
ejpam-3298	217	5	,	,	PUNCT
ejpam-3298	217	6	b(t	b(t	PROPN
ejpam-3298	217	7	(	(	PUNCT
ejpam-3298	217	8	x	x	X
ejpam-3298	217	9	,	,	PUNCT
ejpam-3298	217	10	z	z	NOUN
ejpam-3298	217	11	)	)	PUNCT
ejpam-3298	217	12	)	)	PUNCT
ejpam-3298	217	13	)	)	PUNCT
ejpam-3298	218	1	+	+	CCONJ
ejpam-3298	218	2	ε	ε	PROPN
ejpam-3298	218	3	f(a(x	f(a(x	PROPN
ejpam-3298	218	4	)	)	PUNCT
ejpam-3298	218	5	)	)	PUNCT
ejpam-3298	218	6	≥	≥	NOUN
ejpam-3298	218	7	u(x	u(x	NOUN
ejpam-3298	218	8	,	,	PUNCT
ejpam-3298	218	9	z	z	NOUN
ejpam-3298	218	10	)	)	PUNCT
ejpam-3298	219	1	+	+	NOUN
ejpam-3298	219	2	h1(x	h1(x	NOUN
ejpam-3298	219	3	,	,	PUNCT
ejpam-3298	219	4	z	z	NOUN
ejpam-3298	219	5	,	,	PUNCT
ejpam-3298	219	6	a(t	a(t	NOUN
ejpam-3298	219	7	(	(	PUNCT
ejpam-3298	219	8	x	x	X
ejpam-3298	219	9	,	,	PUNCT
ejpam-3298	219	10	z	z	NOUN
ejpam-3298	219	11	)	)	PUNCT
ejpam-3298	219	12	)	)	PUNCT
ejpam-3298	219	13	)	)	PUNCT
ejpam-3298	220	1	+	+	CCONJ
ejpam-3298	220	2	ε	ε	PROPN
ejpam-3298	220	3	g(b(x	g(b(x	PROPN
ejpam-3298	220	4	)	)	PUNCT
ejpam-3298	220	5	)	)	PUNCT
ejpam-3298	221	1	≥	≥	NOUN
ejpam-3298	221	2	u(x	u(x	PROPN
ejpam-3298	221	3	,	,	PUNCT
ejpam-3298	221	4	y	y	NOUN
ejpam-3298	221	5	)	)	PUNCT
ejpam-3298	222	1	+	+	PROPN
ejpam-3298	222	2	h2(x	h2(x	PROPN
ejpam-3298	222	3	,	,	PUNCT
ejpam-3298	222	4	y	y	PROPN
ejpam-3298	222	5	,	,	PUNCT
ejpam-3298	222	6	b(t	b(t	PROPN
ejpam-3298	222	7	(	(	PUNCT
ejpam-3298	222	8	x	x	X
ejpam-3298	222	9	,	,	PUNCT
ejpam-3298	222	10	y	y	NOUN
ejpam-3298	222	11	)	)	PUNCT
ejpam-3298	222	12	)	)	PUNCT
ejpam-3298	222	13	)	)	PUNCT
ejpam-3298	223	1	+	+	CCONJ
ejpam-3298	223	2	ε	ε	PROPN
ejpam-3298	223	3	combining	combine	VERB
ejpam-3298	223	4	above	above	ADP
ejpam-3298	223	5	inequalities	inequality	NOUN
ejpam-3298	223	6	with	with	ADP
ejpam-3298	223	7	(	(	PUNCT
ejpam-3298	223	8	c2	c2	PROPN
ejpam-3298	223	9	)	)	PUNCT
ejpam-3298	223	10	,	,	PUNCT
ejpam-3298	223	11	we	we	PRON
ejpam-3298	223	12	obtain	obtain	VERB
ejpam-3298	223	13	the	the	DET
ejpam-3298	223	14	following	following	NOUN
ejpam-3298	223	15	:	:	PUNCT
ejpam-3298	223	16	ψ(|f(a(x))−	ψ(|f(a(x))−	NUM
ejpam-3298	223	17	g(b(x))|	g(b(x))|	NOUN
ejpam-3298	223	18	)	)	PUNCT
ejpam-3298	223	19	≤	≤	PROPN
ejpam-3298	223	20	ψ(ε	ψ(ε	PROPN
ejpam-3298	223	21	)	)	PUNCT
ejpam-3298	224	1	+	+	CCONJ
ejpam-3298	224	2	ψ(max{|h1(x	ψ(max{|h1(x	PROPN
ejpam-3298	224	3	,	,	PUNCT
ejpam-3298	224	4	y	y	NOUN
ejpam-3298	224	5	,	,	PUNCT
ejpam-3298	224	6	a(t	a(t	NOUN
ejpam-3298	224	7	(	(	PUNCT
ejpam-3298	224	8	x	x	X
ejpam-3298	224	9	,	,	PUNCT
ejpam-3298	224	10	y)))−h2(x	y)))−h2(x	PROPN
ejpam-3298	224	11	,	,	PUNCT
ejpam-3298	224	12	y	y	PROPN
ejpam-3298	224	13	,	,	PUNCT
ejpam-3298	224	14	b(t	b(t	PROPN
ejpam-3298	224	15	(	(	PUNCT
ejpam-3298	224	16	x	x	X
ejpam-3298	224	17	,	,	PUNCT
ejpam-3298	224	18	y)))|	y)))|	PROPN
ejpam-3298	224	19	,	,	PUNCT
ejpam-3298	224	20	|h1(x	|h1(x	NUM
ejpam-3298	224	21	,	,	PUNCT
ejpam-3298	224	22	z	z	NOUN
ejpam-3298	224	23	,	,	PUNCT
ejpam-3298	224	24	a(t	a(t	NOUN
ejpam-3298	224	25	(	(	PUNCT
ejpam-3298	224	26	x	x	X
ejpam-3298	224	27	,	,	PUNCT
ejpam-3298	224	28	z)))−h2(x	z)))−h2(x	NUM
ejpam-3298	224	29	,	,	PUNCT
ejpam-3298	224	30	z	z	PROPN
ejpam-3298	224	31	,	,	PUNCT
ejpam-3298	224	32	b(t	b(t	PROPN
ejpam-3298	224	33	(	(	PUNCT
ejpam-3298	224	34	x	x	X
ejpam-3298	224	35	,	,	PUNCT
ejpam-3298	224	36	z)))|	z)))|	PROPN
ejpam-3298	224	37	}	}	PUNCT
ejpam-3298	224	38	)	)	PUNCT
ejpam-3298	224	39	≤	≤	PROPN
ejpam-3298	224	40	ψ(ε	ψ(ε	PROPN
ejpam-3298	224	41	)	)	PUNCT
ejpam-3298	225	1	+	+	ADV
ejpam-3298	225	2	max{φ(d(ha	max{φ(d(ha	NOUN
ejpam-3298	225	3	,	,	PUNCT
ejpam-3298	225	4	hb	hb	NOUN
ejpam-3298	225	5	)	)	PUNCT
ejpam-3298	225	6	)	)	PUNCT
ejpam-3298	225	7	,	,	PUNCT
ejpam-3298	225	8	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	225	9	,	,	PUNCT
ejpam-3298	225	10	fa	fa	NOUN
ejpam-3298	225	11	)	)	PUNCT
ejpam-3298	225	12	)	)	PUNCT
ejpam-3298	225	13	,	,	PUNCT
ejpam-3298	225	14	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	225	15	,	,	PUNCT
ejpam-3298	225	16	gb	gb	NOUN
ejpam-3298	225	17	)	)	PUNCT
ejpam-3298	225	18	)	)	PUNCT
ejpam-3298	225	19	,	,	PUNCT
ejpam-3298	225	20	φ	φ	X
ejpam-3298	225	21	(	(	PUNCT
ejpam-3298	225	22	1	1	NUM
ejpam-3298	225	23	2	2	NUM
ejpam-3298	225	24	[	[	X
ejpam-3298	225	25	d(ha	d(ha	NOUN
ejpam-3298	225	26	,	,	PUNCT
ejpam-3298	225	27	hb	hb	PROPN
ejpam-3298	225	28	)	)	PUNCT
ejpam-3298	225	29	+	+	NUM
ejpam-3298	225	30	d(fa	d(fa	NOUN
ejpam-3298	225	31	,	,	PUNCT
ejpam-3298	225	32	gb	gb	NOUN
ejpam-3298	225	33	)	)	PUNCT
ejpam-3298	225	34	]	]	PUNCT
ejpam-3298	225	35	)	)	PUNCT
ejpam-3298	225	36	}	}	PUNCT
ejpam-3298	225	37	−	−	PROPN
ejpam-3298	225	38	w(max{φ(d(ha	w(max{φ(d(ha	NOUN
ejpam-3298	225	39	,	,	PUNCT
ejpam-3298	225	40	hb	hb	PROPN
ejpam-3298	225	41	)	)	PUNCT
ejpam-3298	225	42	)	)	PUNCT
ejpam-3298	225	43	,	,	PUNCT
ejpam-3298	225	44	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	225	45	,	,	PUNCT
ejpam-3298	225	46	fa	fa	NOUN
ejpam-3298	225	47	)	)	PUNCT
ejpam-3298	225	48	)	)	PUNCT
ejpam-3298	225	49	,	,	PUNCT
ejpam-3298	225	50	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	225	51	,	,	PUNCT
ejpam-3298	225	52	gb	gb	NOUN
ejpam-3298	225	53	)	)	PUNCT
ejpam-3298	225	54	)	)	PUNCT
ejpam-3298	225	55	,	,	PUNCT
ejpam-3298	225	56	φ	φ	X
ejpam-3298	225	57	(	(	PUNCT
ejpam-3298	225	58	1	1	NUM
ejpam-3298	225	59	2	2	NUM
ejpam-3298	225	60	[	[	X
ejpam-3298	225	61	d(ha	d(ha	NOUN
ejpam-3298	225	62	,	,	PUNCT
ejpam-3298	225	63	hb	hb	PROPN
ejpam-3298	225	64	)	)	PUNCT
ejpam-3298	225	65	+	+	NUM
ejpam-3298	225	66	d(fa	d(fa	NOUN
ejpam-3298	225	67	,	,	PUNCT
ejpam-3298	225	68	gb	gb	NOUN
ejpam-3298	225	69	)	)	PUNCT
ejpam-3298	225	70	]	]	PUNCT
ejpam-3298	225	71	)	)	PUNCT
ejpam-3298	225	72	}	}	PUNCT
ejpam-3298	225	73	)	)	PUNCT
ejpam-3298	226	1	letting	let	VERB
ejpam-3298	226	2	ε→∞	ε→∞	NUM
ejpam-3298	226	3	we	we	PRON
ejpam-3298	226	4	get	get	VERB
ejpam-3298	226	5	ψ(|f(a(x))−	ψ(|f(a(x))−	NUM
ejpam-3298	226	6	g(b(x))|	g(b(x))|	NOUN
ejpam-3298	226	7	)	)	PUNCT
ejpam-3298	226	8	≤	≤	NOUN
ejpam-3298	226	9	max{φ(d(ha	max{φ(d(ha	NOUN
ejpam-3298	226	10	,	,	PUNCT
ejpam-3298	226	11	hb	hb	PROPN
ejpam-3298	226	12	)	)	PUNCT
ejpam-3298	226	13	)	)	PUNCT
ejpam-3298	226	14	,	,	PUNCT
ejpam-3298	226	15	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	226	16	,	,	PUNCT
ejpam-3298	226	17	fa	fa	NOUN
ejpam-3298	226	18	)	)	PUNCT
ejpam-3298	226	19	)	)	PUNCT
ejpam-3298	226	20	,	,	PUNCT
ejpam-3298	226	21	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	226	22	,	,	PUNCT
ejpam-3298	226	23	gb	gb	NOUN
ejpam-3298	226	24	)	)	PUNCT
ejpam-3298	226	25	)	)	PUNCT
ejpam-3298	226	26	,	,	PUNCT
ejpam-3298	226	27	φ	φ	X
ejpam-3298	226	28	(	(	PUNCT
ejpam-3298	226	29	1	1	NUM
ejpam-3298	226	30	2	2	NUM
ejpam-3298	226	31	)	)	PUNCT
ejpam-3298	226	32	[	[	X
ejpam-3298	226	33	d(ha	d(ha	NOUN
ejpam-3298	226	34	,	,	PUNCT
ejpam-3298	226	35	hb	hb	PROPN
ejpam-3298	226	36	)	)	PUNCT
ejpam-3298	226	37	+	+	NUM
ejpam-3298	226	38	d(fa	d(fa	NOUN
ejpam-3298	226	39	,	,	PUNCT
ejpam-3298	226	40	gb	gb	NOUN
ejpam-3298	226	41	)	)	PUNCT
ejpam-3298	226	42	]	]	PUNCT
ejpam-3298	226	43	}	}	PUNCT
ejpam-3298	226	44	−	−	PROPN
ejpam-3298	226	45	w(max{φ(d(ha	w(max{φ(d(ha	NOUN
ejpam-3298	226	46	,	,	PUNCT
ejpam-3298	226	47	hb	hb	PROPN
ejpam-3298	226	48	)	)	PUNCT
ejpam-3298	226	49	)	)	PUNCT
ejpam-3298	226	50	,	,	PUNCT
ejpam-3298	226	51	φ(d(ha	φ(d(ha	NOUN
ejpam-3298	226	52	,	,	PUNCT
ejpam-3298	226	53	fa	fa	NOUN
ejpam-3298	226	54	)	)	PUNCT
ejpam-3298	226	55	)	)	PUNCT
ejpam-3298	226	56	,	,	PUNCT
ejpam-3298	226	57	φ(d(hb	φ(d(hb	NOUN
ejpam-3298	226	58	,	,	PUNCT
ejpam-3298	226	59	gb	gb	NOUN
ejpam-3298	226	60	)	)	PUNCT
ejpam-3298	226	61	)	)	PUNCT
ejpam-3298	226	62	,	,	PUNCT
ejpam-3298	226	63	φ	φ	X
ejpam-3298	226	64	(	(	PUNCT
ejpam-3298	226	65	1	1	NUM
ejpam-3298	226	66	2	2	NUM
ejpam-3298	226	67	[	[	X
ejpam-3298	226	68	d(ha	d(ha	NOUN
ejpam-3298	226	69	,	,	PUNCT
ejpam-3298	226	70	hb	hb	PROPN
ejpam-3298	226	71	)	)	PUNCT
ejpam-3298	226	72	+	+	NUM
ejpam-3298	226	73	d(fa	d(fa	NOUN
ejpam-3298	226	74	,	,	PUNCT
ejpam-3298	226	75	gb	gb	NOUN
ejpam-3298	226	76	)	)	PUNCT
ejpam-3298	226	77	]	]	PUNCT
ejpam-3298	226	78	)	)	PUNCT
ejpam-3298	226	79	}	}	PUNCT
ejpam-3298	226	80	)	)	PUNCT
ejpam-3298	226	81	therefore	therefore	ADV
ejpam-3298	226	82	,	,	PUNCT
ejpam-3298	226	83	theorem	theorem	VERB
ejpam-3298	226	84	3.1	3.1	NUM
ejpam-3298	226	85	ensures	ensure	VERB
ejpam-3298	226	86	that	that	SCONJ
ejpam-3298	226	87	f	f	PROPN
ejpam-3298	226	88	,	,	PUNCT
ejpam-3298	226	89	g	g	PROPN
ejpam-3298	226	90	and	and	CCONJ
ejpam-3298	226	91	h	h	NOUN
ejpam-3298	226	92	have	have	VERB
ejpam-3298	226	93	a	a	DET
ejpam-3298	226	94	unique	unique	ADJ
ejpam-3298	226	95	common	common	ADJ
ejpam-3298	226	96	fixed	fix	VERB
ejpam-3298	226	97	point	point	NOUN
ejpam-3298	226	98	in	in	ADP
ejpam-3298	226	99	b(s	b(	NOUN
ejpam-3298	226	100	)	)	PUNCT
ejpam-3298	226	101	.	.	PUNCT
ejpam-3298	227	1	that	that	PRON
ejpam-3298	227	2	is	be	AUX
ejpam-3298	227	3	,	,	PUNCT
ejpam-3298	227	4	the	the	DET
ejpam-3298	227	5	system	system	NOUN
ejpam-3298	227	6	of	of	ADP
ejpam-3298	227	7	functional	functional	ADJ
ejpam-3298	227	8	equations	equation	NOUN
ejpam-3298	227	9	(	(	PUNCT
ejpam-3298	227	10	7	7	X
ejpam-3298	227	11	)	)	PUNCT
ejpam-3298	227	12	possesses	possess	VERB
ejpam-3298	227	13	a	a	DET
ejpam-3298	227	14	unique	unique	ADJ
ejpam-3298	227	15	common	common	ADJ
ejpam-3298	227	16	solution	solution	NOUN
ejpam-3298	227	17	b(s	b(	NOUN
ejpam-3298	227	18	)	)	PUNCT
ejpam-3298	227	19	.	.	PUNCT
ejpam-3298	228	1	similarly	similarly	ADV
ejpam-3298	228	2	we	we	PRON
ejpam-3298	228	3	can	can	AUX
ejpam-3298	228	4	change	change	VERB
ejpam-3298	228	5	the	the	DET
ejpam-3298	228	6	condition	condition	NOUN
ejpam-3298	228	7	(	(	PUNCT
ejpam-3298	228	8	c2	c2	PROPN
ejpam-3298	228	9	)	)	PUNCT
ejpam-3298	228	10	in	in	ADP
ejpam-3298	228	11	theorem	theorem	ADJ
ejpam-3298	228	12	3.1	3.1	NUM
ejpam-3298	228	13	and	and	CCONJ
ejpam-3298	228	14	get	get	VERB
ejpam-3298	228	15	the	the	DET
ejpam-3298	228	16	common	common	ADJ
ejpam-3298	228	17	solution	solution	NOUN
ejpam-3298	228	18	using	use	VERB
ejpam-3298	228	19	corollaries	corollary	NOUN
ejpam-3298	228	20	.	.	PUNCT
ejpam-3298	229	1	taking	take	VERB
ejpam-3298	229	2	h	h	NOUN
ejpam-3298	230	1	=	=	PUNCT
ejpam-3298	230	2	i	i	PROPN
ejpam-3298	230	3	in	in	ADP
ejpam-3298	230	4	theorem	theorem	PROPN
ejpam-3298	230	5	,	,	PUNCT
ejpam-3298	230	6	we	we	PRON
ejpam-3298	230	7	conclude	conclude	VERB
ejpam-3298	230	8	that	that	SCONJ
ejpam-3298	230	9	references	reference	NOUN
ejpam-3298	230	10	1188	1188	NUM
ejpam-3298	230	11	theorem	theorem	NOUN
ejpam-3298	230	12	4	4	NUM
ejpam-3298	230	13	.	.	PUNCT
ejpam-3298	231	1	let	let	VERB
ejpam-3298	231	2	the	the	DET
ejpam-3298	231	3	following	follow	VERB
ejpam-3298	231	4	condition	condition	NOUN
ejpam-3298	231	5	hold	hold	VERB
ejpam-3298	231	6	:	:	PUNCT
ejpam-3298	231	7	(	(	PUNCT
ejpam-3298	231	8	c4	c4	NOUN
ejpam-3298	231	9	)	)	PUNCT
ejpam-3298	231	10	u	u	NOUN
ejpam-3298	231	11	and	and	CCONJ
ejpam-3298	231	12	hi	hi	INTJ
ejpam-3298	231	13	are	be	AUX
ejpam-3298	231	14	bounded	bound	VERB
ejpam-3298	231	15	for	for	ADP
ejpam-3298	231	16	i	i	PROPN
ejpam-3298	231	17	∈	∈	PROPN
ejpam-3298	231	18	{	{	PUNCT
ejpam-3298	231	19	1	1	NUM
ejpam-3298	231	20	,	,	PUNCT
ejpam-3298	231	21	2	2	NUM
ejpam-3298	231	22	}	}	PUNCT
ejpam-3298	231	23	.	.	PUNCT
ejpam-3298	232	1	(	(	PUNCT
ejpam-3298	232	2	c5	c5	PROPN
ejpam-3298	232	3	)	)	PUNCT
ejpam-3298	232	4	there	there	PRON
ejpam-3298	232	5	exist	exist	VERB
ejpam-3298	232	6	a	a	DET
ejpam-3298	232	7	w	w	PROPN
ejpam-3298	232	8	∈	∈	PROPN
ejpam-3298	232	9	{	{	PUNCT
ejpam-3298	232	10	w	w	NOUN
ejpam-3298	232	11	}	}	PUNCT
ejpam-3298	232	12	satisfying	satisfy	VERB
ejpam-3298	232	13	|h1(x	|h1(x	NUM
ejpam-3298	232	14	,	,	PUNCT
ejpam-3298	232	15	y	y	PROPN
ejpam-3298	232	16	,	,	PUNCT
ejpam-3298	232	17	a(t))−h2(x	a(t))−h2(x	PROPN
ejpam-3298	232	18	,	,	PUNCT
ejpam-3298	232	19	y	y	PROPN
ejpam-3298	232	20	,	,	PUNCT
ejpam-3298	232	21	b(t))|	b(t))|	NOUN
ejpam-3298	232	22	≤	≤	PRON
ejpam-3298	233	1	max{d(a	max{d(a	PROPN
ejpam-3298	233	2	,	,	PUNCT
ejpam-3298	233	3	b	b	NOUN
ejpam-3298	233	4	)	)	PUNCT
ejpam-3298	233	5	,	,	PUNCT
ejpam-3298	233	6	d(a	d(a	PROPN
ejpam-3298	233	7	,	,	PUNCT
ejpam-3298	233	8	fa	fa	NOUN
ejpam-3298	233	9	)	)	PUNCT
ejpam-3298	233	10	,	,	PUNCT
ejpam-3298	233	11	d(b	d(b	PROPN
ejpam-3298	233	12	,	,	PUNCT
ejpam-3298	233	13	gb	gb	NOUN
ejpam-3298	233	14	)	)	PUNCT
ejpam-3298	233	15	,	,	PUNCT
ejpam-3298	233	16	1	1	NUM
ejpam-3298	233	17	2	2	NUM
ejpam-3298	233	18	[	[	X
ejpam-3298	233	19	d(a	d(a	PROPN
ejpam-3298	233	20	,	,	PUNCT
ejpam-3298	233	21	b	b	NOUN
ejpam-3298	233	22	)	)	PUNCT
ejpam-3298	233	23	+	+	CCONJ
ejpam-3298	233	24	d(fa	d(fa	NOUN
ejpam-3298	233	25	,	,	PUNCT
ejpam-3298	233	26	gb	gb	NOUN
ejpam-3298	233	27	)	)	PUNCT
ejpam-3298	233	28	]	]	PUNCT
ejpam-3298	233	29	)	)	PUNCT
ejpam-3298	233	30	}	}	PUNCT
ejpam-3298	234	1	−w(max{d(a	−w(max{d(a	PROPN
ejpam-3298	234	2	,	,	PUNCT
ejpam-3298	234	3	b	b	NOUN
ejpam-3298	234	4	)	)	PUNCT
ejpam-3298	234	5	,	,	PUNCT
ejpam-3298	234	6	d(a	d(a	PROPN
ejpam-3298	234	7	,	,	PUNCT
ejpam-3298	234	8	fa	fa	NOUN
ejpam-3298	234	9	)	)	PUNCT
ejpam-3298	234	10	,	,	PUNCT
ejpam-3298	234	11	d(b	d(b	PROPN
ejpam-3298	234	12	,	,	PUNCT
ejpam-3298	234	13	gb	gb	NOUN
ejpam-3298	234	14	)	)	PUNCT
ejpam-3298	234	15	,	,	PUNCT
ejpam-3298	234	16	1	1	NUM
ejpam-3298	234	17	2	2	NUM
ejpam-3298	234	18	[	[	X
ejpam-3298	234	19	d(a	d(a	PROPN
ejpam-3298	234	20	,	,	PUNCT
ejpam-3298	234	21	b	b	NOUN
ejpam-3298	234	22	)	)	PUNCT
ejpam-3298	234	23	+	+	CCONJ
ejpam-3298	234	24	d(fa	d(fa	NOUN
ejpam-3298	234	25	,	,	PUNCT
ejpam-3298	234	26	gb	gb	NOUN
ejpam-3298	234	27	)	)	PUNCT
ejpam-3298	234	28	]	]	PUNCT
ejpam-3298	234	29	)	)	PUNCT
ejpam-3298	234	30	}	}	PUNCT
ejpam-3298	234	31	)	)	PUNCT
ejpam-3298	234	32	for	for	ADP
ejpam-3298	234	33	all	all	DET
ejpam-3298	234	34	(	(	PUNCT
ejpam-3298	234	35	x	x	NOUN
ejpam-3298	234	36	,	,	PUNCT
ejpam-3298	234	37	y	y	NOUN
ejpam-3298	234	38	)	)	PUNCT
ejpam-3298	234	39	∈	∈	PROPN
ejpam-3298	234	40	s	s	PART
ejpam-3298	234	41	×d	×d	NOUN
ejpam-3298	234	42	;	;	PUNCT
ejpam-3298	234	43	a	a	DET
ejpam-3298	234	44	,	,	PUNCT
ejpam-3298	234	45	b	b	PROPN
ejpam-3298	234	46	∈	∈	PROPN
ejpam-3298	234	47	b(s	b(	NOUN
ejpam-3298	234	48	)	)	PUNCT
ejpam-3298	234	49	and	and	CCONJ
ejpam-3298	234	50	t	t	NOUN
ejpam-3298	234	51	∈	∈	PROPN
ejpam-3298	234	52	s.where	s.where	SCONJ
ejpam-3298	234	53	f	f	PROPN
ejpam-3298	234	54	and	and	CCONJ
ejpam-3298	234	55	g	g	PROPN
ejpam-3298	234	56	are	be	AUX
ejpam-3298	234	57	defined	define	VERB
ejpam-3298	234	58	as	as	SCONJ
ejpam-3298	234	59	follows	follow	VERB
ejpam-3298	234	60	:	:	PUNCT
ejpam-3298	234	61	for	for	ADP
ejpam-3298	234	62	all	all	PRON
ejpam-3298	234	63	x	x	SYM
ejpam-3298	234	64	∈	∈	PROPN
ejpam-3298	234	65	s	s	NOUN
ejpam-3298	234	66	,	,	PUNCT
ejpam-3298	234	67	ai	ai	VERB
ejpam-3298	234	68	∈	∈	PROPN
ejpam-3298	234	69	b(s	b(	NOUN
ejpam-3298	234	70	)	)	PUNCT
ejpam-3298	234	71	and	and	CCONJ
ejpam-3298	234	72	i	i	PRON
ejpam-3298	234	73	=	=	PUNCT
ejpam-3298	234	74	{	{	PUNCT
ejpam-3298	234	75	1	1	NUM
ejpam-3298	234	76	,	,	PUNCT
ejpam-3298	234	77	2	2	NUM
ejpam-3298	234	78	,	,	PUNCT
ejpam-3298	234	79	3	3	NUM
ejpam-3298	234	80	}	}	SYM
ejpam-3298	234	81	f(a1(x	f(a1(x	NOUN
ejpam-3298	234	82	)	)	PUNCT
ejpam-3298	234	83	)	)	PUNCT
ejpam-3298	235	1	=	=	SYM
ejpam-3298	235	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	235	3	,	,	PUNCT
ejpam-3298	235	4	y	y	NOUN
ejpam-3298	235	5	)	)	PUNCT
ejpam-3298	236	1	+	+	NOUN
ejpam-3298	236	2	h1(x	h1(x	PROPN
ejpam-3298	236	3	,	,	PUNCT
ejpam-3298	236	4	y	y	PROPN
ejpam-3298	236	5	,	,	PUNCT
ejpam-3298	236	6	a1(t	a1(t	PROPN
ejpam-3298	236	7	(	(	PUNCT
ejpam-3298	236	8	x	x	NOUN
ejpam-3298	236	9	,	,	PUNCT
ejpam-3298	236	10	y	y	NOUN
ejpam-3298	236	11	)	)	PUNCT
ejpam-3298	236	12	)	)	PUNCT
ejpam-3298	236	13	)	)	PUNCT
ejpam-3298	236	14	}	}	PUNCT
ejpam-3298	236	15	g(a2(x	g(a2(x	PROPN
ejpam-3298	236	16	)	)	PUNCT
ejpam-3298	236	17	)	)	PUNCT
ejpam-3298	237	1	=	=	SYM
ejpam-3298	237	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	237	3	,	,	PUNCT
ejpam-3298	237	4	y	y	NOUN
ejpam-3298	237	5	)	)	PUNCT
ejpam-3298	238	1	+	+	PROPN
ejpam-3298	238	2	h2(x	h2(x	PROPN
ejpam-3298	238	3	,	,	PUNCT
ejpam-3298	238	4	y	y	PROPN
ejpam-3298	238	5	,	,	PUNCT
ejpam-3298	238	6	a2(t	a2(t	PRON
ejpam-3298	238	7	(	(	PUNCT
ejpam-3298	238	8	x	x	NOUN
ejpam-3298	238	9	,	,	PUNCT
ejpam-3298	238	10	y	y	NOUN
ejpam-3298	238	11	)	)	PUNCT
ejpam-3298	238	12	)	)	PUNCT
ejpam-3298	238	13	)	)	PUNCT
ejpam-3298	238	14	}	}	PUNCT
ejpam-3298	238	15	for	for	ADP
ejpam-3298	238	16	all	all	DET
ejpam-3298	238	17	x	x	SYM
ejpam-3298	238	18	∈	∈	PROPN
ejpam-3298	238	19	s	s	NOUN
ejpam-3298	238	20	,	,	PUNCT
ejpam-3298	238	21	a1	a1	NOUN
ejpam-3298	238	22	,	,	PUNCT
ejpam-3298	238	23	a2	a2	PROPN
ejpam-3298	238	24	∈	∈	PROPN
ejpam-3298	238	25	b(s	b(	NOUN
ejpam-3298	238	26	)	)	PUNCT
ejpam-3298	238	27	.	.	PUNCT
ejpam-3298	239	1	then	then	ADV
ejpam-3298	239	2	the	the	DET
ejpam-3298	239	3	system	system	NOUN
ejpam-3298	239	4	of	of	ADP
ejpam-3298	239	5	functional	functional	ADJ
ejpam-3298	239	6	equations	equation	NOUN
ejpam-3298	239	7	f(x	f(x	PROPN
ejpam-3298	239	8	)	)	PUNCT
ejpam-3298	240	1	=	=	SYM
ejpam-3298	240	2	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	240	3	,	,	PUNCT
ejpam-3298	240	4	y	y	NOUN
ejpam-3298	240	5	)	)	PUNCT
ejpam-3298	241	1	+	+	NOUN
ejpam-3298	241	2	h1(x	h1(x	PROPN
ejpam-3298	241	3	,	,	PUNCT
ejpam-3298	241	4	y	y	PROPN
ejpam-3298	241	5	,	,	PUNCT
ejpam-3298	241	6	f(t	f(t	PROPN
ejpam-3298	241	7	(	(	PUNCT
ejpam-3298	241	8	x	x	X
ejpam-3298	241	9	,	,	PUNCT
ejpam-3298	241	10	y	y	NOUN
ejpam-3298	241	11	)	)	PUNCT
ejpam-3298	241	12	)	)	PUNCT
ejpam-3298	241	13	)	)	PUNCT
ejpam-3298	241	14	}	}	PUNCT
ejpam-3298	241	15	g(x	g(x	NOUN
ejpam-3298	241	16	)	)	PUNCT
ejpam-3298	241	17	=	=	SYM
ejpam-3298	241	18	opty∈d{u(x	opty∈d{u(x	NOUN
ejpam-3298	241	19	,	,	PUNCT
ejpam-3298	241	20	y	y	NOUN
ejpam-3298	241	21	)	)	PUNCT
ejpam-3298	242	1	+	+	PROPN
ejpam-3298	242	2	h2(x	h2(x	PROPN
ejpam-3298	242	3	,	,	PUNCT
ejpam-3298	242	4	y	y	PROPN
ejpam-3298	242	5	,	,	PUNCT
ejpam-3298	242	6	g(t	g(t	PROPN
ejpam-3298	242	7	(	(	PUNCT
ejpam-3298	242	8	x	x	X
ejpam-3298	242	9	,	,	PUNCT
ejpam-3298	242	10	y	y	NOUN
ejpam-3298	242	11	)	)	PUNCT
ejpam-3298	242	12	)	)	PUNCT
ejpam-3298	242	13	)	)	PUNCT
ejpam-3298	242	14	}	}	PUNCT
ejpam-3298	242	15	possesses	possess	VERB
ejpam-3298	242	16	a	a	DET
ejpam-3298	242	17	unique	unique	ADJ
ejpam-3298	242	18	common	common	ADJ
ejpam-3298	242	19	solution	solution	NOUN
ejpam-3298	242	20	in	in	ADP
ejpam-3298	242	21	b(s	b(	NOUN
ejpam-3298	242	22	)	)	PUNCT
ejpam-3298	242	23	.	.	PUNCT
ejpam-3298	243	1	acknowledgements	acknowledgement	VERB
ejpam-3298	243	2	the	the	DET
ejpam-3298	243	3	first	first	ADJ
ejpam-3298	243	4	author	author	NOUN
ejpam-3298	243	5	is	be	AUX
ejpam-3298	243	6	thankful	thankful	ADJ
ejpam-3298	243	7	to	to	ADP
ejpam-3298	243	8	the	the	DET
ejpam-3298	243	9	national	national	PROPN
ejpam-3298	243	10	board	board	PROPN
ejpam-3298	243	11	for	for	ADP
ejpam-3298	243	12	higher	high	ADJ
ejpam-3298	243	13	mathematics(nbhm),india	mathematics(nbhm),india	PROPN
ejpam-3298	243	14	for	for	ADP
ejpam-3298	243	15	providing	provide	VERB
ejpam-3298	243	16	financial	financial	ADJ
ejpam-3298	243	17	assistance	assistance	NOUN
ejpam-3298	243	18	during	during	ADP
ejpam-3298	243	19	this	this	DET
ejpam-3298	243	20	research	research	NOUN
ejpam-3298	243	21	study	study	NOUN
ejpam-3298	243	22	.	.	PUNCT
ejpam-3298	244	1	references	reference	NOUN
ejpam-3298	244	2	[	[	X
ejpam-3298	244	3	1	1	NUM
ejpam-3298	244	4	]	]	PUNCT
ejpam-3298	244	5	r.	r.	NOUN
ejpam-3298	244	6	baskaran	baskaran	PROPN
ejpam-3298	244	7	and	and	CCONJ
ejpam-3298	244	8	p.	p.	NOUN
ejpam-3298	244	9	v.	v.	ADP
ejpam-3298	244	10	subrahmanyam	subrahmanyam	NOUN
ejpam-3298	244	11	.	.	PUNCT
ejpam-3298	245	1	a	a	DET
ejpam-3298	245	2	note	note	NOUN
ejpam-3298	245	3	on	on	ADP
ejpam-3298	245	4	the	the	DET
ejpam-3298	245	5	solution	solution	NOUN
ejpam-3298	245	6	of	of	ADP
ejpam-3298	245	7	a	a	DET
ejpam-3298	245	8	class	class	NOUN
ejpam-3298	245	9	of	of	ADP
ejpam-3298	245	10	functional	functional	ADJ
ejpam-3298	245	11	equations	equation	NOUN
ejpam-3298	245	12	principle	principle	NOUN
ejpam-3298	245	13	.	.	PUNCT
ejpam-3298	246	1	appl	appl	PROPN
ejpam-3298	246	2	.	.	PUNCT
ejpam-3298	247	1	anal	anal	PROPN
ejpam-3298	247	2	,	,	PUNCT
ejpam-3298	247	3	volume	volume	NOUN
ejpam-3298	247	4	22	22	NUM
ejpam-3298	247	5	(	(	PUNCT
ejpam-3298	247	6	3	3	NUM
ejpam-3298	247	7	-	-	SYM
ejpam-3298	247	8	4	4	NUM
ejpam-3298	247	9	)	)	PUNCT
ejpam-3298	247	10	;	;	PUNCT
ejpam-3298	247	11	pages	page	NOUN
ejpam-3298	247	12	235–241	235–241	NUM
ejpam-3298	247	13	,	,	PUNCT
ejpam-3298	247	14	1986	1986	NUM
ejpam-3298	247	15	.	.	PUNCT
ejpam-3298	248	1	[	[	X
ejpam-3298	248	2	2	2	NUM
ejpam-3298	248	3	]	]	PUNCT
ejpam-3298	248	4	r.	r.	PROPN
ejpam-3298	248	5	bellman	bellman	PROPN
ejpam-3298	248	6	.	.	PUNCT
ejpam-3298	249	1	dynamic	dynamic	ADJ
ejpam-3298	249	2	programming	programming	NOUN
ejpam-3298	249	3	,	,	PUNCT
ejpam-3298	249	4	princeton	princeton	PROPN
ejpam-3298	249	5	university	university	PROPN
ejpam-3298	249	6	press	press	NOUN
ejpam-3298	249	7	.	.	PUNCT
ejpam-3298	250	1	princeton	princeton	PROPN
ejpam-3298	250	2	,	,	PUNCT
ejpam-3298	250	3	new	new	PROPN
ejpam-3298	250	4	jersey	jersey	PROPN
ejpam-3298	250	5	,	,	PUNCT
ejpam-3298	250	6	1957	1957	NUM
ejpam-3298	250	7	.	.	PUNCT
ejpam-3298	251	1	[	[	X
ejpam-3298	251	2	3	3	X
ejpam-3298	251	3	]	]	X
ejpam-3298	251	4	r.	r.	PROPN
ejpam-3298	251	5	bellman	bellman	PROPN
ejpam-3298	251	6	and	and	CCONJ
ejpam-3298	251	7	e.	e.	PROPN
ejpam-3298	251	8	s.	s.	PROPN
ejpam-3298	251	9	lee	lee	PROPN
ejpam-3298	251	10	.	.	PUNCT
ejpam-3298	252	1	functional	functional	ADJ
ejpam-3298	252	2	equations	equation	NOUN
ejpam-3298	252	3	in	in	ADP
ejpam-3298	252	4	dynamic	dynamic	ADJ
ejpam-3298	252	5	programming	programming	NOUN
ejpam-3298	252	6	.	.	PUNCT
ejpam-3298	253	1	aequationes	aequatione	NOUN
ejpam-3298	253	2	math	math	PROPN
ejpam-3298	253	3	.	.	PUNCT
ejpam-3298	254	1	17(1):1–18	17(1):1–18	NUM
ejpam-3298	254	2	,	,	PUNCT
ejpam-3298	254	3	1978	1978	NUM
ejpam-3298	254	4	.	.	PUNCT
ejpam-3298	255	1	[	[	X
ejpam-3298	255	2	4	4	X
ejpam-3298	255	3	]	]	X
ejpam-3298	255	4	p.	p.	NOUN
ejpam-3298	255	5	c.	c.	NOUN
ejpam-3298	255	6	bhakta	bhakta	NOUN
ejpam-3298	255	7	and	and	CCONJ
ejpam-3298	255	8	s.	s.	PROPN
ejpam-3298	255	9	r.	r.	PROPN
ejpam-3298	255	10	choudhury	choudhury	PROPN
ejpam-3298	255	11	.	.	PUNCT
ejpam-3298	256	1	some	some	DET
ejpam-3298	256	2	existence	existence	NOUN
ejpam-3298	256	3	theorems	theorem	VERB
ejpam-3298	256	4	for	for	ADP
ejpam-3298	256	5	functional	functional	ADJ
ejpam-3298	256	6	equations	equation	NOUN
ejpam-3298	256	7	arising	arise	VERB
ejpam-3298	256	8	in	in	ADP
ejpam-3298	256	9	dynamic	dynamic	ADJ
ejpam-3298	256	10	programming	programming	NOUN
ejpam-3298	256	11	.	.	PUNCT
ejpam-3298	257	1	ii	ii	PROPN
ejpam-3298	257	2	j.	j.	PROPN
ejpam-3298	257	3	math	math	PROPN
ejpam-3298	257	4	.	.	PUNCT
ejpam-3298	258	1	anal	anal	PROPN
ejpam-3298	258	2	.	.	PUNCT
ejpam-3298	259	1	appl	appl	PROPN
ejpam-3298	259	2	.	.	PROPN
ejpam-3298	260	1	,131(1);217–231	,131(1);217–231	PROPN
ejpam-3298	260	2	,	,	PUNCT
ejpam-3298	260	3	1988	1988	NUM
ejpam-3298	260	4	.	.	PUNCT
ejpam-3298	261	1	[	[	X
ejpam-3298	261	2	5	5	NUM
ejpam-3298	261	3	]	]	PUNCT
ejpam-3298	261	4	p.	p.	NOUN
ejpam-3298	261	5	c.	c.	NOUN
ejpam-3298	261	6	bhakta	bhakta	PROPN
ejpam-3298	261	7	and	and	CCONJ
ejpam-3298	261	8	s.	s.	PROPN
ejpam-3298	261	9	mitra	mitra	PROPN
ejpam-3298	261	10	.	.	PUNCT
ejpam-3298	262	1	some	some	DET
ejpam-3298	262	2	existence	existence	NOUN
ejpam-3298	262	3	theorems	theorem	VERB
ejpam-3298	262	4	for	for	ADP
ejpam-3298	262	5	functional	functional	ADJ
ejpam-3298	262	6	equations	equation	NOUN
ejpam-3298	262	7	arising	arise	VERB
ejpam-3298	262	8	in	in	ADP
ejpam-3298	262	9	dynamic	dynamic	ADJ
ejpam-3298	262	10	programming	programming	NOUN
ejpam-3298	262	11	j.	j.	PROPN
ejpam-3298	262	12	math	math	PROPN
ejpam-3298	262	13	.	.	PUNCT
ejpam-3298	263	1	anal	anal	PROPN
ejpam-3298	263	2	.	.	PUNCT
ejpam-3298	264	1	appl	appl	PROPN
ejpam-3298	264	2	.	.	PROPN
ejpam-3298	265	1	,98(2):348–362	,98(2):348–362	PROPN
ejpam-3298	265	2	,	,	PUNCT
ejpam-3298	265	3	1984	1984	NUM
ejpam-3298	265	4	.	.	PUNCT
ejpam-3298	266	1	references	reference	NOUN
ejpam-3298	266	2	1189	1189	NUM
ejpam-3298	266	3	[	[	X
ejpam-3298	266	4	6	6	NUM
ejpam-3298	266	5	]	]	X
ejpam-3298	266	6	f.e	f.e	PROPN
ejpam-3298	266	7	brawder	brawder	NOUN
ejpam-3298	266	8	,	,	PUNCT
ejpam-3298	266	9	w.v	w.v	PROPN
ejpam-3298	266	10	.	.	PROPN
ejpam-3298	266	11	petryshyn	petryshyn	PROPN
ejpam-3298	266	12	.	.	PUNCT
ejpam-3298	267	1	contraction	contraction	NOUN
ejpam-3298	267	2	of	of	ADP
ejpam-3298	267	3	fixed	fix	VERB
ejpam-3298	267	4	points	point	NOUN
ejpam-3298	267	5	of	of	ADP
ejpam-3298	267	6	nonlinear	nonlinear	ADJ
ejpam-3298	267	7	mappings	mapping	NOUN
ejpam-3298	267	8	in	in	ADP
ejpam-3298	267	9	hilbert	hilbert	PROPN
ejpam-3298	267	10	space	space	PROPN
ejpam-3298	267	11	j.	j.	PROPN
ejpam-3298	267	12	math	math	PROPN
ejpam-3298	267	13	.	.	PUNCT
ejpam-3298	268	1	anal	anal	PROPN
ejpam-3298	268	2	.	.	PUNCT
ejpam-3298	268	3	appl	appl	PROPN
ejpam-3298	268	4	,	,	PUNCT
ejpam-3298	268	5	20:197–228,1967	20:197–228,1967	NOUN
ejpam-3298	268	6	.	.	PUNCT
ejpam-3298	269	1	[	[	X
ejpam-3298	269	2	7	7	X
ejpam-3298	269	3	]	]	PUNCT
ejpam-3298	269	4	s.	s.	PROPN
ejpam-3298	269	5	s.	s.	PROPN
ejpam-3298	269	6	chang	chang	PROPN
ejpam-3298	269	7	and	and	CCONJ
ejpam-3298	269	8	y.	y.	PROPN
ejpam-3298	269	9	h.	h.	PROPN
ejpam-3298	269	10	ma	ma	PROPN
ejpam-3298	269	11	.	.	PROPN
ejpam-3298	269	12	coupled	couple	VERB
ejpam-3298	269	13	fixed	fix	VERB
ejpam-3298	269	14	points	point	NOUN
ejpam-3298	269	15	for	for	ADP
ejpam-3298	269	16	mixed	mixed	ADJ
ejpam-3298	269	17	monotone	monotone	ADJ
ejpam-3298	269	18	condensing	condense	VERB
ejpam-3298	269	19	operators	operator	NOUN
ejpam-3298	269	20	and	and	CCONJ
ejpam-3298	269	21	an	an	DET
ejpam-3298	269	22	existence	existence	NOUN
ejpam-3298	269	23	theorem	theorem	NOUN
ejpam-3298	269	24	of	of	ADP
ejpam-3298	269	25	the	the	DET
ejpam-3298	269	26	solutions	solution	NOUN
ejpam-3298	269	27	for	for	ADP
ejpam-3298	269	28	a	a	DET
ejpam-3298	269	29	class	class	NOUN
ejpam-3298	269	30	of	of	ADP
ejpam-3298	269	31	functional	functional	ADJ
ejpam-3298	269	32	equations	equation	NOUN
ejpam-3298	269	33	arising	arise	VERB
ejpam-3298	269	34	in	in	ADP
ejpam-3298	269	35	dynamic	dynamic	ADJ
ejpam-3298	269	36	programming	programming	NOUN
ejpam-3298	269	37	j.	j.	PROPN
ejpam-3298	269	38	math	math	PROPN
ejpam-3298	269	39	.	.	PUNCT
ejpam-3298	270	1	anal	anal	PROPN
ejpam-3298	270	2	.	.	PUNCT
ejpam-3298	270	3	appl	appl	PROPN
ejpam-3298	270	4	,	,	PUNCT
ejpam-3298	270	5	160(2):468–479,1991	160(2):468–479,1991	NUM
ejpam-3298	270	6	.	.	PUNCT
ejpam-3298	271	1	[	[	X
ejpam-3298	271	2	8	8	NUM
ejpam-3298	271	3	]	]	SYM
ejpam-3298	271	4	p.chumki	p.chumki	NOUN
ejpam-3298	271	5	and	and	CCONJ
ejpam-3298	271	6	a.p	a.p	PROPN
ejpam-3298	271	7	.	.	PROPN
ejpam-3298	271	8	baisnab	baisnab	PROPN
ejpam-3298	271	9	.	.	PUNCT
ejpam-3298	272	1	asymptotically	asymptotically	ADV
ejpam-3298	272	2	regularity	regularity	NOUN
ejpam-3298	272	3	and	and	CCONJ
ejpam-3298	272	4	fixed	fix	VERB
ejpam-3298	272	5	point	point	NOUN
ejpam-3298	272	6	theorems	theorem	VERB
ejpam-3298	272	7	the	the	DET
ejpam-3298	272	8	math	math	NOUN
ejpam-3298	272	9	.	.	PUNCT
ejpam-3298	273	1	student	student	NOUN
ejpam-3298	273	2	,	,	PUNCT
ejpam-3298	273	3	46:54–59,1978	46:54–59,1978	NUM
ejpam-3298	273	4	.	.	PUNCT
ejpam-3298	274	1	[	[	X
ejpam-3298	274	2	9	9	NUM
ejpam-3298	274	3	]	]	SYM
ejpam-3298	274	4	lj.b	lj.b	NOUN
ejpam-3298	274	5	.	.	PUNCT
ejpam-3298	275	1	ciric	ciric	ADJ
ejpam-3298	275	2	.	.	PUNCT
ejpam-3298	276	1	a	a	DET
ejpam-3298	276	2	generalization	generalization	NOUN
ejpam-3298	276	3	of	of	ADP
ejpam-3298	276	4	banachs	banachs	PROPN
ejpam-3298	276	5	contraction	contraction	NOUN
ejpam-3298	276	6	principle	principle	PROPN
ejpam-3298	276	7	proc	proc	NOUN
ejpam-3298	276	8	.	.	PUNCT
ejpam-3298	277	1	am	be	AUX
ejpam-3298	277	2	.	.	PUNCT
ejpam-3298	278	1	math	math	NOUN
ejpam-3298	278	2	.	.	PUNCT
ejpam-3298	279	1	soc	soc	PROPN
ejpam-3298	279	2	.	.	PUNCT
ejpam-3298	280	1	,45:267–273	,45:267–273	PROPN
ejpam-3298	280	2	,	,	PUNCT
ejpam-3298	280	3	1974	1974	NUM
ejpam-3298	280	4	.	.	PUNCT
ejpam-3298	281	1	[	[	X
ejpam-3298	281	2	10	10	NUM
ejpam-3298	281	3	]	]	X
ejpam-3298	281	4	b.	b.	PROPN
ejpam-3298	281	5	fisher	fisher	PROPN
ejpam-3298	281	6	.	.	PUNCT
ejpam-3298	282	1	results	result	NOUN
ejpam-3298	282	2	on	on	ADP
ejpam-3298	282	3	common	common	ADJ
ejpam-3298	282	4	fixed	fix	VERB
ejpam-3298	282	5	points	point	NOUN
ejpam-3298	282	6	on	on	ADP
ejpam-3298	282	7	bounded	bounded	ADJ
ejpam-3298	282	8	metric	metric	ADJ
ejpam-3298	282	9	spaces	space	NOUN
ejpam-3298	282	10	math	math	NOUN
ejpam-3298	282	11	.	.	PUNCT
ejpam-3298	283	1	sem	sem	PROPN
ejpam-3298	283	2	.	.	PUNCT
ejpam-3298	284	1	notes,7:73–80	notes,7:73–80	PROPN
ejpam-3298	284	2	,	,	PUNCT
ejpam-3298	284	3	1979	1979	NUM
ejpam-3298	284	4	.	.	PUNCT
ejpam-3298	285	1	[	[	X
ejpam-3298	285	2	11	11	NUM
ejpam-3298	285	3	]	]	PUNCT
ejpam-3298	285	4	m.	m.	PROPN
ejpam-3298	285	5	d.	d.	PROPN
ejpam-3298	285	6	guay	guay	PROPN
ejpam-3298	285	7	,	,	PUNCT
ejpam-3298	285	8	k.	k.	PROPN
ejpam-3298	285	9	l.	l.	PROPN
ejpam-3298	285	10	singh	singh	PROPN
ejpam-3298	285	11	.	.	PUNCT
ejpam-3298	286	1	fixed	fix	VERB
ejpam-3298	286	2	points	point	NOUN
ejpam-3298	286	3	of	of	ADP
ejpam-3298	286	4	asymptotically	asymptotically	ADV
ejpam-3298	286	5	regular	regular	ADJ
ejpam-3298	286	6	mappings	mapping	NOUN
ejpam-3298	286	7	math	math	NOUN
ejpam-3298	286	8	.	.	PUNCT
ejpam-3298	287	1	vesnik,35:101–106	vesnik,35:101–106	NOUN
ejpam-3298	287	2	,	,	PUNCT
ejpam-3298	287	3	1983	1983	NUM
ejpam-3298	287	4	.	.	PUNCT
ejpam-3298	288	1	[	[	X
ejpam-3298	288	2	12	12	NUM
ejpam-3298	288	3	]	]	X
ejpam-3298	288	4	k.p.r	k.p.r	PROPN
ejpam-3298	288	5	.	.	PROPN
ejpam-3298	288	6	sastry	sastry	PROPN
ejpam-3298	288	7	,	,	PUNCT
ejpam-3298	288	8	s.r	s.r	PROPN
ejpam-3298	288	9	.	.	PROPN
ejpam-3298	288	10	naidu	naidu	PROPN
ejpam-3298	288	11	,	,	PUNCT
ejpam-3298	288	12	i.h.n	i.h.n	ADJ
ejpam-3298	288	13	.	.	PUNCT
ejpam-3298	288	14	rao	rao	PROPN
ejpam-3298	288	15	and	and	CCONJ
ejpam-3298	288	16	k.p.r	k.p.r	PROPN
ejpam-3298	288	17	.	.	PROPN
ejpam-3298	288	18	rao	rao	PROPN
ejpam-3298	288	19	.	.	PUNCT
ejpam-3298	289	1	common	common	ADJ
ejpam-3298	289	2	fixed	fix	VERB
ejpam-3298	289	3	point	point	NOUN
ejpam-3298	289	4	for	for	ADP
ejpam-3298	289	5	asymptotically	asymptotically	ADV
ejpam-3298	289	6	regular	regular	ADJ
ejpam-3298	289	7	mappings	mapping	NOUN
ejpam-3298	289	8	int.j.pure	int.j.pure	NOUN
ejpam-3298	289	9	appl	appl	PROPN
ejpam-3298	289	10	.	.	PUNCT
ejpam-3298	289	11	math	math	NOUN
ejpam-3298	289	12	.	.	PUNCT
ejpam-3298	290	1	,15:849–854	,15:849–854	PUNCT
ejpam-3298	290	2	,	,	PUNCT
ejpam-3298	290	3	1984	1984	NUM
ejpam-3298	290	4	.	.	PUNCT
ejpam-3298	291	1	[	[	X
ejpam-3298	291	2	13	13	NUM
ejpam-3298	291	3	]	]	X
ejpam-3298	291	4	s.l.singh	s.l.singh	PROPN
ejpam-3298	291	5	and	and	CCONJ
ejpam-3298	291	6	s.p	s.p	PROPN
ejpam-3298	291	7	.	.	PROPN
ejpam-3298	291	8	singh	singh	PROPN
ejpam-3298	291	9	.	.	PUNCT
ejpam-3298	292	1	a	a	DET
ejpam-3298	292	2	fixed	fix	VERB
ejpam-3298	292	3	point	point	NOUN
ejpam-3298	292	4	theorems	theorem	VERB
ejpam-3298	292	5	indian	indian	PROPN
ejpam-3298	292	6	j.	j.	PROPN
ejpam-3298	292	7	pure	pure	PROPN
ejpam-3298	292	8	appl	appl	PROPN
ejpam-3298	292	9	.	.	PUNCT
ejpam-3298	292	10	math	math	PROPN
ejpam-3298	292	11	.	.	PUNCT
ejpam-3298	293	1	,11:1584	,11:1584	PUNCT
ejpam-3298	293	2	–	–	PUNCT
ejpam-3298	293	3	1586	1586	NUM
ejpam-3298	293	4	,	,	PUNCT
ejpam-3298	293	5	1980	1980	NUM
ejpam-3298	293	6	.	.	PUNCT
ejpam-3298	294	1	[	[	X
ejpam-3298	294	2	14	14	NUM
ejpam-3298	294	3	]	]	X
ejpam-3298	294	4	p.l	p.l	PROPN
ejpam-3298	294	5	.	.	PROPN
ejpam-3298	294	6	sharma	sharma	PROPN
ejpam-3298	294	7	and	and	CCONJ
ejpam-3298	294	8	a.k	a.k	PROPN
ejpam-3298	294	9	.	.	PROPN
ejpam-3298	294	10	yud	yud	PROPN
ejpam-3298	294	11	.	.	PUNCT
ejpam-3298	295	1	fixed	fix	VERB
ejpam-3298	295	2	point	point	NOUN
ejpam-3298	295	3	theorems	theorem	NOUN
ejpam-3298	295	4	under	under	ADP
ejpam-3298	295	5	asymptotic	asymptotic	ADJ
ejpam-3298	295	6	regularity	regularity	NOUN
ejpam-3298	295	7	at	at	ADP
ejpam-3298	295	8	a	a	DET
ejpam-3298	295	9	point	point	NOUN
ejpam-3298	295	10	ii	ii	PROPN
ejpam-3298	295	11	jnanabha,11:127–131	jnanabha,11:127–131	PROPN
ejpam-3298	295	12	,	,	PUNCT
ejpam-3298	295	13	1981	1981	NUM
ejpam-3298	295	14	.	.	PUNCT
ejpam-3298	296	1	[	[	X
ejpam-3298	296	2	15	15	NUM
ejpam-3298	296	3	]	]	PUNCT
ejpam-3298	297	1	z.	z.	PROPN
ejpam-3298	297	2	liu	liu	PROPN
ejpam-3298	297	3	.	.	PUNCT
ejpam-3298	298	1	a	a	DET
ejpam-3298	298	2	note	note	NOUN
ejpam-3298	298	3	on	on	ADP
ejpam-3298	298	4	unique	unique	ADJ
ejpam-3298	298	5	common	common	ADJ
ejpam-3298	298	6	fixed	fix	VERB
ejpam-3298	298	7	point	point	NOUN
ejpam-3298	298	8	bull	bull	NOUN
ejpam-3298	298	9	.	.	PUNCT
ejpam-3298	299	1	calcutta	calcutta	PROPN
ejpam-3298	299	2	math	math	PROPN
ejpam-3298	299	3	.	.	PUNCT
ejpam-3298	300	1	soc	soc	PROPN
ejpam-3298	300	2	.	.	PUNCT
ejpam-3298	301	1	,85(5):469	,85(5):469	PROPN
ejpam-3298	301	2	–	–	PUNCT
ejpam-3298	301	3	472	472	NUM
ejpam-3298	301	4	,	,	PUNCT
ejpam-3298	301	5	1993	1993	NUM
ejpam-3298	301	6	.	.	PUNCT
ejpam-3298	302	1	[	[	X
ejpam-3298	302	2	16	16	NUM
ejpam-3298	302	3	]	]	PUNCT
ejpam-3298	303	1	z.	z.	PROPN
ejpam-3298	303	2	liu	liu	PROPN
ejpam-3298	303	3	.	.	PUNCT
ejpam-3298	304	1	existence	existence	NOUN
ejpam-3298	304	2	theorems	theorem	NOUN
ejpam-3298	304	3	of	of	ADP
ejpam-3298	304	4	solutions	solution	NOUN
ejpam-3298	304	5	for	for	ADP
ejpam-3298	304	6	certain	certain	ADJ
ejpam-3298	304	7	classes	class	NOUN
ejpam-3298	304	8	of	of	ADP
ejpam-3298	304	9	functional	functional	ADJ
ejpam-3298	304	10	equations	equation	NOUN
ejpam-3298	304	11	arising	arise	VERB
ejpam-3298	304	12	in	in	ADP
ejpam-3298	304	13	dynamic	dynamic	ADJ
ejpam-3298	304	14	programming	programming	NOUN
ejpam-3298	304	15	,	,	PUNCT
ejpam-3298	304	16	j.	j.	PROPN
ejpam-3298	304	17	math	math	PROPN
ejpam-3298	304	18	.	.	PUNCT
ejpam-3298	305	1	anal	anal	PROPN
ejpam-3298	305	2	.	.	PUNCT
ejpam-3298	305	3	appl	appl	PROPN
ejpam-3298	305	4	.	.	PUNCT
ejpam-3298	306	1	262	262	NUM
ejpam-3298	306	2	(	(	PUNCT
ejpam-3298	306	3	2	2	NUM
ejpam-3298	306	4	):	):	PUNCT
ejpam-3298	306	5	529	529	NUM
ejpam-3298	306	6	-	-	SYM
ejpam-3298	306	7	553	553	NUM
ejpam-3298	306	8	,	,	PUNCT
ejpam-3298	306	9	2001	2001	NUM
ejpam-3298	306	10	.	.	PUNCT
ejpam-3298	307	1	[	[	X
ejpam-3298	307	2	17	17	NUM
ejpam-3298	307	3	]	]	PUNCT
ejpam-3298	308	1	z.	z.	PROPN
ejpam-3298	308	2	liu	liu	PROPN
ejpam-3298	308	3	.	.	PUNCT
ejpam-3298	309	1	coincidence	coincidence	NOUN
ejpam-3298	309	2	theorems	theorem	NOUN
ejpam-3298	309	3	for	for	ADP
ejpam-3298	309	4	expansion	expansion	NOUN
ejpam-3298	309	5	mappings	mapping	NOUN
ejpam-3298	309	6	with	with	ADP
ejpam-3298	309	7	applications	application	NOUN
ejpam-3298	309	8	to	to	ADP
ejpam-3298	309	9	the	the	DET
ejpam-3298	309	10	solutions	solution	NOUN
ejpam-3298	309	11	of	of	ADP
ejpam-3298	309	12	functional	functional	ADJ
ejpam-3298	309	13	equations	equation	NOUN
ejpam-3298	309	14	arising	arise	VERB
ejpam-3298	309	15	in	in	ADP
ejpam-3298	309	16	dynamic	dynamic	ADJ
ejpam-3298	309	17	programming	programming	NOUN
ejpam-3298	309	18	,	,	PUNCT
ejpam-3298	309	19	acta	acta	PROPN
ejpam-3298	309	20	sci	sci	PROPN
ejpam-3298	309	21	.	.	PUNCT
ejpam-3298	309	22	math	math	PROPN
ejpam-3298	309	23	.	.	PUNCT
ejpam-3298	310	1	(	(	PUNCT
ejpam-3298	310	2	szeged	szeged	PROPN
ejpam-3298	310	3	)	)	PUNCT
ejpam-3298	310	4	65	65	NUM
ejpam-3298	310	5	(	(	PUNCT
ejpam-3298	310	6	1	1	NUM
ejpam-3298	310	7	):	):	PUNCT
ejpam-3298	310	8	359	359	NUM
ejpam-3298	310	9	-	-	PUNCT
ejpam-3298	310	10	369,1999	369,1999	NUM
ejpam-3298	310	11	.	.	PUNCT
ejpam-3298	311	1	[	[	X
ejpam-3298	311	2	18	18	NUM
ejpam-3298	311	3	]	]	PUNCT
ejpam-3298	312	1	z.	z.	PROPN
ejpam-3298	312	2	liu	liu	PROPN
ejpam-3298	312	3	.	.	PUNCT
ejpam-3298	313	1	compatible	compatible	ADJ
ejpam-3298	313	2	mappings	mapping	NOUN
ejpam-3298	313	3	and	and	CCONJ
ejpam-3298	313	4	fixed	fix	VERB
ejpam-3298	313	5	points	point	NOUN
ejpam-3298	313	6	,	,	PUNCT
ejpam-3298	313	7	acta	acta	PROPN
ejpam-3298	313	8	sci	sci	PROPN
ejpam-3298	313	9	.	.	PUNCT
ejpam-3298	313	10	math	math	PROPN
ejpam-3298	313	11	.	.	PUNCT
ejpam-3298	314	1	(	(	PUNCT
ejpam-3298	314	2	szeged	szeged	PROPN
ejpam-3298	314	3	)	)	PUNCT
ejpam-3298	314	4	65(2	65(2	NOUN
ejpam-3298	314	5	)	)	PUNCT
ejpam-3298	314	6	,	,	PUNCT
ejpam-3298	314	7	371	371	NUM
ejpam-3298	314	8	-	-	SYM
ejpam-3298	314	9	383,1999	383,1999	NUM
ejpam-3298	314	10	.	.	PUNCT
ejpam-3298	315	1	[	[	X
ejpam-3298	315	2	19	19	NUM
ejpam-3298	315	3	]	]	PUNCT
ejpam-3298	315	4	z.	z.	PROPN
ejpam-3298	315	5	liu	liu	PROPN
ejpam-3298	315	6	,	,	PUNCT
ejpam-3298	315	7	r.	r.	PROPN
ejpam-3298	315	8	p.	p.	PROPN
ejpam-3298	315	9	agarwal	agarwal	PROPN
ejpam-3298	315	10	,	,	PUNCT
ejpam-3298	315	11	and	and	CCONJ
ejpam-3298	315	12	s.	s.	PROPN
ejpam-3298	315	13	m.	m.	PROPN
ejpam-3298	315	14	kang	kang	PROPN
ejpam-3298	315	15	on	on	ADP
ejpam-3298	315	16	solvability	solvability	NOUN
ejpam-3298	315	17	of	of	ADP
ejpam-3298	315	18	functional	functional	ADJ
ejpam-3298	315	19	equations	equation	NOUN
ejpam-3298	315	20	and	and	CCONJ
ejpam-3298	315	21	system	system	NOUN
ejpam-3298	315	22	of	of	ADP
ejpam-3298	315	23	functional	functional	ADJ
ejpam-3298	315	24	equations	equation	NOUN
ejpam-3298	315	25	arising	arise	VERB
ejpam-3298	315	26	in	in	ADP
ejpam-3298	315	27	dynamic	dynamic	ADJ
ejpam-3298	315	28	programming	programming	NOUN
ejpam-3298	315	29	,	,	PUNCT
ejpam-3298	315	30	j.	j.	PROPN
ejpam-3298	315	31	math	math	PROPN
ejpam-3298	315	32	.	.	PUNCT
ejpam-3298	316	1	anal	anal	PROPN
ejpam-3298	316	2	.	.	PUNCT
ejpam-3298	317	1	appl	appl	PROPN
ejpam-3298	317	2	.	.	PROPN
ejpam-3298	318	1	297	297	NUM
ejpam-3298	318	2	(	(	PUNCT
ejpam-3298	318	3	1	1	NUM
ejpam-3298	318	4	)	)	PUNCT
ejpam-3298	318	5	,	,	PUNCT
ejpam-3298	318	6	111	111	NUM
ejpam-3298	318	7	-	-	SYM
ejpam-3298	318	8	130,2004	130,2004	NUM
ejpam-3298	318	9	.	.	PUNCT
ejpam-3298	319	1	[	[	X
ejpam-3298	319	2	20	20	NUM
ejpam-3298	319	3	]	]	PUNCT
ejpam-3298	319	4	z.	z.	PROPN
ejpam-3298	319	5	liu	liu	PROPN
ejpam-3298	319	6	and	and	CCONJ
ejpam-3298	319	7	j.	j.	PROPN
ejpam-3298	319	8	s.	s.	PROPN
ejpam-3298	319	9	ume	ume	PROPN
ejpam-3298	319	10	on	on	ADP
ejpam-3298	319	11	properties	property	NOUN
ejpam-3298	319	12	of	of	ADP
ejpam-3298	319	13	solutions	solution	NOUN
ejpam-3298	319	14	for	for	ADP
ejpam-3298	319	15	a	a	DET
ejpam-3298	319	16	class	class	NOUN
ejpam-3298	319	17	of	of	ADP
ejpam-3298	319	18	functional	functional	ADJ
ejpam-3298	319	19	equations	equation	NOUN
ejpam-3298	319	20	arising	arise	VERB
ejpam-3298	319	21	in	in	ADP
ejpam-3298	319	22	dynamic	dynamic	ADJ
ejpam-3298	319	23	programming	programming	NOUN
ejpam-3298	319	24	,	,	PUNCT
ejpam-3298	319	25	j.	j.	PROPN
ejpam-3298	319	26	optim	optim	PROPN
ejpam-3298	319	27	.	.	PUNCT
ejpam-3298	320	1	theory	theory	NOUN
ejpam-3298	320	2	appl	appl	PROPN
ejpam-3298	320	3	.	.	PROPN
ejpam-3298	321	1	117	117	NUM
ejpam-3298	321	2	(	(	PUNCT
ejpam-3298	321	3	3	3	NUM
ejpam-3298	321	4	)	)	PUNCT
ejpam-3298	321	5	,	,	PUNCT
ejpam-3298	321	6	533	533	NUM
ejpam-3298	321	7	-	-	SYM
ejpam-3298	321	8	551,2003	551,2003	NUM
ejpam-3298	321	9	.	.	PUNCT
ejpam-3298	321	10	references	reference	NOUN
ejpam-3298	321	11	1190	1190	NUM
ejpam-3298	322	1	[	[	X
ejpam-3298	322	2	21	21	NUM
ejpam-3298	322	3	]	]	PUNCT
ejpam-3298	322	4	h.	h.	PROPN
ejpam-3298	322	5	k.	k.	PROPN
ejpam-3298	322	6	pathak	pathak	PROPN
ejpam-3298	322	7	and	and	CCONJ
ejpam-3298	322	8	b.	b.	PROPN
ejpam-3298	322	9	fisher	fisher	PROPN
ejpam-3298	322	10	common	common	ADJ
ejpam-3298	322	11	fixed	fix	VERB
ejpam-3298	322	12	point	point	NOUN
ejpam-3298	322	13	theorems	theorem	NOUN
ejpam-3298	322	14	with	with	ADP
ejpam-3298	322	15	applications	application	NOUN
ejpam-3298	322	16	in	in	ADP
ejpam-3298	322	17	dynamic	dynamic	ADJ
ejpam-3298	322	18	programming	programming	NOUN
ejpam-3298	322	19	,	,	PUNCT
ejpam-3298	322	20	glas	glas	PROPN
ejpam-3298	322	21	.	.	PUNCT
ejpam-3298	322	22	mat	mat	PROPN
ejpam-3298	322	23	.	.	PUNCT
ejpam-3298	322	24	ser	ser	PROPN
ejpam-3298	322	25	.	.	PUNCT
ejpam-3298	323	1	iii	iii	NUM
ejpam-3298	323	2	31(51)(2	31(51)(2	NUM
ejpam-3298	323	3	)	)	PUNCT
ejpam-3298	323	4	,	,	PUNCT
ejpam-3298	323	5	321	321	NUM
ejpam-3298	323	6	-	-	SYM
ejpam-3298	323	7	328,1996	328,1996	NUM
ejpam-3298	323	8	.	.	PUNCT
ejpam-3298	324	1	[	[	X
ejpam-3298	324	2	22	22	NUM
ejpam-3298	324	3	]	]	PUNCT
ejpam-3298	324	4	b.	b.	PROPN
ejpam-3298	324	5	n.	n.	PROPN
ejpam-3298	324	6	ray	ray	PROPN
ejpam-3298	324	7	on	on	ADP
ejpam-3298	324	8	common	common	ADJ
ejpam-3298	324	9	fixed	fix	VERB
ejpam-3298	324	10	points	point	NOUN
ejpam-3298	324	11	in	in	ADP
ejpam-3298	324	12	metric	metric	ADJ
ejpam-3298	324	13	spaces	space	NOUN
ejpam-3298	324	14	,	,	PUNCT
ejpam-3298	324	15	indian	indian	PROPN
ejpam-3298	324	16	j.	j.	PROPN
ejpam-3298	324	17	pure	pure	PROPN
ejpam-3298	324	18	appl	appl	PROPN
ejpam-3298	324	19	.	.	PUNCT
ejpam-3298	324	20	math	math	NOUN
ejpam-3298	324	21	.	.	PUNCT
ejpam-3298	325	1	19	19	NUM
ejpam-3298	325	2	(	(	PUNCT
ejpam-3298	325	3	10	10	NUM
ejpam-3298	325	4	)	)	PUNCT
ejpam-3298	325	5	,	,	PUNCT
ejpam-3298	325	6	960	960	NUM
ejpam-3298	325	7	-	-	SYM
ejpam-3298	325	8	962,1988	962,1988	NUM
ejpam-3298	325	9	.	.	PUNCT
ejpam-3298	326	1	[	[	X
ejpam-3298	326	2	23	23	NUM
ejpam-3298	326	3	]	]	X
ejpam-3298	326	4	b.	b.	PROPN
ejpam-3298	326	5	e.	e.	PROPN
ejpam-3298	326	6	rhoades	rhoades	PROPN
ejpam-3298	326	7	,	,	PUNCT
ejpam-3298	326	8	s.	s.	PROPN
ejpam-3298	326	9	sessa	sessa	PROPN
ejpam-3298	326	10	,	,	PUNCT
ejpam-3298	326	11	m.	m.	NOUN
ejpam-3298	326	12	s.	s.	PROPN
ejpam-3298	326	13	khan	khan	PROPN
ejpam-3298	326	14	and	and	CCONJ
ejpam-3298	326	15	m.	m.	NOUN
ejpam-3298	326	16	swaleh	swaleh	NOUN
ejpam-3298	326	17	on	on	ADP
ejpam-3298	326	18	fixed	fix	VERB
ejpam-3298	326	19	point	point	NOUN
ejpam-3298	326	20	of	of	ADP
ejpam-3298	326	21	asymptotically	asymptotically	ADV
ejpam-3298	326	22	regular	regular	ADJ
ejpam-3298	326	23	mappings	mapping	NOUN
ejpam-3298	326	24	,	,	PUNCT
ejpam-3298	326	25	j.	j.	PROPN
ejpam-3298	326	26	austral	austral	PROPN
ejpam-3298	326	27	.	.	PUNCT
ejpam-3298	327	1	math	math	NOUN
ejpam-3298	327	2	.	.	PUNCT
ejpam-3298	328	1	soc	soc	PROPN
ejpam-3298	328	2	.	.	PUNCT
ejpam-3298	329	1	(	(	PUNCT
ejpam-3298	329	2	series	series	NOUN
ejpam-3298	329	3	a	a	NOUN
ejpam-3298	329	4	)	)	PUNCT
ejpam-3298	329	5	43	43	NUM
ejpam-3298	329	6	,	,	PUNCT
ejpam-3298	329	7	328–346,1987	328–346,1987	NUM
ejpam-3298	329	8	.	.	PUNCT
ejpam-3298	330	1	[	[	X
ejpam-3298	330	2	24	24	NUM
ejpam-3298	330	3	]	]	PUNCT
ejpam-3298	330	4	s.	s.	PROPN
ejpam-3298	330	5	s.	s.	PROPN
ejpam-3298	330	6	zhang	zhang	PROPN
ejpam-3298	331	1	some	some	DET
ejpam-3298	331	2	existence	existence	NOUN
ejpam-3298	331	3	theorems	theorem	NOUN
ejpam-3298	331	4	of	of	ADP
ejpam-3298	331	5	common	common	ADJ
ejpam-3298	331	6	and	and	CCONJ
ejpam-3298	331	7	coincidence	coincidence	NOUN
ejpam-3298	331	8	solutions	solution	NOUN
ejpam-3298	331	9	for	for	ADP
ejpam-3298	331	10	a	a	DET
ejpam-3298	331	11	class	class	NOUN
ejpam-3298	331	12	of	of	ADP
ejpam-3298	331	13	systems	system	NOUN
ejpam-3298	331	14	of	of	ADP
ejpam-3298	331	15	functional	functional	ADJ
ejpam-3298	331	16	equations	equation	NOUN
ejpam-3298	331	17	arising	arise	VERB
ejpam-3298	331	18	in	in	ADP
ejpam-3298	331	19	dynamic	dynamic	ADJ
ejpam-3298	331	20	programming	programming	NOUN
ejpam-3298	331	21	,	,	PUNCT
ejpam-3298	331	22	appl	appl	PROPN
ejpam-3298	331	23	.	.	PROPN
ejpam-3298	331	24	math	math	PROPN
ejpam-3298	331	25	.	.	PUNCT
ejpam-3298	332	1	mech	mech	PROPN
ejpam-3298	332	2	.	.	PUNCT
ejpam-3298	333	1	12	12	NUM
ejpam-3298	333	2	(	(	PUNCT
ejpam-3298	333	3	1	1	NUM
ejpam-3298	333	4	)	)	PUNCT
ejpam-3298	333	5	,	,	PUNCT
ejpam-3298	333	6	31	31	NUM
ejpam-3298	333	7	-	-	SYM
ejpam-3298	333	8	37,1991	37,1991	NUM
ejpam-3298	333	9	.	.	PUNCT