id	sid	tid	token	lemma	pos
ejpam-3019	1	1	european	european	PROPN
ejpam-3019	1	2	journal	journal	PROPN
ejpam-3019	1	3	of	of	ADP
ejpam-3019	1	4	pure	pure	ADJ
ejpam-3019	1	5	and	and	CCONJ
ejpam-3019	1	6	applied	apply	VERB
ejpam-3019	1	7	mathematics	mathematic	NOUN
ejpam-3019	1	8	vol	vol	NOUN
ejpam-3019	1	9	.	.	PROPN
ejpam-3019	2	1	10	10	NUM
ejpam-3019	2	2	,	,	PUNCT
ejpam-3019	2	3	no	no	INTJ
ejpam-3019	2	4	.	.	NOUN
ejpam-3019	2	5	4	4	NUM
ejpam-3019	2	6	,	,	PUNCT
ejpam-3019	2	7	2017	2017	NUM
ejpam-3019	2	8	,	,	PUNCT
ejpam-3019	2	9	655	655	NUM
ejpam-3019	2	10	-	-	SYM
ejpam-3019	2	11	667	667	NUM
ejpam-3019	2	12	issn	issn	PROPN
ejpam-3019	2	13	1307	1307	NUM
ejpam-3019	2	14	-	-	SYM
ejpam-3019	2	15	5543	5543	NUM
ejpam-3019	2	16	–	–	PUNCT
ejpam-3019	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3019	2	18	published	publish	VERB
ejpam-3019	2	19	by	by	ADP
ejpam-3019	2	20	new	new	PROPN
ejpam-3019	2	21	york	york	PROPN
ejpam-3019	2	22	business	business	PROPN
ejpam-3019	2	23	global	global	PROPN
ejpam-3019	2	24	coupled	couple	VERB
ejpam-3019	2	25	fixed	fix	VERB
ejpam-3019	2	26	point	point	NOUN
ejpam-3019	2	27	theorems	theorem	NOUN
ejpam-3019	2	28	on	on	ADP
ejpam-3019	2	29	bipolar	bipolar	ADJ
ejpam-3019	2	30	metric	metric	ADJ
ejpam-3019	2	31	spaces	space	NOUN
ejpam-3019	2	32	ali	ali	PROPN
ejpam-3019	2	33	mutlu1,∗	mutlu1,∗	PROPN
ejpam-3019	2	34	,	,	PUNCT
ejpam-3019	2	35	kübra	kübra	PROPN
ejpam-3019	2	36	özkan1	özkan1	ADJ
ejpam-3019	2	37	,	,	PUNCT
ejpam-3019	2	38	utku	utku	ADJ
ejpam-3019	2	39	gürdal1	gürdal1	ADJ
ejpam-3019	2	40	1	1	NUM
ejpam-3019	2	41	manisa	manisa	PROPN
ejpam-3019	2	42	celal	celal	PROPN
ejpam-3019	2	43	bayar	bayar	PROPN
ejpam-3019	2	44	university	university	PROPN
ejpam-3019	2	45	,	,	PUNCT
ejpam-3019	2	46	faculty	faculty	NOUN
ejpam-3019	2	47	of	of	ADP
ejpam-3019	2	48	science	science	NOUN
ejpam-3019	2	49	and	and	CCONJ
ejpam-3019	2	50	arts	art	NOUN
ejpam-3019	2	51	,	,	PUNCT
ejpam-3019	2	52	department	department	NOUN
ejpam-3019	2	53	of	of	ADP
ejpam-3019	2	54	mathematics	mathematics	PROPN
ejpam-3019	2	55	turkey	turkey	PROPN
ejpam-3019	2	56	abstract	abstract	NOUN
ejpam-3019	2	57	.	.	PUNCT
ejpam-3019	3	1	in	in	ADP
ejpam-3019	3	2	this	this	DET
ejpam-3019	3	3	article	article	NOUN
ejpam-3019	3	4	,	,	PUNCT
ejpam-3019	3	5	certain	certain	ADJ
ejpam-3019	3	6	coupled	couple	VERB
ejpam-3019	3	7	fixed	fix	VERB
ejpam-3019	3	8	point	point	NOUN
ejpam-3019	3	9	theorems	theorem	NOUN
ejpam-3019	3	10	,	,	PUNCT
ejpam-3019	3	11	which	which	PRON
ejpam-3019	3	12	can	can	AUX
ejpam-3019	3	13	be	be	AUX
ejpam-3019	3	14	considered	consider	VERB
ejpam-3019	3	15	as	as	ADP
ejpam-3019	3	16	generalizations	generalization	NOUN
ejpam-3019	3	17	of	of	ADP
ejpam-3019	3	18	banach	banach	ADV
ejpam-3019	3	19	fixed	fix	VERB
ejpam-3019	3	20	point	point	NOUN
ejpam-3019	3	21	theorem	theorem	VERB
ejpam-3019	3	22	,	,	PUNCT
ejpam-3019	3	23	are	be	AUX
ejpam-3019	3	24	extended	extend	VERB
ejpam-3019	3	25	to	to	ADP
ejpam-3019	3	26	bipolar	bipolar	ADJ
ejpam-3019	3	27	metric	metric	ADJ
ejpam-3019	3	28	spaces	space	NOUN
ejpam-3019	3	29	.	.	PUNCT
ejpam-3019	4	1	also	also	ADV
ejpam-3019	4	2	,	,	PUNCT
ejpam-3019	4	3	some	some	DET
ejpam-3019	4	4	results	result	NOUN
ejpam-3019	4	5	which	which	PRON
ejpam-3019	4	6	are	be	AUX
ejpam-3019	4	7	related	relate	VERB
ejpam-3019	4	8	to	to	ADP
ejpam-3019	4	9	these	these	DET
ejpam-3019	4	10	theorems	theorem	NOUN
ejpam-3019	4	11	are	be	AUX
ejpam-3019	4	12	obtained	obtain	VERB
ejpam-3019	4	13	.	.	PUNCT
ejpam-3019	5	1	finally	finally	ADV
ejpam-3019	5	2	,	,	PUNCT
ejpam-3019	5	3	it	it	PRON
ejpam-3019	5	4	is	be	AUX
ejpam-3019	5	5	given	give	VERB
ejpam-3019	5	6	an	an	DET
ejpam-3019	5	7	example	example	NOUN
ejpam-3019	5	8	which	which	PRON
ejpam-3019	5	9	presents	present	VERB
ejpam-3019	5	10	the	the	DET
ejpam-3019	5	11	applicability	applicability	NOUN
ejpam-3019	5	12	of	of	ADP
ejpam-3019	5	13	obtained	obtain	VERB
ejpam-3019	5	14	results	result	NOUN
ejpam-3019	5	15	.	.	PUNCT
ejpam-3019	6	1	2010	2010	NUM
ejpam-3019	6	2	mathematics	mathematic	NOUN
ejpam-3019	6	3	subject	subject	NOUN
ejpam-3019	6	4	classifications	classification	NOUN
ejpam-3019	6	5	:	:	PUNCT
ejpam-3019	6	6	46a80	46a80	NUM
ejpam-3019	6	7	,	,	PUNCT
ejpam-3019	6	8	47h10	47h10	NUM
ejpam-3019	6	9	,	,	PUNCT
ejpam-3019	6	10	54h25	54h25	NUM
ejpam-3019	6	11	key	key	ADJ
ejpam-3019	6	12	words	word	NOUN
ejpam-3019	6	13	and	and	CCONJ
ejpam-3019	6	14	phrases	phrase	NOUN
ejpam-3019	6	15	:	:	PUNCT
ejpam-3019	6	16	bipolar	bipolar	ADJ
ejpam-3019	6	17	metric	metric	ADJ
ejpam-3019	6	18	space	space	NOUN
ejpam-3019	6	19	,	,	PUNCT
ejpam-3019	6	20	coupled	couple	VERB
ejpam-3019	6	21	fixed	fix	VERB
ejpam-3019	6	22	point	point	NOUN
ejpam-3019	6	23	,	,	PUNCT
ejpam-3019	6	24	completeness	completeness	NOUN
ejpam-3019	6	25	1	1	NUM
ejpam-3019	6	26	.	.	PUNCT
ejpam-3019	6	27	introduction	introduction	NOUN
ejpam-3019	6	28	in	in	ADP
ejpam-3019	6	29	literature	literature	NOUN
ejpam-3019	6	30	,	,	PUNCT
ejpam-3019	6	31	the	the	DET
ejpam-3019	6	32	notion	notion	NOUN
ejpam-3019	6	33	of	of	ADP
ejpam-3019	6	34	coupled	couple	VERB
ejpam-3019	6	35	fixed	fix	VERB
ejpam-3019	6	36	point	point	NOUN
ejpam-3019	6	37	has	have	AUX
ejpam-3019	6	38	been	be	AUX
ejpam-3019	6	39	introduced	introduce	VERB
ejpam-3019	6	40	by	by	ADP
ejpam-3019	6	41	guo	guo	PROPN
ejpam-3019	6	42	and	and	CCONJ
ejpam-3019	6	43	lakshmikantham	lakshmikantham	VERB
ejpam-3019	6	44	[	[	X
ejpam-3019	6	45	6	6	NUM
ejpam-3019	6	46	]	]	PUNCT
ejpam-3019	6	47	in	in	ADP
ejpam-3019	6	48	1987	1987	NUM
ejpam-3019	6	49	.	.	PUNCT
ejpam-3019	7	1	afterward	afterward	ADV
ejpam-3019	7	2	,	,	PUNCT
ejpam-3019	7	3	bhaskar	bhaskar	NOUN
ejpam-3019	7	4	and	and	CCONJ
ejpam-3019	7	5	lakshmikantham	lakshmikantham	VERB
ejpam-3019	7	6	[	[	X
ejpam-3019	7	7	3	3	X
ejpam-3019	7	8	]	]	PUNCT
ejpam-3019	7	9	introduced	introduce	VERB
ejpam-3019	7	10	certain	certain	ADJ
ejpam-3019	7	11	coupled	couple	VERB
ejpam-3019	7	12	fixed	fix	VERB
ejpam-3019	7	13	point	point	NOUN
ejpam-3019	7	14	theorems	theorem	NOUN
ejpam-3019	7	15	in	in	ADP
ejpam-3019	7	16	partially	partially	ADV
ejpam-3019	7	17	ordered	order	VERB
ejpam-3019	7	18	metric	metric	ADJ
ejpam-3019	7	19	spaces	space	NOUN
ejpam-3019	7	20	.	.	PUNCT
ejpam-3019	8	1	since	since	SCONJ
ejpam-3019	8	2	then	then	ADV
ejpam-3019	8	3	,	,	PUNCT
ejpam-3019	8	4	when	when	SCONJ
ejpam-3019	8	5	many	many	ADJ
ejpam-3019	8	6	authors	author	NOUN
ejpam-3019	8	7	saw	see	VERB
ejpam-3019	8	8	that	that	SCONJ
ejpam-3019	8	9	these	these	DET
ejpam-3019	8	10	fixed	fix	VERB
ejpam-3019	8	11	point	point	NOUN
ejpam-3019	8	12	theorems	theorem	NOUN
ejpam-3019	8	13	can	can	AUX
ejpam-3019	8	14	be	be	AUX
ejpam-3019	8	15	utilized	utilize	VERB
ejpam-3019	8	16	to	to	PART
ejpam-3019	8	17	investigate	investigate	VERB
ejpam-3019	8	18	existence	existence	NOUN
ejpam-3019	8	19	and	and	CCONJ
ejpam-3019	8	20	uniqueness	uniqueness	NOUN
ejpam-3019	8	21	of	of	ADP
ejpam-3019	8	22	solutions	solution	NOUN
ejpam-3019	8	23	of	of	ADP
ejpam-3019	8	24	periodic	periodic	ADJ
ejpam-3019	8	25	boundary	boundary	ADJ
ejpam-3019	8	26	value	value	NOUN
ejpam-3019	8	27	problems	problem	NOUN
ejpam-3019	8	28	,	,	PUNCT
ejpam-3019	8	29	differential	differential	ADJ
ejpam-3019	8	30	equations	equation	NOUN
ejpam-3019	8	31	and	and	CCONJ
ejpam-3019	8	32	nonlinear	nonlinear	ADJ
ejpam-3019	8	33	integral	integral	ADJ
ejpam-3019	8	34	equations	equation	NOUN
ejpam-3019	8	35	,	,	PUNCT
ejpam-3019	8	36	these	these	DET
ejpam-3019	8	37	theorems	theorem	NOUN
ejpam-3019	8	38	attracted	attract	VERB
ejpam-3019	8	39	their	their	PRON
ejpam-3019	8	40	attention	attention	NOUN
ejpam-3019	8	41	.	.	PUNCT
ejpam-3019	9	1	and	and	CCONJ
ejpam-3019	9	2	,	,	PUNCT
ejpam-3019	9	3	they	they	PRON
ejpam-3019	9	4	extended	extend	VERB
ejpam-3019	9	5	these	these	DET
ejpam-3019	9	6	theorems	theorem	NOUN
ejpam-3019	9	7	to	to	ADP
ejpam-3019	9	8	various	various	ADJ
ejpam-3019	9	9	generalizations	generalization	NOUN
ejpam-3019	9	10	of	of	ADP
ejpam-3019	9	11	metric	metric	ADJ
ejpam-3019	9	12	spaces	space	NOUN
ejpam-3019	9	13	as	as	ADP
ejpam-3019	9	14	cone	cone	NOUN
ejpam-3019	9	15	,	,	PUNCT
ejpam-3019	9	16	partial	partial	ADJ
ejpam-3019	9	17	and	and	CCONJ
ejpam-3019	9	18	modular	modular	ADJ
ejpam-3019	9	19	,	,	PUNCT
ejpam-3019	9	20	e.g.	e.g.	ADV
ejpam-3019	9	21	[	[	X
ejpam-3019	9	22	1	1	NUM
ejpam-3019	9	23	,	,	PUNCT
ejpam-3019	9	24	2	2	NUM
ejpam-3019	9	25	,	,	PUNCT
ejpam-3019	9	26	4	4	NUM
ejpam-3019	9	27	,	,	PUNCT
ejpam-3019	9	28	5	5	NUM
ejpam-3019	9	29	,	,	PUNCT
ejpam-3019	9	30	7–12	7–12	PROPN
ejpam-3019	9	31	,	,	PUNCT
ejpam-3019	9	32	14–20	14–20	NUM
ejpam-3019	9	33	]	]	PUNCT
ejpam-3019	9	34	.	.	PUNCT
ejpam-3019	10	1	the	the	DET
ejpam-3019	10	2	notion	notion	NOUN
ejpam-3019	10	3	of	of	ADP
ejpam-3019	10	4	metric	metric	ADJ
ejpam-3019	10	5	space	space	NOUN
ejpam-3019	10	6	has	have	VERB
ejpam-3019	10	7	many	many	ADJ
ejpam-3019	10	8	generalizations	generalization	NOUN
ejpam-3019	10	9	in	in	ADP
ejpam-3019	10	10	literature	literature	NOUN
ejpam-3019	10	11	.	.	PUNCT
ejpam-3019	11	1	one	one	NUM
ejpam-3019	11	2	of	of	ADP
ejpam-3019	11	3	the	the	DET
ejpam-3019	11	4	most	most	ADV
ejpam-3019	11	5	recent	recent	ADJ
ejpam-3019	11	6	of	of	ADP
ejpam-3019	11	7	them	they	PRON
ejpam-3019	11	8	is	be	AUX
ejpam-3019	11	9	bipolar	bipolar	ADJ
ejpam-3019	11	10	metric	metric	ADJ
ejpam-3019	11	11	space	space	NOUN
ejpam-3019	11	12	which	which	PRON
ejpam-3019	11	13	is	be	AUX
ejpam-3019	11	14	introduced	introduce	VERB
ejpam-3019	11	15	by	by	ADP
ejpam-3019	11	16	mutlu	mutlu	NOUN
ejpam-3019	11	17	and	and	CCONJ
ejpam-3019	11	18	gürdal	gürdal	VERB
ejpam-3019	11	19	[	[	X
ejpam-3019	11	20	13	13	NUM
ejpam-3019	11	21	]	]	PUNCT
ejpam-3019	11	22	in	in	ADP
ejpam-3019	11	23	2016	2016	NUM
ejpam-3019	11	24	.	.	PUNCT
ejpam-3019	12	1	also	also	ADV
ejpam-3019	12	2	,	,	PUNCT
ejpam-3019	12	3	they	they	PRON
ejpam-3019	12	4	established	establish	VERB
ejpam-3019	12	5	some	some	DET
ejpam-3019	12	6	fixed	fix	VERB
ejpam-3019	12	7	point	point	NOUN
ejpam-3019	12	8	theorems	theorem	NOUN
ejpam-3019	12	9	as	as	ADP
ejpam-3019	12	10	banach	banach	NOUN
ejpam-3019	12	11	’s	’s	ADJ
ejpam-3019	12	12	and	and	CCONJ
ejpam-3019	12	13	kannan	kannan	PROPN
ejpam-3019	12	14	’s	’s	X
ejpam-3019	12	15	on	on	ADP
ejpam-3019	12	16	this	this	DET
ejpam-3019	12	17	space	space	NOUN
ejpam-3019	12	18	.	.	PUNCT
ejpam-3019	13	1	in	in	ADP
ejpam-3019	13	2	this	this	DET
ejpam-3019	13	3	paper	paper	NOUN
ejpam-3019	13	4	,	,	PUNCT
ejpam-3019	13	5	we	we	PRON
ejpam-3019	13	6	extend	extend	VERB
ejpam-3019	13	7	certain	certain	ADJ
ejpam-3019	13	8	coupled	couple	VERB
ejpam-3019	13	9	fixed	fix	VERB
ejpam-3019	13	10	point	point	NOUN
ejpam-3019	13	11	theorems	theorem	NOUN
ejpam-3019	13	12	,	,	PUNCT
ejpam-3019	13	13	which	which	PRON
ejpam-3019	13	14	can	can	AUX
ejpam-3019	13	15	be	be	AUX
ejpam-3019	13	16	considered	consider	VERB
ejpam-3019	13	17	as	as	SCONJ
ejpam-3019	13	18	generalization	generalization	NOUN
ejpam-3019	13	19	of	of	ADP
ejpam-3019	13	20	banach	banach	ADV
ejpam-3019	13	21	fixed	fix	VERB
ejpam-3019	13	22	point	point	NOUN
ejpam-3019	13	23	theorem	theorem	VERB
ejpam-3019	13	24	,	,	PUNCT
ejpam-3019	13	25	to	to	ADP
ejpam-3019	13	26	bipolar	bipolar	ADJ
ejpam-3019	13	27	metric	metric	ADJ
ejpam-3019	13	28	spaces	space	NOUN
ejpam-3019	13	29	.	.	PUNCT
ejpam-3019	14	1	also	also	ADV
ejpam-3019	14	2	,	,	PUNCT
ejpam-3019	14	3	we	we	PRON
ejpam-3019	14	4	obtain	obtain	VERB
ejpam-3019	14	5	some	some	DET
ejpam-3019	14	6	results	result	NOUN
ejpam-3019	14	7	which	which	PRON
ejpam-3019	14	8	are	be	AUX
ejpam-3019	14	9	related	relate	VERB
ejpam-3019	14	10	to	to	ADP
ejpam-3019	14	11	these	these	DET
ejpam-3019	14	12	theorems	theorem	NOUN
ejpam-3019	14	13	.	.	PUNCT
ejpam-3019	15	1	finally	finally	ADV
ejpam-3019	15	2	,	,	PUNCT
ejpam-3019	15	3	we	we	PRON
ejpam-3019	15	4	give	give	VERB
ejpam-3019	15	5	an	an	DET
ejpam-3019	15	6	example	example	NOUN
ejpam-3019	15	7	which	which	PRON
ejpam-3019	15	8	presents	present	VERB
ejpam-3019	15	9	the	the	DET
ejpam-3019	15	10	applicability	applicability	NOUN
ejpam-3019	15	11	of	of	ADP
ejpam-3019	15	12	our	our	PRON
ejpam-3019	15	13	obtained	obtain	VERB
ejpam-3019	15	14	results	result	NOUN
ejpam-3019	15	15	.	.	PUNCT
ejpam-3019	16	1	∗corresponding	∗corresponde	VERB
ejpam-3019	16	2	author	author	NOUN
ejpam-3019	16	3	.	.	PUNCT
ejpam-3019	17	1	email	email	NOUN
ejpam-3019	17	2	addresses	address	NOUN
ejpam-3019	17	3	:	:	PUNCT
ejpam-3019	17	4	abgamutlu@gmail.com	abgamutlu@gmail.com	X
ejpam-3019	17	5	(	(	PUNCT
ejpam-3019	17	6	a.	a.	PROPN
ejpam-3019	17	7	mutlu	mutlu	PROPN
ejpam-3019	17	8	)	)	PUNCT
ejpam-3019	17	9	,	,	PUNCT
ejpam-3019	17	10	kubra.ozkan@hotmail.com	kubra.ozkan@hotmail.com	X
ejpam-3019	17	11	(	(	PUNCT
ejpam-3019	17	12	k.	k.	PROPN
ejpam-3019	17	13	özkan	özkan	PROPN
ejpam-3019	17	14	)	)	PUNCT
ejpam-3019	17	15	,	,	PUNCT
ejpam-3019	17	16	utkugurdal@gmail.com	utkugurdal@gmail.com	X
ejpam-3019	17	17	(	(	PUNCT
ejpam-3019	17	18	u.	u.	PROPN
ejpam-3019	17	19	gürdal	gürdal	PROPN
ejpam-3019	17	20	)	)	PUNCT
ejpam-3019	17	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3019	18	1	655	655	NUM
ejpam-3019	18	2	c	c	NOUN
ejpam-3019	18	3	©	©	PROPN
ejpam-3019	18	4	2017	2017	NUM
ejpam-3019	18	5	ejpam	ejpam	NOUN
ejpam-3019	18	6	all	all	DET
ejpam-3019	18	7	rights	right	NOUN
ejpam-3019	18	8	reserved	reserve	VERB
ejpam-3019	18	9	.	.	PUNCT
ejpam-3019	19	1	a.	a.	PROPN
ejpam-3019	19	2	mutlu	mutlu	PROPN
ejpam-3019	19	3	,	,	PUNCT
ejpam-3019	19	4	k.	k.	PROPN
ejpam-3019	19	5	özkan	özkan	PROPN
ejpam-3019	19	6	,	,	PUNCT
ejpam-3019	19	7	u.	u.	PROPN
ejpam-3019	19	8	gürdal	gürdal	PROPN
ejpam-3019	19	9	/	/	SYM
ejpam-3019	19	10	eur	eur	PROPN
ejpam-3019	19	11	.	.	PUNCT
ejpam-3019	20	1	j.	j.	PROPN
ejpam-3019	20	2	pure	pure	PROPN
ejpam-3019	20	3	appl	appl	PROPN
ejpam-3019	20	4	.	.	PROPN
ejpam-3019	20	5	math	math	PROPN
ejpam-3019	20	6	,	,	PUNCT
ejpam-3019	20	7	10	10	NUM
ejpam-3019	20	8	(	(	PUNCT
ejpam-3019	20	9	4	4	NUM
ejpam-3019	20	10	)	)	PUNCT
ejpam-3019	20	11	(	(	PUNCT
ejpam-3019	20	12	2017	2017	NUM
ejpam-3019	20	13	)	)	PUNCT
ejpam-3019	20	14	,	,	PUNCT
ejpam-3019	20	15	655	655	NUM
ejpam-3019	20	16	-	-	SYM
ejpam-3019	20	17	667	667	NUM
ejpam-3019	20	18	656	656	NUM
ejpam-3019	20	19	2	2	NUM
ejpam-3019	20	20	.	.	PUNCT
ejpam-3019	21	1	bipolar	bipolar	ADJ
ejpam-3019	21	2	metric	metric	ADJ
ejpam-3019	21	3	spaces	space	NOUN
ejpam-3019	21	4	we	we	PRON
ejpam-3019	21	5	express	express	VERB
ejpam-3019	21	6	a	a	DET
ejpam-3019	21	7	series	series	NOUN
ejpam-3019	21	8	of	of	ADP
ejpam-3019	21	9	definitions	definition	NOUN
ejpam-3019	21	10	of	of	ADP
ejpam-3019	21	11	some	some	DET
ejpam-3019	21	12	fundamental	fundamental	ADJ
ejpam-3019	21	13	notions	notion	NOUN
ejpam-3019	21	14	related	relate	VERB
ejpam-3019	21	15	to	to	ADP
ejpam-3019	21	16	bipolar	bipolar	ADJ
ejpam-3019	21	17	metric	metric	ADJ
ejpam-3019	21	18	spaces	space	NOUN
ejpam-3019	21	19	.	.	PUNCT
ejpam-3019	22	1	definition	definition	NOUN
ejpam-3019	22	2	1	1	NUM
ejpam-3019	22	3	.	.	PUNCT
ejpam-3019	23	1	[	[	X
ejpam-3019	23	2	13	13	NUM
ejpam-3019	23	3	]	]	PUNCT
ejpam-3019	23	4	a	a	DET
ejpam-3019	23	5	bipolar	bipolar	ADJ
ejpam-3019	23	6	metric	metric	ADJ
ejpam-3019	23	7	space	space	NOUN
ejpam-3019	23	8	is	be	AUX
ejpam-3019	23	9	a	a	DET
ejpam-3019	23	10	triple	triple	ADJ
ejpam-3019	23	11	(	(	PUNCT
ejpam-3019	23	12	x	x	NOUN
ejpam-3019	23	13	,	,	PUNCT
ejpam-3019	23	14	y	y	PROPN
ejpam-3019	23	15	,	,	PUNCT
ejpam-3019	23	16	d	d	NOUN
ejpam-3019	23	17	)	)	PUNCT
ejpam-3019	23	18	such	such	ADJ
ejpam-3019	23	19	that	that	SCONJ
ejpam-3019	23	20	x	x	NOUN
ejpam-3019	23	21	,	,	PUNCT
ejpam-3019	23	22	y	y	PROPN
ejpam-3019	23	23	6=	6=	NOUN
ejpam-3019	23	24	∅	∅	NOUN
ejpam-3019	23	25	and	and	CCONJ
ejpam-3019	23	26	d	d	NOUN
ejpam-3019	23	27	:	:	PUNCT
ejpam-3019	23	28	x	x	SYM
ejpam-3019	23	29	×	×	NOUN
ejpam-3019	23	30	y	y	PROPN
ejpam-3019	23	31	→	→	X
ejpam-3019	23	32	r+	r+	PRON
ejpam-3019	23	33	is	be	AUX
ejpam-3019	23	34	a	a	DET
ejpam-3019	23	35	function	function	NOUN
ejpam-3019	23	36	satisfying	satisfy	VERB
ejpam-3019	23	37	the	the	DET
ejpam-3019	23	38	properties	property	NOUN
ejpam-3019	23	39	(	(	PUNCT
ejpam-3019	23	40	b0	b0	NOUN
ejpam-3019	23	41	)	)	PUNCT
ejpam-3019	23	42	if	if	SCONJ
ejpam-3019	23	43	d	d	PROPN
ejpam-3019	23	44	(	(	PUNCT
ejpam-3019	23	45	x	x	NOUN
ejpam-3019	23	46	,	,	PUNCT
ejpam-3019	23	47	y	y	NOUN
ejpam-3019	23	48	)	)	PUNCT
ejpam-3019	23	49	=	=	SYM
ejpam-3019	23	50	0	0	NUM
ejpam-3019	23	51	,	,	PUNCT
ejpam-3019	23	52	then	then	ADV
ejpam-3019	23	53	x	x	X
ejpam-3019	23	54	=	=	SYM
ejpam-3019	23	55	y	y	PROPN
ejpam-3019	23	56	,	,	PUNCT
ejpam-3019	23	57	(	(	PUNCT
ejpam-3019	23	58	b1	b1	NOUN
ejpam-3019	23	59	)	)	PUNCT
ejpam-3019	23	60	if	if	SCONJ
ejpam-3019	23	61	x	x	X
ejpam-3019	23	62	=	=	SYM
ejpam-3019	23	63	y	y	PROPN
ejpam-3019	23	64	,	,	PUNCT
ejpam-3019	23	65	then	then	ADV
ejpam-3019	23	66	d	d	X
ejpam-3019	23	67	(	(	PUNCT
ejpam-3019	23	68	x	x	NOUN
ejpam-3019	23	69	,	,	PUNCT
ejpam-3019	23	70	y	y	NOUN
ejpam-3019	23	71	)	)	PUNCT
ejpam-3019	23	72	=	=	SYM
ejpam-3019	23	73	0	0	NUM
ejpam-3019	23	74	,	,	PUNCT
ejpam-3019	23	75	(	(	PUNCT
ejpam-3019	23	76	b2	b2	NOUN
ejpam-3019	23	77	)	)	PUNCT
ejpam-3019	23	78	if	if	SCONJ
ejpam-3019	23	79	x	x	X
ejpam-3019	23	80	,	,	PUNCT
ejpam-3019	23	81	y	y	PROPN
ejpam-3019	23	82	∈	∈	PROPN
ejpam-3019	23	83	x	x	SYM
ejpam-3019	23	84	∩	∩	PROPN
ejpam-3019	23	85	y	y	PROPN
ejpam-3019	23	86	,	,	PUNCT
ejpam-3019	23	87	then	then	ADV
ejpam-3019	23	88	d	d	X
ejpam-3019	23	89	(	(	PUNCT
ejpam-3019	23	90	x	x	NOUN
ejpam-3019	23	91	,	,	PUNCT
ejpam-3019	23	92	y	y	NOUN
ejpam-3019	23	93	)	)	PUNCT
ejpam-3019	23	94	=	=	SYM
ejpam-3019	24	1	d	d	X
ejpam-3019	24	2	(	(	PUNCT
ejpam-3019	24	3	y	y	PROPN
ejpam-3019	24	4	,	,	PUNCT
ejpam-3019	24	5	x	x	NOUN
ejpam-3019	24	6	)	)	PUNCT
ejpam-3019	24	7	,	,	PUNCT
ejpam-3019	24	8	(	(	PUNCT
ejpam-3019	24	9	b3	b3	NOUN
ejpam-3019	24	10	)	)	PUNCT
ejpam-3019	24	11	d(x1	d(x1	NOUN
ejpam-3019	24	12	,	,	PUNCT
ejpam-3019	24	13	y2	y2	NOUN
ejpam-3019	24	14	)	)	PUNCT
ejpam-3019	24	15	≤	≤	NOUN
ejpam-3019	24	16	d(x1	d(x1	NOUN
ejpam-3019	24	17	,	,	PUNCT
ejpam-3019	24	18	y1	y1	NOUN
ejpam-3019	24	19	)	)	PUNCT
ejpam-3019	24	20	+	+	NUM
ejpam-3019	24	21	d(x2	d(x2	NOUN
ejpam-3019	24	22	,	,	PUNCT
ejpam-3019	24	23	y1	y1	PROPN
ejpam-3019	24	24	)	)	PUNCT
ejpam-3019	24	25	+	+	NUM
ejpam-3019	24	26	d(x2	d(x2	NOUN
ejpam-3019	24	27	,	,	PUNCT
ejpam-3019	24	28	y2	y2	PROPN
ejpam-3019	24	29	)	)	PUNCT
ejpam-3019	24	30	,	,	PUNCT
ejpam-3019	24	31	for	for	ADP
ejpam-3019	24	32	all	all	PRON
ejpam-3019	24	33	(	(	PUNCT
ejpam-3019	24	34	x	x	NOUN
ejpam-3019	24	35	,	,	PUNCT
ejpam-3019	24	36	y	y	PROPN
ejpam-3019	24	37	)	)	PUNCT
ejpam-3019	24	38	,	,	PUNCT
ejpam-3019	24	39	(	(	PUNCT
ejpam-3019	24	40	x1	x1	PROPN
ejpam-3019	24	41	,	,	PUNCT
ejpam-3019	24	42	y1	y1	PROPN
ejpam-3019	24	43	)	)	PUNCT
ejpam-3019	24	44	,	,	PUNCT
ejpam-3019	24	45	(	(	PUNCT
ejpam-3019	24	46	x2	x2	PROPN
ejpam-3019	24	47	,	,	PUNCT
ejpam-3019	24	48	y2	y2	NOUN
ejpam-3019	24	49	)	)	PUNCT
ejpam-3019	24	50	∈	∈	PROPN
ejpam-3019	25	1	x	x	SYM
ejpam-3019	25	2	×	×	PROPN
ejpam-3019	25	3	y	y	PROPN
ejpam-3019	25	4	,	,	PUNCT
ejpam-3019	25	5	where	where	SCONJ
ejpam-3019	25	6	r+	r+	PUNCT
ejpam-3019	25	7	symbolises	symbolise	VERB
ejpam-3019	25	8	the	the	DET
ejpam-3019	25	9	set	set	NOUN
ejpam-3019	25	10	of	of	ADP
ejpam-3019	25	11	all	all	DET
ejpam-3019	25	12	non	non	ADJ
ejpam-3019	25	13	-	-	ADJ
ejpam-3019	25	14	negative	negative	ADJ
ejpam-3019	25	15	real	real	ADJ
ejpam-3019	25	16	numbers	number	NOUN
ejpam-3019	25	17	.	.	PUNCT
ejpam-3019	26	1	then	then	ADV
ejpam-3019	26	2	d	d	PROPN
ejpam-3019	26	3	is	be	AUX
ejpam-3019	26	4	called	call	VERB
ejpam-3019	26	5	a	a	DET
ejpam-3019	26	6	bipolar	bipolar	ADJ
ejpam-3019	26	7	metric	metric	NOUN
ejpam-3019	26	8	on	on	ADP
ejpam-3019	26	9	the	the	DET
ejpam-3019	26	10	pair	pair	NOUN
ejpam-3019	26	11	(	(	PUNCT
ejpam-3019	26	12	x	x	X
ejpam-3019	26	13	,	,	PUNCT
ejpam-3019	26	14	y	y	PROPN
ejpam-3019	26	15	)	)	PUNCT
ejpam-3019	26	16	.	.	PUNCT
ejpam-3019	27	1	definition	definition	NOUN
ejpam-3019	27	2	2	2	NUM
ejpam-3019	27	3	.	.	PUNCT
ejpam-3019	28	1	[	[	X
ejpam-3019	28	2	13	13	NUM
ejpam-3019	28	3	]	]	PUNCT
ejpam-3019	28	4	let	let	VERB
ejpam-3019	28	5	(	(	PUNCT
ejpam-3019	28	6	x1	x1	ADJ
ejpam-3019	28	7	,	,	PUNCT
ejpam-3019	28	8	y1	y1	PROPN
ejpam-3019	28	9	)	)	PUNCT
ejpam-3019	28	10	and	and	CCONJ
ejpam-3019	28	11	(	(	PUNCT
ejpam-3019	28	12	x2	x2	PROPN
ejpam-3019	28	13	,	,	PUNCT
ejpam-3019	28	14	y2	y2	PROPN
ejpam-3019	28	15	)	)	PUNCT
ejpam-3019	28	16	be	be	AUX
ejpam-3019	28	17	pairs	pair	NOUN
ejpam-3019	28	18	of	of	ADP
ejpam-3019	28	19	sets	set	NOUN
ejpam-3019	28	20	and	and	CCONJ
ejpam-3019	28	21	given	give	VERB
ejpam-3019	28	22	a	a	DET
ejpam-3019	28	23	function	function	NOUN
ejpam-3019	28	24	f	f	NOUN
ejpam-3019	28	25	:	:	PUNCT
ejpam-3019	29	1	x1	x1	PROPN
ejpam-3019	29	2	∪	∪	NOUN
ejpam-3019	29	3	y1	y1	NOUN
ejpam-3019	29	4	→	→	SYM
ejpam-3019	29	5	x2	x2	PROPN
ejpam-3019	29	6	∪	∪	NOUN
ejpam-3019	29	7	y2	y2	NOUN
ejpam-3019	29	8	.	.	PUNCT
ejpam-3019	30	1	if	if	SCONJ
ejpam-3019	30	2	f(x1	f(x1	NOUN
ejpam-3019	30	3	)	)	PUNCT
ejpam-3019	30	4	⊆	⊆	NUM
ejpam-3019	30	5	x2	x2	NOUN
ejpam-3019	30	6	and	and	CCONJ
ejpam-3019	30	7	f(y1	f(y1	NOUN
ejpam-3019	30	8	)	)	PUNCT
ejpam-3019	30	9	⊆	⊆	NUM
ejpam-3019	30	10	y2	y2	NOUN
ejpam-3019	30	11	,	,	PUNCT
ejpam-3019	30	12	we	we	PRON
ejpam-3019	30	13	call	call	VERB
ejpam-3019	30	14	f	f	PROPN
ejpam-3019	30	15	a	a	DET
ejpam-3019	30	16	covariant	covariant	ADJ
ejpam-3019	30	17	map	map	NOUN
ejpam-3019	30	18	from	from	ADP
ejpam-3019	30	19	(	(	PUNCT
ejpam-3019	30	20	x1	x1	PROPN
ejpam-3019	30	21	,	,	PUNCT
ejpam-3019	30	22	y1	y1	PROPN
ejpam-3019	30	23	)	)	PUNCT
ejpam-3019	30	24	to	to	ADP
ejpam-3019	30	25	(	(	PUNCT
ejpam-3019	30	26	x2	x2	PROPN
ejpam-3019	30	27	,	,	PUNCT
ejpam-3019	30	28	y2	y2	PROPN
ejpam-3019	30	29	)	)	PUNCT
ejpam-3019	30	30	and	and	CCONJ
ejpam-3019	30	31	denote	denote	VERB
ejpam-3019	30	32	this	this	PRON
ejpam-3019	30	33	with	with	ADP
ejpam-3019	30	34	f	f	PROPN
ejpam-3019	30	35	:	:	PUNCT
ejpam-3019	30	36	(	(	PUNCT
ejpam-3019	30	37	x1	x1	PROPN
ejpam-3019	30	38	,	,	PUNCT
ejpam-3019	30	39	y1	y1	NOUN
ejpam-3019	30	40	)	)	PUNCT
ejpam-3019	30	41	⇒	⇒	NOUN
ejpam-3019	30	42	(	(	PUNCT
ejpam-3019	30	43	x2	x2	PROPN
ejpam-3019	30	44	,	,	PUNCT
ejpam-3019	30	45	y2	y2	PROPN
ejpam-3019	30	46	)	)	PUNCT
ejpam-3019	30	47	.	.	PUNCT
ejpam-3019	31	1	if	if	SCONJ
ejpam-3019	31	2	f(x1	f(x1	NOUN
ejpam-3019	31	3	)	)	PUNCT
ejpam-3019	31	4	⊆	⊆	NUM
ejpam-3019	31	5	y2	y2	NOUN
ejpam-3019	31	6	and	and	CCONJ
ejpam-3019	31	7	f(y1	f(y1	NOUN
ejpam-3019	31	8	)	)	PUNCT
ejpam-3019	31	9	⊆	⊆	NUM
ejpam-3019	31	10	x2	x2	NOUN
ejpam-3019	31	11	,	,	PUNCT
ejpam-3019	31	12	then	then	ADV
ejpam-3019	31	13	we	we	PRON
ejpam-3019	31	14	call	call	VERB
ejpam-3019	31	15	f	f	PROPN
ejpam-3019	31	16	a	a	DET
ejpam-3019	31	17	contravariant	contravariant	ADJ
ejpam-3019	31	18	map	map	NOUN
ejpam-3019	31	19	from	from	ADP
ejpam-3019	31	20	(	(	PUNCT
ejpam-3019	31	21	x1	x1	PROPN
ejpam-3019	31	22	,	,	PUNCT
ejpam-3019	31	23	y1	y1	PROPN
ejpam-3019	31	24	)	)	PUNCT
ejpam-3019	31	25	to	to	ADP
ejpam-3019	31	26	(	(	PUNCT
ejpam-3019	31	27	x2	x2	PROPN
ejpam-3019	31	28	,	,	PUNCT
ejpam-3019	31	29	y2	y2	PROPN
ejpam-3019	31	30	)	)	PUNCT
ejpam-3019	31	31	and	and	CCONJ
ejpam-3019	31	32	write	write	VERB
ejpam-3019	31	33	f	f	PROPN
ejpam-3019	31	34	:	:	PUNCT
ejpam-3019	31	35	(	(	PUNCT
ejpam-3019	31	36	x1	x1	PROPN
ejpam-3019	31	37	,	,	PUNCT
ejpam-3019	31	38	y1	y1	PROPN
ejpam-3019	31	39	)	)	PUNCT
ejpam-3019	31	40	↘	↘	PROPN
ejpam-3019	31	41	↗	↗	PROPN
ejpam-3019	31	42	(	(	PUNCT
ejpam-3019	31	43	x2	x2	PROPN
ejpam-3019	31	44	,	,	PUNCT
ejpam-3019	31	45	y2	y2	PROPN
ejpam-3019	31	46	)	)	PUNCT
ejpam-3019	31	47	.	.	PUNCT
ejpam-3019	32	1	in	in	ADP
ejpam-3019	32	2	particular	particular	ADJ
ejpam-3019	32	3	,	,	PUNCT
ejpam-3019	32	4	if	if	SCONJ
ejpam-3019	32	5	d1	d1	PROPN
ejpam-3019	32	6	and	and	CCONJ
ejpam-3019	32	7	d2	d2	PROPN
ejpam-3019	32	8	are	be	AUX
ejpam-3019	32	9	bipolar	bipolar	ADJ
ejpam-3019	32	10	metrics	metric	NOUN
ejpam-3019	32	11	on	on	ADP
ejpam-3019	32	12	(	(	PUNCT
ejpam-3019	32	13	x1	x1	PROPN
ejpam-3019	32	14	,	,	PUNCT
ejpam-3019	32	15	y1	y1	PROPN
ejpam-3019	32	16	)	)	PUNCT
ejpam-3019	32	17	and	and	CCONJ
ejpam-3019	32	18	(	(	PUNCT
ejpam-3019	32	19	x2	x2	PROPN
ejpam-3019	32	20	,	,	PUNCT
ejpam-3019	32	21	y2	y2	PROPN
ejpam-3019	32	22	)	)	PUNCT
ejpam-3019	32	23	,	,	PUNCT
ejpam-3019	32	24	respectively	respectively	ADV
ejpam-3019	32	25	,	,	PUNCT
ejpam-3019	32	26	we	we	PRON
ejpam-3019	32	27	sometimes	sometimes	ADV
ejpam-3019	32	28	use	use	VERB
ejpam-3019	32	29	the	the	DET
ejpam-3019	32	30	notations	notation	NOUN
ejpam-3019	32	31	f	f	X
ejpam-3019	32	32	:	:	PUNCT
ejpam-3019	32	33	(	(	PUNCT
ejpam-3019	32	34	x1	x1	PROPN
ejpam-3019	32	35	,	,	PUNCT
ejpam-3019	32	36	y1	y1	NOUN
ejpam-3019	32	37	,	,	PUNCT
ejpam-3019	32	38	d1	d1	NOUN
ejpam-3019	32	39	)	)	PUNCT
ejpam-3019	32	40	⇒	⇒	NOUN
ejpam-3019	32	41	(	(	PUNCT
ejpam-3019	32	42	x2	x2	PROPN
ejpam-3019	32	43	,	,	PUNCT
ejpam-3019	32	44	y2	y2	PROPN
ejpam-3019	32	45	,	,	PUNCT
ejpam-3019	32	46	d2	d2	PROPN
ejpam-3019	32	47	)	)	PUNCT
ejpam-3019	32	48	and	and	CCONJ
ejpam-3019	32	49	f	f	NOUN
ejpam-3019	32	50	:	:	PUNCT
ejpam-3019	32	51	(	(	PUNCT
ejpam-3019	32	52	x1	x1	PROPN
ejpam-3019	32	53	,	,	PUNCT
ejpam-3019	32	54	y1	y1	NOUN
ejpam-3019	32	55	,	,	PUNCT
ejpam-3019	32	56	d1	d1	PROPN
ejpam-3019	32	57	)	)	PUNCT
ejpam-3019	32	58	↘	↘	PROPN
ejpam-3019	32	59	↗	↗	PROPN
ejpam-3019	32	60	(	(	PUNCT
ejpam-3019	32	61	x2	x2	PROPN
ejpam-3019	32	62	,	,	PUNCT
ejpam-3019	32	63	y2	y2	PROPN
ejpam-3019	32	64	,	,	PUNCT
ejpam-3019	32	65	d2	d2	PROPN
ejpam-3019	32	66	)	)	PUNCT
ejpam-3019	32	67	.	.	PUNCT
ejpam-3019	33	1	definition	definition	NOUN
ejpam-3019	33	2	3	3	NUM
ejpam-3019	33	3	.	.	PUNCT
ejpam-3019	34	1	[	[	X
ejpam-3019	34	2	13	13	NUM
ejpam-3019	34	3	]	]	PUNCT
ejpam-3019	34	4	let	let	VERB
ejpam-3019	34	5	(	(	PUNCT
ejpam-3019	34	6	x	x	NOUN
ejpam-3019	34	7	,	,	PUNCT
ejpam-3019	34	8	y	y	PROPN
ejpam-3019	34	9	,	,	PUNCT
ejpam-3019	34	10	d	d	NOUN
ejpam-3019	34	11	)	)	PUNCT
ejpam-3019	34	12	be	be	AUX
ejpam-3019	34	13	a	a	DET
ejpam-3019	34	14	bipolar	bipolar	ADJ
ejpam-3019	34	15	metric	metric	ADJ
ejpam-3019	34	16	space	space	NOUN
ejpam-3019	34	17	.	.	PUNCT
ejpam-3019	35	1	a	a	DET
ejpam-3019	35	2	point	point	NOUN
ejpam-3019	35	3	u	u	NOUN
ejpam-3019	35	4	∈	∈	PROPN
ejpam-3019	35	5	x	x	PUNCT
ejpam-3019	35	6	∪	∪	ADP
ejpam-3019	35	7	y	y	PROPN
ejpam-3019	35	8	is	be	AUX
ejpam-3019	35	9	called	call	VERB
ejpam-3019	35	10	a	a	DET
ejpam-3019	35	11	left	left	ADJ
ejpam-3019	35	12	point	point	NOUN
ejpam-3019	35	13	if	if	SCONJ
ejpam-3019	35	14	u	u	PROPN
ejpam-3019	35	15	∈	∈	PROPN
ejpam-3019	35	16	x	x	NOUN
ejpam-3019	35	17	,	,	PUNCT
ejpam-3019	35	18	a	a	DET
ejpam-3019	35	19	right	right	ADJ
ejpam-3019	35	20	point	point	NOUN
ejpam-3019	35	21	if	if	SCONJ
ejpam-3019	35	22	u	u	PROPN
ejpam-3019	35	23	∈	∈	PROPN
ejpam-3019	35	24	y	y	PROPN
ejpam-3019	35	25	and	and	CCONJ
ejpam-3019	35	26	a	a	DET
ejpam-3019	35	27	central	central	ADJ
ejpam-3019	35	28	point	point	NOUN
ejpam-3019	35	29	if	if	SCONJ
ejpam-3019	35	30	it	it	PRON
ejpam-3019	35	31	is	be	AUX
ejpam-3019	35	32	both	both	PRON
ejpam-3019	35	33	left	leave	VERB
ejpam-3019	35	34	and	and	CCONJ
ejpam-3019	35	35	right	right	ADJ
ejpam-3019	35	36	point	point	NOUN
ejpam-3019	35	37	.	.	PUNCT
ejpam-3019	36	1	similarly	similarly	ADV
ejpam-3019	36	2	a	a	DET
ejpam-3019	36	3	sequence	sequence	NOUN
ejpam-3019	36	4	(	(	PUNCT
ejpam-3019	36	5	xn	xn	PROPN
ejpam-3019	36	6	)	)	PUNCT
ejpam-3019	36	7	on	on	ADP
ejpam-3019	36	8	the	the	DET
ejpam-3019	36	9	set	set	NOUN
ejpam-3019	36	10	x	x	PUNCT
ejpam-3019	36	11	is	be	AUX
ejpam-3019	36	12	called	call	VERB
ejpam-3019	36	13	a	a	DET
ejpam-3019	36	14	left	left	ADJ
ejpam-3019	36	15	sequence	sequence	NOUN
ejpam-3019	36	16	and	and	CCONJ
ejpam-3019	36	17	a	a	DET
ejpam-3019	36	18	sequence	sequence	NOUN
ejpam-3019	36	19	(	(	PUNCT
ejpam-3019	36	20	yn	yn	NOUN
ejpam-3019	36	21	)	)	PUNCT
ejpam-3019	36	22	on	on	ADP
ejpam-3019	36	23	y	y	PROPN
ejpam-3019	36	24	is	be	AUX
ejpam-3019	36	25	called	call	VERB
ejpam-3019	36	26	a	a	DET
ejpam-3019	36	27	right	right	ADJ
ejpam-3019	36	28	sequence	sequence	NOUN
ejpam-3019	36	29	.	.	PUNCT
ejpam-3019	37	1	in	in	ADP
ejpam-3019	37	2	a	a	DET
ejpam-3019	37	3	bipolar	bipolar	ADJ
ejpam-3019	37	4	metric	metric	ADJ
ejpam-3019	37	5	space	space	NOUN
ejpam-3019	37	6	,	,	PUNCT
ejpam-3019	37	7	a	a	DET
ejpam-3019	37	8	left	left	NOUN
ejpam-3019	37	9	or	or	CCONJ
ejpam-3019	37	10	a	a	DET
ejpam-3019	37	11	right	right	ADJ
ejpam-3019	37	12	sequence	sequence	NOUN
ejpam-3019	37	13	is	be	AUX
ejpam-3019	37	14	called	call	VERB
ejpam-3019	37	15	simply	simply	ADV
ejpam-3019	37	16	a	a	DET
ejpam-3019	37	17	sequence	sequence	NOUN
ejpam-3019	37	18	.	.	PUNCT
ejpam-3019	38	1	a	a	DET
ejpam-3019	38	2	sequence	sequence	NOUN
ejpam-3019	38	3	(	(	PUNCT
ejpam-3019	38	4	un	un	PROPN
ejpam-3019	38	5	)	)	PUNCT
ejpam-3019	38	6	is	be	AUX
ejpam-3019	38	7	said	say	VERB
ejpam-3019	38	8	to	to	PART
ejpam-3019	38	9	be	be	AUX
ejpam-3019	38	10	convergent	convergent	ADJ
ejpam-3019	38	11	to	to	ADP
ejpam-3019	38	12	a	a	DET
ejpam-3019	38	13	point	point	NOUN
ejpam-3019	38	14	u	u	NOUN
ejpam-3019	38	15	,	,	PUNCT
ejpam-3019	38	16	iff	iff	PROPN
ejpam-3019	38	17	(	(	PUNCT
ejpam-3019	38	18	un	un	PROPN
ejpam-3019	38	19	)	)	PUNCT
ejpam-3019	38	20	is	be	AUX
ejpam-3019	38	21	a	a	DET
ejpam-3019	38	22	left	left	ADJ
ejpam-3019	38	23	sequence	sequence	NOUN
ejpam-3019	38	24	,	,	PUNCT
ejpam-3019	38	25	u	u	NOUN
ejpam-3019	38	26	is	be	AUX
ejpam-3019	38	27	a	a	DET
ejpam-3019	38	28	right	right	ADJ
ejpam-3019	38	29	point	point	NOUN
ejpam-3019	38	30	and	and	CCONJ
ejpam-3019	38	31	lim	lim	PROPN
ejpam-3019	38	32	n→∞	n→∞	NUM
ejpam-3019	38	33	d(un	d(un	PROPN
ejpam-3019	38	34	,	,	PUNCT
ejpam-3019	38	35	u	u	NOUN
ejpam-3019	38	36	)	)	PUNCT
ejpam-3019	38	37	=	=	SYM
ejpam-3019	38	38	0	0	NUM
ejpam-3019	38	39	;	;	PUNCT
ejpam-3019	38	40	or	or	CCONJ
ejpam-3019	38	41	(	(	PUNCT
ejpam-3019	38	42	un	un	PROPN
ejpam-3019	38	43	)	)	PUNCT
ejpam-3019	38	44	is	be	AUX
ejpam-3019	38	45	a	a	DET
ejpam-3019	38	46	right	right	ADJ
ejpam-3019	38	47	sequence	sequence	NOUN
ejpam-3019	38	48	,	,	PUNCT
ejpam-3019	38	49	u	u	NOUN
ejpam-3019	38	50	is	be	AUX
ejpam-3019	38	51	a	a	DET
ejpam-3019	38	52	left	left	ADJ
ejpam-3019	38	53	point	point	NOUN
ejpam-3019	38	54	and	and	CCONJ
ejpam-3019	38	55	lim	lim	PROPN
ejpam-3019	38	56	n→∞	n→∞	PROPN
ejpam-3019	38	57	d(u	d(u	PROPN
ejpam-3019	38	58	,	,	PUNCT
ejpam-3019	38	59	un	un	PROPN
ejpam-3019	38	60	)	)	PUNCT
ejpam-3019	38	61	=	=	SYM
ejpam-3019	39	1	0	0	X
ejpam-3019	39	2	.	.	PUNCT
ejpam-3019	40	1	a	a	DET
ejpam-3019	40	2	bisequence	bisequence	NOUN
ejpam-3019	40	3	(	(	PUNCT
ejpam-3019	40	4	xn	xn	PROPN
ejpam-3019	40	5	,	,	PUNCT
ejpam-3019	40	6	yn	yn	PROPN
ejpam-3019	40	7	)	)	PUNCT
ejpam-3019	40	8	on	on	ADP
ejpam-3019	40	9	(	(	PUNCT
ejpam-3019	40	10	x	x	NOUN
ejpam-3019	40	11	,	,	PUNCT
ejpam-3019	40	12	y	y	PROPN
ejpam-3019	40	13	,	,	PUNCT
ejpam-3019	40	14	d	d	NOUN
ejpam-3019	40	15	)	)	PUNCT
ejpam-3019	40	16	is	be	AUX
ejpam-3019	40	17	a	a	DET
ejpam-3019	40	18	sequence	sequence	NOUN
ejpam-3019	40	19	on	on	ADP
ejpam-3019	40	20	the	the	DET
ejpam-3019	40	21	set	set	NOUN
ejpam-3019	40	22	x	x	X
ejpam-3019	40	23	×	×	PROPN
ejpam-3019	40	24	y	y	PROPN
ejpam-3019	40	25	.	.	PUNCT
ejpam-3019	41	1	if	if	SCONJ
ejpam-3019	41	2	the	the	DET
ejpam-3019	41	3	sequences	sequence	NOUN
ejpam-3019	41	4	(	(	PUNCT
ejpam-3019	41	5	xn	xn	NUM
ejpam-3019	41	6	)	)	PUNCT
ejpam-3019	41	7	and	and	CCONJ
ejpam-3019	41	8	(	(	PUNCT
ejpam-3019	41	9	yn	yn	NOUN
ejpam-3019	41	10	)	)	PUNCT
ejpam-3019	41	11	are	be	AUX
ejpam-3019	41	12	convergent	convergent	ADJ
ejpam-3019	41	13	,	,	PUNCT
ejpam-3019	41	14	then	then	ADV
ejpam-3019	41	15	the	the	DET
ejpam-3019	41	16	bisequence	bisequence	NOUN
ejpam-3019	41	17	(	(	PUNCT
ejpam-3019	41	18	xn	xn	PROPN
ejpam-3019	41	19	,	,	PUNCT
ejpam-3019	41	20	yn	yn	PROPN
ejpam-3019	41	21	)	)	PUNCT
ejpam-3019	41	22	is	be	AUX
ejpam-3019	41	23	said	say	VERB
ejpam-3019	41	24	to	to	PART
ejpam-3019	41	25	be	be	AUX
ejpam-3019	41	26	convergent	convergent	ADJ
ejpam-3019	41	27	,	,	PUNCT
ejpam-3019	41	28	and	and	CCONJ
ejpam-3019	41	29	if	if	SCONJ
ejpam-3019	41	30	(	(	PUNCT
ejpam-3019	41	31	xn	xn	X
ejpam-3019	41	32	)	)	PUNCT
ejpam-3019	41	33	and	and	CCONJ
ejpam-3019	41	34	(	(	PUNCT
ejpam-3019	41	35	yn	yn	NOUN
ejpam-3019	41	36	)	)	PUNCT
ejpam-3019	41	37	converge	converge	VERB
ejpam-3019	41	38	to	to	ADP
ejpam-3019	41	39	a	a	DET
ejpam-3019	41	40	common	common	ADJ
ejpam-3019	41	41	point	point	NOUN
ejpam-3019	41	42	,	,	PUNCT
ejpam-3019	41	43	then	then	ADV
ejpam-3019	41	44	(	(	PUNCT
ejpam-3019	41	45	xn	xn	PROPN
ejpam-3019	41	46	,	,	PUNCT
ejpam-3019	41	47	yn	yn	PROPN
ejpam-3019	41	48	)	)	PUNCT
ejpam-3019	41	49	is	be	AUX
ejpam-3019	41	50	called	call	VERB
ejpam-3019	41	51	biconvergent	biconvergent	NOUN
ejpam-3019	41	52	.	.	PUNCT
ejpam-3019	42	1	(	(	PUNCT
ejpam-3019	42	2	xn	xn	PROPN
ejpam-3019	42	3	,	,	PUNCT
ejpam-3019	42	4	yn	yn	PROPN
ejpam-3019	42	5	)	)	PUNCT
ejpam-3019	42	6	is	be	AUX
ejpam-3019	42	7	a	a	DET
ejpam-3019	42	8	cauchy	cauchy	ADJ
ejpam-3019	42	9	bisequence	bisequence	NOUN
ejpam-3019	42	10	,	,	PUNCT
ejpam-3019	42	11	if	if	SCONJ
ejpam-3019	42	12	lim	lim	PROPN
ejpam-3019	42	13	n	n	CCONJ
ejpam-3019	42	14	,	,	PUNCT
ejpam-3019	42	15	m→∞	m→∞	NOUN
ejpam-3019	42	16	d(xn	d(xn	PROPN
ejpam-3019	42	17	,	,	PUNCT
ejpam-3019	42	18	ym	ym	NOUN
ejpam-3019	42	19	)	)	PUNCT
ejpam-3019	42	20	=	=	NOUN
ejpam-3019	43	1	0	0	X
ejpam-3019	43	2	.	.	PUNCT
ejpam-3019	44	1	in	in	ADP
ejpam-3019	44	2	a	a	DET
ejpam-3019	44	3	bipolar	bipolar	ADJ
ejpam-3019	44	4	metric	metric	ADJ
ejpam-3019	44	5	space	space	NOUN
ejpam-3019	44	6	,	,	PUNCT
ejpam-3019	44	7	every	every	DET
ejpam-3019	44	8	convergent	convergent	NOUN
ejpam-3019	44	9	cauchy	cauchy	ADJ
ejpam-3019	44	10	bisequence	bisequence	NOUN
ejpam-3019	44	11	is	be	AUX
ejpam-3019	44	12	biconvergent	biconvergent	NOUN
ejpam-3019	44	13	.	.	PUNCT
ejpam-3019	45	1	a	a	DET
ejpam-3019	45	2	bipolar	bipolar	ADJ
ejpam-3019	45	3	metric	metric	ADJ
ejpam-3019	45	4	space	space	NOUN
ejpam-3019	45	5	is	be	AUX
ejpam-3019	45	6	called	call	VERB
ejpam-3019	45	7	complete	complete	ADJ
ejpam-3019	45	8	,	,	PUNCT
ejpam-3019	45	9	if	if	SCONJ
ejpam-3019	45	10	every	every	DET
ejpam-3019	45	11	cauchy	cauchy	ADJ
ejpam-3019	45	12	bisequence	bisequence	NOUN
ejpam-3019	45	13	is	be	AUX
ejpam-3019	45	14	convergent	convergent	NOUN
ejpam-3019	45	15	,	,	PUNCT
ejpam-3019	45	16	hence	hence	ADV
ejpam-3019	45	17	biconvergent	biconvergent	NOUN
ejpam-3019	45	18	.	.	PUNCT
ejpam-3019	46	1	definition	definition	NOUN
ejpam-3019	46	2	4	4	NUM
ejpam-3019	46	3	.	.	PUNCT
ejpam-3019	47	1	[	[	X
ejpam-3019	47	2	13	13	NUM
ejpam-3019	47	3	]	]	PUNCT
ejpam-3019	47	4	let	let	VERB
ejpam-3019	47	5	(	(	PUNCT
ejpam-3019	47	6	x1	x1	ADJ
ejpam-3019	47	7	,	,	PUNCT
ejpam-3019	47	8	y1	y1	NOUN
ejpam-3019	47	9	,	,	PUNCT
ejpam-3019	47	10	d1	d1	NOUN
ejpam-3019	47	11	)	)	PUNCT
ejpam-3019	47	12	and	and	CCONJ
ejpam-3019	47	13	(	(	PUNCT
ejpam-3019	47	14	x2	x2	PROPN
ejpam-3019	47	15	,	,	PUNCT
ejpam-3019	47	16	y2	y2	PROPN
ejpam-3019	47	17	,	,	PUNCT
ejpam-3019	47	18	d2	d2	PROPN
ejpam-3019	47	19	)	)	PUNCT
ejpam-3019	47	20	be	be	AUX
ejpam-3019	47	21	bipolar	bipolar	ADJ
ejpam-3019	47	22	metric	metric	ADJ
ejpam-3019	47	23	spaces	space	NOUN
ejpam-3019	47	24	.	.	PUNCT
ejpam-3019	48	1	(	(	PUNCT
ejpam-3019	48	2	1	1	X
ejpam-3019	48	3	)	)	PUNCT
ejpam-3019	48	4	a	a	DET
ejpam-3019	48	5	map	map	NOUN
ejpam-3019	48	6	f	f	X
ejpam-3019	48	7	:	:	PUNCT
ejpam-3019	48	8	(	(	PUNCT
ejpam-3019	48	9	x1	x1	PROPN
ejpam-3019	48	10	,	,	PUNCT
ejpam-3019	48	11	y1	y1	NOUN
ejpam-3019	48	12	,	,	PUNCT
ejpam-3019	48	13	d1	d1	NOUN
ejpam-3019	48	14	)	)	PUNCT
ejpam-3019	48	15	⇒	⇒	NOUN
ejpam-3019	48	16	(	(	PUNCT
ejpam-3019	48	17	x2	x2	PROPN
ejpam-3019	48	18	,	,	PUNCT
ejpam-3019	48	19	y2	y2	PROPN
ejpam-3019	48	20	,	,	PUNCT
ejpam-3019	48	21	d2	d2	PROPN
ejpam-3019	48	22	)	)	PUNCT
ejpam-3019	48	23	is	be	AUX
ejpam-3019	48	24	called	call	VERB
ejpam-3019	48	25	left	left	ADJ
ejpam-3019	48	26	-	-	PUNCT
ejpam-3019	48	27	continuous	continuous	ADJ
ejpam-3019	48	28	at	at	ADP
ejpam-3019	48	29	a	a	DET
ejpam-3019	48	30	point	point	NOUN
ejpam-3019	48	31	x0	x0	PROPN
ejpam-3019	48	32	∈	∈	PROPN
ejpam-3019	49	1	x1	x1	PROPN
ejpam-3019	49	2	,	,	PUNCT
ejpam-3019	49	3	if	if	SCONJ
ejpam-3019	49	4	for	for	ADP
ejpam-3019	49	5	every	every	DET
ejpam-3019	49	6	ε	ε	PROPN
ejpam-3019	49	7	>	>	X
ejpam-3019	49	8	0	0	PROPN
ejpam-3019	49	9	,	,	PUNCT
ejpam-3019	49	10	there	there	PRON
ejpam-3019	49	11	exists	exist	VERB
ejpam-3019	49	12	a	a	DET
ejpam-3019	49	13	δ	δ	PROPN
ejpam-3019	49	14	>	>	X
ejpam-3019	49	15	0	0	NUM
ejpam-3019	50	1	such	such	ADJ
ejpam-3019	50	2	that	that	SCONJ
ejpam-3019	50	3	d1	d1	PROPN
ejpam-3019	50	4	(	(	PUNCT
ejpam-3019	50	5	x0	x0	PROPN
ejpam-3019	50	6	,	,	PUNCT
ejpam-3019	50	7	y	y	PROPN
ejpam-3019	50	8	)	)	PUNCT
ejpam-3019	50	9	<	<	X
ejpam-3019	50	10	δ	δ	PROPN
ejpam-3019	50	11	implies	imply	VERB
ejpam-3019	50	12	d2	d2	PROPN
ejpam-3019	50	13	(	(	PUNCT
ejpam-3019	50	14	f	f	PROPN
ejpam-3019	50	15	(	(	PUNCT
ejpam-3019	50	16	x0	x0	PROPN
ejpam-3019	50	17	)	)	PUNCT
ejpam-3019	50	18	,	,	PUNCT
ejpam-3019	50	19	f	f	PROPN
ejpam-3019	50	20	(	(	PUNCT
ejpam-3019	50	21	y	y	NOUN
ejpam-3019	50	22	)	)	PUNCT
ejpam-3019	50	23	)	)	PUNCT
ejpam-3019	51	1	<	<	X
ejpam-3019	51	2	ε	ε	PROPN
ejpam-3019	51	3	all	all	DET
ejpam-3019	51	4	y	y	PROPN
ejpam-3019	51	5	∈	∈	PROPN
ejpam-3019	51	6	y1	y1	PROPN
ejpam-3019	51	7	.	.	PUNCT
ejpam-3019	52	1	(	(	PUNCT
ejpam-3019	52	2	2	2	X
ejpam-3019	52	3	)	)	PUNCT
ejpam-3019	52	4	a	a	DET
ejpam-3019	52	5	map	map	NOUN
ejpam-3019	52	6	f	f	X
ejpam-3019	52	7	:	:	PUNCT
ejpam-3019	52	8	(	(	PUNCT
ejpam-3019	52	9	x1	x1	PROPN
ejpam-3019	52	10	,	,	PUNCT
ejpam-3019	52	11	y1	y1	NOUN
ejpam-3019	52	12	,	,	PUNCT
ejpam-3019	52	13	d1	d1	NOUN
ejpam-3019	52	14	)	)	PUNCT
ejpam-3019	52	15	⇒	⇒	NOUN
ejpam-3019	52	16	(	(	PUNCT
ejpam-3019	52	17	x2	x2	PROPN
ejpam-3019	52	18	,	,	PUNCT
ejpam-3019	52	19	y2	y2	PROPN
ejpam-3019	52	20	,	,	PUNCT
ejpam-3019	52	21	d2	d2	PROPN
ejpam-3019	52	22	)	)	PUNCT
ejpam-3019	52	23	is	be	AUX
ejpam-3019	52	24	called	call	VERB
ejpam-3019	52	25	right	right	ADV
ejpam-3019	52	26	-	-	PUNCT
ejpam-3019	52	27	continuous	continuous	ADJ
ejpam-3019	52	28	at	at	ADP
ejpam-3019	52	29	a	a	DET
ejpam-3019	52	30	point	point	NOUN
ejpam-3019	52	31	y0	y0	PROPN
ejpam-3019	52	32	∈	∈	NOUN
ejpam-3019	52	33	y1	y1	NOUN
ejpam-3019	52	34	,	,	PUNCT
ejpam-3019	52	35	if	if	SCONJ
ejpam-3019	52	36	for	for	ADP
ejpam-3019	52	37	every	every	DET
ejpam-3019	52	38	ε	ε	PROPN
ejpam-3019	52	39	>	>	X
ejpam-3019	52	40	0	0	PROPN
ejpam-3019	52	41	,	,	PUNCT
ejpam-3019	52	42	there	there	PRON
ejpam-3019	52	43	exists	exist	VERB
ejpam-3019	52	44	a	a	DET
ejpam-3019	52	45	δ	δ	PROPN
ejpam-3019	52	46	>	>	X
ejpam-3019	52	47	0	0	NUM
ejpam-3019	53	1	such	such	ADJ
ejpam-3019	53	2	that	that	SCONJ
ejpam-3019	53	3	d1	d1	PROPN
ejpam-3019	53	4	(	(	PUNCT
ejpam-3019	53	5	x	x	NOUN
ejpam-3019	53	6	,	,	PUNCT
ejpam-3019	53	7	y0	y0	NOUN
ejpam-3019	53	8	)	)	PUNCT
ejpam-3019	53	9	<	<	X
ejpam-3019	53	10	δ	δ	PROPN
ejpam-3019	53	11	implies	imply	VERB
ejpam-3019	53	12	d2	d2	PROPN
ejpam-3019	53	13	(	(	PUNCT
ejpam-3019	53	14	f	f	X
ejpam-3019	53	15	(	(	PUNCT
ejpam-3019	53	16	x	x	NOUN
ejpam-3019	53	17	)	)	PUNCT
ejpam-3019	53	18	,	,	PUNCT
ejpam-3019	53	19	f	f	PROPN
ejpam-3019	53	20	(	(	PUNCT
ejpam-3019	53	21	y0	y0	NOUN
ejpam-3019	53	22	)	)	PUNCT
ejpam-3019	53	23	)	)	PUNCT
ejpam-3019	53	24	<	<	X
ejpam-3019	53	25	ε	ε	PROPN
ejpam-3019	53	26	for	for	ADP
ejpam-3019	53	27	all	all	DET
ejpam-3019	53	28	x	x	SYM
ejpam-3019	53	29	∈	∈	PROPN
ejpam-3019	53	30	x1	x1	PROPN
ejpam-3019	53	31	.	.	PUNCT
ejpam-3019	54	1	(	(	PUNCT
ejpam-3019	54	2	3	3	X
ejpam-3019	54	3	)	)	PUNCT
ejpam-3019	54	4	a	a	DET
ejpam-3019	54	5	map	map	NOUN
ejpam-3019	54	6	f	f	NOUN
ejpam-3019	54	7	is	be	AUX
ejpam-3019	54	8	called	call	VERB
ejpam-3019	54	9	continuous	continuous	ADJ
ejpam-3019	54	10	,	,	PUNCT
ejpam-3019	54	11	if	if	SCONJ
ejpam-3019	54	12	it	it	PRON
ejpam-3019	54	13	is	be	AUX
ejpam-3019	54	14	left	leave	VERB
ejpam-3019	54	15	-	-	PUNCT
ejpam-3019	54	16	continuous	continuous	ADJ
ejpam-3019	54	17	at	at	ADP
ejpam-3019	54	18	each	each	DET
ejpam-3019	54	19	point	point	NOUN
ejpam-3019	54	20	x	x	X
ejpam-3019	54	21	∈	∈	NOUN
ejpam-3019	54	22	x1	x1	ADJ
ejpam-3019	54	23	and	and	CCONJ
ejpam-3019	54	24	right	right	ADJ
ejpam-3019	54	25	-	-	PUNCT
ejpam-3019	54	26	continuous	continuous	ADJ
ejpam-3019	54	27	at	at	ADP
ejpam-3019	54	28	each	each	DET
ejpam-3019	54	29	point	point	NOUN
ejpam-3019	54	30	y	y	PROPN
ejpam-3019	54	31	∈	∈	PROPN
ejpam-3019	54	32	y1	y1	PROPN
ejpam-3019	54	33	.	.	PUNCT
ejpam-3019	54	34	a.	a.	PROPN
ejpam-3019	54	35	mutlu	mutlu	PROPN
ejpam-3019	54	36	,	,	PUNCT
ejpam-3019	54	37	k.	k.	PROPN
ejpam-3019	54	38	özkan	özkan	PROPN
ejpam-3019	54	39	,	,	PUNCT
ejpam-3019	54	40	u.	u.	PROPN
ejpam-3019	54	41	gürdal	gürdal	PROPN
ejpam-3019	54	42	/	/	SYM
ejpam-3019	54	43	eur	eur	PROPN
ejpam-3019	54	44	.	.	PUNCT
ejpam-3019	55	1	j.	j.	PROPN
ejpam-3019	55	2	pure	pure	PROPN
ejpam-3019	55	3	appl	appl	PROPN
ejpam-3019	55	4	.	.	PROPN
ejpam-3019	55	5	math	math	PROPN
ejpam-3019	55	6	,	,	PUNCT
ejpam-3019	55	7	10	10	NUM
ejpam-3019	55	8	(	(	PUNCT
ejpam-3019	55	9	4	4	NUM
ejpam-3019	55	10	)	)	PUNCT
ejpam-3019	55	11	(	(	PUNCT
ejpam-3019	55	12	2017	2017	NUM
ejpam-3019	55	13	)	)	PUNCT
ejpam-3019	55	14	,	,	PUNCT
ejpam-3019	55	15	655	655	NUM
ejpam-3019	55	16	-	-	SYM
ejpam-3019	55	17	667	667	NUM
ejpam-3019	55	18	657	657	NUM
ejpam-3019	55	19	(	(	PUNCT
ejpam-3019	55	20	4	4	NUM
ejpam-3019	55	21	)	)	PUNCT
ejpam-3019	55	22	a	a	DET
ejpam-3019	55	23	contravariant	contravariant	ADJ
ejpam-3019	55	24	map	map	NOUN
ejpam-3019	56	1	f	f	X
ejpam-3019	56	2	:	:	PUNCT
ejpam-3019	56	3	(	(	PUNCT
ejpam-3019	56	4	x1	x1	PROPN
ejpam-3019	56	5	,	,	PUNCT
ejpam-3019	56	6	y1	y1	NOUN
ejpam-3019	56	7	,	,	PUNCT
ejpam-3019	56	8	d1	d1	PROPN
ejpam-3019	56	9	)	)	PUNCT
ejpam-3019	56	10	↘	↘	PROPN
ejpam-3019	56	11	↗	↗	PROPN
ejpam-3019	56	12	(	(	PUNCT
ejpam-3019	56	13	x2	x2	PROPN
ejpam-3019	56	14	,	,	PUNCT
ejpam-3019	56	15	y2	y2	PROPN
ejpam-3019	56	16	,	,	PUNCT
ejpam-3019	56	17	d2	d2	PROPN
ejpam-3019	56	18	)	)	PUNCT
ejpam-3019	56	19	is	be	AUX
ejpam-3019	56	20	continuous	continuous	ADJ
ejpam-3019	56	21	if	if	SCONJ
ejpam-3019	56	22	and	and	CCONJ
ejpam-3019	56	23	only	only	ADV
ejpam-3019	56	24	if	if	SCONJ
ejpam-3019	56	25	it	it	PRON
ejpam-3019	56	26	is	be	AUX
ejpam-3019	56	27	continuous	continuous	ADJ
ejpam-3019	56	28	as	as	ADP
ejpam-3019	56	29	a	a	DET
ejpam-3019	56	30	covariant	covariant	ADJ
ejpam-3019	56	31	map	map	NOUN
ejpam-3019	56	32	f	f	X
ejpam-3019	56	33	:	:	PUNCT
ejpam-3019	56	34	(	(	PUNCT
ejpam-3019	56	35	x1	x1	PROPN
ejpam-3019	56	36	,	,	PUNCT
ejpam-3019	56	37	y1	y1	NOUN
ejpam-3019	56	38	,	,	PUNCT
ejpam-3019	56	39	d1	d1	NOUN
ejpam-3019	56	40	)	)	PUNCT
ejpam-3019	56	41	⇒	⇒	NOUN
ejpam-3019	56	42	(	(	PUNCT
ejpam-3019	56	43	y2	y2	PROPN
ejpam-3019	56	44	,	,	PUNCT
ejpam-3019	56	45	x2	x2	PROPN
ejpam-3019	56	46	,	,	PUNCT
ejpam-3019	56	47	d̄2	d̄2	PROPN
ejpam-3019	56	48	)	)	PUNCT
ejpam-3019	57	1	it	it	PRON
ejpam-3019	57	2	can	can	AUX
ejpam-3019	57	3	be	be	AUX
ejpam-3019	57	4	seen	see	VERB
ejpam-3019	57	5	from	from	ADP
ejpam-3019	57	6	the	the	DET
ejpam-3019	57	7	definition	definition	NOUN
ejpam-3019	57	8	4	4	NUM
ejpam-3019	57	9	that	that	SCONJ
ejpam-3019	57	10	a	a	DET
ejpam-3019	57	11	covariant	covariant	NOUN
ejpam-3019	57	12	or	or	CCONJ
ejpam-3019	57	13	a	a	DET
ejpam-3019	57	14	contravariant	contravariant	ADJ
ejpam-3019	57	15	map	map	NOUN
ejpam-3019	57	16	f	f	PROPN
ejpam-3019	57	17	from	from	ADP
ejpam-3019	57	18	(	(	PUNCT
ejpam-3019	57	19	x1	x1	PROPN
ejpam-3019	57	20	,	,	PUNCT
ejpam-3019	57	21	y1	y1	NOUN
ejpam-3019	57	22	,	,	PUNCT
ejpam-3019	57	23	d1	d1	NOUN
ejpam-3019	57	24	)	)	PUNCT
ejpam-3019	57	25	to	to	ADP
ejpam-3019	57	26	(	(	PUNCT
ejpam-3019	57	27	x2	x2	PROPN
ejpam-3019	57	28	,	,	PUNCT
ejpam-3019	57	29	y2	y2	PROPN
ejpam-3019	57	30	,	,	PUNCT
ejpam-3019	57	31	d2	d2	PROPN
ejpam-3019	57	32	)	)	PUNCT
ejpam-3019	57	33	is	be	AUX
ejpam-3019	57	34	continuous	continuous	ADJ
ejpam-3019	57	35	if	if	SCONJ
ejpam-3019	57	36	and	and	CCONJ
ejpam-3019	57	37	only	only	ADV
ejpam-3019	57	38	if	if	SCONJ
ejpam-3019	57	39	(	(	PUNCT
ejpam-3019	57	40	un	un	PROPN
ejpam-3019	57	41	)	)	PUNCT
ejpam-3019	57	42	→	→	SYM
ejpam-3019	57	43	v	v	NOUN
ejpam-3019	57	44	on	on	ADP
ejpam-3019	57	45	(	(	PUNCT
ejpam-3019	57	46	x1	x1	PROPN
ejpam-3019	57	47	,	,	PUNCT
ejpam-3019	57	48	y1	y1	NOUN
ejpam-3019	57	49	,	,	PUNCT
ejpam-3019	57	50	d1	d1	PROPN
ejpam-3019	57	51	)	)	PUNCT
ejpam-3019	57	52	implies	imply	VERB
ejpam-3019	57	53	(	(	PUNCT
ejpam-3019	57	54	f	f	X
ejpam-3019	57	55	(	(	PUNCT
ejpam-3019	57	56	un))→	un))→	ADJ
ejpam-3019	57	57	f	f	PROPN
ejpam-3019	57	58	(	(	PUNCT
ejpam-3019	57	59	v	v	NOUN
ejpam-3019	57	60	)	)	PUNCT
ejpam-3019	57	61	on	on	ADP
ejpam-3019	57	62	(	(	PUNCT
ejpam-3019	57	63	x2	x2	PROPN
ejpam-3019	57	64	,	,	PUNCT
ejpam-3019	57	65	y2	y2	PROPN
ejpam-3019	57	66	,	,	PUNCT
ejpam-3019	57	67	d2	d2	PROPN
ejpam-3019	57	68	)	)	PUNCT
ejpam-3019	57	69	.	.	PUNCT
ejpam-3019	58	1	3	3	X
ejpam-3019	58	2	.	.	X
ejpam-3019	58	3	main	main	ADJ
ejpam-3019	58	4	results	result	NOUN
ejpam-3019	58	5	definition	definition	NOUN
ejpam-3019	58	6	5	5	NUM
ejpam-3019	58	7	.	.	PUNCT
ejpam-3019	59	1	let	let	VERB
ejpam-3019	59	2	(	(	PUNCT
ejpam-3019	59	3	x	x	X
ejpam-3019	59	4	,	,	PUNCT
ejpam-3019	59	5	y	y	PROPN
ejpam-3019	59	6	,	,	PUNCT
ejpam-3019	59	7	d	d	NOUN
ejpam-3019	59	8	)	)	PUNCT
ejpam-3019	59	9	be	be	AUX
ejpam-3019	59	10	a	a	DET
ejpam-3019	59	11	bipolar	bipolar	ADJ
ejpam-3019	59	12	metric	metric	ADJ
ejpam-3019	59	13	space	space	NOUN
ejpam-3019	59	14	,	,	PUNCT
ejpam-3019	59	15	f	f	X
ejpam-3019	59	16	:	:	PUNCT
ejpam-3019	59	17	(	(	PUNCT
ejpam-3019	59	18	x2	x2	INTJ
ejpam-3019	59	19	,	,	PUNCT
ejpam-3019	59	20	y	y	PROPN
ejpam-3019	59	21	2	2	NUM
ejpam-3019	59	22	)	)	PUNCT
ejpam-3019	59	23	⇒	⇒	NOUN
ejpam-3019	59	24	(	(	PUNCT
ejpam-3019	59	25	x	x	X
ejpam-3019	59	26	,	,	PUNCT
ejpam-3019	59	27	y	y	PROPN
ejpam-3019	59	28	)	)	PUNCT
ejpam-3019	59	29	be	be	AUX
ejpam-3019	59	30	a	a	DET
ejpam-3019	59	31	covariant	covariant	ADJ
ejpam-3019	59	32	mapping	mapping	NOUN
ejpam-3019	59	33	.	.	PUNCT
ejpam-3019	60	1	(	(	PUNCT
ejpam-3019	60	2	a	a	PRON
ejpam-3019	60	3	,	,	PUNCT
ejpam-3019	60	4	b	b	NOUN
ejpam-3019	60	5	)	)	PUNCT
ejpam-3019	60	6	∈	∈	NOUN
ejpam-3019	60	7	x2	x2	PROPN
ejpam-3019	60	8	∪	∪	ADP
ejpam-3019	60	9	y	y	PROPN
ejpam-3019	60	10	2	2	NUM
ejpam-3019	60	11	is	be	AUX
ejpam-3019	60	12	said	say	VERB
ejpam-3019	60	13	to	to	PART
ejpam-3019	60	14	be	be	AUX
ejpam-3019	60	15	a	a	DET
ejpam-3019	60	16	coupled	couple	VERB
ejpam-3019	60	17	fixed	fix	VERB
ejpam-3019	60	18	point	point	NOUN
ejpam-3019	60	19	of	of	ADP
ejpam-3019	60	20	f	f	PROPN
ejpam-3019	60	21	if	if	SCONJ
ejpam-3019	60	22	f	f	PROPN
ejpam-3019	60	23	(	(	PUNCT
ejpam-3019	60	24	a	a	DET
ejpam-3019	60	25	,	,	PUNCT
ejpam-3019	60	26	b	b	NOUN
ejpam-3019	60	27	)	)	PUNCT
ejpam-3019	60	28	=	=	PUNCT
ejpam-3019	60	29	a	a	PROPN
ejpam-3019	60	30	and	and	CCONJ
ejpam-3019	60	31	f	f	PROPN
ejpam-3019	60	32	(	(	PUNCT
ejpam-3019	60	33	b	b	NOUN
ejpam-3019	60	34	,	,	PUNCT
ejpam-3019	60	35	a	a	PRON
ejpam-3019	60	36	)	)	PUNCT
ejpam-3019	60	37	=	=	SYM
ejpam-3019	60	38	b.	b.	PROPN
ejpam-3019	60	39	theorem	theorem	NOUN
ejpam-3019	60	40	1	1	X
ejpam-3019	60	41	.	.	PUNCT
ejpam-3019	61	1	let	let	AUX
ejpam-3019	61	2	(	(	PUNCT
ejpam-3019	61	3	x	x	X
ejpam-3019	61	4	,	,	PUNCT
ejpam-3019	61	5	y	y	PROPN
ejpam-3019	61	6	,	,	PUNCT
ejpam-3019	61	7	d	d	NOUN
ejpam-3019	61	8	)	)	PUNCT
ejpam-3019	61	9	be	be	AUX
ejpam-3019	61	10	a	a	DET
ejpam-3019	61	11	complete	complete	ADJ
ejpam-3019	61	12	bipolar	bipolar	ADJ
ejpam-3019	61	13	metric	metric	ADJ
ejpam-3019	61	14	space	space	NOUN
ejpam-3019	61	15	,	,	PUNCT
ejpam-3019	61	16	f	f	X
ejpam-3019	61	17	:	:	PUNCT
ejpam-3019	61	18	(	(	PUNCT
ejpam-3019	61	19	x2	x2	INTJ
ejpam-3019	61	20	,	,	PUNCT
ejpam-3019	61	21	y	y	PROPN
ejpam-3019	61	22	2	2	NUM
ejpam-3019	61	23	)	)	PUNCT
ejpam-3019	61	24	⇒	⇒	NOUN
ejpam-3019	61	25	(	(	PUNCT
ejpam-3019	61	26	x	x	X
ejpam-3019	61	27	,	,	PUNCT
ejpam-3019	61	28	y	y	PROPN
ejpam-3019	61	29	)	)	PUNCT
ejpam-3019	61	30	be	be	AUX
ejpam-3019	61	31	a	a	DET
ejpam-3019	61	32	covariant	covariant	ADJ
ejpam-3019	61	33	mapping	mapping	NOUN
ejpam-3019	61	34	and	and	CCONJ
ejpam-3019	61	35	k	k	NOUN
ejpam-3019	61	36	,	,	PUNCT
ejpam-3019	61	37	l	l	NOUN
ejpam-3019	61	38	be	be	VERB
ejpam-3019	61	39	non	non	ADJ
ejpam-3019	61	40	-	-	ADJ
ejpam-3019	61	41	negative	negative	ADJ
ejpam-3019	61	42	constants	constant	NOUN
ejpam-3019	61	43	.	.	PUNCT
ejpam-3019	62	1	if	if	SCONJ
ejpam-3019	62	2	f	f	PROPN
ejpam-3019	62	3	satisfies	satisfy	VERB
ejpam-3019	62	4	the	the	DET
ejpam-3019	62	5	condition	condition	NOUN
ejpam-3019	62	6	d(f	d(f	NOUN
ejpam-3019	62	7	(	(	PUNCT
ejpam-3019	62	8	a	a	DET
ejpam-3019	62	9	,	,	PUNCT
ejpam-3019	62	10	b	b	NOUN
ejpam-3019	62	11	)	)	PUNCT
ejpam-3019	62	12	,	,	PUNCT
ejpam-3019	62	13	f	f	PROPN
ejpam-3019	62	14	(	(	PUNCT
ejpam-3019	62	15	p	p	X
ejpam-3019	62	16	,	,	PUNCT
ejpam-3019	62	17	q	q	NOUN
ejpam-3019	62	18	)	)	PUNCT
ejpam-3019	62	19	)	)	PUNCT
ejpam-3019	62	20	≤	≤	NOUN
ejpam-3019	63	1	kd(a	kd(a	X
ejpam-3019	63	2	,	,	PUNCT
ejpam-3019	63	3	p	p	X
ejpam-3019	63	4	)	)	PUNCT
ejpam-3019	63	5	+	+	CCONJ
ejpam-3019	63	6	ld(b	ld(b	ADJ
ejpam-3019	63	7	,	,	PUNCT
ejpam-3019	63	8	q	q	NOUN
ejpam-3019	63	9	)	)	PUNCT
ejpam-3019	63	10	,	,	PUNCT
ejpam-3019	63	11	k	k	PROPN
ejpam-3019	64	1	+	+	CCONJ
ejpam-3019	64	2	l	l	X
ejpam-3019	64	3	<	<	X
ejpam-3019	64	4	1	1	NUM
ejpam-3019	64	5	(	(	PUNCT
ejpam-3019	64	6	1	1	NUM
ejpam-3019	64	7	)	)	PUNCT
ejpam-3019	64	8	for	for	ADP
ejpam-3019	64	9	all	all	DET
ejpam-3019	64	10	a	a	DET
ejpam-3019	64	11	,	,	PUNCT
ejpam-3019	64	12	b	b	X
ejpam-3019	64	13	∈	∈	PROPN
ejpam-3019	64	14	x	x	SYM
ejpam-3019	64	15	,	,	PUNCT
ejpam-3019	64	16	p	p	X
ejpam-3019	64	17	,	,	PUNCT
ejpam-3019	64	18	q	q	PROPN
ejpam-3019	64	19	∈	∈	PROPN
ejpam-3019	64	20	y	y	PROPN
ejpam-3019	64	21	,	,	PUNCT
ejpam-3019	64	22	then	then	ADV
ejpam-3019	64	23	f	f	X
ejpam-3019	64	24	:	:	PUNCT
ejpam-3019	65	1	x2	x2	PROPN
ejpam-3019	65	2	∪	∪	VERB
ejpam-3019	65	3	y	y	PROPN
ejpam-3019	65	4	2	2	NUM
ejpam-3019	65	5	→	→	SYM
ejpam-3019	65	6	x	x	SYM
ejpam-3019	65	7	∪	∪	ADP
ejpam-3019	65	8	y	y	PROPN
ejpam-3019	65	9	has	have	VERB
ejpam-3019	65	10	a	a	DET
ejpam-3019	65	11	unique	unique	ADJ
ejpam-3019	65	12	coupled	couple	VERB
ejpam-3019	65	13	fixed	fix	VERB
ejpam-3019	65	14	point	point	NOUN
ejpam-3019	65	15	.	.	PUNCT
ejpam-3019	66	1	proof	proof	NOUN
ejpam-3019	66	2	.	.	PUNCT
ejpam-3019	67	1	let	let	VERB
ejpam-3019	67	2	a0	a0	PROPN
ejpam-3019	67	3	,	,	PUNCT
ejpam-3019	67	4	b0	b0	NOUN
ejpam-3019	67	5	∈	∈	PROPN
ejpam-3019	67	6	x	x	X
ejpam-3019	67	7	and	and	CCONJ
ejpam-3019	67	8	p0	p0	NOUN
ejpam-3019	67	9	,	,	PUNCT
ejpam-3019	67	10	q0	q0	PROPN
ejpam-3019	67	11	∈	∈	PROPN
ejpam-3019	67	12	y	y	PROPN
ejpam-3019	67	13	.	.	PUNCT
ejpam-3019	68	1	we	we	PRON
ejpam-3019	68	2	take	take	VERB
ejpam-3019	68	3	a1	a1	NOUN
ejpam-3019	68	4	,	,	PUNCT
ejpam-3019	68	5	b1	b1	NOUN
ejpam-3019	68	6	∈	∈	PROPN
ejpam-3019	68	7	x	x	X
ejpam-3019	68	8	and	and	CCONJ
ejpam-3019	68	9	p1	p1	PROPN
ejpam-3019	68	10	,	,	PUNCT
ejpam-3019	68	11	q1	q1	PROPN
ejpam-3019	68	12	∈	∈	PROPN
ejpam-3019	68	13	y	y	PROPN
ejpam-3019	68	14	with	with	ADP
ejpam-3019	68	15	a1	a1	NOUN
ejpam-3019	68	16	=	=	SYM
ejpam-3019	68	17	f	f	PROPN
ejpam-3019	68	18	(	(	PUNCT
ejpam-3019	68	19	a0	a0	PROPN
ejpam-3019	68	20	,	,	PUNCT
ejpam-3019	68	21	b0	b0	NOUN
ejpam-3019	68	22	)	)	PUNCT
ejpam-3019	68	23	,	,	PUNCT
ejpam-3019	68	24	b1	b1	NOUN
ejpam-3019	68	25	=	=	SYM
ejpam-3019	68	26	f	f	PROPN
ejpam-3019	68	27	(	(	PUNCT
ejpam-3019	68	28	b0	b0	NOUN
ejpam-3019	68	29	,	,	PUNCT
ejpam-3019	68	30	a0	a0	PROPN
ejpam-3019	68	31	)	)	PUNCT
ejpam-3019	68	32	,	,	PUNCT
ejpam-3019	68	33	p1	p1	NOUN
ejpam-3019	68	34	=	=	SYM
ejpam-3019	68	35	f	f	PROPN
ejpam-3019	68	36	(	(	PUNCT
ejpam-3019	68	37	p0	p0	NOUN
ejpam-3019	68	38	,	,	PUNCT
ejpam-3019	68	39	q0	q0	PROPN
ejpam-3019	68	40	)	)	PUNCT
ejpam-3019	68	41	,	,	PUNCT
ejpam-3019	68	42	q1	q1	PROPN
ejpam-3019	68	43	=	=	SYM
ejpam-3019	68	44	f	f	PROPN
ejpam-3019	68	45	(	(	PUNCT
ejpam-3019	68	46	q0	q0	PROPN
ejpam-3019	68	47	,	,	PUNCT
ejpam-3019	68	48	p0	p0	NOUN
ejpam-3019	68	49	)	)	PUNCT
ejpam-3019	68	50	.	.	PUNCT
ejpam-3019	69	1	and	and	CCONJ
ejpam-3019	69	2	similarly	similarly	ADV
ejpam-3019	69	3	,	,	PUNCT
ejpam-3019	69	4	we	we	PRON
ejpam-3019	69	5	take	take	VERB
ejpam-3019	69	6	a2	a2	NOUN
ejpam-3019	69	7	,	,	PUNCT
ejpam-3019	69	8	b2	b2	NOUN
ejpam-3019	69	9	∈	∈	NOUN
ejpam-3019	69	10	x	x	X
ejpam-3019	69	11	and	and	CCONJ
ejpam-3019	69	12	p2	p2	NOUN
ejpam-3019	69	13	,	,	PUNCT
ejpam-3019	69	14	q2	q2	PROPN
ejpam-3019	69	15	∈	∈	PROPN
ejpam-3019	69	16	y	y	PROPN
ejpam-3019	69	17	with	with	ADP
ejpam-3019	69	18	a2	a2	PROPN
ejpam-3019	69	19	=	=	SYM
ejpam-3019	69	20	f	f	PROPN
ejpam-3019	69	21	(	(	PUNCT
ejpam-3019	69	22	a1	a1	PROPN
ejpam-3019	69	23	,	,	PUNCT
ejpam-3019	69	24	b1	b1	NOUN
ejpam-3019	69	25	)	)	PUNCT
ejpam-3019	69	26	,	,	PUNCT
ejpam-3019	69	27	b2	b2	NOUN
ejpam-3019	69	28	=	=	SYM
ejpam-3019	69	29	f	f	PROPN
ejpam-3019	69	30	(	(	PUNCT
ejpam-3019	69	31	b1	b1	NOUN
ejpam-3019	69	32	,	,	PUNCT
ejpam-3019	69	33	a1	a1	NOUN
ejpam-3019	69	34	)	)	PUNCT
ejpam-3019	69	35	,	,	PUNCT
ejpam-3019	69	36	p2	p2	PROPN
ejpam-3019	69	37	=	=	SYM
ejpam-3019	69	38	f	f	PROPN
ejpam-3019	69	39	(	(	PUNCT
ejpam-3019	69	40	p1	p1	PROPN
ejpam-3019	69	41	,	,	PUNCT
ejpam-3019	69	42	q1	q1	PROPN
ejpam-3019	69	43	)	)	PUNCT
ejpam-3019	69	44	,	,	PUNCT
ejpam-3019	69	45	q2	q2	NOUN
ejpam-3019	69	46	=	=	SYM
ejpam-3019	69	47	f	f	PROPN
ejpam-3019	69	48	(	(	PUNCT
ejpam-3019	69	49	q1	q1	PROPN
ejpam-3019	69	50	,	,	PUNCT
ejpam-3019	69	51	p1	p1	PROPN
ejpam-3019	69	52	)	)	PUNCT
ejpam-3019	69	53	.	.	PUNCT
ejpam-3019	70	1	in	in	ADP
ejpam-3019	70	2	this	this	DET
ejpam-3019	70	3	way	way	NOUN
ejpam-3019	70	4	,	,	PUNCT
ejpam-3019	70	5	we	we	PRON
ejpam-3019	70	6	obtain	obtain	VERB
ejpam-3019	70	7	bisequences	bisequence	NOUN
ejpam-3019	70	8	(	(	PUNCT
ejpam-3019	70	9	an	an	PRON
ejpam-3019	70	10	,	,	PUNCT
ejpam-3019	70	11	bn	bn	NOUN
ejpam-3019	70	12	)	)	PUNCT
ejpam-3019	70	13	and	and	CCONJ
ejpam-3019	70	14	(	(	PUNCT
ejpam-3019	70	15	pn	pn	PROPN
ejpam-3019	70	16	,	,	PUNCT
ejpam-3019	70	17	qn	qn	NOUN
ejpam-3019	70	18	)	)	PUNCT
ejpam-3019	70	19	with	with	ADP
ejpam-3019	70	20	an+1	an+1	NOUN
ejpam-3019	70	21	=	=	SYM
ejpam-3019	70	22	f	f	X
ejpam-3019	70	23	(	(	PUNCT
ejpam-3019	70	24	an	an	PRON
ejpam-3019	70	25	,	,	PUNCT
ejpam-3019	70	26	bn	bn	NOUN
ejpam-3019	70	27	)	)	PUNCT
ejpam-3019	70	28	,	,	PUNCT
ejpam-3019	70	29	bn+1	bn+1	X
ejpam-3019	70	30	=	=	SYM
ejpam-3019	70	31	f	f	PROPN
ejpam-3019	70	32	(	(	PUNCT
ejpam-3019	70	33	bn	bn	PROPN
ejpam-3019	70	34	,	,	PUNCT
ejpam-3019	70	35	an	an	PRON
ejpam-3019	70	36	)	)	PUNCT
ejpam-3019	70	37	,	,	PUNCT
ejpam-3019	70	38	pn+1	pn+1	PROPN
ejpam-3019	70	39	=	=	SYM
ejpam-3019	70	40	f	f	PROPN
ejpam-3019	70	41	(	(	PUNCT
ejpam-3019	70	42	pn	pn	PROPN
ejpam-3019	70	43	,	,	PUNCT
ejpam-3019	70	44	qn	qn	NOUN
ejpam-3019	70	45	)	)	PUNCT
ejpam-3019	70	46	and	and	CCONJ
ejpam-3019	70	47	qn+1	qn+1	NUM
ejpam-3019	70	48	=	=	SYM
ejpam-3019	70	49	f	f	PROPN
ejpam-3019	70	50	(	(	PUNCT
ejpam-3019	70	51	qn	qn	INTJ
ejpam-3019	70	52	,	,	PUNCT
ejpam-3019	70	53	pn	pn	NOUN
ejpam-3019	70	54	)	)	PUNCT
ejpam-3019	70	55	for	for	ADP
ejpam-3019	70	56	all	all	DET
ejpam-3019	70	57	n	n	PRON
ejpam-3019	70	58	∈	∈	PROPN
ejpam-3019	70	59	n+	n+	PROPN
ejpam-3019	70	60	.	.	PUNCT
ejpam-3019	71	1	let	let	VERB
ejpam-3019	72	1	k	k	NOUN
ejpam-3019	72	2	+	+	NOUN
ejpam-3019	72	3	l	l	NOUN
ejpam-3019	72	4	=	=	SYM
ejpam-3019	72	5	λ	λ	PROPN
ejpam-3019	72	6	.	.	PROPN
ejpam-3019	72	7	from	from	ADP
ejpam-3019	72	8	(	(	PUNCT
ejpam-3019	72	9	1	1	NUM
ejpam-3019	72	10	)	)	PUNCT
ejpam-3019	72	11	,	,	PUNCT
ejpam-3019	72	12	we	we	PRON
ejpam-3019	72	13	get	get	VERB
ejpam-3019	72	14	d(an	d(an	NOUN
ejpam-3019	72	15	,	,	PUNCT
ejpam-3019	72	16	pn+1	pn+1	NOUN
ejpam-3019	72	17	)	)	PUNCT
ejpam-3019	72	18	=	=	SYM
ejpam-3019	72	19	d(f	d(f	NOUN
ejpam-3019	72	20	(	(	PUNCT
ejpam-3019	72	21	an−1	an−1	ADJ
ejpam-3019	72	22	,	,	PUNCT
ejpam-3019	72	23	bn−1	bn−1	NOUN
ejpam-3019	72	24	)	)	PUNCT
ejpam-3019	72	25	,	,	PUNCT
ejpam-3019	72	26	f	f	PROPN
ejpam-3019	72	27	(	(	PUNCT
ejpam-3019	72	28	pn	pn	PROPN
ejpam-3019	72	29	,	,	PUNCT
ejpam-3019	72	30	qn	qn	NOUN
ejpam-3019	72	31	)	)	PUNCT
ejpam-3019	72	32	)	)	PUNCT
ejpam-3019	72	33	,	,	PUNCT
ejpam-3019	72	34	(	(	PUNCT
ejpam-3019	72	35	2	2	X
ejpam-3019	72	36	)	)	PUNCT
ejpam-3019	72	37	≤	≤	NOUN
ejpam-3019	72	38	kd(an−1	kd(an−1	PROPN
ejpam-3019	72	39	,	,	PUNCT
ejpam-3019	72	40	pn	pn	NOUN
ejpam-3019	72	41	)	)	PUNCT
ejpam-3019	72	42	+	+	CCONJ
ejpam-3019	73	1	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	73	2	,	,	PUNCT
ejpam-3019	73	3	qn	qn	NOUN
ejpam-3019	73	4	)	)	PUNCT
ejpam-3019	73	5	and	and	CCONJ
ejpam-3019	73	6	d(bn	d(bn	PROPN
ejpam-3019	73	7	,	,	PUNCT
ejpam-3019	73	8	qn+1	qn+1	NUM
ejpam-3019	73	9	)	)	PUNCT
ejpam-3019	73	10	=	=	SYM
ejpam-3019	73	11	d(f	d(f	NOUN
ejpam-3019	73	12	(	(	PUNCT
ejpam-3019	73	13	bn−1	bn−1	ADJ
ejpam-3019	73	14	,	,	PUNCT
ejpam-3019	73	15	an−1	an−1	ADJ
ejpam-3019	73	16	)	)	PUNCT
ejpam-3019	73	17	,	,	PUNCT
ejpam-3019	73	18	f	f	PROPN
ejpam-3019	73	19	(	(	PUNCT
ejpam-3019	73	20	qn	qn	INTJ
ejpam-3019	73	21	,	,	PUNCT
ejpam-3019	73	22	pn	pn	NOUN
ejpam-3019	73	23	)	)	PUNCT
ejpam-3019	73	24	)	)	PUNCT
ejpam-3019	73	25	,	,	PUNCT
ejpam-3019	73	26	(	(	PUNCT
ejpam-3019	73	27	3	3	X
ejpam-3019	73	28	)	)	PUNCT
ejpam-3019	73	29	≤	≤	NOUN
ejpam-3019	73	30	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	73	31	,	,	PUNCT
ejpam-3019	73	32	qn	qn	NOUN
ejpam-3019	73	33	)	)	PUNCT
ejpam-3019	73	34	+	+	CCONJ
ejpam-3019	73	35	ld(an−1	ld(an−1	ADJ
ejpam-3019	73	36	,	,	PUNCT
ejpam-3019	73	37	pn	pn	NOUN
ejpam-3019	73	38	)	)	PUNCT
ejpam-3019	73	39	for	for	ADP
ejpam-3019	73	40	all	all	DET
ejpam-3019	73	41	n	n	PRON
ejpam-3019	73	42	∈	∈	ADJ
ejpam-3019	73	43	n+	n+	PUNCT
ejpam-3019	73	44	and	and	CCONJ
ejpam-3019	73	45	λ	λ	X
ejpam-3019	73	46	<	<	X
ejpam-3019	73	47	1	1	X
ejpam-3019	73	48	.	.	PUNCT
ejpam-3019	74	1	let	let	VERB
ejpam-3019	74	2	en	en	ADV
ejpam-3019	74	3	=	=	SYM
ejpam-3019	74	4	d(an	d(an	X
ejpam-3019	74	5	,	,	PUNCT
ejpam-3019	74	6	pn+1	pn+1	NOUN
ejpam-3019	74	7	)	)	PUNCT
ejpam-3019	75	1	+	+	CCONJ
ejpam-3019	75	2	d(bn	d(bn	NUM
ejpam-3019	75	3	,	,	PUNCT
ejpam-3019	75	4	qn+1	qn+1	NUM
ejpam-3019	75	5	)	)	PUNCT
ejpam-3019	75	6	for	for	ADP
ejpam-3019	75	7	all	all	DET
ejpam-3019	75	8	n	n	PRON
ejpam-3019	75	9	∈	∈	PROPN
ejpam-3019	75	10	n+	n+	PROPN
ejpam-3019	75	11	.	.	PUNCT
ejpam-3019	76	1	combining	combine	VERB
ejpam-3019	76	2	(	(	PUNCT
ejpam-3019	76	3	2	2	NUM
ejpam-3019	76	4	)	)	PUNCT
ejpam-3019	76	5	and	and	CCONJ
ejpam-3019	76	6	(	(	PUNCT
ejpam-3019	76	7	3	3	NUM
ejpam-3019	76	8	)	)	PUNCT
ejpam-3019	76	9	,	,	PUNCT
ejpam-3019	76	10	we	we	PRON
ejpam-3019	76	11	observe	observe	VERB
ejpam-3019	76	12	that	that	SCONJ
ejpam-3019	76	13	en	en	PROPN
ejpam-3019	76	14	=	=	SYM
ejpam-3019	76	15	d(an	d(an	PROPN
ejpam-3019	76	16	,	,	PUNCT
ejpam-3019	76	17	pn+1	pn+1	NOUN
ejpam-3019	76	18	)	)	PUNCT
ejpam-3019	77	1	+	+	CCONJ
ejpam-3019	77	2	d(bn	d(bn	NUM
ejpam-3019	77	3	,	,	PUNCT
ejpam-3019	77	4	qn+1	qn+1	NUM
ejpam-3019	77	5	)	)	PUNCT
ejpam-3019	77	6	≤	≤	NOUN
ejpam-3019	77	7	kd(an−1	kd(an−1	PROPN
ejpam-3019	77	8	,	,	PUNCT
ejpam-3019	77	9	pn	pn	NOUN
ejpam-3019	77	10	)	)	PUNCT
ejpam-3019	78	1	+	+	CCONJ
ejpam-3019	78	2	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	78	3	,	,	PUNCT
ejpam-3019	78	4	qn	qn	NOUN
ejpam-3019	78	5	)	)	PUNCT
ejpam-3019	78	6	+	+	CCONJ
ejpam-3019	78	7	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	78	8	,	,	PUNCT
ejpam-3019	78	9	qn	qn	NOUN
ejpam-3019	78	10	)	)	PUNCT
ejpam-3019	78	11	+	+	CCONJ
ejpam-3019	78	12	ld(an−1	ld(an−1	ADJ
ejpam-3019	78	13	,	,	PUNCT
ejpam-3019	78	14	pn	pn	ADJ
ejpam-3019	78	15	)	)	PUNCT
ejpam-3019	78	16	a.	a.	NOUN
ejpam-3019	78	17	mutlu	mutlu	PROPN
ejpam-3019	78	18	,	,	PUNCT
ejpam-3019	78	19	k.	k.	PROPN
ejpam-3019	78	20	özkan	özkan	PROPN
ejpam-3019	78	21	,	,	PUNCT
ejpam-3019	78	22	u.	u.	PROPN
ejpam-3019	78	23	gürdal	gürdal	PROPN
ejpam-3019	78	24	/	/	SYM
ejpam-3019	78	25	eur	eur	PROPN
ejpam-3019	78	26	.	.	PUNCT
ejpam-3019	79	1	j.	j.	PROPN
ejpam-3019	79	2	pure	pure	PROPN
ejpam-3019	79	3	appl	appl	PROPN
ejpam-3019	79	4	.	.	PROPN
ejpam-3019	79	5	math	math	PROPN
ejpam-3019	79	6	,	,	PUNCT
ejpam-3019	79	7	10	10	NUM
ejpam-3019	79	8	(	(	PUNCT
ejpam-3019	79	9	4	4	NUM
ejpam-3019	79	10	)	)	PUNCT
ejpam-3019	79	11	(	(	PUNCT
ejpam-3019	79	12	2017	2017	NUM
ejpam-3019	79	13	)	)	PUNCT
ejpam-3019	79	14	,	,	PUNCT
ejpam-3019	79	15	655	655	NUM
ejpam-3019	79	16	-	-	SYM
ejpam-3019	79	17	667	667	NUM
ejpam-3019	79	18	658	658	NUM
ejpam-3019	79	19	=	=	SYM
ejpam-3019	79	20	(	(	PUNCT
ejpam-3019	79	21	k	k	PROPN
ejpam-3019	79	22	+	+	X
ejpam-3019	79	23	l)(d(an−1	l)(d(an−1	PROPN
ejpam-3019	79	24	,	,	PUNCT
ejpam-3019	79	25	pn	pn	NOUN
ejpam-3019	79	26	)	)	PUNCT
ejpam-3019	79	27	+	+	CCONJ
ejpam-3019	79	28	d(bn−1	d(bn−1	NOUN
ejpam-3019	79	29	,	,	PUNCT
ejpam-3019	79	30	qn	qn	NOUN
ejpam-3019	79	31	)	)	PUNCT
ejpam-3019	79	32	)	)	PUNCT
ejpam-3019	80	1	=	=	SYM
ejpam-3019	80	2	λen−1	λen−1	PROPN
ejpam-3019	80	3	.	.	PUNCT
ejpam-3019	81	1	then	then	ADV
ejpam-3019	81	2	we	we	PRON
ejpam-3019	81	3	get	get	VERB
ejpam-3019	81	4	0	0	NUM
ejpam-3019	81	5	≤	≤	NUM
ejpam-3019	81	6	en	en	ADP
ejpam-3019	81	7	≤	≤	X
ejpam-3019	81	8	λen−1	λen−1	PROPN
ejpam-3019	81	9	≤	≤	NOUN
ejpam-3019	81	10	λ2en−2	λ2en−2	X
ejpam-3019	81	11	≤	≤	NUM
ejpam-3019	81	12	·	·	PUNCT
ejpam-3019	81	13	·	·	PUNCT
ejpam-3019	81	14	·	·	PUNCT
ejpam-3019	81	15	≤	≤	NUM
ejpam-3019	81	16	λne0	λne0	PROPN
ejpam-3019	81	17	.	.	PUNCT
ejpam-3019	82	1	(	(	PUNCT
ejpam-3019	82	2	4	4	X
ejpam-3019	82	3	)	)	PUNCT
ejpam-3019	82	4	on	on	ADP
ejpam-3019	82	5	the	the	DET
ejpam-3019	82	6	other	other	ADJ
ejpam-3019	82	7	hand	hand	NOUN
ejpam-3019	82	8	,	,	PUNCT
ejpam-3019	82	9	d(an+1	d(an+1	NUM
ejpam-3019	82	10	,	,	PUNCT
ejpam-3019	82	11	pn	pn	NOUN
ejpam-3019	82	12	)	)	PUNCT
ejpam-3019	83	1	=	=	NOUN
ejpam-3019	83	2	d(f	d(f	NOUN
ejpam-3019	83	3	(	(	PUNCT
ejpam-3019	83	4	an	an	DET
ejpam-3019	83	5	,	,	PUNCT
ejpam-3019	83	6	bn	bn	NOUN
ejpam-3019	83	7	)	)	PUNCT
ejpam-3019	83	8	,	,	PUNCT
ejpam-3019	83	9	f	f	PROPN
ejpam-3019	83	10	(	(	PUNCT
ejpam-3019	83	11	pn−1	pn−1	PROPN
ejpam-3019	83	12	,	,	PUNCT
ejpam-3019	83	13	qn−1	qn−1	PROPN
ejpam-3019	83	14	)	)	PUNCT
ejpam-3019	83	15	)	)	PUNCT
ejpam-3019	83	16	,	,	PUNCT
ejpam-3019	83	17	(	(	PUNCT
ejpam-3019	83	18	5	5	X
ejpam-3019	83	19	)	)	PUNCT
ejpam-3019	83	20	≤	≤	NOUN
ejpam-3019	83	21	kd(an	kd(an	PROPN
ejpam-3019	83	22	,	,	PUNCT
ejpam-3019	83	23	pn−1	pn−1	PROPN
ejpam-3019	83	24	)	)	PUNCT
ejpam-3019	83	25	+	+	CCONJ
ejpam-3019	83	26	ld(bn	ld(bn	PROPN
ejpam-3019	83	27	,	,	PUNCT
ejpam-3019	83	28	qn−1	qn−1	PROPN
ejpam-3019	83	29	)	)	PUNCT
ejpam-3019	83	30	and	and	CCONJ
ejpam-3019	83	31	d(bn+1	d(bn+1	PROPN
ejpam-3019	83	32	,	,	PUNCT
ejpam-3019	83	33	qn	qn	NOUN
ejpam-3019	83	34	)	)	PUNCT
ejpam-3019	83	35	=	=	NOUN
ejpam-3019	83	36	d(f	d(f	NOUN
ejpam-3019	83	37	(	(	PUNCT
ejpam-3019	83	38	bn	bn	X
ejpam-3019	83	39	,	,	PUNCT
ejpam-3019	83	40	an	an	NOUN
ejpam-3019	83	41	)	)	PUNCT
ejpam-3019	83	42	,	,	PUNCT
ejpam-3019	83	43	f	f	PROPN
ejpam-3019	83	44	(	(	PUNCT
ejpam-3019	83	45	qn−1	qn−1	PROPN
ejpam-3019	83	46	,	,	PUNCT
ejpam-3019	83	47	pn−1	pn−1	PROPN
ejpam-3019	83	48	)	)	PUNCT
ejpam-3019	83	49	)	)	PUNCT
ejpam-3019	83	50	,	,	PUNCT
ejpam-3019	83	51	(	(	PUNCT
ejpam-3019	83	52	6	6	X
ejpam-3019	83	53	)	)	PUNCT
ejpam-3019	83	54	≤	≤	NOUN
ejpam-3019	83	55	kd(bn	kd(bn	NOUN
ejpam-3019	83	56	,	,	PUNCT
ejpam-3019	83	57	qn−1	qn−1	ADJ
ejpam-3019	83	58	)	)	PUNCT
ejpam-3019	83	59	+	+	CCONJ
ejpam-3019	84	1	ld(an	ld(an	NOUN
ejpam-3019	84	2	,	,	PUNCT
ejpam-3019	84	3	pn−1	pn−1	PROPN
ejpam-3019	84	4	)	)	PUNCT
ejpam-3019	84	5	for	for	ADP
ejpam-3019	84	6	all	all	DET
ejpam-3019	84	7	n	n	PRON
ejpam-3019	84	8	∈	∈	ADJ
ejpam-3019	84	9	n+	n+	PUNCT
ejpam-3019	84	10	and	and	CCONJ
ejpam-3019	84	11	λ	λ	X
ejpam-3019	84	12	<	<	X
ejpam-3019	84	13	1	1	X
ejpam-3019	84	14	.	.	PUNCT
ejpam-3019	85	1	let	let	VERB
ejpam-3019	85	2	sn	sn	PROPN
ejpam-3019	85	3	=	=	PUNCT
ejpam-3019	85	4	d(an+1	d(an+1	PROPN
ejpam-3019	85	5	,	,	PUNCT
ejpam-3019	85	6	pn	pn	NOUN
ejpam-3019	85	7	)	)	PUNCT
ejpam-3019	85	8	+	+	X
ejpam-3019	85	9	d(bn+1	d(bn+1	PROPN
ejpam-3019	85	10	,	,	PUNCT
ejpam-3019	85	11	qn	qn	NOUN
ejpam-3019	85	12	)	)	PUNCT
ejpam-3019	85	13	for	for	ADP
ejpam-3019	85	14	all	all	DET
ejpam-3019	85	15	n	n	PRON
ejpam-3019	85	16	∈	∈	PROPN
ejpam-3019	85	17	n+	n+	PROPN
ejpam-3019	85	18	.	.	PUNCT
ejpam-3019	86	1	combining	combine	VERB
ejpam-3019	86	2	(	(	PUNCT
ejpam-3019	86	3	5	5	NUM
ejpam-3019	86	4	)	)	PUNCT
ejpam-3019	86	5	and	and	CCONJ
ejpam-3019	86	6	(	(	PUNCT
ejpam-3019	86	7	6	6	NUM
ejpam-3019	86	8	)	)	PUNCT
ejpam-3019	86	9	,	,	PUNCT
ejpam-3019	86	10	we	we	PRON
ejpam-3019	86	11	observe	observe	VERB
ejpam-3019	86	12	that	that	SCONJ
ejpam-3019	86	13	sn	sn	PROPN
ejpam-3019	86	14	=	=	SYM
ejpam-3019	86	15	d(an+1	d(an+1	PROPN
ejpam-3019	86	16	,	,	PUNCT
ejpam-3019	86	17	pn	pn	NOUN
ejpam-3019	86	18	)	)	PUNCT
ejpam-3019	86	19	+	+	X
ejpam-3019	86	20	d(bn+1	d(bn+1	PROPN
ejpam-3019	86	21	,	,	PUNCT
ejpam-3019	86	22	qn	qn	NOUN
ejpam-3019	86	23	)	)	PUNCT
ejpam-3019	86	24	≤	≤	NOUN
ejpam-3019	87	1	kd(an	kd(an	PROPN
ejpam-3019	87	2	,	,	PUNCT
ejpam-3019	87	3	pn−1	pn−1	PROPN
ejpam-3019	87	4	)	)	PUNCT
ejpam-3019	87	5	+	+	CCONJ
ejpam-3019	87	6	ld(bn	ld(bn	PROPN
ejpam-3019	87	7	,	,	PUNCT
ejpam-3019	87	8	qn−1	qn−1	PROPN
ejpam-3019	87	9	)	)	PUNCT
ejpam-3019	87	10	+	+	CCONJ
ejpam-3019	87	11	kd(bn	kd(bn	X
ejpam-3019	87	12	,	,	PUNCT
ejpam-3019	87	13	qn−1	qn−1	ADJ
ejpam-3019	87	14	)	)	PUNCT
ejpam-3019	87	15	+	+	CCONJ
ejpam-3019	87	16	ld(an	ld(an	NOUN
ejpam-3019	87	17	,	,	PUNCT
ejpam-3019	87	18	pn−1	pn−1	PROPN
ejpam-3019	87	19	)	)	PUNCT
ejpam-3019	87	20	=	=	SYM
ejpam-3019	88	1	(	(	PUNCT
ejpam-3019	88	2	k	k	PROPN
ejpam-3019	88	3	+	+	CCONJ
ejpam-3019	88	4	l)(d(an	l)(d(an	PROPN
ejpam-3019	88	5	,	,	PUNCT
ejpam-3019	88	6	pn−1	pn−1	PROPN
ejpam-3019	88	7	)	)	PUNCT
ejpam-3019	88	8	+	+	CCONJ
ejpam-3019	88	9	d(bn	d(bn	NUM
ejpam-3019	88	10	,	,	PUNCT
ejpam-3019	88	11	qn−1	qn−1	ADJ
ejpam-3019	88	12	)	)	PUNCT
ejpam-3019	88	13	)	)	PUNCT
ejpam-3019	89	1	=	=	PUNCT
ejpam-3019	90	1	λsn−1	λsn−1	PROPN
ejpam-3019	90	2	.	.	PUNCT
ejpam-3019	91	1	then	then	ADV
ejpam-3019	91	2	similar	similar	ADJ
ejpam-3019	91	3	to	to	ADP
ejpam-3019	91	4	equation	equation	NOUN
ejpam-3019	91	5	(	(	PUNCT
ejpam-3019	91	6	4	4	NUM
ejpam-3019	91	7	)	)	PUNCT
ejpam-3019	91	8	,	,	PUNCT
ejpam-3019	91	9	we	we	PRON
ejpam-3019	91	10	obtain	obtain	VERB
ejpam-3019	91	11	that	that	DET
ejpam-3019	91	12	0	0	NUM
ejpam-3019	91	13	≤	≤	NUM
ejpam-3019	91	14	sn	sn	NOUN
ejpam-3019	91	15	≤	≤	X
ejpam-3019	92	1	λsn−1	λsn−1	ADV
ejpam-3019	92	2	≤	≤	NOUN
ejpam-3019	92	3	λ2sn−2	λ2sn−2	PROPN
ejpam-3019	92	4	≤	≤	NOUN
ejpam-3019	92	5	·	·	PUNCT
ejpam-3019	92	6	·	·	PUNCT
ejpam-3019	92	7	·	·	PUNCT
ejpam-3019	92	8	≤	≤	NUM
ejpam-3019	92	9	λns0	λns0	PROPN
ejpam-3019	92	10	.	.	PUNCT
ejpam-3019	93	1	(	(	PUNCT
ejpam-3019	93	2	7	7	X
ejpam-3019	93	3	)	)	PUNCT
ejpam-3019	93	4	moreover	moreover	ADV
ejpam-3019	93	5	,	,	PUNCT
ejpam-3019	93	6	d(an	d(an	PROPN
ejpam-3019	93	7	,	,	PUNCT
ejpam-3019	93	8	pn	pn	NOUN
ejpam-3019	93	9	)	)	PUNCT
ejpam-3019	94	1	=	=	NOUN
ejpam-3019	94	2	d(f	d(f	NOUN
ejpam-3019	94	3	(	(	PUNCT
ejpam-3019	94	4	an−1	an−1	ADJ
ejpam-3019	94	5	,	,	PUNCT
ejpam-3019	94	6	bn−1	bn−1	NOUN
ejpam-3019	94	7	)	)	PUNCT
ejpam-3019	94	8	,	,	PUNCT
ejpam-3019	94	9	f	f	PROPN
ejpam-3019	94	10	(	(	PUNCT
ejpam-3019	94	11	pn−1	pn−1	PROPN
ejpam-3019	94	12	,	,	PUNCT
ejpam-3019	94	13	qn−1	qn−1	PROPN
ejpam-3019	94	14	)	)	PUNCT
ejpam-3019	94	15	)	)	PUNCT
ejpam-3019	94	16	,	,	PUNCT
ejpam-3019	94	17	(	(	PUNCT
ejpam-3019	94	18	8)	8)	NUM
ejpam-3019	94	19	≤	≤	X
ejpam-3019	94	20	kd(an−1	kd(an−1	PROPN
ejpam-3019	94	21	,	,	PUNCT
ejpam-3019	94	22	pn−1	pn−1	PROPN
ejpam-3019	94	23	)	)	PUNCT
ejpam-3019	94	24	+	+	CCONJ
ejpam-3019	94	25	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	94	26	,	,	PUNCT
ejpam-3019	94	27	qn−1	qn−1	ADJ
ejpam-3019	94	28	)	)	PUNCT
ejpam-3019	94	29	and	and	CCONJ
ejpam-3019	94	30	d(bn	d(bn	NOUN
ejpam-3019	94	31	,	,	PUNCT
ejpam-3019	94	32	qn	qn	NOUN
ejpam-3019	94	33	)	)	PUNCT
ejpam-3019	94	34	=	=	NOUN
ejpam-3019	94	35	d(f	d(f	NOUN
ejpam-3019	94	36	(	(	PUNCT
ejpam-3019	94	37	bn−1	bn−1	ADJ
ejpam-3019	94	38	,	,	PUNCT
ejpam-3019	94	39	an−1	an−1	ADJ
ejpam-3019	94	40	)	)	PUNCT
ejpam-3019	94	41	,	,	PUNCT
ejpam-3019	94	42	f	f	PROPN
ejpam-3019	94	43	(	(	PUNCT
ejpam-3019	94	44	qn−1	qn−1	PROPN
ejpam-3019	94	45	,	,	PUNCT
ejpam-3019	94	46	pn−1	pn−1	PROPN
ejpam-3019	94	47	)	)	PUNCT
ejpam-3019	94	48	)	)	PUNCT
ejpam-3019	94	49	,	,	PUNCT
ejpam-3019	94	50	(	(	PUNCT
ejpam-3019	94	51	9	9	X
ejpam-3019	94	52	)	)	PUNCT
ejpam-3019	94	53	≤	≤	NOUN
ejpam-3019	94	54	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	94	55	,	,	PUNCT
ejpam-3019	94	56	qn−1	qn−1	PROPN
ejpam-3019	94	57	)	)	PUNCT
ejpam-3019	94	58	+	+	CCONJ
ejpam-3019	94	59	ld(an−1	ld(an−1	ADJ
ejpam-3019	94	60	,	,	PUNCT
ejpam-3019	94	61	pn−1	pn−1	ADJ
ejpam-3019	94	62	)	)	PUNCT
ejpam-3019	94	63	for	for	ADP
ejpam-3019	94	64	all	all	DET
ejpam-3019	94	65	n	n	PRON
ejpam-3019	94	66	∈	∈	ADJ
ejpam-3019	94	67	n+	n+	PUNCT
ejpam-3019	94	68	and	and	CCONJ
ejpam-3019	94	69	λ	λ	X
ejpam-3019	94	70	<	<	X
ejpam-3019	94	71	1	1	NUM
ejpam-3019	94	72	.	.	PUNCT
ejpam-3019	94	73	therefore	therefore	ADV
ejpam-3019	94	74	,	,	PUNCT
ejpam-3019	94	75	let	let	VERB
ejpam-3019	94	76	tn	tn	NOUN
ejpam-3019	94	77	=	=	SYM
ejpam-3019	94	78	d(an	d(an	PROPN
ejpam-3019	94	79	,	,	PUNCT
ejpam-3019	94	80	pn	pn	NOUN
ejpam-3019	94	81	)	)	PUNCT
ejpam-3019	94	82	+	+	CCONJ
ejpam-3019	94	83	d(bn	d(bn	NUM
ejpam-3019	94	84	,	,	PUNCT
ejpam-3019	94	85	qn	qn	NOUN
ejpam-3019	94	86	)	)	PUNCT
ejpam-3019	94	87	a.	a.	NOUN
ejpam-3019	94	88	mutlu	mutlu	PROPN
ejpam-3019	94	89	,	,	PUNCT
ejpam-3019	94	90	k.	k.	PROPN
ejpam-3019	94	91	özkan	özkan	PROPN
ejpam-3019	94	92	,	,	PUNCT
ejpam-3019	94	93	u.	u.	PROPN
ejpam-3019	94	94	gürdal	gürdal	PROPN
ejpam-3019	94	95	/	/	SYM
ejpam-3019	94	96	eur	eur	PROPN
ejpam-3019	94	97	.	.	PUNCT
ejpam-3019	95	1	j.	j.	PROPN
ejpam-3019	95	2	pure	pure	PROPN
ejpam-3019	95	3	appl	appl	PROPN
ejpam-3019	95	4	.	.	PROPN
ejpam-3019	95	5	math	math	PROPN
ejpam-3019	95	6	,	,	PUNCT
ejpam-3019	95	7	10	10	NUM
ejpam-3019	95	8	(	(	PUNCT
ejpam-3019	95	9	4	4	NUM
ejpam-3019	95	10	)	)	PUNCT
ejpam-3019	95	11	(	(	PUNCT
ejpam-3019	95	12	2017	2017	NUM
ejpam-3019	95	13	)	)	PUNCT
ejpam-3019	95	14	,	,	PUNCT
ejpam-3019	95	15	655	655	NUM
ejpam-3019	95	16	-	-	SYM
ejpam-3019	95	17	667	667	NUM
ejpam-3019	95	18	659	659	NUM
ejpam-3019	95	19	for	for	ADP
ejpam-3019	95	20	all	all	DET
ejpam-3019	95	21	n	n	PRON
ejpam-3019	95	22	∈	∈	PROPN
ejpam-3019	95	23	n+	n+	PROPN
ejpam-3019	95	24	.	.	PUNCT
ejpam-3019	96	1	combining	combine	VERB
ejpam-3019	96	2	(	(	PUNCT
ejpam-3019	96	3	8)	8)	NUM
ejpam-3019	96	4	and	and	CCONJ
ejpam-3019	96	5	(	(	PUNCT
ejpam-3019	96	6	9	9	NUM
ejpam-3019	96	7	)	)	PUNCT
ejpam-3019	96	8	,	,	PUNCT
ejpam-3019	96	9	we	we	PRON
ejpam-3019	96	10	observe	observe	VERB
ejpam-3019	96	11	that	that	SCONJ
ejpam-3019	96	12	tn	tn	NOUN
ejpam-3019	97	1	=	=	SYM
ejpam-3019	97	2	d(an	d(an	PROPN
ejpam-3019	97	3	,	,	PUNCT
ejpam-3019	97	4	pn	pn	NOUN
ejpam-3019	97	5	)	)	PUNCT
ejpam-3019	97	6	+	+	CCONJ
ejpam-3019	97	7	d(bn	d(bn	NUM
ejpam-3019	97	8	,	,	PUNCT
ejpam-3019	97	9	qn	qn	NOUN
ejpam-3019	97	10	)	)	PUNCT
ejpam-3019	97	11	≤	≤	NOUN
ejpam-3019	97	12	kd(an−1	kd(an−1	PROPN
ejpam-3019	97	13	,	,	PUNCT
ejpam-3019	97	14	pn−1	pn−1	PROPN
ejpam-3019	97	15	)	)	PUNCT
ejpam-3019	97	16	+	+	CCONJ
ejpam-3019	97	17	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	97	18	,	,	PUNCT
ejpam-3019	97	19	qn−1	qn−1	ADJ
ejpam-3019	97	20	)	)	PUNCT
ejpam-3019	97	21	+	+	X
ejpam-3019	98	1	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	98	2	,	,	PUNCT
ejpam-3019	98	3	qn−1	qn−1	PROPN
ejpam-3019	98	4	)	)	PUNCT
ejpam-3019	99	1	+	+	CCONJ
ejpam-3019	99	2	ld(an−1	ld(an−1	ADJ
ejpam-3019	99	3	,	,	PUNCT
ejpam-3019	99	4	pn−1	pn−1	ADJ
ejpam-3019	99	5	)	)	PUNCT
ejpam-3019	99	6	=	=	SYM
ejpam-3019	100	1	(	(	PUNCT
ejpam-3019	100	2	k	k	PROPN
ejpam-3019	100	3	+	+	X
ejpam-3019	100	4	l)(d(an−1	l)(d(an−1	PROPN
ejpam-3019	100	5	,	,	PUNCT
ejpam-3019	100	6	pn−1	pn−1	PROPN
ejpam-3019	100	7	)	)	PUNCT
ejpam-3019	100	8	+	+	NUM
ejpam-3019	100	9	d(bn−1	d(bn−1	NOUN
ejpam-3019	100	10	,	,	PUNCT
ejpam-3019	100	11	qn−1	qn−1	ADJ
ejpam-3019	100	12	)	)	PUNCT
ejpam-3019	100	13	)	)	PUNCT
ejpam-3019	101	1	=	=	PUNCT
ejpam-3019	101	2	λtn−1	λtn−1	PROPN
ejpam-3019	101	3	.	.	PUNCT
ejpam-3019	102	1	thus	thus	ADV
ejpam-3019	102	2	,	,	PUNCT
ejpam-3019	102	3	we	we	PRON
ejpam-3019	102	4	obtain	obtain	VERB
ejpam-3019	102	5	that	that	DET
ejpam-3019	102	6	0	0	NUM
ejpam-3019	102	7	≤	≤	NUM
ejpam-3019	102	8	tn	tn	NOUN
ejpam-3019	102	9	≤	≤	NOUN
ejpam-3019	102	10	λtn−1	λtn−1	PROPN
ejpam-3019	102	11	≤	≤	NOUN
ejpam-3019	102	12	λ2tn−2	λ2tn−2	NUM
ejpam-3019	102	13	≤	≤	NOUN
ejpam-3019	102	14	·	·	PUNCT
ejpam-3019	102	15	·	·	PUNCT
ejpam-3019	102	16	·	·	PUNCT
ejpam-3019	103	1	≤	≤	NUM
ejpam-3019	103	2	λnt0	λnt0	NOUN
ejpam-3019	103	3	.	.	PUNCT
ejpam-3019	104	1	(	(	PUNCT
ejpam-3019	104	2	10	10	NUM
ejpam-3019	104	3	)	)	PUNCT
ejpam-3019	104	4	using	use	VERB
ejpam-3019	104	5	the	the	DET
ejpam-3019	104	6	property	property	NOUN
ejpam-3019	104	7	(	(	PUNCT
ejpam-3019	104	8	b3	b3	PROPN
ejpam-3019	104	9	)	)	PUNCT
ejpam-3019	104	10	,	,	PUNCT
ejpam-3019	104	11	we	we	PRON
ejpam-3019	104	12	get	get	VERB
ejpam-3019	104	13	d(an	d(an	NOUN
ejpam-3019	104	14	,	,	PUNCT
ejpam-3019	104	15	pm	pm	NOUN
ejpam-3019	104	16	)	)	PUNCT
ejpam-3019	104	17	≤	≤	NOUN
ejpam-3019	104	18	d(an	d(an	PROPN
ejpam-3019	104	19	,	,	PUNCT
ejpam-3019	104	20	pn+1	pn+1	NOUN
ejpam-3019	104	21	)	)	PUNCT
ejpam-3019	104	22	+	+	CCONJ
ejpam-3019	104	23	d(an+1	d(an+1	ADJ
ejpam-3019	104	24	,	,	PUNCT
ejpam-3019	104	25	pn+1	pn+1	NOUN
ejpam-3019	104	26	)	)	PUNCT
ejpam-3019	104	27	+	+	CCONJ
ejpam-3019	104	28	·	·	PUNCT
ejpam-3019	104	29	·	·	PUNCT
ejpam-3019	104	30	·	·	PUNCT
ejpam-3019	105	1	+	+	CCONJ
ejpam-3019	105	2	d(am−1	d(am−1	PROPN
ejpam-3019	105	3	,	,	PUNCT
ejpam-3019	105	4	pm	pm	NOUN
ejpam-3019	105	5	)	)	PUNCT
ejpam-3019	105	6	,	,	PUNCT
ejpam-3019	105	7	d(bn	d(bn	PROPN
ejpam-3019	105	8	,	,	PUNCT
ejpam-3019	105	9	qm	qm	PROPN
ejpam-3019	105	10	)	)	PUNCT
ejpam-3019	105	11	≤	≤	NOUN
ejpam-3019	105	12	d(bn	d(bn	NOUN
ejpam-3019	105	13	,	,	PUNCT
ejpam-3019	105	14	qn+1	qn+1	NUM
ejpam-3019	105	15	)	)	PUNCT
ejpam-3019	106	1	+	+	X
ejpam-3019	106	2	d(bn+1	d(bn+1	PROPN
ejpam-3019	106	3	,	,	PUNCT
ejpam-3019	106	4	qn+1	qn+1	NUM
ejpam-3019	106	5	)	)	PUNCT
ejpam-3019	107	1	+	+	CCONJ
ejpam-3019	108	1	·	·	PUNCT
ejpam-3019	108	2	·	·	PUNCT
ejpam-3019	108	3	·	·	PUNCT
ejpam-3019	108	4	+	+	NUM
ejpam-3019	108	5	d(bm−1	d(bm−1	PROPN
ejpam-3019	108	6	,	,	PUNCT
ejpam-3019	108	7	qm	qm	PROPN
ejpam-3019	108	8	)	)	PUNCT
ejpam-3019	108	9	(	(	PUNCT
ejpam-3019	108	10	11	11	NUM
ejpam-3019	108	11	)	)	PUNCT
ejpam-3019	108	12	and	and	CCONJ
ejpam-3019	108	13	d(am	d(am	PROPN
ejpam-3019	108	14	,	,	PUNCT
ejpam-3019	108	15	pn	pn	NOUN
ejpam-3019	108	16	)	)	PUNCT
ejpam-3019	108	17	≤	≤	NOUN
ejpam-3019	108	18	d(am	d(am	NOUN
ejpam-3019	108	19	,	,	PUNCT
ejpam-3019	108	20	pm−1	pm−1	NOUN
ejpam-3019	108	21	)	)	PUNCT
ejpam-3019	108	22	+	+	CCONJ
ejpam-3019	108	23	d(am−1	d(am−1	PROPN
ejpam-3019	108	24	,	,	PUNCT
ejpam-3019	108	25	pm−1	pm−1	NOUN
ejpam-3019	108	26	)	)	PUNCT
ejpam-3019	109	1	+	+	PUNCT
ejpam-3019	109	2	·	·	PUNCT
ejpam-3019	109	3	·	·	PUNCT
ejpam-3019	109	4	·	·	PUNCT
ejpam-3019	109	5	+	+	CCONJ
ejpam-3019	109	6	d(an+1	d(an+1	ADJ
ejpam-3019	109	7	,	,	PUNCT
ejpam-3019	109	8	pn	pn	NOUN
ejpam-3019	109	9	)	)	PUNCT
ejpam-3019	109	10	,	,	PUNCT
ejpam-3019	109	11	d(bm	d(bm	PROPN
ejpam-3019	109	12	,	,	PUNCT
ejpam-3019	109	13	qn	qn	NOUN
ejpam-3019	109	14	)	)	PUNCT
ejpam-3019	109	15	≤	≤	NOUN
ejpam-3019	109	16	d(bm	d(bm	PROPN
ejpam-3019	109	17	,	,	PUNCT
ejpam-3019	109	18	qm−1	qm−1	NOUN
ejpam-3019	109	19	)	)	PUNCT
ejpam-3019	110	1	+	+	CCONJ
ejpam-3019	110	2	d(bm−1	d(bm−1	PROPN
ejpam-3019	110	3	,	,	PUNCT
ejpam-3019	110	4	qm−1	qm−1	NOUN
ejpam-3019	110	5	)	)	PUNCT
ejpam-3019	110	6	+	+	CCONJ
ejpam-3019	110	7	·	·	PUNCT
ejpam-3019	110	8	·	·	PUNCT
ejpam-3019	110	9	·	·	PUNCT
ejpam-3019	110	10	+	+	SYM
ejpam-3019	110	11	d(bn+1	d(bn+1	PROPN
ejpam-3019	110	12	,	,	PUNCT
ejpam-3019	110	13	qn	qn	NOUN
ejpam-3019	110	14	)	)	PUNCT
ejpam-3019	110	15	(	(	PUNCT
ejpam-3019	110	16	12	12	NUM
ejpam-3019	110	17	)	)	PUNCT
ejpam-3019	110	18	for	for	ADP
ejpam-3019	110	19	each	each	DET
ejpam-3019	110	20	n	n	NOUN
ejpam-3019	110	21	,	,	PUNCT
ejpam-3019	110	22	m	m	PROPN
ejpam-3019	110	23	∈	∈	PROPN
ejpam-3019	110	24	n	n	CCONJ
ejpam-3019	110	25	,	,	PUNCT
ejpam-3019	110	26	n	n	CCONJ
ejpam-3019	110	27	<	<	X
ejpam-3019	110	28	m.	m.	NOUN
ejpam-3019	110	29	then	then	ADV
ejpam-3019	110	30	,	,	PUNCT
ejpam-3019	110	31	from	from	ADP
ejpam-3019	110	32	(	(	PUNCT
ejpam-3019	110	33	4	4	NUM
ejpam-3019	110	34	)	)	PUNCT
ejpam-3019	110	35	,	,	PUNCT
ejpam-3019	110	36	(	(	PUNCT
ejpam-3019	110	37	7	7	X
ejpam-3019	110	38	)	)	PUNCT
ejpam-3019	110	39	(	(	PUNCT
ejpam-3019	110	40	10	10	NUM
ejpam-3019	110	41	)	)	PUNCT
ejpam-3019	110	42	,	,	PUNCT
ejpam-3019	110	43	(	(	PUNCT
ejpam-3019	110	44	11	11	NUM
ejpam-3019	110	45	)	)	PUNCT
ejpam-3019	110	46	and	and	CCONJ
ejpam-3019	110	47	(	(	PUNCT
ejpam-3019	110	48	12	12	NUM
ejpam-3019	110	49	)	)	PUNCT
ejpam-3019	110	50	,	,	PUNCT
ejpam-3019	110	51	we	we	PRON
ejpam-3019	110	52	have	have	VERB
ejpam-3019	110	53	d(an	d(an	NOUN
ejpam-3019	110	54	,	,	PUNCT
ejpam-3019	110	55	pm	pm	NOUN
ejpam-3019	110	56	)	)	PUNCT
ejpam-3019	110	57	+	+	CCONJ
ejpam-3019	110	58	d(bn	d(bn	NUM
ejpam-3019	110	59	,	,	PUNCT
ejpam-3019	110	60	qm	qm	PROPN
ejpam-3019	110	61	)	)	PUNCT
ejpam-3019	110	62	≤	≤	NOUN
ejpam-3019	110	63	(	(	PUNCT
ejpam-3019	110	64	d(an	d(an	NOUN
ejpam-3019	110	65	,	,	PUNCT
ejpam-3019	110	66	pn+1	pn+1	NOUN
ejpam-3019	110	67	)	)	PUNCT
ejpam-3019	111	1	+	+	CCONJ
ejpam-3019	111	2	d(bn	d(bn	NUM
ejpam-3019	111	3	,	,	PUNCT
ejpam-3019	111	4	qn+1	qn+1	NUM
ejpam-3019	111	5	)	)	PUNCT
ejpam-3019	111	6	)	)	PUNCT
ejpam-3019	112	1	+	+	ADJ
ejpam-3019	112	2	(	(	PUNCT
ejpam-3019	112	3	d(an+1	d(an+1	ADJ
ejpam-3019	112	4	,	,	PUNCT
ejpam-3019	112	5	pn+1	pn+1	NOUN
ejpam-3019	112	6	)	)	PUNCT
ejpam-3019	112	7	+	+	X
ejpam-3019	112	8	d(bn+1	d(bn+1	PROPN
ejpam-3019	112	9	,	,	PUNCT
ejpam-3019	112	10	qn+1	qn+1	NUM
ejpam-3019	112	11	)	)	PUNCT
ejpam-3019	112	12	)	)	PUNCT
ejpam-3019	113	1	+	+	CCONJ
ejpam-3019	113	2	·	·	PUNCT
ejpam-3019	113	3	·	·	PUNCT
ejpam-3019	113	4	·	·	PUNCT
ejpam-3019	114	1	+	+	X
ejpam-3019	114	2	(	(	PUNCT
ejpam-3019	114	3	d(am−1	d(am−1	PROPN
ejpam-3019	114	4	,	,	PUNCT
ejpam-3019	114	5	pm−1	pm−1	NOUN
ejpam-3019	114	6	)	)	PUNCT
ejpam-3019	114	7	+	+	CCONJ
ejpam-3019	114	8	d(bm−1	d(bm−1	PROPN
ejpam-3019	114	9	,	,	PUNCT
ejpam-3019	114	10	qm−1	qm−1	NOUN
ejpam-3019	114	11	)	)	PUNCT
ejpam-3019	114	12	)	)	PUNCT
ejpam-3019	115	1	+	+	ADV
ejpam-3019	115	2	(	(	PUNCT
ejpam-3019	115	3	d(am−1	d(am−1	ADJ
ejpam-3019	115	4	,	,	PUNCT
ejpam-3019	115	5	pm	pm	NOUN
ejpam-3019	115	6	)	)	PUNCT
ejpam-3019	115	7	+	+	CCONJ
ejpam-3019	115	8	d(bm−1	d(bm−1	PROPN
ejpam-3019	115	9	,	,	PUNCT
ejpam-3019	115	10	qm	qm	PROPN
ejpam-3019	115	11	)	)	PUNCT
ejpam-3019	115	12	)	)	PUNCT
ejpam-3019	115	13	,	,	PUNCT
ejpam-3019	115	14	=	=	SYM
ejpam-3019	115	15	en	en	X
ejpam-3019	115	16	+	+	X
ejpam-3019	115	17	tn+1	tn+1	X
ejpam-3019	115	18	+	+	CCONJ
ejpam-3019	115	19	en+1	en+1	ADJ
ejpam-3019	115	20	+	+	X
ejpam-3019	115	21	·	·	PUNCT
ejpam-3019	115	22	·	·	PUNCT
ejpam-3019	115	23	·	·	PUNCT
ejpam-3019	115	24	+	+	NUM
ejpam-3019	115	25	tm−1	tm−1	NOUN
ejpam-3019	115	26	+	+	CCONJ
ejpam-3019	115	27	em−1	em−1	PROPN
ejpam-3019	115	28	,	,	PUNCT
ejpam-3019	115	29	≤	≤	ADJ
ejpam-3019	115	30	λne0	λne0	PROPN
ejpam-3019	115	31	+	+	CCONJ
ejpam-3019	115	32	λn+1t0	λn+1t0	PROPN
ejpam-3019	115	33	+	+	CCONJ
ejpam-3019	115	34	λn+1e0	λn+1e0	PROPN
ejpam-3019	115	35	+	+	CCONJ
ejpam-3019	115	36	·	·	PUNCT
ejpam-3019	115	37	·	·	PUNCT
ejpam-3019	115	38	·	·	PUNCT
ejpam-3019	115	39	+	+	SYM
ejpam-3019	115	40	λm−1t0	λm−1t0	X
ejpam-3019	115	41	+	+	CCONJ
ejpam-3019	115	42	λm−1e0	λm−1e0	ADJ
ejpam-3019	115	43	,	,	PUNCT
ejpam-3019	115	44	=	=	SYM
ejpam-3019	115	45	(	(	PUNCT
ejpam-3019	115	46	λn	λn	PROPN
ejpam-3019	115	47	+	+	CCONJ
ejpam-3019	115	48	λn+1	λn+1	PROPN
ejpam-3019	115	49	+	+	CCONJ
ejpam-3019	115	50	·	·	PUNCT
ejpam-3019	115	51	·	·	PUNCT
ejpam-3019	115	52	·	·	PUNCT
ejpam-3019	115	53	+	+	NUM
ejpam-3019	115	54	λm−1)e0	λm−1)e0	NOUN
ejpam-3019	115	55	+	+	CCONJ
ejpam-3019	115	56	(	(	PUNCT
ejpam-3019	115	57	λn+1	λn+1	ADP
ejpam-3019	115	58	+	+	CCONJ
ejpam-3019	115	59	λn+2	λn+2	NUM
ejpam-3019	115	60	+	+	NUM
ejpam-3019	115	61	·	·	PUNCT
ejpam-3019	115	62	·	·	PUNCT
ejpam-3019	115	63	·	·	PUNCT
ejpam-3019	115	64	+	+	CCONJ
ejpam-3019	115	65	λm−1)t0	λm−1)t0	PROPN
ejpam-3019	115	66	,	,	PUNCT
ejpam-3019	115	67	≤	≤	NUM
ejpam-3019	115	68	λn	λn	ADP
ejpam-3019	115	69	1−	1−	NUM
ejpam-3019	115	70	λ	λ	PROPN
ejpam-3019	115	71	e0	e0	PROPN
ejpam-3019	115	72	+	+	CCONJ
ejpam-3019	115	73	λn+1	λn+1	PROPN
ejpam-3019	115	74	1−	1−	NUM
ejpam-3019	115	75	λ	λ	SYM
ejpam-3019	115	76	t0	t0	PROPN
ejpam-3019	115	77	(	(	PUNCT
ejpam-3019	115	78	13	13	NUM
ejpam-3019	115	79	)	)	PUNCT
ejpam-3019	115	80	and	and	CCONJ
ejpam-3019	115	81	d(am	d(am	PROPN
ejpam-3019	115	82	,	,	PUNCT
ejpam-3019	115	83	pn	pn	NOUN
ejpam-3019	115	84	)	)	PUNCT
ejpam-3019	115	85	+	+	CCONJ
ejpam-3019	115	86	d(bm	d(bm	PROPN
ejpam-3019	115	87	,	,	PUNCT
ejpam-3019	115	88	qn	qn	NOUN
ejpam-3019	115	89	)	)	PUNCT
ejpam-3019	115	90	≤	≤	NOUN
ejpam-3019	115	91	(	(	PUNCT
ejpam-3019	115	92	d(am	d(am	NOUN
ejpam-3019	115	93	,	,	PUNCT
ejpam-3019	115	94	pm−1	pm−1	NOUN
ejpam-3019	115	95	)	)	PUNCT
ejpam-3019	115	96	+	+	CCONJ
ejpam-3019	115	97	d(bm	d(bm	NOUN
ejpam-3019	115	98	,	,	PUNCT
ejpam-3019	115	99	qm−1	qm−1	NOUN
ejpam-3019	115	100	)	)	PUNCT
ejpam-3019	115	101	)	)	PUNCT
ejpam-3019	116	1	+	+	ADV
ejpam-3019	116	2	(	(	PUNCT
ejpam-3019	116	3	d(am−1	d(am−1	PROPN
ejpam-3019	116	4	,	,	PUNCT
ejpam-3019	116	5	pm−1	pm−1	NOUN
ejpam-3019	116	6	)	)	PUNCT
ejpam-3019	116	7	+	+	CCONJ
ejpam-3019	116	8	d(bm−1	d(bm−1	PROPN
ejpam-3019	116	9	,	,	PUNCT
ejpam-3019	116	10	qm−1	qm−1	NOUN
ejpam-3019	116	11	)	)	PUNCT
ejpam-3019	116	12	)	)	PUNCT
ejpam-3019	117	1	+	+	CCONJ
ejpam-3019	117	2	·	·	PUNCT
ejpam-3019	117	3	·	·	PUNCT
ejpam-3019	117	4	·	·	PUNCT
ejpam-3019	118	1	+	+	ADJ
ejpam-3019	118	2	(	(	PUNCT
ejpam-3019	118	3	d(an+1	d(an+1	ADJ
ejpam-3019	118	4	,	,	PUNCT
ejpam-3019	118	5	pn+1	pn+1	NOUN
ejpam-3019	118	6	)	)	PUNCT
ejpam-3019	118	7	+	+	X
ejpam-3019	118	8	d(bn+1	d(bn+1	PROPN
ejpam-3019	118	9	,	,	PUNCT
ejpam-3019	118	10	qn+1	qn+1	NUM
ejpam-3019	118	11	)	)	PUNCT
ejpam-3019	118	12	)	)	PUNCT
ejpam-3019	119	1	+	+	ADJ
ejpam-3019	119	2	(	(	PUNCT
ejpam-3019	119	3	d(an+1	d(an+1	ADJ
ejpam-3019	119	4	,	,	PUNCT
ejpam-3019	119	5	pn	pn	NOUN
ejpam-3019	119	6	)	)	PUNCT
ejpam-3019	120	1	+	+	X
ejpam-3019	120	2	d(bn+1	d(bn+1	PROPN
ejpam-3019	120	3	,	,	PUNCT
ejpam-3019	120	4	qn	qn	NOUN
ejpam-3019	120	5	)	)	PUNCT
ejpam-3019	120	6	)	)	PUNCT
ejpam-3019	120	7	,	,	PUNCT
ejpam-3019	120	8	=	=	PUNCT
ejpam-3019	120	9	sm−1	sm−1	NOUN
ejpam-3019	120	10	+	+	CCONJ
ejpam-3019	120	11	tm−1	tm−1	NOUN
ejpam-3019	120	12	+	+	CCONJ
ejpam-3019	120	13	·	·	PUNCT
ejpam-3019	120	14	·	·	PUNCT
ejpam-3019	121	1	·	·	PUNCT
ejpam-3019	121	2	+	+	NUM
ejpam-3019	121	3	sn+1	sn+1	VERB
ejpam-3019	121	4	+	+	SYM
ejpam-3019	121	5	tn+1	tn+1	X
ejpam-3019	121	6	+	+	CCONJ
ejpam-3019	121	7	sn	sn	PROPN
ejpam-3019	121	8	,	,	PUNCT
ejpam-3019	121	9	≤	≤	NOUN
ejpam-3019	122	1	λm−1s0	λm−1s0	PROPN
ejpam-3019	123	1	+	+	NUM
ejpam-3019	123	2	λm−1t0	λm−1t0	X
ejpam-3019	123	3	+	+	X
ejpam-3019	123	4	·	·	PUNCT
ejpam-3019	123	5	·	·	PUNCT
ejpam-3019	123	6	·	·	PUNCT
ejpam-3019	123	7	+	+	CCONJ
ejpam-3019	124	1	λn+1s0	λn+1s0	X
ejpam-3019	124	2	+	+	CCONJ
ejpam-3019	124	3	λn+1t0	λn+1t0	PROPN
ejpam-3019	124	4	+	+	CCONJ
ejpam-3019	124	5	λns0	λns0	PROPN
ejpam-3019	124	6	,	,	PUNCT
ejpam-3019	124	7	=	=	PUNCT
ejpam-3019	124	8	(	(	PUNCT
ejpam-3019	124	9	λn	λn	PROPN
ejpam-3019	124	10	+	+	CCONJ
ejpam-3019	124	11	λn+1	λn+1	PROPN
ejpam-3019	124	12	+	+	CCONJ
ejpam-3019	124	13	·	·	PUNCT
ejpam-3019	124	14	·	·	PUNCT
ejpam-3019	124	15	·	·	PUNCT
ejpam-3019	124	16	+	+	NUM
ejpam-3019	124	17	λm−1)s0	λm−1)s0	X
ejpam-3019	124	18	+	+	CCONJ
ejpam-3019	124	19	(	(	PUNCT
ejpam-3019	124	20	λn+1	λn+1	ADP
ejpam-3019	124	21	+	+	CCONJ
ejpam-3019	124	22	λn+2	λn+2	NUM
ejpam-3019	124	23	+	+	NUM
ejpam-3019	124	24	·	·	PUNCT
ejpam-3019	124	25	·	·	PUNCT
ejpam-3019	124	26	·	·	PUNCT
ejpam-3019	124	27	+	+	CCONJ
ejpam-3019	124	28	λm−1)t0	λm−1)t0	PROPN
ejpam-3019	124	29	,	,	PUNCT
ejpam-3019	124	30	≤	≤	NUM
ejpam-3019	124	31	λn	λn	ADP
ejpam-3019	124	32	1−	1−	NUM
ejpam-3019	124	33	λ	λ	PROPN
ejpam-3019	124	34	s0	s0	NOUN
ejpam-3019	124	35	+	+	CCONJ
ejpam-3019	124	36	λn+1	λn+1	PROPN
ejpam-3019	124	37	1−	1−	NUM
ejpam-3019	124	38	λ	λ	SYM
ejpam-3019	124	39	t0	t0	PROPN
ejpam-3019	124	40	(	(	PUNCT
ejpam-3019	124	41	14	14	NUM
ejpam-3019	124	42	)	)	PUNCT
ejpam-3019	124	43	a.	a.	NOUN
ejpam-3019	124	44	mutlu	mutlu	PROPN
ejpam-3019	124	45	,	,	PUNCT
ejpam-3019	124	46	k.	k.	PROPN
ejpam-3019	124	47	özkan	özkan	PROPN
ejpam-3019	124	48	,	,	PUNCT
ejpam-3019	124	49	u.	u.	PROPN
ejpam-3019	124	50	gürdal	gürdal	PROPN
ejpam-3019	124	51	/	/	SYM
ejpam-3019	124	52	eur	eur	PROPN
ejpam-3019	124	53	.	.	PUNCT
ejpam-3019	125	1	j.	j.	PROPN
ejpam-3019	125	2	pure	pure	PROPN
ejpam-3019	125	3	appl	appl	PROPN
ejpam-3019	125	4	.	.	PROPN
ejpam-3019	125	5	math	math	PROPN
ejpam-3019	125	6	,	,	PUNCT
ejpam-3019	125	7	10	10	NUM
ejpam-3019	125	8	(	(	PUNCT
ejpam-3019	125	9	4	4	NUM
ejpam-3019	125	10	)	)	PUNCT
ejpam-3019	125	11	(	(	PUNCT
ejpam-3019	125	12	2017	2017	NUM
ejpam-3019	125	13	)	)	PUNCT
ejpam-3019	125	14	,	,	PUNCT
ejpam-3019	125	15	655	655	NUM
ejpam-3019	125	16	-	-	SYM
ejpam-3019	125	17	667	667	NUM
ejpam-3019	125	18	660	660	NUM
ejpam-3019	125	19	for	for	ADP
ejpam-3019	125	20	n	n	X
ejpam-3019	125	21	<	<	X
ejpam-3019	125	22	m.	m.	NOUN
ejpam-3019	125	23	since	since	SCONJ
ejpam-3019	125	24	,	,	PUNCT
ejpam-3019	125	25	for	for	ADP
ejpam-3019	125	26	an	an	DET
ejpam-3019	125	27	arbitrary	arbitrary	ADJ
ejpam-3019	125	28	ε	ε	PROPN
ejpam-3019	125	29	>	>	X
ejpam-3019	125	30	0	0	PROPN
ejpam-3019	125	31	,	,	PUNCT
ejpam-3019	125	32	there	there	PRON
ejpam-3019	125	33	exists	exist	VERB
ejpam-3019	125	34	n0	n0	NUM
ejpam-3019	125	35	such	such	ADJ
ejpam-3019	125	36	that	that	SCONJ
ejpam-3019	125	37	λn0	λn0	PROPN
ejpam-3019	125	38	1−λe0	1−λe0	PROPN
ejpam-3019	125	39	+	+	CCONJ
ejpam-3019	125	40	λn0	λn0	ADJ
ejpam-3019	125	41	+	+	PROPN
ejpam-3019	125	42	1	1	NUM
ejpam-3019	125	43	1−λ	1−λ	NUM
ejpam-3019	125	44	t0	t0	NOUN
ejpam-3019	125	45	<	<	X
ejpam-3019	125	46	ε	ε	PROPN
ejpam-3019	125	47	3	3	NUM
ejpam-3019	125	48	and	and	CCONJ
ejpam-3019	125	49	λn0	λn0	ADJ
ejpam-3019	125	50	1−λs0	1−λs0	NUM
ejpam-3019	125	51	+	+	CCONJ
ejpam-3019	125	52	λn0	λn0	ADJ
ejpam-3019	125	53	+	+	PROPN
ejpam-3019	125	54	1	1	NUM
ejpam-3019	125	55	1−λ	1−λ	NUM
ejpam-3019	125	56	t0	t0	NOUN
ejpam-3019	125	57	<	<	X
ejpam-3019	125	58	ε	ε	PROPN
ejpam-3019	125	59	3	3	NUM
ejpam-3019	125	60	,	,	PUNCT
ejpam-3019	125	61	from	from	ADP
ejpam-3019	125	62	(	(	PUNCT
ejpam-3019	125	63	13	13	NUM
ejpam-3019	125	64	)	)	PUNCT
ejpam-3019	125	65	and	and	CCONJ
ejpam-3019	125	66	(	(	PUNCT
ejpam-3019	125	67	14	14	NUM
ejpam-3019	125	68	)	)	PUNCT
ejpam-3019	125	69	,	,	PUNCT
ejpam-3019	125	70	we	we	PRON
ejpam-3019	125	71	have	have	VERB
ejpam-3019	125	72	d(an	d(an	NOUN
ejpam-3019	125	73	,	,	PUNCT
ejpam-3019	125	74	pm	pm	NOUN
ejpam-3019	125	75	)	)	PUNCT
ejpam-3019	125	76	+	+	CCONJ
ejpam-3019	125	77	d(bn	d(bn	NUM
ejpam-3019	125	78	,	,	PUNCT
ejpam-3019	125	79	qm	qm	PROPN
ejpam-3019	125	80	)	)	PUNCT
ejpam-3019	125	81	<	<	X
ejpam-3019	125	82	ε	ε	PROPN
ejpam-3019	125	83	3	3	NUM
ejpam-3019	125	84	for	for	ADP
ejpam-3019	125	85	each	each	DET
ejpam-3019	125	86	n	n	CCONJ
ejpam-3019	125	87	,	,	PUNCT
ejpam-3019	125	88	m	m	PROPN
ejpam-3019	125	89	≥	≥	NOUN
ejpam-3019	125	90	n0	n0	NUM
ejpam-3019	125	91	.	.	PUNCT
ejpam-3019	126	1	then	then	ADV
ejpam-3019	126	2	(	(	PUNCT
ejpam-3019	126	3	an	an	PRON
ejpam-3019	126	4	,	,	PUNCT
ejpam-3019	126	5	pn	pn	NOUN
ejpam-3019	126	6	)	)	PUNCT
ejpam-3019	126	7	and	and	CCONJ
ejpam-3019	126	8	(	(	PUNCT
ejpam-3019	126	9	bn	bn	X
ejpam-3019	126	10	,	,	PUNCT
ejpam-3019	126	11	qn	qn	NOUN
ejpam-3019	126	12	)	)	PUNCT
ejpam-3019	126	13	are	be	AUX
ejpam-3019	126	14	cauchy	cauchy	NOUN
ejpam-3019	126	15	bisequences	bisequence	NOUN
ejpam-3019	126	16	.	.	PUNCT
ejpam-3019	127	1	because	because	SCONJ
ejpam-3019	127	2	of	of	ADP
ejpam-3019	127	3	completeness	completeness	NOUN
ejpam-3019	127	4	of	of	ADP
ejpam-3019	127	5	(	(	PUNCT
ejpam-3019	127	6	x	x	PROPN
ejpam-3019	127	7	,	,	PUNCT
ejpam-3019	127	8	y	y	PROPN
ejpam-3019	127	9	,	,	PUNCT
ejpam-3019	127	10	d	d	PROPN
ejpam-3019	127	11	)	)	PUNCT
ejpam-3019	127	12	,	,	PUNCT
ejpam-3019	127	13	there	there	PRON
ejpam-3019	127	14	exist	exist	VERB
ejpam-3019	127	15	a	a	DET
ejpam-3019	127	16	,	,	PUNCT
ejpam-3019	127	17	b	b	X
ejpam-3019	127	18	∈	∈	PROPN
ejpam-3019	127	19	x	x	X
ejpam-3019	127	20	and	and	CCONJ
ejpam-3019	127	21	p	p	X
ejpam-3019	127	22	,	,	PUNCT
ejpam-3019	127	23	q	q	PROPN
ejpam-3019	127	24	∈	∈	PROPN
ejpam-3019	127	25	y	y	PROPN
ejpam-3019	127	26	with	with	ADP
ejpam-3019	127	27	lim	lim	PROPN
ejpam-3019	127	28	n→∞	n→∞	X
ejpam-3019	127	29	an	an	DET
ejpam-3019	127	30	=	=	SYM
ejpam-3019	127	31	p	p	NOUN
ejpam-3019	127	32	,	,	PUNCT
ejpam-3019	127	33	lim	lim	PROPN
ejpam-3019	127	34	n→∞	n→∞	NUM
ejpam-3019	127	35	bn	bn	NOUN
ejpam-3019	127	36	=	=	SYM
ejpam-3019	127	37	q	q	PROPN
ejpam-3019	127	38	,	,	PUNCT
ejpam-3019	127	39	lim	lim	PROPN
ejpam-3019	127	40	n→∞	n→∞	PRON
ejpam-3019	127	41	pn	pn	PROPN
ejpam-3019	127	42	=	=	PUNCT
ejpam-3019	127	43	a	a	PROPN
ejpam-3019	127	44	and	and	CCONJ
ejpam-3019	127	45	lim	lim	PROPN
ejpam-3019	127	46	n→∞	n→∞	NUM
ejpam-3019	127	47	qn	qn	PROPN
ejpam-3019	127	48	=	=	PROPN
ejpam-3019	127	49	b.	b.	PROPN
ejpam-3019	127	50	(	(	PUNCT
ejpam-3019	127	51	15	15	NUM
ejpam-3019	127	52	)	)	PUNCT
ejpam-3019	127	53	then	then	ADV
ejpam-3019	127	54	there	there	PRON
ejpam-3019	127	55	exists	exist	VERB
ejpam-3019	127	56	n1	n1	PROPN
ejpam-3019	127	57	∈	∈	PROPN
ejpam-3019	127	58	n	n	X
ejpam-3019	127	59	with	with	ADP
ejpam-3019	127	60	d(an	d(an	PROPN
ejpam-3019	127	61	,	,	PUNCT
ejpam-3019	127	62	p	p	NOUN
ejpam-3019	127	63	)	)	PUNCT
ejpam-3019	127	64	<	<	X
ejpam-3019	127	65	ε	ε	PROPN
ejpam-3019	127	66	3	3	NUM
ejpam-3019	127	67	,	,	PUNCT
ejpam-3019	127	68	d(bn	d(bn	PROPN
ejpam-3019	127	69	,	,	PUNCT
ejpam-3019	127	70	q	q	NOUN
ejpam-3019	127	71	)	)	PUNCT
ejpam-3019	127	72	<	<	X
ejpam-3019	127	73	ε	ε	PROPN
ejpam-3019	127	74	3	3	NUM
ejpam-3019	127	75	,	,	PUNCT
ejpam-3019	127	76	d(a	d(a	PROPN
ejpam-3019	127	77	,	,	PUNCT
ejpam-3019	127	78	pn	pn	NOUN
ejpam-3019	127	79	)	)	PUNCT
ejpam-3019	127	80	<	<	X
ejpam-3019	127	81	ε	ε	PROPN
ejpam-3019	127	82	3	3	NUM
ejpam-3019	127	83	and	and	CCONJ
ejpam-3019	127	84	d(b	d(b	PROPN
ejpam-3019	127	85	,	,	PUNCT
ejpam-3019	127	86	qn	qn	NOUN
ejpam-3019	127	87	)	)	PUNCT
ejpam-3019	127	88	<	<	X
ejpam-3019	127	89	ε	ε	PROPN
ejpam-3019	127	90	3	3	NUM
ejpam-3019	127	91	for	for	ADP
ejpam-3019	127	92	all	all	DET
ejpam-3019	127	93	n	n	PRON
ejpam-3019	127	94	≥	≥	NOUN
ejpam-3019	127	95	n1	n1	PROPN
ejpam-3019	127	96	and	and	CCONJ
ejpam-3019	127	97	every	every	DET
ejpam-3019	127	98	ε	ε	PROPN
ejpam-3019	127	99	>	>	X
ejpam-3019	127	100	0	0	PROPN
ejpam-3019	127	101	.	.	PUNCT
ejpam-3019	128	1	since	since	SCONJ
ejpam-3019	128	2	(	(	PUNCT
ejpam-3019	128	3	an	an	DET
ejpam-3019	128	4	,	,	PUNCT
ejpam-3019	128	5	pn	pn	NOUN
ejpam-3019	128	6	)	)	PUNCT
ejpam-3019	128	7	and	and	CCONJ
ejpam-3019	128	8	(	(	PUNCT
ejpam-3019	128	9	bn	bn	X
ejpam-3019	128	10	,	,	PUNCT
ejpam-3019	128	11	qn	qn	NOUN
ejpam-3019	128	12	)	)	PUNCT
ejpam-3019	128	13	are	be	AUX
ejpam-3019	128	14	cauchy	cauchy	NOUN
ejpam-3019	128	15	bisequences	bisequence	NOUN
ejpam-3019	128	16	,	,	PUNCT
ejpam-3019	128	17	we	we	PRON
ejpam-3019	128	18	get	get	VERB
ejpam-3019	128	19	d(an	d(an	NOUN
ejpam-3019	128	20	,	,	PUNCT
ejpam-3019	128	21	pn	pn	NOUN
ejpam-3019	128	22	)	)	PUNCT
ejpam-3019	128	23	<	<	X
ejpam-3019	128	24	ε	ε	PROPN
ejpam-3019	128	25	3	3	NUM
ejpam-3019	128	26	and	and	CCONJ
ejpam-3019	128	27	d(bn	d(bn	NOUN
ejpam-3019	128	28	,	,	PUNCT
ejpam-3019	128	29	qn	qn	NOUN
ejpam-3019	128	30	)	)	PUNCT
ejpam-3019	128	31	<	<	X
ejpam-3019	128	32	ε	ε	PROPN
ejpam-3019	128	33	3	3	NUM
ejpam-3019	128	34	.	.	PUNCT
ejpam-3019	129	1	so	so	ADV
ejpam-3019	129	2	,	,	PUNCT
ejpam-3019	129	3	from	from	ADP
ejpam-3019	129	4	(	(	PUNCT
ejpam-3019	129	5	1	1	NUM
ejpam-3019	129	6	)	)	PUNCT
ejpam-3019	129	7	,	,	PUNCT
ejpam-3019	129	8	we	we	PRON
ejpam-3019	129	9	have	have	VERB
ejpam-3019	129	10	d(f	d(f	NOUN
ejpam-3019	129	11	(	(	PUNCT
ejpam-3019	129	12	a	a	DET
ejpam-3019	129	13	,	,	PUNCT
ejpam-3019	129	14	b	b	NOUN
ejpam-3019	129	15	)	)	PUNCT
ejpam-3019	129	16	,	,	PUNCT
ejpam-3019	129	17	p	p	NOUN
ejpam-3019	129	18	)	)	PUNCT
ejpam-3019	129	19	≤	≤	NOUN
ejpam-3019	129	20	d(f	d(f	NOUN
ejpam-3019	129	21	(	(	PUNCT
ejpam-3019	129	22	a	a	DET
ejpam-3019	129	23	,	,	PUNCT
ejpam-3019	129	24	b	b	NOUN
ejpam-3019	129	25	)	)	PUNCT
ejpam-3019	129	26	,	,	PUNCT
ejpam-3019	129	27	pn+1	pn+1	NOUN
ejpam-3019	129	28	)	)	PUNCT
ejpam-3019	129	29	+	+	CCONJ
ejpam-3019	129	30	d(an+1	d(an+1	ADJ
ejpam-3019	129	31	,	,	PUNCT
ejpam-3019	129	32	pn+1	pn+1	NOUN
ejpam-3019	129	33	)	)	PUNCT
ejpam-3019	129	34	+	+	CCONJ
ejpam-3019	130	1	d(an+1	d(an+1	ADJ
ejpam-3019	130	2	,	,	PUNCT
ejpam-3019	130	3	p	p	NOUN
ejpam-3019	130	4	)	)	PUNCT
ejpam-3019	130	5	=	=	NOUN
ejpam-3019	130	6	d(f	d(f	NOUN
ejpam-3019	130	7	(	(	PUNCT
ejpam-3019	130	8	a	a	DET
ejpam-3019	130	9	,	,	PUNCT
ejpam-3019	130	10	b	b	NOUN
ejpam-3019	130	11	)	)	PUNCT
ejpam-3019	130	12	,	,	PUNCT
ejpam-3019	130	13	f	f	PROPN
ejpam-3019	130	14	(	(	PUNCT
ejpam-3019	130	15	pn	pn	PROPN
ejpam-3019	130	16	,	,	PUNCT
ejpam-3019	130	17	qn	qn	NOUN
ejpam-3019	130	18	)	)	PUNCT
ejpam-3019	130	19	)	)	PUNCT
ejpam-3019	131	1	+	+	CCONJ
ejpam-3019	131	2	d(an+1	d(an+1	ADJ
ejpam-3019	131	3	,	,	PUNCT
ejpam-3019	131	4	pn+1	pn+1	NOUN
ejpam-3019	131	5	)	)	PUNCT
ejpam-3019	132	1	+	+	CCONJ
ejpam-3019	132	2	d(an+1	d(an+1	ADJ
ejpam-3019	132	3	,	,	PUNCT
ejpam-3019	132	4	p	p	NOUN
ejpam-3019	132	5	)	)	PUNCT
ejpam-3019	132	6	≤	≤	NOUN
ejpam-3019	133	1	kd(a	kd(a	X
ejpam-3019	133	2	,	,	PUNCT
ejpam-3019	133	3	pn	pn	NOUN
ejpam-3019	133	4	)	)	PUNCT
ejpam-3019	133	5	+	+	CCONJ
ejpam-3019	133	6	ld(b	ld(b	ADJ
ejpam-3019	133	7	,	,	PUNCT
ejpam-3019	133	8	qn	qn	NOUN
ejpam-3019	133	9	)	)	PUNCT
ejpam-3019	133	10	+	+	CCONJ
ejpam-3019	133	11	d(an+1	d(an+1	ADJ
ejpam-3019	133	12	,	,	PUNCT
ejpam-3019	133	13	pn+1	pn+1	NOUN
ejpam-3019	133	14	)	)	PUNCT
ejpam-3019	133	15	+	+	CCONJ
ejpam-3019	133	16	d(an+1	d(an+1	ADJ
ejpam-3019	133	17	,	,	PUNCT
ejpam-3019	133	18	p	p	NOUN
ejpam-3019	133	19	)	)	PUNCT
ejpam-3019	133	20	<	<	X
ejpam-3019	133	21	k	k	PROPN
ejpam-3019	133	22	ε	ε	PROPN
ejpam-3019	133	23	3	3	NUM
ejpam-3019	133	24	+	+	CCONJ
ejpam-3019	133	25	l	l	NOUN
ejpam-3019	133	26	ε	ε	NOUN
ejpam-3019	133	27	3	3	NUM
ejpam-3019	133	28	+	+	CCONJ
ejpam-3019	133	29	ε	ε	PROPN
ejpam-3019	133	30	3	3	NUM
ejpam-3019	133	31	+	+	CCONJ
ejpam-3019	133	32	ε	ε	PROPN
ejpam-3019	133	33	3	3	NUM
ejpam-3019	133	34	=	=	SYM
ejpam-3019	133	35	λ	λ	X
ejpam-3019	133	36	ε	ε	NOUN
ejpam-3019	133	37	3	3	NUM
ejpam-3019	133	38	+	+	SYM
ejpam-3019	133	39	2	2	NUM
ejpam-3019	133	40	ε	ε	NOUN
ejpam-3019	133	41	3	3	NUM
ejpam-3019	133	42	<	<	X
ejpam-3019	133	43	ε	ε	PROPN
ejpam-3019	133	44	for	for	ADP
ejpam-3019	133	45	each	each	DET
ejpam-3019	133	46	n	n	PRON
ejpam-3019	133	47	∈	∈	PROPN
ejpam-3019	133	48	n	n	NOUN
ejpam-3019	133	49	and	and	CCONJ
ejpam-3019	133	50	λ	λ	X
ejpam-3019	133	51	<	<	X
ejpam-3019	133	52	1	1	NUM
ejpam-3019	133	53	.	.	PUNCT
ejpam-3019	133	54	then	then	ADV
ejpam-3019	133	55	d(f	d(f	NOUN
ejpam-3019	133	56	(	(	PUNCT
ejpam-3019	133	57	a	a	DET
ejpam-3019	133	58	,	,	PUNCT
ejpam-3019	133	59	b	b	NOUN
ejpam-3019	133	60	)	)	PUNCT
ejpam-3019	133	61	,	,	PUNCT
ejpam-3019	133	62	p	p	NOUN
ejpam-3019	133	63	)	)	PUNCT
ejpam-3019	133	64	=	=	SYM
ejpam-3019	133	65	0	0	X
ejpam-3019	133	66	.	.	PUNCT
ejpam-3019	134	1	hence	hence	ADV
ejpam-3019	134	2	,	,	PUNCT
ejpam-3019	134	3	f	f	PROPN
ejpam-3019	134	4	(	(	PUNCT
ejpam-3019	134	5	a	a	DET
ejpam-3019	134	6	,	,	PUNCT
ejpam-3019	134	7	b	b	NOUN
ejpam-3019	134	8	)	)	PUNCT
ejpam-3019	134	9	=	=	VERB
ejpam-3019	135	1	p.	p.	NOUN
ejpam-3019	135	2	similarly	similarly	ADV
ejpam-3019	135	3	,	,	PUNCT
ejpam-3019	135	4	we	we	PRON
ejpam-3019	135	5	get	get	VERB
ejpam-3019	135	6	f	f	PROPN
ejpam-3019	135	7	(	(	PUNCT
ejpam-3019	135	8	b	b	PROPN
ejpam-3019	135	9	,	,	PUNCT
ejpam-3019	135	10	a	a	PRON
ejpam-3019	135	11	)	)	PUNCT
ejpam-3019	136	1	=	=	SYM
ejpam-3019	136	2	q	q	X
ejpam-3019	136	3	,	,	PUNCT
ejpam-3019	136	4	f	f	PROPN
ejpam-3019	136	5	(	(	PUNCT
ejpam-3019	136	6	p	p	X
ejpam-3019	136	7	,	,	PUNCT
ejpam-3019	136	8	q	q	NOUN
ejpam-3019	136	9	)	)	PUNCT
ejpam-3019	136	10	=	=	SYM
ejpam-3019	136	11	a	a	PROPN
ejpam-3019	136	12	and	and	CCONJ
ejpam-3019	136	13	f	f	PROPN
ejpam-3019	136	14	(	(	PUNCT
ejpam-3019	136	15	q	q	NOUN
ejpam-3019	136	16	,	,	PUNCT
ejpam-3019	136	17	p	p	NOUN
ejpam-3019	136	18	)	)	PUNCT
ejpam-3019	136	19	=	=	SYM
ejpam-3019	136	20	b.	b.	PROPN
ejpam-3019	136	21	on	on	ADP
ejpam-3019	136	22	the	the	DET
ejpam-3019	136	23	other	other	ADJ
ejpam-3019	136	24	hand	hand	NOUN
ejpam-3019	136	25	,	,	PUNCT
ejpam-3019	136	26	from	from	ADP
ejpam-3019	136	27	(	(	PUNCT
ejpam-3019	136	28	15	15	NUM
ejpam-3019	136	29	)	)	PUNCT
ejpam-3019	136	30	we	we	PRON
ejpam-3019	136	31	get	get	VERB
ejpam-3019	136	32	d(a	d(a	PROPN
ejpam-3019	136	33	,	,	PUNCT
ejpam-3019	136	34	p	p	NOUN
ejpam-3019	136	35	)	)	PUNCT
ejpam-3019	136	36	=	=	SYM
ejpam-3019	137	1	d	d	X
ejpam-3019	137	2	(	(	PUNCT
ejpam-3019	137	3	lim	lim	PROPN
ejpam-3019	137	4	n→∞	n→∞	NUM
ejpam-3019	137	5	pn	pn	PROPN
ejpam-3019	137	6	,	,	PUNCT
ejpam-3019	137	7	lim	lim	PROPN
ejpam-3019	137	8	n→∞	n→∞	X
ejpam-3019	137	9	an	an	PRON
ejpam-3019	137	10	)	)	PUNCT
ejpam-3019	137	11	=	=	SYM
ejpam-3019	137	12	lim	lim	PROPN
ejpam-3019	137	13	n→∞	n→∞	X
ejpam-3019	137	14	d(an	d(an	PROPN
ejpam-3019	137	15	,	,	PUNCT
ejpam-3019	137	16	pn	pn	NOUN
ejpam-3019	137	17	)	)	PUNCT
ejpam-3019	137	18	=	=	SYM
ejpam-3019	137	19	0	0	NUM
ejpam-3019	137	20	and	and	CCONJ
ejpam-3019	137	21	d(b	d(b	PROPN
ejpam-3019	137	22	,	,	PUNCT
ejpam-3019	137	23	q	q	X
ejpam-3019	137	24	)	)	PUNCT
ejpam-3019	137	25	=	=	SYM
ejpam-3019	138	1	d	d	X
ejpam-3019	138	2	(	(	PUNCT
ejpam-3019	138	3	lim	lim	PROPN
ejpam-3019	138	4	n→∞	n→∞	NUM
ejpam-3019	138	5	qn	qn	PROPN
ejpam-3019	138	6	,	,	PUNCT
ejpam-3019	138	7	lim	lim	PROPN
ejpam-3019	138	8	n→∞	n→∞	NUM
ejpam-3019	138	9	bn	bn	NOUN
ejpam-3019	138	10	)	)	PUNCT
ejpam-3019	138	11	=	=	SYM
ejpam-3019	139	1	lim	lim	PROPN
ejpam-3019	139	2	n→∞	n→∞	X
ejpam-3019	139	3	d(bn	d(bn	PROPN
ejpam-3019	139	4	,	,	PUNCT
ejpam-3019	139	5	qn	qn	NOUN
ejpam-3019	139	6	)	)	PUNCT
ejpam-3019	139	7	=	=	SYM
ejpam-3019	139	8	0	0	X
ejpam-3019	139	9	.	.	PUNCT
ejpam-3019	140	1	so	so	ADV
ejpam-3019	140	2	,	,	PUNCT
ejpam-3019	140	3	a	a	DET
ejpam-3019	140	4	=	=	X
ejpam-3019	140	5	p	p	NOUN
ejpam-3019	140	6	and	and	CCONJ
ejpam-3019	140	7	b	b	X
ejpam-3019	140	8	=	=	SYM
ejpam-3019	140	9	q.	q.	PROPN
ejpam-3019	140	10	therefore	therefore	ADV
ejpam-3019	140	11	,	,	PUNCT
ejpam-3019	140	12	(	(	PUNCT
ejpam-3019	140	13	a	a	DET
ejpam-3019	140	14	,	,	PUNCT
ejpam-3019	140	15	b	b	NOUN
ejpam-3019	140	16	)	)	PUNCT
ejpam-3019	140	17	∈	∈	PROPN
ejpam-3019	140	18	x2	x2	PROPN
ejpam-3019	140	19	∩	∩	NOUN
ejpam-3019	140	20	y	y	PROPN
ejpam-3019	140	21	2	2	NUM
ejpam-3019	140	22	is	be	AUX
ejpam-3019	140	23	a	a	DET
ejpam-3019	140	24	coupled	couple	VERB
ejpam-3019	140	25	fixed	fix	VERB
ejpam-3019	140	26	point	point	NOUN
ejpam-3019	140	27	of	of	ADP
ejpam-3019	140	28	f	f	PROPN
ejpam-3019	140	29	.	.	PUNCT
ejpam-3019	141	1	now	now	ADV
ejpam-3019	141	2	,	,	PUNCT
ejpam-3019	141	3	to	to	PART
ejpam-3019	141	4	show	show	VERB
ejpam-3019	141	5	the	the	DET
ejpam-3019	141	6	uniqueness	uniqueness	NOUN
ejpam-3019	141	7	,	,	PUNCT
ejpam-3019	141	8	we	we	PRON
ejpam-3019	141	9	begin	begin	VERB
ejpam-3019	141	10	by	by	ADP
ejpam-3019	141	11	taking	take	VERB
ejpam-3019	141	12	another	another	DET
ejpam-3019	141	13	coupled	couple	VERB
ejpam-3019	141	14	fixed	fix	VERB
ejpam-3019	141	15	point	point	NOUN
ejpam-3019	141	16	(	(	PUNCT
ejpam-3019	142	1	a∗	a∗	ADJ
ejpam-3019	142	2	,	,	PUNCT
ejpam-3019	142	3	b∗	b∗	ADJ
ejpam-3019	142	4	)	)	PUNCT
ejpam-3019	142	5	∈	∈	PROPN
ejpam-3019	142	6	x2	x2	PROPN
ejpam-3019	142	7	∪	∪	VERB
ejpam-3019	142	8	y	y	PROPN
ejpam-3019	142	9	2	2	NUM
ejpam-3019	142	10	.	.	PUNCT
ejpam-3019	143	1	if	if	SCONJ
ejpam-3019	143	2	(	(	PUNCT
ejpam-3019	143	3	a∗	a∗	ADJ
ejpam-3019	143	4	,	,	PUNCT
ejpam-3019	143	5	b∗	b∗	ADJ
ejpam-3019	143	6	)	)	PUNCT
ejpam-3019	143	7	∈	∈	PROPN
ejpam-3019	143	8	x2	x2	PROPN
ejpam-3019	143	9	,	,	PUNCT
ejpam-3019	143	10	then	then	ADV
ejpam-3019	143	11	we	we	PRON
ejpam-3019	143	12	get	get	VERB
ejpam-3019	143	13	d(a∗	d(a∗	PRON
ejpam-3019	143	14	,	,	PUNCT
ejpam-3019	143	15	a	a	PRON
ejpam-3019	143	16	)	)	PUNCT
ejpam-3019	143	17	=	=	SYM
ejpam-3019	143	18	d(f	d(f	NOUN
ejpam-3019	143	19	(	(	PUNCT
ejpam-3019	143	20	a∗	a∗	ADJ
ejpam-3019	143	21	,	,	PUNCT
ejpam-3019	143	22	b∗	b∗	ADJ
ejpam-3019	143	23	)	)	PUNCT
ejpam-3019	143	24	,	,	PUNCT
ejpam-3019	143	25	f	f	PROPN
ejpam-3019	143	26	(	(	PUNCT
ejpam-3019	143	27	a	a	DET
ejpam-3019	143	28	,	,	PUNCT
ejpam-3019	143	29	b	b	NOUN
ejpam-3019	143	30	)	)	PUNCT
ejpam-3019	143	31	)	)	PUNCT
ejpam-3019	143	32	≤	≤	NUM
ejpam-3019	143	33	kd(a∗	kd(a∗	NOUN
ejpam-3019	143	34	,	,	PUNCT
ejpam-3019	143	35	a	a	NOUN
ejpam-3019	143	36	)	)	PUNCT
ejpam-3019	143	37	+	+	NUM
ejpam-3019	143	38	ld(b∗	ld(b∗	PROPN
ejpam-3019	143	39	,	,	PUNCT
ejpam-3019	143	40	b	b	NOUN
ejpam-3019	143	41	)	)	PUNCT
ejpam-3019	143	42	and	and	CCONJ
ejpam-3019	143	43	d(b∗	d(b∗	PROPN
ejpam-3019	143	44	,	,	PUNCT
ejpam-3019	143	45	b	b	NOUN
ejpam-3019	143	46	)	)	PUNCT
ejpam-3019	143	47	=	=	SYM
ejpam-3019	143	48	d(f	d(f	NOUN
ejpam-3019	143	49	(	(	PUNCT
ejpam-3019	143	50	b∗	b∗	ADJ
ejpam-3019	143	51	,	,	PUNCT
ejpam-3019	143	52	a∗	a∗	PROPN
ejpam-3019	143	53	)	)	PUNCT
ejpam-3019	143	54	,	,	PUNCT
ejpam-3019	143	55	f	f	PROPN
ejpam-3019	143	56	(	(	PUNCT
ejpam-3019	143	57	b	b	PROPN
ejpam-3019	143	58	,	,	PUNCT
ejpam-3019	143	59	a	a	PRON
ejpam-3019	143	60	)	)	PUNCT
ejpam-3019	143	61	)	)	PUNCT
ejpam-3019	143	62	≤	≤	NUM
ejpam-3019	143	63	kd(b∗	kd(b∗	PROPN
ejpam-3019	143	64	,	,	PUNCT
ejpam-3019	143	65	b	b	NOUN
ejpam-3019	143	66	)	)	PUNCT
ejpam-3019	144	1	+	+	NUM
ejpam-3019	144	2	ld(a∗	ld(a∗	NUM
ejpam-3019	144	3	,	,	PUNCT
ejpam-3019	144	4	a	a	PRON
ejpam-3019	144	5	)	)	PUNCT
ejpam-3019	144	6	.	.	PUNCT
ejpam-3019	145	1	therefore	therefore	ADV
ejpam-3019	145	2	,	,	PUNCT
ejpam-3019	145	3	we	we	PRON
ejpam-3019	145	4	have	have	VERB
ejpam-3019	145	5	d(a∗	d(a∗	PRON
ejpam-3019	145	6	,	,	PUNCT
ejpam-3019	145	7	a	a	PRON
ejpam-3019	145	8	)	)	PUNCT
ejpam-3019	145	9	+	+	NOUN
ejpam-3019	145	10	d(b∗	d(b∗	PROPN
ejpam-3019	145	11	,	,	PUNCT
ejpam-3019	145	12	b	b	NOUN
ejpam-3019	145	13	)	)	PUNCT
ejpam-3019	145	14	≤	≤	NOUN
ejpam-3019	146	1	λ(d(a∗	λ(d(a∗	PROPN
ejpam-3019	146	2	,	,	PUNCT
ejpam-3019	146	3	a	a	PRON
ejpam-3019	146	4	)	)	PUNCT
ejpam-3019	146	5	+	+	NOUN
ejpam-3019	146	6	d(b∗	d(b∗	PROPN
ejpam-3019	146	7	,	,	PUNCT
ejpam-3019	146	8	b	b	NOUN
ejpam-3019	146	9	)	)	PUNCT
ejpam-3019	146	10	)	)	PUNCT
ejpam-3019	146	11	.	.	PUNCT
ejpam-3019	147	1	(	(	PUNCT
ejpam-3019	147	2	16	16	NUM
ejpam-3019	147	3	)	)	PUNCT
ejpam-3019	147	4	since	since	SCONJ
ejpam-3019	147	5	λ	λ	X
ejpam-3019	147	6	<	<	X
ejpam-3019	147	7	1	1	NUM
ejpam-3019	147	8	,	,	PUNCT
ejpam-3019	147	9	by	by	ADP
ejpam-3019	147	10	(	(	PUNCT
ejpam-3019	147	11	16	16	NUM
ejpam-3019	147	12	)	)	PUNCT
ejpam-3019	147	13	this	this	PRON
ejpam-3019	147	14	means	mean	VERB
ejpam-3019	147	15	that	that	SCONJ
ejpam-3019	147	16	d(a∗	d(a∗	AUX
ejpam-3019	147	17	,	,	PUNCT
ejpam-3019	147	18	a	a	PRON
ejpam-3019	147	19	)	)	PUNCT
ejpam-3019	148	1	+	+	NOUN
ejpam-3019	148	2	d(b∗	d(b∗	PROPN
ejpam-3019	148	3	,	,	PUNCT
ejpam-3019	148	4	b	b	NOUN
ejpam-3019	148	5	)	)	PUNCT
ejpam-3019	148	6	=	=	SYM
ejpam-3019	148	7	0	0	X
ejpam-3019	148	8	.	.	PUNCT
ejpam-3019	149	1	so	so	ADV
ejpam-3019	149	2	,	,	PUNCT
ejpam-3019	149	3	we	we	PRON
ejpam-3019	149	4	obtain	obtain	VERB
ejpam-3019	149	5	that	that	DET
ejpam-3019	149	6	a∗	a∗	NOUN
ejpam-3019	149	7	=	=	PUNCT
ejpam-3019	149	8	a	a	PRON
ejpam-3019	149	9	and	and	CCONJ
ejpam-3019	149	10	b∗	b∗	ADJ
ejpam-3019	149	11	=	=	SYM
ejpam-3019	149	12	b.	b.	PROPN
ejpam-3019	149	13	similarly	similarly	ADV
ejpam-3019	149	14	,	,	PUNCT
ejpam-3019	149	15	if	if	SCONJ
ejpam-3019	149	16	(	(	PUNCT
ejpam-3019	149	17	a∗	a∗	ADJ
ejpam-3019	149	18	,	,	PUNCT
ejpam-3019	149	19	b∗	b∗	ADJ
ejpam-3019	149	20	)	)	PUNCT
ejpam-3019	149	21	∈	∈	PROPN
ejpam-3019	149	22	y	y	PROPN
ejpam-3019	149	23	2	2	NUM
ejpam-3019	149	24	,	,	PUNCT
ejpam-3019	149	25	we	we	PRON
ejpam-3019	149	26	have	have	VERB
ejpam-3019	149	27	a∗	a∗	NOUN
ejpam-3019	149	28	=	=	PUNCT
ejpam-3019	149	29	a	a	PRON
ejpam-3019	149	30	and	and	CCONJ
ejpam-3019	149	31	b∗	b∗	ADJ
ejpam-3019	149	32	=	=	SYM
ejpam-3019	149	33	b.	b.	PROPN
ejpam-3019	150	1	then	then	ADV
ejpam-3019	150	2	(	(	PUNCT
ejpam-3019	150	3	a	a	DET
ejpam-3019	150	4	,	,	PUNCT
ejpam-3019	150	5	b	b	NOUN
ejpam-3019	150	6	)	)	PUNCT
ejpam-3019	150	7	is	be	AUX
ejpam-3019	150	8	a	a	DET
ejpam-3019	150	9	unique	unique	ADJ
ejpam-3019	150	10	coupled	couple	VERB
ejpam-3019	150	11	fixed	fix	VERB
ejpam-3019	150	12	point	point	NOUN
ejpam-3019	150	13	of	of	ADP
ejpam-3019	150	14	f	f	PROPN
ejpam-3019	150	15	.	.	PUNCT
ejpam-3019	151	1	the	the	DET
ejpam-3019	151	2	following	follow	VERB
ejpam-3019	151	3	corollary	corollary	NOUN
ejpam-3019	151	4	is	be	AUX
ejpam-3019	151	5	obtained	obtain	VERB
ejpam-3019	151	6	,	,	PUNCT
ejpam-3019	151	7	if	if	SCONJ
ejpam-3019	151	8	we	we	PRON
ejpam-3019	151	9	take	take	VERB
ejpam-3019	151	10	equal	equal	ADJ
ejpam-3019	151	11	the	the	DET
ejpam-3019	151	12	constants	constant	NOUN
ejpam-3019	151	13	k	k	NOUN
ejpam-3019	151	14	,	,	PUNCT
ejpam-3019	151	15	l	l	NOUN
ejpam-3019	151	16	in	in	ADP
ejpam-3019	151	17	theorem	theorem	NOUN
ejpam-3019	151	18	1	1	NUM
ejpam-3019	151	19	.	.	PUNCT
ejpam-3019	151	20	a.	a.	NOUN
ejpam-3019	151	21	mutlu	mutlu	PROPN
ejpam-3019	151	22	,	,	PUNCT
ejpam-3019	151	23	k.	k.	PROPN
ejpam-3019	151	24	özkan	özkan	PROPN
ejpam-3019	151	25	,	,	PUNCT
ejpam-3019	151	26	u.	u.	PROPN
ejpam-3019	151	27	gürdal	gürdal	PROPN
ejpam-3019	151	28	/	/	SYM
ejpam-3019	151	29	eur	eur	PROPN
ejpam-3019	151	30	.	.	PUNCT
ejpam-3019	152	1	j.	j.	PROPN
ejpam-3019	152	2	pure	pure	PROPN
ejpam-3019	152	3	appl	appl	PROPN
ejpam-3019	152	4	.	.	PROPN
ejpam-3019	152	5	math	math	PROPN
ejpam-3019	152	6	,	,	PUNCT
ejpam-3019	152	7	10	10	NUM
ejpam-3019	152	8	(	(	PUNCT
ejpam-3019	152	9	4	4	NUM
ejpam-3019	152	10	)	)	PUNCT
ejpam-3019	152	11	(	(	PUNCT
ejpam-3019	152	12	2017	2017	NUM
ejpam-3019	152	13	)	)	PUNCT
ejpam-3019	152	14	,	,	PUNCT
ejpam-3019	152	15	655	655	NUM
ejpam-3019	152	16	-	-	SYM
ejpam-3019	152	17	667	667	NUM
ejpam-3019	152	18	661	661	NUM
ejpam-3019	152	19	corollary	corollary	ADJ
ejpam-3019	152	20	1	1	NUM
ejpam-3019	152	21	.	.	PUNCT
ejpam-3019	153	1	let	let	VERB
ejpam-3019	153	2	(	(	PUNCT
ejpam-3019	153	3	x	x	X
ejpam-3019	153	4	,	,	PUNCT
ejpam-3019	153	5	y	y	PROPN
ejpam-3019	153	6	,	,	PUNCT
ejpam-3019	153	7	d	d	NOUN
ejpam-3019	153	8	)	)	PUNCT
ejpam-3019	153	9	be	be	AUX
ejpam-3019	153	10	a	a	DET
ejpam-3019	153	11	complete	complete	ADJ
ejpam-3019	153	12	bipolar	bipolar	ADJ
ejpam-3019	153	13	metric	metric	ADJ
ejpam-3019	153	14	space	space	NOUN
ejpam-3019	153	15	,	,	PUNCT
ejpam-3019	153	16	f	f	X
ejpam-3019	153	17	:	:	PUNCT
ejpam-3019	153	18	(	(	PUNCT
ejpam-3019	153	19	x2	x2	INTJ
ejpam-3019	153	20	,	,	PUNCT
ejpam-3019	153	21	y	y	PROPN
ejpam-3019	153	22	2	2	NUM
ejpam-3019	153	23	)	)	PUNCT
ejpam-3019	153	24	⇒	⇒	NOUN
ejpam-3019	153	25	(	(	PUNCT
ejpam-3019	153	26	x	x	X
ejpam-3019	153	27	,	,	PUNCT
ejpam-3019	153	28	y	y	PROPN
ejpam-3019	153	29	)	)	PUNCT
ejpam-3019	153	30	be	be	AUX
ejpam-3019	153	31	a	a	DET
ejpam-3019	153	32	covariant	covariant	ADJ
ejpam-3019	153	33	mapping	mapping	NOUN
ejpam-3019	153	34	and	and	CCONJ
ejpam-3019	153	35	k	k	NOUN
ejpam-3019	153	36	,	,	PUNCT
ejpam-3019	153	37	l	l	NOUN
ejpam-3019	153	38	be	be	VERB
ejpam-3019	153	39	non	non	ADJ
ejpam-3019	153	40	-	-	ADJ
ejpam-3019	153	41	negative	negative	ADJ
ejpam-3019	153	42	constants	constant	NOUN
ejpam-3019	153	43	.	.	PUNCT
ejpam-3019	154	1	if	if	SCONJ
ejpam-3019	154	2	the	the	DET
ejpam-3019	154	3	condition	condition	NOUN
ejpam-3019	154	4	d(f	d(f	NOUN
ejpam-3019	154	5	(	(	PUNCT
ejpam-3019	154	6	a	a	DET
ejpam-3019	154	7	,	,	PUNCT
ejpam-3019	154	8	b	b	NOUN
ejpam-3019	154	9	)	)	PUNCT
ejpam-3019	154	10	,	,	PUNCT
ejpam-3019	154	11	f	f	PROPN
ejpam-3019	154	12	(	(	PUNCT
ejpam-3019	154	13	p	p	X
ejpam-3019	154	14	,	,	PUNCT
ejpam-3019	154	15	q	q	NOUN
ejpam-3019	154	16	)	)	PUNCT
ejpam-3019	154	17	)	)	PUNCT
ejpam-3019	154	18	≤	≤	PUNCT
ejpam-3019	155	1	k	k	X
ejpam-3019	155	2	2	2	NUM
ejpam-3019	155	3	(	(	PUNCT
ejpam-3019	155	4	d(a	d(a	PROPN
ejpam-3019	155	5	,	,	PUNCT
ejpam-3019	155	6	p	p	NOUN
ejpam-3019	155	7	)	)	PUNCT
ejpam-3019	156	1	+	+	CCONJ
ejpam-3019	156	2	d(b	d(b	PROPN
ejpam-3019	156	3	,	,	PUNCT
ejpam-3019	156	4	q	q	NOUN
ejpam-3019	156	5	)	)	PUNCT
ejpam-3019	156	6	)	)	PUNCT
ejpam-3019	156	7	,	,	PUNCT
ejpam-3019	156	8	k	k	X
ejpam-3019	156	9	<	<	X
ejpam-3019	156	10	1	1	NUM
ejpam-3019	156	11	(	(	PUNCT
ejpam-3019	156	12	17	17	NUM
ejpam-3019	156	13	)	)	PUNCT
ejpam-3019	156	14	holds	hold	VERB
ejpam-3019	156	15	for	for	ADP
ejpam-3019	156	16	all	all	DET
ejpam-3019	156	17	a	a	PRON
ejpam-3019	156	18	,	,	PUNCT
ejpam-3019	156	19	b	b	X
ejpam-3019	156	20	∈	∈	PROPN
ejpam-3019	156	21	x	x	SYM
ejpam-3019	156	22	,	,	PUNCT
ejpam-3019	156	23	p	p	X
ejpam-3019	156	24	,	,	PUNCT
ejpam-3019	156	25	q	q	PROPN
ejpam-3019	156	26	∈	∈	PROPN
ejpam-3019	156	27	y	y	PROPN
ejpam-3019	156	28	,	,	PUNCT
ejpam-3019	156	29	then	then	ADV
ejpam-3019	156	30	f	f	X
ejpam-3019	156	31	:	:	PUNCT
ejpam-3019	157	1	x2	x2	PROPN
ejpam-3019	157	2	∪	∪	VERB
ejpam-3019	157	3	y	y	PROPN
ejpam-3019	157	4	2	2	NUM
ejpam-3019	157	5	→	→	SYM
ejpam-3019	157	6	x	x	SYM
ejpam-3019	157	7	∪	∪	ADP
ejpam-3019	157	8	y	y	PROPN
ejpam-3019	157	9	has	have	VERB
ejpam-3019	157	10	a	a	DET
ejpam-3019	157	11	unique	unique	ADJ
ejpam-3019	157	12	coupled	couple	VERB
ejpam-3019	157	13	fixed	fix	VERB
ejpam-3019	157	14	point	point	NOUN
ejpam-3019	157	15	.	.	PUNCT
ejpam-3019	158	1	now	now	ADV
ejpam-3019	158	2	,	,	PUNCT
ejpam-3019	158	3	we	we	PRON
ejpam-3019	158	4	express	express	VERB
ejpam-3019	158	5	another	another	DET
ejpam-3019	158	6	generalization	generalization	NOUN
ejpam-3019	158	7	of	of	ADP
ejpam-3019	158	8	coupled	couple	VERB
ejpam-3019	158	9	fixed	fix	VERB
ejpam-3019	158	10	point	point	NOUN
ejpam-3019	158	11	theorem	theorem	VERB
ejpam-3019	158	12	in	in	ADP
ejpam-3019	158	13	bipolar	bipolar	ADJ
ejpam-3019	158	14	metric	metric	ADJ
ejpam-3019	158	15	spaces	space	NOUN
ejpam-3019	158	16	.	.	PUNCT
ejpam-3019	159	1	definition	definition	NOUN
ejpam-3019	159	2	6	6	NUM
ejpam-3019	159	3	.	.	PUNCT
ejpam-3019	160	1	let	let	VERB
ejpam-3019	160	2	(	(	PUNCT
ejpam-3019	160	3	x	x	X
ejpam-3019	160	4	,	,	PUNCT
ejpam-3019	160	5	y	y	PROPN
ejpam-3019	160	6	,	,	PUNCT
ejpam-3019	160	7	d	d	NOUN
ejpam-3019	160	8	)	)	PUNCT
ejpam-3019	160	9	be	be	AUX
ejpam-3019	160	10	a	a	DET
ejpam-3019	160	11	bipolar	bipolar	ADJ
ejpam-3019	160	12	metric	metric	ADJ
ejpam-3019	160	13	space	space	NOUN
ejpam-3019	160	14	,	,	PUNCT
ejpam-3019	160	15	a	a	DET
ejpam-3019	160	16	∈	∈	PROPN
ejpam-3019	160	17	x	x	NOUN
ejpam-3019	160	18	,	,	PUNCT
ejpam-3019	160	19	p	p	PROPN
ejpam-3019	160	20	∈	∈	PROPN
ejpam-3019	160	21	y	y	PROPN
ejpam-3019	160	22	and	and	CCONJ
ejpam-3019	160	23	f	f	PROPN
ejpam-3019	160	24	:	:	PUNCT
ejpam-3019	160	25	(	(	PUNCT
ejpam-3019	160	26	x	x	SYM
ejpam-3019	160	27	×	×	PROPN
ejpam-3019	160	28	y	y	PROPN
ejpam-3019	160	29	,	,	PUNCT
ejpam-3019	160	30	y	y	PROPN
ejpam-3019	160	31	×x	×x	PROPN
ejpam-3019	160	32	)	)	PUNCT
ejpam-3019	160	33	⇒	⇒	NOUN
ejpam-3019	160	34	(	(	PUNCT
ejpam-3019	160	35	x	x	X
ejpam-3019	160	36	,	,	PUNCT
ejpam-3019	160	37	y	y	PROPN
ejpam-3019	160	38	)	)	PUNCT
ejpam-3019	160	39	be	be	AUX
ejpam-3019	160	40	a	a	DET
ejpam-3019	160	41	covariant	covariant	ADJ
ejpam-3019	160	42	mapping	mapping	NOUN
ejpam-3019	160	43	.	.	PUNCT
ejpam-3019	161	1	(	(	PUNCT
ejpam-3019	161	2	a	a	PRON
ejpam-3019	161	3	,	,	PUNCT
ejpam-3019	161	4	p	p	NOUN
ejpam-3019	161	5	)	)	PUNCT
ejpam-3019	161	6	is	be	AUX
ejpam-3019	161	7	said	say	VERB
ejpam-3019	161	8	to	to	PART
ejpam-3019	161	9	be	be	AUX
ejpam-3019	161	10	a	a	DET
ejpam-3019	161	11	coupled	couple	VERB
ejpam-3019	161	12	fixed	fix	VERB
ejpam-3019	161	13	point	point	NOUN
ejpam-3019	161	14	of	of	ADP
ejpam-3019	161	15	f	f	PROPN
ejpam-3019	161	16	if	if	SCONJ
ejpam-3019	161	17	f	f	PROPN
ejpam-3019	161	18	(	(	PUNCT
ejpam-3019	161	19	a	a	DET
ejpam-3019	161	20	,	,	PUNCT
ejpam-3019	161	21	p	p	NOUN
ejpam-3019	161	22	)	)	PUNCT
ejpam-3019	161	23	=	=	SYM
ejpam-3019	161	24	a	a	PROPN
ejpam-3019	161	25	and	and	CCONJ
ejpam-3019	161	26	f	f	PROPN
ejpam-3019	162	1	(	(	PUNCT
ejpam-3019	162	2	p	p	X
ejpam-3019	162	3	,	,	PUNCT
ejpam-3019	162	4	a	a	NOUN
ejpam-3019	162	5	)	)	PUNCT
ejpam-3019	162	6	=	=	SYM
ejpam-3019	163	1	p.	p.	NOUN
ejpam-3019	163	2	theorem	theorem	NOUN
ejpam-3019	163	3	2	2	X
ejpam-3019	163	4	.	.	X
ejpam-3019	164	1	let	let	VERB
ejpam-3019	164	2	(	(	PUNCT
ejpam-3019	164	3	x	x	X
ejpam-3019	164	4	,	,	PUNCT
ejpam-3019	164	5	y	y	PROPN
ejpam-3019	164	6	,	,	PUNCT
ejpam-3019	164	7	d	d	NOUN
ejpam-3019	164	8	)	)	PUNCT
ejpam-3019	164	9	be	be	AUX
ejpam-3019	164	10	a	a	DET
ejpam-3019	164	11	complete	complete	ADJ
ejpam-3019	164	12	bipolar	bipolar	ADJ
ejpam-3019	164	13	metric	metric	ADJ
ejpam-3019	164	14	space	space	NOUN
ejpam-3019	164	15	,	,	PUNCT
ejpam-3019	164	16	f	f	X
ejpam-3019	164	17	:	:	PUNCT
ejpam-3019	164	18	(	(	PUNCT
ejpam-3019	164	19	x	x	SYM
ejpam-3019	164	20	×	×	PROPN
ejpam-3019	164	21	y	y	PROPN
ejpam-3019	164	22	,	,	PUNCT
ejpam-3019	164	23	y	y	PROPN
ejpam-3019	164	24	×x	×x	PROPN
ejpam-3019	164	25	)	)	PUNCT
ejpam-3019	164	26	⇒	⇒	NOUN
ejpam-3019	164	27	(	(	PUNCT
ejpam-3019	164	28	x	x	X
ejpam-3019	164	29	,	,	PUNCT
ejpam-3019	164	30	y	y	PROPN
ejpam-3019	164	31	)	)	PUNCT
ejpam-3019	164	32	be	be	AUX
ejpam-3019	164	33	a	a	DET
ejpam-3019	164	34	covariant	covariant	ADJ
ejpam-3019	164	35	mapping	mapping	NOUN
ejpam-3019	164	36	and	and	CCONJ
ejpam-3019	164	37	k	k	NOUN
ejpam-3019	164	38	,	,	PUNCT
ejpam-3019	164	39	l	l	NOUN
ejpam-3019	164	40	be	be	VERB
ejpam-3019	164	41	non	non	ADJ
ejpam-3019	164	42	-	-	ADJ
ejpam-3019	164	43	negative	negative	ADJ
ejpam-3019	164	44	constants	constant	NOUN
ejpam-3019	164	45	.	.	PUNCT
ejpam-3019	165	1	if	if	SCONJ
ejpam-3019	165	2	the	the	DET
ejpam-3019	165	3	condition	condition	NOUN
ejpam-3019	165	4	d(f	d(f	NOUN
ejpam-3019	165	5	(	(	PUNCT
ejpam-3019	165	6	a	a	DET
ejpam-3019	165	7	,	,	PUNCT
ejpam-3019	165	8	p	p	NOUN
ejpam-3019	165	9	)	)	PUNCT
ejpam-3019	165	10	,	,	PUNCT
ejpam-3019	165	11	f	f	PROPN
ejpam-3019	165	12	(	(	PUNCT
ejpam-3019	165	13	q	q	PROPN
ejpam-3019	165	14	,	,	PUNCT
ejpam-3019	165	15	b	b	NOUN
ejpam-3019	165	16	)	)	PUNCT
ejpam-3019	165	17	)	)	PUNCT
ejpam-3019	165	18	≤	≤	NOUN
ejpam-3019	166	1	kd(a	kd(a	X
ejpam-3019	166	2	,	,	PUNCT
ejpam-3019	166	3	q	q	X
ejpam-3019	166	4	)	)	PUNCT
ejpam-3019	166	5	+	+	CCONJ
ejpam-3019	166	6	ld(b	ld(b	ADJ
ejpam-3019	166	7	,	,	PUNCT
ejpam-3019	166	8	p	p	NOUN
ejpam-3019	166	9	)	)	PUNCT
ejpam-3019	166	10	,	,	PUNCT
ejpam-3019	166	11	k	k	PROPN
ejpam-3019	167	1	+	+	CCONJ
ejpam-3019	167	2	l	l	X
ejpam-3019	167	3	<	<	X
ejpam-3019	167	4	1	1	NUM
ejpam-3019	167	5	(	(	PUNCT
ejpam-3019	167	6	18	18	NUM
ejpam-3019	167	7	)	)	PUNCT
ejpam-3019	167	8	holds	hold	VERB
ejpam-3019	167	9	for	for	ADP
ejpam-3019	167	10	all	all	DET
ejpam-3019	167	11	a	a	PRON
ejpam-3019	167	12	,	,	PUNCT
ejpam-3019	167	13	b	b	X
ejpam-3019	167	14	∈	∈	PROPN
ejpam-3019	167	15	x	x	SYM
ejpam-3019	167	16	,	,	PUNCT
ejpam-3019	167	17	p	p	X
ejpam-3019	167	18	,	,	PUNCT
ejpam-3019	167	19	q	q	PROPN
ejpam-3019	167	20	∈	∈	PROPN
ejpam-3019	167	21	y	y	PROPN
ejpam-3019	167	22	,	,	PUNCT
ejpam-3019	167	23	then	then	ADV
ejpam-3019	167	24	f	f	X
ejpam-3019	167	25	:	:	PUNCT
ejpam-3019	167	26	(	(	PUNCT
ejpam-3019	167	27	x×y	x×y	PUNCT
ejpam-3019	167	28	)	)	PUNCT
ejpam-3019	167	29	∪	∪	NOUN
ejpam-3019	167	30	(	(	PUNCT
ejpam-3019	167	31	y	y	PROPN
ejpam-3019	167	32	×x)→	×x)→	PROPN
ejpam-3019	167	33	x	x	X
ejpam-3019	167	34	∪y	∪y	PROPN
ejpam-3019	167	35	has	have	VERB
ejpam-3019	167	36	a	a	DET
ejpam-3019	167	37	unique	unique	ADJ
ejpam-3019	167	38	coupled	couple	VERB
ejpam-3019	167	39	fixed	fix	VERB
ejpam-3019	167	40	point	point	NOUN
ejpam-3019	167	41	.	.	PUNCT
ejpam-3019	168	1	proof	proof	NOUN
ejpam-3019	168	2	.	.	PUNCT
ejpam-3019	169	1	similar	similar	ADJ
ejpam-3019	169	2	to	to	ADP
ejpam-3019	169	3	the	the	DET
ejpam-3019	169	4	proof	proof	NOUN
ejpam-3019	169	5	of	of	ADP
ejpam-3019	169	6	theorem	theorem	NOUN
ejpam-3019	169	7	1	1	NUM
ejpam-3019	169	8	,	,	PUNCT
ejpam-3019	169	9	we	we	PRON
ejpam-3019	169	10	define	define	VERB
ejpam-3019	169	11	bisequences	bisequence	NOUN
ejpam-3019	169	12	(	(	PUNCT
ejpam-3019	169	13	an	an	DET
ejpam-3019	169	14	,	,	PUNCT
ejpam-3019	169	15	pn	pn	NOUN
ejpam-3019	169	16	)	)	PUNCT
ejpam-3019	169	17	and	and	CCONJ
ejpam-3019	169	18	(	(	PUNCT
ejpam-3019	169	19	bn	bn	X
ejpam-3019	169	20	,	,	PUNCT
ejpam-3019	169	21	qn	qn	NOUN
ejpam-3019	169	22	)	)	PUNCT
ejpam-3019	169	23	as	as	SCONJ
ejpam-3019	169	24	follows	follow	VERB
ejpam-3019	169	25	:	:	PUNCT
ejpam-3019	169	26	an+1	an+1	AUX
ejpam-3019	169	27	=	=	SYM
ejpam-3019	169	28	f	f	PROPN
ejpam-3019	169	29	(	(	PUNCT
ejpam-3019	169	30	an	an	PROPN
ejpam-3019	169	31	,	,	PUNCT
ejpam-3019	169	32	pn	pn	NOUN
ejpam-3019	169	33	)	)	PUNCT
ejpam-3019	169	34	,	,	PUNCT
ejpam-3019	169	35	pn+1	pn+1	PROPN
ejpam-3019	169	36	=	=	SYM
ejpam-3019	169	37	f	f	PROPN
ejpam-3019	169	38	(	(	PUNCT
ejpam-3019	169	39	pn	pn	PROPN
ejpam-3019	169	40	,	,	PUNCT
ejpam-3019	169	41	an	an	NOUN
ejpam-3019	169	42	)	)	PUNCT
ejpam-3019	169	43	,	,	PUNCT
ejpam-3019	169	44	bn+1	bn+1	X
ejpam-3019	170	1	=	=	SYM
ejpam-3019	170	2	f	f	PROPN
ejpam-3019	170	3	(	(	PUNCT
ejpam-3019	170	4	bn	bn	PROPN
ejpam-3019	170	5	,	,	PUNCT
ejpam-3019	170	6	qn	qn	NOUN
ejpam-3019	170	7	)	)	PUNCT
ejpam-3019	170	8	and	and	CCONJ
ejpam-3019	170	9	qn+1	qn+1	NUM
ejpam-3019	170	10	=	=	SYM
ejpam-3019	170	11	f	f	PROPN
ejpam-3019	170	12	(	(	PUNCT
ejpam-3019	170	13	qn	qn	INTJ
ejpam-3019	170	14	,	,	PUNCT
ejpam-3019	170	15	bn	bn	NOUN
ejpam-3019	170	16	)	)	PUNCT
ejpam-3019	170	17	for	for	ADP
ejpam-3019	170	18	all	all	DET
ejpam-3019	170	19	n	n	PRON
ejpam-3019	170	20	∈	∈	PROPN
ejpam-3019	170	21	n+	n+	PROPN
ejpam-3019	170	22	.	.	PUNCT
ejpam-3019	171	1	let	let	VERB
ejpam-3019	172	1	k	k	NOUN
ejpam-3019	172	2	+	+	NOUN
ejpam-3019	172	3	l	l	NOUN
ejpam-3019	172	4	=	=	SYM
ejpam-3019	172	5	λ	λ	PROPN
ejpam-3019	172	6	.	.	PUNCT
ejpam-3019	173	1	then	then	ADV
ejpam-3019	173	2	,	,	PUNCT
ejpam-3019	173	3	from	from	ADP
ejpam-3019	173	4	(	(	PUNCT
ejpam-3019	173	5	18	18	NUM
ejpam-3019	173	6	)	)	PUNCT
ejpam-3019	173	7	,	,	PUNCT
ejpam-3019	173	8	we	we	PRON
ejpam-3019	173	9	get	get	VERB
ejpam-3019	173	10	d(an	d(an	NOUN
ejpam-3019	173	11	,	,	PUNCT
ejpam-3019	173	12	qn+1	qn+1	NUM
ejpam-3019	173	13	)	)	PUNCT
ejpam-3019	173	14	=	=	SYM
ejpam-3019	173	15	d(f	d(f	NOUN
ejpam-3019	173	16	(	(	PUNCT
ejpam-3019	173	17	an−1	an−1	ADJ
ejpam-3019	173	18	,	,	PUNCT
ejpam-3019	173	19	pn−1	pn−1	PROPN
ejpam-3019	173	20	)	)	PUNCT
ejpam-3019	173	21	,	,	PUNCT
ejpam-3019	173	22	f	f	PROPN
ejpam-3019	173	23	(	(	PUNCT
ejpam-3019	173	24	qn	qn	INTJ
ejpam-3019	173	25	,	,	PUNCT
ejpam-3019	173	26	bn	bn	NOUN
ejpam-3019	173	27	)	)	PUNCT
ejpam-3019	173	28	)	)	PUNCT
ejpam-3019	173	29	,	,	PUNCT
ejpam-3019	173	30	(	(	PUNCT
ejpam-3019	173	31	19	19	NUM
ejpam-3019	173	32	)	)	PUNCT
ejpam-3019	173	33	≤	≤	NOUN
ejpam-3019	173	34	kd(an−1	kd(an−1	PROPN
ejpam-3019	173	35	,	,	PUNCT
ejpam-3019	173	36	qn	qn	NOUN
ejpam-3019	173	37	)	)	PUNCT
ejpam-3019	173	38	+	+	CCONJ
ejpam-3019	173	39	ld(bn	ld(bn	PROPN
ejpam-3019	173	40	,	,	PUNCT
ejpam-3019	173	41	pn−1	pn−1	ADJ
ejpam-3019	173	42	)	)	PUNCT
ejpam-3019	173	43	d(an+1	d(an+1	PROPN
ejpam-3019	173	44	,	,	PUNCT
ejpam-3019	173	45	qn	qn	NOUN
ejpam-3019	173	46	)	)	PUNCT
ejpam-3019	173	47	=	=	NOUN
ejpam-3019	173	48	d(f	d(f	NOUN
ejpam-3019	173	49	(	(	PUNCT
ejpam-3019	173	50	an	an	DET
ejpam-3019	173	51	,	,	PUNCT
ejpam-3019	173	52	pn	pn	NOUN
ejpam-3019	173	53	)	)	PUNCT
ejpam-3019	173	54	,	,	PUNCT
ejpam-3019	173	55	f	f	PROPN
ejpam-3019	173	56	(	(	PUNCT
ejpam-3019	173	57	qn−1	qn−1	PROPN
ejpam-3019	173	58	,	,	PUNCT
ejpam-3019	173	59	bn−1	bn−1	NOUN
ejpam-3019	173	60	)	)	PUNCT
ejpam-3019	173	61	)	)	PUNCT
ejpam-3019	173	62	,	,	PUNCT
ejpam-3019	173	63	(	(	PUNCT
ejpam-3019	173	64	20	20	X
ejpam-3019	173	65	)	)	PUNCT
ejpam-3019	173	66	≤	≤	NOUN
ejpam-3019	173	67	kd(an	kd(an	PROPN
ejpam-3019	173	68	,	,	PUNCT
ejpam-3019	173	69	qn−1	qn−1	PROPN
ejpam-3019	173	70	)	)	PUNCT
ejpam-3019	173	71	+	+	CCONJ
ejpam-3019	173	72	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	173	73	,	,	PUNCT
ejpam-3019	173	74	pn	pn	NOUN
ejpam-3019	173	75	)	)	PUNCT
ejpam-3019	173	76	d(bn	d(bn	PROPN
ejpam-3019	173	77	,	,	PUNCT
ejpam-3019	173	78	pn+1	pn+1	NOUN
ejpam-3019	173	79	)	)	PUNCT
ejpam-3019	173	80	=	=	SYM
ejpam-3019	173	81	d(f	d(f	NOUN
ejpam-3019	173	82	(	(	PUNCT
ejpam-3019	173	83	bn−1	bn−1	PRON
ejpam-3019	173	84	,	,	PUNCT
ejpam-3019	173	85	qn−1	qn−1	PROPN
ejpam-3019	173	86	)	)	PUNCT
ejpam-3019	173	87	,	,	PUNCT
ejpam-3019	173	88	f	f	PROPN
ejpam-3019	173	89	(	(	PUNCT
ejpam-3019	173	90	pn	pn	PROPN
ejpam-3019	173	91	,	,	PUNCT
ejpam-3019	173	92	an	an	NOUN
ejpam-3019	173	93	)	)	PUNCT
ejpam-3019	173	94	)	)	PUNCT
ejpam-3019	173	95	,	,	PUNCT
ejpam-3019	173	96	(	(	PUNCT
ejpam-3019	173	97	21	21	NUM
ejpam-3019	173	98	)	)	PUNCT
ejpam-3019	173	99	≤	≤	NOUN
ejpam-3019	173	100	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	173	101	,	,	PUNCT
ejpam-3019	173	102	pn	pn	NOUN
ejpam-3019	173	103	)	)	PUNCT
ejpam-3019	174	1	+	+	CCONJ
ejpam-3019	174	2	ld(an	ld(an	PROPN
ejpam-3019	174	3	,	,	PUNCT
ejpam-3019	174	4	qn−1	qn−1	ADJ
ejpam-3019	174	5	)	)	PUNCT
ejpam-3019	174	6	d(bn+1	d(bn+1	PROPN
ejpam-3019	174	7	,	,	PUNCT
ejpam-3019	174	8	pn	pn	NOUN
ejpam-3019	174	9	)	)	PUNCT
ejpam-3019	174	10	=	=	NOUN
ejpam-3019	175	1	d(f	d(f	NOUN
ejpam-3019	175	2	(	(	PUNCT
ejpam-3019	175	3	bn	bn	X
ejpam-3019	175	4	,	,	PUNCT
ejpam-3019	175	5	qn	qn	NOUN
ejpam-3019	175	6	)	)	PUNCT
ejpam-3019	175	7	,	,	PUNCT
ejpam-3019	175	8	f	f	PROPN
ejpam-3019	175	9	(	(	PUNCT
ejpam-3019	175	10	pn−1	pn−1	PROPN
ejpam-3019	175	11	,	,	PUNCT
ejpam-3019	175	12	an−1	an−1	ADJ
ejpam-3019	175	13	)	)	PUNCT
ejpam-3019	175	14	)	)	PUNCT
ejpam-3019	175	15	,	,	PUNCT
ejpam-3019	175	16	(	(	PUNCT
ejpam-3019	175	17	22	22	X
ejpam-3019	175	18	)	)	PUNCT
ejpam-3019	175	19	≤	≤	NOUN
ejpam-3019	175	20	kd(bn	kd(bn	X
ejpam-3019	175	21	,	,	PUNCT
ejpam-3019	175	22	pn−1	pn−1	PROPN
ejpam-3019	175	23	)	)	PUNCT
ejpam-3019	175	24	+	+	PUNCT
ejpam-3019	175	25	ld(an−1	ld(an−1	ADJ
ejpam-3019	175	26	,	,	PUNCT
ejpam-3019	175	27	qn	qn	ADJ
ejpam-3019	175	28	)	)	PUNCT
ejpam-3019	175	29	a.	a.	NOUN
ejpam-3019	175	30	mutlu	mutlu	PROPN
ejpam-3019	175	31	,	,	PUNCT
ejpam-3019	175	32	k.	k.	PROPN
ejpam-3019	175	33	özkan	özkan	PROPN
ejpam-3019	175	34	,	,	PUNCT
ejpam-3019	175	35	u.	u.	PROPN
ejpam-3019	175	36	gürdal	gürdal	PROPN
ejpam-3019	175	37	/	/	SYM
ejpam-3019	175	38	eur	eur	PROPN
ejpam-3019	175	39	.	.	PUNCT
ejpam-3019	176	1	j.	j.	PROPN
ejpam-3019	176	2	pure	pure	PROPN
ejpam-3019	176	3	appl	appl	PROPN
ejpam-3019	176	4	.	.	PROPN
ejpam-3019	176	5	math	math	PROPN
ejpam-3019	176	6	,	,	PUNCT
ejpam-3019	176	7	10	10	NUM
ejpam-3019	176	8	(	(	PUNCT
ejpam-3019	176	9	4	4	NUM
ejpam-3019	176	10	)	)	PUNCT
ejpam-3019	176	11	(	(	PUNCT
ejpam-3019	176	12	2017	2017	NUM
ejpam-3019	176	13	)	)	PUNCT
ejpam-3019	176	14	,	,	PUNCT
ejpam-3019	176	15	655	655	NUM
ejpam-3019	176	16	-	-	SYM
ejpam-3019	176	17	667	667	NUM
ejpam-3019	176	18	662	662	NUM
ejpam-3019	176	19	for	for	ADP
ejpam-3019	176	20	all	all	PRON
ejpam-3019	176	21	n	n	PRON
ejpam-3019	176	22	∈	∈	ADJ
ejpam-3019	176	23	n+	n+	PUNCT
ejpam-3019	176	24	and	and	CCONJ
ejpam-3019	176	25	λ	λ	X
ejpam-3019	176	26	<	<	X
ejpam-3019	176	27	1	1	X
ejpam-3019	176	28	.	.	PUNCT
ejpam-3019	177	1	let	let	VERB
ejpam-3019	177	2	en	en	ADV
ejpam-3019	177	3	=	=	SYM
ejpam-3019	177	4	d(an	d(an	X
ejpam-3019	177	5	,	,	PUNCT
ejpam-3019	177	6	qn+1	qn+1	NUM
ejpam-3019	177	7	)	)	PUNCT
ejpam-3019	178	1	+	+	X
ejpam-3019	178	2	d(bn+1	d(bn+1	ADJ
ejpam-3019	178	3	,	,	PUNCT
ejpam-3019	178	4	pn	pn	NOUN
ejpam-3019	178	5	)	)	PUNCT
ejpam-3019	178	6	and	and	CCONJ
ejpam-3019	178	7	sn	sn	NOUN
ejpam-3019	178	8	=	=	PUNCT
ejpam-3019	178	9	d(an+1	d(an+1	PROPN
ejpam-3019	178	10	,	,	PUNCT
ejpam-3019	178	11	qn	qn	NOUN
ejpam-3019	178	12	)	)	PUNCT
ejpam-3019	178	13	+	+	CCONJ
ejpam-3019	178	14	d(bn	d(bn	NUM
ejpam-3019	178	15	,	,	PUNCT
ejpam-3019	178	16	pn+1	pn+1	NOUN
ejpam-3019	178	17	)	)	PUNCT
ejpam-3019	178	18	for	for	ADP
ejpam-3019	178	19	all	all	DET
ejpam-3019	178	20	n	n	PRON
ejpam-3019	178	21	∈	∈	PROPN
ejpam-3019	178	22	n+	n+	PROPN
ejpam-3019	178	23	.	.	PUNCT
ejpam-3019	179	1	using	use	VERB
ejpam-3019	179	2	equations	equation	NOUN
ejpam-3019	179	3	(	(	PUNCT
ejpam-3019	179	4	19	19	NUM
ejpam-3019	179	5	)	)	PUNCT
ejpam-3019	179	6	,	,	PUNCT
ejpam-3019	179	7	(	(	PUNCT
ejpam-3019	179	8	20	20	NUM
ejpam-3019	179	9	)	)	PUNCT
ejpam-3019	179	10	,	,	PUNCT
ejpam-3019	179	11	(	(	PUNCT
ejpam-3019	179	12	21	21	NUM
ejpam-3019	179	13	)	)	PUNCT
ejpam-3019	179	14	and	and	CCONJ
ejpam-3019	179	15	(	(	PUNCT
ejpam-3019	179	16	22	22	NUM
ejpam-3019	179	17	)	)	PUNCT
ejpam-3019	179	18	,	,	PUNCT
ejpam-3019	179	19	we	we	PRON
ejpam-3019	179	20	get	get	VERB
ejpam-3019	179	21	en	en	ADV
ejpam-3019	179	22	=	=	SYM
ejpam-3019	179	23	d(an	d(an	X
ejpam-3019	179	24	,	,	PUNCT
ejpam-3019	179	25	qn+1	qn+1	NUM
ejpam-3019	179	26	)	)	PUNCT
ejpam-3019	180	1	+	+	X
ejpam-3019	181	1	d(bn+1	d(bn+1	ADJ
ejpam-3019	181	2	,	,	PUNCT
ejpam-3019	181	3	pn	pn	NOUN
ejpam-3019	181	4	)	)	PUNCT
ejpam-3019	181	5	≤	≤	NOUN
ejpam-3019	181	6	kd(an−1	kd(an−1	PROPN
ejpam-3019	181	7	,	,	PUNCT
ejpam-3019	181	8	qn	qn	NOUN
ejpam-3019	181	9	)	)	PUNCT
ejpam-3019	181	10	+	+	CCONJ
ejpam-3019	181	11	ld(bn	ld(bn	PROPN
ejpam-3019	181	12	,	,	PUNCT
ejpam-3019	181	13	pn−1	pn−1	PROPN
ejpam-3019	181	14	)	)	PUNCT
ejpam-3019	181	15	+	+	CCONJ
ejpam-3019	181	16	kd(bn	kd(bn	X
ejpam-3019	181	17	,	,	PUNCT
ejpam-3019	181	18	pn−1	pn−1	ADJ
ejpam-3019	181	19	)	)	PUNCT
ejpam-3019	181	20	+	+	PUNCT
ejpam-3019	181	21	ld(an−1	ld(an−1	ADJ
ejpam-3019	181	22	,	,	PUNCT
ejpam-3019	181	23	qn	qn	NOUN
ejpam-3019	181	24	)	)	PUNCT
ejpam-3019	181	25	=	=	SYM
ejpam-3019	182	1	(	(	PUNCT
ejpam-3019	182	2	k	k	PROPN
ejpam-3019	182	3	+	+	X
ejpam-3019	182	4	l)(d(an−1	l)(d(an−1	PROPN
ejpam-3019	182	5	,	,	PUNCT
ejpam-3019	182	6	qn	qn	NOUN
ejpam-3019	182	7	)	)	PUNCT
ejpam-3019	182	8	+	+	CCONJ
ejpam-3019	182	9	d(bn	d(bn	NUM
ejpam-3019	182	10	,	,	PUNCT
ejpam-3019	182	11	pn−1	pn−1	ADJ
ejpam-3019	182	12	)	)	PUNCT
ejpam-3019	182	13	)	)	PUNCT
ejpam-3019	183	1	=	=	SYM
ejpam-3019	184	1	λen−1	λen−1	PROPN
ejpam-3019	184	2	and	and	CCONJ
ejpam-3019	184	3	sn	sn	NOUN
ejpam-3019	184	4	=	=	PUNCT
ejpam-3019	184	5	d(an+1	d(an+1	PROPN
ejpam-3019	184	6	,	,	PUNCT
ejpam-3019	184	7	qn	qn	NOUN
ejpam-3019	184	8	)	)	PUNCT
ejpam-3019	184	9	+	+	CCONJ
ejpam-3019	184	10	d(bn	d(bn	NUM
ejpam-3019	184	11	,	,	PUNCT
ejpam-3019	184	12	pn+1	pn+1	NOUN
ejpam-3019	184	13	)	)	PUNCT
ejpam-3019	184	14	≤	≤	NOUN
ejpam-3019	185	1	kd(an	kd(an	PROPN
ejpam-3019	185	2	,	,	PUNCT
ejpam-3019	185	3	qn−1	qn−1	PROPN
ejpam-3019	185	4	)	)	PUNCT
ejpam-3019	185	5	+	+	CCONJ
ejpam-3019	185	6	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	185	7	,	,	PUNCT
ejpam-3019	185	8	pn	pn	NOUN
ejpam-3019	185	9	)	)	PUNCT
ejpam-3019	185	10	+	+	X
ejpam-3019	185	11	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	185	12	,	,	PUNCT
ejpam-3019	185	13	pn	pn	NOUN
ejpam-3019	185	14	)	)	PUNCT
ejpam-3019	185	15	+	+	CCONJ
ejpam-3019	185	16	ld(an	ld(an	PROPN
ejpam-3019	185	17	,	,	PUNCT
ejpam-3019	185	18	qn−1	qn−1	PROPN
ejpam-3019	185	19	)	)	PUNCT
ejpam-3019	185	20	=	=	PUNCT
ejpam-3019	186	1	(	(	PUNCT
ejpam-3019	186	2	k	k	PROPN
ejpam-3019	186	3	+	+	CCONJ
ejpam-3019	186	4	l)(d(an	l)(d(an	PROPN
ejpam-3019	186	5	,	,	PUNCT
ejpam-3019	186	6	qn−1	qn−1	PROPN
ejpam-3019	186	7	)	)	PUNCT
ejpam-3019	186	8	+	+	CCONJ
ejpam-3019	186	9	d(bn−1	d(bn−1	NOUN
ejpam-3019	186	10	,	,	PUNCT
ejpam-3019	186	11	pn	pn	NOUN
ejpam-3019	186	12	)	)	PUNCT
ejpam-3019	186	13	)	)	PUNCT
ejpam-3019	187	1	=	=	PUNCT
ejpam-3019	188	1	λsn−1	λsn−1	PROPN
ejpam-3019	188	2	.	.	PUNCT
ejpam-3019	189	1	then	then	ADV
ejpam-3019	189	2	we	we	PRON
ejpam-3019	189	3	obtain	obtain	VERB
ejpam-3019	189	4	that	that	DET
ejpam-3019	189	5	0	0	NUM
ejpam-3019	189	6	≤	≤	NUM
ejpam-3019	189	7	en	en	ADP
ejpam-3019	189	8	≤	≤	X
ejpam-3019	189	9	λen−1	λen−1	PROPN
ejpam-3019	189	10	≤	≤	NOUN
ejpam-3019	189	11	λ2en−2	λ2en−2	X
ejpam-3019	189	12	≤	≤	NUM
ejpam-3019	189	13	·	·	PUNCT
ejpam-3019	189	14	·	·	PUNCT
ejpam-3019	189	15	·	·	PUNCT
ejpam-3019	190	1	≤	≤	NUM
ejpam-3019	190	2	λne0	λne0	NOUN
ejpam-3019	190	3	(	(	PUNCT
ejpam-3019	190	4	23	23	NUM
ejpam-3019	190	5	)	)	PUNCT
ejpam-3019	190	6	and	and	CCONJ
ejpam-3019	190	7	0	0	NUM
ejpam-3019	190	8	≤	≤	NUM
ejpam-3019	190	9	sn	sn	NOUN
ejpam-3019	190	10	≤	≤	X
ejpam-3019	190	11	λsn−1	λsn−1	ADV
ejpam-3019	190	12	≤	≤	NOUN
ejpam-3019	190	13	λ2sn−2	λ2sn−2	PROPN
ejpam-3019	190	14	≤	≤	NOUN
ejpam-3019	190	15	·	·	PUNCT
ejpam-3019	190	16	·	·	PUNCT
ejpam-3019	190	17	·	·	PUNCT
ejpam-3019	190	18	≤	≤	NUM
ejpam-3019	190	19	λns0	λns0	PROPN
ejpam-3019	190	20	.	.	PUNCT
ejpam-3019	191	1	(	(	PUNCT
ejpam-3019	191	2	24	24	NUM
ejpam-3019	191	3	)	)	PUNCT
ejpam-3019	191	4	on	on	ADP
ejpam-3019	191	5	the	the	DET
ejpam-3019	191	6	other	other	ADJ
ejpam-3019	191	7	hand	hand	NOUN
ejpam-3019	191	8	,	,	PUNCT
ejpam-3019	191	9	d(an	d(an	PROPN
ejpam-3019	191	10	,	,	PUNCT
ejpam-3019	191	11	qn	qn	NOUN
ejpam-3019	191	12	)	)	PUNCT
ejpam-3019	191	13	=	=	NOUN
ejpam-3019	191	14	d(f	d(f	NOUN
ejpam-3019	191	15	(	(	PUNCT
ejpam-3019	191	16	an−1	an−1	ADJ
ejpam-3019	191	17	,	,	PUNCT
ejpam-3019	191	18	pn−1	pn−1	PROPN
ejpam-3019	191	19	)	)	PUNCT
ejpam-3019	191	20	,	,	PUNCT
ejpam-3019	191	21	f	f	PROPN
ejpam-3019	191	22	(	(	PUNCT
ejpam-3019	191	23	qn−1	qn−1	PROPN
ejpam-3019	191	24	,	,	PUNCT
ejpam-3019	191	25	bn−1	bn−1	NOUN
ejpam-3019	191	26	)	)	PUNCT
ejpam-3019	191	27	)	)	PUNCT
ejpam-3019	191	28	,	,	PUNCT
ejpam-3019	191	29	(	(	PUNCT
ejpam-3019	191	30	25	25	NUM
ejpam-3019	191	31	)	)	PUNCT
ejpam-3019	191	32	≤	≤	NOUN
ejpam-3019	191	33	kd(an−1	kd(an−1	PROPN
ejpam-3019	191	34	,	,	PUNCT
ejpam-3019	191	35	qn−1	qn−1	PROPN
ejpam-3019	191	36	)	)	PUNCT
ejpam-3019	191	37	+	+	CCONJ
ejpam-3019	192	1	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	192	2	,	,	PUNCT
ejpam-3019	192	3	pn−1	pn−1	ADJ
ejpam-3019	192	4	)	)	PUNCT
ejpam-3019	192	5	and	and	CCONJ
ejpam-3019	192	6	d(bn	d(bn	PROPN
ejpam-3019	192	7	,	,	PUNCT
ejpam-3019	192	8	pn	pn	NOUN
ejpam-3019	192	9	)	)	PUNCT
ejpam-3019	192	10	=	=	NOUN
ejpam-3019	193	1	d(f	d(f	NOUN
ejpam-3019	193	2	(	(	PUNCT
ejpam-3019	193	3	bn−1	bn−1	ADJ
ejpam-3019	193	4	,	,	PUNCT
ejpam-3019	193	5	pn−1	pn−1	PROPN
ejpam-3019	193	6	)	)	PUNCT
ejpam-3019	193	7	,	,	PUNCT
ejpam-3019	193	8	f	f	PROPN
ejpam-3019	193	9	(	(	PUNCT
ejpam-3019	193	10	pn−1	pn−1	PROPN
ejpam-3019	193	11	,	,	PUNCT
ejpam-3019	193	12	an−1	an−1	ADJ
ejpam-3019	193	13	)	)	PUNCT
ejpam-3019	193	14	)	)	PUNCT
ejpam-3019	193	15	,	,	PUNCT
ejpam-3019	193	16	(	(	PUNCT
ejpam-3019	193	17	26	26	NUM
ejpam-3019	193	18	)	)	PUNCT
ejpam-3019	193	19	≤	≤	NOUN
ejpam-3019	194	1	kd(bn−1	kd(bn−1	PROPN
ejpam-3019	194	2	,	,	PUNCT
ejpam-3019	194	3	pn−1	pn−1	PROPN
ejpam-3019	194	4	)	)	PUNCT
ejpam-3019	194	5	+	+	CCONJ
ejpam-3019	194	6	ld(an−1	ld(an−1	ADJ
ejpam-3019	194	7	,	,	PUNCT
ejpam-3019	194	8	qn−1	qn−1	ADJ
ejpam-3019	194	9	)	)	PUNCT
ejpam-3019	194	10	for	for	ADP
ejpam-3019	194	11	all	all	DET
ejpam-3019	194	12	n	n	PRON
ejpam-3019	194	13	∈	∈	ADJ
ejpam-3019	194	14	n+	n+	PUNCT
ejpam-3019	194	15	and	and	CCONJ
ejpam-3019	194	16	λ	λ	X
ejpam-3019	194	17	<	<	X
ejpam-3019	194	18	1	1	NUM
ejpam-3019	194	19	.	.	PUNCT
ejpam-3019	195	1	if	if	SCONJ
ejpam-3019	195	2	we	we	PRON
ejpam-3019	195	3	take	take	VERB
ejpam-3019	195	4	tn	tn	NOUN
ejpam-3019	195	5	=	=	SYM
ejpam-3019	195	6	d(an	d(an	PROPN
ejpam-3019	195	7	,	,	PUNCT
ejpam-3019	195	8	qn	qn	NOUN
ejpam-3019	195	9	)	)	PUNCT
ejpam-3019	195	10	+	+	CCONJ
ejpam-3019	195	11	d(bn	d(bn	NUM
ejpam-3019	195	12	,	,	PUNCT
ejpam-3019	195	13	pn	pn	NOUN
ejpam-3019	195	14	)	)	PUNCT
ejpam-3019	195	15	for	for	ADP
ejpam-3019	195	16	all	all	PRON
ejpam-3019	195	17	n	n	PRON
ejpam-3019	195	18	∈	∈	ADJ
ejpam-3019	195	19	n+	n+	PUNCT
ejpam-3019	195	20	and	and	CCONJ
ejpam-3019	195	21	combine	combine	VERB
ejpam-3019	195	22	(	(	PUNCT
ejpam-3019	195	23	25	25	NUM
ejpam-3019	195	24	)	)	PUNCT
ejpam-3019	195	25	and	and	CCONJ
ejpam-3019	195	26	(	(	PUNCT
ejpam-3019	195	27	26	26	NUM
ejpam-3019	195	28	)	)	PUNCT
ejpam-3019	195	29	,	,	PUNCT
ejpam-3019	195	30	we	we	PRON
ejpam-3019	195	31	have	have	VERB
ejpam-3019	195	32	tn	tn	NOUN
ejpam-3019	195	33	=	=	SYM
ejpam-3019	195	34	d(an	d(an	PROPN
ejpam-3019	195	35	,	,	PUNCT
ejpam-3019	195	36	qn	qn	NOUN
ejpam-3019	195	37	)	)	PUNCT
ejpam-3019	195	38	+	+	CCONJ
ejpam-3019	195	39	d(bn	d(bn	NUM
ejpam-3019	195	40	,	,	PUNCT
ejpam-3019	195	41	pn	pn	NOUN
ejpam-3019	195	42	)	)	PUNCT
ejpam-3019	195	43	≤	≤	NOUN
ejpam-3019	195	44	kd(an−1	kd(an−1	PROPN
ejpam-3019	195	45	,	,	PUNCT
ejpam-3019	195	46	qn−1	qn−1	PROPN
ejpam-3019	195	47	)	)	PUNCT
ejpam-3019	195	48	+	+	CCONJ
ejpam-3019	195	49	ld(bn−1	ld(bn−1	ADJ
ejpam-3019	195	50	,	,	PUNCT
ejpam-3019	195	51	pn−1	pn−1	ADJ
ejpam-3019	195	52	)	)	PUNCT
ejpam-3019	196	1	+	+	X
ejpam-3019	196	2	kd(bn−1	kd(bn−1	ADJ
ejpam-3019	196	3	,	,	PUNCT
ejpam-3019	196	4	pn−1	pn−1	PROPN
ejpam-3019	196	5	)	)	PUNCT
ejpam-3019	197	1	+	+	CCONJ
ejpam-3019	197	2	ld(an−1	ld(an−1	ADJ
ejpam-3019	197	3	,	,	PUNCT
ejpam-3019	197	4	qn−1	qn−1	ADJ
ejpam-3019	197	5	)	)	PUNCT
ejpam-3019	197	6	=	=	PUNCT
ejpam-3019	198	1	(	(	PUNCT
ejpam-3019	198	2	k	k	PROPN
ejpam-3019	198	3	+	+	X
ejpam-3019	198	4	l)(d(an−1	l)(d(an−1	PROPN
ejpam-3019	198	5	,	,	PUNCT
ejpam-3019	198	6	qn−1	qn−1	PROPN
ejpam-3019	198	7	)	)	PUNCT
ejpam-3019	198	8	+	+	CCONJ
ejpam-3019	198	9	d(bn−1	d(bn−1	NOUN
ejpam-3019	198	10	,	,	PUNCT
ejpam-3019	198	11	pn−1	pn−1	ADJ
ejpam-3019	198	12	)	)	PUNCT
ejpam-3019	198	13	)	)	PUNCT
ejpam-3019	198	14	a.	a.	NOUN
ejpam-3019	198	15	mutlu	mutlu	PROPN
ejpam-3019	198	16	,	,	PUNCT
ejpam-3019	198	17	k.	k.	PROPN
ejpam-3019	198	18	özkan	özkan	PROPN
ejpam-3019	198	19	,	,	PUNCT
ejpam-3019	198	20	u.	u.	PROPN
ejpam-3019	198	21	gürdal	gürdal	PROPN
ejpam-3019	198	22	/	/	SYM
ejpam-3019	198	23	eur	eur	PROPN
ejpam-3019	198	24	.	.	PUNCT
ejpam-3019	199	1	j.	j.	PROPN
ejpam-3019	199	2	pure	pure	PROPN
ejpam-3019	199	3	appl	appl	PROPN
ejpam-3019	199	4	.	.	PROPN
ejpam-3019	199	5	math	math	PROPN
ejpam-3019	199	6	,	,	PUNCT
ejpam-3019	199	7	10	10	NUM
ejpam-3019	199	8	(	(	PUNCT
ejpam-3019	199	9	4	4	NUM
ejpam-3019	199	10	)	)	PUNCT
ejpam-3019	199	11	(	(	PUNCT
ejpam-3019	199	12	2017	2017	NUM
ejpam-3019	199	13	)	)	PUNCT
ejpam-3019	199	14	,	,	PUNCT
ejpam-3019	199	15	655	655	NUM
ejpam-3019	199	16	-	-	SYM
ejpam-3019	199	17	667	667	NUM
ejpam-3019	199	18	663	663	NUM
ejpam-3019	199	19	=	=	SYM
ejpam-3019	199	20	λtn−1	λtn−1	PROPN
ejpam-3019	199	21	.	.	PUNCT
ejpam-3019	200	1	so	so	ADV
ejpam-3019	200	2	,	,	PUNCT
ejpam-3019	200	3	we	we	PRON
ejpam-3019	200	4	get	get	VERB
ejpam-3019	200	5	0	0	NUM
ejpam-3019	200	6	≤	≤	NUM
ejpam-3019	200	7	tn	tn	NOUN
ejpam-3019	200	8	≤	≤	NOUN
ejpam-3019	200	9	λtn−1	λtn−1	PROPN
ejpam-3019	200	10	≤	≤	NOUN
ejpam-3019	200	11	λ2tn−2	λ2tn−2	NUM
ejpam-3019	200	12	≤	≤	NOUN
ejpam-3019	200	13	·	·	PUNCT
ejpam-3019	200	14	·	·	PUNCT
ejpam-3019	200	15	·	·	PUNCT
ejpam-3019	201	1	≤	≤	NUM
ejpam-3019	201	2	λnt0	λnt0	NOUN
ejpam-3019	201	3	.	.	PUNCT
ejpam-3019	202	1	(	(	PUNCT
ejpam-3019	202	2	27	27	NUM
ejpam-3019	202	3	)	)	PUNCT
ejpam-3019	202	4	we	we	PRON
ejpam-3019	202	5	obtain	obtain	VERB
ejpam-3019	202	6	that	that	SCONJ
ejpam-3019	202	7	d(an	d(an	PROPN
ejpam-3019	202	8	,	,	PUNCT
ejpam-3019	202	9	qm	qm	PROPN
ejpam-3019	202	10	)	)	PUNCT
ejpam-3019	202	11	≤	≤	NOUN
ejpam-3019	202	12	d(an	d(an	PROPN
ejpam-3019	202	13	,	,	PUNCT
ejpam-3019	202	14	qn+1	qn+1	NUM
ejpam-3019	202	15	)	)	PUNCT
ejpam-3019	202	16	+	+	NUM
ejpam-3019	202	17	d(an+1	d(an+1	ADJ
ejpam-3019	202	18	,	,	PUNCT
ejpam-3019	202	19	qn+1	qn+1	NUM
ejpam-3019	202	20	)	)	PUNCT
ejpam-3019	203	1	+	+	CCONJ
ejpam-3019	203	2	·	·	PUNCT
ejpam-3019	203	3	·	·	PUNCT
ejpam-3019	203	4	·	·	PUNCT
ejpam-3019	203	5	+	+	NUM
ejpam-3019	203	6	d(am−1qm	d(am−1qm	NOUN
ejpam-3019	203	7	)	)	PUNCT
ejpam-3019	203	8	,	,	PUNCT
ejpam-3019	203	9	d(bn	d(bn	PROPN
ejpam-3019	203	10	,	,	PUNCT
ejpam-3019	203	11	pm	pm	NOUN
ejpam-3019	203	12	)	)	PUNCT
ejpam-3019	203	13	≤	≤	NOUN
ejpam-3019	203	14	d(bn	d(bn	NOUN
ejpam-3019	203	15	,	,	PUNCT
ejpam-3019	203	16	pn+1	pn+1	NOUN
ejpam-3019	203	17	)	)	PUNCT
ejpam-3019	204	1	+	+	SYM
ejpam-3019	204	2	d(bn+1	d(bn+1	PROPN
ejpam-3019	204	3	,	,	PUNCT
ejpam-3019	204	4	pn+1	pn+1	NOUN
ejpam-3019	204	5	)	)	PUNCT
ejpam-3019	204	6	+	+	CCONJ
ejpam-3019	204	7	·	·	PUNCT
ejpam-3019	204	8	·	·	PUNCT
ejpam-3019	204	9	·	·	PUNCT
ejpam-3019	204	10	+	+	NUM
ejpam-3019	204	11	d(bm−1	d(bm−1	PROPN
ejpam-3019	204	12	,	,	PUNCT
ejpam-3019	204	13	pm	pm	NOUN
ejpam-3019	204	14	)	)	PUNCT
ejpam-3019	204	15	,	,	PUNCT
ejpam-3019	204	16	d(am	d(am	PROPN
ejpam-3019	204	17	,	,	PUNCT
ejpam-3019	204	18	qn	qn	NOUN
ejpam-3019	204	19	)	)	PUNCT
ejpam-3019	204	20	≤	≤	NOUN
ejpam-3019	204	21	d(am	d(am	PROPN
ejpam-3019	204	22	,	,	PUNCT
ejpam-3019	204	23	qm−1	qm−1	NOUN
ejpam-3019	204	24	)	)	PUNCT
ejpam-3019	205	1	+	+	CCONJ
ejpam-3019	205	2	d(am−1	d(am−1	PROPN
ejpam-3019	205	3	,	,	PUNCT
ejpam-3019	205	4	qm−1	qm−1	NOUN
ejpam-3019	205	5	)	)	PUNCT
ejpam-3019	206	1	+	+	CCONJ
ejpam-3019	206	2	·	·	PUNCT
ejpam-3019	206	3	·	·	PUNCT
ejpam-3019	206	4	·	·	PUNCT
ejpam-3019	206	5	+	+	CCONJ
ejpam-3019	206	6	d(an+1	d(an+1	ADJ
ejpam-3019	206	7	,	,	PUNCT
ejpam-3019	206	8	qn	qn	NOUN
ejpam-3019	206	9	)	)	PUNCT
ejpam-3019	206	10	,	,	PUNCT
ejpam-3019	206	11	d(bm	d(bm	PROPN
ejpam-3019	206	12	,	,	PUNCT
ejpam-3019	206	13	pn	pn	NOUN
ejpam-3019	206	14	)	)	PUNCT
ejpam-3019	206	15	≤	≤	NOUN
ejpam-3019	206	16	d(bm	d(bm	PROPN
ejpam-3019	206	17	,	,	PUNCT
ejpam-3019	206	18	pm−1	pm−1	NOUN
ejpam-3019	206	19	)	)	PUNCT
ejpam-3019	206	20	+	+	CCONJ
ejpam-3019	206	21	d(bm−1	d(bm−1	PROPN
ejpam-3019	206	22	,	,	PUNCT
ejpam-3019	206	23	pm−1	pm−1	NOUN
ejpam-3019	206	24	)	)	PUNCT
ejpam-3019	207	1	+	+	PUNCT
ejpam-3019	208	1	·	·	PUNCT
ejpam-3019	208	2	·	·	PUNCT
ejpam-3019	208	3	·	·	PUNCT
ejpam-3019	208	4	+	+	SYM
ejpam-3019	208	5	d(bn+1	d(bn+1	PROPN
ejpam-3019	208	6	,	,	PUNCT
ejpam-3019	208	7	pn	pn	NOUN
ejpam-3019	208	8	)	)	PUNCT
ejpam-3019	208	9	(	(	PUNCT
ejpam-3019	208	10	28	28	NUM
ejpam-3019	208	11	)	)	PUNCT
ejpam-3019	208	12	for	for	ADP
ejpam-3019	208	13	each	each	DET
ejpam-3019	208	14	n	n	NOUN
ejpam-3019	208	15	,	,	PUNCT
ejpam-3019	208	16	m	m	PROPN
ejpam-3019	208	17	∈	∈	PROPN
ejpam-3019	208	18	n	n	CCONJ
ejpam-3019	208	19	,	,	PUNCT
ejpam-3019	208	20	n	n	CCONJ
ejpam-3019	208	21	<	<	X
ejpam-3019	208	22	m.	m.	NOUN
ejpam-3019	208	23	thus	thus	ADV
ejpam-3019	208	24	,	,	PUNCT
ejpam-3019	208	25	from	from	ADP
ejpam-3019	208	26	(	(	PUNCT
ejpam-3019	208	27	23	23	NUM
ejpam-3019	208	28	)	)	PUNCT
ejpam-3019	208	29	,	,	PUNCT
ejpam-3019	208	30	(	(	PUNCT
ejpam-3019	208	31	24	24	NUM
ejpam-3019	208	32	)	)	PUNCT
ejpam-3019	208	33	(	(	PUNCT
ejpam-3019	208	34	27	27	NUM
ejpam-3019	208	35	)	)	PUNCT
ejpam-3019	208	36	and	and	CCONJ
ejpam-3019	208	37	(	(	PUNCT
ejpam-3019	208	38	28	28	NUM
ejpam-3019	208	39	)	)	PUNCT
ejpam-3019	208	40	,	,	PUNCT
ejpam-3019	208	41	we	we	PRON
ejpam-3019	208	42	have	have	VERB
ejpam-3019	208	43	d(an	d(an	PROPN
ejpam-3019	208	44	,	,	PUNCT
ejpam-3019	208	45	qm	qm	PROPN
ejpam-3019	208	46	)	)	PUNCT
ejpam-3019	209	1	+	+	CCONJ
ejpam-3019	209	2	d(bm	d(bm	PROPN
ejpam-3019	209	3	,	,	PUNCT
ejpam-3019	209	4	pn	pn	NOUN
ejpam-3019	209	5	)	)	PUNCT
ejpam-3019	209	6	≤	≤	NOUN
ejpam-3019	209	7	(	(	PUNCT
ejpam-3019	209	8	d(an	d(an	NOUN
ejpam-3019	209	9	,	,	PUNCT
ejpam-3019	209	10	qn+1	qn+1	NUM
ejpam-3019	209	11	)	)	PUNCT
ejpam-3019	209	12	+	+	X
ejpam-3019	209	13	d(bn+1	d(bn+1	PROPN
ejpam-3019	209	14	,	,	PUNCT
ejpam-3019	209	15	pn	pn	NOUN
ejpam-3019	209	16	)	)	PUNCT
ejpam-3019	209	17	)	)	PUNCT
ejpam-3019	210	1	+	+	ADJ
ejpam-3019	210	2	(	(	PUNCT
ejpam-3019	210	3	d(an+1	d(an+1	ADJ
ejpam-3019	210	4	,	,	PUNCT
ejpam-3019	210	5	qn+1	qn+1	NUM
ejpam-3019	210	6	)	)	PUNCT
ejpam-3019	210	7	+	+	X
ejpam-3019	210	8	d(bn+1	d(bn+1	PROPN
ejpam-3019	210	9	,	,	PUNCT
ejpam-3019	210	10	pn+1	pn+1	NOUN
ejpam-3019	210	11	)	)	PUNCT
ejpam-3019	210	12	)	)	PUNCT
ejpam-3019	210	13	+	+	CCONJ
ejpam-3019	210	14	·	·	PUNCT
ejpam-3019	210	15	·	·	PUNCT
ejpam-3019	210	16	·	·	PUNCT
ejpam-3019	211	1	+	+	X
ejpam-3019	211	2	(	(	PUNCT
ejpam-3019	211	3	d(am−1	d(am−1	ADJ
ejpam-3019	211	4	,	,	PUNCT
ejpam-3019	211	5	qm−1	qm−1	NOUN
ejpam-3019	211	6	)	)	PUNCT
ejpam-3019	212	1	+	+	CCONJ
ejpam-3019	212	2	d(bm−1	d(bm−1	PROPN
ejpam-3019	212	3	,	,	PUNCT
ejpam-3019	212	4	pm−1	pm−1	NOUN
ejpam-3019	212	5	)	)	PUNCT
ejpam-3019	212	6	)	)	PUNCT
ejpam-3019	213	1	+	+	ADV
ejpam-3019	213	2	(	(	PUNCT
ejpam-3019	213	3	d(am−1	d(am−1	PROPN
ejpam-3019	213	4	,	,	PUNCT
ejpam-3019	213	5	qm	qm	PROPN
ejpam-3019	213	6	)	)	PUNCT
ejpam-3019	213	7	+	+	CCONJ
ejpam-3019	213	8	d(bm	d(bm	NOUN
ejpam-3019	213	9	,	,	PUNCT
ejpam-3019	213	10	pm−1	pm−1	NOUN
ejpam-3019	213	11	)	)	PUNCT
ejpam-3019	213	12	)	)	PUNCT
ejpam-3019	213	13	,	,	PUNCT
ejpam-3019	213	14	=	=	SYM
ejpam-3019	213	15	en	en	X
ejpam-3019	213	16	+	+	X
ejpam-3019	213	17	tn+1	tn+1	X
ejpam-3019	213	18	+	+	CCONJ
ejpam-3019	213	19	en+1	en+1	ADJ
ejpam-3019	213	20	+	+	X
ejpam-3019	213	21	·	·	PUNCT
ejpam-3019	213	22	·	·	PUNCT
ejpam-3019	213	23	·	·	PUNCT
ejpam-3019	213	24	+	+	NUM
ejpam-3019	213	25	tm−1	tm−1	NOUN
ejpam-3019	213	26	+	+	CCONJ
ejpam-3019	213	27	em−1	em−1	PROPN
ejpam-3019	213	28	,	,	PUNCT
ejpam-3019	213	29	≤	≤	ADJ
ejpam-3019	213	30	λne0	λne0	PROPN
ejpam-3019	213	31	+	+	CCONJ
ejpam-3019	213	32	λn+1t0	λn+1t0	PROPN
ejpam-3019	213	33	+	+	CCONJ
ejpam-3019	213	34	λn+1e0	λn+1e0	PROPN
ejpam-3019	213	35	+	+	CCONJ
ejpam-3019	213	36	·	·	PUNCT
ejpam-3019	213	37	·	·	PUNCT
ejpam-3019	213	38	·	·	PUNCT
ejpam-3019	213	39	+	+	SYM
ejpam-3019	213	40	λm−1t0	λm−1t0	X
ejpam-3019	213	41	+	+	CCONJ
ejpam-3019	213	42	λm−1e0	λm−1e0	ADJ
ejpam-3019	213	43	,	,	PUNCT
ejpam-3019	213	44	=	=	SYM
ejpam-3019	213	45	(	(	PUNCT
ejpam-3019	213	46	λn	λn	PROPN
ejpam-3019	213	47	+	+	CCONJ
ejpam-3019	213	48	λn+1	λn+1	PROPN
ejpam-3019	213	49	+	+	CCONJ
ejpam-3019	213	50	·	·	PUNCT
ejpam-3019	213	51	·	·	PUNCT
ejpam-3019	213	52	·	·	PUNCT
ejpam-3019	213	53	+	+	NUM
ejpam-3019	213	54	λm−1)e0	λm−1)e0	NOUN
ejpam-3019	213	55	+	+	CCONJ
ejpam-3019	213	56	(	(	PUNCT
ejpam-3019	213	57	λn+1	λn+1	ADP
ejpam-3019	213	58	+	+	CCONJ
ejpam-3019	213	59	λn+2	λn+2	NUM
ejpam-3019	213	60	+	+	NUM
ejpam-3019	213	61	·	·	PUNCT
ejpam-3019	213	62	·	·	PUNCT
ejpam-3019	213	63	·	·	PUNCT
ejpam-3019	213	64	+	+	CCONJ
ejpam-3019	213	65	λm−1)t0	λm−1)t0	PROPN
ejpam-3019	213	66	,	,	PUNCT
ejpam-3019	213	67	≤	≤	NUM
ejpam-3019	213	68	λn	λn	ADP
ejpam-3019	213	69	1−	1−	NUM
ejpam-3019	213	70	λ	λ	PROPN
ejpam-3019	213	71	e0	e0	PROPN
ejpam-3019	213	72	+	+	CCONJ
ejpam-3019	213	73	λn+1	λn+1	PROPN
ejpam-3019	213	74	1−	1−	NUM
ejpam-3019	213	75	λ	λ	SYM
ejpam-3019	213	76	t0	t0	PROPN
ejpam-3019	213	77	(	(	PUNCT
ejpam-3019	213	78	29	29	NUM
ejpam-3019	213	79	)	)	PUNCT
ejpam-3019	213	80	and	and	CCONJ
ejpam-3019	213	81	d(am	d(am	PROPN
ejpam-3019	213	82	,	,	PUNCT
ejpam-3019	213	83	qn	qn	NOUN
ejpam-3019	213	84	)	)	PUNCT
ejpam-3019	213	85	+	+	CCONJ
ejpam-3019	213	86	d(bn	d(bn	NUM
ejpam-3019	213	87	,	,	PUNCT
ejpam-3019	213	88	pm	pm	NOUN
ejpam-3019	213	89	)	)	PUNCT
ejpam-3019	213	90	≤	≤	NOUN
ejpam-3019	213	91	(	(	PUNCT
ejpam-3019	213	92	d(am	d(am	NOUN
ejpam-3019	213	93	,	,	PUNCT
ejpam-3019	213	94	qm−1	qm−1	NOUN
ejpam-3019	213	95	)	)	PUNCT
ejpam-3019	213	96	+	+	CCONJ
ejpam-3019	213	97	d(bm−1	d(bm−1	PROPN
ejpam-3019	213	98	,	,	PUNCT
ejpam-3019	213	99	pm	pm	NOUN
ejpam-3019	213	100	)	)	PUNCT
ejpam-3019	213	101	)	)	PUNCT
ejpam-3019	214	1	+	+	PROPN
ejpam-3019	214	2	(	(	PUNCT
ejpam-3019	214	3	d(am−1	d(am−1	PROPN
ejpam-3019	214	4	,	,	PUNCT
ejpam-3019	214	5	qm−1	qm−1	NOUN
ejpam-3019	214	6	)	)	PUNCT
ejpam-3019	215	1	+	+	CCONJ
ejpam-3019	215	2	d(bm−1	d(bm−1	PROPN
ejpam-3019	215	3	,	,	PUNCT
ejpam-3019	215	4	pm−1	pm−1	NOUN
ejpam-3019	215	5	)	)	PUNCT
ejpam-3019	215	6	)	)	PUNCT
ejpam-3019	216	1	+	+	CCONJ
ejpam-3019	216	2	·	·	PUNCT
ejpam-3019	216	3	·	·	PUNCT
ejpam-3019	216	4	·	·	PUNCT
ejpam-3019	217	1	+	+	ADJ
ejpam-3019	217	2	(	(	PUNCT
ejpam-3019	217	3	d(an+1	d(an+1	ADJ
ejpam-3019	217	4	,	,	PUNCT
ejpam-3019	217	5	qn+1	qn+1	NUM
ejpam-3019	217	6	)	)	PUNCT
ejpam-3019	217	7	+	+	X
ejpam-3019	217	8	d(bn+1	d(bn+1	PROPN
ejpam-3019	217	9	,	,	PUNCT
ejpam-3019	217	10	pn+1	pn+1	NOUN
ejpam-3019	217	11	)	)	PUNCT
ejpam-3019	217	12	)	)	PUNCT
ejpam-3019	218	1	+	+	ADJ
ejpam-3019	218	2	(	(	PUNCT
ejpam-3019	218	3	d(an+1	d(an+1	ADJ
ejpam-3019	218	4	,	,	PUNCT
ejpam-3019	218	5	qn	qn	NOUN
ejpam-3019	218	6	)	)	PUNCT
ejpam-3019	218	7	+	+	CCONJ
ejpam-3019	218	8	d(bn	d(bn	NUM
ejpam-3019	218	9	,	,	PUNCT
ejpam-3019	218	10	pn+1	pn+1	NOUN
ejpam-3019	218	11	)	)	PUNCT
ejpam-3019	218	12	)	)	PUNCT
ejpam-3019	218	13	,	,	PUNCT
ejpam-3019	218	14	=	=	PUNCT
ejpam-3019	218	15	sm−1	sm−1	NOUN
ejpam-3019	218	16	+	+	CCONJ
ejpam-3019	218	17	tm−1	tm−1	NOUN
ejpam-3019	218	18	+	+	CCONJ
ejpam-3019	218	19	·	·	PUNCT
ejpam-3019	218	20	·	·	PUNCT
ejpam-3019	218	21	·	·	PUNCT
ejpam-3019	218	22	+	+	NUM
ejpam-3019	218	23	sn+1	sn+1	VERB
ejpam-3019	218	24	+	+	SYM
ejpam-3019	218	25	tn+1	tn+1	X
ejpam-3019	218	26	+	+	CCONJ
ejpam-3019	218	27	sn	sn	PROPN
ejpam-3019	218	28	,	,	PUNCT
ejpam-3019	218	29	≤	≤	NOUN
ejpam-3019	219	1	λm−1s0	λm−1s0	PROPN
ejpam-3019	220	1	+	+	NUM
ejpam-3019	220	2	λm−1t0	λm−1t0	X
ejpam-3019	220	3	+	+	X
ejpam-3019	220	4	·	·	PUNCT
ejpam-3019	220	5	·	·	PUNCT
ejpam-3019	220	6	·	·	PUNCT
ejpam-3019	220	7	+	+	CCONJ
ejpam-3019	221	1	λn+1s0	λn+1s0	X
ejpam-3019	221	2	+	+	CCONJ
ejpam-3019	221	3	λn+1t0	λn+1t0	PROPN
ejpam-3019	221	4	+	+	CCONJ
ejpam-3019	221	5	λns0	λns0	PROPN
ejpam-3019	221	6	,	,	PUNCT
ejpam-3019	221	7	=	=	PUNCT
ejpam-3019	221	8	(	(	PUNCT
ejpam-3019	221	9	λn	λn	PROPN
ejpam-3019	221	10	+	+	CCONJ
ejpam-3019	221	11	λn+1	λn+1	PROPN
ejpam-3019	221	12	+	+	CCONJ
ejpam-3019	221	13	·	·	PUNCT
ejpam-3019	221	14	·	·	PUNCT
ejpam-3019	221	15	·	·	PUNCT
ejpam-3019	221	16	+	+	NUM
ejpam-3019	221	17	λm−1)s0	λm−1)s0	X
ejpam-3019	221	18	+	+	CCONJ
ejpam-3019	221	19	(	(	PUNCT
ejpam-3019	221	20	λn+1	λn+1	ADP
ejpam-3019	221	21	+	+	CCONJ
ejpam-3019	221	22	λn+2	λn+2	NUM
ejpam-3019	221	23	+	+	NUM
ejpam-3019	221	24	·	·	PUNCT
ejpam-3019	221	25	·	·	PUNCT
ejpam-3019	221	26	·	·	PUNCT
ejpam-3019	221	27	+	+	CCONJ
ejpam-3019	221	28	λm−1)t0	λm−1)t0	PROPN
ejpam-3019	221	29	,	,	PUNCT
ejpam-3019	221	30	≤	≤	NUM
ejpam-3019	221	31	λn	λn	ADP
ejpam-3019	221	32	1−	1−	NUM
ejpam-3019	221	33	λ	λ	PROPN
ejpam-3019	221	34	s0	s0	NOUN
ejpam-3019	221	35	+	+	CCONJ
ejpam-3019	221	36	λn+1	λn+1	PROPN
ejpam-3019	221	37	1−	1−	NUM
ejpam-3019	221	38	λ	λ	X
ejpam-3019	221	39	t0	t0	PROPN
ejpam-3019	221	40	(	(	PUNCT
ejpam-3019	221	41	30	30	NUM
ejpam-3019	221	42	)	)	PUNCT
ejpam-3019	221	43	for	for	ADP
ejpam-3019	221	44	n	n	X
ejpam-3019	221	45	<	<	X
ejpam-3019	221	46	m.	m.	NOUN
ejpam-3019	221	47	since	since	SCONJ
ejpam-3019	221	48	,	,	PUNCT
ejpam-3019	221	49	for	for	ADP
ejpam-3019	221	50	an	an	DET
ejpam-3019	221	51	arbitrary	arbitrary	ADJ
ejpam-3019	221	52	ε	ε	PROPN
ejpam-3019	221	53	>	>	X
ejpam-3019	221	54	0	0	PROPN
ejpam-3019	221	55	,	,	PUNCT
ejpam-3019	221	56	there	there	PRON
ejpam-3019	221	57	exists	exist	VERB
ejpam-3019	221	58	n0	n0	NUM
ejpam-3019	221	59	such	such	ADJ
ejpam-3019	221	60	that	that	SCONJ
ejpam-3019	221	61	λn0	λn0	PROPN
ejpam-3019	221	62	1−λe0	1−λe0	PROPN
ejpam-3019	221	63	+	+	CCONJ
ejpam-3019	221	64	λn0	λn0	ADJ
ejpam-3019	221	65	+	+	PROPN
ejpam-3019	221	66	1	1	NUM
ejpam-3019	221	67	1−λ	1−λ	NUM
ejpam-3019	221	68	t0	t0	NOUN
ejpam-3019	221	69	<	<	X
ejpam-3019	221	70	ε	ε	PROPN
ejpam-3019	221	71	3	3	NUM
ejpam-3019	221	72	and	and	CCONJ
ejpam-3019	221	73	λn0	λn0	ADJ
ejpam-3019	221	74	1−λs0	1−λs0	NUM
ejpam-3019	221	75	+	+	CCONJ
ejpam-3019	221	76	λn0	λn0	ADJ
ejpam-3019	221	77	+	+	PROPN
ejpam-3019	221	78	1	1	NUM
ejpam-3019	221	79	1−λ	1−λ	NUM
ejpam-3019	221	80	t0	t0	NOUN
ejpam-3019	221	81	<	<	X
ejpam-3019	221	82	ε	ε	PROPN
ejpam-3019	221	83	3	3	NUM
ejpam-3019	221	84	,	,	PUNCT
ejpam-3019	221	85	from	from	ADP
ejpam-3019	221	86	(	(	PUNCT
ejpam-3019	221	87	29	29	NUM
ejpam-3019	221	88	)	)	PUNCT
ejpam-3019	221	89	and	and	CCONJ
ejpam-3019	221	90	(	(	PUNCT
ejpam-3019	221	91	30	30	NUM
ejpam-3019	221	92	)	)	PUNCT
ejpam-3019	221	93	,	,	PUNCT
ejpam-3019	221	94	we	we	PRON
ejpam-3019	221	95	have	have	VERB
ejpam-3019	221	96	for	for	ADP
ejpam-3019	221	97	each	each	DET
ejpam-3019	221	98	n	n	CCONJ
ejpam-3019	221	99	,	,	PUNCT
ejpam-3019	221	100	m	m	PROPN
ejpam-3019	221	101	≥	≥	NOUN
ejpam-3019	221	102	n0	n0	NUM
ejpam-3019	221	103	that	that	SCONJ
ejpam-3019	221	104	d(an	d(an	PROPN
ejpam-3019	221	105	,	,	PUNCT
ejpam-3019	221	106	qm	qm	PROPN
ejpam-3019	221	107	)	)	PUNCT
ejpam-3019	221	108	+	+	CCONJ
ejpam-3019	221	109	d(bm	d(bm	PROPN
ejpam-3019	221	110	,	,	PUNCT
ejpam-3019	221	111	pn	pn	NOUN
ejpam-3019	221	112	)	)	PUNCT
ejpam-3019	221	113	<	<	X
ejpam-3019	221	114	ε	ε	PROPN
ejpam-3019	221	115	3	3	NUM
ejpam-3019	221	116	.	.	PUNCT
ejpam-3019	222	1	then	then	ADV
ejpam-3019	222	2	(	(	PUNCT
ejpam-3019	222	3	an	an	PRON
ejpam-3019	222	4	,	,	PUNCT
ejpam-3019	222	5	qn	qn	NOUN
ejpam-3019	222	6	)	)	PUNCT
ejpam-3019	222	7	and	and	CCONJ
ejpam-3019	222	8	(	(	PUNCT
ejpam-3019	222	9	bn	bn	X
ejpam-3019	222	10	,	,	PUNCT
ejpam-3019	222	11	pn	pn	PROPN
ejpam-3019	222	12	)	)	PUNCT
ejpam-3019	222	13	are	be	AUX
ejpam-3019	222	14	cauchy	cauchy	NOUN
ejpam-3019	222	15	bisequences	bisequence	NOUN
ejpam-3019	222	16	.	.	PUNCT
ejpam-3019	223	1	using	use	VERB
ejpam-3019	223	2	completeness	completeness	NOUN
ejpam-3019	223	3	of	of	ADP
ejpam-3019	223	4	(	(	PUNCT
ejpam-3019	223	5	x	x	PROPN
ejpam-3019	223	6	,	,	PUNCT
ejpam-3019	223	7	y	y	PROPN
ejpam-3019	223	8	,	,	PUNCT
ejpam-3019	223	9	d	d	PROPN
ejpam-3019	223	10	)	)	PUNCT
ejpam-3019	223	11	,	,	PUNCT
ejpam-3019	223	12	we	we	PRON
ejpam-3019	223	13	say	say	VERB
ejpam-3019	223	14	that	that	SCONJ
ejpam-3019	223	15	there	there	PRON
ejpam-3019	223	16	exist	exist	VERB
ejpam-3019	223	17	a	a	DET
ejpam-3019	223	18	,	,	PUNCT
ejpam-3019	223	19	b	b	X
ejpam-3019	223	20	∈	∈	PROPN
ejpam-3019	223	21	x	x	X
ejpam-3019	223	22	and	and	CCONJ
ejpam-3019	223	23	p	p	X
ejpam-3019	223	24	,	,	PUNCT
ejpam-3019	223	25	q	q	PROPN
ejpam-3019	223	26	∈	∈	PROPN
ejpam-3019	223	27	y	y	PROPN
ejpam-3019	223	28	with	with	ADP
ejpam-3019	223	29	lim	lim	PROPN
ejpam-3019	223	30	n→∞	n→∞	PRON
ejpam-3019	224	1	an	an	DET
ejpam-3019	224	2	=	=	X
ejpam-3019	224	3	q	q	NOUN
ejpam-3019	224	4	,	,	PUNCT
ejpam-3019	224	5	lim	lim	PROPN
ejpam-3019	224	6	n→∞	n→∞	X
ejpam-3019	225	1	bn	bn	NOUN
ejpam-3019	225	2	=	=	SYM
ejpam-3019	225	3	p	p	PROPN
ejpam-3019	225	4	,	,	PUNCT
ejpam-3019	225	5	lim	lim	PROPN
ejpam-3019	225	6	n→∞	n→∞	X
ejpam-3019	225	7	pn	pn	PROPN
ejpam-3019	225	8	=	=	SYM
ejpam-3019	225	9	b	b	PROPN
ejpam-3019	225	10	and	and	CCONJ
ejpam-3019	225	11	lim	lim	PROPN
ejpam-3019	225	12	n→∞	n→∞	NUM
ejpam-3019	225	13	qn	qn	PROPN
ejpam-3019	225	14	=	=	NOUN
ejpam-3019	225	15	a.	a.	NOUN
ejpam-3019	225	16	(	(	PUNCT
ejpam-3019	225	17	31	31	NUM
ejpam-3019	225	18	)	)	PUNCT
ejpam-3019	225	19	a.	a.	NOUN
ejpam-3019	225	20	mutlu	mutlu	PROPN
ejpam-3019	225	21	,	,	PUNCT
ejpam-3019	225	22	k.	k.	PROPN
ejpam-3019	225	23	özkan	özkan	PROPN
ejpam-3019	225	24	,	,	PUNCT
ejpam-3019	225	25	u.	u.	PROPN
ejpam-3019	225	26	gürdal	gürdal	PROPN
ejpam-3019	225	27	/	/	SYM
ejpam-3019	225	28	eur	eur	PROPN
ejpam-3019	225	29	.	.	PUNCT
ejpam-3019	226	1	j.	j.	PROPN
ejpam-3019	226	2	pure	pure	PROPN
ejpam-3019	226	3	appl	appl	PROPN
ejpam-3019	226	4	.	.	PROPN
ejpam-3019	226	5	math	math	PROPN
ejpam-3019	226	6	,	,	PUNCT
ejpam-3019	226	7	10	10	NUM
ejpam-3019	226	8	(	(	PUNCT
ejpam-3019	226	9	4	4	NUM
ejpam-3019	226	10	)	)	PUNCT
ejpam-3019	226	11	(	(	PUNCT
ejpam-3019	226	12	2017	2017	NUM
ejpam-3019	226	13	)	)	PUNCT
ejpam-3019	226	14	,	,	PUNCT
ejpam-3019	226	15	655	655	NUM
ejpam-3019	226	16	-	-	SYM
ejpam-3019	226	17	667	667	NUM
ejpam-3019	226	18	664	664	NUM
ejpam-3019	226	19	then	then	ADV
ejpam-3019	226	20	there	there	PRON
ejpam-3019	226	21	exists	exist	VERB
ejpam-3019	226	22	n1	n1	PROPN
ejpam-3019	226	23	∈	∈	PROPN
ejpam-3019	226	24	n	n	X
ejpam-3019	226	25	with	with	ADP
ejpam-3019	226	26	d(an	d(an	PROPN
ejpam-3019	226	27	,	,	PUNCT
ejpam-3019	226	28	q	q	NOUN
ejpam-3019	226	29	)	)	PUNCT
ejpam-3019	226	30	<	<	X
ejpam-3019	226	31	ε	ε	PROPN
ejpam-3019	226	32	3	3	NUM
ejpam-3019	226	33	,	,	PUNCT
ejpam-3019	226	34	d(bn	d(bn	PROPN
ejpam-3019	226	35	,	,	PUNCT
ejpam-3019	226	36	p	p	NOUN
ejpam-3019	226	37	)	)	PUNCT
ejpam-3019	226	38	<	<	X
ejpam-3019	226	39	ε	ε	PROPN
ejpam-3019	226	40	3	3	NUM
ejpam-3019	226	41	,	,	PUNCT
ejpam-3019	226	42	d(b	d(b	PROPN
ejpam-3019	226	43	,	,	PUNCT
ejpam-3019	226	44	pn	pn	NOUN
ejpam-3019	226	45	)	)	PUNCT
ejpam-3019	226	46	<	<	X
ejpam-3019	226	47	ε	ε	PROPN
ejpam-3019	226	48	3	3	NUM
ejpam-3019	226	49	and	and	CCONJ
ejpam-3019	226	50	d(a	d(a	PROPN
ejpam-3019	226	51	,	,	PUNCT
ejpam-3019	226	52	qn	qn	NOUN
ejpam-3019	226	53	)	)	PUNCT
ejpam-3019	226	54	<	<	X
ejpam-3019	226	55	ε	ε	PROPN
ejpam-3019	226	56	3	3	NUM
ejpam-3019	226	57	for	for	ADP
ejpam-3019	226	58	all	all	DET
ejpam-3019	226	59	n	n	PRON
ejpam-3019	226	60	≥	≥	NOUN
ejpam-3019	226	61	n1	n1	PROPN
ejpam-3019	226	62	and	and	CCONJ
ejpam-3019	226	63	every	every	DET
ejpam-3019	226	64	ε	ε	PROPN
ejpam-3019	226	65	>	>	X
ejpam-3019	226	66	0	0	PROPN
ejpam-3019	226	67	.	.	PUNCT
ejpam-3019	227	1	since	since	SCONJ
ejpam-3019	227	2	(	(	PUNCT
ejpam-3019	227	3	an	an	DET
ejpam-3019	227	4	,	,	PUNCT
ejpam-3019	227	5	qn	qn	NOUN
ejpam-3019	227	6	)	)	PUNCT
ejpam-3019	227	7	and	and	CCONJ
ejpam-3019	227	8	(	(	PUNCT
ejpam-3019	227	9	bn	bn	X
ejpam-3019	227	10	,	,	PUNCT
ejpam-3019	227	11	pn	pn	PROPN
ejpam-3019	227	12	)	)	PUNCT
ejpam-3019	227	13	are	be	AUX
ejpam-3019	227	14	cauchy	cauchy	NOUN
ejpam-3019	227	15	bisequences	bisequence	NOUN
ejpam-3019	227	16	,	,	PUNCT
ejpam-3019	227	17	we	we	PRON
ejpam-3019	227	18	get	get	VERB
ejpam-3019	227	19	d(an	d(an	NOUN
ejpam-3019	227	20	,	,	PUNCT
ejpam-3019	227	21	qn	qn	NOUN
ejpam-3019	227	22	)	)	PUNCT
ejpam-3019	227	23	<	<	X
ejpam-3019	227	24	ε	ε	PROPN
ejpam-3019	227	25	3	3	NUM
ejpam-3019	227	26	and	and	CCONJ
ejpam-3019	227	27	d(bn	d(bn	NOUN
ejpam-3019	227	28	,	,	PUNCT
ejpam-3019	227	29	pn	pn	NOUN
ejpam-3019	227	30	)	)	PUNCT
ejpam-3019	227	31	<	<	X
ejpam-3019	227	32	ε	ε	PROPN
ejpam-3019	227	33	3	3	NUM
ejpam-3019	227	34	.	.	PUNCT
ejpam-3019	228	1	thus	thus	ADV
ejpam-3019	228	2	,	,	PUNCT
ejpam-3019	228	3	from	from	ADP
ejpam-3019	228	4	(	(	PUNCT
ejpam-3019	228	5	18	18	NUM
ejpam-3019	228	6	)	)	PUNCT
ejpam-3019	228	7	,	,	PUNCT
ejpam-3019	228	8	we	we	PRON
ejpam-3019	228	9	have	have	VERB
ejpam-3019	228	10	d(f	d(f	NOUN
ejpam-3019	228	11	(	(	PUNCT
ejpam-3019	228	12	a	a	DET
ejpam-3019	228	13	,	,	PUNCT
ejpam-3019	228	14	p	p	NOUN
ejpam-3019	228	15	)	)	PUNCT
ejpam-3019	228	16	,	,	PUNCT
ejpam-3019	228	17	q	q	X
ejpam-3019	228	18	)	)	PUNCT
ejpam-3019	228	19	≤	≤	NOUN
ejpam-3019	228	20	d(f	d(f	NOUN
ejpam-3019	228	21	(	(	PUNCT
ejpam-3019	228	22	a	a	DET
ejpam-3019	228	23	,	,	PUNCT
ejpam-3019	228	24	p	p	NOUN
ejpam-3019	228	25	)	)	PUNCT
ejpam-3019	228	26	,	,	PUNCT
ejpam-3019	228	27	qn+1	qn+1	NUM
ejpam-3019	228	28	)	)	PUNCT
ejpam-3019	228	29	+	+	NUM
ejpam-3019	228	30	d(an+1	d(an+1	ADJ
ejpam-3019	228	31	,	,	PUNCT
ejpam-3019	228	32	qn+1	qn+1	NUM
ejpam-3019	228	33	)	)	PUNCT
ejpam-3019	228	34	+	+	CCONJ
ejpam-3019	228	35	d(an+1	d(an+1	ADJ
ejpam-3019	228	36	,	,	PUNCT
ejpam-3019	228	37	q	q	NOUN
ejpam-3019	228	38	)	)	PUNCT
ejpam-3019	228	39	=	=	SYM
ejpam-3019	228	40	d(f	d(f	NOUN
ejpam-3019	228	41	(	(	PUNCT
ejpam-3019	228	42	a	a	DET
ejpam-3019	228	43	,	,	PUNCT
ejpam-3019	228	44	p	p	NOUN
ejpam-3019	228	45	)	)	PUNCT
ejpam-3019	228	46	,	,	PUNCT
ejpam-3019	228	47	f	f	PROPN
ejpam-3019	228	48	(	(	PUNCT
ejpam-3019	228	49	pn	pn	PROPN
ejpam-3019	228	50	,	,	PUNCT
ejpam-3019	228	51	bn	bn	NOUN
ejpam-3019	228	52	)	)	PUNCT
ejpam-3019	228	53	)	)	PUNCT
ejpam-3019	229	1	+	+	CCONJ
ejpam-3019	229	2	d(an+1	d(an+1	ADJ
ejpam-3019	229	3	,	,	PUNCT
ejpam-3019	229	4	qn+1	qn+1	NUM
ejpam-3019	229	5	)	)	PUNCT
ejpam-3019	229	6	+	+	CCONJ
ejpam-3019	229	7	d(an+1	d(an+1	ADJ
ejpam-3019	229	8	,	,	PUNCT
ejpam-3019	229	9	q	q	NOUN
ejpam-3019	229	10	)	)	PUNCT
ejpam-3019	229	11	≤	≤	NOUN
ejpam-3019	230	1	kd(a	kd(a	X
ejpam-3019	230	2	,	,	PUNCT
ejpam-3019	230	3	qn	qn	NOUN
ejpam-3019	230	4	)	)	PUNCT
ejpam-3019	230	5	+	+	CCONJ
ejpam-3019	230	6	ld(bn	ld(bn	PROPN
ejpam-3019	230	7	,	,	PUNCT
ejpam-3019	230	8	p	p	NOUN
ejpam-3019	230	9	)	)	PUNCT
ejpam-3019	230	10	+	+	CCONJ
ejpam-3019	230	11	d(an+1	d(an+1	ADJ
ejpam-3019	230	12	,	,	PUNCT
ejpam-3019	230	13	qn+1	qn+1	NUM
ejpam-3019	230	14	)	)	PUNCT
ejpam-3019	230	15	+	+	CCONJ
ejpam-3019	230	16	d(an+1	d(an+1	ADJ
ejpam-3019	230	17	,	,	PUNCT
ejpam-3019	230	18	q	q	NOUN
ejpam-3019	230	19	)	)	PUNCT
ejpam-3019	230	20	<	<	X
ejpam-3019	230	21	k	k	PROPN
ejpam-3019	230	22	ε	ε	PROPN
ejpam-3019	230	23	3	3	NUM
ejpam-3019	230	24	+	+	CCONJ
ejpam-3019	230	25	l	l	NOUN
ejpam-3019	230	26	ε	ε	NOUN
ejpam-3019	230	27	3	3	NUM
ejpam-3019	230	28	+	+	CCONJ
ejpam-3019	230	29	ε	ε	PROPN
ejpam-3019	230	30	3	3	NUM
ejpam-3019	230	31	+	+	CCONJ
ejpam-3019	230	32	ε	ε	PROPN
ejpam-3019	230	33	3	3	NUM
ejpam-3019	230	34	=	=	SYM
ejpam-3019	230	35	λ	λ	X
ejpam-3019	230	36	ε	ε	NOUN
ejpam-3019	230	37	3	3	NUM
ejpam-3019	230	38	+	+	SYM
ejpam-3019	230	39	2	2	NUM
ejpam-3019	230	40	ε	ε	NOUN
ejpam-3019	230	41	3	3	NUM
ejpam-3019	230	42	<	<	X
ejpam-3019	230	43	ε	ε	PROPN
ejpam-3019	230	44	for	for	ADP
ejpam-3019	230	45	each	each	DET
ejpam-3019	230	46	n	n	PRON
ejpam-3019	230	47	∈	∈	PROPN
ejpam-3019	230	48	n	n	NOUN
ejpam-3019	230	49	and	and	CCONJ
ejpam-3019	230	50	λ	λ	X
ejpam-3019	230	51	<	<	X
ejpam-3019	230	52	1	1	NUM
ejpam-3019	230	53	.	.	PUNCT
ejpam-3019	230	54	then	then	ADV
ejpam-3019	230	55	d(f	d(f	NOUN
ejpam-3019	230	56	(	(	PUNCT
ejpam-3019	230	57	a	a	DET
ejpam-3019	230	58	,	,	PUNCT
ejpam-3019	230	59	p	p	NOUN
ejpam-3019	230	60	)	)	PUNCT
ejpam-3019	230	61	,	,	PUNCT
ejpam-3019	230	62	q	q	X
ejpam-3019	230	63	)	)	PUNCT
ejpam-3019	230	64	=	=	SYM
ejpam-3019	231	1	0⇒	0⇒	NUM
ejpam-3019	232	1	f	f	NOUN
ejpam-3019	232	2	(	(	PUNCT
ejpam-3019	232	3	a	a	DET
ejpam-3019	232	4	,	,	PUNCT
ejpam-3019	232	5	p	p	NOUN
ejpam-3019	232	6	)	)	PUNCT
ejpam-3019	232	7	=	=	VERB
ejpam-3019	232	8	q.	q.	NOUN
ejpam-3019	232	9	in	in	ADP
ejpam-3019	232	10	a	a	DET
ejpam-3019	232	11	similar	similar	ADJ
ejpam-3019	232	12	manner	manner	NOUN
ejpam-3019	232	13	,	,	PUNCT
ejpam-3019	232	14	we	we	PRON
ejpam-3019	232	15	get	get	VERB
ejpam-3019	232	16	f	f	X
ejpam-3019	232	17	(	(	PUNCT
ejpam-3019	232	18	p	p	X
ejpam-3019	232	19	,	,	PUNCT
ejpam-3019	232	20	a	a	NOUN
ejpam-3019	232	21	)	)	PUNCT
ejpam-3019	232	22	=	=	SYM
ejpam-3019	232	23	b	b	PROPN
ejpam-3019	232	24	,	,	PUNCT
ejpam-3019	232	25	f	f	PROPN
ejpam-3019	232	26	(	(	PUNCT
ejpam-3019	232	27	b	b	NOUN
ejpam-3019	232	28	,	,	PUNCT
ejpam-3019	232	29	q	q	NOUN
ejpam-3019	232	30	)	)	PUNCT
ejpam-3019	232	31	=	=	SYM
ejpam-3019	233	1	p	p	PROPN
ejpam-3019	233	2	and	and	CCONJ
ejpam-3019	233	3	f	f	PROPN
ejpam-3019	233	4	(	(	PUNCT
ejpam-3019	233	5	q	q	PROPN
ejpam-3019	233	6	,	,	PUNCT
ejpam-3019	233	7	b	b	NOUN
ejpam-3019	233	8	)	)	PUNCT
ejpam-3019	233	9	=	=	SYM
ejpam-3019	233	10	a.	a.	NOUN
ejpam-3019	234	1	and	and	CCONJ
ejpam-3019	234	2	,	,	PUNCT
ejpam-3019	234	3	from	from	ADP
ejpam-3019	234	4	(	(	PUNCT
ejpam-3019	234	5	31	31	NUM
ejpam-3019	234	6	)	)	PUNCT
ejpam-3019	234	7	we	we	PRON
ejpam-3019	234	8	have	have	VERB
ejpam-3019	234	9	d(a	d(a	PROPN
ejpam-3019	234	10	,	,	PUNCT
ejpam-3019	234	11	q	q	NOUN
ejpam-3019	234	12	)	)	PUNCT
ejpam-3019	234	13	=	=	SYM
ejpam-3019	235	1	d	d	X
ejpam-3019	235	2	(	(	PUNCT
ejpam-3019	235	3	lim	lim	PROPN
ejpam-3019	235	4	n→∞	n→∞	NUM
ejpam-3019	235	5	qn	qn	PROPN
ejpam-3019	235	6	,	,	PUNCT
ejpam-3019	235	7	lim	lim	PROPN
ejpam-3019	235	8	n→∞	n→∞	X
ejpam-3019	235	9	an	an	PRON
ejpam-3019	235	10	)	)	PUNCT
ejpam-3019	235	11	=	=	SYM
ejpam-3019	235	12	lim	lim	PROPN
ejpam-3019	235	13	n→∞	n→∞	X
ejpam-3019	236	1	d(an	d(an	PROPN
ejpam-3019	236	2	,	,	PUNCT
ejpam-3019	236	3	qn	qn	NOUN
ejpam-3019	236	4	)	)	PUNCT
ejpam-3019	236	5	=	=	SYM
ejpam-3019	236	6	0	0	NUM
ejpam-3019	236	7	and	and	CCONJ
ejpam-3019	236	8	d(b	d(b	PROPN
ejpam-3019	236	9	,	,	PUNCT
ejpam-3019	236	10	p	p	NOUN
ejpam-3019	236	11	)	)	PUNCT
ejpam-3019	236	12	=	=	SYM
ejpam-3019	237	1	d	d	X
ejpam-3019	237	2	(	(	PUNCT
ejpam-3019	237	3	lim	lim	PROPN
ejpam-3019	237	4	n→∞	n→∞	NUM
ejpam-3019	237	5	pn	pn	PROPN
ejpam-3019	237	6	,	,	PUNCT
ejpam-3019	237	7	lim	lim	PROPN
ejpam-3019	237	8	n→∞	n→∞	NUM
ejpam-3019	237	9	bn	bn	NOUN
ejpam-3019	237	10	)	)	PUNCT
ejpam-3019	237	11	=	=	SYM
ejpam-3019	238	1	lim	lim	PROPN
ejpam-3019	238	2	n→∞	n→∞	X
ejpam-3019	238	3	d(bn	d(bn	PROPN
ejpam-3019	238	4	,	,	PUNCT
ejpam-3019	238	5	pn	pn	NOUN
ejpam-3019	238	6	)	)	PUNCT
ejpam-3019	238	7	=	=	SYM
ejpam-3019	238	8	0	0	X
ejpam-3019	238	9	.	.	PUNCT
ejpam-3019	239	1	therefore	therefore	ADV
ejpam-3019	239	2	,	,	PUNCT
ejpam-3019	239	3	a	a	DET
ejpam-3019	239	4	=	=	X
ejpam-3019	239	5	q	q	NOUN
ejpam-3019	239	6	and	and	CCONJ
ejpam-3019	239	7	b	b	X
ejpam-3019	239	8	=	=	SYM
ejpam-3019	240	1	p.	p.	NOUN
ejpam-3019	240	2	then	then	ADV
ejpam-3019	240	3	(	(	PUNCT
ejpam-3019	240	4	a	a	PRON
ejpam-3019	240	5	,	,	PUNCT
ejpam-3019	240	6	p	p	NOUN
ejpam-3019	240	7	)	)	PUNCT
ejpam-3019	240	8	∈	∈	PROPN
ejpam-3019	240	9	(	(	PUNCT
ejpam-3019	240	10	x	x	SYM
ejpam-3019	240	11	×	×	PROPN
ejpam-3019	240	12	y	y	PROPN
ejpam-3019	240	13	)	)	PUNCT
ejpam-3019	240	14	∩	∩	NOUN
ejpam-3019	240	15	(	(	PUNCT
ejpam-3019	240	16	y	y	PROPN
ejpam-3019	240	17	×x	×x	PROPN
ejpam-3019	240	18	)	)	PUNCT
ejpam-3019	240	19	is	be	AUX
ejpam-3019	240	20	a	a	DET
ejpam-3019	240	21	coupled	couple	VERB
ejpam-3019	240	22	fixed	fix	VERB
ejpam-3019	240	23	point	point	NOUN
ejpam-3019	240	24	of	of	ADP
ejpam-3019	240	25	f	f	PROPN
ejpam-3019	240	26	.	.	PUNCT
ejpam-3019	241	1	as	as	ADP
ejpam-3019	241	2	in	in	ADP
ejpam-3019	241	3	the	the	DET
ejpam-3019	241	4	proof	proof	NOUN
ejpam-3019	241	5	of	of	ADP
ejpam-3019	241	6	the	the	DET
ejpam-3019	241	7	theorem	theorem	ADJ
ejpam-3019	241	8	1	1	NUM
ejpam-3019	241	9	,	,	PUNCT
ejpam-3019	241	10	uniqueness	uniqueness	NOUN
ejpam-3019	241	11	of	of	ADP
ejpam-3019	241	12	the	the	DET
ejpam-3019	241	13	coupled	couple	VERB
ejpam-3019	241	14	fixed	fix	VERB
ejpam-3019	241	15	point	point	NOUN
ejpam-3019	241	16	of	of	ADP
ejpam-3019	241	17	f	f	PROPN
ejpam-3019	241	18	can	can	AUX
ejpam-3019	241	19	be	be	AUX
ejpam-3019	241	20	shown	show	VERB
ejpam-3019	241	21	easily	easily	ADV
ejpam-3019	241	22	.	.	PUNCT
ejpam-3019	242	1	corollary	corollary	ADJ
ejpam-3019	242	2	2	2	NUM
ejpam-3019	242	3	.	.	PUNCT
ejpam-3019	243	1	let	let	VERB
ejpam-3019	243	2	(	(	PUNCT
ejpam-3019	243	3	x	x	X
ejpam-3019	243	4	,	,	PUNCT
ejpam-3019	243	5	y	y	PROPN
ejpam-3019	243	6	,	,	PUNCT
ejpam-3019	243	7	d	d	NOUN
ejpam-3019	243	8	)	)	PUNCT
ejpam-3019	243	9	be	be	AUX
ejpam-3019	243	10	a	a	DET
ejpam-3019	243	11	complete	complete	ADJ
ejpam-3019	243	12	bipolar	bipolar	ADJ
ejpam-3019	243	13	metric	metric	ADJ
ejpam-3019	243	14	space	space	NOUN
ejpam-3019	243	15	.	.	PUNCT
ejpam-3019	244	1	f	f	X
ejpam-3019	244	2	:	:	PUNCT
ejpam-3019	244	3	(	(	PUNCT
ejpam-3019	244	4	x	x	SYM
ejpam-3019	244	5	×	×	PROPN
ejpam-3019	244	6	y	y	PROPN
ejpam-3019	244	7	,	,	PUNCT
ejpam-3019	244	8	y	y	PROPN
ejpam-3019	244	9	×x	×x	PROPN
ejpam-3019	244	10	)	)	PUNCT
ejpam-3019	244	11	⇒	⇒	NOUN
ejpam-3019	244	12	(	(	PUNCT
ejpam-3019	244	13	x	x	X
ejpam-3019	244	14	,	,	PUNCT
ejpam-3019	244	15	y	y	PROPN
ejpam-3019	244	16	)	)	PUNCT
ejpam-3019	244	17	be	be	AUX
ejpam-3019	244	18	a	a	DET
ejpam-3019	244	19	covariant	covariant	ADJ
ejpam-3019	244	20	mapping	mapping	NOUN
ejpam-3019	244	21	and	and	CCONJ
ejpam-3019	244	22	k	k	NOUN
ejpam-3019	244	23	,	,	PUNCT
ejpam-3019	244	24	l	l	NOUN
ejpam-3019	244	25	be	be	VERB
ejpam-3019	244	26	non	non	ADJ
ejpam-3019	244	27	-	-	ADJ
ejpam-3019	244	28	negative	negative	ADJ
ejpam-3019	244	29	constants	constant	NOUN
ejpam-3019	244	30	.	.	PUNCT
ejpam-3019	245	1	if	if	SCONJ
ejpam-3019	245	2	the	the	DET
ejpam-3019	245	3	condition	condition	NOUN
ejpam-3019	245	4	d(f	d(f	NOUN
ejpam-3019	245	5	(	(	PUNCT
ejpam-3019	245	6	a	a	DET
ejpam-3019	245	7	,	,	PUNCT
ejpam-3019	245	8	p	p	NOUN
ejpam-3019	245	9	)	)	PUNCT
ejpam-3019	245	10	,	,	PUNCT
ejpam-3019	245	11	f	f	PROPN
ejpam-3019	245	12	(	(	PUNCT
ejpam-3019	245	13	q	q	PROPN
ejpam-3019	245	14	,	,	PUNCT
ejpam-3019	245	15	b	b	NOUN
ejpam-3019	245	16	)	)	PUNCT
ejpam-3019	245	17	)	)	PUNCT
ejpam-3019	245	18	≤	≤	PUNCT
ejpam-3019	246	1	k	k	X
ejpam-3019	246	2	2	2	NUM
ejpam-3019	246	3	(	(	PUNCT
ejpam-3019	246	4	d(a	d(a	PROPN
ejpam-3019	246	5	,	,	PUNCT
ejpam-3019	246	6	q	q	NOUN
ejpam-3019	246	7	)	)	PUNCT
ejpam-3019	247	1	+	+	CCONJ
ejpam-3019	247	2	d(b	d(b	PROPN
ejpam-3019	247	3	,	,	PUNCT
ejpam-3019	247	4	p	p	NOUN
ejpam-3019	247	5	)	)	PUNCT
ejpam-3019	247	6	)	)	PUNCT
ejpam-3019	247	7	,	,	PUNCT
ejpam-3019	247	8	k	k	X
ejpam-3019	247	9	<	<	X
ejpam-3019	247	10	1	1	NUM
ejpam-3019	247	11	(	(	PUNCT
ejpam-3019	247	12	32	32	NUM
ejpam-3019	247	13	)	)	PUNCT
ejpam-3019	247	14	holds	hold	VERB
ejpam-3019	247	15	for	for	ADP
ejpam-3019	247	16	all	all	DET
ejpam-3019	247	17	a	a	PRON
ejpam-3019	247	18	,	,	PUNCT
ejpam-3019	247	19	b	b	X
ejpam-3019	247	20	∈	∈	PROPN
ejpam-3019	247	21	x	x	SYM
ejpam-3019	247	22	,	,	PUNCT
ejpam-3019	247	23	p	p	X
ejpam-3019	247	24	,	,	PUNCT
ejpam-3019	247	25	q	q	PROPN
ejpam-3019	247	26	∈	∈	PROPN
ejpam-3019	247	27	y	y	PROPN
ejpam-3019	247	28	,	,	PUNCT
ejpam-3019	247	29	then	then	ADV
ejpam-3019	247	30	f	f	X
ejpam-3019	247	31	:	:	PUNCT
ejpam-3019	247	32	(	(	PUNCT
ejpam-3019	247	33	x×y	x×y	PUNCT
ejpam-3019	247	34	)	)	PUNCT
ejpam-3019	247	35	∪	∪	NOUN
ejpam-3019	247	36	(	(	PUNCT
ejpam-3019	247	37	y	y	PROPN
ejpam-3019	247	38	×x)→	×x)→	PROPN
ejpam-3019	247	39	x	x	X
ejpam-3019	247	40	∪y	∪y	PROPN
ejpam-3019	247	41	has	have	VERB
ejpam-3019	247	42	a	a	DET
ejpam-3019	247	43	unique	unique	ADJ
ejpam-3019	247	44	coupled	couple	VERB
ejpam-3019	247	45	fixed	fix	VERB
ejpam-3019	247	46	point	point	NOUN
ejpam-3019	247	47	.	.	PUNCT
ejpam-3019	248	1	example	example	NOUN
ejpam-3019	249	1	1	1	NUM
ejpam-3019	249	2	.	.	PUNCT
ejpam-3019	249	3	let	let	VERB
ejpam-3019	249	4	un(r	un(r	PRON
ejpam-3019	249	5	)	)	PUNCT
ejpam-3019	249	6	and	and	CCONJ
ejpam-3019	249	7	ln(r	ln(r	NOUN
ejpam-3019	249	8	)	)	PUNCT
ejpam-3019	249	9	be	be	AUX
ejpam-3019	249	10	the	the	DET
ejpam-3019	249	11	sets	set	NOUN
ejpam-3019	249	12	of	of	ADP
ejpam-3019	249	13	all	all	DET
ejpam-3019	249	14	n	n	PRON
ejpam-3019	249	15	×	×	NOUN
ejpam-3019	249	16	n	n	CCONJ
ejpam-3019	249	17	upper	upper	ADJ
ejpam-3019	249	18	and	and	CCONJ
ejpam-3019	249	19	lower	low	ADJ
ejpam-3019	249	20	triangular	triangular	NOUN
ejpam-3019	249	21	matrices	matrix	NOUN
ejpam-3019	249	22	over	over	ADP
ejpam-3019	249	23	r	r	NOUN
ejpam-3019	249	24	,	,	PUNCT
ejpam-3019	249	25	respectively	respectively	ADV
ejpam-3019	249	26	.	.	PUNCT
ejpam-3019	250	1	a	a	DET
ejpam-3019	250	2	function	function	NOUN
ejpam-3019	250	3	d	d	NOUN
ejpam-3019	250	4	:	:	PUNCT
ejpam-3019	250	5	un(r)×	un(r)×	PROPN
ejpam-3019	250	6	ln(r)→	ln(r)→	PROPN
ejpam-3019	250	7	r+	r+	X
ejpam-3019	250	8	be	be	AUX
ejpam-3019	250	9	defined	define	VERB
ejpam-3019	250	10	as	as	ADP
ejpam-3019	250	11	d(a	d(a	PROPN
ejpam-3019	250	12	,	,	PUNCT
ejpam-3019	250	13	b	b	NOUN
ejpam-3019	250	14	)	)	PUNCT
ejpam-3019	251	1	=	=	SYM
ejpam-3019	251	2	n∑	n∑	NOUN
ejpam-3019	252	1	i	i	PROPN
ejpam-3019	252	2	,	,	PUNCT
ejpam-3019	252	3	j=1	j=1	PROPN
ejpam-3019	252	4	|aij	|aij	PROPN
ejpam-3019	252	5	−	−	PROPN
ejpam-3019	252	6	bij	bij	VERB
ejpam-3019	252	7	|	|	ADV
ejpam-3019	252	8	for	for	ADP
ejpam-3019	252	9	all	all	DET
ejpam-3019	252	10	a	a	DET
ejpam-3019	252	11	=	=	PUNCT
ejpam-3019	252	12	(	(	PUNCT
ejpam-3019	252	13	aij)n×n	aij)n×n	NOUN
ejpam-3019	252	14	∈	∈	NOUN
ejpam-3019	252	15	un(r	un(r	NOUN
ejpam-3019	252	16	)	)	PUNCT
ejpam-3019	252	17	and	and	CCONJ
ejpam-3019	252	18	b	b	X
ejpam-3019	252	19	=	=	SYM
ejpam-3019	252	20	(	(	PUNCT
ejpam-3019	252	21	bij)n×n	bij)n×n	PROPN
ejpam-3019	252	22	∈	∈	PROPN
ejpam-3019	252	23	ln(r	ln(r	NOUN
ejpam-3019	252	24	)	)	PUNCT
ejpam-3019	252	25	.	.	PUNCT
ejpam-3019	253	1	then	then	ADV
ejpam-3019	253	2	it	it	PRON
ejpam-3019	253	3	is	be	AUX
ejpam-3019	253	4	apparent	apparent	ADJ
ejpam-3019	253	5	that	that	SCONJ
ejpam-3019	253	6	(	(	PUNCT
ejpam-3019	253	7	un(r	un(r	NOUN
ejpam-3019	253	8	)	)	PUNCT
ejpam-3019	253	9	,	,	PUNCT
ejpam-3019	253	10	ln(r	ln(r	NOUN
ejpam-3019	253	11	)	)	PUNCT
ejpam-3019	253	12	,	,	PUNCT
ejpam-3019	253	13	d	d	X
ejpam-3019	253	14	)	)	PUNCT
ejpam-3019	253	15	is	be	AUX
ejpam-3019	253	16	a	a	DET
ejpam-3019	253	17	complete	complete	ADJ
ejpam-3019	253	18	bipolar	bipolar	ADJ
ejpam-3019	253	19	metric	metric	ADJ
ejpam-3019	253	20	space	space	NOUN
ejpam-3019	253	21	.	.	PUNCT
ejpam-3019	254	1	we	we	PRON
ejpam-3019	254	2	take	take	VERB
ejpam-3019	254	3	a	a	DET
ejpam-3019	254	4	covariant	covariant	ADJ
ejpam-3019	254	5	mapping	mapping	NOUN
ejpam-3019	254	6	f	f	NOUN
ejpam-3019	254	7	:	:	PUNCT
ejpam-3019	254	8	(	(	PUNCT
ejpam-3019	254	9	un(r)2	un(r)2	PROPN
ejpam-3019	254	10	,	,	PUNCT
ejpam-3019	254	11	ln(r)2	ln(r)2	PROPN
ejpam-3019	254	12	)	)	PUNCT
ejpam-3019	254	13	⇒	⇒	NOUN
ejpam-3019	254	14	(	(	PUNCT
ejpam-3019	254	15	un(r	un(r	NOUN
ejpam-3019	254	16	)	)	PUNCT
ejpam-3019	254	17	,	,	PUNCT
ejpam-3019	254	18	ln(r	ln(r	NOUN
ejpam-3019	254	19	)	)	PUNCT
ejpam-3019	254	20	)	)	PUNCT
ejpam-3019	254	21	such	such	ADJ
ejpam-3019	254	22	as	as	ADP
ejpam-3019	254	23	f	f	PROPN
ejpam-3019	254	24	(	(	PUNCT
ejpam-3019	254	25	a	a	DET
ejpam-3019	254	26	,	,	PUNCT
ejpam-3019	254	27	b	b	NOUN
ejpam-3019	254	28	)	)	PUNCT
ejpam-3019	254	29	=	=	SYM
ejpam-3019	254	30	(	(	PUNCT
ejpam-3019	254	31	aij+bij	aij+bij	PROPN
ejpam-3019	254	32	3	3	NUM
ejpam-3019	254	33	)	)	PUNCT
ejpam-3019	255	1	n×n	n×n	PROPN
ejpam-3019	255	2	where	where	SCONJ
ejpam-3019	255	3	(	(	PUNCT
ejpam-3019	255	4	a	a	PRON
ejpam-3019	255	5	=	=	X
ejpam-3019	255	6	(	(	PUNCT
ejpam-3019	255	7	aij)n×n	aij)n×n	PROPN
ejpam-3019	255	8	,	,	PUNCT
ejpam-3019	255	9	b	b	PROPN
ejpam-3019	255	10	=	=	SYM
ejpam-3019	255	11	(	(	PUNCT
ejpam-3019	255	12	bij)n×n	bij)n×n	PROPN
ejpam-3019	255	13	)	)	PUNCT
ejpam-3019	255	14	∈	∈	PROPN
ejpam-3019	256	1	un(r)2	un(r)2	PROPN
ejpam-3019	256	2	∪	∪	ADP
ejpam-3019	256	3	ln(r)2	ln(r)2	PROPN
ejpam-3019	256	4	.	.	PUNCT
ejpam-3019	257	1	then	then	ADV
ejpam-3019	257	2	we	we	PRON
ejpam-3019	257	3	get	get	VERB
ejpam-3019	257	4	d(f	d(f	NOUN
ejpam-3019	257	5	(	(	PUNCT
ejpam-3019	257	6	a	a	DET
ejpam-3019	257	7	,	,	PUNCT
ejpam-3019	257	8	b	b	NOUN
ejpam-3019	257	9	)	)	PUNCT
ejpam-3019	257	10	,	,	PUNCT
ejpam-3019	257	11	f	f	PROPN
ejpam-3019	257	12	(	(	PUNCT
ejpam-3019	257	13	c	c	X
ejpam-3019	257	14	,	,	PUNCT
ejpam-3019	257	15	d	d	NOUN
ejpam-3019	257	16	)	)	PUNCT
ejpam-3019	257	17	)	)	PUNCT
ejpam-3019	258	1	=	=	PUNCT
ejpam-3019	258	2	d	d	X
ejpam-3019	258	3	(	(	PUNCT
ejpam-3019	258	4	(	(	PUNCT
ejpam-3019	258	5	aij	aij	PROPN
ejpam-3019	258	6	+	+	CCONJ
ejpam-3019	258	7	bij	bij	NOUN
ejpam-3019	258	8	3	3	NUM
ejpam-3019	258	9	)	)	PUNCT
ejpam-3019	258	10	n×n	n×n	PROPN
ejpam-3019	258	11	,	,	PUNCT
ejpam-3019	258	12	(	(	PUNCT
ejpam-3019	258	13	cij	cij	PROPN
ejpam-3019	258	14	+	+	CCONJ
ejpam-3019	258	15	dij	dij	PROPN
ejpam-3019	258	16	3	3	NUM
ejpam-3019	258	17	)	)	PUNCT
ejpam-3019	258	18	n×n	n×n	PROPN
ejpam-3019	258	19	)	)	PUNCT
ejpam-3019	258	20	references	reference	NOUN
ejpam-3019	258	21	665	665	NUM
ejpam-3019	258	22	=	=	SYM
ejpam-3019	258	23	n∑	n∑	NOUN
ejpam-3019	258	24	i	i	PROPN
ejpam-3019	258	25	,	,	PUNCT
ejpam-3019	258	26	j=1	j=1	PROPN
ejpam-3019	258	27	∣∣∣∣aij	∣∣∣∣aij	PROPN
ejpam-3019	258	28	+	+	PROPN
ejpam-3019	258	29	bij	bij	PROPN
ejpam-3019	258	30	−	−	PROPN
ejpam-3019	258	31	cij	cij	PROPN
ejpam-3019	258	32	−	−	PROPN
ejpam-3019	258	33	dij	dij	NOUN
ejpam-3019	258	34	3	3	NUM
ejpam-3019	258	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3019	258	36	≤	≤	PUNCT
ejpam-3019	258	37	n∑	n∑	NOUN
ejpam-3019	259	1	i	i	PRON
ejpam-3019	259	2	,	,	PUNCT
ejpam-3019	259	3	j=1	j=1	PROPN
ejpam-3019	260	1	∣∣∣∣aij	∣∣∣∣aij	PRON
ejpam-3019	260	2	−	−	PROPN
ejpam-3019	260	3	cij3	cij3	NOUN
ejpam-3019	260	4	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3019	260	5	∣∣∣∣bij	∣∣∣∣bij	VERB
ejpam-3019	260	6	−	−	PROPN
ejpam-3019	260	7	dij3	dij3	NOUN
ejpam-3019	260	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3019	260	9	=	=	SYM
ejpam-3019	260	10	1	1	NUM
ejpam-3019	260	11	3	3	NUM
ejpam-3019	260	12	(	(	PUNCT
ejpam-3019	260	13	d(a	d(a	PROPN
ejpam-3019	260	14	,	,	PUNCT
ejpam-3019	260	15	c	c	NOUN
ejpam-3019	260	16	)	)	PUNCT
ejpam-3019	260	17	+	+	CCONJ
ejpam-3019	261	1	d(b	d(b	PROPN
ejpam-3019	261	2	,	,	PUNCT
ejpam-3019	261	3	d	d	NOUN
ejpam-3019	261	4	)	)	PUNCT
ejpam-3019	261	5	)	)	PUNCT
ejpam-3019	261	6	for	for	ADP
ejpam-3019	261	7	all	all	DET
ejpam-3019	261	8	a	a	PRON
ejpam-3019	261	9	=	=	SYM
ejpam-3019	261	10	(	(	PUNCT
ejpam-3019	261	11	aij)n×n	aij)n×n	PROPN
ejpam-3019	261	12	,	,	PUNCT
ejpam-3019	261	13	b	b	PROPN
ejpam-3019	261	14	=	=	PUNCT
ejpam-3019	261	15	(	(	PUNCT
ejpam-3019	261	16	bij)n×n	bij)n×n	NOUN
ejpam-3019	261	17	∈	∈	NOUN
ejpam-3019	261	18	un(r	un(r	NOUN
ejpam-3019	261	19	)	)	PUNCT
ejpam-3019	261	20	and	and	CCONJ
ejpam-3019	261	21	c	c	X
ejpam-3019	261	22	=	=	SYM
ejpam-3019	261	23	(	(	PUNCT
ejpam-3019	261	24	cij)n×n	cij)n×n	PROPN
ejpam-3019	261	25	,	,	PUNCT
ejpam-3019	261	26	d	d	NOUN
ejpam-3019	261	27	=	=	SYM
ejpam-3019	261	28	(	(	PUNCT
ejpam-3019	261	29	dij)n×n	dij)n×n	PROPN
ejpam-3019	261	30	∈	∈	PROPN
ejpam-3019	261	31	ln(r	ln(r	NOUN
ejpam-3019	261	32	)	)	PUNCT
ejpam-3019	261	33	.	.	PUNCT
ejpam-3019	262	1	therefore	therefore	ADV
ejpam-3019	262	2	,	,	PUNCT
ejpam-3019	262	3	the	the	DET
ejpam-3019	262	4	equation	equation	NOUN
ejpam-3019	262	5	(	(	PUNCT
ejpam-3019	262	6	17	17	NUM
ejpam-3019	262	7	)	)	PUNCT
ejpam-3019	262	8	is	be	AUX
ejpam-3019	262	9	satisfied	satisfied	ADJ
ejpam-3019	262	10	for	for	ADP
ejpam-3019	262	11	k	k	X
ejpam-3019	262	12	=	=	SYM
ejpam-3019	262	13	2	2	NUM
ejpam-3019	262	14	3	3	NUM
ejpam-3019	262	15	.	.	PUNCT
ejpam-3019	263	1	then	then	ADV
ejpam-3019	263	2	from	from	ADP
ejpam-3019	263	3	corollary	corollary	ADJ
ejpam-3019	263	4	1	1	NUM
ejpam-3019	263	5	,	,	PUNCT
ejpam-3019	263	6	f	f	PROPN
ejpam-3019	263	7	has	have	VERB
ejpam-3019	263	8	a	a	DET
ejpam-3019	263	9	unique	unique	ADJ
ejpam-3019	263	10	coupled	couple	VERB
ejpam-3019	263	11	fixed	fix	VERB
ejpam-3019	263	12	point	point	NOUN
ejpam-3019	263	13	.	.	PUNCT
ejpam-3019	264	1	it	it	PRON
ejpam-3019	264	2	is	be	AUX
ejpam-3019	264	3	obvious	obvious	ADJ
ejpam-3019	264	4	that	that	SCONJ
ejpam-3019	264	5	the	the	DET
ejpam-3019	264	6	coupled	couple	VERB
ejpam-3019	264	7	fixed	fix	VERB
ejpam-3019	264	8	point	point	NOUN
ejpam-3019	264	9	is	be	AUX
ejpam-3019	264	10	(	(	PUNCT
ejpam-3019	264	11	0n×n	0n×n	ADJ
ejpam-3019	264	12	,	,	PUNCT
ejpam-3019	264	13	0n×n	0n×n	NUM
ejpam-3019	264	14	)	)	PUNCT
ejpam-3019	264	15	∈	∈	NOUN
ejpam-3019	264	16	un(r	un(r	NOUN
ejpam-3019	264	17	)	)	PUNCT
ejpam-3019	264	18	∩	∩	NOUN
ejpam-3019	264	19	ln(r	ln(r	NOUN
ejpam-3019	264	20	)	)	PUNCT
ejpam-3019	264	21	where	where	SCONJ
ejpam-3019	264	22	0n×n	0n×n	PROPN
ejpam-3019	264	23	is	be	AUX
ejpam-3019	264	24	the	the	DET
ejpam-3019	264	25	null	null	ADJ
ejpam-3019	264	26	matrix	matrix	NOUN
ejpam-3019	264	27	.	.	PUNCT
ejpam-3019	265	1	on	on	ADP
ejpam-3019	265	2	the	the	DET
ejpam-3019	265	3	other	other	ADJ
ejpam-3019	265	4	hand	hand	NOUN
ejpam-3019	265	5	,	,	PUNCT
ejpam-3019	265	6	if	if	SCONJ
ejpam-3019	265	7	f	f	X
ejpam-3019	265	8	:	:	PUNCT
ejpam-3019	265	9	(	(	PUNCT
ejpam-3019	265	10	un(r)2	un(r)2	PROPN
ejpam-3019	265	11	,	,	PUNCT
ejpam-3019	265	12	ln(r)2	ln(r)2	PROPN
ejpam-3019	265	13	)	)	PUNCT
ejpam-3019	265	14	⇒	⇒	NOUN
ejpam-3019	265	15	(	(	PUNCT
ejpam-3019	265	16	un(r	un(r	NOUN
ejpam-3019	265	17	)	)	PUNCT
ejpam-3019	265	18	,	,	PUNCT
ejpam-3019	265	19	ln(r	ln(r	NOUN
ejpam-3019	265	20	)	)	PUNCT
ejpam-3019	265	21	)	)	PUNCT
ejpam-3019	265	22	is	be	AUX
ejpam-3019	265	23	defined	define	VERB
ejpam-3019	265	24	by	by	ADP
ejpam-3019	265	25	f	f	PROPN
ejpam-3019	265	26	(	(	PUNCT
ejpam-3019	265	27	a	a	DET
ejpam-3019	265	28	,	,	PUNCT
ejpam-3019	265	29	b	b	NOUN
ejpam-3019	265	30	)	)	PUNCT
ejpam-3019	265	31	=	=	SYM
ejpam-3019	265	32	(	(	PUNCT
ejpam-3019	265	33	aij+bij	aij+bij	PROPN
ejpam-3019	265	34	2	2	NUM
ejpam-3019	265	35	)	)	PUNCT
ejpam-3019	266	1	n×n	n×n	PROPN
ejpam-3019	267	1	where	where	SCONJ
ejpam-3019	267	2	a	a	DET
ejpam-3019	267	3	=	=	X
ejpam-3019	267	4	(	(	PUNCT
ejpam-3019	267	5	aij)n×n	aij)n×n	PROPN
ejpam-3019	267	6	,	,	PUNCT
ejpam-3019	267	7	b	b	PROPN
ejpam-3019	267	8	=	=	PUNCT
ejpam-3019	267	9	(	(	PUNCT
ejpam-3019	267	10	bij)n×n	bij)n×n	PROPN
ejpam-3019	267	11	∈	∈	PROPN
ejpam-3019	267	12	un(r)2	un(r)2	PROPN
ejpam-3019	267	13	∪	∪	ADP
ejpam-3019	267	14	ln(r)2	ln(r)2	PROPN
ejpam-3019	267	15	.	.	PUNCT
ejpam-3019	268	1	then	then	ADV
ejpam-3019	268	2	it	it	PRON
ejpam-3019	268	3	can	can	AUX
ejpam-3019	268	4	be	be	AUX
ejpam-3019	268	5	observed	observe	VERB
ejpam-3019	268	6	that	that	SCONJ
ejpam-3019	268	7	d(f	d(f	NOUN
ejpam-3019	268	8	(	(	PUNCT
ejpam-3019	268	9	a	a	DET
ejpam-3019	268	10	,	,	PUNCT
ejpam-3019	268	11	b	b	NOUN
ejpam-3019	268	12	)	)	PUNCT
ejpam-3019	268	13	,	,	PUNCT
ejpam-3019	268	14	f	f	PROPN
ejpam-3019	268	15	(	(	PUNCT
ejpam-3019	268	16	c	c	X
ejpam-3019	268	17	,	,	PUNCT
ejpam-3019	268	18	d	d	NOUN
ejpam-3019	268	19	)	)	PUNCT
ejpam-3019	268	20	)	)	PUNCT
ejpam-3019	268	21	≤	≤	NUM
ejpam-3019	268	22	1	1	NUM
ejpam-3019	268	23	2	2	NUM
ejpam-3019	268	24	(	(	PUNCT
ejpam-3019	268	25	d(a	d(a	PROPN
ejpam-3019	268	26	,	,	PUNCT
ejpam-3019	268	27	c	c	NOUN
ejpam-3019	268	28	)	)	PUNCT
ejpam-3019	268	29	+	+	CCONJ
ejpam-3019	268	30	d(b	d(b	PROPN
ejpam-3019	268	31	,	,	PUNCT
ejpam-3019	268	32	d	d	NOUN
ejpam-3019	268	33	)	)	PUNCT
ejpam-3019	268	34	)	)	PUNCT
ejpam-3019	268	35	.	.	PUNCT
ejpam-3019	269	1	then	then	ADV
ejpam-3019	269	2	f	f	PROPN
ejpam-3019	269	3	satisfies	satisfy	VERB
ejpam-3019	269	4	the	the	DET
ejpam-3019	269	5	equation	equation	NOUN
ejpam-3019	269	6	(	(	PUNCT
ejpam-3019	269	7	17	17	NUM
ejpam-3019	269	8	)	)	PUNCT
ejpam-3019	269	9	for	for	ADP
ejpam-3019	269	10	k	k	PROPN
ejpam-3019	269	11	=	=	SYM
ejpam-3019	269	12	1	1	X
ejpam-3019	269	13	.	.	PUNCT
ejpam-3019	269	14	therefore	therefore	ADV
ejpam-3019	269	15	,	,	PUNCT
ejpam-3019	269	16	coupled	couple	VERB
ejpam-3019	269	17	fixed	fix	VERB
ejpam-3019	269	18	points	point	NOUN
ejpam-3019	269	19	of	of	ADP
ejpam-3019	269	20	f	f	PROPN
ejpam-3019	269	21	are	be	AUX
ejpam-3019	269	22	both	both	PRON
ejpam-3019	269	23	(	(	PUNCT
ejpam-3019	269	24	0n×n	0n×n	ADJ
ejpam-3019	269	25	,	,	PUNCT
ejpam-3019	269	26	0n×n	0n×n	NUM
ejpam-3019	269	27	)	)	PUNCT
ejpam-3019	269	28	∈	∈	NOUN
ejpam-3019	269	29	un(r)∩ln(r	un(r)∩ln(r	NOUN
ejpam-3019	269	30	)	)	PUNCT
ejpam-3019	269	31	and	and	CCONJ
ejpam-3019	269	32	(	(	PUNCT
ejpam-3019	269	33	in	in	ADP
ejpam-3019	269	34	,	,	PUNCT
ejpam-3019	269	35	in	in	ADP
ejpam-3019	269	36	)	)	PUNCT
ejpam-3019	269	37	∈	∈	NOUN
ejpam-3019	269	38	un(r)∩ln(r	un(r)∩ln(r	NOUN
ejpam-3019	269	39	)	)	PUNCT
ejpam-3019	269	40	where	where	SCONJ
ejpam-3019	269	41	0n×n	0n×n	PROPN
ejpam-3019	269	42	is	be	AUX
ejpam-3019	269	43	the	the	DET
ejpam-3019	269	44	null	null	ADJ
ejpam-3019	269	45	matrix	matrix	NOUN
ejpam-3019	269	46	and	and	CCONJ
ejpam-3019	269	47	in	in	ADP
ejpam-3019	269	48	is	be	AUX
ejpam-3019	269	49	the	the	DET
ejpam-3019	269	50	identity	identity	NOUN
ejpam-3019	269	51	matrix	matrix	NOUN
ejpam-3019	269	52	.	.	PUNCT
ejpam-3019	270	1	as	as	SCONJ
ejpam-3019	270	2	it	it	PRON
ejpam-3019	270	3	can	can	AUX
ejpam-3019	270	4	be	be	AUX
ejpam-3019	270	5	seen	see	VERB
ejpam-3019	270	6	from	from	ADP
ejpam-3019	270	7	this	this	DET
ejpam-3019	270	8	expression	expression	NOUN
ejpam-3019	270	9	,	,	PUNCT
ejpam-3019	270	10	f	f	PROPN
ejpam-3019	270	11	has	have	VERB
ejpam-3019	270	12	not	not	PART
ejpam-3019	270	13	a	a	DET
ejpam-3019	270	14	unique	unique	ADJ
ejpam-3019	270	15	coupled	couple	VERB
ejpam-3019	270	16	fixed	fix	VERB
ejpam-3019	270	17	point	point	NOUN
ejpam-3019	270	18	.	.	PUNCT
ejpam-3019	271	1	thus	thus	ADV
ejpam-3019	271	2	,	,	PUNCT
ejpam-3019	271	3	the	the	DET
ejpam-3019	271	4	conditions	condition	NOUN
ejpam-3019	271	5	k	k	X
ejpam-3019	271	6	<	<	X
ejpam-3019	271	7	1	1	NUM
ejpam-3019	271	8	in	in	ADP
ejpam-3019	271	9	corollary	corollary	ADJ
ejpam-3019	271	10	1	1	NUM
ejpam-3019	271	11	and	and	CCONJ
ejpam-3019	271	12	k	k	PROPN
ejpam-3019	272	1	+	+	CCONJ
ejpam-3019	272	2	l	l	NOUN
ejpam-3019	272	3	<	<	X
ejpam-3019	272	4	1	1	NUM
ejpam-3019	272	5	in	in	ADP
ejpam-3019	272	6	theorem	theorem	NOUN
ejpam-3019	272	7	1	1	NUM
ejpam-3019	272	8	are	be	AUX
ejpam-3019	272	9	the	the	DET
ejpam-3019	272	10	most	most	ADV
ejpam-3019	272	11	appropriate	appropriate	ADJ
ejpam-3019	272	12	conditions	condition	NOUN
ejpam-3019	272	13	for	for	ADP
ejpam-3019	272	14	satisfing	satisfe	VERB
ejpam-3019	272	15	the	the	DET
ejpam-3019	272	16	uniqueness	uniqueness	NOUN
ejpam-3019	272	17	of	of	ADP
ejpam-3019	272	18	coupled	couple	VERB
ejpam-3019	272	19	fixed	fix	VERB
ejpam-3019	272	20	point	point	NOUN
ejpam-3019	272	21	.	.	PUNCT
ejpam-3019	273	1	references	reference	NOUN
ejpam-3019	273	2	[	[	X
ejpam-3019	273	3	1	1	NUM
ejpam-3019	273	4	]	]	PUNCT
ejpam-3019	273	5	m.	m.	NOUN
ejpam-3019	273	6	abbas	abbas	PROPN
ejpam-3019	273	7	,	,	PUNCT
ejpam-3019	273	8	m.	m.	PROPN
ejpam-3019	273	9	ali	ali	PROPN
ejpam-3019	273	10	khan	khan	PROPN
ejpam-3019	273	11	,	,	PUNCT
ejpam-3019	273	12	s.	s.	PROPN
ejpam-3019	273	13	radenovic	radenovic	PROPN
ejpam-3019	273	14	.	.	PUNCT
ejpam-3019	274	1	common	common	ADJ
ejpam-3019	274	2	coupled	couple	VERB
ejpam-3019	274	3	fixed	fix	VERB
ejpam-3019	274	4	point	point	NOUN
ejpam-3019	274	5	theorems	theorem	NOUN
ejpam-3019	274	6	in	in	ADP
ejpam-3019	274	7	cone	cone	NOUN
ejpam-3019	274	8	metric	metric	ADJ
ejpam-3019	274	9	spaces	space	NOUN
ejpam-3019	274	10	for	for	ADP
ejpam-3019	274	11	w	w	ADJ
ejpam-3019	274	12	-	-	PUNCT
ejpam-3019	274	13	compatible	compatible	ADJ
ejpam-3019	274	14	mappings	mapping	NOUN
ejpam-3019	274	15	,	,	PUNCT
ejpam-3019	274	16	appl	appl	PROPN
ejpam-3019	274	17	.	.	PROPN
ejpam-3019	274	18	math	math	NOUN
ejpam-3019	274	19	.	.	PUNCT
ejpam-3019	275	1	comput	comput	NOUN
ejpam-3019	275	2	.	.	PUNCT
ejpam-3019	276	1	217	217	NUM
ejpam-3019	276	2	,	,	PUNCT
ejpam-3019	276	3	195	195	NUM
ejpam-3019	276	4	-	-	SYM
ejpam-3019	276	5	202	202	NUM
ejpam-3019	276	6	,	,	PUNCT
ejpam-3019	276	7	2010	2010	NUM
ejpam-3019	276	8	.	.	PUNCT
ejpam-3019	277	1	[	[	X
ejpam-3019	277	2	2	2	NUM
ejpam-3019	277	3	]	]	PUNCT
ejpam-3019	277	4	i.	i.	NOUN
ejpam-3019	277	5	altun	altun	PROPN
ejpam-3019	277	6	,	,	PUNCT
ejpam-3019	277	7	h.	h.	PROPN
ejpam-3019	277	8	simsek	simsek	PROPN
ejpam-3019	277	9	.	.	PUNCT
ejpam-3019	278	1	some	some	DET
ejpam-3019	278	2	fixed	fix	VERB
ejpam-3019	278	3	point	point	NOUN
ejpam-3019	278	4	theorems	theorem	NOUN
ejpam-3019	278	5	on	on	ADP
ejpam-3019	278	6	ordered	order	VERB
ejpam-3019	278	7	metric	metric	ADJ
ejpam-3019	278	8	spaces	space	NOUN
ejpam-3019	278	9	and	and	CCONJ
ejpam-3019	278	10	application	application	NOUN
ejpam-3019	278	11	,	,	PUNCT
ejpam-3019	278	12	fixed	fix	VERB
ejpam-3019	278	13	point	point	NOUN
ejpam-3019	278	14	theory	theory	NOUN
ejpam-3019	278	15	appl	appl	NOUN
ejpam-3019	278	16	.	.	PUNCT
ejpam-3019	279	1	2010	2010	NUM
ejpam-3019	279	2	,	,	PUNCT
ejpam-3019	279	3	17	17	NUM
ejpam-3019	279	4	pages	page	NOUN
ejpam-3019	279	5	,	,	PUNCT
ejpam-3019	279	6	article	article	NOUN
ejpam-3019	279	7	i	i	PROPN
ejpam-3019	279	8	d	d	PROPN
ejpam-3019	279	9	621492	621492	NUM
ejpam-3019	279	10	,	,	PUNCT
ejpam-3019	279	11	2010	2010	NUM
ejpam-3019	279	12	.	.	PUNCT
ejpam-3019	280	1	[	[	X
ejpam-3019	280	2	3	3	X
ejpam-3019	280	3	]	]	X
ejpam-3019	280	4	t.g	t.g	PROPN
ejpam-3019	280	5	.	.	PROPN
ejpam-3019	280	6	bhaskar	bhaskar	NOUN
ejpam-3019	280	7	,	,	PUNCT
ejpam-3019	280	8	v.	v.	ADP
ejpam-3019	280	9	lakshmikantham	lakshmikantham	NOUN
ejpam-3019	280	10	.	.	PUNCT
ejpam-3019	281	1	fixed	fix	VERB
ejpam-3019	281	2	point	point	NOUN
ejpam-3019	281	3	theorems	theorem	NOUN
ejpam-3019	281	4	in	in	ADP
ejpam-3019	281	5	partially	partially	ADV
ejpam-3019	281	6	ordered	order	VERB
ejpam-3019	281	7	metric	metric	ADJ
ejpam-3019	281	8	spaces	space	NOUN
ejpam-3019	281	9	and	and	CCONJ
ejpam-3019	281	10	applications	application	NOUN
ejpam-3019	281	11	,	,	PUNCT
ejpam-3019	281	12	nonlinear	nonlinear	ADJ
ejpam-3019	281	13	anal	anal	NOUN
ejpam-3019	281	14	.	.	PUNCT
ejpam-3019	282	1	65	65	NUM
ejpam-3019	282	2	,	,	PUNCT
ejpam-3019	282	3	1379	1379	NUM
ejpam-3019	282	4	-	-	SYM
ejpam-3019	282	5	1393	1393	NUM
ejpam-3019	282	6	,	,	PUNCT
ejpam-3019	282	7	2006	2006	NUM
ejpam-3019	282	8	.	.	PUNCT
ejpam-3019	283	1	[	[	X
ejpam-3019	283	2	4	4	NUM
ejpam-3019	283	3	]	]	X
ejpam-3019	283	4	y.j	y.j	PROPN
ejpam-3019	283	5	.	.	PUNCT
ejpam-3019	283	6	cho	cho	PROPN
ejpam-3019	283	7	,	,	PUNCT
ejpam-3019	283	8	b.e	b.e	PROPN
ejpam-3019	283	9	.	.	PROPN
ejpam-3019	283	10	rhoades	rhoades	PROPN
ejpam-3019	283	11	,	,	PUNCT
ejpam-3019	283	12	r.	r.	PROPN
ejpam-3019	283	13	saadati	saadati	PROPN
ejpam-3019	283	14	,	,	PUNCT
ejpam-3019	283	15	b.	b.	PROPN
ejpam-3019	283	16	samet	samet	PROPN
ejpam-3019	283	17	,	,	PUNCT
ejpam-3019	283	18	w.	w.	PROPN
ejpam-3019	283	19	shatanawi	shatanawi	PROPN
ejpam-3019	283	20	.	.	PUNCT
ejpam-3019	284	1	nonlinear	nonlinear	PROPN
ejpam-3019	284	2	coupled	couple	VERB
ejpam-3019	284	3	fixed	fix	VERB
ejpam-3019	284	4	point	point	NOUN
ejpam-3019	284	5	theorems	theorem	NOUN
ejpam-3019	284	6	in	in	ADP
ejpam-3019	284	7	ordered	order	VERB
ejpam-3019	284	8	generalized	generalized	ADJ
ejpam-3019	284	9	metric	metric	ADJ
ejpam-3019	284	10	spaces	space	NOUN
ejpam-3019	284	11	with	with	ADP
ejpam-3019	284	12	integral	integral	ADJ
ejpam-3019	284	13	type	type	NOUN
ejpam-3019	284	14	,	,	PUNCT
ejpam-3019	284	15	fixed	fix	VERB
ejpam-3019	284	16	point	point	NOUN
ejpam-3019	284	17	theory	theory	NOUN
ejpam-3019	284	18	appl	appl	NOUN
ejpam-3019	284	19	.	.	PUNCT
ejpam-3019	285	1	2012(8	2012(8	NUM
ejpam-3019	285	2	)	)	PUNCT
ejpam-3019	285	3	,	,	PUNCT
ejpam-3019	285	4	1–14	1–14	PROPN
ejpam-3019	285	5	,	,	PUNCT
ejpam-3019	285	6	2012	2012	NUM
ejpam-3019	285	7	.	.	PUNCT
ejpam-3019	286	1	[	[	X
ejpam-3019	286	2	5	5	NUM
ejpam-3019	286	3	]	]	X
ejpam-3019	286	4	l.j	l.j	PROPN
ejpam-3019	286	5	.	.	PROPN
ejpam-3019	286	6	ćıŕıc	ćıŕıc	PROPN
ejpam-3019	286	7	,	,	PUNCT
ejpam-3019	286	8	v.	v.	ADP
ejpam-3019	286	9	lakshmikantham	lakshmikantham	NOUN
ejpam-3019	286	10	.	.	PUNCT
ejpam-3019	287	1	coupled	couple	VERB
ejpam-3019	287	2	random	random	ADJ
ejpam-3019	287	3	fixed	fix	VERB
ejpam-3019	287	4	point	point	NOUN
ejpam-3019	287	5	theorems	theorem	NOUN
ejpam-3019	287	6	for	for	ADP
ejpam-3019	287	7	nonlinear	nonlinear	ADJ
ejpam-3019	287	8	contractions	contraction	NOUN
ejpam-3019	287	9	in	in	ADP
ejpam-3019	287	10	partially	partially	ADV
ejpam-3019	287	11	ordered	order	VERB
ejpam-3019	287	12	metric	metric	ADJ
ejpam-3019	287	13	spaces	space	NOUN
ejpam-3019	287	14	,	,	PUNCT
ejpam-3019	287	15	stoch	stoch	NOUN
ejpam-3019	287	16	.	.	PUNCT
ejpam-3019	288	1	anal	anal	PROPN
ejpam-3019	288	2	.	.	PUNCT
ejpam-3019	289	1	appl	appl	PROPN
ejpam-3019	289	2	.	.	PROPN
ejpam-3019	290	1	27	27	NUM
ejpam-3019	290	2	,	,	PUNCT
ejpam-3019	290	3	1246	1246	NUM
ejpam-3019	290	4	-	-	SYM
ejpam-3019	290	5	1259	1259	NUM
ejpam-3019	290	6	,	,	PUNCT
ejpam-3019	290	7	2009	2009	NUM
ejpam-3019	290	8	.	.	PUNCT
ejpam-3019	291	1	references	reference	NOUN
ejpam-3019	291	2	666	666	NUM
ejpam-3019	292	1	[	[	X
ejpam-3019	292	2	6	6	NUM
ejpam-3019	292	3	]	]	PUNCT
ejpam-3019	292	4	d.	d.	PROPN
ejpam-3019	292	5	guo	guo	PROPN
ejpam-3019	292	6	,	,	PUNCT
ejpam-3019	292	7	v.	v.	ADP
ejpam-3019	292	8	lakshmikantham	lakshmikantham	ADV
ejpam-3019	292	9	.	.	PUNCT
ejpam-3019	293	1	coupled	couple	VERB
ejpam-3019	293	2	fixed	fix	VERB
ejpam-3019	293	3	points	point	NOUN
ejpam-3019	293	4	of	of	ADP
ejpam-3019	293	5	nonlinear	nonlinear	ADJ
ejpam-3019	293	6	operators	operator	NOUN
ejpam-3019	293	7	with	with	ADP
ejpam-3019	293	8	applications	application	NOUN
ejpam-3019	293	9	,	,	PUNCT
ejpam-3019	293	10	nonlinear	nonlinear	ADJ
ejpam-3019	293	11	anal	anal	NOUN
ejpam-3019	293	12	.	.	PUNCT
ejpam-3019	294	1	11	11	NUM
ejpam-3019	294	2	,	,	PUNCT
ejpam-3019	294	3	623	623	NUM
ejpam-3019	294	4	-	-	SYM
ejpam-3019	294	5	632	632	NUM
ejpam-3019	294	6	,	,	PUNCT
ejpam-3019	294	7	1987	1987	NUM
ejpam-3019	294	8	.	.	PUNCT
ejpam-3019	295	1	[	[	X
ejpam-3019	295	2	7	7	X
ejpam-3019	295	3	]	]	X
ejpam-3019	295	4	e.	e.	PROPN
ejpam-3019	295	5	karapinar	karapinar	PROPN
ejpam-3019	295	6	.	.	PUNCT
ejpam-3019	295	7	coupled	couple	VERB
ejpam-3019	295	8	fixed	fix	VERB
ejpam-3019	295	9	point	point	NOUN
ejpam-3019	295	10	theorems	theorem	NOUN
ejpam-3019	295	11	for	for	ADP
ejpam-3019	295	12	nonlinear	nonlinear	ADJ
ejpam-3019	295	13	contractions	contraction	NOUN
ejpam-3019	295	14	in	in	ADP
ejpam-3019	295	15	cone	cone	NOUN
ejpam-3019	295	16	metric	metric	ADJ
ejpam-3019	295	17	spaces	space	NOUN
ejpam-3019	295	18	,	,	PUNCT
ejpam-3019	295	19	comput	comput	NOUN
ejpam-3019	295	20	.	.	PUNCT
ejpam-3019	296	1	math	math	NOUN
ejpam-3019	296	2	.	.	PUNCT
ejpam-3019	297	1	appl	appl	PROPN
ejpam-3019	297	2	.	.	PROPN
ejpam-3019	298	1	59	59	NUM
ejpam-3019	298	2	,	,	PUNCT
ejpam-3019	298	3	3656	3656	NUM
ejpam-3019	298	4	-	-	SYM
ejpam-3019	298	5	3668	3668	NUM
ejpam-3019	298	6	,	,	PUNCT
ejpam-3019	298	7	2010	2010	NUM
ejpam-3019	298	8	.	.	PUNCT
ejpam-3019	299	1	[	[	X
ejpam-3019	299	2	8	8	NUM
ejpam-3019	299	3	]	]	PUNCT
ejpam-3019	299	4	v.	v.	CCONJ
ejpam-3019	299	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3019	299	6	,	,	PUNCT
ejpam-3019	299	7	l.j	l.j	PROPN
ejpam-3019	299	8	.	.	PROPN
ejpam-3019	299	9	ćıŕıc	ćıŕıc	PROPN
ejpam-3019	299	10	.	.	PUNCT
ejpam-3019	299	11	coupled	couple	VERB
ejpam-3019	299	12	fixed	fix	VERB
ejpam-3019	299	13	point	point	NOUN
ejpam-3019	299	14	theorems	theorem	NOUN
ejpam-3019	299	15	for	for	ADP
ejpam-3019	299	16	nonlinear	nonlinear	ADJ
ejpam-3019	299	17	contractions	contraction	NOUN
ejpam-3019	299	18	in	in	ADP
ejpam-3019	299	19	partially	partially	ADV
ejpam-3019	299	20	ordered	order	VERB
ejpam-3019	299	21	metric	metric	ADJ
ejpam-3019	299	22	spaces	space	NOUN
ejpam-3019	299	23	,	,	PUNCT
ejpam-3019	299	24	nonlinear	nonlinear	ADJ
ejpam-3019	299	25	anal	anal	NOUN
ejpam-3019	299	26	.	.	PUNCT
ejpam-3019	300	1	70	70	NUM
ejpam-3019	300	2	,	,	PUNCT
ejpam-3019	300	3	4341	4341	NUM
ejpam-3019	300	4	-	-	SYM
ejpam-3019	300	5	4349	4349	NUM
ejpam-3019	300	6	,	,	PUNCT
ejpam-3019	300	7	2009	2009	NUM
ejpam-3019	300	8	.	.	PUNCT
ejpam-3019	301	1	[	[	X
ejpam-3019	301	2	9	9	NUM
ejpam-3019	301	3	]	]	X
ejpam-3019	301	4	n.v	n.v	PROPN
ejpam-3019	301	5	.	.	PROPN
ejpam-3019	301	6	luong	luong	PROPN
ejpam-3019	301	7	,	,	PUNCT
ejpam-3019	301	8	n.x	n.x	PROPN
ejpam-3019	301	9	.	.	PROPN
ejpam-3019	301	10	thuan	thuan	PROPN
ejpam-3019	301	11	.	.	PUNCT
ejpam-3019	301	12	coupled	couple	VERB
ejpam-3019	301	13	fixed	fix	VERB
ejpam-3019	301	14	points	point	NOUN
ejpam-3019	301	15	in	in	ADP
ejpam-3019	301	16	partially	partially	ADV
ejpam-3019	301	17	ordered	order	VERB
ejpam-3019	301	18	metric	metric	ADJ
ejpam-3019	301	19	spaces	space	NOUN
ejpam-3019	301	20	and	and	CCONJ
ejpam-3019	301	21	application	application	NOUN
ejpam-3019	301	22	,	,	PUNCT
ejpam-3019	301	23	nonlinear	nonlinear	ADJ
ejpam-3019	301	24	anal	anal	NOUN
ejpam-3019	301	25	.	.	PUNCT
ejpam-3019	302	1	74	74	NUM
ejpam-3019	302	2	,	,	PUNCT
ejpam-3019	302	3	983	983	NUM
ejpam-3019	302	4	-	-	SYM
ejpam-3019	302	5	992	992	NUM
ejpam-3019	302	6	,	,	PUNCT
ejpam-3019	302	7	2011	2011	NUM
ejpam-3019	302	8	.	.	PUNCT
ejpam-3019	303	1	[	[	X
ejpam-3019	303	2	10	10	NUM
ejpam-3019	303	3	]	]	PUNCT
ejpam-3019	303	4	a.	a.	NOUN
ejpam-3019	303	5	mutlu	mutlu	PROPN
ejpam-3019	303	6	,	,	PUNCT
ejpam-3019	303	7	n.	n.	PROPN
ejpam-3019	303	8	yolcu	yolcu	PROPN
ejpam-3019	303	9	,	,	PUNCT
ejpam-3019	303	10	b.	b.	PROPN
ejpam-3019	303	11	mutlu	mutlu	PROPN
ejpam-3019	303	12	,	,	PUNCT
ejpam-3019	303	13	n.	n.	PROPN
ejpam-3019	303	14	bildik	bildik	VERB
ejpam-3019	303	15	.	.	PUNCT
ejpam-3019	304	1	on	on	ADP
ejpam-3019	304	2	common	common	ADJ
ejpam-3019	304	3	coupled	couple	VERB
ejpam-3019	304	4	fixed	fix	VERB
ejpam-3019	304	5	point	point	NOUN
ejpam-3019	304	6	theorems	theorem	NOUN
ejpam-3019	304	7	for	for	ADP
ejpam-3019	304	8	comparable	comparable	ADJ
ejpam-3019	304	9	mappings	mapping	NOUN
ejpam-3019	304	10	in	in	ADP
ejpam-3019	304	11	ordered	order	VERB
ejpam-3019	304	12	partially	partially	ADV
ejpam-3019	304	13	metric	metric	ADJ
ejpam-3019	304	14	spaces	space	NOUN
ejpam-3019	304	15	,	,	PUNCT
ejpam-3019	304	16	abstract	abstract	ADJ
ejpam-3019	304	17	and	and	CCONJ
ejpam-3019	304	18	applied	apply	VERB
ejpam-3019	304	19	analysis	analysis	NOUN
ejpam-3019	304	20	2014	2014	NUM
ejpam-3019	304	21	,	,	PUNCT
ejpam-3019	304	22	6	6	NUM
ejpam-3019	304	23	pages	page	NOUN
ejpam-3019	304	24	article	article	NOUN
ejpam-3019	304	25	i	i	PROPN
ejpam-3019	304	26	d	d	PROPN
ejpam-3019	304	27	486384	486384	NUM
ejpam-3019	304	28	,	,	PUNCT
ejpam-3019	304	29	2014	2014	NUM
ejpam-3019	304	30	.	.	PUNCT
ejpam-3019	305	1	[	[	X
ejpam-3019	305	2	11	11	NUM
ejpam-3019	305	3	]	]	PUNCT
ejpam-3019	305	4	a.	a.	NOUN
ejpam-3019	305	5	mutlu	mutlu	PROPN
ejpam-3019	305	6	,	,	PUNCT
ejpam-3019	305	7	n.	n.	PROPN
ejpam-3019	305	8	yolcu	yolcu	PROPN
ejpam-3019	305	9	,	,	PUNCT
ejpam-3019	305	10	b.	b.	PROPN
ejpam-3019	305	11	mutlu	mutlu	PROPN
ejpam-3019	305	12	.	.	PUNCT
ejpam-3019	305	13	coupled	couple	VERB
ejpam-3019	305	14	fixed	fix	VERB
ejpam-3019	305	15	point	point	NOUN
ejpam-3019	305	16	theorem	theorem	NOUN
ejpam-3019	305	17	for	for	ADP
ejpam-3019	305	18	mixed	mixed	ADJ
ejpam-3019	305	19	monotone	monotone	ADJ
ejpam-3019	305	20	mappings	mapping	NOUN
ejpam-3019	305	21	on	on	ADP
ejpam-3019	305	22	partially	partially	ADV
ejpam-3019	305	23	ordered	order	VERB
ejpam-3019	305	24	dislocated	dislocated	ADJ
ejpam-3019	305	25	quasi	quasi	ADJ
ejpam-3019	305	26	metric	metric	ADJ
ejpam-3019	305	27	spaces	space	NOUN
ejpam-3019	305	28	,	,	PUNCT
ejpam-3019	305	29	global	global	ADJ
ejpam-3019	305	30	journal	journal	NOUN
ejpam-3019	305	31	of	of	ADP
ejpam-3019	305	32	mathematics	mathematic	NOUN
ejpam-3019	305	33	1(1	1(1	NUM
ejpam-3019	305	34	)	)	PUNCT
ejpam-3019	305	35	,	,	PUNCT
ejpam-3019	305	36	12	12	NUM
ejpam-3019	305	37	-	-	SYM
ejpam-3019	305	38	17	17	NUM
ejpam-3019	305	39	,	,	PUNCT
ejpam-3019	305	40	2015	2015	NUM
ejpam-3019	305	41	.	.	PUNCT
ejpam-3019	306	1	[	[	X
ejpam-3019	306	2	12	12	NUM
ejpam-3019	306	3	]	]	PUNCT
ejpam-3019	306	4	a.	a.	NOUN
ejpam-3019	306	5	mutlu	mutlu	PROPN
ejpam-3019	306	6	,	,	PUNCT
ejpam-3019	306	7	n.	n.	PROPN
ejpam-3019	306	8	yolcu	yolcu	PROPN
ejpam-3019	306	9	,	,	PUNCT
ejpam-3019	306	10	b.	b.	PROPN
ejpam-3019	306	11	mutlu	mutlu	PROPN
ejpam-3019	306	12	.	.	PUNCT
ejpam-3019	307	1	fixed	fix	VERB
ejpam-3019	307	2	point	point	NOUN
ejpam-3019	307	3	theorems	theorem	NOUN
ejpam-3019	307	4	in	in	ADP
ejpam-3019	307	5	partially	partially	ADV
ejpam-3019	307	6	ordered	order	VERB
ejpam-3019	307	7	rectangular	rectangular	ADJ
ejpam-3019	307	8	metric	metric	ADJ
ejpam-3019	307	9	spaces	space	NOUN
ejpam-3019	307	10	,	,	PUNCT
ejpam-3019	307	11	british	british	ADJ
ejpam-3019	307	12	journal	journal	PROPN
ejpam-3019	307	13	of	of	ADP
ejpam-3019	307	14	mathematics	mathematics	PROPN
ejpam-3019	307	15	&	&	CCONJ
ejpam-3019	307	16	computer	computer	PROPN
ejpam-3019	307	17	science	science	NOUN
ejpam-3019	307	18	15(2	15(2	NUM
ejpam-3019	307	19	)	)	PUNCT
ejpam-3019	307	20	,	,	PUNCT
ejpam-3019	307	21	1	1	NUM
ejpam-3019	307	22	-	-	SYM
ejpam-3019	307	23	9	9	NUM
ejpam-3019	307	24	,	,	PUNCT
ejpam-3019	307	25	2016	2016	NUM
ejpam-3019	307	26	.	.	PUNCT
ejpam-3019	308	1	[	[	X
ejpam-3019	308	2	13	13	NUM
ejpam-3019	308	3	]	]	PUNCT
ejpam-3019	308	4	a.	a.	NOUN
ejpam-3019	308	5	mutlu	mutlu	PROPN
ejpam-3019	308	6	,	,	PUNCT
ejpam-3019	308	7	u.	u.	PROPN
ejpam-3019	308	8	gürdal	gürdal	PROPN
ejpam-3019	308	9	.	.	PUNCT
ejpam-3019	309	1	bipolar	bipolar	ADJ
ejpam-3019	309	2	metric	metric	ADJ
ejpam-3019	309	3	spaces	space	NOUN
ejpam-3019	309	4	and	and	CCONJ
ejpam-3019	309	5	some	some	DET
ejpam-3019	309	6	fixed	fix	VERB
ejpam-3019	309	7	point	point	NOUN
ejpam-3019	309	8	theorems	theorem	NOUN
ejpam-3019	309	9	,	,	PUNCT
ejpam-3019	309	10	j.	j.	PROPN
ejpam-3019	309	11	nonlinear	nonlinear	PROPN
ejpam-3019	309	12	sci	sci	PROPN
ejpam-3019	309	13	.	.	PUNCT
ejpam-3019	309	14	appl	appl	PROPN
ejpam-3019	309	15	.	.	PUNCT
ejpam-3019	310	1	9(9	9(9	NUM
ejpam-3019	310	2	)	)	PUNCT
ejpam-3019	310	3	,	,	PUNCT
ejpam-3019	310	4	5362–5373	5362–5373	NUM
ejpam-3019	310	5	,	,	PUNCT
ejpam-3019	310	6	2016	2016	NUM
ejpam-3019	310	7	.	.	PUNCT
ejpam-3019	311	1	[	[	X
ejpam-3019	311	2	14	14	NUM
ejpam-3019	311	3	]	]	PUNCT
ejpam-3019	311	4	a.	a.	NOUN
ejpam-3019	311	5	mutlu	mutlu	PROPN
ejpam-3019	311	6	,	,	PUNCT
ejpam-3019	311	7	,	,	PUNCT
ejpam-3019	311	8	k.	k.	PROPN
ejpam-3019	311	9	özkan	özkan	PROPN
ejpam-3019	311	10	,	,	PUNCT
ejpam-3019	311	11	u.	u.	PROPN
ejpam-3019	311	12	gürdal	gürdal	PROPN
ejpam-3019	311	13	.	.	PUNCT
ejpam-3019	311	14	coupled	couple	VERB
ejpam-3019	311	15	fixed	fix	VERB
ejpam-3019	311	16	point	point	NOUN
ejpam-3019	311	17	theorem	theorem	VERB
ejpam-3019	311	18	in	in	ADP
ejpam-3019	311	19	partially	partially	ADV
ejpam-3019	311	20	ordered	order	VERB
ejpam-3019	311	21	modular	modular	ADJ
ejpam-3019	311	22	metric	metric	ADJ
ejpam-3019	311	23	spaces	space	NOUN
ejpam-3019	311	24	and	and	CCONJ
ejpam-3019	311	25	its	its	PRON
ejpam-3019	311	26	an	an	DET
ejpam-3019	311	27	application	application	NOUN
ejpam-3019	311	28	,	,	PUNCT
ejpam-3019	311	29	j.	j.	PROPN
ejpam-3019	311	30	comput	comput	PROPN
ejpam-3019	311	31	.	.	PUNCT
ejpam-3019	312	1	anal	anal	PROPN
ejpam-3019	312	2	.	.	PUNCT
ejpam-3019	312	3	appl	appl	PROPN
ejpam-3019	312	4	.	.	PUNCT
ejpam-3019	313	1	25(2	25(2	NUM
ejpam-3019	313	2	)	)	PUNCT
ejpam-3019	313	3	,	,	PUNCT
ejpam-3019	313	4	207–216	207–216	NUM
ejpam-3019	313	5	,	,	PUNCT
ejpam-3019	313	6	2018	2018	NUM
ejpam-3019	313	7	.	.	PUNCT
ejpam-3019	314	1	[	[	X
ejpam-3019	314	2	15	15	NUM
ejpam-3019	314	3	]	]	PUNCT
ejpam-3019	314	4	a.	a.	NOUN
ejpam-3019	314	5	petruşel	petruşel	PROPN
ejpam-3019	314	6	,	,	PUNCT
ejpam-3019	314	7	g.	g.	PROPN
ejpam-3019	314	8	petruşel	petruşel	PROPN
ejpam-3019	314	9	,	,	PUNCT
ejpam-3019	314	10	b.	b.	PROPN
ejpam-3019	314	11	samet	samet	PROPN
ejpam-3019	314	12	,	,	PUNCT
ejpam-3019	314	13	j.c	j.c	PROPN
ejpam-3019	314	14	.	.	PROPN
ejpam-3019	314	15	yao	yao	PROPN
ejpam-3019	314	16	.	.	PUNCT
ejpam-3019	314	17	coupled	couple	VERB
ejpam-3019	314	18	fixed	fix	VERB
ejpam-3019	314	19	point	point	NOUN
ejpam-3019	314	20	theorems	theorem	NOUN
ejpam-3019	314	21	for	for	ADP
ejpam-3019	314	22	symmetric	symmetric	ADJ
ejpam-3019	314	23	contractions	contraction	NOUN
ejpam-3019	314	24	in	in	ADP
ejpam-3019	314	25	b	b	NOUN
ejpam-3019	314	26	-	-	ADJ
ejpam-3019	314	27	metric	metric	ADJ
ejpam-3019	314	28	spaces	space	NOUN
ejpam-3019	314	29	with	with	ADP
ejpam-3019	314	30	applications	application	NOUN
ejpam-3019	314	31	to	to	PART
ejpam-3019	314	32	operator	operator	VERB
ejpam-3019	314	33	equation	equation	NOUN
ejpam-3019	314	34	systems	system	NOUN
ejpam-3019	314	35	,	,	PUNCT
ejpam-3019	314	36	fixed	fix	VERB
ejpam-3019	314	37	point	point	NOUN
ejpam-3019	314	38	theory	theory	NOUN
ejpam-3019	314	39	17(2	17(2	NUM
ejpam-3019	314	40	)	)	PUNCT
ejpam-3019	314	41	,	,	PUNCT
ejpam-3019	314	42	457–476	457–476	NUM
ejpam-3019	314	43	,	,	PUNCT
ejpam-3019	314	44	2016	2016	NUM
ejpam-3019	314	45	.	.	PUNCT
ejpam-3019	315	1	[	[	X
ejpam-3019	315	2	16	16	NUM
ejpam-3019	315	3	]	]	X
ejpam-3019	315	4	f.	f.	PROPN
ejpam-3019	315	5	sabetghadam	sabetghadam	PROPN
ejpam-3019	315	6	,	,	PUNCT
ejpam-3019	315	7	h.p	h.p	PROPN
ejpam-3019	315	8	.	.	PROPN
ejpam-3019	315	9	masiha	masiha	PROPN
ejpam-3019	315	10	,	,	PUNCT
ejpam-3019	315	11	a.h	a.h	PROPN
ejpam-3019	315	12	.	.	PROPN
ejpam-3019	315	13	sanatpour	sanatpour	PROPN
ejpam-3019	315	14	.	.	PUNCT
ejpam-3019	316	1	some	some	DET
ejpam-3019	316	2	coupled	couple	VERB
ejpam-3019	316	3	fixed	fix	VERB
ejpam-3019	316	4	point	point	NOUN
ejpam-3019	316	5	theorems	theorem	NOUN
ejpam-3019	316	6	in	in	ADP
ejpam-3019	316	7	cone	cone	NOUN
ejpam-3019	316	8	metric	metric	ADJ
ejpam-3019	316	9	spaces	space	NOUN
ejpam-3019	316	10	,	,	PUNCT
ejpam-3019	316	11	fixed	fix	VERB
ejpam-3019	316	12	point	point	NOUN
ejpam-3019	316	13	theory	theory	NOUN
ejpam-3019	316	14	appl	appl	NOUN
ejpam-3019	316	15	.	.	PROPN
ejpam-3019	316	16	8	8	NUM
ejpam-3019	316	17	pages	page	NOUN
ejpam-3019	316	18	article	article	NOUN
ejpam-3019	316	19	i	i	PROPN
ejpam-3019	316	20	d	d	PROPN
ejpam-3019	316	21	125426	125426	NUM
ejpam-3019	316	22	(	(	PUNCT
ejpam-3019	316	23	2009	2009	NUM
ejpam-3019	316	24	)	)	PUNCT
ejpam-3019	316	25	doi:10.1155/2009/125426	doi:10.1155/2009/125426	PROPN
ejpam-3019	316	26	.	.	PUNCT
ejpam-3019	317	1	[	[	X
ejpam-3019	317	2	17	17	NUM
ejpam-3019	317	3	]	]	X
ejpam-3019	317	4	b.	b.	PROPN
ejpam-3019	317	5	samet	samet	PROPN
ejpam-3019	317	6	.	.	PUNCT
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ejpam-3019	318	2	fixed	fix	VERB
ejpam-3019	318	3	point	point	NOUN
ejpam-3019	318	4	theorems	theorem	NOUN
ejpam-3019	318	5	for	for	ADP
ejpam-3019	318	6	a	a	DET
ejpam-3019	318	7	generalized	generalized	ADJ
ejpam-3019	318	8	meir	meir	PROPN
ejpam-3019	318	9	-	-	PUNCT
ejpam-3019	318	10	keeler	keeler	PROPN
ejpam-3019	318	11	contraction	contraction	NOUN
ejpam-3019	318	12	in	in	ADP
ejpam-3019	318	13	partially	partially	ADV
ejpam-3019	318	14	ordered	order	VERB
ejpam-3019	318	15	metric	metric	ADJ
ejpam-3019	318	16	spaces	space	NOUN
ejpam-3019	318	17	,	,	PUNCT
ejpam-3019	318	18	nonlinear	nonlinear	ADJ
ejpam-3019	318	19	anal	anal	NOUN
ejpam-3019	318	20	.	.	PUNCT
ejpam-3019	319	1	72	72	NUM
ejpam-3019	319	2	,	,	PUNCT
ejpam-3019	319	3	4508	4508	NUM
ejpam-3019	319	4	-	-	SYM
ejpam-3019	319	5	4517	4517	NUM
ejpam-3019	319	6	,	,	PUNCT
ejpam-3019	319	7	2010	2010	NUM
ejpam-3019	319	8	.	.	PUNCT
ejpam-3019	320	1	[	[	X
ejpam-3019	320	2	18	18	NUM
ejpam-3019	320	3	]	]	X
ejpam-3019	320	4	w.	w.	PROPN
ejpam-3019	320	5	shatanawi	shatanawi	PROPN
ejpam-3019	320	6	,	,	PUNCT
ejpam-3019	320	7	e.	e.	PROPN
ejpam-3019	320	8	karapinar	karapinar	PROPN
ejpam-3019	320	9	,	,	PUNCT
ejpam-3019	320	10	h.	h.	PROPN
ejpam-3019	320	11	aydi	aydi	VERB
ejpam-3019	320	12	.	.	PUNCT
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ejpam-3019	321	2	coincidence	coincidence	NOUN
ejpam-3019	321	3	points	point	NOUN
ejpam-3019	321	4	in	in	ADP
ejpam-3019	321	5	partially	partially	ADV
ejpam-3019	321	6	ordered	order	VERB
ejpam-3019	321	7	cone	cone	NOUN
ejpam-3019	321	8	metric	metric	ADJ
ejpam-3019	321	9	spaces	space	NOUN
ejpam-3019	321	10	with	with	ADP
ejpam-3019	321	11	a	a	DET
ejpam-3019	321	12	c	c	NOUN
ejpam-3019	321	13	-	-	PUNCT
ejpam-3019	321	14	distance	distance	NOUN
ejpam-3019	321	15	,	,	PUNCT
ejpam-3019	321	16	journal	journal	NOUN
ejpam-3019	321	17	of	of	ADP
ejpam-3019	321	18	applied	apply	VERB
ejpam-3019	321	19	mathematics	mathematic	NOUN
ejpam-3019	321	20	2012	2012	NUM
ejpam-3019	321	21	,	,	PUNCT
ejpam-3019	321	22	article	article	NOUN
ejpam-3019	321	23	i	i	PROPN
ejpam-3019	321	24	d	d	PROPN
ejpam-3019	321	25	312078	312078	NUM
ejpam-3019	321	26	,	,	PUNCT
ejpam-3019	321	27	2012	2012	NUM
ejpam-3019	321	28	.	.	PUNCT
ejpam-3019	322	1	[	[	X
ejpam-3019	322	2	19	19	NUM
ejpam-3019	322	3	]	]	X
ejpam-3019	322	4	w.	w.	PROPN
ejpam-3019	322	5	shatanawi	shatanawi	PROPN
ejpam-3019	322	6	,	,	PUNCT
ejpam-3019	322	7	a.	a.	NOUN
ejpam-3019	322	8	pitea	pitea	NOUN
ejpam-3019	322	9	.	.	PUNCT
ejpam-3019	323	1	some	some	DET
ejpam-3019	323	2	coupled	couple	VERB
ejpam-3019	323	3	fixed	fix	VERB
ejpam-3019	323	4	point	point	NOUN
ejpam-3019	323	5	theorems	theorem	NOUN
ejpam-3019	323	6	in	in	ADP
ejpam-3019	323	7	quasi	quasi	ADJ
ejpam-3019	323	8	-	-	ADJ
ejpam-3019	323	9	partial	partial	ADJ
ejpam-3019	323	10	metric	metric	ADJ
ejpam-3019	323	11	spaces	space	NOUN
ejpam-3019	323	12	,	,	PUNCT
ejpam-3019	323	13	fixed	fix	VERB
ejpam-3019	323	14	point	point	NOUN
ejpam-3019	323	15	theory	theory	NOUN
ejpam-3019	323	16	appl	appl	NOUN
ejpam-3019	323	17	.	.	PUNCT
ejpam-3019	323	18	2013(153	2013(153	NUM
ejpam-3019	323	19	)	)	PUNCT
ejpam-3019	323	20	,	,	PUNCT
ejpam-3019	323	21	1	1	NUM
ejpam-3019	323	22	-	-	SYM
ejpam-3019	323	23	15	15	NUM
ejpam-3019	323	24	,	,	PUNCT
ejpam-3019	323	25	2013	2013	NUM
ejpam-3019	323	26	.	.	PUNCT
ejpam-3019	323	27	references	reference	NOUN
ejpam-3019	323	28	667	667	NUM
ejpam-3019	323	29	[	[	SYM
ejpam-3019	323	30	20	20	NUM
ejpam-3019	323	31	]	]	X
ejpam-3019	323	32	n.	n.	PROPN
ejpam-3019	323	33	tahat	tahat	PROPN
ejpam-3019	323	34	,	,	PUNCT
ejpam-3019	323	35	h.	h.	PROPN
ejpam-3019	323	36	aydi	aydi	PROPN
ejpam-3019	323	37	,	,	PUNCT
ejpam-3019	323	38	e.	e.	PROPN
ejpam-3019	323	39	karapinar	karapinar	PROPN
ejpam-3019	323	40	,	,	PUNCT
ejpam-3019	323	41	w.	w.	PROPN
ejpam-3019	323	42	shatanawi	shatanawi	PROPN
ejpam-3019	323	43	.	.	PUNCT
ejpam-3019	324	1	common	common	ADJ
ejpam-3019	324	2	fixed	fix	VERB
ejpam-3019	324	3	points	point	NOUN
ejpam-3019	324	4	for	for	ADP
ejpam-3019	324	5	singlevalued	singlevalue	VERB
ejpam-3019	324	6	and	and	CCONJ
ejpam-3019	324	7	multi	multi	ADJ
ejpam-3019	324	8	-	-	ADJ
ejpam-3019	324	9	valued	value	VERB
ejpam-3019	324	10	maps	map	NOUN
ejpam-3019	324	11	satisfying	satisfy	VERB
ejpam-3019	324	12	a	a	DET
ejpam-3019	324	13	generalized	generalized	ADJ
ejpam-3019	324	14	contraction	contraction	NOUN
ejpam-3019	324	15	in	in	ADP
ejpam-3019	324	16	g	g	NOUN
ejpam-3019	324	17	-	-	PUNCT
ejpam-3019	324	18	metric	metric	ADJ
ejpam-3019	324	19	spaces	space	NOUN
ejpam-3019	324	20	,	,	PUNCT
ejpam-3019	324	21	fixed	fix	VERB
ejpam-3019	324	22	point	point	NOUN
ejpam-3019	324	23	theory	theory	NOUN
ejpam-3019	324	24	appl	appl	NOUN
ejpam-3019	324	25	.	.	PUNCT
ejpam-3019	325	1	2012(48	2012(48	NUM
ejpam-3019	325	2	)	)	PUNCT
ejpam-3019	325	3	,	,	PUNCT
ejpam-3019	325	4	2012	2012	NUM
ejpam-3019	325	5	,	,	PUNCT
ejpam-3019	325	6	doi:10.1186/1687	doi:10.1186/1687	NOUN
ejpam-3019	325	7	-	-	PUNCT
ejpam-3019	325	8	1812	1812	NUM
ejpam-3019	325	9	-	-	PUNCT
ejpam-3019	325	10	2012	2012	NUM
ejpam-3019	325	11	-	-	SYM
ejpam-3019	325	12	48	48	NUM
ejpam-3019	325	13	.	.	PUNCT