id	sid	tid	token	lemma	pos
ejpam-3391	1	1	european	european	PROPN
ejpam-3391	1	2	journal	journal	PROPN
ejpam-3391	1	3	of	of	ADP
ejpam-3391	1	4	pure	pure	ADJ
ejpam-3391	1	5	and	and	CCONJ
ejpam-3391	1	6	applied	apply	VERB
ejpam-3391	1	7	mathematics	mathematic	NOUN
ejpam-3391	1	8	vol	vol	NOUN
ejpam-3391	1	9	.	.	PROPN
ejpam-3391	2	1	12	12	NUM
ejpam-3391	2	2	,	,	PUNCT
ejpam-3391	2	3	no	no	INTJ
ejpam-3391	2	4	.	.	NOUN
ejpam-3391	2	5	2	2	NUM
ejpam-3391	2	6	,	,	PUNCT
ejpam-3391	2	7	2019	2019	NUM
ejpam-3391	2	8	,	,	PUNCT
ejpam-3391	2	9	418	418	NUM
ejpam-3391	2	10	-	-	SYM
ejpam-3391	2	11	431	431	NUM
ejpam-3391	2	12	issn	issn	PROPN
ejpam-3391	2	13	1307	1307	NUM
ejpam-3391	2	14	-	-	SYM
ejpam-3391	2	15	5543	5543	NUM
ejpam-3391	2	16	–	–	PUNCT
ejpam-3391	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3391	2	18	published	publish	VERB
ejpam-3391	2	19	by	by	ADP
ejpam-3391	2	20	new	new	PROPN
ejpam-3391	2	21	york	york	PROPN
ejpam-3391	2	22	business	business	PROPN
ejpam-3391	2	23	global	global	ADJ
ejpam-3391	2	24	convergence	convergence	NOUN
ejpam-3391	2	25	of	of	ADP
ejpam-3391	2	26	β	β	NOUN
ejpam-3391	2	27	-	-	ADJ
ejpam-3391	2	28	modified	modify	VERB
ejpam-3391	2	29	jacobi	jacobi	PROPN
ejpam-3391	2	30	-	-	PUNCT
ejpam-3391	2	31	perron	perron	PROPN
ejpam-3391	2	32	algorithm	algorithm	NOUN
ejpam-3391	2	33	over	over	ADP
ejpam-3391	2	34	the	the	DET
ejpam-3391	2	35	field	field	NOUN
ejpam-3391	2	36	of	of	ADP
ejpam-3391	2	37	formal	formal	ADJ
ejpam-3391	2	38	power	power	NOUN
ejpam-3391	2	39	series	series	PROPN
ejpam-3391	2	40	amara	amara	PROPN
ejpam-3391	2	41	chandoul1	chandoul1	PROPN
ejpam-3391	2	42	,	,	PUNCT
ejpam-3391	2	43	fahad	fahad	PROPN
ejpam-3391	2	44	aljuaydi2,∗	aljuaydi2,∗	NOUN
ejpam-3391	2	45	1	1	NUM
ejpam-3391	2	46	departamento	departamento	PROPN
ejpam-3391	2	47	de	de	PROPN
ejpam-3391	2	48	matemática	matemática	PROPN
ejpam-3391	2	49	,	,	PUNCT
ejpam-3391	2	50	universidade	universidade	PROPN
ejpam-3391	2	51	de	de	PROPN
ejpam-3391	2	52	braśılia	braśılia	PROPN
ejpam-3391	2	53	,	,	PUNCT
ejpam-3391	2	54	campus	campus	PROPN
ejpam-3391	2	55	universitário	universitário	ADP
ejpam-3391	2	56	darcy	darcy	PROPN
ejpam-3391	2	57	ribeiro	ribeiro	PROPN
ejpam-3391	2	58	braśılia	braśılia	PROPN
ejpam-3391	2	59	df	df	PROPN
ejpam-3391	2	60	70910	70910	NUM
ejpam-3391	2	61	-	-	SYM
ejpam-3391	2	62	900	900	NUM
ejpam-3391	2	63	,	,	PUNCT
ejpam-3391	2	64	brazil	brazil	PROPN
ejpam-3391	2	65	2	2	NUM
ejpam-3391	2	66	department	department	NOUN
ejpam-3391	2	67	of	of	ADP
ejpam-3391	2	68	mathematics	mathematic	NOUN
ejpam-3391	2	69	,	,	PUNCT
ejpam-3391	2	70	college	college	NOUN
ejpam-3391	2	71	of	of	ADP
ejpam-3391	2	72	sciences	science	NOUN
ejpam-3391	2	73	and	and	CCONJ
ejpam-3391	2	74	humanities	humanity	NOUN
ejpam-3391	2	75	,	,	PUNCT
ejpam-3391	2	76	prince	prince	PROPN
ejpam-3391	2	77	sattam	sattam	PROPN
ejpam-3391	2	78	bin	bin	PROPN
ejpam-3391	2	79	abdulaziz	abdulaziz	PROPN
ejpam-3391	2	80	university	university	PROPN
ejpam-3391	2	81	,	,	PUNCT
ejpam-3391	2	82	al	al	PROPN
ejpam-3391	2	83	-	-	PUNCT
ejpam-3391	2	84	kharj	kharj	PROPN
ejpam-3391	2	85	,	,	PUNCT
ejpam-3391	2	86	saudi	saudi	PROPN
ejpam-3391	2	87	arabia	arabia	PROPN
ejpam-3391	2	88	abstract	abstract	NOUN
ejpam-3391	2	89	.	.	PUNCT
ejpam-3391	3	1	the	the	DET
ejpam-3391	3	2	aim	aim	NOUN
ejpam-3391	3	3	of	of	ADP
ejpam-3391	3	4	this	this	DET
ejpam-3391	3	5	paper	paper	NOUN
ejpam-3391	3	6	is	be	AUX
ejpam-3391	3	7	to	to	PART
ejpam-3391	3	8	study	study	VERB
ejpam-3391	3	9	multidimentional	multidimentional	ADJ
ejpam-3391	3	10	β	β	X
ejpam-3391	3	11	-	-	ADJ
ejpam-3391	3	12	continued	continue	VERB
ejpam-3391	3	13	fraction	fraction	NOUN
ejpam-3391	3	14	algorithm	algorithm	NOUN
ejpam-3391	3	15	over	over	ADP
ejpam-3391	3	16	the	the	DET
ejpam-3391	3	17	field	field	NOUN
ejpam-3391	3	18	of	of	ADP
ejpam-3391	3	19	formal	formal	ADJ
ejpam-3391	3	20	power	power	NOUN
ejpam-3391	3	21	series	series	NOUN
ejpam-3391	3	22	.	.	PUNCT
ejpam-3391	4	1	in	in	ADP
ejpam-3391	4	2	the	the	DET
ejpam-3391	4	3	case	case	NOUN
ejpam-3391	4	4	of	of	ADP
ejpam-3391	4	5	the	the	DET
ejpam-3391	4	6	modified	modify	VERB
ejpam-3391	4	7	jacobi	jacobi	PROPN
ejpam-3391	4	8	-	-	PUNCT
ejpam-3391	4	9	perron	perron	PROPN
ejpam-3391	4	10	algorithm	algorithm	NOUN
ejpam-3391	4	11	,	,	PUNCT
ejpam-3391	4	12	we	we	PRON
ejpam-3391	4	13	prove	prove	VERB
ejpam-3391	4	14	that	that	SCONJ
ejpam-3391	4	15	it	it	PRON
ejpam-3391	4	16	converges	converge	VERB
ejpam-3391	4	17	.	.	PUNCT
ejpam-3391	5	1	2010	2010	NUM
ejpam-3391	5	2	mathematics	mathematic	NOUN
ejpam-3391	5	3	subject	subject	NOUN
ejpam-3391	5	4	classifications	classification	NOUN
ejpam-3391	5	5	:	:	PUNCT
ejpam-3391	5	6	40a15	40a15	NUM
ejpam-3391	5	7	key	key	ADJ
ejpam-3391	5	8	words	word	NOUN
ejpam-3391	5	9	and	and	CCONJ
ejpam-3391	5	10	phrases	phrase	NOUN
ejpam-3391	5	11	:	:	PUNCT
ejpam-3391	5	12	β	β	X
ejpam-3391	5	13	-	-	ADJ
ejpam-3391	5	14	continued	continue	VERB
ejpam-3391	5	15	fractions	fraction	NOUN
ejpam-3391	5	16	,	,	PUNCT
ejpam-3391	5	17	modidied	modidie	VERB
ejpam-3391	5	18	jacobi	jacobi	PROPN
ejpam-3391	5	19	-	-	PUNCT
ejpam-3391	5	20	perron	perron	PROPN
ejpam-3391	5	21	algorithm	algorithm	NOUN
ejpam-3391	5	22	,	,	PUNCT
ejpam-3391	5	23	convergence	convergence	NOUN
ejpam-3391	5	24	,	,	PUNCT
ejpam-3391	5	25	formal	formal	ADJ
ejpam-3391	5	26	power	power	NOUN
ejpam-3391	5	27	series	series	NOUN
ejpam-3391	5	28	.	.	PUNCT
ejpam-3391	6	1	1	1	X
ejpam-3391	6	2	.	.	X
ejpam-3391	6	3	introduction	introduction	NOUN
ejpam-3391	6	4	in	in	ADP
ejpam-3391	6	5	[	[	X
ejpam-3391	6	6	4	4	NUM
ejpam-3391	6	7	]	]	PUNCT
ejpam-3391	6	8	,	,	PUNCT
ejpam-3391	6	9	we	we	PRON
ejpam-3391	6	10	studied	study	VERB
ejpam-3391	6	11	multidimensional	multidimensional	ADJ
ejpam-3391	6	12	continued	continued	ADJ
ejpam-3391	6	13	fraction	fraction	NOUN
ejpam-3391	6	14	algorithm	algorithm	NOUN
ejpam-3391	6	15	over	over	ADP
ejpam-3391	6	16	the	the	DET
ejpam-3391	6	17	field	field	NOUN
ejpam-3391	6	18	of	of	ADP
ejpam-3391	6	19	formal	formal	ADJ
ejpam-3391	6	20	power	power	NOUN
ejpam-3391	6	21	series	series	NOUN
ejpam-3391	6	22	.	.	PUNCT
ejpam-3391	7	1	in	in	ADP
ejpam-3391	7	2	the	the	DET
ejpam-3391	7	3	case	case	NOUN
ejpam-3391	7	4	of	of	ADP
ejpam-3391	7	5	the	the	DET
ejpam-3391	7	6	brun	brun	NOUN
ejpam-3391	7	7	algorithm	algorithm	NOUN
ejpam-3391	7	8	by	by	ADP
ejpam-3391	7	9	using	use	VERB
ejpam-3391	7	10	its	its	PRON
ejpam-3391	7	11	homogenous	homogenous	ADJ
ejpam-3391	7	12	version	version	NOUN
ejpam-3391	7	13	,	,	PUNCT
ejpam-3391	7	14	we	we	PRON
ejpam-3391	7	15	prove	prove	VERB
ejpam-3391	7	16	that	that	SCONJ
ejpam-3391	7	17	it	it	PRON
ejpam-3391	7	18	converges	converge	VERB
ejpam-3391	7	19	.	.	PUNCT
ejpam-3391	8	1	in	in	ADP
ejpam-3391	8	2	this	this	DET
ejpam-3391	8	3	paper	paper	NOUN
ejpam-3391	8	4	,	,	PUNCT
ejpam-3391	8	5	we	we	PRON
ejpam-3391	8	6	study	study	VERB
ejpam-3391	8	7	multidimentional	multidimentional	ADJ
ejpam-3391	8	8	β	β	X
ejpam-3391	8	9	-	-	ADJ
ejpam-3391	8	10	continued	continue	VERB
ejpam-3391	8	11	fraction	fraction	NOUN
ejpam-3391	8	12	in	in	ADP
ejpam-3391	8	13	the	the	DET
ejpam-3391	8	14	case	case	NOUN
ejpam-3391	8	15	of	of	ADP
ejpam-3391	8	16	the	the	DET
ejpam-3391	8	17	modified	modify	VERB
ejpam-3391	8	18	jacobi	jacobi	PROPN
ejpam-3391	8	19	perron	perron	PROPN
ejpam-3391	8	20	algorithm	algorithm	PROPN
ejpam-3391	8	21	(	(	PUNCT
ejpam-3391	8	22	mjpa	mjpa	PROPN
ejpam-3391	8	23	)	)	PUNCT
ejpam-3391	8	24	,	,	PUNCT
ejpam-3391	8	25	we	we	PRON
ejpam-3391	8	26	prove	prove	VERB
ejpam-3391	8	27	that	that	SCONJ
ejpam-3391	8	28	it	it	PRON
ejpam-3391	8	29	converges	converge	VERB
ejpam-3391	8	30	.	.	PUNCT
ejpam-3391	9	1	2	2	X
ejpam-3391	9	2	.	.	X
ejpam-3391	9	3	the	the	DET
ejpam-3391	9	4	field	field	NOUN
ejpam-3391	9	5	of	of	ADP
ejpam-3391	9	6	formal	formal	ADJ
ejpam-3391	9	7	power	power	NOUN
ejpam-3391	9	8	series	series	NOUN
ejpam-3391	9	9	in	in	ADP
ejpam-3391	9	10	order	order	NOUN
ejpam-3391	9	11	to	to	PART
ejpam-3391	9	12	state	state	VERB
ejpam-3391	9	13	our	our	PRON
ejpam-3391	9	14	results	result	NOUN
ejpam-3391	9	15	,	,	PUNCT
ejpam-3391	9	16	we	we	PRON
ejpam-3391	9	17	need	need	VERB
ejpam-3391	9	18	to	to	PART
ejpam-3391	9	19	introduce	introduce	VERB
ejpam-3391	9	20	some	some	DET
ejpam-3391	9	21	basic	basic	ADJ
ejpam-3391	9	22	notion	notion	NOUN
ejpam-3391	9	23	of	of	ADP
ejpam-3391	9	24	the	the	DET
ejpam-3391	9	25	field	field	NOUN
ejpam-3391	9	26	of	of	ADP
ejpam-3391	9	27	formal	formal	ADJ
ejpam-3391	9	28	power	power	NOUN
ejpam-3391	9	29	series	series	NOUN
ejpam-3391	9	30	.	.	PUNCT
ejpam-3391	10	1	let	let	VERB
ejpam-3391	10	2	fq	fq	PRON
ejpam-3391	10	3	be	be	AUX
ejpam-3391	10	4	a	a	DET
ejpam-3391	10	5	field	field	NOUN
ejpam-3391	10	6	with	with	ADP
ejpam-3391	10	7	q	q	ADJ
ejpam-3391	10	8	elements	element	NOUN
ejpam-3391	10	9	of	of	ADP
ejpam-3391	10	10	characteristic	characteristic	ADJ
ejpam-3391	10	11	p	p	X
ejpam-3391	10	12	,	,	PUNCT
ejpam-3391	10	13	fq[x	fq[x	PROPN
ejpam-3391	10	14	]	]	PUNCT
ejpam-3391	10	15	the	the	DET
ejpam-3391	10	16	set	set	NOUN
ejpam-3391	10	17	of	of	ADP
ejpam-3391	10	18	polynomials	polynomial	NOUN
ejpam-3391	10	19	of	of	ADP
ejpam-3391	10	20	coefficients	coefficient	NOUN
ejpam-3391	10	21	in	in	ADP
ejpam-3391	10	22	fq	fq	PROPN
ejpam-3391	10	23	and	and	CCONJ
ejpam-3391	10	24	fq(x	fq(x	NOUN
ejpam-3391	10	25	)	)	PUNCT
ejpam-3391	10	26	its	its	PRON
ejpam-3391	10	27	field	field	NOUN
ejpam-3391	10	28	of	of	ADP
ejpam-3391	10	29	fractions	fraction	NOUN
ejpam-3391	10	30	.	.	PUNCT
ejpam-3391	11	1	the	the	DET
ejpam-3391	11	2	set	set	PROPN
ejpam-3391	11	3	fq((x−1	fq((x−1	NOUN
ejpam-3391	11	4	)	)	PUNCT
ejpam-3391	11	5	)	)	PUNCT
ejpam-3391	11	6	is	be	AUX
ejpam-3391	11	7	the	the	DET
ejpam-3391	11	8	field	field	NOUN
ejpam-3391	11	9	of	of	ADP
ejpam-3391	11	10	formal	formal	ADJ
ejpam-3391	11	11	power	power	NOUN
ejpam-3391	11	12	series	series	NOUN
ejpam-3391	11	13	over	over	ADP
ejpam-3391	11	14	fq	fq	PROPN
ejpam-3391	11	15	fq((x−1	fq((x−1	NOUN
ejpam-3391	11	16	)	)	PUNCT
ejpam-3391	11	17	)	)	PUNCT
ejpam-3391	12	1	=	=	PRON
ejpam-3391	12	2	{	{	PUNCT
ejpam-3391	13	1	f	f	X
ejpam-3391	13	2	=	=	PUNCT
ejpam-3391	14	1	+	+	ADJ
ejpam-3391	14	2	∞∑	∞∑	NUM
ejpam-3391	14	3	j	j	NOUN
ejpam-3391	14	4	=	=	NOUN
ejpam-3391	14	5	s	s	PART
ejpam-3391	14	6	fjx	fjx	NOUN
ejpam-3391	14	7	−j	−j	NOUN
ejpam-3391	14	8	:	:	PUNCT
ejpam-3391	14	9	fj	fj	PROPN
ejpam-3391	14	10	∈	∈	PROPN
ejpam-3391	14	11	fq	fq	PROPN
ejpam-3391	14	12	,	,	PUNCT
ejpam-3391	14	13	s	s	PART
ejpam-3391	14	14	∈	∈	PROPN
ejpam-3391	14	15	z	z	NOUN
ejpam-3391	14	16	}	}	PUNCT
ejpam-3391	14	17	.	.	PUNCT
ejpam-3391	15	1	∗corresponding	∗corresponde	VERB
ejpam-3391	15	2	author	author	NOUN
ejpam-3391	15	3	.	.	PUNCT
ejpam-3391	16	1	doi	doi	NOUN
ejpam-3391	16	2	:	:	PUNCT
ejpam-3391	16	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3391	https://doi.org/10.29020/nybg.ejpam.v12i2.3391	PROPN
ejpam-3391	16	4	email	email	NOUN
ejpam-3391	16	5	addresses	address	NOUN
ejpam-3391	16	6	:	:	PUNCT
ejpam-3391	16	7	amarachandoul@yahoo.fr	amarachandoul@yahoo.fr	PROPN
ejpam-3391	16	8	(	(	PUNCT
ejpam-3391	16	9	a.	a.	NOUN
ejpam-3391	16	10	chandoul	chandoul	PROPN
ejpam-3391	16	11	)	)	PUNCT
ejpam-3391	16	12	,	,	PUNCT
ejpam-3391	16	13	f.m.427@hotmail.com	f.m.427@hotmail.com	PROPN
ejpam-3391	16	14	(	(	PUNCT
ejpam-3391	16	15	f.	f.	PROPN
ejpam-3391	16	16	aljuaydi	aljuaydi	PROPN
ejpam-3391	16	17	)	)	PUNCT
ejpam-3391	16	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3391	17	1	418	418	NUM
ejpam-3391	18	1	c	c	X
ejpam-3391	18	2	©	©	PROPN
ejpam-3391	18	3	2019	2019	NUM
ejpam-3391	18	4	ejpam	ejpam	NOUN
ejpam-3391	18	5	all	all	DET
ejpam-3391	18	6	rights	right	NOUN
ejpam-3391	18	7	reserved	reserve	VERB
ejpam-3391	18	8	.	.	PUNCT
ejpam-3391	19	1	a.	a.	PROPN
ejpam-3391	19	2	chandoul	chandoul	PROPN
ejpam-3391	19	3	,	,	PUNCT
ejpam-3391	19	4	f.	f.	PROPN
ejpam-3391	19	5	aljuaydi	aljuaydi	PROPN
ejpam-3391	19	6	/	/	SYM
ejpam-3391	19	7	eur	eur	NOUN
ejpam-3391	19	8	.	.	PUNCT
ejpam-3391	20	1	j.	j.	PROPN
ejpam-3391	20	2	pure	pure	PROPN
ejpam-3391	20	3	appl	appl	PROPN
ejpam-3391	20	4	.	.	PROPN
ejpam-3391	20	5	math	math	PROPN
ejpam-3391	20	6	,	,	PUNCT
ejpam-3391	20	7	12	12	NUM
ejpam-3391	20	8	(	(	PUNCT
ejpam-3391	20	9	2	2	NUM
ejpam-3391	20	10	)	)	PUNCT
ejpam-3391	20	11	(	(	PUNCT
ejpam-3391	20	12	2019	2019	NUM
ejpam-3391	20	13	)	)	PUNCT
ejpam-3391	20	14	,	,	PUNCT
ejpam-3391	20	15	418	418	NUM
ejpam-3391	20	16	-	-	SYM
ejpam-3391	20	17	431	431	NUM
ejpam-3391	20	18	419	419	NUM
ejpam-3391	20	19	let	let	VERB
ejpam-3391	20	20	f	f	NOUN
ejpam-3391	20	21	=	=	PUNCT
ejpam-3391	21	1	+	+	ADJ
ejpam-3391	21	2	∞∑	∞∑	NUM
ejpam-3391	21	3	j	j	NOUN
ejpam-3391	21	4	=	=	NOUN
ejpam-3391	21	5	s	s	PART
ejpam-3391	21	6	fjx	fjx	NOUN
ejpam-3391	21	7	−j	−j	NOUN
ejpam-3391	21	8	∈	∈	PROPN
ejpam-3391	21	9	fq((x−1	fq((x−1	NOUN
ejpam-3391	21	10	)	)	PUNCT
ejpam-3391	21	11	)	)	PUNCT
ejpam-3391	21	12	,	,	PUNCT
ejpam-3391	21	13	where	where	SCONJ
ejpam-3391	21	14	fs	fs	ADP
ejpam-3391	21	15	6=	6=	PRON
ejpam-3391	21	16	0	0	NUM
ejpam-3391	21	17	.	.	PUNCT
ejpam-3391	22	1	we	we	PRON
ejpam-3391	22	2	denote	denote	VERB
ejpam-3391	22	3	its	its	PRON
ejpam-3391	22	4	polynomial	polynomial	ADJ
ejpam-3391	22	5	part	part	NOUN
ejpam-3391	22	6	by	by	ADP
ejpam-3391	22	7	[	[	X
ejpam-3391	22	8	f	f	X
ejpam-3391	22	9	]	]	PUNCT
ejpam-3391	22	10	and	and	CCONJ
ejpam-3391	22	11	by	by	ADP
ejpam-3391	22	12	{	{	PUNCT
ejpam-3391	22	13	f	f	X
ejpam-3391	22	14	}	}	PUNCT
ejpam-3391	22	15	its	its	PRON
ejpam-3391	22	16	fractional	fractional	ADJ
ejpam-3391	22	17	part	part	NOUN
ejpam-3391	22	18	.	.	PUNCT
ejpam-3391	23	1	we	we	PRON
ejpam-3391	23	2	remark	remark	VERB
ejpam-3391	23	3	that	that	SCONJ
ejpam-3391	23	4	f	f	PROPN
ejpam-3391	24	1	=	=	PUNCT
ejpam-3391	25	1	[	[	X
ejpam-3391	25	2	f	f	X
ejpam-3391	25	3	]	]	X
ejpam-3391	25	4	+	+	CCONJ
ejpam-3391	25	5	{	{	PUNCT
ejpam-3391	25	6	f	f	X
ejpam-3391	25	7	}	}	PUNCT
ejpam-3391	25	8	.	.	PUNCT
ejpam-3391	26	1	we	we	PRON
ejpam-3391	26	2	define	define	VERB
ejpam-3391	26	3	a	a	DET
ejpam-3391	26	4	non	non	ADJ
ejpam-3391	26	5	-	-	ADJ
ejpam-3391	26	6	archimedean	archimedean	ADJ
ejpam-3391	26	7	absolute	absolute	ADJ
ejpam-3391	26	8	value	value	NOUN
ejpam-3391	26	9	on	on	ADP
ejpam-3391	26	10	fq((x−1	fq((x−1	NOUN
ejpam-3391	26	11	)	)	PUNCT
ejpam-3391	26	12	)	)	PUNCT
ejpam-3391	26	13	by	by	ADP
ejpam-3391	26	14	|	|	ADV
ejpam-3391	26	15	f	f	PROPN
ejpam-3391	26	16	|=	|=	PUNCT
ejpam-3391	26	17	e−s	e−s	NOUN
ejpam-3391	26	18	and	and	CCONJ
ejpam-3391	26	19	|	|	ADV
ejpam-3391	26	20	0	0	NUM
ejpam-3391	26	21	|=	|=	NOUN
ejpam-3391	26	22	0	0	NUM
ejpam-3391	26	23	.	.	PUNCT
ejpam-3391	27	1	it	it	PRON
ejpam-3391	27	2	is	be	AUX
ejpam-3391	27	3	clear	clear	ADJ
ejpam-3391	27	4	that	that	SCONJ
ejpam-3391	27	5	,	,	PUNCT
ejpam-3391	27	6	for	for	ADP
ejpam-3391	27	7	any	any	DET
ejpam-3391	27	8	p	p	PROPN
ejpam-3391	27	9	∈	∈	PROPN
ejpam-3391	27	10	fq[x	fq[x	NOUN
ejpam-3391	27	11	]	]	PUNCT
ejpam-3391	27	12	,	,	PUNCT
ejpam-3391	27	13	|	|	ADV
ejpam-3391	27	14	p	p	ADJ
ejpam-3391	27	15	|=	|=	PUNCT
ejpam-3391	27	16	edegp	edegp	NOUN
ejpam-3391	27	17	and	and	CCONJ
ejpam-3391	27	18	,	,	PUNCT
ejpam-3391	27	19	for	for	ADP
ejpam-3391	27	20	any	any	DET
ejpam-3391	27	21	q	q	PROPN
ejpam-3391	27	22	∈	∈	PROPN
ejpam-3391	27	23	fq[x	fq[x	PROPN
ejpam-3391	27	24	]	]	PUNCT
ejpam-3391	27	25	,	,	PUNCT
ejpam-3391	27	26	such	such	ADJ
ejpam-3391	27	27	that	that	DET
ejpam-3391	27	28	q	q	NOUN
ejpam-3391	27	29	6=	6=	NUM
ejpam-3391	27	30	0	0	NUM
ejpam-3391	27	31	,	,	PUNCT
ejpam-3391	27	32	|	|	ADV
ejpam-3391	27	33	p	p	NOUN
ejpam-3391	27	34	q	q	ADJ
ejpam-3391	27	35	|=	|=	NOUN
ejpam-3391	27	36	edegp	edegp	ADJ
ejpam-3391	27	37	−	−	PROPN
ejpam-3391	27	38	degq	degq	NOUN
ejpam-3391	27	39	.	.	PUNCT
ejpam-3391	28	1	let	let	VERB
ejpam-3391	28	2	β0	β0	PROPN
ejpam-3391	28	3	∈	∈	PROPN
ejpam-3391	28	4	fq((x−1	fq((x−1	NOUN
ejpam-3391	28	5	)	)	PUNCT
ejpam-3391	28	6	)	)	PUNCT
ejpam-3391	28	7	\	\	NOUN
ejpam-3391	28	8	{	{	PUNCT
ejpam-3391	28	9	0	0	NUM
ejpam-3391	28	10	}	}	PUNCT
ejpam-3391	28	11	,	,	PUNCT
ejpam-3391	28	12	then	then	ADV
ejpam-3391	28	13	,	,	PUNCT
ejpam-3391	28	14	we	we	PRON
ejpam-3391	28	15	define	define	VERB
ejpam-3391	28	16	l	l	NOUN
ejpam-3391	28	17	=	=	SYM
ejpam-3391	28	18	{	{	PUNCT
ejpam-3391	28	19	ω	ω	NUM
ejpam-3391	28	20	∈	∈	PROPN
ejpam-3391	28	21	fq((x−1	fq((x−1	NOUN
ejpam-3391	28	22	)	)	PUNCT
ejpam-3391	28	23	)	)	PUNCT
ejpam-3391	28	24	,	,	PUNCT
ejpam-3391	28	25	|ϕ|	|ϕ|	VERB
ejpam-3391	28	26	<	<	X
ejpam-3391	28	27	|β0|	|β0|	PROPN
ejpam-3391	28	28	}	}	PUNCT
ejpam-3391	28	29	,	,	PUNCT
ejpam-3391	28	30	which	which	PRON
ejpam-3391	28	31	is	be	AUX
ejpam-3391	28	32	a	a	DET
ejpam-3391	28	33	compact	compact	ADJ
ejpam-3391	28	34	abelian	abelian	ADJ
ejpam-3391	28	35	group	group	NOUN
ejpam-3391	28	36	with	with	ADP
ejpam-3391	28	37	the	the	DET
ejpam-3391	28	38	addition	addition	NOUN
ejpam-3391	28	39	and	and	CCONJ
ejpam-3391	28	40	the	the	DET
ejpam-3391	28	41	metric	metric	ADJ
ejpam-3391	28	42	d(ϕ	d(ϕ	PROPN
ejpam-3391	28	43	,	,	PUNCT
ejpam-3391	28	44	ω	ω	NUM
ejpam-3391	28	45	)	)	PUNCT
ejpam-3391	28	46	=	=	PUNCT
ejpam-3391	28	47	|ϕ	|ϕ	NOUN
ejpam-3391	28	48	−	−	NOUN
ejpam-3391	28	49	ω|	ω|	NOUN
ejpam-3391	28	50	:	:	PUNCT
ejpam-3391	28	51	∀ϕ	∀ϕ	NUM
ejpam-3391	28	52	,	,	PUNCT
ejpam-3391	28	53	ω	ω	PROPN
ejpam-3391	28	54	∈	∈	PROPN
ejpam-3391	28	55	fq((x−1	fq((x−1	NOUN
ejpam-3391	28	56	)	)	PUNCT
ejpam-3391	28	57	)	)	PUNCT
ejpam-3391	28	58	.	.	PUNCT
ejpam-3391	29	1	now	now	ADV
ejpam-3391	29	2	,	,	PUNCT
ejpam-3391	29	3	for	for	ADP
ejpam-3391	29	4	1	1	NUM
ejpam-3391	29	5	≤	≤	NUM
ejpam-3391	29	6	j	j	PROPN
ejpam-3391	29	7	≤	≤	NUM
ejpam-3391	29	8	n	n	CCONJ
ejpam-3391	29	9	,	,	PUNCT
ejpam-3391	29	10	we	we	PRON
ejpam-3391	29	11	put	put	VERB
ejpam-3391	29	12	l(n	l(n	NOUN
ejpam-3391	29	13	)	)	PUNCT
ejpam-3391	29	14	j	j	PROPN
ejpam-3391	30	1	=	=	PRON
ejpam-3391	30	2	{	{	PUNCT
ejpam-3391	30	3	(	(	PUNCT
ejpam-3391	30	4	ϕ1	ϕ1	NOUN
ejpam-3391	30	5	,	,	PUNCT
ejpam-3391	30	6	·	·	PUNCT
ejpam-3391	30	7	·	·	PUNCT
ejpam-3391	30	8	·	·	PUNCT
ejpam-3391	30	9	,	,	PUNCT
ejpam-3391	30	10	ϕn	ϕn	X
ejpam-3391	30	11	)	)	PUNCT
ejpam-3391	30	12	∈	∈	PROPN
ejpam-3391	31	1	ln	ln	ADJ
ejpam-3391	31	2	,	,	PUNCT
ejpam-3391	31	3	{	{	PUNCT
ejpam-3391	31	4	|ϕj	|ϕj	PUNCT
ejpam-3391	31	5	|	|	NOUN
ejpam-3391	31	6	>	>	X
ejpam-3391	31	7	|ϕi|	|ϕi|	NOUN
ejpam-3391	31	8	for	for	ADP
ejpam-3391	31	9	1	1	NUM
ejpam-3391	31	10	≤	≤	NUM
ejpam-3391	32	1	i	i	PRON
ejpam-3391	32	2	<	<	X
ejpam-3391	32	3	j	j	PROPN
ejpam-3391	32	4	,	,	PUNCT
ejpam-3391	32	5	|ϕj	|ϕj	PUNCT
ejpam-3391	32	6	|	|	ADV
ejpam-3391	32	7	≥	≥	AUX
ejpam-3391	32	8	|ϕi|	|ϕi|	NOUN
ejpam-3391	32	9	for	for	ADP
ejpam-3391	32	10	j	j	PROPN
ejpam-3391	32	11	<	<	X
ejpam-3391	32	12	i	i	PROPN
ejpam-3391	32	13	≤	≤	PUNCT
ejpam-3391	32	14	n	n	CCONJ
ejpam-3391	32	15	}	}	PUNCT
ejpam-3391	32	16	,	,	PUNCT
ejpam-3391	32	17	and	and	CCONJ
ejpam-3391	32	18	lnj	lnj	PROPN
ejpam-3391	32	19	=	=	PROPN
ejpam-3391	32	20	l×	l×	PROPN
ejpam-3391	32	21	l×	l×	PROPN
ejpam-3391	32	22	·	·	PUNCT
ejpam-3391	32	23	·	·	PUNCT
ejpam-3391	32	24	·	·	PUNCT
ejpam-3391	32	25	×	×	PROPN
ejpam-3391	32	26	l	l	NOUN
ejpam-3391	32	27	,	,	PUNCT
ejpam-3391	32	28	n	n	PRON
ejpam-3391	32	29	times	time	NOUN
ejpam-3391	32	30	then	then	ADV
ejpam-3391	32	31	l(n	l(n	PROPN
ejpam-3391	32	32	)	)	PUNCT
ejpam-3391	32	33	j	j	PROPN
ejpam-3391	33	1	⊂	⊂	PROPN
ejpam-3391	33	2	lnj	lnj	PROPN
ejpam-3391	33	3	and	and	CCONJ
ejpam-3391	33	4	ln	ln	NOUN
ejpam-3391	33	5	=	=	PUNCT
ejpam-3391	33	6	⋃	⋃	PROPN
ejpam-3391	33	7	1≤i≤n	1≤i≤n	NUM
ejpam-3391	33	8	l(n	l(n	NOUN
ejpam-3391	33	9	)	)	PUNCT
ejpam-3391	34	1	i	i	PRON
ejpam-3391	34	2	.	.	PUNCT
ejpam-3391	35	1	3	3	X
ejpam-3391	35	2	.	.	X
ejpam-3391	35	3	β	β	X
ejpam-3391	35	4	-	-	VERB
ejpam-3391	35	5	continued	continue	VERB
ejpam-3391	35	6	fraction	fraction	NOUN
ejpam-3391	35	7	in	in	ADP
ejpam-3391	35	8	fq((x−1	fq((x−1	NOUN
ejpam-3391	35	9	)	)	PUNCT
ejpam-3391	35	10	)	)	PUNCT
ejpam-3391	35	11	let	let	VERB
ejpam-3391	35	12	β	β	X
ejpam-3391	35	13	=	=	SYM
ejpam-3391	35	14	(	(	PUNCT
ejpam-3391	35	15	βi)i∈z	βi)i∈z	X
ejpam-3391	35	16	with	with	ADP
ejpam-3391	35	17	βi	βi	PROPN
ejpam-3391	35	18	∈	∈	PROPN
ejpam-3391	35	19	fq((x−1	fq((x−1	NOUN
ejpam-3391	35	20	)	)	PUNCT
ejpam-3391	35	21	)	)	PUNCT
ejpam-3391	35	22	\	\	NOUN
ejpam-3391	35	23	{	{	PUNCT
ejpam-3391	35	24	0	0	NUM
ejpam-3391	35	25	}	}	PUNCT
ejpam-3391	35	26	,	,	PUNCT
ejpam-3391	35	27	such	such	ADJ
ejpam-3391	35	28	that	that	SCONJ
ejpam-3391	35	29	deg(βi)i∈z	deg(βi)i∈z	PROPN
ejpam-3391	35	30	is	be	AUX
ejpam-3391	35	31	a	a	DET
ejpam-3391	35	32	strictly	strictly	ADV
ejpam-3391	35	33	increasing	increase	VERB
ejpam-3391	35	34	sequence	sequence	NOUN
ejpam-3391	35	35	of	of	ADP
ejpam-3391	35	36	integers	integer	NOUN
ejpam-3391	35	37	.	.	PUNCT
ejpam-3391	36	1	β	β	X
ejpam-3391	36	2	is	be	AUX
ejpam-3391	36	3	called	call	VERB
ejpam-3391	36	4	base	base	NOUN
ejpam-3391	36	5	sequence	sequence	NOUN
ejpam-3391	36	6	.	.	PUNCT
ejpam-3391	37	1	let	let	VERB
ejpam-3391	37	2	s	s	PRON
ejpam-3391	37	3	=	=	VERB
ejpam-3391	37	4	{	{	PUNCT
ejpam-3391	37	5	(	(	PUNCT
ejpam-3391	37	6	di)−∞<i≤k	di)−∞<i≤k	PROPN
ejpam-3391	37	7	:	:	PUNCT
ejpam-3391	37	8	k	k	PROPN
ejpam-3391	37	9	∈	∈	PROPN
ejpam-3391	37	10	z	z	PROPN
ejpam-3391	37	11	,	,	PUNCT
ejpam-3391	37	12	di	di	PROPN
ejpam-3391	37	13	∈	∈	PROPN
ejpam-3391	37	14	fq[x	fq[x	PROPN
ejpam-3391	37	15	]	]	PUNCT
ejpam-3391	37	16	,	,	PUNCT
ejpam-3391	37	17	deg	deg	X
ejpam-3391	37	18	di	di	X
ejpam-3391	37	19	<	<	X
ejpam-3391	37	20	deg	deg	PROPN
ejpam-3391	37	21	βi+1	βi+1	NUM
ejpam-3391	37	22	−	−	PROPN
ejpam-3391	37	23	deg	deg	PROPN
ejpam-3391	37	24	βi	βi	PRON
ejpam-3391	37	25	}	}	PUNCT
ejpam-3391	37	26	be	be	AUX
ejpam-3391	37	27	the	the	DET
ejpam-3391	37	28	set	set	NOUN
ejpam-3391	37	29	of	of	ADP
ejpam-3391	37	30	admissible	admissible	ADJ
ejpam-3391	37	31	digit	digit	NOUN
ejpam-3391	37	32	strings	string	NOUN
ejpam-3391	37	33	associated	associate	VERB
ejpam-3391	37	34	to	to	ADP
ejpam-3391	37	35	the	the	DET
ejpam-3391	37	36	sequence	sequence	NOUN
ejpam-3391	37	37	β	β	NOUN
ejpam-3391	37	38	.	.	PUNCT
ejpam-3391	38	1	lemma	lemma	PROPN
ejpam-3391	38	2	1	1	X
ejpam-3391	38	3	.	.	PUNCT
ejpam-3391	39	1	let	let	VERB
ejpam-3391	39	2	β	β	X
ejpam-3391	39	3	=	=	SYM
ejpam-3391	39	4	(	(	PUNCT
ejpam-3391	39	5	βi)i∈z	βi)i∈z	X
ejpam-3391	39	6	be	be	AUX
ejpam-3391	39	7	a	a	DET
ejpam-3391	39	8	base	base	NOUN
ejpam-3391	39	9	sequence	sequence	NOUN
ejpam-3391	39	10	and	and	CCONJ
ejpam-3391	39	11	s	s	VERB
ejpam-3391	39	12	the	the	DET
ejpam-3391	39	13	associated	associated	ADJ
ejpam-3391	39	14	set	set	NOUN
ejpam-3391	39	15	of	of	ADP
ejpam-3391	39	16	admissible	admissible	ADJ
ejpam-3391	39	17	digit	digit	NOUN
ejpam-3391	39	18	strings	string	NOUN
ejpam-3391	39	19	.	.	PUNCT
ejpam-3391	40	1	then	then	ADV
ejpam-3391	40	2	each	each	DET
ejpam-3391	40	3	ω	ω	PROPN
ejpam-3391	40	4	∈	∈	PROPN
ejpam-3391	40	5	fq((x−1	fq((x−1	NOUN
ejpam-3391	40	6	)	)	PUNCT
ejpam-3391	40	7	)	)	PUNCT
ejpam-3391	40	8	admits	admit	VERB
ejpam-3391	40	9	a	a	DET
ejpam-3391	40	10	unique	unique	ADJ
ejpam-3391	40	11	representation	representation	NOUN
ejpam-3391	40	12	of	of	ADP
ejpam-3391	40	13	the	the	DET
ejpam-3391	40	14	form	form	NOUN
ejpam-3391	40	15	ω	ω	NOUN
ejpam-3391	40	16	=	=	SYM
ejpam-3391	40	17	∑	∑	PUNCT
ejpam-3391	40	18	−∞<i≤k	−∞<i≤k	NOUN
ejpam-3391	40	19	diβi	diβi	ADJ
ejpam-3391	40	20	,	,	PUNCT
ejpam-3391	40	21	(	(	PUNCT
ejpam-3391	40	22	di)−∞<i≤k	di)−∞<i≤k	PROPN
ejpam-3391	40	23	∈	∈	PROPN
ejpam-3391	40	24	s	s	VERB
ejpam-3391	40	25	the	the	DET
ejpam-3391	40	26	above	above	ADJ
ejpam-3391	40	27	lemma	lemma	PROPN
ejpam-3391	40	28	justifies	justify	VERB
ejpam-3391	40	29	that	that	SCONJ
ejpam-3391	40	30	we	we	PRON
ejpam-3391	40	31	call	call	VERB
ejpam-3391	40	32	(	(	PUNCT
ejpam-3391	40	33	β	β	X
ejpam-3391	40	34	,	,	PUNCT
ejpam-3391	40	35	s	s	PART
ejpam-3391	40	36	)	)	PUNCT
ejpam-3391	40	37	a	a	DET
ejpam-3391	40	38	digit	digit	NOUN
ejpam-3391	40	39	system	system	NOUN
ejpam-3391	40	40	.	.	PUNCT
ejpam-3391	41	1	conversly	conversly	ADV
ejpam-3391	41	2	,	,	PUNCT
ejpam-3391	41	3	a	a	DET
ejpam-3391	41	4	formal	formal	ADJ
ejpam-3391	41	5	power	power	NOUN
ejpam-3391	41	6	series	series	NOUN
ejpam-3391	41	7	associated	associate	VERB
ejpam-3391	41	8	to	to	ADP
ejpam-3391	41	9	a	a	DET
ejpam-3391	41	10	given	give	VERB
ejpam-3391	41	11	string	string	NOUN
ejpam-3391	41	12	in	in	ADP
ejpam-3391	41	13	the	the	DET
ejpam-3391	41	14	digit	digit	NOUN
ejpam-3391	41	15	system	system	NOUN
ejpam-3391	41	16	(	(	PUNCT
ejpam-3391	41	17	β	β	X
ejpam-3391	41	18	,	,	PUNCT
ejpam-3391	41	19	s	s	PART
ejpam-3391	41	20	)	)	PUNCT
ejpam-3391	41	21	is	be	AUX
ejpam-3391	41	22	given	give	VERB
ejpam-3391	41	23	by	by	ADP
ejpam-3391	41	24	the	the	DET
ejpam-3391	41	25	evaluation	evaluation	NOUN
ejpam-3391	41	26	map	map	NOUN
ejpam-3391	41	27	π	π	X
ejpam-3391	41	28	:	:	PUNCT
ejpam-3391	42	1	s	s	VERB
ejpam-3391	42	2	−→	−→	NOUN
ejpam-3391	42	3	fq((x−1	fq((x−1	NOUN
ejpam-3391	42	4	)	)	PUNCT
ejpam-3391	42	5	)	)	PUNCT
ejpam-3391	42	6	,	,	PUNCT
ejpam-3391	42	7	(	(	PUNCT
ejpam-3391	42	8	di)−∞<i≤k	di)−∞<i≤k	PROPN
ejpam-3391	42	9	−→	−→	NOUN
ejpam-3391	42	10	∑	∑	PUNCT
ejpam-3391	42	11	−∞<i≤k	−∞<i≤k	NOUN
ejpam-3391	42	12	diβi	diβi	ADJ
ejpam-3391	42	13	.	.	PUNCT
ejpam-3391	43	1	if	if	SCONJ
ejpam-3391	43	2	a	a	DET
ejpam-3391	43	3	representation	representation	NOUN
ejpam-3391	43	4	ends	end	VERB
ejpam-3391	43	5	in	in	ADP
ejpam-3391	43	6	infinitely	infinitely	ADV
ejpam-3391	43	7	many	many	ADJ
ejpam-3391	43	8	zeros	zero	NOUN
ejpam-3391	43	9	,	,	PUNCT
ejpam-3391	43	10	it	it	PRON
ejpam-3391	43	11	said	say	VERB
ejpam-3391	43	12	to	to	PART
ejpam-3391	43	13	be	be	AUX
ejpam-3391	43	14	finite	finite	ADJ
ejpam-3391	43	15	,	,	PUNCT
ejpam-3391	43	16	and	and	CCONJ
ejpam-3391	43	17	the	the	DET
ejpam-3391	43	18	final	final	ADJ
ejpam-3391	43	19	zeros	zero	NOUN
ejpam-3391	43	20	are	be	AUX
ejpam-3391	43	21	omitted	omit	VERB
ejpam-3391	43	22	.	.	PUNCT
ejpam-3391	44	1	a.	a.	PROPN
ejpam-3391	44	2	chandoul	chandoul	PROPN
ejpam-3391	44	3	,	,	PUNCT
ejpam-3391	44	4	f.	f.	PROPN
ejpam-3391	44	5	aljuaydi	aljuaydi	PROPN
ejpam-3391	44	6	/	/	SYM
ejpam-3391	44	7	eur	eur	NOUN
ejpam-3391	44	8	.	.	PUNCT
ejpam-3391	45	1	j.	j.	PROPN
ejpam-3391	45	2	pure	pure	PROPN
ejpam-3391	45	3	appl	appl	PROPN
ejpam-3391	45	4	.	.	PROPN
ejpam-3391	45	5	math	math	PROPN
ejpam-3391	45	6	,	,	PUNCT
ejpam-3391	45	7	12	12	NUM
ejpam-3391	45	8	(	(	PUNCT
ejpam-3391	45	9	2	2	NUM
ejpam-3391	45	10	)	)	PUNCT
ejpam-3391	45	11	(	(	PUNCT
ejpam-3391	45	12	2019	2019	NUM
ejpam-3391	45	13	)	)	PUNCT
ejpam-3391	45	14	,	,	PUNCT
ejpam-3391	45	15	418	418	NUM
ejpam-3391	45	16	-	-	SYM
ejpam-3391	45	17	431	431	NUM
ejpam-3391	45	18	420	420	NUM
ejpam-3391	45	19	if	if	SCONJ
ejpam-3391	45	20	all	all	DET
ejpam-3391	45	21	the	the	DET
ejpam-3391	45	22	si	si	NOUN
ejpam-3391	45	23	on	on	ADP
ejpam-3391	45	24	the	the	DET
ejpam-3391	45	25	right	right	ADJ
ejpam-3391	45	26	hand	hand	NOUN
ejpam-3391	45	27	side	side	NOUN
ejpam-3391	45	28	of	of	ADP
ejpam-3391	45	29	the	the	DET
ejpam-3391	45	30	radix	radix	PROPN
ejpam-3391	45	31	point	point	NOUN
ejpam-3391	45	32	are	be	AUX
ejpam-3391	45	33	zeros	zero	NOUN
ejpam-3391	45	34	,	,	PUNCT
ejpam-3391	45	35	the	the	DET
ejpam-3391	45	36	representation	representation	NOUN
ejpam-3391	45	37	is	be	AUX
ejpam-3391	45	38	said	say	VERB
ejpam-3391	45	39	to	to	PART
ejpam-3391	45	40	be	be	AUX
ejpam-3391	45	41	an	an	DET
ejpam-3391	45	42	integer	integer	NOUN
ejpam-3391	45	43	representation	representation	NOUN
ejpam-3391	45	44	.	.	PUNCT
ejpam-3391	46	1	the	the	DET
ejpam-3391	46	2	set	set	NOUN
ejpam-3391	46	3	of	of	ADP
ejpam-3391	46	4	all	all	DET
ejpam-3391	46	5	ω	ω	NUM
ejpam-3391	46	6	∈	∈	PROPN
ejpam-3391	46	7	fq((x−1	fq((x−1	NOUN
ejpam-3391	46	8	)	)	PUNCT
ejpam-3391	46	9	)	)	PUNCT
ejpam-3391	46	10	admitting	admit	VERB
ejpam-3391	46	11	an	an	DET
ejpam-3391	46	12	integer	integer	NOUN
ejpam-3391	46	13	representation	representation	NOUN
ejpam-3391	46	14	is	be	AUX
ejpam-3391	46	15	called	call	VERB
ejpam-3391	46	16	the	the	DET
ejpam-3391	46	17	set	set	NOUN
ejpam-3391	46	18	of	of	ADP
ejpam-3391	46	19	β−integers	β−integer	NOUN
ejpam-3391	46	20	.	.	PUNCT
ejpam-3391	47	1	for	for	ADP
ejpam-3391	47	2	ω	ω	PROPN
ejpam-3391	47	3	∈	∈	PROPN
ejpam-3391	47	4	fq((x−1	fq((x−1	NOUN
ejpam-3391	47	5	)	)	PUNCT
ejpam-3391	47	6	)	)	PUNCT
ejpam-3391	47	7	,	,	PUNCT
ejpam-3391	47	8	we	we	PRON
ejpam-3391	47	9	define	define	VERB
ejpam-3391	47	10	the	the	DET
ejpam-3391	47	11	β−integer	β−integer	NOUN
ejpam-3391	47	12	and	and	CCONJ
ejpam-3391	47	13	the	the	DET
ejpam-3391	47	14	β−fractional	β−fractional	ADJ
ejpam-3391	47	15	part	part	NOUN
ejpam-3391	47	16	by	by	ADP
ejpam-3391	47	17	[	[	X
ejpam-3391	47	18	β]β	β]β	X
ejpam-3391	47	19	=	=	SYM
ejpam-3391	47	20	π(dk	π(dk	X
ejpam-3391	47	21	·	·	PUNCT
ejpam-3391	47	22	·	·	PUNCT
ejpam-3391	47	23	·	·	PUNCT
ejpam-3391	47	24	d0)β	d0)β	NOUN
ejpam-3391	47	25	and	and	CCONJ
ejpam-3391	47	26	{	{	PUNCT
ejpam-3391	47	27	β}β	β}β	PROPN
ejpam-3391	47	28	=	=	SYM
ejpam-3391	47	29	π(d−1d−2	π(d−1d−2	PROPN
ejpam-3391	47	30	·	·	PUNCT
ejpam-3391	47	31	·	·	PUNCT
ejpam-3391	47	32	·	·	PUNCT
ejpam-3391	47	33	)	)	PUNCT
ejpam-3391	47	34	β	β	X
ejpam-3391	47	35	,	,	PUNCT
ejpam-3391	47	36	respectively	respectively	ADV
ejpam-3391	47	37	.	.	PUNCT
ejpam-3391	48	1	now	now	ADV
ejpam-3391	48	2	we	we	PRON
ejpam-3391	48	3	are	be	AUX
ejpam-3391	48	4	in	in	ADP
ejpam-3391	48	5	a	a	DET
ejpam-3391	48	6	position	position	NOUN
ejpam-3391	48	7	to	to	PART
ejpam-3391	48	8	introduce	introduce	VERB
ejpam-3391	48	9	our	our	PRON
ejpam-3391	48	10	new	new	ADJ
ejpam-3391	48	11	algorithm	algorithm	NOUN
ejpam-3391	48	12	,	,	PUNCT
ejpam-3391	48	13	called	call	VERB
ejpam-3391	48	14	β−continued	β−continued	NUM
ejpam-3391	48	15	fraction	fraction	NOUN
ejpam-3391	48	16	algorithm	algorithm	NOUN
ejpam-3391	48	17	.	.	PUNCT
ejpam-3391	49	1	the	the	DET
ejpam-3391	49	2	study	study	NOUN
ejpam-3391	49	3	of	of	ADP
ejpam-3391	49	4	this	this	DET
ejpam-3391	49	5	algorithm	algorithm	NOUN
ejpam-3391	49	6	is	be	AUX
ejpam-3391	49	7	similar	similar	ADJ
ejpam-3391	49	8	to	to	ADP
ejpam-3391	49	9	the	the	DET
ejpam-3391	49	10	study	study	NOUN
ejpam-3391	49	11	of	of	ADP
ejpam-3391	49	12	the	the	DET
ejpam-3391	49	13	usual	usual	ADJ
ejpam-3391	49	14	continued	continue	VERB
ejpam-3391	49	15	fraction	fraction	NOUN
ejpam-3391	49	16	expansions	expansion	NOUN
ejpam-3391	49	17	.	.	PUNCT
ejpam-3391	50	1	let	let	VERB
ejpam-3391	50	2	β	β	X
ejpam-3391	50	3	=	=	SYM
ejpam-3391	50	4	(	(	PUNCT
ejpam-3391	50	5	βi)i∈z	βi)i∈z	X
ejpam-3391	50	6	be	be	AUX
ejpam-3391	50	7	a	a	DET
ejpam-3391	50	8	base	base	NOUN
ejpam-3391	50	9	sequence	sequence	NOUN
ejpam-3391	50	10	and	and	CCONJ
ejpam-3391	50	11	let	let	VERB
ejpam-3391	50	12	h′0(β	h′0(β	VERB
ejpam-3391	50	13	)	)	PUNCT
ejpam-3391	50	14	=	=	PRON
ejpam-3391	50	15	{	{	PUNCT
ejpam-3391	50	16	dβ0	dβ0	NOUN
ejpam-3391	50	17	∈	∈	PROPN
ejpam-3391	50	18	fq[x	fq[x	PROPN
ejpam-3391	50	19	]	]	PUNCT
ejpam-3391	50	20	,	,	PUNCT
ejpam-3391	50	21	0	0	PUNCT
ejpam-3391	50	22	<	<	X
ejpam-3391	50	23	deg	deg	PROPN
ejpam-3391	50	24	d	d	X
ejpam-3391	50	25	<	<	X
ejpam-3391	50	26	deg	deg	PROPN
ejpam-3391	50	27	β1	β1	PROPN
ejpam-3391	50	28	−	−	PROPN
ejpam-3391	50	29	deg	deg	PROPN
ejpam-3391	50	30	β0	β0	PROPN
ejpam-3391	50	31	}	}	PUNCT
ejpam-3391	50	32	,	,	PUNCT
ejpam-3391	50	33	h′′0(β	h′′0(β	ADJ
ejpam-3391	50	34	)	)	PUNCT
ejpam-3391	50	35	=	=	SYM
ejpam-3391	50	36	{	{	PUNCT
ejpam-3391	50	37	dβ0	dβ0	NOUN
ejpam-3391	50	38	∈	∈	PROPN
ejpam-3391	50	39	fq[x],deg	fq[x],deg	PUNCT
ejpam-3391	51	1	d	d	X
ejpam-3391	51	2	<	<	X
ejpam-3391	51	3	deg	deg	PROPN
ejpam-3391	51	4	β1	β1	PROPN
ejpam-3391	51	5	−	−	PROPN
ejpam-3391	51	6	deg	deg	PROPN
ejpam-3391	51	7	β0	β0	PROPN
ejpam-3391	51	8	}	}	PUNCT
ejpam-3391	51	9	,	,	PUNCT
ejpam-3391	51	10	hn(β	hn(β	PROPN
ejpam-3391	51	11	)	)	PUNCT
ejpam-3391	51	12	=	=	SYM
ejpam-3391	51	13	{	{	PUNCT
ejpam-3391	51	14	d0β0	d0β0	PROPN
ejpam-3391	51	15	+	+	X
ejpam-3391	51	16	·	·	PUNCT
ejpam-3391	51	17	·	·	PUNCT
ejpam-3391	51	18	·	·	PUNCT
ejpam-3391	51	19	+	+	NUM
ejpam-3391	51	20	dnβn	dnβn	NOUN
ejpam-3391	51	21	,	,	PUNCT
ejpam-3391	51	22	di	di	NOUN
ejpam-3391	51	23	∈	∈	PROPN
ejpam-3391	51	24	fq[x	fq[x	PROPN
ejpam-3391	51	25	]	]	PUNCT
ejpam-3391	51	26	,	,	PUNCT
ejpam-3391	51	27	deg	deg	X
ejpam-3391	51	28	di	di	X
ejpam-3391	51	29	<	<	X
ejpam-3391	51	30	deg	deg	PROPN
ejpam-3391	51	31	βi+1	βi+1	NUM
ejpam-3391	51	32	−	−	PROPN
ejpam-3391	51	33	deg	deg	PROPN
ejpam-3391	51	34	βi	βi	PROPN
ejpam-3391	51	35	,	,	PUNCT
ejpam-3391	51	36	dn	dn	ADP
ejpam-3391	51	37	6=	6=	PROPN
ejpam-3391	51	38	0	0	NUM
ejpam-3391	51	39	}	}	PUNCT
ejpam-3391	51	40	for	for	ADP
ejpam-3391	51	41	all	all	DET
ejpam-3391	51	42	n	n	PRON
ejpam-3391	51	43	≥	≥	NOUN
ejpam-3391	51	44	1	1	NUM
ejpam-3391	51	45	,	,	PUNCT
ejpam-3391	51	46	and	and	CCONJ
ejpam-3391	51	47	h(β	h(β	PROPN
ejpam-3391	51	48	)	)	PUNCT
ejpam-3391	51	49	=	=	SYM
ejpam-3391	51	50	h′0(β	h′0(β	VERB
ejpam-3391	51	51	)	)	PUNCT
ejpam-3391	51	52	∪	∪	ADP
ejpam-3391	51	53	⋃	⋃	PROPN
ejpam-3391	51	54	n≥1	n≥1	NOUN
ejpam-3391	51	55	hn(β	hn(β	NUM
ejpam-3391	51	56	)	)	PUNCT
ejpam-3391	51	57	,	,	PUNCT
ejpam-3391	51	58	i(β	i(β	NOUN
ejpam-3391	51	59	)	)	PUNCT
ejpam-3391	52	1	=	=	PUNCT
ejpam-3391	52	2	h′′0(β	h′′0(β	X
ejpam-3391	52	3	)	)	PUNCT
ejpam-3391	52	4	∪	∪	ADP
ejpam-3391	52	5	⋃	⋃	NOUN
ejpam-3391	52	6	n≥0	n≥0	ADJ
ejpam-3391	52	7	hn(β	hn(β	NUM
ejpam-3391	52	8	)	)	PUNCT
ejpam-3391	52	9	.	.	PUNCT
ejpam-3391	53	1	remark	remark	PROPN
ejpam-3391	53	2	1	1	NUM
ejpam-3391	53	3	.	.	PUNCT
ejpam-3391	54	1	note	note	VERB
ejpam-3391	54	2	that	that	SCONJ
ejpam-3391	55	1	|	|	ADV
ejpam-3391	55	2	z	z	NOUN
ejpam-3391	55	3	|≥|	|≥|	NOUN
ejpam-3391	55	4	β0	β0	NOUN
ejpam-3391	55	5	|	|	ADV
ejpam-3391	55	6	for	for	ADP
ejpam-3391	55	7	all	all	DET
ejpam-3391	55	8	z	z	NOUN
ejpam-3391	55	9	∈	∈	PROPN
ejpam-3391	55	10	i(β	i(β	PROPN
ejpam-3391	55	11	)	)	PUNCT
ejpam-3391	55	12	and	and	CCONJ
ejpam-3391	55	13	|	|	ADV
ejpam-3391	55	14	z	z	PROPN
ejpam-3391	55	15	|>|	|>|	PROPN
ejpam-3391	55	16	β0	β0	ADV
ejpam-3391	55	17	|	|	ADV
ejpam-3391	55	18	for	for	ADP
ejpam-3391	55	19	all	all	DET
ejpam-3391	55	20	z	z	NOUN
ejpam-3391	55	21	∈	∈	NOUN
ejpam-3391	55	22	h(β	h(β	PROPN
ejpam-3391	55	23	)	)	PUNCT
ejpam-3391	55	24	.	.	PUNCT
ejpam-3391	56	1	we	we	PRON
ejpam-3391	56	2	can	can	AUX
ejpam-3391	56	3	define	define	VERB
ejpam-3391	56	4	the	the	DET
ejpam-3391	56	5	β	β	X
ejpam-3391	56	6	-	-	ADJ
ejpam-3391	56	7	continued	continue	VERB
ejpam-3391	56	8	fraction	fraction	NOUN
ejpam-3391	56	9	by	by	ADP
ejpam-3391	56	10	the	the	DET
ejpam-3391	56	11	β	β	NOUN
ejpam-3391	56	12	-	-	NOUN
ejpam-3391	56	13	transformation	transformation	NOUN
ejpam-3391	56	14	tβ	tβ	NOUN
ejpam-3391	56	15	on	on	ADP
ejpam-3391	56	16	d(0	d(0	PROPN
ejpam-3391	56	17	,	,	PUNCT
ejpam-3391	56	18	|β0|	|β0|	PROPN
ejpam-3391	56	19	)	)	PUNCT
ejpam-3391	56	20	,	,	PUNCT
ejpam-3391	56	21	which	which	PRON
ejpam-3391	56	22	is	be	AUX
ejpam-3391	56	23	given	give	VERB
ejpam-3391	56	24	by	by	ADP
ejpam-3391	56	25	the	the	DET
ejpam-3391	56	26	following	follow	VERB
ejpam-3391	56	27	mapping	map	VERB
ejpam-3391	56	28	tβ	tβ	PROPN
ejpam-3391	56	29	:	:	PUNCT
ejpam-3391	56	30	d(0	d(0	NOUN
ejpam-3391	56	31	,	,	PUNCT
ejpam-3391	56	32	|β0|	|β0|	NOUN
ejpam-3391	56	33	)	)	PUNCT
ejpam-3391	56	34	→	→	SYM
ejpam-3391	56	35	d(0	d(0	NOUN
ejpam-3391	56	36	,	,	PUNCT
ejpam-3391	56	37	|β0|	|β0|	PROPN
ejpam-3391	56	38	)	)	PUNCT
ejpam-3391	56	39	ω	ω	NUM
ejpam-3391	56	40	7→	7→	NUM
ejpam-3391	56	41			PUNCT
ejpam-3391	56	42	{	{	PUNCT
ejpam-3391	56	43	β20	β20	PROPN
ejpam-3391	56	44	ω	ω	PROPN
ejpam-3391	56	45	}	}	PUNCT
ejpam-3391	56	46	β	β	X
ejpam-3391	56	47	if	if	SCONJ
ejpam-3391	56	48	f	f	PROPN
ejpam-3391	56	49	6=	6=	ADP
ejpam-3391	56	50	0	0	NUM
ejpam-3391	56	51	0	0	NUM
ejpam-3391	56	52	else	else	ADV
ejpam-3391	56	53	for	for	ADP
ejpam-3391	56	54	any	any	DET
ejpam-3391	56	55	base	base	NOUN
ejpam-3391	56	56	sequence	sequence	NOUN
ejpam-3391	56	57	β	β	NOUN
ejpam-3391	56	58	,	,	PUNCT
ejpam-3391	56	59	the	the	DET
ejpam-3391	56	60	so	so	ADV
ejpam-3391	56	61	-	-	PUNCT
ejpam-3391	56	62	called	call	VERB
ejpam-3391	56	63	β	β	NOUN
ejpam-3391	56	64	-	-	VERB
ejpam-3391	56	65	continued	continue	VERB
ejpam-3391	56	66	fraction	fraction	NOUN
ejpam-3391	56	67	is	be	AUX
ejpam-3391	56	68	introduced	introduce	VERB
ejpam-3391	56	69	in	in	ADP
ejpam-3391	56	70	[	[	X
ejpam-3391	56	71	7	7	NUM
ejpam-3391	56	72	]	]	PUNCT
ejpam-3391	56	73	.	.	PUNCT
ejpam-3391	57	1	a	a	DET
ejpam-3391	57	2	β	β	X
ejpam-3391	57	3	-	-	ADJ
ejpam-3391	57	4	continued	continue	VERB
ejpam-3391	57	5	fraction	fraction	NOUN
ejpam-3391	57	6	is	be	AUX
ejpam-3391	57	7	an	an	DET
ejpam-3391	57	8	expression	expression	NOUN
ejpam-3391	57	9	of	of	ADP
ejpam-3391	57	10	the	the	DET
ejpam-3391	57	11	form	form	NOUN
ejpam-3391	57	12	ω	ω	NOUN
ejpam-3391	57	13	=	=	PROPN
ejpam-3391	57	14	a0	a0	PROPN
ejpam-3391	57	15	+	+	CCONJ
ejpam-3391	57	16	β20	β20	PROPN
ejpam-3391	57	17	a1	a1	PROPN
ejpam-3391	57	18	+	+	CCONJ
ejpam-3391	57	19	β20	β20	PROPN
ejpam-3391	57	20	·	·	PUNCT
ejpam-3391	57	21	·	·	PUNCT
ejpam-3391	58	1	·	·	PUNCT
ejpam-3391	58	2	+	+	NUM
ejpam-3391	58	3	β20	β20	PRON
ejpam-3391	58	4	an	an	DET
ejpam-3391	58	5	+	+	X
ejpam-3391	58	6	·	·	PUNCT
ejpam-3391	58	7	·	·	PUNCT
ejpam-3391	58	8	·	·	PUNCT
ejpam-3391	59	1	=	=	PUNCT
ejpam-3391	60	1	[	[	X
ejpam-3391	60	2	a0	a0	NOUN
ejpam-3391	60	3	;	;	PUNCT
ejpam-3391	60	4	a1	a1	NOUN
ejpam-3391	60	5	,	,	PUNCT
ejpam-3391	60	6	·	·	PUNCT
ejpam-3391	60	7	·	·	PUNCT
ejpam-3391	60	8	·	·	PUNCT
ejpam-3391	61	1	]	]	PUNCT
ejpam-3391	61	2	β	β	X
ejpam-3391	61	3	,	,	PUNCT
ejpam-3391	61	4	where	where	SCONJ
ejpam-3391	61	5	a0	a0	PROPN
ejpam-3391	61	6	∈	∈	PROPN
ejpam-3391	61	7	i(β	i(β	PROPN
ejpam-3391	61	8	)	)	PUNCT
ejpam-3391	61	9	and	and	CCONJ
ejpam-3391	61	10	ai	ai	VERB
ejpam-3391	61	11	∈	∈	PROPN
ejpam-3391	61	12	h(β	h(β	PROPN
ejpam-3391	61	13	)	)	PUNCT
ejpam-3391	61	14	for	for	SCONJ
ejpam-3391	61	15	i	i	PRON
ejpam-3391	61	16	≥	≥	NOUN
ejpam-3391	61	17	1	1	X
ejpam-3391	61	18	.	.	PUNCT
ejpam-3391	62	1	it	it	PRON
ejpam-3391	62	2	is	be	AUX
ejpam-3391	62	3	easy	easy	ADJ
ejpam-3391	62	4	to	to	PART
ejpam-3391	62	5	prove	prove	VERB
ejpam-3391	62	6	that	that	SCONJ
ejpam-3391	62	7	deg	deg	NOUN
ejpam-3391	62	8	ai	ai	VERB
ejpam-3391	62	9	>	>	X
ejpam-3391	62	10	deg	deg	PROPN
ejpam-3391	62	11	β0	β0	PROPN
ejpam-3391	62	12	for	for	ADP
ejpam-3391	62	13	all	all	PRON
ejpam-3391	62	14	i	i	PRON
ejpam-3391	62	15	≥	≥	VERB
ejpam-3391	62	16	1	1	NUM
ejpam-3391	62	17	.	.	PUNCT
ejpam-3391	62	18	remark	remark	NOUN
ejpam-3391	62	19	2	2	NUM
ejpam-3391	62	20	.	.	PUNCT
ejpam-3391	63	1	if	if	SCONJ
ejpam-3391	63	2	β	β	X
ejpam-3391	63	3	=	=	SYM
ejpam-3391	63	4	(	(	PUNCT
ejpam-3391	63	5	xi)i∈n	xi)i∈n	NUM
ejpam-3391	63	6	,	,	PUNCT
ejpam-3391	63	7	then	then	ADV
ejpam-3391	63	8	the	the	DET
ejpam-3391	63	9	transformation	transformation	NOUN
ejpam-3391	63	10	tβ	tβ	PRON
ejpam-3391	63	11	describe	describe	VERB
ejpam-3391	63	12	the	the	DET
ejpam-3391	63	13	regular	regular	ADJ
ejpam-3391	63	14	continued	continue	VERB
ejpam-3391	63	15	fraction	fraction	NOUN
ejpam-3391	63	16	over	over	ADP
ejpam-3391	63	17	the	the	DET
ejpam-3391	63	18	field	field	NOUN
ejpam-3391	63	19	of	of	ADP
ejpam-3391	63	20	formal	formal	ADJ
ejpam-3391	63	21	power	power	NOUN
ejpam-3391	63	22	series	series	NOUN
ejpam-3391	63	23	and	and	CCONJ
ejpam-3391	63	24	has	have	AUX
ejpam-3391	63	25	been	be	AUX
ejpam-3391	63	26	introduced	introduce	VERB
ejpam-3391	63	27	by	by	ADP
ejpam-3391	63	28	artin	artin	PROPN
ejpam-3391	63	29	[	[	X
ejpam-3391	63	30	8	8	NUM
ejpam-3391	63	31	]	]	PUNCT
ejpam-3391	63	32	.	.	PUNCT
ejpam-3391	64	1	a.	a.	PROPN
ejpam-3391	64	2	chandoul	chandoul	PROPN
ejpam-3391	64	3	,	,	PUNCT
ejpam-3391	64	4	f.	f.	PROPN
ejpam-3391	64	5	aljuaydi	aljuaydi	PROPN
ejpam-3391	64	6	/	/	SYM
ejpam-3391	64	7	eur	eur	NOUN
ejpam-3391	64	8	.	.	PUNCT
ejpam-3391	65	1	j.	j.	PROPN
ejpam-3391	65	2	pure	pure	PROPN
ejpam-3391	65	3	appl	appl	PROPN
ejpam-3391	65	4	.	.	PROPN
ejpam-3391	65	5	math	math	PROPN
ejpam-3391	65	6	,	,	PUNCT
ejpam-3391	65	7	12	12	NUM
ejpam-3391	65	8	(	(	PUNCT
ejpam-3391	65	9	2	2	NUM
ejpam-3391	65	10	)	)	PUNCT
ejpam-3391	65	11	(	(	PUNCT
ejpam-3391	65	12	2019	2019	NUM
ejpam-3391	65	13	)	)	PUNCT
ejpam-3391	65	14	,	,	PUNCT
ejpam-3391	65	15	418	418	NUM
ejpam-3391	65	16	-	-	SYM
ejpam-3391	65	17	431	431	NUM
ejpam-3391	65	18	421	421	NUM
ejpam-3391	65	19	4	4	NUM
ejpam-3391	65	20	.	.	PUNCT
ejpam-3391	66	1	multidimensional	multidimensional	ADJ
ejpam-3391	66	2	continued	continued	ADJ
ejpam-3391	66	3	fractions	fraction	NOUN
ejpam-3391	66	4	let	let	VERB
ejpam-3391	66	5	b	b	PROPN
ejpam-3391	66	6	⊂	⊂	PROPN
ejpam-3391	66	7	e	e	PROPN
ejpam-3391	66	8	and	and	CCONJ
ejpam-3391	66	9	t	t	PROPN
ejpam-3391	66	10	:	:	PUNCT
ejpam-3391	66	11	b	b	X
ejpam-3391	66	12	−→	−→	NOUN
ejpam-3391	66	13	b	b	NOUN
ejpam-3391	66	14	be	be	AUX
ejpam-3391	66	15	a	a	DET
ejpam-3391	66	16	map	map	NOUN
ejpam-3391	66	17	.	.	PUNCT
ejpam-3391	67	1	the	the	DET
ejpam-3391	67	2	pair	pair	NOUN
ejpam-3391	67	3	(	(	PUNCT
ejpam-3391	67	4	b	b	NOUN
ejpam-3391	67	5	,	,	PUNCT
ejpam-3391	67	6	t	t	PROPN
ejpam-3391	67	7	)	)	PUNCT
ejpam-3391	67	8	is	be	AUX
ejpam-3391	67	9	called	call	VERB
ejpam-3391	67	10	a	a	DET
ejpam-3391	67	11	fibred	fibre	VERB
ejpam-3391	67	12	system	system	NOUN
ejpam-3391	67	13	if	if	SCONJ
ejpam-3391	67	14	there	there	PRON
ejpam-3391	67	15	exists	exist	VERB
ejpam-3391	67	16	a	a	DET
ejpam-3391	67	17	finite	finite	NOUN
ejpam-3391	67	18	or	or	CCONJ
ejpam-3391	67	19	countable	countable	ADJ
ejpam-3391	67	20	partition	partition	NOUN
ejpam-3391	67	21	{	{	PUNCT
ejpam-3391	67	22	b(p	b(p	PROPN
ejpam-3391	67	23	)	)	PUNCT
ejpam-3391	67	24	:	:	PUNCT
ejpam-3391	68	1	p	p	X
ejpam-3391	68	2	∈	∈	PROPN
ejpam-3391	68	3	i	i	X
ejpam-3391	68	4	}	}	PUNCT
ejpam-3391	68	5	of	of	ADP
ejpam-3391	68	6	b	b	NOUN
ejpam-3391	68	7	,	,	PUNCT
ejpam-3391	68	8	where	where	SCONJ
ejpam-3391	68	9	i	i	PRON
ejpam-3391	68	10	⊂	⊂	PROPN
ejpam-3391	68	11	fq[x]n	fq[x]n	PROPN
ejpam-3391	68	12	,	,	PUNCT
ejpam-3391	68	13	such	such	ADJ
ejpam-3391	68	14	that	that	SCONJ
ejpam-3391	68	15	the	the	DET
ejpam-3391	68	16	restriction	restriction	NOUN
ejpam-3391	68	17	of	of	ADP
ejpam-3391	68	18	t	t	PROPN
ejpam-3391	68	19	to	to	ADP
ejpam-3391	68	20	any	any	DET
ejpam-3391	68	21	b(p	b(p	PROPN
ejpam-3391	68	22	)	)	PUNCT
ejpam-3391	68	23	is	be	AUX
ejpam-3391	68	24	an	an	DET
ejpam-3391	68	25	injective	injective	ADJ
ejpam-3391	68	26	map	map	NOUN
ejpam-3391	68	27	.	.	PUNCT
ejpam-3391	69	1	as	as	SCONJ
ejpam-3391	69	2	e	e	PROPN
ejpam-3391	69	3	is	be	AUX
ejpam-3391	69	4	a	a	DET
ejpam-3391	69	5	normed	normed	ADJ
ejpam-3391	69	6	space	space	NOUN
ejpam-3391	69	7	,	,	PUNCT
ejpam-3391	69	8	we	we	PRON
ejpam-3391	69	9	assume	assume	VERB
ejpam-3391	69	10	that	that	SCONJ
ejpam-3391	69	11	a	a	DET
ejpam-3391	69	12	system	system	NOUN
ejpam-3391	69	13	defines	define	VERB
ejpam-3391	69	14	an	an	DET
ejpam-3391	69	15	algorithm	algorithm	NOUN
ejpam-3391	69	16	of	of	ADP
ejpam-3391	69	17	multidimensional	multidimensional	ADJ
ejpam-3391	69	18	continued	continue	VERB
ejpam-3391	69	19	fractions	fraction	NOUN
ejpam-3391	69	20	if	if	SCONJ
ejpam-3391	69	21	for	for	ADP
ejpam-3391	69	22	all	all	DET
ejpam-3391	69	23	p	p	NOUN
ejpam-3391	69	24	=	=	X
ejpam-3391	69	25	(	(	PUNCT
ejpam-3391	69	26	p1	p1	PROPN
ejpam-3391	69	27	,	,	PUNCT
ejpam-3391	69	28	.	.	PUNCT
ejpam-3391	69	29	.	.	PUNCT
ejpam-3391	70	1	.	.	PUNCT
ejpam-3391	71	1	,	,	PUNCT
ejpam-3391	71	2	pn	pn	PROPN
ejpam-3391	71	3	)	)	PUNCT
ejpam-3391	71	4	∈	∈	PROPN
ejpam-3391	72	1	i	i	PRON
ejpam-3391	72	2	,	,	PUNCT
ejpam-3391	72	3	there	there	PRON
ejpam-3391	72	4	exists	exist	VERB
ejpam-3391	72	5	an	an	DET
ejpam-3391	72	6	(	(	PUNCT
ejpam-3391	72	7	n+	n+	NUM
ejpam-3391	72	8	1)×	1)×	NUM
ejpam-3391	72	9	(	(	PUNCT
ejpam-3391	72	10	n+	n+	NOUN
ejpam-3391	72	11	1	1	NUM
ejpam-3391	72	12	)	)	PUNCT
ejpam-3391	72	13	invertible	invertible	ADJ
ejpam-3391	72	14	matrix	matrix	NOUN
ejpam-3391	72	15	α(p	α(p	PROPN
ejpam-3391	72	16	)	)	PUNCT
ejpam-3391	73	1	=	=	SYM
ejpam-3391	73	2	(	(	PUNCT
ejpam-3391	73	3	ci	ci	PROPN
ejpam-3391	73	4	,	,	PUNCT
ejpam-3391	73	5	j	j	PROPN
ejpam-3391	73	6	)	)	PUNCT
ejpam-3391	73	7	with	with	ADP
ejpam-3391	73	8	entries	entry	NOUN
ejpam-3391	73	9	in	in	ADP
ejpam-3391	73	10	fq[x	fq[x	PROPN
ejpam-3391	73	11	]	]	PUNCT
ejpam-3391	73	12	such	such	ADJ
ejpam-3391	73	13	that	that	SCONJ
ejpam-3391	73	14	if	if	SCONJ
ejpam-3391	73	15	y	y	PROPN
ejpam-3391	73	16	=	=	PUNCT
ejpam-3391	73	17	tf	tf	INTJ
ejpam-3391	73	18	where	where	SCONJ
ejpam-3391	73	19	f	f	PROPN
ejpam-3391	73	20	∈	∈	PROPN
ejpam-3391	73	21	b(p	b(p	PROPN
ejpam-3391	73	22	)	)	PUNCT
ejpam-3391	73	23	,	,	PUNCT
ejpam-3391	73	24	then	then	ADV
ejpam-3391	73	25	yi	yi	PROPN
ejpam-3391	74	1	=	=	PUNCT
ejpam-3391	74	2	ci0	ci0	PROPN
ejpam-3391	74	3	+	+	PUNCT
ejpam-3391	74	4	∑n	∑n	PROPN
ejpam-3391	74	5	j=1cijfj	j=1cijfj	PROPN
ejpam-3391	74	6	c00	c00	NOUN
ejpam-3391	74	7	+	+	CCONJ
ejpam-3391	74	8	∑n	∑n	PROPN
ejpam-3391	74	9	j=1c0jfj	j=1c0jfj	NOUN
ejpam-3391	74	10	for	for	ADP
ejpam-3391	74	11	all	all	DET
ejpam-3391	74	12	1	1	NUM
ejpam-3391	74	13	≤	≤	NUM
ejpam-3391	74	14	i	i	PRON
ejpam-3391	74	15	≤	≤	PUNCT
ejpam-3391	74	16	n.	n.	VERB
ejpam-3391	74	17	the	the	DET
ejpam-3391	74	18	map	map	NOUN
ejpam-3391	74	19	t	t	PROPN
ejpam-3391	74	20	is	be	AUX
ejpam-3391	74	21	called	call	VERB
ejpam-3391	74	22	a	a	DET
ejpam-3391	74	23	multidimensional	multidimensional	ADJ
ejpam-3391	74	24	continued	continue	VERB
ejpam-3391	74	25	fraction	fraction	NOUN
ejpam-3391	74	26	algorithm	algorithm	NOUN
ejpam-3391	74	27	.	.	PUNCT
ejpam-3391	75	1	for	for	ADP
ejpam-3391	75	2	all	all	DET
ejpam-3391	75	3	1	1	NUM
ejpam-3391	75	4	≤	≤	NUM
ejpam-3391	75	5	i	i	PRON
ejpam-3391	75	6	≤	≤	NOUN
ejpam-3391	75	7	n	n	CCONJ
ejpam-3391	75	8	,	,	PUNCT
ejpam-3391	75	9	if	if	SCONJ
ejpam-3391	75	10	f	f	PROPN
ejpam-3391	75	11	∈	∈	PROPN
ejpam-3391	75	12	b(p	b(p	X
ejpam-3391	75	13	(	(	PUNCT
ejpam-3391	75	14	1	1	NUM
ejpam-3391	75	15	)	)	PUNCT
ejpam-3391	75	16	)	)	PUNCT
ejpam-3391	75	17	,	,	PUNCT
ejpam-3391	75	18	then	then	ADV
ejpam-3391	75	19	t	t	PROPN
ejpam-3391	75	20	if	if	SCONJ
ejpam-3391	75	21	∈	∈	PROPN
ejpam-3391	75	22	b(p	b(p	PROPN
ejpam-3391	75	23	(	(	PUNCT
ejpam-3391	75	24	i	i	NOUN
ejpam-3391	75	25	)	)	PUNCT
ejpam-3391	75	26	)	)	PUNCT
ejpam-3391	75	27	.	.	PUNCT
ejpam-3391	76	1	the	the	DET
ejpam-3391	76	2	sequence	sequence	NOUN
ejpam-3391	76	3	p	p	NOUN
ejpam-3391	76	4	(	(	PUNCT
ejpam-3391	76	5	1	1	NUM
ejpam-3391	76	6	)	)	PUNCT
ejpam-3391	76	7	,	,	PUNCT
ejpam-3391	76	8	p	p	X
ejpam-3391	76	9	(	(	PUNCT
ejpam-3391	76	10	2	2	NUM
ejpam-3391	76	11	)	)	PUNCT
ejpam-3391	76	12	,	,	PUNCT
ejpam-3391	76	13	.	.	PUNCT
ejpam-3391	76	14	.	.	PUNCT
ejpam-3391	76	15	.	.	PUNCT
ejpam-3391	77	1	,	,	PUNCT
ejpam-3391	77	2	p	p	X
ejpam-3391	77	3	(	(	PUNCT
ejpam-3391	77	4	n	n	CCONJ
ejpam-3391	77	5	)	)	PUNCT
ejpam-3391	77	6	,	,	PUNCT
ejpam-3391	77	7	.	.	PUNCT
ejpam-3391	77	8	.	.	PUNCT
ejpam-3391	78	1	.	.	PUNCT
ejpam-3391	79	1	is	be	AUX
ejpam-3391	79	2	called	call	VERB
ejpam-3391	79	3	the	the	DET
ejpam-3391	79	4	expansion	expansion	NOUN
ejpam-3391	79	5	of	of	ADP
ejpam-3391	79	6	f	f	PROPN
ejpam-3391	79	7	by	by	ADP
ejpam-3391	79	8	the	the	DET
ejpam-3391	79	9	algorithm	algorithm	NOUN
ejpam-3391	79	10	t.	t.	PROPN
ejpam-3391	79	11	let	let	VERB
ejpam-3391	79	12	β(p	β(p	PROPN
ejpam-3391	79	13	)	)	PUNCT
ejpam-3391	80	1	=	=	PUNCT
ejpam-3391	80	2	(	(	PUNCT
ejpam-3391	80	3	bi	bi	PROPN
ejpam-3391	80	4	,	,	PUNCT
ejpam-3391	80	5	j	j	NOUN
ejpam-3391	80	6	)	)	PUNCT
ejpam-3391	80	7	be	be	VERB
ejpam-3391	80	8	the	the	DET
ejpam-3391	80	9	inverse	inverse	ADJ
ejpam-3391	80	10	matrix	matrix	NOUN
ejpam-3391	80	11	of	of	ADP
ejpam-3391	80	12	α(p	α(p	PROPN
ejpam-3391	80	13	)	)	PUNCT
ejpam-3391	80	14	,	,	PUNCT
ejpam-3391	80	15	we	we	PRON
ejpam-3391	80	16	set	set	VERB
ejpam-3391	80	17	β(p	β(p	PROPN
ejpam-3391	80	18	(	(	PUNCT
ejpam-3391	80	19	1	1	NUM
ejpam-3391	80	20	)	)	PUNCT
ejpam-3391	80	21	,	,	PUNCT
ejpam-3391	80	22	·	·	PUNCT
ejpam-3391	80	23	·	·	PUNCT
ejpam-3391	80	24	·	·	PUNCT
ejpam-3391	80	25	,	,	PUNCT
ejpam-3391	80	26	p	p	X
ejpam-3391	80	27	(	(	PUNCT
ejpam-3391	80	28	s	s	NOUN
ejpam-3391	80	29	)	)	PUNCT
ejpam-3391	80	30	)	)	PUNCT
ejpam-3391	81	1	=	=	SYM
ejpam-3391	82	1	β(p	β(p	PROPN
ejpam-3391	82	2	(	(	PUNCT
ejpam-3391	82	3	1	1	NUM
ejpam-3391	82	4	)	)	PUNCT
ejpam-3391	82	5	)	)	PUNCT
ejpam-3391	82	6	·	·	PUNCT
ejpam-3391	82	7	·	·	PUNCT
ejpam-3391	83	1	·	·	PUNCT
ejpam-3391	83	2	β(p	β(p	NOUN
ejpam-3391	83	3	(	(	PUNCT
ejpam-3391	83	4	s	s	NOUN
ejpam-3391	83	5	)	)	PUNCT
ejpam-3391	83	6	)	)	PUNCT
ejpam-3391	84	1	=	=	SYM
ejpam-3391	84	2	(	(	PUNCT
ejpam-3391	84	3	(	(	PUNCT
ejpam-3391	84	4	b	b	X
ejpam-3391	84	5	(	(	PUNCT
ejpam-3391	84	6	s	s	NOUN
ejpam-3391	84	7	)	)	PUNCT
ejpam-3391	84	8	ij	ij	NOUN
ejpam-3391	84	9	)	)	PUNCT
ejpam-3391	84	10	)	)	PUNCT
ejpam-3391	84	11	,	,	PUNCT
ejpam-3391	84	12	where	where	SCONJ
ejpam-3391	84	13	0	0	NUM
ejpam-3391	84	14	≤	≤	NOUN
ejpam-3391	84	15	i	i	PROPN
ejpam-3391	84	16	,	,	PUNCT
ejpam-3391	84	17	j	j	PROPN
ejpam-3391	84	18	≤	≤	PROPN
ejpam-3391	84	19	n	n	CCONJ
ejpam-3391	84	20	,	,	PUNCT
ejpam-3391	84	21	then	then	ADV
ejpam-3391	84	22	y	y	PROPN
ejpam-3391	84	23	=	=	SYM
ejpam-3391	84	24	t	t	PROPN
ejpam-3391	84	25	sf	sf	INTJ
ejpam-3391	84	26	if	if	SCONJ
ejpam-3391	84	27	,	,	PUNCT
ejpam-3391	84	28	and	and	CCONJ
ejpam-3391	84	29	only	only	ADV
ejpam-3391	84	30	if	if	SCONJ
ejpam-3391	84	31	,	,	PUNCT
ejpam-3391	84	32	fi	fi	NOUN
ejpam-3391	84	33	=	=	SYM
ejpam-3391	84	34	b	b	X
ejpam-3391	84	35	(	(	PUNCT
ejpam-3391	84	36	s	s	NOUN
ejpam-3391	84	37	)	)	PUNCT
ejpam-3391	84	38	i0	i0	PROPN
ejpam-3391	84	39	+	+	PROPN
ejpam-3391	84	40	n∑	n∑	PROPN
ejpam-3391	84	41	g=1	g=1	PROPN
ejpam-3391	84	42	b	b	PROPN
ejpam-3391	84	43	(	(	PUNCT
ejpam-3391	84	44	s	s	NOUN
ejpam-3391	84	45	)	)	PUNCT
ejpam-3391	84	46	ig	ig	PROPN
ejpam-3391	84	47	yg	yg	PROPN
ejpam-3391	84	48	b	b	PROPN
ejpam-3391	84	49	(	(	PUNCT
ejpam-3391	84	50	s	s	NOUN
ejpam-3391	84	51	)	)	PUNCT
ejpam-3391	84	52	00	00	PUNCT
ejpam-3391	85	1	+	+	NUM
ejpam-3391	85	2	n∑	n∑	PROPN
ejpam-3391	85	3	g=1	g=1	PROPN
ejpam-3391	85	4	b	b	PROPN
ejpam-3391	85	5	(	(	PUNCT
ejpam-3391	85	6	s	s	NOUN
ejpam-3391	85	7	)	)	PUNCT
ejpam-3391	85	8	0	0	PROPN
ejpam-3391	85	9	g	g	PROPN
ejpam-3391	85	10	yg	yg	PROPN
ejpam-3391	85	11	.	.	PUNCT
ejpam-3391	86	1	the	the	DET
ejpam-3391	86	2	algorithm	algorithm	PROPN
ejpam-3391	86	3	t	t	PROPN
ejpam-3391	86	4	is	be	AUX
ejpam-3391	86	5	said	say	VERB
ejpam-3391	86	6	convergent	convergent	NOUN
ejpam-3391	86	7	,	,	PUNCT
ejpam-3391	86	8	if	if	SCONJ
ejpam-3391	86	9	for	for	ADP
ejpam-3391	86	10	all	all	DET
ejpam-3391	86	11	f	f	PROPN
ejpam-3391	86	12	∈	∈	PROPN
ejpam-3391	86	13	b	b	PROPN
ejpam-3391	86	14	,	,	PUNCT
ejpam-3391	86	15	lim	lim	PROPN
ejpam-3391	86	16	s→+∞	s→+∞	PROPN
ejpam-3391	86	17	(	(	PUNCT
ejpam-3391	86	18	b	b	PROPN
ejpam-3391	86	19	(	(	PUNCT
ejpam-3391	86	20	s	s	NOUN
ejpam-3391	86	21	)	)	PUNCT
ejpam-3391	86	22	10	10	NUM
ejpam-3391	86	23	b	b	X
ejpam-3391	86	24	(	(	PUNCT
ejpam-3391	86	25	s	s	NOUN
ejpam-3391	86	26	)	)	PUNCT
ejpam-3391	86	27	00	00	PUNCT
ejpam-3391	86	28	,	,	PUNCT
ejpam-3391	86	29	.	.	PUNCT
ejpam-3391	86	30	.	.	PUNCT
ejpam-3391	86	31	.	.	PUNCT
ejpam-3391	87	1	,	,	PUNCT
ejpam-3391	87	2	b	b	X
ejpam-3391	87	3	(	(	PUNCT
ejpam-3391	87	4	s	s	NOUN
ejpam-3391	87	5	)	)	PUNCT
ejpam-3391	87	6	n0	n0	PROPN
ejpam-3391	87	7	b	b	PROPN
ejpam-3391	87	8	(	(	PUNCT
ejpam-3391	87	9	s	s	PROPN
ejpam-3391	87	10	)	)	PUNCT
ejpam-3391	87	11	00	00	PUNCT
ejpam-3391	87	12	)	)	PUNCT
ejpam-3391	88	1	=	=	SYM
ejpam-3391	88	2	f.	f.	NOUN
ejpam-3391	88	3	(	(	PUNCT
ejpam-3391	88	4	4.1	4.1	NUM
ejpam-3391	88	5	)	)	PUNCT
ejpam-3391	88	6	the	the	DET
ejpam-3391	88	7	vectors	vector	NOUN
ejpam-3391	88	8	(	(	PUNCT
ejpam-3391	88	9	b	b	X
ejpam-3391	88	10	(	(	PUNCT
ejpam-3391	88	11	s	s	NOUN
ejpam-3391	88	12	)	)	PUNCT
ejpam-3391	88	13	10	10	NUM
ejpam-3391	88	14	b	b	X
ejpam-3391	88	15	(	(	PUNCT
ejpam-3391	88	16	s	s	NOUN
ejpam-3391	88	17	)	)	PUNCT
ejpam-3391	88	18	00	00	PUNCT
ejpam-3391	88	19	,	,	PUNCT
ejpam-3391	88	20	.	.	PUNCT
ejpam-3391	88	21	.	.	PUNCT
ejpam-3391	88	22	.	.	PUNCT
ejpam-3391	89	1	,	,	PUNCT
ejpam-3391	89	2	b	b	X
ejpam-3391	89	3	(	(	PUNCT
ejpam-3391	89	4	s	s	NOUN
ejpam-3391	89	5	)	)	PUNCT
ejpam-3391	89	6	n0	n0	PROPN
ejpam-3391	89	7	b	b	PROPN
ejpam-3391	89	8	(	(	PUNCT
ejpam-3391	89	9	s	s	PROPN
ejpam-3391	89	10	)	)	PUNCT
ejpam-3391	89	11	00	00	NUM
ejpam-3391	89	12	)	)	PUNCT
ejpam-3391	89	13	are	be	AUX
ejpam-3391	89	14	the	the	DET
ejpam-3391	89	15	convergents	convergent	NOUN
ejpam-3391	89	16	of	of	ADP
ejpam-3391	89	17	f.	f.	PROPN
ejpam-3391	89	18	5	5	NUM
ejpam-3391	89	19	.	.	PUNCT
ejpam-3391	90	1	definitions	definition	NOUN
ejpam-3391	90	2	in	in	ADP
ejpam-3391	90	3	this	this	DET
ejpam-3391	90	4	section	section	NOUN
ejpam-3391	90	5	,	,	PUNCT
ejpam-3391	90	6	we	we	PRON
ejpam-3391	90	7	define	define	VERB
ejpam-3391	90	8	a	a	DET
ejpam-3391	90	9	map	map	NOUN
ejpam-3391	90	10	tβ	tβ	PRON
ejpam-3391	90	11	which	which	PRON
ejpam-3391	90	12	is	be	AUX
ejpam-3391	90	13	arisen	arise	VERB
ejpam-3391	90	14	from	from	ADP
ejpam-3391	90	15	β	β	NOUN
ejpam-3391	90	16	-	-	PUNCT
ejpam-3391	90	17	mjpa	mjpa	NOUN
ejpam-3391	90	18	.	.	PUNCT
ejpam-3391	91	1	let	let	VERB
ejpam-3391	91	2	β	β	X
ejpam-3391	91	3	=	=	SYM
ejpam-3391	91	4	(	(	PUNCT
ejpam-3391	91	5	βi)i∈z	βi)i∈z	X
ejpam-3391	91	6	be	be	AUX
ejpam-3391	91	7	a	a	DET
ejpam-3391	91	8	base	base	NOUN
ejpam-3391	91	9	sequense	sequense	NOUN
ejpam-3391	91	10	.	.	PUNCT
ejpam-3391	92	1	the	the	DET
ejpam-3391	92	2	map	map	NOUN
ejpam-3391	92	3	tβ	tβ	INTJ
ejpam-3391	92	4	:	:	PUNCT
ejpam-3391	92	5	ln	ln	ADJ
ejpam-3391	92	6	→	→	SYM
ejpam-3391	92	7	ln	ln	ADJ
ejpam-3391	92	8	by	by	ADP
ejpam-3391	92	9	tβ(ϕ1	tβ(ϕ1	NOUN
ejpam-3391	92	10	,	,	PUNCT
ejpam-3391	92	11	.	.	PUNCT
ejpam-3391	92	12	.	.	PUNCT
ejpam-3391	92	13	.	.	PUNCT
ejpam-3391	93	1	,	,	PUNCT
ejpam-3391	93	2	ϕn	ϕn	X
ejpam-3391	93	3	)	)	PUNCT
ejpam-3391	93	4	=	=	SYM
ejpam-3391	93	5	(	(	PUNCT
ejpam-3391	93	6	ϕ2	ϕ2	ADV
ejpam-3391	93	7	ϕj	ϕj	INTJ
ejpam-3391	93	8	,	,	PUNCT
ejpam-3391	93	9	.	.	PUNCT
ejpam-3391	93	10	.	.	PUNCT
ejpam-3391	93	11	.	.	PUNCT
ejpam-3391	94	1	,	,	PUNCT
ejpam-3391	94	2	ϕj−1	ϕj−1	INTJ
ejpam-3391	94	3	ϕj	ϕj	INTJ
ejpam-3391	94	4	,	,	PUNCT
ejpam-3391	94	5	{	{	PUNCT
ejpam-3391	94	6	β20	β20	ADV
ejpam-3391	94	7	ϕj	ϕj	INTJ
ejpam-3391	94	8	}	}	PUNCT
ejpam-3391	94	9	β	β	PROPN
ejpam-3391	94	10	,	,	PUNCT
ejpam-3391	94	11	{	{	PUNCT
ejpam-3391	94	12	ϕj+1	ϕj+1	X
ejpam-3391	94	13	ϕj	ϕj	NOUN
ejpam-3391	94	14	}	}	PUNCT
ejpam-3391	94	15	β	β	PROPN
ejpam-3391	94	16	,	,	PUNCT
ejpam-3391	94	17	.	.	PUNCT
ejpam-3391	94	18	.	.	PUNCT
ejpam-3391	94	19	.	.	PUNCT
ejpam-3391	95	1	,	,	PUNCT
ejpam-3391	95	2	{	{	PUNCT
ejpam-3391	95	3	ϕn	ϕn	NOUN
ejpam-3391	95	4	ϕj	ϕj	INTJ
ejpam-3391	95	5	}	}	PUNCT
ejpam-3391	95	6	β	β	PROPN
ejpam-3391	95	7	)	)	PUNCT
ejpam-3391	96	1	=	=	PUNCT
ejpam-3391	96	2	(	(	PUNCT
ejpam-3391	96	3	ϕ2	ϕ2	ADV
ejpam-3391	96	4	ϕj	ϕj	INTJ
ejpam-3391	96	5	,	,	PUNCT
ejpam-3391	96	6	.	.	PUNCT
ejpam-3391	96	7	.	.	PUNCT
ejpam-3391	96	8	.	.	PUNCT
ejpam-3391	97	1	,	,	PUNCT
ejpam-3391	97	2	ϕj−1	ϕj−1	INTJ
ejpam-3391	97	3	ϕj	ϕj	INTJ
ejpam-3391	97	4	,	,	PUNCT
ejpam-3391	97	5	1	1	NUM
ejpam-3391	97	6	ϕj	ϕj	ADP
ejpam-3391	97	7	−	−	PROPN
ejpam-3391	97	8	an+1	an+1	NOUN
ejpam-3391	97	9	,	,	PUNCT
ejpam-3391	97	10	ϕj+1	ϕj+1	X
ejpam-3391	97	11	ϕj	ϕj	ADP
ejpam-3391	97	12	−	−	PROPN
ejpam-3391	97	13	aj+1	aj+1	NOUN
ejpam-3391	97	14	,	,	PUNCT
ejpam-3391	97	15	.	.	PUNCT
ejpam-3391	97	16	.	.	PUNCT
ejpam-3391	98	1	.	.	PUNCT
ejpam-3391	99	1	,	,	PUNCT
ejpam-3391	99	2	ϕn	ϕn	INTJ
ejpam-3391	99	3	ϕj	ϕj	ADP
ejpam-3391	99	4	−	−	PROPN
ejpam-3391	99	5	an	an	DET
ejpam-3391	99	6	)	)	PUNCT
ejpam-3391	99	7	a.	a.	NOUN
ejpam-3391	99	8	chandoul	chandoul	PROPN
ejpam-3391	99	9	,	,	PUNCT
ejpam-3391	99	10	f.	f.	PROPN
ejpam-3391	99	11	aljuaydi	aljuaydi	PROPN
ejpam-3391	99	12	/	/	SYM
ejpam-3391	99	13	eur	eur	NOUN
ejpam-3391	99	14	.	.	PUNCT
ejpam-3391	100	1	j.	j.	PROPN
ejpam-3391	100	2	pure	pure	PROPN
ejpam-3391	100	3	appl	appl	PROPN
ejpam-3391	100	4	.	.	PROPN
ejpam-3391	100	5	math	math	PROPN
ejpam-3391	100	6	,	,	PUNCT
ejpam-3391	100	7	12	12	NUM
ejpam-3391	100	8	(	(	PUNCT
ejpam-3391	100	9	2	2	NUM
ejpam-3391	100	10	)	)	PUNCT
ejpam-3391	100	11	(	(	PUNCT
ejpam-3391	100	12	2019	2019	NUM
ejpam-3391	100	13	)	)	PUNCT
ejpam-3391	100	14	,	,	PUNCT
ejpam-3391	100	15	418	418	NUM
ejpam-3391	100	16	-	-	SYM
ejpam-3391	100	17	431	431	NUM
ejpam-3391	100	18	422	422	NUM
ejpam-3391	100	19	where	where	SCONJ
ejpam-3391	100	20	an+1	an+1	NOUN
ejpam-3391	100	21	[	[	PUNCT
ejpam-3391	100	22	β20	β20	NOUN
ejpam-3391	100	23	ϕj	ϕj	X
ejpam-3391	100	24	]	]	X
ejpam-3391	100	25	β	β	X
ejpam-3391	100	26	and	and	CCONJ
ejpam-3391	100	27	ai	ai	VERB
ejpam-3391	100	28	=	=	PUNCT
ejpam-3391	101	1	[	[	PUNCT
ejpam-3391	101	2	ϕi	ϕi	ADP
ejpam-3391	101	3	ϕj	ϕj	X
ejpam-3391	101	4	]	]	X
ejpam-3391	101	5	β	β	X
ejpam-3391	101	6	:	:	PUNCT
ejpam-3391	101	7	i	i	PRON
ejpam-3391	101	8	≥	≥	VERB
ejpam-3391	101	9	j	j	NOUN
ejpam-3391	102	1	+	+	CCONJ
ejpam-3391	102	2	1	1	NUM
ejpam-3391	102	3	,	,	PUNCT
ejpam-3391	102	4	for	for	ADP
ejpam-3391	102	5	(	(	PUNCT
ejpam-3391	102	6	ϕ1	ϕ1	NOUN
ejpam-3391	102	7	,	,	PUNCT
ejpam-3391	102	8	.	.	PUNCT
ejpam-3391	102	9	.	.	PUNCT
ejpam-3391	103	1	.	.	PUNCT
ejpam-3391	104	1	,	,	PUNCT
ejpam-3391	104	2	ϕn	ϕn	X
ejpam-3391	104	3	)	)	PUNCT
ejpam-3391	104	4	∈	∈	PROPN
ejpam-3391	104	5	lnj	lnj	PROPN
ejpam-3391	104	6	,	,	PUNCT
ejpam-3391	104	7	(	(	PUNCT
ejpam-3391	104	8	ϕ1	ϕ1	NOUN
ejpam-3391	104	9	,	,	PUNCT
ejpam-3391	104	10	.	.	PUNCT
ejpam-3391	104	11	.	.	PUNCT
ejpam-3391	104	12	.	.	PUNCT
ejpam-3391	105	1	,	,	PUNCT
ejpam-3391	105	2	ϕn	ϕn	PROPN
ejpam-3391	105	3	)	)	PUNCT
ejpam-3391	105	4	6=	6=	X
ejpam-3391	105	5	(	(	PUNCT
ejpam-3391	105	6	0	0	NUM
ejpam-3391	105	7	,	,	PUNCT
ejpam-3391	105	8	.	.	PUNCT
ejpam-3391	105	9	.	.	PUNCT
ejpam-3391	106	1	.	.	PUNCT
ejpam-3391	107	1	,	,	PUNCT
ejpam-3391	107	2	0	0	NUM
ejpam-3391	107	3	)	)	PUNCT
ejpam-3391	107	4	and	and	CCONJ
ejpam-3391	107	5	tβ(0	tβ(0	PROPN
ejpam-3391	107	6	,	,	PUNCT
ejpam-3391	107	7	.	.	PUNCT
ejpam-3391	107	8	.	.	PUNCT
ejpam-3391	108	1	.	.	PUNCT
ejpam-3391	109	1	,	,	PUNCT
ejpam-3391	109	2	0	0	X
ejpam-3391	109	3	)	)	PUNCT
ejpam-3391	109	4	=	=	SYM
ejpam-3391	109	5	(	(	PUNCT
ejpam-3391	109	6	0	0	NUM
ejpam-3391	109	7	,	,	PUNCT
ejpam-3391	109	8	.	.	PUNCT
ejpam-3391	109	9	.	.	PUNCT
ejpam-3391	110	1	.	.	PUNCT
ejpam-3391	111	1	,	,	PUNCT
ejpam-3391	111	2	0	0	NUM
ejpam-3391	111	3	)	)	PUNCT
ejpam-3391	111	4	.	.	PUNCT
ejpam-3391	112	1	for	for	ADP
ejpam-3391	112	2	s	s	PRON
ejpam-3391	112	3	≥	≥	NOUN
ejpam-3391	112	4	1	1	NUM
ejpam-3391	112	5	,	,	PUNCT
ejpam-3391	112	6	we	we	PRON
ejpam-3391	112	7	put	put	VERB
ejpam-3391	112	8	(	(	PUNCT
ejpam-3391	112	9	ϕ	ϕ	X
ejpam-3391	112	10	(	(	PUNCT
ejpam-3391	112	11	s	s	NOUN
ejpam-3391	112	12	)	)	PUNCT
ejpam-3391	112	13	1	1	NUM
ejpam-3391	112	14	,	,	PUNCT
ejpam-3391	112	15	.	.	PUNCT
ejpam-3391	112	16	.	.	PUNCT
ejpam-3391	113	1	.	.	PUNCT
ejpam-3391	114	1	,	,	PUNCT
ejpam-3391	114	2	ϕ	ϕ	X
ejpam-3391	114	3	(	(	PUNCT
ejpam-3391	114	4	s	s	NOUN
ejpam-3391	114	5	)	)	PUNCT
ejpam-3391	114	6	n	n	CCONJ
ejpam-3391	114	7	)	)	PUNCT
ejpam-3391	115	1	=	=	SYM
ejpam-3391	115	2	t	t	PROPN
ejpam-3391	115	3	sβ(ϕ1	sβ(ϕ1	NOUN
ejpam-3391	115	4	,	,	PUNCT
ejpam-3391	115	5	.	.	PUNCT
ejpam-3391	115	6	.	.	PUNCT
ejpam-3391	115	7	.	.	PUNCT
ejpam-3391	116	1	,	,	PUNCT
ejpam-3391	116	2	ϕn	ϕn	X
ejpam-3391	116	3	)	)	PUNCT
ejpam-3391	116	4	and	and	CCONJ
ejpam-3391	116	5	a	a	DET
ejpam-3391	116	6	(	(	PUNCT
ejpam-3391	116	7	s	s	X
ejpam-3391	116	8	)	)	PUNCT
ejpam-3391	116	9	i	i	PRON
ejpam-3391	116	10	=	=	PUNCT
ejpam-3391	116	11	ai(ϕ	ai(ϕ	X
ejpam-3391	116	12	(	(	PUNCT
ejpam-3391	116	13	s−1	s−1	PROPN
ejpam-3391	116	14	)	)	PUNCT
ejpam-3391	116	15	1	1	NUM
ejpam-3391	116	16	,	,	PUNCT
ejpam-3391	116	17	.	.	PUNCT
ejpam-3391	116	18	.	.	PUNCT
ejpam-3391	117	1	.	.	PUNCT
ejpam-3391	118	1	,	,	PUNCT
ejpam-3391	118	2	ϕ	ϕ	X
ejpam-3391	118	3	(	(	PUNCT
ejpam-3391	118	4	s−1	s−1	PROPN
ejpam-3391	118	5	)	)	PUNCT
ejpam-3391	118	6	n	n	CCONJ
ejpam-3391	118	7	)	)	PUNCT
ejpam-3391	119	1	=	=	NOUN
ejpam-3391	119	2	0	0	NOUN
ejpam-3391	119	3	,	,	PUNCT
ejpam-3391	119	4	·	·	PUNCT
ejpam-3391	119	5	·	·	PUNCT
ejpam-3391	119	6	·	·	PUNCT
ejpam-3391	119	7	,	,	PUNCT
ejpam-3391	119	8	0	0	NUM
ejpam-3391	119	9	,	,	PUNCT
ejpam-3391	119	10	[	[	PUNCT
ejpam-3391	119	11	β20	β20	NOUN
ejpam-3391	119	12	ϕ	ϕ	X
ejpam-3391	119	13	(	(	PUNCT
ejpam-3391	119	14	s−1	s−1	PROPN
ejpam-3391	119	15	)	)	PUNCT
ejpam-3391	119	16	j	j	NOUN
ejpam-3391	119	17	]	]	PUNCT
ejpam-3391	119	18	β	β	X
ejpam-3391	119	19	,	,	PUNCT
ejpam-3391	119	20	[	[	PUNCT
ejpam-3391	119	21	ϕ	ϕ	X
ejpam-3391	119	22	(	(	PUNCT
ejpam-3391	119	23	s−1	s−1	PROPN
ejpam-3391	119	24	)	)	PUNCT
ejpam-3391	119	25	j+1	j+1	NUM
ejpam-3391	119	26	ϕ	ϕ	NOUN
ejpam-3391	119	27	(	(	PUNCT
ejpam-3391	119	28	s−1	s−1	PROPN
ejpam-3391	119	29	)	)	PUNCT
ejpam-3391	119	30	j	j	NOUN
ejpam-3391	119	31	]	]	PUNCT
ejpam-3391	119	32	β	β	X
ejpam-3391	119	33	,	,	PUNCT
ejpam-3391	119	34	.	.	PUNCT
ejpam-3391	119	35	.	.	PUNCT
ejpam-3391	119	36	.	.	PUNCT
ejpam-3391	120	1	,	,	PUNCT
ejpam-3391	120	2	[	[	PUNCT
ejpam-3391	120	3	ϕ	ϕ	X
ejpam-3391	120	4	(	(	PUNCT
ejpam-3391	120	5	s−1	s−1	PROPN
ejpam-3391	120	6	)	)	PUNCT
ejpam-3391	120	7	n	n	PRON
ejpam-3391	120	8	ϕ	ϕ	NOUN
ejpam-3391	120	9	(	(	PUNCT
ejpam-3391	120	10	s−1	s−1	PROPN
ejpam-3391	120	11	)	)	PUNCT
ejpam-3391	120	12	j	j	NOUN
ejpam-3391	120	13	]	]	PUNCT
ejpam-3391	120	14	β	β	X
ejpam-3391	120	15			PROPN
ejpam-3391	120	16	=	=	SYM
ejpam-3391	120	17	(	(	PUNCT
ejpam-3391	120	18	0	0	NUM
ejpam-3391	120	19	,	,	PUNCT
ejpam-3391	120	20	·	·	PUNCT
ejpam-3391	120	21	·	·	PUNCT
ejpam-3391	120	22	·	·	PUNCT
ejpam-3391	120	23	,	,	PUNCT
ejpam-3391	120	24	0	0	NUM
ejpam-3391	120	25	,	,	PUNCT
ejpam-3391	120	26	an+1	an+1	NOUN
ejpam-3391	120	27	,	,	PUNCT
ejpam-3391	120	28	aj+1	aj+1	NUM
ejpam-3391	120	29	,	,	PUNCT
ejpam-3391	120	30	·	·	PUNCT
ejpam-3391	120	31	·	·	PUNCT
ejpam-3391	120	32	·	·	PUNCT
ejpam-3391	120	33	,	,	PUNCT
ejpam-3391	120	34	an	an	X
ejpam-3391	120	35	)	)	PUNCT
ejpam-3391	120	36	for	for	ADP
ejpam-3391	120	37	1	1	NUM
ejpam-3391	120	38	≤	≤	NUM
ejpam-3391	120	39	i	i	PRON
ejpam-3391	120	40	≤	≤	NOUN
ejpam-3391	120	41	n+	n+	PUNCT
ejpam-3391	120	42	1	1	NUM
ejpam-3391	120	43	,	,	PUNCT
ejpam-3391	120	44	that	that	PRON
ejpam-3391	120	45	is	is	ADV
ejpam-3391	120	46	t	t	NOUN
ejpam-3391	120	47	sβ(ϕ1	sβ(ϕ1	NOUN
ejpam-3391	120	48	,	,	PUNCT
ejpam-3391	120	49	.	.	PUNCT
ejpam-3391	120	50	.	.	PUNCT
ejpam-3391	120	51	.	.	PUNCT
ejpam-3391	120	52	,	,	PUNCT
ejpam-3391	120	53	ϕn	ϕn	X
ejpam-3391	120	54	)	)	PUNCT
ejpam-3391	120	55	=	=	SYM
ejpam-3391	120	56	t	t	PROPN
ejpam-3391	120	57	(	(	PUNCT
ejpam-3391	120	58	ϕ	ϕ	X
ejpam-3391	120	59	(	(	PUNCT
ejpam-3391	120	60	s−1	s−1	PROPN
ejpam-3391	120	61	)	)	PUNCT
ejpam-3391	120	62	1	1	NUM
ejpam-3391	120	63	,	,	PUNCT
ejpam-3391	120	64	.	.	PUNCT
ejpam-3391	120	65	.	.	PUNCT
ejpam-3391	120	66	.	.	PUNCT
ejpam-3391	121	1	,	,	PUNCT
ejpam-3391	121	2	ϕ	ϕ	X
ejpam-3391	121	3	(	(	PUNCT
ejpam-3391	121	4	s−1	s−1	PROPN
ejpam-3391	121	5	)	)	PUNCT
ejpam-3391	121	6	n	n	NOUN
ejpam-3391	121	7	)	)	PUNCT
ejpam-3391	121	8	=	=	SYM
ejpam-3391	121	9	ϕ(s−1	ϕ(s−1	NOUN
ejpam-3391	121	10	)	)	PUNCT
ejpam-3391	121	11	2	2	NUM
ejpam-3391	121	12	ϕ	ϕ	X
ejpam-3391	121	13	(	(	PUNCT
ejpam-3391	121	14	s−1	s−1	PROPN
ejpam-3391	121	15	)	)	PUNCT
ejpam-3391	121	16	j	j	NOUN
ejpam-3391	121	17	,	,	PUNCT
ejpam-3391	121	18	.	.	PUNCT
ejpam-3391	121	19	.	.	PUNCT
ejpam-3391	122	1	.	.	PUNCT
ejpam-3391	123	1	,	,	PUNCT
ejpam-3391	123	2	ϕ	ϕ	X
ejpam-3391	123	3	(	(	PUNCT
ejpam-3391	123	4	s−1	s−1	PROPN
ejpam-3391	123	5	)	)	PUNCT
ejpam-3391	123	6	j−1	j−1	PROPN
ejpam-3391	123	7	ϕ	ϕ	NOUN
ejpam-3391	123	8	(	(	PUNCT
ejpam-3391	123	9	s−1	s−1	PROPN
ejpam-3391	123	10	)	)	PUNCT
ejpam-3391	123	11	j	j	PROPN
ejpam-3391	123	12	,	,	PUNCT
ejpam-3391	123	13	{	{	PUNCT
ejpam-3391	123	14	β20	β20	PROPN
ejpam-3391	123	15	ϕ	ϕ	PROPN
ejpam-3391	123	16	(	(	PUNCT
ejpam-3391	123	17	s−1	s−1	PROPN
ejpam-3391	123	18	)	)	PUNCT
ejpam-3391	123	19	j	j	NOUN
ejpam-3391	123	20	}	}	PUNCT
ejpam-3391	123	21	β	β	PROPN
ejpam-3391	123	22	,	,	PUNCT
ejpam-3391	123	23	{	{	PUNCT
ejpam-3391	123	24	ϕ	ϕ	X
ejpam-3391	123	25	(	(	PUNCT
ejpam-3391	123	26	s−1	s−1	PROPN
ejpam-3391	123	27	)	)	PUNCT
ejpam-3391	123	28	j+1	j+1	NUM
ejpam-3391	123	29	ϕ	ϕ	NOUN
ejpam-3391	123	30	(	(	PUNCT
ejpam-3391	123	31	s−1	s−1	PROPN
ejpam-3391	123	32	)	)	PUNCT
ejpam-3391	123	33	j	j	NOUN
ejpam-3391	123	34	}	}	PUNCT
ejpam-3391	123	35	β	β	PROPN
ejpam-3391	123	36	,	,	PUNCT
ejpam-3391	123	37	.	.	PUNCT
ejpam-3391	123	38	.	.	PUNCT
ejpam-3391	123	39	.	.	PUNCT
ejpam-3391	124	1	,	,	PUNCT
ejpam-3391	124	2	{	{	PUNCT
ejpam-3391	124	3	ϕ	ϕ	X
ejpam-3391	124	4	(	(	PUNCT
ejpam-3391	124	5	s−1	s−1	PROPN
ejpam-3391	124	6	)	)	PUNCT
ejpam-3391	124	7	n	n	PRON
ejpam-3391	124	8	ϕ	ϕ	NOUN
ejpam-3391	124	9	(	(	PUNCT
ejpam-3391	124	10	s−1	s−1	PROPN
ejpam-3391	124	11	)	)	PUNCT
ejpam-3391	124	12	j	j	NOUN
ejpam-3391	124	13	}	}	PUNCT
ejpam-3391	124	14	β	β	X
ejpam-3391	124	15			PROPN
ejpam-3391	124	16	=	=	PUNCT
ejpam-3391	124	17	(	(	PUNCT
ejpam-3391	124	18	ϕ	ϕ	X
ejpam-3391	124	19	(	(	PUNCT
ejpam-3391	124	20	s−1	s−1	PROPN
ejpam-3391	124	21	)	)	PUNCT
ejpam-3391	124	22	2	2	NUM
ejpam-3391	124	23	ϕ	ϕ	X
ejpam-3391	124	24	(	(	PUNCT
ejpam-3391	124	25	s−1	s−1	PROPN
ejpam-3391	124	26	)	)	PUNCT
ejpam-3391	124	27	j	j	NOUN
ejpam-3391	124	28	,	,	PUNCT
ejpam-3391	124	29	.	.	PUNCT
ejpam-3391	124	30	.	.	PUNCT
ejpam-3391	124	31	.	.	PUNCT
ejpam-3391	125	1	,	,	PUNCT
ejpam-3391	125	2	ϕ	ϕ	X
ejpam-3391	125	3	(	(	PUNCT
ejpam-3391	125	4	s−1	s−1	PROPN
ejpam-3391	125	5	)	)	PUNCT
ejpam-3391	125	6	j−1	j−1	PROPN
ejpam-3391	125	7	ϕ	ϕ	NOUN
ejpam-3391	125	8	(	(	PUNCT
ejpam-3391	125	9	s−1	s−1	PROPN
ejpam-3391	125	10	)	)	PUNCT
ejpam-3391	125	11	j	j	NOUN
ejpam-3391	125	12	,	,	PUNCT
ejpam-3391	125	13	1	1	NUM
ejpam-3391	125	14	ϕ	ϕ	X
ejpam-3391	125	15	(	(	PUNCT
ejpam-3391	125	16	s−1	s−1	PROPN
ejpam-3391	125	17	)	)	PUNCT
ejpam-3391	125	18	j	j	NOUN
ejpam-3391	125	19	−	−	PROPN
ejpam-3391	125	20	a(s)n+1	a(s)n+1	PROPN
ejpam-3391	125	21	,	,	PUNCT
ejpam-3391	125	22	ϕ	ϕ	X
ejpam-3391	125	23	(	(	PUNCT
ejpam-3391	125	24	s−1	s−1	PROPN
ejpam-3391	125	25	)	)	PUNCT
ejpam-3391	125	26	j+1	j+1	NUM
ejpam-3391	125	27	ϕ	ϕ	NOUN
ejpam-3391	125	28	(	(	PUNCT
ejpam-3391	125	29	s−1	s−1	PROPN
ejpam-3391	125	30	)	)	PUNCT
ejpam-3391	125	31	j	j	NOUN
ejpam-3391	125	32	−	−	PROPN
ejpam-3391	125	33	a(s)j+1	a(s)j+1	PROPN
ejpam-3391	125	34	,	,	PUNCT
ejpam-3391	125	35	.	.	PUNCT
ejpam-3391	125	36	.	.	PUNCT
ejpam-3391	125	37	.	.	PUNCT
ejpam-3391	126	1	,	,	PUNCT
ejpam-3391	126	2	ϕ	ϕ	X
ejpam-3391	126	3	(	(	PUNCT
ejpam-3391	126	4	s−1	s−1	PROPN
ejpam-3391	126	5	)	)	PUNCT
ejpam-3391	126	6	n	n	PRON
ejpam-3391	126	7	ϕ	ϕ	NOUN
ejpam-3391	126	8	(	(	PUNCT
ejpam-3391	126	9	s−1	s−1	PROPN
ejpam-3391	126	10	)	)	PUNCT
ejpam-3391	126	11	j	j	NOUN
ejpam-3391	126	12	−	−	PROPN
ejpam-3391	126	13	a(s)n	a(s)n	PROPN
ejpam-3391	126	14	)	)	PUNCT
ejpam-3391	126	15	for	for	ADP
ejpam-3391	126	16	(	(	PUNCT
ejpam-3391	126	17	ϕ	ϕ	X
ejpam-3391	126	18	(	(	PUNCT
ejpam-3391	126	19	s−1	s−1	PROPN
ejpam-3391	126	20	)	)	PUNCT
ejpam-3391	126	21	1	1	NUM
ejpam-3391	126	22	,	,	PUNCT
ejpam-3391	126	23	.	.	PUNCT
ejpam-3391	126	24	.	.	PUNCT
ejpam-3391	126	25	.	.	PUNCT
ejpam-3391	127	1	,	,	PUNCT
ejpam-3391	127	2	ϕ	ϕ	X
ejpam-3391	127	3	(	(	PUNCT
ejpam-3391	127	4	s−1	s−1	PROPN
ejpam-3391	127	5	)	)	PUNCT
ejpam-3391	127	6	n	n	CCONJ
ejpam-3391	127	7	)	)	PUNCT
ejpam-3391	127	8	∈	∈	PROPN
ejpam-3391	127	9	lnj	lnj	PROPN
ejpam-3391	127	10	.	.	PUNCT
ejpam-3391	128	1	also	also	ADV
ejpam-3391	128	2	we	we	PRON
ejpam-3391	128	3	put	put	VERB
ejpam-3391	128	4	κ(s	κ(s	PROPN
ejpam-3391	128	5	)	)	PUNCT
ejpam-3391	128	6	:	:	PUNCT
ejpam-3391	129	1	=	=	PUNCT
ejpam-3391	129	2	j	j	PROPN
ejpam-3391	129	3	such	such	ADJ
ejpam-3391	129	4	that	that	DET
ejpam-3391	129	5	degϕ	degϕ	NOUN
ejpam-3391	129	6	(	(	PUNCT
ejpam-3391	129	7	s−1	s−1	PROPN
ejpam-3391	129	8	)	)	PUNCT
ejpam-3391	129	9	j	j	PROPN
ejpam-3391	129	10	>	>	X
ejpam-3391	129	11	ϕ	ϕ	X
ejpam-3391	129	12	(	(	PUNCT
ejpam-3391	129	13	s−1	s−1	PROPN
ejpam-3391	129	14	)	)	PUNCT
ejpam-3391	129	15	i	i	PRON
ejpam-3391	129	16	for	for	ADP
ejpam-3391	129	17	1	1	NUM
ejpam-3391	129	18	≤	≤	NUM
ejpam-3391	130	1	i	i	PRON
ejpam-3391	130	2	<	<	X
ejpam-3391	130	3	j	j	PROPN
ejpam-3391	130	4	and	and	CCONJ
ejpam-3391	130	5	degϕ	degϕ	PROPN
ejpam-3391	130	6	(	(	PUNCT
ejpam-3391	130	7	s−1	s−1	PROPN
ejpam-3391	130	8	)	)	PUNCT
ejpam-3391	130	9	j	j	PROPN
ejpam-3391	130	10	≥	≥	NUM
ejpam-3391	130	11	ϕ(s−1	ϕ(s−1	PROPN
ejpam-3391	130	12	)	)	PUNCT
ejpam-3391	130	13	i	i	PRON
ejpam-3391	130	14	for	for	ADP
ejpam-3391	130	15	j	j	PROPN
ejpam-3391	130	16	<	<	X
ejpam-3391	130	17	i	i	PROPN
ejpam-3391	130	18	≤	≤	PROPN
ejpam-3391	130	19	n.	n.	PROPN
ejpam-3391	130	20	5.1	5.1	NUM
ejpam-3391	130	21	.	.	PUNCT
ejpam-3391	131	1	the	the	DET
ejpam-3391	131	2	matrix	matrix	NOUN
ejpam-3391	131	3	let	let	VERB
ejpam-3391	131	4	(	(	PUNCT
ejpam-3391	131	5	ϕ1	ϕ1	NOUN
ejpam-3391	131	6	,	,	PUNCT
ejpam-3391	131	7	.	.	PUNCT
ejpam-3391	131	8	.	.	PUNCT
ejpam-3391	132	1	.	.	PUNCT
ejpam-3391	133	1	,	,	PUNCT
ejpam-3391	133	2	ϕn	ϕn	X
ejpam-3391	133	3	)	)	PUNCT
ejpam-3391	133	4	∈	∈	PROPN
ejpam-3391	133	5	lnj	lnj	PROPN
ejpam-3391	133	6	,	,	PUNCT
ejpam-3391	133	7	(	(	PUNCT
ejpam-3391	133	8	ϕ1	ϕ1	NOUN
ejpam-3391	133	9	,	,	PUNCT
ejpam-3391	133	10	.	.	PUNCT
ejpam-3391	133	11	.	.	PUNCT
ejpam-3391	133	12	.	.	PUNCT
ejpam-3391	134	1	,	,	PUNCT
ejpam-3391	134	2	ϕn	ϕn	PROPN
ejpam-3391	134	3	)	)	PUNCT
ejpam-3391	134	4	6=	6=	X
ejpam-3391	134	5	(	(	PUNCT
ejpam-3391	134	6	0	0	NUM
ejpam-3391	134	7	,	,	PUNCT
ejpam-3391	134	8	.	.	PUNCT
ejpam-3391	134	9	.	.	PUNCT
ejpam-3391	135	1	.	.	PUNCT
ejpam-3391	136	1	,	,	PUNCT
ejpam-3391	136	2	0	0	NUM
ejpam-3391	136	3	)	)	PUNCT
ejpam-3391	136	4	.	.	PUNCT
ejpam-3391	137	1	we	we	PRON
ejpam-3391	137	2	define	define	VERB
ejpam-3391	137	3	the	the	DET
ejpam-3391	137	4	(	(	PUNCT
ejpam-3391	137	5	n+1)×(n+1	n+1)×(n+1	NOUN
ejpam-3391	137	6	)	)	PUNCT
ejpam-3391	137	7	matrix	matrix	NOUN
ejpam-3391	137	8	m	m	NOUN
ejpam-3391	137	9	=	=	SYM
ejpam-3391	137	10	(	(	PUNCT
ejpam-3391	137	11	mi1i2	mi1i2	PROPN
ejpam-3391	137	12	)	)	PUNCT
ejpam-3391	137	13	,	,	PUNCT
ejpam-3391	137	14	mi1i2	mi1i2	PROPN
ejpam-3391	137	15	∈	∈	PROPN
ejpam-3391	137	16	fq((x−1	fq((x−1	NOUN
ejpam-3391	137	17	)	)	PUNCT
ejpam-3391	137	18	)	)	PUNCT
ejpam-3391	137	19	,	,	PUNCT
ejpam-3391	137	20	associated	associate	VERB
ejpam-3391	137	21	to	to	ADP
ejpam-3391	137	22	(	(	PUNCT
ejpam-3391	137	23	ϕ1	ϕ1	NOUN
ejpam-3391	137	24	,	,	PUNCT
ejpam-3391	137	25	.	.	PUNCT
ejpam-3391	137	26	.	.	PUNCT
ejpam-3391	137	27	.	.	PUNCT
ejpam-3391	138	1	,	,	PUNCT
ejpam-3391	138	2	ϕn	ϕn	X
ejpam-3391	138	3	)	)	PUNCT
ejpam-3391	138	4	in	in	ADP
ejpam-3391	138	5	the	the	DET
ejpam-3391	138	6	following	following	ADJ
ejpam-3391	138	7	way	way	NOUN
ejpam-3391	138	8	:	:	PUNCT
ejpam-3391	138	9	(	(	PUNCT
ejpam-3391	138	10	i	i	NOUN
ejpam-3391	138	11	)	)	PUNCT
ejpam-3391	139	1	1	1	NUM
ejpam-3391	139	2	≤	≤	PROPN
ejpam-3391	139	3	i2	i2	PROPN
ejpam-3391	139	4	≤	≤	PROPN
ejpam-3391	139	5	n	n	CCONJ
ejpam-3391	139	6	,	,	PUNCT
ejpam-3391	139	7	i2	i2	PROPN
ejpam-3391	139	8	6=	6=	PROPN
ejpam-3391	139	9	j	j	PROPN
ejpam-3391	139	10	mi1i2	mi1i2	PROPN
ejpam-3391	139	11	=	=	PROPN
ejpam-3391	139	12	δi1i2	δi1i2	PROPN
ejpam-3391	139	13	for	for	ADP
ejpam-3391	139	14	1	1	NUM
ejpam-3391	139	15	≤	≤	PROPN
ejpam-3391	139	16	i1	i1	PROPN
ejpam-3391	139	17	≤	≤	PROPN
ejpam-3391	139	18	n+	n+	PUNCT
ejpam-3391	139	19	1	1	NUM
ejpam-3391	139	20	,	,	PUNCT
ejpam-3391	139	21	(	(	PUNCT
ejpam-3391	139	22	1	1	NUM
ejpam-3391	139	23	)	)	PUNCT
ejpam-3391	139	24	(	(	PUNCT
ejpam-3391	139	25	ii	ii	NOUN
ejpam-3391	139	26	)	)	PUNCT
ejpam-3391	139	27	i2	i2	PROPN
ejpam-3391	139	28	=	=	SYM
ejpam-3391	139	29	j	j	PROPN
ejpam-3391	139	30	mi1i2	mi1i2	PROPN
ejpam-3391	139	31	=	=	PROPN
ejpam-3391	139	32	{	{	PUNCT
ejpam-3391	139	33	1	1	NUM
ejpam-3391	139	34	for	for	ADP
ejpam-3391	139	35	i1	i1	PROPN
ejpam-3391	139	36	=	=	PUNCT
ejpam-3391	139	37	n+	n+	PUNCT
ejpam-3391	139	38	1	1	NUM
ejpam-3391	139	39	0	0	NUM
ejpam-3391	139	40	for	for	ADP
ejpam-3391	139	41	1	1	NUM
ejpam-3391	139	42	≤	≤	PROPN
ejpam-3391	139	43	i1	i1	PROPN
ejpam-3391	139	44	≤	≤	PROPN
ejpam-3391	139	45	n	n	CCONJ
ejpam-3391	139	46	(	(	PUNCT
ejpam-3391	139	47	2	2	NUM
ejpam-3391	139	48	)	)	PUNCT
ejpam-3391	139	49	(	(	PUNCT
ejpam-3391	139	50	iii	iii	X
ejpam-3391	139	51	)	)	PUNCT
ejpam-3391	139	52	i2	i2	NOUN
ejpam-3391	139	53	=	=	SYM
ejpam-3391	139	54	n+	n+	PUNCT
ejpam-3391	139	55	1	1	NUM
ejpam-3391	139	56	,	,	PUNCT
ejpam-3391	139	57	1	1	NUM
ejpam-3391	139	58	≤	≤	PROPN
ejpam-3391	139	59	i1	i1	PROPN
ejpam-3391	139	60	≤	≤	PROPN
ejpam-3391	139	61	n+	n+	PUNCT
ejpam-3391	139	62	1	1	NUM
ejpam-3391	139	63	mi1i2	mi1i2	PROPN
ejpam-3391	139	64	=	=	PUNCT
ejpam-3391	139	65	ai1	ai1	PROPN
ejpam-3391	139	66	,	,	PUNCT
ejpam-3391	139	67	(	(	PUNCT
ejpam-3391	139	68	3	3	X
ejpam-3391	139	69	)	)	PUNCT
ejpam-3391	139	70	a.	a.	NOUN
ejpam-3391	139	71	chandoul	chandoul	PROPN
ejpam-3391	139	72	,	,	PUNCT
ejpam-3391	139	73	f.	f.	PROPN
ejpam-3391	139	74	aljuaydi	aljuaydi	PROPN
ejpam-3391	139	75	/	/	SYM
ejpam-3391	139	76	eur	eur	NOUN
ejpam-3391	139	77	.	.	PUNCT
ejpam-3391	140	1	j.	j.	PROPN
ejpam-3391	140	2	pure	pure	PROPN
ejpam-3391	140	3	appl	appl	PROPN
ejpam-3391	140	4	.	.	PROPN
ejpam-3391	140	5	math	math	PROPN
ejpam-3391	140	6	,	,	PUNCT
ejpam-3391	140	7	12	12	NUM
ejpam-3391	140	8	(	(	PUNCT
ejpam-3391	140	9	2	2	NUM
ejpam-3391	140	10	)	)	PUNCT
ejpam-3391	140	11	(	(	PUNCT
ejpam-3391	140	12	2019	2019	NUM
ejpam-3391	140	13	)	)	PUNCT
ejpam-3391	140	14	,	,	PUNCT
ejpam-3391	140	15	418	418	NUM
ejpam-3391	140	16	-	-	SYM
ejpam-3391	140	17	431	431	NUM
ejpam-3391	140	18	423	423	NUM
ejpam-3391	140	19	that	that	PRON
ejpam-3391	140	20	is	be	AUX
ejpam-3391	140	21	,	,	PUNCT
ejpam-3391	140	22	m	m	VERB
ejpam-3391	140	23	=	=	ADJ
ejpam-3391	140	24	m(ϕ1	m(ϕ1	ADJ
ejpam-3391	140	25	,	,	PUNCT
ejpam-3391	140	26	.	.	PUNCT
ejpam-3391	140	27	.	.	PUNCT
ejpam-3391	141	1	.	.	PUNCT
ejpam-3391	142	1	,	,	PUNCT
ejpam-3391	142	2	ϕn	ϕn	X
ejpam-3391	142	3	)	)	PUNCT
ejpam-3391	142	4	=	=	SYM
ejpam-3391	142	5			NOUN
ejpam-3391	142	6	1	1	NUM
ejpam-3391	142	7	0	0	NUM
ejpam-3391	142	8	.	.	PUNCT
ejpam-3391	142	9	.	.	PUNCT
ejpam-3391	143	1	.	.	PUNCT
ejpam-3391	144	1	0	0	NUM
ejpam-3391	145	1	0	0	NUM
ejpam-3391	145	2	0	0	NUM
ejpam-3391	145	3	.	.	PUNCT
ejpam-3391	145	4	.	.	PUNCT
ejpam-3391	145	5	.	.	PUNCT
ejpam-3391	146	1	0	0	NUM
ejpam-3391	146	2	0	0	NUM
ejpam-3391	146	3	0	0	NUM
ejpam-3391	146	4	1	1	NUM
ejpam-3391	146	5	.	.	PUNCT
ejpam-3391	146	6	.	.	PUNCT
ejpam-3391	146	7	.	.	PUNCT
ejpam-3391	147	1	0	0	NUM
ejpam-3391	148	1	0	0	NUM
ejpam-3391	148	2	0	0	NUM
ejpam-3391	148	3	.	.	PUNCT
ejpam-3391	148	4	.	.	PUNCT
ejpam-3391	148	5	.	.	PUNCT
ejpam-3391	149	1	0	0	NUM
ejpam-3391	149	2	0	0	NUM
ejpam-3391	149	3	...	...	PUNCT
ejpam-3391	149	4	...	...	PUNCT
ejpam-3391	149	5	.	.	PUNCT
ejpam-3391	149	6	.	.	PUNCT
ejpam-3391	149	7	.	.	PUNCT
ejpam-3391	150	1	...	...	PUNCT
ejpam-3391	150	2	...	...	PUNCT
ejpam-3391	150	3	...	...	PUNCT
ejpam-3391	150	4	.	.	PUNCT
ejpam-3391	150	5	.	.	PUNCT
ejpam-3391	151	1	.	.	PUNCT
ejpam-3391	152	1	...	...	PUNCT
ejpam-3391	153	1	...	...	PUNCT
ejpam-3391	154	1	0	0	NUM
ejpam-3391	154	2	0	0	NUM
ejpam-3391	154	3	.	.	PUNCT
ejpam-3391	154	4	.	.	PUNCT
ejpam-3391	154	5	.	.	PUNCT
ejpam-3391	155	1	1	1	NUM
ejpam-3391	155	2	0	0	NUM
ejpam-3391	155	3	0	0	NUM
ejpam-3391	155	4	.	.	PUNCT
ejpam-3391	155	5	.	.	PUNCT
ejpam-3391	155	6	.	.	PUNCT
ejpam-3391	156	1	0	0	NUM
ejpam-3391	157	1	0	0	NUM
ejpam-3391	157	2	0	0	NUM
ejpam-3391	157	3	0	0	NUM
ejpam-3391	157	4	.	.	PUNCT
ejpam-3391	157	5	.	.	PUNCT
ejpam-3391	157	6	.	.	PUNCT
ejpam-3391	158	1	0	0	NUM
ejpam-3391	159	1	0	0	NUM
ejpam-3391	159	2	0	0	NUM
ejpam-3391	159	3	.	.	PUNCT
ejpam-3391	159	4	.	.	PUNCT
ejpam-3391	159	5	.	.	PUNCT
ejpam-3391	160	1	0	0	NUM
ejpam-3391	161	1	1	1	NUM
ejpam-3391	161	2	0	0	NUM
ejpam-3391	161	3	0	0	NUM
ejpam-3391	161	4	.	.	PUNCT
ejpam-3391	161	5	.	.	PUNCT
ejpam-3391	161	6	.	.	PUNCT
ejpam-3391	162	1	0	0	NUM
ejpam-3391	162	2	0	0	NUM
ejpam-3391	162	3	1	1	NUM
ejpam-3391	162	4	.	.	PUNCT
ejpam-3391	162	5	.	.	PUNCT
ejpam-3391	162	6	.	.	PUNCT
ejpam-3391	163	1	0	0	NUM
ejpam-3391	164	1	aj+1	aj+1	NUM
ejpam-3391	164	2	...	...	PUNCT
ejpam-3391	164	3	...	...	PUNCT
ejpam-3391	164	4	.	.	PUNCT
ejpam-3391	164	5	.	.	PUNCT
ejpam-3391	164	6	.	.	PUNCT
ejpam-3391	164	7	...	...	PUNCT
ejpam-3391	164	8	...	...	PUNCT
ejpam-3391	164	9	...	...	PUNCT
ejpam-3391	164	10	.	.	PUNCT
ejpam-3391	164	11	.	.	PUNCT
ejpam-3391	164	12	.	.	PUNCT
ejpam-3391	165	1	...	...	PUNCT
ejpam-3391	166	1	...	...	PUNCT
ejpam-3391	167	1	0	0	NUM
ejpam-3391	167	2	0	0	NUM
ejpam-3391	167	3	.	.	PUNCT
ejpam-3391	167	4	.	.	PUNCT
ejpam-3391	167	5	.	.	PUNCT
ejpam-3391	168	1	0	0	NUM
ejpam-3391	169	1	0	0	NUM
ejpam-3391	169	2	0	0	NUM
ejpam-3391	169	3	.	.	PUNCT
ejpam-3391	169	4	.	.	PUNCT
ejpam-3391	170	1	.	.	PUNCT
ejpam-3391	171	1	1	1	NUM
ejpam-3391	171	2	an	an	DET
ejpam-3391	171	3	0	0	NUM
ejpam-3391	171	4	0	0	NUM
ejpam-3391	171	5	.	.	PUNCT
ejpam-3391	171	6	.	.	PUNCT
ejpam-3391	171	7	.	.	PUNCT
ejpam-3391	172	1	0	0	NUM
ejpam-3391	173	1	1	1	NUM
ejpam-3391	173	2	0	0	NUM
ejpam-3391	173	3	.	.	PUNCT
ejpam-3391	173	4	.	.	PUNCT
ejpam-3391	174	1	.	.	PUNCT
ejpam-3391	175	1	0	0	NUM
ejpam-3391	175	2	an+1	an+1	PROPN
ejpam-3391	175	3			PROPN
ejpam-3391	175	4	.	.	PUNCT
ejpam-3391	176	1	(	(	PUNCT
ejpam-3391	176	2	4	4	X
ejpam-3391	176	3	)	)	PUNCT
ejpam-3391	176	4	for	for	ADP
ejpam-3391	176	5	(	(	PUNCT
ejpam-3391	176	6	ϕ1	ϕ1	NOUN
ejpam-3391	176	7	,	,	PUNCT
ejpam-3391	176	8	.	.	PUNCT
ejpam-3391	176	9	.	.	PUNCT
ejpam-3391	176	10	.	.	PUNCT
ejpam-3391	177	1	,	,	PUNCT
ejpam-3391	177	2	ϕn	ϕn	X
ejpam-3391	177	3	)	)	PUNCT
ejpam-3391	177	4	=	=	SYM
ejpam-3391	177	5	(	(	PUNCT
ejpam-3391	177	6	0	0	NUM
ejpam-3391	177	7	,	,	PUNCT
ejpam-3391	177	8	.	.	PUNCT
ejpam-3391	177	9	.	.	PUNCT
ejpam-3391	178	1	.	.	PUNCT
ejpam-3391	179	1	,	,	PUNCT
ejpam-3391	179	2	0	0	NUM
ejpam-3391	179	3	)	)	PUNCT
ejpam-3391	179	4	,	,	PUNCT
ejpam-3391	179	5	we	we	PRON
ejpam-3391	179	6	define	define	VERB
ejpam-3391	179	7	m	m	VERB
ejpam-3391	179	8	the	the	DET
ejpam-3391	179	9	(	(	PUNCT
ejpam-3391	179	10	n+	n+	NUM
ejpam-3391	179	11	1)×	1)×	NUM
ejpam-3391	179	12	(	(	PUNCT
ejpam-3391	179	13	n+	n+	NOUN
ejpam-3391	179	14	1	1	NUM
ejpam-3391	179	15	)	)	PUNCT
ejpam-3391	179	16	unit	unit	NOUN
ejpam-3391	179	17	matrix	matrix	NOUN
ejpam-3391	179	18	in+1	in+1	NOUN
ejpam-3391	179	19	.	.	PUNCT
ejpam-3391	180	1	we	we	PRON
ejpam-3391	180	2	put	put	VERB
ejpam-3391	180	3	m	m	PROPN
ejpam-3391	180	4	(	(	PUNCT
ejpam-3391	180	5	0	0	NUM
ejpam-3391	180	6	)	)	PUNCT
ejpam-3391	180	7	=	=	SYM
ejpam-3391	180	8	in+1	in+1	PROPN
ejpam-3391	180	9	,	,	PUNCT
ejpam-3391	180	10	m	m	VERB
ejpam-3391	180	11	(	(	PUNCT
ejpam-3391	180	12	s	s	X
ejpam-3391	180	13	)	)	PUNCT
ejpam-3391	180	14	=	=	SYM
ejpam-3391	181	1	m(ϕ	m(ϕ	INTJ
ejpam-3391	181	2	(	(	PUNCT
ejpam-3391	181	3	s−1	s−1	PROPN
ejpam-3391	181	4	)	)	PUNCT
ejpam-3391	181	5	1	1	NUM
ejpam-3391	181	6	,	,	PUNCT
ejpam-3391	181	7	.	.	PUNCT
ejpam-3391	181	8	.	.	PUNCT
ejpam-3391	181	9	.	.	PUNCT
ejpam-3391	182	1	,	,	PUNCT
ejpam-3391	182	2	ϕ(s−1	ϕ(s−1	PROPN
ejpam-3391	182	3	)	)	PUNCT
ejpam-3391	182	4	n	n	CCONJ
ejpam-3391	182	5	)	)	PUNCT
ejpam-3391	182	6	for	for	ADP
ejpam-3391	182	7	s	s	PRON
ejpam-3391	182	8	≥	≥	NOUN
ejpam-3391	182	9	1	1	NUM
ejpam-3391	182	10	,	,	PUNCT
ejpam-3391	182	11	where	where	SCONJ
ejpam-3391	182	12	(	(	PUNCT
ejpam-3391	182	13	ϕ	ϕ	X
ejpam-3391	182	14	(	(	PUNCT
ejpam-3391	182	15	0	0	NUM
ejpam-3391	182	16	)	)	PUNCT
ejpam-3391	182	17	1	1	NUM
ejpam-3391	182	18	,	,	PUNCT
ejpam-3391	182	19	.	.	PUNCT
ejpam-3391	182	20	.	.	PUNCT
ejpam-3391	183	1	.	.	PUNCT
ejpam-3391	184	1	,	,	PUNCT
ejpam-3391	184	2	ϕ	ϕ	X
ejpam-3391	184	3	(	(	PUNCT
ejpam-3391	184	4	0	0	NUM
ejpam-3391	184	5	)	)	PUNCT
ejpam-3391	184	6	n	n	NOUN
ejpam-3391	184	7	)	)	PUNCT
ejpam-3391	185	1	=	=	SYM
ejpam-3391	185	2	(	(	PUNCT
ejpam-3391	185	3	ϕ1	ϕ1	NOUN
ejpam-3391	185	4	,	,	PUNCT
ejpam-3391	185	5	.	.	PUNCT
ejpam-3391	185	6	.	.	PUNCT
ejpam-3391	185	7	.	.	PUNCT
ejpam-3391	186	1	,	,	PUNCT
ejpam-3391	186	2	ϕn	ϕn	INTJ
ejpam-3391	186	3	)	)	PUNCT
ejpam-3391	186	4	.	.	PUNCT
ejpam-3391	187	1	since	since	SCONJ
ejpam-3391	187	2	,	,	PUNCT
ejpam-3391	187	3	we	we	PRON
ejpam-3391	187	4	consider	consider	VERB
ejpam-3391	187	5	the	the	DET
ejpam-3391	187	6	columns	column	NOUN
ejpam-3391	187	7	of	of	ADP
ejpam-3391	187	8	the	the	DET
ejpam-3391	187	9	matrixm	matrixm	NOUN
ejpam-3391	187	10	(	(	PUNCT
ejpam-3391	187	11	1	1	NUM
ejpam-3391	187	12	)	)	PUNCT
ejpam-3391	187	13	,	,	PUNCT
ejpam-3391	187	14	.	.	PUNCT
ejpam-3391	187	15	.	.	PUNCT
ejpam-3391	188	1	.	.	PUNCT
ejpam-3391	189	1	,	,	PUNCT
ejpam-3391	189	2	m	m	PROPN
ejpam-3391	189	3	(	(	PUNCT
ejpam-3391	189	4	s	s	NOUN
ejpam-3391	189	5	)	)	PUNCT
ejpam-3391	189	6	,	,	PUNCT
ejpam-3391	189	7	we	we	PRON
ejpam-3391	189	8	denote	denote	VERB
ejpam-3391	189	9	m	m	PROPN
ejpam-3391	189	10	(	(	PUNCT
ejpam-3391	189	11	1	1	NUM
ejpam-3391	189	12	)	)	PUNCT
ejpam-3391	189	13	.	.	PUNCT
ejpam-3391	189	14	.	.	PUNCT
ejpam-3391	190	1	.m	.m	PROPN
ejpam-3391	191	1	(	(	PUNCT
ejpam-3391	191	2	s	s	X
ejpam-3391	191	3	)	)	PUNCT
ejpam-3391	191	4	=	=	SYM
ejpam-3391	191	5			ADV
ejpam-3391	191	6	a	a	DET
ejpam-3391	191	7	(	(	PUNCT
ejpam-3391	191	8	s	s	NOUN
ejpam-3391	191	9	)	)	PUNCT
ejpam-3391	191	10	11	11	NUM
ejpam-3391	191	11	.	.	PUNCT
ejpam-3391	191	12	.	.	PUNCT
ejpam-3391	191	13	.	.	PUNCT
ejpam-3391	191	14	.	.	PUNCT
ejpam-3391	191	15	.	.	PUNCT
ejpam-3391	191	16	.	.	PUNCT
ejpam-3391	192	1	a	a	DET
ejpam-3391	192	2	(	(	PUNCT
ejpam-3391	192	3	s	s	NOUN
ejpam-3391	192	4	)	)	PUNCT
ejpam-3391	192	5	1n	1n	PROPN
ejpam-3391	192	6	b	b	X
ejpam-3391	192	7	(	(	PUNCT
ejpam-3391	192	8	s	s	X
ejpam-3391	192	9	)	)	PUNCT
ejpam-3391	192	10	1	1	NUM
ejpam-3391	192	11	...	...	PUNCT
ejpam-3391	192	12	...	...	PUNCT
ejpam-3391	192	13	...	...	PUNCT
ejpam-3391	193	1	a	a	DET
ejpam-3391	193	2	(	(	PUNCT
ejpam-3391	193	3	s	s	X
ejpam-3391	193	4	)	)	PUNCT
ejpam-3391	193	5	κ(s)1	κ(s)1	ADV
ejpam-3391	193	6	.	.	PUNCT
ejpam-3391	193	7	.	.	PUNCT
ejpam-3391	193	8	.	.	PUNCT
ejpam-3391	193	9	.	.	PUNCT
ejpam-3391	193	10	.	.	PUNCT
ejpam-3391	194	1	.	.	PUNCT
ejpam-3391	195	1	a	a	DET
ejpam-3391	195	2	(	(	PUNCT
ejpam-3391	195	3	s	s	NOUN
ejpam-3391	195	4	)	)	PUNCT
ejpam-3391	195	5	κ(s)n	κ(s)n	PROPN
ejpam-3391	195	6	b	b	PROPN
ejpam-3391	195	7	(	(	PUNCT
ejpam-3391	195	8	s	s	NOUN
ejpam-3391	195	9	)	)	PUNCT
ejpam-3391	195	10	j	j	PROPN
ejpam-3391	195	11	...	...	PUNCT
ejpam-3391	195	12	...	...	PUNCT
ejpam-3391	195	13	...	...	PUNCT
ejpam-3391	196	1	a	a	DET
ejpam-3391	196	2	(	(	PUNCT
ejpam-3391	196	3	s	s	NOUN
ejpam-3391	196	4	)	)	PUNCT
ejpam-3391	196	5	n1	n1	NOUN
ejpam-3391	196	6	.	.	PUNCT
ejpam-3391	196	7	.	.	PUNCT
ejpam-3391	196	8	.	.	PUNCT
ejpam-3391	196	9	.	.	PUNCT
ejpam-3391	196	10	.	.	PUNCT
ejpam-3391	196	11	.	.	PUNCT
ejpam-3391	197	1	a	a	DET
ejpam-3391	197	2	(	(	PUNCT
ejpam-3391	197	3	s	s	NOUN
ejpam-3391	197	4	)	)	PUNCT
ejpam-3391	197	5	nn	nn	PROPN
ejpam-3391	197	6	b	b	PROPN
ejpam-3391	197	7	(	(	PUNCT
ejpam-3391	197	8	s	s	NOUN
ejpam-3391	197	9	)	)	PUNCT
ejpam-3391	197	10	n	n	ADV
ejpam-3391	197	11	a	a	DET
ejpam-3391	197	12	(	(	PUNCT
ejpam-3391	197	13	s	s	NOUN
ejpam-3391	197	14	)	)	PUNCT
ejpam-3391	197	15	01	01	NUM
ejpam-3391	197	16	.	.	PUNCT
ejpam-3391	197	17	.	.	PUNCT
ejpam-3391	197	18	.	.	PUNCT
ejpam-3391	197	19	.	.	PUNCT
ejpam-3391	197	20	.	.	PUNCT
ejpam-3391	197	21	.	.	PUNCT
ejpam-3391	198	1	a	a	DET
ejpam-3391	198	2	(	(	PUNCT
ejpam-3391	198	3	s	s	NOUN
ejpam-3391	198	4	)	)	PUNCT
ejpam-3391	198	5	0n	0n	NOUN
ejpam-3391	198	6	b	b	X
ejpam-3391	198	7	(	(	PUNCT
ejpam-3391	198	8	s	s	NOUN
ejpam-3391	198	9	)	)	PUNCT
ejpam-3391	198	10	0	0	NUM
ejpam-3391	199	1			PROPN
ejpam-3391	199	2	.	.	PUNCT
ejpam-3391	200	1	and	and	CCONJ
ejpam-3391	200	2	m	m	PROPN
ejpam-3391	200	3	(	(	PUNCT
ejpam-3391	200	4	0	0	NUM
ejpam-3391	200	5	)	)	PUNCT
ejpam-3391	200	6	=	=	VERB
ejpam-3391	200	7			NOUN
ejpam-3391	200	8	b	b	PROPN
ejpam-3391	200	9	(	(	PUNCT
ejpam-3391	200	10	−d	−d	PROPN
ejpam-3391	200	11	)	)	PUNCT
ejpam-3391	200	12	1	1	NUM
ejpam-3391	200	13	.	.	PUNCT
ejpam-3391	200	14	.	.	PUNCT
ejpam-3391	200	15	.	.	PUNCT
ejpam-3391	201	1	b	b	X
ejpam-3391	201	2	(	(	PUNCT
ejpam-3391	201	3	−1	−1	NOUN
ejpam-3391	201	4	)	)	PUNCT
ejpam-3391	201	5	1	1	NUM
ejpam-3391	201	6	b	b	X
ejpam-3391	201	7	(	(	PUNCT
ejpam-3391	201	8	0	0	NUM
ejpam-3391	201	9	)	)	PUNCT
ejpam-3391	201	10	1	1	NUM
ejpam-3391	201	11	...	...	PUNCT
ejpam-3391	201	12	...	...	PUNCT
ejpam-3391	201	13	...	...	PUNCT
ejpam-3391	202	1	b	b	X
ejpam-3391	202	2	(	(	PUNCT
ejpam-3391	202	3	−n	−n	NOUN
ejpam-3391	202	4	)	)	PUNCT
ejpam-3391	202	5	n	n	NOUN
ejpam-3391	202	6	.	.	PUNCT
ejpam-3391	202	7	.	.	PUNCT
ejpam-3391	202	8	.	.	PUNCT
ejpam-3391	203	1	a	a	DET
ejpam-3391	203	2	(	(	PUNCT
ejpam-3391	203	3	s	s	NOUN
ejpam-3391	203	4	)	)	PUNCT
ejpam-3391	203	5	nn	nn	PROPN
ejpam-3391	203	6	b	b	PROPN
ejpam-3391	203	7	(	(	PUNCT
ejpam-3391	203	8	0	0	NUM
ejpam-3391	203	9	)	)	PUNCT
ejpam-3391	203	10	n	n	ADV
ejpam-3391	203	11	a	a	DET
ejpam-3391	203	12	(	(	PUNCT
ejpam-3391	203	13	−n	−n	NOUN
ejpam-3391	203	14	)	)	PUNCT
ejpam-3391	203	15	0	0	PUNCT
ejpam-3391	203	16	.	.	PUNCT
ejpam-3391	203	17	.	.	PUNCT
ejpam-3391	203	18	.	.	PUNCT
ejpam-3391	204	1	b	b	X
ejpam-3391	204	2	(	(	PUNCT
ejpam-3391	204	3	−1	−1	NOUN
ejpam-3391	204	4	)	)	PUNCT
ejpam-3391	204	5	0	0	NUM
ejpam-3391	205	1	b	b	X
ejpam-3391	205	2	(	(	PUNCT
ejpam-3391	205	3	0	0	NUM
ejpam-3391	205	4	)	)	PUNCT
ejpam-3391	205	5	0	0	NUM
ejpam-3391	205	6			NOUN
ejpam-3391	205	7	.	.	PUNCT
ejpam-3391	206	1	using	use	VERB
ejpam-3391	206	2	definition	definition	NOUN
ejpam-3391	206	3	of	of	ADP
ejpam-3391	206	4	b	b	PROPN
ejpam-3391	206	5	(	(	PUNCT
ejpam-3391	206	6	s	s	NOUN
ejpam-3391	206	7	)	)	PUNCT
ejpam-3391	206	8	0	0	NUM
ejpam-3391	206	9	,	,	PUNCT
ejpam-3391	206	10	it	it	PRON
ejpam-3391	206	11	is	be	AUX
ejpam-3391	206	12	clear	clear	ADJ
ejpam-3391	206	13	that	that	SCONJ
ejpam-3391	206	14	degb	degb	ADJ
ejpam-3391	206	15	(	(	PUNCT
ejpam-3391	206	16	s	s	NOUN
ejpam-3391	206	17	)	)	PUNCT
ejpam-3391	206	18	0	0	NUM
ejpam-3391	207	1	=	=	SYM
ejpam-3391	207	2	s∑	s∑	PROPN
ejpam-3391	208	1	i=1	i=1	PROPN
ejpam-3391	208	2	deg	deg	VERB
ejpam-3391	208	3	a	a	DET
ejpam-3391	208	4	(	(	PUNCT
ejpam-3391	208	5	i	i	NOUN
ejpam-3391	208	6	)	)	PUNCT
ejpam-3391	208	7	n+1	n+1	NUM
ejpam-3391	208	8	which	which	PRON
ejpam-3391	208	9	we	we	PRON
ejpam-3391	208	10	use	use	VERB
ejpam-3391	208	11	often	often	ADV
ejpam-3391	208	12	.	.	PUNCT
ejpam-3391	209	1	b	b	X
ejpam-3391	209	2	(	(	PUNCT
ejpam-3391	209	3	s	s	X
ejpam-3391	209	4	)	)	PUNCT
ejpam-3391	209	5	0	0	NUM
ejpam-3391	209	6	will	will	AUX
ejpam-3391	209	7	be	be	AUX
ejpam-3391	209	8	the	the	DET
ejpam-3391	209	9	denominator	denominator	NOUN
ejpam-3391	209	10	of	of	ADP
ejpam-3391	209	11	the	the	DET
ejpam-3391	209	12	s−th	s−th	NOUN
ejpam-3391	209	13	convergent	convergent	NOUN
ejpam-3391	209	14	and	and	CCONJ
ejpam-3391	209	15	b	b	PROPN
ejpam-3391	209	16	(	(	PUNCT
ejpam-3391	209	17	s	s	X
ejpam-3391	209	18	)	)	PUNCT
ejpam-3391	209	19	i	i	PRON
ejpam-3391	209	20	,	,	PUNCT
ejpam-3391	209	21	1	1	NUM
ejpam-3391	209	22	≤	≤	NUM
ejpam-3391	209	23	i	i	PRON
ejpam-3391	209	24	≤	≤	PROPN
ejpam-3391	209	25	n	n	CCONJ
ejpam-3391	209	26	,	,	PUNCT
ejpam-3391	209	27	will	will	AUX
ejpam-3391	209	28	be	be	AUX
ejpam-3391	209	29	numerator	numerator	NOUN
ejpam-3391	209	30	.	.	PUNCT
ejpam-3391	210	1	a.	a.	PROPN
ejpam-3391	210	2	chandoul	chandoul	PROPN
ejpam-3391	210	3	,	,	PUNCT
ejpam-3391	210	4	f.	f.	PROPN
ejpam-3391	210	5	aljuaydi	aljuaydi	PROPN
ejpam-3391	210	6	/	/	SYM
ejpam-3391	210	7	eur	eur	NOUN
ejpam-3391	210	8	.	.	PUNCT
ejpam-3391	211	1	j.	j.	PROPN
ejpam-3391	211	2	pure	pure	PROPN
ejpam-3391	211	3	appl	appl	PROPN
ejpam-3391	211	4	.	.	PROPN
ejpam-3391	211	5	math	math	PROPN
ejpam-3391	211	6	,	,	PUNCT
ejpam-3391	211	7	12	12	NUM
ejpam-3391	211	8	(	(	PUNCT
ejpam-3391	211	9	2	2	NUM
ejpam-3391	211	10	)	)	PUNCT
ejpam-3391	211	11	(	(	PUNCT
ejpam-3391	211	12	2019	2019	NUM
ejpam-3391	211	13	)	)	PUNCT
ejpam-3391	211	14	,	,	PUNCT
ejpam-3391	211	15	418	418	NUM
ejpam-3391	211	16	-	-	SYM
ejpam-3391	211	17	431	431	NUM
ejpam-3391	211	18	424	424	NUM
ejpam-3391	211	19	evidently	evidently	ADV
ejpam-3391	211	20	,	,	PUNCT
ejpam-3391	211	21	m	m	VERB
ejpam-3391	211	22	(	(	PUNCT
ejpam-3391	211	23	1	1	NUM
ejpam-3391	211	24	)	)	PUNCT
ejpam-3391	211	25	.	.	PUNCT
ejpam-3391	211	26	.	.	PUNCT
ejpam-3391	212	1	.m	.m	PROPN
ejpam-3391	213	1	(	(	PUNCT
ejpam-3391	213	2	s	s	X
ejpam-3391	213	3	)	)	PUNCT
ejpam-3391	213	4	=	=	SYM
ejpam-3391	213	5			ADV
ejpam-3391	213	6	a	a	DET
ejpam-3391	213	7	(	(	PUNCT
ejpam-3391	213	8	s−1	s−1	PROPN
ejpam-3391	213	9	)	)	PUNCT
ejpam-3391	213	10	11	11	NUM
ejpam-3391	213	11	.	.	PUNCT
ejpam-3391	213	12	.	.	PUNCT
ejpam-3391	213	13	.	.	PUNCT
ejpam-3391	213	14	.	.	PUNCT
ejpam-3391	213	15	.	.	PUNCT
ejpam-3391	213	16	.	.	PUNCT
ejpam-3391	214	1	a	a	DET
ejpam-3391	214	2	(	(	PUNCT
ejpam-3391	214	3	s−1	s−1	PROPN
ejpam-3391	214	4	)	)	PUNCT
ejpam-3391	214	5	1n	1n	PROPN
ejpam-3391	214	6	b	b	X
ejpam-3391	214	7	(	(	PUNCT
ejpam-3391	214	8	s−1	s−1	PROPN
ejpam-3391	214	9	)	)	PUNCT
ejpam-3391	214	10	1	1	NUM
ejpam-3391	214	11	...	...	PUNCT
ejpam-3391	214	12	...	...	PUNCT
ejpam-3391	214	13	...	...	PUNCT
ejpam-3391	215	1	a	a	DET
ejpam-3391	215	2	(	(	PUNCT
ejpam-3391	215	3	s−1	s−1	PROPN
ejpam-3391	215	4	)	)	PUNCT
ejpam-3391	215	5	κ(s)1	κ(s)1	ADV
ejpam-3391	215	6	.	.	PUNCT
ejpam-3391	215	7	.	.	PUNCT
ejpam-3391	215	8	.	.	PUNCT
ejpam-3391	215	9	.	.	PUNCT
ejpam-3391	215	10	.	.	PUNCT
ejpam-3391	215	11	.	.	PUNCT
ejpam-3391	216	1	a	a	DET
ejpam-3391	216	2	(	(	PUNCT
ejpam-3391	216	3	s−1	s−1	PROPN
ejpam-3391	216	4	)	)	PUNCT
ejpam-3391	216	5	κ(s)n	κ(s)n	PROPN
ejpam-3391	216	6	b	b	PROPN
ejpam-3391	216	7	(	(	PUNCT
ejpam-3391	216	8	s−1	s−1	PROPN
ejpam-3391	216	9	)	)	PUNCT
ejpam-3391	216	10	κ(s	κ(s	PROPN
ejpam-3391	216	11	)	)	PUNCT
ejpam-3391	216	12	...	...	PUNCT
ejpam-3391	217	1	...	...	PUNCT
ejpam-3391	217	2	...	...	PUNCT
ejpam-3391	218	1	a	a	DET
ejpam-3391	218	2	(	(	PUNCT
ejpam-3391	218	3	s−1	s−1	PROPN
ejpam-3391	218	4	)	)	PUNCT
ejpam-3391	218	5	n1	n1	NOUN
ejpam-3391	218	6	.	.	PUNCT
ejpam-3391	218	7	.	.	PUNCT
ejpam-3391	218	8	.	.	PUNCT
ejpam-3391	218	9	.	.	PUNCT
ejpam-3391	218	10	.	.	PUNCT
ejpam-3391	218	11	.	.	PUNCT
ejpam-3391	219	1	a	a	DET
ejpam-3391	219	2	(	(	PUNCT
ejpam-3391	219	3	s−1	s−1	PROPN
ejpam-3391	219	4	)	)	PUNCT
ejpam-3391	219	5	nn	nn	PROPN
ejpam-3391	219	6	b	b	PROPN
ejpam-3391	219	7	(	(	PUNCT
ejpam-3391	219	8	s−1	s−1	PROPN
ejpam-3391	219	9	)	)	PUNCT
ejpam-3391	219	10	n	n	CCONJ
ejpam-3391	219	11	a	a	DET
ejpam-3391	219	12	(	(	PUNCT
ejpam-3391	219	13	s−1	s−1	PROPN
ejpam-3391	219	14	)	)	PUNCT
ejpam-3391	219	15	01	01	NUM
ejpam-3391	219	16	.	.	PUNCT
ejpam-3391	219	17	.	.	PUNCT
ejpam-3391	219	18	.	.	PUNCT
ejpam-3391	219	19	.	.	PUNCT
ejpam-3391	219	20	.	.	PUNCT
ejpam-3391	219	21	.	.	PUNCT
ejpam-3391	220	1	a	a	DET
ejpam-3391	220	2	(	(	PUNCT
ejpam-3391	220	3	s−1	s−1	PROPN
ejpam-3391	220	4	)	)	PUNCT
ejpam-3391	220	5	0n	0n	NOUN
ejpam-3391	220	6	b	b	X
ejpam-3391	220	7	(	(	PUNCT
ejpam-3391	220	8	s−1	s−1	PROPN
ejpam-3391	220	9	)	)	PUNCT
ejpam-3391	220	10	0	0	NUM
ejpam-3391	221	1			NOUN
ejpam-3391	221	2			NOUN
ejpam-3391	221	3	1	1	NUM
ejpam-3391	221	4	0	0	NUM
ejpam-3391	221	5	.	.	PUNCT
ejpam-3391	221	6	.	.	PUNCT
ejpam-3391	221	7	.	.	PUNCT
ejpam-3391	222	1	0	0	NUM
ejpam-3391	223	1	0	0	NUM
ejpam-3391	223	2	0	0	NUM
ejpam-3391	223	3	.	.	PUNCT
ejpam-3391	223	4	.	.	PUNCT
ejpam-3391	223	5	.	.	PUNCT
ejpam-3391	224	1	0	0	NUM
ejpam-3391	224	2	0	0	NUM
ejpam-3391	224	3	0	0	NUM
ejpam-3391	224	4	1	1	NUM
ejpam-3391	224	5	.	.	PUNCT
ejpam-3391	224	6	.	.	PUNCT
ejpam-3391	224	7	.	.	PUNCT
ejpam-3391	225	1	0	0	NUM
ejpam-3391	226	1	0	0	NUM
ejpam-3391	226	2	0	0	NUM
ejpam-3391	226	3	.	.	PUNCT
ejpam-3391	226	4	.	.	PUNCT
ejpam-3391	226	5	.	.	PUNCT
ejpam-3391	227	1	0	0	NUM
ejpam-3391	227	2	0	0	NUM
ejpam-3391	227	3	...	...	PUNCT
ejpam-3391	227	4	...	...	PUNCT
ejpam-3391	227	5	.	.	PUNCT
ejpam-3391	227	6	.	.	PUNCT
ejpam-3391	227	7	.	.	PUNCT
ejpam-3391	228	1	...	...	PUNCT
ejpam-3391	228	2	...	...	PUNCT
ejpam-3391	228	3	...	...	PUNCT
ejpam-3391	228	4	.	.	PUNCT
ejpam-3391	228	5	.	.	PUNCT
ejpam-3391	229	1	.	.	PUNCT
ejpam-3391	230	1	...	...	PUNCT
ejpam-3391	231	1	...	...	PUNCT
ejpam-3391	232	1	0	0	NUM
ejpam-3391	232	2	0	0	NUM
ejpam-3391	232	3	.	.	PUNCT
ejpam-3391	232	4	.	.	PUNCT
ejpam-3391	232	5	.	.	PUNCT
ejpam-3391	233	1	1	1	NUM
ejpam-3391	233	2	0	0	NUM
ejpam-3391	233	3	0	0	NUM
ejpam-3391	233	4	.	.	PUNCT
ejpam-3391	233	5	.	.	PUNCT
ejpam-3391	233	6	.	.	PUNCT
ejpam-3391	234	1	0	0	NUM
ejpam-3391	235	1	0	0	NUM
ejpam-3391	235	2	0	0	NUM
ejpam-3391	235	3	0	0	NUM
ejpam-3391	235	4	.	.	PUNCT
ejpam-3391	235	5	.	.	PUNCT
ejpam-3391	235	6	.	.	PUNCT
ejpam-3391	236	1	0	0	NUM
ejpam-3391	237	1	0	0	NUM
ejpam-3391	237	2	0	0	NUM
ejpam-3391	237	3	.	.	PUNCT
ejpam-3391	237	4	.	.	PUNCT
ejpam-3391	237	5	.	.	PUNCT
ejpam-3391	238	1	0	0	NUM
ejpam-3391	239	1	1	1	NUM
ejpam-3391	239	2	0	0	NUM
ejpam-3391	239	3	0	0	NUM
ejpam-3391	239	4	.	.	PUNCT
ejpam-3391	239	5	.	.	PUNCT
ejpam-3391	239	6	.	.	PUNCT
ejpam-3391	240	1	0	0	NUM
ejpam-3391	240	2	0	0	NUM
ejpam-3391	240	3	1	1	NUM
ejpam-3391	240	4	.	.	PUNCT
ejpam-3391	240	5	.	.	PUNCT
ejpam-3391	240	6	.	.	PUNCT
ejpam-3391	241	1	0	0	NUM
ejpam-3391	242	1	aj+1	aj+1	NUM
ejpam-3391	242	2	...	...	PUNCT
ejpam-3391	242	3	...	...	PUNCT
ejpam-3391	242	4	.	.	PUNCT
ejpam-3391	242	5	.	.	PUNCT
ejpam-3391	242	6	.	.	PUNCT
ejpam-3391	242	7	...	...	PUNCT
ejpam-3391	242	8	...	...	PUNCT
ejpam-3391	242	9	...	...	PUNCT
ejpam-3391	242	10	.	.	PUNCT
ejpam-3391	242	11	.	.	PUNCT
ejpam-3391	242	12	.	.	PUNCT
ejpam-3391	243	1	...	...	PUNCT
ejpam-3391	244	1	...	...	PUNCT
ejpam-3391	245	1	0	0	NUM
ejpam-3391	245	2	0	0	NUM
ejpam-3391	245	3	.	.	PUNCT
ejpam-3391	245	4	.	.	PUNCT
ejpam-3391	245	5	.	.	PUNCT
ejpam-3391	246	1	0	0	NUM
ejpam-3391	247	1	0	0	NUM
ejpam-3391	247	2	0	0	NUM
ejpam-3391	247	3	.	.	PUNCT
ejpam-3391	247	4	.	.	PUNCT
ejpam-3391	248	1	.	.	PUNCT
ejpam-3391	249	1	1	1	NUM
ejpam-3391	249	2	an	an	DET
ejpam-3391	249	3	0	0	NUM
ejpam-3391	249	4	0	0	NUM
ejpam-3391	249	5	.	.	PUNCT
ejpam-3391	249	6	.	.	PUNCT
ejpam-3391	249	7	.	.	PUNCT
ejpam-3391	250	1	0	0	NUM
ejpam-3391	251	1	1	1	NUM
ejpam-3391	251	2	0	0	NUM
ejpam-3391	251	3	.	.	PUNCT
ejpam-3391	251	4	.	.	PUNCT
ejpam-3391	252	1	.	.	PUNCT
ejpam-3391	253	1	0	0	NUM
ejpam-3391	253	2	an+1	an+1	NOUN
ejpam-3391	253	3			NOUN
ejpam-3391	253	4	=	=	SYM
ejpam-3391	253	5			ADJ
ejpam-3391	253	6	a	a	DET
ejpam-3391	253	7	(	(	PUNCT
ejpam-3391	253	8	s−1	s−1	PROPN
ejpam-3391	253	9	)	)	PUNCT
ejpam-3391	253	10	11	11	NUM
ejpam-3391	253	11	.	.	PUNCT
ejpam-3391	253	12	.	.	PUNCT
ejpam-3391	253	13	.	.	PUNCT
ejpam-3391	254	1	a	a	DET
ejpam-3391	254	2	(	(	PUNCT
ejpam-3391	254	3	s−1	s−1	PROPN
ejpam-3391	254	4	)	)	PUNCT
ejpam-3391	254	5	1,κ(s)−1	1,κ(s)−1	NUM
ejpam-3391	254	6	b	b	X
ejpam-3391	254	7	(	(	PUNCT
ejpam-3391	254	8	s−1	s−1	PROPN
ejpam-3391	254	9	)	)	PUNCT
ejpam-3391	254	10	1	1	NUM
ejpam-3391	254	11	a	a	DET
ejpam-3391	254	12	(	(	PUNCT
ejpam-3391	254	13	s−1	s−1	PROPN
ejpam-3391	254	14	)	)	PUNCT
ejpam-3391	254	15	1,κ(s)+1	1,κ(s)+1	NUM
ejpam-3391	254	16	.	.	PUNCT
ejpam-3391	254	17	.	.	PUNCT
ejpam-3391	254	18	.	.	PUNCT
ejpam-3391	255	1	a	a	DET
ejpam-3391	255	2	(	(	PUNCT
ejpam-3391	255	3	s−1	s−1	PROPN
ejpam-3391	255	4	)	)	PUNCT
ejpam-3391	255	5	1n	1n	PROPN
ejpam-3391	255	6	b	b	X
ejpam-3391	255	7	(	(	PUNCT
ejpam-3391	255	8	s	s	X
ejpam-3391	255	9	)	)	PUNCT
ejpam-3391	255	10	1	1	NUM
ejpam-3391	255	11	...	...	PUNCT
ejpam-3391	255	12	...	...	PUNCT
ejpam-3391	255	13	...	...	PUNCT
ejpam-3391	255	14	...	...	PUNCT
ejpam-3391	255	15	...	...	PUNCT
ejpam-3391	255	16	...	...	PUNCT
ejpam-3391	255	17	...	...	PUNCT
ejpam-3391	255	18	...	...	PUNCT
ejpam-3391	256	1	a	a	DET
ejpam-3391	256	2	(	(	PUNCT
ejpam-3391	256	3	s−1	s−1	PROPN
ejpam-3391	256	4	)	)	PUNCT
ejpam-3391	256	5	κ(s)1	κ(s)1	ADV
ejpam-3391	256	6	.	.	PUNCT
ejpam-3391	256	7	.	.	PUNCT
ejpam-3391	256	8	.	.	PUNCT
ejpam-3391	257	1	a	a	DET
ejpam-3391	257	2	(	(	PUNCT
ejpam-3391	257	3	s−1	s−1	PROPN
ejpam-3391	257	4	)	)	PUNCT
ejpam-3391	257	5	κ(s),κ(s)−1	κ(s),κ(s)−1	NOUN
ejpam-3391	257	6	b	b	PROPN
ejpam-3391	257	7	(	(	PUNCT
ejpam-3391	257	8	s−1	s−1	PROPN
ejpam-3391	257	9	)	)	PUNCT
ejpam-3391	257	10	κ(s	κ(s	NOUN
ejpam-3391	257	11	)	)	PUNCT
ejpam-3391	257	12	a	a	DET
ejpam-3391	257	13	(	(	PUNCT
ejpam-3391	257	14	s−1	s−1	PROPN
ejpam-3391	257	15	)	)	PUNCT
ejpam-3391	257	16	κ(s),κ(s)+1	κ(s),κ(s)+1	NOUN
ejpam-3391	257	17	.	.	PUNCT
ejpam-3391	257	18	.	.	PUNCT
ejpam-3391	257	19	.	.	PUNCT
ejpam-3391	258	1	a	a	DET
ejpam-3391	258	2	(	(	PUNCT
ejpam-3391	258	3	s−1	s−1	PROPN
ejpam-3391	258	4	)	)	PUNCT
ejpam-3391	258	5	κ(s),n	κ(s),n	PROPN
ejpam-3391	258	6	b	b	PROPN
ejpam-3391	258	7	(	(	PUNCT
ejpam-3391	258	8	s	s	NOUN
ejpam-3391	258	9	)	)	PUNCT
ejpam-3391	258	10	κ(s	κ(s	PROPN
ejpam-3391	258	11	)	)	PUNCT
ejpam-3391	258	12	...	...	PUNCT
ejpam-3391	258	13	...	...	PUNCT
ejpam-3391	258	14	...	...	PUNCT
ejpam-3391	258	15	...	...	PUNCT
ejpam-3391	258	16	...	...	PUNCT
ejpam-3391	258	17	...	...	PUNCT
ejpam-3391	258	18	...	...	PUNCT
ejpam-3391	258	19	...	...	PUNCT
ejpam-3391	259	1	a	a	DET
ejpam-3391	259	2	(	(	PUNCT
ejpam-3391	259	3	s−1	s−1	PROPN
ejpam-3391	259	4	)	)	PUNCT
ejpam-3391	259	5	n1	n1	NOUN
ejpam-3391	259	6	.	.	PUNCT
ejpam-3391	259	7	.	.	PUNCT
ejpam-3391	259	8	.	.	PUNCT
ejpam-3391	260	1	a	a	DET
ejpam-3391	260	2	(	(	PUNCT
ejpam-3391	260	3	s−1	s−1	PROPN
ejpam-3391	260	4	)	)	PUNCT
ejpam-3391	260	5	n	n	CCONJ
ejpam-3391	260	6	,	,	PUNCT
ejpam-3391	260	7	κ(s)−1	κ(s)−1	PROPN
ejpam-3391	260	8	b	b	X
ejpam-3391	260	9	(	(	PUNCT
ejpam-3391	260	10	s−1	s−1	PROPN
ejpam-3391	260	11	)	)	PUNCT
ejpam-3391	260	12	n	n	CCONJ
ejpam-3391	260	13	a	a	DET
ejpam-3391	260	14	(	(	PUNCT
ejpam-3391	260	15	s−1	s−1	PROPN
ejpam-3391	260	16	)	)	PUNCT
ejpam-3391	260	17	n	n	CCONJ
ejpam-3391	260	18	,	,	PUNCT
ejpam-3391	260	19	κ(s)+1	κ(s)+1	NOUN
ejpam-3391	260	20	.	.	PUNCT
ejpam-3391	260	21	.	.	PUNCT
ejpam-3391	260	22	.	.	PUNCT
ejpam-3391	261	1	a	a	DET
ejpam-3391	261	2	(	(	PUNCT
ejpam-3391	261	3	s−1	s−1	PROPN
ejpam-3391	261	4	)	)	PUNCT
ejpam-3391	261	5	nn	nn	PROPN
ejpam-3391	261	6	b	b	PROPN
ejpam-3391	261	7	(	(	PUNCT
ejpam-3391	261	8	s	s	NOUN
ejpam-3391	261	9	)	)	PUNCT
ejpam-3391	261	10	n	n	ADV
ejpam-3391	261	11	a	a	DET
ejpam-3391	261	12	(	(	PUNCT
ejpam-3391	261	13	s−1	s−1	PROPN
ejpam-3391	261	14	)	)	PUNCT
ejpam-3391	261	15	01	01	NUM
ejpam-3391	261	16	.	.	PUNCT
ejpam-3391	261	17	.	.	PUNCT
ejpam-3391	261	18	.	.	PUNCT
ejpam-3391	262	1	a	a	DET
ejpam-3391	262	2	(	(	PUNCT
ejpam-3391	262	3	s−1	s−1	PROPN
ejpam-3391	262	4	)	)	PUNCT
ejpam-3391	262	5	0,κ(s)−1	0,κ(s)−1	PROPN
ejpam-3391	262	6	b	b	PROPN
ejpam-3391	262	7	(	(	PUNCT
ejpam-3391	262	8	s−1	s−1	PROPN
ejpam-3391	262	9	)	)	PUNCT
ejpam-3391	262	10	0	0	PUNCT
ejpam-3391	263	1	a	a	DET
ejpam-3391	263	2	(	(	PUNCT
ejpam-3391	263	3	s−1	s−1	PROPN
ejpam-3391	263	4	)	)	PUNCT
ejpam-3391	263	5	0,κ(s)+1	0,κ(s)+1	NUM
ejpam-3391	263	6	.	.	PUNCT
ejpam-3391	263	7	.	.	PUNCT
ejpam-3391	263	8	.	.	PUNCT
ejpam-3391	264	1	a	a	DET
ejpam-3391	264	2	(	(	PUNCT
ejpam-3391	264	3	s−1	s−1	PROPN
ejpam-3391	264	4	)	)	PUNCT
ejpam-3391	264	5	0n	0n	NOUN
ejpam-3391	264	6	b	b	X
ejpam-3391	264	7	(	(	PUNCT
ejpam-3391	264	8	s	s	NOUN
ejpam-3391	264	9	)	)	PUNCT
ejpam-3391	264	10	0	0	NUM
ejpam-3391	265	1			NOUN
ejpam-3391	265	2	.	.	PUNCT
ejpam-3391	266	1	(	(	PUNCT
ejpam-3391	266	2	5	5	X
ejpam-3391	266	3	)	)	PUNCT
ejpam-3391	266	4	where	where	SCONJ
ejpam-3391	266	5	b	b	X
ejpam-3391	266	6	(	(	PUNCT
ejpam-3391	266	7	s	s	X
ejpam-3391	266	8	)	)	PUNCT
ejpam-3391	266	9	i	i	PRON
ejpam-3391	266	10	=	=	PUNCT
ejpam-3391	266	11	a	a	DET
ejpam-3391	266	12	(	(	PUNCT
ejpam-3391	266	13	s−1	s−1	PROPN
ejpam-3391	266	14	)	)	PUNCT
ejpam-3391	266	15	iκ(s	iκ(s	NOUN
ejpam-3391	266	16	)	)	PUNCT
ejpam-3391	267	1	+	+	NUM
ejpam-3391	267	2	n∑	n∑	ADJ
ejpam-3391	267	3	k	k	X
ejpam-3391	267	4	=	=	NOUN
ejpam-3391	267	5	κ(s)+1	κ(s)+1	NOUN
ejpam-3391	267	6	a	a	DET
ejpam-3391	267	7	(	(	PUNCT
ejpam-3391	267	8	s	s	NOUN
ejpam-3391	267	9	)	)	PUNCT
ejpam-3391	267	10	k	k	PROPN
ejpam-3391	267	11	a	a	DET
ejpam-3391	267	12	(	(	PUNCT
ejpam-3391	267	13	s−1	s−1	PROPN
ejpam-3391	267	14	)	)	PUNCT
ejpam-3391	267	15	ik	ik	PROPN
ejpam-3391	267	16	+	+	CCONJ
ejpam-3391	267	17	asn+1b	asn+1b	PROPN
ejpam-3391	268	1	s−1	s−1	PROPN
ejpam-3391	268	2	i	i	PROPN
ejpam-3391	268	3	,	,	PUNCT
ejpam-3391	268	4	0	0	NUM
ejpam-3391	268	5	≤	≤	NUM
ejpam-3391	268	6	i	i	PRON
ejpam-3391	268	7	≤	≤	PROPN
ejpam-3391	268	8	n.	n.	NOUN
ejpam-3391	268	9	since	since	SCONJ
ejpam-3391	268	10	detm	detm	NOUN
ejpam-3391	268	11	(	(	PUNCT
ejpam-3391	268	12	1	1	NUM
ejpam-3391	268	13	)	)	PUNCT
ejpam-3391	268	14	.	.	PUNCT
ejpam-3391	268	15	.	.	PUNCT
ejpam-3391	269	1	.m	.m	PROPN
ejpam-3391	270	1	(	(	PUNCT
ejpam-3391	270	2	s	s	X
ejpam-3391	270	3	)	)	PUNCT
ejpam-3391	270	4	=	=	SYM
ejpam-3391	270	5	±1	±1	VERB
ejpam-3391	270	6	,	,	PUNCT
ejpam-3391	270	7	which	which	PRON
ejpam-3391	270	8	follows	follow	VERB
ejpam-3391	270	9	from	from	ADP
ejpam-3391	270	10	(	(	PUNCT
ejpam-3391	270	11	4	4	NUM
ejpam-3391	270	12	)	)	PUNCT
ejpam-3391	270	13	,	,	PUNCT
ejpam-3391	270	14	we	we	PRON
ejpam-3391	270	15	see	see	VERB
ejpam-3391	270	16	that	that	DET
ejpam-3391	270	17	b	b	PROPN
ejpam-3391	270	18	(	(	PUNCT
ejpam-3391	270	19	s	s	NOUN
ejpam-3391	270	20	)	)	PUNCT
ejpam-3391	270	21	0	0	NUM
ejpam-3391	270	22	,	,	PUNCT
ejpam-3391	270	23	.	.	PUNCT
ejpam-3391	270	24	.	.	PUNCT
ejpam-3391	270	25	.	.	PUNCT
ejpam-3391	271	1	,	,	PUNCT
ejpam-3391	271	2	b	b	X
ejpam-3391	271	3	(	(	PUNCT
ejpam-3391	271	4	s	s	NOUN
ejpam-3391	271	5	)	)	PUNCT
ejpam-3391	271	6	n−1	n−1	PROPN
ejpam-3391	271	7	and	and	CCONJ
ejpam-3391	271	8	b	b	PROPN
ejpam-3391	271	9	(	(	PUNCT
ejpam-3391	271	10	s	s	NOUN
ejpam-3391	271	11	)	)	PUNCT
ejpam-3391	271	12	n	n	AUX
ejpam-3391	271	13	have	have	VERB
ejpam-3391	271	14	no	no	DET
ejpam-3391	271	15	non	non	ADJ
ejpam-3391	271	16	-	-	ADJ
ejpam-3391	271	17	trivial	trivial	ADJ
ejpam-3391	271	18	common	common	ADJ
ejpam-3391	271	19	factor	factor	NOUN
ejpam-3391	271	20	.	.	PUNCT
ejpam-3391	272	1	by	by	ADP
ejpam-3391	272	2	a	a	DET
ejpam-3391	272	3	simple	simple	ADJ
ejpam-3391	272	4	calculation	calculation	NOUN
ejpam-3391	272	5	for	for	ADP
ejpam-3391	272	6	(	(	PUNCT
ejpam-3391	272	7	ϕ1	ϕ1	NOUN
ejpam-3391	272	8	,	,	PUNCT
ejpam-3391	272	9	.	.	PUNCT
ejpam-3391	272	10	.	.	PUNCT
ejpam-3391	272	11	.	.	PUNCT
ejpam-3391	273	1	,	,	PUNCT
ejpam-3391	273	2	ϕn	ϕn	X
ejpam-3391	273	3	)	)	PUNCT
ejpam-3391	273	4	∈	∈	PROPN
ejpam-3391	273	5	lnκ(s	lnκ(s	NOUN
ejpam-3391	273	6	)	)	PUNCT
ejpam-3391	273	7	,	,	PUNCT
ejpam-3391	273	8	we	we	PRON
ejpam-3391	273	9	see	see	VERB
ejpam-3391	273	10	that	that	SCONJ
ejpam-3391	273	11	(	(	PUNCT
ejpam-3391	273	12	i	i	NOUN
ejpam-3391	273	13	)	)	PUNCT
ejpam-3391	273	14	i2	i2	PROPN
ejpam-3391	273	15	6=	6=	PROPN
ejpam-3391	273	16	κ(s	κ(s	PROPN
ejpam-3391	273	17	)	)	PUNCT
ejpam-3391	273	18	,	,	PUNCT
ejpam-3391	273	19	n+	n+	ADP
ejpam-3391	273	20	1	1	NUM
ejpam-3391	273	21	a	a	DET
ejpam-3391	273	22	(	(	PUNCT
ejpam-3391	273	23	s	s	X
ejpam-3391	273	24	)	)	PUNCT
ejpam-3391	273	25	i1i2	i1i2	NOUN
ejpam-3391	273	26	=	=	SYM
ejpam-3391	273	27	a	a	DET
ejpam-3391	273	28	(	(	PUNCT
ejpam-3391	273	29	s−1	s−1	PROPN
ejpam-3391	273	30	)	)	PUNCT
ejpam-3391	273	31	i1i2	i1i2	NOUN
ejpam-3391	273	32	for	for	ADP
ejpam-3391	273	33	1	1	NUM
ejpam-3391	273	34	≤	≤	PROPN
ejpam-3391	273	35	i1	i1	PROPN
ejpam-3391	273	36	≤	≤	PROPN
ejpam-3391	273	37	n	n	CCONJ
ejpam-3391	273	38	,	,	PUNCT
ejpam-3391	273	39	(	(	PUNCT
ejpam-3391	273	40	6	6	NUM
ejpam-3391	273	41	)	)	PUNCT
ejpam-3391	273	42	(	(	PUNCT
ejpam-3391	273	43	ii	ii	NOUN
ejpam-3391	273	44	)	)	PUNCT
ejpam-3391	273	45	i2	i2	PROPN
ejpam-3391	273	46	=	=	SYM
ejpam-3391	273	47	κ(s	κ(s	PROPN
ejpam-3391	273	48	)	)	PUNCT
ejpam-3391	273	49	a	a	DET
ejpam-3391	273	50	(	(	PUNCT
ejpam-3391	273	51	s	s	X
ejpam-3391	273	52	)	)	PUNCT
ejpam-3391	273	53	i1i2	i1i2	NOUN
ejpam-3391	273	54	=	=	SYM
ejpam-3391	273	55	b	b	PROPN
ejpam-3391	273	56	(	(	PUNCT
ejpam-3391	273	57	s−1	s−1	PROPN
ejpam-3391	273	58	)	)	PUNCT
ejpam-3391	273	59	i1	i1	NOUN
ejpam-3391	273	60	for	for	ADP
ejpam-3391	273	61	0	0	NUM
ejpam-3391	273	62	≤	≤	PROPN
ejpam-3391	273	63	i1	i1	PROPN
ejpam-3391	273	64	≤	≤	PROPN
ejpam-3391	273	65	n	n	CCONJ
ejpam-3391	273	66	,	,	PUNCT
ejpam-3391	273	67	(	(	PUNCT
ejpam-3391	273	68	7	7	NUM
ejpam-3391	273	69	)	)	PUNCT
ejpam-3391	273	70	(	(	PUNCT
ejpam-3391	273	71	iii	iii	X
ejpam-3391	273	72	)	)	PUNCT
ejpam-3391	273	73	i2	i2	NOUN
ejpam-3391	273	74	=	=	PUNCT
ejpam-3391	273	75	n+	n+	ADP
ejpam-3391	273	76	1	1	NUM
ejpam-3391	273	77	a	a	DET
ejpam-3391	273	78	(	(	PUNCT
ejpam-3391	273	79	s	s	X
ejpam-3391	273	80	)	)	PUNCT
ejpam-3391	273	81	i1i2	i1i2	NOUN
ejpam-3391	273	82	=	=	SYM
ejpam-3391	273	83	b	b	PROPN
ejpam-3391	273	84	(	(	PUNCT
ejpam-3391	273	85	s	s	NOUN
ejpam-3391	273	86	)	)	PUNCT
ejpam-3391	273	87	i1	i1	NOUN
ejpam-3391	273	88	=	=	SYM
ejpam-3391	273	89	b	b	PROPN
ejpam-3391	273	90	(	(	PUNCT
ejpam-3391	273	91	s	s	X
ejpam-3391	273	92	)	)	PUNCT
ejpam-3391	273	93	i	i	PRON
ejpam-3391	273	94	=	=	PUNCT
ejpam-3391	273	95	a	a	DET
ejpam-3391	273	96	(	(	PUNCT
ejpam-3391	273	97	s−1	s−1	PROPN
ejpam-3391	273	98	)	)	PUNCT
ejpam-3391	273	99	iκ(s	iκ(s	NOUN
ejpam-3391	273	100	)	)	PUNCT
ejpam-3391	274	1	+	+	NUM
ejpam-3391	274	2	n∑	n∑	ADJ
ejpam-3391	274	3	k	k	X
ejpam-3391	274	4	=	=	NOUN
ejpam-3391	274	5	κ(s)+1	κ(s)+1	NOUN
ejpam-3391	274	6	a	a	DET
ejpam-3391	274	7	(	(	PUNCT
ejpam-3391	274	8	s	s	NOUN
ejpam-3391	274	9	)	)	PUNCT
ejpam-3391	274	10	k	k	PROPN
ejpam-3391	274	11	a	a	DET
ejpam-3391	274	12	(	(	PUNCT
ejpam-3391	274	13	s−1	s−1	PROPN
ejpam-3391	274	14	)	)	PUNCT
ejpam-3391	274	15	ik	ik	PROPN
ejpam-3391	274	16	+	+	CCONJ
ejpam-3391	274	17	asn+1b	asn+1b	PROPN
ejpam-3391	275	1	s−1	s−1	PROPN
ejpam-3391	275	2	i	i	PRON
ejpam-3391	275	3	for	for	ADP
ejpam-3391	275	4	0	0	NUM
ejpam-3391	275	5	≤	≤	NUM
ejpam-3391	275	6	i	i	PRON
ejpam-3391	275	7	≤	≤	ADJ
ejpam-3391	276	1	n.	n.	NOUN
ejpam-3391	276	2	(	(	PUNCT
ejpam-3391	276	3	8)	8)	NUM
ejpam-3391	276	4	from	from	ADP
ejpam-3391	276	5	(	(	PUNCT
ejpam-3391	276	6	5	5	NUM
ejpam-3391	276	7	)	)	PUNCT
ejpam-3391	276	8	,	,	PUNCT
ejpam-3391	276	9	we	we	PRON
ejpam-3391	276	10	find	find	VERB
ejpam-3391	276	11	that	that	SCONJ
ejpam-3391	276	12	b	b	X
ejpam-3391	276	13	(	(	PUNCT
ejpam-3391	276	14	s	s	X
ejpam-3391	276	15	)	)	PUNCT
ejpam-3391	276	16	i	i	PRON
ejpam-3391	276	17	increases	increase	VERB
ejpam-3391	276	18	as	as	ADP
ejpam-3391	276	19	s	s	NOUN
ejpam-3391	276	20	increases	increase	NOUN
ejpam-3391	276	21	and	and	CCONJ
ejpam-3391	276	22	degb	degb	ADJ
ejpam-3391	276	23	(	(	PUNCT
ejpam-3391	276	24	s	s	NOUN
ejpam-3391	276	25	)	)	PUNCT
ejpam-3391	276	26	i1	i1	PROPN
ejpam-3391	276	27	>	>	X
ejpam-3391	276	28	dega	dega	PROPN
ejpam-3391	276	29	(	(	PUNCT
ejpam-3391	276	30	s	s	NOUN
ejpam-3391	276	31	)	)	PUNCT
ejpam-3391	276	32	i1,κ(s	i1,κ(s	PROPN
ejpam-3391	276	33	)	)	PUNCT
ejpam-3391	276	34	>	>	X
ejpam-3391	277	1	dega	dega	PROPN
ejpam-3391	277	2	(	(	PUNCT
ejpam-3391	277	3	s	s	NOUN
ejpam-3391	277	4	)	)	PUNCT
ejpam-3391	277	5	i1,i2	i1,i2	PROPN
ejpam-3391	277	6	a.	a.	NOUN
ejpam-3391	277	7	chandoul	chandoul	PROPN
ejpam-3391	277	8	,	,	PUNCT
ejpam-3391	277	9	f.	f.	PROPN
ejpam-3391	277	10	aljuaydi	aljuaydi	PROPN
ejpam-3391	277	11	/	/	SYM
ejpam-3391	277	12	eur	eur	NOUN
ejpam-3391	277	13	.	.	PUNCT
ejpam-3391	278	1	j.	j.	PROPN
ejpam-3391	278	2	pure	pure	PROPN
ejpam-3391	278	3	appl	appl	PROPN
ejpam-3391	278	4	.	.	PROPN
ejpam-3391	278	5	math	math	PROPN
ejpam-3391	278	6	,	,	PUNCT
ejpam-3391	278	7	12	12	NUM
ejpam-3391	278	8	(	(	PUNCT
ejpam-3391	278	9	2	2	NUM
ejpam-3391	278	10	)	)	PUNCT
ejpam-3391	278	11	(	(	PUNCT
ejpam-3391	278	12	2019	2019	NUM
ejpam-3391	278	13	)	)	PUNCT
ejpam-3391	278	14	,	,	PUNCT
ejpam-3391	278	15	418	418	NUM
ejpam-3391	278	16	-	-	SYM
ejpam-3391	278	17	431	431	NUM
ejpam-3391	278	18	425	425	NUM
ejpam-3391	278	19	if	if	SCONJ
ejpam-3391	278	20	i2	i2	PROPN
ejpam-3391	278	21	6=	6=	PROPN
ejpam-3391	278	22	κ(s	κ(s	PROPN
ejpam-3391	278	23	)	)	PUNCT
ejpam-3391	278	24	,	,	PUNCT
ejpam-3391	278	25	n+	n+	ADP
ejpam-3391	278	26	1	1	NUM
ejpam-3391	278	27	for	for	ADP
ejpam-3391	278	28	0	0	NUM
ejpam-3391	278	29	≤	≤	PROPN
ejpam-3391	278	30	i1	i1	PROPN
ejpam-3391	278	31	≤	≤	PROPN
ejpam-3391	278	32	n.	n.	NOUN
ejpam-3391	278	33	we	we	PRON
ejpam-3391	278	34	put	put	VERB
ejpam-3391	278	35	m	m	PROPN
ejpam-3391	278	36	(	(	PUNCT
ejpam-3391	278	37	1	1	NUM
ejpam-3391	278	38	)	)	PUNCT
ejpam-3391	278	39	.	.	PUNCT
ejpam-3391	278	40	.	.	PUNCT
ejpam-3391	279	1	.m	.m	PROPN
ejpam-3391	280	1	(	(	PUNCT
ejpam-3391	280	2	s	s	NOUN
ejpam-3391	280	3	)	)	PUNCT
ejpam-3391	280	4			NOUN
ejpam-3391	280	5	ϕ	ϕ	PROPN
ejpam-3391	280	6	(	(	PUNCT
ejpam-3391	280	7	s	s	NOUN
ejpam-3391	280	8	)	)	PUNCT
ejpam-3391	280	9	1	1	NUM
ejpam-3391	280	10	...	...	PUNCT
ejpam-3391	280	11	ϕ	ϕ	X
ejpam-3391	280	12	(	(	PUNCT
ejpam-3391	280	13	s	s	NOUN
ejpam-3391	280	14	)	)	PUNCT
ejpam-3391	280	15	n	n	PRON
ejpam-3391	280	16	1	1	NUM
ejpam-3391	280	17			NOUN
ejpam-3391	280	18	=	=	NOUN
ejpam-3391	280	19			NOUN
ejpam-3391	280	20	a	a	DET
ejpam-3391	280	21	(	(	PUNCT
ejpam-3391	280	22	s	s	NOUN
ejpam-3391	280	23	)	)	PUNCT
ejpam-3391	280	24	11	11	NUM
ejpam-3391	280	25	ϕ	ϕ	X
ejpam-3391	280	26	(	(	PUNCT
ejpam-3391	280	27	s	s	NOUN
ejpam-3391	280	28	)	)	PUNCT
ejpam-3391	280	29	1	1	NUM
ejpam-3391	280	30	+	+	CCONJ
ejpam-3391	280	31	.	.	PUNCT
ejpam-3391	280	32	.	.	PUNCT
ejpam-3391	281	1	.+a	.+a	PUNCT
ejpam-3391	281	2	(	(	PUNCT
ejpam-3391	281	3	s	s	NOUN
ejpam-3391	281	4	)	)	PUNCT
ejpam-3391	281	5	1nϕ	1nϕ	NOUN
ejpam-3391	281	6	(	(	PUNCT
ejpam-3391	281	7	s	s	NOUN
ejpam-3391	281	8	)	)	PUNCT
ejpam-3391	281	9	n	n	PRON
ejpam-3391	281	10	+	+	ADP
ejpam-3391	281	11	b	b	PROPN
ejpam-3391	281	12	(	(	PUNCT
ejpam-3391	281	13	s	s	NOUN
ejpam-3391	281	14	)	)	PUNCT
ejpam-3391	281	15	1	1	NUM
ejpam-3391	281	16	...	...	PUNCT
ejpam-3391	281	17	a	a	DET
ejpam-3391	281	18	(	(	PUNCT
ejpam-3391	281	19	s	s	NOUN
ejpam-3391	281	20	)	)	PUNCT
ejpam-3391	281	21	n1ϕ	n1ϕ	NOUN
ejpam-3391	281	22	(	(	PUNCT
ejpam-3391	281	23	s	s	X
ejpam-3391	281	24	)	)	PUNCT
ejpam-3391	281	25	1	1	NUM
ejpam-3391	282	1	+	+	CCONJ
ejpam-3391	282	2	.	.	PUNCT
ejpam-3391	282	3	.	.	PUNCT
ejpam-3391	283	1	.+a	.+a	PUNCT
ejpam-3391	283	2	(	(	PUNCT
ejpam-3391	283	3	s	s	NOUN
ejpam-3391	283	4	)	)	PUNCT
ejpam-3391	283	5	nnϕ	nnϕ	NOUN
ejpam-3391	283	6	(	(	PUNCT
ejpam-3391	283	7	s	s	NOUN
ejpam-3391	283	8	)	)	PUNCT
ejpam-3391	283	9	n	n	PRON
ejpam-3391	283	10	+	+	ADP
ejpam-3391	283	11	b	b	PROPN
ejpam-3391	283	12	(	(	PUNCT
ejpam-3391	283	13	s	s	NOUN
ejpam-3391	283	14	)	)	PUNCT
ejpam-3391	283	15	n	n	ADV
ejpam-3391	283	16	a	a	DET
ejpam-3391	283	17	(	(	PUNCT
ejpam-3391	283	18	s	s	NOUN
ejpam-3391	283	19	)	)	PUNCT
ejpam-3391	283	20	01	01	NUM
ejpam-3391	283	21	ϕ	ϕ	X
ejpam-3391	283	22	(	(	PUNCT
ejpam-3391	283	23	s	s	NOUN
ejpam-3391	283	24	)	)	PUNCT
ejpam-3391	283	25	1	1	NUM
ejpam-3391	283	26	+	+	CCONJ
ejpam-3391	283	27	.	.	PUNCT
ejpam-3391	283	28	.	.	PUNCT
ejpam-3391	284	1	.+a	.+a	PUNCT
ejpam-3391	284	2	(	(	PUNCT
ejpam-3391	284	3	s	s	NOUN
ejpam-3391	284	4	)	)	PUNCT
ejpam-3391	284	5	0nϕ	0nϕ	NOUN
ejpam-3391	284	6	(	(	PUNCT
ejpam-3391	284	7	s	s	NOUN
ejpam-3391	284	8	)	)	PUNCT
ejpam-3391	284	9	n	n	PRON
ejpam-3391	284	10	+	+	ADP
ejpam-3391	284	11	b	b	PROPN
ejpam-3391	284	12	(	(	PUNCT
ejpam-3391	284	13	s	s	NOUN
ejpam-3391	284	14	)	)	PUNCT
ejpam-3391	284	15	0	0	NUM
ejpam-3391	284	16			NOUN
ejpam-3391	284	17	and	and	CCONJ
ejpam-3391	284	18	obtain	obtain	VERB
ejpam-3391	284	19	following	follow	VERB
ejpam-3391	284	20	theorem	theorem	VERB
ejpam-3391	284	21	.	.	PUNCT
ejpam-3391	284	22	theorem	theorem	NOUN
ejpam-3391	284	23	1	1	NUM
ejpam-3391	284	24	.	.	X
ejpam-3391	285	1	for	for	ADP
ejpam-3391	285	2	any	any	DET
ejpam-3391	285	3	(	(	PUNCT
ejpam-3391	285	4	ϕ1	ϕ1	NOUN
ejpam-3391	285	5	,	,	PUNCT
ejpam-3391	285	6	.	.	PUNCT
ejpam-3391	285	7	.	.	PUNCT
ejpam-3391	285	8	.	.	PUNCT
ejpam-3391	286	1	,	,	PUNCT
ejpam-3391	286	2	ϕn	ϕn	X
ejpam-3391	286	3	)	)	PUNCT
ejpam-3391	286	4	∈	∈	PROPN
ejpam-3391	287	1	ln	ln	ADJ
ejpam-3391	287	2	,	,	PUNCT
ejpam-3391	287	3	we	we	PRON
ejpam-3391	287	4	have	have	VERB
ejpam-3391	287	5	ϕi	ϕi	ADP
ejpam-3391	287	6	=	=	SYM
ejpam-3391	287	7	a	a	DET
ejpam-3391	287	8	(	(	PUNCT
ejpam-3391	287	9	s	s	NOUN
ejpam-3391	287	10	)	)	PUNCT
ejpam-3391	287	11	i1	i1	PROPN
ejpam-3391	287	12	ϕ	ϕ	PROPN
ejpam-3391	287	13	(	(	PUNCT
ejpam-3391	287	14	s	s	NOUN
ejpam-3391	287	15	)	)	PUNCT
ejpam-3391	287	16	1	1	NUM
ejpam-3391	287	17	+	+	CCONJ
ejpam-3391	287	18	.	.	PUNCT
ejpam-3391	287	19	.	.	PUNCT
ejpam-3391	288	1	.+a	.+a	PUNCT
ejpam-3391	288	2	(	(	PUNCT
ejpam-3391	288	3	s	s	X
ejpam-3391	288	4	)	)	PUNCT
ejpam-3391	288	5	in	in	ADP
ejpam-3391	288	6	ϕ	ϕ	PROPN
ejpam-3391	288	7	(	(	PUNCT
ejpam-3391	288	8	s	s	NOUN
ejpam-3391	288	9	)	)	PUNCT
ejpam-3391	288	10	n	n	PRON
ejpam-3391	288	11	+	+	ADP
ejpam-3391	288	12	b	b	PROPN
ejpam-3391	288	13	(	(	PUNCT
ejpam-3391	288	14	s	s	X
ejpam-3391	288	15	)	)	PUNCT
ejpam-3391	288	16	i	i	PRON
ejpam-3391	289	1	a	a	PRON
ejpam-3391	289	2	(	(	PUNCT
ejpam-3391	289	3	s	s	NOUN
ejpam-3391	289	4	)	)	PUNCT
ejpam-3391	289	5	01	01	NUM
ejpam-3391	289	6	ϕ	ϕ	X
ejpam-3391	289	7	(	(	PUNCT
ejpam-3391	289	8	s	s	NOUN
ejpam-3391	289	9	)	)	PUNCT
ejpam-3391	289	10	1	1	NUM
ejpam-3391	289	11	+	+	CCONJ
ejpam-3391	289	12	.	.	PUNCT
ejpam-3391	289	13	.	.	PUNCT
ejpam-3391	290	1	.+a	.+a	PUNCT
ejpam-3391	290	2	(	(	PUNCT
ejpam-3391	290	3	s	s	NOUN
ejpam-3391	290	4	)	)	PUNCT
ejpam-3391	290	5	0nϕ	0nϕ	NOUN
ejpam-3391	290	6	(	(	PUNCT
ejpam-3391	290	7	s	s	NOUN
ejpam-3391	290	8	)	)	PUNCT
ejpam-3391	290	9	n	n	PRON
ejpam-3391	290	10	+	+	ADP
ejpam-3391	290	11	b	b	PROPN
ejpam-3391	290	12	(	(	PUNCT
ejpam-3391	290	13	s	s	NOUN
ejpam-3391	290	14	)	)	PUNCT
ejpam-3391	290	15	0	0	NUM
ejpam-3391	290	16	,	,	PUNCT
ejpam-3391	290	17	for	for	ADP
ejpam-3391	290	18	1	1	NUM
ejpam-3391	290	19	≤	≤	NUM
ejpam-3391	290	20	i	i	PRON
ejpam-3391	290	21	≤	≤	PROPN
ejpam-3391	290	22	n	n	CCONJ
ejpam-3391	290	23	,	,	PUNCT
ejpam-3391	290	24	whenever	whenever	SCONJ
ejpam-3391	290	25	t	t	PROPN
ejpam-3391	290	26	s	s	VERB
ejpam-3391	290	27	′	′	NUM
ejpam-3391	290	28	β	β	X
ejpam-3391	290	29	(	(	PUNCT
ejpam-3391	290	30	ϕ1	ϕ1	PROPN
ejpam-3391	290	31	,	,	PUNCT
ejpam-3391	290	32	.	.	PUNCT
ejpam-3391	290	33	.	.	PUNCT
ejpam-3391	290	34	.	.	PUNCT
ejpam-3391	291	1	,	,	PUNCT
ejpam-3391	291	2	ϕn	ϕn	PROPN
ejpam-3391	291	3	)	)	PUNCT
ejpam-3391	291	4	6=	6=	X
ejpam-3391	291	5	(	(	PUNCT
ejpam-3391	291	6	0	0	NUM
ejpam-3391	291	7	,	,	PUNCT
ejpam-3391	291	8	.	.	PUNCT
ejpam-3391	291	9	.	.	PUNCT
ejpam-3391	292	1	.	.	PUNCT
ejpam-3391	293	1	,	,	PUNCT
ejpam-3391	293	2	0	0	NUM
ejpam-3391	293	3	)	)	PUNCT
ejpam-3391	293	4	,	,	PUNCT
ejpam-3391	293	5	for	for	ADP
ejpam-3391	293	6	any	any	DET
ejpam-3391	293	7	0	0	NUM
ejpam-3391	293	8	≤	≤	NOUN
ejpam-3391	293	9	s′	s′	ADJ
ejpam-3391	293	10	≤	≤	NUM
ejpam-3391	293	11	s.	s.	PROPN
ejpam-3391	293	12	proof	proof	NOUN
ejpam-3391	293	13	.	.	PUNCT
ejpam-3391	294	1	we	we	PRON
ejpam-3391	294	2	prove	prove	VERB
ejpam-3391	294	3	the	the	DET
ejpam-3391	294	4	theorem	theorem	NOUN
ejpam-3391	294	5	using	use	VERB
ejpam-3391	294	6	the	the	DET
ejpam-3391	294	7	method	method	NOUN
ejpam-3391	294	8	of	of	ADP
ejpam-3391	294	9	mathematical	mathematical	ADJ
ejpam-3391	294	10	induction	induction	NOUN
ejpam-3391	294	11	.	.	PUNCT
ejpam-3391	295	1	for	for	ADP
ejpam-3391	295	2	n	n	NOUN
ejpam-3391	295	3	=	=	SYM
ejpam-3391	295	4	1	1	NUM
ejpam-3391	295	5	,	,	PUNCT
ejpam-3391	295	6	we	we	PRON
ejpam-3391	295	7	have	have	VERB
ejpam-3391	295	8	from	from	ADP
ejpam-3391	295	9	the	the	DET
ejpam-3391	295	10	definition	definition	NOUN
ejpam-3391	295	11	,	,	PUNCT
ejpam-3391	295	12	for	for	ADP
ejpam-3391	295	13	(	(	PUNCT
ejpam-3391	295	14	ϕ1	ϕ1	NOUN
ejpam-3391	295	15	,	,	PUNCT
ejpam-3391	295	16	.	.	PUNCT
ejpam-3391	295	17	.	.	PUNCT
ejpam-3391	296	1	.	.	PUNCT
ejpam-3391	297	1	,	,	PUNCT
ejpam-3391	297	2	ϕn	ϕn	X
ejpam-3391	297	3	)	)	PUNCT
ejpam-3391	297	4	∈	∈	PROPN
ejpam-3391	297	5	l(n	l(n	PROPN
ejpam-3391	297	6	)	)	PUNCT
ejpam-3391	297	7	j	j	PROPN
ejpam-3391	297	8	,	,	PUNCT
ejpam-3391	297	9	tβ(ϕ1	tβ(ϕ1	ADP
ejpam-3391	297	10	,	,	PUNCT
ejpam-3391	297	11	.	.	PUNCT
ejpam-3391	297	12	.	.	PUNCT
ejpam-3391	298	1	.	.	PUNCT
ejpam-3391	299	1	,	,	PUNCT
ejpam-3391	299	2	ϕn	ϕn	X
ejpam-3391	299	3	)	)	PUNCT
ejpam-3391	299	4	=	=	SYM
ejpam-3391	300	1	(	(	PUNCT
ejpam-3391	300	2	ϕ	ϕ	X
ejpam-3391	300	3	(	(	PUNCT
ejpam-3391	300	4	1	1	NUM
ejpam-3391	300	5	)	)	PUNCT
ejpam-3391	300	6	1	1	NUM
ejpam-3391	300	7	,	,	PUNCT
ejpam-3391	300	8	.	.	PUNCT
ejpam-3391	300	9	.	.	PUNCT
ejpam-3391	301	1	.	.	PUNCT
ejpam-3391	302	1	,	,	PUNCT
ejpam-3391	302	2	ϕ	ϕ	X
ejpam-3391	302	3	(	(	PUNCT
ejpam-3391	302	4	1	1	NUM
ejpam-3391	302	5	)	)	PUNCT
ejpam-3391	302	6	n	n	CCONJ
ejpam-3391	302	7	)	)	PUNCT
ejpam-3391	302	8	=	=	SYM
ejpam-3391	302	9	(	(	PUNCT
ejpam-3391	302	10	ϕ2	ϕ2	ADV
ejpam-3391	302	11	ϕj	ϕj	INTJ
ejpam-3391	302	12	,	,	PUNCT
ejpam-3391	302	13	.	.	PUNCT
ejpam-3391	302	14	.	.	PUNCT
ejpam-3391	302	15	.	.	PUNCT
ejpam-3391	303	1	,	,	PUNCT
ejpam-3391	303	2	ϕj−1	ϕj−1	INTJ
ejpam-3391	303	3	ϕj	ϕj	INTJ
ejpam-3391	303	4	,	,	PUNCT
ejpam-3391	303	5	1	1	NUM
ejpam-3391	303	6	ϕj	ϕj	ADP
ejpam-3391	303	7	−	−	PROPN
ejpam-3391	303	8	a(1)n+1	a(1)n+1	PROPN
ejpam-3391	303	9	,	,	PUNCT
ejpam-3391	303	10	ϕj+1	ϕj+1	PROPN
ejpam-3391	303	11	ϕj	ϕj	ADP
ejpam-3391	303	12	−	−	PROPN
ejpam-3391	303	13	a(1)j+1	a(1)j+1	ADJ
ejpam-3391	303	14	,	,	PUNCT
ejpam-3391	303	15	.	.	PUNCT
ejpam-3391	303	16	.	.	PUNCT
ejpam-3391	304	1	.	.	PUNCT
ejpam-3391	305	1	,	,	PUNCT
ejpam-3391	305	2	ϕn	ϕn	INTJ
ejpam-3391	305	3	ϕj	ϕj	ADP
ejpam-3391	305	4	−	−	PROPN
ejpam-3391	305	5	a(1)n	a(1)n	PROPN
ejpam-3391	305	6	)	)	PUNCT
ejpam-3391	305	7	then	then	ADV
ejpam-3391	305	8	ϕi	ϕi	ADP
ejpam-3391	305	9	=	=	PUNCT
ejpam-3391	305	10			PROPN
ejpam-3391	305	11	1.ϕ	1.ϕ	NUM
ejpam-3391	305	12	(	(	PUNCT
ejpam-3391	305	13	1	1	NUM
ejpam-3391	305	14	)	)	PUNCT
ejpam-3391	305	15	i	i	PRON
ejpam-3391	305	16	1.ϕ	1.ϕ	NUM
ejpam-3391	305	17	(	(	PUNCT
ejpam-3391	305	18	1	1	NUM
ejpam-3391	305	19	)	)	PUNCT
ejpam-3391	305	20	j	j	NOUN
ejpam-3391	306	1	+	+	CCONJ
ejpam-3391	306	2	a	a	DET
ejpam-3391	306	3	(	(	PUNCT
ejpam-3391	306	4	1	1	NUM
ejpam-3391	306	5	)	)	PUNCT
ejpam-3391	306	6	n+1	n+1	PROPN
ejpam-3391	306	7	for	for	ADP
ejpam-3391	306	8	1	1	NUM
ejpam-3391	306	9	≤	≤	NUM
ejpam-3391	306	10	i	i	PRON
ejpam-3391	306	11	<	<	X
ejpam-3391	306	12	j	j	PROPN
ejpam-3391	306	13	1	1	NUM
ejpam-3391	306	14	1.ϕ	1.ϕ	NUM
ejpam-3391	306	15	(	(	PUNCT
ejpam-3391	306	16	1	1	NUM
ejpam-3391	306	17	)	)	PUNCT
ejpam-3391	306	18	j	j	NOUN
ejpam-3391	306	19	+	+	CCONJ
ejpam-3391	306	20	a	a	DET
ejpam-3391	306	21	(	(	PUNCT
ejpam-3391	306	22	1	1	NUM
ejpam-3391	306	23	)	)	PUNCT
ejpam-3391	306	24	n+1	n+1	PROPN
ejpam-3391	306	25	for	for	ADP
ejpam-3391	306	26	i	i	PRON
ejpam-3391	306	27	=	=	SYM
ejpam-3391	306	28	j	j	PROPN
ejpam-3391	306	29	1.ϕ	1.ϕ	NUM
ejpam-3391	306	30	(	(	PUNCT
ejpam-3391	306	31	1	1	NUM
ejpam-3391	306	32	)	)	PUNCT
ejpam-3391	306	33	i	i	PRON
ejpam-3391	307	1	+	+	CCONJ
ejpam-3391	307	2	a	a	DET
ejpam-3391	307	3	(	(	PUNCT
ejpam-3391	307	4	1	1	NUM
ejpam-3391	307	5	)	)	PUNCT
ejpam-3391	307	6	i	i	PRON
ejpam-3391	307	7	1.ϕ	1.ϕ	NUM
ejpam-3391	307	8	(	(	PUNCT
ejpam-3391	307	9	1	1	NUM
ejpam-3391	307	10	)	)	PUNCT
ejpam-3391	307	11	j	j	NOUN
ejpam-3391	308	1	+	+	CCONJ
ejpam-3391	308	2	a	a	DET
ejpam-3391	308	3	(	(	PUNCT
ejpam-3391	308	4	1	1	NUM
ejpam-3391	308	5	)	)	PUNCT
ejpam-3391	308	6	n+1	n+1	PROPN
ejpam-3391	308	7	for	for	ADP
ejpam-3391	308	8	j	j	PROPN
ejpam-3391	308	9	<	<	X
ejpam-3391	308	10	i	i	PROPN
ejpam-3391	308	11	≤	≤	PUNCT
ejpam-3391	308	12	n	n	CCONJ
ejpam-3391	308	13	(	(	PUNCT
ejpam-3391	308	14	9	9	NUM
ejpam-3391	308	15	)	)	PUNCT
ejpam-3391	308	16	on	on	ADP
ejpam-3391	308	17	the	the	DET
ejpam-3391	308	18	other	other	ADJ
ejpam-3391	308	19	hand	hand	NOUN
ejpam-3391	308	20	,	,	PUNCT
ejpam-3391	308	21	for	for	ADP
ejpam-3391	308	22	(	(	PUNCT
ejpam-3391	308	23	ϕ1	ϕ1	NOUN
ejpam-3391	308	24	,	,	PUNCT
ejpam-3391	308	25	.	.	PUNCT
ejpam-3391	308	26	.	.	PUNCT
ejpam-3391	309	1	.	.	PUNCT
ejpam-3391	310	1	,	,	PUNCT
ejpam-3391	310	2	ϕn	ϕn	X
ejpam-3391	310	3	)	)	PUNCT
ejpam-3391	310	4	∈	∈	PROPN
ejpam-3391	310	5	l(n	l(n	PROPN
ejpam-3391	310	6	)	)	PUNCT
ejpam-3391	310	7	j	j	PROPN
ejpam-3391	310	8	,	,	PUNCT
ejpam-3391	310	9	a	a	DET
ejpam-3391	310	10	(	(	PUNCT
ejpam-3391	310	11	1	1	NUM
ejpam-3391	310	12	)	)	PUNCT
ejpam-3391	310	13	i1	i1	PROPN
ejpam-3391	310	14	ϕ	ϕ	PROPN
ejpam-3391	310	15	(	(	PUNCT
ejpam-3391	310	16	1	1	NUM
ejpam-3391	310	17	)	)	PUNCT
ejpam-3391	310	18	1	1	NUM
ejpam-3391	311	1	+	+	CCONJ
ejpam-3391	311	2	.	.	PUNCT
ejpam-3391	311	3	.	.	PUNCT
ejpam-3391	312	1	.+a	.+a	PUNCT
ejpam-3391	312	2	(	(	PUNCT
ejpam-3391	312	3	1	1	X
ejpam-3391	312	4	)	)	PUNCT
ejpam-3391	312	5	in	in	ADP
ejpam-3391	312	6	ϕ	ϕ	NOUN
ejpam-3391	312	7	(	(	PUNCT
ejpam-3391	312	8	1	1	NUM
ejpam-3391	312	9	)	)	PUNCT
ejpam-3391	312	10	n	n	PRON
ejpam-3391	312	11	+	+	ADP
ejpam-3391	312	12	b	b	X
ejpam-3391	312	13	(	(	PUNCT
ejpam-3391	312	14	1	1	NUM
ejpam-3391	312	15	)	)	PUNCT
ejpam-3391	312	16	i	i	PRON
ejpam-3391	312	17	a	a	DET
ejpam-3391	312	18	(	(	PUNCT
ejpam-3391	312	19	1	1	NUM
ejpam-3391	312	20	)	)	PUNCT
ejpam-3391	312	21	01	01	NUM
ejpam-3391	312	22	ϕ	ϕ	NOUN
ejpam-3391	312	23	(	(	PUNCT
ejpam-3391	312	24	1	1	NUM
ejpam-3391	312	25	)	)	PUNCT
ejpam-3391	312	26	1	1	NUM
ejpam-3391	312	27	+	+	CCONJ
ejpam-3391	312	28	.	.	PUNCT
ejpam-3391	312	29	.	.	PUNCT
ejpam-3391	313	1	.+a	.+a	PUNCT
ejpam-3391	313	2	(	(	PUNCT
ejpam-3391	313	3	1	1	NUM
ejpam-3391	313	4	)	)	PUNCT
ejpam-3391	313	5	0nϕ	0nϕ	NOUN
ejpam-3391	313	6	(	(	PUNCT
ejpam-3391	313	7	1	1	NUM
ejpam-3391	313	8	)	)	PUNCT
ejpam-3391	313	9	n	n	PRON
ejpam-3391	313	10	+	+	ADP
ejpam-3391	313	11	b	b	X
ejpam-3391	313	12	(	(	PUNCT
ejpam-3391	313	13	1	1	NUM
ejpam-3391	313	14	)	)	PUNCT
ejpam-3391	313	15	0	0	NUM
ejpam-3391	314	1	=	=	SYM
ejpam-3391	314	2			PROPN
ejpam-3391	314	3	1.ϕ	1.ϕ	NUM
ejpam-3391	314	4	(	(	PUNCT
ejpam-3391	314	5	1	1	NUM
ejpam-3391	314	6	)	)	PUNCT
ejpam-3391	314	7	i	i	PRON
ejpam-3391	314	8	1.ϕ	1.ϕ	NUM
ejpam-3391	314	9	(	(	PUNCT
ejpam-3391	314	10	1	1	NUM
ejpam-3391	314	11	)	)	PUNCT
ejpam-3391	314	12	j	j	NOUN
ejpam-3391	315	1	+	+	CCONJ
ejpam-3391	315	2	a	a	DET
ejpam-3391	315	3	(	(	PUNCT
ejpam-3391	315	4	1	1	NUM
ejpam-3391	315	5	)	)	PUNCT
ejpam-3391	315	6	n+1	n+1	PROPN
ejpam-3391	315	7	for	for	ADP
ejpam-3391	315	8	1	1	NUM
ejpam-3391	315	9	≤	≤	NUM
ejpam-3391	315	10	i	i	PRON
ejpam-3391	315	11	<	<	X
ejpam-3391	315	12	j	j	PROPN
ejpam-3391	315	13	1	1	NUM
ejpam-3391	315	14	1.ϕ	1.ϕ	NUM
ejpam-3391	315	15	(	(	PUNCT
ejpam-3391	315	16	1	1	NUM
ejpam-3391	315	17	)	)	PUNCT
ejpam-3391	315	18	j	j	NOUN
ejpam-3391	315	19	+	+	CCONJ
ejpam-3391	315	20	a	a	DET
ejpam-3391	315	21	(	(	PUNCT
ejpam-3391	315	22	1	1	NUM
ejpam-3391	315	23	)	)	PUNCT
ejpam-3391	315	24	n+1	n+1	PROPN
ejpam-3391	315	25	for	for	ADP
ejpam-3391	315	26	i	i	PRON
ejpam-3391	315	27	=	=	SYM
ejpam-3391	315	28	j	j	PROPN
ejpam-3391	315	29	1.ϕ	1.ϕ	NUM
ejpam-3391	315	30	(	(	PUNCT
ejpam-3391	315	31	1	1	NUM
ejpam-3391	315	32	)	)	PUNCT
ejpam-3391	315	33	i	i	PRON
ejpam-3391	316	1	+	+	CCONJ
ejpam-3391	316	2	a	a	DET
ejpam-3391	316	3	(	(	PUNCT
ejpam-3391	316	4	1	1	NUM
ejpam-3391	316	5	)	)	PUNCT
ejpam-3391	316	6	i	i	PRON
ejpam-3391	316	7	1.ϕ	1.ϕ	NUM
ejpam-3391	316	8	(	(	PUNCT
ejpam-3391	316	9	1	1	NUM
ejpam-3391	316	10	)	)	PUNCT
ejpam-3391	316	11	j	j	NOUN
ejpam-3391	317	1	+	+	CCONJ
ejpam-3391	317	2	a	a	DET
ejpam-3391	317	3	(	(	PUNCT
ejpam-3391	317	4	1	1	NUM
ejpam-3391	317	5	)	)	PUNCT
ejpam-3391	317	6	n+1	n+1	PROPN
ejpam-3391	317	7	for	for	ADP
ejpam-3391	317	8	j	j	PROPN
ejpam-3391	317	9	<	<	X
ejpam-3391	317	10	i	i	PROPN
ejpam-3391	317	11	≤	≤	PUNCT
ejpam-3391	317	12	n	n	CCONJ
ejpam-3391	317	13	(	(	PUNCT
ejpam-3391	317	14	10	10	NUM
ejpam-3391	317	15	)	)	PUNCT
ejpam-3391	317	16	from	from	ADP
ejpam-3391	317	17	(	(	PUNCT
ejpam-3391	317	18	9	9	NUM
ejpam-3391	317	19	)	)	PUNCT
ejpam-3391	317	20	and	and	CCONJ
ejpam-3391	317	21	(	(	PUNCT
ejpam-3391	317	22	10	10	NUM
ejpam-3391	317	23	)	)	PUNCT
ejpam-3391	317	24	,	,	PUNCT
ejpam-3391	317	25	the	the	DET
ejpam-3391	317	26	assertion	assertion	NOUN
ejpam-3391	317	27	of	of	ADP
ejpam-3391	317	28	theorem	theorem	NOUN
ejpam-3391	317	29	holds	hold	NOUN
ejpam-3391	317	30	for	for	ADP
ejpam-3391	317	31	s	s	NOUN
ejpam-3391	317	32	=	=	SYM
ejpam-3391	317	33	1	1	NUM
ejpam-3391	317	34	.	.	PUNCT
ejpam-3391	318	1	now	now	ADV
ejpam-3391	318	2	,	,	PUNCT
ejpam-3391	318	3	we	we	PRON
ejpam-3391	318	4	assume	assume	VERB
ejpam-3391	318	5	that	that	SCONJ
ejpam-3391	318	6	the	the	DET
ejpam-3391	318	7	assertion	assertion	NOUN
ejpam-3391	318	8	of	of	ADP
ejpam-3391	318	9	the	the	DET
ejpam-3391	318	10	theorem	theorem	NOUN
ejpam-3391	318	11	holds	hold	VERB
ejpam-3391	318	12	by	by	ADP
ejpam-3391	318	13	s	s	NOUN
ejpam-3391	318	14	,	,	PUNCT
ejpam-3391	318	15	and	and	CCONJ
ejpam-3391	318	16	we	we	PRON
ejpam-3391	318	17	will	will	AUX
ejpam-3391	318	18	show	show	VERB
ejpam-3391	318	19	that	that	SCONJ
ejpam-3391	318	20	the	the	DET
ejpam-3391	318	21	assertion	assertion	NOUN
ejpam-3391	318	22	holds	hold	VERB
ejpam-3391	318	23	for	for	ADP
ejpam-3391	318	24	s	s	PROPN
ejpam-3391	318	25	+	+	NOUN
ejpam-3391	318	26	1	1	X
ejpam-3391	318	27	.	.	X
ejpam-3391	318	28	note	note	VERB
ejpam-3391	318	29	that	that	SCONJ
ejpam-3391	318	30	κ(s+	κ(s+	NOUN
ejpam-3391	318	31	1	1	NUM
ejpam-3391	318	32	)	)	PUNCT
ejpam-3391	318	33	is	be	AUX
ejpam-3391	318	34	chosen	choose	VERB
ejpam-3391	318	35	by	by	ADP
ejpam-3391	318	36	(	(	PUNCT
ejpam-3391	318	37	ϕ	ϕ	X
ejpam-3391	318	38	(	(	PUNCT
ejpam-3391	318	39	s	s	NOUN
ejpam-3391	318	40	)	)	PUNCT
ejpam-3391	318	41	1	1	NUM
ejpam-3391	318	42	,	,	PUNCT
ejpam-3391	318	43	.	.	PUNCT
ejpam-3391	318	44	.	.	PUNCT
ejpam-3391	319	1	.	.	PUNCT
ejpam-3391	320	1	,	,	PUNCT
ejpam-3391	320	2	ϕ	ϕ	X
ejpam-3391	320	3	(	(	PUNCT
ejpam-3391	320	4	s	s	NOUN
ejpam-3391	320	5	)	)	PUNCT
ejpam-3391	320	6	n	n	CCONJ
ejpam-3391	320	7	)	)	PUNCT
ejpam-3391	320	8	∈	∈	PROPN
ejpam-3391	320	9	l(n	l(n	PROPN
ejpam-3391	320	10	)	)	PUNCT
ejpam-3391	320	11	κ(s+1	κ(s+1	NOUN
ejpam-3391	320	12	)	)	PUNCT
ejpam-3391	320	13	,	,	PUNCT
ejpam-3391	320	14	a.	a.	PROPN
ejpam-3391	320	15	chandoul	chandoul	PROPN
ejpam-3391	320	16	,	,	PUNCT
ejpam-3391	320	17	f.	f.	PROPN
ejpam-3391	320	18	aljuaydi	aljuaydi	PROPN
ejpam-3391	320	19	/	/	SYM
ejpam-3391	320	20	eur	eur	NOUN
ejpam-3391	320	21	.	.	PUNCT
ejpam-3391	321	1	j.	j.	PROPN
ejpam-3391	321	2	pure	pure	PROPN
ejpam-3391	321	3	appl	appl	PROPN
ejpam-3391	321	4	.	.	PROPN
ejpam-3391	321	5	math	math	PROPN
ejpam-3391	321	6	,	,	PUNCT
ejpam-3391	321	7	12	12	NUM
ejpam-3391	321	8	(	(	PUNCT
ejpam-3391	321	9	2	2	NUM
ejpam-3391	321	10	)	)	PUNCT
ejpam-3391	321	11	(	(	PUNCT
ejpam-3391	321	12	2019	2019	NUM
ejpam-3391	321	13	)	)	PUNCT
ejpam-3391	321	14	,	,	PUNCT
ejpam-3391	321	15	418	418	NUM
ejpam-3391	321	16	-	-	SYM
ejpam-3391	321	17	431	431	NUM
ejpam-3391	321	18	426	426	NUM
ejpam-3391	321	19	a	a	DET
ejpam-3391	321	20	(	(	PUNCT
ejpam-3391	321	21	s+1	s+1	NOUN
ejpam-3391	321	22	)	)	PUNCT
ejpam-3391	321	23	i1	i1	PROPN
ejpam-3391	321	24	ϕ	ϕ	PROPN
ejpam-3391	322	1	(	(	PUNCT
ejpam-3391	322	2	s+1	s+1	NOUN
ejpam-3391	322	3	)	)	PUNCT
ejpam-3391	322	4	1	1	NUM
ejpam-3391	323	1	+	+	CCONJ
ejpam-3391	323	2	.	.	PUNCT
ejpam-3391	323	3	.	.	PUNCT
ejpam-3391	324	1	.+a	.+a	PUNCT
ejpam-3391	324	2	(	(	PUNCT
ejpam-3391	324	3	s+1	s+1	NOUN
ejpam-3391	324	4	)	)	PUNCT
ejpam-3391	324	5	in	in	ADP
ejpam-3391	324	6	ϕ	ϕ	PROPN
ejpam-3391	324	7	(	(	PUNCT
ejpam-3391	324	8	s+1	s+1	NOUN
ejpam-3391	324	9	)	)	PUNCT
ejpam-3391	324	10	n	n	PRON
ejpam-3391	325	1	+	+	ADP
ejpam-3391	325	2	b	b	PROPN
ejpam-3391	325	3	(	(	PUNCT
ejpam-3391	325	4	s+1	s+1	NOUN
ejpam-3391	325	5	)	)	PUNCT
ejpam-3391	325	6	i	i	PRON
ejpam-3391	325	7	a	a	PRON
ejpam-3391	325	8	(	(	PUNCT
ejpam-3391	325	9	s+1	s+1	NOUN
ejpam-3391	325	10	)	)	PUNCT
ejpam-3391	325	11	01	01	NUM
ejpam-3391	325	12	ϕ	ϕ	X
ejpam-3391	325	13	(	(	PUNCT
ejpam-3391	325	14	s+1	s+1	NOUN
ejpam-3391	325	15	)	)	PUNCT
ejpam-3391	325	16	1	1	NUM
ejpam-3391	326	1	+	+	CCONJ
ejpam-3391	326	2	.	.	PUNCT
ejpam-3391	326	3	.	.	PUNCT
ejpam-3391	327	1	.+a	.+a	PUNCT
ejpam-3391	327	2	(	(	PUNCT
ejpam-3391	327	3	s+1	s+1	NOUN
ejpam-3391	327	4	)	)	PUNCT
ejpam-3391	327	5	0n	0n	NOUN
ejpam-3391	328	1	ϕ	ϕ	PROPN
ejpam-3391	328	2	(	(	PUNCT
ejpam-3391	328	3	s+1	s+1	NOUN
ejpam-3391	328	4	)	)	PUNCT
ejpam-3391	328	5	n	n	PRON
ejpam-3391	329	1	+	+	ADP
ejpam-3391	329	2	b	b	PROPN
ejpam-3391	329	3	(	(	PUNCT
ejpam-3391	329	4	s+1	s+1	NOUN
ejpam-3391	329	5	)	)	PUNCT
ejpam-3391	329	6	0	0	NUM
ejpam-3391	329	7	=	=	SYM
ejpam-3391	329	8	κ(s+1)∑	κ(s+1)∑	X
ejpam-3391	329	9	k=1	k=1	PROPN
ejpam-3391	329	10	a	a	DET
ejpam-3391	329	11	(	(	PUNCT
ejpam-3391	329	12	s+1	s+1	NOUN
ejpam-3391	329	13	)	)	PUNCT
ejpam-3391	329	14	ik	ik	PROPN
ejpam-3391	329	15	ϕ	ϕ	PROPN
ejpam-3391	329	16	(	(	PUNCT
ejpam-3391	329	17	s	s	NOUN
ejpam-3391	329	18	)	)	PUNCT
ejpam-3391	329	19	k	k	PROPN
ejpam-3391	329	20	ϕ	ϕ	X
ejpam-3391	329	21	(	(	PUNCT
ejpam-3391	329	22	s	s	NOUN
ejpam-3391	329	23	)	)	PUNCT
ejpam-3391	329	24	κ(s+1	κ(s+1	ADJ
ejpam-3391	329	25	)	)	PUNCT
ejpam-3391	330	1	+	+	ADP
ejpam-3391	330	2	a	a	DET
ejpam-3391	330	3	(	(	PUNCT
ejpam-3391	330	4	s+1	s+1	NOUN
ejpam-3391	330	5	)	)	PUNCT
ejpam-3391	330	6	i	i	PROPN
ejpam-3391	330	7	,	,	PUNCT
ejpam-3391	330	8	κ(s+1	κ(s+1	PROPN
ejpam-3391	330	9	)	)	PUNCT
ejpam-3391	330	10	(	(	PUNCT
ejpam-3391	330	11	1	1	NUM
ejpam-3391	330	12	ϕ	ϕ	X
ejpam-3391	330	13	(	(	PUNCT
ejpam-3391	330	14	s	s	NOUN
ejpam-3391	330	15	)	)	PUNCT
ejpam-3391	330	16	κ(s+1	κ(s+1	ADJ
ejpam-3391	330	17	)	)	PUNCT
ejpam-3391	330	18	−	−	PROPN
ejpam-3391	330	19	a(s)n+1	a(s)n+1	ADV
ejpam-3391	330	20	)	)	PUNCT
ejpam-3391	331	1	+	+	PROPN
ejpam-3391	331	2	n∑	n∑	NOUN
ejpam-3391	331	3	k	k	X
ejpam-3391	331	4	=	=	NOUN
ejpam-3391	331	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	331	6	a	a	DET
ejpam-3391	331	7	(	(	PUNCT
ejpam-3391	331	8	s+1	s+1	NOUN
ejpam-3391	331	9	)	)	PUNCT
ejpam-3391	331	10	ik	ik	PROPN
ejpam-3391	331	11	(	(	PUNCT
ejpam-3391	331	12	ϕ	ϕ	X
ejpam-3391	331	13	(	(	PUNCT
ejpam-3391	331	14	s	s	NOUN
ejpam-3391	331	15	)	)	PUNCT
ejpam-3391	331	16	k	k	PROPN
ejpam-3391	331	17	ϕ	ϕ	X
ejpam-3391	331	18	(	(	PUNCT
ejpam-3391	331	19	s	s	NOUN
ejpam-3391	331	20	)	)	PUNCT
ejpam-3391	331	21	κ(s+1	κ(s+1	ADJ
ejpam-3391	331	22	)	)	PUNCT
ejpam-3391	331	23	−	−	PROPN
ejpam-3391	331	24	a(s)n+1	a(s)n+1	ADV
ejpam-3391	331	25	)	)	PUNCT
ejpam-3391	332	1	+	+	PROPN
ejpam-3391	332	2	b	b	PROPN
ejpam-3391	332	3	(	(	PUNCT
ejpam-3391	332	4	s+1	s+1	NOUN
ejpam-3391	332	5	)	)	PUNCT
ejpam-3391	332	6	i	i	PRON
ejpam-3391	332	7	κ(s+1)∑	κ(s+1)∑	VERB
ejpam-3391	332	8	k=1	k=1	PROPN
ejpam-3391	332	9	a	a	DET
ejpam-3391	332	10	(	(	PUNCT
ejpam-3391	332	11	s+1	s+1	NOUN
ejpam-3391	332	12	)	)	PUNCT
ejpam-3391	332	13	0k	0k	NOUN
ejpam-3391	332	14	ϕ	ϕ	X
ejpam-3391	332	15	(	(	PUNCT
ejpam-3391	332	16	s	s	NOUN
ejpam-3391	332	17	)	)	PUNCT
ejpam-3391	332	18	k	k	PROPN
ejpam-3391	332	19	ϕ	ϕ	X
ejpam-3391	332	20	(	(	PUNCT
ejpam-3391	332	21	s	s	NOUN
ejpam-3391	332	22	)	)	PUNCT
ejpam-3391	332	23	κ(s+1	κ(s+1	ADJ
ejpam-3391	332	24	)	)	PUNCT
ejpam-3391	333	1	+	+	ADP
ejpam-3391	333	2	a	a	DET
ejpam-3391	333	3	(	(	PUNCT
ejpam-3391	333	4	s+1	s+1	NOUN
ejpam-3391	333	5	)	)	PUNCT
ejpam-3391	333	6	0,κ(s+1	0,κ(s+1	NUM
ejpam-3391	333	7	)	)	PUNCT
ejpam-3391	333	8	(	(	PUNCT
ejpam-3391	333	9	1	1	NUM
ejpam-3391	333	10	ϕ	ϕ	X
ejpam-3391	333	11	(	(	PUNCT
ejpam-3391	333	12	s	s	NOUN
ejpam-3391	333	13	)	)	PUNCT
ejpam-3391	333	14	κ(s+1	κ(s+1	ADJ
ejpam-3391	333	15	)	)	PUNCT
ejpam-3391	333	16	−	−	PROPN
ejpam-3391	333	17	a(s)n+1	a(s)n+1	ADV
ejpam-3391	333	18	)	)	PUNCT
ejpam-3391	334	1	+	+	PROPN
ejpam-3391	334	2	n∑	n∑	NOUN
ejpam-3391	334	3	k	k	X
ejpam-3391	334	4	=	=	NOUN
ejpam-3391	334	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	334	6	a	a	DET
ejpam-3391	334	7	(	(	PUNCT
ejpam-3391	334	8	s+1	s+1	NOUN
ejpam-3391	334	9	)	)	PUNCT
ejpam-3391	334	10	0k	0k	NOUN
ejpam-3391	334	11	(	(	PUNCT
ejpam-3391	334	12	ϕ	ϕ	X
ejpam-3391	334	13	(	(	PUNCT
ejpam-3391	334	14	s	s	NOUN
ejpam-3391	334	15	)	)	PUNCT
ejpam-3391	334	16	k	k	PROPN
ejpam-3391	334	17	ϕ	ϕ	X
ejpam-3391	334	18	(	(	PUNCT
ejpam-3391	334	19	s	s	NOUN
ejpam-3391	334	20	)	)	PUNCT
ejpam-3391	334	21	κ(s+1	κ(s+1	ADJ
ejpam-3391	334	22	)	)	PUNCT
ejpam-3391	334	23	−	−	PROPN
ejpam-3391	335	1	a(s)n+1	a(s)n+1	ADV
ejpam-3391	335	2	)	)	PUNCT
ejpam-3391	336	1	+	+	PROPN
ejpam-3391	336	2	b	b	PROPN
ejpam-3391	336	3	(	(	PUNCT
ejpam-3391	336	4	s+1	s+1	NOUN
ejpam-3391	336	5	)	)	PUNCT
ejpam-3391	336	6	0	0	NUM
ejpam-3391	336	7	=	=	SYM
ejpam-3391	336	8	κ(s+1)∑	κ(s+1)∑	X
ejpam-3391	336	9	k=1	k=1	PROPN
ejpam-3391	336	10	a	a	DET
ejpam-3391	336	11	(	(	PUNCT
ejpam-3391	336	12	s+1	s+1	NOUN
ejpam-3391	336	13	)	)	PUNCT
ejpam-3391	336	14	ik	ik	PROPN
ejpam-3391	336	15	ϕ	ϕ	PROPN
ejpam-3391	336	16	(	(	PUNCT
ejpam-3391	336	17	s	s	NOUN
ejpam-3391	336	18	)	)	PUNCT
ejpam-3391	336	19	k	k	PROPN
ejpam-3391	336	20	ϕ	ϕ	X
ejpam-3391	336	21	(	(	PUNCT
ejpam-3391	336	22	s	s	NOUN
ejpam-3391	336	23	)	)	PUNCT
ejpam-3391	336	24	κ(s+1	κ(s+1	ADJ
ejpam-3391	336	25	)	)	PUNCT
ejpam-3391	337	1	+	+	NOUN
ejpam-3391	337	2	b	b	PROPN
ejpam-3391	337	3	(	(	PUNCT
ejpam-3391	337	4	s	s	X
ejpam-3391	337	5	)	)	PUNCT
ejpam-3391	337	6	i	i	PRON
ejpam-3391	337	7	(	(	PUNCT
ejpam-3391	337	8	1	1	NUM
ejpam-3391	337	9	ϕ	ϕ	X
ejpam-3391	337	10	(	(	PUNCT
ejpam-3391	337	11	s	s	NOUN
ejpam-3391	337	12	)	)	PUNCT
ejpam-3391	337	13	κ(s+1	κ(s+1	ADJ
ejpam-3391	337	14	)	)	PUNCT
ejpam-3391	338	1	−	−	PROPN
ejpam-3391	338	2	a(s)n+1	a(s)n+1	ADV
ejpam-3391	338	3	)	)	PUNCT
ejpam-3391	339	1	+	+	PROPN
ejpam-3391	339	2	n∑	n∑	NOUN
ejpam-3391	339	3	k	k	X
ejpam-3391	339	4	=	=	NOUN
ejpam-3391	339	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	339	6	a	a	DET
ejpam-3391	339	7	(	(	PUNCT
ejpam-3391	339	8	s	s	X
ejpam-3391	339	9	)	)	PUNCT
ejpam-3391	339	10	ik	ik	PROPN
ejpam-3391	339	11	(	(	PUNCT
ejpam-3391	339	12	ϕ	ϕ	X
ejpam-3391	339	13	(	(	PUNCT
ejpam-3391	339	14	s	s	NOUN
ejpam-3391	339	15	)	)	PUNCT
ejpam-3391	339	16	k	k	PROPN
ejpam-3391	339	17	ϕ	ϕ	X
ejpam-3391	339	18	(	(	PUNCT
ejpam-3391	339	19	s	s	NOUN
ejpam-3391	339	20	)	)	PUNCT
ejpam-3391	339	21	κ(s+1	κ(s+1	ADJ
ejpam-3391	339	22	)	)	PUNCT
ejpam-3391	339	23	−	−	PROPN
ejpam-3391	339	24	a(s)n+1	a(s)n+1	ADV
ejpam-3391	339	25	)	)	PUNCT
ejpam-3391	340	1	+	+	PROPN
ejpam-3391	340	2	b	b	PROPN
ejpam-3391	340	3	(	(	PUNCT
ejpam-3391	340	4	s+1	s+1	NOUN
ejpam-3391	340	5	)	)	PUNCT
ejpam-3391	340	6	i	i	PRON
ejpam-3391	340	7	κ(s+1)∑	κ(s+1)∑	VERB
ejpam-3391	340	8	k=1	k=1	PROPN
ejpam-3391	340	9	a	a	DET
ejpam-3391	340	10	(	(	PUNCT
ejpam-3391	340	11	s+1	s+1	NOUN
ejpam-3391	340	12	)	)	PUNCT
ejpam-3391	340	13	0k	0k	NOUN
ejpam-3391	340	14	ϕ	ϕ	X
ejpam-3391	340	15	(	(	PUNCT
ejpam-3391	340	16	s	s	NOUN
ejpam-3391	340	17	)	)	PUNCT
ejpam-3391	340	18	k	k	PROPN
ejpam-3391	340	19	ϕ	ϕ	X
ejpam-3391	340	20	(	(	PUNCT
ejpam-3391	340	21	s	s	NOUN
ejpam-3391	340	22	)	)	PUNCT
ejpam-3391	340	23	κ(s+1	κ(s+1	ADJ
ejpam-3391	340	24	)	)	PUNCT
ejpam-3391	341	1	+	+	NOUN
ejpam-3391	341	2	b	b	PROPN
ejpam-3391	341	3	(	(	PUNCT
ejpam-3391	341	4	s	s	NOUN
ejpam-3391	341	5	)	)	PUNCT
ejpam-3391	341	6	0	0	NUM
ejpam-3391	342	1	(	(	PUNCT
ejpam-3391	342	2	1	1	NUM
ejpam-3391	342	3	ϕ	ϕ	X
ejpam-3391	342	4	(	(	PUNCT
ejpam-3391	342	5	s	s	NOUN
ejpam-3391	342	6	)	)	PUNCT
ejpam-3391	342	7	κ(s+1	κ(s+1	ADJ
ejpam-3391	342	8	)	)	PUNCT
ejpam-3391	342	9	−	−	PROPN
ejpam-3391	342	10	a(s)n+1	a(s)n+1	ADV
ejpam-3391	342	11	)	)	PUNCT
ejpam-3391	343	1	+	+	PROPN
ejpam-3391	343	2	n∑	n∑	NOUN
ejpam-3391	343	3	k	k	X
ejpam-3391	343	4	=	=	NOUN
ejpam-3391	343	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	343	6	a	a	DET
ejpam-3391	343	7	(	(	PUNCT
ejpam-3391	343	8	s	s	NOUN
ejpam-3391	343	9	)	)	PUNCT
ejpam-3391	343	10	0k	0k	NOUN
ejpam-3391	343	11	(	(	PUNCT
ejpam-3391	343	12	ϕ	ϕ	X
ejpam-3391	343	13	(	(	PUNCT
ejpam-3391	343	14	s	s	NOUN
ejpam-3391	343	15	)	)	PUNCT
ejpam-3391	343	16	k	k	PROPN
ejpam-3391	343	17	ϕ	ϕ	X
ejpam-3391	343	18	(	(	PUNCT
ejpam-3391	343	19	s	s	NOUN
ejpam-3391	343	20	)	)	PUNCT
ejpam-3391	343	21	κ(s+1	κ(s+1	ADJ
ejpam-3391	343	22	)	)	PUNCT
ejpam-3391	343	23	−	−	PROPN
ejpam-3391	344	1	a(s)n+1	a(s)n+1	ADV
ejpam-3391	344	2	)	)	PUNCT
ejpam-3391	345	1	+	+	PROPN
ejpam-3391	345	2	b	b	PROPN
ejpam-3391	345	3	(	(	PUNCT
ejpam-3391	345	4	s+1	s+1	NOUN
ejpam-3391	345	5	)	)	PUNCT
ejpam-3391	345	6	0	0	PUNCT
ejpam-3391	345	7	from	from	ADP
ejpam-3391	345	8	(	(	PUNCT
ejpam-3391	345	9	8)	8)	NUM
ejpam-3391	345	10	,	,	PUNCT
ejpam-3391	345	11	a	a	DET
ejpam-3391	345	12	(	(	PUNCT
ejpam-3391	345	13	s+1	s+1	NOUN
ejpam-3391	345	14	)	)	PUNCT
ejpam-3391	345	15	i1	i1	PROPN
ejpam-3391	345	16	ϕ	ϕ	PROPN
ejpam-3391	345	17	(	(	PUNCT
ejpam-3391	345	18	s+1	s+1	NOUN
ejpam-3391	345	19	)	)	PUNCT
ejpam-3391	345	20	1	1	NUM
ejpam-3391	346	1	+	+	CCONJ
ejpam-3391	346	2	.	.	PUNCT
ejpam-3391	346	3	.	.	PUNCT
ejpam-3391	347	1	.+a	.+a	PUNCT
ejpam-3391	347	2	(	(	PUNCT
ejpam-3391	347	3	s+1	s+1	NOUN
ejpam-3391	347	4	)	)	PUNCT
ejpam-3391	347	5	in	in	ADP
ejpam-3391	347	6	ϕ	ϕ	PROPN
ejpam-3391	347	7	(	(	PUNCT
ejpam-3391	347	8	s+1	s+1	NOUN
ejpam-3391	347	9	)	)	PUNCT
ejpam-3391	347	10	n	n	PRON
ejpam-3391	348	1	+	+	ADP
ejpam-3391	348	2	b	b	PROPN
ejpam-3391	348	3	(	(	PUNCT
ejpam-3391	348	4	s+1	s+1	NOUN
ejpam-3391	348	5	)	)	PUNCT
ejpam-3391	348	6	i	i	PRON
ejpam-3391	348	7	a	a	PRON
ejpam-3391	348	8	(	(	PUNCT
ejpam-3391	348	9	s+1	s+1	NOUN
ejpam-3391	348	10	)	)	PUNCT
ejpam-3391	348	11	01	01	NUM
ejpam-3391	348	12	ϕ	ϕ	X
ejpam-3391	348	13	(	(	PUNCT
ejpam-3391	348	14	s+1	s+1	NOUN
ejpam-3391	348	15	)	)	PUNCT
ejpam-3391	348	16	1	1	NUM
ejpam-3391	349	1	+	+	CCONJ
ejpam-3391	349	2	.	.	PUNCT
ejpam-3391	349	3	.	.	PUNCT
ejpam-3391	350	1	.+a	.+a	PUNCT
ejpam-3391	350	2	(	(	PUNCT
ejpam-3391	350	3	s+1	s+1	NOUN
ejpam-3391	350	4	)	)	PUNCT
ejpam-3391	350	5	0n	0n	NOUN
ejpam-3391	351	1	ϕ	ϕ	PROPN
ejpam-3391	351	2	(	(	PUNCT
ejpam-3391	351	3	s+1	s+1	NOUN
ejpam-3391	351	4	)	)	PUNCT
ejpam-3391	351	5	n	n	PRON
ejpam-3391	352	1	+	+	ADP
ejpam-3391	352	2	b	b	PROPN
ejpam-3391	352	3	(	(	PUNCT
ejpam-3391	352	4	s+1	s+1	NOUN
ejpam-3391	352	5	)	)	PUNCT
ejpam-3391	352	6	0	0	NUM
ejpam-3391	352	7	=	=	SYM
ejpam-3391	352	8	κ(s+1)∑	κ(s+1)∑	X
ejpam-3391	352	9	k=1	k=1	PROPN
ejpam-3391	352	10	a	a	DET
ejpam-3391	352	11	(	(	PUNCT
ejpam-3391	352	12	s	s	X
ejpam-3391	352	13	)	)	PUNCT
ejpam-3391	352	14	ik	ik	PROPN
ejpam-3391	352	15	ϕ	ϕ	PROPN
ejpam-3391	352	16	(	(	PUNCT
ejpam-3391	352	17	s	s	NOUN
ejpam-3391	352	18	)	)	PUNCT
ejpam-3391	352	19	k	k	PROPN
ejpam-3391	352	20	ϕ	ϕ	X
ejpam-3391	352	21	(	(	PUNCT
ejpam-3391	352	22	s	s	NOUN
ejpam-3391	352	23	)	)	PUNCT
ejpam-3391	352	24	κ(s+1	κ(s+1	ADJ
ejpam-3391	352	25	)	)	PUNCT
ejpam-3391	353	1	+	+	NOUN
ejpam-3391	353	2	b	b	PROPN
ejpam-3391	353	3	(	(	PUNCT
ejpam-3391	353	4	s	s	X
ejpam-3391	353	5	)	)	PUNCT
ejpam-3391	353	6	i	i	PRON
ejpam-3391	353	7	.	.	PUNCT
ejpam-3391	354	1	1	1	NUM
ejpam-3391	354	2	ϕ	ϕ	X
ejpam-3391	354	3	(	(	PUNCT
ejpam-3391	354	4	s	s	NOUN
ejpam-3391	354	5	)	)	PUNCT
ejpam-3391	354	6	κ(s+1	κ(s+1	ADJ
ejpam-3391	354	7	)	)	PUNCT
ejpam-3391	355	1	+	+	NUM
ejpam-3391	356	1	n∑	n∑	NOUN
ejpam-3391	356	2	k	k	X
ejpam-3391	356	3	=	=	NOUN
ejpam-3391	356	4	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	356	5	a	a	DET
ejpam-3391	356	6	(	(	PUNCT
ejpam-3391	356	7	s	s	X
ejpam-3391	356	8	)	)	PUNCT
ejpam-3391	356	9	ik	ik	PROPN
ejpam-3391	356	10	ϕ	ϕ	PROPN
ejpam-3391	356	11	(	(	PUNCT
ejpam-3391	356	12	s	s	NOUN
ejpam-3391	356	13	)	)	PUNCT
ejpam-3391	356	14	k	k	PROPN
ejpam-3391	356	15	ϕ	ϕ	X
ejpam-3391	356	16	(	(	PUNCT
ejpam-3391	356	17	s	s	NOUN
ejpam-3391	356	18	)	)	PUNCT
ejpam-3391	356	19	κ(s+1	κ(s+1	ADJ
ejpam-3391	356	20	)	)	PUNCT
ejpam-3391	356	21	+	+	ADP
ejpam-3391	356	22	a	a	DET
ejpam-3391	356	23	(	(	PUNCT
ejpam-3391	356	24	s	s	X
ejpam-3391	356	25	)	)	PUNCT
ejpam-3391	356	26	i	i	PROPN
ejpam-3391	356	27	,	,	PUNCT
ejpam-3391	356	28	κ(s+1	κ(s+1	PROPN
ejpam-3391	356	29	)	)	PUNCT
ejpam-3391	356	30	κ(s+1)∑	κ(s+1)∑	X
ejpam-3391	356	31	k=1	k=1	PROPN
ejpam-3391	356	32	a	a	DET
ejpam-3391	356	33	(	(	PUNCT
ejpam-3391	356	34	s	s	NOUN
ejpam-3391	356	35	)	)	PUNCT
ejpam-3391	356	36	0k	0k	NOUN
ejpam-3391	356	37	ϕ	ϕ	X
ejpam-3391	356	38	(	(	PUNCT
ejpam-3391	356	39	s	s	NOUN
ejpam-3391	356	40	)	)	PUNCT
ejpam-3391	356	41	k	k	PROPN
ejpam-3391	356	42	ϕ	ϕ	X
ejpam-3391	356	43	(	(	PUNCT
ejpam-3391	356	44	s	s	NOUN
ejpam-3391	356	45	)	)	PUNCT
ejpam-3391	356	46	κ(s+1	κ(s+1	ADJ
ejpam-3391	356	47	)	)	PUNCT
ejpam-3391	357	1	+	+	NOUN
ejpam-3391	357	2	b	b	PROPN
ejpam-3391	357	3	(	(	PUNCT
ejpam-3391	357	4	s	s	NOUN
ejpam-3391	357	5	)	)	PUNCT
ejpam-3391	357	6	0	0	NUM
ejpam-3391	357	7	.	.	PUNCT
ejpam-3391	358	1	1	1	NUM
ejpam-3391	358	2	ϕ	ϕ	X
ejpam-3391	358	3	(	(	PUNCT
ejpam-3391	358	4	s	s	NOUN
ejpam-3391	358	5	)	)	PUNCT
ejpam-3391	358	6	κ(s+1	κ(s+1	ADJ
ejpam-3391	358	7	)	)	PUNCT
ejpam-3391	359	1	+	+	NUM
ejpam-3391	359	2	n∑	n∑	NOUN
ejpam-3391	359	3	k	k	X
ejpam-3391	359	4	=	=	NOUN
ejpam-3391	359	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	359	6	a	a	DET
ejpam-3391	359	7	(	(	PUNCT
ejpam-3391	359	8	s	s	NOUN
ejpam-3391	359	9	)	)	PUNCT
ejpam-3391	359	10	0k	0k	NOUN
ejpam-3391	359	11	ϕ	ϕ	X
ejpam-3391	359	12	(	(	PUNCT
ejpam-3391	359	13	s	s	NOUN
ejpam-3391	359	14	)	)	PUNCT
ejpam-3391	359	15	k	k	PROPN
ejpam-3391	359	16	ϕ	ϕ	X
ejpam-3391	359	17	(	(	PUNCT
ejpam-3391	359	18	s	s	NOUN
ejpam-3391	359	19	)	)	PUNCT
ejpam-3391	359	20	κ(s+1	κ(s+1	ADJ
ejpam-3391	359	21	)	)	PUNCT
ejpam-3391	359	22	+	+	ADP
ejpam-3391	359	23	a	a	DET
ejpam-3391	359	24	(	(	PUNCT
ejpam-3391	359	25	s	s	NOUN
ejpam-3391	359	26	)	)	PUNCT
ejpam-3391	359	27	0,κ(s+1	0,κ(s+1	NUM
ejpam-3391	359	28	)	)	PUNCT
ejpam-3391	359	29	=	=	SYM
ejpam-3391	359	30	a	a	DET
ejpam-3391	359	31	(	(	PUNCT
ejpam-3391	359	32	s	s	NOUN
ejpam-3391	359	33	)	)	PUNCT
ejpam-3391	359	34	i1	i1	PROPN
ejpam-3391	359	35	ϕ	ϕ	PROPN
ejpam-3391	359	36	(	(	PUNCT
ejpam-3391	359	37	s	s	NOUN
ejpam-3391	359	38	)	)	PUNCT
ejpam-3391	359	39	1	1	NUM
ejpam-3391	359	40	+	+	CCONJ
ejpam-3391	359	41	.	.	PUNCT
ejpam-3391	359	42	.	.	PUNCT
ejpam-3391	360	1	.+a	.+a	PUNCT
ejpam-3391	360	2	(	(	PUNCT
ejpam-3391	360	3	s	s	X
ejpam-3391	360	4	)	)	PUNCT
ejpam-3391	360	5	in	in	ADP
ejpam-3391	360	6	ϕ	ϕ	PROPN
ejpam-3391	360	7	(	(	PUNCT
ejpam-3391	360	8	s	s	NOUN
ejpam-3391	360	9	)	)	PUNCT
ejpam-3391	360	10	n	n	PRON
ejpam-3391	360	11	+	+	ADP
ejpam-3391	360	12	b	b	PROPN
ejpam-3391	360	13	(	(	PUNCT
ejpam-3391	360	14	s	s	X
ejpam-3391	360	15	)	)	PUNCT
ejpam-3391	360	16	i	i	PRON
ejpam-3391	361	1	a	a	PRON
ejpam-3391	361	2	(	(	PUNCT
ejpam-3391	361	3	s	s	NOUN
ejpam-3391	361	4	)	)	PUNCT
ejpam-3391	361	5	01	01	NUM
ejpam-3391	361	6	ϕ	ϕ	X
ejpam-3391	361	7	(	(	PUNCT
ejpam-3391	361	8	s	s	NOUN
ejpam-3391	361	9	)	)	PUNCT
ejpam-3391	361	10	1	1	NUM
ejpam-3391	361	11	+	+	CCONJ
ejpam-3391	361	12	.	.	PUNCT
ejpam-3391	361	13	.	.	PUNCT
ejpam-3391	362	1	.+a	.+a	PUNCT
ejpam-3391	362	2	(	(	PUNCT
ejpam-3391	362	3	s	s	NOUN
ejpam-3391	362	4	)	)	PUNCT
ejpam-3391	362	5	0nϕ	0nϕ	NOUN
ejpam-3391	362	6	(	(	PUNCT
ejpam-3391	362	7	s	s	NOUN
ejpam-3391	362	8	)	)	PUNCT
ejpam-3391	362	9	n	n	PRON
ejpam-3391	362	10	+	+	ADP
ejpam-3391	362	11	b	b	PROPN
ejpam-3391	362	12	(	(	PUNCT
ejpam-3391	362	13	s	s	NOUN
ejpam-3391	362	14	)	)	PUNCT
ejpam-3391	362	15	0	0	NUM
ejpam-3391	363	1	=	=	SYM
ejpam-3391	363	2	ϕi	ϕi	PROPN
ejpam-3391	363	3	.	.	PUNCT
ejpam-3391	364	1	thus	thus	ADV
ejpam-3391	364	2	the	the	DET
ejpam-3391	364	3	assertion	assertion	NOUN
ejpam-3391	364	4	holds	hold	VERB
ejpam-3391	364	5	for	for	ADP
ejpam-3391	364	6	s+	s+	ADJ
ejpam-3391	364	7	1	1	NUM
ejpam-3391	364	8	,	,	PUNCT
ejpam-3391	364	9	completing	complete	VERB
ejpam-3391	364	10	the	the	DET
ejpam-3391	364	11	proof	proof	NOUN
ejpam-3391	364	12	.	.	PUNCT
ejpam-3391	365	1	�	�	PROPN
ejpam-3391	365	2	the	the	DET
ejpam-3391	365	3	vector	vector	PROPN
ejpam-3391	365	4	v	v	X
ejpam-3391	365	5	(	(	PUNCT
ejpam-3391	365	6	s	s	NOUN
ejpam-3391	365	7	)	)	PUNCT
ejpam-3391	365	8	0	0	NUM
ejpam-3391	365	9	=	=	SYM
ejpam-3391	365	10	(	(	PUNCT
ejpam-3391	365	11	b	b	X
ejpam-3391	365	12	(	(	PUNCT
ejpam-3391	365	13	s	s	NOUN
ejpam-3391	365	14	)	)	PUNCT
ejpam-3391	365	15	1	1	NUM
ejpam-3391	365	16	b	b	X
ejpam-3391	365	17	(	(	PUNCT
ejpam-3391	365	18	s	s	NOUN
ejpam-3391	365	19	)	)	PUNCT
ejpam-3391	365	20	0	0	NUM
ejpam-3391	365	21	,	,	PUNCT
ejpam-3391	365	22	.	.	PUNCT
ejpam-3391	365	23	.	.	PUNCT
ejpam-3391	366	1	.	.	PUNCT
ejpam-3391	367	1	,	,	PUNCT
ejpam-3391	367	2	b	b	X
ejpam-3391	367	3	(	(	PUNCT
ejpam-3391	367	4	s	s	NOUN
ejpam-3391	367	5	)	)	PUNCT
ejpam-3391	367	6	n	n	PRON
ejpam-3391	367	7	b	b	PROPN
ejpam-3391	367	8	(	(	PUNCT
ejpam-3391	367	9	s	s	NOUN
ejpam-3391	367	10	)	)	PUNCT
ejpam-3391	367	11	0	0	NUM
ejpam-3391	367	12	)	)	PUNCT
ejpam-3391	367	13	is	be	AUX
ejpam-3391	367	14	called	call	VERB
ejpam-3391	367	15	the	the	DET
ejpam-3391	367	16	s	s	NOUN
ejpam-3391	367	17	-	-	PUNCT
ejpam-3391	367	18	th	th	VERB
ejpam-3391	367	19	convergent	convergent	NOUN
ejpam-3391	367	20	of	of	ADP
ejpam-3391	367	21	ϕ	ϕ	NOUN
ejpam-3391	367	22	=	=	PUNCT
ejpam-3391	367	23	(	(	PUNCT
ejpam-3391	367	24	ϕ1	ϕ1	NOUN
ejpam-3391	367	25	,	,	PUNCT
ejpam-3391	367	26	.	.	PUNCT
ejpam-3391	367	27	.	.	PUNCT
ejpam-3391	368	1	.	.	PUNCT
ejpam-3391	369	1	,	,	PUNCT
ejpam-3391	369	2	ϕn	ϕn	X
ejpam-3391	369	3	)	)	PUNCT
ejpam-3391	369	4	by	by	ADP
ejpam-3391	369	5	the	the	DET
ejpam-3391	369	6	β	β	NOUN
ejpam-3391	369	7	-	-	NOUN
ejpam-3391	369	8	mjpa	mjpa	NOUN
ejpam-3391	369	9	and	and	CCONJ
ejpam-3391	369	10	m	m	PRON
ejpam-3391	369	11	(	(	PUNCT
ejpam-3391	369	12	1	1	NUM
ejpam-3391	369	13	)	)	PUNCT
ejpam-3391	369	14	.	.	PUNCT
ejpam-3391	369	15	.	.	PUNCT
ejpam-3391	370	1	.m	.m	PROPN
ejpam-3391	371	1	(	(	PUNCT
ejpam-3391	371	2	s	s	X
ejpam-3391	371	3	)	)	PUNCT
ejpam-3391	371	4	the	the	DET
ejpam-3391	371	5	matrices	matrix	NOUN
ejpam-3391	371	6	expansion	expansion	NOUN
ejpam-3391	371	7	by	by	ADP
ejpam-3391	371	8	this	this	DET
ejpam-3391	371	9	algorithm	algorithm	NOUN
ejpam-3391	371	10	.	.	PUNCT
ejpam-3391	372	1	morover	morover	VERB
ejpam-3391	372	2	the	the	DET
ejpam-3391	372	3	expansion	expansion	NOUN
ejpam-3391	372	4	by	by	ADP
ejpam-3391	372	5	the	the	DET
ejpam-3391	372	6	β	β	NOUN
ejpam-3391	372	7	-	-	NOUN
ejpam-3391	372	8	mjpa	mjpa	NOUN
ejpam-3391	372	9	is	be	AUX
ejpam-3391	372	10	said	say	VERB
ejpam-3391	372	11	to	to	PART
ejpam-3391	372	12	be	be	AUX
ejpam-3391	372	13	finite	finite	ADJ
ejpam-3391	372	14	or	or	CCONJ
ejpam-3391	372	15	infinite	infinite	ADJ
ejpam-3391	372	16	if	if	SCONJ
ejpam-3391	372	17	t	t	PROPN
ejpam-3391	372	18	sβ(ϕ1	sβ(ϕ1	NOUN
ejpam-3391	372	19	,	,	PUNCT
ejpam-3391	372	20	.	.	PUNCT
ejpam-3391	372	21	.	.	PUNCT
ejpam-3391	373	1	.	.	PUNCT
ejpam-3391	374	1	,	,	PUNCT
ejpam-3391	374	2	ϕn	ϕn	X
ejpam-3391	374	3	)	)	PUNCT
ejpam-3391	374	4	=	=	SYM
ejpam-3391	374	5	(	(	PUNCT
ejpam-3391	374	6	0	0	NUM
ejpam-3391	374	7	,	,	PUNCT
ejpam-3391	374	8	.	.	PUNCT
ejpam-3391	374	9	.	.	PUNCT
ejpam-3391	375	1	.	.	PUNCT
ejpam-3391	376	1	,	,	PUNCT
ejpam-3391	376	2	0	0	NUM
ejpam-3391	376	3	)	)	PUNCT
ejpam-3391	376	4	for	for	ADP
ejpam-3391	376	5	some	some	PRON
ejpam-3391	376	6	s	s	PART
ejpam-3391	376	7	≥	≥	NOUN
ejpam-3391	376	8	0	0	NUM
ejpam-3391	376	9	or	or	CCONJ
ejpam-3391	376	10	t	t	PROPN
ejpam-3391	376	11	sβ(ϕ1	sβ(ϕ1	VERB
ejpam-3391	376	12	,	,	PUNCT
ejpam-3391	376	13	.	.	PUNCT
ejpam-3391	376	14	.	.	PUNCT
ejpam-3391	377	1	.	.	PUNCT
ejpam-3391	378	1	,	,	PUNCT
ejpam-3391	378	2	ϕn	ϕn	PROPN
ejpam-3391	378	3	)	)	PUNCT
ejpam-3391	378	4	6=	6=	X
ejpam-3391	378	5	(	(	PUNCT
ejpam-3391	378	6	0	0	NUM
ejpam-3391	378	7	,	,	PUNCT
ejpam-3391	378	8	.	.	PUNCT
ejpam-3391	378	9	.	.	PUNCT
ejpam-3391	379	1	.	.	PUNCT
ejpam-3391	380	1	,	,	PUNCT
ejpam-3391	380	2	0	0	X
ejpam-3391	380	3	)	)	PUNCT
ejpam-3391	380	4	for	for	ADP
ejpam-3391	380	5	any	any	PRON
ejpam-3391	380	6	s	s	PART
ejpam-3391	380	7	≥	≥	NOUN
ejpam-3391	380	8	0	0	NUM
ejpam-3391	380	9	,	,	PUNCT
ejpam-3391	380	10	respectively	respectively	ADV
ejpam-3391	380	11	.	.	PUNCT
ejpam-3391	381	1	a.	a.	PROPN
ejpam-3391	381	2	chandoul	chandoul	PROPN
ejpam-3391	381	3	,	,	PUNCT
ejpam-3391	381	4	f.	f.	PROPN
ejpam-3391	381	5	aljuaydi	aljuaydi	PROPN
ejpam-3391	381	6	/	/	SYM
ejpam-3391	381	7	eur	eur	NOUN
ejpam-3391	381	8	.	.	PUNCT
ejpam-3391	382	1	j.	j.	PROPN
ejpam-3391	382	2	pure	pure	PROPN
ejpam-3391	382	3	appl	appl	PROPN
ejpam-3391	382	4	.	.	PROPN
ejpam-3391	382	5	math	math	PROPN
ejpam-3391	382	6	,	,	PUNCT
ejpam-3391	382	7	12	12	NUM
ejpam-3391	382	8	(	(	PUNCT
ejpam-3391	382	9	2	2	NUM
ejpam-3391	382	10	)	)	PUNCT
ejpam-3391	382	11	(	(	PUNCT
ejpam-3391	382	12	2019	2019	NUM
ejpam-3391	382	13	)	)	PUNCT
ejpam-3391	382	14	,	,	PUNCT
ejpam-3391	382	15	418	418	NUM
ejpam-3391	382	16	-	-	SYM
ejpam-3391	382	17	431	431	NUM
ejpam-3391	382	18	427	427	NUM
ejpam-3391	382	19	6	6	NUM
ejpam-3391	382	20	.	.	PUNCT
ejpam-3391	383	1	convergence	convergence	NOUN
ejpam-3391	383	2	of	of	ADP
ejpam-3391	383	3	a	a	PRON
ejpam-3391	383	4	-	-	PUNCT
ejpam-3391	383	5	modified	modify	VERB
ejpam-3391	383	6	jacobi	jacobi	PROPN
ejpam-3391	383	7	-	-	PUNCT
ejpam-3391	383	8	perron	perron	PROPN
ejpam-3391	383	9	algorithm	algorithm	NOUN
ejpam-3391	383	10	over	over	ADP
ejpam-3391	383	11	the	the	DET
ejpam-3391	383	12	field	field	NOUN
ejpam-3391	383	13	of	of	ADP
ejpam-3391	383	14	formal	formal	ADJ
ejpam-3391	383	15	power	power	NOUN
ejpam-3391	383	16	series	series	NOUN
ejpam-3391	383	17	now	now	ADV
ejpam-3391	383	18	,	,	PUNCT
ejpam-3391	383	19	we	we	PRON
ejpam-3391	383	20	give	give	VERB
ejpam-3391	383	21	the	the	DET
ejpam-3391	383	22	main	main	ADJ
ejpam-3391	383	23	result	result	NOUN
ejpam-3391	383	24	.	.	PUNCT
ejpam-3391	384	1	theorem	theorem	NOUN
ejpam-3391	384	2	2	2	NUM
ejpam-3391	384	3	.	.	PUNCT
ejpam-3391	385	1	let	let	VERB
ejpam-3391	385	2	ϕ	ϕ	X
ejpam-3391	385	3	=	=	SYM
ejpam-3391	385	4	(	(	PUNCT
ejpam-3391	385	5	ϕ1	ϕ1	NOUN
ejpam-3391	385	6	,	,	PUNCT
ejpam-3391	385	7	.	.	PUNCT
ejpam-3391	385	8	.	.	PUNCT
ejpam-3391	386	1	.	.	PUNCT
ejpam-3391	387	1	,	,	PUNCT
ejpam-3391	387	2	ϕn	ϕn	X
ejpam-3391	387	3	)	)	PUNCT
ejpam-3391	387	4	∈	∈	PROPN
ejpam-3391	387	5	ln	ln	NOUN
ejpam-3391	387	6	and	and	CCONJ
ejpam-3391	387	7	v	v	NOUN
ejpam-3391	387	8	(	(	PUNCT
ejpam-3391	387	9	s	s	NOUN
ejpam-3391	387	10	)	)	PUNCT
ejpam-3391	387	11	0	0	NUM
ejpam-3391	388	1	=	=	SYM
ejpam-3391	388	2	v	v	X
ejpam-3391	388	3	(	(	PUNCT
ejpam-3391	388	4	s	s	NOUN
ejpam-3391	388	5	)	)	PUNCT
ejpam-3391	388	6	0	0	NUM
ejpam-3391	388	7	(	(	PUNCT
ejpam-3391	388	8	ϕ	ϕ	NOUN
ejpam-3391	388	9	)	)	PUNCT
ejpam-3391	388	10	for	for	ADP
ejpam-3391	388	11	all	all	PRON
ejpam-3391	388	12	s	s	PART
ejpam-3391	388	13	≥	≥	NOUN
ejpam-3391	388	14	1	1	NUM
ejpam-3391	388	15	,	,	PUNCT
ejpam-3391	388	16	then	then	ADV
ejpam-3391	388	17	the	the	DET
ejpam-3391	388	18	sequence	sequence	NOUN
ejpam-3391	388	19	(	(	PUNCT
ejpam-3391	388	20	v	v	X
ejpam-3391	388	21	(	(	PUNCT
ejpam-3391	388	22	s	s	NOUN
ejpam-3391	388	23	)	)	PUNCT
ejpam-3391	388	24	0	0	NUM
ejpam-3391	388	25	)	)	PUNCT
ejpam-3391	388	26	s≥1	s≥1	ADJ
ejpam-3391	388	27	converges	converge	NOUN
ejpam-3391	388	28	to	to	ADP
ejpam-3391	388	29	ϕ.	ϕ.	PROPN
ejpam-3391	388	30	in	in	ADP
ejpam-3391	388	31	order	order	NOUN
ejpam-3391	388	32	to	to	PART
ejpam-3391	388	33	prove	prove	VERB
ejpam-3391	388	34	this	this	DET
ejpam-3391	388	35	theorem	theorem	NOUN
ejpam-3391	388	36	we	we	PRON
ejpam-3391	388	37	need	need	VERB
ejpam-3391	388	38	the	the	DET
ejpam-3391	388	39	following	follow	VERB
ejpam-3391	388	40	lemma	lemma	PROPN
ejpam-3391	388	41	lemma	lemma	PROPN
ejpam-3391	388	42	2	2	NUM
ejpam-3391	388	43	.	.	PUNCT
ejpam-3391	388	44	for	for	ADP
ejpam-3391	388	45	any	any	DET
ejpam-3391	388	46	sequence	sequence	NOUN
ejpam-3391	388	47	m	m	NOUN
ejpam-3391	388	48	(	(	PUNCT
ejpam-3391	388	49	1	1	NUM
ejpam-3391	388	50	)	)	PUNCT
ejpam-3391	388	51	,	,	PUNCT
ejpam-3391	388	52	·	·	PUNCT
ejpam-3391	388	53	·	·	PUNCT
ejpam-3391	388	54	·	·	PUNCT
ejpam-3391	388	55	,	,	PUNCT
ejpam-3391	388	56	m	m	PROPN
ejpam-3391	388	57	(	(	PUNCT
ejpam-3391	388	58	s+1	s+1	NOUN
ejpam-3391	388	59	)	)	PUNCT
ejpam-3391	388	60	,	,	PUNCT
ejpam-3391	388	61	·	·	PUNCT
ejpam-3391	388	62	·	·	PUNCT
ejpam-3391	388	63	·	·	PUNCT
ejpam-3391	388	64	of	of	ADP
ejpam-3391	388	65	the	the	DET
ejpam-3391	388	66	form	form	NOUN
ejpam-3391	388	67	(	(	PUNCT
ejpam-3391	388	68	5	5	X
ejpam-3391	388	69	)	)	PUNCT
ejpam-3391	388	70	|b(s	|b(s	PROPN
ejpam-3391	388	71	)	)	PUNCT
ejpam-3391	388	72	0	0	PUNCT
ejpam-3391	389	1	|	|	CCONJ
ejpam-3391	389	2	∣∣∣∣∣b(s+1	∣∣∣∣∣b(s+1	X
ejpam-3391	389	3	)	)	PUNCT
ejpam-3391	389	4	i	i	PRON
ejpam-3391	389	5	b	b	PROPN
ejpam-3391	389	6	(	(	PUNCT
ejpam-3391	389	7	s+1	s+1	NOUN
ejpam-3391	389	8	)	)	PUNCT
ejpam-3391	389	9	0	0	NUM
ejpam-3391	390	1	−	−	PROPN
ejpam-3391	390	2	b	b	PROPN
ejpam-3391	390	3	(	(	PUNCT
ejpam-3391	390	4	s	s	X
ejpam-3391	390	5	)	)	PUNCT
ejpam-3391	390	6	i	i	PROPN
ejpam-3391	390	7	b	b	X
ejpam-3391	390	8	(	(	PUNCT
ejpam-3391	390	9	s	s	NOUN
ejpam-3391	390	10	)	)	PUNCT
ejpam-3391	390	11	0	0	NUM
ejpam-3391	391	1	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-3391	391	2	≤	≤	PROPN
ejpam-3391	391	3	e−1	e−1	PROPN
ejpam-3391	391	4	holds	hold	VERB
ejpam-3391	391	5	for	for	ADP
ejpam-3391	391	6	any	any	DET
ejpam-3391	391	7	s	s	NOUN
ejpam-3391	391	8	≥	≥	NOUN
ejpam-3391	391	9	1	1	NUM
ejpam-3391	391	10	.	.	PUNCT
ejpam-3391	392	1	proof	proof	NOUN
ejpam-3391	392	2	.	.	PUNCT
ejpam-3391	393	1	we	we	PRON
ejpam-3391	393	2	prove	prove	VERB
ejpam-3391	393	3	this	this	DET
ejpam-3391	393	4	result	result	NOUN
ejpam-3391	393	5	by	by	ADP
ejpam-3391	393	6	using	use	VERB
ejpam-3391	393	7	the	the	DET
ejpam-3391	393	8	mathematical	mathematical	ADJ
ejpam-3391	393	9	induction	induction	NOUN
ejpam-3391	393	10	on	on	ADP
ejpam-3391	393	11	s.	s.	PROPN
ejpam-3391	393	12	note	note	VERB
ejpam-3391	393	13	that	that	SCONJ
ejpam-3391	393	14	κ(s	κ(s	PROPN
ejpam-3391	393	15	)	)	PUNCT
ejpam-3391	393	16	=	=	SYM
ejpam-3391	394	1	min	min	PROPN
ejpam-3391	394	2	1≤i≤n+1	1≤i≤n+1	NUM
ejpam-3391	394	3	{	{	PUNCT
ejpam-3391	394	4	i	i	NOUN
ejpam-3391	394	5	:	:	PUNCT
ejpam-3391	394	6	m	m	VERB
ejpam-3391	394	7	(	(	PUNCT
ejpam-3391	394	8	s	s	X
ejpam-3391	394	9	)	)	PUNCT
ejpam-3391	394	10	i	i	PRON
ejpam-3391	394	11	,	,	PUNCT
ejpam-3391	394	12	n+1	n+1	PROPN
ejpam-3391	394	13	6=	6=	NUM
ejpam-3391	394	14	0	0	NUM
ejpam-3391	394	15	}	}	PUNCT
ejpam-3391	394	16	where	where	SCONJ
ejpam-3391	394	17	m	m	VERB
ejpam-3391	394	18	(	(	PUNCT
ejpam-3391	394	19	s	s	X
ejpam-3391	394	20	)	)	PUNCT
ejpam-3391	394	21	i	i	PRON
ejpam-3391	394	22	,	,	PUNCT
ejpam-3391	394	23	n+1	n+1	PROPN
ejpam-3391	394	24	is	be	AUX
ejpam-3391	394	25	the	the	DET
ejpam-3391	394	26	(	(	PUNCT
ejpam-3391	394	27	i	i	NOUN
ejpam-3391	394	28	,	,	PUNCT
ejpam-3391	394	29	n+	n+	NUM
ejpam-3391	394	30	1	1	NUM
ejpam-3391	394	31	)	)	PUNCT
ejpam-3391	394	32	component	component	NOUN
ejpam-3391	394	33	of	of	ADP
ejpam-3391	394	34	m	m	PROPN
ejpam-3391	394	35	(	(	PUNCT
ejpam-3391	394	36	s	s	NOUN
ejpam-3391	394	37	)	)	PUNCT
ejpam-3391	394	38	.	.	PUNCT
ejpam-3391	395	1	then	then	ADV
ejpam-3391	395	2	if	if	SCONJ
ejpam-3391	395	3	1	1	NUM
ejpam-3391	395	4	≤	≤	NUM
ejpam-3391	395	5	κ(1	κ(1	NOUN
ejpam-3391	395	6	)	)	PUNCT
ejpam-3391	396	1	<	<	X
ejpam-3391	396	2	κ(2	κ(2	PROPN
ejpam-3391	396	3	)	)	PUNCT
ejpam-3391	396	4	,	,	PUNCT
ejpam-3391	396	5	∣∣∣∣∣b(2	∣∣∣∣∣b(2	PROPN
ejpam-3391	396	6	)	)	PUNCT
ejpam-3391	396	7	i	i	PROPN
ejpam-3391	397	1	b	b	X
ejpam-3391	397	2	(	(	PUNCT
ejpam-3391	397	3	2	2	NUM
ejpam-3391	397	4	)	)	PUNCT
ejpam-3391	397	5	0	0	NUM
ejpam-3391	398	1	−	−	PROPN
ejpam-3391	398	2	b	b	X
ejpam-3391	398	3	(	(	PUNCT
ejpam-3391	398	4	1	1	NUM
ejpam-3391	398	5	)	)	PUNCT
ejpam-3391	398	6	i	i	PRON
ejpam-3391	398	7	b	b	X
ejpam-3391	398	8	(	(	PUNCT
ejpam-3391	398	9	1	1	NUM
ejpam-3391	398	10	)	)	PUNCT
ejpam-3391	398	11	0	0	NUM
ejpam-3391	399	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	399	2	=	=	SYM
ejpam-3391	400	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	400	2	a	a	DET
ejpam-3391	400	3	(	(	PUNCT
ejpam-3391	400	4	2	2	NUM
ejpam-3391	400	5	)	)	PUNCT
ejpam-3391	400	6	i	i	PRON
ejpam-3391	400	7	a	a	PRON
ejpam-3391	400	8	(	(	PUNCT
ejpam-3391	400	9	1	1	X
ejpam-3391	400	10	)	)	PUNCT
ejpam-3391	400	11	n+1a	n+1a	NOUN
ejpam-3391	400	12	(	(	PUNCT
ejpam-3391	400	13	2	2	NUM
ejpam-3391	400	14	)	)	PUNCT
ejpam-3391	400	15	n+1	n+1	NUM
ejpam-3391	400	16	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3391	400	17	for	for	ADP
ejpam-3391	400	18	1	1	NUM
ejpam-3391	400	19	≤	≤	NUM
ejpam-3391	400	20	i	i	PRON
ejpam-3391	400	21	≤	≤	PROPN
ejpam-3391	400	22	n.	n.	NOUN
ejpam-3391	400	23	since	since	SCONJ
ejpam-3391	400	24	deg	deg	PROPN
ejpam-3391	400	25	a	a	DET
ejpam-3391	400	26	(	(	PUNCT
ejpam-3391	400	27	s	s	X
ejpam-3391	400	28	)	)	PUNCT
ejpam-3391	400	29	n+1	n+1	NUM
ejpam-3391	400	30	≥	≥	NOUN
ejpam-3391	400	31	1	1	NUM
ejpam-3391	400	32	and	and	CCONJ
ejpam-3391	400	33	deg	deg	VERB
ejpam-3391	400	34	a	a	DET
ejpam-3391	400	35	(	(	PUNCT
ejpam-3391	400	36	s	s	X
ejpam-3391	400	37	)	)	PUNCT
ejpam-3391	400	38	n+1	n+1	NUM
ejpam-3391	400	39	≥	≥	NUM
ejpam-3391	400	40	deg	deg	VERB
ejpam-3391	400	41	a	a	DET
ejpam-3391	400	42	(	(	PUNCT
ejpam-3391	400	43	s	s	X
ejpam-3391	400	44	)	)	PUNCT
ejpam-3391	400	45	i	i	PRON
ejpam-3391	400	46	,	,	PUNCT
ejpam-3391	400	47	1	1	NUM
ejpam-3391	400	48	≤	≤	NUM
ejpam-3391	400	49	i	i	PRON
ejpam-3391	400	50	≤	≤	NOUN
ejpam-3391	400	51	n	n	CCONJ
ejpam-3391	400	52	,	,	PUNCT
ejpam-3391	400	53	for	for	ADP
ejpam-3391	400	54	s	s	PRON
ejpam-3391	400	55	≥	≥	NOUN
ejpam-3391	400	56	1	1	NUM
ejpam-3391	400	57	,	,	PUNCT
ejpam-3391	400	58	we	we	PRON
ejpam-3391	400	59	have	have	AUX
ejpam-3391	400	60	|b(1	|b(1	VERB
ejpam-3391	400	61	)	)	PUNCT
ejpam-3391	400	62	0	0	PUNCT
ejpam-3391	401	1	|	|	CCONJ
ejpam-3391	401	2	∣∣∣∣∣b(2	∣∣∣∣∣b(2	NOUN
ejpam-3391	401	3	)	)	PUNCT
ejpam-3391	402	1	i	i	PROPN
ejpam-3391	402	2	b	b	X
ejpam-3391	402	3	(	(	PUNCT
ejpam-3391	402	4	2	2	NUM
ejpam-3391	402	5	)	)	PUNCT
ejpam-3391	402	6	0	0	NUM
ejpam-3391	403	1	−	−	PROPN
ejpam-3391	403	2	b	b	X
ejpam-3391	403	3	(	(	PUNCT
ejpam-3391	403	4	1	1	NUM
ejpam-3391	403	5	)	)	PUNCT
ejpam-3391	403	6	i	i	PRON
ejpam-3391	403	7	b	b	X
ejpam-3391	403	8	(	(	PUNCT
ejpam-3391	403	9	1	1	NUM
ejpam-3391	403	10	)	)	PUNCT
ejpam-3391	403	11	0	0	NUM
ejpam-3391	404	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	404	2	≤	≤	ADJ
ejpam-3391	404	3	e−1	e−1	PROPN
ejpam-3391	404	4	(	(	PUNCT
ejpam-3391	404	5	11	11	NUM
ejpam-3391	404	6	)	)	PUNCT
ejpam-3391	404	7	moreover	moreover	ADV
ejpam-3391	404	8	,	,	PUNCT
ejpam-3391	404	9	if	if	SCONJ
ejpam-3391	404	10	κ(1	κ(1	PROPN
ejpam-3391	404	11	)	)	PUNCT
ejpam-3391	404	12	=	=	SYM
ejpam-3391	405	1	κ(2	κ(2	PROPN
ejpam-3391	405	2	)	)	PUNCT
ejpam-3391	405	3	,	,	PUNCT
ejpam-3391	405	4	we	we	PRON
ejpam-3391	405	5	have	have	VERB
ejpam-3391	405	6	∣∣∣∣∣b(2	∣∣∣∣∣b(2	NOUN
ejpam-3391	405	7	)	)	PUNCT
ejpam-3391	406	1	i	i	PROPN
ejpam-3391	406	2	b	b	X
ejpam-3391	406	3	(	(	PUNCT
ejpam-3391	406	4	2	2	NUM
ejpam-3391	406	5	)	)	PUNCT
ejpam-3391	406	6	0	0	NUM
ejpam-3391	407	1	−	−	PROPN
ejpam-3391	407	2	b	b	X
ejpam-3391	407	3	(	(	PUNCT
ejpam-3391	407	4	1	1	NUM
ejpam-3391	407	5	)	)	PUNCT
ejpam-3391	407	6	i	i	PRON
ejpam-3391	407	7	b	b	X
ejpam-3391	407	8	(	(	PUNCT
ejpam-3391	407	9	1	1	NUM
ejpam-3391	407	10	)	)	PUNCT
ejpam-3391	407	11	0	0	NUM
ejpam-3391	408	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	408	2	=	=	PUNCT
ejpam-3391	409	1			NUM
ejpam-3391	409	2	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3391	409	3	a	a	DET
ejpam-3391	409	4	(	(	PUNCT
ejpam-3391	409	5	2	2	NUM
ejpam-3391	409	6	)	)	PUNCT
ejpam-3391	409	7	i	i	PRON
ejpam-3391	409	8	(	(	PUNCT
ejpam-3391	409	9	1	1	NUM
ejpam-3391	409	10	+	+	CCONJ
ejpam-3391	409	11	a	a	DET
ejpam-3391	409	12	(	(	PUNCT
ejpam-3391	409	13	1	1	X
ejpam-3391	409	14	)	)	PUNCT
ejpam-3391	409	15	n+1a	n+1a	NOUN
ejpam-3391	409	16	(	(	PUNCT
ejpam-3391	409	17	2	2	NUM
ejpam-3391	409	18	)	)	PUNCT
ejpam-3391	409	19	n+1)a	n+1)a	NOUN
ejpam-3391	409	20	(	(	PUNCT
ejpam-3391	409	21	1	1	NUM
ejpam-3391	409	22	)	)	PUNCT
ejpam-3391	409	23	n+1	n+1	NUM
ejpam-3391	409	24	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3391	409	25	for	for	ADP
ejpam-3391	409	26	1	1	NUM
ejpam-3391	409	27	≤	≤	NUM
ejpam-3391	409	28	i	i	PROPN
ejpam-3391	409	29	≤	≤	PROPN
ejpam-3391	409	30	κ(1	κ(1	PROPN
ejpam-3391	409	31	)	)	PUNCT
ejpam-3391	409	32	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	409	33	a	a	DET
ejpam-3391	409	34	(	(	PUNCT
ejpam-3391	409	35	1	1	X
ejpam-3391	409	36	)	)	PUNCT
ejpam-3391	409	37	n+1a	n+1a	NOUN
ejpam-3391	409	38	(	(	PUNCT
ejpam-3391	409	39	2	2	NUM
ejpam-3391	409	40	)	)	PUNCT
ejpam-3391	409	41	i	i	PRON
ejpam-3391	409	42	−	−	VERB
ejpam-3391	409	43	a	a	DET
ejpam-3391	409	44	(	(	PUNCT
ejpam-3391	409	45	1	1	NUM
ejpam-3391	409	46	)	)	PUNCT
ejpam-3391	409	47	i	i	PRON
ejpam-3391	409	48	(	(	PUNCT
ejpam-3391	410	1	1	1	NUM
ejpam-3391	410	2	+	+	CCONJ
ejpam-3391	410	3	a	a	DET
ejpam-3391	410	4	(	(	PUNCT
ejpam-3391	410	5	1	1	X
ejpam-3391	410	6	)	)	PUNCT
ejpam-3391	410	7	n+1a	n+1a	NOUN
ejpam-3391	410	8	(	(	PUNCT
ejpam-3391	410	9	2	2	NUM
ejpam-3391	410	10	)	)	PUNCT
ejpam-3391	410	11	n+1)a	n+1)a	NOUN
ejpam-3391	410	12	(	(	PUNCT
ejpam-3391	410	13	1	1	NUM
ejpam-3391	410	14	)	)	PUNCT
ejpam-3391	410	15	n+1	n+1	NUM
ejpam-3391	410	16	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3391	410	17	for	for	ADP
ejpam-3391	410	18	κ(1	κ(1	PROPN
ejpam-3391	410	19	)	)	PUNCT
ejpam-3391	410	20	≤	≤	PUNCT
ejpam-3391	411	1	i	i	PRON
ejpam-3391	411	2	≤	≤	ADJ
ejpam-3391	411	3	n	n	CCONJ
ejpam-3391	411	4	(	(	PUNCT
ejpam-3391	411	5	12	12	NUM
ejpam-3391	411	6	)	)	PUNCT
ejpam-3391	411	7	and	and	CCONJ
ejpam-3391	411	8	if	if	SCONJ
ejpam-3391	411	9	κ(2	κ(2	PROPN
ejpam-3391	411	10	)	)	PUNCT
ejpam-3391	411	11	<	<	X
ejpam-3391	411	12	κ(1	κ(1	PROPN
ejpam-3391	411	13	)	)	PUNCT
ejpam-3391	411	14	≤	≤	NOUN
ejpam-3391	412	1	n	n	CCONJ
ejpam-3391	412	2	,	,	PUNCT
ejpam-3391	412	3	we	we	PRON
ejpam-3391	412	4	have	have	VERB
ejpam-3391	412	5	∣∣∣∣∣b(2	∣∣∣∣∣b(2	NOUN
ejpam-3391	412	6	)	)	PUNCT
ejpam-3391	413	1	i	i	PROPN
ejpam-3391	413	2	b	b	X
ejpam-3391	413	3	(	(	PUNCT
ejpam-3391	413	4	2	2	NUM
ejpam-3391	413	5	)	)	PUNCT
ejpam-3391	413	6	0	0	NUM
ejpam-3391	414	1	−	−	PROPN
ejpam-3391	414	2	b	b	X
ejpam-3391	414	3	(	(	PUNCT
ejpam-3391	414	4	1	1	NUM
ejpam-3391	414	5	)	)	PUNCT
ejpam-3391	414	6	i	i	PRON
ejpam-3391	414	7	b	b	X
ejpam-3391	414	8	(	(	PUNCT
ejpam-3391	414	9	1	1	NUM
ejpam-3391	414	10	)	)	PUNCT
ejpam-3391	414	11	0	0	NUM
ejpam-3391	415	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	415	2	=	=	PUNCT
ejpam-3391	416	1			ADV
ejpam-3391	416	2	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	416	3	a	a	DET
ejpam-3391	416	4	(	(	PUNCT
ejpam-3391	416	5	2	2	NUM
ejpam-3391	416	6	)	)	PUNCT
ejpam-3391	416	7	i	i	PRON
ejpam-3391	416	8	(	(	PUNCT
ejpam-3391	416	9	a	a	DET
ejpam-3391	416	10	(	(	PUNCT
ejpam-3391	416	11	1	1	NUM
ejpam-3391	416	12	)	)	PUNCT
ejpam-3391	416	13	n+1a	n+1a	NOUN
ejpam-3391	416	14	(	(	PUNCT
ejpam-3391	416	15	2	2	NUM
ejpam-3391	416	16	)	)	PUNCT
ejpam-3391	416	17	n+1	n+1	PROPN
ejpam-3391	417	1	+	+	NUM
ejpam-3391	417	2	a	a	DET
ejpam-3391	417	3	(	(	PUNCT
ejpam-3391	417	4	2	2	NUM
ejpam-3391	417	5	)	)	PUNCT
ejpam-3391	417	6	κ(1	κ(1	PROPN
ejpam-3391	417	7	)	)	PUNCT
ejpam-3391	417	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	417	9	for	for	ADP
ejpam-3391	417	10	1	1	NUM
ejpam-3391	417	11	≤	≤	NUM
ejpam-3391	417	12	i	i	PRON
ejpam-3391	417	13	≤	≤	PROPN
ejpam-3391	417	14	κ(1)∣∣∣∣∣∣	κ(1)∣∣∣∣∣∣	PROPN
ejpam-3391	417	15	a	a	DET
ejpam-3391	417	16	(	(	PUNCT
ejpam-3391	417	17	1	1	X
ejpam-3391	417	18	)	)	PUNCT
ejpam-3391	417	19	n+1a	n+1a	NOUN
ejpam-3391	417	20	(	(	PUNCT
ejpam-3391	417	21	2	2	NUM
ejpam-3391	417	22	)	)	PUNCT
ejpam-3391	417	23	i	i	PRON
ejpam-3391	417	24	−	−	VERB
ejpam-3391	418	1	a	a	DET
ejpam-3391	418	2	(	(	PUNCT
ejpam-3391	418	3	1	1	NUM
ejpam-3391	418	4	)	)	PUNCT
ejpam-3391	418	5	i	i	PRON
ejpam-3391	418	6	a	a	DET
ejpam-3391	418	7	(	(	PUNCT
ejpam-3391	418	8	2	2	NUM
ejpam-3391	418	9	)	)	PUNCT
ejpam-3391	418	10	κ(1	κ(1	PROPN
ejpam-3391	418	11	)	)	PUNCT
ejpam-3391	418	12	(	(	PUNCT
ejpam-3391	418	13	a	a	DET
ejpam-3391	418	14	(	(	PUNCT
ejpam-3391	418	15	2	2	NUM
ejpam-3391	418	16	)	)	PUNCT
ejpam-3391	418	17	κ(1	κ(1	PROPN
ejpam-3391	418	18	)	)	PUNCT
ejpam-3391	419	1	+	+	CCONJ
ejpam-3391	419	2	a	a	DET
ejpam-3391	419	3	(	(	PUNCT
ejpam-3391	419	4	1	1	X
ejpam-3391	419	5	)	)	PUNCT
ejpam-3391	419	6	n+1a	n+1a	NOUN
ejpam-3391	419	7	(	(	PUNCT
ejpam-3391	419	8	2	2	NUM
ejpam-3391	419	9	)	)	PUNCT
ejpam-3391	419	10	n+1)a	n+1)a	NOUN
ejpam-3391	419	11	(	(	PUNCT
ejpam-3391	419	12	1	1	NUM
ejpam-3391	419	13	)	)	PUNCT
ejpam-3391	419	14	n+1	n+1	PROPN
ejpam-3391	419	15	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3391	419	16	for	for	ADP
ejpam-3391	419	17	κ(1	κ(1	PROPN
ejpam-3391	419	18	)	)	PUNCT
ejpam-3391	419	19	≤	≤	PUNCT
ejpam-3391	420	1	i	i	PRON
ejpam-3391	420	2	≤	≤	ADJ
ejpam-3391	420	3	n	n	CCONJ
ejpam-3391	420	4	(	(	PUNCT
ejpam-3391	420	5	13	13	NUM
ejpam-3391	420	6	)	)	PUNCT
ejpam-3391	420	7	a.	a.	NOUN
ejpam-3391	420	8	chandoul	chandoul	PROPN
ejpam-3391	420	9	,	,	PUNCT
ejpam-3391	420	10	f.	f.	PROPN
ejpam-3391	420	11	aljuaydi	aljuaydi	PROPN
ejpam-3391	420	12	/	/	SYM
ejpam-3391	420	13	eur	eur	NOUN
ejpam-3391	420	14	.	.	PUNCT
ejpam-3391	421	1	j.	j.	PROPN
ejpam-3391	421	2	pure	pure	PROPN
ejpam-3391	421	3	appl	appl	PROPN
ejpam-3391	421	4	.	.	PROPN
ejpam-3391	421	5	math	math	PROPN
ejpam-3391	421	6	,	,	PUNCT
ejpam-3391	421	7	12	12	NUM
ejpam-3391	421	8	(	(	PUNCT
ejpam-3391	421	9	2	2	NUM
ejpam-3391	421	10	)	)	PUNCT
ejpam-3391	421	11	(	(	PUNCT
ejpam-3391	421	12	2019	2019	NUM
ejpam-3391	421	13	)	)	PUNCT
ejpam-3391	421	14	,	,	PUNCT
ejpam-3391	421	15	418	418	NUM
ejpam-3391	421	16	-	-	SYM
ejpam-3391	421	17	431	431	NUM
ejpam-3391	421	18	428	428	NUM
ejpam-3391	421	19	then	then	ADV
ejpam-3391	421	20	similarly	similarly	ADV
ejpam-3391	421	21	,	,	PUNCT
ejpam-3391	421	22	we	we	PRON
ejpam-3391	421	23	have	have	AUX
ejpam-3391	421	24	∣∣∣b(1	∣∣∣b(1	NOUN
ejpam-3391	421	25	)	)	PUNCT
ejpam-3391	421	26	0	0	NUM
ejpam-3391	421	27	∣∣∣	∣∣∣	ADJ
ejpam-3391	421	28	∣∣∣∣∣b(2	∣∣∣∣∣b(2	PROPN
ejpam-3391	421	29	)	)	PUNCT
ejpam-3391	422	1	i	i	PROPN
ejpam-3391	422	2	b	b	X
ejpam-3391	422	3	(	(	PUNCT
ejpam-3391	422	4	2	2	NUM
ejpam-3391	422	5	)	)	PUNCT
ejpam-3391	422	6	0	0	NUM
ejpam-3391	423	1	−	−	PROPN
ejpam-3391	423	2	b	b	X
ejpam-3391	423	3	(	(	PUNCT
ejpam-3391	423	4	1	1	NUM
ejpam-3391	423	5	)	)	PUNCT
ejpam-3391	423	6	i	i	PRON
ejpam-3391	423	7	b	b	X
ejpam-3391	423	8	(	(	PUNCT
ejpam-3391	423	9	1	1	NUM
ejpam-3391	423	10	)	)	PUNCT
ejpam-3391	423	11	0	0	NUM
ejpam-3391	424	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	424	2	≤	≤	ADJ
ejpam-3391	424	3	e−1	e−1	PROPN
ejpam-3391	424	4	(	(	PUNCT
ejpam-3391	424	5	14	14	NUM
ejpam-3391	424	6	)	)	PUNCT
ejpam-3391	424	7	now	now	ADV
ejpam-3391	424	8	we	we	PRON
ejpam-3391	424	9	suppose	suppose	VERB
ejpam-3391	424	10	the	the	DET
ejpam-3391	424	11	assertion	assertion	NOUN
ejpam-3391	424	12	of	of	ADP
ejpam-3391	424	13	(	(	PUNCT
ejpam-3391	424	14	lemma	lemma	PROPN
ejpam-3391	424	15	2	2	NUM
ejpam-3391	424	16	)	)	PUNCT
ejpam-3391	424	17	holds	hold	VERB
ejpam-3391	424	18	by	by	ADP
ejpam-3391	424	19	s−	s−	PROPN
ejpam-3391	424	20	1	1	NUM
ejpam-3391	424	21	.	.	PUNCT
ejpam-3391	425	1	for	for	ADP
ejpam-3391	425	2	s	s	PRON
ejpam-3391	425	3	≥	≥	NUM
ejpam-3391	425	4	2	2	NUM
ejpam-3391	425	5	∣∣∣∣∣b(s+1	∣∣∣∣∣b(s+1	NOUN
ejpam-3391	425	6	)	)	PUNCT
ejpam-3391	425	7	i	i	PRON
ejpam-3391	426	1	b	b	PROPN
ejpam-3391	426	2	(	(	PUNCT
ejpam-3391	426	3	s+1	s+1	NOUN
ejpam-3391	426	4	)	)	PUNCT
ejpam-3391	426	5	0	0	NUM
ejpam-3391	427	1	−	−	PROPN
ejpam-3391	427	2	b	b	PROPN
ejpam-3391	427	3	(	(	PUNCT
ejpam-3391	427	4	s	s	X
ejpam-3391	427	5	)	)	PUNCT
ejpam-3391	427	6	i	i	PROPN
ejpam-3391	427	7	b	b	X
ejpam-3391	427	8	(	(	PUNCT
ejpam-3391	427	9	s	s	NOUN
ejpam-3391	427	10	)	)	PUNCT
ejpam-3391	427	11	0	0	NUM
ejpam-3391	428	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	428	2	=	=	PUNCT
ejpam-3391	429	1	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	429	2	a	a	DET
ejpam-3391	429	3	(	(	PUNCT
ejpam-3391	429	4	s	s	NOUN
ejpam-3391	429	5	)	)	PUNCT
ejpam-3391	429	6	iκ(s+1	iκ(s+1	NOUN
ejpam-3391	429	7	)	)	PUNCT
ejpam-3391	430	1	+	+	CCONJ
ejpam-3391	431	1	n∑	n∑	NOUN
ejpam-3391	431	2	k	k	X
ejpam-3391	431	3	=	=	NOUN
ejpam-3391	431	4	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	431	5	a	a	DET
ejpam-3391	431	6	(	(	PUNCT
ejpam-3391	431	7	s+1	s+1	NOUN
ejpam-3391	431	8	)	)	PUNCT
ejpam-3391	431	9	k	k	NOUN
ejpam-3391	431	10	a	a	DET
ejpam-3391	431	11	(	(	PUNCT
ejpam-3391	431	12	s	s	X
ejpam-3391	431	13	)	)	PUNCT
ejpam-3391	431	14	ik	ik	PROPN
ejpam-3391	431	15	+	+	CCONJ
ejpam-3391	431	16	a	a	DET
ejpam-3391	431	17	(	(	PUNCT
ejpam-3391	431	18	s+1	s+1	NOUN
ejpam-3391	431	19	)	)	PUNCT
ejpam-3391	431	20	n+1	n+1	PROPN
ejpam-3391	431	21	b	b	PROPN
ejpam-3391	431	22	(	(	PUNCT
ejpam-3391	431	23	s	s	X
ejpam-3391	431	24	)	)	PUNCT
ejpam-3391	431	25	i	i	PRON
ejpam-3391	431	26	a	a	PRON
ejpam-3391	431	27	(	(	PUNCT
ejpam-3391	431	28	s	s	NOUN
ejpam-3391	431	29	)	)	PUNCT
ejpam-3391	431	30	0κ(s+1	0κ(s+1	NOUN
ejpam-3391	431	31	)	)	PUNCT
ejpam-3391	432	1	+	+	NUM
ejpam-3391	432	2	n∑	n∑	NOUN
ejpam-3391	432	3	k	k	X
ejpam-3391	432	4	=	=	NOUN
ejpam-3391	432	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	432	6	a	a	DET
ejpam-3391	432	7	(	(	PUNCT
ejpam-3391	432	8	s+1	s+1	NOUN
ejpam-3391	432	9	)	)	PUNCT
ejpam-3391	432	10	k	k	NOUN
ejpam-3391	432	11	a	a	DET
ejpam-3391	432	12	(	(	PUNCT
ejpam-3391	432	13	s	s	NOUN
ejpam-3391	432	14	)	)	PUNCT
ejpam-3391	432	15	0k	0k	NOUN
ejpam-3391	432	16	+	+	CCONJ
ejpam-3391	432	17	a	a	DET
ejpam-3391	432	18	(	(	PUNCT
ejpam-3391	432	19	s+1	s+1	NOUN
ejpam-3391	432	20	)	)	PUNCT
ejpam-3391	432	21	n+1	n+1	PROPN
ejpam-3391	432	22	b	b	X
ejpam-3391	432	23	(	(	PUNCT
ejpam-3391	432	24	s	s	NOUN
ejpam-3391	432	25	)	)	PUNCT
ejpam-3391	432	26	0	0	NUM
ejpam-3391	433	1	−	−	PROPN
ejpam-3391	433	2	b	b	X
ejpam-3391	433	3	(	(	PUNCT
ejpam-3391	433	4	s	s	X
ejpam-3391	433	5	)	)	PUNCT
ejpam-3391	433	6	i	i	PROPN
ejpam-3391	433	7	b	b	X
ejpam-3391	433	8	(	(	PUNCT
ejpam-3391	433	9	s	s	NOUN
ejpam-3391	433	10	)	)	PUNCT
ejpam-3391	433	11	0	0	NUM
ejpam-3391	433	12	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	433	13	=	=	SYM
ejpam-3391	433	14	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	433	15	a	a	DET
ejpam-3391	433	16	(	(	PUNCT
ejpam-3391	433	17	s	s	NOUN
ejpam-3391	433	18	)	)	PUNCT
ejpam-3391	433	19	iκ(s+1)b	iκ(s+1)b	NOUN
ejpam-3391	433	20	(	(	PUNCT
ejpam-3391	433	21	s	s	NOUN
ejpam-3391	433	22	)	)	PUNCT
ejpam-3391	433	23	0	0	NUM
ejpam-3391	433	24	−a	−a	NOUN
ejpam-3391	433	25	(	(	PUNCT
ejpam-3391	433	26	s	s	NOUN
ejpam-3391	433	27	)	)	PUNCT
ejpam-3391	433	28	0κ(s+1)b	0κ(s+1)b	NOUN
ejpam-3391	433	29	(	(	PUNCT
ejpam-3391	433	30	s	s	X
ejpam-3391	433	31	)	)	PUNCT
ejpam-3391	433	32	i	i	PROPN
ejpam-3391	433	33	+	+	PROPN
ejpam-3391	433	34	n∑	n∑	ADJ
ejpam-3391	433	35	k	k	X
ejpam-3391	433	36	=	=	NOUN
ejpam-3391	433	37	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	433	38	a	a	DET
ejpam-3391	433	39	(	(	PUNCT
ejpam-3391	433	40	s+1	s+1	NOUN
ejpam-3391	433	41	)	)	PUNCT
ejpam-3391	433	42	k	k	NOUN
ejpam-3391	433	43	(	(	PUNCT
ejpam-3391	433	44	a	a	DET
ejpam-3391	433	45	(	(	PUNCT
ejpam-3391	433	46	s	s	NOUN
ejpam-3391	433	47	)	)	PUNCT
ejpam-3391	433	48	ik	ik	PROPN
ejpam-3391	433	49	b	b	PROPN
ejpam-3391	433	50	(	(	PUNCT
ejpam-3391	433	51	s	s	NOUN
ejpam-3391	433	52	)	)	PUNCT
ejpam-3391	433	53	0	0	NUM
ejpam-3391	433	54	−a	−a	NOUN
ejpam-3391	433	55	(	(	PUNCT
ejpam-3391	433	56	s	s	NOUN
ejpam-3391	433	57	)	)	PUNCT
ejpam-3391	433	58	0	0	NUM
ejpam-3391	433	59	kb	kb	X
ejpam-3391	433	60	(	(	PUNCT
ejpam-3391	433	61	s	s	NOUN
ejpam-3391	433	62	)	)	PUNCT
ejpam-3391	433	63	i	i	NOUN
ejpam-3391	433	64	)	)	PUNCT
ejpam-3391	433	65	(	(	PUNCT
ejpam-3391	433	66	a	a	DET
ejpam-3391	433	67	(	(	PUNCT
ejpam-3391	433	68	s	s	NOUN
ejpam-3391	433	69	)	)	PUNCT
ejpam-3391	433	70	0κ(s+1	0κ(s+1	NOUN
ejpam-3391	433	71	)	)	PUNCT
ejpam-3391	434	1	+	+	NUM
ejpam-3391	434	2	n∑	n∑	NOUN
ejpam-3391	434	3	k	k	X
ejpam-3391	434	4	=	=	NOUN
ejpam-3391	434	5	κ(s+1)+1	κ(s+1)+1	X
ejpam-3391	434	6	a	a	DET
ejpam-3391	434	7	(	(	PUNCT
ejpam-3391	434	8	s+1	s+1	NOUN
ejpam-3391	434	9	)	)	PUNCT
ejpam-3391	434	10	k	k	NOUN
ejpam-3391	434	11	a	a	DET
ejpam-3391	434	12	(	(	PUNCT
ejpam-3391	434	13	s	s	NOUN
ejpam-3391	434	14	)	)	PUNCT
ejpam-3391	434	15	0k	0k	NOUN
ejpam-3391	434	16	+	+	CCONJ
ejpam-3391	434	17	a	a	DET
ejpam-3391	434	18	(	(	PUNCT
ejpam-3391	434	19	s+1	s+1	NOUN
ejpam-3391	434	20	)	)	PUNCT
ejpam-3391	434	21	n+1	n+1	PROPN
ejpam-3391	434	22	b	b	X
ejpam-3391	434	23	(	(	PUNCT
ejpam-3391	434	24	s	s	NOUN
ejpam-3391	434	25	)	)	PUNCT
ejpam-3391	434	26	0	0	NUM
ejpam-3391	434	27	)	)	PUNCT
ejpam-3391	434	28	b	b	X
ejpam-3391	434	29	(	(	PUNCT
ejpam-3391	434	30	s	s	NOUN
ejpam-3391	434	31	)	)	PUNCT
ejpam-3391	434	32	0	0	NUM
ejpam-3391	435	1	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-3391	435	2	using	use	VERB
ejpam-3391	435	3	the	the	DET
ejpam-3391	435	4	fact	fact	NOUN
ejpam-3391	435	5	that	that	SCONJ
ejpam-3391	435	6	deg	deg	PROPN
ejpam-3391	435	7	a	a	DET
ejpam-3391	435	8	(	(	PUNCT
ejpam-3391	435	9	s+1	s+1	NOUN
ejpam-3391	435	10	)	)	PUNCT
ejpam-3391	435	11	k	k	NOUN
ejpam-3391	435	12	a	a	DET
ejpam-3391	435	13	(	(	PUNCT
ejpam-3391	435	14	s	s	NOUN
ejpam-3391	435	15	)	)	PUNCT
ejpam-3391	435	16	0k	0k	NOUN
ejpam-3391	435	17	<	<	X
ejpam-3391	435	18	a	a	PRON
ejpam-3391	435	19	(	(	PUNCT
ejpam-3391	435	20	s	s	NOUN
ejpam-3391	435	21	)	)	PUNCT
ejpam-3391	435	22	n+1b	n+1b	PROPN
ejpam-3391	435	23	(	(	PUNCT
ejpam-3391	435	24	s	s	NOUN
ejpam-3391	435	25	)	)	PUNCT
ejpam-3391	435	26	0	0	PUNCT
ejpam-3391	436	1	∣∣∣∣∣b(s+1	∣∣∣∣∣b(s+1	NOUN
ejpam-3391	436	2	)	)	PUNCT
ejpam-3391	437	1	i	i	PRON
ejpam-3391	437	2	b	b	PROPN
ejpam-3391	437	3	(	(	PUNCT
ejpam-3391	437	4	s+1	s+1	NOUN
ejpam-3391	437	5	)	)	PUNCT
ejpam-3391	437	6	0	0	NUM
ejpam-3391	438	1	−	−	PROPN
ejpam-3391	438	2	b	b	PROPN
ejpam-3391	438	3	(	(	PUNCT
ejpam-3391	438	4	s	s	X
ejpam-3391	438	5	)	)	PUNCT
ejpam-3391	438	6	i	i	PROPN
ejpam-3391	438	7	b	b	X
ejpam-3391	438	8	(	(	PUNCT
ejpam-3391	438	9	s	s	NOUN
ejpam-3391	438	10	)	)	PUNCT
ejpam-3391	438	11	0	0	NUM
ejpam-3391	439	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	439	2	=	=	SYM
ejpam-3391	439	3	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3391	439	4	n∑	n∑	PROPN
ejpam-3391	439	5	k	k	PROPN
ejpam-3391	439	6	=	=	PROPN
ejpam-3391	439	7	κ(s+1	κ(s+1	NOUN
ejpam-3391	439	8	)	)	PUNCT
ejpam-3391	440	1	a	a	DET
ejpam-3391	440	2	(	(	PUNCT
ejpam-3391	440	3	s+1	s+1	NOUN
ejpam-3391	440	4	)	)	PUNCT
ejpam-3391	440	5	k	k	NOUN
ejpam-3391	440	6	(	(	PUNCT
ejpam-3391	440	7	a	a	DET
ejpam-3391	440	8	(	(	PUNCT
ejpam-3391	440	9	s	s	NOUN
ejpam-3391	440	10	)	)	PUNCT
ejpam-3391	440	11	ik	ik	PROPN
ejpam-3391	440	12	b	b	PROPN
ejpam-3391	440	13	(	(	PUNCT
ejpam-3391	440	14	s	s	NOUN
ejpam-3391	440	15	)	)	PUNCT
ejpam-3391	440	16	0	0	NUM
ejpam-3391	441	1	−a	−a	NOUN
ejpam-3391	441	2	(	(	PUNCT
ejpam-3391	441	3	s	s	NOUN
ejpam-3391	441	4	)	)	PUNCT
ejpam-3391	441	5	0	0	NUM
ejpam-3391	441	6	kb	kb	X
ejpam-3391	441	7	(	(	PUNCT
ejpam-3391	441	8	s	s	NOUN
ejpam-3391	441	9	)	)	PUNCT
ejpam-3391	441	10	i	i	NOUN
ejpam-3391	441	11	)	)	PUNCT
ejpam-3391	442	1	∣∣∣∣∣∣∣∣∣a(s+1	∣∣∣∣∣∣∣∣∣a(s+1	PROPN
ejpam-3391	442	2	)	)	PUNCT
ejpam-3391	442	3	n+1	n+1	PROPN
ejpam-3391	442	4	(	(	PUNCT
ejpam-3391	442	5	b	b	X
ejpam-3391	442	6	(	(	PUNCT
ejpam-3391	442	7	s	s	NOUN
ejpam-3391	442	8	)	)	PUNCT
ejpam-3391	442	9	0	0	NUM
ejpam-3391	442	10	)	)	PUNCT
ejpam-3391	442	11	2	2	NUM
ejpam-3391	442	12	∣∣∣	∣∣∣	NOUN
ejpam-3391	442	13	=	=	SYM
ejpam-3391	442	14	1∣∣∣a(s+1	1∣∣∣a(s+1	NUM
ejpam-3391	442	15	)	)	PUNCT
ejpam-3391	442	16	n+1	n+1	PROPN
ejpam-3391	442	17	b	b	PROPN
ejpam-3391	442	18	(	(	PUNCT
ejpam-3391	442	19	s	s	NOUN
ejpam-3391	442	20	)	)	PUNCT
ejpam-3391	442	21	0	0	NUM
ejpam-3391	442	22	∣∣∣	∣∣∣	NOUN
ejpam-3391	442	23	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	442	24	n∑	n∑	PROPN
ejpam-3391	442	25	k	k	PROPN
ejpam-3391	442	26	=	=	PROPN
ejpam-3391	442	27	κ(s+1	κ(s+1	NOUN
ejpam-3391	442	28	)	)	PUNCT
ejpam-3391	442	29	a	a	DET
ejpam-3391	442	30	(	(	PUNCT
ejpam-3391	442	31	s+1	s+1	NOUN
ejpam-3391	442	32	)	)	PUNCT
ejpam-3391	442	33	k	k	NOUN
ejpam-3391	442	34	a	a	DET
ejpam-3391	442	35	(	(	PUNCT
ejpam-3391	442	36	s	s	NOUN
ejpam-3391	442	37	)	)	PUNCT
ejpam-3391	442	38	0k	0k	NOUN
ejpam-3391	442	39	(	(	PUNCT
ejpam-3391	442	40	a	a	DET
ejpam-3391	442	41	(	(	PUNCT
ejpam-3391	442	42	s	s	NOUN
ejpam-3391	442	43	)	)	PUNCT
ejpam-3391	442	44	ik	ik	PROPN
ejpam-3391	442	45	a	a	PROPN
ejpam-3391	442	46	(	(	PUNCT
ejpam-3391	442	47	s	s	NOUN
ejpam-3391	442	48	)	)	PUNCT
ejpam-3391	442	49	0k	0k	NOUN
ejpam-3391	442	50	−	−	PROPN
ejpam-3391	442	51	b	b	PROPN
ejpam-3391	442	52	(	(	PUNCT
ejpam-3391	442	53	s	s	X
ejpam-3391	442	54	)	)	PUNCT
ejpam-3391	442	55	i	i	PROPN
ejpam-3391	442	56	b	b	X
ejpam-3391	442	57	(	(	PUNCT
ejpam-3391	442	58	s	s	NOUN
ejpam-3391	442	59	)	)	PUNCT
ejpam-3391	442	60	0	0	NUM
ejpam-3391	442	61	)	)	PUNCT
ejpam-3391	442	62	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	442	63	by	by	ADP
ejpam-3391	442	64	(	(	PUNCT
ejpam-3391	442	65	6	6	NUM
ejpam-3391	442	66	)	)	PUNCT
ejpam-3391	442	67	and	and	CCONJ
ejpam-3391	442	68	(	(	PUNCT
ejpam-3391	442	69	7	7	NUM
ejpam-3391	442	70	)	)	PUNCT
ejpam-3391	442	71	,	,	PUNCT
ejpam-3391	442	72	we	we	PRON
ejpam-3391	442	73	replace	replace	VERB
ejpam-3391	442	74	a	a	DET
ejpam-3391	442	75	(	(	PUNCT
ejpam-3391	442	76	s	s	X
ejpam-3391	442	77	)	)	PUNCT
ejpam-3391	442	78	ik	ik	PROPN
ejpam-3391	442	79	by	by	ADP
ejpam-3391	442	80	b	b	PROPN
ejpam-3391	442	81	(	(	PUNCT
ejpam-3391	442	82	lk	lk	PROPN
ejpam-3391	442	83	)	)	PUNCT
ejpam-3391	442	84	i	i	PRON
ejpam-3391	442	85	,	,	PUNCT
ejpam-3391	442	86	for	for	ADP
ejpam-3391	442	87	some	some	DET
ejpam-3391	442	88	lk	lk	NOUN
ejpam-3391	442	89	,	,	PUNCT
ejpam-3391	442	90	lk	lk	X
ejpam-3391	442	91	<	<	X
ejpam-3391	442	92	s.	s.	PROPN
ejpam-3391	442	93	∣∣∣b(s	∣∣∣b(s	PROPN
ejpam-3391	442	94	)	)	PUNCT
ejpam-3391	442	95	0	0	PUNCT
ejpam-3391	442	96	∣∣∣	∣∣∣	PROPN
ejpam-3391	442	97	∣∣∣∣∣b(s+1	∣∣∣∣∣b(s+1	NOUN
ejpam-3391	442	98	)	)	PUNCT
ejpam-3391	443	1	i	i	PROPN
ejpam-3391	443	2	b	b	PROPN
ejpam-3391	443	3	(	(	PUNCT
ejpam-3391	443	4	s+1	s+1	NOUN
ejpam-3391	443	5	)	)	PUNCT
ejpam-3391	443	6	0	0	NUM
ejpam-3391	444	1	−	−	PROPN
ejpam-3391	444	2	b	b	PROPN
ejpam-3391	444	3	(	(	PUNCT
ejpam-3391	444	4	s	s	X
ejpam-3391	444	5	)	)	PUNCT
ejpam-3391	444	6	i	i	PROPN
ejpam-3391	444	7	b	b	X
ejpam-3391	444	8	(	(	PUNCT
ejpam-3391	444	9	s	s	NOUN
ejpam-3391	444	10	)	)	PUNCT
ejpam-3391	444	11	0	0	NUM
ejpam-3391	445	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	445	2	=	=	SYM
ejpam-3391	446	1	1∣∣∣a(s+1	1∣∣∣a(s+1	NUM
ejpam-3391	446	2	)	)	PUNCT
ejpam-3391	446	3	n+1	n+1	ADV
ejpam-3391	446	4	∣∣∣	∣∣∣	NOUN
ejpam-3391	446	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	446	6	n∑	n∑	PROPN
ejpam-3391	446	7	k	k	PROPN
ejpam-3391	446	8	=	=	PROPN
ejpam-3391	446	9	κ(s+1	κ(s+1	NOUN
ejpam-3391	446	10	)	)	PUNCT
ejpam-3391	446	11	a	a	PRON
ejpam-3391	446	12	(	(	PUNCT
ejpam-3391	446	13	s+1	s+1	NOUN
ejpam-3391	446	14	)	)	PUNCT
ejpam-3391	446	15	k	k	PROPN
ejpam-3391	446	16	b	b	PROPN
ejpam-3391	446	17	(	(	PUNCT
ejpam-3391	446	18	lk	lk	PROPN
ejpam-3391	446	19	)	)	PUNCT
ejpam-3391	446	20	0	0	NUM
ejpam-3391	447	1	(	(	PUNCT
ejpam-3391	447	2	b	b	X
ejpam-3391	447	3	(	(	PUNCT
ejpam-3391	447	4	lk	lk	PROPN
ejpam-3391	447	5	)	)	PUNCT
ejpam-3391	447	6	i	i	PROPN
ejpam-3391	447	7	b	b	X
ejpam-3391	447	8	(	(	PUNCT
ejpam-3391	447	9	lk	lk	PROPN
ejpam-3391	447	10	)	)	PUNCT
ejpam-3391	447	11	0	0	NUM
ejpam-3391	448	1	−	−	PROPN
ejpam-3391	448	2	b	b	PROPN
ejpam-3391	448	3	(	(	PUNCT
ejpam-3391	448	4	s	s	X
ejpam-3391	448	5	)	)	PUNCT
ejpam-3391	448	6	i	i	PROPN
ejpam-3391	448	7	b	b	X
ejpam-3391	448	8	(	(	PUNCT
ejpam-3391	448	9	s	s	NOUN
ejpam-3391	448	10	)	)	PUNCT
ejpam-3391	448	11	0	0	NUM
ejpam-3391	448	12	)	)	PUNCT
ejpam-3391	448	13	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	448	14	≤	≤	NOUN
ejpam-3391	448	15	1∣∣∣a(s+1	1∣∣∣a(s+1	NUM
ejpam-3391	448	16	)	)	PUNCT
ejpam-3391	448	17	n+1	n+1	PROPN
ejpam-3391	448	18	∣∣∣	∣∣∣	NOUN
ejpam-3391	448	19	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	448	20	n∑	n∑	PROPN
ejpam-3391	448	21	k	k	PROPN
ejpam-3391	448	22	=	=	PROPN
ejpam-3391	448	23	κ(s+1	κ(s+1	NOUN
ejpam-3391	448	24	)	)	PUNCT
ejpam-3391	448	25	a	a	PRON
ejpam-3391	448	26	(	(	PUNCT
ejpam-3391	448	27	s+1	s+1	NOUN
ejpam-3391	448	28	)	)	PUNCT
ejpam-3391	448	29	k	k	PROPN
ejpam-3391	448	30	b	b	PROPN
ejpam-3391	448	31	(	(	PUNCT
ejpam-3391	448	32	lk	lk	PROPN
ejpam-3391	448	33	)	)	PUNCT
ejpam-3391	448	34	0	0	NUM
ejpam-3391	449	1	s−1∑	s−1∑	NUM
ejpam-3391	449	2	k=1	k=1	PUNCT
ejpam-3391	450	1	(	(	PUNCT
ejpam-3391	450	2	b	b	X
ejpam-3391	450	3	(	(	PUNCT
ejpam-3391	450	4	l	l	NOUN
ejpam-3391	450	5	)	)	PUNCT
ejpam-3391	450	6	i	i	PROPN
ejpam-3391	450	7	b	b	PROPN
ejpam-3391	450	8	(	(	PUNCT
ejpam-3391	450	9	l	l	NOUN
ejpam-3391	450	10	)	)	PUNCT
ejpam-3391	450	11	0	0	NUM
ejpam-3391	451	1	−	−	PROPN
ejpam-3391	451	2	b	b	PROPN
ejpam-3391	451	3	(	(	PUNCT
ejpam-3391	451	4	l+1	l+1	PROPN
ejpam-3391	451	5	)	)	PUNCT
ejpam-3391	451	6	i	i	PROPN
ejpam-3391	451	7	b	b	PROPN
ejpam-3391	451	8	(	(	PUNCT
ejpam-3391	451	9	l+1	l+1	X
ejpam-3391	451	10	)	)	PUNCT
ejpam-3391	451	11	0	0	NUM
ejpam-3391	451	12	)	)	PUNCT
ejpam-3391	451	13	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3391	451	14	≤	≤	NOUN
ejpam-3391	451	15	1∣∣∣a(s+1	1∣∣∣a(s+1	NUM
ejpam-3391	451	16	)	)	PUNCT
ejpam-3391	451	17	n+1	n+1	NUM
ejpam-3391	451	18	∣∣∣	∣∣∣	NOUN
ejpam-3391	451	19	max	max	PROPN
ejpam-3391	451	20	1≤k≤s−1	1≤k≤s−1	NUM
ejpam-3391	451	21	max	max	PROPN
ejpam-3391	451	22	k≤l≤s−1	k≤l≤s−1	PROPN
ejpam-3391	451	23	∣∣∣b(k	∣∣∣b(k	NOUN
ejpam-3391	451	24	)	)	PUNCT
ejpam-3391	451	25	0	0	NUM
ejpam-3391	451	26	∣∣∣	∣∣∣	PROPN
ejpam-3391	451	27	∣∣∣∣∣b(l	∣∣∣∣∣b(l	PROPN
ejpam-3391	451	28	)	)	PUNCT
ejpam-3391	452	1	i	i	PROPN
ejpam-3391	452	2	b	b	X
ejpam-3391	452	3	(	(	PUNCT
ejpam-3391	452	4	l	l	NOUN
ejpam-3391	452	5	)	)	PUNCT
ejpam-3391	452	6	0	0	NUM
ejpam-3391	453	1	−	−	PROPN
ejpam-3391	453	2	b	b	PROPN
ejpam-3391	453	3	(	(	PUNCT
ejpam-3391	453	4	l+1	l+1	PROPN
ejpam-3391	453	5	)	)	PUNCT
ejpam-3391	453	6	i	i	PROPN
ejpam-3391	453	7	b	b	PROPN
ejpam-3391	453	8	(	(	PUNCT
ejpam-3391	453	9	l+1	l+1	X
ejpam-3391	453	10	)	)	PUNCT
ejpam-3391	453	11	0	0	PUNCT
ejpam-3391	454	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	454	2	≤	≤	PROPN
ejpam-3391	455	1	e−2	e−2	PROPN
ejpam-3391	455	2	≤	≤	ADV
ejpam-3391	455	3	e−1	e−1	PROPN
ejpam-3391	455	4	a.	a.	NOUN
ejpam-3391	455	5	chandoul	chandoul	PROPN
ejpam-3391	455	6	,	,	PUNCT
ejpam-3391	455	7	f.	f.	PROPN
ejpam-3391	455	8	aljuaydi	aljuaydi	PROPN
ejpam-3391	455	9	/	/	SYM
ejpam-3391	455	10	eur	eur	NOUN
ejpam-3391	455	11	.	.	PUNCT
ejpam-3391	456	1	j.	j.	PROPN
ejpam-3391	456	2	pure	pure	PROPN
ejpam-3391	456	3	appl	appl	PROPN
ejpam-3391	456	4	.	.	PROPN
ejpam-3391	456	5	math	math	PROPN
ejpam-3391	456	6	,	,	PUNCT
ejpam-3391	456	7	12	12	NUM
ejpam-3391	456	8	(	(	PUNCT
ejpam-3391	456	9	2	2	NUM
ejpam-3391	456	10	)	)	PUNCT
ejpam-3391	456	11	(	(	PUNCT
ejpam-3391	456	12	2019	2019	NUM
ejpam-3391	456	13	)	)	PUNCT
ejpam-3391	456	14	,	,	PUNCT
ejpam-3391	456	15	418	418	NUM
ejpam-3391	456	16	-	-	SYM
ejpam-3391	456	17	431	431	NUM
ejpam-3391	456	18	429	429	NUM
ejpam-3391	456	19	then	then	ADV
ejpam-3391	456	20	,	,	PUNCT
ejpam-3391	456	21	from	from	ADP
ejpam-3391	456	22	the	the	DET
ejpam-3391	456	23	assumption	assumption	NOUN
ejpam-3391	456	24	of	of	ADP
ejpam-3391	456	25	the	the	DET
ejpam-3391	456	26	induction	induction	NOUN
ejpam-3391	456	27	,	,	PUNCT
ejpam-3391	456	28	∣∣∣b(s	∣∣∣b(	NOUN
ejpam-3391	456	29	)	)	PUNCT
ejpam-3391	456	30	0	0	PUNCT
ejpam-3391	457	1	∣∣∣	∣∣∣	PROPN
ejpam-3391	457	2	∣∣∣∣∣b(s+1	∣∣∣∣∣b(s+1	NOUN
ejpam-3391	457	3	)	)	PUNCT
ejpam-3391	457	4	i	i	PROPN
ejpam-3391	457	5	b	b	PROPN
ejpam-3391	457	6	(	(	PUNCT
ejpam-3391	457	7	s+1	s+1	NOUN
ejpam-3391	457	8	)	)	PUNCT
ejpam-3391	457	9	0	0	NUM
ejpam-3391	458	1	−	−	PROPN
ejpam-3391	458	2	b	b	PROPN
ejpam-3391	458	3	(	(	PUNCT
ejpam-3391	458	4	s	s	X
ejpam-3391	458	5	)	)	PUNCT
ejpam-3391	458	6	i	i	PROPN
ejpam-3391	458	7	b	b	X
ejpam-3391	458	8	(	(	PUNCT
ejpam-3391	458	9	s	s	NOUN
ejpam-3391	458	10	)	)	PUNCT
ejpam-3391	458	11	0	0	NUM
ejpam-3391	459	1	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-3391	459	2	≤	≤	PROPN
ejpam-3391	459	3	e−1	e−1	NOUN
ejpam-3391	459	4	completing	complete	VERB
ejpam-3391	459	5	the	the	DET
ejpam-3391	459	6	proof	proof	NOUN
ejpam-3391	459	7	.	.	PUNCT
ejpam-3391	460	1	�	�	PROPN
ejpam-3391	460	2	proof	proof	NOUN
ejpam-3391	460	3	.	.	PUNCT
ejpam-3391	461	1	(	(	PUNCT
ejpam-3391	461	2	of	of	ADP
ejpam-3391	461	3	theorem	theorem	NOUN
ejpam-3391	461	4	2	2	NUM
ejpam-3391	461	5	)	)	PUNCT
ejpam-3391	461	6	.	.	PUNCT
ejpam-3391	462	1	we	we	PRON
ejpam-3391	462	2	see∣∣∣∣∣ϕi	see∣∣∣∣∣ϕi	VERB
ejpam-3391	462	3	−	−	PROPN
ejpam-3391	462	4	b	b	PROPN
ejpam-3391	462	5	(	(	PUNCT
ejpam-3391	462	6	s	s	X
ejpam-3391	462	7	)	)	PUNCT
ejpam-3391	462	8	i	i	PROPN
ejpam-3391	462	9	b	b	X
ejpam-3391	462	10	(	(	PUNCT
ejpam-3391	462	11	s	s	NOUN
ejpam-3391	462	12	)	)	PUNCT
ejpam-3391	462	13	0	0	NUM
ejpam-3391	463	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	463	2	=	=	SYM
ejpam-3391	463	3	∣∣∣∣∣a(s	∣∣∣∣∣a(s	PROPN
ejpam-3391	463	4	)	)	PUNCT
ejpam-3391	463	5	i1	i1	PROPN
ejpam-3391	463	6	ϕ	ϕ	PROPN
ejpam-3391	463	7	(	(	PUNCT
ejpam-3391	463	8	s	s	NOUN
ejpam-3391	463	9	)	)	PUNCT
ejpam-3391	463	10	1	1	NUM
ejpam-3391	463	11	+	+	CCONJ
ejpam-3391	463	12	.	.	PUNCT
ejpam-3391	463	13	.	.	PUNCT
ejpam-3391	464	1	.+a	.+a	PUNCT
ejpam-3391	464	2	(	(	PUNCT
ejpam-3391	464	3	s	s	X
ejpam-3391	464	4	)	)	PUNCT
ejpam-3391	464	5	in	in	ADP
ejpam-3391	464	6	ϕ	ϕ	PROPN
ejpam-3391	464	7	(	(	PUNCT
ejpam-3391	464	8	s	s	NOUN
ejpam-3391	464	9	)	)	PUNCT
ejpam-3391	464	10	n	n	PRON
ejpam-3391	464	11	+	+	ADP
ejpam-3391	464	12	b	b	PROPN
ejpam-3391	464	13	(	(	PUNCT
ejpam-3391	464	14	s	s	X
ejpam-3391	464	15	)	)	PUNCT
ejpam-3391	464	16	i	i	PRON
ejpam-3391	465	1	a	a	PRON
ejpam-3391	465	2	(	(	PUNCT
ejpam-3391	465	3	s	s	NOUN
ejpam-3391	465	4	)	)	PUNCT
ejpam-3391	465	5	01	01	NUM
ejpam-3391	465	6	ϕ	ϕ	X
ejpam-3391	465	7	(	(	PUNCT
ejpam-3391	465	8	s	s	NOUN
ejpam-3391	465	9	)	)	PUNCT
ejpam-3391	465	10	1	1	NUM
ejpam-3391	465	11	+	+	CCONJ
ejpam-3391	465	12	.	.	PUNCT
ejpam-3391	465	13	.	.	PUNCT
ejpam-3391	466	1	.+a	.+a	PUNCT
ejpam-3391	466	2	(	(	PUNCT
ejpam-3391	466	3	s	s	NOUN
ejpam-3391	466	4	)	)	PUNCT
ejpam-3391	466	5	0nϕ	0nϕ	NOUN
ejpam-3391	466	6	(	(	PUNCT
ejpam-3391	466	7	s	s	NOUN
ejpam-3391	466	8	)	)	PUNCT
ejpam-3391	466	9	n	n	PRON
ejpam-3391	466	10	+	+	ADP
ejpam-3391	466	11	b	b	PROPN
ejpam-3391	466	12	(	(	PUNCT
ejpam-3391	466	13	s	s	NOUN
ejpam-3391	466	14	)	)	PUNCT
ejpam-3391	466	15	0	0	NUM
ejpam-3391	467	1	−	−	PROPN
ejpam-3391	467	2	b	b	X
ejpam-3391	467	3	(	(	PUNCT
ejpam-3391	467	4	s	s	X
ejpam-3391	467	5	)	)	PUNCT
ejpam-3391	467	6	i	i	PROPN
ejpam-3391	467	7	b	b	X
ejpam-3391	467	8	(	(	PUNCT
ejpam-3391	467	9	s	s	NOUN
ejpam-3391	467	10	)	)	PUNCT
ejpam-3391	467	11	0	0	NUM
ejpam-3391	468	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	468	2	=	=	PUNCT
ejpam-3391	469	1	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	469	2	n∑	n∑	INTJ
ejpam-3391	470	1	k=1	k=1	X
ejpam-3391	470	2	(	(	PUNCT
ejpam-3391	470	3	a	a	DET
ejpam-3391	470	4	(	(	PUNCT
ejpam-3391	470	5	s	s	NOUN
ejpam-3391	470	6	)	)	PUNCT
ejpam-3391	470	7	ik	ik	PROPN
ejpam-3391	470	8	b	b	PROPN
ejpam-3391	470	9	(	(	PUNCT
ejpam-3391	470	10	s	s	NOUN
ejpam-3391	470	11	)	)	PUNCT
ejpam-3391	470	12	0	0	NUM
ejpam-3391	471	1	−a	−a	NOUN
ejpam-3391	471	2	(	(	PUNCT
ejpam-3391	471	3	s	s	NOUN
ejpam-3391	471	4	)	)	PUNCT
ejpam-3391	471	5	0	0	NUM
ejpam-3391	471	6	kb	kb	X
ejpam-3391	471	7	(	(	PUNCT
ejpam-3391	471	8	s	s	NOUN
ejpam-3391	471	9	)	)	PUNCT
ejpam-3391	471	10	i	i	NOUN
ejpam-3391	471	11	)	)	PUNCT
ejpam-3391	471	12	ϕ	ϕ	PROPN
ejpam-3391	471	13	(	(	PUNCT
ejpam-3391	471	14	s	s	NOUN
ejpam-3391	471	15	)	)	PUNCT
ejpam-3391	471	16	k	k	NOUN
ejpam-3391	471	17	(	(	PUNCT
ejpam-3391	471	18	a	a	DET
ejpam-3391	471	19	(	(	PUNCT
ejpam-3391	471	20	s	s	NOUN
ejpam-3391	471	21	)	)	PUNCT
ejpam-3391	471	22	01	01	NUM
ejpam-3391	471	23	ϕ	ϕ	X
ejpam-3391	471	24	(	(	PUNCT
ejpam-3391	471	25	s	s	NOUN
ejpam-3391	471	26	)	)	PUNCT
ejpam-3391	471	27	1	1	NUM
ejpam-3391	471	28	+	+	CCONJ
ejpam-3391	471	29	.	.	PUNCT
ejpam-3391	471	30	.	.	PUNCT
ejpam-3391	472	1	.+a	.+a	PUNCT
ejpam-3391	472	2	(	(	PUNCT
ejpam-3391	472	3	s	s	NOUN
ejpam-3391	472	4	)	)	PUNCT
ejpam-3391	472	5	0nϕ	0nϕ	NOUN
ejpam-3391	472	6	(	(	PUNCT
ejpam-3391	472	7	s	s	NOUN
ejpam-3391	472	8	)	)	PUNCT
ejpam-3391	472	9	n	n	PRON
ejpam-3391	472	10	+	+	ADP
ejpam-3391	472	11	b	b	PROPN
ejpam-3391	472	12	(	(	PUNCT
ejpam-3391	472	13	s	s	NOUN
ejpam-3391	472	14	)	)	PUNCT
ejpam-3391	472	15	0	0	NUM
ejpam-3391	472	16	)	)	PUNCT
ejpam-3391	472	17	b	b	X
ejpam-3391	472	18	(	(	PUNCT
ejpam-3391	472	19	s	s	NOUN
ejpam-3391	472	20	)	)	PUNCT
ejpam-3391	472	21	0	0	NUM
ejpam-3391	473	1	∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣	NOUN
ejpam-3391	473	2	=	=	PUNCT
ejpam-3391	474	1	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	474	2	n∑	n∑	NOUN
ejpam-3391	474	3	k=1	k=1	PROPN
ejpam-3391	475	1	(	(	PUNCT
ejpam-3391	475	2	a	a	DET
ejpam-3391	475	3	(	(	PUNCT
ejpam-3391	475	4	s	s	NOUN
ejpam-3391	475	5	)	)	PUNCT
ejpam-3391	475	6	ik	ik	PROPN
ejpam-3391	475	7	a	a	PROPN
ejpam-3391	475	8	(	(	PUNCT
ejpam-3391	475	9	s	s	NOUN
ejpam-3391	475	10	)	)	PUNCT
ejpam-3391	475	11	0k	0k	NOUN
ejpam-3391	475	12	−	−	PROPN
ejpam-3391	475	13	b	b	PROPN
ejpam-3391	475	14	(	(	PUNCT
ejpam-3391	475	15	s	s	X
ejpam-3391	475	16	)	)	PUNCT
ejpam-3391	475	17	i	i	PROPN
ejpam-3391	475	18	b	b	X
ejpam-3391	475	19	(	(	PUNCT
ejpam-3391	475	20	s	s	NOUN
ejpam-3391	475	21	)	)	PUNCT
ejpam-3391	475	22	0	0	NUM
ejpam-3391	475	23	)	)	PUNCT
ejpam-3391	475	24	a	a	DET
ejpam-3391	475	25	(	(	PUNCT
ejpam-3391	475	26	s	s	NOUN
ejpam-3391	475	27	)	)	PUNCT
ejpam-3391	475	28	0k	0k	NOUN
ejpam-3391	475	29	ϕ	ϕ	X
ejpam-3391	475	30	(	(	PUNCT
ejpam-3391	475	31	s	s	PROPN
ejpam-3391	475	32	)	)	PUNCT
ejpam-3391	475	33	k	k	PROPN
ejpam-3391	475	34	a	a	DET
ejpam-3391	475	35	(	(	PUNCT
ejpam-3391	475	36	s	s	NOUN
ejpam-3391	475	37	)	)	PUNCT
ejpam-3391	475	38	01	01	NUM
ejpam-3391	475	39	ϕ	ϕ	X
ejpam-3391	475	40	(	(	PUNCT
ejpam-3391	475	41	s	s	NOUN
ejpam-3391	475	42	)	)	PUNCT
ejpam-3391	475	43	1	1	NUM
ejpam-3391	475	44	+	+	CCONJ
ejpam-3391	475	45	.	.	PUNCT
ejpam-3391	475	46	.	.	PUNCT
ejpam-3391	476	1	.+a	.+a	PUNCT
ejpam-3391	476	2	(	(	PUNCT
ejpam-3391	476	3	s	s	NOUN
ejpam-3391	476	4	)	)	PUNCT
ejpam-3391	476	5	0nϕ	0nϕ	NOUN
ejpam-3391	476	6	(	(	PUNCT
ejpam-3391	476	7	s	s	NOUN
ejpam-3391	476	8	)	)	PUNCT
ejpam-3391	476	9	n	n	PRON
ejpam-3391	476	10	+	+	ADP
ejpam-3391	476	11	b	b	PROPN
ejpam-3391	476	12	(	(	PUNCT
ejpam-3391	476	13	s	s	NOUN
ejpam-3391	476	14	)	)	PUNCT
ejpam-3391	476	15	0	0	NUM
ejpam-3391	477	1	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	477	2	for	for	ADP
ejpam-3391	477	3	each	each	DET
ejpam-3391	477	4	k	k	NOUN
ejpam-3391	477	5	,	,	PUNCT
ejpam-3391	477	6	1	1	NUM
ejpam-3391	477	7	≤	≤	NUM
ejpam-3391	477	8	k	k	X
ejpam-3391	477	9	≤	≤	PROPN
ejpam-3391	477	10	n	n	CCONJ
ejpam-3391	477	11	,	,	PUNCT
ejpam-3391	477	12	there	there	PRON
ejpam-3391	477	13	exists	exist	VERB
ejpam-3391	477	14	an	an	DET
ejpam-3391	477	15	increasing	increase	VERB
ejpam-3391	477	16	sequence	sequence	NOUN
ejpam-3391	477	17	lk	lk	NOUN
ejpam-3391	477	18	,	,	PUNCT
ejpam-3391	477	19	lk	lk	X
ejpam-3391	477	20	<	<	X
ejpam-3391	477	21	s	s	PROPN
ejpam-3391	477	22	,	,	PUNCT
ejpam-3391	477	23	such	such	ADJ
ejpam-3391	477	24	that	that	SCONJ
ejpam-3391	477	25	j(lk	j(lk	NOUN
ejpam-3391	477	26	)	)	PUNCT
ejpam-3391	478	1	=	=	SYM
ejpam-3391	478	2	k	k	NOUN
ejpam-3391	478	3	,	,	PUNCT
ejpam-3391	478	4	one	one	PRON
ejpam-3391	478	5	gets	get	VERB
ejpam-3391	478	6	a	a	DET
ejpam-3391	478	7	(	(	PUNCT
ejpam-3391	478	8	s	s	NOUN
ejpam-3391	478	9	)	)	PUNCT
ejpam-3391	478	10	ik	ik	PROPN
ejpam-3391	478	11	=	=	SYM
ejpam-3391	478	12	b	b	PROPN
ejpam-3391	478	13	(	(	PUNCT
ejpam-3391	478	14	lk	lk	PROPN
ejpam-3391	478	15	)	)	PUNCT
ejpam-3391	478	16	i	i	PRON
ejpam-3391	478	17	.	.	PUNCT
ejpam-3391	479	1	then	then	ADV
ejpam-3391	479	2	we	we	PRON
ejpam-3391	479	3	have	have	VERB
ejpam-3391	479	4	a.	a.	NOUN
ejpam-3391	479	5	chandoul	chandoul	PROPN
ejpam-3391	479	6	,	,	PUNCT
ejpam-3391	479	7	f.	f.	PROPN
ejpam-3391	479	8	aljuaydi	aljuaydi	PROPN
ejpam-3391	479	9	/	/	SYM
ejpam-3391	479	10	eur	eur	NOUN
ejpam-3391	479	11	.	.	PUNCT
ejpam-3391	480	1	j.	j.	PROPN
ejpam-3391	480	2	pure	pure	PROPN
ejpam-3391	480	3	appl	appl	PROPN
ejpam-3391	480	4	.	.	PROPN
ejpam-3391	480	5	math	math	PROPN
ejpam-3391	480	6	,	,	PUNCT
ejpam-3391	480	7	12	12	NUM
ejpam-3391	480	8	(	(	PUNCT
ejpam-3391	480	9	2	2	NUM
ejpam-3391	480	10	)	)	PUNCT
ejpam-3391	480	11	(	(	PUNCT
ejpam-3391	480	12	2019	2019	NUM
ejpam-3391	480	13	)	)	PUNCT
ejpam-3391	480	14	,	,	PUNCT
ejpam-3391	480	15	418	418	NUM
ejpam-3391	480	16	-	-	SYM
ejpam-3391	480	17	431	431	NUM
ejpam-3391	480	18	430	430	NUM
ejpam-3391	480	19	∣∣∣∣∣ϕi	∣∣∣∣∣ϕi	NOUN
ejpam-3391	480	20	−	−	PROPN
ejpam-3391	480	21	b	b	PROPN
ejpam-3391	480	22	(	(	PUNCT
ejpam-3391	480	23	s	s	X
ejpam-3391	480	24	)	)	PUNCT
ejpam-3391	480	25	i	i	PROPN
ejpam-3391	480	26	b	b	X
ejpam-3391	480	27	(	(	PUNCT
ejpam-3391	480	28	s	s	NOUN
ejpam-3391	480	29	)	)	PUNCT
ejpam-3391	480	30	0	0	NUM
ejpam-3391	481	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3391	481	2	=	=	PUNCT
ejpam-3391	482	1	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	482	2	n∑	n∑	NOUN
ejpam-3391	482	3	k=1	k=1	PROPN
ejpam-3391	483	1	(	(	PUNCT
ejpam-3391	483	2	a	a	DET
ejpam-3391	483	3	(	(	PUNCT
ejpam-3391	483	4	s	s	NOUN
ejpam-3391	483	5	)	)	PUNCT
ejpam-3391	483	6	ik	ik	PROPN
ejpam-3391	483	7	a	a	PROPN
ejpam-3391	483	8	(	(	PUNCT
ejpam-3391	483	9	s	s	NOUN
ejpam-3391	483	10	)	)	PUNCT
ejpam-3391	483	11	0k	0k	NOUN
ejpam-3391	483	12	−	−	PROPN
ejpam-3391	483	13	b	b	PROPN
ejpam-3391	483	14	(	(	PUNCT
ejpam-3391	483	15	s	s	X
ejpam-3391	483	16	)	)	PUNCT
ejpam-3391	483	17	i	i	PROPN
ejpam-3391	483	18	b	b	X
ejpam-3391	483	19	(	(	PUNCT
ejpam-3391	483	20	s	s	NOUN
ejpam-3391	483	21	)	)	PUNCT
ejpam-3391	483	22	0	0	NUM
ejpam-3391	483	23	)	)	PUNCT
ejpam-3391	483	24	a	a	DET
ejpam-3391	483	25	(	(	PUNCT
ejpam-3391	483	26	s	s	NOUN
ejpam-3391	483	27	)	)	PUNCT
ejpam-3391	483	28	0k	0k	NOUN
ejpam-3391	483	29	ϕ	ϕ	X
ejpam-3391	483	30	(	(	PUNCT
ejpam-3391	483	31	s	s	PROPN
ejpam-3391	483	32	)	)	PUNCT
ejpam-3391	483	33	k	k	PROPN
ejpam-3391	483	34	a	a	DET
ejpam-3391	483	35	(	(	PUNCT
ejpam-3391	483	36	s	s	NOUN
ejpam-3391	483	37	)	)	PUNCT
ejpam-3391	483	38	01	01	NUM
ejpam-3391	483	39	ϕ	ϕ	X
ejpam-3391	483	40	(	(	PUNCT
ejpam-3391	483	41	s	s	NOUN
ejpam-3391	483	42	)	)	PUNCT
ejpam-3391	483	43	1	1	NUM
ejpam-3391	483	44	+	+	CCONJ
ejpam-3391	483	45	.	.	PUNCT
ejpam-3391	483	46	.	.	PUNCT
ejpam-3391	484	1	.+a	.+a	PUNCT
ejpam-3391	484	2	(	(	PUNCT
ejpam-3391	484	3	s	s	NOUN
ejpam-3391	484	4	)	)	PUNCT
ejpam-3391	484	5	0nϕ	0nϕ	NOUN
ejpam-3391	484	6	(	(	PUNCT
ejpam-3391	484	7	s	s	NOUN
ejpam-3391	484	8	)	)	PUNCT
ejpam-3391	484	9	n	n	PRON
ejpam-3391	484	10	+	+	ADP
ejpam-3391	484	11	b	b	PROPN
ejpam-3391	484	12	(	(	PUNCT
ejpam-3391	484	13	s	s	NOUN
ejpam-3391	484	14	)	)	PUNCT
ejpam-3391	484	15	0	0	NUM
ejpam-3391	484	16	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	484	17	=	=	SYM
ejpam-3391	484	18	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	485	1	n∑	n∑	NOUN
ejpam-3391	485	2	k=1	k=1	PROPN
ejpam-3391	486	1	(	(	PUNCT
ejpam-3391	486	2	a	a	DET
ejpam-3391	486	3	(	(	PUNCT
ejpam-3391	486	4	lk	lk	NOUN
ejpam-3391	486	5	)	)	PUNCT
ejpam-3391	486	6	ik	ik	PROPN
ejpam-3391	486	7	a	a	DET
ejpam-3391	486	8	(	(	PUNCT
ejpam-3391	486	9	lk	lk	NOUN
ejpam-3391	486	10	)	)	PUNCT
ejpam-3391	486	11	0k	0k	NOUN
ejpam-3391	486	12	−	−	PROPN
ejpam-3391	486	13	b	b	PROPN
ejpam-3391	486	14	(	(	PUNCT
ejpam-3391	486	15	s	s	X
ejpam-3391	486	16	)	)	PUNCT
ejpam-3391	486	17	i	i	PROPN
ejpam-3391	486	18	b	b	X
ejpam-3391	486	19	(	(	PUNCT
ejpam-3391	486	20	s	s	NOUN
ejpam-3391	486	21	)	)	PUNCT
ejpam-3391	486	22	0	0	NUM
ejpam-3391	486	23	)	)	PUNCT
ejpam-3391	486	24	b	b	X
ejpam-3391	486	25	(	(	PUNCT
ejpam-3391	486	26	lk	lk	PROPN
ejpam-3391	486	27	)	)	PUNCT
ejpam-3391	486	28	0	0	NUM
ejpam-3391	487	1	ϕ	ϕ	X
ejpam-3391	487	2	(	(	PUNCT
ejpam-3391	487	3	s	s	NOUN
ejpam-3391	487	4	)	)	PUNCT
ejpam-3391	487	5	k	k	PROPN
ejpam-3391	487	6	a	a	DET
ejpam-3391	487	7	(	(	PUNCT
ejpam-3391	487	8	s	s	NOUN
ejpam-3391	487	9	)	)	PUNCT
ejpam-3391	487	10	01	01	NUM
ejpam-3391	487	11	ϕ	ϕ	X
ejpam-3391	487	12	(	(	PUNCT
ejpam-3391	487	13	s	s	NOUN
ejpam-3391	487	14	)	)	PUNCT
ejpam-3391	487	15	1	1	NUM
ejpam-3391	487	16	+	+	CCONJ
ejpam-3391	487	17	.	.	PUNCT
ejpam-3391	487	18	.	.	PUNCT
ejpam-3391	488	1	.+a	.+a	PUNCT
ejpam-3391	488	2	(	(	PUNCT
ejpam-3391	488	3	s	s	NOUN
ejpam-3391	488	4	)	)	PUNCT
ejpam-3391	488	5	0nϕ	0nϕ	NOUN
ejpam-3391	488	6	(	(	PUNCT
ejpam-3391	488	7	s	s	NOUN
ejpam-3391	488	8	)	)	PUNCT
ejpam-3391	488	9	n	n	PRON
ejpam-3391	488	10	+	+	ADP
ejpam-3391	488	11	b	b	PROPN
ejpam-3391	488	12	(	(	PUNCT
ejpam-3391	488	13	s	s	NOUN
ejpam-3391	488	14	)	)	PUNCT
ejpam-3391	488	15	0	0	NUM
ejpam-3391	488	16	∣∣∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3391	488	17	=	=	SYM
ejpam-3391	488	18	n∑	n∑	NOUN
ejpam-3391	488	19	k=1	k=1	X
ejpam-3391	489	1	∣∣∣b(lk	∣∣∣b(lk	ADV
ejpam-3391	489	2	)	)	PUNCT
ejpam-3391	489	3	0	0	NUM
ejpam-3391	490	1	∣∣∣	∣∣∣	NOUN
ejpam-3391	490	2	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	490	3	(	(	PUNCT
ejpam-3391	490	4	a	a	DET
ejpam-3391	490	5	(	(	PUNCT
ejpam-3391	490	6	lk	lk	NOUN
ejpam-3391	490	7	)	)	PUNCT
ejpam-3391	490	8	ik	ik	PROPN
ejpam-3391	490	9	a	a	DET
ejpam-3391	490	10	(	(	PUNCT
ejpam-3391	490	11	lk	lk	NOUN
ejpam-3391	490	12	)	)	PUNCT
ejpam-3391	490	13	0k	0k	NOUN
ejpam-3391	490	14	−	−	PROPN
ejpam-3391	490	15	b	b	PROPN
ejpam-3391	490	16	(	(	PUNCT
ejpam-3391	490	17	s	s	X
ejpam-3391	490	18	)	)	PUNCT
ejpam-3391	490	19	i	i	PROPN
ejpam-3391	490	20	b	b	X
ejpam-3391	490	21	(	(	PUNCT
ejpam-3391	490	22	s	s	NOUN
ejpam-3391	490	23	)	)	PUNCT
ejpam-3391	490	24	0	0	NUM
ejpam-3391	490	25	)	)	PUNCT
ejpam-3391	490	26	ϕ	ϕ	NOUN
ejpam-3391	490	27	(	(	PUNCT
ejpam-3391	490	28	s	s	NOUN
ejpam-3391	490	29	)	)	PUNCT
ejpam-3391	490	30	k	k	PROPN
ejpam-3391	490	31	∣∣∣∣∣∣∣∣a(s	∣∣∣∣∣∣∣∣a(s	PROPN
ejpam-3391	490	32	)	)	PUNCT
ejpam-3391	490	33	01	01	NUM
ejpam-3391	490	34	ϕ	ϕ	X
ejpam-3391	490	35	(	(	PUNCT
ejpam-3391	490	36	s	s	NOUN
ejpam-3391	490	37	)	)	PUNCT
ejpam-3391	490	38	1	1	NUM
ejpam-3391	490	39	+	+	CCONJ
ejpam-3391	490	40	.	.	PUNCT
ejpam-3391	490	41	.	.	PUNCT
ejpam-3391	491	1	.+a	.+a	PUNCT
ejpam-3391	491	2	(	(	PUNCT
ejpam-3391	491	3	s	s	NOUN
ejpam-3391	491	4	)	)	PUNCT
ejpam-3391	491	5	0nϕ	0nϕ	NOUN
ejpam-3391	491	6	(	(	PUNCT
ejpam-3391	491	7	s	s	NOUN
ejpam-3391	491	8	)	)	PUNCT
ejpam-3391	491	9	n	n	PRON
ejpam-3391	491	10	+	+	ADP
ejpam-3391	491	11	b	b	PROPN
ejpam-3391	491	12	(	(	PUNCT
ejpam-3391	491	13	s	s	NOUN
ejpam-3391	491	14	)	)	PUNCT
ejpam-3391	491	15	0	0	NUM
ejpam-3391	491	16	∣∣∣	∣∣∣	PROPN
ejpam-3391	491	17	≤	≤	NUM
ejpam-3391	491	18	max	max	PROPN
ejpam-3391	491	19	1≤l≤s−1	1≤l≤s−1	NUM
ejpam-3391	491	20	∣∣∣b(lk	∣∣∣b(lk	ADV
ejpam-3391	491	21	)	)	PUNCT
ejpam-3391	491	22	0	0	PUNCT
ejpam-3391	491	23	∣∣∣	∣∣∣	NOUN
ejpam-3391	492	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3391	492	2	(	(	PUNCT
ejpam-3391	492	3	a	a	DET
ejpam-3391	492	4	(	(	PUNCT
ejpam-3391	492	5	lk	lk	NOUN
ejpam-3391	492	6	)	)	PUNCT
ejpam-3391	492	7	ik	ik	PROPN
ejpam-3391	492	8	a	a	DET
ejpam-3391	492	9	(	(	PUNCT
ejpam-3391	492	10	lk	lk	NOUN
ejpam-3391	492	11	)	)	PUNCT
ejpam-3391	492	12	0k	0k	NOUN
ejpam-3391	492	13	−	−	PROPN
ejpam-3391	492	14	b	b	PROPN
ejpam-3391	492	15	(	(	PUNCT
ejpam-3391	492	16	s	s	X
ejpam-3391	492	17	)	)	PUNCT
ejpam-3391	492	18	i	i	PROPN
ejpam-3391	492	19	b	b	X
ejpam-3391	492	20	(	(	PUNCT
ejpam-3391	492	21	s	s	NOUN
ejpam-3391	492	22	)	)	PUNCT
ejpam-3391	492	23	0	0	NUM
ejpam-3391	492	24	)	)	PUNCT
ejpam-3391	492	25	ϕ	ϕ	NOUN
ejpam-3391	492	26	(	(	PUNCT
ejpam-3391	492	27	s	s	NOUN
ejpam-3391	492	28	)	)	PUNCT
ejpam-3391	492	29	k	k	PROPN
ejpam-3391	492	30	∣∣∣∣∣∣∣∣a(s	∣∣∣∣∣∣∣∣a(s	PROPN
ejpam-3391	492	31	)	)	PUNCT
ejpam-3391	492	32	01	01	NUM
ejpam-3391	492	33	ϕ	ϕ	X
ejpam-3391	492	34	(	(	PUNCT
ejpam-3391	492	35	s	s	NOUN
ejpam-3391	492	36	)	)	PUNCT
ejpam-3391	492	37	1	1	NUM
ejpam-3391	492	38	+	+	CCONJ
ejpam-3391	492	39	.	.	PUNCT
ejpam-3391	492	40	.	.	PUNCT
ejpam-3391	493	1	.+a	.+a	PUNCT
ejpam-3391	493	2	(	(	PUNCT
ejpam-3391	493	3	s	s	NOUN
ejpam-3391	493	4	)	)	PUNCT
ejpam-3391	493	5	0nϕ	0nϕ	NOUN
ejpam-3391	493	6	(	(	PUNCT
ejpam-3391	493	7	s	s	NOUN
ejpam-3391	493	8	)	)	PUNCT
ejpam-3391	493	9	n	n	PRON
ejpam-3391	493	10	+	+	ADP
ejpam-3391	493	11	b	b	PROPN
ejpam-3391	493	12	(	(	PUNCT
ejpam-3391	493	13	s	s	NOUN
ejpam-3391	493	14	)	)	PUNCT
ejpam-3391	493	15	0	0	NUM
ejpam-3391	493	16	∣∣∣	∣∣∣	ADJ
ejpam-3391	493	17	using	use	VERB
ejpam-3391	493	18	(	(	PUNCT
ejpam-3391	493	19	lemma	lemma	PROPN
ejpam-3391	493	20	2	2	NUM
ejpam-3391	493	21	)	)	PUNCT
ejpam-3391	493	22	,	,	PUNCT
ejpam-3391	493	23	we	we	PRON
ejpam-3391	493	24	get∣∣∣∣∣ϕi	get∣∣∣∣∣ϕi	VERB
ejpam-3391	493	25	−	−	PROPN
ejpam-3391	493	26	b	b	PROPN
ejpam-3391	493	27	(	(	PUNCT
ejpam-3391	493	28	s	s	X
ejpam-3391	493	29	)	)	PUNCT
ejpam-3391	493	30	i	i	PROPN
ejpam-3391	493	31	b	b	X
ejpam-3391	493	32	(	(	PUNCT
ejpam-3391	493	33	s	s	NOUN
ejpam-3391	493	34	)	)	PUNCT
ejpam-3391	493	35	0	0	NUM
ejpam-3391	494	1	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-3391	494	2	≤	≤	PROPN
ejpam-3391	494	3	e−1	e−1	PROPN
ejpam-3391	494	4	∣∣∣ϕ(s	∣∣∣ϕ(	NOUN
ejpam-3391	494	5	)	)	PUNCT
ejpam-3391	495	1	k	k	X
ejpam-3391	495	2	∣∣∣∣∣∣a(s	∣∣∣∣∣∣a(s	PROPN
ejpam-3391	495	3	)	)	PUNCT
ejpam-3391	495	4	01	01	NUM
ejpam-3391	495	5	ϕ	ϕ	X
ejpam-3391	495	6	(	(	PUNCT
ejpam-3391	495	7	s	s	NOUN
ejpam-3391	495	8	)	)	PUNCT
ejpam-3391	495	9	1	1	NUM
ejpam-3391	495	10	+	+	CCONJ
ejpam-3391	495	11	.	.	PUNCT
ejpam-3391	495	12	.	.	PUNCT
ejpam-3391	496	1	.+a	.+a	PUNCT
ejpam-3391	496	2	(	(	PUNCT
ejpam-3391	496	3	s	s	NOUN
ejpam-3391	496	4	)	)	PUNCT
ejpam-3391	496	5	0nϕ	0nϕ	NOUN
ejpam-3391	496	6	(	(	PUNCT
ejpam-3391	496	7	s	s	NOUN
ejpam-3391	496	8	)	)	PUNCT
ejpam-3391	496	9	n	n	PRON
ejpam-3391	496	10	+	+	ADP
ejpam-3391	496	11	b	b	PROPN
ejpam-3391	496	12	(	(	PUNCT
ejpam-3391	496	13	s	s	NOUN
ejpam-3391	496	14	)	)	PUNCT
ejpam-3391	496	15	0	0	NUM
ejpam-3391	496	16	∣∣∣	∣∣∣	NOUN
ejpam-3391	496	17	since	since	SCONJ
ejpam-3391	496	18	degb	degb	NOUN
ejpam-3391	496	19	(	(	PUNCT
ejpam-3391	496	20	s	s	NOUN
ejpam-3391	496	21	)	)	PUNCT
ejpam-3391	496	22	0	0	NUM
ejpam-3391	497	1	=	=	SYM
ejpam-3391	497	2	s∑	s∑	PROPN
ejpam-3391	498	1	k=1	k=1	PROPN
ejpam-3391	498	2	deg	deg	VERB
ejpam-3391	498	3	a	a	DET
ejpam-3391	498	4	(	(	PUNCT
ejpam-3391	498	5	k	k	NOUN
ejpam-3391	498	6	)	)	PUNCT
ejpam-3391	498	7	n+1	n+1	NUM
ejpam-3391	498	8	≥	≥	NUM
ejpam-3391	498	9	s	s	NOUN
ejpam-3391	498	10	,	,	PUNCT
ejpam-3391	498	11	then	then	ADV
ejpam-3391	498	12	,	,	PUNCT
ejpam-3391	498	13	for	for	ADP
ejpam-3391	498	14	any	any	DET
ejpam-3391	498	15	ε	ε	PROPN
ejpam-3391	498	16	>	>	X
ejpam-3391	498	17	0	0	PROPN
ejpam-3391	498	18	,	,	PUNCT
ejpam-3391	498	19	there	there	PRON
ejpam-3391	498	20	exists	exist	VERB
ejpam-3391	498	21	s0	s0	PROPN
ejpam-3391	498	22	≥	≥	NUM
ejpam-3391	498	23	1	1	NUM
ejpam-3391	498	24	such	such	ADJ
ejpam-3391	498	25	that∣∣∣∣∣ϕi	that∣∣∣∣∣ϕi	PROPN
ejpam-3391	498	26	−	−	PROPN
ejpam-3391	498	27	b	b	PROPN
ejpam-3391	498	28	(	(	PUNCT
ejpam-3391	498	29	s	s	X
ejpam-3391	498	30	)	)	PUNCT
ejpam-3391	498	31	i	i	PROPN
ejpam-3391	498	32	b	b	X
ejpam-3391	498	33	(	(	PUNCT
ejpam-3391	498	34	s	s	NOUN
ejpam-3391	498	35	)	)	PUNCT
ejpam-3391	498	36	0	0	NUM
ejpam-3391	499	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-3391	499	2	≤	≤	NOUN
ejpam-3391	499	3	e−1∣∣∣b(s	e−1∣∣∣b(s	PUNCT
ejpam-3391	499	4	)	)	PUNCT
ejpam-3391	499	5	0	0	NUM
ejpam-3391	499	6	∣∣∣	∣∣∣	NOUN
ejpam-3391	499	7	<	<	X
ejpam-3391	499	8	ε	ε	PROPN
ejpam-3391	499	9	,	,	PUNCT
ejpam-3391	499	10	for	for	ADP
ejpam-3391	499	11	any	any	DET
ejpam-3391	499	12	s	s	PART
ejpam-3391	499	13	≥	≥	NOUN
ejpam-3391	499	14	s0	s0	NOUN
ejpam-3391	499	15	this	this	PRON
ejpam-3391	499	16	implies	imply	VERB
ejpam-3391	499	17	lim	lim	PROPN
ejpam-3391	499	18	s−→∞	s−→∞	PROPN
ejpam-3391	499	19	b	b	PROPN
ejpam-3391	499	20	(	(	PUNCT
ejpam-3391	499	21	s	s	X
ejpam-3391	499	22	)	)	PUNCT
ejpam-3391	499	23	i	i	PROPN
ejpam-3391	499	24	b	b	X
ejpam-3391	499	25	(	(	PUNCT
ejpam-3391	499	26	s	s	NOUN
ejpam-3391	499	27	)	)	PUNCT
ejpam-3391	499	28	0	0	NUM
ejpam-3391	500	1	=	=	NOUN
ejpam-3391	500	2	ϕi	ϕi	ADP
ejpam-3391	500	3	for	for	ADP
ejpam-3391	500	4	1	1	NUM
ejpam-3391	500	5	≤	≤	NUM
ejpam-3391	500	6	i	i	PRON
ejpam-3391	500	7	≤	≤	NOUN
ejpam-3391	500	8	n	n	CCONJ
ejpam-3391	500	9	which	which	PRON
ejpam-3391	500	10	proves	prove	VERB
ejpam-3391	500	11	the	the	DET
ejpam-3391	500	12	theorem	theorem	PROPN
ejpam-3391	500	13	.	.	PUNCT
ejpam-3391	500	14	�	�	PROPN
ejpam-3391	500	15	references	reference	VERB
ejpam-3391	500	16	431	431	NUM
ejpam-3391	500	17	references	reference	NOUN
ejpam-3391	500	18	[	[	X
ejpam-3391	500	19	1	1	NUM
ejpam-3391	500	20	]	]	PUNCT
ejpam-3391	500	21	a.	a.	NOUN
ejpam-3391	500	22	chandoul	chandoul	PROPN
ejpam-3391	500	23	.	.	PUNCT
ejpam-3391	501	1	simpler	simple	ADJ
ejpam-3391	501	2	proof	proof	NOUN
ejpam-3391	501	3	of	of	ADP
ejpam-3391	501	4	convergence	convergence	NOUN
ejpam-3391	501	5	of	of	ADP
ejpam-3391	501	6	brun	brun	NOUN
ejpam-3391	501	7	algorithm	algorithm	NOUN
ejpam-3391	501	8	over	over	ADP
ejpam-3391	501	9	the	the	DET
ejpam-3391	501	10	field	field	NOUN
ejpam-3391	501	11	of	of	ADP
ejpam-3391	501	12	formal	formal	ADJ
ejpam-3391	501	13	power	power	NOUN
ejpam-3391	501	14	series	series	NOUN
ejpam-3391	501	15	,	,	PUNCT
ejpam-3391	501	16	international	international	ADJ
ejpam-3391	501	17	journal	journal	NOUN
ejpam-3391	501	18	of	of	ADP
ejpam-3391	501	19	algebra	algebra	PROPN
ejpam-3391	501	20	,	,	PUNCT
ejpam-3391	501	21	v.	v.	ADP
ejpam-3391	501	22	5	5	NUM
ejpam-3391	501	23	,	,	PUNCT
ejpam-3391	501	24	p.	p.	NOUN
ejpam-3391	501	25	25	25	NUM
ejpam-3391	501	26	-	-	SYM
ejpam-3391	501	27	30	30	NUM
ejpam-3391	501	28	,	,	PUNCT
ejpam-3391	501	29	2011	2011	NUM
ejpam-3391	501	30	.	.	PUNCT
ejpam-3391	502	1	[	[	X
ejpam-3391	502	2	2	2	NUM
ejpam-3391	502	3	]	]	PUNCT
ejpam-3391	502	4	a.	a.	NOUN
ejpam-3391	502	5	chandoul	chandoul	PROPN
ejpam-3391	502	6	.	.	PUNCT
ejpam-3391	503	1	on	on	ADP
ejpam-3391	503	2	continued	continue	VERB
ejpam-3391	503	3	fractions	fraction	NOUN
ejpam-3391	503	4	over	over	ADP
ejpam-3391	503	5	the	the	DET
ejpam-3391	503	6	field	field	NOUN
ejpam-3391	503	7	of	of	ADP
ejpam-3391	503	8	formal	formal	ADJ
ejpam-3391	503	9	power	power	NOUN
ejpam-3391	503	10	series	series	NOUN
ejpam-3391	503	11	,	,	PUNCT
ejpam-3391	503	12	international	international	ADJ
ejpam-3391	503	13	journal	journal	NOUN
ejpam-3391	503	14	of	of	ADP
ejpam-3391	503	15	contomporary	contomporary	PROPN
ejpam-3391	503	16	mathematical	mathematical	PROPN
ejpam-3391	503	17	sciences	sciences	PROPN
ejpam-3391	503	18	,	,	PUNCT
ejpam-3391	503	19	v.	v.	ADP
ejpam-3391	503	20	6	6	NUM
ejpam-3391	503	21	,	,	PUNCT
ejpam-3391	503	22	p.	p.	NOUN
ejpam-3391	503	23	1351	1351	NUM
ejpam-3391	503	24	-	-	SYM
ejpam-3391	503	25	1356	1356	NUM
ejpam-3391	503	26	,	,	PUNCT
ejpam-3391	503	27	2011	2011	NUM
ejpam-3391	503	28	.	.	PUNCT
ejpam-3391	504	1	[	[	X
ejpam-3391	504	2	3	3	NUM
ejpam-3391	504	3	]	]	X
ejpam-3391	504	4	a.	a.	NOUN
ejpam-3391	504	5	chandoul	chandoul	PROPN
ejpam-3391	504	6	,	,	PUNCT
ejpam-3391	504	7	on	on	ADP
ejpam-3391	504	8	periodic	periodic	ADJ
ejpam-3391	504	9	jacobi	jacobi	PROPN
ejpam-3391	504	10	-	-	PUNCT
ejpam-3391	504	11	perron	perron	PROPN
ejpam-3391	504	12	algorithm	algorithm	NOUN
ejpam-3391	504	13	over	over	ADP
ejpam-3391	504	14	the	the	DET
ejpam-3391	504	15	field	field	NOUN
ejpam-3391	504	16	of	of	ADP
ejpam-3391	504	17	formal	formal	ADJ
ejpam-3391	504	18	power	power	NOUN
ejpam-3391	504	19	series	series	NOUN
ejpam-3391	504	20	,	,	PUNCT
ejpam-3391	504	21	new	new	ADJ
ejpam-3391	504	22	trends	trend	NOUN
ejpam-3391	504	23	in	in	ADP
ejpam-3391	504	24	mathematical	mathematical	ADJ
ejpam-3391	504	25	science	science	NOUN
ejpam-3391	504	26	,	,	PUNCT
ejpam-3391	504	27	v.	v.	ADP
ejpam-3391	504	28	1	1	NUM
ejpam-3391	504	29	,	,	PUNCT
ejpam-3391	504	30	p.	p.	NOUN
ejpam-3391	504	31	145	145	NUM
ejpam-3391	504	32	-	-	SYM
ejpam-3391	504	33	152	152	NUM
ejpam-3391	504	34	,	,	PUNCT
ejpam-3391	504	35	2018	2018	NUM
ejpam-3391	504	36	.	.	PUNCT
ejpam-3391	505	1	[	[	X
ejpam-3391	505	2	4	4	X
ejpam-3391	505	3	]	]	PUNCT
ejpam-3391	505	4	h.	h.	PROPN
ejpam-3391	505	5	ben	ben	PROPN
ejpam-3391	505	6	amar	amar	PROPN
ejpam-3391	505	7	and	and	CCONJ
ejpam-3391	505	8	a.	a.	PROPN
ejpam-3391	505	9	chandoul	chandoul	PROPN
ejpam-3391	505	10	,	,	PUNCT
ejpam-3391	505	11	convergence	convergence	NOUN
ejpam-3391	505	12	of	of	ADP
ejpam-3391	505	13	the	the	DET
ejpam-3391	505	14	brun	brun	NOUN
ejpam-3391	505	15	algorithm	algorithm	NOUN
ejpam-3391	505	16	over	over	ADP
ejpam-3391	505	17	the	the	DET
ejpam-3391	505	18	field	field	NOUN
ejpam-3391	505	19	of	of	ADP
ejpam-3391	505	20	formal	formal	ADJ
ejpam-3391	505	21	power	power	NOUN
ejpam-3391	505	22	series	series	NOUN
ejpam-3391	505	23	,	,	PUNCT
ejpam-3391	505	24	journal	journal	NOUN
ejpam-3391	505	25	of	of	ADP
ejpam-3391	505	26	number	number	NOUN
ejpam-3391	505	27	theory	theory	NOUN
ejpam-3391	505	28	197	197	NUM
ejpam-3391	505	29	,	,	PUNCT
ejpam-3391	505	30	621	621	NUM
ejpam-3391	505	31	-	-	SYM
ejpam-3391	505	32	631	631	NUM
ejpam-3391	505	33	,	,	PUNCT
ejpam-3391	505	34	2009	2009	NUM
ejpam-3391	505	35	.	.	PUNCT
ejpam-3391	506	1	[	[	X
ejpam-3391	506	2	5	5	NUM
ejpam-3391	506	3	]	]	PUNCT
ejpam-3391	506	4	a.	a.	NOUN
ejpam-3391	506	5	chandoul	chandoul	PROPN
ejpam-3391	506	6	et	et	PROPN
ejpam-3391	506	7	al	al	PROPN
ejpam-3391	506	8	.	.	PROPN
ejpam-3391	507	1	on	on	ADP
ejpam-3391	507	2	periodic	periodic	ADJ
ejpam-3391	507	3	p	p	ADV
ejpam-3391	507	4	-	-	PUNCT
ejpam-3391	507	5	continued	continue	VERB
ejpam-3391	507	6	fraction	fraction	NOUN
ejpam-3391	507	7	having	have	VERB
ejpam-3391	507	8	period	period	NOUN
ejpam-3391	507	9	lenght	lenght	ADJ
ejpam-3391	507	10	one	one	NOUN
ejpam-3391	507	11	,	,	PUNCT
ejpam-3391	507	12	bulletin	bulletin	NOUN
ejpam-3391	507	13	of	of	ADP
ejpam-3391	507	14	the	the	DET
ejpam-3391	507	15	korean	korean	PROPN
ejpam-3391	507	16	mathematical	mathematical	ADJ
ejpam-3391	507	17	society	society	NOUN
ejpam-3391	507	18	,	,	PUNCT
ejpam-3391	507	19	v.	v.	ADP
ejpam-3391	507	20	50	50	NUM
ejpam-3391	507	21	,	,	PUNCT
ejpam-3391	507	22	p.	p.	NOUN
ejpam-3391	507	23	1623	1623	NUM
ejpam-3391	507	24	-	-	SYM
ejpam-3391	507	25	1630	1630	NUM
ejpam-3391	507	26	,	,	PUNCT
ejpam-3391	507	27	2013	2013	NUM
ejpam-3391	507	28	.	.	PUNCT
ejpam-3391	508	1	[	[	X
ejpam-3391	508	2	6	6	NUM
ejpam-3391	508	3	]	]	PUNCT
ejpam-3391	508	4	a.	a.	NOUN
ejpam-3391	508	5	chandoul	chandoul	PROPN
ejpam-3391	508	6	et	et	PROPN
ejpam-3391	508	7	al	al	PROPN
ejpam-3391	508	8	.	.	PROPN
ejpam-3391	509	1	on	on	ADP
ejpam-3391	509	2	the	the	DET
ejpam-3391	509	3	continued	continue	VERB
ejpam-3391	509	4	fraction	fraction	NOUN
ejpam-3391	509	5	expansion	expansion	NOUN
ejpam-3391	509	6	of	of	ADP
ejpam-3391	509	7	fixed	fix	VERB
ejpam-3391	509	8	period	period	NOUN
ejpam-3391	509	9	in	in	ADP
ejpam-3391	509	10	finite	finite	ADJ
ejpam-3391	509	11	fields	field	NOUN
ejpam-3391	509	12	,	,	PUNCT
ejpam-3391	509	13	canadian	canadian	ADJ
ejpam-3391	509	14	mathematical	mathematical	ADJ
ejpam-3391	509	15	bulletin	bulletin	NOUN
ejpam-3391	509	16	,	,	PUNCT
ejpam-3391	509	17	v.	v.	ADP
ejpam-3391	509	18	58	58	NUM
ejpam-3391	509	19	,	,	PUNCT
ejpam-3391	509	20	p.	p.	NOUN
ejpam-3391	509	21	704	704	NUM
ejpam-3391	509	22	-	-	SYM
ejpam-3391	509	23	712	712	NUM
ejpam-3391	509	24	,	,	PUNCT
ejpam-3391	509	25	2015	2015	NUM
ejpam-3391	509	26	.	.	PUNCT
ejpam-3391	510	1	[	[	X
ejpam-3391	510	2	7	7	X
ejpam-3391	510	3	]	]	X
ejpam-3391	510	4	m.	m.	NOUN
ejpam-3391	510	5	jellali	jellali	PROPN
ejpam-3391	510	6	et	et	PROPN
ejpam-3391	510	7	al	al	PROPN
ejpam-3391	510	8	.	.	PUNCT
ejpam-3391	510	9	beta	beta	NOUN
ejpam-3391	510	10	-	-	PUNCT
ejpam-3391	510	11	continued	continue	VERB
ejpam-3391	510	12	fraction	fraction	NOUN
ejpam-3391	510	13	over	over	ADP
ejpam-3391	510	14	laurent	laurent	PROPN
ejpam-3391	510	15	series	series	PROPN
ejpam-3391	510	16	,	,	PUNCT
ejpam-3391	510	17	pub	pub	NOUN
ejpam-3391	510	18	math	math	NOUN
ejpam-3391	510	19	.	.	PUNCT
ejpam-3391	511	1	debrecen	debrecen	NOUN
ejpam-3391	511	2	77/3	77/3	NUM
ejpam-3391	511	3	-	-	PUNCT
ejpam-3391	511	4	4,443	4,443	NUM
ejpam-3391	511	5	-	-	SYM
ejpam-3391	511	6	463	463	NUM
ejpam-3391	511	7	,	,	PUNCT
ejpam-3391	511	8	2010	2010	NUM
ejpam-3391	511	9	.	.	PUNCT
ejpam-3391	512	1	[	[	X
ejpam-3391	512	2	8	8	NUM
ejpam-3391	512	3	]	]	X
ejpam-3391	512	4	e.	e.	PROPN
ejpam-3391	512	5	artin	artin	PROPN
ejpam-3391	512	6	,	,	PUNCT
ejpam-3391	512	7	quadratische	quadratische	PROPN
ejpam-3391	512	8	körper	körper	AUX
ejpam-3391	513	1	i	i	NOUN
ejpam-3391	513	2	m	m	PROPN
ejpam-3391	513	3	gebiete	gebiete	ADJ
ejpam-3391	513	4	der	der	NOUN
ejpam-3391	513	5	höhern	höhern	VERB
ejpam-3391	513	6	kongruenzen	kongruenzen	PROPN
ejpam-3391	513	7	i.	i.	NOUN
ejpam-3391	513	8	,	,	PUNCT
ejpam-3391	513	9	arithmetischer	arithmetischer	ADJ
ejpam-3391	513	10	teil	teil	PROPN
ejpam-3391	513	11	.	.	PUNCT
ejpam-3391	514	1	ii	ii	PROPN
ejpam-3391	514	2	.	.	PUNCT
ejpam-3391	515	1	(	(	PUNCT
ejpam-3391	515	2	analytischer	analytischer	NOUN
ejpam-3391	515	3	teil	teil	PROPN
ejpam-3391	515	4	.	.	PUNCT
ejpam-3391	515	5	)	)	PUNCT
ejpam-3391	515	6	,	,	PUNCT
ejpam-3391	515	7	1924	1924	NUM
ejpam-3391	515	8	.	.	PUNCT
ejpam-3391	516	1	[	[	X
ejpam-3391	516	2	9	9	NUM
ejpam-3391	516	3	]	]	X
ejpam-3391	516	4	v.	v.	ADP
ejpam-3391	516	5	berthé	berthé	NOUN
ejpam-3391	516	6	and	and	CCONJ
ejpam-3391	516	7	h.	h.	PROPN
ejpam-3391	516	8	nakada	nakada	PROPN
ejpam-3391	516	9	.	.	PUNCT
ejpam-3391	517	1	on	on	ADP
ejpam-3391	517	2	continued	continue	VERB
ejpam-3391	517	3	fraction	fraction	NOUN
ejpam-3391	517	4	expansions	expansion	NOUN
ejpam-3391	517	5	in	in	ADP
ejpam-3391	517	6	positive	positive	ADJ
ejpam-3391	517	7	characteristic	characteristic	NOUN
ejpam-3391	517	8	:	:	PUNCT
ejpam-3391	517	9	equivalence	equivalence	NOUN
ejpam-3391	517	10	relations	relation	NOUN
ejpam-3391	517	11	and	and	CCONJ
ejpam-3391	517	12	some	some	DET
ejpam-3391	517	13	metric	metric	ADJ
ejpam-3391	517	14	properties	property	NOUN
ejpam-3391	517	15	,	,	PUNCT
ejpam-3391	517	16	expo	expo	NOUN
ejpam-3391	517	17	.	.	PUNCT
ejpam-3391	518	1	math	math	NOUN
ejpam-3391	518	2	.	.	PUNCT
ejpam-3391	518	3	,	,	PUNCT
ejpam-3391	518	4	18(4	18(4	NUM
ejpam-3391	518	5	)	)	PUNCT
ejpam-3391	518	6	,	,	PUNCT
ejpam-3391	518	7	257	257	NUM
ejpam-3391	518	8	-	-	SYM
ejpam-3391	518	9	284	284	NUM
ejpam-3391	518	10	,	,	PUNCT
ejpam-3391	518	11	2000	2000	NUM
ejpam-3391	518	12	.	.	PUNCT
ejpam-3391	519	1	[	[	X
ejpam-3391	519	2	10	10	NUM
ejpam-3391	519	3	]	]	PUNCT
ejpam-3391	519	4	m.	m.	NOUN
ejpam-3391	519	5	fochs	fochs	PROPN
ejpam-3391	519	6	.	.	PUNCT
ejpam-3391	520	1	an	an	DET
ejpam-3391	520	2	analogue	analogue	NOUN
ejpam-3391	520	3	of	of	ADP
ejpam-3391	520	4	a	a	DET
ejpam-3391	520	5	theorem	theorem	NOUN
ejpam-3391	520	6	of	of	ADP
ejpam-3391	520	7	szusz	szusz	PROPN
ejpam-3391	520	8	for	for	ADP
ejpam-3391	520	9	formal	formal	ADJ
ejpam-3391	520	10	laurent	laurent	NOUN
ejpam-3391	520	11	series	series	PROPN
ejpam-3391	520	12	over	over	ADP
ejpam-3391	520	13	finite	finite	PROPN
ejpam-3391	520	14	fields	field	NOUN
ejpam-3391	520	15	,	,	PUNCT
ejpam-3391	520	16	journal	journal	NOUN
ejpam-3391	520	17	of	of	ADP
ejpam-3391	520	18	number	number	NOUN
ejpam-3391	520	19	theory	theory	NOUN
ejpam-3391	520	20	,	,	PUNCT
ejpam-3391	520	21	101(1	101(1	NUM
ejpam-3391	520	22	)	)	PUNCT
ejpam-3391	520	23	,	,	PUNCT
ejpam-3391	520	24	105	105	NUM
ejpam-3391	520	25	-	-	SYM
ejpam-3391	520	26	130	130	NUM
ejpam-3391	520	27	,	,	PUNCT
ejpam-3391	520	28	2003	2003	NUM
ejpam-3391	520	29	.	.	PUNCT
ejpam-3391	521	1	[	[	X
ejpam-3391	521	2	11	11	NUM
ejpam-3391	521	3	]	]	PUNCT
ejpam-3391	521	4	k.	k.	PROPN
ejpam-3391	521	5	schmidt	schmidt	PROPN
ejpam-3391	521	6	.	.	PUNCT
ejpam-3391	522	1	on	on	ADP
ejpam-3391	522	2	periodic	periodic	ADJ
ejpam-3391	522	3	expansions	expansion	NOUN
ejpam-3391	522	4	of	of	ADP
ejpam-3391	522	5	pisot	pisot	ADJ
ejpam-3391	522	6	numbers	number	NOUN
ejpam-3391	522	7	and	and	CCONJ
ejpam-3391	522	8	salem	salem	NOUN
ejpam-3391	522	9	numbers	number	NOUN
ejpam-3391	522	10	.	.	PUNCT
ejpam-3391	523	1	bull	bull	NOUN
ejpam-3391	523	2	.	.	PUNCT
ejpam-3391	524	1	london	london	PROPN
ejpam-3391	524	2	math	math	PROPN
ejpam-3391	524	3	.	.	PUNCT
ejpam-3391	525	1	soc	soc	PROPN
ejpam-3391	525	2	.	.	PUNCT
ejpam-3391	525	3	,	,	PUNCT
ejpam-3391	525	4	12(4):269	12(4):269	NUM
ejpam-3391	525	5	-	-	SYM
ejpam-3391	525	6	278	278	NUM
ejpam-3391	525	7	,	,	PUNCT
ejpam-3391	525	8	1980	1980	NUM
ejpam-3391	525	9	.	.	PUNCT