id	sid	tid	token	lemma	pos
ejpam-4348	1	1	european	european	PROPN
ejpam-4348	1	2	journal	journal	PROPN
ejpam-4348	1	3	of	of	ADP
ejpam-4348	1	4	pure	pure	ADJ
ejpam-4348	1	5	and	and	CCONJ
ejpam-4348	1	6	applied	apply	VERB
ejpam-4348	1	7	mathematics	mathematic	NOUN
ejpam-4348	1	8	vol	vol	NOUN
ejpam-4348	1	9	.	.	PROPN
ejpam-4348	2	1	15	15	NUM
ejpam-4348	2	2	,	,	PUNCT
ejpam-4348	2	3	no	no	INTJ
ejpam-4348	2	4	.	.	NOUN
ejpam-4348	2	5	2	2	NUM
ejpam-4348	2	6	,	,	PUNCT
ejpam-4348	2	7	2022	2022	NUM
ejpam-4348	2	8	,	,	PUNCT
ejpam-4348	2	9	681	681	NUM
ejpam-4348	2	10	-	-	SYM
ejpam-4348	2	11	725	725	NUM
ejpam-4348	2	12	issn	issn	PROPN
ejpam-4348	2	13	1307	1307	NUM
ejpam-4348	2	14	-	-	SYM
ejpam-4348	2	15	5543	5543	NUM
ejpam-4348	2	16	–	–	PUNCT
ejpam-4348	2	17	ejpam.com	ejpam.com	X
ejpam-4348	2	18	published	publish	VERB
ejpam-4348	2	19	by	by	ADP
ejpam-4348	2	20	new	new	PROPN
ejpam-4348	2	21	york	york	PROPN
ejpam-4348	2	22	business	business	PROPN
ejpam-4348	2	23	global	global	ADJ
ejpam-4348	2	24	spectral	spectral	ADJ
ejpam-4348	2	25	dichotomy	dichotomy	NOUN
ejpam-4348	2	26	methods	method	NOUN
ejpam-4348	2	27	of	of	ADP
ejpam-4348	2	28	a	a	DET
ejpam-4348	2	29	matrix	matrix	NOUN
ejpam-4348	2	30	with	with	ADP
ejpam-4348	2	31	respect	respect	NOUN
ejpam-4348	2	32	to	to	ADP
ejpam-4348	2	33	the	the	DET
ejpam-4348	2	34	general	general	ADJ
ejpam-4348	2	35	equation	equation	NOUN
ejpam-4348	2	36	of	of	ADP
ejpam-4348	2	37	the	the	DET
ejpam-4348	2	38	parabola	parabola	PROPN
ejpam-4348	2	39	seydou	seydou	PROPN
ejpam-4348	2	40	traoré1,∗	traoré1,∗	PROPN
ejpam-4348	2	41	,	,	PUNCT
ejpam-4348	2	42	mouhamadou	mouhamadou	NOUN
ejpam-4348	2	43	dosso1	dosso1	NOUN
ejpam-4348	2	44	1	1	NUM
ejpam-4348	2	45	laboratoire	laboratoire	PROPN
ejpam-4348	2	46	de	de	PROPN
ejpam-4348	2	47	de	de	PROPN
ejpam-4348	2	48	mathématiques	mathématiques	PROPN
ejpam-4348	2	49	fondammatales	fondammatale	NOUN
ejpam-4348	2	50	et	et	NOUN
ejpam-4348	2	51	applications	application	NOUN
ejpam-4348	2	52	,	,	PUNCT
ejpam-4348	2	53	ufr	ufr	PROPN
ejpam-4348	2	54	mathématiques	mathématiques	INTJ
ejpam-4348	2	55	et	et	PROPN
ejpam-4348	2	56	informatique	informatique	NOUN
ejpam-4348	2	57	,	,	PUNCT
ejpam-4348	2	58	université	université	ADJ
ejpam-4348	2	59	félix	félix	ADJ
ejpam-4348	2	60	houphouët	houphouët	PROPN
ejpam-4348	2	61	-	-	PUNCT
ejpam-4348	2	62	boigny	boigny	PROPN
ejpam-4348	2	63	,	,	PUNCT
ejpam-4348	2	64	abidjan	abidjan	PROPN
ejpam-4348	2	65	,	,	PUNCT
ejpam-4348	2	66	côte	côte	X
ejpam-4348	2	67	d’ivoire	d’ivoire	NOUN
ejpam-4348	2	68	abstract	abstract	NOUN
ejpam-4348	2	69	.	.	PUNCT
ejpam-4348	3	1	this	this	DET
ejpam-4348	3	2	paper	paper	NOUN
ejpam-4348	3	3	presents	present	VERB
ejpam-4348	3	4	methods	method	NOUN
ejpam-4348	3	5	of	of	ADP
ejpam-4348	3	6	spectral	spectral	ADJ
ejpam-4348	3	7	dichotomy	dichotomy	NOUN
ejpam-4348	3	8	of	of	ADP
ejpam-4348	3	9	a	a	DET
ejpam-4348	3	10	matrix	matrix	NOUN
ejpam-4348	3	11	which	which	PRON
ejpam-4348	3	12	compute	compute	VERB
ejpam-4348	3	13	spectral	spectral	ADJ
ejpam-4348	3	14	projectors	projector	NOUN
ejpam-4348	3	15	on	on	ADP
ejpam-4348	3	16	the	the	DET
ejpam-4348	3	17	subspace	subspace	NOUN
ejpam-4348	3	18	associated	associate	VERB
ejpam-4348	3	19	with	with	ADP
ejpam-4348	3	20	the	the	DET
ejpam-4348	3	21	eigenvalues	eigenvalue	NOUN
ejpam-4348	3	22	external	external	ADJ
ejpam-4348	3	23	to	to	ADP
ejpam-4348	3	24	the	the	DET
ejpam-4348	3	25	parabolas	parabola	NOUN
ejpam-4348	3	26	described	describe	VERB
ejpam-4348	3	27	by	by	ADP
ejpam-4348	3	28	a	a	DET
ejpam-4348	3	29	general	general	ADJ
ejpam-4348	3	30	equation	equation	NOUN
ejpam-4348	3	31	.	.	PUNCT
ejpam-4348	4	1	these	these	DET
ejpam-4348	4	2	methods	method	NOUN
ejpam-4348	4	3	are	be	AUX
ejpam-4348	4	4	modifications	modification	NOUN
ejpam-4348	4	5	of	of	ADP
ejpam-4348	4	6	the	the	DET
ejpam-4348	4	7	one	one	NOUN
ejpam-4348	4	8	proposed	propose	VERB
ejpam-4348	4	9	in	in	ADP
ejpam-4348	4	10	[	[	X
ejpam-4348	4	11	a.	a.	NOUN
ejpam-4348	4	12	n.	n.	PROPN
ejpam-4348	4	13	malyshev	malyshev	PROPN
ejpam-4348	4	14	and	and	CCONJ
ejpam-4348	4	15	m.	m.	NOUN
ejpam-4348	4	16	sadkane	sadkane	PROPN
ejpam-4348	4	17	,	,	PUNCT
ejpam-4348	4	18	siam	siam	ADJ
ejpam-4348	4	19	j.	j.	PROPN
ejpam-4348	4	20	matrix	matrix	PROPN
ejpam-4348	4	21	anal	anal	PROPN
ejpam-4348	4	22	.	.	PUNCT
ejpam-4348	5	1	appl	appl	PROPN
ejpam-4348	5	2	.	.	PROPN
ejpam-4348	6	1	18	18	NUM
ejpam-4348	6	2	(	(	PUNCT
ejpam-4348	6	3	2	2	NUM
ejpam-4348	6	4	)	)	PUNCT
ejpam-4348	6	5	,	,	PUNCT
ejpam-4348	6	6	265	265	NUM
ejpam-4348	6	7	-	-	SYM
ejpam-4348	6	8	278	278	NUM
ejpam-4348	6	9	,	,	PUNCT
ejpam-4348	6	10	1997	1997	NUM
ejpam-4348	6	11	]	]	PUNCT
ejpam-4348	6	12	which	which	PRON
ejpam-4348	6	13	uses	use	VERB
ejpam-4348	6	14	the	the	DET
ejpam-4348	6	15	spectral	spectral	ADJ
ejpam-4348	6	16	dichotomy	dichotomy	NOUN
ejpam-4348	6	17	theoretical	theoretical	ADJ
ejpam-4348	6	18	and	and	CCONJ
ejpam-4348	6	19	method	method	NOUN
ejpam-4348	6	20	of	of	ADP
ejpam-4348	6	21	a	a	DET
ejpam-4348	6	22	matrix	matrix	NOUN
ejpam-4348	6	23	with	with	ADP
ejpam-4348	6	24	respect	respect	NOUN
ejpam-4348	6	25	to	to	ADP
ejpam-4348	6	26	the	the	DET
ejpam-4348	6	27	imaginary	imaginary	ADJ
ejpam-4348	6	28	axis	axis	NOUN
ejpam-4348	6	29	.	.	PUNCT
ejpam-4348	7	1	algorithmic	algorithmic	ADJ
ejpam-4348	7	2	aspects	aspect	NOUN
ejpam-4348	7	3	of	of	ADP
ejpam-4348	7	4	the	the	DET
ejpam-4348	7	5	methods	method	NOUN
ejpam-4348	7	6	are	be	AUX
ejpam-4348	7	7	developed	develop	VERB
ejpam-4348	7	8	.	.	PUNCT
ejpam-4348	8	1	numerical	numerical	ADJ
ejpam-4348	8	2	results	result	NOUN
ejpam-4348	8	3	obtained	obtain	VERB
ejpam-4348	8	4	by	by	ADP
ejpam-4348	8	5	applying	apply	VERB
ejpam-4348	8	6	methods	method	NOUN
ejpam-4348	8	7	presented	present	VERB
ejpam-4348	8	8	on	on	ADP
ejpam-4348	8	9	matrices	matrix	NOUN
ejpam-4348	8	10	are	be	AUX
ejpam-4348	8	11	reported	report	VERB
ejpam-4348	8	12	.	.	PUNCT
ejpam-4348	9	1	2020	2020	NUM
ejpam-4348	9	2	mathematics	mathematic	NOUN
ejpam-4348	9	3	subject	subject	NOUN
ejpam-4348	9	4	classifications	classification	NOUN
ejpam-4348	9	5	:	:	PUNCT
ejpam-4348	9	6	65f15	65f15	NUM
ejpam-4348	9	7	,	,	PUNCT
ejpam-4348	9	8	34d09	34d09	NUM
ejpam-4348	9	9	,	,	PUNCT
ejpam-4348	9	10	47a46	47a46	NUM
ejpam-4348	9	11	key	key	ADJ
ejpam-4348	9	12	words	word	NOUN
ejpam-4348	9	13	and	and	CCONJ
ejpam-4348	9	14	phrases	phrase	NOUN
ejpam-4348	9	15	:	:	PUNCT
ejpam-4348	9	16	spectral	spectral	ADJ
ejpam-4348	9	17	dichotomy	dichotomy	NOUN
ejpam-4348	9	18	method	method	NOUN
ejpam-4348	9	19	,	,	PUNCT
ejpam-4348	9	20	spectral	spectral	ADJ
ejpam-4348	9	21	projector	projector	NOUN
ejpam-4348	9	22	,	,	PUNCT
ejpam-4348	9	23	eigensubspaces	eigensubspace	NOUN
ejpam-4348	9	24	,	,	PUNCT
ejpam-4348	9	25	eigenvalues	eigenvalue	VERB
ejpam-4348	9	26	.	.	PUNCT
ejpam-4348	10	1	1	1	X
ejpam-4348	10	2	.	.	X
ejpam-4348	10	3	introduction	introduction	NOUN
ejpam-4348	10	4	let	let	VERB
ejpam-4348	10	5	a	a	DET
ejpam-4348	10	6	∈	∈	ADJ
ejpam-4348	10	7	rn×n	rn×n	NOUN
ejpam-4348	10	8	(	(	PUNCT
ejpam-4348	10	9	n	n	CCONJ
ejpam-4348	10	10	>	>	SYM
ejpam-4348	10	11	1	1	X
ejpam-4348	10	12	)	)	PUNCT
ejpam-4348	10	13	be	be	AUX
ejpam-4348	10	14	a	a	DET
ejpam-4348	10	15	matrix	matrix	NOUN
ejpam-4348	10	16	and	and	CCONJ
ejpam-4348	10	17	γ(a	γ(a	PROPN
ejpam-4348	10	18	,	,	PUNCT
ejpam-4348	10	19	b	b	NOUN
ejpam-4348	10	20	,	,	PUNCT
ejpam-4348	10	21	c	c	NOUN
ejpam-4348	10	22	)	)	PUNCT
ejpam-4348	10	23	a	a	DET
ejpam-4348	10	24	parabola	parabola	NOUN
ejpam-4348	10	25	with	with	ADP
ejpam-4348	10	26	an	an	DET
ejpam-4348	10	27	equation	equation	NOUN
ejpam-4348	10	28	of	of	ADP
ejpam-4348	10	29	the	the	DET
ejpam-4348	10	30	type	type	NOUN
ejpam-4348	10	31	x	x	X
ejpam-4348	11	1	=	=	PUNCT
ejpam-4348	11	2	ay2	ay2	NOUN
ejpam-4348	11	3	+	+	X
ejpam-4348	11	4	by	by	ADV
ejpam-4348	11	5	+	+	CCONJ
ejpam-4348	11	6	c	c	PROPN
ejpam-4348	11	7	a	a	DET
ejpam-4348	11	8	̸=	̸=	PROPN
ejpam-4348	11	9	0	0	NUM
ejpam-4348	11	10	.	.	PUNCT
ejpam-4348	12	1	(	(	PUNCT
ejpam-4348	12	2	1	1	X
ejpam-4348	12	3	)	)	PUNCT
ejpam-4348	12	4	the	the	DET
ejpam-4348	12	5	aim	aim	NOUN
ejpam-4348	12	6	of	of	ADP
ejpam-4348	12	7	this	this	DET
ejpam-4348	12	8	paper	paper	NOUN
ejpam-4348	12	9	is	be	AUX
ejpam-4348	12	10	to	to	PART
ejpam-4348	12	11	propose	propose	VERB
ejpam-4348	12	12	spectral	spectral	ADJ
ejpam-4348	12	13	dichotomy	dichotomy	NOUN
ejpam-4348	12	14	methods	method	NOUN
ejpam-4348	12	15	which	which	PRON
ejpam-4348	12	16	partition	partition	VERB
ejpam-4348	12	17	the	the	DET
ejpam-4348	12	18	spectrum	spectrum	NOUN
ejpam-4348	12	19	of	of	ADP
ejpam-4348	12	20	matrix	matrix	NOUN
ejpam-4348	12	21	a	a	PRON
ejpam-4348	12	22	into	into	ADP
ejpam-4348	12	23	two	two	NUM
ejpam-4348	12	24	parts	part	NOUN
ejpam-4348	12	25	:	:	PUNCT
ejpam-4348	12	26	a	a	DET
ejpam-4348	12	27	first	first	ADJ
ejpam-4348	12	28	part	part	NOUN
ejpam-4348	12	29	inside	inside	ADP
ejpam-4348	12	30	the	the	DET
ejpam-4348	12	31	parabola	parabola	NOUN
ejpam-4348	12	32	and	and	CCONJ
ejpam-4348	12	33	a	a	DET
ejpam-4348	12	34	second	second	ADJ
ejpam-4348	12	35	one	one	NUM
ejpam-4348	12	36	outside	outside	ADV
ejpam-4348	12	37	.	.	PUNCT
ejpam-4348	13	1	this	this	PRON
ejpam-4348	13	2	will	will	AUX
ejpam-4348	13	3	lead	lead	VERB
ejpam-4348	13	4	to	to	ADP
ejpam-4348	13	5	the	the	DET
ejpam-4348	13	6	calculation	calculation	NOUN
ejpam-4348	13	7	of	of	ADP
ejpam-4348	13	8	the	the	DET
ejpam-4348	13	9	projectors	projector	NOUN
ejpam-4348	13	10	associated	associate	VERB
ejpam-4348	13	11	respectively	respectively	ADV
ejpam-4348	13	12	with	with	ADP
ejpam-4348	13	13	the	the	DET
ejpam-4348	13	14	eigenvalues	eigenvalue	NOUN
ejpam-4348	13	15	inside	inside	ADP
ejpam-4348	13	16	and	and	CCONJ
ejpam-4348	13	17	outside	outside	ADP
ejpam-4348	13	18	the	the	DET
ejpam-4348	13	19	parabola	parabola	PROPN
ejpam-4348	13	20	.	.	PUNCT
ejpam-4348	14	1	equation	equation	NOUN
ejpam-4348	14	2	(	(	PUNCT
ejpam-4348	14	3	1	1	X
ejpam-4348	14	4	)	)	PUNCT
ejpam-4348	14	5	reduces	reduce	VERB
ejpam-4348	14	6	to	to	ADP
ejpam-4348	14	7	the	the	DET
ejpam-4348	14	8	following	follow	VERB
ejpam-4348	14	9	form	form	NOUN
ejpam-4348	14	10	x	x	PUNCT
ejpam-4348	14	11	=	=	PUNCT
ejpam-4348	14	12	a	a	PRON
ejpam-4348	14	13	[	[	X
ejpam-4348	14	14	(	(	PUNCT
ejpam-4348	14	15	y	y	PROPN
ejpam-4348	14	16	+	+	CCONJ
ejpam-4348	14	17	b	b	PROPN
ejpam-4348	14	18	2a	2a	NUM
ejpam-4348	14	19	)	)	PUNCT
ejpam-4348	14	20	2	2	NUM
ejpam-4348	14	21	−	−	NOUN
ejpam-4348	14	22	disc	disc	NOUN
ejpam-4348	14	23	4a2	4a2	NUM
ejpam-4348	14	24	]	]	PUNCT
ejpam-4348	14	25	(	(	PUNCT
ejpam-4348	14	26	2	2	X
ejpam-4348	14	27	)	)	PUNCT
ejpam-4348	14	28	∗corresponding	∗corresponde	VERB
ejpam-4348	14	29	author	author	NOUN
ejpam-4348	14	30	.	.	PUNCT
ejpam-4348	15	1	doi	doi	NOUN
ejpam-4348	15	2	:	:	PUNCT
ejpam-4348	15	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4348	https://doi.org/10.29020/nybg.ejpam.v15i2.4348	ADJ
ejpam-4348	15	4	email	email	NOUN
ejpam-4348	15	5	addresses	address	NOUN
ejpam-4348	15	6	:	:	PUNCT
ejpam-4348	15	7	tsaid06@yahoo.fr	tsaid06@yahoo.fr	PROPN
ejpam-4348	15	8	(	(	PUNCT
ejpam-4348	15	9	s.	s.	PROPN
ejpam-4348	15	10	traoré	traoré	PROPN
ejpam-4348	15	11	)	)	PUNCT
ejpam-4348	15	12	,	,	PUNCT
ejpam-4348	15	13	mouhamadou.dosso@univ-fhb.edu.ci	mouhamadou.dosso@univ-fhb.edu.ci	NOUN
ejpam-4348	15	14	(	(	PUNCT
ejpam-4348	15	15	m.	m.	NOUN
ejpam-4348	15	16	dosso	dosso	PROPN
ejpam-4348	15	17	)	)	PUNCT
ejpam-4348	15	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4348	16	1	681	681	NUM
ejpam-4348	16	2	©	©	PROPN
ejpam-4348	16	3	2022	2022	NUM
ejpam-4348	16	4	ejpam	ejpam	VERB
ejpam-4348	16	5	all	all	DET
ejpam-4348	16	6	rights	right	NOUN
ejpam-4348	16	7	reserved	reserve	VERB
ejpam-4348	16	8	.	.	PUNCT
ejpam-4348	17	1	s.	s.	PROPN
ejpam-4348	17	2	traoré	traoré	PROPN
ejpam-4348	17	3	,	,	PUNCT
ejpam-4348	17	4	m.	m.	NOUN
ejpam-4348	17	5	dosso	dosso	PROPN
ejpam-4348	17	6	/	/	SYM
ejpam-4348	17	7	eur	eur	PROPN
ejpam-4348	17	8	.	.	PUNCT
ejpam-4348	18	1	j.	j.	PROPN
ejpam-4348	18	2	pure	pure	PROPN
ejpam-4348	18	3	appl	appl	PROPN
ejpam-4348	18	4	.	.	PROPN
ejpam-4348	18	5	math	math	PROPN
ejpam-4348	18	6	,	,	PUNCT
ejpam-4348	18	7	15	15	NUM
ejpam-4348	18	8	(	(	PUNCT
ejpam-4348	18	9	2	2	NUM
ejpam-4348	18	10	)	)	PUNCT
ejpam-4348	18	11	(	(	PUNCT
ejpam-4348	18	12	2022	2022	NUM
ejpam-4348	18	13	)	)	PUNCT
ejpam-4348	18	14	,	,	PUNCT
ejpam-4348	18	15	681	681	NUM
ejpam-4348	18	16	-	-	SYM
ejpam-4348	18	17	725	725	NUM
ejpam-4348	18	18	682	682	NUM
ejpam-4348	18	19	where	where	SCONJ
ejpam-4348	18	20	disc	disc	NOUN
ejpam-4348	18	21	=	=	SYM
ejpam-4348	18	22	b2	b2	NOUN
ejpam-4348	18	23	−	−	NOUN
ejpam-4348	18	24	4ac	4ac	NOUN
ejpam-4348	18	25	;	;	PUNCT
ejpam-4348	18	26	or	or	CCONJ
ejpam-4348	18	27	again	again	ADV
ejpam-4348	18	28	1	1	NUM
ejpam-4348	18	29	a	a	DET
ejpam-4348	18	30	(	(	PUNCT
ejpam-4348	18	31	x+	x+	ADJ
ejpam-4348	18	32	disc	disc	NOUN
ejpam-4348	18	33	4a	4a	NOUN
ejpam-4348	18	34	)	)	PUNCT
ejpam-4348	19	1	=	=	PUNCT
ejpam-4348	19	2	(	(	PUNCT
ejpam-4348	19	3	y	y	PROPN
ejpam-4348	19	4	+	+	CCONJ
ejpam-4348	19	5	b	b	PROPN
ejpam-4348	19	6	2a	2a	NUM
ejpam-4348	19	7	)	)	PUNCT
ejpam-4348	19	8	2	2	NUM
ejpam-4348	19	9	(	(	PUNCT
ejpam-4348	19	10	3	3	NUM
ejpam-4348	19	11	)	)	PUNCT
ejpam-4348	19	12	throughout	throughout	ADP
ejpam-4348	19	13	this	this	DET
ejpam-4348	19	14	paper	paper	NOUN
ejpam-4348	19	15	we	we	PRON
ejpam-4348	19	16	assume	assume	VERB
ejpam-4348	19	17	that	that	SCONJ
ejpam-4348	19	18	the	the	DET
ejpam-4348	19	19	coefficient	coefficient	NOUN
ejpam-4348	19	20	a	a	PRON
ejpam-4348	19	21	has	have	VERB
ejpam-4348	19	22	a	a	DET
ejpam-4348	19	23	negative	negative	ADJ
ejpam-4348	19	24	sign	sign	NOUN
ejpam-4348	19	25	.	.	PUNCT
ejpam-4348	20	1	thus	thus	ADV
ejpam-4348	20	2	,	,	PUNCT
ejpam-4348	20	3	the	the	DET
ejpam-4348	20	4	parabola	parabola	NOUN
ejpam-4348	20	5	with	with	ADP
ejpam-4348	20	6	equation	equation	NOUN
ejpam-4348	20	7	(	(	PUNCT
ejpam-4348	20	8	3	3	X
ejpam-4348	20	9	)	)	PUNCT
ejpam-4348	20	10	takes	take	VERB
ejpam-4348	20	11	the	the	DET
ejpam-4348	20	12	form	form	NOUN
ejpam-4348	20	13	2p(d−	2p(d−	NUM
ejpam-4348	20	14	x	x	X
ejpam-4348	20	15	)	)	PUNCT
ejpam-4348	20	16	=	=	SYM
ejpam-4348	20	17	(	(	PUNCT
ejpam-4348	20	18	y	y	PROPN
ejpam-4348	20	19	−	−	PROPN
ejpam-4348	20	20	pb)2	pb)2	PROPN
ejpam-4348	20	21	(	(	PUNCT
ejpam-4348	20	22	4	4	NUM
ejpam-4348	20	23	)	)	PUNCT
ejpam-4348	20	24	by	by	ADP
ejpam-4348	20	25	setting	set	VERB
ejpam-4348	20	26	p	p	X
ejpam-4348	20	27	=	=	PUNCT
ejpam-4348	20	28	−	−	PROPN
ejpam-4348	20	29	1	1	NUM
ejpam-4348	20	30	2a	2a	NUM
ejpam-4348	20	31	and	and	CCONJ
ejpam-4348	20	32	d	d	NOUN
ejpam-4348	20	33	=	=	SYM
ejpam-4348	20	34	−disc	−disc	NOUN
ejpam-4348	20	35	4a	4a	NOUN
ejpam-4348	20	36	=	=	SYM
ejpam-4348	20	37	−b2	−b2	ADV
ejpam-4348	20	38	−	−	PROPN
ejpam-4348	20	39	4ac	4ac	NOUN
ejpam-4348	20	40	4a	4a	NOUN
ejpam-4348	20	41	we	we	PRON
ejpam-4348	20	42	assume	assume	VERB
ejpam-4348	20	43	that	that	SCONJ
ejpam-4348	20	44	the	the	DET
ejpam-4348	20	45	matrix	matrix	NOUN
ejpam-4348	20	46	a	a	PRON
ejpam-4348	20	47	has	have	VERB
ejpam-4348	20	48	no	no	DET
ejpam-4348	20	49	eigenvalues	eigenvalue	NOUN
ejpam-4348	20	50	on	on	ADP
ejpam-4348	20	51	the	the	DET
ejpam-4348	20	52	parabola	parabola	PROPN
ejpam-4348	20	53	γ(a	γ(a	PROPN
ejpam-4348	20	54	,	,	PUNCT
ejpam-4348	20	55	b	b	NOUN
ejpam-4348	20	56	,	,	PUNCT
ejpam-4348	20	57	c	c	NOUN
ejpam-4348	20	58	)	)	PUNCT
ejpam-4348	20	59	for	for	ADP
ejpam-4348	20	60	any	any	DET
ejpam-4348	20	61	variation	variation	NOUN
ejpam-4348	20	62	of	of	ADP
ejpam-4348	20	63	the	the	DET
ejpam-4348	20	64	parameters	parameter	NOUN
ejpam-4348	20	65	a	a	DET
ejpam-4348	20	66	,	,	PUNCT
ejpam-4348	20	67	b	b	PROPN
ejpam-4348	20	68	and	and	CCONJ
ejpam-4348	20	69	c	c	NOUN
ejpam-4348	20	70	with	with	ADP
ejpam-4348	20	71	a	a	DET
ejpam-4348	20	72	̸=	̸=	PROPN
ejpam-4348	20	73	0	0	NUM
ejpam-4348	20	74	.	.	PUNCT
ejpam-4348	21	1	from	from	ADP
ejpam-4348	21	2	the	the	DET
ejpam-4348	21	3	work	work	NOUN
ejpam-4348	21	4	done	do	VERB
ejpam-4348	21	5	in	in	ADP
ejpam-4348	21	6	[	[	X
ejpam-4348	21	7	13	13	NUM
ejpam-4348	21	8	,	,	PUNCT
ejpam-4348	21	9	15	15	NUM
ejpam-4348	21	10	]	]	PUNCT
ejpam-4348	21	11	,	,	PUNCT
ejpam-4348	21	12	we	we	PRON
ejpam-4348	21	13	propose	propose	VERB
ejpam-4348	21	14	in	in	ADP
ejpam-4348	21	15	this	this	DET
ejpam-4348	21	16	paper	paper	NOUN
ejpam-4348	21	17	spectral	spectral	ADJ
ejpam-4348	21	18	dichotomy	dichotomy	NOUN
ejpam-4348	21	19	methods	method	NOUN
ejpam-4348	21	20	which	which	PRON
ejpam-4348	21	21	give	give	VERB
ejpam-4348	21	22	the	the	DET
ejpam-4348	21	23	projector	projector	NOUN
ejpam-4348	21	24	p	p	NOUN
ejpam-4348	21	25	on	on	ADP
ejpam-4348	21	26	the	the	DET
ejpam-4348	21	27	subspace	subspace	NOUN
ejpam-4348	21	28	associated	associate	VERB
ejpam-4348	21	29	with	with	ADP
ejpam-4348	21	30	the	the	DET
ejpam-4348	21	31	eigenvalues	eigenvalue	NOUN
ejpam-4348	21	32	located	locate	VERB
ejpam-4348	21	33	outside	outside	ADP
ejpam-4348	21	34	of	of	ADP
ejpam-4348	21	35	γ(a	γ(a	PROPN
ejpam-4348	21	36	,	,	PUNCT
ejpam-4348	21	37	b	b	NOUN
ejpam-4348	21	38	,	,	PUNCT
ejpam-4348	21	39	c	c	NOUN
ejpam-4348	21	40	)	)	PUNCT
ejpam-4348	21	41	.	.	PUNCT
ejpam-4348	22	1	the	the	DET
ejpam-4348	22	2	paper	paper	NOUN
ejpam-4348	22	3	is	be	AUX
ejpam-4348	22	4	organized	organize	VERB
ejpam-4348	22	5	as	as	SCONJ
ejpam-4348	22	6	follows	follow	VERB
ejpam-4348	22	7	.	.	PUNCT
ejpam-4348	23	1	section	section	NOUN
ejpam-4348	23	2	2	2	NUM
ejpam-4348	23	3	gives	give	VERB
ejpam-4348	23	4	preliminaries	preliminary	NOUN
ejpam-4348	23	5	used	use	VERB
ejpam-4348	23	6	in	in	ADP
ejpam-4348	23	7	the	the	DET
ejpam-4348	23	8	implementation	implementation	NOUN
ejpam-4348	23	9	of	of	ADP
ejpam-4348	23	10	our	our	PRON
ejpam-4348	23	11	proposed	propose	VERB
ejpam-4348	23	12	methods	method	NOUN
ejpam-4348	23	13	.	.	PUNCT
ejpam-4348	24	1	it	it	PRON
ejpam-4348	24	2	consists	consist	VERB
ejpam-4348	24	3	of	of	ADP
ejpam-4348	24	4	three	three	NUM
ejpam-4348	24	5	subsections	subsection	NOUN
ejpam-4348	24	6	.	.	PUNCT
ejpam-4348	25	1	the	the	DET
ejpam-4348	25	2	first	first	ADJ
ejpam-4348	25	3	subsection	subsection	NOUN
ejpam-4348	25	4	summarizes	summarize	VERB
ejpam-4348	25	5	the	the	DET
ejpam-4348	25	6	methods	method	NOUN
ejpam-4348	25	7	of	of	ADP
ejpam-4348	25	8	spectral	spectral	ADJ
ejpam-4348	25	9	dichotomy	dichotomy	NOUN
ejpam-4348	25	10	of	of	ADP
ejpam-4348	25	11	a	a	DET
ejpam-4348	25	12	matrix	matrix	NOUN
ejpam-4348	25	13	and	and	CCONJ
ejpam-4348	25	14	a	a	DET
ejpam-4348	25	15	pencil	pencil	NOUN
ejpam-4348	25	16	of	of	ADP
ejpam-4348	25	17	matrices	matrix	NOUN
ejpam-4348	25	18	with	with	ADP
ejpam-4348	25	19	respect	respect	NOUN
ejpam-4348	25	20	to	to	ADP
ejpam-4348	25	21	a	a	DET
ejpam-4348	25	22	circle	circle	NOUN
ejpam-4348	25	23	developed	develop	VERB
ejpam-4348	25	24	respectively	respectively	ADV
ejpam-4348	25	25	by	by	ADP
ejpam-4348	25	26	m.	m.	NOUN
ejpam-4348	25	27	dosso	dosso	NOUN
ejpam-4348	25	28	and	and	CCONJ
ejpam-4348	25	29	al	al	PROPN
ejpam-4348	25	30	.	.	PUNCT
ejpam-4348	26	1	in	in	ADP
ejpam-4348	26	2	[	[	X
ejpam-4348	26	3	2	2	NUM
ejpam-4348	26	4	,	,	PUNCT
ejpam-4348	26	5	4	4	NUM
ejpam-4348	26	6	]	]	PUNCT
ejpam-4348	26	7	and	and	CCONJ
ejpam-4348	26	8	m.	m.	NOUN
ejpam-4348	26	9	sadkane	sadkane	NOUN
ejpam-4348	26	10	and	and	CCONJ
ejpam-4348	26	11	al	al	PROPN
ejpam-4348	26	12	.	.	PUNCT
ejpam-4348	27	1	in	in	ADP
ejpam-4348	27	2	[	[	X
ejpam-4348	27	3	15	15	NUM
ejpam-4348	27	4	]	]	PUNCT
ejpam-4348	27	5	.	.	PUNCT
ejpam-4348	28	1	the	the	DET
ejpam-4348	28	2	second	second	ADJ
ejpam-4348	28	3	subsection	subsection	NOUN
ejpam-4348	28	4	makes	make	VERB
ejpam-4348	28	5	a	a	DET
ejpam-4348	28	6	brief	brief	ADJ
ejpam-4348	28	7	presentation	presentation	NOUN
ejpam-4348	28	8	of	of	ADP
ejpam-4348	28	9	the	the	DET
ejpam-4348	28	10	spectral	spectral	ADJ
ejpam-4348	28	11	dichotomy	dichotomy	NOUN
ejpam-4348	28	12	method	method	NOUN
ejpam-4348	28	13	of	of	ADP
ejpam-4348	28	14	a	a	DET
ejpam-4348	28	15	matrix	matrix	NOUN
ejpam-4348	28	16	with	with	ADP
ejpam-4348	28	17	respect	respect	NOUN
ejpam-4348	28	18	to	to	ADP
ejpam-4348	28	19	the	the	DET
ejpam-4348	28	20	imaginary	imaginary	ADJ
ejpam-4348	28	21	axis	axis	NOUN
ejpam-4348	28	22	(	(	PUNCT
ejpam-4348	28	23	see	see	VERB
ejpam-4348	28	24	[	[	X
ejpam-4348	28	25	15	15	NUM
ejpam-4348	28	26	]	]	NUM
ejpam-4348	28	27	)	)	PUNCT
ejpam-4348	28	28	.	.	PUNCT
ejpam-4348	29	1	the	the	DET
ejpam-4348	29	2	last	last	ADJ
ejpam-4348	29	3	subsection	subsection	NOUN
ejpam-4348	29	4	presents	present	VERB
ejpam-4348	29	5	the	the	DET
ejpam-4348	29	6	study	study	NOUN
ejpam-4348	29	7	made	make	VERB
ejpam-4348	29	8	by	by	ADP
ejpam-4348	29	9	a.n.malyshev	a.n.malyshev	NOUN
ejpam-4348	29	10	and	and	CCONJ
ejpam-4348	29	11	m.sadkane	m.sadkane	ADJ
ejpam-4348	29	12	in	in	ADP
ejpam-4348	29	13	[	[	X
ejpam-4348	29	14	13	13	NUM
ejpam-4348	29	15	]	]	PUNCT
ejpam-4348	29	16	.	.	PUNCT
ejpam-4348	30	1	section	section	NOUN
ejpam-4348	30	2	3	3	NUM
ejpam-4348	30	3	presents	present	VERB
ejpam-4348	30	4	new	new	ADJ
ejpam-4348	30	5	methods	method	NOUN
ejpam-4348	30	6	of	of	ADP
ejpam-4348	30	7	spectral	spectral	ADJ
ejpam-4348	30	8	dichotomy	dichotomy	NOUN
ejpam-4348	30	9	of	of	ADP
ejpam-4348	30	10	a	a	DET
ejpam-4348	30	11	matrix	matrix	NOUN
ejpam-4348	30	12	with	with	ADP
ejpam-4348	30	13	respect	respect	NOUN
ejpam-4348	30	14	to	to	ADP
ejpam-4348	30	15	the	the	DET
ejpam-4348	30	16	curve	curve	PROPN
ejpam-4348	30	17	γ(a	γ(a	PROPN
ejpam-4348	30	18	,	,	PUNCT
ejpam-4348	30	19	b	b	NOUN
ejpam-4348	30	20	,	,	PUNCT
ejpam-4348	30	21	c	c	NOUN
ejpam-4348	30	22	)	)	PUNCT
ejpam-4348	30	23	for	for	ADP
ejpam-4348	30	24	variations	variation	NOUN
ejpam-4348	30	25	of	of	ADP
ejpam-4348	30	26	parameters	parameter	NOUN
ejpam-4348	30	27	a	a	DET
ejpam-4348	30	28	,	,	PUNCT
ejpam-4348	30	29	b	b	PROPN
ejpam-4348	30	30	and	and	CCONJ
ejpam-4348	30	31	c	c	NOUN
ejpam-4348	30	32	with	with	ADP
ejpam-4348	30	33	a	a	DET
ejpam-4348	30	34	̸=	̸=	PROPN
ejpam-4348	30	35	0	0	NUM
ejpam-4348	30	36	.	.	PUNCT
ejpam-4348	31	1	finally	finally	ADV
ejpam-4348	31	2	in	in	ADP
ejpam-4348	31	3	section	section	NOUN
ejpam-4348	31	4	4	4	NUM
ejpam-4348	31	5	,	,	PUNCT
ejpam-4348	31	6	numerical	numerical	ADJ
ejpam-4348	31	7	tests	test	NOUN
ejpam-4348	31	8	are	be	AUX
ejpam-4348	31	9	used	use	VERB
ejpam-4348	31	10	on	on	ADP
ejpam-4348	31	11	various	various	ADJ
ejpam-4348	31	12	examples	example	NOUN
ejpam-4348	31	13	to	to	PART
ejpam-4348	31	14	illustrate	illustrate	VERB
ejpam-4348	31	15	the	the	DET
ejpam-4348	31	16	effectiveness	effectiveness	NOUN
ejpam-4348	31	17	of	of	ADP
ejpam-4348	31	18	the	the	DET
ejpam-4348	31	19	methods	method	NOUN
ejpam-4348	31	20	presented	present	VERB
ejpam-4348	31	21	.	.	PUNCT
ejpam-4348	32	1	throughout	throughout	ADP
ejpam-4348	32	2	this	this	DET
ejpam-4348	32	3	paper	paper	NOUN
ejpam-4348	32	4	,	,	PUNCT
ejpam-4348	32	5	the	the	DET
ejpam-4348	32	6	identity	identity	NOUN
ejpam-4348	32	7	and	and	CCONJ
ejpam-4348	32	8	zero	zero	NUM
ejpam-4348	32	9	matrices	matrix	NOUN
ejpam-4348	32	10	of	of	ADP
ejpam-4348	32	11	order	order	NOUN
ejpam-4348	32	12	k	k	PRON
ejpam-4348	32	13	are	be	AUX
ejpam-4348	32	14	denoted	denote	VERB
ejpam-4348	32	15	by	by	ADP
ejpam-4348	32	16	ik	ik	PROPN
ejpam-4348	32	17	and	and	CCONJ
ejpam-4348	32	18	0k	0k	NOUN
ejpam-4348	32	19	or	or	CCONJ
ejpam-4348	32	20	just	just	ADV
ejpam-4348	32	21	i	i	PRON
ejpam-4348	32	22	and	and	CCONJ
ejpam-4348	32	23	0	0	NUM
ejpam-4348	32	24	whenever	whenever	SCONJ
ejpam-4348	32	25	the	the	DET
ejpam-4348	32	26	order	order	NOUN
ejpam-4348	32	27	is	be	AUX
ejpam-4348	32	28	clear	clear	ADJ
ejpam-4348	32	29	from	from	ADP
ejpam-4348	32	30	the	the	DET
ejpam-4348	32	31	context	context	NOUN
ejpam-4348	32	32	.	.	PUNCT
ejpam-4348	33	1	the	the	DET
ejpam-4348	33	2	2	2	NUM
ejpam-4348	33	3	-	-	PUNCT
ejpam-4348	33	4	norm	norm	NOUN
ejpam-4348	33	5	of	of	ADP
ejpam-4348	33	6	a	a	DET
ejpam-4348	33	7	matrix	matrix	NOUN
ejpam-4348	33	8	a	a	PRON
ejpam-4348	33	9	is	be	AUX
ejpam-4348	33	10	denoted	denote	VERB
ejpam-4348	33	11	by	by	ADP
ejpam-4348	33	12	∥a∥.	∥a∥.	PROPN
ejpam-4348	33	13	2	2	NUM
ejpam-4348	33	14	.	.	PUNCT
ejpam-4348	33	15	preliminaries	preliminary	NOUN
ejpam-4348	33	16	on	on	ADP
ejpam-4348	33	17	spectral	spectral	ADJ
ejpam-4348	33	18	dichotomy	dichotomy	NOUN
ejpam-4348	33	19	methods	method	NOUN
ejpam-4348	33	20	2.1	2.1	NUM
ejpam-4348	33	21	.	.	PUNCT
ejpam-4348	34	1	spectral	spectral	ADJ
ejpam-4348	34	2	dichotomy	dichotomy	NOUN
ejpam-4348	34	3	with	with	ADP
ejpam-4348	34	4	respect	respect	NOUN
ejpam-4348	34	5	to	to	ADP
ejpam-4348	34	6	a	a	DET
ejpam-4348	34	7	circle	circle	NOUN
ejpam-4348	34	8	let	let	VERB
ejpam-4348	34	9	a	a	PRON
ejpam-4348	34	10	be	be	AUX
ejpam-4348	34	11	a	a	DET
ejpam-4348	34	12	matrix	matrix	NOUN
ejpam-4348	34	13	having	have	VERB
ejpam-4348	34	14	no	no	DET
ejpam-4348	34	15	eigenvalues	eigenvalue	NOUN
ejpam-4348	34	16	on	on	ADP
ejpam-4348	34	17	the	the	DET
ejpam-4348	34	18	circle	circle	NOUN
ejpam-4348	34	19	c(0	c(0	PROPN
ejpam-4348	34	20	,	,	PUNCT
ejpam-4348	34	21	r	r	NOUN
ejpam-4348	34	22	)	)	PUNCT
ejpam-4348	34	23	(	(	PUNCT
ejpam-4348	34	24	where	where	SCONJ
ejpam-4348	34	25	r	r	NOUN
ejpam-4348	34	26	>	>	X
ejpam-4348	34	27	0	0	NUM
ejpam-4348	34	28	)	)	PUNCT
ejpam-4348	34	29	.	.	PUNCT
ejpam-4348	35	1	the	the	DET
ejpam-4348	35	2	spectral	spectral	ADJ
ejpam-4348	35	3	projector	projector	NOUN
ejpam-4348	35	4	on	on	ADP
ejpam-4348	35	5	the	the	DET
ejpam-4348	35	6	subspace	subspace	NOUN
ejpam-4348	35	7	corresponding	correspond	VERB
ejpam-4348	35	8	to	to	ADP
ejpam-4348	35	9	the	the	DET
ejpam-4348	35	10	eigenvalues	eigenvalue	NOUN
ejpam-4348	35	11	inside	inside	ADP
ejpam-4348	35	12	the	the	DET
ejpam-4348	35	13	unit	unit	NOUN
ejpam-4348	35	14	circle	circle	NOUN
ejpam-4348	35	15	is	be	AUX
ejpam-4348	35	16	defined	define	VERB
ejpam-4348	35	17	by	by	ADP
ejpam-4348	35	18	p	p	NOUN
ejpam-4348	35	19	=	=	NOUN
ejpam-4348	35	20	1	1	NUM
ejpam-4348	35	21	2iπ	2iπ	NOUN
ejpam-4348	35	22	∫	∫	PROPN
ejpam-4348	35	23	c	c	NOUN
ejpam-4348	35	24	(	(	PUNCT
ejpam-4348	35	25	zin	zin	NOUN
ejpam-4348	35	26	−a)−1dz	−a)−1dz	PUNCT
ejpam-4348	35	27	=	=	SYM
ejpam-4348	36	1	1	1	NUM
ejpam-4348	36	2	2π	2π	NUM
ejpam-4348	36	3	∫	∫	PROPN
ejpam-4348	36	4	2π	2π	NOUN
ejpam-4348	36	5	0	0	PUNCT
ejpam-4348	37	1	(	(	PUNCT
ejpam-4348	37	2	in	in	ADP
ejpam-4348	37	3	−	−	PROPN
ejpam-4348	37	4	e−iθ	e−iθ	NOUN
ejpam-4348	37	5	r	r	NOUN
ejpam-4348	37	6	a	a	PRON
ejpam-4348	37	7	)	)	PUNCT
ejpam-4348	37	8	−1	−1	NOUN
ejpam-4348	37	9	dθ	dθ	NOUN
ejpam-4348	37	10	(	(	PUNCT
ejpam-4348	37	11	5	5	NUM
ejpam-4348	37	12	)	)	PUNCT
ejpam-4348	37	13	the	the	DET
ejpam-4348	37	14	computation	computation	NOUN
ejpam-4348	37	15	of	of	ADP
ejpam-4348	37	16	the	the	DET
ejpam-4348	37	17	spectral	spectral	ADJ
ejpam-4348	37	18	projector	projector	NOUN
ejpam-4348	37	19	is	be	AUX
ejpam-4348	37	20	accompanied	accompany	VERB
ejpam-4348	37	21	by	by	ADP
ejpam-4348	37	22	that	that	PRON
ejpam-4348	37	23	of	of	ADP
ejpam-4348	37	24	the	the	DET
ejpam-4348	37	25	hermitian	hermitian	ADJ
ejpam-4348	37	26	matrix	matrix	NOUN
ejpam-4348	37	27	defined	define	VERB
ejpam-4348	37	28	by	by	ADP
ejpam-4348	37	29	:	:	PUNCT
ejpam-4348	37	30	s.	s.	PROPN
ejpam-4348	37	31	traoré	traoré	PROPN
ejpam-4348	37	32	,	,	PUNCT
ejpam-4348	37	33	m.	m.	NOUN
ejpam-4348	37	34	dosso	dosso	PROPN
ejpam-4348	37	35	/	/	SYM
ejpam-4348	37	36	eur	eur	PROPN
ejpam-4348	37	37	.	.	PUNCT
ejpam-4348	38	1	j.	j.	PROPN
ejpam-4348	38	2	pure	pure	PROPN
ejpam-4348	38	3	appl	appl	PROPN
ejpam-4348	38	4	.	.	PROPN
ejpam-4348	38	5	math	math	PROPN
ejpam-4348	38	6	,	,	PUNCT
ejpam-4348	38	7	15	15	NUM
ejpam-4348	38	8	(	(	PUNCT
ejpam-4348	38	9	2	2	NUM
ejpam-4348	38	10	)	)	PUNCT
ejpam-4348	38	11	(	(	PUNCT
ejpam-4348	38	12	2022	2022	NUM
ejpam-4348	38	13	)	)	PUNCT
ejpam-4348	38	14	,	,	PUNCT
ejpam-4348	38	15	681	681	NUM
ejpam-4348	38	16	-	-	SYM
ejpam-4348	38	17	725	725	NUM
ejpam-4348	38	18	683	683	NUM
ejpam-4348	38	19	h	h	NOUN
ejpam-4348	38	20	=	=	SYM
ejpam-4348	38	21	h(r	h(r	NOUN
ejpam-4348	38	22	)	)	PUNCT
ejpam-4348	38	23	=	=	SYM
ejpam-4348	39	1	1	1	NUM
ejpam-4348	39	2	2π	2π	NUM
ejpam-4348	39	3	∫	∫	PROPN
ejpam-4348	39	4	2π	2π	NOUN
ejpam-4348	39	5	0	0	PUNCT
ejpam-4348	40	1	(	(	PUNCT
ejpam-4348	40	2	i	i	PRON
ejpam-4348	40	3	−	−	VERB
ejpam-4348	40	4	e−iθa	e−iθa	ADJ
ejpam-4348	40	5	r	r	NOUN
ejpam-4348	40	6	)	)	PUNCT
ejpam-4348	40	7	−∗	−∗	X
ejpam-4348	41	1	h(0	h(0	PROPN
ejpam-4348	41	2	)	)	PUNCT
ejpam-4348	41	3	(	(	PUNCT
ejpam-4348	41	4	i	i	PRON
ejpam-4348	41	5	−	−	VERB
ejpam-4348	41	6	e−iθa	e−iθa	ADJ
ejpam-4348	41	7	r	r	NOUN
ejpam-4348	41	8	)	)	PUNCT
ejpam-4348	41	9	−1	−1	NOUN
ejpam-4348	41	10	dθ	dθ	PROPN
ejpam-4348	41	11	,	,	PUNCT
ejpam-4348	41	12	(	(	PUNCT
ejpam-4348	41	13	6	6	NUM
ejpam-4348	41	14	)	)	PUNCT
ejpam-4348	41	15	with	with	ADP
ejpam-4348	41	16	h(0	h(0	PROPN
ejpam-4348	41	17	)	)	PUNCT
ejpam-4348	41	18	=	=	PRON
ejpam-4348	41	19	(	(	PUNCT
ejpam-4348	41	20	h(0))∗	h(0))∗	X
ejpam-4348	41	21	>	>	X
ejpam-4348	41	22	0	0	PROPN
ejpam-4348	41	23	,	,	PUNCT
ejpam-4348	41	24	an	an	DET
ejpam-4348	41	25	arbitrary	arbitrary	ADJ
ejpam-4348	41	26	hermitian	hermitian	ADJ
ejpam-4348	41	27	positive	positive	ADJ
ejpam-4348	41	28	definite	definite	ADJ
ejpam-4348	41	29	matrix	matrix	NOUN
ejpam-4348	41	30	used	use	VERB
ejpam-4348	41	31	for	for	ADP
ejpam-4348	41	32	scaling	scale	VERB
ejpam-4348	41	33	purpose	purpose	NOUN
ejpam-4348	41	34	.	.	PUNCT
ejpam-4348	42	1	remark	remark	NOUN
ejpam-4348	42	2	1	1	NUM
ejpam-4348	42	3	.	.	PUNCT
ejpam-4348	43	1	the	the	DET
ejpam-4348	43	2	spectral	spectral	ADJ
ejpam-4348	43	3	norm	norm	NOUN
ejpam-4348	43	4	of	of	ADP
ejpam-4348	43	5	h	h	NOUN
ejpam-4348	43	6	indicates	indicate	VERB
ejpam-4348	43	7	the	the	DET
ejpam-4348	43	8	behavior	behavior	NOUN
ejpam-4348	43	9	of	of	ADP
ejpam-4348	43	10	the	the	DET
ejpam-4348	43	11	spectral	spectral	ADJ
ejpam-4348	43	12	projector	projector	NOUN
ejpam-4348	43	13	p.	p.	NOUN
ejpam-4348	43	14	the	the	DET
ejpam-4348	43	15	smaller	small	ADJ
ejpam-4348	43	16	∥h∥	∥h∥	NOUN
ejpam-4348	43	17	is	be	AUX
ejpam-4348	43	18	,	,	PUNCT
ejpam-4348	43	19	better	well	ADJ
ejpam-4348	43	20	is	be	AUX
ejpam-4348	43	21	the	the	DET
ejpam-4348	43	22	quality	quality	NOUN
ejpam-4348	43	23	of	of	ADP
ejpam-4348	43	24	the	the	DET
ejpam-4348	43	25	dichotomy	dichotomy	NOUN
ejpam-4348	43	26	.	.	PUNCT
ejpam-4348	44	1	the	the	DET
ejpam-4348	44	2	couple	couple	NOUN
ejpam-4348	44	3	of	of	ADP
ejpam-4348	44	4	matrices	matrix	NOUN
ejpam-4348	44	5	(	(	PUNCT
ejpam-4348	44	6	p	p	X
ejpam-4348	44	7	,	,	PUNCT
ejpam-4348	44	8	h	h	NOUN
ejpam-4348	44	9	)	)	PUNCT
ejpam-4348	44	10	is	be	AUX
ejpam-4348	44	11	the	the	DET
ejpam-4348	44	12	only	only	ADJ
ejpam-4348	44	13	solution	solution	NOUN
ejpam-4348	44	14	of	of	ADP
ejpam-4348	44	15	the	the	DET
ejpam-4348	44	16	generalized	generalized	ADJ
ejpam-4348	44	17	lyapunov	lyapunov	NOUN
ejpam-4348	44	18	’s	’s	PART
ejpam-4348	44	19	equation	equation	NOUN
ejpam-4348	44	20	[	[	X
ejpam-4348	44	21	8	8	NUM
ejpam-4348	44	22	]	]	PUNCT
ejpam-4348	44	23			NUM
ejpam-4348	44	24	r2h−a∗ha	r2h−a∗ha	PROPN
ejpam-4348	44	25	=	=	SYM
ejpam-4348	44	26	p∗h(0)p−	p∗h(0)p−	PROPN
ejpam-4348	44	27	(	(	PUNCT
ejpam-4348	44	28	i	i	PRON
ejpam-4348	44	29	−	−	PROPN
ejpam-4348	45	1	p)∗h(0)(i	p)∗h(0)(i	NOUN
ejpam-4348	45	2	−	−	PROPN
ejpam-4348	46	1	p	p	X
ejpam-4348	46	2	)	)	PUNCT
ejpam-4348	46	3	pa	pa	PROPN
ejpam-4348	46	4	=	=	PROPN
ejpam-4348	46	5	ap	ap	PROPN
ejpam-4348	46	6	p2	p2	PROPN
ejpam-4348	47	1	=	=	PUNCT
ejpam-4348	47	2	p	p	X
ejpam-4348	47	3	ph	ph	NOUN
ejpam-4348	47	4	=	=	SYM
ejpam-4348	47	5	(	(	PUNCT
ejpam-4348	47	6	ph)∗	ph)∗	PROPN
ejpam-4348	47	7	(	(	PUNCT
ejpam-4348	47	8	7	7	NUM
ejpam-4348	47	9	)	)	PUNCT
ejpam-4348	47	10	that	that	PRON
ejpam-4348	47	11	generalized	generalized	ADJ
ejpam-4348	47	12	equation	equation	NOUN
ejpam-4348	47	13	was	be	AUX
ejpam-4348	47	14	first	first	ADV
ejpam-4348	47	15	proposed	propose	VERB
ejpam-4348	47	16	by	by	ADP
ejpam-4348	47	17	godunov	godunov	NOUN
ejpam-4348	47	18	in	in	ADP
ejpam-4348	47	19	partial	partial	ADJ
ejpam-4348	47	20	form	form	NOUN
ejpam-4348	47	21	in	in	ADP
ejpam-4348	47	22	[	[	X
ejpam-4348	47	23	7	7	NUM
ejpam-4348	47	24	]	]	PUNCT
ejpam-4348	47	25	and	and	CCONJ
ejpam-4348	47	26	later	later	ADV
ejpam-4348	47	27	by	by	ADP
ejpam-4348	47	28	bulgakov	bulgakov	NOUN
ejpam-4348	47	29	in	in	ADP
ejpam-4348	47	30	complete	complete	ADJ
ejpam-4348	47	31	form	form	NOUN
ejpam-4348	47	32	(	(	PUNCT
ejpam-4348	47	33	7	7	NUM
ejpam-4348	47	34	)	)	PUNCT
ejpam-4348	47	35	in	in	ADP
ejpam-4348	47	36	[	[	X
ejpam-4348	47	37	1	1	NUM
ejpam-4348	47	38	]	]	PUNCT
ejpam-4348	47	39	.	.	PUNCT
ejpam-4348	48	1	the	the	DET
ejpam-4348	48	2	most	most	ADV
ejpam-4348	48	3	efficient	efficient	ADJ
ejpam-4348	48	4	numerical	numerical	ADJ
ejpam-4348	48	5	method	method	NOUN
ejpam-4348	48	6	for	for	ADP
ejpam-4348	48	7	the	the	DET
ejpam-4348	48	8	circular	circular	ADJ
ejpam-4348	48	9	dichotomy	dichotomy	NOUN
ejpam-4348	48	10	was	be	AUX
ejpam-4348	48	11	first	first	ADV
ejpam-4348	48	12	proposed	propose	VERB
ejpam-4348	48	13	in	in	ADP
ejpam-4348	48	14	[	[	X
ejpam-4348	48	15	10	10	NUM
ejpam-4348	48	16	]	]	PUNCT
ejpam-4348	48	17	and	and	CCONJ
ejpam-4348	48	18	[	[	X
ejpam-4348	48	19	12	12	NUM
ejpam-4348	48	20	]	]	PUNCT
ejpam-4348	48	21	.	.	PUNCT
ejpam-4348	49	1	moreover	moreover	ADV
ejpam-4348	49	2	,	,	PUNCT
ejpam-4348	49	3	for	for	ADP
ejpam-4348	49	4	any	any	DET
ejpam-4348	49	5	vector	vector	NOUN
ejpam-4348	49	6	x	x	PUNCT
ejpam-4348	49	7	and	and	CCONJ
ejpam-4348	49	8	for	for	ADP
ejpam-4348	49	9	any	any	DET
ejpam-4348	49	10	integer	integer	NOUN
ejpam-4348	49	11	k	k	NOUN
ejpam-4348	49	12	,	,	PUNCT
ejpam-4348	49	13	we	we	PRON
ejpam-4348	49	14	have	have	VERB
ejpam-4348	49	15	the	the	DET
ejpam-4348	49	16	estimates	estimate	NOUN
ejpam-4348	49	17	[	[	X
ejpam-4348	49	18	4	4	NUM
ejpam-4348	49	19	,	,	PUNCT
ejpam-4348	49	20	6	6	NUM
ejpam-4348	49	21	,	,	PUNCT
ejpam-4348	49	22	14	14	NUM
ejpam-4348	49	23	]	]	PUNCT
ejpam-4348	49	24	∥akpx∥	∥akpx∥	ADP
ejpam-4348	49	25	≤	≤	NOUN
ejpam-4348	49	26	√	√	NUM
ejpam-4348	49	27	∥h∥∥h−1∥∥	∥h∥∥h−1∥∥	NOUN
ejpam-4348	49	28	(	(	PUNCT
ejpam-4348	49	29	1−	1−	NUM
ejpam-4348	49	30	1	1	NUM
ejpam-4348	49	31	∥h∥	∥h∥	NOUN
ejpam-4348	49	32	)	)	PUNCT
ejpam-4348	49	33	k	k	NOUN
ejpam-4348	49	34	2	2	NUM
ejpam-4348	49	35	∥x∥	∥x∥	NOUN
ejpam-4348	49	36	∥akpx∥	∥akpx∥	NOUN
ejpam-4348	49	37	≥	≥	NOUN
ejpam-4348	49	38	1√	1√	NUM
ejpam-4348	49	39	∥h∥∥h−1∥∥	∥h∥∥h−1∥∥	NOUN
ejpam-4348	49	40	(	(	PUNCT
ejpam-4348	49	41	1	1	NUM
ejpam-4348	49	42	+	+	NUM
ejpam-4348	49	43	1	1	NUM
ejpam-4348	49	44	∥h∥	∥h∥	NOUN
ejpam-4348	49	45	)	)	PUNCT
ejpam-4348	49	46	k	k	NOUN
ejpam-4348	49	47	2	2	NUM
ejpam-4348	49	48	∥(i	∥(i	NOUN
ejpam-4348	49	49	−	−	NOUN
ejpam-4348	49	50	p)x∥	p)x∥	NOUN
ejpam-4348	49	51	(	(	PUNCT
ejpam-4348	49	52	8)	8)	NUM
ejpam-4348	49	53	which	which	PRON
ejpam-4348	49	54	shows	show	VERB
ejpam-4348	49	55	the	the	DET
ejpam-4348	49	56	importance	importance	NOUN
ejpam-4348	49	57	of	of	ADP
ejpam-4348	49	58	the	the	DET
ejpam-4348	49	59	quantity	quantity	NOUN
ejpam-4348	49	60	∥h∥	∥h∥	NOUN
ejpam-4348	49	61	on	on	ADP
ejpam-4348	49	62	asymptotic	asymptotic	ADJ
ejpam-4348	49	63	decay	decay	NOUN
ejpam-4348	49	64	to	to	ADP
ejpam-4348	49	65	0	0	NUM
ejpam-4348	49	66	(	(	PUNCT
ejpam-4348	49	67	or	or	CCONJ
ejpam-4348	49	68	growth	growth	NOUN
ejpam-4348	49	69	to	to	ADP
ejpam-4348	49	70	+	+	NOUN
ejpam-4348	49	71	∞	∞	NOUN
ejpam-4348	49	72	)	)	PUNCT
ejpam-4348	49	73	of	of	ADP
ejpam-4348	49	74	the	the	DET
ejpam-4348	49	75	powers	power	NOUN
ejpam-4348	49	76	of	of	ADP
ejpam-4348	49	77	a.	a.	NOUN
ejpam-4348	49	78	different	different	ADJ
ejpam-4348	49	79	authors	author	NOUN
ejpam-4348	49	80	have	have	AUX
ejpam-4348	49	81	proposed	propose	VERB
ejpam-4348	49	82	methods	method	NOUN
ejpam-4348	49	83	for	for	ADP
ejpam-4348	49	84	determining	determine	VERB
ejpam-4348	49	85	the	the	DET
ejpam-4348	49	86	projector	projector	NOUN
ejpam-4348	49	87	p	p	NOUN
ejpam-4348	49	88	and	and	CCONJ
ejpam-4348	49	89	the	the	DET
ejpam-4348	49	90	matrix	matrix	NOUN
ejpam-4348	49	91	h.	h.	NOUN
ejpam-4348	49	92	we	we	PRON
ejpam-4348	49	93	summarize	summarize	VERB
ejpam-4348	49	94	the	the	DET
ejpam-4348	49	95	most	most	ADV
ejpam-4348	49	96	important	important	ADJ
ejpam-4348	49	97	steps	step	NOUN
ejpam-4348	49	98	of	of	ADP
ejpam-4348	49	99	the	the	DET
ejpam-4348	49	100	method	method	NOUN
ejpam-4348	49	101	proposed	propose	VERB
ejpam-4348	49	102	in	in	ADP
ejpam-4348	49	103	[	[	X
ejpam-4348	49	104	2	2	NUM
ejpam-4348	49	105	,	,	PUNCT
ejpam-4348	49	106	4	4	NUM
ejpam-4348	49	107	]	]	PUNCT
ejpam-4348	49	108	.	.	PUNCT
ejpam-4348	50	1	note	note	VERB
ejpam-4348	50	2	that	that	SCONJ
ejpam-4348	50	3	this	this	DET
ejpam-4348	50	4	method	method	NOUN
ejpam-4348	50	5	is	be	AUX
ejpam-4348	50	6	a	a	DET
ejpam-4348	50	7	variant	variant	NOUN
ejpam-4348	50	8	of	of	ADP
ejpam-4348	50	9	an	an	DET
ejpam-4348	50	10	initial	initial	ADJ
ejpam-4348	50	11	method	method	NOUN
ejpam-4348	50	12	proposed	propose	VERB
ejpam-4348	50	13	by	by	ADP
ejpam-4348	50	14	s.k	s.k	PROPN
ejpam-4348	50	15	.	.	PROPN
ejpam-4348	50	16	godunov	godunov	PROPN
ejpam-4348	50	17	and	and	CCONJ
ejpam-4348	50	18	m.	m.	NOUN
ejpam-4348	50	19	sadkane	sadkane	NOUN
ejpam-4348	50	20	in	in	ADP
ejpam-4348	50	21	[	[	X
ejpam-4348	50	22	9	9	NUM
ejpam-4348	50	23	]	]	PUNCT
ejpam-4348	50	24	.	.	PUNCT
ejpam-4348	51	1	during	during	ADP
ejpam-4348	51	2	their	their	PRON
ejpam-4348	51	3	work	work	NOUN
ejpam-4348	51	4	,	,	PUNCT
ejpam-4348	51	5	these	these	DET
ejpam-4348	51	6	authors	author	NOUN
ejpam-4348	51	7	have	have	AUX
ejpam-4348	51	8	given	give	VERB
ejpam-4348	51	9	some	some	DET
ejpam-4348	51	10	important	important	ADJ
ejpam-4348	51	11	results	result	NOUN
ejpam-4348	51	12	.	.	PUNCT
ejpam-4348	52	1	the	the	DET
ejpam-4348	52	2	first	first	ADJ
ejpam-4348	52	3	proposition	proposition	NOUN
ejpam-4348	52	4	gives	give	VERB
ejpam-4348	52	5	the	the	DET
ejpam-4348	52	6	link	link	NOUN
ejpam-4348	52	7	in	in	ADP
ejpam-4348	52	8	the	the	DET
ejpam-4348	52	9	one	one	NUM
ejpam-4348	52	10	hand	hand	NOUN
ejpam-4348	52	11	between	between	ADP
ejpam-4348	52	12	the	the	DET
ejpam-4348	52	13	sequences	sequence	NOUN
ejpam-4348	52	14	of	of	ADP
ejpam-4348	52	15	matrices	matrix	NOUN
ejpam-4348	52	16	z	z	NOUN
ejpam-4348	52	17	(	(	PUNCT
ejpam-4348	52	18	2j+1	2j+1	NUM
ejpam-4348	52	19	)	)	PUNCT
ejpam-4348	52	20	k	k	PROPN
ejpam-4348	52	21	and	and	CCONJ
ejpam-4348	52	22	z	z	PROPN
ejpam-4348	52	23	(	(	PUNCT
ejpam-4348	52	24	2j	2j	NUM
ejpam-4348	52	25	)	)	PUNCT
ejpam-4348	52	26	k	k	NOUN
ejpam-4348	52	27	,	,	PUNCT
ejpam-4348	52	28	and	and	CCONJ
ejpam-4348	52	29	in	in	ADP
ejpam-4348	52	30	the	the	DET
ejpam-4348	52	31	other	other	ADJ
ejpam-4348	52	32	hand	hand	NOUN
ejpam-4348	52	33	between	between	ADP
ejpam-4348	52	34	hj+1	hj+1	PROPN
ejpam-4348	52	35	and	and	CCONJ
ejpam-4348	52	36	hj	hj	PROPN
ejpam-4348	52	37	.	.	PUNCT
ejpam-4348	53	1	proposition	proposition	NOUN
ejpam-4348	53	2	1	1	NUM
ejpam-4348	53	3	.	.	X
ejpam-4348	54	1	for	for	ADP
ejpam-4348	54	2	j	j	PROPN
ejpam-4348	54	3	=	=	SYM
ejpam-4348	54	4	0	0	PROPN
ejpam-4348	54	5	,	,	PUNCT
ejpam-4348	54	6	1	1	NUM
ejpam-4348	54	7	,	,	PUNCT
ejpam-4348	54	8	·	·	PUNCT
ejpam-4348	54	9	·	·	PUNCT
ejpam-4348	54	10	·	·	PUNCT
ejpam-4348	54	11	and	and	CCONJ
ejpam-4348	54	12	k	k	X
ejpam-4348	54	13	=	=	SYM
ejpam-4348	54	14	0	0	NUM
ejpam-4348	54	15	,	,	PUNCT
ejpam-4348	54	16	1	1	NUM
ejpam-4348	54	17	,	,	PUNCT
ejpam-4348	54	18	·	·	PUNCT
ejpam-4348	54	19	·	·	PUNCT
ejpam-4348	54	20	·	·	PUNCT
ejpam-4348	54	21	,	,	PUNCT
ejpam-4348	54	22	2j	2j	X
ejpam-4348	54	23	,	,	PUNCT
ejpam-4348	54	24	we	we	PRON
ejpam-4348	54	25	have	have	AUX
ejpam-4348	54	26	z	z	NOUN
ejpam-4348	54	27	(	(	PUNCT
ejpam-4348	54	28	2j+1	2j+1	NUM
ejpam-4348	54	29	)	)	PUNCT
ejpam-4348	55	1	k	k	NOUN
ejpam-4348	56	1	=	=	PUNCT
ejpam-4348	56	2	z	z	NOUN
ejpam-4348	56	3	(	(	PUNCT
ejpam-4348	56	4	2j	2j	NUM
ejpam-4348	56	5	)	)	PUNCT
ejpam-4348	56	6	k	k	NOUN
ejpam-4348	56	7	kj+1	kj+1	X
ejpam-4348	56	8	(	(	PUNCT
ejpam-4348	56	9	9	9	NUM
ejpam-4348	56	10	)	)	PUNCT
ejpam-4348	56	11	z	z	NOUN
ejpam-4348	56	12	(	(	PUNCT
ejpam-4348	56	13	2j+1	2j+1	NUM
ejpam-4348	56	14	)	)	PUNCT
ejpam-4348	56	15	2j+k	2j+k	NUM
ejpam-4348	57	1	=	=	SYM
ejpam-4348	57	2	z	z	NOUN
ejpam-4348	57	3	(	(	PUNCT
ejpam-4348	57	4	2j	2j	NUM
ejpam-4348	57	5	)	)	PUNCT
ejpam-4348	58	1	k	k	NOUN
ejpam-4348	58	2	lj+1	lj+1	X
ejpam-4348	58	3	(	(	PUNCT
ejpam-4348	58	4	10	10	NUM
ejpam-4348	58	5	)	)	PUNCT
ejpam-4348	58	6	hj+1	hj+1	X
ejpam-4348	58	7	=	=	SYM
ejpam-4348	58	8	(	(	PUNCT
ejpam-4348	58	9	kj+1	kj+1	NOUN
ejpam-4348	58	10	)	)	PUNCT
ejpam-4348	58	11	∗hjkj+1	∗hjkj+1	NOUN
ejpam-4348	58	12	+	+	CCONJ
ejpam-4348	58	13	(	(	PUNCT
ejpam-4348	58	14	lj+1	lj+1	X
ejpam-4348	58	15	)	)	PUNCT
ejpam-4348	58	16	∗hjlj+1	∗hjlj+1	NOUN
ejpam-4348	58	17	.	.	PUNCT
ejpam-4348	59	1	(	(	PUNCT
ejpam-4348	59	2	11	11	NUM
ejpam-4348	59	3	)	)	PUNCT
ejpam-4348	59	4	for	for	ADP
ejpam-4348	59	5	the	the	DET
ejpam-4348	59	6	details	detail	NOUN
ejpam-4348	59	7	of	of	ADP
ejpam-4348	59	8	the	the	DET
ejpam-4348	59	9	proof	proof	NOUN
ejpam-4348	59	10	,	,	PUNCT
ejpam-4348	59	11	see	see	VERB
ejpam-4348	59	12	in	in	ADP
ejpam-4348	59	13	[	[	X
ejpam-4348	59	14	2	2	NUM
ejpam-4348	59	15	,	,	PUNCT
ejpam-4348	59	16	4	4	NUM
ejpam-4348	59	17	]	]	PUNCT
ejpam-4348	59	18	.	.	PUNCT
ejpam-4348	60	1	in	in	ADP
ejpam-4348	60	2	the	the	DET
ejpam-4348	60	3	second	second	ADJ
ejpam-4348	60	4	proposition	proposition	NOUN
ejpam-4348	60	5	,	,	PUNCT
ejpam-4348	60	6	the	the	DET
ejpam-4348	60	7	sequences	sequence	NOUN
ejpam-4348	60	8	of	of	ADP
ejpam-4348	60	9	matrices	matrix	NOUN
ejpam-4348	60	10	(	(	PUNCT
ejpam-4348	60	11	lk)k≥0	lk)k≥0	NOUN
ejpam-4348	60	12	and	and	CCONJ
ejpam-4348	60	13	(	(	PUNCT
ejpam-4348	60	14	kr)r≥0	kr)r≥0	PROPN
ejpam-4348	60	15	are	be	AUX
ejpam-4348	60	16	computed	compute	VERB
ejpam-4348	60	17	iteratively	iteratively	ADV
ejpam-4348	60	18	s.	s.	PROPN
ejpam-4348	60	19	traoré	traoré	PROPN
ejpam-4348	60	20	,	,	PUNCT
ejpam-4348	60	21	m.	m.	NOUN
ejpam-4348	60	22	dosso	dosso	PROPN
ejpam-4348	60	23	/	/	SYM
ejpam-4348	60	24	eur	eur	PROPN
ejpam-4348	60	25	.	.	PUNCT
ejpam-4348	61	1	j.	j.	PROPN
ejpam-4348	61	2	pure	pure	PROPN
ejpam-4348	61	3	appl	appl	PROPN
ejpam-4348	61	4	.	.	PROPN
ejpam-4348	61	5	math	math	PROPN
ejpam-4348	61	6	,	,	PUNCT
ejpam-4348	61	7	15	15	NUM
ejpam-4348	61	8	(	(	PUNCT
ejpam-4348	61	9	2	2	NUM
ejpam-4348	61	10	)	)	PUNCT
ejpam-4348	61	11	(	(	PUNCT
ejpam-4348	61	12	2022	2022	NUM
ejpam-4348	61	13	)	)	PUNCT
ejpam-4348	61	14	,	,	PUNCT
ejpam-4348	61	15	681	681	NUM
ejpam-4348	61	16	-	-	SYM
ejpam-4348	61	17	725	725	NUM
ejpam-4348	61	18	684	684	NUM
ejpam-4348	61	19	proposition	proposition	NOUN
ejpam-4348	61	20	2	2	NUM
ejpam-4348	61	21	.	.	X
ejpam-4348	62	1	for	for	ADP
ejpam-4348	62	2	j	j	PROPN
ejpam-4348	62	3	=	=	SYM
ejpam-4348	62	4	0	0	PROPN
ejpam-4348	62	5	,	,	PUNCT
ejpam-4348	62	6	1	1	NUM
ejpam-4348	62	7	,	,	PUNCT
ejpam-4348	62	8	·	·	PUNCT
ejpam-4348	62	9	·	·	PUNCT
ejpam-4348	62	10	·	·	PUNCT
ejpam-4348	62	11	,	,	PUNCT
ejpam-4348	62	12	we	we	PRON
ejpam-4348	62	13	have	have	AUX
ejpam-4348	62	14	(	(	PUNCT
ejpam-4348	62	15	bj	bj	VERB
ejpam-4348	62	16	aj	aj	PROPN
ejpam-4348	62	17	aj	aj	PROPN
ejpam-4348	62	18	bj	bj	VERB
ejpam-4348	62	19	)	)	PUNCT
ejpam-4348	62	20	.	.	PUNCT
ejpam-4348	63	1	(	(	PUNCT
ejpam-4348	63	2	kj+1	kj+1	NOUN
ejpam-4348	63	3	lj+1	lj+1	PROPN
ejpam-4348	63	4	)	)	PUNCT
ejpam-4348	63	5	=	=	PUNCT
ejpam-4348	64	1	(	(	PUNCT
ejpam-4348	64	2	0	0	NUM
ejpam-4348	64	3	in	in	ADP
ejpam-4348	64	4	)	)	PUNCT
ejpam-4348	64	5	(	(	PUNCT
ejpam-4348	64	6	12	12	NUM
ejpam-4348	64	7	)	)	PUNCT
ejpam-4348	64	8	with	with	ADP
ejpam-4348	64	9	aj	aj	PROPN
ejpam-4348	64	10	=	=	PROPN
ejpam-4348	64	11	−az	−az	PROPN
ejpam-4348	64	12	(	(	PUNCT
ejpam-4348	64	13	2j	2j	NUM
ejpam-4348	64	14	)	)	PUNCT
ejpam-4348	64	15	1	1	NUM
ejpam-4348	64	16	,	,	PUNCT
ejpam-4348	64	17	bj	bj	ADP
ejpam-4348	64	18	=	=	SYM
ejpam-4348	64	19	z	z	NOUN
ejpam-4348	64	20	(	(	PUNCT
ejpam-4348	64	21	2j	2j	NOUN
ejpam-4348	64	22	)	)	PUNCT
ejpam-4348	64	23	2j	2j	NOUN
ejpam-4348	64	24	for	for	ADP
ejpam-4348	64	25	the	the	DET
ejpam-4348	64	26	details	detail	NOUN
ejpam-4348	64	27	of	of	ADP
ejpam-4348	64	28	the	the	DET
ejpam-4348	64	29	proof	proof	NOUN
ejpam-4348	64	30	,	,	PUNCT
ejpam-4348	64	31	see	see	VERB
ejpam-4348	64	32	in	in	ADP
ejpam-4348	64	33	[	[	X
ejpam-4348	64	34	2	2	NUM
ejpam-4348	64	35	,	,	PUNCT
ejpam-4348	64	36	4	4	NUM
ejpam-4348	64	37	]	]	PUNCT
ejpam-4348	64	38	.	.	PUNCT
ejpam-4348	65	1	the	the	DET
ejpam-4348	65	2	third	third	ADJ
ejpam-4348	65	3	important	important	ADJ
ejpam-4348	65	4	result	result	NOUN
ejpam-4348	65	5	gives	give	VERB
ejpam-4348	65	6	an	an	DET
ejpam-4348	65	7	estimate	estimate	NOUN
ejpam-4348	65	8	of	of	ADP
ejpam-4348	65	9	the	the	DET
ejpam-4348	65	10	error	error	NOUN
ejpam-4348	65	11	z	z	NOUN
ejpam-4348	65	12	(	(	PUNCT
ejpam-4348	65	13	2j+1	2j+1	NUM
ejpam-4348	65	14	)	)	PUNCT
ejpam-4348	65	15	2j+1	2j+1	NOUN
ejpam-4348	65	16	−p	−p	ADJ
ejpam-4348	65	17	when	when	SCONJ
ejpam-4348	65	18	j	j	PROPN
ejpam-4348	65	19	takes	take	VERB
ejpam-4348	65	20	large	large	ADJ
ejpam-4348	65	21	values	value	NOUN
ejpam-4348	65	22	theorem	theorem	VERB
ejpam-4348	65	23	1	1	X
ejpam-4348	65	24	.	.	PUNCT
ejpam-4348	66	1	there	there	PRON
ejpam-4348	66	2	exists	exist	VERB
ejpam-4348	66	3	j0	j0	PROPN
ejpam-4348	66	4	∈	∈	PROPN
ejpam-4348	66	5	n	n	PRON
ejpam-4348	66	6	such	such	ADJ
ejpam-4348	66	7	that	that	PRON
ejpam-4348	66	8	for	for	ADP
ejpam-4348	66	9	all	all	PRON
ejpam-4348	66	10	j	j	PROPN
ejpam-4348	66	11	≥	≥	PROPN
ejpam-4348	66	12	j0	j0	PROPN
ejpam-4348	66	13	,	,	PUNCT
ejpam-4348	66	14	we	we	PRON
ejpam-4348	66	15	have	have	VERB
ejpam-4348	66	16	∥z(2j+1	∥z(2j+1	NOUN
ejpam-4348	66	17	)	)	PUNCT
ejpam-4348	67	1	2j+1	2j+1	NOUN
ejpam-4348	67	2	−	−	NOUN
ejpam-4348	67	3	p∥	p∥	NOUN
ejpam-4348	67	4	≤	≤	NOUN
ejpam-4348	67	5	κ2(x	κ2(x	PROPN
ejpam-4348	67	6	)	)	PUNCT
ejpam-4348	67	7	ωγ2	ωγ2	NOUN
ejpam-4348	67	8	j+1	j+1	PROPN
ejpam-4348	67	9	1−	1−	NUM
ejpam-4348	67	10	ωγ2j+1	ωγ2j+1	NUM
ejpam-4348	67	11	.	.	PUNCT
ejpam-4348	68	1	with	with	ADP
ejpam-4348	68	2	ω	ω	PROPN
ejpam-4348	68	3	>	>	SYM
ejpam-4348	68	4	1	1	NUM
ejpam-4348	68	5	and	and	CCONJ
ejpam-4348	68	6	0	0	NUM
ejpam-4348	68	7	<	<	X
ejpam-4348	68	8	γ	γ	X
ejpam-4348	68	9	<	<	X
ejpam-4348	68	10	1	1	NUM
ejpam-4348	68	11	.	.	PUNCT
ejpam-4348	68	12	for	for	ADP
ejpam-4348	68	13	the	the	DET
ejpam-4348	68	14	details	detail	NOUN
ejpam-4348	68	15	of	of	ADP
ejpam-4348	68	16	the	the	DET
ejpam-4348	68	17	proof	proof	NOUN
ejpam-4348	68	18	,	,	PUNCT
ejpam-4348	68	19	see	see	VERB
ejpam-4348	68	20	in	in	ADP
ejpam-4348	68	21	[	[	X
ejpam-4348	68	22	2	2	NUM
ejpam-4348	68	23	,	,	PUNCT
ejpam-4348	68	24	4	4	NUM
ejpam-4348	68	25	]	]	PUNCT
ejpam-4348	68	26	.	.	PUNCT
ejpam-4348	69	1	this	this	DET
ejpam-4348	69	2	last	last	ADJ
ejpam-4348	69	3	result	result	NOUN
ejpam-4348	69	4	shows	show	VERB
ejpam-4348	69	5	the	the	DET
ejpam-4348	69	6	fast	fast	ADJ
ejpam-4348	69	7	convergence	convergence	NOUN
ejpam-4348	69	8	of	of	ADP
ejpam-4348	69	9	z	z	PROPN
ejpam-4348	69	10	(	(	PUNCT
ejpam-4348	69	11	2j+1	2j+1	NUM
ejpam-4348	69	12	)	)	PUNCT
ejpam-4348	69	13	2j+1	2j+1	NOUN
ejpam-4348	69	14	to	to	ADP
ejpam-4348	69	15	the	the	DET
ejpam-4348	69	16	projector	projector	NOUN
ejpam-4348	69	17	p.	p.	NOUN
ejpam-4348	70	1	these	these	DET
ejpam-4348	70	2	results	result	NOUN
ejpam-4348	70	3	led	lead	VERB
ejpam-4348	70	4	to	to	ADP
ejpam-4348	70	5	the	the	DET
ejpam-4348	70	6	following	follow	VERB
ejpam-4348	70	7	algorithm	algorithm	NOUN
ejpam-4348	70	8	algorithm	algorithm	NOUN
ejpam-4348	70	9	1	1	NUM
ejpam-4348	70	10	(	(	PUNCT
ejpam-4348	70	11	dichoc1	dichoc1	NOUN
ejpam-4348	70	12	)	)	PUNCT
ejpam-4348	70	13	.	.	PUNCT
ejpam-4348	71	1	•	•	NUM
ejpam-4348	71	2	input	input	NOUN
ejpam-4348	71	3	variables	variable	NOUN
ejpam-4348	71	4	:	:	PUNCT
ejpam-4348	71	5	a	a	X
ejpam-4348	71	6	and	and	CCONJ
ejpam-4348	71	7	in	in	ADP
ejpam-4348	71	8	such	such	ADJ
ejpam-4348	71	9	that	that	SCONJ
ejpam-4348	71	10	the	the	DET
ejpam-4348	71	11	matrix	matrix	NOUN
ejpam-4348	71	12	pencil	pencil	NOUN
ejpam-4348	71	13	zin−a	zin−a	PROPN
ejpam-4348	71	14	has	have	AUX
ejpam-4348	71	15	no	no	DET
ejpam-4348	71	16	eigenvalues	eigenvalue	NOUN
ejpam-4348	71	17	on	on	ADP
ejpam-4348	71	18	the	the	DET
ejpam-4348	71	19	circle	circle	NOUN
ejpam-4348	71	20	c(o	c(o	NOUN
ejpam-4348	71	21	,	,	PUNCT
ejpam-4348	71	22	r	r	NOUN
ejpam-4348	71	23	)	)	PUNCT
ejpam-4348	71	24	with	with	ADP
ejpam-4348	71	25	center	center	NOUN
ejpam-4348	71	26	o	o	NOUN
ejpam-4348	71	27	and	and	CCONJ
ejpam-4348	71	28	the	the	DET
ejpam-4348	71	29	radius	radius	PROPN
ejpam-4348	71	30	r.	r.	PROPN
ejpam-4348	71	31	•	•	PROPN
ejpam-4348	71	32	output	output	NOUN
ejpam-4348	71	33	variables	variable	NOUN
ejpam-4348	71	34	:	:	PUNCT
ejpam-4348	71	35	the	the	DET
ejpam-4348	71	36	spectral	spectral	ADJ
ejpam-4348	71	37	projector	projector	NOUN
ejpam-4348	71	38	p	p	NOUN
ejpam-4348	71	39	and	and	CCONJ
ejpam-4348	71	40	the	the	DET
ejpam-4348	71	41	dichotomy	dichotomy	NOUN
ejpam-4348	71	42	criterion	criterion	NOUN
ejpam-4348	71	43	h.	h.	PROPN
ejpam-4348	72	1	p	p	PROPN
ejpam-4348	72	2	being	be	AUX
ejpam-4348	72	3	the	the	DET
ejpam-4348	72	4	projector	projector	NOUN
ejpam-4348	72	5	on	on	ADP
ejpam-4348	72	6	the	the	DET
ejpam-4348	72	7	right	right	ADJ
ejpam-4348	72	8	invariant	invariant	ADJ
ejpam-4348	72	9	space	space	NOUN
ejpam-4348	72	10	of	of	ADP
ejpam-4348	72	11	zin	zin	NOUN
ejpam-4348	72	12	−	−	PROPN
ejpam-4348	72	13	a	a	DET
ejpam-4348	72	14	corresponding	corresponding	NOUN
ejpam-4348	72	15	to	to	ADP
ejpam-4348	72	16	the	the	DET
ejpam-4348	72	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	72	18	inside	inside	ADP
ejpam-4348	72	19	the	the	DET
ejpam-4348	72	20	circle	circle	NOUN
ejpam-4348	72	21	c(o	c(o	NOUN
ejpam-4348	72	22	,	,	PUNCT
ejpam-4348	72	23	r	r	NOUN
ejpam-4348	72	24	)	)	PUNCT
ejpam-4348	72	25	and	and	CCONJ
ejpam-4348	72	26	h	h	DET
ejpam-4348	72	27	the	the	DET
ejpam-4348	72	28	dichotomy	dichotomy	NOUN
ejpam-4348	72	29	criterion	criterion	NOUN
ejpam-4348	72	30	.	.	PUNCT
ejpam-4348	73	1	(	(	PUNCT
ejpam-4348	73	2	i	i	NOUN
ejpam-4348	73	3	)	)	PUNCT
ejpam-4348	73	4	initialize	initialize	NOUN
ejpam-4348	73	5	(	(	PUNCT
ejpam-4348	73	6	a	a	PRON
ejpam-4348	73	7	)	)	PUNCT
ejpam-4348	73	8	a0	a0	NOUN
ejpam-4348	73	9	=	=	SYM
ejpam-4348	73	10	−a	−a	NOUN
ejpam-4348	73	11	r	r	NOUN
ejpam-4348	73	12	.	.	PUNCT
ejpam-4348	74	1	(	(	PUNCT
ejpam-4348	74	2	b	b	X
ejpam-4348	74	3	)	)	PUNCT
ejpam-4348	74	4	resolve	resolve	NOUN
ejpam-4348	74	5	(	(	PUNCT
ejpam-4348	74	6	a0	a0	VERB
ejpam-4348	74	7	in	in	ADP
ejpam-4348	74	8	in	in	ADP
ejpam-4348	74	9	a0	a0	NOUN
ejpam-4348	74	10	)	)	PUNCT
ejpam-4348	74	11	(	(	PUNCT
ejpam-4348	74	12	k1	k1	PROPN
ejpam-4348	74	13	l1	l1	PROPN
ejpam-4348	74	14	)	)	PUNCT
ejpam-4348	75	1	=	=	PUNCT
ejpam-4348	75	2	(	(	PUNCT
ejpam-4348	75	3	0	0	NUM
ejpam-4348	75	4	in	in	ADP
ejpam-4348	75	5	)	)	PUNCT
ejpam-4348	75	6	.	.	PUNCT
ejpam-4348	76	1	(	(	PUNCT
ejpam-4348	76	2	c	c	X
ejpam-4348	76	3	)	)	PUNCT
ejpam-4348	76	4	put	put	VERB
ejpam-4348	76	5	z	z	NOUN
ejpam-4348	76	6	(	(	PUNCT
ejpam-4348	76	7	2	2	NUM
ejpam-4348	76	8	)	)	SYM
ejpam-4348	76	9	1	1	NUM
ejpam-4348	76	10	=	=	SYM
ejpam-4348	76	11	k1	k1	X
ejpam-4348	76	12	,	,	PUNCT
ejpam-4348	76	13	z	z	NOUN
ejpam-4348	76	14	(	(	PUNCT
ejpam-4348	76	15	2	2	NUM
ejpam-4348	76	16	)	)	SYM
ejpam-4348	76	17	2	2	NUM
ejpam-4348	76	18	=	=	SYM
ejpam-4348	76	19	l1	l1	PROPN
ejpam-4348	76	20	and	and	CCONJ
ejpam-4348	76	21	compute	compute	NOUN
ejpam-4348	76	22	h1	h1	NOUN
ejpam-4348	76	23	=	=	PUNCT
ejpam-4348	76	24	(	(	PUNCT
ejpam-4348	76	25	z	z	NOUN
ejpam-4348	76	26	(	(	PUNCT
ejpam-4348	76	27	2	2	NUM
ejpam-4348	76	28	)	)	PUNCT
ejpam-4348	76	29	1	1	NUM
ejpam-4348	76	30	)	)	PUNCT
ejpam-4348	76	31	∗(z	∗(z	PROPN
ejpam-4348	76	32	(	(	PUNCT
ejpam-4348	76	33	2	2	NUM
ejpam-4348	76	34	)	)	PUNCT
ejpam-4348	76	35	1	1	NUM
ejpam-4348	76	36	)	)	PUNCT
ejpam-4348	77	1	+	+	CCONJ
ejpam-4348	77	2	(	(	PUNCT
ejpam-4348	77	3	z	z	NOUN
ejpam-4348	77	4	(	(	PUNCT
ejpam-4348	77	5	2	2	NUM
ejpam-4348	77	6	)	)	SYM
ejpam-4348	77	7	2	2	NUM
ejpam-4348	77	8	)	)	PUNCT
ejpam-4348	77	9	∗(z	∗(z	NOUN
ejpam-4348	77	10	(	(	PUNCT
ejpam-4348	77	11	2	2	NUM
ejpam-4348	77	12	)	)	PUNCT
ejpam-4348	77	13	2	2	NUM
ejpam-4348	77	14	)	)	PUNCT
ejpam-4348	77	15	.	.	PUNCT
ejpam-4348	78	1	(	(	PUNCT
ejpam-4348	78	2	ii	ii	NOUN
ejpam-4348	78	3	)	)	PUNCT
ejpam-4348	78	4	iterate	iterate	NOUN
ejpam-4348	78	5	:	:	PUNCT
ejpam-4348	78	6	for	for	ADP
ejpam-4348	78	7	j	j	PROPN
ejpam-4348	78	8	=	=	SYM
ejpam-4348	78	9	1	1	NUM
ejpam-4348	78	10	,	,	PUNCT
ejpam-4348	78	11	2	2	NUM
ejpam-4348	78	12	,	,	PUNCT
ejpam-4348	78	13	...	...	PUNCT
ejpam-4348	79	1	(	(	PUNCT
ejpam-4348	79	2	a	a	X
ejpam-4348	79	3	)	)	PUNCT
ejpam-4348	79	4	put	put	VERB
ejpam-4348	79	5	aj	aj	PROPN
ejpam-4348	79	6	=	=	PROPN
ejpam-4348	79	7	a0z	a0z	X
ejpam-4348	79	8	(	(	PUNCT
ejpam-4348	79	9	2j	2j	NUM
ejpam-4348	79	10	)	)	PUNCT
ejpam-4348	79	11	1	1	NUM
ejpam-4348	79	12	,	,	PUNCT
ejpam-4348	79	13	bj	bj	ADP
ejpam-4348	79	14	=	=	SYM
ejpam-4348	79	15	z	z	NOUN
ejpam-4348	79	16	(	(	PUNCT
ejpam-4348	79	17	2j	2j	NOUN
ejpam-4348	79	18	)	)	PUNCT
ejpam-4348	79	19	2j	2j	NOUN
ejpam-4348	79	20	.	.	PUNCT
ejpam-4348	80	1	s.	s.	PROPN
ejpam-4348	80	2	traoré	traoré	PROPN
ejpam-4348	80	3	,	,	PUNCT
ejpam-4348	80	4	m.	m.	NOUN
ejpam-4348	80	5	dosso	dosso	PROPN
ejpam-4348	80	6	/	/	SYM
ejpam-4348	80	7	eur	eur	PROPN
ejpam-4348	80	8	.	.	PUNCT
ejpam-4348	81	1	j.	j.	PROPN
ejpam-4348	81	2	pure	pure	PROPN
ejpam-4348	81	3	appl	appl	PROPN
ejpam-4348	81	4	.	.	PROPN
ejpam-4348	81	5	math	math	PROPN
ejpam-4348	81	6	,	,	PUNCT
ejpam-4348	81	7	15	15	NUM
ejpam-4348	81	8	(	(	PUNCT
ejpam-4348	81	9	2	2	NUM
ejpam-4348	81	10	)	)	PUNCT
ejpam-4348	81	11	(	(	PUNCT
ejpam-4348	81	12	2022	2022	NUM
ejpam-4348	81	13	)	)	PUNCT
ejpam-4348	81	14	,	,	PUNCT
ejpam-4348	81	15	681	681	NUM
ejpam-4348	81	16	-	-	SYM
ejpam-4348	81	17	725	725	NUM
ejpam-4348	81	18	685	685	NUM
ejpam-4348	81	19	(	(	PUNCT
ejpam-4348	81	20	b	b	NOUN
ejpam-4348	81	21	)	)	PUNCT
ejpam-4348	81	22	resolve	resolve	NOUN
ejpam-4348	81	23	(	(	PUNCT
ejpam-4348	81	24	bj	bj	VERB
ejpam-4348	81	25	aj	aj	PROPN
ejpam-4348	81	26	aj	aj	PROPN
ejpam-4348	81	27	bj	bj	VERB
ejpam-4348	81	28	)	)	PUNCT
ejpam-4348	81	29	(	(	PUNCT
ejpam-4348	81	30	kj+1	kj+1	NOUN
ejpam-4348	81	31	lj+1	lj+1	PROPN
ejpam-4348	81	32	)	)	PUNCT
ejpam-4348	82	1	=	=	PUNCT
ejpam-4348	82	2	(	(	PUNCT
ejpam-4348	82	3	0	0	NUM
ejpam-4348	82	4	in	in	ADP
ejpam-4348	82	5	)	)	PUNCT
ejpam-4348	82	6	.	.	PUNCT
ejpam-4348	83	1	(	(	PUNCT
ejpam-4348	83	2	c	c	X
ejpam-4348	83	3	)	)	PUNCT
ejpam-4348	83	4	compute	compute	NOUN
ejpam-4348	83	5	z	z	PROPN
ejpam-4348	83	6	(	(	PUNCT
ejpam-4348	83	7	2j+1	2j+1	NUM
ejpam-4348	83	8	)	)	PUNCT
ejpam-4348	83	9	1	1	NUM
ejpam-4348	84	1	=	=	NOUN
ejpam-4348	84	2	z	z	X
ejpam-4348	84	3	(	(	PUNCT
ejpam-4348	84	4	2j	2j	NUM
ejpam-4348	84	5	)	)	PUNCT
ejpam-4348	84	6	1	1	NUM
ejpam-4348	84	7	kj+1	kj+1	PROPN
ejpam-4348	84	8	z	z	NOUN
ejpam-4348	84	9	(	(	PUNCT
ejpam-4348	84	10	2j+1	2j+1	NUM
ejpam-4348	84	11	)	)	PUNCT
ejpam-4348	84	12	2j+1	2j+1	PROPN
ejpam-4348	84	13	=	=	SYM
ejpam-4348	84	14	z	z	NOUN
ejpam-4348	84	15	(	(	PUNCT
ejpam-4348	84	16	2j	2j	NOUN
ejpam-4348	84	17	)	)	PUNCT
ejpam-4348	84	18	2j	2j	NOUN
ejpam-4348	84	19	lj+1	lj+1	PROPN
ejpam-4348	84	20	hj+1	hj+1	NUM
ejpam-4348	84	21	=(	=(	NOUN
ejpam-4348	84	22	kj+1	kj+1	NOUN
ejpam-4348	84	23	)	)	PUNCT
ejpam-4348	84	24	∗hjkj+1	∗hjkj+1	NOUN
ejpam-4348	84	25	+	+	CCONJ
ejpam-4348	84	26	(	(	PUNCT
ejpam-4348	84	27	lj+1	lj+1	X
ejpam-4348	84	28	)	)	PUNCT
ejpam-4348	84	29	∗hjlj+1	∗hjlj+1	PROPN
ejpam-4348	84	30	.	.	PUNCT
ejpam-4348	85	1	(	(	PUNCT
ejpam-4348	85	2	iii	iii	X
ejpam-4348	85	3	)	)	PUNCT
ejpam-4348	85	4	p	p	NOUN
ejpam-4348	85	5	=	=	PUNCT
ejpam-4348	85	6	z	z	X
ejpam-4348	85	7	(	(	PUNCT
ejpam-4348	85	8	2j+1	2j+1	NUM
ejpam-4348	85	9	)	)	PUNCT
ejpam-4348	85	10	2j+1	2j+1	PROPN
ejpam-4348	85	11	and	and	CCONJ
ejpam-4348	85	12	h	h	NOUN
ejpam-4348	85	13	=	=	SYM
ejpam-4348	85	14	hj+1	hj+1	PROPN
ejpam-4348	85	15	.	.	PUNCT
ejpam-4348	86	1	another	another	DET
ejpam-4348	86	2	spectral	spectral	ADJ
ejpam-4348	86	3	dichotomy	dichotomy	NOUN
ejpam-4348	86	4	method	method	NOUN
ejpam-4348	86	5	has	have	AUX
ejpam-4348	86	6	been	be	AUX
ejpam-4348	86	7	proposed	propose	VERB
ejpam-4348	86	8	by	by	ADP
ejpam-4348	86	9	m.	m.	NOUN
ejpam-4348	86	10	sadkane	sadkane	PROPN
ejpam-4348	86	11	and	and	CCONJ
ejpam-4348	86	12	a.	a.	NOUN
ejpam-4348	86	13	touhami	touhami	NOUN
ejpam-4348	86	14	in	in	ADP
ejpam-4348	86	15	[	[	X
ejpam-4348	86	16	15	15	NUM
ejpam-4348	86	17	]	]	PUNCT
ejpam-4348	86	18	.	.	PUNCT
ejpam-4348	87	1	we	we	PRON
ejpam-4348	87	2	will	will	AUX
ejpam-4348	87	3	just	just	ADV
ejpam-4348	87	4	present	present	VERB
ejpam-4348	87	5	the	the	DET
ejpam-4348	87	6	resulting	result	VERB
ejpam-4348	87	7	algorithm	algorithm	NOUN
ejpam-4348	87	8	of	of	ADP
ejpam-4348	87	9	their	their	PRON
ejpam-4348	87	10	work	work	NOUN
ejpam-4348	87	11	within	within	ADP
ejpam-4348	87	12	the	the	DET
ejpam-4348	87	13	framework	framework	NOUN
ejpam-4348	87	14	of	of	ADP
ejpam-4348	87	15	the	the	DET
ejpam-4348	87	16	spectral	spectral	ADJ
ejpam-4348	87	17	dichotomy	dichotomy	NOUN
ejpam-4348	87	18	method	method	NOUN
ejpam-4348	87	19	of	of	ADP
ejpam-4348	87	20	a	a	DET
ejpam-4348	87	21	pencil	pencil	NOUN
ejpam-4348	87	22	λb	λb	ADP
ejpam-4348	87	23	−a	−a	ADJ
ejpam-4348	87	24	algorithm	algorithm	NOUN
ejpam-4348	87	25	2	2	NUM
ejpam-4348	87	26	(	(	PUNCT
ejpam-4348	87	27	dichoc2	dichoc2	PROPN
ejpam-4348	87	28	)	)	PUNCT
ejpam-4348	87	29	.	.	PUNCT
ejpam-4348	88	1	•	•	NUM
ejpam-4348	88	2	input	input	NOUN
ejpam-4348	88	3	:	:	PUNCT
ejpam-4348	88	4	a	a	DET
ejpam-4348	88	5	,	,	PUNCT
ejpam-4348	88	6	b	b	NOUN
ejpam-4348	88	7	∈	∈	PROPN
ejpam-4348	88	8	cn×n	cn×n	NOUN
ejpam-4348	88	9	such	such	ADJ
ejpam-4348	88	10	that	that	SCONJ
ejpam-4348	88	11	the	the	DET
ejpam-4348	88	12	pencil	pencil	NOUN
ejpam-4348	88	13	λb	λb	ADP
ejpam-4348	88	14	−	−	PROPN
ejpam-4348	88	15	a	a	PRON
ejpam-4348	88	16	is	be	AUX
ejpam-4348	88	17	regular	regular	ADJ
ejpam-4348	88	18	having	have	VERB
ejpam-4348	88	19	no	no	DET
ejpam-4348	88	20	eigenvalues	eigenvalue	NOUN
ejpam-4348	88	21	on	on	ADP
ejpam-4348	88	22	the	the	DET
ejpam-4348	88	23	unit	unit	NOUN
ejpam-4348	88	24	circle	circle	NOUN
ejpam-4348	88	25	.	.	PUNCT
ejpam-4348	89	1	h(0	h(0	PROPN
ejpam-4348	89	2	)	)	PUNCT
ejpam-4348	89	3	=	=	PRON
ejpam-4348	90	1	(	(	PUNCT
ejpam-4348	90	2	h(0))∗	h(0))∗	NOUN
ejpam-4348	90	3	used	use	VERB
ejpam-4348	90	4	for	for	ADP
ejpam-4348	90	5	scaling	scaling	NOUN
ejpam-4348	90	6	.	.	PUNCT
ejpam-4348	91	1	for	for	ADP
ejpam-4348	91	2	instance	instance	NOUN
ejpam-4348	91	3	h(0	h(0	PROPN
ejpam-4348	91	4	)	)	PUNCT
ejpam-4348	91	5	=	=	NOUN
ejpam-4348	91	6	in	in	ADP
ejpam-4348	91	7	•	•	NUM
ejpam-4348	91	8	output	output	NOUN
ejpam-4348	91	9	:	:	PUNCT
ejpam-4348	91	10	p	p	X
ejpam-4348	91	11	the	the	DET
ejpam-4348	91	12	spectral	spectral	ADJ
ejpam-4348	91	13	projector	projector	NOUN
ejpam-4348	91	14	onto	onto	ADP
ejpam-4348	91	15	the	the	DET
ejpam-4348	91	16	right	right	ADJ
ejpam-4348	91	17	deflating	deflate	VERB
ejpam-4348	91	18	subspace	subspace	NOUN
ejpam-4348	91	19	of	of	ADP
ejpam-4348	91	20	λb	λb	ADP
ejpam-4348	91	21	−	−	PROPN
ejpam-4348	91	22	a	a	DET
ejpam-4348	91	23	associated	associate	VERB
ejpam-4348	91	24	with	with	ADP
ejpam-4348	91	25	the	the	DET
ejpam-4348	91	26	eigenvalues	eigenvalue	NOUN
ejpam-4348	91	27	inside	inside	ADP
ejpam-4348	91	28	the	the	DET
ejpam-4348	91	29	unit	unit	NOUN
ejpam-4348	91	30	circle	circle	NOUN
ejpam-4348	91	31	.	.	PUNCT
ejpam-4348	92	1	h	h	PROPN
ejpam-4348	93	1	the	the	DET
ejpam-4348	93	2	matrix	matrix	NOUN
ejpam-4348	93	3	integral	integral	ADJ
ejpam-4348	93	4	whose	whose	DET
ejpam-4348	93	5	norm	norm	NOUN
ejpam-4348	93	6	∥h∥	∥h∥	NOUN
ejpam-4348	93	7	indicates	indicate	VERB
ejpam-4348	93	8	the	the	DET
ejpam-4348	93	9	quality	quality	NOUN
ejpam-4348	93	10	of	of	ADP
ejpam-4348	93	11	the	the	DET
ejpam-4348	93	12	projector	projector	NOUN
ejpam-4348	93	13	p.	p.	NOUN
ejpam-4348	93	14	1	1	NUM
ejpam-4348	93	15	.	.	X
ejpam-4348	93	16	initialization	initialization	PROPN
ejpam-4348	93	17	h0	h0	PROPN
ejpam-4348	93	18	=	=	PROPN
ejpam-4348	93	19	h0	h0	PROPN
ejpam-4348	93	20	first	first	ADJ
ejpam-4348	93	21	iteration	iteration	NOUN
ejpam-4348	93	22	(	(	PUNCT
ejpam-4348	93	23	i	i	NOUN
ejpam-4348	93	24	)	)	PUNCT
ejpam-4348	93	25	compute	compute	PROPN
ejpam-4348	93	26	x	x	NOUN
ejpam-4348	93	27	,	,	PUNCT
ejpam-4348	93	28	y	y	PROPN
ejpam-4348	93	29	solutions	solution	NOUN
ejpam-4348	93	30	of	of	ADP
ejpam-4348	93	31	the	the	DET
ejpam-4348	93	32	equations	equation	NOUN
ejpam-4348	93	33	x(b	x(b	PROPN
ejpam-4348	93	34	−a	−a	ADV
ejpam-4348	93	35	)	)	PUNCT
ejpam-4348	94	1	=	=	SYM
ejpam-4348	94	2	a	a	PRON
ejpam-4348	94	3	,	,	PUNCT
ejpam-4348	94	4	and	and	CCONJ
ejpam-4348	94	5	y	y	PROPN
ejpam-4348	94	6	(	(	PUNCT
ejpam-4348	94	7	b	b	NOUN
ejpam-4348	94	8	−a	−a	NOUN
ejpam-4348	94	9	)	)	PUNCT
ejpam-4348	94	10	=	=	SYM
ejpam-4348	94	11	b	b	PROPN
ejpam-4348	94	12	(	(	PUNCT
ejpam-4348	94	13	ii	ii	NOUN
ejpam-4348	94	14	)	)	PUNCT
ejpam-4348	94	15	compute	compute	NOUN
ejpam-4348	94	16	∆0,∇0	∆0,∇0	NOUN
ejpam-4348	94	17	solutions	solution	NOUN
ejpam-4348	94	18	of	of	ADP
ejpam-4348	94	19	the	the	DET
ejpam-4348	94	20	equations	equation	NOUN
ejpam-4348	94	21	(	(	PUNCT
ejpam-4348	94	22	a+b)∆0	a+b)∆0	NOUN
ejpam-4348	94	23	=	=	SYM
ejpam-4348	94	24	x	x	NOUN
ejpam-4348	94	25	,	,	PUNCT
ejpam-4348	94	26	and	and	CCONJ
ejpam-4348	94	27	(	(	PUNCT
ejpam-4348	94	28	a+b)∇0	a+b)∇0	NOUN
ejpam-4348	94	29	=	=	SYM
ejpam-4348	94	30	y	y	PROPN
ejpam-4348	94	31	(	(	PUNCT
ejpam-4348	94	32	iii	iii	NOUN
ejpam-4348	94	33	)	)	PUNCT
ejpam-4348	94	34	compute	compute	NOUN
ejpam-4348	94	35	h1	h1	NOUN
ejpam-4348	94	36	,	,	PUNCT
ejpam-4348	94	37	z	z	NOUN
ejpam-4348	94	38	(	(	PUNCT
ejpam-4348	94	39	2	2	NUM
ejpam-4348	94	40	)	)	PUNCT
ejpam-4348	94	41	1	1	NUM
ejpam-4348	94	42	,	,	PUNCT
ejpam-4348	94	43	z	z	NOUN
ejpam-4348	94	44	(	(	PUNCT
ejpam-4348	94	45	2	2	NUM
ejpam-4348	94	46	)	)	PUNCT
ejpam-4348	94	47	2	2	NUM
ejpam-4348	94	48	:	:	PUNCT
ejpam-4348	94	49	h1	h1	PROPN
ejpam-4348	94	50	=	=	PUNCT
ejpam-4348	94	51	∆∗	∆∗	NOUN
ejpam-4348	94	52	0h0∆+∇∗	0h0∆+∇∗	NOUN
ejpam-4348	94	53	0h0∇0	0h0∇0	PUNCT
ejpam-4348	95	1	z2	z2	NOUN
ejpam-4348	95	2	1	1	NUM
ejpam-4348	95	3	=	=	SYM
ejpam-4348	95	4	∆0	∆0	NOUN
ejpam-4348	95	5	,	,	PUNCT
ejpam-4348	95	6	z	z	NOUN
ejpam-4348	95	7	(	(	PUNCT
ejpam-4348	95	8	2	2	NUM
ejpam-4348	95	9	)	)	SYM
ejpam-4348	95	10	2	2	NUM
ejpam-4348	95	11	=	=	SYM
ejpam-4348	95	12	∇0	∇0	NUM
ejpam-4348	95	13	2	2	NUM
ejpam-4348	95	14	.	.	PUNCT
ejpam-4348	96	1	next	next	ADJ
ejpam-4348	96	2	iterations	iteration	NOUN
ejpam-4348	96	3	for	for	ADP
ejpam-4348	96	4	j	j	PROPN
ejpam-4348	96	5	=	=	SYM
ejpam-4348	96	6	2	2	NUM
ejpam-4348	96	7	,	,	PUNCT
ejpam-4348	96	8	3	3	NUM
ejpam-4348	96	9	·	·	PUNCT
ejpam-4348	96	10	·	·	PUNCT
ejpam-4348	96	11	·	·	PUNCT
ejpam-4348	96	12	until	until	SCONJ
ejpam-4348	96	13	convergence	convergence	NOUN
ejpam-4348	96	14	do	do	VERB
ejpam-4348	96	15	:	:	PUNCT
ejpam-4348	96	16	update	update	NOUN
ejpam-4348	96	17	of	of	ADP
ejpam-4348	96	18	aj−1	aj−1	NOUN
ejpam-4348	96	19	s.	s.	PROPN
ejpam-4348	96	20	traoré	traoré	PROPN
ejpam-4348	96	21	,	,	PUNCT
ejpam-4348	96	22	m.	m.	NOUN
ejpam-4348	96	23	dosso	dosso	PROPN
ejpam-4348	96	24	/	/	SYM
ejpam-4348	96	25	eur	eur	PROPN
ejpam-4348	96	26	.	.	PUNCT
ejpam-4348	97	1	j.	j.	PROPN
ejpam-4348	97	2	pure	pure	PROPN
ejpam-4348	97	3	appl	appl	PROPN
ejpam-4348	97	4	.	.	PROPN
ejpam-4348	97	5	math	math	PROPN
ejpam-4348	97	6	,	,	PUNCT
ejpam-4348	97	7	15	15	NUM
ejpam-4348	97	8	(	(	PUNCT
ejpam-4348	97	9	2	2	NUM
ejpam-4348	97	10	)	)	PUNCT
ejpam-4348	97	11	(	(	PUNCT
ejpam-4348	97	12	2022	2022	NUM
ejpam-4348	97	13	)	)	PUNCT
ejpam-4348	97	14	,	,	PUNCT
ejpam-4348	97	15	681	681	NUM
ejpam-4348	97	16	-	-	SYM
ejpam-4348	97	17	725	725	NUM
ejpam-4348	97	18	686	686	NUM
ejpam-4348	97	19	(	(	PUNCT
ejpam-4348	97	20	i	i	NOUN
ejpam-4348	97	21	)	)	PUNCT
ejpam-4348	97	22	aj−1	aj−1	NOUN
ejpam-4348	98	1	=	=	SYM
ejpam-4348	98	2	−az	−az	PROPN
ejpam-4348	98	3	(	(	PUNCT
ejpam-4348	98	4	2j−1	2j−1	NUM
ejpam-4348	98	5	)	)	PUNCT
ejpam-4348	98	6	1	1	NUM
ejpam-4348	98	7	(	(	PUNCT
ejpam-4348	98	8	ii	ii	NOUN
ejpam-4348	98	9	)	)	PUNCT
ejpam-4348	98	10	compute	compute	NOUN
ejpam-4348	98	11	∆j−1	∆j−1	PROPN
ejpam-4348	98	12	(	(	PUNCT
ejpam-4348	98	13	2aj−1	2aj−1	NUM
ejpam-4348	98	14	−	−	NOUN
ejpam-4348	98	15	in)∆j−1	in)∆j−1	NOUN
ejpam-4348	98	16	=	=	PUNCT
ejpam-4348	99	1	aj−1	aj−1	NOUN
ejpam-4348	99	2	computation	computation	NOUN
ejpam-4348	99	3	of	of	ADP
ejpam-4348	99	4	hj	hj	PROPN
ejpam-4348	99	5	,	,	PUNCT
ejpam-4348	99	6	z	z	PROPN
ejpam-4348	99	7	(	(	PUNCT
ejpam-4348	99	8	2j	2j	NUM
ejpam-4348	99	9	)	)	PUNCT
ejpam-4348	99	10	1	1	NUM
ejpam-4348	99	11	,	,	PUNCT
ejpam-4348	99	12	z	z	NOUN
ejpam-4348	99	13	(	(	PUNCT
ejpam-4348	99	14	2j	2j	NUM
ejpam-4348	99	15	)	)	PUNCT
ejpam-4348	99	16	2j	2j	NOUN
ejpam-4348	99	17	:	:	PUNCT
ejpam-4348	99	18	(	(	PUNCT
ejpam-4348	99	19	iii	iii	X
ejpam-4348	99	20	)	)	PUNCT
ejpam-4348	99	21	hj	hj	NOUN
ejpam-4348	99	22	=	=	PUNCT
ejpam-4348	99	23	∆∗	∆∗	NOUN
ejpam-4348	99	24	j−1hj−1∆j−1	j−1hj−1∆j−1	NOUN
ejpam-4348	99	25	+	+	CCONJ
ejpam-4348	99	26	(	(	PUNCT
ejpam-4348	99	27	i	i	NOUN
ejpam-4348	99	28	−∆j−1	−∆j−1	PROPN
ejpam-4348	99	29	)	)	PUNCT
ejpam-4348	99	30	∗hj−1(in	∗hj−1(in	PROPN
ejpam-4348	99	31	−∆j−1	−∆j−1	PROPN
ejpam-4348	99	32	)	)	PUNCT
ejpam-4348	99	33	(	(	PUNCT
ejpam-4348	99	34	iv	iv	X
ejpam-4348	99	35	)	)	PUNCT
ejpam-4348	99	36	z	z	NOUN
ejpam-4348	99	37	(	(	PUNCT
ejpam-4348	99	38	2j	2j	NUM
ejpam-4348	99	39	)	)	PUNCT
ejpam-4348	99	40	1	1	NUM
ejpam-4348	99	41	=	=	SYM
ejpam-4348	99	42	z	z	NOUN
ejpam-4348	99	43	(	(	PUNCT
ejpam-4348	99	44	2j−1	2j−1	NUM
ejpam-4348	99	45	)	)	PUNCT
ejpam-4348	99	46	1	1	NUM
ejpam-4348	99	47	∆j−1	∆j−1	NOUN
ejpam-4348	99	48	,	,	PUNCT
ejpam-4348	99	49	z	z	X
ejpam-4348	99	50	(	(	PUNCT
ejpam-4348	99	51	2j	2j	NOUN
ejpam-4348	99	52	)	)	PUNCT
ejpam-4348	99	53	2j	2j	NOUN
ejpam-4348	99	54	=	=	SYM
ejpam-4348	99	55	z	z	NOUN
ejpam-4348	99	56	(	(	PUNCT
ejpam-4348	99	57	2j−1	2j−1	NUM
ejpam-4348	99	58	)	)	PUNCT
ejpam-4348	99	59	2j−1	2j−1	NUM
ejpam-4348	99	60	(	(	PUNCT
ejpam-4348	99	61	in	in	ADP
ejpam-4348	99	62	−∆j−1	−∆j−1	PROPN
ejpam-4348	99	63	)	)	PUNCT
ejpam-4348	99	64	endfor	endfor	NOUN
ejpam-4348	99	65	3	3	NUM
ejpam-4348	99	66	.	.	PUNCT
ejpam-4348	100	1	p	p	X
ejpam-4348	100	2	=	=	PUNCT
ejpam-4348	100	3	z	z	NOUN
ejpam-4348	100	4	(	(	PUNCT
ejpam-4348	100	5	2j	2j	NOUN
ejpam-4348	100	6	)	)	PUNCT
ejpam-4348	100	7	2j	2j	PROPN
ejpam-4348	100	8	b	b	NOUN
ejpam-4348	100	9	and	and	CCONJ
ejpam-4348	100	10	h	h	NOUN
ejpam-4348	100	11	=	=	SYM
ejpam-4348	100	12	hj	hj	PROPN
ejpam-4348	100	13	2.2	2.2	NUM
ejpam-4348	100	14	.	.	PUNCT
ejpam-4348	101	1	spectral	spectral	ADJ
ejpam-4348	101	2	dichotomy	dichotomy	NOUN
ejpam-4348	101	3	with	with	ADP
ejpam-4348	101	4	respect	respect	NOUN
ejpam-4348	101	5	to	to	ADP
ejpam-4348	101	6	the	the	DET
ejpam-4348	101	7	imaginary	imaginary	ADJ
ejpam-4348	101	8	axis	axis	NOUN
ejpam-4348	101	9	we	we	PRON
ejpam-4348	101	10	assume	assume	VERB
ejpam-4348	101	11	that	that	SCONJ
ejpam-4348	101	12	λin−a	λin−a	NOUN
ejpam-4348	101	13	does	do	AUX
ejpam-4348	101	14	not	not	PART
ejpam-4348	101	15	have	have	VERB
ejpam-4348	101	16	any	any	DET
ejpam-4348	101	17	eigenvalue	eigenvalue	NOUN
ejpam-4348	101	18	on	on	ADP
ejpam-4348	101	19	the	the	DET
ejpam-4348	101	20	imaginary	imaginary	ADJ
ejpam-4348	101	21	axis	axis	NOUN
ejpam-4348	101	22	.	.	PUNCT
ejpam-4348	102	1	we	we	PRON
ejpam-4348	102	2	summarize	summarize	VERB
ejpam-4348	102	3	the	the	DET
ejpam-4348	102	4	computation	computation	NOUN
ejpam-4348	102	5	of	of	ADP
ejpam-4348	102	6	the	the	DET
ejpam-4348	102	7	spectral	spectral	ADJ
ejpam-4348	102	8	projector	projector	NOUN
ejpam-4348	102	9	on	on	ADP
ejpam-4348	102	10	the	the	DET
ejpam-4348	102	11	right	right	ADJ
ejpam-4348	102	12	eigenspace	eigenspace	NOUN
ejpam-4348	102	13	corresponding	correspond	VERB
ejpam-4348	102	14	to	to	ADP
ejpam-4348	102	15	the	the	DET
ejpam-4348	102	16	eigenvalues	eigenvalue	NOUN
ejpam-4348	102	17	with	with	ADP
ejpam-4348	102	18	positive	positive	ADJ
ejpam-4348	102	19	real	real	ADJ
ejpam-4348	102	20	parts	part	NOUN
ejpam-4348	102	21	.	.	PUNCT
ejpam-4348	103	1	using	use	VERB
ejpam-4348	103	2	the	the	DET
ejpam-4348	103	3	cayley	cayley	ADJ
ejpam-4348	103	4	transformation	transformation	NOUN
ejpam-4348	103	5	φ	φ	X
ejpam-4348	103	6	:	:	PUNCT
ejpam-4348	104	1	λ	λ	X
ejpam-4348	104	2	∈	∈	PROPN
ejpam-4348	104	3	c	c	X
ejpam-4348	104	4	\	\	X
ejpam-4348	104	5	{	{	PUNCT
ejpam-4348	104	6	1	1	NUM
ejpam-4348	104	7	}	}	PUNCT
ejpam-4348	104	8	−→	−→	NOUN
ejpam-4348	104	9	z	z	NOUN
ejpam-4348	104	10	∈	∈	PROPN
ejpam-4348	104	11	c	c	NOUN
ejpam-4348	104	12	\	\	X
ejpam-4348	104	13	{	{	PUNCT
ejpam-4348	104	14	1	1	NUM
ejpam-4348	104	15	}	}	PUNCT
ejpam-4348	104	16	,	,	PUNCT
ejpam-4348	104	17	defined	define	VERB
ejpam-4348	104	18	by	by	ADP
ejpam-4348	104	19	φ(λ	φ(λ	PROPN
ejpam-4348	104	20	)	)	PUNCT
ejpam-4348	104	21	=	=	PUNCT
ejpam-4348	105	1	z	z	NOUN
ejpam-4348	105	2	=	=	PUNCT
ejpam-4348	105	3	(	(	PUNCT
ejpam-4348	105	4	λ+	λ+	NUM
ejpam-4348	105	5	1	1	NUM
ejpam-4348	105	6	)	)	PUNCT
ejpam-4348	105	7	(	(	PUNCT
ejpam-4348	105	8	λ−	λ−	PROPN
ejpam-4348	105	9	1	1	NUM
ejpam-4348	105	10	)	)	PUNCT
ejpam-4348	105	11	(	(	PUNCT
ejpam-4348	105	12	13	13	NUM
ejpam-4348	105	13	)	)	PUNCT
ejpam-4348	105	14	φ	φ	PROPN
ejpam-4348	105	15	is	be	AUX
ejpam-4348	105	16	a	a	DET
ejpam-4348	105	17	bijection	bijection	NOUN
ejpam-4348	105	18	from	from	ADP
ejpam-4348	105	19	c	c	PROPN
ejpam-4348	105	20	\	\	PROPN
ejpam-4348	105	21	{	{	PUNCT
ejpam-4348	105	22	1	1	NUM
ejpam-4348	105	23	}	}	PUNCT
ejpam-4348	105	24	to	to	ADP
ejpam-4348	105	25	c	c	PROPN
ejpam-4348	105	26	\	\	X
ejpam-4348	105	27	{	{	PUNCT
ejpam-4348	105	28	1	1	NUM
ejpam-4348	105	29	}	}	PUNCT
ejpam-4348	105	30	.	.	PUNCT
ejpam-4348	106	1	the	the	DET
ejpam-4348	106	2	spectral	spectral	ADJ
ejpam-4348	106	3	dichotomy	dichotomy	NOUN
ejpam-4348	106	4	with	with	ADP
ejpam-4348	106	5	respect	respect	NOUN
ejpam-4348	106	6	to	to	ADP
ejpam-4348	106	7	the	the	DET
ejpam-4348	106	8	imaginary	imaginary	ADJ
ejpam-4348	106	9	axis	axis	NOUN
ejpam-4348	106	10	can	can	AUX
ejpam-4348	106	11	be	be	AUX
ejpam-4348	106	12	transformed	transform	VERB
ejpam-4348	106	13	to	to	ADP
ejpam-4348	106	14	the	the	DET
ejpam-4348	106	15	spectral	spectral	ADJ
ejpam-4348	106	16	dichotomy	dichotomy	NOUN
ejpam-4348	106	17	to	to	ADP
ejpam-4348	106	18	the	the	DET
ejpam-4348	106	19	circle	circle	NOUN
ejpam-4348	106	20	by	by	ADP
ejpam-4348	106	21	the	the	DET
ejpam-4348	106	22	inverse	inverse	NOUN
ejpam-4348	106	23	of	of	ADP
ejpam-4348	106	24	φ	φ	PROPN
ejpam-4348	106	25	.	.	PUNCT
ejpam-4348	107	1	it	it	PRON
ejpam-4348	107	2	is	be	AUX
ejpam-4348	107	3	not	not	PART
ejpam-4348	107	4	difficult	difficult	ADJ
ejpam-4348	107	5	to	to	PART
ejpam-4348	107	6	show	show	VERB
ejpam-4348	107	7	that	that	SCONJ
ejpam-4348	107	8	the	the	DET
ejpam-4348	107	9	bijection	bijection	NOUN
ejpam-4348	107	10	φ	φ	PROPN
ejpam-4348	107	11	transforms	transform	VERB
ejpam-4348	107	12	the	the	DET
ejpam-4348	107	13	interior	interior	ADJ
ejpam-4348	107	14	(	(	PUNCT
ejpam-4348	107	15	respectively	respectively	ADV
ejpam-4348	107	16	exterior	exterior	NOUN
ejpam-4348	107	17	)	)	PUNCT
ejpam-4348	107	18	of	of	ADP
ejpam-4348	107	19	the	the	DET
ejpam-4348	107	20	circle	circle	NOUN
ejpam-4348	107	21	to	to	ADP
ejpam-4348	107	22	the	the	DET
ejpam-4348	107	23	left	left	NOUN
ejpam-4348	107	24	(	(	PUNCT
ejpam-4348	107	25	respectively	respectively	ADV
ejpam-4348	107	26	the	the	DET
ejpam-4348	107	27	right	right	NOUN
ejpam-4348	107	28	)	)	PUNCT
ejpam-4348	107	29	half	half	NOUN
ejpam-4348	107	30	plane	plane	NOUN
ejpam-4348	107	31	and	and	CCONJ
ejpam-4348	107	32	the	the	DET
ejpam-4348	107	33	circle	circle	NOUN
ejpam-4348	107	34	to	to	ADP
ejpam-4348	107	35	the	the	DET
ejpam-4348	107	36	imaginary	imaginary	ADJ
ejpam-4348	107	37	axis	axis	NOUN
ejpam-4348	107	38	.	.	PUNCT
ejpam-4348	108	1	we	we	PRON
ejpam-4348	108	2	will	will	AUX
ejpam-4348	108	3	briefly	briefly	ADV
ejpam-4348	108	4	prove	prove	VERB
ejpam-4348	108	5	it	it	PRON
ejpam-4348	108	6	below	below	ADV
ejpam-4348	108	7	.	.	PUNCT
ejpam-4348	109	1	let	let	VERB
ejpam-4348	109	2	’s	’s	PRON
ejpam-4348	109	3	assume	assume	VERB
ejpam-4348	109	4	that	that	SCONJ
ejpam-4348	109	5	z	z	NOUN
ejpam-4348	109	6	=	=	SYM
ejpam-4348	109	7	x+	x+	PROPN
ejpam-4348	110	1	iy	iy	INTJ
ejpam-4348	110	2	then	then	ADV
ejpam-4348	110	3	z	z	PROPN
ejpam-4348	110	4	=	=	SYM
ejpam-4348	110	5	ℜ(λ	ℜ(λ	NOUN
ejpam-4348	110	6	)	)	PUNCT
ejpam-4348	110	7	+	+	NUM
ejpam-4348	110	8	iℑ(λ	iℑ(λ	ADV
ejpam-4348	110	9	)	)	PUNCT
ejpam-4348	110	10	+	+	CCONJ
ejpam-4348	110	11	1	1	NUM
ejpam-4348	110	12	ℜ(λ	ℜ(λ	NOUN
ejpam-4348	110	13	)	)	PUNCT
ejpam-4348	111	1	+	+	CCONJ
ejpam-4348	112	1	iℑ(λ)−	iℑ(λ)−	CCONJ
ejpam-4348	112	2	1	1	NUM
ejpam-4348	112	3	=	=	SYM
ejpam-4348	112	4	ℜ(λ)2	ℜ(λ)2	NOUN
ejpam-4348	112	5	−	−	PROPN
ejpam-4348	112	6	1	1	NUM
ejpam-4348	112	7	+	+	NOUN
ejpam-4348	112	8	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	112	9	−	−	NOUN
ejpam-4348	112	10	2iℑ(λ	2iℑ(λ	NUM
ejpam-4348	112	11	)	)	PUNCT
ejpam-4348	112	12	(	(	PUNCT
ejpam-4348	112	13	ℜ(λ)−	ℜ(λ)−	PROPN
ejpam-4348	112	14	1)2	1)2	NUM
ejpam-4348	112	15	+	+	NOUN
ejpam-4348	112	16	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	112	17	s.	s.	NOUN
ejpam-4348	112	18	traoré	traoré	NOUN
ejpam-4348	112	19	,	,	PUNCT
ejpam-4348	112	20	m.	m.	NOUN
ejpam-4348	112	21	dosso	dosso	PROPN
ejpam-4348	112	22	/	/	SYM
ejpam-4348	112	23	eur	eur	PROPN
ejpam-4348	112	24	.	.	PUNCT
ejpam-4348	113	1	j.	j.	PROPN
ejpam-4348	113	2	pure	pure	PROPN
ejpam-4348	113	3	appl	appl	PROPN
ejpam-4348	113	4	.	.	PROPN
ejpam-4348	113	5	math	math	PROPN
ejpam-4348	113	6	,	,	PUNCT
ejpam-4348	113	7	15	15	NUM
ejpam-4348	113	8	(	(	PUNCT
ejpam-4348	113	9	2	2	NUM
ejpam-4348	113	10	)	)	PUNCT
ejpam-4348	113	11	(	(	PUNCT
ejpam-4348	113	12	2022	2022	NUM
ejpam-4348	113	13	)	)	PUNCT
ejpam-4348	113	14	,	,	PUNCT
ejpam-4348	113	15	681	681	NUM
ejpam-4348	113	16	-	-	SYM
ejpam-4348	113	17	725	725	NUM
ejpam-4348	113	18	687	687	NUM
ejpam-4348	113	19	so	so	NOUN
ejpam-4348	113	20	x	x	NOUN
ejpam-4348	113	21	=	=	SYM
ejpam-4348	113	22	ℜ(λ)2	ℜ(λ)2	NOUN
ejpam-4348	113	23	−	−	PROPN
ejpam-4348	113	24	1	1	NUM
ejpam-4348	113	25	+	+	NOUN
ejpam-4348	113	26	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	113	27	(	(	PUNCT
ejpam-4348	113	28	ℜ(λ)−	ℜ(λ)−	PROPN
ejpam-4348	113	29	1)2	1)2	NUM
ejpam-4348	113	30	+	+	CCONJ
ejpam-4348	113	31	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	113	32	and	and	CCONJ
ejpam-4348	113	33	y	y	NOUN
ejpam-4348	113	34	=	=	PUNCT
ejpam-4348	113	35	−2ℑ(λ	−2ℑ(λ	ADV
ejpam-4348	113	36	)	)	PUNCT
ejpam-4348	113	37	(	(	PUNCT
ejpam-4348	114	1	ℜ(λ)−	ℜ(λ)−	PROPN
ejpam-4348	114	2	1)2	1)2	NUM
ejpam-4348	115	1	+	+	NOUN
ejpam-4348	115	2	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	115	3	we	we	PRON
ejpam-4348	115	4	have	have	VERB
ejpam-4348	115	5	:	:	PUNCT
ejpam-4348	115	6	λ	λ	PROPN
ejpam-4348	115	7	∈	∈	PROPN
ejpam-4348	115	8	c(o	c(o	NOUN
ejpam-4348	115	9	,	,	PUNCT
ejpam-4348	115	10	1	1	X
ejpam-4348	115	11	)	)	PUNCT
ejpam-4348	115	12	⇔	⇔	PROPN
ejpam-4348	115	13	|λ|	|λ|	PROPN
ejpam-4348	115	14	=	=	SYM
ejpam-4348	115	15	1	1	NUM
ejpam-4348	115	16	⇔	⇔	X
ejpam-4348	115	17	ℜ(λ)2	ℜ(λ)2	NOUN
ejpam-4348	115	18	+	+	CCONJ
ejpam-4348	115	19	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	115	20	=	=	SYM
ejpam-4348	115	21	1	1	NUM
ejpam-4348	115	22	⇔	⇔	NOUN
ejpam-4348	115	23	x	x	PUNCT
ejpam-4348	115	24	=	=	SYM
ejpam-4348	115	25	0	0	NUM
ejpam-4348	115	26	which	which	PRON
ejpam-4348	115	27	proves	prove	VERB
ejpam-4348	115	28	that	that	SCONJ
ejpam-4348	115	29	φ	φ	PROPN
ejpam-4348	115	30	maps	map	VERB
ejpam-4348	115	31	bijectively	bijectively	ADV
ejpam-4348	115	32	the	the	DET
ejpam-4348	115	33	circle	circle	NOUN
ejpam-4348	115	34	c(o	c(o	NOUN
ejpam-4348	115	35	,	,	PUNCT
ejpam-4348	115	36	1)\{(1	1)\{(1	NUM
ejpam-4348	115	37	,	,	PUNCT
ejpam-4348	115	38	0	0	NUM
ejpam-4348	115	39	)	)	PUNCT
ejpam-4348	115	40	}	}	PUNCT
ejpam-4348	115	41	onto	onto	ADP
ejpam-4348	115	42	the	the	DET
ejpam-4348	115	43	imaginary	imaginary	ADJ
ejpam-4348	115	44	axis	axis	NOUN
ejpam-4348	115	45	.	.	PUNCT
ejpam-4348	116	1	similarly	similarly	ADV
ejpam-4348	116	2	we	we	PRON
ejpam-4348	116	3	have	have	AUX
ejpam-4348	116	4	,	,	PUNCT
ejpam-4348	116	5	|λ|	|λ|	ADP
ejpam-4348	116	6	<	<	X
ejpam-4348	116	7	1	1	NUM
ejpam-4348	116	8	⇔	⇔	X
ejpam-4348	116	9	ℜ(λ)2	ℜ(λ)2	NOUN
ejpam-4348	116	10	+	+	CCONJ
ejpam-4348	116	11	ℑ(λ)2	ℑ(λ)2	NOUN
ejpam-4348	116	12	<	<	X
ejpam-4348	116	13	1	1	NUM
ejpam-4348	116	14	⇔	⇔	X
ejpam-4348	116	15	x	x	PUNCT
ejpam-4348	116	16	<	<	X
ejpam-4348	116	17	0	0	PUNCT
ejpam-4348	116	18	consider	consider	VERB
ejpam-4348	116	19	the	the	DET
ejpam-4348	116	20	pencil	pencil	NOUN
ejpam-4348	116	21	λb	λb	ADP
ejpam-4348	116	22	−	−	PROPN
ejpam-4348	116	23	a	a	DET
ejpam-4348	116	24	where	where	SCONJ
ejpam-4348	116	25	b	b	NOUN
ejpam-4348	116	26	=	=	SYM
ejpam-4348	116	27	a−	a−	PROPN
ejpam-4348	116	28	in	in	ADP
ejpam-4348	116	29	and	and	CCONJ
ejpam-4348	116	30	a	a	DET
ejpam-4348	116	31	=	=	X
ejpam-4348	116	32	a+	a+	PUNCT
ejpam-4348	116	33	in	in	ADV
ejpam-4348	116	34	.	.	PUNCT
ejpam-4348	117	1	the	the	DET
ejpam-4348	117	2	eigenvalues	eigenvalues	PROPN
ejpam-4348	117	3	z	z	PROPN
ejpam-4348	117	4	of	of	ADP
ejpam-4348	117	5	the	the	DET
ejpam-4348	117	6	matrix	matrix	NOUN
ejpam-4348	117	7	a	a	PRON
ejpam-4348	117	8	and	and	CCONJ
ejpam-4348	117	9	λ	λ	NOUN
ejpam-4348	117	10	are	be	AUX
ejpam-4348	117	11	linked	link	VERB
ejpam-4348	117	12	by	by	ADP
ejpam-4348	117	13	the	the	DET
ejpam-4348	117	14	relation	relation	NOUN
ejpam-4348	117	15	z	z	PROPN
ejpam-4348	117	16	=	=	PUNCT
ejpam-4348	117	17	λ+	λ+	PUNCT
ejpam-4348	117	18	1	1	NUM
ejpam-4348	117	19	λ−	λ−	PROPN
ejpam-4348	117	20	1	1	NUM
ejpam-4348	117	21	.	.	PUNCT
ejpam-4348	118	1	therefore	therefore	ADV
ejpam-4348	118	2	,	,	PUNCT
ejpam-4348	118	3	the	the	DET
ejpam-4348	118	4	spectral	spectral	ADJ
ejpam-4348	118	5	dichotomy	dichotomy	NOUN
ejpam-4348	118	6	with	with	ADP
ejpam-4348	118	7	respect	respect	NOUN
ejpam-4348	118	8	to	to	ADP
ejpam-4348	118	9	the	the	DET
ejpam-4348	118	10	imaginary	imaginary	ADJ
ejpam-4348	118	11	axis	axis	NOUN
ejpam-4348	118	12	can	can	AUX
ejpam-4348	118	13	be	be	AUX
ejpam-4348	118	14	transformed	transform	VERB
ejpam-4348	118	15	to	to	ADP
ejpam-4348	118	16	the	the	DET
ejpam-4348	118	17	spectral	spectral	ADJ
ejpam-4348	118	18	dichotomy	dichotomy	NOUN
ejpam-4348	118	19	to	to	ADP
ejpam-4348	118	20	the	the	DET
ejpam-4348	118	21	unit	unit	NOUN
ejpam-4348	118	22	circle	circle	NOUN
ejpam-4348	118	23	and	and	CCONJ
ejpam-4348	118	24	their	their	PRON
ejpam-4348	118	25	spectral	spectral	ADJ
ejpam-4348	118	26	projectors	projector	NOUN
ejpam-4348	118	27	are	be	AUX
ejpam-4348	118	28	the	the	DET
ejpam-4348	118	29	same	same	ADJ
ejpam-4348	118	30	.	.	PUNCT
ejpam-4348	119	1	according	accord	VERB
ejpam-4348	119	2	to	to	ADP
ejpam-4348	119	3	[	[	X
ejpam-4348	119	4	3],[11],[12	3],[11],[12	NUM
ejpam-4348	119	5	]	]	PUNCT
ejpam-4348	119	6	,	,	PUNCT
ejpam-4348	119	7	the	the	DET
ejpam-4348	119	8	quality	quality	NOUN
ejpam-4348	119	9	of	of	ADP
ejpam-4348	119	10	the	the	DET
ejpam-4348	119	11	spectral	spectral	ADJ
ejpam-4348	119	12	dichotomy	dichotomy	NOUN
ejpam-4348	119	13	with	with	ADP
ejpam-4348	119	14	respect	respect	NOUN
ejpam-4348	119	15	to	to	ADP
ejpam-4348	119	16	the	the	DET
ejpam-4348	119	17	imaginary	imaginary	ADJ
ejpam-4348	119	18	axis	axis	NOUN
ejpam-4348	119	19	is	be	AUX
ejpam-4348	119	20	characterized	characterize	VERB
ejpam-4348	119	21	by	by	ADP
ejpam-4348	119	22	the	the	DET
ejpam-4348	119	23	numerical	numerical	ADJ
ejpam-4348	119	24	parameter	parameter	PROPN
ejpam-4348	119	25	α	α	PROPN
ejpam-4348	119	26	=	=	NOUN
ejpam-4348	119	27	sup	sup	NOUN
ejpam-4348	119	28	ℜ(z)=0	ℜ(z)=0	PUNCT
ejpam-4348	119	29	∥(zin	∥(zin	PROPN
ejpam-4348	119	30	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	119	31	(	(	PUNCT
ejpam-4348	119	32	14	14	NUM
ejpam-4348	119	33	)	)	PUNCT
ejpam-4348	119	34	similarly	similarly	ADV
ejpam-4348	119	35	,	,	PUNCT
ejpam-4348	119	36	the	the	DET
ejpam-4348	119	37	quality	quality	NOUN
ejpam-4348	119	38	of	of	ADP
ejpam-4348	119	39	the	the	DET
ejpam-4348	119	40	dichotomy	dichotomy	NOUN
ejpam-4348	119	41	for	for	ADP
ejpam-4348	119	42	the	the	DET
ejpam-4348	119	43	matrix	matrix	NOUN
ejpam-4348	119	44	pencil	pencil	NOUN
ejpam-4348	119	45	λb	λb	ADP
ejpam-4348	119	46	−	−	PROPN
ejpam-4348	119	47	a	a	PRON
ejpam-4348	119	48	with	with	ADP
ejpam-4348	119	49	respect	respect	NOUN
ejpam-4348	119	50	to	to	ADP
ejpam-4348	119	51	the	the	DET
ejpam-4348	119	52	unit	unit	NOUN
ejpam-4348	119	53	circle	circle	NOUN
ejpam-4348	119	54	is	be	AUX
ejpam-4348	119	55	also	also	ADV
ejpam-4348	119	56	given	give	VERB
ejpam-4348	119	57	by	by	ADP
ejpam-4348	119	58	α̃	α̃	PROPN
ejpam-4348	119	59	=	=	SYM
ejpam-4348	119	60	sup	sup	NOUN
ejpam-4348	120	1	|λ|=1	|λ|=1	NOUN
ejpam-4348	120	2	∥(λb	∥(λb	ADV
ejpam-4348	120	3	−a)−1∥	−a)−1∥	PROPN
ejpam-4348	120	4	(	(	PUNCT
ejpam-4348	120	5	15	15	NUM
ejpam-4348	120	6	)	)	PUNCT
ejpam-4348	120	7	the	the	DET
ejpam-4348	120	8	following	follow	VERB
ejpam-4348	120	9	proposition	proposition	NOUN
ejpam-4348	120	10	shows	show	VERB
ejpam-4348	120	11	the	the	DET
ejpam-4348	120	12	relation	relation	NOUN
ejpam-4348	120	13	between	between	ADP
ejpam-4348	120	14	the	the	DET
ejpam-4348	120	15	two	two	NUM
ejpam-4348	120	16	parameters	parameter	NOUN
ejpam-4348	120	17	.	.	PUNCT
ejpam-4348	121	1	proposition	proposition	NOUN
ejpam-4348	121	2	3	3	NUM
ejpam-4348	121	3	.	.	PUNCT
ejpam-4348	122	1	we	we	PRON
ejpam-4348	122	2	assume	assume	VERB
ejpam-4348	122	3	that	that	SCONJ
ejpam-4348	122	4	∥a∥	∥a∥	NOUN
ejpam-4348	122	5	=	=	SYM
ejpam-4348	122	6	1	1	NUM
ejpam-4348	122	7	and	and	CCONJ
ejpam-4348	122	8	let	let	VERB
ejpam-4348	122	9	α	α	PRON
ejpam-4348	122	10	and	and	CCONJ
ejpam-4348	122	11	α̃	α̃	PROPN
ejpam-4348	122	12	be	be	VERB
ejpam-4348	122	13	the	the	DET
ejpam-4348	122	14	two	two	NUM
ejpam-4348	122	15	parameters	parameter	NOUN
ejpam-4348	122	16	defined	define	VERB
ejpam-4348	122	17	by	by	ADP
ejpam-4348	122	18	(	(	PUNCT
ejpam-4348	122	19	14	14	NUM
ejpam-4348	122	20	)	)	PUNCT
ejpam-4348	122	21	and	and	CCONJ
ejpam-4348	122	22	(	(	PUNCT
ejpam-4348	122	23	15	15	NUM
ejpam-4348	122	24	)	)	PUNCT
ejpam-4348	122	25	.	.	PUNCT
ejpam-4348	123	1	then	then	ADV
ejpam-4348	123	2	1	1	NUM
ejpam-4348	123	3	2	2	NUM
ejpam-4348	123	4	α	α	NOUN
ejpam-4348	123	5	≤	≤	NUM
ejpam-4348	123	6	α̃	α̃	PROPN
ejpam-4348	123	7	≤	≤	NOUN
ejpam-4348	123	8	α+	α+	PUNCT
ejpam-4348	123	9	1	1	NUM
ejpam-4348	123	10	2	2	NUM
ejpam-4348	123	11	(	(	PUNCT
ejpam-4348	123	12	16	16	NUM
ejpam-4348	123	13	)	)	PUNCT
ejpam-4348	123	14	proof	proof	NOUN
ejpam-4348	123	15	.	.	PUNCT
ejpam-4348	124	1	since	since	SCONJ
ejpam-4348	124	2	λb	λb	ADP
ejpam-4348	124	3	−a	−a	NOUN
ejpam-4348	124	4	=	=	PUNCT
ejpam-4348	124	5	z	z	NOUN
ejpam-4348	124	6	+	+	NOUN
ejpam-4348	124	7	1	1	NUM
ejpam-4348	124	8	z	z	NOUN
ejpam-4348	124	9	−	−	NUM
ejpam-4348	124	10	1	1	NUM
ejpam-4348	124	11	b	b	NOUN
ejpam-4348	124	12	−	−	PROPN
ejpam-4348	124	13	(	(	PUNCT
ejpam-4348	124	14	a+	a+	PUNCT
ejpam-4348	124	15	in	in	ADP
ejpam-4348	124	16	)	)	PUNCT
ejpam-4348	124	17	=	=	SYM
ejpam-4348	124	18	1	1	NUM
ejpam-4348	124	19	z	z	NOUN
ejpam-4348	124	20	−	−	NOUN
ejpam-4348	124	21	1	1	NUM
ejpam-4348	124	22	[	[	X
ejpam-4348	124	23	(	(	PUNCT
ejpam-4348	124	24	z	z	NOUN
ejpam-4348	124	25	+	+	NOUN
ejpam-4348	124	26	1)(a−	1)(a−	NUM
ejpam-4348	124	27	in)−	in)−	NOUN
ejpam-4348	124	28	(	(	PUNCT
ejpam-4348	124	29	z	z	NOUN
ejpam-4348	124	30	−	−	PROPN
ejpam-4348	124	31	1)(a+	1)(a+	NUM
ejpam-4348	124	32	in	in	ADP
ejpam-4348	124	33	)	)	PUNCT
ejpam-4348	124	34	]	]	PUNCT
ejpam-4348	125	1	=	=	PUNCT
ejpam-4348	125	2	−2	−2	NOUN
ejpam-4348	125	3	z	z	NOUN
ejpam-4348	125	4	−	−	NOUN
ejpam-4348	125	5	1	1	NUM
ejpam-4348	125	6	(	(	PUNCT
ejpam-4348	125	7	zin	zin	NOUN
ejpam-4348	125	8	−a	−a	NOUN
ejpam-4348	125	9	)	)	PUNCT
ejpam-4348	125	10	s.	s.	PROPN
ejpam-4348	125	11	traoré	traoré	PROPN
ejpam-4348	125	12	,	,	PUNCT
ejpam-4348	125	13	m.	m.	NOUN
ejpam-4348	125	14	dosso	dosso	PROPN
ejpam-4348	125	15	/	/	SYM
ejpam-4348	125	16	eur	eur	PROPN
ejpam-4348	125	17	.	.	PUNCT
ejpam-4348	126	1	j.	j.	PROPN
ejpam-4348	126	2	pure	pure	PROPN
ejpam-4348	126	3	appl	appl	PROPN
ejpam-4348	126	4	.	.	PROPN
ejpam-4348	126	5	math	math	PROPN
ejpam-4348	126	6	,	,	PUNCT
ejpam-4348	126	7	15	15	NUM
ejpam-4348	126	8	(	(	PUNCT
ejpam-4348	126	9	2	2	NUM
ejpam-4348	126	10	)	)	PUNCT
ejpam-4348	126	11	(	(	PUNCT
ejpam-4348	126	12	2022	2022	NUM
ejpam-4348	126	13	)	)	PUNCT
ejpam-4348	126	14	,	,	PUNCT
ejpam-4348	126	15	681	681	NUM
ejpam-4348	126	16	-	-	SYM
ejpam-4348	126	17	725	725	NUM
ejpam-4348	126	18	688	688	NUM
ejpam-4348	126	19	then	then	ADV
ejpam-4348	126	20	(	(	PUNCT
ejpam-4348	126	21	λb	λb	NOUN
ejpam-4348	126	22	−a)−1	−a)−1	NOUN
ejpam-4348	126	23	=	=	PUNCT
ejpam-4348	126	24	−z	−z	NOUN
ejpam-4348	126	25	−	−	NOUN
ejpam-4348	126	26	1	1	NUM
ejpam-4348	126	27	2	2	NUM
ejpam-4348	126	28	(	(	PUNCT
ejpam-4348	126	29	zin	zin	NOUN
ejpam-4348	126	30	−a)−1	−a)−1	NOUN
ejpam-4348	126	31	and	and	CCONJ
ejpam-4348	126	32	thus	thus	ADV
ejpam-4348	126	33	α̃	α̃	PROPN
ejpam-4348	126	34	=	=	SYM
ejpam-4348	126	35	sup	sup	NOUN
ejpam-4348	126	36	ℜ(z)=0	ℜ(z)=0	X
ejpam-4348	126	37	1	1	NUM
ejpam-4348	126	38	2	2	NUM
ejpam-4348	127	1	|	|	NOUN
ejpam-4348	127	2	z	z	NOUN
ejpam-4348	127	3	−	−	NOUN
ejpam-4348	127	4	1	1	NUM
ejpam-4348	128	1	|	|	ADV
ejpam-4348	128	2	∥(zin	∥(zin	PROPN
ejpam-4348	128	3	−a)−1∥	−a)−1∥	NUM
ejpam-4348	128	4	≥	≥	NUM
ejpam-4348	128	5	1	1	NUM
ejpam-4348	128	6	2	2	NUM
ejpam-4348	128	7	α	α	NOUN
ejpam-4348	128	8	we	we	PRON
ejpam-4348	128	9	also	also	ADV
ejpam-4348	128	10	have	have	VERB
ejpam-4348	128	11	∥	∥	NUM
ejpam-4348	128	12	(	(	PUNCT
ejpam-4348	128	13	λb	λb	PART
ejpam-4348	128	14	−a)−1	−a)−1	NOUN
ejpam-4348	128	15	∥	∥	PUNCT
ejpam-4348	128	16	≤	≤	NUM
ejpam-4348	128	17	1	1	NUM
ejpam-4348	128	18	2	2	NUM
ejpam-4348	128	19	(	(	PUNCT
ejpam-4348	128	20	1	1	NUM
ejpam-4348	128	21	+	+	NUM
ejpam-4348	128	22	|z|)∥	|z|)∥	PROPN
ejpam-4348	128	23	(	(	PUNCT
ejpam-4348	129	1	zin	zin	NOUN
ejpam-4348	129	2	−a)−1	−a)−1	NOUN
ejpam-4348	129	3	∥	∥	NOUN
ejpam-4348	129	4	we	we	PRON
ejpam-4348	129	5	will	will	AUX
ejpam-4348	129	6	discuss	discuss	VERB
ejpam-4348	129	7	according	accord	VERB
ejpam-4348	129	8	to	to	ADP
ejpam-4348	129	9	the	the	DET
ejpam-4348	129	10	values	value	NOUN
ejpam-4348	129	11	of	of	ADP
ejpam-4348	129	12	|z|	|z|	NOUN
ejpam-4348	129	13	•	•	ADV
ejpam-4348	129	14	if	if	SCONJ
ejpam-4348	129	15	|z|	|z|	NOUN
ejpam-4348	129	16	≤	≤	NOUN
ejpam-4348	129	17	α+	α+	PUNCT
ejpam-4348	129	18	1	1	NUM
ejpam-4348	129	19	α	α	NOUN
ejpam-4348	129	20	sup	sup	NOUN
ejpam-4348	129	21	|λ|=1	|λ|=1	PUNCT
ejpam-4348	129	22	∥	∥	X
ejpam-4348	129	23	(	(	PUNCT
ejpam-4348	129	24	λb	λb	PART
ejpam-4348	129	25	−a)−1	−a)−1	NOUN
ejpam-4348	129	26	∥	∥	NOUN
ejpam-4348	129	27	≤	≤	NUM
ejpam-4348	129	28	1	1	NUM
ejpam-4348	129	29	2	2	NUM
ejpam-4348	129	30	sup	sup	NOUN
ejpam-4348	129	31	ℜ(z)=0	ℜ(z)=0	PUNCT
ejpam-4348	129	32	(	(	PUNCT
ejpam-4348	129	33	1	1	NUM
ejpam-4348	129	34	+	+	NUM
ejpam-4348	129	35	|z|)∥	|z|)∥	PROPN
ejpam-4348	129	36	(	(	PUNCT
ejpam-4348	129	37	zin	zin	NOUN
ejpam-4348	129	38	−a)−1	−a)−1	NOUN
ejpam-4348	129	39	∥	∥	NOUN
ejpam-4348	129	40	≤	≤	NOUN
ejpam-4348	129	41	α+	α+	PUNCT
ejpam-4348	129	42	1	1	NUM
ejpam-4348	129	43	2	2	NUM
ejpam-4348	129	44	then	then	ADV
ejpam-4348	129	45	α̃	α̃	PROPN
ejpam-4348	129	46	≤	≤	NOUN
ejpam-4348	129	47	α+	α+	PUNCT
ejpam-4348	129	48	1	1	NUM
ejpam-4348	129	49	2	2	NUM
ejpam-4348	129	50	•	•	NOUN
ejpam-4348	129	51	if	if	SCONJ
ejpam-4348	129	52	|z|	|z|	NOUN
ejpam-4348	129	53	≥	≥	PUNCT
ejpam-4348	129	54	α+	α+	PUNCT
ejpam-4348	129	55	1	1	NUM
ejpam-4348	129	56	α	α	NOUN
ejpam-4348	129	57	then	then	ADV
ejpam-4348	129	58	with	with	ADP
ejpam-4348	129	59	the	the	DET
ejpam-4348	129	60	assumption	assumption	NOUN
ejpam-4348	129	61	∥a∥	∥a∥	NOUN
ejpam-4348	129	62	=	=	SYM
ejpam-4348	129	63	1	1	NUM
ejpam-4348	129	64	it	it	PRON
ejpam-4348	129	65	follows	follow	VERB
ejpam-4348	129	66	that	that	SCONJ
ejpam-4348	129	67	∥∥∥∥az	∥∥∥∥az	PROPN
ejpam-4348	129	68	∥∥∥∥	∥∥∥∥	NUM
ejpam-4348	129	69	≤	≤	NUM
ejpam-4348	129	70	1	1	NUM
ejpam-4348	129	71	.	.	PUNCT
ejpam-4348	129	72	which	which	PRON
ejpam-4348	129	73	leads	lead	VERB
ejpam-4348	129	74	to	to	ADP
ejpam-4348	129	75	(	(	PUNCT
ejpam-4348	129	76	zin	zin	NOUN
ejpam-4348	129	77	−a)−1	−a)−1	NOUN
ejpam-4348	129	78	=	=	SYM
ejpam-4348	129	79	1	1	NUM
ejpam-4348	129	80	z	z	NOUN
ejpam-4348	129	81	(	(	PUNCT
ejpam-4348	129	82	in	in	ADP
ejpam-4348	129	83	−	−	PROPN
ejpam-4348	129	84	a	a	DET
ejpam-4348	129	85	z	z	NOUN
ejpam-4348	129	86	)	)	PUNCT
ejpam-4348	129	87	−1	−1	NOUN
ejpam-4348	129	88	=	=	SYM
ejpam-4348	130	1	1	1	NUM
ejpam-4348	130	2	z	z	NOUN
ejpam-4348	130	3	(	(	PUNCT
ejpam-4348	130	4	in	in	ADP
ejpam-4348	130	5	+	+	CCONJ
ejpam-4348	130	6	a	a	DET
ejpam-4348	130	7	z	z	NOUN
ejpam-4348	131	1	+	+	NOUN
ejpam-4348	131	2	∞∑	∞∑	PROPN
ejpam-4348	131	3	m=0	m=0	PROPN
ejpam-4348	131	4	am	be	AUX
ejpam-4348	131	5	zm	zm	PROPN
ejpam-4348	131	6	)	)	PUNCT
ejpam-4348	132	1	=	=	PUNCT
ejpam-4348	133	1	1	1	NUM
ejpam-4348	133	2	z	z	NOUN
ejpam-4348	133	3	(	(	PUNCT
ejpam-4348	133	4	in	in	ADP
ejpam-4348	133	5	+	+	NOUN
ejpam-4348	133	6	a(zin	a(zin	NOUN
ejpam-4348	133	7	−a)−1	−a)−1	NOUN
ejpam-4348	133	8	)	)	PUNCT
ejpam-4348	133	9	)	)	PUNCT
ejpam-4348	133	10	consequently	consequently	ADV
ejpam-4348	133	11	,	,	PUNCT
ejpam-4348	133	12	we	we	PRON
ejpam-4348	133	13	obtain	obtain	VERB
ejpam-4348	133	14	∥(λb	∥(λb	ADJ
ejpam-4348	133	15	−a)−1∥	−a)−1∥	NOUN
ejpam-4348	133	16	≤	≤	NUM
ejpam-4348	133	17	1	1	NUM
ejpam-4348	133	18	2	2	NUM
ejpam-4348	133	19	(	(	PUNCT
ejpam-4348	133	20	1	1	NUM
ejpam-4348	133	21	+	+	CCONJ
ejpam-4348	133	22	|z|)∥(zin	|z|)∥(zin	PRON
ejpam-4348	133	23	−a)−1∥	−a)−1∥	NOUN
ejpam-4348	133	24	≤	≤	ADV
ejpam-4348	133	25	1	1	NUM
ejpam-4348	133	26	2	2	NUM
ejpam-4348	133	27	(	(	PUNCT
ejpam-4348	133	28	1	1	NUM
ejpam-4348	133	29	+	+	SYM
ejpam-4348	133	30	1	1	NUM
ejpam-4348	133	31	|z|	|z|	NOUN
ejpam-4348	133	32	)	)	PUNCT
ejpam-4348	133	33	(	(	PUNCT
ejpam-4348	133	34	1	1	NUM
ejpam-4348	133	35	+	+	NUM
ejpam-4348	133	36	∥(zin	∥(zin	PROPN
ejpam-4348	133	37	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	133	38	)	)	PUNCT
ejpam-4348	133	39	≤	≤	NOUN
ejpam-4348	133	40	2α+	2α+	NUM
ejpam-4348	133	41	1	1	NUM
ejpam-4348	133	42	2(α+	2(α+	NUM
ejpam-4348	133	43	1	1	NUM
ejpam-4348	133	44	)	)	PUNCT
ejpam-4348	133	45	(	(	PUNCT
ejpam-4348	133	46	1	1	NUM
ejpam-4348	133	47	+	+	NUM
ejpam-4348	133	48	∥(zin	∥(zin	PROPN
ejpam-4348	133	49	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	133	50	)	)	PUNCT
ejpam-4348	133	51	hence	hence	ADV
ejpam-4348	133	52	α̃	α̃	PROPN
ejpam-4348	133	53	≤	≤	ADV
ejpam-4348	133	54	2α+	2α+	NUM
ejpam-4348	133	55	1	1	NUM
ejpam-4348	133	56	2(α+	2(α+	NUM
ejpam-4348	133	57	1	1	NUM
ejpam-4348	133	58	)	)	PUNCT
ejpam-4348	133	59	(	(	PUNCT
ejpam-4348	133	60	1	1	NUM
ejpam-4348	133	61	+	+	NUM
ejpam-4348	133	62	α	α	X
ejpam-4348	133	63	)	)	PUNCT
ejpam-4348	133	64	=	=	SYM
ejpam-4348	134	1	α+	α+	PUNCT
ejpam-4348	134	2	1	1	NUM
ejpam-4348	134	3	2	2	NUM
ejpam-4348	134	4	s.	s.	PROPN
ejpam-4348	134	5	traoré	traoré	NOUN
ejpam-4348	134	6	,	,	PUNCT
ejpam-4348	134	7	m.	m.	NOUN
ejpam-4348	134	8	dosso	dosso	PROPN
ejpam-4348	134	9	/	/	SYM
ejpam-4348	134	10	eur	eur	PROPN
ejpam-4348	134	11	.	.	PUNCT
ejpam-4348	135	1	j.	j.	PROPN
ejpam-4348	135	2	pure	pure	PROPN
ejpam-4348	135	3	appl	appl	PROPN
ejpam-4348	135	4	.	.	PROPN
ejpam-4348	135	5	math	math	PROPN
ejpam-4348	135	6	,	,	PUNCT
ejpam-4348	135	7	15	15	NUM
ejpam-4348	135	8	(	(	PUNCT
ejpam-4348	135	9	2	2	NUM
ejpam-4348	135	10	)	)	PUNCT
ejpam-4348	135	11	(	(	PUNCT
ejpam-4348	135	12	2022	2022	NUM
ejpam-4348	135	13	)	)	PUNCT
ejpam-4348	135	14	,	,	PUNCT
ejpam-4348	135	15	681	681	NUM
ejpam-4348	135	16	-	-	SYM
ejpam-4348	135	17	725	725	NUM
ejpam-4348	135	18	689	689	NUM
ejpam-4348	135	19	in	in	ADP
ejpam-4348	135	20	both	both	DET
ejpam-4348	135	21	cases	case	NOUN
ejpam-4348	135	22	α̃	α̃	PROPN
ejpam-4348	135	23	≤	≤	NOUN
ejpam-4348	135	24	α+	α+	DET
ejpam-4348	135	25	1	1	NUM
ejpam-4348	135	26	2	2	NUM
ejpam-4348	135	27	in	in	ADP
ejpam-4348	135	28	conclusion	conclusion	NOUN
ejpam-4348	135	29	1	1	NUM
ejpam-4348	135	30	2	2	NUM
ejpam-4348	135	31	α	α	NOUN
ejpam-4348	135	32	≤	≤	NUM
ejpam-4348	135	33	α̃	α̃	PROPN
ejpam-4348	135	34	≤	≤	NOUN
ejpam-4348	135	35	α+	α+	PUNCT
ejpam-4348	135	36	1	1	NUM
ejpam-4348	135	37	2	2	NUM
ejpam-4348	135	38	this	this	DET
ejpam-4348	135	39	proposition	proposition	NOUN
ejpam-4348	135	40	shows	show	VERB
ejpam-4348	135	41	that	that	SCONJ
ejpam-4348	135	42	the	the	DET
ejpam-4348	135	43	quality	quality	NOUN
ejpam-4348	135	44	of	of	ADP
ejpam-4348	135	45	the	the	DET
ejpam-4348	135	46	dichotomy	dichotomy	NOUN
ejpam-4348	135	47	of	of	ADP
ejpam-4348	135	48	a	a	PRON
ejpam-4348	135	49	with	with	ADP
ejpam-4348	135	50	respect	respect	NOUN
ejpam-4348	135	51	to	to	ADP
ejpam-4348	135	52	the	the	DET
ejpam-4348	135	53	imaginary	imaginary	ADJ
ejpam-4348	135	54	axis	axis	NOUN
ejpam-4348	135	55	is	be	AUX
ejpam-4348	135	56	equivalent	equivalent	ADJ
ejpam-4348	135	57	to	to	ADP
ejpam-4348	135	58	the	the	DET
ejpam-4348	135	59	dichotomy	dichotomy	NOUN
ejpam-4348	135	60	of	of	ADP
ejpam-4348	135	61	the	the	DET
ejpam-4348	135	62	matrix	matrix	NOUN
ejpam-4348	135	63	pencil	pencil	NOUN
ejpam-4348	135	64	λb	λb	ADP
ejpam-4348	135	65	−	−	PROPN
ejpam-4348	135	66	a	a	PRON
ejpam-4348	135	67	with	with	ADP
ejpam-4348	135	68	respect	respect	NOUN
ejpam-4348	135	69	to	to	ADP
ejpam-4348	135	70	the	the	DET
ejpam-4348	135	71	unit	unit	NOUN
ejpam-4348	135	72	circle	circle	NOUN
ejpam-4348	135	73	.	.	PUNCT
ejpam-4348	136	1	the	the	DET
ejpam-4348	136	2	following	follow	VERB
ejpam-4348	136	3	algorithm	algorithm	NOUN
ejpam-4348	136	4	is	be	AUX
ejpam-4348	136	5	used	use	VERB
ejpam-4348	136	6	to	to	PART
ejpam-4348	136	7	calculate	calculate	VERB
ejpam-4348	136	8	the	the	DET
ejpam-4348	136	9	values	value	NOUN
ejpam-4348	136	10	of	of	ADP
ejpam-4348	136	11	the	the	DET
ejpam-4348	136	12	projector	projector	NOUN
ejpam-4348	136	13	and	and	CCONJ
ejpam-4348	136	14	the	the	DET
ejpam-4348	136	15	dichotomy	dichotomy	NOUN
ejpam-4348	136	16	criterion	criterion	NOUN
ejpam-4348	136	17	algorithm	algorithm	NOUN
ejpam-4348	136	18	3	3	NUM
ejpam-4348	136	19	(	(	PUNCT
ejpam-4348	136	20	dichoi	dichoi	NOUN
ejpam-4348	136	21	)	)	PUNCT
ejpam-4348	136	22	.	.	PUNCT
ejpam-4348	137	1	•	•	NOUN
ejpam-4348	137	2	input	input	NOUN
ejpam-4348	137	3	variables	variable	NOUN
ejpam-4348	137	4	:	:	PUNCT
ejpam-4348	137	5	a	a	X
ejpam-4348	137	6	and	and	CCONJ
ejpam-4348	137	7	in	in	ADP
ejpam-4348	137	8	such	such	ADJ
ejpam-4348	137	9	that	that	SCONJ
ejpam-4348	137	10	the	the	DET
ejpam-4348	137	11	matrix	matrix	NOUN
ejpam-4348	137	12	sheaf	sheaf	NOUN
ejpam-4348	137	13	zin	zin	NOUN
ejpam-4348	137	14	−a	−a	NOUN
ejpam-4348	137	15	has	have	AUX
ejpam-4348	137	16	no	no	DET
ejpam-4348	137	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	137	18	on	on	ADP
ejpam-4348	137	19	the	the	DET
ejpam-4348	137	20	imaginary	imaginary	ADJ
ejpam-4348	137	21	axis	axis	NOUN
ejpam-4348	137	22	.	.	PUNCT
ejpam-4348	138	1	•	•	NUM
ejpam-4348	138	2	output	output	NOUN
ejpam-4348	138	3	variables	variable	NOUN
ejpam-4348	138	4	:	:	PUNCT
ejpam-4348	139	1	p	p	NOUN
ejpam-4348	139	2	and	and	CCONJ
ejpam-4348	139	3	h.	h.	PROPN
ejpam-4348	139	4	p	p	PROPN
ejpam-4348	139	5	is	be	AUX
ejpam-4348	139	6	the	the	DET
ejpam-4348	139	7	projector	projector	NOUN
ejpam-4348	139	8	onto	onto	ADP
ejpam-4348	139	9	the	the	DET
ejpam-4348	139	10	left	left	ADJ
ejpam-4348	139	11	deflating	deflate	VERB
ejpam-4348	139	12	subspace	subspace	NOUN
ejpam-4348	139	13	of	of	ADP
ejpam-4348	139	14	a	a	DET
ejpam-4348	139	15	corresponding	corresponding	NOUN
ejpam-4348	139	16	to	to	ADP
ejpam-4348	139	17	the	the	DET
ejpam-4348	139	18	eigenvalues	eigenvalue	NOUN
ejpam-4348	139	19	with	with	ADP
ejpam-4348	139	20	real	real	ADJ
ejpam-4348	139	21	positives	positive	NOUN
ejpam-4348	139	22	parts	part	NOUN
ejpam-4348	139	23	and	and	CCONJ
ejpam-4348	139	24	h	h	NOUN
ejpam-4348	139	25	the	the	DET
ejpam-4348	139	26	dichotomy	dichotomy	NOUN
ejpam-4348	139	27	’s	’s	PART
ejpam-4348	139	28	criterion	criterion	NOUN
ejpam-4348	139	29	.	.	PUNCT
ejpam-4348	140	1	1	1	X
ejpam-4348	140	2	.	.	X
ejpam-4348	140	3	set	set	VERB
ejpam-4348	140	4	a	a	DET
ejpam-4348	140	5	=	=	X
ejpam-4348	140	6	a+	a+	PUNCT
ejpam-4348	140	7	i	i	PROPN
ejpam-4348	140	8	and	and	CCONJ
ejpam-4348	140	9	b	b	NOUN
ejpam-4348	140	10	=	=	SYM
ejpam-4348	140	11	a−	a−	PROPN
ejpam-4348	140	12	i.	i.	NOUN
ejpam-4348	140	13	2	2	NUM
ejpam-4348	140	14	.	.	PUNCT
ejpam-4348	140	15	using	use	VERB
ejpam-4348	140	16	algorithm	algorithm	NOUN
ejpam-4348	140	17	2	2	NUM
ejpam-4348	140	18	to	to	ADP
ejpam-4348	140	19	λb−a	λb−a	NUM
ejpam-4348	140	20	,	,	PUNCT
ejpam-4348	140	21	compute	compute	VERB
ejpam-4348	140	22	the	the	DET
ejpam-4348	140	23	projectors	projector	NOUN
ejpam-4348	140	24	pi	pi	INTJ
ejpam-4348	140	25	onto	onto	ADP
ejpam-4348	140	26	the	the	DET
ejpam-4348	140	27	right	right	ADJ
ejpam-4348	140	28	eigenspace	eigenspace	NOUN
ejpam-4348	140	29	of	of	ADP
ejpam-4348	140	30	a	a	DET
ejpam-4348	140	31	associated	associate	VERB
ejpam-4348	140	32	with	with	ADP
ejpam-4348	140	33	the	the	DET
ejpam-4348	140	34	eigenvalues	eigenvalue	NOUN
ejpam-4348	140	35	inside	inside	ADP
ejpam-4348	140	36	the	the	DET
ejpam-4348	140	37	unit	unit	NOUN
ejpam-4348	140	38	circle	circle	NOUN
ejpam-4348	140	39	and	and	CCONJ
ejpam-4348	140	40	the	the	DET
ejpam-4348	140	41	hermitian	hermitian	PROPN
ejpam-4348	140	42	matrice	matrice	PROPN
ejpam-4348	140	43	h.	h.	PROPN
ejpam-4348	140	44	3	3	X
ejpam-4348	140	45	.	.	PUNCT
ejpam-4348	141	1	p	p	X
ejpam-4348	142	1	=	=	NOUN
ejpam-4348	142	2	in	in	ADP
ejpam-4348	142	3	−	−	PROPN
ejpam-4348	142	4	pi	pi	NOUN
ejpam-4348	142	5	.	.	PUNCT
ejpam-4348	143	1	2.3	2.3	NUM
ejpam-4348	143	2	.	.	PUNCT
ejpam-4348	143	3	spectral	spectral	ADJ
ejpam-4348	143	4	dichotomy	dichotomy	NOUN
ejpam-4348	143	5	with	with	ADP
ejpam-4348	143	6	respect	respect	NOUN
ejpam-4348	143	7	to	to	ADP
ejpam-4348	143	8	a	a	DET
ejpam-4348	143	9	parabola	parabola	NOUN
ejpam-4348	143	10	consider	consider	VERB
ejpam-4348	143	11	the	the	DET
ejpam-4348	143	12	equation	equation	NOUN
ejpam-4348	143	13	of	of	ADP
ejpam-4348	143	14	the	the	DET
ejpam-4348	143	15	following	follow	VERB
ejpam-4348	143	16	parabola	parabola	PROPN
ejpam-4348	143	17	2p	2p	PROPN
ejpam-4348	143	18	(	(	PUNCT
ejpam-4348	143	19	p	p	NOUN
ejpam-4348	143	20	2	2	NUM
ejpam-4348	143	21	−	−	NOUN
ejpam-4348	143	22	x	x	PUNCT
ejpam-4348	143	23	)	)	PUNCT
ejpam-4348	144	1	=	=	SYM
ejpam-4348	144	2	y2	y2	PROPN
ejpam-4348	144	3	with	with	ADP
ejpam-4348	144	4	p	p	PROPN
ejpam-4348	144	5	>	>	X
ejpam-4348	144	6	0	0	PUNCT
ejpam-4348	145	1	(	(	PUNCT
ejpam-4348	145	2	17	17	NUM
ejpam-4348	145	3	)	)	PUNCT
ejpam-4348	145	4	which	which	PRON
ejpam-4348	145	5	was	be	AUX
ejpam-4348	145	6	studied	study	VERB
ejpam-4348	145	7	by	by	ADP
ejpam-4348	145	8	malyshev	malyshev	NOUN
ejpam-4348	145	9	and	and	CCONJ
ejpam-4348	145	10	sadkane	sadkane	NOUN
ejpam-4348	145	11	in	in	ADP
ejpam-4348	145	12	[	[	X
ejpam-4348	145	13	13	13	NUM
ejpam-4348	145	14	]	]	PUNCT
ejpam-4348	145	15	.	.	PUNCT
ejpam-4348	146	1	we	we	PRON
ejpam-4348	146	2	make	make	VERB
ejpam-4348	146	3	a	a	DET
ejpam-4348	146	4	brief	brief	ADJ
ejpam-4348	146	5	summary	summary	NOUN
ejpam-4348	146	6	:	:	PUNCT
ejpam-4348	146	7	consider	consider	VERB
ejpam-4348	146	8	the	the	DET
ejpam-4348	146	9	matrix	matrix	NOUN
ejpam-4348	146	10	a	a	PRON
ejpam-4348	146	11	of	of	ADP
ejpam-4348	146	12	order	order	NOUN
ejpam-4348	146	13	n	n	X
ejpam-4348	146	14	(	(	PUNCT
ejpam-4348	146	15	n	n	CCONJ
ejpam-4348	146	16	>	>	X
ejpam-4348	146	17	1	1	X
ejpam-4348	146	18	)	)	PUNCT
ejpam-4348	146	19	having	have	VERB
ejpam-4348	146	20	no	no	DET
ejpam-4348	146	21	eigenvalues	eigenvalue	NOUN
ejpam-4348	146	22	on	on	ADP
ejpam-4348	146	23	the	the	DET
ejpam-4348	146	24	parabola	parabola	PROPN
ejpam-4348	146	25	γ	γ	X
ejpam-4348	146	26	=	=	SYM
ejpam-4348	146	27	γ(a	γ(a	PROPN
ejpam-4348	146	28	,	,	PUNCT
ejpam-4348	146	29	0	0	NUM
ejpam-4348	146	30	,	,	PUNCT
ejpam-4348	146	31	c	c	NOUN
ejpam-4348	146	32	)	)	PUNCT
ejpam-4348	146	33	of	of	ADP
ejpam-4348	146	34	equation	equation	NOUN
ejpam-4348	146	35	(	(	PUNCT
ejpam-4348	146	36	17	17	NUM
ejpam-4348	146	37	)	)	PUNCT
ejpam-4348	146	38	.	.	PUNCT
ejpam-4348	147	1	let	let	VERB
ejpam-4348	147	2	a	a	PRON
ejpam-4348	147	3	be	be	AUX
ejpam-4348	147	4	the	the	DET
ejpam-4348	147	5	matrix	matrix	NOUN
ejpam-4348	147	6	of	of	ADP
ejpam-4348	147	7	order	order	NOUN
ejpam-4348	147	8	2n	2n	NUM
ejpam-4348	147	9	defined	define	VERB
ejpam-4348	147	10	by	by	ADP
ejpam-4348	147	11	a	a	DET
ejpam-4348	147	12	=	=	NOUN
ejpam-4348	147	13			NOUN
ejpam-4348	147	14	−	−	NOUN
ejpam-4348	148	1	√	√	NOUN
ejpam-4348	149	1	p	p	NOUN
ejpam-4348	149	2	2	2	NUM
ejpam-4348	149	3	in	in	ADP
ejpam-4348	149	4	a	a	PRON
ejpam-4348	149	5	in	in	ADP
ejpam-4348	149	6	−	−	PROPN
ejpam-4348	149	7	√	√	PROPN
ejpam-4348	149	8	p	p	NOUN
ejpam-4348	149	9	2	2	NUM
ejpam-4348	149	10	in	in	ADP
ejpam-4348	149	11			NOUN
ejpam-4348	149	12	the	the	DET
ejpam-4348	149	13	respective	respective	ADJ
ejpam-4348	149	14	eigenvalues	eigenvalue	NOUN
ejpam-4348	149	15	λ	λ	PROPN
ejpam-4348	149	16	and	and	CCONJ
ejpam-4348	149	17	z	z	PROPN
ejpam-4348	149	18	of	of	ADP
ejpam-4348	149	19	the	the	DET
ejpam-4348	149	20	matrices	matrix	NOUN
ejpam-4348	149	21	a	a	PRON
ejpam-4348	149	22	and	and	CCONJ
ejpam-4348	149	23	a	a	DET
ejpam-4348	149	24	satisfy	satisfy	NOUN
ejpam-4348	149	25	the	the	DET
ejpam-4348	149	26	relation	relation	NOUN
ejpam-4348	149	27	s.	s.	PROPN
ejpam-4348	149	28	traoré	traoré	PROPN
ejpam-4348	149	29	,	,	PUNCT
ejpam-4348	149	30	m.	m.	NOUN
ejpam-4348	149	31	dosso	dosso	PROPN
ejpam-4348	149	32	/	/	SYM
ejpam-4348	149	33	eur	eur	PROPN
ejpam-4348	149	34	.	.	PUNCT
ejpam-4348	150	1	j.	j.	PROPN
ejpam-4348	150	2	pure	pure	PROPN
ejpam-4348	150	3	appl	appl	PROPN
ejpam-4348	150	4	.	.	PROPN
ejpam-4348	150	5	math	math	PROPN
ejpam-4348	150	6	,	,	PUNCT
ejpam-4348	150	7	15	15	NUM
ejpam-4348	150	8	(	(	PUNCT
ejpam-4348	150	9	2	2	NUM
ejpam-4348	150	10	)	)	PUNCT
ejpam-4348	150	11	(	(	PUNCT
ejpam-4348	150	12	2022	2022	NUM
ejpam-4348	150	13	)	)	PUNCT
ejpam-4348	150	14	,	,	PUNCT
ejpam-4348	150	15	681	681	NUM
ejpam-4348	150	16	-	-	SYM
ejpam-4348	150	17	725	725	NUM
ejpam-4348	150	18	690	690	NUM
ejpam-4348	150	19	z	z	NOUN
ejpam-4348	150	20	=	=	PUNCT
ejpam-4348	150	21	(	(	PUNCT
ejpam-4348	150	22	λ+	λ+	NUM
ejpam-4348	150	23	√	√	VERB
ejpam-4348	150	24	p	p	NOUN
ejpam-4348	150	25	2	2	NUM
ejpam-4348	150	26	)	)	PUNCT
ejpam-4348	150	27	2	2	NUM
ejpam-4348	150	28	in	in	ADP
ejpam-4348	150	29	their	their	PRON
ejpam-4348	150	30	study	study	NOUN
ejpam-4348	150	31	,	,	PUNCT
ejpam-4348	150	32	malyshev	malyshev	NOUN
ejpam-4348	150	33	and	and	CCONJ
ejpam-4348	150	34	sadkane	sadkane	NOUN
ejpam-4348	150	35	assumed	assume	VERB
ejpam-4348	150	36	in	in	ADP
ejpam-4348	150	37	(	(	PUNCT
ejpam-4348	150	38	[	[	X
ejpam-4348	150	39	13	13	NUM
ejpam-4348	150	40	]	]	PUNCT
ejpam-4348	150	41	)	)	PUNCT
ejpam-4348	150	42	that	that	SCONJ
ejpam-4348	150	43	∥a∥	∥a∥	VERB
ejpam-4348	150	44	=	=	SYM
ejpam-4348	150	45	1	1	X
ejpam-4348	150	46	.	.	PUNCT
ejpam-4348	151	1	otherwise	otherwise	ADV
ejpam-4348	151	2	we	we	PRON
ejpam-4348	151	3	set	set	VERB
ejpam-4348	151	4	a1	a1	NOUN
ejpam-4348	151	5	=	=	SYM
ejpam-4348	151	6	1	1	NUM
ejpam-4348	151	7	∥a∥	∥a∥	NOUN
ejpam-4348	151	8	a	a	PRON
ejpam-4348	151	9	and	and	CCONJ
ejpam-4348	151	10	p1	p1	NOUN
ejpam-4348	151	11	=	=	PUNCT
ejpam-4348	151	12	p	p	NOUN
ejpam-4348	151	13	∥a∥	∥a∥	NOUN
ejpam-4348	151	14	.	.	PUNCT
ejpam-4348	152	1	according	accord	VERB
ejpam-4348	152	2	to	to	ADP
ejpam-4348	152	3	[	[	X
ejpam-4348	152	4	13	13	NUM
ejpam-4348	152	5	]	]	PUNCT
ejpam-4348	152	6	,	,	PUNCT
ejpam-4348	152	7	the	the	DET
ejpam-4348	152	8	quality	quality	NOUN
ejpam-4348	152	9	of	of	ADP
ejpam-4348	152	10	the	the	DET
ejpam-4348	152	11	spectral	spectral	ADJ
ejpam-4348	152	12	dichotomy	dichotomy	NOUN
ejpam-4348	152	13	with	with	ADP
ejpam-4348	152	14	respect	respect	NOUN
ejpam-4348	152	15	to	to	ADP
ejpam-4348	152	16	the	the	DET
ejpam-4348	152	17	imaginary	imaginary	ADJ
ejpam-4348	152	18	axis	axis	NOUN
ejpam-4348	152	19	is	be	AUX
ejpam-4348	152	20	characterized	characterize	VERB
ejpam-4348	152	21	by	by	ADP
ejpam-4348	152	22	the	the	DET
ejpam-4348	152	23	numerical	numerical	ADJ
ejpam-4348	152	24	value	value	NOUN
ejpam-4348	152	25	αa	αa	NOUN
ejpam-4348	152	26	=	=	NOUN
ejpam-4348	152	27	sup	sup	NOUN
ejpam-4348	152	28	ℜ(λ)=0	ℜ(λ)=0	PUNCT
ejpam-4348	152	29	∥(λi2n	∥(λi2n	PROPN
ejpam-4348	152	30	−a)−1∥.	−a)−1∥.	PROPN
ejpam-4348	152	31	(	(	PUNCT
ejpam-4348	152	32	18	18	NUM
ejpam-4348	152	33	)	)	PUNCT
ejpam-4348	152	34	similarly	similarly	ADV
ejpam-4348	152	35	,	,	PUNCT
ejpam-4348	152	36	the	the	DET
ejpam-4348	152	37	spectral	spectral	ADJ
ejpam-4348	152	38	dichotomy	dichotomy	NOUN
ejpam-4348	152	39	with	with	ADP
ejpam-4348	152	40	respect	respect	NOUN
ejpam-4348	152	41	to	to	ADP
ejpam-4348	152	42	the	the	DET
ejpam-4348	152	43	parabola	parabola	NOUN
ejpam-4348	152	44	is	be	AUX
ejpam-4348	152	45	also	also	ADV
ejpam-4348	152	46	characterized	characterize	VERB
ejpam-4348	152	47	by	by	ADP
ejpam-4348	152	48	the	the	DET
ejpam-4348	152	49	numerical	numerical	ADJ
ejpam-4348	152	50	parameter	parameter	PROPN
ejpam-4348	152	51	αa	αa	PROPN
ejpam-4348	153	1	=	=	PUNCT
ejpam-4348	153	2	sup	sup	NOUN
ejpam-4348	153	3	z∈γ	z∈γ	NOUN
ejpam-4348	153	4	∥(zin	∥(zin	PROPN
ejpam-4348	153	5	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	153	6	(	(	PUNCT
ejpam-4348	153	7	19	19	NUM
ejpam-4348	153	8	)	)	PUNCT
ejpam-4348	153	9	the	the	DET
ejpam-4348	153	10	following	follow	VERB
ejpam-4348	153	11	proposition	proposition	NOUN
ejpam-4348	153	12	gives	give	VERB
ejpam-4348	153	13	a	a	DET
ejpam-4348	153	14	relation	relation	NOUN
ejpam-4348	153	15	between	between	ADP
ejpam-4348	153	16	the	the	DET
ejpam-4348	153	17	parameters	parameter	NOUN
ejpam-4348	153	18	αa	αa	X
ejpam-4348	153	19	and	and	CCONJ
ejpam-4348	153	20	αa	αa	PROPN
ejpam-4348	153	21	.	.	PUNCT
ejpam-4348	153	22	proposition	proposition	NOUN
ejpam-4348	153	23	4	4	NUM
ejpam-4348	153	24	.	.	PUNCT
ejpam-4348	154	1	(	(	PUNCT
ejpam-4348	154	2	[	[	X
ejpam-4348	154	3	13	13	NUM
ejpam-4348	154	4	]	]	PUNCT
ejpam-4348	154	5	)	)	PUNCT
ejpam-4348	154	6	let	let	VERB
ejpam-4348	154	7	αa	αa	INTJ
ejpam-4348	154	8	and	and	CCONJ
ejpam-4348	154	9	αa	αa	ADV
ejpam-4348	154	10	be	be	AUX
ejpam-4348	154	11	the	the	DET
ejpam-4348	154	12	two	two	NUM
ejpam-4348	154	13	parameters	parameter	NOUN
ejpam-4348	154	14	defined	define	VERB
ejpam-4348	154	15	by	by	ADP
ejpam-4348	154	16	(	(	PUNCT
ejpam-4348	154	17	18	18	NUM
ejpam-4348	154	18	)	)	PUNCT
ejpam-4348	154	19	and	and	CCONJ
ejpam-4348	154	20	(	(	PUNCT
ejpam-4348	154	21	19	19	NUM
ejpam-4348	154	22	)	)	PUNCT
ejpam-4348	154	23	.	.	PUNCT
ejpam-4348	155	1	we	we	PRON
ejpam-4348	155	2	have	have	VERB
ejpam-4348	155	3	αa	αa	NOUN
ejpam-4348	155	4	≤	≤	NUM
ejpam-4348	155	5	αa	αa	INTJ
ejpam-4348	155	6	≤	≤	NUM
ejpam-4348	155	7	αa	αa	NOUN
ejpam-4348	156	1	+	+	CCONJ
ejpam-4348	156	2	√	√	ADJ
ejpam-4348	156	3	αa	αa	ADV
ejpam-4348	156	4	√	√	NUM
ejpam-4348	156	5	1	1	NUM
ejpam-4348	157	1	+	+	NUM
ejpam-4348	157	2	αa	αa	PROPN
ejpam-4348	157	3	(	(	PUNCT
ejpam-4348	157	4	20	20	NUM
ejpam-4348	157	5	)	)	PUNCT
ejpam-4348	157	6	consider	consider	VERB
ejpam-4348	157	7	the	the	DET
ejpam-4348	157	8	spectral	spectral	ADJ
ejpam-4348	157	9	projectors	projector	NOUN
ejpam-4348	157	10	•	•	ADP
ejpam-4348	157	11	p	p	X
ejpam-4348	157	12	∈	∈	ADJ
ejpam-4348	157	13	cn×n	cn×n	NOUN
ejpam-4348	157	14	on	on	ADP
ejpam-4348	157	15	the	the	DET
ejpam-4348	157	16	right	right	ADJ
ejpam-4348	157	17	eigenspace	eigenspace	NOUN
ejpam-4348	157	18	of	of	ADP
ejpam-4348	157	19	a	a	DET
ejpam-4348	157	20	associated	associate	VERB
ejpam-4348	157	21	with	with	ADP
ejpam-4348	157	22	the	the	DET
ejpam-4348	157	23	eigenvalues	eigenvalue	NOUN
ejpam-4348	157	24	outside	outside	ADP
ejpam-4348	157	25	the	the	DET
ejpam-4348	157	26	parabola	parabola	PROPN
ejpam-4348	157	27	γ	γ	X
ejpam-4348	157	28	;	;	PUNCT
ejpam-4348	157	29	•	•	ADP
ejpam-4348	157	30	p	p	NOUN
ejpam-4348	157	31	∈	∈	PROPN
ejpam-4348	157	32	c2n×2n	c2n×2n	VERB
ejpam-4348	157	33	on	on	ADP
ejpam-4348	157	34	the	the	DET
ejpam-4348	157	35	right	right	ADJ
ejpam-4348	157	36	eigenspace	eigenspace	NOUN
ejpam-4348	157	37	of	of	ADP
ejpam-4348	157	38	a	a	DET
ejpam-4348	157	39	associated	associate	VERB
ejpam-4348	157	40	with	with	ADP
ejpam-4348	157	41	the	the	DET
ejpam-4348	157	42	eigenvalues	eigenvalue	NOUN
ejpam-4348	157	43	in	in	ADP
ejpam-4348	157	44	the	the	DET
ejpam-4348	157	45	right	right	ADJ
ejpam-4348	157	46	complex	complex	ADJ
ejpam-4348	157	47	half	half	ADJ
ejpam-4348	157	48	-	-	PUNCT
ejpam-4348	157	49	plane	plane	NOUN
ejpam-4348	157	50	.	.	PUNCT
ejpam-4348	158	1	the	the	DET
ejpam-4348	158	2	following	follow	VERB
ejpam-4348	158	3	proposition	proposition	NOUN
ejpam-4348	158	4	characterizes	characterize	VERB
ejpam-4348	158	5	the	the	DET
ejpam-4348	158	6	relation	relation	NOUN
ejpam-4348	158	7	between	between	ADP
ejpam-4348	158	8	p	p	PROPN
ejpam-4348	158	9	and	and	CCONJ
ejpam-4348	158	10	p	p	NOUN
ejpam-4348	158	11	proposition	proposition	NOUN
ejpam-4348	158	12	5	5	NUM
ejpam-4348	158	13	.	.	PUNCT
ejpam-4348	159	1	(	(	PUNCT
ejpam-4348	159	2	[	[	X
ejpam-4348	159	3	13	13	NUM
ejpam-4348	159	4	]	]	PUNCT
ejpam-4348	159	5	)	)	PUNCT
ejpam-4348	159	6	consider	consider	VERB
ejpam-4348	159	7	a	a	DET
ejpam-4348	159	8	partition	partition	NOUN
ejpam-4348	159	9	of	of	ADP
ejpam-4348	159	10	the	the	DET
ejpam-4348	159	11	matrix	matrix	NOUN
ejpam-4348	159	12	p	p	NOUN
ejpam-4348	159	13	in	in	ADP
ejpam-4348	159	14	the	the	DET
ejpam-4348	159	15	form	form	NOUN
ejpam-4348	159	16	p	p	NOUN
ejpam-4348	159	17	=	=	X
ejpam-4348	159	18	(	(	PUNCT
ejpam-4348	159	19	p1	p1	PROPN
ejpam-4348	159	20	p2	p2	PROPN
ejpam-4348	159	21	p3	p3	PROPN
ejpam-4348	159	22	p4	p4	PROPN
ejpam-4348	159	23	)	)	PUNCT
ejpam-4348	159	24	with	with	ADP
ejpam-4348	159	25	pi	pi	PROPN
ejpam-4348	159	26	∈	∈	PROPN
ejpam-4348	159	27	cn×n	cn×n	NOUN
ejpam-4348	159	28	,	,	PUNCT
ejpam-4348	159	29	i	i	NOUN
ejpam-4348	159	30	=	=	NOUN
ejpam-4348	159	31	1	1	NUM
ejpam-4348	159	32	,	,	PUNCT
ejpam-4348	159	33	4	4	NUM
ejpam-4348	159	34	(	(	PUNCT
ejpam-4348	159	35	21	21	NUM
ejpam-4348	159	36	)	)	PUNCT
ejpam-4348	160	1	then	then	ADV
ejpam-4348	160	2	p	p	X
ejpam-4348	160	3	=	=	SYM
ejpam-4348	160	4	2p1	2p1	NUM
ejpam-4348	160	5	=	=	SYM
ejpam-4348	160	6	2p4	2p4	NUM
ejpam-4348	160	7	=	=	SYM
ejpam-4348	160	8	4p2p3	4p2p3	NUM
ejpam-4348	160	9	(	(	PUNCT
ejpam-4348	160	10	22	22	NUM
ejpam-4348	160	11	)	)	PUNCT
ejpam-4348	160	12	moreover	moreover	ADV
ejpam-4348	160	13	p2	p2	X
ejpam-4348	160	14	=	=	SYM
ejpam-4348	160	15	1	1	NUM
ejpam-4348	160	16	2	2	NUM
ejpam-4348	160	17	(	(	PUNCT
ejpam-4348	160	18	pa	pa	PROPN
ejpam-4348	160	19	)	)	PUNCT
ejpam-4348	160	20	1	1	NUM
ejpam-4348	160	21	2	2	NUM
ejpam-4348	160	22	(	(	PUNCT
ejpam-4348	160	23	23	23	NUM
ejpam-4348	160	24	)	)	PUNCT
ejpam-4348	160	25	s.	s.	PROPN
ejpam-4348	160	26	traoré	traoré	PROPN
ejpam-4348	160	27	,	,	PUNCT
ejpam-4348	160	28	m.	m.	NOUN
ejpam-4348	160	29	dosso	dosso	PROPN
ejpam-4348	160	30	/	/	SYM
ejpam-4348	160	31	eur	eur	PROPN
ejpam-4348	160	32	.	.	PUNCT
ejpam-4348	161	1	j.	j.	PROPN
ejpam-4348	161	2	pure	pure	PROPN
ejpam-4348	161	3	appl	appl	PROPN
ejpam-4348	161	4	.	.	PROPN
ejpam-4348	161	5	math	math	PROPN
ejpam-4348	161	6	,	,	PUNCT
ejpam-4348	161	7	15	15	NUM
ejpam-4348	161	8	(	(	PUNCT
ejpam-4348	161	9	2	2	NUM
ejpam-4348	161	10	)	)	PUNCT
ejpam-4348	161	11	(	(	PUNCT
ejpam-4348	161	12	2022	2022	NUM
ejpam-4348	161	13	)	)	PUNCT
ejpam-4348	161	14	,	,	PUNCT
ejpam-4348	161	15	681	681	NUM
ejpam-4348	161	16	-	-	SYM
ejpam-4348	161	17	725	725	NUM
ejpam-4348	161	18	691	691	NUM
ejpam-4348	161	19	algorithm	algorithm	NOUN
ejpam-4348	161	20	4	4	NUM
ejpam-4348	161	21	(	(	PUNCT
ejpam-4348	161	22	dichop	dichop	PROPN
ejpam-4348	161	23	)	)	PUNCT
ejpam-4348	161	24	.	.	PUNCT
ejpam-4348	162	1	•	•	NOUN
ejpam-4348	162	2	input	input	NOUN
ejpam-4348	162	3	variables	variable	NOUN
ejpam-4348	162	4	:	:	PUNCT
ejpam-4348	162	5	a	a	X
ejpam-4348	162	6	and	and	CCONJ
ejpam-4348	162	7	in	in	ADP
ejpam-4348	162	8	such	such	ADJ
ejpam-4348	162	9	that	that	SCONJ
ejpam-4348	162	10	the	the	DET
ejpam-4348	162	11	matrix	matrix	NOUN
ejpam-4348	162	12	sheaf	sheaf	NOUN
ejpam-4348	162	13	zin	zin	NOUN
ejpam-4348	162	14	−a	−a	NOUN
ejpam-4348	162	15	has	have	AUX
ejpam-4348	162	16	no	no	DET
ejpam-4348	162	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	162	18	on	on	ADP
ejpam-4348	162	19	the	the	DET
ejpam-4348	162	20	parabola	parabola	NOUN
ejpam-4348	162	21	of	of	ADP
ejpam-4348	162	22	the	the	DET
ejpam-4348	162	23	equation	equation	NOUN
ejpam-4348	162	24	2p	2p	NOUN
ejpam-4348	162	25	(	(	PUNCT
ejpam-4348	162	26	p	p	NOUN
ejpam-4348	162	27	2	2	NUM
ejpam-4348	162	28	−	−	NOUN
ejpam-4348	162	29	x	x	SYM
ejpam-4348	162	30	)	)	PUNCT
ejpam-4348	162	31	2	2	NUM
ejpam-4348	162	32	=	=	SYM
ejpam-4348	162	33	y2	y2	VERB
ejpam-4348	162	34	with	with	ADP
ejpam-4348	162	35	p	p	PROPN
ejpam-4348	162	36	>	>	SYM
ejpam-4348	162	37	0	0	NUM
ejpam-4348	162	38	•	•	NOUN
ejpam-4348	162	39	output	output	NOUN
ejpam-4348	162	40	variables	variable	NOUN
ejpam-4348	162	41	:	:	PUNCT
ejpam-4348	162	42	the	the	DET
ejpam-4348	162	43	spectral	spectral	ADJ
ejpam-4348	162	44	projector	projector	NOUN
ejpam-4348	162	45	p	p	NOUN
ejpam-4348	162	46	and	and	CCONJ
ejpam-4348	162	47	the	the	DET
ejpam-4348	162	48	dichotomy	dichotomy	NOUN
ejpam-4348	162	49	criterion	criterion	NOUN
ejpam-4348	162	50	h.	h.	PROPN
ejpam-4348	163	1	p	p	PROPN
ejpam-4348	163	2	being	be	AUX
ejpam-4348	163	3	the	the	DET
ejpam-4348	163	4	projector	projector	NOUN
ejpam-4348	163	5	on	on	ADP
ejpam-4348	163	6	the	the	DET
ejpam-4348	163	7	right	right	ADJ
ejpam-4348	163	8	invariant	invariant	ADJ
ejpam-4348	163	9	space	space	NOUN
ejpam-4348	163	10	of	of	ADP
ejpam-4348	163	11	zin	zin	NOUN
ejpam-4348	163	12	−	−	PROPN
ejpam-4348	163	13	a	a	DET
ejpam-4348	163	14	corresponding	corresponding	NOUN
ejpam-4348	163	15	to	to	ADP
ejpam-4348	163	16	the	the	DET
ejpam-4348	163	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	163	18	outside	outside	ADP
ejpam-4348	163	19	the	the	DET
ejpam-4348	163	20	parabola	parabola	NOUN
ejpam-4348	163	21	and	and	CCONJ
ejpam-4348	163	22	h	h	DET
ejpam-4348	163	23	the	the	DET
ejpam-4348	163	24	dichotomy	dichotomy	NOUN
ejpam-4348	163	25	criterion	criterion	NOUN
ejpam-4348	163	26	.	.	PUNCT
ejpam-4348	164	1	1	1	X
ejpam-4348	164	2	.	.	X
ejpam-4348	164	3	compute	compute	VERB
ejpam-4348	164	4	the	the	DET
ejpam-4348	164	5	matrix	matrix	NOUN
ejpam-4348	164	6	a	a	DET
ejpam-4348	164	7	=	=	SYM
ejpam-4348	164	8			PROPN
ejpam-4348	164	9	−	−	ADP
ejpam-4348	164	10	√	√	NOUN
ejpam-4348	164	11	p	p	NOUN
ejpam-4348	164	12	2	2	NUM
ejpam-4348	164	13	in	in	ADP
ejpam-4348	164	14	a	a	PRON
ejpam-4348	164	15	in	in	ADP
ejpam-4348	164	16	−	−	PROPN
ejpam-4348	164	17	√	√	PROPN
ejpam-4348	164	18	p	p	NOUN
ejpam-4348	164	19	2	2	NUM
ejpam-4348	164	20	in	in	ADP
ejpam-4348	164	21			NOUN
ejpam-4348	164	22	2	2	NUM
ejpam-4348	164	23	.	.	PUNCT
ejpam-4348	164	24	using	use	VERB
ejpam-4348	164	25	algorithm	algorithm	NOUN
ejpam-4348	164	26	3	3	NUM
ejpam-4348	164	27	to	to	ADP
ejpam-4348	164	28	λi2n	λi2n	PROPN
ejpam-4348	164	29	−	−	PROPN
ejpam-4348	164	30	a	a	X
ejpam-4348	164	31	,	,	PUNCT
ejpam-4348	164	32	compute	compute	VERB
ejpam-4348	164	33	the	the	DET
ejpam-4348	164	34	projector	projector	NOUN
ejpam-4348	164	35	p	p	X
ejpam-4348	164	36	onto	onto	ADP
ejpam-4348	164	37	the	the	DET
ejpam-4348	164	38	right	right	ADJ
ejpam-4348	164	39	eigenspace	eigenspace	NOUN
ejpam-4348	164	40	of	of	ADP
ejpam-4348	164	41	a	a	DET
ejpam-4348	164	42	associated	associate	VERB
ejpam-4348	164	43	with	with	ADP
ejpam-4348	164	44	the	the	DET
ejpam-4348	164	45	eigenvalues	eigenvalue	NOUN
ejpam-4348	164	46	on	on	ADP
ejpam-4348	164	47	the	the	DET
ejpam-4348	164	48	right	right	ADJ
ejpam-4348	164	49	half	half	ADJ
ejpam-4348	164	50	-	-	PUNCT
ejpam-4348	164	51	plane	plane	NOUN
ejpam-4348	164	52	of	of	ADP
ejpam-4348	164	53	the	the	DET
ejpam-4348	164	54	complex	complex	ADJ
ejpam-4348	164	55	plane	plane	NOUN
ejpam-4348	164	56	and	and	CCONJ
ejpam-4348	164	57	the	the	DET
ejpam-4348	164	58	matrix	matrix	NOUN
ejpam-4348	164	59	h	h	NOUN
ejpam-4348	164	60	;	;	PUNCT
ejpam-4348	164	61	3	3	X
ejpam-4348	164	62	.	.	X
ejpam-4348	164	63	if	if	SCONJ
ejpam-4348	164	64	∥h∥	∥h∥	NOUN
ejpam-4348	164	65	is	be	AUX
ejpam-4348	164	66	not	not	PART
ejpam-4348	164	67	large	large	ADJ
ejpam-4348	164	68	then	then	ADV
ejpam-4348	164	69	determine	determine	VERB
ejpam-4348	164	70	the	the	DET
ejpam-4348	164	71	projector	projector	NOUN
ejpam-4348	164	72	p	p	NOUN
ejpam-4348	164	73	by	by	ADP
ejpam-4348	164	74	p	p	NOUN
ejpam-4348	164	75	=	=	PROPN
ejpam-4348	164	76	2p1	2p1	NUM
ejpam-4348	164	77	3	3	NUM
ejpam-4348	164	78	.	.	PUNCT
ejpam-4348	164	79	presentation	presentation	NOUN
ejpam-4348	164	80	of	of	ADP
ejpam-4348	164	81	new	new	ADJ
ejpam-4348	164	82	methods	method	NOUN
ejpam-4348	164	83	in	in	ADP
ejpam-4348	164	84	what	what	PRON
ejpam-4348	164	85	follows	follow	VERB
ejpam-4348	164	86	,	,	PUNCT
ejpam-4348	164	87	we	we	PRON
ejpam-4348	164	88	will	will	AUX
ejpam-4348	164	89	consider	consider	VERB
ejpam-4348	164	90	the	the	DET
ejpam-4348	164	91	general	general	ADJ
ejpam-4348	164	92	equation	equation	NOUN
ejpam-4348	164	93	of	of	ADP
ejpam-4348	164	94	the	the	DET
ejpam-4348	164	95	parabola	parabola	NOUN
ejpam-4348	164	96	(	(	PUNCT
ejpam-4348	164	97	1	1	NUM
ejpam-4348	164	98	)	)	PUNCT
ejpam-4348	164	99	as	as	SCONJ
ejpam-4348	164	100	announced	announce	VERB
ejpam-4348	164	101	in	in	ADP
ejpam-4348	164	102	the	the	DET
ejpam-4348	164	103	introduction	introduction	NOUN
ejpam-4348	164	104	and	and	CCONJ
ejpam-4348	164	105	we	we	PRON
ejpam-4348	164	106	will	will	AUX
ejpam-4348	164	107	determine	determine	VERB
ejpam-4348	164	108	the	the	DET
ejpam-4348	164	109	projector	projector	NOUN
ejpam-4348	164	110	p	p	NOUN
ejpam-4348	164	111	for	for	ADP
ejpam-4348	164	112	parameters	parameter	NOUN
ejpam-4348	164	113	a	a	PRON
ejpam-4348	164	114	,	,	PUNCT
ejpam-4348	164	115	b	b	NOUN
ejpam-4348	164	116	and	and	CCONJ
ejpam-4348	164	117	c	c	NOUN
ejpam-4348	164	118	∈	∈	NOUN
ejpam-4348	164	119	r	r	NOUN
ejpam-4348	164	120	with	with	ADP
ejpam-4348	164	121	a	a	DET
ejpam-4348	164	122	̸=	̸=	PROPN
ejpam-4348	164	123	0	0	NUM
ejpam-4348	164	124	.	.	PROPN
ejpam-4348	164	125	3.1	3.1	NUM
ejpam-4348	164	126	.	.	PUNCT
ejpam-4348	165	1	the	the	DET
ejpam-4348	165	2	case	case	NOUN
ejpam-4348	165	3	of	of	ADP
ejpam-4348	165	4	a	a	DET
ejpam-4348	165	5	parabola	parabola	NOUN
ejpam-4348	165	6	of	of	ADP
ejpam-4348	165	7	equation	equation	NOUN
ejpam-4348	165	8	of	of	ADP
ejpam-4348	165	9	type	type	NOUN
ejpam-4348	165	10	(	(	PUNCT
ejpam-4348	165	11	1	1	NUM
ejpam-4348	165	12	)	)	PUNCT
ejpam-4348	165	13	with	with	ADP
ejpam-4348	165	14	discriminant	discriminant	NOUN
ejpam-4348	165	15	equal	equal	ADJ
ejpam-4348	165	16	to	to	ADP
ejpam-4348	165	17	1	1	NUM
ejpam-4348	165	18	.	.	PUNCT
ejpam-4348	166	1	equation	equation	NOUN
ejpam-4348	166	2	(	(	PUNCT
ejpam-4348	166	3	1	1	NUM
ejpam-4348	166	4	)	)	PUNCT
ejpam-4348	166	5	of	of	ADP
ejpam-4348	166	6	the	the	DET
ejpam-4348	166	7	parabola	parabola	NOUN
ejpam-4348	166	8	becomes	become	VERB
ejpam-4348	166	9	2p	2p	NUM
ejpam-4348	166	10	(	(	PUNCT
ejpam-4348	166	11	p	p	NOUN
ejpam-4348	166	12	2	2	NUM
ejpam-4348	166	13	−	−	NOUN
ejpam-4348	166	14	x	x	SYM
ejpam-4348	166	15	)	)	PUNCT
ejpam-4348	167	1	=	=	SYM
ejpam-4348	167	2	(	(	PUNCT
ejpam-4348	167	3	y	y	PROPN
ejpam-4348	167	4	−	−	PROPN
ejpam-4348	167	5	pb)2	pb)2	PROPN
ejpam-4348	167	6	(	(	PUNCT
ejpam-4348	167	7	24	24	NUM
ejpam-4348	167	8	)	)	PUNCT
ejpam-4348	167	9	with	with	ADP
ejpam-4348	167	10	p	p	PROPN
ejpam-4348	167	11	>	>	X
ejpam-4348	167	12	0	0	NUM
ejpam-4348	167	13	.	.	PUNCT
ejpam-4348	168	1	for	for	ADP
ejpam-4348	168	2	the	the	DET
ejpam-4348	168	3	parameter	parameter	NOUN
ejpam-4348	168	4	b	b	PROPN
ejpam-4348	168	5	=	=	SYM
ejpam-4348	168	6	0	0	PROPN
ejpam-4348	168	7	,	,	PUNCT
ejpam-4348	168	8	we	we	PRON
ejpam-4348	168	9	are	be	AUX
ejpam-4348	168	10	in	in	ADP
ejpam-4348	168	11	the	the	DET
ejpam-4348	168	12	case	case	NOUN
ejpam-4348	168	13	of	of	ADP
ejpam-4348	168	14	the	the	DET
ejpam-4348	168	15	parabola	parabola	NOUN
ejpam-4348	168	16	studied	study	VERB
ejpam-4348	168	17	by	by	ADP
ejpam-4348	168	18	malyshev	malyshev	NOUN
ejpam-4348	168	19	and	and	CCONJ
ejpam-4348	168	20	sadkane	sadkane	NOUN
ejpam-4348	168	21	in	in	ADP
ejpam-4348	168	22	[	[	X
ejpam-4348	168	23	13	13	NUM
ejpam-4348	168	24	]	]	PUNCT
ejpam-4348	168	25	.	.	PUNCT
ejpam-4348	169	1	on	on	ADP
ejpam-4348	169	2	the	the	DET
ejpam-4348	169	3	other	other	ADJ
ejpam-4348	169	4	hand	hand	NOUN
ejpam-4348	169	5	,	,	PUNCT
ejpam-4348	169	6	in	in	ADP
ejpam-4348	169	7	this	this	DET
ejpam-4348	169	8	section	section	NOUN
ejpam-4348	169	9	,	,	PUNCT
ejpam-4348	169	10	we	we	PRON
ejpam-4348	169	11	are	be	AUX
ejpam-4348	169	12	going	go	VERB
ejpam-4348	169	13	to	to	PART
ejpam-4348	169	14	consider	consider	VERB
ejpam-4348	169	15	the	the	DET
ejpam-4348	169	16	coefficient	coefficient	NOUN
ejpam-4348	169	17	b	b	PROPN
ejpam-4348	169	18	̸=	̸=	PROPN
ejpam-4348	169	19	0	0	NUM
ejpam-4348	169	20	.	.	PUNCT
ejpam-4348	170	1	which	which	PRON
ejpam-4348	170	2	leads	lead	VERB
ejpam-4348	170	3	us	we	PRON
ejpam-4348	170	4	to	to	PART
ejpam-4348	170	5	define	define	VERB
ejpam-4348	170	6	the	the	DET
ejpam-4348	170	7	following	follow	VERB
ejpam-4348	170	8	parabola	parabola	PROPN
ejpam-4348	170	9	γ̃	γ̃	PROPN
ejpam-4348	170	10	=	=	PUNCT
ejpam-4348	170	11	{	{	PUNCT
ejpam-4348	170	12	z	z	NOUN
ejpam-4348	170	13	=	=	SYM
ejpam-4348	170	14	x+	x+	PROPN
ejpam-4348	170	15	iy	iy	PROPN
ejpam-4348	170	16	\	\	PROPN
ejpam-4348	170	17	x+	x+	PROPN
ejpam-4348	170	18	i(y	i(y	PROPN
ejpam-4348	170	19	−	−	PROPN
ejpam-4348	170	20	pb	pb	NOUN
ejpam-4348	170	21	)	)	PUNCT
ejpam-4348	170	22	∈	∈	PROPN
ejpam-4348	170	23	γ	γ	X
ejpam-4348	170	24	}	}	PUNCT
ejpam-4348	170	25	s.	s.	PROPN
ejpam-4348	170	26	traoré	traoré	PROPN
ejpam-4348	170	27	,	,	PUNCT
ejpam-4348	170	28	m.	m.	NOUN
ejpam-4348	170	29	dosso	dosso	PROPN
ejpam-4348	170	30	/	/	SYM
ejpam-4348	170	31	eur	eur	PROPN
ejpam-4348	170	32	.	.	PUNCT
ejpam-4348	171	1	j.	j.	PROPN
ejpam-4348	171	2	pure	pure	PROPN
ejpam-4348	171	3	appl	appl	PROPN
ejpam-4348	171	4	.	.	PROPN
ejpam-4348	171	5	math	math	PROPN
ejpam-4348	171	6	,	,	PUNCT
ejpam-4348	171	7	15	15	NUM
ejpam-4348	171	8	(	(	PUNCT
ejpam-4348	171	9	2	2	NUM
ejpam-4348	171	10	)	)	PUNCT
ejpam-4348	171	11	(	(	PUNCT
ejpam-4348	171	12	2022	2022	NUM
ejpam-4348	171	13	)	)	PUNCT
ejpam-4348	171	14	,	,	PUNCT
ejpam-4348	171	15	681	681	NUM
ejpam-4348	171	16	-	-	SYM
ejpam-4348	171	17	725	725	NUM
ejpam-4348	171	18	692	692	NUM
ejpam-4348	171	19	of	of	ADP
ejpam-4348	171	20	the	the	DET
ejpam-4348	171	21	equation	equation	NOUN
ejpam-4348	171	22	2p	2p	NOUN
ejpam-4348	171	23	(	(	PUNCT
ejpam-4348	171	24	p	p	NOUN
ejpam-4348	171	25	2	2	NUM
ejpam-4348	171	26	−	−	NOUN
ejpam-4348	171	27	x	x	SYM
ejpam-4348	171	28	)	)	PUNCT
ejpam-4348	172	1	=	=	SYM
ejpam-4348	172	2	ỹ2	ỹ2	PROPN
ejpam-4348	172	3	(	(	PUNCT
ejpam-4348	172	4	25	25	NUM
ejpam-4348	172	5	)	)	PUNCT
ejpam-4348	172	6	where	where	SCONJ
ejpam-4348	172	7	ỹ	ỹ	PROPN
ejpam-4348	172	8	=	=	SYM
ejpam-4348	172	9	y	y	PROPN
ejpam-4348	172	10	−	−	NOUN
ejpam-4348	172	11	pb	pb	X
ejpam-4348	172	12	.	.	PUNCT
ejpam-4348	172	13	consider	consider	VERB
ejpam-4348	172	14	the	the	DET
ejpam-4348	172	15	matrix	matrix	NOUN
ejpam-4348	172	16	of	of	ADP
ejpam-4348	172	17	order	order	NOUN
ejpam-4348	172	18	2n	2n	NUM
ejpam-4348	172	19	defined	define	VERB
ejpam-4348	172	20	by	by	ADP
ejpam-4348	172	21	ã	ã	PROPN
ejpam-4348	172	22	=	=	PUNCT
ejpam-4348	172	23			NOUN
ejpam-4348	173	1	−	−	ADP
ejpam-4348	173	2	√	√	NOUN
ejpam-4348	174	1	p	p	NOUN
ejpam-4348	174	2	2	2	NUM
ejpam-4348	174	3	in	in	ADP
ejpam-4348	174	4	ab	ab	PROPN
ejpam-4348	174	5	in	in	ADP
ejpam-4348	174	6	−	−	PROPN
ejpam-4348	174	7	√	√	PROPN
ejpam-4348	174	8	p	p	NOUN
ejpam-4348	174	9	2	2	NUM
ejpam-4348	174	10	in	in	ADP
ejpam-4348	174	11			NUM
ejpam-4348	174	12	where	where	SCONJ
ejpam-4348	174	13	ab	ab	PROPN
ejpam-4348	174	14	=	=	SYM
ejpam-4348	174	15	a−	a−	PROPN
ejpam-4348	174	16	ipbin	ipbin	ADJ
ejpam-4348	174	17	remark	remark	NOUN
ejpam-4348	174	18	2	2	NUM
ejpam-4348	174	19	.	.	PUNCT
ejpam-4348	175	1	the	the	DET
ejpam-4348	175	2	respective	respective	ADJ
ejpam-4348	175	3	eigenvalues	eigenvalue	VERB
ejpam-4348	175	4	λ̃	λ̃	PROPN
ejpam-4348	175	5	and	and	CCONJ
ejpam-4348	175	6	z	z	NOUN
ejpam-4348	175	7	of	of	ADP
ejpam-4348	175	8	the	the	DET
ejpam-4348	175	9	matrices	matrix	NOUN
ejpam-4348	175	10	ã	ã	PROPN
ejpam-4348	175	11	and	and	CCONJ
ejpam-4348	175	12	a	a	PRON
ejpam-4348	175	13	are	be	AUX
ejpam-4348	175	14	such	such	ADJ
ejpam-4348	175	15	that	that	SCONJ
ejpam-4348	175	16	z	z	NOUN
ejpam-4348	175	17	=	=	SYM
ejpam-4348	175	18	(	(	PUNCT
ejpam-4348	175	19	λ̃+	λ̃+	X
ejpam-4348	175	20	√	√	ADJ
ejpam-4348	175	21	p	p	NOUN
ejpam-4348	175	22	2	2	NUM
ejpam-4348	175	23	)	)	SYM
ejpam-4348	175	24	2	2	NUM
ejpam-4348	176	1	+	+	CCONJ
ejpam-4348	176	2	ipb	ipb	NOUN
ejpam-4348	176	3	we	we	PRON
ejpam-4348	176	4	also	also	ADV
ejpam-4348	176	5	assume	assume	VERB
ejpam-4348	176	6	that	that	SCONJ
ejpam-4348	176	7	∥ab∥	∥ab∥	ADV
ejpam-4348	176	8	=	=	SYM
ejpam-4348	176	9	1	1	X
ejpam-4348	176	10	.	.	PUNCT
ejpam-4348	176	11	otherwise	otherwise	ADV
ejpam-4348	176	12	(	(	PUNCT
ejpam-4348	176	13	i.e.	i.e.	X
ejpam-4348	176	14	∥ab∥	∥ab∥	X
ejpam-4348	176	15	=	=	NOUN
ejpam-4348	176	16	̸	̸	NUM
ejpam-4348	176	17	1	1	NUM
ejpam-4348	176	18	)	)	PUNCT
ejpam-4348	176	19	,	,	PUNCT
ejpam-4348	176	20	we	we	PRON
ejpam-4348	176	21	can	can	AUX
ejpam-4348	176	22	take	take	VERB
ejpam-4348	176	23	a1	a1	NOUN
ejpam-4348	176	24	b	b	NOUN
ejpam-4348	176	25	=	=	SYM
ejpam-4348	176	26	1	1	NUM
ejpam-4348	176	27	∥ab∥	∥ab∥	VERB
ejpam-4348	176	28	ab	ab	PROPN
ejpam-4348	176	29	and	and	CCONJ
ejpam-4348	176	30	p1	p1	PROPN
ejpam-4348	176	31	=	=	SYM
ejpam-4348	176	32	1	1	NUM
ejpam-4348	176	33	∥ab∥	∥ab∥	ADJ
ejpam-4348	176	34	p.	p.	NOUN
ejpam-4348	176	35	consider	consider	VERB
ejpam-4348	176	36	the	the	DET
ejpam-4348	176	37	dichotomy	dichotomy	NOUN
ejpam-4348	176	38	quantities	quantity	NOUN
ejpam-4348	176	39	characterized	characterize	VERB
ejpam-4348	176	40	by	by	ADP
ejpam-4348	176	41	the	the	DET
ejpam-4348	176	42	following	follow	VERB
ejpam-4348	176	43	numerical	numerical	ADJ
ejpam-4348	176	44	parameters	parameter	NOUN
ejpam-4348	176	45	αã	αã	X
ejpam-4348	176	46	=	=	NOUN
ejpam-4348	176	47	sup	sup	NOUN
ejpam-4348	176	48	ℜ(λ̃)=0	ℜ(λ̃)=0	ADV
ejpam-4348	176	49	∥(λ̃i2n	∥(λ̃i2n	PROPN
ejpam-4348	176	50	−	−	PROPN
ejpam-4348	176	51	ã)−1∥	ã)−1∥	PROPN
ejpam-4348	177	1	and	and	CCONJ
ejpam-4348	177	2	αab	αab	VERB
ejpam-4348	177	3	=	=	NOUN
ejpam-4348	177	4	sup	sup	NOUN
ejpam-4348	177	5	z∈γ̃	z∈γ̃	NOUN
ejpam-4348	177	6	∥(zin	∥(zin	PROPN
ejpam-4348	177	7	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	177	8	(	(	PUNCT
ejpam-4348	177	9	26	26	NUM
ejpam-4348	177	10	)	)	PUNCT
ejpam-4348	177	11	we	we	PRON
ejpam-4348	177	12	have	have	VERB
ejpam-4348	177	13	the	the	DET
ejpam-4348	177	14	following	follow	VERB
ejpam-4348	177	15	proposition	proposition	NOUN
ejpam-4348	177	16	proposition	proposition	NOUN
ejpam-4348	177	17	6	6	NUM
ejpam-4348	177	18	.	.	PUNCT
ejpam-4348	178	1	let	let	VERB
ejpam-4348	178	2	αã	αã	PRON
ejpam-4348	178	3	and	and	CCONJ
ejpam-4348	178	4	αab	αab	VERB
ejpam-4348	178	5	be	be	AUX
ejpam-4348	178	6	the	the	DET
ejpam-4348	178	7	two	two	NUM
ejpam-4348	178	8	parameters	parameter	NOUN
ejpam-4348	178	9	defined	define	VERB
ejpam-4348	178	10	in	in	ADP
ejpam-4348	178	11	(	(	PUNCT
ejpam-4348	178	12	26	26	NUM
ejpam-4348	178	13	)	)	PUNCT
ejpam-4348	178	14	.	.	PUNCT
ejpam-4348	179	1	assume	assume	VERB
ejpam-4348	179	2	that	that	SCONJ
ejpam-4348	179	3	∥ab∥	∥ab∥	ADV
ejpam-4348	179	4	=	=	SYM
ejpam-4348	179	5	1	1	NUM
ejpam-4348	179	6	and	and	CCONJ
ejpam-4348	179	7	|pb|	|pb|	ADJ
ejpam-4348	179	8	<	<	X
ejpam-4348	179	9	1	1	NUM
ejpam-4348	179	10	αab	αab	NOUN
ejpam-4348	179	11	.	.	PUNCT
ejpam-4348	180	1	(	(	PUNCT
ejpam-4348	180	2	27	27	NUM
ejpam-4348	180	3	)	)	PUNCT
ejpam-4348	180	4	then	then	ADV
ejpam-4348	180	5	αab	αab	VERB
ejpam-4348	180	6	≤	≤	ADJ
ejpam-4348	180	7	αã	αã	PRON
ejpam-4348	180	8	≤	≤	ADJ
ejpam-4348	180	9	2	2	NUM
ejpam-4348	180	10	(	(	PUNCT
ejpam-4348	180	11	αab	αab	VERB
ejpam-4348	180	12	+	+	CCONJ
ejpam-4348	180	13	√	√	INTJ
ejpam-4348	180	14	αab	αab	NOUN
ejpam-4348	180	15	(	(	PUNCT
ejpam-4348	180	16	1	1	NUM
ejpam-4348	180	17	+	+	CCONJ
ejpam-4348	180	18	√	√	ADJ
ejpam-4348	180	19	αab	αab	VERB
ejpam-4348	180	20	+	+	NOUN
ejpam-4348	180	21	1	1	NUM
ejpam-4348	180	22	)	)	PUNCT
ejpam-4348	180	23	)	)	PUNCT
ejpam-4348	181	1	(	(	PUNCT
ejpam-4348	181	2	28	28	X
ejpam-4348	181	3	)	)	PUNCT
ejpam-4348	181	4	proof	proof	NOUN
ejpam-4348	181	5	.	.	PUNCT
ejpam-4348	182	1	consider	consider	VERB
ejpam-4348	182	2	the	the	DET
ejpam-4348	182	3	matrix	matrix	NOUN
ejpam-4348	182	4	(	(	PUNCT
ejpam-4348	182	5	λ̃i2n	λ̃i2n	NOUN
ejpam-4348	182	6	−	−	PROPN
ejpam-4348	182	7	ã	ã	PROPN
ejpam-4348	182	8	)	)	PUNCT
ejpam-4348	182	9	=	=	SYM
ejpam-4348	182	10			NOUN
ejpam-4348	182	11	(	(	PUNCT
ejpam-4348	182	12	λ̃+	λ̃+	X
ejpam-4348	183	1	√	√	X
ejpam-4348	183	2	p	p	X
ejpam-4348	183	3	2)in	2)in	NUM
ejpam-4348	183	4	−ab	−ab	NUM
ejpam-4348	183	5	−in	−in	PROPN
ejpam-4348	183	6	(	(	PUNCT
ejpam-4348	183	7	λ̃+	λ̃+	X
ejpam-4348	183	8	√	√	INTJ
ejpam-4348	183	9	p	p	X
ejpam-4348	183	10	2)in	2)in	PROPN
ejpam-4348	183	11			NOUN
ejpam-4348	183	12	.	.	PUNCT
ejpam-4348	184	1	s.	s.	PROPN
ejpam-4348	184	2	traoré	traoré	PROPN
ejpam-4348	184	3	,	,	PUNCT
ejpam-4348	184	4	m.	m.	NOUN
ejpam-4348	184	5	dosso	dosso	PROPN
ejpam-4348	184	6	/	/	SYM
ejpam-4348	184	7	eur	eur	PROPN
ejpam-4348	184	8	.	.	PUNCT
ejpam-4348	185	1	j.	j.	PROPN
ejpam-4348	185	2	pure	pure	PROPN
ejpam-4348	185	3	appl	appl	PROPN
ejpam-4348	185	4	.	.	PROPN
ejpam-4348	185	5	math	math	PROPN
ejpam-4348	185	6	,	,	PUNCT
ejpam-4348	185	7	15	15	NUM
ejpam-4348	185	8	(	(	PUNCT
ejpam-4348	185	9	2	2	NUM
ejpam-4348	185	10	)	)	PUNCT
ejpam-4348	185	11	(	(	PUNCT
ejpam-4348	185	12	2022	2022	NUM
ejpam-4348	185	13	)	)	PUNCT
ejpam-4348	185	14	,	,	PUNCT
ejpam-4348	185	15	681	681	NUM
ejpam-4348	185	16	-	-	SYM
ejpam-4348	185	17	725	725	NUM
ejpam-4348	185	18	693	693	NUM
ejpam-4348	185	19	we	we	PRON
ejpam-4348	185	20	have	have	VERB
ejpam-4348	185	21			NOUN
ejpam-4348	185	22	(	(	PUNCT
ejpam-4348	185	23	λ̃+	λ̃+	X
ejpam-4348	185	24	√	√	X
ejpam-4348	185	25	p	p	X
ejpam-4348	185	26	2)in	2)in	PROPN
ejpam-4348	185	27	ab	ab	PROPN
ejpam-4348	185	28	in	in	ADP
ejpam-4348	185	29	(	(	PUNCT
ejpam-4348	185	30	λ̃+	λ̃+	X
ejpam-4348	185	31	√	√	PROPN
ejpam-4348	185	32	p	p	NOUN
ejpam-4348	185	33	2)in	2)in	PROPN
ejpam-4348	185	34	×	×	NOUN
ejpam-4348	185	35			NOUN
ejpam-4348	185	36	(	(	PUNCT
ejpam-4348	185	37	λ̃+	λ̃+	X
ejpam-4348	185	38	√	√	X
ejpam-4348	186	1	p	p	X
ejpam-4348	186	2	2)in	2)in	NUM
ejpam-4348	186	3	−ab	−ab	NUM
ejpam-4348	186	4	−in	−in	PROPN
ejpam-4348	186	5	(	(	PUNCT
ejpam-4348	186	6	λ̃+	λ̃+	X
ejpam-4348	186	7	√	√	INTJ
ejpam-4348	186	8	p	p	X
ejpam-4348	186	9	2)in	2)in	PROPN
ejpam-4348	186	10			NOUN
ejpam-4348	186	11	=	=	PUNCT
ejpam-4348	186	12			NOUN
ejpam-4348	186	13	(	(	PUNCT
ejpam-4348	186	14	λ̃+	λ̃+	X
ejpam-4348	186	15	√	√	X
ejpam-4348	186	16	p	p	NOUN
ejpam-4348	186	17	2	2	NUM
ejpam-4348	186	18	)	)	PUNCT
ejpam-4348	186	19	2	2	NUM
ejpam-4348	186	20	in	in	ADP
ejpam-4348	186	21	−ab	−ab	NUM
ejpam-4348	186	22	0	0	NUM
ejpam-4348	186	23	0	0	NUM
ejpam-4348	186	24	(	(	PUNCT
ejpam-4348	186	25	λ̃+	λ̃+	X
ejpam-4348	186	26	√	√	X
ejpam-4348	186	27	p	p	NOUN
ejpam-4348	186	28	2	2	NUM
ejpam-4348	186	29	)	)	PUNCT
ejpam-4348	186	30	2	2	NUM
ejpam-4348	186	31	in	in	ADP
ejpam-4348	186	32	−ab	−ab	NUM
ejpam-4348	186	33			NOUN
ejpam-4348	186	34	therefore	therefore	ADV
ejpam-4348	186	35	(	(	PUNCT
ejpam-4348	186	36	λ̃i2n	λ̃i2n	NOUN
ejpam-4348	186	37	−	−	X
ejpam-4348	187	1	ã)−1	ã)−1	PRON
ejpam-4348	187	2	=	=	NOUN
ejpam-4348	187	3			NOUN
ejpam-4348	187	4	(	(	PUNCT
ejpam-4348	187	5	λ̃+	λ̃+	X
ejpam-4348	187	6	√	√	X
ejpam-4348	187	7	p	p	NOUN
ejpam-4348	187	8	2	2	NUM
ejpam-4348	187	9	)	)	PUNCT
ejpam-4348	187	10	2	2	NUM
ejpam-4348	187	11	in	in	ADP
ejpam-4348	187	12	−ab	−ab	NUM
ejpam-4348	187	13	0	0	NUM
ejpam-4348	187	14	0	0	NUM
ejpam-4348	187	15	(	(	PUNCT
ejpam-4348	187	16	λ̃+	λ̃+	X
ejpam-4348	187	17	√	√	X
ejpam-4348	187	18	p	p	NOUN
ejpam-4348	187	19	2	2	NUM
ejpam-4348	187	20	)	)	PUNCT
ejpam-4348	187	21	2	2	NUM
ejpam-4348	187	22	in	in	ADP
ejpam-4348	187	23	−ab	−ab	NUM
ejpam-4348	187	24			NOUN
ejpam-4348	187	25	−1	−1	NOUN
ejpam-4348	187	26	×	×	NOUN
ejpam-4348	187	27			NOUN
ejpam-4348	187	28	(	(	PUNCT
ejpam-4348	187	29	λ̃+	λ̃+	X
ejpam-4348	187	30	√	√	X
ejpam-4348	187	31	p	p	X
ejpam-4348	187	32	2)in	2)in	PROPN
ejpam-4348	187	33	ab	ab	PROPN
ejpam-4348	187	34	in	in	ADP
ejpam-4348	187	35	(	(	PUNCT
ejpam-4348	187	36	λ̃+	λ̃+	X
ejpam-4348	187	37	√	√	PROPN
ejpam-4348	187	38	p	p	X
ejpam-4348	187	39	2)in	2)in	PROPN
ejpam-4348	187	40			NOUN
ejpam-4348	187	41	=	=	SYM
ejpam-4348	187	42			NOUN
ejpam-4348	188	1	(	(	PUNCT
ejpam-4348	188	2	(	(	PUNCT
ejpam-4348	188	3	λ̃+	λ̃+	X
ejpam-4348	188	4	√	√	X
ejpam-4348	188	5	p	p	NOUN
ejpam-4348	188	6	2	2	NUM
ejpam-4348	188	7	)	)	PUNCT
ejpam-4348	188	8	2	2	NUM
ejpam-4348	189	1	+	+	CCONJ
ejpam-4348	189	2	ipb)in	ipb)in	ADJ
ejpam-4348	189	3	−a	−a	NOUN
ejpam-4348	189	4	0	0	NUM
ejpam-4348	189	5	0	0	NUM
ejpam-4348	189	6	(	(	PUNCT
ejpam-4348	189	7	(	(	PUNCT
ejpam-4348	189	8	λ̃+	λ̃+	X
ejpam-4348	189	9	√	√	X
ejpam-4348	189	10	p	p	NOUN
ejpam-4348	189	11	2	2	NUM
ejpam-4348	189	12	)	)	PUNCT
ejpam-4348	189	13	2	2	NUM
ejpam-4348	190	1	+	+	CCONJ
ejpam-4348	190	2	ipb)in	ipb)in	ADJ
ejpam-4348	190	3	−a	−a	ADJ
ejpam-4348	190	4			ADJ
ejpam-4348	190	5	−1	−1	NOUN
ejpam-4348	190	6	×	×	NOUN
ejpam-4348	190	7			NOUN
ejpam-4348	190	8	(	(	PUNCT
ejpam-4348	190	9	λ̃+	λ̃+	X
ejpam-4348	190	10	√	√	X
ejpam-4348	190	11	p	p	X
ejpam-4348	190	12	2)in	2)in	PROPN
ejpam-4348	190	13	a−	a−	PROPN
ejpam-4348	190	14	ipbin	ipbin	NOUN
ejpam-4348	190	15	in	in	ADP
ejpam-4348	190	16	(	(	PUNCT
ejpam-4348	190	17	λ̃+	λ̃+	X
ejpam-4348	190	18	√	√	PROPN
ejpam-4348	190	19	p	p	X
ejpam-4348	190	20	2)in	2)in	PROPN
ejpam-4348	190	21			NOUN
ejpam-4348	190	22	=	=	SYM
ejpam-4348	190	23	(zin	(zin	NOUN
ejpam-4348	190	24	−a)−1	−a)−1	NOUN
ejpam-4348	190	25	0	0	NUM
ejpam-4348	190	26	0	0	NUM
ejpam-4348	190	27	(	(	PUNCT
ejpam-4348	190	28	zin	zin	NOUN
ejpam-4348	190	29	−a)−1	−a)−1	NOUN
ejpam-4348	190	30	×	×	NOUN
ejpam-4348	190	31	√z	√z	NOUN
ejpam-4348	190	32	−	−	PROPN
ejpam-4348	190	33	ipbin	ipbin	ADJ
ejpam-4348	190	34	a−	a−	PROPN
ejpam-4348	190	35	ipbin	ipbin	NOUN
ejpam-4348	190	36	in	in	ADP
ejpam-4348	190	37	√	√	PROPN
ejpam-4348	190	38	z	z	NOUN
ejpam-4348	190	39	−	−	NOUN
ejpam-4348	190	40	ipbin	ipbin	ADJ
ejpam-4348	190	41			NOUN
ejpam-4348	190	42	=	=	SYM
ejpam-4348	190	43	√z	√z	VERB
ejpam-4348	191	1	−	−	PROPN
ejpam-4348	191	2	ipb(zin	ipb(zin	NOUN
ejpam-4348	191	3	−a)−1	−a)−1	NOUN
ejpam-4348	191	4	(	(	PUNCT
ejpam-4348	191	5	zin	zin	NOUN
ejpam-4348	191	6	−a)−1(a−	−a)−1(a−	PROPN
ejpam-4348	191	7	ipbin	ipbin	NOUN
ejpam-4348	191	8	)	)	PUNCT
ejpam-4348	191	9	(	(	PUNCT
ejpam-4348	191	10	zin	zin	NOUN
ejpam-4348	191	11	−a)−1	−a)−1	NOUN
ejpam-4348	191	12	√	√	NOUN
ejpam-4348	191	13	z	z	NOUN
ejpam-4348	191	14	−	−	PROPN
ejpam-4348	191	15	ipb(zin	ipb(zin	NOUN
ejpam-4348	192	1	−a)−1	−a)−1	NOUN
ejpam-4348	192	2			NOUN
ejpam-4348	192	3	knowing	know	VERB
ejpam-4348	192	4	that	that	SCONJ
ejpam-4348	192	5	the	the	DET
ejpam-4348	192	6	norm	norm	NOUN
ejpam-4348	192	7	(	(	PUNCT
ejpam-4348	192	8	λ̃i2n	λ̃i2n	NOUN
ejpam-4348	192	9	−	−	X
ejpam-4348	192	10	ã)−1	ã)−1	PRON
ejpam-4348	192	11	is	be	AUX
ejpam-4348	192	12	greater	great	ADJ
ejpam-4348	192	13	than	than	ADP
ejpam-4348	192	14	or	or	CCONJ
ejpam-4348	192	15	equal	equal	ADJ
ejpam-4348	192	16	to	to	ADP
ejpam-4348	192	17	the	the	DET
ejpam-4348	192	18	norm	norm	NOUN
ejpam-4348	192	19	of	of	ADP
ejpam-4348	192	20	each	each	PRON
ejpam-4348	192	21	of	of	ADP
ejpam-4348	192	22	its	its	PRON
ejpam-4348	192	23	block	block	NOUN
ejpam-4348	192	24	components	component	NOUN
ejpam-4348	192	25	taken	take	VERB
ejpam-4348	192	26	individually	individually	ADV
ejpam-4348	192	27	,	,	PUNCT
ejpam-4348	192	28	we	we	PRON
ejpam-4348	192	29	can	can	AUX
ejpam-4348	192	30	deduce	deduce	VERB
ejpam-4348	192	31	that	that	PRON
ejpam-4348	192	32	α̃	α̃	PROPN
ejpam-4348	192	33	=	=	PUNCT
ejpam-4348	192	34	sup	sup	X
ejpam-4348	192	35	ℜ(λ̃)=0	ℜ(λ̃)=0	ADV
ejpam-4348	192	36	∥(λ̃i2n	∥(λ̃i2n	PROPN
ejpam-4348	192	37	−	−	PROPN
ejpam-4348	192	38	ã)−1∥	ã)−1∥	NOUN
ejpam-4348	192	39	≥	≥	NOUN
ejpam-4348	192	40	sup	sup	NOUN
ejpam-4348	192	41	z∈γ̃	z∈γ̃	VERB
ejpam-4348	192	42	∥(zin	∥(zin	PROPN
ejpam-4348	192	43	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	193	1	=	=	SYM
ejpam-4348	193	2	αab	αab	PROPN
ejpam-4348	193	3	s.	s.	PROPN
ejpam-4348	193	4	traoré	traoré	PROPN
ejpam-4348	193	5	,	,	PUNCT
ejpam-4348	193	6	m.	m.	NOUN
ejpam-4348	193	7	dosso	dosso	PROPN
ejpam-4348	193	8	/	/	SYM
ejpam-4348	193	9	eur	eur	PROPN
ejpam-4348	193	10	.	.	PUNCT
ejpam-4348	194	1	j.	j.	PROPN
ejpam-4348	194	2	pure	pure	PROPN
ejpam-4348	194	3	appl	appl	PROPN
ejpam-4348	194	4	.	.	PROPN
ejpam-4348	194	5	math	math	PROPN
ejpam-4348	194	6	,	,	PUNCT
ejpam-4348	194	7	15	15	NUM
ejpam-4348	194	8	(	(	PUNCT
ejpam-4348	194	9	2	2	NUM
ejpam-4348	194	10	)	)	PUNCT
ejpam-4348	194	11	(	(	PUNCT
ejpam-4348	194	12	2022	2022	NUM
ejpam-4348	194	13	)	)	PUNCT
ejpam-4348	194	14	,	,	PUNCT
ejpam-4348	194	15	681	681	NUM
ejpam-4348	194	16	-	-	SYM
ejpam-4348	194	17	725	725	NUM
ejpam-4348	194	18	694	694	NUM
ejpam-4348	194	19	and	and	CCONJ
ejpam-4348	194	20	also	also	ADV
ejpam-4348	194	21	∥(λ̃i2n	∥(λ̃i2n	PROPN
ejpam-4348	194	22	−	−	PROPN
ejpam-4348	194	23	ã)−1∥	ã)−1∥	PROPN
ejpam-4348	194	24	≤	≤	PROPN
ejpam-4348	194	25	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4348	195	1	√	√	PROPN
ejpam-4348	195	2	z	z	NOUN
ejpam-4348	195	3	−	−	PROPN
ejpam-4348	195	4	ipbin	ipbin	ADJ
ejpam-4348	195	5	a−	a−	PROPN
ejpam-4348	195	6	ipbin	ipbin	NOUN
ejpam-4348	195	7	in	in	ADP
ejpam-4348	195	8	√	√	PROPN
ejpam-4348	195	9	z	z	NOUN
ejpam-4348	195	10	−	−	PROPN
ejpam-4348	196	1	ipbin	ipbin	INTJ
ejpam-4348	196	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ejpam-4348	197	1	∥(zin	∥(zin	PROPN
ejpam-4348	198	1	−a)−1∥	−a)−1∥	CCONJ
ejpam-4348	198	2	≤	≤	NUM
ejpam-4348	198	3	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ejpam-4348	199	1	∥	∥	NOUN
ejpam-4348	199	2	√	√	PROPN
ejpam-4348	199	3	z	z	NOUN
ejpam-4348	199	4	−	−	PROPN
ejpam-4348	199	5	ipbin∥	ipbin∥	PROPN
ejpam-4348	199	6	∥a−	∥a−	PUNCT
ejpam-4348	199	7	ipbin∥	ipbin∥	PROPN
ejpam-4348	199	8	∥in∥	∥in∥	X
ejpam-4348	199	9	∥	∥	PRON
ejpam-4348	200	1	√	√	ADV
ejpam-4348	200	2	z	z	NOUN
ejpam-4348	200	3	−	−	PROPN
ejpam-4348	200	4	ipbin∥	ipbin∥	PROPN
ejpam-4348	200	5	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4348	201	1	∥(zin	∥(zin	PROPN
ejpam-4348	201	2	−a)−1∥	−a)−1∥	CCONJ
ejpam-4348	201	3	≤	≤	NUM
ejpam-4348	201	4	∥∥∥∥∥∥	∥∥∥∥∥∥	X
ejpam-4348	202	1			PROPN
ejpam-4348	202	2	√	√	NOUN
ejpam-4348	202	3	|z|+	|z|+	VERB
ejpam-4348	202	4	√	√	NOUN
ejpam-4348	202	5	|pb|	|pb|	ADJ
ejpam-4348	202	6	1	1	NUM
ejpam-4348	202	7	1	1	NUM
ejpam-4348	202	8	√	√	NOUN
ejpam-4348	202	9	|z|+	|z|+	VERB
ejpam-4348	202	10	√	√	NOUN
ejpam-4348	202	11	|pb|	|pb|	PROPN
ejpam-4348	202	12	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ejpam-4348	203	1	∥(zin	∥(zin	PROPN
ejpam-4348	203	2	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	203	3	≤	≤	NUM
ejpam-4348	203	4	(	(	PUNCT
ejpam-4348	203	5	(	(	PUNCT
ejpam-4348	203	6	1	1	NUM
ejpam-4348	203	7	+	+	NOUN
ejpam-4348	203	8	√	√	PROPN
ejpam-4348	203	9	|z|+	|z|+	VERB
ejpam-4348	203	10	√	√	NOUN
ejpam-4348	203	11	|pb|	|pb|	ADJ
ejpam-4348	203	12	)	)	PUNCT
ejpam-4348	204	1	∥(zin	∥(zin	PROPN
ejpam-4348	204	2	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	204	3	•	•	NOUN
ejpam-4348	204	4	if	if	SCONJ
ejpam-4348	204	5	|z|	|z|	NOUN
ejpam-4348	204	6	≤	≤	NUM
ejpam-4348	204	7	αab	αab	VERB
ejpam-4348	204	8	+	+	NOUN
ejpam-4348	204	9	1	1	NUM
ejpam-4348	204	10	αab	αab	AUX
ejpam-4348	204	11	then	then	ADV
ejpam-4348	204	12	∥(λi2n	∥(λi2n	VERB
ejpam-4348	204	13	−	−	PROPN
ejpam-4348	204	14	ã)−1∥	ã)−1∥	PROPN
ejpam-4348	204	15	≤	≤	NOUN
ejpam-4348	204	16	αab	αab	VERB
ejpam-4348	204	17	(	(	PUNCT
ejpam-4348	204	18	√	√	INTJ
ejpam-4348	204	19	|z|+	|z|+	VERB
ejpam-4348	204	20	√	√	NUM
ejpam-4348	204	21	|pb|+	|pb|+	NOUN
ejpam-4348	204	22	1	1	NUM
ejpam-4348	204	23	)	)	PUNCT
ejpam-4348	204	24	≤	≤	NOUN
ejpam-4348	205	1	αab	αab	VERB
ejpam-4348	205	2	(	(	PUNCT
ejpam-4348	205	3	√	√	VERB
ejpam-4348	205	4	αab	αab	VERB
ejpam-4348	205	5	+	+	NOUN
ejpam-4348	205	6	1	1	NUM
ejpam-4348	205	7	αab	αab	NOUN
ejpam-4348	205	8	+	+	CCONJ
ejpam-4348	205	9	√	√	NUM
ejpam-4348	205	10	1	1	NUM
ejpam-4348	205	11	αab	αab	VERB
ejpam-4348	205	12	+	+	NOUN
ejpam-4348	205	13	1	1	NUM
ejpam-4348	205	14	)	)	PUNCT
ejpam-4348	205	15	≤	≤	NOUN
ejpam-4348	206	1	αab	αab	VERB
ejpam-4348	206	2	+	+	CCONJ
ejpam-4348	206	3	√	√	NUM
ejpam-4348	206	4	αab	αab	NOUN
ejpam-4348	206	5	(	(	PUNCT
ejpam-4348	206	6	1	1	NUM
ejpam-4348	206	7	+	+	CCONJ
ejpam-4348	206	8	√	√	ADJ
ejpam-4348	206	9	αab	αab	VERB
ejpam-4348	206	10	+	+	NOUN
ejpam-4348	206	11	1	1	NUM
ejpam-4348	206	12	)	)	PUNCT
ejpam-4348	206	13	•	•	NOUN
ejpam-4348	206	14	if	if	SCONJ
ejpam-4348	206	15	|z|	|z|	NOUN
ejpam-4348	206	16	>	>	X
ejpam-4348	206	17	αab	αab	NOUN
ejpam-4348	207	1	+	+	NOUN
ejpam-4348	207	2	1	1	NUM
ejpam-4348	207	3	αab	αab	VERB
ejpam-4348	207	4	then	then	ADV
ejpam-4348	207	5	with	with	ADP
ejpam-4348	207	6	the	the	DET
ejpam-4348	207	7	assumptions	assumption	NOUN
ejpam-4348	207	8	∥ab∥	∥ab∥	ADJ
ejpam-4348	207	9	=	=	SYM
ejpam-4348	207	10	1	1	NUM
ejpam-4348	207	11	and	and	CCONJ
ejpam-4348	207	12	|pb|	|pb|	ADJ
ejpam-4348	207	13	<	<	X
ejpam-4348	207	14	1	1	NUM
ejpam-4348	207	15	αab	αab	INTJ
ejpam-4348	207	16	we	we	PRON
ejpam-4348	207	17	note	note	VERB
ejpam-4348	207	18	that	that	SCONJ
ejpam-4348	207	19	∥∥∥∥az	∥∥∥∥az	PROPN
ejpam-4348	207	20	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-4348	207	21	<	<	X
ejpam-4348	207	22	αab	αab	VERB
ejpam-4348	207	23	αab	αab	ADV
ejpam-4348	207	24	+	+	X
ejpam-4348	207	25	1	1	NUM
ejpam-4348	207	26	(	(	PUNCT
ejpam-4348	207	27	∥ab∥+	∥ab∥+	NOUN
ejpam-4348	207	28	|pb|	|pb|	ADV
ejpam-4348	207	29	)	)	PUNCT
ejpam-4348	207	30	<	<	X
ejpam-4348	207	31	αab	αab	VERB
ejpam-4348	207	32	αab	αab	ADV
ejpam-4348	207	33	+	+	X
ejpam-4348	207	34	1	1	NUM
ejpam-4348	207	35	(	(	PUNCT
ejpam-4348	207	36	1	1	NUM
ejpam-4348	207	37	+	+	SYM
ejpam-4348	207	38	1	1	NUM
ejpam-4348	207	39	αab	αab	NOUN
ejpam-4348	207	40	)	)	PUNCT
ejpam-4348	207	41	<	<	X
ejpam-4348	207	42	1	1	NUM
ejpam-4348	207	43	which	which	PRON
ejpam-4348	207	44	leads	lead	VERB
ejpam-4348	207	45	to	to	ADP
ejpam-4348	207	46	(	(	PUNCT
ejpam-4348	207	47	zin	zin	NOUN
ejpam-4348	207	48	−a)−1	−a)−1	NOUN
ejpam-4348	208	1	=	=	SYM
ejpam-4348	208	2	1	1	NUM
ejpam-4348	208	3	z	z	NOUN
ejpam-4348	208	4	(	(	PUNCT
ejpam-4348	208	5	in	in	ADP
ejpam-4348	208	6	−	−	PROPN
ejpam-4348	208	7	a	a	DET
ejpam-4348	208	8	z	z	NOUN
ejpam-4348	208	9	)	)	PUNCT
ejpam-4348	208	10	−1	−1	NOUN
ejpam-4348	208	11	=	=	SYM
ejpam-4348	208	12	1	1	NUM
ejpam-4348	208	13	z	z	NOUN
ejpam-4348	208	14	(	(	PUNCT
ejpam-4348	208	15	in	in	ADP
ejpam-4348	208	16	+	+	CCONJ
ejpam-4348	208	17	a	a	DET
ejpam-4348	208	18	z	z	NOUN
ejpam-4348	209	1	+	+	NOUN
ejpam-4348	209	2	∞∑	∞∑	PROPN
ejpam-4348	209	3	m=0	m=0	PROPN
ejpam-4348	209	4	am	be	AUX
ejpam-4348	209	5	zm	zm	PROPN
ejpam-4348	209	6	)	)	PUNCT
ejpam-4348	210	1	=	=	PUNCT
ejpam-4348	211	1	1	1	NUM
ejpam-4348	211	2	z	z	NOUN
ejpam-4348	211	3	(	(	PUNCT
ejpam-4348	211	4	in	in	ADP
ejpam-4348	211	5	+	+	NOUN
ejpam-4348	211	6	a(zin	a(zin	NOUN
ejpam-4348	211	7	−a)−1	−a)−1	NOUN
ejpam-4348	211	8	)	)	PUNCT
ejpam-4348	211	9	)	)	PUNCT
ejpam-4348	211	10	therefore	therefore	ADV
ejpam-4348	211	11	s.	s.	PROPN
ejpam-4348	211	12	traoré	traoré	PROPN
ejpam-4348	211	13	,	,	PUNCT
ejpam-4348	211	14	m.	m.	NOUN
ejpam-4348	211	15	dosso	dosso	PROPN
ejpam-4348	211	16	/	/	SYM
ejpam-4348	211	17	eur	eur	PROPN
ejpam-4348	211	18	.	.	PUNCT
ejpam-4348	212	1	j.	j.	PROPN
ejpam-4348	212	2	pure	pure	PROPN
ejpam-4348	212	3	appl	appl	PROPN
ejpam-4348	212	4	.	.	PROPN
ejpam-4348	212	5	math	math	PROPN
ejpam-4348	212	6	,	,	PUNCT
ejpam-4348	212	7	15	15	NUM
ejpam-4348	212	8	(	(	PUNCT
ejpam-4348	212	9	2	2	NUM
ejpam-4348	212	10	)	)	PUNCT
ejpam-4348	212	11	(	(	PUNCT
ejpam-4348	212	12	2022	2022	NUM
ejpam-4348	212	13	)	)	PUNCT
ejpam-4348	212	14	,	,	PUNCT
ejpam-4348	212	15	681	681	NUM
ejpam-4348	212	16	-	-	SYM
ejpam-4348	212	17	725	725	NUM
ejpam-4348	212	18	695	695	NUM
ejpam-4348	212	19	∥(λ̃i2n	∥(λ̃i2n	PROPN
ejpam-4348	212	20	−	−	PROPN
ejpam-4348	212	21	ã)−1∥	ã)−1∥	NOUN
ejpam-4348	212	22	≤	≤	NOUN
ejpam-4348	212	23	∥∥∥∥1z	∥∥∥∥1z	PROPN
ejpam-4348	212	24	in	in	ADP
ejpam-4348	212	25	+	+	NUM
ejpam-4348	212	26	1	1	NUM
ejpam-4348	212	27	z	z	NOUN
ejpam-4348	212	28	a	a	DET
ejpam-4348	212	29	(	(	PUNCT
ejpam-4348	212	30	zin	zin	NOUN
ejpam-4348	212	31	−a)−1	−a)−1	NOUN
ejpam-4348	212	32	∥∥∥∥×	∥∥∥∥×	X
ejpam-4348	212	33	∥∥∥1	∥∥∥1	NOUN
ejpam-4348	213	1	+	+	ADJ
ejpam-4348	213	2	√|z|+	√|z|+	ADJ
ejpam-4348	213	3	√	√	VERB
ejpam-4348	213	4	|pb|	|pb|	PROPN
ejpam-4348	213	5	∥∥∥	∥∥∥	PROPN
ejpam-4348	213	6	≤	≤	NUM
ejpam-4348	213	7	(	(	PUNCT
ejpam-4348	213	8	∥a∥∥(zin	∥a∥∥(zin	NOUN
ejpam-4348	213	9	−a)−1∥+	−a)−1∥+	NOUN
ejpam-4348	213	10	1	1	NUM
ejpam-4348	213	11	)	)	PUNCT
ejpam-4348	213	12	1	1	NUM
ejpam-4348	213	13	+	+	CCONJ
ejpam-4348	213	14	√	√	PROPN
ejpam-4348	213	15	|z|+	|z|+	VERB
ejpam-4348	213	16	√	√	ADJ
ejpam-4348	213	17	|pb|	|pb|	ADJ
ejpam-4348	213	18	|z|	|z|	NOUN
ejpam-4348	213	19	≤	≤	NUM
ejpam-4348	213	20	(	(	PUNCT
ejpam-4348	213	21	(	(	PUNCT
ejpam-4348	213	22	1	1	NUM
ejpam-4348	213	23	+	+	NUM
ejpam-4348	213	24	|pb|)αab	|pb|)αab	PROPN
ejpam-4348	213	25	+	+	CCONJ
ejpam-4348	213	26	1	1	NUM
ejpam-4348	213	27	)	)	PUNCT
ejpam-4348	213	28	(	(	PUNCT
ejpam-4348	213	29	αab	αab	AUX
ejpam-4348	213	30	αab	αab	VERB
ejpam-4348	213	31	+	+	CCONJ
ejpam-4348	213	32	1	1	NUM
ejpam-4348	213	33	+	+	CCONJ
ejpam-4348	213	34	√	√	PROPN
ejpam-4348	213	35	αab√	αab√	NUM
ejpam-4348	213	36	αab	αab	VERB
ejpam-4348	213	37	+	+	CCONJ
ejpam-4348	213	38	1	1	NUM
ejpam-4348	213	39	+	+	CCONJ
ejpam-4348	213	40	αab	αab	VERB
ejpam-4348	213	41	√	√	PROPN
ejpam-4348	213	42	|pb|	|pb|	PROPN
ejpam-4348	213	43	αab	αab	VERB
ejpam-4348	214	1	+	+	CCONJ
ejpam-4348	214	2	1	1	NUM
ejpam-4348	214	3	)	)	PUNCT
ejpam-4348	214	4	≤	≤	NOUN
ejpam-4348	214	5	(	(	PUNCT
ejpam-4348	214	6	(	(	PUNCT
ejpam-4348	214	7	1	1	NUM
ejpam-4348	214	8	+	+	SYM
ejpam-4348	214	9	1	1	NUM
ejpam-4348	214	10	αab	αab	NOUN
ejpam-4348	214	11	)	)	PUNCT
ejpam-4348	214	12	αab	αab	VERB
ejpam-4348	214	13	+	+	NOUN
ejpam-4348	214	14	1	1	X
ejpam-4348	214	15	)	)	PUNCT
ejpam-4348	214	16	(	(	PUNCT
ejpam-4348	214	17	αab	αab	AUX
ejpam-4348	214	18	αab	αab	VERB
ejpam-4348	214	19	+	+	CCONJ
ejpam-4348	214	20	1	1	NUM
ejpam-4348	214	21	+	+	CCONJ
ejpam-4348	214	22	√	√	PROPN
ejpam-4348	214	23	αab√	αab√	NUM
ejpam-4348	214	24	αab	αab	VERB
ejpam-4348	214	25	+	+	CCONJ
ejpam-4348	214	26	1	1	NUM
ejpam-4348	214	27	+	+	CCONJ
ejpam-4348	214	28	√	√	ADJ
ejpam-4348	214	29	αab	αab	VERB
ejpam-4348	214	30	αab	αab	VERB
ejpam-4348	215	1	+	+	NOUN
ejpam-4348	215	2	1	1	NUM
ejpam-4348	215	3	)	)	PUNCT
ejpam-4348	215	4	≤	≤	NOUN
ejpam-4348	215	5	2	2	NUM
ejpam-4348	216	1	+	+	CCONJ
ejpam-4348	216	2	αab	αab	VERB
ejpam-4348	216	3	αab	αab	ADV
ejpam-4348	216	4	+	+	X
ejpam-4348	216	5	1	1	NUM
ejpam-4348	216	6	(	(	PUNCT
ejpam-4348	216	7	αab	αab	VERB
ejpam-4348	216	8	+	+	CCONJ
ejpam-4348	216	9	√	√	NUM
ejpam-4348	216	10	αab	αab	VERB
ejpam-4348	216	11	√	√	PROPN
ejpam-4348	216	12	αab	αab	VERB
ejpam-4348	216	13	+	+	CCONJ
ejpam-4348	216	14	1	1	NUM
ejpam-4348	216	15	+	+	CCONJ
ejpam-4348	216	16	√	√	NOUN
ejpam-4348	216	17	αab	αab	VERB
ejpam-4348	216	18	)	)	PUNCT
ejpam-4348	216	19	≤	≤	NOUN
ejpam-4348	216	20	2	2	NUM
ejpam-4348	216	21	(	(	PUNCT
ejpam-4348	216	22	αab	αab	VERB
ejpam-4348	216	23	+	+	CCONJ
ejpam-4348	216	24	√	√	INTJ
ejpam-4348	216	25	αab	αab	NOUN
ejpam-4348	216	26	(	(	PUNCT
ejpam-4348	216	27	1	1	NUM
ejpam-4348	216	28	+	+	CCONJ
ejpam-4348	216	29	√	√	ADJ
ejpam-4348	216	30	αab	αab	VERB
ejpam-4348	216	31	+	+	NOUN
ejpam-4348	216	32	1	1	NUM
ejpam-4348	216	33	)	)	PUNCT
ejpam-4348	216	34	)	)	PUNCT
ejpam-4348	216	35	.	.	PUNCT
ejpam-4348	217	1	hence	hence	ADV
ejpam-4348	217	2	αab	αab	VERB
ejpam-4348	217	3	≤	≤	NUM
ejpam-4348	217	4	α̃	α̃	PROPN
ejpam-4348	217	5	≤	≤	ADV
ejpam-4348	217	6	2	2	NUM
ejpam-4348	217	7	(	(	PUNCT
ejpam-4348	217	8	αab	αab	VERB
ejpam-4348	217	9	+	+	CCONJ
ejpam-4348	217	10	√	√	INTJ
ejpam-4348	217	11	αab	αab	NOUN
ejpam-4348	217	12	(	(	PUNCT
ejpam-4348	217	13	1	1	NUM
ejpam-4348	217	14	+	+	CCONJ
ejpam-4348	217	15	√	√	ADJ
ejpam-4348	217	16	αab	αab	VERB
ejpam-4348	217	17	+	+	NOUN
ejpam-4348	217	18	1	1	NUM
ejpam-4348	217	19	)	)	PUNCT
ejpam-4348	217	20	)	)	PUNCT
ejpam-4348	217	21	.	.	PUNCT
ejpam-4348	218	1	this	this	PRON
ejpam-4348	218	2	proves	prove	VERB
ejpam-4348	218	3	that	that	SCONJ
ejpam-4348	218	4	the	the	DET
ejpam-4348	218	5	dichotomy	dichotomy	NOUN
ejpam-4348	218	6	parameters	parameter	NOUN
ejpam-4348	218	7	of	of	ADP
ejpam-4348	218	8	a	a	DET
ejpam-4348	218	9	matrix	matrix	NOUN
ejpam-4348	218	10	with	with	ADP
ejpam-4348	218	11	respect	respect	NOUN
ejpam-4348	218	12	to	to	ADP
ejpam-4348	218	13	a	a	DET
ejpam-4348	218	14	parabola	parabola	NOUN
ejpam-4348	218	15	and	and	CCONJ
ejpam-4348	218	16	with	with	ADP
ejpam-4348	218	17	respect	respect	NOUN
ejpam-4348	218	18	to	to	ADP
ejpam-4348	218	19	the	the	DET
ejpam-4348	218	20	imaginary	imaginary	ADJ
ejpam-4348	218	21	axis	axis	NOUN
ejpam-4348	218	22	are	be	AUX
ejpam-4348	218	23	equivalent	equivalent	ADJ
ejpam-4348	218	24	.	.	PUNCT
ejpam-4348	219	1	consider	consider	VERB
ejpam-4348	219	2	spectral	spectral	ADJ
ejpam-4348	219	3	projectors	projector	NOUN
ejpam-4348	219	4	•	•	PRON
ejpam-4348	219	5	p̃	p̃	PROPN
ejpam-4348	219	6	∈	∈	PROPN
ejpam-4348	219	7	cn×n	cn×n	NOUN
ejpam-4348	219	8	on	on	ADP
ejpam-4348	219	9	the	the	DET
ejpam-4348	219	10	right	right	ADJ
ejpam-4348	219	11	subspace	subspace	NOUN
ejpam-4348	219	12	of	of	ADP
ejpam-4348	219	13	a	a	DET
ejpam-4348	219	14	associated	associate	VERB
ejpam-4348	219	15	with	with	ADP
ejpam-4348	219	16	its	its	PRON
ejpam-4348	219	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	219	18	outside	outside	ADP
ejpam-4348	219	19	the	the	DET
ejpam-4348	219	20	parabola	parabola	PROPN
ejpam-4348	219	21	γ̃.	γ̃.	PROPN
ejpam-4348	219	22	•	•	NUM
ejpam-4348	219	23	p̃	p̃	PROPN
ejpam-4348	219	24	∈	∈	PROPN
ejpam-4348	219	25	c2n×2n	c2n×2n	VERB
ejpam-4348	219	26	on	on	ADP
ejpam-4348	219	27	the	the	DET
ejpam-4348	219	28	right	right	ADJ
ejpam-4348	219	29	subspace	subspace	NOUN
ejpam-4348	219	30	of	of	ADP
ejpam-4348	219	31	ã	ã	PROPN
ejpam-4348	219	32	associated	associate	VERB
ejpam-4348	219	33	with	with	ADP
ejpam-4348	219	34	its	its	PRON
ejpam-4348	219	35	eigenvalues	eigenvalue	NOUN
ejpam-4348	219	36	in	in	ADP
ejpam-4348	219	37	the	the	DET
ejpam-4348	219	38	complex	complex	ADJ
ejpam-4348	219	39	right	right	ADJ
ejpam-4348	219	40	half	half	ADJ
ejpam-4348	219	41	-	-	PUNCT
ejpam-4348	219	42	plane	plane	NOUN
ejpam-4348	219	43	.	.	PUNCT
ejpam-4348	220	1	we	we	PRON
ejpam-4348	220	2	obtain	obtain	VERB
ejpam-4348	220	3	the	the	DET
ejpam-4348	220	4	following	follow	VERB
ejpam-4348	220	5	proposition	proposition	NOUN
ejpam-4348	220	6	which	which	PRON
ejpam-4348	220	7	characterizes	characterize	VERB
ejpam-4348	220	8	the	the	DET
ejpam-4348	220	9	relation	relation	NOUN
ejpam-4348	220	10	between	between	ADP
ejpam-4348	220	11	p̃	p̃	PROPN
ejpam-4348	220	12	and	and	CCONJ
ejpam-4348	220	13	p̃	p̃	PROPN
ejpam-4348	220	14	proposition	proposition	NOUN
ejpam-4348	220	15	7	7	NUM
ejpam-4348	220	16	.	.	PUNCT
ejpam-4348	220	17	consider	consider	VERB
ejpam-4348	220	18	a	a	DET
ejpam-4348	220	19	partition	partition	NOUN
ejpam-4348	220	20	of	of	ADP
ejpam-4348	220	21	the	the	DET
ejpam-4348	220	22	matrix	matrix	NOUN
ejpam-4348	220	23	p̃	p̃	PROPN
ejpam-4348	220	24	in	in	ADP
ejpam-4348	220	25	the	the	DET
ejpam-4348	220	26	form	form	NOUN
ejpam-4348	220	27	p̃	p̃	PROPN
ejpam-4348	220	28	=	=	PUNCT
ejpam-4348	220	29	(	(	PUNCT
ejpam-4348	220	30	p̃1	p̃1	PROPN
ejpam-4348	220	31	p̃2	p̃2	PROPN
ejpam-4348	220	32	p̃3	p̃3	PROPN
ejpam-4348	220	33	p̃4	p̃4	PROPN
ejpam-4348	220	34	)	)	PUNCT
ejpam-4348	220	35	avec	avec	PROPN
ejpam-4348	220	36	p̃i	p̃i	PROPN
ejpam-4348	220	37	∈	∈	PROPN
ejpam-4348	220	38	cn×n	cn×n	PROPN
ejpam-4348	220	39	,	,	PUNCT
ejpam-4348	220	40	i	i	NOUN
ejpam-4348	220	41	=	=	NOUN
ejpam-4348	220	42	1	1	NUM
ejpam-4348	220	43	,	,	PUNCT
ejpam-4348	220	44	4	4	NUM
ejpam-4348	220	45	(	(	PUNCT
ejpam-4348	220	46	29	29	NUM
ejpam-4348	220	47	)	)	PUNCT
ejpam-4348	220	48	then	then	ADV
ejpam-4348	220	49	p̃	p̃	PROPN
ejpam-4348	220	50	=	=	SYM
ejpam-4348	220	51	2p̃1	2p̃1	PROPN
ejpam-4348	220	52	=	=	PUNCT
ejpam-4348	221	1	2p̃4	2p̃4	X
ejpam-4348	221	2	=	=	SYM
ejpam-4348	221	3	4p̃2p̃3	4p̃2p̃3	NUM
ejpam-4348	221	4	(	(	PUNCT
ejpam-4348	221	5	30	30	NUM
ejpam-4348	221	6	)	)	PUNCT
ejpam-4348	221	7	s.	s.	PROPN
ejpam-4348	221	8	traoré	traoré	PROPN
ejpam-4348	221	9	,	,	PUNCT
ejpam-4348	221	10	m.	m.	NOUN
ejpam-4348	221	11	dosso	dosso	PROPN
ejpam-4348	221	12	/	/	SYM
ejpam-4348	221	13	eur	eur	PROPN
ejpam-4348	221	14	.	.	PUNCT
ejpam-4348	222	1	j.	j.	PROPN
ejpam-4348	222	2	pure	pure	PROPN
ejpam-4348	222	3	appl	appl	PROPN
ejpam-4348	222	4	.	.	PROPN
ejpam-4348	222	5	math	math	PROPN
ejpam-4348	222	6	,	,	PUNCT
ejpam-4348	222	7	15	15	NUM
ejpam-4348	222	8	(	(	PUNCT
ejpam-4348	222	9	2	2	NUM
ejpam-4348	222	10	)	)	PUNCT
ejpam-4348	222	11	(	(	PUNCT
ejpam-4348	222	12	2022	2022	NUM
ejpam-4348	222	13	)	)	PUNCT
ejpam-4348	222	14	,	,	PUNCT
ejpam-4348	222	15	681	681	NUM
ejpam-4348	222	16	-	-	SYM
ejpam-4348	222	17	725	725	NUM
ejpam-4348	222	18	696	696	NUM
ejpam-4348	222	19	moreover	moreover	ADV
ejpam-4348	222	20	p̃a	p̃a	NOUN
ejpam-4348	222	21	=	=	SYM
ejpam-4348	222	22	4×	4×	NOUN
ejpam-4348	222	23	(	(	PUNCT
ejpam-4348	222	24	p̃2	p̃2	NOUN
ejpam-4348	222	25	)	)	PUNCT
ejpam-4348	222	26	2	2	NUM
ejpam-4348	223	1	+	+	CCONJ
ejpam-4348	223	2	2ipbp̃1	2ipbp̃1	NUM
ejpam-4348	223	3	(	(	PUNCT
ejpam-4348	223	4	31	31	NUM
ejpam-4348	223	5	)	)	PUNCT
ejpam-4348	223	6	proof	proof	NOUN
ejpam-4348	223	7	.	.	PUNCT
ejpam-4348	224	1	let	let	VERB
ejpam-4348	224	2	x̃	x̃	PROPN
ejpam-4348	224	3	be	be	AUX
ejpam-4348	224	4	a	a	DET
ejpam-4348	224	5	solution	solution	NOUN
ejpam-4348	224	6	to	to	ADP
ejpam-4348	224	7	the	the	DET
ejpam-4348	224	8	matrix	matrix	NOUN
ejpam-4348	224	9	equation	equation	NOUN
ejpam-4348	224	10	(	(	PUNCT
ejpam-4348	224	11	x̃	x̃	PROPN
ejpam-4348	225	1	+	+	CCONJ
ejpam-4348	225	2	√	√	PROPN
ejpam-4348	225	3	p	p	NOUN
ejpam-4348	225	4	2	2	NUM
ejpam-4348	225	5	in	in	ADP
ejpam-4348	225	6	)	)	PUNCT
ejpam-4348	225	7	2	2	NUM
ejpam-4348	225	8	=	=	SYM
ejpam-4348	225	9	ab	ab	X
ejpam-4348	225	10	(	(	PUNCT
ejpam-4348	225	11	32	32	NUM
ejpam-4348	225	12	)	)	PUNCT
ejpam-4348	225	13	consider	consider	VERB
ejpam-4348	225	14	the	the	DET
ejpam-4348	225	15	matrix	matrix	NOUN
ejpam-4348	225	16	x̃1	x̃1	PROPN
ejpam-4348	225	17	defined	define	VERB
ejpam-4348	225	18	by	by	ADP
ejpam-4348	225	19	x̃1	x̃1	PROPN
ejpam-4348	225	20	=	=	PUNCT
ejpam-4348	225	21	−x̃	−x̃	NUM
ejpam-4348	226	1	−	−	PROPN
ejpam-4348	226	2	2	2	NUM
ejpam-4348	226	3	√	√	NOUN
ejpam-4348	226	4	p	p	NOUN
ejpam-4348	226	5	2	2	NUM
ejpam-4348	226	6	in	in	ADV
ejpam-4348	226	7	.	.	PUNCT
ejpam-4348	227	1	we	we	PRON
ejpam-4348	227	2	notice	notice	VERB
ejpam-4348	227	3	that	that	SCONJ
ejpam-4348	227	4	(	(	PUNCT
ejpam-4348	227	5	x̃1	x̃1	PROPN
ejpam-4348	227	6	+	+	CCONJ
ejpam-4348	227	7	√	√	PROPN
ejpam-4348	227	8	p	p	NOUN
ejpam-4348	227	9	2	2	NUM
ejpam-4348	227	10	in	in	ADP
ejpam-4348	227	11	)	)	PUNCT
ejpam-4348	227	12	2	2	NUM
ejpam-4348	227	13	=	=	SYM
ejpam-4348	227	14	(	(	PUNCT
ejpam-4348	227	15	x̃	x̃	PROPN
ejpam-4348	227	16	+	+	CCONJ
ejpam-4348	227	17	√	√	PROPN
ejpam-4348	227	18	p	p	NOUN
ejpam-4348	227	19	2	2	NUM
ejpam-4348	227	20	in	in	ADP
ejpam-4348	227	21	)	)	PUNCT
ejpam-4348	227	22	2	2	NUM
ejpam-4348	227	23	=	=	SYM
ejpam-4348	227	24	ab	ab	PROPN
ejpam-4348	227	25	hence	hence	ADV
ejpam-4348	227	26	x̃1	x̃1	PROPN
ejpam-4348	227	27	is	be	AUX
ejpam-4348	227	28	also	also	ADV
ejpam-4348	227	29	a	a	DET
ejpam-4348	227	30	solution	solution	NOUN
ejpam-4348	227	31	of	of	ADP
ejpam-4348	227	32	matrix	matrix	NOUN
ejpam-4348	227	33	equation	equation	NOUN
ejpam-4348	227	34	(	(	PUNCT
ejpam-4348	227	35	32	32	NUM
ejpam-4348	227	36	)	)	PUNCT
ejpam-4348	227	37	.	.	PUNCT
ejpam-4348	228	1	x̃	x̃	NUM
ejpam-4348	229	1	+	+	CCONJ
ejpam-4348	229	2	√	√	ADJ
ejpam-4348	229	3	p	p	NOUN
ejpam-4348	229	4	2	2	NUM
ejpam-4348	229	5	in	in	ADP
ejpam-4348	229	6	−x̃	−x̃	NOUN
ejpam-4348	229	7	−	−	PROPN
ejpam-4348	230	1	√	√	PROPN
ejpam-4348	230	2	p	p	NOUN
ejpam-4348	230	3	2	2	NUM
ejpam-4348	230	4	in	in	ADV
ejpam-4348	230	5	in	in	ADV
ejpam-4348	230	6	in	in	ADP
ejpam-4348	230	7	×	×	NOUN
ejpam-4348	230	8	x̃	x̃	ADV
ejpam-4348	230	9	0	0	NUM
ejpam-4348	230	10	0	0	NUM
ejpam-4348	230	11	−x̃	−x̃	PUNCT
ejpam-4348	231	1	−	−	PROPN
ejpam-4348	231	2	2	2	NUM
ejpam-4348	231	3	√	√	NOUN
ejpam-4348	231	4	p	p	NOUN
ejpam-4348	231	5	2	2	NUM
ejpam-4348	231	6	in	in	ADP
ejpam-4348	231	7	×	×	NOUN
ejpam-4348	231	8			NOUN
ejpam-4348	231	9	1	1	NUM
ejpam-4348	231	10	2(x̃	2(x̃	NUM
ejpam-4348	231	11	+	+	CCONJ
ejpam-4348	231	12	√	√	PROPN
ejpam-4348	231	13	p	p	ADJ
ejpam-4348	231	14	2	2	NUM
ejpam-4348	231	15	in	in	ADP
ejpam-4348	231	16	)	)	PUNCT
ejpam-4348	231	17	−1	−1	NOUN
ejpam-4348	231	18	1	1	NUM
ejpam-4348	231	19	2	2	NUM
ejpam-4348	231	20	in	in	ADP
ejpam-4348	231	21	−1	−1	NOUN
ejpam-4348	231	22	2(x̃	2(x̃	NUM
ejpam-4348	231	23	+	+	CCONJ
ejpam-4348	231	24	√	√	PROPN
ejpam-4348	231	25	p	p	ADJ
ejpam-4348	231	26	2	2	NUM
ejpam-4348	231	27	in	in	ADP
ejpam-4348	231	28	)	)	PUNCT
ejpam-4348	231	29	−1	−1	NOUN
ejpam-4348	231	30	1	1	NUM
ejpam-4348	231	31	2	2	NUM
ejpam-4348	231	32	in	in	ADP
ejpam-4348	231	33			NOUN
ejpam-4348	231	34	=	=	PUNCT
ejpam-4348	231	35			NOUN
ejpam-4348	231	36	x̃(x̃	x̃(x̃	X
ejpam-4348	232	1	+	+	CCONJ
ejpam-4348	232	2	√	√	PROPN
ejpam-4348	232	3	p	p	ADJ
ejpam-4348	232	4	2	2	NUM
ejpam-4348	232	5	in	in	ADP
ejpam-4348	232	6	)	)	PUNCT
ejpam-4348	232	7	(	(	PUNCT
ejpam-4348	232	8	−x̃	−x̃	NOUN
ejpam-4348	232	9	−	−	NOUN
ejpam-4348	233	1	√	√	PROPN
ejpam-4348	233	2	p	p	NOUN
ejpam-4348	233	3	2in)(−x̃	2in)(−x̃	NUM
ejpam-4348	233	4	−	−	NUM
ejpam-4348	233	5	2	2	NUM
ejpam-4348	233	6	√	√	NOUN
ejpam-4348	233	7	p	p	NOUN
ejpam-4348	233	8	2	2	NUM
ejpam-4348	233	9	in	in	ADP
ejpam-4348	233	10	)	)	PUNCT
ejpam-4348	234	1	x̃	x̃	PROPN
ejpam-4348	234	2	−x̃	−x̃	PUNCT
ejpam-4348	235	1	−	−	PROPN
ejpam-4348	235	2	2	2	NUM
ejpam-4348	235	3	√	√	NOUN
ejpam-4348	235	4	p	p	NOUN
ejpam-4348	235	5	2	2	NUM
ejpam-4348	235	6	in	in	ADP
ejpam-4348	235	7	×	×	NOUN
ejpam-4348	235	8			NOUN
ejpam-4348	235	9	1	1	NUM
ejpam-4348	235	10	2(x̃	2(x̃	NUM
ejpam-4348	235	11	+	+	CCONJ
ejpam-4348	235	12	√	√	PROPN
ejpam-4348	235	13	p	p	ADJ
ejpam-4348	235	14	2	2	NUM
ejpam-4348	235	15	in	in	ADP
ejpam-4348	235	16	)	)	PUNCT
ejpam-4348	235	17	−1	−1	NOUN
ejpam-4348	235	18	1	1	NUM
ejpam-4348	235	19	2	2	NUM
ejpam-4348	235	20	in	in	ADP
ejpam-4348	235	21	−1	−1	NOUN
ejpam-4348	235	22	2(x̃	2(x̃	NUM
ejpam-4348	235	23	+	+	CCONJ
ejpam-4348	235	24	√	√	PROPN
ejpam-4348	235	25	p	p	ADJ
ejpam-4348	235	26	2	2	NUM
ejpam-4348	235	27	in	in	ADP
ejpam-4348	235	28	)	)	PUNCT
ejpam-4348	235	29	−1	−1	NOUN
ejpam-4348	235	30	1	1	NUM
ejpam-4348	235	31	2	2	NUM
ejpam-4348	235	32	in	in	ADP
ejpam-4348	235	33			NOUN
ejpam-4348	235	34	=	=	PUNCT
ejpam-4348	235	35			NOUN
ejpam-4348	235	36	1	1	NUM
ejpam-4348	235	37	2x̃	2x̃	NUM
ejpam-4348	235	38	−	−	NOUN
ejpam-4348	235	39	1	1	NUM
ejpam-4348	235	40	2(x̃	2(x̃	NUM
ejpam-4348	235	41	+	+	CCONJ
ejpam-4348	235	42	2	2	NUM
ejpam-4348	235	43	√	√	NOUN
ejpam-4348	235	44	p	p	NOUN
ejpam-4348	235	45	2	2	NUM
ejpam-4348	235	46	in	in	ADP
ejpam-4348	235	47	)	)	PUNCT
ejpam-4348	235	48	1	1	NUM
ejpam-4348	235	49	2(x̃	2(x̃	NUM
ejpam-4348	235	50	+	+	CCONJ
ejpam-4348	235	51	√	√	PROPN
ejpam-4348	235	52	p	p	X
ejpam-4348	235	53	2in)(2x̃	2in)(2x̃	NUM
ejpam-4348	235	54	+	+	CCONJ
ejpam-4348	235	55	2	2	NUM
ejpam-4348	235	56	√	√	NOUN
ejpam-4348	235	57	p	p	NOUN
ejpam-4348	235	58	2	2	NUM
ejpam-4348	235	59	in	in	ADP
ejpam-4348	235	60	)	)	PUNCT
ejpam-4348	235	61	1	1	NUM
ejpam-4348	235	62	2(x̃	2(x̃	NUM
ejpam-4348	235	63	+	+	CCONJ
ejpam-4348	235	64	√	√	PROPN
ejpam-4348	235	65	p	p	ADJ
ejpam-4348	235	66	2	2	NUM
ejpam-4348	235	67	in	in	ADP
ejpam-4348	235	68	)	)	PUNCT
ejpam-4348	236	1	−1(2x̃	−1(2x̃	PROPN
ejpam-4348	236	2	+	+	CCONJ
ejpam-4348	236	3	2	2	NUM
ejpam-4348	236	4	√	√	NOUN
ejpam-4348	236	5	p	p	NOUN
ejpam-4348	236	6	2	2	NUM
ejpam-4348	236	7	in	in	ADP
ejpam-4348	236	8	)	)	PUNCT
ejpam-4348	236	9	1	1	NUM
ejpam-4348	236	10	2x	2x	NUM
ejpam-4348	236	11	−	−	NUM
ejpam-4348	236	12	1	1	NUM
ejpam-4348	236	13	2(x	2(x	NUM
ejpam-4348	236	14	+	+	CCONJ
ejpam-4348	236	15	2	2	NUM
ejpam-4348	236	16	√	√	NOUN
ejpam-4348	236	17	p	p	NOUN
ejpam-4348	236	18	2	2	NUM
ejpam-4348	236	19	in	in	NOUN
ejpam-4348	236	20	)	)	PUNCT
ejpam-4348	236	21			NOUN
ejpam-4348	236	22	=	=	PUNCT
ejpam-4348	236	23			NOUN
ejpam-4348	237	1	−	−	NOUN
ejpam-4348	237	2	√	√	NOUN
ejpam-4348	238	1	p	p	NOUN
ejpam-4348	238	2	2	2	NUM
ejpam-4348	238	3	in	in	ADP
ejpam-4348	238	4	ab	ab	NOUN
ejpam-4348	238	5	in	in	ADP
ejpam-4348	238	6	−	−	PROPN
ejpam-4348	238	7	√	√	PROPN
ejpam-4348	238	8	p	p	NOUN
ejpam-4348	238	9	2	2	NUM
ejpam-4348	238	10	in	in	ADP
ejpam-4348	238	11			ADJ
ejpam-4348	238	12	s.	s.	PROPN
ejpam-4348	238	13	traoré	traoré	NOUN
ejpam-4348	238	14	,	,	PUNCT
ejpam-4348	238	15	m.	m.	NOUN
ejpam-4348	238	16	dosso	dosso	PROPN
ejpam-4348	238	17	/	/	SYM
ejpam-4348	238	18	eur	eur	PROPN
ejpam-4348	238	19	.	.	PUNCT
ejpam-4348	239	1	j.	j.	PROPN
ejpam-4348	239	2	pure	pure	PROPN
ejpam-4348	239	3	appl	appl	PROPN
ejpam-4348	239	4	.	.	PROPN
ejpam-4348	239	5	math	math	PROPN
ejpam-4348	239	6	,	,	PUNCT
ejpam-4348	239	7	15	15	NUM
ejpam-4348	239	8	(	(	PUNCT
ejpam-4348	239	9	2	2	NUM
ejpam-4348	239	10	)	)	PUNCT
ejpam-4348	239	11	(	(	PUNCT
ejpam-4348	239	12	2022	2022	NUM
ejpam-4348	239	13	)	)	PUNCT
ejpam-4348	239	14	,	,	PUNCT
ejpam-4348	239	15	681	681	NUM
ejpam-4348	239	16	-	-	SYM
ejpam-4348	239	17	725	725	NUM
ejpam-4348	239	18	697	697	NUM
ejpam-4348	239	19	=	=	SYM
ejpam-4348	239	20	ã.	ã.	NOUN
ejpam-4348	239	21	let	let	VERB
ejpam-4348	239	22	x̃	x̃	PROPN
ejpam-4348	239	23	=	=	PUNCT
ejpam-4348	239	24	q	q	X
ejpam-4348	240	1	[	[	PUNCT
ejpam-4348	240	2	j+	j+	NUM
ejpam-4348	240	3	0	0	NUM
ejpam-4348	240	4	0	0	NUM
ejpam-4348	240	5	j−	j−	PROPN
ejpam-4348	240	6	]	]	PUNCT
ejpam-4348	241	1	q−1	q−1	PRON
ejpam-4348	241	2	be	be	VERB
ejpam-4348	241	3	the	the	DET
ejpam-4348	241	4	canonical	canonical	ADJ
ejpam-4348	241	5	jordan	jordan	PROPN
ejpam-4348	241	6	form	form	NOUN
ejpam-4348	241	7	of	of	ADP
ejpam-4348	241	8	the	the	DET
ejpam-4348	241	9	matrix	matrix	NOUN
ejpam-4348	241	10	x̃	x̃	PROPN
ejpam-4348	241	11	with	with	ADP
ejpam-4348	241	12	j+	j+	NUM
ejpam-4348	241	13	and	and	CCONJ
ejpam-4348	241	14	j−	j−	VERB
ejpam-4348	241	15	the	the	DET
ejpam-4348	241	16	jordan	jordan	PROPN
ejpam-4348	241	17	blocks	block	NOUN
ejpam-4348	241	18	associated	associate	VERB
ejpam-4348	241	19	respectively	respectively	ADV
ejpam-4348	241	20	with	with	ADP
ejpam-4348	241	21	the	the	DET
ejpam-4348	241	22	eigenvalues	eigenvalue	NOUN
ejpam-4348	241	23	located	locate	VERB
ejpam-4348	241	24	in	in	ADP
ejpam-4348	241	25	the	the	DET
ejpam-4348	241	26	right	right	ADJ
ejpam-4348	241	27	half	half	ADJ
ejpam-4348	241	28	-	-	PUNCT
ejpam-4348	241	29	plane	plane	NOUN
ejpam-4348	241	30	and	and	CCONJ
ejpam-4348	241	31	the	the	DET
ejpam-4348	241	32	left	left	ADJ
ejpam-4348	241	33	half	half	ADJ
ejpam-4348	241	34	-	-	PUNCT
ejpam-4348	241	35	plane	plane	NOUN
ejpam-4348	241	36	where	where	SCONJ
ejpam-4348	241	37	j+	j+	NUM
ejpam-4348	241	38	if	if	SCONJ
ejpam-4348	241	39	of	of	ADP
ejpam-4348	241	40	order	order	NOUN
ejpam-4348	241	41	k.	k.	INTJ
ejpam-4348	241	42	by	by	ADP
ejpam-4348	241	43	replacing	replace	VERB
ejpam-4348	241	44	the	the	DET
ejpam-4348	241	45	decomposition	decomposition	NOUN
ejpam-4348	241	46	of	of	ADP
ejpam-4348	241	47	x̃	x̃	PROPN
ejpam-4348	241	48	in	in	ADP
ejpam-4348	241	49	the	the	DET
ejpam-4348	241	50	matrix	matrix	NOUN
ejpam-4348	241	51	ã	ã	PROPN
ejpam-4348	241	52	,	,	PUNCT
ejpam-4348	241	53	we	we	PRON
ejpam-4348	241	54	get	get	VERB
ejpam-4348	242	1	ã	ã	PROPN
ejpam-4348	242	2	=	=	SYM
ejpam-4348	242	3	q	q	PROPN
ejpam-4348	242	4	[	[	PUNCT
ejpam-4348	242	5	j+	j+	NUM
ejpam-4348	242	6	0	0	NUM
ejpam-4348	242	7	0	0	NUM
ejpam-4348	242	8	j−	j−	PROPN
ejpam-4348	242	9	]	]	PUNCT
ejpam-4348	243	1	q−1	q−1	PROPN
ejpam-4348	243	2	+	+	CCONJ
ejpam-4348	244	1	√	√	PROPN
ejpam-4348	244	2	p	p	NOUN
ejpam-4348	244	3	2	2	NUM
ejpam-4348	244	4	in	in	ADP
ejpam-4348	244	5	−q	−q	ADJ
ejpam-4348	244	6	[	[	PUNCT
ejpam-4348	244	7	j+	j+	NUM
ejpam-4348	244	8	0	0	NUM
ejpam-4348	244	9	0	0	NUM
ejpam-4348	245	1	j−	j−	PROPN
ejpam-4348	245	2	]	]	PUNCT
ejpam-4348	246	1	q−1	q−1	PROPN
ejpam-4348	246	2	−	−	NOUN
ejpam-4348	247	1	√	√	PROPN
ejpam-4348	247	2	p	p	NOUN
ejpam-4348	247	3	2	2	NUM
ejpam-4348	247	4	in	in	ADV
ejpam-4348	247	5	in	in	ADV
ejpam-4348	247	6	in	in	ADP
ejpam-4348	247	7	×	×	NOUN
ejpam-4348	247	8			NOUN
ejpam-4348	248	1	q	q	NOUN
ejpam-4348	249	1	[	[	PUNCT
ejpam-4348	249	2	j+	j+	NUM
ejpam-4348	249	3	0	0	NUM
ejpam-4348	249	4	0	0	NUM
ejpam-4348	249	5	j−	j−	PROPN
ejpam-4348	249	6	]	]	PUNCT
ejpam-4348	250	1	q−1	q−1	PROPN
ejpam-4348	250	2	0	0	NUM
ejpam-4348	250	3	0	0	NUM
ejpam-4348	250	4	q	q	NOUN
ejpam-4348	251	1	[	[	PUNCT
ejpam-4348	251	2	j+	j+	NUM
ejpam-4348	251	3	0	0	NUM
ejpam-4348	251	4	0	0	NUM
ejpam-4348	251	5	j−	j−	PROPN
ejpam-4348	251	6	]	]	PUNCT
ejpam-4348	252	1	q−1	q−1	PROPN
ejpam-4348	253	1	−	−	NUM
ejpam-4348	253	2	2	2	NUM
ejpam-4348	254	1	√	√	NOUN
ejpam-4348	254	2	p	p	NOUN
ejpam-4348	254	3	2	2	NUM
ejpam-4348	254	4	in	in	ADP
ejpam-4348	254	5	×	×	NOUN
ejpam-4348	254	6			VERB
ejpam-4348	254	7	1	1	NUM
ejpam-4348	254	8	2	2	NUM
ejpam-4348	254	9	(	(	PUNCT
ejpam-4348	254	10	q	q	X
ejpam-4348	254	11	[	[	PUNCT
ejpam-4348	255	1	j+	j+	NUM
ejpam-4348	255	2	0	0	NUM
ejpam-4348	255	3	0	0	NUM
ejpam-4348	255	4	j−	j−	PROPN
ejpam-4348	255	5	]	]	PUNCT
ejpam-4348	256	1	q−1	q−1	PROPN
ejpam-4348	256	2	+	+	CCONJ
ejpam-4348	257	1	√	√	PROPN
ejpam-4348	257	2	p	p	NOUN
ejpam-4348	257	3	2	2	NUM
ejpam-4348	257	4	in	in	ADP
ejpam-4348	257	5	)	)	PUNCT
ejpam-4348	257	6	−1	−1	NOUN
ejpam-4348	257	7	1	1	NUM
ejpam-4348	257	8	2	2	NUM
ejpam-4348	257	9	in	in	ADP
ejpam-4348	257	10	−1	−1	NOUN
ejpam-4348	257	11	2	2	NUM
ejpam-4348	257	12	(	(	PUNCT
ejpam-4348	257	13	q	q	X
ejpam-4348	257	14	[	[	PUNCT
ejpam-4348	257	15	j+	j+	NUM
ejpam-4348	257	16	0	0	NUM
ejpam-4348	257	17	0	0	NUM
ejpam-4348	258	1	j−	j−	PROPN
ejpam-4348	258	2	]	]	PUNCT
ejpam-4348	259	1	q−1	q−1	PROPN
ejpam-4348	259	2	−	−	NOUN
ejpam-4348	260	1	√	√	PROPN
ejpam-4348	260	2	p	p	NOUN
ejpam-4348	260	3	2	2	NUM
ejpam-4348	260	4	in	in	ADP
ejpam-4348	260	5	)	)	PUNCT
ejpam-4348	260	6	−1	−1	NOUN
ejpam-4348	260	7	1	1	NUM
ejpam-4348	260	8	2	2	NUM
ejpam-4348	260	9	in	in	ADP
ejpam-4348	260	10			NOUN
ejpam-4348	260	11	=	=	SYM
ejpam-4348	260	12	q	q	PROPN
ejpam-4348	260	13	0	0	NUM
ejpam-4348	260	14	0	0	NUM
ejpam-4348	260	15	q	q	NOUN
ejpam-4348	260	16			NOUN
ejpam-4348	260	17			NOUN
ejpam-4348	260	18	[	[	PUNCT
ejpam-4348	260	19	j+	j+	NUM
ejpam-4348	260	20	0	0	NUM
ejpam-4348	260	21	0	0	NUM
ejpam-4348	260	22	j−	j−	PROPN
ejpam-4348	260	23	]	]	PUNCT
ejpam-4348	261	1	+	+	CCONJ
ejpam-4348	261	2	√	√	ADJ
ejpam-4348	261	3	p	p	NOUN
ejpam-4348	261	4	2	2	NUM
ejpam-4348	261	5	in	in	ADP
ejpam-4348	261	6	−	−	PROPN
ejpam-4348	261	7	[	[	PUNCT
ejpam-4348	261	8	j+	j+	NUM
ejpam-4348	261	9	0	0	NUM
ejpam-4348	261	10	0	0	NUM
ejpam-4348	261	11	j−	j−	PROPN
ejpam-4348	261	12	]	]	PUNCT
ejpam-4348	261	13	−	−	PROPN
ejpam-4348	262	1	√	√	NOUN
ejpam-4348	262	2	p	p	NOUN
ejpam-4348	262	3	2	2	NUM
ejpam-4348	262	4	in	in	ADV
ejpam-4348	262	5	in	in	ADV
ejpam-4348	262	6	in	in	ADP
ejpam-4348	262	7	×	×	NOUN
ejpam-4348	262	8			NOUN
ejpam-4348	262	9	[	[	PUNCT
ejpam-4348	262	10	j+	j+	NUM
ejpam-4348	262	11	0	0	NUM
ejpam-4348	262	12	0	0	NUM
ejpam-4348	263	1	j−	j−	PROPN
ejpam-4348	263	2	]	]	PUNCT
ejpam-4348	263	3	0	0	NUM
ejpam-4348	263	4	0	0	NUM
ejpam-4348	264	1	[	[	PUNCT
ejpam-4348	264	2	j+	j+	NUM
ejpam-4348	264	3	0	0	NUM
ejpam-4348	264	4	0	0	NUM
ejpam-4348	264	5	j−	j−	PROPN
ejpam-4348	264	6	]	]	PUNCT
ejpam-4348	264	7	−	−	PROPN
ejpam-4348	264	8	2	2	NUM
ejpam-4348	265	1	√	√	NOUN
ejpam-4348	265	2	p	p	NOUN
ejpam-4348	265	3	2	2	NUM
ejpam-4348	265	4	in	in	ADP
ejpam-4348	265	5	×	×	NOUN
ejpam-4348	265	6			VERB
ejpam-4348	265	7	1	1	NUM
ejpam-4348	265	8	2	2	NUM
ejpam-4348	265	9	(	(	PUNCT
ejpam-4348	265	10	[	[	PUNCT
ejpam-4348	265	11	j+	j+	NUM
ejpam-4348	265	12	0	0	NUM
ejpam-4348	265	13	0	0	NUM
ejpam-4348	265	14	j−	j−	PROPN
ejpam-4348	265	15	]	]	PUNCT
ejpam-4348	266	1	+	+	CCONJ
ejpam-4348	266	2	√	√	ADJ
ejpam-4348	266	3	p	p	NOUN
ejpam-4348	266	4	2	2	NUM
ejpam-4348	266	5	in	in	ADP
ejpam-4348	266	6	)	)	PUNCT
ejpam-4348	266	7	−1	−1	NOUN
ejpam-4348	266	8	1	1	NUM
ejpam-4348	266	9	2	2	NUM
ejpam-4348	266	10	in	in	ADP
ejpam-4348	266	11	−1	−1	NOUN
ejpam-4348	266	12	2	2	NUM
ejpam-4348	266	13	(	(	PUNCT
ejpam-4348	266	14	[	[	PUNCT
ejpam-4348	266	15	j+	j+	NUM
ejpam-4348	266	16	0	0	NUM
ejpam-4348	266	17	0	0	NUM
ejpam-4348	266	18	j−	j−	PROPN
ejpam-4348	266	19	]	]	PUNCT
ejpam-4348	266	20	−	−	PROPN
ejpam-4348	267	1	√	√	NUM
ejpam-4348	267	2	p	p	NOUN
ejpam-4348	267	3	2	2	NUM
ejpam-4348	267	4	in	in	ADP
ejpam-4348	267	5	)	)	PUNCT
ejpam-4348	267	6	−1	−1	NOUN
ejpam-4348	267	7	1	1	NUM
ejpam-4348	267	8	2	2	NUM
ejpam-4348	267	9	in	in	ADP
ejpam-4348	267	10			PROPN
ejpam-4348	267	11	q−1	q−1	X
ejpam-4348	267	12	0	0	PUNCT
ejpam-4348	267	13	0	0	NUM
ejpam-4348	268	1	q−1	q−1	PROPN
ejpam-4348	268	2			NOUN
ejpam-4348	268	3	=	=	X
ejpam-4348	268	4	q̃j	q̃j	VERB
ejpam-4348	268	5	q̃−1	q̃−1	ADV
ejpam-4348	268	6	with	with	ADP
ejpam-4348	268	7	s.	s.	PROPN
ejpam-4348	268	8	traoré	traoré	PROPN
ejpam-4348	268	9	,	,	PUNCT
ejpam-4348	268	10	m.	m.	NOUN
ejpam-4348	268	11	dosso	dosso	PROPN
ejpam-4348	268	12	/	/	SYM
ejpam-4348	268	13	eur	eur	PROPN
ejpam-4348	268	14	.	.	PUNCT
ejpam-4348	269	1	j.	j.	PROPN
ejpam-4348	269	2	pure	pure	PROPN
ejpam-4348	269	3	appl	appl	PROPN
ejpam-4348	269	4	.	.	PROPN
ejpam-4348	269	5	math	math	PROPN
ejpam-4348	269	6	,	,	PUNCT
ejpam-4348	269	7	15	15	NUM
ejpam-4348	269	8	(	(	PUNCT
ejpam-4348	269	9	2	2	NUM
ejpam-4348	269	10	)	)	PUNCT
ejpam-4348	269	11	(	(	PUNCT
ejpam-4348	269	12	2022	2022	NUM
ejpam-4348	269	13	)	)	PUNCT
ejpam-4348	269	14	,	,	PUNCT
ejpam-4348	269	15	681	681	NUM
ejpam-4348	269	16	-	-	SYM
ejpam-4348	269	17	725	725	NUM
ejpam-4348	269	18	698	698	NUM
ejpam-4348	269	19	q̃	q̃	NOUN
ejpam-4348	269	20	=	=	SYM
ejpam-4348	269	21	q	q	PROPN
ejpam-4348	269	22	0	0	NUM
ejpam-4348	269	23	0	0	NUM
ejpam-4348	269	24	q	q	NOUN
ejpam-4348	269	25			NOUN
ejpam-4348	269	26			NOUN
ejpam-4348	269	27	(	(	PUNCT
ejpam-4348	269	28	j+	j+	NUM
ejpam-4348	269	29	0	0	NUM
ejpam-4348	269	30	0	0	NUM
ejpam-4348	269	31	j−	j−	PROPN
ejpam-4348	269	32	)	)	PUNCT
ejpam-4348	270	1	+	+	CCONJ
ejpam-4348	270	2	√	√	ADJ
ejpam-4348	270	3	p	p	NOUN
ejpam-4348	270	4	2	2	NUM
ejpam-4348	270	5	in	in	ADP
ejpam-4348	270	6	−	−	PROPN
ejpam-4348	270	7	[	[	PUNCT
ejpam-4348	270	8	j+	j+	NUM
ejpam-4348	270	9	0	0	NUM
ejpam-4348	270	10	0	0	NUM
ejpam-4348	271	1	j−	j−	PROPN
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ejpam-4348	271	3	−	−	PROPN
ejpam-4348	272	1	√	√	NOUN
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ejpam-4348	272	3	2	2	NUM
ejpam-4348	272	4	in	in	ADV
ejpam-4348	272	5	in	in	ADP
ejpam-4348	272	6	in	in	ADP
ejpam-4348	272	7			NOUN
ejpam-4348	272	8	and	and	CCONJ
ejpam-4348	272	9	j	j	NOUN
ejpam-4348	272	10	=	=	PUNCT
ejpam-4348	272	11			NOUN
ejpam-4348	272	12	[	[	PUNCT
ejpam-4348	272	13	j+	j+	NUM
ejpam-4348	272	14	0	0	NUM
ejpam-4348	272	15	0	0	NUM
ejpam-4348	273	1	j−	j−	PROPN
ejpam-4348	273	2	]	]	PUNCT
ejpam-4348	273	3	0	0	NUM
ejpam-4348	273	4	0	0	NUM
ejpam-4348	274	1	[	[	PUNCT
ejpam-4348	274	2	j+	j+	NUM
ejpam-4348	274	3	0	0	NUM
ejpam-4348	274	4	0	0	NUM
ejpam-4348	274	5	j−	j−	PROPN
ejpam-4348	274	6	]	]	PUNCT
ejpam-4348	274	7	−	−	PROPN
ejpam-4348	274	8	2	2	NUM
ejpam-4348	275	1	√	√	NOUN
ejpam-4348	275	2	p	p	NOUN
ejpam-4348	275	3	2	2	NUM
ejpam-4348	275	4	in	in	ADP
ejpam-4348	275	5			NOUN
ejpam-4348	275	6	knowing	know	VERB
ejpam-4348	275	7	that	that	SCONJ
ejpam-4348	275	8	we	we	PRON
ejpam-4348	275	9	have	have	VERB
ejpam-4348	275	10	k	k	PROPN
ejpam-4348	275	11	eigenvalues	eigenvalue	NOUN
ejpam-4348	275	12	of	of	ADP
ejpam-4348	275	13	the	the	DET
ejpam-4348	275	14	matrix	matrix	NOUN
ejpam-4348	275	15	ab	ab	PROPN
ejpam-4348	275	16	in	in	ADP
ejpam-4348	275	17	the	the	DET
ejpam-4348	275	18	right	right	ADJ
ejpam-4348	275	19	half	half	ADJ
ejpam-4348	275	20	-	-	PUNCT
ejpam-4348	275	21	plane	plane	NOUN
ejpam-4348	275	22	,	,	PUNCT
ejpam-4348	275	23	we	we	PRON
ejpam-4348	275	24	can	can	AUX
ejpam-4348	275	25	therefore	therefore	ADV
ejpam-4348	275	26	compute	compute	VERB
ejpam-4348	275	27	the	the	DET
ejpam-4348	275	28	associated	associated	ADJ
ejpam-4348	275	29	projector	projector	NOUN
ejpam-4348	275	30	p̃	p̃	PROPN
ejpam-4348	275	31	=	=	SYM
ejpam-4348	275	32	q̃	q̃	PROPN
ejpam-4348	275	33	[	[	PUNCT
ejpam-4348	275	34	ik	ik	X
ejpam-4348	275	35	0	0	PROPN
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ejpam-4348	275	37	0	0	NUM
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ejpam-4348	275	39	q̃−1	q̃−1	ADV
ejpam-4348	275	40	=	=	SYM
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ejpam-4348	276	3	0	0	NUM
ejpam-4348	276	4	q	q	NOUN
ejpam-4348	276	5			NOUN
ejpam-4348	276	6			NOUN
ejpam-4348	276	7	[	[	PUNCT
ejpam-4348	276	8	j+	j+	NUM
ejpam-4348	276	9	0	0	NUM
ejpam-4348	276	10	0	0	NUM
ejpam-4348	276	11	j−	j−	PROPN
ejpam-4348	276	12	]	]	PUNCT
ejpam-4348	277	1	+	+	CCONJ
ejpam-4348	277	2	√	√	ADJ
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ejpam-4348	277	4	2	2	NUM
ejpam-4348	277	5	in	in	ADP
ejpam-4348	277	6	−	−	PROPN
ejpam-4348	277	7	[	[	PUNCT
ejpam-4348	277	8	j+	j+	NUM
ejpam-4348	277	9	0	0	NUM
ejpam-4348	277	10	0	0	NUM
ejpam-4348	277	11	j−	j−	PROPN
ejpam-4348	277	12	]	]	PUNCT
ejpam-4348	277	13	−	−	PROPN
ejpam-4348	278	1	√	√	NOUN
ejpam-4348	278	2	p	p	NOUN
ejpam-4348	278	3	2	2	NUM
ejpam-4348	278	4	in	in	ADV
ejpam-4348	278	5	in	in	ADV
ejpam-4348	278	6	in	in	ADP
ejpam-4348	278	7	×	×	NOUN
ejpam-4348	278	8			NOUN
ejpam-4348	278	9	[	[	PUNCT
ejpam-4348	278	10	ik	ik	X
ejpam-4348	278	11	0	0	PROPN
ejpam-4348	278	12	0	0	NUM
ejpam-4348	278	13	0	0	NUM
ejpam-4348	278	14	]	]	PUNCT
ejpam-4348	279	1	[	[	PUNCT
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ejpam-4348	279	5	0	0	NUM
ejpam-4348	279	6	]	]	PUNCT
ejpam-4348	279	7	[	[	PUNCT
ejpam-4348	279	8	0	0	NUM
ejpam-4348	279	9	0	0	NUM
ejpam-4348	279	10	0	0	NUM
ejpam-4348	279	11	0	0	NUM
ejpam-4348	279	12	]	]	PUNCT
ejpam-4348	280	1	[	[	PUNCT
ejpam-4348	280	2	0	0	NUM
ejpam-4348	280	3	0	0	NUM
ejpam-4348	280	4	0	0	NUM
ejpam-4348	280	5	0	0	NUM
ejpam-4348	280	6	]	]	PUNCT
ejpam-4348	280	7			PROPN
ejpam-4348	280	8	×	×	NOUN
ejpam-4348	280	9			NOUN
ejpam-4348	280	10	1	1	NUM
ejpam-4348	280	11	2	2	NUM
ejpam-4348	280	12	(	(	PUNCT
ejpam-4348	280	13	[	[	PUNCT
ejpam-4348	280	14	j+	j+	NUM
ejpam-4348	280	15	0	0	NUM
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ejpam-4348	280	17	j−	j−	PROPN
ejpam-4348	280	18	]	]	PUNCT
ejpam-4348	281	1	+	+	CCONJ
ejpam-4348	281	2	√	√	ADJ
ejpam-4348	281	3	p	p	NOUN
ejpam-4348	281	4	2	2	NUM
ejpam-4348	281	5	in	in	ADP
ejpam-4348	281	6	)	)	PUNCT
ejpam-4348	281	7	−1	−1	NOUN
ejpam-4348	281	8	1	1	NUM
ejpam-4348	281	9	2	2	NUM
ejpam-4348	281	10	in	in	ADP
ejpam-4348	281	11	−1	−1	NOUN
ejpam-4348	281	12	2	2	NUM
ejpam-4348	281	13	j+	j+	NOUN
ejpam-4348	281	14	0	0	NUM
ejpam-4348	281	15	0	0	NUM
ejpam-4348	281	16	j−	j−	PROPN
ejpam-4348	281	17	+	+	PROPN
ejpam-4348	281	18	√	√	PUNCT
ejpam-4348	281	19	p	p	NOUN
ejpam-4348	281	20	2	2	NUM
ejpam-4348	281	21	in	in	ADP
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ejpam-4348	281	24	2	2	NUM
ejpam-4348	281	25	in	in	ADP
ejpam-4348	281	26			NOUN
ejpam-4348	281	27	q−1	q−1	NOUN
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ejpam-4348	282	1	q−1	q−1	PROPN
ejpam-4348	282	2			NOUN
ejpam-4348	282	3	=	=	PUNCT
ejpam-4348	282	4	q	q	PROPN
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ejpam-4348	282	6	0	0	NUM
ejpam-4348	282	7	q	q	NOUN
ejpam-4348	282	8			NOUN
ejpam-4348	282	9			NOUN
ejpam-4348	282	10	j+	j+	PUNCT
ejpam-4348	283	1	+	+	CCONJ
ejpam-4348	284	1	√	√	PROPN
ejpam-4348	284	2	p	p	NOUN
ejpam-4348	284	3	2	2	NUM
ejpam-4348	284	4	ik	ik	X
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ejpam-4348	284	6	0	0	NUM
ejpam-4348	284	7	0	0	NUM
ejpam-4348	284	8			NOUN
ejpam-4348	284	9	[	[	PUNCT
ejpam-4348	284	10	0	0	NUM
ejpam-4348	284	11	0	0	NUM
ejpam-4348	284	12	0	0	NUM
ejpam-4348	284	13	0	0	NUM
ejpam-4348	284	14	]	]	PUNCT
ejpam-4348	284	15	[	[	PUNCT
ejpam-4348	284	16	ik	ik	X
ejpam-4348	284	17	0	0	PROPN
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ejpam-4348	284	19	0	0	NUM
ejpam-4348	284	20	]	]	PUNCT
ejpam-4348	285	1	[	[	PUNCT
ejpam-4348	285	2	0	0	NUM
ejpam-4348	285	3	0	0	NUM
ejpam-4348	285	4	0	0	NUM
ejpam-4348	285	5	0	0	NUM
ejpam-4348	285	6	]	]	PUNCT
ejpam-4348	285	7			NUM
ejpam-4348	285	8	×	×	PROPN
ejpam-4348	285	9			NOUN
ejpam-4348	285	10	1	1	NUM
ejpam-4348	285	11	2	2	NUM
ejpam-4348	285	12	(j+	(j+	NOUN
ejpam-4348	285	13	+	+	CCONJ
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ejpam-4348	285	16	2	2	NUM
ejpam-4348	285	17	ik	ik	NOUN
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ejpam-4348	285	19	−1	−1	NOUN
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ejpam-4348	285	21	0	0	NUM
ejpam-4348	285	22	(	(	PUNCT
ejpam-4348	285	23	j−	j−	VERB
ejpam-4348	285	24	+	+	CCONJ
ejpam-4348	285	25	√	√	PROPN
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ejpam-4348	285	29	)	)	PUNCT
ejpam-4348	285	30	−1	−1	NOUN
ejpam-4348	285	31			NOUN
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ejpam-4348	285	35	ik	ik	X
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ejpam-4348	285	40	−1	−1	NOUN
ejpam-4348	285	41	2	2	NUM
ejpam-4348	285	42	(j+	(j+	NOUN
ejpam-4348	285	43	+	+	CCONJ
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ejpam-4348	285	49	−1	−1	NOUN
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ejpam-4348	285	51	0	0	NUM
ejpam-4348	285	52	(	(	PUNCT
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ejpam-4348	285	54	+	+	CCONJ
ejpam-4348	285	55	√	√	PROPN
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ejpam-4348	285	57	2	2	NUM
ejpam-4348	285	58	in−k	in−k	NOUN
ejpam-4348	285	59	)	)	PUNCT
ejpam-4348	285	60	−1	−1	NOUN
ejpam-4348	285	61			NOUN
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ejpam-4348	285	63	2	2	NUM
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ejpam-4348	285	65	ik	ik	X
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ejpam-4348	285	68	in−k	in−k	NOUN
ejpam-4348	285	69	]	]	PUNCT
ejpam-4348	285	70			NOUN
ejpam-4348	285	71	q−1	q−1	X
ejpam-4348	285	72	0	0	SYM
ejpam-4348	285	73	0	0	NUM
ejpam-4348	286	1	q−1	q−1	PROPN
ejpam-4348	286	2			VERB
ejpam-4348	286	3	s.	s.	PROPN
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ejpam-4348	286	7	dosso	dosso	PROPN
ejpam-4348	286	8	/	/	SYM
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ejpam-4348	286	10	.	.	PUNCT
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ejpam-4348	287	2	pure	pure	PROPN
ejpam-4348	287	3	appl	appl	PROPN
ejpam-4348	287	4	.	.	PROPN
ejpam-4348	287	5	math	math	PROPN
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ejpam-4348	287	9	2	2	NUM
ejpam-4348	287	10	)	)	PUNCT
ejpam-4348	287	11	(	(	PUNCT
ejpam-4348	287	12	2022	2022	NUM
ejpam-4348	287	13	)	)	PUNCT
ejpam-4348	287	14	,	,	PUNCT
ejpam-4348	287	15	681	681	NUM
ejpam-4348	287	16	-	-	SYM
ejpam-4348	287	17	725	725	NUM
ejpam-4348	287	18	699	699	NUM
ejpam-4348	287	19	=	=	SYM
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ejpam-4348	287	22	0	0	NUM
ejpam-4348	287	23	q	q	NOUN
ejpam-4348	287	24			NOUN
ejpam-4348	287	25			NOUN
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ejpam-4348	287	37	+	+	CCONJ
ejpam-4348	287	38	√	√	PROPN
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ejpam-4348	287	44	0	0	NUM
ejpam-4348	287	45			NOUN
ejpam-4348	287	46	1	1	NUM
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ejpam-4348	288	17	0	0	NUM
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ejpam-4348	288	20	q−1	q−1	NUM
ejpam-4348	288	21	0	0	PUNCT
ejpam-4348	288	22	0	0	NUM
ejpam-4348	289	1	q−1	q−1	PROPN
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ejpam-4348	289	5	q	q	X
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ejpam-4348	291	3	12(j+	12(j+	PROPN
ejpam-4348	291	4	+	+	CCONJ
ejpam-4348	291	5	√	√	PROPN
ejpam-4348	291	6	p	p	SYM
ejpam-4348	291	7	2	2	NUM
ejpam-4348	291	8	ik	ik	NOUN
ejpam-4348	291	9	)	)	PUNCT
ejpam-4348	291	10	0	0	NUM
ejpam-4348	291	11	0	0	NUM
ejpam-4348	291	12	0	0	NUM
ejpam-4348	292	1	q−1	q−1	PRON
ejpam-4348	292	2	q	q	X
ejpam-4348	292	3	12(j+	12(j+	PROPN
ejpam-4348	292	4	+	+	CCONJ
ejpam-4348	292	5	√	√	PROPN
ejpam-4348	292	6	p	p	SYM
ejpam-4348	292	7	2	2	NUM
ejpam-4348	292	8	ik	ik	NOUN
ejpam-4348	292	9	)	)	PUNCT
ejpam-4348	292	10	−1	−1	NOUN
ejpam-4348	292	11	0	0	NUM
ejpam-4348	292	12	0	0	NUM
ejpam-4348	292	13	0	0	NUM
ejpam-4348	293	1	q−1	q−1	PRON
ejpam-4348	293	2	q	q	X
ejpam-4348	294	1	[	[	X
ejpam-4348	294	2	1	1	NUM
ejpam-4348	294	3	2	2	NUM
ejpam-4348	294	4	ik	ik	X
ejpam-4348	294	5	0	0	PROPN
ejpam-4348	294	6	0	0	NUM
ejpam-4348	294	7	0	0	NUM
ejpam-4348	294	8	]	]	PUNCT
ejpam-4348	295	1	q−1	q−1	PROPN
ejpam-4348	295	2			NUM
ejpam-4348	295	3	=	=	PUNCT
ejpam-4348	295	4	[	[	PUNCT
ejpam-4348	295	5	p̃1	p̃1	PROPN
ejpam-4348	295	6	p̃2	p̃2	PROPN
ejpam-4348	295	7	p̃3	p̃3	PROPN
ejpam-4348	295	8	p̃4	p̃4	PROPN
ejpam-4348	295	9	]	]	PUNCT
ejpam-4348	295	10	it	it	PRON
ejpam-4348	295	11	follows	follow	VERB
ejpam-4348	295	12	that	that	SCONJ
ejpam-4348	295	13	p̃1	p̃1	PROPN
ejpam-4348	295	14	=	=	PUNCT
ejpam-4348	295	15	q	q	X
ejpam-4348	296	1	[	[	X
ejpam-4348	296	2	1	1	NUM
ejpam-4348	296	3	2	2	NUM
ejpam-4348	296	4	ik	ik	X
ejpam-4348	296	5	0	0	PROPN
ejpam-4348	296	6	0	0	NUM
ejpam-4348	296	7	0	0	NUM
ejpam-4348	296	8	]	]	PUNCT
ejpam-4348	297	1	q−1	q−1	PROPN
ejpam-4348	297	2	=	=	NOUN
ejpam-4348	297	3	1	1	NUM
ejpam-4348	297	4	2	2	NUM
ejpam-4348	297	5	p̃	p̃	PROPN
ejpam-4348	297	6	p̃2	p̃2	PROPN
ejpam-4348	297	7	=	=	PUNCT
ejpam-4348	297	8	q	q	NOUN
ejpam-4348	297	9	1	1	NUM
ejpam-4348	297	10	2	2	NUM
ejpam-4348	297	11	j+	j+	NUM
ejpam-4348	297	12	+	+	CCONJ
ejpam-4348	297	13	√	√	PROPN
ejpam-4348	297	14	p	p	NOUN
ejpam-4348	297	15	2	2	NUM
ejpam-4348	297	16	ik	ik	X
ejpam-4348	297	17	0	0	NUM
ejpam-4348	297	18	0	0	SYM
ejpam-4348	297	19	0	0	NUM
ejpam-4348	298	1	q−1	q−1	PRON
ejpam-4348	299	1	p̃3	p̃3	X
ejpam-4348	299	2	=	=	SYM
ejpam-4348	299	3	q	q	NOUN
ejpam-4348	299	4	1	1	NUM
ejpam-4348	299	5	2	2	NUM
ejpam-4348	299	6	(j+	(j+	ADJ
ejpam-4348	299	7	+	+	CCONJ
ejpam-4348	299	8	√	√	PROPN
ejpam-4348	299	9	p	p	SYM
ejpam-4348	299	10	2	2	NUM
ejpam-4348	299	11	ik	ik	NOUN
ejpam-4348	299	12	)	)	PUNCT
ejpam-4348	299	13	−1	−1	NOUN
ejpam-4348	299	14	0	0	NUM
ejpam-4348	299	15	0	0	NUM
ejpam-4348	299	16	0	0	X
ejpam-4348	300	1	q−1	q−1	DET
ejpam-4348	300	2			NUM
ejpam-4348	300	3	=	=	VERB
ejpam-4348	300	4	⇒	⇒	NOUN
ejpam-4348	300	5	pb	pb	ADP
ejpam-4348	300	6	=	=	SYM
ejpam-4348	300	7	4p̃2p̃3	4p̃2p̃3	PUNCT
ejpam-4348	301	1	p̃4	p̃4	NOUN
ejpam-4348	301	2	=	=	PUNCT
ejpam-4348	301	3	q	q	X
ejpam-4348	302	1	[	[	X
ejpam-4348	302	2	1	1	NUM
ejpam-4348	302	3	2	2	NUM
ejpam-4348	302	4	ik	ik	X
ejpam-4348	302	5	0	0	PROPN
ejpam-4348	302	6	0	0	NUM
ejpam-4348	302	7	0	0	NUM
ejpam-4348	302	8	]	]	PUNCT
ejpam-4348	303	1	q−1	q−1	PROPN
ejpam-4348	303	2	=	=	NOUN
ejpam-4348	303	3	1	1	NUM
ejpam-4348	303	4	2	2	NUM
ejpam-4348	303	5	pb	pb	ADP
ejpam-4348	303	6	we	we	PRON
ejpam-4348	303	7	also	also	ADV
ejpam-4348	303	8	note	note	VERB
ejpam-4348	303	9	that	that	SCONJ
ejpam-4348	303	10	with	with	ADP
ejpam-4348	303	11	a	a	PRON
ejpam-4348	303	12	=	=	X
ejpam-4348	303	13	ab	ab	PROPN
ejpam-4348	303	14	+	+	CCONJ
ejpam-4348	303	15	ipbin	ipbin	NOUN
ejpam-4348	303	16	=	=	PUNCT
ejpam-4348	303	17	q	q	NOUN
ejpam-4348	303	18			NOUN
ejpam-4348	303	19	(	(	PUNCT
ejpam-4348	303	20	j+	j+	PROPN
ejpam-4348	303	21	+	+	CCONJ
ejpam-4348	303	22	√	√	PROPN
ejpam-4348	303	23	p	p	SYM
ejpam-4348	303	24	2	2	NUM
ejpam-4348	303	25	ik	ik	X
ejpam-4348	303	26	)	)	PUNCT
ejpam-4348	303	27	2	2	PROPN
ejpam-4348	304	1	+	+	NUM
ejpam-4348	304	2	ipbik	ipbik	PROPN
ejpam-4348	304	3	0	0	NUM
ejpam-4348	304	4	0	0	NUM
ejpam-4348	304	5	(	(	PUNCT
ejpam-4348	304	6	j−	j−	VERB
ejpam-4348	304	7	+	+	CCONJ
ejpam-4348	304	8	√	√	PROPN
ejpam-4348	304	9	p	p	NOUN
ejpam-4348	304	10	2	2	NUM
ejpam-4348	304	11	in−k	in−k	NOUN
ejpam-4348	304	12	)	)	PUNCT
ejpam-4348	304	13	2	2	NUM
ejpam-4348	304	14	+	+	NUM
ejpam-4348	304	15	ipbin−k	ipbin−k	NOUN
ejpam-4348	304	16	q−1	q−1	PROPN
ejpam-4348	304	17	s.	s.	PROPN
ejpam-4348	304	18	traoré	traoré	PROPN
ejpam-4348	304	19	,	,	PUNCT
ejpam-4348	304	20	m.	m.	NOUN
ejpam-4348	304	21	dosso	dosso	PROPN
ejpam-4348	304	22	/	/	SYM
ejpam-4348	304	23	eur	eur	PROPN
ejpam-4348	304	24	.	.	PUNCT
ejpam-4348	305	1	j.	j.	PROPN
ejpam-4348	305	2	pure	pure	PROPN
ejpam-4348	305	3	appl	appl	PROPN
ejpam-4348	305	4	.	.	PROPN
ejpam-4348	305	5	math	math	PROPN
ejpam-4348	305	6	,	,	PUNCT
ejpam-4348	305	7	15	15	NUM
ejpam-4348	305	8	(	(	PUNCT
ejpam-4348	305	9	2	2	NUM
ejpam-4348	305	10	)	)	PUNCT
ejpam-4348	305	11	(	(	PUNCT
ejpam-4348	305	12	2022	2022	NUM
ejpam-4348	305	13	)	)	PUNCT
ejpam-4348	305	14	,	,	PUNCT
ejpam-4348	305	15	681	681	NUM
ejpam-4348	305	16	-	-	SYM
ejpam-4348	305	17	725	725	NUM
ejpam-4348	305	18	700	700	NUM
ejpam-4348	305	19	we	we	PRON
ejpam-4348	305	20	have	have	VERB
ejpam-4348	305	21	p̃a	p̃a	NOUN
ejpam-4348	306	1	=	=	PUNCT
ejpam-4348	306	2	q	q	X
ejpam-4348	306	3	[	[	PUNCT
ejpam-4348	306	4	ik	ik	X
ejpam-4348	306	5	0	0	PROPN
ejpam-4348	306	6	0	0	NUM
ejpam-4348	306	7	0	0	NUM
ejpam-4348	306	8	]	]	PUNCT
ejpam-4348	307	1	q−1	q−1	PROPN
ejpam-4348	307	2	×q	×q	VERB
ejpam-4348	307	3			NOUN
ejpam-4348	307	4	(	(	PUNCT
ejpam-4348	307	5	j+	j+	PROPN
ejpam-4348	307	6	+	+	CCONJ
ejpam-4348	307	7	√	√	PROPN
ejpam-4348	307	8	p	p	SYM
ejpam-4348	307	9	2	2	NUM
ejpam-4348	307	10	ik	ik	X
ejpam-4348	307	11	)	)	PUNCT
ejpam-4348	307	12	2	2	PROPN
ejpam-4348	307	13	+	+	NUM
ejpam-4348	307	14	ipbik	ipbik	PROPN
ejpam-4348	307	15	0	0	NUM
ejpam-4348	307	16	0	0	NUM
ejpam-4348	308	1	(	(	PUNCT
ejpam-4348	309	1	j−	j−	VERB
ejpam-4348	309	2	+	+	CCONJ
ejpam-4348	309	3	√	√	PROPN
ejpam-4348	309	4	p	p	NOUN
ejpam-4348	309	5	2	2	NUM
ejpam-4348	309	6	in−k	in−k	NOUN
ejpam-4348	309	7	)	)	PUNCT
ejpam-4348	309	8	2	2	NUM
ejpam-4348	310	1	+	+	NUM
ejpam-4348	310	2	ipbin−k	ipbin−k	NOUN
ejpam-4348	310	3	q−1	q−1	X
ejpam-4348	311	1	=	=	PUNCT
ejpam-4348	311	2	q	q	PUNCT
ejpam-4348	311	3	(j+	(j+	PROPN
ejpam-4348	311	4	+	+	CCONJ
ejpam-4348	311	5	(	(	PUNCT
ejpam-4348	311	6	√	√	PROPN
ejpam-4348	311	7	p	p	SYM
ejpam-4348	311	8	2	2	NUM
ejpam-4348	311	9	ik	ik	X
ejpam-4348	311	10	)	)	PUNCT
ejpam-4348	311	11	2	2	PROPN
ejpam-4348	312	1	+	+	NUM
ejpam-4348	312	2	ipbik	ipbik	PROPN
ejpam-4348	312	3	0	0	NUM
ejpam-4348	312	4	0	0	NUM
ejpam-4348	312	5	0	0	NUM
ejpam-4348	313	1	q−1	q−1	NOUN
ejpam-4348	313	2	=	=	PUNCT
ejpam-4348	314	1	4p̃2	4p̃2	NUM
ejpam-4348	314	2	2	2	NUM
ejpam-4348	314	3	+	+	CCONJ
ejpam-4348	314	4	2ipbp̃1	2ipbp̃1	NUM
ejpam-4348	314	5	thus	thus	ADV
ejpam-4348	314	6	we	we	PRON
ejpam-4348	314	7	obtain	obtain	VERB
ejpam-4348	314	8	the	the	DET
ejpam-4348	314	9	equality	equality	NOUN
ejpam-4348	314	10	(	(	PUNCT
ejpam-4348	314	11	30	30	NUM
ejpam-4348	314	12	)	)	PUNCT
ejpam-4348	314	13	and	and	CCONJ
ejpam-4348	314	14	(	(	PUNCT
ejpam-4348	314	15	31	31	NUM
ejpam-4348	314	16	)	)	PUNCT
ejpam-4348	314	17	remark	remark	NOUN
ejpam-4348	314	18	3	3	NUM
ejpam-4348	314	19	.	.	PUNCT
ejpam-4348	315	1	if	if	SCONJ
ejpam-4348	315	2	the	the	DET
ejpam-4348	315	3	parameter	parameter	NOUN
ejpam-4348	315	4	b	b	PROPN
ejpam-4348	315	5	=	=	SYM
ejpam-4348	315	6	0	0	NUM
ejpam-4348	315	7	,	,	PUNCT
ejpam-4348	315	8	whence	whence	ADJ
ejpam-4348	315	9	equalities	equality	NOUN
ejpam-4348	315	10	(	(	PUNCT
ejpam-4348	315	11	31	31	NUM
ejpam-4348	315	12	)	)	PUNCT
ejpam-4348	315	13	are	be	AUX
ejpam-4348	315	14	reduced	reduce	VERB
ejpam-4348	315	15	to	to	ADP
ejpam-4348	315	16	those	those	PRON
ejpam-4348	315	17	of	of	ADP
ejpam-4348	315	18	(	(	PUNCT
ejpam-4348	315	19	23	23	NUM
ejpam-4348	315	20	)	)	PUNCT
ejpam-4348	315	21	algorithm	algorithm	NOUN
ejpam-4348	315	22	5	5	NUM
ejpam-4348	315	23	(	(	PUNCT
ejpam-4348	315	24	dichopb	dichopb	ADJ
ejpam-4348	315	25	)	)	PUNCT
ejpam-4348	315	26	.	.	PUNCT
ejpam-4348	316	1	•	•	NUM
ejpam-4348	316	2	input	input	NOUN
ejpam-4348	316	3	variables	variable	NOUN
ejpam-4348	316	4	:	:	PUNCT
ejpam-4348	316	5	a	a	X
ejpam-4348	316	6	and	and	CCONJ
ejpam-4348	316	7	in	in	ADP
ejpam-4348	316	8	such	such	ADJ
ejpam-4348	316	9	that	that	SCONJ
ejpam-4348	316	10	the	the	DET
ejpam-4348	316	11	matrix	matrix	NOUN
ejpam-4348	316	12	bundle	bundle	NOUN
ejpam-4348	316	13	zin	zin	NOUN
ejpam-4348	316	14	−	−	NOUN
ejpam-4348	316	15	a	a	PRON
ejpam-4348	316	16	has	have	AUX
ejpam-4348	316	17	no	no	DET
ejpam-4348	316	18	eigenvalues	eigenvalue	NOUN
ejpam-4348	316	19	on	on	ADP
ejpam-4348	316	20	the	the	DET
ejpam-4348	316	21	parabola	parabola	NOUN
ejpam-4348	316	22	with	with	ADP
ejpam-4348	316	23	equation	equation	NOUN
ejpam-4348	316	24	2p	2p	NOUN
ejpam-4348	316	25	(	(	PUNCT
ejpam-4348	316	26	p	p	NOUN
ejpam-4348	316	27	2	2	NUM
ejpam-4348	316	28	−	−	NOUN
ejpam-4348	316	29	x	x	SYM
ejpam-4348	316	30	)	)	PUNCT
ejpam-4348	316	31	2	2	NUM
ejpam-4348	316	32	=	=	SYM
ejpam-4348	316	33	(	(	PUNCT
ejpam-4348	316	34	y	y	PROPN
ejpam-4348	316	35	−	−	PROPN
ejpam-4348	316	36	pb)2	pb)2	PROPN
ejpam-4348	316	37	with	with	ADP
ejpam-4348	316	38	p	p	PROPN
ejpam-4348	316	39	>	>	SYM
ejpam-4348	316	40	0	0	NUM
ejpam-4348	316	41	•	•	NOUN
ejpam-4348	316	42	output	output	NOUN
ejpam-4348	316	43	variables	variable	NOUN
ejpam-4348	316	44	:	:	PUNCT
ejpam-4348	317	1	p̃	p̃	PROPN
ejpam-4348	317	2	and	and	CCONJ
ejpam-4348	317	3	h̃	h̃	PROPN
ejpam-4348	317	4	p̃	p̃	PROPN
ejpam-4348	317	5	being	be	AUX
ejpam-4348	317	6	the	the	DET
ejpam-4348	317	7	projector	projector	NOUN
ejpam-4348	317	8	on	on	ADP
ejpam-4348	317	9	the	the	DET
ejpam-4348	317	10	right	right	ADJ
ejpam-4348	317	11	subspace	subspace	NOUN
ejpam-4348	317	12	of	of	ADP
ejpam-4348	317	13	zin−a	zin−a	PROPN
ejpam-4348	317	14	associated	associate	VERB
ejpam-4348	317	15	with	with	ADP
ejpam-4348	317	16	the	the	DET
ejpam-4348	317	17	eigenvalues	eigenvalue	NOUN
ejpam-4348	317	18	outside	outside	ADP
ejpam-4348	317	19	the	the	DET
ejpam-4348	317	20	parabola	parabola	NOUN
ejpam-4348	317	21	and	and	CCONJ
ejpam-4348	317	22	the	the	DET
ejpam-4348	317	23	matrix	matrix	NOUN
ejpam-4348	317	24	h̃	h̃	PROPN
ejpam-4348	317	25	whose	whose	DET
ejpam-4348	317	26	norm	norm	NOUN
ejpam-4348	317	27	gives	give	VERB
ejpam-4348	317	28	the	the	DET
ejpam-4348	317	29	dichotomy	dichotomy	NOUN
ejpam-4348	317	30	criterion	criterion	NOUN
ejpam-4348	317	31	.	.	PUNCT
ejpam-4348	318	1	1	1	X
ejpam-4348	318	2	.	.	X
ejpam-4348	318	3	determine	determine	VERB
ejpam-4348	318	4	the	the	DET
ejpam-4348	318	5	matrix	matrix	NOUN
ejpam-4348	318	6	ã	ã	PROPN
ejpam-4348	318	7	=	=	SYM
ejpam-4348	318	8			PROPN
ejpam-4348	318	9	−	−	ADP
ejpam-4348	318	10	√	√	NOUN
ejpam-4348	318	11	p	p	NOUN
ejpam-4348	318	12	2	2	NUM
ejpam-4348	318	13	in	in	ADP
ejpam-4348	318	14	a−	a−	PROPN
ejpam-4348	318	15	ipbin	ipbin	NOUN
ejpam-4348	318	16	in	in	ADP
ejpam-4348	318	17	−	−	PROPN
ejpam-4348	318	18	√	√	PROPN
ejpam-4348	319	1	p	p	NOUN
ejpam-4348	319	2	2	2	NUM
ejpam-4348	319	3	in	in	ADP
ejpam-4348	319	4			NOUN
ejpam-4348	319	5	2	2	NUM
ejpam-4348	319	6	.	.	PUNCT
ejpam-4348	319	7	using	use	VERB
ejpam-4348	319	8	algorithm	algorithm	NOUN
ejpam-4348	319	9	3	3	NUM
ejpam-4348	319	10	to	to	ADP
ejpam-4348	319	11	λ̃i2n	λ̃i2n	NOUN
ejpam-4348	319	12	−	−	PROPN
ejpam-4348	319	13	ã	ã	PROPN
ejpam-4348	319	14	,	,	PUNCT
ejpam-4348	319	15	compute	compute	VERB
ejpam-4348	319	16	the	the	DET
ejpam-4348	319	17	projector	projector	NOUN
ejpam-4348	319	18	p̃	p̃	PROPN
ejpam-4348	319	19	onto	onto	ADP
ejpam-4348	319	20	the	the	DET
ejpam-4348	319	21	right	right	ADJ
ejpam-4348	319	22	eigenspace	eigenspace	NOUN
ejpam-4348	319	23	of	of	ADP
ejpam-4348	319	24	ã	ã	PROPN
ejpam-4348	319	25	associted	associte	VERB
ejpam-4348	319	26	with	with	ADP
ejpam-4348	319	27	the	the	DET
ejpam-4348	319	28	eigenvalues	eigenvalue	NOUN
ejpam-4348	319	29	on	on	ADP
ejpam-4348	319	30	the	the	DET
ejpam-4348	319	31	right	right	ADJ
ejpam-4348	319	32	half	half	ADJ
ejpam-4348	319	33	-	-	PUNCT
ejpam-4348	319	34	plane	plane	NOUN
ejpam-4348	319	35	of	of	ADP
ejpam-4348	319	36	the	the	DET
ejpam-4348	319	37	complex	complex	ADJ
ejpam-4348	319	38	plane	plane	NOUN
ejpam-4348	319	39	and	and	CCONJ
ejpam-4348	319	40	the	the	DET
ejpam-4348	319	41	matrix	matrix	NOUN
ejpam-4348	319	42	h̃	h̃	PROPN
ejpam-4348	319	43	;	;	PUNCT
ejpam-4348	320	1	3	3	X
ejpam-4348	320	2	.	.	X
ejpam-4348	321	1	if	if	SCONJ
ejpam-4348	321	2	∥h̃∥	∥h̃∥	PROPN
ejpam-4348	321	3	is	be	AUX
ejpam-4348	321	4	not	not	PART
ejpam-4348	321	5	large	large	ADJ
ejpam-4348	321	6	,	,	PUNCT
ejpam-4348	321	7	determine	determine	VERB
ejpam-4348	321	8	the	the	DET
ejpam-4348	321	9	projectors	projector	NOUN
ejpam-4348	321	10	p̃	p̃	PROPN
ejpam-4348	321	11	by	by	ADP
ejpam-4348	321	12	p̃	p̃	PROPN
ejpam-4348	321	13	=	=	PROPN
ejpam-4348	321	14	2p̃1	2p̃1	PROPN
ejpam-4348	321	15	s.	s.	PROPN
ejpam-4348	321	16	traoré	traoré	NOUN
ejpam-4348	321	17	,	,	PUNCT
ejpam-4348	321	18	m.	m.	NOUN
ejpam-4348	321	19	dosso	dosso	PROPN
ejpam-4348	321	20	/	/	SYM
ejpam-4348	321	21	eur	eur	PROPN
ejpam-4348	321	22	.	.	PUNCT
ejpam-4348	322	1	j.	j.	PROPN
ejpam-4348	322	2	pure	pure	PROPN
ejpam-4348	322	3	appl	appl	PROPN
ejpam-4348	322	4	.	.	PROPN
ejpam-4348	322	5	math	math	PROPN
ejpam-4348	322	6	,	,	PUNCT
ejpam-4348	322	7	15	15	NUM
ejpam-4348	322	8	(	(	PUNCT
ejpam-4348	322	9	2	2	NUM
ejpam-4348	322	10	)	)	PUNCT
ejpam-4348	322	11	(	(	PUNCT
ejpam-4348	322	12	2022	2022	NUM
ejpam-4348	322	13	)	)	PUNCT
ejpam-4348	322	14	,	,	PUNCT
ejpam-4348	322	15	681	681	NUM
ejpam-4348	322	16	-	-	SYM
ejpam-4348	322	17	725	725	NUM
ejpam-4348	322	18	701	701	NUM
ejpam-4348	322	19	3.2	3.2	NUM
ejpam-4348	322	20	.	.	PUNCT
ejpam-4348	323	1	the	the	DET
ejpam-4348	323	2	case	case	NOUN
ejpam-4348	323	3	of	of	ADP
ejpam-4348	323	4	a	a	DET
ejpam-4348	323	5	parabola	parabola	NOUN
ejpam-4348	323	6	of	of	ADP
ejpam-4348	323	7	equation	equation	NOUN
ejpam-4348	323	8	of	of	ADP
ejpam-4348	323	9	type	type	NOUN
ejpam-4348	323	10	(	(	PUNCT
ejpam-4348	323	11	1	1	NUM
ejpam-4348	323	12	)	)	PUNCT
ejpam-4348	323	13	with	with	ADP
ejpam-4348	323	14	discriminant	discriminant	NOUN
ejpam-4348	323	15	different	different	ADJ
ejpam-4348	323	16	from	from	ADP
ejpam-4348	323	17	1	1	NUM
ejpam-4348	323	18	we	we	PRON
ejpam-4348	323	19	consider	consider	VERB
ejpam-4348	323	20	the	the	DET
ejpam-4348	323	21	following	follow	VERB
ejpam-4348	323	22	change	change	NOUN
ejpam-4348	323	23	of	of	ADP
ejpam-4348	323	24	variable	variable	NOUN
ejpam-4348	323	25	in	in	ADP
ejpam-4348	323	26	equation	equation	NOUN
ejpam-4348	323	27	(	(	PUNCT
ejpam-4348	323	28	4	4	NUM
ejpam-4348	323	29	)	)	PUNCT
ejpam-4348	323	30	x̃	x̃	PROPN
ejpam-4348	323	31	=	=	PUNCT
ejpam-4348	324	1	x+	x+	PUNCT
ejpam-4348	324	2	p	p	NOUN
ejpam-4348	324	3	2	2	NUM
ejpam-4348	324	4	−	−	NOUN
ejpam-4348	325	1	d	d	NOUN
ejpam-4348	325	2	we	we	PRON
ejpam-4348	325	3	get	get	VERB
ejpam-4348	325	4	2p	2p	NUM
ejpam-4348	325	5	(	(	PUNCT
ejpam-4348	325	6	p	p	NOUN
ejpam-4348	325	7	2	2	NUM
ejpam-4348	325	8	−	−	PROPN
ejpam-4348	325	9	x̃	x̃	PROPN
ejpam-4348	325	10	)	)	PUNCT
ejpam-4348	326	1	=	=	PUNCT
ejpam-4348	326	2	(	(	PUNCT
ejpam-4348	326	3	y	y	PROPN
ejpam-4348	326	4	−	−	PROPN
ejpam-4348	326	5	pb)2	pb)2	PROPN
ejpam-4348	326	6	(	(	PUNCT
ejpam-4348	326	7	33	33	NUM
ejpam-4348	326	8	)	)	PUNCT
ejpam-4348	326	9	3.2.1	3.2.1	NUM
ejpam-4348	326	10	.	.	PUNCT
ejpam-4348	327	1	the	the	DET
ejpam-4348	327	2	spectral	spectral	ADJ
ejpam-4348	327	3	dichotomy	dichotomy	NOUN
ejpam-4348	327	4	method	method	NOUN
ejpam-4348	327	5	with	with	ADP
ejpam-4348	327	6	the	the	DET
ejpam-4348	327	7	coefficient	coefficient	NOUN
ejpam-4348	327	8	b	b	NOUN
ejpam-4348	327	9	=	=	SYM
ejpam-4348	327	10	0	0	PUNCT
ejpam-4348	327	11	consider	consider	VERB
ejpam-4348	327	12	the	the	DET
ejpam-4348	327	13	set	set	NOUN
ejpam-4348	327	14	γd	γd	ADP
ejpam-4348	327	15	=	=	PUNCT
ejpam-4348	327	16	{	{	PUNCT
ejpam-4348	327	17	zd	zd	PROPN
ejpam-4348	327	18	=	=	SYM
ejpam-4348	327	19	x+	x+	PROPN
ejpam-4348	327	20	iy	iy	PROPN
ejpam-4348	327	21	/	/	SYM
ejpam-4348	327	22	x+	x+	PROPN
ejpam-4348	327	23	(	(	PUNCT
ejpam-4348	327	24	p	p	NOUN
ejpam-4348	327	25	2	2	NUM
ejpam-4348	327	26	−	−	NOUN
ejpam-4348	327	27	d	d	NOUN
ejpam-4348	327	28	)	)	PUNCT
ejpam-4348	328	1	+	+	CCONJ
ejpam-4348	328	2	iy	iy	PROPN
ejpam-4348	328	3	∈	∈	PROPN
ejpam-4348	328	4	γ	γ	PROPN
ejpam-4348	328	5	}	}	PUNCT
ejpam-4348	328	6	described	describe	VERB
ejpam-4348	328	7	by	by	ADP
ejpam-4348	328	8	the	the	DET
ejpam-4348	328	9	following	follow	VERB
ejpam-4348	328	10	equation	equation	NOUN
ejpam-4348	328	11	y2	y2	NOUN
ejpam-4348	328	12	=	=	NOUN
ejpam-4348	328	13	2p	2p	NOUN
ejpam-4348	328	14	(	(	PUNCT
ejpam-4348	328	15	p	p	NOUN
ejpam-4348	328	16	2	2	NUM
ejpam-4348	328	17	−	−	PROPN
ejpam-4348	328	18	x̃	x̃	PROPN
ejpam-4348	328	19	)	)	PUNCT
ejpam-4348	328	20	.	.	PUNCT
ejpam-4348	329	1	let	let	VERB
ejpam-4348	329	2	the	the	DET
ejpam-4348	329	3	matrix	matrix	NOUN
ejpam-4348	329	4	ad	ad	NOUN
ejpam-4348	329	5	=	=	SYM
ejpam-4348	329	6	−	−	PROPN
ejpam-4348	329	7	√	√	NUM
ejpam-4348	330	1	p	p	NOUN
ejpam-4348	330	2	2	2	NUM
ejpam-4348	330	3	in	in	ADP
ejpam-4348	330	4	ad	ad	NOUN
ejpam-4348	330	5	in	in	ADP
ejpam-4348	330	6	−	−	PROPN
ejpam-4348	330	7	√	√	PROPN
ejpam-4348	330	8	p	p	NOUN
ejpam-4348	330	9	2	2	NUM
ejpam-4348	330	10	in	in	ADP
ejpam-4348	330	11			NOUN
ejpam-4348	330	12	where	where	SCONJ
ejpam-4348	330	13	ad	ad	NOUN
ejpam-4348	330	14	=	=	SYM
ejpam-4348	330	15	a+	a+	PUNCT
ejpam-4348	330	16	(	(	PUNCT
ejpam-4348	330	17	p	p	NOUN
ejpam-4348	330	18	2	2	NUM
ejpam-4348	330	19	−	−	PROPN
ejpam-4348	330	20	d	d	NOUN
ejpam-4348	330	21	)	)	PUNCT
ejpam-4348	330	22	in	in	ADP
ejpam-4348	330	23	(	(	PUNCT
ejpam-4348	330	24	34	34	NUM
ejpam-4348	330	25	)	)	PUNCT
ejpam-4348	330	26	knowing	know	VERB
ejpam-4348	330	27	that	that	SCONJ
ejpam-4348	330	28	the	the	DET
ejpam-4348	330	29	eigenvalues	eigenvalues	PROPN
ejpam-4348	330	30	zd	zd	PROPN
ejpam-4348	330	31	and	and	CCONJ
ejpam-4348	330	32	z	z	PROPN
ejpam-4348	330	33	of	of	ADP
ejpam-4348	330	34	the	the	DET
ejpam-4348	330	35	matrices	matrix	NOUN
ejpam-4348	330	36	ad	ad	NOUN
ejpam-4348	330	37	and	and	CCONJ
ejpam-4348	330	38	a	a	PRON
ejpam-4348	330	39	are	be	AUX
ejpam-4348	330	40	linked	link	VERB
ejpam-4348	330	41	by	by	ADP
ejpam-4348	330	42	zd	zd	PROPN
ejpam-4348	330	43	=	=	SYM
ejpam-4348	330	44	z	z	PROPN
ejpam-4348	331	1	+	+	NOUN
ejpam-4348	331	2	p	p	X
ejpam-4348	331	3	2	2	NUM
ejpam-4348	331	4	−	−	NOUN
ejpam-4348	331	5	d	d	NOUN
ejpam-4348	331	6	,	,	PUNCT
ejpam-4348	331	7	remark	remark	NOUN
ejpam-4348	331	8	4	4	NUM
ejpam-4348	331	9	.	.	PUNCT
ejpam-4348	332	1	the	the	DET
ejpam-4348	332	2	respective	respective	ADJ
ejpam-4348	332	3	eigenvalues	eigenvalue	VERB
ejpam-4348	332	4	λd	λd	NOUN
ejpam-4348	332	5	and	and	CCONJ
ejpam-4348	332	6	z	z	NOUN
ejpam-4348	332	7	of	of	ADP
ejpam-4348	332	8	the	the	DET
ejpam-4348	332	9	matrices	matrix	NOUN
ejpam-4348	332	10	ad	ad	NOUN
ejpam-4348	332	11	and	and	CCONJ
ejpam-4348	332	12	a	a	PRON
ejpam-4348	332	13	are	be	AUX
ejpam-4348	332	14	such	such	ADJ
ejpam-4348	332	15	that	that	SCONJ
ejpam-4348	332	16	z	z	NOUN
ejpam-4348	332	17	=	=	PUNCT
ejpam-4348	332	18	(	(	PUNCT
ejpam-4348	332	19	λd	λd	NOUN
ejpam-4348	332	20	+	+	CCONJ
ejpam-4348	332	21	√	√	PROPN
ejpam-4348	332	22	p	p	NOUN
ejpam-4348	332	23	2	2	NUM
ejpam-4348	332	24	)	)	SYM
ejpam-4348	332	25	2	2	NUM
ejpam-4348	332	26	−	−	NOUN
ejpam-4348	332	27	p	p	NOUN
ejpam-4348	332	28	2	2	NUM
ejpam-4348	332	29	+	+	CCONJ
ejpam-4348	332	30	d	d	NOUN
ejpam-4348	332	31	furthermore	furthermore	ADV
ejpam-4348	332	32	,	,	PUNCT
ejpam-4348	332	33	since	since	SCONJ
ejpam-4348	332	34	z	z	NOUN
ejpam-4348	332	35	=	=	SYM
ejpam-4348	332	36	x+	x+	PROPN
ejpam-4348	332	37	iy	iy	INTJ
ejpam-4348	332	38	,	,	PUNCT
ejpam-4348	332	39	then	then	ADV
ejpam-4348	332	40	we	we	PRON
ejpam-4348	332	41	have	have	PROPN
ejpam-4348	332	42	x	x	PUNCT
ejpam-4348	333	1	=	=	PRON
ejpam-4348	333	2	(	(	PUNCT
ejpam-4348	333	3	ℜ(λd	ℜ(λd	PROPN
ejpam-4348	333	4	)	)	PUNCT
ejpam-4348	334	1	+	+	CCONJ
ejpam-4348	334	2	√	√	ADJ
ejpam-4348	334	3	p	p	NOUN
ejpam-4348	334	4	2	2	NUM
ejpam-4348	334	5	)	)	SYM
ejpam-4348	334	6	2	2	NUM
ejpam-4348	334	7	−ℑ(λd	−ℑ(λd	NOUN
ejpam-4348	334	8	)	)	PUNCT
ejpam-4348	334	9	2	2	NUM
ejpam-4348	334	10	−	−	NOUN
ejpam-4348	334	11	p	p	NOUN
ejpam-4348	334	12	2	2	NUM
ejpam-4348	334	13	+	+	CCONJ
ejpam-4348	334	14	d	d	PROPN
ejpam-4348	334	15	y	y	NOUN
ejpam-4348	334	16	=	=	SYM
ejpam-4348	334	17	2	2	NUM
ejpam-4348	334	18	(	(	PUNCT
ejpam-4348	334	19	ℜ(λd	ℜ(λd	PROPN
ejpam-4348	334	20	)	)	PUNCT
ejpam-4348	335	1	+	+	CCONJ
ejpam-4348	335	2	√	√	PROPN
ejpam-4348	335	3	p	p	NOUN
ejpam-4348	335	4	2	2	NUM
ejpam-4348	335	5	)	)	PUNCT
ejpam-4348	335	6	ℑ(λd	ℑ(λd	PROPN
ejpam-4348	335	7	)	)	PUNCT
ejpam-4348	335	8	by	by	ADP
ejpam-4348	335	9	setting	set	VERB
ejpam-4348	335	10	that	that	SCONJ
ejpam-4348	335	11	s.	s.	PROPN
ejpam-4348	335	12	traoré	traoré	PROPN
ejpam-4348	335	13	,	,	PUNCT
ejpam-4348	335	14	m.	m.	NOUN
ejpam-4348	335	15	dosso	dosso	PROPN
ejpam-4348	335	16	/	/	SYM
ejpam-4348	335	17	eur	eur	PROPN
ejpam-4348	335	18	.	.	PUNCT
ejpam-4348	336	1	j.	j.	PROPN
ejpam-4348	336	2	pure	pure	PROPN
ejpam-4348	336	3	appl	appl	PROPN
ejpam-4348	336	4	.	.	PROPN
ejpam-4348	336	5	math	math	PROPN
ejpam-4348	336	6	,	,	PUNCT
ejpam-4348	336	7	15	15	NUM
ejpam-4348	336	8	(	(	PUNCT
ejpam-4348	336	9	2	2	NUM
ejpam-4348	336	10	)	)	PUNCT
ejpam-4348	336	11	(	(	PUNCT
ejpam-4348	336	12	2022	2022	NUM
ejpam-4348	336	13	)	)	PUNCT
ejpam-4348	336	14	,	,	PUNCT
ejpam-4348	336	15	681	681	NUM
ejpam-4348	336	16	-	-	SYM
ejpam-4348	336	17	725	725	NUM
ejpam-4348	336	18	702	702	NUM
ejpam-4348	336	19	pd	pd	NOUN
ejpam-4348	336	20	=	=	SYM
ejpam-4348	336	21	2	2	NUM
ejpam-4348	336	22	(	(	PUNCT
ejpam-4348	336	23	ℜ(λd	ℜ(λd	PROPN
ejpam-4348	336	24	)	)	PUNCT
ejpam-4348	337	1	+	+	CCONJ
ejpam-4348	337	2	√	√	ADJ
ejpam-4348	337	3	p	p	NOUN
ejpam-4348	337	4	2	2	NUM
ejpam-4348	337	5	)	)	SYM
ejpam-4348	337	6	2	2	NUM
ejpam-4348	337	7	then	then	ADV
ejpam-4348	338	1	y2	y2	NOUN
ejpam-4348	338	2	=	=	SYM
ejpam-4348	338	3	2pd	2pd	ADJ
ejpam-4348	339	1	[	[	X
ejpam-4348	339	2	pd	pd	NOUN
ejpam-4348	339	3	2	2	NUM
ejpam-4348	339	4	−	−	NOUN
ejpam-4348	339	5	x−	x−	PROPN
ejpam-4348	339	6	p	p	PROPN
ejpam-4348	339	7	2	2	NUM
ejpam-4348	340	1	+	+	CCONJ
ejpam-4348	340	2	d	d	NOUN
ejpam-4348	340	3	]	]	X
ejpam-4348	340	4	=	=	SYM
ejpam-4348	340	5	2pd	2pd	ADJ
ejpam-4348	340	6	(	(	PUNCT
ejpam-4348	340	7	pd	pd	PROPN
ejpam-4348	340	8	2	2	NUM
ejpam-4348	340	9	−	−	PROPN
ejpam-4348	340	10	x̃	x̃	PROPN
ejpam-4348	340	11	)	)	PUNCT
ejpam-4348	340	12	we	we	PRON
ejpam-4348	340	13	also	also	ADV
ejpam-4348	340	14	assume	assume	VERB
ejpam-4348	340	15	that	that	SCONJ
ejpam-4348	340	16	∥ad∥	∥ad∥	PRON
ejpam-4348	340	17	=	=	SYM
ejpam-4348	340	18	1	1	X
ejpam-4348	340	19	.	.	PUNCT
ejpam-4348	341	1	otherwise	otherwise	ADV
ejpam-4348	341	2	we	we	PRON
ejpam-4348	341	3	set	set	VERB
ejpam-4348	341	4	(	(	PUNCT
ejpam-4348	341	5	i.e.	i.e.	X
ejpam-4348	341	6	∥ad|	∥ad|	X
ejpam-4348	341	7	=	=	NOUN
ejpam-4348	341	8	̸	̸	NUM
ejpam-4348	341	9	1	1	NUM
ejpam-4348	341	10	)	)	PUNCT
ejpam-4348	341	11	,	,	PUNCT
ejpam-4348	341	12	we	we	PRON
ejpam-4348	341	13	can	can	AUX
ejpam-4348	341	14	take	take	VERB
ejpam-4348	341	15	a1	a1	NOUN
ejpam-4348	341	16	d	d	NOUN
ejpam-4348	341	17	=	=	SYM
ejpam-4348	341	18	1	1	NUM
ejpam-4348	341	19	∥ad∥	∥ad∥	NOUN
ejpam-4348	341	20	ad	ad	NOUN
ejpam-4348	341	21	and	and	CCONJ
ejpam-4348	341	22	p1	p1	NOUN
ejpam-4348	341	23	=	=	SYM
ejpam-4348	341	24	1	1	NUM
ejpam-4348	341	25	∥ad∥	∥ad∥	NOUN
ejpam-4348	341	26	.	.	PUNCT
ejpam-4348	342	1	consider	consider	VERB
ejpam-4348	342	2	the	the	DET
ejpam-4348	342	3	numerical	numerical	ADJ
ejpam-4348	342	4	parameters	parameter	NOUN
ejpam-4348	342	5	αad	αad	PROPN
ejpam-4348	342	6	and	and	CCONJ
ejpam-4348	342	7	αad	αad	NOUN
ejpam-4348	342	8	defined	define	VERB
ejpam-4348	342	9	by	by	ADP
ejpam-4348	342	10	αad	αad	NOUN
ejpam-4348	342	11	=	=	NOUN
ejpam-4348	342	12	sup	sup	NOUN
ejpam-4348	342	13	ℜ(λd)=0	ℜ(λd)=0	VERB
ejpam-4348	342	14	∥(λdi2n	∥(λdi2n	NUM
ejpam-4348	342	15	−ad	−ad	NUM
ejpam-4348	342	16	)	)	PUNCT
ejpam-4348	342	17	−1∥	−1∥	VERB
ejpam-4348	342	18	et	et	NOUN
ejpam-4348	342	19	αad	αad	NOUN
ejpam-4348	342	20	=	=	NOUN
ejpam-4348	342	21	sup	sup	PROPN
ejpam-4348	342	22	z∈γd	z∈γd	NOUN
ejpam-4348	342	23	∥(zin	∥(zin	PROPN
ejpam-4348	342	24	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	342	25	(	(	PUNCT
ejpam-4348	342	26	35	35	NUM
ejpam-4348	342	27	)	)	PUNCT
ejpam-4348	342	28	the	the	DET
ejpam-4348	342	29	following	follow	VERB
ejpam-4348	342	30	proposition	proposition	NOUN
ejpam-4348	342	31	gives	give	VERB
ejpam-4348	342	32	a	a	DET
ejpam-4348	342	33	relation	relation	NOUN
ejpam-4348	342	34	between	between	ADP
ejpam-4348	342	35	the	the	DET
ejpam-4348	342	36	parameters	parameter	NOUN
ejpam-4348	342	37	αad	αad	NOUN
ejpam-4348	342	38	and	and	CCONJ
ejpam-4348	342	39	αad	αad	NOUN
ejpam-4348	342	40	.	.	PUNCT
ejpam-4348	343	1	proposition	proposition	NOUN
ejpam-4348	343	2	8	8	NUM
ejpam-4348	343	3	.	.	PUNCT
ejpam-4348	344	1	let	let	VERB
ejpam-4348	344	2	αad	αad	NOUN
ejpam-4348	344	3	and	and	CCONJ
ejpam-4348	344	4	αad	αad	NOUN
ejpam-4348	344	5	be	be	AUX
ejpam-4348	344	6	the	the	DET
ejpam-4348	344	7	two	two	NUM
ejpam-4348	344	8	parameters	parameter	NOUN
ejpam-4348	344	9	defined	define	VERB
ejpam-4348	344	10	in	in	ADP
ejpam-4348	344	11	(	(	PUNCT
ejpam-4348	344	12	35	35	NUM
ejpam-4348	344	13	)	)	PUNCT
ejpam-4348	344	14	.	.	PUNCT
ejpam-4348	345	1	assume	assume	VERB
ejpam-4348	345	2	that	that	SCONJ
ejpam-4348	345	3	∥ad∥	∥ad∥	PRON
ejpam-4348	345	4	=	=	SYM
ejpam-4348	345	5	1	1	NUM
ejpam-4348	345	6	and	and	CCONJ
ejpam-4348	345	7	∣∣∣p	∣∣∣p	NOUN
ejpam-4348	345	8	2	2	NUM
ejpam-4348	345	9	−	−	NOUN
ejpam-4348	345	10	d	d	NOUN
ejpam-4348	345	11	∣∣∣	∣∣∣	NOUN
ejpam-4348	345	12	<	<	X
ejpam-4348	345	13	1	1	NUM
ejpam-4348	345	14	αad	αad	NOUN
ejpam-4348	345	15	.	.	PUNCT
ejpam-4348	346	1	(	(	PUNCT
ejpam-4348	346	2	36	36	NUM
ejpam-4348	346	3	)	)	PUNCT
ejpam-4348	346	4	then	then	ADV
ejpam-4348	346	5	αad	αad	VERB
ejpam-4348	346	6	≤	≤	X
ejpam-4348	346	7	αad	αad	NOUN
ejpam-4348	346	8	≤	≤	ADJ
ejpam-4348	346	9	2	2	NUM
ejpam-4348	346	10	(	(	PUNCT
ejpam-4348	346	11	αad	αad	NOUN
ejpam-4348	346	12	+	+	NOUN
ejpam-4348	346	13	√	√	PROPN
ejpam-4348	346	14	αad	αad	NOUN
ejpam-4348	346	15	(	(	PUNCT
ejpam-4348	346	16	1	1	NUM
ejpam-4348	346	17	+	+	CCONJ
ejpam-4348	346	18	√	√	PROPN
ejpam-4348	346	19	αad	αad	NOUN
ejpam-4348	346	20	+	+	NOUN
ejpam-4348	346	21	1	1	NUM
ejpam-4348	346	22	)	)	PUNCT
ejpam-4348	346	23	)	)	PUNCT
ejpam-4348	346	24	.	.	PUNCT
ejpam-4348	347	1	(	(	PUNCT
ejpam-4348	347	2	37	37	NUM
ejpam-4348	347	3	)	)	PUNCT
ejpam-4348	347	4	proof	proof	NOUN
ejpam-4348	347	5	.	.	PUNCT
ejpam-4348	348	1	let	let	VERB
ejpam-4348	348	2	the	the	DET
ejpam-4348	348	3	matrix	matrix	NOUN
ejpam-4348	348	4	(	(	PUNCT
ejpam-4348	348	5	λdi2n	λdi2n	NUM
ejpam-4348	348	6	−ad	−ad	NOUN
ejpam-4348	348	7	)	)	PUNCT
ejpam-4348	348	8	=	=	SYM
ejpam-4348	348	9			NOUN
ejpam-4348	348	10	(	(	PUNCT
ejpam-4348	348	11	λd	λd	NOUN
ejpam-4348	348	12	+	+	NOUN
ejpam-4348	348	13	√	√	PROPN
ejpam-4348	349	1	p	p	X
ejpam-4348	349	2	2)in	2)in	PROPN
ejpam-4348	349	3	−ad	−ad	NUM
ejpam-4348	349	4	−in	−in	PROPN
ejpam-4348	349	5	(	(	PUNCT
ejpam-4348	349	6	λd	λd	NOUN
ejpam-4348	349	7	+	+	NOUN
ejpam-4348	349	8	√	√	PROPN
ejpam-4348	349	9	p	p	X
ejpam-4348	349	10	2)in	2)in	PROPN
ejpam-4348	349	11			NOUN
ejpam-4348	349	12	we	we	PRON
ejpam-4348	349	13	have	have	VERB
ejpam-4348	349	14			NOUN
ejpam-4348	349	15	(	(	PUNCT
ejpam-4348	349	16	λd	λd	NOUN
ejpam-4348	349	17	+	+	NOUN
ejpam-4348	349	18	√	√	PROPN
ejpam-4348	349	19	p	p	X
ejpam-4348	349	20	2)in	2)in	NUM
ejpam-4348	349	21	ad	ad	NOUN
ejpam-4348	349	22	in	in	ADP
ejpam-4348	349	23	(	(	PUNCT
ejpam-4348	349	24	λd	λd	NOUN
ejpam-4348	349	25	+	+	NOUN
ejpam-4348	349	26	√	√	PROPN
ejpam-4348	349	27	p	p	X
ejpam-4348	349	28	2)in	2)in	PROPN
ejpam-4348	349	29	×	×	NOUN
ejpam-4348	349	30			NOUN
ejpam-4348	349	31	(	(	PUNCT
ejpam-4348	349	32	λd	λd	NOUN
ejpam-4348	349	33	+	+	NOUN
ejpam-4348	349	34	√	√	PROPN
ejpam-4348	350	1	p	p	X
ejpam-4348	350	2	2)in	2)in	PROPN
ejpam-4348	350	3	−ad	−ad	NUM
ejpam-4348	350	4	−in	−in	PROPN
ejpam-4348	350	5	(	(	PUNCT
ejpam-4348	350	6	λd	λd	NOUN
ejpam-4348	350	7	+	+	NOUN
ejpam-4348	350	8	√	√	PROPN
ejpam-4348	350	9	p	p	X
ejpam-4348	350	10	2)in	2)in	PROPN
ejpam-4348	350	11			NOUN
ejpam-4348	350	12	=	=	SYM
ejpam-4348	350	13			NOUN
ejpam-4348	350	14	(	(	PUNCT
ejpam-4348	350	15	λd	λd	NOUN
ejpam-4348	350	16	+	+	CCONJ
ejpam-4348	350	17	√	√	PROPN
ejpam-4348	350	18	p	p	NOUN
ejpam-4348	350	19	2	2	NUM
ejpam-4348	350	20	)	)	PUNCT
ejpam-4348	350	21	2	2	NUM
ejpam-4348	350	22	in	in	ADP
ejpam-4348	350	23	−ad	−ad	NUM
ejpam-4348	350	24	0	0	NUM
ejpam-4348	350	25	0	0	NUM
ejpam-4348	350	26	(	(	PUNCT
ejpam-4348	350	27	λd	λd	NOUN
ejpam-4348	350	28	+	+	CCONJ
ejpam-4348	350	29	√	√	PROPN
ejpam-4348	350	30	p	p	NOUN
ejpam-4348	350	31	2	2	NUM
ejpam-4348	350	32	)	)	PUNCT
ejpam-4348	350	33	2	2	NUM
ejpam-4348	350	34	in	in	ADP
ejpam-4348	350	35	−ad	−ad	NUM
ejpam-4348	350	36			NOUN
ejpam-4348	350	37	with	with	ADP
ejpam-4348	350	38	s.	s.	PROPN
ejpam-4348	350	39	traoré	traoré	PROPN
ejpam-4348	350	40	,	,	PUNCT
ejpam-4348	350	41	m.	m.	NOUN
ejpam-4348	350	42	dosso	dosso	PROPN
ejpam-4348	350	43	/	/	SYM
ejpam-4348	350	44	eur	eur	PROPN
ejpam-4348	350	45	.	.	PUNCT
ejpam-4348	351	1	j.	j.	PROPN
ejpam-4348	351	2	pure	pure	PROPN
ejpam-4348	351	3	appl	appl	PROPN
ejpam-4348	351	4	.	.	PROPN
ejpam-4348	351	5	math	math	PROPN
ejpam-4348	351	6	,	,	PUNCT
ejpam-4348	351	7	15	15	NUM
ejpam-4348	351	8	(	(	PUNCT
ejpam-4348	351	9	2	2	NUM
ejpam-4348	351	10	)	)	PUNCT
ejpam-4348	351	11	(	(	PUNCT
ejpam-4348	351	12	2022	2022	NUM
ejpam-4348	351	13	)	)	PUNCT
ejpam-4348	351	14	,	,	PUNCT
ejpam-4348	351	15	681	681	NUM
ejpam-4348	351	16	-	-	SYM
ejpam-4348	351	17	725	725	NUM
ejpam-4348	351	18	703	703	NUM
ejpam-4348	351	19	(	(	PUNCT
ejpam-4348	351	20	λdi2n	λdi2n	NUM
ejpam-4348	351	21	−ad	−ad	NOUN
ejpam-4348	351	22	)	)	PUNCT
ejpam-4348	351	23	−1	−1	NOUN
ejpam-4348	351	24	=	=	NOUN
ejpam-4348	351	25			NOUN
ejpam-4348	351	26	(	(	PUNCT
ejpam-4348	351	27	λd	λd	NOUN
ejpam-4348	351	28	+	+	CCONJ
ejpam-4348	351	29	√	√	PROPN
ejpam-4348	351	30	p	p	NOUN
ejpam-4348	351	31	2	2	NUM
ejpam-4348	351	32	)	)	PUNCT
ejpam-4348	351	33	2	2	NUM
ejpam-4348	351	34	in	in	ADP
ejpam-4348	351	35	−ad	−ad	NUM
ejpam-4348	351	36	0	0	NUM
ejpam-4348	351	37	0	0	NUM
ejpam-4348	351	38	(	(	PUNCT
ejpam-4348	351	39	λd	λd	NOUN
ejpam-4348	351	40	+	+	CCONJ
ejpam-4348	351	41	√	√	PROPN
ejpam-4348	351	42	p	p	NOUN
ejpam-4348	351	43	2	2	NUM
ejpam-4348	351	44	)	)	PUNCT
ejpam-4348	351	45	2	2	NUM
ejpam-4348	351	46	in	in	ADP
ejpam-4348	351	47	−ad	−ad	NUM
ejpam-4348	351	48			NOUN
ejpam-4348	351	49	−1	−1	NOUN
ejpam-4348	351	50	×	×	NOUN
ejpam-4348	351	51			NOUN
ejpam-4348	351	52	(	(	PUNCT
ejpam-4348	351	53	λd	λd	NOUN
ejpam-4348	351	54	+	+	NOUN
ejpam-4348	351	55	√	√	PROPN
ejpam-4348	351	56	p	p	X
ejpam-4348	351	57	2)in	2)in	NUM
ejpam-4348	351	58	ad	ad	NOUN
ejpam-4348	351	59	in	in	ADP
ejpam-4348	351	60	(	(	PUNCT
ejpam-4348	351	61	λd	λd	NOUN
ejpam-4348	351	62	+	+	NOUN
ejpam-4348	351	63	√	√	PROPN
ejpam-4348	351	64	p	p	X
ejpam-4348	351	65	2)in	2)in	PROPN
ejpam-4348	351	66			NOUN
ejpam-4348	351	67	=	=	SYM
ejpam-4348	351	68			NOUN
ejpam-4348	351	69	(	(	PUNCT
ejpam-4348	351	70	λd	λd	NOUN
ejpam-4348	351	71	+	+	CCONJ
ejpam-4348	351	72	√	√	PROPN
ejpam-4348	351	73	p	p	NOUN
ejpam-4348	351	74	2	2	NUM
ejpam-4348	351	75	)	)	PUNCT
ejpam-4348	351	76	2	2	NUM
ejpam-4348	351	77	in	in	ADP
ejpam-4348	351	78	−	−	PROPN
ejpam-4348	351	79	(	(	PUNCT
ejpam-4348	351	80	a+	a+	X
ejpam-4348	351	81	(	(	PUNCT
ejpam-4348	351	82	p2	p2	PROPN
ejpam-4348	351	83	−	−	PROPN
ejpam-4348	351	84	d)in	d)in	PROPN
ejpam-4348	351	85	)	)	PUNCT
ejpam-4348	351	86	0	0	NUM
ejpam-4348	351	87	0	0	NUM
ejpam-4348	351	88	(	(	PUNCT
ejpam-4348	351	89	λd	λd	NOUN
ejpam-4348	351	90	+	+	CCONJ
ejpam-4348	352	1	√	√	PROPN
ejpam-4348	352	2	p	p	NOUN
ejpam-4348	352	3	2	2	NUM
ejpam-4348	352	4	)	)	PUNCT
ejpam-4348	352	5	2	2	NUM
ejpam-4348	352	6	in	in	ADP
ejpam-4348	352	7	−	−	PROPN
ejpam-4348	352	8	(	(	PUNCT
ejpam-4348	352	9	a+	a+	X
ejpam-4348	352	10	(	(	PUNCT
ejpam-4348	352	11	p2	p2	PROPN
ejpam-4348	352	12	−	−	PROPN
ejpam-4348	352	13	d)in	d)in	PROPN
ejpam-4348	352	14	)	)	PUNCT
ejpam-4348	352	15			PROPN
ejpam-4348	352	16	−1	−1	NOUN
ejpam-4348	352	17	×	×	NOUN
ejpam-4348	352	18			NOUN
ejpam-4348	352	19	(	(	PUNCT
ejpam-4348	352	20	λd	λd	NOUN
ejpam-4348	352	21	+	+	NOUN
ejpam-4348	352	22	√	√	PROPN
ejpam-4348	352	23	p	p	PROPN
ejpam-4348	352	24	2)in	2)in	PROPN
ejpam-4348	352	25	(	(	PUNCT
ejpam-4348	352	26	a+	a+	X
ejpam-4348	352	27	(	(	PUNCT
ejpam-4348	352	28	p2	p2	PROPN
ejpam-4348	352	29	−	−	PROPN
ejpam-4348	352	30	d)in	d)in	PROPN
ejpam-4348	352	31	)	)	PUNCT
ejpam-4348	352	32	in	in	ADP
ejpam-4348	352	33	(	(	PUNCT
ejpam-4348	352	34	λd	λd	NOUN
ejpam-4348	352	35	+	+	NOUN
ejpam-4348	352	36	√	√	PROPN
ejpam-4348	352	37	p	p	X
ejpam-4348	352	38	2)in	2)in	PROPN
ejpam-4348	352	39			NOUN
ejpam-4348	352	40	=	=	SYM
ejpam-4348	352	41			NOUN
ejpam-4348	352	42	(	(	PUNCT
ejpam-4348	352	43	λd	λd	NOUN
ejpam-4348	352	44	+	+	CCONJ
ejpam-4348	352	45	√	√	PROPN
ejpam-4348	352	46	p	p	NOUN
ejpam-4348	352	47	2	2	NUM
ejpam-4348	352	48	)	)	PUNCT
ejpam-4348	352	49	2	2	NUM
ejpam-4348	352	50	−	−	NOUN
ejpam-4348	352	51	p	p	NOUN
ejpam-4348	352	52	2	2	NUM
ejpam-4348	353	1	+	+	CCONJ
ejpam-4348	353	2	d)in	d)in	NOUN
ejpam-4348	353	3	−a	−a	NOUN
ejpam-4348	353	4	0	0	NUM
ejpam-4348	353	5	0	0	NUM
ejpam-4348	353	6	(	(	PUNCT
ejpam-4348	353	7	(	(	PUNCT
ejpam-4348	353	8	λd	λd	NOUN
ejpam-4348	353	9	+	+	CCONJ
ejpam-4348	353	10	√	√	PROPN
ejpam-4348	353	11	p	p	NOUN
ejpam-4348	353	12	2	2	NUM
ejpam-4348	353	13	)	)	PUNCT
ejpam-4348	353	14	2	2	NUM
ejpam-4348	353	15	−	−	NOUN
ejpam-4348	353	16	p	p	NOUN
ejpam-4348	353	17	2	2	NUM
ejpam-4348	353	18	+	+	CCONJ
ejpam-4348	353	19	d)in	d)in	NOUN
ejpam-4348	353	20	−a	−a	ADJ
ejpam-4348	353	21			ADJ
ejpam-4348	353	22	−1	−1	NOUN
ejpam-4348	353	23	×	×	NOUN
ejpam-4348	353	24			NOUN
ejpam-4348	353	25	(	(	PUNCT
ejpam-4348	353	26	λd	λd	NOUN
ejpam-4348	353	27	+	+	NOUN
ejpam-4348	353	28	√	√	PROPN
ejpam-4348	353	29	p	p	X
ejpam-4348	353	30	2)in	2)in	PROPN
ejpam-4348	353	31	a+	a+	PUNCT
ejpam-4348	353	32	(	(	PUNCT
ejpam-4348	353	33	p2	p2	PROPN
ejpam-4348	353	34	−	−	PROPN
ejpam-4348	354	1	d)in	d)in	PROPN
ejpam-4348	354	2	in	in	ADP
ejpam-4348	354	3	(	(	PUNCT
ejpam-4348	354	4	λd	λd	NOUN
ejpam-4348	354	5	+	+	NOUN
ejpam-4348	354	6	√	√	PROPN
ejpam-4348	354	7	p	p	X
ejpam-4348	354	8	2)in	2)in	PROPN
ejpam-4348	354	9			NOUN
ejpam-4348	354	10	=	=	SYM
ejpam-4348	354	11	(zin	(zin	NOUN
ejpam-4348	354	12	−a)−1	−a)−1	NOUN
ejpam-4348	354	13	0	0	NUM
ejpam-4348	354	14	0	0	NUM
ejpam-4348	354	15	(	(	PUNCT
ejpam-4348	354	16	zin	zin	NOUN
ejpam-4348	354	17	−a)−1	−a)−1	NOUN
ejpam-4348	354	18	×	×	NOUN
ejpam-4348	354	19			NOUN
ejpam-4348	354	20	√	√	NOUN
ejpam-4348	354	21	z	z	NOUN
ejpam-4348	355	1	+	+	CCONJ
ejpam-4348	355	2	p	p	X
ejpam-4348	355	3	2	2	NUM
ejpam-4348	355	4	−	−	NOUN
ejpam-4348	355	5	din	din	VERB
ejpam-4348	355	6	a+	a+	PUNCT
ejpam-4348	355	7	(	(	PUNCT
ejpam-4348	355	8	p2	p2	PROPN
ejpam-4348	355	9	−	−	PROPN
ejpam-4348	355	10	d)in	d)in	PROPN
ejpam-4348	355	11	in	in	ADP
ejpam-4348	355	12	√	√	NOUN
ejpam-4348	355	13	z	z	NOUN
ejpam-4348	356	1	+	+	CCONJ
ejpam-4348	356	2	p	p	X
ejpam-4348	356	3	2	2	NUM
ejpam-4348	356	4	−	−	NOUN
ejpam-4348	356	5	din	din	NOUN
ejpam-4348	356	6			NOUN
ejpam-4348	356	7	=	=	PUNCT
ejpam-4348	356	8			NOUN
ejpam-4348	356	9	√	√	NOUN
ejpam-4348	356	10	z	z	NOUN
ejpam-4348	357	1	+	+	CCONJ
ejpam-4348	357	2	p	p	NOUN
ejpam-4348	357	3	2	2	NUM
ejpam-4348	357	4	−	−	NOUN
ejpam-4348	357	5	d(zin	d(zin	NOUN
ejpam-4348	357	6	−a)−1	−a)−1	NOUN
ejpam-4348	357	7	(	(	PUNCT
ejpam-4348	357	8	zin	zin	NOUN
ejpam-4348	357	9	−a)−1(a+	−a)−1(a+	PROPN
ejpam-4348	357	10	(	(	PUNCT
ejpam-4348	357	11	p2	p2	PROPN
ejpam-4348	357	12	−	−	PROPN
ejpam-4348	357	13	d)in	d)in	PROPN
ejpam-4348	357	14	)	)	PUNCT
ejpam-4348	357	15	(	(	PUNCT
ejpam-4348	357	16	zin	zin	NOUN
ejpam-4348	357	17	−a)−1	−a)−1	NOUN
ejpam-4348	358	1	√	√	NOUN
ejpam-4348	358	2	z	z	NOUN
ejpam-4348	359	1	+	+	NOUN
ejpam-4348	359	2	p	p	NOUN
ejpam-4348	359	3	2	2	NUM
ejpam-4348	359	4	−	−	NOUN
ejpam-4348	359	5	d(zin	d(zin	NOUN
ejpam-4348	359	6	−a)−1	−a)−1	NOUN
ejpam-4348	359	7			NOUN
ejpam-4348	359	8	knowing	know	VERB
ejpam-4348	359	9	that	that	SCONJ
ejpam-4348	359	10	the	the	DET
ejpam-4348	359	11	norm	norm	NOUN
ejpam-4348	359	12	of	of	ADP
ejpam-4348	359	13	(	(	PUNCT
ejpam-4348	359	14	λdi2n−ad	λdi2n−ad	NOUN
ejpam-4348	359	15	)	)	PUNCT
ejpam-4348	359	16	−1	−1	NOUN
ejpam-4348	359	17	is	be	AUX
ejpam-4348	359	18	greater	great	ADJ
ejpam-4348	359	19	than	than	ADP
ejpam-4348	359	20	or	or	CCONJ
ejpam-4348	359	21	equal	equal	ADJ
ejpam-4348	359	22	to	to	ADP
ejpam-4348	359	23	the	the	DET
ejpam-4348	359	24	norm	norm	NOUN
ejpam-4348	359	25	of	of	ADP
ejpam-4348	359	26	each	each	PRON
ejpam-4348	359	27	of	of	ADP
ejpam-4348	359	28	its	its	PRON
ejpam-4348	359	29	block	block	NOUN
ejpam-4348	359	30	components	component	NOUN
ejpam-4348	359	31	taken	take	VERB
ejpam-4348	359	32	individually	individually	ADV
ejpam-4348	359	33	,	,	PUNCT
ejpam-4348	359	34	we	we	PRON
ejpam-4348	359	35	can	can	AUX
ejpam-4348	359	36	deduce	deduce	VERB
ejpam-4348	359	37	that	that	SCONJ
ejpam-4348	359	38	s.	s.	PROPN
ejpam-4348	359	39	traoré	traoré	PROPN
ejpam-4348	359	40	,	,	PUNCT
ejpam-4348	359	41	m.	m.	NOUN
ejpam-4348	359	42	dosso	dosso	PROPN
ejpam-4348	359	43	/	/	SYM
ejpam-4348	359	44	eur	eur	PROPN
ejpam-4348	359	45	.	.	PUNCT
ejpam-4348	360	1	j.	j.	PROPN
ejpam-4348	360	2	pure	pure	PROPN
ejpam-4348	360	3	appl	appl	PROPN
ejpam-4348	360	4	.	.	PROPN
ejpam-4348	360	5	math	math	PROPN
ejpam-4348	360	6	,	,	PUNCT
ejpam-4348	360	7	15	15	NUM
ejpam-4348	360	8	(	(	PUNCT
ejpam-4348	360	9	2	2	NUM
ejpam-4348	360	10	)	)	PUNCT
ejpam-4348	360	11	(	(	PUNCT
ejpam-4348	360	12	2022	2022	NUM
ejpam-4348	360	13	)	)	PUNCT
ejpam-4348	360	14	,	,	PUNCT
ejpam-4348	360	15	681	681	NUM
ejpam-4348	360	16	-	-	SYM
ejpam-4348	360	17	725	725	NUM
ejpam-4348	360	18	704	704	NUM
ejpam-4348	360	19	αad	αad	NOUN
ejpam-4348	360	20	=	=	NOUN
ejpam-4348	360	21	sup	sup	NOUN
ejpam-4348	360	22	ℜ(λd)=0	ℜ(λd)=0	VERB
ejpam-4348	360	23	∥(λdi2n	∥(λdi2n	NUM
ejpam-4348	360	24	−ad	−ad	NUM
ejpam-4348	360	25	)	)	PUNCT
ejpam-4348	360	26	−1∥	−1∥	NOUN
ejpam-4348	360	27	≥	≥	NUM
ejpam-4348	360	28	sup	sup	NOUN
ejpam-4348	360	29	z∈γd	z∈γd	NOUN
ejpam-4348	360	30	∥(zin	∥(zin	PROPN
ejpam-4348	360	31	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	360	32	=	=	SYM
ejpam-4348	360	33	αad	αad	NOUN
ejpam-4348	360	34	and	and	CCONJ
ejpam-4348	360	35	also	also	ADV
ejpam-4348	360	36	∥∥(λdi2n	∥∥(λdi2n	AUX
ejpam-4348	360	37	−ad	−ad	NOUN
ejpam-4348	360	38	)	)	PUNCT
ejpam-4348	360	39	−1	−1	NOUN
ejpam-4348	360	40	∥∥	∥∥	PRON
ejpam-4348	360	41	≤	≤	PROPN
ejpam-4348	360	42	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	361	1			NUM
ejpam-4348	361	2	√	√	PUNCT
ejpam-4348	361	3	z	z	NOUN
ejpam-4348	362	1	+	+	NOUN
ejpam-4348	362	2	p	p	NOUN
ejpam-4348	362	3	2	2	NUM
ejpam-4348	362	4	−	−	NOUN
ejpam-4348	362	5	din	din	VERB
ejpam-4348	362	6	a+	a+	PUNCT
ejpam-4348	362	7	(	(	PUNCT
ejpam-4348	362	8	p2	p2	PROPN
ejpam-4348	362	9	−	−	PROPN
ejpam-4348	362	10	d)in	d)in	PROPN
ejpam-4348	362	11	in	in	ADP
ejpam-4348	362	12	√	√	NOUN
ejpam-4348	362	13	z	z	NOUN
ejpam-4348	363	1	+	+	CCONJ
ejpam-4348	363	2	p	p	X
ejpam-4348	363	3	2	2	NUM
ejpam-4348	363	4	−	−	NOUN
ejpam-4348	363	5	din	din	NOUN
ejpam-4348	363	6			NOUN
ejpam-4348	363	7	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	364	1	∥∥(zin	∥∥(zin	ADP
ejpam-4348	364	2	−a)−1	−a)−1	X
ejpam-4348	364	3	∥∥	∥∥	PROPN
ejpam-4348	364	4	≤	≤	PROPN
ejpam-4348	364	5	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	365	1			PROPN
ejpam-4348	365	2	∥	∥	PUNCT
ejpam-4348	365	3	√	√	PUNCT
ejpam-4348	365	4	z	z	NOUN
ejpam-4348	366	1	+	+	CCONJ
ejpam-4348	366	2	p	p	X
ejpam-4348	366	3	2	2	NUM
ejpam-4348	366	4	−	−	PRON
ejpam-4348	366	5	din∥	din∥	NOUN
ejpam-4348	366	6	∥a+	∥a+	PROPN
ejpam-4348	366	7	(	(	PUNCT
ejpam-4348	366	8	p2	p2	PROPN
ejpam-4348	366	9	−	−	PROPN
ejpam-4348	366	10	d)in∥	d)in∥	X
ejpam-4348	366	11	∥in∥	∥in∥	X
ejpam-4348	366	12	∥	∥	X
ejpam-4348	366	13	√	√	NOUN
ejpam-4348	366	14	z	z	NOUN
ejpam-4348	367	1	+	+	CCONJ
ejpam-4348	367	2	p	p	X
ejpam-4348	367	3	2	2	NUM
ejpam-4348	367	4	−	−	PRON
ejpam-4348	367	5	din∥	din∥	NUM
ejpam-4348	367	6			NOUN
ejpam-4348	367	7	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	367	8	∥∥(zin	∥∥(zin	ADP
ejpam-4348	367	9	−a)−1	−a)−1	X
ejpam-4348	367	10	∥∥	∥∥	PROPN
ejpam-4348	367	11	≤	≤	PROPN
ejpam-4348	367	12	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	367	13			NOUN
ejpam-4348	367	14	√	√	PROPN
ejpam-4348	367	15	|z|+	|z|+	NOUN
ejpam-4348	367	16	√	√	NUM
ejpam-4348	367	17	|p2	|p2	NOUN
ejpam-4348	367	18	−	−	PROPN
ejpam-4348	367	19	d|	d|	PROPN
ejpam-4348	367	20	1	1	NUM
ejpam-4348	367	21	1	1	NUM
ejpam-4348	367	22	√	√	NOUN
ejpam-4348	367	23	|z|+	|z|+	NOUN
ejpam-4348	367	24	√	√	PROPN
ejpam-4348	367	25	|p2	|p2	NOUN
ejpam-4348	367	26	−	−	PROPN
ejpam-4348	367	27	d|	d|	PROPN
ejpam-4348	367	28			NOUN
ejpam-4348	367	29	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	367	30	∥∥(zin	∥∥(zin	ADP
ejpam-4348	367	31	−a)−1	−a)−1	X
ejpam-4348	367	32	∥∥	∥∥	PUNCT
ejpam-4348	367	33	≤	≤	X
ejpam-4348	367	34	(	(	PUNCT
ejpam-4348	367	35	√	√	ADP
ejpam-4348	367	36	|z|+	|z|+	VERB
ejpam-4348	367	37	√	√	NUM
ejpam-4348	367	38	|p	|p	NOUN
ejpam-4348	367	39	2	2	NUM
ejpam-4348	367	40	−	−	NOUN
ejpam-4348	367	41	d|+	d|+	NOUN
ejpam-4348	367	42	1	1	NUM
ejpam-4348	367	43	)	)	PUNCT
ejpam-4348	367	44	∥∥(zin	∥∥(zin	ADP
ejpam-4348	367	45	−a)−1	−a)−1	X
ejpam-4348	367	46	∥∥	∥∥	X
ejpam-4348	367	47	•	•	NOUN
ejpam-4348	367	48	if	if	SCONJ
ejpam-4348	367	49	|z|	|z|	NOUN
ejpam-4348	367	50	≤	≤	X
ejpam-4348	367	51	αad	αad	NOUN
ejpam-4348	367	52	+	+	NOUN
ejpam-4348	367	53	1	1	NUM
ejpam-4348	367	54	αad	αad	NOUN
ejpam-4348	367	55	then	then	ADV
ejpam-4348	367	56	∥(λi2n	∥(λi2n	PROPN
ejpam-4348	367	57	−ad	−ad	NOUN
ejpam-4348	367	58	)	)	PUNCT
ejpam-4348	367	59	−1∥	−1∥	VERB
ejpam-4348	367	60	≤	≤	NUM
ejpam-4348	367	61	αad	αad	NOUN
ejpam-4348	367	62	(	(	PUNCT
ejpam-4348	367	63	√	√	PROPN
ejpam-4348	367	64	αad	αad	NOUN
ejpam-4348	367	65	+	+	NOUN
ejpam-4348	367	66	1	1	NUM
ejpam-4348	367	67	αad	αad	NOUN
ejpam-4348	367	68	+	+	NOUN
ejpam-4348	367	69	√∣∣∣p	√∣∣∣p	ADP
ejpam-4348	367	70	2	2	NUM
ejpam-4348	367	71	−	−	NOUN
ejpam-4348	367	72	d	d	NOUN
ejpam-4348	367	73	∣∣∣+	∣∣∣+	PROPN
ejpam-4348	367	74	1	1	NUM
ejpam-4348	367	75	)	)	PUNCT
ejpam-4348	367	76	≤	≤	PROPN
ejpam-4348	368	1	αad	αad	NOUN
ejpam-4348	369	1	(	(	PUNCT
ejpam-4348	370	1	1	1	NUM
ejpam-4348	370	2	+	+	CCONJ
ejpam-4348	370	3	√	√	NUM
ejpam-4348	370	4	1	1	NUM
ejpam-4348	370	5	αad	αad	NOUN
ejpam-4348	370	6	)	)	PUNCT
ejpam-4348	371	1	+	+	CCONJ
ejpam-4348	371	2	√	√	NUM
ejpam-4348	371	3	αad	αad	VERB
ejpam-4348	371	4	√	√	VERB
ejpam-4348	371	5	1	1	NUM
ejpam-4348	372	1	+	+	NUM
ejpam-4348	372	2	αad	αad	NOUN
ejpam-4348	372	3	≤	≤	X
ejpam-4348	372	4	αad	αad	NOUN
ejpam-4348	372	5	+	+	CCONJ
ejpam-4348	372	6	√	√	PROPN
ejpam-4348	372	7	αad	αad	NOUN
ejpam-4348	372	8	(	(	PUNCT
ejpam-4348	372	9	1	1	NUM
ejpam-4348	372	10	+	+	CCONJ
ejpam-4348	372	11	√	√	PROPN
ejpam-4348	372	12	αad	αad	NOUN
ejpam-4348	372	13	+	+	NOUN
ejpam-4348	372	14	1	1	NUM
ejpam-4348	372	15	)	)	PUNCT
ejpam-4348	372	16	•	•	NOUN
ejpam-4348	372	17	if	if	SCONJ
ejpam-4348	372	18	|z|	|z|	NOUN
ejpam-4348	372	19	>	>	X
ejpam-4348	372	20	αad	αad	NOUN
ejpam-4348	372	21	+	+	PROPN
ejpam-4348	372	22	1	1	NUM
ejpam-4348	372	23	αad	αad	NOUN
ejpam-4348	372	24	with	with	ADP
ejpam-4348	372	25	the	the	DET
ejpam-4348	372	26	conditions	condition	NOUN
ejpam-4348	372	27	(	(	PUNCT
ejpam-4348	372	28	36	36	NUM
ejpam-4348	372	29	)	)	PUNCT
ejpam-4348	372	30	we	we	PRON
ejpam-4348	372	31	have	have	VERB
ejpam-4348	372	32	∥∥∥∥az	∥∥∥∥az	PROPN
ejpam-4348	372	33	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-4348	372	34	<	<	X
ejpam-4348	372	35	1	1	NUM
ejpam-4348	372	36	.	.	NOUN
ejpam-4348	372	37	which	which	PRON
ejpam-4348	372	38	leads	lead	VERB
ejpam-4348	372	39	to	to	ADP
ejpam-4348	372	40	(	(	PUNCT
ejpam-4348	372	41	zin	zin	NOUN
ejpam-4348	372	42	−a)−1	−a)−1	NOUN
ejpam-4348	372	43	=	=	SYM
ejpam-4348	372	44	1	1	NUM
ejpam-4348	372	45	z	z	NOUN
ejpam-4348	372	46	(	(	PUNCT
ejpam-4348	372	47	in	in	ADP
ejpam-4348	372	48	−	−	PROPN
ejpam-4348	372	49	a	a	DET
ejpam-4348	372	50	z	z	NOUN
ejpam-4348	372	51	)	)	PUNCT
ejpam-4348	372	52	−1	−1	NOUN
ejpam-4348	372	53	=	=	SYM
ejpam-4348	372	54	1	1	NUM
ejpam-4348	372	55	z	z	X
ejpam-4348	372	56	+	+	ADP
ejpam-4348	372	57	∞∑	∞∑	DET
ejpam-4348	372	58	k=0	k=0	PROPN
ejpam-4348	372	59	ak	ak	PROPN
ejpam-4348	372	60	zk	zk	PROPN
ejpam-4348	372	61	s.	s.	PROPN
ejpam-4348	372	62	traoré	traoré	PROPN
ejpam-4348	372	63	,	,	PUNCT
ejpam-4348	372	64	m.	m.	NOUN
ejpam-4348	372	65	dosso	dosso	PROPN
ejpam-4348	372	66	/	/	SYM
ejpam-4348	372	67	eur	eur	PROPN
ejpam-4348	372	68	.	.	PUNCT
ejpam-4348	373	1	j.	j.	PROPN
ejpam-4348	373	2	pure	pure	PROPN
ejpam-4348	373	3	appl	appl	PROPN
ejpam-4348	373	4	.	.	PROPN
ejpam-4348	373	5	math	math	PROPN
ejpam-4348	373	6	,	,	PUNCT
ejpam-4348	373	7	15	15	NUM
ejpam-4348	373	8	(	(	PUNCT
ejpam-4348	373	9	2	2	NUM
ejpam-4348	373	10	)	)	PUNCT
ejpam-4348	373	11	(	(	PUNCT
ejpam-4348	373	12	2022	2022	NUM
ejpam-4348	373	13	)	)	PUNCT
ejpam-4348	373	14	,	,	PUNCT
ejpam-4348	373	15	681	681	NUM
ejpam-4348	373	16	-	-	SYM
ejpam-4348	373	17	725	725	NUM
ejpam-4348	373	18	705	705	NUM
ejpam-4348	373	19	=	=	SYM
ejpam-4348	373	20	1	1	NUM
ejpam-4348	373	21	z	z	NOUN
ejpam-4348	373	22	(	(	PUNCT
ejpam-4348	373	23	in	in	ADP
ejpam-4348	373	24	+	+	CCONJ
ejpam-4348	373	25	a	a	DET
ejpam-4348	373	26	z	z	NOUN
ejpam-4348	374	1	+	+	NOUN
ejpam-4348	374	2	∞∑	∞∑	PROPN
ejpam-4348	374	3	m=0	m=0	PROPN
ejpam-4348	374	4	am	be	AUX
ejpam-4348	374	5	zm	zm	PROPN
ejpam-4348	374	6	)	)	PUNCT
ejpam-4348	375	1	=	=	PUNCT
ejpam-4348	376	1	1	1	NUM
ejpam-4348	376	2	z	z	NOUN
ejpam-4348	376	3	(	(	PUNCT
ejpam-4348	376	4	in	in	ADP
ejpam-4348	376	5	+	+	CCONJ
ejpam-4348	376	6	a	a	DET
ejpam-4348	376	7	z	z	NOUN
ejpam-4348	376	8	(	(	PUNCT
ejpam-4348	376	9	in	in	ADP
ejpam-4348	376	10	−	−	PROPN
ejpam-4348	376	11	a	a	DET
ejpam-4348	376	12	z	z	NOUN
ejpam-4348	376	13	)	)	PUNCT
ejpam-4348	376	14	−1	−1	NOUN
ejpam-4348	376	15	)	)	PUNCT
ejpam-4348	376	16	consequently	consequently	ADV
ejpam-4348	376	17	∥(λdi2n	∥(λdi2n	NUM
ejpam-4348	376	18	−ad	−ad	NUM
ejpam-4348	376	19	)	)	PUNCT
ejpam-4348	376	20	−1∥	−1∥	NOUN
ejpam-4348	376	21	≤	≤	NUM
ejpam-4348	376	22	∥∥∥∥1z	∥∥∥∥1z	VERB
ejpam-4348	376	23	in	in	ADP
ejpam-4348	376	24	+	+	NUM
ejpam-4348	376	25	1	1	NUM
ejpam-4348	376	26	z	z	NOUN
ejpam-4348	376	27	a	a	PRON
ejpam-4348	376	28	(	(	PUNCT
ejpam-4348	376	29	zin	zin	NOUN
ejpam-4348	376	30	−a)−1	−a)−1	NOUN
ejpam-4348	376	31	∥∥∥∥×	∥∥∥∥×	X
ejpam-4348	376	32	(	(	PUNCT
ejpam-4348	376	33	1	1	NUM
ejpam-4348	376	34	+	+	ADJ
ejpam-4348	376	35	√|z|+	√|z|+	ADJ
ejpam-4348	376	36	√	√	PRON
ejpam-4348	376	37	|p	|p	VERB
ejpam-4348	376	38	2	2	NUM
ejpam-4348	376	39	−	−	NOUN
ejpam-4348	376	40	d|	d|	PROPN
ejpam-4348	376	41	)	)	PUNCT
ejpam-4348	377	1	≤	≤	NUM
ejpam-4348	377	2	∥a(zin	∥a(zin	NOUN
ejpam-4348	377	3	−a)−1	−a)−1	NOUN
ejpam-4348	377	4	+	+	CCONJ
ejpam-4348	377	5	in∥	in∥	PROPN
ejpam-4348	377	6	×	×	PROPN
ejpam-4348	377	7			ADJ
ejpam-4348	377	8	1	1	NUM
ejpam-4348	377	9	|z|	|z|	NOUN
ejpam-4348	377	10	+	+	CCONJ
ejpam-4348	377	11	1√	1√	ADJ
ejpam-4348	377	12	|z|	|z|	NOUN
ejpam-4348	377	13	+	+	CCONJ
ejpam-4348	377	14	√	√	PROPN
ejpam-4348	377	15	|p	|p	VERB
ejpam-4348	377	16	2	2	NUM
ejpam-4348	377	17	−	−	NOUN
ejpam-4348	377	18	d|	d|	PROPN
ejpam-4348	377	19	|z|	|z|	VERB
ejpam-4348	377	20			NOUN
ejpam-4348	377	21	≤	≤	NUM
ejpam-4348	377	22	(	(	PUNCT
ejpam-4348	377	23	(	(	PUNCT
ejpam-4348	377	24	1	1	NUM
ejpam-4348	377	25	+	+	NUM
ejpam-4348	377	26	∣∣∣p	∣∣∣p	NOUN
ejpam-4348	377	27	2	2	NUM
ejpam-4348	377	28	−	−	NOUN
ejpam-4348	377	29	d	d	PROPN
ejpam-4348	377	30	∣∣∣)αad	∣∣∣)αad	NOUN
ejpam-4348	377	31	+	+	NOUN
ejpam-4348	377	32	1	1	NUM
ejpam-4348	377	33	)	)	PUNCT
ejpam-4348	377	34	×	×	NOUN
ejpam-4348	377	35	(	(	PUNCT
ejpam-4348	377	36	αad	αad	NOUN
ejpam-4348	377	37	αad	αad	NOUN
ejpam-4348	377	38	+	+	NOUN
ejpam-4348	377	39	1	1	NUM
ejpam-4348	377	40	+	+	CCONJ
ejpam-4348	377	41	√	√	PROPN
ejpam-4348	377	42	αad√	αad√	NUM
ejpam-4348	377	43	αad	αad	NOUN
ejpam-4348	377	44	+	+	NOUN
ejpam-4348	377	45	1	1	NUM
ejpam-4348	377	46	+	+	CCONJ
ejpam-4348	377	47	√	√	NOUN
ejpam-4348	377	48	αad	αad	NOUN
ejpam-4348	377	49	αad	αad	NOUN
ejpam-4348	377	50	+	+	NOUN
ejpam-4348	377	51	1	1	NUM
ejpam-4348	377	52	)	)	PUNCT
ejpam-4348	377	53	≤	≤	NOUN
ejpam-4348	377	54	(	(	PUNCT
ejpam-4348	377	55	2	2	NUM
ejpam-4348	377	56	+	+	NUM
ejpam-4348	377	57	αad	αad	NOUN
ejpam-4348	377	58	)	)	PUNCT
ejpam-4348	377	59	αad	αad	NOUN
ejpam-4348	378	1	+	+	NOUN
ejpam-4348	378	2	1	1	NUM
ejpam-4348	378	3	(	(	PUNCT
ejpam-4348	378	4	αad	αad	NOUN
ejpam-4348	378	5	+	+	NOUN
ejpam-4348	378	6	√	√	PROPN
ejpam-4348	378	7	αad	αad	NOUN
ejpam-4348	378	8	√	√	PROPN
ejpam-4348	378	9	αad	αad	NOUN
ejpam-4348	378	10	+	+	NOUN
ejpam-4348	378	11	1	1	NUM
ejpam-4348	378	12	+	+	CCONJ
ejpam-4348	378	13	√	√	PROPN
ejpam-4348	378	14	αad	αad	NOUN
ejpam-4348	378	15	)	)	PUNCT
ejpam-4348	378	16	≤	≤	NOUN
ejpam-4348	378	17	2	2	NUM
ejpam-4348	378	18	(	(	PUNCT
ejpam-4348	378	19	αad	αad	NOUN
ejpam-4348	378	20	+	+	NOUN
ejpam-4348	378	21	√	√	PROPN
ejpam-4348	378	22	αad	αad	NOUN
ejpam-4348	378	23	(	(	PUNCT
ejpam-4348	378	24	1	1	NUM
ejpam-4348	378	25	+	+	CCONJ
ejpam-4348	378	26	√	√	PROPN
ejpam-4348	378	27	αad	αad	NOUN
ejpam-4348	378	28	+	+	NOUN
ejpam-4348	378	29	1	1	NUM
ejpam-4348	378	30	)	)	PUNCT
ejpam-4348	378	31	)	)	PUNCT
ejpam-4348	378	32	.	.	PUNCT
ejpam-4348	379	1	consider	consider	VERB
ejpam-4348	379	2	spectral	spectral	ADJ
ejpam-4348	379	3	projectors	projector	NOUN
ejpam-4348	379	4	•	•	ADP
ejpam-4348	379	5	pd	pd	PROPN
ejpam-4348	379	6	∈	∈	PROPN
ejpam-4348	379	7	cn×n	cn×n	PROPN
ejpam-4348	379	8	on	on	ADP
ejpam-4348	379	9	the	the	DET
ejpam-4348	379	10	right	right	ADJ
ejpam-4348	379	11	eigensubspace	eigensubspace	NOUN
ejpam-4348	379	12	associated	associate	VERB
ejpam-4348	379	13	with	with	ADP
ejpam-4348	379	14	the	the	DET
ejpam-4348	379	15	eigenvalues	eigenvalue	NOUN
ejpam-4348	379	16	of	of	ADP
ejpam-4348	379	17	a	a	DET
ejpam-4348	379	18	outside	outside	NOUN
ejpam-4348	379	19	the	the	DET
ejpam-4348	379	20	parabola	parabola	NOUN
ejpam-4348	379	21	γd	γd	ADP
ejpam-4348	379	22	•	•	NUM
ejpam-4348	379	23	pd	pd	PROPN
ejpam-4348	379	24	∈	∈	PROPN
ejpam-4348	379	25	c2n×2n	c2n×2n	VERB
ejpam-4348	379	26	on	on	ADP
ejpam-4348	379	27	the	the	DET
ejpam-4348	379	28	right	right	ADJ
ejpam-4348	379	29	eigensubspace	eigensubspace	NOUN
ejpam-4348	379	30	associated	associate	VERB
ejpam-4348	379	31	to	to	ADP
ejpam-4348	379	32	the	the	DET
ejpam-4348	379	33	eigenvalues	eigenvalue	NOUN
ejpam-4348	379	34	of	of	ADP
ejpam-4348	379	35	ad	ad	NOUN
ejpam-4348	379	36	in	in	ADP
ejpam-4348	379	37	the	the	DET
ejpam-4348	379	38	right	right	ADJ
ejpam-4348	379	39	complex	complex	ADJ
ejpam-4348	379	40	half	half	ADJ
ejpam-4348	379	41	-	-	PUNCT
ejpam-4348	379	42	plane	plane	NOUN
ejpam-4348	379	43	.	.	PUNCT
ejpam-4348	380	1	the	the	DET
ejpam-4348	380	2	following	follow	VERB
ejpam-4348	380	3	proposition	proposition	NOUN
ejpam-4348	380	4	characterizes	characterize	VERB
ejpam-4348	380	5	the	the	DET
ejpam-4348	380	6	relation	relation	NOUN
ejpam-4348	380	7	between	between	ADP
ejpam-4348	380	8	pd	pd	PROPN
ejpam-4348	380	9	and	and	CCONJ
ejpam-4348	380	10	pd	pd	PROPN
ejpam-4348	380	11	proposition	proposition	NOUN
ejpam-4348	380	12	9	9	NUM
ejpam-4348	380	13	.	.	PUNCT
ejpam-4348	380	14	consider	consider	VERB
ejpam-4348	380	15	a	a	DET
ejpam-4348	380	16	partition	partition	NOUN
ejpam-4348	380	17	of	of	ADP
ejpam-4348	380	18	the	the	DET
ejpam-4348	380	19	matrix	matrix	NOUN
ejpam-4348	380	20	pd	pd	NOUN
ejpam-4348	380	21	in	in	ADP
ejpam-4348	380	22	the	the	DET
ejpam-4348	380	23	form	form	NOUN
ejpam-4348	380	24	pd	pd	X
ejpam-4348	380	25	=	=	PUNCT
ejpam-4348	380	26	(	(	PUNCT
ejpam-4348	380	27	p(d	p(d	PROPN
ejpam-4348	380	28	)	)	PUNCT
ejpam-4348	380	29	1	1	NUM
ejpam-4348	380	30	p(d	p(d	NOUN
ejpam-4348	380	31	)	)	PUNCT
ejpam-4348	380	32	2	2	NUM
ejpam-4348	380	33	p(d	p(d	NOUN
ejpam-4348	380	34	)	)	PUNCT
ejpam-4348	380	35	3	3	NUM
ejpam-4348	380	36	p(d	p(d	NOUN
ejpam-4348	380	37	)	)	PUNCT
ejpam-4348	380	38	4	4	NUM
ejpam-4348	380	39	)	)	PUNCT
ejpam-4348	380	40	with	with	ADP
ejpam-4348	380	41	p(d	p(d	NOUN
ejpam-4348	380	42	)	)	PUNCT
ejpam-4348	381	1	i	i	PRON
ejpam-4348	381	2	∈	∈	PROPN
ejpam-4348	381	3	cn×n	cn×n	NOUN
ejpam-4348	381	4	,	,	PUNCT
ejpam-4348	381	5	i	i	NOUN
ejpam-4348	381	6	=	=	NOUN
ejpam-4348	381	7	1	1	NUM
ejpam-4348	381	8	,	,	PUNCT
ejpam-4348	381	9	4	4	NUM
ejpam-4348	381	10	(	(	PUNCT
ejpam-4348	381	11	38	38	NUM
ejpam-4348	381	12	)	)	PUNCT
ejpam-4348	381	13	then	then	ADV
ejpam-4348	381	14	s.	s.	PROPN
ejpam-4348	381	15	traoré	traoré	PROPN
ejpam-4348	381	16	,	,	PUNCT
ejpam-4348	381	17	m.	m.	NOUN
ejpam-4348	381	18	dosso	dosso	PROPN
ejpam-4348	381	19	/	/	SYM
ejpam-4348	381	20	eur	eur	PROPN
ejpam-4348	381	21	.	.	PUNCT
ejpam-4348	382	1	j.	j.	PROPN
ejpam-4348	382	2	pure	pure	PROPN
ejpam-4348	382	3	appl	appl	PROPN
ejpam-4348	382	4	.	.	PROPN
ejpam-4348	382	5	math	math	PROPN
ejpam-4348	382	6	,	,	PUNCT
ejpam-4348	382	7	15	15	NUM
ejpam-4348	382	8	(	(	PUNCT
ejpam-4348	382	9	2	2	NUM
ejpam-4348	382	10	)	)	PUNCT
ejpam-4348	382	11	(	(	PUNCT
ejpam-4348	382	12	2022	2022	NUM
ejpam-4348	382	13	)	)	PUNCT
ejpam-4348	382	14	,	,	PUNCT
ejpam-4348	382	15	681	681	NUM
ejpam-4348	382	16	-	-	SYM
ejpam-4348	382	17	725	725	NUM
ejpam-4348	382	18	706	706	NUM
ejpam-4348	382	19	pd	pd	NOUN
ejpam-4348	382	20	=	=	PROPN
ejpam-4348	382	21	2p(d	2p(d	PROPN
ejpam-4348	382	22	)	)	PUNCT
ejpam-4348	382	23	1	1	NUM
ejpam-4348	382	24	=	=	SYM
ejpam-4348	382	25	2p(d	2p(d	PROPN
ejpam-4348	382	26	)	)	PUNCT
ejpam-4348	382	27	4	4	NUM
ejpam-4348	382	28	=	=	SYM
ejpam-4348	382	29	4p(d	4p(d	NOUN
ejpam-4348	382	30	)	)	PUNCT
ejpam-4348	382	31	2	2	NUM
ejpam-4348	382	32	p(d	p(d	NOUN
ejpam-4348	382	33	)	)	PUNCT
ejpam-4348	382	34	3	3	NUM
ejpam-4348	382	35	(	(	PUNCT
ejpam-4348	382	36	39	39	NUM
ejpam-4348	382	37	)	)	PUNCT
ejpam-4348	382	38	moreover	moreover	ADV
ejpam-4348	382	39	pda	pda	NOUN
ejpam-4348	382	40	=	=	SYM
ejpam-4348	382	41	4(p(d	4(p(d	NUM
ejpam-4348	382	42	)	)	PUNCT
ejpam-4348	382	43	2	2	NUM
ejpam-4348	382	44	)	)	SYM
ejpam-4348	382	45	2	2	NUM
ejpam-4348	382	46	−	−	NOUN
ejpam-4348	382	47	(	(	PUNCT
ejpam-4348	382	48	p−	p−	NOUN
ejpam-4348	382	49	2d)p(d	2d)p(d	PROPN
ejpam-4348	382	50	)	)	PUNCT
ejpam-4348	382	51	1	1	NUM
ejpam-4348	382	52	(	(	PUNCT
ejpam-4348	382	53	40	40	NUM
ejpam-4348	382	54	)	)	PUNCT
ejpam-4348	382	55	proof	proof	NOUN
ejpam-4348	382	56	.	.	PUNCT
ejpam-4348	383	1	let	let	VERB
ejpam-4348	383	2	xd	xd	INTJ
ejpam-4348	383	3	be	be	AUX
ejpam-4348	383	4	a	a	DET
ejpam-4348	383	5	solution	solution	NOUN
ejpam-4348	383	6	of	of	ADP
ejpam-4348	383	7	the	the	DET
ejpam-4348	383	8	matrix	matrix	NOUN
ejpam-4348	383	9	equation	equation	NOUN
ejpam-4348	383	10	(	(	PUNCT
ejpam-4348	383	11	xd	xd	INTJ
ejpam-4348	383	12	+	+	CCONJ
ejpam-4348	383	13	√	√	PROPN
ejpam-4348	383	14	p	p	NOUN
ejpam-4348	383	15	2	2	NUM
ejpam-4348	383	16	in	in	ADP
ejpam-4348	383	17	)	)	PUNCT
ejpam-4348	383	18	2	2	NUM
ejpam-4348	383	19	=	=	NOUN
ejpam-4348	383	20	ad	ad	NOUN
ejpam-4348	383	21	.	.	PUNCT
ejpam-4348	384	1	(	(	PUNCT
ejpam-4348	384	2	41	41	NUM
ejpam-4348	384	3	)	)	PUNCT
ejpam-4348	384	4	following	follow	VERB
ejpam-4348	384	5	the	the	DET
ejpam-4348	384	6	same	same	ADJ
ejpam-4348	384	7	calculation	calculation	NOUN
ejpam-4348	384	8	as	as	ADP
ejpam-4348	384	9	in	in	ADP
ejpam-4348	384	10	the	the	DET
ejpam-4348	384	11	proof	proof	NOUN
ejpam-4348	384	12	of	of	ADP
ejpam-4348	384	13	proposition	proposition	NOUN
ejpam-4348	384	14	7	7	NUM
ejpam-4348	384	15	,	,	PUNCT
ejpam-4348	384	16	we	we	PRON
ejpam-4348	384	17	get	get	VERB
ejpam-4348	384	18	ad	ad	NOUN
ejpam-4348	384	19	=	=	SYM
ejpam-4348	384	20	xd	xd	NOUN
ejpam-4348	384	21	+	+	CCONJ
ejpam-4348	384	22	√	√	PROPN
ejpam-4348	384	23	p	p	ADJ
ejpam-4348	384	24	2	2	NUM
ejpam-4348	384	25	in	in	ADP
ejpam-4348	384	26	−xd	−xd	NOUN
ejpam-4348	384	27	−	−	PROPN
ejpam-4348	384	28	√	√	PROPN
ejpam-4348	385	1	p	p	NOUN
ejpam-4348	385	2	2	2	NUM
ejpam-4348	385	3	in	in	ADV
ejpam-4348	385	4	in	in	ADV
ejpam-4348	385	5	in	in	ADP
ejpam-4348	385	6	×	×	X
ejpam-4348	385	7			NOUN
ejpam-4348	385	8	xd	xd	ADP
ejpam-4348	385	9	0	0	NUM
ejpam-4348	385	10	0	0	NUM
ejpam-4348	385	11	−xd	−xd	NOUN
ejpam-4348	385	12	−	−	PROPN
ejpam-4348	385	13	2	2	NUM
ejpam-4348	385	14	√	√	NOUN
ejpam-4348	385	15	p	p	NOUN
ejpam-4348	385	16	2	2	NUM
ejpam-4348	385	17	in	in	ADP
ejpam-4348	385	18	×	×	NOUN
ejpam-4348	385	19			NOUN
ejpam-4348	385	20	1	1	NUM
ejpam-4348	385	21	2	2	NUM
ejpam-4348	385	22	(	(	PUNCT
ejpam-4348	385	23	xd	xd	INTJ
ejpam-4348	385	24	+	+	CCONJ
ejpam-4348	385	25	√	√	PROPN
ejpam-4348	385	26	p	p	NOUN
ejpam-4348	385	27	2	2	NUM
ejpam-4348	385	28	in	in	ADP
ejpam-4348	385	29	)	)	PUNCT
ejpam-4348	385	30	−1	−1	NOUN
ejpam-4348	385	31	1	1	NUM
ejpam-4348	385	32	2	2	NUM
ejpam-4348	385	33	in	in	ADP
ejpam-4348	385	34	−1	−1	NOUN
ejpam-4348	385	35	2	2	NUM
ejpam-4348	385	36	(	(	PUNCT
ejpam-4348	385	37	xd	xd	INTJ
ejpam-4348	385	38	+	+	CCONJ
ejpam-4348	385	39	√	√	PROPN
ejpam-4348	385	40	p	p	NOUN
ejpam-4348	385	41	2	2	NUM
ejpam-4348	385	42	in	in	ADP
ejpam-4348	385	43	)	)	PUNCT
ejpam-4348	385	44	−1	−1	NOUN
ejpam-4348	385	45	1	1	NUM
ejpam-4348	385	46	2	2	NUM
ejpam-4348	385	47	in	in	ADP
ejpam-4348	385	48			NOUN
ejpam-4348	385	49	let	let	VERB
ejpam-4348	385	50	xd	xd	INTJ
ejpam-4348	385	51	=	=	SYM
ejpam-4348	385	52	qd	qd	PROPN
ejpam-4348	385	53	[	[	PUNCT
ejpam-4348	385	54	m+	m+	NOUN
ejpam-4348	385	55	0	0	NUM
ejpam-4348	385	56	0	0	NUM
ejpam-4348	386	1	m−	m−	PROPN
ejpam-4348	386	2	]	]	PUNCT
ejpam-4348	387	1	q−1	q−1	PROPN
ejpam-4348	388	1	d	d	X
ejpam-4348	388	2	be	be	VERB
ejpam-4348	388	3	the	the	DET
ejpam-4348	388	4	canonical	canonical	ADJ
ejpam-4348	388	5	jordan	jordan	PROPN
ejpam-4348	388	6	form	form	NOUN
ejpam-4348	388	7	of	of	ADP
ejpam-4348	388	8	the	the	DET
ejpam-4348	388	9	matrix	matrix	NOUN
ejpam-4348	388	10	xd	xd	INTJ
ejpam-4348	388	11	with	with	ADP
ejpam-4348	388	12	m+	m+	NUM
ejpam-4348	388	13	and	and	CCONJ
ejpam-4348	388	14	m−	m−	PROPN
ejpam-4348	388	15	the	the	DET
ejpam-4348	388	16	jordan	jordan	PROPN
ejpam-4348	388	17	blocks	block	NOUN
ejpam-4348	388	18	associated	associate	VERB
ejpam-4348	388	19	respectively	respectively	ADV
ejpam-4348	388	20	with	with	ADP
ejpam-4348	388	21	the	the	DET
ejpam-4348	388	22	eigenvalues	eigenvalue	NOUN
ejpam-4348	388	23	of	of	ADP
ejpam-4348	388	24	xd	xd	INTJ
ejpam-4348	388	25	located	locate	VERB
ejpam-4348	388	26	in	in	ADP
ejpam-4348	388	27	the	the	DET
ejpam-4348	388	28	right	right	ADJ
ejpam-4348	388	29	half	half	ADJ
ejpam-4348	388	30	-	-	PUNCT
ejpam-4348	388	31	plane	plane	NOUN
ejpam-4348	388	32	and	and	CCONJ
ejpam-4348	388	33	the	the	DET
ejpam-4348	388	34	left	left	ADJ
ejpam-4348	388	35	half	half	ADJ
ejpam-4348	388	36	-	-	PUNCT
ejpam-4348	388	37	plane	plane	NOUN
ejpam-4348	388	38	.	.	PUNCT
ejpam-4348	389	1	by	by	ADP
ejpam-4348	389	2	replacing	replace	VERB
ejpam-4348	389	3	the	the	DET
ejpam-4348	389	4	decomposition	decomposition	NOUN
ejpam-4348	389	5	of	of	ADP
ejpam-4348	389	6	xd	xd	INTJ
ejpam-4348	389	7	in	in	ADP
ejpam-4348	389	8	the	the	DET
ejpam-4348	389	9	matrix	matrix	NOUN
ejpam-4348	389	10	ad	ad	NOUN
ejpam-4348	389	11	,	,	PUNCT
ejpam-4348	389	12	we	we	PRON
ejpam-4348	389	13	get	get	VERB
ejpam-4348	389	14	ad	ad	NOUN
ejpam-4348	389	15	=	=	SYM
ejpam-4348	389	16	q̃dm(q̃d	q̃dm(q̃d	PROPN
ejpam-4348	389	17	)	)	PUNCT
ejpam-4348	389	18	−1	−1	NOUN
ejpam-4348	389	19	with	with	ADP
ejpam-4348	389	20	q̃d	q̃d	PROPN
ejpam-4348	389	21	=	=	PUNCT
ejpam-4348	389	22	qd	qd	PROPN
ejpam-4348	389	23	0	0	NUM
ejpam-4348	389	24	0	0	NUM
ejpam-4348	389	25	qd	qd	NOUN
ejpam-4348	389	26			NOUN
ejpam-4348	389	27			NOUN
ejpam-4348	389	28	(	(	PUNCT
ejpam-4348	389	29	m+	m+	NUM
ejpam-4348	389	30	0	0	NUM
ejpam-4348	389	31	0	0	NUM
ejpam-4348	389	32	m−	m−	PROPN
ejpam-4348	389	33	)	)	PUNCT
ejpam-4348	390	1	+	+	CCONJ
ejpam-4348	390	2	√	√	ADJ
ejpam-4348	390	3	p	p	NOUN
ejpam-4348	390	4	2	2	NUM
ejpam-4348	390	5	in	in	ADP
ejpam-4348	390	6	−	−	PROPN
ejpam-4348	390	7	[	[	PUNCT
ejpam-4348	390	8	m+	m+	NUM
ejpam-4348	390	9	0	0	NUM
ejpam-4348	390	10	0	0	NUM
ejpam-4348	391	1	m−	m−	PROPN
ejpam-4348	391	2	]	]	PUNCT
ejpam-4348	392	1	−	−	PROPN
ejpam-4348	393	1	√	√	NOUN
ejpam-4348	393	2	p	p	NOUN
ejpam-4348	393	3	2	2	NUM
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ejpam-4348	393	5	in	in	ADP
ejpam-4348	393	6	in	in	ADP
ejpam-4348	393	7			ADJ
ejpam-4348	393	8	and	and	CCONJ
ejpam-4348	393	9	m	m	NOUN
ejpam-4348	393	10	=	=	ADJ
ejpam-4348	393	11			NOUN
ejpam-4348	393	12	[	[	PUNCT
ejpam-4348	393	13	m+	m+	NUM
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ejpam-4348	393	15	0	0	NUM
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ejpam-4348	393	17	]	]	PUNCT
ejpam-4348	393	18	0	0	PUNCT
ejpam-4348	393	19	0	0	PUNCT
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ejpam-4348	394	2	m+	m+	NUM
ejpam-4348	394	3	0	0	NUM
ejpam-4348	394	4	0	0	NUM
ejpam-4348	395	1	m−	m−	PROPN
ejpam-4348	395	2	]	]	PUNCT
ejpam-4348	396	1	−	−	PROPN
ejpam-4348	396	2	2	2	NUM
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ejpam-4348	397	2	p	p	NOUN
ejpam-4348	397	3	2	2	NUM
ejpam-4348	397	4	in	in	ADP
ejpam-4348	397	5			NOUN
ejpam-4348	397	6	therefore	therefore	ADV
ejpam-4348	397	7	we	we	PRON
ejpam-4348	397	8	can	can	AUX
ejpam-4348	397	9	compute	compute	VERB
ejpam-4348	397	10	the	the	DET
ejpam-4348	397	11	associated	associated	ADJ
ejpam-4348	397	12	projector	projector	NOUN
ejpam-4348	397	13	pd	pd	X
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ejpam-4348	398	2	(	(	PUNCT
ejpam-4348	398	3	q̃d	q̃d	NOUN
ejpam-4348	398	4	)	)	PUNCT
ejpam-4348	398	5	[	[	PUNCT
ejpam-4348	398	6	ik	ik	X
ejpam-4348	398	7	0	0	NUM
ejpam-4348	398	8	0	0	NUM
ejpam-4348	398	9	0	0	NUM
ejpam-4348	398	10	]	]	PUNCT
ejpam-4348	398	11	(	(	PUNCT
ejpam-4348	398	12	q̃d	q̃d	NOUN
ejpam-4348	398	13	)	)	PUNCT
ejpam-4348	398	14	−1	−1	NOUN
ejpam-4348	398	15	s.	s.	PROPN
ejpam-4348	398	16	traoré	traoré	PROPN
ejpam-4348	398	17	,	,	PUNCT
ejpam-4348	398	18	m.	m.	NOUN
ejpam-4348	398	19	dosso	dosso	PROPN
ejpam-4348	398	20	/	/	SYM
ejpam-4348	398	21	eur	eur	PROPN
ejpam-4348	398	22	.	.	PUNCT
ejpam-4348	399	1	j.	j.	PROPN
ejpam-4348	399	2	pure	pure	PROPN
ejpam-4348	399	3	appl	appl	PROPN
ejpam-4348	399	4	.	.	PROPN
ejpam-4348	399	5	math	math	PROPN
ejpam-4348	399	6	,	,	PUNCT
ejpam-4348	399	7	15	15	NUM
ejpam-4348	399	8	(	(	PUNCT
ejpam-4348	399	9	2	2	NUM
ejpam-4348	399	10	)	)	PUNCT
ejpam-4348	399	11	(	(	PUNCT
ejpam-4348	399	12	2022	2022	NUM
ejpam-4348	399	13	)	)	PUNCT
ejpam-4348	399	14	,	,	PUNCT
ejpam-4348	399	15	681	681	NUM
ejpam-4348	399	16	-	-	SYM
ejpam-4348	399	17	725	725	NUM
ejpam-4348	399	18	707	707	NUM
ejpam-4348	399	19	=	=	SYM
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ejpam-4348	399	21	0	0	NUM
ejpam-4348	399	22	0	0	NUM
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ejpam-4348	399	27	m+	m+	NUM
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ejpam-4348	401	4	2	2	NUM
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ejpam-4348	401	8	m+	m+	NUM
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ejpam-4348	403	1	−	−	PROPN
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ejpam-4348	404	5	in	in	ADV
ejpam-4348	404	6	in	in	ADP
ejpam-4348	404	7	×	×	NOUN
ejpam-4348	404	8			NOUN
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ejpam-4348	405	7	[	[	PUNCT
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ejpam-4348	405	11	0	0	NUM
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ejpam-4348	406	1	[	[	PUNCT
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ejpam-4348	406	7			PROPN
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ejpam-4348	406	9			NOUN
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ejpam-4348	418	17	]	]	SYM
ejpam-4348	418	18	1	1	NUM
ejpam-4348	418	19	2	2	NUM
ejpam-4348	418	20	m+	m+	NOUN
ejpam-4348	419	1	+	+	CCONJ
ejpam-4348	419	2	√	√	PROPN
ejpam-4348	420	1	p	p	SYM
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ejpam-4348	420	4	0	0	PROPN
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ejpam-4348	420	6	0	0	NUM
ejpam-4348	420	7			NOUN
ejpam-4348	420	8	1	1	NUM
ejpam-4348	420	9	2	2	NUM
ejpam-4348	420	10	(m+	(m+	NOUN
ejpam-4348	420	11	+	+	CCONJ
ejpam-4348	420	12	√	√	PROPN
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ejpam-4348	420	16	)	)	PUNCT
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ejpam-4348	420	18	0	0	NUM
ejpam-4348	420	19	0	0	NUM
ejpam-4348	420	20	0	0	NUM
ejpam-4348	420	21			NOUN
ejpam-4348	420	22	1	1	NUM
ejpam-4348	420	23	2	2	NUM
ejpam-4348	420	24	[	[	PUNCT
ejpam-4348	420	25	ik	ik	X
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ejpam-4348	420	28	0	0	NUM
ejpam-4348	420	29	]	]	PUNCT
ejpam-4348	420	30			NUM
ejpam-4348	420	31	q−1	q−1	X
ejpam-4348	421	1	d	d	X
ejpam-4348	421	2	0	0	NUM
ejpam-4348	421	3	0	0	NUM
ejpam-4348	422	1	q−1	q−1	PROPN
ejpam-4348	423	1	d	d	ADP
ejpam-4348	423	2			NOUN
ejpam-4348	423	3	=	=	SYM
ejpam-4348	423	4			NOUN
ejpam-4348	423	5	qd	qd	NOUN
ejpam-4348	424	1	[	[	X
ejpam-4348	424	2	1	1	NUM
ejpam-4348	424	3	2	2	NUM
ejpam-4348	424	4	ik	ik	X
ejpam-4348	424	5	0	0	PROPN
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ejpam-4348	424	7	0	0	NUM
ejpam-4348	424	8	]	]	PUNCT
ejpam-4348	425	1	q−1	q−1	PROPN
ejpam-4348	426	1	d	d	X
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ejpam-4348	427	1	+	+	NOUN
ejpam-4348	427	2	√	√	PROPN
ejpam-4348	427	3	p	p	SYM
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ejpam-4348	427	5	ik	ik	NOUN
ejpam-4348	427	6	)	)	PUNCT
ejpam-4348	427	7	0	0	NUM
ejpam-4348	428	1	0	0	NUM
ejpam-4348	428	2	0	0	NUM
ejpam-4348	429	1	q−1	q−1	NOUN
ejpam-4348	429	2	d	d	NOUN
ejpam-4348	429	3	qd	qd	ADP
ejpam-4348	429	4	12(m+	12(m+	NUM
ejpam-4348	429	5	+	+	CCONJ
ejpam-4348	430	1	√	√	PROPN
ejpam-4348	430	2	p	p	SYM
ejpam-4348	430	3	2	2	NUM
ejpam-4348	430	4	ik	ik	NOUN
ejpam-4348	430	5	)	)	PUNCT
ejpam-4348	430	6	−1	−1	NOUN
ejpam-4348	430	7	0	0	NUM
ejpam-4348	430	8	0	0	NUM
ejpam-4348	430	9	0	0	NUM
ejpam-4348	431	1	q−1	q−1	NOUN
ejpam-4348	431	2	d	d	X
ejpam-4348	431	3	qd	qd	NOUN
ejpam-4348	432	1	[	[	X
ejpam-4348	432	2	1	1	NUM
ejpam-4348	432	3	2	2	NUM
ejpam-4348	432	4	ik	ik	X
ejpam-4348	432	5	0	0	PROPN
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ejpam-4348	432	7	0	0	NUM
ejpam-4348	432	8	]	]	PUNCT
ejpam-4348	433	1	q−1	q−1	PROPN
ejpam-4348	433	2			VERB
ejpam-4348	433	3	s.	s.	PROPN
ejpam-4348	433	4	traoré	traoré	PROPN
ejpam-4348	433	5	,	,	PUNCT
ejpam-4348	433	6	m.	m.	NOUN
ejpam-4348	433	7	dosso	dosso	PROPN
ejpam-4348	433	8	/	/	SYM
ejpam-4348	433	9	eur	eur	PROPN
ejpam-4348	433	10	.	.	PUNCT
ejpam-4348	434	1	j.	j.	PROPN
ejpam-4348	434	2	pure	pure	PROPN
ejpam-4348	434	3	appl	appl	PROPN
ejpam-4348	434	4	.	.	PROPN
ejpam-4348	434	5	math	math	PROPN
ejpam-4348	434	6	,	,	PUNCT
ejpam-4348	434	7	15	15	NUM
ejpam-4348	434	8	(	(	PUNCT
ejpam-4348	434	9	2	2	NUM
ejpam-4348	434	10	)	)	PUNCT
ejpam-4348	434	11	(	(	PUNCT
ejpam-4348	434	12	2022	2022	NUM
ejpam-4348	434	13	)	)	PUNCT
ejpam-4348	434	14	,	,	PUNCT
ejpam-4348	434	15	681	681	NUM
ejpam-4348	434	16	-	-	SYM
ejpam-4348	434	17	725	725	NUM
ejpam-4348	434	18	708	708	NUM
ejpam-4348	434	19	=	=	SYM
ejpam-4348	434	20	[	[	PUNCT
ejpam-4348	434	21	p(d	p(d	NOUN
ejpam-4348	434	22	)	)	PUNCT
ejpam-4348	434	23	1	1	NUM
ejpam-4348	434	24	p(d	p(d	NOUN
ejpam-4348	434	25	)	)	PUNCT
ejpam-4348	434	26	2	2	NUM
ejpam-4348	434	27	p(d	p(d	NOUN
ejpam-4348	434	28	)	)	PUNCT
ejpam-4348	434	29	3	3	NUM
ejpam-4348	434	30	p(d	p(d	NOUN
ejpam-4348	434	31	)	)	PUNCT
ejpam-4348	434	32	4	4	NUM
ejpam-4348	434	33	]	]	PUNCT
ejpam-4348	435	1	it	it	PRON
ejpam-4348	435	2	follows	follow	VERB
ejpam-4348	435	3	that	that	PRON
ejpam-4348	435	4	p(d	p(d	NOUN
ejpam-4348	435	5	)	)	PUNCT
ejpam-4348	435	6	1	1	NUM
ejpam-4348	435	7	=	=	SYM
ejpam-4348	435	8	qd	qd	NOUN
ejpam-4348	436	1	[	[	X
ejpam-4348	436	2	1	1	NUM
ejpam-4348	436	3	2	2	NUM
ejpam-4348	436	4	ik	ik	X
ejpam-4348	436	5	0	0	PROPN
ejpam-4348	436	6	0	0	NUM
ejpam-4348	436	7	0	0	NUM
ejpam-4348	436	8	]	]	PUNCT
ejpam-4348	437	1	q−1	q−1	PROPN
ejpam-4348	437	2	d	d	NOUN
ejpam-4348	437	3	=	=	SYM
ejpam-4348	437	4	1	1	NUM
ejpam-4348	437	5	2	2	NUM
ejpam-4348	437	6	pd	pd	X
ejpam-4348	437	7	p(d	p(d	PROPN
ejpam-4348	437	8	)	)	PUNCT
ejpam-4348	437	9	2	2	NUM
ejpam-4348	437	10	=	=	SYM
ejpam-4348	437	11	qd	qd	NOUN
ejpam-4348	437	12	1	1	NUM
ejpam-4348	437	13	2	2	NUM
ejpam-4348	437	14	m+	m+	NOUN
ejpam-4348	438	1	+	+	CCONJ
ejpam-4348	438	2	√	√	PROPN
ejpam-4348	439	1	p	p	SYM
ejpam-4348	439	2	2	2	NUM
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ejpam-4348	439	5	0	0	SYM
ejpam-4348	439	6	0	0	NUM
ejpam-4348	440	1	q−1	q−1	NOUN
ejpam-4348	440	2	d	d	X
ejpam-4348	440	3	p(d	p(d	NOUN
ejpam-4348	440	4	)	)	PUNCT
ejpam-4348	440	5	3	3	NUM
ejpam-4348	440	6	=	=	SYM
ejpam-4348	440	7	qd	qd	NOUN
ejpam-4348	440	8	1	1	NUM
ejpam-4348	440	9	2	2	NUM
ejpam-4348	440	10	(m+	(m+	NOUN
ejpam-4348	440	11	+	+	CCONJ
ejpam-4348	441	1	√	√	PROPN
ejpam-4348	441	2	p	p	SYM
ejpam-4348	441	3	2	2	NUM
ejpam-4348	441	4	ik	ik	NOUN
ejpam-4348	441	5	)	)	PUNCT
ejpam-4348	441	6	−1	−1	NOUN
ejpam-4348	441	7	0	0	NUM
ejpam-4348	441	8	0	0	NUM
ejpam-4348	441	9	0	0	NUM
ejpam-4348	442	1	q−1	q−1	NOUN
ejpam-4348	443	1	d	d	ADP
ejpam-4348	443	2			NOUN
ejpam-4348	443	3	=	=	VERB
ejpam-4348	443	4	⇒	⇒	X
ejpam-4348	443	5	pd	pd	PROPN
ejpam-4348	443	6	=	=	PROPN
ejpam-4348	443	7	4p(d	4p(d	PROPN
ejpam-4348	443	8	)	)	PUNCT
ejpam-4348	443	9	2	2	NUM
ejpam-4348	443	10	p(d	p(d	NOUN
ejpam-4348	443	11	)	)	PUNCT
ejpam-4348	443	12	3	3	NUM
ejpam-4348	443	13	p(d	p(d	NOUN
ejpam-4348	443	14	)	)	PUNCT
ejpam-4348	443	15	4	4	NUM
ejpam-4348	443	16	=	=	SYM
ejpam-4348	443	17	qd	qd	NOUN
ejpam-4348	444	1	[	[	X
ejpam-4348	444	2	1	1	NUM
ejpam-4348	444	3	2	2	NUM
ejpam-4348	444	4	ik	ik	X
ejpam-4348	444	5	0	0	PROPN
ejpam-4348	444	6	0	0	NUM
ejpam-4348	444	7	0	0	NUM
ejpam-4348	444	8	]	]	PUNCT
ejpam-4348	445	1	q−1	q−1	PROPN
ejpam-4348	445	2	d	d	NOUN
ejpam-4348	445	3	=	=	SYM
ejpam-4348	445	4	1	1	NUM
ejpam-4348	445	5	2	2	NUM
ejpam-4348	445	6	pd	pd	NOUN
ejpam-4348	445	7	with	with	ADP
ejpam-4348	445	8	xd	xd	PROPN
ejpam-4348	445	9	=	=	SYM
ejpam-4348	445	10	q	q	X
ejpam-4348	446	1	[	[	PUNCT
ejpam-4348	446	2	m+	m+	NUM
ejpam-4348	446	3	0	0	NUM
ejpam-4348	446	4	0	0	NUM
ejpam-4348	447	1	m−	m−	PROPN
ejpam-4348	447	2	]	]	PUNCT
ejpam-4348	448	1	q−1	q−1	PROPN
ejpam-4348	449	1	d	d	INTJ
ejpam-4348	449	2	we	we	PRON
ejpam-4348	449	3	have	have	VERB
ejpam-4348	449	4	a	a	DET
ejpam-4348	449	5	=	=	NOUN
ejpam-4348	449	6	ad	ad	NOUN
ejpam-4348	449	7	−	−	PROPN
ejpam-4348	450	1	(	(	PUNCT
ejpam-4348	450	2	p	p	NOUN
ejpam-4348	450	3	2	2	NUM
ejpam-4348	450	4	−	−	PROPN
ejpam-4348	450	5	d	d	NOUN
ejpam-4348	450	6	)	)	PUNCT
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ejpam-4348	450	8	=	=	PUNCT
ejpam-4348	450	9	qd	qd	NOUN
ejpam-4348	450	10			NOUN
ejpam-4348	450	11	(	(	PUNCT
ejpam-4348	450	12	m+	m+	NUM
ejpam-4348	451	1	+	+	CCONJ
ejpam-4348	451	2	√	√	PROPN
ejpam-4348	452	1	p	p	NOUN
ejpam-4348	452	2	2	2	NUM
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ejpam-4348	452	4	)	)	PUNCT
ejpam-4348	452	5	2	2	NUM
ejpam-4348	452	6	−	−	PROPN
ejpam-4348	452	7	(	(	PUNCT
ejpam-4348	452	8	p	p	NOUN
ejpam-4348	452	9	2	2	NUM
ejpam-4348	452	10	−	−	PROPN
ejpam-4348	452	11	d	d	PROPN
ejpam-4348	452	12	)	)	PUNCT
ejpam-4348	452	13	ik	ik	PROPN
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ejpam-4348	452	15	0	0	NUM
ejpam-4348	453	1	(	(	PUNCT
ejpam-4348	453	2	m−	m−	PROPN
ejpam-4348	453	3	+	+	CCONJ
ejpam-4348	454	1	√	√	PROPN
ejpam-4348	454	2	p	p	SYM
ejpam-4348	454	3	2	2	NUM
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ejpam-4348	454	5	)	)	PUNCT
ejpam-4348	454	6	2	2	NUM
ejpam-4348	454	7	−	−	NOUN
ejpam-4348	454	8	(	(	PUNCT
ejpam-4348	454	9	p	p	NOUN
ejpam-4348	454	10	2	2	NUM
ejpam-4348	454	11	−	−	PROPN
ejpam-4348	454	12	d	d	PROPN
ejpam-4348	454	13	)	)	PUNCT
ejpam-4348	454	14	in−k	in−k	NOUN
ejpam-4348	454	15	q−1	q−1	PROPN
ejpam-4348	454	16	and	and	CCONJ
ejpam-4348	454	17	pda	pda	NOUN
ejpam-4348	454	18	=	=	SYM
ejpam-4348	454	19	q	q	X
ejpam-4348	454	20	[	[	PUNCT
ejpam-4348	454	21	ik	ik	X
ejpam-4348	454	22	0	0	PROPN
ejpam-4348	454	23	0	0	NUM
ejpam-4348	454	24	0	0	NUM
ejpam-4348	454	25	]	]	PUNCT
ejpam-4348	455	1	q−1	q−1	PROPN
ejpam-4348	456	1	d	d	X
ejpam-4348	456	2	×q	×q	ADJ
ejpam-4348	456	3			NOUN
ejpam-4348	456	4	(	(	PUNCT
ejpam-4348	456	5	m+	m+	NUM
ejpam-4348	456	6	+	+	CCONJ
ejpam-4348	456	7	√	√	PROPN
ejpam-4348	456	8	p	p	NOUN
ejpam-4348	456	9	2	2	NUM
ejpam-4348	456	10	ik	ik	X
ejpam-4348	456	11	)	)	PUNCT
ejpam-4348	456	12	2	2	NUM
ejpam-4348	456	13	−	−	PROPN
ejpam-4348	456	14	(	(	PUNCT
ejpam-4348	456	15	p	p	NOUN
ejpam-4348	456	16	2	2	NUM
ejpam-4348	456	17	−	−	PROPN
ejpam-4348	457	1	d)ik	d)ik	PROPN
ejpam-4348	457	2	0	0	NUM
ejpam-4348	457	3	0	0	NUM
ejpam-4348	457	4	(	(	PUNCT
ejpam-4348	457	5	m−	m−	PROPN
ejpam-4348	457	6	+	+	CCONJ
ejpam-4348	457	7	√	√	PROPN
ejpam-4348	457	8	p	p	SYM
ejpam-4348	457	9	2	2	NUM
ejpam-4348	457	10	in−k	in−k	NOUN
ejpam-4348	457	11	)	)	PUNCT
ejpam-4348	457	12	2	2	NUM
ejpam-4348	457	13	−	−	PROPN
ejpam-4348	457	14	(	(	PUNCT
ejpam-4348	457	15	p	p	NOUN
ejpam-4348	457	16	2	2	NUM
ejpam-4348	457	17	−	−	NOUN
ejpam-4348	457	18	d)in−k	d)in−k	NOUN
ejpam-4348	457	19	q−1	q−1	PUNCT
ejpam-4348	458	1	d	d	X
ejpam-4348	458	2	=	=	PUNCT
ejpam-4348	458	3	qd	qd	NOUN
ejpam-4348	458	4	(m+	(m+	NOUN
ejpam-4348	458	5	+	+	CCONJ
ejpam-4348	458	6	√	√	PROPN
ejpam-4348	458	7	p	p	SYM
ejpam-4348	458	8	2	2	NUM
ejpam-4348	458	9	ik	ik	X
ejpam-4348	458	10	)	)	PUNCT
ejpam-4348	458	11	2	2	NUM
ejpam-4348	458	12	−	−	PROPN
ejpam-4348	458	13	(	(	PUNCT
ejpam-4348	458	14	p	p	NOUN
ejpam-4348	458	15	2	2	NUM
ejpam-4348	458	16	−	−	PROPN
ejpam-4348	458	17	d)ik	d)ik	PROPN
ejpam-4348	458	18	0	0	NUM
ejpam-4348	458	19	0	0	NUM
ejpam-4348	458	20	0	0	NUM
ejpam-4348	459	1	q−1	q−1	PRON
ejpam-4348	459	2	d	d	NOUN
ejpam-4348	459	3	=	=	SYM
ejpam-4348	459	4	4(p(d	4(p(d	NUM
ejpam-4348	459	5	)	)	PUNCT
ejpam-4348	459	6	2	2	NUM
ejpam-4348	459	7	)	)	SYM
ejpam-4348	459	8	2	2	NUM
ejpam-4348	459	9	−	−	NOUN
ejpam-4348	459	10	(	(	PUNCT
ejpam-4348	459	11	p−	p−	NOUN
ejpam-4348	459	12	2d)p(d	2d)p(d	NOUN
ejpam-4348	459	13	)	)	PUNCT
ejpam-4348	459	14	1	1	NUM
ejpam-4348	459	15	hence	hence	ADV
ejpam-4348	459	16	(	(	PUNCT
ejpam-4348	459	17	39	39	NUM
ejpam-4348	459	18	)	)	PUNCT
ejpam-4348	459	19	and	and	CCONJ
ejpam-4348	459	20	(	(	PUNCT
ejpam-4348	459	21	40	40	NUM
ejpam-4348	459	22	)	)	PUNCT
ejpam-4348	459	23	.	.	PUNCT
ejpam-4348	460	1	remark	remark	NOUN
ejpam-4348	460	2	5	5	NUM
ejpam-4348	460	3	.	.	PUNCT
ejpam-4348	461	1	if	if	SCONJ
ejpam-4348	461	2	the	the	DET
ejpam-4348	461	3	parameter	parameter	NOUN
ejpam-4348	461	4	d	d	PROPN
ejpam-4348	462	1	=	=	SYM
ejpam-4348	463	1	p	p	NOUN
ejpam-4348	463	2	2	2	NUM
ejpam-4348	463	3	,	,	PUNCT
ejpam-4348	463	4	whence	whence	NOUN
ejpam-4348	463	5	equalities	equality	NOUN
ejpam-4348	463	6	(	(	PUNCT
ejpam-4348	463	7	40	40	NUM
ejpam-4348	463	8	)	)	PUNCT
ejpam-4348	463	9	are	be	AUX
ejpam-4348	463	10	reduced	reduce	VERB
ejpam-4348	463	11	to	to	ADP
ejpam-4348	463	12	those	those	PRON
ejpam-4348	463	13	of	of	ADP
ejpam-4348	463	14	equalities	equality	NOUN
ejpam-4348	463	15	(	(	PUNCT
ejpam-4348	463	16	23	23	NUM
ejpam-4348	463	17	)	)	PUNCT
ejpam-4348	463	18	.	.	PUNCT
ejpam-4348	464	1	s.	s.	PROPN
ejpam-4348	464	2	traoré	traoré	PROPN
ejpam-4348	464	3	,	,	PUNCT
ejpam-4348	464	4	m.	m.	NOUN
ejpam-4348	464	5	dosso	dosso	PROPN
ejpam-4348	464	6	/	/	SYM
ejpam-4348	464	7	eur	eur	PROPN
ejpam-4348	464	8	.	.	PUNCT
ejpam-4348	465	1	j.	j.	PROPN
ejpam-4348	465	2	pure	pure	PROPN
ejpam-4348	465	3	appl	appl	PROPN
ejpam-4348	465	4	.	.	PROPN
ejpam-4348	465	5	math	math	PROPN
ejpam-4348	465	6	,	,	PUNCT
ejpam-4348	465	7	15	15	NUM
ejpam-4348	465	8	(	(	PUNCT
ejpam-4348	465	9	2	2	NUM
ejpam-4348	465	10	)	)	PUNCT
ejpam-4348	465	11	(	(	PUNCT
ejpam-4348	465	12	2022	2022	NUM
ejpam-4348	465	13	)	)	PUNCT
ejpam-4348	465	14	,	,	PUNCT
ejpam-4348	465	15	681	681	NUM
ejpam-4348	465	16	-	-	SYM
ejpam-4348	465	17	725	725	NUM
ejpam-4348	465	18	709	709	NUM
ejpam-4348	465	19	algorithm	algorithm	NOUN
ejpam-4348	465	20	6	6	NUM
ejpam-4348	465	21	(	(	PUNCT
ejpam-4348	465	22	dichopd	dichopd	NOUN
ejpam-4348	465	23	)	)	PUNCT
ejpam-4348	465	24	.	.	PUNCT
ejpam-4348	466	1	•	•	NOUN
ejpam-4348	466	2	input	input	NOUN
ejpam-4348	466	3	variables	variable	NOUN
ejpam-4348	466	4	:	:	PUNCT
ejpam-4348	466	5	the	the	DET
ejpam-4348	466	6	matrices	matrix	NOUN
ejpam-4348	466	7	a	a	PRON
ejpam-4348	466	8	,	,	PUNCT
ejpam-4348	466	9	in	in	ADV
ejpam-4348	466	10	and	and	CCONJ
ejpam-4348	466	11	the	the	DET
ejpam-4348	466	12	real	real	ADJ
ejpam-4348	466	13	numbers	number	NOUN
ejpam-4348	466	14	d	d	NOUN
ejpam-4348	466	15	and	and	CCONJ
ejpam-4348	466	16	p	p	NOUN
ejpam-4348	466	17	such	such	ADJ
ejpam-4348	466	18	that	that	SCONJ
ejpam-4348	466	19	the	the	DET
ejpam-4348	466	20	matrix	matrix	NOUN
ejpam-4348	466	21	pencil	pencil	NOUN
ejpam-4348	466	22	zin−a	zin−a	PROPN
ejpam-4348	466	23	has	have	VERB
ejpam-4348	466	24	no	no	DET
ejpam-4348	466	25	eigenvalues	eigenvalue	NOUN
ejpam-4348	466	26	on	on	ADP
ejpam-4348	466	27	the	the	DET
ejpam-4348	466	28	parabola	parabola	NOUN
ejpam-4348	466	29	with	with	ADP
ejpam-4348	466	30	equation	equation	NOUN
ejpam-4348	466	31	2p	2p	NOUN
ejpam-4348	466	32	(	(	PUNCT
ejpam-4348	466	33	d−	d−	PROPN
ejpam-4348	466	34	x	x	PRON
ejpam-4348	466	35	)	)	PUNCT
ejpam-4348	466	36	=	=	PUNCT
ejpam-4348	467	1	y2	y2	PROPN
ejpam-4348	467	2	with	with	ADP
ejpam-4348	467	3	p	p	PROPN
ejpam-4348	467	4	>	>	X
ejpam-4348	467	5	0	0	PUNCT
ejpam-4348	467	6	et	et	NOUN
ejpam-4348	467	7	d	d	X
ejpam-4348	467	8	>	>	X
ejpam-4348	467	9	0	0	NUM
ejpam-4348	467	10	•	•	NUM
ejpam-4348	467	11	output	output	NOUN
ejpam-4348	467	12	variables	variable	NOUN
ejpam-4348	467	13	:	:	PUNCT
ejpam-4348	467	14	pd	pd	PROPN
ejpam-4348	467	15	and	and	CCONJ
ejpam-4348	467	16	hd	hd	PROPN
ejpam-4348	467	17	.	.	PROPN
ejpam-4348	468	1	pd	pd	PROPN
ejpam-4348	468	2	being	be	AUX
ejpam-4348	468	3	the	the	DET
ejpam-4348	468	4	projector	projector	NOUN
ejpam-4348	468	5	on	on	ADP
ejpam-4348	468	6	the	the	DET
ejpam-4348	468	7	right	right	ADJ
ejpam-4348	468	8	subspace	subspace	NOUN
ejpam-4348	468	9	of	of	ADP
ejpam-4348	468	10	zin−a	zin−a	PROPN
ejpam-4348	468	11	associated	associate	VERB
ejpam-4348	468	12	with	with	ADP
ejpam-4348	468	13	the	the	DET
ejpam-4348	468	14	eigenvalues	eigenvalue	NOUN
ejpam-4348	468	15	outside	outside	ADP
ejpam-4348	468	16	the	the	DET
ejpam-4348	468	17	parabola	parabola	NOUN
ejpam-4348	468	18	and	and	CCONJ
ejpam-4348	468	19	hd	hd	VERB
ejpam-4348	468	20	the	the	DET
ejpam-4348	468	21	matrix	matrix	NOUN
ejpam-4348	468	22	whose	whose	DET
ejpam-4348	468	23	norm	norm	NOUN
ejpam-4348	468	24	defines	define	VERB
ejpam-4348	468	25	the	the	DET
ejpam-4348	468	26	dichotomy	dichotomy	NOUN
ejpam-4348	468	27	criterion	criterion	NOUN
ejpam-4348	468	28	.	.	PUNCT
ejpam-4348	469	1	1	1	X
ejpam-4348	469	2	.	.	X
ejpam-4348	469	3	determine	determine	VERB
ejpam-4348	469	4	the	the	DET
ejpam-4348	469	5	matrix	matrix	NOUN
ejpam-4348	469	6	ad	ad	NOUN
ejpam-4348	469	7	=	=	NOUN
ejpam-4348	469	8			NOUN
ejpam-4348	470	1	−	−	PROPN
ejpam-4348	470	2	√	√	PROPN
ejpam-4348	470	3	p	p	NOUN
ejpam-4348	470	4	2	2	NUM
ejpam-4348	470	5	in	in	ADP
ejpam-4348	470	6	a+	a+	PUNCT
ejpam-4348	470	7	(	(	PUNCT
ejpam-4348	470	8	p	p	NOUN
ejpam-4348	470	9	2	2	NUM
ejpam-4348	470	10	−	−	NOUN
ejpam-4348	470	11	d)in	d)in	PROPN
ejpam-4348	470	12	in	in	ADP
ejpam-4348	470	13	−	−	PROPN
ejpam-4348	470	14	√	√	NUM
ejpam-4348	470	15	p	p	NOUN
ejpam-4348	470	16	2	2	NUM
ejpam-4348	470	17	in	in	ADP
ejpam-4348	470	18			NOUN
ejpam-4348	470	19	2	2	NUM
ejpam-4348	470	20	.	.	PUNCT
ejpam-4348	470	21	using	use	VERB
ejpam-4348	470	22	algorithm	algorithm	NOUN
ejpam-4348	470	23	3	3	NUM
ejpam-4348	470	24	to	to	ADP
ejpam-4348	470	25	λdi2n−ad	λdi2n−ad	PRON
ejpam-4348	470	26	,	,	PUNCT
ejpam-4348	470	27	compute	compute	VERB
ejpam-4348	470	28	the	the	DET
ejpam-4348	470	29	projector	projector	NOUN
ejpam-4348	470	30	pd	pd	NOUN
ejpam-4348	470	31	onto	onto	ADP
ejpam-4348	470	32	the	the	DET
ejpam-4348	470	33	right	right	ADJ
ejpam-4348	470	34	eigenspace	eigenspace	NOUN
ejpam-4348	470	35	of	of	ADP
ejpam-4348	470	36	ad	ad	NOUN
ejpam-4348	470	37	associted	associte	VERB
ejpam-4348	470	38	with	with	ADP
ejpam-4348	470	39	the	the	DET
ejpam-4348	470	40	eigenvalues	eigenvalue	NOUN
ejpam-4348	470	41	on	on	ADP
ejpam-4348	470	42	the	the	DET
ejpam-4348	470	43	right	right	ADJ
ejpam-4348	470	44	half	half	ADJ
ejpam-4348	470	45	-	-	PUNCT
ejpam-4348	470	46	plane	plane	NOUN
ejpam-4348	470	47	of	of	ADP
ejpam-4348	470	48	the	the	DET
ejpam-4348	470	49	complex	complex	ADJ
ejpam-4348	470	50	plane	plane	NOUN
ejpam-4348	470	51	and	and	CCONJ
ejpam-4348	470	52	the	the	DET
ejpam-4348	470	53	matrix	matrix	NOUN
ejpam-4348	470	54	hd	hd	NOUN
ejpam-4348	470	55	.	.	PROPN
ejpam-4348	471	1	3	3	X
ejpam-4348	471	2	.	.	X
ejpam-4348	472	1	if	if	SCONJ
ejpam-4348	472	2	∥hd∥	∥hd∥	NOUN
ejpam-4348	472	3	is	be	AUX
ejpam-4348	472	4	not	not	PART
ejpam-4348	472	5	large	large	ADJ
ejpam-4348	472	6	,	,	PUNCT
ejpam-4348	472	7	determine	determine	VERB
ejpam-4348	472	8	the	the	DET
ejpam-4348	472	9	projector	projector	NOUN
ejpam-4348	472	10	pd	pd	NOUN
ejpam-4348	472	11	by	by	ADP
ejpam-4348	472	12	pd	pd	PROPN
ejpam-4348	472	13	=	=	PROPN
ejpam-4348	472	14	2p(d	2p(d	PROPN
ejpam-4348	472	15	)	)	PUNCT
ejpam-4348	472	16	1	1	NUM
ejpam-4348	472	17	.	.	PUNCT
ejpam-4348	473	1	3.2.2	3.2.2	X
ejpam-4348	473	2	.	.	PUNCT
ejpam-4348	474	1	the	the	DET
ejpam-4348	474	2	spectral	spectral	ADJ
ejpam-4348	474	3	dichotomy	dichotomy	NOUN
ejpam-4348	474	4	method	method	NOUN
ejpam-4348	474	5	with	with	ADP
ejpam-4348	474	6	the	the	DET
ejpam-4348	474	7	coefficient	coefficient	NOUN
ejpam-4348	474	8	b	b	PROPN
ejpam-4348	474	9	̸=	̸=	PROPN
ejpam-4348	474	10	0	0	NUM
ejpam-4348	474	11	consider	consider	VERB
ejpam-4348	474	12	the	the	DET
ejpam-4348	474	13	set	set	NOUN
ejpam-4348	474	14	γ̃d	γ̃d	PROPN
ejpam-4348	474	15	=	=	PUNCT
ejpam-4348	474	16	{	{	PUNCT
ejpam-4348	474	17	z	z	NOUN
ejpam-4348	474	18	=	=	SYM
ejpam-4348	474	19	x+	x+	PROPN
ejpam-4348	474	20	iy	iy	PROPN
ejpam-4348	474	21	/	/	SYM
ejpam-4348	474	22	x+	x+	PROPN
ejpam-4348	474	23	(	(	PUNCT
ejpam-4348	474	24	p	p	NOUN
ejpam-4348	474	25	2	2	NUM
ejpam-4348	474	26	−	−	PROPN
ejpam-4348	474	27	d	d	NOUN
ejpam-4348	474	28	)	)	PUNCT
ejpam-4348	475	1	+	+	CCONJ
ejpam-4348	475	2	i(y	i(y	NOUN
ejpam-4348	475	3	−	−	NOUN
ejpam-4348	475	4	pb	pb	NOUN
ejpam-4348	475	5	)	)	PUNCT
ejpam-4348	475	6	∈	∈	PROPN
ejpam-4348	475	7	γ	γ	PROPN
ejpam-4348	475	8	}	}	PUNCT
ejpam-4348	475	9	described	describe	VERB
ejpam-4348	475	10	by	by	ADP
ejpam-4348	475	11	the	the	DET
ejpam-4348	475	12	following	follow	VERB
ejpam-4348	475	13	equation	equation	NOUN
ejpam-4348	475	14	(	(	PUNCT
ejpam-4348	475	15	33	33	NUM
ejpam-4348	475	16	)	)	PUNCT
ejpam-4348	475	17	.	.	PUNCT
ejpam-4348	476	1	we	we	PRON
ejpam-4348	476	2	consider	consider	VERB
ejpam-4348	476	3	the	the	DET
ejpam-4348	476	4	following	follow	VERB
ejpam-4348	476	5	order	order	NOUN
ejpam-4348	476	6	matrix	matrix	NOUN
ejpam-4348	476	7	2n	2n	NUM
ejpam-4348	476	8	ãd	ãd	NOUN
ejpam-4348	477	1	=	=	PUNCT
ejpam-4348	477	2	−	−	PROPN
ejpam-4348	477	3	√	√	NUM
ejpam-4348	478	1	p	p	NOUN
ejpam-4348	478	2	2	2	NUM
ejpam-4348	478	3	in	in	ADP
ejpam-4348	478	4	adb	adb	NOUN
ejpam-4348	478	5	in	in	ADP
ejpam-4348	478	6	−	−	PROPN
ejpam-4348	478	7	√	√	PROPN
ejpam-4348	478	8	p	p	NOUN
ejpam-4348	478	9	2	2	NUM
ejpam-4348	478	10	in	in	ADP
ejpam-4348	478	11			NOUN
ejpam-4348	478	12	with	with	ADP
ejpam-4348	478	13	adb	adb	NOUN
ejpam-4348	478	14	=	=	SYM
ejpam-4348	478	15	a+	a+	PUNCT
ejpam-4348	478	16	(	(	PUNCT
ejpam-4348	478	17	p	p	NOUN
ejpam-4348	478	18	2	2	NUM
ejpam-4348	478	19	−	−	NUM
ejpam-4348	478	20	d−	d−	PROPN
ejpam-4348	478	21	ipb	ipb	PROPN
ejpam-4348	478	22	)	)	PUNCT
ejpam-4348	478	23	in	in	ADP
ejpam-4348	478	24	.	.	PUNCT
ejpam-4348	479	1	the	the	DET
ejpam-4348	479	2	respective	respective	ADJ
ejpam-4348	479	3	eigenvalues	eigenvalue	VERB
ejpam-4348	479	4	λ̃d	λ̃d	NOUN
ejpam-4348	479	5	and	and	CCONJ
ejpam-4348	479	6	zdb	zdb	NOUN
ejpam-4348	479	7	of	of	ADP
ejpam-4348	479	8	the	the	DET
ejpam-4348	479	9	matrices	matrix	NOUN
ejpam-4348	479	10	ãd	ãd	VERB
ejpam-4348	479	11	and	and	CCONJ
ejpam-4348	479	12	adb	adb	PROPN
ejpam-4348	479	13	verify	verify	VERB
ejpam-4348	479	14	the	the	DET
ejpam-4348	479	15	relationship	relationship	NOUN
ejpam-4348	479	16	zdb	zdb	NOUN
ejpam-4348	479	17	=	=	PUNCT
ejpam-4348	479	18	(	(	PUNCT
ejpam-4348	479	19	√	√	PROPN
ejpam-4348	479	20	p	p	NOUN
ejpam-4348	479	21	2	2	NUM
ejpam-4348	479	22	+	+	CCONJ
ejpam-4348	479	23	λ̃d	λ̃d	NOUN
ejpam-4348	479	24	)	)	PUNCT
ejpam-4348	479	25	2	2	X
ejpam-4348	479	26	.	.	PUNCT
ejpam-4348	480	1	this	this	PRON
ejpam-4348	480	2	leads	lead	VERB
ejpam-4348	480	3	to	to	ADP
ejpam-4348	480	4	the	the	DET
ejpam-4348	480	5	following	follow	VERB
ejpam-4348	480	6	remark	remark	NOUN
ejpam-4348	480	7	s.	s.	PROPN
ejpam-4348	480	8	traoré	traoré	PROPN
ejpam-4348	480	9	,	,	PUNCT
ejpam-4348	480	10	m.	m.	NOUN
ejpam-4348	480	11	dosso	dosso	PROPN
ejpam-4348	480	12	/	/	SYM
ejpam-4348	480	13	eur	eur	PROPN
ejpam-4348	480	14	.	.	PUNCT
ejpam-4348	481	1	j.	j.	PROPN
ejpam-4348	481	2	pure	pure	PROPN
ejpam-4348	481	3	appl	appl	PROPN
ejpam-4348	481	4	.	.	PROPN
ejpam-4348	481	5	math	math	PROPN
ejpam-4348	481	6	,	,	PUNCT
ejpam-4348	481	7	15	15	NUM
ejpam-4348	481	8	(	(	PUNCT
ejpam-4348	481	9	2	2	NUM
ejpam-4348	481	10	)	)	PUNCT
ejpam-4348	481	11	(	(	PUNCT
ejpam-4348	481	12	2022	2022	NUM
ejpam-4348	481	13	)	)	PUNCT
ejpam-4348	481	14	,	,	PUNCT
ejpam-4348	481	15	681	681	NUM
ejpam-4348	481	16	-	-	SYM
ejpam-4348	481	17	725	725	NUM
ejpam-4348	481	18	710	710	NUM
ejpam-4348	481	19	remark	remark	NOUN
ejpam-4348	481	20	6	6	NUM
ejpam-4348	481	21	.	.	PUNCT
ejpam-4348	482	1	the	the	DET
ejpam-4348	482	2	respective	respective	ADJ
ejpam-4348	482	3	eigenvalues	eigenvalue	VERB
ejpam-4348	482	4	λ̃d	λ̃d	NOUN
ejpam-4348	482	5	and	and	CCONJ
ejpam-4348	482	6	z	z	PROPN
ejpam-4348	482	7	of	of	ADP
ejpam-4348	482	8	the	the	DET
ejpam-4348	482	9	matrices	matrix	NOUN
ejpam-4348	482	10	ãd	ãd	NOUN
ejpam-4348	482	11	and	and	CCONJ
ejpam-4348	482	12	a	a	DET
ejpam-4348	482	13	satisfy	satisfy	NOUN
ejpam-4348	482	14	the	the	DET
ejpam-4348	482	15	relation	relation	NOUN
ejpam-4348	482	16	z	z	NOUN
ejpam-4348	482	17	=	=	SYM
ejpam-4348	482	18	(	(	PUNCT
ejpam-4348	482	19	√	√	PROPN
ejpam-4348	482	20	p	p	NOUN
ejpam-4348	482	21	2	2	NUM
ejpam-4348	482	22	+	+	CCONJ
ejpam-4348	482	23	λ̃d	λ̃d	NOUN
ejpam-4348	482	24	)	)	PUNCT
ejpam-4348	482	25	2	2	NUM
ejpam-4348	482	26	−	−	PROPN
ejpam-4348	482	27	(	(	PUNCT
ejpam-4348	482	28	p	p	NOUN
ejpam-4348	482	29	2	2	NUM
ejpam-4348	482	30	−	−	NUM
ejpam-4348	482	31	d−	d−	PROPN
ejpam-4348	482	32	ipb	ipb	PROPN
ejpam-4348	482	33	)	)	PUNCT
ejpam-4348	482	34	furthermore	furthermore	ADV
ejpam-4348	482	35	,	,	PUNCT
ejpam-4348	482	36	we	we	PRON
ejpam-4348	482	37	get	get	VERB
ejpam-4348	482	38	x	x	PUNCT
ejpam-4348	483	1	=	=	PRON
ejpam-4348	483	2	(	(	PUNCT
ejpam-4348	483	3	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	483	4	)	)	PUNCT
ejpam-4348	484	1	+	+	CCONJ
ejpam-4348	484	2	√	√	ADJ
ejpam-4348	484	3	p	p	NOUN
ejpam-4348	484	4	2	2	NUM
ejpam-4348	484	5	)	)	SYM
ejpam-4348	484	6	2	2	NUM
ejpam-4348	484	7	−ℑ(λ̃d	−ℑ(λ̃d	NUM
ejpam-4348	484	8	)	)	PUNCT
ejpam-4348	484	9	2	2	NUM
ejpam-4348	485	1	+	+	CCONJ
ejpam-4348	485	2	p	p	NOUN
ejpam-4348	485	3	2	2	NUM
ejpam-4348	485	4	−	−	NOUN
ejpam-4348	485	5	d	d	X
ejpam-4348	485	6	y	y	NOUN
ejpam-4348	485	7	=	=	SYM
ejpam-4348	485	8	2	2	NUM
ejpam-4348	485	9	(	(	PUNCT
ejpam-4348	485	10	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	485	11	)	)	PUNCT
ejpam-4348	486	1	+	+	CCONJ
ejpam-4348	486	2	√	√	PROPN
ejpam-4348	486	3	p	p	NOUN
ejpam-4348	486	4	2	2	NUM
ejpam-4348	486	5	)	)	PUNCT
ejpam-4348	486	6	ℑ(λ̃d)−	ℑ(λ̃d)−	ADV
ejpam-4348	486	7	pb	pb	ADP
ejpam-4348	486	8	thus	thus	ADV
ejpam-4348	486	9	y2	y2	VERB
ejpam-4348	486	10	=	=	SYM
ejpam-4348	486	11	4	4	NUM
ejpam-4348	486	12	(	(	PUNCT
ejpam-4348	486	13	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	486	14	)	)	PUNCT
ejpam-4348	487	1	+	+	CCONJ
ejpam-4348	487	2	√	√	ADJ
ejpam-4348	487	3	p	p	NOUN
ejpam-4348	487	4	2	2	NUM
ejpam-4348	487	5	)	)	SYM
ejpam-4348	487	6	2	2	NUM
ejpam-4348	487	7	ℑ(λ̃d	ℑ(λ̃d	NOUN
ejpam-4348	487	8	)	)	PUNCT
ejpam-4348	487	9	2	2	NUM
ejpam-4348	487	10	−	−	NOUN
ejpam-4348	487	11	4	4	NUM
ejpam-4348	487	12	(	(	PUNCT
ejpam-4348	487	13	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	487	14	)	)	PUNCT
ejpam-4348	488	1	+	+	CCONJ
ejpam-4348	488	2	√	√	PROPN
ejpam-4348	488	3	p	p	NOUN
ejpam-4348	488	4	2	2	NUM
ejpam-4348	488	5	)	)	PUNCT
ejpam-4348	488	6	ℑ(λ̃db)pb+	ℑ(λ̃db)pb+	NOUN
ejpam-4348	488	7	p2b2	p2b2	X
ejpam-4348	489	1	=	=	PUNCT
ejpam-4348	489	2	[	[	X
ejpam-4348	489	3	(	(	PUNCT
ejpam-4348	489	4	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	489	5	)	)	PUNCT
ejpam-4348	489	6	+	+	CCONJ
ejpam-4348	489	7	√	√	ADJ
ejpam-4348	489	8	p	p	NOUN
ejpam-4348	489	9	2	2	NUM
ejpam-4348	489	10	)	)	SYM
ejpam-4348	489	11	2	2	NUM
ejpam-4348	489	12	−	−	NOUN
ejpam-4348	489	13	x+	x+	PUNCT
ejpam-4348	489	14	√	√	PROPN
ejpam-4348	489	15	p	p	NOUN
ejpam-4348	489	16	2	2	NUM
ejpam-4348	489	17	−	−	NUM
ejpam-4348	489	18	d−	d−	PROPN
ejpam-4348	489	19	ipb	ipb	PROPN
ejpam-4348	489	20	]	]	PUNCT
ejpam-4348	489	21	by	by	ADP
ejpam-4348	489	22	setting	set	VERB
ejpam-4348	489	23	p̃d	p̃d	NOUN
ejpam-4348	489	24	=	=	SYM
ejpam-4348	489	25	2	2	NUM
ejpam-4348	489	26	(	(	PUNCT
ejpam-4348	489	27	ℜ(λ̃d	ℜ(λ̃d	PROPN
ejpam-4348	489	28	)	)	PUNCT
ejpam-4348	490	1	+	+	CCONJ
ejpam-4348	490	2	√	√	ADJ
ejpam-4348	490	3	p	p	NOUN
ejpam-4348	490	4	2	2	NUM
ejpam-4348	490	5	−	−	NOUN
ejpam-4348	490	6	pb	pb	ADP
ejpam-4348	490	7	)	)	PUNCT
ejpam-4348	490	8	2	2	NUM
ejpam-4348	490	9	we	we	PRON
ejpam-4348	490	10	have	have	AUX
ejpam-4348	490	11	y2	y2	VERB
ejpam-4348	490	12	=	=	SYM
ejpam-4348	490	13	2p̃db	2p̃db	NUM
ejpam-4348	490	14	(	(	PUNCT
ejpam-4348	490	15	p̃db	p̃db	PROPN
ejpam-4348	490	16	2	2	NUM
ejpam-4348	490	17	−	−	NOUN
ejpam-4348	490	18	x−	x−	PROPN
ejpam-4348	490	19	p	p	PROPN
ejpam-4348	490	20	2	2	NUM
ejpam-4348	490	21	+	+	CCONJ
ejpam-4348	490	22	db	db	PROPN
ejpam-4348	490	23	)	)	PUNCT
ejpam-4348	491	1	=	=	SYM
ejpam-4348	491	2	2p̃db	2p̃db	NUM
ejpam-4348	491	3	(	(	PUNCT
ejpam-4348	491	4	p̃db	p̃db	SYM
ejpam-4348	491	5	2	2	NUM
ejpam-4348	491	6	−	−	PROPN
ejpam-4348	491	7	x̃	x̃	PROPN
ejpam-4348	491	8	)	)	PUNCT
ejpam-4348	492	1	we	we	PRON
ejpam-4348	492	2	also	also	ADV
ejpam-4348	492	3	assume	assume	VERB
ejpam-4348	492	4	that	that	SCONJ
ejpam-4348	492	5	∥adb∥	∥adb∥	AUX
ejpam-4348	493	1	=	=	SYM
ejpam-4348	493	2	1	1	X
ejpam-4348	493	3	.	.	PUNCT
ejpam-4348	494	1	otherwise	otherwise	ADV
ejpam-4348	494	2	(	(	PUNCT
ejpam-4348	494	3	if	if	SCONJ
ejpam-4348	494	4	∥adb∥	∥adb∥	NOUN
ejpam-4348	494	5	=	=	NOUN
ejpam-4348	494	6	̸	̸	NUM
ejpam-4348	494	7	1	1	NUM
ejpam-4348	494	8	)	)	PUNCT
ejpam-4348	494	9	,	,	PUNCT
ejpam-4348	494	10	we	we	PRON
ejpam-4348	494	11	can	can	AUX
ejpam-4348	494	12	take	take	VERB
ejpam-4348	494	13	a1	a1	NOUN
ejpam-4348	494	14	db	db	NOUN
ejpam-4348	494	15	=	=	SYM
ejpam-4348	494	16	1	1	NUM
ejpam-4348	494	17	∥adb∥	∥adb∥	NOUN
ejpam-4348	494	18	adb	adb	NOUN
ejpam-4348	494	19	and	and	CCONJ
ejpam-4348	494	20	p̃1db	p̃1db	NOUN
ejpam-4348	494	21	=	=	SYM
ejpam-4348	494	22	1	1	NUM
ejpam-4348	494	23	∥adb∥	∥adb∥	NOUN
ejpam-4348	494	24	.	.	PUNCT
ejpam-4348	495	1	consider	consider	VERB
ejpam-4348	495	2	the	the	DET
ejpam-4348	495	3	numerical	numerical	ADJ
ejpam-4348	495	4	parameters	parameter	NOUN
ejpam-4348	495	5	αãd	αãd	VERB
ejpam-4348	495	6	and	and	CCONJ
ejpam-4348	495	7	αadb	αadb	PROPN
ejpam-4348	495	8	defined	define	VERB
ejpam-4348	495	9	by	by	ADP
ejpam-4348	495	10	αãd	αãd	PROPN
ejpam-4348	495	11	=	=	SYM
ejpam-4348	495	12	sup	sup	NUM
ejpam-4348	495	13	ℜ(λ̃d)=0	ℜ(λ̃d)=0	NUM
ejpam-4348	495	14	∥(λ̃di2n	∥(λ̃di2n	PRON
ejpam-4348	495	15	−	−	PROPN
ejpam-4348	495	16	ãd	ãd	NOUN
ejpam-4348	495	17	)	)	PUNCT
ejpam-4348	495	18	−1∥	−1∥	NOUN
ejpam-4348	495	19	and	and	CCONJ
ejpam-4348	495	20	αadb	αadb	NOUN
ejpam-4348	495	21	=	=	NOUN
ejpam-4348	496	1	sup	sup	NOUN
ejpam-4348	496	2	z∈γ̃d	z∈γ̃d	NOUN
ejpam-4348	496	3	∥(zin	∥(zin	PROPN
ejpam-4348	496	4	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	496	5	(	(	PUNCT
ejpam-4348	496	6	42	42	NUM
ejpam-4348	496	7	)	)	PUNCT
ejpam-4348	496	8	the	the	DET
ejpam-4348	496	9	following	follow	VERB
ejpam-4348	496	10	proposition	proposition	NOUN
ejpam-4348	496	11	gives	give	VERB
ejpam-4348	496	12	a	a	DET
ejpam-4348	496	13	relation	relation	NOUN
ejpam-4348	496	14	between	between	ADP
ejpam-4348	496	15	the	the	DET
ejpam-4348	496	16	parameters	parameter	NOUN
ejpam-4348	496	17	αãd	αãd	VERB
ejpam-4348	496	18	and	and	CCONJ
ejpam-4348	496	19	αadb	αadb	PROPN
ejpam-4348	496	20	.	.	PUNCT
ejpam-4348	497	1	proposition	proposition	NOUN
ejpam-4348	497	2	10	10	NUM
ejpam-4348	497	3	.	.	PUNCT
ejpam-4348	498	1	let	let	VERB
ejpam-4348	498	2	αãd	αãd	PRON
ejpam-4348	498	3	and	and	CCONJ
ejpam-4348	498	4	αadb	αadb	PROPN
ejpam-4348	498	5	be	be	AUX
ejpam-4348	498	6	the	the	DET
ejpam-4348	498	7	two	two	NUM
ejpam-4348	498	8	parameters	parameter	NOUN
ejpam-4348	498	9	defined	define	VERB
ejpam-4348	498	10	in	in	ADP
ejpam-4348	498	11	(	(	PUNCT
ejpam-4348	498	12	46	46	NUM
ejpam-4348	498	13	)	)	PUNCT
ejpam-4348	498	14	.	.	PUNCT
ejpam-4348	499	1	assume	assume	VERB
ejpam-4348	499	2	that	that	SCONJ
ejpam-4348	499	3	∥adb∥	∥adb∥	PUNCT
ejpam-4348	500	1	=	=	SYM
ejpam-4348	500	2	1	1	NUM
ejpam-4348	500	3	and	and	CCONJ
ejpam-4348	500	4	∣∣∣p	∣∣∣p	NOUN
ejpam-4348	500	5	2	2	NUM
ejpam-4348	500	6	−	−	NUM
ejpam-4348	501	1	d−	d−	PROPN
ejpam-4348	501	2	ipb	ipb	PROPN
ejpam-4348	501	3	∣∣∣	∣∣∣	NOUN
ejpam-4348	501	4	<	<	X
ejpam-4348	501	5	1	1	NUM
ejpam-4348	501	6	αdb	αdb	NOUN
ejpam-4348	501	7	(	(	PUNCT
ejpam-4348	501	8	43	43	NUM
ejpam-4348	501	9	)	)	PUNCT
ejpam-4348	501	10	then	then	ADV
ejpam-4348	501	11	αadb	αadb	PROPN
ejpam-4348	501	12	≤	≤	NUM
ejpam-4348	501	13	αãd	αãd	VERB
ejpam-4348	501	14	≤	≤	ADV
ejpam-4348	501	15	2	2	NUM
ejpam-4348	501	16	(	(	PUNCT
ejpam-4348	501	17	αadb	αadb	NOUN
ejpam-4348	501	18	+	+	CCONJ
ejpam-4348	501	19	√	√	PROPN
ejpam-4348	501	20	αadb	αadb	NOUN
ejpam-4348	501	21	(	(	PUNCT
ejpam-4348	501	22	√	√	PROPN
ejpam-4348	501	23	1	1	NUM
ejpam-4348	501	24	+	+	CCONJ
ejpam-4348	501	25	αadb	αadb	NOUN
ejpam-4348	501	26	+	+	NOUN
ejpam-4348	501	27	1	1	NUM
ejpam-4348	501	28	)	)	PUNCT
ejpam-4348	501	29	)	)	PUNCT
ejpam-4348	501	30	.	.	PUNCT
ejpam-4348	502	1	(	(	PUNCT
ejpam-4348	502	2	44	44	NUM
ejpam-4348	502	3	)	)	PUNCT
ejpam-4348	502	4	s.	s.	PROPN
ejpam-4348	502	5	traoré	traoré	PROPN
ejpam-4348	502	6	,	,	PUNCT
ejpam-4348	502	7	m.	m.	NOUN
ejpam-4348	502	8	dosso	dosso	PROPN
ejpam-4348	502	9	/	/	SYM
ejpam-4348	502	10	eur	eur	PROPN
ejpam-4348	502	11	.	.	PUNCT
ejpam-4348	503	1	j.	j.	PROPN
ejpam-4348	503	2	pure	pure	PROPN
ejpam-4348	503	3	appl	appl	PROPN
ejpam-4348	503	4	.	.	PROPN
ejpam-4348	503	5	math	math	PROPN
ejpam-4348	503	6	,	,	PUNCT
ejpam-4348	503	7	15	15	NUM
ejpam-4348	503	8	(	(	PUNCT
ejpam-4348	503	9	2	2	NUM
ejpam-4348	503	10	)	)	PUNCT
ejpam-4348	503	11	(	(	PUNCT
ejpam-4348	503	12	2022	2022	NUM
ejpam-4348	503	13	)	)	PUNCT
ejpam-4348	503	14	,	,	PUNCT
ejpam-4348	503	15	681	681	NUM
ejpam-4348	503	16	-	-	SYM
ejpam-4348	503	17	725	725	NUM
ejpam-4348	503	18	711	711	NUM
ejpam-4348	503	19	proof	proof	NOUN
ejpam-4348	503	20	.	.	PUNCT
ejpam-4348	504	1	let	let	VERB
ejpam-4348	504	2	the	the	DET
ejpam-4348	504	3	matrix	matrix	NOUN
ejpam-4348	504	4	(	(	PUNCT
ejpam-4348	504	5	λ̃i2n	λ̃i2n	NOUN
ejpam-4348	504	6	−	−	PROPN
ejpam-4348	504	7	ãd	ãd	NOUN
ejpam-4348	504	8	)	)	PUNCT
ejpam-4348	505	1	=	=	SYM
ejpam-4348	505	2			NOUN
ejpam-4348	506	1	(	(	PUNCT
ejpam-4348	507	1	λ̃d	λ̃d	X
ejpam-4348	508	1	+	+	NOUN
ejpam-4348	508	2	√	√	PROPN
ejpam-4348	509	1	p	p	X
ejpam-4348	509	2	2)in	2)in	NUM
ejpam-4348	509	3	−adb	−adb	NOUN
ejpam-4348	510	1	−in	−in	PROPN
ejpam-4348	510	2	(	(	PUNCT
ejpam-4348	510	3	λ̃d	λ̃d	X
ejpam-4348	511	1	+	+	NOUN
ejpam-4348	511	2	√	√	PROPN
ejpam-4348	511	3	p	p	X
ejpam-4348	511	4	2)in	2)in	PROPN
ejpam-4348	511	5			NOUN
ejpam-4348	511	6	we	we	PRON
ejpam-4348	511	7	have	have	AUX
ejpam-4348	511	8			NOUN
ejpam-4348	511	9	(	(	PUNCT
ejpam-4348	511	10	λ̃d	λ̃d	X
ejpam-4348	512	1	+	+	NOUN
ejpam-4348	512	2	√	√	PROPN
ejpam-4348	512	3	p	p	X
ejpam-4348	512	4	2)in	2)in	PROPN
ejpam-4348	512	5	adb	adb	NOUN
ejpam-4348	512	6	in	in	ADP
ejpam-4348	512	7	(	(	PUNCT
ejpam-4348	512	8	λ̃d	λ̃d	X
ejpam-4348	512	9	+	+	CCONJ
ejpam-4348	512	10	√	√	PROPN
ejpam-4348	512	11	p	p	PROPN
ejpam-4348	512	12	2)in	2)in	PROPN
ejpam-4348	512	13	!	!	PUNCT
ejpam-4348	512	14	×	×	NOUN
ejpam-4348	512	15			NOUN
ejpam-4348	512	16	(	(	PUNCT
ejpam-4348	512	17	λ̃d	λ̃d	X
ejpam-4348	513	1	+	+	NOUN
ejpam-4348	513	2	√	√	PROPN
ejpam-4348	514	1	p	p	X
ejpam-4348	514	2	2)in	2)in	NUM
ejpam-4348	514	3	−adb	−adb	NOUN
ejpam-4348	515	1	−in	−in	PROPN
ejpam-4348	515	2	(	(	PUNCT
ejpam-4348	515	3	λ̃d	λ̃d	X
ejpam-4348	516	1	+	+	NOUN
ejpam-4348	516	2	√	√	PROPN
ejpam-4348	517	1	p	p	X
ejpam-4348	517	2	2)in	2)in	PROPN
ejpam-4348	517	3			NOUN
ejpam-4348	517	4	=	=	PUNCT
ejpam-4348	517	5			NOUN
ejpam-4348	517	6	(	(	PUNCT
ejpam-4348	517	7	λ̃d	λ̃d	X
ejpam-4348	518	1	+	+	CCONJ
ejpam-4348	518	2	√	√	PROPN
ejpam-4348	518	3	p	p	NOUN
ejpam-4348	518	4	2	2	NUM
ejpam-4348	518	5	)	)	PUNCT
ejpam-4348	518	6	2	2	NUM
ejpam-4348	518	7	in	in	ADP
ejpam-4348	518	8	−adb	−adb	NOUN
ejpam-4348	518	9	0	0	NUM
ejpam-4348	518	10	0	0	NUM
ejpam-4348	518	11	(	(	PUNCT
ejpam-4348	518	12	λ̃d	λ̃d	X
ejpam-4348	519	1	+	+	CCONJ
ejpam-4348	519	2	√	√	PROPN
ejpam-4348	519	3	p	p	NOUN
ejpam-4348	519	4	2	2	NUM
ejpam-4348	519	5	)	)	PUNCT
ejpam-4348	519	6	2	2	NUM
ejpam-4348	519	7	in	in	ADP
ejpam-4348	519	8	−adb	−adb	NOUN
ejpam-4348	519	9			NOUN
ejpam-4348	519	10	with	with	ADP
ejpam-4348	519	11	(	(	PUNCT
ejpam-4348	519	12	λ̃di2n	λ̃di2n	NOUN
ejpam-4348	519	13	−	−	NOUN
ejpam-4348	519	14	ãd	ãd	NOUN
ejpam-4348	519	15	)	)	PUNCT
ejpam-4348	519	16	−1	−1	NOUN
ejpam-4348	519	17	=	=	NOUN
ejpam-4348	519	18			NOUN
ejpam-4348	519	19	(	(	PUNCT
ejpam-4348	519	20	λ̃d	λ̃d	X
ejpam-4348	520	1	+	+	CCONJ
ejpam-4348	520	2	√	√	PROPN
ejpam-4348	520	3	p	p	NOUN
ejpam-4348	520	4	2	2	NUM
ejpam-4348	520	5	)	)	PUNCT
ejpam-4348	520	6	2	2	NUM
ejpam-4348	520	7	in	in	ADP
ejpam-4348	520	8	−adb	−adb	NOUN
ejpam-4348	520	9	0	0	NUM
ejpam-4348	520	10	0	0	NUM
ejpam-4348	520	11	(	(	PUNCT
ejpam-4348	520	12	λ̃d	λ̃d	X
ejpam-4348	521	1	+	+	CCONJ
ejpam-4348	521	2	√	√	PROPN
ejpam-4348	521	3	p	p	NOUN
ejpam-4348	521	4	2	2	NUM
ejpam-4348	521	5	)	)	PUNCT
ejpam-4348	521	6	2	2	NUM
ejpam-4348	521	7	in	in	ADP
ejpam-4348	521	8	−adb	−adb	NOUN
ejpam-4348	521	9			ADJ
ejpam-4348	521	10	−1	−1	NOUN
ejpam-4348	521	11	×	×	NOUN
ejpam-4348	521	12			NOUN
ejpam-4348	521	13	(	(	PUNCT
ejpam-4348	521	14	λ̃d	λ̃d	X
ejpam-4348	522	1	+	+	NOUN
ejpam-4348	522	2	√	√	PROPN
ejpam-4348	522	3	p	p	X
ejpam-4348	522	4	2)in	2)in	PROPN
ejpam-4348	522	5	adb	adb	NOUN
ejpam-4348	522	6	in	in	ADP
ejpam-4348	522	7	(	(	PUNCT
ejpam-4348	522	8	λ̃d	λ̃d	X
ejpam-4348	522	9	+	+	NOUN
ejpam-4348	522	10	√	√	PROPN
ejpam-4348	522	11	p	p	X
ejpam-4348	522	12	2)in	2)in	PROPN
ejpam-4348	522	13			NOUN
ejpam-4348	522	14	=	=	PUNCT
ejpam-4348	522	15			NOUN
ejpam-4348	522	16	(	(	PUNCT
ejpam-4348	522	17	λ̃d	λ̃d	X
ejpam-4348	523	1	+	+	CCONJ
ejpam-4348	523	2	√	√	PROPN
ejpam-4348	523	3	p	p	NOUN
ejpam-4348	523	4	2	2	NUM
ejpam-4348	523	5	)	)	PUNCT
ejpam-4348	523	6	2	2	NUM
ejpam-4348	523	7	in	in	ADP
ejpam-4348	523	8	−	−	PROPN
ejpam-4348	523	9	(	(	PUNCT
ejpam-4348	523	10	a+	a+	X
ejpam-4348	523	11	(	(	PUNCT
ejpam-4348	523	12	p2	p2	PROPN
ejpam-4348	523	13	−	−	PROPN
ejpam-4348	523	14	d−	d−	PROPN
ejpam-4348	523	15	ipb)in	ipb)in	NOUN
ejpam-4348	523	16	)	)	PUNCT
ejpam-4348	523	17	0	0	NUM
ejpam-4348	523	18	0	0	NUM
ejpam-4348	523	19	(	(	PUNCT
ejpam-4348	523	20	λ̃d	λ̃d	X
ejpam-4348	524	1	+	+	CCONJ
ejpam-4348	524	2	√	√	PROPN
ejpam-4348	524	3	p	p	NOUN
ejpam-4348	524	4	2	2	NUM
ejpam-4348	524	5	)	)	PUNCT
ejpam-4348	524	6	2	2	NUM
ejpam-4348	524	7	in	in	ADP
ejpam-4348	524	8	−	−	PROPN
ejpam-4348	524	9	(	(	PUNCT
ejpam-4348	524	10	a+	a+	X
ejpam-4348	524	11	(	(	PUNCT
ejpam-4348	524	12	p2	p2	PROPN
ejpam-4348	524	13	−	−	PROPN
ejpam-4348	524	14	d−	d−	PROPN
ejpam-4348	524	15	ipb)in	ipb)in	NOUN
ejpam-4348	524	16	)	)	PUNCT
ejpam-4348	525	1			ADJ
ejpam-4348	525	2	−1	−1	NOUN
ejpam-4348	525	3	×	×	NOUN
ejpam-4348	525	4			NOUN
ejpam-4348	525	5	(	(	PUNCT
ejpam-4348	525	6	λ̃d	λ̃d	X
ejpam-4348	525	7	+	+	NOUN
ejpam-4348	525	8	√	√	PROPN
ejpam-4348	525	9	p	p	PROPN
ejpam-4348	525	10	2)in	2)in	PROPN
ejpam-4348	525	11	(	(	PUNCT
ejpam-4348	525	12	a+	a+	X
ejpam-4348	525	13	(	(	PUNCT
ejpam-4348	525	14	p2	p2	PROPN
ejpam-4348	525	15	−	−	PROPN
ejpam-4348	525	16	d−	d−	PROPN
ejpam-4348	525	17	ipb)in	ipb)in	NOUN
ejpam-4348	525	18	)	)	PUNCT
ejpam-4348	525	19	in	in	ADP
ejpam-4348	525	20	(	(	PUNCT
ejpam-4348	525	21	λ̃d	λ̃d	X
ejpam-4348	525	22	+	+	NOUN
ejpam-4348	525	23	√	√	PROPN
ejpam-4348	525	24	p	p	X
ejpam-4348	525	25	2)in	2)in	PROPN
ejpam-4348	525	26			NOUN
ejpam-4348	525	27	=	=	SYM
ejpam-4348	525	28			NOUN
ejpam-4348	525	29	(	(	PUNCT
ejpam-4348	525	30	(	(	PUNCT
ejpam-4348	525	31	λ̃d	λ̃d	X
ejpam-4348	525	32	+	+	NOUN
ejpam-4348	525	33	√	√	PROPN
ejpam-4348	525	34	p	p	NOUN
ejpam-4348	525	35	2	2	NUM
ejpam-4348	525	36	)	)	PUNCT
ejpam-4348	525	37	2	2	NUM
ejpam-4348	525	38	−	−	NOUN
ejpam-4348	525	39	p	p	NOUN
ejpam-4348	525	40	2	2	NUM
ejpam-4348	525	41	+	+	CCONJ
ejpam-4348	525	42	d−	d−	PROPN
ejpam-4348	525	43	ipb)in	ipb)in	ADJ
ejpam-4348	525	44	−a	−a	NOUN
ejpam-4348	525	45	0	0	NUM
ejpam-4348	525	46	0	0	PUNCT
ejpam-4348	526	1	(	(	PUNCT
ejpam-4348	526	2	(	(	PUNCT
ejpam-4348	526	3	λ̃d	λ̃d	X
ejpam-4348	526	4	+	+	NOUN
ejpam-4348	526	5	√	√	PROPN
ejpam-4348	526	6	p	p	NOUN
ejpam-4348	526	7	2	2	NUM
ejpam-4348	526	8	)	)	PUNCT
ejpam-4348	526	9	2	2	NUM
ejpam-4348	526	10	−	−	NOUN
ejpam-4348	526	11	p	p	NOUN
ejpam-4348	526	12	2	2	NUM
ejpam-4348	526	13	+	+	CCONJ
ejpam-4348	526	14	d−	d−	PROPN
ejpam-4348	526	15	ipb)in	ipb)in	ADJ
ejpam-4348	526	16	−a	−a	NOUN
ejpam-4348	526	17			ADJ
ejpam-4348	526	18	−1	−1	NOUN
ejpam-4348	526	19	×	×	NOUN
ejpam-4348	526	20	s.	s.	PROPN
ejpam-4348	526	21	traoré	traoré	PROPN
ejpam-4348	526	22	,	,	PUNCT
ejpam-4348	526	23	m.	m.	NOUN
ejpam-4348	526	24	dosso	dosso	PROPN
ejpam-4348	526	25	/	/	SYM
ejpam-4348	526	26	eur	eur	PROPN
ejpam-4348	526	27	.	.	PUNCT
ejpam-4348	527	1	j.	j.	PROPN
ejpam-4348	527	2	pure	pure	PROPN
ejpam-4348	527	3	appl	appl	PROPN
ejpam-4348	527	4	.	.	PROPN
ejpam-4348	527	5	math	math	PROPN
ejpam-4348	527	6	,	,	PUNCT
ejpam-4348	527	7	15	15	NUM
ejpam-4348	527	8	(	(	PUNCT
ejpam-4348	527	9	2	2	NUM
ejpam-4348	527	10	)	)	PUNCT
ejpam-4348	527	11	(	(	PUNCT
ejpam-4348	527	12	2022	2022	NUM
ejpam-4348	527	13	)	)	PUNCT
ejpam-4348	527	14	,	,	PUNCT
ejpam-4348	527	15	681	681	NUM
ejpam-4348	527	16	-	-	SYM
ejpam-4348	527	17	725	725	NUM
ejpam-4348	527	18	712	712	NOUN
ejpam-4348	527	19	(	(	PUNCT
ejpam-4348	527	20	λ̃d	λ̃d	X
ejpam-4348	527	21	+	+	NOUN
ejpam-4348	527	22	√	√	PROPN
ejpam-4348	527	23	p	p	X
ejpam-4348	527	24	2)in	2)in	PROPN
ejpam-4348	527	25	a+	a+	PUNCT
ejpam-4348	527	26	(	(	PUNCT
ejpam-4348	527	27	p2	p2	PROPN
ejpam-4348	527	28	−	−	PROPN
ejpam-4348	527	29	d−	d−	PROPN
ejpam-4348	527	30	ipb)in	ipb)in	NOUN
ejpam-4348	527	31	)	)	PUNCT
ejpam-4348	527	32	in	in	ADP
ejpam-4348	527	33	(	(	PUNCT
ejpam-4348	527	34	λ̃d	λ̃d	X
ejpam-4348	527	35	+	+	NOUN
ejpam-4348	527	36	√	√	PROPN
ejpam-4348	527	37	p	p	X
ejpam-4348	527	38	2)in	2)in	PROPN
ejpam-4348	527	39			NOUN
ejpam-4348	527	40	=	=	SYM
ejpam-4348	527	41	(zin	(zin	NOUN
ejpam-4348	527	42	−a)−1	−a)−1	NOUN
ejpam-4348	527	43	0	0	NUM
ejpam-4348	527	44	0	0	NUM
ejpam-4348	527	45	(	(	PUNCT
ejpam-4348	527	46	zin	zin	NOUN
ejpam-4348	527	47	−a)−1	−a)−1	NOUN
ejpam-4348	527	48	×	×	NOUN
ejpam-4348	527	49			NOUN
ejpam-4348	527	50	√	√	NOUN
ejpam-4348	527	51	z	z	NOUN
ejpam-4348	528	1	+	+	CCONJ
ejpam-4348	528	2	p	p	X
ejpam-4348	528	3	2	2	NUM
ejpam-4348	528	4	−	−	NUM
ejpam-4348	528	5	d−	d−	PROPN
ejpam-4348	528	6	ipbin	ipbin	NOUN
ejpam-4348	528	7	a+	a+	PUNCT
ejpam-4348	528	8	(	(	PUNCT
ejpam-4348	528	9	p2	p2	PROPN
ejpam-4348	528	10	−	−	NOUN
ejpam-4348	528	11	d−	d−	PROPN
ejpam-4348	528	12	ipb)in	ipb)in	NOUN
ejpam-4348	528	13	in	in	ADP
ejpam-4348	528	14	√	√	PROPN
ejpam-4348	528	15	z	z	NOUN
ejpam-4348	529	1	+	+	CCONJ
ejpam-4348	529	2	p	p	NOUN
ejpam-4348	529	3	2	2	NUM
ejpam-4348	529	4	−	−	ADP
ejpam-4348	529	5	d−	d−	PROPN
ejpam-4348	529	6	ipbin	ipbin	NOUN
ejpam-4348	529	7			NOUN
ejpam-4348	529	8	=	=	PUNCT
ejpam-4348	529	9			NOUN
ejpam-4348	529	10	√	√	NOUN
ejpam-4348	529	11	z	z	NOUN
ejpam-4348	530	1	+	+	CCONJ
ejpam-4348	531	1	p	p	X
ejpam-4348	531	2	2	2	NUM
ejpam-4348	531	3	−	−	ADP
ejpam-4348	531	4	d−	d−	PROPN
ejpam-4348	531	5	ipb(zin	ipb(zin	NOUN
ejpam-4348	531	6	−a)−1	−a)−1	NOUN
ejpam-4348	531	7	(	(	PUNCT
ejpam-4348	531	8	zin	zin	NOUN
ejpam-4348	531	9	−a)−1(a+	−a)−1(a+	PROPN
ejpam-4348	531	10	(	(	PUNCT
ejpam-4348	531	11	p2	p2	PROPN
ejpam-4348	531	12	−	−	PROPN
ejpam-4348	531	13	d−	d−	PROPN
ejpam-4348	531	14	ipb)in	ipb)in	NOUN
ejpam-4348	531	15	)	)	PUNCT
ejpam-4348	531	16	(	(	PUNCT
ejpam-4348	531	17	zin	zin	NOUN
ejpam-4348	531	18	−a)−1	−a)−1	NOUN
ejpam-4348	532	1	√	√	NOUN
ejpam-4348	532	2	z	z	NOUN
ejpam-4348	533	1	+	+	NOUN
ejpam-4348	533	2	p	p	X
ejpam-4348	533	3	2	2	NUM
ejpam-4348	533	4	−	−	ADP
ejpam-4348	533	5	d−	d−	PROPN
ejpam-4348	533	6	ipb(zin	ipb(zin	NOUN
ejpam-4348	533	7	−a)−1	−a)−1	NOUN
ejpam-4348	533	8			NOUN
ejpam-4348	533	9	knowing	know	VERB
ejpam-4348	533	10	that	that	SCONJ
ejpam-4348	533	11	the	the	DET
ejpam-4348	533	12	norm	norm	NOUN
ejpam-4348	533	13	of	of	ADP
ejpam-4348	533	14	(	(	PUNCT
ejpam-4348	533	15	λ̃di2n−ãd	λ̃di2n−ãd	NOUN
ejpam-4348	533	16	)	)	PUNCT
ejpam-4348	533	17	−1	−1	NOUN
ejpam-4348	533	18	is	be	AUX
ejpam-4348	533	19	greater	great	ADJ
ejpam-4348	533	20	than	than	ADP
ejpam-4348	533	21	or	or	CCONJ
ejpam-4348	533	22	equal	equal	ADJ
ejpam-4348	533	23	to	to	ADP
ejpam-4348	533	24	the	the	DET
ejpam-4348	533	25	norm	norm	NOUN
ejpam-4348	533	26	of	of	ADP
ejpam-4348	533	27	each	each	PRON
ejpam-4348	533	28	of	of	ADP
ejpam-4348	533	29	its	its	PRON
ejpam-4348	533	30	block	block	NOUN
ejpam-4348	533	31	components	component	NOUN
ejpam-4348	533	32	taken	take	VERB
ejpam-4348	533	33	individually	individually	ADV
ejpam-4348	533	34	,	,	PUNCT
ejpam-4348	533	35	we	we	PRON
ejpam-4348	533	36	can	can	AUX
ejpam-4348	533	37	deduce	deduce	VERB
ejpam-4348	533	38	that	that	PRON
ejpam-4348	533	39	αãd	αãd	VERB
ejpam-4348	534	1	=	=	SYM
ejpam-4348	534	2	sup	sup	NUM
ejpam-4348	534	3	ℜ(λ̃d)=0	ℜ(λ̃d)=0	NUM
ejpam-4348	534	4	∥(λ̃di2n	∥(λ̃di2n	PRON
ejpam-4348	534	5	−	−	PROPN
ejpam-4348	534	6	ãd	ãd	NOUN
ejpam-4348	534	7	)	)	PUNCT
ejpam-4348	534	8	−1∥	−1∥	NOUN
ejpam-4348	534	9	≥	≥	NOUN
ejpam-4348	534	10	sup	sup	NOUN
ejpam-4348	534	11	z∈γ̃d	z∈γ̃d	X
ejpam-4348	534	12	∥(zin	∥(zin	PROPN
ejpam-4348	534	13	−a)−1∥	−a)−1∥	INTJ
ejpam-4348	534	14	=	=	SYM
ejpam-4348	534	15	αadb	αadb	NOUN
ejpam-4348	534	16	and	and	CCONJ
ejpam-4348	534	17	also	also	ADV
ejpam-4348	534	18	∥∥∥(λ̃di2n	∥∥∥(λ̃di2n	PROPN
ejpam-4348	534	19	−	−	PROPN
ejpam-4348	534	20	ãd	ãd	NOUN
ejpam-4348	534	21	)	)	PUNCT
ejpam-4348	534	22	−1	−1	NOUN
ejpam-4348	534	23	∥∥∥	∥∥∥	PROPN
ejpam-4348	534	24	≤	≤	NUM
ejpam-4348	534	25	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	535	1			NOUN
ejpam-4348	535	2	√	√	PUNCT
ejpam-4348	535	3	z	z	NOUN
ejpam-4348	536	1	+	+	NOUN
ejpam-4348	536	2	p	p	NOUN
ejpam-4348	536	3	2	2	NUM
ejpam-4348	536	4	−	−	NUM
ejpam-4348	536	5	d−	d−	PROPN
ejpam-4348	536	6	ipbin	ipbin	NOUN
ejpam-4348	536	7	a+	a+	PUNCT
ejpam-4348	536	8	(	(	PUNCT
ejpam-4348	536	9	p2	p2	PROPN
ejpam-4348	536	10	−	−	NOUN
ejpam-4348	536	11	d−	d−	PROPN
ejpam-4348	536	12	ipb)in	ipb)in	NOUN
ejpam-4348	536	13	in	in	ADP
ejpam-4348	536	14	√	√	PROPN
ejpam-4348	536	15	z	z	NOUN
ejpam-4348	537	1	+	+	CCONJ
ejpam-4348	537	2	p	p	NOUN
ejpam-4348	537	3	2	2	NUM
ejpam-4348	537	4	−	−	NUM
ejpam-4348	537	5	d−	d−	PROPN
ejpam-4348	537	6	ipbin	ipbin	ADJ
ejpam-4348	537	7			NOUN
ejpam-4348	537	8	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	538	1	∥∥(zin	∥∥(zin	ADP
ejpam-4348	538	2	−a)−1	−a)−1	X
ejpam-4348	538	3	∥∥	∥∥	PROPN
ejpam-4348	538	4	≤	≤	PROPN
ejpam-4348	538	5	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	539	1			PROPN
ejpam-4348	539	2	∥	∥	PUNCT
ejpam-4348	539	3	√	√	PUNCT
ejpam-4348	539	4	z	z	NOUN
ejpam-4348	540	1	+	+	CCONJ
ejpam-4348	541	1	p	p	NOUN
ejpam-4348	541	2	2	2	NUM
ejpam-4348	541	3	−	−	ADP
ejpam-4348	541	4	d−	d−	PROPN
ejpam-4348	541	5	ipbin∥	ipbin∥	PROPN
ejpam-4348	541	6	∥a+	∥a+	PROPN
ejpam-4348	541	7	(	(	PUNCT
ejpam-4348	541	8	p2	p2	PROPN
ejpam-4348	541	9	−	−	PROPN
ejpam-4348	541	10	d−	d−	PROPN
ejpam-4348	541	11	ipb)in∥	ipb)in∥	PROPN
ejpam-4348	541	12	∥in∥	∥in∥	X
ejpam-4348	541	13	∥	∥	PRON
ejpam-4348	541	14	√	√	VERB
ejpam-4348	541	15	z	z	NOUN
ejpam-4348	542	1	+	+	CCONJ
ejpam-4348	542	2	p	p	NOUN
ejpam-4348	542	3	2	2	NUM
ejpam-4348	542	4	−	−	ADP
ejpam-4348	542	5	d−	d−	PROPN
ejpam-4348	542	6	ipbin∥	ipbin∥	PROPN
ejpam-4348	542	7			NOUN
ejpam-4348	542	8	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	542	9	∥∥(zin	∥∥(zin	ADP
ejpam-4348	542	10	−a)−1	−a)−1	X
ejpam-4348	542	11	∥∥	∥∥	PROPN
ejpam-4348	542	12	≤	≤	PROPN
ejpam-4348	542	13	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	PROPN
ejpam-4348	542	14			NOUN
ejpam-4348	542	15	√	√	PROPN
ejpam-4348	542	16	|z|+	|z|+	PROPN
ejpam-4348	542	17	√	√	NUM
ejpam-4348	542	18	|p2	|p2	NOUN
ejpam-4348	542	19	−	−	ADP
ejpam-4348	542	20	d−	d−	PROPN
ejpam-4348	542	21	ipb|	ipb|	ADJ
ejpam-4348	542	22	1	1	NUM
ejpam-4348	542	23	1	1	NUM
ejpam-4348	542	24	√	√	NOUN
ejpam-4348	542	25	|z|+	|z|+	NOUN
ejpam-4348	542	26	√	√	NUM
ejpam-4348	542	27	|p2	|p2	NOUN
ejpam-4348	542	28	−	−	ADP
ejpam-4348	542	29	d−	d−	PROPN
ejpam-4348	542	30	ipb|	ipb|	ADJ
ejpam-4348	542	31			NOUN
ejpam-4348	542	32	∥∥∥∥∥∥∥∥	∥∥∥∥∥∥∥∥	NUM
ejpam-4348	542	33	∥∥(zin	∥∥(zin	ADP
ejpam-4348	542	34	−a)−1	−a)−1	X
ejpam-4348	542	35	∥∥	∥∥	PUNCT
ejpam-4348	542	36	≤	≤	X
ejpam-4348	542	37	(	(	PUNCT
ejpam-4348	542	38	√	√	ADP
ejpam-4348	542	39	|z|+	|z|+	VERB
ejpam-4348	542	40	√	√	NUM
ejpam-4348	542	41	|p	|p	NOUN
ejpam-4348	542	42	2	2	NUM
ejpam-4348	542	43	−	−	NUM
ejpam-4348	542	44	d−	d−	PROPN
ejpam-4348	542	45	ipb|+	ipb|+	NOUN
ejpam-4348	542	46	1	1	NUM
ejpam-4348	542	47	)	)	PUNCT
ejpam-4348	542	48	∥∥(zin	∥∥(zin	ADP
ejpam-4348	542	49	−a)−1	−a)−1	NOUN
ejpam-4348	542	50	∥∥	∥∥	X
ejpam-4348	542	51	s.	s.	PROPN
ejpam-4348	542	52	traoré	traoré	PROPN
ejpam-4348	542	53	,	,	PUNCT
ejpam-4348	542	54	m.	m.	NOUN
ejpam-4348	542	55	dosso	dosso	PROPN
ejpam-4348	542	56	/	/	SYM
ejpam-4348	542	57	eur	eur	PROPN
ejpam-4348	542	58	.	.	PUNCT
ejpam-4348	543	1	j.	j.	PROPN
ejpam-4348	543	2	pure	pure	PROPN
ejpam-4348	543	3	appl	appl	PROPN
ejpam-4348	543	4	.	.	PROPN
ejpam-4348	543	5	math	math	PROPN
ejpam-4348	543	6	,	,	PUNCT
ejpam-4348	543	7	15	15	NUM
ejpam-4348	543	8	(	(	PUNCT
ejpam-4348	543	9	2	2	NUM
ejpam-4348	543	10	)	)	PUNCT
ejpam-4348	543	11	(	(	PUNCT
ejpam-4348	543	12	2022	2022	NUM
ejpam-4348	543	13	)	)	PUNCT
ejpam-4348	543	14	,	,	PUNCT
ejpam-4348	543	15	681	681	NUM
ejpam-4348	543	16	-	-	SYM
ejpam-4348	543	17	725	725	NUM
ejpam-4348	543	18	713	713	NUM
ejpam-4348	543	19	•	•	NOUN
ejpam-4348	543	20	if	if	SCONJ
ejpam-4348	543	21	|z|	|z|	NOUN
ejpam-4348	543	22	≤	≤	NUM
ejpam-4348	543	23	αadb	αadb	NOUN
ejpam-4348	543	24	+	+	CCONJ
ejpam-4348	543	25	1	1	NUM
ejpam-4348	543	26	αadb	αadb	NOUN
ejpam-4348	543	27	then	then	ADV
ejpam-4348	543	28	∥(λi2n	∥(λi2n	VERB
ejpam-4348	543	29	−	−	PROPN
ejpam-4348	543	30	ãd	ãd	NOUN
ejpam-4348	543	31	)	)	PUNCT
ejpam-4348	543	32	−1∥	−1∥	VERB
ejpam-4348	543	33	≤	≤	NUM
ejpam-4348	543	34	αadb	αadb	NOUN
ejpam-4348	543	35	(	(	PUNCT
ejpam-4348	543	36	√	√	ADP
ejpam-4348	543	37	|z|+	|z|+	VERB
ejpam-4348	543	38	√	√	NUM
ejpam-4348	543	39	|p	|p	NOUN
ejpam-4348	543	40	2	2	NUM
ejpam-4348	543	41	−	−	NUM
ejpam-4348	543	42	d−	d−	PROPN
ejpam-4348	543	43	ipb|+	ipb|+	NOUN
ejpam-4348	543	44	1	1	NUM
ejpam-4348	543	45	)	)	PUNCT
ejpam-4348	543	46	≤	≤	NOUN
ejpam-4348	543	47	αadb	αadb	NOUN
ejpam-4348	543	48	(	(	PUNCT
ejpam-4348	543	49	√	√	PROPN
ejpam-4348	543	50	αadb	αadb	NOUN
ejpam-4348	543	51	+	+	CCONJ
ejpam-4348	543	52	1	1	NUM
ejpam-4348	543	53	αadb	αadb	NOUN
ejpam-4348	544	1	+	+	CCONJ
ejpam-4348	544	2	1√	1√	ADJ
ejpam-4348	544	3	α	α	NOUN
ejpam-4348	544	4	+	+	CCONJ
ejpam-4348	544	5	1	1	NUM
ejpam-4348	544	6	)	)	PUNCT
ejpam-4348	544	7	≤	≤	NOUN
ejpam-4348	544	8	αadb	αadb	NOUN
ejpam-4348	544	9	+	+	CCONJ
ejpam-4348	544	10	√	√	NUM
ejpam-4348	544	11	αdb	αdb	NOUN
ejpam-4348	544	12	(	(	PUNCT
ejpam-4348	544	13	√	√	NUM
ejpam-4348	544	14	αdb	αdb	NOUN
ejpam-4348	544	15	+	+	CCONJ
ejpam-4348	544	16	1	1	NUM
ejpam-4348	544	17	+	+	NUM
ejpam-4348	544	18	1	1	NUM
ejpam-4348	544	19	)	)	PUNCT
ejpam-4348	544	20	•	•	NOUN
ejpam-4348	544	21	if	if	SCONJ
ejpam-4348	544	22	|z|	|z|	NOUN
ejpam-4348	544	23	>	>	X
ejpam-4348	544	24	αadb	αadb	NOUN
ejpam-4348	544	25	+	+	CCONJ
ejpam-4348	544	26	1	1	NUM
ejpam-4348	544	27	αadb	αadb	NOUN
ejpam-4348	544	28	with	with	ADP
ejpam-4348	544	29	the	the	DET
ejpam-4348	544	30	conditions	condition	NOUN
ejpam-4348	544	31	(	(	PUNCT
ejpam-4348	544	32	43	43	NUM
ejpam-4348	544	33	)	)	PUNCT
ejpam-4348	544	34	we	we	PRON
ejpam-4348	544	35	have	have	VERB
ejpam-4348	544	36	∥∥∥∥az	∥∥∥∥az	PROPN
ejpam-4348	544	37	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-4348	544	38	<	<	X
ejpam-4348	544	39	1	1	X
ejpam-4348	544	40	.	.	X
ejpam-4348	545	1	we	we	PRON
ejpam-4348	545	2	note	note	VERB
ejpam-4348	545	3	that	that	SCONJ
ejpam-4348	545	4	∥∥∥∥az	∥∥∥∥az	PROPN
ejpam-4348	545	5	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-4348	545	6	<	<	X
ejpam-4348	545	7	αdb	αdb	NOUN
ejpam-4348	545	8	αdb	αdb	NOUN
ejpam-4348	545	9	+	+	CCONJ
ejpam-4348	545	10	1	1	NUM
ejpam-4348	545	11	(	(	PUNCT
ejpam-4348	545	12	∥adb∥+	∥adb∥+	NUM
ejpam-4348	545	13	|p	|p	VERB
ejpam-4348	545	14	2	2	NUM
ejpam-4348	545	15	−	−	NUM
ejpam-4348	545	16	d−	d−	PROPN
ejpam-4348	545	17	ipb|	ipb|	ADJ
ejpam-4348	545	18	)	)	PUNCT
ejpam-4348	545	19	<	<	X
ejpam-4348	545	20	αdb	αdb	NOUN
ejpam-4348	545	21	αdb	αdb	NOUN
ejpam-4348	545	22	+	+	CCONJ
ejpam-4348	545	23	1	1	NUM
ejpam-4348	545	24	(	(	PUNCT
ejpam-4348	545	25	1	1	NUM
ejpam-4348	545	26	+	+	SYM
ejpam-4348	545	27	1	1	NUM
ejpam-4348	545	28	αdb	αdb	NOUN
ejpam-4348	545	29	)	)	PUNCT
ejpam-4348	545	30	<	<	X
ejpam-4348	545	31	1	1	NUM
ejpam-4348	545	32	which	which	PRON
ejpam-4348	545	33	leads	lead	VERB
ejpam-4348	545	34	to	to	ADP
ejpam-4348	545	35	(	(	PUNCT
ejpam-4348	545	36	zin	zin	NOUN
ejpam-4348	545	37	−a)−1	−a)−1	NOUN
ejpam-4348	545	38	=	=	SYM
ejpam-4348	545	39	1	1	NUM
ejpam-4348	545	40	z	z	NOUN
ejpam-4348	545	41	(	(	PUNCT
ejpam-4348	545	42	in	in	ADP
ejpam-4348	545	43	−	−	PROPN
ejpam-4348	545	44	a	a	DET
ejpam-4348	545	45	z	z	NOUN
ejpam-4348	545	46	)	)	PUNCT
ejpam-4348	545	47	−1	−1	NOUN
ejpam-4348	545	48	=	=	SYM
ejpam-4348	545	49	1	1	NUM
ejpam-4348	545	50	z	z	NOUN
ejpam-4348	545	51	(	(	PUNCT
ejpam-4348	545	52	in	in	ADP
ejpam-4348	545	53	+	+	CCONJ
ejpam-4348	545	54	+	+	ADP
ejpam-4348	545	55	∞∑	∞∑	NUM
ejpam-4348	545	56	k=1	k=1	PROPN
ejpam-4348	545	57	ak	ak	PROPN
ejpam-4348	545	58	zk	zk	PROPN
ejpam-4348	545	59	)	)	PUNCT
ejpam-4348	546	1	=	=	PUNCT
ejpam-4348	546	2	1	1	NUM
ejpam-4348	546	3	z	z	NOUN
ejpam-4348	546	4	(	(	PUNCT
ejpam-4348	546	5	in	in	ADP
ejpam-4348	546	6	+	+	CCONJ
ejpam-4348	546	7	a	a	DET
ejpam-4348	546	8	z	z	NOUN
ejpam-4348	547	1	+	+	NOUN
ejpam-4348	547	2	∞∑	∞∑	PROPN
ejpam-4348	547	3	m=0	m=0	PROPN
ejpam-4348	547	4	am	be	AUX
ejpam-4348	547	5	zm	zm	PROPN
ejpam-4348	547	6	)	)	PUNCT
ejpam-4348	548	1	=	=	PUNCT
ejpam-4348	549	1	1	1	NUM
ejpam-4348	549	2	z	z	NOUN
ejpam-4348	549	3	(	(	PUNCT
ejpam-4348	549	4	in	in	ADP
ejpam-4348	549	5	+	+	CCONJ
ejpam-4348	549	6	a	a	DET
ejpam-4348	549	7	z	z	NOUN
ejpam-4348	549	8	(	(	PUNCT
ejpam-4348	549	9	in	in	ADP
ejpam-4348	549	10	−	−	PROPN
ejpam-4348	549	11	a	a	DET
ejpam-4348	549	12	z	z	NOUN
ejpam-4348	549	13	)	)	PUNCT
ejpam-4348	549	14	−1	−1	NOUN
ejpam-4348	549	15	)	)	PUNCT
ejpam-4348	549	16	consequently	consequently	ADV
ejpam-4348	549	17	∥(λ̃di2n	∥(λ̃di2n	PRON
ejpam-4348	550	1	−	−	PROPN
ejpam-4348	550	2	ãd	ãd	NOUN
ejpam-4348	550	3	)	)	PUNCT
ejpam-4348	550	4	−1∥	−1∥	NOUN
ejpam-4348	550	5	≤	≤	NUM
ejpam-4348	550	6	∥∥∥∥1z	∥∥∥∥1z	VERB
ejpam-4348	550	7	in	in	ADP
ejpam-4348	550	8	+	+	NUM
ejpam-4348	550	9	1	1	NUM
ejpam-4348	550	10	z	z	NOUN
ejpam-4348	550	11	a	a	PRON
ejpam-4348	550	12	(	(	PUNCT
ejpam-4348	550	13	zin	zin	NOUN
ejpam-4348	550	14	−a)−1	−a)−1	NOUN
ejpam-4348	550	15	∥∥∥∥×	∥∥∥∥×	X
ejpam-4348	550	16	∥∥∥∥1	∥∥∥∥1	NOUN
ejpam-4348	550	17	+	+	NOUN
ejpam-4348	550	18	√|z|+	√|z|+	ADJ
ejpam-4348	550	19	√∣∣∣p	√∣∣∣p	ADP
ejpam-4348	550	20	2	2	NUM
ejpam-4348	550	21	−	−	NUM
ejpam-4348	550	22	d−	d−	PROPN
ejpam-4348	550	23	ipb	ipb	PROPN
ejpam-4348	550	24	∣∣∣∥∥∥∥	∣∣∣∥∥∥∥	PROPN
ejpam-4348	550	25	≤	≤	PROPN
ejpam-4348	550	26	(	(	PUNCT
ejpam-4348	550	27	∥a(zin	∥a(zin	NOUN
ejpam-4348	550	28	−a)−1∥+	−a)−1∥+	NOUN
ejpam-4348	550	29	1	1	NUM
ejpam-4348	550	30	)	)	PUNCT
ejpam-4348	550	31	1	1	NUM
ejpam-4348	550	32	+	+	CCONJ
ejpam-4348	550	33	√	√	NOUN
ejpam-4348	550	34	|z|+	|z|+	NOUN
ejpam-4348	550	35	√∣∣p	√∣∣p	PROPN
ejpam-4348	550	36	2	2	NUM
ejpam-4348	550	37	−	−	PROPN
ejpam-4348	550	38	d−	d−	PROPN
ejpam-4348	550	39	ipb	ipb	PROPN
ejpam-4348	550	40	∣∣	∣∣	NUM
ejpam-4348	550	41	|z|	|z|	VERB
ejpam-4348	550	42	s.	s.	PROPN
ejpam-4348	550	43	traoré	traoré	PROPN
ejpam-4348	550	44	,	,	PUNCT
ejpam-4348	550	45	m.	m.	NOUN
ejpam-4348	550	46	dosso	dosso	PROPN
ejpam-4348	550	47	/	/	SYM
ejpam-4348	550	48	eur	eur	PROPN
ejpam-4348	550	49	.	.	PUNCT
ejpam-4348	551	1	j.	j.	PROPN
ejpam-4348	551	2	pure	pure	PROPN
ejpam-4348	551	3	appl	appl	PROPN
ejpam-4348	551	4	.	.	PROPN
ejpam-4348	551	5	math	math	PROPN
ejpam-4348	551	6	,	,	PUNCT
ejpam-4348	551	7	15	15	NUM
ejpam-4348	551	8	(	(	PUNCT
ejpam-4348	551	9	2	2	NUM
ejpam-4348	551	10	)	)	PUNCT
ejpam-4348	551	11	(	(	PUNCT
ejpam-4348	551	12	2022	2022	NUM
ejpam-4348	551	13	)	)	PUNCT
ejpam-4348	551	14	,	,	PUNCT
ejpam-4348	551	15	681	681	NUM
ejpam-4348	551	16	-	-	SYM
ejpam-4348	551	17	725	725	NUM
ejpam-4348	551	18	714	714	NUM
ejpam-4348	551	19	≤	≤	NOUN
ejpam-4348	551	20	(	(	PUNCT
ejpam-4348	551	21	(	(	PUNCT
ejpam-4348	551	22	1	1	NUM
ejpam-4348	551	23	+	+	NUM
ejpam-4348	551	24	|p	|p	VERB
ejpam-4348	551	25	2	2	NUM
ejpam-4348	551	26	−	−	NOUN
ejpam-4348	551	27	p−	p−	NOUN
ejpam-4348	551	28	ipb|	ipb|	ADJ
ejpam-4348	551	29	)	)	PUNCT
ejpam-4348	552	1	αadb	αadb	NOUN
ejpam-4348	553	1	+	+	CCONJ
ejpam-4348	553	2	1	1	X
ejpam-4348	553	3	)	)	PUNCT
ejpam-4348	553	4			PROPN
ejpam-4348	553	5	1√	1√	NOUN
ejpam-4348	553	6	|z|	|z|	NOUN
ejpam-4348	553	7	+	+	CCONJ
ejpam-4348	553	8	1	1	NUM
ejpam-4348	553	9	|z|	|z|	NOUN
ejpam-4348	553	10	+	+	CCONJ
ejpam-4348	553	11	√	√	PROPN
ejpam-4348	553	12	|p2	|p2	NOUN
ejpam-4348	553	13	−	−	ADP
ejpam-4348	553	14	d−	d−	PROPN
ejpam-4348	553	15	ipb|	ipb|	ADJ
ejpam-4348	553	16	|z|	|z|	NOUN
ejpam-4348	553	17			PROPN
ejpam-4348	553	18	≤	≤	NUM
ejpam-4348	553	19	(	(	PUNCT
ejpam-4348	553	20	(	(	PUNCT
ejpam-4348	553	21	1	1	NUM
ejpam-4348	553	22	+	+	SYM
ejpam-4348	553	23	1	1	NUM
ejpam-4348	553	24	αadb	αadb	NOUN
ejpam-4348	553	25	)	)	PUNCT
ejpam-4348	554	1	+	+	CCONJ
ejpam-4348	554	2	1	1	X
ejpam-4348	554	3	)	)	PUNCT
ejpam-4348	554	4	(	(	PUNCT
ejpam-4348	554	5	√	√	NUM
ejpam-4348	554	6	αadb√	αadb√	PROPN
ejpam-4348	554	7	αadb	αadb	NOUN
ejpam-4348	554	8	+	+	CCONJ
ejpam-4348	554	9	1	1	NUM
ejpam-4348	554	10	+	+	NUM
ejpam-4348	554	11	αadb	αadb	ADJ
ejpam-4348	554	12	αadb	αadb	NOUN
ejpam-4348	555	1	+	+	CCONJ
ejpam-4348	555	2	1	1	NUM
ejpam-4348	555	3	+	+	CCONJ
ejpam-4348	555	4	√	√	NUM
ejpam-4348	555	5	αadb	αadb	NOUN
ejpam-4348	555	6	αadb+1	αadb+1	PROPN
ejpam-4348	555	7	)	)	PUNCT
ejpam-4348	556	1	≤	≤	NUM
ejpam-4348	556	2	(	(	PUNCT
ejpam-4348	556	3	αadb	αadb	NOUN
ejpam-4348	556	4	+	+	CCONJ
ejpam-4348	556	5	2	2	NUM
ejpam-4348	556	6	αadb	αadb	NOUN
ejpam-4348	556	7	+	+	X
ejpam-4348	556	8	1	1	NUM
ejpam-4348	556	9	)	)	PUNCT
ejpam-4348	556	10	(	(	PUNCT
ejpam-4348	556	11	√	√	NUM
ejpam-4348	556	12	αadb	αadb	NOUN
ejpam-4348	556	13	√	√	PROPN
ejpam-4348	556	14	αadb	αadb	NOUN
ejpam-4348	556	15	+	+	CCONJ
ejpam-4348	556	16	1	1	NUM
ejpam-4348	556	17	+	+	CCONJ
ejpam-4348	556	18	√	√	NOUN
ejpam-4348	556	19	αadb	αadb	NOUN
ejpam-4348	556	20	+	+	CCONJ
ejpam-4348	556	21	αdb	αdb	NOUN
ejpam-4348	556	22	)	)	PUNCT
ejpam-4348	556	23	≤	≤	NOUN
ejpam-4348	556	24	2	2	NUM
ejpam-4348	556	25	(	(	PUNCT
ejpam-4348	556	26	αadb	αadb	NOUN
ejpam-4348	556	27	+	+	CCONJ
ejpam-4348	556	28	√	√	PROPN
ejpam-4348	556	29	αadb	αadb	NOUN
ejpam-4348	556	30	(	(	PUNCT
ejpam-4348	556	31	√	√	PROPN
ejpam-4348	556	32	αadb+1	αadb+1	NOUN
ejpam-4348	556	33	+	+	CCONJ
ejpam-4348	556	34	1	1	NUM
ejpam-4348	556	35	)	)	PUNCT
ejpam-4348	556	36	)	)	PUNCT
ejpam-4348	557	1	finally	finally	ADV
ejpam-4348	557	2	αadb	αadb	VERB
ejpam-4348	557	3	≤	≤	NUM
ejpam-4348	557	4	αadb	αadb	NOUN
ejpam-4348	557	5	≤	≤	ADJ
ejpam-4348	557	6	2	2	NUM
ejpam-4348	557	7	(	(	PUNCT
ejpam-4348	557	8	αadb	αadb	NOUN
ejpam-4348	557	9	+	+	CCONJ
ejpam-4348	557	10	√	√	PROPN
ejpam-4348	557	11	αadb	αadb	NOUN
ejpam-4348	557	12	(	(	PUNCT
ejpam-4348	557	13	√	√	PROPN
ejpam-4348	557	14	αadb+1	αadb+1	NOUN
ejpam-4348	557	15	+	+	CCONJ
ejpam-4348	557	16	1	1	NUM
ejpam-4348	557	17	)	)	PUNCT
ejpam-4348	557	18	)	)	PUNCT
ejpam-4348	557	19	.	.	PUNCT
ejpam-4348	558	1	consider	consider	VERB
ejpam-4348	558	2	the	the	DET
ejpam-4348	558	3	projector	projector	NOUN
ejpam-4348	558	4	•	•	NOUN
ejpam-4348	558	5	p̃d	p̃d	NOUN
ejpam-4348	558	6	∈	∈	PROPN
ejpam-4348	558	7	cn×n	cn×n	PROPN
ejpam-4348	558	8	on	on	ADP
ejpam-4348	558	9	right	right	ADJ
ejpam-4348	558	10	eigenspace	eigenspace	NOUN
ejpam-4348	558	11	of	of	ADP
ejpam-4348	558	12	adb	adb	PROPN
ejpam-4348	558	13	associated	associate	VERB
ejpam-4348	558	14	with	with	ADP
ejpam-4348	558	15	eigenvalues	eigenvalue	NOUN
ejpam-4348	558	16	outside	outside	ADP
ejpam-4348	558	17	the	the	DET
ejpam-4348	558	18	parabola	parabola	PROPN
ejpam-4348	558	19	γ̃d	γ̃d	PROPN
ejpam-4348	559	1	•	•	NUM
ejpam-4348	559	2	p̃d	p̃d	VERB
ejpam-4348	559	3	∈	∈	NOUN
ejpam-4348	559	4	c2n×2n	c2n×2n	VERB
ejpam-4348	559	5	on	on	ADP
ejpam-4348	559	6	right	right	ADJ
ejpam-4348	559	7	eigenspace	eigenspace	NOUN
ejpam-4348	559	8	of	of	ADP
ejpam-4348	559	9	ãd	ãd	PROPN
ejpam-4348	559	10	associated	associate	VERB
ejpam-4348	559	11	with	with	ADP
ejpam-4348	559	12	eigenvalues	eigenvalue	NOUN
ejpam-4348	559	13	in	in	ADP
ejpam-4348	559	14	the	the	DET
ejpam-4348	559	15	right	right	ADJ
ejpam-4348	559	16	complex	complex	ADJ
ejpam-4348	559	17	half	half	ADJ
ejpam-4348	559	18	-	-	PUNCT
ejpam-4348	559	19	plane	plane	NOUN
ejpam-4348	559	20	.	.	PUNCT
ejpam-4348	560	1	the	the	DET
ejpam-4348	560	2	following	follow	VERB
ejpam-4348	560	3	proposition	proposition	NOUN
ejpam-4348	560	4	characterizes	characterize	VERB
ejpam-4348	560	5	the	the	DET
ejpam-4348	560	6	relation	relation	NOUN
ejpam-4348	560	7	between	between	ADP
ejpam-4348	560	8	p̃d	p̃d	NOUN
ejpam-4348	560	9	and	and	CCONJ
ejpam-4348	560	10	p̃d	p̃d	NOUN
ejpam-4348	560	11	proposition	proposition	NOUN
ejpam-4348	560	12	11	11	NUM
ejpam-4348	560	13	.	.	PUNCT
ejpam-4348	561	1	consider	consider	VERB
ejpam-4348	561	2	a	a	DET
ejpam-4348	561	3	partition	partition	NOUN
ejpam-4348	561	4	of	of	ADP
ejpam-4348	561	5	the	the	DET
ejpam-4348	561	6	matrix	matrix	NOUN
ejpam-4348	561	7	p̃d	p̃d	NOUN
ejpam-4348	561	8	in	in	ADP
ejpam-4348	561	9	the	the	DET
ejpam-4348	561	10	form	form	NOUN
ejpam-4348	561	11	p̃d	p̃d	VERB
ejpam-4348	561	12	=	=	SYM
ejpam-4348	561	13	(	(	PUNCT
ejpam-4348	561	14	p̃(d	p̃(d	PROPN
ejpam-4348	561	15	)	)	PUNCT
ejpam-4348	561	16	1	1	NUM
ejpam-4348	561	17	p̃(d	p̃(d	PROPN
ejpam-4348	561	18	)	)	PUNCT
ejpam-4348	561	19	2	2	NUM
ejpam-4348	561	20	p̃(d	p̃(d	PROPN
ejpam-4348	561	21	)	)	PUNCT
ejpam-4348	561	22	3	3	NUM
ejpam-4348	561	23	p̃(d	p̃(d	PROPN
ejpam-4348	561	24	)	)	PUNCT
ejpam-4348	561	25	4	4	NUM
ejpam-4348	561	26	)	)	PUNCT
ejpam-4348	561	27	with	with	ADP
ejpam-4348	561	28	p̃(d	p̃(d	PROPN
ejpam-4348	561	29	)	)	PUNCT
ejpam-4348	561	30	i	i	PRON
ejpam-4348	561	31	∈	∈	PROPN
ejpam-4348	561	32	cn×n	cn×n	NOUN
ejpam-4348	561	33	,	,	PUNCT
ejpam-4348	561	34	i	i	NOUN
ejpam-4348	561	35	=	=	NOUN
ejpam-4348	561	36	1	1	NUM
ejpam-4348	561	37	,	,	PUNCT
ejpam-4348	561	38	4	4	NUM
ejpam-4348	561	39	(	(	PUNCT
ejpam-4348	561	40	45	45	NUM
ejpam-4348	561	41	)	)	PUNCT
ejpam-4348	561	42	then	then	ADV
ejpam-4348	561	43	p̃d	p̃d	VERB
ejpam-4348	561	44	=	=	NOUN
ejpam-4348	561	45	2p̃(d	2p̃(d	NUM
ejpam-4348	561	46	)	)	PUNCT
ejpam-4348	561	47	1	1	NUM
ejpam-4348	561	48	=	=	SYM
ejpam-4348	561	49	2p̃(d	2p̃(d	NUM
ejpam-4348	561	50	)	)	PUNCT
ejpam-4348	561	51	4	4	NUM
ejpam-4348	561	52	=	=	SYM
ejpam-4348	561	53	4p̃(d	4p̃(d	NUM
ejpam-4348	561	54	)	)	PUNCT
ejpam-4348	561	55	2	2	NUM
ejpam-4348	561	56	p̃(d	p̃(d	PROPN
ejpam-4348	561	57	)	)	PUNCT
ejpam-4348	561	58	3	3	NUM
ejpam-4348	561	59	(	(	PUNCT
ejpam-4348	561	60	46	46	NUM
ejpam-4348	561	61	)	)	PUNCT
ejpam-4348	562	1	moreover	moreover	ADV
ejpam-4348	562	2	p̃da	p̃da	PROPN
ejpam-4348	562	3	=	=	SYM
ejpam-4348	562	4	4(p̃(d	4(p̃(d	NUM
ejpam-4348	562	5	)	)	PUNCT
ejpam-4348	562	6	2	2	NUM
ejpam-4348	562	7	)	)	PUNCT
ejpam-4348	562	8	2	2	NUM
ejpam-4348	562	9	−	−	NOUN
ejpam-4348	562	10	(	(	PUNCT
ejpam-4348	562	11	p−	p−	NOUN
ejpam-4348	562	12	2d−	2d−	PROPN
ejpam-4348	562	13	2ipb)p̃(d	2ipb)p̃(d	NUM
ejpam-4348	562	14	)	)	PUNCT
ejpam-4348	562	15	1	1	NUM
ejpam-4348	562	16	(	(	PUNCT
ejpam-4348	562	17	47	47	NUM
ejpam-4348	562	18	)	)	PUNCT
ejpam-4348	562	19	proof	proof	NOUN
ejpam-4348	562	20	.	.	PUNCT
ejpam-4348	563	1	let	let	VERB
ejpam-4348	563	2	x̃d	x̃d	PROPN
ejpam-4348	563	3	be	be	AUX
ejpam-4348	563	4	a	a	DET
ejpam-4348	563	5	solution	solution	NOUN
ejpam-4348	563	6	of	of	ADP
ejpam-4348	563	7	the	the	DET
ejpam-4348	563	8	matrix	matrix	NOUN
ejpam-4348	563	9	equation	equation	NOUN
ejpam-4348	563	10	(	(	PUNCT
ejpam-4348	563	11	x̃d	x̃d	PROPN
ejpam-4348	564	1	+	+	CCONJ
ejpam-4348	564	2	√	√	PROPN
ejpam-4348	564	3	p	p	NOUN
ejpam-4348	564	4	2	2	NUM
ejpam-4348	564	5	in	in	ADP
ejpam-4348	564	6	)	)	PUNCT
ejpam-4348	564	7	2	2	NUM
ejpam-4348	564	8	=	=	SYM
ejpam-4348	564	9	adb	adb	NOUN
ejpam-4348	564	10	.	.	PUNCT
ejpam-4348	565	1	(	(	PUNCT
ejpam-4348	565	2	48	48	NUM
ejpam-4348	565	3	)	)	PUNCT
ejpam-4348	565	4	following	follow	VERB
ejpam-4348	565	5	the	the	DET
ejpam-4348	565	6	same	same	ADJ
ejpam-4348	565	7	calculation	calculation	NOUN
ejpam-4348	565	8	as	as	ADP
ejpam-4348	565	9	in	in	ADP
ejpam-4348	565	10	the	the	DET
ejpam-4348	565	11	proof	proof	NOUN
ejpam-4348	565	12	of	of	ADP
ejpam-4348	565	13	proposition	proposition	NOUN
ejpam-4348	565	14	7	7	NUM
ejpam-4348	565	15	,	,	PUNCT
ejpam-4348	565	16	we	we	PRON
ejpam-4348	565	17	get	get	VERB
ejpam-4348	565	18	s.	s.	PROPN
ejpam-4348	565	19	traoré	traoré	PROPN
ejpam-4348	565	20	,	,	PUNCT
ejpam-4348	565	21	m.	m.	NOUN
ejpam-4348	565	22	dosso	dosso	PROPN
ejpam-4348	565	23	/	/	SYM
ejpam-4348	565	24	eur	eur	PROPN
ejpam-4348	565	25	.	.	PUNCT
ejpam-4348	566	1	j.	j.	PROPN
ejpam-4348	566	2	pure	pure	PROPN
ejpam-4348	566	3	appl	appl	PROPN
ejpam-4348	566	4	.	.	PROPN
ejpam-4348	566	5	math	math	PROPN
ejpam-4348	566	6	,	,	PUNCT
ejpam-4348	566	7	15	15	NUM
ejpam-4348	566	8	(	(	PUNCT
ejpam-4348	566	9	2	2	NUM
ejpam-4348	566	10	)	)	PUNCT
ejpam-4348	566	11	(	(	PUNCT
ejpam-4348	566	12	2022	2022	NUM
ejpam-4348	566	13	)	)	PUNCT
ejpam-4348	566	14	,	,	PUNCT
ejpam-4348	566	15	681	681	NUM
ejpam-4348	566	16	-	-	SYM
ejpam-4348	566	17	725	725	NUM
ejpam-4348	566	18	715	715	NUM
ejpam-4348	566	19	ãd	ãd	NOUN
ejpam-4348	566	20	=	=	VERB
ejpam-4348	566	21	x̃d	x̃d	NOUN
ejpam-4348	566	22	+	+	NOUN
ejpam-4348	566	23	√	√	PROPN
ejpam-4348	566	24	p	p	ADJ
ejpam-4348	566	25	2	2	NUM
ejpam-4348	566	26	in	in	ADP
ejpam-4348	566	27	−x̃d	−x̃d	ADP
ejpam-4348	566	28	−	−	NOUN
ejpam-4348	566	29	√	√	PROPN
ejpam-4348	566	30	p	p	NOUN
ejpam-4348	566	31	2	2	NUM
ejpam-4348	566	32	in	in	ADV
ejpam-4348	566	33	in	in	ADV
ejpam-4348	566	34	in	in	ADP
ejpam-4348	566	35	×	×	X
ejpam-4348	566	36			NOUN
ejpam-4348	566	37	x̃d	x̃d	PROPN
ejpam-4348	566	38	0	0	NUM
ejpam-4348	566	39	0	0	NUM
ejpam-4348	567	1	−x̃d	−x̃d	ADP
ejpam-4348	567	2	−	−	PROPN
ejpam-4348	567	3	2	2	NUM
ejpam-4348	567	4	√	√	PROPN
ejpam-4348	567	5	p	p	NOUN
ejpam-4348	567	6	2	2	NUM
ejpam-4348	567	7	in	in	ADP
ejpam-4348	567	8	×	×	NOUN
ejpam-4348	567	9			NOUN
ejpam-4348	567	10	1	1	NUM
ejpam-4348	567	11	2	2	NUM
ejpam-4348	567	12	(	(	PUNCT
ejpam-4348	567	13	x̃d	x̃d	PROPN
ejpam-4348	568	1	+	+	CCONJ
ejpam-4348	568	2	√	√	PROPN
ejpam-4348	568	3	p	p	NOUN
ejpam-4348	568	4	2	2	NUM
ejpam-4348	568	5	in	in	ADP
ejpam-4348	568	6	)	)	PUNCT
ejpam-4348	568	7	−1	−1	NOUN
ejpam-4348	568	8	1	1	NUM
ejpam-4348	568	9	2	2	NUM
ejpam-4348	568	10	in	in	ADP
ejpam-4348	568	11	−1	−1	NOUN
ejpam-4348	568	12	2	2	NUM
ejpam-4348	568	13	(	(	PUNCT
ejpam-4348	568	14	x̃d	x̃d	PROPN
ejpam-4348	569	1	+	+	CCONJ
ejpam-4348	569	2	√	√	PROPN
ejpam-4348	569	3	p	p	NOUN
ejpam-4348	569	4	2	2	NUM
ejpam-4348	569	5	in	in	ADP
ejpam-4348	569	6	)	)	PUNCT
ejpam-4348	569	7	−1	−1	NOUN
ejpam-4348	569	8	1	1	NUM
ejpam-4348	569	9	2	2	NUM
ejpam-4348	569	10	in	in	ADP
ejpam-4348	569	11			NOUN
ejpam-4348	569	12	let	let	VERB
ejpam-4348	569	13	x̃d	x̃d	PUNCT
ejpam-4348	570	1	=	=	PUNCT
ejpam-4348	570	2	qdb	qdb	PROPN
ejpam-4348	570	3	[	[	PUNCT
ejpam-4348	570	4	m+	m+	NOUN
ejpam-4348	570	5	0	0	NUM
ejpam-4348	570	6	0	0	NUM
ejpam-4348	571	1	m−	m−	PROPN
ejpam-4348	571	2	]	]	PUNCT
ejpam-4348	572	1	q−1	q−1	PRON
ejpam-4348	572	2	db	db	AUX
ejpam-4348	572	3	be	be	AUX
ejpam-4348	572	4	the	the	DET
ejpam-4348	572	5	canonical	canonical	ADJ
ejpam-4348	572	6	jordan	jordan	PROPN
ejpam-4348	572	7	form	form	NOUN
ejpam-4348	572	8	of	of	ADP
ejpam-4348	572	9	the	the	DET
ejpam-4348	572	10	matrix	matrix	NOUN
ejpam-4348	572	11	x̃d	x̃d	PUNCT
ejpam-4348	573	1	with	with	ADP
ejpam-4348	573	2	m+	m+	NUM
ejpam-4348	573	3	and	and	CCONJ
ejpam-4348	573	4	m−	m−	PROPN
ejpam-4348	573	5	the	the	DET
ejpam-4348	573	6	jordan	jordan	PROPN
ejpam-4348	573	7	blocks	block	NOUN
ejpam-4348	573	8	associated	associate	VERB
ejpam-4348	573	9	respectively	respectively	ADV
ejpam-4348	573	10	with	with	ADP
ejpam-4348	573	11	the	the	DET
ejpam-4348	573	12	eigenvalues	eigenvalue	NOUN
ejpam-4348	573	13	of	of	ADP
ejpam-4348	573	14	x̃d	x̃d	PROPN
ejpam-4348	573	15	located	locate	VERB
ejpam-4348	573	16	in	in	ADP
ejpam-4348	573	17	the	the	DET
ejpam-4348	573	18	right	right	ADJ
ejpam-4348	573	19	half	half	ADJ
ejpam-4348	573	20	-	-	PUNCT
ejpam-4348	573	21	plane	plane	NOUN
ejpam-4348	573	22	and	and	CCONJ
ejpam-4348	573	23	the	the	DET
ejpam-4348	573	24	left	left	ADJ
ejpam-4348	573	25	half	half	ADJ
ejpam-4348	573	26	-	-	PUNCT
ejpam-4348	573	27	plane	plane	NOUN
ejpam-4348	573	28	.	.	PUNCT
ejpam-4348	574	1	by	by	ADP
ejpam-4348	574	2	replacing	replace	VERB
ejpam-4348	574	3	the	the	DET
ejpam-4348	574	4	decomposition	decomposition	NOUN
ejpam-4348	574	5	of	of	ADP
ejpam-4348	574	6	x̃d	x̃d	PROPN
ejpam-4348	574	7	in	in	ADP
ejpam-4348	574	8	the	the	DET
ejpam-4348	574	9	matrix	matrix	NOUN
ejpam-4348	574	10	ãd	ãd	NOUN
ejpam-4348	574	11	,	,	PUNCT
ejpam-4348	574	12	we	we	PRON
ejpam-4348	574	13	get	get	AUX
ejpam-4348	574	14	ãd	ãd	VERB
ejpam-4348	574	15	=	=	SYM
ejpam-4348	574	16	q̃dbm(q̃db	q̃dbm(q̃db	PROPN
ejpam-4348	574	17	)	)	PUNCT
ejpam-4348	574	18	−1	−1	NOUN
ejpam-4348	574	19	with	with	ADP
ejpam-4348	574	20	q̃db	q̃db	NOUN
ejpam-4348	574	21	=	=	SYM
ejpam-4348	574	22	qdb	qdb	NOUN
ejpam-4348	574	23	0	0	NUM
ejpam-4348	574	24	0	0	NUM
ejpam-4348	574	25	qdb	qdb	NOUN
ejpam-4348	574	26			NOUN
ejpam-4348	574	27			NOUN
ejpam-4348	574	28	(	(	PUNCT
ejpam-4348	574	29	m+	m+	NOUN
ejpam-4348	574	30	0	0	NUM
ejpam-4348	574	31	0	0	NUM
ejpam-4348	574	32	m−	m−	PROPN
ejpam-4348	574	33	)	)	PUNCT
ejpam-4348	575	1	+	+	CCONJ
ejpam-4348	575	2	√	√	ADJ
ejpam-4348	575	3	p	p	NOUN
ejpam-4348	575	4	2	2	NUM
ejpam-4348	575	5	in	in	ADP
ejpam-4348	575	6	−	−	PROPN
ejpam-4348	575	7	[	[	PUNCT
ejpam-4348	575	8	m+	m+	NUM
ejpam-4348	575	9	0	0	NUM
ejpam-4348	575	10	0	0	NUM
ejpam-4348	576	1	m−	m−	PROPN
ejpam-4348	576	2	]	]	PUNCT
ejpam-4348	577	1	−	−	PROPN
ejpam-4348	578	1	√	√	NOUN
ejpam-4348	578	2	p	p	NOUN
ejpam-4348	578	3	2	2	NUM
ejpam-4348	578	4	in	in	ADV
ejpam-4348	578	5	in	in	ADP
ejpam-4348	578	6	in	in	ADP
ejpam-4348	578	7			PROPN
ejpam-4348	578	8	et	et	NOUN
ejpam-4348	578	9	m	m	VERB
ejpam-4348	578	10	=	=	VERB
ejpam-4348	578	11			NOUN
ejpam-4348	578	12	[	[	PUNCT
ejpam-4348	578	13	m+	m+	NUM
ejpam-4348	578	14	0	0	NUM
ejpam-4348	578	15	0	0	NUM
ejpam-4348	578	16	m−	m−	PROPN
ejpam-4348	578	17	]	]	PUNCT
ejpam-4348	578	18	0	0	PUNCT
ejpam-4348	578	19	0	0	PUNCT
ejpam-4348	579	1	[	[	PUNCT
ejpam-4348	579	2	m+	m+	NUM
ejpam-4348	579	3	0	0	NUM
ejpam-4348	579	4	0	0	NUM
ejpam-4348	580	1	m−	m−	PROPN
ejpam-4348	580	2	]	]	PUNCT
ejpam-4348	581	1	−	−	PROPN
ejpam-4348	581	2	2	2	NUM
ejpam-4348	582	1	√	√	NOUN
ejpam-4348	582	2	p	p	NOUN
ejpam-4348	582	3	2	2	NUM
ejpam-4348	582	4	in	in	ADP
ejpam-4348	582	5			NOUN
ejpam-4348	582	6	we	we	PRON
ejpam-4348	582	7	can	can	AUX
ejpam-4348	582	8	therefore	therefore	ADV
ejpam-4348	582	9	calculate	calculate	VERB
ejpam-4348	582	10	the	the	DET
ejpam-4348	582	11	associated	associated	ADJ
ejpam-4348	582	12	projector	projector	NOUN
ejpam-4348	582	13	p̃d	p̃d	NOUN
ejpam-4348	582	14	=	=	SYM
ejpam-4348	582	15	(	(	PUNCT
ejpam-4348	582	16	q̃db	q̃db	X
ejpam-4348	582	17	)	)	PUNCT
ejpam-4348	582	18	[	[	PUNCT
ejpam-4348	582	19	ik	ik	X
ejpam-4348	582	20	0	0	NUM
ejpam-4348	582	21	0	0	NUM
ejpam-4348	582	22	0	0	NUM
ejpam-4348	582	23	]	]	PUNCT
ejpam-4348	582	24	(	(	PUNCT
ejpam-4348	582	25	q̃db	q̃db	NOUN
ejpam-4348	582	26	)	)	PUNCT
ejpam-4348	582	27	−1	−1	NOUN
ejpam-4348	582	28	=	=	SYM
ejpam-4348	582	29	qdb	qdb	X
ejpam-4348	582	30	0	0	NUM
ejpam-4348	582	31	0	0	NUM
ejpam-4348	582	32	qdb	qdb	NOUN
ejpam-4348	582	33			NOUN
ejpam-4348	582	34			NOUN
ejpam-4348	582	35	[	[	PUNCT
ejpam-4348	582	36	m+	m+	NUM
ejpam-4348	582	37	0	0	NUM
ejpam-4348	582	38	0	0	NUM
ejpam-4348	583	1	m−	m−	PROPN
ejpam-4348	583	2	]	]	PUNCT
ejpam-4348	584	1	+	+	CCONJ
ejpam-4348	584	2	√	√	ADJ
ejpam-4348	584	3	p	p	NOUN
ejpam-4348	584	4	2	2	NUM
ejpam-4348	584	5	in	in	ADP
ejpam-4348	584	6	−	−	PROPN
ejpam-4348	584	7	[	[	PUNCT
ejpam-4348	584	8	m+	m+	NUM
ejpam-4348	584	9	0	0	NUM
ejpam-4348	584	10	0	0	NUM
ejpam-4348	585	1	m−	m−	PROPN
ejpam-4348	585	2	]	]	PUNCT
ejpam-4348	586	1	−	−	PROPN
ejpam-4348	587	1	√	√	NOUN
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ejpam-4348	587	3	2	2	NUM
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ejpam-4348	587	5	in	in	ADV
ejpam-4348	587	6	in	in	ADP
ejpam-4348	587	7	×	×	NOUN
ejpam-4348	587	8			NOUN
ejpam-4348	587	9	[	[	PUNCT
ejpam-4348	587	10	ik	ik	X
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ejpam-4348	587	13	0	0	NUM
ejpam-4348	587	14	]	]	PUNCT
ejpam-4348	588	1	[	[	PUNCT
ejpam-4348	588	2	0	0	NUM
ejpam-4348	588	3	0	0	NUM
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ejpam-4348	588	5	0	0	NUM
ejpam-4348	588	6	]	]	PUNCT
ejpam-4348	588	7	[	[	PUNCT
ejpam-4348	588	8	0	0	NUM
ejpam-4348	588	9	0	0	NUM
ejpam-4348	588	10	0	0	NUM
ejpam-4348	588	11	0	0	NUM
ejpam-4348	588	12	]	]	PUNCT
ejpam-4348	589	1	[	[	PUNCT
ejpam-4348	589	2	0	0	NUM
ejpam-4348	589	3	0	0	NUM
ejpam-4348	589	4	0	0	NUM
ejpam-4348	589	5	0	0	NUM
ejpam-4348	589	6	]	]	PUNCT
ejpam-4348	589	7			PROPN
ejpam-4348	589	8	×	×	NOUN
ejpam-4348	589	9			NOUN
ejpam-4348	589	10	1	1	NUM
ejpam-4348	589	11	2	2	NUM
ejpam-4348	589	12	(	(	PUNCT
ejpam-4348	589	13	[	[	PUNCT
ejpam-4348	589	14	m+	m+	NOUN
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ejpam-4348	590	1	m−	m−	PROPN
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ejpam-4348	591	1	+	+	CCONJ
ejpam-4348	591	2	√	√	ADJ
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ejpam-4348	591	4	2	2	NUM
ejpam-4348	591	5	in	in	ADP
ejpam-4348	591	6	)	)	PUNCT
ejpam-4348	591	7	−1	−1	NOUN
ejpam-4348	591	8	1	1	NUM
ejpam-4348	591	9	2	2	NUM
ejpam-4348	591	10	in	in	ADP
ejpam-4348	591	11	−1	−1	NOUN
ejpam-4348	591	12	2	2	NUM
ejpam-4348	591	13	m+	m+	NOUN
ejpam-4348	591	14	0	0	NUM
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ejpam-4348	592	1	m−	m−	PROPN
ejpam-4348	592	2	−	−	VERB
ejpam-4348	592	3	√	√	ADP
ejpam-4348	592	4	p	p	PRON
ejpam-4348	592	5	2	2	NUM
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ejpam-4348	592	7	−1	−1	PROPN
ejpam-4348	592	8	1	1	NUM
ejpam-4348	592	9	2	2	NUM
ejpam-4348	592	10	in	in	ADP
ejpam-4348	592	11			NOUN
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ejpam-4348	592	13	db	db	PROPN
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ejpam-4348	593	1	q−1	q−1	PRON
ejpam-4348	593	2	db	db	VERB
ejpam-4348	593	3			NOUN
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ejpam-4348	593	8	dosso	dosso	PROPN
ejpam-4348	593	9	/	/	SYM
ejpam-4348	593	10	eur	eur	PROPN
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ejpam-4348	594	3	appl	appl	PROPN
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ejpam-4348	594	6	,	,	PUNCT
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ejpam-4348	594	9	2	2	NUM
ejpam-4348	594	10	)	)	PUNCT
ejpam-4348	594	11	(	(	PUNCT
ejpam-4348	594	12	2022	2022	NUM
ejpam-4348	594	13	)	)	PUNCT
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ejpam-4348	594	19	=	=	NOUN
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ejpam-4348	594	24			NOUN
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ejpam-4348	594	26	m+	m+	NOUN
ejpam-4348	595	1	+	+	CCONJ
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ejpam-4348	595	8	0	0	NUM
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ejpam-4348	595	15	]	]	PUNCT
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ejpam-4348	597	5	0	0	NUM
ejpam-4348	597	6	]	]	PUNCT
ejpam-4348	597	7			NUM
ejpam-4348	597	8	×	×	PROPN
ejpam-4348	597	9			NOUN
ejpam-4348	597	10	1	1	NUM
ejpam-4348	597	11	2	2	NUM
ejpam-4348	597	12	(m+	(m+	NOUN
ejpam-4348	597	13	+	+	NOUN
ejpam-4348	597	14	√	√	PROPN
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ejpam-4348	597	16	2	2	NUM
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ejpam-4348	597	18	)	)	PUNCT
ejpam-4348	597	19	−1	−1	NOUN
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ejpam-4348	597	23	m−	m−	PROPN
ejpam-4348	597	24	+	+	CCONJ
ejpam-4348	597	25	√	√	PROPN
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ejpam-4348	597	31			NOUN
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ejpam-4348	597	41	2	2	NUM
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ejpam-4348	597	43	+	+	ADP
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ejpam-4348	598	12	√	√	PROPN
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ejpam-4348	598	29	db	db	PROPN
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ejpam-4348	610	1	q−1	q−1	PROPN
ejpam-4348	610	2	db	db	PROPN
ejpam-4348	610	3			NUM
ejpam-4348	610	4	=	=	SYM
ejpam-4348	610	5	[	[	PUNCT
ejpam-4348	610	6	p̃(d	p̃(d	PROPN
ejpam-4348	610	7	)	)	PUNCT
ejpam-4348	610	8	1	1	NUM
ejpam-4348	610	9	p̃(d	p̃(d	PROPN
ejpam-4348	610	10	)	)	PUNCT
ejpam-4348	610	11	2	2	NUM
ejpam-4348	610	12	p̃(d	p̃(d	PROPN
ejpam-4348	610	13	)	)	PUNCT
ejpam-4348	610	14	3	3	NUM
ejpam-4348	610	15	p̃(d	p̃(d	PROPN
ejpam-4348	610	16	)	)	PUNCT
ejpam-4348	610	17	4	4	NUM
ejpam-4348	610	18	]	]	PUNCT
ejpam-4348	610	19	it	it	PRON
ejpam-4348	610	20	follows	follow	VERB
ejpam-4348	610	21	that	that	SCONJ
ejpam-4348	610	22	p̃(d	p̃(d	PROPN
ejpam-4348	610	23	)	)	PUNCT
ejpam-4348	610	24	1	1	NUM
ejpam-4348	610	25	=	=	SYM
ejpam-4348	610	26	qd	qd	NOUN
ejpam-4348	611	1	[	[	X
ejpam-4348	611	2	1	1	NUM
ejpam-4348	611	3	2	2	NUM
ejpam-4348	611	4	ik	ik	X
ejpam-4348	611	5	0	0	PROPN
ejpam-4348	611	6	0	0	NUM
ejpam-4348	611	7	0	0	NUM
ejpam-4348	611	8	]	]	PUNCT
ejpam-4348	612	1	q−1	q−1	PROPN
ejpam-4348	612	2	db	db	PROPN
ejpam-4348	612	3	=	=	NOUN
ejpam-4348	612	4	1	1	NUM
ejpam-4348	612	5	2	2	NUM
ejpam-4348	612	6	p̃d	p̃d	NOUN
ejpam-4348	612	7	p̃(d	p̃(d	PROPN
ejpam-4348	612	8	)	)	PUNCT
ejpam-4348	612	9	2	2	NUM
ejpam-4348	612	10	=	=	SYM
ejpam-4348	612	11	1	1	NUM
ejpam-4348	612	12	2	2	NUM
ejpam-4348	612	13	qdb	qdb	NOUN
ejpam-4348	612	14	m+	m+	NOUN
ejpam-4348	613	1	+	+	CCONJ
ejpam-4348	613	2	√	√	PROPN
ejpam-4348	614	1	p	p	SYM
ejpam-4348	614	2	2	2	NUM
ejpam-4348	614	3	ik	ik	X
ejpam-4348	614	4	0	0	PROPN
ejpam-4348	614	5	0	0	SYM
ejpam-4348	614	6	0	0	NUM
ejpam-4348	615	1	q−1	q−1	PRON
ejpam-4348	615	2	db	db	PROPN
ejpam-4348	615	3	s.	s.	PROPN
ejpam-4348	615	4	traoré	traoré	PROPN
ejpam-4348	615	5	,	,	PUNCT
ejpam-4348	615	6	m.	m.	NOUN
ejpam-4348	615	7	dosso	dosso	PROPN
ejpam-4348	615	8	/	/	SYM
ejpam-4348	615	9	eur	eur	PROPN
ejpam-4348	615	10	.	.	PUNCT
ejpam-4348	616	1	j.	j.	PROPN
ejpam-4348	616	2	pure	pure	PROPN
ejpam-4348	616	3	appl	appl	PROPN
ejpam-4348	616	4	.	.	PROPN
ejpam-4348	616	5	math	math	PROPN
ejpam-4348	616	6	,	,	PUNCT
ejpam-4348	616	7	15	15	NUM
ejpam-4348	616	8	(	(	PUNCT
ejpam-4348	616	9	2	2	NUM
ejpam-4348	616	10	)	)	PUNCT
ejpam-4348	616	11	(	(	PUNCT
ejpam-4348	616	12	2022	2022	NUM
ejpam-4348	616	13	)	)	PUNCT
ejpam-4348	616	14	,	,	PUNCT
ejpam-4348	616	15	681	681	NUM
ejpam-4348	616	16	-	-	SYM
ejpam-4348	616	17	725	725	NUM
ejpam-4348	616	18	717	717	NUM
ejpam-4348	616	19	p̃(d	p̃(d	PROPN
ejpam-4348	616	20	)	)	PUNCT
ejpam-4348	616	21	3	3	NUM
ejpam-4348	616	22	=	=	SYM
ejpam-4348	616	23	1	1	NUM
ejpam-4348	616	24	2	2	NUM
ejpam-4348	616	25	qdb	qdb	NOUN
ejpam-4348	616	26	(m+	(m+	NOUN
ejpam-4348	616	27	+	+	CCONJ
ejpam-4348	616	28	√	√	PROPN
ejpam-4348	616	29	p	p	SYM
ejpam-4348	616	30	2	2	NUM
ejpam-4348	616	31	ik	ik	NOUN
ejpam-4348	616	32	)	)	PUNCT
ejpam-4348	616	33	−1	−1	NOUN
ejpam-4348	616	34	0	0	NUM
ejpam-4348	616	35	0	0	NUM
ejpam-4348	616	36	0	0	NUM
ejpam-4348	617	1	q−1	q−1	NOUN
ejpam-4348	617	2	db	db	ADP
ejpam-4348	617	3	p̃(d	p̃(d	PROPN
ejpam-4348	617	4	)	)	PUNCT
ejpam-4348	617	5	4	4	NUM
ejpam-4348	617	6	=	=	NOUN
ejpam-4348	617	7	qdb	qdb	NOUN
ejpam-4348	618	1	[	[	PUNCT
ejpam-4348	618	2	1	1	NUM
ejpam-4348	618	3	2	2	NUM
ejpam-4348	618	4	ik	ik	X
ejpam-4348	618	5	0	0	PROPN
ejpam-4348	618	6	0	0	NUM
ejpam-4348	618	7	0	0	NUM
ejpam-4348	618	8	]	]	PUNCT
ejpam-4348	619	1	q−1	q−1	PROPN
ejpam-4348	619	2	db	db	PROPN
ejpam-4348	619	3	=	=	NOUN
ejpam-4348	619	4	1	1	NUM
ejpam-4348	619	5	2	2	NUM
ejpam-4348	619	6	p̃d	p̃d	NOUN
ejpam-4348	619	7	with	with	ADP
ejpam-4348	619	8	x̃d	x̃d	PROPN
ejpam-4348	619	9	=	=	PUNCT
ejpam-4348	619	10	qdb	qdb	PROPN
ejpam-4348	619	11	[	[	PUNCT
ejpam-4348	619	12	m+	m+	NOUN
ejpam-4348	619	13	0	0	NUM
ejpam-4348	619	14	0	0	NUM
ejpam-4348	620	1	m−	m−	PROPN
ejpam-4348	620	2	]	]	PUNCT
ejpam-4348	621	1	q−1	q−1	PROPN
ejpam-4348	621	2	db	db	VERB
ejpam-4348	621	3	we	we	PRON
ejpam-4348	621	4	have	have	VERB
ejpam-4348	621	5	a	a	DET
ejpam-4348	621	6	=	=	ADJ
ejpam-4348	621	7	adb	adb	NOUN
ejpam-4348	622	1	−	−	PROPN
ejpam-4348	623	1	(	(	PUNCT
ejpam-4348	623	2	p	p	NOUN
ejpam-4348	623	3	2	2	NUM
ejpam-4348	623	4	−	−	NUM
ejpam-4348	623	5	d−	d−	PROPN
ejpam-4348	623	6	ipb	ipb	PROPN
ejpam-4348	623	7	)	)	PUNCT
ejpam-4348	623	8	in	in	ADP
ejpam-4348	623	9	=	=	PUNCT
ejpam-4348	623	10	qd	qd	NOUN
ejpam-4348	623	11			NOUN
ejpam-4348	623	12	(	(	PUNCT
ejpam-4348	623	13	m+	m+	NUM
ejpam-4348	624	1	+	+	CCONJ
ejpam-4348	624	2	√	√	PROPN
ejpam-4348	625	1	p	p	NOUN
ejpam-4348	625	2	2	2	NUM
ejpam-4348	625	3	ik	ik	X
ejpam-4348	625	4	)	)	PUNCT
ejpam-4348	625	5	2	2	NUM
ejpam-4348	625	6	−	−	PROPN
ejpam-4348	625	7	(	(	PUNCT
ejpam-4348	625	8	p	p	NOUN
ejpam-4348	625	9	2	2	NUM
ejpam-4348	625	10	−	−	NUM
ejpam-4348	625	11	d−	d−	PROPN
ejpam-4348	625	12	ipb	ipb	PROPN
ejpam-4348	625	13	)	)	PUNCT
ejpam-4348	625	14	ik	ik	PROPN
ejpam-4348	625	15	0	0	PROPN
ejpam-4348	625	16	0	0	NUM
ejpam-4348	626	1	(	(	PUNCT
ejpam-4348	626	2	m−	m−	PROPN
ejpam-4348	626	3	+	+	CCONJ
ejpam-4348	627	1	√	√	PROPN
ejpam-4348	627	2	p	p	SYM
ejpam-4348	627	3	2	2	NUM
ejpam-4348	627	4	in−k	in−k	NOUN
ejpam-4348	627	5	)	)	PUNCT
ejpam-4348	627	6	2	2	NUM
ejpam-4348	627	7	−	−	NOUN
ejpam-4348	627	8	(	(	PUNCT
ejpam-4348	627	9	p	p	NOUN
ejpam-4348	627	10	2	2	NUM
ejpam-4348	627	11	−	−	NUM
ejpam-4348	627	12	d−	d−	PROPN
ejpam-4348	627	13	ipb	ipb	PROPN
ejpam-4348	627	14	)	)	PUNCT
ejpam-4348	627	15	in−k	in−k	VERB
ejpam-4348	627	16	q−1	q−1	PUNCT
ejpam-4348	627	17	and	and	CCONJ
ejpam-4348	627	18	p̃da	p̃da	PROPN
ejpam-4348	627	19	=	=	SYM
ejpam-4348	627	20	qdb	qdb	NOUN
ejpam-4348	627	21	[	[	PUNCT
ejpam-4348	627	22	ik	ik	X
ejpam-4348	627	23	0	0	PROPN
ejpam-4348	627	24	0	0	NUM
ejpam-4348	627	25	0	0	NUM
ejpam-4348	627	26	]	]	SYM
ejpam-4348	627	27			NOUN
ejpam-4348	627	28	(	(	PUNCT
ejpam-4348	627	29	m+	m+	NUM
ejpam-4348	628	1	+	+	CCONJ
ejpam-4348	628	2	√	√	PROPN
ejpam-4348	629	1	p	p	NOUN
ejpam-4348	629	2	2	2	NUM
ejpam-4348	629	3	ik	ik	X
ejpam-4348	629	4	)	)	PUNCT
ejpam-4348	629	5	2	2	NUM
ejpam-4348	629	6	−	−	PROPN
ejpam-4348	629	7	(	(	PUNCT
ejpam-4348	629	8	p	p	NOUN
ejpam-4348	629	9	2	2	NUM
ejpam-4348	629	10	−	−	ADP
ejpam-4348	629	11	d−	d−	PROPN
ejpam-4348	629	12	ipb)ik	ipb)ik	NOUN
ejpam-4348	629	13	0	0	NUM
ejpam-4348	629	14	0	0	NUM
ejpam-4348	630	1	(	(	PUNCT
ejpam-4348	630	2	m−	m−	PROPN
ejpam-4348	630	3	+	+	CCONJ
ejpam-4348	631	1	√	√	PROPN
ejpam-4348	631	2	p	p	SYM
ejpam-4348	631	3	2	2	NUM
ejpam-4348	631	4	in−k	in−k	NOUN
ejpam-4348	631	5	)	)	PUNCT
ejpam-4348	631	6	2	2	NUM
ejpam-4348	631	7	−	−	PROPN
ejpam-4348	632	1	(	(	PUNCT
ejpam-4348	632	2	p	p	NOUN
ejpam-4348	632	3	2	2	NUM
ejpam-4348	632	4	−	−	NUM
ejpam-4348	632	5	d−	d−	PROPN
ejpam-4348	632	6	ipb)in−k	ipb)in−k	PROPN
ejpam-4348	632	7	q−1	q−1	PROPN
ejpam-4348	632	8	db	db	PROPN
ejpam-4348	632	9	=	=	PUNCT
ejpam-4348	632	10	qdb	qdb	NOUN
ejpam-4348	632	11	(m+	(m+	NOUN
ejpam-4348	632	12	+	+	CCONJ
ejpam-4348	632	13	√	√	PROPN
ejpam-4348	632	14	p	p	SYM
ejpam-4348	632	15	2	2	NUM
ejpam-4348	632	16	ik	ik	X
ejpam-4348	632	17	)	)	PUNCT
ejpam-4348	632	18	2	2	NUM
ejpam-4348	632	19	−	−	PROPN
ejpam-4348	633	1	(	(	PUNCT
ejpam-4348	633	2	p	p	NOUN
ejpam-4348	633	3	2	2	NUM
ejpam-4348	633	4	−	−	ADP
ejpam-4348	633	5	d−	d−	PROPN
ejpam-4348	633	6	ipb)ik	ipb)ik	NOUN
ejpam-4348	633	7	0	0	NUM
ejpam-4348	633	8	0	0	NUM
ejpam-4348	633	9	0	0	NUM
ejpam-4348	634	1	q−1	q−1	NOUN
ejpam-4348	634	2	db	db	PROPN
ejpam-4348	634	3	=	=	SYM
ejpam-4348	634	4	4(p̃(d	4(p̃(d	NUM
ejpam-4348	634	5	)	)	PUNCT
ejpam-4348	634	6	2	2	NUM
ejpam-4348	634	7	)	)	PUNCT
ejpam-4348	634	8	2	2	NUM
ejpam-4348	634	9	−	−	NOUN
ejpam-4348	634	10	(	(	PUNCT
ejpam-4348	634	11	p−	p−	NOUN
ejpam-4348	634	12	2d−	2d−	NUM
ejpam-4348	634	13	2ipb)p̃(db	2ipb)p̃(db	NUM
ejpam-4348	634	14	)	)	PUNCT
ejpam-4348	634	15	1	1	NUM
ejpam-4348	634	16	hence	hence	ADV
ejpam-4348	634	17	(	(	PUNCT
ejpam-4348	634	18	46	46	NUM
ejpam-4348	634	19	)	)	PUNCT
ejpam-4348	634	20	and	and	CCONJ
ejpam-4348	634	21	(	(	PUNCT
ejpam-4348	634	22	47	47	NUM
ejpam-4348	634	23	)	)	PUNCT
ejpam-4348	634	24	.	.	PUNCT
ejpam-4348	635	1	remark	remark	VERB
ejpam-4348	635	2	7	7	NUM
ejpam-4348	635	3	.	.	PUNCT
ejpam-4348	636	1	we	we	PRON
ejpam-4348	636	2	note	note	VERB
ejpam-4348	636	3	that	that	SCONJ
ejpam-4348	636	4	:	:	PUNCT
ejpam-4348	636	5	•	•	X
ejpam-4348	636	6	if	if	SCONJ
ejpam-4348	636	7	the	the	DET
ejpam-4348	636	8	parameter	parameter	NOUN
ejpam-4348	637	1	d	d	PROPN
ejpam-4348	637	2	=	=	SYM
ejpam-4348	637	3	p	p	NOUN
ejpam-4348	637	4	2	2	NUM
ejpam-4348	637	5	,	,	PUNCT
ejpam-4348	637	6	whence	whence	NOUN
ejpam-4348	637	7	equalities	equality	NOUN
ejpam-4348	637	8	(	(	PUNCT
ejpam-4348	637	9	47	47	NUM
ejpam-4348	637	10	)	)	PUNCT
ejpam-4348	637	11	are	be	AUX
ejpam-4348	637	12	reduced	reduce	VERB
ejpam-4348	637	13	to	to	ADP
ejpam-4348	637	14	those	those	PRON
ejpam-4348	637	15	of	of	ADP
ejpam-4348	637	16	equalities	equality	NOUN
ejpam-4348	637	17	(	(	PUNCT
ejpam-4348	637	18	31	31	NUM
ejpam-4348	637	19	)	)	PUNCT
ejpam-4348	637	20	.	.	PUNCT
ejpam-4348	638	1	•	•	INTJ
ejpam-4348	638	2	if	if	SCONJ
ejpam-4348	638	3	the	the	DET
ejpam-4348	638	4	parameter	parameter	NOUN
ejpam-4348	638	5	b	b	PROPN
ejpam-4348	638	6	=	=	SYM
ejpam-4348	638	7	0	0	NUM
ejpam-4348	638	8	,	,	PUNCT
ejpam-4348	638	9	whence	whence	ADJ
ejpam-4348	638	10	equalities	equality	NOUN
ejpam-4348	638	11	(	(	PUNCT
ejpam-4348	638	12	47	47	NUM
ejpam-4348	638	13	)	)	PUNCT
ejpam-4348	638	14	are	be	AUX
ejpam-4348	638	15	reduced	reduce	VERB
ejpam-4348	638	16	to	to	ADP
ejpam-4348	638	17	those	those	PRON
ejpam-4348	638	18	of	of	ADP
ejpam-4348	638	19	equalities	equality	NOUN
ejpam-4348	638	20	(	(	PUNCT
ejpam-4348	638	21	40	40	NUM
ejpam-4348	638	22	)	)	PUNCT
ejpam-4348	638	23	.	.	PUNCT
ejpam-4348	639	1	•	•	INTJ
ejpam-4348	639	2	if	if	SCONJ
ejpam-4348	639	3	the	the	DET
ejpam-4348	639	4	parameters	parameter	NOUN
ejpam-4348	640	1	b	b	NOUN
ejpam-4348	640	2	=	=	SYM
ejpam-4348	640	3	0	0	PROPN
ejpam-4348	640	4	,	,	PUNCT
ejpam-4348	640	5	d	d	NOUN
ejpam-4348	640	6	=	=	SYM
ejpam-4348	641	1	p	p	NOUN
ejpam-4348	641	2	2	2	NUM
ejpam-4348	641	3	,	,	PUNCT
ejpam-4348	641	4	whence	whence	NOUN
ejpam-4348	641	5	equalities	equality	NOUN
ejpam-4348	641	6	(	(	PUNCT
ejpam-4348	641	7	47	47	NUM
ejpam-4348	641	8	)	)	PUNCT
ejpam-4348	641	9	are	be	AUX
ejpam-4348	641	10	reduced	reduce	VERB
ejpam-4348	641	11	to	to	ADP
ejpam-4348	641	12	those	those	PRON
ejpam-4348	641	13	of	of	ADP
ejpam-4348	641	14	equalities	equality	NOUN
ejpam-4348	641	15	(	(	PUNCT
ejpam-4348	641	16	23	23	NUM
ejpam-4348	641	17	)	)	PUNCT
ejpam-4348	641	18	.	.	PUNCT
ejpam-4348	642	1	algorithm	algorithm	NOUN
ejpam-4348	642	2	7	7	NUM
ejpam-4348	642	3	(	(	PUNCT
ejpam-4348	642	4	dichopdb	dichopdb	PROPN
ejpam-4348	642	5	)	)	PUNCT
ejpam-4348	642	6	.	.	PUNCT
ejpam-4348	643	1	s.	s.	PROPN
ejpam-4348	643	2	traoré	traoré	PROPN
ejpam-4348	643	3	,	,	PUNCT
ejpam-4348	643	4	m.	m.	NOUN
ejpam-4348	643	5	dosso	dosso	PROPN
ejpam-4348	643	6	/	/	SYM
ejpam-4348	643	7	eur	eur	PROPN
ejpam-4348	643	8	.	.	PUNCT
ejpam-4348	644	1	j.	j.	PROPN
ejpam-4348	644	2	pure	pure	PROPN
ejpam-4348	644	3	appl	appl	PROPN
ejpam-4348	644	4	.	.	PROPN
ejpam-4348	644	5	math	math	PROPN
ejpam-4348	644	6	,	,	PUNCT
ejpam-4348	644	7	15	15	NUM
ejpam-4348	644	8	(	(	PUNCT
ejpam-4348	644	9	2	2	NUM
ejpam-4348	644	10	)	)	PUNCT
ejpam-4348	644	11	(	(	PUNCT
ejpam-4348	644	12	2022	2022	NUM
ejpam-4348	644	13	)	)	PUNCT
ejpam-4348	644	14	,	,	PUNCT
ejpam-4348	644	15	681	681	NUM
ejpam-4348	644	16	-	-	SYM
ejpam-4348	644	17	725	725	NUM
ejpam-4348	644	18	718	718	NUM
ejpam-4348	644	19	•	•	NOUN
ejpam-4348	644	20	input	input	NOUN
ejpam-4348	644	21	variables	variable	NOUN
ejpam-4348	644	22	:	:	PUNCT
ejpam-4348	644	23	the	the	DET
ejpam-4348	644	24	matrices	matrix	NOUN
ejpam-4348	644	25	a	a	PRON
ejpam-4348	644	26	,	,	PUNCT
ejpam-4348	644	27	in	in	ADV
ejpam-4348	644	28	and	and	CCONJ
ejpam-4348	644	29	the	the	DET
ejpam-4348	644	30	real	real	ADJ
ejpam-4348	644	31	numbers	number	NOUN
ejpam-4348	644	32	b	b	PROPN
ejpam-4348	644	33	,	,	PUNCT
ejpam-4348	644	34	d	d	NOUN
ejpam-4348	644	35	and	and	CCONJ
ejpam-4348	644	36	p	p	X
ejpam-4348	644	37	such	such	ADJ
ejpam-4348	645	1	that	that	SCONJ
ejpam-4348	645	2	the	the	DET
ejpam-4348	645	3	matrix	matrix	NOUN
ejpam-4348	645	4	pencil	pencil	NOUN
ejpam-4348	645	5	zin	zin	NOUN
ejpam-4348	645	6	−a	−a	NOUN
ejpam-4348	645	7	has	have	VERB
ejpam-4348	645	8	no	no	DET
ejpam-4348	645	9	eigenvalues	eigenvalue	NOUN
ejpam-4348	645	10	on	on	ADP
ejpam-4348	645	11	the	the	DET
ejpam-4348	645	12	parabola	parabola	NOUN
ejpam-4348	645	13	with	with	ADP
ejpam-4348	645	14	equation	equation	NOUN
ejpam-4348	645	15	2p	2p	NOUN
ejpam-4348	645	16	(	(	PUNCT
ejpam-4348	645	17	d−	d−	PROPN
ejpam-4348	645	18	x	x	PRON
ejpam-4348	645	19	)	)	PUNCT
ejpam-4348	645	20	=	=	SYM
ejpam-4348	645	21	(	(	PUNCT
ejpam-4348	645	22	y	y	NOUN
ejpam-4348	646	1	−	−	PROPN
ejpam-4348	646	2	ipb)2	ipb)2	PROPN
ejpam-4348	646	3	with	with	ADP
ejpam-4348	646	4	p	p	PROPN
ejpam-4348	646	5	>	>	X
ejpam-4348	646	6	0	0	PUNCT
ejpam-4348	646	7	et	et	NOUN
ejpam-4348	646	8	d	d	X
ejpam-4348	646	9	>	>	X
ejpam-4348	646	10	0	0	NUM
ejpam-4348	646	11	•	•	NUM
ejpam-4348	646	12	output	output	NOUN
ejpam-4348	646	13	variables	variable	NOUN
ejpam-4348	646	14	:	:	PUNCT
ejpam-4348	646	15	p̃d	p̃d	NOUN
ejpam-4348	646	16	,	,	PUNCT
ejpam-4348	646	17	h̃d	h̃d	NOUN
ejpam-4348	646	18	and	and	CCONJ
ejpam-4348	646	19	b	b	NOUN
ejpam-4348	646	20	̸=	̸=	PROPN
ejpam-4348	646	21	0	0	NUM
ejpam-4348	646	22	.	.	PUNCT
ejpam-4348	647	1	p̃d	p̃d	NOUN
ejpam-4348	647	2	being	be	AUX
ejpam-4348	647	3	the	the	DET
ejpam-4348	647	4	projector	projector	NOUN
ejpam-4348	647	5	on	on	ADP
ejpam-4348	647	6	the	the	DET
ejpam-4348	647	7	right	right	ADJ
ejpam-4348	647	8	subspace	subspace	NOUN
ejpam-4348	647	9	of	of	ADP
ejpam-4348	647	10	zin−a	zin−a	PROPN
ejpam-4348	647	11	associated	associate	VERB
ejpam-4348	647	12	with	with	ADP
ejpam-4348	647	13	the	the	DET
ejpam-4348	647	14	eigenvalues	eigenvalue	NOUN
ejpam-4348	647	15	outside	outside	ADP
ejpam-4348	647	16	the	the	DET
ejpam-4348	647	17	parabola	parabola	NOUN
ejpam-4348	647	18	and	and	CCONJ
ejpam-4348	647	19	h̃d	h̃d	NOUN
ejpam-4348	647	20	the	the	DET
ejpam-4348	647	21	matrix	matrix	NOUN
ejpam-4348	647	22	whose	whose	DET
ejpam-4348	647	23	norm	norm	NOUN
ejpam-4348	647	24	defines	define	VERB
ejpam-4348	647	25	the	the	DET
ejpam-4348	647	26	dichotomy	dichotomy	NOUN
ejpam-4348	647	27	criterion	criterion	NOUN
ejpam-4348	647	28	.	.	PUNCT
ejpam-4348	648	1	1	1	X
ejpam-4348	648	2	.	.	X
ejpam-4348	648	3	determine	determine	VERB
ejpam-4348	648	4	the	the	DET
ejpam-4348	648	5	matrix	matrix	NOUN
ejpam-4348	648	6	ãd	ãd	NOUN
ejpam-4348	648	7	=	=	SYM
ejpam-4348	648	8			NOUN
ejpam-4348	648	9	−	−	PROPN
ejpam-4348	649	1	√	√	PROPN
ejpam-4348	649	2	p	p	NOUN
ejpam-4348	649	3	2	2	NUM
ejpam-4348	649	4	in	in	ADP
ejpam-4348	649	5	a+	a+	PUNCT
ejpam-4348	649	6	(	(	PUNCT
ejpam-4348	649	7	p	p	NOUN
ejpam-4348	649	8	2	2	NUM
ejpam-4348	649	9	−	−	ADP
ejpam-4348	649	10	d−	d−	PROPN
ejpam-4348	649	11	ipb)in	ipb)in	NOUN
ejpam-4348	649	12	in	in	ADP
ejpam-4348	649	13	−	−	PROPN
ejpam-4348	649	14	√	√	PROPN
ejpam-4348	649	15	p	p	NOUN
ejpam-4348	649	16	2	2	NUM
ejpam-4348	649	17	in	in	ADP
ejpam-4348	649	18			NOUN
ejpam-4348	649	19	2	2	NUM
ejpam-4348	649	20	.	.	PUNCT
ejpam-4348	649	21	using	use	VERB
ejpam-4348	649	22	algorithm	algorithm	NOUN
ejpam-4348	649	23	3	3	NUM
ejpam-4348	649	24	to	to	ADP
ejpam-4348	649	25	λ̃di2n−ãd	λ̃di2n−ãd	NOUN
ejpam-4348	649	26	,	,	PUNCT
ejpam-4348	649	27	compute	compute	VERB
ejpam-4348	649	28	the	the	DET
ejpam-4348	649	29	projector	projector	NOUN
ejpam-4348	649	30	p̃d	p̃d	VERB
ejpam-4348	649	31	onto	onto	ADP
ejpam-4348	649	32	the	the	DET
ejpam-4348	649	33	right	right	ADJ
ejpam-4348	649	34	eigenspace	eigenspace	NOUN
ejpam-4348	649	35	of	of	ADP
ejpam-4348	649	36	ãd	ãd	PROPN
ejpam-4348	649	37	associted	associte	VERB
ejpam-4348	649	38	with	with	ADP
ejpam-4348	649	39	the	the	DET
ejpam-4348	649	40	eigenvalues	eigenvalue	NOUN
ejpam-4348	649	41	on	on	ADP
ejpam-4348	649	42	the	the	DET
ejpam-4348	649	43	right	right	ADJ
ejpam-4348	649	44	half	half	ADJ
ejpam-4348	649	45	-	-	PUNCT
ejpam-4348	649	46	plane	plane	NOUN
ejpam-4348	649	47	of	of	ADP
ejpam-4348	649	48	the	the	DET
ejpam-4348	649	49	complex	complex	ADJ
ejpam-4348	649	50	plane	plane	NOUN
ejpam-4348	649	51	and	and	CCONJ
ejpam-4348	649	52	the	the	DET
ejpam-4348	649	53	matrix	matrix	NOUN
ejpam-4348	649	54	h̃d	h̃d	NOUN
ejpam-4348	649	55	.	.	PROPN
ejpam-4348	650	1	3	3	X
ejpam-4348	650	2	.	.	X
ejpam-4348	651	1	if	if	SCONJ
ejpam-4348	651	2	∥h̃d∥	∥h̃d∥	ADJ
ejpam-4348	651	3	is	be	AUX
ejpam-4348	651	4	not	not	PART
ejpam-4348	651	5	large	large	ADJ
ejpam-4348	651	6	,	,	PUNCT
ejpam-4348	651	7	determine	determine	VERB
ejpam-4348	651	8	the	the	DET
ejpam-4348	651	9	projector	projector	NOUN
ejpam-4348	651	10	p̃d	p̃d	NOUN
ejpam-4348	651	11	by	by	ADP
ejpam-4348	651	12	p̃d	p̃d	NOUN
ejpam-4348	651	13	=	=	SYM
ejpam-4348	651	14	2p̃(d	2p̃(d	NUM
ejpam-4348	651	15	)	)	PUNCT
ejpam-4348	651	16	1	1	NUM
ejpam-4348	651	17	.	.	X
ejpam-4348	652	1	4	4	X
ejpam-4348	652	2	.	.	NOUN
ejpam-4348	652	3	numerical	numerical	ADJ
ejpam-4348	652	4	experiments	experiment	NOUN
ejpam-4348	652	5	in	in	ADP
ejpam-4348	652	6	this	this	DET
ejpam-4348	652	7	section	section	NOUN
ejpam-4348	652	8	,	,	PUNCT
ejpam-4348	652	9	we	we	PRON
ejpam-4348	652	10	illustrate	illustrate	VERB
ejpam-4348	652	11	numerical	numerical	ADJ
ejpam-4348	652	12	examples	example	NOUN
ejpam-4348	652	13	using	use	VERB
ejpam-4348	652	14	a	a	DET
ejpam-4348	652	15	matrix	matrix	NOUN
ejpam-4348	652	16	function	function	NOUN
ejpam-4348	652	17	from	from	ADP
ejpam-4348	652	18	[	[	X
ejpam-4348	652	19	2	2	NUM
ejpam-4348	652	20	,	,	PUNCT
ejpam-4348	652	21	4	4	NUM
ejpam-4348	652	22	,	,	PUNCT
ejpam-4348	652	23	5	5	NUM
ejpam-4348	652	24	]	]	PUNCT
ejpam-4348	652	25	on	on	ADP
ejpam-4348	652	26	which	which	PRON
ejpam-4348	652	27	we	we	PRON
ejpam-4348	652	28	apply	apply	VERB
ejpam-4348	652	29	the	the	DET
ejpam-4348	652	30	algorithms	algorithm	NOUN
ejpam-4348	652	31	4	4	NUM
ejpam-4348	652	32	,	,	PUNCT
ejpam-4348	652	33	5	5	NUM
ejpam-4348	652	34	,	,	PUNCT
ejpam-4348	652	35	6	6	NUM
ejpam-4348	652	36	and	and	CCONJ
ejpam-4348	652	37	7	7	NUM
ejpam-4348	652	38	for	for	ADP
ejpam-4348	652	39	positive	positive	ADJ
ejpam-4348	652	40	parameters	parameter	NOUN
ejpam-4348	652	41	p	p	X
ejpam-4348	652	42	,	,	PUNCT
ejpam-4348	652	43	b	b	PROPN
ejpam-4348	652	44	and	and	CCONJ
ejpam-4348	652	45	d	d	AUX
ejpam-4348	652	46	given	give	VERB
ejpam-4348	652	47	.	.	PUNCT
ejpam-4348	653	1	w	w	PROPN
ejpam-4348	653	2	(	(	PUNCT
ejpam-4348	653	3	t	t	PROPN
ejpam-4348	653	4	)	)	PUNCT
ejpam-4348	653	5	=	=	SYM
ejpam-4348	654	1	−(a(s(t)))−t	−(a(s(t)))−t	PROPN
ejpam-4348	654	2	cos(w(t	cos(w(t	NOUN
ejpam-4348	654	3	)	)	PUNCT
ejpam-4348	654	4	)	)	PUNCT
ejpam-4348	654	5	−(a(s(t)))−t	−(a(s(t)))−t	PROPN
ejpam-4348	654	6	sin(w(t	sin(w(t	PROPN
ejpam-4348	654	7	)	)	PUNCT
ejpam-4348	654	8	)	)	PUNCT
ejpam-4348	654	9	a(s(t	a(s(t	NOUN
ejpam-4348	654	10	)	)	PUNCT
ejpam-4348	654	11	)	)	PUNCT
ejpam-4348	654	12	sin(w(t	sin(w(t	NOUN
ejpam-4348	654	13	)	)	PUNCT
ejpam-4348	654	14	)	)	PUNCT
ejpam-4348	655	1	(	(	PUNCT
ejpam-4348	655	2	a(s(t)))−t	a(s(t)))−t	PROPN
ejpam-4348	655	3	cos(w(t	cos(w(t	PROPN
ejpam-4348	655	4	)	)	PUNCT
ejpam-4348	655	5	)	)	PUNCT
ejpam-4348	656	1			NOUN
ejpam-4348	656	2	(	(	PUNCT
ejpam-4348	656	3	49	49	NUM
ejpam-4348	656	4	)	)	PUNCT
ejpam-4348	656	5	avec	avec	NOUN
ejpam-4348	656	6	a(s	a(s	PROPN
ejpam-4348	656	7	)	)	PUNCT
ejpam-4348	656	8	=	=	PRON
ejpam-4348	656	9	(	(	PUNCT
ejpam-4348	656	10	1−	1−	NUM
ejpam-4348	656	11	s2	s2	NOUN
ejpam-4348	656	12	−1	−1	NOUN
ejpam-4348	656	13	s2	s2	NOUN
ejpam-4348	656	14	1−	1−	NUM
ejpam-4348	656	15	s2	s2	PROPN
ejpam-4348	656	16	)	)	PUNCT
ejpam-4348	656	17	,	,	PUNCT
ejpam-4348	656	18	w(t	w(t	PROPN
ejpam-4348	656	19	)	)	PUNCT
ejpam-4348	657	1	=	=	PUNCT
ejpam-4348	657	2	π	π	X
ejpam-4348	657	3	(	(	PUNCT
ejpam-4348	657	4	1	1	NUM
ejpam-4348	657	5	2	2	NUM
ejpam-4348	657	6	−	−	NUM
ejpam-4348	657	7	1	1	NUM
ejpam-4348	657	8	3	3	NUM
ejpam-4348	657	9	sin(3	sin(3	NOUN
ejpam-4348	657	10	t	t	NOUN
ejpam-4348	657	11	)	)	PUNCT
ejpam-4348	657	12	)	)	PUNCT
ejpam-4348	657	13	et	et	PROPN
ejpam-4348	657	14	s(t	s(t	PROPN
ejpam-4348	657	15	)	)	PUNCT
ejpam-4348	657	16	=	=	SYM
ejpam-4348	657	17	4	4	NUM
ejpam-4348	657	18	sin(3	sin(3	NOUN
ejpam-4348	657	19	t	t	NOUN
ejpam-4348	657	20	)	)	PUNCT
ejpam-4348	657	21	•	•	NUM
ejpam-4348	657	22	applying	apply	VERB
ejpam-4348	657	23	algorithm	algorithm	NOUN
ejpam-4348	657	24	4	4	NUM
ejpam-4348	657	25	to	to	PART
ejpam-4348	657	26	matrix	matrix	VERB
ejpam-4348	657	27	function	function	NOUN
ejpam-4348	657	28	(	(	PUNCT
ejpam-4348	657	29	49	49	NUM
ejpam-4348	657	30	)	)	PUNCT
ejpam-4348	657	31	gives	give	VERB
ejpam-4348	657	32	the	the	DET
ejpam-4348	657	33	following	follow	VERB
ejpam-4348	657	34	results	result	NOUN
ejpam-4348	657	35	:	:	PUNCT
ejpam-4348	657	36	·	·	PUNCT
ejpam-4348	657	37	at	at	ADP
ejpam-4348	657	38	t	t	NOUN
ejpam-4348	657	39	=	=	SYM
ejpam-4348	657	40	3.5	3.5	NUM
ejpam-4348	657	41	,	,	PUNCT
ejpam-4348	657	42	those	those	DET
ejpam-4348	657	43	different	different	ADJ
ejpam-4348	657	44	graphs	graph	NOUN
ejpam-4348	657	45	on	on	ADP
ejpam-4348	657	46	figure	figure	NOUN
ejpam-4348	657	47	1	1	NUM
ejpam-4348	657	48	show	show	VERB
ejpam-4348	657	49	how	how	SCONJ
ejpam-4348	657	50	a	a	DET
ejpam-4348	657	51	parabola	parabola	NOUN
ejpam-4348	657	52	γ	γ	X
ejpam-4348	657	53	can	can	AUX
ejpam-4348	657	54	realise	realise	VERB
ejpam-4348	657	55	a	a	DET
ejpam-4348	657	56	dichotomy	dichotomy	NOUN
ejpam-4348	657	57	on	on	ADP
ejpam-4348	657	58	the	the	DET
ejpam-4348	657	59	eigenvalues	eigenvalue	NOUN
ejpam-4348	657	60	of	of	ADP
ejpam-4348	657	61	a	a	DET
ejpam-4348	657	62	given	give	VERB
ejpam-4348	657	63	matrix	matrix	NOUN
ejpam-4348	657	64	.	.	PUNCT
ejpam-4348	658	1	we	we	PRON
ejpam-4348	658	2	have	have	VERB
ejpam-4348	658	3	three	three	NUM
ejpam-4348	658	4	possibilities	possibility	NOUN
ejpam-4348	658	5	:	:	PUNCT
ejpam-4348	658	6	when	when	SCONJ
ejpam-4348	658	7	all	all	DET
ejpam-4348	658	8	the	the	DET
ejpam-4348	658	9	eigenvalues	eigenvalue	NOUN
ejpam-4348	658	10	are	be	AUX
ejpam-4348	658	11	in	in	ADP
ejpam-4348	658	12	the	the	DET
ejpam-4348	658	13	interior	interior	NOUN
ejpam-4348	658	14	,	,	PUNCT
ejpam-4348	658	15	then	then	ADV
ejpam-4348	658	16	the	the	DET
ejpam-4348	658	17	computed	computed	ADJ
ejpam-4348	658	18	projector	projector	NOUN
ejpam-4348	658	19	is	be	AUX
ejpam-4348	658	20	the	the	DET
ejpam-4348	658	21	null	null	ADJ
ejpam-4348	658	22	matrix	matrix	NOUN
ejpam-4348	658	23	.	.	PUNCT
ejpam-4348	659	1	when	when	SCONJ
ejpam-4348	659	2	all	all	DET
ejpam-4348	659	3	the	the	DET
ejpam-4348	659	4	eigenvalues	eigenvalue	NOUN
ejpam-4348	659	5	are	be	AUX
ejpam-4348	659	6	at	at	ADP
ejpam-4348	659	7	the	the	DET
ejpam-4348	659	8	exterior	exterior	NOUN
ejpam-4348	659	9	of	of	ADP
ejpam-4348	659	10	the	the	DET
ejpam-4348	659	11	parabola	parabola	NOUN
ejpam-4348	659	12	,	,	PUNCT
ejpam-4348	659	13	the	the	DET
ejpam-4348	659	14	s.	s.	PROPN
ejpam-4348	659	15	traoré	traoré	PROPN
ejpam-4348	659	16	,	,	PUNCT
ejpam-4348	659	17	m.	m.	NOUN
ejpam-4348	659	18	dosso	dosso	PROPN
ejpam-4348	659	19	/	/	SYM
ejpam-4348	659	20	eur	eur	PROPN
ejpam-4348	659	21	.	.	PUNCT
ejpam-4348	660	1	j.	j.	PROPN
ejpam-4348	660	2	pure	pure	PROPN
ejpam-4348	660	3	appl	appl	PROPN
ejpam-4348	660	4	.	.	PROPN
ejpam-4348	660	5	math	math	PROPN
ejpam-4348	660	6	,	,	PUNCT
ejpam-4348	660	7	15	15	NUM
ejpam-4348	660	8	(	(	PUNCT
ejpam-4348	660	9	2	2	NUM
ejpam-4348	660	10	)	)	PUNCT
ejpam-4348	660	11	(	(	PUNCT
ejpam-4348	660	12	2022	2022	NUM
ejpam-4348	660	13	)	)	PUNCT
ejpam-4348	660	14	,	,	PUNCT
ejpam-4348	660	15	681	681	NUM
ejpam-4348	660	16	-	-	SYM
ejpam-4348	660	17	725	725	NUM
ejpam-4348	660	18	719	719	NUM
ejpam-4348	660	19	−10	−10	NOUN
ejpam-4348	660	20	0	0	NUM
ejpam-4348	660	21	10	10	NUM
ejpam-4348	660	22	−15	−15	NOUN
ejpam-4348	660	23	−10	−10	X
ejpam-4348	660	24	−5	−5	ADV
ejpam-4348	660	25	0	0	NUM
ejpam-4348	660	26	5	5	NUM
ejpam-4348	660	27	10	10	NUM
ejpam-4348	660	28	15	15	NUM
ejpam-4348	660	29	the	the	DET
ejpam-4348	660	30	abscissa	abscissa	ADJ
ejpam-4348	660	31	axis	axis	NOUN
ejpam-4348	660	32	t	t	PROPN
ejpam-4348	660	33	h	h	NOUN
ejpam-4348	660	34	e	e	PROPN
ejpam-4348	660	35	o	o	PROPN
ejpam-4348	660	36	rd	rd	NOUN
ejpam-4348	660	37	in	in	ADP
ejpam-4348	660	38	a	a	DET
ejpam-4348	660	39	te	te	PROPN
ejpam-4348	660	40	a	a	PRON
ejpam-4348	660	41	x	x	PUNCT
ejpam-4348	660	42	is	be	AUX
ejpam-4348	660	43	p=4	p=4	X
ejpam-4348	660	44	and	and	CCONJ
ejpam-4348	660	45	t=3.5	t=3.5	NOUN
ejpam-4348	660	46	−10	−10	X
ejpam-4348	660	47	0	0	NUM
ejpam-4348	660	48	10	10	NUM
ejpam-4348	661	1	−8	−8	NOUN
ejpam-4348	662	1	−6	−6	NOUN
ejpam-4348	662	2	−4	−4	X
ejpam-4348	662	3	−2	−2	NOUN
ejpam-4348	662	4	0	0	NUM
ejpam-4348	662	5	2	2	NUM
ejpam-4348	662	6	4	4	NUM
ejpam-4348	662	7	6	6	NUM
ejpam-4348	662	8	8	8	NUM
ejpam-4348	662	9	the	the	DET
ejpam-4348	662	10	abscissa	abscissa	ADJ
ejpam-4348	662	11	axis	axis	NOUN
ejpam-4348	662	12	t	t	PROPN
ejpam-4348	662	13	h	h	NOUN
ejpam-4348	662	14	e	e	PROPN
ejpam-4348	662	15	o	o	PROPN
ejpam-4348	662	16	rd	rd	NOUN
ejpam-4348	662	17	in	in	ADP
ejpam-4348	662	18	a	a	DET
ejpam-4348	662	19	te	te	PROPN
ejpam-4348	662	20	a	a	DET
ejpam-4348	662	21	x	x	PUNCT
ejpam-4348	662	22	is	be	AUX
ejpam-4348	662	23	p=1.3	p=1.3	ADJ
ejpam-4348	662	24	and	and	CCONJ
ejpam-4348	662	25	t=3.5	t=3.5	NOUN
ejpam-4348	662	26	−10	−10	PUNCT
ejpam-4348	662	27	0	0	NUM
ejpam-4348	662	28	10	10	NUM
ejpam-4348	662	29	−2.5	−2.5	NUM
ejpam-4348	662	30	−2	−2	NOUN
ejpam-4348	662	31	−1.5	−1.5	NOUN
ejpam-4348	662	32	−1	−1	NOUN
ejpam-4348	662	33	−0.5	−0.5	NOUN
ejpam-4348	662	34	0	0	NUM
ejpam-4348	662	35	0.5	0.5	NUM
ejpam-4348	662	36	1	1	NUM
ejpam-4348	662	37	1.5	1.5	NUM
ejpam-4348	662	38	2	2	NUM
ejpam-4348	662	39	2.5	2.5	NUM
ejpam-4348	662	40	the	the	DET
ejpam-4348	662	41	abscissa	abscissa	ADJ
ejpam-4348	662	42	axis	axis	NOUN
ejpam-4348	662	43	t	t	PROPN
ejpam-4348	662	44	h	h	NOUN
ejpam-4348	662	45	e	e	PROPN
ejpam-4348	662	46	o	o	PROPN
ejpam-4348	662	47	rd	rd	NOUN
ejpam-4348	662	48	in	in	ADP
ejpam-4348	662	49	a	a	DET
ejpam-4348	662	50	te	te	PROPN
ejpam-4348	662	51	a	a	PRON
ejpam-4348	662	52	x	x	NOUN
ejpam-4348	662	53	is	be	AUX
ejpam-4348	662	54	p=0.2	p=0.2	NOUN
ejpam-4348	662	55	and	and	CCONJ
ejpam-4348	662	56	t=3.5	t=3.5	NOUN
ejpam-4348	662	57	figure	figure	VERB
ejpam-4348	662	58	1	1	NUM
ejpam-4348	662	59	:	:	PUNCT
ejpam-4348	662	60	partition	partition	NOUN
ejpam-4348	662	61	of	of	ADP
ejpam-4348	662	62	the	the	DET
ejpam-4348	662	63	spectrum	spectrum	NOUN
ejpam-4348	662	64	of	of	ADP
ejpam-4348	662	65	the	the	DET
ejpam-4348	662	66	matrix	matrix	NOUN
ejpam-4348	662	67	w	w	PROPN
ejpam-4348	662	68	(	(	PUNCT
ejpam-4348	662	69	t	t	PROPN
ejpam-4348	662	70	)	)	PUNCT
ejpam-4348	662	71	for	for	ADP
ejpam-4348	662	72	t	t	NOUN
ejpam-4348	662	73	=	=	SYM
ejpam-4348	662	74	3.5	3.5	NUM
ejpam-4348	662	75	by	by	ADP
ejpam-4348	662	76	parabolas	parabola	NOUN
ejpam-4348	662	77	of	of	ADP
ejpam-4348	662	78	equation	equation	NOUN
ejpam-4348	662	79	2p	2p	NUM
ejpam-4348	662	80	(	(	PUNCT
ejpam-4348	662	81	p	p	NOUN
ejpam-4348	662	82	2	2	NUM
ejpam-4348	662	83	−	−	NOUN
ejpam-4348	662	84	x	x	NOUN
ejpam-4348	662	85	)	)	PUNCT
ejpam-4348	662	86	=	=	SYM
ejpam-4348	662	87	y2	y2	PROPN
ejpam-4348	662	88	.	.	PUNCT
ejpam-4348	663	1	table	table	NOUN
ejpam-4348	663	2	1	1	NUM
ejpam-4348	663	3	:	:	SYM
ejpam-4348	663	4	traces	trace	NOUN
ejpam-4348	663	5	,	,	PUNCT
ejpam-4348	663	6	norms	norm	NOUN
ejpam-4348	663	7	and	and	CCONJ
ejpam-4348	663	8	quality	quality	NOUN
ejpam-4348	663	9	of	of	ADP
ejpam-4348	663	10	spectral	spectral	ADJ
ejpam-4348	663	11	projectors	projector	NOUN
ejpam-4348	663	12	p	p	NOUN
ejpam-4348	663	13	by	by	ADP
ejpam-4348	663	14	applying	apply	VERB
ejpam-4348	663	15	the	the	DET
ejpam-4348	663	16	dichop	dichop	NOUN
ejpam-4348	663	17	algorithm	algorithm	NOUN
ejpam-4348	663	18	for	for	ADP
ejpam-4348	663	19	three	three	NUM
ejpam-4348	663	20	values	value	NOUN
ejpam-4348	663	21	of	of	ADP
ejpam-4348	663	22	p	p	NOUN
ejpam-4348	663	23	p	p	NOUN
ejpam-4348	663	24	tr(p	tr(p	NOUN
ejpam-4348	663	25	)	)	PUNCT
ejpam-4348	663	26	∥p∥	∥p∥	PROPN
ejpam-4348	663	27	∥p2	∥p2	NUM
ejpam-4348	663	28	−	−	PROPN
ejpam-4348	663	29	p∥	p∥	NOUN
ejpam-4348	663	30	∥pw	∥pw	PROPN
ejpam-4348	663	31	(	(	PUNCT
ejpam-4348	663	32	t)−w	t)−w	PROPN
ejpam-4348	663	33	(	(	PUNCT
ejpam-4348	663	34	t)p∥	t)p∥	X
ejpam-4348	663	35	∥h∥	∥h∥	PROPN
ejpam-4348	663	36	4	4	NUM
ejpam-4348	663	37	0	0	NUM
ejpam-4348	663	38	0	0	NUM
ejpam-4348	663	39	0	0	NUM
ejpam-4348	663	40	0	0	NUM
ejpam-4348	663	41	4.0502	4.0502	NUM
ejpam-4348	663	42	1.3	1.3	NUM
ejpam-4348	663	43	2	2	NUM
ejpam-4348	663	44	1.6305	1.6305	NUM
ejpam-4348	663	45	2.3747	2.3747	NUM
ejpam-4348	663	46	10−15	10−15	PROPN
ejpam-4348	663	47	5.6077	5.6077	NUM
ejpam-4348	663	48	10−15	10−15	PROPN
ejpam-4348	663	49	63.1478	63.1478	NUM
ejpam-4348	663	50	0.2	0.2	NUM
ejpam-4348	663	51	4	4	NUM
ejpam-4348	663	52	1	1	NUM
ejpam-4348	663	53	2.0540	2.0540	NUM
ejpam-4348	663	54	10−15	10−15	NOUN
ejpam-4348	663	55	5.3639	5.3639	NUM
ejpam-4348	663	56	10−15	10−15	NOUN
ejpam-4348	663	57	6.2228	6.2228	NUM
ejpam-4348	663	58	computed	compute	VERB
ejpam-4348	663	59	projector	projector	NOUN
ejpam-4348	663	60	is	be	AUX
ejpam-4348	663	61	the	the	DET
ejpam-4348	663	62	identity	identity	NOUN
ejpam-4348	663	63	matrix	matrix	NOUN
ejpam-4348	663	64	.	.	PUNCT
ejpam-4348	664	1	a	a	DET
ejpam-4348	664	2	part	part	NOUN
ejpam-4348	664	3	of	of	ADP
ejpam-4348	664	4	the	the	DET
ejpam-4348	664	5	eigenvalues	eigenvalue	NOUN
ejpam-4348	664	6	can	can	AUX
ejpam-4348	664	7	be	be	AUX
ejpam-4348	664	8	in	in	ADP
ejpam-4348	664	9	the	the	DET
ejpam-4348	664	10	interior	interior	NOUN
ejpam-4348	664	11	of	of	ADP
ejpam-4348	664	12	the	the	DET
ejpam-4348	664	13	parabola	parabola	NOUN
ejpam-4348	664	14	and	and	CCONJ
ejpam-4348	664	15	another	another	DET
ejpam-4348	664	16	part	part	NOUN
ejpam-4348	664	17	of	of	ADP
ejpam-4348	664	18	the	the	DET
ejpam-4348	664	19	eigenvalues	eigenvalue	NOUN
ejpam-4348	664	20	can	can	AUX
ejpam-4348	664	21	be	be	AUX
ejpam-4348	664	22	at	at	ADP
ejpam-4348	664	23	the	the	DET
ejpam-4348	664	24	exterior	exterior	NOUN
ejpam-4348	664	25	.	.	PUNCT
ejpam-4348	665	1	in	in	ADP
ejpam-4348	665	2	this	this	DET
ejpam-4348	665	3	case	case	NOUN
ejpam-4348	665	4	,	,	PUNCT
ejpam-4348	665	5	the	the	DET
ejpam-4348	665	6	projector	projector	NOUN
ejpam-4348	665	7	is	be	AUX
ejpam-4348	665	8	different	different	ADJ
ejpam-4348	665	9	of	of	ADP
ejpam-4348	665	10	the	the	DET
ejpam-4348	665	11	null	null	ADJ
ejpam-4348	665	12	matrix	matrix	NOUN
ejpam-4348	665	13	and	and	CCONJ
ejpam-4348	665	14	the	the	DET
ejpam-4348	665	15	identity	identity	NOUN
ejpam-4348	665	16	matrix	matrix	NOUN
ejpam-4348	665	17	.	.	PUNCT
ejpam-4348	666	1	in	in	ADP
ejpam-4348	666	2	the	the	DET
ejpam-4348	666	3	above	above	ADJ
ejpam-4348	666	4	table	table	NOUN
ejpam-4348	666	5	of	of	ADP
ejpam-4348	666	6	values	value	NOUN
ejpam-4348	666	7	,	,	PUNCT
ejpam-4348	666	8	the	the	DET
ejpam-4348	666	9	trace	trace	NOUN
ejpam-4348	666	10	tr(p	tr(p	PUNCT
ejpam-4348	666	11	)	)	PUNCT
ejpam-4348	666	12	of	of	ADP
ejpam-4348	666	13	p	p	NOUN
ejpam-4348	666	14	denotes	denote	VERB
ejpam-4348	666	15	the	the	DET
ejpam-4348	666	16	number	number	NOUN
ejpam-4348	666	17	of	of	ADP
ejpam-4348	666	18	eigenvalues	eigenvalue	NOUN
ejpam-4348	666	19	outside	outside	ADV
ejpam-4348	666	20	of	of	ADP
ejpam-4348	666	21	the	the	DET
ejpam-4348	666	22	parabola	parabola	NOUN
ejpam-4348	666	23	.	.	PUNCT
ejpam-4348	667	1	moreover	moreover	ADV
ejpam-4348	667	2	,	,	PUNCT
ejpam-4348	667	3	the	the	DET
ejpam-4348	667	4	values	value	NOUN
ejpam-4348	667	5	of	of	ADP
ejpam-4348	667	6	∥p∥	∥p∥	NUM
ejpam-4348	667	7	confirm	confirm	VERB
ejpam-4348	667	8	what	what	PRON
ejpam-4348	667	9	was	be	AUX
ejpam-4348	667	10	said	say	VERB
ejpam-4348	667	11	above	above	ADV
ejpam-4348	667	12	.	.	PUNCT
ejpam-4348	668	1	the	the	DET
ejpam-4348	668	2	computing	computing	NOUN
ejpam-4348	668	3	of	of	ADP
ejpam-4348	668	4	∥p2	∥p2	NOUN
ejpam-4348	668	5	−	−	PROPN
ejpam-4348	668	6	p∥	p∥	NOUN
ejpam-4348	668	7	and	and	CCONJ
ejpam-4348	668	8	∥pw	∥pw	PROPN
ejpam-4348	668	9	(	(	PUNCT
ejpam-4348	668	10	t)−w	t)−w	NUM
ejpam-4348	668	11	(	(	PUNCT
ejpam-4348	668	12	t)p∥	t)p∥	NOUN
ejpam-4348	668	13	prove	prove	VERB
ejpam-4348	668	14	that	that	SCONJ
ejpam-4348	668	15	p	p	NOUN
ejpam-4348	668	16	is	be	AUX
ejpam-4348	668	17	a	a	DET
ejpam-4348	668	18	projector	projector	NOUN
ejpam-4348	668	19	and	and	CCONJ
ejpam-4348	668	20	the	the	DET
ejpam-4348	668	21	values	value	NOUN
ejpam-4348	668	22	obtained	obtain	VERB
ejpam-4348	668	23	for	for	ADP
ejpam-4348	668	24	∥h∥	∥h∥	NOUN
ejpam-4348	668	25	show	show	VERB
ejpam-4348	668	26	the	the	DET
ejpam-4348	668	27	good	good	ADJ
ejpam-4348	668	28	quality	quality	NOUN
ejpam-4348	668	29	of	of	ADP
ejpam-4348	668	30	the	the	DET
ejpam-4348	668	31	dichotomy	dichotomy	NOUN
ejpam-4348	668	32	.	.	PUNCT
ejpam-4348	669	1	this	this	PRON
ejpam-4348	669	2	shows	show	VERB
ejpam-4348	669	3	the	the	DET
ejpam-4348	669	4	effectiveness	effectiveness	NOUN
ejpam-4348	669	5	of	of	ADP
ejpam-4348	669	6	the	the	DET
ejpam-4348	669	7	method	method	NOUN
ejpam-4348	669	8	.	.	PUNCT
ejpam-4348	669	9	·	·	PUNCT
ejpam-4348	670	1	the	the	DET
ejpam-4348	670	2	partition	partition	NOUN
ejpam-4348	670	3	of	of	ADP
ejpam-4348	670	4	the	the	DET
ejpam-4348	670	5	eigenvalues	eigenvalue	NOUN
ejpam-4348	670	6	of	of	ADP
ejpam-4348	670	7	w	w	PROPN
ejpam-4348	670	8	(	(	PUNCT
ejpam-4348	670	9	t	t	PROPN
ejpam-4348	670	10	)	)	PUNCT
ejpam-4348	670	11	,	,	PUNCT
ejpam-4348	670	12	∀t	∀t	PROPN
ejpam-4348	670	13	∈	∈	PROPN
ejpam-4348	671	1	[	[	X
ejpam-4348	671	2	0	0	NUM
ejpam-4348	671	3	,	,	PUNCT
ejpam-4348	671	4	π	π	X
ejpam-4348	671	5	]	]	X
ejpam-4348	671	6	with	with	ADP
ejpam-4348	671	7	the	the	DET
ejpam-4348	671	8	parameters	parameter	NOUN
ejpam-4348	671	9	p	p	PROPN
ejpam-4348	671	10	∈	∈	PROPN
ejpam-4348	671	11	{	{	PUNCT
ejpam-4348	671	12	0.5	0.5	NUM
ejpam-4348	671	13	,	,	PUNCT
ejpam-4348	671	14	1	1	NUM
ejpam-4348	671	15	,	,	PUNCT
ejpam-4348	671	16	2	2	NUM
ejpam-4348	671	17	,	,	PUNCT
ejpam-4348	671	18	4	4	NUM
ejpam-4348	671	19	}	}	PUNCT
ejpam-4348	671	20	gives	give	VERB
ejpam-4348	671	21	us	we	PRON
ejpam-4348	671	22	figure	figure	NOUN
ejpam-4348	671	23	2	2	NUM
ejpam-4348	671	24	.	.	PUNCT
ejpam-4348	672	1	those	those	DET
ejpam-4348	672	2	graphs	graph	NOUN
ejpam-4348	672	3	describe	describe	VERB
ejpam-4348	672	4	the	the	DET
ejpam-4348	672	5	spectral	spectral	ADJ
ejpam-4348	672	6	portrait	portrait	NOUN
ejpam-4348	672	7	of	of	ADP
ejpam-4348	672	8	w	w	PROPN
ejpam-4348	672	9	(	(	PUNCT
ejpam-4348	672	10	t),∀t	t),∀t	PROPN
ejpam-4348	672	11	∈	∈	PROPN
ejpam-4348	673	1	[	[	X
ejpam-4348	673	2	0	0	NUM
ejpam-4348	673	3	;	;	PUNCT
ejpam-4348	673	4	2π	2π	NOUN
ejpam-4348	673	5	]	]	PUNCT
ejpam-4348	673	6	this	this	DET
ejpam-4348	673	7	spectrum	spectrum	NOUN
ejpam-4348	673	8	dichotomy	dichotomy	NOUN
ejpam-4348	673	9	realised	realise	VERB
ejpam-4348	673	10	by	by	ADP
ejpam-4348	673	11	the	the	DET
ejpam-4348	673	12	parabola	parabola	PROPN
ejpam-4348	673	13	γ	γ	PROPN
ejpam-4348	673	14	is	be	AUX
ejpam-4348	673	15	illustrated	illustrate	VERB
ejpam-4348	673	16	with	with	ADP
ejpam-4348	673	17	colors	color	NOUN
ejpam-4348	673	18	(	(	PUNCT
ejpam-4348	673	19	the	the	DET
ejpam-4348	673	20	green	green	ADJ
ejpam-4348	673	21	color	color	NOUN
ejpam-4348	673	22	for	for	ADP
ejpam-4348	673	23	the	the	DET
ejpam-4348	673	24	inside	inside	ADJ
ejpam-4348	673	25	eigenvalues	eigenvalue	NOUN
ejpam-4348	673	26	and	and	CCONJ
ejpam-4348	673	27	the	the	DET
ejpam-4348	673	28	red	red	ADJ
ejpam-4348	673	29	color	color	NOUN
ejpam-4348	673	30	for	for	ADP
ejpam-4348	673	31	the	the	DET
ejpam-4348	673	32	outside	outside	ADJ
ejpam-4348	673	33	eigenvalues	eigenvalue	NOUN
ejpam-4348	673	34	)	)	PUNCT
ejpam-4348	673	35	.	.	PUNCT
ejpam-4348	674	1	•	•	NUM
ejpam-4348	674	2	applying	apply	VERB
ejpam-4348	674	3	algorithm	algorithm	NOUN
ejpam-4348	674	4	5	5	NUM
ejpam-4348	674	5	to	to	PART
ejpam-4348	674	6	matrix	matrix	VERB
ejpam-4348	674	7	function	function	NOUN
ejpam-4348	674	8	49	49	NUM
ejpam-4348	674	9	gives	give	VERB
ejpam-4348	674	10	the	the	DET
ejpam-4348	674	11	following	follow	VERB
ejpam-4348	674	12	results	result	NOUN
ejpam-4348	674	13	:	:	PUNCT
ejpam-4348	674	14	·	·	PUNCT
ejpam-4348	674	15	at	at	ADP
ejpam-4348	674	16	t	t	NOUN
ejpam-4348	674	17	=	=	SYM
ejpam-4348	674	18	6	6	NUM
ejpam-4348	674	19	,	,	PUNCT
ejpam-4348	674	20	those	those	DET
ejpam-4348	674	21	different	different	ADJ
ejpam-4348	674	22	graphs	graph	NOUN
ejpam-4348	674	23	on	on	ADP
ejpam-4348	674	24	figure	figure	NOUN
ejpam-4348	674	25	3	3	NUM
ejpam-4348	674	26	show	show	VERB
ejpam-4348	674	27	how	how	SCONJ
ejpam-4348	674	28	a	a	DET
ejpam-4348	674	29	parabola	parabola	PROPN
ejpam-4348	674	30	γ̃	γ̃	PROPN
ejpam-4348	674	31	can	can	AUX
ejpam-4348	674	32	realise	realise	VERB
ejpam-4348	674	33	a	a	DET
ejpam-4348	674	34	dichotomy	dichotomy	NOUN
ejpam-4348	674	35	on	on	ADP
ejpam-4348	674	36	the	the	DET
ejpam-4348	674	37	eigenvalues	eigenvalue	NOUN
ejpam-4348	674	38	of	of	ADP
ejpam-4348	674	39	a	a	DET
ejpam-4348	674	40	given	give	VERB
ejpam-4348	674	41	matrix	matrix	NOUN
ejpam-4348	674	42	.	.	PUNCT
ejpam-4348	675	1	similarly	similarly	ADV
ejpam-4348	675	2	to	to	ADP
ejpam-4348	675	3	the	the	DET
ejpam-4348	675	4	case	case	NOUN
ejpam-4348	675	5	seen	see	VERB
ejpam-4348	675	6	for	for	ADP
ejpam-4348	675	7	s.	s.	PROPN
ejpam-4348	675	8	traoré	traoré	PROPN
ejpam-4348	675	9	,	,	PUNCT
ejpam-4348	675	10	m.	m.	NOUN
ejpam-4348	675	11	dosso	dosso	PROPN
ejpam-4348	675	12	/	/	SYM
ejpam-4348	675	13	eur	eur	PROPN
ejpam-4348	675	14	.	.	PUNCT
ejpam-4348	676	1	j.	j.	PROPN
ejpam-4348	676	2	pure	pure	PROPN
ejpam-4348	676	3	appl	appl	PROPN
ejpam-4348	676	4	.	.	PROPN
ejpam-4348	676	5	math	math	PROPN
ejpam-4348	676	6	,	,	PUNCT
ejpam-4348	676	7	15	15	NUM
ejpam-4348	676	8	(	(	PUNCT
ejpam-4348	676	9	2	2	NUM
ejpam-4348	676	10	)	)	PUNCT
ejpam-4348	676	11	(	(	PUNCT
ejpam-4348	676	12	2022	2022	NUM
ejpam-4348	676	13	)	)	PUNCT
ejpam-4348	676	14	,	,	PUNCT
ejpam-4348	676	15	681	681	NUM
ejpam-4348	676	16	-	-	SYM
ejpam-4348	676	17	725	725	NUM
ejpam-4348	676	18	720	720	NUM
ejpam-4348	676	19	−15	−15	NOUN
ejpam-4348	676	20	−10	−10	PRON
ejpam-4348	676	21	−5	−5	ADV
ejpam-4348	676	22	0	0	NUM
ejpam-4348	676	23	5	5	NUM
ejpam-4348	676	24	−4	−4	NOUN
ejpam-4348	676	25	−2	−2	NOUN
ejpam-4348	676	26	0	0	NUM
ejpam-4348	676	27	2	2	NUM
ejpam-4348	676	28	4	4	NUM
ejpam-4348	676	29	the	the	DET
ejpam-4348	676	30	abscissa	abscissa	ADJ
ejpam-4348	676	31	axis	axis	NOUN
ejpam-4348	676	32	th	th	X
ejpam-4348	676	33	e	e	X
ejpam-4348	676	34	o	o	PROPN
ejpam-4348	676	35	rd	rd	NOUN
ejpam-4348	676	36	in	in	ADP
ejpam-4348	676	37	a	a	DET
ejpam-4348	676	38	te	te	PROPN
ejpam-4348	676	39	a	a	DET
ejpam-4348	676	40	x	x	PUNCT
ejpam-4348	676	41	is	be	AUX
ejpam-4348	676	42	p=0.5	p=0.5	NOUN
ejpam-4348	676	43	−15	−15	NOUN
ejpam-4348	676	44	−10	−10	X
ejpam-4348	676	45	−5	−5	ADV
ejpam-4348	676	46	0	0	NUM
ejpam-4348	676	47	5	5	NUM
ejpam-4348	676	48	−10	−10	SYM
ejpam-4348	676	49	−5	−5	ADV
ejpam-4348	676	50	0	0	NUM
ejpam-4348	676	51	5	5	NUM
ejpam-4348	676	52	10	10	NUM
ejpam-4348	676	53	the	the	DET
ejpam-4348	676	54	abscissa	abscissa	ADJ
ejpam-4348	676	55	axis	axis	NOUN
ejpam-4348	676	56	th	th	X
ejpam-4348	676	57	e	e	X
ejpam-4348	676	58	o	o	PROPN
ejpam-4348	676	59	rd	rd	NOUN
ejpam-4348	676	60	in	in	ADP
ejpam-4348	676	61	a	a	DET
ejpam-4348	676	62	te	te	PROPN
ejpam-4348	676	63	a	a	PRON
ejpam-4348	676	64	x	x	X
ejpam-4348	676	65	is	be	AUX
ejpam-4348	676	66	p=1	p=1	NUM
ejpam-4348	676	67	−15	−15	NOUN
ejpam-4348	676	68	−10	−10	NOUN
ejpam-4348	676	69	−5	−5	ADV
ejpam-4348	676	70	0	0	NUM
ejpam-4348	676	71	5	5	NUM
ejpam-4348	676	72	−10	−10	SYM
ejpam-4348	676	73	−5	−5	ADV
ejpam-4348	676	74	0	0	NUM
ejpam-4348	676	75	5	5	NUM
ejpam-4348	676	76	10	10	NUM
ejpam-4348	676	77	the	the	DET
ejpam-4348	676	78	abscissa	abscissa	ADJ
ejpam-4348	676	79	axis	axis	NOUN
ejpam-4348	676	80	th	th	X
ejpam-4348	676	81	e	e	X
ejpam-4348	676	82	o	o	PROPN
ejpam-4348	676	83	rd	rd	NOUN
ejpam-4348	676	84	in	in	ADP
ejpam-4348	676	85	a	a	DET
ejpam-4348	676	86	te	te	PROPN
ejpam-4348	676	87	a	a	PRON
ejpam-4348	676	88	x	x	X
ejpam-4348	676	89	is	be	AUX
ejpam-4348	676	90	p=2	p=2	PROPN
ejpam-4348	676	91	−15	−15	NOUN
ejpam-4348	676	92	−10	−10	X
ejpam-4348	676	93	−5	−5	ADV
ejpam-4348	676	94	0	0	NUM
ejpam-4348	676	95	5	5	NUM
ejpam-4348	676	96	−20	−20	NOUN
ejpam-4348	676	97	−10	−10	X
ejpam-4348	676	98	0	0	NUM
ejpam-4348	676	99	10	10	NUM
ejpam-4348	676	100	20	20	NUM
ejpam-4348	676	101	the	the	DET
ejpam-4348	676	102	abscissa	abscissa	ADJ
ejpam-4348	676	103	axis	axis	NOUN
ejpam-4348	676	104	th	th	X
ejpam-4348	676	105	e	e	X
ejpam-4348	676	106	o	o	PROPN
ejpam-4348	676	107	rd	rd	NOUN
ejpam-4348	676	108	in	in	ADP
ejpam-4348	676	109	a	a	DET
ejpam-4348	676	110	te	te	PROPN
ejpam-4348	676	111	a	a	PRON
ejpam-4348	676	112	x	x	X
ejpam-4348	676	113	is	be	AUX
ejpam-4348	676	114	p=4	p=4	PRON
ejpam-4348	676	115	figure	figure	NOUN
ejpam-4348	676	116	2	2	NUM
ejpam-4348	676	117	:	:	PUNCT
ejpam-4348	676	118	partition	partition	NOUN
ejpam-4348	676	119	of	of	ADP
ejpam-4348	676	120	the	the	DET
ejpam-4348	676	121	eigenvalues	eigenvalue	NOUN
ejpam-4348	676	122	of	of	ADP
ejpam-4348	676	123	w	w	PROPN
ejpam-4348	676	124	(	(	PUNCT
ejpam-4348	676	125	t	t	PROPN
ejpam-4348	676	126	)	)	PUNCT
ejpam-4348	676	127	,	,	PUNCT
ejpam-4348	676	128	∀t	∀t	PROPN
ejpam-4348	676	129	∈	∈	PROPN
ejpam-4348	677	1	[	[	X
ejpam-4348	677	2	0	0	NUM
ejpam-4348	677	3	,	,	PUNCT
ejpam-4348	677	4	π	π	X
ejpam-4348	677	5	]	]	X
ejpam-4348	677	6	for	for	ADP
ejpam-4348	677	7	p	p	PROPN
ejpam-4348	677	8	∈	∈	PROPN
ejpam-4348	677	9	{	{	PUNCT
ejpam-4348	677	10	0.5	0.5	NUM
ejpam-4348	677	11	,	,	PUNCT
ejpam-4348	677	12	1	1	NUM
ejpam-4348	677	13	,	,	PUNCT
ejpam-4348	677	14	2	2	NUM
ejpam-4348	677	15	,	,	PUNCT
ejpam-4348	677	16	4	4	NUM
ejpam-4348	677	17	}	}	PUNCT
ejpam-4348	677	18	.	.	PUNCT
ejpam-4348	678	1	table	table	NOUN
ejpam-4348	678	2	2	2	NUM
ejpam-4348	678	3	:	:	PUNCT
ejpam-4348	678	4	traces	trace	NOUN
ejpam-4348	678	5	,	,	PUNCT
ejpam-4348	678	6	norms	norm	NOUN
ejpam-4348	678	7	and	and	CCONJ
ejpam-4348	678	8	quality	quality	NOUN
ejpam-4348	678	9	of	of	ADP
ejpam-4348	678	10	spectral	spectral	ADJ
ejpam-4348	678	11	projectors	projector	NOUN
ejpam-4348	678	12	p̃	p̃	PROPN
ejpam-4348	678	13	by	by	ADP
ejpam-4348	678	14	applying	apply	VERB
ejpam-4348	678	15	the	the	DET
ejpam-4348	678	16	dichopb	dichopb	ADJ
ejpam-4348	678	17	algorithm	algorithm	NOUN
ejpam-4348	678	18	for	for	ADP
ejpam-4348	678	19	differents	different	NOUN
ejpam-4348	678	20	values	value	NOUN
ejpam-4348	678	21	of	of	ADP
ejpam-4348	678	22	p	p	NOUN
ejpam-4348	678	23	and	and	CCONJ
ejpam-4348	678	24	b	b	PROPN
ejpam-4348	678	25	p	p	PROPN
ejpam-4348	678	26	b	b	PROPN
ejpam-4348	678	27	tr(p̃	tr(p̃	PROPN
ejpam-4348	678	28	)	)	PUNCT
ejpam-4348	679	1	∥p̃∥	∥p̃∥	NOUN
ejpam-4348	679	2	∥p̃2	∥p̃2	PROPN
ejpam-4348	679	3	−	−	PROPN
ejpam-4348	679	4	p̃∥	p̃∥	NOUN
ejpam-4348	679	5	∥p̃w	∥p̃w	NOUN
ejpam-4348	679	6	(	(	PUNCT
ejpam-4348	679	7	t)−w	t)−w	NUM
ejpam-4348	679	8	(	(	PUNCT
ejpam-4348	679	9	t)p̃∥	t)p̃∥	NOUN
ejpam-4348	679	10	∥h̃∥	∥h̃∥	VERB
ejpam-4348	679	11	2	2	NUM
ejpam-4348	679	12	1	1	NUM
ejpam-4348	679	13	3	3	NUM
ejpam-4348	679	14	1.0268	1.0268	NUM
ejpam-4348	679	15	1.4726	1.4726	NUM
ejpam-4348	679	16	10−15	10−15	PROPN
ejpam-4348	679	17	2.2659	2.2659	NUM
ejpam-4348	679	18	10−15	10−15	NOUN
ejpam-4348	679	19	3.9802	3.9802	NUM
ejpam-4348	679	20	2	2	NUM
ejpam-4348	679	21	3	3	NUM
ejpam-4348	679	22	4	4	NUM
ejpam-4348	679	23	1	1	NUM
ejpam-4348	679	24	2.6170	2.6170	NUM
ejpam-4348	679	25	10−15	10−15	NOUN
ejpam-4348	679	26	3.9255	3.9255	NUM
ejpam-4348	679	27	10−15	10−15	NOUN
ejpam-4348	679	28	0.9799	0.9799	NUM
ejpam-4348	679	29	2	2	NUM
ejpam-4348	679	30	0.1	0.1	NUM
ejpam-4348	679	31	0	0	NUM
ejpam-4348	679	32	4.9838	4.9838	NUM
ejpam-4348	679	33	10−16	10−16	NOUN
ejpam-4348	679	34	4.9838	4.9838	NUM
ejpam-4348	679	35	10−16	10−16	NOUN
ejpam-4348	679	36	8.0143	8.0143	NUM
ejpam-4348	679	37	10−16	10−16	PROPN
ejpam-4348	679	38	29.4351	29.4351	NUM
ejpam-4348	679	39	0.1	0.1	NUM
ejpam-4348	679	40	0.5	0.5	NUM
ejpam-4348	679	41	4	4	NUM
ejpam-4348	679	42	1	1	NUM
ejpam-4348	679	43	2.8478	2.8478	NUM
ejpam-4348	679	44	10−15	10−15	NUM
ejpam-4348	679	45	5.1651	5.1651	NUM
ejpam-4348	679	46	10−15	10−15	PROPN
ejpam-4348	679	47	1.1260	1.1260	NUM
ejpam-4348	679	48	1	1	NUM
ejpam-4348	679	49	0.5	0.5	NUM
ejpam-4348	679	50	3	3	NUM
ejpam-4348	679	51	1.6455	1.6455	NUM
ejpam-4348	679	52	2.6392	2.6392	NUM
ejpam-4348	679	53	10−15	10−15	PROPN
ejpam-4348	679	54	2.6392	2.6392	NUM
ejpam-4348	679	55	10−15	10−15	NOUN
ejpam-4348	679	56	7.7339	7.7339	NUM
ejpam-4348	679	57	4	4	NUM
ejpam-4348	679	58	0.5	0.5	NUM
ejpam-4348	679	59	0	0	NUM
ejpam-4348	679	60	4.8120	4.8120	NUM
ejpam-4348	679	61	10−16	10−16	NOUN
ejpam-4348	679	62	4.8120	4.8120	NUM
ejpam-4348	679	63	10−16	10−16	PROPN
ejpam-4348	679	64	6.0288	6.0288	NUM
ejpam-4348	679	65	10−16	10−16	NOUN
ejpam-4348	679	66	3.7896	3.7896	NUM
ejpam-4348	679	67	the	the	DET
ejpam-4348	679	68	parabola	parabola	PROPN
ejpam-4348	679	69	γ	γ	PROPN
ejpam-4348	679	70	,	,	PUNCT
ejpam-4348	679	71	the	the	DET
ejpam-4348	679	72	values	value	NOUN
ejpam-4348	679	73	obtained	obtain	VERB
ejpam-4348	679	74	for	for	ADP
ejpam-4348	679	75	∥p̃2−	∥p̃2−	NOUN
ejpam-4348	679	76	p̃∥	p̃∥	PUNCT
ejpam-4348	679	77	and	and	CCONJ
ejpam-4348	679	78	∥p̃w	∥p̃w	X
ejpam-4348	679	79	(	(	PUNCT
ejpam-4348	679	80	t)−w	t)−w	PROPN
ejpam-4348	679	81	(	(	PUNCT
ejpam-4348	679	82	t)p̃∥	t)p̃∥	PRON
ejpam-4348	679	83	proved	prove	VERB
ejpam-4348	679	84	that	that	SCONJ
ejpam-4348	679	85	p̃	p̃	PROPN
ejpam-4348	679	86	is	be	AUX
ejpam-4348	679	87	a	a	DET
ejpam-4348	679	88	projector	projector	NOUN
ejpam-4348	679	89	.	.	PUNCT
ejpam-4348	680	1	moreover	moreover	ADV
ejpam-4348	680	2	,	,	PUNCT
ejpam-4348	680	3	the	the	DET
ejpam-4348	680	4	values	value	NOUN
ejpam-4348	680	5	of	of	ADP
ejpam-4348	680	6	∥h̃∥	∥h̃∥	PROPN
ejpam-4348	680	7	show	show	VERB
ejpam-4348	680	8	the	the	DET
ejpam-4348	680	9	good	good	ADJ
ejpam-4348	680	10	quality	quality	NOUN
ejpam-4348	680	11	of	of	ADP
ejpam-4348	680	12	the	the	DET
ejpam-4348	680	13	dichotomy	dichotomy	NOUN
ejpam-4348	680	14	.	.	PUNCT
ejpam-4348	680	15	·	·	PUNCT
ejpam-4348	681	1	the	the	DET
ejpam-4348	681	2	partition	partition	NOUN
ejpam-4348	681	3	of	of	ADP
ejpam-4348	681	4	the	the	DET
ejpam-4348	681	5	eigenvalues	eigenvalues	PROPN
ejpam-4348	681	6	ofw	ofw	PROPN
ejpam-4348	681	7	(	(	PUNCT
ejpam-4348	681	8	t	t	PROPN
ejpam-4348	681	9	)	)	PUNCT
ejpam-4348	681	10	,	,	PUNCT
ejpam-4348	681	11	∀t	∀t	PROPN
ejpam-4348	681	12	∈	∈	PROPN
ejpam-4348	682	1	[	[	X
ejpam-4348	682	2	0	0	NUM
ejpam-4348	682	3	,	,	PUNCT
ejpam-4348	682	4	π	π	X
ejpam-4348	682	5	]	]	X
ejpam-4348	682	6	with	with	ADP
ejpam-4348	682	7	the	the	DET
ejpam-4348	682	8	parameters	parameter	NOUN
ejpam-4348	682	9	(	(	PUNCT
ejpam-4348	682	10	p	p	X
ejpam-4348	682	11	,	,	PUNCT
ejpam-4348	682	12	b	b	NOUN
ejpam-4348	682	13	)	)	PUNCT
ejpam-4348	682	14	∈	∈	NOUN
ejpam-4348	682	15	{	{	PUNCT
ejpam-4348	682	16	(	(	PUNCT
ejpam-4348	682	17	0.5	0.5	NUM
ejpam-4348	682	18	,	,	PUNCT
ejpam-4348	682	19	2	2	NUM
ejpam-4348	682	20	)	)	PUNCT
ejpam-4348	682	21	,	,	PUNCT
ejpam-4348	682	22	(	(	PUNCT
ejpam-4348	682	23	1,−2	1,−2	NUM
ejpam-4348	682	24	)	)	PUNCT
ejpam-4348	682	25	,	,	PUNCT
ejpam-4348	682	26	(	(	PUNCT
ejpam-4348	682	27	2	2	NUM
ejpam-4348	682	28	,	,	PUNCT
ejpam-4348	682	29	0	0	NUM
ejpam-4348	682	30	)	)	PUNCT
ejpam-4348	682	31	,	,	PUNCT
ejpam-4348	682	32	(	(	PUNCT
ejpam-4348	682	33	4	4	NUM
ejpam-4348	682	34	,	,	PUNCT
ejpam-4348	682	35	3	3	NUM
ejpam-4348	682	36	)	)	PUNCT
ejpam-4348	682	37	}	}	PUNCT
ejpam-4348	682	38	gives	give	VERB
ejpam-4348	682	39	us	we	PRON
ejpam-4348	682	40	figure	figure	NOUN
ejpam-4348	682	41	4	4	NUM
ejpam-4348	682	42	.	.	PUNCT
ejpam-4348	683	1	this	this	PRON
ejpam-4348	683	2	shows	show	VERB
ejpam-4348	683	3	the	the	DET
ejpam-4348	683	4	effectiveness	effectiveness	NOUN
ejpam-4348	683	5	of	of	ADP
ejpam-4348	683	6	the	the	DET
ejpam-4348	683	7	method	method	NOUN
ejpam-4348	683	8	.	.	PUNCT
ejpam-4348	684	1	those	those	DET
ejpam-4348	684	2	graphs	graph	NOUN
ejpam-4348	684	3	describe	describe	VERB
ejpam-4348	684	4	the	the	DET
ejpam-4348	684	5	spectral	spectral	ADJ
ejpam-4348	684	6	portrait	portrait	NOUN
ejpam-4348	684	7	of	of	ADP
ejpam-4348	684	8	w	w	PROPN
ejpam-4348	684	9	(	(	PUNCT
ejpam-4348	684	10	t),∀t	t),∀t	PROPN
ejpam-4348	684	11	∈	∈	PROPN
ejpam-4348	685	1	[	[	X
ejpam-4348	685	2	0	0	NUM
ejpam-4348	685	3	;	;	PUNCT
ejpam-4348	685	4	2π	2π	NOUN
ejpam-4348	685	5	]	]	PUNCT
ejpam-4348	685	6	.	.	PUNCT
ejpam-4348	686	1	this	this	DET
ejpam-4348	686	2	spectrum	spectrum	NOUN
ejpam-4348	686	3	dichotomy	dichotomy	NOUN
ejpam-4348	686	4	realised	realise	VERB
ejpam-4348	686	5	by	by	ADP
ejpam-4348	686	6	the	the	DET
ejpam-4348	686	7	parabola	parabola	PROPN
ejpam-4348	686	8	γ̃	γ̃	PROPN
ejpam-4348	686	9	is	be	AUX
ejpam-4348	686	10	illustrated	illustrate	VERB
ejpam-4348	686	11	with	with	ADP
ejpam-4348	686	12	colors	color	NOUN
ejpam-4348	686	13	(	(	PUNCT
ejpam-4348	686	14	the	the	DET
ejpam-4348	686	15	green	green	ADJ
ejpam-4348	686	16	color	color	NOUN
ejpam-4348	686	17	for	for	ADP
ejpam-4348	686	18	the	the	DET
ejpam-4348	686	19	inside	inside	ADJ
ejpam-4348	686	20	eigenvalues	eigenvalue	NOUN
ejpam-4348	686	21	and	and	CCONJ
ejpam-4348	686	22	the	the	DET
ejpam-4348	686	23	red	red	ADJ
ejpam-4348	686	24	color	color	NOUN
ejpam-4348	686	25	for	for	ADP
ejpam-4348	686	26	the	the	DET
ejpam-4348	686	27	outside	outside	ADJ
ejpam-4348	686	28	eigenvalues	eigenvalue	NOUN
ejpam-4348	686	29	)	)	PUNCT
ejpam-4348	686	30	.	.	PUNCT
ejpam-4348	687	1	•	•	NUM
ejpam-4348	687	2	applying	apply	VERB
ejpam-4348	687	3	algorithm	algorithm	NOUN
ejpam-4348	687	4	6	6	NUM
ejpam-4348	687	5	to	to	PART
ejpam-4348	687	6	matrix	matrix	VERB
ejpam-4348	687	7	function	function	NOUN
ejpam-4348	687	8	49	49	NUM
ejpam-4348	687	9	gives	give	VERB
ejpam-4348	687	10	the	the	DET
ejpam-4348	687	11	following	follow	VERB
ejpam-4348	687	12	results	result	NOUN
ejpam-4348	687	13	:	:	PUNCT
ejpam-4348	687	14	·	·	PUNCT
ejpam-4348	687	15	at	at	ADP
ejpam-4348	687	16	t	t	NOUN
ejpam-4348	687	17	=	=	PUNCT
ejpam-4348	687	18	2π	2π	NOUN
ejpam-4348	687	19	,	,	PUNCT
ejpam-4348	687	20	those	those	DET
ejpam-4348	687	21	different	different	ADJ
ejpam-4348	687	22	graphs	graph	NOUN
ejpam-4348	687	23	on	on	ADP
ejpam-4348	687	24	figure	figure	NOUN
ejpam-4348	687	25	5	5	NUM
ejpam-4348	687	26	show	show	VERB
ejpam-4348	687	27	how	how	SCONJ
ejpam-4348	687	28	a	a	DET
ejpam-4348	687	29	parabola	parabola	NOUN
ejpam-4348	687	30	γd	γd	ADV
ejpam-4348	687	31	can	can	AUX
ejpam-4348	687	32	realise	realise	VERB
ejpam-4348	687	33	a	a	DET
ejpam-4348	687	34	dichotomy	dichotomy	NOUN
ejpam-4348	687	35	on	on	ADP
ejpam-4348	687	36	the	the	DET
ejpam-4348	687	37	eigenvalues	eigenvalue	NOUN
ejpam-4348	687	38	of	of	ADP
ejpam-4348	687	39	a	a	DET
ejpam-4348	687	40	given	give	VERB
ejpam-4348	687	41	matrix	matrix	NOUN
ejpam-4348	687	42	.	.	PUNCT
ejpam-4348	688	1	similarly	similarly	ADV
ejpam-4348	688	2	to	to	ADP
ejpam-4348	688	3	the	the	DET
ejpam-4348	688	4	case	case	NOUN
ejpam-4348	688	5	seen	see	VERB
ejpam-4348	688	6	for	for	ADP
ejpam-4348	688	7	the	the	DET
ejpam-4348	688	8	parabola	parabola	PROPN
ejpam-4348	688	9	γ	γ	PROPN
ejpam-4348	688	10	,	,	PUNCT
ejpam-4348	688	11	the	the	DET
ejpam-4348	688	12	values	value	NOUN
ejpam-4348	688	13	obtained	obtain	VERB
ejpam-4348	688	14	for	for	ADP
ejpam-4348	688	15	∥p2	∥p2	NOUN
ejpam-4348	688	16	d−pd∥	d−pd∥	PROPN
ejpam-4348	688	17	s.	s.	PROPN
ejpam-4348	688	18	traoré	traoré	PROPN
ejpam-4348	688	19	,	,	PUNCT
ejpam-4348	688	20	m.	m.	NOUN
ejpam-4348	688	21	dosso	dosso	PROPN
ejpam-4348	688	22	/	/	SYM
ejpam-4348	688	23	eur	eur	PROPN
ejpam-4348	688	24	.	.	PUNCT
ejpam-4348	689	1	j.	j.	PROPN
ejpam-4348	689	2	pure	pure	PROPN
ejpam-4348	689	3	appl	appl	PROPN
ejpam-4348	689	4	.	.	PROPN
ejpam-4348	689	5	math	math	PROPN
ejpam-4348	689	6	,	,	PUNCT
ejpam-4348	689	7	15	15	NUM
ejpam-4348	689	8	(	(	PUNCT
ejpam-4348	689	9	2	2	NUM
ejpam-4348	689	10	)	)	PUNCT
ejpam-4348	689	11	(	(	PUNCT
ejpam-4348	689	12	2022	2022	NUM
ejpam-4348	689	13	)	)	PUNCT
ejpam-4348	689	14	,	,	PUNCT
ejpam-4348	689	15	681	681	NUM
ejpam-4348	689	16	-	-	SYM
ejpam-4348	689	17	725	725	NUM
ejpam-4348	689	18	721	721	NUM
ejpam-4348	689	19	−15	−15	NOUN
ejpam-4348	689	20	−10	−10	X
ejpam-4348	689	21	−5	−5	ADV
ejpam-4348	689	22	0	0	NUM
ejpam-4348	689	23	5	5	NUM
ejpam-4348	689	24	10	10	NUM
ejpam-4348	689	25	15	15	NUM
ejpam-4348	689	26	−10	−10	NOUN
ejpam-4348	689	27	−5	−5	ADV
ejpam-4348	689	28	0	0	NUM
ejpam-4348	689	29	5	5	NUM
ejpam-4348	689	30	10	10	NUM
ejpam-4348	689	31	15	15	NUM
ejpam-4348	689	32	abscisses	abscisse	NOUN
ejpam-4348	689	33	o	o	X
ejpam-4348	689	34	rd	rd	NOUN
ejpam-4348	689	35	o	o	NOUN
ejpam-4348	689	36	n	n	CCONJ
ejpam-4348	689	37	n	n	PRON
ejpam-4348	689	38	�	�	PROPN
ejpam-4348	689	39	e	e	NOUN
ejpam-4348	689	40	s	s	X
ejpam-4348	689	41	for	for	ADP
ejpam-4348	689	42	t=3.5	t=3.5	NOUN
ejpam-4348	689	43	with	with	ADP
ejpam-4348	689	44	p=3	p=3	PROPN
ejpam-4348	689	45	and	and	CCONJ
ejpam-4348	689	46	b=1	b=1	PUNCT
ejpam-4348	689	47	−15	−15	VERB
ejpam-4348	689	48	−10	−10	PRON
ejpam-4348	689	49	−5	−5	ADV
ejpam-4348	689	50	0	0	NUM
ejpam-4348	689	51	5	5	NUM
ejpam-4348	689	52	10	10	NUM
ejpam-4348	689	53	15	15	NUM
ejpam-4348	689	54	−5	−5	NOUN
ejpam-4348	689	55	0	0	NUM
ejpam-4348	689	56	5	5	NUM
ejpam-4348	689	57	10	10	NUM
ejpam-4348	689	58	15	15	NUM
ejpam-4348	689	59	20	20	NUM
ejpam-4348	689	60	abscisses	abscisse	NOUN
ejpam-4348	689	61	o	o	X
ejpam-4348	689	62	rd	rd	NOUN
ejpam-4348	689	63	o	o	NOUN
ejpam-4348	689	64	n	n	CCONJ
ejpam-4348	689	65	n	n	PRON
ejpam-4348	689	66	�	�	PROPN
ejpam-4348	689	67	e	e	NOUN
ejpam-4348	689	68	s	s	X
ejpam-4348	689	69	for	for	ADP
ejpam-4348	689	70	t=3.5	t=3.5	NOUN
ejpam-4348	689	71	with	with	ADP
ejpam-4348	689	72	p=3	p=3	PROPN
ejpam-4348	689	73	and	and	CCONJ
ejpam-4348	689	74	b=0.2	b=0.2	VERB
ejpam-4348	689	75	−15	−15	PROPN
ejpam-4348	689	76	−10	−10	X
ejpam-4348	689	77	−5	−5	ADV
ejpam-4348	689	78	0	0	NUM
ejpam-4348	689	79	5	5	NUM
ejpam-4348	689	80	10	10	NUM
ejpam-4348	689	81	15	15	NUM
ejpam-4348	689	82	−10	−10	NOUN
ejpam-4348	689	83	−5	−5	ADV
ejpam-4348	689	84	0	0	NUM
ejpam-4348	689	85	5	5	NUM
ejpam-4348	689	86	10	10	NUM
ejpam-4348	689	87	15	15	NUM
ejpam-4348	689	88	abscisses	abscisse	NOUN
ejpam-4348	689	89	o	o	X
ejpam-4348	689	90	rd	rd	NOUN
ejpam-4348	689	91	o	o	NOUN
ejpam-4348	689	92	n	n	CCONJ
ejpam-4348	689	93	n	n	PRON
ejpam-4348	689	94	�	�	PROPN
ejpam-4348	689	95	e	e	NOUN
ejpam-4348	689	96	s	s	X
ejpam-4348	689	97	for	for	ADP
ejpam-4348	689	98	t=3.5	t=3.5	NOUN
ejpam-4348	689	99	with	with	ADP
ejpam-4348	689	100	p=3	p=3	PROPN
ejpam-4348	689	101	and	and	CCONJ
ejpam-4348	689	102	b=3	b=3	PROPN
ejpam-4348	689	103	−15	−15	NOUN
ejpam-4348	689	104	−10	−10	X
ejpam-4348	689	105	−5	−5	ADV
ejpam-4348	689	106	0	0	NUM
ejpam-4348	689	107	5	5	NUM
ejpam-4348	689	108	10	10	NUM
ejpam-4348	689	109	15	15	NUM
ejpam-4348	689	110	−10	−10	NOUN
ejpam-4348	689	111	−5	−5	ADV
ejpam-4348	689	112	0	0	NUM
ejpam-4348	689	113	5	5	NUM
ejpam-4348	689	114	10	10	NUM
ejpam-4348	689	115	15	15	NUM
ejpam-4348	689	116	abscisses	abscisse	NOUN
ejpam-4348	689	117	o	o	X
ejpam-4348	689	118	rd	rd	NOUN
ejpam-4348	689	119	o	o	NOUN
ejpam-4348	689	120	n	n	CCONJ
ejpam-4348	689	121	n	n	PRON
ejpam-4348	689	122	�	�	PROPN
ejpam-4348	689	123	e	e	NOUN
ejpam-4348	689	124	s	s	X
ejpam-4348	689	125	for	for	ADP
ejpam-4348	689	126	t=3.5	t=3.5	NOUN
ejpam-4348	689	127	with	with	ADP
ejpam-4348	689	128	p=4	p=4	ADP
ejpam-4348	689	129	and	and	CCONJ
ejpam-4348	689	130	b=0.5	b=0.5	NOUN
ejpam-4348	689	131	−15	−15	NOUN
ejpam-4348	689	132	−10	−10	X
ejpam-4348	689	133	−5	−5	ADV
ejpam-4348	689	134	0	0	NUM
ejpam-4348	689	135	5	5	NUM
ejpam-4348	689	136	10	10	NUM
ejpam-4348	689	137	15	15	NUM
ejpam-4348	689	138	−6	−6	NOUN
ejpam-4348	690	1	−4	−4	NOUN
ejpam-4348	690	2	−2	−2	NOUN
ejpam-4348	690	3	0	0	NUM
ejpam-4348	690	4	2	2	NUM
ejpam-4348	690	5	4	4	NUM
ejpam-4348	690	6	6	6	NUM
ejpam-4348	690	7	8	8	NUM
ejpam-4348	690	8	abscisses	abscisse	NOUN
ejpam-4348	690	9	o	o	X
ejpam-4348	690	10	rd	rd	NOUN
ejpam-4348	690	11	o	o	NOUN
ejpam-4348	690	12	n	n	CCONJ
ejpam-4348	690	13	n	n	PRON
ejpam-4348	690	14	�	�	PROPN
ejpam-4348	690	15	e	e	NOUN
ejpam-4348	690	16	s	s	X
ejpam-4348	690	17	for	for	ADP
ejpam-4348	690	18	t=3.5	t=3.5	NOUN
ejpam-4348	690	19	with	with	ADP
ejpam-4348	690	20	p=1	p=1	PROPN
ejpam-4348	690	21	and	and	CCONJ
ejpam-4348	690	22	b=0.5	b=0.5	NOUN
ejpam-4348	690	23	−15	−15	NOUN
ejpam-4348	690	24	−10	−10	X
ejpam-4348	690	25	−5	−5	ADV
ejpam-4348	690	26	0	0	NUM
ejpam-4348	690	27	5	5	NUM
ejpam-4348	690	28	10	10	NUM
ejpam-4348	690	29	15	15	NUM
ejpam-4348	690	30	−3	−3	ADJ
ejpam-4348	690	31	−2	−2	NOUN
ejpam-4348	690	32	−1	−1	NOUN
ejpam-4348	690	33	0	0	NUM
ejpam-4348	690	34	1	1	NUM
ejpam-4348	690	35	2	2	NUM
ejpam-4348	690	36	3	3	NUM
ejpam-4348	690	37	abscisses	abscisse	NOUN
ejpam-4348	690	38	o	o	X
ejpam-4348	690	39	rd	rd	NOUN
ejpam-4348	690	40	o	o	NOUN
ejpam-4348	690	41	n	n	CCONJ
ejpam-4348	690	42	n	n	PRON
ejpam-4348	690	43	�	�	PROPN
ejpam-4348	690	44	e	e	NOUN
ejpam-4348	690	45	s	s	X
ejpam-4348	690	46	for	for	ADP
ejpam-4348	690	47	t=3.5	t=3.5	NOUN
ejpam-4348	690	48	with	with	ADP
ejpam-4348	690	49	p=0.2	p=0.2	NOUN
ejpam-4348	690	50	and	and	CCONJ
ejpam-4348	690	51	b=0.5	b=0.5	ADJ
ejpam-4348	690	52	figure	figure	NOUN
ejpam-4348	690	53	3	3	NUM
ejpam-4348	690	54	:	:	PUNCT
ejpam-4348	690	55	partition	partition	NOUN
ejpam-4348	690	56	of	of	ADP
ejpam-4348	690	57	the	the	DET
ejpam-4348	690	58	spectrum	spectrum	NOUN
ejpam-4348	690	59	of	of	ADP
ejpam-4348	690	60	the	the	DET
ejpam-4348	690	61	matrix	matrix	NOUN
ejpam-4348	690	62	w	w	PROPN
ejpam-4348	690	63	(	(	PUNCT
ejpam-4348	690	64	t	t	PROPN
ejpam-4348	690	65	)	)	PUNCT
ejpam-4348	690	66	for	for	ADP
ejpam-4348	690	67	t	t	NOUN
ejpam-4348	690	68	=	=	SYM
ejpam-4348	690	69	6	6	NUM
ejpam-4348	690	70	by	by	ADP
ejpam-4348	690	71	parabolas	parabola	NOUN
ejpam-4348	690	72	of	of	ADP
ejpam-4348	690	73	equation	equation	NOUN
ejpam-4348	690	74	2p	2p	NUM
ejpam-4348	690	75	(	(	PUNCT
ejpam-4348	690	76	p	p	NOUN
ejpam-4348	690	77	2	2	NUM
ejpam-4348	690	78	−x	−x	NOUN
ejpam-4348	690	79	)	)	PUNCT
ejpam-4348	690	80	=	=	SYM
ejpam-4348	691	1	(	(	PUNCT
ejpam-4348	691	2	y−ipb)2	y−ipb)2	PROPN
ejpam-4348	691	3	.	.	PROPN
ejpam-4348	691	4	table	table	NOUN
ejpam-4348	691	5	3	3	NUM
ejpam-4348	691	6	:	:	SYM
ejpam-4348	691	7	traces	trace	NOUN
ejpam-4348	691	8	,	,	PUNCT
ejpam-4348	691	9	norms	norm	NOUN
ejpam-4348	691	10	and	and	CCONJ
ejpam-4348	691	11	quality	quality	NOUN
ejpam-4348	691	12	of	of	ADP
ejpam-4348	691	13	spectral	spectral	ADJ
ejpam-4348	691	14	projectors	projector	NOUN
ejpam-4348	691	15	pd	pd	X
ejpam-4348	691	16	by	by	ADP
ejpam-4348	691	17	applying	apply	VERB
ejpam-4348	691	18	the	the	DET
ejpam-4348	691	19	dichopd	dichopd	NOUN
ejpam-4348	691	20	algorithm	algorithm	NOUN
ejpam-4348	691	21	for	for	ADP
ejpam-4348	691	22	differents	different	NOUN
ejpam-4348	691	23	values	value	NOUN
ejpam-4348	691	24	of	of	ADP
ejpam-4348	691	25	p	p	NOUN
ejpam-4348	691	26	and	and	CCONJ
ejpam-4348	691	27	d	d	PROPN
ejpam-4348	691	28	p	p	PROPN
ejpam-4348	691	29	d	d	PROPN
ejpam-4348	691	30	tr(pd	tr(pd	NOUN
ejpam-4348	691	31	)	)	PUNCT
ejpam-4348	691	32	∥pd∥	∥pd∥	NOUN
ejpam-4348	691	33	∥p2	∥p2	PUNCT
ejpam-4348	692	1	d	d	ADP
ejpam-4348	692	2	−	−	PROPN
ejpam-4348	692	3	pd∥	pd∥	NOUN
ejpam-4348	692	4	∥pdw	∥pdw	NUM
ejpam-4348	692	5	(	(	PUNCT
ejpam-4348	692	6	t)−w	t)−w	PROPN
ejpam-4348	692	7	(	(	PUNCT
ejpam-4348	692	8	t)pd∥	t)pd∥	X
ejpam-4348	692	9	∥hd∥	∥hd∥	NOUN
ejpam-4348	692	10	0.1	0.1	NUM
ejpam-4348	692	11	5	5	NUM
ejpam-4348	692	12	0	0	NUM
ejpam-4348	692	13	1.9703	1.9703	NUM
ejpam-4348	692	14	10−17	10−17	NUM
ejpam-4348	692	15	1.9703	1.9703	NUM
ejpam-4348	692	16	10−17	10−17	NUM
ejpam-4348	692	17	4.1735	4.1735	NUM
ejpam-4348	692	18	10−17	10−17	NUM
ejpam-4348	692	19	37.0029	37.0029	NUM
ejpam-4348	692	20	0.1	0.1	NUM
ejpam-4348	692	21	2	2	NUM
ejpam-4348	692	22	4	4	NUM
ejpam-4348	692	23	1	1	NUM
ejpam-4348	692	24	1.3784	1.3784	NUM
ejpam-4348	692	25	10−15	10−15	NUM
ejpam-4348	692	26	1.9182	1.9182	NUM
ejpam-4348	692	27	10−15	10−15	NOUN
ejpam-4348	692	28	11.0360	11.0360	NUM
ejpam-4348	692	29	0.1	0.1	NUM
ejpam-4348	692	30	3.5	3.5	NUM
ejpam-4348	692	31	2	2	NUM
ejpam-4348	692	32	1	1	NUM
ejpam-4348	692	33	2.8954	2.8954	NUM
ejpam-4348	692	34	10−15	10−15	NOUN
ejpam-4348	692	35	5.0227	5.0227	NUM
ejpam-4348	692	36	10−15	10−15	NOUN
ejpam-4348	692	37	96.0484	96.0484	NUM
ejpam-4348	692	38	0.15	0.15	NUM
ejpam-4348	692	39	1.5	1.5	NUM
ejpam-4348	692	40	4	4	NUM
ejpam-4348	692	41	1	1	NUM
ejpam-4348	692	42	2.1579	2.1579	NUM
ejpam-4348	692	43	10−15	10−15	PROPN
ejpam-4348	692	44	3.6774	3.6774	NUM
ejpam-4348	692	45	10−15	10−15	NUM
ejpam-4348	692	46	15.1757	15.1757	NUM
ejpam-4348	692	47	0.25	0.25	NUM
ejpam-4348	692	48	1.5	1.5	NUM
ejpam-4348	692	49	2	2	NUM
ejpam-4348	692	50	1	1	NUM
ejpam-4348	692	51	4.4977	4.4977	NUM
ejpam-4348	692	52	10−16	10−16	NOUN
ejpam-4348	692	53	2.0476	2.0476	NUM
ejpam-4348	692	54	10−15	10−15	NUM
ejpam-4348	692	55	9.6088	9.6088	NUM
ejpam-4348	692	56	2	2	NUM
ejpam-4348	692	57	1.5	1.5	NUM
ejpam-4348	692	58	0	0	NUM
ejpam-4348	693	1	6.2936	6.2936	NUM
ejpam-4348	693	2	10−17	10−17	NUM
ejpam-4348	693	3	6.2936	6.2936	NUM
ejpam-4348	693	4	10−17	10−17	NUM
ejpam-4348	693	5	1.0107	1.0107	NUM
ejpam-4348	693	6	10−16	10−16	NOUN
ejpam-4348	693	7	1.1828	1.1828	NUM
ejpam-4348	693	8	and	and	CCONJ
ejpam-4348	693	9	∥pdw	∥pdw	VERB
ejpam-4348	693	10	−wpd∥	−wpd∥	NOUN
ejpam-4348	693	11	proved	prove	VERB
ejpam-4348	693	12	that	that	SCONJ
ejpam-4348	693	13	pd	pd	PROPN
ejpam-4348	693	14	is	be	AUX
ejpam-4348	693	15	a	a	DET
ejpam-4348	693	16	projector	projector	NOUN
ejpam-4348	693	17	.	.	PUNCT
ejpam-4348	694	1	moreover	moreover	ADV
ejpam-4348	694	2	,	,	PUNCT
ejpam-4348	694	3	the	the	DET
ejpam-4348	694	4	values	value	NOUN
ejpam-4348	694	5	of	of	ADP
ejpam-4348	694	6	∥hd∥	∥hd∥	NOUN
ejpam-4348	694	7	show	show	VERB
ejpam-4348	694	8	the	the	DET
ejpam-4348	694	9	good	good	ADJ
ejpam-4348	694	10	quality	quality	NOUN
ejpam-4348	694	11	of	of	ADP
ejpam-4348	694	12	the	the	DET
ejpam-4348	694	13	dichotomy	dichotomy	NOUN
ejpam-4348	694	14	.	.	PUNCT
ejpam-4348	694	15	·	·	PUNCT
ejpam-4348	695	1	the	the	DET
ejpam-4348	695	2	partition	partition	NOUN
ejpam-4348	695	3	of	of	ADP
ejpam-4348	695	4	the	the	DET
ejpam-4348	695	5	eigenvalues	eigenvalues	PROPN
ejpam-4348	695	6	ofw	ofw	PROPN
ejpam-4348	695	7	(	(	PUNCT
ejpam-4348	695	8	t	t	PROPN
ejpam-4348	695	9	)	)	PUNCT
ejpam-4348	695	10	,	,	PUNCT
ejpam-4348	695	11	∀t	∀t	PROPN
ejpam-4348	695	12	∈	∈	PROPN
ejpam-4348	696	1	[	[	X
ejpam-4348	696	2	0	0	NUM
ejpam-4348	696	3	,	,	PUNCT
ejpam-4348	696	4	π	π	X
ejpam-4348	696	5	]	]	X
ejpam-4348	696	6	with	with	ADP
ejpam-4348	696	7	the	the	DET
ejpam-4348	696	8	parameters	parameter	NOUN
ejpam-4348	696	9	(	(	PUNCT
ejpam-4348	696	10	p	p	X
ejpam-4348	696	11	,	,	PUNCT
ejpam-4348	696	12	d	d	NOUN
ejpam-4348	696	13	)	)	PUNCT
ejpam-4348	696	14	∈	∈	NOUN
ejpam-4348	696	15	{	{	PUNCT
ejpam-4348	696	16	(	(	PUNCT
ejpam-4348	696	17	0.5	0.5	NUM
ejpam-4348	696	18	,	,	PUNCT
ejpam-4348	696	19	0.5	0.5	NUM
ejpam-4348	696	20	)	)	PUNCT
ejpam-4348	696	21	,	,	PUNCT
ejpam-4348	696	22	(	(	PUNCT
ejpam-4348	696	23	2	2	NUM
ejpam-4348	696	24	,	,	PUNCT
ejpam-4348	696	25	1	1	NUM
ejpam-4348	696	26	)	)	PUNCT
ejpam-4348	696	27	,	,	PUNCT
ejpam-4348	696	28	(	(	PUNCT
ejpam-4348	696	29	0.2	0.2	NUM
ejpam-4348	696	30	,	,	PUNCT
ejpam-4348	696	31	2	2	NUM
ejpam-4348	696	32	)	)	PUNCT
ejpam-4348	696	33	,	,	PUNCT
ejpam-4348	696	34	(	(	PUNCT
ejpam-4348	696	35	0.2	0.2	NUM
ejpam-4348	696	36	,	,	PUNCT
ejpam-4348	696	37	7	7	NUM
ejpam-4348	696	38	)	)	PUNCT
ejpam-4348	696	39	}	}	PUNCT
ejpam-4348	696	40	gives	give	VERB
ejpam-4348	696	41	us	we	PRON
ejpam-4348	696	42	figure	figure	NOUN
ejpam-4348	696	43	6	6	NUM
ejpam-4348	696	44	.	.	PUNCT
ejpam-4348	697	1	this	this	PRON
ejpam-4348	697	2	shows	show	VERB
ejpam-4348	697	3	the	the	DET
ejpam-4348	697	4	effectiveness	effectiveness	NOUN
ejpam-4348	697	5	of	of	ADP
ejpam-4348	697	6	the	the	DET
ejpam-4348	697	7	method	method	NOUN
ejpam-4348	697	8	.	.	PUNCT
ejpam-4348	698	1	those	those	DET
ejpam-4348	698	2	graphs	graph	NOUN
ejpam-4348	698	3	describe	describe	VERB
ejpam-4348	698	4	the	the	DET
ejpam-4348	698	5	spectral	spectral	ADJ
ejpam-4348	698	6	portrait	portrait	NOUN
ejpam-4348	698	7	of	of	ADP
ejpam-4348	698	8	w	w	PROPN
ejpam-4348	698	9	(	(	PUNCT
ejpam-4348	698	10	t),∀t	t),∀t	PROPN
ejpam-4348	698	11	∈	∈	PROPN
ejpam-4348	699	1	[	[	X
ejpam-4348	699	2	0	0	NUM
ejpam-4348	699	3	;	;	PUNCT
ejpam-4348	699	4	2π	2π	NOUN
ejpam-4348	699	5	]	]	PUNCT
ejpam-4348	699	6	this	this	DET
ejpam-4348	699	7	spectrum	spectrum	NOUN
ejpam-4348	699	8	dichotomy	dichotomy	NOUN
ejpam-4348	699	9	realised	realise	VERB
ejpam-4348	699	10	by	by	ADP
ejpam-4348	699	11	the	the	DET
ejpam-4348	699	12	parabola	parabola	PROPN
ejpam-4348	699	13	γd	γd	ADP
ejpam-4348	699	14	is	be	AUX
ejpam-4348	699	15	illustrated	illustrate	VERB
ejpam-4348	699	16	with	with	ADP
ejpam-4348	699	17	colors	color	NOUN
ejpam-4348	699	18	(	(	PUNCT
ejpam-4348	699	19	the	the	DET
ejpam-4348	699	20	green	green	ADJ
ejpam-4348	699	21	color	color	NOUN
ejpam-4348	699	22	for	for	ADP
ejpam-4348	699	23	the	the	DET
ejpam-4348	699	24	inside	inside	ADJ
ejpam-4348	699	25	eigenvalues	eigenvalue	NOUN
ejpam-4348	699	26	and	and	CCONJ
ejpam-4348	699	27	the	the	DET
ejpam-4348	699	28	red	red	ADJ
ejpam-4348	699	29	color	color	NOUN
ejpam-4348	699	30	for	for	ADP
ejpam-4348	699	31	the	the	DET
ejpam-4348	699	32	outside	outside	ADJ
ejpam-4348	699	33	eigenvalues	eigenvalue	NOUN
ejpam-4348	699	34	)	)	PUNCT
ejpam-4348	699	35	.	.	PUNCT
ejpam-4348	700	1	•	•	NUM
ejpam-4348	700	2	applying	apply	VERB
ejpam-4348	700	3	algorithm	algorithm	NOUN
ejpam-4348	700	4	7	7	NUM
ejpam-4348	700	5	to	to	PART
ejpam-4348	700	6	matrix	matrix	VERB
ejpam-4348	700	7	function	function	NOUN
ejpam-4348	700	8	49	49	NUM
ejpam-4348	700	9	gives	give	VERB
ejpam-4348	700	10	the	the	DET
ejpam-4348	700	11	following	follow	VERB
ejpam-4348	700	12	results	result	NOUN
ejpam-4348	700	13	:	:	PUNCT
ejpam-4348	700	14	·	·	PUNCT
ejpam-4348	700	15	at	at	ADP
ejpam-4348	700	16	t	t	NOUN
ejpam-4348	700	17	=	=	SYM
ejpam-4348	700	18	3.5	3.5	NUM
ejpam-4348	700	19	,	,	PUNCT
ejpam-4348	700	20	those	those	DET
ejpam-4348	700	21	different	different	ADJ
ejpam-4348	700	22	graphs	graph	NOUN
ejpam-4348	700	23	on	on	ADP
ejpam-4348	700	24	figure	figure	NOUN
ejpam-4348	700	25	7	7	NUM
ejpam-4348	700	26	show	show	VERB
ejpam-4348	700	27	how	how	SCONJ
ejpam-4348	700	28	a	a	DET
ejpam-4348	700	29	parabola	parabola	NOUN
ejpam-4348	700	30	γ̃d	γ̃d	X
ejpam-4348	700	31	can	can	AUX
ejpam-4348	700	32	realise	realise	VERB
ejpam-4348	700	33	a	a	DET
ejpam-4348	700	34	dichotomy	dichotomy	NOUN
ejpam-4348	700	35	on	on	ADP
ejpam-4348	700	36	the	the	DET
ejpam-4348	700	37	eigenvalues	eigenvalue	NOUN
ejpam-4348	700	38	of	of	ADP
ejpam-4348	700	39	a	a	DET
ejpam-4348	700	40	given	give	VERB
ejpam-4348	700	41	matrix	matrix	NOUN
ejpam-4348	700	42	.	.	PUNCT
ejpam-4348	701	1	similarly	similarly	ADV
ejpam-4348	701	2	to	to	ADP
ejpam-4348	701	3	the	the	DET
ejpam-4348	701	4	case	case	NOUN
ejpam-4348	701	5	seen	see	VERB
ejpam-4348	701	6	for	for	ADP
ejpam-4348	701	7	the	the	DET
ejpam-4348	701	8	parabola	parabola	PROPN
ejpam-4348	701	9	γ	γ	PROPN
ejpam-4348	701	10	,	,	PUNCT
ejpam-4348	701	11	the	the	DET
ejpam-4348	701	12	values	value	NOUN
ejpam-4348	701	13	obtained	obtain	VERB
ejpam-4348	701	14	for	for	ADP
ejpam-4348	701	15	∥p̃d	∥p̃d	NOUN
ejpam-4348	701	16	2	2	NUM
ejpam-4348	701	17	−	−	NOUN
ejpam-4348	701	18	p̃d∥	p̃d∥	NOUN
ejpam-4348	701	19	and	and	CCONJ
ejpam-4348	701	20	∥p̃dw	∥p̃dw	PROPN
ejpam-4348	701	21	(	(	PUNCT
ejpam-4348	701	22	t)−w	t)−w	PROPN
ejpam-4348	701	23	(	(	PUNCT
ejpam-4348	701	24	t)p̃d∥	t)p̃d∥	PROPN
ejpam-4348	701	25	proved	prove	VERB
ejpam-4348	701	26	that	that	SCONJ
ejpam-4348	701	27	p̃d	p̃d	NOUN
ejpam-4348	701	28	is	be	AUX
ejpam-4348	701	29	a	a	DET
ejpam-4348	701	30	projector	projector	NOUN
ejpam-4348	701	31	.	.	PUNCT
ejpam-4348	702	1	moreover	moreover	ADV
ejpam-4348	702	2	,	,	PUNCT
ejpam-4348	702	3	the	the	DET
ejpam-4348	702	4	values	value	NOUN
ejpam-4348	702	5	of	of	ADP
ejpam-4348	702	6	∥h̃d∥	∥h̃d∥	ADJ
ejpam-4348	702	7	show	show	VERB
ejpam-4348	702	8	the	the	DET
ejpam-4348	702	9	good	good	ADJ
ejpam-4348	702	10	quality	quality	NOUN
ejpam-4348	702	11	of	of	ADP
ejpam-4348	702	12	the	the	DET
ejpam-4348	702	13	dichotomy	dichotomy	NOUN
ejpam-4348	702	14	.	.	PUNCT
ejpam-4348	703	1	s.	s.	PROPN
ejpam-4348	703	2	traoré	traoré	PROPN
ejpam-4348	703	3	,	,	PUNCT
ejpam-4348	703	4	m.	m.	NOUN
ejpam-4348	703	5	dosso	dosso	PROPN
ejpam-4348	703	6	/	/	SYM
ejpam-4348	703	7	eur	eur	PROPN
ejpam-4348	703	8	.	.	PUNCT
ejpam-4348	704	1	j.	j.	PROPN
ejpam-4348	704	2	pure	pure	PROPN
ejpam-4348	704	3	appl	appl	PROPN
ejpam-4348	704	4	.	.	PROPN
ejpam-4348	704	5	math	math	PROPN
ejpam-4348	704	6	,	,	PUNCT
ejpam-4348	704	7	15	15	NUM
ejpam-4348	704	8	(	(	PUNCT
ejpam-4348	704	9	2	2	NUM
ejpam-4348	704	10	)	)	PUNCT
ejpam-4348	704	11	(	(	PUNCT
ejpam-4348	704	12	2022	2022	NUM
ejpam-4348	704	13	)	)	PUNCT
ejpam-4348	704	14	,	,	PUNCT
ejpam-4348	704	15	681	681	NUM
ejpam-4348	704	16	-	-	SYM
ejpam-4348	704	17	725	725	NUM
ejpam-4348	704	18	722	722	NUM
ejpam-4348	704	19	−10	−10	NOUN
ejpam-4348	704	20	0	0	NUM
ejpam-4348	704	21	10	10	NUM
ejpam-4348	704	22	−5	−5	NOUN
ejpam-4348	704	23	0	0	NUM
ejpam-4348	704	24	5	5	NUM
ejpam-4348	704	25	the	the	DET
ejpam-4348	704	26	abscissa	abscissa	ADJ
ejpam-4348	704	27	axis	axis	NOUN
ejpam-4348	704	28	t	t	PROPN
ejpam-4348	704	29	h	h	NOUN
ejpam-4348	704	30	e	e	PROPN
ejpam-4348	704	31	o	o	PROPN
ejpam-4348	704	32	rd	rd	NOUN
ejpam-4348	704	33	in	in	ADP
ejpam-4348	704	34	a	a	DET
ejpam-4348	704	35	te	te	PROPN
ejpam-4348	704	36	a	a	DET
ejpam-4348	704	37	x	x	PUNCT
ejpam-4348	704	38	is	be	AUX
ejpam-4348	704	39	p=0.5	p=0.5	NOUN
ejpam-4348	704	40	et	et	NOUN
ejpam-4348	704	41	b=2	b=2	NOUN
ejpam-4348	704	42	−10	−10	X
ejpam-4348	704	43	0	0	NUM
ejpam-4348	704	44	10	10	NUM
ejpam-4348	704	45	−5	−5	NOUN
ejpam-4348	704	46	0	0	NUM
ejpam-4348	704	47	5	5	NUM
ejpam-4348	704	48	10	10	NUM
ejpam-4348	704	49	the	the	DET
ejpam-4348	704	50	abscissa	abscissa	ADJ
ejpam-4348	704	51	axis	axis	NOUN
ejpam-4348	704	52	t	t	PROPN
ejpam-4348	704	53	h	h	NOUN
ejpam-4348	704	54	e	e	PROPN
ejpam-4348	704	55	o	o	PROPN
ejpam-4348	704	56	rd	rd	NOUN
ejpam-4348	704	57	in	in	ADP
ejpam-4348	704	58	a	a	DET
ejpam-4348	704	59	te	te	PROPN
ejpam-4348	704	60	a	a	PRON
ejpam-4348	704	61	x	x	X
ejpam-4348	704	62	is	be	AUX
ejpam-4348	704	63	p=1	p=1	NOUN
ejpam-4348	704	64	et	et	NOUN
ejpam-4348	704	65	b=−2	b=−2	NOUN
ejpam-4348	704	66	−10	−10	PROPN
ejpam-4348	704	67	0	0	NUM
ejpam-4348	704	68	10	10	NUM
ejpam-4348	704	69	−10	−10	SYM
ejpam-4348	704	70	−5	−5	ADV
ejpam-4348	704	71	0	0	NUM
ejpam-4348	704	72	5	5	NUM
ejpam-4348	704	73	10	10	NUM
ejpam-4348	704	74	the	the	DET
ejpam-4348	704	75	abscissa	abscissa	ADJ
ejpam-4348	704	76	axis	axis	NOUN
ejpam-4348	704	77	t	t	PROPN
ejpam-4348	704	78	h	h	NOUN
ejpam-4348	704	79	e	e	PROPN
ejpam-4348	704	80	o	o	PROPN
ejpam-4348	704	81	rd	rd	NOUN
ejpam-4348	704	82	in	in	ADP
ejpam-4348	704	83	a	a	DET
ejpam-4348	704	84	te	te	PROPN
ejpam-4348	704	85	a	a	PRON
ejpam-4348	704	86	x	x	PUNCT
ejpam-4348	704	87	is	be	AUX
ejpam-4348	704	88	p=3	p=3	PROPN
ejpam-4348	704	89	et	et	NOUN
ejpam-4348	704	90	b=0	b=0	NOUN
ejpam-4348	704	91	−10	−10	PUNCT
ejpam-4348	704	92	0	0	NUM
ejpam-4348	704	93	10	10	NUM
ejpam-4348	704	94	−30	−30	NOUN
ejpam-4348	704	95	−20	−20	PROPN
ejpam-4348	704	96	−10	−10	NOUN
ejpam-4348	704	97	0	0	NUM
ejpam-4348	704	98	10	10	NUM
ejpam-4348	704	99	the	the	DET
ejpam-4348	704	100	abscissa	abscissa	ADJ
ejpam-4348	704	101	axis	axis	NOUN
ejpam-4348	704	102	t	t	PROPN
ejpam-4348	704	103	h	h	NOUN
ejpam-4348	704	104	e	e	PROPN
ejpam-4348	704	105	o	o	PROPN
ejpam-4348	704	106	rd	rd	NOUN
ejpam-4348	704	107	in	in	ADP
ejpam-4348	704	108	a	a	DET
ejpam-4348	704	109	te	te	PROPN
ejpam-4348	704	110	a	a	PRON
ejpam-4348	704	111	x	x	PUNCT
ejpam-4348	704	112	is	be	AUX
ejpam-4348	704	113	p=4	p=4	NUM
ejpam-4348	704	114	et	et	NOUN
ejpam-4348	704	115	b=3	b=3	NOUN
ejpam-4348	704	116	figure	figure	NOUN
ejpam-4348	704	117	4	4	NUM
ejpam-4348	704	118	:	:	PUNCT
ejpam-4348	704	119	partition	partition	NOUN
ejpam-4348	704	120	of	of	ADP
ejpam-4348	704	121	the	the	DET
ejpam-4348	704	122	eigenvalues	eigenvalue	NOUN
ejpam-4348	704	123	of	of	ADP
ejpam-4348	704	124	w	w	PROPN
ejpam-4348	704	125	(	(	PUNCT
ejpam-4348	704	126	t	t	PROPN
ejpam-4348	704	127	)	)	PUNCT
ejpam-4348	704	128	,	,	PUNCT
ejpam-4348	704	129	∀t	∀t	PROPN
ejpam-4348	704	130	∈	∈	PROPN
ejpam-4348	705	1	[	[	X
ejpam-4348	705	2	0	0	NUM
ejpam-4348	705	3	,	,	PUNCT
ejpam-4348	705	4	π	π	X
ejpam-4348	705	5	]	]	X
ejpam-4348	705	6	with	with	ADP
ejpam-4348	705	7	(	(	PUNCT
ejpam-4348	705	8	p	p	X
ejpam-4348	705	9	,	,	PUNCT
ejpam-4348	705	10	b	b	NOUN
ejpam-4348	705	11	)	)	PUNCT
ejpam-4348	705	12	∈	∈	NOUN
ejpam-4348	705	13	{	{	PUNCT
ejpam-4348	705	14	(	(	PUNCT
ejpam-4348	705	15	0.5	0.5	NUM
ejpam-4348	705	16	,	,	PUNCT
ejpam-4348	705	17	2	2	NUM
ejpam-4348	705	18	)	)	PUNCT
ejpam-4348	705	19	,	,	PUNCT
ejpam-4348	705	20	(	(	PUNCT
ejpam-4348	705	21	1,−2	1,−2	NUM
ejpam-4348	705	22	)	)	PUNCT
ejpam-4348	705	23	,	,	PUNCT
ejpam-4348	705	24	(	(	PUNCT
ejpam-4348	705	25	2	2	NUM
ejpam-4348	705	26	,	,	PUNCT
ejpam-4348	705	27	0	0	NUM
ejpam-4348	705	28	)	)	PUNCT
ejpam-4348	705	29	,	,	PUNCT
ejpam-4348	705	30	(	(	PUNCT
ejpam-4348	705	31	4	4	NUM
ejpam-4348	705	32	,	,	PUNCT
ejpam-4348	705	33	3	3	NUM
ejpam-4348	705	34	)	)	PUNCT
ejpam-4348	705	35	}	}	PUNCT
ejpam-4348	705	36	.	.	PUNCT
ejpam-4348	706	1	−15	−15	PROPN
ejpam-4348	706	2	−10	−10	PRON
ejpam-4348	706	3	−5	−5	ADV
ejpam-4348	707	1	0	0	NUM
ejpam-4348	707	2	5	5	NUM
ejpam-4348	707	3	−6	−6	NOUN
ejpam-4348	707	4	−4	−4	X
ejpam-4348	707	5	−2	−2	NOUN
ejpam-4348	707	6	0	0	NUM
ejpam-4348	707	7	2	2	NUM
ejpam-4348	707	8	4	4	NUM
ejpam-4348	707	9	6	6	NUM
ejpam-4348	707	10	abscisses	abscisse	NOUN
ejpam-4348	707	11	o	o	X
ejpam-4348	707	12	rd	rd	NOUN
ejpam-4348	707	13	o	o	NOUN
ejpam-4348	707	14	n	n	CCONJ
ejpam-4348	707	15	n	n	PRON
ejpam-4348	707	16	�	�	PROPN
ejpam-4348	707	17	e	e	NOUN
ejpam-4348	707	18	s	s	X
ejpam-4348	707	19	for	for	ADP
ejpam-4348	707	20	t=3.5	t=3.5	NOUN
ejpam-4348	707	21	with	with	ADP
ejpam-4348	707	22	p=1	p=1	NOUN
ejpam-4348	707	23	and	and	CCONJ
ejpam-4348	707	24	d=0.6	d=0.6	ADJ
ejpam-4348	707	25	−15	−15	NOUN
ejpam-4348	707	26	−10	−10	PRON
ejpam-4348	707	27	−5	−5	ADV
ejpam-4348	707	28	0	0	NUM
ejpam-4348	707	29	5	5	NUM
ejpam-4348	707	30	−6	−6	NOUN
ejpam-4348	708	1	−4	−4	X
ejpam-4348	709	1	−2	−2	NOUN
ejpam-4348	709	2	0	0	NUM
ejpam-4348	709	3	2	2	NUM
ejpam-4348	709	4	4	4	NUM
ejpam-4348	709	5	6	6	NUM
ejpam-4348	709	6	abscisses	abscisse	NOUN
ejpam-4348	709	7	o	o	X
ejpam-4348	709	8	rd	rd	NOUN
ejpam-4348	709	9	o	o	NOUN
ejpam-4348	709	10	n	n	CCONJ
ejpam-4348	709	11	n	n	PRON
ejpam-4348	709	12	�	�	PROPN
ejpam-4348	709	13	e	e	NOUN
ejpam-4348	709	14	s	s	X
ejpam-4348	709	15	for	for	ADP
ejpam-4348	709	16	t=3.5	t=3.5	NOUN
ejpam-4348	709	17	with	with	ADP
ejpam-4348	709	18	p=1	p=1	PROPN
ejpam-4348	709	19	and	and	CCONJ
ejpam-4348	709	20	d=0.8	d=0.8	VERB
ejpam-4348	709	21	−15	−15	NOUN
ejpam-4348	709	22	−10	−10	X
ejpam-4348	709	23	−5	−5	ADV
ejpam-4348	710	1	0	0	NUM
ejpam-4348	710	2	5	5	NUM
ejpam-4348	710	3	−6	−6	NOUN
ejpam-4348	710	4	−4	−4	X
ejpam-4348	710	5	−2	−2	NOUN
ejpam-4348	710	6	0	0	NUM
ejpam-4348	710	7	2	2	NUM
ejpam-4348	710	8	4	4	NUM
ejpam-4348	710	9	6	6	NUM
ejpam-4348	710	10	abscisses	abscisse	NOUN
ejpam-4348	710	11	o	o	X
ejpam-4348	710	12	rd	rd	NOUN
ejpam-4348	710	13	o	o	NOUN
ejpam-4348	710	14	n	n	CCONJ
ejpam-4348	710	15	n	n	PRON
ejpam-4348	710	16	�	�	PROPN
ejpam-4348	710	17	e	e	NOUN
ejpam-4348	710	18	s	s	X
ejpam-4348	710	19	for	for	ADP
ejpam-4348	710	20	t=3.5	t=3.5	NOUN
ejpam-4348	710	21	with	with	ADP
ejpam-4348	710	22	p=1	p=1	PROPN
ejpam-4348	710	23	and	and	CCONJ
ejpam-4348	710	24	d=2	d=2	PROPN
ejpam-4348	710	25	−15	−15	NOUN
ejpam-4348	710	26	−10	−10	X
ejpam-4348	710	27	−5	−5	ADV
ejpam-4348	710	28	0	0	NUM
ejpam-4348	710	29	5	5	NUM
ejpam-4348	710	30	−4	−4	NOUN
ejpam-4348	710	31	−3	−3	PROPN
ejpam-4348	710	32	−2	−2	PROPN
ejpam-4348	710	33	−1	−1	NOUN
ejpam-4348	710	34	0	0	NUM
ejpam-4348	710	35	1	1	NUM
ejpam-4348	710	36	2	2	NUM
ejpam-4348	710	37	3	3	NUM
ejpam-4348	710	38	4	4	NUM
ejpam-4348	710	39	abscisses	abscisse	NOUN
ejpam-4348	710	40	o	o	X
ejpam-4348	710	41	rd	rd	NOUN
ejpam-4348	710	42	o	o	NOUN
ejpam-4348	710	43	n	n	CCONJ
ejpam-4348	710	44	n	n	PRON
ejpam-4348	710	45	�	�	PROPN
ejpam-4348	710	46	e	e	NOUN
ejpam-4348	710	47	s	s	X
ejpam-4348	710	48	for	for	ADP
ejpam-4348	710	49	t=3.5	t=3.5	NOUN
ejpam-4348	710	50	with	with	ADP
ejpam-4348	710	51	p=0.35	p=0.35	NOUN
ejpam-4348	710	52	and	and	CCONJ
ejpam-4348	710	53	d=1.3	d=1.3	ADJ
ejpam-4348	710	54	−15	−15	NOUN
ejpam-4348	710	55	−10	−10	X
ejpam-4348	710	56	−5	−5	ADV
ejpam-4348	710	57	0	0	NUM
ejpam-4348	710	58	5	5	NUM
ejpam-4348	710	59	−10	−10	SYM
ejpam-4348	710	60	−5	−5	ADV
ejpam-4348	710	61	0	0	NUM
ejpam-4348	710	62	5	5	NUM
ejpam-4348	710	63	10	10	NUM
ejpam-4348	710	64	abscisses	abscisse	NOUN
ejpam-4348	710	65	o	o	X
ejpam-4348	710	66	rd	rd	NOUN
ejpam-4348	710	67	o	o	NOUN
ejpam-4348	710	68	n	n	CCONJ
ejpam-4348	710	69	n	n	PRON
ejpam-4348	710	70	�	�	PROPN
ejpam-4348	710	71	e	e	NOUN
ejpam-4348	710	72	s	s	X
ejpam-4348	710	73	for	for	ADP
ejpam-4348	710	74	t=3.5	t=3.5	NOUN
ejpam-4348	710	75	with	with	ADP
ejpam-4348	710	76	p=2	p=2	PROPN
ejpam-4348	710	77	and	and	CCONJ
ejpam-4348	710	78	d=1.3	d=1.3	ADJ
ejpam-4348	710	79	−15	−15	NOUN
ejpam-4348	710	80	−10	−10	X
ejpam-4348	710	81	−5	−5	ADV
ejpam-4348	710	82	0	0	NUM
ejpam-4348	710	83	5	5	NUM
ejpam-4348	710	84	−3	−3	NOUN
ejpam-4348	710	85	−2	−2	NOUN
ejpam-4348	710	86	−1	−1	NOUN
ejpam-4348	710	87	0	0	NUM
ejpam-4348	710	88	1	1	NUM
ejpam-4348	710	89	2	2	NUM
ejpam-4348	710	90	3	3	NUM
ejpam-4348	710	91	abscisses	abscisse	NOUN
ejpam-4348	710	92	o	o	X
ejpam-4348	710	93	rd	rd	NOUN
ejpam-4348	710	94	o	o	NOUN
ejpam-4348	710	95	n	n	CCONJ
ejpam-4348	710	96	n	n	PRON
ejpam-4348	710	97	�	�	PROPN
ejpam-4348	710	98	e	e	NOUN
ejpam-4348	710	99	s	s	X
ejpam-4348	710	100	for	for	ADP
ejpam-4348	710	101	t=3.5	t=3.5	NOUN
ejpam-4348	710	102	with	with	ADP
ejpam-4348	710	103	p=0.2	p=0.2	NOUN
ejpam-4348	710	104	and	and	CCONJ
ejpam-4348	710	105	d=1.3	d=1.3	ADJ
ejpam-4348	710	106	figure	figure	NOUN
ejpam-4348	710	107	5	5	NUM
ejpam-4348	710	108	:	:	PUNCT
ejpam-4348	710	109	partition	partition	NOUN
ejpam-4348	710	110	of	of	ADP
ejpam-4348	710	111	the	the	DET
ejpam-4348	710	112	spectrum	spectrum	NOUN
ejpam-4348	710	113	of	of	ADP
ejpam-4348	710	114	the	the	DET
ejpam-4348	710	115	matrix	matrix	NOUN
ejpam-4348	710	116	w	w	PROPN
ejpam-4348	710	117	(	(	PUNCT
ejpam-4348	710	118	t	t	PROPN
ejpam-4348	710	119	)	)	PUNCT
ejpam-4348	710	120	for	for	ADP
ejpam-4348	710	121	t	t	NOUN
ejpam-4348	710	122	=	=	PUNCT
ejpam-4348	710	123	2π	2π	NOUN
ejpam-4348	710	124	by	by	ADP
ejpam-4348	710	125	parabolas	parabola	NOUN
ejpam-4348	710	126	of	of	ADP
ejpam-4348	710	127	equation	equation	NOUN
ejpam-4348	710	128	2p(d−	2p(d−	NUM
ejpam-4348	710	129	x	x	X
ejpam-4348	710	130	)	)	PUNCT
ejpam-4348	710	131	=	=	SYM
ejpam-4348	710	132	y2	y2	PROPN
ejpam-4348	710	133	.	.	PUNCT
ejpam-4348	710	134	·	·	PUNCT
ejpam-4348	711	1	the	the	DET
ejpam-4348	711	2	partition	partition	NOUN
ejpam-4348	711	3	of	of	ADP
ejpam-4348	711	4	the	the	DET
ejpam-4348	711	5	eigenvalues	eigenvalue	NOUN
ejpam-4348	711	6	of	of	ADP
ejpam-4348	711	7	w	w	PROPN
ejpam-4348	711	8	(	(	PUNCT
ejpam-4348	711	9	t	t	PROPN
ejpam-4348	711	10	)	)	PUNCT
ejpam-4348	711	11	,	,	PUNCT
ejpam-4348	711	12	∀t	∀t	PROPN
ejpam-4348	711	13	∈	∈	PROPN
ejpam-4348	712	1	[	[	X
ejpam-4348	712	2	0	0	NUM
ejpam-4348	712	3	,	,	PUNCT
ejpam-4348	712	4	π	π	X
ejpam-4348	712	5	]	]	X
ejpam-4348	712	6	with	with	ADP
ejpam-4348	712	7	the	the	DET
ejpam-4348	712	8	parameters	parameter	NOUN
ejpam-4348	712	9	(	(	PUNCT
ejpam-4348	712	10	p	p	X
ejpam-4348	712	11	,	,	PUNCT
ejpam-4348	712	12	d	d	PROPN
ejpam-4348	712	13	,	,	PUNCT
ejpam-4348	712	14	b	b	NOUN
ejpam-4348	712	15	)	)	PUNCT
ejpam-4348	712	16	∈	∈	NOUN
ejpam-4348	712	17	{	{	PUNCT
ejpam-4348	712	18	(	(	PUNCT
ejpam-4348	712	19	0.5	0.5	NUM
ejpam-4348	712	20	,	,	PUNCT
ejpam-4348	712	21	0.5	0.5	NUM
ejpam-4348	712	22	,	,	PUNCT
ejpam-4348	712	23	2	2	NUM
ejpam-4348	712	24	)	)	PUNCT
ejpam-4348	712	25	,	,	PUNCT
ejpam-4348	712	26	(	(	PUNCT
ejpam-4348	712	27	2	2	NUM
ejpam-4348	712	28	,	,	PUNCT
ejpam-4348	712	29	1,−2	1,−2	NUM
ejpam-4348	712	30	)	)	PUNCT
ejpam-4348	712	31	,	,	PUNCT
ejpam-4348	712	32	(	(	PUNCT
ejpam-4348	712	33	0.2	0.2	NUM
ejpam-4348	712	34	,	,	PUNCT
ejpam-4348	712	35	2	2	NUM
ejpam-4348	712	36	,	,	PUNCT
ejpam-4348	712	37	0	0	NUM
ejpam-4348	712	38	)	)	PUNCT
ejpam-4348	712	39	,	,	PUNCT
ejpam-4348	712	40	(	(	PUNCT
ejpam-4348	712	41	0.2	0.2	NUM
ejpam-4348	712	42	,	,	PUNCT
ejpam-4348	712	43	7	7	NUM
ejpam-4348	712	44	,	,	PUNCT
ejpam-4348	712	45	3	3	NUM
ejpam-4348	712	46	)	)	PUNCT
ejpam-4348	712	47	}	}	PUNCT
ejpam-4348	712	48	gives	give	VERB
ejpam-4348	712	49	us	we	PRON
ejpam-4348	712	50	figure	figure	NOUN
ejpam-4348	712	51	8	8	NUM
ejpam-4348	712	52	.	.	PUNCT
ejpam-4348	713	1	this	this	PRON
ejpam-4348	713	2	shows	show	VERB
ejpam-4348	713	3	the	the	DET
ejpam-4348	713	4	effectiveness	effectiveness	NOUN
ejpam-4348	713	5	of	of	ADP
ejpam-4348	713	6	the	the	DET
ejpam-4348	713	7	method	method	NOUN
ejpam-4348	713	8	.	.	PUNCT
ejpam-4348	714	1	those	those	DET
ejpam-4348	714	2	graphs	graph	NOUN
ejpam-4348	714	3	describe	describe	VERB
ejpam-4348	714	4	the	the	DET
ejpam-4348	714	5	spectral	spectral	ADJ
ejpam-4348	714	6	portrait	portrait	NOUN
ejpam-4348	714	7	of	of	ADP
ejpam-4348	714	8	w	w	PROPN
ejpam-4348	714	9	(	(	PUNCT
ejpam-4348	714	10	t),∀t	t),∀t	PROPN
ejpam-4348	714	11	∈	∈	PROPN
ejpam-4348	715	1	[	[	X
ejpam-4348	715	2	0	0	NUM
ejpam-4348	715	3	;	;	PUNCT
ejpam-4348	715	4	2π	2π	NOUN
ejpam-4348	715	5	]	]	PUNCT
ejpam-4348	715	6	this	this	DET
ejpam-4348	715	7	spectrum	spectrum	NOUN
ejpam-4348	715	8	dichotomy	dichotomy	NOUN
ejpam-4348	715	9	realised	realise	VERB
ejpam-4348	715	10	by	by	ADP
ejpam-4348	715	11	the	the	DET
ejpam-4348	715	12	parabola	parabola	PROPN
ejpam-4348	715	13	γ̃d	γ̃d	PROPN
ejpam-4348	715	14	is	be	AUX
ejpam-4348	715	15	illustrated	illustrate	VERB
ejpam-4348	715	16	with	with	ADP
ejpam-4348	715	17	colors	color	NOUN
ejpam-4348	715	18	(	(	PUNCT
ejpam-4348	715	19	the	the	DET
ejpam-4348	715	20	green	green	ADJ
ejpam-4348	715	21	color	color	NOUN
ejpam-4348	715	22	for	for	ADP
ejpam-4348	715	23	the	the	DET
ejpam-4348	715	24	inside	inside	ADJ
ejpam-4348	715	25	eigenvalues	eigenvalue	NOUN
ejpam-4348	715	26	and	and	CCONJ
ejpam-4348	715	27	the	the	DET
ejpam-4348	715	28	red	red	ADJ
ejpam-4348	715	29	color	color	NOUN
ejpam-4348	715	30	for	for	ADP
ejpam-4348	715	31	the	the	DET
ejpam-4348	715	32	outside	outside	ADJ
ejpam-4348	715	33	eigenvalues	eigenvalue	NOUN
ejpam-4348	715	34	)	)	PUNCT
ejpam-4348	715	35	.	.	PUNCT
ejpam-4348	716	1	5	5	X
ejpam-4348	716	2	.	.	X
ejpam-4348	716	3	conclusion	conclusion	NOUN
ejpam-4348	716	4	in	in	ADP
ejpam-4348	716	5	this	this	DET
ejpam-4348	716	6	work	work	NOUN
ejpam-4348	716	7	,	,	PUNCT
ejpam-4348	716	8	we	we	PRON
ejpam-4348	716	9	proposed	propose	VERB
ejpam-4348	716	10	methods	method	NOUN
ejpam-4348	716	11	of	of	ADP
ejpam-4348	716	12	spectral	spectral	ADJ
ejpam-4348	716	13	dichotomies	dichotomy	NOUN
ejpam-4348	716	14	of	of	ADP
ejpam-4348	716	15	a	a	DET
ejpam-4348	716	16	matrix	matrix	NOUN
ejpam-4348	716	17	with	with	ADP
ejpam-4348	716	18	respect	respect	NOUN
ejpam-4348	716	19	to	to	ADP
ejpam-4348	716	20	the	the	DET
ejpam-4348	716	21	general	general	ADJ
ejpam-4348	716	22	equation	equation	NOUN
ejpam-4348	716	23	x	x	PUNCT
ejpam-4348	716	24	=	=	PUNCT
ejpam-4348	717	1	ay2	ay2	NOUN
ejpam-4348	717	2	+	+	NUM
ejpam-4348	717	3	by+	by+	NOUN
ejpam-4348	717	4	c	c	NOUN
ejpam-4348	717	5	wth	wth	VERB
ejpam-4348	717	6	a	a	DET
ejpam-4348	717	7	̸=	̸=	PROPN
ejpam-4348	717	8	0	0	NUM
ejpam-4348	717	9	of	of	ADP
ejpam-4348	717	10	a	a	DET
ejpam-4348	717	11	parabola	parabola	PROPN
ejpam-4348	717	12	γa	γa	PROPN
ejpam-4348	717	13	,	,	PUNCT
ejpam-4348	717	14	b	b	PROPN
ejpam-4348	717	15	,	,	PUNCT
ejpam-4348	717	16	c.	c.	NOUN
ejpam-4348	717	17	these	these	DET
ejpam-4348	717	18	methods	method	NOUN
ejpam-4348	717	19	are	be	AUX
ejpam-4348	717	20	modifications	modification	NOUN
ejpam-4348	717	21	of	of	ADP
ejpam-4348	717	22	the	the	DET
ejpam-4348	717	23	algorithm	algorithm	NOUN
ejpam-4348	717	24	proposed	propose	VERB
ejpam-4348	717	25	by	by	ADP
ejpam-4348	717	26	a.	a.	PROPN
ejpam-4348	717	27	n.	n.	PROPN
ejpam-4348	717	28	malyshev	malyshev	PROPN
ejpam-4348	717	29	and	and	CCONJ
ejpam-4348	717	30	m.	m.	NOUN
ejpam-4348	717	31	sadkane	sadkane	NOUN
ejpam-4348	717	32	in	in	ADP
ejpam-4348	717	33	[	[	X
ejpam-4348	717	34	13	13	NUM
ejpam-4348	717	35	]	]	PUNCT
ejpam-4348	717	36	.	.	PUNCT
ejpam-4348	718	1	in	in	ADP
ejpam-4348	718	2	s.	s.	PROPN
ejpam-4348	718	3	traoré	traoré	PROPN
ejpam-4348	718	4	,	,	PUNCT
ejpam-4348	718	5	m.	m.	NOUN
ejpam-4348	718	6	dosso	dosso	PROPN
ejpam-4348	718	7	/	/	SYM
ejpam-4348	718	8	eur	eur	PROPN
ejpam-4348	718	9	.	.	PUNCT
ejpam-4348	719	1	j.	j.	PROPN
ejpam-4348	719	2	pure	pure	PROPN
ejpam-4348	719	3	appl	appl	PROPN
ejpam-4348	719	4	.	.	PROPN
ejpam-4348	719	5	math	math	PROPN
ejpam-4348	719	6	,	,	PUNCT
ejpam-4348	719	7	15	15	NUM
ejpam-4348	719	8	(	(	PUNCT
ejpam-4348	719	9	2	2	NUM
ejpam-4348	719	10	)	)	PUNCT
ejpam-4348	719	11	(	(	PUNCT
ejpam-4348	719	12	2022	2022	NUM
ejpam-4348	719	13	)	)	PUNCT
ejpam-4348	719	14	,	,	PUNCT
ejpam-4348	719	15	681	681	NUM
ejpam-4348	719	16	-	-	SYM
ejpam-4348	719	17	725	725	NUM
ejpam-4348	719	18	723	723	NUM
ejpam-4348	719	19	−15	−15	NOUN
ejpam-4348	719	20	−10	−10	NOUN
ejpam-4348	719	21	−5	−5	ADV
ejpam-4348	719	22	0	0	NUM
ejpam-4348	719	23	5	5	NUM
ejpam-4348	719	24	−4	−4	NOUN
ejpam-4348	719	25	−2	−2	NOUN
ejpam-4348	719	26	0	0	NUM
ejpam-4348	719	27	2	2	NUM
ejpam-4348	719	28	4	4	NUM
ejpam-4348	719	29	l’axe	l’axe	VERB
ejpam-4348	719	30	des	des	PROPN
ejpam-4348	719	31	abscisses	abscisses	PROPN
ejpam-4348	719	32	l’a	l’a	PROPN
ejpam-4348	719	33	x	x	X
ejpam-4348	719	34	e	e	X
ejpam-4348	719	35	d	d	X
ejpam-4348	719	36	e	e	X
ejpam-4348	719	37	s	s	PROPN
ejpam-4348	719	38	o	o	PROPN
ejpam-4348	719	39	rd	rd	NOUN
ejpam-4348	719	40	o	o	NOUN
ejpam-4348	719	41	n	n	CCONJ
ejpam-4348	719	42	n	n	ADV
ejpam-4348	719	43	é	é	NOUN
ejpam-4348	719	44	e	e	NOUN
ejpam-4348	719	45	s	s	PROPN
ejpam-4348	719	46	p=0.5	p=0.5	NOUN
ejpam-4348	719	47	et	et	NOUN
ejpam-4348	719	48	d=0.5	d=0.5	NOUN
ejpam-4348	719	49	−15	−15	X
ejpam-4348	719	50	−10	−10	NOUN
ejpam-4348	719	51	−5	−5	ADV
ejpam-4348	719	52	0	0	NUM
ejpam-4348	719	53	5	5	NUM
ejpam-4348	719	54	−10	−10	SYM
ejpam-4348	719	55	−5	−5	ADV
ejpam-4348	719	56	0	0	NUM
ejpam-4348	719	57	5	5	NUM
ejpam-4348	719	58	10	10	NUM
ejpam-4348	719	59	l’axe	l’axe	VERB
ejpam-4348	719	60	des	des	PROPN
ejpam-4348	719	61	abscisses	abscisses	PROPN
ejpam-4348	719	62	l’a	l’a	PROPN
ejpam-4348	719	63	x	x	X
ejpam-4348	719	64	e	e	X
ejpam-4348	719	65	d	d	X
ejpam-4348	719	66	e	e	X
ejpam-4348	719	67	s	s	PROPN
ejpam-4348	719	68	o	o	PROPN
ejpam-4348	719	69	rd	rd	NOUN
ejpam-4348	719	70	o	o	NOUN
ejpam-4348	719	71	n	n	CCONJ
ejpam-4348	719	72	n	n	ADV
ejpam-4348	719	73	é	é	PROPN
ejpam-4348	719	74	e	e	X
ejpam-4348	719	75	s	s	PROPN
ejpam-4348	719	76	p=2	p=2	PROPN
ejpam-4348	719	77	et	et	NOUN
ejpam-4348	719	78	d=1	d=1	NOUN
ejpam-4348	719	79	−15	−15	NOUN
ejpam-4348	719	80	−10	−10	X
ejpam-4348	719	81	−5	−5	ADV
ejpam-4348	719	82	0	0	NUM
ejpam-4348	719	83	5	5	NUM
ejpam-4348	719	84	−5	−5	NOUN
ejpam-4348	719	85	0	0	NUM
ejpam-4348	719	86	5	5	NUM
ejpam-4348	719	87	l’axe	l’axe	VERB
ejpam-4348	719	88	des	des	PROPN
ejpam-4348	719	89	abscisses	abscisses	PROPN
ejpam-4348	719	90	l’a	l’a	PROPN
ejpam-4348	719	91	x	x	X
ejpam-4348	719	92	e	e	X
ejpam-4348	719	93	d	d	X
ejpam-4348	719	94	e	e	X
ejpam-4348	719	95	s	s	PROPN
ejpam-4348	719	96	o	o	PROPN
ejpam-4348	719	97	rd	rd	NOUN
ejpam-4348	719	98	o	o	NOUN
ejpam-4348	719	99	n	n	CCONJ
ejpam-4348	719	100	n	n	ADV
ejpam-4348	719	101	é	é	NOUN
ejpam-4348	719	102	e	e	NOUN
ejpam-4348	719	103	s	s	X
ejpam-4348	719	104	p=0.2	p=0.2	NOUN
ejpam-4348	719	105	et	et	NOUN
ejpam-4348	719	106	d=2	d=2	X
ejpam-4348	719	107	−15	−15	X
ejpam-4348	719	108	−10	−10	NOUN
ejpam-4348	719	109	−5	−5	ADV
ejpam-4348	719	110	0	0	NUM
ejpam-4348	719	111	5	5	NUM
ejpam-4348	719	112	−10	−10	SYM
ejpam-4348	719	113	−5	−5	ADV
ejpam-4348	719	114	0	0	NUM
ejpam-4348	719	115	5	5	NUM
ejpam-4348	719	116	10	10	NUM
ejpam-4348	719	117	l’axe	l’axe	VERB
ejpam-4348	719	118	des	des	PROPN
ejpam-4348	719	119	abscisses	abscisses	PROPN
ejpam-4348	719	120	l’a	l’a	PROPN
ejpam-4348	719	121	x	x	X
ejpam-4348	719	122	e	e	X
ejpam-4348	719	123	d	d	X
ejpam-4348	719	124	e	e	X
ejpam-4348	719	125	s	s	PROPN
ejpam-4348	719	126	o	o	PROPN
ejpam-4348	719	127	rd	rd	NOUN
ejpam-4348	719	128	o	o	NOUN
ejpam-4348	719	129	n	n	CCONJ
ejpam-4348	719	130	n	n	ADV
ejpam-4348	719	131	é	é	NOUN
ejpam-4348	719	132	e	e	NOUN
ejpam-4348	719	133	s	s	PROPN
ejpam-4348	719	134	p=0.2	p=0.2	NOUN
ejpam-4348	719	135	et	et	NOUN
ejpam-4348	719	136	d=7	d=7	NOUN
ejpam-4348	719	137	figure	figure	NOUN
ejpam-4348	719	138	6	6	NUM
ejpam-4348	719	139	:	:	PUNCT
ejpam-4348	719	140	partition	partition	NOUN
ejpam-4348	719	141	of	of	ADP
ejpam-4348	719	142	the	the	DET
ejpam-4348	719	143	eigenvalues	eigenvalue	NOUN
ejpam-4348	719	144	of	of	ADP
ejpam-4348	719	145	w	w	PROPN
ejpam-4348	719	146	(	(	PUNCT
ejpam-4348	719	147	t	t	PROPN
ejpam-4348	719	148	)	)	PUNCT
ejpam-4348	719	149	,	,	PUNCT
ejpam-4348	719	150	∀t	∀t	PROPN
ejpam-4348	719	151	∈	∈	PROPN
ejpam-4348	720	1	[	[	X
ejpam-4348	720	2	0	0	NUM
ejpam-4348	720	3	,	,	PUNCT
ejpam-4348	720	4	π	π	X
ejpam-4348	720	5	]	]	X
ejpam-4348	720	6	with	with	ADP
ejpam-4348	720	7	(	(	PUNCT
ejpam-4348	720	8	p	p	X
ejpam-4348	720	9	,	,	PUNCT
ejpam-4348	720	10	d	d	NOUN
ejpam-4348	720	11	)	)	PUNCT
ejpam-4348	720	12	∈	∈	NOUN
ejpam-4348	720	13	{	{	PUNCT
ejpam-4348	720	14	(	(	PUNCT
ejpam-4348	720	15	0.5	0.5	NUM
ejpam-4348	720	16	,	,	PUNCT
ejpam-4348	720	17	0.5	0.5	NUM
ejpam-4348	720	18	)	)	PUNCT
ejpam-4348	720	19	,	,	PUNCT
ejpam-4348	720	20	(	(	PUNCT
ejpam-4348	720	21	2	2	NUM
ejpam-4348	720	22	,	,	PUNCT
ejpam-4348	720	23	1	1	NUM
ejpam-4348	720	24	)	)	PUNCT
ejpam-4348	720	25	,	,	PUNCT
ejpam-4348	720	26	(	(	PUNCT
ejpam-4348	720	27	0.2	0.2	NUM
ejpam-4348	720	28	,	,	PUNCT
ejpam-4348	720	29	2	2	NUM
ejpam-4348	720	30	)	)	PUNCT
ejpam-4348	720	31	,	,	PUNCT
ejpam-4348	720	32	(	(	PUNCT
ejpam-4348	720	33	0.2	0.2	NUM
ejpam-4348	720	34	,	,	PUNCT
ejpam-4348	720	35	7	7	NUM
ejpam-4348	720	36	)	)	PUNCT
ejpam-4348	720	37	}	}	PUNCT
ejpam-4348	720	38	.	.	PUNCT
ejpam-4348	721	1	−15	−15	PROPN
ejpam-4348	721	2	−10	−10	PRON
ejpam-4348	721	3	−5	−5	ADV
ejpam-4348	722	1	0	0	NUM
ejpam-4348	722	2	5	5	NUM
ejpam-4348	722	3	−6	−6	NOUN
ejpam-4348	722	4	−4	−4	X
ejpam-4348	722	5	−2	−2	NOUN
ejpam-4348	722	6	0	0	NUM
ejpam-4348	722	7	2	2	NUM
ejpam-4348	722	8	4	4	NUM
ejpam-4348	722	9	6	6	NUM
ejpam-4348	722	10	abscisses	abscisse	NOUN
ejpam-4348	722	11	o	o	X
ejpam-4348	722	12	rd	rd	NOUN
ejpam-4348	722	13	o	o	NOUN
ejpam-4348	722	14	n	n	CCONJ
ejpam-4348	722	15	n	n	PRON
ejpam-4348	722	16	�	�	PROPN
ejpam-4348	722	17	e	e	NOUN
ejpam-4348	722	18	s	s	X
ejpam-4348	722	19	for	for	ADP
ejpam-4348	722	20	t=3.5	t=3.5	NOUN
ejpam-4348	722	21	with	with	ADP
ejpam-4348	722	22	p=1,b=0.2	p=1,b=0.2	ADJ
ejpam-4348	722	23	and	and	CCONJ
ejpam-4348	722	24	d=0.2	d=0.2	ADJ
ejpam-4348	722	25	−15	−15	X
ejpam-4348	722	26	−10	−10	X
ejpam-4348	722	27	−5	−5	ADV
ejpam-4348	722	28	0	0	NUM
ejpam-4348	722	29	5	5	NUM
ejpam-4348	722	30	−4	−4	NOUN
ejpam-4348	722	31	−2	−2	NOUN
ejpam-4348	722	32	0	0	NUM
ejpam-4348	722	33	2	2	NUM
ejpam-4348	722	34	4	4	NUM
ejpam-4348	722	35	6	6	NUM
ejpam-4348	722	36	8	8	NUM
ejpam-4348	722	37	abscisses	abscisse	NOUN
ejpam-4348	722	38	o	o	X
ejpam-4348	722	39	rd	rd	NOUN
ejpam-4348	722	40	o	o	NOUN
ejpam-4348	722	41	n	n	CCONJ
ejpam-4348	722	42	n	n	PRON
ejpam-4348	722	43	�	�	PROPN
ejpam-4348	722	44	e	e	NOUN
ejpam-4348	722	45	s	s	X
ejpam-4348	722	46	for	for	ADP
ejpam-4348	722	47	t=3.5	t=3.5	NOUN
ejpam-4348	722	48	with	with	ADP
ejpam-4348	722	49	p=1,b=2	p=1,b=2	ADJ
ejpam-4348	722	50	and	and	CCONJ
ejpam-4348	722	51	d=1	d=1	NOUN
ejpam-4348	722	52	−15	−15	NOUN
ejpam-4348	722	53	−10	−10	X
ejpam-4348	722	54	−5	−5	ADV
ejpam-4348	722	55	0	0	NUM
ejpam-4348	722	56	5	5	NUM
ejpam-4348	722	57	−4	−4	NOUN
ejpam-4348	722	58	−2	−2	NOUN
ejpam-4348	722	59	0	0	NUM
ejpam-4348	722	60	2	2	NUM
ejpam-4348	722	61	4	4	NUM
ejpam-4348	722	62	6	6	NUM
ejpam-4348	722	63	abscisses	abscisse	NOUN
ejpam-4348	722	64	o	o	X
ejpam-4348	722	65	rd	rd	NOUN
ejpam-4348	722	66	o	o	NOUN
ejpam-4348	722	67	n	n	CCONJ
ejpam-4348	722	68	n	n	PRON
ejpam-4348	722	69	�	�	PROPN
ejpam-4348	722	70	e	e	NOUN
ejpam-4348	722	71	s	s	X
ejpam-4348	722	72	for	for	ADP
ejpam-4348	722	73	t=3.5	t=3.5	NOUN
ejpam-4348	722	74	with	with	ADP
ejpam-4348	722	75	p=0.5,b=0.5	p=0.5,b=0.5	PROPN
ejpam-4348	722	76	and	and	CCONJ
ejpam-4348	722	77	d=2	d=2	PROPN
ejpam-4348	722	78	−15	−15	NOUN
ejpam-4348	722	79	−10	−10	X
ejpam-4348	722	80	−5	−5	ADV
ejpam-4348	722	81	0	0	NUM
ejpam-4348	722	82	5	5	NUM
ejpam-4348	722	83	−10	−10	SYM
ejpam-4348	722	84	−5	−5	ADV
ejpam-4348	722	85	0	0	NUM
ejpam-4348	722	86	5	5	NUM
ejpam-4348	722	87	10	10	NUM
ejpam-4348	722	88	abscisses	abscisse	NOUN
ejpam-4348	722	89	o	o	X
ejpam-4348	722	90	rd	rd	NOUN
ejpam-4348	722	91	o	o	NOUN
ejpam-4348	722	92	n	n	CCONJ
ejpam-4348	722	93	n	n	PRON
ejpam-4348	722	94	�	�	PROPN
ejpam-4348	722	95	e	e	NOUN
ejpam-4348	722	96	s	s	X
ejpam-4348	722	97	for	for	ADP
ejpam-4348	722	98	t=3.5	t=3.5	NOUN
ejpam-4348	722	99	with	with	ADP
ejpam-4348	722	100	p=2,b=0.5	p=2,b=0.5	PROPN
ejpam-4348	722	101	and	and	CCONJ
ejpam-4348	722	102	d=0.3	d=0.3	PROPN
ejpam-4348	722	103	−15	−15	VERB
ejpam-4348	722	104	−10	−10	PRON
ejpam-4348	722	105	−5	−5	ADV
ejpam-4348	722	106	0	0	NUM
ejpam-4348	722	107	5	5	NUM
ejpam-4348	722	108	−8	−8	PRON
ejpam-4348	723	1	−6	−6	NOUN
ejpam-4348	724	1	−4	−4	X
ejpam-4348	725	1	−2	−2	NOUN
ejpam-4348	725	2	0	0	NUM
ejpam-4348	725	3	2	2	NUM
ejpam-4348	725	4	4	4	NUM
ejpam-4348	725	5	6	6	NUM
ejpam-4348	725	6	8	8	NUM
ejpam-4348	725	7	abscisses	abscisse	NOUN
ejpam-4348	725	8	o	o	X
ejpam-4348	725	9	rd	rd	NOUN
ejpam-4348	725	10	o	o	NOUN
ejpam-4348	725	11	n	n	CCONJ
ejpam-4348	725	12	n	n	PRON
ejpam-4348	725	13	�	�	PROPN
ejpam-4348	725	14	e	e	NOUN
ejpam-4348	725	15	s	s	X
ejpam-4348	725	16	for	for	ADP
ejpam-4348	725	17	t=3.5	t=3.5	NOUN
ejpam-4348	725	18	with	with	ADP
ejpam-4348	725	19	p=1.3,b=0.2	p=1.3,b=0.2	NOUN
ejpam-4348	725	20	and	and	CCONJ
ejpam-4348	725	21	d=3	d=3	PROPN
ejpam-4348	725	22	−15	−15	VERB
ejpam-4348	725	23	−10	−10	PRON
ejpam-4348	725	24	−5	−5	ADV
ejpam-4348	725	25	0	0	NUM
ejpam-4348	725	26	5	5	NUM
ejpam-4348	725	27	−5	−5	NOUN
ejpam-4348	725	28	0	0	NUM
ejpam-4348	725	29	5	5	NUM
ejpam-4348	725	30	10	10	NUM
ejpam-4348	725	31	15	15	NUM
ejpam-4348	725	32	abscisses	abscisse	NOUN
ejpam-4348	726	1	o	o	X
ejpam-4348	726	2	rd	rd	NOUN
ejpam-4348	726	3	o	o	NOUN
ejpam-4348	726	4	n	n	CCONJ
ejpam-4348	726	5	n	n	PRON
ejpam-4348	726	6	�	�	PROPN
ejpam-4348	726	7	e	e	NOUN
ejpam-4348	726	8	s	s	X
ejpam-4348	726	9	for	for	ADP
ejpam-4348	726	10	t=3.5	t=3.5	NOUN
ejpam-4348	726	11	with	with	ADP
ejpam-4348	726	12	p=1.8,b=3	p=1.8,b=3	ADJ
ejpam-4348	726	13	and	and	CCONJ
ejpam-4348	726	14	d=3	d=3	PRON
ejpam-4348	726	15	figure	figure	VERB
ejpam-4348	726	16	7	7	NUM
ejpam-4348	726	17	:	:	PUNCT
ejpam-4348	726	18	partition	partition	NOUN
ejpam-4348	726	19	of	of	ADP
ejpam-4348	726	20	the	the	DET
ejpam-4348	726	21	spectrum	spectrum	NOUN
ejpam-4348	726	22	of	of	ADP
ejpam-4348	726	23	the	the	DET
ejpam-4348	726	24	matrixw	matrixw	ADJ
ejpam-4348	726	25	(	(	PUNCT
ejpam-4348	726	26	t	t	NOUN
ejpam-4348	726	27	)	)	PUNCT
ejpam-4348	726	28	for	for	ADP
ejpam-4348	726	29	t	t	NOUN
ejpam-4348	726	30	=	=	SYM
ejpam-4348	726	31	2.8	2.8	NUM
ejpam-4348	726	32	by	by	ADP
ejpam-4348	726	33	parabolas	parabola	NOUN
ejpam-4348	726	34	of	of	ADP
ejpam-4348	726	35	equation	equation	NOUN
ejpam-4348	726	36	2p(d−x	2p(d−x	NUM
ejpam-4348	726	37	)	)	PUNCT
ejpam-4348	726	38	=	=	SYM
ejpam-4348	726	39	(	(	PUNCT
ejpam-4348	726	40	y−pb)2	y−pb)2	PROPN
ejpam-4348	726	41	.	.	PUNCT
ejpam-4348	727	1	this	this	DET
ejpam-4348	727	2	study	study	NOUN
ejpam-4348	727	3	,	,	PUNCT
ejpam-4348	727	4	if	if	SCONJ
ejpam-4348	727	5	the	the	DET
ejpam-4348	727	6	discriminant	discriminant	NOUN
ejpam-4348	727	7	is	be	AUX
ejpam-4348	727	8	equal	equal	ADJ
ejpam-4348	727	9	to	to	ADP
ejpam-4348	727	10	1	1	NUM
ejpam-4348	727	11	in	in	ADP
ejpam-4348	727	12	the	the	DET
ejpam-4348	727	13	canonical	canonical	ADJ
ejpam-4348	727	14	form	form	NOUN
ejpam-4348	727	15	of	of	ADP
ejpam-4348	727	16	the	the	DET
ejpam-4348	727	17	general	general	ADJ
ejpam-4348	727	18	equation	equation	NOUN
ejpam-4348	727	19	with	with	ADP
ejpam-4348	727	20	non	non	ADJ
ejpam-4348	727	21	-	-	ADJ
ejpam-4348	727	22	zero	zero	NUM
ejpam-4348	727	23	parameter	parameter	NOUN
ejpam-4348	727	24	b	b	PROPN
ejpam-4348	727	25	,	,	PUNCT
ejpam-4348	727	26	the	the	DET
ejpam-4348	727	27	matrix	matrix	NOUN
ejpam-4348	727	28	a	a	PRON
ejpam-4348	727	29	is	be	AUX
ejpam-4348	727	30	replaced	replace	VERB
ejpam-4348	727	31	by	by	ADP
ejpam-4348	727	32	the	the	DET
ejpam-4348	727	33	matrix	matrix	NOUN
ejpam-4348	727	34	ab	ab	NOUN
ejpam-4348	727	35	=	=	SYM
ejpam-4348	727	36	a−	a−	PROPN
ejpam-4348	727	37	ipbin	ipbin	NOUN
ejpam-4348	727	38	in	in	ADP
ejpam-4348	727	39	the	the	DET
ejpam-4348	727	40	algorithm	algorithm	NOUN
ejpam-4348	727	41	.	.	PUNCT
ejpam-4348	728	1	moreover	moreover	ADV
ejpam-4348	728	2	,	,	PUNCT
ejpam-4348	728	3	if	if	SCONJ
ejpam-4348	728	4	the	the	DET
ejpam-4348	728	5	discriminant	discriminant	NOUN
ejpam-4348	728	6	is	be	AUX
ejpam-4348	728	7	different	different	ADJ
ejpam-4348	728	8	from	from	ADP
ejpam-4348	728	9	1	1	NUM
ejpam-4348	728	10	,	,	PUNCT
ejpam-4348	728	11	we	we	PRON
ejpam-4348	728	12	replace	replace	VERB
ejpam-4348	728	13	the	the	DET
ejpam-4348	728	14	matrix	matrix	NOUN
ejpam-4348	728	15	a	a	PRON
ejpam-4348	728	16	by	by	ADP
ejpam-4348	728	17	ad	ad	NOUN
ejpam-4348	728	18	=	=	SYM
ejpam-4348	728	19	a+	a+	PUNCT
ejpam-4348	728	20	(	(	PUNCT
ejpam-4348	728	21	p	p	NOUN
ejpam-4348	728	22	2	2	NUM
ejpam-4348	728	23	−	−	PROPN
ejpam-4348	728	24	d	d	NOUN
ejpam-4348	728	25	)	)	PUNCT
ejpam-4348	728	26	in	in	ADP
ejpam-4348	728	27	(	(	PUNCT
ejpam-4348	728	28	respectively	respectively	ADV
ejpam-4348	728	29	adb	adb	PROPN
ejpam-4348	728	30	=	=	SYM
ejpam-4348	728	31	a+	a+	PUNCT
ejpam-4348	729	1	(	(	PUNCT
ejpam-4348	729	2	p	p	NOUN
ejpam-4348	729	3	2	2	NUM
ejpam-4348	729	4	−	−	NUM
ejpam-4348	729	5	d−	d−	PROPN
ejpam-4348	729	6	ipb	ipb	PROPN
ejpam-4348	729	7	)	)	PUNCT
ejpam-4348	729	8	in	in	ADP
ejpam-4348	729	9	)	)	PUNCT
ejpam-4348	729	10	in	in	ADP
ejpam-4348	729	11	the	the	DET
ejpam-4348	729	12	dichop	dichop	NOUN
ejpam-4348	729	13	algorithm	algorithm	NOUN
ejpam-4348	729	14	when	when	SCONJ
ejpam-4348	729	15	the	the	DET
ejpam-4348	729	16	parameter	parameter	PROPN
ejpam-4348	729	17	b	b	PROPN
ejpam-4348	729	18	is	be	AUX
ejpam-4348	729	19	zero	zero	NUM
ejpam-4348	729	20	(	(	PUNCT
ejpam-4348	729	21	respectively	respectively	ADV
ejpam-4348	729	22	b	b	PROPN
ejpam-4348	729	23	is	be	AUX
ejpam-4348	729	24	not	not	PART
ejpam-4348	729	25	zero	zero	NUM
ejpam-4348	729	26	)	)	PUNCT
ejpam-4348	729	27	.	.	PUNCT
ejpam-4348	730	1	a	a	DET
ejpam-4348	730	2	theoretical	theoretical	ADJ
ejpam-4348	730	3	analysis	analysis	NOUN
ejpam-4348	730	4	of	of	ADP
ejpam-4348	730	5	the	the	DET
ejpam-4348	730	6	proposed	propose	VERB
ejpam-4348	730	7	new	new	ADJ
ejpam-4348	730	8	methods	method	NOUN
ejpam-4348	730	9	shows	show	VERB
ejpam-4348	730	10	how	how	SCONJ
ejpam-4348	730	11	to	to	PART
ejpam-4348	730	12	calculate	calculate	VERB
ejpam-4348	730	13	the	the	DET
ejpam-4348	730	14	projector	projector	NOUN
ejpam-4348	730	15	spectral	spectral	NOUN
ejpam-4348	730	16	associated	associate	VERB
ejpam-4348	730	17	with	with	ADP
ejpam-4348	730	18	the	the	DET
ejpam-4348	730	19	eigenvalues	eigenvalue	NOUN
ejpam-4348	730	20	outside	outside	ADV
ejpam-4348	730	21	at	at	ADP
ejpam-4348	730	22	a	a	DET
ejpam-4348	730	23	given	give	VERB
ejpam-4348	730	24	parabola	parabola	PROPN
ejpam-4348	730	25	γ(a	γ(a	PROPN
ejpam-4348	730	26	,	,	PUNCT
ejpam-4348	730	27	b	b	NOUN
ejpam-4348	730	28	,	,	PUNCT
ejpam-4348	730	29	c	c	NOUN
ejpam-4348	730	30	)	)	PUNCT
ejpam-4348	730	31	.	.	PUNCT
ejpam-4348	731	1	an	an	DET
ejpam-4348	731	2	analysis	analysis	NOUN
ejpam-4348	731	3	of	of	ADP
ejpam-4348	731	4	the	the	DET
ejpam-4348	731	5	new	new	ADJ
ejpam-4348	731	6	method	method	NOUN
ejpam-4348	731	7	shows	show	VERB
ejpam-4348	731	8	how	how	SCONJ
ejpam-4348	731	9	to	to	PART
ejpam-4348	731	10	extract	extract	VERB
ejpam-4348	731	11	the	the	DET
ejpam-4348	731	12	projector	projector	NOUN
ejpam-4348	731	13	.	.	PUNCT
ejpam-4348	732	1	thus	thus	ADV
ejpam-4348	732	2	,	,	PUNCT
ejpam-4348	732	3	in	in	ADP
ejpam-4348	732	4	the	the	DET
ejpam-4348	732	5	numerical	numerical	ADJ
ejpam-4348	732	6	experiments	experiment	NOUN
ejpam-4348	732	7	,	,	PUNCT
ejpam-4348	732	8	the	the	DET
ejpam-4348	732	9	application	application	NOUN
ejpam-4348	732	10	of	of	ADP
ejpam-4348	732	11	the	the	DET
ejpam-4348	732	12	four	four	NUM
ejpam-4348	732	13	algorithms	algorithms	NOUN
ejpam-4348	732	14	dichop	dichop	NOUN
ejpam-4348	732	15	,	,	PUNCT
ejpam-4348	732	16	dichopb	dichopb	ADJ
ejpam-4348	732	17	,	,	PUNCT
ejpam-4348	732	18	dichopd	dichopd	NOUN
ejpam-4348	732	19	and	and	CCONJ
ejpam-4348	732	20	dichopdb	dichopdb	ADJ
ejpam-4348	732	21	to	to	ADP
ejpam-4348	732	22	a	a	DET
ejpam-4348	732	23	matrix	matrix	NOUN
ejpam-4348	732	24	function	function	NOUN
ejpam-4348	732	25	shows	show	VERB
ejpam-4348	732	26	the	the	DET
ejpam-4348	732	27	efficient	efficient	ADJ
ejpam-4348	732	28	calculation	calculation	NOUN
ejpam-4348	732	29	of	of	ADP
ejpam-4348	732	30	the	the	DET
ejpam-4348	732	31	projector	projector	NOUN
ejpam-4348	732	32	which	which	PRON
ejpam-4348	732	33	allows	allow	VERB
ejpam-4348	732	34	a	a	DET
ejpam-4348	732	35	separation	separation	NOUN
ejpam-4348	732	36	of	of	ADP
ejpam-4348	732	37	its	its	PRON
ejpam-4348	732	38	spectrum	spectrum	NOUN
ejpam-4348	732	39	into	into	ADP
ejpam-4348	732	40	two	two	NUM
ejpam-4348	732	41	parts	part	NOUN
ejpam-4348	732	42	with	with	ADP
ejpam-4348	732	43	respect	respect	NOUN
ejpam-4348	732	44	to	to	ADP
ejpam-4348	732	45	the	the	DET
ejpam-4348	732	46	parabola	parabola	PROPN
ejpam-4348	732	47	(	(	PUNCT
ejpam-4348	732	48	i.	i.	PROPN
ejpam-4348	732	49	e.	e.	PROPN
ejpam-4348	732	50	inside	inside	PROPN
ejpam-4348	732	51	and	and	CCONJ
ejpam-4348	732	52	outside	outside	ADP
ejpam-4348	732	53	the	the	DET
ejpam-4348	732	54	parabola	parabola	NOUN
ejpam-4348	732	55	)	)	PUNCT
ejpam-4348	732	56	.	.	PUNCT
ejpam-4348	733	1	references	reference	NOUN
ejpam-4348	733	2	724	724	NUM
ejpam-4348	733	3	table	table	NOUN
ejpam-4348	733	4	4	4	NUM
ejpam-4348	733	5	:	:	SYM
ejpam-4348	733	6	traces	trace	NOUN
ejpam-4348	733	7	,	,	PUNCT
ejpam-4348	733	8	norms	norm	NOUN
ejpam-4348	733	9	and	and	CCONJ
ejpam-4348	733	10	quality	quality	NOUN
ejpam-4348	733	11	of	of	ADP
ejpam-4348	733	12	spectral	spectral	ADJ
ejpam-4348	733	13	projectors	projector	NOUN
ejpam-4348	733	14	p̃d	p̃d	NOUN
ejpam-4348	733	15	by	by	ADP
ejpam-4348	733	16	applying	apply	VERB
ejpam-4348	733	17	the	the	DET
ejpam-4348	733	18	dichopdb	dichopdb	ADJ
ejpam-4348	733	19	algorithm	algorithm	NOUN
ejpam-4348	733	20	for	for	ADP
ejpam-4348	733	21	different	different	ADJ
ejpam-4348	733	22	values	value	NOUN
ejpam-4348	733	23	of	of	ADP
ejpam-4348	733	24	p	p	PROPN
ejpam-4348	733	25	b	b	PROPN
ejpam-4348	733	26	and	and	CCONJ
ejpam-4348	733	27	d	d	PROPN
ejpam-4348	733	28	p	p	PROPN
ejpam-4348	733	29	b	b	PROPN
ejpam-4348	733	30	d	d	PRON
ejpam-4348	733	31	tr(p̃d	tr(p̃d	NOUN
ejpam-4348	733	32	)	)	PUNCT
ejpam-4348	733	33	∥p̃d∥	∥p̃d∥	NOUN
ejpam-4348	733	34	∥p̃d	∥p̃d	NOUN
ejpam-4348	733	35	2	2	NUM
ejpam-4348	733	36	−	−	NOUN
ejpam-4348	733	37	p̃d∥	p̃d∥	NOUN
ejpam-4348	733	38	∥p̃dw	∥p̃dw	PROPN
ejpam-4348	733	39	(	(	PUNCT
ejpam-4348	733	40	t)−w	t)−w	PROPN
ejpam-4348	733	41	(	(	PUNCT
ejpam-4348	733	42	t)p̃d∥	t)p̃d∥	PROPN
ejpam-4348	733	43	∥h̃d∥	∥h̃d∥	ADJ
ejpam-4348	733	44	1	1	NUM
ejpam-4348	733	45	0.2	0.2	NUM
ejpam-4348	733	46	0.2	0.2	NUM
ejpam-4348	733	47	2	2	NUM
ejpam-4348	733	48	1.3292	1.3292	NUM
ejpam-4348	733	49	3.3183	3.3183	NUM
ejpam-4348	733	50	10−15	10−15	PROPN
ejpam-4348	733	51	7.2032	7.2032	NUM
ejpam-4348	733	52	10−15	10−15	NUM
ejpam-4348	733	53	7.3681	7.3681	NUM
ejpam-4348	733	54	1	1	NUM
ejpam-4348	733	55	4	4	NUM
ejpam-4348	733	56	1	1	NUM
ejpam-4348	733	57	4	4	NUM
ejpam-4348	733	58	1	1	NUM
ejpam-4348	733	59	3.8213	3.8213	NUM
ejpam-4348	733	60	10−15	10−15	NOUN
ejpam-4348	733	61	5.3470	5.3470	NUM
ejpam-4348	733	62	10−15	10−15	NOUN
ejpam-4348	733	63	1.3453	1.3453	NUM
ejpam-4348	733	64	0.5	0.5	NUM
ejpam-4348	733	65	0.5	0.5	NUM
ejpam-4348	733	66	2	2	NUM
ejpam-4348	733	67	0	0	NUM
ejpam-4348	733	68	3.2139	3.2139	NUM
ejpam-4348	733	69	10−17	10−17	NUM
ejpam-4348	733	70	3.2139	3.2139	NUM
ejpam-4348	733	71	10−17	10−17	NUM
ejpam-4348	733	72	4.7630	4.7630	NUM
ejpam-4348	733	73	10−16	10−16	NOUN
ejpam-4348	733	74	9.9291	9.9291	NUM
ejpam-4348	733	75	2	2	NUM
ejpam-4348	733	76	0.5	0.5	NUM
ejpam-4348	733	77	0.3	0.3	NUM
ejpam-4348	733	78	1	1	NUM
ejpam-4348	733	79	1.3499	1.3499	NUM
ejpam-4348	733	80	1.7537	1.7537	NUM
ejpam-4348	733	81	10−15	10−15	PROPN
ejpam-4348	733	82	5.6241	5.6241	NUM
ejpam-4348	733	83	10−15	10−15	NOUN
ejpam-4348	733	84	4.3035	4.3035	NUM
ejpam-4348	733	85	1.3	1.3	NUM
ejpam-4348	733	86	0.2	0.2	NUM
ejpam-4348	733	87	3	3	NUM
ejpam-4348	733	88	0	0	NUM
ejpam-4348	733	89	3.6050	3.6050	NUM
ejpam-4348	733	90	10−17	10−17	NUM
ejpam-4348	733	91	3.6050	3.6050	NUM
ejpam-4348	733	92	10−17	10−17	NUM
ejpam-4348	733	93	6.0976	6.0976	NUM
ejpam-4348	733	94	10−17	10−17	NUM
ejpam-4348	733	95	1.3319	1.3319	NUM
ejpam-4348	733	96	3	3	NUM
ejpam-4348	733	97	5	5	NUM
ejpam-4348	733	98	3	3	NUM
ejpam-4348	733	99	4	4	NUM
ejpam-4348	733	100	1	1	NUM
ejpam-4348	733	101	2.6922	2.6922	NUM
ejpam-4348	733	102	10−15	10−15	NOUN
ejpam-4348	733	103	5.4784	5.4784	NUM
ejpam-4348	733	104	10−15	10−15	NOUN
ejpam-4348	733	105	1.1007	1.1007	NUM
ejpam-4348	733	106	−10	−10	X
ejpam-4348	733	107	0	0	NUM
ejpam-4348	733	108	10	10	NUM
ejpam-4348	733	109	−5	−5	NOUN
ejpam-4348	733	110	0	0	NUM
ejpam-4348	733	111	5	5	NUM
ejpam-4348	733	112	the	the	DET
ejpam-4348	733	113	abscissa	abscissa	ADJ
ejpam-4348	733	114	axis	axis	NOUN
ejpam-4348	733	115	th	th	X
ejpam-4348	733	116	e	e	X
ejpam-4348	733	117	o	o	PROPN
ejpam-4348	733	118	rd	rd	NOUN
ejpam-4348	733	119	in	in	ADP
ejpam-4348	733	120	a	a	DET
ejpam-4348	733	121	te	te	PROPN
ejpam-4348	733	122	a	a	DET
ejpam-4348	733	123	x	x	X
ejpam-4348	733	124	is	be	AUX
ejpam-4348	733	125	p=0.5	p=0.5	NOUN
ejpam-4348	733	126	,	,	PUNCT
ejpam-4348	733	127	d=0.5	d=0.5	NOUN
ejpam-4348	733	128	et	et	NOUN
ejpam-4348	733	129	b=2	b=2	X
ejpam-4348	733	130	−10	−10	X
ejpam-4348	733	131	0	0	NUM
ejpam-4348	733	132	10	10	NUM
ejpam-4348	733	133	−5	−5	NOUN
ejpam-4348	733	134	0	0	NUM
ejpam-4348	733	135	5	5	NUM
ejpam-4348	733	136	10	10	NUM
ejpam-4348	733	137	15	15	NUM
ejpam-4348	733	138	the	the	DET
ejpam-4348	733	139	abscissa	abscissa	ADJ
ejpam-4348	733	140	axis	axis	NOUN
ejpam-4348	733	141	th	th	X
ejpam-4348	733	142	e	e	X
ejpam-4348	733	143	o	o	PROPN
ejpam-4348	733	144	rd	rd	NOUN
ejpam-4348	733	145	in	in	ADP
ejpam-4348	733	146	a	a	DET
ejpam-4348	733	147	te	te	PROPN
ejpam-4348	733	148	a	a	DET
ejpam-4348	733	149	x	x	X
ejpam-4348	733	150	is	be	AUX
ejpam-4348	733	151	p=2	p=2	PROPN
ejpam-4348	733	152	,	,	PUNCT
ejpam-4348	733	153	d=1	d=1	NOUN
ejpam-4348	733	154	et	et	NOUN
ejpam-4348	733	155	b=−2	b=−2	NOUN
ejpam-4348	733	156	−10	−10	PROPN
ejpam-4348	733	157	0	0	NUM
ejpam-4348	733	158	10	10	NUM
ejpam-4348	733	159	−5	−5	NOUN
ejpam-4348	733	160	0	0	NUM
ejpam-4348	733	161	5	5	NUM
ejpam-4348	733	162	the	the	DET
ejpam-4348	733	163	abscissa	abscissa	ADJ
ejpam-4348	733	164	axis	axis	NOUN
ejpam-4348	733	165	th	th	X
ejpam-4348	733	166	e	e	X
ejpam-4348	733	167	o	o	PROPN
ejpam-4348	733	168	rd	rd	NOUN
ejpam-4348	733	169	in	in	ADP
ejpam-4348	733	170	a	a	DET
ejpam-4348	733	171	te	te	PROPN
ejpam-4348	733	172	a	a	PRON
ejpam-4348	733	173	x	x	NOUN
ejpam-4348	733	174	is	be	AUX
ejpam-4348	733	175	p=0.2	p=0.2	ADJ
ejpam-4348	733	176	,	,	PUNCT
ejpam-4348	733	177	d=2	d=2	X
ejpam-4348	733	178	et	et	PROPN
ejpam-4348	733	179	b=0	b=0	NOUN
ejpam-4348	733	180	−10	−10	SYM
ejpam-4348	733	181	0	0	NUM
ejpam-4348	733	182	10	10	NUM
ejpam-4348	733	183	−20	−20	NOUN
ejpam-4348	733	184	−10	−10	NOUN
ejpam-4348	733	185	0	0	NUM
ejpam-4348	733	186	10	10	NUM
ejpam-4348	733	187	the	the	DET
ejpam-4348	733	188	abscissa	abscissa	ADJ
ejpam-4348	733	189	axis	axis	NOUN
ejpam-4348	733	190	th	th	X
ejpam-4348	733	191	e	e	X
ejpam-4348	733	192	o	o	PROPN
ejpam-4348	733	193	rd	rd	NOUN
ejpam-4348	733	194	in	in	ADP
ejpam-4348	733	195	a	a	DET
ejpam-4348	733	196	te	te	PROPN
ejpam-4348	733	197	a	a	PRON
ejpam-4348	733	198	x	x	NOUN
ejpam-4348	733	199	is	be	AUX
ejpam-4348	733	200	p=0.2	p=0.2	ADJ
ejpam-4348	733	201	,	,	PUNCT
ejpam-4348	733	202	d=7	d=7	PROPN
ejpam-4348	733	203	et	et	NOUN
ejpam-4348	733	204	b=3	b=3	NOUN
ejpam-4348	733	205	figure	figure	NOUN
ejpam-4348	733	206	8	8	NUM
ejpam-4348	733	207	:	:	PUNCT
ejpam-4348	733	208	partition	partition	NOUN
ejpam-4348	733	209	of	of	ADP
ejpam-4348	733	210	the	the	DET
ejpam-4348	733	211	eigenvalues	eigenvalue	NOUN
ejpam-4348	733	212	of	of	ADP
ejpam-4348	733	213	w	w	PROPN
ejpam-4348	733	214	(	(	PUNCT
ejpam-4348	733	215	t	t	PROPN
ejpam-4348	733	216	)	)	PUNCT
ejpam-4348	733	217	,	,	PUNCT
ejpam-4348	733	218	∀t	∀t	PROPN
ejpam-4348	733	219	∈	∈	PROPN
ejpam-4348	734	1	[	[	X
ejpam-4348	734	2	0	0	NUM
ejpam-4348	734	3	,	,	PUNCT
ejpam-4348	734	4	π	π	X
ejpam-4348	734	5	]	]	X
ejpam-4348	734	6	with	with	ADP
ejpam-4348	734	7	(	(	PUNCT
ejpam-4348	734	8	p	p	X
ejpam-4348	734	9	,	,	PUNCT
ejpam-4348	734	10	d	d	PROPN
ejpam-4348	734	11	,	,	PUNCT
ejpam-4348	734	12	b	b	NOUN
ejpam-4348	734	13	)	)	PUNCT
ejpam-4348	734	14	∈	∈	NOUN
ejpam-4348	734	15	{	{	PUNCT
ejpam-4348	734	16	(	(	PUNCT
ejpam-4348	734	17	0.5	0.5	NUM
ejpam-4348	734	18	,	,	PUNCT
ejpam-4348	734	19	0.5	0.5	NUM
ejpam-4348	734	20	,	,	PUNCT
ejpam-4348	734	21	2	2	NUM
ejpam-4348	734	22	)	)	PUNCT
ejpam-4348	734	23	,	,	PUNCT
ejpam-4348	734	24	(	(	PUNCT
ejpam-4348	734	25	2	2	NUM
ejpam-4348	734	26	,	,	PUNCT
ejpam-4348	734	27	1,−2	1,−2	NUM
ejpam-4348	734	28	)	)	PUNCT
ejpam-4348	734	29	,	,	PUNCT
ejpam-4348	734	30	(	(	PUNCT
ejpam-4348	734	31	0.2	0.2	NUM
ejpam-4348	734	32	,	,	PUNCT
ejpam-4348	734	33	2	2	NUM
ejpam-4348	734	34	,	,	PUNCT
ejpam-4348	734	35	0	0	NUM
ejpam-4348	734	36	)	)	PUNCT
ejpam-4348	734	37	,	,	PUNCT
ejpam-4348	734	38	(	(	PUNCT
ejpam-4348	734	39	0.2	0.2	NUM
ejpam-4348	734	40	,	,	PUNCT
ejpam-4348	734	41	7	7	NUM
ejpam-4348	734	42	,	,	PUNCT
ejpam-4348	734	43	3	3	NUM
ejpam-4348	734	44	)	)	PUNCT
ejpam-4348	734	45	}	}	PUNCT
ejpam-4348	734	46	.	.	PUNCT
ejpam-4348	735	1	acknowledgements	acknowledgement	NOUN
ejpam-4348	735	2	the	the	DET
ejpam-4348	735	3	authors	author	NOUN
ejpam-4348	735	4	thank	thank	VERB
ejpam-4348	735	5	the	the	DET
ejpam-4348	735	6	referees	referee	NOUN
ejpam-4348	735	7	for	for	ADP
ejpam-4348	735	8	their	their	PRON
ejpam-4348	735	9	useful	useful	ADJ
ejpam-4348	735	10	suggestions	suggestion	NOUN
ejpam-4348	735	11	that	that	PRON
ejpam-4348	735	12	helped	help	VERB
ejpam-4348	735	13	to	to	PART
ejpam-4348	735	14	improve	improve	VERB
ejpam-4348	735	15	this	this	DET
ejpam-4348	735	16	article	article	NOUN
ejpam-4348	735	17	.	.	PUNCT
ejpam-4348	736	1	references	reference	NOUN
ejpam-4348	736	2	[	[	X
ejpam-4348	736	3	1	1	X
ejpam-4348	736	4	]	]	PUNCT
ejpam-4348	736	5	a	a	DET
ejpam-4348	736	6	ya	ya	PROPN
ejpam-4348	736	7	bulgakov	bulgakov	PROPN
ejpam-4348	736	8	.	.	PUNCT
ejpam-4348	737	1	generalization	generalization	NOUN
ejpam-4348	737	2	of	of	ADP
ejpam-4348	737	3	a	a	DET
ejpam-4348	737	4	matrix	matrix	NOUN
ejpam-4348	737	5	lyapunov	lyapunov	NOUN
ejpam-4348	737	6	equation	equation	NOUN
ejpam-4348	737	7	.	.	PUNCT
ejpam-4348	738	1	(	(	PUNCT
ejpam-4348	738	2	russian	russian	ADJ
ejpam-4348	738	3	)	)	PUNCT
ejpam-4348	738	4	sibirsk	sibirsk	NOUN
ejpam-4348	738	5	.	.	PUNCT
ejpam-4348	739	1	mat	mat	NOUN
ejpam-4348	739	2	.	.	PUNCT
ejpam-4348	740	1	zh	zh	PROPN
ejpam-4348	740	2	.	.	PROPN
ejpam-4348	740	3	,	,	PUNCT
ejpam-4348	740	4	30(4):30–39	30(4):30–39	NUM
ejpam-4348	740	5	,	,	PUNCT
ejpam-4348	740	6	1989	1989	NUM
ejpam-4348	740	7	.	.	PUNCT
ejpam-4348	741	1	[	[	X
ejpam-4348	741	2	2	2	NUM
ejpam-4348	741	3	]	]	PUNCT
ejpam-4348	741	4	m	m	VERB
ejpam-4348	741	5	dosso	dosso	NOUN
ejpam-4348	741	6	n	n	PRON
ejpam-4348	741	7	coulibaly	coulibaly	NOUN
ejpam-4348	741	8	and	and	CCONJ
ejpam-4348	741	9	l	l	PROPN
ejpam-4348	741	10	samassi	samassi	PROPN
ejpam-4348	741	11	.	.	PUNCT
ejpam-4348	742	1	strong	strong	ADJ
ejpam-4348	742	2	stability	stability	NOUN
ejpam-4348	742	3	of	of	ADP
ejpam-4348	742	4	symplectic	symplectic	ADJ
ejpam-4348	742	5	matrices	matrix	NOUN
ejpam-4348	742	6	using	use	VERB
ejpam-4348	742	7	a	a	DET
ejpam-4348	742	8	spectral	spectral	ADJ
ejpam-4348	742	9	dichotomy	dichotomy	NOUN
ejpam-4348	742	10	method	method	NOUN
ejpam-4348	742	11	.	.	PUNCT
ejpam-4348	743	1	far	far	PROPN
ejpam-4348	743	2	east	east	PROPN
ejpam-4348	743	3	journal	journal	PROPN
ejpam-4348	743	4	applied	apply	VERB
ejpam-4348	743	5	mathematics	mathematic	NOUN
ejpam-4348	743	6	,	,	PUNCT
ejpam-4348	743	7	79(2):73–110	79(2):73–110	NUM
ejpam-4348	743	8	,	,	PUNCT
ejpam-4348	743	9	2013	2013	NUM
ejpam-4348	743	10	.	.	PUNCT
ejpam-4348	744	1	[	[	X
ejpam-4348	744	2	3	3	X
ejpam-4348	744	3	]	]	X
ejpam-4348	744	4	z	z	PROPN
ejpam-4348	744	5	bai	bai	PROPN
ejpam-4348	744	6	j	j	PROPN
ejpam-4348	744	7	demmel	demmel	PROPN
ejpam-4348	744	8	and	and	CCONJ
ejpam-4348	744	9	m	m	PROPN
ejpam-4348	744	10	gu	gu	PROPN
ejpam-4348	744	11	.	.	PROPN
ejpam-4348	744	12	inverse	inverse	PROPN
ejpam-4348	744	13	free	free	PROPN
ejpam-4348	744	14	parallel	parallel	ADJ
ejpam-4348	744	15	spectral	spectral	ADJ
ejpam-4348	744	16	divide	divide	NOUN
ejpam-4348	744	17	and	and	CCONJ
ejpam-4348	744	18	conquer	conquer	VERB
ejpam-4348	744	19	algorithms	algorithm	NOUN
ejpam-4348	744	20	for	for	ADP
ejpam-4348	744	21	nonsymmetric	nonsymmetric	ADJ
ejpam-4348	744	22	eigenproblems	eigenproblem	NOUN
ejpam-4348	744	23	.	.	PUNCT
ejpam-4348	745	1	numerische	numerische	PROPN
ejpam-4348	745	2	mathematik	mathematik	PROPN
ejpam-4348	745	3	.	.	PROPN
ejpam-4348	745	4	,	,	PUNCT
ejpam-4348	746	1	76:279–308	76:279–308	NUM
ejpam-4348	746	2	,	,	PUNCT
ejpam-4348	746	3	1997	1997	NUM
ejpam-4348	746	4	.	.	PUNCT
ejpam-4348	747	1	references	reference	NOUN
ejpam-4348	747	2	725	725	NUM
ejpam-4348	747	3	[	[	X
ejpam-4348	747	4	4	4	NUM
ejpam-4348	747	5	]	]	PUNCT
ejpam-4348	747	6	m	m	NOUN
ejpam-4348	747	7	dosso	dosso	PROPN
ejpam-4348	747	8	.	.	PUNCT
ejpam-4348	748	1	sur	sur	PROPN
ejpam-4348	748	2	quelques	quelques	PROPN
ejpam-4348	748	3	algorithms	algorithms	NOUN
ejpam-4348	748	4	d’analyse	d’analyse	PROPN
ejpam-4348	748	5	de	de	PROPN
ejpam-4348	748	6	stabilité	stabilité	PROPN
ejpam-4348	748	7	forte	forte	NOUN
ejpam-4348	748	8	de	de	X
ejpam-4348	748	9	matrices	matrix	NOUN
ejpam-4348	748	10	symplectiques	symplectique	NOUN
ejpam-4348	748	11	.	.	PUNCT
ejpam-4348	749	1	phd	phd	NOUN
ejpam-4348	749	2	thesis	thesis	NOUN
ejpam-4348	749	3	,	,	PUNCT
ejpam-4348	749	4	université	université	ADJ
ejpam-4348	749	5	de	de	X
ejpam-4348	749	6	bretagne	bretagne	PROPN
ejpam-4348	749	7	occidentale	occidentale	PROPN
ejpam-4348	749	8	.	.	PUNCT
ejpam-4348	749	9	ecole	ecole	PROPN
ejpam-4348	749	10	doctorale	doctorale	PROPN
ejpam-4348	749	11	smis	smis	PROPN
ejpam-4348	749	12	,	,	PUNCT
ejpam-4348	749	13	laboratoire	laboratoire	PROPN
ejpam-4348	749	14	de	de	PROPN
ejpam-4348	749	15	mathématiques	mathématiques	PROPN
ejpam-4348	749	16	,	,	PUNCT
ejpam-4348	749	17	ufr	ufr	PROPN
ejpam-4348	749	18	sciences	sciences	PROPN
ejpam-4348	749	19	et	et	NOUN
ejpam-4348	749	20	techniques	technique	NOUN
ejpam-4348	749	21	.	.	PUNCT
ejpam-4348	749	22	,	,	PUNCT
ejpam-4348	749	23	2006	2006	NUM
ejpam-4348	749	24	.	.	PUNCT
ejpam-4348	750	1	[	[	X
ejpam-4348	750	2	5	5	NUM
ejpam-4348	750	3	]	]	PUNCT
ejpam-4348	750	4	m	m	VERB
ejpam-4348	750	5	dosso	dosso	NOUN
ejpam-4348	750	6	and	and	CCONJ
ejpam-4348	750	7	m	m	PROPN
ejpam-4348	750	8	sadkane	sadkane	ADJ
ejpam-4348	750	9	.	.	PUNCT
ejpam-4348	751	1	on	on	ADP
ejpam-4348	751	2	the	the	DET
ejpam-4348	751	3	strong	strong	ADJ
ejpam-4348	751	4	stability	stability	NOUN
ejpam-4348	751	5	of	of	ADP
ejpam-4348	751	6	symplectic	symplectic	ADJ
ejpam-4348	751	7	matrices	matrix	NOUN
ejpam-4348	751	8	.	.	PUNCT
ejpam-4348	752	1	numerical	numerical	PROPN
ejpam-4348	752	2	linear	linear	PROPN
ejpam-4348	752	3	algebra	algebra	PROPN
ejpam-4348	752	4	with	with	ADP
ejpam-4348	752	5	applications	application	NOUN
ejpam-4348	752	6	,	,	PUNCT
ejpam-4348	752	7	20	20	NUM
ejpam-4348	752	8	,	,	PUNCT
ejpam-4348	752	9	2013	2013	NUM
ejpam-4348	752	10	.	.	PUNCT
ejpam-4348	753	1	[	[	X
ejpam-4348	753	2	6	6	NUM
ejpam-4348	753	3	]	]	PUNCT
ejpam-4348	753	4	a	a	DET
ejpam-4348	753	5	ya	ya	PROPN
ejpam-4348	753	6	bulgakov	bulgakov	PROPN
ejpam-4348	753	7	s	s	PART
ejpam-4348	753	8	k	k	NOUN
ejpam-4348	753	9	godunov	godunov	PROPN
ejpam-4348	753	10	.	.	PUNCT
ejpam-4348	754	1	circular	circular	ADJ
ejpam-4348	754	2	dichotomy	dichotomy	NOUN
ejpam-4348	754	3	of	of	ADP
ejpam-4348	754	4	a	a	DET
ejpam-4348	754	5	matrix	matrix	NOUN
ejpam-4348	754	6	spectrum	spectrum	NOUN
ejpam-4348	754	7	.	.	PUNCT
ejpam-4348	755	1	(	(	PUNCT
ejpam-4348	755	2	russian	russian	ADJ
ejpam-4348	755	3	)	)	PUNCT
ejpam-4348	755	4	sibirsk	sibirsk	NOUN
ejpam-4348	755	5	.	.	PUNCT
ejpam-4348	756	1	mat	mat	NOUN
ejpam-4348	756	2	.	.	PUNCT
ejpam-4348	757	1	zh	zh	PROPN
ejpam-4348	757	2	.	.	PROPN
ejpam-4348	757	3	,	,	PUNCT
ejpam-4348	757	4	29(5):59–70	29(5):59–70	NUM
ejpam-4348	757	5	,	,	PUNCT
ejpam-4348	757	6	1988	1988	NUM
ejpam-4348	757	7	.	.	PUNCT
ejpam-4348	758	1	[	[	X
ejpam-4348	758	2	7	7	NUM
ejpam-4348	758	3	]	]	SYM
ejpam-4348	758	4	s	s	PART
ejpam-4348	758	5	k	k	NOUN
ejpam-4348	758	6	godunov	godunov	NOUN
ejpam-4348	758	7	.	.	PUNCT
ejpam-4348	759	1	the	the	DET
ejpam-4348	759	2	problem	problem	NOUN
ejpam-4348	759	3	of	of	ADP
ejpam-4348	759	4	the	the	DET
ejpam-4348	759	5	dichotomy	dichotomy	NOUN
ejpam-4348	759	6	of	of	ADP
ejpam-4348	759	7	spectrum	spectrum	NOUN
ejpam-4348	759	8	of	of	ADP
ejpam-4348	759	9	a	a	DET
ejpam-4348	759	10	matrix	matrix	NOUN
ejpam-4348	759	11	.	.	PUNCT
ejpam-4348	760	1	(	(	PUNCT
ejpam-4348	760	2	russian	russian	ADJ
ejpam-4348	760	3	)	)	PUNCT
ejpam-4348	760	4	sibirsk	sibirsk	NOUN
ejpam-4348	760	5	.	.	PUNCT
ejpam-4348	761	1	mat	mat	NOUN
ejpam-4348	761	2	.	.	PUNCT
ejpam-4348	762	1	zh	zh	PROPN
ejpam-4348	762	2	.	.	PROPN
ejpam-4348	762	3	,	,	PUNCT
ejpam-4348	762	4	27(5):24–37	27(5):24–37	NUM
ejpam-4348	762	5	,	,	PUNCT
ejpam-4348	762	6	1986	1986	NUM
ejpam-4348	762	7	.	.	PUNCT
ejpam-4348	763	1	[	[	X
ejpam-4348	763	2	8	8	NUM
ejpam-4348	763	3	]	]	SYM
ejpam-4348	763	4	s	s	PART
ejpam-4348	763	5	k	k	NOUN
ejpam-4348	763	6	godunov	godunov	NOUN
ejpam-4348	763	7	.	.	PUNCT
ejpam-4348	764	1	modern	modern	ADJ
ejpam-4348	764	2	aspects	aspect	NOUN
ejpam-4348	764	3	of	of	ADP
ejpam-4348	764	4	linear	linear	PROPN
ejpam-4348	764	5	algebra	algebra	NOUN
ejpam-4348	764	6	.	.	PUNCT
ejpam-4348	765	1	the	the	DET
ejpam-4348	765	2	scientific	scientific	ADJ
ejpam-4348	765	3	book	book	NOUN
ejpam-4348	765	4	,	,	PUNCT
ejpam-4348	765	5	,	,	PUNCT
ejpam-4348	765	6	novosibirsk	novosibirsk	PROPN
ejpam-4348	765	7	,	,	PUNCT
ejpam-4348	765	8	1998	1998	NUM
ejpam-4348	765	9	.	.	PUNCT
ejpam-4348	766	1	[	[	X
ejpam-4348	766	2	9	9	NUM
ejpam-4348	766	3	]	]	SYM
ejpam-4348	766	4	s	s	PART
ejpam-4348	766	5	k	k	NOUN
ejpam-4348	766	6	godunov	godunov	PROPN
ejpam-4348	766	7	and	and	CCONJ
ejpam-4348	766	8	m	m	PRON
ejpam-4348	766	9	sadkane	sadkane	ADJ
ejpam-4348	766	10	.	.	PUNCT
ejpam-4348	767	1	some	some	DET
ejpam-4348	767	2	new	new	ADJ
ejpam-4348	767	3	algorithms	algorithm	NOUN
ejpam-4348	767	4	for	for	ADP
ejpam-4348	767	5	the	the	DET
ejpam-4348	767	6	spectral	spectral	ADJ
ejpam-4348	767	7	dichotomy	dichotomy	NOUN
ejpam-4348	767	8	methods	method	NOUN
ejpam-4348	767	9	.	.	PUNCT
ejpam-4348	768	1	linear	linear	ADJ
ejpam-4348	768	2	algebra	algebra	PROPN
ejpam-4348	768	3	appl	appl	NOUN
ejpam-4348	768	4	.	.	PUNCT
ejpam-4348	768	5	,	,	PUNCT
ejpam-4348	768	6	358	358	NUM
ejpam-4348	768	7	,	,	PUNCT
ejpam-4348	768	8	2003	2003	NUM
ejpam-4348	768	9	.	.	PUNCT
ejpam-4348	769	1	[	[	X
ejpam-4348	769	2	10	10	NUM
ejpam-4348	769	3	]	]	X
ejpam-4348	769	4	a	a	PRON
ejpam-4348	769	5	n	n	ADV
ejpam-4348	769	6	malyshev	malyshev	NOUN
ejpam-4348	769	7	.	.	PUNCT
ejpam-4348	770	1	calculation	calculation	NOUN
ejpam-4348	770	2	of	of	ADP
ejpam-4348	770	3	invariant	invariant	ADJ
ejpam-4348	770	4	subspaces	subspace	NOUN
ejpam-4348	770	5	of	of	ADP
ejpam-4348	770	6	a	a	DET
ejpam-4348	770	7	regular	regular	ADJ
ejpam-4348	770	8	linear	linear	ADJ
ejpam-4348	770	9	matrix	matrix	NOUN
ejpam-4348	770	10	pencil	pencil	NOUN
ejpam-4348	770	11	.	.	PUNCT
ejpam-4348	771	1	(	(	PUNCT
ejpam-4348	771	2	russian	russian	ADJ
ejpam-4348	771	3	)	)	PUNCT
ejpam-4348	771	4	sibirsk	sibirsk	NOUN
ejpam-4348	771	5	.	.	PUNCT
ejpam-4348	772	1	mat	mat	NOUN
ejpam-4348	772	2	.	.	PUNCT
ejpam-4348	773	1	zh	zh	PROPN
ejpam-4348	773	2	.	.	PROPN
ejpam-4348	773	3	,	,	PUNCT
ejpam-4348	773	4	30(4):76–86	30(4):76–86	NUM
ejpam-4348	773	5	,	,	PUNCT
ejpam-4348	773	6	1989	1989	NUM
ejpam-4348	773	7	.	.	PUNCT
ejpam-4348	774	1	[	[	X
ejpam-4348	774	2	11	11	NUM
ejpam-4348	774	3	]	]	PUNCT
ejpam-4348	774	4	a	a	DET
ejpam-4348	774	5	n	n	DET
ejpam-4348	774	6	malyshev	malyshev	NOUN
ejpam-4348	774	7	.	.	PUNCT
ejpam-4348	775	1	guaranted	guarante	VERB
ejpam-4348	775	2	accuracy	accuracy	NOUN
ejpam-4348	775	3	in	in	ADP
ejpam-4348	775	4	spectral	spectral	ADJ
ejpam-4348	775	5	problems	problem	NOUN
ejpam-4348	775	6	of	of	ADP
ejpam-4348	775	7	linear	linear	PROPN
ejpam-4348	775	8	algebra	algebra	PROPN
ejpam-4348	775	9	.	.	PUNCT
ejpam-4348	776	1	siberian	siberian	PROPN
ejpam-4348	776	2	adv	adv	PROPN
ejpam-4348	776	3	.	.	PUNCT
ejpam-4348	776	4	math	math	PROPN
ejpam-4348	776	5	.	.	PUNCT
ejpam-4348	777	1	j.	j.	PROPN
ejpam-4348	777	2	,	,	PUNCT
ejpam-4348	777	3	i	i	PRON
ejpam-4348	777	4	,	,	PUNCT
ejpam-4348	777	5	ii(2):144–197	ii(2):144–197	PROPN
ejpam-4348	777	6	,	,	PUNCT
ejpam-4348	777	7	1992	1992	NUM
ejpam-4348	777	8	.	.	PUNCT
ejpam-4348	778	1	[	[	X
ejpam-4348	778	2	12	12	NUM
ejpam-4348	778	3	]	]	PUNCT
ejpam-4348	778	4	a	a	PRON
ejpam-4348	778	5	n	n	ADV
ejpam-4348	778	6	malyshev	malyshev	NOUN
ejpam-4348	778	7	.	.	PUNCT
ejpam-4348	779	1	parallel	parallel	ADJ
ejpam-4348	779	2	algorithm	algorithm	NOUN
ejpam-4348	779	3	for	for	ADP
ejpam-4348	779	4	solving	solve	VERB
ejpam-4348	779	5	some	some	DET
ejpam-4348	779	6	spectral	spectral	ADJ
ejpam-4348	779	7	problems	problem	NOUN
ejpam-4348	779	8	of	of	ADP
ejpam-4348	779	9	linear	linear	PROPN
ejpam-4348	779	10	algebra	algebra	PROPN
ejpam-4348	779	11	.	.	PUNCT
ejpam-4348	780	1	linear	linear	PROPN
ejpam-4348	780	2	algebra	algebra	PROPN
ejpam-4348	780	3	appl	appl	PROPN
ejpam-4348	780	4	.	.	PROPN
ejpam-4348	780	5	,	,	PUNCT
ejpam-4348	780	6	1993	1993	NUM
ejpam-4348	780	7	.	.	PUNCT
ejpam-4348	781	1	[	[	X
ejpam-4348	781	2	13	13	NUM
ejpam-4348	781	3	]	]	SYM
ejpam-4348	781	4	a	a	DET
ejpam-4348	781	5	n	n	ADV
ejpam-4348	781	6	malyshev	malyshev	NOUN
ejpam-4348	781	7	m	m	PROPN
ejpam-4348	781	8	sadkane	sadkane	ADJ
ejpam-4348	781	9	.	.	PUNCT
ejpam-4348	782	1	on	on	ADP
ejpam-4348	782	2	parabolic	parabolic	ADJ
ejpam-4348	782	3	and	and	CCONJ
ejpam-4348	782	4	elliptic	elliptic	ADJ
ejpam-4348	782	5	spectral	spectral	ADJ
ejpam-4348	782	6	dichotomy	dichotomy	NOUN
ejpam-4348	782	7	.	.	PUNCT
ejpam-4348	783	1	siam	siam	ADJ
ejpam-4348	783	2	j.	j.	PROPN
ejpam-4348	783	3	matrix	matrix	PROPN
ejpam-4348	783	4	anal.appl	anal.appl	PROPN
ejpam-4348	783	5	.	.	PROPN
ejpam-4348	783	6	,	,	PUNCT
ejpam-4348	783	7	18(2):265–278	18(2):265–278	PROPN
ejpam-4348	783	8	,	,	PUNCT
ejpam-4348	783	9	1997	1997	NUM
ejpam-4348	783	10	.	.	PUNCT
ejpam-4348	784	1	[	[	X
ejpam-4348	784	2	14	14	NUM
ejpam-4348	784	3	]	]	X
ejpam-4348	784	4	m	m	VERB
ejpam-4348	784	5	sadkane	sadkane	ADJ
ejpam-4348	784	6	.	.	PUNCT
ejpam-4348	785	1	estimates	estimate	NOUN
ejpam-4348	785	2	from	from	ADP
ejpam-4348	785	3	the	the	DET
ejpam-4348	785	4	discrete	discrete	ADJ
ejpam-4348	785	5	-	-	PUNCT
ejpam-4348	785	6	time	time	NOUN
ejpam-4348	785	7	lyapunov	lyapunov	ADJ
ejpam-4348	785	8	equation	equation	NOUN
ejpam-4348	785	9	.	.	PUNCT
ejpam-4348	786	1	appli	appli	PROPN
ejpam-4348	786	2	.	.	PUNCT
ejpam-4348	786	3	math	math	PROPN
ejpam-4348	786	4	.	.	PUNCT
ejpam-4348	787	1	lett	lett	PROPN
ejpam-4348	787	2	.	.	PROPN
ejpam-4348	787	3	,	,	PUNCT
ejpam-4348	787	4	16	16	NUM
ejpam-4348	787	5	,	,	PUNCT
ejpam-4348	787	6	2003	2003	NUM
ejpam-4348	787	7	.	.	PUNCT
ejpam-4348	788	1	[	[	X
ejpam-4348	788	2	15	15	NUM
ejpam-4348	788	3	]	]	X
ejpam-4348	788	4	m	m	AUX
ejpam-4348	788	5	sadkane	sadkane	NOUN
ejpam-4348	788	6	and	and	CCONJ
ejpam-4348	788	7	a	a	DET
ejpam-4348	788	8	touhami	touhami	NOUN
ejpam-4348	788	9	.	.	PUNCT
ejpam-4348	789	1	on	on	ADP
ejpam-4348	789	2	modifications	modification	NOUN
ejpam-4348	789	3	to	to	ADP
ejpam-4348	789	4	the	the	DET
ejpam-4348	789	5	spectral	spectral	ADJ
ejpam-4348	789	6	dichotomy	dichotomy	NOUN
ejpam-4348	789	7	algorithm	algorithm	NOUN
ejpam-4348	789	8	.	.	PUNCT
ejpam-4348	790	1	numerical	numerical	ADJ
ejpam-4348	790	2	functional	functional	ADJ
ejpam-4348	790	3	analysis	analysis	NOUN
ejpam-4348	790	4	and	and	CCONJ
ejpam-4348	790	5	optimization	optimization	NOUN
ejpam-4348	790	6	,	,	PUNCT
ejpam-4348	790	7	34(7):791–817	34(7):791–817	PROPN
ejpam-4348	790	8	,	,	PUNCT
ejpam-4348	790	9	2013	2013	NUM
ejpam-4348	790	10	.	.	PUNCT