id	sid	tid	token	lemma	pos
ejpam-3574	1	1	european	european	PROPN
ejpam-3574	1	2	journal	journal	PROPN
ejpam-3574	1	3	of	of	ADP
ejpam-3574	1	4	pure	pure	ADJ
ejpam-3574	1	5	and	and	CCONJ
ejpam-3574	1	6	applied	apply	VERB
ejpam-3574	1	7	mathematics	mathematic	NOUN
ejpam-3574	1	8	vol	vol	NOUN
ejpam-3574	1	9	.	.	PROPN
ejpam-3574	2	1	12	12	NUM
ejpam-3574	2	2	,	,	PUNCT
ejpam-3574	2	3	no	no	INTJ
ejpam-3574	2	4	.	.	NOUN
ejpam-3574	2	5	4	4	NUM
ejpam-3574	2	6	,	,	PUNCT
ejpam-3574	2	7	2019	2019	NUM
ejpam-3574	2	8	,	,	PUNCT
ejpam-3574	2	9	1744	1744	NUM
ejpam-3574	2	10	-	-	SYM
ejpam-3574	2	11	1770	1770	NUM
ejpam-3574	2	12	issn	issn	PROPN
ejpam-3574	2	13	1307	1307	NUM
ejpam-3574	2	14	-	-	SYM
ejpam-3574	2	15	5543	5543	NUM
ejpam-3574	2	16	–	–	PUNCT
ejpam-3574	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3574	2	18	published	publish	VERB
ejpam-3574	2	19	by	by	ADP
ejpam-3574	2	20	new	new	PROPN
ejpam-3574	2	21	york	york	PROPN
ejpam-3574	2	22	business	business	PROPN
ejpam-3574	2	23	global	global	PROPN
ejpam-3574	2	24	rank	rank	PROPN
ejpam-3574	2	25	-	-	PUNCT
ejpam-3574	2	26	k	k	NOUN
ejpam-3574	2	27	perturbation	perturbation	NOUN
ejpam-3574	2	28	of	of	ADP
ejpam-3574	2	29	hamiltonian	hamiltonian	ADJ
ejpam-3574	2	30	systems	system	NOUN
ejpam-3574	2	31	with	with	ADP
ejpam-3574	2	32	periodic	periodic	ADJ
ejpam-3574	2	33	coefficients	coefficient	NOUN
ejpam-3574	2	34	and	and	CCONJ
ejpam-3574	2	35	applications	application	NOUN
ejpam-3574	2	36	mouhamadou	mouhamadou	NOUN
ejpam-3574	2	37	dosso1,∗	dosso1,∗	NOUN
ejpam-3574	2	38	,	,	PUNCT
ejpam-3574	2	39	traoré	traoré	NOUN
ejpam-3574	2	40	g.	g.	PROPN
ejpam-3574	2	41	y.	y.	PROPN
ejpam-3574	2	42	arouna1	arouna1	PROPN
ejpam-3574	2	43	,	,	PUNCT
ejpam-3574	2	44	jean	jean	PROPN
ejpam-3574	2	45	-	-	PUNCT
ejpam-3574	2	46	claude	claude	PROPN
ejpam-3574	2	47	koua	koua	PROPN
ejpam-3574	2	48	brou1	brou1	AUX
ejpam-3574	2	49	1	1	NUM
ejpam-3574	2	50	ufr	ufr	NOUN
ejpam-3574	2	51	mathématiques	mathématique	NOUN
ejpam-3574	2	52	et	et	PROPN
ejpam-3574	2	53	informatique	informatique	NOUN
ejpam-3574	2	54	,	,	PUNCT
ejpam-3574	2	55	université	université	ADJ
ejpam-3574	2	56	félix	félix	ADJ
ejpam-3574	2	57	houphouët	houphouët	PROPN
ejpam-3574	2	58	-	-	PUNCT
ejpam-3574	2	59	boigny	boigny	PROPN
ejpam-3574	2	60	,	,	PUNCT
ejpam-3574	2	61	côte	côte	VERB
ejpam-3574	2	62	d’ivoire	d’ivoire	NOUN
ejpam-3574	2	63	abstract	abstract	NOUN
ejpam-3574	2	64	.	.	PUNCT
ejpam-3574	3	1	jordan	jordan	PROPN
ejpam-3574	3	2	canonical	canonical	ADJ
ejpam-3574	3	3	forms	form	NOUN
ejpam-3574	3	4	of	of	ADP
ejpam-3574	3	5	a	a	DET
ejpam-3574	3	6	rank	rank	NOUN
ejpam-3574	3	7	-	-	PUNCT
ejpam-3574	3	8	k	k	NOUN
ejpam-3574	3	9	perturbation	perturbation	NOUN
ejpam-3574	3	10	of	of	ADP
ejpam-3574	3	11	symplectic	symplectic	ADJ
ejpam-3574	3	12	matrices	matrix	NOUN
ejpam-3574	3	13	and	and	CCONJ
ejpam-3574	3	14	the	the	DET
ejpam-3574	3	15	fundamental	fundamental	ADJ
ejpam-3574	3	16	solutions	solution	NOUN
ejpam-3574	3	17	of	of	ADP
ejpam-3574	3	18	hamiltonian	hamiltonian	ADJ
ejpam-3574	3	19	systems	system	NOUN
ejpam-3574	3	20	are	be	AUX
ejpam-3574	3	21	presented	present	VERB
ejpam-3574	3	22	on	on	ADP
ejpam-3574	3	23	the	the	DET
ejpam-3574	3	24	basis	basis	NOUN
ejpam-3574	3	25	of	of	ADP
ejpam-3574	3	26	work	work	NOUN
ejpam-3574	3	27	done	do	VERB
ejpam-3574	3	28	by	by	ADP
ejpam-3574	3	29	c.	c.	PROPN
ejpam-3574	3	30	mehl	mehl	PROPN
ejpam-3574	3	31	et	et	PROPN
ejpam-3574	3	32	,	,	PUNCT
ejpam-3574	3	33	al	al	PROPN
ejpam-3574	3	34	..	..	PROPN
ejpam-3574	3	35	small	small	ADJ
ejpam-3574	3	36	rank	rank	PROPN
ejpam-3574	3	37	-	-	PUNCT
ejpam-3574	3	38	k	k	NOUN
ejpam-3574	3	39	perturbations	perturbation	NOUN
ejpam-3574	3	40	of	of	ADP
ejpam-3574	3	41	mathieu	mathieu	PROPN
ejpam-3574	3	42	systems	system	NOUN
ejpam-3574	3	43	are	be	AUX
ejpam-3574	3	44	analyzed	analyze	VERB
ejpam-3574	3	45	.	.	PUNCT
ejpam-3574	4	1	more	more	ADV
ejpam-3574	4	2	precisely	precisely	ADV
ejpam-3574	4	3	,	,	PUNCT
ejpam-3574	4	4	it	it	PRON
ejpam-3574	4	5	is	be	AUX
ejpam-3574	4	6	shown	show	VERB
ejpam-3574	4	7	that	that	SCONJ
ejpam-3574	4	8	the	the	DET
ejpam-3574	4	9	rank	rank	NOUN
ejpam-3574	4	10	-	-	PUNCT
ejpam-3574	4	11	k	k	NOUN
ejpam-3574	4	12	perturbations	perturbation	NOUN
ejpam-3574	4	13	of	of	ADP
ejpam-3574	4	14	coupled	couple	VERB
ejpam-3574	4	15	or	or	CCONJ
ejpam-3574	4	16	non	non	ADJ
ejpam-3574	4	17	-	-	ADJ
ejpam-3574	4	18	coupled	couple	VERB
ejpam-3574	4	19	double	double	ADJ
ejpam-3574	4	20	pendulums	pendulum	NOUN
ejpam-3574	4	21	and	and	CCONJ
ejpam-3574	4	22	the	the	DET
ejpam-3574	4	23	motion	motion	NOUN
ejpam-3574	4	24	of	of	ADP
ejpam-3574	4	25	an	an	DET
ejpam-3574	4	26	ion	ion	NOUN
ejpam-3574	4	27	through	through	ADP
ejpam-3574	4	28	a	a	DET
ejpam-3574	4	29	quadrupole	quadrupole	NOUN
ejpam-3574	4	30	analyzer	analyzer	NOUN
ejpam-3574	4	31	slightly	slightly	ADV
ejpam-3574	4	32	perturb	perturb	VERB
ejpam-3574	4	33	the	the	DET
ejpam-3574	4	34	behavior	behavior	NOUN
ejpam-3574	4	35	of	of	ADP
ejpam-3574	4	36	their	their	PRON
ejpam-3574	4	37	spectra	spectra	NOUN
ejpam-3574	4	38	and	and	CCONJ
ejpam-3574	4	39	their	their	PRON
ejpam-3574	4	40	stabilities	stability	NOUN
ejpam-3574	4	41	.	.	PUNCT
ejpam-3574	5	1	2010	2010	NUM
ejpam-3574	5	2	mathematics	mathematic	NOUN
ejpam-3574	5	3	subject	subject	NOUN
ejpam-3574	5	4	classifications	classification	NOUN
ejpam-3574	5	5	:	:	PUNCT
ejpam-3574	5	6	35e05	35e05	NUM
ejpam-3574	5	7	,	,	PUNCT
ejpam-3574	5	8	39a30	39a30	NUM
ejpam-3574	5	9	,	,	PUNCT
ejpam-3574	5	10	70h05	70h05	NUM
ejpam-3574	5	11	,	,	PUNCT
ejpam-3574	5	12	70h09	70h09	NUM
ejpam-3574	5	13	,	,	PUNCT
ejpam-3574	5	14	93c15	93c15	NOUN
ejpam-3574	5	15	key	key	ADJ
ejpam-3574	5	16	words	word	NOUN
ejpam-3574	5	17	and	and	CCONJ
ejpam-3574	5	18	phrases	phrase	NOUN
ejpam-3574	5	19	:	:	PUNCT
ejpam-3574	5	20	symplectic	symplectic	ADJ
ejpam-3574	5	21	matrices	matrix	NOUN
ejpam-3574	5	22	,	,	PUNCT
ejpam-3574	5	23	isotropic	isotropic	ADJ
ejpam-3574	5	24	subspaces	subspace	NOUN
ejpam-3574	5	25	,	,	PUNCT
ejpam-3574	5	26	hamiltonian	hamiltonian	ADJ
ejpam-3574	5	27	systems	system	NOUN
ejpam-3574	5	28	,	,	PUNCT
ejpam-3574	5	29	fundamental	fundamental	ADJ
ejpam-3574	5	30	solutions	solution	NOUN
ejpam-3574	5	31	,	,	PUNCT
ejpam-3574	5	32	rang	rang	PROPN
ejpam-3574	5	33	-	-	PUNCT
ejpam-3574	5	34	k	k	PROPN
ejpam-3574	5	35	perturbation	perturbation	NOUN
ejpam-3574	5	36	,	,	PUNCT
ejpam-3574	5	37	stability(strong	stability(strong	PROPN
ejpam-3574	5	38	)	)	PUNCT
ejpam-3574	5	39	,	,	PUNCT
ejpam-3574	5	40	mathieu	mathieu	PROPN
ejpam-3574	5	41	systems	systems	PROPN
ejpam-3574	5	42	1	1	NUM
ejpam-3574	5	43	.	.	PUNCT
ejpam-3574	6	1	introduction	introduction	NOUN
ejpam-3574	6	2	let	let	VERB
ejpam-3574	6	3	j	j	PROPN
ejpam-3574	6	4	,	,	PUNCT
ejpam-3574	6	5	w	w	PROPN
ejpam-3574	6	6	∈	∈	PROPN
ejpam-3574	6	7	r2n×2n	r2n×2n	NOUN
ejpam-3574	6	8	such	such	ADJ
ejpam-3574	6	9	that	that	SCONJ
ejpam-3574	6	10	j	j	PROPN
ejpam-3574	6	11	is	be	AUX
ejpam-3574	6	12	a	a	DET
ejpam-3574	6	13	skew	skew	ADJ
ejpam-3574	6	14	-	-	PUNCT
ejpam-3574	6	15	symmetric	symmetric	ADJ
ejpam-3574	6	16	matrix	matrix	NOUN
ejpam-3574	6	17	.	.	PUNCT
ejpam-3574	7	1	we	we	PRON
ejpam-3574	7	2	say	say	VERB
ejpam-3574	7	3	that	that	SCONJ
ejpam-3574	7	4	the	the	DET
ejpam-3574	7	5	matrix	matrix	NOUN
ejpam-3574	7	6	w	w	NOUN
ejpam-3574	7	7	is	be	AUX
ejpam-3574	7	8	j	j	NOUN
ejpam-3574	7	9	-	-	PUNCT
ejpam-3574	7	10	symplectic	symplectic	ADJ
ejpam-3574	7	11	or	or	CCONJ
ejpam-3574	7	12	j	j	NOUN
ejpam-3574	7	13	-	-	NOUN
ejpam-3574	7	14	orthogonal	orthogonal	ADJ
ejpam-3574	7	15	if	if	SCONJ
ejpam-3574	7	16	and	and	CCONJ
ejpam-3574	7	17	only	only	ADV
ejpam-3574	7	18	if	if	SCONJ
ejpam-3574	7	19	w	w	NOUN
ejpam-3574	7	20	tjw	tjw	NOUN
ejpam-3574	7	21	=	=	SYM
ejpam-3574	7	22	j	j	PROPN
ejpam-3574	8	1	[	[	X
ejpam-3574	8	2	4	4	NUM
ejpam-3574	8	3	,	,	PUNCT
ejpam-3574	8	4	18	18	NUM
ejpam-3574	8	5	]	]	PUNCT
ejpam-3574	8	6	.	.	PUNCT
ejpam-3574	9	1	these	these	DET
ejpam-3574	9	2	types	type	NOUN
ejpam-3574	9	3	of	of	ADP
ejpam-3574	9	4	matrices	matrix	NOUN
ejpam-3574	9	5	generally	generally	ADV
ejpam-3574	9	6	appear	appear	VERB
ejpam-3574	9	7	in	in	ADP
ejpam-3574	9	8	control	control	NOUN
ejpam-3574	9	9	theory	theory	NOUN
ejpam-3574	9	10	[	[	X
ejpam-3574	9	11	3	3	NUM
ejpam-3574	9	12	,	,	PUNCT
ejpam-3574	9	13	11	11	NUM
ejpam-3574	9	14	,	,	PUNCT
ejpam-3574	9	15	15	15	NUM
ejpam-3574	9	16	,	,	PUNCT
ejpam-3574	9	17	18	18	NUM
ejpam-3574	9	18	]	]	PUNCT
ejpam-3574	9	19	,	,	PUNCT
ejpam-3574	9	20	especially	especially	ADV
ejpam-3574	9	21	in	in	ADP
ejpam-3574	9	22	optimal	optimal	ADJ
ejpam-3574	9	23	control	control	NOUN
ejpam-3574	10	1	[	[	X
ejpam-3574	10	2	11	11	NUM
ejpam-3574	10	3	]	]	PUNCT
ejpam-3574	10	4	and	and	CCONJ
ejpam-3574	10	5	in	in	ADP
ejpam-3574	10	6	parametric	parametric	ADJ
ejpam-3574	10	7	resonance	resonance	NOUN
ejpam-3574	10	8	theory	theory	NOUN
ejpam-3574	10	9	[	[	X
ejpam-3574	10	10	15	15	NUM
ejpam-3574	10	11	]	]	PUNCT
ejpam-3574	10	12	.	.	PUNCT
ejpam-3574	11	1	the	the	DET
ejpam-3574	11	2	spectra	spectra	NOUN
ejpam-3574	11	3	of	of	ADP
ejpam-3574	11	4	the	the	DET
ejpam-3574	11	5	symplectic	symplectic	ADJ
ejpam-3574	11	6	matrices	matrix	NOUN
ejpam-3574	11	7	is	be	AUX
ejpam-3574	11	8	generally	generally	ADV
ejpam-3574	11	9	composed	compose	VERB
ejpam-3574	11	10	of	of	ADP
ejpam-3574	11	11	three	three	NUM
ejpam-3574	11	12	groups	group	NOUN
ejpam-3574	11	13	with	with	ADP
ejpam-3574	11	14	respect	respect	NOUN
ejpam-3574	11	15	to	to	ADP
ejpam-3574	11	16	the	the	DET
ejpam-3574	11	17	unit	unit	NOUN
ejpam-3574	11	18	circle	circle	NOUN
ejpam-3574	11	19	(	(	PUNCT
ejpam-3574	11	20	see	see	VERB
ejpam-3574	12	1	e.g.	e.g.	ADV
ejpam-3574	12	2	[	[	X
ejpam-3574	12	3	7	7	NUM
ejpam-3574	12	4	,	,	PUNCT
ejpam-3574	12	5	8	8	NUM
ejpam-3574	12	6	,	,	PUNCT
ejpam-3574	12	7	18	18	NUM
ejpam-3574	12	8	]	]	PUNCT
ejpam-3574	12	9	)	)	PUNCT
ejpam-3574	13	1	:	:	PUNCT
ejpam-3574	13	2	n0	n0	NUM
ejpam-3574	13	3	eigenvalues	eigenvalue	VERB
ejpam-3574	13	4	outside	outside	ADP
ejpam-3574	13	5	the	the	DET
ejpam-3574	13	6	unit	unit	NOUN
ejpam-3574	13	7	circle	circle	NOUN
ejpam-3574	13	8	,	,	PUNCT
ejpam-3574	13	9	n0	n0	X
ejpam-3574	13	10	=	=	SYM
ejpam-3574	13	11	n∞	n∞	PROPN
ejpam-3574	13	12	eigenvalues	eigenvalue	VERB
ejpam-3574	13	13	inside	inside	ADP
ejpam-3574	13	14	the	the	DET
ejpam-3574	13	15	unit	unit	NOUN
ejpam-3574	13	16	circle	circle	NOUN
ejpam-3574	13	17	and	and	CCONJ
ejpam-3574	14	1	2n1	2n1	NUM
ejpam-3574	14	2	=	=	SYM
ejpam-3574	14	3	2(n	2(n	NUM
ejpam-3574	14	4	−n0	−n0	NOUN
ejpam-3574	14	5	)	)	PUNCT
ejpam-3574	14	6	eigenvalues	eigenvalue	VERB
ejpam-3574	14	7	on	on	ADP
ejpam-3574	14	8	the	the	DET
ejpam-3574	14	9	unit	unit	NOUN
ejpam-3574	14	10	circle	circle	NOUN
ejpam-3574	14	11	.	.	PUNCT
ejpam-3574	15	1	a	a	DET
ejpam-3574	15	2	symplectic	symplectic	ADJ
ejpam-3574	15	3	matrix	matrix	NOUN
ejpam-3574	15	4	w	w	NOUN
ejpam-3574	15	5	is	be	AUX
ejpam-3574	15	6	stable	stable	ADJ
ejpam-3574	15	7	if	if	SCONJ
ejpam-3574	15	8	all	all	DET
ejpam-3574	15	9	its	its	PRON
ejpam-3574	15	10	powers	power	NOUN
ejpam-3574	15	11	are	be	AUX
ejpam-3574	15	12	bounded	bound	VERB
ejpam-3574	15	13	.	.	PUNCT
ejpam-3574	16	1	in	in	ADP
ejpam-3574	16	2	other	other	ADJ
ejpam-3574	16	3	words	word	NOUN
ejpam-3574	16	4	,	,	PUNCT
ejpam-3574	16	5	if	if	SCONJ
ejpam-3574	16	6	the	the	DET
ejpam-3574	16	7	eigenvalues	eigenvalue	NOUN
ejpam-3574	16	8	of	of	ADP
ejpam-3574	16	9	w	w	PROPN
ejpam-3574	16	10	lie	lie	NOUN
ejpam-3574	16	11	on	on	ADP
ejpam-3574	16	12	the	the	DET
ejpam-3574	16	13	unit	unit	NOUN
ejpam-3574	16	14	circle	circle	NOUN
ejpam-3574	16	15	and	and	CCONJ
ejpam-3574	16	16	are	be	AUX
ejpam-3574	16	17	semi	semi	ADJ
ejpam-3574	16	18	-	-	ADJ
ejpam-3574	16	19	simple	simple	ADJ
ejpam-3574	16	20	.	.	PUNCT
ejpam-3574	17	1	some	some	DET
ejpam-3574	17	2	classifications	classification	NOUN
ejpam-3574	17	3	of	of	ADP
ejpam-3574	17	4	eigenvalues	eigenvalue	NOUN
ejpam-3574	17	5	of	of	ADP
ejpam-3574	17	6	w	w	NOUN
ejpam-3574	17	7	are	be	AUX
ejpam-3574	17	8	given	give	VERB
ejpam-3574	17	9	by	by	ADP
ejpam-3574	17	10	the	the	DET
ejpam-3574	17	11	following	follow	VERB
ejpam-3574	17	12	definitions	definition	NOUN
ejpam-3574	17	13	[	[	X
ejpam-3574	17	14	4	4	NUM
ejpam-3574	17	15	,	,	PUNCT
ejpam-3574	17	16	7	7	NUM
ejpam-3574	17	17	,	,	PUNCT
ejpam-3574	17	18	10	10	NUM
ejpam-3574	17	19	,	,	PUNCT
ejpam-3574	17	20	18	18	NUM
ejpam-3574	17	21	]	]	PUNCT
ejpam-3574	17	22	definition	definition	NOUN
ejpam-3574	17	23	1	1	NUM
ejpam-3574	17	24	.	.	PUNCT
ejpam-3574	18	1	let	let	VERB
ejpam-3574	18	2	λ	λ	PRON
ejpam-3574	18	3	be	be	AUX
ejpam-3574	18	4	a	a	DET
ejpam-3574	18	5	semi	semi	ADJ
ejpam-3574	18	6	-	-	ADJ
ejpam-3574	18	7	simple	simple	ADJ
ejpam-3574	18	8	eigenvalue	eigenvalue	NOUN
ejpam-3574	18	9	of	of	ADP
ejpam-3574	18	10	w	w	PROPN
ejpam-3574	18	11	lying	lie	VERB
ejpam-3574	18	12	on	on	ADP
ejpam-3574	18	13	the	the	DET
ejpam-3574	18	14	unit	unit	NOUN
ejpam-3574	18	15	circle	circle	NOUN
ejpam-3574	18	16	.	.	PUNCT
ejpam-3574	19	1	(	(	PUNCT
ejpam-3574	19	2	i	i	NOUN
ejpam-3574	19	3	)	)	PUNCT
ejpam-3574	19	4	then	then	ADV
ejpam-3574	19	5	λ	λ	NOUN
ejpam-3574	19	6	is	be	AUX
ejpam-3574	19	7	called	call	VERB
ejpam-3574	19	8	an	an	DET
ejpam-3574	19	9	eigenvalue	eigenvalue	NOUN
ejpam-3574	19	10	of	of	ADP
ejpam-3574	19	11	the	the	DET
ejpam-3574	19	12	first	first	ADJ
ejpam-3574	19	13	(	(	PUNCT
ejpam-3574	19	14	second	second	ADJ
ejpam-3574	19	15	)	)	PUNCT
ejpam-3574	19	16	kind	kind	NOUN
ejpam-3574	19	17	if	if	SCONJ
ejpam-3574	19	18	the	the	DET
ejpam-3574	19	19	quadratic	quadratic	ADJ
ejpam-3574	19	20	form	form	NOUN
ejpam-3574	19	21	(	(	PUNCT
ejpam-3574	19	22	ijx	ijx	NOUN
ejpam-3574	19	23	,	,	PUNCT
ejpam-3574	19	24	x	x	PRON
ejpam-3574	19	25	)	)	PUNCT
ejpam-3574	19	26	is	be	AUX
ejpam-3574	19	27	positive	positive	ADJ
ejpam-3574	19	28	(	(	PUNCT
ejpam-3574	19	29	negative	negative	ADJ
ejpam-3574	19	30	)	)	PUNCT
ejpam-3574	19	31	on	on	ADP
ejpam-3574	19	32	the	the	DET
ejpam-3574	19	33	eigenspace	eigenspace	NOUN
ejpam-3574	19	34	associated	associate	VERB
ejpam-3574	19	35	with	with	ADP
ejpam-3574	19	36	λ	λ	PROPN
ejpam-3574	19	37	.	.	PUNCT
ejpam-3574	20	1	when	when	SCONJ
ejpam-3574	20	2	(	(	PUNCT
ejpam-3574	20	3	jx	jx	PROPN
ejpam-3574	20	4	,	,	PUNCT
ejpam-3574	20	5	x	x	NOUN
ejpam-3574	20	6	)	)	PUNCT
ejpam-3574	20	7	=	=	SYM
ejpam-3574	20	8	0	0	NUM
ejpam-3574	20	9	,	,	PUNCT
ejpam-3574	20	10	then	then	ADV
ejpam-3574	20	11	λ	λ	PROPN
ejpam-3574	20	12	is	be	AUX
ejpam-3574	20	13	of	of	ADP
ejpam-3574	20	14	mixed	mixed	ADJ
ejpam-3574	20	15	kind	kind	NOUN
ejpam-3574	20	16	.	.	PUNCT
ejpam-3574	21	1	∗corresponding	∗corresponde	VERB
ejpam-3574	21	2	author	author	NOUN
ejpam-3574	21	3	.	.	PUNCT
ejpam-3574	22	1	doi	doi	NOUN
ejpam-3574	22	2	:	:	PUNCT
ejpam-3574	22	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3574	https://doi.org/10.29020/nybg.ejpam.v12i4.3574	ADJ
ejpam-3574	22	4	email	email	NOUN
ejpam-3574	22	5	addresses	address	NOUN
ejpam-3574	22	6	:	:	PUNCT
ejpam-3574	22	7	mouhamadou.dosso@univ-fhb.edu.ci	mouhamadou.dosso@univ-fhb.edu.ci	PROPN
ejpam-3574	22	8	(	(	PUNCT
ejpam-3574	22	9	m.	m.	NOUN
ejpam-3574	22	10	dosso	dosso	PROPN
ejpam-3574	22	11	)	)	PUNCT
ejpam-3574	22	12	,	,	PUNCT
ejpam-3574	23	1	k	k	PROPN
ejpam-3574	23	2	brou@hotmail.com	brou@hotmail.com	PROPN
ejpam-3574	23	3	(	(	PUNCT
ejpam-3574	23	4	j.-c	j.-c	PROPN
ejpam-3574	23	5	.	.	PUNCT
ejpam-3574	24	1	koua	koua	PROPN
ejpam-3574	24	2	brou	brou	PROPN
ejpam-3574	24	3	)	)	PUNCT
ejpam-3574	24	4	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3574	25	1	1744	1744	NUM
ejpam-3574	25	2	c	c	X
ejpam-3574	25	3	©	©	PROPN
ejpam-3574	25	4	2019	2019	NUM
ejpam-3574	25	5	ejpam	ejpam	NOUN
ejpam-3574	25	6	all	all	DET
ejpam-3574	25	7	rights	right	NOUN
ejpam-3574	25	8	reserved	reserve	VERB
ejpam-3574	25	9	.	.	PUNCT
ejpam-3574	26	1	m.	m.	NOUN
ejpam-3574	26	2	dosso	dosso	PROPN
ejpam-3574	26	3	,	,	PUNCT
ejpam-3574	26	4	t.	t.	PROPN
ejpam-3574	26	5	g.	g.	PROPN
ejpam-3574	26	6	y.	y.	PROPN
ejpam-3574	26	7	arouna	arouna	PROPN
ejpam-3574	26	8	,	,	PUNCT
ejpam-3574	26	9	j.-c	j.-c	PROPN
ejpam-3574	26	10	.	.	PUNCT
ejpam-3574	27	1	koua	koua	PROPN
ejpam-3574	27	2	brou	brou	PROPN
ejpam-3574	27	3	/	/	SYM
ejpam-3574	27	4	eur	eur	PROPN
ejpam-3574	27	5	.	.	PUNCT
ejpam-3574	28	1	j.	j.	PROPN
ejpam-3574	28	2	pure	pure	PROPN
ejpam-3574	28	3	appl	appl	PROPN
ejpam-3574	28	4	.	.	PROPN
ejpam-3574	28	5	math	math	PROPN
ejpam-3574	28	6	,	,	PUNCT
ejpam-3574	28	7	12	12	NUM
ejpam-3574	28	8	(	(	PUNCT
ejpam-3574	28	9	4	4	NUM
ejpam-3574	28	10	)	)	PUNCT
ejpam-3574	28	11	(	(	PUNCT
ejpam-3574	28	12	2019	2019	NUM
ejpam-3574	28	13	)	)	PUNCT
ejpam-3574	28	14	,	,	PUNCT
ejpam-3574	28	15	1744	1744	NUM
ejpam-3574	28	16	-	-	SYM
ejpam-3574	28	17	1770	1770	NUM
ejpam-3574	28	18	1745	1745	NUM
ejpam-3574	28	19	(	(	PUNCT
ejpam-3574	28	20	ii	ii	NOUN
ejpam-3574	28	21	)	)	PUNCT
ejpam-3574	28	22	then	then	ADV
ejpam-3574	28	23	λ	λ	PROPN
ejpam-3574	28	24	is	be	AUX
ejpam-3574	28	25	an	an	DET
ejpam-3574	28	26	eigenvalue	eigenvalue	NOUN
ejpam-3574	28	27	of	of	ADP
ejpam-3574	28	28	a	a	DET
ejpam-3574	28	29	red	red	ADJ
ejpam-3574	28	30	(	(	PUNCT
ejpam-3574	28	31	green	green	ADJ
ejpam-3574	28	32	)	)	PUNCT
ejpam-3574	28	33	color	color	NOUN
ejpam-3574	28	34	or	or	CCONJ
ejpam-3574	28	35	in	in	ADP
ejpam-3574	28	36	short	short	ADJ
ejpam-3574	28	37	r	r	NOUN
ejpam-3574	28	38	-	-	PUNCT
ejpam-3574	28	39	eigenvalue	eigenvalue	ADJ
ejpam-3574	28	40	(	(	PUNCT
ejpam-3574	28	41	g	g	NOUN
ejpam-3574	28	42	-	-	PUNCT
ejpam-3574	28	43	eigenvalue	eigenvalue	NOUN
ejpam-3574	28	44	)	)	PUNCT
ejpam-3574	28	45	if	if	SCONJ
ejpam-3574	28	46	(	(	PUNCT
ejpam-3574	28	47	s(0)x	s(0)x	X
ejpam-3574	28	48	,	,	PUNCT
ejpam-3574	28	49	x	x	X
ejpam-3574	28	50	)	)	PUNCT
ejpam-3574	28	51	is	be	AUX
ejpam-3574	28	52	positive	positive	ADJ
ejpam-3574	28	53	(	(	PUNCT
ejpam-3574	28	54	negative	negative	ADJ
ejpam-3574	28	55	)	)	PUNCT
ejpam-3574	28	56	on	on	ADP
ejpam-3574	28	57	the	the	DET
ejpam-3574	28	58	eigenspace	eigenspace	NOUN
ejpam-3574	28	59	associated	associate	VERB
ejpam-3574	28	60	with	with	ADP
ejpam-3574	28	61	λ	λ	PROPN
ejpam-3574	29	1	where	where	SCONJ
ejpam-3574	29	2	s(0	s(0	PROPN
ejpam-3574	29	3	)	)	PUNCT
ejpam-3574	29	4	=	=	SYM
ejpam-3574	29	5	1	1	NUM
ejpam-3574	29	6	2	2	NUM
ejpam-3574	29	7	(	(	PUNCT
ejpam-3574	29	8	jw	jw	PROPN
ejpam-3574	29	9	+	+	CCONJ
ejpam-3574	29	10	(	(	PUNCT
ejpam-3574	29	11	jw	jw	PROPN
ejpam-3574	29	12	)	)	PUNCT
ejpam-3574	29	13	t	t	PROPN
ejpam-3574	29	14	)	)	PUNCT
ejpam-3574	29	15	.	.	PUNCT
ejpam-3574	30	1	this	this	PRON
ejpam-3574	30	2	leads	lead	VERB
ejpam-3574	30	3	us	we	PRON
ejpam-3574	30	4	to	to	ADP
ejpam-3574	30	5	the	the	DET
ejpam-3574	30	6	characterization	characterization	NOUN
ejpam-3574	30	7	of	of	ADP
ejpam-3574	30	8	the	the	DET
ejpam-3574	30	9	strong	strong	ADJ
ejpam-3574	30	10	stability	stability	NOUN
ejpam-3574	30	11	by	by	ADP
ejpam-3574	30	12	the	the	DET
ejpam-3574	30	13	following	follow	VERB
ejpam-3574	30	14	theorem	theorem	NOUN
ejpam-3574	30	15	(	(	PUNCT
ejpam-3574	30	16	see	see	VERB
ejpam-3574	30	17	[	[	X
ejpam-3574	30	18	6	6	NUM
ejpam-3574	30	19	,	,	PUNCT
ejpam-3574	30	20	7	7	NUM
ejpam-3574	30	21	]	]	PUNCT
ejpam-3574	30	22	)	)	PUNCT
ejpam-3574	30	23	theorem	theorem	NOUN
ejpam-3574	30	24	1	1	NUM
ejpam-3574	30	25	.	.	PUNCT
ejpam-3574	31	1	a	a	DET
ejpam-3574	31	2	symplectic	symplectic	ADJ
ejpam-3574	31	3	matrix	matrix	NOUN
ejpam-3574	31	4	w	w	NOUN
ejpam-3574	31	5	is	be	AUX
ejpam-3574	31	6	strongly	strongly	ADV
ejpam-3574	31	7	stable	stable	ADJ
ejpam-3574	31	8	if	if	SCONJ
ejpam-3574	31	9	all	all	DET
ejpam-3574	31	10	the	the	DET
ejpam-3574	31	11	eigenvalues	eigenvalue	NOUN
ejpam-3574	31	12	are	be	AUX
ejpam-3574	31	13	on	on	ADP
ejpam-3574	31	14	the	the	DET
ejpam-3574	31	15	unit	unit	NOUN
ejpam-3574	31	16	circle	circle	NOUN
ejpam-3574	31	17	and	and	CCONJ
ejpam-3574	31	18	verifies	verifie	NOUN
ejpam-3574	31	19	one	one	NUM
ejpam-3574	31	20	of	of	ADP
ejpam-3574	31	21	the	the	DET
ejpam-3574	31	22	following	follow	VERB
ejpam-3574	31	23	assertion	assertion	NOUN
ejpam-3574	31	24	:	:	PUNCT
ejpam-3574	31	25	(	(	PUNCT
ejpam-3574	31	26	i	i	NOUN
ejpam-3574	31	27	)	)	PUNCT
ejpam-3574	31	28	the	the	DET
ejpam-3574	31	29	eigenvalues	eigenvalue	NOUN
ejpam-3574	31	30	are	be	AUX
ejpam-3574	31	31	either	either	PRON
ejpam-3574	31	32	of	of	ADP
ejpam-3574	31	33	the	the	DET
ejpam-3574	31	34	first	first	ADJ
ejpam-3574	31	35	or	or	CCONJ
ejpam-3574	31	36	second	second	ADJ
ejpam-3574	31	37	kind	kind	NOUN
ejpam-3574	31	38	and	and	CCONJ
ejpam-3574	31	39	there	there	PRON
ejpam-3574	31	40	is	be	VERB
ejpam-3574	31	41	a	a	DET
ejpam-3574	31	42	sufficient	sufficient	ADJ
ejpam-3574	31	43	gap	gap	NOUN
ejpam-3574	31	44	between	between	ADP
ejpam-3574	31	45	the	the	DET
ejpam-3574	31	46	eigenvalues	eigenvalue	NOUN
ejpam-3574	31	47	of	of	ADP
ejpam-3574	31	48	first	first	ADJ
ejpam-3574	31	49	and	and	CCONJ
ejpam-3574	31	50	second	second	ADJ
ejpam-3574	31	51	kind	kind	NOUN
ejpam-3574	31	52	.	.	PUNCT
ejpam-3574	32	1	in	in	ADP
ejpam-3574	32	2	other	other	ADJ
ejpam-3574	32	3	words	word	NOUN
ejpam-3574	32	4	,	,	PUNCT
ejpam-3574	32	5	the	the	DET
ejpam-3574	32	6	quantity	quantity	NOUN
ejpam-3574	32	7	δkgl(w	δkgl(w	NOUN
ejpam-3574	32	8	)	)	PUNCT
ejpam-3574	33	1	=	=	SYM
ejpam-3574	33	2	min	min	NOUN
ejpam-3574	33	3	{	{	PUNCT
ejpam-3574	33	4	|eiθk	|eiθk	NOUN
ejpam-3574	33	5	−	−	PROPN
ejpam-3574	33	6	eiθl	eiθl	ADV
ejpam-3574	33	7	|	|	ADV
ejpam-3574	33	8	such	such	ADJ
ejpam-3574	33	9	that	that	DET
ejpam-3574	33	10	eiθk	eiθk	NOUN
ejpam-3574	33	11	,	,	PUNCT
ejpam-3574	33	12	eiθl	eiθl	ADV
ejpam-3574	33	13	are	be	AUX
ejpam-3574	33	14	eigenvalues	eigenvalue	NOUN
ejpam-3574	33	15	of	of	ADP
ejpam-3574	33	16	w	w	NOUN
ejpam-3574	33	17	of	of	ADP
ejpam-3574	33	18	different	different	ADJ
ejpam-3574	33	19	kinds	kind	NOUN
ejpam-3574	33	20	}	}	PUNCT
ejpam-3574	33	21	should	should	AUX
ejpam-3574	33	22	not	not	PART
ejpam-3574	33	23	be	be	AUX
ejpam-3574	33	24	close	close	ADJ
ejpam-3574	33	25	to	to	ADP
ejpam-3574	33	26	zero	zero	NUM
ejpam-3574	33	27	.	.	PUNCT
ejpam-3574	34	1	(	(	PUNCT
ejpam-3574	34	2	ii	ii	NOUN
ejpam-3574	34	3	)	)	PUNCT
ejpam-3574	34	4	the	the	DET
ejpam-3574	34	5	eigenvalues	eigenvalue	NOUN
ejpam-3574	34	6	are	be	AUX
ejpam-3574	34	7	either	either	PRON
ejpam-3574	34	8	of	of	ADP
ejpam-3574	34	9	red	red	ADJ
ejpam-3574	34	10	color	color	NOUN
ejpam-3574	34	11	or	or	CCONJ
ejpam-3574	34	12	green	green	ADJ
ejpam-3574	34	13	color	color	NOUN
ejpam-3574	34	14	and	and	CCONJ
ejpam-3574	34	15	there	there	PRON
ejpam-3574	34	16	is	be	VERB
ejpam-3574	34	17	a	a	DET
ejpam-3574	34	18	sufficient	sufficient	ADJ
ejpam-3574	34	19	gap	gap	NOUN
ejpam-3574	34	20	between	between	ADP
ejpam-3574	34	21	the	the	DET
ejpam-3574	34	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	34	23	of	of	ADP
ejpam-3574	34	24	red	red	ADJ
ejpam-3574	34	25	and	and	CCONJ
ejpam-3574	34	26	green	green	ADJ
ejpam-3574	34	27	color	color	NOUN
ejpam-3574	34	28	.	.	PUNCT
ejpam-3574	35	1	in	in	ADP
ejpam-3574	35	2	other	other	ADJ
ejpam-3574	35	3	words	word	NOUN
ejpam-3574	35	4	,	,	PUNCT
ejpam-3574	35	5	the	the	DET
ejpam-3574	35	6	quantity	quantity	NOUN
ejpam-3574	35	7	δs(w	δs(w	PRON
ejpam-3574	35	8	)	)	PUNCT
ejpam-3574	35	9	=	=	SYM
ejpam-3574	35	10	min	min	NOUN
ejpam-3574	35	11	{	{	PUNCT
ejpam-3574	35	12	|eiθk	|eiθk	NOUN
ejpam-3574	35	13	−	−	PROPN
ejpam-3574	35	14	eiθl	eiθl	ADV
ejpam-3574	35	15	|	|	ADV
ejpam-3574	35	16	such	such	ADJ
ejpam-3574	35	17	that	that	DET
ejpam-3574	35	18	eiθk	eiθk	NOUN
ejpam-3574	35	19	,	,	PUNCT
ejpam-3574	35	20	eiθl	eiθl	ADV
ejpam-3574	35	21	are	be	AUX
ejpam-3574	35	22	rand	rand	NOUN
ejpam-3574	35	23	g	g	NOUN
ejpam-3574	35	24	-	-	PUNCT
ejpam-3574	35	25	eigenvalues	eigenvalue	NOUN
ejpam-3574	35	26	of	of	ADP
ejpam-3574	35	27	w	w	NOUN
ejpam-3574	35	28	}	}	PUNCT
ejpam-3574	35	29	should	should	AUX
ejpam-3574	35	30	not	not	PART
ejpam-3574	35	31	be	be	AUX
ejpam-3574	35	32	close	close	ADJ
ejpam-3574	35	33	to	to	ADP
ejpam-3574	35	34	zero	zero	NUM
ejpam-3574	35	35	.	.	PUNCT
ejpam-3574	36	1	these	these	DET
ejpam-3574	36	2	symplectic	symplectic	ADJ
ejpam-3574	36	3	matrices	matrix	NOUN
ejpam-3574	36	4	are	be	AUX
ejpam-3574	36	5	often	often	ADV
ejpam-3574	36	6	obtained	obtain	VERB
ejpam-3574	36	7	as	as	ADP
ejpam-3574	36	8	solutions	solution	NOUN
ejpam-3574	36	9	of	of	ADP
ejpam-3574	36	10	hamiltonian	hamiltonian	ADJ
ejpam-3574	36	11	systems	system	NOUN
ejpam-3574	36	12	with	with	ADP
ejpam-3574	36	13	periodic	periodic	ADJ
ejpam-3574	36	14	coefficients	coefficient	NOUN
ejpam-3574	36	15	i.e.	i.e.	X
ejpam-3574	36	16	the	the	DET
ejpam-3574	36	17	differential	differential	ADJ
ejpam-3574	36	18	systems	system	NOUN
ejpam-3574	36	19	of	of	ADP
ejpam-3574	36	20	the	the	DET
ejpam-3574	36	21	form	form	NOUN
ejpam-3574	36	22	j	j	PROPN
ejpam-3574	36	23	dx(t	dx(t	X
ejpam-3574	36	24	)	)	PUNCT
ejpam-3574	36	25	dt	dt	NOUN
ejpam-3574	36	26	=	=	SYM
ejpam-3574	36	27	h(t)x(t	h(t)x(t	PROPN
ejpam-3574	36	28	)	)	PUNCT
ejpam-3574	36	29	,	,	PUNCT
ejpam-3574	36	30	t	t	PROPN
ejpam-3574	36	31	∈	∈	PROPN
ejpam-3574	36	32	r	r	NOUN
ejpam-3574	36	33	(	(	PUNCT
ejpam-3574	36	34	1	1	NUM
ejpam-3574	36	35	)	)	PUNCT
ejpam-3574	36	36	where	where	SCONJ
ejpam-3574	36	37	h(t	h(t	PROPN
ejpam-3574	36	38	)	)	PUNCT
ejpam-3574	36	39	∈	∈	PROPN
ejpam-3574	36	40	r2n×2n	r2n×2n	NOUN
ejpam-3574	36	41	is	be	AUX
ejpam-3574	36	42	symmetric	symmetric	ADJ
ejpam-3574	36	43	and	and	CCONJ
ejpam-3574	36	44	p	p	NOUN
ejpam-3574	36	45	-periodic	-periodic	ADJ
ejpam-3574	36	46	(	(	PUNCT
ejpam-3574	36	47	i.e.	i.e.	X
ejpam-3574	36	48	h(t	h(t	PROPN
ejpam-3574	36	49	+	+	CCONJ
ejpam-3574	36	50	p	p	NOUN
ejpam-3574	36	51	)	)	PUNCT
ejpam-3574	36	52	=	=	SYM
ejpam-3574	36	53	h(t	h(t	PROPN
ejpam-3574	36	54	)	)	PUNCT
ejpam-3574	36	55	=	=	PRON
ejpam-3574	36	56	(	(	PUNCT
ejpam-3574	36	57	h(t))t	h(t))t	PROPN
ejpam-3574	36	58	)	)	PUNCT
ejpam-3574	36	59	.	.	PUNCT
ejpam-3574	37	1	we	we	PRON
ejpam-3574	37	2	know	know	VERB
ejpam-3574	37	3	that	that	SCONJ
ejpam-3574	37	4	the	the	DET
ejpam-3574	37	5	fundamental	fundamental	ADJ
ejpam-3574	37	6	solution	solution	NOUN
ejpam-3574	37	7	x(t	x(t	PROPN
ejpam-3574	37	8	)	)	PUNCT
ejpam-3574	37	9	of	of	ADP
ejpam-3574	37	10	(	(	PUNCT
ejpam-3574	37	11	1	1	NUM
ejpam-3574	37	12	)	)	PUNCT
ejpam-3574	37	13	,	,	PUNCT
ejpam-3574	37	14	in	in	ADP
ejpam-3574	37	15	other	other	ADJ
ejpam-3574	37	16	words	word	NOUN
ejpam-3574	37	17	,	,	PUNCT
ejpam-3574	37	18	the	the	DET
ejpam-3574	37	19	solution	solution	NOUN
ejpam-3574	37	20	of	of	ADP
ejpam-3574	37	21	the	the	DET
ejpam-3574	37	22	system	system	NOUN
ejpam-3574	37	23			PROPN
ejpam-3574	37	24	j	j	PROPN
ejpam-3574	37	25	dx(t	dx(t	X
ejpam-3574	37	26	)	)	PUNCT
ejpam-3574	37	27	dt	dt	NOUN
ejpam-3574	37	28	=	=	SYM
ejpam-3574	37	29	h(t)x(t	h(t)x(t	PROPN
ejpam-3574	37	30	)	)	PUNCT
ejpam-3574	37	31	,	,	PUNCT
ejpam-3574	37	32	t	t	PROPN
ejpam-3574	37	33	∈	∈	PROPN
ejpam-3574	37	34	r	r	PROPN
ejpam-3574	37	35	x(0	x(0	PROPN
ejpam-3574	37	36	)	)	PUNCT
ejpam-3574	38	1	=	=	NOUN
ejpam-3574	39	1	i	i	PRON
ejpam-3574	39	2	,	,	PUNCT
ejpam-3574	39	3	(	(	PUNCT
ejpam-3574	39	4	2	2	X
ejpam-3574	39	5	)	)	PUNCT
ejpam-3574	39	6	satisfies	satisfy	VERB
ejpam-3574	39	7	the	the	DET
ejpam-3574	39	8	relationship	relationship	NOUN
ejpam-3574	39	9	x(t	x(t	PROPN
ejpam-3574	40	1	+	+	CCONJ
ejpam-3574	40	2	np	np	INTJ
ejpam-3574	40	3	)	)	PUNCT
ejpam-3574	40	4	=	=	PUNCT
ejpam-3574	41	1	x(t)xn(p	x(t)xn(p	X
ejpam-3574	41	2	)	)	PUNCT
ejpam-3574	41	3	(	(	PUNCT
ejpam-3574	41	4	6=	6=	NUM
ejpam-3574	41	5	xn(p	xn(p	ADJ
ejpam-3574	41	6	)	)	PUNCT
ejpam-3574	41	7	x(t	x(t	PROPN
ejpam-3574	41	8	)	)	PUNCT
ejpam-3574	41	9	)	)	PUNCT
ejpam-3574	41	10	,	,	PUNCT
ejpam-3574	41	11	∀	∀	X
ejpam-3574	41	12	(	(	PUNCT
ejpam-3574	41	13	t	t	PROPN
ejpam-3574	41	14	,	,	PUNCT
ejpam-3574	41	15	n	n	CCONJ
ejpam-3574	41	16	)	)	PUNCT
ejpam-3574	41	17	∈	∈	PROPN
ejpam-3574	41	18	r	r	NOUN
ejpam-3574	41	19	×	×	NOUN
ejpam-3574	41	20	n	n	NOUN
ejpam-3574	41	21	and	and	CCONJ
ejpam-3574	41	22	is	be	AUX
ejpam-3574	41	23	j	j	NOUN
ejpam-3574	41	24	-	-	PUNCT
ejpam-3574	41	25	symplectic	symplectic	ADJ
ejpam-3574	41	26	[	[	X
ejpam-3574	41	27	18	18	NUM
ejpam-3574	41	28	,	,	PUNCT
ejpam-3574	41	29	vol	vol	NOUN
ejpam-3574	41	30	.	.	NOUN
ejpam-3574	41	31	1	1	NUM
ejpam-3574	41	32	,	,	PUNCT
ejpam-3574	41	33	chap	chap	NOUN
ejpam-3574	41	34	.	.	PUNCT
ejpam-3574	42	1	2	2	NUM
ejpam-3574	42	2	]	]	PUNCT
ejpam-3574	42	3	.	.	PUNCT
ejpam-3574	43	1	regarding	regard	VERB
ejpam-3574	43	2	stability	stability	NOUN
ejpam-3574	43	3	(	(	PUNCT
ejpam-3574	43	4	strong	strong	ADJ
ejpam-3574	43	5	stability	stability	NOUN
ejpam-3574	43	6	)	)	PUNCT
ejpam-3574	43	7	,	,	PUNCT
ejpam-3574	43	8	we	we	PRON
ejpam-3574	43	9	have	have	VERB
ejpam-3574	43	10	the	the	DET
ejpam-3574	43	11	following	follow	VERB
ejpam-3574	43	12	definitions	definition	NOUN
ejpam-3574	43	13	[	[	X
ejpam-3574	43	14	6	6	NUM
ejpam-3574	43	15	,	,	PUNCT
ejpam-3574	43	16	18	18	NUM
ejpam-3574	43	17	]	]	PUNCT
ejpam-3574	43	18	definition	definition	NOUN
ejpam-3574	43	19	2	2	NUM
ejpam-3574	43	20	.	.	PUNCT
ejpam-3574	44	1	(	(	PUNCT
ejpam-3574	44	2	i	i	NOUN
ejpam-3574	44	3	)	)	PUNCT
ejpam-3574	44	4	system	system	NOUN
ejpam-3574	44	5	(	(	PUNCT
ejpam-3574	44	6	1	1	X
ejpam-3574	44	7	)	)	PUNCT
ejpam-3574	44	8	is	be	AUX
ejpam-3574	44	9	stable	stable	ADJ
ejpam-3574	44	10	if	if	SCONJ
ejpam-3574	44	11	each	each	PRON
ejpam-3574	44	12	of	of	ADP
ejpam-3574	44	13	its	its	PRON
ejpam-3574	44	14	solutions	solution	NOUN
ejpam-3574	44	15	x(t	x(t	PROPN
ejpam-3574	44	16	)	)	PUNCT
ejpam-3574	44	17	remains	remain	VERB
ejpam-3574	44	18	bounded	bounded	ADJ
ejpam-3574	44	19	for	for	ADP
ejpam-3574	44	20	t	t	PROPN
ejpam-3574	44	21	∈	∈	PROPN
ejpam-3574	44	22	r.	r.	PROPN
ejpam-3574	44	23	(	(	PUNCT
ejpam-3574	44	24	ii	ii	NOUN
ejpam-3574	44	25	)	)	PUNCT
ejpam-3574	44	26	system	system	NOUN
ejpam-3574	44	27	(	(	PUNCT
ejpam-3574	44	28	1	1	X
ejpam-3574	44	29	)	)	PUNCT
ejpam-3574	44	30	is	be	AUX
ejpam-3574	44	31	strongly	strongly	ADV
ejpam-3574	44	32	stable	stable	ADJ
ejpam-3574	44	33	if	if	SCONJ
ejpam-3574	44	34	any	any	DET
ejpam-3574	44	35	hamiltonian	hamiltonian	ADJ
ejpam-3574	44	36	system	system	NOUN
ejpam-3574	44	37	with	with	ADP
ejpam-3574	44	38	p	p	NOUN
ejpam-3574	44	39	-periodic	-periodic	ADJ
ejpam-3574	44	40	coefficients	coefficient	NOUN
ejpam-3574	44	41	to	to	ADP
ejpam-3574	44	42	sufficiently	sufficiently	ADV
ejpam-3574	44	43	close	close	ADJ
ejpam-3574	44	44	to	to	ADP
ejpam-3574	44	45	(	(	PUNCT
ejpam-3574	44	46	1	1	NUM
ejpam-3574	44	47	)	)	PUNCT
ejpam-3574	44	48	,	,	PUNCT
ejpam-3574	44	49	is	be	AUX
ejpam-3574	44	50	stable	stable	ADJ
ejpam-3574	44	51	.	.	PUNCT
ejpam-3574	45	1	m.	m.	NOUN
ejpam-3574	45	2	dosso	dosso	PROPN
ejpam-3574	45	3	,	,	PUNCT
ejpam-3574	45	4	t.	t.	PROPN
ejpam-3574	45	5	g.	g.	PROPN
ejpam-3574	45	6	y.	y.	PROPN
ejpam-3574	45	7	arouna	arouna	PROPN
ejpam-3574	45	8	,	,	PUNCT
ejpam-3574	45	9	j.-c	j.-c	PROPN
ejpam-3574	45	10	.	.	PUNCT
ejpam-3574	46	1	koua	koua	PROPN
ejpam-3574	46	2	brou	brou	PROPN
ejpam-3574	46	3	/	/	SYM
ejpam-3574	46	4	eur	eur	PROPN
ejpam-3574	46	5	.	.	PUNCT
ejpam-3574	47	1	j.	j.	PROPN
ejpam-3574	47	2	pure	pure	PROPN
ejpam-3574	47	3	appl	appl	PROPN
ejpam-3574	47	4	.	.	PROPN
ejpam-3574	47	5	math	math	PROPN
ejpam-3574	47	6	,	,	PUNCT
ejpam-3574	47	7	12	12	NUM
ejpam-3574	47	8	(	(	PUNCT
ejpam-3574	47	9	4	4	NUM
ejpam-3574	47	10	)	)	PUNCT
ejpam-3574	47	11	(	(	PUNCT
ejpam-3574	47	12	2019	2019	NUM
ejpam-3574	47	13	)	)	PUNCT
ejpam-3574	47	14	,	,	PUNCT
ejpam-3574	47	15	1744	1744	NUM
ejpam-3574	47	16	-	-	SYM
ejpam-3574	47	17	1770	1770	NUM
ejpam-3574	47	18	1746	1746	NUM
ejpam-3574	47	19	specifically	specifically	ADV
ejpam-3574	47	20	,	,	PUNCT
ejpam-3574	47	21	system	system	NOUN
ejpam-3574	47	22	(	(	PUNCT
ejpam-3574	47	23	1	1	NUM
ejpam-3574	47	24	)	)	PUNCT
ejpam-3574	47	25	(	(	PUNCT
ejpam-3574	47	26	or	or	CCONJ
ejpam-3574	47	27	system	system	NOUN
ejpam-3574	47	28	(	(	PUNCT
ejpam-3574	47	29	2	2	NUM
ejpam-3574	47	30	)	)	PUNCT
ejpam-3574	47	31	)	)	PUNCT
ejpam-3574	47	32	is	be	AUX
ejpam-3574	47	33	strongly	strongly	ADV
ejpam-3574	47	34	stable	stable	ADJ
ejpam-3574	47	35	if	if	SCONJ
ejpam-3574	47	36	there	there	PRON
ejpam-3574	47	37	exists	exist	VERB
ejpam-3574	47	38	ε	ε	PROPN
ejpam-3574	47	39	>	>	X
ejpam-3574	47	40	0	0	NUM
ejpam-3574	48	1	such	such	ADJ
ejpam-3574	48	2	that	that	SCONJ
ejpam-3574	48	3	any	any	DET
ejpam-3574	48	4	hamiltonian	hamiltonian	ADJ
ejpam-3574	48	5	system	system	NOUN
ejpam-3574	48	6	with	with	ADP
ejpam-3574	48	7	p	p	NOUN
ejpam-3574	48	8	-periodic	-periodic	ADJ
ejpam-3574	48	9	coefficients	coefficient	NOUN
ejpam-3574	48	10	of	of	ADP
ejpam-3574	48	11	the	the	DET
ejpam-3574	48	12	form	form	NOUN
ejpam-3574	48	13	j	j	PROPN
ejpam-3574	48	14	dx(t	dx(t	X
ejpam-3574	48	15	)	)	PUNCT
ejpam-3574	48	16	dt	dt	NOUN
ejpam-3574	48	17	=	=	SYM
ejpam-3574	48	18	h̃(t)x(t	h̃(t)x(t	NOUN
ejpam-3574	48	19	)	)	PUNCT
ejpam-3574	48	20	and	and	CCONJ
ejpam-3574	48	21	satisfying	satisfy	VERB
ejpam-3574	48	22	‖h	‖h	PUNCT
ejpam-3574	49	1	−	−	PROPN
ejpam-3574	49	2	h̃‖	h̃‖	NOUN
ejpam-3574	50	1	=	=	SYM
ejpam-3574	50	2	∫	∫	PROPN
ejpam-3574	50	3	t	t	PROPN
ejpam-3574	50	4	0	0	NUM
ejpam-3574	50	5	‖h(t)−	‖h(t)−	PROPN
ejpam-3574	50	6	h̃(t)‖dt	h̃(t)‖dt	PROPN
ejpam-3574	50	7	<	<	X
ejpam-3574	50	8	ε	ε	PROPN
ejpam-3574	50	9	,	,	PUNCT
ejpam-3574	50	10	is	be	AUX
ejpam-3574	50	11	stable	stable	ADJ
ejpam-3574	50	12	.	.	PUNCT
ejpam-3574	51	1	we	we	PRON
ejpam-3574	51	2	also	also	ADV
ejpam-3574	51	3	have	have	VERB
ejpam-3574	51	4	the	the	DET
ejpam-3574	51	5	following	follow	VERB
ejpam-3574	51	6	theorem	theorem	NOUN
ejpam-3574	51	7	[	[	X
ejpam-3574	51	8	18	18	NUM
ejpam-3574	51	9	,	,	PUNCT
ejpam-3574	51	10	p.	p.	NOUN
ejpam-3574	51	11	196	196	NUM
ejpam-3574	51	12	]	]	PUNCT
ejpam-3574	51	13	theorem	theorem	VERB
ejpam-3574	51	14	2	2	NUM
ejpam-3574	51	15	.	.	PUNCT
ejpam-3574	51	16	system	system	NOUN
ejpam-3574	51	17	1	1	NUM
ejpam-3574	51	18	is	be	AUX
ejpam-3574	51	19	strongly	strongly	ADV
ejpam-3574	51	20	stable	stable	ADJ
ejpam-3574	51	21	if	if	SCONJ
ejpam-3574	51	22	and	and	CCONJ
ejpam-3574	51	23	only	only	ADV
ejpam-3574	51	24	if	if	SCONJ
ejpam-3574	51	25	the	the	DET
ejpam-3574	51	26	j	j	PROPN
ejpam-3574	51	27	-	-	PUNCT
ejpam-3574	51	28	symplectic	symplectic	ADJ
ejpam-3574	51	29	matrix	matrix	NOUN
ejpam-3574	51	30	x(p	x(p	PROPN
ejpam-3574	51	31	)	)	PUNCT
ejpam-3574	51	32	is	be	AUX
ejpam-3574	51	33	strongly	strongly	ADV
ejpam-3574	51	34	stable	stable	ADJ
ejpam-3574	51	35	.	.	PUNCT
ejpam-3574	52	1	since	since	SCONJ
ejpam-3574	52	2	the	the	DET
ejpam-3574	52	3	strong	strong	ADJ
ejpam-3574	52	4	stability	stability	NOUN
ejpam-3574	52	5	analysis	analysis	NOUN
ejpam-3574	52	6	of	of	ADP
ejpam-3574	52	7	the	the	DET
ejpam-3574	52	8	hamiltonian	hamiltonian	ADJ
ejpam-3574	52	9	systems	system	NOUN
ejpam-3574	52	10	with	with	ADP
ejpam-3574	52	11	p	p	NOUN
ejpam-3574	52	12	-periodic	-periodic	ADJ
ejpam-3574	52	13	coefficients	coefficient	NOUN
ejpam-3574	52	14	is	be	AUX
ejpam-3574	52	15	related	relate	VERB
ejpam-3574	52	16	to	to	ADP
ejpam-3574	52	17	the	the	DET
ejpam-3574	52	18	study	study	NOUN
ejpam-3574	52	19	of	of	ADP
ejpam-3574	52	20	their	their	PRON
ejpam-3574	52	21	perturbation	perturbation	NOUN
ejpam-3574	52	22	,	,	PUNCT
ejpam-3574	52	23	we	we	PRON
ejpam-3574	52	24	will	will	AUX
ejpam-3574	52	25	dwell	dwell	VERB
ejpam-3574	52	26	on	on	ADP
ejpam-3574	52	27	a	a	DET
ejpam-3574	52	28	type	type	NOUN
ejpam-3574	52	29	of	of	ADP
ejpam-3574	52	30	the	the	DET
ejpam-3574	52	31	perturbation	perturbation	NOUN
ejpam-3574	52	32	which	which	PRON
ejpam-3574	52	33	we	we	PRON
ejpam-3574	52	34	call	call	VERB
ejpam-3574	52	35	rank	rank	NOUN
ejpam-3574	52	36	-	-	PUNCT
ejpam-3574	52	37	k	k	NOUN
ejpam-3574	52	38	perturbation	perturbation	NOUN
ejpam-3574	52	39	.	.	PUNCT
ejpam-3574	53	1	thus	thus	ADV
ejpam-3574	53	2	,	,	PUNCT
ejpam-3574	53	3	we	we	PRON
ejpam-3574	53	4	present	present	VERB
ejpam-3574	53	5	in	in	ADP
ejpam-3574	53	6	section	section	NOUN
ejpam-3574	53	7	2	2	NUM
ejpam-3574	53	8	,	,	PUNCT
ejpam-3574	53	9	preliminaries	preliminary	NOUN
ejpam-3574	53	10	necessary	necessary	ADJ
ejpam-3574	53	11	to	to	ADP
ejpam-3574	53	12	the	the	DET
ejpam-3574	53	13	study	study	NOUN
ejpam-3574	53	14	of	of	ADP
ejpam-3574	53	15	the	the	DET
ejpam-3574	53	16	isotropic	isotropic	ADJ
ejpam-3574	53	17	subspaces	subspace	NOUN
ejpam-3574	53	18	,	,	PUNCT
ejpam-3574	53	19	on	on	ADP
ejpam-3574	53	20	the	the	DET
ejpam-3574	53	21	rank	rank	NOUN
ejpam-3574	53	22	-	-	PUNCT
ejpam-3574	53	23	k	k	NOUN
ejpam-3574	53	24	perturbation	perturbation	NOUN
ejpam-3574	53	25	of	of	ADP
ejpam-3574	53	26	a	a	DET
ejpam-3574	53	27	symplectic	symplectic	ADJ
ejpam-3574	53	28	matrix	matrix	NOUN
ejpam-3574	53	29	and	and	CCONJ
ejpam-3574	53	30	rank	rank	NOUN
ejpam-3574	53	31	-	-	PUNCT
ejpam-3574	53	32	k	k	NOUN
ejpam-3574	53	33	perturbation	perturbation	NOUN
ejpam-3574	53	34	of	of	ADP
ejpam-3574	53	35	a	a	DET
ejpam-3574	53	36	hamiltonian	hamiltonian	ADJ
ejpam-3574	53	37	system	system	NOUN
ejpam-3574	53	38	with	with	ADP
ejpam-3574	53	39	p	p	NOUN
ejpam-3574	53	40	-	-	PUNCT
ejpam-3574	53	41	periodic	periodic	ADJ
ejpam-3574	53	42	coefficients	coefficient	NOUN
ejpam-3574	53	43	.	.	PUNCT
ejpam-3574	54	1	in	in	ADP
ejpam-3574	54	2	sections	section	NOUN
ejpam-3574	54	3	3	3	NUM
ejpam-3574	54	4	and	and	CCONJ
ejpam-3574	54	5	4	4	NUM
ejpam-3574	54	6	,	,	PUNCT
ejpam-3574	54	7	we	we	PRON
ejpam-3574	54	8	give	give	VERB
ejpam-3574	54	9	respectively	respectively	ADV
ejpam-3574	54	10	the	the	DET
ejpam-3574	54	11	jordan	jordan	PROPN
ejpam-3574	54	12	canonical	canonical	ADJ
ejpam-3574	54	13	forms	form	NOUN
ejpam-3574	54	14	of	of	ADP
ejpam-3574	54	15	a	a	DET
ejpam-3574	54	16	rank	rank	NOUN
ejpam-3574	54	17	-	-	PUNCT
ejpam-3574	54	18	k	k	NOUN
ejpam-3574	54	19	perturbation	perturbation	NOUN
ejpam-3574	54	20	of	of	ADP
ejpam-3574	54	21	a	a	DET
ejpam-3574	54	22	symplectic	symplectic	ADJ
ejpam-3574	54	23	matrix	matrix	NOUN
ejpam-3574	54	24	and	and	CCONJ
ejpam-3574	54	25	of	of	ADP
ejpam-3574	54	26	a	a	DET
ejpam-3574	54	27	rang	ring	VERB
ejpam-3574	54	28	-	-	PUNCT
ejpam-3574	54	29	k	k	NOUN
ejpam-3574	54	30	perturbation	perturbation	NOUN
ejpam-3574	54	31	of	of	ADP
ejpam-3574	54	32	the	the	DET
ejpam-3574	54	33	fundamental	fundamental	ADJ
ejpam-3574	54	34	solution	solution	NOUN
ejpam-3574	54	35	of	of	ADP
ejpam-3574	54	36	(	(	PUNCT
ejpam-3574	54	37	1	1	NUM
ejpam-3574	54	38	)	)	PUNCT
ejpam-3574	54	39	.	.	PUNCT
ejpam-3574	55	1	finally	finally	ADV
ejpam-3574	55	2	in	in	ADP
ejpam-3574	55	3	section	section	NOUN
ejpam-3574	55	4	5	5	NUM
ejpam-3574	55	5	,	,	PUNCT
ejpam-3574	55	6	we	we	PRON
ejpam-3574	55	7	present	present	VERB
ejpam-3574	55	8	some	some	DET
ejpam-3574	55	9	applications	application	NOUN
ejpam-3574	55	10	for	for	ADP
ejpam-3574	55	11	some	some	DET
ejpam-3574	55	12	systems	system	NOUN
ejpam-3574	55	13	of	of	ADP
ejpam-3574	55	14	mathieu	mathieu	PROPN
ejpam-3574	55	15	:	:	PUNCT
ejpam-3574	55	16	namely	namely	ADV
ejpam-3574	55	17	systems	system	NOUN
ejpam-3574	55	18	that	that	PRON
ejpam-3574	55	19	describe	describe	VERB
ejpam-3574	55	20	the	the	DET
ejpam-3574	55	21	movement	movement	NOUN
ejpam-3574	55	22	of	of	ADP
ejpam-3574	55	23	a	a	DET
ejpam-3574	55	24	double	double	ADJ
ejpam-3574	55	25	pendulum	pendulum	NOUN
ejpam-3574	55	26	with	with	ADP
ejpam-3574	55	27	oscillating	oscillate	VERB
ejpam-3574	55	28	support	support	NOUN
ejpam-3574	55	29	and	and	CCONJ
ejpam-3574	55	30	those	those	PRON
ejpam-3574	55	31	that	that	PRON
ejpam-3574	55	32	describe	describe	VERB
ejpam-3574	55	33	the	the	DET
ejpam-3574	55	34	motion	motion	NOUN
ejpam-3574	55	35	of	of	ADP
ejpam-3574	55	36	an	an	DET
ejpam-3574	55	37	ion	ion	NOUN
ejpam-3574	55	38	through	through	ADP
ejpam-3574	55	39	a	a	DET
ejpam-3574	55	40	quadrupole	quadrupole	NOUN
ejpam-3574	55	41	analyzer	analyzer	NOUN
ejpam-3574	55	42	.	.	PUNCT
ejpam-3574	56	1	2	2	X
ejpam-3574	56	2	.	.	NUM
ejpam-3574	56	3	preliminaries	preliminary	NOUN
ejpam-3574	56	4	2.1	2.1	NUM
ejpam-3574	56	5	.	.	PUNCT
ejpam-3574	56	6	isotropic	isotropic	NOUN
ejpam-3574	56	7	subspaces	subspace	NOUN
ejpam-3574	56	8	definition	definition	NOUN
ejpam-3574	56	9	3	3	NUM
ejpam-3574	56	10	.	.	PUNCT
ejpam-3574	57	1	a	a	DET
ejpam-3574	57	2	subspace	subspace	NOUN
ejpam-3574	57	3	x	x	PUNCT
ejpam-3574	57	4	⊆	⊆	NUM
ejpam-3574	57	5	r2n	r2n	NOUN
ejpam-3574	57	6	is	be	AUX
ejpam-3574	57	7	called	call	VERB
ejpam-3574	57	8	isotropic	isotropic	NOUN
ejpam-3574	57	9	if	if	SCONJ
ejpam-3574	57	10	x	x	PROPN
ejpam-3574	57	11	⊥	⊥	PROPN
ejpam-3574	57	12	jx	jx	PROPN
ejpam-3574	57	13	.	.	PUNCT
ejpam-3574	58	1	a	a	DET
ejpam-3574	58	2	maximal	maximal	ADJ
ejpam-3574	58	3	isotropic	isotropic	NOUN
ejpam-3574	58	4	subspace	subspace	NOUN
ejpam-3574	58	5	is	be	AUX
ejpam-3574	58	6	called	call	VERB
ejpam-3574	58	7	lagrangian	lagrangian	ADJ
ejpam-3574	58	8	.	.	PUNCT
ejpam-3574	59	1	the	the	DET
ejpam-3574	59	2	maximum	maximum	ADJ
ejpam-3574	59	3	isotropic	isotropic	NOUN
ejpam-3574	59	4	subspaces	subspace	NOUN
ejpam-3574	59	5	containing	contain	VERB
ejpam-3574	59	6	x	x	SYM
ejpam-3574	59	7	are	be	AUX
ejpam-3574	59	8	of	of	ADP
ejpam-3574	59	9	dimension	dimension	NOUN
ejpam-3574	59	10	n	n	ADV
ejpam-3574	59	11	.	.	PUNCT
ejpam-3574	60	1	hence	hence	ADV
ejpam-3574	60	2	the	the	DET
ejpam-3574	60	3	following	follow	VERB
ejpam-3574	60	4	definition	definition	NOUN
ejpam-3574	60	5	(	(	PUNCT
ejpam-3574	60	6	see	see	VERB
ejpam-3574	60	7	[	[	X
ejpam-3574	60	8	9	9	NUM
ejpam-3574	60	9	]	]	SYM
ejpam-3574	60	10	)	)	PUNCT
ejpam-3574	60	11	definition	definition	NOUN
ejpam-3574	60	12	4	4	NUM
ejpam-3574	60	13	.	.	PUNCT
ejpam-3574	61	1	a	a	DET
ejpam-3574	61	2	subspace	subspace	NOUN
ejpam-3574	61	3	l	l	NOUN
ejpam-3574	61	4	of	of	ADP
ejpam-3574	61	5	rn	rn	PROPN
ejpam-3574	61	6	is	be	AUX
ejpam-3574	61	7	called	call	VERB
ejpam-3574	61	8	a	a	DET
ejpam-3574	61	9	lagrangian	lagrangian	ADJ
ejpam-3574	61	10	subspace	subspace	NOUN
ejpam-3574	61	11	if	if	SCONJ
ejpam-3574	61	12	it	it	PRON
ejpam-3574	61	13	has	have	VERB
ejpam-3574	61	14	the	the	DET
ejpam-3574	61	15	dimension	dimension	NOUN
ejpam-3574	61	16	n	n	NOUN
ejpam-3574	61	17	and	and	CCONJ
ejpam-3574	61	18	xtjy	xtjy	ADP
ejpam-3574	61	19	=	=	SYM
ejpam-3574	61	20	0	0	NUM
ejpam-3574	61	21	,	,	PUNCT
ejpam-3574	61	22	∀x	∀x	X
ejpam-3574	61	23	,	,	PUNCT
ejpam-3574	61	24	y	y	PROPN
ejpam-3574	61	25	∈	∈	PROPN
ejpam-3574	61	26	l.	l.	NOUN
ejpam-3574	61	27	in	in	ADP
ejpam-3574	61	28	other	other	ADJ
ejpam-3574	61	29	words	word	NOUN
ejpam-3574	61	30	,	,	PUNCT
ejpam-3574	61	31	we	we	PRON
ejpam-3574	61	32	say	say	VERB
ejpam-3574	61	33	that	that	SCONJ
ejpam-3574	61	34	a	a	DET
ejpam-3574	61	35	subspace	subspace	NOUN
ejpam-3574	61	36	l	l	NOUN
ejpam-3574	61	37	is	be	AUX
ejpam-3574	61	38	lagrangian	lagrangian	ADJ
ejpam-3574	61	39	if	if	SCONJ
ejpam-3574	61	40	and	and	CCONJ
ejpam-3574	61	41	only	only	ADV
ejpam-3574	61	42	if	if	SCONJ
ejpam-3574	61	43	every	every	DET
ejpam-3574	61	44	matrix	matrix	NOUN
ejpam-3574	61	45	l	l	NOUN
ejpam-3574	61	46	whose	whose	DET
ejpam-3574	61	47	columns	column	NOUN
ejpam-3574	61	48	span	span	NOUN
ejpam-3574	61	49	l	l	NOUN
ejpam-3574	61	50	satisfies	satisfie	NOUN
ejpam-3574	61	51	rankl	rankl	VERB
ejpam-3574	61	52	=	=	SYM
ejpam-3574	61	53	n	n	PROPN
ejpam-3574	61	54	and	and	CCONJ
ejpam-3574	61	55	ltjl	ltjl	NOUN
ejpam-3574	61	56	=	=	NOUN
ejpam-3574	61	57	0	0	X
ejpam-3574	61	58	.	.	PUNCT
ejpam-3574	62	1	we	we	PRON
ejpam-3574	62	2	list	list	VERB
ejpam-3574	62	3	a	a	DET
ejpam-3574	62	4	set	set	NOUN
ejpam-3574	62	5	of	of	ADP
ejpam-3574	62	6	properties	property	NOUN
ejpam-3574	62	7	on	on	ADP
ejpam-3574	62	8	the	the	DET
ejpam-3574	62	9	isotropic	isotropic	ADJ
ejpam-3574	62	10	subspaces	subspace	NOUN
ejpam-3574	62	11	in	in	ADP
ejpam-3574	62	12	the	the	DET
ejpam-3574	62	13	following	follow	VERB
ejpam-3574	62	14	proposition	proposition	NOUN
ejpam-3574	62	15	proposition	proposition	NOUN
ejpam-3574	62	16	1	1	NUM
ejpam-3574	62	17	.	.	PUNCT
ejpam-3574	63	1	(	(	PUNCT
ejpam-3574	63	2	i	i	NOUN
ejpam-3574	63	3	)	)	PUNCT
ejpam-3574	63	4	let	let	VERB
ejpam-3574	63	5	x	x	PRON
ejpam-3574	63	6	be	be	AUX
ejpam-3574	63	7	an	an	DET
ejpam-3574	63	8	isotropic	isotropic	ADJ
ejpam-3574	63	9	subspace	subspace	NOUN
ejpam-3574	63	10	.	.	PUNCT
ejpam-3574	64	1	then	then	ADV
ejpam-3574	64	2	the	the	DET
ejpam-3574	64	3	dimension	dimension	NOUN
ejpam-3574	64	4	of	of	ADP
ejpam-3574	64	5	x	x	PUNCT
ejpam-3574	64	6	is	be	AUX
ejpam-3574	64	7	less	less	ADJ
ejpam-3574	64	8	than	than	ADP
ejpam-3574	64	9	or	or	CCONJ
ejpam-3574	64	10	equal	equal	ADJ
ejpam-3574	64	11	to	to	ADP
ejpam-3574	64	12	n	n	PRON
ejpam-3574	64	13	.	.	PUNCT
ejpam-3574	65	1	(	(	PUNCT
ejpam-3574	65	2	ii	ii	NOUN
ejpam-3574	65	3	)	)	PUNCT
ejpam-3574	65	4	every	every	DET
ejpam-3574	65	5	isotropic	isotropic	NOUN
ejpam-3574	65	6	subspace	subspace	NOUN
ejpam-3574	65	7	is	be	AUX
ejpam-3574	65	8	contained	contain	VERB
ejpam-3574	65	9	in	in	ADP
ejpam-3574	65	10	a	a	DET
ejpam-3574	65	11	lagrangian	lagrangian	ADJ
ejpam-3574	65	12	subspaces	subspace	NOUN
ejpam-3574	65	13	.	.	PUNCT
ejpam-3574	66	1	(	(	PUNCT
ejpam-3574	66	2	iii	iii	X
ejpam-3574	66	3	)	)	PUNCT
ejpam-3574	66	4	let	let	VERB
ejpam-3574	66	5	s	s	PRON
ejpam-3574	66	6	=	=	PUNCT
ejpam-3574	67	1	[	[	X
ejpam-3574	67	2	s1	s1	PROPN
ejpam-3574	67	3	s2	s2	PROPN
ejpam-3574	67	4	]	]	PUNCT
ejpam-3574	67	5	∈	∈	PROPN
ejpam-3574	67	6	r2n×2n	r2n×2n	NOUN
ejpam-3574	67	7	be	be	VERB
ejpam-3574	67	8	a	a	DET
ejpam-3574	67	9	symplectic	symplectic	ADJ
ejpam-3574	67	10	matrix	matrix	NOUN
ejpam-3574	67	11	with	with	ADP
ejpam-3574	67	12	si	si	PROPN
ejpam-3574	67	13	∈	∈	PROPN
ejpam-3574	67	14	r2n×n	r2n×n	PROPN
ejpam-3574	67	15	,	,	PUNCT
ejpam-3574	67	16	i	i	PRON
ejpam-3574	67	17	=	=	NOUN
ejpam-3574	67	18	1	1	NUM
ejpam-3574	67	19	,	,	PUNCT
ejpam-3574	67	20	2	2	NUM
ejpam-3574	67	21	;	;	PUNCT
ejpam-3574	67	22	then	then	ADV
ejpam-3574	67	23	the	the	DET
ejpam-3574	67	24	columns	column	NOUN
ejpam-3574	67	25	of	of	ADP
ejpam-3574	67	26	s1	s1	PROPN
ejpam-3574	67	27	and	and	CCONJ
ejpam-3574	67	28	s2	s2	PROPN
ejpam-3574	67	29	span	span	VERB
ejpam-3574	67	30	isotropic	isotropic	ADJ
ejpam-3574	67	31	subspaces	subspace	NOUN
ejpam-3574	67	32	.	.	PUNCT
ejpam-3574	68	1	m.	m.	NOUN
ejpam-3574	68	2	dosso	dosso	PROPN
ejpam-3574	68	3	,	,	PUNCT
ejpam-3574	68	4	t.	t.	PROPN
ejpam-3574	68	5	g.	g.	PROPN
ejpam-3574	68	6	y.	y.	PROPN
ejpam-3574	68	7	arouna	arouna	PROPN
ejpam-3574	68	8	,	,	PUNCT
ejpam-3574	68	9	j.-c	j.-c	PROPN
ejpam-3574	68	10	.	.	PUNCT
ejpam-3574	69	1	koua	koua	PROPN
ejpam-3574	69	2	brou	brou	PROPN
ejpam-3574	69	3	/	/	SYM
ejpam-3574	69	4	eur	eur	PROPN
ejpam-3574	69	5	.	.	PUNCT
ejpam-3574	70	1	j.	j.	PROPN
ejpam-3574	70	2	pure	pure	PROPN
ejpam-3574	70	3	appl	appl	PROPN
ejpam-3574	70	4	.	.	PROPN
ejpam-3574	70	5	math	math	PROPN
ejpam-3574	70	6	,	,	PUNCT
ejpam-3574	70	7	12	12	NUM
ejpam-3574	70	8	(	(	PUNCT
ejpam-3574	70	9	4	4	NUM
ejpam-3574	70	10	)	)	PUNCT
ejpam-3574	70	11	(	(	PUNCT
ejpam-3574	70	12	2019	2019	NUM
ejpam-3574	70	13	)	)	PUNCT
ejpam-3574	70	14	,	,	PUNCT
ejpam-3574	70	15	1744	1744	NUM
ejpam-3574	70	16	-	-	SYM
ejpam-3574	70	17	1770	1770	NUM
ejpam-3574	70	18	1747	1747	NUM
ejpam-3574	70	19	recall	recall	NOUN
ejpam-3574	70	20	the	the	DET
ejpam-3574	70	21	two	two	NUM
ejpam-3574	70	22	lemmas	lemma	NOUN
ejpam-3574	70	23	below	below	ADV
ejpam-3574	70	24	(	(	PUNCT
ejpam-3574	70	25	see	see	VERB
ejpam-3574	70	26	[	[	X
ejpam-3574	70	27	13	13	NUM
ejpam-3574	70	28	]	]	SYM
ejpam-3574	70	29	)	)	PUNCT
ejpam-3574	70	30	lemma	lemma	PROPN
ejpam-3574	71	1	1	1	X
ejpam-3574	71	2	.	.	PUNCT
ejpam-3574	72	1	let	let	VERB
ejpam-3574	72	2	xs	xs	PRON
ejpam-3574	72	3	⊆	⊆	NUM
ejpam-3574	72	4	r2n	r2n	NOUN
ejpam-3574	72	5	be	be	AUX
ejpam-3574	72	6	a	a	DET
ejpam-3574	72	7	subspace	subspace	NOUN
ejpam-3574	72	8	that	that	PRON
ejpam-3574	72	9	is	be	AUX
ejpam-3574	72	10	invariant	invariant	ADJ
ejpam-3574	72	11	under	under	ADP
ejpam-3574	72	12	a	a	DET
ejpam-3574	72	13	hamiltonian	hamiltonian	ADJ
ejpam-3574	72	14	matrix	matrix	NOUN
ejpam-3574	72	15	s	s	PART
ejpam-3574	72	16	which	which	PRON
ejpam-3574	72	17	has	have	VERB
ejpam-3574	72	18	all	all	PRON
ejpam-3574	72	19	its	its	PRON
ejpam-3574	72	20	eigenvalues	eigenvalue	NOUN
ejpam-3574	72	21	associated	associate	VERB
ejpam-3574	72	22	with	with	ADP
ejpam-3574	72	23	xs	xs	PROPN
ejpam-3574	72	24	having	have	VERB
ejpam-3574	72	25	their	their	PRON
ejpam-3574	72	26	real	real	ADJ
ejpam-3574	72	27	part	part	NOUN
ejpam-3574	72	28	negative	negative	ADJ
ejpam-3574	72	29	.	.	PUNCT
ejpam-3574	73	1	then	then	ADV
ejpam-3574	73	2	xs	xs	PROPN
ejpam-3574	73	3	is	be	AUX
ejpam-3574	73	4	isotropic	isotropic	ADJ
ejpam-3574	73	5	.	.	PUNCT
ejpam-3574	74	1	lemma	lemma	PROPN
ejpam-3574	74	2	2	2	X
ejpam-3574	74	3	.	.	PUNCT
ejpam-3574	75	1	let	let	VERB
ejpam-3574	75	2	s	s	PRON
ejpam-3574	75	3	∈	∈	NOUN
ejpam-3574	75	4	r2n×2n	r2n×2n	NOUN
ejpam-3574	75	5	be	be	AUX
ejpam-3574	75	6	a	a	DET
ejpam-3574	75	7	skew	skew	ADJ
ejpam-3574	75	8	-	-	PUNCT
ejpam-3574	75	9	hamiltonian	hamiltonian	ADJ
ejpam-3574	75	10	matrix	matrix	NOUN
ejpam-3574	75	11	and	and	CCONJ
ejpam-3574	75	12	x	x	PUNCT
ejpam-3574	75	13	∈	∈	PROPN
ejpam-3574	75	14	r2n×k(k	r2n×k(k	NOUN
ejpam-3574	75	15	≤	≤	NOUN
ejpam-3574	75	16	n	n	CCONJ
ejpam-3574	75	17	)	)	PUNCT
ejpam-3574	75	18	with	with	ADP
ejpam-3574	75	19	orthogonal	orthogonal	ADJ
ejpam-3574	75	20	columns	column	NOUN
ejpam-3574	75	21	.	.	PUNCT
ejpam-3574	76	1	then	then	ADV
ejpam-3574	76	2	the	the	DET
ejpam-3574	76	3	columns	column	NOUN
ejpam-3574	76	4	of	of	ADP
ejpam-3574	76	5	x	x	PUNCT
ejpam-3574	76	6	span	span	VERB
ejpam-3574	76	7	an	an	DET
ejpam-3574	76	8	isotropic	isotropic	ADJ
ejpam-3574	76	9	invariant	invariant	ADJ
ejpam-3574	76	10	subspace	subspace	NOUN
ejpam-3574	76	11	of	of	ADP
ejpam-3574	76	12	s	s	PRON
ejpam-3574	76	13	if	if	SCONJ
ejpam-3574	77	1	and	and	CCONJ
ejpam-3574	77	2	only	only	ADV
ejpam-3574	77	3	if	if	SCONJ
ejpam-3574	77	4	there	there	PRON
ejpam-3574	77	5	exists	exist	VERB
ejpam-3574	77	6	an	an	DET
ejpam-3574	77	7	orthogonal	orthogonal	ADJ
ejpam-3574	77	8	symplectic	symplectic	ADJ
ejpam-3574	77	9	matrix	matrix	NOUN
ejpam-3574	77	10	u	u	NOUN
ejpam-3574	77	11	=	=	PUNCT
ejpam-3574	78	1	[	[	X
ejpam-3574	78	2	x	x	X
ejpam-3574	78	3	,	,	PUNCT
ejpam-3574	78	4	z	z	PROPN
ejpam-3574	78	5	,	,	PUNCT
ejpam-3574	78	6	jtx	jtx	PROPN
ejpam-3574	78	7	,	,	PUNCT
ejpam-3574	78	8	jtz	jtz	NOUN
ejpam-3574	78	9	]	]	PUNCT
ejpam-3574	78	10	with	with	ADP
ejpam-3574	78	11	some	some	DET
ejpam-3574	78	12	z	z	NOUN
ejpam-3574	78	13	∈	∈	PROPN
ejpam-3574	78	14	r2n×(n−k	r2n×(n−k	PROPN
ejpam-3574	78	15	)	)	PUNCT
ejpam-3574	78	16	so	so	SCONJ
ejpam-3574	78	17	that	that	DET
ejpam-3574	78	18	utsu	utsu	NOUN
ejpam-3574	78	19	=	=	PROPN
ejpam-3574	78	20	k	k	PROPN
ejpam-3574	79	1	n	n	CCONJ
ejpam-3574	80	1	−	−	PROPN
ejpam-3574	80	2	k	k	PROPN
ejpam-3574	80	3	k	k	PROPN
ejpam-3574	80	4	n	n	CCONJ
ejpam-3574	80	5	−	−	PROPN
ejpam-3574	81	1	k	k	PROPN
ejpam-3574	82	1	k	k	PROPN
ejpam-3574	83	1	n	n	CCONJ
ejpam-3574	83	2	−	−	PROPN
ejpam-3574	84	1	k	k	PROPN
ejpam-3574	84	2	k	k	PROPN
ejpam-3574	84	3	n	n	CCONJ
ejpam-3574	85	1	−	−	PROPN
ejpam-3574	85	2	k	k	PROPN
ejpam-3574	85	3			NOUN
ejpam-3574	85	4	a11	a11	PROPN
ejpam-3574	85	5	a12	a12	PROPN
ejpam-3574	85	6	g11	g11	PROPN
ejpam-3574	85	7	g12	g12	PROPN
ejpam-3574	85	8	0	0	PROPN
ejpam-3574	85	9	a22	a22	PROPN
ejpam-3574	85	10	−gt12	−gt12	PROPN
ejpam-3574	85	11	g22	g22	NOUN
ejpam-3574	85	12	0	0	NUM
ejpam-3574	85	13	0	0	NUM
ejpam-3574	86	1	at11	at11	PROPN
ejpam-3574	86	2	0	0	NUM
ejpam-3574	86	3	0	0	PUNCT
ejpam-3574	86	4	h22	h22	PROPN
ejpam-3574	86	5	at12	at12	PROPN
ejpam-3574	86	6	at22	at22	PROPN
ejpam-3574	86	7			NOUN
ejpam-3574	86	8	on	on	ADP
ejpam-3574	86	9	the	the	DET
ejpam-3574	86	10	other	other	ADJ
ejpam-3574	86	11	hand	hand	NOUN
ejpam-3574	86	12	,	,	PUNCT
ejpam-3574	86	13	if	if	SCONJ
ejpam-3574	86	14	we	we	PRON
ejpam-3574	86	15	consider	consider	VERB
ejpam-3574	86	16	the	the	DET
ejpam-3574	86	17	krylov	krylov	NOUN
ejpam-3574	86	18	subspace	subspace	NOUN
ejpam-3574	86	19	defined	define	VERB
ejpam-3574	86	20	below	below	ADP
ejpam-3574	86	21	km	km	PROPN
ejpam-3574	86	22	≡	≡	PROPN
ejpam-3574	86	23	km(a	km(a	PROPN
ejpam-3574	86	24	,	,	PUNCT
ejpam-3574	86	25	v	v	NOUN
ejpam-3574	86	26	)	)	PUNCT
ejpam-3574	86	27	=	=	PRON
ejpam-3574	86	28	span	span	NOUN
ejpam-3574	86	29	{	{	PUNCT
ejpam-3574	86	30	v	v	NOUN
ejpam-3574	86	31	,	,	PUNCT
ejpam-3574	86	32	av	av	PRON
ejpam-3574	86	33	,	,	PUNCT
ejpam-3574	86	34	a2v	a2v	ADV
ejpam-3574	86	35	,	,	PUNCT
ejpam-3574	86	36	.	.	PUNCT
ejpam-3574	86	37	.	.	PUNCT
ejpam-3574	86	38	.	.	PUNCT
ejpam-3574	87	1	,	,	PUNCT
ejpam-3574	87	2	am−1v	am−1v	PROPN
ejpam-3574	87	3	}	}	PUNCT
ejpam-3574	87	4	,	,	PUNCT
ejpam-3574	87	5	where	where	SCONJ
ejpam-3574	87	6	a	a	DET
ejpam-3574	87	7	∈	∈	PROPN
ejpam-3574	87	8	rn×m	rn×m	NOUN
ejpam-3574	87	9	(	(	PUNCT
ejpam-3574	87	10	with	with	ADP
ejpam-3574	87	11	n	n	NOUN
ejpam-3574	87	12	>	>	SYM
ejpam-3574	87	13	1	1	NUM
ejpam-3574	87	14	)	)	PUNCT
ejpam-3574	87	15	and	and	CCONJ
ejpam-3574	87	16	v	v	ADP
ejpam-3574	87	17	∈	∈	PROPN
ejpam-3574	87	18	rm	rm	NOUN
ejpam-3574	87	19	.	.	PUNCT
ejpam-3574	88	1	then	then	ADV
ejpam-3574	88	2	we	we	PRON
ejpam-3574	88	3	have	have	VERB
ejpam-3574	88	4	the	the	DET
ejpam-3574	88	5	following	follow	VERB
ejpam-3574	88	6	proposition	proposition	NOUN
ejpam-3574	88	7	which	which	PRON
ejpam-3574	88	8	shows	show	VERB
ejpam-3574	88	9	that	that	SCONJ
ejpam-3574	88	10	we	we	PRON
ejpam-3574	88	11	can	can	AUX
ejpam-3574	88	12	construct	construct	VERB
ejpam-3574	88	13	isotropic	isotropic	ADJ
ejpam-3574	88	14	invariant	invariant	ADJ
ejpam-3574	88	15	subspaces	subspace	NOUN
ejpam-3574	88	16	from	from	ADP
ejpam-3574	88	17	krylov	krylov	NOUN
ejpam-3574	88	18	process	process	NOUN
ejpam-3574	88	19	(	(	PUNCT
ejpam-3574	88	20	see	see	VERB
ejpam-3574	88	21	[	[	X
ejpam-3574	88	22	17	17	NUM
ejpam-3574	88	23	,	,	PUNCT
ejpam-3574	88	24	p.	p.	NOUN
ejpam-3574	88	25	399	399	NUM
ejpam-3574	88	26	]	]	PUNCT
ejpam-3574	88	27	)	)	PUNCT
ejpam-3574	88	28	proposition	proposition	NOUN
ejpam-3574	88	29	2	2	NUM
ejpam-3574	88	30	.	.	PUNCT
ejpam-3574	89	1	let	let	VERB
ejpam-3574	89	2	s	s	PRON
ejpam-3574	89	3	∈	∈	NOUN
ejpam-3574	89	4	r2n×2n	r2n×2n	NOUN
ejpam-3574	89	5	be	be	AUX
ejpam-3574	89	6	a	a	DET
ejpam-3574	89	7	skew	skew	ADJ
ejpam-3574	89	8	-	-	PUNCT
ejpam-3574	89	9	hamiltonian	hamiltonian	ADJ
ejpam-3574	89	10	matrix	matrix	NOUN
ejpam-3574	89	11	and	and	CCONJ
ejpam-3574	89	12	u	u	PROPN
ejpam-3574	89	13	∈	∈	PROPN
ejpam-3574	89	14	r2n	r2n	NOUN
ejpam-3574	89	15	be	be	AUX
ejpam-3574	89	16	an	an	DET
ejpam-3574	89	17	arbitrary	arbitrary	ADJ
ejpam-3574	89	18	nonzero	nonzero	NOUN
ejpam-3574	89	19	vector	vector	NOUN
ejpam-3574	89	20	.	.	PUNCT
ejpam-3574	90	1	then	then	ADV
ejpam-3574	90	2	the	the	DET
ejpam-3574	90	3	krylov	krylov	PROPN
ejpam-3574	90	4	subspace	subspace	PROPN
ejpam-3574	90	5	kj(s	kj(s	PROPN
ejpam-3574	90	6	,	,	PUNCT
ejpam-3574	90	7	u	u	NOUN
ejpam-3574	90	8	)	)	PUNCT
ejpam-3574	90	9	is	be	AUX
ejpam-3574	90	10	isotropic	isotropic	NOUN
ejpam-3574	90	11	for	for	ADP
ejpam-3574	90	12	all	all	PRON
ejpam-3574	90	13	j.	j.	PROPN
ejpam-3574	90	14	2.2	2.2	NUM
ejpam-3574	90	15	.	.	PUNCT
ejpam-3574	91	1	rank	rank	NOUN
ejpam-3574	91	2	-	-	PUNCT
ejpam-3574	91	3	k	k	PROPN
ejpam-3574	91	4	perturbation	perturbation	NOUN
ejpam-3574	91	5	of	of	ADP
ejpam-3574	91	6	symplectic	symplectic	ADJ
ejpam-3574	91	7	matrices	matrix	NOUN
ejpam-3574	91	8	let	let	VERB
ejpam-3574	91	9	w	w	NOUN
ejpam-3574	91	10	∈	∈	NOUN
ejpam-3574	91	11	r2n×2n	r2n×2n	NOUN
ejpam-3574	91	12	and	and	CCONJ
ejpam-3574	91	13	l	l	NOUN
ejpam-3574	91	14	be	be	AUX
ejpam-3574	91	15	respectively	respectively	ADV
ejpam-3574	91	16	a	a	DET
ejpam-3574	91	17	symplectic	symplectic	ADJ
ejpam-3574	91	18	matrix	matrix	NOUN
ejpam-3574	91	19	and	and	CCONJ
ejpam-3574	91	20	a	a	DET
ejpam-3574	91	21	j	j	NOUN
ejpam-3574	91	22	-	-	PUNCT
ejpam-3574	91	23	lagrangian	lagrangian	ADJ
ejpam-3574	91	24	subspace	subspace	NOUN
ejpam-3574	91	25	.	.	PUNCT
ejpam-3574	92	1	consider	consider	VERB
ejpam-3574	92	2	k	k	PROPN
ejpam-3574	92	3	vectors	vector	NOUN
ejpam-3574	92	4	u1	u1	VERB
ejpam-3574	92	5	,	,	PUNCT
ejpam-3574	92	6	·	·	PUNCT
ejpam-3574	92	7	·	·	PUNCT
ejpam-3574	92	8	·	·	PUNCT
ejpam-3574	92	9	,	,	PUNCT
ejpam-3574	92	10	uk	uk	PROPN
ejpam-3574	92	11	of	of	ADP
ejpam-3574	92	12	l	l	PROPN
ejpam-3574	92	13	,	,	PUNCT
ejpam-3574	92	14	where	where	SCONJ
ejpam-3574	92	15	k	k	PROPN
ejpam-3574	92	16	≤	≤	PROPN
ejpam-3574	92	17	n	n	CCONJ
ejpam-3574	92	18	.	.	PUNCT
ejpam-3574	93	1	setting	set	VERB
ejpam-3574	93	2	u	u	NOUN
ejpam-3574	93	3	=	=	PUNCT
ejpam-3574	94	1	[	[	X
ejpam-3574	94	2	u1	u1	NOUN
ejpam-3574	94	3	;	;	PUNCT
ejpam-3574	94	4	.	.	PUNCT
ejpam-3574	94	5	.	.	PUNCT
ejpam-3574	94	6	.	.	PUNCT
ejpam-3574	95	1	;	;	PUNCT
ejpam-3574	95	2	uk	uk	PROPN
ejpam-3574	95	3	]	]	PUNCT
ejpam-3574	95	4	,	,	PUNCT
ejpam-3574	95	5	and	and	CCONJ
ejpam-3574	95	6	w̃	w̃	PROPN
ejpam-3574	95	7	=	=	SYM
ejpam-3574	95	8	(	(	PUNCT
ejpam-3574	95	9	i	i	PRON
ejpam-3574	95	10	+	+	CCONJ
ejpam-3574	95	11	uutj	uutj	ADJ
ejpam-3574	95	12	)	)	PUNCT
ejpam-3574	95	13	w	w	NOUN
ejpam-3574	95	14	,	,	PUNCT
ejpam-3574	95	15	we	we	PRON
ejpam-3574	95	16	have	have	VERB
ejpam-3574	95	17	the	the	DET
ejpam-3574	95	18	following	follow	VERB
ejpam-3574	95	19	proposition	proposition	NOUN
ejpam-3574	95	20	proposition	proposition	NOUN
ejpam-3574	95	21	3	3	NUM
ejpam-3574	95	22	.	.	PUNCT
ejpam-3574	96	1	the	the	DET
ejpam-3574	96	2	matrix	matrix	NOUN
ejpam-3574	96	3	w̃	w̃	PROPN
ejpam-3574	96	4	is	be	AUX
ejpam-3574	96	5	j	j	NOUN
ejpam-3574	96	6	-	-	PUNCT
ejpam-3574	96	7	symplectic	symplectic	ADJ
ejpam-3574	96	8	.	.	PUNCT
ejpam-3574	97	1	proof	proof	NOUN
ejpam-3574	97	2	.	.	PUNCT
ejpam-3574	98	1	for	for	ADP
ejpam-3574	98	2	the	the	DET
ejpam-3574	98	3	proof	proof	NOUN
ejpam-3574	98	4	,	,	PUNCT
ejpam-3574	98	5	see	see	VERB
ejpam-3574	98	6	[	[	X
ejpam-3574	98	7	2	2	NUM
ejpam-3574	98	8	]	]	PUNCT
ejpam-3574	98	9	.	.	PUNCT
ejpam-3574	99	1	definition	definition	NOUN
ejpam-3574	99	2	5	5	NUM
ejpam-3574	99	3	.	.	PUNCT
ejpam-3574	100	1	we	we	PRON
ejpam-3574	100	2	call	call	VERB
ejpam-3574	100	3	rank	rank	NOUN
ejpam-3574	100	4	-	-	PUNCT
ejpam-3574	100	5	k	k	NOUN
ejpam-3574	100	6	perturbation	perturbation	NOUN
ejpam-3574	100	7	of	of	ADP
ejpam-3574	100	8	w	w	PROPN
ejpam-3574	100	9	,	,	PUNCT
ejpam-3574	100	10	any	any	DET
ejpam-3574	100	11	matrix	matrix	NOUN
ejpam-3574	100	12	of	of	ADP
ejpam-3574	100	13	the	the	DET
ejpam-3574	100	14	form	form	NOUN
ejpam-3574	100	15	w̃	w̃	PROPN
ejpam-3574	100	16	=	=	PUNCT
ejpam-3574	100	17	(	(	PUNCT
ejpam-3574	100	18	i	i	NOUN
ejpam-3574	100	19	+	+	X
ejpam-3574	100	20	uutj)w	uutj)w	PROPN
ejpam-3574	100	21	,	,	PUNCT
ejpam-3574	100	22	(	(	PUNCT
ejpam-3574	100	23	3	3	X
ejpam-3574	100	24	)	)	PUNCT
ejpam-3574	100	25	where	where	SCONJ
ejpam-3574	100	26	u	u	NOUN
ejpam-3574	100	27	is	be	AUX
ejpam-3574	100	28	a	a	DET
ejpam-3574	100	29	matrix	matrix	NOUN
ejpam-3574	100	30	of	of	ADP
ejpam-3574	100	31	rank	rank	NOUN
ejpam-3574	100	32	k	k	PROPN
ejpam-3574	100	33	whose	whose	DET
ejpam-3574	100	34	columns	column	NOUN
ejpam-3574	100	35	belong	belong	VERB
ejpam-3574	100	36	to	to	ADP
ejpam-3574	100	37	a	a	DET
ejpam-3574	100	38	j	j	NOUN
ejpam-3574	100	39	-	-	ADJ
ejpam-3574	100	40	lagrangian	lagrangian	ADJ
ejpam-3574	100	41	subspace	subspace	NOUN
ejpam-3574	100	42	.	.	PUNCT
ejpam-3574	101	1	m.	m.	NOUN
ejpam-3574	101	2	dosso	dosso	PROPN
ejpam-3574	101	3	,	,	PUNCT
ejpam-3574	101	4	t.	t.	PROPN
ejpam-3574	101	5	g.	g.	PROPN
ejpam-3574	101	6	y.	y.	PROPN
ejpam-3574	101	7	arouna	arouna	PROPN
ejpam-3574	101	8	,	,	PUNCT
ejpam-3574	101	9	j.-c	j.-c	PROPN
ejpam-3574	101	10	.	.	PUNCT
ejpam-3574	102	1	koua	koua	PROPN
ejpam-3574	102	2	brou	brou	PROPN
ejpam-3574	102	3	/	/	SYM
ejpam-3574	102	4	eur	eur	PROPN
ejpam-3574	102	5	.	.	PUNCT
ejpam-3574	103	1	j.	j.	PROPN
ejpam-3574	103	2	pure	pure	PROPN
ejpam-3574	103	3	appl	appl	PROPN
ejpam-3574	103	4	.	.	PROPN
ejpam-3574	103	5	math	math	PROPN
ejpam-3574	103	6	,	,	PUNCT
ejpam-3574	103	7	12	12	NUM
ejpam-3574	103	8	(	(	PUNCT
ejpam-3574	103	9	4	4	NUM
ejpam-3574	103	10	)	)	PUNCT
ejpam-3574	103	11	(	(	PUNCT
ejpam-3574	103	12	2019	2019	NUM
ejpam-3574	103	13	)	)	PUNCT
ejpam-3574	103	14	,	,	PUNCT
ejpam-3574	103	15	1744	1744	NUM
ejpam-3574	103	16	-	-	SYM
ejpam-3574	103	17	1770	1770	NUM
ejpam-3574	103	18	1748	1748	NUM
ejpam-3574	103	19	the	the	DET
ejpam-3574	103	20	matrix	matrix	NOUN
ejpam-3574	103	21	w̃	w̃	PROPN
ejpam-3574	103	22	can	can	AUX
ejpam-3574	103	23	be	be	AUX
ejpam-3574	103	24	put	put	VERB
ejpam-3574	103	25	in	in	ADP
ejpam-3574	103	26	the	the	DET
ejpam-3574	103	27	form	form	NOUN
ejpam-3574	103	28	w̃	w̃	PROPN
ejpam-3574	103	29	=	=	PUNCT
ejpam-3574	103	30	(	(	PUNCT
ejpam-3574	103	31	i	i	PRON
ejpam-3574	103	32	+	+	CCONJ
ejpam-3574	103	33	k∑	k∑	ADJ
ejpam-3574	104	1	j=1	j=1	PROPN
ejpam-3574	104	2	uju	uju	PROPN
ejpam-3574	104	3	t	t	PROPN
ejpam-3574	104	4	j	j	PROPN
ejpam-3574	104	5	j)w	j)w	NOUN
ejpam-3574	104	6	.	.	PUNCT
ejpam-3574	105	1	more	more	ADV
ejpam-3574	105	2	specially	specially	ADV
ejpam-3574	105	3	,	,	PUNCT
ejpam-3574	105	4	this	this	PRON
ejpam-3574	105	5	shows	show	VERB
ejpam-3574	105	6	that	that	SCONJ
ejpam-3574	105	7	any	any	DET
ejpam-3574	105	8	rank	rank	NOUN
ejpam-3574	105	9	-	-	PUNCT
ejpam-3574	105	10	k	k	NOUN
ejpam-3574	105	11	perturbation	perturbation	NOUN
ejpam-3574	105	12	of	of	ADP
ejpam-3574	105	13	w	w	PROPN
ejpam-3574	105	14	is	be	AUX
ejpam-3574	105	15	k	k	PROPN
ejpam-3574	105	16	rank	rank	PROPN
ejpam-3574	105	17	-	-	PUNCT
ejpam-3574	105	18	one	one	NUM
ejpam-3574	105	19	perturbations	perturbation	NOUN
ejpam-3574	105	20	of	of	ADP
ejpam-3574	105	21	the	the	DET
ejpam-3574	105	22	symplectic	symplectic	ADJ
ejpam-3574	105	23	matrix	matrix	NOUN
ejpam-3574	105	24	w	w	NOUN
ejpam-3574	105	25	.	.	PUNCT
ejpam-3574	106	1	we	we	PRON
ejpam-3574	106	2	have	have	VERB
ejpam-3574	106	3	k∏	k∏	PROPN
ejpam-3574	106	4	j=1	j=1	PROPN
ejpam-3574	106	5	(	(	PUNCT
ejpam-3574	106	6	i	i	PRON
ejpam-3574	106	7	+	+	NUM
ejpam-3574	106	8	uju	uju	PROPN
ejpam-3574	106	9	t	t	PROPN
ejpam-3574	106	10	j	j	PROPN
ejpam-3574	106	11	j	j	PROPN
ejpam-3574	106	12	)	)	PUNCT
ejpam-3574	106	13	w	w	PUNCT
ejpam-3574	107	1	=	=	SYM
ejpam-3574	107	2	i	i	PROPN
ejpam-3574	107	3	+	+	CCONJ
ejpam-3574	107	4	k∑	k∑	PROPN
ejpam-3574	108	1	j=1	j=1	PROPN
ejpam-3574	108	2	uju	uju	PROPN
ejpam-3574	108	3	t	t	PROPN
ejpam-3574	108	4	j	j	PROPN
ejpam-3574	109	1	j	j	PROPN
ejpam-3574	109	2	w	w	PROPN
ejpam-3574	109	3	.	.	PUNCT
ejpam-3574	109	4	consider	consider	VERB
ejpam-3574	109	5	a	a	DET
ejpam-3574	109	6	symplectic	symplectic	ADJ
ejpam-3574	109	7	matrix	matrix	NOUN
ejpam-3574	109	8	of	of	ADP
ejpam-3574	109	9	function	function	NOUN
ejpam-3574	109	10	(	(	PUNCT
ejpam-3574	109	11	x(t))t∈r	x(t))t∈r	PROPN
ejpam-3574	109	12	;	;	PUNCT
ejpam-3574	109	13	we	we	PRON
ejpam-3574	109	14	can	can	AUX
ejpam-3574	109	15	consider	consider	VERB
ejpam-3574	109	16	for	for	ADP
ejpam-3574	109	17	example	example	NOUN
ejpam-3574	109	18	the	the	DET
ejpam-3574	109	19	solution	solution	NOUN
ejpam-3574	109	20	of	of	ADP
ejpam-3574	109	21	system	system	NOUN
ejpam-3574	109	22	(	(	PUNCT
ejpam-3574	109	23	2	2	X
ejpam-3574	109	24	)	)	PUNCT
ejpam-3574	109	25	which	which	PRON
ejpam-3574	109	26	is	be	AUX
ejpam-3574	109	27	j	j	NOUN
ejpam-3574	109	28	-	-	NOUN
ejpam-3574	109	29	symplectic	symplectic	ADJ
ejpam-3574	109	30	.	.	PUNCT
ejpam-3574	110	1	we	we	PRON
ejpam-3574	110	2	have	have	VERB
ejpam-3574	110	3	the	the	DET
ejpam-3574	110	4	following	follow	VERB
ejpam-3574	110	5	definition	definition	NOUN
ejpam-3574	110	6	definition	definition	NOUN
ejpam-3574	110	7	6	6	NUM
ejpam-3574	110	8	.	.	PUNCT
ejpam-3574	111	1	we	we	PRON
ejpam-3574	111	2	call	call	VERB
ejpam-3574	111	3	rank	rank	NOUN
ejpam-3574	111	4	-	-	PUNCT
ejpam-3574	111	5	k	k	NOUN
ejpam-3574	111	6	perturbation	perturbation	NOUN
ejpam-3574	111	7	of	of	ADP
ejpam-3574	111	8	x(t	x(t	PROPN
ejpam-3574	111	9	)	)	PUNCT
ejpam-3574	111	10	any	any	DET
ejpam-3574	111	11	matrix	matrix	NOUN
ejpam-3574	111	12	function	function	NOUN
ejpam-3574	111	13	of	of	ADP
ejpam-3574	111	14	the	the	DET
ejpam-3574	111	15	form	form	NOUN
ejpam-3574	111	16	x̃(t	x̃(t	PROPN
ejpam-3574	111	17	)	)	PUNCT
ejpam-3574	112	1	=	=	PUNCT
ejpam-3574	112	2	(	(	PUNCT
ejpam-3574	112	3	i	i	PRON
ejpam-3574	112	4	+	+	X
ejpam-3574	112	5	uutj)x(t	uutj)x(t	NOUN
ejpam-3574	112	6	)	)	PUNCT
ejpam-3574	112	7	,	,	PUNCT
ejpam-3574	112	8	(	(	PUNCT
ejpam-3574	112	9	4	4	X
ejpam-3574	112	10	)	)	PUNCT
ejpam-3574	112	11	where	where	SCONJ
ejpam-3574	112	12	rank(u	rank(u	VERB
ejpam-3574	112	13	)	)	PUNCT
ejpam-3574	112	14	=	=	SYM
ejpam-3574	112	15	k	k	PROPN
ejpam-3574	112	16	and	and	CCONJ
ejpam-3574	112	17	the	the	DET
ejpam-3574	112	18	columns	column	NOUN
ejpam-3574	112	19	of	of	ADP
ejpam-3574	112	20	u	u	PROPN
ejpam-3574	112	21	belong	belong	VERB
ejpam-3574	112	22	in	in	ADP
ejpam-3574	112	23	a	a	DET
ejpam-3574	112	24	j	j	NOUN
ejpam-3574	112	25	-	-	PUNCT
ejpam-3574	112	26	lagrangian	lagrangian	ADJ
ejpam-3574	112	27	subspace	subspace	NOUN
ejpam-3574	112	28	.	.	PUNCT
ejpam-3574	113	1	remark	remark	PROPN
ejpam-3574	113	2	1	1	NUM
ejpam-3574	113	3	.	.	PUNCT
ejpam-3574	114	1	since	since	SCONJ
ejpam-3574	114	2	the	the	DET
ejpam-3574	114	3	matrix	matrix	NOUN
ejpam-3574	114	4	function	function	NOUN
ejpam-3574	114	5	(	(	PUNCT
ejpam-3574	114	6	x(t))t∈r	x(t))t∈r	PROPN
ejpam-3574	114	7	is	be	AUX
ejpam-3574	114	8	j	j	NOUN
ejpam-3574	114	9	-	-	PUNCT
ejpam-3574	114	10	symplectic	symplectic	ADJ
ejpam-3574	114	11	,	,	PUNCT
ejpam-3574	114	12	its	its	PRON
ejpam-3574	114	13	rank	rank	NOUN
ejpam-3574	114	14	-	-	PUNCT
ejpam-3574	114	15	k	k	NOUN
ejpam-3574	114	16	perturbation	perturbation	NOUN
ejpam-3574	114	17	will	will	AUX
ejpam-3574	114	18	be	be	AUX
ejpam-3574	114	19	j−symplectic	j−symplectic	ADJ
ejpam-3574	114	20	.	.	PROPN
ejpam-3574	114	21	2.3	2.3	NUM
ejpam-3574	114	22	.	.	PUNCT
ejpam-3574	115	1	rank	rank	NOUN
ejpam-3574	115	2	-	-	PUNCT
ejpam-3574	115	3	k	k	PROPN
ejpam-3574	115	4	perturbation	perturbation	NOUN
ejpam-3574	115	5	of	of	ADP
ejpam-3574	115	6	hamiltonian	hamiltonian	ADJ
ejpam-3574	115	7	system	system	NOUN
ejpam-3574	115	8	with	with	ADP
ejpam-3574	115	9	periodic	periodic	ADJ
ejpam-3574	115	10	coefficients	coefficient	NOUN
ejpam-3574	115	11	let	let	VERB
ejpam-3574	115	12	u	u	PRON
ejpam-3574	115	13	∈	∈	PROPN
ejpam-3574	115	14	r2n×k	r2n×k	PROPN
ejpam-3574	115	15	(	(	PUNCT
ejpam-3574	115	16	with	with	ADP
ejpam-3574	115	17	k	k	PROPN
ejpam-3574	115	18	≤	≤	NUM
ejpam-3574	115	19	n	n	CCONJ
ejpam-3574	115	20	)	)	PUNCT
ejpam-3574	115	21	be	be	AUX
ejpam-3574	115	22	a	a	DET
ejpam-3574	115	23	constant	constant	ADJ
ejpam-3574	115	24	matrix	matrix	NOUN
ejpam-3574	115	25	of	of	ADP
ejpam-3574	115	26	rank	rank	NOUN
ejpam-3574	115	27	k	k	PROPN
ejpam-3574	115	28	such	such	ADJ
ejpam-3574	115	29	that	that	SCONJ
ejpam-3574	115	30	its	its	PRON
ejpam-3574	115	31	columns	column	NOUN
ejpam-3574	115	32	belong	belong	VERB
ejpam-3574	115	33	to	to	ADP
ejpam-3574	115	34	a	a	DET
ejpam-3574	115	35	j	j	PROPN
ejpam-3574	115	36	-	-	ADJ
ejpam-3574	115	37	lagrangian	lagrangian	ADJ
ejpam-3574	115	38	subspace	subspace	NOUN
ejpam-3574	115	39	and	and	CCONJ
ejpam-3574	115	40	(	(	PUNCT
ejpam-3574	115	41	x(t))t≥0	x(t))t≥0	NOUN
ejpam-3574	115	42	be	be	VERB
ejpam-3574	115	43	the	the	DET
ejpam-3574	115	44	fundamental	fundamental	ADJ
ejpam-3574	115	45	solution	solution	NOUN
ejpam-3574	115	46	of	of	ADP
ejpam-3574	115	47	(	(	PUNCT
ejpam-3574	115	48	2	2	NUM
ejpam-3574	115	49	)	)	PUNCT
ejpam-3574	115	50	.	.	PUNCT
ejpam-3574	116	1	we	we	PRON
ejpam-3574	116	2	have	have	VERB
ejpam-3574	116	3	the	the	DET
ejpam-3574	116	4	following	follow	VERB
ejpam-3574	116	5	proposition	proposition	NOUN
ejpam-3574	116	6	proposition	proposition	NOUN
ejpam-3574	116	7	4	4	NUM
ejpam-3574	116	8	.	.	PUNCT
ejpam-3574	117	1	a	a	PRON
ejpam-3574	117	2	consider	consider	VERB
ejpam-3574	117	3	the	the	DET
ejpam-3574	117	4	following	follow	VERB
ejpam-3574	117	5	perturbed	perturb	VERB
ejpam-3574	117	6	hamiltonian	hamiltonian	ADJ
ejpam-3574	117	7	system	system	NOUN
ejpam-3574	117	8	j	j	PROPN
ejpam-3574	117	9	dx̃(t	dx̃(t	PROPN
ejpam-3574	117	10	)	)	PUNCT
ejpam-3574	118	1	dt	dt	NOUN
ejpam-3574	119	1	=	=	PUNCT
ejpam-3574	120	1	[	[	X
ejpam-3574	120	2	h(t	h(t	X
ejpam-3574	120	3	)	)	PUNCT
ejpam-3574	120	4	+	+	SYM
ejpam-3574	120	5	e(t	e(t	NOUN
ejpam-3574	120	6	)	)	PUNCT
ejpam-3574	120	7	]	]	PUNCT
ejpam-3574	121	1	x̃(t	x̃(t	PROPN
ejpam-3574	121	2	)	)	PUNCT
ejpam-3574	121	3	,	,	PUNCT
ejpam-3574	121	4	(	(	PUNCT
ejpam-3574	121	5	5	5	X
ejpam-3574	121	6	)	)	PUNCT
ejpam-3574	121	7	where	where	SCONJ
ejpam-3574	121	8	e(t	e(t	NOUN
ejpam-3574	121	9	)	)	PUNCT
ejpam-3574	121	10	=	=	SYM
ejpam-3574	121	11	(	(	PUNCT
ejpam-3574	121	12	juuth(t))t	juuth(t))t	PROPN
ejpam-3574	121	13	+	+	CCONJ
ejpam-3574	121	14	juuth(t	juuth(t	NOUN
ejpam-3574	121	15	)	)	PUNCT
ejpam-3574	122	1	+	+	CCONJ
ejpam-3574	122	2	(	(	PUNCT
ejpam-3574	122	3	uutj)th(t)(uutj	uutj)th(t)(uutj	ADJ
ejpam-3574	122	4	)	)	PUNCT
ejpam-3574	122	5	.	.	PUNCT
ejpam-3574	123	1	(	(	PUNCT
ejpam-3574	123	2	i	i	NOUN
ejpam-3574	123	3	)	)	PUNCT
ejpam-3574	123	4	then	then	ADV
ejpam-3574	123	5	x̃(t	x̃(t	PROPN
ejpam-3574	123	6	)	)	PUNCT
ejpam-3574	123	7	=	=	PUNCT
ejpam-3574	124	1	(	(	PUNCT
ejpam-3574	124	2	i	i	PRON
ejpam-3574	124	3	+	+	PUNCT
ejpam-3574	124	4	uutj)x(t	uutj)x(t	NOUN
ejpam-3574	124	5	)	)	PUNCT
ejpam-3574	124	6	is	be	AUX
ejpam-3574	124	7	a	a	DET
ejpam-3574	124	8	solution	solution	NOUN
ejpam-3574	124	9	of	of	ADP
ejpam-3574	124	10	system	system	NOUN
ejpam-3574	124	11	(	(	PUNCT
ejpam-3574	124	12	5	5	NUM
ejpam-3574	124	13	)	)	PUNCT
ejpam-3574	124	14	.	.	PUNCT
ejpam-3574	125	1	(	(	PUNCT
ejpam-3574	125	2	ii	ii	NOUN
ejpam-3574	125	3	)	)	PUNCT
ejpam-3574	125	4	equation	equation	NOUN
ejpam-3574	125	5	(	(	PUNCT
ejpam-3574	125	6	5	5	X
ejpam-3574	125	7	)	)	PUNCT
ejpam-3574	125	8	can	can	AUX
ejpam-3574	125	9	be	be	AUX
ejpam-3574	125	10	put	put	VERB
ejpam-3574	125	11	in	in	ADP
ejpam-3574	125	12	the	the	DET
ejpam-3574	125	13	form	form	NUM
ejpam-3574	125	14	j	j	PROPN
ejpam-3574	125	15	dx̃(t	dx̃(t	NOUN
ejpam-3574	125	16	)	)	PUNCT
ejpam-3574	125	17	dt	dt	NOUN
ejpam-3574	126	1	=	=	PUNCT
ejpam-3574	126	2	(	(	PUNCT
ejpam-3574	126	3	i	i	PRON
ejpam-3574	126	4	−	−	PROPN
ejpam-3574	126	5	uutj	uutj	ADJ
ejpam-3574	126	6	)	)	PUNCT
ejpam-3574	126	7	t	t	PROPN
ejpam-3574	126	8	h(t	h(t	PROPN
ejpam-3574	126	9	)	)	PUNCT
ejpam-3574	127	1	(	(	PUNCT
ejpam-3574	127	2	i	i	PRON
ejpam-3574	127	3	−	−	PROPN
ejpam-3574	127	4	uutj	uutj	ADJ
ejpam-3574	127	5	)	)	PUNCT
ejpam-3574	127	6	x̃(t	x̃(t	PROPN
ejpam-3574	127	7	)	)	PUNCT
ejpam-3574	127	8	,	,	PUNCT
ejpam-3574	127	9	t	t	PROPN
ejpam-3574	127	10	∈	∈	PROPN
ejpam-3574	127	11	r+	r+	X
ejpam-3574	127	12	,	,	PUNCT
ejpam-3574	127	13	x̃(0	x̃(0	X
ejpam-3574	127	14	)	)	PUNCT
ejpam-3574	127	15	=	=	SYM
ejpam-3574	128	1	i	i	PRON
ejpam-3574	128	2	+	+	CCONJ
ejpam-3574	128	3	uutj	uutj	ADJ
ejpam-3574	128	4	(	(	PUNCT
ejpam-3574	128	5	6	6	NUM
ejpam-3574	128	6	)	)	PUNCT
ejpam-3574	128	7	m.	m.	NOUN
ejpam-3574	128	8	dosso	dosso	NOUN
ejpam-3574	128	9	,	,	PUNCT
ejpam-3574	128	10	t.	t.	PROPN
ejpam-3574	128	11	g.	g.	PROPN
ejpam-3574	128	12	y.	y.	PROPN
ejpam-3574	128	13	arouna	arouna	PROPN
ejpam-3574	128	14	,	,	PUNCT
ejpam-3574	128	15	j.-c	j.-c	PROPN
ejpam-3574	128	16	.	.	PUNCT
ejpam-3574	129	1	koua	koua	PROPN
ejpam-3574	129	2	brou	brou	PROPN
ejpam-3574	129	3	/	/	SYM
ejpam-3574	129	4	eur	eur	PROPN
ejpam-3574	129	5	.	.	PUNCT
ejpam-3574	130	1	j.	j.	PROPN
ejpam-3574	130	2	pure	pure	PROPN
ejpam-3574	130	3	appl	appl	PROPN
ejpam-3574	130	4	.	.	PROPN
ejpam-3574	130	5	math	math	PROPN
ejpam-3574	130	6	,	,	PUNCT
ejpam-3574	130	7	12	12	NUM
ejpam-3574	130	8	(	(	PUNCT
ejpam-3574	130	9	4	4	NUM
ejpam-3574	130	10	)	)	PUNCT
ejpam-3574	130	11	(	(	PUNCT
ejpam-3574	130	12	2019	2019	NUM
ejpam-3574	130	13	)	)	PUNCT
ejpam-3574	130	14	,	,	PUNCT
ejpam-3574	130	15	1744	1744	NUM
ejpam-3574	130	16	-	-	SYM
ejpam-3574	130	17	1770	1770	NUM
ejpam-3574	130	18	1749	1749	NUM
ejpam-3574	130	19	(	(	PUNCT
ejpam-3574	130	20	iii	iii	NOUN
ejpam-3574	130	21	)	)	PUNCT
ejpam-3574	130	22	any	any	DET
ejpam-3574	130	23	solution	solution	NOUN
ejpam-3574	130	24	(	(	PUNCT
ejpam-3574	130	25	x̃(t))t≥0	x̃(t))t≥0	NOUN
ejpam-3574	130	26	of	of	ADP
ejpam-3574	130	27	perturbed	perturb	VERB
ejpam-3574	130	28	system	system	NOUN
ejpam-3574	130	29	(	(	PUNCT
ejpam-3574	130	30	5	5	NUM
ejpam-3574	130	31	)	)	PUNCT
ejpam-3574	130	32	of	of	ADP
ejpam-3574	130	33	system	system	NOUN
ejpam-3574	130	34	(	(	PUNCT
ejpam-3574	130	35	2	2	NUM
ejpam-3574	130	36	)	)	PUNCT
ejpam-3574	130	37	,	,	PUNCT
ejpam-3574	130	38	is	be	AUX
ejpam-3574	130	39	of	of	ADP
ejpam-3574	130	40	the	the	DET
ejpam-3574	130	41	form	form	NOUN
ejpam-3574	130	42	x̃(t	x̃(t	PROPN
ejpam-3574	130	43	)	)	PUNCT
ejpam-3574	130	44	=	=	PUNCT
ejpam-3574	131	1	(	(	PUNCT
ejpam-3574	131	2	i	i	PRON
ejpam-3574	131	3	+	+	X
ejpam-3574	131	4	uutj)x(t	uutj)x(t	NOUN
ejpam-3574	131	5	)	)	PUNCT
ejpam-3574	131	6	,	,	PUNCT
ejpam-3574	131	7	where	where	SCONJ
ejpam-3574	131	8	(	(	PUNCT
ejpam-3574	131	9	x(t))t≥0	x(t))t≥0	PROPN
ejpam-3574	131	10	is	be	AUX
ejpam-3574	131	11	the	the	DET
ejpam-3574	131	12	fundamental	fundamental	ADJ
ejpam-3574	131	13	solution	solution	NOUN
ejpam-3574	131	14	of	of	ADP
ejpam-3574	131	15	system	system	NOUN
ejpam-3574	131	16	(	(	PUNCT
ejpam-3574	131	17	2	2	NUM
ejpam-3574	131	18	)	)	PUNCT
ejpam-3574	131	19	.	.	PUNCT
ejpam-3574	132	1	proof	proof	NOUN
ejpam-3574	132	2	.	.	PUNCT
ejpam-3574	133	1	for	for	ADP
ejpam-3574	133	2	the	the	DET
ejpam-3574	133	3	proof	proof	NOUN
ejpam-3574	133	4	,	,	PUNCT
ejpam-3574	133	5	see	see	VERB
ejpam-3574	133	6	[	[	X
ejpam-3574	133	7	2	2	NUM
ejpam-3574	133	8	]	]	PUNCT
ejpam-3574	133	9	.	.	PUNCT
ejpam-3574	134	1	system	system	NOUN
ejpam-3574	134	2	(	(	PUNCT
ejpam-3574	134	3	6	6	NUM
ejpam-3574	134	4	)	)	PUNCT
ejpam-3574	134	5	can	can	AUX
ejpam-3574	134	6	be	be	AUX
ejpam-3574	134	7	written	write	VERB
ejpam-3574	134	8	as	as	ADP
ejpam-3574	134	9	below	below	PROPN
ejpam-3574	134	10	j	j	PROPN
ejpam-3574	134	11	dx̃(t	dx̃(t	PROPN
ejpam-3574	134	12	)	)	PUNCT
ejpam-3574	134	13	dt	dt	NOUN
ejpam-3574	135	1	=	=	PUNCT
ejpam-3574	135	2	(	(	PUNCT
ejpam-3574	135	3	i	i	PRON
ejpam-3574	135	4	−	−	PROPN
ejpam-3574	136	1	∑k	∑k	PROPN
ejpam-3574	136	2	j=1	j=1	PROPN
ejpam-3574	136	3	uju	uju	PROPN
ejpam-3574	136	4	t	t	PROPN
ejpam-3574	136	5	j	j	PROPN
ejpam-3574	136	6	j	j	PROPN
ejpam-3574	136	7	)	)	PUNCT
ejpam-3574	136	8	t	t	PROPN
ejpam-3574	136	9	h(t	h(t	PROPN
ejpam-3574	136	10	)	)	PUNCT
ejpam-3574	136	11	(	(	PUNCT
ejpam-3574	136	12	i	i	PRON
ejpam-3574	136	13	−	−	PROPN
ejpam-3574	137	1	∑k	∑k	PROPN
ejpam-3574	137	2	j=1	j=1	PROPN
ejpam-3574	137	3	uju	uju	PROPN
ejpam-3574	137	4	t	t	PROPN
ejpam-3574	137	5	j	j	PROPN
ejpam-3574	137	6	j	j	PROPN
ejpam-3574	137	7	)	)	PUNCT
ejpam-3574	137	8	x̃(t	x̃(t	PROPN
ejpam-3574	137	9	)	)	PUNCT
ejpam-3574	137	10	x̃(0	x̃(0	X
ejpam-3574	137	11	)	)	PUNCT
ejpam-3574	137	12	=	=	SYM
ejpam-3574	138	1	(	(	PUNCT
ejpam-3574	138	2	i	i	PRON
ejpam-3574	138	3	+	+	X
ejpam-3574	139	1	∑k	∑k	PROPN
ejpam-3574	139	2	j=1	j=1	PROPN
ejpam-3574	139	3	uju	uju	PROPN
ejpam-3574	139	4	t	t	PROPN
ejpam-3574	139	5	j	j	PROPN
ejpam-3574	139	6	j	j	PROPN
ejpam-3574	139	7	)	)	PUNCT
ejpam-3574	139	8	,	,	PUNCT
ejpam-3574	139	9	(	(	PUNCT
ejpam-3574	139	10	7	7	X
ejpam-3574	139	11	)	)	PUNCT
ejpam-3574	139	12	where	where	SCONJ
ejpam-3574	139	13	each	each	DET
ejpam-3574	139	14	vector	vector	NOUN
ejpam-3574	139	15	(	(	PUNCT
ejpam-3574	139	16	uj)1≤j≤k	uj)1≤j≤k	PROPN
ejpam-3574	139	17	⊂	⊂	PROPN
ejpam-3574	139	18	r2n	r2n	NOUN
ejpam-3574	139	19	belongs	belong	VERB
ejpam-3574	139	20	to	to	ADP
ejpam-3574	139	21	a	a	DET
ejpam-3574	139	22	same	same	ADJ
ejpam-3574	139	23	j	j	NOUN
ejpam-3574	139	24	-	-	ADJ
ejpam-3574	139	25	lagrangian	lagrangian	ADJ
ejpam-3574	139	26	subspace	subspace	NOUN
ejpam-3574	139	27	.	.	PUNCT
ejpam-3574	140	1	we	we	PRON
ejpam-3574	140	2	can	can	AUX
ejpam-3574	140	3	immediately	immediately	ADV
ejpam-3574	140	4	see	see	VERB
ejpam-3574	140	5	that	that	SCONJ
ejpam-3574	140	6	the	the	DET
ejpam-3574	140	7	rank	rank	NOUN
ejpam-3574	140	8	-	-	PUNCT
ejpam-3574	140	9	k	k	NOUN
ejpam-3574	140	10	perturbation	perturbation	NOUN
ejpam-3574	140	11	of	of	ADP
ejpam-3574	140	12	(	(	PUNCT
ejpam-3574	140	13	2	2	X
ejpam-3574	140	14	)	)	PUNCT
ejpam-3574	140	15	can	can	AUX
ejpam-3574	140	16	be	be	AUX
ejpam-3574	140	17	interpreted	interpret	VERB
ejpam-3574	140	18	as	as	ADP
ejpam-3574	140	19	k	k	PROPN
ejpam-3574	140	20	rank	rank	PROPN
ejpam-3574	140	21	-	-	PUNCT
ejpam-3574	140	22	one	one	NUM
ejpam-3574	140	23	perturbations	perturbation	NOUN
ejpam-3574	140	24	of	of	ADP
ejpam-3574	140	25	(	(	PUNCT
ejpam-3574	140	26	2	2	NUM
ejpam-3574	140	27	)	)	PUNCT
ejpam-3574	140	28	.	.	PUNCT
ejpam-3574	141	1	in	in	ADP
ejpam-3574	141	2	fact	fact	NOUN
ejpam-3574	141	3	,	,	PUNCT
ejpam-3574	141	4	since	since	SCONJ
ejpam-3574	141	5	i	i	PRON
ejpam-3574	141	6	−	−	VERB
ejpam-3574	141	7	uutj	uutj	ADJ
ejpam-3574	142	1	=	=	PUNCT
ejpam-3574	142	2	i	i	PRON
ejpam-3574	142	3	−	−	PROPN
ejpam-3574	142	4	k∑	k∑	PROPN
ejpam-3574	143	1	j=1	j=1	PROPN
ejpam-3574	143	2	uju	uju	PROPN
ejpam-3574	143	3	t	t	PROPN
ejpam-3574	143	4	j	j	PROPN
ejpam-3574	143	5	j	j	PROPN
ejpam-3574	143	6	=	=	SYM
ejpam-3574	143	7	k∏	k∏	PROPN
ejpam-3574	143	8	j=1	j=1	NOUN
ejpam-3574	143	9	(	(	PUNCT
ejpam-3574	143	10	i	i	PRON
ejpam-3574	143	11	−	−	PROPN
ejpam-3574	143	12	ujutj	ujutj	PROPN
ejpam-3574	143	13	j	j	PROPN
ejpam-3574	143	14	)	)	PUNCT
ejpam-3574	143	15	,	,	PUNCT
ejpam-3574	143	16	we	we	PRON
ejpam-3574	143	17	easily	easily	ADV
ejpam-3574	143	18	see	see	VERB
ejpam-3574	143	19	that	that	DET
ejpam-3574	143	20	system	system	NOUN
ejpam-3574	143	21	(	(	PUNCT
ejpam-3574	143	22	7	7	X
ejpam-3574	143	23	)	)	PUNCT
ejpam-3574	143	24	can	can	AUX
ejpam-3574	143	25	be	be	AUX
ejpam-3574	143	26	put	put	VERB
ejpam-3574	143	27	in	in	ADP
ejpam-3574	143	28	the	the	DET
ejpam-3574	143	29	following	follow	VERB
ejpam-3574	143	30	form	form	PROPN
ejpam-3574	143	31	j	j	PROPN
ejpam-3574	143	32	dx̃(t	dx̃(t	PROPN
ejpam-3574	143	33	)	)	PUNCT
ejpam-3574	143	34	dt	dt	PUNCT
ejpam-3574	144	1	=	=	PUNCT
ejpam-3574	144	2	(	(	PUNCT
ejpam-3574	144	3	∏k	∏k	X
ejpam-3574	144	4	j=1	j=1	NOUN
ejpam-3574	144	5	(	(	PUNCT
ejpam-3574	144	6	i	i	PRON
ejpam-3574	144	7	−	−	PROPN
ejpam-3574	144	8	ujutj	ujutj	PROPN
ejpam-3574	144	9	j	j	PROPN
ejpam-3574	144	10	)	)	PUNCT
ejpam-3574	144	11	)	)	PUNCT
ejpam-3574	144	12	t	t	PROPN
ejpam-3574	144	13	h(t	h(t	PROPN
ejpam-3574	144	14	)	)	PUNCT
ejpam-3574	144	15	(	(	PUNCT
ejpam-3574	144	16	∏k	∏k	X
ejpam-3574	144	17	j=1	j=1	NOUN
ejpam-3574	144	18	(	(	PUNCT
ejpam-3574	144	19	i	i	PRON
ejpam-3574	144	20	−	−	PROPN
ejpam-3574	144	21	ujutj	ujutj	PROPN
ejpam-3574	144	22	j	j	PROPN
ejpam-3574	144	23	)	)	PUNCT
ejpam-3574	144	24	)	)	PUNCT
ejpam-3574	145	1	x̃(t	x̃(t	PROPN
ejpam-3574	145	2	)	)	PUNCT
ejpam-3574	145	3	x̃(0	x̃(0	X
ejpam-3574	145	4	)	)	PUNCT
ejpam-3574	145	5	=	=	PUNCT
ejpam-3574	146	1	∏k	∏k	NOUN
ejpam-3574	146	2	j=1	j=1	NOUN
ejpam-3574	146	3	(	(	PUNCT
ejpam-3574	146	4	i	i	PRON
ejpam-3574	146	5	+	+	NUM
ejpam-3574	147	1	uju	uju	PROPN
ejpam-3574	147	2	t	t	PROPN
ejpam-3574	147	3	j	j	PROPN
ejpam-3574	147	4	j	j	PROPN
ejpam-3574	147	5	)	)	PUNCT
ejpam-3574	147	6	(	(	PUNCT
ejpam-3574	147	7	8)	8)	NUM
ejpam-3574	147	8	which	which	PRON
ejpam-3574	147	9	is	be	AUX
ejpam-3574	147	10	the	the	DET
ejpam-3574	147	11	same	same	ADJ
ejpam-3574	147	12	as	as	ADP
ejpam-3574	147	13	the	the	DET
ejpam-3574	147	14	bellow	bellow	ADJ
ejpam-3574	147	15	system	system	NOUN
ejpam-3574	147	16	,	,	PUNCT
ejpam-3574	147	17	for	for	ADP
ejpam-3574	147	18	all	all	PRON
ejpam-3574	147	19	p	p	NOUN
ejpam-3574	147	20	∈	∈	PROPN
ejpam-3574	147	21	{	{	PUNCT
ejpam-3574	147	22	1	1	NUM
ejpam-3574	147	23	,	,	PUNCT
ejpam-3574	147	24	2	2	NUM
ejpam-3574	147	25	,	,	PUNCT
ejpam-3574	147	26	...	...	PUNCT
ejpam-3574	147	27	,	,	PUNCT
ejpam-3574	147	28	k	k	PROPN
ejpam-3574	148	1	−	−	PROPN
ejpam-3574	148	2	1	1	NUM
ejpam-3574	148	3	}	}	PUNCT
ejpam-3574	148	4	:	:	PUNCT
ejpam-3574	148	5			PROPN
ejpam-3574	148	6	j	j	PROPN
ejpam-3574	148	7	dx̃(t	dx̃(t	PROPN
ejpam-3574	148	8	)	)	PUNCT
ejpam-3574	148	9	dt	dt	PUNCT
ejpam-3574	149	1	=	=	PUNCT
ejpam-3574	149	2	(	(	PUNCT
ejpam-3574	149	3	∏k	∏k	X
ejpam-3574	149	4	j	j	PROPN
ejpam-3574	149	5	=	=	PROPN
ejpam-3574	149	6	p+1(i	p+1(i	PROPN
ejpam-3574	149	7	−	−	PROPN
ejpam-3574	149	8	ujutj	ujutj	PROPN
ejpam-3574	149	9	j	j	PROPN
ejpam-3574	149	10	)	)	PUNCT
ejpam-3574	149	11	)	)	PUNCT
ejpam-3574	149	12	t	t	PROPN
ejpam-3574	149	13	h(p)(t	h(p)(t	NOUN
ejpam-3574	149	14	)	)	PUNCT
ejpam-3574	149	15	(	(	PUNCT
ejpam-3574	149	16	∏k	∏k	X
ejpam-3574	149	17	j	j	PROPN
ejpam-3574	149	18	=	=	PROPN
ejpam-3574	149	19	p+1(i	p+1(i	PROPN
ejpam-3574	149	20	−	−	PROPN
ejpam-3574	149	21	ujutj	ujutj	PROPN
ejpam-3574	149	22	j	j	PROPN
ejpam-3574	149	23	)	)	PUNCT
ejpam-3574	149	24	)	)	PUNCT
ejpam-3574	150	1	x̃(t	x̃(t	PROPN
ejpam-3574	150	2	)	)	PUNCT
ejpam-3574	150	3	x̃(0	x̃(0	X
ejpam-3574	150	4	)	)	PUNCT
ejpam-3574	150	5	=	=	PUNCT
ejpam-3574	151	1	(	(	PUNCT
ejpam-3574	151	2	∏k	∏k	X
ejpam-3574	151	3	j	j	PROPN
ejpam-3574	151	4	=	=	PROPN
ejpam-3574	151	5	p+1(i	p+1(i	PROPN
ejpam-3574	151	6	+	+	CCONJ
ejpam-3574	151	7	u(k+p−j+1)u	u(k+p−j+1)u	ADJ
ejpam-3574	151	8	t	t	NOUN
ejpam-3574	151	9	(	(	PUNCT
ejpam-3574	151	10	k+p−j+1)j	k+p−j+1)j	PROPN
ejpam-3574	151	11	)	)	PUNCT
ejpam-3574	151	12	)	)	PUNCT
ejpam-3574	152	1	x	x	X
ejpam-3574	152	2	(	(	PUNCT
ejpam-3574	152	3	p	p	NOUN
ejpam-3574	152	4	)	)	PUNCT
ejpam-3574	152	5	(	(	PUNCT
ejpam-3574	152	6	0	0	NUM
ejpam-3574	152	7	)	)	PUNCT
ejpam-3574	152	8	,	,	PUNCT
ejpam-3574	152	9	(	(	PUNCT
ejpam-3574	152	10	9	9	X
ejpam-3574	152	11	)	)	PUNCT
ejpam-3574	152	12	where	where	SCONJ
ejpam-3574	152	13	h(p)(t	h(p)(t	VERB
ejpam-3574	152	14	)	)	PUNCT
ejpam-3574	152	15	=	=	NOUN
ejpam-3574	153	1			PROPN
ejpam-3574	153	2	p∏	p∏	PROPN
ejpam-3574	153	3	j=1	j=1	NOUN
ejpam-3574	153	4	(	(	PUNCT
ejpam-3574	153	5	i	i	PRON
ejpam-3574	153	6	−	−	PROPN
ejpam-3574	153	7	ujutj	ujutj	PROPN
ejpam-3574	153	8	j	j	PROPN
ejpam-3574	153	9	)	)	PUNCT
ejpam-3574	153	10	t	t	PUNCT
ejpam-3574	153	11	h(t	h(t	PROPN
ejpam-3574	153	12	)	)	PUNCT
ejpam-3574	153	13			PROPN
ejpam-3574	153	14	p∏	p∏	PROPN
ejpam-3574	153	15	j=1	j=1	NOUN
ejpam-3574	153	16	(	(	PUNCT
ejpam-3574	153	17	i	i	PRON
ejpam-3574	153	18	−	−	PROPN
ejpam-3574	153	19	ujutj	ujutj	PROPN
ejpam-3574	153	20	j	j	PROPN
ejpam-3574	153	21	)	)	PUNCT
ejpam-3574	153	22			PROPN
ejpam-3574	153	23	and	and	CCONJ
ejpam-3574	153	24	x	x	PRON
ejpam-3574	153	25	(	(	PUNCT
ejpam-3574	153	26	p	p	NOUN
ejpam-3574	153	27	)	)	PUNCT
ejpam-3574	153	28	(	(	PUNCT
ejpam-3574	153	29	0	0	NUM
ejpam-3574	153	30	)	)	PUNCT
ejpam-3574	153	31	=	=	SYM
ejpam-3574	154	1	p∏	p∏	X
ejpam-3574	154	2	j=1	j=1	NOUN
ejpam-3574	154	3	(	(	PUNCT
ejpam-3574	154	4	i	i	PRON
ejpam-3574	154	5	+	+	CCONJ
ejpam-3574	154	6	u(p−j+1)u	u(p−j+1)u	PROPN
ejpam-3574	154	7	t	t	PROPN
ejpam-3574	154	8	(	(	PUNCT
ejpam-3574	154	9	p−j+1)j	p−j+1)j	PROPN
ejpam-3574	154	10	)	)	PUNCT
ejpam-3574	154	11	.	.	PUNCT
ejpam-3574	155	1	m.	m.	NOUN
ejpam-3574	155	2	dosso	dosso	PROPN
ejpam-3574	155	3	,	,	PUNCT
ejpam-3574	155	4	t.	t.	PROPN
ejpam-3574	155	5	g.	g.	PROPN
ejpam-3574	155	6	y.	y.	PROPN
ejpam-3574	155	7	arouna	arouna	PROPN
ejpam-3574	155	8	,	,	PUNCT
ejpam-3574	155	9	j.-c	j.-c	PROPN
ejpam-3574	155	10	.	.	PUNCT
ejpam-3574	156	1	koua	koua	PROPN
ejpam-3574	156	2	brou	brou	PROPN
ejpam-3574	156	3	/	/	SYM
ejpam-3574	156	4	eur	eur	PROPN
ejpam-3574	156	5	.	.	PUNCT
ejpam-3574	157	1	j.	j.	PROPN
ejpam-3574	157	2	pure	pure	PROPN
ejpam-3574	157	3	appl	appl	PROPN
ejpam-3574	157	4	.	.	PROPN
ejpam-3574	157	5	math	math	PROPN
ejpam-3574	157	6	,	,	PUNCT
ejpam-3574	157	7	12	12	NUM
ejpam-3574	157	8	(	(	PUNCT
ejpam-3574	157	9	4	4	NUM
ejpam-3574	157	10	)	)	PUNCT
ejpam-3574	157	11	(	(	PUNCT
ejpam-3574	157	12	2019	2019	NUM
ejpam-3574	157	13	)	)	PUNCT
ejpam-3574	157	14	,	,	PUNCT
ejpam-3574	157	15	1744	1744	NUM
ejpam-3574	157	16	-	-	SYM
ejpam-3574	157	17	1770	1770	NUM
ejpam-3574	157	18	1750	1750	NUM
ejpam-3574	157	19	3	3	NUM
ejpam-3574	157	20	.	.	PUNCT
ejpam-3574	158	1	jordan	jordan	PROPN
ejpam-3574	158	2	canonical	canonical	ADJ
ejpam-3574	158	3	form	form	NOUN
ejpam-3574	158	4	of	of	ADP
ejpam-3574	158	5	rank	rank	NOUN
ejpam-3574	158	6	-	-	PUNCT
ejpam-3574	158	7	k	k	NOUN
ejpam-3574	158	8	perturbation	perturbation	NOUN
ejpam-3574	158	9	of	of	ADP
ejpam-3574	158	10	a	a	DET
ejpam-3574	158	11	symplectic	symplectic	ADJ
ejpam-3574	158	12	matrix	matrix	NOUN
ejpam-3574	158	13	let	let	VERB
ejpam-3574	158	14	w	w	NOUN
ejpam-3574	158	15	,	,	PUNCT
ejpam-3574	158	16	j	j	PROPN
ejpam-3574	158	17	∈	∈	PROPN
ejpam-3574	158	18	r2n×2n	r2n×2n	NOUN
ejpam-3574	158	19	be	be	VERB
ejpam-3574	158	20	two	two	NUM
ejpam-3574	158	21	matrices	matrix	NOUN
ejpam-3574	158	22	and	and	CCONJ
ejpam-3574	158	23	λ	λ	X
ejpam-3574	158	24	∈	∈	PROPN
ejpam-3574	158	25	c	c	NOUN
ejpam-3574	158	26	such	such	ADJ
ejpam-3574	158	27	that	that	SCONJ
ejpam-3574	158	28	j	j	PROPN
ejpam-3574	158	29	is	be	AUX
ejpam-3574	158	30	skew	skew	ADJ
ejpam-3574	158	31	-	-	PUNCT
ejpam-3574	158	32	symmetric	symmetric	ADJ
ejpam-3574	158	33	,	,	PUNCT
ejpam-3574	158	34	w	w	PROPN
ejpam-3574	158	35	is	be	AUX
ejpam-3574	158	36	j	j	NOUN
ejpam-3574	158	37	-	-	PUNCT
ejpam-3574	158	38	symplectic	symplectic	ADJ
ejpam-3574	158	39	and	and	CCONJ
ejpam-3574	158	40	λ	λ	X
ejpam-3574	158	41	an	an	DET
ejpam-3574	158	42	eigenvalue	eigenvalue	NOUN
ejpam-3574	158	43	of	of	ADP
ejpam-3574	158	44	w	w	PROPN
ejpam-3574	158	45	.	.	PUNCT
ejpam-3574	159	1	we	we	PRON
ejpam-3574	159	2	have	have	VERB
ejpam-3574	159	3	the	the	DET
ejpam-3574	159	4	following	follow	VERB
ejpam-3574	159	5	theorem	theorem	NOUN
ejpam-3574	159	6	theorem	theorem	NOUN
ejpam-3574	159	7	3	3	X
ejpam-3574	159	8	.	.	PUNCT
ejpam-3574	159	9	suppose	suppose	VERB
ejpam-3574	159	10	that	that	SCONJ
ejpam-3574	159	11	w	w	PROPN
ejpam-3574	159	12	has	have	VERB
ejpam-3574	159	13	the	the	DET
ejpam-3574	159	14	following	follow	VERB
ejpam-3574	159	15	jordan	jordan	PROPN
ejpam-3574	159	16	canonical	canonical	ADJ
ejpam-3574	159	17	form	form	NOUN
ejpam-3574	159	18	:	:	PUNCT
ejpam-3574	160	1			PROPN
ejpam-3574	160	2	l1⊕	l1⊕	PROPN
ejpam-3574	160	3	j=1	j=1	PROPN
ejpam-3574	160	4	jn1(λ	jn1(λ	PROPN
ejpam-3574	160	5	)	)	PUNCT
ejpam-3574	160	6	⊕	⊕	PROPN
ejpam-3574	160	7			PROPN
ejpam-3574	160	8	l2⊕	l2⊕	PROPN
ejpam-3574	160	9	j=1	j=1	PROPN
ejpam-3574	160	10	jn2(λ	jn2(λ	PROPN
ejpam-3574	160	11	)	)	PUNCT
ejpam-3574	160	12	⊕	⊕	PROPN
ejpam-3574	160	13	·	·	PUNCT
ejpam-3574	160	14	·	·	PUNCT
ejpam-3574	160	15	·	·	PUNCT
ejpam-3574	160	16	⊕	⊕	NOUN
ejpam-3574	161	1			PROPN
ejpam-3574	161	2	lm⊕	lm⊕	PROPN
ejpam-3574	161	3	j=1	j=1	PROPN
ejpam-3574	161	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	161	5	)	)	PUNCT
ejpam-3574	162	1	⊕	⊕	PROPN
ejpam-3574	162	2	j	j	PROPN
ejpam-3574	162	3	,	,	PUNCT
ejpam-3574	162	4	where	where	SCONJ
ejpam-3574	162	5	n1	n1	PROPN
ejpam-3574	162	6	>	>	X
ejpam-3574	162	7	·	·	PUNCT
ejpam-3574	162	8	·	·	PUNCT
ejpam-3574	162	9	·	·	PUNCT
ejpam-3574	163	1	>	>	PUNCT
ejpam-3574	163	2	nm	nm	PROPN
ejpam-3574	163	3	,	,	PUNCT
ejpam-3574	163	4	m	m	PROPN
ejpam-3574	163	5	∈	∈	NOUN
ejpam-3574	163	6	n∗	n∗	NOUN
ejpam-3574	163	7	such	such	ADJ
ejpam-3574	163	8	that	that	SCONJ
ejpam-3574	163	9	the	the	DET
ejpam-3574	163	10	algebraic	algebraic	ADJ
ejpam-3574	163	11	multiplicity	multiplicity	NOUN
ejpam-3574	163	12	a	a	PRON
ejpam-3574	163	13	of	of	ADP
ejpam-3574	163	14	λ	λ	PROPN
ejpam-3574	163	15	is	be	AUX
ejpam-3574	163	16	of	of	ADP
ejpam-3574	163	17	the	the	DET
ejpam-3574	163	18	form	form	NOUN
ejpam-3574	163	19	a	a	DET
ejpam-3574	163	20	=	=	PUNCT
ejpam-3574	163	21	m∑	m∑	ADV
ejpam-3574	163	22	j=1	j=1	PROPN
ejpam-3574	163	23	ljnj	ljnj	PROPN
ejpam-3574	163	24	and	and	CCONJ
ejpam-3574	163	25	j	j	PROPN
ejpam-3574	163	26	contains	contain	VERB
ejpam-3574	163	27	all	all	DET
ejpam-3574	163	28	the	the	DET
ejpam-3574	163	29	forms	form	NOUN
ejpam-3574	163	30	in	in	ADP
ejpam-3574	163	31	jordan	jordan	PROPN
ejpam-3574	163	32	blocks	block	NOUN
ejpam-3574	163	33	associated	associate	VERB
ejpam-3574	163	34	with	with	ADP
ejpam-3574	163	35	eigenvalues	eigenvalue	NOUN
ejpam-3574	163	36	of	of	ADP
ejpam-3574	163	37	w	w	PROPN
ejpam-3574	163	38	that	that	PRON
ejpam-3574	163	39	are	be	AUX
ejpam-3574	163	40	different	different	ADJ
ejpam-3574	163	41	from	from	ADP
ejpam-3574	163	42	λ	λ	PROPN
ejpam-3574	163	43	.	.	PUNCT
ejpam-3574	164	1	moreover	moreover	ADV
ejpam-3574	164	2	let	let	VERB
ejpam-3574	164	3	b	b	NOUN
ejpam-3574	164	4	=	=	PUNCT
ejpam-3574	164	5	uutjw	uutjw	NOUN
ejpam-3574	164	6	where	where	SCONJ
ejpam-3574	164	7	u	u	PROPN
ejpam-3574	164	8	∈	∈	PROPN
ejpam-3574	164	9	r2n×k	r2n×k	VERB
ejpam-3574	164	10	is	be	AUX
ejpam-3574	164	11	such	such	ADJ
ejpam-3574	164	12	that	that	SCONJ
ejpam-3574	164	13	its	its	PRON
ejpam-3574	164	14	columns	column	NOUN
ejpam-3574	164	15	generate	generate	VERB
ejpam-3574	164	16	an	an	DET
ejpam-3574	164	17	isotropic	isotropic	ADJ
ejpam-3574	164	18	subspace	subspace	NOUN
ejpam-3574	164	19	.	.	PUNCT
ejpam-3574	165	1	(	(	PUNCT
ejpam-3574	165	2	1	1	X
ejpam-3574	165	3	)	)	PUNCT
ejpam-3574	165	4	if	if	SCONJ
ejpam-3574	165	5	λ	λ	PROPN
ejpam-3574	165	6	6∈	6∈	NOUN
ejpam-3574	165	7	{	{	PUNCT
ejpam-3574	165	8	−1	−1	NOUN
ejpam-3574	165	9	,	,	PUNCT
ejpam-3574	165	10	1	1	NUM
ejpam-3574	165	11	}	}	PUNCT
ejpam-3574	165	12	,	,	PUNCT
ejpam-3574	165	13	then	then	ADV
ejpam-3574	165	14	generally	generally	ADV
ejpam-3574	165	15	with	with	ADP
ejpam-3574	165	16	respect	respect	NOUN
ejpam-3574	165	17	to	to	ADP
ejpam-3574	165	18	the	the	DET
ejpam-3574	165	19	components	component	NOUN
ejpam-3574	165	20	of	of	ADP
ejpam-3574	165	21	u	u	PROPN
ejpam-3574	165	22	,	,	PUNCT
ejpam-3574	165	23	the	the	DET
ejpam-3574	165	24	matrix	matrix	NOUN
ejpam-3574	165	25	w+b	w+b	PUNCT
ejpam-3574	165	26	has	have	VERB
ejpam-3574	165	27	the	the	DET
ejpam-3574	165	28	jordan	jordan	PROPN
ejpam-3574	165	29	canonical	canonical	PROPN
ejpam-3574	165	30	form	form	NOUN
ejpam-3574	165	31			X
ejpam-3574	165	32	l1−k⊕	l1−k⊕	X
ejpam-3574	165	33	j=1	j=1	PROPN
ejpam-3574	165	34	jn1(λ	jn1(λ	PROPN
ejpam-3574	165	35	)	)	PUNCT
ejpam-3574	166	1	⊕	⊕	PROPN
ejpam-3574	166	2			PROPN
ejpam-3574	166	3	l2⊕	l2⊕	PROPN
ejpam-3574	166	4	j=1	j=1	PROPN
ejpam-3574	166	5	jn2(λ	jn2(λ	PROPN
ejpam-3574	166	6	)	)	PUNCT
ejpam-3574	166	7	⊕	⊕	PROPN
ejpam-3574	166	8	·	·	PUNCT
ejpam-3574	166	9	·	·	PUNCT
ejpam-3574	166	10	·	·	PUNCT
ejpam-3574	167	1	⊕	⊕	NOUN
ejpam-3574	168	1			PROPN
ejpam-3574	168	2	lm⊕	lm⊕	PROPN
ejpam-3574	168	3	j=1	j=1	PROPN
ejpam-3574	168	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	168	5	)	)	PUNCT
ejpam-3574	169	1	⊕	⊕	PROPN
ejpam-3574	169	2	j̃	j̃	PROPN
ejpam-3574	169	3	,	,	PUNCT
ejpam-3574	169	4	if	if	SCONJ
ejpam-3574	169	5	k	k	PROPN
ejpam-3574	169	6	<	<	X
ejpam-3574	169	7	l1	l1	PROPN
ejpam-3574	169	8	li−ki⊕	li−ki⊕	VERB
ejpam-3574	169	9	j=1	j=1	PROPN
ejpam-3574	169	10	jni(λ	jni(λ	PROPN
ejpam-3574	169	11	)	)	PUNCT
ejpam-3574	169	12	⊕	⊕	PROPN
ejpam-3574	170	1			PROPN
ejpam-3574	170	2	li+1⊕	li+1⊕	NOUN
ejpam-3574	170	3	j=1	j=1	PROPN
ejpam-3574	170	4	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	170	5	)	)	PUNCT
ejpam-3574	170	6	⊕	⊕	PROPN
ejpam-3574	170	7	·	·	PUNCT
ejpam-3574	170	8	·	·	PUNCT
ejpam-3574	170	9	·	·	PUNCT
ejpam-3574	171	1	⊕	⊕	NOUN
ejpam-3574	172	1			PROPN
ejpam-3574	172	2	lm⊕	lm⊕	PROPN
ejpam-3574	172	3	j=1	j=1	PROPN
ejpam-3574	172	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	172	5	)	)	PUNCT
ejpam-3574	173	1	⊕	⊕	PROPN
ejpam-3574	173	2	j̃	j̃	PROPN
ejpam-3574	173	3	,	,	PUNCT
ejpam-3574	173	4	if	if	SCONJ
ejpam-3574	173	5			PROPN
ejpam-3574	173	6	k	k	NOUN
ejpam-3574	173	7	=	=	PUNCT
ejpam-3574	173	8	i−1∑	i−1∑	NOUN
ejpam-3574	173	9	s=1	s=1	PUNCT
ejpam-3574	173	10	ls	ls	X
ejpam-3574	174	1	+	+	X
ejpam-3574	174	2	ki	ki	PROPN
ejpam-3574	174	3	,	,	PUNCT
ejpam-3574	174	4	with	with	ADP
ejpam-3574	174	5	ki	ki	PROPN
ejpam-3574	174	6	<	<	X
ejpam-3574	174	7	li	li	PROPN
ejpam-3574	174	8	and	and	CCONJ
ejpam-3574	174	9	i	i	PRON
ejpam-3574	174	10	>	>	X
ejpam-3574	174	11	1	1	NUM
ejpam-3574	175	1	where	where	SCONJ
ejpam-3574	175	2	j̃	j̃	PROPN
ejpam-3574	175	3	contains	contain	VERB
ejpam-3574	175	4	all	all	DET
ejpam-3574	175	5	the	the	DET
ejpam-3574	175	6	forms	form	NOUN
ejpam-3574	175	7	in	in	ADP
ejpam-3574	175	8	jordan	jordan	PROPN
ejpam-3574	175	9	blocks	block	NOUN
ejpam-3574	175	10	of	of	ADP
ejpam-3574	175	11	w+b	w+b	PROPN
ejpam-3574	175	12	associated	associate	VERB
ejpam-3574	175	13	with	with	ADP
ejpam-3574	175	14	eigenvalues	eigenvalue	NOUN
ejpam-3574	175	15	different	different	ADJ
ejpam-3574	175	16	from	from	ADP
ejpam-3574	175	17	λ	λ	PROPN
ejpam-3574	175	18	.	.	PUNCT
ejpam-3574	176	1	(	(	PUNCT
ejpam-3574	176	2	2	2	X
ejpam-3574	176	3	)	)	PUNCT
ejpam-3574	176	4	if	if	SCONJ
ejpam-3574	176	5	λ	λ	PROPN
ejpam-3574	176	6	∈	∈	PROPN
ejpam-3574	176	7	{	{	PUNCT
ejpam-3574	176	8	−1	−1	NOUN
ejpam-3574	176	9	,	,	PUNCT
ejpam-3574	176	10	1	1	NUM
ejpam-3574	176	11	}	}	PUNCT
ejpam-3574	176	12	,	,	PUNCT
ejpam-3574	176	13	then	then	ADV
ejpam-3574	176	14	(	(	PUNCT
ejpam-3574	176	15	2a	2a	NUM
ejpam-3574	176	16	)	)	PUNCT
ejpam-3574	176	17	if	if	SCONJ
ejpam-3574	176	18	k	k	NOUN
ejpam-3574	176	19	=	=	PUNCT
ejpam-3574	176	20	i−1∑	i−1∑	PUNCT
ejpam-3574	177	1	s=1	s=1	PUNCT
ejpam-3574	177	2	ls	ls	X
ejpam-3574	178	1	+	+	CCONJ
ejpam-3574	178	2	ki	ki	PROPN
ejpam-3574	178	3	where	where	SCONJ
ejpam-3574	178	4	the	the	DET
ejpam-3574	178	5	n1	n1	NOUN
ejpam-3574	178	6	,	,	PUNCT
ejpam-3574	178	7	n2	n2	NOUN
ejpam-3574	178	8	,	,	PUNCT
ejpam-3574	178	9	.	.	PUNCT
ejpam-3574	178	10	.	.	PUNCT
ejpam-3574	178	11	.	.	PUNCT
ejpam-3574	179	1	,	,	PUNCT
ejpam-3574	179	2	ni	ni	PROPN
ejpam-3574	179	3	are	be	AUX
ejpam-3574	179	4	even	even	ADV
ejpam-3574	179	5	and	and	CCONJ
ejpam-3574	179	6	ki	ki	PROPN
ejpam-3574	179	7	<	<	X
ejpam-3574	179	8	li	li	PROPN
ejpam-3574	179	9	,	,	PUNCT
ejpam-3574	179	10	then	then	ADV
ejpam-3574	179	11	generally	generally	ADV
ejpam-3574	179	12	with	with	ADP
ejpam-3574	179	13	respect	respect	NOUN
ejpam-3574	179	14	to	to	ADP
ejpam-3574	179	15	the	the	DET
ejpam-3574	179	16	components	component	NOUN
ejpam-3574	179	17	of	of	ADP
ejpam-3574	179	18	u	u	PROPN
ejpam-3574	179	19	,	,	PUNCT
ejpam-3574	179	20	then	then	ADV
ejpam-3574	179	21	matrix	matrix	VERB
ejpam-3574	179	22	w	w	PROPN
ejpam-3574	180	1	+	+	NOUN
ejpam-3574	180	2	b	b	PROPN
ejpam-3574	180	3	has	have	VERB
ejpam-3574	180	4	the	the	DET
ejpam-3574	180	5	jordan	jordan	PROPN
ejpam-3574	180	6	canonical	canonical	PROPN
ejpam-3574	180	7	formli−ki⊕	formli−ki⊕	X
ejpam-3574	180	8	j=1	j=1	PROPN
ejpam-3574	180	9	jni(λ	jni(λ	PROPN
ejpam-3574	181	1	)	)	PUNCT
ejpam-3574	181	2	⊕	⊕	PROPN
ejpam-3574	181	3			PROPN
ejpam-3574	181	4	li+1⊕	li+1⊕	NOUN
ejpam-3574	181	5	j=1	j=1	PROPN
ejpam-3574	181	6	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	181	7	)	)	PUNCT
ejpam-3574	181	8	⊕	⊕	PROPN
ejpam-3574	181	9	·	·	PUNCT
ejpam-3574	181	10	·	·	PUNCT
ejpam-3574	181	11	·	·	PUNCT
ejpam-3574	181	12	⊕	⊕	NOUN
ejpam-3574	182	1			PROPN
ejpam-3574	182	2	lm⊕	lm⊕	PROPN
ejpam-3574	182	3	j=1	j=1	PROPN
ejpam-3574	182	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	182	5	)	)	PUNCT
ejpam-3574	183	1	⊕	⊕	PROPN
ejpam-3574	183	2	j̃	j̃	PROPN
ejpam-3574	183	3	,	,	PUNCT
ejpam-3574	183	4	where	where	SCONJ
ejpam-3574	183	5	j̃	j̃	PROPN
ejpam-3574	183	6	contains	contain	VERB
ejpam-3574	183	7	all	all	DET
ejpam-3574	183	8	the	the	DET
ejpam-3574	183	9	forms	form	NOUN
ejpam-3574	183	10	in	in	ADP
ejpam-3574	183	11	jordan	jordan	PROPN
ejpam-3574	183	12	blocks	block	NOUN
ejpam-3574	183	13	of	of	ADP
ejpam-3574	183	14	w	w	PROPN
ejpam-3574	183	15	+	+	NOUN
ejpam-3574	183	16	b	b	NOUN
ejpam-3574	183	17	associated	associate	VERB
ejpam-3574	183	18	with	with	ADP
ejpam-3574	183	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	183	20	different	different	ADJ
ejpam-3574	183	21	from	from	ADP
ejpam-3574	183	22	λ	λ	PROPN
ejpam-3574	183	23	.	.	PROPN
ejpam-3574	183	24	m.	m.	NOUN
ejpam-3574	183	25	dosso	dosso	PROPN
ejpam-3574	183	26	,	,	PUNCT
ejpam-3574	183	27	t.	t.	PROPN
ejpam-3574	183	28	g.	g.	PROPN
ejpam-3574	183	29	y.	y.	PROPN
ejpam-3574	183	30	arouna	arouna	PROPN
ejpam-3574	183	31	,	,	PUNCT
ejpam-3574	183	32	j.-c	j.-c	PROPN
ejpam-3574	183	33	.	.	PUNCT
ejpam-3574	184	1	koua	koua	PROPN
ejpam-3574	184	2	brou	brou	PROPN
ejpam-3574	184	3	/	/	SYM
ejpam-3574	184	4	eur	eur	PROPN
ejpam-3574	184	5	.	.	PUNCT
ejpam-3574	185	1	j.	j.	PROPN
ejpam-3574	185	2	pure	pure	PROPN
ejpam-3574	185	3	appl	appl	PROPN
ejpam-3574	185	4	.	.	PROPN
ejpam-3574	185	5	math	math	PROPN
ejpam-3574	185	6	,	,	PUNCT
ejpam-3574	185	7	12	12	NUM
ejpam-3574	185	8	(	(	PUNCT
ejpam-3574	185	9	4	4	NUM
ejpam-3574	185	10	)	)	PUNCT
ejpam-3574	185	11	(	(	PUNCT
ejpam-3574	185	12	2019	2019	NUM
ejpam-3574	185	13	)	)	PUNCT
ejpam-3574	185	14	,	,	PUNCT
ejpam-3574	185	15	1744	1744	NUM
ejpam-3574	185	16	-	-	SYM
ejpam-3574	185	17	1770	1770	NUM
ejpam-3574	185	18	1751	1751	NUM
ejpam-3574	185	19	(	(	PUNCT
ejpam-3574	185	20	2b	2b	NOUN
ejpam-3574	185	21	)	)	PUNCT
ejpam-3574	185	22	if	if	SCONJ
ejpam-3574	185	23	k	k	PROPN
ejpam-3574	185	24	=	=	PUNCT
ejpam-3574	185	25	i−1∑	i−1∑	PUNCT
ejpam-3574	186	1	s=1	s=1	PUNCT
ejpam-3574	186	2	ls	ls	X
ejpam-3574	186	3	+	+	CCONJ
ejpam-3574	186	4	2ki	2ki	ADJ
ejpam-3574	186	5	−	−	NOUN
ejpam-3574	186	6	1	1	NUM
ejpam-3574	186	7	with	with	ADP
ejpam-3574	186	8	2ki	2ki	ADJ
ejpam-3574	186	9	≤	≤	NUM
ejpam-3574	186	10	li	li	PROPN
ejpam-3574	186	11	and	and	CCONJ
ejpam-3574	186	12	ni	ni	PROPN
ejpam-3574	186	13	is	be	AUX
ejpam-3574	186	14	odd	odd	ADJ
ejpam-3574	186	15	,	,	PUNCT
ejpam-3574	186	16	then	then	ADV
ejpam-3574	186	17	li	li	PROPN
ejpam-3574	186	18	is	be	AUX
ejpam-3574	186	19	even	even	ADV
ejpam-3574	186	20	and	and	CCONJ
ejpam-3574	186	21	generally	generally	ADV
ejpam-3574	186	22	with	with	ADP
ejpam-3574	186	23	respect	respect	NOUN
ejpam-3574	186	24	to	to	ADP
ejpam-3574	186	25	the	the	DET
ejpam-3574	186	26	components	component	NOUN
ejpam-3574	186	27	of	of	ADP
ejpam-3574	186	28	u	u	PROPN
ejpam-3574	186	29	,	,	PUNCT
ejpam-3574	186	30	then	then	ADV
ejpam-3574	186	31	matrix	matrix	VERB
ejpam-3574	186	32	w	w	NOUN
ejpam-3574	187	1	+	+	NUM
ejpam-3574	187	2	b	b	NOUN
ejpam-3574	187	3	has	have	VERB
ejpam-3574	187	4	the	the	DET
ejpam-3574	187	5	jordan	jordan	PROPN
ejpam-3574	187	6	canonical	canonical	ADJ
ejpam-3574	187	7	form	form	NOUN
ejpam-3574	187	8	jni+1(λ)⊕	jni+1(λ)⊕	ADJ
ejpam-3574	187	9	li−2ki⊕	li−2ki⊕	NUM
ejpam-3574	187	10	j=1	j=1	ADJ
ejpam-3574	187	11	jni(λ	jni(λ	PROPN
ejpam-3574	187	12	)	)	PUNCT
ejpam-3574	187	13	⊕	⊕	PROPN
ejpam-3574	187	14	·	·	PUNCT
ejpam-3574	187	15	·	·	PUNCT
ejpam-3574	187	16	·	·	PUNCT
ejpam-3574	188	1	⊕	⊕	NOUN
ejpam-3574	189	1			PROPN
ejpam-3574	189	2	lm⊕	lm⊕	PROPN
ejpam-3574	189	3	j=1	j=1	PROPN
ejpam-3574	189	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	189	5	)	)	PUNCT
ejpam-3574	190	1	⊕	⊕	PROPN
ejpam-3574	190	2	j̃	j̃	PROPN
ejpam-3574	190	3	,	,	PUNCT
ejpam-3574	190	4	where	where	SCONJ
ejpam-3574	190	5	j̃	j̃	PROPN
ejpam-3574	190	6	contains	contain	VERB
ejpam-3574	190	7	all	all	DET
ejpam-3574	190	8	the	the	DET
ejpam-3574	190	9	forms	form	NOUN
ejpam-3574	190	10	in	in	ADP
ejpam-3574	190	11	jordan	jordan	PROPN
ejpam-3574	190	12	blocks	block	NOUN
ejpam-3574	190	13	of	of	ADP
ejpam-3574	190	14	w	w	PROPN
ejpam-3574	190	15	+	+	NOUN
ejpam-3574	190	16	b	b	NOUN
ejpam-3574	190	17	associated	associate	VERB
ejpam-3574	190	18	with	with	ADP
ejpam-3574	190	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	190	20	,	,	PUNCT
ejpam-3574	190	21	different	different	ADJ
ejpam-3574	190	22	from	from	ADP
ejpam-3574	190	23	λ	λ	PROPN
ejpam-3574	190	24	.	.	PUNCT
ejpam-3574	190	25	proof	proof	NOUN
ejpam-3574	190	26	.	.	PUNCT
ejpam-3574	191	1	we	we	PRON
ejpam-3574	191	2	know	know	VERB
ejpam-3574	191	3	that	that	SCONJ
ejpam-3574	191	4	the	the	DET
ejpam-3574	191	5	rang	rang	PROPN
ejpam-3574	191	6	-	-	PUNCT
ejpam-3574	191	7	k	k	PROPN
ejpam-3574	191	8	perturbation	perturbation	NOUN
ejpam-3574	191	9	w̃	w̃	PROPN
ejpam-3574	191	10	=	=	PROPN
ejpam-3574	191	11	w	w	PROPN
ejpam-3574	192	1	+	+	PROPN
ejpam-3574	192	2	b	b	NOUN
ejpam-3574	192	3	of	of	ADP
ejpam-3574	192	4	w	w	NOUN
ejpam-3574	192	5	can	can	AUX
ejpam-3574	192	6	be	be	AUX
ejpam-3574	192	7	written	write	VERB
ejpam-3574	192	8	in	in	ADP
ejpam-3574	192	9	the	the	DET
ejpam-3574	192	10	form	form	NOUN
ejpam-3574	192	11	w̃	w̃	PROPN
ejpam-3574	192	12	=	=	PUNCT
ejpam-3574	192	13			PROPN
ejpam-3574	192	14	k∏	k∏	NOUN
ejpam-3574	192	15	j=1	j=1	NOUN
ejpam-3574	192	16	(	(	PUNCT
ejpam-3574	192	17	i	i	PRON
ejpam-3574	192	18	+	+	CCONJ
ejpam-3574	192	19	uk−j+1u	uk−j+1u	PROPN
ejpam-3574	192	20	t	t	PROPN
ejpam-3574	192	21	k−j+1j	k−j+1j	PROPN
ejpam-3574	192	22	)	)	PUNCT
ejpam-3574	192	23	w	w	NOUN
ejpam-3574	192	24	,	,	PUNCT
ejpam-3574	192	25	where	where	SCONJ
ejpam-3574	192	26	each	each	DET
ejpam-3574	192	27	vector	vector	NOUN
ejpam-3574	192	28	uj	uj	PROPN
ejpam-3574	192	29	is	be	AUX
ejpam-3574	192	30	a	a	DET
ejpam-3574	192	31	column	column	NOUN
ejpam-3574	192	32	of	of	ADP
ejpam-3574	192	33	u	u	PROPN
ejpam-3574	192	34	.	.	PUNCT
ejpam-3574	193	1	therefore	therefore	ADV
ejpam-3574	193	2	1	1	X
ejpam-3574	193	3	)	)	PUNCT
ejpam-3574	193	4	if	if	SCONJ
ejpam-3574	193	5	λ	λ	X
ejpam-3574	193	6	/∈	/∈	PUNCT
ejpam-3574	193	7	{	{	PUNCT
ejpam-3574	193	8	−1	−1	NOUN
ejpam-3574	193	9	,	,	PUNCT
ejpam-3574	193	10	1	1	NUM
ejpam-3574	193	11	}	}	PUNCT
ejpam-3574	193	12	,	,	PUNCT
ejpam-3574	193	13	then	then	ADV
ejpam-3574	193	14	•	•	VERB
ejpam-3574	193	15	for	for	ADP
ejpam-3574	193	16	k	k	PROPN
ejpam-3574	193	17	<	<	X
ejpam-3574	193	18	l1	l1	PROPN
ejpam-3574	193	19	;	;	PUNCT
ejpam-3574	193	20	–	–	PUNCT
ejpam-3574	193	21	set	set	VERB
ejpam-3574	193	22	w̃1	w̃1	NOUN
ejpam-3574	193	23	=	=	PUNCT
ejpam-3574	193	24	(	(	PUNCT
ejpam-3574	193	25	i	i	PRON
ejpam-3574	193	26	+	+	CCONJ
ejpam-3574	194	1	u1u	u1u	PROPN
ejpam-3574	195	1	t	t	PROPN
ejpam-3574	195	2	1	1	NUM
ejpam-3574	195	3	j	j	PROPN
ejpam-3574	195	4	)	)	PUNCT
ejpam-3574	195	5	w	w	PROPN
ejpam-3574	195	6	.	.	PUNCT
ejpam-3574	196	1	according	accord	VERB
ejpam-3574	196	2	to	to	ADP
ejpam-3574	196	3	1	1	NUM
ejpam-3574	196	4	)	)	PUNCT
ejpam-3574	196	5	of	of	ADP
ejpam-3574	196	6	theorem	theorem	ADJ
ejpam-3574	196	7	7.1	7.1	NUM
ejpam-3574	196	8	of	of	ADP
ejpam-3574	196	9	[	[	X
ejpam-3574	196	10	16	16	NUM
ejpam-3574	196	11	]	]	PUNCT
ejpam-3574	196	12	,	,	PUNCT
ejpam-3574	196	13	w̃1	w̃1	PROPN
ejpam-3574	196	14	has	have	VERB
ejpam-3574	196	15	the	the	DET
ejpam-3574	196	16	jordan	jordan	PROPN
ejpam-3574	196	17	canonicall1−1⊕	canonicall1−1⊕	PROPN
ejpam-3574	197	1	j=1	j=1	PROPN
ejpam-3574	197	2	jn1(λ	jn1(λ	PROPN
ejpam-3574	197	3	)	)	PUNCT
ejpam-3574	198	1	⊕	⊕	PROPN
ejpam-3574	198	2			PROPN
ejpam-3574	198	3	l2⊕	l2⊕	PROPN
ejpam-3574	198	4	j=1	j=1	PROPN
ejpam-3574	198	5	jn2(λ	jn2(λ	PROPN
ejpam-3574	198	6	)	)	PUNCT
ejpam-3574	198	7	⊕	⊕	PROPN
ejpam-3574	198	8	·	·	PUNCT
ejpam-3574	198	9	·	·	PUNCT
ejpam-3574	198	10	·	·	PUNCT
ejpam-3574	199	1	⊕	⊕	NOUN
ejpam-3574	200	1			PROPN
ejpam-3574	200	2	lm⊕	lm⊕	PROPN
ejpam-3574	200	3	j=1	j=1	PROPN
ejpam-3574	200	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	200	5	)	)	PUNCT
ejpam-3574	200	6	⊕	⊕	PROPN
ejpam-3574	200	7	j̃1	j̃1	PROPN
ejpam-3574	200	8	,	,	PUNCT
ejpam-3574	200	9	where	where	SCONJ
ejpam-3574	200	10	j̃1	j̃1	PROPN
ejpam-3574	200	11	contains	contain	VERB
ejpam-3574	200	12	all	all	DET
ejpam-3574	200	13	the	the	DET
ejpam-3574	200	14	forms	form	NOUN
ejpam-3574	200	15	in	in	ADP
ejpam-3574	200	16	blocks	block	NOUN
ejpam-3574	200	17	of	of	ADP
ejpam-3574	200	18	jordan	jordan	PROPN
ejpam-3574	200	19	of	of	ADP
ejpam-3574	200	20	w̃1	w̃1	PROPN
ejpam-3574	200	21	associated	associate	VERB
ejpam-3574	200	22	with	with	ADP
ejpam-3574	200	23	eigenvalues	eigenvalue	NOUN
ejpam-3574	200	24	different	different	ADJ
ejpam-3574	200	25	from	from	ADP
ejpam-3574	200	26	λ	λ	PROPN
ejpam-3574	200	27	.	.	PUNCT
ejpam-3574	200	28	–	–	PUNCT
ejpam-3574	200	29	set	set	VERB
ejpam-3574	200	30	w̃2	w̃2	PROPN
ejpam-3574	200	31	=	=	PUNCT
ejpam-3574	200	32	(	(	PUNCT
ejpam-3574	200	33	i	i	PRON
ejpam-3574	200	34	+	+	CCONJ
ejpam-3574	200	35	u2u	u2u	ADJ
ejpam-3574	200	36	t	t	PROPN
ejpam-3574	200	37	2	2	NUM
ejpam-3574	200	38	j	j	NOUN
ejpam-3574	200	39	)	)	PUNCT
ejpam-3574	201	1	w̃1	w̃1	PROPN
ejpam-3574	201	2	.	.	PUNCT
ejpam-3574	202	1	according	accord	VERB
ejpam-3574	202	2	to	to	ADP
ejpam-3574	202	3	1	1	NUM
ejpam-3574	202	4	)	)	PUNCT
ejpam-3574	202	5	of	of	ADP
ejpam-3574	202	6	theorem	theorem	ADJ
ejpam-3574	202	7	7.1	7.1	NUM
ejpam-3574	202	8	of	of	ADP
ejpam-3574	202	9	[	[	X
ejpam-3574	202	10	16	16	NUM
ejpam-3574	202	11	]	]	PUNCT
ejpam-3574	202	12	,	,	PUNCT
ejpam-3574	202	13	w̃2	w̃2	PROPN
ejpam-3574	202	14	has	have	VERB
ejpam-3574	202	15	the	the	DET
ejpam-3574	202	16	jordan	jordan	PROPN
ejpam-3574	202	17	canonical	canonical	PROPN
ejpam-3574	203	1	forml1−2⊕	forml1−2⊕	ADP
ejpam-3574	203	2	j=1	j=1	PROPN
ejpam-3574	203	3	jn1(λ	jn1(λ	PROPN
ejpam-3574	203	4	)	)	PUNCT
ejpam-3574	203	5	⊕	⊕	PROPN
ejpam-3574	203	6			PROPN
ejpam-3574	203	7	l2⊕	l2⊕	PROPN
ejpam-3574	203	8	j=1	j=1	PROPN
ejpam-3574	203	9	jn2(λ	jn2(λ	PROPN
ejpam-3574	203	10	)	)	PUNCT
ejpam-3574	203	11	⊕	⊕	PROPN
ejpam-3574	203	12	·	·	PUNCT
ejpam-3574	203	13	·	·	PUNCT
ejpam-3574	203	14	·	·	PUNCT
ejpam-3574	203	15	⊕	⊕	NOUN
ejpam-3574	204	1			PROPN
ejpam-3574	204	2	lm⊕	lm⊕	PROPN
ejpam-3574	204	3	j=1	j=1	PROPN
ejpam-3574	204	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	204	5	)	)	PUNCT
ejpam-3574	204	6	⊕	⊕	PROPN
ejpam-3574	204	7	j̃2	j̃2	PROPN
ejpam-3574	204	8	,	,	PUNCT
ejpam-3574	204	9	with	with	ADP
ejpam-3574	204	10	j̃2	j̃2	PROPN
ejpam-3574	204	11	containing	contain	VERB
ejpam-3574	204	12	all	all	DET
ejpam-3574	204	13	the	the	DET
ejpam-3574	204	14	forms	form	NOUN
ejpam-3574	204	15	in	in	ADP
ejpam-3574	204	16	jordan	jordan	PROPN
ejpam-3574	204	17	blocks	block	NOUN
ejpam-3574	204	18	of	of	ADP
ejpam-3574	204	19	w̃2	w̃2	PROPN
ejpam-3574	204	20	associated	associate	VERB
ejpam-3574	204	21	with	with	ADP
ejpam-3574	204	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	204	23	different	different	ADJ
ejpam-3574	204	24	from	from	ADP
ejpam-3574	204	25	λ	λ	PROPN
ejpam-3574	204	26	.	.	PUNCT
ejpam-3574	204	27	–	–	PUNCT
ejpam-3574	204	28	on	on	ADP
ejpam-3574	204	29	the	the	DET
ejpam-3574	204	30	other	other	ADJ
ejpam-3574	204	31	hand	hand	NOUN
ejpam-3574	204	32	,	,	PUNCT
ejpam-3574	204	33	w̃k	w̃k	ADV
ejpam-3574	204	34	=	=	PUNCT
ejpam-3574	205	1	w	w	PUNCT
ejpam-3574	205	2	+	+	NOUN
ejpam-3574	205	3	b	b	NOUN
ejpam-3574	205	4	=	=	SYM
ejpam-3574	205	5	(	(	PUNCT
ejpam-3574	205	6	i	i	PRON
ejpam-3574	205	7	+	+	NUM
ejpam-3574	205	8	uku	uku	PROPN
ejpam-3574	205	9	t	t	PROPN
ejpam-3574	205	10	k	k	PROPN
ejpam-3574	205	11	j	j	PROPN
ejpam-3574	205	12	)	)	PUNCT
ejpam-3574	206	1	(	(	PUNCT
ejpam-3574	206	2	i	i	PRON
ejpam-3574	206	3	+	+	CCONJ
ejpam-3574	207	1	uk−1u	uk−1u	NUM
ejpam-3574	207	2	t	t	NOUN
ejpam-3574	207	3	k−1j	k−1j	NOUN
ejpam-3574	207	4	)	)	PUNCT
ejpam-3574	207	5	×	×	NOUN
ejpam-3574	207	6	...	...	PUNCT
ejpam-3574	207	7	×	×	NOUN
ejpam-3574	208	1	(	(	PUNCT
ejpam-3574	208	2	i	i	PRON
ejpam-3574	208	3	+	+	CCONJ
ejpam-3574	208	4	u3u	u3u	PROPN
ejpam-3574	208	5	t	t	PROPN
ejpam-3574	208	6	3	3	NUM
ejpam-3574	208	7	j	j	PROPN
ejpam-3574	208	8	)	)	PUNCT
ejpam-3574	208	9	w̃2	w̃2	PROPN
ejpam-3574	208	10	,	,	PUNCT
ejpam-3574	208	11	m.	m.	NOUN
ejpam-3574	208	12	dosso	dosso	PROPN
ejpam-3574	208	13	,	,	PUNCT
ejpam-3574	208	14	t.	t.	PROPN
ejpam-3574	208	15	g.	g.	PROPN
ejpam-3574	208	16	y.	y.	PROPN
ejpam-3574	208	17	arouna	arouna	PROPN
ejpam-3574	208	18	,	,	PUNCT
ejpam-3574	208	19	j.-c	j.-c	PROPN
ejpam-3574	208	20	.	.	PUNCT
ejpam-3574	209	1	koua	koua	PROPN
ejpam-3574	209	2	brou	brou	PROPN
ejpam-3574	209	3	/	/	SYM
ejpam-3574	209	4	eur	eur	PROPN
ejpam-3574	209	5	.	.	PUNCT
ejpam-3574	210	1	j.	j.	PROPN
ejpam-3574	210	2	pure	pure	PROPN
ejpam-3574	210	3	appl	appl	PROPN
ejpam-3574	210	4	.	.	PROPN
ejpam-3574	210	5	math	math	PROPN
ejpam-3574	210	6	,	,	PUNCT
ejpam-3574	210	7	12	12	NUM
ejpam-3574	210	8	(	(	PUNCT
ejpam-3574	210	9	4	4	NUM
ejpam-3574	210	10	)	)	PUNCT
ejpam-3574	210	11	(	(	PUNCT
ejpam-3574	210	12	2019	2019	NUM
ejpam-3574	210	13	)	)	PUNCT
ejpam-3574	210	14	,	,	PUNCT
ejpam-3574	210	15	1744	1744	NUM
ejpam-3574	210	16	-	-	SYM
ejpam-3574	210	17	1770	1770	NUM
ejpam-3574	210	18	1752	1752	NUM
ejpam-3574	210	19	by	by	ADP
ejpam-3574	210	20	applying	apply	VERB
ejpam-3574	210	21	(	(	PUNCT
ejpam-3574	210	22	k	k	PROPN
ejpam-3574	210	23	−	−	PROPN
ejpam-3574	210	24	2)-times	2)-times	NUM
ejpam-3574	210	25	1	1	NUM
ejpam-3574	210	26	)	)	PUNCT
ejpam-3574	210	27	of	of	ADP
ejpam-3574	210	28	theorem	theorem	ADJ
ejpam-3574	210	29	7.1	7.1	NUM
ejpam-3574	210	30	of	of	ADP
ejpam-3574	210	31	[	[	X
ejpam-3574	210	32	16	16	NUM
ejpam-3574	210	33	]	]	PUNCT
ejpam-3574	210	34	to	to	ADP
ejpam-3574	210	35	the	the	DET
ejpam-3574	210	36	matrix	matrix	NOUN
ejpam-3574	210	37	w̃2	w̃2	PROPN
ejpam-3574	210	38	,	,	PUNCT
ejpam-3574	210	39	we	we	PRON
ejpam-3574	210	40	get	get	VERB
ejpam-3574	210	41	that	that	DET
ejpam-3574	210	42	w̃k	w̃k	PRON
ejpam-3574	210	43	has	have	VERB
ejpam-3574	210	44	the	the	DET
ejpam-3574	210	45	following	follow	VERB
ejpam-3574	210	46	jordan	jordan	PROPN
ejpam-3574	210	47	canonical	canonical	ADJ
ejpam-3574	210	48	form	form	NOUN
ejpam-3574	210	49	:	:	PUNCT
ejpam-3574	210	50	l1−k⊕	l1−k⊕	X
ejpam-3574	210	51	j=1	j=1	PROPN
ejpam-3574	210	52	jn1(λ	jn1(λ	PROPN
ejpam-3574	210	53	)	)	PUNCT
ejpam-3574	211	1	⊕	⊕	PROPN
ejpam-3574	211	2			PROPN
ejpam-3574	211	3	l2⊕	l2⊕	PROPN
ejpam-3574	211	4	j=1	j=1	PROPN
ejpam-3574	211	5	jn2(λ	jn2(λ	PROPN
ejpam-3574	211	6	)	)	PUNCT
ejpam-3574	211	7	⊕	⊕	PROPN
ejpam-3574	211	8	·	·	PUNCT
ejpam-3574	211	9	·	·	PUNCT
ejpam-3574	211	10	·	·	PUNCT
ejpam-3574	212	1	⊕	⊕	NOUN
ejpam-3574	213	1			PROPN
ejpam-3574	213	2	lm⊕	lm⊕	PROPN
ejpam-3574	213	3	j=1	j=1	PROPN
ejpam-3574	213	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	213	5	)	)	PUNCT
ejpam-3574	214	1	⊕	⊕	PROPN
ejpam-3574	214	2	j̃	j̃	PROPN
ejpam-3574	214	3	,	,	PUNCT
ejpam-3574	214	4	where	where	SCONJ
ejpam-3574	214	5	j̃	j̃	PROPN
ejpam-3574	214	6	=	=	SYM
ejpam-3574	214	7	j̃k	j̃k	PROPN
ejpam-3574	214	8	contains	contain	VERB
ejpam-3574	214	9	all	all	DET
ejpam-3574	214	10	the	the	DET
ejpam-3574	214	11	forms	form	NOUN
ejpam-3574	214	12	in	in	ADP
ejpam-3574	214	13	jordan	jordan	PROPN
ejpam-3574	214	14	blocks	block	NOUN
ejpam-3574	214	15	of	of	ADP
ejpam-3574	214	16	w	w	PROPN
ejpam-3574	214	17	+	+	PROPN
ejpam-3574	214	18	b	b	NOUN
ejpam-3574	214	19	associated	associate	VERB
ejpam-3574	214	20	with	with	ADP
ejpam-3574	214	21	eigenvalues	eigenvalue	NOUN
ejpam-3574	214	22	different	different	ADJ
ejpam-3574	214	23	from	from	ADP
ejpam-3574	214	24	λ	λ	PROPN
ejpam-3574	214	25	.	.	PROPN
ejpam-3574	214	26	•	•	NUM
ejpam-3574	214	27	for	for	ADP
ejpam-3574	214	28	k	k	NOUN
ejpam-3574	214	29	=	=	PUNCT
ejpam-3574	214	30	i−1∑	i−1∑	NOUN
ejpam-3574	214	31	s=1	s=1	PUNCT
ejpam-3574	214	32	ls	ls	X
ejpam-3574	215	1	+	+	X
ejpam-3574	215	2	ki	ki	PROPN
ejpam-3574	215	3	,	,	PUNCT
ejpam-3574	215	4	with	with	ADP
ejpam-3574	215	5	ki	ki	PROPN
ejpam-3574	215	6	<	<	X
ejpam-3574	215	7	li	li	PROPN
ejpam-3574	216	1	:	:	PUNCT
ejpam-3574	216	2	–	–	PUNCT
ejpam-3574	216	3	i	i	NOUN
ejpam-3574	216	4	=	=	NOUN
ejpam-3574	216	5	2	2	NUM
ejpam-3574	216	6	,	,	PUNCT
ejpam-3574	216	7	we	we	PRON
ejpam-3574	216	8	have	have	VERB
ejpam-3574	216	9	k	k	PROPN
ejpam-3574	216	10	=	=	PROPN
ejpam-3574	216	11	l1	l1	PROPN
ejpam-3574	216	12	+	+	CCONJ
ejpam-3574	216	13	k2	k2	PROPN
ejpam-3574	216	14	with	with	ADP
ejpam-3574	216	15	k2	k2	ADJ
ejpam-3574	216	16	<	<	X
ejpam-3574	216	17	l2	l2	NOUN
ejpam-3574	216	18	.	.	PUNCT
ejpam-3574	217	1	we	we	PRON
ejpam-3574	217	2	know	know	VERB
ejpam-3574	217	3	that	that	SCONJ
ejpam-3574	217	4	w̃k	w̃k	ADV
ejpam-3574	218	1	=	=	PUNCT
ejpam-3574	219	1	(	(	PUNCT
ejpam-3574	219	2	i	i	PRON
ejpam-3574	219	3	+	+	CCONJ
ejpam-3574	219	4	uku	uku	PROPN
ejpam-3574	219	5	t	t	PROPN
ejpam-3574	219	6	k	k	PROPN
ejpam-3574	219	7	j	j	PROPN
ejpam-3574	219	8	)	)	PUNCT
ejpam-3574	219	9	(	(	PUNCT
ejpam-3574	219	10	i	i	PRON
ejpam-3574	219	11	+	+	CCONJ
ejpam-3574	220	1	uk−1u	uk−1u	NUM
ejpam-3574	220	2	t	t	NOUN
ejpam-3574	220	3	k−1j	k−1j	NOUN
ejpam-3574	220	4	)	)	PUNCT
ejpam-3574	220	5	×	×	NOUN
ejpam-3574	220	6	...	...	PUNCT
ejpam-3574	220	7	×	×	NOUN
ejpam-3574	221	1	(	(	PUNCT
ejpam-3574	221	2	i	i	PRON
ejpam-3574	221	3	+	+	CCONJ
ejpam-3574	221	4	ul1	ul1	PROPN
ejpam-3574	221	5	+	+	PROPN
ejpam-3574	221	6	1u	1u	NUM
ejpam-3574	221	7	t	t	PROPN
ejpam-3574	221	8	l1	l1	PROPN
ejpam-3574	221	9	+	+	PROPN
ejpam-3574	221	10	1j	1j	NUM
ejpam-3574	221	11	)	)	PUNCT
ejpam-3574	221	12	×	×	NOUN
ejpam-3574	221	13	(	(	PUNCT
ejpam-3574	221	14	i	i	PRON
ejpam-3574	221	15	+	+	CCONJ
ejpam-3574	222	1	ul1u	ul1u	PROPN
ejpam-3574	222	2	t	t	X
ejpam-3574	222	3	l1j	l1j	PROPN
ejpam-3574	222	4	)	)	PUNCT
ejpam-3574	223	1	(	(	PUNCT
ejpam-3574	223	2	i	i	PRON
ejpam-3574	223	3	+	+	CCONJ
ejpam-3574	224	1	ul1−1u	ul1−1u	PROPN
ejpam-3574	224	2	t	t	PROPN
ejpam-3574	224	3	l1−1j	l1−1j	PROPN
ejpam-3574	224	4	)	)	PUNCT
ejpam-3574	224	5	×	×	NOUN
ejpam-3574	224	6	...	...	PUNCT
ejpam-3574	225	1	×	×	NOUN
ejpam-3574	225	2	(	(	PUNCT
ejpam-3574	225	3	i	i	PRON
ejpam-3574	225	4	+	+	CCONJ
ejpam-3574	225	5	u1u	u1u	PROPN
ejpam-3574	225	6	t	t	PROPN
ejpam-3574	225	7	1	1	NUM
ejpam-3574	225	8	j	j	PROPN
ejpam-3574	225	9	)	)	PUNCT
ejpam-3574	225	10	w︸	w︸	VERB
ejpam-3574	225	11	︷︷	︷︷	PROPN
ejpam-3574	225	12	︸	︸	X
ejpam-3574	225	13	w̃l1	w̃l1	NOUN
ejpam-3574	225	14	=	=	SYM
ejpam-3574	226	1	(	(	PUNCT
ejpam-3574	226	2	i	i	PRON
ejpam-3574	226	3	+	+	CCONJ
ejpam-3574	226	4	uku	uku	PROPN
ejpam-3574	226	5	t	t	PROPN
ejpam-3574	226	6	k	k	PROPN
ejpam-3574	226	7	j	j	PROPN
ejpam-3574	226	8	)	)	PUNCT
ejpam-3574	227	1	(	(	PUNCT
ejpam-3574	227	2	i	i	PRON
ejpam-3574	227	3	+	+	CCONJ
ejpam-3574	228	1	uk−1u	uk−1u	NUM
ejpam-3574	228	2	t	t	NOUN
ejpam-3574	228	3	k−1j	k−1j	NOUN
ejpam-3574	228	4	)	)	PUNCT
ejpam-3574	228	5	×	×	NOUN
ejpam-3574	228	6	...	...	PUNCT
ejpam-3574	228	7	×	×	NOUN
ejpam-3574	229	1	(	(	PUNCT
ejpam-3574	229	2	i	i	PRON
ejpam-3574	229	3	+	+	CCONJ
ejpam-3574	229	4	ul1	ul1	PROPN
ejpam-3574	229	5	+	+	PROPN
ejpam-3574	229	6	1u	1u	NUM
ejpam-3574	229	7	t	t	PROPN
ejpam-3574	229	8	l1	l1	PROPN
ejpam-3574	229	9	+	+	PROPN
ejpam-3574	229	10	1j	1j	NUM
ejpam-3574	229	11	)	)	PUNCT
ejpam-3574	229	12	w̃l1	w̃l1	NOUN
ejpam-3574	229	13	=	=	SYM
ejpam-3574	229	14	(	(	PUNCT
ejpam-3574	229	15	i	i	PRON
ejpam-3574	229	16	+	+	CCONJ
ejpam-3574	229	17	uku	uku	PROPN
ejpam-3574	229	18	t	t	PROPN
ejpam-3574	229	19	k	k	PROPN
ejpam-3574	229	20	j	j	PROPN
ejpam-3574	229	21	)	)	PUNCT
ejpam-3574	230	1	(	(	PUNCT
ejpam-3574	230	2	i	i	PRON
ejpam-3574	230	3	+	+	CCONJ
ejpam-3574	231	1	uk−1u	uk−1u	NUM
ejpam-3574	231	2	t	t	NOUN
ejpam-3574	231	3	k−1j	k−1j	NOUN
ejpam-3574	231	4	)	)	PUNCT
ejpam-3574	231	5	×	×	NOUN
ejpam-3574	231	6	...	...	PUNCT
ejpam-3574	231	7	×	×	NOUN
ejpam-3574	232	1	(	(	PUNCT
ejpam-3574	232	2	i	i	PRON
ejpam-3574	232	3	+	+	X
ejpam-3574	232	4	uk−k2	uk−k2	PROPN
ejpam-3574	232	5	+	+	ADJ
ejpam-3574	232	6	1u	1u	NUM
ejpam-3574	232	7	t	t	NOUN
ejpam-3574	232	8	k−k2	k−k2	X
ejpam-3574	232	9	+	+	PROPN
ejpam-3574	232	10	1j	1j	NUM
ejpam-3574	232	11	)	)	PUNCT
ejpam-3574	232	12	w̃l1	w̃l1	NOUN
ejpam-3574	232	13	,	,	PUNCT
ejpam-3574	232	14	because	because	SCONJ
ejpam-3574	232	15	l1	l1	PROPN
ejpam-3574	232	16	=	=	PROPN
ejpam-3574	232	17	k	k	PROPN
ejpam-3574	232	18	−	−	PROPN
ejpam-3574	232	19	k2	k2	PROPN
ejpam-3574	232	20	.	.	PUNCT
ejpam-3574	233	1	as	as	SCONJ
ejpam-3574	233	2	w̃l1	w̃l1	PROPN
ejpam-3574	233	3	has	have	VERB
ejpam-3574	233	4	the	the	DET
ejpam-3574	233	5	following	follow	VERB
ejpam-3574	233	6	jordan	jordan	PROPN
ejpam-3574	233	7	canonical	canonical	ADJ
ejpam-3574	233	8	form	form	NOUN
ejpam-3574	233	9	:	:	PUNCT
ejpam-3574	233	10			PROPN
ejpam-3574	233	11	l2⊕	l2⊕	PROPN
ejpam-3574	233	12	j=1	j=1	PROPN
ejpam-3574	233	13	jn2(λ	jn2(λ	PROPN
ejpam-3574	233	14	)	)	PUNCT
ejpam-3574	233	15	⊕	⊕	PROPN
ejpam-3574	234	1	·	·	PUNCT
ejpam-3574	234	2	·	·	PUNCT
ejpam-3574	234	3	·	·	PUNCT
ejpam-3574	234	4	⊕	⊕	NOUN
ejpam-3574	235	1			PROPN
ejpam-3574	235	2	lm⊕	lm⊕	PROPN
ejpam-3574	235	3	j=1	j=1	PROPN
ejpam-3574	235	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	235	5	)	)	PUNCT
ejpam-3574	235	6	⊕	⊕	PROPN
ejpam-3574	235	7	j̃l1	j̃l1	PROPN
ejpam-3574	235	8	,	,	PUNCT
ejpam-3574	235	9	where	where	SCONJ
ejpam-3574	235	10	j̃l1	j̃l1	PROPN
ejpam-3574	235	11	contains	contain	VERB
ejpam-3574	235	12	all	all	DET
ejpam-3574	235	13	the	the	DET
ejpam-3574	235	14	forms	form	NOUN
ejpam-3574	235	15	in	in	ADP
ejpam-3574	235	16	jordan	jordan	PROPN
ejpam-3574	235	17	blocks	block	NOUN
ejpam-3574	235	18	of	of	ADP
ejpam-3574	235	19	w̃l1	w̃l1	NOUN
ejpam-3574	235	20	associated	associate	VERB
ejpam-3574	235	21	with	with	ADP
ejpam-3574	235	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	235	23	different	different	ADJ
ejpam-3574	235	24	from	from	ADP
ejpam-3574	235	25	λ	λ	PROPN
ejpam-3574	235	26	because	because	SCONJ
ejpam-3574	235	27	w̃k	w̃k	PRON
ejpam-3574	235	28	is	be	AUX
ejpam-3574	235	29	a	a	DET
ejpam-3574	235	30	rang	ring	VERB
ejpam-3574	235	31	-	-	PUNCT
ejpam-3574	235	32	k2	k2	NOUN
ejpam-3574	235	33	perturbation	perturbation	NOUN
ejpam-3574	235	34	of	of	ADP
ejpam-3574	235	35	w̃l1	w̃l1	PROPN
ejpam-3574	235	36	,	,	PUNCT
ejpam-3574	235	37	then	then	ADV
ejpam-3574	235	38	w̃k	w̃k	PRON
ejpam-3574	235	39	has	have	VERB
ejpam-3574	235	40	the	the	DET
ejpam-3574	235	41	following	follow	VERB
ejpam-3574	235	42	jordan	jordan	PROPN
ejpam-3574	235	43	canonical	canonical	ADJ
ejpam-3574	235	44	form	form	NOUN
ejpam-3574	235	45	:	:	PUNCT
ejpam-3574	235	46	l2−k2⊕	l2−k2⊕	NOUN
ejpam-3574	235	47	j=1	j=1	PROPN
ejpam-3574	235	48	jn2(λ	jn2(λ	PROPN
ejpam-3574	235	49	)	)	PUNCT
ejpam-3574	235	50			PUNCT
ejpam-3574	236	1	l3⊕	l3⊕	PROPN
ejpam-3574	236	2	j=1	j=1	PROPN
ejpam-3574	236	3	jn3(λ	jn3(λ	PROPN
ejpam-3574	236	4	)	)	PUNCT
ejpam-3574	236	5	⊕	⊕	PROPN
ejpam-3574	236	6	·	·	PUNCT
ejpam-3574	236	7	·	·	PUNCT
ejpam-3574	236	8	·	·	PUNCT
ejpam-3574	236	9	⊕	⊕	NOUN
ejpam-3574	237	1			PROPN
ejpam-3574	237	2	lm⊕	lm⊕	PROPN
ejpam-3574	237	3	j=1	j=1	PROPN
ejpam-3574	237	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	237	5	)	)	PUNCT
ejpam-3574	237	6	⊕	⊕	PROPN
ejpam-3574	237	7	j̃k2	j̃k2	PROPN
ejpam-3574	237	8	,	,	PUNCT
ejpam-3574	237	9	where	where	SCONJ
ejpam-3574	237	10	j̃k2	j̃k2	NOUN
ejpam-3574	237	11	contains	contain	VERB
ejpam-3574	237	12	all	all	DET
ejpam-3574	237	13	the	the	DET
ejpam-3574	237	14	forms	form	NOUN
ejpam-3574	237	15	in	in	ADP
ejpam-3574	237	16	jordan	jordan	PROPN
ejpam-3574	237	17	blocks	block	NOUN
ejpam-3574	237	18	of	of	ADP
ejpam-3574	237	19	w̃k	w̃k	NOUN
ejpam-3574	237	20	=	=	SYM
ejpam-3574	237	21	w+b	w+b	NOUN
ejpam-3574	237	22	associated	associate	VERB
ejpam-3574	237	23	with	with	ADP
ejpam-3574	237	24	eigenvalues	eigenvalue	NOUN
ejpam-3574	237	25	different	different	ADJ
ejpam-3574	237	26	from	from	ADP
ejpam-3574	237	27	λ	λ	PROPN
ejpam-3574	237	28	.	.	PUNCT
ejpam-3574	237	29	–	–	PUNCT
ejpam-3574	237	30	i	i	PRON
ejpam-3574	237	31	>	>	X
ejpam-3574	237	32	2	2	NUM
ejpam-3574	237	33	,	,	PUNCT
ejpam-3574	237	34	k	k	NOUN
ejpam-3574	237	35	=	=	PUNCT
ejpam-3574	237	36	i−1∑	i−1∑	NOUN
ejpam-3574	237	37	s=1	s=1	PUNCT
ejpam-3574	237	38	ls	ls	X
ejpam-3574	238	1	+	+	X
ejpam-3574	238	2	ki	ki	PROPN
ejpam-3574	238	3	,	,	PUNCT
ejpam-3574	238	4	with	with	ADP
ejpam-3574	238	5	ki	ki	PROPN
ejpam-3574	238	6	<	<	X
ejpam-3574	238	7	li	li	PROPN
ejpam-3574	238	8	.	.	PROPN
ejpam-3574	238	9	set	set	PROPN
ejpam-3574	238	10	γ(i	γ(i	NOUN
ejpam-3574	238	11	)	)	PUNCT
ejpam-3574	239	1	=	=	SYM
ejpam-3574	239	2	i∑	i∑	NOUN
ejpam-3574	240	1	s=1	s=1	SYM
ejpam-3574	240	2	ls	ls	ADJ
ejpam-3574	240	3	,	,	PUNCT
ejpam-3574	240	4	∀	∀	VERB
ejpam-3574	241	1	i	i	PRON
ejpam-3574	241	2	≥	≥	VERB
ejpam-3574	241	3	1	1	NUM
ejpam-3574	241	4	.	.	PUNCT
ejpam-3574	241	5	m.	m.	NOUN
ejpam-3574	241	6	dosso	dosso	PROPN
ejpam-3574	241	7	,	,	PUNCT
ejpam-3574	241	8	t.	t.	PROPN
ejpam-3574	241	9	g.	g.	PROPN
ejpam-3574	241	10	y.	y.	PROPN
ejpam-3574	241	11	arouna	arouna	PROPN
ejpam-3574	241	12	,	,	PUNCT
ejpam-3574	241	13	j.-c	j.-c	PROPN
ejpam-3574	241	14	.	.	PUNCT
ejpam-3574	242	1	koua	koua	PROPN
ejpam-3574	242	2	brou	brou	PROPN
ejpam-3574	242	3	/	/	SYM
ejpam-3574	242	4	eur	eur	PROPN
ejpam-3574	242	5	.	.	PUNCT
ejpam-3574	243	1	j.	j.	PROPN
ejpam-3574	243	2	pure	pure	PROPN
ejpam-3574	243	3	appl	appl	PROPN
ejpam-3574	243	4	.	.	PROPN
ejpam-3574	243	5	math	math	PROPN
ejpam-3574	243	6	,	,	PUNCT
ejpam-3574	243	7	12	12	NUM
ejpam-3574	243	8	(	(	PUNCT
ejpam-3574	243	9	4	4	NUM
ejpam-3574	243	10	)	)	PUNCT
ejpam-3574	243	11	(	(	PUNCT
ejpam-3574	243	12	2019	2019	NUM
ejpam-3574	243	13	)	)	PUNCT
ejpam-3574	243	14	,	,	PUNCT
ejpam-3574	243	15	1744	1744	NUM
ejpam-3574	243	16	-	-	SYM
ejpam-3574	243	17	1770	1770	NUM
ejpam-3574	243	18	1753	1753	NUM
ejpam-3574	243	19	we	we	PRON
ejpam-3574	243	20	have	have	VERB
ejpam-3574	243	21	w̃k	w̃k	PRON
ejpam-3574	243	22	=	=	PUNCT
ejpam-3574	243	23	(	(	PUNCT
ejpam-3574	243	24	i	i	PRON
ejpam-3574	243	25	+	+	CCONJ
ejpam-3574	243	26	uku	uku	PROPN
ejpam-3574	243	27	t	t	PROPN
ejpam-3574	243	28	k	k	PROPN
ejpam-3574	243	29	j	j	PROPN
ejpam-3574	243	30	)	)	PUNCT
ejpam-3574	244	1	(	(	PUNCT
ejpam-3574	244	2	i	i	PRON
ejpam-3574	244	3	+	+	CCONJ
ejpam-3574	245	1	uk−1u	uk−1u	NUM
ejpam-3574	245	2	t	t	NOUN
ejpam-3574	245	3	k−1j	k−1j	NOUN
ejpam-3574	245	4	)	)	PUNCT
ejpam-3574	245	5	×	×	NOUN
ejpam-3574	245	6	·	·	PUNCT
ejpam-3574	245	7	·	·	PUNCT
ejpam-3574	245	8	·	·	PUNCT
ejpam-3574	246	1	×	×	NOUN
ejpam-3574	246	2	(	(	PUNCT
ejpam-3574	246	3	i	i	PRON
ejpam-3574	246	4	+	+	CCONJ
ejpam-3574	246	5	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	246	6	t	t	NOUN
ejpam-3574	246	7	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	246	8	)	)	PUNCT
ejpam-3574	246	9	×	×	NOUN
ejpam-3574	246	10	(	(	PUNCT
ejpam-3574	246	11	i	i	PRON
ejpam-3574	246	12	+	+	CCONJ
ejpam-3574	246	13	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	246	14	t	t	X
ejpam-3574	246	15	γ(i−1)j	γ(i−1)j	NOUN
ejpam-3574	246	16	)	)	PUNCT
ejpam-3574	246	17	×	×	PROPN
ejpam-3574	246	18	·	·	PUNCT
ejpam-3574	246	19	·	·	PUNCT
ejpam-3574	246	20	·	·	PUNCT
ejpam-3574	247	1	×	×	NOUN
ejpam-3574	247	2	(	(	PUNCT
ejpam-3574	247	3	i	i	PRON
ejpam-3574	247	4	+	+	NUM
ejpam-3574	247	5	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	247	6	t	t	NOUN
ejpam-3574	247	7	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	247	8	)	)	PUNCT
ejpam-3574	248	1	(	(	PUNCT
ejpam-3574	248	2	i	i	PRON
ejpam-3574	248	3	+	+	NUM
ejpam-3574	248	4	uγ(3)u	uγ(3)u	PROPN
ejpam-3574	248	5	t	t	NOUN
ejpam-3574	248	6	γ(3)j	γ(3)j	NUM
ejpam-3574	248	7	)	)	PUNCT
ejpam-3574	248	8	×	×	NOUN
ejpam-3574	248	9	·	·	PUNCT
ejpam-3574	248	10	·	·	PUNCT
ejpam-3574	248	11	·	·	PUNCT
ejpam-3574	249	1	×	×	NOUN
ejpam-3574	249	2	(	(	PUNCT
ejpam-3574	249	3	i	i	PRON
ejpam-3574	249	4	+	+	X
ejpam-3574	249	5	uγ(2)+1u	uγ(2)+1u	PROPN
ejpam-3574	249	6	t	t	NOUN
ejpam-3574	249	7	γ(2)+1j	γ(2)+1j	NOUN
ejpam-3574	249	8	)	)	PUNCT
ejpam-3574	250	1	(	(	PUNCT
ejpam-3574	250	2	i	i	PRON
ejpam-3574	250	3	+	+	NUM
ejpam-3574	250	4	uγ(2)u	uγ(2)u	PROPN
ejpam-3574	250	5	t	t	NOUN
ejpam-3574	250	6	γ(2)j	γ(2)j	PRON
ejpam-3574	250	7	)	)	PUNCT
ejpam-3574	250	8	×	×	NOUN
ejpam-3574	250	9	·	·	PUNCT
ejpam-3574	250	10	·	·	PUNCT
ejpam-3574	250	11	·	·	PUNCT
ejpam-3574	251	1	×	×	NOUN
ejpam-3574	251	2	(	(	PUNCT
ejpam-3574	251	3	i	i	PRON
ejpam-3574	251	4	+	+	CCONJ
ejpam-3574	251	5	u1u	u1u	PROPN
ejpam-3574	251	6	t	t	PROPN
ejpam-3574	251	7	1	1	NUM
ejpam-3574	251	8	j	j	PROPN
ejpam-3574	251	9	)	)	PUNCT
ejpam-3574	251	10	w︸	w︸	VERB
ejpam-3574	251	11	︷︷	︷︷	PROPN
ejpam-3574	251	12	︸	︸	PRON
ejpam-3574	251	13	w̃γ(2	w̃γ(2	PROPN
ejpam-3574	251	14	)	)	PUNCT
ejpam-3574	251	15	=	=	PRON
ejpam-3574	252	1	(	(	PUNCT
ejpam-3574	252	2	i	i	PRON
ejpam-3574	252	3	+	+	CCONJ
ejpam-3574	252	4	uku	uku	PROPN
ejpam-3574	252	5	t	t	PROPN
ejpam-3574	252	6	k	k	PROPN
ejpam-3574	252	7	j	j	PROPN
ejpam-3574	252	8	)	)	PUNCT
ejpam-3574	253	1	(	(	PUNCT
ejpam-3574	253	2	i	i	PRON
ejpam-3574	253	3	+	+	CCONJ
ejpam-3574	254	1	uk−1u	uk−1u	NUM
ejpam-3574	254	2	t	t	NOUN
ejpam-3574	254	3	k−1j	k−1j	NOUN
ejpam-3574	254	4	)	)	PUNCT
ejpam-3574	254	5	×	×	NOUN
ejpam-3574	254	6	·	·	PUNCT
ejpam-3574	254	7	·	·	PUNCT
ejpam-3574	254	8	·	·	PUNCT
ejpam-3574	255	1	×	×	NOUN
ejpam-3574	255	2	(	(	PUNCT
ejpam-3574	255	3	i	i	PRON
ejpam-3574	255	4	+	+	CCONJ
ejpam-3574	255	5	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	255	6	t	t	NOUN
ejpam-3574	255	7	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	255	8	)	)	PUNCT
ejpam-3574	255	9	×	×	NOUN
ejpam-3574	255	10	(	(	PUNCT
ejpam-3574	255	11	i	i	PRON
ejpam-3574	255	12	+	+	CCONJ
ejpam-3574	255	13	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	255	14	t	t	X
ejpam-3574	255	15	γ(i−1)j	γ(i−1)j	NOUN
ejpam-3574	255	16	)	)	PUNCT
ejpam-3574	255	17	×	×	PROPN
ejpam-3574	255	18	·	·	PUNCT
ejpam-3574	255	19	·	·	PUNCT
ejpam-3574	255	20	·	·	PUNCT
ejpam-3574	256	1	×	×	NOUN
ejpam-3574	256	2	(	(	PUNCT
ejpam-3574	256	3	i	i	PRON
ejpam-3574	256	4	+	+	NUM
ejpam-3574	256	5	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	256	6	t	t	NOUN
ejpam-3574	256	7	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	256	8	)	)	PUNCT
ejpam-3574	256	9	×	×	NOUN
ejpam-3574	256	10	(	(	PUNCT
ejpam-3574	256	11	i	i	PRON
ejpam-3574	256	12	+	+	NUM
ejpam-3574	256	13	uγ(3)u	uγ(3)u	PROPN
ejpam-3574	256	14	t	t	NOUN
ejpam-3574	256	15	γ(3)j	γ(3)j	NUM
ejpam-3574	256	16	)	)	PUNCT
ejpam-3574	256	17	×	×	NOUN
ejpam-3574	256	18	·	·	PUNCT
ejpam-3574	256	19	·	·	PUNCT
ejpam-3574	256	20	·	·	PUNCT
ejpam-3574	257	1	×	×	NOUN
ejpam-3574	257	2	(	(	PUNCT
ejpam-3574	257	3	i	i	PRON
ejpam-3574	257	4	+	+	X
ejpam-3574	257	5	uγ(2)+1u	uγ(2)+1u	PROPN
ejpam-3574	257	6	t	t	NOUN
ejpam-3574	257	7	γ(2)+1j	γ(2)+1j	NOUN
ejpam-3574	257	8	)	)	PUNCT
ejpam-3574	257	9	w̃γ(2)︸	w̃γ(2)︸	VERB
ejpam-3574	257	10	︷︷	︷︷	PROPN
ejpam-3574	257	11	︸	︸	ADP
ejpam-3574	257	12	w̃γ(3	w̃γ(3	PROPN
ejpam-3574	257	13	)	)	PUNCT
ejpam-3574	257	14	=	=	NOUN
ejpam-3574	258	1	(	(	PUNCT
ejpam-3574	258	2	i	i	PRON
ejpam-3574	258	3	+	+	CCONJ
ejpam-3574	258	4	uku	uku	PROPN
ejpam-3574	258	5	t	t	PROPN
ejpam-3574	258	6	k	k	PROPN
ejpam-3574	258	7	j	j	PROPN
ejpam-3574	258	8	)	)	PUNCT
ejpam-3574	259	1	(	(	PUNCT
ejpam-3574	259	2	i	i	PRON
ejpam-3574	259	3	+	+	CCONJ
ejpam-3574	260	1	uk−1u	uk−1u	NUM
ejpam-3574	260	2	t	t	NOUN
ejpam-3574	260	3	k−1j	k−1j	NOUN
ejpam-3574	260	4	)	)	PUNCT
ejpam-3574	260	5	×	×	NOUN
ejpam-3574	260	6	·	·	PUNCT
ejpam-3574	260	7	·	·	PUNCT
ejpam-3574	260	8	·	·	PUNCT
ejpam-3574	261	1	×	×	NOUN
ejpam-3574	261	2	(	(	PUNCT
ejpam-3574	261	3	i	i	PRON
ejpam-3574	261	4	+	+	CCONJ
ejpam-3574	261	5	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	261	6	t	t	NOUN
ejpam-3574	261	7	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	261	8	)	)	PUNCT
ejpam-3574	261	9	×	×	NOUN
ejpam-3574	261	10	(	(	PUNCT
ejpam-3574	261	11	i	i	PRON
ejpam-3574	261	12	+	+	CCONJ
ejpam-3574	261	13	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	261	14	t	t	X
ejpam-3574	261	15	γ(i−1)j	γ(i−1)j	NOUN
ejpam-3574	261	16	)	)	PUNCT
ejpam-3574	261	17	×	×	PROPN
ejpam-3574	261	18	·	·	PUNCT
ejpam-3574	261	19	·	·	PUNCT
ejpam-3574	261	20	·	·	PUNCT
ejpam-3574	262	1	×	×	NOUN
ejpam-3574	262	2	(	(	PUNCT
ejpam-3574	262	3	i	i	PRON
ejpam-3574	262	4	+	+	NUM
ejpam-3574	262	5	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	262	6	t	t	NOUN
ejpam-3574	262	7	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	262	8	)	)	PUNCT
ejpam-3574	262	9	w̃γ(3)︸	w̃γ(3)︸	VERB
ejpam-3574	262	10	︷︷	︷︷	PROPN
ejpam-3574	262	11	︸	︸	X
ejpam-3574	262	12	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	262	13	)	)	PUNCT
ejpam-3574	262	14	=	=	PUNCT
ejpam-3574	263	1	(	(	PUNCT
ejpam-3574	263	2	i	i	PRON
ejpam-3574	263	3	+	+	CCONJ
ejpam-3574	263	4	uku	uku	PROPN
ejpam-3574	263	5	t	t	PROPN
ejpam-3574	263	6	k	k	PROPN
ejpam-3574	263	7	j	j	PROPN
ejpam-3574	263	8	)	)	PUNCT
ejpam-3574	264	1	(	(	PUNCT
ejpam-3574	264	2	i	i	PRON
ejpam-3574	264	3	+	+	CCONJ
ejpam-3574	265	1	uk−1u	uk−1u	NUM
ejpam-3574	265	2	t	t	NOUN
ejpam-3574	265	3	k−1j	k−1j	NOUN
ejpam-3574	265	4	)	)	PUNCT
ejpam-3574	265	5	×	×	NOUN
ejpam-3574	265	6	·	·	PUNCT
ejpam-3574	265	7	·	·	PUNCT
ejpam-3574	265	8	·	·	PUNCT
ejpam-3574	266	1	×	×	NOUN
ejpam-3574	266	2	(	(	PUNCT
ejpam-3574	266	3	i	i	PRON
ejpam-3574	266	4	+	+	CCONJ
ejpam-3574	266	5	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	266	6	t	t	NOUN
ejpam-3574	266	7	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	266	8	)	)	PUNCT
ejpam-3574	266	9	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	266	10	)	)	PUNCT
ejpam-3574	266	11	=	=	PUNCT
ejpam-3574	267	1	(	(	PUNCT
ejpam-3574	267	2	i	i	PRON
ejpam-3574	267	3	+	+	CCONJ
ejpam-3574	267	4	uku	uku	PROPN
ejpam-3574	267	5	t	t	PROPN
ejpam-3574	267	6	k	k	PROPN
ejpam-3574	267	7	j	j	PROPN
ejpam-3574	267	8	)	)	PUNCT
ejpam-3574	268	1	(	(	PUNCT
ejpam-3574	268	2	i	i	PRON
ejpam-3574	268	3	+	+	CCONJ
ejpam-3574	269	1	uk−1u	uk−1u	NUM
ejpam-3574	269	2	t	t	NOUN
ejpam-3574	269	3	k−1j	k−1j	NOUN
ejpam-3574	269	4	)	)	PUNCT
ejpam-3574	269	5	×	×	NOUN
ejpam-3574	269	6	·	·	PUNCT
ejpam-3574	269	7	·	·	PUNCT
ejpam-3574	269	8	·	·	PUNCT
ejpam-3574	270	1	×	×	NOUN
ejpam-3574	270	2	(	(	PUNCT
ejpam-3574	270	3	i	i	PRON
ejpam-3574	270	4	+	+	CCONJ
ejpam-3574	270	5	uk−ki+1u	uk−ki+1u	PROPN
ejpam-3574	270	6	t	t	PROPN
ejpam-3574	270	7	k−ki+1j	k−ki+1j	PROPN
ejpam-3574	270	8	)	)	PUNCT
ejpam-3574	270	9	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	270	10	)	)	PUNCT
ejpam-3574	270	11	,	,	PUNCT
ejpam-3574	270	12	where	where	SCONJ
ejpam-3574	270	13	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	270	14	)	)	PUNCT
ejpam-3574	270	15	is	be	AUX
ejpam-3574	270	16	γ(i−	γ(i−	NOUN
ejpam-3574	270	17	1	1	NUM
ejpam-3574	270	18	)	)	PUNCT
ejpam-3574	270	19	rank	rank	NOUN
ejpam-3574	270	20	-	-	PUNCT
ejpam-3574	270	21	one	one	NUM
ejpam-3574	270	22	perturbations	perturbation	NOUN
ejpam-3574	270	23	of	of	ADP
ejpam-3574	270	24	the	the	DET
ejpam-3574	270	25	symplectic	symplectic	ADJ
ejpam-3574	270	26	matrix	matrix	NOUN
ejpam-3574	270	27	w	w	NOUN
ejpam-3574	270	28	.	.	PUNCT
ejpam-3574	271	1	then	then	ADV
ejpam-3574	271	2	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	271	3	)	)	PUNCT
ejpam-3574	271	4	has	have	VERB
ejpam-3574	271	5	the	the	DET
ejpam-3574	271	6	following	follow	VERB
ejpam-3574	271	7	jordan	jordan	PROPN
ejpam-3574	271	8	canonical	canonical	ADJ
ejpam-3574	271	9	form	form	NOUN
ejpam-3574	271	10	:	:	PUNCT
ejpam-3574	272	1			PROPN
ejpam-3574	272	2	li⊕	li⊕	PUNCT
ejpam-3574	272	3	j=1	j=1	PROPN
ejpam-3574	272	4	jni(λ	jni(λ	PROPN
ejpam-3574	272	5	)	)	PUNCT
ejpam-3574	272	6	⊕	⊕	PROPN
ejpam-3574	272	7	·	·	PUNCT
ejpam-3574	272	8	·	·	PUNCT
ejpam-3574	272	9	·	·	PUNCT
ejpam-3574	272	10	⊕	⊕	NOUN
ejpam-3574	273	1			PROPN
ejpam-3574	273	2	lm⊕	lm⊕	PROPN
ejpam-3574	273	3	j=1	j=1	PROPN
ejpam-3574	273	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	273	5	)	)	PUNCT
ejpam-3574	273	6	⊕	⊕	PROPN
ejpam-3574	273	7	j̃γ(i−1	j̃γ(i−1	PROPN
ejpam-3574	273	8	)	)	PUNCT
ejpam-3574	273	9	,	,	PUNCT
ejpam-3574	273	10	where	where	SCONJ
ejpam-3574	273	11	j̃γ(i−1	j̃γ(i−1	NOUN
ejpam-3574	273	12	)	)	PUNCT
ejpam-3574	273	13	contains	contain	VERB
ejpam-3574	273	14	all	all	DET
ejpam-3574	273	15	the	the	DET
ejpam-3574	273	16	forms	form	NOUN
ejpam-3574	273	17	in	in	ADP
ejpam-3574	273	18	jordan	jordan	PROPN
ejpam-3574	273	19	blocks	block	NOUN
ejpam-3574	273	20	of	of	ADP
ejpam-3574	273	21	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	273	22	)	)	PUNCT
ejpam-3574	273	23	associated	associate	VERB
ejpam-3574	273	24	with	with	ADP
ejpam-3574	273	25	eigenvalues	eigenvalue	NOUN
ejpam-3574	273	26	different	different	ADJ
ejpam-3574	273	27	from	from	ADP
ejpam-3574	273	28	λ	λ	PROPN
ejpam-3574	273	29	.	.	PUNCT
ejpam-3574	273	30	finally	finally	ADV
ejpam-3574	273	31	,	,	PUNCT
ejpam-3574	273	32	using	use	VERB
ejpam-3574	273	33	the	the	DET
ejpam-3574	273	34	fact	fact	NOUN
ejpam-3574	273	35	that	that	SCONJ
ejpam-3574	273	36	w̃k	w̃k	PRON
ejpam-3574	273	37	is	be	AUX
ejpam-3574	273	38	ki	ki	PROPN
ejpam-3574	273	39	rank	rank	VERB
ejpam-3574	273	40	one	one	NUM
ejpam-3574	273	41	perturbation	perturbation	NOUN
ejpam-3574	273	42	of	of	ADP
ejpam-3574	273	43	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	273	44	)	)	PUNCT
ejpam-3574	273	45	,	,	PUNCT
ejpam-3574	273	46	according	accord	VERB
ejpam-3574	273	47	to	to	ADP
ejpam-3574	273	48	1	1	NUM
ejpam-3574	273	49	)	)	PUNCT
ejpam-3574	273	50	of	of	ADP
ejpam-3574	273	51	theorem	theorem	ADJ
ejpam-3574	273	52	7.1	7.1	NUM
ejpam-3574	273	53	of	of	ADP
ejpam-3574	273	54	[	[	X
ejpam-3574	273	55	16	16	NUM
ejpam-3574	273	56	]	]	PUNCT
ejpam-3574	273	57	and	and	CCONJ
ejpam-3574	273	58	it	it	PRON
ejpam-3574	273	59	follows	follow	VERB
ejpam-3574	273	60	that	that	SCONJ
ejpam-3574	273	61	the	the	DET
ejpam-3574	273	62	jordan	jordan	PROPN
ejpam-3574	273	63	canonical	canonical	ADJ
ejpam-3574	273	64	form	form	NOUN
ejpam-3574	273	65	of	of	ADP
ejpam-3574	273	66	w̃	w̃	PROPN
ejpam-3574	273	67	=	=	PRON
ejpam-3574	273	68	w̃k	w̃k	PRON
ejpam-3574	273	69	is	be	AUX
ejpam-3574	273	70	given	give	VERB
ejpam-3574	273	71	byli−ki⊕	byli−ki⊕	ADJ
ejpam-3574	273	72	j=1	j=1	ADJ
ejpam-3574	273	73	jni(λ	jni(λ	PROPN
ejpam-3574	273	74	)	)	PUNCT
ejpam-3574	273	75			PUNCT
ejpam-3574	274	1	li+1⊕	li+1⊕	PROPN
ejpam-3574	274	2	j=1	j=1	PROPN
ejpam-3574	274	3	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	274	4	)	)	PUNCT
ejpam-3574	274	5	⊕	⊕	PROPN
ejpam-3574	274	6	·	·	PUNCT
ejpam-3574	274	7	·	·	PUNCT
ejpam-3574	274	8	·	·	PUNCT
ejpam-3574	275	1	⊕	⊕	NOUN
ejpam-3574	276	1			PROPN
ejpam-3574	276	2	lm⊕	lm⊕	PROPN
ejpam-3574	276	3	j=1	j=1	PROPN
ejpam-3574	276	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	276	5	)	)	PUNCT
ejpam-3574	277	1	⊕	⊕	PROPN
ejpam-3574	277	2	j̃	j̃	PROPN
ejpam-3574	277	3	,	,	PUNCT
ejpam-3574	277	4	where	where	SCONJ
ejpam-3574	277	5	j̃	j̃	PROPN
ejpam-3574	277	6	=	=	SYM
ejpam-3574	277	7	j̃k	j̃k	PROPN
ejpam-3574	277	8	contains	contain	VERB
ejpam-3574	277	9	all	all	DET
ejpam-3574	277	10	the	the	DET
ejpam-3574	277	11	form	form	NOUN
ejpam-3574	277	12	in	in	ADP
ejpam-3574	277	13	jordan	jordan	PROPN
ejpam-3574	277	14	blocks	block	NOUN
ejpam-3574	277	15	of	of	ADP
ejpam-3574	277	16	w̃k	w̃k	ADV
ejpam-3574	277	17	associated	associate	VERB
ejpam-3574	277	18	with	with	ADP
ejpam-3574	277	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	277	20	different	different	ADJ
ejpam-3574	277	21	from	from	ADP
ejpam-3574	277	22	λ	λ	PROPN
ejpam-3574	277	23	.	.	PROPN
ejpam-3574	277	24	m.	m.	NOUN
ejpam-3574	277	25	dosso	dosso	PROPN
ejpam-3574	277	26	,	,	PUNCT
ejpam-3574	277	27	t.	t.	PROPN
ejpam-3574	277	28	g.	g.	PROPN
ejpam-3574	277	29	y.	y.	PROPN
ejpam-3574	277	30	arouna	arouna	PROPN
ejpam-3574	277	31	,	,	PUNCT
ejpam-3574	277	32	j.-c	j.-c	PROPN
ejpam-3574	277	33	.	.	PUNCT
ejpam-3574	278	1	koua	koua	PROPN
ejpam-3574	278	2	brou	brou	PROPN
ejpam-3574	278	3	/	/	SYM
ejpam-3574	278	4	eur	eur	PROPN
ejpam-3574	278	5	.	.	PUNCT
ejpam-3574	279	1	j.	j.	PROPN
ejpam-3574	279	2	pure	pure	PROPN
ejpam-3574	279	3	appl	appl	PROPN
ejpam-3574	279	4	.	.	PROPN
ejpam-3574	279	5	math	math	PROPN
ejpam-3574	279	6	,	,	PUNCT
ejpam-3574	279	7	12	12	NUM
ejpam-3574	279	8	(	(	PUNCT
ejpam-3574	279	9	4	4	NUM
ejpam-3574	279	10	)	)	PUNCT
ejpam-3574	279	11	(	(	PUNCT
ejpam-3574	279	12	2019	2019	NUM
ejpam-3574	279	13	)	)	PUNCT
ejpam-3574	279	14	,	,	PUNCT
ejpam-3574	279	15	1744	1744	NUM
ejpam-3574	279	16	-	-	SYM
ejpam-3574	279	17	1770	1770	NUM
ejpam-3574	279	18	1754	1754	NUM
ejpam-3574	279	19	2	2	NUM
ejpam-3574	279	20	)	)	PUNCT
ejpam-3574	279	21	if	if	SCONJ
ejpam-3574	279	22	λ	λ	PROPN
ejpam-3574	279	23	∈	∈	PROPN
ejpam-3574	279	24	{	{	PUNCT
ejpam-3574	279	25	−1	−1	NOUN
ejpam-3574	279	26	,	,	PUNCT
ejpam-3574	279	27	1	1	NUM
ejpam-3574	279	28	}	}	PUNCT
ejpam-3574	279	29	,	,	PUNCT
ejpam-3574	279	30	then	then	ADV
ejpam-3574	279	31	:	:	PUNCT
ejpam-3574	279	32	2a	2a	X
ejpam-3574	279	33	)	)	PUNCT
ejpam-3574	279	34	if	if	SCONJ
ejpam-3574	279	35	k	k	NOUN
ejpam-3574	279	36	=	=	PUNCT
ejpam-3574	279	37	i−1∑	i−1∑	PUNCT
ejpam-3574	279	38	s=1	s=1	PUNCT
ejpam-3574	279	39	ls	ls	X
ejpam-3574	280	1	+	+	CCONJ
ejpam-3574	280	2	ki	ki	PROPN
ejpam-3574	280	3	,	,	PUNCT
ejpam-3574	280	4	where	where	SCONJ
ejpam-3574	280	5	the	the	DET
ejpam-3574	280	6	n1	n1	NOUN
ejpam-3574	280	7	,	,	PUNCT
ejpam-3574	280	8	n2	n2	NOUN
ejpam-3574	280	9	,	,	PUNCT
ejpam-3574	280	10	.	.	PUNCT
ejpam-3574	280	11	.	.	PUNCT
ejpam-3574	280	12	.	.	PUNCT
ejpam-3574	281	1	,	,	PUNCT
ejpam-3574	281	2	ni	ni	PROPN
ejpam-3574	281	3	are	be	AUX
ejpam-3574	281	4	even	even	ADV
ejpam-3574	281	5	and	and	CCONJ
ejpam-3574	281	6	ki	ki	PROPN
ejpam-3574	281	7	<	<	X
ejpam-3574	281	8	li	li	PROPN
ejpam-3574	281	9	,	,	PUNCT
ejpam-3574	281	10	then	then	ADV
ejpam-3574	281	11	–	–	PUNCT
ejpam-3574	281	12	i	i	NOUN
ejpam-3574	281	13	=	=	NOUN
ejpam-3574	281	14	1	1	NUM
ejpam-3574	281	15	,	,	PUNCT
ejpam-3574	281	16	we	we	PRON
ejpam-3574	281	17	have	have	VERB
ejpam-3574	281	18	k	k	NOUN
ejpam-3574	281	19	=	=	SYM
ejpam-3574	281	20	k1	k1	PROPN
ejpam-3574	281	21	and	and	CCONJ
ejpam-3574	281	22	n1	n1	NOUN
ejpam-3574	281	23	is	be	AUX
ejpam-3574	281	24	even	even	ADV
ejpam-3574	281	25	.	.	PUNCT
ejpam-3574	282	1	w̃k	w̃k	X
ejpam-3574	283	1	=	=	PUNCT
ejpam-3574	284	1	(	(	PUNCT
ejpam-3574	284	2	i	i	PRON
ejpam-3574	284	3	+	+	CCONJ
ejpam-3574	284	4	uku	uku	PROPN
ejpam-3574	284	5	t	t	PROPN
ejpam-3574	284	6	k	k	PROPN
ejpam-3574	284	7	j	j	PROPN
ejpam-3574	284	8	)	)	PUNCT
ejpam-3574	285	1	(	(	PUNCT
ejpam-3574	285	2	i	i	PRON
ejpam-3574	285	3	+	+	CCONJ
ejpam-3574	286	1	uk−1u	uk−1u	NUM
ejpam-3574	286	2	t	t	NOUN
ejpam-3574	286	3	k−1j	k−1j	NOUN
ejpam-3574	286	4	)	)	PUNCT
ejpam-3574	286	5	×	×	NOUN
ejpam-3574	286	6	...	...	PUNCT
ejpam-3574	286	7	×	×	NOUN
ejpam-3574	287	1	(	(	PUNCT
ejpam-3574	287	2	i	i	PRON
ejpam-3574	287	3	+	+	CCONJ
ejpam-3574	287	4	u2u	u2u	ADJ
ejpam-3574	287	5	t	t	PROPN
ejpam-3574	287	6	2	2	NUM
ejpam-3574	287	7	j	j	NOUN
ejpam-3574	287	8	)	)	PUNCT
ejpam-3574	287	9	(	(	PUNCT
ejpam-3574	287	10	i	i	PRON
ejpam-3574	287	11	+	+	CCONJ
ejpam-3574	287	12	u1u	u1u	PROPN
ejpam-3574	287	13	t	t	PROPN
ejpam-3574	287	14	1	1	NUM
ejpam-3574	287	15	j	j	PROPN
ejpam-3574	287	16	)	)	PUNCT
ejpam-3574	287	17	w︸	w︸	VERB
ejpam-3574	287	18	︷︷	︷︷	PROPN
ejpam-3574	287	19	︸	︸	PRON
ejpam-3574	288	1	=	=	ADJ
ejpam-3574	288	2	w̃1	w̃1	PROPN
ejpam-3574	288	3	=	=	PUNCT
ejpam-3574	288	4	(	(	PUNCT
ejpam-3574	288	5	i	i	PRON
ejpam-3574	288	6	+	+	NUM
ejpam-3574	288	7	uku	uku	PROPN
ejpam-3574	288	8	t	t	PROPN
ejpam-3574	288	9	k	k	PROPN
ejpam-3574	288	10	j	j	PROPN
ejpam-3574	288	11	)	)	PUNCT
ejpam-3574	289	1	(	(	PUNCT
ejpam-3574	289	2	i	i	PRON
ejpam-3574	289	3	+	+	CCONJ
ejpam-3574	290	1	uk−1u	uk−1u	NUM
ejpam-3574	290	2	t	t	NOUN
ejpam-3574	290	3	k−1j	k−1j	NOUN
ejpam-3574	290	4	)	)	PUNCT
ejpam-3574	290	5	×	×	NOUN
ejpam-3574	290	6	...	...	PUNCT
ejpam-3574	290	7	×	×	NOUN
ejpam-3574	291	1	(	(	PUNCT
ejpam-3574	291	2	i	i	PRON
ejpam-3574	291	3	+	+	CCONJ
ejpam-3574	291	4	u2u	u2u	ADJ
ejpam-3574	291	5	t	t	PROPN
ejpam-3574	291	6	2	2	NUM
ejpam-3574	291	7	j	j	NOUN
ejpam-3574	291	8	)	)	PUNCT
ejpam-3574	291	9	w̃1︸	w̃1︸	PUNCT
ejpam-3574	291	10	︷︷	︷︷	PROPN
ejpam-3574	291	11	︸	︸	X
ejpam-3574	292	1	=	=	NOUN
ejpam-3574	292	2	w̃2	w̃2	PROPN
ejpam-3574	292	3	=	=	PUNCT
ejpam-3574	292	4	(	(	PUNCT
ejpam-3574	292	5	i	i	PRON
ejpam-3574	292	6	+	+	CCONJ
ejpam-3574	292	7	uku	uku	PROPN
ejpam-3574	292	8	t	t	PROPN
ejpam-3574	292	9	k	k	PROPN
ejpam-3574	292	10	j	j	PROPN
ejpam-3574	292	11	)	)	PUNCT
ejpam-3574	293	1	(	(	PUNCT
ejpam-3574	293	2	i	i	PRON
ejpam-3574	293	3	+	+	CCONJ
ejpam-3574	294	1	uk−1u	uk−1u	NUM
ejpam-3574	294	2	t	t	NOUN
ejpam-3574	294	3	k−1j	k−1j	NOUN
ejpam-3574	294	4	)	)	PUNCT
ejpam-3574	294	5	×	×	NOUN
ejpam-3574	294	6	...	...	PUNCT
ejpam-3574	294	7	×	×	NOUN
ejpam-3574	295	1	(	(	PUNCT
ejpam-3574	295	2	i	i	PRON
ejpam-3574	295	3	+	+	CCONJ
ejpam-3574	295	4	u3u	u3u	PROPN
ejpam-3574	295	5	t	t	PROPN
ejpam-3574	295	6	3	3	NUM
ejpam-3574	295	7	j	j	PROPN
ejpam-3574	295	8	)	)	PUNCT
ejpam-3574	295	9	w̃2	w̃2	PROPN
ejpam-3574	295	10	.	.	PUNCT
ejpam-3574	296	1	as	as	SCONJ
ejpam-3574	296	2	w̃1	w̃1	PROPN
ejpam-3574	296	3	is	be	AUX
ejpam-3574	296	4	a	a	DET
ejpam-3574	296	5	rank	rank	NOUN
ejpam-3574	296	6	-	-	PUNCT
ejpam-3574	296	7	one	one	NUM
ejpam-3574	296	8	perturbation	perturbation	NOUN
ejpam-3574	296	9	of	of	ADP
ejpam-3574	296	10	w	w	PROPN
ejpam-3574	296	11	,	,	PUNCT
ejpam-3574	296	12	according	accord	VERB
ejpam-3574	296	13	to	to	ADP
ejpam-3574	296	14	2a	2a	NUM
ejpam-3574	296	15	)	)	PUNCT
ejpam-3574	296	16	of	of	ADP
ejpam-3574	296	17	theorem	theorem	ADJ
ejpam-3574	296	18	7.1	7.1	NUM
ejpam-3574	296	19	of	of	ADP
ejpam-3574	296	20	[	[	X
ejpam-3574	296	21	16	16	NUM
ejpam-3574	296	22	]	]	PUNCT
ejpam-3574	296	23	,	,	PUNCT
ejpam-3574	296	24	it	it	PRON
ejpam-3574	296	25	has	have	VERB
ejpam-3574	296	26	the	the	DET
ejpam-3574	296	27	following	follow	VERB
ejpam-3574	296	28	jordan	jordan	PROPN
ejpam-3574	296	29	canonical	canonical	ADJ
ejpam-3574	296	30	form	form	NOUN
ejpam-3574	296	31	:	:	PUNCT
ejpam-3574	296	32	l1−1⊕	l1−1⊕	NUM
ejpam-3574	296	33	j=1	j=1	PROPN
ejpam-3574	296	34	jn1(λ	jn1(λ	PROPN
ejpam-3574	296	35	)	)	PUNCT
ejpam-3574	296	36	⊕	⊕	PROPN
ejpam-3574	296	37			PROPN
ejpam-3574	296	38	l2⊕	l2⊕	PROPN
ejpam-3574	296	39	j=1	j=1	PROPN
ejpam-3574	296	40	jn2(λ	jn2(λ	PROPN
ejpam-3574	296	41	)	)	PUNCT
ejpam-3574	296	42	⊕	⊕	PROPN
ejpam-3574	296	43	·	·	PUNCT
ejpam-3574	296	44	·	·	PUNCT
ejpam-3574	296	45	·	·	PUNCT
ejpam-3574	297	1	⊕	⊕	NOUN
ejpam-3574	298	1			PROPN
ejpam-3574	298	2	lm⊕	lm⊕	PROPN
ejpam-3574	298	3	j=1	j=1	PROPN
ejpam-3574	298	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	298	5	)	)	PUNCT
ejpam-3574	298	6	⊕	⊕	PROPN
ejpam-3574	298	7	j̃1	j̃1	PROPN
ejpam-3574	298	8	,	,	PUNCT
ejpam-3574	298	9	where	where	SCONJ
ejpam-3574	298	10	j̃1	j̃1	PROPN
ejpam-3574	298	11	contains	contain	VERB
ejpam-3574	298	12	all	all	DET
ejpam-3574	298	13	the	the	DET
ejpam-3574	298	14	forms	form	NOUN
ejpam-3574	298	15	in	in	ADP
ejpam-3574	298	16	jordan	jordan	PROPN
ejpam-3574	298	17	blocks	block	NOUN
ejpam-3574	298	18	of	of	ADP
ejpam-3574	298	19	w̃1	w̃1	PROPN
ejpam-3574	298	20	associated	associate	VERB
ejpam-3574	298	21	with	with	ADP
ejpam-3574	298	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	298	23	different	different	ADJ
ejpam-3574	298	24	from	from	ADP
ejpam-3574	298	25	λ	λ	PROPN
ejpam-3574	298	26	.	.	PUNCT
ejpam-3574	299	1	using	use	VERB
ejpam-3574	299	2	the	the	DET
ejpam-3574	299	3	fact	fact	NOUN
ejpam-3574	299	4	that	that	SCONJ
ejpam-3574	299	5	w̃2	w̃2	PROPN
ejpam-3574	299	6	is	be	AUX
ejpam-3574	299	7	a	a	DET
ejpam-3574	299	8	rank	rank	NOUN
ejpam-3574	299	9	-	-	PUNCT
ejpam-3574	299	10	one	one	NUM
ejpam-3574	299	11	perturbation	perturbation	NOUN
ejpam-3574	299	12	of	of	ADP
ejpam-3574	299	13	w̃1	w̃1	PROPN
ejpam-3574	299	14	,	,	PUNCT
ejpam-3574	299	15	2a	2a	NUM
ejpam-3574	299	16	)	)	PUNCT
ejpam-3574	299	17	of	of	ADP
ejpam-3574	299	18	theorem	theorem	ADJ
ejpam-3574	299	19	7.1	7.1	NUM
ejpam-3574	299	20	of	of	ADP
ejpam-3574	299	21	[	[	X
ejpam-3574	299	22	16	16	NUM
ejpam-3574	299	23	]	]	PUNCT
ejpam-3574	299	24	implies	imply	VERB
ejpam-3574	299	25	that	that	SCONJ
ejpam-3574	299	26	the	the	DET
ejpam-3574	299	27	jordan	jordan	PROPN
ejpam-3574	299	28	canonical	canonical	ADJ
ejpam-3574	299	29	form	form	NOUN
ejpam-3574	299	30	of	of	ADP
ejpam-3574	299	31	w̃2	w̃2	PROPN
ejpam-3574	299	32	is	be	AUX
ejpam-3574	299	33	given	give	VERB
ejpam-3574	299	34	byl1−2⊕	byl1−2⊕	PROPN
ejpam-3574	299	35	j=1	j=1	PROPN
ejpam-3574	299	36	jn1(λ	jn1(λ	PROPN
ejpam-3574	299	37	)	)	PUNCT
ejpam-3574	300	1	⊕	⊕	PROPN
ejpam-3574	300	2			PROPN
ejpam-3574	300	3	l2⊕	l2⊕	PROPN
ejpam-3574	300	4	j=1	j=1	PROPN
ejpam-3574	300	5	jn2(λ	jn2(λ	PROPN
ejpam-3574	300	6	)	)	PUNCT
ejpam-3574	300	7	⊕	⊕	PROPN
ejpam-3574	300	8	·	·	PUNCT
ejpam-3574	300	9	·	·	PUNCT
ejpam-3574	300	10	·	·	PUNCT
ejpam-3574	301	1	⊕	⊕	NOUN
ejpam-3574	302	1			PROPN
ejpam-3574	302	2	lm⊕	lm⊕	PROPN
ejpam-3574	302	3	j=1	j=1	PROPN
ejpam-3574	302	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	302	5	)	)	PUNCT
ejpam-3574	302	6	⊕	⊕	PROPN
ejpam-3574	302	7	j̃2	j̃2	PROPN
ejpam-3574	302	8	,	,	PUNCT
ejpam-3574	302	9	where	where	SCONJ
ejpam-3574	302	10	j̃2	j̃2	PROPN
ejpam-3574	302	11	contains	contain	VERB
ejpam-3574	302	12	all	all	DET
ejpam-3574	302	13	the	the	DET
ejpam-3574	302	14	forms	form	NOUN
ejpam-3574	302	15	in	in	ADP
ejpam-3574	302	16	jordan	jordan	PROPN
ejpam-3574	302	17	blocks	block	NOUN
ejpam-3574	302	18	of	of	ADP
ejpam-3574	302	19	w̃2	w̃2	PROPN
ejpam-3574	302	20	associated	associate	VERB
ejpam-3574	302	21	with	with	ADP
ejpam-3574	302	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	302	23	different	different	ADJ
ejpam-3574	302	24	from	from	ADP
ejpam-3574	302	25	λ	λ	PROPN
ejpam-3574	302	26	.	.	PUNCT
ejpam-3574	302	27	hence	hence	ADV
ejpam-3574	302	28	,	,	PUNCT
ejpam-3574	302	29	applying	apply	VERB
ejpam-3574	302	30	(	(	PUNCT
ejpam-3574	302	31	k1−2)-times	k1−2)-times	PROPN
ejpam-3574	302	32	2a	2a	NUM
ejpam-3574	302	33	)	)	PUNCT
ejpam-3574	302	34	of	of	ADP
ejpam-3574	302	35	theorem	theorem	ADJ
ejpam-3574	302	36	7.1	7.1	NUM
ejpam-3574	302	37	of	of	ADP
ejpam-3574	302	38	[	[	X
ejpam-3574	302	39	16	16	NUM
ejpam-3574	302	40	]	]	PUNCT
ejpam-3574	302	41	to	to	ADP
ejpam-3574	302	42	the	the	DET
ejpam-3574	302	43	matrix	matrix	NOUN
ejpam-3574	302	44	w̃2	w̃2	PROPN
ejpam-3574	302	45	,	,	PUNCT
ejpam-3574	302	46	we	we	PRON
ejpam-3574	302	47	have	have	VERB
ejpam-3574	302	48	the	the	DET
ejpam-3574	302	49	following	follow	VERB
ejpam-3574	302	50	jordan	jordan	PROPN
ejpam-3574	302	51	canonical	canonical	ADJ
ejpam-3574	302	52	form	form	NOUN
ejpam-3574	302	53	of	of	ADP
ejpam-3574	302	54	w̃k1l1−k1⊕	w̃k1l1−k1⊕	NOUN
ejpam-3574	302	55	j=1	j=1	PROPN
ejpam-3574	302	56	jn1(λ	jn1(λ	PROPN
ejpam-3574	302	57	)	)	PUNCT
ejpam-3574	303	1	⊕	⊕	PROPN
ejpam-3574	303	2			PROPN
ejpam-3574	303	3	l2⊕	l2⊕	PROPN
ejpam-3574	303	4	j=1	j=1	PROPN
ejpam-3574	303	5	jn2(λ	jn2(λ	PROPN
ejpam-3574	303	6	)	)	PUNCT
ejpam-3574	303	7	⊕	⊕	PROPN
ejpam-3574	303	8	·	·	PUNCT
ejpam-3574	303	9	·	·	PUNCT
ejpam-3574	303	10	·	·	PUNCT
ejpam-3574	304	1	⊕	⊕	NOUN
ejpam-3574	305	1			PROPN
ejpam-3574	305	2	lm⊕	lm⊕	PROPN
ejpam-3574	305	3	j=1	j=1	PROPN
ejpam-3574	305	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	305	5	)	)	PUNCT
ejpam-3574	305	6	⊕	⊕	PROPN
ejpam-3574	305	7	j̃k1	j̃k1	PROPN
ejpam-3574	305	8	,	,	PUNCT
ejpam-3574	305	9	where	where	SCONJ
ejpam-3574	305	10	j̃k1	j̃k1	NOUN
ejpam-3574	305	11	contains	contain	VERB
ejpam-3574	305	12	all	all	DET
ejpam-3574	305	13	the	the	DET
ejpam-3574	305	14	forms	form	NOUN
ejpam-3574	305	15	in	in	ADP
ejpam-3574	305	16	jordan	jordan	PROPN
ejpam-3574	305	17	blocks	block	NOUN
ejpam-3574	305	18	of	of	ADP
ejpam-3574	305	19	w̃k1	w̃k1	NOUN
ejpam-3574	305	20	associated	associate	VERB
ejpam-3574	305	21	with	with	ADP
ejpam-3574	305	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	305	23	different	different	ADJ
ejpam-3574	305	24	from	from	ADP
ejpam-3574	305	25	λ	λ	PROPN
ejpam-3574	305	26	.	.	PROPN
ejpam-3574	305	27	–	–	PUNCT
ejpam-3574	305	28	for	for	ADP
ejpam-3574	305	29	i	i	PRON
ejpam-3574	305	30	>	>	X
ejpam-3574	305	31	1	1	NUM
ejpam-3574	305	32	,	,	PUNCT
ejpam-3574	305	33	we	we	PRON
ejpam-3574	305	34	have	have	VERB
ejpam-3574	305	35	k	k	NOUN
ejpam-3574	305	36	=	=	PUNCT
ejpam-3574	305	37	i−1∑	i−1∑	NOUN
ejpam-3574	305	38	s=1	s=1	PUNCT
ejpam-3574	305	39	ls	ls	X
ejpam-3574	306	1	+	+	X
ejpam-3574	306	2	ki	ki	PROPN
ejpam-3574	306	3	,	,	PUNCT
ejpam-3574	306	4	with	with	ADP
ejpam-3574	306	5	ki	ki	PROPN
ejpam-3574	306	6	<	<	X
ejpam-3574	306	7	li	li	PROPN
ejpam-3574	306	8	and	and	CCONJ
ejpam-3574	306	9	n1	n1	PROPN
ejpam-3574	306	10	,	,	PUNCT
ejpam-3574	306	11	n2	n2	NOUN
ejpam-3574	306	12	,	,	PUNCT
ejpam-3574	306	13	...	...	PUNCT
ejpam-3574	306	14	,	,	PUNCT
ejpam-3574	306	15	ni	ni	PROPN
ejpam-3574	306	16	are	be	AUX
ejpam-3574	306	17	even	even	ADV
ejpam-3574	306	18	.	.	PUNCT
ejpam-3574	307	1	m.	m.	NOUN
ejpam-3574	307	2	dosso	dosso	PROPN
ejpam-3574	307	3	,	,	PUNCT
ejpam-3574	307	4	t.	t.	PROPN
ejpam-3574	307	5	g.	g.	PROPN
ejpam-3574	307	6	y.	y.	PROPN
ejpam-3574	307	7	arouna	arouna	PROPN
ejpam-3574	307	8	,	,	PUNCT
ejpam-3574	307	9	j.-c	j.-c	PROPN
ejpam-3574	307	10	.	.	PUNCT
ejpam-3574	308	1	koua	koua	PROPN
ejpam-3574	308	2	brou	brou	PROPN
ejpam-3574	308	3	/	/	SYM
ejpam-3574	308	4	eur	eur	PROPN
ejpam-3574	308	5	.	.	PUNCT
ejpam-3574	309	1	j.	j.	PROPN
ejpam-3574	309	2	pure	pure	PROPN
ejpam-3574	309	3	appl	appl	PROPN
ejpam-3574	309	4	.	.	PROPN
ejpam-3574	309	5	math	math	PROPN
ejpam-3574	309	6	,	,	PUNCT
ejpam-3574	309	7	12	12	NUM
ejpam-3574	309	8	(	(	PUNCT
ejpam-3574	309	9	4	4	NUM
ejpam-3574	309	10	)	)	PUNCT
ejpam-3574	309	11	(	(	PUNCT
ejpam-3574	309	12	2019	2019	NUM
ejpam-3574	309	13	)	)	PUNCT
ejpam-3574	309	14	,	,	PUNCT
ejpam-3574	309	15	1744	1744	NUM
ejpam-3574	309	16	-	-	SYM
ejpam-3574	309	17	1770	1770	NUM
ejpam-3574	309	18	1755	1755	NUM
ejpam-3574	309	19	with	with	ADP
ejpam-3574	309	20	γ(i	γ(i	NOUN
ejpam-3574	309	21	)	)	PUNCT
ejpam-3574	309	22	=	=	SYM
ejpam-3574	310	1	i∑	i∑	NOUN
ejpam-3574	310	2	s=1	s=1	SYM
ejpam-3574	310	3	ls	ls	ADJ
ejpam-3574	310	4	,	,	PUNCT
ejpam-3574	310	5	∀	∀	VERB
ejpam-3574	311	1	i	i	X
ejpam-3574	311	2	>	>	X
ejpam-3574	311	3	1	1	NUM
ejpam-3574	311	4	,	,	PUNCT
ejpam-3574	311	5	we	we	PRON
ejpam-3574	311	6	have	have	VERB
ejpam-3574	311	7	:	:	PUNCT
ejpam-3574	311	8	w̃k	w̃k	X
ejpam-3574	311	9	=	=	PUNCT
ejpam-3574	312	1	(	(	PUNCT
ejpam-3574	312	2	i	i	PRON
ejpam-3574	312	3	+	+	CCONJ
ejpam-3574	312	4	uku	uku	PROPN
ejpam-3574	312	5	t	t	PROPN
ejpam-3574	312	6	k	k	PROPN
ejpam-3574	312	7	j	j	PROPN
ejpam-3574	312	8	)	)	PUNCT
ejpam-3574	312	9	(	(	PUNCT
ejpam-3574	312	10	i	i	PRON
ejpam-3574	312	11	+	+	CCONJ
ejpam-3574	312	12	uk−1u	uk−1u	NUM
ejpam-3574	312	13	t	t	NOUN
ejpam-3574	312	14	k−1j	k−1j	NOUN
ejpam-3574	312	15	)	)	PUNCT
ejpam-3574	312	16	×	×	NOUN
ejpam-3574	312	17	...	...	PUNCT
ejpam-3574	312	18	×	×	NOUN
ejpam-3574	312	19	(	(	PUNCT
ejpam-3574	312	20	i	i	PRON
ejpam-3574	312	21	+	+	X
ejpam-3574	312	22	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	312	23	t	t	NOUN
ejpam-3574	312	24	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	312	25	)	)	PUNCT
ejpam-3574	312	26	×	×	NOUN
ejpam-3574	312	27	(	(	PUNCT
ejpam-3574	312	28	i	i	PRON
ejpam-3574	312	29	+	+	CCONJ
ejpam-3574	312	30	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	312	31	t	t	X
ejpam-3574	312	32	γ(i−1)j	γ(i−1)j	PROPN
ejpam-3574	312	33	)	)	PUNCT
ejpam-3574	312	34	×	×	NOUN
ejpam-3574	312	35	...	...	PUNCT
ejpam-3574	312	36	×	×	NOUN
ejpam-3574	312	37	(	(	PUNCT
ejpam-3574	312	38	i	i	PRON
ejpam-3574	312	39	+	+	NUM
ejpam-3574	312	40	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	312	41	t	t	NOUN
ejpam-3574	312	42	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	312	43	)	)	PUNCT
ejpam-3574	312	44	(	(	PUNCT
ejpam-3574	312	45	i	i	PRON
ejpam-3574	312	46	+	+	NUM
ejpam-3574	312	47	uγ(3)u	uγ(3)u	PROPN
ejpam-3574	312	48	t	t	NOUN
ejpam-3574	312	49	γ(3)j	γ(3)j	NUM
ejpam-3574	312	50	)	)	PUNCT
ejpam-3574	312	51	×	×	NOUN
ejpam-3574	312	52	...	...	SYM
ejpam-3574	312	53	×	×	NOUN
ejpam-3574	312	54	(	(	PUNCT
ejpam-3574	312	55	i	i	PRON
ejpam-3574	312	56	+	+	X
ejpam-3574	312	57	uγ(2)+1u	uγ(2)+1u	PROPN
ejpam-3574	312	58	t	t	NOUN
ejpam-3574	312	59	γ(2)+1j	γ(2)+1j	NOUN
ejpam-3574	312	60	)	)	PUNCT
ejpam-3574	312	61	(	(	PUNCT
ejpam-3574	312	62	i	i	PRON
ejpam-3574	312	63	+	+	NUM
ejpam-3574	312	64	uγ(2)u	uγ(2)u	PROPN
ejpam-3574	312	65	t	t	NOUN
ejpam-3574	312	66	γ(2)j	γ(2)j	PRON
ejpam-3574	312	67	)	)	PUNCT
ejpam-3574	312	68	×	×	NOUN
ejpam-3574	312	69	...	...	PUNCT
ejpam-3574	312	70	×	×	NOUN
ejpam-3574	312	71	(	(	PUNCT
ejpam-3574	312	72	i	i	PRON
ejpam-3574	312	73	+	+	CCONJ
ejpam-3574	312	74	u1u	u1u	PROPN
ejpam-3574	312	75	t	t	PROPN
ejpam-3574	312	76	1	1	NUM
ejpam-3574	312	77	j	j	PROPN
ejpam-3574	312	78	)	)	PUNCT
ejpam-3574	312	79	w︸	w︸	VERB
ejpam-3574	312	80	︷︷	︷︷	PROPN
ejpam-3574	312	81	︸	︸	PRON
ejpam-3574	312	82	w̃γ(2	w̃γ(2	PROPN
ejpam-3574	312	83	)	)	PUNCT
ejpam-3574	312	84	=	=	PRON
ejpam-3574	313	1	(	(	PUNCT
ejpam-3574	313	2	i	i	PRON
ejpam-3574	313	3	+	+	CCONJ
ejpam-3574	313	4	uku	uku	PROPN
ejpam-3574	313	5	t	t	PROPN
ejpam-3574	313	6	k	k	PROPN
ejpam-3574	313	7	j	j	PROPN
ejpam-3574	313	8	)	)	PUNCT
ejpam-3574	314	1	(	(	PUNCT
ejpam-3574	314	2	i	i	PRON
ejpam-3574	314	3	+	+	CCONJ
ejpam-3574	315	1	uk−1u	uk−1u	NUM
ejpam-3574	315	2	t	t	NOUN
ejpam-3574	315	3	k−1j	k−1j	NOUN
ejpam-3574	315	4	)	)	PUNCT
ejpam-3574	315	5	×	×	NOUN
ejpam-3574	315	6	...	...	PUNCT
ejpam-3574	315	7	×	×	NOUN
ejpam-3574	316	1	(	(	PUNCT
ejpam-3574	316	2	i	i	PRON
ejpam-3574	316	3	+	+	X
ejpam-3574	316	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	316	5	t	t	NOUN
ejpam-3574	316	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	316	7	)	)	PUNCT
ejpam-3574	316	8	×	×	NOUN
ejpam-3574	316	9	(	(	PUNCT
ejpam-3574	316	10	i	i	PRON
ejpam-3574	316	11	+	+	CCONJ
ejpam-3574	316	12	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	316	13	t	t	X
ejpam-3574	316	14	γ(i−1)j	γ(i−1)j	PROPN
ejpam-3574	316	15	)	)	PUNCT
ejpam-3574	316	16	×	×	NOUN
ejpam-3574	316	17	...	...	PUNCT
ejpam-3574	316	18	×	×	NOUN
ejpam-3574	316	19	(	(	PUNCT
ejpam-3574	316	20	i	i	PRON
ejpam-3574	316	21	+	+	NUM
ejpam-3574	316	22	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	316	23	t	t	NOUN
ejpam-3574	316	24	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	316	25	)	)	PUNCT
ejpam-3574	316	26	×	×	NOUN
ejpam-3574	316	27	(	(	PUNCT
ejpam-3574	316	28	i	i	PRON
ejpam-3574	316	29	+	+	NUM
ejpam-3574	316	30	uγ(3)u	uγ(3)u	PROPN
ejpam-3574	316	31	t	t	NOUN
ejpam-3574	316	32	γ(3)j	γ(3)j	NUM
ejpam-3574	316	33	)	)	PUNCT
ejpam-3574	316	34	×	×	NOUN
ejpam-3574	316	35	...	...	PUNCT
ejpam-3574	316	36	×	×	NOUN
ejpam-3574	316	37	(	(	PUNCT
ejpam-3574	316	38	i	i	PRON
ejpam-3574	316	39	+	+	X
ejpam-3574	316	40	uγ(2)+1u	uγ(2)+1u	PROPN
ejpam-3574	316	41	t	t	NOUN
ejpam-3574	316	42	γ(2)+1j	γ(2)+1j	NOUN
ejpam-3574	316	43	)	)	PUNCT
ejpam-3574	316	44	w̃γ(2)︸	w̃γ(2)︸	VERB
ejpam-3574	316	45	︷︷	︷︷	PROPN
ejpam-3574	316	46	︸	︸	ADP
ejpam-3574	316	47	w̃γ(3	w̃γ(3	PROPN
ejpam-3574	316	48	)	)	PUNCT
ejpam-3574	316	49	=	=	NOUN
ejpam-3574	317	1	(	(	PUNCT
ejpam-3574	317	2	i	i	PRON
ejpam-3574	317	3	+	+	CCONJ
ejpam-3574	317	4	uku	uku	PROPN
ejpam-3574	317	5	t	t	PROPN
ejpam-3574	317	6	k	k	PROPN
ejpam-3574	317	7	j	j	PROPN
ejpam-3574	317	8	)	)	PUNCT
ejpam-3574	318	1	(	(	PUNCT
ejpam-3574	318	2	i	i	PRON
ejpam-3574	318	3	+	+	CCONJ
ejpam-3574	319	1	uk−1u	uk−1u	NUM
ejpam-3574	319	2	t	t	NOUN
ejpam-3574	319	3	k−1j	k−1j	NOUN
ejpam-3574	319	4	)	)	PUNCT
ejpam-3574	319	5	×	×	NOUN
ejpam-3574	319	6	...	...	PUNCT
ejpam-3574	319	7	×	×	NOUN
ejpam-3574	320	1	(	(	PUNCT
ejpam-3574	320	2	i	i	PRON
ejpam-3574	320	3	+	+	X
ejpam-3574	320	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	320	5	t	t	NOUN
ejpam-3574	320	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	320	7	)	)	PUNCT
ejpam-3574	320	8	×	×	NOUN
ejpam-3574	320	9	(	(	PUNCT
ejpam-3574	320	10	i	i	PRON
ejpam-3574	320	11	+	+	CCONJ
ejpam-3574	320	12	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	320	13	t	t	X
ejpam-3574	320	14	γ(i−1)j	γ(i−1)j	PROPN
ejpam-3574	320	15	)	)	PUNCT
ejpam-3574	320	16	×	×	NOUN
ejpam-3574	320	17	...	...	PUNCT
ejpam-3574	320	18	×	×	NOUN
ejpam-3574	320	19	(	(	PUNCT
ejpam-3574	320	20	i	i	PRON
ejpam-3574	320	21	+	+	NUM
ejpam-3574	320	22	uγ(3)+1u	uγ(3)+1u	PROPN
ejpam-3574	320	23	t	t	NOUN
ejpam-3574	320	24	γ(3)+1j	γ(3)+1j	NOUN
ejpam-3574	320	25	)	)	PUNCT
ejpam-3574	320	26	w̃γ(3)︸	w̃γ(3)︸	VERB
ejpam-3574	320	27	︷︷	︷︷	PROPN
ejpam-3574	320	28	︸	︸	X
ejpam-3574	320	29	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	320	30	)	)	PUNCT
ejpam-3574	321	1	=	=	PUNCT
ejpam-3574	322	1	(	(	PUNCT
ejpam-3574	322	2	i	i	PRON
ejpam-3574	322	3	+	+	CCONJ
ejpam-3574	322	4	uku	uku	PROPN
ejpam-3574	322	5	t	t	PROPN
ejpam-3574	322	6	k	k	PROPN
ejpam-3574	322	7	j	j	PROPN
ejpam-3574	322	8	)	)	PUNCT
ejpam-3574	323	1	(	(	PUNCT
ejpam-3574	323	2	i	i	PRON
ejpam-3574	323	3	+	+	CCONJ
ejpam-3574	324	1	uk−1u	uk−1u	NUM
ejpam-3574	324	2	t	t	NOUN
ejpam-3574	324	3	k−1j	k−1j	NOUN
ejpam-3574	324	4	)	)	PUNCT
ejpam-3574	324	5	×	×	NOUN
ejpam-3574	324	6	...	...	PUNCT
ejpam-3574	324	7	×	×	NOUN
ejpam-3574	325	1	(	(	PUNCT
ejpam-3574	325	2	i	i	PRON
ejpam-3574	325	3	+	+	X
ejpam-3574	325	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	325	5	t	t	NOUN
ejpam-3574	325	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	325	7	)	)	PUNCT
ejpam-3574	325	8	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	325	9	)	)	PUNCT
ejpam-3574	325	10	=	=	PUNCT
ejpam-3574	326	1	(	(	PUNCT
ejpam-3574	326	2	i	i	PRON
ejpam-3574	326	3	+	+	CCONJ
ejpam-3574	326	4	uku	uku	PROPN
ejpam-3574	326	5	t	t	PROPN
ejpam-3574	326	6	k	k	PROPN
ejpam-3574	326	7	j	j	PROPN
ejpam-3574	326	8	)	)	PUNCT
ejpam-3574	327	1	(	(	PUNCT
ejpam-3574	327	2	i	i	PRON
ejpam-3574	327	3	+	+	CCONJ
ejpam-3574	328	1	uk−1u	uk−1u	NUM
ejpam-3574	328	2	t	t	NOUN
ejpam-3574	328	3	k−1j	k−1j	NOUN
ejpam-3574	328	4	)	)	PUNCT
ejpam-3574	328	5	×	×	NOUN
ejpam-3574	328	6	...	...	PUNCT
ejpam-3574	328	7	×	×	NOUN
ejpam-3574	329	1	(	(	PUNCT
ejpam-3574	329	2	i	i	PRON
ejpam-3574	329	3	+	+	CCONJ
ejpam-3574	329	4	uk−ki+1u	uk−ki+1u	PROPN
ejpam-3574	329	5	t	t	PROPN
ejpam-3574	329	6	k−ki+1j	k−ki+1j	PROPN
ejpam-3574	329	7	)	)	PUNCT
ejpam-3574	329	8	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	329	9	)	)	PUNCT
ejpam-3574	329	10	.	.	PUNCT
ejpam-3574	330	1	knowing	know	VERB
ejpam-3574	330	2	that	that	SCONJ
ejpam-3574	330	3	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	330	4	)	)	PUNCT
ejpam-3574	330	5	is	be	AUX
ejpam-3574	330	6	γ(i−	γ(i−	NOUN
ejpam-3574	330	7	1	1	NUM
ejpam-3574	330	8	)	)	PUNCT
ejpam-3574	330	9	rank	rank	NOUN
ejpam-3574	330	10	-	-	PUNCT
ejpam-3574	330	11	one	one	NUM
ejpam-3574	330	12	perturbations	perturbation	NOUN
ejpam-3574	330	13	of	of	ADP
ejpam-3574	330	14	the	the	DET
ejpam-3574	330	15	symplectic	symplectic	ADJ
ejpam-3574	330	16	matrixw	matrixw	NOUN
ejpam-3574	330	17	,	,	PUNCT
ejpam-3574	330	18	according	accord	VERB
ejpam-3574	330	19	to	to	ADP
ejpam-3574	330	20	2a	2a	NUM
ejpam-3574	330	21	)	)	PUNCT
ejpam-3574	330	22	of	of	ADP
ejpam-3574	330	23	theorem	theorem	ADJ
ejpam-3574	330	24	7.1	7.1	NUM
ejpam-3574	330	25	of	of	ADP
ejpam-3574	330	26	[	[	X
ejpam-3574	330	27	16	16	NUM
ejpam-3574	330	28	]	]	PUNCT
ejpam-3574	330	29	,	,	PUNCT
ejpam-3574	330	30	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	330	31	)	)	PUNCT
ejpam-3574	330	32	has	have	VERB
ejpam-3574	330	33	the	the	DET
ejpam-3574	330	34	following	follow	VERB
ejpam-3574	330	35	jordan	jordan	PROPN
ejpam-3574	330	36	canonical	canonical	PROPN
ejpam-3574	330	37	form	form	PROPN
ejpam-3574	330	38	li⊕	li⊕	PUNCT
ejpam-3574	331	1	j=1	j=1	ADJ
ejpam-3574	331	2	jni(λ	jni(λ	PROPN
ejpam-3574	331	3	)	)	PUNCT
ejpam-3574	331	4	⊕	⊕	PROPN
ejpam-3574	331	5	·	·	PUNCT
ejpam-3574	331	6	·	·	PUNCT
ejpam-3574	331	7	·	·	PUNCT
ejpam-3574	331	8	⊕	⊕	NOUN
ejpam-3574	332	1			PROPN
ejpam-3574	332	2	lm⊕	lm⊕	PROPN
ejpam-3574	332	3	j=1	j=1	PROPN
ejpam-3574	332	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	332	5	)	)	PUNCT
ejpam-3574	332	6	⊕	⊕	PROPN
ejpam-3574	332	7	j̃γ(i−1	j̃γ(i−1	PROPN
ejpam-3574	332	8	)	)	PUNCT
ejpam-3574	332	9	,	,	PUNCT
ejpam-3574	332	10	where	where	SCONJ
ejpam-3574	332	11	j̃γ(i−1	j̃γ(i−1	NOUN
ejpam-3574	332	12	)	)	PUNCT
ejpam-3574	332	13	contains	contain	VERB
ejpam-3574	332	14	all	all	DET
ejpam-3574	332	15	the	the	DET
ejpam-3574	332	16	forms	form	NOUN
ejpam-3574	332	17	in	in	ADP
ejpam-3574	332	18	jordan	jordan	PROPN
ejpam-3574	332	19	blocks	block	NOUN
ejpam-3574	332	20	of	of	ADP
ejpam-3574	332	21	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	332	22	)	)	PUNCT
ejpam-3574	332	23	associated	associate	VERB
ejpam-3574	332	24	with	with	ADP
ejpam-3574	332	25	eigenvalues	eigenvalue	NOUN
ejpam-3574	332	26	different	different	ADJ
ejpam-3574	332	27	from	from	ADP
ejpam-3574	332	28	λ	λ	PROPN
ejpam-3574	332	29	.	.	PUNCT
ejpam-3574	333	1	finally	finally	ADV
ejpam-3574	333	2	,	,	PUNCT
ejpam-3574	333	3	as	as	SCONJ
ejpam-3574	333	4	w̃k	w̃k	PRON
ejpam-3574	333	5	is	be	AUX
ejpam-3574	333	6	ki	ki	PROPN
ejpam-3574	333	7	rank	rank	PROPN
ejpam-3574	333	8	-	-	PUNCT
ejpam-3574	333	9	one	one	NUM
ejpam-3574	333	10	perturbations	perturbation	NOUN
ejpam-3574	333	11	of	of	ADP
ejpam-3574	333	12	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	333	13	)	)	PUNCT
ejpam-3574	333	14	,	,	PUNCT
ejpam-3574	333	15	according	accord	VERB
ejpam-3574	333	16	to	to	ADP
ejpam-3574	333	17	2a	2a	NUM
ejpam-3574	333	18	)	)	PUNCT
ejpam-3574	333	19	of	of	ADP
ejpam-3574	333	20	theorem	theorem	ADJ
ejpam-3574	333	21	7.1	7.1	NUM
ejpam-3574	333	22	of	of	ADP
ejpam-3574	333	23	[	[	X
ejpam-3574	333	24	16	16	NUM
ejpam-3574	333	25	]	]	PUNCT
ejpam-3574	333	26	the	the	DET
ejpam-3574	333	27	jordan	jordan	PROPN
ejpam-3574	333	28	canonical	canonical	ADJ
ejpam-3574	333	29	form	form	NOUN
ejpam-3574	333	30	of	of	ADP
ejpam-3574	333	31	w̃k	w̃k	PRON
ejpam-3574	333	32	is	be	AUX
ejpam-3574	333	33	given	give	VERB
ejpam-3574	333	34	by	by	ADP
ejpam-3574	333	35	:	:	PUNCT
ejpam-3574	333	36	li−ki⊕	li−ki⊕	PROPN
ejpam-3574	333	37	j=1	j=1	PROPN
ejpam-3574	333	38	jni(λ	jni(λ	PROPN
ejpam-3574	333	39	)	)	PUNCT
ejpam-3574	333	40			PUNCT
ejpam-3574	334	1	li+1⊕	li+1⊕	PROPN
ejpam-3574	334	2	j=1	j=1	PROPN
ejpam-3574	334	3	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	334	4	)	)	PUNCT
ejpam-3574	334	5	⊕	⊕	PROPN
ejpam-3574	334	6	·	·	PUNCT
ejpam-3574	334	7	·	·	PUNCT
ejpam-3574	334	8	·	·	PUNCT
ejpam-3574	335	1	⊕	⊕	NOUN
ejpam-3574	336	1			PROPN
ejpam-3574	336	2	lm⊕	lm⊕	PROPN
ejpam-3574	336	3	j=1	j=1	PROPN
ejpam-3574	336	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	336	5	)	)	PUNCT
ejpam-3574	337	1	⊕	⊕	PROPN
ejpam-3574	337	2	j̃	j̃	PROPN
ejpam-3574	337	3	,	,	PUNCT
ejpam-3574	337	4	where	where	SCONJ
ejpam-3574	337	5	j̃	j̃	PROPN
ejpam-3574	337	6	=	=	SYM
ejpam-3574	337	7	j̃k	j̃k	PROPN
ejpam-3574	337	8	contains	contain	VERB
ejpam-3574	337	9	all	all	DET
ejpam-3574	337	10	the	the	DET
ejpam-3574	337	11	form	form	NOUN
ejpam-3574	337	12	in	in	ADP
ejpam-3574	337	13	jordan	jordan	PROPN
ejpam-3574	337	14	blocks	block	NOUN
ejpam-3574	337	15	from	from	ADP
ejpam-3574	337	16	w̃k	w̃k	NOUN
ejpam-3574	337	17	associated	associate	VERB
ejpam-3574	337	18	with	with	ADP
ejpam-3574	337	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	337	20	different	different	ADJ
ejpam-3574	337	21	from	from	ADP
ejpam-3574	337	22	λ	λ	PROPN
ejpam-3574	337	23	.	.	PROPN
ejpam-3574	337	24	m.	m.	NOUN
ejpam-3574	337	25	dosso	dosso	PROPN
ejpam-3574	337	26	,	,	PUNCT
ejpam-3574	337	27	t.	t.	PROPN
ejpam-3574	337	28	g.	g.	PROPN
ejpam-3574	337	29	y.	y.	PROPN
ejpam-3574	337	30	arouna	arouna	PROPN
ejpam-3574	337	31	,	,	PUNCT
ejpam-3574	337	32	j.-c	j.-c	PROPN
ejpam-3574	337	33	.	.	PUNCT
ejpam-3574	338	1	koua	koua	PROPN
ejpam-3574	338	2	brou	brou	PROPN
ejpam-3574	338	3	/	/	SYM
ejpam-3574	338	4	eur	eur	PROPN
ejpam-3574	338	5	.	.	PUNCT
ejpam-3574	339	1	j.	j.	PROPN
ejpam-3574	339	2	pure	pure	PROPN
ejpam-3574	339	3	appl	appl	PROPN
ejpam-3574	339	4	.	.	PROPN
ejpam-3574	339	5	math	math	PROPN
ejpam-3574	339	6	,	,	PUNCT
ejpam-3574	339	7	12	12	NUM
ejpam-3574	339	8	(	(	PUNCT
ejpam-3574	339	9	4	4	NUM
ejpam-3574	339	10	)	)	PUNCT
ejpam-3574	339	11	(	(	PUNCT
ejpam-3574	339	12	2019	2019	NUM
ejpam-3574	339	13	)	)	PUNCT
ejpam-3574	339	14	,	,	PUNCT
ejpam-3574	339	15	1744	1744	NUM
ejpam-3574	339	16	-	-	SYM
ejpam-3574	339	17	1770	1770	NUM
ejpam-3574	339	18	1756	1756	NUM
ejpam-3574	339	19	2b	2b	NOUN
ejpam-3574	339	20	)	)	PUNCT
ejpam-3574	339	21	if	if	SCONJ
ejpam-3574	339	22	k	k	PROPN
ejpam-3574	339	23	=	=	PUNCT
ejpam-3574	339	24	i−1∑	i−1∑	PUNCT
ejpam-3574	340	1	s=1	s=1	PUNCT
ejpam-3574	340	2	ls	ls	X
ejpam-3574	341	1	+	+	CCONJ
ejpam-3574	341	2	2ki	2ki	ADJ
ejpam-3574	341	3	−	−	NOUN
ejpam-3574	341	4	1	1	NUM
ejpam-3574	341	5	,	,	PUNCT
ejpam-3574	341	6	with	with	ADP
ejpam-3574	341	7	2ki	2ki	ADJ
ejpam-3574	341	8	≤	≤	NUM
ejpam-3574	341	9	li	li	PROPN
ejpam-3574	341	10	and	and	CCONJ
ejpam-3574	341	11	ni	ni	PROPN
ejpam-3574	341	12	is	be	AUX
ejpam-3574	341	13	even	even	ADV
ejpam-3574	341	14	.	.	PUNCT
ejpam-3574	341	15	–	–	PUNCT
ejpam-3574	341	16	for	for	ADP
ejpam-3574	341	17	i	i	PRON
ejpam-3574	341	18	=	=	NOUN
ejpam-3574	341	19	1	1	NUM
ejpam-3574	341	20	,	,	PUNCT
ejpam-3574	341	21	we	we	PRON
ejpam-3574	341	22	have	have	VERB
ejpam-3574	341	23	k	k	NOUN
ejpam-3574	341	24	=	=	SYM
ejpam-3574	341	25	2k1	2k1	NUM
ejpam-3574	341	26	−	−	NOUN
ejpam-3574	341	27	1	1	NUM
ejpam-3574	341	28	with	with	ADP
ejpam-3574	341	29	2k1	2k1	NUM
ejpam-3574	341	30	≤	≤	NOUN
ejpam-3574	341	31	l1	l1	PROPN
ejpam-3574	341	32	and	and	CCONJ
ejpam-3574	341	33	n1	n1	PROPN
ejpam-3574	341	34	is	be	AUX
ejpam-3574	341	35	odd	odd	ADJ
ejpam-3574	341	36	.	.	PUNCT
ejpam-3574	342	1	according	accord	VERB
ejpam-3574	342	2	to	to	ADP
ejpam-3574	342	3	the	the	DET
ejpam-3574	342	4	property	property	NOUN
ejpam-3574	342	5	2b	2b	NOUN
ejpam-3574	342	6	)	)	PUNCT
ejpam-3574	342	7	of	of	ADP
ejpam-3574	342	8	theorem	theorem	NOUN
ejpam-3574	342	9	10	10	NUM
ejpam-3574	342	10	of	of	ADP
ejpam-3574	342	11	[	[	X
ejpam-3574	342	12	5	5	NUM
ejpam-3574	342	13	]	]	PUNCT
ejpam-3574	342	14	,	,	PUNCT
ejpam-3574	342	15	l1	l1	PROPN
ejpam-3574	342	16	is	be	AUX
ejpam-3574	342	17	even	even	ADV
ejpam-3574	342	18	and	and	CCONJ
ejpam-3574	342	19	we	we	PRON
ejpam-3574	342	20	have	have	VERB
ejpam-3574	342	21	w̃k	w̃k	ADV
ejpam-3574	342	22	=	=	PUNCT
ejpam-3574	343	1	(	(	PUNCT
ejpam-3574	343	2	i	i	PRON
ejpam-3574	343	3	+	+	CCONJ
ejpam-3574	343	4	uku	uku	PROPN
ejpam-3574	343	5	t	t	PROPN
ejpam-3574	343	6	k	k	PROPN
ejpam-3574	343	7	j	j	PROPN
ejpam-3574	343	8	)	)	PUNCT
ejpam-3574	344	1	(	(	PUNCT
ejpam-3574	344	2	i	i	PRON
ejpam-3574	344	3	+	+	CCONJ
ejpam-3574	345	1	uk−1u	uk−1u	NUM
ejpam-3574	345	2	t	t	NOUN
ejpam-3574	345	3	k−1j	k−1j	NOUN
ejpam-3574	345	4	)	)	PUNCT
ejpam-3574	345	5	×	×	NOUN
ejpam-3574	345	6	...	...	PUNCT
ejpam-3574	345	7	×	×	NOUN
ejpam-3574	346	1	(	(	PUNCT
ejpam-3574	346	2	i	i	PRON
ejpam-3574	346	3	+	+	CCONJ
ejpam-3574	346	4	u3u	u3u	PROPN
ejpam-3574	346	5	t	t	PROPN
ejpam-3574	346	6	3	3	NUM
ejpam-3574	346	7	j	j	NOUN
ejpam-3574	346	8	)	)	PUNCT
ejpam-3574	346	9	(	(	PUNCT
ejpam-3574	346	10	i	i	PRON
ejpam-3574	346	11	+	+	CCONJ
ejpam-3574	346	12	u2u	u2u	ADJ
ejpam-3574	346	13	t	t	PROPN
ejpam-3574	346	14	2	2	NUM
ejpam-3574	346	15	j	j	PROPN
ejpam-3574	346	16	)	)	PUNCT
ejpam-3574	346	17	×	×	NOUN
ejpam-3574	346	18	(	(	PUNCT
ejpam-3574	346	19	i	i	PRON
ejpam-3574	346	20	+	+	CCONJ
ejpam-3574	346	21	u1u	u1u	PROPN
ejpam-3574	346	22	t	t	PROPN
ejpam-3574	346	23	1	1	NUM
ejpam-3574	346	24	j	j	PROPN
ejpam-3574	346	25	)	)	PUNCT
ejpam-3574	346	26	w︸	w︸	VERB
ejpam-3574	346	27	︷︷	︷︷	PROPN
ejpam-3574	346	28	︸	︸	PRON
ejpam-3574	347	1	w̃1	w̃1	PROPN
ejpam-3574	347	2	=	=	PUNCT
ejpam-3574	348	1	(	(	PUNCT
ejpam-3574	348	2	i	i	PRON
ejpam-3574	348	3	+	+	NUM
ejpam-3574	348	4	uku	uku	PROPN
ejpam-3574	348	5	t	t	PROPN
ejpam-3574	348	6	k	k	PROPN
ejpam-3574	348	7	j	j	PROPN
ejpam-3574	348	8	)	)	PUNCT
ejpam-3574	349	1	(	(	PUNCT
ejpam-3574	349	2	i	i	PRON
ejpam-3574	349	3	+	+	CCONJ
ejpam-3574	350	1	uk−1u	uk−1u	NUM
ejpam-3574	350	2	t	t	NOUN
ejpam-3574	350	3	k−1j	k−1j	NOUN
ejpam-3574	350	4	)	)	PUNCT
ejpam-3574	350	5	×	×	NOUN
ejpam-3574	350	6	...	...	PUNCT
ejpam-3574	350	7	×	×	NOUN
ejpam-3574	351	1	(	(	PUNCT
ejpam-3574	351	2	i	i	PRON
ejpam-3574	351	3	+	+	CCONJ
ejpam-3574	351	4	u3u	u3u	PROPN
ejpam-3574	351	5	t	t	PROPN
ejpam-3574	351	6	3	3	NUM
ejpam-3574	351	7	j	j	NOUN
ejpam-3574	351	8	)	)	PUNCT
ejpam-3574	351	9	(	(	PUNCT
ejpam-3574	351	10	i	i	PRON
ejpam-3574	351	11	+	+	CCONJ
ejpam-3574	351	12	u2u	u2u	ADJ
ejpam-3574	351	13	t	t	PROPN
ejpam-3574	351	14	2	2	NUM
ejpam-3574	351	15	j	j	NOUN
ejpam-3574	351	16	)	)	PUNCT
ejpam-3574	351	17	w̃1︸	w̃1︸	PUNCT
ejpam-3574	351	18	︷︷	︷︷	PROPN
ejpam-3574	351	19	︸	︸	X
ejpam-3574	351	20	w̃2	w̃2	PROPN
ejpam-3574	351	21	=	=	SYM
ejpam-3574	351	22	(	(	PUNCT
ejpam-3574	351	23	i	i	PRON
ejpam-3574	351	24	+	+	CCONJ
ejpam-3574	351	25	uku	uku	PROPN
ejpam-3574	351	26	t	t	PROPN
ejpam-3574	351	27	k	k	PROPN
ejpam-3574	351	28	j	j	PROPN
ejpam-3574	351	29	)	)	PUNCT
ejpam-3574	352	1	(	(	PUNCT
ejpam-3574	352	2	i	i	PRON
ejpam-3574	352	3	+	+	CCONJ
ejpam-3574	353	1	uk−1u	uk−1u	NUM
ejpam-3574	353	2	t	t	NOUN
ejpam-3574	353	3	k−1j	k−1j	NOUN
ejpam-3574	353	4	)	)	PUNCT
ejpam-3574	353	5	×	×	NOUN
ejpam-3574	353	6	...	...	PUNCT
ejpam-3574	353	7	×	×	NOUN
ejpam-3574	354	1	(	(	PUNCT
ejpam-3574	354	2	i	i	PRON
ejpam-3574	354	3	+	+	CCONJ
ejpam-3574	355	1	u4u	u4u	PROPN
ejpam-3574	355	2	t	t	PROPN
ejpam-3574	355	3	4	4	NUM
ejpam-3574	355	4	j	j	NOUN
ejpam-3574	355	5	)	)	PUNCT
ejpam-3574	356	1	(	(	PUNCT
ejpam-3574	356	2	i	i	PRON
ejpam-3574	356	3	+	+	CCONJ
ejpam-3574	356	4	u3u	u3u	PROPN
ejpam-3574	356	5	t	t	PROPN
ejpam-3574	356	6	3	3	NUM
ejpam-3574	356	7	j	j	PROPN
ejpam-3574	356	8	)	)	PUNCT
ejpam-3574	356	9	w̃2︸	w̃2︸	PUNCT
ejpam-3574	356	10	︷︷	︷︷	PROPN
ejpam-3574	356	11	︸	︸	X
ejpam-3574	357	1	w̃3	w̃3	PROPN
ejpam-3574	357	2	=	=	SYM
ejpam-3574	357	3	(	(	PUNCT
ejpam-3574	357	4	i	i	PRON
ejpam-3574	357	5	+	+	NUM
ejpam-3574	357	6	uku	uku	PROPN
ejpam-3574	357	7	t	t	PROPN
ejpam-3574	357	8	k	k	PROPN
ejpam-3574	357	9	j	j	PROPN
ejpam-3574	357	10	)	)	PUNCT
ejpam-3574	358	1	(	(	PUNCT
ejpam-3574	358	2	i	i	PRON
ejpam-3574	358	3	+	+	CCONJ
ejpam-3574	359	1	uk−1u	uk−1u	NUM
ejpam-3574	359	2	t	t	NOUN
ejpam-3574	359	3	k−1j	k−1j	NOUN
ejpam-3574	359	4	)	)	PUNCT
ejpam-3574	359	5	×	×	NOUN
ejpam-3574	359	6	...	...	PUNCT
ejpam-3574	359	7	×	×	NOUN
ejpam-3574	360	1	(	(	PUNCT
ejpam-3574	360	2	i	i	PRON
ejpam-3574	360	3	+	+	CCONJ
ejpam-3574	361	1	u4u	u4u	PROPN
ejpam-3574	361	2	t	t	PROPN
ejpam-3574	361	3	4	4	NUM
ejpam-3574	361	4	j	j	PROPN
ejpam-3574	361	5	)	)	PUNCT
ejpam-3574	362	1	w̃3	w̃3	PROPN
ejpam-3574	362	2	.	.	PUNCT
ejpam-3574	363	1	we	we	PRON
ejpam-3574	363	2	know	know	VERB
ejpam-3574	363	3	that	that	SCONJ
ejpam-3574	363	4	w̃1	w̃1	PROPN
ejpam-3574	363	5	is	be	AUX
ejpam-3574	363	6	a	a	DET
ejpam-3574	363	7	rank	rank	NOUN
ejpam-3574	363	8	-	-	PUNCT
ejpam-3574	363	9	one	one	NUM
ejpam-3574	363	10	perturbation	perturbation	NOUN
ejpam-3574	363	11	of	of	ADP
ejpam-3574	363	12	w	w	PROPN
ejpam-3574	363	13	and	and	CCONJ
ejpam-3574	363	14	its	its	PRON
ejpam-3574	363	15	jordan	jordan	PROPN
ejpam-3574	363	16	canonical	canonical	ADJ
ejpam-3574	363	17	form	form	NOUN
ejpam-3574	363	18	in	in	ADP
ejpam-3574	363	19	block	block	NOUN
ejpam-3574	363	20	of	of	ADP
ejpam-3574	363	21	jordan	jordan	PROPN
ejpam-3574	363	22	is	be	AUX
ejpam-3574	363	23	given	give	VERB
ejpam-3574	363	24	by	by	ADP
ejpam-3574	363	25	(	(	PUNCT
ejpam-3574	363	26	see	see	VERB
ejpam-3574	363	27	[	[	X
ejpam-3574	363	28	16	16	NUM
ejpam-3574	363	29	,	,	PUNCT
ejpam-3574	363	30	theorem	theorem	ADJ
ejpam-3574	363	31	7.1,2b	7.1,2b	NOUN
ejpam-3574	363	32	)	)	PUNCT
ejpam-3574	363	33	]	]	PUNCT
ejpam-3574	363	34	)	)	PUNCT
ejpam-3574	363	35	jn1	jn1	VERB
ejpam-3574	364	1	+	+	PROPN
ejpam-3574	364	2	1(λ)⊕	1(λ)⊕	NUM
ejpam-3574	364	3	l1−2⊕	l1−2⊕	X
ejpam-3574	364	4	j=1	j=1	PROPN
ejpam-3574	364	5	jn1(λ	jn1(λ	PROPN
ejpam-3574	364	6	)	)	PUNCT
ejpam-3574	364	7			PUNCT
ejpam-3574	364	8	l2⊕	l2⊕	PUNCT
ejpam-3574	364	9	j=1	j=1	PROPN
ejpam-3574	364	10	jn2(λ	jn2(λ	PROPN
ejpam-3574	364	11	)	)	PUNCT
ejpam-3574	364	12	⊕	⊕	PROPN
ejpam-3574	364	13	·	·	PUNCT
ejpam-3574	364	14	·	·	PUNCT
ejpam-3574	364	15	·	·	PUNCT
ejpam-3574	365	1	⊕	⊕	NOUN
ejpam-3574	366	1			PROPN
ejpam-3574	366	2	lm⊕	lm⊕	PROPN
ejpam-3574	366	3	j=1	j=1	PROPN
ejpam-3574	366	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	366	5	)	)	PUNCT
ejpam-3574	366	6	⊕	⊕	PROPN
ejpam-3574	366	7	j̃1	j̃1	PROPN
ejpam-3574	366	8	,	,	PUNCT
ejpam-3574	366	9	where	where	SCONJ
ejpam-3574	366	10	j̃1	j̃1	PROPN
ejpam-3574	366	11	contains	contain	VERB
ejpam-3574	366	12	all	all	DET
ejpam-3574	366	13	the	the	DET
ejpam-3574	366	14	form	form	NOUN
ejpam-3574	366	15	in	in	ADP
ejpam-3574	366	16	jordan	jordan	PROPN
ejpam-3574	366	17	blocks	block	NOUN
ejpam-3574	366	18	of	of	ADP
ejpam-3574	366	19	w̃1	w̃1	PROPN
ejpam-3574	366	20	associated	associate	VERB
ejpam-3574	366	21	with	with	ADP
ejpam-3574	366	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	366	23	different	different	ADJ
ejpam-3574	366	24	from	from	ADP
ejpam-3574	366	25	λ	λ	PROPN
ejpam-3574	366	26	.	.	PUNCT
ejpam-3574	367	1	so	so	ADV
ejpam-3574	367	2	w̃2	w̃2	PROPN
ejpam-3574	367	3	has	have	VERB
ejpam-3574	367	4	the	the	DET
ejpam-3574	367	5	following	follow	VERB
ejpam-3574	367	6	jordan	jordan	PROPN
ejpam-3574	367	7	canonical	canonical	ADJ
ejpam-3574	367	8	form	form	NOUN
ejpam-3574	367	9	(	(	PUNCT
ejpam-3574	367	10	see	see	VERB
ejpam-3574	367	11	[	[	X
ejpam-3574	367	12	16	16	NUM
ejpam-3574	367	13	,	,	PUNCT
ejpam-3574	367	14	2b	2b	NUM
ejpam-3574	367	15	)	)	PUNCT
ejpam-3574	367	16	theorem	theorem	VERB
ejpam-3574	367	17	7.1	7.1	NUM
ejpam-3574	367	18	]	]	PUNCT
ejpam-3574	367	19	)	)	PUNCT
ejpam-3574	367	20	:	:	PUNCT
ejpam-3574	367	21	l1−2⊕	l1−2⊕	VERB
ejpam-3574	367	22	j=1	j=1	PROPN
ejpam-3574	367	23	jn1(λ	jn1(λ	PROPN
ejpam-3574	367	24	)	)	PUNCT
ejpam-3574	367	25			PUNCT
ejpam-3574	367	26	l2⊕	l2⊕	PUNCT
ejpam-3574	367	27	j=1	j=1	PROPN
ejpam-3574	367	28	jn2(λ	jn2(λ	PROPN
ejpam-3574	367	29	)	)	PUNCT
ejpam-3574	367	30	⊕	⊕	PROPN
ejpam-3574	367	31	·	·	PUNCT
ejpam-3574	367	32	·	·	PUNCT
ejpam-3574	367	33	·	·	PUNCT
ejpam-3574	368	1	⊕	⊕	NOUN
ejpam-3574	369	1			PROPN
ejpam-3574	369	2	lm⊕	lm⊕	PROPN
ejpam-3574	369	3	j=1	j=1	PROPN
ejpam-3574	369	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	369	5	)	)	PUNCT
ejpam-3574	369	6	⊕	⊕	PROPN
ejpam-3574	369	7	j̃2	j̃2	PROPN
ejpam-3574	369	8	,	,	PUNCT
ejpam-3574	369	9	where	where	SCONJ
ejpam-3574	369	10	j̃2	j̃2	PROPN
ejpam-3574	369	11	contains	contain	VERB
ejpam-3574	369	12	all	all	DET
ejpam-3574	369	13	the	the	DET
ejpam-3574	369	14	forms	form	NOUN
ejpam-3574	369	15	in	in	ADP
ejpam-3574	369	16	jordan	jordan	PROPN
ejpam-3574	369	17	blocks	block	NOUN
ejpam-3574	369	18	of	of	ADP
ejpam-3574	369	19	w̃2	w̃2	PROPN
ejpam-3574	369	20	associated	associate	VERB
ejpam-3574	369	21	with	with	ADP
ejpam-3574	369	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	369	23	different	different	ADJ
ejpam-3574	369	24	from	from	ADP
ejpam-3574	369	25	λ	λ	PROPN
ejpam-3574	369	26	,	,	PUNCT
ejpam-3574	369	27	because	because	SCONJ
ejpam-3574	369	28	it	it	PRON
ejpam-3574	369	29	is	be	AUX
ejpam-3574	369	30	a	a	DET
ejpam-3574	369	31	rank	rank	NOUN
ejpam-3574	369	32	-	-	PUNCT
ejpam-3574	369	33	one	one	NUM
ejpam-3574	369	34	perturbation	perturbation	NOUN
ejpam-3574	369	35	of	of	ADP
ejpam-3574	369	36	w̃1	w̃1	PROPN
ejpam-3574	369	37	.	.	PUNCT
ejpam-3574	370	1	similarly	similarly	ADV
ejpam-3574	370	2	the	the	DET
ejpam-3574	370	3	jordan	jordan	PROPN
ejpam-3574	370	4	canonical	canonical	ADJ
ejpam-3574	370	5	form	form	NOUN
ejpam-3574	370	6	of	of	ADP
ejpam-3574	370	7	w̃3	w̃3	PROPN
ejpam-3574	370	8	[	[	X
ejpam-3574	370	9	16	16	NUM
ejpam-3574	370	10	,	,	PUNCT
ejpam-3574	370	11	part	part	NOUN
ejpam-3574	370	12	2b	2b	NOUN
ejpam-3574	370	13	)	)	PUNCT
ejpam-3574	370	14	du	du	PROPN
ejpam-3574	370	15	theorem	theorem	VERB
ejpam-3574	370	16	7.1	7.1	NUM
ejpam-3574	370	17	]	]	PUNCT
ejpam-3574	370	18	is	be	AUX
ejpam-3574	370	19	given	give	VERB
ejpam-3574	370	20	by	by	ADP
ejpam-3574	370	21	jn1	jn1	PROPN
ejpam-3574	370	22	+	+	PROPN
ejpam-3574	370	23	1(λ)⊕	1(λ)⊕	ADJ
ejpam-3574	370	24	l1−2×2⊕	l1−2×2⊕	PROPN
ejpam-3574	370	25	j=1	j=1	PROPN
ejpam-3574	370	26	jn1(λ	jn1(λ	PROPN
ejpam-3574	370	27	)	)	PUNCT
ejpam-3574	370	28			PUNCT
ejpam-3574	370	29	l2⊕	l2⊕	PUNCT
ejpam-3574	370	30	j=1	j=1	PROPN
ejpam-3574	370	31	jn2(λ	jn2(λ	PROPN
ejpam-3574	370	32	)	)	PUNCT
ejpam-3574	370	33	⊕	⊕	PROPN
ejpam-3574	370	34	·	·	PUNCT
ejpam-3574	370	35	·	·	PUNCT
ejpam-3574	370	36	·	·	PUNCT
ejpam-3574	371	1	⊕	⊕	NOUN
ejpam-3574	372	1			PROPN
ejpam-3574	372	2	lm⊕	lm⊕	PROPN
ejpam-3574	372	3	j=1	j=1	PROPN
ejpam-3574	372	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	372	5	)	)	PUNCT
ejpam-3574	372	6	⊕	⊕	PROPN
ejpam-3574	372	7	j̃3	j̃3	PROPN
ejpam-3574	372	8	,	,	PUNCT
ejpam-3574	372	9	where	where	SCONJ
ejpam-3574	372	10	j̃3	j̃3	ADV
ejpam-3574	372	11	contains	contain	VERB
ejpam-3574	372	12	all	all	DET
ejpam-3574	372	13	the	the	DET
ejpam-3574	372	14	forms	form	NOUN
ejpam-3574	372	15	in	in	ADP
ejpam-3574	372	16	jordan	jordan	PROPN
ejpam-3574	372	17	blocks	block	NOUN
ejpam-3574	372	18	of	of	ADP
ejpam-3574	372	19	w̃3	w̃3	PROPN
ejpam-3574	372	20	associated	associate	VERB
ejpam-3574	372	21	with	with	ADP
ejpam-3574	372	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	372	23	different	different	ADJ
ejpam-3574	372	24	from	from	ADP
ejpam-3574	372	25	λ	λ	PROPN
ejpam-3574	372	26	.	.	PUNCT
ejpam-3574	372	27	hence	hence	ADV
ejpam-3574	372	28	,	,	PUNCT
ejpam-3574	372	29	applying	apply	VERB
ejpam-3574	372	30	(	(	PUNCT
ejpam-3574	372	31	2k1	2k1	NUM
ejpam-3574	372	32	−	−	NOUN
ejpam-3574	372	33	4)-times	4)-times	NUM
ejpam-3574	372	34	this	this	DET
ejpam-3574	372	35	process	process	NOUN
ejpam-3574	372	36	m.	m.	NOUN
ejpam-3574	372	37	dosso	dosso	PROPN
ejpam-3574	372	38	,	,	PUNCT
ejpam-3574	372	39	t.	t.	PROPN
ejpam-3574	372	40	g.	g.	PROPN
ejpam-3574	372	41	y.	y.	PROPN
ejpam-3574	372	42	arouna	arouna	PROPN
ejpam-3574	372	43	,	,	PUNCT
ejpam-3574	372	44	j.-c	j.-c	PROPN
ejpam-3574	372	45	.	.	PUNCT
ejpam-3574	373	1	koua	koua	PROPN
ejpam-3574	373	2	brou	brou	PROPN
ejpam-3574	373	3	/	/	SYM
ejpam-3574	373	4	eur	eur	PROPN
ejpam-3574	373	5	.	.	PUNCT
ejpam-3574	374	1	j.	j.	PROPN
ejpam-3574	374	2	pure	pure	PROPN
ejpam-3574	374	3	appl	appl	PROPN
ejpam-3574	374	4	.	.	PROPN
ejpam-3574	374	5	math	math	PROPN
ejpam-3574	374	6	,	,	PUNCT
ejpam-3574	374	7	12	12	NUM
ejpam-3574	374	8	(	(	PUNCT
ejpam-3574	374	9	4	4	NUM
ejpam-3574	374	10	)	)	PUNCT
ejpam-3574	374	11	(	(	PUNCT
ejpam-3574	374	12	2019	2019	NUM
ejpam-3574	374	13	)	)	PUNCT
ejpam-3574	374	14	,	,	PUNCT
ejpam-3574	374	15	1744	1744	NUM
ejpam-3574	374	16	-	-	SYM
ejpam-3574	374	17	1770	1770	NUM
ejpam-3574	374	18	1757	1757	NUM
ejpam-3574	374	19	to	to	PART
ejpam-3574	374	20	matrix	matrix	VERB
ejpam-3574	374	21	w̃3	w̃3	PROPN
ejpam-3574	374	22	,	,	PUNCT
ejpam-3574	374	23	we	we	PRON
ejpam-3574	374	24	obtain	obtain	VERB
ejpam-3574	374	25	the	the	DET
ejpam-3574	374	26	canonical	canonical	ADJ
ejpam-3574	374	27	form	form	NOUN
ejpam-3574	374	28	of	of	ADP
ejpam-3574	374	29	jordan	jordan	PROPN
ejpam-3574	374	30	below	below	ADP
ejpam-3574	374	31	jn1	jn1	PROPN
ejpam-3574	375	1	+	+	PROPN
ejpam-3574	375	2	1(λ)⊕	1(λ)⊕	ADJ
ejpam-3574	375	3	l1−2k1⊕	l1−2k1⊕	ADP
ejpam-3574	375	4	j=1	j=1	PROPN
ejpam-3574	375	5	jn1(λ	jn1(λ	PROPN
ejpam-3574	375	6	)	)	PUNCT
ejpam-3574	375	7			PUNCT
ejpam-3574	375	8	l2⊕	l2⊕	PUNCT
ejpam-3574	375	9	j=1	j=1	PROPN
ejpam-3574	375	10	jn2(λ	jn2(λ	PROPN
ejpam-3574	375	11	)	)	PUNCT
ejpam-3574	376	1	⊕	⊕	PROPN
ejpam-3574	376	2	·	·	PUNCT
ejpam-3574	376	3	·	·	PUNCT
ejpam-3574	376	4	·	·	PUNCT
ejpam-3574	376	5	⊕	⊕	NOUN
ejpam-3574	377	1			PROPN
ejpam-3574	377	2	lm⊕	lm⊕	PROPN
ejpam-3574	377	3	j=1	j=1	PROPN
ejpam-3574	377	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	377	5	)	)	PUNCT
ejpam-3574	378	1	⊕	⊕	PROPN
ejpam-3574	378	2	j̃	j̃	PROPN
ejpam-3574	378	3	,	,	PUNCT
ejpam-3574	378	4	where	where	SCONJ
ejpam-3574	378	5	j̃	j̃	PROPN
ejpam-3574	378	6	=	=	SYM
ejpam-3574	378	7	j̃k	j̃k	PROPN
ejpam-3574	378	8	contains	contain	VERB
ejpam-3574	378	9	all	all	DET
ejpam-3574	378	10	the	the	DET
ejpam-3574	378	11	forms	form	NOUN
ejpam-3574	378	12	in	in	ADP
ejpam-3574	378	13	jordan	jordan	PROPN
ejpam-3574	378	14	blocks	block	NOUN
ejpam-3574	378	15	of	of	ADP
ejpam-3574	378	16	w	w	PROPN
ejpam-3574	378	17	+	+	PROPN
ejpam-3574	378	18	b	b	NOUN
ejpam-3574	378	19	associated	associate	VERB
ejpam-3574	378	20	with	with	ADP
ejpam-3574	378	21	eigenvalues	eigenvalue	NOUN
ejpam-3574	378	22	different	different	ADJ
ejpam-3574	378	23	from	from	ADP
ejpam-3574	378	24	λ	λ	PROPN
ejpam-3574	378	25	.	.	PROPN
ejpam-3574	378	26	–	–	PUNCT
ejpam-3574	378	27	for	for	ADP
ejpam-3574	378	28	i	i	PRON
ejpam-3574	378	29	=	=	SYM
ejpam-3574	378	30	2	2	NUM
ejpam-3574	378	31	,	,	PUNCT
ejpam-3574	378	32	we	we	PRON
ejpam-3574	378	33	have	have	VERB
ejpam-3574	378	34	k	k	PROPN
ejpam-3574	378	35	=	=	PROPN
ejpam-3574	378	36	l1	l1	PROPN
ejpam-3574	378	37	+	+	CCONJ
ejpam-3574	378	38	2k2	2k2	NUM
ejpam-3574	378	39	−	−	NOUN
ejpam-3574	378	40	1	1	NUM
ejpam-3574	378	41	with	with	ADP
ejpam-3574	378	42	2k2	2k2	NUM
ejpam-3574	378	43	≤	≤	NOUN
ejpam-3574	378	44	l2	l2	NOUN
ejpam-3574	378	45	and	and	CCONJ
ejpam-3574	378	46	n2	n2	NOUN
ejpam-3574	378	47	is	be	AUX
ejpam-3574	378	48	odd	odd	ADJ
ejpam-3574	378	49	.	.	PUNCT
ejpam-3574	379	1	w̃k	w̃k	PUNCT
ejpam-3574	380	1	=	=	PUNCT
ejpam-3574	380	2	(	(	PUNCT
ejpam-3574	380	3	i	i	PRON
ejpam-3574	380	4	+	+	CCONJ
ejpam-3574	380	5	uku	uku	PROPN
ejpam-3574	380	6	t	t	PROPN
ejpam-3574	380	7	k	k	PROPN
ejpam-3574	380	8	j	j	PROPN
ejpam-3574	380	9	)	)	PUNCT
ejpam-3574	381	1	(	(	PUNCT
ejpam-3574	381	2	i	i	PRON
ejpam-3574	381	3	+	+	CCONJ
ejpam-3574	382	1	uk−1u	uk−1u	NUM
ejpam-3574	382	2	t	t	NOUN
ejpam-3574	382	3	k−1j	k−1j	NOUN
ejpam-3574	382	4	)	)	PUNCT
ejpam-3574	382	5	×	×	NOUN
ejpam-3574	382	6	...	...	PUNCT
ejpam-3574	382	7	×	×	NOUN
ejpam-3574	383	1	(	(	PUNCT
ejpam-3574	383	2	i	i	PRON
ejpam-3574	383	3	+	+	CCONJ
ejpam-3574	383	4	ul1	ul1	PROPN
ejpam-3574	383	5	+	+	PROPN
ejpam-3574	383	6	1u	1u	NUM
ejpam-3574	383	7	t	t	PROPN
ejpam-3574	383	8	l1	l1	PROPN
ejpam-3574	383	9	+	+	PROPN
ejpam-3574	383	10	1j	1j	NUM
ejpam-3574	383	11	)	)	PUNCT
ejpam-3574	383	12	×	×	NOUN
ejpam-3574	383	13	(	(	PUNCT
ejpam-3574	383	14	i	i	PRON
ejpam-3574	383	15	+	+	CCONJ
ejpam-3574	384	1	ul1u	ul1u	PROPN
ejpam-3574	384	2	t	t	X
ejpam-3574	384	3	l1j	l1j	PROPN
ejpam-3574	384	4	)	)	PUNCT
ejpam-3574	385	1	×	×	NOUN
ejpam-3574	385	2	...	...	PUNCT
ejpam-3574	385	3	×	×	NOUN
ejpam-3574	386	1	(	(	PUNCT
ejpam-3574	386	2	i	i	PRON
ejpam-3574	386	3	+	+	CCONJ
ejpam-3574	386	4	u1u	u1u	PROPN
ejpam-3574	386	5	t	t	PROPN
ejpam-3574	386	6	1	1	NUM
ejpam-3574	386	7	j	j	PROPN
ejpam-3574	386	8	)	)	PUNCT
ejpam-3574	386	9	w︸	w︸	VERB
ejpam-3574	386	10	︷︷	︷︷	PROPN
ejpam-3574	386	11	︸	︸	X
ejpam-3574	386	12	w̃l1	w̃l1	NOUN
ejpam-3574	386	13	=	=	SYM
ejpam-3574	387	1	(	(	PUNCT
ejpam-3574	387	2	i	i	PRON
ejpam-3574	387	3	+	+	CCONJ
ejpam-3574	387	4	uku	uku	PROPN
ejpam-3574	387	5	t	t	PROPN
ejpam-3574	387	6	k	k	PROPN
ejpam-3574	387	7	j	j	PROPN
ejpam-3574	387	8	)	)	PUNCT
ejpam-3574	388	1	(	(	PUNCT
ejpam-3574	388	2	i	i	PRON
ejpam-3574	388	3	+	+	CCONJ
ejpam-3574	389	1	uk−1u	uk−1u	NUM
ejpam-3574	389	2	t	t	NOUN
ejpam-3574	389	3	k−1j	k−1j	NOUN
ejpam-3574	389	4	)	)	PUNCT
ejpam-3574	389	5	×	×	NOUN
ejpam-3574	389	6	...	...	PUNCT
ejpam-3574	389	7	×	×	NOUN
ejpam-3574	390	1	(	(	PUNCT
ejpam-3574	390	2	i	i	PRON
ejpam-3574	390	3	+	+	CCONJ
ejpam-3574	390	4	ul1	ul1	PROPN
ejpam-3574	390	5	+	+	PROPN
ejpam-3574	390	6	1u	1u	NUM
ejpam-3574	390	7	t	t	PROPN
ejpam-3574	390	8	l1	l1	PROPN
ejpam-3574	390	9	+	+	PROPN
ejpam-3574	390	10	1j	1j	NUM
ejpam-3574	390	11	)	)	PUNCT
ejpam-3574	390	12	w̃l1	w̃l1	NOUN
ejpam-3574	390	13	=	=	SYM
ejpam-3574	390	14	(	(	PUNCT
ejpam-3574	390	15	i	i	PRON
ejpam-3574	390	16	+	+	CCONJ
ejpam-3574	390	17	uku	uku	PROPN
ejpam-3574	390	18	t	t	PROPN
ejpam-3574	390	19	k	k	PROPN
ejpam-3574	390	20	j	j	PROPN
ejpam-3574	390	21	)	)	PUNCT
ejpam-3574	391	1	(	(	PUNCT
ejpam-3574	391	2	i	i	PRON
ejpam-3574	391	3	+	+	CCONJ
ejpam-3574	392	1	uk−1u	uk−1u	NUM
ejpam-3574	392	2	t	t	NOUN
ejpam-3574	392	3	k−1j	k−1j	NOUN
ejpam-3574	392	4	)	)	PUNCT
ejpam-3574	392	5	×	×	NOUN
ejpam-3574	392	6	...	...	PUNCT
ejpam-3574	392	7	×	×	NOUN
ejpam-3574	393	1	(	(	PUNCT
ejpam-3574	393	2	i	i	PRON
ejpam-3574	393	3	+	+	CCONJ
ejpam-3574	393	4	uk−2k2	uk−2k2	VERB
ejpam-3574	393	5	+	+	NOUN
ejpam-3574	393	6	2u	2u	NOUN
ejpam-3574	393	7	t	t	PROPN
ejpam-3574	393	8	k−2k2	k−2k2	PROPN
ejpam-3574	393	9	+	+	PROPN
ejpam-3574	393	10	2j	2j	NUM
ejpam-3574	393	11	)	)	PUNCT
ejpam-3574	393	12	w̃l1	w̃l1	NOUN
ejpam-3574	393	13	,	,	PUNCT
ejpam-3574	393	14	knowing	know	VERB
ejpam-3574	393	15	that	that	SCONJ
ejpam-3574	393	16	l1	l1	PROPN
ejpam-3574	393	17	=	=	PROPN
ejpam-3574	393	18	k	k	PROPN
ejpam-3574	394	1	−	−	PROPN
ejpam-3574	394	2	2k2	2k2	NUM
ejpam-3574	395	1	+	+	CCONJ
ejpam-3574	395	2	1	1	X
ejpam-3574	395	3	.	.	X
ejpam-3574	396	1	i	i	PRON
ejpam-3574	396	2	)	)	PUNCT
ejpam-3574	396	3	if	if	SCONJ
ejpam-3574	396	4	n1	n1	PROPN
ejpam-3574	396	5	is	be	AUX
ejpam-3574	396	6	even	even	ADV
ejpam-3574	396	7	,	,	PUNCT
ejpam-3574	396	8	according	accord	VERB
ejpam-3574	396	9	to	to	ADP
ejpam-3574	396	10	the	the	DET
ejpam-3574	396	11	property	property	NOUN
ejpam-3574	396	12	2a	2a	NUM
ejpam-3574	396	13	)	)	PUNCT
ejpam-3574	396	14	of	of	ADP
ejpam-3574	396	15	theorem	theorem	ADJ
ejpam-3574	396	16	7.1	7.1	NUM
ejpam-3574	396	17	of	of	ADP
ejpam-3574	396	18	[	[	X
ejpam-3574	396	19	16	16	NUM
ejpam-3574	396	20	]	]	PUNCT
ejpam-3574	396	21	,	,	PUNCT
ejpam-3574	396	22	w̃l1	w̃l1	PROPN
ejpam-3574	396	23	has	have	VERB
ejpam-3574	396	24	the	the	DET
ejpam-3574	396	25	jordan	jordan	PROPN
ejpam-3574	396	26	canonical	canonical	ADJ
ejpam-3574	396	27	form	form	NOUN
ejpam-3574	396	28	bellow	bellow	PROPN
ejpam-3574	396	29	l2⊕	l2⊕	PUNCT
ejpam-3574	396	30	j=1	j=1	PROPN
ejpam-3574	396	31	jn2(λ	jn2(λ	PROPN
ejpam-3574	396	32	)	)	PUNCT
ejpam-3574	397	1	⊕	⊕	PROPN
ejpam-3574	397	2	...	...	PUNCT
ejpam-3574	397	3	⊕	⊕	PROPN
ejpam-3574	398	1			PROPN
ejpam-3574	398	2	lm⊕	lm⊕	PROPN
ejpam-3574	398	3	j=1	j=1	PROPN
ejpam-3574	398	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	398	5	)	)	PUNCT
ejpam-3574	398	6	⊕	⊕	PROPN
ejpam-3574	398	7	j̃l1	j̃l1	PROPN
ejpam-3574	398	8	,	,	PUNCT
ejpam-3574	398	9	where	where	SCONJ
ejpam-3574	398	10	j̃l1	j̃l1	PROPN
ejpam-3574	398	11	contains	contain	VERB
ejpam-3574	398	12	all	all	DET
ejpam-3574	398	13	the	the	DET
ejpam-3574	398	14	forms	form	NOUN
ejpam-3574	398	15	in	in	ADP
ejpam-3574	398	16	jordan	jordan	PROPN
ejpam-3574	398	17	blocks	block	NOUN
ejpam-3574	398	18	of	of	ADP
ejpam-3574	398	19	w̃l1	w̃l1	NOUN
ejpam-3574	398	20	associated	associate	VERB
ejpam-3574	398	21	with	with	ADP
ejpam-3574	398	22	the	the	DET
ejpam-3574	398	23	eigenvalues	eigenvalue	NOUN
ejpam-3574	398	24	different	different	ADJ
ejpam-3574	398	25	from	from	ADP
ejpam-3574	398	26	λ	λ	PROPN
ejpam-3574	398	27	.	.	PUNCT
ejpam-3574	398	28	finally	finally	ADV
ejpam-3574	398	29	,	,	PUNCT
ejpam-3574	398	30	as	as	SCONJ
ejpam-3574	398	31	w̃k	w̃k	PRON
ejpam-3574	398	32	is	be	AUX
ejpam-3574	398	33	(	(	PUNCT
ejpam-3574	398	34	2k2	2k2	NUM
ejpam-3574	398	35	−	−	NUM
ejpam-3574	398	36	1	1	NUM
ejpam-3574	398	37	)	)	PUNCT
ejpam-3574	398	38	rank	rank	NOUN
ejpam-3574	398	39	-	-	PUNCT
ejpam-3574	398	40	one	one	NUM
ejpam-3574	398	41	perturbations	perturbation	NOUN
ejpam-3574	398	42	of	of	ADP
ejpam-3574	398	43	w̃l1	w̃l1	NOUN
ejpam-3574	398	44	and	and	CCONJ
ejpam-3574	398	45	n2	n2	NOUN
ejpam-3574	398	46	is	be	AUX
ejpam-3574	398	47	odd	odd	ADJ
ejpam-3574	398	48	,	,	PUNCT
ejpam-3574	398	49	according	accord	VERB
ejpam-3574	398	50	to	to	ADP
ejpam-3574	398	51	2b	2b	NUM
ejpam-3574	398	52	)	)	PUNCT
ejpam-3574	398	53	of	of	ADP
ejpam-3574	398	54	theorem	theorem	ADJ
ejpam-3574	398	55	7.1	7.1	NUM
ejpam-3574	398	56	of	of	ADP
ejpam-3574	398	57	[	[	X
ejpam-3574	398	58	16	16	NUM
ejpam-3574	398	59	]	]	PUNCT
ejpam-3574	398	60	,	,	PUNCT
ejpam-3574	398	61	l2	l2	NOUN
ejpam-3574	398	62	is	be	AUX
ejpam-3574	398	63	even	even	ADV
ejpam-3574	398	64	and	and	CCONJ
ejpam-3574	398	65	the	the	DET
ejpam-3574	398	66	jordan	jordan	PROPN
ejpam-3574	398	67	canonical	canonical	ADJ
ejpam-3574	398	68	form	form	NOUN
ejpam-3574	398	69	of	of	ADP
ejpam-3574	398	70	w̃k	w̃k	PRON
ejpam-3574	398	71	is	be	AUX
ejpam-3574	398	72	given	give	VERB
ejpam-3574	398	73	by	by	ADP
ejpam-3574	398	74	:	:	PUNCT
ejpam-3574	398	75	jn2	jn2	VERB
ejpam-3574	398	76	+	+	PROPN
ejpam-3574	398	77	1(λ)⊕	1(λ)⊕	ADJ
ejpam-3574	398	78	l2−2k2⊕	l2−2k2⊕	NOUN
ejpam-3574	398	79	j=1	j=1	PROPN
ejpam-3574	398	80	jn2(λ	jn2(λ	PROPN
ejpam-3574	398	81	)	)	PUNCT
ejpam-3574	399	1	⊕	⊕	PROPN
ejpam-3574	399	2			PROPN
ejpam-3574	399	3	l3⊕	l3⊕	PROPN
ejpam-3574	399	4	j=1	j=1	PROPN
ejpam-3574	399	5	jn3(λ	jn3(λ	PROPN
ejpam-3574	399	6	)	)	PUNCT
ejpam-3574	399	7	⊕	⊕	PROPN
ejpam-3574	399	8	...	...	PUNCT
ejpam-3574	399	9	⊕	⊕	PROPN
ejpam-3574	400	1			PROPN
ejpam-3574	400	2	lm⊕	lm⊕	PROPN
ejpam-3574	400	3	j=1	j=1	PROPN
ejpam-3574	400	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	400	5	)	)	PUNCT
ejpam-3574	400	6	⊕j̃k	⊕j̃k	NOUN
ejpam-3574	400	7	,	,	PUNCT
ejpam-3574	400	8	where	where	SCONJ
ejpam-3574	400	9	j̃k	j̃k	PROPN
ejpam-3574	400	10	contains	contain	VERB
ejpam-3574	400	11	all	all	DET
ejpam-3574	400	12	the	the	DET
ejpam-3574	400	13	forms	form	NOUN
ejpam-3574	400	14	in	in	ADP
ejpam-3574	400	15	jordan	jordan	PROPN
ejpam-3574	400	16	blocks	block	NOUN
ejpam-3574	400	17	of	of	ADP
ejpam-3574	400	18	w̃k	w̃k	ADV
ejpam-3574	400	19	associated	associate	VERB
ejpam-3574	400	20	to	to	PART
ejpam-3574	400	21	eigenvalues	eigenvalues	VERB
ejpam-3574	400	22	different	different	ADJ
ejpam-3574	400	23	from	from	ADP
ejpam-3574	400	24	λ	λ	PROPN
ejpam-3574	400	25	.	.	PROPN
ejpam-3574	400	26	ii	ii	PROPN
ejpam-3574	400	27	)	)	PUNCT
ejpam-3574	400	28	if	if	SCONJ
ejpam-3574	400	29	n1	n1	PROPN
ejpam-3574	400	30	is	be	AUX
ejpam-3574	400	31	odd	odd	ADJ
ejpam-3574	400	32	,	,	PUNCT
ejpam-3574	400	33	in	in	ADP
ejpam-3574	400	34	this	this	DET
ejpam-3574	400	35	case	case	NOUN
ejpam-3574	400	36	l1	l1	PROPN
ejpam-3574	400	37	is	be	AUX
ejpam-3574	400	38	even	even	ADV
ejpam-3574	400	39	[	[	X
ejpam-3574	400	40	16	16	NUM
ejpam-3574	400	41	,	,	PUNCT
ejpam-3574	400	42	theorem	theorem	VERB
ejpam-3574	400	43	7.1,2b	7.1,2b	NOUN
ejpam-3574	400	44	]	]	PUNCT
ejpam-3574	400	45	.	.	PUNCT
ejpam-3574	401	1	applying	apply	VERB
ejpam-3574	401	2	l1times	l1time	VERB
ejpam-3574	401	3	the	the	DET
ejpam-3574	401	4	2b	2b	NOUN
ejpam-3574	401	5	)	)	PUNCT
ejpam-3574	401	6	of	of	ADP
ejpam-3574	401	7	theorem	theorem	ADJ
ejpam-3574	401	8	7.1	7.1	NUM
ejpam-3574	401	9	of	of	ADP
ejpam-3574	401	10	[	[	X
ejpam-3574	401	11	16	16	NUM
ejpam-3574	401	12	]	]	PUNCT
ejpam-3574	401	13	to	to	ADP
ejpam-3574	401	14	w	w	PROPN
ejpam-3574	401	15	,	,	PUNCT
ejpam-3574	401	16	we	we	PRON
ejpam-3574	401	17	have	have	VERB
ejpam-3574	401	18	the	the	DET
ejpam-3574	401	19	jordan	jordan	PROPN
ejpam-3574	401	20	canonical	canonical	ADJ
ejpam-3574	401	21	form	form	NOUN
ejpam-3574	401	22	of	of	ADP
ejpam-3574	401	23	w̃l1	w̃l1	NOUN
ejpam-3574	401	24			PROPN
ejpam-3574	401	25	l2⊕	l2⊕	PROPN
ejpam-3574	401	26	j=1	j=1	PROPN
ejpam-3574	401	27	jn2(λ	jn2(λ	PROPN
ejpam-3574	401	28	)	)	PUNCT
ejpam-3574	402	1	⊕	⊕	PROPN
ejpam-3574	402	2	...	...	PUNCT
ejpam-3574	402	3	⊕	⊕	PROPN
ejpam-3574	403	1			PROPN
ejpam-3574	403	2	lm⊕	lm⊕	PROPN
ejpam-3574	403	3	j=1	j=1	PROPN
ejpam-3574	403	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	403	5	)	)	PUNCT
ejpam-3574	403	6	⊕	⊕	PROPN
ejpam-3574	403	7	j̃l1	j̃l1	PROPN
ejpam-3574	403	8	,	,	PUNCT
ejpam-3574	403	9	(	(	PUNCT
ejpam-3574	403	10	10	10	NUM
ejpam-3574	403	11	)	)	PUNCT
ejpam-3574	403	12	m.	m.	NOUN
ejpam-3574	403	13	dosso	dosso	PROPN
ejpam-3574	403	14	,	,	PUNCT
ejpam-3574	403	15	t.	t.	PROPN
ejpam-3574	403	16	g.	g.	PROPN
ejpam-3574	403	17	y.	y.	PROPN
ejpam-3574	403	18	arouna	arouna	PROPN
ejpam-3574	403	19	,	,	PUNCT
ejpam-3574	403	20	j.-c	j.-c	PROPN
ejpam-3574	403	21	.	.	PUNCT
ejpam-3574	404	1	koua	koua	PROPN
ejpam-3574	404	2	brou	brou	PROPN
ejpam-3574	404	3	/	/	SYM
ejpam-3574	404	4	eur	eur	PROPN
ejpam-3574	404	5	.	.	PUNCT
ejpam-3574	405	1	j.	j.	PROPN
ejpam-3574	405	2	pure	pure	PROPN
ejpam-3574	405	3	appl	appl	PROPN
ejpam-3574	405	4	.	.	PROPN
ejpam-3574	405	5	math	math	PROPN
ejpam-3574	405	6	,	,	PUNCT
ejpam-3574	405	7	12	12	NUM
ejpam-3574	405	8	(	(	PUNCT
ejpam-3574	405	9	4	4	NUM
ejpam-3574	405	10	)	)	PUNCT
ejpam-3574	405	11	(	(	PUNCT
ejpam-3574	405	12	2019	2019	NUM
ejpam-3574	405	13	)	)	PUNCT
ejpam-3574	405	14	,	,	PUNCT
ejpam-3574	405	15	1744	1744	NUM
ejpam-3574	405	16	-	-	SYM
ejpam-3574	405	17	1770	1770	NUM
ejpam-3574	405	18	1758	1758	NUM
ejpam-3574	405	19	where	where	SCONJ
ejpam-3574	405	20	j̃l1	j̃l1	PROPN
ejpam-3574	405	21	contains	contain	VERB
ejpam-3574	405	22	all	all	DET
ejpam-3574	405	23	the	the	DET
ejpam-3574	405	24	forms	form	NOUN
ejpam-3574	405	25	in	in	ADP
ejpam-3574	405	26	jordan	jordan	PROPN
ejpam-3574	405	27	blocks	block	NOUN
ejpam-3574	405	28	of	of	ADP
ejpam-3574	405	29	w̃l1	w̃l1	NOUN
ejpam-3574	405	30	associated	associate	VERB
ejpam-3574	405	31	with	with	ADP
ejpam-3574	405	32	the	the	DET
ejpam-3574	405	33	eigenvalues	eigenvalue	NOUN
ejpam-3574	405	34	different	different	ADJ
ejpam-3574	405	35	from	from	ADP
ejpam-3574	405	36	λ	λ	PROPN
ejpam-3574	405	37	.	.	PUNCT
ejpam-3574	406	1	since	since	SCONJ
ejpam-3574	406	2	n2	n2	PROPN
ejpam-3574	406	3	is	be	AUX
ejpam-3574	406	4	odd	odd	ADJ
ejpam-3574	406	5	and	and	CCONJ
ejpam-3574	406	6	w̃k	w̃k	PRON
ejpam-3574	406	7	is	be	AUX
ejpam-3574	406	8	(	(	PUNCT
ejpam-3574	406	9	2k2	2k2	NUM
ejpam-3574	406	10	−	−	NUM
ejpam-3574	406	11	1	1	NUM
ejpam-3574	406	12	)	)	PUNCT
ejpam-3574	406	13	rank	rank	NOUN
ejpam-3574	406	14	-	-	PUNCT
ejpam-3574	406	15	one	one	NUM
ejpam-3574	406	16	perturbations	perturbation	NOUN
ejpam-3574	406	17	of	of	ADP
ejpam-3574	406	18	the	the	DET
ejpam-3574	406	19	symplectic	symplectic	ADJ
ejpam-3574	406	20	matrix	matrix	NOUN
ejpam-3574	406	21	w̃l1	w̃l1	NOUN
ejpam-3574	406	22	,	,	PUNCT
ejpam-3574	406	23	according	accord	VERB
ejpam-3574	406	24	the	the	DET
ejpam-3574	406	25	property	property	NOUN
ejpam-3574	406	26	2b	2b	NOUN
ejpam-3574	406	27	)	)	PUNCT
ejpam-3574	406	28	of	of	ADP
ejpam-3574	406	29	theorem	theorem	ADJ
ejpam-3574	406	30	7.1	7.1	NUM
ejpam-3574	406	31	of	of	ADP
ejpam-3574	406	32	[	[	X
ejpam-3574	406	33	16	16	NUM
ejpam-3574	406	34	]	]	PUNCT
ejpam-3574	406	35	,	,	PUNCT
ejpam-3574	406	36	l2	l2	NOUN
ejpam-3574	406	37	is	be	AUX
ejpam-3574	406	38	even	even	ADV
ejpam-3574	406	39	and	and	CCONJ
ejpam-3574	406	40	w̃k	w̃k	ADV
ejpam-3574	406	41	has	have	VERB
ejpam-3574	406	42	the	the	DET
ejpam-3574	406	43	following	follow	VERB
ejpam-3574	406	44	jordan	jordan	PROPN
ejpam-3574	406	45	canonical	canonical	ADJ
ejpam-3574	406	46	form	form	NOUN
ejpam-3574	406	47	:	:	PUNCT
ejpam-3574	406	48	jn2	jn2	VERB
ejpam-3574	406	49	+	+	PROPN
ejpam-3574	406	50	1(λ)⊕	1(λ)⊕	ADJ
ejpam-3574	406	51	l2−2k2⊕	l2−2k2⊕	NOUN
ejpam-3574	406	52	j=1	j=1	PROPN
ejpam-3574	406	53	jn2(λ	jn2(λ	PROPN
ejpam-3574	406	54	)	)	PUNCT
ejpam-3574	407	1	⊕	⊕	PROPN
ejpam-3574	407	2	...	...	PUNCT
ejpam-3574	407	3	⊕	⊕	PROPN
ejpam-3574	408	1			PROPN
ejpam-3574	408	2	lm⊕	lm⊕	PROPN
ejpam-3574	408	3	j=1	j=1	PROPN
ejpam-3574	408	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	408	5	)	)	PUNCT
ejpam-3574	408	6	⊕	⊕	PROPN
ejpam-3574	408	7	j̃k	j̃k	PROPN
ejpam-3574	408	8	,	,	PUNCT
ejpam-3574	408	9	where	where	SCONJ
ejpam-3574	408	10	j̃k	j̃k	PROPN
ejpam-3574	408	11	contains	contain	VERB
ejpam-3574	408	12	all	all	DET
ejpam-3574	408	13	the	the	DET
ejpam-3574	408	14	forms	form	NOUN
ejpam-3574	408	15	in	in	ADP
ejpam-3574	408	16	jordan	jordan	PROPN
ejpam-3574	408	17	blocks	block	NOUN
ejpam-3574	408	18	of	of	ADP
ejpam-3574	408	19	w̃k	w̃k	ADV
ejpam-3574	408	20	associated	associate	VERB
ejpam-3574	408	21	with	with	ADP
ejpam-3574	408	22	eigenvalues	eigenvalue	NOUN
ejpam-3574	408	23	different	different	ADJ
ejpam-3574	408	24	from	from	ADP
ejpam-3574	408	25	λ	λ	PROPN
ejpam-3574	408	26	.	.	PROPN
ejpam-3574	408	27	•	•	NUM
ejpam-3574	408	28	for	for	ADP
ejpam-3574	408	29	i	i	PRON
ejpam-3574	408	30	>	>	X
ejpam-3574	408	31	2	2	NUM
ejpam-3574	408	32	,	,	PUNCT
ejpam-3574	408	33	we	we	PRON
ejpam-3574	408	34	have	have	VERB
ejpam-3574	408	35	k	k	NOUN
ejpam-3574	408	36	=	=	PUNCT
ejpam-3574	408	37	i−1∑	i−1∑	NOUN
ejpam-3574	409	1	s=1	s=1	PUNCT
ejpam-3574	410	1	ls	ls	X
ejpam-3574	411	1	+	+	CCONJ
ejpam-3574	411	2	2ki	2ki	ADJ
ejpam-3574	411	3	−	−	NOUN
ejpam-3574	411	4	1	1	NUM
ejpam-3574	411	5	,	,	PUNCT
ejpam-3574	411	6	with	with	ADP
ejpam-3574	411	7	2ki	2ki	ADJ
ejpam-3574	411	8	≤	≤	NUM
ejpam-3574	411	9	li	li	PROPN
ejpam-3574	411	10	and	and	CCONJ
ejpam-3574	411	11	ni	ni	PROPN
ejpam-3574	411	12	is	be	AUX
ejpam-3574	411	13	odd	odd	ADJ
ejpam-3574	411	14	.	.	PUNCT
ejpam-3574	412	1	set	set	ADJ
ejpam-3574	412	2	γ(i	γ(i	NOUN
ejpam-3574	412	3	)	)	PUNCT
ejpam-3574	413	1	=	=	SYM
ejpam-3574	413	2	i∑	i∑	NOUN
ejpam-3574	414	1	s=1	s=1	SYM
ejpam-3574	414	2	ls	ls	ADJ
ejpam-3574	414	3	,	,	PUNCT
ejpam-3574	414	4	∀	∀	VERB
ejpam-3574	414	5	i	i	X
ejpam-3574	414	6	>	>	X
ejpam-3574	415	1	2	2	X
ejpam-3574	415	2	.	.	PUNCT
ejpam-3574	415	3	w̃k	w̃k	NOUN
ejpam-3574	416	1	=	=	PUNCT
ejpam-3574	416	2	(	(	PUNCT
ejpam-3574	416	3	i	i	PRON
ejpam-3574	416	4	+	+	CCONJ
ejpam-3574	416	5	uku	uku	PROPN
ejpam-3574	416	6	t	t	PROPN
ejpam-3574	416	7	k	k	PROPN
ejpam-3574	416	8	j	j	PROPN
ejpam-3574	416	9	)	)	PUNCT
ejpam-3574	417	1	(	(	PUNCT
ejpam-3574	417	2	i	i	PRON
ejpam-3574	417	3	+	+	CCONJ
ejpam-3574	418	1	uk−1u	uk−1u	NUM
ejpam-3574	418	2	t	t	NOUN
ejpam-3574	418	3	k−1j	k−1j	NOUN
ejpam-3574	418	4	)	)	PUNCT
ejpam-3574	418	5	×	×	NOUN
ejpam-3574	418	6	...	...	PUNCT
ejpam-3574	418	7	×	×	NOUN
ejpam-3574	419	1	(	(	PUNCT
ejpam-3574	419	2	i	i	PRON
ejpam-3574	419	3	+	+	X
ejpam-3574	419	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	419	5	t	t	NOUN
ejpam-3574	419	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	419	7	)	)	PUNCT
ejpam-3574	419	8	×	×	NOUN
ejpam-3574	419	9	(	(	PUNCT
ejpam-3574	419	10	i	i	PRON
ejpam-3574	419	11	+	+	CCONJ
ejpam-3574	419	12	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	419	13	t	t	X
ejpam-3574	419	14	γ(i−1)j	γ(i−1)j	PROPN
ejpam-3574	419	15	)	)	PUNCT
ejpam-3574	419	16	×	×	NOUN
ejpam-3574	419	17	...	...	PUNCT
ejpam-3574	419	18	×	×	NOUN
ejpam-3574	419	19	(	(	PUNCT
ejpam-3574	419	20	i	i	PRON
ejpam-3574	419	21	+	+	CCONJ
ejpam-3574	419	22	u1u	u1u	PROPN
ejpam-3574	419	23	t	t	PROPN
ejpam-3574	419	24	1	1	NUM
ejpam-3574	419	25	j	j	PROPN
ejpam-3574	419	26	)	)	PUNCT
ejpam-3574	419	27	w︸	w︸	VERB
ejpam-3574	419	28	︷︷	︷︷	PROPN
ejpam-3574	419	29	︸	︸	X
ejpam-3574	419	30	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	419	31	)	)	PUNCT
ejpam-3574	420	1	=	=	PUNCT
ejpam-3574	421	1	(	(	PUNCT
ejpam-3574	421	2	i	i	PRON
ejpam-3574	421	3	+	+	CCONJ
ejpam-3574	421	4	uku	uku	PROPN
ejpam-3574	421	5	t	t	PROPN
ejpam-3574	421	6	k	k	PROPN
ejpam-3574	421	7	j	j	PROPN
ejpam-3574	421	8	)	)	PUNCT
ejpam-3574	422	1	(	(	PUNCT
ejpam-3574	422	2	i	i	PRON
ejpam-3574	422	3	+	+	CCONJ
ejpam-3574	423	1	uk−1u	uk−1u	NUM
ejpam-3574	423	2	t	t	NOUN
ejpam-3574	423	3	k−1j	k−1j	NOUN
ejpam-3574	423	4	)	)	PUNCT
ejpam-3574	423	5	×	×	NOUN
ejpam-3574	423	6	...	...	PUNCT
ejpam-3574	423	7	×	×	NOUN
ejpam-3574	424	1	(	(	PUNCT
ejpam-3574	424	2	i	i	PRON
ejpam-3574	424	3	+	+	X
ejpam-3574	424	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	424	5	t	t	NOUN
ejpam-3574	424	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	424	7	)	)	PUNCT
ejpam-3574	424	8	×w̃γ(i−1	×w̃γ(i−1	PROPN
ejpam-3574	424	9	)	)	PUNCT
ejpam-3574	424	10	.	.	PUNCT
ejpam-3574	425	1	from	from	ADP
ejpam-3574	425	2	2a	2a	NUM
ejpam-3574	425	3	)	)	PUNCT
ejpam-3574	425	4	and	and	CCONJ
ejpam-3574	425	5	2b	2b	NOUN
ejpam-3574	425	6	)	)	PUNCT
ejpam-3574	425	7	of	of	ADP
ejpam-3574	425	8	theorem	theorem	ADJ
ejpam-3574	425	9	7.1	7.1	NUM
ejpam-3574	425	10	of	of	ADP
ejpam-3574	425	11	[	[	X
ejpam-3574	425	12	16],we	16],we	NUM
ejpam-3574	425	13	deduce	deduce	NOUN
ejpam-3574	425	14	that	that	SCONJ
ejpam-3574	425	15	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	425	16	)	)	PUNCT
ejpam-3574	425	17	has	have	VERB
ejpam-3574	425	18	the	the	DET
ejpam-3574	425	19	following	follow	VERB
ejpam-3574	425	20	jordan	jordan	PROPN
ejpam-3574	425	21	canonical	canonical	ADJ
ejpam-3574	425	22	form	form	NOUN
ejpam-3574	425	23	:	:	PUNCT
ejpam-3574	425	24			PROPN
ejpam-3574	425	25	li⊕	li⊕	PUNCT
ejpam-3574	425	26	j=1	j=1	PROPN
ejpam-3574	425	27	jni(λ	jni(λ	PROPN
ejpam-3574	425	28	)	)	PUNCT
ejpam-3574	426	1	⊕	⊕	PROPN
ejpam-3574	426	2			PROPN
ejpam-3574	426	3	li+1⊕	li+1⊕	NOUN
ejpam-3574	426	4	j=1	j=1	PROPN
ejpam-3574	426	5	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	426	6	)	)	PUNCT
ejpam-3574	426	7	⊕	⊕	PROPN
ejpam-3574	426	8	·	·	PUNCT
ejpam-3574	426	9	·	·	PUNCT
ejpam-3574	426	10	·	·	PUNCT
ejpam-3574	427	1	⊕	⊕	NOUN
ejpam-3574	428	1			PROPN
ejpam-3574	428	2	lm⊕	lm⊕	PROPN
ejpam-3574	428	3	j=1	j=1	PROPN
ejpam-3574	428	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	428	5	)	)	PUNCT
ejpam-3574	428	6	⊕	⊕	PROPN
ejpam-3574	428	7	j̃γ(i−1	j̃γ(i−1	PROPN
ejpam-3574	428	8	)	)	PUNCT
ejpam-3574	428	9	,	,	PUNCT
ejpam-3574	428	10	where	where	SCONJ
ejpam-3574	428	11	j̃γ(i−1	j̃γ(i−1	NOUN
ejpam-3574	428	12	)	)	PUNCT
ejpam-3574	428	13	contains	contain	VERB
ejpam-3574	428	14	all	all	DET
ejpam-3574	428	15	the	the	DET
ejpam-3574	428	16	forms	form	NOUN
ejpam-3574	428	17	in	in	ADP
ejpam-3574	428	18	jordan	jordan	PROPN
ejpam-3574	428	19	blocks	block	NOUN
ejpam-3574	428	20	of	of	ADP
ejpam-3574	428	21	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	428	22	)	)	PUNCT
ejpam-3574	428	23	associated	associate	VERB
ejpam-3574	428	24	with	with	ADP
ejpam-3574	428	25	the	the	DET
ejpam-3574	428	26	eigenvalues	eigenvalue	NOUN
ejpam-3574	428	27	different	different	ADJ
ejpam-3574	428	28	from	from	ADP
ejpam-3574	428	29	λ	λ	PROPN
ejpam-3574	428	30	.	.	PUNCT
ejpam-3574	429	1	thus	thus	ADV
ejpam-3574	429	2	w̃k	w̃k	ADV
ejpam-3574	429	3	has	have	VERB
ejpam-3574	429	4	the	the	DET
ejpam-3574	429	5	following	follow	VERB
ejpam-3574	429	6	jordan	jordan	PROPN
ejpam-3574	429	7	canonical	canonical	ADJ
ejpam-3574	429	8	form	form	NOUN
ejpam-3574	429	9	:	:	PUNCT
ejpam-3574	429	10	jni+1(λ)⊕	jni+1(λ)⊕	ADJ
ejpam-3574	429	11	li−2ki⊕	li−2ki⊕	NUM
ejpam-3574	429	12	j=1	j=1	PROPN
ejpam-3574	429	13	jni(λ	jni(λ	PROPN
ejpam-3574	429	14	)	)	PUNCT
ejpam-3574	430	1	⊕	⊕	PROPN
ejpam-3574	430	2			PROPN
ejpam-3574	430	3	li+1⊕	li+1⊕	NOUN
ejpam-3574	430	4	j=1	j=1	PROPN
ejpam-3574	430	5	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	430	6	)	)	PUNCT
ejpam-3574	430	7	⊕	⊕	PROPN
ejpam-3574	430	8	·	·	PUNCT
ejpam-3574	430	9	·	·	PUNCT
ejpam-3574	430	10	·	·	PUNCT
ejpam-3574	430	11	⊕	⊕	PROPN
ejpam-3574	431	1			PROPN
ejpam-3574	431	2	lm⊕	lm⊕	PROPN
ejpam-3574	431	3	j=1	j=1	PROPN
ejpam-3574	431	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	431	5	)	)	PUNCT
ejpam-3574	431	6	⊕j̃	⊕j̃	NOUN
ejpam-3574	431	7	,	,	PUNCT
ejpam-3574	431	8	where	where	SCONJ
ejpam-3574	431	9	j̃	j̃	PROPN
ejpam-3574	431	10	=	=	SYM
ejpam-3574	431	11	j̃k	j̃k	PROPN
ejpam-3574	431	12	contains	contain	VERB
ejpam-3574	431	13	all	all	DET
ejpam-3574	431	14	the	the	DET
ejpam-3574	431	15	forms	form	NOUN
ejpam-3574	431	16	in	in	ADP
ejpam-3574	431	17	jordan	jordan	PROPN
ejpam-3574	431	18	blocks	block	NOUN
ejpam-3574	431	19	of	of	ADP
ejpam-3574	431	20	w̃k	w̃k	ADV
ejpam-3574	431	21	associated	associate	VERB
ejpam-3574	431	22	with	with	ADP
ejpam-3574	431	23	eigenvalues	eigenvalue	NOUN
ejpam-3574	431	24	different	different	ADJ
ejpam-3574	431	25	from	from	ADP
ejpam-3574	431	26	λ	λ	PROPN
ejpam-3574	431	27	because	because	SCONJ
ejpam-3574	431	28	w̃k	w̃k	PRON
ejpam-3574	431	29	is	be	AUX
ejpam-3574	431	30	(	(	PUNCT
ejpam-3574	431	31	2ki−	2ki−	NUM
ejpam-3574	431	32	1	1	NUM
ejpam-3574	431	33	)	)	PUNCT
ejpam-3574	431	34	rank	rank	NOUN
ejpam-3574	431	35	-	-	PUNCT
ejpam-3574	431	36	one	one	NUM
ejpam-3574	431	37	perturbation	perturbation	NOUN
ejpam-3574	431	38	of	of	ADP
ejpam-3574	431	39	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	431	40	)	)	PUNCT
ejpam-3574	431	41	.	.	PUNCT
ejpam-3574	432	1	m.	m.	NOUN
ejpam-3574	432	2	dosso	dosso	PROPN
ejpam-3574	432	3	,	,	PUNCT
ejpam-3574	432	4	t.	t.	PROPN
ejpam-3574	432	5	g.	g.	PROPN
ejpam-3574	432	6	y.	y.	PROPN
ejpam-3574	432	7	arouna	arouna	PROPN
ejpam-3574	432	8	,	,	PUNCT
ejpam-3574	432	9	j.-c	j.-c	PROPN
ejpam-3574	432	10	.	.	PUNCT
ejpam-3574	433	1	koua	koua	PROPN
ejpam-3574	433	2	brou	brou	PROPN
ejpam-3574	433	3	/	/	SYM
ejpam-3574	433	4	eur	eur	PROPN
ejpam-3574	433	5	.	.	PUNCT
ejpam-3574	434	1	j.	j.	PROPN
ejpam-3574	434	2	pure	pure	PROPN
ejpam-3574	434	3	appl	appl	PROPN
ejpam-3574	434	4	.	.	PROPN
ejpam-3574	434	5	math	math	PROPN
ejpam-3574	434	6	,	,	PUNCT
ejpam-3574	434	7	12	12	NUM
ejpam-3574	434	8	(	(	PUNCT
ejpam-3574	434	9	4	4	NUM
ejpam-3574	434	10	)	)	PUNCT
ejpam-3574	434	11	(	(	PUNCT
ejpam-3574	434	12	2019	2019	NUM
ejpam-3574	434	13	)	)	PUNCT
ejpam-3574	434	14	,	,	PUNCT
ejpam-3574	434	15	1744	1744	NUM
ejpam-3574	434	16	-	-	SYM
ejpam-3574	434	17	1770	1770	NUM
ejpam-3574	434	18	1759	1759	NUM
ejpam-3574	434	19	remark	remark	NOUN
ejpam-3574	434	20	2	2	NUM
ejpam-3574	434	21	.	.	PUNCT
ejpam-3574	435	1	in	in	ADP
ejpam-3574	435	2	the	the	DET
ejpam-3574	435	3	property	property	NOUN
ejpam-3574	435	4	(	(	PUNCT
ejpam-3574	435	5	2	2	NUM
ejpam-3574	435	6	)	)	PUNCT
ejpam-3574	435	7	of	of	ADP
ejpam-3574	435	8	theorem	theorem	ADJ
ejpam-3574	435	9	3	3	NUM
ejpam-3574	435	10	,	,	PUNCT
ejpam-3574	435	11	if	if	SCONJ
ejpam-3574	435	12	k	k	PROPN
ejpam-3574	435	13	=	=	PUNCT
ejpam-3574	435	14	i−1∑	i−1∑	NUM
ejpam-3574	435	15	j=1	j=1	NOUN
ejpam-3574	435	16	ls	ls	X
ejpam-3574	436	1	+	+	CCONJ
ejpam-3574	436	2	2ki	2ki	ADJ
ejpam-3574	436	3	,	,	PUNCT
ejpam-3574	436	4	with	with	ADP
ejpam-3574	436	5	2ki	2ki	ADJ
ejpam-3574	436	6	<	<	X
ejpam-3574	436	7	li	li	PROPN
ejpam-3574	436	8	and	and	CCONJ
ejpam-3574	436	9	the	the	DET
ejpam-3574	436	10	ni	ni	PROPN
ejpam-3574	436	11	is	be	AUX
ejpam-3574	436	12	odd	odd	ADJ
ejpam-3574	436	13	,	,	PUNCT
ejpam-3574	436	14	then	then	ADV
ejpam-3574	436	15	the	the	DET
ejpam-3574	436	16	li	li	PROPN
ejpam-3574	436	17	are	be	AUX
ejpam-3574	436	18	even	even	ADV
ejpam-3574	436	19	and	and	CCONJ
ejpam-3574	436	20	generally	generally	ADV
ejpam-3574	436	21	with	with	ADP
ejpam-3574	436	22	respect	respect	NOUN
ejpam-3574	436	23	to	to	ADP
ejpam-3574	436	24	the	the	DET
ejpam-3574	436	25	components	component	NOUN
ejpam-3574	436	26	of	of	ADP
ejpam-3574	436	27	u	u	PROPN
ejpam-3574	436	28	,	,	PUNCT
ejpam-3574	436	29	the	the	DET
ejpam-3574	436	30	rank	rank	NOUN
ejpam-3574	436	31	-	-	PUNCT
ejpam-3574	436	32	k	k	NOUN
ejpam-3574	436	33	perturbation	perturbation	NOUN
ejpam-3574	437	1	w̃	w̃	PROPN
ejpam-3574	437	2	=	=	PROPN
ejpam-3574	438	1	w	w	PROPN
ejpam-3574	438	2	+	+	PROPN
ejpam-3574	438	3	b	b	NOUN
ejpam-3574	438	4	of	of	ADP
ejpam-3574	438	5	w	w	PROPN
ejpam-3574	438	6	has	have	VERB
ejpam-3574	438	7	the	the	DET
ejpam-3574	438	8	following	follow	VERB
ejpam-3574	438	9	jordan	jordan	PROPN
ejpam-3574	438	10	canonical	canonical	ADJ
ejpam-3574	438	11	form	form	NOUN
ejpam-3574	438	12	:	:	PUNCT
ejpam-3574	438	13	li−2ki⊕	li−2ki⊕	NUM
ejpam-3574	438	14	j=1	j=1	ADJ
ejpam-3574	438	15	jni(λ	jni(λ	PROPN
ejpam-3574	438	16	)	)	PUNCT
ejpam-3574	438	17	⊕	⊕	PROPN
ejpam-3574	438	18	·	·	PUNCT
ejpam-3574	438	19	·	·	PUNCT
ejpam-3574	438	20	·	·	PUNCT
ejpam-3574	439	1	⊕	⊕	NOUN
ejpam-3574	440	1			PROPN
ejpam-3574	440	2	lm⊕	lm⊕	PROPN
ejpam-3574	440	3	j=1	j=1	PROPN
ejpam-3574	440	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	440	5	)	)	PUNCT
ejpam-3574	440	6	⊕	⊕	PROPN
ejpam-3574	440	7	j̃k	j̃k	PROPN
ejpam-3574	440	8	,	,	PUNCT
ejpam-3574	440	9	where	where	SCONJ
ejpam-3574	440	10	j̃	j̃	PROPN
ejpam-3574	440	11	=	=	SYM
ejpam-3574	440	12	j̃k	j̃k	PROPN
ejpam-3574	440	13	contains	contain	VERB
ejpam-3574	440	14	all	all	DET
ejpam-3574	440	15	the	the	DET
ejpam-3574	440	16	forms	form	NOUN
ejpam-3574	440	17	in	in	ADP
ejpam-3574	440	18	jordan	jordan	PROPN
ejpam-3574	440	19	blocks	block	NOUN
ejpam-3574	440	20	of	of	ADP
ejpam-3574	440	21	w̃	w̃	PROPN
ejpam-3574	440	22	associated	associate	VERB
ejpam-3574	440	23	with	with	ADP
ejpam-3574	440	24	the	the	DET
ejpam-3574	440	25	eigenvalues	eigenvalue	NOUN
ejpam-3574	440	26	different	different	ADJ
ejpam-3574	440	27	from	from	ADP
ejpam-3574	440	28	λ	λ	PROPN
ejpam-3574	440	29	.	.	PUNCT
ejpam-3574	441	1	using	use	VERB
ejpam-3574	441	2	(	(	PUNCT
ejpam-3574	441	3	2a	2a	NUM
ejpam-3574	441	4	)	)	PUNCT
ejpam-3574	441	5	and	and	CCONJ
ejpam-3574	441	6	(	(	PUNCT
ejpam-3574	441	7	2b	2b	NOUN
ejpam-3574	441	8	)	)	PUNCT
ejpam-3574	441	9	of	of	ADP
ejpam-3574	441	10	theorem	theorem	NOUN
ejpam-3574	441	11	3	3	NUM
ejpam-3574	441	12	,	,	PUNCT
ejpam-3574	441	13	we	we	PRON
ejpam-3574	441	14	have	have	VERB
ejpam-3574	441	15	the	the	DET
ejpam-3574	441	16	following	follow	VERB
ejpam-3574	441	17	corollary	corollary	ADJ
ejpam-3574	441	18	:	:	PUNCT
ejpam-3574	441	19	corollary	corollary	ADJ
ejpam-3574	441	20	1	1	PROPN
ejpam-3574	441	21	.	.	PUNCT
ejpam-3574	441	22	suppose	suppose	VERB
ejpam-3574	441	23	that	that	SCONJ
ejpam-3574	441	24	λ	λ	PROPN
ejpam-3574	441	25	∈	∈	PROPN
ejpam-3574	441	26	{	{	PUNCT
ejpam-3574	441	27	−1	−1	NOUN
ejpam-3574	441	28	,	,	PUNCT
ejpam-3574	441	29	1	1	NUM
ejpam-3574	441	30	}	}	PUNCT
ejpam-3574	441	31	.	.	PUNCT
ejpam-3574	442	1	if	if	SCONJ
ejpam-3574	442	2	k	k	PROPN
ejpam-3574	442	3	=	=	PUNCT
ejpam-3574	442	4	i−1∑	i−1∑	PUNCT
ejpam-3574	442	5	s=1	s=1	PUNCT
ejpam-3574	442	6	ls	ls	X
ejpam-3574	443	1	+	+	X
ejpam-3574	443	2	ki	ki	PROPN
ejpam-3574	443	3	,	,	PUNCT
ejpam-3574	443	4	with	with	ADP
ejpam-3574	443	5	ki	ki	PROPN
ejpam-3574	443	6	<	<	X
ejpam-3574	443	7	li	li	PROPN
ejpam-3574	443	8	and	and	CCONJ
ejpam-3574	443	9	only	only	ADV
ejpam-3574	443	10	ni	ni	PROPN
ejpam-3574	443	11	is	be	AUX
ejpam-3574	443	12	even	even	ADV
ejpam-3574	443	13	,	,	PUNCT
ejpam-3574	443	14	then	then	ADV
ejpam-3574	443	15	generally	generally	ADV
ejpam-3574	443	16	with	with	ADP
ejpam-3574	443	17	respect	respect	NOUN
ejpam-3574	443	18	to	to	ADP
ejpam-3574	443	19	the	the	DET
ejpam-3574	443	20	components	component	NOUN
ejpam-3574	443	21	of	of	ADP
ejpam-3574	443	22	u	u	PROPN
ejpam-3574	443	23	,	,	PUNCT
ejpam-3574	443	24	the	the	DET
ejpam-3574	443	25	w	w	PROPN
ejpam-3574	443	26	+	+	PROPN
ejpam-3574	443	27	b	b	NOUN
ejpam-3574	443	28	has	have	VERB
ejpam-3574	443	29	the	the	DET
ejpam-3574	443	30	jordan	jordan	PROPN
ejpam-3574	443	31	canonical	canonical	PROPN
ejpam-3574	443	32	formli−ki⊕	formli−ki⊕	X
ejpam-3574	443	33	j=1	j=1	PROPN
ejpam-3574	443	34	jni(λ	jni(λ	PROPN
ejpam-3574	444	1	)	)	PUNCT
ejpam-3574	444	2	⊕	⊕	PROPN
ejpam-3574	444	3			PROPN
ejpam-3574	444	4	li+1⊕	li+1⊕	NOUN
ejpam-3574	444	5	j=1	j=1	PROPN
ejpam-3574	444	6	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	444	7	)	)	PUNCT
ejpam-3574	444	8	⊕	⊕	PROPN
ejpam-3574	444	9	·	·	PUNCT
ejpam-3574	444	10	·	·	PUNCT
ejpam-3574	444	11	·	·	PUNCT
ejpam-3574	444	12	⊕	⊕	NOUN
ejpam-3574	445	1			PROPN
ejpam-3574	445	2	lm⊕	lm⊕	PROPN
ejpam-3574	445	3	j=1	j=1	PROPN
ejpam-3574	445	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	445	5	)	)	PUNCT
ejpam-3574	446	1	⊕	⊕	PROPN
ejpam-3574	446	2	j̃	j̃	PROPN
ejpam-3574	446	3	,	,	PUNCT
ejpam-3574	446	4	where	where	SCONJ
ejpam-3574	446	5	j̃	j̃	PROPN
ejpam-3574	446	6	contains	contain	VERB
ejpam-3574	446	7	all	all	DET
ejpam-3574	446	8	the	the	DET
ejpam-3574	446	9	forms	form	NOUN
ejpam-3574	446	10	in	in	ADP
ejpam-3574	446	11	jordan	jordan	PROPN
ejpam-3574	446	12	blocks	block	NOUN
ejpam-3574	446	13	of	of	ADP
ejpam-3574	446	14	w	w	PROPN
ejpam-3574	446	15	+	+	NOUN
ejpam-3574	446	16	b	b	NOUN
ejpam-3574	446	17	associated	associate	VERB
ejpam-3574	446	18	with	with	ADP
ejpam-3574	446	19	the	the	DET
ejpam-3574	446	20	eigenvalues	eigenvalue	NOUN
ejpam-3574	446	21	different	different	ADJ
ejpam-3574	446	22	from	from	ADP
ejpam-3574	446	23	λ	λ	PROPN
ejpam-3574	446	24	.	.	PUNCT
ejpam-3574	446	25	proof	proof	NOUN
ejpam-3574	446	26	.	.	PUNCT
ejpam-3574	447	1	•	•	INTJ
ejpam-3574	447	2	if	if	SCONJ
ejpam-3574	447	3	i	i	PRON
ejpam-3574	447	4	=	=	NOUN
ejpam-3574	447	5	1	1	NUM
ejpam-3574	447	6	,	,	PUNCT
ejpam-3574	447	7	then	then	ADV
ejpam-3574	447	8	k	k	PROPN
ejpam-3574	447	9	=	=	SYM
ejpam-3574	447	10	k1	k1	PROPN
ejpam-3574	447	11	and	and	CCONJ
ejpam-3574	447	12	n1	n1	NOUN
ejpam-3574	447	13	is	be	AUX
ejpam-3574	447	14	even	even	ADV
ejpam-3574	447	15	.	.	PUNCT
ejpam-3574	448	1	according	accord	VERB
ejpam-3574	448	2	to	to	ADP
ejpam-3574	448	3	(	(	PUNCT
ejpam-3574	448	4	2a	2a	NUM
ejpam-3574	448	5	)	)	PUNCT
ejpam-3574	448	6	of	of	ADP
ejpam-3574	448	7	theorem	theorem	NOUN
ejpam-3574	448	8	3	3	NUM
ejpam-3574	448	9	,	,	PUNCT
ejpam-3574	448	10	w̃k	w̃k	PRON
ejpam-3574	448	11	has	have	VERB
ejpam-3574	448	12	the	the	DET
ejpam-3574	448	13	following	follow	VERB
ejpam-3574	448	14	jordan	jordan	PROPN
ejpam-3574	448	15	canonical	canonical	ADJ
ejpam-3574	448	16	forml1−k1⊕	forml1−k1⊕	NOUN
ejpam-3574	448	17	j=1	j=1	PROPN
ejpam-3574	448	18	jn1(λ	jn1(λ	PROPN
ejpam-3574	448	19	)	)	PUNCT
ejpam-3574	448	20	⊕	⊕	PROPN
ejpam-3574	448	21			PROPN
ejpam-3574	448	22	l2⊕	l2⊕	PROPN
ejpam-3574	448	23	j=1	j=1	PROPN
ejpam-3574	448	24	jn2(λ	jn2(λ	PROPN
ejpam-3574	448	25	)	)	PUNCT
ejpam-3574	448	26	⊕	⊕	PROPN
ejpam-3574	448	27	·	·	PUNCT
ejpam-3574	448	28	·	·	PUNCT
ejpam-3574	448	29	·	·	PUNCT
ejpam-3574	449	1	⊕	⊕	NOUN
ejpam-3574	450	1			PROPN
ejpam-3574	450	2	lm⊕	lm⊕	PROPN
ejpam-3574	450	3	j=1	j=1	PROPN
ejpam-3574	450	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	450	5	)	)	PUNCT
ejpam-3574	451	1	⊕	⊕	PROPN
ejpam-3574	451	2	j̃	j̃	PROPN
ejpam-3574	451	3	,	,	PUNCT
ejpam-3574	451	4	where	where	SCONJ
ejpam-3574	451	5	j̃	j̃	PROPN
ejpam-3574	451	6	=	=	SYM
ejpam-3574	451	7	j̃k1	j̃k1	PROPN
ejpam-3574	451	8	contains	contain	VERB
ejpam-3574	451	9	all	all	DET
ejpam-3574	451	10	the	the	DET
ejpam-3574	451	11	forms	form	NOUN
ejpam-3574	451	12	in	in	ADP
ejpam-3574	451	13	jordan	jordan	PROPN
ejpam-3574	451	14	blocks	block	NOUN
ejpam-3574	451	15	of	of	ADP
ejpam-3574	451	16	w̃k1	w̃k1	NOUN
ejpam-3574	451	17	associated	associate	VERB
ejpam-3574	451	18	with	with	ADP
ejpam-3574	451	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	451	20	different	different	ADJ
ejpam-3574	451	21	from	from	ADP
ejpam-3574	451	22	λ	λ	PROPN
ejpam-3574	451	23	.	.	PROPN
ejpam-3574	451	24	•	•	NUM
ejpam-3574	451	25	if	if	SCONJ
ejpam-3574	451	26	i	i	PRON
ejpam-3574	451	27	=	=	NOUN
ejpam-3574	451	28	2	2	NUM
ejpam-3574	451	29	,	,	PUNCT
ejpam-3574	451	30	then	then	ADV
ejpam-3574	451	31	k	k	PROPN
ejpam-3574	451	32	=	=	PROPN
ejpam-3574	451	33	l1	l1	PROPN
ejpam-3574	451	34	+	+	CCONJ
ejpam-3574	451	35	k2	k2	PROPN
ejpam-3574	451	36	,	,	PUNCT
ejpam-3574	451	37	with	with	ADP
ejpam-3574	451	38	(	(	PUNCT
ejpam-3574	451	39	k2	k2	ADJ
ejpam-3574	451	40	<	<	X
ejpam-3574	451	41	l2	l2	NOUN
ejpam-3574	451	42	)	)	PUNCT
ejpam-3574	451	43	and	and	CCONJ
ejpam-3574	451	44	n2	n2	NOUN
ejpam-3574	451	45	is	be	AUX
ejpam-3574	451	46	even	even	ADV
ejpam-3574	451	47	.	.	PUNCT
ejpam-3574	452	1	we	we	PRON
ejpam-3574	452	2	know	know	VERB
ejpam-3574	452	3	that	that	SCONJ
ejpam-3574	452	4	w̃k	w̃k	ADV
ejpam-3574	453	1	=	=	PUNCT
ejpam-3574	454	1	(	(	PUNCT
ejpam-3574	454	2	i	i	PRON
ejpam-3574	454	3	+	+	CCONJ
ejpam-3574	454	4	uku	uku	PROPN
ejpam-3574	454	5	t	t	PROPN
ejpam-3574	454	6	k	k	PROPN
ejpam-3574	454	7	j	j	PROPN
ejpam-3574	454	8	)	)	PUNCT
ejpam-3574	454	9	(	(	PUNCT
ejpam-3574	454	10	i	i	PRON
ejpam-3574	454	11	+	+	CCONJ
ejpam-3574	455	1	uk−1u	uk−1u	NUM
ejpam-3574	455	2	t	t	NOUN
ejpam-3574	455	3	k−1j	k−1j	NOUN
ejpam-3574	455	4	)	)	PUNCT
ejpam-3574	455	5	×	×	NOUN
ejpam-3574	455	6	...	...	PUNCT
ejpam-3574	455	7	×	×	NOUN
ejpam-3574	456	1	(	(	PUNCT
ejpam-3574	456	2	i	i	PRON
ejpam-3574	456	3	+	+	CCONJ
ejpam-3574	456	4	ul1	ul1	PROPN
ejpam-3574	456	5	+	+	PROPN
ejpam-3574	456	6	1u	1u	NUM
ejpam-3574	456	7	t	t	PROPN
ejpam-3574	456	8	l1	l1	PROPN
ejpam-3574	456	9	+	+	PROPN
ejpam-3574	456	10	1j	1j	NUM
ejpam-3574	456	11	)	)	PUNCT
ejpam-3574	456	12	×	×	NOUN
ejpam-3574	456	13	(	(	PUNCT
ejpam-3574	456	14	i	i	PRON
ejpam-3574	456	15	+	+	CCONJ
ejpam-3574	457	1	ul1u	ul1u	PROPN
ejpam-3574	457	2	t	t	X
ejpam-3574	457	3	l1j	l1j	PROPN
ejpam-3574	457	4	)	)	PUNCT
ejpam-3574	458	1	×	×	NOUN
ejpam-3574	458	2	...	...	PUNCT
ejpam-3574	458	3	×	×	NOUN
ejpam-3574	459	1	(	(	PUNCT
ejpam-3574	459	2	i	i	PRON
ejpam-3574	459	3	+	+	CCONJ
ejpam-3574	459	4	u1u	u1u	PROPN
ejpam-3574	459	5	t	t	PROPN
ejpam-3574	459	6	1	1	NUM
ejpam-3574	459	7	j	j	PROPN
ejpam-3574	459	8	)	)	PUNCT
ejpam-3574	459	9	w︸	w︸	VERB
ejpam-3574	459	10	︷︷	︷︷	PROPN
ejpam-3574	459	11	︸	︸	X
ejpam-3574	459	12	w̃l1	w̃l1	NOUN
ejpam-3574	459	13	=	=	SYM
ejpam-3574	460	1	(	(	PUNCT
ejpam-3574	460	2	i	i	PRON
ejpam-3574	460	3	+	+	CCONJ
ejpam-3574	460	4	uku	uku	PROPN
ejpam-3574	460	5	t	t	PROPN
ejpam-3574	460	6	k	k	PROPN
ejpam-3574	460	7	j	j	PROPN
ejpam-3574	460	8	)	)	PUNCT
ejpam-3574	461	1	(	(	PUNCT
ejpam-3574	461	2	i	i	PRON
ejpam-3574	461	3	+	+	CCONJ
ejpam-3574	462	1	uk−1u	uk−1u	NUM
ejpam-3574	462	2	t	t	NOUN
ejpam-3574	462	3	k−1j	k−1j	NOUN
ejpam-3574	462	4	)	)	PUNCT
ejpam-3574	462	5	×	×	NOUN
ejpam-3574	462	6	...	...	PUNCT
ejpam-3574	462	7	×	×	NOUN
ejpam-3574	463	1	(	(	PUNCT
ejpam-3574	463	2	i	i	PRON
ejpam-3574	463	3	+	+	CCONJ
ejpam-3574	463	4	ul1	ul1	PROPN
ejpam-3574	463	5	+	+	PROPN
ejpam-3574	463	6	1u	1u	NUM
ejpam-3574	463	7	t	t	PROPN
ejpam-3574	463	8	l1	l1	PROPN
ejpam-3574	463	9	+	+	PROPN
ejpam-3574	463	10	1j	1j	NUM
ejpam-3574	463	11	)	)	PUNCT
ejpam-3574	463	12	w̃l1	w̃l1	NOUN
ejpam-3574	463	13	.	.	PUNCT
ejpam-3574	464	1	so	so	ADV
ejpam-3574	464	2	m.	m.	NOUN
ejpam-3574	464	3	dosso	dosso	PROPN
ejpam-3574	464	4	,	,	PUNCT
ejpam-3574	464	5	t.	t.	PROPN
ejpam-3574	464	6	g.	g.	PROPN
ejpam-3574	464	7	y.	y.	PROPN
ejpam-3574	464	8	arouna	arouna	PROPN
ejpam-3574	464	9	,	,	PUNCT
ejpam-3574	464	10	j.-c	j.-c	PROPN
ejpam-3574	464	11	.	.	PUNCT
ejpam-3574	465	1	koua	koua	PROPN
ejpam-3574	465	2	brou	brou	PROPN
ejpam-3574	465	3	/	/	SYM
ejpam-3574	465	4	eur	eur	PROPN
ejpam-3574	465	5	.	.	PUNCT
ejpam-3574	466	1	j.	j.	PROPN
ejpam-3574	466	2	pure	pure	PROPN
ejpam-3574	466	3	appl	appl	PROPN
ejpam-3574	466	4	.	.	PROPN
ejpam-3574	466	5	math	math	PROPN
ejpam-3574	466	6	,	,	PUNCT
ejpam-3574	466	7	12	12	NUM
ejpam-3574	466	8	(	(	PUNCT
ejpam-3574	466	9	4	4	NUM
ejpam-3574	466	10	)	)	PUNCT
ejpam-3574	466	11	(	(	PUNCT
ejpam-3574	466	12	2019	2019	NUM
ejpam-3574	466	13	)	)	PUNCT
ejpam-3574	466	14	,	,	PUNCT
ejpam-3574	466	15	1744	1744	NUM
ejpam-3574	466	16	-	-	SYM
ejpam-3574	466	17	1770	1770	NUM
ejpam-3574	466	18	1760	1760	NUM
ejpam-3574	466	19	(	(	PUNCT
ejpam-3574	466	20	a	a	X
ejpam-3574	466	21	)	)	PUNCT
ejpam-3574	466	22	if	if	SCONJ
ejpam-3574	466	23	n1	n1	PROPN
ejpam-3574	466	24	is	be	AUX
ejpam-3574	466	25	even	even	ADV
ejpam-3574	466	26	,	,	PUNCT
ejpam-3574	466	27	according	accord	VERB
ejpam-3574	466	28	to	to	ADP
ejpam-3574	466	29	the	the	DET
ejpam-3574	466	30	property	property	NOUN
ejpam-3574	466	31	2a	2a	NUM
ejpam-3574	466	32	)	)	PUNCT
ejpam-3574	466	33	of	of	ADP
ejpam-3574	466	34	theorem	theorem	ADJ
ejpam-3574	466	35	3	3	NUM
ejpam-3574	466	36	,	,	PUNCT
ejpam-3574	466	37	w̃l1	w̃l1	PROPN
ejpam-3574	466	38	has	have	VERB
ejpam-3574	466	39	the	the	DET
ejpam-3574	466	40	following	follow	VERB
ejpam-3574	466	41	jordan	jordan	PROPN
ejpam-3574	466	42	canonical	canonical	PROPN
ejpam-3574	466	43	form	form	PROPN
ejpam-3574	466	44	l2⊕	l2⊕	X
ejpam-3574	466	45	j=1	j=1	PROPN
ejpam-3574	466	46	jn2(λ	jn2(λ	PROPN
ejpam-3574	466	47	)	)	PUNCT
ejpam-3574	466	48	⊕	⊕	PROPN
ejpam-3574	466	49	·	·	PUNCT
ejpam-3574	466	50	·	·	PUNCT
ejpam-3574	466	51	·	·	PUNCT
ejpam-3574	467	1	⊕	⊕	NOUN
ejpam-3574	468	1			PROPN
ejpam-3574	468	2	lm⊕	lm⊕	PROPN
ejpam-3574	468	3	j=1	j=1	PROPN
ejpam-3574	468	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	468	5	)	)	PUNCT
ejpam-3574	468	6	⊕	⊕	PROPN
ejpam-3574	468	7	j̃l1	j̃l1	PROPN
ejpam-3574	468	8	,	,	PUNCT
ejpam-3574	468	9	(	(	PUNCT
ejpam-3574	468	10	11	11	NUM
ejpam-3574	468	11	)	)	PUNCT
ejpam-3574	468	12	where	where	SCONJ
ejpam-3574	468	13	j̃	j̃	PROPN
ejpam-3574	468	14	=	=	SYM
ejpam-3574	468	15	j̃l1	j̃l1	PROPN
ejpam-3574	468	16	contains	contain	VERB
ejpam-3574	468	17	all	all	DET
ejpam-3574	468	18	the	the	DET
ejpam-3574	468	19	forms	form	NOUN
ejpam-3574	468	20	in	in	ADP
ejpam-3574	468	21	jordan	jordan	PROPN
ejpam-3574	468	22	blocks	block	NOUN
ejpam-3574	468	23	of	of	ADP
ejpam-3574	468	24	w̃l1	w̃l1	NOUN
ejpam-3574	468	25	associated	associate	VERB
ejpam-3574	468	26	with	with	ADP
ejpam-3574	468	27	all	all	DET
ejpam-3574	468	28	eigenvalues	eigenvalue	VERB
ejpam-3574	468	29	different	different	ADJ
ejpam-3574	468	30	from	from	ADP
ejpam-3574	468	31	λ	λ	X
ejpam-3574	468	32	.	.	PROPN
ejpam-3574	468	33	w̃k	w̃k	PRON
ejpam-3574	468	34	being	be	AUX
ejpam-3574	468	35	k2	k2	ADJ
ejpam-3574	468	36	rank	rank	NOUN
ejpam-3574	468	37	-	-	PUNCT
ejpam-3574	468	38	one	one	NUM
ejpam-3574	468	39	perturbations	perturbation	NOUN
ejpam-3574	468	40	of	of	ADP
ejpam-3574	468	41	w̃l1	w̃l1	NOUN
ejpam-3574	468	42	,	,	PUNCT
ejpam-3574	468	43	according	accord	VERB
ejpam-3574	468	44	to	to	ADP
ejpam-3574	468	45	2a	2a	NUM
ejpam-3574	468	46	)	)	PUNCT
ejpam-3574	468	47	of	of	ADP
ejpam-3574	468	48	theorem	theorem	NOUN
ejpam-3574	468	49	3	3	NUM
ejpam-3574	468	50	,	,	PUNCT
ejpam-3574	468	51	the	the	DET
ejpam-3574	468	52	jordan	jordan	PROPN
ejpam-3574	468	53	canonical	canonical	ADJ
ejpam-3574	468	54	form	form	NOUN
ejpam-3574	468	55	of	of	ADP
ejpam-3574	468	56	w̃k	w̃k	PRON
ejpam-3574	468	57	is	be	AUX
ejpam-3574	468	58	given	give	VERB
ejpam-3574	468	59	byl2−k2⊕	byl2−k2⊕	NOUN
ejpam-3574	468	60	j=1	j=1	PROPN
ejpam-3574	468	61	jn2(λ	jn2(λ	PROPN
ejpam-3574	468	62	)	)	PUNCT
ejpam-3574	469	1	⊕	⊕	PROPN
ejpam-3574	469	2			PROPN
ejpam-3574	469	3	l3⊕	l3⊕	PROPN
ejpam-3574	469	4	j=1	j=1	PROPN
ejpam-3574	469	5	jn3(λ	jn3(λ	PROPN
ejpam-3574	469	6	)	)	PUNCT
ejpam-3574	469	7	⊕	⊕	PROPN
ejpam-3574	469	8	·	·	PUNCT
ejpam-3574	469	9	·	·	PUNCT
ejpam-3574	469	10	·	·	PUNCT
ejpam-3574	469	11	⊕	⊕	NOUN
ejpam-3574	470	1			PROPN
ejpam-3574	470	2	lm⊕	lm⊕	PROPN
ejpam-3574	470	3	j=1	j=1	PROPN
ejpam-3574	470	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	470	5	)	)	PUNCT
ejpam-3574	471	1	⊕	⊕	PROPN
ejpam-3574	471	2	j̃	j̃	PROPN
ejpam-3574	471	3	,	,	PUNCT
ejpam-3574	471	4	where	where	SCONJ
ejpam-3574	471	5	j̃	j̃	PROPN
ejpam-3574	471	6	=	=	SYM
ejpam-3574	471	7	j̃k	j̃k	PROPN
ejpam-3574	471	8	contains	contain	VERB
ejpam-3574	471	9	all	all	DET
ejpam-3574	471	10	the	the	DET
ejpam-3574	471	11	forms	form	NOUN
ejpam-3574	471	12	in	in	ADP
ejpam-3574	471	13	jordan	jordan	PROPN
ejpam-3574	471	14	blocks	block	NOUN
ejpam-3574	471	15	of	of	ADP
ejpam-3574	471	16	w̃k	w̃k	ADV
ejpam-3574	471	17	associated	associate	VERB
ejpam-3574	471	18	with	with	ADP
ejpam-3574	471	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	471	20	different	different	ADJ
ejpam-3574	471	21	from	from	ADP
ejpam-3574	471	22	λ	λ	PROPN
ejpam-3574	471	23	.	.	PUNCT
ejpam-3574	472	1	(	(	PUNCT
ejpam-3574	472	2	b	b	X
ejpam-3574	472	3	)	)	PUNCT
ejpam-3574	472	4	if	if	SCONJ
ejpam-3574	472	5	n1	n1	PROPN
ejpam-3574	472	6	is	be	AUX
ejpam-3574	472	7	odd	odd	ADJ
ejpam-3574	472	8	,	,	PUNCT
ejpam-3574	472	9	according	accord	VERB
ejpam-3574	472	10	to	to	ADP
ejpam-3574	472	11	2b	2b	NUM
ejpam-3574	472	12	)	)	PUNCT
ejpam-3574	472	13	of	of	ADP
ejpam-3574	472	14	theorem	theorem	NOUN
ejpam-3574	472	15	3	3	NUM
ejpam-3574	472	16	,	,	PUNCT
ejpam-3574	472	17	the	the	DET
ejpam-3574	472	18	jordan	jordan	PROPN
ejpam-3574	472	19	canonical	canonical	ADJ
ejpam-3574	472	20	form	form	NOUN
ejpam-3574	472	21	of	of	ADP
ejpam-3574	472	22	w̃l1	w̃l1	PROPN
ejpam-3574	472	23	is	be	AUX
ejpam-3574	472	24	given	give	VERB
ejpam-3574	472	25	by	by	ADP
ejpam-3574	472	26	(	(	PUNCT
ejpam-3574	472	27	11	11	NUM
ejpam-3574	472	28	)	)	PUNCT
ejpam-3574	472	29	.	.	PUNCT
ejpam-3574	473	1	knowing	know	VERB
ejpam-3574	473	2	that	that	DET
ejpam-3574	473	3	n2	n2	NOUN
ejpam-3574	473	4	is	be	AUX
ejpam-3574	473	5	even	even	ADV
ejpam-3574	473	6	and	and	CCONJ
ejpam-3574	473	7	w̃k	w̃k	PRON
ejpam-3574	473	8	is	be	AUX
ejpam-3574	473	9	k2	k2	ADJ
ejpam-3574	473	10	rank	rank	NOUN
ejpam-3574	473	11	-	-	PUNCT
ejpam-3574	473	12	one	one	NUM
ejpam-3574	473	13	perturbations	perturbation	NOUN
ejpam-3574	473	14	of	of	ADP
ejpam-3574	473	15	w̃l1	w̃l1	NOUN
ejpam-3574	473	16	,	,	PUNCT
ejpam-3574	473	17	we	we	PRON
ejpam-3574	473	18	obtain	obtain	AUX
ejpam-3574	473	19	from	from	ADP
ejpam-3574	473	20	2a	2a	NUM
ejpam-3574	473	21	)	)	PUNCT
ejpam-3574	473	22	of	of	ADP
ejpam-3574	473	23	theorem	theorem	NOUN
ejpam-3574	473	24	3	3	NUM
ejpam-3574	473	25	that	that	PRON
ejpam-3574	473	26	w̃k	w̃k	ADV
ejpam-3574	473	27	has	have	VERB
ejpam-3574	473	28	the	the	DET
ejpam-3574	473	29	following	follow	VERB
ejpam-3574	473	30	jordan	jordan	PROPN
ejpam-3574	473	31	canonical	canonical	PROPN
ejpam-3574	473	32	forml2−k2⊕	forml2−k2⊕	VERB
ejpam-3574	473	33	j=1	j=1	PROPN
ejpam-3574	473	34	jn2(λ	jn2(λ	PROPN
ejpam-3574	473	35	)	)	PUNCT
ejpam-3574	474	1	⊕	⊕	PROPN
ejpam-3574	474	2			PROPN
ejpam-3574	474	3	l3⊕	l3⊕	PROPN
ejpam-3574	474	4	j=1	j=1	PROPN
ejpam-3574	474	5	jn3(λ	jn3(λ	PROPN
ejpam-3574	474	6	)	)	PUNCT
ejpam-3574	474	7	⊕	⊕	PROPN
ejpam-3574	474	8	·	·	PUNCT
ejpam-3574	474	9	·	·	PUNCT
ejpam-3574	474	10	·	·	PUNCT
ejpam-3574	474	11	⊕	⊕	NOUN
ejpam-3574	475	1			PROPN
ejpam-3574	475	2	lm⊕	lm⊕	PROPN
ejpam-3574	475	3	j=1	j=1	PROPN
ejpam-3574	475	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	475	5	)	)	PUNCT
ejpam-3574	476	1	⊕	⊕	PROPN
ejpam-3574	476	2	j̃	j̃	PROPN
ejpam-3574	476	3	,	,	PUNCT
ejpam-3574	476	4	where	where	SCONJ
ejpam-3574	476	5	j̃	j̃	PROPN
ejpam-3574	476	6	=	=	SYM
ejpam-3574	476	7	j̃k	j̃k	PROPN
ejpam-3574	476	8	contains	contain	VERB
ejpam-3574	476	9	all	all	DET
ejpam-3574	476	10	the	the	DET
ejpam-3574	476	11	forms	form	NOUN
ejpam-3574	476	12	in	in	ADP
ejpam-3574	476	13	jordan	jordan	PROPN
ejpam-3574	476	14	blocks	block	NOUN
ejpam-3574	476	15	of	of	ADP
ejpam-3574	476	16	w̃k	w̃k	ADV
ejpam-3574	476	17	associated	associate	VERB
ejpam-3574	476	18	with	with	ADP
ejpam-3574	476	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	476	20	different	different	ADJ
ejpam-3574	476	21	from	from	ADP
ejpam-3574	476	22	λ	λ	PROPN
ejpam-3574	476	23	.	.	PROPN
ejpam-3574	476	24	•	•	NUM
ejpam-3574	476	25	for	for	ADP
ejpam-3574	476	26	i	i	PRON
ejpam-3574	476	27	>	>	X
ejpam-3574	476	28	2	2	NUM
ejpam-3574	476	29	,	,	PUNCT
ejpam-3574	476	30	we	we	PRON
ejpam-3574	476	31	have	have	VERB
ejpam-3574	476	32	k	k	NOUN
ejpam-3574	476	33	=	=	PUNCT
ejpam-3574	476	34	i−1∑	i−1∑	NOUN
ejpam-3574	476	35	s=1	s=1	PUNCT
ejpam-3574	476	36	ls	ls	X
ejpam-3574	477	1	+	+	X
ejpam-3574	477	2	ki	ki	PROPN
ejpam-3574	477	3	,	,	PUNCT
ejpam-3574	477	4	with	with	ADP
ejpam-3574	477	5	ki	ki	PROPN
ejpam-3574	477	6	<	<	X
ejpam-3574	477	7	li	li	PROPN
ejpam-3574	477	8	and	and	CCONJ
ejpam-3574	477	9	ni	ni	PROPN
ejpam-3574	477	10	is	be	AUX
ejpam-3574	477	11	even	even	ADV
ejpam-3574	477	12	.	.	PUNCT
ejpam-3574	478	1	let	let	VERB
ejpam-3574	478	2	’s	’s	NOUN
ejpam-3574	478	3	put	put	VERB
ejpam-3574	478	4	γ(i	γ(i	NOUN
ejpam-3574	478	5	)	)	PUNCT
ejpam-3574	479	1	=	=	SYM
ejpam-3574	480	1	∑i	∑i	NOUN
ejpam-3574	480	2	s=1	s=1	X
ejpam-3574	480	3	ls	ls	ADJ
ejpam-3574	480	4	.	.	PUNCT
ejpam-3574	481	1	we	we	PRON
ejpam-3574	481	2	know	know	VERB
ejpam-3574	481	3	that	that	SCONJ
ejpam-3574	481	4	w̃k	w̃k	ADV
ejpam-3574	482	1	=	=	PUNCT
ejpam-3574	483	1	(	(	PUNCT
ejpam-3574	483	2	i	i	PRON
ejpam-3574	483	3	+	+	CCONJ
ejpam-3574	483	4	uku	uku	PROPN
ejpam-3574	483	5	t	t	PROPN
ejpam-3574	483	6	k	k	PROPN
ejpam-3574	483	7	j	j	PROPN
ejpam-3574	483	8	)	)	PUNCT
ejpam-3574	483	9	(	(	PUNCT
ejpam-3574	483	10	i	i	PRON
ejpam-3574	483	11	+	+	CCONJ
ejpam-3574	484	1	uk−1u	uk−1u	NUM
ejpam-3574	484	2	t	t	NOUN
ejpam-3574	484	3	k−1j	k−1j	NOUN
ejpam-3574	484	4	)	)	PUNCT
ejpam-3574	484	5	×	×	NOUN
ejpam-3574	484	6	...	...	PUNCT
ejpam-3574	484	7	×	×	NOUN
ejpam-3574	485	1	(	(	PUNCT
ejpam-3574	485	2	i	i	PRON
ejpam-3574	485	3	+	+	X
ejpam-3574	485	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	485	5	t	t	NOUN
ejpam-3574	485	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	485	7	)	)	PUNCT
ejpam-3574	485	8	×	×	NOUN
ejpam-3574	485	9	(	(	PUNCT
ejpam-3574	485	10	i	i	PRON
ejpam-3574	485	11	+	+	CCONJ
ejpam-3574	485	12	uγ(i−1)u	uγ(i−1)u	PROPN
ejpam-3574	485	13	t	t	X
ejpam-3574	485	14	γ(i−1)j	γ(i−1)j	PROPN
ejpam-3574	485	15	)	)	PUNCT
ejpam-3574	485	16	×	×	NOUN
ejpam-3574	485	17	...	...	PUNCT
ejpam-3574	485	18	×	×	NOUN
ejpam-3574	485	19	(	(	PUNCT
ejpam-3574	485	20	i	i	PRON
ejpam-3574	485	21	+	+	CCONJ
ejpam-3574	485	22	u1u	u1u	PROPN
ejpam-3574	485	23	t	t	PROPN
ejpam-3574	485	24	1	1	NUM
ejpam-3574	485	25	j	j	PROPN
ejpam-3574	485	26	)	)	PUNCT
ejpam-3574	485	27	w︸	w︸	VERB
ejpam-3574	485	28	︷︷	︷︷	PROPN
ejpam-3574	485	29	︸	︸	ADP
ejpam-3574	486	1	=	=	ADJ
ejpam-3574	486	2	w̃γ(i−1	w̃γ(i−1	X
ejpam-3574	486	3	)	)	PUNCT
ejpam-3574	486	4	=	=	PUNCT
ejpam-3574	487	1	(	(	PUNCT
ejpam-3574	487	2	i	i	PRON
ejpam-3574	487	3	+	+	CCONJ
ejpam-3574	487	4	uku	uku	PROPN
ejpam-3574	487	5	t	t	PROPN
ejpam-3574	487	6	k	k	PROPN
ejpam-3574	487	7	j	j	PROPN
ejpam-3574	487	8	)	)	PUNCT
ejpam-3574	488	1	(	(	PUNCT
ejpam-3574	488	2	i	i	PRON
ejpam-3574	488	3	+	+	CCONJ
ejpam-3574	489	1	uk−1u	uk−1u	NUM
ejpam-3574	489	2	t	t	NOUN
ejpam-3574	489	3	k−1j	k−1j	NOUN
ejpam-3574	489	4	)	)	PUNCT
ejpam-3574	489	5	×	×	NOUN
ejpam-3574	489	6	...	...	PUNCT
ejpam-3574	489	7	×	×	NOUN
ejpam-3574	490	1	(	(	PUNCT
ejpam-3574	490	2	i	i	PRON
ejpam-3574	490	3	+	+	X
ejpam-3574	490	4	uγ(i−1)+1u	uγ(i−1)+1u	PROPN
ejpam-3574	490	5	t	t	NOUN
ejpam-3574	490	6	γ(i−1)+1j	γ(i−1)+1j	NOUN
ejpam-3574	490	7	)	)	PUNCT
ejpam-3574	490	8	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	490	9	)	)	PUNCT
ejpam-3574	490	10	=	=	PUNCT
ejpam-3574	491	1	(	(	PUNCT
ejpam-3574	491	2	i	i	PRON
ejpam-3574	491	3	+	+	CCONJ
ejpam-3574	491	4	uku	uku	PROPN
ejpam-3574	491	5	t	t	PROPN
ejpam-3574	491	6	k	k	PROPN
ejpam-3574	491	7	j	j	PROPN
ejpam-3574	491	8	)	)	PUNCT
ejpam-3574	492	1	(	(	PUNCT
ejpam-3574	492	2	i	i	PRON
ejpam-3574	492	3	+	+	CCONJ
ejpam-3574	493	1	uk−1u	uk−1u	NUM
ejpam-3574	493	2	t	t	NOUN
ejpam-3574	493	3	k−1j	k−1j	NOUN
ejpam-3574	493	4	)	)	PUNCT
ejpam-3574	493	5	×	×	NOUN
ejpam-3574	493	6	...	...	PUNCT
ejpam-3574	493	7	×	×	NOUN
ejpam-3574	494	1	(	(	PUNCT
ejpam-3574	494	2	i	i	PRON
ejpam-3574	494	3	+	+	CCONJ
ejpam-3574	494	4	uk−ki+1u	uk−ki+1u	PROPN
ejpam-3574	494	5	t	t	PROPN
ejpam-3574	494	6	k−ki+1j	k−ki+1j	PROPN
ejpam-3574	494	7	)	)	PUNCT
ejpam-3574	494	8	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	494	9	)	)	PUNCT
ejpam-3574	494	10	,	,	PUNCT
ejpam-3574	494	11	because	because	SCONJ
ejpam-3574	494	12	γ(i−	γ(i−	NOUN
ejpam-3574	494	13	1	1	NUM
ejpam-3574	494	14	)	)	PUNCT
ejpam-3574	494	15	=	=	PUNCT
ejpam-3574	495	1	k	k	PROPN
ejpam-3574	495	2	−	−	PROPN
ejpam-3574	496	1	ki	ki	INTJ
ejpam-3574	496	2	.	.	PUNCT
ejpam-3574	497	1	so	so	ADV
ejpam-3574	497	2	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	497	3	)	)	PUNCT
ejpam-3574	497	4	has	have	VERB
ejpam-3574	497	5	the	the	DET
ejpam-3574	497	6	following	follow	VERB
ejpam-3574	497	7	jordan	jordan	PROPN
ejpam-3574	497	8	canonical	canonical	PROPN
ejpam-3574	497	9	form	form	PROPN
ejpam-3574	497	10	li⊕	li⊕	PUNCT
ejpam-3574	498	1	j=1	j=1	ADJ
ejpam-3574	498	2	jni(λ	jni(λ	PROPN
ejpam-3574	498	3	)	)	PUNCT
ejpam-3574	498	4	⊕	⊕	PROPN
ejpam-3574	498	5			PROPN
ejpam-3574	498	6	li+1⊕	li+1⊕	NOUN
ejpam-3574	498	7	j=1	j=1	PROPN
ejpam-3574	498	8	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	498	9	)	)	PUNCT
ejpam-3574	498	10	⊕	⊕	PROPN
ejpam-3574	498	11	·	·	PUNCT
ejpam-3574	498	12	·	·	PUNCT
ejpam-3574	498	13	·	·	PUNCT
ejpam-3574	499	1	⊕	⊕	NOUN
ejpam-3574	500	1			PROPN
ejpam-3574	500	2	lm⊕	lm⊕	PROPN
ejpam-3574	500	3	j=1	j=1	PROPN
ejpam-3574	500	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	500	5	)	)	PUNCT
ejpam-3574	500	6	⊕	⊕	PROPN
ejpam-3574	500	7	j̃γ(i−1	j̃γ(i−1	PROPN
ejpam-3574	500	8	)	)	PUNCT
ejpam-3574	500	9	,	,	PUNCT
ejpam-3574	500	10	m.	m.	NOUN
ejpam-3574	500	11	dosso	dosso	PROPN
ejpam-3574	500	12	,	,	PUNCT
ejpam-3574	500	13	t.	t.	PROPN
ejpam-3574	500	14	g.	g.	PROPN
ejpam-3574	500	15	y.	y.	PROPN
ejpam-3574	500	16	arouna	arouna	PROPN
ejpam-3574	500	17	,	,	PUNCT
ejpam-3574	500	18	j.-c	j.-c	PROPN
ejpam-3574	500	19	.	.	PUNCT
ejpam-3574	501	1	koua	koua	PROPN
ejpam-3574	501	2	brou	brou	PROPN
ejpam-3574	501	3	/	/	SYM
ejpam-3574	501	4	eur	eur	PROPN
ejpam-3574	501	5	.	.	PUNCT
ejpam-3574	502	1	j.	j.	PROPN
ejpam-3574	502	2	pure	pure	PROPN
ejpam-3574	502	3	appl	appl	PROPN
ejpam-3574	502	4	.	.	PROPN
ejpam-3574	502	5	math	math	PROPN
ejpam-3574	502	6	,	,	PUNCT
ejpam-3574	502	7	12	12	NUM
ejpam-3574	502	8	(	(	PUNCT
ejpam-3574	502	9	4	4	NUM
ejpam-3574	502	10	)	)	PUNCT
ejpam-3574	502	11	(	(	PUNCT
ejpam-3574	502	12	2019	2019	NUM
ejpam-3574	502	13	)	)	PUNCT
ejpam-3574	502	14	,	,	PUNCT
ejpam-3574	502	15	1744	1744	NUM
ejpam-3574	502	16	-	-	SYM
ejpam-3574	502	17	1770	1770	NUM
ejpam-3574	502	18	1761	1761	NUM
ejpam-3574	502	19	where	where	SCONJ
ejpam-3574	502	20	j̃γ(i−1	j̃γ(i−1	NOUN
ejpam-3574	502	21	)	)	PUNCT
ejpam-3574	502	22	contains	contain	VERB
ejpam-3574	502	23	all	all	DET
ejpam-3574	502	24	the	the	DET
ejpam-3574	502	25	forms	form	NOUN
ejpam-3574	502	26	in	in	ADP
ejpam-3574	502	27	jordan	jordan	PROPN
ejpam-3574	502	28	blocks	block	NOUN
ejpam-3574	502	29	of	of	ADP
ejpam-3574	502	30	w̃γ(i−1	w̃γ(i−1	NOUN
ejpam-3574	502	31	)	)	PUNCT
ejpam-3574	502	32	associated	associate	VERB
ejpam-3574	502	33	with	with	ADP
ejpam-3574	502	34	eigenvalues	eigenvalue	NOUN
ejpam-3574	502	35	different	different	ADJ
ejpam-3574	502	36	from	from	ADP
ejpam-3574	502	37	λ	λ	PROPN
ejpam-3574	502	38	.	.	PUNCT
ejpam-3574	502	39	applying	apply	VERB
ejpam-3574	502	40	thereafter	thereafter	ADV
ejpam-3574	502	41	ki	ki	PROPN
ejpam-3574	502	42	times	time	NOUN
ejpam-3574	502	43	2a	2a	NUM
ejpam-3574	502	44	)	)	PUNCT
ejpam-3574	502	45	of	of	ADP
ejpam-3574	502	46	theorem	theorem	NOUN
ejpam-3574	502	47	3	3	NUM
ejpam-3574	502	48	to	to	ADP
ejpam-3574	502	49	the	the	DET
ejpam-3574	502	50	matrix	matrix	NOUN
ejpam-3574	502	51	w̃γ(i−1	w̃γ(i−1	PROPN
ejpam-3574	502	52	)	)	PUNCT
ejpam-3574	503	1	,	,	PUNCT
ejpam-3574	503	2	we	we	PRON
ejpam-3574	503	3	obtain	obtain	VERB
ejpam-3574	503	4	the	the	DET
ejpam-3574	503	5	jordan	jordan	PROPN
ejpam-3574	503	6	canonical	canonical	ADJ
ejpam-3574	503	7	form	form	NOUN
ejpam-3574	503	8	of	of	ADP
ejpam-3574	503	9	w̃kli−ki⊕	w̃kli−ki⊕	NOUN
ejpam-3574	503	10	j=1	j=1	ADJ
ejpam-3574	503	11	jni(λ	jni(λ	PROPN
ejpam-3574	503	12	)	)	PUNCT
ejpam-3574	504	1	⊕	⊕	PROPN
ejpam-3574	504	2			PROPN
ejpam-3574	504	3	li+1⊕	li+1⊕	NOUN
ejpam-3574	504	4	j=1	j=1	PROPN
ejpam-3574	504	5	jni+1(λ	jni+1(λ	PROPN
ejpam-3574	504	6	)	)	PUNCT
ejpam-3574	504	7	⊕	⊕	PROPN
ejpam-3574	504	8	·	·	PUNCT
ejpam-3574	504	9	·	·	PUNCT
ejpam-3574	504	10	·	·	PUNCT
ejpam-3574	505	1	⊕	⊕	NOUN
ejpam-3574	506	1			PROPN
ejpam-3574	506	2	lm⊕	lm⊕	PROPN
ejpam-3574	506	3	j=1	j=1	PROPN
ejpam-3574	506	4	jnm(λ	jnm(λ	PROPN
ejpam-3574	506	5	)	)	PUNCT
ejpam-3574	507	1	⊕	⊕	PROPN
ejpam-3574	507	2	j̃	j̃	PROPN
ejpam-3574	507	3	,	,	PUNCT
ejpam-3574	507	4	where	where	SCONJ
ejpam-3574	507	5	j̃	j̃	PROPN
ejpam-3574	507	6	=	=	SYM
ejpam-3574	507	7	j̃k	j̃k	PROPN
ejpam-3574	507	8	contains	contain	VERB
ejpam-3574	507	9	all	all	DET
ejpam-3574	507	10	the	the	DET
ejpam-3574	507	11	forms	form	NOUN
ejpam-3574	507	12	in	in	ADP
ejpam-3574	507	13	jordan	jordan	PROPN
ejpam-3574	507	14	blocks	block	NOUN
ejpam-3574	507	15	of	of	ADP
ejpam-3574	507	16	w	w	PROPN
ejpam-3574	507	17	+	+	NOUN
ejpam-3574	507	18	b	b	NOUN
ejpam-3574	507	19	associated	associate	VERB
ejpam-3574	507	20	with	with	ADP
ejpam-3574	507	21	eigenvalues	eigenvalue	NOUN
ejpam-3574	507	22	different	different	ADJ
ejpam-3574	507	23	from	from	ADP
ejpam-3574	507	24	λ	λ	PROPN
ejpam-3574	507	25	.	.	PROPN
ejpam-3574	507	26	4	4	NUM
ejpam-3574	507	27	.	.	X
ejpam-3574	507	28	jordan	jordan	PROPN
ejpam-3574	507	29	canonical	canonical	ADJ
ejpam-3574	507	30	form	form	NOUN
ejpam-3574	507	31	of	of	ADP
ejpam-3574	507	32	(	(	PUNCT
ejpam-3574	507	33	x̃(t))t>0	x̃(t))t>0	PROPN
ejpam-3574	507	34	theorem	theorem	NOUN
ejpam-3574	507	35	4	4	NUM
ejpam-3574	507	36	.	.	PUNCT
ejpam-3574	508	1	let	let	VERB
ejpam-3574	508	2	t	t	PROPN
ejpam-3574	508	3	>	>	X
ejpam-3574	508	4	0	0	PROPN
ejpam-3574	508	5	,	,	PUNCT
ejpam-3574	508	6	j	j	PROPN
ejpam-3574	508	7	∈	∈	PROPN
ejpam-3574	508	8	r2n×2n	r2n×2n	NOUN
ejpam-3574	508	9	be	be	VERB
ejpam-3574	508	10	a	a	DET
ejpam-3574	508	11	skew	skew	ADJ
ejpam-3574	508	12	-	-	PUNCT
ejpam-3574	508	13	symmtric	symmtric	ADJ
ejpam-3574	508	14	and	and	CCONJ
ejpam-3574	508	15	invertible	invertible	ADJ
ejpam-3574	508	16	matrix	matrix	NOUN
ejpam-3574	508	17	,	,	PUNCT
ejpam-3574	508	18	(	(	PUNCT
ejpam-3574	508	19	x(t))t>0	x(t))t>0	X
ejpam-3574	508	20	be	be	AUX
ejpam-3574	508	21	the	the	DET
ejpam-3574	508	22	fundamental	fundamental	ADJ
ejpam-3574	508	23	solution	solution	NOUN
ejpam-3574	508	24	of	of	ADP
ejpam-3574	508	25	the	the	DET
ejpam-3574	508	26	system	system	NOUN
ejpam-3574	508	27	(	(	PUNCT
ejpam-3574	508	28	2	2	NUM
ejpam-3574	508	29	)	)	PUNCT
ejpam-3574	508	30	and	and	CCONJ
ejpam-3574	509	1	λ(t	λ(t	NOUN
ejpam-3574	509	2	)	)	PUNCT
ejpam-3574	509	3	∈	∈	PROPN
ejpam-3574	509	4	c	c	NOUN
ejpam-3574	509	5	be	be	AUX
ejpam-3574	509	6	an	an	DET
ejpam-3574	509	7	eigenvalue	eigenvalue	NOUN
ejpam-3574	509	8	of	of	ADP
ejpam-3574	509	9	(	(	PUNCT
ejpam-3574	509	10	x(t))t>0	x(t))t>0	NUM
ejpam-3574	509	11	.	.	PUNCT
ejpam-3574	509	12	suppose	suppose	VERB
ejpam-3574	509	13	that	that	SCONJ
ejpam-3574	509	14	x(t	x(t	PROPN
ejpam-3574	509	15	)	)	PUNCT
ejpam-3574	509	16	has	have	VERB
ejpam-3574	509	17	the	the	DET
ejpam-3574	509	18	following	follow	VERB
ejpam-3574	509	19	jordan	jordan	PROPN
ejpam-3574	509	20	canonical	canonical	PROPN
ejpam-3574	509	21	form	form	PROPN
ejpam-3574	509	22	l1⊕	l1⊕	PROPN
ejpam-3574	509	23	j=1	j=1	PROPN
ejpam-3574	509	24	jn1(λ(t	jn1(λ(t	NOUN
ejpam-3574	509	25	)	)	PUNCT
ejpam-3574	509	26	)	)	PUNCT
ejpam-3574	510	1	⊕	⊕	PROPN
ejpam-3574	510	2			PROPN
ejpam-3574	510	3	l2⊕	l2⊕	PROPN
ejpam-3574	510	4	j=1	j=1	PROPN
ejpam-3574	510	5	jn2(λ(t	jn2(λ(t	NOUN
ejpam-3574	510	6	)	)	PUNCT
ejpam-3574	510	7	)	)	PUNCT
ejpam-3574	511	1	⊕	⊕	PROPN
ejpam-3574	511	2	·	·	PUNCT
ejpam-3574	511	3	·	·	PUNCT
ejpam-3574	511	4	·	·	PUNCT
ejpam-3574	511	5	⊕	⊕	PROPN
ejpam-3574	512	1	lm(t)⊕	lm(t)⊕	PROPN
ejpam-3574	512	2	j=1	j=1	PROPN
ejpam-3574	512	3	jnm(t	jnm(t	PROPN
ejpam-3574	512	4	)	)	PUNCT
ejpam-3574	512	5	(	(	PUNCT
ejpam-3574	512	6	λ(t	λ(t	NOUN
ejpam-3574	512	7	)	)	PUNCT
ejpam-3574	512	8	)	)	PUNCT
ejpam-3574	513	1	⊕	⊕	PROPN
ejpam-3574	513	2	j	j	PROPN
ejpam-3574	513	3	(	(	PUNCT
ejpam-3574	513	4	t	t	PROPN
ejpam-3574	513	5	)	)	PUNCT
ejpam-3574	513	6	,	,	PUNCT
ejpam-3574	513	7	where	where	SCONJ
ejpam-3574	513	8	n1	n1	PROPN
ejpam-3574	513	9	>	>	X
ejpam-3574	513	10	·	·	PUNCT
ejpam-3574	513	11	·	·	PUNCT
ejpam-3574	513	12	·	·	PUNCT
ejpam-3574	513	13	>	>	X
ejpam-3574	513	14	nm(t	nm(t	NUM
ejpam-3574	513	15	)	)	PUNCT
ejpam-3574	513	16	et	et	NOUN
ejpam-3574	513	17	m	m	VERB
ejpam-3574	513	18	:	:	PUNCT
ejpam-3574	513	19	r	r	NOUN
ejpam-3574	513	20	−→	−→	NOUN
ejpam-3574	513	21	n∗	n∗	PROPN
ejpam-3574	513	22	is	be	AUX
ejpam-3574	513	23	a	a	DET
ejpam-3574	513	24	index	index	NOUN
ejpam-3574	513	25	function	function	NOUN
ejpam-3574	513	26	such	such	ADJ
ejpam-3574	513	27	that	that	SCONJ
ejpam-3574	513	28	the	the	DET
ejpam-3574	513	29	algebraic	algebraic	ADJ
ejpam-3574	513	30	multiplicity	multiplicity	NOUN
ejpam-3574	513	31	a(t	a(t	NOUN
ejpam-3574	513	32	)	)	PUNCT
ejpam-3574	513	33	of	of	ADP
ejpam-3574	513	34	λ(t	λ(t	NOUN
ejpam-3574	513	35	)	)	PUNCT
ejpam-3574	513	36	is	be	AUX
ejpam-3574	513	37	of	of	ADP
ejpam-3574	513	38	the	the	DET
ejpam-3574	513	39	form	form	NOUN
ejpam-3574	513	40	a(t	a(t	NOUN
ejpam-3574	513	41	)	)	PUNCT
ejpam-3574	514	1	=	=	NOUN
ejpam-3574	514	2	m(t)∑	m(t)∑	NOUN
ejpam-3574	514	3	j=1	j=1	PROPN
ejpam-3574	514	4	ljnj	ljnj	PROPN
ejpam-3574	514	5	and	and	CCONJ
ejpam-3574	514	6	j	j	PROPN
ejpam-3574	514	7	(	(	PUNCT
ejpam-3574	514	8	t	t	PROPN
ejpam-3574	514	9	)	)	PUNCT
ejpam-3574	514	10	contains	contain	VERB
ejpam-3574	514	11	all	all	DET
ejpam-3574	514	12	the	the	DET
ejpam-3574	514	13	forms	form	NOUN
ejpam-3574	514	14	in	in	ADP
ejpam-3574	514	15	jordan	jordan	PROPN
ejpam-3574	514	16	blocks	block	NOUN
ejpam-3574	514	17	associated	associate	VERB
ejpam-3574	514	18	with	with	ADP
ejpam-3574	514	19	eigenvalues	eigenvalue	NOUN
ejpam-3574	514	20	of	of	ADP
ejpam-3574	514	21	x(t	x(t	PROPN
ejpam-3574	514	22	)	)	PUNCT
ejpam-3574	514	23	different	different	ADJ
ejpam-3574	514	24	from	from	ADP
ejpam-3574	514	25	λ(t	λ(t	NOUN
ejpam-3574	514	26	)	)	PUNCT
ejpam-3574	514	27	.	.	PUNCT
ejpam-3574	515	1	moreover	moreover	ADV
ejpam-3574	515	2	,	,	PUNCT
ejpam-3574	515	3	set	set	ADJ
ejpam-3574	515	4	b(t	b(t	NOUN
ejpam-3574	515	5	)	)	PUNCT
ejpam-3574	516	1	=	=	SYM
ejpam-3574	516	2	uutjx(t	uutjx(t	PROPN
ejpam-3574	516	3	)	)	PUNCT
ejpam-3574	516	4	where	where	SCONJ
ejpam-3574	516	5	u	u	PROPN
ejpam-3574	516	6	∈	∈	PROPN
ejpam-3574	516	7	r2n×k	r2n×k	VERB
ejpam-3574	516	8	is	be	AUX
ejpam-3574	516	9	such	such	ADJ
ejpam-3574	516	10	that	that	SCONJ
ejpam-3574	516	11	its	its	PRON
ejpam-3574	516	12	columns	column	NOUN
ejpam-3574	516	13	generate	generate	VERB
ejpam-3574	516	14	an	an	DET
ejpam-3574	516	15	isotropic	isotropic	ADJ
ejpam-3574	516	16	subspace	subspace	NOUN
ejpam-3574	516	17	.	.	PUNCT
ejpam-3574	517	1	(	(	PUNCT
ejpam-3574	517	2	1	1	X
ejpam-3574	517	3	)	)	PUNCT
ejpam-3574	517	4	if	if	SCONJ
ejpam-3574	517	5	λ(t	λ(t	NOUN
ejpam-3574	517	6	)	)	PUNCT
ejpam-3574	517	7	6∈	6∈	PROPN
ejpam-3574	517	8	{	{	PUNCT
ejpam-3574	517	9	−1	−1	NOUN
ejpam-3574	517	10	,	,	PUNCT
ejpam-3574	517	11	1	1	NUM
ejpam-3574	517	12	}	}	PUNCT
ejpam-3574	517	13	,	,	PUNCT
ejpam-3574	517	14	then	then	ADV
ejpam-3574	517	15	generally	generally	ADV
ejpam-3574	517	16	with	with	ADP
ejpam-3574	517	17	respect	respect	NOUN
ejpam-3574	517	18	to	to	ADP
ejpam-3574	517	19	the	the	DET
ejpam-3574	517	20	components	component	NOUN
ejpam-3574	517	21	of	of	ADP
ejpam-3574	517	22	u	u	NOUN
ejpam-3574	517	23	,	,	PUNCT
ejpam-3574	517	24	x(t	x(t	PROPN
ejpam-3574	517	25	)	)	PUNCT
ejpam-3574	517	26	+	+	NUM
ejpam-3574	517	27	b(t	b(t	NOUN
ejpam-3574	517	28	)	)	PUNCT
ejpam-3574	517	29	has	have	VERB
ejpam-3574	517	30	the	the	DET
ejpam-3574	517	31	following	follow	VERB
ejpam-3574	517	32	jordan	jordan	PROPN
ejpam-3574	517	33	canonical	canonical	ADJ
ejpam-3574	517	34	form	form	NOUN
ejpam-3574	517	35			X
ejpam-3574	517	36	l1−k⊕	l1−k⊕	X
ejpam-3574	517	37	j=1	j=1	PROPN
ejpam-3574	517	38	jn1(λ(t	jn1(λ(t	NOUN
ejpam-3574	517	39	)	)	PUNCT
ejpam-3574	517	40	)	)	PUNCT
ejpam-3574	518	1	⊕	⊕	PROPN
ejpam-3574	518	2			PROPN
ejpam-3574	518	3	l2⊕	l2⊕	PROPN
ejpam-3574	518	4	j=1	j=1	PROPN
ejpam-3574	518	5	jn2(λ(t	jn2(λ(t	NOUN
ejpam-3574	518	6	)	)	PUNCT
ejpam-3574	518	7	)	)	PUNCT
ejpam-3574	519	1	⊕	⊕	PROPN
ejpam-3574	519	2	·	·	PUNCT
ejpam-3574	519	3	·	·	PUNCT
ejpam-3574	519	4	·	·	PUNCT
ejpam-3574	519	5	⊕	⊕	PROPN
ejpam-3574	520	1	lm(t)⊕	lm(t)⊕	PROPN
ejpam-3574	520	2	j=1	j=1	PROPN
ejpam-3574	520	3	jnm(t	jnm(t	PROPN
ejpam-3574	520	4	)	)	PUNCT
ejpam-3574	520	5	(	(	PUNCT
ejpam-3574	520	6	λ(t	λ(t	NOUN
ejpam-3574	520	7	)	)	PUNCT
ejpam-3574	520	8	)	)	PUNCT
ejpam-3574	521	1	⊕	⊕	PROPN
ejpam-3574	521	2	j̃	j̃	PROPN
ejpam-3574	521	3	(	(	PUNCT
ejpam-3574	521	4	t	t	PROPN
ejpam-3574	521	5	)	)	PUNCT
ejpam-3574	521	6	,	,	PUNCT
ejpam-3574	521	7	if	if	SCONJ
ejpam-3574	521	8	k	k	PROPN
ejpam-3574	521	9	<	<	X
ejpam-3574	521	10	l1	l1	PROPN
ejpam-3574	521	11	li−ki⊕	li−ki⊕	VERB
ejpam-3574	521	12	j=1	j=1	PROPN
ejpam-3574	521	13	jni(λ(t	jni(λ(t	PROPN
ejpam-3574	521	14	)	)	PUNCT
ejpam-3574	521	15	)	)	PUNCT
ejpam-3574	522	1	⊕	⊕	PROPN
ejpam-3574	522	2			PROPN
ejpam-3574	522	3	li+1⊕	li+1⊕	NOUN
ejpam-3574	522	4	j=1	j=1	PROPN
ejpam-3574	522	5	jni+1(λ(t	jni+1(λ(t	PROPN
ejpam-3574	522	6	)	)	PUNCT
ejpam-3574	522	7	)	)	PUNCT
ejpam-3574	523	1	⊕	⊕	PROPN
ejpam-3574	523	2	·	·	PUNCT
ejpam-3574	523	3	·	·	PUNCT
ejpam-3574	523	4	·	·	PUNCT
ejpam-3574	523	5	⊕	⊕	PROPN
ejpam-3574	524	1	lm(t)⊕	lm(t)⊕	PROPN
ejpam-3574	524	2	j=1	j=1	PROPN
ejpam-3574	524	3	jnm(t	jnm(t	PROPN
ejpam-3574	524	4	)	)	PUNCT
ejpam-3574	524	5	(	(	PUNCT
ejpam-3574	524	6	λ(t	λ(t	NOUN
ejpam-3574	524	7	)	)	PUNCT
ejpam-3574	524	8	)	)	PUNCT
ejpam-3574	525	1	⊕	⊕	PROPN
ejpam-3574	525	2	j̃	j̃	PROPN
ejpam-3574	525	3	(	(	PUNCT
ejpam-3574	525	4	t	t	PROPN
ejpam-3574	525	5	)	)	PUNCT
ejpam-3574	525	6	,	,	PUNCT
ejpam-3574	525	7	if	if	SCONJ
ejpam-3574	525	8			PROPN
ejpam-3574	525	9	k	k	NOUN
ejpam-3574	525	10	=	=	PUNCT
ejpam-3574	525	11	i−1∑	i−1∑	NOUN
ejpam-3574	525	12	s=1	s=1	PUNCT
ejpam-3574	525	13	ls	ls	X
ejpam-3574	526	1	+	+	X
ejpam-3574	526	2	ki	ki	PROPN
ejpam-3574	526	3	,	,	PUNCT
ejpam-3574	526	4	with	with	ADP
ejpam-3574	526	5	ki	ki	PROPN
ejpam-3574	526	6	<	<	X
ejpam-3574	526	7	li	li	PROPN
ejpam-3574	526	8	et	et	PROPN
ejpam-3574	526	9	i	i	PROPN
ejpam-3574	526	10	>	>	X
ejpam-3574	526	11	1	1	NUM
ejpam-3574	526	12	m.	m.	NOUN
ejpam-3574	526	13	dosso	dosso	NOUN
ejpam-3574	526	14	,	,	PUNCT
ejpam-3574	526	15	t.	t.	PROPN
ejpam-3574	526	16	g.	g.	PROPN
ejpam-3574	526	17	y.	y.	PROPN
ejpam-3574	526	18	arouna	arouna	PROPN
ejpam-3574	526	19	,	,	PUNCT
ejpam-3574	526	20	j.-c	j.-c	PROPN
ejpam-3574	526	21	.	.	PUNCT
ejpam-3574	527	1	koua	koua	PROPN
ejpam-3574	527	2	brou	brou	PROPN
ejpam-3574	527	3	/	/	SYM
ejpam-3574	527	4	eur	eur	PROPN
ejpam-3574	527	5	.	.	PUNCT
ejpam-3574	528	1	j.	j.	PROPN
ejpam-3574	528	2	pure	pure	PROPN
ejpam-3574	528	3	appl	appl	PROPN
ejpam-3574	528	4	.	.	PROPN
ejpam-3574	528	5	math	math	PROPN
ejpam-3574	528	6	,	,	PUNCT
ejpam-3574	528	7	12	12	NUM
ejpam-3574	528	8	(	(	PUNCT
ejpam-3574	528	9	4	4	NUM
ejpam-3574	528	10	)	)	PUNCT
ejpam-3574	528	11	(	(	PUNCT
ejpam-3574	528	12	2019	2019	NUM
ejpam-3574	528	13	)	)	PUNCT
ejpam-3574	528	14	,	,	PUNCT
ejpam-3574	528	15	1744	1744	NUM
ejpam-3574	528	16	-	-	SYM
ejpam-3574	528	17	1770	1770	NUM
ejpam-3574	528	18	1762	1762	NUM
ejpam-3574	528	19	where	where	SCONJ
ejpam-3574	528	20	j̃	j̃	PROPN
ejpam-3574	528	21	(	(	PUNCT
ejpam-3574	528	22	t	t	PROPN
ejpam-3574	528	23	)	)	PUNCT
ejpam-3574	528	24	contains	contain	VERB
ejpam-3574	528	25	all	all	DET
ejpam-3574	528	26	the	the	DET
ejpam-3574	528	27	form	form	NOUN
ejpam-3574	528	28	in	in	ADP
ejpam-3574	528	29	jordan	jordan	PROPN
ejpam-3574	528	30	blocks	block	NOUN
ejpam-3574	528	31	of	of	ADP
ejpam-3574	528	32	x(t	x(t	PROPN
ejpam-3574	528	33	)	)	PUNCT
ejpam-3574	529	1	+	+	NUM
ejpam-3574	529	2	b(t	b(t	NOUN
ejpam-3574	529	3	)	)	PUNCT
ejpam-3574	529	4	associated	associate	VERB
ejpam-3574	529	5	with	with	ADP
ejpam-3574	529	6	eigenvalues	eigenvalue	NOUN
ejpam-3574	529	7	different	different	ADJ
ejpam-3574	529	8	from	from	ADP
ejpam-3574	529	9	λ(t	λ(t	NOUN
ejpam-3574	529	10	)	)	PUNCT
ejpam-3574	529	11	.	.	PUNCT
ejpam-3574	530	1	(	(	PUNCT
ejpam-3574	530	2	2	2	X
ejpam-3574	530	3	)	)	PUNCT
ejpam-3574	530	4	if	if	SCONJ
ejpam-3574	530	5	∃	∃	PROPN
ejpam-3574	530	6	t0	t0	PROPN
ejpam-3574	530	7	>	>	X
ejpam-3574	530	8	0	0	PUNCT
ejpam-3574	530	9	such	such	ADJ
ejpam-3574	530	10	that	that	DET
ejpam-3574	530	11	λ(t0	λ(t0	NOUN
ejpam-3574	530	12	)	)	PUNCT
ejpam-3574	530	13	∈	∈	PROPN
ejpam-3574	530	14	{	{	PUNCT
ejpam-3574	530	15	−1	−1	NOUN
ejpam-3574	530	16	,	,	PUNCT
ejpam-3574	530	17	1	1	NUM
ejpam-3574	530	18	}	}	PUNCT
ejpam-3574	530	19	,	,	PUNCT
ejpam-3574	530	20	then	then	ADV
ejpam-3574	530	21	(	(	PUNCT
ejpam-3574	530	22	2a	2a	NUM
ejpam-3574	530	23	)	)	PUNCT
ejpam-3574	530	24	if	if	SCONJ
ejpam-3574	530	25	k	k	NOUN
ejpam-3574	530	26	=	=	PUNCT
ejpam-3574	530	27	i−1∑	i−1∑	PUNCT
ejpam-3574	530	28	s=1	s=1	PUNCT
ejpam-3574	530	29	ls	ls	X
ejpam-3574	531	1	+	+	CCONJ
ejpam-3574	531	2	ki	ki	PROPN
ejpam-3574	531	3	where	where	SCONJ
ejpam-3574	531	4	the	the	DET
ejpam-3574	531	5	n1	n1	NOUN
ejpam-3574	531	6	,	,	PUNCT
ejpam-3574	531	7	n2	n2	NOUN
ejpam-3574	531	8	,	,	PUNCT
ejpam-3574	531	9	.	.	PUNCT
ejpam-3574	531	10	.	.	PUNCT
ejpam-3574	531	11	.	.	PUNCT
ejpam-3574	532	1	,	,	PUNCT
ejpam-3574	532	2	ni	ni	PROPN
ejpam-3574	532	3	are	be	AUX
ejpam-3574	532	4	even	even	ADV
ejpam-3574	532	5	and	and	CCONJ
ejpam-3574	532	6	ki	ki	PROPN
ejpam-3574	532	7	<	<	X
ejpam-3574	532	8	li	li	PROPN
ejpam-3574	532	9	,	,	PUNCT
ejpam-3574	532	10	then	then	ADV
ejpam-3574	532	11	generally	generally	ADV
ejpam-3574	532	12	with	with	ADP
ejpam-3574	532	13	respect	respect	NOUN
ejpam-3574	532	14	to	to	ADP
ejpam-3574	532	15	the	the	DET
ejpam-3574	532	16	components	component	NOUN
ejpam-3574	532	17	of	of	ADP
ejpam-3574	532	18	u	u	NOUN
ejpam-3574	532	19	,	,	PUNCT
ejpam-3574	532	20	x(t	x(t	PROPN
ejpam-3574	532	21	)	)	PUNCT
ejpam-3574	532	22	+	+	NUM
ejpam-3574	532	23	b(t	b(t	NOUN
ejpam-3574	532	24	)	)	PUNCT
ejpam-3574	532	25	has	have	VERB
ejpam-3574	532	26	the	the	DET
ejpam-3574	532	27	following	follow	VERB
ejpam-3574	532	28	jordan	jordan	PROPN
ejpam-3574	532	29	canonical	canonical	PROPN
ejpam-3574	532	30	formli−ki⊕	formli−ki⊕	PROPN
ejpam-3574	532	31	j=1	j=1	PROPN
ejpam-3574	532	32	jni(λ(t0	jni(λ(t0	PROPN
ejpam-3574	532	33	)	)	PUNCT
ejpam-3574	532	34	)	)	PUNCT
ejpam-3574	533	1	⊕	⊕	PROPN
ejpam-3574	533	2			PROPN
ejpam-3574	533	3	li+1⊕	li+1⊕	NOUN
ejpam-3574	533	4	j=1	j=1	PROPN
ejpam-3574	533	5	jni+1(λ(t0	jni+1(λ(t0	PROPN
ejpam-3574	533	6	)	)	PUNCT
ejpam-3574	533	7	)	)	PUNCT
ejpam-3574	534	1	⊕	⊕	PROPN
ejpam-3574	534	2	·	·	PUNCT
ejpam-3574	534	3	·	·	PUNCT
ejpam-3574	534	4	·	·	PUNCT
ejpam-3574	534	5	⊕	⊕	PROPN
ejpam-3574	534	6	lm(t0)⊕	lm(t0)⊕	VERB
ejpam-3574	534	7	j=1	j=1	PROPN
ejpam-3574	534	8	jnm(t0	jnm(t0	PROPN
ejpam-3574	534	9	)	)	PUNCT
ejpam-3574	534	10	(	(	PUNCT
ejpam-3574	534	11	λ(t0	λ(t0	NOUN
ejpam-3574	534	12	)	)	PUNCT
ejpam-3574	534	13	)	)	PUNCT
ejpam-3574	535	1	⊕j̃	⊕j̃	VERB
ejpam-3574	535	2	(	(	PUNCT
ejpam-3574	535	3	t0	t0	NOUN
ejpam-3574	535	4	)	)	PUNCT
ejpam-3574	535	5	,	,	PUNCT
ejpam-3574	535	6	where	where	SCONJ
ejpam-3574	535	7	j̃	j̃	PROPN
ejpam-3574	535	8	(	(	PUNCT
ejpam-3574	535	9	t0	t0	PROPN
ejpam-3574	535	10	)	)	PUNCT
ejpam-3574	535	11	contains	contain	VERB
ejpam-3574	535	12	all	all	DET
ejpam-3574	535	13	the	the	DET
ejpam-3574	535	14	form	form	NOUN
ejpam-3574	535	15	in	in	ADP
ejpam-3574	535	16	jordan	jordan	PROPN
ejpam-3574	535	17	blocks	block	NOUN
ejpam-3574	535	18	of	of	ADP
ejpam-3574	535	19	x(t0	x(t0	PROPN
ejpam-3574	535	20	)	)	PUNCT
ejpam-3574	536	1	+	+	NOUN
ejpam-3574	536	2	b(t0	b(t0	NOUN
ejpam-3574	536	3	)	)	PUNCT
ejpam-3574	536	4	associated	associate	VERB
ejpam-3574	536	5	with	with	ADP
ejpam-3574	536	6	eigenvalues	eigenvalue	NOUN
ejpam-3574	536	7	different	different	ADJ
ejpam-3574	536	8	from	from	ADP
ejpam-3574	536	9	λ(t0	λ(t0	PROPN
ejpam-3574	536	10	)	)	PUNCT
ejpam-3574	536	11	.	.	PUNCT
ejpam-3574	537	1	(	(	PUNCT
ejpam-3574	537	2	2b	2b	NUM
ejpam-3574	537	3	)	)	PUNCT
ejpam-3574	537	4	if	if	SCONJ
ejpam-3574	537	5	k	k	PROPN
ejpam-3574	537	6	=	=	PUNCT
ejpam-3574	537	7	i−1∑	i−1∑	PUNCT
ejpam-3574	538	1	s=1	s=1	PUNCT
ejpam-3574	538	2	ls	ls	X
ejpam-3574	538	3	+	+	CCONJ
ejpam-3574	538	4	2ki	2ki	ADJ
ejpam-3574	538	5	−	−	NOUN
ejpam-3574	538	6	1	1	NUM
ejpam-3574	538	7	with	with	ADP
ejpam-3574	538	8	2ki	2ki	ADJ
ejpam-3574	538	9	≤	≤	NUM
ejpam-3574	538	10	li	li	PROPN
ejpam-3574	538	11	and	and	CCONJ
ejpam-3574	538	12	ni	ni	PROPN
ejpam-3574	538	13	is	be	AUX
ejpam-3574	538	14	odd	odd	ADJ
ejpam-3574	538	15	,	,	PUNCT
ejpam-3574	538	16	then	then	ADV
ejpam-3574	538	17	li	li	PROPN
ejpam-3574	538	18	is	be	AUX
ejpam-3574	538	19	even	even	ADV
ejpam-3574	538	20	and	and	CCONJ
ejpam-3574	538	21	generally	generally	ADV
ejpam-3574	538	22	with	with	ADP
ejpam-3574	538	23	respect	respect	NOUN
ejpam-3574	538	24	to	to	ADP
ejpam-3574	538	25	the	the	DET
ejpam-3574	538	26	components	component	NOUN
ejpam-3574	538	27	of	of	ADP
ejpam-3574	538	28	u	u	PROPN
ejpam-3574	538	29	,	,	PUNCT
ejpam-3574	538	30	x(t0	x(t0	PROPN
ejpam-3574	538	31	)	)	PUNCT
ejpam-3574	539	1	+	+	NUM
ejpam-3574	539	2	b(t0	b(t0	NOUN
ejpam-3574	539	3	)	)	PUNCT
ejpam-3574	539	4	has	have	VERB
ejpam-3574	539	5	the	the	DET
ejpam-3574	539	6	following	follow	VERB
ejpam-3574	539	7	jordan	jordan	PROPN
ejpam-3574	539	8	canonical	canonical	ADJ
ejpam-3574	539	9	form	form	NOUN
ejpam-3574	539	10	jni+1(λ(t0))⊕	jni+1(λ(t0))⊕	PROPN
ejpam-3574	539	11	li−2ki⊕	li−2ki⊕	NUM
ejpam-3574	539	12	j=1	j=1	PROPN
ejpam-3574	539	13	jni(λ(t0	jni(λ(t0	PROPN
ejpam-3574	539	14	)	)	PUNCT
ejpam-3574	539	15	)	)	PUNCT
ejpam-3574	540	1	⊕	⊕	PROPN
ejpam-3574	540	2	·	·	PUNCT
ejpam-3574	540	3	·	·	PUNCT
ejpam-3574	540	4	·	·	PUNCT
ejpam-3574	540	5	⊕	⊕	PROPN
ejpam-3574	540	6	lm(t0)⊕	lm(t0)⊕	VERB
ejpam-3574	540	7	j=1	j=1	PROPN
ejpam-3574	540	8	jnm(t0	jnm(t0	PROPN
ejpam-3574	540	9	)	)	PUNCT
ejpam-3574	540	10	(	(	PUNCT
ejpam-3574	540	11	λ(t0	λ(t0	NOUN
ejpam-3574	540	12	)	)	PUNCT
ejpam-3574	540	13	)	)	PUNCT
ejpam-3574	541	1	⊕	⊕	PROPN
ejpam-3574	541	2	j̃	j̃	PROPN
ejpam-3574	541	3	(	(	PUNCT
ejpam-3574	541	4	t0	t0	PROPN
ejpam-3574	541	5	)	)	PUNCT
ejpam-3574	541	6	,	,	PUNCT
ejpam-3574	541	7	where	where	SCONJ
ejpam-3574	541	8	j̃	j̃	PROPN
ejpam-3574	541	9	(	(	PUNCT
ejpam-3574	541	10	t0	t0	PROPN
ejpam-3574	541	11	)	)	PUNCT
ejpam-3574	541	12	contains	contain	VERB
ejpam-3574	541	13	all	all	DET
ejpam-3574	541	14	the	the	DET
ejpam-3574	541	15	form	form	NOUN
ejpam-3574	541	16	in	in	ADP
ejpam-3574	541	17	jordan	jordan	PROPN
ejpam-3574	541	18	blocks	block	NOUN
ejpam-3574	541	19	of	of	ADP
ejpam-3574	541	20	x(t0	x(t0	PROPN
ejpam-3574	541	21	)	)	PUNCT
ejpam-3574	542	1	+	+	NOUN
ejpam-3574	542	2	b(t0	b(t0	NOUN
ejpam-3574	542	3	)	)	PUNCT
ejpam-3574	542	4	associated	associate	VERB
ejpam-3574	542	5	with	with	ADP
ejpam-3574	542	6	eigenvalues	eigenvalue	NOUN
ejpam-3574	542	7	different	different	ADJ
ejpam-3574	542	8	from	from	ADP
ejpam-3574	542	9	λ(t0	λ(t0	PROPN
ejpam-3574	542	10	)	)	PUNCT
ejpam-3574	542	11	.	.	PUNCT
ejpam-3574	543	1	proof	proof	NOUN
ejpam-3574	543	2	.	.	PUNCT
ejpam-3574	544	1	it	it	PRON
ejpam-3574	544	2	suffices	suffice	VERB
ejpam-3574	544	3	to	to	PART
ejpam-3574	544	4	adapt	adapt	VERB
ejpam-3574	544	5	the	the	DET
ejpam-3574	544	6	proof	proof	NOUN
ejpam-3574	544	7	of	of	ADP
ejpam-3574	544	8	theorem	theorem	NOUN
ejpam-3574	544	9	3	3	NUM
ejpam-3574	544	10	to	to	ADP
ejpam-3574	544	11	the	the	DET
ejpam-3574	544	12	solution	solution	NOUN
ejpam-3574	544	13	(	(	PUNCT
ejpam-3574	544	14	x(t))t≥0	x(t))t≥0	NOUN
ejpam-3574	544	15	of	of	ADP
ejpam-3574	544	16	(	(	PUNCT
ejpam-3574	544	17	2	2	NUM
ejpam-3574	544	18	)	)	PUNCT
ejpam-3574	544	19	and	and	CCONJ
ejpam-3574	544	20	to	to	ADP
ejpam-3574	544	21	its	its	PRON
ejpam-3574	544	22	rank	rank	NOUN
ejpam-3574	544	23	-	-	PUNCT
ejpam-3574	544	24	k	k	NOUN
ejpam-3574	544	25	perturbation	perturbation	NOUN
ejpam-3574	544	26	(	(	PUNCT
ejpam-3574	544	27	x̃(t	x̃(t	PROPN
ejpam-3574	544	28	)	)	PUNCT
ejpam-3574	544	29	)	)	PUNCT
ejpam-3574	544	30	t≥0	t≥0	NOUN
ejpam-3574	544	31	(	(	PUNCT
ejpam-3574	544	32	which	which	PRON
ejpam-3574	544	33	is	be	AUX
ejpam-3574	544	34	the	the	DET
ejpam-3574	544	35	fundamental	fundamental	ADJ
ejpam-3574	544	36	solution	solution	NOUN
ejpam-3574	544	37	of	of	ADP
ejpam-3574	544	38	(	(	PUNCT
ejpam-3574	544	39	6	6	NUM
ejpam-3574	544	40	)	)	PUNCT
ejpam-3574	544	41	)	)	PUNCT
ejpam-3574	544	42	.	.	PUNCT
ejpam-3574	545	1	5	5	X
ejpam-3574	545	2	.	.	X
ejpam-3574	545	3	application	application	NOUN
ejpam-3574	545	4	to	to	ADP
ejpam-3574	545	5	some	some	DET
ejpam-3574	545	6	mathieu	mathieu	PROPN
ejpam-3574	545	7	systems	system	NOUN
ejpam-3574	545	8	5.1	5.1	NUM
ejpam-3574	545	9	.	.	PUNCT
ejpam-3574	546	1	double	double	ADJ
ejpam-3574	546	2	pendulum	pendulum	NOUN
ejpam-3574	546	3	with	with	ADP
ejpam-3574	546	4	oscillating	oscillating	NOUN
ejpam-3574	546	5	supports	support	NOUN
ejpam-3574	546	6	consider	consider	VERB
ejpam-3574	546	7	two	two	NUM
ejpam-3574	546	8	identical	identical	ADJ
ejpam-3574	546	9	simple	simple	ADJ
ejpam-3574	546	10	pendulums	pendulum	NOUN
ejpam-3574	546	11	attached	attach	VERB
ejpam-3574	546	12	to	to	ADP
ejpam-3574	546	13	the	the	DET
ejpam-3574	546	14	same	same	ADJ
ejpam-3574	546	15	support	support	NOUN
ejpam-3574	546	16	.	.	PUNCT
ejpam-3574	547	1	when	when	SCONJ
ejpam-3574	547	2	the	the	DET
ejpam-3574	547	3	support	support	NOUN
ejpam-3574	547	4	of	of	ADP
ejpam-3574	547	5	each	each	DET
ejpam-3574	547	6	pendulum	pendulum	NOUN
ejpam-3574	547	7	is	be	AUX
ejpam-3574	547	8	subjected	subject	VERB
ejpam-3574	547	9	to	to	ADP
ejpam-3574	547	10	an	an	DET
ejpam-3574	547	11	oscillatory	oscillatory	ADJ
ejpam-3574	547	12	movement	movement	NOUN
ejpam-3574	547	13	f(t	f(t	NOUN
ejpam-3574	547	14	)	)	PUNCT
ejpam-3574	547	15	of	of	ADP
ejpam-3574	547	16	amplitude	amplitude	NOUN
ejpam-3574	547	17	α	α	NOUN
ejpam-3574	547	18	and	and	CCONJ
ejpam-3574	547	19	of	of	ADP
ejpam-3574	547	20	a	a	DET
ejpam-3574	547	21	pulsation	pulsation	NOUN
ejpam-3574	547	22	ω	ω	NOUN
ejpam-3574	547	23	,	,	PUNCT
ejpam-3574	547	24	defined	define	VERB
ejpam-3574	547	25	by	by	ADP
ejpam-3574	547	26	f(t	f(t	NOUN
ejpam-3574	547	27	)	)	PUNCT
ejpam-3574	547	28	=	=	PUNCT
ejpam-3574	547	29	α	α	NUM
ejpam-3574	547	30	cos(ωt	cos(ωt	NOUN
ejpam-3574	547	31	)	)	PUNCT
ejpam-3574	548	1	[	[	X
ejpam-3574	548	2	14	14	NUM
ejpam-3574	548	3	]	]	PUNCT
ejpam-3574	548	4	,	,	PUNCT
ejpam-3574	548	5	we	we	PRON
ejpam-3574	548	6	present	present	VERB
ejpam-3574	548	7	two	two	NUM
ejpam-3574	548	8	cases	case	NOUN
ejpam-3574	548	9	:	:	PUNCT
ejpam-3574	548	10	m.	m.	NOUN
ejpam-3574	548	11	dosso	dosso	PROPN
ejpam-3574	548	12	,	,	PUNCT
ejpam-3574	548	13	t.	t.	PROPN
ejpam-3574	548	14	g.	g.	PROPN
ejpam-3574	548	15	y.	y.	PROPN
ejpam-3574	548	16	arouna	arouna	PROPN
ejpam-3574	548	17	,	,	PUNCT
ejpam-3574	548	18	j.-c	j.-c	PROPN
ejpam-3574	548	19	.	.	PUNCT
ejpam-3574	549	1	koua	koua	PROPN
ejpam-3574	549	2	brou	brou	PROPN
ejpam-3574	549	3	/	/	SYM
ejpam-3574	549	4	eur	eur	PROPN
ejpam-3574	549	5	.	.	PUNCT
ejpam-3574	550	1	j.	j.	PROPN
ejpam-3574	550	2	pure	pure	PROPN
ejpam-3574	550	3	appl	appl	PROPN
ejpam-3574	550	4	.	.	PROPN
ejpam-3574	550	5	math	math	PROPN
ejpam-3574	550	6	,	,	PUNCT
ejpam-3574	550	7	12	12	NUM
ejpam-3574	550	8	(	(	PUNCT
ejpam-3574	550	9	4	4	NUM
ejpam-3574	550	10	)	)	PUNCT
ejpam-3574	550	11	(	(	PUNCT
ejpam-3574	550	12	2019	2019	NUM
ejpam-3574	550	13	)	)	PUNCT
ejpam-3574	550	14	,	,	PUNCT
ejpam-3574	550	15	1744	1744	NUM
ejpam-3574	550	16	-	-	SYM
ejpam-3574	550	17	1770	1770	NUM
ejpam-3574	550	18	1763	1763	NUM
ejpam-3574	550	19	figure	figure	NOUN
ejpam-3574	550	20	1	1	NUM
ejpam-3574	550	21	:	:	PUNCT
ejpam-3574	550	22	model	model	NOUN
ejpam-3574	550	23	of	of	ADP
ejpam-3574	550	24	the	the	DET
ejpam-3574	550	25	uncoupled	uncoupled	ADJ
ejpam-3574	550	26	double	double	ADJ
ejpam-3574	550	27	pendulum	pendulum	NOUN
ejpam-3574	550	28	with	with	ADP
ejpam-3574	550	29	oscillating	oscillating	NOUN
ejpam-3574	550	30	supports	support	NOUN
ejpam-3574	550	31	.	.	PUNCT
ejpam-3574	551	1	5.1.1	5.1.1	NUM
ejpam-3574	551	2	.	.	NOUN
ejpam-3574	551	3	uncoupled	uncoupled	ADJ
ejpam-3574	551	4	double	double	ADJ
ejpam-3574	551	5	pendulums	pendulum	NOUN
ejpam-3574	551	6	with	with	ADP
ejpam-3574	551	7	oscillating	oscillating	NOUN
ejpam-3574	551	8	supports	support	NOUN
ejpam-3574	551	9	according	accord	VERB
ejpam-3574	551	10	to	to	ADP
ejpam-3574	551	11	[	[	X
ejpam-3574	551	12	14	14	NUM
ejpam-3574	551	13	]	]	PUNCT
ejpam-3574	551	14	,	,	PUNCT
ejpam-3574	551	15	the	the	DET
ejpam-3574	551	16	differential	differential	ADJ
ejpam-3574	551	17	equation	equation	NOUN
ejpam-3574	551	18	of	of	ADP
ejpam-3574	551	19	the	the	DET
ejpam-3574	551	20	movement	movement	NOUN
ejpam-3574	551	21	of	of	ADP
ejpam-3574	551	22	the	the	DET
ejpam-3574	551	23	two	two	NUM
ejpam-3574	551	24	pendulums	pendulum	NOUN
ejpam-3574	551	25	will	will	AUX
ejpam-3574	551	26	be	be	AUX
ejpam-3574	551	27	the	the	DET
ejpam-3574	551	28	same	same	ADJ
ejpam-3574	551	29	.	.	PUNCT
ejpam-3574	552	1	thus	thus	ADV
ejpam-3574	552	2	,	,	PUNCT
ejpam-3574	552	3	the	the	DET
ejpam-3574	552	4	equation	equation	NOUN
ejpam-3574	552	5	of	of	ADP
ejpam-3574	552	6	motion	motion	NOUN
ejpam-3574	552	7	is	be	AUX
ejpam-3574	552	8	given	give	VERB
ejpam-3574	552	9	by	by	ADP
ejpam-3574	552	10	:	:	PUNCT
ejpam-3574	552	11	d2xi	d2xi	PROPN
ejpam-3574	552	12	dt2	dt2	PROPN
ejpam-3574	552	13	+	+	CCONJ
ejpam-3574	552	14	cg	cg	NOUN
ejpam-3574	552	15	k20	k20	NOUN
ejpam-3574	552	16	(	(	PUNCT
ejpam-3574	552	17	1−	1−	NUM
ejpam-3574	552	18	1	1	NUM
ejpam-3574	552	19	g	g	PROPN
ejpam-3574	552	20	d2f	d2f	PROPN
ejpam-3574	552	21	dt2	dt2	PROPN
ejpam-3574	552	22	)	)	PUNCT
ejpam-3574	552	23	xi	xi	X
ejpam-3574	553	1	=	=	SYM
ejpam-3574	553	2	0	0	PROPN
ejpam-3574	553	3	,	,	PUNCT
ejpam-3574	553	4	i	i	PRON
ejpam-3574	553	5	=	=	NOUN
ejpam-3574	553	6	1	1	NUM
ejpam-3574	553	7	,	,	PUNCT
ejpam-3574	553	8	2	2	NUM
ejpam-3574	553	9	,	,	PUNCT
ejpam-3574	553	10	(	(	PUNCT
ejpam-3574	553	11	12	12	NUM
ejpam-3574	553	12	)	)	PUNCT
ejpam-3574	553	13	where	where	SCONJ
ejpam-3574	553	14	k0	k0	PROPN
ejpam-3574	553	15	is	be	AUX
ejpam-3574	553	16	the	the	DET
ejpam-3574	553	17	radius	radius	NOUN
ejpam-3574	553	18	of	of	ADP
ejpam-3574	553	19	gyration	gyration	NOUN
ejpam-3574	553	20	of	of	ADP
ejpam-3574	553	21	the	the	DET
ejpam-3574	553	22	pendulum	pendulum	NOUN
ejpam-3574	553	23	around	around	ADP
ejpam-3574	553	24	its	its	PRON
ejpam-3574	553	25	point	point	NOUN
ejpam-3574	553	26	of	of	ADP
ejpam-3574	553	27	suspension	suspension	NOUN
ejpam-3574	553	28	,	,	PUNCT
ejpam-3574	553	29	and	and	CCONJ
ejpam-3574	553	30	c	c	NOUN
ejpam-3574	553	31	is	be	AUX
ejpam-3574	553	32	the	the	DET
ejpam-3574	553	33	distance	distance	NOUN
ejpam-3574	553	34	between	between	ADP
ejpam-3574	553	35	the	the	DET
ejpam-3574	553	36	point	point	NOUN
ejpam-3574	553	37	of	of	ADP
ejpam-3574	553	38	suspension	suspension	NOUN
ejpam-3574	553	39	and	and	CCONJ
ejpam-3574	553	40	the	the	DET
ejpam-3574	553	41	center	center	NOUN
ejpam-3574	553	42	of	of	ADP
ejpam-3574	553	43	the	the	DET
ejpam-3574	553	44	pendulum	pendulum	NOUN
ejpam-3574	553	45	.	.	PUNCT
ejpam-3574	554	1	since	since	SCONJ
ejpam-3574	554	2	f(t	f(t	NOUN
ejpam-3574	554	3	)	)	PUNCT
ejpam-3574	554	4	=	=	PUNCT
ejpam-3574	554	5	α	α	PRON
ejpam-3574	554	6	cos(ωt	cos(ωt	NOUN
ejpam-3574	554	7	)	)	PUNCT
ejpam-3574	554	8	,	,	PUNCT
ejpam-3574	554	9	then	then	ADV
ejpam-3574	554	10	system	system	NOUN
ejpam-3574	554	11	(	(	PUNCT
ejpam-3574	554	12	12	12	NUM
ejpam-3574	554	13	)	)	PUNCT
ejpam-3574	554	14	becomes	become	VERB
ejpam-3574	554	15	:	:	PUNCT
ejpam-3574	554	16	d2xi	d2xi	PROPN
ejpam-3574	554	17	dt2	dt2	PROPN
ejpam-3574	554	18	+	+	CCONJ
ejpam-3574	554	19	cg	cg	NOUN
ejpam-3574	554	20	k20	k20	NOUN
ejpam-3574	554	21	(	(	PUNCT
ejpam-3574	554	22	1	1	NUM
ejpam-3574	554	23	+	+	CCONJ
ejpam-3574	554	24	αω2	αω2	NOUN
ejpam-3574	554	25	g	g	NOUN
ejpam-3574	554	26	cos(ωt	cos(ωt	NOUN
ejpam-3574	554	27	)	)	PUNCT
ejpam-3574	554	28	)	)	PUNCT
ejpam-3574	554	29	xi	xi	X
ejpam-3574	555	1	=	=	SYM
ejpam-3574	555	2	0	0	PROPN
ejpam-3574	555	3	,	,	PUNCT
ejpam-3574	555	4	i	i	PRON
ejpam-3574	555	5	=	=	NOUN
ejpam-3574	555	6	1	1	NUM
ejpam-3574	555	7	,	,	PUNCT
ejpam-3574	555	8	2	2	NUM
ejpam-3574	555	9	,	,	PUNCT
ejpam-3574	555	10	(	(	PUNCT
ejpam-3574	555	11	13	13	NUM
ejpam-3574	555	12	)	)	PUNCT
ejpam-3574	555	13	and	and	CCONJ
ejpam-3574	555	14	by	by	ADP
ejpam-3574	555	15	the	the	DET
ejpam-3574	555	16	change	change	NOUN
ejpam-3574	555	17	of	of	ADP
ejpam-3574	555	18	variable	variable	NOUN
ejpam-3574	555	19	τ	τ	X
ejpam-3574	556	1	=	=	SYM
ejpam-3574	556	2	ωt	ωt	PROPN
ejpam-3574	557	1	[	[	X
ejpam-3574	557	2	14	14	NUM
ejpam-3574	557	3	]	]	PUNCT
ejpam-3574	557	4	,	,	PUNCT
ejpam-3574	557	5	equation	equation	NOUN
ejpam-3574	557	6	(	(	PUNCT
ejpam-3574	557	7	13	13	NUM
ejpam-3574	557	8	)	)	PUNCT
ejpam-3574	557	9	becomes	become	VERB
ejpam-3574	557	10	:	:	PUNCT
ejpam-3574	557	11	d2xi	d2xi	NOUN
ejpam-3574	557	12	dτ2	dτ2	NOUN
ejpam-3574	557	13	+	+	CCONJ
ejpam-3574	557	14	(	(	PUNCT
ejpam-3574	557	15	δ	δ	PROPN
ejpam-3574	557	16	+	+	CCONJ
ejpam-3574	557	17	ε	ε	PROPN
ejpam-3574	557	18	cos(τ))xi	cos(τ))xi	NOUN
ejpam-3574	557	19	=	=	SYM
ejpam-3574	557	20	0	0	NUM
ejpam-3574	557	21	,	,	PUNCT
ejpam-3574	557	22	i	i	PRON
ejpam-3574	557	23	=	=	NOUN
ejpam-3574	557	24	1	1	NUM
ejpam-3574	557	25	,	,	PUNCT
ejpam-3574	557	26	2	2	NUM
ejpam-3574	557	27	,	,	PUNCT
ejpam-3574	557	28	(	(	PUNCT
ejpam-3574	557	29	14	14	NUM
ejpam-3574	557	30	)	)	PUNCT
ejpam-3574	557	31	where	where	SCONJ
ejpam-3574	557	32	ε	ε	X
ejpam-3574	557	33	=	=	SYM
ejpam-3574	557	34	cα	cα	ADP
ejpam-3574	557	35	k20	k20	NOUN
ejpam-3574	557	36	and	and	CCONJ
ejpam-3574	557	37	δ	δ	NOUN
ejpam-3574	557	38	=	=	SYM
ejpam-3574	558	1	cg	cg	PROPN
ejpam-3574	558	2	k20ω2	k20ω2	PROPN
ejpam-3574	558	3	.	.	PUNCT
ejpam-3574	559	1	finally	finally	ADV
ejpam-3574	559	2	,	,	PUNCT
ejpam-3574	559	3	using	use	VERB
ejpam-3574	559	4	the	the	DET
ejpam-3574	559	5	following	follow	VERB
ejpam-3574	559	6	change	change	NOUN
ejpam-3574	559	7	of	of	ADP
ejpam-3574	559	8	variables	variable	NOUN
ejpam-3574	559	9	x(τ	x(τ	PROPN
ejpam-3574	559	10	)	)	PUNCT
ejpam-3574	560	1	=	=	PRON
ejpam-3574	560	2	[	[	PUNCT
ejpam-3574	560	3	x(τ	x(τ	PROPN
ejpam-3574	560	4	)	)	PUNCT
ejpam-3574	560	5	dx	dx	PROPN
ejpam-3574	560	6	dτ	dτ	PROPN
ejpam-3574	560	7	(	(	PUNCT
ejpam-3574	560	8	τ	τ	X
ejpam-3574	560	9	)	)	PUNCT
ejpam-3574	560	10	]	]	PUNCT
ejpam-3574	560	11	,	,	PUNCT
ejpam-3574	560	12	j	j	X
ejpam-3574	561	1	=	=	PUNCT
ejpam-3574	562	1	[	[	PUNCT
ejpam-3574	562	2	02	02	NUM
ejpam-3574	562	3	−i2	−i2	PROPN
ejpam-3574	562	4	i2	i2	NOUN
ejpam-3574	562	5	02	02	NUM
ejpam-3574	562	6	]	]	PUNCT
ejpam-3574	562	7	and	and	CCONJ
ejpam-3574	562	8	h(τ	h(τ	PROPN
ejpam-3574	562	9	,	,	PUNCT
ejpam-3574	562	10	δ	δ	PROPN
ejpam-3574	562	11	,	,	PUNCT
ejpam-3574	562	12	ε	ε	PROPN
ejpam-3574	562	13	)	)	PUNCT
ejpam-3574	562	14	=	=	PUNCT
ejpam-3574	563	1	[	[	PUNCT
ejpam-3574	563	2	p	p	X
ejpam-3574	563	3	(	(	PUNCT
ejpam-3574	563	4	τ	τ	PROPN
ejpam-3574	563	5	,	,	PUNCT
ejpam-3574	563	6	δ	δ	PROPN
ejpam-3574	563	7	,	,	PUNCT
ejpam-3574	563	8	ε	ε	PROPN
ejpam-3574	563	9	)	)	PUNCT
ejpam-3574	563	10	02	02	NUM
ejpam-3574	563	11	02	02	NUM
ejpam-3574	563	12	i2	i2	PROPN
ejpam-3574	563	13	]	]	PUNCT
ejpam-3574	563	14	,	,	PUNCT
ejpam-3574	563	15	(	(	PUNCT
ejpam-3574	563	16	15	15	NUM
ejpam-3574	563	17	)	)	PUNCT
ejpam-3574	563	18	with	with	ADP
ejpam-3574	563	19	x(τ	x(τ	PROPN
ejpam-3574	563	20	)	)	PUNCT
ejpam-3574	563	21	=	=	PUNCT
ejpam-3574	564	1	[	[	PUNCT
ejpam-3574	564	2	x1(τ	x1(τ	PROPN
ejpam-3574	564	3	)	)	PUNCT
ejpam-3574	564	4	x2(τ	x2(τ	PROPN
ejpam-3574	564	5	)	)	PUNCT
ejpam-3574	564	6	]	]	PUNCT
ejpam-3574	564	7	and	and	CCONJ
ejpam-3574	564	8	p	p	X
ejpam-3574	564	9	(	(	PUNCT
ejpam-3574	564	10	τ	τ	PROPN
ejpam-3574	564	11	,	,	PUNCT
ejpam-3574	564	12	δ	δ	PROPN
ejpam-3574	564	13	,	,	PUNCT
ejpam-3574	564	14	ε	ε	PROPN
ejpam-3574	564	15	)	)	PUNCT
ejpam-3574	564	16	=	=	SYM
ejpam-3574	564	17	(	(	PUNCT
ejpam-3574	564	18	δ	δ	PROPN
ejpam-3574	564	19	+	+	CCONJ
ejpam-3574	564	20	ε	ε	PROPN
ejpam-3574	564	21	cos(τ))i2	cos(τ))i2	PUNCT
ejpam-3574	564	22	,	,	PUNCT
ejpam-3574	564	23	we	we	PRON
ejpam-3574	564	24	obtain	obtain	VERB
ejpam-3574	564	25	equation	equation	NOUN
ejpam-3574	564	26	(	(	PUNCT
ejpam-3574	564	27	1	1	NUM
ejpam-3574	564	28	)	)	PUNCT
ejpam-3574	564	29	.	.	PUNCT
ejpam-3574	565	1	now	now	ADV
ejpam-3574	565	2	,	,	PUNCT
ejpam-3574	565	3	consider	consider	VERB
ejpam-3574	565	4	the	the	DET
ejpam-3574	565	5	rank-2	rank-2	NOUN
ejpam-3574	565	6	perturbation	perturbation	NOUN
ejpam-3574	565	7	of	of	ADP
ejpam-3574	565	8	the	the	DET
ejpam-3574	565	9	fundamental	fundamental	ADJ
ejpam-3574	565	10	solution	solution	NOUN
ejpam-3574	565	11	x(τ	x(τ	PROPN
ejpam-3574	565	12	,	,	PUNCT
ejpam-3574	565	13	δ	δ	PROPN
ejpam-3574	565	14	,	,	PUNCT
ejpam-3574	565	15	ε	ε	PROPN
ejpam-3574	565	16	)	)	PUNCT
ejpam-3574	565	17	of	of	ADP
ejpam-3574	565	18	its	its	PRON
ejpam-3574	565	19	corresponding	corresponding	ADJ
ejpam-3574	565	20	hamiltonian	hamiltonian	ADJ
ejpam-3574	565	21	system	system	NOUN
ejpam-3574	565	22	by	by	ADP
ejpam-3574	565	23	the	the	DET
ejpam-3574	565	24	following	follow	VERB
ejpam-3574	565	25	matrix	matrix	NOUN
ejpam-3574	565	26	of	of	ADP
ejpam-3574	565	27	rank	rank	PROPN
ejpam-3574	565	28	2	2	NUM
ejpam-3574	565	29	ea(τ	ea(τ	PROPN
ejpam-3574	565	30	,	,	PUNCT
ejpam-3574	565	31	δ	δ	PROPN
ejpam-3574	565	32	,	,	PUNCT
ejpam-3574	565	33	ε	ε	PROPN
ejpam-3574	565	34	)	)	PUNCT
ejpam-3574	566	1	=	=	PUNCT
ejpam-3574	566	2	uau	uau	PROPN
ejpam-3574	566	3	t	t	PROPN
ejpam-3574	566	4	a	a	DET
ejpam-3574	566	5	jx(τ	jx(τ	NOUN
ejpam-3574	566	6	,	,	PUNCT
ejpam-3574	566	7	δ	δ	PROPN
ejpam-3574	566	8	,	,	PUNCT
ejpam-3574	566	9	ε	ε	PROPN
ejpam-3574	566	10	)	)	PUNCT
ejpam-3574	566	11	,	,	PUNCT
ejpam-3574	566	12	(	(	PUNCT
ejpam-3574	566	13	16	16	NUM
ejpam-3574	566	14	)	)	PUNCT
ejpam-3574	567	1	where	where	SCONJ
ejpam-3574	567	2	ua	ua	NOUN
ejpam-3574	567	3	=	=	PUNCT
ejpam-3574	567	4	a	a	DET
ejpam-3574	567	5			ADJ
ejpam-3574	567	6	1	1	NUM
ejpam-3574	567	7	0	0	NUM
ejpam-3574	567	8	0	0	NUM
ejpam-3574	567	9	1	1	NUM
ejpam-3574	567	10	0	0	NUM
ejpam-3574	567	11	0	0	NUM
ejpam-3574	567	12	0	0	NUM
ejpam-3574	567	13	0	0	NUM
ejpam-3574	567	14			NOUN
ejpam-3574	567	15	and	and	CCONJ
ejpam-3574	567	16	a	a	DET
ejpam-3574	567	17	∈	∈	NOUN
ejpam-3574	567	18	[	[	X
ejpam-3574	567	19	0	0	NUM
ejpam-3574	567	20	,	,	PUNCT
ejpam-3574	567	21	1	1	NUM
ejpam-3574	567	22	[	[	NOUN
ejpam-3574	567	23	.	.	PUNCT
ejpam-3574	568	1	(	(	PUNCT
ejpam-3574	568	2	17	17	NUM
ejpam-3574	568	3	)	)	PUNCT
ejpam-3574	568	4	according	accord	VERB
ejpam-3574	568	5	to	to	ADP
ejpam-3574	568	6	[	[	X
ejpam-3574	568	7	2	2	NUM
ejpam-3574	568	8	,	,	PUNCT
ejpam-3574	568	9	5	5	NUM
ejpam-3574	568	10	]	]	PUNCT
ejpam-3574	568	11	,	,	PUNCT
ejpam-3574	568	12	its	its	PRON
ejpam-3574	568	13	rank-2	rank-2	PROPN
ejpam-3574	568	14	perturbation	perturbation	NOUN
ejpam-3574	568	15	x̃a(τ	x̃a(τ	NOUN
ejpam-3574	568	16	,	,	PUNCT
ejpam-3574	568	17	δ	δ	PROPN
ejpam-3574	568	18	,	,	PUNCT
ejpam-3574	568	19	ε	ε	PROPN
ejpam-3574	568	20	)	)	PUNCT
ejpam-3574	568	21	=	=	NOUN
ejpam-3574	569	1	(	(	PUNCT
ejpam-3574	569	2	i	i	PRON
ejpam-3574	569	3	+	+	CCONJ
ejpam-3574	570	1	uau	uau	PROPN
ejpam-3574	570	2	t	t	PROPN
ejpam-3574	570	3	a	a	DET
ejpam-3574	570	4	j	j	PROPN
ejpam-3574	570	5	)	)	PUNCT
ejpam-3574	571	1	x(τ	x(τ	PROPN
ejpam-3574	571	2	,	,	PUNCT
ejpam-3574	571	3	δ	δ	PROPN
ejpam-3574	571	4	,	,	PUNCT
ejpam-3574	571	5	ε	ε	PROPN
ejpam-3574	571	6	)	)	PUNCT
ejpam-3574	571	7	.	.	PUNCT
ejpam-3574	572	1	(	(	PUNCT
ejpam-3574	572	2	18	18	NUM
ejpam-3574	572	3	)	)	PUNCT
ejpam-3574	572	4	m.	m.	NOUN
ejpam-3574	572	5	dosso	dosso	PROPN
ejpam-3574	572	6	,	,	PUNCT
ejpam-3574	572	7	t.	t.	PROPN
ejpam-3574	572	8	g.	g.	PROPN
ejpam-3574	572	9	y.	y.	PROPN
ejpam-3574	572	10	arouna	arouna	PROPN
ejpam-3574	572	11	,	,	PUNCT
ejpam-3574	572	12	j.-c	j.-c	PROPN
ejpam-3574	572	13	.	.	PUNCT
ejpam-3574	573	1	koua	koua	PROPN
ejpam-3574	573	2	brou	brou	PROPN
ejpam-3574	573	3	/	/	SYM
ejpam-3574	573	4	eur	eur	PROPN
ejpam-3574	573	5	.	.	PUNCT
ejpam-3574	574	1	j.	j.	PROPN
ejpam-3574	574	2	pure	pure	PROPN
ejpam-3574	574	3	appl	appl	PROPN
ejpam-3574	574	4	.	.	PROPN
ejpam-3574	574	5	math	math	PROPN
ejpam-3574	574	6	,	,	PUNCT
ejpam-3574	574	7	12	12	NUM
ejpam-3574	574	8	(	(	PUNCT
ejpam-3574	574	9	4	4	NUM
ejpam-3574	574	10	)	)	PUNCT
ejpam-3574	574	11	(	(	PUNCT
ejpam-3574	574	12	2019	2019	NUM
ejpam-3574	574	13	)	)	PUNCT
ejpam-3574	574	14	,	,	PUNCT
ejpam-3574	574	15	1744	1744	NUM
ejpam-3574	574	16	-	-	SYM
ejpam-3574	574	17	1770	1770	NUM
ejpam-3574	574	18	1764	1764	NUM
ejpam-3574	574	19	is	be	AUX
ejpam-3574	574	20	the	the	DET
ejpam-3574	574	21	solution	solution	NOUN
ejpam-3574	574	22	of	of	ADP
ejpam-3574	574	23	the	the	DET
ejpam-3574	574	24	following	follow	VERB
ejpam-3574	574	25	rank	rank	NOUN
ejpam-3574	574	26	-	-	PUNCT
ejpam-3574	574	27	k	k	NOUN
ejpam-3574	574	28	perturbation	perturbation	NOUN
ejpam-3574	574	29	hamiltonian	hamiltonian	NOUN
ejpam-3574	574	30	system	system	PROPN
ejpam-3574	574	31	j	j	PROPN
ejpam-3574	574	32	dx̃a(τ	dx̃a(τ	X
ejpam-3574	574	33	,	,	PUNCT
ejpam-3574	574	34	δ	δ	PROPN
ejpam-3574	574	35	,	,	PUNCT
ejpam-3574	574	36	ε	ε	PROPN
ejpam-3574	574	37	)	)	PUNCT
ejpam-3574	574	38	dτ	dτ	NOUN
ejpam-3574	575	1	=	=	SYM
ejpam-3574	575	2	(	(	PUNCT
ejpam-3574	575	3	i	i	PRON
ejpam-3574	575	4	−	−	PROPN
ejpam-3574	576	1	uauta	uauta	PROPN
ejpam-3574	576	2	j)th(τ	j)th(τ	PROPN
ejpam-3574	576	3	,	,	PUNCT
ejpam-3574	576	4	δ	δ	PROPN
ejpam-3574	576	5	,	,	PUNCT
ejpam-3574	576	6	ε)(i	ε)(i	NUM
ejpam-3574	576	7	−	−	PROPN
ejpam-3574	577	1	uauta	uauta	NOUN
ejpam-3574	577	2	j)︸	j)︸	NOUN
ejpam-3574	577	3	︷︷	︷︷	PROPN
ejpam-3574	577	4	︸	︸	X
ejpam-3574	577	5	h̃(τ	h̃(τ	PROPN
ejpam-3574	577	6	,	,	PUNCT
ejpam-3574	577	7	δ	δ	PROPN
ejpam-3574	577	8	,	,	PUNCT
ejpam-3574	577	9	ε	ε	PROPN
ejpam-3574	577	10	,	,	PUNCT
ejpam-3574	577	11	a	a	PRON
ejpam-3574	577	12	)	)	PUNCT
ejpam-3574	577	13	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	577	14	,	,	PUNCT
ejpam-3574	577	15	δ	δ	PROPN
ejpam-3574	577	16	,	,	PUNCT
ejpam-3574	577	17	ε	ε	PROPN
ejpam-3574	577	18	)	)	PUNCT
ejpam-3574	577	19	,	,	PUNCT
ejpam-3574	577	20	x̃a(0	x̃a(0	PROPN
ejpam-3574	577	21	,	,	PUNCT
ejpam-3574	577	22	δ	δ	PROPN
ejpam-3574	577	23	,	,	PUNCT
ejpam-3574	577	24	ε	ε	PROPN
ejpam-3574	577	25	)	)	PUNCT
ejpam-3574	578	1	=	=	VERB
ejpam-3574	579	1	i	i	PRON
ejpam-3574	579	2	+	+	NOUN
ejpam-3574	580	1	uau	uau	PROPN
ejpam-3574	580	2	t	t	PROPN
ejpam-3574	580	3	a	a	DET
ejpam-3574	580	4	j	j	PROPN
ejpam-3574	580	5	(	(	PUNCT
ejpam-3574	580	6	19	19	NUM
ejpam-3574	580	7	)	)	PUNCT
ejpam-3574	580	8	figure	figure	NOUN
ejpam-3574	580	9	2	2	NUM
ejpam-3574	580	10	represents	represent	VERB
ejpam-3574	580	11	the	the	DET
ejpam-3574	580	12	movement	movement	NOUN
ejpam-3574	580	13	of	of	ADP
ejpam-3574	580	14	eigenvalues	eigenvalue	NOUN
ejpam-3574	580	15	of	of	ADP
ejpam-3574	580	16	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	580	17	,	,	PUNCT
ejpam-3574	580	18	δ	δ	PROPN
ejpam-3574	580	19	,	,	PUNCT
ejpam-3574	580	20	ε	ε	PROPN
ejpam-3574	580	21	)	)	PUNCT
ejpam-3574	580	22	for	for	ADP
ejpam-3574	580	23	(	(	PUNCT
ejpam-3574	580	24	δ	δ	PROPN
ejpam-3574	580	25	,	,	PUNCT
ejpam-3574	580	26	ε	ε	PROPN
ejpam-3574	580	27	)	)	PUNCT
ejpam-3574	580	28	∈	∈	PROPN
ejpam-3574	580	29	{	{	PUNCT
ejpam-3574	580	30	(	(	PUNCT
ejpam-3574	580	31	1	1	NUM
ejpam-3574	580	32	,	,	PUNCT
ejpam-3574	580	33	0.8	0.8	NUM
ejpam-3574	580	34	)	)	PUNCT
ejpam-3574	580	35	,	,	PUNCT
ejpam-3574	580	36	(	(	PUNCT
ejpam-3574	580	37	1.93	1.93	NUM
ejpam-3574	580	38	,	,	PUNCT
ejpam-3574	580	39	1.93	1.93	NUM
ejpam-3574	580	40	)	)	PUNCT
ejpam-3574	580	41	}	}	PUNCT
ejpam-3574	580	42	and	and	CCONJ
ejpam-3574	580	43	a	a	DET
ejpam-3574	580	44	∈	∈	PROPN
ejpam-3574	580	45	{	{	PUNCT
ejpam-3574	580	46	0	0	NUM
ejpam-3574	580	47	,	,	PUNCT
ejpam-3574	580	48	0.35	0.35	NUM
ejpam-3574	580	49	}	}	PUNCT
ejpam-3574	580	50	,	,	PUNCT
ejpam-3574	580	51	with	with	ADP
ejpam-3574	580	52	τ	τ	PROPN
ejpam-3574	580	53	∈	∈	PROPN
ejpam-3574	581	1	[	[	X
ejpam-3574	581	2	0	0	NUM
ejpam-3574	581	3	,	,	PUNCT
ejpam-3574	581	4	2π	2π	NOUN
ejpam-3574	581	5	]	]	PUNCT
ejpam-3574	581	6	.	.	PUNCT
ejpam-3574	582	1	these	these	DET
ejpam-3574	582	2	figures	figure	NOUN
ejpam-3574	582	3	show	show	VERB
ejpam-3574	582	4	that	that	SCONJ
ejpam-3574	582	5	small	small	ADJ
ejpam-3574	582	6	rank	rank	NOUN
ejpam-3574	582	7	-	-	PUNCT
ejpam-3574	582	8	k	k	NOUN
ejpam-3574	582	9	−1	−1	NOUN
ejpam-3574	582	10	0	0	NUM
ejpam-3574	582	11	1	1	NUM
ejpam-3574	582	12	−1	−1	NOUN
ejpam-3574	582	13	0	0	NUM
ejpam-3574	582	14	1	1	NUM
ejpam-3574	582	15	0	0	NUM
ejpam-3574	582	16	2	2	NUM
ejpam-3574	582	17	4	4	NUM
ejpam-3574	582	18	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	582	19	)	)	PUNCT
ejpam-3574	582	20	)	)	PUNCT
ejpam-3574	583	1	δ=1	δ=1	ADP
ejpam-3574	583	2	and	and	CCONJ
ejpam-3574	583	3	ε=0.8	ε=0.8	ADV
ejpam-3574	583	4	,	,	PUNCT
ejpam-3574	583	5	with	with	ADP
ejpam-3574	583	6	a=0.35	a=0.35	PRON
ejpam-3574	583	7	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	583	8	)	)	PUNCT
ejpam-3574	583	9	)	)	PUNCT
ejpam-3574	584	1	τ	τ	X
ejpam-3574	584	2	−1	−1	NOUN
ejpam-3574	584	3	0	0	NUM
ejpam-3574	584	4	1	1	NUM
ejpam-3574	584	5	−1	−1	NOUN
ejpam-3574	584	6	0	0	NUM
ejpam-3574	584	7	1	1	NUM
ejpam-3574	584	8	0	0	NUM
ejpam-3574	584	9	2	2	NUM
ejpam-3574	584	10	4	4	NUM
ejpam-3574	584	11	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	584	12	)	)	PUNCT
ejpam-3574	584	13	)	)	PUNCT
ejpam-3574	585	1	δ=1	δ=1	ADP
ejpam-3574	585	2	and	and	CCONJ
ejpam-3574	585	3	ε=0.8	ε=0.8	ADV
ejpam-3574	585	4	,	,	PUNCT
ejpam-3574	585	5	with	with	ADP
ejpam-3574	585	6	a=0	a=0	DET
ejpam-3574	585	7	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	585	8	)	)	PUNCT
ejpam-3574	585	9	)	)	PUNCT
ejpam-3574	586	1	τ	τ	X
ejpam-3574	586	2	−1	−1	NOUN
ejpam-3574	586	3	0	0	NUM
ejpam-3574	586	4	1	1	NUM
ejpam-3574	586	5	−1	−1	NOUN
ejpam-3574	586	6	0	0	NUM
ejpam-3574	586	7	1	1	NUM
ejpam-3574	586	8	0	0	NUM
ejpam-3574	586	9	2	2	NUM
ejpam-3574	586	10	4	4	NUM
ejpam-3574	586	11	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	586	12	)	)	PUNCT
ejpam-3574	586	13	)	)	PUNCT
ejpam-3574	586	14	δ=1.93	δ=1.93	NOUN
ejpam-3574	586	15	and	and	CCONJ
ejpam-3574	586	16	ε=1.93	ε=1.93	NOUN
ejpam-3574	586	17	,	,	PUNCT
ejpam-3574	586	18	with	with	ADP
ejpam-3574	586	19	a=0.35	a=0.35	PRON
ejpam-3574	586	20	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	586	21	)	)	PUNCT
ejpam-3574	586	22	)	)	PUNCT
ejpam-3574	587	1	τ	τ	X
ejpam-3574	587	2	−1	−1	NOUN
ejpam-3574	587	3	0	0	NUM
ejpam-3574	587	4	1	1	NUM
ejpam-3574	587	5	−1	−1	NOUN
ejpam-3574	587	6	0	0	NUM
ejpam-3574	587	7	1	1	NUM
ejpam-3574	587	8	0	0	NUM
ejpam-3574	587	9	2	2	NUM
ejpam-3574	587	10	4	4	NUM
ejpam-3574	587	11	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	587	12	)	)	PUNCT
ejpam-3574	587	13	)	)	PUNCT
ejpam-3574	587	14	δ=1.93	δ=1.93	NOUN
ejpam-3574	587	15	and	and	CCONJ
ejpam-3574	587	16	ε=1.93	ε=1.93	PROPN
ejpam-3574	587	17	,	,	PUNCT
ejpam-3574	587	18	with	with	ADP
ejpam-3574	587	19	a=0	a=0	DET
ejpam-3574	587	20	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	587	21	)	)	PUNCT
ejpam-3574	587	22	)	)	PUNCT
ejpam-3574	588	1	τ	τ	PROPN
ejpam-3574	588	2	figure	figure	NOUN
ejpam-3574	588	3	2	2	NUM
ejpam-3574	588	4	:	:	PUNCT
ejpam-3574	588	5	spectral	spectral	ADJ
ejpam-3574	588	6	portrait	portrait	NOUN
ejpam-3574	588	7	of	of	ADP
ejpam-3574	588	8	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	588	9	,	,	PUNCT
ejpam-3574	588	10	δ	δ	PROPN
ejpam-3574	588	11	,	,	PUNCT
ejpam-3574	588	12	ε	ε	PROPN
ejpam-3574	588	13	)	)	PUNCT
ejpam-3574	588	14	for	for	ADP
ejpam-3574	588	15	τ	τ	PROPN
ejpam-3574	588	16	∈	∈	PROPN
ejpam-3574	589	1	[	[	X
ejpam-3574	589	2	0	0	NUM
ejpam-3574	589	3	,	,	PUNCT
ejpam-3574	589	4	2π	2π	NOUN
ejpam-3574	589	5	]	]	PUNCT
ejpam-3574	589	6	and	and	CCONJ
ejpam-3574	589	7	(	(	PUNCT
ejpam-3574	589	8	δ	δ	PROPN
ejpam-3574	589	9	,	,	PUNCT
ejpam-3574	589	10	ε	ε	PROPN
ejpam-3574	589	11	)	)	PUNCT
ejpam-3574	589	12	∈	∈	PROPN
ejpam-3574	589	13	{	{	PUNCT
ejpam-3574	589	14	(	(	PUNCT
ejpam-3574	589	15	1	1	NUM
ejpam-3574	589	16	,	,	PUNCT
ejpam-3574	589	17	0.8	0.8	NUM
ejpam-3574	589	18	)	)	PUNCT
ejpam-3574	589	19	,	,	PUNCT
ejpam-3574	589	20	(	(	PUNCT
ejpam-3574	589	21	1.93	1.93	NUM
ejpam-3574	589	22	,	,	PUNCT
ejpam-3574	589	23	1.93	1.93	NUM
ejpam-3574	589	24	)	)	PUNCT
ejpam-3574	589	25	}	}	PUNCT
ejpam-3574	589	26	with	with	ADP
ejpam-3574	589	27	a	a	DET
ejpam-3574	589	28	∈	∈	PROPN
ejpam-3574	589	29	{	{	PUNCT
ejpam-3574	589	30	0	0	NUM
ejpam-3574	589	31	,	,	PUNCT
ejpam-3574	589	32	0.35	0.35	NUM
ejpam-3574	589	33	}	}	PUNCT
ejpam-3574	589	34	.	.	PUNCT
ejpam-3574	590	1	perturbations	perturbation	NOUN
ejpam-3574	590	2	on	on	ADP
ejpam-3574	590	3	the	the	DET
ejpam-3574	590	4	movement	movement	NOUN
ejpam-3574	590	5	of	of	ADP
ejpam-3574	590	6	pendulums	pendulum	NOUN
ejpam-3574	590	7	do	do	AUX
ejpam-3574	590	8	not	not	PART
ejpam-3574	590	9	change	change	VERB
ejpam-3574	590	10	the	the	DET
ejpam-3574	590	11	nature	nature	NOUN
ejpam-3574	590	12	of	of	ADP
ejpam-3574	590	13	the	the	DET
ejpam-3574	590	14	spectral	spectral	ADJ
ejpam-3574	590	15	portrait	portrait	NOUN
ejpam-3574	590	16	of	of	ADP
ejpam-3574	590	17	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	590	18	,	,	PUNCT
ejpam-3574	590	19	δ	δ	PROPN
ejpam-3574	590	20	,	,	PUNCT
ejpam-3574	590	21	ε	ε	PROPN
ejpam-3574	590	22	)	)	PUNCT
ejpam-3574	590	23	.	.	PUNCT
ejpam-3574	591	1	for	for	ADP
ejpam-3574	591	2	all	all	DET
ejpam-3574	591	3	(	(	PUNCT
ejpam-3574	591	4	δ	δ	PROPN
ejpam-3574	591	5	,	,	PUNCT
ejpam-3574	591	6	ε	ε	PROPN
ejpam-3574	591	7	)	)	PUNCT
ejpam-3574	591	8	∈	∈	PROPN
ejpam-3574	592	1	[	[	X
ejpam-3574	592	2	0	0	NUM
ejpam-3574	592	3	,	,	PUNCT
ejpam-3574	592	4	1.98	1.98	NUM
ejpam-3574	592	5	]	]	PUNCT
ejpam-3574	592	6	×	×	NOUN
ejpam-3574	593	1	[	[	X
ejpam-3574	593	2	0	0	NUM
ejpam-3574	593	3	,	,	PUNCT
ejpam-3574	593	4	2	2	NUM
ejpam-3574	593	5	]	]	PUNCT
ejpam-3574	593	6	,	,	PUNCT
ejpam-3574	593	7	figure	figure	NOUN
ejpam-3574	593	8	3	3	NUM
ejpam-3574	593	9	shows	show	VERB
ejpam-3574	593	10	the	the	DET
ejpam-3574	593	11	stability	stability	NOUN
ejpam-3574	593	12	region	region	NOUN
ejpam-3574	593	13	of	of	ADP
ejpam-3574	593	14	x̃a(2π	x̃a(2π	PROPN
ejpam-3574	593	15	,	,	PUNCT
ejpam-3574	593	16	δ	δ	PROPN
ejpam-3574	593	17	,	,	PUNCT
ejpam-3574	593	18	ε	ε	PROPN
ejpam-3574	593	19	)	)	PUNCT
ejpam-3574	593	20	.	.	PUNCT
ejpam-3574	594	1	the	the	DET
ejpam-3574	594	2	first	first	ADJ
ejpam-3574	594	3	figure	figure	NOUN
ejpam-3574	594	4	(	(	PUNCT
ejpam-3574	594	5	left	left	ADJ
ejpam-3574	594	6	)	)	PUNCT
ejpam-3574	594	7	shows	show	VERB
ejpam-3574	594	8	areas	area	NOUN
ejpam-3574	594	9	of	of	ADP
ejpam-3574	594	10	stability	stability	NOUN
ejpam-3574	594	11	in	in	ADP
ejpam-3574	594	12	blue	blue	ADJ
ejpam-3574	594	13	and	and	CCONJ
ejpam-3574	594	14	of	of	ADP
ejpam-3574	594	15	instability	instability	NOUN
ejpam-3574	594	16	in	in	ADP
ejpam-3574	594	17	red	red	NOUN
ejpam-3574	594	18	when	when	SCONJ
ejpam-3574	594	19	our	our	PRON
ejpam-3574	594	20	system	system	NOUN
ejpam-3574	594	21	is	be	AUX
ejpam-3574	594	22	subject	subject	ADJ
ejpam-3574	594	23	to	to	ADP
ejpam-3574	594	24	a	a	DET
ejpam-3574	594	25	rank-2	rank-2	PROPN
ejpam-3574	594	26	perturbation	perturbation	NOUN
ejpam-3574	594	27	(	(	PUNCT
ejpam-3574	594	28	with	with	ADP
ejpam-3574	594	29	a	a	DET
ejpam-3574	594	30	=	=	NOUN
ejpam-3574	594	31	0.35	0.35	NUM
ejpam-3574	594	32	)	)	PUNCT
ejpam-3574	594	33	.	.	PUNCT
ejpam-3574	595	1	the	the	DET
ejpam-3574	595	2	second	second	ADJ
ejpam-3574	595	3	figure	figure	NOUN
ejpam-3574	595	4	(	(	PUNCT
ejpam-3574	595	5	right	right	ADJ
ejpam-3574	595	6	)	)	PUNCT
ejpam-3574	595	7	also	also	ADV
ejpam-3574	595	8	shows	show	VERB
ejpam-3574	595	9	the	the	DET
ejpam-3574	595	10	zone	zone	NOUN
ejpam-3574	595	11	of	of	ADP
ejpam-3574	595	12	stability	stability	NOUN
ejpam-3574	595	13	in	in	ADP
ejpam-3574	595	14	blue	blue	ADJ
ejpam-3574	595	15	and	and	CCONJ
ejpam-3574	595	16	of	of	ADP
ejpam-3574	595	17	instability	instability	NOUN
ejpam-3574	595	18	in	in	ADP
ejpam-3574	595	19	red	red	NOUN
ejpam-3574	595	20	of	of	ADP
ejpam-3574	595	21	the	the	DET
ejpam-3574	595	22	unperturbed	unperturbed	ADJ
ejpam-3574	595	23	system	system	NOUN
ejpam-3574	595	24	(	(	PUNCT
ejpam-3574	595	25	i.e.	i.e.	X
ejpam-3574	595	26	a	a	DET
ejpam-3574	595	27	=	=	NOUN
ejpam-3574	595	28	0	0	NUM
ejpam-3574	595	29	)	)	PUNCT
ejpam-3574	595	30	.	.	PUNCT
ejpam-3574	596	1	thus	thus	ADV
ejpam-3574	596	2	we	we	PRON
ejpam-3574	596	3	notice	notice	VERB
ejpam-3574	596	4	a	a	DET
ejpam-3574	596	5	slight	slight	ADJ
ejpam-3574	596	6	difference	difference	NOUN
ejpam-3574	596	7	between	between	ADP
ejpam-3574	596	8	the	the	DET
ejpam-3574	596	9	two	two	NUM
ejpam-3574	596	10	figures	figure	NOUN
ejpam-3574	596	11	due	due	ADP
ejpam-3574	596	12	to	to	ADP
ejpam-3574	596	13	the	the	DET
ejpam-3574	596	14	small	small	ADJ
ejpam-3574	596	15	rank	rank	NOUN
ejpam-3574	596	16	-	-	PUNCT
ejpam-3574	596	17	k	k	NOUN
ejpam-3574	596	18	perturbation	perturbation	NOUN
ejpam-3574	596	19	of	of	ADP
ejpam-3574	596	20	the	the	DET
ejpam-3574	596	21	system	system	NOUN
ejpam-3574	596	22	described	describe	VERB
ejpam-3574	596	23	by	by	ADP
ejpam-3574	596	24	our	our	PRON
ejpam-3574	596	25	two	two	NUM
ejpam-3574	596	26	uncoupled	uncoupled	ADJ
ejpam-3574	596	27	pendulums	pendulum	NOUN
ejpam-3574	596	28	.	.	PUNCT
ejpam-3574	597	1	5.1.2	5.1.2	X
ejpam-3574	597	2	.	.	NUM
ejpam-3574	597	3	coupled	couple	VERB
ejpam-3574	597	4	double	double	ADJ
ejpam-3574	597	5	pendulums	pendulum	NOUN
ejpam-3574	597	6	with	with	ADP
ejpam-3574	597	7	oscillating	oscillating	NOUN
ejpam-3574	597	8	supports	support	NOUN
ejpam-3574	597	9	in	in	ADP
ejpam-3574	597	10	this	this	DET
ejpam-3574	597	11	part	part	NOUN
ejpam-3574	597	12	,	,	PUNCT
ejpam-3574	597	13	the	the	DET
ejpam-3574	597	14	two	two	NUM
ejpam-3574	597	15	simple	simple	ADJ
ejpam-3574	597	16	pendulums	pendulum	NOUN
ejpam-3574	597	17	are	be	AUX
ejpam-3574	597	18	coupled	couple	VERB
ejpam-3574	597	19	by	by	ADP
ejpam-3574	597	20	a	a	DET
ejpam-3574	597	21	spring	spring	NOUN
ejpam-3574	597	22	of	of	ADP
ejpam-3574	597	23	constant	constant	ADJ
ejpam-3574	597	24	stiffness	stiffness	NOUN
ejpam-3574	597	25	k	k	PROPN
ejpam-3574	597	26	(	(	PUNCT
ejpam-3574	597	27	see	see	VERB
ejpam-3574	597	28	figure	figure	NOUN
ejpam-3574	597	29	4	4	NUM
ejpam-3574	597	30	)	)	PUNCT
ejpam-3574	597	31	.	.	PUNCT
ejpam-3574	598	1	according	accord	VERB
ejpam-3574	598	2	to	to	ADP
ejpam-3574	598	3	[	[	X
ejpam-3574	598	4	14	14	NUM
ejpam-3574	598	5	]	]	PUNCT
ejpam-3574	598	6	,	,	PUNCT
ejpam-3574	598	7	the	the	DET
ejpam-3574	598	8	motion	motion	NOUN
ejpam-3574	598	9	of	of	ADP
ejpam-3574	598	10	the	the	DET
ejpam-3574	598	11	system	system	NOUN
ejpam-3574	598	12	is	be	AUX
ejpam-3574	598	13	governed	govern	VERB
ejpam-3574	598	14	by	by	ADP
ejpam-3574	598	15	the	the	DET
ejpam-3574	598	16	following	follow	VERB
ejpam-3574	598	17	differential	differential	NOUN
ejpam-3574	598	18	system	system	NOUN
ejpam-3574	598	19	:	:	PUNCT
ejpam-3574	598	20	d2x	d2x	PROPN
ejpam-3574	598	21	dt2	dt2	PROPN
ejpam-3574	598	22	+	+	CCONJ
ejpam-3574	598	23	(	(	PUNCT
ejpam-3574	598	24	b0	b0	NOUN
ejpam-3574	598	25	−	−	PROPN
ejpam-3574	598	26	c	c	NOUN
ejpam-3574	598	27	k20	k20	PROPN
ejpam-3574	598	28	d2f	d2f	PROPN
ejpam-3574	598	29	dt2	dt2	PROPN
ejpam-3574	598	30	i2	i2	PROPN
ejpam-3574	598	31	)	)	PUNCT
ejpam-3574	598	32	x	x	PUNCT
ejpam-3574	599	1	=	=	SYM
ejpam-3574	599	2	0	0	NUM
ejpam-3574	599	3	,	,	PUNCT
ejpam-3574	599	4	(	(	PUNCT
ejpam-3574	599	5	20	20	NUM
ejpam-3574	599	6	)	)	PUNCT
ejpam-3574	599	7	where	where	SCONJ
ejpam-3574	599	8	x	x	X
ejpam-3574	599	9	=	=	PUNCT
ejpam-3574	599	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3574	599	11	x1x2	x1x2	X
ejpam-3574	599	12	]	]	PUNCT
ejpam-3574	599	13	and	and	CCONJ
ejpam-3574	599	14	b0	b0	NOUN
ejpam-3574	599	15	=	=	SYM
ejpam-3574	599	16			NOUN
ejpam-3574	599	17	cg	cg	NOUN
ejpam-3574	599	18	k20	k20	NOUN
ejpam-3574	599	19	+	+	CCONJ
ejpam-3574	599	20	kb2	kb2	ADJ
ejpam-3574	599	21	mk20	mk20	PROPN
ejpam-3574	599	22	−	−	NOUN
ejpam-3574	600	1	kb2	kb2	NOUN
ejpam-3574	600	2	mk20	mk20	PROPN
ejpam-3574	600	3	−	−	PROPN
ejpam-3574	601	1	kb2	kb2	NOUN
ejpam-3574	602	1	mk20	mk20	PROPN
ejpam-3574	602	2	cg	cg	NOUN
ejpam-3574	602	3	k20	k20	NOUN
ejpam-3574	602	4	+	+	CCONJ
ejpam-3574	602	5	kb2	kb2	ADJ
ejpam-3574	602	6	mk20	mk20	PROPN
ejpam-3574	602	7			NUM
ejpam-3574	602	8	,	,	PUNCT
ejpam-3574	602	9	m.	m.	NOUN
ejpam-3574	602	10	dosso	dosso	PROPN
ejpam-3574	602	11	,	,	PUNCT
ejpam-3574	602	12	t.	t.	PROPN
ejpam-3574	602	13	g.	g.	PROPN
ejpam-3574	602	14	y.	y.	PROPN
ejpam-3574	602	15	arouna	arouna	PROPN
ejpam-3574	602	16	,	,	PUNCT
ejpam-3574	602	17	j.-c	j.-c	PROPN
ejpam-3574	602	18	.	.	PUNCT
ejpam-3574	603	1	koua	koua	PROPN
ejpam-3574	603	2	brou	brou	PROPN
ejpam-3574	603	3	/	/	SYM
ejpam-3574	603	4	eur	eur	PROPN
ejpam-3574	603	5	.	.	PUNCT
ejpam-3574	604	1	j.	j.	PROPN
ejpam-3574	604	2	pure	pure	PROPN
ejpam-3574	604	3	appl	appl	PROPN
ejpam-3574	604	4	.	.	PROPN
ejpam-3574	604	5	math	math	PROPN
ejpam-3574	604	6	,	,	PUNCT
ejpam-3574	604	7	12	12	NUM
ejpam-3574	604	8	(	(	PUNCT
ejpam-3574	604	9	4	4	NUM
ejpam-3574	604	10	)	)	PUNCT
ejpam-3574	604	11	(	(	PUNCT
ejpam-3574	604	12	2019	2019	NUM
ejpam-3574	604	13	)	)	PUNCT
ejpam-3574	604	14	,	,	PUNCT
ejpam-3574	604	15	1744	1744	NUM
ejpam-3574	604	16	-	-	SYM
ejpam-3574	604	17	1770	1770	NUM
ejpam-3574	604	18	1765	1765	NUM
ejpam-3574	604	19	0	0	NUM
ejpam-3574	605	1	0.5	0.5	NUM
ejpam-3574	605	2	1	1	NUM
ejpam-3574	605	3	1.5	1.5	NUM
ejpam-3574	605	4	0	0	NUM
ejpam-3574	605	5	0.2	0.2	NUM
ejpam-3574	605	6	0.4	0.4	NUM
ejpam-3574	605	7	0.6	0.6	NUM
ejpam-3574	605	8	0.8	0.8	NUM
ejpam-3574	605	9	1	1	NUM
ejpam-3574	605	10	1.2	1.2	NUM
ejpam-3574	605	11	1.4	1.4	NUM
ejpam-3574	605	12	1.6	1.6	NUM
ejpam-3574	605	13	1.8	1.8	NUM
ejpam-3574	605	14	2	2	NUM
ejpam-3574	605	15	δ	δ	PROPN
ejpam-3574	605	16	ε	ε	X
ejpam-3574	605	17	a=0.35	a=0.35	NOUN
ejpam-3574	605	18	0	0	NUM
ejpam-3574	605	19	0.5	0.5	NUM
ejpam-3574	605	20	1	1	NUM
ejpam-3574	605	21	1.5	1.5	NUM
ejpam-3574	605	22	0	0	NUM
ejpam-3574	605	23	0.2	0.2	NUM
ejpam-3574	605	24	0.4	0.4	NUM
ejpam-3574	605	25	0.6	0.6	NUM
ejpam-3574	605	26	0.8	0.8	NUM
ejpam-3574	605	27	1	1	NUM
ejpam-3574	605	28	1.2	1.2	NUM
ejpam-3574	605	29	1.4	1.4	NUM
ejpam-3574	605	30	1.6	1.6	NUM
ejpam-3574	605	31	1.8	1.8	NUM
ejpam-3574	605	32	2	2	NUM
ejpam-3574	605	33	δ	δ	NOUN
ejpam-3574	605	34	ε	ε	PROPN
ejpam-3574	605	35	a=0	a=0	PRON
ejpam-3574	605	36	figure	figure	NOUN
ejpam-3574	605	37	3	3	NUM
ejpam-3574	605	38	:	:	PUNCT
ejpam-3574	605	39	stability	stability	NOUN
ejpam-3574	605	40	zone	zone	NOUN
ejpam-3574	605	41	of	of	ADP
ejpam-3574	605	42	matrix	matrix	NOUN
ejpam-3574	605	43	x̃a(2π	x̃a(2π	NUM
ejpam-3574	605	44	,	,	PUNCT
ejpam-3574	605	45	δ	δ	PROPN
ejpam-3574	605	46	,	,	PUNCT
ejpam-3574	605	47	ε	ε	PROPN
ejpam-3574	605	48	)	)	PUNCT
ejpam-3574	605	49	,	,	PUNCT
ejpam-3574	605	50	∀	∀	X
ejpam-3574	605	51	(	(	PUNCT
ejpam-3574	605	52	δ	δ	PROPN
ejpam-3574	605	53	,	,	PUNCT
ejpam-3574	605	54	ε	ε	PROPN
ejpam-3574	605	55	)	)	PUNCT
ejpam-3574	605	56	∈	∈	PROPN
ejpam-3574	606	1	[	[	X
ejpam-3574	606	2	0	0	NUM
ejpam-3574	606	3	,	,	PUNCT
ejpam-3574	606	4	1.98]×	1.98]×	NUM
ejpam-3574	606	5	[	[	X
ejpam-3574	606	6	0	0	NUM
ejpam-3574	606	7	,	,	PUNCT
ejpam-3574	606	8	2	2	NUM
ejpam-3574	606	9	]	]	PUNCT
ejpam-3574	606	10	and	and	CCONJ
ejpam-3574	606	11	a	a	DET
ejpam-3574	606	12	∈	∈	PROPN
ejpam-3574	606	13	{	{	PUNCT
ejpam-3574	606	14	0	0	NUM
ejpam-3574	606	15	,	,	PUNCT
ejpam-3574	606	16	0.35	0.35	NUM
ejpam-3574	606	17	}	}	PUNCT
ejpam-3574	606	18	.	.	PUNCT
ejpam-3574	607	1	figure	figure	VERB
ejpam-3574	607	2	4	4	NUM
ejpam-3574	607	3	:	:	PUNCT
ejpam-3574	607	4	model	model	NOUN
ejpam-3574	607	5	of	of	ADP
ejpam-3574	607	6	the	the	DET
ejpam-3574	607	7	coupled	couple	VERB
ejpam-3574	607	8	double	double	ADJ
ejpam-3574	607	9	pendulum	pendulum	NOUN
ejpam-3574	607	10	with	with	ADP
ejpam-3574	607	11	oscillating	oscillating	NOUN
ejpam-3574	607	12	supports	support	NOUN
ejpam-3574	607	13	.	.	PUNCT
ejpam-3574	608	1	with	with	ADP
ejpam-3574	608	2	m	m	PROPN
ejpam-3574	608	3	is	be	AUX
ejpam-3574	608	4	the	the	DET
ejpam-3574	608	5	mass	mass	NOUN
ejpam-3574	608	6	of	of	ADP
ejpam-3574	608	7	each	each	DET
ejpam-3574	608	8	pendulum	pendulum	NOUN
ejpam-3574	608	9	and	and	CCONJ
ejpam-3574	608	10	b	b	NOUN
ejpam-3574	608	11	is	be	AUX
ejpam-3574	608	12	the	the	DET
ejpam-3574	608	13	distance	distance	NOUN
ejpam-3574	608	14	between	between	ADP
ejpam-3574	608	15	the	the	DET
ejpam-3574	608	16	point	point	NOUN
ejpam-3574	608	17	of	of	ADP
ejpam-3574	608	18	suspension	suspension	NOUN
ejpam-3574	608	19	and	and	CCONJ
ejpam-3574	608	20	the	the	DET
ejpam-3574	608	21	point	point	NOUN
ejpam-3574	608	22	of	of	ADP
ejpam-3574	608	23	attachment	attachment	NOUN
ejpam-3574	608	24	of	of	ADP
ejpam-3574	608	25	the	the	DET
ejpam-3574	608	26	coupling	coupling	NOUN
ejpam-3574	608	27	spring	spring	NOUN
ejpam-3574	608	28	.	.	PUNCT
ejpam-3574	609	1	replacing	replace	VERB
ejpam-3574	609	2	f(t	f(t	NOUN
ejpam-3574	609	3	)	)	PUNCT
ejpam-3574	609	4	by	by	ADP
ejpam-3574	609	5	its	its	PRON
ejpam-3574	609	6	expression	expression	NOUN
ejpam-3574	609	7	in	in	ADP
ejpam-3574	609	8	(	(	PUNCT
ejpam-3574	609	9	20	20	NUM
ejpam-3574	609	10	)	)	PUNCT
ejpam-3574	609	11	,	,	PUNCT
ejpam-3574	609	12	equation	equation	NOUN
ejpam-3574	609	13	(	(	PUNCT
ejpam-3574	609	14	20	20	NUM
ejpam-3574	609	15	)	)	PUNCT
ejpam-3574	609	16	becomes	become	VERB
ejpam-3574	609	17	:	:	PUNCT
ejpam-3574	609	18	d2x	d2x	PROPN
ejpam-3574	609	19	dt2	dt2	PROPN
ejpam-3574	609	20	+	+	CCONJ
ejpam-3574	609	21	(	(	PUNCT
ejpam-3574	609	22	b0	b0	NOUN
ejpam-3574	609	23	+	+	CCONJ
ejpam-3574	609	24	cαω2	cαω2	NOUN
ejpam-3574	609	25	k20	k20	NOUN
ejpam-3574	609	26	cos(ωt)i2	cos(ωt)i2	NOUN
ejpam-3574	609	27	)	)	PUNCT
ejpam-3574	609	28	x	x	X
ejpam-3574	610	1	=	=	PUNCT
ejpam-3574	610	2	0	0	NUM
ejpam-3574	610	3	.	.	PUNCT
ejpam-3574	611	1	(	(	PUNCT
ejpam-3574	611	2	21	21	NUM
ejpam-3574	611	3	)	)	PUNCT
ejpam-3574	611	4	using	use	VERB
ejpam-3574	611	5	successively	successively	ADV
ejpam-3574	611	6	the	the	DET
ejpam-3574	611	7	change	change	NOUN
ejpam-3574	611	8	of	of	ADP
ejpam-3574	611	9	variables	variable	NOUN
ejpam-3574	611	10	z	z	PROPN
ejpam-3574	612	1	=	=	SYM
ejpam-3574	612	2	(	(	PUNCT
ejpam-3574	612	3	z1	z1	PROPN
ejpam-3574	612	4	z2	z2	PROPN
ejpam-3574	612	5	)	)	PUNCT
ejpam-3574	612	6	=	=	PUNCT
ejpam-3574	613	1	(	(	PUNCT
ejpam-3574	613	2	x1	x1	PROPN
ejpam-3574	613	3	+	+	CCONJ
ejpam-3574	614	1	x2	x2	NOUN
ejpam-3574	615	1	x1	x1	NUM
ejpam-3574	616	1	−	−	PROPN
ejpam-3574	617	1	x2	x2	PROPN
ejpam-3574	617	2	)	)	PUNCT
ejpam-3574	617	3	and	and	CCONJ
ejpam-3574	617	4	τ	τ	PROPN
ejpam-3574	617	5	=	=	SYM
ejpam-3574	617	6	ωt	ωt	PROPN
ejpam-3574	617	7	,	,	PUNCT
ejpam-3574	617	8	the	the	DET
ejpam-3574	617	9	equation	equation	NOUN
ejpam-3574	617	10	of	of	ADP
ejpam-3574	617	11	motion	motion	NOUN
ejpam-3574	617	12	of	of	ADP
ejpam-3574	617	13	the	the	DET
ejpam-3574	617	14	system	system	NOUN
ejpam-3574	617	15	can	can	AUX
ejpam-3574	617	16	be	be	AUX
ejpam-3574	617	17	reduced	reduce	VERB
ejpam-3574	617	18	as	as	ADP
ejpam-3574	617	19	(	(	PUNCT
ejpam-3574	617	20	see	see	VERB
ejpam-3574	617	21	[	[	X
ejpam-3574	617	22	14	14	NUM
ejpam-3574	617	23	]	]	SYM
ejpam-3574	617	24	)	)	PUNCT
ejpam-3574	617	25	d2zi	d2zi	NOUN
ejpam-3574	617	26	dτ2	dτ2	NOUN
ejpam-3574	617	27	+	+	CCONJ
ejpam-3574	617	28	(	(	PUNCT
ejpam-3574	617	29	δi	δi	X
ejpam-3574	617	30	+	+	CCONJ
ejpam-3574	617	31	εi	εi	PRON
ejpam-3574	617	32	cos(τ	cos(τ	PROPN
ejpam-3574	617	33	)	)	PUNCT
ejpam-3574	617	34	)	)	PUNCT
ejpam-3574	618	1	zi	zi	NOUN
ejpam-3574	618	2	=	=	PUNCT
ejpam-3574	619	1	0	0	NUM
ejpam-3574	619	2	,	,	PUNCT
ejpam-3574	619	3	i	i	PRON
ejpam-3574	619	4	=	=	NOUN
ejpam-3574	619	5	1	1	NUM
ejpam-3574	619	6	,	,	PUNCT
ejpam-3574	619	7	2	2	NUM
ejpam-3574	619	8	(	(	PUNCT
ejpam-3574	619	9	22	22	NUM
ejpam-3574	619	10	)	)	PUNCT
ejpam-3574	619	11	where	where	SCONJ
ejpam-3574	619	12	δ1	δ1	NOUN
ejpam-3574	619	13	=	=	SYM
ejpam-3574	619	14	δ	δ	PROPN
ejpam-3574	619	15	=	=	PUNCT
ejpam-3574	619	16	cg	cg	PROPN
ejpam-3574	619	17	k20ω2	k20ω2	PROPN
ejpam-3574	619	18	,	,	PUNCT
ejpam-3574	619	19	ε1	ε1	PROPN
ejpam-3574	619	20	=	=	SYM
ejpam-3574	619	21	ε	ε	PROPN
ejpam-3574	619	22	=	=	SYM
ejpam-3574	619	23	cα	cα	ADP
ejpam-3574	619	24	k20	k20	NOUN
ejpam-3574	619	25	and	and	CCONJ
ejpam-3574	619	26	ε2	ε2	NOUN
ejpam-3574	619	27	=	=	SYM
ejpam-3574	619	28	ε+	ε+	X
ejpam-3574	619	29	2e	2e	NOUN
ejpam-3574	619	30	,	,	PUNCT
ejpam-3574	619	31	with	with	ADP
ejpam-3574	619	32	e	e	NOUN
ejpam-3574	619	33	=	=	SYM
ejpam-3574	619	34	kb2	kb2	PROPN
ejpam-3574	619	35	mk20ω2	mk20ω2	PROPN
ejpam-3574	619	36	.	.	PUNCT
ejpam-3574	620	1	m.	m.	NOUN
ejpam-3574	620	2	dosso	dosso	PROPN
ejpam-3574	620	3	,	,	PUNCT
ejpam-3574	620	4	t.	t.	PROPN
ejpam-3574	620	5	g.	g.	PROPN
ejpam-3574	620	6	y.	y.	PROPN
ejpam-3574	620	7	arouna	arouna	PROPN
ejpam-3574	620	8	,	,	PUNCT
ejpam-3574	620	9	j.-c	j.-c	PROPN
ejpam-3574	620	10	.	.	PUNCT
ejpam-3574	621	1	koua	koua	PROPN
ejpam-3574	621	2	brou	brou	PROPN
ejpam-3574	621	3	/	/	SYM
ejpam-3574	621	4	eur	eur	PROPN
ejpam-3574	621	5	.	.	PUNCT
ejpam-3574	622	1	j.	j.	PROPN
ejpam-3574	622	2	pure	pure	PROPN
ejpam-3574	622	3	appl	appl	PROPN
ejpam-3574	622	4	.	.	PROPN
ejpam-3574	622	5	math	math	PROPN
ejpam-3574	622	6	,	,	PUNCT
ejpam-3574	622	7	12	12	NUM
ejpam-3574	622	8	(	(	PUNCT
ejpam-3574	622	9	4	4	NUM
ejpam-3574	622	10	)	)	PUNCT
ejpam-3574	622	11	(	(	PUNCT
ejpam-3574	622	12	2019	2019	NUM
ejpam-3574	622	13	)	)	PUNCT
ejpam-3574	622	14	,	,	PUNCT
ejpam-3574	622	15	1744	1744	NUM
ejpam-3574	622	16	-	-	SYM
ejpam-3574	622	17	1770	1770	NUM
ejpam-3574	622	18	1766	1766	NUM
ejpam-3574	622	19	finally	finally	ADV
ejpam-3574	622	20	,	,	PUNCT
ejpam-3574	622	21	using	use	VERB
ejpam-3574	622	22	the	the	DET
ejpam-3574	622	23	change	change	NOUN
ejpam-3574	622	24	of	of	ADP
ejpam-3574	622	25	variables	variable	NOUN
ejpam-3574	622	26	given	give	VERB
ejpam-3574	622	27	in	in	ADP
ejpam-3574	622	28	(	(	PUNCT
ejpam-3574	622	29	15	15	NUM
ejpam-3574	622	30	)	)	PUNCT
ejpam-3574	622	31	with	with	ADP
ejpam-3574	622	32	n	n	NOUN
ejpam-3574	622	33	=	=	SYM
ejpam-3574	622	34	2	2	NUM
ejpam-3574	622	35	,	,	PUNCT
ejpam-3574	622	36	it	it	PRON
ejpam-3574	622	37	is	be	AUX
ejpam-3574	622	38	easy	easy	ADJ
ejpam-3574	622	39	to	to	PART
ejpam-3574	622	40	see	see	VERB
ejpam-3574	622	41	that	that	SCONJ
ejpam-3574	622	42	the	the	DET
ejpam-3574	622	43	equation	equation	NOUN
ejpam-3574	622	44	of	of	ADP
ejpam-3574	622	45	motion	motion	NOUN
ejpam-3574	622	46	of	of	ADP
ejpam-3574	622	47	the	the	DET
ejpam-3574	622	48	coupled	couple	VERB
ejpam-3574	622	49	system	system	NOUN
ejpam-3574	622	50	can	can	AUX
ejpam-3574	622	51	be	be	AUX
ejpam-3574	622	52	reduce	reduce	VERB
ejpam-3574	622	53	to	to	ADP
ejpam-3574	622	54	form	form	NOUN
ejpam-3574	622	55	(	(	PUNCT
ejpam-3574	622	56	1	1	NUM
ejpam-3574	622	57	)	)	PUNCT
ejpam-3574	622	58	with	with	ADP
ejpam-3574	622	59	h(τ	h(τ	PROPN
ejpam-3574	622	60	,	,	PUNCT
ejpam-3574	622	61	δ	δ	PROPN
ejpam-3574	622	62	,	,	PUNCT
ejpam-3574	622	63	ε	ε	PROPN
ejpam-3574	622	64	,	,	PUNCT
ejpam-3574	622	65	e	e	NOUN
ejpam-3574	622	66	)	)	PUNCT
ejpam-3574	622	67	=	=	SYM
ejpam-3574	623	1	(	(	PUNCT
ejpam-3574	623	2	p	p	X
ejpam-3574	623	3	(	(	PUNCT
ejpam-3574	623	4	τ	τ	PROPN
ejpam-3574	623	5	,	,	PUNCT
ejpam-3574	623	6	δ	δ	PROPN
ejpam-3574	623	7	,	,	PUNCT
ejpam-3574	623	8	ε	ε	PROPN
ejpam-3574	623	9	,	,	PUNCT
ejpam-3574	623	10	e	e	NOUN
ejpam-3574	623	11	)	)	PUNCT
ejpam-3574	623	12	02	02	NUM
ejpam-3574	623	13	02	02	NUM
ejpam-3574	623	14	i2	i2	PROPN
ejpam-3574	623	15	)	)	PUNCT
ejpam-3574	623	16	and	and	CCONJ
ejpam-3574	623	17	p	p	X
ejpam-3574	623	18	(	(	PUNCT
ejpam-3574	623	19	τ	τ	PROPN
ejpam-3574	623	20	,	,	PUNCT
ejpam-3574	623	21	δ	δ	PROPN
ejpam-3574	623	22	,	,	PUNCT
ejpam-3574	623	23	ε	ε	PROPN
ejpam-3574	623	24	,	,	PUNCT
ejpam-3574	623	25	e	e	NOUN
ejpam-3574	623	26	)	)	PUNCT
ejpam-3574	623	27	=	=	SYM
ejpam-3574	623	28			PROPN
ejpam-3574	623	29	δ	δ	PROPN
ejpam-3574	623	30	+	+	CCONJ
ejpam-3574	623	31	ε	ε	PROPN
ejpam-3574	623	32	cos(τ	cos(τ	PROPN
ejpam-3574	623	33	)	)	PUNCT
ejpam-3574	623	34	0	0	NUM
ejpam-3574	624	1	0	0	NUM
ejpam-3574	624	2	δ	δ	PROPN
ejpam-3574	624	3	+	+	X
ejpam-3574	624	4	2e+	2e+	NUM
ejpam-3574	624	5	ε	ε	PROPN
ejpam-3574	624	6	cos(τ	cos(τ	PROPN
ejpam-3574	624	7	)	)	PUNCT
ejpam-3574	624	8			PROPN
ejpam-3574	624	9	.	.	PUNCT
ejpam-3574	625	1	consider	consider	VERB
ejpam-3574	625	2	the	the	DET
ejpam-3574	625	3	rank-2	rank-2	NOUN
ejpam-3574	625	4	perturbation	perturbation	NOUN
ejpam-3574	625	5	of	of	ADP
ejpam-3574	625	6	the	the	DET
ejpam-3574	625	7	fundamental	fundamental	ADJ
ejpam-3574	625	8	solution	solution	NOUN
ejpam-3574	625	9	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	625	10	,	,	PUNCT
ejpam-3574	625	11	δ	δ	PROPN
ejpam-3574	625	12	,	,	PUNCT
ejpam-3574	625	13	ε	ε	PROPN
ejpam-3574	625	14	,	,	PUNCT
ejpam-3574	625	15	e	e	NOUN
ejpam-3574	625	16	)	)	PUNCT
ejpam-3574	625	17	of	of	ADP
ejpam-3574	625	18	its	its	PRON
ejpam-3574	625	19	corresponding	corresponding	ADJ
ejpam-3574	625	20	hamiltonian	hamiltonian	ADJ
ejpam-3574	625	21	system	system	NOUN
ejpam-3574	625	22	ea(τ	ea(τ	NOUN
ejpam-3574	625	23	,	,	PUNCT
ejpam-3574	625	24	δ	δ	PROPN
ejpam-3574	625	25	,	,	PUNCT
ejpam-3574	625	26	ε	ε	PROPN
ejpam-3574	625	27	,	,	PUNCT
ejpam-3574	625	28	e	e	NOUN
ejpam-3574	625	29	)	)	PUNCT
ejpam-3574	625	30	=	=	SYM
ejpam-3574	625	31	uau	uau	PROPN
ejpam-3574	625	32	t	t	PROPN
ejpam-3574	625	33	a	a	DET
ejpam-3574	625	34	jx(τ	jx(τ	NOUN
ejpam-3574	625	35	,	,	PUNCT
ejpam-3574	625	36	δ	δ	PROPN
ejpam-3574	625	37	,	,	PUNCT
ejpam-3574	625	38	ε	ε	PROPN
ejpam-3574	625	39	,	,	PUNCT
ejpam-3574	625	40	e	e	NOUN
ejpam-3574	625	41	)	)	PUNCT
ejpam-3574	625	42	,	,	PUNCT
ejpam-3574	625	43	(	(	PUNCT
ejpam-3574	625	44	23	23	NUM
ejpam-3574	625	45	)	)	PUNCT
ejpam-3574	625	46	where	where	SCONJ
ejpam-3574	625	47	ua	ua	PROPN
ejpam-3574	625	48	is	be	AUX
ejpam-3574	625	49	defined	define	VERB
ejpam-3574	625	50	in	in	ADP
ejpam-3574	625	51	(	(	PUNCT
ejpam-3574	625	52	17	17	NUM
ejpam-3574	625	53	)	)	PUNCT
ejpam-3574	625	54	.	.	PUNCT
ejpam-3574	626	1	in	in	ADP
ejpam-3574	626	2	this	this	DET
ejpam-3574	626	3	case	case	NOUN
ejpam-3574	626	4	,	,	PUNCT
ejpam-3574	626	5	it	it	PRON
ejpam-3574	626	6	is	be	AUX
ejpam-3574	626	7	easy	easy	ADJ
ejpam-3574	626	8	to	to	PART
ejpam-3574	626	9	see	see	VERB
ejpam-3574	626	10	that	that	SCONJ
ejpam-3574	626	11	the	the	DET
ejpam-3574	626	12	equation	equation	NOUN
ejpam-3574	626	13	of	of	ADP
ejpam-3574	626	14	motion	motion	NOUN
ejpam-3574	626	15	is	be	AUX
ejpam-3574	626	16	of	of	ADP
ejpam-3574	626	17	the	the	DET
ejpam-3574	626	18	form	form	NOUN
ejpam-3574	626	19	(	(	PUNCT
ejpam-3574	626	20	19	19	NUM
ejpam-3574	626	21	)	)	PUNCT
ejpam-3574	627	1	[	[	X
ejpam-3574	627	2	1	1	NUM
ejpam-3574	627	3	,	,	PUNCT
ejpam-3574	627	4	2	2	NUM
ejpam-3574	627	5	,	,	PUNCT
ejpam-3574	627	6	5	5	NUM
ejpam-3574	627	7	]	]	PUNCT
ejpam-3574	627	8	.	.	PUNCT
ejpam-3574	628	1	figure	figure	NOUN
ejpam-3574	628	2	5	5	NUM
ejpam-3574	628	3	represents	represent	VERB
ejpam-3574	628	4	the	the	DET
ejpam-3574	628	5	spectral	spectral	ADJ
ejpam-3574	628	6	portrait	portrait	NOUN
ejpam-3574	628	7	of	of	ADP
ejpam-3574	628	8	the	the	DET
ejpam-3574	628	9	matrix	matrix	NOUN
ejpam-3574	628	10	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	628	11	,	,	PUNCT
ejpam-3574	628	12	δ	δ	PROPN
ejpam-3574	628	13	,	,	PUNCT
ejpam-3574	628	14	ε	ε	PROPN
ejpam-3574	628	15	,	,	PUNCT
ejpam-3574	628	16	e	e	NOUN
ejpam-3574	628	17	)	)	PUNCT
ejpam-3574	628	18	,	,	PUNCT
ejpam-3574	628	19	∀	∀	X
ejpam-3574	628	20	(	(	PUNCT
ejpam-3574	628	21	δ	δ	PROPN
ejpam-3574	628	22	,	,	PUNCT
ejpam-3574	628	23	ε	ε	PROPN
ejpam-3574	628	24	,	,	PUNCT
ejpam-3574	628	25	e	e	NOUN
ejpam-3574	628	26	)	)	PUNCT
ejpam-3574	628	27	∈	∈	NOUN
ejpam-3574	628	28	{	{	PUNCT
ejpam-3574	628	29	(	(	PUNCT
ejpam-3574	628	30	1	1	NUM
ejpam-3574	628	31	,	,	PUNCT
ejpam-3574	628	32	0.8	0.8	NUM
ejpam-3574	628	33	,	,	PUNCT
ejpam-3574	628	34	0.5	0.5	NUM
ejpam-3574	628	35	)	)	PUNCT
ejpam-3574	628	36	,	,	PUNCT
ejpam-3574	628	37	(	(	PUNCT
ejpam-3574	628	38	1.93	1.93	NUM
ejpam-3574	628	39	,	,	PUNCT
ejpam-3574	628	40	1.93	1.93	NUM
ejpam-3574	628	41	,	,	PUNCT
ejpam-3574	628	42	0.5	0.5	NUM
ejpam-3574	628	43	)	)	PUNCT
ejpam-3574	628	44	}	}	PUNCT
ejpam-3574	628	45	and	and	CCONJ
ejpam-3574	628	46	a	a	DET
ejpam-3574	628	47	∈	∈	PROPN
ejpam-3574	628	48	{	{	PUNCT
ejpam-3574	628	49	0	0	NUM
ejpam-3574	628	50	,	,	PUNCT
ejpam-3574	628	51	0.35	0.35	NUM
ejpam-3574	628	52	}	}	PUNCT
ejpam-3574	628	53	,	,	PUNCT
ejpam-3574	628	54	∀τ	∀τ	SYM
ejpam-3574	628	55	∈	∈	PROPN
ejpam-3574	629	1	[	[	X
ejpam-3574	629	2	0	0	NUM
ejpam-3574	629	3	,	,	PUNCT
ejpam-3574	629	4	2π	2π	NOUN
ejpam-3574	629	5	]	]	PUNCT
ejpam-3574	629	6	.	.	PUNCT
ejpam-3574	630	1	the	the	DET
ejpam-3574	630	2	figures	figure	NOUN
ejpam-3574	630	3	also	also	ADV
ejpam-3574	630	4	show	show	VERB
ejpam-3574	630	5	that	that	SCONJ
ejpam-3574	630	6	the	the	DET
ejpam-3574	630	7	small	small	ADJ
ejpam-3574	630	8	−1	−1	NOUN
ejpam-3574	630	9	0	0	NUM
ejpam-3574	630	10	1	1	NUM
ejpam-3574	630	11	−1	−1	NOUN
ejpam-3574	630	12	0	0	NUM
ejpam-3574	630	13	1	1	NUM
ejpam-3574	630	14	0	0	NUM
ejpam-3574	630	15	1	1	NUM
ejpam-3574	630	16	2	2	NUM
ejpam-3574	630	17	3	3	NUM
ejpam-3574	630	18	4	4	NUM
ejpam-3574	630	19	5	5	NUM
ejpam-3574	630	20	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	630	21	)	)	PUNCT
ejpam-3574	630	22	)	)	PUNCT
ejpam-3574	631	1	δ=1	δ=1	ADV
ejpam-3574	631	2	,	,	PUNCT
ejpam-3574	631	3	ε=0.8	ε=0.8	ADJ
ejpam-3574	631	4	and	and	CCONJ
ejpam-3574	631	5	e=0.5	e=0.5	NOUN
ejpam-3574	631	6	,	,	PUNCT
ejpam-3574	631	7	with	with	ADP
ejpam-3574	631	8	a=0.35	a=0.35	PRON
ejpam-3574	631	9	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	631	10	)	)	PUNCT
ejpam-3574	631	11	)	)	PUNCT
ejpam-3574	632	1	τ	τ	X
ejpam-3574	632	2	−1	−1	NOUN
ejpam-3574	632	3	0	0	NUM
ejpam-3574	632	4	1	1	NUM
ejpam-3574	632	5	−1	−1	NOUN
ejpam-3574	632	6	0	0	NUM
ejpam-3574	632	7	1	1	NUM
ejpam-3574	632	8	0	0	NUM
ejpam-3574	632	9	1	1	NUM
ejpam-3574	632	10	2	2	NUM
ejpam-3574	632	11	3	3	NUM
ejpam-3574	632	12	4	4	NUM
ejpam-3574	632	13	5	5	NUM
ejpam-3574	632	14	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	632	15	)	)	PUNCT
ejpam-3574	632	16	)	)	PUNCT
ejpam-3574	633	1	δ=1	δ=1	ADV
ejpam-3574	633	2	,	,	PUNCT
ejpam-3574	633	3	ε=0.8	ε=0.8	ADJ
ejpam-3574	633	4	and	and	CCONJ
ejpam-3574	633	5	e=0.5	e=0.5	NOUN
ejpam-3574	633	6	,	,	PUNCT
ejpam-3574	633	7	with	with	ADP
ejpam-3574	633	8	a=0	a=0	DET
ejpam-3574	633	9	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	633	10	)	)	PUNCT
ejpam-3574	633	11	)	)	PUNCT
ejpam-3574	634	1	τ	τ	X
ejpam-3574	634	2	−1	−1	NOUN
ejpam-3574	634	3	0	0	NUM
ejpam-3574	634	4	1	1	NUM
ejpam-3574	634	5	−1	−1	NOUN
ejpam-3574	634	6	0	0	NUM
ejpam-3574	634	7	1	1	NUM
ejpam-3574	634	8	0	0	NUM
ejpam-3574	634	9	1	1	NUM
ejpam-3574	634	10	2	2	NUM
ejpam-3574	634	11	3	3	NUM
ejpam-3574	634	12	4	4	NUM
ejpam-3574	634	13	5	5	NUM
ejpam-3574	634	14	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	634	15	)	)	PUNCT
ejpam-3574	634	16	)	)	PUNCT
ejpam-3574	634	17	δ=1.93	δ=1.93	NOUN
ejpam-3574	634	18	,	,	PUNCT
ejpam-3574	634	19	ε=1.93	ε=1.93	NOUN
ejpam-3574	634	20	and	and	CCONJ
ejpam-3574	634	21	e=0.5	e=0.5	NOUN
ejpam-3574	634	22	,	,	PUNCT
ejpam-3574	634	23	with	with	ADP
ejpam-3574	634	24	a=0.35	a=0.35	PRON
ejpam-3574	634	25	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	634	26	)	)	PUNCT
ejpam-3574	634	27	)	)	PUNCT
ejpam-3574	635	1	τ	τ	X
ejpam-3574	635	2	−1	−1	NOUN
ejpam-3574	635	3	0	0	NUM
ejpam-3574	635	4	1	1	NUM
ejpam-3574	635	5	−1	−1	NOUN
ejpam-3574	635	6	0	0	NUM
ejpam-3574	635	7	1	1	NUM
ejpam-3574	635	8	0	0	NUM
ejpam-3574	635	9	1	1	NUM
ejpam-3574	635	10	2	2	NUM
ejpam-3574	635	11	3	3	NUM
ejpam-3574	635	12	4	4	NUM
ejpam-3574	635	13	5	5	NUM
ejpam-3574	635	14	ℜ(λ(τ	ℜ(λ(τ	NOUN
ejpam-3574	635	15	)	)	PUNCT
ejpam-3574	635	16	)	)	PUNCT
ejpam-3574	635	17	δ=1.93	δ=1.93	NOUN
ejpam-3574	635	18	,	,	PUNCT
ejpam-3574	635	19	ε=1.93	ε=1.93	NOUN
ejpam-3574	635	20	and	and	CCONJ
ejpam-3574	635	21	e=0.5	e=0.5	NOUN
ejpam-3574	635	22	,	,	PUNCT
ejpam-3574	635	23	with	with	ADP
ejpam-3574	635	24	a=0	a=0	DET
ejpam-3574	635	25	ℑ(λ(τ	ℑ(λ(τ	NOUN
ejpam-3574	635	26	)	)	PUNCT
ejpam-3574	635	27	)	)	PUNCT
ejpam-3574	636	1	τ	τ	PRON
ejpam-3574	636	2	figure	figure	NOUN
ejpam-3574	636	3	5	5	NUM
ejpam-3574	636	4	:	:	PUNCT
ejpam-3574	636	5	spectral	spectral	ADJ
ejpam-3574	636	6	portrait	portrait	NOUN
ejpam-3574	636	7	of	of	ADP
ejpam-3574	636	8	x̃a(τ	x̃a(τ	PROPN
ejpam-3574	636	9	,	,	PUNCT
ejpam-3574	636	10	δ	δ	PROPN
ejpam-3574	636	11	,	,	PUNCT
ejpam-3574	636	12	ε	ε	PROPN
ejpam-3574	636	13	,	,	PUNCT
ejpam-3574	636	14	e	e	NOUN
ejpam-3574	636	15	)	)	PUNCT
ejpam-3574	636	16	,	,	PUNCT
ejpam-3574	636	17	∀τ	∀τ	SYM
ejpam-3574	636	18	∈	∈	PROPN
ejpam-3574	637	1	[	[	X
ejpam-3574	637	2	0	0	NUM
ejpam-3574	637	3	,	,	PUNCT
ejpam-3574	637	4	2π	2π	NOUN
ejpam-3574	637	5	]	]	PUNCT
ejpam-3574	637	6	and	and	CCONJ
ejpam-3574	637	7	(	(	PUNCT
ejpam-3574	637	8	δ	δ	PROPN
ejpam-3574	637	9	,	,	PUNCT
ejpam-3574	637	10	ε	ε	PROPN
ejpam-3574	637	11	,	,	PUNCT
ejpam-3574	637	12	e	e	NOUN
ejpam-3574	637	13	)	)	PUNCT
ejpam-3574	637	14	∈	∈	NOUN
ejpam-3574	637	15	{	{	PUNCT
ejpam-3574	637	16	(	(	PUNCT
ejpam-3574	637	17	1	1	NUM
ejpam-3574	637	18	,	,	PUNCT
ejpam-3574	637	19	0.8	0.8	NUM
ejpam-3574	637	20	,	,	PUNCT
ejpam-3574	637	21	0.5	0.5	NUM
ejpam-3574	637	22	)	)	PUNCT
ejpam-3574	637	23	,	,	PUNCT
ejpam-3574	637	24	(	(	PUNCT
ejpam-3574	637	25	1.93	1.93	NUM
ejpam-3574	637	26	,	,	PUNCT
ejpam-3574	637	27	1.93	1.93	NUM
ejpam-3574	637	28	,	,	PUNCT
ejpam-3574	637	29	0.5	0.5	NUM
ejpam-3574	637	30	)	)	PUNCT
ejpam-3574	637	31	}	}	PUNCT
ejpam-3574	637	32	,	,	PUNCT
ejpam-3574	637	33	with	with	ADP
ejpam-3574	637	34	a	a	DET
ejpam-3574	637	35	∈	∈	PROPN
ejpam-3574	637	36	{	{	PUNCT
ejpam-3574	637	37	0	0	NUM
ejpam-3574	637	38	,	,	PUNCT
ejpam-3574	637	39	0.35	0.35	NUM
ejpam-3574	637	40	}	}	PUNCT
ejpam-3574	637	41	.	.	PUNCT
ejpam-3574	638	1	perturbation	perturbation	NOUN
ejpam-3574	638	2	of	of	ADP
ejpam-3574	638	3	rank-2	rank-2	PROPN
ejpam-3574	638	4	on	on	ADP
ejpam-3574	638	5	the	the	DET
ejpam-3574	638	6	movement	movement	NOUN
ejpam-3574	638	7	of	of	ADP
ejpam-3574	638	8	pendulums	pendulum	NOUN
ejpam-3574	638	9	do	do	AUX
ejpam-3574	638	10	not	not	PART
ejpam-3574	638	11	change	change	VERB
ejpam-3574	638	12	the	the	DET
ejpam-3574	638	13	nature	nature	NOUN
ejpam-3574	638	14	of	of	ADP
ejpam-3574	638	15	the	the	DET
ejpam-3574	638	16	spectral	spectral	ADJ
ejpam-3574	638	17	portrait	portrait	NOUN
ejpam-3574	638	18	of	of	ADP
ejpam-3574	638	19	the	the	DET
ejpam-3574	638	20	fundamental	fundamental	ADJ
ejpam-3574	638	21	solution	solution	NOUN
ejpam-3574	638	22	x̃(τ	x̃(τ	PROPN
ejpam-3574	638	23	,	,	PUNCT
ejpam-3574	638	24	δ	δ	PROPN
ejpam-3574	638	25	,	,	PUNCT
ejpam-3574	638	26	ε	ε	PROPN
ejpam-3574	638	27	,	,	PUNCT
ejpam-3574	638	28	e	e	NOUN
ejpam-3574	638	29	)	)	PUNCT
ejpam-3574	638	30	.	.	PUNCT
ejpam-3574	639	1	for	for	ADP
ejpam-3574	639	2	all	all	DET
ejpam-3574	639	3	(	(	PUNCT
ejpam-3574	639	4	δ	δ	PROPN
ejpam-3574	639	5	,	,	PUNCT
ejpam-3574	639	6	ε	ε	PROPN
ejpam-3574	639	7	)	)	PUNCT
ejpam-3574	639	8	∈	∈	PROPN
ejpam-3574	640	1	[	[	X
ejpam-3574	640	2	0	0	NUM
ejpam-3574	640	3	,	,	PUNCT
ejpam-3574	640	4	1.98]×[0	1.98]×[0	NUM
ejpam-3574	640	5	,	,	PUNCT
ejpam-3574	640	6	2	2	NUM
ejpam-3574	640	7	]	]	PUNCT
ejpam-3574	640	8	,	,	PUNCT
ejpam-3574	640	9	figure	figure	NOUN
ejpam-3574	640	10	6	6	NUM
ejpam-3574	640	11	shows	show	VERB
ejpam-3574	640	12	the	the	DET
ejpam-3574	640	13	stability(strong	stability(strong	PROPN
ejpam-3574	640	14	)	)	PUNCT
ejpam-3574	640	15	region	region	NOUN
ejpam-3574	640	16	of	of	ADP
ejpam-3574	640	17	x̃a(2π	x̃a(2π	PROPN
ejpam-3574	640	18	,	,	PUNCT
ejpam-3574	640	19	δ	δ	PROPN
ejpam-3574	640	20	,	,	PUNCT
ejpam-3574	640	21	ε	ε	PROPN
ejpam-3574	640	22	,	,	PUNCT
ejpam-3574	640	23	e	e	NOUN
ejpam-3574	640	24	)	)	PUNCT
ejpam-3574	640	25	.	.	PUNCT
ejpam-3574	641	1	the	the	DET
ejpam-3574	641	2	first	first	ADJ
ejpam-3574	641	3	figure	figure	NOUN
ejpam-3574	641	4	(	(	PUNCT
ejpam-3574	641	5	left	left	ADJ
ejpam-3574	641	6	)	)	PUNCT
ejpam-3574	641	7	shows	show	VERB
ejpam-3574	641	8	the	the	DET
ejpam-3574	641	9	zone	zone	NOUN
ejpam-3574	641	10	of	of	ADP
ejpam-3574	641	11	strong	strong	ADJ
ejpam-3574	641	12	stability	stability	NOUN
ejpam-3574	641	13	in	in	ADP
ejpam-3574	641	14	white	white	ADJ
ejpam-3574	641	15	and	and	CCONJ
ejpam-3574	641	16	instability	instability	NOUN
ejpam-3574	641	17	in	in	ADP
ejpam-3574	641	18	red	red	NOUN
ejpam-3574	641	19	when	when	SCONJ
ejpam-3574	641	20	our	our	PRON
ejpam-3574	641	21	system	system	NOUN
ejpam-3574	641	22	is	be	AUX
ejpam-3574	641	23	subject	subject	ADJ
ejpam-3574	641	24	to	to	ADP
ejpam-3574	641	25	a	a	DET
ejpam-3574	641	26	rank-2	rank-2	PROPN
ejpam-3574	641	27	perturbation	perturbation	NOUN
ejpam-3574	641	28	with	with	ADP
ejpam-3574	641	29	a	a	DET
ejpam-3574	641	30	=	=	SYM
ejpam-3574	641	31	0.35	0.35	NUM
ejpam-3574	641	32	.	.	PUNCT
ejpam-3574	642	1	the	the	DET
ejpam-3574	642	2	second	second	ADJ
ejpam-3574	642	3	figure	figure	NOUN
ejpam-3574	642	4	(	(	PUNCT
ejpam-3574	642	5	right	right	ADJ
ejpam-3574	642	6	)	)	PUNCT
ejpam-3574	642	7	also	also	ADV
ejpam-3574	642	8	shows	show	VERB
ejpam-3574	642	9	the	the	DET
ejpam-3574	642	10	zone	zone	NOUN
ejpam-3574	642	11	of	of	ADP
ejpam-3574	642	12	strong	strong	ADJ
ejpam-3574	642	13	stability	stability	NOUN
ejpam-3574	642	14	in	in	ADP
ejpam-3574	642	15	white	white	ADJ
ejpam-3574	642	16	and	and	CCONJ
ejpam-3574	642	17	instability	instability	NOUN
ejpam-3574	642	18	in	in	ADP
ejpam-3574	642	19	red	red	NOUN
ejpam-3574	642	20	of	of	ADP
ejpam-3574	642	21	the	the	DET
ejpam-3574	642	22	unperturbed	unperturbed	ADJ
ejpam-3574	642	23	system	system	NOUN
ejpam-3574	642	24	(	(	PUNCT
ejpam-3574	642	25	a	a	DET
ejpam-3574	642	26	=	=	NOUN
ejpam-3574	642	27	0	0	NUM
ejpam-3574	642	28	)	)	PUNCT
ejpam-3574	642	29	.	.	PUNCT
ejpam-3574	643	1	however	however	ADV
ejpam-3574	643	2	,	,	PUNCT
ejpam-3574	643	3	we	we	PRON
ejpam-3574	643	4	observe	observe	VERB
ejpam-3574	643	5	some	some	DET
ejpam-3574	643	6	points	point	NOUN
ejpam-3574	643	7	of	of	ADP
ejpam-3574	643	8	stability	stability	NOUN
ejpam-3574	643	9	in	in	ADP
ejpam-3574	643	10	blue	blue	ADJ
ejpam-3574	643	11	.	.	PUNCT
ejpam-3574	644	1	thus	thus	ADV
ejpam-3574	644	2	we	we	PRON
ejpam-3574	644	3	notice	notice	VERB
ejpam-3574	644	4	a	a	DET
ejpam-3574	644	5	slight	slight	ADJ
ejpam-3574	644	6	difference	difference	NOUN
ejpam-3574	644	7	between	between	ADP
ejpam-3574	644	8	the	the	DET
ejpam-3574	644	9	two	two	NUM
ejpam-3574	644	10	figures	figure	NOUN
ejpam-3574	644	11	due	due	ADP
ejpam-3574	644	12	to	to	ADP
ejpam-3574	644	13	the	the	DET
ejpam-3574	644	14	small	small	ADJ
ejpam-3574	644	15	rank-2	rank-2	PROPN
ejpam-3574	644	16	perturbations	perturbation	NOUN
ejpam-3574	644	17	of	of	ADP
ejpam-3574	644	18	the	the	DET
ejpam-3574	644	19	system	system	NOUN
ejpam-3574	644	20	described	describe	VERB
ejpam-3574	644	21	by	by	ADP
ejpam-3574	644	22	our	our	PRON
ejpam-3574	644	23	two	two	NUM
ejpam-3574	644	24	coupled	couple	VERB
ejpam-3574	644	25	pendulums	pendulum	NOUN
ejpam-3574	644	26	.	.	PUNCT
ejpam-3574	645	1	m.	m.	NOUN
ejpam-3574	645	2	dosso	dosso	PROPN
ejpam-3574	645	3	,	,	PUNCT
ejpam-3574	645	4	t.	t.	PROPN
ejpam-3574	645	5	g.	g.	PROPN
ejpam-3574	645	6	y.	y.	PROPN
ejpam-3574	645	7	arouna	arouna	PROPN
ejpam-3574	645	8	,	,	PUNCT
ejpam-3574	645	9	j.-c	j.-c	PROPN
ejpam-3574	645	10	.	.	PUNCT
ejpam-3574	646	1	koua	koua	PROPN
ejpam-3574	646	2	brou	brou	PROPN
ejpam-3574	646	3	/	/	SYM
ejpam-3574	646	4	eur	eur	PROPN
ejpam-3574	646	5	.	.	PUNCT
ejpam-3574	647	1	j.	j.	PROPN
ejpam-3574	647	2	pure	pure	PROPN
ejpam-3574	647	3	appl	appl	PROPN
ejpam-3574	647	4	.	.	PROPN
ejpam-3574	647	5	math	math	PROPN
ejpam-3574	647	6	,	,	PUNCT
ejpam-3574	647	7	12	12	NUM
ejpam-3574	647	8	(	(	PUNCT
ejpam-3574	647	9	4	4	NUM
ejpam-3574	647	10	)	)	PUNCT
ejpam-3574	647	11	(	(	PUNCT
ejpam-3574	647	12	2019	2019	NUM
ejpam-3574	647	13	)	)	PUNCT
ejpam-3574	647	14	,	,	PUNCT
ejpam-3574	647	15	1744	1744	NUM
ejpam-3574	647	16	-	-	SYM
ejpam-3574	647	17	1770	1770	NUM
ejpam-3574	647	18	1767	1767	NUM
ejpam-3574	647	19	figure	figure	NOUN
ejpam-3574	647	20	6	6	NUM
ejpam-3574	647	21	:	:	PUNCT
ejpam-3574	647	22	stability(strong	stability(strong	PROPN
ejpam-3574	647	23	)	)	PUNCT
ejpam-3574	647	24	of	of	ADP
ejpam-3574	647	25	the	the	DET
ejpam-3574	647	26	matrix	matrix	NOUN
ejpam-3574	647	27	x̃a(2π	x̃a(2π	NUM
ejpam-3574	647	28	,	,	PUNCT
ejpam-3574	647	29	δ	δ	PROPN
ejpam-3574	647	30	,	,	PUNCT
ejpam-3574	647	31	ε	ε	PROPN
ejpam-3574	647	32	,	,	PUNCT
ejpam-3574	647	33	e	e	NOUN
ejpam-3574	647	34	)	)	PUNCT
ejpam-3574	647	35	,	,	PUNCT
ejpam-3574	647	36	∀	∀	X
ejpam-3574	647	37	(	(	PUNCT
ejpam-3574	647	38	δ	δ	PROPN
ejpam-3574	647	39	,	,	PUNCT
ejpam-3574	647	40	ε	ε	PROPN
ejpam-3574	647	41	)	)	PUNCT
ejpam-3574	647	42	∈	∈	PROPN
ejpam-3574	648	1	[	[	X
ejpam-3574	648	2	0	0	NUM
ejpam-3574	648	3	,	,	PUNCT
ejpam-3574	648	4	1.98]×	1.98]×	NUM
ejpam-3574	648	5	[	[	X
ejpam-3574	648	6	0	0	NUM
ejpam-3574	648	7	,	,	PUNCT
ejpam-3574	648	8	2	2	NUM
ejpam-3574	648	9	]	]	PUNCT
ejpam-3574	648	10	,	,	PUNCT
ejpam-3574	648	11	a	a	DET
ejpam-3574	648	12	∈	∈	PROPN
ejpam-3574	648	13	{	{	PUNCT
ejpam-3574	648	14	0	0	NUM
ejpam-3574	648	15	,	,	PUNCT
ejpam-3574	648	16	0.35	0.35	NUM
ejpam-3574	648	17	}	}	PUNCT
ejpam-3574	648	18	and	and	CCONJ
ejpam-3574	648	19	e	e	X
ejpam-3574	648	20	=	=	SYM
ejpam-3574	648	21	0.5	0.5	NUM
ejpam-3574	648	22	.	.	PUNCT
ejpam-3574	649	1	5.2	5.2	NUM
ejpam-3574	649	2	.	.	PUNCT
ejpam-3574	649	3	motion	motion	NOUN
ejpam-3574	649	4	of	of	ADP
ejpam-3574	649	5	an	an	DET
ejpam-3574	649	6	ion	ion	NOUN
ejpam-3574	649	7	through	through	ADP
ejpam-3574	649	8	a	a	DET
ejpam-3574	649	9	quadrupole	quadrupole	NOUN
ejpam-3574	649	10	analyser	analyser	NOUN
ejpam-3574	649	11	consider	consider	VERB
ejpam-3574	649	12	an	an	DET
ejpam-3574	649	13	ion	ion	NOUN
ejpam-3574	649	14	of	of	ADP
ejpam-3574	649	15	mass	mass	NOUN
ejpam-3574	649	16	m	m	PROPN
ejpam-3574	649	17	and	and	CCONJ
ejpam-3574	649	18	of	of	ADP
ejpam-3574	649	19	electric	electric	ADJ
ejpam-3574	649	20	charge	charge	NOUN
ejpam-3574	649	21	|ze|	|ze|	PROPN
ejpam-3574	649	22	which	which	PRON
ejpam-3574	649	23	moves	move	VERB
ejpam-3574	649	24	with	with	ADP
ejpam-3574	649	25	a	a	DET
ejpam-3574	649	26	velocity	velocity	NOUN
ejpam-3574	649	27	v	v	NOUN
ejpam-3574	649	28	through	through	ADP
ejpam-3574	649	29	a	a	DET
ejpam-3574	649	30	quadrupole	quadrupole	NOUN
ejpam-3574	649	31	analyzer	analyzer	NOUN
ejpam-3574	649	32	of	of	ADP
ejpam-3574	649	33	potential	potential	ADJ
ejpam-3574	649	34	φ0	φ0	PROPN
ejpam-3574	649	35	=	=	PUNCT
ejpam-3574	649	36	u	u	PROPN
ejpam-3574	649	37	−v	−v	NOUN
ejpam-3574	649	38	cos(ωt	cos(ωt	NOUN
ejpam-3574	649	39	)	)	PUNCT
ejpam-3574	649	40	.	.	PUNCT
ejpam-3574	650	1	within	within	ADP
ejpam-3574	650	2	the	the	DET
ejpam-3574	650	3	analyzer	analyzer	NOUN
ejpam-3574	650	4	,	,	PUNCT
ejpam-3574	650	5	the	the	DET
ejpam-3574	650	6	ion	ion	NOUN
ejpam-3574	650	7	experiences	experience	VERB
ejpam-3574	650	8	a	a	DET
ejpam-3574	650	9	force	force	NOUN
ejpam-3574	650	10	f(x	f(x	PROPN
ejpam-3574	650	11	,	,	PUNCT
ejpam-3574	650	12	y	y	PROPN
ejpam-3574	650	13	,	,	PUNCT
ejpam-3574	650	14	t	t	PROPN
ejpam-3574	650	15	)	)	PUNCT
ejpam-3574	650	16	=	=	SYM
ejpam-3574	651	1	−ze∇v(x	−ze∇v(x	PROPN
ejpam-3574	651	2	,	,	PUNCT
ejpam-3574	651	3	y	y	PROPN
ejpam-3574	651	4	,	,	PUNCT
ejpam-3574	651	5	t	t	PROPN
ejpam-3574	651	6	)	)	PUNCT
ejpam-3574	651	7	,	,	PUNCT
ejpam-3574	651	8	where	where	SCONJ
ejpam-3574	651	9	z	z	NOUN
ejpam-3574	651	10	is	be	AUX
ejpam-3574	651	11	the	the	DET
ejpam-3574	651	12	number	number	NOUN
ejpam-3574	651	13	of	of	ADP
ejpam-3574	651	14	protons	proton	NOUN
ejpam-3574	651	15	and	and	CCONJ
ejpam-3574	651	16	e	e	NOUN
ejpam-3574	651	17	is	be	AUX
ejpam-3574	651	18	the	the	DET
ejpam-3574	651	19	charge	charge	NOUN
ejpam-3574	651	20	of	of	ADP
ejpam-3574	651	21	a	a	DET
ejpam-3574	651	22	proton	proton	NOUN
ejpam-3574	651	23	.	.	PUNCT
ejpam-3574	652	1	we	we	PRON
ejpam-3574	652	2	assume	assume	VERB
ejpam-3574	652	3	that	that	SCONJ
ejpam-3574	652	4	the	the	DET
ejpam-3574	652	5	component	component	NOUN
ejpam-3574	652	6	of	of	ADP
ejpam-3574	652	7	the	the	DET
ejpam-3574	652	8	electric	electric	ADJ
ejpam-3574	652	9	field	field	NOUN
ejpam-3574	652	10	along	along	ADP
ejpam-3574	652	11	the	the	DET
ejpam-3574	652	12	axis	axis	NOUN
ejpam-3574	652	13	oz	oz	NOUN
ejpam-3574	652	14	is	be	AUX
ejpam-3574	652	15	zero	zero	NUM
ejpam-3574	652	16	,	,	PUNCT
ejpam-3574	652	17	and	and	CCONJ
ejpam-3574	652	18	the	the	DET
ejpam-3574	652	19	component	component	NOUN
ejpam-3574	652	20	z	z	NOUN
ejpam-3574	652	21	of	of	ADP
ejpam-3574	652	22	the	the	DET
ejpam-3574	652	23	velocity	velocity	NOUN
ejpam-3574	652	24	remains	remain	VERB
ejpam-3574	652	25	constant	constant	ADJ
ejpam-3574	652	26	.	.	PUNCT
ejpam-3574	653	1	figure	figure	VERB
ejpam-3574	653	2	7	7	NUM
ejpam-3574	653	3	:	:	PUNCT
ejpam-3574	653	4	model	model	NOUN
ejpam-3574	653	5	of	of	ADP
ejpam-3574	653	6	a	a	DET
ejpam-3574	653	7	quadrupole	quadrupole	NOUN
ejpam-3574	653	8	analyzer	analyzer	NOUN
ejpam-3574	653	9	.	.	PUNCT
ejpam-3574	654	1	according	accord	VERB
ejpam-3574	654	2	to	to	ADP
ejpam-3574	654	3	[	[	X
ejpam-3574	654	4	12	12	NUM
ejpam-3574	654	5	]	]	PUNCT
ejpam-3574	654	6	,	,	PUNCT
ejpam-3574	654	7	the	the	DET
ejpam-3574	654	8	motion	motion	NOUN
ejpam-3574	654	9	of	of	ADP
ejpam-3574	654	10	the	the	DET
ejpam-3574	654	11	ion	ion	NOUN
ejpam-3574	654	12	through	through	ADP
ejpam-3574	654	13	the	the	DET
ejpam-3574	654	14	analyzer	analyzer	NOUN
ejpam-3574	654	15	is	be	AUX
ejpam-3574	654	16	governed	govern	VERB
ejpam-3574	654	17	by	by	ADP
ejpam-3574	654	18	the	the	DET
ejpam-3574	654	19	following	follow	VERB
ejpam-3574	654	20	equation	equation	NOUN
ejpam-3574	654	21			NOUN
ejpam-3574	654	22	d2x	d2x	VERB
ejpam-3574	654	23	dξ2	dξ2	VERB
ejpam-3574	654	24	+	+	CCONJ
ejpam-3574	654	25	(	(	PUNCT
ejpam-3574	654	26	α−	α−	ADP
ejpam-3574	654	27	2q	2q	NUM
ejpam-3574	654	28	cos(2ξ))x	cos(2ξ))x	X
ejpam-3574	654	29	=	=	SYM
ejpam-3574	654	30	0	0	NUM
ejpam-3574	654	31	d2y	d2y	NOUN
ejpam-3574	654	32	dξ2	dξ2	NOUN
ejpam-3574	654	33	−	−	PROPN
ejpam-3574	654	34	(	(	PUNCT
ejpam-3574	654	35	α−	α−	ADP
ejpam-3574	654	36	2q	2q	NUM
ejpam-3574	654	37	cos(2ξ	cos(2ξ	NOUN
ejpam-3574	654	38	)	)	PUNCT
ejpam-3574	654	39	)	)	PUNCT
ejpam-3574	655	1	y	y	PROPN
ejpam-3574	655	2	=	=	SYM
ejpam-3574	655	3	0	0	PROPN
ejpam-3574	656	1	(	(	PUNCT
ejpam-3574	656	2	24	24	NUM
ejpam-3574	656	3	)	)	PUNCT
ejpam-3574	656	4	where	where	SCONJ
ejpam-3574	656	5	α	α	NOUN
ejpam-3574	656	6	=	=	PROPN
ejpam-3574	656	7	8zeu	8zeu	PROPN
ejpam-3574	656	8	r20mω	r20mω	NOUN
ejpam-3574	656	9	2	2	NUM
ejpam-3574	656	10	,	,	PUNCT
ejpam-3574	656	11	q	q	NOUN
ejpam-3574	656	12	=	=	SYM
ejpam-3574	656	13	4zev	4zev	NOUN
ejpam-3574	656	14	r20mω	r20mω	NOUN
ejpam-3574	656	15	2	2	NUM
ejpam-3574	656	16	and	and	CCONJ
ejpam-3574	656	17	ξ	ξ	NOUN
ejpam-3574	656	18	=	=	SYM
ejpam-3574	656	19	ωt	ωt	ADP
ejpam-3574	656	20	2	2	NUM
ejpam-3574	656	21	.	.	PUNCT
ejpam-3574	657	1	m.	m.	NOUN
ejpam-3574	657	2	dosso	dosso	PROPN
ejpam-3574	657	3	,	,	PUNCT
ejpam-3574	657	4	t.	t.	PROPN
ejpam-3574	657	5	g.	g.	PROPN
ejpam-3574	657	6	y.	y.	PROPN
ejpam-3574	657	7	arouna	arouna	PROPN
ejpam-3574	657	8	,	,	PUNCT
ejpam-3574	657	9	j.-c	j.-c	PROPN
ejpam-3574	657	10	.	.	PUNCT
ejpam-3574	658	1	koua	koua	PROPN
ejpam-3574	658	2	brou	brou	PROPN
ejpam-3574	658	3	/	/	SYM
ejpam-3574	658	4	eur	eur	PROPN
ejpam-3574	658	5	.	.	PUNCT
ejpam-3574	659	1	j.	j.	PROPN
ejpam-3574	659	2	pure	pure	PROPN
ejpam-3574	659	3	appl	appl	PROPN
ejpam-3574	659	4	.	.	PROPN
ejpam-3574	659	5	math	math	PROPN
ejpam-3574	659	6	,	,	PUNCT
ejpam-3574	659	7	12	12	NUM
ejpam-3574	659	8	(	(	PUNCT
ejpam-3574	659	9	4	4	NUM
ejpam-3574	659	10	)	)	PUNCT
ejpam-3574	659	11	(	(	PUNCT
ejpam-3574	659	12	2019	2019	NUM
ejpam-3574	659	13	)	)	PUNCT
ejpam-3574	659	14	,	,	PUNCT
ejpam-3574	659	15	1744	1744	NUM
ejpam-3574	659	16	-	-	SYM
ejpam-3574	659	17	1770	1770	NUM
ejpam-3574	659	18	1768	1768	NUM
ejpam-3574	659	19	this	this	DET
ejpam-3574	659	20	equation	equation	NOUN
ejpam-3574	659	21	was	be	AUX
ejpam-3574	659	22	proposed	propose	VERB
ejpam-3574	659	23	in	in	ADP
ejpam-3574	659	24	1866	1866	NUM
ejpam-3574	659	25	by	by	ADP
ejpam-3574	659	26	physicist	physicist	NOUN
ejpam-3574	659	27	mathieu	mathieu	PROPN
ejpam-3574	659	28	to	to	PART
ejpam-3574	659	29	describe	describe	VERB
ejpam-3574	659	30	the	the	DET
ejpam-3574	659	31	propagation	propagation	NOUN
ejpam-3574	659	32	of	of	ADP
ejpam-3574	659	33	waves	wave	NOUN
ejpam-3574	659	34	in	in	ADP
ejpam-3574	659	35	membranes	membrane	NOUN
ejpam-3574	659	36	.	.	PUNCT
ejpam-3574	660	1	we	we	PRON
ejpam-3574	660	2	apply	apply	VERB
ejpam-3574	660	3	the	the	DET
ejpam-3574	660	4	rank	rank	NOUN
ejpam-3574	660	5	-	-	PUNCT
ejpam-3574	660	6	k	k	NOUN
ejpam-3574	660	7	perturbation	perturbation	NOUN
ejpam-3574	660	8	to	to	ADP
ejpam-3574	660	9	this	this	DET
ejpam-3574	660	10	system	system	NOUN
ejpam-3574	660	11	in	in	ADP
ejpam-3574	660	12	view	view	NOUN
ejpam-3574	660	13	of	of	ADP
ejpam-3574	660	14	comparing	compare	VERB
ejpam-3574	660	15	the	the	DET
ejpam-3574	660	16	spectral	spectral	ADJ
ejpam-3574	660	17	portraits	portrait	NOUN
ejpam-3574	660	18	and	and	CCONJ
ejpam-3574	660	19	the	the	DET
ejpam-3574	660	20	stability	stability	NOUN
ejpam-3574	660	21	zones	zone	NOUN
ejpam-3574	660	22	of	of	ADP
ejpam-3574	660	23	the	the	DET
ejpam-3574	660	24	perturbed	perturb	VERB
ejpam-3574	660	25	and	and	CCONJ
ejpam-3574	660	26	unperturbed	unperturbed	ADJ
ejpam-3574	660	27	systems	system	NOUN
ejpam-3574	660	28	.	.	PUNCT
ejpam-3574	661	1	using	use	VERB
ejpam-3574	661	2	the	the	DET
ejpam-3574	661	3	change	change	NOUN
ejpam-3574	661	4	of	of	ADP
ejpam-3574	661	5	variable	variable	NOUN
ejpam-3574	661	6	given	give	VERB
ejpam-3574	661	7	in	in	ADP
ejpam-3574	661	8	(	(	PUNCT
ejpam-3574	661	9	15	15	NUM
ejpam-3574	661	10	)	)	PUNCT
ejpam-3574	661	11	with	with	ADP
ejpam-3574	661	12	n	n	NOUN
ejpam-3574	661	13	=	=	SYM
ejpam-3574	661	14	2	2	NUM
ejpam-3574	661	15	,	,	PUNCT
ejpam-3574	661	16	we	we	PRON
ejpam-3574	661	17	obtain	obtain	VERB
ejpam-3574	661	18	hamiltonian	hamiltonian	ADJ
ejpam-3574	661	19	system	system	NOUN
ejpam-3574	661	20	(	(	PUNCT
ejpam-3574	661	21	1	1	NUM
ejpam-3574	661	22	)	)	PUNCT
ejpam-3574	661	23	with	with	ADP
ejpam-3574	661	24	h(ξ	h(ξ	NOUN
ejpam-3574	661	25	)	)	PUNCT
ejpam-3574	661	26	=	=	NOUN
ejpam-3574	662	1	(	(	PUNCT
ejpam-3574	662	2	p	p	X
ejpam-3574	662	3	(	(	PUNCT
ejpam-3574	662	4	ξ	ξ	NOUN
ejpam-3574	662	5	)	)	PUNCT
ejpam-3574	662	6	02	02	NUM
ejpam-3574	662	7	02	02	NUM
ejpam-3574	662	8	i2	i2	PROPN
ejpam-3574	662	9	)	)	PUNCT
ejpam-3574	662	10	and	and	CCONJ
ejpam-3574	662	11	p	p	X
ejpam-3574	662	12	(	(	PUNCT
ejpam-3574	662	13	ξ	ξ	NOUN
ejpam-3574	662	14	)	)	PUNCT
ejpam-3574	662	15	=	=	SYM
ejpam-3574	663	1			PROPN
ejpam-3574	663	2	α−	α−	ADP
ejpam-3574	663	3	2q	2q	NUM
ejpam-3574	663	4	cos(2ξ	cos(2ξ	NOUN
ejpam-3574	663	5	)	)	PUNCT
ejpam-3574	663	6	0	0	NUM
ejpam-3574	663	7	0	0	NUM
ejpam-3574	663	8	−α+	−α+	NOUN
ejpam-3574	663	9	2q	2q	NUM
ejpam-3574	663	10	cos(2ξ	cos(2ξ	ADJ
ejpam-3574	663	11	)	)	PUNCT
ejpam-3574	663	12			PROPN
ejpam-3574	663	13	.	.	PUNCT
ejpam-3574	664	1	considering	consider	VERB
ejpam-3574	664	2	that	that	SCONJ
ejpam-3574	664	3	the	the	DET
ejpam-3574	664	4	motion	motion	NOUN
ejpam-3574	664	5	of	of	ADP
ejpam-3574	664	6	the	the	DET
ejpam-3574	664	7	ion	ion	NOUN
ejpam-3574	664	8	is	be	AUX
ejpam-3574	664	9	subjected	subject	VERB
ejpam-3574	664	10	to	to	ADP
ejpam-3574	664	11	a	a	DET
ejpam-3574	664	12	perturbation	perturbation	NOUN
ejpam-3574	664	13	of	of	ADP
ejpam-3574	664	14	the	the	DET
ejpam-3574	664	15	type	type	NOUN
ejpam-3574	664	16	(	(	PUNCT
ejpam-3574	664	17	16	16	NUM
ejpam-3574	664	18	)	)	PUNCT
ejpam-3574	664	19	,	,	PUNCT
ejpam-3574	664	20	the	the	DET
ejpam-3574	664	21	equation	equation	NOUN
ejpam-3574	664	22	of	of	ADP
ejpam-3574	664	23	the	the	DET
ejpam-3574	664	24	motion	motion	NOUN
ejpam-3574	664	25	of	of	ADP
ejpam-3574	664	26	the	the	DET
ejpam-3574	664	27	ion	ion	NOUN
ejpam-3574	664	28	then	then	ADV
ejpam-3574	664	29	becomes	become	VERB
ejpam-3574	664	30	[	[	X
ejpam-3574	664	31	2	2	NUM
ejpam-3574	664	32	,	,	PUNCT
ejpam-3574	664	33	5]	5]	NUM
ejpam-3574	664	34	j	j	NOUN
ejpam-3574	664	35	dx̃a(ξ	dx̃a(ξ	PROPN
ejpam-3574	664	36	,	,	PUNCT
ejpam-3574	664	37	α	α	X
ejpam-3574	664	38	,	,	PUNCT
ejpam-3574	664	39	q	q	NOUN
ejpam-3574	664	40	)	)	PUNCT
ejpam-3574	664	41	dξ	dξ	PROPN
ejpam-3574	665	1	=	=	PUNCT
ejpam-3574	665	2	(	(	PUNCT
ejpam-3574	665	3	i	i	PRON
ejpam-3574	665	4	−	−	PROPN
ejpam-3574	665	5	uutj)th(ξ	uutj)th(ξ	PROPN
ejpam-3574	665	6	,	,	PUNCT
ejpam-3574	665	7	α	α	NOUN
ejpam-3574	665	8	,	,	PUNCT
ejpam-3574	665	9	q)(i	q)(i	NOUN
ejpam-3574	665	10	−	−	PRON
ejpam-3574	665	11	uutj)︸	uutj)︸	NOUN
ejpam-3574	665	12	︷︷	︷︷	PROPN
ejpam-3574	665	13	︸	︸	X
ejpam-3574	665	14	h̃(ξ	h̃(ξ	PROPN
ejpam-3574	665	15	,	,	PUNCT
ejpam-3574	665	16	α	α	NOUN
ejpam-3574	665	17	,	,	PUNCT
ejpam-3574	665	18	q	q	NOUN
ejpam-3574	665	19	)	)	PUNCT
ejpam-3574	665	20	x̃a(ξ	x̃a(ξ	PROPN
ejpam-3574	665	21	,	,	PUNCT
ejpam-3574	665	22	α	α	X
ejpam-3574	665	23	,	,	PUNCT
ejpam-3574	665	24	q	q	NOUN
ejpam-3574	665	25	)	)	PUNCT
ejpam-3574	665	26	,	,	PUNCT
ejpam-3574	665	27	x̃a(0	x̃a(0	NUM
ejpam-3574	665	28	,	,	PUNCT
ejpam-3574	665	29	α	α	NOUN
ejpam-3574	665	30	,	,	PUNCT
ejpam-3574	665	31	q	q	NOUN
ejpam-3574	665	32	)	)	PUNCT
ejpam-3574	666	1	=	=	SYM
ejpam-3574	666	2	i	i	PRON
ejpam-3574	667	1	+	+	CCONJ
ejpam-3574	667	2	uutj	uutj	ADJ
ejpam-3574	667	3	(	(	PUNCT
ejpam-3574	667	4	25	25	NUM
ejpam-3574	667	5	)	)	PUNCT
ejpam-3574	667	6	where	where	SCONJ
ejpam-3574	667	7	u	u	NOUN
ejpam-3574	667	8	=	=	PUNCT
ejpam-3574	667	9	a	a	DET
ejpam-3574	667	10			ADJ
ejpam-3574	667	11	1	1	NUM
ejpam-3574	667	12	0	0	NUM
ejpam-3574	667	13	0	0	NUM
ejpam-3574	667	14	1	1	NUM
ejpam-3574	667	15	0	0	NUM
ejpam-3574	667	16	0	0	NUM
ejpam-3574	667	17	0	0	NUM
ejpam-3574	667	18	0	0	NUM
ejpam-3574	667	19			NOUN
ejpam-3574	667	20	and	and	CCONJ
ejpam-3574	667	21	a	a	DET
ejpam-3574	667	22	∈	∈	NOUN
ejpam-3574	668	1	[	[	X
ejpam-3574	668	2	0	0	NUM
ejpam-3574	668	3	,	,	PUNCT
ejpam-3574	668	4	1	1	NUM
ejpam-3574	668	5	[	[	NOUN
ejpam-3574	668	6	.	.	PUNCT
ejpam-3574	669	1	figure	figure	NOUN
ejpam-3574	669	2	8	8	NUM
ejpam-3574	669	3	represents	represent	VERB
ejpam-3574	669	4	the	the	DET
ejpam-3574	669	5	spectral	spectral	ADJ
ejpam-3574	669	6	portrait	portrait	NOUN
ejpam-3574	669	7	of	of	ADP
ejpam-3574	669	8	the	the	DET
ejpam-3574	669	9	matrix	matrix	NOUN
ejpam-3574	669	10	x̃a(α	x̃a(α	PROPN
ejpam-3574	669	11	,	,	PUNCT
ejpam-3574	669	12	q	q	X
ejpam-3574	669	13	,	,	PUNCT
ejpam-3574	669	14	ξ	ξ	NOUN
ejpam-3574	669	15	)	)	PUNCT
ejpam-3574	669	16	,	,	PUNCT
ejpam-3574	669	17	∀	∀	X
ejpam-3574	669	18	(	(	PUNCT
ejpam-3574	669	19	α	α	NOUN
ejpam-3574	669	20	,	,	PUNCT
ejpam-3574	669	21	q	q	ADJ
ejpam-3574	669	22	)	)	PUNCT
ejpam-3574	669	23	∈	∈	NOUN
ejpam-3574	669	24	{	{	PUNCT
ejpam-3574	669	25	(	(	PUNCT
ejpam-3574	669	26	0	0	NUM
ejpam-3574	669	27	,	,	PUNCT
ejpam-3574	669	28	0.025	0.025	NUM
ejpam-3574	669	29	)	)	PUNCT
ejpam-3574	669	30	,	,	PUNCT
ejpam-3574	669	31	(	(	PUNCT
ejpam-3574	669	32	0.1	0.1	NUM
ejpam-3574	669	33	,	,	PUNCT
ejpam-3574	669	34	0.7	0.7	NUM
ejpam-3574	669	35	)	)	PUNCT
ejpam-3574	669	36	}	}	PUNCT
ejpam-3574	669	37	,	,	PUNCT
ejpam-3574	669	38	and	and	CCONJ
ejpam-3574	669	39	a	a	DET
ejpam-3574	669	40	=	=	SYM
ejpam-3574	669	41	0	0	NUM
ejpam-3574	669	42	,	,	PUNCT
ejpam-3574	669	43	0.3003	0.3003	NUM
ejpam-3574	669	44	,	,	PUNCT
ejpam-3574	669	45	∀ξ	∀ξ	X
ejpam-3574	669	46	∈	∈	NOUN
ejpam-3574	670	1	[	[	X
ejpam-3574	670	2	0	0	NUM
ejpam-3574	670	3	,	,	PUNCT
ejpam-3574	670	4	π	π	NOUN
ejpam-3574	670	5	]	]	X
ejpam-3574	670	6	.	.	PUNCT
ejpam-3574	671	1	once	once	ADV
ejpam-3574	671	2	again	again	ADV
ejpam-3574	671	3	,	,	PUNCT
ejpam-3574	671	4	these	these	DET
ejpam-3574	671	5	figures	figure	NOUN
ejpam-3574	671	6	show	show	VERB
ejpam-3574	671	7	that	that	SCONJ
ejpam-3574	671	8	the	the	DET
ejpam-3574	671	9	small	small	ADJ
ejpam-3574	671	10	0.8	0.8	NUM
ejpam-3574	671	11	1	1	NUM
ejpam-3574	671	12	1.2	1.2	NUM
ejpam-3574	671	13	1.4	1.4	NUM
ejpam-3574	671	14	−0.4	−0.4	NUM
ejpam-3574	671	15	−0.2	−0.2	NOUN
ejpam-3574	671	16	0	0	NUM
ejpam-3574	671	17	0.2	0.2	NUM
ejpam-3574	671	18	0	0	NUM
ejpam-3574	671	19	1	1	NUM
ejpam-3574	671	20	2	2	NUM
ejpam-3574	671	21	3	3	NUM
ejpam-3574	671	22	4	4	NUM
ejpam-3574	671	23	5	5	NUM
ejpam-3574	671	24	ℜ(λ(ξ	ℜ(λ(ξ	NOUN
ejpam-3574	671	25	)	)	PUNCT
ejpam-3574	671	26	)	)	PUNCT
ejpam-3574	672	1	α=0	α=0	PROPN
ejpam-3574	672	2	and	and	CCONJ
ejpam-3574	672	3	q=0.025	q=0.025	PUNCT
ejpam-3574	672	4	,	,	PUNCT
ejpam-3574	672	5	with	with	ADP
ejpam-3574	672	6	a=0.3003	a=0.3003	NOUN
ejpam-3574	672	7	ℑ(λ(ξ	ℑ(λ(ξ	NOUN
ejpam-3574	672	8	)	)	PUNCT
ejpam-3574	672	9	)	)	PUNCT
ejpam-3574	673	1	ξ	ξ	X
ejpam-3574	673	2	0.8	0.8	NUM
ejpam-3574	673	3	1	1	NUM
ejpam-3574	673	4	1.2	1.2	NUM
ejpam-3574	673	5	1.4	1.4	NUM
ejpam-3574	673	6	−0.4	−0.4	NUM
ejpam-3574	673	7	−0.2	−0.2	NOUN
ejpam-3574	673	8	0	0	NUM
ejpam-3574	673	9	0.2	0.2	NUM
ejpam-3574	673	10	0	0	NUM
ejpam-3574	673	11	1	1	NUM
ejpam-3574	673	12	2	2	NUM
ejpam-3574	673	13	3	3	NUM
ejpam-3574	673	14	4	4	NUM
ejpam-3574	673	15	5	5	NUM
ejpam-3574	673	16	ℜ(λ(ξ	ℜ(λ(ξ	NOUN
ejpam-3574	673	17	)	)	PUNCT
ejpam-3574	673	18	)	)	PUNCT
ejpam-3574	674	1	α=0	α=0	PROPN
ejpam-3574	674	2	and	and	CCONJ
ejpam-3574	674	3	q=0.025	q=0.025	ADV
ejpam-3574	674	4	,	,	PUNCT
ejpam-3574	674	5	with	with	ADP
ejpam-3574	674	6	a=0	a=0	DET
ejpam-3574	674	7	ℑ(λ(ξ	ℑ(λ(ξ	NOUN
ejpam-3574	674	8	)	)	PUNCT
ejpam-3574	674	9	)	)	PUNCT
ejpam-3574	675	1	ξ	ξ	X
ejpam-3574	675	2	0	0	NUM
ejpam-3574	675	3	2	2	NUM
ejpam-3574	675	4	4	4	NUM
ejpam-3574	675	5	−1	−1	NOUN
ejpam-3574	675	6	0	0	NUM
ejpam-3574	675	7	1	1	NUM
ejpam-3574	675	8	0	0	NUM
ejpam-3574	675	9	1	1	NUM
ejpam-3574	675	10	2	2	NUM
ejpam-3574	675	11	3	3	NUM
ejpam-3574	675	12	4	4	NUM
ejpam-3574	675	13	5	5	NUM
ejpam-3574	675	14	ℜ(λ(ξ	ℜ(λ(ξ	NOUN
ejpam-3574	675	15	)	)	PUNCT
ejpam-3574	675	16	)	)	PUNCT
ejpam-3574	675	17	α=0.1	α=0.1	NOUN
ejpam-3574	675	18	and	and	CCONJ
ejpam-3574	675	19	q=0.7	q=0.7	PROPN
ejpam-3574	675	20	,	,	PUNCT
ejpam-3574	675	21	with	with	ADP
ejpam-3574	675	22	a=0.3003	a=0.3003	NOUN
ejpam-3574	675	23	ℑ(λ(ξ	ℑ(λ(ξ	NOUN
ejpam-3574	675	24	)	)	PUNCT
ejpam-3574	675	25	)	)	PUNCT
ejpam-3574	676	1	ξ	ξ	X
ejpam-3574	676	2	0	0	NUM
ejpam-3574	676	3	2	2	NUM
ejpam-3574	676	4	4	4	NUM
ejpam-3574	676	5	−1	−1	NOUN
ejpam-3574	676	6	0	0	NUM
ejpam-3574	676	7	1	1	NUM
ejpam-3574	676	8	0	0	NUM
ejpam-3574	676	9	1	1	NUM
ejpam-3574	676	10	2	2	NUM
ejpam-3574	676	11	3	3	NUM
ejpam-3574	676	12	4	4	NUM
ejpam-3574	676	13	5	5	NUM
ejpam-3574	676	14	ℜ(λ(ξ	ℜ(λ(ξ	NOUN
ejpam-3574	676	15	)	)	PUNCT
ejpam-3574	676	16	)	)	PUNCT
ejpam-3574	676	17	α=0.1	α=0.1	NOUN
ejpam-3574	676	18	and	and	CCONJ
ejpam-3574	676	19	q=0.7	q=0.7	PROPN
ejpam-3574	676	20	,	,	PUNCT
ejpam-3574	676	21	with	with	ADP
ejpam-3574	676	22	a=0	a=0	DET
ejpam-3574	676	23	ℑ(λ(ξ	ℑ(λ(ξ	NOUN
ejpam-3574	676	24	)	)	PUNCT
ejpam-3574	676	25	)	)	PUNCT
ejpam-3574	677	1	ξ	ξ	X
ejpam-3574	677	2	figure	figure	NOUN
ejpam-3574	677	3	8	8	NUM
ejpam-3574	677	4	:	:	PUNCT
ejpam-3574	677	5	spectral	spectral	ADJ
ejpam-3574	677	6	porttait	porttait	NOUN
ejpam-3574	677	7	of	of	ADP
ejpam-3574	677	8	the	the	DET
ejpam-3574	677	9	matrix	matrix	NOUN
ejpam-3574	677	10	x̃a(ξ	x̃a(ξ	PROPN
ejpam-3574	677	11	,	,	PUNCT
ejpam-3574	677	12	α	α	X
ejpam-3574	677	13	,	,	PUNCT
ejpam-3574	677	14	q	q	NOUN
ejpam-3574	677	15	)	)	PUNCT
ejpam-3574	677	16	,	,	PUNCT
ejpam-3574	677	17	∀ξ	∀ξ	X
ejpam-3574	677	18	∈	∈	NOUN
ejpam-3574	678	1	[	[	X
ejpam-3574	678	2	0	0	NUM
ejpam-3574	678	3	,	,	PUNCT
ejpam-3574	678	4	π	π	X
ejpam-3574	678	5	]	]	X
ejpam-3574	678	6	and	and	CCONJ
ejpam-3574	678	7	(	(	PUNCT
ejpam-3574	678	8	α	α	NOUN
ejpam-3574	678	9	,	,	PUNCT
ejpam-3574	678	10	q	q	ADJ
ejpam-3574	678	11	)	)	PUNCT
ejpam-3574	678	12	∈	∈	NOUN
ejpam-3574	678	13	{	{	PUNCT
ejpam-3574	678	14	(	(	PUNCT
ejpam-3574	678	15	0	0	NUM
ejpam-3574	678	16	,	,	PUNCT
ejpam-3574	678	17	0.025	0.025	NUM
ejpam-3574	678	18	)	)	PUNCT
ejpam-3574	678	19	,	,	PUNCT
ejpam-3574	678	20	(	(	PUNCT
ejpam-3574	678	21	0.1	0.1	NUM
ejpam-3574	678	22	,	,	PUNCT
ejpam-3574	678	23	0.7	0.7	NUM
ejpam-3574	678	24	)	)	PUNCT
ejpam-3574	678	25	}	}	PUNCT
ejpam-3574	678	26	with	with	ADP
ejpam-3574	678	27	a	a	DET
ejpam-3574	678	28	∈	∈	PROPN
ejpam-3574	678	29	{	{	PUNCT
ejpam-3574	678	30	0	0	NUM
ejpam-3574	678	31	,	,	PUNCT
ejpam-3574	678	32	0.3003	0.3003	NUM
ejpam-3574	678	33	}	}	PUNCT
ejpam-3574	678	34	.	.	PUNCT
ejpam-3574	679	1	rang-2	rang-2	NUM
ejpam-3574	679	2	perturbation	perturbation	NOUN
ejpam-3574	679	3	on	on	ADP
ejpam-3574	679	4	the	the	DET
ejpam-3574	679	5	movement	movement	NOUN
ejpam-3574	679	6	of	of	ADP
ejpam-3574	679	7	an	an	DET
ejpam-3574	679	8	ion	ion	NOUN
ejpam-3574	679	9	through	through	ADP
ejpam-3574	679	10	a	a	DET
ejpam-3574	679	11	quadrupole	quadrupole	NOUN
ejpam-3574	679	12	analyzer	analyzer	NOUN
ejpam-3574	679	13	do	do	AUX
ejpam-3574	679	14	not	not	PART
ejpam-3574	679	15	change	change	VERB
ejpam-3574	679	16	the	the	DET
ejpam-3574	679	17	nature	nature	NOUN
ejpam-3574	679	18	of	of	ADP
ejpam-3574	679	19	the	the	DET
ejpam-3574	679	20	spectral	spectral	ADJ
ejpam-3574	679	21	portrait	portrait	NOUN
ejpam-3574	679	22	of	of	ADP
ejpam-3574	679	23	x̃a(ξ	x̃a(ξ	PROPN
ejpam-3574	679	24	,	,	PUNCT
ejpam-3574	679	25	α	α	X
ejpam-3574	679	26	,	,	PUNCT
ejpam-3574	679	27	q	q	NOUN
ejpam-3574	679	28	)	)	PUNCT
ejpam-3574	679	29	.	.	PUNCT
ejpam-3574	680	1	∀	∀	X
ejpam-3574	681	1	(	(	PUNCT
ejpam-3574	681	2	α	α	NOUN
ejpam-3574	681	3	,	,	PUNCT
ejpam-3574	681	4	q	q	NOUN
ejpam-3574	681	5	)	)	PUNCT
ejpam-3574	681	6	∈	∈	PROPN
ejpam-3574	682	1	[	[	X
ejpam-3574	682	2	0	0	NUM
ejpam-3574	682	3	,	,	PUNCT
ejpam-3574	682	4	0.2	0.2	NUM
ejpam-3574	682	5	]	]	PUNCT
ejpam-3574	682	6	×	×	NOUN
ejpam-3574	683	1	[	[	X
ejpam-3574	683	2	0	0	NUM
ejpam-3574	683	3	,	,	PUNCT
ejpam-3574	683	4	0.9	0.9	NUM
ejpam-3574	683	5	]	]	PUNCT
ejpam-3574	683	6	,	,	PUNCT
ejpam-3574	683	7	figure	figure	NOUN
ejpam-3574	683	8	9	9	NUM
ejpam-3574	683	9	shows	show	VERB
ejpam-3574	683	10	the	the	DET
ejpam-3574	683	11	stability(strong	stability(strong	PROPN
ejpam-3574	683	12	)	)	PUNCT
ejpam-3574	683	13	zone	zone	NOUN
ejpam-3574	683	14	of	of	ADP
ejpam-3574	683	15	the	the	DET
ejpam-3574	683	16	matrix	matrix	NOUN
ejpam-3574	683	17	x̃a(π	x̃a(π	PROPN
ejpam-3574	683	18	,	,	PUNCT
ejpam-3574	683	19	α	α	NOUN
ejpam-3574	683	20	,	,	PUNCT
ejpam-3574	683	21	q	q	NOUN
ejpam-3574	683	22	)	)	PUNCT
ejpam-3574	683	23	.	.	PUNCT
ejpam-3574	684	1	the	the	DET
ejpam-3574	684	2	first	first	ADJ
ejpam-3574	684	3	figure	figure	NOUN
ejpam-3574	684	4	(	(	PUNCT
ejpam-3574	684	5	to	to	ADP
ejpam-3574	684	6	the	the	DET
ejpam-3574	684	7	left	left	NOUN
ejpam-3574	684	8	)	)	PUNCT
ejpam-3574	684	9	shows	show	VERB
ejpam-3574	684	10	the	the	DET
ejpam-3574	684	11	zone	zone	NOUN
ejpam-3574	684	12	of	of	ADP
ejpam-3574	684	13	strong	strong	ADJ
ejpam-3574	684	14	stability	stability	NOUN
ejpam-3574	684	15	in	in	ADP
ejpam-3574	684	16	white	white	ADJ
ejpam-3574	684	17	color	color	NOUN
ejpam-3574	684	18	references	reference	NOUN
ejpam-3574	684	19	1769	1769	NUM
ejpam-3574	684	20	and	and	CCONJ
ejpam-3574	684	21	the	the	DET
ejpam-3574	684	22	zone	zone	NOUN
ejpam-3574	684	23	of	of	ADP
ejpam-3574	684	24	instability	instability	NOUN
ejpam-3574	684	25	in	in	ADP
ejpam-3574	684	26	red	red	ADJ
ejpam-3574	684	27	color	color	NOUN
ejpam-3574	684	28	when	when	SCONJ
ejpam-3574	684	29	our	our	PRON
ejpam-3574	684	30	system	system	NOUN
ejpam-3574	684	31	is	be	AUX
ejpam-3574	684	32	subject	subject	ADJ
ejpam-3574	684	33	to	to	ADP
ejpam-3574	684	34	a	a	DET
ejpam-3574	684	35	rank-2	rank-2	PROPN
ejpam-3574	684	36	perturbation	perturbation	NOUN
ejpam-3574	684	37	with	with	ADP
ejpam-3574	684	38	a	a	DET
ejpam-3574	684	39	=	=	SYM
ejpam-3574	684	40	0.35	0.35	NUM
ejpam-3574	684	41	.	.	PUNCT
ejpam-3574	685	1	the	the	DET
ejpam-3574	685	2	second	second	ADJ
ejpam-3574	685	3	figure	figure	NOUN
ejpam-3574	685	4	(	(	PUNCT
ejpam-3574	685	5	to	to	ADP
ejpam-3574	685	6	the	the	DET
ejpam-3574	685	7	right	right	NOUN
ejpam-3574	685	8	)	)	PUNCT
ejpam-3574	685	9	also	also	ADV
ejpam-3574	685	10	shows	show	VERB
ejpam-3574	685	11	the	the	DET
ejpam-3574	685	12	zone	zone	NOUN
ejpam-3574	685	13	of	of	ADP
ejpam-3574	685	14	strong	strong	ADJ
ejpam-3574	685	15	stability	stability	NOUN
ejpam-3574	685	16	in	in	ADP
ejpam-3574	685	17	white	white	ADJ
ejpam-3574	685	18	color	color	NOUN
ejpam-3574	685	19	and	and	CCONJ
ejpam-3574	685	20	instability	instability	NOUN
ejpam-3574	685	21	in	in	ADP
ejpam-3574	685	22	red	red	ADJ
ejpam-3574	685	23	color	color	NOUN
ejpam-3574	685	24	of	of	ADP
ejpam-3574	685	25	the	the	DET
ejpam-3574	685	26	unperturbed	unperturbed	ADJ
ejpam-3574	685	27	system	system	NOUN
ejpam-3574	685	28	(	(	PUNCT
ejpam-3574	685	29	a	a	DET
ejpam-3574	685	30	=	=	NOUN
ejpam-3574	685	31	0	0	NUM
ejpam-3574	685	32	)	)	PUNCT
ejpam-3574	685	33	.	.	PUNCT
ejpam-3574	686	1	however	however	ADV
ejpam-3574	686	2	,	,	PUNCT
ejpam-3574	686	3	we	we	PRON
ejpam-3574	686	4	also	also	ADV
ejpam-3574	686	5	see	see	VERB
ejpam-3574	686	6	points	point	NOUN
ejpam-3574	686	7	of	of	ADP
ejpam-3574	686	8	stability	stability	NOUN
ejpam-3574	686	9	visible	visible	ADJ
ejpam-3574	686	10	in	in	ADP
ejpam-3574	686	11	blue	blue	NOUN
ejpam-3574	686	12	on	on	ADP
ejpam-3574	686	13	the	the	DET
ejpam-3574	686	14	first	first	ADJ
ejpam-3574	686	15	figure	figure	NOUN
ejpam-3574	686	16	compared	compare	VERB
ejpam-3574	686	17	to	to	ADP
ejpam-3574	686	18	the	the	DET
ejpam-3574	686	19	second	second	NOUN
ejpam-3574	686	20	.	.	PUNCT
ejpam-3574	687	1	thus	thus	ADV
ejpam-3574	687	2	we	we	PRON
ejpam-3574	687	3	notice	notice	VERB
ejpam-3574	687	4	a	a	DET
ejpam-3574	687	5	slight	slight	ADJ
ejpam-3574	687	6	difference	difference	NOUN
ejpam-3574	687	7	between	between	ADP
ejpam-3574	687	8	the	the	DET
ejpam-3574	687	9	two	two	NUM
ejpam-3574	687	10	figures	figure	NOUN
ejpam-3574	687	11	due	due	ADP
ejpam-3574	687	12	to	to	ADP
ejpam-3574	687	13	the	the	DET
ejpam-3574	687	14	small	small	ADJ
ejpam-3574	687	15	rank-2	rank-2	PROPN
ejpam-3574	687	16	perturbation	perturbation	NOUN
ejpam-3574	687	17	of	of	ADP
ejpam-3574	687	18	the	the	DET
ejpam-3574	687	19	system	system	NOUN
ejpam-3574	687	20	described	describe	VERB
ejpam-3574	687	21	by	by	ADP
ejpam-3574	687	22	the	the	DET
ejpam-3574	687	23	movement	movement	NOUN
ejpam-3574	687	24	of	of	ADP
ejpam-3574	687	25	an	an	DET
ejpam-3574	687	26	ion	ion	NOUN
ejpam-3574	687	27	through	through	ADP
ejpam-3574	687	28	a	a	DET
ejpam-3574	687	29	quadrupole	quadrupole	NOUN
ejpam-3574	687	30	analyzer	analyzer	NOUN
ejpam-3574	687	31	.	.	PUNCT
ejpam-3574	688	1	0	0	NUM
ejpam-3574	689	1	0.05	0.05	NUM
ejpam-3574	689	2	0.1	0.1	NUM
ejpam-3574	689	3	0.15	0.15	NUM
ejpam-3574	689	4	0.2	0.2	NUM
ejpam-3574	689	5	0	0	NUM
ejpam-3574	689	6	0.1	0.1	NUM
ejpam-3574	689	7	0.2	0.2	NUM
ejpam-3574	689	8	0.3	0.3	NUM
ejpam-3574	689	9	0.4	0.4	NUM
ejpam-3574	689	10	0.5	0.5	NUM
ejpam-3574	689	11	0.6	0.6	NUM
ejpam-3574	689	12	0.7	0.7	NUM
ejpam-3574	689	13	0.8	0.8	NUM
ejpam-3574	689	14	0.9	0.9	NUM
ejpam-3574	689	15	α	α	PRON
ejpam-3574	689	16	q	q	PROPN
ejpam-3574	689	17	a=0.3003	a=0.3003	PROPN
ejpam-3574	689	18	0	0	NUM
ejpam-3574	689	19	0.05	0.05	NUM
ejpam-3574	689	20	0.1	0.1	NUM
ejpam-3574	689	21	0.15	0.15	NUM
ejpam-3574	689	22	0.2	0.2	NUM
ejpam-3574	689	23	0	0	NUM
ejpam-3574	689	24	0.1	0.1	NUM
ejpam-3574	689	25	0.2	0.2	NUM
ejpam-3574	689	26	0.3	0.3	NUM
ejpam-3574	689	27	0.4	0.4	NUM
ejpam-3574	689	28	0.5	0.5	NUM
ejpam-3574	689	29	0.6	0.6	NUM
ejpam-3574	689	30	0.7	0.7	NUM
ejpam-3574	689	31	0.8	0.8	NUM
ejpam-3574	689	32	0.9	0.9	NUM
ejpam-3574	689	33	α	α	DET
ejpam-3574	689	34	q	q	NOUN
ejpam-3574	689	35	a=0	a=0	DET
ejpam-3574	689	36	figure	figure	NOUN
ejpam-3574	689	37	9	9	NUM
ejpam-3574	689	38	:	:	PUNCT
ejpam-3574	689	39	stability(strong	stability(strong	PROPN
ejpam-3574	689	40	)	)	PUNCT
ejpam-3574	689	41	zone	zone	NOUN
ejpam-3574	689	42	of	of	ADP
ejpam-3574	689	43	the	the	DET
ejpam-3574	689	44	matrix	matrix	NOUN
ejpam-3574	689	45	x̃a(π	x̃a(π	PROPN
ejpam-3574	689	46	,	,	PUNCT
ejpam-3574	689	47	α	α	NOUN
ejpam-3574	689	48	,	,	PUNCT
ejpam-3574	689	49	q	q	NOUN
ejpam-3574	689	50	)	)	PUNCT
ejpam-3574	689	51	,	,	PUNCT
ejpam-3574	689	52	∀	∀	X
ejpam-3574	689	53	(	(	PUNCT
ejpam-3574	689	54	α	α	NOUN
ejpam-3574	689	55	,	,	PUNCT
ejpam-3574	689	56	q	q	NOUN
ejpam-3574	689	57	)	)	PUNCT
ejpam-3574	689	58	∈	∈	PROPN
ejpam-3574	690	1	[	[	X
ejpam-3574	690	2	0	0	NUM
ejpam-3574	690	3	,	,	PUNCT
ejpam-3574	690	4	0.2]×	0.2]×	NOUN
ejpam-3574	691	1	[	[	X
ejpam-3574	691	2	0	0	NUM
ejpam-3574	691	3	,	,	PUNCT
ejpam-3574	691	4	0.9	0.9	NUM
ejpam-3574	691	5	]	]	PUNCT
ejpam-3574	691	6	and	and	CCONJ
ejpam-3574	691	7	a	a	DET
ejpam-3574	691	8	∈	∈	PROPN
ejpam-3574	691	9	{	{	PUNCT
ejpam-3574	691	10	0	0	NUM
ejpam-3574	691	11	,	,	PUNCT
ejpam-3574	691	12	0.3003	0.3003	NUM
ejpam-3574	691	13	}	}	PUNCT
ejpam-3574	691	14	.	.	PUNCT
ejpam-3574	692	1	6	6	X
ejpam-3574	692	2	.	.	X
ejpam-3574	692	3	concluding	conclude	VERB
ejpam-3574	692	4	remarks	remark	NOUN
ejpam-3574	692	5	from	from	ADP
ejpam-3574	692	6	works	work	NOUN
ejpam-3574	692	7	by	by	ADP
ejpam-3574	692	8	c.	c.	PROPN
ejpam-3574	692	9	mehl	mehl	PROPN
ejpam-3574	692	10	,	,	PUNCT
ejpam-3574	692	11	et	et	PROPN
ejpam-3574	692	12	al.[16	al.[16	PROPN
ejpam-3574	692	13	]	]	PUNCT
ejpam-3574	692	14	on	on	ADP
ejpam-3574	692	15	the	the	DET
ejpam-3574	692	16	perturbation	perturbation	NOUN
ejpam-3574	692	17	theory	theory	NOUN
ejpam-3574	692	18	of	of	ADP
ejpam-3574	692	19	structured	structured	ADJ
ejpam-3574	692	20	matrices	matrix	NOUN
ejpam-3574	692	21	,	,	PUNCT
ejpam-3574	692	22	we	we	PRON
ejpam-3574	692	23	presented	present	VERB
ejpam-3574	692	24	jordan	jordan	PROPN
ejpam-3574	692	25	canonical	canonical	ADJ
ejpam-3574	692	26	forms	form	NOUN
ejpam-3574	692	27	of	of	ADP
ejpam-3574	692	28	rank	rank	NOUN
ejpam-3574	692	29	-	-	PUNCT
ejpam-3574	692	30	k	k	NOUN
ejpam-3574	692	31	perturbations	perturbation	NOUN
ejpam-3574	692	32	of	of	ADP
ejpam-3574	692	33	symplectic	symplectic	ADJ
ejpam-3574	692	34	matrices	matrix	NOUN
ejpam-3574	692	35	and	and	CCONJ
ejpam-3574	692	36	fundamental	fundamental	ADJ
ejpam-3574	692	37	solutions	solution	NOUN
ejpam-3574	692	38	of	of	ADP
ejpam-3574	692	39	hamiltonian	hamiltonian	ADJ
ejpam-3574	692	40	system	system	NOUN
ejpam-3574	692	41	with	with	ADP
ejpam-3574	692	42	periodic	periodic	ADJ
ejpam-3574	692	43	coefficients	coefficient	NOUN
ejpam-3574	692	44	.	.	PUNCT
ejpam-3574	693	1	these	these	DET
ejpam-3574	693	2	results	result	NOUN
ejpam-3574	693	3	show	show	VERB
ejpam-3574	693	4	the	the	DET
ejpam-3574	693	5	effect	effect	NOUN
ejpam-3574	693	6	of	of	ADP
ejpam-3574	693	7	a	a	DET
ejpam-3574	693	8	k	k	ADJ
ejpam-3574	693	9	-	-	PUNCT
ejpam-3574	693	10	rank	rank	ADJ
ejpam-3574	693	11	perturbation	perturbation	NOUN
ejpam-3574	693	12	on	on	ADP
ejpam-3574	693	13	spectra	spectra	NOUN
ejpam-3574	693	14	of	of	ADP
ejpam-3574	693	15	periodic	periodic	ADJ
ejpam-3574	693	16	hamiltonian	hamiltonian	ADJ
ejpam-3574	693	17	systems	system	NOUN
ejpam-3574	693	18	.	.	PUNCT
ejpam-3574	694	1	examples	example	NOUN
ejpam-3574	694	2	of	of	ADP
ejpam-3574	694	3	applications	application	NOUN
ejpam-3574	694	4	on	on	ADP
ejpam-3574	694	5	mathieu	mathieu	PROPN
ejpam-3574	694	6	systems	system	NOUN
ejpam-3574	694	7	have	have	AUX
ejpam-3574	694	8	been	be	AUX
ejpam-3574	694	9	proposed	propose	VERB
ejpam-3574	694	10	to	to	PART
ejpam-3574	694	11	check	check	VERB
ejpam-3574	694	12	the	the	DET
ejpam-3574	694	13	small	small	ADJ
ejpam-3574	694	14	change	change	NOUN
ejpam-3574	694	15	of	of	ADP
ejpam-3574	694	16	spectrum	spectrum	NOUN
ejpam-3574	694	17	under	under	ADP
ejpam-3574	694	18	small	small	ADJ
ejpam-3574	694	19	perturbations	perturbation	NOUN
ejpam-3574	694	20	.	.	PUNCT
ejpam-3574	695	1	numerical	numerical	ADJ
ejpam-3574	695	2	simulations	simulation	NOUN
ejpam-3574	695	3	on	on	ADP
ejpam-3574	695	4	the	the	DET
ejpam-3574	695	5	differential	differential	ADJ
ejpam-3574	695	6	equations	equation	NOUN
ejpam-3574	695	7	of	of	ADP
ejpam-3574	695	8	the	the	DET
ejpam-3574	695	9	motion	motion	NOUN
ejpam-3574	695	10	of	of	ADP
ejpam-3574	695	11	two	two	NUM
ejpam-3574	695	12	uncoupled	uncoupled	ADJ
ejpam-3574	695	13	or	or	CCONJ
ejpam-3574	695	14	coupled	couple	VERB
ejpam-3574	695	15	pendulums	pendulum	NOUN
ejpam-3574	695	16	and	and	CCONJ
ejpam-3574	695	17	the	the	DET
ejpam-3574	695	18	movement	movement	NOUN
ejpam-3574	695	19	of	of	ADP
ejpam-3574	695	20	an	an	DET
ejpam-3574	695	21	ion	ion	NOUN
ejpam-3574	695	22	through	through	ADP
ejpam-3574	695	23	a	a	DET
ejpam-3574	695	24	quadrupole	quadrupole	NOUN
ejpam-3574	695	25	analyzer	analyzer	NOUN
ejpam-3574	695	26	show	show	VERB
ejpam-3574	695	27	a	a	DET
ejpam-3574	695	28	slight	slight	ADJ
ejpam-3574	695	29	change	change	NOUN
ejpam-3574	695	30	in	in	ADP
ejpam-3574	695	31	their	their	PRON
ejpam-3574	695	32	spectra	spectra	NOUN
ejpam-3574	695	33	(	(	PUNCT
ejpam-3574	695	34	thus	thus	ADV
ejpam-3574	695	35	in	in	ADP
ejpam-3574	695	36	their	their	PRON
ejpam-3574	695	37	stability	stability	NOUN
ejpam-3574	695	38	zones	zone	NOUN
ejpam-3574	695	39	)	)	PUNCT
ejpam-3574	695	40	.	.	PUNCT
ejpam-3574	696	1	references	reference	NOUN
ejpam-3574	696	2	[	[	X
ejpam-3574	696	3	1	1	X
ejpam-3574	696	4	]	]	PUNCT
ejpam-3574	696	5	t.	t.	PROPN
ejpam-3574	696	6	g.	g.	PROPN
ejpam-3574	696	7	y.	y.	PROPN
ejpam-3574	696	8	arouna	arouna	PROPN
ejpam-3574	696	9	and	and	CCONJ
ejpam-3574	696	10	m.	m.	NOUN
ejpam-3574	696	11	dosso	dosso	PROPN
ejpam-3574	696	12	,	,	PUNCT
ejpam-3574	696	13	a	a	DET
ejpam-3574	696	14	structured	structured	ADJ
ejpam-3574	696	15	approach	approach	NOUN
ejpam-3574	696	16	to	to	ADP
ejpam-3574	696	17	a	a	DET
ejpam-3574	696	18	perturbation	perturbation	NOUN
ejpam-3574	696	19	of	of	ADP
ejpam-3574	696	20	hamiltonian	hamiltonian	ADJ
ejpam-3574	696	21	systems	system	NOUN
ejpam-3574	696	22	with	with	ADP
ejpam-3574	696	23	periodic	periodic	ADJ
ejpam-3574	696	24	coefficients.int	coefficients.int	NOUN
ejpam-3574	696	25	j	j	NOUN
ejpam-3574	696	26	recent	recent	ADJ
ejpam-3574	696	27	sci	sci	PROPN
ejpam-3574	696	28	res	re	NOUN
ejpam-3574	696	29	.	.	PUNCT
ejpam-3574	697	1	vol9	vol9	PROPN
ejpam-3574	697	2	,	,	PUNCT
ejpam-3574	697	3	no	no	DET
ejpam-3574	697	4	3	3	NUM
ejpam-3574	697	5	,	,	PUNCT
ejpam-3574	697	6	p.25846	p.25846	PROPN
ejpam-3574	697	7	-	-	PUNCT
ejpam-3574	697	8	25856	25856	NUM
ejpam-3574	697	9	,	,	PUNCT
ejpam-3574	697	10	2018	2018	NUM
ejpam-3574	697	11	.	.	PUNCT
ejpam-3574	698	1	[	[	X
ejpam-3574	698	2	2	2	X
ejpam-3574	698	3	]	]	PUNCT
ejpam-3574	698	4	t.	t.	PROPN
ejpam-3574	698	5	g.	g.	PROPN
ejpam-3574	698	6	y.	y.	PROPN
ejpam-3574	698	7	arouna	arouna	PROPN
ejpam-3574	698	8	,	,	PUNCT
ejpam-3574	698	9	m.	m.	NOUN
ejpam-3574	698	10	dosso	dosso	NOUN
ejpam-3574	698	11	and	and	CCONJ
ejpam-3574	698	12	j.c	j.c	PROPN
ejpam-3574	698	13	.	.	PROPN
ejpam-3574	698	14	koua	koua	PROPN
ejpam-3574	698	15	brou	brou	PROPN
ejpam-3574	698	16	,	,	PUNCT
ejpam-3574	698	17	on	on	ADP
ejpam-3574	698	18	a	a	DET
ejpam-3574	698	19	pertubation	pertubation	NOUN
ejpam-3574	698	20	theory	theory	NOUN
ejpam-3574	698	21	of	of	ADP
ejpam-3574	698	22	hamiltonian	hamiltonian	ADJ
ejpam-3574	698	23	systems	system	NOUN
ejpam-3574	698	24	with	with	ADP
ejpam-3574	698	25	periodic	periodic	ADJ
ejpam-3574	698	26	coefficients	coefficient	NOUN
ejpam-3574	698	27	.	.	PUNCT
ejpam-3574	699	1	international	international	ADJ
ejpam-3574	699	2	journal	journal	PROPN
ejpam-3574	699	3	of	of	ADP
ejpam-3574	699	4	numerical	numerical	ADJ
ejpam-3574	699	5	methods	method	NOUN
ejpam-3574	699	6	and	and	CCONJ
ejpam-3574	699	7	applications	application	NOUN
ejpam-3574	699	8	,	,	PUNCT
ejpam-3574	699	9	vol	vol	NOUN
ejpam-3574	699	10	.	.	PROPN
ejpam-3574	699	11	17	17	NUM
ejpam-3574	699	12	,	,	PUNCT
ejpam-3574	699	13	no	no	DET
ejpam-3574	699	14	2	2	NUM
ejpam-3574	699	15	,	,	PUNCT
ejpam-3574	699	16	pages	page	NOUN
ejpam-3574	699	17	47	47	NUM
ejpam-3574	699	18	-	-	SYM
ejpam-3574	699	19	89	89	NUM
ejpam-3574	699	20	,	,	PUNCT
ejpam-3574	699	21	2018	2018	NUM
ejpam-3574	699	22	.	.	PUNCT
ejpam-3574	700	1	[	[	X
ejpam-3574	700	2	3	3	X
ejpam-3574	700	3	]	]	PUNCT
ejpam-3574	700	4	c.	c.	NOUN
ejpam-3574	700	5	brezinski	brezinski	PROPN
ejpam-3574	700	6	,	,	PUNCT
ejpam-3574	700	7	computational	computational	ADJ
ejpam-3574	700	8	aspects	aspect	NOUN
ejpam-3574	700	9	of	of	ADP
ejpam-3574	700	10	linear	linear	PROPN
ejpam-3574	700	11	control	control	NOUN
ejpam-3574	700	12	,	,	PUNCT
ejpam-3574	700	13	kluwer	kluwer	NOUN
ejpam-3574	700	14	academic	academic	ADJ
ejpam-3574	700	15	publishers	publisher	NOUN
ejpam-3574	700	16	,	,	PUNCT
ejpam-3574	700	17	2002	2002	NUM
ejpam-3574	700	18	.	.	PUNCT
ejpam-3574	701	1	references	reference	NOUN
ejpam-3574	701	2	1770	1770	NUM
ejpam-3574	701	3	[	[	X
ejpam-3574	701	4	4	4	NUM
ejpam-3574	701	5	]	]	PUNCT
ejpam-3574	701	6	m.	m.	NOUN
ejpam-3574	701	7	dosso	dosso	PROPN
ejpam-3574	701	8	,	,	PUNCT
ejpam-3574	701	9	sur	sur	PROPN
ejpam-3574	701	10	quelques	quelques	PROPN
ejpam-3574	701	11	algorithms	algorithms	NOUN
ejpam-3574	701	12	d’analyse	d’analyse	PROPN
ejpam-3574	701	13	de	de	PROPN
ejpam-3574	701	14	stabilité	stabilité	PROPN
ejpam-3574	701	15	forte	forte	NOUN
ejpam-3574	701	16	de	de	X
ejpam-3574	701	17	matrices	matrix	NOUN
ejpam-3574	701	18	symplectiques	symplectique	NOUN
ejpam-3574	701	19	,	,	PUNCT
ejpam-3574	701	20	phd	phd	NOUN
ejpam-3574	701	21	thesis	thesis	NOUN
ejpam-3574	701	22	,	,	PUNCT
ejpam-3574	701	23	université	université	ADJ
ejpam-3574	701	24	de	de	X
ejpam-3574	701	25	bretagne	bretagne	PROPN
ejpam-3574	701	26	occidentale	occidentale	PROPN
ejpam-3574	701	27	.	.	PUNCT
ejpam-3574	701	28	ecole	ecole	PROPN
ejpam-3574	701	29	doctorale	doctorale	PROPN
ejpam-3574	701	30	smis	smis	PROPN
ejpam-3574	701	31	,	,	PUNCT
ejpam-3574	701	32	laboratoire	laboratoire	PROPN
ejpam-3574	701	33	de	de	PROPN
ejpam-3574	701	34	mathématiques	mathématiques	PROPN
ejpam-3574	701	35	,	,	PUNCT
ejpam-3574	701	36	ufr	ufr	PROPN
ejpam-3574	701	37	sciences	sciences	PROPN
ejpam-3574	701	38	et	et	NOUN
ejpam-3574	701	39	techniques	technique	NOUN
ejpam-3574	701	40	,	,	PUNCT
ejpam-3574	701	41	september	september	PROPN
ejpam-3574	701	42	2006	2006	NUM
ejpam-3574	701	43	.	.	PUNCT
ejpam-3574	702	1	[	[	X
ejpam-3574	702	2	5	5	NUM
ejpam-3574	702	3	]	]	PUNCT
ejpam-3574	702	4	m.	m.	NOUN
ejpam-3574	702	5	dosso	dosso	PROPN
ejpam-3574	702	6	,	,	PUNCT
ejpam-3574	702	7	t.	t.	PROPN
ejpam-3574	702	8	g.	g.	PROPN
ejpam-3574	702	9	y.	y.	PROPN
ejpam-3574	702	10	arouna	arouna	PROPN
ejpam-3574	702	11	and	and	CCONJ
ejpam-3574	702	12	j.c	j.c	PROPN
ejpam-3574	702	13	.	.	PROPN
ejpam-3574	702	14	koua	koua	PROPN
ejpam-3574	702	15	brou	brou	PROPN
ejpam-3574	702	16	,	,	PUNCT
ejpam-3574	702	17	on	on	ADP
ejpam-3574	702	18	rank	rank	NOUN
ejpam-3574	702	19	one	one	NUM
ejpam-3574	702	20	perturbation	perturbation	NOUN
ejpam-3574	702	21	of	of	ADP
ejpam-3574	702	22	hamiltonian	hamiltonian	ADJ
ejpam-3574	702	23	system	system	NOUN
ejpam-3574	702	24	with	with	ADP
ejpam-3574	702	25	periodic	periodic	ADJ
ejpam-3574	702	26	coefficients	coefficient	NOUN
ejpam-3574	702	27	.	.	PUNCT
ejpam-3574	703	1	wseas	wseas	NOUN
ejpam-3574	703	2	translations	translation	NOUN
ejpam-3574	703	3	on	on	ADP
ejpam-3574	703	4	mathematics	mathematic	NOUN
ejpam-3574	703	5	,	,	PUNCT
ejpam-3574	703	6	volume	volume	NOUN
ejpam-3574	703	7	15	15	NUM
ejpam-3574	703	8	,	,	PUNCT
ejpam-3574	703	9	p.	p.	NOUN
ejpam-3574	703	10	502	502	NUM
ejpam-3574	703	11	-	-	SYM
ejpam-3574	703	12	510	510	NUM
ejpam-3574	703	13	,	,	PUNCT
ejpam-3574	703	14	2016	2016	NUM
ejpam-3574	703	15	.	.	PUNCT
ejpam-3574	704	1	[	[	X
ejpam-3574	704	2	6	6	NUM
ejpam-3574	704	3	]	]	PUNCT
ejpam-3574	704	4	m.	m.	NOUN
ejpam-3574	704	5	dosso	dosso	NOUN
ejpam-3574	704	6	and	and	CCONJ
ejpam-3574	704	7	n.	n.	PROPN
ejpam-3574	704	8	coulibaly	coulibaly	PROPN
ejpam-3574	704	9	,	,	PUNCT
ejpam-3574	704	10	symplectic	symplectic	ADJ
ejpam-3574	704	11	matrices	matrix	NOUN
ejpam-3574	704	12	and	and	CCONJ
ejpam-3574	704	13	strong	strong	ADJ
ejpam-3574	704	14	stability	stability	NOUN
ejpam-3574	704	15	of	of	ADP
ejpam-3574	704	16	hamiltonian	hamiltonian	ADJ
ejpam-3574	704	17	systems	system	NOUN
ejpam-3574	704	18	with	with	ADP
ejpam-3574	704	19	periodic	periodic	ADJ
ejpam-3574	704	20	coefficients	coefficient	NOUN
ejpam-3574	704	21	.	.	PUNCT
ejpam-3574	705	1	journal	journal	NOUN
ejpam-3574	705	2	of	of	ADP
ejpam-3574	705	3	mathematical	mathematical	ADJ
ejpam-3574	705	4	sciences	science	NOUN
ejpam-3574	705	5	:	:	PUNCT
ejpam-3574	705	6	advances	advance	NOUN
ejpam-3574	705	7	and	and	CCONJ
ejpam-3574	705	8	applications	application	NOUN
ejpam-3574	705	9	.	.	PUNCT
ejpam-3574	706	1	vol	vol	NOUN
ejpam-3574	706	2	.	.	PROPN
ejpam-3574	706	3	28	28	NUM
ejpam-3574	706	4	,	,	PUNCT
ejpam-3574	706	5	15	15	NUM
ejpam-3574	706	6	-	-	SYM
ejpam-3574	706	7	38	38	NUM
ejpam-3574	706	8	,	,	PUNCT
ejpam-3574	706	9	2014	2014	NUM
ejpam-3574	706	10	.	.	PUNCT
ejpam-3574	707	1	[	[	X
ejpam-3574	707	2	7	7	X
ejpam-3574	707	3	]	]	PUNCT
ejpam-3574	707	4	m.	m.	NOUN
ejpam-3574	707	5	dosso	dosso	NOUN
ejpam-3574	707	6	and	and	CCONJ
ejpam-3574	707	7	m.	m.	NOUN
ejpam-3574	707	8	sadkane	sadkane	NOUN
ejpam-3574	707	9	.	.	PUNCT
ejpam-3574	708	1	on	on	ADP
ejpam-3574	708	2	the	the	DET
ejpam-3574	708	3	strong	strong	ADJ
ejpam-3574	708	4	stability	stability	NOUN
ejpam-3574	708	5	of	of	ADP
ejpam-3574	708	6	symplectic	symplectic	ADJ
ejpam-3574	708	7	matrices	matrix	NOUN
ejpam-3574	708	8	.	.	PUNCT
ejpam-3574	709	1	numerical	numerical	PROPN
ejpam-3574	709	2	linear	linear	PROPN
ejpam-3574	709	3	algebra	algebra	PROPN
ejpam-3574	709	4	with	with	ADP
ejpam-3574	709	5	applications	application	NOUN
ejpam-3574	709	6	,	,	PUNCT
ejpam-3574	709	7	vol	vol	NOUN
ejpam-3574	709	8	.	.	PROPN
ejpam-3574	709	9	20	20	NUM
ejpam-3574	709	10	,	,	PUNCT
ejpam-3574	709	11	no	no	DET
ejpam-3574	709	12	2	2	NUM
ejpam-3574	709	13	,	,	PUNCT
ejpam-3574	709	14	p.	p.	NOUN
ejpam-3574	709	15	234	234	NUM
ejpam-3574	709	16	-	-	SYM
ejpam-3574	709	17	249	249	NUM
ejpam-3574	709	18	,	,	PUNCT
ejpam-3574	709	19	2013	2013	NUM
ejpam-3574	709	20	.	.	PUNCT
ejpam-3574	710	1	[	[	X
ejpam-3574	710	2	8	8	NUM
ejpam-3574	710	3	]	]	PUNCT
ejpam-3574	710	4	m.	m.	NOUN
ejpam-3574	710	5	dosso	dosso	NOUN
ejpam-3574	710	6	and	and	CCONJ
ejpam-3574	710	7	m.	m.	NOUN
ejpam-3574	710	8	sadkane	sadkane	PROPN
ejpam-3574	710	9	,	,	PUNCT
ejpam-3574	710	10	a	a	DET
ejpam-3574	710	11	spectral	spectral	ADJ
ejpam-3574	710	12	trichotomy	trichotomy	NOUN
ejpam-3574	710	13	method	method	NOUN
ejpam-3574	710	14	for	for	ADP
ejpam-3574	710	15	symplectic	symplectic	ADJ
ejpam-3574	710	16	matrices	matrix	NOUN
ejpam-3574	710	17	.	.	PUNCT
ejpam-3574	711	1	numer	numer	PROPN
ejpam-3574	711	2	.	.	PROPN
ejpam-3574	712	1	algor	algor	PROPN
ejpam-3574	712	2	.	.	PUNCT
ejpam-3574	713	1	,	,	PUNCT
ejpam-3574	713	2	52	52	NUM
ejpam-3574	713	3	:	:	SYM
ejpam-3574	713	4	187	187	NUM
ejpam-3574	713	5	-	-	SYM
ejpam-3574	713	6	212	212	NUM
ejpam-3574	713	7	,	,	PUNCT
ejpam-3574	713	8	2009	2009	NUM
ejpam-3574	713	9	.	.	PUNCT
ejpam-3574	714	1	[	[	X
ejpam-3574	714	2	9	9	NUM
ejpam-3574	714	3	]	]	X
ejpam-3574	714	4	g.	g.	PROPN
ejpam-3574	714	5	freiling	freiling	PROPN
ejpam-3574	714	6	,	,	PUNCT
ejpam-3574	714	7	v.	v.	PROPN
ejpam-3574	714	8	mehrmann	mehrmann	PROPN
ejpam-3574	714	9	,	,	PUNCT
ejpam-3574	714	10	and	and	CCONJ
ejpam-3574	714	11	h.	h.	PROPN
ejpam-3574	714	12	xu	xu	PROPN
ejpam-3574	714	13	.	.	PUNCT
ejpam-3574	715	1	existence	existence	NOUN
ejpam-3574	715	2	,	,	PUNCT
ejpam-3574	715	3	uniqueness	uniqueness	NOUN
ejpam-3574	715	4	and	and	CCONJ
ejpam-3574	715	5	parametrization	parametrization	NOUN
ejpam-3574	715	6	of	of	ADP
ejpam-3574	715	7	lagrangian	lagrangian	ADJ
ejpam-3574	715	8	invariant	invariant	ADJ
ejpam-3574	715	9	subspaces	subspace	NOUN
ejpam-3574	715	10	.	.	PUNCT
ejpam-3574	716	1	siam	siam	ADJ
ejpam-3574	716	2	journal	journal	PROPN
ejpam-3574	716	3	on	on	ADP
ejpam-3574	716	4	matrix	matrix	NOUN
ejpam-3574	716	5	analysis	analysis	NOUN
ejpam-3574	716	6	and	and	CCONJ
ejpam-3574	716	7	applications	application	NOUN
ejpam-3574	716	8	,	,	PUNCT
ejpam-3574	716	9	vol	vol	NOUN
ejpam-3574	716	10	.	.	PROPN
ejpam-3574	716	11	23	23	NUM
ejpam-3574	716	12	,	,	PUNCT
ejpam-3574	716	13	no	no	DET
ejpam-3574	716	14	4	4	NUM
ejpam-3574	716	15	,	,	PUNCT
ejpam-3574	716	16	p.	p.	NOUN
ejpam-3574	716	17	1045	1045	NUM
ejpam-3574	716	18	-	-	SYM
ejpam-3574	716	19	1069	1069	NUM
ejpam-3574	716	20	,	,	PUNCT
ejpam-3574	716	21	2002	2002	NUM
ejpam-3574	716	22	.	.	PUNCT
ejpam-3574	717	1	[	[	X
ejpam-3574	717	2	10	10	NUM
ejpam-3574	717	3	]	]	PUNCT
ejpam-3574	717	4	s.	s.	PROPN
ejpam-3574	717	5	k.	k.	PROPN
ejpam-3574	717	6	godunov	godunov	PROPN
ejpam-3574	717	7	,	,	PUNCT
ejpam-3574	717	8	m.	m.	NOUN
ejpam-3574	717	9	sadkane	sadkane	NOUN
ejpam-3574	717	10	,	,	PUNCT
ejpam-3574	717	11	numerical	numerical	ADJ
ejpam-3574	717	12	determination	determination	NOUN
ejpam-3574	717	13	of	of	ADP
ejpam-3574	717	14	a	a	DET
ejpam-3574	717	15	canonical	canonical	ADJ
ejpam-3574	717	16	form	form	NOUN
ejpam-3574	717	17	of	of	ADP
ejpam-3574	717	18	a	a	DET
ejpam-3574	717	19	symplectic	symplectic	ADJ
ejpam-3574	717	20	matrix	matrix	NOUN
ejpam-3574	717	21	.	.	PUNCT
ejpam-3574	718	1	siberian	siberian	ADJ
ejpam-3574	718	2	math	math	NOUN
ejpam-3574	718	3	.	.	PUNCT
ejpam-3574	719	1	j.	j.	PROPN
ejpam-3574	719	2	,	,	PUNCT
ejpam-3574	719	3	42	42	NUM
ejpam-3574	719	4	:	:	PUNCT
ejpam-3574	719	5	629	629	NUM
ejpam-3574	719	6	-	-	SYM
ejpam-3574	719	7	647	647	NUM
ejpam-3574	719	8	,	,	PUNCT
ejpam-3574	719	9	2001	2001	NUM
ejpam-3574	719	10	.	.	PUNCT
ejpam-3574	720	1	[	[	X
ejpam-3574	720	2	11	11	NUM
ejpam-3574	720	3	]	]	X
ejpam-3574	720	4	b.	b.	NOUN
ejpam-3574	720	5	hassibi	hassibi	NOUN
ejpam-3574	720	6	,	,	PUNCT
ejpam-3574	720	7	a.	a.	PROPN
ejpam-3574	720	8	h.	h.	PROPN
ejpam-3574	720	9	sayed	say	VERB
ejpam-3574	720	10	,	,	PUNCT
ejpam-3574	720	11	t.	t.	PROPN
ejpam-3574	720	12	kailath	kailath	PROPN
ejpam-3574	720	13	,	,	PUNCT
ejpam-3574	720	14	indefinite	indefinite	ADJ
ejpam-3574	720	15	-	-	PUNCT
ejpam-3574	720	16	quadratic	quadratic	ADJ
ejpam-3574	720	17	estimation	estimation	NOUN
ejpam-3574	720	18	and	and	CCONJ
ejpam-3574	720	19	control	control	NOUN
ejpam-3574	720	20	,	,	PUNCT
ejpam-3574	720	21	siam	siam	PROPN
ejpam-3574	720	22	,	,	PUNCT
ejpam-3574	720	23	philadelphia	philadelphia	PROPN
ejpam-3574	720	24	,	,	PUNCT
ejpam-3574	720	25	pa	pa	PROPN
ejpam-3574	720	26	,	,	PUNCT
ejpam-3574	720	27	1999	1999	NUM
ejpam-3574	720	28	.	.	PUNCT
ejpam-3574	721	1	[	[	X
ejpam-3574	721	2	12	12	NUM
ejpam-3574	721	3	]	]	X
ejpam-3574	721	4	e.	e.	PROPN
ejpam-3574	721	5	hoffmann	hoffmann	PROPN
ejpam-3574	721	6	and	and	CCONJ
ejpam-3574	721	7	v.	v.	ADP
ejpam-3574	721	8	stroobant	stroobant	ADJ
ejpam-3574	721	9	,	,	PUNCT
ejpam-3574	721	10	mass	mass	ADJ
ejpam-3574	721	11	spectrometry	spectrometry	NOUN
ejpam-3574	721	12	.	.	PUNCT
ejpam-3574	722	1	principles	principle	NOUN
ejpam-3574	722	2	and	and	CCONJ
ejpam-3574	722	3	applications	application	NOUN
ejpam-3574	722	4	,	,	PUNCT
ejpam-3574	722	5	3rd	3rd	ADJ
ejpam-3574	722	6	edition	edition	NOUN
ejpam-3574	722	7	,	,	PUNCT
ejpam-3574	722	8	september	september	PROPN
ejpam-3574	722	9	2007	2007	NUM
ejpam-3574	722	10	.	.	PUNCT
ejpam-3574	723	1	[	[	X
ejpam-3574	723	2	13	13	NUM
ejpam-3574	723	3	]	]	X
ejpam-3574	723	4	d.	d.	PROPN
ejpam-3574	723	5	kressner	kressner	PROPN
ejpam-3574	723	6	,	,	PUNCT
ejpam-3574	723	7	perturbation	perturbation	NOUN
ejpam-3574	723	8	bounds	bound	VERB
ejpam-3574	723	9	for	for	ADP
ejpam-3574	723	10	isotropic	isotropic	ADJ
ejpam-3574	723	11	invariant	invariant	ADJ
ejpam-3574	723	12	subspaces	subspace	NOUN
ejpam-3574	723	13	of	of	ADP
ejpam-3574	723	14	skewhamiltonian	skewhamiltonian	ADJ
ejpam-3574	723	15	matrices	matrix	NOUN
ejpam-3574	723	16	.	.	PUNCT
ejpam-3574	724	1	siam	siam	ADJ
ejpam-3574	724	2	j.	j.	PROPN
ejpam-3574	724	3	matrix	matrix	PROPN
ejpam-3574	724	4	analysis	analysis	NOUN
ejpam-3574	724	5	applications	application	NOUN
ejpam-3574	724	6	26(4	26(4	NUM
ejpam-3574	724	7	)	)	PUNCT
ejpam-3574	724	8	947	947	NUM
ejpam-3574	724	9	-	-	SYM
ejpam-3574	724	10	961,2005	961,2005	NUM
ejpam-3574	724	11	.	.	PUNCT
ejpam-3574	725	1	[	[	X
ejpam-3574	725	2	14	14	NUM
ejpam-3574	725	3	]	]	X
ejpam-3574	725	4	c.	c.	PROPN
ejpam-3574	725	5	s.	s.	PROPN
ejpam-3574	725	6	hsu	hsu	PROPN
ejpam-3574	725	7	,	,	PUNCT
ejpam-3574	725	8	on	on	ADP
ejpam-3574	725	9	a	a	DET
ejpam-3574	725	10	restricted	restricted	ADJ
ejpam-3574	725	11	class	class	NOUN
ejpam-3574	725	12	of	of	ADP
ejpam-3574	725	13	coupled	couple	VERB
ejpam-3574	725	14	hill	hill	PROPN
ejpam-3574	725	15	’s	’s	PART
ejpam-3574	725	16	equations	equation	NOUN
ejpam-3574	725	17	and	and	CCONJ
ejpam-3574	725	18	some	some	DET
ejpam-3574	725	19	applications	application	NOUN
ejpam-3574	725	20	,	,	PUNCT
ejpam-3574	725	21	journal	journal	NOUN
ejpam-3574	725	22	of	of	ADP
ejpam-3574	725	23	applied	apply	VERB
ejpam-3574	725	24	mechanics	mechanic	NOUN
ejpam-3574	725	25	,	,	PUNCT
ejpam-3574	725	26	vol	vol	NOUN
ejpam-3574	725	27	.	.	PROPN
ejpam-3574	725	28	28	28	NUM
ejpam-3574	725	29	,	,	PUNCT
ejpam-3574	725	30	no	no	DET
ejpam-3574	725	31	4	4	NUM
ejpam-3574	725	32	,	,	PUNCT
ejpam-3574	725	33	p.	p.	NOUN
ejpam-3574	725	34	551	551	NUM
ejpam-3574	725	35	-	-	SYM
ejpam-3574	725	36	556	556	NUM
ejpam-3574	725	37	,	,	PUNCT
ejpam-3574	725	38	1961	1961	NUM
ejpam-3574	725	39	.	.	PUNCT
ejpam-3574	726	1	[	[	X
ejpam-3574	726	2	15	15	NUM
ejpam-3574	726	3	]	]	X
ejpam-3574	726	4	p.	p.	NOUN
ejpam-3574	726	5	lancaster	lancaster	PROPN
ejpam-3574	726	6	,	,	PUNCT
ejpam-3574	726	7	l.	l.	PROPN
ejpam-3574	726	8	rodman	rodman	PROPN
ejpam-3574	726	9	,	,	PUNCT
ejpam-3574	726	10	algebraic	algebraic	PROPN
ejpam-3574	726	11	riccati	riccati	PROPN
ejpam-3574	726	12	equations	equation	NOUN
ejpam-3574	726	13	,	,	PUNCT
ejpam-3574	726	14	clarendon	clarendon	PROPN
ejpam-3574	726	15	press	press	NOUN
ejpam-3574	726	16	,	,	PUNCT
ejpam-3574	726	17	1995	1995	NUM
ejpam-3574	726	18	.	.	PUNCT
ejpam-3574	727	1	[	[	X
ejpam-3574	727	2	16	16	NUM
ejpam-3574	727	3	]	]	X
ejpam-3574	727	4	c.	c.	PROPN
ejpam-3574	727	5	mehl	mehl	PROPN
ejpam-3574	727	6	,	,	PUNCT
ejpam-3574	727	7	v.	v.	PROPN
ejpam-3574	727	8	mehrmann	mehrmann	PROPN
ejpam-3574	727	9	,	,	PUNCT
ejpam-3574	727	10	a.	a.	PROPN
ejpam-3574	727	11	c.	c.	PROPN
ejpam-3574	727	12	m.	m.	PROPN
ejpam-3574	727	13	ran	run	VERB
ejpam-3574	727	14	and	and	CCONJ
ejpam-3574	727	15	l.	l.	PROPN
ejpam-3574	727	16	rodman	rodman	PROPN
ejpam-3574	727	17	.	.	PUNCT
ejpam-3574	728	1	eigenvalues	eigenvalue	VERB
ejpam-3574	728	2	perturbation	perturbation	NOUN
ejpam-3574	728	3	theory	theory	NOUN
ejpam-3574	728	4	of	of	ADP
ejpam-3574	728	5	structured	structured	ADJ
ejpam-3574	728	6	matrices	matrix	NOUN
ejpam-3574	728	7	under	under	ADP
ejpam-3574	728	8	generic	generic	ADJ
ejpam-3574	728	9	structured	structured	ADJ
ejpam-3574	728	10	rank	rank	NOUN
ejpam-3574	728	11	one	one	NUM
ejpam-3574	728	12	perturbations	perturbation	NOUN
ejpam-3574	728	13	;	;	PUNCT
ejpam-3574	728	14	symplectic	symplectic	ADJ
ejpam-3574	728	15	,	,	PUNCT
ejpam-3574	728	16	othogonal	othogonal	ADJ
ejpam-3574	728	17	and	and	CCONJ
ejpam-3574	728	18	unitary	unitary	ADJ
ejpam-3574	728	19	matrices	matrix	NOUN
ejpam-3574	728	20	.	.	PUNCT
ejpam-3574	729	1	bit	bit	NOUN
ejpam-3574	729	2	,	,	PUNCT
ejpam-3574	729	3	54	54	NUM
ejpam-3574	729	4	,	,	PUNCT
ejpam-3574	729	5	219	219	NUM
ejpam-3574	729	6	-	-	SYM
ejpam-3574	729	7	255	255	NUM
ejpam-3574	729	8	,	,	PUNCT
ejpam-3574	729	9	2014	2014	NUM
ejpam-3574	729	10	.	.	PUNCT
ejpam-3574	730	1	[	[	X
ejpam-3574	730	2	17	17	NUM
ejpam-3574	730	3	]	]	X
ejpam-3574	730	4	d.	d.	PROPN
ejpam-3574	730	5	s.	s.	PROPN
ejpam-3574	730	6	watkins	watkins	PROPN
ejpam-3574	730	7	,	,	PUNCT
ejpam-3574	730	8	the	the	DET
ejpam-3574	730	9	matrix	matrix	NOUN
ejpam-3574	730	10	eigenvalue	eigenvalue	NOUN
ejpam-3574	730	11	problem	problem	NOUN
ejpam-3574	730	12	.	.	PUNCT
ejpam-3574	731	1	gr	gr	INTJ
ejpam-3574	731	2	and	and	CCONJ
ejpam-3574	731	3	krylov	krylov	NOUN
ejpam-3574	731	4	subspace	subspace	NOUN
ejpam-3574	731	5	methods	method	NOUN
ejpam-3574	731	6	,	,	PUNCT
ejpam-3574	731	7	siam	siam	NOUN
ejpam-3574	731	8	,	,	PUNCT
ejpam-3574	731	9	philadelphia	philadelphia	PROPN
ejpam-3574	731	10	,	,	PUNCT
ejpam-3574	731	11	2007	2007	NUM
ejpam-3574	731	12	.	.	PUNCT
ejpam-3574	732	1	[	[	X
ejpam-3574	732	2	18	18	NUM
ejpam-3574	732	3	]	]	X
ejpam-3574	732	4	v.	v.	ADP
ejpam-3574	732	5	a.	a.	NOUN
ejpam-3574	732	6	yakubovich	yakubovich	PROPN
ejpam-3574	732	7	,	,	PUNCT
ejpam-3574	732	8	v.	v.	ADP
ejpam-3574	732	9	m.	m.	NOUN
ejpam-3574	732	10	starzhinskii	starzhinskii	PROPN
ejpam-3574	732	11	,	,	PUNCT
ejpam-3574	732	12	linear	linear	ADJ
ejpam-3574	732	13	differential	differential	NOUN
ejpam-3574	732	14	equqtions	equqtion	NOUN
ejpam-3574	732	15	with	with	ADP
ejpam-3574	732	16	periodic	periodic	ADJ
ejpam-3574	732	17	coefficients	coefficient	NOUN
ejpam-3574	732	18	,	,	PUNCT
ejpam-3574	732	19	vol	vol	NOUN
ejpam-3574	732	20	.	.	PROPN
ejpam-3574	732	21	1	1	NUM
ejpam-3574	732	22	&	&	CCONJ
ejpam-3574	732	23	2	2	NUM
ejpam-3574	732	24	,	,	PUNCT
ejpam-3574	732	25	wiley	wiley	NOUN
ejpam-3574	732	26	,	,	PUNCT
ejpam-3574	732	27	new	new	PROPN
ejpam-3574	732	28	york	york	PROPN
ejpam-3574	732	29	,	,	PUNCT
ejpam-3574	732	30	1975	1975	NUM
ejpam-3574	732	31	.	.	PUNCT