id	sid	tid	token	lemma	pos
ejpam-6047	1	1	european	european	PROPN
ejpam-6047	1	2	journal	journal	PROPN
ejpam-6047	1	3	of	of	ADP
ejpam-6047	1	4	pure	pure	ADJ
ejpam-6047	1	5	and	and	CCONJ
ejpam-6047	1	6	applied	applied	ADJ
ejpam-6047	1	7	mathematics	mathematic	NOUN
ejpam-6047	1	8	2025	2025	NUM
ejpam-6047	1	9	,	,	PUNCT
ejpam-6047	1	10	vol	vol	NOUN
ejpam-6047	1	11	.	.	PROPN
ejpam-6047	1	12	18	18	NUM
ejpam-6047	1	13	,	,	PUNCT
ejpam-6047	1	14	issue	issue	NOUN
ejpam-6047	1	15	3	3	NUM
ejpam-6047	1	16	,	,	PUNCT
ejpam-6047	1	17	article	article	NOUN
ejpam-6047	1	18	number	number	NOUN
ejpam-6047	1	19	6047	6047	NUM
ejpam-6047	1	20	issn	issn	VERB
ejpam-6047	1	21	1307	1307	NUM
ejpam-6047	1	22	-	-	SYM
ejpam-6047	1	23	5543	5543	NUM
ejpam-6047	1	24	–	–	PUNCT
ejpam-6047	1	25	ejpam.com	ejpam.com	X
ejpam-6047	1	26	published	publish	VERB
ejpam-6047	1	27	by	by	ADP
ejpam-6047	1	28	new	new	PROPN
ejpam-6047	1	29	york	york	PROPN
ejpam-6047	1	30	business	business	PROPN
ejpam-6047	1	31	global	global	ADJ
ejpam-6047	1	32	stability	stability	NOUN
ejpam-6047	1	33	,	,	PUNCT
ejpam-6047	1	34	d	d	NOUN
ejpam-6047	1	35	-	-	PUNCT
ejpam-6047	1	36	stability	stability	NOUN
ejpam-6047	1	37	,	,	PUNCT
ejpam-6047	1	38	strong	strong	ADJ
ejpam-6047	1	39	d	d	NOUN
ejpam-6047	1	40	-	-	NOUN
ejpam-6047	1	41	stability	stability	NOUN
ejpam-6047	1	42	of	of	ADP
ejpam-6047	1	43	positive	positive	ADJ
ejpam-6047	1	44	linear	linear	ADJ
ejpam-6047	1	45	time	time	NOUN
ejpam-6047	1	46	-	-	PUNCT
ejpam-6047	1	47	invariant	invariant	ADJ
ejpam-6047	1	48	systems	system	NOUN
ejpam-6047	1	49	with	with	ADP
ejpam-6047	1	50	applications	application	NOUN
ejpam-6047	1	51	mutti	mutti	PROPN
ejpam-6047	1	52	-	-	PUNCT
ejpam-6047	1	53	ur	ur	PROPN
ejpam-6047	1	54	rehman1,∗	rehman1,∗	NOUN
ejpam-6047	1	55	,	,	PUNCT
ejpam-6047	1	56	jehad	jehad	ADJ
ejpam-6047	1	57	alzabut2,3,∗	alzabut2,3,∗	PROPN
ejpam-6047	1	58	,	,	PUNCT
ejpam-6047	1	59	amanullah	amanullah	ADJ
ejpam-6047	1	60	phulpoto4	phulpoto4	NOUN
ejpam-6047	1	61	,	,	PUNCT
ejpam-6047	1	62	mohamed	mohamed	PROPN
ejpam-6047	1	63	tounsi5	tounsi5	PROPN
ejpam-6047	1	64	,	,	PUNCT
ejpam-6047	1	65	rajaa	rajaa	PROPN
ejpam-6047	1	66	al	al	PROPN
ejpam-6047	1	67	naimi6	naimi6	PROPN
ejpam-6047	1	68	1	1	NUM
ejpam-6047	1	69	center	center	NOUN
ejpam-6047	1	70	of	of	ADP
ejpam-6047	1	71	research	research	NOUN
ejpam-6047	1	72	and	and	CCONJ
ejpam-6047	1	73	innovation	innovation	NOUN
ejpam-6047	1	74	,	,	PUNCT
ejpam-6047	1	75	asia	asia	PROPN
ejpam-6047	1	76	international	international	PROPN
ejpam-6047	1	77	university	university	PROPN
ejpam-6047	1	78	,	,	PUNCT
ejpam-6047	1	79	yangiobod	yangiobod	ADJ
ejpam-6047	1	80	mfy	mfy	NOUN
ejpam-6047	1	81	,	,	PUNCT
ejpam-6047	1	82	g‘ijduvon	g‘ijduvon	PROPN
ejpam-6047	1	83	street	street	PROPN
ejpam-6047	1	84	,	,	PUNCT
ejpam-6047	1	85	house	house	NOUN
ejpam-6047	1	86	74	74	NUM
ejpam-6047	1	87	,	,	PUNCT
ejpam-6047	1	88	200100	200100	NUM
ejpam-6047	1	89	bukhara	bukhara	PROPN
ejpam-6047	1	90	,	,	PUNCT
ejpam-6047	1	91	uzbekistan	uzbekistan	PROPN
ejpam-6047	1	92	2	2	NUM
ejpam-6047	1	93	department	department	NOUN
ejpam-6047	1	94	of	of	ADP
ejpam-6047	1	95	mathematics	mathematic	NOUN
ejpam-6047	1	96	and	and	CCONJ
ejpam-6047	1	97	sciences	science	NOUN
ejpam-6047	1	98	,	,	PUNCT
ejpam-6047	1	99	prince	prince	PROPN
ejpam-6047	1	100	sultan	sultan	PROPN
ejpam-6047	1	101	university	university	PROPN
ejpam-6047	1	102	,	,	PUNCT
ejpam-6047	1	103	11586	11586	NUM
ejpam-6047	1	104	riyadh	riyadh	NOUN
ejpam-6047	1	105	,	,	PUNCT
ejpam-6047	1	106	saudi	saudi	PROPN
ejpam-6047	1	107	arabia	arabia	PROPN
ejpam-6047	1	108	3	3	NUM
ejpam-6047	1	109	department	department	NOUN
ejpam-6047	1	110	of	of	ADP
ejpam-6047	1	111	industrial	industrial	ADJ
ejpam-6047	1	112	engineering	engineering	NOUN
ejpam-6047	1	113	,	,	PUNCT
ejpam-6047	1	114	ostim	ostim	PROPN
ejpam-6047	1	115	technical	technical	PROPN
ejpam-6047	1	116	university	university	PROPN
ejpam-6047	1	117	,	,	PUNCT
ejpam-6047	1	118	06374	06374	NUM
ejpam-6047	1	119	ankara	ankara	PROPN
ejpam-6047	1	120	,	,	PUNCT
ejpam-6047	1	121	türkiye	türkiye	NOUN
ejpam-6047	1	122	4	4	NUM
ejpam-6047	1	123	department	department	NOUN
ejpam-6047	1	124	of	of	ADP
ejpam-6047	1	125	mathematics	mathematic	NOUN
ejpam-6047	1	126	,	,	PUNCT
ejpam-6047	1	127	sukkur	sukkur	PROPN
ejpam-6047	1	128	iba	iba	PROPN
ejpam-6047	1	129	university	university	PROPN
ejpam-6047	1	130	,	,	PUNCT
ejpam-6047	1	131	sukkur	sukkur	PROPN
ejpam-6047	1	132	65200	65200	NUM
ejpam-6047	1	133	,	,	PUNCT
ejpam-6047	1	134	pakistan	pakistan	PROPN
ejpam-6047	1	135	5	5	NUM
ejpam-6047	1	136	computer	computer	NOUN
ejpam-6047	1	137	science	science	NOUN
ejpam-6047	1	138	department	department	PROPN
ejpam-6047	1	139	,	,	PUNCT
ejpam-6047	1	140	prince	prince	PROPN
ejpam-6047	1	141	sultan	sultan	PROPN
ejpam-6047	1	142	university	university	PROPN
ejpam-6047	1	143	,	,	PUNCT
ejpam-6047	1	144	11586	11586	NUM
ejpam-6047	1	145	riyadh	riyadh	NOUN
ejpam-6047	1	146	,	,	PUNCT
ejpam-6047	1	147	saudi	saudi	PROPN
ejpam-6047	1	148	arabia	arabia	PROPN
ejpam-6047	1	149	6	6	NUM
ejpam-6047	1	150	department	department	NOUN
ejpam-6047	1	151	of	of	ADP
ejpam-6047	1	152	mathematics	mathematic	NOUN
ejpam-6047	1	153	,	,	PUNCT
ejpam-6047	1	154	faculty	faculty	NOUN
ejpam-6047	1	155	of	of	ADP
ejpam-6047	1	156	art	art	NOUN
ejpam-6047	1	157	and	and	CCONJ
ejpam-6047	1	158	science	science	NOUN
ejpam-6047	1	159	,	,	PUNCT
ejpam-6047	1	160	university	university	NOUN
ejpam-6047	1	161	of	of	ADP
ejpam-6047	1	162	petra	petra	PROPN
ejpam-6047	1	163	,	,	PUNCT
ejpam-6047	1	164	11196	11196	NUM
ejpam-6047	1	165	,	,	PUNCT
ejpam-6047	1	166	amman	amman	PROPN
ejpam-6047	1	167	,	,	PUNCT
ejpam-6047	1	168	jordan	jordan	PROPN
ejpam-6047	1	169	abstract	abstract	PROPN
ejpam-6047	1	170	.	.	PUNCT
ejpam-6047	2	1	this	this	DET
ejpam-6047	2	2	paper	paper	NOUN
ejpam-6047	2	3	presents	present	VERB
ejpam-6047	2	4	new	new	ADJ
ejpam-6047	2	5	results	result	NOUN
ejpam-6047	2	6	on	on	ADP
ejpam-6047	2	7	the	the	DET
ejpam-6047	2	8	analysis	analysis	NOUN
ejpam-6047	2	9	of	of	ADP
ejpam-6047	2	10	positive	positive	ADJ
ejpam-6047	2	11	linear	linear	ADJ
ejpam-6047	2	12	time	time	NOUN
ejpam-6047	2	13	-	-	PUNCT
ejpam-6047	2	14	invariant	invariant	ADJ
ejpam-6047	2	15	systems	system	NOUN
ejpam-6047	2	16	with	with	ADP
ejpam-6047	2	17	non	non	ADJ
ejpam-6047	2	18	-	-	ADJ
ejpam-6047	2	19	negative	negative	ADJ
ejpam-6047	2	20	state	state	NOUN
ejpam-6047	2	21	variables	variable	NOUN
ejpam-6047	2	22	and	and	CCONJ
ejpam-6047	2	23	output	output	NOUN
ejpam-6047	2	24	data	datum	NOUN
ejpam-6047	2	25	for	for	ADP
ejpam-6047	2	26	non	non	ADJ
ejpam-6047	2	27	-	-	ADJ
ejpam-6047	2	28	negative	negative	ADJ
ejpam-6047	2	29	initial	initial	ADJ
ejpam-6047	2	30	conditions	condition	NOUN
ejpam-6047	2	31	and	and	CCONJ
ejpam-6047	2	32	inputs	input	NOUN
ejpam-6047	2	33	.	.	PUNCT
ejpam-6047	3	1	the	the	DET
ejpam-6047	3	2	positive	positive	ADJ
ejpam-6047	3	3	linear	linear	ADJ
ejpam-6047	3	4	time	time	NOUN
ejpam-6047	3	5	-	-	PUNCT
ejpam-6047	3	6	invariant	invariant	ADJ
ejpam-6047	3	7	systems	system	NOUN
ejpam-6047	3	8	are	be	AUX
ejpam-6047	3	9	characterized	characterize	VERB
ejpam-6047	3	10	by	by	ADP
ejpam-6047	3	11	the	the	DET
ejpam-6047	3	12	state	state	NOUN
ejpam-6047	3	13	-	-	PUNCT
ejpam-6047	3	14	space	space	NOUN
ejpam-6047	3	15	equations	equation	NOUN
ejpam-6047	3	16	which	which	PRON
ejpam-6047	3	17	offer	offer	VERB
ejpam-6047	3	18	a	a	DET
ejpam-6047	3	19	formal	formal	ADJ
ejpam-6047	3	20	mathematical	mathematical	ADJ
ejpam-6047	3	21	structure	structure	NOUN
ejpam-6047	3	22	of	of	ADP
ejpam-6047	3	23	form	form	NOUN
ejpam-6047	3	24	dx(t	dx(t	NOUN
ejpam-6047	3	25	)	)	PUNCT
ejpam-6047	3	26	dt	dt	NOUN
ejpam-6047	3	27	=	=	SYM
ejpam-6047	3	28	ax(t	ax(t	X
ejpam-6047	3	29	)	)	PUNCT
ejpam-6047	3	30	where	where	SCONJ
ejpam-6047	3	31	the	the	DET
ejpam-6047	3	32	system	system	NOUN
ejpam-6047	3	33	matrix	matrix	VERB
ejpam-6047	3	34	a	a	DET
ejpam-6047	3	35	∈	∈	PROPN
ejpam-6047	3	36	rn	rn	PROPN
ejpam-6047	3	37	,	,	PUNCT
ejpam-6047	3	38	n	n	PROPN
ejpam-6047	3	39	is	be	AUX
ejpam-6047	3	40	metzler	metzler	NOUN
ejpam-6047	3	41	,	,	PUNCT
ejpam-6047	3	42	with	with	ADP
ejpam-6047	3	43	non	non	ADJ
ejpam-6047	3	44	-	-	ADJ
ejpam-6047	3	45	negative	negative	ADJ
ejpam-6047	3	46	off	off	ADP
ejpam-6047	3	47	-	-	PUNCT
ejpam-6047	3	48	diagonal	diagonal	ADJ
ejpam-6047	3	49	components	component	NOUN
ejpam-6047	3	50	.	.	PUNCT
ejpam-6047	4	1	these	these	DET
ejpam-6047	4	2	systems	system	NOUN
ejpam-6047	4	3	exhibit	exhibit	VERB
ejpam-6047	4	4	essential	essential	ADJ
ejpam-6047	4	5	characteristics	characteristic	NOUN
ejpam-6047	4	6	such	such	ADJ
ejpam-6047	4	7	as	as	ADP
ejpam-6047	4	8	monotonicity	monotonicity	NOUN
ejpam-6047	4	9	,	,	PUNCT
ejpam-6047	4	10	stability	stability	NOUN
ejpam-6047	4	11	,	,	PUNCT
ejpam-6047	4	12	and	and	CCONJ
ejpam-6047	4	13	non	non	ADJ
ejpam-6047	4	14	-	-	ADJ
ejpam-6047	4	15	negativity	negativity	ADJ
ejpam-6047	4	16	,	,	PUNCT
ejpam-6047	4	17	making	make	VERB
ejpam-6047	4	18	them	they	PRON
ejpam-6047	4	19	fundamental	fundamental	ADJ
ejpam-6047	4	20	in	in	ADP
ejpam-6047	4	21	applications	application	NOUN
ejpam-6047	4	22	such	such	ADJ
ejpam-6047	4	23	as	as	ADP
ejpam-6047	4	24	biological	biological	ADJ
ejpam-6047	4	25	systems	system	NOUN
ejpam-6047	4	26	,	,	PUNCT
ejpam-6047	4	27	mathematical	mathematical	ADJ
ejpam-6047	4	28	economics	economic	NOUN
ejpam-6047	4	29	,	,	PUNCT
ejpam-6047	4	30	chemical	chemical	NOUN
ejpam-6047	4	31	reaction	reaction	NOUN
ejpam-6047	4	32	networks	network	NOUN
ejpam-6047	4	33	,	,	PUNCT
ejpam-6047	4	34	and	and	CCONJ
ejpam-6047	4	35	transportation	transportation	NOUN
ejpam-6047	4	36	models	model	NOUN
ejpam-6047	4	37	.	.	PUNCT
ejpam-6047	5	1	we	we	PRON
ejpam-6047	5	2	present	present	VERB
ejpam-6047	5	3	the	the	DET
ejpam-6047	5	4	theoretical	theoretical	ADJ
ejpam-6047	5	5	foundations	foundation	NOUN
ejpam-6047	5	6	utilizing	utilize	VERB
ejpam-6047	5	7	a	a	DET
ejpam-6047	5	8	mathematical	mathematical	ADJ
ejpam-6047	5	9	framework	framework	NOUN
ejpam-6047	5	10	from	from	ADP
ejpam-6047	5	11	algebraic	algebraic	ADJ
ejpam-6047	5	12	systems	system	NOUN
ejpam-6047	5	13	,	,	PUNCT
ejpam-6047	5	14	matrix	matrix	NOUN
ejpam-6047	5	15	theory	theory	NOUN
ejpam-6047	5	16	,	,	PUNCT
ejpam-6047	5	17	and	and	CCONJ
ejpam-6047	5	18	stability	stability	NOUN
ejpam-6047	5	19	analysis	analysis	NOUN
ejpam-6047	5	20	to	to	PART
ejpam-6047	5	21	investigate	investigate	VERB
ejpam-6047	5	22	stability	stability	NOUN
ejpam-6047	5	23	,	,	PUNCT
ejpam-6047	5	24	d	d	NOUN
ejpam-6047	5	25	-	-	NOUN
ejpam-6047	5	26	stability	stability	NOUN
ejpam-6047	5	27	,	,	PUNCT
ejpam-6047	5	28	and	and	CCONJ
ejpam-6047	5	29	strong	strong	ADJ
ejpam-6047	5	30	d	d	NOUN
ejpam-6047	5	31	-	-	NOUN
ejpam-6047	5	32	stability	stability	NOUN
ejpam-6047	5	33	of	of	ADP
ejpam-6047	5	34	positive	positive	ADJ
ejpam-6047	5	35	linear	linear	ADJ
ejpam-6047	5	36	time	time	NOUN
ejpam-6047	5	37	-	-	PUNCT
ejpam-6047	5	38	invariant	invariant	ADJ
ejpam-6047	5	39	systems	system	NOUN
ejpam-6047	5	40	in	in	ADP
ejpam-6047	5	41	the	the	DET
ejpam-6047	5	42	presence	presence	NOUN
ejpam-6047	5	43	of	of	ADP
ejpam-6047	5	44	metzler	metzler	PROPN
ejpam-6047	5	45	and	and	CCONJ
ejpam-6047	5	46	hurwitz	hurwitz	PROPN
ejpam-6047	5	47	matrices	matrix	NOUN
ejpam-6047	5	48	.	.	PUNCT
ejpam-6047	6	1	the	the	DET
ejpam-6047	6	2	numerical	numerical	PROPN
ejpam-6047	6	3	testing	testing	NOUN
ejpam-6047	6	4	supports	support	VERB
ejpam-6047	6	5	the	the	DET
ejpam-6047	6	6	spectrum	spectrum	NOUN
ejpam-6047	6	7	analysis	analysis	NOUN
ejpam-6047	6	8	and	and	CCONJ
ejpam-6047	6	9	ϵpseudospectrum	ϵpseudospectrum	NOUN
ejpam-6047	6	10	of	of	ADP
ejpam-6047	6	11	metzler	metzler	NOUN
ejpam-6047	6	12	matrices	matrix	NOUN
ejpam-6047	6	13	.	.	PUNCT
ejpam-6047	7	1	2020	2020	NUM
ejpam-6047	7	2	mathematics	mathematic	NOUN
ejpam-6047	7	3	subject	subject	NOUN
ejpam-6047	7	4	classifications	classification	NOUN
ejpam-6047	7	5	:	:	PUNCT
ejpam-6047	7	6	15a18	15a18	NUM
ejpam-6047	7	7	,	,	PUNCT
ejpam-6047	7	8	15a16	15a16	NUM
ejpam-6047	7	9	,	,	PUNCT
ejpam-6047	7	10	15a23	15a23	NUM
ejpam-6047	7	11	key	key	ADJ
ejpam-6047	7	12	words	word	NOUN
ejpam-6047	7	13	and	and	CCONJ
ejpam-6047	7	14	phrases	phrase	NOUN
ejpam-6047	7	15	:	:	PUNCT
ejpam-6047	7	16	singular	singular	ADJ
ejpam-6047	7	17	values	value	NOUN
ejpam-6047	7	18	,	,	PUNCT
ejpam-6047	7	19	structured	structure	VERB
ejpam-6047	7	20	singular	singular	ADJ
ejpam-6047	7	21	values	value	NOUN
ejpam-6047	7	22	,	,	PUNCT
ejpam-6047	7	23	strong	strong	ADJ
ejpam-6047	7	24	d	d	ADJ
ejpam-6047	7	25	-	-	ADJ
ejpam-6047	7	26	stable	stable	ADJ
ejpam-6047	7	27	matrix	matrix	NOUN
ejpam-6047	7	28	,	,	PUNCT
ejpam-6047	7	29	positive	positive	ADJ
ejpam-6047	7	30	linear	linear	NOUN
ejpam-6047	7	31	systems	system	NOUN
ejpam-6047	7	32	,	,	PUNCT
ejpam-6047	7	33	metzler	metzler	NOUN
ejpam-6047	7	34	matrices	matrix	NOUN
ejpam-6047	7	35	∗corresponding	∗corresponde	VERB
ejpam-6047	7	36	author	author	NOUN
ejpam-6047	7	37	.	.	PUNCT
ejpam-6047	8	1	doi	doi	NOUN
ejpam-6047	8	2	:	:	PUNCT
ejpam-6047	8	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6047	https://doi.org/10.29020/nybg.ejpam.v18i3.6047	ADJ
ejpam-6047	8	4	email	email	NOUN
ejpam-6047	8	5	addresses	address	NOUN
ejpam-6047	8	6	:	:	PUNCT
ejpam-6047	8	7	muttiur.abbasi@oxu.uz	muttiur.abbasi@oxu.uz	NOUN
ejpam-6047	8	8	(	(	PUNCT
ejpam-6047	8	9	m.	m.	NOUN
ejpam-6047	8	10	u.	u.	PROPN
ejpam-6047	8	11	rehman	rehman	PROPN
ejpam-6047	8	12	)	)	PUNCT
ejpam-6047	8	13	,	,	PUNCT
ejpam-6047	8	14	jalzabut@psu.edu.sa	jalzabut@psu.edu.sa	PROPN
ejpam-6047	8	15	(	(	PUNCT
ejpam-6047	8	16	j.	j.	PROPN
ejpam-6047	8	17	alzabut	alzabut	PROPN
ejpam-6047	8	18	)	)	PUNCT
ejpam-6047	8	19	,	,	PUNCT
ejpam-6047	8	20	amanullah@iba-suk.edu.pk	amanullah@iba-suk.edu.pk	PROPN
ejpam-6047	8	21	(	(	PUNCT
ejpam-6047	8	22	a.	a.	NOUN
ejpam-6047	8	23	phulpoto	phulpoto	NOUN
ejpam-6047	8	24	)	)	PUNCT
ejpam-6047	8	25	,	,	PUNCT
ejpam-6047	8	26	mtounsi@psu.edu.sa	mtounsi@psu.edu.sa	NOUN
ejpam-6047	8	27	(	(	PUNCT
ejpam-6047	8	28	m.	m.	NOUN
ejpam-6047	8	29	tounsi	tounsi	PROPN
ejpam-6047	8	30	)	)	PUNCT
ejpam-6047	8	31	,	,	PUNCT
ejpam-6047	8	32	rajaa.alnaimi@uop.edu.jo	rajaa.alnaimi@uop.edu.jo	PROPN
ejpam-6047	8	33	(	(	PUNCT
ejpam-6047	8	34	r.	r.	PROPN
ejpam-6047	8	35	al	al	PROPN
ejpam-6047	8	36	naimi	naimi	PROPN
ejpam-6047	8	37	)	)	PUNCT
ejpam-6047	8	38	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6047	9	1	1	1	NUM
ejpam-6047	9	2	copyright	copyright	NOUN
ejpam-6047	9	3	:	:	PUNCT
ejpam-6047	9	4	©	©	PROPN
ejpam-6047	9	5	2025	2025	NUM
ejpam-6047	9	6	the	the	DET
ejpam-6047	9	7	author(s	author(s	NOUN
ejpam-6047	9	8	)	)	PUNCT
ejpam-6047	9	9	.	.	PUNCT
ejpam-6047	10	1	(	(	PUNCT
ejpam-6047	10	2	cc	cc	NOUN
ejpam-6047	10	3	by	by	ADP
ejpam-6047	10	4	-	-	PUNCT
ejpam-6047	10	5	nc	nc	PROPN
ejpam-6047	10	6	4.0	4.0	NUM
ejpam-6047	10	7	)	)	PUNCT
ejpam-6047	10	8	m.u	m.u	PROPN
ejpam-6047	10	9	.	.	PROPN
ejpam-6047	10	10	rehman	rehman	PROPN
ejpam-6047	10	11	et	et	PROPN
ejpam-6047	10	12	al	al	PROPN
ejpam-6047	10	13	.	.	PUNCT
ejpam-6047	10	14	/	/	SYM
ejpam-6047	10	15	eur	eur	PROPN
ejpam-6047	10	16	.	.	PUNCT
ejpam-6047	11	1	j.	j.	PROPN
ejpam-6047	11	2	pure	pure	PROPN
ejpam-6047	11	3	appl	appl	PROPN
ejpam-6047	11	4	.	.	PROPN
ejpam-6047	11	5	math	math	PROPN
ejpam-6047	11	6	,	,	PUNCT
ejpam-6047	11	7	18	18	NUM
ejpam-6047	11	8	(	(	PUNCT
ejpam-6047	11	9	3	3	NUM
ejpam-6047	11	10	)	)	PUNCT
ejpam-6047	11	11	(	(	PUNCT
ejpam-6047	11	12	2025	2025	NUM
ejpam-6047	11	13	)	)	PUNCT
ejpam-6047	11	14	,	,	PUNCT
ejpam-6047	11	15	6047	6047	NUM
ejpam-6047	11	16	2	2	NUM
ejpam-6047	11	17	of	of	ADP
ejpam-6047	11	18	33	33	NUM
ejpam-6047	11	19	1	1	NUM
ejpam-6047	11	20	.	.	PUNCT
ejpam-6047	12	1	introduction	introduction	NOUN
ejpam-6047	12	2	the	the	DET
ejpam-6047	12	3	stability	stability	NOUN
ejpam-6047	12	4	theory	theory	NOUN
ejpam-6047	12	5	concerning	concern	VERB
ejpam-6047	12	6	positive	positive	ADJ
ejpam-6047	12	7	linear	linear	ADJ
ejpam-6047	12	8	time	time	NOUN
ejpam-6047	12	9	-	-	PUNCT
ejpam-6047	12	10	invariant	invariant	ADJ
ejpam-6047	12	11	(	(	PUNCT
ejpam-6047	12	12	lti	lti	PROPN
ejpam-6047	12	13	)	)	PUNCT
ejpam-6047	12	14	systems	system	NOUN
ejpam-6047	12	15	is	be	AUX
ejpam-6047	12	16	welldocumented	welldocumente	VERB
ejpam-6047	12	17	and	and	CCONJ
ejpam-6047	12	18	widely	widely	ADV
ejpam-6047	12	19	accessible	accessible	ADJ
ejpam-6047	12	20	in	in	ADP
ejpam-6047	12	21	the	the	DET
ejpam-6047	12	22	literature	literature	NOUN
ejpam-6047	12	23	.	.	PUNCT
ejpam-6047	13	1	however	however	ADV
ejpam-6047	13	2	,	,	PUNCT
ejpam-6047	13	3	when	when	SCONJ
ejpam-6047	13	4	extending	extend	VERB
ejpam-6047	13	5	this	this	DET
ejpam-6047	13	6	theory	theory	NOUN
ejpam-6047	13	7	to	to	ADP
ejpam-6047	13	8	nonlinear	nonlinear	ADJ
ejpam-6047	13	9	systems	system	NOUN
ejpam-6047	13	10	,	,	PUNCT
ejpam-6047	13	11	systems	system	NOUN
ejpam-6047	13	12	with	with	ADP
ejpam-6047	13	13	uncertainties	uncertainty	NOUN
ejpam-6047	13	14	,	,	PUNCT
ejpam-6047	13	15	or	or	CCONJ
ejpam-6047	13	16	positive	positive	ADJ
ejpam-6047	13	17	lti	lti	PROPN
ejpam-6047	13	18	systems	system	NOUN
ejpam-6047	13	19	,	,	PUNCT
ejpam-6047	13	20	the	the	DET
ejpam-6047	13	21	framework	framework	NOUN
ejpam-6047	13	22	remains	remain	VERB
ejpam-6047	13	23	less	less	ADV
ejpam-6047	13	24	developed	developed	ADJ
ejpam-6047	13	25	and	and	CCONJ
ejpam-6047	13	26	not	not	PART
ejpam-6047	13	27	well	well	ADV
ejpam-6047	13	28	established	establish	VERB
ejpam-6047	13	29	.	.	PUNCT
ejpam-6047	14	1	the	the	DET
ejpam-6047	14	2	stability	stability	NOUN
ejpam-6047	14	3	characteristics	characteristic	NOUN
ejpam-6047	14	4	of	of	ADP
ejpam-6047	14	5	positive	positive	ADJ
ejpam-6047	14	6	lti	lti	PROPN
ejpam-6047	14	7	systems	system	NOUN
ejpam-6047	14	8	have	have	AUX
ejpam-6047	14	9	been	be	AUX
ejpam-6047	14	10	generalized	generalize	VERB
ejpam-6047	14	11	to	to	PART
ejpam-6047	14	12	include	include	VERB
ejpam-6047	14	13	positive	positive	ADJ
ejpam-6047	14	14	descriptor	descriptor	NOUN
ejpam-6047	14	15	systems	system	NOUN
ejpam-6047	14	16	and	and	CCONJ
ejpam-6047	14	17	were	be	AUX
ejpam-6047	14	18	further	far	ADV
ejpam-6047	14	19	analyzed	analyze	VERB
ejpam-6047	14	20	in	in	ADP
ejpam-6047	14	21	[	[	X
ejpam-6047	14	22	1	1	NUM
ejpam-6047	14	23	]	]	PUNCT
ejpam-6047	14	24	.	.	PUNCT
ejpam-6047	15	1	additionally	additionally	ADV
ejpam-6047	15	2	,	,	PUNCT
ejpam-6047	15	3	in	in	ADP
ejpam-6047	15	4	[	[	PUNCT
ejpam-6047	15	5	2	2	NUM
ejpam-6047	15	6	]	]	PUNCT
ejpam-6047	15	7	,	,	PUNCT
ejpam-6047	15	8	stability	stability	NOUN
ejpam-6047	15	9	theory	theory	NOUN
ejpam-6047	15	10	for	for	ADP
ejpam-6047	15	11	positive	positive	ADJ
ejpam-6047	15	12	lti	lti	PROPN
ejpam-6047	15	13	systems	system	NOUN
ejpam-6047	15	14	was	be	AUX
ejpam-6047	15	15	expanded	expand	VERB
ejpam-6047	15	16	to	to	PART
ejpam-6047	15	17	switched	switch	VERB
ejpam-6047	15	18	positive	positive	ADJ
ejpam-6047	15	19	linear	linear	NOUN
ejpam-6047	15	20	systems	system	NOUN
ejpam-6047	15	21	.	.	PUNCT
ejpam-6047	16	1	moreover	moreover	ADV
ejpam-6047	16	2	,	,	PUNCT
ejpam-6047	16	3	the	the	DET
ejpam-6047	16	4	concept	concept	NOUN
ejpam-6047	16	5	of	of	ADP
ejpam-6047	16	6	d	d	NOUN
ejpam-6047	16	7	-	-	NOUN
ejpam-6047	16	8	stability	stability	NOUN
ejpam-6047	16	9	for	for	ADP
ejpam-6047	16	10	positive	positive	ADJ
ejpam-6047	16	11	switched	switch	VERB
ejpam-6047	16	12	linear	linear	NOUN
ejpam-6047	16	13	systems	system	NOUN
ejpam-6047	16	14	was	be	AUX
ejpam-6047	16	15	further	far	ADV
ejpam-6047	16	16	refined	refine	VERB
ejpam-6047	16	17	,	,	PUNCT
ejpam-6047	16	18	leading	lead	VERB
ejpam-6047	16	19	to	to	ADP
ejpam-6047	16	20	the	the	DET
ejpam-6047	16	21	derivation	derivation	NOUN
ejpam-6047	16	22	and	and	CCONJ
ejpam-6047	16	23	presentation	presentation	NOUN
ejpam-6047	16	24	of	of	ADP
ejpam-6047	16	25	new	new	ADJ
ejpam-6047	16	26	findings	finding	NOUN
ejpam-6047	16	27	in	in	ADP
ejpam-6047	16	28	[	[	X
ejpam-6047	16	29	2	2	NUM
ejpam-6047	16	30	]	]	PUNCT
ejpam-6047	16	31	.	.	PUNCT
ejpam-6047	17	1	the	the	DET
ejpam-6047	17	2	time	time	NOUN
ejpam-6047	17	3	-	-	PUNCT
ejpam-6047	17	4	invariant	invariant	ADJ
ejpam-6047	17	5	linear	linear	ADJ
ejpam-6047	17	6	system	system	NOUN
ejpam-6047	17	7	characterized	characterize	VERB
ejpam-6047	17	8	by	by	ADP
ejpam-6047	17	9	dx(t	dx(t	NOUN
ejpam-6047	17	10	)	)	PUNCT
ejpam-6047	17	11	dt	dt	NOUN
ejpam-6047	17	12	=	=	SYM
ejpam-6047	17	13	ax(t	ax(t	NUM
ejpam-6047	17	14	)	)	PUNCT
ejpam-6047	17	15	,	,	PUNCT
ejpam-6047	17	16	is	be	AUX
ejpam-6047	17	17	classified	classify	VERB
ejpam-6047	17	18	as	as	ADP
ejpam-6047	17	19	positive	positive	ADJ
ejpam-6047	17	20	if	if	SCONJ
ejpam-6047	17	21	and	and	CCONJ
ejpam-6047	17	22	only	only	ADV
ejpam-6047	17	23	if	if	SCONJ
ejpam-6047	17	24	a	a	DET
ejpam-6047	17	25	∈	∈	PROPN
ejpam-6047	17	26	rn	rn	PROPN
ejpam-6047	17	27	,	,	PUNCT
ejpam-6047	17	28	n	n	PRON
ejpam-6047	17	29	is	be	AUX
ejpam-6047	17	30	a	a	DET
ejpam-6047	17	31	metzler	metzler	NOUN
ejpam-6047	17	32	matrix	matrix	NOUN
ejpam-6047	17	33	,	,	PUNCT
ejpam-6047	17	34	meaning	mean	VERB
ejpam-6047	17	35	that	that	SCONJ
ejpam-6047	17	36	all	all	DET
ejpam-6047	17	37	its	its	PRON
ejpam-6047	17	38	off	off	ADJ
ejpam-6047	17	39	-	-	PUNCT
ejpam-6047	17	40	diagonal	diagonal	ADJ
ejpam-6047	17	41	elements	element	NOUN
ejpam-6047	17	42	are	be	AUX
ejpam-6047	17	43	non	non	ADJ
ejpam-6047	17	44	-	-	ADJ
ejpam-6047	17	45	negative	negative	ADJ
ejpam-6047	17	46	.	.	PUNCT
ejpam-6047	18	1	as	as	SCONJ
ejpam-6047	18	2	demonstrated	demonstrate	VERB
ejpam-6047	18	3	in	in	ADP
ejpam-6047	18	4	[	[	X
ejpam-6047	18	5	3	3	NUM
ejpam-6047	18	6	]	]	X
ejpam-6047	18	7	,	,	PUNCT
ejpam-6047	18	8	such	such	DET
ejpam-6047	18	9	a	a	DET
ejpam-6047	18	10	system	system	NOUN
ejpam-6047	18	11	attains	attain	VERB
ejpam-6047	18	12	global	global	ADJ
ejpam-6047	18	13	asymptotic	asymptotic	ADJ
ejpam-6047	18	14	stability	stability	NOUN
ejpam-6047	18	15	if	if	SCONJ
ejpam-6047	18	16	and	and	CCONJ
ejpam-6047	18	17	only	only	ADV
ejpam-6047	18	18	if	if	SCONJ
ejpam-6047	18	19	the	the	DET
ejpam-6047	18	20	system	system	NOUN
ejpam-6047	18	21	dx(t	dx(t	NOUN
ejpam-6047	18	22	)	)	PUNCT
ejpam-6047	18	23	dt	dt	X
ejpam-6047	18	24	=	=	SYM
ejpam-6047	18	25	dax(t	dax(t	PROPN
ejpam-6047	18	26	)	)	PUNCT
ejpam-6047	18	27	,	,	PUNCT
ejpam-6047	18	28	is	be	AUX
ejpam-6047	18	29	asymptotically	asymptotically	ADV
ejpam-6047	18	30	stable	stable	ADJ
ejpam-6047	18	31	,	,	PUNCT
ejpam-6047	18	32	where	where	SCONJ
ejpam-6047	18	33	d	d	NOUN
ejpam-6047	18	34	represents	represent	VERB
ejpam-6047	18	35	a	a	DET
ejpam-6047	18	36	positive	positive	ADJ
ejpam-6047	18	37	diagonal	diagonal	ADJ
ejpam-6047	18	38	matrix	matrix	NOUN
ejpam-6047	18	39	.	.	PUNCT
ejpam-6047	19	1	in	in	ADP
ejpam-6047	19	2	[	[	X
ejpam-6047	19	3	4	4	NUM
ejpam-6047	19	4	]	]	PUNCT
ejpam-6047	19	5	,	,	PUNCT
ejpam-6047	19	6	it	it	PRON
ejpam-6047	19	7	was	be	AUX
ejpam-6047	19	8	demonstrated	demonstrate	VERB
ejpam-6047	19	9	that	that	SCONJ
ejpam-6047	19	10	a	a	DET
ejpam-6047	19	11	delayed	delay	VERB
ejpam-6047	19	12	positive	positive	ADJ
ejpam-6047	19	13	linear	linear	NOUN
ejpam-6047	19	14	system	system	NOUN
ejpam-6047	19	15	of	of	ADP
ejpam-6047	19	16	the	the	DET
ejpam-6047	19	17	form	form	NOUN
ejpam-6047	19	18	dx(t	dx(t	NOUN
ejpam-6047	19	19	)	)	PUNCT
ejpam-6047	19	20	dt	dt	NOUN
ejpam-6047	19	21	=	=	SYM
ejpam-6047	19	22	ax(t	ax(t	NUM
ejpam-6047	19	23	)	)	PUNCT
ejpam-6047	20	1	+	+	NUM
ejpam-6047	20	2	bx(t−	bx(t−	CCONJ
ejpam-6047	20	3	τ	τ	PROPN
ejpam-6047	20	4	)	)	PUNCT
ejpam-6047	20	5	,	,	PUNCT
ejpam-6047	20	6	τ	τ	PROPN
ejpam-6047	20	7	≥	≥	NOUN
ejpam-6047	20	8	0	0	NUM
ejpam-6047	20	9	,	,	PUNCT
ejpam-6047	20	10	where	where	SCONJ
ejpam-6047	20	11	a	a	PRON
ejpam-6047	20	12	is	be	AUX
ejpam-6047	20	13	a	a	DET
ejpam-6047	20	14	metzler	metzler	NOUN
ejpam-6047	20	15	matrix	matrix	NOUN
ejpam-6047	20	16	and	and	CCONJ
ejpam-6047	20	17	b	b	NOUN
ejpam-6047	20	18	is	be	AUX
ejpam-6047	20	19	a	a	DET
ejpam-6047	20	20	non	non	ADJ
ejpam-6047	20	21	-	-	ADJ
ejpam-6047	20	22	negative	negative	ADJ
ejpam-6047	20	23	matrix	matrix	NOUN
ejpam-6047	20	24	,	,	PUNCT
ejpam-6047	20	25	exhibits	exhibit	VERB
ejpam-6047	20	26	global	global	ADJ
ejpam-6047	20	27	asymptotic	asymptotic	ADJ
ejpam-6047	20	28	stability	stability	NOUN
ejpam-6047	20	29	.	.	PUNCT
ejpam-6047	21	1	furthermore	furthermore	ADV
ejpam-6047	21	2	,	,	PUNCT
ejpam-6047	21	3	[	[	X
ejpam-6047	21	4	5	5	NUM
ejpam-6047	21	5	]	]	PUNCT
ejpam-6047	21	6	explored	explore	VERB
ejpam-6047	21	7	theoretical	theoretical	ADJ
ejpam-6047	21	8	developments	development	NOUN
ejpam-6047	21	9	in	in	ADP
ejpam-6047	21	10	cooperative	cooperative	ADJ
ejpam-6047	21	11	systems	system	NOUN
ejpam-6047	21	12	that	that	PRON
ejpam-6047	21	13	maintain	maintain	VERB
ejpam-6047	21	14	homogeneity	homogeneity	NOUN
ejpam-6047	21	15	of	of	ADP
ejpam-6047	21	16	arbitrary	arbitrary	ADJ
ejpam-6047	21	17	degree	degree	NOUN
ejpam-6047	21	18	under	under	ADP
ejpam-6047	21	19	certain	certain	ADJ
ejpam-6047	21	20	dilation	dilation	NOUN
ejpam-6047	21	21	mappings	mapping	NOUN
ejpam-6047	21	22	.	.	PUNCT
ejpam-6047	22	1	considering	consider	VERB
ejpam-6047	22	2	the	the	DET
ejpam-6047	22	3	linear	linear	ADJ
ejpam-6047	22	4	time	time	NOUN
ejpam-6047	22	5	-	-	PUNCT
ejpam-6047	22	6	invariant	invariant	ADJ
ejpam-6047	22	7	system	system	NOUN
ejpam-6047	22	8	:	:	PUNCT
ejpam-6047	22	9	dx(t	dx(t	X
ejpam-6047	22	10	)	)	PUNCT
ejpam-6047	22	11	dt	dt	AUX
ejpam-6047	22	12	=	=	SYM
ejpam-6047	22	13	ax(t	ax(t	NUM
ejpam-6047	22	14	)	)	PUNCT
ejpam-6047	22	15	,	,	PUNCT
ejpam-6047	22	16	where	where	SCONJ
ejpam-6047	22	17	a	a	PRON
ejpam-6047	22	18	is	be	AUX
ejpam-6047	22	19	an	an	DET
ejpam-6047	22	20	n	n	NUM
ejpam-6047	22	21	×	×	NOUN
ejpam-6047	22	22	n	n	CCONJ
ejpam-6047	22	23	real	real	ADJ
ejpam-6047	22	24	metzler	metzler	NOUN
ejpam-6047	22	25	matrix	matrix	NOUN
ejpam-6047	22	26	and	and	CCONJ
ejpam-6047	22	27	x(t	x(t	PROPN
ejpam-6047	22	28	)	)	PUNCT
ejpam-6047	22	29	∈	∈	PROPN
ejpam-6047	22	30	rn,1	rn,1	PROPN
ejpam-6047	22	31	,	,	PUNCT
ejpam-6047	22	32	the	the	DET
ejpam-6047	22	33	system	system	NOUN
ejpam-6047	22	34	is	be	AUX
ejpam-6047	22	35	deemed	deem	VERB
ejpam-6047	22	36	stable	stable	ADJ
ejpam-6047	22	37	if	if	SCONJ
ejpam-6047	22	38	the	the	DET
ejpam-6047	22	39	real	real	ADJ
ejpam-6047	22	40	parts	part	NOUN
ejpam-6047	22	41	of	of	ADP
ejpam-6047	22	42	all	all	DET
ejpam-6047	22	43	eigenvalues	eigenvalue	NOUN
ejpam-6047	22	44	of	of	ADP
ejpam-6047	22	45	a	a	PRON
ejpam-6047	22	46	are	be	AUX
ejpam-6047	22	47	strictly	strictly	ADV
ejpam-6047	22	48	negative	negative	ADJ
ejpam-6047	22	49	.	.	PUNCT
ejpam-6047	23	1	such	such	DET
ejpam-6047	23	2	a	a	DET
ejpam-6047	23	3	system	system	NOUN
ejpam-6047	23	4	satisfies	satisfy	VERB
ejpam-6047	23	5	the	the	DET
ejpam-6047	23	6	hurwitz	hurwitz	PROPN
ejpam-6047	23	7	condition	condition	NOUN
ejpam-6047	23	8	,	,	PUNCT
ejpam-6047	23	9	ensuring	ensure	VERB
ejpam-6047	23	10	that	that	SCONJ
ejpam-6047	23	11	all	all	PRON
ejpam-6047	23	12	eigenvalues	eigenvalue	NOUN
ejpam-6047	23	13	reside	reside	VERB
ejpam-6047	23	14	within	within	ADP
ejpam-6047	23	15	the	the	DET
ejpam-6047	23	16	open	open	ADJ
ejpam-6047	23	17	left	left	ADJ
ejpam-6047	23	18	half	half	ADJ
ejpam-6047	23	19	-	-	PUNCT
ejpam-6047	23	20	plane	plane	NOUN
ejpam-6047	23	21	of	of	ADP
ejpam-6047	23	22	the	the	DET
ejpam-6047	23	23	complex	complex	ADJ
ejpam-6047	23	24	domain	domain	NOUN
ejpam-6047	23	25	.	.	PUNCT
ejpam-6047	24	1	for	for	ADP
ejpam-6047	24	2	a	a	DET
ejpam-6047	24	3	system	system	NOUN
ejpam-6047	24	4	of	of	ADP
ejpam-6047	24	5	this	this	DET
ejpam-6047	24	6	type	type	NOUN
ejpam-6047	24	7	,	,	PUNCT
ejpam-6047	24	8	one	one	PRON
ejpam-6047	24	9	can	can	AUX
ejpam-6047	24	10	deduce	deduce	VERB
ejpam-6047	24	11	that	that	DET
ejpam-6047	24	12	stability	stability	NOUN
ejpam-6047	24	13	implies	imply	VERB
ejpam-6047	24	14	the	the	DET
ejpam-6047	24	15	existence	existence	NOUN
ejpam-6047	24	16	of	of	ADP
ejpam-6047	24	17	a	a	DET
ejpam-6047	24	18	positive	positive	ADJ
ejpam-6047	24	19	matrix	matrix	NOUN
ejpam-6047	24	20	p	p	NOUN
ejpam-6047	24	21	such	such	ADJ
ejpam-6047	24	22	that	that	PRON
ejpam-6047	24	23	:	:	PUNCT
ejpam-6047	25	1	atp	atp	PROPN
ejpam-6047	25	2	+	+	CCONJ
ejpam-6047	25	3	pa	pa	PROPN
ejpam-6047	25	4	<	<	X
ejpam-6047	25	5	0	0	NUM
ejpam-6047	25	6	.	.	PUNCT
ejpam-6047	26	1	additionally	additionally	ADV
ejpam-6047	26	2	,	,	PUNCT
ejpam-6047	26	3	the	the	DET
ejpam-6047	26	4	stability	stability	NOUN
ejpam-6047	26	5	condition	condition	NOUN
ejpam-6047	26	6	ensures	ensure	VERB
ejpam-6047	26	7	that	that	SCONJ
ejpam-6047	26	8	there	there	PRON
ejpam-6047	26	9	exists	exist	VERB
ejpam-6047	26	10	a	a	DET
ejpam-6047	26	11	positive	positive	ADJ
ejpam-6047	26	12	diagonal	diagonal	ADJ
ejpam-6047	26	13	matrix	matrix	NOUN
ejpam-6047	26	14	d.	d.	PROPN
ejpam-6047	26	15	m.u	m.u	PROPN
ejpam-6047	26	16	.	.	PROPN
ejpam-6047	27	1	rehman	rehman	PROPN
ejpam-6047	27	2	et	et	PROPN
ejpam-6047	27	3	al	al	PROPN
ejpam-6047	27	4	.	.	PUNCT
ejpam-6047	27	5	/	/	SYM
ejpam-6047	27	6	eur	eur	PROPN
ejpam-6047	27	7	.	.	PUNCT
ejpam-6047	28	1	j.	j.	PROPN
ejpam-6047	28	2	pure	pure	PROPN
ejpam-6047	28	3	appl	appl	PROPN
ejpam-6047	28	4	.	.	PROPN
ejpam-6047	28	5	math	math	PROPN
ejpam-6047	28	6	,	,	PUNCT
ejpam-6047	28	7	18	18	NUM
ejpam-6047	28	8	(	(	PUNCT
ejpam-6047	28	9	3	3	NUM
ejpam-6047	28	10	)	)	PUNCT
ejpam-6047	28	11	(	(	PUNCT
ejpam-6047	28	12	2025	2025	NUM
ejpam-6047	28	13	)	)	PUNCT
ejpam-6047	28	14	,	,	PUNCT
ejpam-6047	28	15	6047	6047	NUM
ejpam-6047	28	16	3	3	NUM
ejpam-6047	28	17	of	of	ADP
ejpam-6047	28	18	33	33	NUM
ejpam-6047	28	19	the	the	DET
ejpam-6047	28	20	notion	notion	NOUN
ejpam-6047	28	21	of	of	ADP
ejpam-6047	28	22	d	d	NOUN
ejpam-6047	28	23	-	-	NOUN
ejpam-6047	28	24	stability	stability	NOUN
ejpam-6047	28	25	for	for	ADP
ejpam-6047	28	26	real	real	ADV
ejpam-6047	28	27	-	-	PUNCT
ejpam-6047	28	28	valued	value	VERB
ejpam-6047	28	29	matrices	matrix	NOUN
ejpam-6047	28	30	was	be	AUX
ejpam-6047	28	31	given	give	VERB
ejpam-6047	28	32	by	by	ADP
ejpam-6047	28	33	arrow	arrow	NOUN
ejpam-6047	28	34	and	and	CCONJ
ejpam-6047	28	35	mcmanus	mcmanus	PROPN
ejpam-6047	29	1	[	[	X
ejpam-6047	29	2	6	6	NUM
ejpam-6047	29	3	]	]	PUNCT
ejpam-6047	29	4	in	in	ADP
ejpam-6047	29	5	their	their	PRON
ejpam-6047	29	6	classical	classical	ADJ
ejpam-6047	29	7	paper	paper	NOUN
ejpam-6047	29	8	.	.	PUNCT
ejpam-6047	30	1	it	it	PRON
ejpam-6047	30	2	was	be	AUX
ejpam-6047	30	3	then	then	ADV
ejpam-6047	30	4	introduced	introduce	VERB
ejpam-6047	30	5	by	by	ADP
ejpam-6047	30	6	enthoven	enthoven	ADV
ejpam-6047	30	7	and	and	CCONJ
ejpam-6047	30	8	arrow	arrow	NOUN
ejpam-6047	30	9	[	[	X
ejpam-6047	30	10	7	7	NUM
ejpam-6047	30	11	]	]	PUNCT
ejpam-6047	30	12	for	for	ADP
ejpam-6047	30	13	the	the	DET
ejpam-6047	30	14	analysis	analysis	NOUN
ejpam-6047	30	15	and	and	CCONJ
ejpam-6047	30	16	interpretations	interpretation	NOUN
ejpam-6047	30	17	of	of	ADP
ejpam-6047	30	18	stability	stability	NOUN
ejpam-6047	30	19	of	of	ADP
ejpam-6047	30	20	competitive	competitive	ADJ
ejpam-6047	30	21	markets	market	NOUN
ejpam-6047	30	22	.	.	PUNCT
ejpam-6047	31	1	the	the	DET
ejpam-6047	31	2	concept	concept	NOUN
ejpam-6047	31	3	of	of	ADP
ejpam-6047	31	4	d	d	NOUN
ejpam-6047	31	5	-	-	NOUN
ejpam-6047	31	6	stability	stability	NOUN
ejpam-6047	31	7	holds	hold	VERB
ejpam-6047	31	8	significant	significant	ADJ
ejpam-6047	31	9	importance	importance	NOUN
ejpam-6047	31	10	across	across	ADP
ejpam-6047	31	11	various	various	ADJ
ejpam-6047	31	12	fields	field	NOUN
ejpam-6047	31	13	,	,	PUNCT
ejpam-6047	31	14	for	for	ADP
ejpam-6047	31	15	instance	instance	NOUN
ejpam-6047	31	16	,	,	PUNCT
ejpam-6047	31	17	in	in	ADP
ejpam-6047	31	18	the	the	DET
ejpam-6047	31	19	study	study	NOUN
ejpam-6047	31	20	of	of	ADP
ejpam-6047	31	21	models	model	NOUN
ejpam-6047	31	22	in	in	ADP
ejpam-6047	31	23	economics	economic	NOUN
ejpam-6047	31	24	,	,	PUNCT
ejpam-6047	31	25	see	see	VERB
ejpam-6047	31	26	[	[	X
ejpam-6047	31	27	8–14	8–14	PROPN
ejpam-6047	31	28	]	]	X
ejpam-6047	31	29	.	.	PUNCT
ejpam-6047	32	1	an	an	DET
ejpam-6047	32	2	n	n	ADV
ejpam-6047	32	3	-	-	PUNCT
ejpam-6047	32	4	dimensional	dimensional	ADJ
ejpam-6047	32	5	real	real	ADJ
ejpam-6047	32	6	matrix	matrix	NOUN
ejpam-6047	32	7	a	a	PRON
ejpam-6047	32	8	is	be	AUX
ejpam-6047	32	9	considered	consider	VERB
ejpam-6047	32	10	d	d	ADJ
ejpam-6047	32	11	-	-	ADJ
ejpam-6047	32	12	stable	stable	ADJ
ejpam-6047	32	13	if	if	SCONJ
ejpam-6047	32	14	there	there	PRON
ejpam-6047	32	15	exists	exist	VERB
ejpam-6047	32	16	a	a	DET
ejpam-6047	32	17	positive	positive	ADJ
ejpam-6047	32	18	diagonal	diagonal	ADJ
ejpam-6047	32	19	matrix	matrix	NOUN
ejpam-6047	32	20	d	d	ADP
ejpam-6047	32	21	such	such	ADJ
ejpam-6047	32	22	that	that	SCONJ
ejpam-6047	32	23	either	either	CCONJ
ejpam-6047	32	24	da	da	NOUN
ejpam-6047	32	25	or	or	CCONJ
ejpam-6047	32	26	ad	ad	NOUN
ejpam-6047	32	27	remains	remain	VERB
ejpam-6047	32	28	positive	positive	ADJ
ejpam-6047	32	29	stable	stable	ADJ
ejpam-6047	32	30	.	.	PUNCT
ejpam-6047	33	1	characterizing	characterize	VERB
ejpam-6047	33	2	d	d	NOUN
ejpam-6047	33	3	-	-	NOUN
ejpam-6047	33	4	stability	stability	NOUN
ejpam-6047	33	5	is	be	AUX
ejpam-6047	33	6	highly	highly	ADV
ejpam-6047	33	7	challenging	challenging	ADJ
ejpam-6047	33	8	,	,	PUNCT
ejpam-6047	33	9	and	and	CCONJ
ejpam-6047	33	10	in	in	ADP
ejpam-6047	33	11	certain	certain	ADJ
ejpam-6047	33	12	cases	case	NOUN
ejpam-6047	33	13	,	,	PUNCT
ejpam-6047	33	14	it	it	PRON
ejpam-6047	33	15	leads	lead	VERB
ejpam-6047	33	16	to	to	ADP
ejpam-6047	33	17	computationally	computationally	ADV
ejpam-6047	33	18	intractable	intractable	ADJ
ejpam-6047	33	19	(	(	PUNCT
ejpam-6047	33	20	np	np	INTJ
ejpam-6047	33	21	-	-	PUNCT
ejpam-6047	33	22	hard	hard	ADJ
ejpam-6047	33	23	)	)	PUNCT
ejpam-6047	33	24	problems	problem	NOUN
ejpam-6047	33	25	;	;	PUNCT
ejpam-6047	33	26	see	see	VERB
ejpam-6047	33	27	[	[	X
ejpam-6047	33	28	15	15	NUM
ejpam-6047	33	29	,	,	PUNCT
ejpam-6047	33	30	16	16	NUM
ejpam-6047	33	31	]	]	PUNCT
ejpam-6047	33	32	.	.	PUNCT
ejpam-6047	34	1	the	the	DET
ejpam-6047	34	2	problems	problem	NOUN
ejpam-6047	34	3	concerning	concern	VERB
ejpam-6047	34	4	d	d	NOUN
ejpam-6047	34	5	-	-	NOUN
ejpam-6047	34	6	stability	stability	NOUN
ejpam-6047	34	7	for	for	ADP
ejpam-6047	34	8	the	the	DET
ejpam-6047	34	9	linear	linear	PROPN
ejpam-6047	34	10	systems	system	NOUN
ejpam-6047	34	11	have	have	AUX
ejpam-6047	34	12	received	receive	VERB
ejpam-6047	34	13	a	a	DET
ejpam-6047	34	14	great	great	ADJ
ejpam-6047	34	15	attention	attention	NOUN
ejpam-6047	34	16	over	over	ADP
ejpam-6047	34	17	the	the	DET
ejpam-6047	34	18	last	last	ADJ
ejpam-6047	34	19	few	few	ADJ
ejpam-6047	34	20	decades	decade	NOUN
ejpam-6047	34	21	.	.	PUNCT
ejpam-6047	35	1	numerous	numerous	ADJ
ejpam-6047	35	2	significant	significant	ADJ
ejpam-6047	35	3	findings	finding	NOUN
ejpam-6047	35	4	and	and	CCONJ
ejpam-6047	35	5	mathematical	mathematical	ADJ
ejpam-6047	35	6	approaches	approach	NOUN
ejpam-6047	35	7	were	be	AUX
ejpam-6047	35	8	established	establish	VERB
ejpam-6047	35	9	in	in	ADP
ejpam-6047	35	10	the	the	DET
ejpam-6047	35	11	literature	literature	NOUN
ejpam-6047	35	12	;	;	PUNCT
ejpam-6047	35	13	refer	refer	VERB
ejpam-6047	35	14	to	to	ADP
ejpam-6047	35	15	[	[	X
ejpam-6047	35	16	17–25	17–25	NUM
ejpam-6047	35	17	]	]	X
ejpam-6047	35	18	and	and	CCONJ
ejpam-6047	35	19	the	the	DET
ejpam-6047	35	20	associated	associated	ADJ
ejpam-6047	35	21	references	reference	NOUN
ejpam-6047	35	22	.	.	PUNCT
ejpam-6047	36	1	the	the	DET
ejpam-6047	36	2	selection	selection	NOUN
ejpam-6047	36	3	of	of	ADP
ejpam-6047	36	4	an	an	DET
ejpam-6047	36	5	appropriate	appropriate	ADJ
ejpam-6047	36	6	region(s	region(s	NOUN
ejpam-6047	36	7	)	)	PUNCT
ejpam-6047	36	8	in	in	ADP
ejpam-6047	36	9	the	the	DET
ejpam-6047	36	10	complex	complex	ADJ
ejpam-6047	36	11	plane	plane	NOUN
ejpam-6047	36	12	,	,	PUNCT
ejpam-6047	36	13	for	for	ADP
ejpam-6047	36	14	instance	instance	NOUN
ejpam-6047	36	15	,	,	PUNCT
ejpam-6047	36	16	d(α	d(α	PROPN
ejpam-6047	36	17	,	,	PUNCT
ejpam-6047	36	18	r	r	NOUN
ejpam-6047	36	19	)	)	PUNCT
ejpam-6047	36	20	is	be	AUX
ejpam-6047	36	21	a	a	DET
ejpam-6047	36	22	disk	disk	NOUN
ejpam-6047	36	23	,	,	PUNCT
ejpam-6047	36	24	centered	center	VERB
ejpam-6047	36	25	at	at	ADP
ejpam-6047	36	26	α	α	PROPN
ejpam-6047	36	27	+	+	CCONJ
ejpam-6047	36	28	i0	i0	PROPN
ejpam-6047	36	29	,	,	PUNCT
ejpam-6047	36	30	having	have	VERB
ejpam-6047	36	31	radius	radius	NOUN
ejpam-6047	36	32	r	r	NOUN
ejpam-6047	36	33	(	(	PUNCT
ejpam-6047	36	34	see	see	VERB
ejpam-6047	36	35	[	[	X
ejpam-6047	36	36	26	26	NUM
ejpam-6047	36	37	]	]	PUNCT
ejpam-6047	36	38	)	)	PUNCT
ejpam-6047	36	39	plays	play	VERB
ejpam-6047	36	40	a	a	DET
ejpam-6047	36	41	vital	vital	ADJ
ejpam-6047	36	42	role	role	NOUN
ejpam-6047	36	43	for	for	ADP
ejpam-6047	36	44	the	the	DET
ejpam-6047	36	45	characterization	characterization	NOUN
ejpam-6047	36	46	of	of	ADP
ejpam-6047	36	47	d	d	NOUN
ejpam-6047	36	48	-	-	NOUN
ejpam-6047	36	49	stability	stability	NOUN
ejpam-6047	36	50	.	.	PUNCT
ejpam-6047	37	1	the	the	DET
ejpam-6047	37	2	analysis	analysis	NOUN
ejpam-6047	37	3	on	on	ADP
ejpam-6047	37	4	d	d	NOUN
ejpam-6047	37	5	-	-	NOUN
ejpam-6047	37	6	stability	stability	NOUN
ejpam-6047	37	7	for	for	ADP
ejpam-6047	37	8	singular	singular	ADJ
ejpam-6047	37	9	systems	system	NOUN
ejpam-6047	37	10	is	be	AUX
ejpam-6047	37	11	indeed	indeed	ADV
ejpam-6047	37	12	very	very	ADV
ejpam-6047	37	13	complicated	complicated	ADJ
ejpam-6047	37	14	and	and	CCONJ
ejpam-6047	37	15	a	a	DET
ejpam-6047	37	16	challenging	challenging	ADJ
ejpam-6047	37	17	problem	problem	NOUN
ejpam-6047	37	18	as	as	ADP
ejpam-6047	37	19	compared	compare	VERB
ejpam-6047	37	20	to	to	ADP
ejpam-6047	37	21	normal	normal	ADJ
ejpam-6047	37	22	state	state	NOUN
ejpam-6047	37	23	space	space	NOUN
ejpam-6047	37	24	systems	system	NOUN
ejpam-6047	37	25	.	.	PUNCT
ejpam-6047	38	1	the	the	DET
ejpam-6047	38	2	establishment	establishment	NOUN
ejpam-6047	38	3	of	of	ADP
ejpam-6047	38	4	numerous	numerous	ADJ
ejpam-6047	38	5	significant	significant	ADJ
ejpam-6047	38	6	results	result	NOUN
ejpam-6047	38	7	for	for	ADP
ejpam-6047	38	8	d	d	NOUN
ejpam-6047	38	9	-	-	NOUN
ejpam-6047	38	10	stability	stability	NOUN
ejpam-6047	38	11	,	,	PUNCT
ejpam-6047	38	12	regularity	regularity	NOUN
ejpam-6047	38	13	,	,	PUNCT
ejpam-6047	38	14	and	and	CCONJ
ejpam-6047	38	15	causality	causality	NOUN
ejpam-6047	38	16	is	be	AUX
ejpam-6047	38	17	documented	document	VERB
ejpam-6047	38	18	in	in	ADP
ejpam-6047	38	19	[	[	X
ejpam-6047	38	20	27–30	27–30	NUM
ejpam-6047	38	21	]	]	PUNCT
ejpam-6047	38	22	and	and	CCONJ
ejpam-6047	38	23	the	the	DET
ejpam-6047	38	24	cited	cite	VERB
ejpam-6047	38	25	sources	source	NOUN
ejpam-6047	38	26	.	.	PUNCT
ejpam-6047	39	1	for	for	ADP
ejpam-6047	39	2	a	a	DET
ejpam-6047	39	3	given	give	VERB
ejpam-6047	39	4	stable	stable	ADJ
ejpam-6047	39	5	matrix	matrix	NOUN
ejpam-6047	39	6	a	a	DET
ejpam-6047	39	7	∈	∈	PROPN
ejpam-6047	39	8	rn	rn	PROPN
ejpam-6047	39	9	,	,	PUNCT
ejpam-6047	39	10	n	n	CCONJ
ejpam-6047	39	11	,	,	PUNCT
ejpam-6047	39	12	it	it	PRON
ejpam-6047	39	13	is	be	AUX
ejpam-6047	39	14	well	well	ADV
ejpam-6047	39	15	established	establish	VERB
ejpam-6047	39	16	that	that	SCONJ
ejpam-6047	39	17	the	the	DET
ejpam-6047	39	18	matrix	matrix	NOUN
ejpam-6047	39	19	a+m	a+m	NUM
ejpam-6047	39	20	remains	remain	VERB
ejpam-6047	39	21	stable	stable	ADJ
ejpam-6047	39	22	,	,	PUNCT
ejpam-6047	39	23	provided	provide	VERB
ejpam-6047	39	24	that	that	DET
ejpam-6047	39	25	∥m∥	∥m∥	VERB
ejpam-6047	39	26	<	<	X
ejpam-6047	39	27	γ	γ	NOUN
ejpam-6047	39	28	for	for	ADP
ejpam-6047	39	29	some	some	DET
ejpam-6047	39	30	γ	γ	X
ejpam-6047	39	31	>	>	X
ejpam-6047	39	32	0	0	PROPN
ejpam-6047	39	33	.	.	PUNCT
ejpam-6047	40	1	see	see	VERB
ejpam-6047	40	2	[	[	X
ejpam-6047	40	3	31	31	NUM
ejpam-6047	40	4	,	,	PUNCT
ejpam-6047	40	5	32	32	NUM
ejpam-6047	40	6	]	]	PUNCT
ejpam-6047	40	7	.	.	PUNCT
ejpam-6047	41	1	this	this	PRON
ejpam-6047	41	2	further	further	ADJ
ejpam-6047	41	3	ensures	ensure	VERB
ejpam-6047	41	4	that	that	SCONJ
ejpam-6047	41	5	the	the	DET
ejpam-6047	41	6	stability	stability	NOUN
ejpam-6047	41	7	is	be	AUX
ejpam-6047	41	8	a	a	DET
ejpam-6047	41	9	property	property	NOUN
ejpam-6047	41	10	that	that	PRON
ejpam-6047	41	11	is	be	AUX
ejpam-6047	41	12	very	very	ADV
ejpam-6047	41	13	much	much	ADV
ejpam-6047	41	14	robust	robust	ADJ
ejpam-6047	41	15	to	to	ADP
ejpam-6047	41	16	some	some	DET
ejpam-6047	41	17	small	small	ADJ
ejpam-6047	41	18	admissible	admissible	ADJ
ejpam-6047	41	19	perturbations	perturbation	NOUN
ejpam-6047	41	20	appearing	appear	VERB
ejpam-6047	41	21	across	across	ADP
ejpam-6047	41	22	the	the	DET
ejpam-6047	41	23	system	system	NOUN
ejpam-6047	41	24	.	.	PUNCT
ejpam-6047	42	1	for	for	ADP
ejpam-6047	42	2	given	give	VERB
ejpam-6047	42	3	d	d	PROPN
ejpam-6047	42	4	,	,	PUNCT
ejpam-6047	42	5	a	a	DET
ejpam-6047	42	6	positive	positive	ADJ
ejpam-6047	42	7	diagonal	diagonal	ADJ
ejpam-6047	42	8	matrix	matrix	NOUN
ejpam-6047	42	9	,	,	PUNCT
ejpam-6047	42	10	assume	assume	VERB
ejpam-6047	42	11	that	that	SCONJ
ejpam-6047	42	12	a	a	DET
ejpam-6047	42	13	∈	∈	PROPN
ejpam-6047	42	14	rn	rn	PROPN
ejpam-6047	42	15	,	,	PUNCT
ejpam-6047	42	16	n	n	CCONJ
ejpam-6047	42	17	,	,	PUNCT
ejpam-6047	42	18	is	be	AUX
ejpam-6047	42	19	d	d	ADJ
ejpam-6047	42	20	-	-	ADJ
ejpam-6047	42	21	stable	stable	ADJ
ejpam-6047	42	22	matrix	matrix	NOUN
ejpam-6047	42	23	,	,	PUNCT
ejpam-6047	42	24	then	then	ADV
ejpam-6047	42	25	one	one	PRON
ejpam-6047	42	26	can	can	AUX
ejpam-6047	42	27	easily	easily	ADV
ejpam-6047	42	28	observe	observe	VERB
ejpam-6047	42	29	that	that	DET
ejpam-6047	42	30	matrix	matrix	NOUN
ejpam-6047	42	31	products	product	NOUN
ejpam-6047	42	32	da	da	NOUN
ejpam-6047	42	33	,	,	PUNCT
ejpam-6047	42	34	and	and	CCONJ
ejpam-6047	42	35	d(a+m	d(a+m	PRON
ejpam-6047	42	36	)	)	PUNCT
ejpam-6047	42	37	are	be	AUX
ejpam-6047	42	38	also	also	ADV
ejpam-6047	42	39	stable	stable	ADJ
ejpam-6047	42	40	.	.	PUNCT
ejpam-6047	43	1	the	the	DET
ejpam-6047	43	2	important	important	ADJ
ejpam-6047	43	3	question	question	NOUN
ejpam-6047	43	4	that	that	PRON
ejpam-6047	43	5	arises	arise	VERB
ejpam-6047	43	6	at	at	ADP
ejpam-6047	43	7	this	this	DET
ejpam-6047	43	8	stage	stage	NOUN
ejpam-6047	43	9	is	be	AUX
ejpam-6047	43	10	then	then	ADV
ejpam-6047	43	11	to	to	PART
ejpam-6047	43	12	ask	ask	VERB
ejpam-6047	43	13	if	if	SCONJ
ejpam-6047	43	14	it	it	PRON
ejpam-6047	43	15	is	be	AUX
ejpam-6047	43	16	possible	possible	ADJ
ejpam-6047	43	17	to	to	PART
ejpam-6047	43	18	search	search	VERB
ejpam-6047	43	19	for	for	ADP
ejpam-6047	43	20	a	a	DET
ejpam-6047	43	21	suitable	suitable	ADJ
ejpam-6047	43	22	γ	γ	X
ejpam-6047	43	23	>	>	X
ejpam-6047	43	24	0	0	NUM
ejpam-6047	43	25	,	,	PUNCT
ejpam-6047	43	26	so	so	SCONJ
ejpam-6047	43	27	that	that	SCONJ
ejpam-6047	43	28	a	a	DET
ejpam-6047	43	29	+	+	NOUN
ejpam-6047	43	30	m	m	VERB
ejpam-6047	43	31	is	be	AUX
ejpam-6047	43	32	a	a	DET
ejpam-6047	43	33	d	d	ADJ
ejpam-6047	43	34	-	-	ADJ
ejpam-6047	43	35	stable	stable	ADJ
ejpam-6047	43	36	matrix	matrix	NOUN
ejpam-6047	43	37	for	for	ADP
ejpam-6047	43	38	|m	|m	NOUN
ejpam-6047	43	39	|	|	ADV
ejpam-6047	43	40	<	<	X
ejpam-6047	43	41	γ	γ	X
ejpam-6047	43	42	.	.	PROPN
ejpam-6047	44	1	but	but	CCONJ
ejpam-6047	44	2	,	,	PUNCT
ejpam-6047	44	3	unfortunately	unfortunately	ADV
ejpam-6047	44	4	,	,	PUNCT
ejpam-6047	44	5	in	in	ADP
ejpam-6047	44	6	general	general	ADJ
ejpam-6047	44	7	,	,	PUNCT
ejpam-6047	44	8	the	the	DET
ejpam-6047	44	9	response	response	NOUN
ejpam-6047	44	10	is	be	AUX
ejpam-6047	44	11	a	a	DET
ejpam-6047	44	12	no	no	NOUN
ejpam-6047	44	13	.	.	PUNCT
ejpam-6047	45	1	however	however	ADV
ejpam-6047	45	2	,	,	PUNCT
ejpam-6047	45	3	in	in	ADP
ejpam-6047	45	4	certain	certain	ADJ
ejpam-6047	45	5	special	special	ADJ
ejpam-6047	45	6	cases	case	NOUN
ejpam-6047	45	7	,	,	PUNCT
ejpam-6047	45	8	it	it	PRON
ejpam-6047	45	9	is	be	AUX
ejpam-6047	45	10	indeed	indeed	ADV
ejpam-6047	45	11	feasible	feasible	ADJ
ejpam-6047	45	12	to	to	PART
ejpam-6047	45	13	identify	identify	VERB
ejpam-6047	45	14	a	a	DET
ejpam-6047	45	15	class	class	NOUN
ejpam-6047	45	16	of	of	ADP
ejpam-6047	45	17	d	d	ADJ
ejpam-6047	45	18	-	-	ADJ
ejpam-6047	45	19	stable	stable	ADJ
ejpam-6047	45	20	matrices	matrix	NOUN
ejpam-6047	45	21	where	where	SCONJ
ejpam-6047	45	22	small	small	ADJ
ejpam-6047	45	23	,	,	PUNCT
ejpam-6047	45	24	permissible	permissible	ADJ
ejpam-6047	45	25	perturbations	perturbation	NOUN
ejpam-6047	45	26	result	result	VERB
ejpam-6047	45	27	exclusively	exclusively	ADV
ejpam-6047	45	28	in	in	ADP
ejpam-6047	45	29	d	d	ADJ
ejpam-6047	45	30	-	-	ADJ
ejpam-6047	45	31	stable	stable	ADJ
ejpam-6047	45	32	matrices	matrix	NOUN
ejpam-6047	45	33	.	.	PUNCT
ejpam-6047	46	1	the	the	DET
ejpam-6047	46	2	given	give	VERB
ejpam-6047	46	3	a	a	DET
ejpam-6047	46	4	∈	∈	PROPN
ejpam-6047	46	5	rn	rn	PROPN
ejpam-6047	46	6	,	,	PUNCT
ejpam-6047	46	7	n	n	PRON
ejpam-6047	46	8	is	be	AUX
ejpam-6047	46	9	strongly	strongly	ADV
ejpam-6047	46	10	d	d	ADJ
ejpam-6047	46	11	-	-	ADJ
ejpam-6047	46	12	stable	stable	ADJ
ejpam-6047	46	13	if	if	SCONJ
ejpam-6047	46	14	there	there	PRON
ejpam-6047	46	15	exist	exist	VERB
ejpam-6047	46	16	a	a	DET
ejpam-6047	46	17	γ	γ	X
ejpam-6047	46	18	>	>	X
ejpam-6047	46	19	0	0	NUM
ejpam-6047	46	20	such	such	ADJ
ejpam-6047	46	21	that	that	SCONJ
ejpam-6047	46	22	a	a	DET
ejpam-6047	46	23	+	+	NOUN
ejpam-6047	46	24	m	m	VERB
ejpam-6047	46	25	is	be	AUX
ejpam-6047	46	26	a	a	DET
ejpam-6047	46	27	d	d	NOUN
ejpam-6047	46	28	-	-	NOUN
ejpam-6047	46	29	stable	stable	ADJ
ejpam-6047	46	30	for	for	ADP
ejpam-6047	46	31	each	each	DET
ejpam-6047	46	32	m	m	PROPN
ejpam-6047	46	33	∈	∈	PROPN
ejpam-6047	46	34	rn	rn	PROPN
ejpam-6047	46	35	,	,	PUNCT
ejpam-6047	46	36	n	n	CCONJ
ejpam-6047	46	37	,	,	PUNCT
ejpam-6047	46	38	with	with	ADP
ejpam-6047	46	39	|m	|m	NOUN
ejpam-6047	46	40	|	|	ADV
ejpam-6047	46	41	<	<	X
ejpam-6047	46	42	γ	γ	X
ejpam-6047	46	43	.	.	PROPN
ejpam-6047	47	1	furthermore	furthermore	ADV
ejpam-6047	47	2	,	,	PUNCT
ejpam-6047	47	3	one	one	PRON
ejpam-6047	47	4	can	can	AUX
ejpam-6047	47	5	easily	easily	ADV
ejpam-6047	47	6	notice	notice	VERB
ejpam-6047	47	7	that	that	SCONJ
ejpam-6047	47	8	each	each	DET
ejpam-6047	47	9	strongly	strongly	ADV
ejpam-6047	47	10	d	d	ADJ
ejpam-6047	47	11	-	-	ADJ
ejpam-6047	47	12	stable	stable	ADJ
ejpam-6047	47	13	matrix	matrix	NOUN
ejpam-6047	47	14	must	must	AUX
ejpam-6047	47	15	be	be	AUX
ejpam-6047	47	16	a	a	DET
ejpam-6047	47	17	d	d	ADJ
ejpam-6047	47	18	-	-	ADJ
ejpam-6047	47	19	stable	stable	ADJ
ejpam-6047	47	20	matrix	matrix	NOUN
ejpam-6047	47	21	.	.	PUNCT
ejpam-6047	48	1	the	the	DET
ejpam-6047	48	2	mathematical	mathematical	ADJ
ejpam-6047	48	3	problem	problem	NOUN
ejpam-6047	48	4	of	of	ADP
ejpam-6047	48	5	optimization	optimization	NOUN
ejpam-6047	48	6	of	of	ADP
ejpam-6047	48	7	spectral	spectral	ADJ
ejpam-6047	48	8	abscissa	abscissa	NOUN
ejpam-6047	48	9	over	over	ADP
ejpam-6047	48	10	the	the	DET
ejpam-6047	48	11	families	family	NOUN
ejpam-6047	48	12	of	of	ADP
ejpam-6047	48	13	metzler	metzler	NOUN
ejpam-6047	48	14	matrices	matrix	NOUN
ejpam-6047	48	15	is	be	AUX
ejpam-6047	48	16	helpful	helpful	ADJ
ejpam-6047	48	17	to	to	PART
ejpam-6047	48	18	study	study	VERB
ejpam-6047	48	19	and	and	CCONJ
ejpam-6047	48	20	analyze	analyze	VERB
ejpam-6047	48	21	the	the	DET
ejpam-6047	48	22	stabilization	stabilization	NOUN
ejpam-6047	48	23	of	of	ADP
ejpam-6047	48	24	the	the	DET
ejpam-6047	48	25	metzler	metzler	NOUN
ejpam-6047	48	26	matrices	matrix	NOUN
ejpam-6047	48	27	.	.	PUNCT
ejpam-6047	49	1	the	the	DET
ejpam-6047	49	2	objective	objective	ADJ
ejpam-6047	49	3	function	function	NOUN
ejpam-6047	49	4	is	be	AUX
ejpam-6047	49	5	neither	neither	CCONJ
ejpam-6047	49	6	convex	convex	ADJ
ejpam-6047	49	7	not	not	PART
ejpam-6047	49	8	concave	concave	VERB
ejpam-6047	49	9	,	,	PUNCT
ejpam-6047	49	10	not	not	PART
ejpam-6047	49	11	lipschitz	lipschitz	VERB
ejpam-6047	49	12	and	and	CCONJ
ejpam-6047	49	13	this	this	PRON
ejpam-6047	49	14	cause	cause	VERB
ejpam-6047	49	15	the	the	DET
ejpam-6047	49	16	problem	problem	NOUN
ejpam-6047	49	17	to	to	PART
ejpam-6047	49	18	be	be	AUX
ejpam-6047	49	19	very	very	ADV
ejpam-6047	49	20	hard	hard	ADJ
ejpam-6047	49	21	.	.	PUNCT
ejpam-6047	50	1	further	far	ADV
ejpam-6047	50	2	,	,	PUNCT
ejpam-6047	50	3	from	from	ADP
ejpam-6047	50	4	this	this	DET
ejpam-6047	50	5	one	one	NOUN
ejpam-6047	50	6	might	might	AUX
ejpam-6047	50	7	obtained	obtain	VERB
ejpam-6047	50	8	many	many	ADJ
ejpam-6047	50	9	local	local	ADJ
ejpam-6047	50	10	extrema	extrema	NOUN
ejpam-6047	50	11	which	which	PRON
ejpam-6047	50	12	in	in	ADP
ejpam-6047	50	13	turn	turn	NOUN
ejpam-6047	50	14	are	be	AUX
ejpam-6047	50	15	very	very	ADV
ejpam-6047	50	16	hard	hard	ADJ
ejpam-6047	50	17	to	to	PART
ejpam-6047	50	18	localize	localize	VERB
ejpam-6047	50	19	,	,	PUNCT
ejpam-6047	50	20	see	see	VERB
ejpam-6047	50	21	[	[	X
ejpam-6047	50	22	33	33	NUM
ejpam-6047	50	23	]	]	PUNCT
ejpam-6047	50	24	.	.	PUNCT
ejpam-6047	51	1	the	the	DET
ejpam-6047	51	2	necessary	necessary	ADJ
ejpam-6047	51	3	and	and	CCONJ
ejpam-6047	51	4	sufficient	sufficient	ADJ
ejpam-6047	51	5	condition	condition	NOUN
ejpam-6047	51	6	for	for	ADP
ejpam-6047	51	7	a	a	DET
ejpam-6047	51	8	given	give	VERB
ejpam-6047	51	9	matrix	matrix	NOUN
ejpam-6047	51	10	to	to	PART
ejpam-6047	51	11	be	be	AUX
ejpam-6047	51	12	d	d	ADJ
ejpam-6047	51	13	-	-	NOUN
ejpam-6047	51	14	stable	stable	ADJ
ejpam-6047	51	15	by	by	ADP
ejpam-6047	51	16	using	use	VERB
ejpam-6047	51	17	kalman	kalman	NOUN
ejpam-6047	51	18	-	-	PUNCT
ejpam-6047	51	19	yacubovich	yacubovich	PROPN
ejpam-6047	51	20	-	-	PUNCT
ejpam-6047	51	21	popov	popov	NOUN
ejpam-6047	51	22	lemma	lemma	PROPN
ejpam-6047	51	23	were	be	AUX
ejpam-6047	51	24	given	give	VERB
ejpam-6047	51	25	in	in	ADP
ejpam-6047	51	26	[	[	X
ejpam-6047	51	27	34	34	NUM
ejpam-6047	51	28	]	]	PUNCT
ejpam-6047	51	29	.	.	PUNCT
ejpam-6047	52	1	it	it	PRON
ejpam-6047	52	2	was	be	AUX
ejpam-6047	52	3	shown	show	VERB
ejpam-6047	52	4	that	that	SCONJ
ejpam-6047	52	5	obtained	obtain	VERB
ejpam-6047	52	6	condition	condition	NOUN
ejpam-6047	52	7	is	be	AUX
ejpam-6047	52	8	mathematically	mathematically	ADV
ejpam-6047	52	9	equivalent	equivalent	ADJ
ejpam-6047	52	10	to	to	PART
ejpam-6047	52	11	requirement	requirement	VERB
ejpam-6047	52	12	that	that	SCONJ
ejpam-6047	52	13	pair	pair	NOUN
ejpam-6047	52	14	of	of	ADP
ejpam-6047	52	15	linear	linear	ADJ
ejpam-6047	52	16	-	-	PUNCT
ejpam-6047	52	17	time	time	NOUN
ejpam-6047	52	18	-	-	PUNCT
ejpam-6047	52	19	invariant	invariant	ADJ
ejpam-6047	52	20	systems	system	NOUN
ejpam-6047	52	21	have	have	VERB
ejpam-6047	52	22	common	common	ADJ
ejpam-6047	52	23	lyapunov	lyapunov	ADJ
ejpam-6047	52	24	function	function	NOUN
ejpam-6047	52	25	in	in	ADP
ejpam-6047	52	26	the	the	DET
ejpam-6047	52	27	lower	low	ADJ
ejpam-6047	52	28	dimensions	dimension	NOUN
ejpam-6047	52	29	.	.	PUNCT
ejpam-6047	53	1	furthermore	furthermore	ADV
ejpam-6047	53	2	,	,	PUNCT
ejpam-6047	53	3	the	the	DET
ejpam-6047	53	4	simple	simple	ADJ
ejpam-6047	53	5	conditions	condition	NOUN
ejpam-6047	53	6	for	for	ADP
ejpam-6047	53	7	hurwitz	hurwitz	PROPN
ejpam-6047	53	8	stability	stability	NOUN
ejpam-6047	53	9	of	of	ADP
ejpam-6047	53	10	a	a	DET
ejpam-6047	53	11	given	give	VERB
ejpam-6047	53	12	metzler	metzler	NOUN
ejpam-6047	53	13	matrix	matrix	NOUN
ejpam-6047	53	14	were	be	AUX
ejpam-6047	53	15	derived	derive	VERB
ejpam-6047	53	16	.	.	PUNCT
ejpam-6047	54	1	in	in	ADP
ejpam-6047	54	2	recent	recent	ADJ
ejpam-6047	54	3	years	year	NOUN
ejpam-6047	54	4	,	,	PUNCT
ejpam-6047	54	5	the	the	DET
ejpam-6047	54	6	study	study	NOUN
ejpam-6047	54	7	of	of	ADP
ejpam-6047	54	8	fractional	fractional	ADJ
ejpam-6047	54	9	differential	differential	ADJ
ejpam-6047	54	10	equations	equation	NOUN
ejpam-6047	54	11	(	(	PUNCT
ejpam-6047	54	12	fdes	fde	NOUN
ejpam-6047	54	13	)	)	PUNCT
ejpam-6047	54	14	has	have	AUX
ejpam-6047	54	15	gained	gain	VERB
ejpam-6047	54	16	signifm.u	signifm.u	NOUN
ejpam-6047	54	17	.	.	PUNCT
ejpam-6047	55	1	rehman	rehman	NOUN
ejpam-6047	55	2	et	et	PROPN
ejpam-6047	55	3	al	al	PROPN
ejpam-6047	55	4	.	.	PUNCT
ejpam-6047	55	5	/	/	SYM
ejpam-6047	55	6	eur	eur	PROPN
ejpam-6047	55	7	.	.	PUNCT
ejpam-6047	56	1	j.	j.	PROPN
ejpam-6047	56	2	pure	pure	PROPN
ejpam-6047	56	3	appl	appl	PROPN
ejpam-6047	56	4	.	.	PROPN
ejpam-6047	56	5	math	math	PROPN
ejpam-6047	56	6	,	,	PUNCT
ejpam-6047	56	7	18	18	NUM
ejpam-6047	56	8	(	(	PUNCT
ejpam-6047	56	9	3	3	NUM
ejpam-6047	56	10	)	)	PUNCT
ejpam-6047	56	11	(	(	PUNCT
ejpam-6047	56	12	2025	2025	NUM
ejpam-6047	56	13	)	)	PUNCT
ejpam-6047	56	14	,	,	PUNCT
ejpam-6047	56	15	6047	6047	NUM
ejpam-6047	56	16	4	4	NUM
ejpam-6047	56	17	of	of	ADP
ejpam-6047	56	18	33	33	NUM
ejpam-6047	56	19	icant	icant	ADJ
ejpam-6047	56	20	attention	attention	NOUN
ejpam-6047	56	21	due	due	ADP
ejpam-6047	56	22	to	to	ADP
ejpam-6047	56	23	their	their	PRON
ejpam-6047	56	24	ability	ability	NOUN
ejpam-6047	56	25	to	to	PART
ejpam-6047	56	26	model	model	VERB
ejpam-6047	56	27	memory	memory	NOUN
ejpam-6047	56	28	and	and	CCONJ
ejpam-6047	56	29	hereditary	hereditary	ADJ
ejpam-6047	56	30	properties	property	NOUN
ejpam-6047	56	31	in	in	ADP
ejpam-6047	56	32	various	various	ADJ
ejpam-6047	56	33	physical	physical	ADJ
ejpam-6047	56	34	and	and	CCONJ
ejpam-6047	56	35	engineering	engineering	NOUN
ejpam-6047	56	36	systems	system	NOUN
ejpam-6047	56	37	.	.	PUNCT
ejpam-6047	57	1	analytical	analytical	ADJ
ejpam-6047	57	2	methods	method	NOUN
ejpam-6047	57	3	such	such	ADJ
ejpam-6047	57	4	as	as	ADP
ejpam-6047	57	5	the	the	DET
ejpam-6047	57	6	laplace	laplace	NOUN
ejpam-6047	57	7	transform	transform	NOUN
ejpam-6047	57	8	method	method	NOUN
ejpam-6047	57	9	,	,	PUNCT
ejpam-6047	57	10	adomian	adomian	NOUN
ejpam-6047	57	11	decomposition	decomposition	NOUN
ejpam-6047	57	12	method	method	NOUN
ejpam-6047	57	13	(	(	PUNCT
ejpam-6047	57	14	adm	adm	PROPN
ejpam-6047	57	15	)	)	PUNCT
ejpam-6047	57	16	,	,	PUNCT
ejpam-6047	57	17	and	and	CCONJ
ejpam-6047	57	18	the	the	DET
ejpam-6047	57	19	homotopy	homotopy	NOUN
ejpam-6047	57	20	analysis	analysis	NOUN
ejpam-6047	57	21	method	method	NOUN
ejpam-6047	57	22	(	(	PUNCT
ejpam-6047	57	23	ham	ham	NOUN
ejpam-6047	57	24	)	)	PUNCT
ejpam-6047	57	25	have	have	AUX
ejpam-6047	57	26	been	be	AUX
ejpam-6047	57	27	widely	widely	ADV
ejpam-6047	57	28	applied	apply	VERB
ejpam-6047	57	29	to	to	PART
ejpam-6047	57	30	obtain	obtain	VERB
ejpam-6047	57	31	exact	exact	ADJ
ejpam-6047	57	32	or	or	CCONJ
ejpam-6047	57	33	approximate	approximate	ADJ
ejpam-6047	57	34	solutions	solution	NOUN
ejpam-6047	57	35	to	to	ADP
ejpam-6047	57	36	fdes	fde	NOUN
ejpam-6047	57	37	.	.	PUNCT
ejpam-6047	58	1	these	these	DET
ejpam-6047	58	2	approaches	approach	NOUN
ejpam-6047	58	3	are	be	AUX
ejpam-6047	58	4	especially	especially	ADV
ejpam-6047	58	5	useful	useful	ADJ
ejpam-6047	58	6	for	for	ADP
ejpam-6047	58	7	linear	linear	ADJ
ejpam-6047	58	8	or	or	CCONJ
ejpam-6047	58	9	weakly	weakly	ADJ
ejpam-6047	58	10	nonlinear	nonlinear	ADJ
ejpam-6047	58	11	problems	problem	NOUN
ejpam-6047	58	12	,	,	PUNCT
ejpam-6047	58	13	offering	offer	VERB
ejpam-6047	58	14	insight	insight	NOUN
ejpam-6047	58	15	into	into	ADP
ejpam-6047	58	16	the	the	DET
ejpam-6047	58	17	qualitative	qualitative	ADJ
ejpam-6047	58	18	behavior	behavior	NOUN
ejpam-6047	58	19	of	of	ADP
ejpam-6047	58	20	solutions	solution	NOUN
ejpam-6047	58	21	.	.	PUNCT
ejpam-6047	59	1	on	on	ADP
ejpam-6047	59	2	the	the	DET
ejpam-6047	59	3	numerical	numerical	ADJ
ejpam-6047	59	4	side	side	NOUN
ejpam-6047	59	5	,	,	PUNCT
ejpam-6047	59	6	methods	method	NOUN
ejpam-6047	59	7	like	like	ADP
ejpam-6047	59	8	the	the	DET
ejpam-6047	59	9	finite	finite	ADJ
ejpam-6047	59	10	difference	difference	NOUN
ejpam-6047	59	11	method	method	NOUN
ejpam-6047	59	12	(	(	PUNCT
ejpam-6047	59	13	fdm	fdm	NOUN
ejpam-6047	59	14	)	)	PUNCT
ejpam-6047	59	15	,	,	PUNCT
ejpam-6047	59	16	finite	finite	PROPN
ejpam-6047	59	17	element	element	NOUN
ejpam-6047	59	18	method	method	NOUN
ejpam-6047	59	19	(	(	PUNCT
ejpam-6047	59	20	fem	fem	NOUN
ejpam-6047	59	21	)	)	PUNCT
ejpam-6047	59	22	,	,	PUNCT
ejpam-6047	59	23	and	and	CCONJ
ejpam-6047	59	24	spectral	spectral	ADJ
ejpam-6047	59	25	methods	method	NOUN
ejpam-6047	59	26	have	have	AUX
ejpam-6047	59	27	proven	prove	VERB
ejpam-6047	59	28	effective	effective	ADJ
ejpam-6047	59	29	in	in	ADP
ejpam-6047	59	30	handling	handle	VERB
ejpam-6047	59	31	more	more	ADV
ejpam-6047	59	32	complex	complex	ADJ
ejpam-6047	59	33	or	or	CCONJ
ejpam-6047	59	34	strongly	strongly	ADV
ejpam-6047	59	35	nonlinear	nonlinear	ADJ
ejpam-6047	59	36	problems	problem	NOUN
ejpam-6047	59	37	,	,	PUNCT
ejpam-6047	59	38	particularly	particularly	ADV
ejpam-6047	59	39	when	when	SCONJ
ejpam-6047	59	40	closed	close	VERB
ejpam-6047	59	41	-	-	PUNCT
ejpam-6047	59	42	form	form	NOUN
ejpam-6047	59	43	solutions	solution	NOUN
ejpam-6047	59	44	are	be	AUX
ejpam-6047	59	45	not	not	PART
ejpam-6047	59	46	attainable	attainable	ADJ
ejpam-6047	59	47	.	.	PUNCT
ejpam-6047	60	1	more	more	ADV
ejpam-6047	60	2	recent	recent	ADJ
ejpam-6047	60	3	advancements	advancement	NOUN
ejpam-6047	60	4	include	include	VERB
ejpam-6047	60	5	the	the	DET
ejpam-6047	60	6	development	development	NOUN
ejpam-6047	60	7	of	of	ADP
ejpam-6047	60	8	grünwald	grünwald	ADJ
ejpam-6047	60	9	–	–	PUNCT
ejpam-6047	60	10	letnikov	letnikov	NOUN
ejpam-6047	60	11	and	and	CCONJ
ejpam-6047	60	12	caputo	caputo	PROPN
ejpam-6047	60	13	-	-	PUNCT
ejpam-6047	60	14	based	base	VERB
ejpam-6047	60	15	numerical	numerical	ADJ
ejpam-6047	60	16	schemes	scheme	NOUN
ejpam-6047	60	17	,	,	PUNCT
ejpam-6047	60	18	which	which	PRON
ejpam-6047	60	19	are	be	AUX
ejpam-6047	60	20	particularly	particularly	ADV
ejpam-6047	60	21	suited	suit	VERB
ejpam-6047	60	22	for	for	ADP
ejpam-6047	60	23	time	time	NOUN
ejpam-6047	60	24	-	-	PUNCT
ejpam-6047	60	25	fractional	fractional	ADJ
ejpam-6047	60	26	models	model	NOUN
ejpam-6047	60	27	,	,	PUNCT
ejpam-6047	60	28	as	as	ADV
ejpam-6047	60	29	well	well	ADV
ejpam-6047	60	30	as	as	ADP
ejpam-6047	60	31	predictor	predictor	NOUN
ejpam-6047	60	32	–	–	PUNCT
ejpam-6047	60	33	corrector	corrector	NOUN
ejpam-6047	60	34	algorithms	algorithm	NOUN
ejpam-6047	60	35	and	and	CCONJ
ejpam-6047	60	36	adaptive	adaptive	ADJ
ejpam-6047	60	37	mesh	mesh	NOUN
ejpam-6047	60	38	techniques	technique	NOUN
ejpam-6047	60	39	that	that	PRON
ejpam-6047	60	40	improve	improve	VERB
ejpam-6047	60	41	accuracy	accuracy	NOUN
ejpam-6047	60	42	and	and	CCONJ
ejpam-6047	60	43	efficiency	efficiency	NOUN
ejpam-6047	60	44	.	.	PUNCT
ejpam-6047	61	1	for	for	ADP
ejpam-6047	61	2	a	a	DET
ejpam-6047	61	3	comprehensive	comprehensive	ADJ
ejpam-6047	61	4	overview	overview	NOUN
ejpam-6047	61	5	,	,	PUNCT
ejpam-6047	61	6	the	the	DET
ejpam-6047	61	7	works	work	NOUN
ejpam-6047	61	8	of	of	ADP
ejpam-6047	61	9	[	[	X
ejpam-6047	61	10	35–40	35–40	NUM
ejpam-6047	61	11	]	]	PUNCT
ejpam-6047	61	12	provide	provide	VERB
ejpam-6047	61	13	foundational	foundational	ADJ
ejpam-6047	61	14	insights	insight	NOUN
ejpam-6047	61	15	into	into	ADP
ejpam-6047	61	16	both	both	CCONJ
ejpam-6047	61	17	the	the	DET
ejpam-6047	61	18	theoretical	theoretical	ADJ
ejpam-6047	61	19	and	and	CCONJ
ejpam-6047	61	20	practical	practical	ADJ
ejpam-6047	61	21	aspects	aspect	NOUN
ejpam-6047	61	22	of	of	ADP
ejpam-6047	61	23	these	these	DET
ejpam-6047	61	24	methods	method	NOUN
ejpam-6047	61	25	.	.	PUNCT
ejpam-6047	62	1	the	the	DET
ejpam-6047	62	2	spectra	spectra	NOUN
ejpam-6047	62	3	and	and	CCONJ
ejpam-6047	62	4	pseudo	pseudo	NOUN
ejpam-6047	62	5	-	-	NOUN
ejpam-6047	62	6	spectra	spectra	NOUN
ejpam-6047	62	7	of	of	ADP
ejpam-6047	62	8	structured	structured	ADJ
ejpam-6047	62	9	matrices	matrix	NOUN
ejpam-6047	62	10	to	to	ADP
ejpam-6047	62	11	different	different	ADJ
ejpam-6047	62	12	linear	linear	NOUN
ejpam-6047	62	13	and	and	CCONJ
ejpam-6047	62	14	nonlinear	nonlinear	ADJ
ejpam-6047	62	15	mathematical	mathematical	ADJ
ejpam-6047	62	16	problems	problem	NOUN
ejpam-6047	62	17	helps	help	VERB
ejpam-6047	62	18	to	to	PART
ejpam-6047	62	19	analyze	analyze	VERB
ejpam-6047	62	20	their	their	PRON
ejpam-6047	62	21	behavior	behavior	NOUN
ejpam-6047	62	22	.	.	PUNCT
ejpam-6047	63	1	the	the	DET
ejpam-6047	63	2	spectrum	spectrum	NOUN
ejpam-6047	63	3	and	and	CCONJ
ejpam-6047	63	4	pseudospectrum	pseudospectrum	NOUN
ejpam-6047	63	5	of	of	ADP
ejpam-6047	63	6	d	d	ADJ
ejpam-6047	63	7	-	-	ADJ
ejpam-6047	63	8	stable	stable	ADJ
ejpam-6047	63	9	matrices	matrix	NOUN
ejpam-6047	63	10	for	for	ADP
ejpam-6047	63	11	an	an	DET
ejpam-6047	63	12	economic	economic	ADJ
ejpam-6047	63	13	model	model	NOUN
ejpam-6047	63	14	was	be	AUX
ejpam-6047	63	15	the	the	DET
ejpam-6047	63	16	subject	subject	NOUN
ejpam-6047	63	17	of	of	ADP
ejpam-6047	63	18	some	some	DET
ejpam-6047	63	19	recent	recent	ADJ
ejpam-6047	63	20	novel	novel	ADJ
ejpam-6047	63	21	mathematical	mathematical	ADJ
ejpam-6047	63	22	studies	study	NOUN
ejpam-6047	63	23	,	,	PUNCT
ejpam-6047	63	24	see	see	VERB
ejpam-6047	63	25	[	[	X
ejpam-6047	63	26	41	41	NUM
ejpam-6047	63	27	]	]	PUNCT
ejpam-6047	63	28	.	.	PUNCT
ejpam-6047	64	1	in	in	ADP
ejpam-6047	64	2	[	[	X
ejpam-6047	64	3	42	42	NUM
ejpam-6047	64	4	]	]	PUNCT
ejpam-6047	64	5	a	a	DET
ejpam-6047	64	6	characterization	characterization	NOUN
ejpam-6047	64	7	of	of	ADP
ejpam-6047	64	8	d	d	ADJ
ejpam-6047	64	9	-	-	ADJ
ejpam-6047	64	10	stable	stable	ADJ
ejpam-6047	64	11	matrices	matrix	NOUN
ejpam-6047	64	12	from	from	ADP
ejpam-6047	64	13	transportation	transportation	NOUN
ejpam-6047	64	14	problems	problem	NOUN
ejpam-6047	64	15	were	be	AUX
ejpam-6047	64	16	analyzed	analyze	VERB
ejpam-6047	64	17	.	.	PUNCT
ejpam-6047	65	1	a	a	DET
ejpam-6047	65	2	in	in	ADP
ejpam-6047	65	3	-	-	PUNCT
ejpam-6047	65	4	depth	depth	NOUN
ejpam-6047	65	5	mathematical	mathematical	ADJ
ejpam-6047	65	6	analysis	analysis	NOUN
ejpam-6047	65	7	on	on	ADP
ejpam-6047	65	8	stability	stability	NOUN
ejpam-6047	65	9	,	,	PUNCT
ejpam-6047	65	10	dstability	dstability	NOUN
ejpam-6047	65	11	,	,	PUNCT
ejpam-6047	65	12	and	and	CCONJ
ejpam-6047	65	13	pseudo	pseudo	NOUN
ejpam-6047	65	14	-	-	NOUN
ejpam-6047	65	15	spectrum	spectrum	NOUN
ejpam-6047	65	16	of	of	ADP
ejpam-6047	65	17	structured	structured	ADJ
ejpam-6047	65	18	matrices	matrix	NOUN
ejpam-6047	65	19	arising	arise	VERB
ejpam-6047	65	20	from	from	ADP
ejpam-6047	65	21	economic	economic	ADJ
ejpam-6047	65	22	models	model	NOUN
ejpam-6047	65	23	was	be	AUX
ejpam-6047	65	24	studied	study	VERB
ejpam-6047	65	25	in	in	ADP
ejpam-6047	65	26	[	[	X
ejpam-6047	65	27	43	43	NUM
ejpam-6047	65	28	]	]	PUNCT
ejpam-6047	65	29	.	.	PUNCT
ejpam-6047	66	1	the	the	DET
ejpam-6047	66	2	most	most	ADV
ejpam-6047	66	3	recent	recent	ADJ
ejpam-6047	66	4	mathematical	mathematical	ADJ
ejpam-6047	66	5	findings	finding	NOUN
ejpam-6047	66	6	on	on	ADP
ejpam-6047	66	7	interaction	interaction	NOUN
ejpam-6047	66	8	between	between	ADP
ejpam-6047	66	9	µ-values	µ-value	NOUN
ejpam-6047	66	10	and	and	CCONJ
ejpam-6047	66	11	schur	schur	ADJ
ejpam-6047	66	12	stability	stability	NOUN
ejpam-6047	66	13	were	be	AUX
ejpam-6047	66	14	studied	study	VERB
ejpam-6047	66	15	and	and	CCONJ
ejpam-6047	66	16	analyzed	analyze	VERB
ejpam-6047	66	17	in	in	ADP
ejpam-6047	66	18	[	[	X
ejpam-6047	66	19	44	44	NUM
ejpam-6047	66	20	]	]	PUNCT
ejpam-6047	66	21	.	.	PUNCT
ejpam-6047	67	1	our	our	PRON
ejpam-6047	67	2	main	main	ADJ
ejpam-6047	67	3	objective	objective	NOUN
ejpam-6047	67	4	in	in	ADP
ejpam-6047	67	5	this	this	DET
ejpam-6047	67	6	article	article	NOUN
ejpam-6047	67	7	is	be	AUX
ejpam-6047	67	8	to	to	PART
ejpam-6047	67	9	extend	extend	VERB
ejpam-6047	67	10	the	the	DET
ejpam-6047	67	11	results	result	NOUN
ejpam-6047	67	12	on	on	ADP
ejpam-6047	67	13	stability	stability	NOUN
ejpam-6047	67	14	,	,	PUNCT
ejpam-6047	67	15	d	d	NOUN
ejpam-6047	67	16	-	-	NOUN
ejpam-6047	67	17	stability	stability	NOUN
ejpam-6047	67	18	,	,	PUNCT
ejpam-6047	67	19	and	and	CCONJ
ejpam-6047	67	20	strong	strong	ADJ
ejpam-6047	67	21	d	d	NOUN
ejpam-6047	67	22	-	-	PUNCT
ejpam-6047	67	23	stability	stability	NOUN
ejpam-6047	67	24	theory	theory	NOUN
ejpam-6047	67	25	.	.	PUNCT
ejpam-6047	68	1	mainly	mainly	ADV
ejpam-6047	68	2	,	,	PUNCT
ejpam-6047	68	3	we	we	PRON
ejpam-6047	68	4	target	target	VERB
ejpam-6047	68	5	problems	problem	NOUN
ejpam-6047	68	6	of	of	ADP
ejpam-6047	68	7	linear	linear	ADJ
ejpam-6047	68	8	time	time	NOUN
ejpam-6047	68	9	-	-	PUNCT
ejpam-6047	68	10	invariant	invariant	ADJ
ejpam-6047	68	11	systems	system	NOUN
ejpam-6047	68	12	which	which	PRON
ejpam-6047	68	13	are	be	AUX
ejpam-6047	68	14	positive	positive	ADJ
ejpam-6047	68	15	and	and	CCONJ
ejpam-6047	68	16	have	have	AUX
ejpam-6047	68	17	following	follow	VERB
ejpam-6047	68	18	mathematical	mathematical	ADJ
ejpam-6047	68	19	formulations	formulation	NOUN
ejpam-6047	68	20	:	:	PUNCT
ejpam-6047	68	21	problem	problem	NOUN
ejpam-6047	68	22	-	-	PUNCT
ejpam-6047	68	23	i	i	NOUN
ejpam-6047	68	24	:	:	PUNCT
ejpam-6047	68	25	to	to	PART
ejpam-6047	68	26	extend	extend	VERB
ejpam-6047	68	27	and	and	CCONJ
ejpam-6047	68	28	construct	construct	VERB
ejpam-6047	68	29	some	some	DET
ejpam-6047	68	30	new	new	ADJ
ejpam-6047	68	31	insights	insight	NOUN
ejpam-6047	68	32	on	on	ADP
ejpam-6047	68	33	stability	stability	NOUN
ejpam-6047	68	34	,	,	PUNCT
ejpam-6047	68	35	d	d	NOUN
ejpam-6047	68	36	-	-	PUNCT
ejpam-6047	68	37	stability	stability	NOUN
ejpam-6047	68	38	and	and	CCONJ
ejpam-6047	68	39	strong	strong	ADJ
ejpam-6047	68	40	d	d	NOUN
ejpam-6047	68	41	-	-	PUNCT
ejpam-6047	68	42	stability	stability	NOUN
ejpam-6047	68	43	analysis	analysis	NOUN
ejpam-6047	68	44	of	of	ADP
ejpam-6047	68	45	lti	lti	PROPN
ejpam-6047	68	46	system	system	PROPN
ejpam-6047	68	47	dx(t	dx(t	NOUN
ejpam-6047	68	48	)	)	PUNCT
ejpam-6047	68	49	dt	dt	NOUN
ejpam-6047	68	50	=	=	SYM
ejpam-6047	68	51	ax(t	ax(t	NUM
ejpam-6047	68	52	)	)	PUNCT
ejpam-6047	68	53	;	;	PUNCT
ejpam-6047	68	54	x(t	x(t	PROPN
ejpam-6047	68	55	)	)	PUNCT
ejpam-6047	68	56	∈	∈	PROPN
ejpam-6047	68	57	rn,1	rn,1	PROPN
ejpam-6047	68	58	,	,	PUNCT
ejpam-6047	68	59	a	a	DET
ejpam-6047	68	60	∈	∈	PROPN
ejpam-6047	68	61	rn	rn	PROPN
ejpam-6047	68	62	,	,	PUNCT
ejpam-6047	68	63	n	n	CCONJ
ejpam-6047	68	64	,	,	PUNCT
ejpam-6047	68	65	where	where	SCONJ
ejpam-6047	68	66	a	a	PRON
ejpam-6047	68	67	is	be	AUX
ejpam-6047	68	68	metzler	metzler	NOUN
ejpam-6047	68	69	and	and	CCONJ
ejpam-6047	68	70	hurwitz	hurwitz	PROPN
ejpam-6047	68	71	.	.	PROPN
ejpam-6047	68	72	problem	problem	PROPN
ejpam-6047	68	73	-	-	PUNCT
ejpam-6047	68	74	ii	ii	NOUN
ejpam-6047	68	75	:	:	PUNCT
ejpam-6047	68	76	to	to	PART
ejpam-6047	68	77	extend	extend	VERB
ejpam-6047	68	78	and	and	CCONJ
ejpam-6047	68	79	construct	construct	VERB
ejpam-6047	68	80	some	some	DET
ejpam-6047	68	81	new	new	ADJ
ejpam-6047	68	82	findings	finding	NOUN
ejpam-6047	68	83	on	on	ADP
ejpam-6047	68	84	stability	stability	NOUN
ejpam-6047	68	85	,	,	PUNCT
ejpam-6047	68	86	d	d	NOUN
ejpam-6047	68	87	-	-	PUNCT
ejpam-6047	68	88	stability	stability	NOUN
ejpam-6047	68	89	and	and	CCONJ
ejpam-6047	68	90	strong	strong	ADJ
ejpam-6047	68	91	d	d	NOUN
ejpam-6047	68	92	-	-	PUNCT
ejpam-6047	68	93	stability	stability	NOUN
ejpam-6047	68	94	analysis	analysis	NOUN
ejpam-6047	68	95	of	of	ADP
ejpam-6047	68	96	lti	lti	PROPN
ejpam-6047	68	97	system	system	PROPN
ejpam-6047	68	98	dx(t	dx(t	NOUN
ejpam-6047	68	99	)	)	PUNCT
ejpam-6047	68	100	dt	dt	NOUN
ejpam-6047	68	101	=	=	SYM
ejpam-6047	68	102	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	68	103	)	)	PUNCT
ejpam-6047	68	104	;	;	PUNCT
ejpam-6047	68	105	x(t	x(t	PROPN
ejpam-6047	68	106	)	)	PUNCT
ejpam-6047	68	107	∈	∈	PROPN
ejpam-6047	68	108	rn,1	rn,1	PROPN
ejpam-6047	68	109	,	,	PUNCT
ejpam-6047	68	110	a(t	a(t	NOUN
ejpam-6047	68	111	)	)	PUNCT
ejpam-6047	68	112	∈	∈	PROPN
ejpam-6047	68	113	{	{	PUNCT
ejpam-6047	68	114	a1	a1	NOUN
ejpam-6047	68	115	,	,	PUNCT
ejpam-6047	68	116	a2	a2	PROPN
ejpam-6047	68	117	}	}	PUNCT
ejpam-6047	68	118	,	,	PUNCT
ejpam-6047	68	119	with	with	ADP
ejpam-6047	68	120	a1	a1	NOUN
ejpam-6047	68	121	,	,	PUNCT
ejpam-6047	68	122	a2	a2	NOUN
ejpam-6047	68	123	being	be	AUX
ejpam-6047	68	124	asymptotically	asymptotically	ADV
ejpam-6047	68	125	stable	stable	ADJ
ejpam-6047	68	126	matrices	matrix	NOUN
ejpam-6047	68	127	.	.	PUNCT
ejpam-6047	69	1	problem	problem	NOUN
ejpam-6047	69	2	-	-	PUNCT
ejpam-6047	69	3	iii	iii	NOUN
ejpam-6047	69	4	:	:	PUNCT
ejpam-6047	69	5	to	to	PART
ejpam-6047	69	6	extend	extend	VERB
ejpam-6047	69	7	and	and	CCONJ
ejpam-6047	69	8	construct	construct	VERB
ejpam-6047	69	9	some	some	DET
ejpam-6047	69	10	new	new	ADJ
ejpam-6047	69	11	findings	finding	NOUN
ejpam-6047	69	12	on	on	ADP
ejpam-6047	69	13	stability	stability	NOUN
ejpam-6047	69	14	,	,	PUNCT
ejpam-6047	69	15	d	d	NOUN
ejpam-6047	69	16	-	-	PUNCT
ejpam-6047	69	17	stability	stability	NOUN
ejpam-6047	69	18	and	and	CCONJ
ejpam-6047	69	19	strong	strong	ADJ
ejpam-6047	69	20	d	d	NOUN
ejpam-6047	69	21	-	-	PUNCT
ejpam-6047	69	22	stability	stability	NOUN
ejpam-6047	69	23	analysis	analysis	NOUN
ejpam-6047	69	24	of	of	ADP
ejpam-6047	69	25	lti	lti	PROPN
ejpam-6047	69	26	system	system	PROPN
ejpam-6047	69	27	dx(t	dx(t	NOUN
ejpam-6047	69	28	)	)	PUNCT
ejpam-6047	69	29	dt	dt	NOUN
ejpam-6047	69	30	=	=	SYM
ejpam-6047	69	31	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	69	32	)	)	PUNCT
ejpam-6047	69	33	;	;	PUNCT
ejpam-6047	70	1	x(t	x(t	PROPN
ejpam-6047	70	2	)	)	PUNCT
ejpam-6047	70	3	∈	∈	PROPN
ejpam-6047	70	4	rn,1	rn,1	PROPN
ejpam-6047	70	5	,	,	PUNCT
ejpam-6047	70	6	a(t	a(t	NOUN
ejpam-6047	70	7	)	)	PUNCT
ejpam-6047	70	8	∈	∈	PROPN
ejpam-6047	70	9	{	{	PUNCT
ejpam-6047	70	10	d1a1	d1a1	NOUN
ejpam-6047	70	11	,	,	PUNCT
ejpam-6047	70	12	d2a2	d2a2	NOUN
ejpam-6047	70	13	}	}	PUNCT
ejpam-6047	70	14	,	,	PUNCT
ejpam-6047	70	15	with	with	ADP
ejpam-6047	70	16	a1	a1	NOUN
ejpam-6047	70	17	,	,	PUNCT
ejpam-6047	70	18	a2	a2	NOUN
ejpam-6047	70	19	being	be	AUX
ejpam-6047	70	20	irreducible	irreducible	ADJ
ejpam-6047	70	21	matrices	matrix	NOUN
ejpam-6047	70	22	,	,	PUNCT
ejpam-6047	70	23	and	and	CCONJ
ejpam-6047	70	24	d1	d1	PROPN
ejpam-6047	70	25	,	,	PUNCT
ejpam-6047	70	26	d2	d2	PROPN
ejpam-6047	70	27	>	>	X
ejpam-6047	70	28	0	0	PROPN
ejpam-6047	70	29	.	.	PUNCT
ejpam-6047	71	1	m.u	m.u	PROPN
ejpam-6047	71	2	.	.	PROPN
ejpam-6047	71	3	rehman	rehman	PROPN
ejpam-6047	71	4	et	et	PROPN
ejpam-6047	71	5	al	al	PROPN
ejpam-6047	71	6	.	.	PUNCT
ejpam-6047	71	7	/	/	SYM
ejpam-6047	71	8	eur	eur	PROPN
ejpam-6047	71	9	.	.	PUNCT
ejpam-6047	72	1	j.	j.	PROPN
ejpam-6047	72	2	pure	pure	PROPN
ejpam-6047	72	3	appl	appl	PROPN
ejpam-6047	72	4	.	.	PROPN
ejpam-6047	72	5	math	math	PROPN
ejpam-6047	72	6	,	,	PUNCT
ejpam-6047	72	7	18	18	NUM
ejpam-6047	72	8	(	(	PUNCT
ejpam-6047	72	9	3	3	NUM
ejpam-6047	72	10	)	)	PUNCT
ejpam-6047	72	11	(	(	PUNCT
ejpam-6047	72	12	2025	2025	NUM
ejpam-6047	72	13	)	)	PUNCT
ejpam-6047	72	14	,	,	PUNCT
ejpam-6047	72	15	6047	6047	NUM
ejpam-6047	72	16	5	5	NUM
ejpam-6047	72	17	of	of	ADP
ejpam-6047	72	18	33	33	NUM
ejpam-6047	72	19	overview	overview	NOUN
ejpam-6047	72	20	of	of	ADP
ejpam-6047	72	21	article	article	NOUN
ejpam-6047	72	22	:	:	PUNCT
ejpam-6047	72	23	section	section	NOUN
ejpam-6047	72	24	2	2	NUM
ejpam-6047	72	25	is	be	AUX
ejpam-6047	72	26	about	about	ADP
ejpam-6047	72	27	notations	notation	NOUN
ejpam-6047	72	28	and	and	CCONJ
ejpam-6047	72	29	the	the	DET
ejpam-6047	72	30	preliminary	preliminary	ADJ
ejpam-6047	72	31	findings	finding	NOUN
ejpam-6047	72	32	on	on	ADP
ejpam-6047	72	33	stability	stability	NOUN
ejpam-6047	72	34	,	,	PUNCT
ejpam-6047	72	35	d	d	NOUN
ejpam-6047	72	36	-	-	NOUN
ejpam-6047	72	37	stability	stability	NOUN
ejpam-6047	72	38	,	,	PUNCT
ejpam-6047	72	39	and	and	CCONJ
ejpam-6047	72	40	strong	strong	ADJ
ejpam-6047	72	41	d	d	NOUN
ejpam-6047	72	42	-	-	NOUN
ejpam-6047	72	43	stability	stability	NOUN
ejpam-6047	72	44	.	.	PUNCT
ejpam-6047	73	1	in	in	ADP
ejpam-6047	73	2	section	section	NOUN
ejpam-6047	73	3	3	3	NUM
ejpam-6047	73	4	,	,	PUNCT
ejpam-6047	73	5	we	we	PRON
ejpam-6047	73	6	recall	recall	VERB
ejpam-6047	73	7	some	some	DET
ejpam-6047	73	8	basic	basic	ADJ
ejpam-6047	73	9	and	and	CCONJ
ejpam-6047	73	10	fundamental	fundamental	ADJ
ejpam-6047	73	11	outcomes	outcome	NOUN
ejpam-6047	73	12	on	on	ADP
ejpam-6047	73	13	metzler	metzler	NOUN
ejpam-6047	73	14	matrices	matrix	NOUN
ejpam-6047	73	15	and	and	CCONJ
ejpam-6047	73	16	their	their	PRON
ejpam-6047	73	17	spectrum	spectrum	NOUN
ejpam-6047	73	18	.	.	PUNCT
ejpam-6047	74	1	in	in	ADP
ejpam-6047	74	2	section	section	NOUN
ejpam-6047	74	3	4	4	NUM
ejpam-6047	74	4	,	,	PUNCT
ejpam-6047	74	5	we	we	PRON
ejpam-6047	74	6	present	present	VERB
ejpam-6047	74	7	some	some	DET
ejpam-6047	74	8	new	new	ADJ
ejpam-6047	74	9	results	result	NOUN
ejpam-6047	74	10	on	on	ADP
ejpam-6047	74	11	the	the	DET
ejpam-6047	74	12	extension	extension	NOUN
ejpam-6047	74	13	of	of	ADP
ejpam-6047	74	14	concepts	concept	NOUN
ejpam-6047	74	15	to	to	ADP
ejpam-6047	74	16	stability	stability	NOUN
ejpam-6047	74	17	,	,	PUNCT
ejpam-6047	74	18	d	d	NOUN
ejpam-6047	74	19	-	-	NOUN
ejpam-6047	74	20	stability	stability	NOUN
ejpam-6047	74	21	,	,	PUNCT
ejpam-6047	74	22	and	and	CCONJ
ejpam-6047	74	23	strong	strong	ADJ
ejpam-6047	74	24	d	d	NOUN
ejpam-6047	74	25	-	-	NOUN
ejpam-6047	74	26	stability	stability	NOUN
ejpam-6047	74	27	of	of	ADP
ejpam-6047	74	28	metzler	metzler	PROPN
ejpam-6047	74	29	and	and	CCONJ
ejpam-6047	74	30	hurwitz	hurwitz	PROPN
ejpam-6047	74	31	matrices	matrix	NOUN
ejpam-6047	74	32	.	.	PUNCT
ejpam-6047	75	1	for	for	ADP
ejpam-6047	75	2	this	this	DET
ejpam-6047	75	3	purpose	purpose	NOUN
ejpam-6047	75	4	,	,	PUNCT
ejpam-6047	75	5	we	we	PRON
ejpam-6047	75	6	apply	apply	VERB
ejpam-6047	75	7	different	different	ADJ
ejpam-6047	75	8	approaches	approach	NOUN
ejpam-6047	75	9	drawn	draw	VERB
ejpam-6047	75	10	from	from	ADP
ejpam-6047	75	11	linear	linear	PROPN
ejpam-6047	75	12	algebra	algebra	NOUN
ejpam-6047	75	13	,	,	PUNCT
ejpam-6047	75	14	matrix	matrix	NOUN
ejpam-6047	75	15	analysis	analysis	NOUN
ejpam-6047	75	16	,	,	PUNCT
ejpam-6047	75	17	and	and	CCONJ
ejpam-6047	75	18	system	system	NOUN
ejpam-6047	75	19	theory	theory	NOUN
ejpam-6047	75	20	.	.	PUNCT
ejpam-6047	76	1	the	the	DET
ejpam-6047	76	2	numerical	numerical	ADJ
ejpam-6047	76	3	illustration	illustration	NOUN
ejpam-6047	76	4	is	be	AUX
ejpam-6047	76	5	presented	present	VERB
ejpam-6047	76	6	in	in	ADP
ejpam-6047	76	7	section	section	NOUN
ejpam-6047	76	8	5	5	NUM
ejpam-6047	76	9	.	.	PUNCT
ejpam-6047	77	1	the	the	DET
ejpam-6047	77	2	applications	application	NOUN
ejpam-6047	77	3	to	to	ADP
ejpam-6047	77	4	positive	positive	ADJ
ejpam-6047	77	5	linear	linear	ADJ
ejpam-6047	77	6	time	time	NOUN
ejpam-6047	77	7	-	-	PUNCT
ejpam-6047	77	8	invariant	invariant	ADJ
ejpam-6047	77	9	systems	system	NOUN
ejpam-6047	77	10	having	have	VERB
ejpam-6047	77	11	metzler	metzler	NOUN
ejpam-6047	77	12	and	and	CCONJ
ejpam-6047	77	13	hurwitz	hurwitz	PROPN
ejpam-6047	77	14	as	as	SCONJ
ejpam-6047	77	15	their	their	PRON
ejpam-6047	77	16	coefficient	coefficient	NOUN
ejpam-6047	77	17	matrices	matrix	NOUN
ejpam-6047	77	18	are	be	AUX
ejpam-6047	77	19	presented	present	VERB
ejpam-6047	77	20	in	in	ADP
ejpam-6047	77	21	section	section	NOUN
ejpam-6047	77	22	6	6	NUM
ejpam-6047	77	23	,	,	PUNCT
ejpam-6047	77	24	and	and	CCONJ
ejpam-6047	77	25	then	then	ADV
ejpam-6047	77	26	finally	finally	ADV
ejpam-6047	77	27	in	in	ADP
ejpam-6047	77	28	section	section	NOUN
ejpam-6047	77	29	7	7	NUM
ejpam-6047	77	30	,	,	PUNCT
ejpam-6047	77	31	we	we	PRON
ejpam-6047	77	32	present	present	VERB
ejpam-6047	77	33	the	the	DET
ejpam-6047	77	34	conclusion	conclusion	NOUN
ejpam-6047	77	35	to	to	ADP
ejpam-6047	77	36	our	our	PRON
ejpam-6047	77	37	paper	paper	NOUN
ejpam-6047	77	38	.	.	PUNCT
ejpam-6047	78	1	2	2	X
ejpam-6047	78	2	.	.	X
ejpam-6047	78	3	preliminaries	preliminary	NOUN
ejpam-6047	78	4	the	the	DET
ejpam-6047	78	5	problem	problem	NOUN
ejpam-6047	78	6	on	on	ADP
ejpam-6047	78	7	the	the	DET
ejpam-6047	78	8	analysis	analysis	NOUN
ejpam-6047	78	9	of	of	ADP
ejpam-6047	78	10	stability	stability	NOUN
ejpam-6047	78	11	and	and	CCONJ
ejpam-6047	78	12	its	its	PRON
ejpam-6047	78	13	properties	property	NOUN
ejpam-6047	78	14	for	for	ADP
ejpam-6047	78	15	linear	linear	ADJ
ejpam-6047	78	16	time	time	NOUN
ejpam-6047	78	17	-	-	PUNCT
ejpam-6047	78	18	invariant	invariant	ADJ
ejpam-6047	78	19	system	system	NOUN
ejpam-6047	78	20	with	with	ADP
ejpam-6047	78	21	positive	positive	ADJ
ejpam-6047	78	22	constraints	constraint	NOUN
ejpam-6047	78	23	has	have	AUX
ejpam-6047	78	24	been	be	AUX
ejpam-6047	78	25	thoroughly	thoroughly	ADV
ejpam-6047	78	26	investigated	investigate	VERB
ejpam-6047	78	27	and	and	CCONJ
ejpam-6047	78	28	examined	examine	VERB
ejpam-6047	78	29	in	in	ADP
ejpam-6047	78	30	the	the	DET
ejpam-6047	78	31	literature	literature	NOUN
ejpam-6047	78	32	in	in	ADP
ejpam-6047	78	33	much	much	ADV
ejpam-6047	78	34	greater	great	ADJ
ejpam-6047	78	35	detail	detail	NOUN
ejpam-6047	78	36	.	.	PUNCT
ejpam-6047	79	1	the	the	DET
ejpam-6047	79	2	positive	positive	ADJ
ejpam-6047	79	3	system	system	NOUN
ejpam-6047	79	4	stability	stability	NOUN
ejpam-6047	79	5	is	be	AUX
ejpam-6047	79	6	an	an	DET
ejpam-6047	79	7	important	important	ADJ
ejpam-6047	79	8	focus	focus	NOUN
ejpam-6047	79	9	of	of	ADP
ejpam-6047	79	10	many	many	ADJ
ejpam-6047	79	11	disciplines	discipline	NOUN
ejpam-6047	79	12	,	,	PUNCT
ejpam-6047	79	13	for	for	ADP
ejpam-6047	79	14	instance	instance	NOUN
ejpam-6047	79	15	,	,	PUNCT
ejpam-6047	79	16	applied	apply	VERB
ejpam-6047	79	17	mathematics	mathematic	NOUN
ejpam-6047	79	18	,	,	PUNCT
ejpam-6047	79	19	engineering	engineering	NOUN
ejpam-6047	79	20	,	,	PUNCT
ejpam-6047	79	21	and	and	CCONJ
ejpam-6047	79	22	computational	computational	ADJ
ejpam-6047	79	23	sciences	science	NOUN
ejpam-6047	79	24	.	.	PUNCT
ejpam-6047	80	1	we	we	PRON
ejpam-6047	80	2	study	study	VERB
ejpam-6047	80	3	and	and	CCONJ
ejpam-6047	80	4	analyze	analyze	VERB
ejpam-6047	80	5	the	the	DET
ejpam-6047	80	6	positive	positive	ADJ
ejpam-6047	80	7	system	system	NOUN
ejpam-6047	80	8	of	of	ADP
ejpam-6047	80	9	linear	linear	ADJ
ejpam-6047	80	10	time	time	NOUN
ejpam-6047	80	11	-	-	PUNCT
ejpam-6047	80	12	invariant	invariant	ADJ
ejpam-6047	80	13	of	of	ADP
ejpam-6047	80	14	the	the	DET
ejpam-6047	80	15	form	form	NOUN
ejpam-6047	80	16	dx(t	dx(t	NOUN
ejpam-6047	80	17	)	)	PUNCT
ejpam-6047	80	18	dt	dt	NOUN
ejpam-6047	80	19	=	=	SYM
ejpam-6047	80	20	ax(t	ax(t	NUM
ejpam-6047	80	21	)	)	PUNCT
ejpam-6047	80	22	,	,	PUNCT
ejpam-6047	80	23	a	a	DET
ejpam-6047	80	24	∈	∈	PROPN
ejpam-6047	80	25	rn	rn	PROPN
ejpam-6047	80	26	,	,	PUNCT
ejpam-6047	80	27	n	n	CCONJ
ejpam-6047	80	28	,	,	PUNCT
ejpam-6047	80	29	x(t	x(t	PROPN
ejpam-6047	80	30	)	)	PUNCT
ejpam-6047	80	31	∈	∈	PROPN
ejpam-6047	80	32	rn,1	rn,1	PROPN
ejpam-6047	80	33	,	,	PUNCT
ejpam-6047	80	34	with	with	ADP
ejpam-6047	80	35	a	a	DET
ejpam-6047	80	36	being	be	AUX
ejpam-6047	80	37	metzler	metzler	NOUN
ejpam-6047	80	38	,	,	PUNCT
ejpam-6047	80	39	and	and	CCONJ
ejpam-6047	80	40	hurwitz	hurwitz	PROPN
ejpam-6047	80	41	.	.	PUNCT
ejpam-6047	81	1	definition	definition	NOUN
ejpam-6047	81	2	1	1	NUM
ejpam-6047	81	3	.	.	PUNCT
ejpam-6047	82	1	[	[	X
ejpam-6047	82	2	45	45	NUM
ejpam-6047	82	3	]	]	PUNCT
ejpam-6047	82	4	a	a	DET
ejpam-6047	82	5	matrix	matrix	NOUN
ejpam-6047	82	6	a	a	DET
ejpam-6047	82	7	∈	∈	PROPN
ejpam-6047	82	8	rn	rn	PROPN
ejpam-6047	82	9	,	,	PUNCT
ejpam-6047	82	10	n	n	PRON
ejpam-6047	82	11	is	be	AUX
ejpam-6047	82	12	classified	classify	VERB
ejpam-6047	82	13	as	as	ADP
ejpam-6047	82	14	metzler	metzler	NOUN
ejpam-6047	82	15	if	if	SCONJ
ejpam-6047	82	16	all	all	PRON
ejpam-6047	82	17	of	of	ADP
ejpam-6047	82	18	its	its	PRON
ejpam-6047	82	19	off	off	ADJ
ejpam-6047	82	20	-	-	PUNCT
ejpam-6047	82	21	diagonal	diagonal	ADJ
ejpam-6047	82	22	entries	entry	NOUN
ejpam-6047	82	23	aij	aij	PROPN
ejpam-6047	82	24	,	,	PUNCT
ejpam-6047	82	25	∀	∀	VERB
ejpam-6047	82	26	i	i	NOUN
ejpam-6047	82	27	̸=	̸=	PROPN
ejpam-6047	82	28	j	j	PROPN
ejpam-6047	82	29	are	be	AUX
ejpam-6047	82	30	non	non	ADJ
ejpam-6047	82	31	-	-	ADJ
ejpam-6047	82	32	negative	negative	ADJ
ejpam-6047	82	33	.	.	PUNCT
ejpam-6047	83	1	definition	definition	NOUN
ejpam-6047	83	2	2	2	NUM
ejpam-6047	83	3	.	.	PUNCT
ejpam-6047	84	1	the	the	DET
ejpam-6047	84	2	matrix	matrix	NOUN
ejpam-6047	84	3	a	a	DET
ejpam-6047	84	4	∈	∈	PROPN
ejpam-6047	84	5	rn	rn	PROPN
ejpam-6047	84	6	,	,	PUNCT
ejpam-6047	84	7	n	n	PRON
ejpam-6047	84	8	is	be	AUX
ejpam-6047	84	9	hurwitz	hurwitz	PROPN
ejpam-6047	84	10	if	if	SCONJ
ejpam-6047	84	11	λi(a	λi(a	NOUN
ejpam-6047	84	12	)	)	PUNCT
ejpam-6047	84	13	∀i	∀i	NOUN
ejpam-6047	84	14	is	be	AUX
ejpam-6047	84	15	such	such	ADJ
ejpam-6047	84	16	that	that	SCONJ
ejpam-6047	84	17	re(λi(a	re(λi(a	PROPN
ejpam-6047	84	18	)	)	PUNCT
ejpam-6047	84	19	)	)	PUNCT
ejpam-6047	85	1	<	<	X
ejpam-6047	85	2	1	1	NUM
ejpam-6047	85	3	∀	∀	NOUN
ejpam-6047	85	4	i.	i.	NOUN
ejpam-6047	85	5	the	the	DET
ejpam-6047	85	6	d	d	NOUN
ejpam-6047	85	7	-	-	PUNCT
ejpam-6047	85	8	stability	stability	NOUN
ejpam-6047	85	9	analysis	analysis	NOUN
ejpam-6047	85	10	aims	aim	VERB
ejpam-6047	85	11	to	to	PART
ejpam-6047	85	12	study	study	VERB
ejpam-6047	85	13	and	and	CCONJ
ejpam-6047	85	14	analyze	analyze	VERB
ejpam-6047	85	15	the	the	DET
ejpam-6047	85	16	stability	stability	NOUN
ejpam-6047	85	17	of	of	ADP
ejpam-6047	85	18	an	an	DET
ejpam-6047	85	19	equilibrium	equilibrium	NOUN
ejpam-6047	85	20	of	of	ADP
ejpam-6047	85	21	dynamic	dynamic	ADJ
ejpam-6047	85	22	models	model	NOUN
ejpam-6047	85	23	appearing	appear	VERB
ejpam-6047	85	24	in	in	ADP
ejpam-6047	85	25	competitive	competitive	ADJ
ejpam-6047	85	26	market	market	NOUN
ejpam-6047	85	27	.	.	PUNCT
ejpam-6047	86	1	a	a	DET
ejpam-6047	86	2	given	give	VERB
ejpam-6047	86	3	n	n	CCONJ
ejpam-6047	86	4	-	-	PUNCT
ejpam-6047	86	5	dimensional	dimensional	ADJ
ejpam-6047	86	6	real	real	ADV
ejpam-6047	86	7	-	-	PUNCT
ejpam-6047	86	8	valued	value	VERB
ejpam-6047	86	9	matrix	matrix	NOUN
ejpam-6047	86	10	a	a	PRON
ejpam-6047	86	11	is	be	AUX
ejpam-6047	86	12	a	a	DET
ejpam-6047	86	13	d	d	ADJ
ejpam-6047	86	14	-	-	ADJ
ejpam-6047	86	15	stable	stable	ADJ
ejpam-6047	86	16	matrix	matrix	NOUN
ejpam-6047	86	17	if	if	SCONJ
ejpam-6047	86	18	for	for	ADP
ejpam-6047	86	19	any	any	DET
ejpam-6047	86	20	diagonal	diagonal	ADJ
ejpam-6047	86	21	matrix	matrix	NOUN
ejpam-6047	86	22	d	d	X
ejpam-6047	86	23	=	=	SYM
ejpam-6047	86	24	diag(dii	diag(dii	PROPN
ejpam-6047	86	25	)	)	PUNCT
ejpam-6047	86	26	,	,	PUNCT
ejpam-6047	86	27	dii	dii	INTJ
ejpam-6047	86	28	>	>	X
ejpam-6047	86	29	0	0	NUM
ejpam-6047	86	30	,	,	PUNCT
ejpam-6047	86	31	∀	∀	X
ejpam-6047	87	1	i	i	NOUN
ejpam-6047	87	2	,	,	PUNCT
ejpam-6047	87	3	the	the	DET
ejpam-6047	87	4	matrix	matrix	NOUN
ejpam-6047	87	5	da	da	NOUN
ejpam-6047	87	6	or	or	CCONJ
ejpam-6047	87	7	ad	ad	NOUN
ejpam-6047	87	8	is	be	AUX
ejpam-6047	87	9	a	a	DET
ejpam-6047	87	10	stable	stable	ADJ
ejpam-6047	87	11	matrix	matrix	NOUN
ejpam-6047	87	12	.	.	PUNCT
ejpam-6047	88	1	remark	remark	NOUN
ejpam-6047	88	2	1	1	NUM
ejpam-6047	88	3	.	.	PUNCT
ejpam-6047	89	1	the	the	DET
ejpam-6047	89	2	classification	classification	NOUN
ejpam-6047	89	3	of	of	ADP
ejpam-6047	89	4	d	d	NOUN
ejpam-6047	89	5	-	-	NOUN
ejpam-6047	89	6	stability	stability	NOUN
ejpam-6047	89	7	is	be	AUX
ejpam-6047	89	8	generally	generally	ADV
ejpam-6047	89	9	difficult	difficult	ADJ
ejpam-6047	89	10	,	,	PUNCT
ejpam-6047	89	11	except	except	SCONJ
ejpam-6047	89	12	in	in	ADP
ejpam-6047	89	13	the	the	DET
ejpam-6047	89	14	case	case	NOUN
ejpam-6047	89	15	of	of	ADP
ejpam-6047	89	16	matrices	matrix	NOUN
ejpam-6047	89	17	with	with	ADP
ejpam-6047	89	18	size	size	NOUN
ejpam-6047	89	19	3	3	NUM
ejpam-6047	89	20	,	,	PUNCT
ejpam-6047	89	21	or	or	CCONJ
ejpam-6047	89	22	less	less	ADJ
ejpam-6047	89	23	,	,	PUNCT
ejpam-6047	89	24	see	see	VERB
ejpam-6047	89	25	[	[	X
ejpam-6047	89	26	15	15	NUM
ejpam-6047	89	27	,	,	PUNCT
ejpam-6047	89	28	46	46	NUM
ejpam-6047	89	29	]	]	PUNCT
ejpam-6047	89	30	.	.	PUNCT
ejpam-6047	90	1	the	the	DET
ejpam-6047	90	2	concept	concept	NOUN
ejpam-6047	90	3	of	of	ADP
ejpam-6047	90	4	strong	strong	ADJ
ejpam-6047	90	5	d	d	NOUN
ejpam-6047	90	6	-	-	NOUN
ejpam-6047	90	7	stability	stability	NOUN
ejpam-6047	90	8	for	for	ADP
ejpam-6047	90	9	n	n	CCONJ
ejpam-6047	90	10	-	-	PUNCT
ejpam-6047	90	11	dimensional	dimensional	ADJ
ejpam-6047	90	12	real	real	ADV
ejpam-6047	90	13	-	-	PUNCT
ejpam-6047	90	14	valued	value	VERB
ejpam-6047	90	15	matrix	matrix	NOUN
ejpam-6047	90	16	a	a	PRON
ejpam-6047	90	17	,	,	PUNCT
ejpam-6047	90	18	introduced	introduce	VERB
ejpam-6047	90	19	in	in	ADP
ejpam-6047	90	20	[	[	X
ejpam-6047	90	21	47	47	NUM
ejpam-6047	90	22	]	]	PUNCT
ejpam-6047	90	23	,	,	PUNCT
ejpam-6047	90	24	seeks	seek	VERB
ejpam-6047	90	25	to	to	PART
ejpam-6047	90	26	investigate	investigate	VERB
ejpam-6047	90	27	and	and	CCONJ
ejpam-6047	90	28	characterize	characterize	VERB
ejpam-6047	90	29	the	the	DET
ejpam-6047	90	30	properties	property	NOUN
ejpam-6047	90	31	of	of	ADP
ejpam-6047	90	32	d	d	NOUN
ejpam-6047	90	33	-	-	NOUN
ejpam-6047	90	34	stability	stability	NOUN
ejpam-6047	90	35	.	.	PUNCT
ejpam-6047	91	1	definition	definition	NOUN
ejpam-6047	91	2	3	3	NUM
ejpam-6047	91	3	.	.	PUNCT
ejpam-6047	92	1	the	the	DET
ejpam-6047	92	2	matrix	matrix	NOUN
ejpam-6047	92	3	a	a	DET
ejpam-6047	92	4	∈	∈	PROPN
ejpam-6047	92	5	rn	rn	PROPN
ejpam-6047	92	6	,	,	PUNCT
ejpam-6047	92	7	n	n	PROPN
ejpam-6047	92	8	is	be	AUX
ejpam-6047	92	9	stable	stable	ADJ
ejpam-6047	92	10	if	if	SCONJ
ejpam-6047	92	11	real	real	NOUN
ejpam-6047	92	12	-	-	PUNCT
ejpam-6047	92	13	part	part	NOUN
ejpam-6047	92	14	of	of	ADP
ejpam-6047	92	15	all	all	PRON
ejpam-6047	92	16	of	of	ADP
ejpam-6047	92	17	its	its	PRON
ejpam-6047	92	18	eigenvalues	eigenvalue	NOUN
ejpam-6047	92	19	are	be	AUX
ejpam-6047	92	20	strictly	strictly	ADV
ejpam-6047	92	21	positive	positive	ADJ
ejpam-6047	92	22	(	(	PUNCT
ejpam-6047	92	23	sometime	sometime	ADV
ejpam-6047	92	24	in	in	ADP
ejpam-6047	92	25	literature	literature	NOUN
ejpam-6047	92	26	it	it	PRON
ejpam-6047	92	27	maybe	maybe	ADV
ejpam-6047	92	28	consider	consider	VERB
ejpam-6047	92	29	as	as	ADP
ejpam-6047	92	30	strictly	strictly	ADV
ejpam-6047	92	31	negative	negative	ADJ
ejpam-6047	92	32	)	)	PUNCT
ejpam-6047	92	33	.	.	PUNCT
ejpam-6047	93	1	definition	definition	NOUN
ejpam-6047	93	2	4	4	NUM
ejpam-6047	93	3	.	.	PUNCT
ejpam-6047	94	1	[	[	X
ejpam-6047	94	2	6	6	NUM
ejpam-6047	94	3	]	]	PUNCT
ejpam-6047	94	4	the	the	DET
ejpam-6047	94	5	matrix	matrix	NOUN
ejpam-6047	94	6	a	a	DET
ejpam-6047	94	7	∈	∈	PROPN
ejpam-6047	94	8	rn	rn	PROPN
ejpam-6047	94	9	,	,	PUNCT
ejpam-6047	94	10	n	n	PRON
ejpam-6047	94	11	is	be	AUX
ejpam-6047	94	12	d	d	ADJ
ejpam-6047	94	13	-	-	ADJ
ejpam-6047	94	14	stable	stable	ADJ
ejpam-6047	94	15	if	if	SCONJ
ejpam-6047	94	16	real	real	NOUN
ejpam-6047	94	17	-	-	PUNCT
ejpam-6047	94	18	part	part	NOUN
ejpam-6047	94	19	of	of	ADP
ejpam-6047	94	20	all	all	DET
ejpam-6047	94	21	eigenvalues	eigenvalue	NOUN
ejpam-6047	94	22	of	of	ADP
ejpam-6047	94	23	da	da	NOUN
ejpam-6047	94	24	or	or	CCONJ
ejpam-6047	94	25	ad	ad	NOUN
ejpam-6047	94	26	are	be	AUX
ejpam-6047	94	27	strictly	strictly	ADV
ejpam-6047	94	28	positive	positive	ADJ
ejpam-6047	94	29	(	(	PUNCT
ejpam-6047	94	30	sometime	sometime	ADV
ejpam-6047	94	31	in	in	ADP
ejpam-6047	94	32	literature	literature	NOUN
ejpam-6047	94	33	it	it	PRON
ejpam-6047	94	34	maybe	maybe	ADV
ejpam-6047	94	35	consider	consider	VERB
ejpam-6047	94	36	as	as	ADP
ejpam-6047	94	37	strictly	strictly	ADV
ejpam-6047	94	38	negative	negative	ADJ
ejpam-6047	94	39	)	)	PUNCT
ejpam-6047	94	40	for	for	ADP
ejpam-6047	94	41	a	a	DET
ejpam-6047	94	42	positive	positive	ADJ
ejpam-6047	94	43	diagonal	diagonal	ADJ
ejpam-6047	94	44	matrix	matrix	NOUN
ejpam-6047	94	45	d.	d.	NOUN
ejpam-6047	94	46	definition	definition	NOUN
ejpam-6047	94	47	5	5	NUM
ejpam-6047	94	48	.	.	PUNCT
ejpam-6047	95	1	[	[	X
ejpam-6047	95	2	47	47	NUM
ejpam-6047	95	3	]	]	PUNCT
ejpam-6047	95	4	the	the	DET
ejpam-6047	95	5	matrix	matrix	NOUN
ejpam-6047	95	6	a	a	DET
ejpam-6047	95	7	∈	∈	PROPN
ejpam-6047	95	8	rn	rn	PROPN
ejpam-6047	95	9	,	,	PUNCT
ejpam-6047	95	10	n	n	PRON
ejpam-6047	95	11	is	be	AUX
ejpam-6047	95	12	strongly	strongly	ADV
ejpam-6047	95	13	d	d	ADJ
ejpam-6047	95	14	-	-	ADJ
ejpam-6047	95	15	stable	stable	ADJ
ejpam-6047	95	16	if	if	SCONJ
ejpam-6047	95	17	there	there	PRON
ejpam-6047	95	18	exists	exist	VERB
ejpam-6047	95	19	γ	γ	X
ejpam-6047	95	20	>	>	X
ejpam-6047	95	21	0	0	PUNCT
ejpam-6047	96	1	so	so	SCONJ
ejpam-6047	96	2	that	that	SCONJ
ejpam-6047	96	3	a	a	DET
ejpam-6047	96	4	+	+	NOUN
ejpam-6047	96	5	m	m	VERB
ejpam-6047	96	6	is	be	AUX
ejpam-6047	96	7	a	a	DET
ejpam-6047	96	8	d	d	ADJ
ejpam-6047	96	9	-	-	ADJ
ejpam-6047	96	10	stable	stable	ADJ
ejpam-6047	96	11	matrix	matrix	NOUN
ejpam-6047	96	12	,	,	PUNCT
ejpam-6047	96	13	for	for	ADP
ejpam-6047	96	14	every	every	DET
ejpam-6047	96	15	m	m	PROPN
ejpam-6047	96	16	∈	∈	PROPN
ejpam-6047	96	17	rn	rn	PROPN
ejpam-6047	96	18	,	,	PUNCT
ejpam-6047	96	19	n	n	CCONJ
ejpam-6047	96	20	with	with	ADP
ejpam-6047	96	21	|m	|m	NOUN
ejpam-6047	97	1	|	|	ADV
ejpam-6047	97	2	<	<	X
ejpam-6047	97	3	γ	γ	PROPN
ejpam-6047	97	4	.	.	PROPN
ejpam-6047	97	5	m.u	m.u	PROPN
ejpam-6047	97	6	.	.	PROPN
ejpam-6047	97	7	rehman	rehman	PROPN
ejpam-6047	97	8	et	et	PROPN
ejpam-6047	97	9	al	al	PROPN
ejpam-6047	97	10	.	.	PUNCT
ejpam-6047	97	11	/	/	SYM
ejpam-6047	97	12	eur	eur	PROPN
ejpam-6047	97	13	.	.	PUNCT
ejpam-6047	98	1	j.	j.	PROPN
ejpam-6047	98	2	pure	pure	PROPN
ejpam-6047	98	3	appl	appl	PROPN
ejpam-6047	98	4	.	.	PROPN
ejpam-6047	98	5	math	math	PROPN
ejpam-6047	98	6	,	,	PUNCT
ejpam-6047	98	7	18	18	NUM
ejpam-6047	98	8	(	(	PUNCT
ejpam-6047	98	9	3	3	NUM
ejpam-6047	98	10	)	)	PUNCT
ejpam-6047	98	11	(	(	PUNCT
ejpam-6047	98	12	2025	2025	NUM
ejpam-6047	98	13	)	)	PUNCT
ejpam-6047	98	14	,	,	PUNCT
ejpam-6047	98	15	6047	6047	NUM
ejpam-6047	98	16	6	6	NUM
ejpam-6047	98	17	of	of	ADP
ejpam-6047	98	18	33	33	NUM
ejpam-6047	98	19	remark	remark	NOUN
ejpam-6047	98	20	2	2	NUM
ejpam-6047	98	21	.	.	PUNCT
ejpam-6047	99	1	the	the	DET
ejpam-6047	99	2	d	d	NOUN
ejpam-6047	99	3	-	-	NOUN
ejpam-6047	99	4	stability	stability	NOUN
ejpam-6047	99	5	of	of	ADP
ejpam-6047	99	6	a	a	DET
ejpam-6047	99	7	matrix	matrix	NOUN
ejpam-6047	99	8	needs	need	VERB
ejpam-6047	99	9	to	to	PART
ejpam-6047	99	10	be	be	AUX
ejpam-6047	99	11	a	a	DET
ejpam-6047	99	12	robust	robust	ADJ
ejpam-6047	99	13	property	property	NOUN
ejpam-6047	99	14	.	.	PUNCT
ejpam-6047	100	1	this	this	PRON
ejpam-6047	100	2	can	can	AUX
ejpam-6047	100	3	be	be	AUX
ejpam-6047	100	4	easily	easily	ADV
ejpam-6047	100	5	understand	understand	VERB
ejpam-6047	100	6	with	with	ADP
ejpam-6047	100	7	an	an	DET
ejpam-6047	100	8	example	example	NOUN
ejpam-6047	100	9	(	(	PUNCT
ejpam-6047	100	10	see	see	VERB
ejpam-6047	100	11	[	[	X
ejpam-6047	100	12	47	47	NUM
ejpam-6047	100	13	]	]	NUM
ejpam-6047	100	14	)	)	PUNCT
ejpam-6047	100	15	,	,	PUNCT
ejpam-6047	100	16	for	for	ADP
ejpam-6047	100	17	instance	instance	NOUN
ejpam-6047	100	18	,	,	PUNCT
ejpam-6047	100	19	the	the	DET
ejpam-6047	100	20	matrix	matrix	NOUN
ejpam-6047	100	21	a(0	a(0	VERB
ejpam-6047	100	22	)	)	PUNCT
ejpam-6047	100	23	=	=	PRON
ejpam-6047	101	1	(	(	PUNCT
ejpam-6047	101	2	0	0	NUM
ejpam-6047	101	3	1	1	NUM
ejpam-6047	101	4	−1	−1	NOUN
ejpam-6047	101	5	−1	−1	NOUN
ejpam-6047	101	6	)	)	PUNCT
ejpam-6047	101	7	,	,	PUNCT
ejpam-6047	101	8	is	be	AUX
ejpam-6047	101	9	a	a	DET
ejpam-6047	101	10	d	d	ADJ
ejpam-6047	101	11	-	-	ADJ
ejpam-6047	101	12	stable	stable	ADJ
ejpam-6047	101	13	matrix	matrix	NOUN
ejpam-6047	101	14	,	,	PUNCT
ejpam-6047	101	15	but	but	CCONJ
ejpam-6047	101	16	the	the	DET
ejpam-6047	101	17	perturbed	perturb	VERB
ejpam-6047	101	18	matrix	matrix	NOUN
ejpam-6047	101	19	,	,	PUNCT
ejpam-6047	101	20	that	that	ADV
ejpam-6047	101	21	is	be	AUX
ejpam-6047	101	22	,	,	PUNCT
ejpam-6047	101	23	a(γ	a(γ	ADJ
ejpam-6047	101	24	)	)	PUNCT
ejpam-6047	101	25	=	=	SYM
ejpam-6047	101	26	(	(	PUNCT
ejpam-6047	101	27	γ	γ	X
ejpam-6047	101	28	1	1	NUM
ejpam-6047	101	29	−1	−1	NOUN
ejpam-6047	101	30	−1	−1	NOUN
ejpam-6047	101	31	)	)	PUNCT
ejpam-6047	101	32	,	,	PUNCT
ejpam-6047	101	33	is	be	AUX
ejpam-6047	101	34	not	not	PART
ejpam-6047	101	35	a	a	DET
ejpam-6047	101	36	d	d	ADJ
ejpam-6047	101	37	-	-	ADJ
ejpam-6047	101	38	stable	stable	ADJ
ejpam-6047	101	39	matrix	matrix	NOUN
ejpam-6047	101	40	for	for	ADP
ejpam-6047	101	41	γ	γ	X
ejpam-6047	101	42	>	>	X
ejpam-6047	101	43	0	0	PROPN
ejpam-6047	101	44	.	.	PUNCT
ejpam-6047	102	1	the	the	DET
ejpam-6047	102	2	following	follow	VERB
ejpam-6047	102	3	lemma	lemma	PROPN
ejpam-6047	102	4	is	be	AUX
ejpam-6047	102	5	taken	take	VERB
ejpam-6047	102	6	from	from	ADP
ejpam-6047	102	7	[	[	X
ejpam-6047	102	8	48	48	NUM
ejpam-6047	102	9	]	]	PUNCT
ejpam-6047	102	10	.	.	PUNCT
ejpam-6047	103	1	lemma	lemma	PROPN
ejpam-6047	103	2	1	1	X
ejpam-6047	103	3	.	.	PUNCT
ejpam-6047	104	1	if	if	SCONJ
ejpam-6047	104	2	a	a	PRON
ejpam-6047	104	3	is	be	AUX
ejpam-6047	104	4	a	a	DET
ejpam-6047	104	5	d	d	ADJ
ejpam-6047	104	6	-	-	ADJ
ejpam-6047	104	7	stable	stable	ADJ
ejpam-6047	104	8	matrix	matrix	NOUN
ejpam-6047	104	9	,	,	PUNCT
ejpam-6047	104	10	then	then	ADV
ejpam-6047	104	11	a	a	PRON
ejpam-6047	104	12	is	be	AUX
ejpam-6047	104	13	non	non	ADJ
ejpam-6047	104	14	-	-	ADJ
ejpam-6047	104	15	singular	singular	ADJ
ejpam-6047	104	16	and	and	CCONJ
ejpam-6047	104	17	each	each	PRON
ejpam-6047	104	18	of	of	ADP
ejpam-6047	104	19	following	follow	VERB
ejpam-6047	104	20	matrices	matrix	NOUN
ejpam-6047	104	21	are	be	AUX
ejpam-6047	104	22	d	d	ADJ
ejpam-6047	104	23	-	-	ADJ
ejpam-6047	104	24	stable	stable	ADJ
ejpam-6047	104	25	.	.	PUNCT
ejpam-6047	105	1	1	1	X
ejpam-6047	105	2	.	.	X
ejpam-6047	106	1	at	at	ADP
ejpam-6047	106	2	2	2	NUM
ejpam-6047	106	3	.	.	PUNCT
ejpam-6047	106	4	a−1	a−1	NOUN
ejpam-6047	106	5	3	3	NUM
ejpam-6047	106	6	.	.	PUNCT
ejpam-6047	107	1	p	p	NOUN
ejpam-6047	107	2	tap	tap	NOUN
ejpam-6047	107	3	for	for	ADP
ejpam-6047	107	4	a	a	DET
ejpam-6047	107	5	permutation	permutation	NOUN
ejpam-6047	107	6	matrix	matrix	NOUN
ejpam-6047	107	7	p	p	NOUN
ejpam-6047	107	8	4	4	NUM
ejpam-6047	107	9	.	.	PUNCT
ejpam-6047	107	10	dae	dae	VERB
ejpam-6047	107	11	for	for	ADP
ejpam-6047	107	12	positive	positive	ADJ
ejpam-6047	107	13	diagonal	diagonal	ADJ
ejpam-6047	107	14	matrices	matrix	NOUN
ejpam-6047	107	15	d	d	NOUN
ejpam-6047	107	16	,	,	PUNCT
ejpam-6047	107	17	e.	e.	PROPN
ejpam-6047	107	18	the	the	DET
ejpam-6047	107	19	following	follow	VERB
ejpam-6047	107	20	theorem	theorem	NOUN
ejpam-6047	107	21	is	be	AUX
ejpam-6047	107	22	taken	take	VERB
ejpam-6047	107	23	from	from	ADP
ejpam-6047	107	24	[	[	X
ejpam-6047	107	25	48	48	NUM
ejpam-6047	107	26	]	]	PUNCT
ejpam-6047	107	27	.	.	PUNCT
ejpam-6047	108	1	theorem	theorem	NOUN
ejpam-6047	108	2	1	1	X
ejpam-6047	108	3	.	.	PUNCT
ejpam-6047	109	1	let	let	VERB
ejpam-6047	109	2	a	a	DET
ejpam-6047	109	3	∈	∈	PROPN
ejpam-6047	109	4	cn	cn	PROPN
ejpam-6047	109	5	,	,	PUNCT
ejpam-6047	109	6	n	n	PRON
ejpam-6047	109	7	be	be	VERB
ejpam-6047	109	8	a	a	DET
ejpam-6047	109	9	stable	stable	ADJ
ejpam-6047	109	10	matrix	matrix	NOUN
ejpam-6047	109	11	.	.	PUNCT
ejpam-6047	110	1	then	then	ADV
ejpam-6047	110	2	following	follow	VERB
ejpam-6047	110	3	statements	statement	NOUN
ejpam-6047	110	4	are	be	AUX
ejpam-6047	110	5	equivalent	equivalent	ADJ
ejpam-6047	110	6	.	.	PUNCT
ejpam-6047	111	1	1	1	X
ejpam-6047	111	2	.	.	X
ejpam-6047	111	3	a	a	PRON
ejpam-6047	111	4	is	be	AUX
ejpam-6047	111	5	a	a	DET
ejpam-6047	111	6	d	d	ADJ
ejpam-6047	111	7	-	-	ADJ
ejpam-6047	111	8	stable	stable	ADJ
ejpam-6047	111	9	matrix	matrix	NOUN
ejpam-6047	111	10	2	2	NUM
ejpam-6047	111	11	.	.	PUNCT
ejpam-6047	112	1	det(a±	det(a±	PROPN
ejpam-6047	112	2	i	i	PROPN
ejpam-6047	112	3	d	d	PROPN
ejpam-6047	112	4	)	)	PUNCT
ejpam-6047	112	5	̸=	̸=	NOUN
ejpam-6047	112	6	0	0	NUM
ejpam-6047	112	7	for	for	ADP
ejpam-6047	112	8	each	each	DET
ejpam-6047	112	9	positive	positive	ADJ
ejpam-6047	112	10	diagonal	diagonal	ADJ
ejpam-6047	112	11	matrix	matrix	NOUN
ejpam-6047	112	12	d.	d.	NOUN
ejpam-6047	112	13	let	let	VERB
ejpam-6047	112	14	b	b	PROPN
ejpam-6047	112	15	denotes	denote	NOUN
ejpam-6047	112	16	the	the	DET
ejpam-6047	112	17	set	set	NOUN
ejpam-6047	112	18	of	of	ADP
ejpam-6047	112	19	block	block	NOUN
ejpam-6047	112	20	-	-	PUNCT
ejpam-6047	112	21	diagonal	diagonal	ADJ
ejpam-6047	112	22	matrices	matrix	NOUN
ejpam-6047	112	23	and	and	CCONJ
ejpam-6047	112	24	is	be	AUX
ejpam-6047	112	25	defined	define	VERB
ejpam-6047	112	26	as	as	ADP
ejpam-6047	112	27	b	b	X
ejpam-6047	112	28	=	=	SYM
ejpam-6047	112	29	{	{	PUNCT
ejpam-6047	112	30	diag(δ1ir1	diag(δ1ir1	PROPN
ejpam-6047	112	31	,	,	PUNCT
ejpam-6047	112	32	δ2ir2	δ2ir2	NOUN
ejpam-6047	112	33	,	,	PUNCT
ejpam-6047	112	34	·	·	PUNCT
ejpam-6047	112	35	·	·	PUNCT
ejpam-6047	112	36	·	·	PUNCT
ejpam-6047	112	37	,	,	PUNCT
ejpam-6047	112	38	δsirs	δsir	NOUN
ejpam-6047	112	39	;	;	PUNCT
ejpam-6047	112	40	∆1,∆2	∆1,∆2	NOUN
ejpam-6047	112	41	,	,	PUNCT
ejpam-6047	112	42	·	·	PUNCT
ejpam-6047	112	43	·	·	PUNCT
ejpam-6047	112	44	·	·	PUNCT
ejpam-6047	112	45	,	,	PUNCT
ejpam-6047	112	46	∆f	∆f	PROPN
ejpam-6047	112	47	)	)	PUNCT
ejpam-6047	112	48	:	:	PUNCT
ejpam-6047	112	49	δi	δi	ADP
ejpam-6047	112	50	∈	∈	PROPN
ejpam-6047	112	51	k,∆j	k,∆j	NOUN
ejpam-6047	112	52	∈	∈	PROPN
ejpam-6047	112	53	kmj	kmj	NOUN
ejpam-6047	112	54	,	,	PUNCT
ejpam-6047	112	55	mj	mj	INTJ
ejpam-6047	112	56	,	,	PUNCT
ejpam-6047	112	57	k	k	PROPN
ejpam-6047	113	1	=	=	SYM
ejpam-6047	113	2	r	r	NOUN
ejpam-6047	113	3	or	or	CCONJ
ejpam-6047	113	4	c	c	NOUN
ejpam-6047	113	5	}	}	PUNCT
ejpam-6047	113	6	.	.	PUNCT
ejpam-6047	114	1	the	the	DET
ejpam-6047	114	2	structured	structured	ADJ
ejpam-6047	114	3	singular	singular	NOUN
ejpam-6047	114	4	value	value	NOUN
ejpam-6047	114	5	,	,	PUNCT
ejpam-6047	114	6	denoted	denote	VERB
ejpam-6047	114	7	as	as	ADP
ejpam-6047	114	8	µb(a	µb(a	NOUN
ejpam-6047	114	9	)	)	PUNCT
ejpam-6047	114	10	,	,	PUNCT
ejpam-6047	114	11	of	of	ADP
ejpam-6047	114	12	a	a	DET
ejpam-6047	114	13	real	real	ADJ
ejpam-6047	114	14	matrix	matrix	NOUN
ejpam-6047	114	15	a	a	DET
ejpam-6047	114	16	∈	∈	PROPN
ejpam-6047	114	17	rn	rn	PROPN
ejpam-6047	114	18	,	,	PUNCT
ejpam-6047	114	19	n	n	CCONJ
ejpam-6047	114	20	with	with	ADP
ejpam-6047	114	21	respect	respect	NOUN
ejpam-6047	114	22	to	to	ADP
ejpam-6047	114	23	b	b	NOUN
ejpam-6047	114	24	is	be	AUX
ejpam-6047	114	25	defined	define	VERB
ejpam-6047	114	26	such	such	ADJ
ejpam-6047	114	27	that	that	SCONJ
ejpam-6047	114	28	µb(a	µb(a	NUM
ejpam-6047	114	29	)	)	PUNCT
ejpam-6047	115	1	=	=	SYM
ejpam-6047	115	2	0	0	PUNCT
ejpam-6047	116	1	if	if	SCONJ
ejpam-6047	116	2	and	and	CCONJ
ejpam-6047	116	3	only	only	ADV
ejpam-6047	116	4	if	if	SCONJ
ejpam-6047	116	5	there	there	PRON
ejpam-6047	116	6	exists	exist	VERB
ejpam-6047	116	7	no	no	DET
ejpam-6047	116	8	∆	∆	PROPN
ejpam-6047	116	9	∈	∈	PROPN
ejpam-6047	116	10	b	b	PROPN
ejpam-6047	116	11	for	for	ADP
ejpam-6047	116	12	which	which	PRON
ejpam-6047	116	13	the	the	DET
ejpam-6047	116	14	matrix	matrix	NOUN
ejpam-6047	116	15	in	in	ADP
ejpam-6047	116	16	−	−	PROPN
ejpam-6047	116	17	a∆	a∆	PUNCT
ejpam-6047	116	18	has	have	AUX
ejpam-6047	116	19	at	at	ADV
ejpam-6047	116	20	least	least	ADV
ejpam-6047	116	21	one	one	NUM
ejpam-6047	116	22	eigenvalue	eigenvalue	NOUN
ejpam-6047	116	23	equal	equal	ADJ
ejpam-6047	116	24	to	to	ADP
ejpam-6047	116	25	zero	zero	NUM
ejpam-6047	116	26	,	,	PUNCT
ejpam-6047	116	27	where	where	SCONJ
ejpam-6047	116	28	in	in	ADP
ejpam-6047	116	29	represents	represent	VERB
ejpam-6047	116	30	the	the	DET
ejpam-6047	116	31	n	n	NUM
ejpam-6047	116	32	×	×	NOUN
ejpam-6047	116	33	n	n	CCONJ
ejpam-6047	116	34	identity	identity	NOUN
ejpam-6047	116	35	matrix	matrix	NOUN
ejpam-6047	116	36	.	.	PUNCT
ejpam-6047	117	1	otherwise	otherwise	ADV
ejpam-6047	117	2	,	,	PUNCT
ejpam-6047	117	3	µb(a	µb(a	X
ejpam-6047	117	4	)	)	PUNCT
ejpam-6047	117	5	takes	take	VERB
ejpam-6047	117	6	a	a	DET
ejpam-6047	117	7	nonzero	nonzero	NOUN
ejpam-6047	117	8	(	(	PUNCT
ejpam-6047	117	9	positive	positive	ADJ
ejpam-6047	117	10	)	)	PUNCT
ejpam-6047	117	11	value	value	NOUN
ejpam-6047	117	12	,	,	PUNCT
ejpam-6047	117	13	that	that	PRON
ejpam-6047	117	14	is	be	AUX
ejpam-6047	117	15	µb(a	µb(a	NOUN
ejpam-6047	117	16	)	)	PUNCT
ejpam-6047	117	17	:	:	PUNCT
ejpam-6047	118	1	=	=	SYM
ejpam-6047	118	2	1	1	NUM
ejpam-6047	118	3	min{||∆||2	min{||∆||2	NOUN
ejpam-6047	118	4	:	:	PUNCT
ejpam-6047	118	5	det(in	det(in	NUM
ejpam-6047	118	6	−a∆	−a∆	NOUN
ejpam-6047	118	7	)	)	PUNCT
ejpam-6047	118	8	=	=	SYM
ejpam-6047	118	9	0	0	NUM
ejpam-6047	118	10	}	}	PUNCT
ejpam-6047	118	11	,	,	PUNCT
ejpam-6047	118	12	where	where	SCONJ
ejpam-6047	118	13	min	min	NOUN
ejpam-6047	118	14	is	be	AUX
ejpam-6047	118	15	taken	take	VERB
ejpam-6047	118	16	over	over	ADP
ejpam-6047	118	17	all	all	DET
ejpam-6047	118	18	∆	∆	PROPN
ejpam-6047	118	19	∈	∈	PROPN
ejpam-6047	118	20	b.	b.	PROPN
ejpam-6047	118	21	remark	remark	NOUN
ejpam-6047	118	22	3	3	NUM
ejpam-6047	118	23	.	.	PUNCT
ejpam-6047	119	1	the	the	DET
ejpam-6047	119	2	necessary	necessary	ADJ
ejpam-6047	119	3	condition	condition	NOUN
ejpam-6047	119	4	for	for	ADP
ejpam-6047	119	5	µ-value	µ-value	NOUN
ejpam-6047	119	6	is	be	AUX
ejpam-6047	119	7	that	that	SCONJ
ejpam-6047	119	8	if	if	SCONJ
ejpam-6047	119	9	det(in	det(in	ADJ
ejpam-6047	119	10	−	−	NOUN
ejpam-6047	119	11	a∆	a∆	NUM
ejpam-6047	119	12	)	)	PUNCT
ejpam-6047	119	13	̸=	̸=	PROPN
ejpam-6047	119	14	0	0	NUM
ejpam-6047	119	15	for	for	ADP
ejpam-6047	119	16	any	any	DET
ejpam-6047	119	17	∆	∆	PROPN
ejpam-6047	119	18	∈	∈	PROPN
ejpam-6047	119	19	b.	b.	PROPN
ejpam-6047	119	20	then	then	ADV
ejpam-6047	119	21	,	,	PUNCT
ejpam-6047	119	22	0	0	NUM
ejpam-6047	119	23	≤	≤	NUM
ejpam-6047	119	24	µb(a	µb(a	PUNCT
ejpam-6047	119	25	)	)	PUNCT
ejpam-6047	119	26	<	<	X
ejpam-6047	119	27	1	1	X
ejpam-6047	119	28	.	.	PUNCT
ejpam-6047	119	29	remark	remark	NOUN
ejpam-6047	119	30	4	4	NUM
ejpam-6047	119	31	.	.	PUNCT
ejpam-6047	120	1	the	the	DET
ejpam-6047	120	2	matrix	matrix	NOUN
ejpam-6047	120	3	a	a	DET
ejpam-6047	120	4	∈	∈	PROPN
ejpam-6047	120	5	rn	rn	PROPN
ejpam-6047	120	6	,	,	PUNCT
ejpam-6047	120	7	n	n	PRON
ejpam-6047	120	8	is	be	AUX
ejpam-6047	120	9	d	d	ADJ
ejpam-6047	120	10	-	-	ADJ
ejpam-6047	120	11	stable	stable	ADJ
ejpam-6047	120	12	iff	iff	NOUN
ejpam-6047	120	13	it	it	PRON
ejpam-6047	120	14	is	be	AUX
ejpam-6047	120	15	stable	stable	ADJ
ejpam-6047	120	16	,	,	PUNCT
ejpam-6047	120	17	and	and	CCONJ
ejpam-6047	120	18	det(a+id	det(a+id	NOUN
ejpam-6047	120	19	)	)	PUNCT
ejpam-6047	120	20	̸=	̸=	PROPN
ejpam-6047	120	21	0	0	NUM
ejpam-6047	120	22	,	,	PUNCT
ejpam-6047	120	23	i	i	PRON
ejpam-6047	120	24	=	=	PUNCT
ejpam-6047	120	25	√	√	ADP
ejpam-6047	120	26	−1	−1	NOUN
ejpam-6047	120	27	for	for	ADP
ejpam-6047	120	28	some	some	DET
ejpam-6047	120	29	specific	specific	ADJ
ejpam-6047	120	30	positive	positive	ADJ
ejpam-6047	120	31	diagonal	diagonal	ADJ
ejpam-6047	120	32	matrix	matrix	NOUN
ejpam-6047	120	33	d	d	NOUN
ejpam-6047	120	34	,	,	PUNCT
ejpam-6047	120	35	see	see	VERB
ejpam-6047	120	36	[	[	X
ejpam-6047	120	37	13	13	NUM
ejpam-6047	120	38	]	]	PUNCT
ejpam-6047	120	39	.	.	PUNCT
ejpam-6047	121	1	remark	remark	PROPN
ejpam-6047	121	2	5	5	NUM
ejpam-6047	121	3	.	.	PUNCT
ejpam-6047	122	1	the	the	DET
ejpam-6047	122	2	sufficient	sufficient	ADJ
ejpam-6047	122	3	condition	condition	NOUN
ejpam-6047	122	4	for	for	ADP
ejpam-6047	122	5	µ-value	µ-value	NOUN
ejpam-6047	122	6	is	be	AUX
ejpam-6047	122	7	that	that	SCONJ
ejpam-6047	122	8	if	if	SCONJ
ejpam-6047	122	9	0	0	NUM
ejpam-6047	122	10	≤	≤	NUM
ejpam-6047	122	11	µb(a	µb(a	NOUN
ejpam-6047	122	12	)	)	PUNCT
ejpam-6047	122	13	<	<	X
ejpam-6047	122	14	1	1	NUM
ejpam-6047	122	15	,	,	PUNCT
ejpam-6047	122	16	then	then	ADV
ejpam-6047	122	17	det(in	det(in	ADJ
ejpam-6047	122	18	−	−	PROPN
ejpam-6047	122	19	a∆	a∆	NUM
ejpam-6047	122	20	)	)	PUNCT
ejpam-6047	122	21	̸=	̸=	PROPN
ejpam-6047	122	22	0	0	NUM
ejpam-6047	122	23	,	,	PUNCT
ejpam-6047	122	24	∀∆	∀∆	PROPN
ejpam-6047	122	25	∈	∈	PROPN
ejpam-6047	122	26	b.	b.	PROPN
ejpam-6047	122	27	the	the	DET
ejpam-6047	122	28	analysis	analysis	NOUN
ejpam-6047	122	29	and	and	CCONJ
ejpam-6047	122	30	investigation	investigation	NOUN
ejpam-6047	122	31	on	on	ADP
ejpam-6047	122	32	the	the	DET
ejpam-6047	122	33	behaviour	behaviour	NOUN
ejpam-6047	122	34	of	of	ADP
ejpam-6047	122	35	a	a	DET
ejpam-6047	122	36	∈	∈	PROPN
ejpam-6047	122	37	rn	rn	PROPN
ejpam-6047	122	38	,	,	PUNCT
ejpam-6047	122	39	n	n	X
ejpam-6047	122	40	subject	subject	ADJ
ejpam-6047	122	41	to	to	ADP
ejpam-6047	122	42	an	an	DET
ejpam-6047	122	43	admissible	admissible	ADJ
ejpam-6047	122	44	perturbation	perturbation	NOUN
ejpam-6047	122	45	∆p	∆p	PROPN
ejpam-6047	122	46	,	,	PUNCT
ejpam-6047	122	47	for	for	ADP
ejpam-6047	122	48	ϵ	ϵ	X
ejpam-6047	122	49	>	>	X
ejpam-6047	122	50	0	0	NUM
ejpam-6047	123	1	such	such	ADJ
ejpam-6047	123	2	that	that	PRON
ejpam-6047	123	3	||∆p||	||∆p||	PROPN
ejpam-6047	123	4	≤	≤	PROPN
ejpam-6047	123	5	ϵ	ϵ	PUNCT
ejpam-6047	123	6	,	,	PUNCT
ejpam-6047	123	7	is	be	AUX
ejpam-6047	123	8	to	to	PART
ejpam-6047	123	9	study	study	VERB
ejpam-6047	123	10	the	the	DET
ejpam-6047	123	11	pseudo	pseudo	NOUN
ejpam-6047	123	12	-	-	NOUN
ejpam-6047	123	13	spectrum	spectrum	NOUN
ejpam-6047	123	14	[	[	X
ejpam-6047	123	15	49	49	NUM
ejpam-6047	123	16	]	]	PUNCT
ejpam-6047	123	17	.	.	PUNCT
ejpam-6047	124	1	for	for	ADP
ejpam-6047	124	2	given	give	VERB
ejpam-6047	124	3	a	a	DET
ejpam-6047	124	4	∈	∈	PROPN
ejpam-6047	124	5	rn	rn	PROPN
ejpam-6047	124	6	,	,	PUNCT
ejpam-6047	124	7	n	n	PROPN
ejpam-6047	124	8	and	and	CCONJ
ejpam-6047	124	9	ϵ	ϵ	X
ejpam-6047	124	10	>	>	X
ejpam-6047	124	11	0	0	PROPN
ejpam-6047	124	12	,	,	PUNCT
ejpam-6047	124	13	the	the	DET
ejpam-6047	124	14	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-6047	124	15	is	be	AUX
ejpam-6047	124	16	given	give	VERB
ejpam-6047	124	17	by	by	ADP
ejpam-6047	124	18	λϵ(a	λϵ(a	PROPN
ejpam-6047	124	19	)	)	PUNCT
ejpam-6047	124	20	:	:	PUNCT
ejpam-6047	125	1	=	=	PUNCT
ejpam-6047	125	2	{	{	PUNCT
ejpam-6047	125	3	z	z	NOUN
ejpam-6047	125	4	∈	∈	PROPN
ejpam-6047	125	5	c	c	NOUN
ejpam-6047	125	6	:	:	PUNCT
ejpam-6047	125	7	||(a−	||(a−	PROPN
ejpam-6047	125	8	zin)−1||−1	zin)−1||−1	VERB
ejpam-6047	125	9	<	<	X
ejpam-6047	125	10	ϵ	ϵ	X
ejpam-6047	125	11	}	}	PUNCT
ejpam-6047	125	12	,	,	PUNCT
ejpam-6047	125	13	where	where	SCONJ
ejpam-6047	125	14	||	||	NOUN
ejpam-6047	125	15	·	·	PUNCT
ejpam-6047	125	16	||	||	NUM
ejpam-6047	125	17	is	be	AUX
ejpam-6047	125	18	matrix	matrix	NOUN
ejpam-6047	125	19	-	-	PUNCT
ejpam-6047	125	20	norm	norm	NOUN
ejpam-6047	125	21	.	.	PUNCT
ejpam-6047	126	1	m.u	m.u	PROPN
ejpam-6047	126	2	.	.	PROPN
ejpam-6047	126	3	rehman	rehman	PROPN
ejpam-6047	126	4	et	et	PROPN
ejpam-6047	126	5	al	al	PROPN
ejpam-6047	126	6	.	.	PUNCT
ejpam-6047	126	7	/	/	SYM
ejpam-6047	126	8	eur	eur	PROPN
ejpam-6047	126	9	.	.	PUNCT
ejpam-6047	127	1	j.	j.	PROPN
ejpam-6047	127	2	pure	pure	PROPN
ejpam-6047	127	3	appl	appl	PROPN
ejpam-6047	127	4	.	.	PROPN
ejpam-6047	127	5	math	math	PROPN
ejpam-6047	127	6	,	,	PUNCT
ejpam-6047	127	7	18	18	NUM
ejpam-6047	127	8	(	(	PUNCT
ejpam-6047	127	9	3	3	NUM
ejpam-6047	127	10	)	)	PUNCT
ejpam-6047	127	11	(	(	PUNCT
ejpam-6047	127	12	2025	2025	NUM
ejpam-6047	127	13	)	)	PUNCT
ejpam-6047	127	14	,	,	PUNCT
ejpam-6047	127	15	6047	6047	NUM
ejpam-6047	127	16	7	7	NUM
ejpam-6047	127	17	of	of	ADP
ejpam-6047	127	18	33	33	NUM
ejpam-6047	127	19	remark	remark	NOUN
ejpam-6047	127	20	6	6	NUM
ejpam-6047	127	21	.	.	PUNCT
ejpam-6047	128	1	if	if	SCONJ
ejpam-6047	128	2	||	||	NOUN
ejpam-6047	129	1	·	·	PUNCT
ejpam-6047	129	2	||	||	NUM
ejpam-6047	129	3	is	be	AUX
ejpam-6047	129	4	being	be	AUX
ejpam-6047	129	5	euclidean	euclidean	ADJ
ejpam-6047	129	6	norm	norm	NOUN
ejpam-6047	129	7	,	,	PUNCT
ejpam-6047	129	8	then	then	ADV
ejpam-6047	129	9	λϵ(a	λϵ(a	NUM
ejpam-6047	129	10	)	)	PUNCT
ejpam-6047	130	1	:	:	PUNCT
ejpam-6047	130	2	=	=	PUNCT
ejpam-6047	130	3	{	{	PUNCT
ejpam-6047	130	4	z	z	NOUN
ejpam-6047	130	5	∈	∈	PROPN
ejpam-6047	130	6	c	c	NOUN
ejpam-6047	130	7	:	:	PUNCT
ejpam-6047	130	8	||(a−	||(a−	PROPN
ejpam-6047	130	9	zin)−1||−1	zin)−1||−1	VERB
ejpam-6047	130	10	<	<	X
ejpam-6047	130	11	ϵ	ϵ	X
ejpam-6047	130	12	}	}	PUNCT
ejpam-6047	130	13	=	=	SYM
ejpam-6047	130	14	{	{	PUNCT
ejpam-6047	130	15	z	z	NOUN
ejpam-6047	130	16	∈	∈	PROPN
ejpam-6047	130	17	c	c	NOUN
ejpam-6047	130	18	:	:	PUNCT
ejpam-6047	130	19	σmin(a−	σmin(a−	PROPN
ejpam-6047	130	20	zin	zin	PROPN
ejpam-6047	130	21	)	)	PUNCT
ejpam-6047	130	22	<	<	X
ejpam-6047	130	23	ϵ	ϵ	X
ejpam-6047	130	24	}	}	PUNCT
ejpam-6047	130	25	,	,	PUNCT
ejpam-6047	130	26	where	where	SCONJ
ejpam-6047	130	27	σmin	σmin	X
ejpam-6047	130	28	(	(	PUNCT
ejpam-6047	130	29	·	·	PUNCT
ejpam-6047	130	30	)	)	PUNCT
ejpam-6047	130	31	denotes	denote	NOUN
ejpam-6047	130	32	smallest	small	ADJ
ejpam-6047	130	33	singular	singular	NOUN
ejpam-6047	130	34	-	-	PUNCT
ejpam-6047	130	35	value	value	NOUN
ejpam-6047	130	36	of	of	ADP
ejpam-6047	130	37	a	a	DET
ejpam-6047	130	38	matrix	matrix	NOUN
ejpam-6047	130	39	.	.	PUNCT
ejpam-6047	131	1	2.1	2.1	NUM
ejpam-6047	131	2	.	.	PUNCT
ejpam-6047	131	3	sufficient	sufficient	ADJ
ejpam-6047	131	4	conditions	condition	NOUN
ejpam-6047	131	5	for	for	ADP
ejpam-6047	131	6	d	d	NOUN
ejpam-6047	131	7	-	-	NOUN
ejpam-6047	131	8	stability	stability	NOUN
ejpam-6047	131	9	:	:	PUNCT
ejpam-6047	131	10	we	we	PRON
ejpam-6047	131	11	review	review	VERB
ejpam-6047	131	12	c.r	c.r	PROPN
ejpam-6047	131	13	.	.	PROPN
ejpam-6047	131	14	johnson	johnson	PROPN
ejpam-6047	131	15	’s	’s	PART
ejpam-6047	131	16	[	[	X
ejpam-6047	131	17	15	15	NUM
ejpam-6047	131	18	]	]	SYM
ejpam-6047	131	19	13	13	NUM
ejpam-6047	131	20	sufficient	sufficient	ADJ
ejpam-6047	131	21	conditions	condition	NOUN
ejpam-6047	131	22	for	for	ADP
ejpam-6047	131	23	the	the	DET
ejpam-6047	131	24	d	d	NOUN
ejpam-6047	131	25	-	-	NOUN
ejpam-6047	131	26	stability	stability	NOUN
ejpam-6047	131	27	for	for	ADP
ejpam-6047	131	28	a	a	DET
ejpam-6047	131	29	given	give	VERB
ejpam-6047	131	30	n	n	CCONJ
ejpam-6047	131	31	-	-	PUNCT
ejpam-6047	131	32	dimensional	dimensional	ADJ
ejpam-6047	131	33	real	real	ADV
ejpam-6047	131	34	-	-	PUNCT
ejpam-6047	131	35	valued	value	VERB
ejpam-6047	131	36	matrix	matrix	NOUN
ejpam-6047	131	37	a.	a.	NOUN
ejpam-6047	131	38	c1	c1	PROPN
ejpam-6047	131	39	:	:	PUNCT
ejpam-6047	131	40	all	all	DET
ejpam-6047	131	41	the	the	DET
ejpam-6047	131	42	eigenvalues	eigenvalues	PROPN
ejpam-6047	131	43	λi	λi	INTJ
ejpam-6047	131	44	(	(	PUNCT
ejpam-6047	131	45	da	da	ADJ
ejpam-6047	131	46	+	+	X
ejpam-6047	131	47	atd	atd	PROPN
ejpam-6047	131	48	)	)	PUNCT
ejpam-6047	131	49	>	>	X
ejpam-6047	131	50	0	0	NUM
ejpam-6047	131	51	,	,	PUNCT
ejpam-6047	131	52	∀i	∀i	NOUN
ejpam-6047	131	53	,	,	PUNCT
ejpam-6047	131	54	d	d	PRON
ejpam-6047	131	55	is	be	AUX
ejpam-6047	131	56	a	a	DET
ejpam-6047	131	57	diagonal	diagonal	ADJ
ejpam-6047	131	58	matrix	matrix	NOUN
ejpam-6047	131	59	which	which	PRON
ejpam-6047	131	60	is	be	AUX
ejpam-6047	131	61	positive	positive	ADJ
ejpam-6047	131	62	.	.	PUNCT
ejpam-6047	132	1	c2	c2	PROPN
ejpam-6047	132	2	:	:	PUNCT
ejpam-6047	132	3	the	the	DET
ejpam-6047	132	4	a	a	DET
ejpam-6047	132	5	-	-	PUNCT
ejpam-6047	132	6	matrix	matrix	NOUN
ejpam-6047	132	7	means	mean	VERB
ejpam-6047	132	8	that	that	SCONJ
ejpam-6047	132	9	all	all	PRON
ejpam-6047	132	10	of	of	ADP
ejpam-6047	132	11	the	the	DET
ejpam-6047	132	12	principal	principal	ADJ
ejpam-6047	132	13	minors	minor	NOUN
ejpam-6047	132	14	are	be	AUX
ejpam-6047	132	15	positive	positive	ADJ
ejpam-6047	132	16	and	and	CCONJ
ejpam-6047	132	17	all	all	PRON
ejpam-6047	132	18	of	of	ADP
ejpam-6047	132	19	the	the	DET
ejpam-6047	132	20	offdiagonal	offdiagonal	ADJ
ejpam-6047	132	21	entries	entry	NOUN
ejpam-6047	132	22	are	be	AUX
ejpam-6047	132	23	non	non	ADJ
ejpam-6047	132	24	-	-	ADJ
ejpam-6047	132	25	positive	positive	ADJ
ejpam-6047	132	26	.	.	PUNCT
ejpam-6047	133	1	c3	c3	NOUN
ejpam-6047	133	2	:	:	PUNCT
ejpam-6047	133	3	there	there	PRON
ejpam-6047	133	4	exists	exist	VERB
ejpam-6047	133	5	a	a	DET
ejpam-6047	133	6	positive	positive	ADJ
ejpam-6047	133	7	diagonal	diagonal	ADJ
ejpam-6047	133	8	matrix	matrix	NOUN
ejpam-6047	133	9	d	d	ADP
ejpam-6047	133	10	such	such	ADJ
ejpam-6047	133	11	that	that	DET
ejpam-6047	133	12	ad	ad	NOUN
ejpam-6047	133	13	=	=	SYM
ejpam-6047	133	14	b	b	NOUN
ejpam-6047	133	15	=	=	SYM
ejpam-6047	133	16	(	(	PUNCT
ejpam-6047	133	17	bij	bij	NOUN
ejpam-6047	133	18	)	)	PUNCT
ejpam-6047	133	19	which	which	PRON
ejpam-6047	133	20	satisfies	satisfy	VERB
ejpam-6047	133	21	the	the	DET
ejpam-6047	133	22	condition	condition	NOUN
ejpam-6047	133	23	that	that	SCONJ
ejpam-6047	133	24	re(bii	re(bii	NOUN
ejpam-6047	133	25	)	)	PUNCT
ejpam-6047	133	26	>	>	PUNCT
ejpam-6047	134	1	n∑	n∑	PUNCT
ejpam-6047	134	2	j=1	j=1	PROPN
ejpam-6047	134	3	|bij	|bij	VERB
ejpam-6047	134	4	|	|	ADV
ejpam-6047	134	5	;	;	PUNCT
ejpam-6047	134	6	i	i	NOUN
ejpam-6047	134	7	=	=	NOUN
ejpam-6047	134	8	1	1	NUM
ejpam-6047	134	9	:	:	SYM
ejpam-6047	134	10	n	n	CCONJ
ejpam-6047	134	11	,	,	PUNCT
ejpam-6047	134	12	j	j	PROPN
ejpam-6047	134	13	̸=	̸=	PROPN
ejpam-6047	134	14	i.	i.	NOUN
ejpam-6047	134	15	c4	c4	NOUN
ejpam-6047	134	16	:	:	PUNCT
ejpam-6047	134	17	given	give	VERB
ejpam-6047	134	18	a	a	DET
ejpam-6047	134	19	∈	∈	PROPN
ejpam-6047	134	20	rn	rn	PROPN
ejpam-6047	134	21	,	,	PUNCT
ejpam-6047	134	22	n	n	PRON
ejpam-6047	134	23	is	be	AUX
ejpam-6047	134	24	a	a	DET
ejpam-6047	134	25	triangular	triangular	NOUN
ejpam-6047	134	26	matrix	matrix	NOUN
ejpam-6047	134	27	and	and	CCONJ
ejpam-6047	134	28	the	the	DET
ejpam-6047	134	29	real	real	ADJ
ejpam-6047	134	30	part	part	NOUN
ejpam-6047	134	31	of	of	ADP
ejpam-6047	134	32	all	all	DET
ejpam-6047	134	33	the	the	DET
ejpam-6047	134	34	off	off	ADJ
ejpam-6047	134	35	-	-	PUNCT
ejpam-6047	134	36	diagonal	diagonal	ADJ
ejpam-6047	134	37	entries	entry	NOUN
ejpam-6047	134	38	aii	aii	NOUN
ejpam-6047	134	39	is	be	AUX
ejpam-6047	134	40	strictly	strictly	ADV
ejpam-6047	134	41	positive	positive	ADJ
ejpam-6047	134	42	.	.	PUNCT
ejpam-6047	135	1	c5	c5	PROPN
ejpam-6047	135	2	:	:	PUNCT
ejpam-6047	135	3	given	give	VERB
ejpam-6047	135	4	a	a	DET
ejpam-6047	135	5	∈	∈	PROPN
ejpam-6047	135	6	rn	rn	PROPN
ejpam-6047	135	7	,	,	PUNCT
ejpam-6047	135	8	n	n	PRON
ejpam-6047	135	9	is	be	AUX
ejpam-6047	135	10	a	a	DET
ejpam-6047	135	11	sign	sign	ADJ
ejpam-6047	135	12	stable	stable	ADJ
ejpam-6047	135	13	matrix	matrix	NOUN
ejpam-6047	135	14	.	.	PUNCT
ejpam-6047	136	1	c6	c6	NOUN
ejpam-6047	136	2	:	:	PUNCT
ejpam-6047	136	3	every	every	DET
ejpam-6047	136	4	principal	principal	ADJ
ejpam-6047	136	5	minor	minor	NOUN
ejpam-6047	136	6	of	of	ADP
ejpam-6047	136	7	a	a	DET
ejpam-6047	136	8	∈	∈	PROPN
ejpam-6047	136	9	rn	rn	PROPN
ejpam-6047	136	10	,	,	PUNCT
ejpam-6047	136	11	n	n	PRON
ejpam-6047	136	12	is	be	AUX
ejpam-6047	136	13	positive	positive	ADJ
ejpam-6047	136	14	,	,	PUNCT
ejpam-6047	136	15	and	and	CCONJ
ejpam-6047	136	16	a	a	PRON
ejpam-6047	136	17	is	be	AUX
ejpam-6047	136	18	a	a	DET
ejpam-6047	136	19	tri	tri	ADJ
ejpam-6047	136	20	-	-	ADJ
ejpam-6047	136	21	diagonal	diagonal	ADJ
ejpam-6047	136	22	matrix	matrix	NOUN
ejpam-6047	136	23	.	.	PUNCT
ejpam-6047	137	1	c7	c7	PROPN
ejpam-6047	137	2	:	:	PUNCT
ejpam-6047	137	3	given	give	VERB
ejpam-6047	137	4	a	a	DET
ejpam-6047	137	5	∈	∈	PROPN
ejpam-6047	137	6	rn	rn	PROPN
ejpam-6047	137	7	,	,	PUNCT
ejpam-6047	137	8	n	n	PRON
ejpam-6047	137	9	is	be	AUX
ejpam-6047	137	10	an	an	DET
ejpam-6047	137	11	oscillatory	oscillatory	ADJ
ejpam-6047	137	12	matrix	matrix	NOUN
ejpam-6047	137	13	,	,	PUNCT
ejpam-6047	137	14	that	that	ADV
ejpam-6047	137	15	is	is	ADV
ejpam-6047	137	16	,	,	PUNCT
ejpam-6047	137	17	a	a	PRON
ejpam-6047	137	18	is	be	AUX
ejpam-6047	137	19	totally	totally	ADV
ejpam-6047	137	20	non	non	ADJ
ejpam-6047	137	21	-	-	ADJ
ejpam-6047	137	22	negative	negative	ADJ
ejpam-6047	137	23	matrix	matrix	NOUN
ejpam-6047	137	24	.	.	PUNCT
ejpam-6047	138	1	c8	c8	NOUN
ejpam-6047	138	2	:	:	PUNCT
ejpam-6047	138	3	for	for	ADP
ejpam-6047	138	4	each	each	DET
ejpam-6047	138	5	x	x	SYM
ejpam-6047	138	6	∈	∈	PROPN
ejpam-6047	138	7	rn,1	rn,1	PROPN
ejpam-6047	138	8	,	,	PUNCT
ejpam-6047	138	9	x	x	X
ejpam-6047	138	10	̸=	̸=	PROPN
ejpam-6047	138	11	0	0	NUM
ejpam-6047	138	12	,	,	PUNCT
ejpam-6047	138	13	a	a	DET
ejpam-6047	138	14	positive	positive	ADJ
ejpam-6047	138	15	diagonal	diagonal	ADJ
ejpam-6047	138	16	matrix	matrix	NOUN
ejpam-6047	138	17	d	d	NOUN
ejpam-6047	138	18	exists	exist	VERB
ejpam-6047	138	19	such	such	ADJ
ejpam-6047	138	20	that	that	SCONJ
ejpam-6047	138	21	the	the	DET
ejpam-6047	138	22	real	real	ADJ
ejpam-6047	138	23	part	part	NOUN
ejpam-6047	138	24	of	of	ADP
ejpam-6047	138	25	xtdax	xtdax	PROPN
ejpam-6047	138	26	is	be	AUX
ejpam-6047	138	27	positive	positive	ADJ
ejpam-6047	138	28	.	.	PUNCT
ejpam-6047	139	1	c9	c9	NOUN
ejpam-6047	139	2	:	:	PUNCT
ejpam-6047	139	3	for	for	SCONJ
ejpam-6047	139	4	given	give	VERB
ejpam-6047	139	5	a	a	DET
ejpam-6047	139	6	∈	∈	PROPN
ejpam-6047	139	7	rn	rn	PROPN
ejpam-6047	139	8	,	,	PUNCT
ejpam-6047	139	9	n	n	CCONJ
ejpam-6047	139	10	,	,	PUNCT
ejpam-6047	139	11	and	and	CCONJ
ejpam-6047	139	12	for	for	ADP
ejpam-6047	139	13	every	every	DET
ejpam-6047	139	14	positive	positive	ADJ
ejpam-6047	139	15	definite	definite	ADJ
ejpam-6047	139	16	matrix	matrix	NOUN
ejpam-6047	139	17	p	p	NOUN
ejpam-6047	139	18	,	,	PUNCT
ejpam-6047	139	19	the	the	DET
ejpam-6047	139	20	hadamard	hadamard	ADJ
ejpam-6047	139	21	product	product	NOUN
ejpam-6047	139	22	of	of	ADP
ejpam-6047	139	23	p	p	NOUN
ejpam-6047	139	24	and	and	CCONJ
ejpam-6047	139	25	a	a	PRON
ejpam-6047	139	26	is	be	AUX
ejpam-6047	139	27	a	a	DET
ejpam-6047	139	28	stable	stable	ADJ
ejpam-6047	139	29	matrix	matrix	NOUN
ejpam-6047	139	30	.	.	PUNCT
ejpam-6047	140	1	c10	c10	VERB
ejpam-6047	140	2	:	:	PUNCT
ejpam-6047	140	3	the	the	DET
ejpam-6047	140	4	given	give	VERB
ejpam-6047	140	5	a	a	DET
ejpam-6047	140	6	∈	∈	PROPN
ejpam-6047	140	7	rn	rn	PROPN
ejpam-6047	140	8	,	,	PUNCT
ejpam-6047	140	9	n	n	PRON
ejpam-6047	140	10	is	be	AUX
ejpam-6047	140	11	a	a	DET
ejpam-6047	140	12	strictly	strictly	ADV
ejpam-6047	140	13	sign	sign	VERB
ejpam-6047	140	14	symmetric	symmetric	ADJ
ejpam-6047	140	15	matrix	matrix	NOUN
ejpam-6047	140	16	and	and	CCONJ
ejpam-6047	140	17	its	its	PRON
ejpam-6047	140	18	every	every	DET
ejpam-6047	140	19	minor	minor	NOUN
ejpam-6047	140	20	is	be	AUX
ejpam-6047	140	21	positive	positive	ADJ
ejpam-6047	140	22	.	.	PUNCT
ejpam-6047	141	1	c11	c11	NOUN
ejpam-6047	141	2	:	:	PUNCT
ejpam-6047	141	3	given	give	VERB
ejpam-6047	141	4	a	a	DET
ejpam-6047	141	5	∈	∈	PROPN
ejpam-6047	141	6	rn	rn	PROPN
ejpam-6047	141	7	,	,	PUNCT
ejpam-6047	141	8	n	n	PRON
ejpam-6047	141	9	such	such	ADJ
ejpam-6047	141	10	that	that	SCONJ
ejpam-6047	141	11	a	a	DET
ejpam-6047	141	12	∈	∈	PROPN
ejpam-6047	141	13	r2,2	r2,2	PROPN
ejpam-6047	141	14	∩	∩	NOUN
ejpam-6047	141	15	p+	p+	VERB
ejpam-6047	141	16	0	0	NUM
ejpam-6047	141	17	.	.	PUNCT
ejpam-6047	142	1	c12	c12	PROPN
ejpam-6047	142	2	:	:	PUNCT
ejpam-6047	142	3	given	give	VERB
ejpam-6047	142	4	a	a	DET
ejpam-6047	142	5	∈	∈	PROPN
ejpam-6047	142	6	rn	rn	PROPN
ejpam-6047	142	7	,	,	PUNCT
ejpam-6047	142	8	n	n	PRON
ejpam-6047	142	9	such	such	ADJ
ejpam-6047	142	10	that	that	SCONJ
ejpam-6047	142	11	a	a	DET
ejpam-6047	142	12	∈	∈	PROPN
ejpam-6047	142	13	r3,3	r3,3	PROPN
ejpam-6047	142	14	∩	∩	NOUN
ejpam-6047	142	15	p+	p+	VERB
ejpam-6047	142	16	0	0	NUM
ejpam-6047	142	17	,	,	PUNCT
ejpam-6047	142	18	and	and	CCONJ
ejpam-6047	142	19	a	a	PRON
ejpam-6047	142	20	=	=	X
ejpam-6047	142	21	x	x	ADP
ejpam-6047	142	22	a	a	DET
ejpam-6047	142	23	b	b	NOUN
ejpam-6047	142	24	α	α	NOUN
ejpam-6047	142	25	y	y	NOUN
ejpam-6047	142	26	c	c	NOUN
ejpam-6047	142	27	β	β	X
ejpam-6047	142	28	α	α	X
ejpam-6047	142	29	z	z	PROPN
ejpam-6047	142	30			PROPN
ejpam-6047	142	31	.	.	PUNCT
ejpam-6047	143	1	c13	c13	NOUN
ejpam-6047	143	2	:	:	PUNCT
ejpam-6047	143	3	given	give	VERB
ejpam-6047	143	4	a	a	DET
ejpam-6047	143	5	∈	∈	PROPN
ejpam-6047	143	6	rn	rn	PROPN
ejpam-6047	143	7	,	,	PUNCT
ejpam-6047	143	8	n	n	PRON
ejpam-6047	143	9	such	such	ADJ
ejpam-6047	143	10	that	that	SCONJ
ejpam-6047	143	11	a	a	DET
ejpam-6047	143	12	∈	∈	PROPN
ejpam-6047	143	13	rn	rn	PROPN
ejpam-6047	143	14	,	,	PUNCT
ejpam-6047	143	15	n	n	PRON
ejpam-6047	143	16	∩	∩	NOUN
ejpam-6047	143	17	p+	p+	PART
ejpam-6047	143	18	0	0	NUM
ejpam-6047	143	19	satisfies	satisfy	VERB
ejpam-6047	143	20	gkk	gkk	PROPN
ejpam-6047	143	21	condition	condition	NOUN
ejpam-6047	143	22	with	with	ADP
ejpam-6047	143	23	n	n	PRON
ejpam-6047	143	24	≤	≤	NUM
ejpam-6047	143	25	4	4	NUM
ejpam-6047	143	26	.	.	X
ejpam-6047	143	27	2.2	2.2	NUM
ejpam-6047	143	28	.	.	PUNCT
ejpam-6047	144	1	sufficient	sufficient	ADJ
ejpam-6047	144	2	condition	condition	NOUN
ejpam-6047	144	3	for	for	ADP
ejpam-6047	144	4	strong	strong	ADJ
ejpam-6047	144	5	d	d	NOUN
ejpam-6047	144	6	-	-	NOUN
ejpam-6047	144	7	stability	stability	NOUN
ejpam-6047	144	8	[	[	X
ejpam-6047	144	9	50	50	NUM
ejpam-6047	144	10	]	]	PUNCT
ejpam-6047	144	11	:	:	PUNCT
ejpam-6047	144	12	for	for	ADP
ejpam-6047	144	13	a	a	DET
ejpam-6047	144	14	given	give	VERB
ejpam-6047	144	15	a	a	DET
ejpam-6047	144	16	∈	∈	PROPN
ejpam-6047	144	17	rn	rn	PROPN
ejpam-6047	144	18	,	,	PUNCT
ejpam-6047	144	19	n	n	CCONJ
ejpam-6047	144	20	,	,	PUNCT
ejpam-6047	144	21	the	the	DET
ejpam-6047	144	22	sufficient	sufficient	ADJ
ejpam-6047	144	23	conditions	condition	NOUN
ejpam-6047	144	24	for	for	ADP
ejpam-6047	144	25	the	the	DET
ejpam-6047	144	26	strong	strong	ADJ
ejpam-6047	144	27	d	d	NOUN
ejpam-6047	144	28	-	-	NOUN
ejpam-6047	144	29	stability	stability	NOUN
ejpam-6047	144	30	are	be	AUX
ejpam-6047	144	31	:	:	PUNCT
ejpam-6047	144	32	c1	c1	NOUN
ejpam-6047	144	33	:	:	PUNCT
ejpam-6047	144	34	for	for	ADP
ejpam-6047	144	35	a	a	DET
ejpam-6047	144	36	positive	positive	ADJ
ejpam-6047	144	37	diagonal	diagonal	ADJ
ejpam-6047	144	38	matrix	matrix	NOUN
ejpam-6047	144	39	d	d	NOUN
ejpam-6047	144	40	,	,	PUNCT
ejpam-6047	144	41	all	all	DET
ejpam-6047	144	42	the	the	DET
ejpam-6047	144	43	eigenvalues	eigenvalues	PROPN
ejpam-6047	144	44	λi	λi	INTJ
ejpam-6047	144	45	(	(	PUNCT
ejpam-6047	144	46	da	da	ADJ
ejpam-6047	144	47	+	+	X
ejpam-6047	144	48	atd	atd	NOUN
ejpam-6047	144	49	)	)	PUNCT
ejpam-6047	144	50	<	<	X
ejpam-6047	144	51	0	0	NUM
ejpam-6047	144	52	,	,	PUNCT
ejpam-6047	144	53	∀i	∀i	NOUN
ejpam-6047	144	54	.	.	PUNCT
ejpam-6047	145	1	c2	c2	PROPN
ejpam-6047	145	2	:	:	PUNCT
ejpam-6047	145	3	given	give	VERB
ejpam-6047	145	4	a	a	DET
ejpam-6047	145	5	∈	∈	PROPN
ejpam-6047	145	6	rn	rn	PROPN
ejpam-6047	145	7	,	,	PUNCT
ejpam-6047	145	8	n	n	PRON
ejpam-6047	145	9	is	be	AUX
ejpam-6047	145	10	an	an	DET
ejpam-6047	145	11	a	a	DET
ejpam-6047	145	12	-	-	PUNCT
ejpam-6047	145	13	matrix	matrix	NOUN
ejpam-6047	145	14	,	,	PUNCT
ejpam-6047	145	15	that	that	ADV
ejpam-6047	145	16	is	is	ADV
ejpam-6047	145	17	,	,	PUNCT
ejpam-6047	145	18	all	all	DET
ejpam-6047	145	19	the	the	DET
ejpam-6047	145	20	off	off	ADJ
ejpam-6047	145	21	-	-	PUNCT
ejpam-6047	145	22	diagonal	diagonal	ADJ
ejpam-6047	145	23	entries	entry	NOUN
ejpam-6047	145	24	are	be	AUX
ejpam-6047	145	25	non	non	ADJ
ejpam-6047	145	26	-	-	ADJ
ejpam-6047	145	27	positive	positive	ADJ
ejpam-6047	145	28	and	and	CCONJ
ejpam-6047	145	29	all	all	DET
ejpam-6047	145	30	the	the	DET
ejpam-6047	145	31	principal	principal	ADJ
ejpam-6047	145	32	minors	minor	NOUN
ejpam-6047	145	33	are	be	AUX
ejpam-6047	145	34	positive	positive	ADJ
ejpam-6047	145	35	.	.	PUNCT
ejpam-6047	146	1	c3	c3	NOUN
ejpam-6047	146	2	:	:	PUNCT
ejpam-6047	146	3	there	there	PRON
ejpam-6047	146	4	exists	exist	VERB
ejpam-6047	146	5	a	a	DET
ejpam-6047	146	6	positive	positive	ADJ
ejpam-6047	146	7	diagonal	diagonal	ADJ
ejpam-6047	146	8	matrix	matrix	NOUN
ejpam-6047	146	9	d	d	ADP
ejpam-6047	146	10	such	such	ADJ
ejpam-6047	146	11	that	that	DET
ejpam-6047	146	12	ad	ad	NOUN
ejpam-6047	146	13	=	=	SYM
ejpam-6047	146	14	b	b	NOUN
ejpam-6047	146	15	=	=	SYM
ejpam-6047	146	16	(	(	PUNCT
ejpam-6047	146	17	bij	bij	NOUN
ejpam-6047	146	18	)	)	PUNCT
ejpam-6047	146	19	which	which	PRON
ejpam-6047	146	20	satisfies	satisfy	VERB
ejpam-6047	146	21	the	the	DET
ejpam-6047	146	22	condition	condition	NOUN
ejpam-6047	146	23	that	that	SCONJ
ejpam-6047	146	24	re(bii	re(bii	NOUN
ejpam-6047	146	25	)	)	PUNCT
ejpam-6047	146	26	<	<	X
ejpam-6047	146	27	−	−	PROPN
ejpam-6047	146	28	n∑	n∑	PROPN
ejpam-6047	146	29	1≤j≤n	1≤j≤n	NUM
ejpam-6047	146	30	|bij	|bij	NOUN
ejpam-6047	146	31	|	|	ADV
ejpam-6047	146	32	;	;	PUNCT
ejpam-6047	146	33	1	1	NUM
ejpam-6047	146	34	≤	≤	NUM
ejpam-6047	146	35	i	i	PRON
ejpam-6047	146	36	≤	≤	PROPN
ejpam-6047	146	37	n	n	CCONJ
ejpam-6047	146	38	,	,	PUNCT
ejpam-6047	146	39	j	j	PROPN
ejpam-6047	146	40	̸=	̸=	PROPN
ejpam-6047	146	41	i.	i.	PROPN
ejpam-6047	146	42	m.u	m.u	PROPN
ejpam-6047	146	43	.	.	PROPN
ejpam-6047	147	1	rehman	rehman	PROPN
ejpam-6047	147	2	et	et	PROPN
ejpam-6047	147	3	al	al	PROPN
ejpam-6047	147	4	.	.	PUNCT
ejpam-6047	147	5	/	/	SYM
ejpam-6047	147	6	eur	eur	PROPN
ejpam-6047	147	7	.	.	PUNCT
ejpam-6047	148	1	j.	j.	PROPN
ejpam-6047	148	2	pure	pure	PROPN
ejpam-6047	148	3	appl	appl	PROPN
ejpam-6047	148	4	.	.	PROPN
ejpam-6047	148	5	math	math	PROPN
ejpam-6047	148	6	,	,	PUNCT
ejpam-6047	148	7	18	18	NUM
ejpam-6047	148	8	(	(	PUNCT
ejpam-6047	148	9	3	3	NUM
ejpam-6047	148	10	)	)	PUNCT
ejpam-6047	148	11	(	(	PUNCT
ejpam-6047	148	12	2025	2025	NUM
ejpam-6047	148	13	)	)	PUNCT
ejpam-6047	148	14	,	,	PUNCT
ejpam-6047	148	15	6047	6047	NUM
ejpam-6047	148	16	8	8	NUM
ejpam-6047	148	17	of	of	ADP
ejpam-6047	148	18	33	33	NUM
ejpam-6047	148	19	c4	c4	NOUN
ejpam-6047	148	20	:	:	PUNCT
ejpam-6047	148	21	given	give	VERB
ejpam-6047	148	22	a	a	DET
ejpam-6047	148	23	∈	∈	PROPN
ejpam-6047	148	24	rn	rn	PROPN
ejpam-6047	148	25	,	,	PUNCT
ejpam-6047	148	26	n	n	PRON
ejpam-6047	148	27	is	be	AUX
ejpam-6047	148	28	a	a	DET
ejpam-6047	148	29	sign	sign	NOUN
ejpam-6047	148	30	triangular	triangular	NOUN
ejpam-6047	148	31	matrix	matrix	NOUN
ejpam-6047	148	32	,	,	PUNCT
ejpam-6047	148	33	and	and	CCONJ
ejpam-6047	148	34	aii	aii	X
ejpam-6047	148	35	<	<	X
ejpam-6047	148	36	0	0	NUM
ejpam-6047	148	37	,	,	PUNCT
ejpam-6047	148	38	i	i	PRON
ejpam-6047	148	39	=	=	NOUN
ejpam-6047	148	40	1	1	NUM
ejpam-6047	148	41	:	:	PUNCT
ejpam-6047	148	42	n	n	CCONJ
ejpam-6047	148	43	..	..	PUNCT
ejpam-6047	148	44	c5	c5	PROPN
ejpam-6047	148	45	:	:	PUNCT
ejpam-6047	148	46	given	give	VERB
ejpam-6047	148	47	a	a	DET
ejpam-6047	148	48	∈	∈	PROPN
ejpam-6047	148	49	rn	rn	PROPN
ejpam-6047	148	50	,	,	PUNCT
ejpam-6047	148	51	n	n	PRON
ejpam-6047	148	52	is	be	AUX
ejpam-6047	148	53	a	a	DET
ejpam-6047	148	54	sign	sign	ADJ
ejpam-6047	148	55	stable	stable	ADJ
ejpam-6047	148	56	matrix	matrix	NOUN
ejpam-6047	148	57	without	without	ADP
ejpam-6047	148	58	having	have	VERB
ejpam-6047	148	59	a	a	DET
ejpam-6047	148	60	any	any	PRON
ejpam-6047	148	61	of	of	ADP
ejpam-6047	148	62	non	non	ADJ
ejpam-6047	148	63	-	-	ADJ
ejpam-6047	148	64	zero	zero	NUM
ejpam-6047	148	65	entry	entry	NOUN
ejpam-6047	148	66	.	.	PUNCT
ejpam-6047	149	1	c6	c6	PROPN
ejpam-6047	149	2	:	:	PUNCT
ejpam-6047	149	3	for	for	SCONJ
ejpam-6047	149	4	given	give	VERB
ejpam-6047	149	5	a	a	DET
ejpam-6047	149	6	∈	∈	PROPN
ejpam-6047	149	7	rn	rn	PROPN
ejpam-6047	149	8	,	,	PUNCT
ejpam-6047	149	9	n	n	PRON
ejpam-6047	149	10	is	be	AUX
ejpam-6047	149	11	a	a	DET
ejpam-6047	149	12	jocabi	jocabi	NOUN
ejpam-6047	149	13	matrix	matrix	NOUN
ejpam-6047	149	14	,	,	PUNCT
ejpam-6047	149	15	and	and	CCONJ
ejpam-6047	149	16	each	each	PRON
ejpam-6047	149	17	of	of	ADP
ejpam-6047	149	18	jth	jth	PROPN
ejpam-6047	149	19	-	-	PUNCT
ejpam-6047	149	20	order	order	NOUN
ejpam-6047	149	21	principal	principal	ADJ
ejpam-6047	149	22	minor	minor	ADJ
ejpam-6047	149	23	is	be	AUX
ejpam-6047	149	24	of	of	ADP
ejpam-6047	149	25	sign	sign	NOUN
ejpam-6047	149	26	(	(	PUNCT
ejpam-6047	149	27	−1)j	−1)j	X
ejpam-6047	149	28	.	.	PUNCT
ejpam-6047	150	1	c7	c7	PROPN
ejpam-6047	150	2	:	:	PUNCT
ejpam-6047	150	3	given	give	VERB
ejpam-6047	150	4	a	a	DET
ejpam-6047	150	5	∈	∈	PROPN
ejpam-6047	150	6	rn	rn	PROPN
ejpam-6047	150	7	,	,	PUNCT
ejpam-6047	150	8	n	n	PRON
ejpam-6047	150	9	is	be	AUX
ejpam-6047	150	10	an	an	DET
ejpam-6047	150	11	oscillatory	oscillatory	ADJ
ejpam-6047	150	12	matrix	matrix	NOUN
ejpam-6047	150	13	,	,	PUNCT
ejpam-6047	150	14	that	that	ADV
ejpam-6047	150	15	is	is	ADV
ejpam-6047	150	16	,	,	PUNCT
ejpam-6047	150	17	a	a	PRON
ejpam-6047	150	18	is	be	AUX
ejpam-6047	150	19	totally	totally	ADV
ejpam-6047	150	20	non	non	ADJ
ejpam-6047	150	21	-	-	ADJ
ejpam-6047	150	22	negative	negative	ADJ
ejpam-6047	150	23	matrix	matrix	NOUN
ejpam-6047	150	24	.	.	PUNCT
ejpam-6047	151	1	c8	c8	NOUN
ejpam-6047	151	2	:	:	PUNCT
ejpam-6047	151	3	for	for	ADP
ejpam-6047	151	4	each	each	DET
ejpam-6047	151	5	x	x	SYM
ejpam-6047	151	6	∈	∈	PROPN
ejpam-6047	151	7	rn,1	rn,1	PROPN
ejpam-6047	151	8	,	,	PUNCT
ejpam-6047	151	9	x	x	X
ejpam-6047	151	10	̸=	̸=	PROPN
ejpam-6047	151	11	0	0	NUM
ejpam-6047	151	12	,	,	PUNCT
ejpam-6047	151	13	there	there	PRON
ejpam-6047	151	14	exists	exist	VERB
ejpam-6047	151	15	a	a	DET
ejpam-6047	151	16	positive	positive	ADJ
ejpam-6047	151	17	diagonal	diagonal	ADJ
ejpam-6047	151	18	matrix	matrix	NOUN
ejpam-6047	151	19	d	d	SCONJ
ejpam-6047	151	20	such	such	ADJ
ejpam-6047	151	21	that	that	DET
ejpam-6047	151	22	real	real	ADJ
ejpam-6047	151	23	part	part	NOUN
ejpam-6047	151	24	of	of	ADP
ejpam-6047	151	25	xtdax	xtdax	PROPN
ejpam-6047	151	26	is	be	AUX
ejpam-6047	151	27	strictly	strictly	ADV
ejpam-6047	151	28	positive	positive	ADJ
ejpam-6047	151	29	.	.	PUNCT
ejpam-6047	152	1	c9	c9	NOUN
ejpam-6047	152	2	:	:	PUNCT
ejpam-6047	152	3	for	for	SCONJ
ejpam-6047	152	4	given	give	VERB
ejpam-6047	152	5	a	a	DET
ejpam-6047	152	6	∈	∈	PROPN
ejpam-6047	152	7	rn	rn	PROPN
ejpam-6047	152	8	,	,	PUNCT
ejpam-6047	152	9	n	n	CCONJ
ejpam-6047	152	10	,	,	PUNCT
ejpam-6047	152	11	the	the	DET
ejpam-6047	152	12	hadamard	hadamard	ADJ
ejpam-6047	152	13	product	product	NOUN
ejpam-6047	152	14	(	(	PUNCT
ejpam-6047	152	15	h	h	NOUN
ejpam-6047	152	16	◦	◦	NOUN
ejpam-6047	152	17	(	(	PUNCT
ejpam-6047	152	18	a	a	DET
ejpam-6047	152	19	+	+	NOUN
ejpam-6047	152	20	g	g	NOUN
ejpam-6047	152	21	)	)	PUNCT
ejpam-6047	152	22	)	)	PUNCT
ejpam-6047	152	23	is	be	AUX
ejpam-6047	152	24	schur	schur	ADJ
ejpam-6047	152	25	stable	stable	ADJ
ejpam-6047	152	26	matrix	matrix	NOUN
ejpam-6047	152	27	for	for	ADP
ejpam-6047	152	28	each	each	DET
ejpam-6047	152	29	positive	positive	ADJ
ejpam-6047	152	30	definite	definite	ADJ
ejpam-6047	152	31	symmetric	symmetric	ADJ
ejpam-6047	152	32	matrix	matrix	NOUN
ejpam-6047	152	33	h	h	NOUN
ejpam-6047	152	34	,	,	PUNCT
ejpam-6047	152	35	and	and	CCONJ
ejpam-6047	152	36	a	a	DET
ejpam-6047	152	37	perturbation	perturbation	NOUN
ejpam-6047	152	38	matrix	matrix	NOUN
ejpam-6047	152	39	g	g	ADP
ejpam-6047	152	40	such	such	ADJ
ejpam-6047	152	41	that	that	DET
ejpam-6047	152	42	||g||2	||g||2	PROPN
ejpam-6047	152	43	<	<	X
ejpam-6047	152	44	α	α	PROPN
ejpam-6047	152	45	,	,	PUNCT
ejpam-6047	152	46	α	α	PROPN
ejpam-6047	152	47	∈	∈	PROPN
ejpam-6047	152	48	r.	r.	PROPN
ejpam-6047	152	49	c10	c10	VERB
ejpam-6047	152	50	:	:	PUNCT
ejpam-6047	152	51	for	for	SCONJ
ejpam-6047	152	52	given	give	VERB
ejpam-6047	152	53	a	a	DET
ejpam-6047	152	54	∈	∈	PROPN
ejpam-6047	152	55	rn	rn	PROPN
ejpam-6047	152	56	,	,	PUNCT
ejpam-6047	152	57	n	n	PRON
ejpam-6047	152	58	each	each	DET
ejpam-6047	152	59	jth	jth	PROPN
ejpam-6047	152	60	-	-	PUNCT
ejpam-6047	152	61	order	order	NOUN
ejpam-6047	152	62	principal	principal	ADJ
ejpam-6047	152	63	minor	minor	ADJ
ejpam-6047	152	64	is	be	AUX
ejpam-6047	152	65	of	of	ADP
ejpam-6047	152	66	sign	sign	NOUN
ejpam-6047	152	67	(	(	PUNCT
ejpam-6047	152	68	−1)j	−1)j	X
ejpam-6047	152	69	.	.	PUNCT
ejpam-6047	153	1	c11	c11	NOUN
ejpam-6047	153	2	:	:	PUNCT
ejpam-6047	153	3	given	give	VERB
ejpam-6047	153	4	a	a	DET
ejpam-6047	153	5	∈	∈	PROPN
ejpam-6047	153	6	r2,2	r2,2	PROPN
ejpam-6047	153	7	is	be	AUX
ejpam-6047	153	8	strongly	strongly	ADV
ejpam-6047	153	9	d	d	ADJ
ejpam-6047	153	10	-	-	ADJ
ejpam-6047	153	11	stable	stable	ADJ
ejpam-6047	153	12	iff	iff	NOUN
ejpam-6047	153	13	its	its	PRON
ejpam-6047	153	14	jth	jth	PROPN
ejpam-6047	153	15	-	-	PUNCT
ejpam-6047	153	16	order	order	NOUN
ejpam-6047	153	17	principal	principal	ADJ
ejpam-6047	153	18	minors	minor	NOUN
ejpam-6047	153	19	are	be	AUX
ejpam-6047	153	20	of	of	ADP
ejpam-6047	153	21	sign	sign	NOUN
ejpam-6047	153	22	(	(	PUNCT
ejpam-6047	153	23	−1)j	−1)j	X
ejpam-6047	153	24	.	.	PUNCT
ejpam-6047	154	1	c12	c12	PROPN
ejpam-6047	154	2	:	:	PUNCT
ejpam-6047	154	3	given	give	VERB
ejpam-6047	154	4	a	a	DET
ejpam-6047	154	5	∈	∈	PROPN
ejpam-6047	154	6	r3,3	r3,3	NOUN
ejpam-6047	154	7	with	with	ADP
ejpam-6047	154	8	all	all	PRON
ejpam-6047	154	9	of	of	ADP
ejpam-6047	154	10	its	its	PRON
ejpam-6047	154	11	jth	jth	ADJ
ejpam-6047	154	12	-	-	PUNCT
ejpam-6047	154	13	order	order	NOUN
ejpam-6047	154	14	principal	principal	ADJ
ejpam-6047	154	15	minors	minor	NOUN
ejpam-6047	154	16	are	be	AUX
ejpam-6047	154	17	with	with	ADP
ejpam-6047	154	18	sign	sign	NOUN
ejpam-6047	154	19	(	(	PUNCT
ejpam-6047	154	20	−1)j	−1)j	X
ejpam-6047	154	21	,	,	PUNCT
ejpam-6047	154	22	and	and	CCONJ
ejpam-6047	154	23	a11a22a33	a11a22a33	VERB
ejpam-6047	154	24	<	<	X
ejpam-6047	154	25	a12a23a31	a12a23a31	X
ejpam-6047	154	26	+	+	PUNCT
ejpam-6047	154	27	a21a32a13	a21a32a13	PROPN
ejpam-6047	154	28	2	2	NUM
ejpam-6047	154	29	.	.	PUNCT
ejpam-6047	155	1	c13	c13	NOUN
ejpam-6047	155	2	:	:	PUNCT
ejpam-6047	155	3	given	give	VERB
ejpam-6047	155	4	given	give	VERB
ejpam-6047	155	5	a	a	DET
ejpam-6047	155	6	∈	∈	PROPN
ejpam-6047	155	7	rn	rn	PROPN
ejpam-6047	155	8	,	,	PUNCT
ejpam-6047	155	9	n	n	PRON
ejpam-6047	155	10	is	be	AUX
ejpam-6047	155	11	strongly	strongly	ADV
ejpam-6047	155	12	d	d	ADJ
ejpam-6047	155	13	-	-	ADJ
ejpam-6047	155	14	stable	stable	ADJ
ejpam-6047	155	15	matrix	matrix	NOUN
ejpam-6047	155	16	if	if	SCONJ
ejpam-6047	155	17	for	for	ADP
ejpam-6047	155	18	n	n	DET
ejpam-6047	155	19	≤	≤	NUM
ejpam-6047	155	20	4	4	NUM
ejpam-6047	155	21	,	,	PUNCT
ejpam-6047	155	22	and	and	CCONJ
ejpam-6047	155	23	a	a	DET
ejpam-6047	155	24	satisfies	satisfie	NOUN
ejpam-6047	155	25	gkk	gkk	PROPN
ejpam-6047	155	26	condition	condition	NOUN
ejpam-6047	155	27	.	.	PUNCT
ejpam-6047	156	1	3	3	X
ejpam-6047	156	2	.	.	X
ejpam-6047	156	3	metzler	metzler	NOUN
ejpam-6047	156	4	matrices	matrix	NOUN
ejpam-6047	156	5	and	and	CCONJ
ejpam-6047	156	6	their	their	PRON
ejpam-6047	156	7	spectrum	spectrum	NOUN
ejpam-6047	156	8	in	in	ADP
ejpam-6047	156	9	this	this	DET
ejpam-6047	156	10	section	section	NOUN
ejpam-6047	156	11	,	,	PUNCT
ejpam-6047	156	12	we	we	PRON
ejpam-6047	156	13	provide	provide	VERB
ejpam-6047	156	14	an	an	DET
ejpam-6047	156	15	overview	overview	NOUN
ejpam-6047	156	16	of	of	ADP
ejpam-6047	156	17	metzler	metzler	NOUN
ejpam-6047	156	18	matrices	matrix	NOUN
ejpam-6047	156	19	and	and	CCONJ
ejpam-6047	156	20	their	their	PRON
ejpam-6047	156	21	spectral	spectral	ADJ
ejpam-6047	156	22	properties	property	NOUN
ejpam-6047	156	23	,	,	PUNCT
ejpam-6047	156	24	specifically	specifically	ADV
ejpam-6047	156	25	the	the	DET
ejpam-6047	156	26	set	set	NOUN
ejpam-6047	156	27	of	of	ADP
ejpam-6047	156	28	eigenvalues	eigenvalue	NOUN
ejpam-6047	156	29	.	.	PUNCT
ejpam-6047	157	1	metzler	metzler	NOUN
ejpam-6047	157	2	matrices	matrix	NOUN
ejpam-6047	157	3	are	be	AUX
ejpam-6047	157	4	fundamentally	fundamentally	ADV
ejpam-6047	157	5	linked	link	VERB
ejpam-6047	157	6	to	to	ADP
ejpam-6047	157	7	the	the	DET
ejpam-6047	157	8	study	study	NOUN
ejpam-6047	157	9	and	and	CCONJ
ejpam-6047	157	10	analysis	analysis	NOUN
ejpam-6047	157	11	of	of	ADP
ejpam-6047	157	12	continuous	continuous	ADJ
ejpam-6047	157	13	-	-	PUNCT
ejpam-6047	157	14	time	time	NOUN
ejpam-6047	157	15	linear	linear	PROPN
ejpam-6047	157	16	systems	system	NOUN
ejpam-6047	157	17	.	.	PUNCT
ejpam-6047	158	1	the	the	DET
ejpam-6047	158	2	spectrum	spectrum	NOUN
ejpam-6047	158	3	of	of	ADP
ejpam-6047	158	4	a	a	DET
ejpam-6047	158	5	metzler	metzler	NOUN
ejpam-6047	158	6	matrix	matrix	NOUN
ejpam-6047	158	7	can	can	AUX
ejpam-6047	158	8	be	be	AUX
ejpam-6047	158	9	determined	determine	VERB
ejpam-6047	158	10	by	by	ADP
ejpam-6047	158	11	shifting	shift	VERB
ejpam-6047	158	12	the	the	DET
ejpam-6047	158	13	spectrum	spectrum	NOUN
ejpam-6047	158	14	of	of	ADP
ejpam-6047	158	15	a	a	DET
ejpam-6047	158	16	non	non	ADJ
ejpam-6047	158	17	-	-	ADJ
ejpam-6047	158	18	negative	negative	ADJ
ejpam-6047	158	19	matrix	matrix	NOUN
ejpam-6047	158	20	by	by	ADP
ejpam-6047	158	21	αin	αin	NOUN
ejpam-6047	158	22	,	,	PUNCT
ejpam-6047	158	23	where	where	SCONJ
ejpam-6047	158	24	in	in	ADP
ejpam-6047	158	25	represents	represent	VERB
ejpam-6047	158	26	the	the	DET
ejpam-6047	158	27	n	n	ADV
ejpam-6047	158	28	-	-	PUNCT
ejpam-6047	158	29	dimensional	dimensional	ADJ
ejpam-6047	158	30	identity	identity	NOUN
ejpam-6047	158	31	matrix	matrix	NOUN
ejpam-6047	158	32	,	,	PUNCT
ejpam-6047	158	33	as	as	SCONJ
ejpam-6047	158	34	noted	note	VERB
ejpam-6047	158	35	in	in	ADP
ejpam-6047	158	36	[	[	X
ejpam-6047	158	37	51	51	NUM
ejpam-6047	158	38	]	]	PUNCT
ejpam-6047	158	39	.	.	PUNCT
ejpam-6047	159	1	it	it	PRON
ejpam-6047	159	2	is	be	AUX
ejpam-6047	159	3	well	well	ADV
ejpam-6047	159	4	established	establish	VERB
ejpam-6047	159	5	that	that	SCONJ
ejpam-6047	159	6	the	the	DET
ejpam-6047	159	7	spectrum	spectrum	NOUN
ejpam-6047	159	8	of	of	ADP
ejpam-6047	159	9	a	a	DET
ejpam-6047	159	10	positive	positive	ADJ
ejpam-6047	159	11	matrix	matrix	NOUN
ejpam-6047	159	12	is	be	AUX
ejpam-6047	159	13	positive	positive	ADJ
ejpam-6047	159	14	and	and	CCONJ
ejpam-6047	159	15	corresponds	correspond	VERB
ejpam-6047	159	16	exactly	exactly	ADV
ejpam-6047	159	17	to	to	ADP
ejpam-6047	159	18	its	its	PRON
ejpam-6047	159	19	spectral	spectral	ADJ
ejpam-6047	159	20	radius	radius	NOUN
ejpam-6047	159	21	ρ	ρ	PROPN
ejpam-6047	159	22	,	,	PUNCT
ejpam-6047	159	23	see	see	VERB
ejpam-6047	159	24	[	[	X
ejpam-6047	159	25	52	52	NUM
ejpam-6047	159	26	]	]	PUNCT
ejpam-6047	159	27	.	.	PUNCT
ejpam-6047	160	1	moreover	moreover	ADV
ejpam-6047	160	2	,	,	PUNCT
ejpam-6047	160	3	as	as	SCONJ
ejpam-6047	160	4	demonstrated	demonstrate	VERB
ejpam-6047	160	5	in	in	ADP
ejpam-6047	160	6	[	[	X
ejpam-6047	160	7	53	53	NUM
ejpam-6047	160	8	]	]	PUNCT
ejpam-6047	160	9	,	,	PUNCT
ejpam-6047	160	10	the	the	DET
ejpam-6047	160	11	spectrum	spectrum	NOUN
ejpam-6047	160	12	of	of	ADP
ejpam-6047	160	13	a	a	DET
ejpam-6047	160	14	non	non	ADJ
ejpam-6047	160	15	-	-	ADJ
ejpam-6047	160	16	negative	negative	ADJ
ejpam-6047	160	17	matrix	matrix	NOUN
ejpam-6047	160	18	is	be	AUX
ejpam-6047	160	19	confined	confine	VERB
ejpam-6047	160	20	to	to	ADP
ejpam-6047	160	21	specific	specific	ADJ
ejpam-6047	160	22	regions	region	NOUN
ejpam-6047	160	23	within	within	ADP
ejpam-6047	160	24	the	the	DET
ejpam-6047	160	25	complex	complex	ADJ
ejpam-6047	160	26	plane	plane	NOUN
ejpam-6047	160	27	.	.	PUNCT
ejpam-6047	161	1	these	these	DET
ejpam-6047	161	2	regions	region	NOUN
ejpam-6047	161	3	,	,	PUNCT
ejpam-6047	161	4	referred	refer	VERB
ejpam-6047	161	5	to	to	ADP
ejpam-6047	161	6	as	as	ADP
ejpam-6047	161	7	kerpelevich	kerpelevich	PROPN
ejpam-6047	161	8	regions	region	NOUN
ejpam-6047	161	9	,	,	PUNCT
ejpam-6047	161	10	define	define	VERB
ejpam-6047	161	11	the	the	DET
ejpam-6047	161	12	spectral	spectral	ADJ
ejpam-6047	161	13	behavior	behavior	NOUN
ejpam-6047	161	14	of	of	ADP
ejpam-6047	161	15	such	such	ADJ
ejpam-6047	161	16	matrices	matrix	NOUN
ejpam-6047	161	17	.	.	PUNCT
ejpam-6047	162	1	in	in	ADP
ejpam-6047	162	2	[	[	X
ejpam-6047	162	3	45	45	NUM
ejpam-6047	162	4	]	]	PUNCT
ejpam-6047	162	5	,	,	PUNCT
ejpam-6047	162	6	the	the	DET
ejpam-6047	162	7	metzler	metzler	NOUN
ejpam-6047	162	8	matrix	matrix	NOUN
ejpam-6047	162	9	spectrum	spectrum	NOUN
ejpam-6047	162	10	has	have	AUX
ejpam-6047	162	11	been	be	AUX
ejpam-6047	162	12	proven	prove	VERB
ejpam-6047	162	13	to	to	PART
ejpam-6047	162	14	reside	reside	VERB
ejpam-6047	162	15	within	within	ADP
ejpam-6047	162	16	the	the	DET
ejpam-6047	162	17	kerpelevich	kerpelevich	PROPN
ejpam-6047	162	18	region	region	NOUN
ejpam-6047	162	19	,	,	PUNCT
ejpam-6047	162	20	shaped	shape	VERB
ejpam-6047	162	21	like	like	ADP
ejpam-6047	162	22	a	a	DET
ejpam-6047	162	23	cone	cone	NOUN
ejpam-6047	162	24	in	in	ADP
ejpam-6047	162	25	the	the	DET
ejpam-6047	162	26	complex	complex	ADJ
ejpam-6047	162	27	plane	plane	NOUN
ejpam-6047	162	28	.	.	PUNCT
ejpam-6047	163	1	additionally	additionally	ADV
ejpam-6047	163	2	,	,	PUNCT
ejpam-6047	163	3	it	it	PRON
ejpam-6047	163	4	has	have	AUX
ejpam-6047	163	5	been	be	AUX
ejpam-6047	163	6	demonstrated	demonstrate	VERB
ejpam-6047	163	7	that	that	SCONJ
ejpam-6047	163	8	for	for	ADP
ejpam-6047	163	9	3	3	NUM
ejpam-6047	163	10	×	×	NOUN
ejpam-6047	163	11	3	3	NUM
ejpam-6047	163	12	matrices	matrix	NOUN
ejpam-6047	163	13	,	,	PUNCT
ejpam-6047	163	14	both	both	CCONJ
ejpam-6047	163	15	necessary	necessary	ADJ
ejpam-6047	163	16	and	and	CCONJ
ejpam-6047	163	17	sufficient	sufficient	ADJ
ejpam-6047	163	18	conditions	condition	NOUN
ejpam-6047	163	19	for	for	ADP
ejpam-6047	163	20	the	the	DET
ejpam-6047	163	21	spectrum	spectrum	NOUN
ejpam-6047	163	22	of	of	ADP
ejpam-6047	163	23	metzler	metzler	NOUN
ejpam-6047	163	24	matrices	matrix	NOUN
ejpam-6047	163	25	are	be	AUX
ejpam-6047	163	26	established	establish	VERB
ejpam-6047	163	27	.	.	PUNCT
ejpam-6047	164	1	metzler	metzler	NOUN
ejpam-6047	164	2	matrices	matrix	NOUN
ejpam-6047	164	3	share	share	VERB
ejpam-6047	164	4	a	a	DET
ejpam-6047	164	5	strong	strong	ADJ
ejpam-6047	164	6	connection	connection	NOUN
ejpam-6047	164	7	with	with	ADP
ejpam-6047	164	8	positive	positive	ADJ
ejpam-6047	164	9	matrices	matrix	NOUN
ejpam-6047	164	10	,	,	PUNCT
ejpam-6047	164	11	particularly	particularly	ADV
ejpam-6047	164	12	in	in	ADP
ejpam-6047	164	13	the	the	DET
ejpam-6047	164	14	context	context	NOUN
ejpam-6047	164	15	of	of	ADP
ejpam-6047	164	16	analyzing	analyze	VERB
ejpam-6047	164	17	linear	linear	ADJ
ejpam-6047	164	18	time	time	NOUN
ejpam-6047	164	19	-	-	PUNCT
ejpam-6047	164	20	invariant	invariant	ADJ
ejpam-6047	164	21	systems	system	NOUN
ejpam-6047	164	22	.	.	PUNCT
ejpam-6047	165	1	in	in	ADP
ejpam-6047	165	2	[	[	X
ejpam-6047	165	3	45	45	NUM
ejpam-6047	165	4	]	]	PUNCT
ejpam-6047	165	5	,	,	PUNCT
ejpam-6047	165	6	following	follow	VERB
ejpam-6047	165	7	dynamical	dynamical	ADJ
ejpam-6047	165	8	system	system	NOUN
ejpam-6047	165	9	was	be	AUX
ejpam-6047	165	10	considered	consider	VERB
ejpam-6047	165	11	for	for	ADP
ejpam-6047	165	12	a	a	DET
ejpam-6047	165	13	demonstration.	demonstration.	NOUN
ejpam-6047	165	14	dx(t	dx(t	NOUN
ejpam-6047	165	15	)	)	PUNCT
ejpam-6047	165	16	dt	dt	NOUN
ejpam-6047	165	17	=	=	SYM
ejpam-6047	165	18	ax(t	ax(t	NUM
ejpam-6047	165	19	)	)	PUNCT
ejpam-6047	165	20	x(0	x(0	PROPN
ejpam-6047	165	21	)	)	PUNCT
ejpam-6047	166	1	=	=	PUNCT
ejpam-6047	166	2	x0	x0	PUNCT
ejpam-6047	166	3	x	x	X
ejpam-6047	166	4	∈	∈	PROPN
ejpam-6047	166	5	rn,1	rn,1	PROPN
ejpam-6047	166	6	,	,	PUNCT
ejpam-6047	166	7	a	a	DET
ejpam-6047	166	8	∈	∈	PROPN
ejpam-6047	166	9	rn	rn	PROPN
ejpam-6047	166	10	,	,	PUNCT
ejpam-6047	166	11	n.	n.	PROPN
ejpam-6047	166	12	m.u	m.u	PROPN
ejpam-6047	166	13	.	.	PROPN
ejpam-6047	167	1	rehman	rehman	PROPN
ejpam-6047	167	2	et	et	PROPN
ejpam-6047	167	3	al	al	PROPN
ejpam-6047	167	4	.	.	PUNCT
ejpam-6047	167	5	/	/	SYM
ejpam-6047	167	6	eur	eur	PROPN
ejpam-6047	167	7	.	.	PUNCT
ejpam-6047	168	1	j.	j.	PROPN
ejpam-6047	168	2	pure	pure	PROPN
ejpam-6047	168	3	appl	appl	PROPN
ejpam-6047	168	4	.	.	PROPN
ejpam-6047	168	5	math	math	PROPN
ejpam-6047	168	6	,	,	PUNCT
ejpam-6047	168	7	18	18	NUM
ejpam-6047	168	8	(	(	PUNCT
ejpam-6047	168	9	3	3	NUM
ejpam-6047	168	10	)	)	PUNCT
ejpam-6047	168	11	(	(	PUNCT
ejpam-6047	168	12	2025	2025	NUM
ejpam-6047	168	13	)	)	PUNCT
ejpam-6047	168	14	,	,	PUNCT
ejpam-6047	168	15	6047	6047	NUM
ejpam-6047	168	16	9	9	NUM
ejpam-6047	168	17	of	of	ADP
ejpam-6047	168	18	33	33	NUM
ejpam-6047	168	19	lemma	lemma	PROPN
ejpam-6047	168	20	2	2	NUM
ejpam-6047	168	21	.	.	PUNCT
ejpam-6047	169	1	[	[	X
ejpam-6047	169	2	45	45	NUM
ejpam-6047	169	3	]	]	PUNCT
ejpam-6047	169	4	the	the	DET
ejpam-6047	169	5	dynamical	dynamical	ADJ
ejpam-6047	169	6	system	system	NOUN
ejpam-6047	169	7	(	(	PUNCT
ejpam-6047	169	8	given	give	VERB
ejpam-6047	169	9	as	as	ADP
ejpam-6047	169	10	above	above	ADJ
ejpam-6047	169	11	)	)	PUNCT
ejpam-6047	169	12	is	be	AUX
ejpam-6047	169	13	positive	positive	ADJ
ejpam-6047	169	14	iff	iff	NOUN
ejpam-6047	169	15	a	a	PRON
ejpam-6047	169	16	is	be	AUX
ejpam-6047	169	17	a	a	DET
ejpam-6047	169	18	non	non	ADJ
ejpam-6047	169	19	-	-	ADJ
ejpam-6047	169	20	negative	negative	ADJ
ejpam-6047	169	21	matrix	matrix	NOUN
ejpam-6047	169	22	,	,	PUNCT
ejpam-6047	169	23	and	and	CCONJ
ejpam-6047	169	24	for	for	ADP
ejpam-6047	169	25	all	all	DET
ejpam-6047	169	26	t	t	PROPN
ejpam-6047	169	27	≥	≥	NOUN
ejpam-6047	169	28	0	0	NUM
ejpam-6047	169	29	,	,	PUNCT
ejpam-6047	169	30	the	the	DET
ejpam-6047	169	31	matrix	matrix	NOUN
ejpam-6047	169	32	eat	eat	NOUN
ejpam-6047	169	33	is	be	AUX
ejpam-6047	169	34	non	non	ADJ
ejpam-6047	169	35	-	-	ADJ
ejpam-6047	169	36	negative	negative	ADJ
ejpam-6047	169	37	.	.	PUNCT
ejpam-6047	170	1	lemma	lemma	PROPN
ejpam-6047	170	2	3	3	X
ejpam-6047	170	3	.	.	PUNCT
ejpam-6047	171	1	[	[	X
ejpam-6047	171	2	45	45	NUM
ejpam-6047	171	3	]	]	PUNCT
ejpam-6047	171	4	for	for	ADP
ejpam-6047	171	5	a	a	DET
ejpam-6047	171	6	∈	∈	PROPN
ejpam-6047	171	7	rn	rn	PROPN
ejpam-6047	171	8	,	,	PUNCT
ejpam-6047	171	9	n	n	CCONJ
ejpam-6047	171	10	,	,	PUNCT
ejpam-6047	171	11	the	the	DET
ejpam-6047	171	12	following	following	ADJ
ejpam-6047	171	13	statements	statement	NOUN
ejpam-6047	171	14	are	be	AUX
ejpam-6047	171	15	equivalent	equivalent	ADJ
ejpam-6047	171	16	:	:	PUNCT
ejpam-6047	171	17	(	(	PUNCT
ejpam-6047	171	18	i	i	NOUN
ejpam-6047	171	19	)	)	PUNCT
ejpam-6047	171	20	eat	eat	VERB
ejpam-6047	171	21	≥	≥	NOUN
ejpam-6047	171	22	0	0	NUM
ejpam-6047	171	23	,	,	PUNCT
ejpam-6047	171	24	∀	∀	X
ejpam-6047	171	25	t	t	NOUN
ejpam-6047	171	26	≥	≥	NOUN
ejpam-6047	171	27	0	0	NUM
ejpam-6047	171	28	.	.	PUNCT
ejpam-6047	172	1	(	(	PUNCT
ejpam-6047	172	2	ii	ii	NOUN
ejpam-6047	172	3	)	)	PUNCT
ejpam-6047	172	4	the	the	DET
ejpam-6047	172	5	matrix	matrix	NOUN
ejpam-6047	172	6	a	a	PRON
ejpam-6047	172	7	is	be	AUX
ejpam-6047	172	8	metzler	metzler	NOUN
ejpam-6047	172	9	matrix	matrix	NOUN
ejpam-6047	172	10	.	.	PUNCT
ejpam-6047	173	1	remark	remark	NOUN
ejpam-6047	173	2	7	7	NUM
ejpam-6047	173	3	.	.	PUNCT
ejpam-6047	174	1	the	the	DET
ejpam-6047	174	2	metzler	metzler	PROPN
ejpam-6047	174	3	matrtix	matrtix	NOUN
ejpam-6047	174	4	a	a	DET
ejpam-6047	174	5	∈	∈	PROPN
ejpam-6047	174	6	rn	rn	PROPN
ejpam-6047	174	7	,	,	PUNCT
ejpam-6047	174	8	n	n	PRON
ejpam-6047	174	9	can	can	AUX
ejpam-6047	174	10	be	be	AUX
ejpam-6047	174	11	expressed	express	VERB
ejpam-6047	174	12	as	as	ADP
ejpam-6047	174	13	the	the	DET
ejpam-6047	174	14	sum	sum	NOUN
ejpam-6047	174	15	of	of	ADP
ejpam-6047	174	16	a	a	DET
ejpam-6047	174	17	non	non	ADJ
ejpam-6047	174	18	-	-	ADJ
ejpam-6047	174	19	negative	negative	ADJ
ejpam-6047	174	20	matrix	matrix	NOUN
ejpam-6047	174	21	n	n	NOUN
ejpam-6047	174	22	,	,	PUNCT
ejpam-6047	174	23	and	and	CCONJ
ejpam-6047	174	24	αin	αin	NOUN
ejpam-6047	174	25	,	,	PUNCT
ejpam-6047	174	26	where	where	SCONJ
ejpam-6047	174	27	arbitrary	arbitrary	ADJ
ejpam-6047	174	28	number	number	NOUN
ejpam-6047	174	29	α	α	NOUN
ejpam-6047	174	30	∈	∈	NOUN
ejpam-6047	174	31	r	r	NOUN
ejpam-6047	174	32	satisfies	satisfy	VERB
ejpam-6047	174	33	α	α	PROPN
ejpam-6047	174	34	≥	≥	NUM
ejpam-6047	174	35	diag(n	diag(n	NOUN
ejpam-6047	174	36	)	)	PUNCT
ejpam-6047	174	37	.	.	PUNCT
ejpam-6047	175	1	for	for	ADP
ejpam-6047	175	2	sr	sr	PROPN
ejpam-6047	175	3	n	n	PROPN
ejpam-6047	175	4	:	:	PUNCT
ejpam-6047	175	5	=	=	SYM
ejpam-6047	175	6	{	{	PUNCT
ejpam-6047	175	7	λ	λ	X
ejpam-6047	175	8	∈	∈	NOUN
ejpam-6047	175	9	c	c	NOUN
ejpam-6047	175	10	such	such	ADJ
ejpam-6047	175	11	that	that	SCONJ
ejpam-6047	175	12	∃	∃	PROPN
ejpam-6047	175	13	n	n	PROPN
ejpam-6047	175	14	∈	∈	PROPN
ejpam-6047	175	15	rn	rn	PROPN
ejpam-6047	175	16	,	,	PUNCT
ejpam-6047	175	17	n	n	CCONJ
ejpam-6047	175	18	,	,	PUNCT
ejpam-6047	175	19	λ	λ	PROPN
ejpam-6047	175	20	∈	∈	PROPN
ejpam-6047	175	21	σ(n	σ(n	PROPN
ejpam-6047	175	22	)	)	PUNCT
ejpam-6047	175	23	,	,	PUNCT
ejpam-6047	175	24	n	n	PRON
ejpam-6047	175	25	≥	≥	NOUN
ejpam-6047	175	26	0	0	NUM
ejpam-6047	175	27	,	,	PUNCT
ejpam-6047	175	28	ρ(n	ρ(n	PROPN
ejpam-6047	175	29	)	)	PUNCT
ejpam-6047	176	1	=	=	SYM
ejpam-6047	176	2	r	r	X
ejpam-6047	176	3	}	}	PUNCT
ejpam-6047	176	4	,	,	PUNCT
ejpam-6047	176	5	one	one	PRON
ejpam-6047	176	6	may	may	AUX
ejpam-6047	176	7	easily	easily	ADV
ejpam-6047	176	8	find	find	VERB
ejpam-6047	176	9	that	that	SCONJ
ejpam-6047	176	10	the	the	DET
ejpam-6047	176	11	set	set	NOUN
ejpam-6047	176	12	sr	sr	PROPN
ejpam-6047	176	13	n	n	PRON
ejpam-6047	176	14	can	can	AUX
ejpam-6047	176	15	be	be	AUX
ejpam-6047	176	16	obtained	obtain	VERB
ejpam-6047	176	17	by	by	ADP
ejpam-6047	176	18	the	the	DET
ejpam-6047	176	19	following	follow	VERB
ejpam-6047	176	20	theorem	theorem	ADJ
ejpam-6047	176	21	2	2	NUM
ejpam-6047	176	22	.	.	PUNCT
ejpam-6047	176	23	theorem	theorem	NOUN
ejpam-6047	176	24	2	2	NUM
ejpam-6047	176	25	.	.	PUNCT
ejpam-6047	177	1	[	[	X
ejpam-6047	177	2	45	45	NUM
ejpam-6047	177	3	]	]	PUNCT
ejpam-6047	177	4	the	the	DET
ejpam-6047	177	5	set	set	NOUN
ejpam-6047	177	6	sr	sr	PROPN
ejpam-6047	177	7	n	n	AUX
ejpam-6047	177	8	is	be	AUX
ejpam-6047	177	9	characterized	characterize	VERB
ejpam-6047	177	10	as	as	ADP
ejpam-6047	177	11	:	:	PUNCT
ejpam-6047	177	12	(	(	PUNCT
ejpam-6047	177	13	i	i	NOUN
ejpam-6047	177	14	)	)	PUNCT
ejpam-6047	177	15	the	the	DET
ejpam-6047	177	16	set	set	NOUN
ejpam-6047	177	17	sr	sr	PROPN
ejpam-6047	177	18	n	n	VERB
ejpam-6047	177	19	is	be	AUX
ejpam-6047	177	20	in	in	ADP
ejpam-6047	177	21	a	a	DET
ejpam-6047	177	22	unit	unit	NOUN
ejpam-6047	177	23	disk	disk	NOUN
ejpam-6047	177	24	of	of	ADP
ejpam-6047	177	25	complex	complex	ADJ
ejpam-6047	177	26	plane	plane	NOUN
ejpam-6047	177	27	,	,	PUNCT
ejpam-6047	177	28	and	and	CCONJ
ejpam-6047	177	29	it	it	PRON
ejpam-6047	177	30	’s	’	VERB
ejpam-6047	177	31	spectrum	spectrum	NOUN
ejpam-6047	177	32	is	be	AUX
ejpam-6047	177	33	symmetric	symmetric	ADJ
ejpam-6047	177	34	about	about	ADP
ejpam-6047	177	35	real	real	ADJ
ejpam-6047	177	36	-	-	PUNCT
ejpam-6047	177	37	axis	axis	NOUN
ejpam-6047	177	38	.	.	PUNCT
ejpam-6047	178	1	(	(	PUNCT
ejpam-6047	178	2	ii	ii	NOUN
ejpam-6047	178	3	)	)	PUNCT
ejpam-6047	178	4	the	the	DET
ejpam-6047	178	5	set	set	NOUN
ejpam-6047	178	6	sr	sr	PROPN
ejpam-6047	178	7	n	n	PRON
ejpam-6047	178	8	may	may	AUX
ejpam-6047	178	9	intersect	intersect	VERB
ejpam-6047	178	10	the	the	DET
ejpam-6047	178	11	unit	unit	NOUN
ejpam-6047	178	12	circle	circle	NOUN
ejpam-6047	178	13	in	in	ADP
ejpam-6047	178	14	a	a	DET
ejpam-6047	178	15	finite	finite	ADJ
ejpam-6047	178	16	number	number	NOUN
ejpam-6047	178	17	of	of	ADP
ejpam-6047	178	18	vertices	vertex	NOUN
ejpam-6047	178	19	.	.	PUNCT
ejpam-6047	179	1	4	4	X
ejpam-6047	179	2	.	.	X
ejpam-6047	179	3	new	new	ADJ
ejpam-6047	179	4	results	result	NOUN
ejpam-6047	179	5	in	in	ADP
ejpam-6047	179	6	this	this	DET
ejpam-6047	179	7	section	section	NOUN
ejpam-6047	179	8	,	,	PUNCT
ejpam-6047	179	9	we	we	PRON
ejpam-6047	179	10	provide	provide	VERB
ejpam-6047	179	11	recent	recent	ADJ
ejpam-6047	179	12	findings	finding	NOUN
ejpam-6047	179	13	on	on	ADP
ejpam-6047	179	14	the	the	DET
ejpam-6047	179	15	stability	stability	NOUN
ejpam-6047	179	16	,	,	PUNCT
ejpam-6047	179	17	d	d	NOUN
ejpam-6047	179	18	-	-	PUNCT
ejpam-6047	179	19	stability	stability	NOUN
ejpam-6047	179	20	and	and	CCONJ
ejpam-6047	179	21	strong	strong	ADJ
ejpam-6047	179	22	dstability	dstability	NOUN
ejpam-6047	179	23	analysis	analysis	NOUN
ejpam-6047	179	24	on	on	ADP
ejpam-6047	179	25	positive	positive	ADJ
ejpam-6047	179	26	dynamical	dynamical	ADJ
ejpam-6047	179	27	systems	system	NOUN
ejpam-6047	179	28	whose	whose	DET
ejpam-6047	179	29	coefficient	coefficient	ADJ
ejpam-6047	179	30	matrices	matrix	NOUN
ejpam-6047	179	31	are	be	AUX
ejpam-6047	179	32	metzler	metzler	NOUN
ejpam-6047	179	33	matrices	matrix	NOUN
ejpam-6047	179	34	.	.	PUNCT
ejpam-6047	180	1	mainly	mainly	ADV
ejpam-6047	180	2	,	,	PUNCT
ejpam-6047	180	3	we	we	PRON
ejpam-6047	180	4	analyze	analyze	VERB
ejpam-6047	180	5	positive	positive	ADJ
ejpam-6047	180	6	linear	linear	ADJ
ejpam-6047	180	7	time	time	NOUN
ejpam-6047	180	8	-	-	PUNCT
ejpam-6047	180	9	invariant	invariant	ADJ
ejpam-6047	180	10	systems	system	NOUN
ejpam-6047	180	11	,	,	PUNCT
ejpam-6047	180	12	where	where	SCONJ
ejpam-6047	180	13	the	the	DET
ejpam-6047	180	14	development	development	NOUN
ejpam-6047	180	15	of	of	ADP
ejpam-6047	180	16	these	these	DET
ejpam-6047	180	17	findings	finding	NOUN
ejpam-6047	180	18	incorporates	incorporate	VERB
ejpam-6047	180	19	various	various	ADJ
ejpam-6047	180	20	principles	principle	NOUN
ejpam-6047	180	21	from	from	ADP
ejpam-6047	180	22	linear	linear	PROPN
ejpam-6047	180	23	algebra	algebra	NOUN
ejpam-6047	180	24	,	,	PUNCT
ejpam-6047	180	25	matrix	matrix	NOUN
ejpam-6047	180	26	theory	theory	NOUN
ejpam-6047	180	27	,	,	PUNCT
ejpam-6047	180	28	and	and	CCONJ
ejpam-6047	180	29	system	system	NOUN
ejpam-6047	180	30	theory	theory	NOUN
ejpam-6047	180	31	.	.	PUNCT
ejpam-6047	181	1	we	we	PRON
ejpam-6047	181	2	use	use	VERB
ejpam-6047	181	3	results	result	NOUN
ejpam-6047	181	4	on	on	ADP
ejpam-6047	181	5	the	the	DET
ejpam-6047	181	6	interconnection	interconnection	NOUN
ejpam-6047	181	7	between	between	ADP
ejpam-6047	181	8	µ-theory	µ-theory	ADJ
ejpam-6047	181	9	and	and	CCONJ
ejpam-6047	181	10	d	d	ADJ
ejpam-6047	181	11	-	-	PUNCT
ejpam-6047	181	12	stability	stability	NOUN
ejpam-6047	181	13	theory	theory	NOUN
ejpam-6047	181	14	to	to	PART
ejpam-6047	181	15	formulate	formulate	VERB
ejpam-6047	181	16	and	and	CCONJ
ejpam-6047	181	17	bring	bring	VERB
ejpam-6047	181	18	forth	forth	ADV
ejpam-6047	181	19	new	new	ADJ
ejpam-6047	181	20	findings	finding	NOUN
ejpam-6047	181	21	on	on	ADP
ejpam-6047	181	22	stability	stability	NOUN
ejpam-6047	181	23	,	,	PUNCT
ejpam-6047	181	24	d	d	NOUN
ejpam-6047	181	25	-	-	PUNCT
ejpam-6047	181	26	stability	stability	NOUN
ejpam-6047	181	27	and	and	CCONJ
ejpam-6047	181	28	strong	strong	ADJ
ejpam-6047	181	29	dstability	dstability	NOUN
ejpam-6047	181	30	.	.	PUNCT
ejpam-6047	182	1	4.1	4.1	NUM
ejpam-6047	182	2	.	.	PUNCT
ejpam-6047	183	1	the	the	DET
ejpam-6047	183	2	stability	stability	NOUN
ejpam-6047	183	3	of	of	ADP
ejpam-6047	183	4	positive	positive	ADJ
ejpam-6047	183	5	linear	linear	ADJ
ejpam-6047	183	6	time	time	NOUN
ejpam-6047	183	7	-	-	PUNCT
ejpam-6047	183	8	invariant	invariant	ADJ
ejpam-6047	183	9	systems	system	NOUN
ejpam-6047	183	10	:	:	PUNCT
ejpam-6047	183	11	we	we	PRON
ejpam-6047	183	12	present	present	VERB
ejpam-6047	183	13	some	some	DET
ejpam-6047	183	14	recent	recent	ADJ
ejpam-6047	183	15	findings	finding	NOUN
ejpam-6047	183	16	on	on	ADP
ejpam-6047	183	17	stability	stability	NOUN
ejpam-6047	183	18	analysis	analysis	NOUN
ejpam-6047	183	19	of	of	ADP
ejpam-6047	183	20	positive	positive	ADJ
ejpam-6047	183	21	linear	linear	ADJ
ejpam-6047	183	22	time	time	NOUN
ejpam-6047	183	23	-	-	PUNCT
ejpam-6047	183	24	invariant	invariant	ADJ
ejpam-6047	183	25	systems	system	NOUN
ejpam-6047	183	26	having	have	VERB
ejpam-6047	183	27	the	the	DET
ejpam-6047	183	28	appearance	appearance	NOUN
ejpam-6047	183	29	of	of	ADP
ejpam-6047	183	30	metzler	metzler	NOUN
ejpam-6047	183	31	,	,	PUNCT
ejpam-6047	183	32	and	and	CCONJ
ejpam-6047	183	33	hurwitz	hurwitz	PROPN
ejpam-6047	183	34	matrices	matrix	NOUN
ejpam-6047	183	35	.	.	PUNCT
ejpam-6047	184	1	theorem	theorem	NOUN
ejpam-6047	184	2	3	3	NUM
ejpam-6047	184	3	gives	give	VERB
ejpam-6047	184	4	the	the	DET
ejpam-6047	184	5	conditions	condition	NOUN
ejpam-6047	184	6	under	under	ADP
ejpam-6047	184	7	which	which	PRON
ejpam-6047	184	8	linear	linear	ADJ
ejpam-6047	184	9	time	time	NOUN
ejpam-6047	184	10	-	-	PUNCT
ejpam-6047	184	11	invariant	invariant	ADJ
ejpam-6047	184	12	system	system	NOUN
ejpam-6047	184	13	with	with	ADP
ejpam-6047	184	14	n	n	CCONJ
ejpam-6047	184	15	-	-	PUNCT
ejpam-6047	184	16	dimensional	dimensional	ADJ
ejpam-6047	184	17	real	real	ADV
ejpam-6047	184	18	-	-	PUNCT
ejpam-6047	184	19	valued	value	VERB
ejpam-6047	184	20	metzler	metzler	NOUN
ejpam-6047	184	21	,	,	PUNCT
ejpam-6047	184	22	and	and	CCONJ
ejpam-6047	184	23	hurwitz	hurwitz	PROPN
ejpam-6047	184	24	matrices	matrix	NOUN
ejpam-6047	184	25	,	,	PUNCT
ejpam-6047	184	26	is	be	AUX
ejpam-6047	184	27	stable	stable	ADJ
ejpam-6047	184	28	.	.	PUNCT
ejpam-6047	185	1	theorem	theorem	NOUN
ejpam-6047	185	2	3	3	X
ejpam-6047	185	3	.	.	PUNCT
ejpam-6047	186	1	let	let	VERB
ejpam-6047	186	2	a1	a1	NOUN
ejpam-6047	186	3	,	,	PUNCT
ejpam-6047	186	4	a2	a2	PROPN
ejpam-6047	186	5	∈	∈	PROPN
ejpam-6047	186	6	rn	rn	PROPN
ejpam-6047	186	7	,	,	PUNCT
ejpam-6047	186	8	n	n	PRON
ejpam-6047	186	9	be	be	VERB
ejpam-6047	186	10	metzler	metzler	NOUN
ejpam-6047	186	11	matrices	matrix	NOUN
ejpam-6047	186	12	and	and	CCONJ
ejpam-6047	186	13	hurwitz	hurwitz	PROPN
ejpam-6047	186	14	.	.	PUNCT
ejpam-6047	187	1	the	the	DET
ejpam-6047	187	2	linear	linear	ADJ
ejpam-6047	187	3	system	system	NOUN
ejpam-6047	187	4	:	:	PUNCT
ejpam-6047	187	5	dx(t	dx(t	X
ejpam-6047	187	6	)	)	PUNCT
ejpam-6047	187	7	dt	dt	NOUN
ejpam-6047	187	8	=	=	SYM
ejpam-6047	187	9	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	187	10	)	)	PUNCT
ejpam-6047	187	11	;	;	PUNCT
ejpam-6047	187	12	a(t	a(t	X
ejpam-6047	187	13	)	)	PUNCT
ejpam-6047	187	14	∈	∈	PROPN
ejpam-6047	187	15	{	{	PUNCT
ejpam-6047	187	16	d1a1	d1a1	NOUN
ejpam-6047	187	17	,	,	PUNCT
ejpam-6047	187	18	d2a2	d2a2	NOUN
ejpam-6047	187	19	}	}	PUNCT
ejpam-6047	187	20	:	:	PUNCT
ejpam-6047	187	21	d1	d1	PROPN
ejpam-6047	187	22	,	,	PUNCT
ejpam-6047	187	23	d2	d2	PROPN
ejpam-6047	187	24	>	>	X
ejpam-6047	187	25	0	0	PROPN
ejpam-6047	187	26	,	,	PUNCT
ejpam-6047	187	27	x(t	x(t	PROPN
ejpam-6047	187	28	)	)	PUNCT
ejpam-6047	187	29	∈	∈	PROPN
ejpam-6047	187	30	rn,1	rn,1	PROPN
ejpam-6047	187	31	,	,	PUNCT
ejpam-6047	187	32	is	be	AUX
ejpam-6047	187	33	stable	stable	ADJ
ejpam-6047	187	34	if	if	SCONJ
ejpam-6047	187	35	re	re	ADP
ejpam-6047	187	36	(	(	PUNCT
ejpam-6047	187	37	λ1(d1(a1	λ1(d1(a1	X
ejpam-6047	187	38	+	+	NUM
ejpam-6047	187	39	γd−1	γd−1	PROPN
ejpam-6047	187	40	1	1	NUM
ejpam-6047	187	41	d2a2	d2a2	NOUN
ejpam-6047	187	42	)	)	PUNCT
ejpam-6047	187	43	)	)	PUNCT
ejpam-6047	187	44	)	)	PUNCT
ejpam-6047	188	1	>	>	PUNCT
ejpam-6047	188	2	∣∣re	∣∣re	PROPN
ejpam-6047	188	3	(	(	PUNCT
ejpam-6047	188	4	λk(d1(a1	λk(d1(a1	PROPN
ejpam-6047	188	5	+	+	NUM
ejpam-6047	188	6	γd−1	γd−1	PROPN
ejpam-6047	188	7	1	1	NUM
ejpam-6047	188	8	d2a2	d2a2	NOUN
ejpam-6047	188	9	)	)	PUNCT
ejpam-6047	188	10	)	)	PUNCT
ejpam-6047	189	1	∣∣	∣∣	PROPN
ejpam-6047	189	2	,	,	PUNCT
ejpam-6047	189	3	where	where	SCONJ
ejpam-6047	189	4	λ1	λ1	PROPN
ejpam-6047	189	5	is	be	AUX
ejpam-6047	189	6	largest	large	ADJ
ejpam-6047	189	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	189	8	,	,	PUNCT
ejpam-6047	189	9	and	and	CCONJ
ejpam-6047	189	10	λk	λk	PROPN
ejpam-6047	189	11	denotes	denote	NOUN
ejpam-6047	189	12	all	all	DET
ejpam-6047	189	13	the	the	DET
ejpam-6047	189	14	remaining	remain	VERB
ejpam-6047	189	15	eigenvalues	eigenvalue	NOUN
ejpam-6047	189	16	other	other	ADJ
ejpam-6047	189	17	than	than	ADP
ejpam-6047	189	18	λ1	λ1	ADJ
ejpam-6047	189	19	,	,	PUNCT
ejpam-6047	189	20	and	and	CCONJ
ejpam-6047	189	21	γ	γ	X
ejpam-6047	189	22	≥	≥	NUM
ejpam-6047	189	23	0	0	NUM
ejpam-6047	189	24	.	.	PUNCT
ejpam-6047	190	1	m.u	m.u	PROPN
ejpam-6047	190	2	.	.	PROPN
ejpam-6047	190	3	rehman	rehman	PROPN
ejpam-6047	190	4	et	et	PROPN
ejpam-6047	190	5	al	al	PROPN
ejpam-6047	190	6	.	.	PUNCT
ejpam-6047	190	7	/	/	SYM
ejpam-6047	190	8	eur	eur	PROPN
ejpam-6047	190	9	.	.	PUNCT
ejpam-6047	191	1	j.	j.	PROPN
ejpam-6047	191	2	pure	pure	PROPN
ejpam-6047	191	3	appl	appl	PROPN
ejpam-6047	191	4	.	.	PROPN
ejpam-6047	191	5	math	math	PROPN
ejpam-6047	191	6	,	,	PUNCT
ejpam-6047	191	7	18	18	NUM
ejpam-6047	191	8	(	(	PUNCT
ejpam-6047	191	9	3	3	NUM
ejpam-6047	191	10	)	)	PUNCT
ejpam-6047	191	11	(	(	PUNCT
ejpam-6047	191	12	2025	2025	NUM
ejpam-6047	191	13	)	)	PUNCT
ejpam-6047	191	14	,	,	PUNCT
ejpam-6047	191	15	6047	6047	NUM
ejpam-6047	191	16	10	10	NUM
ejpam-6047	191	17	of	of	ADP
ejpam-6047	191	18	33	33	NUM
ejpam-6047	191	19	proof	proof	NOUN
ejpam-6047	191	20	.	.	PUNCT
ejpam-6047	192	1	for	for	ADP
ejpam-6047	192	2	the	the	DET
ejpam-6047	192	3	largest	large	ADJ
ejpam-6047	192	4	eigenvalue	eigenvalue	ADJ
ejpam-6047	192	5	λ1	λ1	NOUN
ejpam-6047	192	6	,	,	PUNCT
ejpam-6047	192	7	we	we	PRON
ejpam-6047	192	8	have	have	VERB
ejpam-6047	192	9	that	that	PRON
ejpam-6047	192	10	,	,	PUNCT
ejpam-6047	192	11	re	re	ADP
ejpam-6047	192	12	(	(	PUNCT
ejpam-6047	192	13	λ1(d1(a1	λ1(d1(a1	X
ejpam-6047	192	14	+	+	NUM
ejpam-6047	192	15	γd−1d2a2	γd−1d2a2	PROPN
ejpam-6047	192	16	)	)	PUNCT
ejpam-6047	192	17	)	)	PUNCT
ejpam-6047	192	18	)	)	PUNCT
ejpam-6047	193	1	>	>	X
ejpam-6047	193	2	0	0	PUNCT
ejpam-6047	194	1	because	because	SCONJ
ejpam-6047	194	2	λ1	λ1	PROPN
ejpam-6047	194	3	∈	∈	PROPN
ejpam-6047	194	4	r	r	NOUN
ejpam-6047	194	5	,	,	PUNCT
ejpam-6047	194	6	and∑	and∑	AUX
ejpam-6047	194	7	i=1	i=1	X
ejpam-6047	194	8	λi	λi	X
ejpam-6047	194	9	(	(	PUNCT
ejpam-6047	194	10	d1(a1	d1(a1	PROPN
ejpam-6047	194	11	+	+	CCONJ
ejpam-6047	194	12	γd−1d2a2	γd−1d2a2	NOUN
ejpam-6047	194	13	)	)	PUNCT
ejpam-6047	194	14	)	)	PUNCT
ejpam-6047	195	1	=	=	PUNCT
ejpam-6047	195	2	tr	tr	VERB
ejpam-6047	195	3	(	(	PUNCT
ejpam-6047	195	4	d1(a1	d1(a1	NUM
ejpam-6047	195	5	+	+	CCONJ
ejpam-6047	195	6	γd−1	γd−1	PROPN
ejpam-6047	195	7	1	1	NUM
ejpam-6047	195	8	d2a2	d2a2	NOUN
ejpam-6047	195	9	)	)	PUNCT
ejpam-6047	195	10	)	)	PUNCT
ejpam-6047	195	11	,	,	PUNCT
ejpam-6047	195	12	where	where	SCONJ
ejpam-6047	195	13	trace	trace	NOUN
ejpam-6047	195	14	of	of	ADP
ejpam-6047	195	15	the	the	DET
ejpam-6047	195	16	matrix	matrix	NOUN
ejpam-6047	195	17	is	be	AUX
ejpam-6047	195	18	denoted	denote	VERB
ejpam-6047	195	19	by	by	ADP
ejpam-6047	195	20	tr	tr	VERB
ejpam-6047	195	21	(	(	PUNCT
ejpam-6047	195	22	·	·	PUNCT
ejpam-6047	195	23	)	)	PUNCT
ejpam-6047	195	24	.	.	PUNCT
ejpam-6047	196	1	the	the	DET
ejpam-6047	196	2	above	above	ADJ
ejpam-6047	196	3	expression	expression	NOUN
ejpam-6047	196	4	is	be	AUX
ejpam-6047	196	5	strictly	strictly	ADV
ejpam-6047	196	6	positive	positive	ADJ
ejpam-6047	196	7	,	,	PUNCT
ejpam-6047	196	8	and	and	CCONJ
ejpam-6047	196	9	from	from	ADP
ejpam-6047	196	10	this	this	PRON
ejpam-6047	196	11	it	it	PRON
ejpam-6047	196	12	follows	follow	VERB
ejpam-6047	196	13	that	that	SCONJ
ejpam-6047	196	14	λ1	λ1	PROPN
ejpam-6047	196	15	(	(	PUNCT
ejpam-6047	196	16	d1(a1	d1(a1	NOUN
ejpam-6047	196	17	+	+	CCONJ
ejpam-6047	196	18	γd−1	γd−1	PROPN
ejpam-6047	196	19	1	1	NUM
ejpam-6047	196	20	d2a2	d2a2	NOUN
ejpam-6047	196	21	)	)	PUNCT
ejpam-6047	196	22	)	)	PUNCT
ejpam-6047	196	23	>	>	X
ejpam-6047	197	1	0	0	X
ejpam-6047	197	2	.	.	PUNCT
ejpam-6047	198	1	next	next	ADV
ejpam-6047	198	2	,	,	PUNCT
ejpam-6047	198	3	we	we	PRON
ejpam-6047	198	4	aim	aim	VERB
ejpam-6047	198	5	to	to	PART
ejpam-6047	198	6	show	show	VERB
ejpam-6047	198	7	that	that	SCONJ
ejpam-6047	198	8	λ1	λ1	PROPN
ejpam-6047	198	9	̸=	̸=	PROPN
ejpam-6047	198	10	λk	λk	ADV
ejpam-6047	198	11	,	,	PUNCT
ejpam-6047	198	12	and	and	CCONJ
ejpam-6047	198	13	re	re	X
ejpam-6047	198	14	(	(	PUNCT
ejpam-6047	198	15	λ1(d1(a1	λ1(d1(a1	X
ejpam-6047	198	16	+	+	NUM
ejpam-6047	198	17	γd−1	γd−1	PROPN
ejpam-6047	198	18	1	1	NUM
ejpam-6047	198	19	d2a2	d2a2	NOUN
ejpam-6047	198	20	)	)	PUNCT
ejpam-6047	198	21	)	)	PUNCT
ejpam-6047	198	22	)	)	PUNCT
ejpam-6047	199	1	>	>	PUNCT
ejpam-6047	199	2	∣∣re	∣∣re	PROPN
ejpam-6047	199	3	(	(	PUNCT
ejpam-6047	199	4	λk(d1(a1	λk(d1(a1	PROPN
ejpam-6047	199	5	+	+	NUM
ejpam-6047	199	6	γd−1	γd−1	PROPN
ejpam-6047	199	7	1	1	NUM
ejpam-6047	199	8	d2a2	d2a2	NOUN
ejpam-6047	199	9	)	)	PUNCT
ejpam-6047	199	10	)	)	PUNCT
ejpam-6047	199	11	∣∣	∣∣	PROPN
ejpam-6047	199	12	.	.	PUNCT
ejpam-6047	200	1	consider	consider	VERB
ejpam-6047	200	2	for	for	ADP
ejpam-6047	200	3	λ1	λ1	PROPN
ejpam-6047	200	4	>	>	X
ejpam-6047	200	5	λk	λk	PROPN
ejpam-6047	200	6	,	,	PUNCT
ejpam-6047	200	7	v⃗1	v⃗1	X
ejpam-6047	200	8	be	be	AUX
ejpam-6047	200	9	normalized	normalize	VERB
ejpam-6047	200	10	eigenvector	eigenvector	NOUN
ejpam-6047	200	11	then,∑	then,∑	X
ejpam-6047	200	12	i	i	PRON
ejpam-6047	200	13	ai	ai	VERB
ejpam-6047	200	14	,	,	PUNCT
ejpam-6047	200	15	j	j	PROPN
ejpam-6047	200	16	v⃗1	v⃗1	ADV
ejpam-6047	200	17	=	=	PUNCT
ejpam-6047	200	18	λkv⃗1	λkv⃗1	NOUN
ejpam-6047	200	19	,	,	PUNCT
ejpam-6047	200	20	and	and	CCONJ
ejpam-6047	200	21	let	let	VERB
ejpam-6047	200	22	|v⃗1|	|v⃗1|	PROPN
ejpam-6047	200	23	=	=	SYM
ejpam-6047	200	24	x1	x1	PROPN
ejpam-6047	200	25	,	,	PUNCT
ejpam-6047	200	26	then	then	ADV
ejpam-6047	200	27	0	0	NUM
ejpam-6047	200	28	<	<	X
ejpam-6047	200	29	re	re	ADP
ejpam-6047	200	30	(	(	PUNCT
ejpam-6047	200	31	λ1(d1(a1	λ1(d1(a1	X
ejpam-6047	200	32	+	+	NUM
ejpam-6047	200	33	γd−1	γd−1	PROPN
ejpam-6047	200	34	1	1	NUM
ejpam-6047	200	35	d2a2	d2a2	NOUN
ejpam-6047	200	36	)	)	PUNCT
ejpam-6047	200	37	)	)	PUNCT
ejpam-6047	200	38	)	)	PUNCT
ejpam-6047	201	1	=	=	PUNCT
ejpam-6047	201	2	∑	∑	PUNCT
ejpam-6047	201	3	ij	ij	INTJ
ejpam-6047	201	4	aij	aij	PROPN
ejpam-6047	201	5	v⃗1v⃗k	v⃗1v⃗k	PROPN
ejpam-6047	201	6	=	=	SYM
ejpam-6047	201	7	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6047	201	8	∑	∑	PROPN
ejpam-6047	201	9	ij	ij	NOUN
ejpam-6047	201	10	v⃗1v⃗k	v⃗1v⃗k	PROPN
ejpam-6047	201	11	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6047	201	12	≤	≤	PROPN
ejpam-6047	201	13	∑	∑	ADP
ejpam-6047	201	14	ij	ij	NOUN
ejpam-6047	201	15	aijx1x2	aijx1x2	X
ejpam-6047	201	16	.	.	PUNCT
ejpam-6047	201	17	suppose	suppose	VERB
ejpam-6047	201	18	that	that	SCONJ
ejpam-6047	201	19	x2	x2	PRON
ejpam-6047	201	20	be	be	VERB
ejpam-6047	201	21	an	an	DET
ejpam-6047	201	22	eigenvector	eigenvector	NOUN
ejpam-6047	201	23	corresponding	correspond	VERB
ejpam-6047	201	24	to	to	ADP
ejpam-6047	201	25	λ1	λ1	PROPN
ejpam-6047	201	26	(	(	PUNCT
ejpam-6047	201	27	d1(a1	d1(a1	NUM
ejpam-6047	201	28	+	+	CCONJ
ejpam-6047	201	29	γd−1	γd−1	PROPN
ejpam-6047	201	30	1	1	NUM
ejpam-6047	201	31	d2a2	d2a2	NOUN
ejpam-6047	201	32	)	)	PUNCT
ejpam-6047	201	33	)	)	PUNCT
ejpam-6047	201	34	,	,	PUNCT
ejpam-6047	201	35	then	then	ADV
ejpam-6047	201	36	we	we	PRON
ejpam-6047	201	37	have	have	VERB
ejpam-6047	201	38	∑	∑	ADV
ejpam-6047	201	39	ij	ij	INTJ
ejpam-6047	201	40	aijx2	aijx2	PROPN
ejpam-6047	201	41	=	=	PUNCT
ejpam-6047	202	1	λ1x1	λ1x1	PROPN
ejpam-6047	202	2	,	,	PUNCT
ejpam-6047	202	3	x2	x2	PROPN
ejpam-6047	202	4	̸=	̸=	PROPN
ejpam-6047	202	5	0⃗.	0⃗.	NUM
ejpam-6047	202	6	the	the	DET
ejpam-6047	202	7	condition	condition	NOUN
ejpam-6047	202	8	that	that	SCONJ
ejpam-6047	202	9	x2	x2	PROPN
ejpam-6047	202	10	̸=	̸=	PROPN
ejpam-6047	202	11	0⃗	0⃗	PRON
ejpam-6047	202	12	is	be	AUX
ejpam-6047	202	13	a	a	DET
ejpam-6047	202	14	non	non	ADJ
ejpam-6047	202	15	-	-	ADJ
ejpam-6047	202	16	degeneracy	degeneracy	ADJ
ejpam-6047	202	17	condition	condition	NOUN
ejpam-6047	202	18	,	,	PUNCT
ejpam-6047	202	19	and	and	CCONJ
ejpam-6047	202	20	it	it	PRON
ejpam-6047	202	21	then	then	ADV
ejpam-6047	202	22	allows	allow	VERB
ejpam-6047	202	23	to	to	PART
ejpam-6047	202	24	have	have	VERB
ejpam-6047	202	25	re	re	VERB
ejpam-6047	202	26	(	(	PUNCT
ejpam-6047	202	27	λ1(d1(a1	λ1(d1(a1	X
ejpam-6047	202	28	+	+	NUM
ejpam-6047	202	29	γd−1	γd−1	PROPN
ejpam-6047	202	30	1	1	NUM
ejpam-6047	202	31	d2a2	d2a2	NOUN
ejpam-6047	202	32	)	)	PUNCT
ejpam-6047	202	33	)	)	PUNCT
ejpam-6047	202	34	>	>	PUNCT
ejpam-6047	202	35	∑	∑	PUNCT
ejpam-6047	202	36	ij	ij	ADP
ejpam-6047	202	37	aij	aij	PROPN
ejpam-6047	202	38	|v1||vk|	|v1||vk|	X
ejpam-6047	202	39	≥	≥	NUM
ejpam-6047	202	40	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6047	202	41	∑	∑	PROPN
ejpam-6047	202	42	ij	ij	NOUN
ejpam-6047	202	43	aijv1vk	aijv1vk	ADV
ejpam-6047	202	44	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6047	202	45	=	=	SYM
ejpam-6047	202	46	∣∣λk	∣∣λk	PROPN
ejpam-6047	202	47	(	(	PUNCT
ejpam-6047	202	48	d1(a1	d1(a1	NOUN
ejpam-6047	202	49	+	+	CCONJ
ejpam-6047	202	50	γd−1	γd−1	PROPN
ejpam-6047	202	51	1	1	NUM
ejpam-6047	202	52	d2a2	d2a2	NOUN
ejpam-6047	202	53	)	)	PUNCT
ejpam-6047	202	54	)	)	PUNCT
ejpam-6047	202	55	∣∣	∣∣	X
ejpam-6047	202	56	=	=	SYM
ejpam-6047	202	57	∣∣re	∣∣re	PROPN
ejpam-6047	202	58	(	(	PUNCT
ejpam-6047	202	59	λk(d1(a1	λk(d1(a1	PROPN
ejpam-6047	202	60	+	+	NUM
ejpam-6047	202	61	γd−1	γd−1	PROPN
ejpam-6047	202	62	1	1	NUM
ejpam-6047	202	63	d2a2	d2a2	NOUN
ejpam-6047	202	64	)	)	PUNCT
ejpam-6047	202	65	)	)	PUNCT
ejpam-6047	202	66	)	)	PUNCT
ejpam-6047	202	67	∣∣	∣∣	X
ejpam-6047	202	68	>	>	X
ejpam-6047	202	69	0	0	X
ejpam-6047	202	70	.	.	PUNCT
ejpam-6047	202	71	theorem	theorem	ADJ
ejpam-6047	202	72	4	4	NUM
ejpam-6047	202	73	shows	show	VERB
ejpam-6047	202	74	that	that	SCONJ
ejpam-6047	202	75	the	the	DET
ejpam-6047	202	76	positive	positive	ADJ
ejpam-6047	202	77	linear	linear	ADJ
ejpam-6047	202	78	time	time	NOUN
ejpam-6047	202	79	-	-	PUNCT
ejpam-6047	202	80	invariant	invariant	ADJ
ejpam-6047	202	81	system	system	NOUN
ejpam-6047	202	82	with	with	ADP
ejpam-6047	202	83	coefficient	coefficient	NOUN
ejpam-6047	202	84	matrices	matrix	NOUN
ejpam-6047	202	85	a1	a1	NOUN
ejpam-6047	202	86	,	,	PUNCT
ejpam-6047	202	87	a2	a2	PROPN
ejpam-6047	202	88	∈	∈	PROPN
ejpam-6047	202	89	rn	rn	PROPN
ejpam-6047	202	90	,	,	PUNCT
ejpam-6047	202	91	n	n	PRON
ejpam-6047	202	92	being	be	AUX
ejpam-6047	202	93	metzler	metzler	NOUN
ejpam-6047	202	94	and	and	CCONJ
ejpam-6047	202	95	hurwitz	hurwitz	PROPN
ejpam-6047	202	96	,	,	PUNCT
ejpam-6047	202	97	is	be	AUX
ejpam-6047	202	98	stable	stable	ADJ
ejpam-6047	202	99	system	system	NOUN
ejpam-6047	202	100	for	for	ADP
ejpam-6047	202	101	x(t	x(t	PROPN
ejpam-6047	202	102	)	)	PUNCT
ejpam-6047	202	103	∈	∈	PROPN
ejpam-6047	202	104	rn,1	rn,1	PROPN
ejpam-6047	202	105	,	,	PUNCT
ejpam-6047	202	106	γ	γ	X
ejpam-6047	202	107	>	>	X
ejpam-6047	202	108	0	0	PROPN
ejpam-6047	202	109	,	,	PUNCT
ejpam-6047	202	110	the	the	DET
ejpam-6047	202	111	quantity	quantity	NOUN
ejpam-6047	202	112	xt(t	xt(t	NUM
ejpam-6047	202	113	)	)	PUNCT
ejpam-6047	202	114	(	(	PUNCT
ejpam-6047	202	115	d1(a1	d1(a1	NOUN
ejpam-6047	202	116	+	+	CCONJ
ejpam-6047	202	117	γd−1	γd−1	PROPN
ejpam-6047	202	118	1	1	NUM
ejpam-6047	202	119	d2a2	d2a2	NOUN
ejpam-6047	202	120	)	)	PUNCT
ejpam-6047	202	121	)	)	PUNCT
ejpam-6047	203	1	x(t	x(t	PROPN
ejpam-6047	203	2	)	)	PUNCT
ejpam-6047	203	3	is	be	AUX
ejpam-6047	203	4	strictly	strictly	ADV
ejpam-6047	203	5	positive	positive	ADJ
ejpam-6047	203	6	if	if	SCONJ
ejpam-6047	203	7	and	and	CCONJ
ejpam-6047	203	8	only	only	ADV
ejpam-6047	203	9	if	if	SCONJ
ejpam-6047	203	10	re	re	X
ejpam-6047	203	11	(	(	PUNCT
ejpam-6047	203	12	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	203	13	+	+	NUM
ejpam-6047	203	14	γd−1	γd−1	PROPN
ejpam-6047	203	15	1	1	NUM
ejpam-6047	203	16	d2a2	d2a2	NOUN
ejpam-6047	203	17	)	)	PUNCT
ejpam-6047	203	18	)	)	PUNCT
ejpam-6047	203	19	)	)	PUNCT
ejpam-6047	203	20	is	be	AUX
ejpam-6047	203	21	strictly	strictly	ADV
ejpam-6047	203	22	positive	positive	ADJ
ejpam-6047	203	23	.	.	PUNCT
ejpam-6047	204	1	theorem	theorem	ADJ
ejpam-6047	204	2	4	4	NUM
ejpam-6047	204	3	.	.	PUNCT
ejpam-6047	205	1	let	let	VERB
ejpam-6047	205	2	a1	a1	NOUN
ejpam-6047	205	3	,	,	PUNCT
ejpam-6047	205	4	a2	a2	PROPN
ejpam-6047	205	5	∈	∈	PROPN
ejpam-6047	205	6	rn	rn	PROPN
ejpam-6047	205	7	,	,	PUNCT
ejpam-6047	205	8	n	n	PRON
ejpam-6047	205	9	be	be	VERB
ejpam-6047	205	10	metzler	metzler	NOUN
ejpam-6047	205	11	matrices	matrix	NOUN
ejpam-6047	205	12	and	and	CCONJ
ejpam-6047	205	13	hurwitz	hurwitz	PROPN
ejpam-6047	205	14	.	.	PUNCT
ejpam-6047	206	1	the	the	DET
ejpam-6047	206	2	linear	linear	ADJ
ejpam-6047	206	3	system	system	NOUN
ejpam-6047	206	4	dx(t	dx(t	NOUN
ejpam-6047	206	5	)	)	PUNCT
ejpam-6047	206	6	dt	dt	NOUN
ejpam-6047	206	7	=	=	SYM
ejpam-6047	206	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	206	9	)	)	PUNCT
ejpam-6047	206	10	,	,	PUNCT
ejpam-6047	206	11	where	where	SCONJ
ejpam-6047	206	12	a(t	a(t	NOUN
ejpam-6047	206	13	)	)	PUNCT
ejpam-6047	206	14	∈	∈	PROPN
ejpam-6047	206	15	{	{	PUNCT
ejpam-6047	206	16	d1a1	d1a1	NOUN
ejpam-6047	206	17	,	,	PUNCT
ejpam-6047	206	18	d2a2	d2a2	NOUN
ejpam-6047	206	19	}	}	PUNCT
ejpam-6047	206	20	,	,	PUNCT
ejpam-6047	206	21	d1	d1	PROPN
ejpam-6047	206	22	,	,	PUNCT
ejpam-6047	206	23	d2	d2	PROPN
ejpam-6047	206	24	>	>	X
ejpam-6047	206	25	0	0	PROPN
ejpam-6047	206	26	,	,	PUNCT
ejpam-6047	206	27	and	and	CCONJ
ejpam-6047	206	28	x(t	x(t	PROPN
ejpam-6047	206	29	)	)	PUNCT
ejpam-6047	206	30	∈	∈	PROPN
ejpam-6047	206	31	rn,1	rn,1	NOUN
ejpam-6047	206	32	is	be	AUX
ejpam-6047	206	33	stable	stable	ADJ
ejpam-6047	206	34	then	then	ADV
ejpam-6047	206	35	xt	xt	PROPN
ejpam-6047	206	36	(	(	PUNCT
ejpam-6047	206	37	t	t	PROPN
ejpam-6047	206	38	)	)	PUNCT
ejpam-6047	206	39	(	(	PUNCT
ejpam-6047	206	40	d1(a1	d1(a1	NUM
ejpam-6047	206	41	+	+	CCONJ
ejpam-6047	206	42	γd−1	γd−1	PROPN
ejpam-6047	206	43	1	1	NUM
ejpam-6047	206	44	d2a2	d2a2	NOUN
ejpam-6047	206	45	)	)	PUNCT
ejpam-6047	206	46	)	)	PUNCT
ejpam-6047	206	47	x(t	x(t	PROPN
ejpam-6047	206	48	)	)	PUNCT
ejpam-6047	206	49	>	>	SYM
ejpam-6047	206	50	0	0	PUNCT
ejpam-6047	206	51	⇐	⇐	ADJ
ejpam-6047	206	52	⇒	⇒	NOUN
ejpam-6047	206	53	re	re	ADP
ejpam-6047	206	54	(	(	PUNCT
ejpam-6047	206	55	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	206	56	+	+	NUM
ejpam-6047	206	57	γd−1	γd−1	PROPN
ejpam-6047	206	58	1	1	NUM
ejpam-6047	206	59	d2a2	d2a2	NOUN
ejpam-6047	206	60	)	)	PUNCT
ejpam-6047	206	61	)	)	PUNCT
ejpam-6047	206	62	)	)	PUNCT
ejpam-6047	206	63	>	>	X
ejpam-6047	206	64	0	0	X
ejpam-6047	206	65	.	.	PUNCT
ejpam-6047	206	66	m.u	m.u	PROPN
ejpam-6047	206	67	.	.	PROPN
ejpam-6047	206	68	rehman	rehman	PROPN
ejpam-6047	206	69	et	et	PROPN
ejpam-6047	206	70	al	al	PROPN
ejpam-6047	206	71	.	.	PUNCT
ejpam-6047	206	72	/	/	SYM
ejpam-6047	206	73	eur	eur	PROPN
ejpam-6047	206	74	.	.	PUNCT
ejpam-6047	207	1	j.	j.	PROPN
ejpam-6047	207	2	pure	pure	PROPN
ejpam-6047	207	3	appl	appl	PROPN
ejpam-6047	207	4	.	.	PROPN
ejpam-6047	207	5	math	math	PROPN
ejpam-6047	207	6	,	,	PUNCT
ejpam-6047	207	7	18	18	NUM
ejpam-6047	207	8	(	(	PUNCT
ejpam-6047	207	9	3	3	NUM
ejpam-6047	207	10	)	)	PUNCT
ejpam-6047	207	11	(	(	PUNCT
ejpam-6047	207	12	2025	2025	NUM
ejpam-6047	207	13	)	)	PUNCT
ejpam-6047	207	14	,	,	PUNCT
ejpam-6047	207	15	6047	6047	NUM
ejpam-6047	207	16	11	11	NUM
ejpam-6047	207	17	of	of	ADP
ejpam-6047	207	18	33	33	NUM
ejpam-6047	207	19	proof	proof	NOUN
ejpam-6047	207	20	.	.	PUNCT
ejpam-6047	208	1	to	to	PART
ejpam-6047	208	2	ensure	ensure	VERB
ejpam-6047	208	3	stability	stability	NOUN
ejpam-6047	208	4	,	,	PUNCT
ejpam-6047	208	5	it	it	PRON
ejpam-6047	208	6	is	be	AUX
ejpam-6047	208	7	sufficient	sufficient	ADJ
ejpam-6047	208	8	to	to	PART
ejpam-6047	208	9	demonstrate	demonstrate	VERB
ejpam-6047	208	10	that	that	SCONJ
ejpam-6047	208	11	for	for	ADP
ejpam-6047	208	12	z	z	NOUN
ejpam-6047	208	13	=	=	SYM
ejpam-6047	208	14	x+iy	x+iy	NOUN
ejpam-6047	209	1	:	:	PUNCT
ejpam-6047	209	2	x	x	X
ejpam-6047	209	3	,	,	PUNCT
ejpam-6047	209	4	y	y	PROPN
ejpam-6047	209	5	∈	∈	PROPN
ejpam-6047	209	6	rn,1	rn,1	PROPN
ejpam-6047	209	7	,	,	PUNCT
ejpam-6047	209	8	the	the	DET
ejpam-6047	209	9	quadratic	quadratic	ADJ
ejpam-6047	209	10	form	form	NOUN
ejpam-6047	209	11	zt	zt	PROPN
ejpam-6047	209	12	(	(	PUNCT
ejpam-6047	209	13	d1(a1	d1(a1	PROPN
ejpam-6047	209	14	+	+	CCONJ
ejpam-6047	209	15	γd−1	γd−1	PROPN
ejpam-6047	209	16	1	1	NUM
ejpam-6047	209	17	d2a2	d2a2	NOUN
ejpam-6047	209	18	)	)	PUNCT
ejpam-6047	209	19	)	)	PUNCT
ejpam-6047	210	1	z	z	NOUN
ejpam-6047	210	2	>	>	X
ejpam-6047	210	3	0	0	NUM
ejpam-6047	210	4	,	,	PUNCT
ejpam-6047	210	5	z	z	PROPN
ejpam-6047	210	6	∈	∈	PROPN
ejpam-6047	210	7	cn,1	cn,1	PROPN
ejpam-6047	210	8	.	.	PUNCT
ejpam-6047	211	1	further	further	PROPN
ejpam-6047	211	2	yt	yt	PROPN
ejpam-6047	211	3	(	(	PUNCT
ejpam-6047	211	4	d1(a1	d1(a1	PROPN
ejpam-6047	211	5	+	+	CCONJ
ejpam-6047	211	6	γd−1	γd−1	PROPN
ejpam-6047	211	7	1	1	NUM
ejpam-6047	211	8	d2a2)x	d2a2)x	PROPN
ejpam-6047	211	9	)	)	PUNCT
ejpam-6047	211	10	t	t	NOUN
ejpam-6047	211	11	=	=	SYM
ejpam-6047	211	12	xt	xt	PROPN
ejpam-6047	211	13	(	(	PUNCT
ejpam-6047	211	14	d1(a1	d1(a1	PROPN
ejpam-6047	211	15	+	+	CCONJ
ejpam-6047	211	16	γd−1	γd−1	PROPN
ejpam-6047	211	17	1	1	NUM
ejpam-6047	211	18	d2a2	d2a2	NOUN
ejpam-6047	211	19	)	)	PUNCT
ejpam-6047	211	20	)	)	PUNCT
ejpam-6047	212	1	t	t	PROPN
ejpam-6047	212	2	y.	y.	PROPN
ejpam-6047	212	3	also	also	ADV
ejpam-6047	212	4	,	,	PUNCT
ejpam-6047	212	5	zt	zt	PROPN
ejpam-6047	212	6	(	(	PUNCT
ejpam-6047	212	7	d1(a1	d1(a1	PROPN
ejpam-6047	212	8	+	+	CCONJ
ejpam-6047	212	9	γd−1	γd−1	PROPN
ejpam-6047	212	10	1	1	NUM
ejpam-6047	212	11	d2a2	d2a2	NOUN
ejpam-6047	212	12	)	)	PUNCT
ejpam-6047	212	13	)	)	PUNCT
ejpam-6047	212	14	z	z	X
ejpam-6047	212	15	=	=	SYM
ejpam-6047	212	16	xt	xt	PROPN
ejpam-6047	212	17	(	(	PUNCT
ejpam-6047	212	18	d1(a1	d1(a1	PROPN
ejpam-6047	212	19	+	+	CCONJ
ejpam-6047	212	20	γd−1	γd−1	PROPN
ejpam-6047	212	21	1	1	NUM
ejpam-6047	212	22	d2a2	d2a2	NOUN
ejpam-6047	212	23	)	)	PUNCT
ejpam-6047	212	24	)	)	PUNCT
ejpam-6047	212	25	x+yt	x+yt	NOUN
ejpam-6047	212	26	(	(	PUNCT
ejpam-6047	212	27	d1(a1	d1(a1	NOUN
ejpam-6047	212	28	+	+	CCONJ
ejpam-6047	212	29	γd−1	γd−1	PROPN
ejpam-6047	212	30	1	1	NUM
ejpam-6047	212	31	d2a2	d2a2	NOUN
ejpam-6047	212	32	)	)	PUNCT
ejpam-6047	212	33	)	)	PUNCT
ejpam-6047	213	1	y+i	y+i	PROPN
ejpam-6047	213	2	(	(	PUNCT
ejpam-6047	213	3	xt	xt	X
ejpam-6047	213	4	(	(	PUNCT
ejpam-6047	213	5	d1(a1	d1(a1	NOUN
ejpam-6047	213	6	+	+	CCONJ
ejpam-6047	213	7	γd−1	γd−1	PROPN
ejpam-6047	213	8	1	1	NUM
ejpam-6047	213	9	d2a2	d2a2	NOUN
ejpam-6047	213	10	)	)	PUNCT
ejpam-6047	213	11	)	)	PUNCT
ejpam-6047	214	1	y	y	PROPN
ejpam-6047	214	2	−yt	−yt	X
ejpam-6047	214	3	(	(	PUNCT
ejpam-6047	214	4	(	(	PUNCT
ejpam-6047	214	5	d1(a1	d1(a1	NOUN
ejpam-6047	214	6	+	+	NUM
ejpam-6047	214	7	γd−1	γd−1	PROPN
ejpam-6047	214	8	1	1	NUM
ejpam-6047	214	9	d2a2))x	d2a2))x	PROPN
ejpam-6047	214	10	)	)	PUNCT
ejpam-6047	214	11	=	=	SYM
ejpam-6047	214	12	xt	xt	PROPN
ejpam-6047	214	13	(	(	PUNCT
ejpam-6047	214	14	d1(a1	d1(a1	PROPN
ejpam-6047	214	15	+	+	CCONJ
ejpam-6047	214	16	γd−1	γd−1	PROPN
ejpam-6047	214	17	1	1	NUM
ejpam-6047	214	18	d2a2	d2a2	NOUN
ejpam-6047	214	19	)	)	PUNCT
ejpam-6047	214	20	x+yt	x+yt	NOUN
ejpam-6047	214	21	(	(	PUNCT
ejpam-6047	214	22	d1(a1	d1(a1	NOUN
ejpam-6047	214	23	+	+	CCONJ
ejpam-6047	214	24	γd−1	γd−1	PROPN
ejpam-6047	214	25	1	1	NUM
ejpam-6047	214	26	d2a2	d2a2	NOUN
ejpam-6047	214	27	)	)	PUNCT
ejpam-6047	214	28	)	)	PUNCT
ejpam-6047	215	1	y	y	PROPN
ejpam-6047	215	2	>	>	X
ejpam-6047	215	3	0	0	X
ejpam-6047	215	4	.	.	PUNCT
ejpam-6047	216	1	this	this	PRON
ejpam-6047	216	2	is	be	AUX
ejpam-6047	216	3	true	true	ADJ
ejpam-6047	216	4	if	if	SCONJ
ejpam-6047	216	5	x	x	NOUN
ejpam-6047	216	6	,	,	PUNCT
ejpam-6047	216	7	y	y	PROPN
ejpam-6047	216	8	̸=	̸=	PROPN
ejpam-6047	216	9	0⃗	0⃗	NOUN
ejpam-6047	216	10	,	,	PUNCT
ejpam-6047	216	11	and	and	CCONJ
ejpam-6047	216	12	hence	hence	ADV
ejpam-6047	216	13	this	this	PRON
ejpam-6047	216	14	implies	imply	VERB
ejpam-6047	216	15	that	that	SCONJ
ejpam-6047	217	1	re	re	ADP
ejpam-6047	217	2	(	(	PUNCT
ejpam-6047	217	3	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	217	4	+	+	NUM
ejpam-6047	217	5	γd−1	γd−1	PROPN
ejpam-6047	217	6	1	1	NUM
ejpam-6047	217	7	d2a2	d2a2	NOUN
ejpam-6047	217	8	)	)	PUNCT
ejpam-6047	217	9	)	)	PUNCT
ejpam-6047	217	10	>	>	X
ejpam-6047	218	1	0,∀	0,∀	NUM
ejpam-6047	218	2	i.	i.	NOUN
ejpam-6047	218	3	theorem	theorem	VERB
ejpam-6047	218	4	5	5	NUM
ejpam-6047	218	5	.	.	PUNCT
ejpam-6047	219	1	let	let	VERB
ejpam-6047	219	2	a1	a1	NOUN
ejpam-6047	219	3	,	,	PUNCT
ejpam-6047	219	4	a2	a2	PROPN
ejpam-6047	219	5	∈	∈	PROPN
ejpam-6047	219	6	rn	rn	PROPN
ejpam-6047	219	7	,	,	PUNCT
ejpam-6047	219	8	n	n	PRON
ejpam-6047	219	9	be	be	VERB
ejpam-6047	219	10	metzler	metzler	NOUN
ejpam-6047	219	11	matrices	matrix	NOUN
ejpam-6047	219	12	and	and	CCONJ
ejpam-6047	219	13	hurwitz	hurwitz	PROPN
ejpam-6047	219	14	.	.	PUNCT
ejpam-6047	220	1	the	the	DET
ejpam-6047	220	2	linear	linear	ADJ
ejpam-6047	220	3	system	system	NOUN
ejpam-6047	220	4	dx(t	dx(t	NOUN
ejpam-6047	220	5	)	)	PUNCT
ejpam-6047	220	6	dt	dt	NOUN
ejpam-6047	220	7	=	=	SYM
ejpam-6047	220	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	220	9	)	)	PUNCT
ejpam-6047	220	10	,	,	PUNCT
ejpam-6047	220	11	where	where	SCONJ
ejpam-6047	220	12	a(t	a(t	NOUN
ejpam-6047	220	13	)	)	PUNCT
ejpam-6047	220	14	∈	∈	PROPN
ejpam-6047	220	15	{	{	PUNCT
ejpam-6047	220	16	d1a1	d1a1	NOUN
ejpam-6047	220	17	,	,	PUNCT
ejpam-6047	220	18	d2a2	d2a2	NOUN
ejpam-6047	220	19	}	}	PUNCT
ejpam-6047	220	20	,	,	PUNCT
ejpam-6047	220	21	d1	d1	PROPN
ejpam-6047	220	22	,	,	PUNCT
ejpam-6047	220	23	d2	d2	PROPN
ejpam-6047	220	24	>	>	X
ejpam-6047	220	25	0	0	PROPN
ejpam-6047	220	26	,	,	PUNCT
ejpam-6047	220	27	and	and	CCONJ
ejpam-6047	220	28	x(t	x(t	PROPN
ejpam-6047	220	29	)	)	PUNCT
ejpam-6047	220	30	∈	∈	PROPN
ejpam-6047	220	31	rn,1	rn,1	PROPN
ejpam-6047	220	32	,	,	PUNCT
ejpam-6047	220	33	is	be	AUX
ejpam-6047	220	34	stable	stable	ADJ
ejpam-6047	220	35	then	then	ADV
ejpam-6047	220	36	xt	xt	PROPN
ejpam-6047	220	37	(	(	PUNCT
ejpam-6047	220	38	d1(a1	d1(a1	PROPN
ejpam-6047	220	39	+	+	CCONJ
ejpam-6047	220	40	γd−1	γd−1	PROPN
ejpam-6047	220	41	1	1	NUM
ejpam-6047	220	42	d2a2	d2a2	NOUN
ejpam-6047	220	43	)	)	PUNCT
ejpam-6047	220	44	)	)	PUNCT
ejpam-6047	221	1	x	x	PUNCT
ejpam-6047	221	2	>	>	X
ejpam-6047	221	3	0	0	PUNCT
ejpam-6047	222	1	⇐	⇐	ADJ
ejpam-6047	222	2	⇒	⇒	NOUN
ejpam-6047	222	3	re	re	ADP
ejpam-6047	222	4	(	(	PUNCT
ejpam-6047	222	5	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	222	6	+	+	NUM
ejpam-6047	222	7	γd−1	γd−1	PROPN
ejpam-6047	222	8	1	1	NUM
ejpam-6047	222	9	d2a2	d2a2	NOUN
ejpam-6047	222	10	)	)	PUNCT
ejpam-6047	222	11	)	)	PUNCT
ejpam-6047	222	12	)	)	PUNCT
ejpam-6047	223	1	>	>	X
ejpam-6047	223	2	0	0	NUM
ejpam-6047	223	3	,	,	PUNCT
ejpam-6047	223	4	∀	∀	VERB
ejpam-6047	224	1	i	i	NOUN
ejpam-6047	224	2	=	=	NOUN
ejpam-6047	224	3	1	1	X
ejpam-6047	224	4	:	:	PUNCT
ejpam-6047	224	5	n.	n.	NOUN
ejpam-6047	224	6	proof	proof	NOUN
ejpam-6047	224	7	.	.	PUNCT
ejpam-6047	225	1	the	the	DET
ejpam-6047	225	2	quantity	quantity	NOUN
ejpam-6047	225	3	xt	xt	X
ejpam-6047	225	4	(	(	PUNCT
ejpam-6047	225	5	d1(a1	d1(a1	PROPN
ejpam-6047	225	6	+	+	CCONJ
ejpam-6047	225	7	γd−1	γd−1	PROPN
ejpam-6047	225	8	1	1	NUM
ejpam-6047	225	9	d2a2	d2a2	NOUN
ejpam-6047	225	10	)	)	PUNCT
ejpam-6047	225	11	)	)	PUNCT
ejpam-6047	226	1	x	x	X
ejpam-6047	226	2	is	be	AUX
ejpam-6047	226	3	real	real	ADJ
ejpam-6047	226	4	,	,	PUNCT
ejpam-6047	226	5	and	and	CCONJ
ejpam-6047	226	6	positive	positive	ADJ
ejpam-6047	226	7	for	for	ADP
ejpam-6047	226	8	the	the	DET
ejpam-6047	226	9	given	give	VERB
ejpam-6047	226	10	matrix	matrix	NOUN
ejpam-6047	226	11	(	(	PUNCT
ejpam-6047	226	12	d1(a1+γd−1	d1(a1+γd−1	NOUN
ejpam-6047	226	13	1	1	NUM
ejpam-6047	226	14	d2a2	d2a2	NOUN
ejpam-6047	226	15	)	)	PUNCT
ejpam-6047	226	16	)	)	PUNCT
ejpam-6047	226	17	.	.	PUNCT
ejpam-6047	227	1	then	then	ADV
ejpam-6047	227	2	for	for	ADP
ejpam-6047	227	3	x	x	PROPN
ejpam-6047	227	4	∈	∈	PROPN
ejpam-6047	227	5	rn,1	rn,1	PROPN
ejpam-6047	227	6	,	,	PUNCT
ejpam-6047	227	7	the	the	DET
ejpam-6047	227	8	quadratic	quadratic	ADJ
ejpam-6047	227	9	form	form	NOUN
ejpam-6047	227	10	xt	xt	X
ejpam-6047	227	11	(	(	PUNCT
ejpam-6047	227	12	d1(a1	d1(a1	NOUN
ejpam-6047	227	13	+	+	CCONJ
ejpam-6047	227	14	γd−1	γd−1	PROPN
ejpam-6047	227	15	1	1	NUM
ejpam-6047	227	16	d2a2	d2a2	NOUN
ejpam-6047	227	17	)	)	PUNCT
ejpam-6047	227	18	)	)	PUNCT
ejpam-6047	228	1	x	x	X
ejpam-6047	228	2	,	,	PUNCT
ejpam-6047	228	3	x	x	SYM
ejpam-6047	228	4	∈	∈	PROPN
ejpam-6047	228	5	r2,1	r2,1	NOUN
ejpam-6047	228	6	.	.	PUNCT
ejpam-6047	229	1	also	also	ADV
ejpam-6047	229	2	,	,	PUNCT
ejpam-6047	229	3	re	re	ADP
ejpam-6047	229	4	(	(	PUNCT
ejpam-6047	229	5	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	229	6	+	+	NUM
ejpam-6047	229	7	γd−1	γd−1	PROPN
ejpam-6047	229	8	1	1	NUM
ejpam-6047	229	9	d2a2	d2a2	NOUN
ejpam-6047	229	10	)	)	PUNCT
ejpam-6047	229	11	)	)	PUNCT
ejpam-6047	229	12	)	)	PUNCT
ejpam-6047	230	1	>	>	X
ejpam-6047	230	2	0,∀i	0,∀i	PUNCT
ejpam-6047	231	1	=	=	SYM
ejpam-6047	231	2	1	1	NUM
ejpam-6047	231	3	:	:	SYM
ejpam-6047	231	4	2	2	NUM
ejpam-6047	231	5	because	because	SCONJ
ejpam-6047	231	6	for	for	ADP
ejpam-6047	231	7	v1	v1	PROPN
ejpam-6047	231	8	∈	∈	PROPN
ejpam-6047	231	9	rn,1	rn,1	PROPN
ejpam-6047	231	10	,	,	PUNCT
ejpam-6047	231	11	re	re	X
ejpam-6047	231	12	(	(	PUNCT
ejpam-6047	231	13	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	231	14	+	+	NUM
ejpam-6047	231	15	γd−1	γd−1	PROPN
ejpam-6047	231	16	1	1	NUM
ejpam-6047	231	17	d2a2	d2a2	NOUN
ejpam-6047	231	18	)	)	PUNCT
ejpam-6047	231	19	)	)	PUNCT
ejpam-6047	231	20	)	)	PUNCT
ejpam-6047	232	1	=	=	PRON
ejpam-6047	232	2	vt1	vt1	PROPN
ejpam-6047	232	3	(	(	PUNCT
ejpam-6047	232	4	λiv1	λiv1	PROPN
ejpam-6047	232	5	)	)	PUNCT
ejpam-6047	233	1	=	=	SYM
ejpam-6047	233	2	vt1	vt1	PROPN
ejpam-6047	233	3	(	(	PUNCT
ejpam-6047	233	4	d1(a1	d1(a1	PROPN
ejpam-6047	233	5	+	+	CCONJ
ejpam-6047	233	6	γd−1	γd−1	PROPN
ejpam-6047	233	7	1	1	NUM
ejpam-6047	233	8	d2a2	d2a2	NOUN
ejpam-6047	233	9	)	)	PUNCT
ejpam-6047	233	10	)	)	PUNCT
ejpam-6047	233	11	v1	v1	NOUN
ejpam-6047	233	12	,	,	PUNCT
ejpam-6047	233	13	where	where	SCONJ
ejpam-6047	233	14	v1	v1	NOUN
ejpam-6047	233	15	is	be	AUX
ejpam-6047	233	16	unit	unit	NOUN
ejpam-6047	233	17	eigenvector	eigenvector	NOUN
ejpam-6047	233	18	corresponding	correspond	VERB
ejpam-6047	233	19	to	to	ADP
ejpam-6047	233	20	λi	λi	VERB
ejpam-6047	233	21	∀i	∀i	NOUN
ejpam-6047	233	22	=	=	SYM
ejpam-6047	233	23	1	1	NUM
ejpam-6047	233	24	:	:	PUNCT
ejpam-6047	233	25	n.	n.	NOUN
ejpam-6047	233	26	if	if	SCONJ
ejpam-6047	233	27	we	we	PRON
ejpam-6047	233	28	consider	consider	VERB
ejpam-6047	233	29	the	the	DET
ejpam-6047	233	30	matrix	matrix	NOUN
ejpam-6047	233	31	(	(	PUNCT
ejpam-6047	233	32	d1(a1	d1(a1	NOUN
ejpam-6047	233	33	+	+	CCONJ
ejpam-6047	233	34	γd−1	γd−1	PROPN
ejpam-6047	233	35	1	1	NUM
ejpam-6047	233	36	d2a2	d2a2	NOUN
ejpam-6047	233	37	)	)	PUNCT
ejpam-6047	233	38	)	)	PUNCT
ejpam-6047	234	1	such	such	ADJ
ejpam-6047	234	2	that	that	SCONJ
ejpam-6047	234	3	it	it	PRON
ejpam-6047	234	4	has	have	VERB
ejpam-6047	234	5	only	only	ADV
ejpam-6047	234	6	one	one	NUM
ejpam-6047	234	7	positive	positive	ADJ
ejpam-6047	234	8	eigenvalue	eigenvalue	NOUN
ejpam-6047	234	9	,	,	PUNCT
ejpam-6047	234	10	then	then	ADV
ejpam-6047	234	11	(	(	PUNCT
ejpam-6047	234	12	d1(a1	d1(a1	PROPN
ejpam-6047	234	13	+	+	NUM
ejpam-6047	234	14	γd−1	γd−1	PROPN
ejpam-6047	234	15	1	1	NUM
ejpam-6047	234	16	d2a2	d2a2	NOUN
ejpam-6047	234	17	)	)	PUNCT
ejpam-6047	234	18	)	)	PUNCT
ejpam-6047	235	1	=	=	SYM
ejpam-6047	235	2	uλut	uλut	NOUN
ejpam-6047	235	3	,	,	PUNCT
ejpam-6047	235	4	utu	utu	PROPN
ejpam-6047	235	5	=	=	PROPN
ejpam-6047	235	6	uut	uut	PROPN
ejpam-6047	235	7	=	=	NOUN
ejpam-6047	235	8	in	in	ADP
ejpam-6047	235	9	and	and	CCONJ
ejpam-6047	235	10	λ	λ	X
ejpam-6047	235	11	=	=	SYM
ejpam-6047	235	12	diag(λ1	diag(λ1	NOUN
ejpam-6047	235	13	,	,	PUNCT
ejpam-6047	235	14	λ2	λ2	NOUN
ejpam-6047	235	15	,	,	PUNCT
ejpam-6047	235	16	·	·	PUNCT
ejpam-6047	235	17	·	·	PUNCT
ejpam-6047	235	18	·	·	PUNCT
ejpam-6047	235	19	,	,	PUNCT
ejpam-6047	235	20	λn	λn	NOUN
ejpam-6047	235	21	)	)	PUNCT
ejpam-6047	235	22	.	.	PUNCT
ejpam-6047	236	1	this	this	DET
ejpam-6047	236	2	yield	yield	NOUN
ejpam-6047	236	3	xt	xt	PUNCT
ejpam-6047	236	4	(	(	PUNCT
ejpam-6047	236	5	d1(a1	d1(a1	PROPN
ejpam-6047	236	6	+	+	CCONJ
ejpam-6047	236	7	γd−1	γd−1	PROPN
ejpam-6047	236	8	1	1	NUM
ejpam-6047	236	9	d2a2	d2a2	NOUN
ejpam-6047	236	10	)	)	PUNCT
ejpam-6047	236	11	)	)	PUNCT
ejpam-6047	237	1	x	x	X
ejpam-6047	237	2	=	=	PUNCT
ejpam-6047	237	3	xtuλutx	xtuλutx	PROPN
ejpam-6047	237	4	=	=	PUNCT
ejpam-6047	237	5	(	(	PUNCT
ejpam-6047	237	6	u	u	NOUN
ejpam-6047	237	7	tx)tλ(utx	tx)tλ(utx	PROPN
ejpam-6047	237	8	)	)	PUNCT
ejpam-6047	237	9	=	=	PUNCT
ejpam-6047	238	1	∑	∑	PUNCT
ejpam-6047	239	1	i	i	PRON
ejpam-6047	239	2	re(λi)|vt1	re(λi)|vt1	VERB
ejpam-6047	239	3	x|2	x|2	PROPN
ejpam-6047	239	4	≥	≥	NUM
ejpam-6047	239	5	0	0	NUM
ejpam-6047	239	6	,	,	PUNCT
ejpam-6047	239	7	for	for	ADP
ejpam-6047	239	8	re	re	PROPN
ejpam-6047	239	9	(	(	PUNCT
ejpam-6047	239	10	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	239	11	+	+	NUM
ejpam-6047	239	12	γd−1	γd−1	PROPN
ejpam-6047	239	13	1	1	NUM
ejpam-6047	239	14	d2a2	d2a2	NOUN
ejpam-6047	239	15	)	)	PUNCT
ejpam-6047	239	16	)	)	PUNCT
ejpam-6047	239	17	>	>	X
ejpam-6047	240	1	0	0	NUM
ejpam-6047	240	2	,	,	PUNCT
ejpam-6047	240	3	and	and	CCONJ
ejpam-6047	240	4	some	some	DET
ejpam-6047	240	5	vt1	vt1	NOUN
ejpam-6047	240	6	x	x	X
ejpam-6047	240	7	̸=	̸=	PROPN
ejpam-6047	240	8	0	0	NUM
ejpam-6047	240	9	,	,	PUNCT
ejpam-6047	240	10	with	with	ADP
ejpam-6047	240	11	x	x	SYM
ejpam-6047	240	12	̸=	̸=	PROPN
ejpam-6047	240	13	0	0	NUM
ejpam-6047	240	14	.	.	PUNCT
ejpam-6047	240	15	theorem	theorem	VERB
ejpam-6047	240	16	6	6	NUM
ejpam-6047	240	17	shows	show	VERB
ejpam-6047	240	18	that	that	SCONJ
ejpam-6047	240	19	the	the	DET
ejpam-6047	240	20	positive	positive	ADJ
ejpam-6047	240	21	linear	linear	ADJ
ejpam-6047	240	22	time	time	NOUN
ejpam-6047	240	23	-	-	PUNCT
ejpam-6047	240	24	invariant	invariant	ADJ
ejpam-6047	240	25	system	system	NOUN
ejpam-6047	240	26	with	with	ADP
ejpam-6047	240	27	coefficient	coefficient	NOUN
ejpam-6047	240	28	matrices	matrix	NOUN
ejpam-6047	240	29	a1	a1	NOUN
ejpam-6047	240	30	,	,	PUNCT
ejpam-6047	240	31	a2	a2	PROPN
ejpam-6047	240	32	∈	∈	PROPN
ejpam-6047	240	33	rn	rn	PROPN
ejpam-6047	240	34	,	,	PUNCT
ejpam-6047	240	35	n	n	PRON
ejpam-6047	240	36	being	be	AUX
ejpam-6047	240	37	metzler	metzler	NOUN
ejpam-6047	240	38	and	and	CCONJ
ejpam-6047	240	39	hurwitz	hurwitz	PROPN
ejpam-6047	240	40	,	,	PUNCT
ejpam-6047	240	41	is	be	AUX
ejpam-6047	240	42	a	a	DET
ejpam-6047	240	43	stable	stable	ADJ
ejpam-6047	240	44	system	system	NOUN
ejpam-6047	240	45	for	for	ADP
ejpam-6047	240	46	st	st	PROPN
ejpam-6047	240	47	=	=	SYM
ejpam-6047	240	48	s	s	PROPN
ejpam-6047	240	49	,	,	PUNCT
ejpam-6047	240	50	γ	γ	X
ejpam-6047	240	51	>	>	X
ejpam-6047	240	52	0	0	PROPN
ejpam-6047	240	53	,	,	PUNCT
ejpam-6047	240	54	the	the	DET
ejpam-6047	240	55	perturbed	perturb	VERB
ejpam-6047	240	56	matrix	matrix	NOUN
ejpam-6047	240	57	d1	d1	NOUN
ejpam-6047	240	58	(	(	PUNCT
ejpam-6047	240	59	a1	a1	NOUN
ejpam-6047	240	60	+	+	CCONJ
ejpam-6047	240	61	γd−1	γd−1	PROPN
ejpam-6047	240	62	1	1	NUM
ejpam-6047	240	63	d2a2	d2a2	NOUN
ejpam-6047	240	64	)	)	PUNCT
ejpam-6047	240	65	)	)	PUNCT
ejpam-6047	241	1	t	t	PROPN
ejpam-6047	241	2	s	s	PART
ejpam-6047	241	3	(	(	PUNCT
ejpam-6047	241	4	d1(a1	d1(a1	PROPN
ejpam-6047	241	5	+	+	CCONJ
ejpam-6047	241	6	γd−1	γd−1	PROPN
ejpam-6047	241	7	1	1	NUM
ejpam-6047	241	8	d2a2	d2a2	NOUN
ejpam-6047	241	9	)	)	PUNCT
ejpam-6047	241	10	)	)	PUNCT
ejpam-6047	242	1	−	−	PROPN
ejpam-6047	242	2	s	s	VERB
ejpam-6047	242	3	,	,	PUNCT
ejpam-6047	242	4	has	have	VERB
ejpam-6047	242	5	strictly	strictly	ADV
ejpam-6047	242	6	positive	positive	ADJ
ejpam-6047	242	7	real	real	ADJ
ejpam-6047	242	8	part	part	NOUN
ejpam-6047	242	9	for	for	ADP
ejpam-6047	242	10	all	all	PRON
ejpam-6047	242	11	of	of	ADP
ejpam-6047	242	12	it	it	PRON
ejpam-6047	242	13	’s	’s	AUX
ejpam-6047	242	14	eigenvalues	eigenvalue	NOUN
ejpam-6047	242	15	.	.	PUNCT
ejpam-6047	243	1	m.u	m.u	PROPN
ejpam-6047	243	2	.	.	PROPN
ejpam-6047	243	3	rehman	rehman	PROPN
ejpam-6047	243	4	et	et	PROPN
ejpam-6047	243	5	al	al	PROPN
ejpam-6047	243	6	.	.	PUNCT
ejpam-6047	243	7	/	/	SYM
ejpam-6047	243	8	eur	eur	PROPN
ejpam-6047	243	9	.	.	PUNCT
ejpam-6047	244	1	j.	j.	PROPN
ejpam-6047	244	2	pure	pure	PROPN
ejpam-6047	244	3	appl	appl	PROPN
ejpam-6047	244	4	.	.	PROPN
ejpam-6047	244	5	math	math	PROPN
ejpam-6047	244	6	,	,	PUNCT
ejpam-6047	244	7	18	18	NUM
ejpam-6047	244	8	(	(	PUNCT
ejpam-6047	244	9	3	3	NUM
ejpam-6047	244	10	)	)	PUNCT
ejpam-6047	244	11	(	(	PUNCT
ejpam-6047	244	12	2025	2025	NUM
ejpam-6047	244	13	)	)	PUNCT
ejpam-6047	244	14	,	,	PUNCT
ejpam-6047	244	15	6047	6047	NUM
ejpam-6047	244	16	12	12	NUM
ejpam-6047	244	17	of	of	ADP
ejpam-6047	244	18	33	33	NUM
ejpam-6047	244	19	theorem	theorem	NOUN
ejpam-6047	244	20	6	6	NUM
ejpam-6047	244	21	.	.	PUNCT
ejpam-6047	245	1	let	let	VERB
ejpam-6047	245	2	a1	a1	NOUN
ejpam-6047	245	3	,	,	PUNCT
ejpam-6047	245	4	a2	a2	PROPN
ejpam-6047	245	5	∈	∈	PROPN
ejpam-6047	245	6	rn	rn	PROPN
ejpam-6047	245	7	,	,	PUNCT
ejpam-6047	245	8	n	n	PRON
ejpam-6047	245	9	be	be	VERB
ejpam-6047	245	10	metzler	metzler	NOUN
ejpam-6047	245	11	matrices	matrix	NOUN
ejpam-6047	245	12	and	and	CCONJ
ejpam-6047	245	13	hurwitz	hurwitz	PROPN
ejpam-6047	245	14	.	.	PUNCT
ejpam-6047	246	1	the	the	DET
ejpam-6047	246	2	linear	linear	ADJ
ejpam-6047	246	3	system	system	NOUN
ejpam-6047	246	4	dx(t	dx(t	NOUN
ejpam-6047	246	5	)	)	PUNCT
ejpam-6047	246	6	dt	dt	NOUN
ejpam-6047	246	7	=	=	SYM
ejpam-6047	246	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	246	9	)	)	PUNCT
ejpam-6047	246	10	,	,	PUNCT
ejpam-6047	246	11	where	where	SCONJ
ejpam-6047	246	12	a(t	a(t	NOUN
ejpam-6047	246	13	)	)	PUNCT
ejpam-6047	246	14	∈	∈	PROPN
ejpam-6047	246	15	{	{	PUNCT
ejpam-6047	246	16	d1a1	d1a1	NOUN
ejpam-6047	246	17	,	,	PUNCT
ejpam-6047	246	18	d2a2	d2a2	NOUN
ejpam-6047	246	19	}	}	PUNCT
ejpam-6047	246	20	,	,	PUNCT
ejpam-6047	246	21	d1	d1	PROPN
ejpam-6047	246	22	,	,	PUNCT
ejpam-6047	246	23	d2	d2	PROPN
ejpam-6047	246	24	>	>	X
ejpam-6047	246	25	0	0	PROPN
ejpam-6047	246	26	,	,	PUNCT
ejpam-6047	246	27	and	and	CCONJ
ejpam-6047	246	28	x(t	x(t	PROPN
ejpam-6047	246	29	)	)	PUNCT
ejpam-6047	246	30	∈	∈	PROPN
ejpam-6047	246	31	rn,1	rn,1	PROPN
ejpam-6047	246	32	,	,	PUNCT
ejpam-6047	246	33	is	be	AUX
ejpam-6047	246	34	stable	stable	ADJ
ejpam-6047	246	35	if	if	SCONJ
ejpam-6047	246	36	re	re	ADP
ejpam-6047	246	37	[	[	PUNCT
ejpam-6047	246	38	λi	λi	X
ejpam-6047	246	39	(	(	PUNCT
ejpam-6047	246	40	d1(a1	d1(a1	PROPN
ejpam-6047	246	41	+	+	NUM
ejpam-6047	246	42	γd−1	γd−1	PROPN
ejpam-6047	246	43	1	1	NUM
ejpam-6047	246	44	d2a2	d2a2	NOUN
ejpam-6047	246	45	)	)	PUNCT
ejpam-6047	246	46	)	)	PUNCT
ejpam-6047	247	1	t	t	PROPN
ejpam-6047	247	2	s	s	PART
ejpam-6047	247	3	(	(	PUNCT
ejpam-6047	247	4	d1(a1	d1(a1	PROPN
ejpam-6047	247	5	+	+	CCONJ
ejpam-6047	247	6	γd−1	γd−1	PROPN
ejpam-6047	247	7	1	1	NUM
ejpam-6047	247	8	d2a2	d2a2	NOUN
ejpam-6047	247	9	)	)	PUNCT
ejpam-6047	247	10	)	)	PUNCT
ejpam-6047	248	1	−	−	PROPN
ejpam-6047	248	2	s	s	X
ejpam-6047	248	3	]	]	X
ejpam-6047	248	4	>	>	X
ejpam-6047	248	5	0	0	NUM
ejpam-6047	248	6	∀i	∀i	NOUN
ejpam-6047	248	7	=	=	SYM
ejpam-6047	248	8	1	1	NUM
ejpam-6047	248	9	:	:	PUNCT
ejpam-6047	248	10	n	n	X
ejpam-6047	248	11	with	with	ADP
ejpam-6047	248	12	st	st	PROPN
ejpam-6047	248	13	=	=	SYM
ejpam-6047	248	14	s	s	PROPN
ejpam-6047	248	15	and	and	CCONJ
ejpam-6047	248	16	s	s	VERB
ejpam-6047	248	17	>	>	X
ejpam-6047	248	18	0	0	NUM
ejpam-6047	248	19	is	be	AUX
ejpam-6047	248	20	positive	positive	ADJ
ejpam-6047	248	21	definite	definite	ADJ
ejpam-6047	248	22	matrix	matrix	NOUN
ejpam-6047	248	23	.	.	PUNCT
ejpam-6047	249	1	proof	proof	NOUN
ejpam-6047	249	2	.	.	PUNCT
ejpam-6047	250	1	consider	consider	VERB
ejpam-6047	250	2	α	α	PRON
ejpam-6047	250	3	∈	∈	PROPN
ejpam-6047	250	4	{	{	PUNCT
ejpam-6047	250	5	1	1	NUM
ejpam-6047	250	6	,	,	PUNCT
ejpam-6047	250	7	2	2	NUM
ejpam-6047	250	8	,	,	PUNCT
ejpam-6047	250	9	·	·	PUNCT
ejpam-6047	250	10	·	·	PUNCT
ejpam-6047	250	11	·	·	PUNCT
ejpam-6047	250	12	,	,	PUNCT
ejpam-6047	250	13	n	n	CCONJ
ejpam-6047	250	14	}	}	PUNCT
ejpam-6047	250	15	,	,	PUNCT
ejpam-6047	250	16	and	and	CCONJ
ejpam-6047	250	17	let	let	VERB
ejpam-6047	250	18	x(t	x(t	PROPN
ejpam-6047	250	19	)	)	PUNCT
ejpam-6047	250	20	∈	∈	PROPN
ejpam-6047	250	21	rn,1	rn,1	PROPN
ejpam-6047	250	22	,	,	PUNCT
ejpam-6047	250	23	t	t	PROPN
ejpam-6047	250	24	∈	∈	PROPN
ejpam-6047	250	25	r+	r+	X
ejpam-6047	250	26	.	.	PUNCT
ejpam-6047	251	1	also	also	ADV
ejpam-6047	251	2	,	,	PUNCT
ejpam-6047	251	3	assume	assume	VERB
ejpam-6047	251	4	that	that	SCONJ
ejpam-6047	251	5	x[α	x[α	X
ejpam-6047	251	6	]	]	X
ejpam-6047	251	7	̸=	̸=	PROPN
ejpam-6047	251	8	0	0	NUM
ejpam-6047	251	9	.	.	PUNCT
ejpam-6047	252	1	for	for	ADP
ejpam-6047	252	2	the	the	DET
ejpam-6047	252	3	proof	proof	NOUN
ejpam-6047	252	4	of	of	ADP
ejpam-6047	252	5	our	our	PRON
ejpam-6047	252	6	result	result	NOUN
ejpam-6047	252	7	,	,	PUNCT
ejpam-6047	252	8	we	we	PRON
ejpam-6047	252	9	take	take	VERB
ejpam-6047	252	10	a	a	DET
ejpam-6047	252	11	non	non	ADJ
ejpam-6047	252	12	-	-	ADJ
ejpam-6047	252	13	zero	zero	NUM
ejpam-6047	252	14	vector	vector	NOUN
ejpam-6047	252	15	x(t	x(t	PROPN
ejpam-6047	252	16	)	)	PUNCT
ejpam-6047	252	17	,	,	PUNCT
ejpam-6047	252	18	so	so	SCONJ
ejpam-6047	252	19	that	that	SCONJ
ejpam-6047	252	20	x[α]t	x[α]t	PROPN
ejpam-6047	252	21	(	(	PUNCT
ejpam-6047	252	22	d1(a1	d1(a1	PROPN
ejpam-6047	252	23	+	+	CCONJ
ejpam-6047	252	24	γd−1	γd−1	PROPN
ejpam-6047	252	25	1	1	NUM
ejpam-6047	252	26	d2a2	d2a2	PROPN
ejpam-6047	252	27	)	)	PUNCT
ejpam-6047	252	28	t	t	PROPN
ejpam-6047	252	29	s	s	PART
ejpam-6047	252	30	(	(	PUNCT
ejpam-6047	252	31	d1(a1	d1(a1	PROPN
ejpam-6047	252	32	+	+	CCONJ
ejpam-6047	252	33	γd−1	γd−1	PROPN
ejpam-6047	252	34	1	1	NUM
ejpam-6047	252	35	d2a2	d2a2	NOUN
ejpam-6047	252	36	)	)	PUNCT
ejpam-6047	253	1	−	−	PROPN
ejpam-6047	253	2	s	s	NOUN
ejpam-6047	253	3	)	)	PUNCT
ejpam-6047	253	4	)	)	PUNCT
ejpam-6047	254	1	x[α	x[α	NUM
ejpam-6047	254	2	]	]	X
ejpam-6047	254	3	=	=	SYM
ejpam-6047	254	4	xt	xt	X
ejpam-6047	254	5	(	(	PUNCT
ejpam-6047	254	6	t	t	PROPN
ejpam-6047	254	7	)	)	PUNCT
ejpam-6047	254	8	(	(	PUNCT
ejpam-6047	254	9	(	(	PUNCT
ejpam-6047	254	10	d1(a1	d1(a1	NOUN
ejpam-6047	254	11	+	+	NUM
ejpam-6047	254	12	γd−1	γd−1	PROPN
ejpam-6047	254	13	1	1	NUM
ejpam-6047	254	14	d2a2	d2a2	PROPN
ejpam-6047	254	15	)	)	PUNCT
ejpam-6047	254	16	s	s	PROPN
ejpam-6047	254	17	(	(	PUNCT
ejpam-6047	254	18	d1(a1	d1(a1	PROPN
ejpam-6047	254	19	+	+	CCONJ
ejpam-6047	254	20	γd−1	γd−1	PROPN
ejpam-6047	254	21	1	1	NUM
ejpam-6047	254	22	d2a2	d2a2	NOUN
ejpam-6047	254	23	)	)	PUNCT
ejpam-6047	254	24	−	−	PROPN
ejpam-6047	254	25	s)x(t	s)x(t	NOUN
ejpam-6047	254	26	)	)	PUNCT
ejpam-6047	254	27	)	)	PUNCT
ejpam-6047	255	1	>	>	X
ejpam-6047	255	2	0	0	X
ejpam-6047	255	3	.	.	PUNCT
ejpam-6047	256	1	further	far	ADV
ejpam-6047	256	2	,	,	PUNCT
ejpam-6047	256	3	we	we	PRON
ejpam-6047	256	4	have	have	VERB
ejpam-6047	256	5	xt	xt	NUM
ejpam-6047	257	1	(	(	PUNCT
ejpam-6047	257	2	t)re	t)re	PROPN
ejpam-6047	257	3	(	(	PUNCT
ejpam-6047	257	4	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	257	5	+	+	NUM
ejpam-6047	257	6	γd−1	γd−1	PROPN
ejpam-6047	257	7	1	1	NUM
ejpam-6047	257	8	d2a2	d2a2	NOUN
ejpam-6047	257	9	)	)	PUNCT
ejpam-6047	257	10	)	)	PUNCT
ejpam-6047	257	11	x(t	x(t	PROPN
ejpam-6047	257	12	)	)	PUNCT
ejpam-6047	257	13	>	>	X
ejpam-6047	257	14	0	0	NUM
ejpam-6047	257	15	,	,	PUNCT
ejpam-6047	257	16	∀i	∀i	NOUN
ejpam-6047	257	17	=	=	SYM
ejpam-6047	257	18	1	1	NUM
ejpam-6047	257	19	:	:	PUNCT
ejpam-6047	257	20	n.	n.	NOUN
ejpam-6047	257	21	in	in	ADP
ejpam-6047	257	22	turn	turn	NOUN
ejpam-6047	257	23	,	,	PUNCT
ejpam-6047	257	24	this	this	DET
ejpam-6047	257	25	yields	yield	NOUN
ejpam-6047	257	26	re(λi	re(λi	VERB
ejpam-6047	257	27	(	(	PUNCT
ejpam-6047	257	28	d1(a1	d1(a1	NOUN
ejpam-6047	257	29	+	+	CCONJ
ejpam-6047	257	30	γd−1	γd−1	PROPN
ejpam-6047	257	31	1	1	NUM
ejpam-6047	257	32	d2a2	d2a2	NOUN
ejpam-6047	257	33	)	)	PUNCT
ejpam-6047	257	34	)	)	PUNCT
ejpam-6047	257	35	>	>	X
ejpam-6047	257	36	0	0	NUM
ejpam-6047	257	37	,	,	PUNCT
ejpam-6047	257	38	∀i	∀i	NOUN
ejpam-6047	257	39	=	=	SYM
ejpam-6047	257	40	1	1	NUM
ejpam-6047	257	41	:	:	SYM
ejpam-6047	257	42	n	n	NUM
ejpam-6047	257	43	and	and	CCONJ
ejpam-6047	257	44	||x(t)||	||x(t)||	NUM
ejpam-6047	257	45	=	=	NOUN
ejpam-6047	257	46	1	1	NUM
ejpam-6047	257	47	.	.	PUNCT
ejpam-6047	258	1	thus	thus	ADV
ejpam-6047	258	2	,	,	PUNCT
ejpam-6047	258	3	finally	finally	ADV
ejpam-6047	258	4	we	we	PRON
ejpam-6047	258	5	have	have	VERB
ejpam-6047	258	6	that	that	PRON
ejpam-6047	258	7	given	give	VERB
ejpam-6047	258	8	linear	linear	ADJ
ejpam-6047	258	9	system	system	NOUN
ejpam-6047	258	10	is	be	AUX
ejpam-6047	258	11	stable	stable	ADJ
ejpam-6047	258	12	.	.	PUNCT
ejpam-6047	259	1	theorem	theorem	ADJ
ejpam-6047	259	2	7	7	NUM
ejpam-6047	259	3	.	.	PUNCT
ejpam-6047	260	1	let	let	VERB
ejpam-6047	260	2	a1	a1	NOUN
ejpam-6047	260	3	,	,	PUNCT
ejpam-6047	260	4	a2	a2	PROPN
ejpam-6047	260	5	∈	∈	PROPN
ejpam-6047	260	6	rn	rn	PROPN
ejpam-6047	260	7	,	,	PUNCT
ejpam-6047	260	8	n	n	PRON
ejpam-6047	260	9	be	be	VERB
ejpam-6047	260	10	metzler	metzler	NOUN
ejpam-6047	260	11	matrices	matrix	NOUN
ejpam-6047	260	12	and	and	CCONJ
ejpam-6047	260	13	hurwitz	hurwitz	PROPN
ejpam-6047	260	14	.	.	PUNCT
ejpam-6047	261	1	the	the	DET
ejpam-6047	261	2	linear	linear	ADJ
ejpam-6047	261	3	system	system	NOUN
ejpam-6047	261	4	dx(t	dx(t	NOUN
ejpam-6047	261	5	)	)	PUNCT
ejpam-6047	261	6	dt	dt	NOUN
ejpam-6047	261	7	=	=	SYM
ejpam-6047	261	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	261	9	)	)	PUNCT
ejpam-6047	261	10	,	,	PUNCT
ejpam-6047	261	11	where	where	SCONJ
ejpam-6047	261	12	a(t	a(t	NOUN
ejpam-6047	261	13	)	)	PUNCT
ejpam-6047	261	14	∈	∈	PROPN
ejpam-6047	261	15	{	{	PUNCT
ejpam-6047	261	16	d1a1	d1a1	NOUN
ejpam-6047	261	17	,	,	PUNCT
ejpam-6047	261	18	d2a2	d2a2	NOUN
ejpam-6047	261	19	}	}	PUNCT
ejpam-6047	261	20	,	,	PUNCT
ejpam-6047	261	21	d1	d1	PROPN
ejpam-6047	261	22	,	,	PUNCT
ejpam-6047	261	23	d2	d2	PROPN
ejpam-6047	261	24	>	>	X
ejpam-6047	261	25	0	0	PROPN
ejpam-6047	261	26	,	,	PUNCT
ejpam-6047	261	27	and	and	CCONJ
ejpam-6047	261	28	x(t	x(t	PROPN
ejpam-6047	261	29	)	)	PUNCT
ejpam-6047	261	30	∈	∈	PROPN
ejpam-6047	261	31	rn,1	rn,1	NOUN
ejpam-6047	261	32	is	be	AUX
ejpam-6047	261	33	stable	stable	ADJ
ejpam-6047	261	34	if	if	SCONJ
ejpam-6047	261	35	re	re	ADP
ejpam-6047	261	36	[	[	PUNCT
ejpam-6047	261	37	λi	λi	X
ejpam-6047	261	38	(	(	PUNCT
ejpam-6047	261	39	(	(	PUNCT
ejpam-6047	261	40	d1(a1	d1(a1	NOUN
ejpam-6047	261	41	+	+	NUM
ejpam-6047	261	42	γd−1	γd−1	PROPN
ejpam-6047	261	43	1	1	NUM
ejpam-6047	261	44	d2a2	d2a2	NOUN
ejpam-6047	261	45	)	)	PUNCT
ejpam-6047	261	46	)	)	PUNCT
ejpam-6047	262	1	t	t	PROPN
ejpam-6047	262	2	s	s	PART
ejpam-6047	262	3	(	(	PUNCT
ejpam-6047	262	4	d1(a1	d1(a1	PROPN
ejpam-6047	262	5	+	+	CCONJ
ejpam-6047	262	6	γd−1	γd−1	PROPN
ejpam-6047	262	7	1	1	NUM
ejpam-6047	262	8	d2a2	d2a2	NOUN
ejpam-6047	262	9	)	)	PUNCT
ejpam-6047	262	10	)	)	PUNCT
ejpam-6047	263	1	−	−	PROPN
ejpam-6047	263	2	s	s	PART
ejpam-6047	263	3	)	)	PUNCT
ejpam-6047	263	4	]	]	PUNCT
ejpam-6047	264	1	>	>	X
ejpam-6047	264	2	0	0	NUM
ejpam-6047	264	3	∀i	∀i	NOUN
ejpam-6047	264	4	=	=	SYM
ejpam-6047	264	5	1	1	NUM
ejpam-6047	264	6	:	:	PUNCT
ejpam-6047	264	7	n.	n.	NOUN
ejpam-6047	264	8	let	let	VERB
ejpam-6047	264	9	(	(	PUNCT
ejpam-6047	264	10	λi(t	λi(t	NUM
ejpam-6047	264	11	)	)	PUNCT
ejpam-6047	264	12	,	,	PUNCT
ejpam-6047	264	13	xi(t	xi(t	NOUN
ejpam-6047	264	14	)	)	PUNCT
ejpam-6047	264	15	)	)	PUNCT
ejpam-6047	264	16	be	be	AUX
ejpam-6047	264	17	an	an	DET
ejpam-6047	264	18	eigenpair	eigenpair	NOUN
ejpam-6047	264	19	,	,	PUNCT
ejpam-6047	264	20	and	and	CCONJ
ejpam-6047	264	21	assume	assume	VERB
ejpam-6047	264	22	that	that	SCONJ
ejpam-6047	264	23	ρ	ρ	PROPN
ejpam-6047	264	24	=	=	SYM
ejpam-6047	264	25	∣∣∣re	∣∣∣re	PROPN
ejpam-6047	264	26	(	(	PUNCT
ejpam-6047	264	27	λi(d1(a1	λi(d1(a1	PROPN
ejpam-6047	264	28	+	+	NUM
ejpam-6047	264	29	γd−1	γd−1	PROPN
ejpam-6047	264	30	1	1	NUM
ejpam-6047	264	31	d2a2	d2a2	PROPN
ejpam-6047	264	32	)	)	PUNCT
ejpam-6047	264	33	t	t	PROPN
ejpam-6047	264	34	s	s	PART
ejpam-6047	264	35	(	(	PUNCT
ejpam-6047	264	36	d1(a1	d1(a1	PROPN
ejpam-6047	264	37	+	+	CCONJ
ejpam-6047	264	38	γd−1	γd−1	PROPN
ejpam-6047	264	39	1	1	NUM
ejpam-6047	264	40	d2a2	d2a2	NOUN
ejpam-6047	264	41	)	)	PUNCT
ejpam-6047	264	42	)	)	PUNCT
ejpam-6047	265	1	−	−	PROPN
ejpam-6047	265	2	s	s	X
ejpam-6047	265	3	∣∣∣	∣∣∣	NOUN
ejpam-6047	265	4	,	,	PUNCT
ejpam-6047	265	5	then	then	ADV
ejpam-6047	265	6	|x(t)|	|x(t)|	PROPN
ejpam-6047	265	7	>	>	X
ejpam-6047	265	8	0	0	NUM
ejpam-6047	265	9	,	,	PUNCT
ejpam-6047	265	10	t	t	PROPN
ejpam-6047	265	11	∈	∈	PROPN
ejpam-6047	265	12	r+	r+	PUNCT
ejpam-6047	265	13	and	and	CCONJ
ejpam-6047	265	14	(	(	PUNCT
ejpam-6047	265	15	(	(	PUNCT
ejpam-6047	265	16	d1(a1	d1(a1	NOUN
ejpam-6047	265	17	+	+	NUM
ejpam-6047	265	18	γd−1	γd−1	PROPN
ejpam-6047	265	19	1	1	NUM
ejpam-6047	265	20	d2a2	d2a2	NOUN
ejpam-6047	265	21	)	)	PUNCT
ejpam-6047	265	22	)	)	PUNCT
ejpam-6047	266	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	266	2	+	+	NUM
ejpam-6047	266	3	γd−1	γd−1	PROPN
ejpam-6047	266	4	1	1	NUM
ejpam-6047	266	5	d2a2	d2a2	NOUN
ejpam-6047	266	6	)	)	PUNCT
ejpam-6047	266	7	)	)	PUNCT
ejpam-6047	267	1	−	−	PROPN
ejpam-6047	267	2	s	s	PART
ejpam-6047	267	3	)	)	PUNCT
ejpam-6047	267	4	|x(t)|	|x(t)|	PROPN
ejpam-6047	267	5	=	=	SYM
ejpam-6047	267	6	ρ	ρ	PROPN
ejpam-6047	267	7	(	(	PUNCT
ejpam-6047	267	8	(	(	PUNCT
ejpam-6047	267	9	d1(a1	d1(a1	NOUN
ejpam-6047	267	10	+	+	NUM
ejpam-6047	267	11	γd−1	γd−1	PROPN
ejpam-6047	267	12	1	1	NUM
ejpam-6047	267	13	d2a2	d2a2	NOUN
ejpam-6047	267	14	)	)	PUNCT
ejpam-6047	267	15	)	)	PUNCT
ejpam-6047	268	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	268	2	+	+	NUM
ejpam-6047	268	3	γd−1	γd−1	PROPN
ejpam-6047	268	4	1	1	NUM
ejpam-6047	268	5	d2a2	d2a2	NOUN
ejpam-6047	268	6	)	)	PUNCT
ejpam-6047	268	7	)	)	PUNCT
ejpam-6047	269	1	−	−	PROPN
ejpam-6047	269	2	s	s	X
ejpam-6047	269	3	)	)	PUNCT
ejpam-6047	269	4	)	)	PUNCT
ejpam-6047	270	1	|x(t)|	|x(t)|	PROPN
ejpam-6047	270	2	.	.	PUNCT
ejpam-6047	270	3	m.u	m.u	PROPN
ejpam-6047	270	4	.	.	PROPN
ejpam-6047	270	5	rehman	rehman	PROPN
ejpam-6047	270	6	et	et	PROPN
ejpam-6047	270	7	al	al	PROPN
ejpam-6047	270	8	.	.	PUNCT
ejpam-6047	270	9	/	/	SYM
ejpam-6047	270	10	eur	eur	PROPN
ejpam-6047	270	11	.	.	PUNCT
ejpam-6047	271	1	j.	j.	PROPN
ejpam-6047	271	2	pure	pure	PROPN
ejpam-6047	271	3	appl	appl	PROPN
ejpam-6047	271	4	.	.	PROPN
ejpam-6047	271	5	math	math	PROPN
ejpam-6047	271	6	,	,	PUNCT
ejpam-6047	271	7	18	18	NUM
ejpam-6047	271	8	(	(	PUNCT
ejpam-6047	271	9	3	3	NUM
ejpam-6047	271	10	)	)	PUNCT
ejpam-6047	271	11	(	(	PUNCT
ejpam-6047	271	12	2025	2025	NUM
ejpam-6047	271	13	)	)	PUNCT
ejpam-6047	271	14	,	,	PUNCT
ejpam-6047	271	15	6047	6047	NUM
ejpam-6047	271	16	13	13	NUM
ejpam-6047	271	17	of	of	ADP
ejpam-6047	271	18	33	33	NUM
ejpam-6047	271	19	proof	proof	NOUN
ejpam-6047	271	20	.	.	PUNCT
ejpam-6047	272	1	consider	consider	VERB
ejpam-6047	272	2	that	that	PRON
ejpam-6047	272	3	x̃(t	x̃(t	PROPN
ejpam-6047	272	4	)	)	PUNCT
ejpam-6047	273	1	=	=	SYM
ejpam-6047	273	2	(	(	PUNCT
ejpam-6047	273	3	(	(	PUNCT
ejpam-6047	273	4	d1(a1	d1(a1	NOUN
ejpam-6047	273	5	+	+	NUM
ejpam-6047	273	6	γd−1	γd−1	PROPN
ejpam-6047	273	7	1	1	NUM
ejpam-6047	273	8	d2a2	d2a2	NOUN
ejpam-6047	273	9	)	)	PUNCT
ejpam-6047	273	10	)	)	PUNCT
ejpam-6047	274	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	274	2	+	+	NUM
ejpam-6047	274	3	γd−1	γd−1	PROPN
ejpam-6047	274	4	1	1	NUM
ejpam-6047	274	5	d2a2	d2a2	NOUN
ejpam-6047	274	6	)	)	PUNCT
ejpam-6047	274	7	)	)	PUNCT
ejpam-6047	275	1	−	−	PROPN
ejpam-6047	275	2	s	s	X
ejpam-6047	275	3	)	)	PUNCT
ejpam-6047	275	4	)	)	PUNCT
ejpam-6047	276	1	|x(t)|	|x(t)|	ADP
ejpam-6047	276	2	>	>	X
ejpam-6047	276	3	0	0	X
ejpam-6047	276	4	.	.	PUNCT
ejpam-6047	277	1	this	this	DET
ejpam-6047	277	2	further	far	ADV
ejpam-6047	277	3	implies	imply	VERB
ejpam-6047	277	4	that	that	SCONJ
ejpam-6047	277	5	x̃(t	x̃(t	PROPN
ejpam-6047	277	6	)	)	PUNCT
ejpam-6047	277	7	=	=	SYM
ejpam-6047	278	1	re	re	X
ejpam-6047	278	2	[	[	PUNCT
ejpam-6047	278	3	λi	λi	X
ejpam-6047	278	4	(	(	PUNCT
ejpam-6047	278	5	(	(	PUNCT
ejpam-6047	278	6	d1(a1	d1(a1	NOUN
ejpam-6047	278	7	+	+	NUM
ejpam-6047	278	8	γd−1	γd−1	PROPN
ejpam-6047	278	9	1	1	NUM
ejpam-6047	278	10	d2a2	d2a2	NOUN
ejpam-6047	278	11	)	)	PUNCT
ejpam-6047	278	12	)	)	PUNCT
ejpam-6047	279	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	279	2	+	+	NUM
ejpam-6047	279	3	γd−1	γd−1	PROPN
ejpam-6047	279	4	1	1	NUM
ejpam-6047	279	5	d2a2	d2a2	NOUN
ejpam-6047	279	6	)	)	PUNCT
ejpam-6047	279	7	)	)	PUNCT
ejpam-6047	280	1	−	−	PROPN
ejpam-6047	280	2	s	s	X
ejpam-6047	280	3	)	)	PUNCT
ejpam-6047	280	4	)	)	PUNCT
ejpam-6047	280	5	]	]	PUNCT
ejpam-6047	281	1	|x(t)|	|x(t)|	PROPN
ejpam-6047	281	2	.	.	PUNCT
ejpam-6047	281	3	also	also	ADV
ejpam-6047	281	4	,	,	PUNCT
ejpam-6047	281	5	from	from	ADP
ejpam-6047	281	6	this	this	PRON
ejpam-6047	281	7	we	we	PRON
ejpam-6047	281	8	have	have	VERB
ejpam-6047	281	9	that	that	PRON
ejpam-6047	281	10	,	,	PUNCT
ejpam-6047	281	11	x̃(t	x̃(t	PROPN
ejpam-6047	281	12	)	)	PUNCT
ejpam-6047	281	13	=	=	SYM
ejpam-6047	281	14	ρ	ρ	PROPN
ejpam-6047	281	15	(	(	PUNCT
ejpam-6047	281	16	(	(	PUNCT
ejpam-6047	281	17	d1(a1	d1(a1	NOUN
ejpam-6047	281	18	+	+	NUM
ejpam-6047	281	19	γd−1	γd−1	PROPN
ejpam-6047	281	20	1	1	NUM
ejpam-6047	281	21	d2a2	d2a2	NOUN
ejpam-6047	281	22	)	)	PUNCT
ejpam-6047	281	23	)	)	PUNCT
ejpam-6047	282	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	282	2	+	+	NUM
ejpam-6047	282	3	γd−1	γd−1	PROPN
ejpam-6047	282	4	1	1	NUM
ejpam-6047	282	5	d2a2	d2a2	NOUN
ejpam-6047	282	6	)	)	PUNCT
ejpam-6047	282	7	)	)	PUNCT
ejpam-6047	283	1	−	−	PROPN
ejpam-6047	283	2	s	s	X
ejpam-6047	283	3	)	)	PUNCT
ejpam-6047	283	4	)	)	PUNCT
ejpam-6047	284	1	|x(t)|	|x(t)|	PRON
ejpam-6047	284	2	.	.	PUNCT
ejpam-6047	284	3	let	let	VERB
ejpam-6047	284	4	x̂(t	x̂(t	PRON
ejpam-6047	284	5	)	)	PUNCT
ejpam-6047	284	6	=	=	SYM
ejpam-6047	284	7	x(t	x(t	PROPN
ejpam-6047	284	8	)	)	PUNCT
ejpam-6047	284	9	−	−	PROPN
ejpam-6047	284	10	ρ	ρ	PROPN
ejpam-6047	284	11	(	(	PUNCT
ejpam-6047	284	12	(	(	PUNCT
ejpam-6047	284	13	d1(a1	d1(a1	NOUN
ejpam-6047	284	14	+	+	NUM
ejpam-6047	284	15	γd−1	γd−1	PROPN
ejpam-6047	284	16	1	1	NUM
ejpam-6047	284	17	d2a2	d2a2	NOUN
ejpam-6047	284	18	)	)	PUNCT
ejpam-6047	284	19	)	)	PUNCT
ejpam-6047	285	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	285	2	+	+	NUM
ejpam-6047	285	3	γd−1	γd−1	PROPN
ejpam-6047	285	4	1	1	NUM
ejpam-6047	285	5	d2a2	d2a2	NOUN
ejpam-6047	285	6	)	)	PUNCT
ejpam-6047	285	7	)	)	PUNCT
ejpam-6047	286	1	−	−	PROPN
ejpam-6047	286	2	s	s	X
ejpam-6047	286	3	)	)	PUNCT
ejpam-6047	286	4	)	)	PUNCT
ejpam-6047	287	1	|x(t)|	|x(t)|	ADP
ejpam-6047	287	2	≥	≥	NUM
ejpam-6047	287	3	0	0	NUM
ejpam-6047	287	4	.	.	PUNCT
ejpam-6047	288	1	also	also	ADV
ejpam-6047	288	2	,	,	PUNCT
ejpam-6047	288	3	ρ	ρ	PROPN
ejpam-6047	288	4	(	(	PUNCT
ejpam-6047	288	5	(	(	PUNCT
ejpam-6047	288	6	d1(a1	d1(a1	NOUN
ejpam-6047	288	7	+	+	NUM
ejpam-6047	288	8	γd−1	γd−1	PROPN
ejpam-6047	288	9	1	1	NUM
ejpam-6047	288	10	d2a2	d2a2	NOUN
ejpam-6047	288	11	)	)	PUNCT
ejpam-6047	288	12	)	)	PUNCT
ejpam-6047	289	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	289	2	+	+	NUM
ejpam-6047	289	3	γd−1	γd−1	PROPN
ejpam-6047	289	4	1	1	NUM
ejpam-6047	289	5	d2a2	d2a2	NOUN
ejpam-6047	289	6	)	)	PUNCT
ejpam-6047	289	7	)	)	PUNCT
ejpam-6047	290	1	−	−	PROPN
ejpam-6047	290	2	s	s	X
ejpam-6047	290	3	)	)	PUNCT
ejpam-6047	290	4	)	)	PUNCT
ejpam-6047	291	1	≥	≥	NOUN
ejpam-6047	291	2	0	0	NUM
ejpam-6047	291	3	,	,	PUNCT
ejpam-6047	291	4	and	and	CCONJ
ejpam-6047	291	5	|x(t)|	|x(t)|	ADP
ejpam-6047	291	6	>	>	X
ejpam-6047	291	7	0	0	NUM
ejpam-6047	291	8	,	,	PUNCT
ejpam-6047	291	9	x̂(t	x̂(t	PRON
ejpam-6047	291	10	)	)	PUNCT
ejpam-6047	291	11	=	=	SYM
ejpam-6047	292	1	0	0	X
ejpam-6047	292	2	.	.	PUNCT
ejpam-6047	293	1	for	for	ADP
ejpam-6047	293	2	x̃(t	x̃(t	NOUN
ejpam-6047	293	3	)	)	PUNCT
ejpam-6047	293	4	̸=	̸=	PROPN
ejpam-6047	293	5	0	0	NUM
ejpam-6047	293	6	,	,	PUNCT
ejpam-6047	293	7	we	we	PRON
ejpam-6047	293	8	have	have	VERB
ejpam-6047	293	9	(	(	PUNCT
ejpam-6047	293	10	(	(	PUNCT
ejpam-6047	293	11	d1(a1	d1(a1	NOUN
ejpam-6047	293	12	+	+	NUM
ejpam-6047	293	13	γd−1	γd−1	PROPN
ejpam-6047	293	14	1	1	NUM
ejpam-6047	293	15	d2a2	d2a2	NOUN
ejpam-6047	293	16	)	)	PUNCT
ejpam-6047	293	17	)	)	PUNCT
ejpam-6047	294	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	294	2	+	+	NUM
ejpam-6047	294	3	γd−1	γd−1	PROPN
ejpam-6047	294	4	1	1	NUM
ejpam-6047	294	5	d2a2	d2a2	NOUN
ejpam-6047	294	6	)	)	PUNCT
ejpam-6047	294	7	)	)	PUNCT
ejpam-6047	295	1	−	−	PROPN
ejpam-6047	295	2	s	s	X
ejpam-6047	295	3	)	)	PUNCT
ejpam-6047	295	4	)	)	PUNCT
ejpam-6047	296	1	x(t	x(t	PROPN
ejpam-6047	296	2	)	)	PUNCT
ejpam-6047	296	3	>	>	X
ejpam-6047	297	1	ρ	ρ	PROPN
ejpam-6047	297	2	(	(	PUNCT
ejpam-6047	297	3	(	(	PUNCT
ejpam-6047	297	4	d1(a1	d1(a1	NOUN
ejpam-6047	297	5	+	+	NUM
ejpam-6047	297	6	γd−1	γd−1	PROPN
ejpam-6047	297	7	1	1	NUM
ejpam-6047	297	8	d2a2	d2a2	NOUN
ejpam-6047	297	9	)	)	PUNCT
ejpam-6047	297	10	)	)	PUNCT
ejpam-6047	298	1	ts(d1(a1	ts(d1(a1	NOUN
ejpam-6047	298	2	+	+	NUM
ejpam-6047	298	3	γd−1	γd−1	PROPN
ejpam-6047	298	4	1	1	NUM
ejpam-6047	298	5	d2a2	d2a2	NOUN
ejpam-6047	298	6	)	)	PUNCT
ejpam-6047	298	7	)	)	PUNCT
ejpam-6047	299	1	−	−	PROPN
ejpam-6047	299	2	s	s	X
ejpam-6047	299	3	)	)	PUNCT
ejpam-6047	299	4	)	)	PUNCT
ejpam-6047	300	1	x(t	x(t	PROPN
ejpam-6047	300	2	)	)	PUNCT
ejpam-6047	300	3	,	,	PUNCT
ejpam-6047	300	4	which	which	PRON
ejpam-6047	300	5	is	be	AUX
ejpam-6047	300	6	only	only	ADV
ejpam-6047	300	7	possible	possible	ADJ
ejpam-6047	300	8	if	if	SCONJ
ejpam-6047	300	9	we	we	PRON
ejpam-6047	300	10	do	do	AUX
ejpam-6047	300	11	n’t	not	PART
ejpam-6047	300	12	consider	consider	VERB
ejpam-6047	300	13	x(t	x(t	PROPN
ejpam-6047	300	14	)	)	PUNCT
ejpam-6047	300	15	,	,	PUNCT
ejpam-6047	300	16	and	and	CCONJ
ejpam-6047	300	17	this	this	PRON
ejpam-6047	300	18	is	be	AUX
ejpam-6047	300	19	not	not	PART
ejpam-6047	300	20	possible	possible	ADJ
ejpam-6047	300	21	,	,	PUNCT
ejpam-6047	300	22	and	and	CCONJ
ejpam-6047	300	23	hence	hence	ADV
ejpam-6047	300	24	x̃(t	x̃(t	PROPN
ejpam-6047	300	25	)	)	PUNCT
ejpam-6047	300	26	̸=	̸=	PROPN
ejpam-6047	300	27	0	0	NUM
ejpam-6047	300	28	.	.	PROPN
ejpam-6047	301	1	4.2	4.2	NUM
ejpam-6047	301	2	.	.	PUNCT
ejpam-6047	302	1	the	the	DET
ejpam-6047	302	2	d	d	NOUN
ejpam-6047	302	3	-	-	NOUN
ejpam-6047	302	4	stability	stability	NOUN
ejpam-6047	302	5	of	of	ADP
ejpam-6047	302	6	positive	positive	ADJ
ejpam-6047	302	7	linear	linear	ADJ
ejpam-6047	302	8	time	time	NOUN
ejpam-6047	302	9	-	-	PUNCT
ejpam-6047	302	10	invariant	invariant	ADJ
ejpam-6047	302	11	systems	system	NOUN
ejpam-6047	302	12	:	:	PUNCT
ejpam-6047	302	13	we	we	PRON
ejpam-6047	302	14	derive	derive	VERB
ejpam-6047	302	15	some	some	DET
ejpam-6047	302	16	new	new	ADJ
ejpam-6047	302	17	results	result	NOUN
ejpam-6047	302	18	on	on	ADP
ejpam-6047	302	19	d	d	ADJ
ejpam-6047	302	20	-	-	PUNCT
ejpam-6047	302	21	stability	stability	NOUN
ejpam-6047	302	22	analysis	analysis	NOUN
ejpam-6047	302	23	of	of	ADP
ejpam-6047	302	24	positive	positive	ADJ
ejpam-6047	302	25	time	time	NOUN
ejpam-6047	302	26	-	-	PUNCT
ejpam-6047	302	27	invariant	invariant	ADJ
ejpam-6047	302	28	linear	linear	NOUN
ejpam-6047	302	29	systems	system	NOUN
ejpam-6047	302	30	having	have	VERB
ejpam-6047	302	31	the	the	DET
ejpam-6047	302	32	presence	presence	NOUN
ejpam-6047	302	33	of	of	ADP
ejpam-6047	302	34	metzler	metzler	NOUN
ejpam-6047	302	35	,	,	PUNCT
ejpam-6047	302	36	and	and	CCONJ
ejpam-6047	302	37	hurwitz	hurwitz	PROPN
ejpam-6047	302	38	matrices	matrix	NOUN
ejpam-6047	302	39	.	.	PUNCT
ejpam-6047	303	1	the	the	DET
ejpam-6047	303	2	characterization	characterization	NOUN
ejpam-6047	303	3	of	of	ADP
ejpam-6047	303	4	d	d	NOUN
ejpam-6047	303	5	-	-	NOUN
ejpam-6047	303	6	stability	stability	NOUN
ejpam-6047	303	7	[	[	X
ejpam-6047	303	8	54	54	NUM
ejpam-6047	303	9	]	]	PUNCT
ejpam-6047	303	10	for	for	ADP
ejpam-6047	303	11	a	a	DET
ejpam-6047	303	12	given	give	VERB
ejpam-6047	303	13	real	real	ADV
ejpam-6047	303	14	-	-	PUNCT
ejpam-6047	303	15	valued	value	VERB
ejpam-6047	303	16	n	n	CCONJ
ejpam-6047	303	17	-	-	PUNCT
ejpam-6047	303	18	dimensional	dimensional	ADJ
ejpam-6047	303	19	matrix	matrix	NOUN
ejpam-6047	303	20	a	a	PRON
ejpam-6047	303	21	in	in	ADP
ejpam-6047	303	22	terms	term	NOUN
ejpam-6047	303	23	of	of	ADP
ejpam-6047	303	24	the	the	DET
ejpam-6047	303	25	real	real	ADV
ejpam-6047	303	26	structured	structured	ADJ
ejpam-6047	303	27	singular	singular	ADJ
ejpam-6047	303	28	values	value	NOUN
ejpam-6047	303	29	is	be	AUX
ejpam-6047	303	30	given	give	VERB
ejpam-6047	303	31	by	by	ADP
ejpam-6047	303	32	the	the	DET
ejpam-6047	303	33	following	follow	VERB
ejpam-6047	303	34	theorem	theorem	ADJ
ejpam-6047	303	35	8	8	NUM
ejpam-6047	303	36	.	.	PUNCT
ejpam-6047	304	1	theorem	theorem	NOUN
ejpam-6047	304	2	8	8	NUM
ejpam-6047	304	3	.	.	PUNCT
ejpam-6047	305	1	let	let	VERB
ejpam-6047	305	2	a	a	DET
ejpam-6047	305	3	∈	∈	PROPN
ejpam-6047	305	4	rn	rn	PROPN
ejpam-6047	305	5	,	,	PUNCT
ejpam-6047	305	6	n	n	CCONJ
ejpam-6047	305	7	be	be	VERB
ejpam-6047	305	8	the	the	DET
ejpam-6047	305	9	given	give	VERB
ejpam-6047	305	10	matrix	matrix	NOUN
ejpam-6047	305	11	.	.	PUNCT
ejpam-6047	306	1	then	then	ADV
ejpam-6047	306	2	a	a	PRON
ejpam-6047	306	3	is	be	AUX
ejpam-6047	306	4	a	a	DET
ejpam-6047	306	5	d	d	ADJ
ejpam-6047	306	6	-	-	ADJ
ejpam-6047	306	7	stable	stable	ADJ
ejpam-6047	306	8	matrix	matrix	NOUN
ejpam-6047	306	9	if	if	SCONJ
ejpam-6047	306	10	and	and	CCONJ
ejpam-6047	306	11	only	only	ADV
ejpam-6047	306	12	if	if	SCONJ
ejpam-6047	306	13	it	it	PRON
ejpam-6047	306	14	is	be	AUX
ejpam-6047	306	15	stable	stable	ADJ
ejpam-6047	306	16	and	and	CCONJ
ejpam-6047	306	17	none	none	NOUN
ejpam-6047	306	18	of	of	ADP
ejpam-6047	306	19	the	the	DET
ejpam-6047	306	20	eigenvalues	eigenvalue	NOUN
ejpam-6047	306	21	of	of	ADP
ejpam-6047	306	22	a±	a±	PROPN
ejpam-6047	306	23	i	i	PROPN
ejpam-6047	306	24	d	d	PROPN
ejpam-6047	306	25	is	be	AUX
ejpam-6047	306	26	exactly	exactly	ADV
ejpam-6047	306	27	equal	equal	ADJ
ejpam-6047	306	28	to	to	ADP
ejpam-6047	306	29	zero	zero	NUM
ejpam-6047	306	30	,	,	PUNCT
ejpam-6047	306	31	and	and	CCONJ
ejpam-6047	306	32	0	0	NUM
ejpam-6047	306	33	≤	≤	NOUN
ejpam-6047	306	34	µb	µb	VERB
ejpam-6047	306	35	(	(	PUNCT
ejpam-6047	306	36	(	(	PUNCT
ejpam-6047	306	37	ii	ii	X
ejpam-6047	306	38	+	+	CCONJ
ejpam-6047	306	39	a)−1(ii	a)−1(ii	PROPN
ejpam-6047	306	40	−a	−a	NOUN
ejpam-6047	306	41	)	)	PUNCT
ejpam-6047	306	42	)	)	PUNCT
ejpam-6047	307	1	<	<	X
ejpam-6047	307	2	1	1	X
ejpam-6047	307	3	.	.	PUNCT
ejpam-6047	307	4	theorem	theorem	NOUN
ejpam-6047	307	5	9	9	NUM
ejpam-6047	307	6	gives	give	VERB
ejpam-6047	307	7	the	the	DET
ejpam-6047	307	8	conditions	condition	NOUN
ejpam-6047	307	9	under	under	ADP
ejpam-6047	307	10	which	which	PRON
ejpam-6047	307	11	linear	linear	ADJ
ejpam-6047	307	12	time	time	NOUN
ejpam-6047	307	13	-	-	PUNCT
ejpam-6047	307	14	invariant	invariant	ADJ
ejpam-6047	307	15	system	system	NOUN
ejpam-6047	307	16	with	with	ADP
ejpam-6047	307	17	ndimensional	ndimensional	ADJ
ejpam-6047	307	18	real	real	ADV
ejpam-6047	307	19	-	-	PUNCT
ejpam-6047	307	20	valued	value	VERB
ejpam-6047	307	21	metzler	metzler	NOUN
ejpam-6047	307	22	,	,	PUNCT
ejpam-6047	307	23	and	and	CCONJ
ejpam-6047	307	24	hurwitz	hurwitz	PROPN
ejpam-6047	307	25	matrices	matrix	NOUN
ejpam-6047	307	26	,	,	PUNCT
ejpam-6047	307	27	is	be	AUX
ejpam-6047	307	28	d	d	ADJ
ejpam-6047	307	29	-	-	ADJ
ejpam-6047	307	30	stable	stable	ADJ
ejpam-6047	307	31	.	.	PUNCT
ejpam-6047	308	1	theorem	theorem	NOUN
ejpam-6047	308	2	9	9	NUM
ejpam-6047	308	3	.	.	PUNCT
ejpam-6047	309	1	let	let	VERB
ejpam-6047	309	2	a1	a1	NOUN
ejpam-6047	309	3	,	,	PUNCT
ejpam-6047	309	4	a2	a2	PROPN
ejpam-6047	309	5	∈	∈	PROPN
ejpam-6047	309	6	rn	rn	PROPN
ejpam-6047	309	7	,	,	PUNCT
ejpam-6047	309	8	n	n	PRON
ejpam-6047	309	9	be	be	VERB
ejpam-6047	309	10	metzler	metzler	NOUN
ejpam-6047	309	11	matrices	matrix	NOUN
ejpam-6047	309	12	and	and	CCONJ
ejpam-6047	309	13	hurwitz.the	hurwitz.the	DET
ejpam-6047	309	14	time	time	NOUN
ejpam-6047	309	15	-	-	PUNCT
ejpam-6047	309	16	invariant	invariant	ADJ
ejpam-6047	309	17	linear	linear	NOUN
ejpam-6047	309	18	system	system	NOUN
ejpam-6047	309	19	dx(t	dx(t	NOUN
ejpam-6047	309	20	)	)	PUNCT
ejpam-6047	309	21	dt	dt	NOUN
ejpam-6047	310	1	=	=	SYM
ejpam-6047	310	2	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	310	3	)	)	PUNCT
ejpam-6047	310	4	,	,	PUNCT
ejpam-6047	310	5	where	where	SCONJ
ejpam-6047	310	6	a(t	a(t	NOUN
ejpam-6047	310	7	)	)	PUNCT
ejpam-6047	310	8	∈	∈	PROPN
ejpam-6047	310	9	{	{	PUNCT
ejpam-6047	310	10	a1	a1	NOUN
ejpam-6047	310	11	,	,	PUNCT
ejpam-6047	310	12	a2	a2	PROPN
ejpam-6047	310	13	}	}	PUNCT
ejpam-6047	310	14	,	,	PUNCT
ejpam-6047	310	15	and	and	CCONJ
ejpam-6047	310	16	x(t	x(t	PROPN
ejpam-6047	310	17	)	)	PUNCT
ejpam-6047	310	18	∈	∈	PROPN
ejpam-6047	310	19	rn,1	rn,1	PROPN
ejpam-6047	310	20	,	,	PUNCT
ejpam-6047	310	21	is	be	AUX
ejpam-6047	310	22	d	d	NOUN
ejpam-6047	310	23	-	-	ADJ
ejpam-6047	310	24	stable	stable	ADJ
ejpam-6047	310	25	if	if	SCONJ
ejpam-6047	310	26	re	re	X
ejpam-6047	310	27	(	(	PUNCT
ejpam-6047	310	28	λi(a1	λi(a1	X
ejpam-6047	310	29	+	+	CCONJ
ejpam-6047	310	30	da2	da2	PROPN
ejpam-6047	310	31	)	)	PUNCT
ejpam-6047	310	32	)	)	PUNCT
ejpam-6047	311	1	̸=	̸=	PROPN
ejpam-6047	311	2	0	0	NUM
ejpam-6047	311	3	,	,	PUNCT
ejpam-6047	311	4	∀i	∀i	NOUN
ejpam-6047	311	5	=	=	SYM
ejpam-6047	311	6	1	1	NUM
ejpam-6047	311	7	:	:	PUNCT
ejpam-6047	311	8	n	n	NOUN
ejpam-6047	311	9	with	with	ADP
ejpam-6047	311	10	d	d	PROPN
ejpam-6047	311	11	=	=	SYM
ejpam-6047	311	12	diag(dii	diag(dii	PROPN
ejpam-6047	311	13	)	)	PUNCT
ejpam-6047	311	14	:	:	PUNCT
ejpam-6047	311	15	dii	dii	NOUN
ejpam-6047	311	16	>	>	X
ejpam-6047	311	17	0	0	X
ejpam-6047	311	18	.	.	PUNCT
ejpam-6047	312	1	m.u	m.u	PROPN
ejpam-6047	312	2	.	.	PROPN
ejpam-6047	312	3	rehman	rehman	PROPN
ejpam-6047	312	4	et	et	PROPN
ejpam-6047	312	5	al	al	PROPN
ejpam-6047	312	6	.	.	PUNCT
ejpam-6047	312	7	/	/	SYM
ejpam-6047	312	8	eur	eur	PROPN
ejpam-6047	312	9	.	.	PUNCT
ejpam-6047	313	1	j.	j.	PROPN
ejpam-6047	313	2	pure	pure	PROPN
ejpam-6047	313	3	appl	appl	PROPN
ejpam-6047	313	4	.	.	PROPN
ejpam-6047	313	5	math	math	PROPN
ejpam-6047	313	6	,	,	PUNCT
ejpam-6047	313	7	18	18	NUM
ejpam-6047	313	8	(	(	PUNCT
ejpam-6047	313	9	3	3	NUM
ejpam-6047	313	10	)	)	PUNCT
ejpam-6047	313	11	(	(	PUNCT
ejpam-6047	313	12	2025	2025	NUM
ejpam-6047	313	13	)	)	PUNCT
ejpam-6047	313	14	,	,	PUNCT
ejpam-6047	313	15	6047	6047	NUM
ejpam-6047	313	16	14	14	NUM
ejpam-6047	313	17	of	of	ADP
ejpam-6047	313	18	33	33	NUM
ejpam-6047	313	19	proof	proof	NOUN
ejpam-6047	313	20	.	.	PUNCT
ejpam-6047	314	1	let	let	VERB
ejpam-6047	314	2	a(t	a(t	NOUN
ejpam-6047	314	3	)	)	PUNCT
ejpam-6047	314	4	∈	∈	PROPN
ejpam-6047	314	5	{	{	PUNCT
ejpam-6047	314	6	a1	a1	PROPN
ejpam-6047	314	7	,	,	PUNCT
ejpam-6047	314	8	a2	a2	PROPN
ejpam-6047	314	9	}	}	PUNCT
ejpam-6047	314	10	is	be	AUX
ejpam-6047	314	11	d	d	ADJ
ejpam-6047	314	12	-	-	ADJ
ejpam-6047	314	13	stable	stable	ADJ
ejpam-6047	314	14	,	,	PUNCT
ejpam-6047	314	15	which	which	PRON
ejpam-6047	314	16	means	mean	VERB
ejpam-6047	314	17	that	that	SCONJ
ejpam-6047	314	18	re	re	ADP
ejpam-6047	314	19	(	(	PUNCT
ejpam-6047	314	20	λi(a1	λi(a1	X
ejpam-6047	314	21	+	+	CCONJ
ejpam-6047	314	22	da2	da2	PROPN
ejpam-6047	314	23	)	)	PUNCT
ejpam-6047	314	24	)	)	PUNCT
ejpam-6047	315	1	>	>	X
ejpam-6047	315	2	0	0	NUM
ejpam-6047	315	3	,	,	PUNCT
ejpam-6047	315	4	∀i	∀i	NOUN
ejpam-6047	315	5	=	=	SYM
ejpam-6047	315	6	1	1	NUM
ejpam-6047	315	7	:	:	PUNCT
ejpam-6047	316	1	n.	n.	NOUN
ejpam-6047	316	2	further	far	ADV
ejpam-6047	316	3	(	(	PUNCT
ejpam-6047	316	4	a1+da2)+id	a1+da2)+id	PROPN
ejpam-6047	316	5	=	=	SYM
ejpam-6047	316	6	d	d	PROPN
ejpam-6047	316	7	(	(	PUNCT
ejpam-6047	316	8	d−1(a1	d−1(a1	PROPN
ejpam-6047	316	9	+	+	CCONJ
ejpam-6047	316	10	a2d	a2d	PROPN
ejpam-6047	316	11	)	)	PUNCT
ejpam-6047	317	1	+	+	CCONJ
ejpam-6047	317	2	iin	iin	NOUN
ejpam-6047	317	3	)	)	PUNCT
ejpam-6047	318	1	so	so	SCONJ
ejpam-6047	318	2	that	that	PRON
ejpam-6047	318	3	λi	λi	INTJ
ejpam-6047	318	4	(	(	PUNCT
ejpam-6047	318	5	d(d−1(a1	d(d−1(a1	X
ejpam-6047	318	6	+	+	CCONJ
ejpam-6047	318	7	a2d	a2d	PROPN
ejpam-6047	318	8	)	)	PUNCT
ejpam-6047	318	9	+	+	CCONJ
ejpam-6047	318	10	iin	iin	NOUN
ejpam-6047	318	11	)	)	PUNCT
ejpam-6047	318	12	)	)	PUNCT
ejpam-6047	319	1	̸=	̸=	PROPN
ejpam-6047	319	2	0	0	NUM
ejpam-6047	319	3	,	,	PUNCT
ejpam-6047	319	4	∀i	∀i	NOUN
ejpam-6047	319	5	=	=	SYM
ejpam-6047	319	6	1	1	NUM
ejpam-6047	319	7	:	:	SYM
ejpam-6047	319	8	n	n	CCONJ
ejpam-6047	319	9	,	,	PUNCT
ejpam-6047	319	10	with	with	ADP
ejpam-6047	319	11	in	in	ADP
ejpam-6047	319	12	being	be	AUX
ejpam-6047	319	13	n	n	CCONJ
ejpam-6047	319	14	-	-	PUNCT
ejpam-6047	319	15	dimensional	dimensional	ADJ
ejpam-6047	319	16	identity	identity	NOUN
ejpam-6047	319	17	matrix	matrix	NOUN
ejpam-6047	319	18	.	.	PUNCT
ejpam-6047	320	1	assume	assume	VERB
ejpam-6047	320	2	that	that	SCONJ
ejpam-6047	320	3	a(t	a(t	NOUN
ejpam-6047	320	4	)	)	PUNCT
ejpam-6047	320	5	∈	∈	PROPN
ejpam-6047	320	6	{	{	PUNCT
ejpam-6047	320	7	a1	a1	PROPN
ejpam-6047	320	8	,	,	PUNCT
ejpam-6047	320	9	a2	a2	PROPN
ejpam-6047	320	10	}	}	PUNCT
ejpam-6047	320	11	is	be	AUX
ejpam-6047	320	12	not	not	PART
ejpam-6047	320	13	d	d	ADJ
ejpam-6047	320	14	-	-	ADJ
ejpam-6047	320	15	stable	stable	ADJ
ejpam-6047	320	16	matrix	matrix	NOUN
ejpam-6047	320	17	,	,	PUNCT
ejpam-6047	320	18	which	which	PRON
ejpam-6047	320	19	implies	imply	VERB
ejpam-6047	320	20	that	that	SCONJ
ejpam-6047	320	21	re(λi(d(a1	re(λi(d(a1	PROPN
ejpam-6047	320	22	+	+	PROPN
ejpam-6047	320	23	da2	da2	PROPN
ejpam-6047	320	24	)	)	PUNCT
ejpam-6047	320	25	)	)	PUNCT
ejpam-6047	320	26	)	)	PUNCT
ejpam-6047	321	1	̸̸	̸̸	PROPN
ejpam-6047	321	2	>	>	X
ejpam-6047	321	3	0	0	NUM
ejpam-6047	321	4	,	,	PUNCT
ejpam-6047	321	5	∀i	∀i	NOUN
ejpam-6047	321	6	=	=	SYM
ejpam-6047	321	7	1	1	NUM
ejpam-6047	321	8	:	:	PUNCT
ejpam-6047	321	9	n.	n.	NOUN
ejpam-6047	321	10	for	for	ADP
ejpam-6047	321	11	each	each	DET
ejpam-6047	321	12	positive	positive	ADJ
ejpam-6047	321	13	diagonal	diagonal	ADJ
ejpam-6047	321	14	matrix	matrix	NOUN
ejpam-6047	321	15	d̃	d̃	PROPN
ejpam-6047	321	16	,	,	PUNCT
ejpam-6047	321	17	the	the	DET
ejpam-6047	321	18	matrix	matrix	NOUN
ejpam-6047	321	19	d̃d(a1+a2d	d̃d(a1+a2d	NOUN
ejpam-6047	321	20	)	)	PUNCT
ejpam-6047	321	21	is	be	AUX
ejpam-6047	321	22	not	not	PART
ejpam-6047	321	23	stable	stable	ADJ
ejpam-6047	321	24	,	,	PUNCT
ejpam-6047	321	25	but	but	CCONJ
ejpam-6047	321	26	d̃(a1+a2d	d̃(a1+a2d	PROPN
ejpam-6047	321	27	)	)	PUNCT
ejpam-6047	321	28	is	be	AUX
ejpam-6047	321	29	a	a	DET
ejpam-6047	321	30	stable	stable	ADJ
ejpam-6047	321	31	matrix	matrix	NOUN
ejpam-6047	321	32	for	for	ADP
ejpam-6047	321	33	0	0	NUM
ejpam-6047	321	34	<	<	X
ejpam-6047	321	35	t	t	X
ejpam-6047	321	36	≤	≤	NUM
ejpam-6047	321	37	1	1	NUM
ejpam-6047	321	38	and	and	CCONJ
ejpam-6047	321	39	for	for	ADP
ejpam-6047	321	40	some	some	DET
ejpam-6047	321	41	γ	γ	NOUN
ejpam-6047	321	42	>	>	X
ejpam-6047	321	43	0	0	NUM
ejpam-6047	321	44	,	,	PUNCT
ejpam-6047	321	45	we	we	PRON
ejpam-6047	321	46	have	have	VERB
ejpam-6047	321	47	that	that	PRON
ejpam-6047	321	48	1	1	NUM
ejpam-6047	321	49	γ	γ	X
ejpam-6047	321	50	(	(	PUNCT
ejpam-6047	321	51	td+(1−t)in)d̃(a1+da2	td+(1−t)in)d̃(a1+da2	PROPN
ejpam-6047	321	52	)	)	PUNCT
ejpam-6047	321	53	with	with	ADP
ejpam-6047	321	54	d	d	PROPN
ejpam-6047	321	55	=	=	X
ejpam-6047	321	56	γ(td	γ(td	PROPN
ejpam-6047	321	57	+	+	CCONJ
ejpam-6047	321	58	(	(	PUNCT
ejpam-6047	321	59	1	1	NUM
ejpam-6047	321	60	−	−	NOUN
ejpam-6047	321	61	t)in)−1	t)in)−1	NOUN
ejpam-6047	321	62	has	have	VERB
ejpam-6047	321	63	an	an	DET
ejpam-6047	321	64	eigenvalue	eigenvalue	ADJ
ejpam-6047	321	65	i	i	NOUN
ejpam-6047	321	66	=	=	NOUN
ejpam-6047	321	67	√	√	NUM
ejpam-6047	321	68	−1	−1	NOUN
ejpam-6047	321	69	.	.	PUNCT
ejpam-6047	322	1	in	in	ADP
ejpam-6047	322	2	theorem	theorem	NOUN
ejpam-6047	322	3	10	10	NUM
ejpam-6047	322	4	,	,	PUNCT
ejpam-6047	322	5	it	it	PRON
ejpam-6047	322	6	has	have	AUX
ejpam-6047	322	7	been	be	AUX
ejpam-6047	322	8	proven	prove	VERB
ejpam-6047	322	9	that	that	SCONJ
ejpam-6047	322	10	the	the	DET
ejpam-6047	322	11	positive	positive	ADJ
ejpam-6047	322	12	linear	linear	ADJ
ejpam-6047	322	13	time	time	NOUN
ejpam-6047	322	14	-	-	PUNCT
ejpam-6047	322	15	invariant	invariant	ADJ
ejpam-6047	322	16	system	system	NOUN
ejpam-6047	322	17	is	be	AUX
ejpam-6047	322	18	dstable	dstable	ADJ
ejpam-6047	322	19	if	if	SCONJ
ejpam-6047	322	20	the	the	DET
ejpam-6047	322	21	product	product	NOUN
ejpam-6047	322	22	of	of	ADP
ejpam-6047	322	23	all	all	DET
ejpam-6047	322	24	eigenvalues	eigenvalue	NOUN
ejpam-6047	322	25	of	of	ADP
ejpam-6047	322	26	the	the	DET
ejpam-6047	322	27	perturbed	perturb	VERB
ejpam-6047	322	28	matrix	matrix	NOUN
ejpam-6047	322	29	(	(	PUNCT
ejpam-6047	322	30	a1	a1	NOUN
ejpam-6047	322	31	+	+	PROPN
ejpam-6047	322	32	da2)d	da2)d	NOUN
ejpam-6047	322	33	−1	−1	NOUN
ejpam-6047	323	1	+	+	CCONJ
ejpam-6047	323	2	d(a1	d(a1	NOUN
ejpam-6047	323	3	+	+	CCONJ
ejpam-6047	323	4	da2	da2	PROPN
ejpam-6047	323	5	)	)	PUNCT
ejpam-6047	323	6	−1	−1	NOUN
ejpam-6047	323	7	is	be	AUX
ejpam-6047	323	8	strictly	strictly	ADV
ejpam-6047	323	9	positive	positive	ADJ
ejpam-6047	323	10	.	.	PUNCT
ejpam-6047	324	1	theorem	theorem	ADJ
ejpam-6047	324	2	10	10	NUM
ejpam-6047	324	3	.	.	PUNCT
ejpam-6047	325	1	let	let	VERB
ejpam-6047	325	2	a1	a1	NOUN
ejpam-6047	325	3	,	,	PUNCT
ejpam-6047	325	4	a2	a2	PROPN
ejpam-6047	325	5	∈	∈	PROPN
ejpam-6047	325	6	rn	rn	PROPN
ejpam-6047	325	7	,	,	PUNCT
ejpam-6047	325	8	n	n	PRON
ejpam-6047	325	9	be	be	VERB
ejpam-6047	325	10	metzler	metzler	NOUN
ejpam-6047	325	11	,	,	PUNCT
ejpam-6047	325	12	and	and	CCONJ
ejpam-6047	325	13	hurwitz	hurwitz	PROPN
ejpam-6047	325	14	matrices	matrix	NOUN
ejpam-6047	325	15	.	.	PUNCT
ejpam-6047	326	1	the	the	DET
ejpam-6047	326	2	positive	positive	ADJ
ejpam-6047	326	3	linear	linear	ADJ
ejpam-6047	326	4	time	time	NOUN
ejpam-6047	326	5	-	-	PUNCT
ejpam-6047	326	6	invariant	invariant	ADJ
ejpam-6047	326	7	system	system	NOUN
ejpam-6047	326	8	dx(t	dx(t	NOUN
ejpam-6047	326	9	)	)	PUNCT
ejpam-6047	326	10	dt	dt	NOUN
ejpam-6047	326	11	=	=	SYM
ejpam-6047	326	12	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	326	13	)	)	PUNCT
ejpam-6047	326	14	,	,	PUNCT
ejpam-6047	326	15	where	where	SCONJ
ejpam-6047	326	16	a(t	a(t	NOUN
ejpam-6047	326	17	)	)	PUNCT
ejpam-6047	326	18	∈	∈	PROPN
ejpam-6047	326	19	{	{	PUNCT
ejpam-6047	326	20	a1	a1	PROPN
ejpam-6047	326	21	,	,	PUNCT
ejpam-6047	326	22	a2	a2	PROPN
ejpam-6047	326	23	}	}	PUNCT
ejpam-6047	326	24	and	and	CCONJ
ejpam-6047	326	25	x(t	x(t	PROPN
ejpam-6047	326	26	)	)	PUNCT
ejpam-6047	326	27	∈	∈	PROPN
ejpam-6047	326	28	rn,1	rn,1	PROPN
ejpam-6047	326	29	,	,	PUNCT
ejpam-6047	326	30	is	be	AUX
ejpam-6047	326	31	d	d	NOUN
ejpam-6047	326	32	-	-	ADJ
ejpam-6047	326	33	stable	stable	ADJ
ejpam-6047	326	34	if	if	SCONJ
ejpam-6047	326	35	∏n	∏n	ADJ
ejpam-6047	326	36	i=1	i=1	PRON
ejpam-6047	326	37	λi	λi	X
ejpam-6047	326	38	(	(	PUNCT
ejpam-6047	326	39	(	(	PUNCT
ejpam-6047	326	40	a1	a1	NOUN
ejpam-6047	326	41	+	+	CCONJ
ejpam-6047	326	42	da2)d	da2)d	NOUN
ejpam-6047	326	43	−1	−1	NOUN
ejpam-6047	326	44	+	+	CCONJ
ejpam-6047	326	45	d(a1	d(a1	NOUN
ejpam-6047	326	46	+	+	CCONJ
ejpam-6047	326	47	da2	da2	PROPN
ejpam-6047	326	48	)	)	PUNCT
ejpam-6047	326	49	−1	−1	NOUN
ejpam-6047	326	50	)	)	PUNCT
ejpam-6047	326	51	>	>	X
ejpam-6047	327	1	0	0	NUM
ejpam-6047	327	2	,	,	PUNCT
ejpam-6047	327	3	∀	∀	VERB
ejpam-6047	328	1	i	i	NOUN
ejpam-6047	328	2	=	=	NOUN
ejpam-6047	328	3	1	1	X
ejpam-6047	328	4	:	:	PUNCT
ejpam-6047	328	5	n.	n.	NOUN
ejpam-6047	328	6	proof	proof	NOUN
ejpam-6047	328	7	.	.	PUNCT
ejpam-6047	329	1	we	we	PRON
ejpam-6047	329	2	start	start	VERB
ejpam-6047	329	3	with	with	ADP
ejpam-6047	329	4	the	the	DET
ejpam-6047	329	5	partitioned	partition	VERB
ejpam-6047	329	6	matrix	matrix	NOUN
ejpam-6047	329	7	of	of	ADP
ejpam-6047	329	8	the	the	DET
ejpam-6047	329	9	form	form	NOUN
ejpam-6047	329	10	(	(	PUNCT
ejpam-6047	329	11	a1	a1	NOUN
ejpam-6047	329	12	+	+	CCONJ
ejpam-6047	329	13	da2	da2	PROPN
ejpam-6047	329	14	−d	−d	VERB
ejpam-6047	329	15	d	d	X
ejpam-6047	329	16	a1	a1	PROPN
ejpam-6047	329	17	+	+	CCONJ
ejpam-6047	329	18	da2	da2	PROPN
ejpam-6047	329	19	)	)	PUNCT
ejpam-6047	329	20	.	.	PUNCT
ejpam-6047	330	1	the	the	DET
ejpam-6047	330	2	schur	schur	PROPN
ejpam-6047	330	3	complement	complement	NOUN
ejpam-6047	330	4	of	of	ADP
ejpam-6047	330	5	the	the	DET
ejpam-6047	330	6	partitioned	partition	VERB
ejpam-6047	330	7	matrix	matrix	NOUN
ejpam-6047	330	8	is	be	AUX
ejpam-6047	330	9	given	give	VERB
ejpam-6047	330	10	as	as	ADP
ejpam-6047	330	11	(	(	PUNCT
ejpam-6047	330	12	a1	a1	NOUN
ejpam-6047	330	13	+	+	CCONJ
ejpam-6047	330	14	da2	da2	PROPN
ejpam-6047	330	15	)	)	PUNCT
ejpam-6047	331	1	+	+	CCONJ
ejpam-6047	331	2	d(a1	d(a1	NOUN
ejpam-6047	331	3	+	+	CCONJ
ejpam-6047	331	4	da2	da2	PROPN
ejpam-6047	331	5	)	)	PUNCT
ejpam-6047	331	6	−1d	−1d	PROPN
ejpam-6047	331	7	=	=	PUNCT
ejpam-6047	331	8	d(a1	d(a1	NOUN
ejpam-6047	331	9	+	+	CCONJ
ejpam-6047	331	10	da2)d	da2)d	PROPN
ejpam-6047	331	11	−1d	−1d	PROPN
ejpam-6047	331	12	+	+	CCONJ
ejpam-6047	331	13	d(a1	d(a1	NOUN
ejpam-6047	331	14	+	+	CCONJ
ejpam-6047	331	15	da2	da2	PROPN
ejpam-6047	331	16	)	)	PUNCT
ejpam-6047	331	17	−1d	−1d	PROPN
ejpam-6047	331	18	=	=	PUNCT
ejpam-6047	331	19	(	(	PUNCT
ejpam-6047	331	20	(	(	PUNCT
ejpam-6047	331	21	a1	a1	NOUN
ejpam-6047	331	22	+	+	CCONJ
ejpam-6047	331	23	da2	da2	PROPN
ejpam-6047	331	24	)	)	PUNCT
ejpam-6047	331	25	−1	−1	NOUN
ejpam-6047	331	26	+	+	CCONJ
ejpam-6047	331	27	d(a1	d(a1	NOUN
ejpam-6047	331	28	+	+	CCONJ
ejpam-6047	331	29	da2	da2	PROPN
ejpam-6047	331	30	)	)	PUNCT
ejpam-6047	331	31	−1d	−1d	PROPN
ejpam-6047	331	32	)	)	PUNCT
ejpam-6047	331	33	.	.	PUNCT
ejpam-6047	332	1	the	the	DET
ejpam-6047	332	2	eigenvalues	eigenvalue	NOUN
ejpam-6047	332	3	λi	λi	ADP
ejpam-6047	332	4	∀	∀	NOUN
ejpam-6047	332	5	i	i	NOUN
ejpam-6047	332	6	=	=	NOUN
ejpam-6047	332	7	1	1	NUM
ejpam-6047	332	8	:	:	PUNCT
ejpam-6047	332	9	n	n	PRON
ejpam-6047	332	10	are	be	AUX
ejpam-6047	332	11	with	with	ADP
ejpam-6047	332	12	n∏	n∏	PROPN
ejpam-6047	332	13	i=1	i=1	PROPN
ejpam-6047	332	14	λi((a1	λi((a1	PROPN
ejpam-6047	332	15	+	+	CCONJ
ejpam-6047	332	16	da2	da2	PROPN
ejpam-6047	332	17	)	)	PUNCT
ejpam-6047	333	1	+	+	CCONJ
ejpam-6047	333	2	d(a1	d(a1	NOUN
ejpam-6047	333	3	+	+	CCONJ
ejpam-6047	333	4	da2	da2	PROPN
ejpam-6047	333	5	)	)	PUNCT
ejpam-6047	333	6	−1	−1	NOUN
ejpam-6047	333	7	)	)	PUNCT
ejpam-6047	334	1	=	=	PUNCT
ejpam-6047	334	2	n∏	n∏	PROPN
ejpam-6047	334	3	i=1	i=1	X
ejpam-6047	334	4	λi((a1	λi((a1	PUNCT
ejpam-6047	335	1	+	+	CCONJ
ejpam-6047	335	2	da2)d	da2)d	PROPN
ejpam-6047	335	3	−1	−1	NOUN
ejpam-6047	335	4	+	+	CCONJ
ejpam-6047	335	5	d(a1	d(a1	NOUN
ejpam-6047	335	6	+	+	CCONJ
ejpam-6047	335	7	da2	da2	PROPN
ejpam-6047	335	8	)	)	PUNCT
ejpam-6047	335	9	−1)d	−1)d	NOUN
ejpam-6047	335	10	=	=	SYM
ejpam-6047	335	11	n∏	n∏	PROPN
ejpam-6047	335	12	i=1	i=1	X
ejpam-6047	335	13	λi((a1	λi((a1	PUNCT
ejpam-6047	335	14	+	+	CCONJ
ejpam-6047	335	15	da2	da2	PROPN
ejpam-6047	335	16	)	)	PUNCT
ejpam-6047	335	17	n∏	n∏	PROPN
ejpam-6047	335	18	i=1	i=1	X
ejpam-6047	335	19	λi((a1	λi((a1	PUNCT
ejpam-6047	335	20	+	+	CCONJ
ejpam-6047	335	21	da2	da2	PROPN
ejpam-6047	335	22	)	)	PUNCT
ejpam-6047	335	23	−1d−1	−1d−1	PROPN
ejpam-6047	335	24	+	+	CCONJ
ejpam-6047	335	25	d(a1	d(a1	PROPN
ejpam-6047	335	26	+	+	CCONJ
ejpam-6047	335	27	da2	da2	PROPN
ejpam-6047	335	28	)	)	PUNCT
ejpam-6047	335	29	−1	−1	NOUN
ejpam-6047	335	30	)	)	PUNCT
ejpam-6047	335	31	n∏	n∏	PROPN
ejpam-6047	335	32	i=1	i=1	PROPN
ejpam-6047	335	33	λi(d	λi(d	NOUN
ejpam-6047	335	34	)	)	PUNCT
ejpam-6047	335	35	.	.	PUNCT
ejpam-6047	336	1	we	we	PRON
ejpam-6047	336	2	know	know	VERB
ejpam-6047	336	3	that	that	DET
ejpam-6047	336	4	n∏	n∏	PROPN
ejpam-6047	336	5	i=1	i=1	PROPN
ejpam-6047	336	6	λi	λi	X
ejpam-6047	336	7	(	(	PUNCT
ejpam-6047	336	8	(	(	PUNCT
ejpam-6047	336	9	a1	a1	NOUN
ejpam-6047	336	10	+	+	CCONJ
ejpam-6047	336	11	da2	da2	PROPN
ejpam-6047	336	12	)	)	PUNCT
ejpam-6047	337	1	+	+	CCONJ
ejpam-6047	337	2	d(a1	d(a1	NOUN
ejpam-6047	337	3	+	+	CCONJ
ejpam-6047	337	4	da2	da2	PROPN
ejpam-6047	337	5	)	)	PUNCT
ejpam-6047	337	6	−1d	−1d	PROPN
ejpam-6047	337	7	)	)	PUNCT
ejpam-6047	337	8	>	>	X
ejpam-6047	337	9	0	0	NUM
ejpam-6047	338	1	⇔	⇔	PROPN
ejpam-6047	338	2	n∏	n∏	PROPN
ejpam-6047	338	3	i=1	i=1	PROPN
ejpam-6047	339	1	λi	λi	X
ejpam-6047	339	2	(	(	PUNCT
ejpam-6047	339	3	(	(	PUNCT
ejpam-6047	339	4	a1	a1	NOUN
ejpam-6047	339	5	+	+	CCONJ
ejpam-6047	339	6	da2)d	da2)d	NOUN
ejpam-6047	339	7	−1	−1	NOUN
ejpam-6047	339	8	+	+	CCONJ
ejpam-6047	339	9	d(a1	d(a1	NOUN
ejpam-6047	339	10	+	+	CCONJ
ejpam-6047	339	11	da2	da2	PROPN
ejpam-6047	339	12	)	)	PUNCT
ejpam-6047	339	13	−1	−1	NOUN
ejpam-6047	339	14	)	)	PUNCT
ejpam-6047	340	1	>	>	X
ejpam-6047	340	2	0	0	NUM
ejpam-6047	340	3	,	,	PUNCT
ejpam-6047	340	4	m.u	m.u	PROPN
ejpam-6047	340	5	.	.	PROPN
ejpam-6047	340	6	rehman	rehman	PROPN
ejpam-6047	340	7	et	et	PROPN
ejpam-6047	340	8	al	al	PROPN
ejpam-6047	340	9	.	.	PUNCT
ejpam-6047	340	10	/	/	SYM
ejpam-6047	340	11	eur	eur	PROPN
ejpam-6047	340	12	.	.	PUNCT
ejpam-6047	341	1	j.	j.	PROPN
ejpam-6047	341	2	pure	pure	PROPN
ejpam-6047	341	3	appl	appl	PROPN
ejpam-6047	341	4	.	.	PROPN
ejpam-6047	341	5	math	math	PROPN
ejpam-6047	341	6	,	,	PUNCT
ejpam-6047	341	7	18	18	NUM
ejpam-6047	341	8	(	(	PUNCT
ejpam-6047	341	9	3	3	NUM
ejpam-6047	341	10	)	)	PUNCT
ejpam-6047	341	11	(	(	PUNCT
ejpam-6047	341	12	2025	2025	NUM
ejpam-6047	341	13	)	)	PUNCT
ejpam-6047	341	14	,	,	PUNCT
ejpam-6047	341	15	6047	6047	NUM
ejpam-6047	341	16	15	15	NUM
ejpam-6047	341	17	of	of	ADP
ejpam-6047	341	18	33	33	NUM
ejpam-6047	341	19	because	because	SCONJ
ejpam-6047	341	20	λi(a1	λi(a1	X
ejpam-6047	341	21	+	+	CCONJ
ejpam-6047	341	22	da2	da2	PROPN
ejpam-6047	341	23	)	)	PUNCT
ejpam-6047	341	24	>	>	X
ejpam-6047	341	25	0	0	NUM
ejpam-6047	341	26	,	,	PUNCT
ejpam-6047	341	27	λi(d	λi(d	X
ejpam-6047	341	28	)	)	PUNCT
ejpam-6047	341	29	>	>	X
ejpam-6047	341	30	0	0	NUM
ejpam-6047	341	31	,	,	PUNCT
ejpam-6047	341	32	∀i	∀i	NOUN
ejpam-6047	341	33	=	=	SYM
ejpam-6047	341	34	1	1	NUM
ejpam-6047	341	35	:	:	PUNCT
ejpam-6047	341	36	n.	n.	PROPN
ejpam-6047	341	37	also	also	ADV
ejpam-6047	341	38	,	,	PUNCT
ejpam-6047	341	39	λi((a1	λi((a1	PUNCT
ejpam-6047	341	40	+	+	CCONJ
ejpam-6047	341	41	da2	da2	PROPN
ejpam-6047	341	42	)	)	PUNCT
ejpam-6047	341	43	−1	−1	NOUN
ejpam-6047	341	44	)	)	PUNCT
ejpam-6047	341	45	>	>	X
ejpam-6047	341	46	0	0	NUM
ejpam-6047	341	47	,	,	PUNCT
ejpam-6047	341	48	which	which	PRON
ejpam-6047	341	49	implies	imply	VERB
ejpam-6047	341	50	λi(d(a1	λi(d(a1	PROPN
ejpam-6047	341	51	+	+	CCONJ
ejpam-6047	341	52	da2	da2	PROPN
ejpam-6047	341	53	)	)	PUNCT
ejpam-6047	341	54	−1	−1	NOUN
ejpam-6047	341	55	)	)	PUNCT
ejpam-6047	341	56	>	>	X
ejpam-6047	341	57	0	0	NUM
ejpam-6047	341	58	,	,	PUNCT
ejpam-6047	341	59	∀i	∀i	NOUN
ejpam-6047	341	60	=	=	SYM
ejpam-6047	341	61	1	1	NUM
ejpam-6047	341	62	:	:	PUNCT
ejpam-6047	341	63	n.	n.	VERB
ejpam-6047	341	64	the	the	DET
ejpam-6047	341	65	results	result	NOUN
ejpam-6047	341	66	established	establish	VERB
ejpam-6047	341	67	in	in	ADP
ejpam-6047	341	68	theorem	theorem	ADJ
ejpam-6047	341	69	11	11	NUM
ejpam-6047	341	70	show	show	NOUN
ejpam-6047	341	71	that	that	SCONJ
ejpam-6047	341	72	positive	positive	ADJ
ejpam-6047	341	73	linear	linear	ADJ
ejpam-6047	341	74	time	time	NOUN
ejpam-6047	341	75	-	-	PUNCT
ejpam-6047	341	76	invariant	invariant	ADJ
ejpam-6047	341	77	system	system	NOUN
ejpam-6047	341	78	is	be	AUX
ejpam-6047	341	79	d	d	NOUN
ejpam-6047	341	80	-	-	NOUN
ejpam-6047	341	81	stable	stable	ADJ
ejpam-6047	341	82	for	for	ADP
ejpam-6047	341	83	n	n	CCONJ
ejpam-6047	341	84	-	-	PUNCT
ejpam-6047	341	85	dimensional	dimensional	ADJ
ejpam-6047	341	86	real	real	ADV
ejpam-6047	341	87	-	-	PUNCT
ejpam-6047	341	88	valued	value	VERB
ejpam-6047	341	89	metzler	metzler	NOUN
ejpam-6047	341	90	,	,	PUNCT
ejpam-6047	341	91	and	and	CCONJ
ejpam-6047	341	92	hurwitz	hurwitz	PROPN
ejpam-6047	341	93	matrices	matrix	NOUN
ejpam-6047	341	94	a1	a1	PROPN
ejpam-6047	341	95	,	,	PUNCT
ejpam-6047	341	96	a2	a2	PROPN
ejpam-6047	341	97	if	if	SCONJ
ejpam-6047	341	98	λi((a1	λi((a1	PRON
ejpam-6047	341	99	+	+	SYM
ejpam-6047	341	100	da2	da2	PROPN
ejpam-6047	341	101	)	)	PUNCT
ejpam-6047	342	1	+	+	CCONJ
ejpam-6047	342	2	i	i	PROPN
ejpam-6047	342	3	d	d	PROPN
ejpam-6047	342	4	)	)	PUNCT
ejpam-6047	342	5	̸=	̸=	PROPN
ejpam-6047	342	6	0	0	NUM
ejpam-6047	342	7	,	,	PUNCT
ejpam-6047	342	8	∀i	∀i	NOUN
ejpam-6047	342	9	=	=	SYM
ejpam-6047	342	10	1	1	NUM
ejpam-6047	342	11	:	:	PUNCT
ejpam-6047	342	12	n.	n.	NOUN
ejpam-6047	342	13	theorem	theorem	VERB
ejpam-6047	342	14	11	11	NUM
ejpam-6047	342	15	.	.	PUNCT
ejpam-6047	343	1	the	the	DET
ejpam-6047	343	2	dynamical	dynamical	ADJ
ejpam-6047	343	3	system	system	NOUN
ejpam-6047	343	4	dx(t	dx(t	NOUN
ejpam-6047	343	5	)	)	PUNCT
ejpam-6047	343	6	dt	dt	NOUN
ejpam-6047	343	7	=	=	SYM
ejpam-6047	343	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	343	9	)	)	PUNCT
ejpam-6047	343	10	,	,	PUNCT
ejpam-6047	343	11	a(t	a(t	NOUN
ejpam-6047	343	12	)	)	PUNCT
ejpam-6047	343	13	∈	∈	PROPN
ejpam-6047	343	14	{	{	PUNCT
ejpam-6047	343	15	a1	a1	PROPN
ejpam-6047	343	16	,	,	PUNCT
ejpam-6047	343	17	a2	a2	PROPN
ejpam-6047	343	18	}	}	PUNCT
ejpam-6047	343	19	where	where	SCONJ
ejpam-6047	343	20	a1	a1	NOUN
ejpam-6047	343	21	,	,	PUNCT
ejpam-6047	343	22	a2	a2	PROPN
ejpam-6047	343	23	∈	∈	PROPN
ejpam-6047	343	24	rn	rn	PROPN
ejpam-6047	343	25	,	,	PUNCT
ejpam-6047	343	26	n	n	PRON
ejpam-6047	343	27	are	be	AUX
ejpam-6047	343	28	metzlern	metzlern	NOUN
ejpam-6047	343	29	and	and	CCONJ
ejpam-6047	343	30	hurwitz	hurwitz	PROPN
ejpam-6047	343	31	,	,	PUNCT
ejpam-6047	343	32	is	be	AUX
ejpam-6047	343	33	d	d	NOUN
ejpam-6047	343	34	-	-	ADJ
ejpam-6047	343	35	stable	stable	ADJ
ejpam-6047	343	36	if	if	SCONJ
ejpam-6047	343	37	λi((a1	λi((a1	PROPN
ejpam-6047	343	38	+	+	NUM
ejpam-6047	343	39	da2	da2	PROPN
ejpam-6047	343	40	)	)	PUNCT
ejpam-6047	344	1	+	+	CCONJ
ejpam-6047	344	2	i	i	PROPN
ejpam-6047	344	3	d	d	PROPN
ejpam-6047	344	4	)	)	PUNCT
ejpam-6047	345	1	̸=	̸=	PROPN
ejpam-6047	345	2	0,∀i	0,∀i	NUM
ejpam-6047	346	1	=	=	SYM
ejpam-6047	346	2	1	1	NUM
ejpam-6047	346	3	:	:	SYM
ejpam-6047	346	4	n	n	CCONJ
ejpam-6047	346	5	,	,	PUNCT
ejpam-6047	346	6	with	with	ADP
ejpam-6047	346	7	d	d	PROPN
ejpam-6047	346	8	=	=	SYM
ejpam-6047	346	9	diag(dii	diag(dii	PROPN
ejpam-6047	346	10	)	)	PUNCT
ejpam-6047	346	11	,	,	PUNCT
ejpam-6047	346	12	where	where	SCONJ
ejpam-6047	346	13	dii	dii	NOUN
ejpam-6047	346	14	>	>	X
ejpam-6047	346	15	0	0	X
ejpam-6047	346	16	.	.	PUNCT
ejpam-6047	347	1	proof	proof	NOUN
ejpam-6047	347	2	.	.	PUNCT
ejpam-6047	348	1	suppose	suppose	VERB
ejpam-6047	348	2	that	that	SCONJ
ejpam-6047	348	3	a(t	a(t	NOUN
ejpam-6047	348	4	)	)	PUNCT
ejpam-6047	348	5	∈	∈	PROPN
ejpam-6047	348	6	{	{	PUNCT
ejpam-6047	348	7	a1	a1	PROPN
ejpam-6047	348	8	,	,	PUNCT
ejpam-6047	348	9	a2	a2	PROPN
ejpam-6047	348	10	}	}	PUNCT
ejpam-6047	348	11	is	be	AUX
ejpam-6047	348	12	a	a	DET
ejpam-6047	348	13	d	d	ADJ
ejpam-6047	348	14	-	-	ADJ
ejpam-6047	348	15	stable	stable	ADJ
ejpam-6047	348	16	matrix	matrix	NOUN
ejpam-6047	348	17	.	.	PUNCT
ejpam-6047	349	1	this	this	PRON
ejpam-6047	349	2	implies	imply	VERB
ejpam-6047	349	3	that	that	SCONJ
ejpam-6047	349	4	re(λi(d(a1	re(λi(d(a1	PROPN
ejpam-6047	349	5	+	+	CCONJ
ejpam-6047	349	6	da2	da2	PROPN
ejpam-6047	349	7	)	)	PUNCT
ejpam-6047	349	8	)	)	PUNCT
ejpam-6047	349	9	)	)	PUNCT
ejpam-6047	349	10	>	>	X
ejpam-6047	350	1	0,∀i	0,∀i	PUNCT
ejpam-6047	351	1	=	=	SYM
ejpam-6047	351	2	1	1	NUM
ejpam-6047	351	3	:	:	PUNCT
ejpam-6047	351	4	n.	n.	VERB
ejpam-6047	351	5	the	the	DET
ejpam-6047	351	6	eigenvalue	eigenvalue	PROPN
ejpam-6047	351	7	i	i	NOUN
ejpam-6047	351	8	=	=	NOUN
ejpam-6047	351	9	√	√	NUM
ejpam-6047	351	10	−1	−1	NOUN
ejpam-6047	351	11	is	be	AUX
ejpam-6047	351	12	not	not	PART
ejpam-6047	351	13	an	an	DET
ejpam-6047	351	14	eigenvalue	eigenvalue	NOUN
ejpam-6047	351	15	of	of	ADP
ejpam-6047	351	16	the	the	DET
ejpam-6047	351	17	matrix	matrix	NOUN
ejpam-6047	351	18	product	product	NOUN
ejpam-6047	351	19	d(a1	d(a1	NOUN
ejpam-6047	351	20	+	+	CCONJ
ejpam-6047	351	21	da2	da2	PROPN
ejpam-6047	351	22	)	)	PUNCT
ejpam-6047	351	23	.	.	PUNCT
ejpam-6047	352	1	furthermore	furthermore	ADV
ejpam-6047	352	2	,	,	PUNCT
ejpam-6047	352	3	we	we	PRON
ejpam-6047	352	4	have	have	VERB
ejpam-6047	352	5	that	that	DET
ejpam-6047	352	6	(	(	PUNCT
ejpam-6047	352	7	a1	a1	NOUN
ejpam-6047	352	8	+	+	CCONJ
ejpam-6047	352	9	da2	da2	PROPN
ejpam-6047	352	10	)	)	PUNCT
ejpam-6047	353	1	+	+	CCONJ
ejpam-6047	354	1	i	i	PROPN
ejpam-6047	354	2	d	d	NOUN
ejpam-6047	354	3	=	=	PUNCT
ejpam-6047	354	4	d(d−1(a1	d(d−1(a1	PROPN
ejpam-6047	355	1	+	+	CCONJ
ejpam-6047	355	2	da2	da2	PROPN
ejpam-6047	355	3	)	)	PUNCT
ejpam-6047	356	1	+	+	CCONJ
ejpam-6047	356	2	iin	iin	NOUN
ejpam-6047	356	3	)	)	PUNCT
ejpam-6047	356	4	,	,	PUNCT
ejpam-6047	356	5	such	such	ADJ
ejpam-6047	356	6	that	that	SCONJ
ejpam-6047	356	7	λi(d(d−1(a1	λi(d(d−1(a1	X
ejpam-6047	356	8	+	+	CCONJ
ejpam-6047	356	9	da2	da2	PROPN
ejpam-6047	356	10	)	)	PUNCT
ejpam-6047	356	11	+	+	CCONJ
ejpam-6047	356	12	iin	iin	NOUN
ejpam-6047	356	13	)	)	PUNCT
ejpam-6047	356	14	)	)	PUNCT
ejpam-6047	357	1	̸=	̸=	PROPN
ejpam-6047	357	2	0,∀i	0,∀i	NUM
ejpam-6047	358	1	=	=	SYM
ejpam-6047	358	2	1	1	NUM
ejpam-6047	358	3	:	:	PUNCT
ejpam-6047	358	4	n	n	CCONJ
ejpam-6047	358	5	where	where	SCONJ
ejpam-6047	358	6	in	in	ADP
ejpam-6047	358	7	is	be	AUX
ejpam-6047	358	8	n×	n×	PROPN
ejpam-6047	358	9	n	n	PRON
ejpam-6047	358	10	identity	identity	NOUN
ejpam-6047	358	11	matrix	matrix	NOUN
ejpam-6047	358	12	.	.	PUNCT
ejpam-6047	359	1	this	this	PRON
ejpam-6047	359	2	also	also	ADV
ejpam-6047	359	3	hold	hold	VERB
ejpam-6047	359	4	for	for	ADP
ejpam-6047	359	5	a	a	DET
ejpam-6047	359	6	positive	positive	ADJ
ejpam-6047	359	7	diagonal	diagonal	ADJ
ejpam-6047	359	8	matrix	matrix	NOUN
ejpam-6047	359	9	d̃	d̃	PROPN
ejpam-6047	359	10	so	so	SCONJ
ejpam-6047	359	11	that	that	SCONJ
ejpam-6047	359	12	the	the	DET
ejpam-6047	359	13	matrix	matrix	NOUN
ejpam-6047	359	14	d̃d(a1	d̃d(a1	NOUN
ejpam-6047	359	15	+	+	CCONJ
ejpam-6047	359	16	da2	da2	PROPN
ejpam-6047	359	17	)	)	PUNCT
ejpam-6047	359	18	is	be	AUX
ejpam-6047	359	19	not	not	PART
ejpam-6047	359	20	stable	stable	ADJ
ejpam-6047	359	21	,	,	PUNCT
ejpam-6047	359	22	but	but	CCONJ
ejpam-6047	359	23	d̃(a1	d̃(a1	PROPN
ejpam-6047	359	24	+	+	CCONJ
ejpam-6047	359	25	da2	da2	PROPN
ejpam-6047	359	26	)	)	PUNCT
ejpam-6047	359	27	is	be	AUX
ejpam-6047	359	28	stable	stable	ADJ
ejpam-6047	359	29	,	,	PUNCT
ejpam-6047	359	30	means	mean	VERB
ejpam-6047	359	31	that	that	SCONJ
ejpam-6047	359	32	re(λi(d̃(a1	re(λi(d̃(a1	NOUN
ejpam-6047	359	33	+	+	CCONJ
ejpam-6047	359	34	da2	da2	PROPN
ejpam-6047	359	35	)	)	PUNCT
ejpam-6047	359	36	)	)	PUNCT
ejpam-6047	359	37	>	>	X
ejpam-6047	359	38	0,∀i	0,∀i	PUNCT
ejpam-6047	360	1	=	=	SYM
ejpam-6047	360	2	1	1	NUM
ejpam-6047	360	3	:	:	PUNCT
ejpam-6047	360	4	n.	n.	NOUN
ejpam-6047	360	5	this	this	DET
ejpam-6047	360	6	follow	follow	NOUN
ejpam-6047	360	7	from	from	ADP
ejpam-6047	360	8	fact	fact	NOUN
ejpam-6047	360	9	that	that	SCONJ
ejpam-6047	360	10	if	if	SCONJ
ejpam-6047	360	11	0	0	NUM
ejpam-6047	360	12	<	<	X
ejpam-6047	360	13	t	t	X
ejpam-6047	360	14	≤	≤	NUM
ejpam-6047	360	15	1	1	NUM
ejpam-6047	360	16	,	,	PUNCT
ejpam-6047	360	17	and	and	CCONJ
ejpam-6047	360	18	for	for	ADP
ejpam-6047	360	19	γ	γ	X
ejpam-6047	360	20	>	>	X
ejpam-6047	360	21	0	0	PROPN
ejpam-6047	360	22	,	,	PUNCT
ejpam-6047	360	23	the	the	DET
ejpam-6047	360	24	matrix	matrix	NOUN
ejpam-6047	360	25	1	1	NUM
ejpam-6047	360	26	γ	γ	X
ejpam-6047	360	27	(	(	PUNCT
ejpam-6047	360	28	td+	td+	PROPN
ejpam-6047	360	29	(	(	PUNCT
ejpam-6047	360	30	1−	1−	NUM
ejpam-6047	360	31	t)in)d̃(a1	t)in)d̃(a1	PROPN
ejpam-6047	360	32	+	+	CCONJ
ejpam-6047	360	33	da2	da2	PROPN
ejpam-6047	360	34	)	)	PUNCT
ejpam-6047	360	35	)	)	PUNCT
ejpam-6047	360	36	,	,	PUNCT
ejpam-6047	360	37	with	with	ADP
ejpam-6047	360	38	d	d	PROPN
ejpam-6047	360	39	=	=	X
ejpam-6047	360	40	γ(td	γ(td	PROPN
ejpam-6047	360	41	+	+	CCONJ
ejpam-6047	360	42	(	(	PUNCT
ejpam-6047	360	43	1	1	NUM
ejpam-6047	360	44	−	−	NOUN
ejpam-6047	360	45	t)in)−1	t)in)−1	NOUN
ejpam-6047	360	46	has	have	AUX
ejpam-6047	360	47	an	an	DET
ejpam-6047	360	48	eigenvalue	eigenvalue	ADJ
ejpam-6047	360	49	i	i	NOUN
ejpam-6047	360	50	=	=	NOUN
ejpam-6047	360	51	√	√	NUM
ejpam-6047	360	52	−1	−1	NOUN
ejpam-6047	360	53	.	.	PUNCT
ejpam-6047	361	1	theorem	theorem	NOUN
ejpam-6047	361	2	12	12	NUM
ejpam-6047	361	3	provides	provide	VERB
ejpam-6047	361	4	insights	insight	NOUN
ejpam-6047	361	5	into	into	ADP
ejpam-6047	361	6	the	the	DET
ejpam-6047	361	7	d	d	NOUN
ejpam-6047	361	8	-	-	NOUN
ejpam-6047	361	9	stability	stability	NOUN
ejpam-6047	361	10	of	of	ADP
ejpam-6047	361	11	positive	positive	ADJ
ejpam-6047	361	12	linear	linear	ADJ
ejpam-6047	361	13	time	time	NOUN
ejpam-6047	361	14	-	-	PUNCT
ejpam-6047	361	15	invariant	invariant	ADJ
ejpam-6047	361	16	systems	system	NOUN
ejpam-6047	361	17	.	.	PUNCT
ejpam-6047	362	1	it	it	PRON
ejpam-6047	362	2	has	have	AUX
ejpam-6047	362	3	been	be	AUX
ejpam-6047	362	4	established	establish	VERB
ejpam-6047	362	5	that	that	SCONJ
ejpam-6047	362	6	a	a	DET
ejpam-6047	362	7	positive	positive	ADJ
ejpam-6047	362	8	linear	linear	ADJ
ejpam-6047	362	9	time	time	NOUN
ejpam-6047	362	10	-	-	PUNCT
ejpam-6047	362	11	invariant	invariant	ADJ
ejpam-6047	362	12	system	system	NOUN
ejpam-6047	362	13	,	,	PUNCT
ejpam-6047	362	14	where	where	SCONJ
ejpam-6047	362	15	a1	a1	NOUN
ejpam-6047	362	16	,	,	PUNCT
ejpam-6047	362	17	a2	a2	PROPN
ejpam-6047	362	18	∈	∈	PROPN
ejpam-6047	362	19	rn	rn	PROPN
ejpam-6047	362	20	,	,	PUNCT
ejpam-6047	362	21	n	n	PRON
ejpam-6047	362	22	are	be	AUX
ejpam-6047	362	23	metzler	metzler	NOUN
ejpam-6047	362	24	and	and	CCONJ
ejpam-6047	362	25	hurwitz	hurwitz	PROPN
ejpam-6047	362	26	matrices	matrix	NOUN
ejpam-6047	362	27	,	,	PUNCT
ejpam-6047	362	28	is	be	AUX
ejpam-6047	362	29	d	d	NOUN
ejpam-6047	362	30	-	-	ADJ
ejpam-6047	362	31	stable	stable	ADJ
ejpam-6047	362	32	if	if	SCONJ
ejpam-6047	362	33	the	the	DET
ejpam-6047	362	34	µ-value	µ-value	NOUN
ejpam-6047	362	35	of	of	ADP
ejpam-6047	362	36	(	(	PUNCT
ejpam-6047	362	37	a1	a1	NOUN
ejpam-6047	362	38	+	+	PROPN
ejpam-6047	362	39	da2	da2	PROPN
ejpam-6047	362	40	)	)	PUNCT
ejpam-6047	362	41	−2	−2	NOUN
ejpam-6047	362	42	greater	great	ADJ
ejpam-6047	362	43	than	than	ADP
ejpam-6047	362	44	or	or	CCONJ
ejpam-6047	362	45	equal	equal	ADJ
ejpam-6047	362	46	to	to	ADP
ejpam-6047	362	47	0	0	NUM
ejpam-6047	362	48	and	and	CCONJ
ejpam-6047	362	49	less	less	ADJ
ejpam-6047	362	50	than	than	ADP
ejpam-6047	362	51	1	1	NUM
ejpam-6047	362	52	,	,	PUNCT
ejpam-6047	362	53	for	for	ADP
ejpam-6047	362	54	some	some	DET
ejpam-6047	362	55	positive	positive	ADJ
ejpam-6047	362	56	diagonal	diagonal	ADJ
ejpam-6047	362	57	matrix	matrix	NOUN
ejpam-6047	362	58	d.	d.	PROPN
ejpam-6047	362	59	theorem	theorem	VERB
ejpam-6047	362	60	12	12	NUM
ejpam-6047	362	61	.	.	PUNCT
ejpam-6047	363	1	the	the	DET
ejpam-6047	363	2	dynamical	dynamical	ADJ
ejpam-6047	363	3	system	system	NOUN
ejpam-6047	363	4	dx(t	dx(t	NOUN
ejpam-6047	363	5	)	)	PUNCT
ejpam-6047	363	6	dt	dt	NOUN
ejpam-6047	363	7	=	=	SYM
ejpam-6047	363	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	363	9	)	)	PUNCT
ejpam-6047	363	10	,	,	PUNCT
ejpam-6047	363	11	where	where	SCONJ
ejpam-6047	363	12	a(t	a(t	NOUN
ejpam-6047	363	13	)	)	PUNCT
ejpam-6047	363	14	∈	∈	PROPN
ejpam-6047	363	15	{	{	PUNCT
ejpam-6047	363	16	a1	a1	PROPN
ejpam-6047	363	17	,	,	PUNCT
ejpam-6047	363	18	a2	a2	PROPN
ejpam-6047	363	19	}	}	PUNCT
ejpam-6047	363	20	and	and	CCONJ
ejpam-6047	363	21	x(t	x(t	PROPN
ejpam-6047	363	22	)	)	PUNCT
ejpam-6047	363	23	∈	∈	PROPN
ejpam-6047	363	24	rn,1	rn,1	PROPN
ejpam-6047	363	25	,	,	PUNCT
ejpam-6047	363	26	where	where	SCONJ
ejpam-6047	363	27	a1	a1	NOUN
ejpam-6047	363	28	,	,	PUNCT
ejpam-6047	363	29	a2	a2	PROPN
ejpam-6047	363	30	∈	∈	PROPN
ejpam-6047	363	31	rn	rn	PROPN
ejpam-6047	363	32	,	,	PUNCT
ejpam-6047	363	33	n	n	PRON
ejpam-6047	363	34	are	be	AUX
ejpam-6047	363	35	d	d	ADJ
ejpam-6047	363	36	-	-	ADJ
ejpam-6047	363	37	stable	stable	ADJ
ejpam-6047	363	38	metzler	metzler	NOUN
ejpam-6047	363	39	and	and	CCONJ
ejpam-6047	363	40	hurwitz	hurwitz	PROPN
ejpam-6047	363	41	matrices	matrix	NOUN
ejpam-6047	363	42	iff	iff	VERB
ejpam-6047	363	43	0	0	NUM
ejpam-6047	363	44	≤	≤	NOUN
ejpam-6047	363	45	µb((a1	µb((a1	PUNCT
ejpam-6047	363	46	+	+	CCONJ
ejpam-6047	363	47	da2	da2	PROPN
ejpam-6047	363	48	)	)	PUNCT
ejpam-6047	363	49	−2	−2	NOUN
ejpam-6047	363	50	)	)	PUNCT
ejpam-6047	363	51	<	<	X
ejpam-6047	363	52	1	1	NUM
ejpam-6047	363	53	,	,	PUNCT
ejpam-6047	363	54	with	with	ADP
ejpam-6047	363	55	d	d	PROPN
ejpam-6047	363	56	=	=	SYM
ejpam-6047	363	57	diag(dii	diag(dii	PROPN
ejpam-6047	363	58	)	)	PUNCT
ejpam-6047	363	59	;	;	PUNCT
ejpam-6047	363	60	dii	dii	NOUN
ejpam-6047	363	61	>	>	X
ejpam-6047	363	62	0	0	X
ejpam-6047	363	63	.	.	PUNCT
ejpam-6047	364	1	m.u	m.u	PROPN
ejpam-6047	364	2	.	.	PROPN
ejpam-6047	364	3	rehman	rehman	PROPN
ejpam-6047	364	4	et	et	PROPN
ejpam-6047	364	5	al	al	PROPN
ejpam-6047	364	6	.	.	PUNCT
ejpam-6047	364	7	/	/	SYM
ejpam-6047	364	8	eur	eur	PROPN
ejpam-6047	364	9	.	.	PUNCT
ejpam-6047	365	1	j.	j.	PROPN
ejpam-6047	365	2	pure	pure	PROPN
ejpam-6047	365	3	appl	appl	PROPN
ejpam-6047	365	4	.	.	PROPN
ejpam-6047	365	5	math	math	PROPN
ejpam-6047	365	6	,	,	PUNCT
ejpam-6047	365	7	18	18	NUM
ejpam-6047	365	8	(	(	PUNCT
ejpam-6047	365	9	3	3	NUM
ejpam-6047	365	10	)	)	PUNCT
ejpam-6047	365	11	(	(	PUNCT
ejpam-6047	365	12	2025	2025	NUM
ejpam-6047	365	13	)	)	PUNCT
ejpam-6047	365	14	,	,	PUNCT
ejpam-6047	365	15	6047	6047	NUM
ejpam-6047	365	16	16	16	NUM
ejpam-6047	365	17	of	of	ADP
ejpam-6047	365	18	33	33	NUM
ejpam-6047	365	19	proof	proof	NOUN
ejpam-6047	365	20	.	.	PUNCT
ejpam-6047	366	1	from	from	ADP
ejpam-6047	366	2	[	[	X
ejpam-6047	366	3	55	55	NUM
ejpam-6047	366	4	]	]	PUNCT
ejpam-6047	366	5	,	,	PUNCT
ejpam-6047	366	6	it	it	PRON
ejpam-6047	366	7	is	be	AUX
ejpam-6047	366	8	evident	evident	ADJ
ejpam-6047	366	9	that	that	SCONJ
ejpam-6047	366	10	the	the	DET
ejpam-6047	366	11	matrix	matrix	NOUN
ejpam-6047	366	12	(	(	PUNCT
ejpam-6047	366	13	a1	a1	NOUN
ejpam-6047	366	14	+	+	CCONJ
ejpam-6047	366	15	da2	da2	PROPN
ejpam-6047	366	16	)	)	PUNCT
ejpam-6047	366	17	is	be	AUX
ejpam-6047	366	18	d	d	ADJ
ejpam-6047	366	19	-	-	ADJ
ejpam-6047	366	20	stable	stable	ADJ
ejpam-6047	366	21	iff	iff	NOUN
ejpam-6047	366	22	(	(	PUNCT
ejpam-6047	366	23	a1	a1	NOUN
ejpam-6047	366	24	+	+	CCONJ
ejpam-6047	366	25	da2	da2	PROPN
ejpam-6047	366	26	)	)	PUNCT
ejpam-6047	366	27	is	be	AUX
ejpam-6047	366	28	stable	stable	ADJ
ejpam-6047	366	29	and	and	CCONJ
ejpam-6047	366	30	det	det	PROPN
ejpam-6047	366	31	(	(	PUNCT
ejpam-6047	366	32	a1	a1	NOUN
ejpam-6047	366	33	+	+	CCONJ
ejpam-6047	366	34	da2	da2	PROPN
ejpam-6047	366	35	−d	−d	VERB
ejpam-6047	366	36	d	d	X
ejpam-6047	366	37	a1	a1	PROPN
ejpam-6047	366	38	+	+	CCONJ
ejpam-6047	366	39	da2	da2	PROPN
ejpam-6047	366	40	)	)	PUNCT
ejpam-6047	367	1	̸=	̸=	PROPN
ejpam-6047	367	2	0	0	NUM
ejpam-6047	367	3	.	.	PUNCT
ejpam-6047	368	1	as	as	SCONJ
ejpam-6047	368	2	we	we	PRON
ejpam-6047	368	3	know	know	VERB
ejpam-6047	368	4	that	that	PRON
ejpam-6047	368	5	for	for	ADP
ejpam-6047	368	6	a	a	DET
ejpam-6047	368	7	stable	stable	ADJ
ejpam-6047	368	8	matrix	matrix	NOUN
ejpam-6047	368	9	(	(	PUNCT
ejpam-6047	368	10	a1	a1	NOUN
ejpam-6047	368	11	+	+	CCONJ
ejpam-6047	368	12	da2	da2	PROPN
ejpam-6047	368	13	)	)	PUNCT
ejpam-6047	368	14	,	,	PUNCT
ejpam-6047	368	15	we	we	PRON
ejpam-6047	368	16	have	have	VERB
ejpam-6047	368	17	that	that	DET
ejpam-6047	368	18	det	det	PROPN
ejpam-6047	368	19	(	(	PUNCT
ejpam-6047	368	20	a1	a1	NOUN
ejpam-6047	368	21	+	+	CCONJ
ejpam-6047	368	22	da2	da2	PROPN
ejpam-6047	368	23	−d	−d	VERB
ejpam-6047	368	24	d	d	X
ejpam-6047	368	25	a1	a1	PROPN
ejpam-6047	368	26	+	+	CCONJ
ejpam-6047	368	27	da2	da2	PROPN
ejpam-6047	368	28	)	)	PUNCT
ejpam-6047	368	29	̸=	̸=	PROPN
ejpam-6047	368	30	0	0	NUM
ejpam-6047	368	31	.	.	PUNCT
ejpam-6047	369	1	this	this	PRON
ejpam-6047	369	2	implies	imply	VERB
ejpam-6047	369	3	that	that	SCONJ
ejpam-6047	369	4	0	0	NUM
ejpam-6047	369	5	≤	≤	NOUN
ejpam-6047	369	6	µb((a1+da2	µb((a1+da2	PRON
ejpam-6047	369	7	)	)	PUNCT
ejpam-6047	369	8	−2	−2	NOUN
ejpam-6047	369	9	)	)	PUNCT
ejpam-6047	369	10	<	<	X
ejpam-6047	370	1	1	1	X
ejpam-6047	370	2	.	.	PUNCT
ejpam-6047	370	3	also	also	ADV
ejpam-6047	370	4	from	from	ADP
ejpam-6047	370	5	[	[	X
ejpam-6047	370	6	56	56	NUM
ejpam-6047	370	7	]	]	PUNCT
ejpam-6047	370	8	,	,	PUNCT
ejpam-6047	370	9	we	we	PRON
ejpam-6047	370	10	have	have	VERB
ejpam-6047	370	11	det	det	NOUN
ejpam-6047	370	12	(	(	PUNCT
ejpam-6047	370	13	a1	a1	NOUN
ejpam-6047	370	14	+	+	CCONJ
ejpam-6047	370	15	da2	da2	PROPN
ejpam-6047	370	16	−d	−d	VERB
ejpam-6047	370	17	d	d	X
ejpam-6047	370	18	a1	a1	PROPN
ejpam-6047	370	19	+	+	CCONJ
ejpam-6047	370	20	da2	da2	PROPN
ejpam-6047	370	21	)	)	PUNCT
ejpam-6047	371	1	̸=	̸=	PROPN
ejpam-6047	371	2	0	0	NUM
ejpam-6047	371	3	,	,	PUNCT
ejpam-6047	371	4	in	in	ADP
ejpam-6047	371	5	turn	turn	NOUN
ejpam-6047	371	6	this	this	PRON
ejpam-6047	371	7	implies	imply	VERB
ejpam-6047	371	8	det	det	PROPN
ejpam-6047	371	9	(	(	PUNCT
ejpam-6047	371	10	(	(	PUNCT
ejpam-6047	371	11	a1	a1	NOUN
ejpam-6047	371	12	+	+	CCONJ
ejpam-6047	371	13	da2	da2	PROPN
ejpam-6047	371	14	)	)	PUNCT
ejpam-6047	371	15	2	2	NUM
ejpam-6047	371	16	−d(a1	−d(a1	PROPN
ejpam-6047	371	17	+	+	CCONJ
ejpam-6047	371	18	da2	da2	PROPN
ejpam-6047	371	19	)	)	PUNCT
ejpam-6047	372	1	−1d(a1	−1d(a1	PROPN
ejpam-6047	372	2	+	+	CCONJ
ejpam-6047	372	3	da2	da2	PROPN
ejpam-6047	372	4	)	)	PUNCT
ejpam-6047	372	5	)	)	PUNCT
ejpam-6047	373	1	̸=	̸=	PROPN
ejpam-6047	373	2	0	0	NUM
ejpam-6047	373	3	,	,	PUNCT
ejpam-6047	373	4	which	which	PRON
ejpam-6047	373	5	further	far	ADV
ejpam-6047	373	6	yields	yield	VERB
ejpam-6047	373	7	det	det	PROPN
ejpam-6047	373	8	(	(	PUNCT
ejpam-6047	373	9	(	(	PUNCT
ejpam-6047	373	10	a1	a1	NOUN
ejpam-6047	373	11	+	+	CCONJ
ejpam-6047	373	12	da2	da2	PROPN
ejpam-6047	373	13	)	)	PUNCT
ejpam-6047	373	14	2	2	NUM
ejpam-6047	373	15	−d(a1	−d(a1	PROPN
ejpam-6047	373	16	+	+	CCONJ
ejpam-6047	373	17	da2	da2	PROPN
ejpam-6047	373	18	)	)	PUNCT
ejpam-6047	374	1	−1d(a1	−1d(a1	PROPN
ejpam-6047	374	2	+	+	CCONJ
ejpam-6047	374	3	da2	da2	PROPN
ejpam-6047	374	4	)	)	PUNCT
ejpam-6047	374	5	)	)	PUNCT
ejpam-6047	375	1	̸=	̸=	PROPN
ejpam-6047	375	2	0	0	NUM
ejpam-6047	375	3	.	.	PUNCT
ejpam-6047	376	1	this	this	PRON
ejpam-6047	376	2	implies	imply	VERB
ejpam-6047	376	3	that	that	SCONJ
ejpam-6047	376	4	det	det	PROPN
ejpam-6047	376	5	(	(	PUNCT
ejpam-6047	376	6	i2	i2	PROPN
ejpam-6047	376	7	−	−	PROPN
ejpam-6047	376	8	(	(	PUNCT
ejpam-6047	376	9	a1	a1	NOUN
ejpam-6047	376	10	+	+	CCONJ
ejpam-6047	376	11	da2	da2	PROPN
ejpam-6047	376	12	)	)	PUNCT
ejpam-6047	376	13	−2d̃	−2d̃	NOUN
ejpam-6047	376	14	)	)	PUNCT
ejpam-6047	376	15	̸=	̸=	PROPN
ejpam-6047	376	16	0	0	NUM
ejpam-6047	376	17	,	,	PUNCT
ejpam-6047	376	18	where	where	SCONJ
ejpam-6047	376	19	d̃	d̃	PROPN
ejpam-6047	376	20	=	=	SYM
ejpam-6047	376	21	d	d	PROPN
ejpam-6047	376	22	=	=	PUNCT
ejpam-6047	376	23	diag(d11	diag(d11	PROPN
ejpam-6047	376	24	,	,	PUNCT
ejpam-6047	376	25	d22	d22	PROPN
ejpam-6047	376	26	)	)	PUNCT
ejpam-6047	376	27	;	;	PUNCT
ejpam-6047	376	28	dii	dii	NOUN
ejpam-6047	376	29	>	>	X
ejpam-6047	376	30	0	0	X
ejpam-6047	376	31	.	.	PUNCT
ejpam-6047	377	1	thus	thus	ADV
ejpam-6047	377	2	finally	finally	ADV
ejpam-6047	377	3	,	,	PUNCT
ejpam-6047	377	4	det(in	det(in	ADJ
ejpam-6047	377	5	−	−	NOUN
ejpam-6047	377	6	(	(	PUNCT
ejpam-6047	377	7	a1	a1	NOUN
ejpam-6047	377	8	+	+	CCONJ
ejpam-6047	377	9	da2	da2	PROPN
ejpam-6047	377	10	)	)	PUNCT
ejpam-6047	377	11	−2d̃	−2d̃	NOUN
ejpam-6047	377	12	)	)	PUNCT
ejpam-6047	377	13	̸=	̸=	NOUN
ejpam-6047	377	14	0	0	NUM
ejpam-6047	378	1	=	=	NOUN
ejpam-6047	378	2	⇒	⇒	NOUN
ejpam-6047	378	3	0	0	NUM
ejpam-6047	378	4	≤	≤	NOUN
ejpam-6047	378	5	µb((a1	µb((a1	PUNCT
ejpam-6047	378	6	+	+	CCONJ
ejpam-6047	378	7	da2	da2	PROPN
ejpam-6047	378	8	)	)	PUNCT
ejpam-6047	378	9	−2	−2	NOUN
ejpam-6047	378	10	)	)	PUNCT
ejpam-6047	378	11	<	<	X
ejpam-6047	378	12	1	1	X
ejpam-6047	378	13	.	.	PUNCT
ejpam-6047	378	14	theorem	theorem	VERB
ejpam-6047	378	15	13	13	NUM
ejpam-6047	378	16	establishes	establish	VERB
ejpam-6047	378	17	results	result	NOUN
ejpam-6047	378	18	regarding	regard	VERB
ejpam-6047	378	19	the	the	DET
ejpam-6047	378	20	d	d	NOUN
ejpam-6047	378	21	-	-	NOUN
ejpam-6047	378	22	stability	stability	NOUN
ejpam-6047	378	23	of	of	ADP
ejpam-6047	378	24	positive	positive	ADJ
ejpam-6047	378	25	linear	linear	ADJ
ejpam-6047	378	26	time	time	NOUN
ejpam-6047	378	27	-	-	PUNCT
ejpam-6047	378	28	invariant	invariant	ADJ
ejpam-6047	378	29	systems	system	NOUN
ejpam-6047	378	30	.	.	PUNCT
ejpam-6047	379	1	it	it	PRON
ejpam-6047	379	2	has	have	AUX
ejpam-6047	379	3	been	be	AUX
ejpam-6047	379	4	demonstrated	demonstrate	VERB
ejpam-6047	379	5	that	that	SCONJ
ejpam-6047	379	6	a	a	DET
ejpam-6047	379	7	positive	positive	ADJ
ejpam-6047	379	8	linear	linear	ADJ
ejpam-6047	379	9	time	time	NOUN
ejpam-6047	379	10	-	-	PUNCT
ejpam-6047	379	11	invariant	invariant	ADJ
ejpam-6047	379	12	system	system	NOUN
ejpam-6047	379	13	with	with	ADP
ejpam-6047	379	14	a1	a1	NOUN
ejpam-6047	379	15	,	,	PUNCT
ejpam-6047	379	16	a2	a2	PROPN
ejpam-6047	379	17	∈	∈	PROPN
ejpam-6047	379	18	rn	rn	PROPN
ejpam-6047	379	19	,	,	PUNCT
ejpam-6047	379	20	n	n	CCONJ
ejpam-6047	379	21	,	,	PUNCT
ejpam-6047	379	22	where	where	SCONJ
ejpam-6047	379	23	both	both	PRON
ejpam-6047	379	24	are	be	AUX
ejpam-6047	379	25	metzler	metzler	NOUN
ejpam-6047	379	26	and	and	CCONJ
ejpam-6047	379	27	hurwitz	hurwitz	PROPN
ejpam-6047	379	28	matrices	matrix	NOUN
ejpam-6047	379	29	,	,	PUNCT
ejpam-6047	379	30	is	be	AUX
ejpam-6047	379	31	d	d	NOUN
ejpam-6047	379	32	-	-	ADJ
ejpam-6047	379	33	stable	stable	ADJ
ejpam-6047	379	34	if	if	SCONJ
ejpam-6047	379	35	the	the	DET
ejpam-6047	379	36	real	real	ADJ
ejpam-6047	379	37	parts	part	NOUN
ejpam-6047	379	38	of	of	ADP
ejpam-6047	379	39	all	all	DET
ejpam-6047	379	40	eigenvalues	eigenvalue	NOUN
ejpam-6047	379	41	of	of	ADP
ejpam-6047	379	42	the	the	DET
ejpam-6047	379	43	matrix	matrix	NOUN
ejpam-6047	379	44	d(a1	d(a1	NOUN
ejpam-6047	379	45	+	+	CCONJ
ejpam-6047	379	46	da2	da2	PROPN
ejpam-6047	379	47	)	)	PUNCT
ejpam-6047	380	1	+	+	CCONJ
ejpam-6047	380	2	(	(	PUNCT
ejpam-6047	380	3	a1	a1	NOUN
ejpam-6047	380	4	+	+	NOUN
ejpam-6047	380	5	da2	da2	PROPN
ejpam-6047	380	6	)	)	PUNCT
ejpam-6047	380	7	td	td	NOUN
ejpam-6047	380	8	are	be	AUX
ejpam-6047	380	9	strictly	strictly	ADV
ejpam-6047	380	10	positive	positive	ADJ
ejpam-6047	380	11	.	.	PUNCT
ejpam-6047	381	1	additionally	additionally	ADV
ejpam-6047	381	2	,	,	PUNCT
ejpam-6047	381	3	for	for	ADP
ejpam-6047	381	4	a	a	DET
ejpam-6047	381	5	positive	positive	ADJ
ejpam-6047	381	6	diagonal	diagonal	ADJ
ejpam-6047	381	7	matrix	matrix	NOUN
ejpam-6047	381	8	d	d	NOUN
ejpam-6047	381	9	,	,	PUNCT
ejpam-6047	381	10	the	the	DET
ejpam-6047	381	11	system	system	NOUN
ejpam-6047	381	12	remains	remain	VERB
ejpam-6047	381	13	d	d	ADJ
ejpam-6047	381	14	-	-	ADJ
ejpam-6047	381	15	stable	stable	ADJ
ejpam-6047	381	16	if	if	SCONJ
ejpam-6047	381	17	the	the	DET
ejpam-6047	381	18	µ-value	µ-value	NOUN
ejpam-6047	381	19	of	of	ADP
ejpam-6047	381	20	the	the	DET
ejpam-6047	381	21	matrix	matrix	NOUN
ejpam-6047	381	22	m	m	VERB
ejpam-6047	381	23	,	,	PUNCT
ejpam-6047	381	24	derived	derive	VERB
ejpam-6047	381	25	from	from	ADP
ejpam-6047	381	26	a1	a1	NOUN
ejpam-6047	381	27	,	,	PUNCT
ejpam-6047	381	28	a2	a2	PROPN
ejpam-6047	381	29	,	,	PUNCT
ejpam-6047	381	30	and	and	CCONJ
ejpam-6047	381	31	d	d	NOUN
ejpam-6047	381	32	,	,	PUNCT
ejpam-6047	381	33	satisfies	satisfy	VERB
ejpam-6047	381	34	0	0	NUM
ejpam-6047	381	35	≤	≤	NUM
ejpam-6047	381	36	µ(m	µ(m	NOUN
ejpam-6047	381	37	)	)	PUNCT
ejpam-6047	381	38	<	<	X
ejpam-6047	381	39	1	1	X
ejpam-6047	381	40	.	.	PUNCT
ejpam-6047	381	41	theorem	theorem	VERB
ejpam-6047	381	42	13	13	NUM
ejpam-6047	381	43	.	.	PUNCT
ejpam-6047	382	1	the	the	DET
ejpam-6047	382	2	dynamical	dynamical	ADJ
ejpam-6047	382	3	system	system	NOUN
ejpam-6047	382	4	dx(t	dx(t	NOUN
ejpam-6047	382	5	)	)	PUNCT
ejpam-6047	382	6	dt	dt	NOUN
ejpam-6047	382	7	=	=	SYM
ejpam-6047	382	8	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	382	9	)	)	PUNCT
ejpam-6047	382	10	,	,	PUNCT
ejpam-6047	382	11	where	where	SCONJ
ejpam-6047	382	12	a(t	a(t	NOUN
ejpam-6047	382	13	)	)	PUNCT
ejpam-6047	382	14	∈	∈	PROPN
ejpam-6047	382	15	{	{	PUNCT
ejpam-6047	382	16	a1	a1	NOUN
ejpam-6047	382	17	,	,	PUNCT
ejpam-6047	382	18	a2	a2	PROPN
ejpam-6047	382	19	}	}	PUNCT
ejpam-6047	382	20	,	,	PUNCT
ejpam-6047	382	21	x(t	x(t	PROPN
ejpam-6047	382	22	)	)	PUNCT
ejpam-6047	382	23	∈	∈	PROPN
ejpam-6047	382	24	rn,1	rn,1	PROPN
ejpam-6047	382	25	,	,	PUNCT
ejpam-6047	382	26	where	where	SCONJ
ejpam-6047	382	27	a1	a1	NOUN
ejpam-6047	382	28	,	,	PUNCT
ejpam-6047	382	29	a2	a2	PROPN
ejpam-6047	382	30	∈	∈	PROPN
ejpam-6047	382	31	rn	rn	PROPN
ejpam-6047	382	32	,	,	PUNCT
ejpam-6047	382	33	n	n	PRON
ejpam-6047	382	34	are	be	AUX
ejpam-6047	382	35	metzler	metzler	NOUN
ejpam-6047	382	36	,	,	PUNCT
ejpam-6047	382	37	and	and	CCONJ
ejpam-6047	382	38	hurwitz	hurwitz	PROPN
ejpam-6047	382	39	matrices	matrix	NOUN
ejpam-6047	382	40	,	,	PUNCT
ejpam-6047	382	41	is	be	AUX
ejpam-6047	382	42	d	d	NOUN
ejpam-6047	382	43	-	-	ADJ
ejpam-6047	382	44	stable	stable	ADJ
ejpam-6047	382	45	if	if	SCONJ
ejpam-6047	382	46	and	and	CCONJ
ejpam-6047	382	47	only	only	ADV
ejpam-6047	382	48	if	if	SCONJ
ejpam-6047	382	49	re	re	X
ejpam-6047	382	50	(	(	PUNCT
ejpam-6047	382	51	λi(d(a1	λi(d(a1	PROPN
ejpam-6047	382	52	+	+	CCONJ
ejpam-6047	382	53	da2	da2	PROPN
ejpam-6047	382	54	)	)	PUNCT
ejpam-6047	383	1	+	+	CCONJ
ejpam-6047	383	2	(	(	PUNCT
ejpam-6047	383	3	a1	a1	NOUN
ejpam-6047	383	4	+	+	CCONJ
ejpam-6047	383	5	da2	da2	PROPN
ejpam-6047	383	6	)	)	PUNCT
ejpam-6047	383	7	td	td	NOUN
ejpam-6047	383	8	)	)	PUNCT
ejpam-6047	383	9	)	)	PUNCT
ejpam-6047	384	1	>	>	X
ejpam-6047	384	2	0	0	NUM
ejpam-6047	384	3	,	,	PUNCT
ejpam-6047	384	4	∀i	∀i	NOUN
ejpam-6047	384	5	=	=	SYM
ejpam-6047	384	6	1	1	NUM
ejpam-6047	384	7	:	:	PUNCT
ejpam-6047	384	8	n	n	NOUN
ejpam-6047	384	9	with	with	ADP
ejpam-6047	384	10	d	d	PROPN
ejpam-6047	384	11	=	=	SYM
ejpam-6047	384	12	diag(dii	diag(dii	PROPN
ejpam-6047	384	13	)	)	PUNCT
ejpam-6047	384	14	,	,	PUNCT
ejpam-6047	384	15	dii	dii	INTJ
ejpam-6047	384	16	>	>	X
ejpam-6047	384	17	0	0	NUM
ejpam-6047	384	18	,	,	PUNCT
ejpam-6047	384	19	and	and	CCONJ
ejpam-6047	384	20	0	0	NUM
ejpam-6047	384	21	≤	≤	NUM
ejpam-6047	384	22	µb(m	µb(m	ADV
ejpam-6047	384	23	)	)	PUNCT
ejpam-6047	384	24	<	<	X
ejpam-6047	384	25	1	1	X
ejpam-6047	384	26	.	.	PUNCT
ejpam-6047	385	1	the	the	DET
ejpam-6047	385	2	matrix	matrix	NOUN
ejpam-6047	385	3	m	m	AUX
ejpam-6047	385	4	is	be	AUX
ejpam-6047	385	5	defined	define	VERB
ejpam-6047	385	6	as	as	ADP
ejpam-6047	385	7	m	m	NOUN
ejpam-6047	385	8	=	=	PUNCT
ejpam-6047	385	9	(	(	PUNCT
ejpam-6047	385	10	iin	iin	NOUN
ejpam-6047	385	11	+	+	CCONJ
ejpam-6047	385	12	d(a1	d(a1	NOUN
ejpam-6047	385	13	+	+	CCONJ
ejpam-6047	385	14	da2	da2	PROPN
ejpam-6047	385	15	)	)	PUNCT
ejpam-6047	386	1	+	+	CCONJ
ejpam-6047	386	2	(	(	PUNCT
ejpam-6047	386	3	a1	a1	NOUN
ejpam-6047	386	4	+	+	CCONJ
ejpam-6047	386	5	da2	da2	PROPN
ejpam-6047	386	6	)	)	PUNCT
ejpam-6047	386	7	td	td	NOUN
ejpam-6047	386	8	)	)	PUNCT
ejpam-6047	386	9	−1	−1	NOUN
ejpam-6047	386	10	(	(	PUNCT
ejpam-6047	386	11	iin	iin	PROPN
ejpam-6047	386	12	−d(a1	−d(a1	PROPN
ejpam-6047	386	13	+	+	CCONJ
ejpam-6047	386	14	da2	da2	PROPN
ejpam-6047	386	15	)	)	PUNCT
ejpam-6047	386	16	−	−	PROPN
ejpam-6047	387	1	(	(	PUNCT
ejpam-6047	387	2	a1	a1	NOUN
ejpam-6047	387	3	+	+	CCONJ
ejpam-6047	387	4	da2)d	da2)d	PROPN
ejpam-6047	387	5	)	)	PUNCT
ejpam-6047	387	6	.	.	PUNCT
ejpam-6047	388	1	proof	proof	NOUN
ejpam-6047	388	2	.	.	PUNCT
ejpam-6047	389	1	to	to	PART
ejpam-6047	389	2	prove	prove	VERB
ejpam-6047	389	3	that	that	SCONJ
ejpam-6047	389	4	(	(	PUNCT
ejpam-6047	389	5	a1	a1	NOUN
ejpam-6047	389	6	+	+	CCONJ
ejpam-6047	389	7	da2	da2	PROPN
ejpam-6047	389	8	)	)	PUNCT
ejpam-6047	389	9	is	be	AUX
ejpam-6047	389	10	d	d	ADJ
ejpam-6047	389	11	-	-	ADJ
ejpam-6047	389	12	stable	stable	ADJ
ejpam-6047	389	13	iff	iff	PROPN
ejpam-6047	389	14	0	0	NUM
ejpam-6047	389	15	≤	≤	NUM
ejpam-6047	390	1	µb(m	µb(m	ADV
ejpam-6047	390	2	)	)	PUNCT
ejpam-6047	390	3	<	<	X
ejpam-6047	390	4	1	1	NUM
ejpam-6047	390	5	,	,	PUNCT
ejpam-6047	390	6	we	we	PRON
ejpam-6047	390	7	assume	assume	VERB
ejpam-6047	390	8	that	that	SCONJ
ejpam-6047	390	9	(	(	PUNCT
ejpam-6047	390	10	a1	a1	NOUN
ejpam-6047	390	11	+	+	NOUN
ejpam-6047	390	12	da2	da2	PROPN
ejpam-6047	390	13	)	)	PUNCT
ejpam-6047	390	14	is	be	AUX
ejpam-6047	390	15	d	d	ADJ
ejpam-6047	390	16	-	-	ADJ
ejpam-6047	390	17	stable	stable	ADJ
ejpam-6047	390	18	matrix	matrix	NOUN
ejpam-6047	390	19	,	,	PUNCT
ejpam-6047	390	20	means	mean	VERB
ejpam-6047	390	21	that	that	SCONJ
ejpam-6047	390	22	for	for	ADP
ejpam-6047	390	23	all	all	DET
ejpam-6047	390	24	d	d	NOUN
ejpam-6047	390	25	=	=	SYM
ejpam-6047	390	26	diag(dii	diag(dii	PROPN
ejpam-6047	390	27	)	)	PUNCT
ejpam-6047	390	28	,	,	PUNCT
ejpam-6047	390	29	λi((a1	λi((a1	PUNCT
ejpam-6047	391	1	+	+	ADJ
ejpam-6047	391	2	da2	da2	PROPN
ejpam-6047	391	3	)	)	PUNCT
ejpam-6047	392	1	+	+	CCONJ
ejpam-6047	392	2	i	i	PROPN
ejpam-6047	392	3	d	d	PROPN
ejpam-6047	392	4	)	)	PUNCT
ejpam-6047	392	5	̸=	̸=	PROPN
ejpam-6047	392	6	0	0	NUM
ejpam-6047	392	7	,	,	PUNCT
ejpam-6047	392	8	∀	∀	PUNCT
ejpam-6047	393	1	i	i	NOUN
ejpam-6047	393	2	=	=	NOUN
ejpam-6047	393	3	1	1	X
ejpam-6047	393	4	:	:	PUNCT
ejpam-6047	393	5	n.	n.	NOUN
ejpam-6047	393	6	let	let	VERB
ejpam-6047	393	7	∆	∆	PROPN
ejpam-6047	393	8	∈	∈	PROPN
ejpam-6047	393	9	b	b	PROPN
ejpam-6047	393	10	has	have	VERB
ejpam-6047	393	11	block	block	NOUN
ejpam-6047	393	12	-	-	PUNCT
ejpam-6047	393	13	diagonal	diagonal	ADJ
ejpam-6047	393	14	structure	structure	NOUN
ejpam-6047	393	15	,	,	PUNCT
ejpam-6047	393	16	that	that	ADV
ejpam-6047	393	17	is	be	AUX
ejpam-6047	393	18	,	,	PUNCT
ejpam-6047	393	19	∆	∆	X
ejpam-6047	393	20	=	=	PUNCT
ejpam-6047	393	21	(	(	PUNCT
ejpam-6047	393	22	iin	iin	NOUN
ejpam-6047	393	23	−d)(iin	−d)(iin	NOUN
ejpam-6047	393	24	+	+	CCONJ
ejpam-6047	393	25	d)−1	d)−1	NOUN
ejpam-6047	393	26	.	.	PUNCT
ejpam-6047	394	1	then	then	ADV
ejpam-6047	394	2	,	,	PUNCT
ejpam-6047	394	3	d	d	PROPN
ejpam-6047	394	4	=	=	PRON
ejpam-6047	394	5	(	(	PUNCT
ejpam-6047	394	6	iin	iin	NOUN
ejpam-6047	394	7	+	+	CCONJ
ejpam-6047	394	8	∆)−1(iin	∆)−1(iin	PROPN
ejpam-6047	394	9	−	−	PROPN
ejpam-6047	394	10	∆),∆	∆),∆	NOUN
ejpam-6047	394	11	∈	∈	PROPN
ejpam-6047	394	12	b.	b.	NOUN
ejpam-6047	394	13	since	since	SCONJ
ejpam-6047	394	14	λi((a1	λi((a1	PROPN
ejpam-6047	394	15	+	+	CCONJ
ejpam-6047	394	16	da2	da2	PROPN
ejpam-6047	394	17	)	)	PUNCT
ejpam-6047	395	1	+	+	CCONJ
ejpam-6047	396	1	i	i	PROPN
ejpam-6047	396	2	d	d	PROPN
ejpam-6047	396	3	)	)	PUNCT
ejpam-6047	396	4	̸=	̸=	NOUN
ejpam-6047	396	5	0,∀	0,∀	NUM
ejpam-6047	397	1	i	i	NOUN
ejpam-6047	397	2	=	=	NOUN
ejpam-6047	397	3	1	1	NUM
ejpam-6047	397	4	:	:	PUNCT
ejpam-6047	397	5	n	n	CCONJ
ejpam-6047	397	6	for	for	ADP
ejpam-6047	397	7	some	some	DET
ejpam-6047	397	8	d	d	NOUN
ejpam-6047	397	9	,	,	PUNCT
ejpam-6047	397	10	a	a	DET
ejpam-6047	397	11	positive	positive	ADJ
ejpam-6047	397	12	diagonal	diagonal	ADJ
ejpam-6047	397	13	matrix	matrix	NOUN
ejpam-6047	397	14	.	.	PUNCT
ejpam-6047	398	1	this	this	DET
ejpam-6047	398	2	further	far	ADV
ejpam-6047	398	3	implies	imply	VERB
ejpam-6047	398	4	that	that	SCONJ
ejpam-6047	398	5	λi((a1	λi((a1	PUNCT
ejpam-6047	398	6	+	+	NUM
ejpam-6047	398	7	da2	da2	PROPN
ejpam-6047	398	8	)	)	PUNCT
ejpam-6047	399	1	+	+	CCONJ
ejpam-6047	399	2	i(iin	i(iin	NOUN
ejpam-6047	399	3	+	+	CCONJ
ejpam-6047	399	4	∆)−1(iin	∆)−1(iin	NOUN
ejpam-6047	399	5	−	−	PROPN
ejpam-6047	399	6	∆	∆	PROPN
ejpam-6047	399	7	)	)	PUNCT
ejpam-6047	399	8	)	)	PUNCT
ejpam-6047	400	1	̸=	̸=	NOUN
ejpam-6047	400	2	0	0	NUM
ejpam-6047	400	3	∀∆	∀∆	NOUN
ejpam-6047	400	4	∈	∈	PROPN
ejpam-6047	400	5	b,∀	b,∀	PUNCT
ejpam-6047	401	1	i	i	PRON
ejpam-6047	401	2	=	=	NOUN
ejpam-6047	401	3	1	1	X
ejpam-6047	401	4	:	:	PUNCT
ejpam-6047	401	5	n.	n.	PROPN
ejpam-6047	401	6	m.u	m.u	PROPN
ejpam-6047	401	7	.	.	PROPN
ejpam-6047	402	1	rehman	rehman	PROPN
ejpam-6047	402	2	et	et	PROPN
ejpam-6047	402	3	al	al	PROPN
ejpam-6047	402	4	.	.	PUNCT
ejpam-6047	402	5	/	/	SYM
ejpam-6047	402	6	eur	eur	PROPN
ejpam-6047	402	7	.	.	PUNCT
ejpam-6047	403	1	j.	j.	PROPN
ejpam-6047	403	2	pure	pure	PROPN
ejpam-6047	403	3	appl	appl	PROPN
ejpam-6047	403	4	.	.	PROPN
ejpam-6047	403	5	math	math	PROPN
ejpam-6047	403	6	,	,	PUNCT
ejpam-6047	403	7	18	18	NUM
ejpam-6047	403	8	(	(	PUNCT
ejpam-6047	403	9	3	3	NUM
ejpam-6047	403	10	)	)	PUNCT
ejpam-6047	403	11	(	(	PUNCT
ejpam-6047	403	12	2025	2025	NUM
ejpam-6047	403	13	)	)	PUNCT
ejpam-6047	403	14	,	,	PUNCT
ejpam-6047	403	15	6047	6047	NUM
ejpam-6047	403	16	17	17	NUM
ejpam-6047	403	17	of	of	ADP
ejpam-6047	403	18	33	33	NUM
ejpam-6047	403	19	we	we	PRON
ejpam-6047	403	20	also	also	ADV
ejpam-6047	403	21	observe	observe	VERB
ejpam-6047	403	22	that	that	SCONJ
ejpam-6047	403	23	,	,	PUNCT
ejpam-6047	403	24	rank	rank	NOUN
ejpam-6047	403	25	(	(	PUNCT
ejpam-6047	403	26	(	(	PUNCT
ejpam-6047	403	27	a1	a1	NOUN
ejpam-6047	403	28	+	+	CCONJ
ejpam-6047	403	29	da2	da2	PROPN
ejpam-6047	403	30	)	)	PUNCT
ejpam-6047	404	1	+	+	CCONJ
ejpam-6047	404	2	i(iin	i(iin	NOUN
ejpam-6047	404	3	+	+	CCONJ
ejpam-6047	404	4	∆)−1(iin	∆)−1(iin	NOUN
ejpam-6047	404	5	−	−	PROPN
ejpam-6047	404	6	∆	∆	PROPN
ejpam-6047	404	7	)	)	PUNCT
ejpam-6047	404	8	)	)	PUNCT
ejpam-6047	405	1	≈	≈	PROPN
ejpam-6047	405	2	rank	rank	NOUN
ejpam-6047	405	3	(	(	PUNCT
ejpam-6047	405	4	(	(	PUNCT
ejpam-6047	405	5	iin	iin	NOUN
ejpam-6047	405	6	+	+	CCONJ
ejpam-6047	405	7	(	(	PUNCT
ejpam-6047	405	8	a1	a1	NOUN
ejpam-6047	405	9	+	+	CCONJ
ejpam-6047	405	10	da2	da2	PROPN
ejpam-6047	405	11	)	)	PUNCT
ejpam-6047	405	12	−	−	PROPN
ejpam-6047	405	13	(	(	PUNCT
ejpam-6047	405	14	iin	iin	NOUN
ejpam-6047	405	15	−	−	PROPN
ejpam-6047	405	16	(	(	PUNCT
ejpam-6047	405	17	a1	a1	NOUN
ejpam-6047	405	18	+	+	CCONJ
ejpam-6047	405	19	da2)∆	da2)∆	ADJ
ejpam-6047	405	20	)	)	PUNCT
ejpam-6047	405	21	)	)	PUNCT
ejpam-6047	405	22	.	.	PUNCT
ejpam-6047	406	1	this	this	PRON
ejpam-6047	406	2	allows	allow	VERB
ejpam-6047	406	3	us	we	PRON
ejpam-6047	406	4	to	to	PART
ejpam-6047	406	5	arrive	arrive	VERB
ejpam-6047	406	6	at	at	ADP
ejpam-6047	406	7	following	follow	VERB
ejpam-6047	406	8	expression	expression	NOUN
ejpam-6047	406	9	,	,	PUNCT
ejpam-6047	406	10	that	that	ADV
ejpam-6047	406	11	is	is	ADV
ejpam-6047	406	12	,	,	PUNCT
ejpam-6047	406	13	(	(	PUNCT
ejpam-6047	406	14	iin+(a1+da2))−(iin−(a1+da2)∆	iin+(a1+da2))−(iin−(a1+da2)∆	ADJ
ejpam-6047	406	15	)	)	PUNCT
ejpam-6047	406	16	)	)	PUNCT
ejpam-6047	407	1	=	=	PRON
ejpam-6047	407	2	(	(	PUNCT
ejpam-6047	407	3	in−(iin+(a1+da2	in−(iin+(a1+da2	NOUN
ejpam-6047	407	4	)	)	PUNCT
ejpam-6047	407	5	−1)(iin−(a1+da2)∆)),∀∆	−1)(iin−(a1+da2)∆)),∀∆	PROPN
ejpam-6047	407	6	∈	∈	PROPN
ejpam-6047	407	7	b.	b.	NOUN
ejpam-6047	407	8	thus	thus	ADV
ejpam-6047	407	9	λi((in	λi((in	ADP
ejpam-6047	407	10	−	−	PROPN
ejpam-6047	407	11	(	(	PUNCT
ejpam-6047	407	12	iin	iin	NOUN
ejpam-6047	407	13	+	+	CCONJ
ejpam-6047	407	14	(	(	PUNCT
ejpam-6047	407	15	a1	a1	NOUN
ejpam-6047	407	16	+	+	CCONJ
ejpam-6047	407	17	da2	da2	PROPN
ejpam-6047	407	18	)	)	PUNCT
ejpam-6047	408	1	−1(iin	−1(iin	PROPN
ejpam-6047	408	2	−	−	PROPN
ejpam-6047	409	1	(	(	PUNCT
ejpam-6047	409	2	a1	a1	NOUN
ejpam-6047	409	3	+	+	CCONJ
ejpam-6047	409	4	da2))∆	da2))∆	NOUN
ejpam-6047	409	5	)	)	PUNCT
ejpam-6047	409	6	̸=	̸=	PROPN
ejpam-6047	409	7	0,∀∆	0,∀∆	NOUN
ejpam-6047	409	8	∈	∈	PROPN
ejpam-6047	409	9	b,∀i	b,∀i	NOUN
ejpam-6047	410	1	=	=	NOUN
ejpam-6047	410	2	1	1	NUM
ejpam-6047	410	3	:	:	SYM
ejpam-6047	410	4	n	n	PRON
ejpam-6047	410	5	which	which	PRON
ejpam-6047	410	6	yield	yield	VERB
ejpam-6047	410	7	that	that	DET
ejpam-6047	410	8	0	0	NUM
ejpam-6047	410	9	≤	≤	NUM
ejpam-6047	410	10	µb(m	µb(m	ADV
ejpam-6047	410	11	)	)	PUNCT
ejpam-6047	410	12	<	<	X
ejpam-6047	411	1	1	1	X
ejpam-6047	411	2	.	.	PUNCT
ejpam-6047	411	3	conversely	conversely	ADV
ejpam-6047	411	4	,	,	PUNCT
ejpam-6047	411	5	we	we	PRON
ejpam-6047	411	6	assume	assume	VERB
ejpam-6047	411	7	that	that	SCONJ
ejpam-6047	411	8	0	0	NUM
ejpam-6047	411	9	≤	≤	NOUN
ejpam-6047	411	10	µb(m	µb(m	ADV
ejpam-6047	411	11	)	)	PUNCT
ejpam-6047	411	12	<	<	X
ejpam-6047	411	13	1	1	NUM
ejpam-6047	411	14	and	and	CCONJ
ejpam-6047	411	15	we	we	PRON
ejpam-6047	411	16	show	show	VERB
ejpam-6047	411	17	that	that	SCONJ
ejpam-6047	411	18	(	(	PUNCT
ejpam-6047	411	19	a1	a1	NOUN
ejpam-6047	411	20	+	+	CCONJ
ejpam-6047	411	21	da2	da2	PROPN
ejpam-6047	411	22	)	)	PUNCT
ejpam-6047	411	23	is	be	AUX
ejpam-6047	411	24	d	d	ADJ
ejpam-6047	411	25	-	-	ADJ
ejpam-6047	411	26	stable	stable	ADJ
ejpam-6047	411	27	matrix	matrix	NOUN
ejpam-6047	411	28	.	.	PUNCT
ejpam-6047	412	1	for	for	ADP
ejpam-6047	412	2	0	0	NUM
ejpam-6047	412	3	≤	≤	NOUN
ejpam-6047	412	4	µb(m	µb(m	ADV
ejpam-6047	412	5	)	)	PUNCT
ejpam-6047	412	6	<	<	X
ejpam-6047	412	7	1	1	NUM
ejpam-6047	412	8	,	,	PUNCT
ejpam-6047	412	9	a	a	DET
ejpam-6047	412	10	sufficient	sufficient	ADJ
ejpam-6047	412	11	condition	condition	NOUN
ejpam-6047	412	12	is	be	AUX
ejpam-6047	412	13	that	that	PRON
ejpam-6047	412	14	λi((a1	λi((a1	PUNCT
ejpam-6047	412	15	+	+	CCONJ
ejpam-6047	412	16	da2	da2	PROPN
ejpam-6047	412	17	)	)	PUNCT
ejpam-6047	413	1	+	+	CCONJ
ejpam-6047	414	1	i	i	PROPN
ejpam-6047	414	2	d	d	PROPN
ejpam-6047	414	3	)	)	PUNCT
ejpam-6047	414	4	̸=	̸=	NOUN
ejpam-6047	414	5	0,∀	0,∀	NUM
ejpam-6047	415	1	i	i	NOUN
ejpam-6047	415	2	=	=	NOUN
ejpam-6047	415	3	1	1	NUM
ejpam-6047	415	4	:	:	PUNCT
ejpam-6047	415	5	n	n	CCONJ
ejpam-6047	415	6	,	,	PUNCT
ejpam-6047	415	7	and	and	CCONJ
ejpam-6047	415	8	for	for	ADP
ejpam-6047	415	9	some	some	DET
ejpam-6047	415	10	d	d	NOUN
ejpam-6047	415	11	=	=	SYM
ejpam-6047	415	12	diag(dii	diag(dii	PROPN
ejpam-6047	415	13	)	)	PUNCT
ejpam-6047	415	14	,	,	PUNCT
ejpam-6047	415	15	a	a	DET
ejpam-6047	415	16	positive	positive	ADJ
ejpam-6047	415	17	diagonal	diagonal	ADJ
ejpam-6047	415	18	matrix	matrix	NOUN
ejpam-6047	415	19	and	and	CCONJ
ejpam-6047	415	20	this	this	PRON
ejpam-6047	415	21	shows	show	VERB
ejpam-6047	415	22	that	that	SCONJ
ejpam-6047	415	23	(	(	PUNCT
ejpam-6047	415	24	a1	a1	NOUN
ejpam-6047	415	25	+	+	CCONJ
ejpam-6047	415	26	da2	da2	PROPN
ejpam-6047	415	27	)	)	PUNCT
ejpam-6047	415	28	is	be	AUX
ejpam-6047	415	29	a	a	DET
ejpam-6047	415	30	d	d	ADJ
ejpam-6047	415	31	-	-	ADJ
ejpam-6047	415	32	stable	stable	ADJ
ejpam-6047	415	33	matrix	matrix	NOUN
ejpam-6047	415	34	.	.	PUNCT
ejpam-6047	416	1	4.3	4.3	NUM
ejpam-6047	416	2	.	.	PUNCT
ejpam-6047	417	1	the	the	DET
ejpam-6047	417	2	strong	strong	ADJ
ejpam-6047	417	3	d	d	NOUN
ejpam-6047	417	4	-	-	NOUN
ejpam-6047	417	5	stability	stability	NOUN
ejpam-6047	417	6	of	of	ADP
ejpam-6047	417	7	positive	positive	ADJ
ejpam-6047	417	8	linear	linear	ADJ
ejpam-6047	417	9	time	time	NOUN
ejpam-6047	417	10	-	-	PUNCT
ejpam-6047	417	11	invariant	invariant	ADJ
ejpam-6047	417	12	systems	system	NOUN
ejpam-6047	417	13	:	:	PUNCT
ejpam-6047	417	14	we	we	PRON
ejpam-6047	417	15	present	present	VERB
ejpam-6047	417	16	some	some	DET
ejpam-6047	417	17	recent	recent	ADJ
ejpam-6047	417	18	findings	finding	NOUN
ejpam-6047	417	19	on	on	ADP
ejpam-6047	417	20	strong	strong	ADJ
ejpam-6047	417	21	d	d	NOUN
ejpam-6047	417	22	-	-	NOUN
ejpam-6047	417	23	stability	stability	NOUN
ejpam-6047	417	24	analysis	analysis	NOUN
ejpam-6047	417	25	of	of	ADP
ejpam-6047	417	26	positive	positive	ADJ
ejpam-6047	417	27	linear	linear	NOUN
ejpam-6047	417	28	timeinvariant	timeinvariant	NOUN
ejpam-6047	417	29	systems	system	NOUN
ejpam-6047	417	30	having	have	VERB
ejpam-6047	417	31	the	the	DET
ejpam-6047	417	32	presence	presence	NOUN
ejpam-6047	417	33	of	of	ADP
ejpam-6047	417	34	metzler	metzler	NOUN
ejpam-6047	417	35	,	,	PUNCT
ejpam-6047	417	36	and	and	CCONJ
ejpam-6047	417	37	hurwitz	hurwitz	PROPN
ejpam-6047	417	38	matrices	matrix	NOUN
ejpam-6047	417	39	.	.	PUNCT
ejpam-6047	418	1	the	the	DET
ejpam-6047	418	2	characterization	characterization	NOUN
ejpam-6047	418	3	of	of	ADP
ejpam-6047	418	4	strong	strong	ADJ
ejpam-6047	418	5	d	d	NOUN
ejpam-6047	418	6	-	-	NOUN
ejpam-6047	418	7	stability	stability	NOUN
ejpam-6047	418	8	[	[	X
ejpam-6047	418	9	57	57	NUM
ejpam-6047	418	10	]	]	PUNCT
ejpam-6047	418	11	for	for	ADP
ejpam-6047	418	12	a	a	DET
ejpam-6047	418	13	given	give	VERB
ejpam-6047	418	14	real	real	ADV
ejpam-6047	418	15	-	-	PUNCT
ejpam-6047	418	16	valued	value	VERB
ejpam-6047	418	17	n	n	CCONJ
ejpam-6047	418	18	-	-	PUNCT
ejpam-6047	418	19	dimensional	dimensional	ADJ
ejpam-6047	418	20	matrix	matrix	NOUN
ejpam-6047	418	21	a	a	PRON
ejpam-6047	418	22	in	in	ADP
ejpam-6047	418	23	terms	term	NOUN
ejpam-6047	418	24	of	of	ADP
ejpam-6047	418	25	the	the	DET
ejpam-6047	418	26	real	real	ADV
ejpam-6047	418	27	structured	structured	ADJ
ejpam-6047	418	28	singular	singular	ADJ
ejpam-6047	418	29	values	value	NOUN
ejpam-6047	418	30	is	be	AUX
ejpam-6047	418	31	given	give	VERB
ejpam-6047	418	32	by	by	ADP
ejpam-6047	418	33	the	the	DET
ejpam-6047	418	34	following	follow	VERB
ejpam-6047	418	35	theorem	theorem	ADJ
ejpam-6047	418	36	14	14	NUM
ejpam-6047	418	37	.	.	PUNCT
ejpam-6047	419	1	theorem	theorem	NOUN
ejpam-6047	419	2	14	14	NUM
ejpam-6047	419	3	.	.	PUNCT
ejpam-6047	420	1	let	let	VERB
ejpam-6047	420	2	a	a	DET
ejpam-6047	420	3	∈	∈	PROPN
ejpam-6047	420	4	rn	rn	PROPN
ejpam-6047	420	5	,	,	PUNCT
ejpam-6047	420	6	n	n	CCONJ
ejpam-6047	420	7	be	be	VERB
ejpam-6047	420	8	the	the	DET
ejpam-6047	420	9	given	give	VERB
ejpam-6047	420	10	matrix	matrix	NOUN
ejpam-6047	420	11	.	.	PUNCT
ejpam-6047	421	1	then	then	ADV
ejpam-6047	421	2	a	a	PRON
ejpam-6047	421	3	is	be	AUX
ejpam-6047	421	4	a	a	DET
ejpam-6047	421	5	strongly	strongly	ADV
ejpam-6047	421	6	d	d	ADJ
ejpam-6047	421	7	-	-	ADJ
ejpam-6047	421	8	stable	stable	ADJ
ejpam-6047	421	9	matrix	matrix	NOUN
ejpam-6047	421	10	if	if	SCONJ
ejpam-6047	421	11	and	and	CCONJ
ejpam-6047	421	12	only	only	ADV
ejpam-6047	421	13	if	if	SCONJ
ejpam-6047	421	14	it	it	PRON
ejpam-6047	421	15	is	be	AUX
ejpam-6047	421	16	stable	stable	ADJ
ejpam-6047	421	17	and	and	CCONJ
ejpam-6047	421	18	0	0	NUM
ejpam-6047	421	19	≤	≤	NUM
ejpam-6047	421	20	µb	µb	VERB
ejpam-6047	421	21	(	(	PUNCT
ejpam-6047	421	22	(	(	PUNCT
ejpam-6047	421	23	ii	ii	X
ejpam-6047	421	24	+	+	CCONJ
ejpam-6047	421	25	a)−1(ii	a)−1(ii	PROPN
ejpam-6047	421	26	−a	−a	NOUN
ejpam-6047	421	27	)	)	PUNCT
ejpam-6047	421	28	)	)	PUNCT
ejpam-6047	422	1	<	<	X
ejpam-6047	422	2	1	1	X
ejpam-6047	422	3	.	.	PUNCT
ejpam-6047	422	4	theorem	theorem	NOUN
ejpam-6047	422	5	15	15	NUM
ejpam-6047	422	6	gives	give	VERB
ejpam-6047	422	7	the	the	DET
ejpam-6047	422	8	conditions	condition	NOUN
ejpam-6047	422	9	under	under	ADP
ejpam-6047	422	10	which	which	PRON
ejpam-6047	422	11	linear	linear	ADJ
ejpam-6047	422	12	time	time	NOUN
ejpam-6047	422	13	-	-	PUNCT
ejpam-6047	422	14	invariant	invariant	ADJ
ejpam-6047	422	15	system	system	NOUN
ejpam-6047	422	16	with	with	ADP
ejpam-6047	422	17	ndimensional	ndimensional	ADJ
ejpam-6047	422	18	real	real	ADV
ejpam-6047	422	19	-	-	PUNCT
ejpam-6047	422	20	valued	value	VERB
ejpam-6047	422	21	metzler	metzler	NOUN
ejpam-6047	422	22	,	,	PUNCT
ejpam-6047	422	23	and	and	CCONJ
ejpam-6047	422	24	hurwitz	hurwitz	PROPN
ejpam-6047	422	25	matrices	matrix	NOUN
ejpam-6047	422	26	,	,	PUNCT
ejpam-6047	422	27	is	be	AUX
ejpam-6047	422	28	strongly	strongly	ADV
ejpam-6047	422	29	d	d	ADJ
ejpam-6047	422	30	-	-	ADJ
ejpam-6047	422	31	stable	stable	ADJ
ejpam-6047	422	32	.	.	PUNCT
ejpam-6047	423	1	theorem	theorem	NOUN
ejpam-6047	423	2	15	15	NUM
ejpam-6047	423	3	.	.	PUNCT
ejpam-6047	424	1	let	let	VERB
ejpam-6047	424	2	m	m	PROPN
ejpam-6047	424	3	∈	∈	PROPN
ejpam-6047	424	4	rn	rn	PROPN
ejpam-6047	424	5	,	,	PUNCT
ejpam-6047	424	6	n	n	PROPN
ejpam-6047	424	7	and	and	CCONJ
ejpam-6047	424	8	let	let	VERB
ejpam-6047	424	9	a1	a1	NOUN
ejpam-6047	424	10	,	,	PUNCT
ejpam-6047	424	11	a2	a2	PROPN
ejpam-6047	424	12	,	,	PUNCT
ejpam-6047	424	13	...	...	PUNCT
ejpam-6047	424	14	,	,	PUNCT
ejpam-6047	424	15	ar	ar	PROPN
ejpam-6047	424	16	∈	∈	PROPN
ejpam-6047	424	17	rn	rn	PROPN
ejpam-6047	424	18	,	,	PUNCT
ejpam-6047	424	19	n.	n.	VERB
ejpam-6047	424	20	the	the	DET
ejpam-6047	424	21	linear	linear	ADJ
ejpam-6047	424	22	system	system	NOUN
ejpam-6047	424	23	dx(t	dx(t	NOUN
ejpam-6047	424	24	)	)	PUNCT
ejpam-6047	424	25	dt	dt	NOUN
ejpam-6047	425	1	=	=	SYM
ejpam-6047	425	2	ma(t)x(t	ma(t)x(t	PROPN
ejpam-6047	425	3	)	)	PUNCT
ejpam-6047	425	4	;	;	PUNCT
ejpam-6047	425	5	a(t	a(t	X
ejpam-6047	425	6	)	)	PUNCT
ejpam-6047	425	7	∈	∈	PROPN
ejpam-6047	425	8	{	{	PUNCT
ejpam-6047	425	9	a1	a1	PROPN
ejpam-6047	425	10	,	,	PUNCT
ejpam-6047	425	11	a2	a2	PROPN
ejpam-6047	425	12	,	,	PUNCT
ejpam-6047	425	13	...	...	PUNCT
ejpam-6047	425	14	,	,	PUNCT
ejpam-6047	425	15	ar	ar	PROPN
ejpam-6047	425	16	}	}	PUNCT
ejpam-6047	425	17	;	;	PUNCT
ejpam-6047	425	18	x(t	x(t	PROPN
ejpam-6047	425	19	)	)	PUNCT
ejpam-6047	425	20	∈	∈	PROPN
ejpam-6047	425	21	rn,1	rn,1	NOUN
ejpam-6047	425	22	is	be	AUX
ejpam-6047	425	23	strongly	strongly	ADV
ejpam-6047	425	24	d	d	ADJ
ejpam-6047	425	25	-	-	ADJ
ejpam-6047	425	26	stable	stable	ADJ
ejpam-6047	425	27	if	if	SCONJ
ejpam-6047	425	28	there	there	PRON
ejpam-6047	425	29	exist	exist	VERB
ejpam-6047	425	30	γi	γi	ADP
ejpam-6047	425	31	>	>	PROPN
ejpam-6047	425	32	0	0	PROPN
ejpam-6047	425	33	,	,	PUNCT
ejpam-6047	425	34	the	the	DET
ejpam-6047	425	35	matrix	matrix	NOUN
ejpam-6047	425	36	log(m)+	log(m)+	NOUN
ejpam-6047	425	37	(	(	PUNCT
ejpam-6047	425	38	(	(	PUNCT
ejpam-6047	425	39	log(m	log(m	PROPN
ejpam-6047	425	40	)	)	PUNCT
ejpam-6047	425	41	⊗	⊗	NOUN
ejpam-6047	425	42	(	(	PUNCT
ejpam-6047	425	43	a1	a1	NOUN
ejpam-6047	425	44	+	+	CCONJ
ejpam-6047	425	45	γ2a2	γ2a2	PROPN
ejpam-6047	426	1	+	+	CCONJ
ejpam-6047	426	2	....	....	PUNCT
ejpam-6047	426	3	+	+	NUM
ejpam-6047	426	4	γrar	γrar	NOUN
ejpam-6047	426	5	)	)	PUNCT
ejpam-6047	426	6	t∆	t∆	PROPN
ejpam-6047	426	7	+	+	CCONJ
ejpam-6047	426	8	∆((log(m	∆((log(m	ADJ
ejpam-6047	426	9	)	)	PUNCT
ejpam-6047	426	10	⊗	⊗	PROPN
ejpam-6047	426	11	(	(	PUNCT
ejpam-6047	426	12	a1	a1	NOUN
ejpam-6047	426	13	+	+	CCONJ
ejpam-6047	426	14	γ2a2	γ2a2	PROPN
ejpam-6047	426	15	+	+	NUM
ejpam-6047	426	16	...	...	PUNCT
ejpam-6047	427	1	+	+	NUM
ejpam-6047	427	2	γrar	γrar	NOUN
ejpam-6047	427	3	)	)	PUNCT
ejpam-6047	427	4	)	)	PUNCT
ejpam-6047	427	5	is	be	AUX
ejpam-6047	427	6	a	a	DET
ejpam-6047	427	7	d	d	ADJ
ejpam-6047	427	8	-	-	ADJ
ejpam-6047	427	9	stable	stable	ADJ
ejpam-6047	427	10	matrix	matrix	NOUN
ejpam-6047	427	11	with	with	ADP
ejpam-6047	427	12	∆	∆	PROPN
ejpam-6047	427	13	∈	∈	PROPN
ejpam-6047	427	14	b	b	PROPN
ejpam-6047	427	15	and	and	CCONJ
ejpam-6047	427	16	⊗	⊗	PROPN
ejpam-6047	427	17	denotes	denote	NOUN
ejpam-6047	427	18	entry	entry	NOUN
ejpam-6047	427	19	-	-	PUNCT
ejpam-6047	427	20	wise	wise	ADJ
ejpam-6047	427	21	product	product	NOUN
ejpam-6047	427	22	of	of	ADP
ejpam-6047	427	23	matrices	matrix	NOUN
ejpam-6047	427	24	.	.	PUNCT
ejpam-6047	428	1	m.u	m.u	PROPN
ejpam-6047	428	2	.	.	PROPN
ejpam-6047	428	3	rehman	rehman	PROPN
ejpam-6047	428	4	et	et	PROPN
ejpam-6047	428	5	al	al	PROPN
ejpam-6047	428	6	.	.	PUNCT
ejpam-6047	428	7	/	/	SYM
ejpam-6047	428	8	eur	eur	PROPN
ejpam-6047	428	9	.	.	PUNCT
ejpam-6047	429	1	j.	j.	PROPN
ejpam-6047	429	2	pure	pure	PROPN
ejpam-6047	429	3	appl	appl	PROPN
ejpam-6047	429	4	.	.	PROPN
ejpam-6047	429	5	math	math	PROPN
ejpam-6047	429	6	,	,	PUNCT
ejpam-6047	429	7	18	18	NUM
ejpam-6047	429	8	(	(	PUNCT
ejpam-6047	429	9	3	3	NUM
ejpam-6047	429	10	)	)	PUNCT
ejpam-6047	429	11	(	(	PUNCT
ejpam-6047	429	12	2025	2025	NUM
ejpam-6047	429	13	)	)	PUNCT
ejpam-6047	429	14	,	,	PUNCT
ejpam-6047	429	15	6047	6047	NUM
ejpam-6047	429	16	18	18	NUM
ejpam-6047	429	17	of	of	ADP
ejpam-6047	429	18	33	33	NUM
ejpam-6047	429	19	proof	proof	NOUN
ejpam-6047	429	20	.	.	PUNCT
ejpam-6047	430	1	consider	consider	VERB
ejpam-6047	430	2	that	that	PRON
ejpam-6047	430	3	∆	∆	PROPN
ejpam-6047	430	4	=	=	SYM
ejpam-6047	430	5	∆(t	∆(t	PROPN
ejpam-6047	430	6	)	)	PUNCT
ejpam-6047	430	7	∈	∈	PROPN
ejpam-6047	430	8	b	b	NOUN
ejpam-6047	430	9	be	be	AUX
ejpam-6047	430	10	an	an	DET
ejpam-6047	430	11	admissible	admissible	ADJ
ejpam-6047	430	12	perturbation	perturbation	NOUN
ejpam-6047	430	13	and	and	CCONJ
ejpam-6047	430	14	b	b	NOUN
ejpam-6047	430	15	is	be	AUX
ejpam-6047	430	16	the	the	DET
ejpam-6047	430	17	set	set	NOUN
ejpam-6047	430	18	of	of	ADP
ejpam-6047	430	19	block	block	NOUN
ejpam-6047	430	20	diagonal	diagonal	ADJ
ejpam-6047	430	21	matrices	matrix	NOUN
ejpam-6047	430	22	with	with	ADP
ejpam-6047	430	23	real	real	ADJ
ejpam-6047	430	24	or	or	CCONJ
ejpam-6047	430	25	complex	complex	ADJ
ejpam-6047	430	26	uncertainties	uncertainty	NOUN
ejpam-6047	430	27	.	.	PUNCT
ejpam-6047	431	1	let	let	VERB
ejpam-6047	431	2	λ(t	λ(t	PRON
ejpam-6047	431	3	)	)	PUNCT
ejpam-6047	432	1	=	=	PUNCT
ejpam-6047	432	2	|λ(t)|(cos	|λ(t)|(cos	X
ejpam-6047	432	3	θ+i	θ+i	PROPN
ejpam-6047	432	4	sin	sin	PROPN
ejpam-6047	432	5	θ	θ	PROPN
ejpam-6047	432	6	)	)	PUNCT
ejpam-6047	432	7	for	for	ADP
ejpam-6047	432	8	0	0	NUM
ejpam-6047	432	9	<	<	X
ejpam-6047	432	10	θ	θ	PROPN
ejpam-6047	432	11	≤	≤	NOUN
ejpam-6047	432	12	2π	2π	PROPN
ejpam-6047	432	13	be	be	VERB
ejpam-6047	432	14	the	the	DET
ejpam-6047	432	15	largest	large	ADJ
ejpam-6047	432	16	eigenvalue	eigenvalue	NOUN
ejpam-6047	432	17	.	.	PUNCT
ejpam-6047	433	1	assume	assume	VERB
ejpam-6047	433	2	that	that	SCONJ
ejpam-6047	433	3	x̃(t	x̃(t	PROPN
ejpam-6047	433	4	)	)	PUNCT
ejpam-6047	433	5	,	,	PUNCT
ejpam-6047	433	6	ỹ(t	ỹ(t	PROPN
ejpam-6047	433	7	)	)	PUNCT
ejpam-6047	433	8	be	be	VERB
ejpam-6047	433	9	the	the	DET
ejpam-6047	433	10	right	right	NOUN
ejpam-6047	433	11	and	and	CCONJ
ejpam-6047	433	12	left	leave	VERB
ejpam-6047	433	13	eigenvectors	eigenvector	NOUN
ejpam-6047	433	14	and	and	CCONJ
ejpam-6047	433	15	let	let	VERB
ejpam-6047	433	16	z	z	NOUN
ejpam-6047	433	17	=	=	PUNCT
ejpam-6047	433	18	(	(	PUNCT
ejpam-6047	433	19	(	(	PUNCT
ejpam-6047	433	20	log(m	log(m	PROPN
ejpam-6047	433	21	)	)	PUNCT
ejpam-6047	433	22	⊗	⊗	NOUN
ejpam-6047	433	23	(	(	PUNCT
ejpam-6047	433	24	a1	a1	NOUN
ejpam-6047	433	25	+	+	CCONJ
ejpam-6047	433	26	γ2a2	γ2a2	NOUN
ejpam-6047	433	27	+	+	CCONJ
ejpam-6047	433	28	·	·	PUNCT
ejpam-6047	433	29	·	·	PUNCT
ejpam-6047	433	30	·	·	PUNCT
ejpam-6047	434	1	+	+	NUM
ejpam-6047	434	2	γrar	γrar	NOUN
ejpam-6047	434	3	)	)	PUNCT
ejpam-6047	434	4	)	)	PUNCT
ejpam-6047	435	1	t	t	PROPN
ejpam-6047	435	2	∆	∆	X
ejpam-6047	435	3	+	+	CCONJ
ejpam-6047	435	4	∆	∆	PROPN
ejpam-6047	435	5	(	(	PUNCT
ejpam-6047	435	6	log(m	log(m	PROPN
ejpam-6047	435	7	)	)	PUNCT
ejpam-6047	435	8	⊗	⊗	NOUN
ejpam-6047	435	9	(	(	PUNCT
ejpam-6047	435	10	a1	a1	NOUN
ejpam-6047	435	11	+	+	CCONJ
ejpam-6047	435	12	γ2a2	γ2a2	NOUN
ejpam-6047	435	13	+	+	CCONJ
ejpam-6047	435	14	·	·	PUNCT
ejpam-6047	435	15	·	·	PUNCT
ejpam-6047	435	16	·	·	PUNCT
ejpam-6047	436	1	+	+	NUM
ejpam-6047	436	2	γrar	γrar	NOUN
ejpam-6047	436	3	)	)	PUNCT
ejpam-6047	436	4	)	)	PUNCT
ejpam-6047	436	5	)	)	PUNCT
ejpam-6047	437	1	y(t	y(t	NUM
ejpam-6047	437	2	)	)	PUNCT
ejpam-6047	437	3	.	.	PUNCT
ejpam-6047	438	1	we	we	PRON
ejpam-6047	438	2	make	make	VERB
ejpam-6047	438	3	use	use	NOUN
ejpam-6047	438	4	of	of	ADP
ejpam-6047	438	5	an	an	DET
ejpam-6047	438	6	eigenvalue	eigenvalue	ADJ
ejpam-6047	438	7	perturbation	perturbation	NOUN
ejpam-6047	438	8	result	result	NOUN
ejpam-6047	438	9	by	by	ADP
ejpam-6047	438	10	[	[	X
ejpam-6047	438	11	32	32	NUM
ejpam-6047	438	12	]	]	PUNCT
ejpam-6047	438	13	on	on	ADP
ejpam-6047	438	14	the	the	DET
ejpam-6047	438	15	largest	large	ADJ
ejpam-6047	438	16	and	and	CCONJ
ejpam-6047	438	17	simple	simple	ADJ
ejpam-6047	438	18	eigenvalue	eigenvalue	PROPN
ejpam-6047	438	19	λ(t	λ(t	NOUN
ejpam-6047	438	20	)	)	PUNCT
ejpam-6047	438	21	to	to	PART
ejpam-6047	438	22	have	have	VERB
ejpam-6047	438	23	that	that	PRON
ejpam-6047	438	24	d	d	NOUN
ejpam-6047	438	25	dt	dt	PUNCT
ejpam-6047	439	1	|λ(t)|	|λ(t)|	VERB
ejpam-6047	439	2	∣∣∣∣2	∣∣∣∣2	NOUN
ejpam-6047	439	3	t=0	t=0	PRON
ejpam-6047	439	4	=	=	SYM
ejpam-6047	439	5	2ϵ	2ϵ	PROPN
ejpam-6047	439	6	|λ(t)|	|λ(t)|	VERB
ejpam-6047	439	7	α	α	NUM
ejpam-6047	439	8	re(zt∆(t)x	re(zt∆(t)x	NOUN
ejpam-6047	439	9	)	)	PUNCT
ejpam-6047	439	10	,	,	PUNCT
ejpam-6047	439	11	with	with	ADP
ejpam-6047	439	12	α	α	NOUN
ejpam-6047	439	13	=	=	SYM
ejpam-6047	439	14	(	(	PUNCT
ejpam-6047	439	15	cos	cos	PROPN
ejpam-6047	439	16	θ	θ	PROPN
ejpam-6047	440	1	+	+	CCONJ
ejpam-6047	440	2	i	i	PRON
ejpam-6047	440	3	sin	sin	VERB
ejpam-6047	440	4	θ)ytx	θ)ytx	PROPN
ejpam-6047	440	5	>	>	X
ejpam-6047	440	6	0	0	NUM
ejpam-6047	440	7	,	,	PUNCT
ejpam-6047	440	8	ϵ	ϵ	X
ejpam-6047	440	9	>	>	X
ejpam-6047	440	10	0	0	X
ejpam-6047	440	11	.	.	PUNCT
ejpam-6047	441	1	in	in	ADP
ejpam-6047	441	2	turn	turn	NOUN
ejpam-6047	441	3	,	,	PUNCT
ejpam-6047	441	4	this	this	PRON
ejpam-6047	441	5	implies	imply	VERB
ejpam-6047	441	6	that	that	SCONJ
ejpam-6047	441	7	(	(	PUNCT
ejpam-6047	441	8	log(m	log(m	PROPN
ejpam-6047	441	9	)	)	PUNCT
ejpam-6047	441	10	⊗	⊗	NOUN
ejpam-6047	441	11	(	(	PUNCT
ejpam-6047	441	12	a1	a1	NOUN
ejpam-6047	441	13	+	+	CCONJ
ejpam-6047	441	14	γ2a2	γ2a2	NOUN
ejpam-6047	441	15	+	+	CCONJ
ejpam-6047	441	16	·	·	PUNCT
ejpam-6047	441	17	·	·	PUNCT
ejpam-6047	441	18	·	·	PUNCT
ejpam-6047	442	1	+	+	NUM
ejpam-6047	442	2	γrar	γrar	NOUN
ejpam-6047	442	3	)	)	PUNCT
ejpam-6047	442	4	)	)	PUNCT
ejpam-6047	443	1	t	t	PROPN
ejpam-6047	443	2	∆	∆	X
ejpam-6047	443	3	+	+	CCONJ
ejpam-6047	443	4	∆	∆	PROPN
ejpam-6047	443	5	(	(	PUNCT
ejpam-6047	443	6	log(m	log(m	PROPN
ejpam-6047	443	7	)	)	PUNCT
ejpam-6047	443	8	⊗	⊗	NOUN
ejpam-6047	443	9	(	(	PUNCT
ejpam-6047	443	10	a1	a1	NOUN
ejpam-6047	443	11	+	+	CCONJ
ejpam-6047	443	12	γ2a2	γ2a2	NOUN
ejpam-6047	443	13	+	+	CCONJ
ejpam-6047	443	14	·	·	PUNCT
ejpam-6047	443	15	·	·	PUNCT
ejpam-6047	443	16	·	·	PUNCT
ejpam-6047	444	1	+	+	NUM
ejpam-6047	444	2	γrar	γrar	NOUN
ejpam-6047	444	3	)	)	PUNCT
ejpam-6047	444	4	)	)	PUNCT
ejpam-6047	445	1	>	>	X
ejpam-6047	445	2	0	0	NUM
ejpam-6047	445	3	,	,	PUNCT
ejpam-6047	445	4	which	which	PRON
ejpam-6047	445	5	further	further	ADJ
ejpam-6047	445	6	yields	yield	NOUN
ejpam-6047	445	7	that	that	PRON
ejpam-6047	445	8	log(m)+	log(m)+	PROPN
ejpam-6047	445	9	(	(	PUNCT
ejpam-6047	445	10	(	(	PUNCT
ejpam-6047	445	11	log(m	log(m	PROPN
ejpam-6047	445	12	)	)	PUNCT
ejpam-6047	445	13	⊗	⊗	NOUN
ejpam-6047	445	14	(	(	PUNCT
ejpam-6047	445	15	a1	a1	NOUN
ejpam-6047	445	16	+	+	CCONJ
ejpam-6047	445	17	γ2a2	γ2a2	NOUN
ejpam-6047	445	18	+	+	CCONJ
ejpam-6047	445	19	·	·	PUNCT
ejpam-6047	445	20	·	·	PUNCT
ejpam-6047	445	21	·	·	PUNCT
ejpam-6047	446	1	+	+	NUM
ejpam-6047	446	2	γrar	γrar	NOUN
ejpam-6047	446	3	)	)	PUNCT
ejpam-6047	446	4	)	)	PUNCT
ejpam-6047	447	1	t	t	PROPN
ejpam-6047	447	2	∆	∆	X
ejpam-6047	447	3	+	+	CCONJ
ejpam-6047	447	4	∆	∆	PROPN
ejpam-6047	447	5	(	(	PUNCT
ejpam-6047	447	6	log(m	log(m	PROPN
ejpam-6047	447	7	)	)	PUNCT
ejpam-6047	447	8	⊗	⊗	NOUN
ejpam-6047	447	9	(	(	PUNCT
ejpam-6047	447	10	a1	a1	NOUN
ejpam-6047	447	11	+	+	CCONJ
ejpam-6047	447	12	γ2a2	γ2a2	NOUN
ejpam-6047	447	13	+	+	CCONJ
ejpam-6047	447	14	·	·	PUNCT
ejpam-6047	447	15	·	·	PUNCT
ejpam-6047	447	16	·	·	PUNCT
ejpam-6047	448	1	+	+	NUM
ejpam-6047	448	2	γrar	γrar	NOUN
ejpam-6047	448	3	)	)	PUNCT
ejpam-6047	448	4	)	)	PUNCT
ejpam-6047	448	5	)	)	PUNCT
ejpam-6047	448	6	is	be	AUX
ejpam-6047	448	7	d	d	ADJ
ejpam-6047	448	8	-	-	ADJ
ejpam-6047	448	9	stable	stable	ADJ
ejpam-6047	448	10	.	.	PUNCT
ejpam-6047	449	1	theorem	theorem	VERB
ejpam-6047	449	2	16	16	NUM
ejpam-6047	449	3	.	.	PUNCT
ejpam-6047	450	1	let	let	VERB
ejpam-6047	450	2	m	m	PROPN
ejpam-6047	450	3	∈	∈	PROPN
ejpam-6047	450	4	rn	rn	PROPN
ejpam-6047	450	5	,	,	PUNCT
ejpam-6047	450	6	n	n	CCONJ
ejpam-6047	450	7	,	,	PUNCT
ejpam-6047	450	8	and	and	CCONJ
ejpam-6047	450	9	let	let	VERB
ejpam-6047	450	10	m	m	VERB
ejpam-6047	450	11	=	=	NOUN
ejpam-6047	450	12	e{a1+γ2a2+	e{a1+γ2a2+	NOUN
ejpam-6047	450	13	...	...	PUNCT
ejpam-6047	450	14	+γrar	+γrar	NOUN
ejpam-6047	450	15	}	}	PUNCT
ejpam-6047	450	16	where	where	SCONJ
ejpam-6047	450	17	a1	a1	NOUN
ejpam-6047	450	18	,	,	PUNCT
ejpam-6047	450	19	a2	a2	PROPN
ejpam-6047	450	20	,	,	PUNCT
ejpam-6047	450	21	...	...	PUNCT
ejpam-6047	450	22	,	,	PUNCT
ejpam-6047	450	23	ar	ar	PROPN
ejpam-6047	450	24	are	be	AUX
ejpam-6047	450	25	n	n	CCONJ
ejpam-6047	450	26	-	-	PUNCT
ejpam-6047	450	27	dimensional	dimensional	ADJ
ejpam-6047	450	28	hermition	hermition	NOUN
ejpam-6047	450	29	matrices	matrix	NOUN
ejpam-6047	450	30	,	,	PUNCT
ejpam-6047	450	31	then	then	ADV
ejpam-6047	450	32	m	m	NOUN
ejpam-6047	450	33	is	be	AUX
ejpam-6047	450	34	strongly	strongly	ADV
ejpam-6047	450	35	d	d	ADJ
ejpam-6047	450	36	-	-	ADJ
ejpam-6047	450	37	stable	stable	ADJ
ejpam-6047	450	38	matrix	matrix	NOUN
ejpam-6047	450	39	if	if	SCONJ
ejpam-6047	450	40	m	m	NOUN
ejpam-6047	450	41	is	be	AUX
ejpam-6047	450	42	stable	stable	ADJ
ejpam-6047	450	43	and	and	CCONJ
ejpam-6047	450	44	for	for	ADP
ejpam-6047	450	45	some	some	DET
ejpam-6047	450	46	α	α	NOUN
ejpam-6047	450	47	>	>	X
ejpam-6047	450	48	0	0	PUNCT
ejpam-6047	451	1	the	the	DET
ejpam-6047	451	2	matrix	matrix	NOUN
ejpam-6047	451	3	(	(	PUNCT
ejpam-6047	451	4	m	m	VERB
ejpam-6047	451	5	+	+	ADP
ejpam-6047	451	6	g	g	NOUN
ejpam-6047	451	7	)	)	PUNCT
ejpam-6047	451	8	is	be	AUX
ejpam-6047	451	9	d	d	ADJ
ejpam-6047	451	10	-	-	NOUN
ejpam-6047	451	11	stable	stable	ADJ
ejpam-6047	451	12	where	where	SCONJ
ejpam-6047	451	13	g	g	NOUN
ejpam-6047	451	14	=	=	SYM
ejpam-6047	451	15	(	(	PUNCT
ejpam-6047	451	16	m	m	VERB
ejpam-6047	451	17	⊗	⊗	NOUN
ejpam-6047	451	18	(	(	PUNCT
ejpam-6047	451	19	a1	a1	NOUN
ejpam-6047	451	20	+	+	CCONJ
ejpam-6047	451	21	γ2a2	γ2a2	PROPN
ejpam-6047	451	22	+	+	NUM
ejpam-6047	451	23	...	...	PUNCT
ejpam-6047	452	1	+	+	NUM
ejpam-6047	452	2	γrar	γrar	NOUN
ejpam-6047	452	3	)	)	PUNCT
ejpam-6047	452	4	t	t	NOUN
ejpam-6047	452	5	)	)	PUNCT
ejpam-6047	452	6	∆	∆	PROPN
ejpam-6047	453	1	+	+	CCONJ
ejpam-6047	454	1	∆(m	∆(m	VERB
ejpam-6047	454	2	⊗	⊗	NOUN
ejpam-6047	454	3	(	(	PUNCT
ejpam-6047	454	4	a1	a1	NOUN
ejpam-6047	454	5	+	+	CCONJ
ejpam-6047	454	6	γ2a2	γ2a2	PROPN
ejpam-6047	454	7	+	+	NUM
ejpam-6047	454	8	...	...	PUNCT
ejpam-6047	454	9	+	+	NUM
ejpam-6047	454	10	γrar	γrar	NOUN
ejpam-6047	454	11	)	)	PUNCT
ejpam-6047	454	12	)	)	PUNCT
ejpam-6047	455	1	,	,	PUNCT
ejpam-6047	455	2	∆	∆	PROPN
ejpam-6047	455	3	∈	∈	PROPN
ejpam-6047	455	4	b	b	PROPN
ejpam-6047	455	5	,	,	PUNCT
ejpam-6047	455	6	∥g∥	∥g∥	X
ejpam-6047	455	7	<	<	X
ejpam-6047	455	8	α	α	X
ejpam-6047	455	9	.	.	PUNCT
ejpam-6047	455	10	proof	proof	NOUN
ejpam-6047	455	11	.	.	PUNCT
ejpam-6047	456	1	assume	assume	VERB
ejpam-6047	456	2	that	that	SCONJ
ejpam-6047	456	3	∆	∆	PROPN
ejpam-6047	456	4	=	=	SYM
ejpam-6047	456	5	∆(t	∆(t	PROPN
ejpam-6047	456	6	)	)	PUNCT
ejpam-6047	456	7	∈	∈	PROPN
ejpam-6047	456	8	b	b	NOUN
ejpam-6047	456	9	,	,	PUNCT
ejpam-6047	456	10	where	where	SCONJ
ejpam-6047	456	11	b	b	NOUN
ejpam-6047	456	12	is	be	AUX
ejpam-6047	456	13	set	set	VERB
ejpam-6047	456	14	of	of	ADP
ejpam-6047	456	15	block	block	NOUN
ejpam-6047	456	16	diagonal	diagonal	ADJ
ejpam-6047	456	17	matrices	matrix	NOUN
ejpam-6047	456	18	.	.	PUNCT
ejpam-6047	457	1	let	let	VERB
ejpam-6047	457	2	λ(t	λ(t	PRON
ejpam-6047	457	3	)	)	PUNCT
ejpam-6047	458	1	=	=	PUNCT
ejpam-6047	458	2	|λ(t)|(cos	|λ(t)|(cos	X
ejpam-6047	458	3	θ+i	θ+i	PROPN
ejpam-6047	458	4	sin	sin	PROPN
ejpam-6047	458	5	θ	θ	PROPN
ejpam-6047	458	6	)	)	PUNCT
ejpam-6047	458	7	,	,	PUNCT
ejpam-6047	458	8	0	0	NUM
ejpam-6047	458	9	<	<	X
ejpam-6047	458	10	θ	θ	PROPN
ejpam-6047	458	11	≤	≤	NOUN
ejpam-6047	458	12	2π	2π	PROPN
ejpam-6047	458	13	be	be	VERB
ejpam-6047	458	14	the	the	DET
ejpam-6047	458	15	largest	large	ADJ
ejpam-6047	458	16	eigenvalue	eigenvalue	NOUN
ejpam-6047	458	17	.	.	PUNCT
ejpam-6047	459	1	in	in	ADP
ejpam-6047	459	2	addition	addition	NOUN
ejpam-6047	459	3	,	,	PUNCT
ejpam-6047	459	4	assume	assume	VERB
ejpam-6047	459	5	that	that	SCONJ
ejpam-6047	459	6	x(t	x(t	PROPN
ejpam-6047	459	7	)	)	PUNCT
ejpam-6047	459	8	,	,	PUNCT
ejpam-6047	459	9	y(t	y(t	NUM
ejpam-6047	459	10	)	)	PUNCT
ejpam-6047	459	11	are	be	AUX
ejpam-6047	459	12	leftand	leftand	NOUN
ejpam-6047	459	13	right	right	ADJ
ejpam-6047	459	14	-	-	PUNCT
ejpam-6047	459	15	eigenvectors	eigenvector	NOUN
ejpam-6047	459	16	.	.	PUNCT
ejpam-6047	460	1	consider	consider	VERB
ejpam-6047	460	2	z	z	NOUN
ejpam-6047	460	3	=	=	PUNCT
ejpam-6047	460	4	gt	gt	PROPN
ejpam-6047	460	5	y.	y.	NOUN
ejpam-6047	460	6	the	the	DET
ejpam-6047	460	7	eigenvalues	eigenvalue	VERB
ejpam-6047	460	8	perturbation	perturbation	NOUN
ejpam-6047	460	9	findings	finding	NOUN
ejpam-6047	460	10	by	by	ADP
ejpam-6047	460	11	[	[	X
ejpam-6047	460	12	32	32	NUM
ejpam-6047	460	13	]	]	PUNCT
ejpam-6047	460	14	on	on	ADP
ejpam-6047	460	15	λ(t	λ(t	NOUN
ejpam-6047	460	16	)	)	PUNCT
ejpam-6047	460	17	yield	yield	NOUN
ejpam-6047	460	18	d	d	NOUN
ejpam-6047	460	19	dt	dt	NOUN
ejpam-6047	460	20	|λ(t)|2	|λ(t)|2	NOUN
ejpam-6047	461	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6047	461	2	t=0	t=0	VERB
ejpam-6047	461	3	=	=	SYM
ejpam-6047	461	4	2ϵ	2ϵ	PROPN
ejpam-6047	462	1	|λ(t)|	|λ(t)|	VERB
ejpam-6047	462	2	α	α	NUM
ejpam-6047	462	3	re(zt	re(zt	PROPN
ejpam-6047	462	4	∆̇(t)x	∆̇(t)x	NOUN
ejpam-6047	462	5	)	)	PUNCT
ejpam-6047	462	6	with	with	ADP
ejpam-6047	462	7	α	α	NOUN
ejpam-6047	462	8	=	=	SYM
ejpam-6047	462	9	(	(	PUNCT
ejpam-6047	462	10	cos	cos	PROPN
ejpam-6047	462	11	θ	θ	PROPN
ejpam-6047	463	1	+	+	CCONJ
ejpam-6047	463	2	i	i	PRON
ejpam-6047	463	3	sin	sin	VERB
ejpam-6047	463	4	θ)ytx	θ)ytx	PROPN
ejpam-6047	463	5	;	;	PUNCT
ejpam-6047	463	6	α	α	PRON
ejpam-6047	463	7	≥	≥	NOUN
ejpam-6047	463	8	0	0	NUM
ejpam-6047	463	9	.	.	PUNCT
ejpam-6047	464	1	as	as	SCONJ
ejpam-6047	464	2	we	we	PRON
ejpam-6047	464	3	know	know	VERB
ejpam-6047	464	4	that	that	SCONJ
ejpam-6047	464	5	,	,	PUNCT
ejpam-6047	464	6	re(zt	re(zt	PROPN
ejpam-6047	464	7	∆̇(t)x	∆̇(t)x	NOUN
ejpam-6047	464	8	)	)	PUNCT
ejpam-6047	464	9	>	>	X
ejpam-6047	464	10	0	0	NUM
ejpam-6047	464	11	,	,	PUNCT
ejpam-6047	464	12	and	and	CCONJ
ejpam-6047	464	13	in	in	ADP
ejpam-6047	464	14	turn	turn	NOUN
ejpam-6047	464	15	this	this	PRON
ejpam-6047	464	16	implies	imply	VERB
ejpam-6047	464	17	that	that	SCONJ
ejpam-6047	464	18	(	(	PUNCT
ejpam-6047	464	19	m	m	VERB
ejpam-6047	464	20	⊗	⊗	NOUN
ejpam-6047	464	21	(	(	PUNCT
ejpam-6047	464	22	a1	a1	NOUN
ejpam-6047	464	23	+	+	CCONJ
ejpam-6047	464	24	γ2a2	γ2a2	PROPN
ejpam-6047	465	1	+	+	NUM
ejpam-6047	465	2	...	...	PUNCT
ejpam-6047	466	1	+	+	NUM
ejpam-6047	466	2	γrar	γrar	NOUN
ejpam-6047	466	3	)	)	PUNCT
ejpam-6047	466	4	t	t	NOUN
ejpam-6047	466	5	)	)	PUNCT
ejpam-6047	466	6	∆	∆	PROPN
ejpam-6047	467	1	+	+	CCONJ
ejpam-6047	468	1	∆(m	∆(m	VERB
ejpam-6047	468	2	⊗	⊗	NOUN
ejpam-6047	468	3	(	(	PUNCT
ejpam-6047	468	4	a1	a1	NOUN
ejpam-6047	468	5	+	+	CCONJ
ejpam-6047	468	6	γ2a2	γ2a2	PROPN
ejpam-6047	468	7	+	+	NUM
ejpam-6047	468	8	...	...	PUNCT
ejpam-6047	468	9	+	+	NUM
ejpam-6047	468	10	γrar	γrar	NOUN
ejpam-6047	468	11	)	)	PUNCT
ejpam-6047	468	12	)	)	PUNCT
ejpam-6047	468	13	,	,	PUNCT
ejpam-6047	468	14	∆	∆	PROPN
ejpam-6047	468	15	∈	∈	PROPN
ejpam-6047	468	16	b	b	PROPN
ejpam-6047	468	17	is	be	AUX
ejpam-6047	468	18	pd	pd	NOUN
ejpam-6047	468	19	-	-	NOUN
ejpam-6047	468	20	matrix	matrix	NOUN
ejpam-6047	468	21	.	.	PUNCT
ejpam-6047	469	1	finally	finally	ADV
ejpam-6047	469	2	for	for	ADP
ejpam-6047	469	3	d	d	PROPN
ejpam-6047	469	4	=	=	SYM
ejpam-6047	469	5	diag(dii	diag(dii	PROPN
ejpam-6047	469	6	)	)	PUNCT
ejpam-6047	469	7	;	;	PUNCT
ejpam-6047	469	8	dii	dii	NOUN
ejpam-6047	469	9	>	>	X
ejpam-6047	469	10	0	0	PROPN
ejpam-6047	469	11	,	,	PUNCT
ejpam-6047	469	12	the	the	DET
ejpam-6047	469	13	matrix	matrix	NOUN
ejpam-6047	469	14	d	d	X
ejpam-6047	469	15	(	(	PUNCT
ejpam-6047	469	16	e{a1+γ2a2+···+γrar	e{a1+γ2a2+···+γrar	NOUN
ejpam-6047	469	17	}	}	PUNCT
ejpam-6047	469	18	+	+	CCONJ
ejpam-6047	469	19	g	g	NOUN
ejpam-6047	469	20	)	)	PUNCT
ejpam-6047	469	21	and	and	CCONJ
ejpam-6047	469	22	from	from	ADP
ejpam-6047	469	23	this	this	PRON
ejpam-6047	469	24	it	it	PRON
ejpam-6047	469	25	follows	follow	VERB
ejpam-6047	469	26	that	that	SCONJ
ejpam-6047	469	27	m	m	VERB
ejpam-6047	469	28	+	+	ADP
ejpam-6047	469	29	g	g	NOUN
ejpam-6047	469	30	=	=	NOUN
ejpam-6047	469	31	m	m	VERB
ejpam-6047	469	32	+	+	NOUN
ejpam-6047	469	33	(	(	PUNCT
ejpam-6047	469	34	m	m	VERB
ejpam-6047	469	35	⊗	⊗	NOUN
ejpam-6047	469	36	(	(	PUNCT
ejpam-6047	469	37	a1	a1	NOUN
ejpam-6047	469	38	+	+	CCONJ
ejpam-6047	469	39	γ2a2	γ2a2	PROPN
ejpam-6047	469	40	+	+	NUM
ejpam-6047	469	41	...	...	PUNCT
ejpam-6047	470	1	+	+	NUM
ejpam-6047	470	2	γrar	γrar	NOUN
ejpam-6047	470	3	)	)	PUNCT
ejpam-6047	470	4	t	t	NOUN
ejpam-6047	470	5	)	)	PUNCT
ejpam-6047	470	6	∆	∆	PROPN
ejpam-6047	471	1	+	+	CCONJ
ejpam-6047	472	1	∆(m	∆(m	VERB
ejpam-6047	472	2	⊗	⊗	NOUN
ejpam-6047	472	3	(	(	PUNCT
ejpam-6047	472	4	a1	a1	NOUN
ejpam-6047	472	5	+	+	CCONJ
ejpam-6047	472	6	γ2a2	γ2a2	PROPN
ejpam-6047	472	7	+	+	NUM
ejpam-6047	472	8	...	...	PUNCT
ejpam-6047	472	9	+	+	NUM
ejpam-6047	472	10	γrar	γrar	NOUN
ejpam-6047	472	11	)	)	PUNCT
ejpam-6047	472	12	)	)	PUNCT
ejpam-6047	472	13	is	be	AUX
ejpam-6047	472	14	d	d	ADJ
ejpam-6047	472	15	-	-	ADJ
ejpam-6047	472	16	stable	stable	ADJ
ejpam-6047	472	17	matrix	matrix	NOUN
ejpam-6047	472	18	.	.	PUNCT
ejpam-6047	473	1	m.u	m.u	PROPN
ejpam-6047	473	2	.	.	PROPN
ejpam-6047	473	3	rehman	rehman	PROPN
ejpam-6047	473	4	et	et	PROPN
ejpam-6047	473	5	al	al	PROPN
ejpam-6047	473	6	.	.	PUNCT
ejpam-6047	473	7	/	/	SYM
ejpam-6047	473	8	eur	eur	PROPN
ejpam-6047	473	9	.	.	PUNCT
ejpam-6047	474	1	j.	j.	PROPN
ejpam-6047	474	2	pure	pure	PROPN
ejpam-6047	474	3	appl	appl	PROPN
ejpam-6047	474	4	.	.	PROPN
ejpam-6047	474	5	math	math	PROPN
ejpam-6047	474	6	,	,	PUNCT
ejpam-6047	474	7	18	18	NUM
ejpam-6047	474	8	(	(	PUNCT
ejpam-6047	474	9	3	3	NUM
ejpam-6047	474	10	)	)	PUNCT
ejpam-6047	474	11	(	(	PUNCT
ejpam-6047	474	12	2025	2025	NUM
ejpam-6047	474	13	)	)	PUNCT
ejpam-6047	474	14	,	,	PUNCT
ejpam-6047	474	15	6047	6047	NUM
ejpam-6047	474	16	19	19	NUM
ejpam-6047	474	17	of	of	ADP
ejpam-6047	474	18	33	33	NUM
ejpam-6047	474	19	5	5	NUM
ejpam-6047	474	20	.	.	PUNCT
ejpam-6047	474	21	numerical	numerical	PROPN
ejpam-6047	474	22	testing	testing	PROPN
ejpam-6047	474	23	the	the	DET
ejpam-6047	474	24	numerical	numerical	ADJ
ejpam-6047	474	25	experimentation	experimentation	NOUN
ejpam-6047	474	26	illustrate	illustrate	VERB
ejpam-6047	474	27	the	the	DET
ejpam-6047	474	28	computation	computation	NOUN
ejpam-6047	474	29	,	,	PUNCT
ejpam-6047	474	30	and	and	CCONJ
ejpam-6047	474	31	to	to	PART
ejpam-6047	474	32	visualize	visualize	VERB
ejpam-6047	474	33	the	the	DET
ejpam-6047	474	34	spectrum	spectrum	NOUN
ejpam-6047	474	35	,	,	PUNCT
ejpam-6047	474	36	the	the	DET
ejpam-6047	474	37	singular	singular	ADJ
ejpam-6047	474	38	values	value	NOUN
ejpam-6047	474	39	,	,	PUNCT
ejpam-6047	474	40	the	the	DET
ejpam-6047	474	41	structured	structured	ADJ
ejpam-6047	474	42	singular	singular	ADJ
ejpam-6047	474	43	values	value	NOUN
ejpam-6047	474	44	,	,	PUNCT
ejpam-6047	474	45	and	and	CCONJ
ejpam-6047	474	46	the	the	DET
ejpam-6047	474	47	pseudo	pseudo	NOUN
ejpam-6047	474	48	-	-	NOUN
ejpam-6047	474	49	spectra	spectra	NOUN
ejpam-6047	474	50	for	for	ADP
ejpam-6047	474	51	metzler	metzler	NOUN
ejpam-6047	474	52	matrices	matrix	NOUN
ejpam-6047	474	53	appearing	appear	VERB
ejpam-6047	474	54	across	across	ADP
ejpam-6047	474	55	the	the	DET
ejpam-6047	474	56	positive	positive	ADJ
ejpam-6047	474	57	dynamical	dynamical	ADJ
ejpam-6047	474	58	systems	system	NOUN
ejpam-6047	474	59	.	.	PUNCT
ejpam-6047	475	1	the	the	DET
ejpam-6047	475	2	graphical	graphical	ADJ
ejpam-6047	475	3	representations	representation	NOUN
ejpam-6047	475	4	of	of	ADP
ejpam-6047	475	5	the	the	DET
ejpam-6047	475	6	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-6047	475	7	are	be	AUX
ejpam-6047	475	8	the	the	DET
ejpam-6047	475	9	level	level	NOUN
ejpam-6047	475	10	sets	set	NOUN
ejpam-6047	475	11	which	which	PRON
ejpam-6047	475	12	are	be	AUX
ejpam-6047	475	13	corresponding	correspond	VERB
ejpam-6047	475	14	to	to	ADP
ejpam-6047	475	15	resolvent	resolvent	ADJ
ejpam-6047	475	16	norm	norm	NOUN
ejpam-6047	475	17	||(zin	||(zin	ADP
ejpam-6047	475	18	−a)−1||	−a)−1||	PROPN
ejpam-6047	475	19	.	.	PUNCT
ejpam-6047	475	20	example	example	NOUN
ejpam-6047	476	1	1	1	NUM
ejpam-6047	476	2	.	.	X
ejpam-6047	476	3	consider	consider	VERB
ejpam-6047	476	4	dx(t	dx(t	NOUN
ejpam-6047	476	5	)	)	PUNCT
ejpam-6047	476	6	dt	dt	NOUN
ejpam-6047	476	7	=	=	SYM
ejpam-6047	476	8	ax(t	ax(t	X
ejpam-6047	476	9	)	)	PUNCT
ejpam-6047	476	10	is	be	AUX
ejpam-6047	476	11	a	a	DET
ejpam-6047	476	12	positive	positive	ADJ
ejpam-6047	476	13	dynamical	dynamical	ADJ
ejpam-6047	476	14	system	system	NOUN
ejpam-6047	476	15	with	with	ADP
ejpam-6047	476	16	a	a	DET
ejpam-6047	476	17	metzler	metzler	NOUN
ejpam-6047	476	18	matrix	matrix	NOUN
ejpam-6047	476	19	give	give	VERB
ejpam-6047	476	20	by	by	ADP
ejpam-6047	476	21	a	a	DET
ejpam-6047	476	22	=	=	NOUN
ejpam-6047	476	23			ADJ
ejpam-6047	476	24	−10−9	−10−9	NUM
ejpam-6047	477	1	109	109	NUM
ejpam-6047	477	2	0	0	NUM
ejpam-6047	477	3	0	0	NUM
ejpam-6047	477	4	0	0	NUM
ejpam-6047	477	5	0	0	NUM
ejpam-6047	477	6	−10−9	−10−9	NUM
ejpam-6047	477	7	0	0	NUM
ejpam-6047	477	8	0	0	NUM
ejpam-6047	478	1	109	109	NUM
ejpam-6047	478	2	0	0	NUM
ejpam-6047	478	3	109	109	NUM
ejpam-6047	478	4	−10−9	−10−9	NUM
ejpam-6047	478	5	0	0	NUM
ejpam-6047	478	6	0	0	NUM
ejpam-6047	478	7	109	109	NUM
ejpam-6047	478	8	109	109	NUM
ejpam-6047	478	9	0	0	NUM
ejpam-6047	478	10	−10−9	−10−9	NUM
ejpam-6047	478	11	109	109	NUM
ejpam-6047	478	12	0	0	NUM
ejpam-6047	478	13	0	0	NUM
ejpam-6047	478	14	0	0	NUM
ejpam-6047	478	15	0	0	NUM
ejpam-6047	478	16	−10−9	−10−9	NUM
ejpam-6047	478	17			NOUN
ejpam-6047	478	18	.	.	PUNCT
ejpam-6047	479	1	the	the	DET
ejpam-6047	479	2	spectral	spectral	ADJ
ejpam-6047	479	3	properties	property	NOUN
ejpam-6047	479	4	like	like	ADP
ejpam-6047	479	5	the	the	DET
ejpam-6047	479	6	computation	computation	NOUN
ejpam-6047	479	7	of	of	ADP
ejpam-6047	479	8	spectrum	spectrum	NOUN
ejpam-6047	479	9	,	,	PUNCT
ejpam-6047	479	10	singular	singular	PROPN
ejpam-6047	479	11	,	,	PUNCT
ejpam-6047	479	12	structured	structure	VERB
ejpam-6047	479	13	singular	singular	ADJ
ejpam-6047	479	14	values	value	NOUN
ejpam-6047	479	15	,	,	PUNCT
ejpam-6047	479	16	and	and	CCONJ
ejpam-6047	479	17	pseudo	pseudo	NOUN
ejpam-6047	479	18	-	-	NOUN
ejpam-6047	479	19	spectrum	spectrum	NOUN
ejpam-6047	479	20	of	of	ADP
ejpam-6047	479	21	metzler	metzler	NOUN
ejpam-6047	479	22	matrix	matrix	NOUN
ejpam-6047	479	23	a	a	PRON
ejpam-6047	479	24	are	be	AUX
ejpam-6047	479	25	presented	present	VERB
ejpam-6047	479	26	in	in	ADP
ejpam-6047	479	27	figure	figure	NOUN
ejpam-6047	479	28	1	1	NUM
ejpam-6047	479	29	.	.	PUNCT
ejpam-6047	480	1	in	in	ADP
ejpam-6047	480	2	figure	figure	NOUN
ejpam-6047	480	3	2	2	NUM
ejpam-6047	480	4	,	,	PUNCT
ejpam-6047	480	5	we	we	PRON
ejpam-6047	480	6	plot	plot	VERB
ejpam-6047	480	7	the	the	DET
ejpam-6047	480	8	eigenmode	eigenmode	PROPN
ejpam-6047	480	9	corresponding	corresponding	NOUN
ejpam-6047	480	10	to	to	ADP
ejpam-6047	480	11	the	the	DET
ejpam-6047	480	12	eigenvalues	eigenvalue	NOUN
ejpam-6047	480	13	.	.	PUNCT
ejpam-6047	481	1	the	the	DET
ejpam-6047	481	2	top	top	ADJ
ejpam-6047	481	3	plot	plot	NOUN
ejpam-6047	481	4	in	in	ADP
ejpam-6047	481	5	the	the	DET
ejpam-6047	481	6	figure	figure	NOUN
ejpam-6047	481	7	(	(	PUNCT
ejpam-6047	481	8	left	left	ADJ
ejpam-6047	481	9	)	)	PUNCT
ejpam-6047	481	10	shows	show	VERB
ejpam-6047	481	11	an	an	DET
ejpam-6047	481	12	envelope	envelope	NOUN
ejpam-6047	481	13	which	which	PRON
ejpam-6047	481	14	is	be	AUX
ejpam-6047	481	15	produced	produce	VERB
ejpam-6047	481	16	by	by	ADP
ejpam-6047	481	17	plotting	plot	VERB
ejpam-6047	481	18	the	the	DET
ejpam-6047	481	19	absolute	absolute	ADJ
ejpam-6047	481	20	value	value	NOUN
ejpam-6047	481	21	of	of	ADP
ejpam-6047	481	22	an	an	DET
ejpam-6047	481	23	eigenmode	eigenmode	NOUN
ejpam-6047	481	24	and	and	CCONJ
ejpam-6047	481	25	minus	minus	ADP
ejpam-6047	481	26	the	the	DET
ejpam-6047	481	27	absolute	absolute	ADJ
ejpam-6047	481	28	value	value	NOUN
ejpam-6047	481	29	.	.	PUNCT
ejpam-6047	482	1	the	the	DET
ejpam-6047	482	2	real	real	ADJ
ejpam-6047	482	3	part	part	NOUN
ejpam-6047	482	4	is	be	AUX
ejpam-6047	482	5	shown	show	VERB
ejpam-6047	482	6	with	with	ADP
ejpam-6047	482	7	a	a	DET
ejpam-6047	482	8	cyan	cyan	ADJ
ejpam-6047	482	9	line	line	NOUN
ejpam-6047	482	10	.	.	PUNCT
ejpam-6047	483	1	the	the	DET
ejpam-6047	483	2	plot	plot	NOUN
ejpam-6047	483	3	at	at	ADP
ejpam-6047	483	4	the	the	DET
ejpam-6047	483	5	bottom	bottom	ADJ
ejpam-6047	483	6	level	level	NOUN
ejpam-6047	483	7	show	show	VERB
ejpam-6047	483	8	absolute	absolute	ADJ
ejpam-6047	483	9	value	value	NOUN
ejpam-6047	483	10	of	of	ADP
ejpam-6047	483	11	eigenmode	eigenmode	ADJ
ejpam-6047	483	12	being	be	AUX
ejpam-6047	483	13	ploted	plot	VERB
ejpam-6047	483	14	at	at	ADP
ejpam-6047	483	15	a	a	DET
ejpam-6047	483	16	log	log	NOUN
ejpam-6047	483	17	scale	scale	NOUN
ejpam-6047	483	18	.	.	PUNCT
ejpam-6047	484	1	further	far	ADV
ejpam-6047	484	2	,	,	PUNCT
ejpam-6047	484	3	it	it	PRON
ejpam-6047	484	4	shows	show	VERB
ejpam-6047	484	5	that	that	SCONJ
ejpam-6047	484	6	how	how	SCONJ
ejpam-6047	484	7	quickly	quickly	ADV
ejpam-6047	484	8	an	an	DET
ejpam-6047	484	9	eigenmode	eigenmode	NOUN
ejpam-6047	484	10	is	be	AUX
ejpam-6047	484	11	decaying	decay	VERB
ejpam-6047	484	12	with	with	ADP
ejpam-6047	484	13	time	time	NOUN
ejpam-6047	484	14	.	.	PUNCT
ejpam-6047	485	1	the	the	DET
ejpam-6047	485	2	condition	condition	NOUN
ejpam-6047	485	3	number	number	NOUN
ejpam-6047	485	4	computed	compute	VERB
ejpam-6047	485	5	for	for	ADP
ejpam-6047	485	6	an	an	DET
ejpam-6047	485	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	485	8	is	be	AUX
ejpam-6047	485	9	shown	show	VERB
ejpam-6047	485	10	in	in	ADP
ejpam-6047	485	11	the	the	DET
ejpam-6047	485	12	top	top	ADJ
ejpam-6047	485	13	plot	plot	NOUN
ejpam-6047	485	14	.	.	PUNCT
ejpam-6047	486	1	the	the	DET
ejpam-6047	486	2	large	large	ADJ
ejpam-6047	486	3	condition	condition	NOUN
ejpam-6047	486	4	number	number	NOUN
ejpam-6047	486	5	means	mean	VERB
ejpam-6047	486	6	that	that	SCONJ
ejpam-6047	486	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	486	8	is	be	AUX
ejpam-6047	486	9	sensitive	sensitive	ADJ
ejpam-6047	486	10	to	to	ADP
ejpam-6047	486	11	perturbations	perturbation	NOUN
ejpam-6047	486	12	.	.	PUNCT
ejpam-6047	487	1	we	we	PRON
ejpam-6047	487	2	plot	plot	VERB
ejpam-6047	487	3	the	the	DET
ejpam-6047	487	4	value	value	NOUN
ejpam-6047	487	5	of	of	ADP
ejpam-6047	487	6	inverse	inverse	NOUN
ejpam-6047	487	7	of	of	ADP
ejpam-6047	487	8	the	the	DET
ejpam-6047	487	9	resolvent	resolvent	ADJ
ejpam-6047	487	10	norm	norm	NOUN
ejpam-6047	487	11	(	(	PUNCT
ejpam-6047	487	12	right	right	NOUN
ejpam-6047	487	13	)	)	PUNCT
ejpam-6047	487	14	.	.	PUNCT
ejpam-6047	488	1	we	we	PRON
ejpam-6047	488	2	show	show	VERB
ejpam-6047	488	3	real	real	ADJ
ejpam-6047	488	4	part	part	NOUN
ejpam-6047	488	5	of	of	ADP
ejpam-6047	488	6	pseudomode	pseudomode	NOUN
ejpam-6047	488	7	in	in	ADP
ejpam-6047	488	8	magenta.the	magenta.the	DET
ejpam-6047	488	9	right	right	ADJ
ejpam-6047	488	10	singular	singular	PROPN
ejpam-6047	488	11	vector	vector	NOUN
ejpam-6047	488	12	corresponding	correspond	VERB
ejpam-6047	488	13	to	to	ADP
ejpam-6047	488	14	the	the	DET
ejpam-6047	488	15	smallest	small	ADJ
ejpam-6047	488	16	singular	singular	ADJ
ejpam-6047	488	17	value	value	NOUN
ejpam-6047	488	18	of	of	ADP
ejpam-6047	488	19	the	the	DET
ejpam-6047	488	20	matrix	matrix	NOUN
ejpam-6047	488	21	zin	zin	NOUN
ejpam-6047	488	22	−	−	NOUN
ejpam-6047	488	23	a	a	PRON
ejpam-6047	488	24	is	be	AUX
ejpam-6047	488	25	depicted	depict	VERB
ejpam-6047	488	26	in	in	ADP
ejpam-6047	488	27	pseudomode	pseudomode	NOUN
ejpam-6047	488	28	.	.	PUNCT
ejpam-6047	488	29	example	example	NOUN
ejpam-6047	489	1	2	2	NUM
ejpam-6047	489	2	.	.	X
ejpam-6047	489	3	consider	consider	VERB
ejpam-6047	489	4	a	a	DET
ejpam-6047	489	5	positive	positive	ADJ
ejpam-6047	489	6	frobenius	frobenius	NOUN
ejpam-6047	489	7	matrix	matrix	NOUN
ejpam-6047	489	8	[	[	X
ejpam-6047	489	9	58	58	NUM
ejpam-6047	489	10	]	]	X
ejpam-6047	489	11	f	f	X
ejpam-6047	489	12	=	=	SYM
ejpam-6047	489	13			PROPN
ejpam-6047	489	14	0	0	NUM
ejpam-6047	489	15	1	1	NUM
ejpam-6047	489	16	0	0	NUM
ejpam-6047	489	17	0	0	NUM
ejpam-6047	489	18	0	0	NUM
ejpam-6047	489	19	1	1	NUM
ejpam-6047	489	20	0.4714	0.4714	NUM
ejpam-6047	489	21	0.1953	0.1953	NUM
ejpam-6047	489	22	0.3333	0.3333	NUM
ejpam-6047	489	23			NOUN
ejpam-6047	489	24	,	,	PUNCT
ejpam-6047	489	25	and	and	CCONJ
ejpam-6047	489	26	a	a	DET
ejpam-6047	489	27	characteristic	characteristic	ADJ
ejpam-6047	489	28	polynomial	polynomial	NOUN
ejpam-6047	489	29	for	for	ADP
ejpam-6047	489	30	f	f	PROPN
ejpam-6047	489	31	given	give	VERB
ejpam-6047	489	32	as	as	ADP
ejpam-6047	489	33	p	p	NOUN
ejpam-6047	489	34	(	(	PUNCT
ejpam-6047	489	35	β	β	X
ejpam-6047	489	36	,	,	PUNCT
ejpam-6047	489	37	f	f	PROPN
ejpam-6047	489	38	)	)	PUNCT
ejpam-6047	489	39	=	=	SYM
ejpam-6047	489	40	β3	β3	ADP
ejpam-6047	489	41	−	−	NOUN
ejpam-6047	489	42	0.3333β2	0.3333β2	NUM
ejpam-6047	490	1	−	−	NOUN
ejpam-6047	490	2	0.1953β	0.1953β	NOUN
ejpam-6047	490	3	−	−	PROPN
ejpam-6047	490	4	0.4714	0.4714	NUM
ejpam-6047	490	5	,	,	PUNCT
ejpam-6047	490	6	with	with	ADP
ejpam-6047	490	7	β	β	X
ejpam-6047	490	8	=	=	SYM
ejpam-6047	490	9	λ	λ	PROPN
ejpam-6047	490	10	+	+	CCONJ
ejpam-6047	490	11	η	η	PROPN
ejpam-6047	490	12	,	,	PUNCT
ejpam-6047	490	13	η	η	NOUN
ejpam-6047	490	14	=	=	PROPN
ejpam-6047	490	15	1.1	1.1	NUM
ejpam-6047	490	16	>	>	PUNCT
ejpam-6047	490	17	ρ(f	ρ(f	NOUN
ejpam-6047	490	18	)	)	PUNCT
ejpam-6047	491	1	=	=	PUNCT
ejpam-6047	491	2	1	1	X
ejpam-6047	491	3	.	.	PUNCT
ejpam-6047	492	1	the	the	DET
ejpam-6047	492	2	matrix	matrix	NOUN
ejpam-6047	492	3	a	a	DET
ejpam-6047	492	4	=	=	SYM
ejpam-6047	492	5	f	f	X
ejpam-6047	492	6	−	−	PROPN
ejpam-6047	492	7	ηi3	ηi3	NOUN
ejpam-6047	492	8	,	,	PUNCT
ejpam-6047	492	9	is	be	AUX
ejpam-6047	492	10	a	a	DET
ejpam-6047	492	11	metzler	metzler	NOUN
ejpam-6047	492	12	matrix	matrix	NOUN
ejpam-6047	492	13	with	with	ADP
ejpam-6047	492	14	a	a	DET
ejpam-6047	492	15	=	=	SYM
ejpam-6047	492	16			NOUN
ejpam-6047	492	17	−1.1	−1.1	NOUN
ejpam-6047	492	18	1	1	NUM
ejpam-6047	492	19	0	0	NUM
ejpam-6047	492	20	0	0	NUM
ejpam-6047	493	1	−1.1	−1.1	NOUN
ejpam-6047	493	2	1	1	NUM
ejpam-6047	493	3	0.4714	0.4714	NUM
ejpam-6047	493	4	0.1953	0.1953	NUM
ejpam-6047	493	5	0.7667	0.7667	NUM
ejpam-6047	493	6			NOUN
ejpam-6047	493	7	.	.	PUNCT
ejpam-6047	494	1	the	the	DET
ejpam-6047	494	2	spectral	spectral	ADJ
ejpam-6047	494	3	properties	property	NOUN
ejpam-6047	494	4	like	like	ADP
ejpam-6047	494	5	the	the	DET
ejpam-6047	494	6	computation	computation	NOUN
ejpam-6047	494	7	of	of	ADP
ejpam-6047	494	8	spectrum	spectrum	NOUN
ejpam-6047	494	9	,	,	PUNCT
ejpam-6047	494	10	singular	singular	PROPN
ejpam-6047	494	11	,	,	PUNCT
ejpam-6047	494	12	structured	structure	VERB
ejpam-6047	494	13	singular	singular	ADJ
ejpam-6047	494	14	values	value	NOUN
ejpam-6047	494	15	and	and	CCONJ
ejpam-6047	494	16	pseudo	pseudo	NOUN
ejpam-6047	494	17	-	-	NOUN
ejpam-6047	494	18	spectrum	spectrum	NOUN
ejpam-6047	494	19	of	of	ADP
ejpam-6047	494	20	metzler	metzler	NOUN
ejpam-6047	494	21	matrix	matrix	NOUN
ejpam-6047	494	22	a	a	PRON
ejpam-6047	494	23	are	be	AUX
ejpam-6047	494	24	presented	present	VERB
ejpam-6047	494	25	in	in	ADP
ejpam-6047	494	26	figure	figure	NOUN
ejpam-6047	494	27	3	3	NUM
ejpam-6047	494	28	.	.	PUNCT
ejpam-6047	495	1	m.u	m.u	PROPN
ejpam-6047	495	2	.	.	PROPN
ejpam-6047	495	3	rehman	rehman	PROPN
ejpam-6047	495	4	et	et	PROPN
ejpam-6047	495	5	al	al	PROPN
ejpam-6047	495	6	.	.	PUNCT
ejpam-6047	495	7	/	/	SYM
ejpam-6047	495	8	eur	eur	PROPN
ejpam-6047	495	9	.	.	PUNCT
ejpam-6047	496	1	j.	j.	PROPN
ejpam-6047	496	2	pure	pure	PROPN
ejpam-6047	496	3	appl	appl	PROPN
ejpam-6047	496	4	.	.	PROPN
ejpam-6047	496	5	math	math	PROPN
ejpam-6047	496	6	,	,	PUNCT
ejpam-6047	496	7	18	18	NUM
ejpam-6047	496	8	(	(	PUNCT
ejpam-6047	496	9	3	3	NUM
ejpam-6047	496	10	)	)	PUNCT
ejpam-6047	496	11	(	(	PUNCT
ejpam-6047	496	12	2025	2025	NUM
ejpam-6047	496	13	)	)	PUNCT
ejpam-6047	496	14	,	,	PUNCT
ejpam-6047	496	15	6047	6047	NUM
ejpam-6047	496	16	20	20	NUM
ejpam-6047	496	17	of	of	ADP
ejpam-6047	496	18	33	33	NUM
ejpam-6047	496	19	figure	figure	NOUN
ejpam-6047	496	20	1	1	NUM
ejpam-6047	496	21	:	:	PUNCT
ejpam-6047	496	22	spectral	spectral	ADJ
ejpam-6047	496	23	properties	property	NOUN
ejpam-6047	496	24	of	of	ADP
ejpam-6047	496	25	metzler	metzler	NOUN
ejpam-6047	496	26	matrix	matrix	NOUN
ejpam-6047	496	27	a	a	PRON
ejpam-6047	496	28	in	in	ADP
ejpam-6047	496	29	example-1	example-1	PROPN
ejpam-6047	496	30	.	.	PUNCT
ejpam-6047	497	1	in	in	ADP
ejpam-6047	497	2	figure	figure	NOUN
ejpam-6047	497	3	4	4	NUM
ejpam-6047	497	4	,	,	PUNCT
ejpam-6047	497	5	we	we	PRON
ejpam-6047	497	6	plot	plot	VERB
ejpam-6047	497	7	the	the	DET
ejpam-6047	497	8	eigenmode	eigenmode	PROPN
ejpam-6047	497	9	corresponding	corresponding	NOUN
ejpam-6047	497	10	to	to	ADP
ejpam-6047	497	11	the	the	DET
ejpam-6047	497	12	eigenvalues	eigenvalue	NOUN
ejpam-6047	497	13	.	.	PUNCT
ejpam-6047	498	1	the	the	DET
ejpam-6047	498	2	top	top	ADJ
ejpam-6047	498	3	plot	plot	NOUN
ejpam-6047	498	4	(	(	PUNCT
ejpam-6047	498	5	left	leave	VERB
ejpam-6047	498	6	)	)	PUNCT
ejpam-6047	498	7	in	in	ADP
ejpam-6047	498	8	the	the	DET
ejpam-6047	498	9	figure	figure	NOUN
ejpam-6047	498	10	shows	show	VERB
ejpam-6047	498	11	an	an	DET
ejpam-6047	498	12	envelope	envelope	NOUN
ejpam-6047	498	13	which	which	PRON
ejpam-6047	498	14	is	be	AUX
ejpam-6047	498	15	produced	produce	VERB
ejpam-6047	498	16	by	by	ADP
ejpam-6047	498	17	plotting	plot	VERB
ejpam-6047	498	18	the	the	DET
ejpam-6047	498	19	absolute	absolute	ADJ
ejpam-6047	498	20	value	value	NOUN
ejpam-6047	498	21	of	of	ADP
ejpam-6047	498	22	an	an	DET
ejpam-6047	498	23	eigenmode	eigenmode	NOUN
ejpam-6047	498	24	and	and	CCONJ
ejpam-6047	498	25	minus	minus	ADP
ejpam-6047	498	26	the	the	DET
ejpam-6047	498	27	absolute	absolute	ADJ
ejpam-6047	498	28	value	value	NOUN
ejpam-6047	498	29	.	.	PUNCT
ejpam-6047	499	1	the	the	DET
ejpam-6047	499	2	real	real	ADJ
ejpam-6047	499	3	part	part	NOUN
ejpam-6047	499	4	is	be	AUX
ejpam-6047	499	5	shown	show	VERB
ejpam-6047	499	6	with	with	ADP
ejpam-6047	499	7	a	a	DET
ejpam-6047	499	8	cyan	cyan	ADJ
ejpam-6047	499	9	line	line	NOUN
ejpam-6047	499	10	.	.	PUNCT
ejpam-6047	500	1	the	the	DET
ejpam-6047	500	2	plot	plot	NOUN
ejpam-6047	500	3	at	at	ADP
ejpam-6047	500	4	the	the	DET
ejpam-6047	500	5	bottom	bottom	ADJ
ejpam-6047	500	6	level	level	NOUN
ejpam-6047	500	7	show	show	VERB
ejpam-6047	500	8	absolute	absolute	ADJ
ejpam-6047	500	9	value	value	NOUN
ejpam-6047	500	10	of	of	ADP
ejpam-6047	500	11	eigenmode	eigenmode	ADJ
ejpam-6047	500	12	being	be	AUX
ejpam-6047	500	13	ploted	plot	VERB
ejpam-6047	500	14	at	at	ADP
ejpam-6047	500	15	a	a	DET
ejpam-6047	500	16	log	log	NOUN
ejpam-6047	500	17	scale	scale	NOUN
ejpam-6047	500	18	.	.	PUNCT
ejpam-6047	501	1	further	far	ADV
ejpam-6047	501	2	,	,	PUNCT
ejpam-6047	501	3	it	it	PRON
ejpam-6047	501	4	shows	show	VERB
ejpam-6047	501	5	that	that	SCONJ
ejpam-6047	501	6	how	how	SCONJ
ejpam-6047	501	7	quickly	quickly	ADV
ejpam-6047	501	8	an	an	DET
ejpam-6047	501	9	eigenmode	eigenmode	NOUN
ejpam-6047	501	10	is	be	AUX
ejpam-6047	501	11	decaying	decay	VERB
ejpam-6047	501	12	with	with	ADP
ejpam-6047	501	13	time	time	NOUN
ejpam-6047	501	14	.	.	PUNCT
ejpam-6047	502	1	the	the	DET
ejpam-6047	502	2	condition	condition	NOUN
ejpam-6047	502	3	number	number	NOUN
ejpam-6047	502	4	computed	compute	VERB
ejpam-6047	502	5	for	for	ADP
ejpam-6047	502	6	an	an	DET
ejpam-6047	502	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	502	8	is	be	AUX
ejpam-6047	502	9	shown	show	VERB
ejpam-6047	502	10	in	in	ADP
ejpam-6047	502	11	the	the	DET
ejpam-6047	502	12	top	top	ADJ
ejpam-6047	502	13	plot	plot	NOUN
ejpam-6047	502	14	.	.	PUNCT
ejpam-6047	503	1	the	the	DET
ejpam-6047	503	2	large	large	ADJ
ejpam-6047	503	3	condition	condition	NOUN
ejpam-6047	503	4	number	number	NOUN
ejpam-6047	503	5	means	mean	VERB
ejpam-6047	503	6	that	that	SCONJ
ejpam-6047	503	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	503	8	is	be	AUX
ejpam-6047	503	9	sensitive	sensitive	ADJ
ejpam-6047	503	10	to	to	ADP
ejpam-6047	503	11	perturbations	perturbation	NOUN
ejpam-6047	503	12	.	.	PUNCT
ejpam-6047	504	1	we	we	PRON
ejpam-6047	504	2	plot	plot	VERB
ejpam-6047	504	3	the	the	DET
ejpam-6047	504	4	value	value	NOUN
ejpam-6047	504	5	of	of	ADP
ejpam-6047	504	6	inverse	inverse	NOUN
ejpam-6047	504	7	of	of	ADP
ejpam-6047	504	8	the	the	DET
ejpam-6047	504	9	resolvent	resolvent	ADJ
ejpam-6047	504	10	norm	norm	NOUN
ejpam-6047	504	11	(	(	PUNCT
ejpam-6047	504	12	right	right	NOUN
ejpam-6047	504	13	)	)	PUNCT
ejpam-6047	504	14	.	.	PUNCT
ejpam-6047	505	1	we	we	PRON
ejpam-6047	505	2	show	show	VERB
ejpam-6047	505	3	real	real	ADJ
ejpam-6047	505	4	part	part	NOUN
ejpam-6047	505	5	of	of	ADP
ejpam-6047	505	6	pseudomode	pseudomode	NOUN
ejpam-6047	505	7	in	in	ADP
ejpam-6047	505	8	magenta	magenta	NOUN
ejpam-6047	505	9	.	.	PUNCT
ejpam-6047	506	1	the	the	DET
ejpam-6047	506	2	right	right	ADJ
ejpam-6047	506	3	singular	singular	PROPN
ejpam-6047	506	4	vector	vector	NOUN
ejpam-6047	506	5	corresponding	correspond	VERB
ejpam-6047	506	6	to	to	ADP
ejpam-6047	506	7	the	the	DET
ejpam-6047	506	8	smallest	small	ADJ
ejpam-6047	506	9	singular	singular	ADJ
ejpam-6047	506	10	value	value	NOUN
ejpam-6047	506	11	of	of	ADP
ejpam-6047	506	12	the	the	DET
ejpam-6047	506	13	matrix	matrix	NOUN
ejpam-6047	506	14	zin	zin	NOUN
ejpam-6047	506	15	−	−	NOUN
ejpam-6047	506	16	a	a	PRON
ejpam-6047	506	17	is	be	AUX
ejpam-6047	506	18	depicted	depict	VERB
ejpam-6047	506	19	in	in	ADP
ejpam-6047	506	20	pseudomode	pseudomode	NOUN
ejpam-6047	506	21	.	.	PUNCT
ejpam-6047	507	1	example	example	NOUN
ejpam-6047	508	1	3	3	X
ejpam-6047	508	2	.	.	X
ejpam-6047	508	3	we	we	PRON
ejpam-6047	508	4	consider	consider	VERB
ejpam-6047	508	5	metzler	metzler	NOUN
ejpam-6047	508	6	matrices	matrix	NOUN
ejpam-6047	508	7	with	with	ADP
ejpam-6047	508	8	sizes	size	NOUN
ejpam-6047	508	9	50	50	NUM
ejpam-6047	508	10	,	,	PUNCT
ejpam-6047	508	11	100	100	NUM
ejpam-6047	508	12	,	,	PUNCT
ejpam-6047	508	13	and	and	CCONJ
ejpam-6047	508	14	500	500	NUM
ejpam-6047	508	15	,	,	PUNCT
ejpam-6047	508	16	respectively	respectively	ADV
ejpam-6047	508	17	.	.	PUNCT
ejpam-6047	509	1	the	the	DET
ejpam-6047	509	2	spectral	spectral	ADJ
ejpam-6047	509	3	properties	property	NOUN
ejpam-6047	509	4	like	like	ADP
ejpam-6047	509	5	the	the	DET
ejpam-6047	509	6	computation	computation	NOUN
ejpam-6047	509	7	of	of	ADP
ejpam-6047	509	8	spectrum	spectrum	NOUN
ejpam-6047	509	9	,	,	PUNCT
ejpam-6047	509	10	singular	singular	PROPN
ejpam-6047	509	11	,	,	PUNCT
ejpam-6047	509	12	structured	structure	VERB
ejpam-6047	509	13	singular	singular	ADJ
ejpam-6047	509	14	values	value	NOUN
ejpam-6047	509	15	and	and	CCONJ
ejpam-6047	509	16	pseudo	pseudo	NOUN
ejpam-6047	509	17	-	-	NOUN
ejpam-6047	509	18	spectrum	spectrum	NOUN
ejpam-6047	509	19	of	of	ADP
ejpam-6047	509	20	metzler	metzler	NOUN
ejpam-6047	509	21	matrix	matrix	NOUN
ejpam-6047	509	22	a	a	PRON
ejpam-6047	509	23	are	be	AUX
ejpam-6047	509	24	presented	present	VERB
ejpam-6047	509	25	in	in	ADP
ejpam-6047	509	26	figures	figure	NOUN
ejpam-6047	509	27	5,7	5,7	NUM
ejpam-6047	509	28	,	,	PUNCT
ejpam-6047	509	29	and	and	CCONJ
ejpam-6047	509	30	9	9	NUM
ejpam-6047	509	31	.	.	PUNCT
ejpam-6047	510	1	in	in	ADP
ejpam-6047	510	2	figures	figure	NOUN
ejpam-6047	510	3	6,8	6,8	NUM
ejpam-6047	510	4	,	,	PUNCT
ejpam-6047	510	5	and	and	CCONJ
ejpam-6047	510	6	10	10	NUM
ejpam-6047	510	7	,	,	PUNCT
ejpam-6047	510	8	we	we	PRON
ejpam-6047	510	9	plot	plot	VERB
ejpam-6047	510	10	(	(	PUNCT
ejpam-6047	510	11	left	leave	VERB
ejpam-6047	510	12	)	)	PUNCT
ejpam-6047	510	13	the	the	DET
ejpam-6047	510	14	eigenmode	eigenmode	PROPN
ejpam-6047	510	15	corresponding	correspond	VERB
ejpam-6047	510	16	to	to	ADP
ejpam-6047	510	17	the	the	DET
ejpam-6047	510	18	eigenvalues	eigenvalue	NOUN
ejpam-6047	510	19	.	.	PUNCT
ejpam-6047	511	1	the	the	DET
ejpam-6047	511	2	top	top	ADJ
ejpam-6047	511	3	plot	plot	NOUN
ejpam-6047	511	4	in	in	ADP
ejpam-6047	511	5	the	the	DET
ejpam-6047	511	6	figure	figure	NOUN
ejpam-6047	511	7	shows	show	VERB
ejpam-6047	511	8	an	an	DET
ejpam-6047	511	9	envelope	envelope	NOUN
ejpam-6047	511	10	which	which	PRON
ejpam-6047	511	11	is	be	AUX
ejpam-6047	511	12	produced	produce	VERB
ejpam-6047	511	13	by	by	ADP
ejpam-6047	511	14	plotting	plot	VERB
ejpam-6047	511	15	the	the	DET
ejpam-6047	511	16	absolute	absolute	ADJ
ejpam-6047	511	17	value	value	NOUN
ejpam-6047	511	18	of	of	ADP
ejpam-6047	511	19	an	an	DET
ejpam-6047	511	20	eigenmode	eigenmode	NOUN
ejpam-6047	511	21	and	and	CCONJ
ejpam-6047	511	22	minus	minus	ADP
ejpam-6047	511	23	the	the	DET
ejpam-6047	511	24	absolute	absolute	ADJ
ejpam-6047	511	25	value	value	NOUN
ejpam-6047	511	26	.	.	PUNCT
ejpam-6047	512	1	the	the	DET
ejpam-6047	512	2	real	real	ADJ
ejpam-6047	512	3	part	part	NOUN
ejpam-6047	512	4	is	be	AUX
ejpam-6047	512	5	shown	show	VERB
ejpam-6047	512	6	with	with	ADP
ejpam-6047	512	7	a	a	DET
ejpam-6047	512	8	cyan	cyan	ADJ
ejpam-6047	512	9	line	line	NOUN
ejpam-6047	512	10	.	.	PUNCT
ejpam-6047	513	1	the	the	DET
ejpam-6047	513	2	plot	plot	NOUN
ejpam-6047	513	3	at	at	ADP
ejpam-6047	513	4	the	the	DET
ejpam-6047	513	5	bottom	bottom	ADJ
ejpam-6047	513	6	level	level	NOUN
ejpam-6047	513	7	show	show	VERB
ejpam-6047	513	8	absolute	absolute	ADJ
ejpam-6047	513	9	value	value	NOUN
ejpam-6047	513	10	of	of	ADP
ejpam-6047	513	11	eigenmode	eigenmode	ADJ
ejpam-6047	513	12	being	be	AUX
ejpam-6047	513	13	ploted	plot	VERB
ejpam-6047	513	14	at	at	ADP
ejpam-6047	513	15	a	a	DET
ejpam-6047	513	16	log	log	NOUN
ejpam-6047	513	17	scale	scale	NOUN
ejpam-6047	513	18	.	.	PUNCT
ejpam-6047	514	1	further	far	ADV
ejpam-6047	514	2	,	,	PUNCT
ejpam-6047	514	3	it	it	PRON
ejpam-6047	514	4	shows	show	VERB
ejpam-6047	514	5	that	that	SCONJ
ejpam-6047	514	6	how	how	SCONJ
ejpam-6047	514	7	quickly	quickly	ADV
ejpam-6047	514	8	an	an	DET
ejpam-6047	514	9	eigenmode	eigenmode	NOUN
ejpam-6047	514	10	is	be	AUX
ejpam-6047	514	11	decaying	decay	VERB
ejpam-6047	514	12	with	with	ADP
ejpam-6047	514	13	time	time	NOUN
ejpam-6047	514	14	.	.	PUNCT
ejpam-6047	515	1	the	the	DET
ejpam-6047	515	2	condition	condition	NOUN
ejpam-6047	515	3	number	number	NOUN
ejpam-6047	515	4	computed	compute	VERB
ejpam-6047	515	5	for	for	ADP
ejpam-6047	515	6	an	an	DET
ejpam-6047	515	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	515	8	is	be	AUX
ejpam-6047	515	9	shown	show	VERB
ejpam-6047	515	10	in	in	ADP
ejpam-6047	515	11	the	the	DET
ejpam-6047	515	12	top	top	ADJ
ejpam-6047	515	13	plot	plot	NOUN
ejpam-6047	515	14	.	.	PUNCT
ejpam-6047	516	1	the	the	DET
ejpam-6047	516	2	large	large	ADJ
ejpam-6047	516	3	condition	condition	NOUN
ejpam-6047	516	4	number	number	NOUN
ejpam-6047	516	5	means	mean	VERB
ejpam-6047	516	6	that	that	SCONJ
ejpam-6047	516	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	516	8	is	be	AUX
ejpam-6047	516	9	sensitive	sensitive	ADJ
ejpam-6047	516	10	to	to	ADP
ejpam-6047	516	11	perturbations	perturbation	NOUN
ejpam-6047	516	12	.	.	PUNCT
ejpam-6047	517	1	we	we	PRON
ejpam-6047	517	2	plot	plot	VERB
ejpam-6047	517	3	the	the	DET
ejpam-6047	517	4	value	value	NOUN
ejpam-6047	517	5	of	of	ADP
ejpam-6047	517	6	inverse	inverse	NOUN
ejpam-6047	517	7	of	of	ADP
ejpam-6047	517	8	the	the	DET
ejpam-6047	517	9	resolvent	resolvent	ADJ
ejpam-6047	517	10	norm	norm	NOUN
ejpam-6047	517	11	(	(	PUNCT
ejpam-6047	517	12	right	right	NOUN
ejpam-6047	517	13	)	)	PUNCT
ejpam-6047	517	14	.	.	PUNCT
ejpam-6047	518	1	we	we	PRON
ejpam-6047	518	2	show	show	VERB
ejpam-6047	518	3	real	real	ADJ
ejpam-6047	518	4	part	part	NOUN
ejpam-6047	518	5	of	of	ADP
ejpam-6047	518	6	pseudomode	pseudomode	NOUN
ejpam-6047	518	7	in	in	ADP
ejpam-6047	518	8	magenta	magenta	NOUN
ejpam-6047	518	9	.	.	PUNCT
ejpam-6047	519	1	the	the	DET
ejpam-6047	519	2	right	right	ADJ
ejpam-6047	519	3	singular	singular	PROPN
ejpam-6047	519	4	vector	vector	NOUN
ejpam-6047	519	5	corresponding	correspond	VERB
ejpam-6047	519	6	to	to	ADP
ejpam-6047	519	7	the	the	DET
ejpam-6047	519	8	smallest	small	ADJ
ejpam-6047	519	9	singular	singular	ADJ
ejpam-6047	519	10	value	value	NOUN
ejpam-6047	519	11	of	of	ADP
ejpam-6047	519	12	the	the	DET
ejpam-6047	519	13	matrix	matrix	NOUN
ejpam-6047	519	14	zin	zin	NOUN
ejpam-6047	519	15	−a	−a	NOUN
ejpam-6047	519	16	is	be	AUX
ejpam-6047	519	17	depicted	depict	VERB
ejpam-6047	519	18	in	in	ADP
ejpam-6047	519	19	pseudomode	pseudomode	NOUN
ejpam-6047	519	20	.	.	PUNCT
ejpam-6047	520	1	m.u	m.u	PROPN
ejpam-6047	520	2	.	.	PROPN
ejpam-6047	520	3	rehman	rehman	PROPN
ejpam-6047	520	4	et	et	PROPN
ejpam-6047	520	5	al	al	PROPN
ejpam-6047	520	6	.	.	PUNCT
ejpam-6047	520	7	/	/	SYM
ejpam-6047	520	8	eur	eur	PROPN
ejpam-6047	520	9	.	.	PUNCT
ejpam-6047	521	1	j.	j.	PROPN
ejpam-6047	521	2	pure	pure	PROPN
ejpam-6047	521	3	appl	appl	PROPN
ejpam-6047	521	4	.	.	PROPN
ejpam-6047	521	5	math	math	PROPN
ejpam-6047	521	6	,	,	PUNCT
ejpam-6047	521	7	18	18	NUM
ejpam-6047	521	8	(	(	PUNCT
ejpam-6047	521	9	3	3	NUM
ejpam-6047	521	10	)	)	PUNCT
ejpam-6047	521	11	(	(	PUNCT
ejpam-6047	521	12	2025	2025	NUM
ejpam-6047	521	13	)	)	PUNCT
ejpam-6047	521	14	,	,	PUNCT
ejpam-6047	521	15	6047	6047	NUM
ejpam-6047	521	16	21	21	NUM
ejpam-6047	521	17	of	of	ADP
ejpam-6047	521	18	33	33	NUM
ejpam-6047	521	19	figure	figure	NOUN
ejpam-6047	521	20	2	2	NUM
ejpam-6047	521	21	:	:	PUNCT
ejpam-6047	521	22	eigenmode	eigenmode	ADJ
ejpam-6047	521	23	(	(	PUNCT
ejpam-6047	521	24	left	left	ADJ
ejpam-6047	521	25	)	)	PUNCT
ejpam-6047	521	26	and	and	CCONJ
ejpam-6047	521	27	inverse	inverse	NOUN
ejpam-6047	521	28	of	of	ADP
ejpam-6047	521	29	resolvent	resolvent	ADJ
ejpam-6047	521	30	norm	norm	NOUN
ejpam-6047	521	31	(	(	PUNCT
ejpam-6047	521	32	right	right	NOUN
ejpam-6047	521	33	)	)	PUNCT
ejpam-6047	521	34	of	of	ADP
ejpam-6047	521	35	metzler	metzler	NOUN
ejpam-6047	521	36	matrix	matrix	NOUN
ejpam-6047	521	37	a	a	PRON
ejpam-6047	521	38	in	in	ADP
ejpam-6047	521	39	example-1	example-1	NOUN
ejpam-6047	521	40	example	example	NOUN
ejpam-6047	521	41	4	4	NUM
ejpam-6047	521	42	.	.	PUNCT
ejpam-6047	522	1	we	we	PRON
ejpam-6047	522	2	consider	consider	VERB
ejpam-6047	522	3	hurwitz	hurwitz	PROPN
ejpam-6047	522	4	matrices	matrix	NOUN
ejpam-6047	522	5	with	with	ADP
ejpam-6047	522	6	sizes	size	NOUN
ejpam-6047	522	7	50	50	NUM
ejpam-6047	522	8	,	,	PUNCT
ejpam-6047	522	9	100	100	NUM
ejpam-6047	522	10	,	,	PUNCT
ejpam-6047	522	11	and	and	CCONJ
ejpam-6047	522	12	500	500	NUM
ejpam-6047	522	13	,	,	PUNCT
ejpam-6047	522	14	respectively	respectively	ADV
ejpam-6047	522	15	.	.	PUNCT
ejpam-6047	523	1	the	the	DET
ejpam-6047	523	2	spectral	spectral	ADJ
ejpam-6047	523	3	properties	property	NOUN
ejpam-6047	523	4	like	like	ADP
ejpam-6047	523	5	the	the	DET
ejpam-6047	523	6	computation	computation	NOUN
ejpam-6047	523	7	of	of	ADP
ejpam-6047	523	8	spectrum	spectrum	NOUN
ejpam-6047	523	9	,	,	PUNCT
ejpam-6047	523	10	singular	singular	PROPN
ejpam-6047	523	11	,	,	PUNCT
ejpam-6047	523	12	structured	structure	VERB
ejpam-6047	523	13	singular	singular	ADJ
ejpam-6047	523	14	values	value	NOUN
ejpam-6047	523	15	and	and	CCONJ
ejpam-6047	523	16	pseudo	pseudo	NOUN
ejpam-6047	523	17	-	-	NOUN
ejpam-6047	523	18	spectrum	spectrum	NOUN
ejpam-6047	523	19	of	of	ADP
ejpam-6047	523	20	hurwitz	hurwitz	PROPN
ejpam-6047	523	21	matrix	matrix	NOUN
ejpam-6047	523	22	a	a	PRON
ejpam-6047	523	23	are	be	AUX
ejpam-6047	523	24	presented	present	VERB
ejpam-6047	523	25	in	in	ADP
ejpam-6047	523	26	figures	figure	NOUN
ejpam-6047	523	27	11,13	11,13	NUM
ejpam-6047	523	28	,	,	PUNCT
ejpam-6047	523	29	and	and	CCONJ
ejpam-6047	523	30	15	15	NUM
ejpam-6047	523	31	.	.	PUNCT
ejpam-6047	524	1	in	in	ADP
ejpam-6047	524	2	figures	figure	NOUN
ejpam-6047	524	3	12,14	12,14	ADV
ejpam-6047	524	4	,	,	PUNCT
ejpam-6047	524	5	and	and	CCONJ
ejpam-6047	524	6	16	16	NUM
ejpam-6047	524	7	,	,	PUNCT
ejpam-6047	524	8	we	we	PRON
ejpam-6047	524	9	plot	plot	VERB
ejpam-6047	524	10	(	(	PUNCT
ejpam-6047	524	11	left	leave	VERB
ejpam-6047	524	12	)	)	PUNCT
ejpam-6047	524	13	the	the	DET
ejpam-6047	524	14	eigenmode	eigenmode	PROPN
ejpam-6047	524	15	corresponding	correspond	VERB
ejpam-6047	524	16	to	to	ADP
ejpam-6047	524	17	the	the	DET
ejpam-6047	524	18	eigenvalues	eigenvalue	NOUN
ejpam-6047	524	19	.	.	PUNCT
ejpam-6047	525	1	the	the	DET
ejpam-6047	525	2	top	top	ADJ
ejpam-6047	525	3	plot	plot	NOUN
ejpam-6047	525	4	in	in	ADP
ejpam-6047	525	5	the	the	DET
ejpam-6047	525	6	figure	figure	NOUN
ejpam-6047	525	7	shows	show	VERB
ejpam-6047	525	8	an	an	DET
ejpam-6047	525	9	envelope	envelope	NOUN
ejpam-6047	525	10	which	which	PRON
ejpam-6047	525	11	is	be	AUX
ejpam-6047	525	12	produced	produce	VERB
ejpam-6047	525	13	by	by	ADP
ejpam-6047	525	14	plotting	plot	VERB
ejpam-6047	525	15	the	the	DET
ejpam-6047	525	16	absolute	absolute	ADJ
ejpam-6047	525	17	value	value	NOUN
ejpam-6047	525	18	of	of	ADP
ejpam-6047	525	19	an	an	DET
ejpam-6047	525	20	eigenmode	eigenmode	NOUN
ejpam-6047	525	21	and	and	CCONJ
ejpam-6047	525	22	minus	minus	ADP
ejpam-6047	525	23	the	the	DET
ejpam-6047	525	24	absolute	absolute	ADJ
ejpam-6047	525	25	value	value	NOUN
ejpam-6047	525	26	.	.	PUNCT
ejpam-6047	526	1	the	the	DET
ejpam-6047	526	2	real	real	ADJ
ejpam-6047	526	3	part	part	NOUN
ejpam-6047	526	4	is	be	AUX
ejpam-6047	526	5	shown	show	VERB
ejpam-6047	526	6	with	with	ADP
ejpam-6047	526	7	a	a	DET
ejpam-6047	526	8	cyan	cyan	ADJ
ejpam-6047	526	9	line	line	NOUN
ejpam-6047	526	10	.	.	PUNCT
ejpam-6047	527	1	the	the	DET
ejpam-6047	527	2	plot	plot	NOUN
ejpam-6047	527	3	at	at	ADP
ejpam-6047	527	4	the	the	DET
ejpam-6047	527	5	bottom	bottom	ADJ
ejpam-6047	527	6	level	level	NOUN
ejpam-6047	527	7	show	show	VERB
ejpam-6047	527	8	absolute	absolute	ADJ
ejpam-6047	527	9	value	value	NOUN
ejpam-6047	527	10	of	of	ADP
ejpam-6047	527	11	eigenmode	eigenmode	ADJ
ejpam-6047	527	12	being	be	AUX
ejpam-6047	527	13	ploted	plot	VERB
ejpam-6047	527	14	at	at	ADP
ejpam-6047	527	15	a	a	DET
ejpam-6047	527	16	log	log	NOUN
ejpam-6047	527	17	scale	scale	NOUN
ejpam-6047	527	18	.	.	PUNCT
ejpam-6047	528	1	further	far	ADV
ejpam-6047	528	2	,	,	PUNCT
ejpam-6047	528	3	it	it	PRON
ejpam-6047	528	4	shows	show	VERB
ejpam-6047	528	5	that	that	SCONJ
ejpam-6047	528	6	how	how	SCONJ
ejpam-6047	528	7	quickly	quickly	ADV
ejpam-6047	528	8	an	an	DET
ejpam-6047	528	9	eigenmode	eigenmode	NOUN
ejpam-6047	528	10	is	be	AUX
ejpam-6047	528	11	decaying	decay	VERB
ejpam-6047	528	12	with	with	ADP
ejpam-6047	528	13	time	time	NOUN
ejpam-6047	528	14	.	.	PUNCT
ejpam-6047	529	1	the	the	DET
ejpam-6047	529	2	condition	condition	NOUN
ejpam-6047	529	3	number	number	NOUN
ejpam-6047	529	4	computed	compute	VERB
ejpam-6047	529	5	for	for	ADP
ejpam-6047	529	6	an	an	DET
ejpam-6047	529	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	529	8	is	be	AUX
ejpam-6047	529	9	shown	show	VERB
ejpam-6047	529	10	in	in	ADP
ejpam-6047	529	11	the	the	DET
ejpam-6047	529	12	top	top	ADJ
ejpam-6047	529	13	plot	plot	NOUN
ejpam-6047	529	14	.	.	PUNCT
ejpam-6047	530	1	the	the	DET
ejpam-6047	530	2	large	large	ADJ
ejpam-6047	530	3	condition	condition	NOUN
ejpam-6047	530	4	number	number	NOUN
ejpam-6047	530	5	means	mean	VERB
ejpam-6047	530	6	that	that	SCONJ
ejpam-6047	530	7	eigenvalue	eigenvalue	NOUN
ejpam-6047	530	8	is	be	AUX
ejpam-6047	530	9	sensitive	sensitive	ADJ
ejpam-6047	530	10	to	to	ADP
ejpam-6047	530	11	perturbations	perturbation	NOUN
ejpam-6047	530	12	.	.	PUNCT
ejpam-6047	531	1	we	we	PRON
ejpam-6047	531	2	plot	plot	VERB
ejpam-6047	531	3	the	the	DET
ejpam-6047	531	4	value	value	NOUN
ejpam-6047	531	5	of	of	ADP
ejpam-6047	531	6	inverse	inverse	NOUN
ejpam-6047	531	7	of	of	ADP
ejpam-6047	531	8	the	the	DET
ejpam-6047	531	9	resolvent	resolvent	ADJ
ejpam-6047	531	10	norm	norm	NOUN
ejpam-6047	531	11	(	(	PUNCT
ejpam-6047	531	12	right	right	NOUN
ejpam-6047	531	13	)	)	PUNCT
ejpam-6047	531	14	.	.	PUNCT
ejpam-6047	532	1	we	we	PRON
ejpam-6047	532	2	show	show	VERB
ejpam-6047	532	3	real	real	ADJ
ejpam-6047	532	4	part	part	NOUN
ejpam-6047	532	5	of	of	ADP
ejpam-6047	532	6	pseudomode	pseudomode	NOUN
ejpam-6047	532	7	in	in	ADP
ejpam-6047	532	8	magenta	magenta	NOUN
ejpam-6047	532	9	.	.	PUNCT
ejpam-6047	533	1	the	the	DET
ejpam-6047	533	2	right	right	ADJ
ejpam-6047	533	3	singular	singular	PROPN
ejpam-6047	533	4	vector	vector	NOUN
ejpam-6047	533	5	corresponding	correspond	VERB
ejpam-6047	533	6	to	to	ADP
ejpam-6047	533	7	the	the	DET
ejpam-6047	533	8	smallest	small	ADJ
ejpam-6047	533	9	singular	singular	ADJ
ejpam-6047	533	10	value	value	NOUN
ejpam-6047	533	11	of	of	ADP
ejpam-6047	533	12	the	the	DET
ejpam-6047	533	13	matrix	matrix	NOUN
ejpam-6047	533	14	zin	zin	NOUN
ejpam-6047	533	15	−	−	NOUN
ejpam-6047	533	16	a	a	PRON
ejpam-6047	533	17	is	be	AUX
ejpam-6047	533	18	depicted	depict	VERB
ejpam-6047	533	19	in	in	ADP
ejpam-6047	533	20	pseudomode	pseudomode	NOUN
ejpam-6047	533	21	.	.	PUNCT
ejpam-6047	534	1	m.u	m.u	PROPN
ejpam-6047	534	2	.	.	PROPN
ejpam-6047	534	3	rehman	rehman	PROPN
ejpam-6047	534	4	et	et	PROPN
ejpam-6047	534	5	al	al	PROPN
ejpam-6047	534	6	.	.	PUNCT
ejpam-6047	534	7	/	/	SYM
ejpam-6047	534	8	eur	eur	PROPN
ejpam-6047	534	9	.	.	PUNCT
ejpam-6047	535	1	j.	j.	PROPN
ejpam-6047	535	2	pure	pure	PROPN
ejpam-6047	535	3	appl	appl	PROPN
ejpam-6047	535	4	.	.	PROPN
ejpam-6047	535	5	math	math	PROPN
ejpam-6047	535	6	,	,	PUNCT
ejpam-6047	535	7	18	18	NUM
ejpam-6047	535	8	(	(	PUNCT
ejpam-6047	535	9	3	3	NUM
ejpam-6047	535	10	)	)	PUNCT
ejpam-6047	535	11	(	(	PUNCT
ejpam-6047	535	12	2025	2025	NUM
ejpam-6047	535	13	)	)	PUNCT
ejpam-6047	535	14	,	,	PUNCT
ejpam-6047	535	15	6047	6047	NUM
ejpam-6047	535	16	22	22	NUM
ejpam-6047	535	17	of	of	ADP
ejpam-6047	535	18	33	33	NUM
ejpam-6047	535	19	figure	figure	NOUN
ejpam-6047	535	20	3	3	NUM
ejpam-6047	535	21	:	:	PUNCT
ejpam-6047	535	22	spectral	spectral	ADJ
ejpam-6047	535	23	properties	property	NOUN
ejpam-6047	535	24	of	of	ADP
ejpam-6047	535	25	metzler	metzler	NOUN
ejpam-6047	535	26	matrix	matrix	NOUN
ejpam-6047	535	27	a	a	PRON
ejpam-6047	535	28	in	in	ADP
ejpam-6047	535	29	example-2	example-2	PROPN
ejpam-6047	535	30	.	.	PUNCT
ejpam-6047	535	31	figure	figure	NOUN
ejpam-6047	535	32	4	4	NUM
ejpam-6047	535	33	:	:	PUNCT
ejpam-6047	535	34	eigenmode	eigenmode	ADJ
ejpam-6047	535	35	(	(	PUNCT
ejpam-6047	535	36	left	left	ADJ
ejpam-6047	535	37	)	)	PUNCT
ejpam-6047	535	38	and	and	CCONJ
ejpam-6047	535	39	inverse	inverse	NOUN
ejpam-6047	535	40	of	of	ADP
ejpam-6047	535	41	resolvent	resolvent	ADJ
ejpam-6047	535	42	norm	norm	NOUN
ejpam-6047	535	43	(	(	PUNCT
ejpam-6047	535	44	right	right	NOUN
ejpam-6047	535	45	)	)	PUNCT
ejpam-6047	535	46	of	of	ADP
ejpam-6047	535	47	metzler	metzler	NOUN
ejpam-6047	535	48	matrix	matrix	NOUN
ejpam-6047	535	49	a	a	DET
ejpam-6047	535	50	in	in	ADP
ejpam-6047	535	51	example-2	example-2	NUM
ejpam-6047	535	52	m.u	m.u	PROPN
ejpam-6047	535	53	.	.	PROPN
ejpam-6047	535	54	rehman	rehman	PROPN
ejpam-6047	535	55	et	et	PROPN
ejpam-6047	535	56	al	al	PROPN
ejpam-6047	535	57	.	.	PUNCT
ejpam-6047	535	58	/	/	SYM
ejpam-6047	535	59	eur	eur	PROPN
ejpam-6047	535	60	.	.	PUNCT
ejpam-6047	536	1	j.	j.	PROPN
ejpam-6047	536	2	pure	pure	PROPN
ejpam-6047	536	3	appl	appl	PROPN
ejpam-6047	536	4	.	.	PROPN
ejpam-6047	536	5	math	math	PROPN
ejpam-6047	536	6	,	,	PUNCT
ejpam-6047	536	7	18	18	NUM
ejpam-6047	536	8	(	(	PUNCT
ejpam-6047	536	9	3	3	NUM
ejpam-6047	536	10	)	)	PUNCT
ejpam-6047	536	11	(	(	PUNCT
ejpam-6047	536	12	2025	2025	NUM
ejpam-6047	536	13	)	)	PUNCT
ejpam-6047	536	14	,	,	PUNCT
ejpam-6047	536	15	6047	6047	NUM
ejpam-6047	536	16	23	23	NUM
ejpam-6047	536	17	of	of	ADP
ejpam-6047	536	18	33	33	NUM
ejpam-6047	536	19	figure	figure	NOUN
ejpam-6047	536	20	5	5	NUM
ejpam-6047	536	21	:	:	PUNCT
ejpam-6047	536	22	spectral	spectral	ADJ
ejpam-6047	536	23	properties	property	NOUN
ejpam-6047	536	24	of	of	ADP
ejpam-6047	536	25	metzler	metzler	NOUN
ejpam-6047	536	26	matrix	matrix	NOUN
ejpam-6047	536	27	(	(	PUNCT
ejpam-6047	536	28	size	size	NOUN
ejpam-6047	536	29	=	=	SYM
ejpam-6047	536	30	50	50	NUM
ejpam-6047	536	31	)	)	PUNCT
ejpam-6047	536	32	in	in	ADP
ejpam-6047	536	33	example-3	example-3	PROPN
ejpam-6047	536	34	.	.	PUNCT
ejpam-6047	536	35	figure	figure	NOUN
ejpam-6047	536	36	6	6	NUM
ejpam-6047	536	37	:	:	PUNCT
ejpam-6047	536	38	eigenmode	eigenmode	ADJ
ejpam-6047	536	39	(	(	PUNCT
ejpam-6047	536	40	left	left	ADJ
ejpam-6047	536	41	)	)	PUNCT
ejpam-6047	536	42	and	and	CCONJ
ejpam-6047	536	43	inverse	inverse	NOUN
ejpam-6047	536	44	of	of	ADP
ejpam-6047	536	45	resolvent	resolvent	ADJ
ejpam-6047	536	46	norm	norm	NOUN
ejpam-6047	536	47	(	(	PUNCT
ejpam-6047	536	48	right	right	NOUN
ejpam-6047	536	49	)	)	PUNCT
ejpam-6047	536	50	of	of	ADP
ejpam-6047	536	51	metzler	metzler	NOUN
ejpam-6047	536	52	matrix	matrix	NOUN
ejpam-6047	536	53	(	(	PUNCT
ejpam-6047	536	54	size	size	NOUN
ejpam-6047	536	55	=	=	SYM
ejpam-6047	536	56	50	50	NUM
ejpam-6047	536	57	)	)	PUNCT
ejpam-6047	536	58	in	in	ADP
ejpam-6047	536	59	example-3	example-3	PROPN
ejpam-6047	536	60	m.u	m.u	PROPN
ejpam-6047	536	61	.	.	PROPN
ejpam-6047	536	62	rehman	rehman	PROPN
ejpam-6047	536	63	et	et	PROPN
ejpam-6047	536	64	al	al	PROPN
ejpam-6047	536	65	.	.	PUNCT
ejpam-6047	536	66	/	/	SYM
ejpam-6047	536	67	eur	eur	PROPN
ejpam-6047	536	68	.	.	PUNCT
ejpam-6047	537	1	j.	j.	PROPN
ejpam-6047	537	2	pure	pure	PROPN
ejpam-6047	537	3	appl	appl	PROPN
ejpam-6047	537	4	.	.	PROPN
ejpam-6047	537	5	math	math	PROPN
ejpam-6047	537	6	,	,	PUNCT
ejpam-6047	537	7	18	18	NUM
ejpam-6047	537	8	(	(	PUNCT
ejpam-6047	537	9	3	3	NUM
ejpam-6047	537	10	)	)	PUNCT
ejpam-6047	537	11	(	(	PUNCT
ejpam-6047	537	12	2025	2025	NUM
ejpam-6047	537	13	)	)	PUNCT
ejpam-6047	537	14	,	,	PUNCT
ejpam-6047	537	15	6047	6047	NUM
ejpam-6047	537	16	24	24	NUM
ejpam-6047	537	17	of	of	ADP
ejpam-6047	537	18	33	33	NUM
ejpam-6047	537	19	figure	figure	NOUN
ejpam-6047	537	20	7	7	NUM
ejpam-6047	537	21	:	:	PUNCT
ejpam-6047	537	22	spectral	spectral	ADJ
ejpam-6047	537	23	properties	property	NOUN
ejpam-6047	537	24	of	of	ADP
ejpam-6047	537	25	metzler	metzler	NOUN
ejpam-6047	537	26	matrix	matrix	NOUN
ejpam-6047	537	27	(	(	PUNCT
ejpam-6047	537	28	size	size	NOUN
ejpam-6047	537	29	=	=	SYM
ejpam-6047	537	30	100	100	NUM
ejpam-6047	537	31	)	)	PUNCT
ejpam-6047	537	32	in	in	ADP
ejpam-6047	537	33	example-3	example-3	PROPN
ejpam-6047	537	34	.	.	PUNCT
ejpam-6047	537	35	figure	figure	NOUN
ejpam-6047	537	36	8	8	NUM
ejpam-6047	537	37	:	:	PUNCT
ejpam-6047	537	38	eigenmode	eigenmode	PROPN
ejpam-6047	537	39	(	(	PUNCT
ejpam-6047	537	40	left	left	ADJ
ejpam-6047	537	41	)	)	PUNCT
ejpam-6047	537	42	and	and	CCONJ
ejpam-6047	537	43	inverse	inverse	NOUN
ejpam-6047	537	44	of	of	ADP
ejpam-6047	537	45	resolvent	resolvent	ADJ
ejpam-6047	537	46	norm	norm	NOUN
ejpam-6047	537	47	(	(	PUNCT
ejpam-6047	537	48	right	right	NOUN
ejpam-6047	537	49	)	)	PUNCT
ejpam-6047	537	50	of	of	ADP
ejpam-6047	537	51	metzler	metzler	NOUN
ejpam-6047	537	52	matrix	matrix	NOUN
ejpam-6047	537	53	(	(	PUNCT
ejpam-6047	537	54	size	size	NOUN
ejpam-6047	537	55	=	=	SYM
ejpam-6047	537	56	100	100	NUM
ejpam-6047	537	57	)	)	PUNCT
ejpam-6047	537	58	in	in	ADP
ejpam-6047	537	59	example-3	example-3	PROPN
ejpam-6047	537	60	m.u	m.u	PROPN
ejpam-6047	537	61	.	.	PROPN
ejpam-6047	537	62	rehman	rehman	PROPN
ejpam-6047	537	63	et	et	PROPN
ejpam-6047	537	64	al	al	PROPN
ejpam-6047	537	65	.	.	PUNCT
ejpam-6047	537	66	/	/	SYM
ejpam-6047	537	67	eur	eur	PROPN
ejpam-6047	537	68	.	.	PUNCT
ejpam-6047	538	1	j.	j.	PROPN
ejpam-6047	538	2	pure	pure	PROPN
ejpam-6047	538	3	appl	appl	PROPN
ejpam-6047	538	4	.	.	PROPN
ejpam-6047	538	5	math	math	PROPN
ejpam-6047	538	6	,	,	PUNCT
ejpam-6047	538	7	18	18	NUM
ejpam-6047	538	8	(	(	PUNCT
ejpam-6047	538	9	3	3	NUM
ejpam-6047	538	10	)	)	PUNCT
ejpam-6047	538	11	(	(	PUNCT
ejpam-6047	538	12	2025	2025	NUM
ejpam-6047	538	13	)	)	PUNCT
ejpam-6047	538	14	,	,	PUNCT
ejpam-6047	538	15	6047	6047	NUM
ejpam-6047	538	16	25	25	NUM
ejpam-6047	538	17	of	of	ADP
ejpam-6047	538	18	33	33	NUM
ejpam-6047	538	19	figure	figure	NOUN
ejpam-6047	538	20	9	9	NUM
ejpam-6047	538	21	:	:	PUNCT
ejpam-6047	538	22	spectral	spectral	ADJ
ejpam-6047	538	23	properties	property	NOUN
ejpam-6047	538	24	of	of	ADP
ejpam-6047	538	25	metzler	metzler	NOUN
ejpam-6047	538	26	matrix	matrix	NOUN
ejpam-6047	538	27	(	(	PUNCT
ejpam-6047	538	28	size	size	NOUN
ejpam-6047	538	29	=	=	SYM
ejpam-6047	538	30	500	500	NUM
ejpam-6047	538	31	)	)	PUNCT
ejpam-6047	538	32	in	in	ADP
ejpam-6047	538	33	example-3	example-3	PROPN
ejpam-6047	538	34	.	.	PUNCT
ejpam-6047	538	35	figure	figure	NOUN
ejpam-6047	538	36	10	10	NUM
ejpam-6047	538	37	:	:	PUNCT
ejpam-6047	538	38	eigenmode	eigenmode	PROPN
ejpam-6047	538	39	(	(	PUNCT
ejpam-6047	538	40	left	left	ADJ
ejpam-6047	538	41	)	)	PUNCT
ejpam-6047	538	42	and	and	CCONJ
ejpam-6047	538	43	inverse	inverse	NOUN
ejpam-6047	538	44	of	of	ADP
ejpam-6047	538	45	resolvent	resolvent	ADJ
ejpam-6047	538	46	norm	norm	NOUN
ejpam-6047	538	47	(	(	PUNCT
ejpam-6047	538	48	right	right	NOUN
ejpam-6047	538	49	)	)	PUNCT
ejpam-6047	538	50	of	of	ADP
ejpam-6047	538	51	metzler	metzler	NOUN
ejpam-6047	538	52	matrix	matrix	NOUN
ejpam-6047	538	53	(	(	PUNCT
ejpam-6047	538	54	size	size	NOUN
ejpam-6047	538	55	=	=	SYM
ejpam-6047	538	56	500	500	NUM
ejpam-6047	538	57	)	)	PUNCT
ejpam-6047	538	58	in	in	ADP
ejpam-6047	538	59	example-3	example-3	PROPN
ejpam-6047	538	60	m.u	m.u	PROPN
ejpam-6047	538	61	.	.	PROPN
ejpam-6047	538	62	rehman	rehman	PROPN
ejpam-6047	538	63	et	et	PROPN
ejpam-6047	538	64	al	al	PROPN
ejpam-6047	538	65	.	.	PUNCT
ejpam-6047	538	66	/	/	SYM
ejpam-6047	538	67	eur	eur	PROPN
ejpam-6047	538	68	.	.	PUNCT
ejpam-6047	539	1	j.	j.	PROPN
ejpam-6047	539	2	pure	pure	PROPN
ejpam-6047	539	3	appl	appl	PROPN
ejpam-6047	539	4	.	.	PROPN
ejpam-6047	539	5	math	math	PROPN
ejpam-6047	539	6	,	,	PUNCT
ejpam-6047	539	7	18	18	NUM
ejpam-6047	539	8	(	(	PUNCT
ejpam-6047	539	9	3	3	NUM
ejpam-6047	539	10	)	)	PUNCT
ejpam-6047	539	11	(	(	PUNCT
ejpam-6047	539	12	2025	2025	NUM
ejpam-6047	539	13	)	)	PUNCT
ejpam-6047	539	14	,	,	PUNCT
ejpam-6047	539	15	6047	6047	NUM
ejpam-6047	539	16	26	26	NUM
ejpam-6047	539	17	of	of	ADP
ejpam-6047	539	18	33	33	NUM
ejpam-6047	539	19	figure	figure	NOUN
ejpam-6047	539	20	11	11	NUM
ejpam-6047	539	21	:	:	PUNCT
ejpam-6047	539	22	spectral	spectral	ADJ
ejpam-6047	539	23	properties	property	NOUN
ejpam-6047	539	24	of	of	ADP
ejpam-6047	539	25	hurwitz	hurwitz	PROPN
ejpam-6047	539	26	matrix	matrix	NOUN
ejpam-6047	539	27	(	(	PUNCT
ejpam-6047	539	28	size	size	NOUN
ejpam-6047	539	29	=	=	SYM
ejpam-6047	539	30	50	50	NUM
ejpam-6047	539	31	)	)	PUNCT
ejpam-6047	539	32	in	in	ADP
ejpam-6047	539	33	example-4	example-4	PROPN
ejpam-6047	539	34	.	.	PUNCT
ejpam-6047	540	1	figure	figure	NOUN
ejpam-6047	540	2	12	12	NUM
ejpam-6047	540	3	:	:	PUNCT
ejpam-6047	540	4	eigenmode	eigenmode	ADJ
ejpam-6047	540	5	(	(	PUNCT
ejpam-6047	540	6	left	left	ADJ
ejpam-6047	540	7	)	)	PUNCT
ejpam-6047	540	8	and	and	CCONJ
ejpam-6047	540	9	inverse	inverse	NOUN
ejpam-6047	540	10	of	of	ADP
ejpam-6047	540	11	resolvent	resolvent	ADJ
ejpam-6047	540	12	norm	norm	NOUN
ejpam-6047	540	13	(	(	PUNCT
ejpam-6047	540	14	right	right	NOUN
ejpam-6047	540	15	)	)	PUNCT
ejpam-6047	540	16	of	of	ADP
ejpam-6047	540	17	hurwitz	hurwitz	PROPN
ejpam-6047	540	18	matrix	matrix	NOUN
ejpam-6047	540	19	(	(	PUNCT
ejpam-6047	540	20	size	size	NOUN
ejpam-6047	540	21	=	=	SYM
ejpam-6047	540	22	50	50	NUM
ejpam-6047	540	23	)	)	PUNCT
ejpam-6047	540	24	in	in	ADP
ejpam-6047	540	25	example-4	example-4	NUM
ejpam-6047	540	26	m.u	m.u	PROPN
ejpam-6047	540	27	.	.	PUNCT
ejpam-6047	541	1	rehman	rehman	PROPN
ejpam-6047	541	2	et	et	PROPN
ejpam-6047	541	3	al	al	PROPN
ejpam-6047	541	4	.	.	PUNCT
ejpam-6047	541	5	/	/	SYM
ejpam-6047	541	6	eur	eur	PROPN
ejpam-6047	541	7	.	.	PUNCT
ejpam-6047	542	1	j.	j.	PROPN
ejpam-6047	542	2	pure	pure	PROPN
ejpam-6047	542	3	appl	appl	PROPN
ejpam-6047	542	4	.	.	PROPN
ejpam-6047	542	5	math	math	PROPN
ejpam-6047	542	6	,	,	PUNCT
ejpam-6047	542	7	18	18	NUM
ejpam-6047	542	8	(	(	PUNCT
ejpam-6047	542	9	3	3	NUM
ejpam-6047	542	10	)	)	PUNCT
ejpam-6047	542	11	(	(	PUNCT
ejpam-6047	542	12	2025	2025	NUM
ejpam-6047	542	13	)	)	PUNCT
ejpam-6047	542	14	,	,	PUNCT
ejpam-6047	542	15	6047	6047	NUM
ejpam-6047	542	16	27	27	NUM
ejpam-6047	542	17	of	of	ADP
ejpam-6047	542	18	33	33	NUM
ejpam-6047	542	19	figure	figure	NOUN
ejpam-6047	542	20	13	13	NUM
ejpam-6047	542	21	:	:	PUNCT
ejpam-6047	542	22	spectral	spectral	ADJ
ejpam-6047	542	23	properties	property	NOUN
ejpam-6047	542	24	of	of	ADP
ejpam-6047	542	25	hurwitz	hurwitz	PROPN
ejpam-6047	542	26	matrix	matrix	NOUN
ejpam-6047	542	27	(	(	PUNCT
ejpam-6047	542	28	size	size	NOUN
ejpam-6047	542	29	=	=	SYM
ejpam-6047	542	30	100	100	NUM
ejpam-6047	542	31	)	)	PUNCT
ejpam-6047	542	32	in	in	ADP
ejpam-6047	542	33	example-4	example-4	PROPN
ejpam-6047	542	34	.	.	PUNCT
ejpam-6047	542	35	figure	figure	NOUN
ejpam-6047	542	36	14	14	NUM
ejpam-6047	542	37	:	:	PUNCT
ejpam-6047	542	38	eigenmode	eigenmode	PROPN
ejpam-6047	542	39	(	(	PUNCT
ejpam-6047	542	40	left	left	ADJ
ejpam-6047	542	41	)	)	PUNCT
ejpam-6047	542	42	and	and	CCONJ
ejpam-6047	542	43	inverse	inverse	NOUN
ejpam-6047	542	44	of	of	ADP
ejpam-6047	542	45	resolvent	resolvent	ADJ
ejpam-6047	542	46	norm	norm	NOUN
ejpam-6047	542	47	(	(	PUNCT
ejpam-6047	542	48	right	right	NOUN
ejpam-6047	542	49	)	)	PUNCT
ejpam-6047	542	50	of	of	ADP
ejpam-6047	542	51	hurwitz	hurwitz	PROPN
ejpam-6047	542	52	matrix	matrix	NOUN
ejpam-6047	542	53	(	(	PUNCT
ejpam-6047	542	54	size	size	NOUN
ejpam-6047	542	55	=	=	SYM
ejpam-6047	542	56	100	100	NUM
ejpam-6047	542	57	)	)	PUNCT
ejpam-6047	542	58	in	in	ADP
ejpam-6047	542	59	example-4	example-4	NUM
ejpam-6047	542	60	m.u	m.u	PROPN
ejpam-6047	542	61	.	.	PUNCT
ejpam-6047	543	1	rehman	rehman	PROPN
ejpam-6047	543	2	et	et	PROPN
ejpam-6047	543	3	al	al	PROPN
ejpam-6047	543	4	.	.	PUNCT
ejpam-6047	543	5	/	/	SYM
ejpam-6047	543	6	eur	eur	PROPN
ejpam-6047	543	7	.	.	PUNCT
ejpam-6047	544	1	j.	j.	PROPN
ejpam-6047	544	2	pure	pure	PROPN
ejpam-6047	544	3	appl	appl	PROPN
ejpam-6047	544	4	.	.	PROPN
ejpam-6047	544	5	math	math	PROPN
ejpam-6047	544	6	,	,	PUNCT
ejpam-6047	544	7	18	18	NUM
ejpam-6047	544	8	(	(	PUNCT
ejpam-6047	544	9	3	3	NUM
ejpam-6047	544	10	)	)	PUNCT
ejpam-6047	544	11	(	(	PUNCT
ejpam-6047	544	12	2025	2025	NUM
ejpam-6047	544	13	)	)	PUNCT
ejpam-6047	544	14	,	,	PUNCT
ejpam-6047	544	15	6047	6047	NUM
ejpam-6047	544	16	28	28	NUM
ejpam-6047	544	17	of	of	ADP
ejpam-6047	544	18	33	33	NUM
ejpam-6047	544	19	figure	figure	NOUN
ejpam-6047	544	20	15	15	NUM
ejpam-6047	544	21	:	:	PUNCT
ejpam-6047	544	22	spectral	spectral	ADJ
ejpam-6047	544	23	properties	property	NOUN
ejpam-6047	544	24	of	of	ADP
ejpam-6047	544	25	hurwitz	hurwitz	PROPN
ejpam-6047	544	26	matrix	matrix	NOUN
ejpam-6047	544	27	(	(	PUNCT
ejpam-6047	544	28	size	size	NOUN
ejpam-6047	544	29	=	=	SYM
ejpam-6047	544	30	500	500	NUM
ejpam-6047	544	31	)	)	PUNCT
ejpam-6047	544	32	in	in	ADP
ejpam-6047	544	33	example-4	example-4	PROPN
ejpam-6047	544	34	.	.	PUNCT
ejpam-6047	544	35	figure	figure	NOUN
ejpam-6047	544	36	16	16	NUM
ejpam-6047	544	37	:	:	PUNCT
ejpam-6047	544	38	eigenmode	eigenmode	PROPN
ejpam-6047	544	39	(	(	PUNCT
ejpam-6047	544	40	left	left	ADJ
ejpam-6047	544	41	)	)	PUNCT
ejpam-6047	544	42	and	and	CCONJ
ejpam-6047	544	43	inverse	inverse	NOUN
ejpam-6047	544	44	of	of	ADP
ejpam-6047	544	45	resolvent	resolvent	ADJ
ejpam-6047	544	46	norm	norm	NOUN
ejpam-6047	544	47	(	(	PUNCT
ejpam-6047	544	48	right	right	NOUN
ejpam-6047	544	49	)	)	PUNCT
ejpam-6047	544	50	of	of	ADP
ejpam-6047	544	51	hurwitz	hurwitz	PROPN
ejpam-6047	544	52	matrix	matrix	NOUN
ejpam-6047	544	53	(	(	PUNCT
ejpam-6047	544	54	size	size	NOUN
ejpam-6047	544	55	=	=	SYM
ejpam-6047	544	56	500	500	NUM
ejpam-6047	544	57	)	)	PUNCT
ejpam-6047	544	58	in	in	ADP
ejpam-6047	544	59	example-4	example-4	NUM
ejpam-6047	544	60	m.u	m.u	PROPN
ejpam-6047	544	61	.	.	PUNCT
ejpam-6047	545	1	rehman	rehman	PROPN
ejpam-6047	545	2	et	et	PROPN
ejpam-6047	545	3	al	al	PROPN
ejpam-6047	545	4	.	.	PUNCT
ejpam-6047	545	5	/	/	SYM
ejpam-6047	545	6	eur	eur	PROPN
ejpam-6047	545	7	.	.	PUNCT
ejpam-6047	546	1	j.	j.	PROPN
ejpam-6047	546	2	pure	pure	PROPN
ejpam-6047	546	3	appl	appl	PROPN
ejpam-6047	546	4	.	.	PROPN
ejpam-6047	546	5	math	math	PROPN
ejpam-6047	546	6	,	,	PUNCT
ejpam-6047	546	7	18	18	NUM
ejpam-6047	546	8	(	(	PUNCT
ejpam-6047	546	9	3	3	NUM
ejpam-6047	546	10	)	)	PUNCT
ejpam-6047	546	11	(	(	PUNCT
ejpam-6047	546	12	2025	2025	NUM
ejpam-6047	546	13	)	)	PUNCT
ejpam-6047	546	14	,	,	PUNCT
ejpam-6047	546	15	6047	6047	NUM
ejpam-6047	546	16	29	29	NUM
ejpam-6047	546	17	of	of	ADP
ejpam-6047	546	18	33	33	NUM
ejpam-6047	546	19	6	6	NUM
ejpam-6047	546	20	.	.	PUNCT
ejpam-6047	546	21	applications	application	NOUN
ejpam-6047	546	22	1	1	NUM
ejpam-6047	546	23	.	.	PUNCT
ejpam-6047	546	24	mathematical	mathematical	ADJ
ejpam-6047	546	25	modeling	modeling	NOUN
ejpam-6047	546	26	:	:	PUNCT
ejpam-6047	546	27	the	the	DET
ejpam-6047	546	28	metzler	metzler	NOUN
ejpam-6047	546	29	matrices	matrix	NOUN
ejpam-6047	546	30	play	play	VERB
ejpam-6047	546	31	an	an	DET
ejpam-6047	546	32	important	important	ADJ
ejpam-6047	546	33	role	role	NOUN
ejpam-6047	546	34	for	for	ADP
ejpam-6047	546	35	mathematical	mathematical	ADJ
ejpam-6047	546	36	modeling	modeling	NOUN
ejpam-6047	546	37	of	of	ADP
ejpam-6047	546	38	various	various	ADJ
ejpam-6047	546	39	problems	problem	NOUN
ejpam-6047	546	40	,	,	PUNCT
ejpam-6047	546	41	see	see	VERB
ejpam-6047	546	42	[	[	X
ejpam-6047	546	43	59–61	59–61	NUM
ejpam-6047	546	44	]	]	PUNCT
ejpam-6047	546	45	.	.	PUNCT
ejpam-6047	547	1	for	for	ADP
ejpam-6047	547	2	an	an	DET
ejpam-6047	547	3	input	input	NOUN
ejpam-6047	547	4	data	data	NOUN
ejpam-6047	547	5	vector	vector	NOUN
ejpam-6047	547	6	x(t	x(t	PROPN
ejpam-6047	547	7	)	)	PUNCT
ejpam-6047	547	8	∈	∈	PROPN
ejpam-6047	547	9	rn,1	rn,1	PROPN
ejpam-6047	547	10	,	,	PUNCT
ejpam-6047	547	11	the	the	DET
ejpam-6047	547	12	most	most	ADV
ejpam-6047	547	13	common	common	ADJ
ejpam-6047	547	14	problem	problem	NOUN
ejpam-6047	547	15	is	be	AUX
ejpam-6047	547	16	to	to	PART
ejpam-6047	547	17	analyze	analyze	VERB
ejpam-6047	547	18	the	the	DET
ejpam-6047	547	19	given	give	VERB
ejpam-6047	547	20	linear	linear	NOUN
ejpam-6047	547	21	system	system	NOUN
ejpam-6047	547	22	having	have	VERB
ejpam-6047	547	23	the	the	DET
ejpam-6047	547	24	form	form	NOUN
ejpam-6047	547	25	dx(t	dx(t	NOUN
ejpam-6047	547	26	)	)	PUNCT
ejpam-6047	547	27	dt	dt	NOUN
ejpam-6047	547	28	=	=	SYM
ejpam-6047	547	29	ax(t	ax(t	NUM
ejpam-6047	547	30	)	)	PUNCT
ejpam-6047	547	31	,	,	PUNCT
ejpam-6047	547	32	with	with	ADP
ejpam-6047	547	33	a	a	PRON
ejpam-6047	547	34	being	be	AUX
ejpam-6047	547	35	a	a	DET
ejpam-6047	547	36	metzler	metzler	NOUN
ejpam-6047	547	37	matrix	matrix	NOUN
ejpam-6047	547	38	.	.	PUNCT
ejpam-6047	548	1	the	the	DET
ejpam-6047	548	2	analysis	analysis	NOUN
ejpam-6047	548	3	on	on	ADP
ejpam-6047	548	4	positive	positive	ADJ
ejpam-6047	548	5	linear	linear	NOUN
ejpam-6047	548	6	switching	switch	VERB
ejpam-6047	548	7	systems	system	NOUN
ejpam-6047	548	8	also	also	ADV
ejpam-6047	548	9	play	play	VERB
ejpam-6047	548	10	an	an	DET
ejpam-6047	548	11	important	important	ADJ
ejpam-6047	548	12	and	and	CCONJ
ejpam-6047	548	13	vital	vital	ADJ
ejpam-6047	548	14	role	role	NOUN
ejpam-6047	548	15	to	to	ADP
ejpam-6047	548	16	the	the	DET
ejpam-6047	548	17	mathematical	mathematical	ADJ
ejpam-6047	548	18	modeling	modeling	NOUN
ejpam-6047	548	19	.	.	PUNCT
ejpam-6047	549	1	an	an	DET
ejpam-6047	549	2	extensive	extensive	ADJ
ejpam-6047	549	3	amount	amount	NOUN
ejpam-6047	549	4	of	of	ADP
ejpam-6047	549	5	research	research	NOUN
ejpam-6047	549	6	work	work	NOUN
ejpam-6047	549	7	has	have	AUX
ejpam-6047	549	8	already	already	ADV
ejpam-6047	549	9	been	be	AUX
ejpam-6047	549	10	done	do	VERB
ejpam-6047	549	11	in	in	ADP
ejpam-6047	549	12	this	this	DET
ejpam-6047	549	13	directions	direction	NOUN
ejpam-6047	549	14	,	,	PUNCT
ejpam-6047	549	15	see	see	VERB
ejpam-6047	549	16	[	[	X
ejpam-6047	549	17	18	18	NUM
ejpam-6047	549	18	,	,	PUNCT
ejpam-6047	549	19	62	62	NUM
ejpam-6047	549	20	,	,	PUNCT
ejpam-6047	549	21	63	63	NUM
ejpam-6047	549	22	]	]	PUNCT
ejpam-6047	549	23	.	.	PUNCT
ejpam-6047	550	1	2	2	X
ejpam-6047	550	2	.	.	X
ejpam-6047	550	3	dynamics	dynamic	NOUN
ejpam-6047	550	4	of	of	ADP
ejpam-6047	550	5	love	love	NOUN
ejpam-6047	550	6	:	:	PUNCT
ejpam-6047	550	7	a	a	DET
ejpam-6047	550	8	mathematical	mathematical	ADJ
ejpam-6047	550	9	model	model	NOUN
ejpam-6047	550	10	was	be	AUX
ejpam-6047	550	11	proposed	propose	VERB
ejpam-6047	550	12	by	by	ADP
ejpam-6047	550	13	s.	s.	PROPN
ejpam-6047	550	14	rinaldi	rinaldi	PROPN
ejpam-6047	551	1	[	[	X
ejpam-6047	551	2	64	64	NUM
ejpam-6047	551	3	]	]	PUNCT
ejpam-6047	551	4	to	to	PART
ejpam-6047	551	5	describe	describe	VERB
ejpam-6047	551	6	the	the	DET
ejpam-6047	551	7	dynamics	dynamic	NOUN
ejpam-6047	551	8	of	of	ADP
ejpam-6047	551	9	love	love	NOUN
ejpam-6047	551	10	of	of	ADP
ejpam-6047	551	11	laura	laura	PROPN
ejpam-6047	551	12	de	de	ADP
ejpam-6047	551	13	noves	noves	PROPN
ejpam-6047	551	14	and	and	CCONJ
ejpam-6047	551	15	petrarch	petrarch	PROPN
ejpam-6047	551	16	,	,	PUNCT
ejpam-6047	551	17	which	which	PRON
ejpam-6047	551	18	leads	lead	VERB
ejpam-6047	551	19	to	to	ADP
ejpam-6047	551	20	a	a	DET
ejpam-6047	551	21	periodic	periodic	ADJ
ejpam-6047	551	22	dynamics	dynamic	NOUN
ejpam-6047	551	23	.	.	PUNCT
ejpam-6047	552	1	for	for	ADP
ejpam-6047	552	2	the	the	DET
ejpam-6047	552	3	implementation	implementation	NOUN
ejpam-6047	552	4	of	of	ADP
ejpam-6047	552	5	model	model	NOUN
ejpam-6047	552	6	,	,	PUNCT
ejpam-6047	552	7	23	23	NUM
ejpam-6047	552	8	dated	date	VERB
ejpam-6047	552	9	poems	poem	NOUN
ejpam-6047	552	10	out	out	ADP
ejpam-6047	552	11	of	of	ADP
ejpam-6047	552	12	366	366	NUM
ejpam-6047	552	13	poems	poem	NOUN
ejpam-6047	552	14	petrarch	petrarch	NOUN
ejpam-6047	552	15	wrote	write	VERB
ejpam-6047	552	16	in	in	ADP
ejpam-6047	552	17	canzoniere	canzoniere	NOUN
ejpam-6047	552	18	during	during	ADP
ejpam-6047	552	19	21	21	NUM
ejpam-6047	552	20	years	year	NOUN
ejpam-6047	552	21	were	be	AUX
ejpam-6047	552	22	analyzed	analyze	VERB
ejpam-6047	552	23	,	,	PUNCT
ejpam-6047	552	24	see	see	VERB
ejpam-6047	552	25	[	[	X
ejpam-6047	552	26	65	65	NUM
ejpam-6047	552	27	]	]	X
ejpam-6047	552	28	.	.	PUNCT
ejpam-6047	553	1	rinaldi	rinaldi	PROPN
ejpam-6047	553	2	’s	’s	PART
ejpam-6047	553	3	model	model	NOUN
ejpam-6047	553	4	describes	describe	VERB
ejpam-6047	553	5	love	love	VERB
ejpam-6047	553	6	dynamic	dynamic	ADJ
ejpam-6047	553	7	in	in	ADP
ejpam-6047	553	8	three	three	NUM
ejpam-6047	553	9	variables	variable	NOUN
ejpam-6047	553	10	,	,	PUNCT
ejpam-6047	553	11	l	l	NOUN
ejpam-6047	553	12	denotes	denote	NOUN
ejpam-6047	553	13	love	love	VERB
ejpam-6047	553	14	of	of	ADP
ejpam-6047	553	15	laura	laura	NOUN
ejpam-6047	553	16	for	for	ADP
ejpam-6047	553	17	petrarch	petrarch	PROPN
ejpam-6047	553	18	,	,	PUNCT
ejpam-6047	553	19	p	p	NOUN
ejpam-6047	553	20	denotes	denote	NOUN
ejpam-6047	553	21	love	love	VERB
ejpam-6047	553	22	of	of	ADP
ejpam-6047	553	23	petrarch	petrarch	NOUN
ejpam-6047	553	24	for	for	ADP
ejpam-6047	553	25	laura	laura	NOUN
ejpam-6047	553	26	,	,	PUNCT
ejpam-6047	553	27	and	and	CCONJ
ejpam-6047	553	28	z	z	NOUN
ejpam-6047	553	29	denotes	denote	VERB
ejpam-6047	553	30	the	the	DET
ejpam-6047	553	31	poetic	poetic	ADJ
ejpam-6047	553	32	inspiration	inspiration	NOUN
ejpam-6047	553	33	.	.	PUNCT
ejpam-6047	554	1	the	the	DET
ejpam-6047	554	2	mathematical	mathematical	ADJ
ejpam-6047	554	3	model	model	NOUN
ejpam-6047	554	4	is:	is:	PROPN
ejpam-6047	554	5	d	d	PROPN
ejpam-6047	554	6	dt(l(t	dt(l(t	NOUN
ejpam-6047	554	7	)	)	PUNCT
ejpam-6047	554	8	)	)	PUNCT
ejpam-6047	555	1	=	=	PUNCT
ejpam-6047	555	2	−α1l(t	−α1l(t	PROPN
ejpam-6047	555	3	)	)	PUNCT
ejpam-6047	556	1	+	+	NUM
ejpam-6047	556	2	rl(p	rl(p	X
ejpam-6047	556	3	(	(	PUNCT
ejpam-6047	556	4	t	t	NOUN
ejpam-6047	556	5	)	)	PUNCT
ejpam-6047	556	6	)	)	PUNCT
ejpam-6047	557	1	+	+	CCONJ
ejpam-6047	557	2	ap	ap	PROPN
ejpam-6047	557	3	d	d	PROPN
ejpam-6047	557	4	dt(p	dt(p	X
ejpam-6047	557	5	(	(	PUNCT
ejpam-6047	557	6	t	t	NOUN
ejpam-6047	557	7	)	)	PUNCT
ejpam-6047	557	8	)	)	PUNCT
ejpam-6047	558	1	=	=	SYM
ejpam-6047	558	2	−α2p	−α2p	PROPN
ejpam-6047	558	3	(	(	PUNCT
ejpam-6047	558	4	t	t	PROPN
ejpam-6047	558	5	)	)	PUNCT
ejpam-6047	559	1	+	+	CCONJ
ejpam-6047	559	2	rp	rp	NOUN
ejpam-6047	559	3	(	(	PUNCT
ejpam-6047	559	4	l(t	l(t	PROPN
ejpam-6047	559	5	)	)	PUNCT
ejpam-6047	559	6	)	)	PUNCT
ejpam-6047	559	7	+	+	CCONJ
ejpam-6047	559	8	β2al(z(t	β2al(z(t	NOUN
ejpam-6047	559	9	)	)	PUNCT
ejpam-6047	559	10	)	)	PUNCT
ejpam-6047	559	11	d	d	X
ejpam-6047	559	12	dtz(t	dtz(t	PROPN
ejpam-6047	559	13	)	)	PUNCT
ejpam-6047	559	14	=	=	SYM
ejpam-6047	559	15	−α3z(t	−α3z(t	NOUN
ejpam-6047	559	16	)	)	PUNCT
ejpam-6047	560	1	+	+	NUM
ejpam-6047	560	2	β4p	β4p	SYM
ejpam-6047	560	3	(	(	PUNCT
ejpam-6047	560	4	t	t	PROPN
ejpam-6047	560	5	)	)	PUNCT
ejpam-6047	560	6	,	,	PUNCT
ejpam-6047	560	7	where	where	SCONJ
ejpam-6047	560	8	all	all	DET
ejpam-6047	560	9	parameters	parameter	NOUN
ejpam-6047	560	10	involved	involve	VERB
ejpam-6047	560	11	are	be	AUX
ejpam-6047	560	12	defined	define	VERB
ejpam-6047	560	13	and	and	CCONJ
ejpam-6047	560	14	described	describe	VERB
ejpam-6047	560	15	in	in	ADP
ejpam-6047	560	16	[	[	X
ejpam-6047	560	17	65	65	NUM
ejpam-6047	560	18	]	]	PUNCT
ejpam-6047	560	19	.	.	PUNCT
ejpam-6047	561	1	this	this	DET
ejpam-6047	561	2	love	love	NOUN
ejpam-6047	561	3	model	model	NOUN
ejpam-6047	561	4	can	can	AUX
ejpam-6047	561	5	be	be	AUX
ejpam-6047	561	6	expressed	express	VERB
ejpam-6047	561	7	as	as	ADP
ejpam-6047	561	8	dx(t	dx(t	NOUN
ejpam-6047	561	9	)	)	PUNCT
ejpam-6047	561	10	dt	dt	NOUN
ejpam-6047	562	1	=	=	SYM
ejpam-6047	562	2	a0x(t	a0x(t	PROPN
ejpam-6047	562	3	)	)	PUNCT
ejpam-6047	563	1	+	+	NUM
ejpam-6047	563	2	b	b	X
ejpam-6047	563	3	=	=	SYM
ejpam-6047	563	4	ϕ(t	ϕ(t	NUM
ejpam-6047	563	5	)	)	PUNCT
ejpam-6047	563	6	,	,	PUNCT
ejpam-6047	563	7	where	where	SCONJ
ejpam-6047	563	8	a0	a0	PROPN
ejpam-6047	563	9	=	=	SYM
ejpam-6047	563	10	−α1	−α1	NUM
ejpam-6047	563	11	0	0	NUM
ejpam-6047	563	12	0	0	NUM
ejpam-6047	563	13	0	0	NUM
ejpam-6047	563	14	−α2	−α2	PROPN
ejpam-6047	563	15	−β3	−β3	NOUN
ejpam-6047	563	16	0	0	NUM
ejpam-6047	563	17	β4	β4	PROPN
ejpam-6047	563	18	−α3	−α3	PROPN
ejpam-6047	563	19			NOUN
ejpam-6047	563	20	;	;	PUNCT
ejpam-6047	563	21	b	b	X
ejpam-6047	563	22	=	=	SYM
ejpam-6047	563	23	β1β2	β1β2	NOUN
ejpam-6047	563	24	0	0	NUM
ejpam-6047	563	25			NOUN
ejpam-6047	563	26	;	;	PUNCT
ejpam-6047	563	27	ϕ(t	ϕ(t	NUM
ejpam-6047	563	28	)	)	PUNCT
ejpam-6047	564	1	=	=	PUNCT
ejpam-6047	565	1	[	[	X
ejpam-6047	565	2	rl(p	rl(p	X
ejpam-6047	565	3	(	(	PUNCT
ejpam-6047	565	4	t	t	NOUN
ejpam-6047	565	5	)	)	PUNCT
ejpam-6047	565	6	,	,	PUNCT
ejpam-6047	565	7	0	0	NUM
ejpam-6047	565	8	,	,	PUNCT
ejpam-6047	565	9	0)]t	0)]t	NUM
ejpam-6047	565	10	.	.	PUNCT
ejpam-6047	566	1	for	for	ADP
ejpam-6047	566	2	a	a	DET
ejpam-6047	566	3	matrix	matrix	NOUN
ejpam-6047	566	4	q̃	q̃	PROPN
ejpam-6047	566	5	,	,	PUNCT
ejpam-6047	566	6	and	and	CCONJ
ejpam-6047	566	7	using	use	VERB
ejpam-6047	566	8	matrix	matrix	NOUN
ejpam-6047	566	9	a0	a0	NOUN
ejpam-6047	566	10	,	,	PUNCT
ejpam-6047	566	11	one	one	PRON
ejpam-6047	566	12	can	can	AUX
ejpam-6047	566	13	have	have	VERB
ejpam-6047	566	14	that	that	DET
ejpam-6047	566	15	a	a	DET
ejpam-6047	566	16	=	=	SYM
ejpam-6047	566	17	q̃a0q̃	q̃a0q̃	NOUN
ejpam-6047	566	18	,	,	PUNCT
ejpam-6047	566	19	where	where	SCONJ
ejpam-6047	566	20	the	the	DET
ejpam-6047	566	21	matrix	matrix	NOUN
ejpam-6047	566	22	a	a	PRON
ejpam-6047	566	23	is	be	AUX
ejpam-6047	566	24	same	same	ADJ
ejpam-6047	566	25	as	as	ADP
ejpam-6047	566	26	metzler	metzler	NOUN
ejpam-6047	566	27	matrix	matrix	NOUN
ejpam-6047	566	28	.	.	PUNCT
ejpam-6047	567	1	thus	thus	ADV
ejpam-6047	567	2	,	,	PUNCT
ejpam-6047	567	3	finally	finally	ADV
ejpam-6047	567	4	,	,	PUNCT
ejpam-6047	567	5	the	the	DET
ejpam-6047	567	6	analysis	analysis	NOUN
ejpam-6047	567	7	on	on	ADP
ejpam-6047	567	8	a	a	PRON
ejpam-6047	567	9	can	can	AUX
ejpam-6047	567	10	lead	lead	VERB
ejpam-6047	567	11	to	to	ADP
ejpam-6047	567	12	interesting	interesting	ADJ
ejpam-6047	567	13	results	result	NOUN
ejpam-6047	567	14	for	for	ADP
ejpam-6047	567	15	the	the	DET
ejpam-6047	567	16	love	love	NOUN
ejpam-6047	567	17	dynamic	dynamic	ADJ
ejpam-6047	567	18	model	model	NOUN
ejpam-6047	567	19	.	.	PUNCT
ejpam-6047	568	1	7	7	X
ejpam-6047	568	2	.	.	X
ejpam-6047	568	3	conclusion	conclusion	NOUN
ejpam-6047	568	4	in	in	ADP
ejpam-6047	568	5	this	this	DET
ejpam-6047	568	6	paper	paper	NOUN
ejpam-6047	568	7	,	,	PUNCT
ejpam-6047	568	8	we	we	PRON
ejpam-6047	568	9	have	have	AUX
ejpam-6047	568	10	studied	study	VERB
ejpam-6047	568	11	and	and	CCONJ
ejpam-6047	568	12	analyzed	analyze	VERB
ejpam-6047	568	13	mathematical	mathematical	ADJ
ejpam-6047	568	14	problems	problem	NOUN
ejpam-6047	568	15	related	relate	VERB
ejpam-6047	568	16	to	to	ADP
ejpam-6047	568	17	positive	positive	ADJ
ejpam-6047	568	18	linear	linear	ADJ
ejpam-6047	568	19	time	time	NOUN
ejpam-6047	568	20	-	-	PUNCT
ejpam-6047	568	21	invariant	invariant	ADJ
ejpam-6047	568	22	systems	system	NOUN
ejpam-6047	568	23	whose	whose	DET
ejpam-6047	568	24	coefficient	coefficient	ADJ
ejpam-6047	568	25	matrices	matrix	NOUN
ejpam-6047	568	26	are	be	AUX
ejpam-6047	568	27	metzler	metzler	NOUN
ejpam-6047	568	28	and	and	CCONJ
ejpam-6047	568	29	hurwitz	hurwitz	PROPN
ejpam-6047	568	30	matrices	matrix	NOUN
ejpam-6047	568	31	.	.	PUNCT
ejpam-6047	569	1	we	we	PRON
ejpam-6047	569	2	have	have	AUX
ejpam-6047	569	3	established	establish	VERB
ejpam-6047	569	4	and	and	CCONJ
ejpam-6047	569	5	presented	present	VERB
ejpam-6047	569	6	some	some	DET
ejpam-6047	569	7	new	new	ADJ
ejpam-6047	569	8	theoretical	theoretical	ADJ
ejpam-6047	569	9	results	result	NOUN
ejpam-6047	569	10	on	on	ADP
ejpam-6047	569	11	stability	stability	NOUN
ejpam-6047	569	12	,	,	PUNCT
ejpam-6047	569	13	d	d	NOUN
ejpam-6047	569	14	-	-	NOUN
ejpam-6047	569	15	stability	stability	NOUN
ejpam-6047	569	16	,	,	PUNCT
ejpam-6047	569	17	and	and	CCONJ
ejpam-6047	569	18	strong	strong	ADJ
ejpam-6047	569	19	d	d	NOUN
ejpam-6047	569	20	-	-	NOUN
ejpam-6047	569	21	stability	stability	NOUN
ejpam-6047	569	22	to	to	ADP
ejpam-6047	569	23	the	the	DET
ejpam-6047	569	24	following	follow	VERB
ejpam-6047	569	25	three	three	NUM
ejpam-6047	569	26	mathematical	mathematical	ADJ
ejpam-6047	569	27	problems	problem	NOUN
ejpam-6047	569	28	:	:	PUNCT
ejpam-6047	569	29	problem	problem	NOUN
ejpam-6047	569	30	-	-	PUNCT
ejpam-6047	569	31	i	i	NOUN
ejpam-6047	569	32	:	:	PUNCT
ejpam-6047	569	33	to	to	PART
ejpam-6047	569	34	extend	extend	VERB
ejpam-6047	569	35	and	and	CCONJ
ejpam-6047	569	36	construct	construct	VERB
ejpam-6047	569	37	some	some	DET
ejpam-6047	569	38	recent	recent	ADJ
ejpam-6047	569	39	findings	finding	NOUN
ejpam-6047	569	40	on	on	ADP
ejpam-6047	569	41	stability	stability	NOUN
ejpam-6047	569	42	,	,	PUNCT
ejpam-6047	569	43	d	d	NOUN
ejpam-6047	569	44	-	-	PUNCT
ejpam-6047	569	45	stability	stability	NOUN
ejpam-6047	569	46	and	and	CCONJ
ejpam-6047	569	47	strong	strong	ADJ
ejpam-6047	569	48	d	d	NOUN
ejpam-6047	569	49	-	-	PUNCT
ejpam-6047	569	50	stability	stability	NOUN
ejpam-6047	569	51	analysis	analysis	NOUN
ejpam-6047	569	52	of	of	ADP
ejpam-6047	569	53	lti	lti	PROPN
ejpam-6047	569	54	system	system	PROPN
ejpam-6047	569	55	dx(t	dx(t	NOUN
ejpam-6047	569	56	)	)	PUNCT
ejpam-6047	569	57	dt	dt	NOUN
ejpam-6047	569	58	=	=	SYM
ejpam-6047	569	59	ax(t	ax(t	NUM
ejpam-6047	569	60	)	)	PUNCT
ejpam-6047	569	61	,	,	PUNCT
ejpam-6047	569	62	where	where	SCONJ
ejpam-6047	569	63	x(t	x(t	PROPN
ejpam-6047	569	64	)	)	PUNCT
ejpam-6047	569	65	∈	∈	PROPN
ejpam-6047	569	66	rn,1	rn,1	PROPN
ejpam-6047	569	67	,	,	PUNCT
ejpam-6047	569	68	a	a	DET
ejpam-6047	569	69	∈	∈	PROPN
ejpam-6047	569	70	rn	rn	PROPN
ejpam-6047	569	71	,	,	PUNCT
ejpam-6047	569	72	n	n	CCONJ
ejpam-6047	569	73	,	,	PUNCT
ejpam-6047	569	74	with	with	ADP
ejpam-6047	569	75	a	a	DET
ejpam-6047	569	76	a	a	DET
ejpam-6047	569	77	metzler	metzler	NOUN
ejpam-6047	569	78	and	and	CCONJ
ejpam-6047	569	79	hurwitz	hurwitz	PROPN
ejpam-6047	569	80	matrix	matrix	NOUN
ejpam-6047	569	81	.	.	PUNCT
ejpam-6047	570	1	m.u	m.u	PROPN
ejpam-6047	570	2	.	.	PROPN
ejpam-6047	570	3	rehman	rehman	PROPN
ejpam-6047	570	4	et	et	PROPN
ejpam-6047	570	5	al	al	PROPN
ejpam-6047	570	6	.	.	PUNCT
ejpam-6047	570	7	/	/	SYM
ejpam-6047	570	8	eur	eur	PROPN
ejpam-6047	570	9	.	.	PUNCT
ejpam-6047	571	1	j.	j.	PROPN
ejpam-6047	571	2	pure	pure	PROPN
ejpam-6047	571	3	appl	appl	PROPN
ejpam-6047	571	4	.	.	PROPN
ejpam-6047	571	5	math	math	PROPN
ejpam-6047	571	6	,	,	PUNCT
ejpam-6047	571	7	18	18	NUM
ejpam-6047	571	8	(	(	PUNCT
ejpam-6047	571	9	3	3	NUM
ejpam-6047	571	10	)	)	PUNCT
ejpam-6047	571	11	(	(	PUNCT
ejpam-6047	571	12	2025	2025	NUM
ejpam-6047	571	13	)	)	PUNCT
ejpam-6047	571	14	,	,	PUNCT
ejpam-6047	571	15	6047	6047	NUM
ejpam-6047	571	16	30	30	NUM
ejpam-6047	571	17	of	of	ADP
ejpam-6047	571	18	33	33	NUM
ejpam-6047	571	19	problem	problem	NOUN
ejpam-6047	571	20	-	-	PUNCT
ejpam-6047	571	21	ii	ii	NOUN
ejpam-6047	571	22	:	:	PUNCT
ejpam-6047	571	23	to	to	PART
ejpam-6047	571	24	extend	extend	VERB
ejpam-6047	571	25	and	and	CCONJ
ejpam-6047	571	26	construct	construct	VERB
ejpam-6047	571	27	some	some	DET
ejpam-6047	571	28	new	new	ADJ
ejpam-6047	571	29	findings	finding	NOUN
ejpam-6047	571	30	on	on	ADP
ejpam-6047	571	31	stability	stability	NOUN
ejpam-6047	571	32	,	,	PUNCT
ejpam-6047	571	33	d	d	NOUN
ejpam-6047	571	34	-	-	PUNCT
ejpam-6047	571	35	stability	stability	NOUN
ejpam-6047	571	36	and	and	CCONJ
ejpam-6047	571	37	strong	strong	ADJ
ejpam-6047	571	38	d	d	NOUN
ejpam-6047	571	39	-	-	PUNCT
ejpam-6047	571	40	stability	stability	NOUN
ejpam-6047	571	41	analysis	analysis	NOUN
ejpam-6047	571	42	of	of	ADP
ejpam-6047	571	43	lti	lti	PROPN
ejpam-6047	571	44	system	system	PROPN
ejpam-6047	571	45	dx(t	dx(t	NOUN
ejpam-6047	571	46	)	)	PUNCT
ejpam-6047	571	47	dt	dt	NOUN
ejpam-6047	572	1	=	=	SYM
ejpam-6047	572	2	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	572	3	)	)	PUNCT
ejpam-6047	572	4	,	,	PUNCT
ejpam-6047	572	5	where	where	SCONJ
ejpam-6047	572	6	x(t	x(t	PROPN
ejpam-6047	572	7	)	)	PUNCT
ejpam-6047	572	8	∈	∈	PROPN
ejpam-6047	572	9	rn,1	rn,1	PROPN
ejpam-6047	572	10	,	,	PUNCT
ejpam-6047	572	11	a(t	a(t	NOUN
ejpam-6047	572	12	)	)	PUNCT
ejpam-6047	572	13	∈	∈	PROPN
ejpam-6047	572	14	{	{	PUNCT
ejpam-6047	572	15	a1	a1	NOUN
ejpam-6047	572	16	,	,	PUNCT
ejpam-6047	572	17	a2	a2	PROPN
ejpam-6047	572	18	}	}	PUNCT
ejpam-6047	572	19	,	,	PUNCT
ejpam-6047	572	20	with	with	ADP
ejpam-6047	572	21	a1	a1	NOUN
ejpam-6047	572	22	,	,	PUNCT
ejpam-6047	572	23	a2	a2	NOUN
ejpam-6047	572	24	being	be	AUX
ejpam-6047	572	25	asymptotically	asymptotically	ADV
ejpam-6047	572	26	stable	stable	ADJ
ejpam-6047	572	27	matrices	matrix	NOUN
ejpam-6047	572	28	.	.	PUNCT
ejpam-6047	573	1	problem	problem	NOUN
ejpam-6047	573	2	-	-	PUNCT
ejpam-6047	573	3	iii	iii	NOUN
ejpam-6047	573	4	:	:	PUNCT
ejpam-6047	573	5	to	to	PART
ejpam-6047	573	6	extend	extend	VERB
ejpam-6047	573	7	and	and	CCONJ
ejpam-6047	573	8	construct	construct	VERB
ejpam-6047	573	9	some	some	DET
ejpam-6047	573	10	new	new	ADJ
ejpam-6047	573	11	findings	finding	NOUN
ejpam-6047	573	12	on	on	ADP
ejpam-6047	573	13	stability	stability	NOUN
ejpam-6047	573	14	,	,	PUNCT
ejpam-6047	573	15	d	d	NOUN
ejpam-6047	573	16	-	-	PUNCT
ejpam-6047	573	17	stability	stability	NOUN
ejpam-6047	573	18	and	and	CCONJ
ejpam-6047	573	19	strong	strong	ADJ
ejpam-6047	573	20	d	d	NOUN
ejpam-6047	573	21	-	-	PUNCT
ejpam-6047	573	22	stability	stability	NOUN
ejpam-6047	573	23	analysis	analysis	NOUN
ejpam-6047	573	24	of	of	ADP
ejpam-6047	573	25	lti	lti	PROPN
ejpam-6047	573	26	system	system	PROPN
ejpam-6047	573	27	dx(t	dx(t	NOUN
ejpam-6047	573	28	)	)	PUNCT
ejpam-6047	573	29	dt	dt	NOUN
ejpam-6047	573	30	=	=	SYM
ejpam-6047	573	31	a(t)x(t	a(t)x(t	PROPN
ejpam-6047	573	32	)	)	PUNCT
ejpam-6047	573	33	,	,	PUNCT
ejpam-6047	573	34	where	where	SCONJ
ejpam-6047	573	35	x(t	x(t	PROPN
ejpam-6047	573	36	)	)	PUNCT
ejpam-6047	573	37	∈	∈	PROPN
ejpam-6047	573	38	rn,1	rn,1	PROPN
ejpam-6047	573	39	,	,	PUNCT
ejpam-6047	573	40	a(t	a(t	NOUN
ejpam-6047	573	41	)	)	PUNCT
ejpam-6047	573	42	∈	∈	PROPN
ejpam-6047	573	43	{	{	PUNCT
ejpam-6047	573	44	d1a1	d1a1	NOUN
ejpam-6047	573	45	,	,	PUNCT
ejpam-6047	573	46	d2a2	d2a2	NOUN
ejpam-6047	573	47	}	}	PUNCT
ejpam-6047	573	48	,	,	PUNCT
ejpam-6047	573	49	with	with	ADP
ejpam-6047	573	50	a1	a1	NOUN
ejpam-6047	573	51	,	,	PUNCT
ejpam-6047	573	52	a2	a2	NOUN
ejpam-6047	573	53	being	be	AUX
ejpam-6047	573	54	irreducible	irreducible	ADJ
ejpam-6047	573	55	matrices	matrix	NOUN
ejpam-6047	573	56	,	,	PUNCT
ejpam-6047	573	57	and	and	CCONJ
ejpam-6047	573	58	d1	d1	PROPN
ejpam-6047	573	59	,	,	PUNCT
ejpam-6047	573	60	d2	d2	PROPN
ejpam-6047	573	61	>	>	X
ejpam-6047	573	62	0	0	PROPN
ejpam-6047	573	63	.	.	PUNCT
ejpam-6047	574	1	conflicts	conflict	NOUN
ejpam-6047	574	2	of	of	ADP
ejpam-6047	574	3	interest	interest	NOUN
ejpam-6047	574	4	the	the	DET
ejpam-6047	574	5	authors	author	NOUN
ejpam-6047	574	6	confirm	confirm	VERB
ejpam-6047	574	7	that	that	SCONJ
ejpam-6047	574	8	they	they	PRON
ejpam-6047	574	9	have	have	VERB
ejpam-6047	574	10	no	no	DET
ejpam-6047	574	11	conflicts	conflict	NOUN
ejpam-6047	574	12	of	of	ADP
ejpam-6047	574	13	interest	interest	NOUN
ejpam-6047	574	14	concerning	concern	VERB
ejpam-6047	574	15	the	the	DET
ejpam-6047	574	16	publication	publication	NOUN
ejpam-6047	574	17	of	of	ADP
ejpam-6047	574	18	this	this	DET
ejpam-6047	574	19	paper	paper	NOUN
ejpam-6047	574	20	.	.	PUNCT
ejpam-6047	575	1	acknowledgements	acknowledgement	NOUN
ejpam-6047	575	2	j.	j.	PROPN
ejpam-6047	575	3	alzabut	alzabut	PROPN
ejpam-6047	575	4	and	and	CCONJ
ejpam-6047	575	5	m.	m.	NOUN
ejpam-6047	575	6	tounsi	tounsi	NOUN
ejpam-6047	575	7	express	express	VERB
ejpam-6047	575	8	their	their	PRON
ejpam-6047	575	9	sincere	sincere	ADJ
ejpam-6047	575	10	thanks	thank	NOUN
ejpam-6047	575	11	to	to	ADP
ejpam-6047	575	12	prince	prince	PROPN
ejpam-6047	575	13	sultan	sultan	PROPN
ejpam-6047	575	14	university	university	PROPN
ejpam-6047	575	15	for	for	ADP
ejpam-6047	575	16	its	its	PRON
ejpam-6047	575	17	endless	endless	ADJ
ejpam-6047	575	18	support	support	NOUN
ejpam-6047	575	19	.	.	PUNCT
ejpam-6047	576	1	m.	m.	NOUN
ejpam-6047	576	2	rehman	rehman	PROPN
ejpam-6047	576	3	expresses	express	VERB
ejpam-6047	576	4	his	his	PRON
ejpam-6047	576	5	gratitude	gratitude	NOUN
ejpam-6047	576	6	to	to	ADP
ejpam-6047	576	7	asia	asia	PROPN
ejpam-6047	576	8	international	international	PROPN
ejpam-6047	576	9	university	university	PROPN
ejpam-6047	576	10	for	for	ADP
ejpam-6047	576	11	its	its	PRON
ejpam-6047	576	12	assistance	assistance	NOUN
ejpam-6047	576	13	.	.	PUNCT
ejpam-6047	577	1	references	reference	NOUN
ejpam-6047	577	2	[	[	X
ejpam-6047	577	3	1	1	X
ejpam-6047	577	4	]	]	PUNCT
ejpam-6047	577	5	abraham	abraham	PROPN
ejpam-6047	577	6	berman	berman	PROPN
ejpam-6047	577	7	and	and	CCONJ
ejpam-6047	577	8	robert	robert	PROPN
ejpam-6047	577	9	j	j	PROPN
ejpam-6047	577	10	plemmons	plemmon	NOUN
ejpam-6047	577	11	.	.	PUNCT
ejpam-6047	578	1	nonnegative	nonnegative	ADJ
ejpam-6047	578	2	matrices	matrix	NOUN
ejpam-6047	578	3	in	in	ADP
ejpam-6047	578	4	the	the	DET
ejpam-6047	578	5	mathematical	mathematical	ADJ
ejpam-6047	578	6	sciences	science	NOUN
ejpam-6047	578	7	.	.	PUNCT
ejpam-6047	579	1	siam	siam	PROPN
ejpam-6047	579	2	,	,	PUNCT
ejpam-6047	579	3	1994	1994	NUM
ejpam-6047	579	4	.	.	PUNCT
ejpam-6047	580	1	[	[	X
ejpam-6047	580	2	2	2	NUM
ejpam-6047	580	3	]	]	X
ejpam-6047	580	4	oliver	oliver	PROPN
ejpam-6047	580	5	mason	mason	PROPN
ejpam-6047	580	6	,	,	PUNCT
ejpam-6047	580	7	vahid	vahid	PROPN
ejpam-6047	580	8	s	s	PART
ejpam-6047	580	9	bokharaie	bokharaie	NOUN
ejpam-6047	580	10	,	,	PUNCT
ejpam-6047	580	11	and	and	CCONJ
ejpam-6047	580	12	robert	robert	PROPN
ejpam-6047	580	13	shorten	shorten	PROPN
ejpam-6047	580	14	.	.	PUNCT
ejpam-6047	581	1	stability	stability	NOUN
ejpam-6047	581	2	and	and	CCONJ
ejpam-6047	581	3	d	d	NOUN
ejpam-6047	581	4	-	-	NOUN
ejpam-6047	581	5	stability	stability	NOUN
ejpam-6047	581	6	for	for	ADP
ejpam-6047	581	7	switched	switch	VERB
ejpam-6047	581	8	positive	positive	ADJ
ejpam-6047	581	9	systems	system	NOUN
ejpam-6047	581	10	.	.	PUNCT
ejpam-6047	582	1	in	in	ADP
ejpam-6047	582	2	positive	positive	ADJ
ejpam-6047	582	3	systems	system	NOUN
ejpam-6047	582	4	:	:	PUNCT
ejpam-6047	582	5	proceedings	proceeding	NOUN
ejpam-6047	582	6	of	of	ADP
ejpam-6047	582	7	the	the	DET
ejpam-6047	582	8	third	third	ADJ
ejpam-6047	582	9	multidisciplinary	multidisciplinary	ADJ
ejpam-6047	582	10	international	international	ADJ
ejpam-6047	582	11	symposium	symposium	NOUN
ejpam-6047	582	12	on	on	ADP
ejpam-6047	582	13	positive	positive	ADJ
ejpam-6047	582	14	systems	system	NOUN
ejpam-6047	582	15	:	:	PUNCT
ejpam-6047	582	16	theory	theory	NOUN
ejpam-6047	582	17	and	and	CCONJ
ejpam-6047	582	18	applications	application	NOUN
ejpam-6047	582	19	(	(	PUNCT
ejpam-6047	582	20	posta	posta	ADJ
ejpam-6047	582	21	2009	2009	NUM
ejpam-6047	582	22	)	)	PUNCT
ejpam-6047	582	23	valencia	valencia	PROPN
ejpam-6047	582	24	,	,	PUNCT
ejpam-6047	582	25	spain	spain	PROPN
ejpam-6047	582	26	,	,	PUNCT
ejpam-6047	582	27	september	september	PROPN
ejpam-6047	582	28	2	2	NUM
ejpam-6047	582	29	-	-	SYM
ejpam-6047	582	30	4	4	NUM
ejpam-6047	582	31	,	,	PUNCT
ejpam-6047	582	32	2009	2009	NUM
ejpam-6047	582	33	,	,	PUNCT
ejpam-6047	582	34	pages	page	NOUN
ejpam-6047	582	35	101–109	101–109	NUM
ejpam-6047	582	36	.	.	PUNCT
ejpam-6047	582	37	springer	springer	NOUN
ejpam-6047	582	38	,	,	PUNCT
ejpam-6047	582	39	2009	2009	NUM
ejpam-6047	582	40	.	.	PUNCT
ejpam-6047	583	1	[	[	X
ejpam-6047	583	2	3	3	X
ejpam-6047	583	3	]	]	X
ejpam-6047	583	4	lorenzo	lorenzo	PROPN
ejpam-6047	583	5	farina	farina	PROPN
ejpam-6047	583	6	and	and	CCONJ
ejpam-6047	583	7	sergio	sergio	PROPN
ejpam-6047	583	8	rinaldi	rinaldi	PROPN
ejpam-6047	583	9	.	.	PROPN
ejpam-6047	583	10	positive	positive	ADJ
ejpam-6047	583	11	linear	linear	PROPN
ejpam-6047	583	12	systems	system	NOUN
ejpam-6047	583	13	:	:	PUNCT
ejpam-6047	583	14	theory	theory	NOUN
ejpam-6047	583	15	and	and	CCONJ
ejpam-6047	583	16	applications	application	NOUN
ejpam-6047	583	17	.	.	PUNCT
ejpam-6047	584	1	john	john	PROPN
ejpam-6047	584	2	wiley	wiley	PROPN
ejpam-6047	584	3	&	&	CCONJ
ejpam-6047	584	4	sons	son	NOUN
ejpam-6047	584	5	,	,	PUNCT
ejpam-6047	584	6	2011	2011	NUM
ejpam-6047	584	7	.	.	PUNCT
ejpam-6047	585	1	[	[	X
ejpam-6047	585	2	4	4	NUM
ejpam-6047	585	3	]	]	PUNCT
ejpam-6047	585	4	wassim	wassim	NOUN
ejpam-6047	585	5	m	m	PROPN
ejpam-6047	585	6	haddad	haddad	PROPN
ejpam-6047	585	7	and	and	CCONJ
ejpam-6047	585	8	vijaysekhar	vijaysekhar	NOUN
ejpam-6047	585	9	chellaboina	chellaboina	NOUN
ejpam-6047	585	10	.	.	PUNCT
ejpam-6047	586	1	stability	stability	NOUN
ejpam-6047	586	2	theory	theory	NOUN
ejpam-6047	586	3	for	for	ADP
ejpam-6047	586	4	nonnegative	nonnegative	ADJ
ejpam-6047	586	5	and	and	CCONJ
ejpam-6047	586	6	compartmental	compartmental	ADJ
ejpam-6047	586	7	dynamical	dynamical	ADJ
ejpam-6047	586	8	systems	system	NOUN
ejpam-6047	586	9	with	with	ADP
ejpam-6047	586	10	time	time	NOUN
ejpam-6047	586	11	delay	delay	NOUN
ejpam-6047	586	12	.	.	PUNCT
ejpam-6047	587	1	in	in	ADP
ejpam-6047	587	2	proceedings	proceeding	NOUN
ejpam-6047	587	3	of	of	ADP
ejpam-6047	587	4	the	the	DET
ejpam-6047	587	5	2004	2004	NUM
ejpam-6047	587	6	american	american	PROPN
ejpam-6047	587	7	control	control	PROPN
ejpam-6047	587	8	conference	conference	PROPN
ejpam-6047	587	9	,	,	PUNCT
ejpam-6047	587	10	volume	volume	NOUN
ejpam-6047	587	11	2	2	NUM
ejpam-6047	587	12	,	,	PUNCT
ejpam-6047	587	13	pages	page	NOUN
ejpam-6047	587	14	1422–1427	1422–1427	NUM
ejpam-6047	587	15	.	.	PUNCT
ejpam-6047	587	16	ieee	ieee	PROPN
ejpam-6047	587	17	,	,	PUNCT
ejpam-6047	587	18	2004	2004	NUM
ejpam-6047	587	19	.	.	PUNCT
ejpam-6047	588	1	[	[	X
ejpam-6047	588	2	5	5	NUM
ejpam-6047	588	3	]	]	PUNCT
ejpam-6047	588	4	vahid	vahid	PROPN
ejpam-6047	588	5	samadi	samadi	PROPN
ejpam-6047	588	6	bokharaie	bokharaie	PROPN
ejpam-6047	588	7	,	,	PUNCT
ejpam-6047	588	8	oliver	oliver	PROPN
ejpam-6047	588	9	mason	mason	PROPN
ejpam-6047	588	10	,	,	PUNCT
ejpam-6047	588	11	and	and	CCONJ
ejpam-6047	588	12	mark	mark	PROPN
ejpam-6047	588	13	verwoerd	verwoerd	NOUN
ejpam-6047	588	14	.	.	PUNCT
ejpam-6047	589	1	d	d	X
ejpam-6047	589	2	-	-	PUNCT
ejpam-6047	589	3	stability	stability	NOUN
ejpam-6047	589	4	and	and	CCONJ
ejpam-6047	589	5	delayindependent	delayindependent	NOUN
ejpam-6047	589	6	stability	stability	NOUN
ejpam-6047	589	7	of	of	ADP
ejpam-6047	589	8	homogeneous	homogeneous	ADJ
ejpam-6047	589	9	cooperative	cooperative	ADJ
ejpam-6047	589	10	systems	system	NOUN
ejpam-6047	589	11	.	.	PUNCT
ejpam-6047	590	1	ieee	ieee	NOUN
ejpam-6047	590	2	transactions	transaction	NOUN
ejpam-6047	590	3	on	on	ADP
ejpam-6047	590	4	automatic	automatic	ADJ
ejpam-6047	590	5	control	control	NOUN
ejpam-6047	590	6	,	,	PUNCT
ejpam-6047	590	7	55(12):2882–2885	55(12):2882–2885	NUM
ejpam-6047	590	8	,	,	PUNCT
ejpam-6047	590	9	2010	2010	NUM
ejpam-6047	590	10	.	.	PUNCT
ejpam-6047	591	1	[	[	X
ejpam-6047	591	2	6	6	NUM
ejpam-6047	591	3	]	]	PUNCT
ejpam-6047	591	4	kenneth	kenneth	PROPN
ejpam-6047	591	5	j	j	PROPN
ejpam-6047	591	6	arrow	arrow	NOUN
ejpam-6047	591	7	and	and	CCONJ
ejpam-6047	591	8	maurice	maurice	PROPN
ejpam-6047	591	9	mcmanus	mcmanus	PROPN
ejpam-6047	591	10	.	.	PUNCT
ejpam-6047	592	1	a	a	DET
ejpam-6047	592	2	note	note	NOUN
ejpam-6047	592	3	on	on	ADP
ejpam-6047	592	4	dynamic	dynamic	ADJ
ejpam-6047	592	5	stability	stability	NOUN
ejpam-6047	592	6	.	.	PUNCT
ejpam-6047	593	1	econometrica	econometrica	PROPN
ejpam-6047	593	2	:	:	PUNCT
ejpam-6047	593	3	journal	journal	NOUN
ejpam-6047	593	4	of	of	ADP
ejpam-6047	593	5	the	the	DET
ejpam-6047	593	6	econometric	econometric	ADJ
ejpam-6047	593	7	society	society	NOUN
ejpam-6047	593	8	,	,	PUNCT
ejpam-6047	593	9	pages	page	NOUN
ejpam-6047	593	10	448–454	448–454	NUM
ejpam-6047	593	11	,	,	PUNCT
ejpam-6047	593	12	1958	1958	NUM
ejpam-6047	593	13	.	.	PUNCT
ejpam-6047	594	1	[	[	X
ejpam-6047	594	2	7	7	X
ejpam-6047	594	3	]	]	X
ejpam-6047	594	4	alain	alain	PROPN
ejpam-6047	594	5	c	c	PROPN
ejpam-6047	594	6	enthoven	enthoven	NOUN
ejpam-6047	594	7	and	and	CCONJ
ejpam-6047	594	8	kenneth	kenneth	PROPN
ejpam-6047	594	9	j	j	PROPN
ejpam-6047	594	10	arrow	arrow	NOUN
ejpam-6047	594	11	.	.	PUNCT
ejpam-6047	595	1	a	a	DET
ejpam-6047	595	2	theorem	theorem	NOUN
ejpam-6047	595	3	on	on	ADP
ejpam-6047	595	4	expectations	expectation	NOUN
ejpam-6047	595	5	and	and	CCONJ
ejpam-6047	595	6	the	the	DET
ejpam-6047	595	7	stability	stability	NOUN
ejpam-6047	595	8	of	of	ADP
ejpam-6047	595	9	equilibrium	equilibrium	NOUN
ejpam-6047	595	10	.	.	PUNCT
ejpam-6047	596	1	econometrica	econometrica	PROPN
ejpam-6047	596	2	:	:	PUNCT
ejpam-6047	596	3	journal	journal	NOUN
ejpam-6047	596	4	of	of	ADP
ejpam-6047	596	5	the	the	DET
ejpam-6047	596	6	econometric	econometric	ADJ
ejpam-6047	596	7	society	society	NOUN
ejpam-6047	596	8	,	,	PUNCT
ejpam-6047	596	9	pages	page	NOUN
ejpam-6047	596	10	288–293	288–293	NUM
ejpam-6047	596	11	,	,	PUNCT
ejpam-6047	596	12	1956	1956	NUM
ejpam-6047	596	13	.	.	PUNCT
ejpam-6047	597	1	[	[	X
ejpam-6047	597	2	8	8	NUM
ejpam-6047	597	3	]	]	PUNCT
ejpam-6047	597	4	giorgio	giorgio	PROPN
ejpam-6047	597	5	giorgi	giorgi	PROPN
ejpam-6047	597	6	.	.	PUNCT
ejpam-6047	598	1	stable	stable	ADJ
ejpam-6047	598	2	and	and	CCONJ
ejpam-6047	598	3	related	related	ADJ
ejpam-6047	598	4	matrices	matrix	NOUN
ejpam-6047	598	5	in	in	ADP
ejpam-6047	598	6	economic	economic	ADJ
ejpam-6047	598	7	theory	theory	NOUN
ejpam-6047	598	8	.	.	PUNCT
ejpam-6047	599	1	control	control	NOUN
ejpam-6047	599	2	and	and	CCONJ
ejpam-6047	599	3	cybernetics	cybernetic	NOUN
ejpam-6047	599	4	,	,	PUNCT
ejpam-6047	599	5	32(2):397–410	32(2):397–410	NUM
ejpam-6047	599	6	,	,	PUNCT
ejpam-6047	599	7	2003	2003	NUM
ejpam-6047	599	8	.	.	PUNCT
ejpam-6047	600	1	[	[	X
ejpam-6047	600	2	9	9	NUM
ejpam-6047	600	3	]	]	X
ejpam-6047	600	4	frank	frank	PROPN
ejpam-6047	600	5	hahn	hahn	PROPN
ejpam-6047	600	6	.	.	PUNCT
ejpam-6047	601	1	stability	stability	NOUN
ejpam-6047	601	2	.	.	PUNCT
ejpam-6047	602	1	handbook	handbook	NOUN
ejpam-6047	602	2	of	of	ADP
ejpam-6047	602	3	mathematical	mathematical	ADJ
ejpam-6047	602	4	economics	economic	NOUN
ejpam-6047	602	5	,	,	PUNCT
ejpam-6047	602	6	2:745–793	2:745–793	NUM
ejpam-6047	602	7	,	,	PUNCT
ejpam-6047	602	8	1982	1982	NUM
ejpam-6047	602	9	.	.	PUNCT
ejpam-6047	603	1	m.u	m.u	PROPN
ejpam-6047	603	2	.	.	PROPN
ejpam-6047	603	3	rehman	rehman	PROPN
ejpam-6047	603	4	et	et	PROPN
ejpam-6047	603	5	al	al	PROPN
ejpam-6047	603	6	.	.	PUNCT
ejpam-6047	603	7	/	/	SYM
ejpam-6047	603	8	eur	eur	PROPN
ejpam-6047	603	9	.	.	PUNCT
ejpam-6047	604	1	j.	j.	PROPN
ejpam-6047	604	2	pure	pure	PROPN
ejpam-6047	604	3	appl	appl	PROPN
ejpam-6047	604	4	.	.	PROPN
ejpam-6047	604	5	math	math	PROPN
ejpam-6047	604	6	,	,	PUNCT
ejpam-6047	604	7	18	18	NUM
ejpam-6047	604	8	(	(	PUNCT
ejpam-6047	604	9	3	3	NUM
ejpam-6047	604	10	)	)	PUNCT
ejpam-6047	604	11	(	(	PUNCT
ejpam-6047	604	12	2025	2025	NUM
ejpam-6047	604	13	)	)	PUNCT
ejpam-6047	604	14	,	,	PUNCT
ejpam-6047	604	15	6047	6047	NUM
ejpam-6047	604	16	31	31	NUM
ejpam-6047	604	17	of	of	ADP
ejpam-6047	604	18	33	33	NUM
ejpam-6047	604	19	[	[	SYM
ejpam-6047	604	20	10	10	NUM
ejpam-6047	604	21	]	]	X
ejpam-6047	604	22	murray	murray	PROPN
ejpam-6047	604	23	c	c	PROPN
ejpam-6047	604	24	kemp	kemp	PROPN
ejpam-6047	604	25	and	and	CCONJ
ejpam-6047	604	26	yoshio	yoshio	PROPN
ejpam-6047	604	27	kimura	kimura	PROPN
ejpam-6047	604	28	.	.	PUNCT
ejpam-6047	605	1	introduction	introduction	NOUN
ejpam-6047	605	2	to	to	ADP
ejpam-6047	605	3	mathematical	mathematical	ADJ
ejpam-6047	605	4	economics	economic	NOUN
ejpam-6047	605	5	.	.	PUNCT
ejpam-6047	606	1	springer	springer	NOUN
ejpam-6047	606	2	,	,	PUNCT
ejpam-6047	606	3	1978	1978	NUM
ejpam-6047	606	4	.	.	PUNCT
ejpam-6047	607	1	[	[	X
ejpam-6047	607	2	11	11	NUM
ejpam-6047	607	3	]	]	X
ejpam-6047	607	4	peter	peter	PROPN
ejpam-6047	607	5	k	k	PROPN
ejpam-6047	607	6	newman	newman	PROPN
ejpam-6047	607	7	.	.	PUNCT
ejpam-6047	608	1	some	some	DET
ejpam-6047	608	2	notes	note	NOUN
ejpam-6047	608	3	on	on	ADP
ejpam-6047	608	4	stability	stability	NOUN
ejpam-6047	608	5	conditions	condition	NOUN
ejpam-6047	608	6	.	.	PUNCT
ejpam-6047	609	1	the	the	DET
ejpam-6047	609	2	review	review	NOUN
ejpam-6047	609	3	of	of	ADP
ejpam-6047	609	4	economic	economic	ADJ
ejpam-6047	609	5	studies	study	NOUN
ejpam-6047	609	6	,	,	PUNCT
ejpam-6047	609	7	27(1):1–9	27(1):1–9	NUM
ejpam-6047	609	8	,	,	PUNCT
ejpam-6047	609	9	1959	1959	NUM
ejpam-6047	609	10	.	.	PUNCT
ejpam-6047	610	1	[	[	X
ejpam-6047	610	2	12	12	NUM
ejpam-6047	610	3	]	]	X
ejpam-6047	610	4	james	james	PROPN
ejpam-6047	610	5	p	p	PROPN
ejpam-6047	610	6	quirk	quirk	PROPN
ejpam-6047	610	7	and	and	CCONJ
ejpam-6047	610	8	rubin	rubin	PROPN
ejpam-6047	610	9	saposnik	saposnik	PROPN
ejpam-6047	610	10	.	.	PUNCT
ejpam-6047	611	1	introduction	introduction	NOUN
ejpam-6047	611	2	to	to	ADP
ejpam-6047	611	3	general	general	ADJ
ejpam-6047	611	4	equilibrium	equilibrium	NOUN
ejpam-6047	611	5	theory	theory	NOUN
ejpam-6047	611	6	and	and	CCONJ
ejpam-6047	611	7	welfare	welfare	NOUN
ejpam-6047	611	8	economics	economic	NOUN
ejpam-6047	611	9	.	.	PUNCT
ejpam-6047	612	1	mcgraw	mcgraw	PROPN
ejpam-6047	612	2	-	-	PUNCT
ejpam-6047	612	3	hill	hill	PROPN
ejpam-6047	612	4	,	,	PUNCT
ejpam-6047	612	5	1968	1968	NUM
ejpam-6047	612	6	.	.	PUNCT
ejpam-6047	613	1	[	[	X
ejpam-6047	613	2	13	13	NUM
ejpam-6047	613	3	]	]	X
ejpam-6047	613	4	john	john	PROPN
ejpam-6047	613	5	e	e	PROPN
ejpam-6047	613	6	woods	woods	PROPN
ejpam-6047	613	7	.	.	PUNCT
ejpam-6047	614	1	mathematical	mathematical	ADJ
ejpam-6047	614	2	economics	economic	NOUN
ejpam-6047	614	3	.	.	PUNCT
ejpam-6047	615	1	(	(	PUNCT
ejpam-6047	615	2	no	no	DET
ejpam-6047	615	3	title	title	NOUN
ejpam-6047	615	4	)	)	PUNCT
ejpam-6047	615	5	,	,	PUNCT
ejpam-6047	615	6	1978	1978	NUM
ejpam-6047	615	7	.	.	PUNCT
ejpam-6047	616	1	[	[	X
ejpam-6047	616	2	14	14	NUM
ejpam-6047	616	3	]	]	X
ejpam-6047	616	4	eugenius	eugenius	PROPN
ejpam-6047	616	5	kaszkurewicz	kaszkurewicz	PROPN
ejpam-6047	616	6	and	and	CCONJ
ejpam-6047	616	7	amit	amit	PROPN
ejpam-6047	616	8	bhaya	bhaya	PROPN
ejpam-6047	616	9	.	.	PUNCT
ejpam-6047	616	10	matrix	matrix	NOUN
ejpam-6047	616	11	diagonal	diagonal	ADJ
ejpam-6047	616	12	stability	stability	NOUN
ejpam-6047	616	13	in	in	ADP
ejpam-6047	616	14	systems	system	NOUN
ejpam-6047	616	15	and	and	CCONJ
ejpam-6047	616	16	computation	computation	NOUN
ejpam-6047	616	17	.	.	PUNCT
ejpam-6047	617	1	springer	springer	NOUN
ejpam-6047	617	2	science	science	PROPN
ejpam-6047	617	3	&	&	CCONJ
ejpam-6047	617	4	business	business	NOUN
ejpam-6047	617	5	media	medium	NOUN
ejpam-6047	617	6	,	,	PUNCT
ejpam-6047	617	7	2012	2012	NUM
ejpam-6047	617	8	.	.	PUNCT
ejpam-6047	618	1	[	[	X
ejpam-6047	618	2	15	15	NUM
ejpam-6047	618	3	]	]	X
ejpam-6047	618	4	charles	charles	PROPN
ejpam-6047	618	5	r	r	PROPN
ejpam-6047	618	6	johnson	johnson	PROPN
ejpam-6047	618	7	.	.	PUNCT
ejpam-6047	619	1	sufficient	sufficient	ADJ
ejpam-6047	619	2	conditions	condition	NOUN
ejpam-6047	619	3	for	for	ADP
ejpam-6047	619	4	d	d	NOUN
ejpam-6047	619	5	-	-	NOUN
ejpam-6047	619	6	stability	stability	NOUN
ejpam-6047	619	7	.	.	PUNCT
ejpam-6047	620	1	journal	journal	NOUN
ejpam-6047	620	2	of	of	ADP
ejpam-6047	620	3	economic	economic	ADJ
ejpam-6047	620	4	theory	theory	NOUN
ejpam-6047	620	5	,	,	PUNCT
ejpam-6047	620	6	9(1):53–62	9(1):53–62	NUM
ejpam-6047	620	7	,	,	PUNCT
ejpam-6047	620	8	1974	1974	NUM
ejpam-6047	620	9	.	.	PUNCT
ejpam-6047	621	1	[	[	X
ejpam-6047	621	2	16	16	NUM
ejpam-6047	621	3	]	]	X
ejpam-6047	621	4	cheng	cheng	PROPN
ejpam-6047	621	5	-	-	PUNCT
ejpam-6047	621	6	ching	ching	PROPN
ejpam-6047	621	7	yu	yu	PROPN
ejpam-6047	621	8	and	and	CCONJ
ejpam-6047	621	9	michael	michael	PROPN
ejpam-6047	621	10	kh	kh	PROPN
ejpam-6047	621	11	fan	fan	PROPN
ejpam-6047	621	12	.	.	PUNCT
ejpam-6047	622	1	decentralized	decentralize	VERB
ejpam-6047	622	2	integral	integral	ADJ
ejpam-6047	622	3	controllability	controllability	NOUN
ejpam-6047	622	4	and	and	CCONJ
ejpam-6047	622	5	d	d	NOUN
ejpam-6047	622	6	-	-	NOUN
ejpam-6047	622	7	stability	stability	NOUN
ejpam-6047	622	8	.	.	PUNCT
ejpam-6047	623	1	chemical	chemical	NOUN
ejpam-6047	623	2	engineering	engineering	NOUN
ejpam-6047	623	3	science	science	PROPN
ejpam-6047	623	4	,	,	PUNCT
ejpam-6047	623	5	45(11):3299–3309	45(11):3299–3309	PROPN
ejpam-6047	623	6	,	,	PUNCT
ejpam-6047	623	7	1990	1990	NUM
ejpam-6047	623	8	.	.	PUNCT
ejpam-6047	624	1	[	[	X
ejpam-6047	624	2	17	17	NUM
ejpam-6047	624	3	]	]	X
ejpam-6047	624	4	mahmoud	mahmoud	PROPN
ejpam-6047	624	5	chilali	chilali	PROPN
ejpam-6047	624	6	,	,	PUNCT
ejpam-6047	624	7	pascal	pascal	ADJ
ejpam-6047	624	8	gahinet	gahinet	NOUN
ejpam-6047	624	9	,	,	PUNCT
ejpam-6047	624	10	and	and	CCONJ
ejpam-6047	624	11	pierre	pierre	PROPN
ejpam-6047	624	12	apkarian	apkarian	PROPN
ejpam-6047	624	13	.	.	PUNCT
ejpam-6047	625	1	robust	robust	ADJ
ejpam-6047	625	2	pole	pole	NOUN
ejpam-6047	625	3	placement	placement	NOUN
ejpam-6047	625	4	in	in	ADP
ejpam-6047	625	5	lmi	lmi	PROPN
ejpam-6047	625	6	regions	region	NOUN
ejpam-6047	625	7	.	.	PUNCT
ejpam-6047	626	1	ieee	ieee	NOUN
ejpam-6047	626	2	transactions	transaction	NOUN
ejpam-6047	626	3	on	on	ADP
ejpam-6047	626	4	automatic	automatic	ADJ
ejpam-6047	626	5	control	control	NOUN
ejpam-6047	626	6	,	,	PUNCT
ejpam-6047	626	7	44(12):2257–2270	44(12):2257–2270	NUM
ejpam-6047	626	8	,	,	PUNCT
ejpam-6047	626	9	2002	2002	NUM
ejpam-6047	626	10	.	.	PUNCT
ejpam-6047	627	1	[	[	X
ejpam-6047	627	2	18	18	NUM
ejpam-6047	627	3	]	]	X
ejpam-6047	627	4	valter	valter	NOUN
ejpam-6047	627	5	js	js	PROPN
ejpam-6047	627	6	leite	leite	PROPN
ejpam-6047	627	7	and	and	CCONJ
ejpam-6047	627	8	pedro	pedro	PROPN
ejpam-6047	627	9	ld	ld	PROPN
ejpam-6047	627	10	peres	peres	PROPN
ejpam-6047	627	11	.	.	PUNCT
ejpam-6047	628	1	an	an	DET
ejpam-6047	628	2	improved	improved	ADJ
ejpam-6047	628	3	lmi	lmi	PROPN
ejpam-6047	628	4	condition	condition	NOUN
ejpam-6047	628	5	for	for	ADP
ejpam-6047	628	6	robust	robust	ADJ
ejpam-6047	628	7	d	d	NOUN
ejpam-6047	628	8	-	-	NOUN
ejpam-6047	628	9	stability	stability	NOUN
ejpam-6047	628	10	of	of	ADP
ejpam-6047	628	11	uncertain	uncertain	ADJ
ejpam-6047	628	12	polytopic	polytopic	NOUN
ejpam-6047	628	13	systems	system	NOUN
ejpam-6047	628	14	.	.	PUNCT
ejpam-6047	629	1	ieee	ieee	NOUN
ejpam-6047	629	2	transactions	transaction	NOUN
ejpam-6047	629	3	on	on	ADP
ejpam-6047	629	4	automatic	automatic	ADJ
ejpam-6047	629	5	control	control	NOUN
ejpam-6047	629	6	,	,	PUNCT
ejpam-6047	629	7	48(3):500	48(3):500	NUM
ejpam-6047	629	8	–	–	PUNCT
ejpam-6047	629	9	504	504	NUM
ejpam-6047	629	10	,	,	PUNCT
ejpam-6047	629	11	2003	2003	NUM
ejpam-6047	629	12	.	.	PUNCT
ejpam-6047	630	1	[	[	X
ejpam-6047	630	2	19	19	NUM
ejpam-6047	630	3	]	]	X
ejpam-6047	630	4	dimitri	dimitri	PROPN
ejpam-6047	630	5	peaucelle	peaucelle	PROPN
ejpam-6047	630	6	,	,	PUNCT
ejpam-6047	630	7	denis	denis	PROPN
ejpam-6047	630	8	arzelier	arzelier	PROPN
ejpam-6047	630	9	,	,	PUNCT
ejpam-6047	630	10	olivier	olivier	PROPN
ejpam-6047	630	11	bachelier	bachelier	PROPN
ejpam-6047	630	12	,	,	PUNCT
ejpam-6047	630	13	and	and	CCONJ
ejpam-6047	630	14	jacques	jacques	PROPN
ejpam-6047	630	15	bernussou	bernussou	PROPN
ejpam-6047	630	16	.	.	PUNCT
ejpam-6047	631	1	a	a	DET
ejpam-6047	631	2	new	new	ADJ
ejpam-6047	631	3	robust	robust	ADJ
ejpam-6047	631	4	d	d	NOUN
ejpam-6047	631	5	-	-	PUNCT
ejpam-6047	631	6	stability	stability	NOUN
ejpam-6047	631	7	condition	condition	NOUN
ejpam-6047	631	8	for	for	ADP
ejpam-6047	631	9	real	real	ADJ
ejpam-6047	631	10	convex	convex	NOUN
ejpam-6047	631	11	polytopic	polytopic	NOUN
ejpam-6047	631	12	uncertainty	uncertainty	NOUN
ejpam-6047	631	13	.	.	PUNCT
ejpam-6047	632	1	systems	system	NOUN
ejpam-6047	632	2	&	&	CCONJ
ejpam-6047	632	3	control	control	PROPN
ejpam-6047	632	4	letters	letter	NOUN
ejpam-6047	632	5	,	,	PUNCT
ejpam-6047	632	6	40(1):21–30	40(1):21–30	NUM
ejpam-6047	632	7	,	,	PUNCT
ejpam-6047	632	8	2000	2000	NUM
ejpam-6047	632	9	.	.	PUNCT
ejpam-6047	633	1	[	[	X
ejpam-6047	633	2	20	20	NUM
ejpam-6047	633	3	]	]	X
ejpam-6047	633	4	d	d	NOUN
ejpam-6047	633	5	arzelier	arzelier	NOUN
ejpam-6047	633	6	,	,	PUNCT
ejpam-6047	633	7	d	d	NOUN
ejpam-6047	633	8	henrion	henrion	NOUN
ejpam-6047	633	9	,	,	PUNCT
ejpam-6047	633	10	and	and	CCONJ
ejpam-6047	633	11	d	d	ADP
ejpam-6047	633	12	peaucelle	peaucelle	NOUN
ejpam-6047	633	13	.	.	PUNCT
ejpam-6047	634	1	robust	robust	ADJ
ejpam-6047	634	2	d	d	NOUN
ejpam-6047	634	3	stabilization	stabilization	NOUN
ejpam-6047	634	4	of	of	ADP
ejpam-6047	634	5	a	a	DET
ejpam-6047	634	6	polytope	polytope	NOUN
ejpam-6047	634	7	of	of	ADP
ejpam-6047	634	8	matrices	matrix	NOUN
ejpam-6047	634	9	.	.	PUNCT
ejpam-6047	635	1	international	international	ADJ
ejpam-6047	635	2	journal	journal	PROPN
ejpam-6047	635	3	of	of	ADP
ejpam-6047	635	4	control	control	PROPN
ejpam-6047	635	5	,	,	PUNCT
ejpam-6047	635	6	75(10):744–752	75(10):744–752	NUM
ejpam-6047	635	7	,	,	PUNCT
ejpam-6047	635	8	2002	2002	NUM
ejpam-6047	635	9	.	.	PUNCT
ejpam-6047	636	1	[	[	X
ejpam-6047	636	2	21	21	NUM
ejpam-6047	636	3	]	]	X
ejpam-6047	636	4	olga	olga	PROPN
ejpam-6047	637	1	i	i	PRON
ejpam-6047	637	2	kosmidou	kosmidou	PROPN
ejpam-6047	637	3	.	.	PUNCT
ejpam-6047	638	1	robust	robust	ADJ
ejpam-6047	638	2	control	control	NOUN
ejpam-6047	638	3	with	with	ADP
ejpam-6047	638	4	pole	pole	NOUN
ejpam-6047	638	5	shifting	shift	VERB
ejpam-6047	638	6	via	via	ADP
ejpam-6047	638	7	performance	performance	NOUN
ejpam-6047	638	8	index	index	NOUN
ejpam-6047	638	9	modification	modification	NOUN
ejpam-6047	638	10	.	.	PUNCT
ejpam-6047	639	1	applied	apply	VERB
ejpam-6047	639	2	mathematics	mathematic	NOUN
ejpam-6047	639	3	and	and	CCONJ
ejpam-6047	639	4	computation	computation	NOUN
ejpam-6047	639	5	,	,	PUNCT
ejpam-6047	639	6	182(1):596–606	182(1):596–606	NUM
ejpam-6047	639	7	,	,	PUNCT
ejpam-6047	639	8	2006	2006	NUM
ejpam-6047	639	9	.	.	PUNCT
ejpam-6047	640	1	[	[	X
ejpam-6047	640	2	22	22	NUM
ejpam-6047	640	3	]	]	X
ejpam-6047	640	4	dong	dong	PROPN
ejpam-6047	640	5	hwan	hwan	PROPN
ejpam-6047	640	6	lee	lee	PROPN
ejpam-6047	640	7	,	,	PUNCT
ejpam-6047	640	8	jin	jin	PROPN
ejpam-6047	640	9	bae	bae	PROPN
ejpam-6047	640	10	park	park	PROPN
ejpam-6047	640	11	,	,	PUNCT
ejpam-6047	640	12	and	and	CCONJ
ejpam-6047	640	13	young	young	ADJ
ejpam-6047	640	14	hoon	hoon	NOUN
ejpam-6047	640	15	joo	joo	PROPN
ejpam-6047	640	16	.	.	PUNCT
ejpam-6047	641	1	a	a	DET
ejpam-6047	641	2	less	less	ADV
ejpam-6047	641	3	conservative	conservative	ADJ
ejpam-6047	641	4	lmi	lmi	PROPN
ejpam-6047	641	5	condition	condition	NOUN
ejpam-6047	641	6	for	for	ADP
ejpam-6047	641	7	d	d	NOUN
ejpam-6047	641	8	-	-	NOUN
ejpam-6047	641	9	stability	stability	NOUN
ejpam-6047	641	10	of	of	ADP
ejpam-6047	641	11	polynomial	polynomial	ADJ
ejpam-6047	641	12	matrix	matrix	NOUN
ejpam-6047	641	13	polytopes	polytope	NOUN
ejpam-6047	641	14	—	—	PUNCT
ejpam-6047	641	15	a	a	DET
ejpam-6047	641	16	projection	projection	NOUN
ejpam-6047	641	17	approach	approach	NOUN
ejpam-6047	641	18	.	.	PUNCT
ejpam-6047	642	1	ieee	ieee	NOUN
ejpam-6047	642	2	transactions	transaction	NOUN
ejpam-6047	642	3	on	on	ADP
ejpam-6047	642	4	automatic	automatic	ADJ
ejpam-6047	642	5	control	control	NOUN
ejpam-6047	642	6	,	,	PUNCT
ejpam-6047	642	7	56(4):868–873	56(4):868–873	PROPN
ejpam-6047	642	8	,	,	PUNCT
ejpam-6047	642	9	2010	2010	NUM
ejpam-6047	642	10	.	.	PUNCT
ejpam-6047	643	1	[	[	X
ejpam-6047	643	2	23	23	NUM
ejpam-6047	643	3	]	]	X
ejpam-6047	643	4	mutti	mutti	PROPN
ejpam-6047	643	5	-	-	PUNCT
ejpam-6047	643	6	ur	ur	PROPN
ejpam-6047	643	7	rehman	rehman	PROPN
ejpam-6047	643	8	et	et	PROPN
ejpam-6047	643	9	al	al	PROPN
ejpam-6047	643	10	.	.	PROPN
ejpam-6047	643	11	spectrum	spectrum	PROPN
ejpam-6047	643	12	and	and	CCONJ
ejpam-6047	643	13	pseudspectrum	pseudspectrum	NOUN
ejpam-6047	643	14	of	of	ADP
ejpam-6047	643	15	d	d	ADJ
ejpam-6047	643	16	-	-	ADJ
ejpam-6047	643	17	stable	stable	ADJ
ejpam-6047	643	18	matrices	matrix	NOUN
ejpam-6047	643	19	of	of	ADP
ejpam-6047	643	20	economy	economy	NOUN
ejpam-6047	643	21	models	model	NOUN
ejpam-6047	643	22	.	.	PUNCT
ejpam-6047	644	1	j.	j.	PROPN
ejpam-6047	644	2	math	math	PROPN
ejpam-6047	644	3	.	.	PUNCT
ejpam-6047	645	1	computer	computer	PROPN
ejpam-6047	645	2	sci	sci	PROPN
ejpam-6047	645	3	,	,	PUNCT
ejpam-6047	645	4	38:298–312	38:298–312	NUM
ejpam-6047	645	5	,	,	PUNCT
ejpam-6047	645	6	2025	2025	NUM
ejpam-6047	645	7	.	.	PUNCT
ejpam-6047	646	1	[	[	X
ejpam-6047	646	2	24	24	NUM
ejpam-6047	646	3	]	]	PUNCT
ejpam-6047	646	4	pierre	pierre	NOUN
ejpam-6047	646	5	rostan	rostan	PROPN
ejpam-6047	646	6	and	and	CCONJ
ejpam-6047	646	7	alexandra	alexandra	PROPN
ejpam-6047	646	8	rostan	rostan	PROPN
ejpam-6047	646	9	.	.	PUNCT
ejpam-6047	647	1	the	the	DET
ejpam-6047	647	2	versatility	versatility	NOUN
ejpam-6047	647	3	of	of	ADP
ejpam-6047	647	4	spectrum	spectrum	NOUN
ejpam-6047	647	5	analysis	analysis	NOUN
ejpam-6047	647	6	for	for	ADP
ejpam-6047	647	7	forecasting	forecast	VERB
ejpam-6047	647	8	financial	financial	ADJ
ejpam-6047	647	9	time	time	NOUN
ejpam-6047	647	10	series	series	PROPN
ejpam-6047	647	11	.	.	PUNCT
ejpam-6047	648	1	journal	journal	PROPN
ejpam-6047	648	2	of	of	ADP
ejpam-6047	648	3	forecasting	forecasting	NOUN
ejpam-6047	648	4	,	,	PUNCT
ejpam-6047	648	5	37(3):327–339	37(3):327–339	PROPN
ejpam-6047	648	6	,	,	PUNCT
ejpam-6047	648	7	2018	2018	NUM
ejpam-6047	648	8	.	.	PUNCT
ejpam-6047	649	1	[	[	X
ejpam-6047	649	2	25	25	NUM
ejpam-6047	649	3	]	]	X
ejpam-6047	649	4	alaa	alaa	PROPN
ejpam-6047	649	5	khadim	khadim	PROPN
ejpam-6047	649	6	mohammed	mohammed	PROPN
ejpam-6047	649	7	and	and	CCONJ
ejpam-6047	649	8	salam	salam	PROPN
ejpam-6047	649	9	jasim	jasim	PROPN
ejpam-6047	649	10	majeed	majeed	PROPN
ejpam-6047	649	11	.	.	PUNCT
ejpam-6047	650	1	bifurcation	bifurcation	NOUN
ejpam-6047	650	2	analysis	analysis	NOUN
ejpam-6047	650	3	of	of	ADP
ejpam-6047	650	4	an	an	DET
ejpam-6047	650	5	ecoepidemiological	ecoepidemiological	ADJ
ejpam-6047	650	6	model	model	NOUN
ejpam-6047	650	7	involving	involve	VERB
ejpam-6047	650	8	prey	prey	PROPN
ejpam-6047	650	9	refuge	refuge	NOUN
ejpam-6047	650	10	,	,	PUNCT
ejpam-6047	650	11	fear	fear	VERB
ejpam-6047	650	12	impact	impact	NOUN
ejpam-6047	650	13	and	and	CCONJ
ejpam-6047	650	14	hunting	hunt	VERB
ejpam-6047	650	15	cooperation	cooperation	NOUN
ejpam-6047	650	16	.	.	PUNCT
ejpam-6047	651	1	journal	journal	PROPN
ejpam-6047	651	2	of	of	ADP
ejpam-6047	651	3	education	education	NOUN
ejpam-6047	651	4	for	for	ADP
ejpam-6047	651	5	pure	pure	ADJ
ejpam-6047	651	6	science	science	NOUN
ejpam-6047	651	7	-	-	PUNCT
ejpam-6047	651	8	university	university	NOUN
ejpam-6047	651	9	of	of	ADP
ejpam-6047	651	10	thi	thi	PROPN
ejpam-6047	651	11	-	-	PUNCT
ejpam-6047	651	12	qar	qar	PROPN
ejpam-6047	651	13	,	,	PUNCT
ejpam-6047	651	14	14(2	14(2	NUM
ejpam-6047	651	15	)	)	PUNCT
ejpam-6047	651	16	,	,	PUNCT
ejpam-6047	651	17	2024	2024	NUM
ejpam-6047	651	18	.	.	PUNCT
ejpam-6047	652	1	[	[	X
ejpam-6047	652	2	26	26	NUM
ejpam-6047	652	3	]	]	PUNCT
ejpam-6047	652	4	katsuhisa	katsuhisa	NOUN
ejpam-6047	652	5	furuta	furuta	PROPN
ejpam-6047	652	6	and	and	CCONJ
ejpam-6047	652	7	s	s	PROPN
ejpam-6047	652	8	kim	kim	PROPN
ejpam-6047	652	9	.	.	PUNCT
ejpam-6047	653	1	pole	pole	PROPN
ejpam-6047	653	2	assignment	assignment	NOUN
ejpam-6047	653	3	in	in	ADP
ejpam-6047	653	4	a	a	DET
ejpam-6047	653	5	specified	specify	VERB
ejpam-6047	653	6	disk	disk	NOUN
ejpam-6047	653	7	.	.	PUNCT
ejpam-6047	654	1	ieee	ieee	NOUN
ejpam-6047	654	2	transactions	transaction	NOUN
ejpam-6047	654	3	on	on	ADP
ejpam-6047	654	4	automatic	automatic	ADJ
ejpam-6047	654	5	control	control	NOUN
ejpam-6047	654	6	,	,	PUNCT
ejpam-6047	654	7	32(5):423–427	32(5):423–427	PROPN
ejpam-6047	654	8	,	,	PUNCT
ejpam-6047	654	9	1987	1987	NUM
ejpam-6047	654	10	.	.	PUNCT
ejpam-6047	655	1	[	[	X
ejpam-6047	655	2	27	27	NUM
ejpam-6047	655	3	]	]	X
ejpam-6047	655	4	chun	chun	PROPN
ejpam-6047	655	5	-	-	PUNCT
ejpam-6047	655	6	hsiung	hsiung	PROPN
ejpam-6047	655	7	fang	fang	PROPN
ejpam-6047	655	8	and	and	CCONJ
ejpam-6047	655	9	li	li	PROPN
ejpam-6047	655	10	lee	lee	PROPN
ejpam-6047	655	11	.	.	PUNCT
ejpam-6047	655	12	robustness	robustness	NOUN
ejpam-6047	655	13	of	of	ADP
ejpam-6047	655	14	regional	regional	ADJ
ejpam-6047	655	15	pole	pole	NOUN
ejpam-6047	655	16	placement	placement	NOUN
ejpam-6047	655	17	for	for	ADP
ejpam-6047	655	18	uncertain	uncertain	ADJ
ejpam-6047	655	19	continuous	continuous	ADJ
ejpam-6047	655	20	-	-	PUNCT
ejpam-6047	655	21	time	time	NOUN
ejpam-6047	655	22	implicit	implicit	ADJ
ejpam-6047	655	23	systems	system	NOUN
ejpam-6047	655	24	.	.	PUNCT
ejpam-6047	656	1	ieee	ieee	NOUN
ejpam-6047	656	2	transactions	transaction	NOUN
ejpam-6047	656	3	on	on	ADP
ejpam-6047	656	4	automatic	automatic	ADJ
ejpam-6047	656	5	control	control	NOUN
ejpam-6047	656	6	,	,	PUNCT
ejpam-6047	656	7	39(11):2303–2307	39(11):2303–2307	NUM
ejpam-6047	656	8	,	,	PUNCT
ejpam-6047	656	9	1994	1994	NUM
ejpam-6047	656	10	.	.	PUNCT
ejpam-6047	657	1	[	[	X
ejpam-6047	657	2	28	28	NUM
ejpam-6047	657	3	]	]	X
ejpam-6047	657	4	chun	chun	PROPN
ejpam-6047	657	5	-	-	PUNCT
ejpam-6047	657	6	hsiung	hsiung	PROPN
ejpam-6047	657	7	fang	fang	PROPN
ejpam-6047	657	8	,	,	PUNCT
ejpam-6047	657	9	li	li	PROPN
ejpam-6047	657	10	lee	lee	PROPN
ejpam-6047	657	11	,	,	PUNCT
ejpam-6047	657	12	and	and	CCONJ
ejpam-6047	657	13	fan	fan	PROPN
ejpam-6047	657	14	-	-	PUNCT
ejpam-6047	657	15	ren	ren	PROPN
ejpam-6047	657	16	chang	chang	PROPN
ejpam-6047	657	17	.	.	PUNCT
ejpam-6047	658	1	robust	robust	ADJ
ejpam-6047	658	2	control	control	NOUN
ejpam-6047	658	3	analysis	analysis	NOUN
ejpam-6047	658	4	and	and	CCONJ
ejpam-6047	658	5	design	design	NOUN
ejpam-6047	658	6	for	for	ADP
ejpam-6047	658	7	discrete	discrete	ADJ
ejpam-6047	658	8	-	-	PUNCT
ejpam-6047	658	9	time	time	NOUN
ejpam-6047	658	10	singular	singular	PROPN
ejpam-6047	658	11	systems	system	NOUN
ejpam-6047	658	12	.	.	PUNCT
ejpam-6047	659	1	automatica	automatica	PROPN
ejpam-6047	659	2	,	,	PUNCT
ejpam-6047	659	3	30(11):1741–1750	30(11):1741–1750	NUM
ejpam-6047	659	4	,	,	PUNCT
ejpam-6047	659	5	1994	1994	NUM
ejpam-6047	659	6	.	.	PUNCT
ejpam-6047	660	1	[	[	X
ejpam-6047	660	2	29	29	NUM
ejpam-6047	660	3	]	]	X
ejpam-6047	660	4	shengyuan	shengyuan	PROPN
ejpam-6047	660	5	xu	xu	PROPN
ejpam-6047	660	6	,	,	PUNCT
ejpam-6047	660	7	james	james	PROPN
ejpam-6047	660	8	lam	lam	PROPN
ejpam-6047	660	9	,	,	PUNCT
ejpam-6047	660	10	and	and	CCONJ
ejpam-6047	660	11	chengwu	chengwu	PROPN
ejpam-6047	660	12	yang	yang	PROPN
ejpam-6047	660	13	.	.	PUNCT
ejpam-6047	661	1	robust	robust	ADJ
ejpam-6047	661	2	h	h	NOUN
ejpam-6047	661	3	control	control	NOUN
ejpam-6047	661	4	for	for	ADP
ejpam-6047	661	5	uncertain	uncertain	ADJ
ejpam-6047	661	6	m.u	m.u	PROPN
ejpam-6047	662	1	.	.	PROPN
ejpam-6047	662	2	rehman	rehman	PROPN
ejpam-6047	662	3	et	et	PROPN
ejpam-6047	662	4	al	al	PROPN
ejpam-6047	662	5	.	.	PUNCT
ejpam-6047	662	6	/	/	SYM
ejpam-6047	662	7	eur	eur	PROPN
ejpam-6047	662	8	.	.	PUNCT
ejpam-6047	663	1	j.	j.	PROPN
ejpam-6047	663	2	pure	pure	PROPN
ejpam-6047	663	3	appl	appl	PROPN
ejpam-6047	663	4	.	.	PROPN
ejpam-6047	663	5	math	math	PROPN
ejpam-6047	663	6	,	,	PUNCT
ejpam-6047	663	7	18	18	NUM
ejpam-6047	663	8	(	(	PUNCT
ejpam-6047	663	9	3	3	NUM
ejpam-6047	663	10	)	)	PUNCT
ejpam-6047	663	11	(	(	PUNCT
ejpam-6047	663	12	2025	2025	NUM
ejpam-6047	663	13	)	)	PUNCT
ejpam-6047	663	14	,	,	PUNCT
ejpam-6047	663	15	6047	6047	NUM
ejpam-6047	663	16	32	32	NUM
ejpam-6047	663	17	of	of	ADP
ejpam-6047	663	18	33	33	NUM
ejpam-6047	663	19	discrete	discrete	ADJ
ejpam-6047	663	20	singular	singular	NOUN
ejpam-6047	663	21	systems	system	NOUN
ejpam-6047	663	22	with	with	ADP
ejpam-6047	663	23	pole	pole	ADJ
ejpam-6047	663	24	placement	placement	NOUN
ejpam-6047	663	25	in	in	ADP
ejpam-6047	663	26	a	a	DET
ejpam-6047	663	27	disk	disk	NOUN
ejpam-6047	663	28	.	.	PUNCT
ejpam-6047	664	1	systems	system	NOUN
ejpam-6047	664	2	&	&	CCONJ
ejpam-6047	664	3	control	control	PROPN
ejpam-6047	664	4	letters	letter	NOUN
ejpam-6047	664	5	,	,	PUNCT
ejpam-6047	664	6	43(2):85–93	43(2):85–93	NUM
ejpam-6047	664	7	,	,	PUNCT
ejpam-6047	664	8	2001	2001	NUM
ejpam-6047	664	9	.	.	PUNCT
ejpam-6047	665	1	[	[	X
ejpam-6047	665	2	30	30	NUM
ejpam-6047	665	3	]	]	X
ejpam-6047	665	4	tung	tung	PROPN
ejpam-6047	665	5	-	-	PUNCT
ejpam-6047	665	6	kuan	kuan	PROPN
ejpam-6047	665	7	liu	liu	PROPN
ejpam-6047	665	8	,	,	PUNCT
ejpam-6047	665	9	shinn	shinn	PROPN
ejpam-6047	665	10	-	-	PUNCT
ejpam-6047	665	11	horng	horng	PROPN
ejpam-6047	665	12	chen	chen	PROPN
ejpam-6047	665	13	,	,	PUNCT
ejpam-6047	665	14	jyh	jyh	NOUN
ejpam-6047	665	15	-	-	PUNCT
ejpam-6047	665	16	horng	horng	ADJ
ejpam-6047	665	17	chou	chou	NOUN
ejpam-6047	665	18	,	,	PUNCT
ejpam-6047	665	19	and	and	CCONJ
ejpam-6047	665	20	cheng	cheng	PROPN
ejpam-6047	665	21	-	-	PUNCT
ejpam-6047	665	22	yi	yi	PROPN
ejpam-6047	665	23	chen	chen	PROPN
ejpam-6047	665	24	.	.	PUNCT
ejpam-6047	666	1	regional	regional	ADJ
ejpam-6047	666	2	eigenvalue	eigenvalue	NOUN
ejpam-6047	666	3	-	-	PUNCT
ejpam-6047	666	4	clustering	cluster	VERB
ejpam-6047	666	5	robustness	robustness	NOUN
ejpam-6047	666	6	of	of	ADP
ejpam-6047	666	7	linear	linear	ADJ
ejpam-6047	666	8	uncertain	uncertain	ADJ
ejpam-6047	666	9	multivariable	multivariable	ADJ
ejpam-6047	666	10	output	output	NOUN
ejpam-6047	666	11	feedback	feedback	NOUN
ejpam-6047	666	12	pid	pid	NOUN
ejpam-6047	666	13	control	control	NOUN
ejpam-6047	666	14	systems	systems	PROPN
ejpam-6047	666	15	.	.	PUNCT
ejpam-6047	667	1	journal	journal	NOUN
ejpam-6047	667	2	of	of	ADP
ejpam-6047	667	3	the	the	DET
ejpam-6047	667	4	franklin	franklin	PROPN
ejpam-6047	667	5	institute	institute	PROPN
ejpam-6047	667	6	,	,	PUNCT
ejpam-6047	667	7	346(3):253–266	346(3):253–266	NUM
ejpam-6047	667	8	,	,	PUNCT
ejpam-6047	667	9	2009	2009	NUM
ejpam-6047	667	10	.	.	PUNCT
ejpam-6047	668	1	[	[	X
ejpam-6047	668	2	31	31	NUM
ejpam-6047	668	3	]	]	PUNCT
ejpam-6047	668	4	roger	roger	PROPN
ejpam-6047	668	5	w	w	PROPN
ejpam-6047	668	6	brockett	brockett	PROPN
ejpam-6047	668	7	.	.	PUNCT
ejpam-6047	669	1	finite	finite	VERB
ejpam-6047	669	2	dimensional	dimensional	ADJ
ejpam-6047	669	3	linear	linear	NOUN
ejpam-6047	669	4	systems	system	NOUN
ejpam-6047	669	5	.	.	PUNCT
ejpam-6047	670	1	siam	siam	PROPN
ejpam-6047	670	2	,	,	PUNCT
ejpam-6047	670	3	2015	2015	NUM
ejpam-6047	670	4	.	.	PUNCT
ejpam-6047	671	1	[	[	X
ejpam-6047	671	2	32	32	NUM
ejpam-6047	671	3	]	]	PUNCT
ejpam-6047	671	4	tosio	tosio	PROPN
ejpam-6047	671	5	kato	kato	PROPN
ejpam-6047	671	6	.	.	PUNCT
ejpam-6047	671	7	perturbation	perturbation	NOUN
ejpam-6047	671	8	theory	theory	NOUN
ejpam-6047	671	9	for	for	ADP
ejpam-6047	671	10	linear	linear	PROPN
ejpam-6047	671	11	operators	operator	NOUN
ejpam-6047	671	12	,	,	PUNCT
ejpam-6047	671	13	volume	volume	NOUN
ejpam-6047	671	14	132	132	NUM
ejpam-6047	671	15	.	.	PUNCT
ejpam-6047	671	16	springer	springer	NOUN
ejpam-6047	671	17	science	science	PROPN
ejpam-6047	671	18	&	&	CCONJ
ejpam-6047	671	19	business	business	NOUN
ejpam-6047	671	20	media	medium	NOUN
ejpam-6047	671	21	,	,	PUNCT
ejpam-6047	671	22	2013	2013	NUM
ejpam-6047	671	23	.	.	PUNCT
ejpam-6047	672	1	[	[	X
ejpam-6047	672	2	33	33	NUM
ejpam-6047	672	3	]	]	PUNCT
ejpam-6047	672	4	aleksandar	aleksandar	PROPN
ejpam-6047	672	5	cvetković.	cvetković.	PROPN
ejpam-6047	672	6	stabilizing	stabilize	VERB
ejpam-6047	672	7	the	the	DET
ejpam-6047	672	8	metzler	metzler	NOUN
ejpam-6047	672	9	matrices	matrix	NOUN
ejpam-6047	672	10	with	with	ADP
ejpam-6047	672	11	applications	application	NOUN
ejpam-6047	672	12	to	to	ADP
ejpam-6047	672	13	dynamical	dynamical	ADJ
ejpam-6047	672	14	systems	system	NOUN
ejpam-6047	672	15	.	.	PUNCT
ejpam-6047	673	1	calcolo	calcolo	PROPN
ejpam-6047	673	2	,	,	PUNCT
ejpam-6047	673	3	57(1):1	57(1):1	NUM
ejpam-6047	673	4	,	,	PUNCT
ejpam-6047	673	5	2020	2020	NUM
ejpam-6047	673	6	.	.	PUNCT
ejpam-6047	674	1	[	[	X
ejpam-6047	674	2	34	34	NUM
ejpam-6047	674	3	]	]	X
ejpam-6047	674	4	kumpati	kumpati	PROPN
ejpam-6047	674	5	s	s	PROPN
ejpam-6047	674	6	narendra	narendra	PROPN
ejpam-6047	674	7	and	and	CCONJ
ejpam-6047	674	8	robert	robert	PROPN
ejpam-6047	674	9	shorten	shorten	PROPN
ejpam-6047	674	10	.	.	PUNCT
ejpam-6047	675	1	hurwitz	hurwitz	PROPN
ejpam-6047	675	2	stability	stability	NOUN
ejpam-6047	675	3	of	of	ADP
ejpam-6047	675	4	metzler	metzler	NOUN
ejpam-6047	675	5	matrices	matrix	NOUN
ejpam-6047	675	6	.	.	PUNCT
ejpam-6047	676	1	ieee	ieee	NOUN
ejpam-6047	676	2	transactions	transaction	NOUN
ejpam-6047	676	3	on	on	ADP
ejpam-6047	676	4	automatic	automatic	ADJ
ejpam-6047	676	5	control	control	NOUN
ejpam-6047	676	6	,	,	PUNCT
ejpam-6047	676	7	55(6):1484–1487	55(6):1484–1487	NUM
ejpam-6047	676	8	,	,	PUNCT
ejpam-6047	676	9	2010	2010	NUM
ejpam-6047	676	10	.	.	PUNCT
ejpam-6047	677	1	[	[	X
ejpam-6047	677	2	35	35	NUM
ejpam-6047	677	3	]	]	X
ejpam-6047	677	4	igor	igor	NOUN
ejpam-6047	677	5	podlubny	podlubny	PROPN
ejpam-6047	677	6	.	.	PUNCT
ejpam-6047	678	1	fractional	fractional	ADJ
ejpam-6047	678	2	differential	differential	ADJ
ejpam-6047	678	3	equations	equation	NOUN
ejpam-6047	678	4	:	:	PUNCT
ejpam-6047	678	5	an	an	DET
ejpam-6047	678	6	introduction	introduction	NOUN
ejpam-6047	678	7	to	to	ADP
ejpam-6047	678	8	fractional	fractional	ADJ
ejpam-6047	678	9	derivatives	derivative	NOUN
ejpam-6047	678	10	,	,	PUNCT
ejpam-6047	678	11	fractional	fractional	ADJ
ejpam-6047	678	12	differential	differential	ADJ
ejpam-6047	678	13	equations	equation	NOUN
ejpam-6047	678	14	,	,	PUNCT
ejpam-6047	678	15	to	to	ADP
ejpam-6047	678	16	methods	method	NOUN
ejpam-6047	678	17	of	of	ADP
ejpam-6047	678	18	their	their	PRON
ejpam-6047	678	19	solution	solution	NOUN
ejpam-6047	678	20	and	and	CCONJ
ejpam-6047	678	21	some	some	PRON
ejpam-6047	678	22	of	of	ADP
ejpam-6047	678	23	their	their	PRON
ejpam-6047	678	24	applications	application	NOUN
ejpam-6047	678	25	,	,	PUNCT
ejpam-6047	678	26	volume	volume	NOUN
ejpam-6047	678	27	198	198	NUM
ejpam-6047	678	28	.	.	PUNCT
ejpam-6047	679	1	elsevier	elsevier	NOUN
ejpam-6047	679	2	,	,	PUNCT
ejpam-6047	679	3	1998	1998	NUM
ejpam-6047	679	4	.	.	PUNCT
ejpam-6047	680	1	[	[	X
ejpam-6047	680	2	36	36	NUM
ejpam-6047	680	3	]	]	X
ejpam-6047	680	4	diethelm	diethelm	PROPN
ejpam-6047	680	5	kai	kai	PROPN
ejpam-6047	680	6	.	.	PUNCT
ejpam-6047	681	1	the	the	DET
ejpam-6047	681	2	analysis	analysis	NOUN
ejpam-6047	681	3	of	of	ADP
ejpam-6047	681	4	fractional	fractional	ADJ
ejpam-6047	681	5	differential	differential	ADJ
ejpam-6047	681	6	equations	equation	NOUN
ejpam-6047	681	7	.	.	PUNCT
ejpam-6047	682	1	an	an	DET
ejpam-6047	682	2	application	application	NOUN
ejpam-6047	682	3	-	-	PUNCT
ejpam-6047	682	4	oriented	orient	VERB
ejpam-6047	682	5	exposition	exposition	NOUN
ejpam-6047	682	6	using	use	VERB
ejpam-6047	682	7	differential	differential	ADJ
ejpam-6047	682	8	operators	operator	NOUN
ejpam-6047	682	9	of	of	ADP
ejpam-6047	682	10	caputo	caputo	PROPN
ejpam-6047	682	11	type	type	PROPN
ejpam-6047	682	12	.	.	PUNCT
ejpam-6047	683	1	lecture	lecture	NOUN
ejpam-6047	683	2	notes	note	NOUN
ejpam-6047	683	3	in	in	ADP
ejpam-6047	683	4	mathematics	mathematic	NOUN
ejpam-6047	683	5	,	,	PUNCT
ejpam-6047	683	6	2010	2010	NUM
ejpam-6047	683	7	.	.	PUNCT
ejpam-6047	684	1	[	[	X
ejpam-6047	684	2	37	37	NUM
ejpam-6047	684	3	]	]	PUNCT
ejpam-6047	684	4	anatoliui	anatoliui	ADJ
ejpam-6047	684	5	aleksandrovich	aleksandrovich	PROPN
ejpam-6047	684	6	kilbas	kilbas	PROPN
ejpam-6047	684	7	,	,	PUNCT
ejpam-6047	684	8	hari	hari	PROPN
ejpam-6047	684	9	m	m	PROPN
ejpam-6047	684	10	srivastava	srivastava	PROPN
ejpam-6047	684	11	,	,	PUNCT
ejpam-6047	684	12	and	and	CCONJ
ejpam-6047	684	13	juan	juan	PROPN
ejpam-6047	684	14	j	j	PROPN
ejpam-6047	684	15	trujillo	trujillo	PROPN
ejpam-6047	684	16	.	.	PUNCT
ejpam-6047	684	17	theory	theory	NOUN
ejpam-6047	684	18	and	and	CCONJ
ejpam-6047	684	19	applications	application	NOUN
ejpam-6047	684	20	of	of	ADP
ejpam-6047	684	21	fractional	fractional	ADJ
ejpam-6047	684	22	differential	differential	ADJ
ejpam-6047	684	23	equations	equation	NOUN
ejpam-6047	684	24	,	,	PUNCT
ejpam-6047	684	25	volume	volume	NOUN
ejpam-6047	684	26	204	204	NUM
ejpam-6047	684	27	.	.	PUNCT
ejpam-6047	685	1	elsevier	elsevier	NOUN
ejpam-6047	685	2	,	,	PUNCT
ejpam-6047	685	3	2006	2006	NUM
ejpam-6047	685	4	.	.	PUNCT
ejpam-6047	686	1	[	[	X
ejpam-6047	686	2	38	38	NUM
ejpam-6047	686	3	]	]	PUNCT
ejpam-6047	686	4	muhammad	muhammad	PROPN
ejpam-6047	686	5	shoaib	shoaib	PROPN
ejpam-6047	686	6	arif	arif	PROPN
ejpam-6047	686	7	,	,	PUNCT
ejpam-6047	686	8	kamaleldin	kamaleldin	NOUN
ejpam-6047	686	9	abodayeh	abodayeh	NOUN
ejpam-6047	686	10	,	,	PUNCT
ejpam-6047	686	11	and	and	CCONJ
ejpam-6047	686	12	yasir	yasir	PROPN
ejpam-6047	686	13	nawaz	nawaz	PROPN
ejpam-6047	686	14	.	.	PUNCT
ejpam-6047	687	1	numerical	numerical	ADJ
ejpam-6047	687	2	schemes	scheme	NOUN
ejpam-6047	687	3	for	for	ADP
ejpam-6047	687	4	fractional	fractional	ADJ
ejpam-6047	687	5	energy	energy	NOUN
ejpam-6047	687	6	balance	balance	NOUN
ejpam-6047	687	7	model	model	NOUN
ejpam-6047	687	8	of	of	ADP
ejpam-6047	687	9	climate	climate	NOUN
ejpam-6047	687	10	change	change	NOUN
ejpam-6047	687	11	with	with	ADP
ejpam-6047	687	12	diffusion	diffusion	NOUN
ejpam-6047	687	13	effects	effect	NOUN
ejpam-6047	687	14	.	.	PUNCT
ejpam-6047	688	1	emerging	emerge	VERB
ejpam-6047	688	2	science	science	NOUN
ejpam-6047	688	3	journal	journal	NOUN
ejpam-6047	688	4	,	,	PUNCT
ejpam-6047	688	5	7(3):808–820	7(3):808–820	NOUN
ejpam-6047	688	6	,	,	PUNCT
ejpam-6047	688	7	2023	2023	NUM
ejpam-6047	688	8	.	.	PUNCT
ejpam-6047	689	1	[	[	X
ejpam-6047	689	2	39	39	NUM
ejpam-6047	689	3	]	]	X
ejpam-6047	689	4	shafiullah	shafiullah	NOUN
ejpam-6047	689	5	,	,	PUNCT
ejpam-6047	689	6	kamal	kamal	PROPN
ejpam-6047	689	7	shah	shah	PROPN
ejpam-6047	689	8	,	,	PUNCT
ejpam-6047	689	9	muhammad	muhammad	PROPN
ejpam-6047	689	10	sarwar	sarwar	PROPN
ejpam-6047	689	11	,	,	PUNCT
ejpam-6047	689	12	and	and	CCONJ
ejpam-6047	689	13	thabet	thabet	ADJ
ejpam-6047	689	14	abdeljawad	abdeljawad	NOUN
ejpam-6047	689	15	.	.	PUNCT
ejpam-6047	690	1	on	on	ADP
ejpam-6047	690	2	theoretical	theoretical	ADJ
ejpam-6047	690	3	and	and	CCONJ
ejpam-6047	690	4	numerical	numerical	ADJ
ejpam-6047	690	5	analysis	analysis	NOUN
ejpam-6047	690	6	of	of	ADP
ejpam-6047	690	7	fractal	fractal	ADJ
ejpam-6047	690	8	–	–	PUNCT
ejpam-6047	690	9	fractional	fractional	ADJ
ejpam-6047	690	10	non	non	ADJ
ejpam-6047	690	11	-	-	ADJ
ejpam-6047	690	12	linear	linear	ADJ
ejpam-6047	690	13	hybrid	hybrid	ADJ
ejpam-6047	690	14	differential	differential	NOUN
ejpam-6047	690	15	equations	equation	NOUN
ejpam-6047	690	16	.	.	PUNCT
ejpam-6047	691	1	nonlinear	nonlinear	ADJ
ejpam-6047	691	2	engineering	engineering	NOUN
ejpam-6047	691	3	,	,	PUNCT
ejpam-6047	691	4	13(1):20220372	13(1):20220372	NUM
ejpam-6047	691	5	,	,	PUNCT
ejpam-6047	691	6	2024	2024	NUM
ejpam-6047	691	7	.	.	PUNCT
ejpam-6047	692	1	[	[	X
ejpam-6047	692	2	40	40	NUM
ejpam-6047	692	3	]	]	PUNCT
ejpam-6047	692	4	mutti	mutti	PROPN
ejpam-6047	692	5	-	-	PUNCT
ejpam-6047	692	6	ur	ur	PROPN
ejpam-6047	692	7	rehman	rehman	PROPN
ejpam-6047	692	8	et	et	PROPN
ejpam-6047	692	9	al	al	PROPN
ejpam-6047	692	10	.	.	PROPN
ejpam-6047	692	11	spectrum	spectrum	PROPN
ejpam-6047	692	12	and	and	CCONJ
ejpam-6047	692	13	pseudspectrum	pseudspectrum	NOUN
ejpam-6047	692	14	of	of	ADP
ejpam-6047	692	15	d	d	ADJ
ejpam-6047	692	16	-	-	ADJ
ejpam-6047	692	17	stable	stable	ADJ
ejpam-6047	692	18	matrices	matrix	NOUN
ejpam-6047	692	19	of	of	ADP
ejpam-6047	692	20	economy	economy	NOUN
ejpam-6047	692	21	models	model	NOUN
ejpam-6047	692	22	.	.	PUNCT
ejpam-6047	693	1	j.	j.	PROPN
ejpam-6047	693	2	math	math	PROPN
ejpam-6047	693	3	.	.	PUNCT
ejpam-6047	694	1	computer	computer	PROPN
ejpam-6047	694	2	sci	sci	PROPN
ejpam-6047	694	3	,	,	PUNCT
ejpam-6047	694	4	38:298–312	38:298–312	NUM
ejpam-6047	694	5	,	,	PUNCT
ejpam-6047	694	6	2025	2025	NUM
ejpam-6047	694	7	.	.	PUNCT
ejpam-6047	695	1	[	[	X
ejpam-6047	695	2	41	41	NUM
ejpam-6047	695	3	]	]	X
ejpam-6047	695	4	mutti	mutti	PROPN
ejpam-6047	695	5	-	-	PUNCT
ejpam-6047	695	6	ur	ur	PROPN
ejpam-6047	695	7	rehman	rehman	PROPN
ejpam-6047	695	8	et	et	PROPN
ejpam-6047	695	9	al	al	PROPN
ejpam-6047	695	10	.	.	PROPN
ejpam-6047	695	11	spectrum	spectrum	PROPN
ejpam-6047	695	12	and	and	CCONJ
ejpam-6047	695	13	pseudspectrum	pseudspectrum	NOUN
ejpam-6047	695	14	of	of	ADP
ejpam-6047	695	15	d	d	ADJ
ejpam-6047	695	16	-	-	ADJ
ejpam-6047	695	17	stable	stable	ADJ
ejpam-6047	695	18	matrices	matrix	NOUN
ejpam-6047	695	19	of	of	ADP
ejpam-6047	695	20	economy	economy	NOUN
ejpam-6047	695	21	models	model	NOUN
ejpam-6047	695	22	.	.	PUNCT
ejpam-6047	696	1	j.	j.	PROPN
ejpam-6047	696	2	math	math	PROPN
ejpam-6047	696	3	.	.	PUNCT
ejpam-6047	697	1	computer	computer	PROPN
ejpam-6047	697	2	sci	sci	PROPN
ejpam-6047	697	3	,	,	PUNCT
ejpam-6047	697	4	38:298–312	38:298–312	NUM
ejpam-6047	697	5	,	,	PUNCT
ejpam-6047	697	6	2025	2025	NUM
ejpam-6047	697	7	.	.	PUNCT
ejpam-6047	698	1	[	[	X
ejpam-6047	698	2	42	42	NUM
ejpam-6047	698	3	]	]	X
ejpam-6047	698	4	mutti	mutti	PROPN
ejpam-6047	698	5	-	-	PUNCT
ejpam-6047	698	6	ur	ur	PROPN
ejpam-6047	698	7	rehman	rehman	PROPN
ejpam-6047	698	8	,	,	PUNCT
ejpam-6047	698	9	behkzod	behkzod	PROPN
ejpam-6047	698	10	aminov	aminov	PROPN
ejpam-6047	698	11	,	,	PUNCT
ejpam-6047	698	12	mohammed	mohammed	PROPN
ejpam-6047	698	13	n	n	PROPN
ejpam-6047	698	14	alshehri	alshehri	PROPN
ejpam-6047	698	15	,	,	PUNCT
ejpam-6047	698	16	mustafa	mustafa	PROPN
ejpam-6047	698	17	m	m	PROPN
ejpam-6047	698	18	mohammed	mohammed	PROPN
ejpam-6047	698	19	,	,	PUNCT
ejpam-6047	698	20	arafa	arafa	NOUN
ejpam-6047	698	21	o	o	PROPN
ejpam-6047	698	22	mustafa	mustafa	PROPN
ejpam-6047	698	23	,	,	PUNCT
ejpam-6047	698	24	nhla	nhla	VERB
ejpam-6047	698	25	a	a	DET
ejpam-6047	698	26	abdalrahman	abdalrahman	NOUN
ejpam-6047	698	27	,	,	PUNCT
ejpam-6047	698	28	mona	mona	PROPN
ejpam-6047	698	29	magzoub	magzoub	PROPN
ejpam-6047	698	30	,	,	PUNCT
ejpam-6047	698	31	hala	hala	PROPN
ejpam-6047	698	32	s	s	PART
ejpam-6047	698	33	mahgoub	mahgoub	NOUN
ejpam-6047	698	34	,	,	PUNCT
ejpam-6047	698	35	sakeena	sakeena	PRON
ejpam-6047	698	36	em	em	PRON
ejpam-6047	698	37	hamed	hamed	PROPN
ejpam-6047	698	38	,	,	PUNCT
ejpam-6047	698	39	runda	runda	PROPN
ejpam-6047	698	40	aa	aa	PROPN
ejpam-6047	698	41	bashir	bashir	PROPN
ejpam-6047	698	42	,	,	PUNCT
ejpam-6047	698	43	et	et	PROPN
ejpam-6047	698	44	al	al	PROPN
ejpam-6047	698	45	.	.	PUNCT
ejpam-6047	699	1	spectral	spectral	ADJ
ejpam-6047	699	2	properties	property	NOUN
ejpam-6047	699	3	of	of	ADP
ejpam-6047	699	4	structured	structured	ADJ
ejpam-6047	699	5	matrices	matrix	NOUN
ejpam-6047	699	6	in	in	ADP
ejpam-6047	699	7	transportation	transportation	NOUN
ejpam-6047	699	8	problems	problem	NOUN
ejpam-6047	699	9	.	.	PUNCT
ejpam-6047	700	1	european	european	ADJ
ejpam-6047	700	2	journal	journal	PROPN
ejpam-6047	700	3	of	of	ADP
ejpam-6047	700	4	pure	pure	ADJ
ejpam-6047	700	5	and	and	CCONJ
ejpam-6047	700	6	applied	applied	ADJ
ejpam-6047	700	7	mathematics	mathematic	NOUN
ejpam-6047	700	8	,	,	PUNCT
ejpam-6047	700	9	18(1):5637–5637	18(1):5637–5637	NUM
ejpam-6047	700	10	,	,	PUNCT
ejpam-6047	700	11	2025	2025	NUM
ejpam-6047	700	12	.	.	PUNCT
ejpam-6047	701	1	[	[	X
ejpam-6047	701	2	43	43	NUM
ejpam-6047	701	3	]	]	X
ejpam-6047	701	4	mutti	mutti	PROPN
ejpam-6047	701	5	-	-	PUNCT
ejpam-6047	701	6	ur	ur	PROPN
ejpam-6047	701	7	rehman	rehman	PROPN
ejpam-6047	701	8	,	,	PUNCT
ejpam-6047	701	9	sakeena	sakeena	PRON
ejpam-6047	701	10	em	em	PRON
ejpam-6047	701	11	hamed	hamed	ADJ
ejpam-6047	701	12	,	,	PUNCT
ejpam-6047	701	13	nidal	nidal	PROPN
ejpam-6047	701	14	e	e	PROPN
ejpam-6047	701	15	taha	taha	PROPN
ejpam-6047	701	16	,	,	PUNCT
ejpam-6047	701	17	arafa	arafa	NOUN
ejpam-6047	701	18	o	o	PROPN
ejpam-6047	701	19	mustafa	mustafa	PROPN
ejpam-6047	701	20	,	,	PUNCT
ejpam-6047	701	21	khurshidbek	khurshidbek	PROPN
ejpam-6047	701	22	dilmurodov	dilmurodov	PROPN
ejpam-6047	701	23	,	,	PUNCT
ejpam-6047	701	24	hala	hala	PROPN
ejpam-6047	701	25	s	s	PART
ejpam-6047	701	26	mahgoub	mahgoub	NOUN
ejpam-6047	701	27	,	,	PUNCT
ejpam-6047	701	28	mona	mona	PROPN
ejpam-6047	701	29	magzoub	magzoub	PROPN
ejpam-6047	701	30	,	,	PUNCT
ejpam-6047	701	31	runda	runda	PROPN
ejpam-6047	701	32	aa	aa	PROPN
ejpam-6047	701	33	bashir	bashir	PROPN
ejpam-6047	701	34	,	,	PUNCT
ejpam-6047	701	35	mustafa	mustafa	PROPN
ejpam-6047	701	36	m	m	PROPN
ejpam-6047	701	37	mohammed	mohammed	PROPN
ejpam-6047	701	38	,	,	PUNCT
ejpam-6047	701	39	and	and	CCONJ
ejpam-6047	701	40	awad	awad	VERB
ejpam-6047	701	41	a	a	DET
ejpam-6047	701	42	bakery	bakery	NOUN
ejpam-6047	701	43	.	.	PUNCT
ejpam-6047	702	1	analysis	analysis	NOUN
ejpam-6047	702	2	of	of	ADP
ejpam-6047	702	3	stability	stability	NOUN
ejpam-6047	702	4	,	,	PUNCT
ejpam-6047	702	5	d	d	NOUN
ejpam-6047	702	6	-	-	NOUN
ejpam-6047	702	7	stability	stability	NOUN
ejpam-6047	702	8	,	,	PUNCT
ejpam-6047	702	9	and	and	CCONJ
ejpam-6047	702	10	pseudospectra	pseudospectra	PROPN
ejpam-6047	702	11	in	in	ADP
ejpam-6047	702	12	economic	economic	ADJ
ejpam-6047	702	13	modeling	modeling	NOUN
ejpam-6047	702	14	.	.	PUNCT
ejpam-6047	703	1	european	european	ADJ
ejpam-6047	703	2	journal	journal	PROPN
ejpam-6047	703	3	of	of	ADP
ejpam-6047	703	4	pure	pure	ADJ
ejpam-6047	703	5	and	and	CCONJ
ejpam-6047	703	6	applied	applied	ADJ
ejpam-6047	703	7	mathematics	mathematic	NOUN
ejpam-6047	703	8	,	,	PUNCT
ejpam-6047	703	9	18(1):5657–5657	18(1):5657–5657	NUM
ejpam-6047	703	10	,	,	PUNCT
ejpam-6047	703	11	2025	2025	NUM
ejpam-6047	703	12	.	.	PUNCT
ejpam-6047	704	1	[	[	X
ejpam-6047	704	2	44	44	NUM
ejpam-6047	704	3	]	]	X
ejpam-6047	704	4	mutti	mutti	PROPN
ejpam-6047	704	5	-	-	PUNCT
ejpam-6047	704	6	ur	ur	PROPN
ejpam-6047	704	7	rehman	rehman	PROPN
ejpam-6047	704	8	,	,	PUNCT
ejpam-6047	704	9	jehad	jehad	PROPN
ejpam-6047	704	10	alzabut	alzabut	PROPN
ejpam-6047	704	11	,	,	PUNCT
ejpam-6047	704	12	muhamad	muhamad	PROPN
ejpam-6047	704	13	tayyab	tayyab	PROPN
ejpam-6047	704	14	,	,	PUNCT
ejpam-6047	704	15	and	and	CCONJ
ejpam-6047	704	16	fouzia	fouzia	AUX
ejpam-6047	704	17	amir	amir	PROPN
ejpam-6047	704	18	.	.	PUNCT
ejpam-6047	705	1	interconnection	interconnection	NOUN
ejpam-6047	705	2	between	between	ADP
ejpam-6047	705	3	schur	schur	PROPN
ejpam-6047	705	4	stability	stability	NOUN
ejpam-6047	705	5	and	and	CCONJ
ejpam-6047	705	6	structured	structure	VERB
ejpam-6047	705	7	singular	singular	ADJ
ejpam-6047	705	8	values	value	NOUN
ejpam-6047	705	9	.	.	PUNCT
ejpam-6047	706	1	contemporary	contemporary	ADJ
ejpam-6047	706	2	mathematics	mathematic	NOUN
ejpam-6047	706	3	,	,	PUNCT
ejpam-6047	706	4	pages	page	NOUN
ejpam-6047	706	5	63–72	63–72	NUM
ejpam-6047	706	6	,	,	PUNCT
ejpam-6047	706	7	2025	2025	NUM
ejpam-6047	706	8	.	.	PUNCT
ejpam-6047	707	1	m.u	m.u	PROPN
ejpam-6047	707	2	.	.	PROPN
ejpam-6047	707	3	rehman	rehman	PROPN
ejpam-6047	707	4	et	et	PROPN
ejpam-6047	707	5	al	al	PROPN
ejpam-6047	707	6	.	.	PUNCT
ejpam-6047	707	7	/	/	SYM
ejpam-6047	707	8	eur	eur	PROPN
ejpam-6047	707	9	.	.	PUNCT
ejpam-6047	708	1	j.	j.	PROPN
ejpam-6047	708	2	pure	pure	PROPN
ejpam-6047	708	3	appl	appl	PROPN
ejpam-6047	708	4	.	.	PROPN
ejpam-6047	708	5	math	math	PROPN
ejpam-6047	708	6	,	,	PUNCT
ejpam-6047	708	7	18	18	NUM
ejpam-6047	708	8	(	(	PUNCT
ejpam-6047	708	9	3	3	NUM
ejpam-6047	708	10	)	)	PUNCT
ejpam-6047	708	11	(	(	PUNCT
ejpam-6047	708	12	2025	2025	NUM
ejpam-6047	708	13	)	)	PUNCT
ejpam-6047	708	14	,	,	PUNCT
ejpam-6047	708	15	6047	6047	NUM
ejpam-6047	708	16	33	33	NUM
ejpam-6047	708	17	of	of	ADP
ejpam-6047	708	18	33	33	NUM
ejpam-6047	708	19	[	[	SYM
ejpam-6047	708	20	45	45	NUM
ejpam-6047	708	21	]	]	PUNCT
ejpam-6047	708	22	micha	micha	PROPN
ejpam-6047	708	23	l	l	PROPN
ejpam-6047	708	24	domka	domka	PROPN
ejpam-6047	708	25	and	and	CCONJ
ejpam-6047	708	26	wojciech	wojciech	PROPN
ejpam-6047	708	27	mitkowski	mitkowski	NOUN
ejpam-6047	708	28	.	.	PUNCT
ejpam-6047	709	1	on	on	ADP
ejpam-6047	709	2	spectrum	spectrum	NOUN
ejpam-6047	709	3	of	of	ADP
ejpam-6047	709	4	metzler	metzler	NOUN
ejpam-6047	709	5	matrices	matrix	NOUN
ejpam-6047	709	6	.	.	PUNCT
ejpam-6047	710	1	przeglad	przeglad	PROPN
ejpam-6047	710	2	elektrotechniczny	elektrotechniczny	NOUN
ejpam-6047	710	3	,	,	PUNCT
ejpam-6047	710	4	98(12	98(12	NUM
ejpam-6047	710	5	)	)	PUNCT
ejpam-6047	710	6	,	,	PUNCT
ejpam-6047	710	7	2022	2022	NUM
ejpam-6047	710	8	.	.	PUNCT
ejpam-6047	711	1	[	[	X
ejpam-6047	711	2	46	46	NUM
ejpam-6047	711	3	]	]	SYM
ejpam-6047	711	4	dragoslav	dragoslav	NOUN
ejpam-6047	711	5	d	d	X
ejpam-6047	711	6	siljak	siljak	ADV
ejpam-6047	711	7	.	.	PUNCT
ejpam-6047	712	1	large	large	ADJ
ejpam-6047	712	2	-	-	PUNCT
ejpam-6047	712	3	scale	scale	NOUN
ejpam-6047	712	4	dynamic	dynamic	ADJ
ejpam-6047	712	5	systems	system	NOUN
ejpam-6047	712	6	:	:	PUNCT
ejpam-6047	712	7	stability	stability	NOUN
ejpam-6047	712	8	and	and	CCONJ
ejpam-6047	712	9	structure	structure	NOUN
ejpam-6047	712	10	.	.	PUNCT
ejpam-6047	713	1	(	(	PUNCT
ejpam-6047	713	2	no	no	DET
ejpam-6047	713	3	title	title	NOUN
ejpam-6047	713	4	)	)	PUNCT
ejpam-6047	713	5	,	,	PUNCT
ejpam-6047	713	6	1978	1978	NUM
ejpam-6047	713	7	.	.	PUNCT
ejpam-6047	714	1	[	[	X
ejpam-6047	714	2	47	47	NUM
ejpam-6047	714	3	]	]	X
ejpam-6047	714	4	eyad	eyad	NOUN
ejpam-6047	714	5	h	h	NOUN
ejpam-6047	714	6	abed	abe	VERB
ejpam-6047	714	7	.	.	PUNCT
ejpam-6047	715	1	strong	strong	ADJ
ejpam-6047	715	2	d	d	NOUN
ejpam-6047	715	3	-	-	NOUN
ejpam-6047	715	4	stability	stability	NOUN
ejpam-6047	715	5	.	.	PUNCT
ejpam-6047	716	1	systems	system	NOUN
ejpam-6047	716	2	&	&	CCONJ
ejpam-6047	716	3	control	control	PROPN
ejpam-6047	716	4	letters	letter	NOUN
ejpam-6047	716	5	,	,	PUNCT
ejpam-6047	716	6	7(3):207–212	7(3):207–212	NUM
ejpam-6047	716	7	,	,	PUNCT
ejpam-6047	716	8	1986	1986	NUM
ejpam-6047	716	9	.	.	PUNCT
ejpam-6047	717	1	[	[	X
ejpam-6047	717	2	48	48	NUM
ejpam-6047	717	3	]	]	X
ejpam-6047	717	4	olga	olga	PROPN
ejpam-6047	717	5	y	y	PROPN
ejpam-6047	717	6	kushel	kushel	PROPN
ejpam-6047	717	7	.	.	PUNCT
ejpam-6047	718	1	how	how	SCONJ
ejpam-6047	718	2	to	to	PART
ejpam-6047	718	3	check	check	VERB
ejpam-6047	718	4	d	d	NOUN
ejpam-6047	718	5	-	-	NOUN
ejpam-6047	718	6	stability	stability	NOUN
ejpam-6047	718	7	:	:	PUNCT
ejpam-6047	718	8	a	a	DET
ejpam-6047	718	9	simple	simple	ADJ
ejpam-6047	718	10	determinantal	determinantal	ADJ
ejpam-6047	718	11	test	test	NOUN
ejpam-6047	718	12	.	.	PUNCT
ejpam-6047	719	1	arxiv	arxiv	PROPN
ejpam-6047	719	2	preprint	preprint	NOUN
ejpam-6047	719	3	arxiv:2210.05711	arxiv:2210.05711	NOUN
ejpam-6047	719	4	,	,	PUNCT
ejpam-6047	719	5	2022	2022	NUM
ejpam-6047	719	6	.	.	PUNCT
ejpam-6047	720	1	[	[	X
ejpam-6047	720	2	49	49	NUM
ejpam-6047	720	3	]	]	X
ejpam-6047	720	4	lloyd	lloyd	PROPN
ejpam-6047	720	5	n	n	PROPN
ejpam-6047	720	6	trefethen	trefethen	NOUN
ejpam-6047	720	7	and	and	CCONJ
ejpam-6047	720	8	mark	mark	PROPN
ejpam-6047	720	9	embree	embree	PROPN
ejpam-6047	720	10	.	.	PUNCT
ejpam-6047	720	11	spectra	spectra	PROPN
ejpam-6047	720	12	and	and	CCONJ
ejpam-6047	720	13	pseudospectra	pseudospectra	PROPN
ejpam-6047	720	14	:	:	PUNCT
ejpam-6047	720	15	the	the	DET
ejpam-6047	720	16	behavior	behavior	NOUN
ejpam-6047	720	17	of	of	ADP
ejpam-6047	720	18	nonnormal	nonnormal	ADJ
ejpam-6047	720	19	matrices	matrix	NOUN
ejpam-6047	720	20	and	and	CCONJ
ejpam-6047	720	21	operators	operator	NOUN
ejpam-6047	720	22	.	.	PUNCT
ejpam-6047	721	1	2020	2020	NUM
ejpam-6047	721	2	.	.	PUNCT
ejpam-6047	722	1	[	[	X
ejpam-6047	722	2	50	50	NUM
ejpam-6047	722	3	]	]	PUNCT
ejpam-6047	722	4	wasfi	wasfi	NOUN
ejpam-6047	722	5	kafri	kafri	PROPN
ejpam-6047	722	6	.	.	PUNCT
ejpam-6047	723	1	robust	robust	ADJ
ejpam-6047	723	2	d	d	NOUN
ejpam-6047	723	3	-	-	NOUN
ejpam-6047	723	4	stability	stability	NOUN
ejpam-6047	723	5	.	.	PUNCT
ejpam-6047	724	1	applied	apply	VERB
ejpam-6047	724	2	mathematics	mathematics	NOUN
ejpam-6047	724	3	letters	letter	NOUN
ejpam-6047	724	4	,	,	PUNCT
ejpam-6047	724	5	15(3):7–10	15(3):7–10	NUM
ejpam-6047	724	6	,	,	PUNCT
ejpam-6047	724	7	2001	2001	NUM
ejpam-6047	724	8	.	.	PUNCT
ejpam-6047	725	1	[	[	X
ejpam-6047	725	2	51	51	NUM
ejpam-6047	725	3	]	]	PUNCT
ejpam-6047	725	4	wojciech	wojciech	NOUN
ejpam-6047	725	5	mitkowski	mitkowski	NOUN
ejpam-6047	725	6	.	.	PUNCT
ejpam-6047	726	1	dynamical	dynamical	ADJ
ejpam-6047	726	2	properties	property	NOUN
ejpam-6047	726	3	of	of	ADP
ejpam-6047	726	4	metzler	metzler	NOUN
ejpam-6047	726	5	systems	system	NOUN
ejpam-6047	726	6	.	.	PUNCT
ejpam-6047	727	1	bulletin	bulletin	NOUN
ejpam-6047	727	2	of	of	ADP
ejpam-6047	727	3	the	the	DET
ejpam-6047	727	4	polish	polish	PROPN
ejpam-6047	727	5	academy	academy	PROPN
ejpam-6047	727	6	of	of	ADP
ejpam-6047	727	7	sciences	sciences	PROPN
ejpam-6047	727	8	:	:	PUNCT
ejpam-6047	727	9	technical	technical	ADJ
ejpam-6047	727	10	sciences	science	NOUN
ejpam-6047	727	11	,	,	PUNCT
ejpam-6047	727	12	56(4	56(4	NOUN
ejpam-6047	727	13	)	)	PUNCT
ejpam-6047	727	14	,	,	PUNCT
ejpam-6047	727	15	2008	2008	NUM
ejpam-6047	727	16	.	.	PUNCT
ejpam-6047	728	1	[	[	X
ejpam-6047	728	2	52	52	NUM
ejpam-6047	728	3	]	]	PUNCT
ejpam-6047	728	4	oskar	oskar	PROPN
ejpam-6047	728	5	perron	perron	PROPN
ejpam-6047	728	6	.	.	PUNCT
ejpam-6047	728	7	zur	zur	PROPN
ejpam-6047	729	1	theorie	theorie	PROPN
ejpam-6047	729	2	der	der	ADJ
ejpam-6047	729	3	matrices	matrix	NOUN
ejpam-6047	729	4	.	.	PUNCT
ejpam-6047	730	1	mathematische	mathematische	PROPN
ejpam-6047	730	2	annalen	annalen	PROPN
ejpam-6047	730	3	,	,	PUNCT
ejpam-6047	730	4	64(2):248–263	64(2):248–263	PROPN
ejpam-6047	730	5	,	,	PUNCT
ejpam-6047	730	6	1907	1907	NUM
ejpam-6047	730	7	.	.	PUNCT
ejpam-6047	731	1	[	[	X
ejpam-6047	731	2	53	53	NUM
ejpam-6047	731	3	]	]	SYM
ejpam-6047	731	4	fridrikh	fridrikh	NOUN
ejpam-6047	731	5	izrailevich	izrailevich	ADJ
ejpam-6047	731	6	karpelevich	karpelevich	X
ejpam-6047	731	7	.	.	PUNCT
ejpam-6047	732	1	on	on	ADP
ejpam-6047	732	2	the	the	DET
ejpam-6047	732	3	characteristic	characteristic	ADJ
ejpam-6047	732	4	roots	root	NOUN
ejpam-6047	732	5	of	of	ADP
ejpam-6047	732	6	matrices	matrix	NOUN
ejpam-6047	732	7	with	with	ADP
ejpam-6047	732	8	nonnegative	nonnegative	ADJ
ejpam-6047	732	9	elements	element	NOUN
ejpam-6047	732	10	.	.	PUNCT
ejpam-6047	733	1	izvestiya	izvestiya	PROPN
ejpam-6047	733	2	rossiiskoi	rossiiskoi	PROPN
ejpam-6047	733	3	akademii	akademii	PROPN
ejpam-6047	733	4	nauk	nauk	PROPN
ejpam-6047	733	5	.	.	PROPN
ejpam-6047	733	6	seriya	seriya	PROPN
ejpam-6047	733	7	matematicheskaya	matematicheskaya	PROPN
ejpam-6047	733	8	,	,	PUNCT
ejpam-6047	733	9	15(4):361–383	15(4):361–383	PROPN
ejpam-6047	733	10	,	,	PUNCT
ejpam-6047	733	11	1951	1951	NUM
ejpam-6047	733	12	.	.	PUNCT
ejpam-6047	734	1	[	[	X
ejpam-6047	734	2	54	54	NUM
ejpam-6047	734	3	]	]	X
ejpam-6047	734	4	jie	jie	PROPN
ejpam-6047	734	5	chen	chen	PROPN
ejpam-6047	734	6	,	,	PUNCT
ejpam-6047	734	7	michael	michael	PROPN
ejpam-6047	734	8	kh	kh	PROPN
ejpam-6047	734	9	fan	fan	PROPN
ejpam-6047	734	10	,	,	PUNCT
ejpam-6047	734	11	and	and	CCONJ
ejpam-6047	734	12	cheng	cheng	PROPN
ejpam-6047	734	13	-	-	PUNCT
ejpam-6047	734	14	ching	ching	PROPN
ejpam-6047	734	15	yu	yu	PROPN
ejpam-6047	734	16	.	.	PUNCT
ejpam-6047	735	1	on	on	ADP
ejpam-6047	735	2	d	d	NOUN
ejpam-6047	735	3	-	-	NOUN
ejpam-6047	735	4	stability	stability	NOUN
ejpam-6047	735	5	and	and	CCONJ
ejpam-6047	735	6	structured	structure	VERB
ejpam-6047	735	7	singular	singular	ADJ
ejpam-6047	735	8	values	value	NOUN
ejpam-6047	735	9	.	.	PUNCT
ejpam-6047	736	1	systems	system	NOUN
ejpam-6047	736	2	&	&	CCONJ
ejpam-6047	736	3	control	control	PROPN
ejpam-6047	736	4	letters	letter	NOUN
ejpam-6047	736	5	,	,	PUNCT
ejpam-6047	736	6	24(1):19–24	24(1):19–24	NUM
ejpam-6047	736	7	,	,	PUNCT
ejpam-6047	736	8	1995	1995	NUM
ejpam-6047	736	9	.	.	PUNCT
ejpam-6047	737	1	[	[	X
ejpam-6047	737	2	55	55	NUM
ejpam-6047	737	3	]	]	X
ejpam-6047	737	4	russell	russell	PROPN
ejpam-6047	737	5	allan	allan	PROPN
ejpam-6047	737	6	johnson	johnson	PROPN
ejpam-6047	737	7	,	,	PUNCT
ejpam-6047	737	8	alberto	alberto	PROPN
ejpam-6047	737	9	tesi	tesi	PROPN
ejpam-6047	737	10	,	,	PUNCT
ejpam-6047	737	11	et	et	PROPN
ejpam-6047	737	12	al	al	PROPN
ejpam-6047	737	13	.	.	PROPN
ejpam-6047	738	1	on	on	ADP
ejpam-6047	738	2	the	the	DET
ejpam-6047	738	3	d	d	NOUN
ejpam-6047	738	4	-	-	PUNCT
ejpam-6047	738	5	stability	stability	NOUN
ejpam-6047	738	6	problem	problem	NOUN
ejpam-6047	738	7	for	for	ADP
ejpam-6047	738	8	real	real	ADJ
ejpam-6047	738	9	matrices	matrix	NOUN
ejpam-6047	738	10	.	.	PUNCT
ejpam-6047	739	1	bollettino	bollettino	PROPN
ejpam-6047	739	2	dell’unione	dell’unione	PROPN
ejpam-6047	739	3	matematica	matematica	PROPN
ejpam-6047	739	4	italiana	italiana	PROPN
ejpam-6047	739	5	.	.	PROPN
ejpam-6047	740	1	b	b	X
ejpam-6047	740	2	,	,	PUNCT
ejpam-6047	740	3	2:299–314	2:299–314	NUM
ejpam-6047	740	4	,	,	PUNCT
ejpam-6047	740	5	1999	1999	NUM
ejpam-6047	740	6	.	.	PUNCT
ejpam-6047	741	1	[	[	X
ejpam-6047	741	2	56	56	NUM
ejpam-6047	741	3	]	]	X
ejpam-6047	741	4	john	john	PROPN
ejpam-6047	741	5	r	r	PROPN
ejpam-6047	741	6	silvester	silvester	NOUN
ejpam-6047	741	7	.	.	PUNCT
ejpam-6047	742	1	determinants	determinant	NOUN
ejpam-6047	742	2	of	of	ADP
ejpam-6047	742	3	block	block	NOUN
ejpam-6047	742	4	matrices	matrix	NOUN
ejpam-6047	742	5	.	.	PUNCT
ejpam-6047	743	1	the	the	DET
ejpam-6047	743	2	mathematical	mathematical	ADJ
ejpam-6047	743	3	gazette	gazette	NOUN
ejpam-6047	743	4	,	,	PUNCT
ejpam-6047	743	5	84(501):460–467	84(501):460–467	PROPN
ejpam-6047	743	6	,	,	PUNCT
ejpam-6047	743	7	2000	2000	NUM
ejpam-6047	743	8	.	.	PUNCT
ejpam-6047	744	1	[	[	X
ejpam-6047	744	2	57	57	NUM
ejpam-6047	744	3	]	]	X
ejpam-6047	744	4	jietae	jietae	PROPN
ejpam-6047	744	5	lee	lee	PROPN
ejpam-6047	744	6	and	and	CCONJ
ejpam-6047	744	7	thomas	thomas	PROPN
ejpam-6047	744	8	f	f	PROPN
ejpam-6047	744	9	edgar	edgar	PROPN
ejpam-6047	744	10	.	.	PUNCT
ejpam-6047	745	1	real	real	ADJ
ejpam-6047	745	2	structured	structure	VERB
ejpam-6047	745	3	singular	singular	ADJ
ejpam-6047	745	4	value	value	NOUN
ejpam-6047	745	5	conditions	condition	NOUN
ejpam-6047	745	6	for	for	ADP
ejpam-6047	745	7	the	the	DET
ejpam-6047	745	8	strong	strong	ADJ
ejpam-6047	745	9	d	d	NOUN
ejpam-6047	745	10	-	-	NOUN
ejpam-6047	745	11	stability	stability	NOUN
ejpam-6047	745	12	.	.	PUNCT
ejpam-6047	746	1	systems	system	NOUN
ejpam-6047	746	2	&	&	CCONJ
ejpam-6047	746	3	control	control	PROPN
ejpam-6047	746	4	letters	letter	NOUN
ejpam-6047	746	5	,	,	PUNCT
ejpam-6047	746	6	44(4):273–277	44(4):273–277	PROPN
ejpam-6047	746	7	,	,	PUNCT
ejpam-6047	746	8	2001	2001	NUM
ejpam-6047	746	9	.	.	PUNCT
ejpam-6047	747	1	[	[	X
ejpam-6047	747	2	58	58	NUM
ejpam-6047	747	3	]	]	PUNCT
ejpam-6047	747	4	wojciech	wojciech	NOUN
ejpam-6047	747	5	mitkowski	mitkowski	NOUN
ejpam-6047	747	6	.	.	PUNCT
ejpam-6047	748	1	dynamical	dynamical	ADJ
ejpam-6047	748	2	properties	property	NOUN
ejpam-6047	748	3	of	of	ADP
ejpam-6047	748	4	metzler	metzler	NOUN
ejpam-6047	748	5	systems	system	NOUN
ejpam-6047	748	6	.	.	PUNCT
ejpam-6047	749	1	bulletin	bulletin	NOUN
ejpam-6047	749	2	of	of	ADP
ejpam-6047	749	3	the	the	DET
ejpam-6047	749	4	polish	polish	PROPN
ejpam-6047	749	5	academy	academy	PROPN
ejpam-6047	749	6	of	of	ADP
ejpam-6047	749	7	sciences	sciences	PROPN
ejpam-6047	749	8	:	:	PUNCT
ejpam-6047	749	9	technical	technical	ADJ
ejpam-6047	749	10	sciences	science	NOUN
ejpam-6047	749	11	,	,	PUNCT
ejpam-6047	749	12	56(4	56(4	NOUN
ejpam-6047	749	13	)	)	PUNCT
ejpam-6047	749	14	,	,	PUNCT
ejpam-6047	749	15	2008	2008	NUM
ejpam-6047	749	16	.	.	PUNCT
ejpam-6047	750	1	[	[	X
ejpam-6047	750	2	59	59	NUM
ejpam-6047	750	3	]	]	X
ejpam-6047	750	4	lorenzo	lorenzo	PROPN
ejpam-6047	750	5	farina	farina	PROPN
ejpam-6047	750	6	and	and	CCONJ
ejpam-6047	750	7	sergio	sergio	PROPN
ejpam-6047	750	8	rinaldi	rinaldi	PROPN
ejpam-6047	750	9	.	.	PROPN
ejpam-6047	751	1	positive	positive	ADJ
ejpam-6047	751	2	linear	linear	PROPN
ejpam-6047	751	3	systems	system	NOUN
ejpam-6047	751	4	:	:	PUNCT
ejpam-6047	751	5	theory	theory	NOUN
ejpam-6047	751	6	and	and	CCONJ
ejpam-6047	751	7	applications	application	NOUN
ejpam-6047	751	8	.	.	PUNCT
ejpam-6047	752	1	john	john	PROPN
ejpam-6047	752	2	wiley	wiley	PROPN
ejpam-6047	752	3	&	&	CCONJ
ejpam-6047	752	4	sons	son	NOUN
ejpam-6047	752	5	,	,	PUNCT
ejpam-6047	752	6	2011	2011	NUM
ejpam-6047	752	7	.	.	PUNCT
ejpam-6047	753	1	[	[	X
ejpam-6047	753	2	60	60	NUM
ejpam-6047	753	3	]	]	X
ejpam-6047	753	4	david	david	PROPN
ejpam-6047	753	5	g	g	PROPN
ejpam-6047	753	6	luenberger	luenberg	ADJ
ejpam-6047	753	7	.	.	PUNCT
ejpam-6047	754	1	introduction	introduction	NOUN
ejpam-6047	754	2	to	to	ADP
ejpam-6047	754	3	dynamic	dynamic	ADJ
ejpam-6047	754	4	systems	system	NOUN
ejpam-6047	754	5	:	:	PUNCT
ejpam-6047	755	1	theory	theory	NOUN
ejpam-6047	755	2	,	,	PUNCT
ejpam-6047	755	3	models	model	NOUN
ejpam-6047	755	4	,	,	PUNCT
ejpam-6047	755	5	and	and	CCONJ
ejpam-6047	755	6	applications	application	NOUN
ejpam-6047	755	7	.	.	PUNCT
ejpam-6047	756	1	(	(	PUNCT
ejpam-6047	756	2	no	no	DET
ejpam-6047	756	3	title	title	NOUN
ejpam-6047	756	4	)	)	PUNCT
ejpam-6047	756	5	,	,	PUNCT
ejpam-6047	756	6	1979	1979	NUM
ejpam-6047	756	7	.	.	PUNCT
ejpam-6047	757	1	[	[	X
ejpam-6047	757	2	61	61	NUM
ejpam-6047	757	3	]	]	PUNCT
ejpam-6047	757	4	corentin	corentin	PROPN
ejpam-6047	757	5	briat	briat	PROPN
ejpam-6047	757	6	.	.	PUNCT
ejpam-6047	758	1	sign	sign	VERB
ejpam-6047	758	2	properties	property	NOUN
ejpam-6047	758	3	of	of	ADP
ejpam-6047	758	4	metzler	metzler	NOUN
ejpam-6047	758	5	matrices	matrix	NOUN
ejpam-6047	758	6	with	with	ADP
ejpam-6047	758	7	applications	application	NOUN
ejpam-6047	758	8	.	.	PUNCT
ejpam-6047	759	1	linear	linear	ADJ
ejpam-6047	759	2	algebra	algebra	NOUN
ejpam-6047	759	3	and	and	CCONJ
ejpam-6047	759	4	its	its	PRON
ejpam-6047	759	5	applications	application	NOUN
ejpam-6047	759	6	,	,	PUNCT
ejpam-6047	759	7	515:53–86	515:53–86	NUM
ejpam-6047	759	8	,	,	PUNCT
ejpam-6047	759	9	2017	2017	NUM
ejpam-6047	759	10	.	.	PUNCT
ejpam-6047	760	1	[	[	X
ejpam-6047	760	2	62	62	NUM
ejpam-6047	760	3	]	]	X
ejpam-6047	760	4	daniel	daniel	PROPN
ejpam-6047	760	5	liberzon	liberzon	PROPN
ejpam-6047	760	6	.	.	PUNCT
ejpam-6047	761	1	switching	switch	VERB
ejpam-6047	761	2	in	in	ADP
ejpam-6047	761	3	systems	system	NOUN
ejpam-6047	761	4	and	and	CCONJ
ejpam-6047	761	5	control	control	NOUN
ejpam-6047	761	6	,	,	PUNCT
ejpam-6047	761	7	volume	volume	NOUN
ejpam-6047	761	8	190	190	NUM
ejpam-6047	761	9	.	.	PUNCT
ejpam-6047	761	10	springer	springer	NOUN
ejpam-6047	761	11	,	,	PUNCT
ejpam-6047	761	12	2003	2003	NUM
ejpam-6047	761	13	.	.	PUNCT
ejpam-6047	762	1	[	[	X
ejpam-6047	762	2	63	63	NUM
ejpam-6047	762	3	]	]	PUNCT
ejpam-6047	762	4	leonid	leonid	PROPN
ejpam-6047	762	5	gurvits	gurvits	PROPN
ejpam-6047	762	6	,	,	PUNCT
ejpam-6047	762	7	robert	robert	PROPN
ejpam-6047	762	8	shorten	shorten	PROPN
ejpam-6047	762	9	,	,	PUNCT
ejpam-6047	762	10	and	and	CCONJ
ejpam-6047	762	11	oliver	oliver	PROPN
ejpam-6047	762	12	mason	mason	PROPN
ejpam-6047	762	13	.	.	PUNCT
ejpam-6047	763	1	on	on	ADP
ejpam-6047	763	2	the	the	DET
ejpam-6047	763	3	stability	stability	NOUN
ejpam-6047	763	4	of	of	ADP
ejpam-6047	763	5	switched	switch	VERB
ejpam-6047	763	6	positive	positive	ADJ
ejpam-6047	763	7	linear	linear	NOUN
ejpam-6047	763	8	systems	system	NOUN
ejpam-6047	763	9	.	.	PUNCT
ejpam-6047	764	1	ieee	ieee	NOUN
ejpam-6047	764	2	transactions	transaction	NOUN
ejpam-6047	764	3	on	on	ADP
ejpam-6047	764	4	automatic	automatic	ADJ
ejpam-6047	764	5	control	control	NOUN
ejpam-6047	764	6	,	,	PUNCT
ejpam-6047	764	7	52(6):1099–1103	52(6):1099–1103	NUM
ejpam-6047	764	8	,	,	PUNCT
ejpam-6047	764	9	2007	2007	NUM
ejpam-6047	764	10	.	.	PUNCT
ejpam-6047	765	1	[	[	X
ejpam-6047	765	2	64	64	NUM
ejpam-6047	765	3	]	]	PUNCT
ejpam-6047	765	4	sergio	sergio	PROPN
ejpam-6047	765	5	rinaldi	rinaldi	PROPN
ejpam-6047	765	6	.	.	PROPN
ejpam-6047	765	7	laura	laura	PROPN
ejpam-6047	765	8	and	and	CCONJ
ejpam-6047	765	9	petrarch	petrarch	PROPN
ejpam-6047	765	10	:	:	PUNCT
ejpam-6047	765	11	an	an	DET
ejpam-6047	765	12	intriguing	intriguing	ADJ
ejpam-6047	765	13	case	case	NOUN
ejpam-6047	765	14	of	of	ADP
ejpam-6047	765	15	cyclical	cyclical	ADJ
ejpam-6047	765	16	love	love	NOUN
ejpam-6047	765	17	dynamics	dynamic	NOUN
ejpam-6047	765	18	.	.	PUNCT
ejpam-6047	766	1	siam	siam	PROPN
ejpam-6047	766	2	journal	journal	PROPN
ejpam-6047	766	3	on	on	ADP
ejpam-6047	766	4	applied	apply	VERB
ejpam-6047	766	5	mathematics	mathematic	NOUN
ejpam-6047	766	6	,	,	PUNCT
ejpam-6047	766	7	58(4):1205–1221	58(4):1205–1221	PROPN
ejpam-6047	766	8	,	,	PUNCT
ejpam-6047	766	9	1998	1998	NUM
ejpam-6047	766	10	.	.	PUNCT
ejpam-6047	767	1	[	[	X
ejpam-6047	767	2	65	65	NUM
ejpam-6047	767	3	]	]	X
ejpam-6047	767	4	frederic	frederic	PROPN
ejpam-6047	767	5	j	j	PROPN
ejpam-6047	767	6	jones	jones	PROPN
ejpam-6047	767	7	.	.	PUNCT
ejpam-6047	768	1	the	the	DET
ejpam-6047	768	2	structure	structure	NOUN
ejpam-6047	768	3	of	of	ADP
ejpam-6047	768	4	petrarch	petrarch	PROPN
ejpam-6047	768	5	’s	’s	PART
ejpam-6047	768	6	canzoniere	canzoniere	NOUN
ejpam-6047	768	7	:	:	PUNCT
ejpam-6047	768	8	a	a	DET
ejpam-6047	768	9	chronological	chronological	ADJ
ejpam-6047	768	10	,	,	PUNCT
ejpam-6047	768	11	psychological	psychological	ADJ
ejpam-6047	768	12	,	,	PUNCT
ejpam-6047	768	13	and	and	CCONJ
ejpam-6047	768	14	stylistic	stylistic	ADJ
ejpam-6047	768	15	analysis	analysis	NOUN
ejpam-6047	768	16	.	.	PUNCT
ejpam-6047	769	1	boydell	boydell	PROPN
ejpam-6047	769	2	&	&	CCONJ
ejpam-6047	769	3	brewer	brewer	PROPN
ejpam-6047	769	4	,	,	PUNCT
ejpam-6047	769	5	1995	1995	NUM
ejpam-6047	769	6	.	.	PUNCT