id	sid	tid	token	lemma	pos
ejpam-5638	1	1	european	european	PROPN
ejpam-5638	1	2	journal	journal	PROPN
ejpam-5638	1	3	of	of	ADP
ejpam-5638	1	4	pure	pure	ADJ
ejpam-5638	1	5	and	and	CCONJ
ejpam-5638	1	6	applied	applied	ADJ
ejpam-5638	1	7	mathematics	mathematic	NOUN
ejpam-5638	1	8	2025	2025	NUM
ejpam-5638	1	9	,	,	PUNCT
ejpam-5638	1	10	vol	vol	NOUN
ejpam-5638	1	11	.	.	PROPN
ejpam-5638	1	12	18	18	NUM
ejpam-5638	1	13	,	,	PUNCT
ejpam-5638	1	14	issue	issue	NOUN
ejpam-5638	1	15	2	2	NUM
ejpam-5638	1	16	,	,	PUNCT
ejpam-5638	1	17	article	article	NOUN
ejpam-5638	1	18	number	number	NOUN
ejpam-5638	1	19	5638	5638	NUM
ejpam-5638	1	20	issn	issn	PROPN
ejpam-5638	1	21	1307	1307	NUM
ejpam-5638	1	22	-	-	SYM
ejpam-5638	1	23	5543	5543	NUM
ejpam-5638	1	24	–	–	PUNCT
ejpam-5638	1	25	ejpam.com	ejpam.com	X
ejpam-5638	1	26	published	publish	VERB
ejpam-5638	1	27	by	by	ADP
ejpam-5638	1	28	new	new	PROPN
ejpam-5638	1	29	york	york	PROPN
ejpam-5638	1	30	business	business	PROPN
ejpam-5638	1	31	global	global	ADJ
ejpam-5638	1	32	d	d	ADJ
ejpam-5638	1	33	-	-	PUNCT
ejpam-5638	1	34	stability	stability	NOUN
ejpam-5638	1	35	analysis	analysis	NOUN
ejpam-5638	1	36	of	of	ADP
ejpam-5638	1	37	structured	structured	ADJ
ejpam-5638	1	38	matrices	matrix	NOUN
ejpam-5638	1	39	appearing	appear	VERB
ejpam-5638	1	40	in	in	ADP
ejpam-5638	1	41	first	first	ADJ
ejpam-5638	1	42	and	and	CCONJ
ejpam-5638	1	43	second	second	ADJ
ejpam-5638	1	44	order	order	NOUN
ejpam-5638	1	45	economy	economy	NOUN
ejpam-5638	1	46	models	model	NOUN
ejpam-5638	1	47	mutti	mutti	PROPN
ejpam-5638	1	48	-	-	PUNCT
ejpam-5638	1	49	ur	ur	PROPN
ejpam-5638	1	50	rehman1	rehman1	NOUN
ejpam-5638	1	51	,	,	PUNCT
ejpam-5638	1	52	salah	salah	PROPN
ejpam-5638	1	53	h.	h.	PROPN
ejpam-5638	1	54	alshabhi2	alshabhi2	PROPN
ejpam-5638	1	55	,	,	PUNCT
ejpam-5638	1	56	om	om	PROPN
ejpam-5638	1	57	kalthum	kalthum	PROPN
ejpam-5638	1	58	s.	s.	PROPN
ejpam-5638	1	59	k.	k.	PROPN
ejpam-5638	1	60	mohamed2	mohamed2	PROPN
ejpam-5638	1	61	,	,	PUNCT
ejpam-5638	1	62	mustafa	mustafa	PROPN
ejpam-5638	1	63	m.	m.	PROPN
ejpam-5638	1	64	mohammed2	mohammed2	PROPN
ejpam-5638	1	65	,	,	PUNCT
ejpam-5638	1	66	runda	runda	PROPN
ejpam-5638	1	67	a.	a.	PROPN
ejpam-5638	1	68	a.	a.	PROPN
ejpam-5638	1	69	bashir2	bashir2	PROPN
ejpam-5638	1	70	,	,	PUNCT
ejpam-5638	1	71	mona	mona	PROPN
ejpam-5638	1	72	magzoub4	magzoub4	PROPN
ejpam-5638	1	73	,	,	PUNCT
ejpam-5638	1	74	sakeena	sakeena	PROPN
ejpam-5638	1	75	e.	e.	PROPN
ejpam-5638	1	76	m.	m.	PROPN
ejpam-5638	1	77	hamed3	hamed3	PROPN
ejpam-5638	1	78	,	,	PUNCT
ejpam-5638	1	79	nhla	nhla	NOUN
ejpam-5638	1	80	a.	a.	PROPN
ejpam-5638	1	81	abdalrahman3	abdalrahman3	PROPN
ejpam-5638	1	82	,	,	PUNCT
ejpam-5638	1	83	arafa	arafa	ADJ
ejpam-5638	1	84	o.	o.	PROPN
ejpam-5638	1	85	mustafa3	mustafa3	PROPN
ejpam-5638	1	86	,	,	PUNCT
ejpam-5638	1	87	awad	awad	PROPN
ejpam-5638	1	88	a.	a.	PROPN
ejpam-5638	1	89	bakery2,5,∗	bakery2,5,∗	PROPN
ejpam-5638	1	90	1	1	NUM
ejpam-5638	1	91	center	center	NOUN
ejpam-5638	1	92	of	of	ADP
ejpam-5638	1	93	research	research	NOUN
ejpam-5638	1	94	and	and	CCONJ
ejpam-5638	1	95	innovation	innovation	NOUN
ejpam-5638	1	96	,	,	PUNCT
ejpam-5638	1	97	asia	asia	PROPN
ejpam-5638	1	98	international	international	PROPN
ejpam-5638	1	99	university	university	PROPN
ejpam-5638	1	100	,	,	PUNCT
ejpam-5638	1	101	yangiobod	yangiobod	ADJ
ejpam-5638	1	102	mfy	mfy	NOUN
ejpam-5638	1	103	,	,	PUNCT
ejpam-5638	1	104	g‘ijduvon	g‘ijduvon	PROPN
ejpam-5638	1	105	street	street	PROPN
ejpam-5638	1	106	,	,	PUNCT
ejpam-5638	1	107	house	house	NOUN
ejpam-5638	1	108	74	74	NUM
ejpam-5638	1	109	,	,	PUNCT
ejpam-5638	1	110	bukhara	bukhara	PROPN
ejpam-5638	1	111	,	,	PUNCT
ejpam-5638	1	112	uzbekistan	uzbekistan	PROPN
ejpam-5638	1	113	2	2	NUM
ejpam-5638	1	114	university	university	NOUN
ejpam-5638	1	115	of	of	ADP
ejpam-5638	1	116	jeddah	jeddah	PROPN
ejpam-5638	1	117	,	,	PUNCT
ejpam-5638	1	118	college	college	NOUN
ejpam-5638	1	119	of	of	ADP
ejpam-5638	1	120	science	science	NOUN
ejpam-5638	1	121	and	and	CCONJ
ejpam-5638	1	122	arts	art	NOUN
ejpam-5638	1	123	at	at	ADP
ejpam-5638	1	124	khulis	khulis	PROPN
ejpam-5638	1	125	,	,	PUNCT
ejpam-5638	1	126	department	department	NOUN
ejpam-5638	1	127	of	of	ADP
ejpam-5638	1	128	mathematics	mathematics	PROPN
ejpam-5638	1	129	,	,	PUNCT
ejpam-5638	1	130	jeddah	jeddah	PROPN
ejpam-5638	1	131	,	,	PUNCT
ejpam-5638	1	132	saudi	saudi	PROPN
ejpam-5638	1	133	arabia	arabia	PROPN
ejpam-5638	1	134	3	3	NUM
ejpam-5638	1	135	university	university	NOUN
ejpam-5638	1	136	of	of	ADP
ejpam-5638	1	137	jeddah	jeddah	PROPN
ejpam-5638	1	138	,	,	PUNCT
ejpam-5638	1	139	college	college	NOUN
ejpam-5638	1	140	of	of	ADP
ejpam-5638	1	141	business	business	NOUN
ejpam-5638	1	142	at	at	ADP
ejpam-5638	1	143	khulis	khulis	PROPN
ejpam-5638	1	144	,	,	PUNCT
ejpam-5638	1	145	jeddah	jeddah	PROPN
ejpam-5638	1	146	,	,	PUNCT
ejpam-5638	1	147	saudi	saudi	PROPN
ejpam-5638	1	148	arabia	arabia	PROPN
ejpam-5638	1	149	4	4	NUM
ejpam-5638	1	150	mathematics	mathematics	PROPN
ejpam-5638	1	151	department	department	NOUN
ejpam-5638	1	152	,	,	PUNCT
ejpam-5638	1	153	faculty	faculty	NOUN
ejpam-5638	1	154	of	of	ADP
ejpam-5638	1	155	sciences	science	NOUN
ejpam-5638	1	156	and	and	CCONJ
ejpam-5638	1	157	arts	art	NOUN
ejpam-5638	1	158	-	-	PUNCT
ejpam-5638	1	159	alkamil	alkamil	NOUN
ejpam-5638	1	160	,	,	PUNCT
ejpam-5638	1	161	university	university	NOUN
ejpam-5638	1	162	of	of	ADP
ejpam-5638	1	163	jeddah	jeddah	PROPN
ejpam-5638	1	164	,	,	PUNCT
ejpam-5638	1	165	saudi	saudi	PROPN
ejpam-5638	1	166	arabia	arabia	PROPN
ejpam-5638	1	167	5	5	NUM
ejpam-5638	1	168	ain	ain	PROPN
ejpam-5638	1	169	shams	sham	NOUN
ejpam-5638	1	170	university	university	NOUN
ejpam-5638	1	171	,	,	PUNCT
ejpam-5638	1	172	faculty	faculty	NOUN
ejpam-5638	1	173	of	of	ADP
ejpam-5638	1	174	science	science	NOUN
ejpam-5638	1	175	,	,	PUNCT
ejpam-5638	1	176	department	department	NOUN
ejpam-5638	1	177	of	of	ADP
ejpam-5638	1	178	mathematics	mathematics	PROPN
ejpam-5638	1	179	,	,	PUNCT
ejpam-5638	1	180	cairo	cairo	PROPN
ejpam-5638	1	181	,	,	PUNCT
ejpam-5638	1	182	abbassia	abbassia	PROPN
ejpam-5638	1	183	,	,	PUNCT
ejpam-5638	1	184	egypt	egypt	PROPN
ejpam-5638	1	185	abstract	abstract	PROPN
ejpam-5638	1	186	.	.	PUNCT
ejpam-5638	2	1	thed	the	VERB
ejpam-5638	2	2	-	-	PUNCT
ejpam-5638	2	3	stability	stability	NOUN
ejpam-5638	2	4	of	of	ADP
ejpam-5638	2	5	structured	structured	ADJ
ejpam-5638	2	6	matrices	matrix	NOUN
ejpam-5638	2	7	has	have	VERB
ejpam-5638	2	8	significant	significant	ADJ
ejpam-5638	2	9	implications	implication	NOUN
ejpam-5638	2	10	in	in	ADP
ejpam-5638	2	11	system	system	NOUN
ejpam-5638	2	12	theory	theory	NOUN
ejpam-5638	2	13	and	and	CCONJ
ejpam-5638	2	14	decision	decision	NOUN
ejpam-5638	2	15	-	-	PUNCT
ejpam-5638	2	16	making	make	VERB
ejpam-5638	2	17	systems	system	NOUN
ejpam-5638	2	18	.	.	PUNCT
ejpam-5638	3	1	the	the	DET
ejpam-5638	3	2	notation	notation	NOUN
ejpam-5638	3	3	of	of	ADP
ejpam-5638	3	4	d	d	NOUN
ejpam-5638	3	5	-	-	NOUN
ejpam-5638	3	6	stability	stability	NOUN
ejpam-5638	3	7	refers	refer	VERB
ejpam-5638	3	8	to	to	ADP
ejpam-5638	3	9	the	the	DET
ejpam-5638	3	10	characterization	characterization	NOUN
ejpam-5638	3	11	of	of	ADP
ejpam-5638	3	12	a	a	DET
ejpam-5638	3	13	dynamical	dynamical	ADJ
ejpam-5638	3	14	model	model	NOUN
ejpam-5638	3	15	where	where	SCONJ
ejpam-5638	3	16	structured	structured	ADJ
ejpam-5638	3	17	stability	stability	NOUN
ejpam-5638	3	18	is	be	AUX
ejpam-5638	3	19	maintained	maintain	VERB
ejpam-5638	3	20	when	when	SCONJ
ejpam-5638	3	21	each	each	DET
ejpam-5638	3	22	eigenvalue	eigenvalue	NOUN
ejpam-5638	3	23	of	of	ADP
ejpam-5638	3	24	the	the	DET
ejpam-5638	3	25	system	system	NOUN
ejpam-5638	3	26	matrix	matrix	NOUN
ejpam-5638	3	27	remains	remain	VERB
ejpam-5638	3	28	within	within	ADP
ejpam-5638	3	29	a	a	DET
ejpam-5638	3	30	designated	designate	VERB
ejpam-5638	3	31	region	region	NOUN
ejpam-5638	3	32	,	,	PUNCT
ejpam-5638	3	33	we	we	PRON
ejpam-5638	3	34	consider	consider	VERB
ejpam-5638	3	35	it	it	PRON
ejpam-5638	3	36	in	in	ADP
ejpam-5638	3	37	half	half	NOUN
ejpam-5638	3	38	of	of	ADP
ejpam-5638	3	39	right	right	ADJ
ejpam-5638	3	40	complex	complex	ADJ
ejpam-5638	3	41	plane	plane	NOUN
ejpam-5638	3	42	c	c	PROPN
ejpam-5638	3	43	subject	subject	NOUN
ejpam-5638	3	44	to	to	ADP
ejpam-5638	3	45	various	various	ADJ
ejpam-5638	3	46	perturbations	perturbation	NOUN
ejpam-5638	3	47	.	.	PUNCT
ejpam-5638	4	1	the	the	DET
ejpam-5638	4	2	structured	structured	ADJ
ejpam-5638	4	3	d	d	NOUN
ejpam-5638	4	4	-	-	PUNCT
ejpam-5638	4	5	stability	stability	NOUN
ejpam-5638	4	6	of	of	ADP
ejpam-5638	4	7	time	time	NOUN
ejpam-5638	4	8	varying	vary	VERB
ejpam-5638	4	9	dynamical	dynamical	ADJ
ejpam-5638	4	10	systems	system	NOUN
ejpam-5638	4	11	implies	imply	VERB
ejpam-5638	4	12	that	that	SCONJ
ejpam-5638	4	13	the	the	DET
ejpam-5638	4	14	system	system	NOUN
ejpam-5638	4	15	will	will	AUX
ejpam-5638	4	16	remain	remain	VERB
ejpam-5638	4	17	stable	stable	ADJ
ejpam-5638	4	18	under	under	ADP
ejpam-5638	4	19	certain	certain	ADJ
ejpam-5638	4	20	diagonal	diagonal	ADJ
ejpam-5638	4	21	transformations	transformation	NOUN
ejpam-5638	4	22	.	.	PUNCT
ejpam-5638	5	1	this	this	DET
ejpam-5638	5	2	concept	concept	NOUN
ejpam-5638	5	3	is	be	AUX
ejpam-5638	5	4	fundamental	fundamental	ADJ
ejpam-5638	5	5	in	in	ADP
ejpam-5638	5	6	system	system	NOUN
ejpam-5638	5	7	theory	theory	NOUN
ejpam-5638	5	8	and	and	CCONJ
ejpam-5638	5	9	ensures	ensure	VERB
ejpam-5638	5	10	the	the	DET
ejpam-5638	5	11	robust	robust	ADJ
ejpam-5638	5	12	stability	stability	NOUN
ejpam-5638	5	13	and	and	CCONJ
ejpam-5638	5	14	performance	performance	NOUN
ejpam-5638	5	15	even	even	ADV
ejpam-5638	5	16	if	if	SCONJ
ejpam-5638	5	17	system	system	NOUN
ejpam-5638	5	18	experiences	experience	VERB
ejpam-5638	5	19	structural	structural	ADJ
ejpam-5638	5	20	changes	change	NOUN
ejpam-5638	5	21	or	or	CCONJ
ejpam-5638	5	22	parameter	parameter	NOUN
ejpam-5638	5	23	uncertainties	uncertainty	NOUN
ejpam-5638	5	24	.	.	PUNCT
ejpam-5638	6	1	in	in	ADP
ejpam-5638	6	2	this	this	DET
ejpam-5638	6	3	paper	paper	NOUN
ejpam-5638	6	4	,	,	PUNCT
ejpam-5638	6	5	novel	novel	ADJ
ejpam-5638	6	6	results	result	NOUN
ejpam-5638	6	7	are	be	AUX
ejpam-5638	6	8	obtained	obtain	VERB
ejpam-5638	6	9	on	on	ADP
ejpam-5638	6	10	the	the	DET
ejpam-5638	6	11	computation	computation	NOUN
ejpam-5638	6	12	of	of	ADP
ejpam-5638	6	13	structured	structured	ADJ
ejpam-5638	6	14	stability	stability	NOUN
ejpam-5638	6	15	and	and	CCONJ
ejpam-5638	6	16	structured	structure	VERB
ejpam-5638	6	17	d	d	X
ejpam-5638	6	18	-	-	NOUN
ejpam-5638	6	19	stability	stability	NOUN
ejpam-5638	6	20	of	of	ADP
ejpam-5638	6	21	first	first	ADJ
ejpam-5638	6	22	order	order	NOUN
ejpam-5638	6	23	and	and	CCONJ
ejpam-5638	6	24	second	second	ADJ
ejpam-5638	6	25	dynamical	dynamical	ADJ
ejpam-5638	6	26	models	model	NOUN
ejpam-5638	6	27	with	with	ADP
ejpam-5638	6	28	mathematical	mathematical	ADJ
ejpam-5638	6	29	forms	form	NOUN
ejpam-5638	6	30	d	d	X
ejpam-5638	6	31	dt	dt	X
ejpam-5638	6	32	(	(	PUNCT
ejpam-5638	6	33	x(t	x(t	PROPN
ejpam-5638	6	34	)	)	PUNCT
ejpam-5638	6	35	)	)	PUNCT
ejpam-5638	7	1	=	=	SYM
ejpam-5638	7	2	ax	ax	NOUN
ejpam-5638	7	3	,	,	PUNCT
ejpam-5638	7	4	d2	d2	PROPN
ejpam-5638	7	5	dt2	dt2	PROPN
ejpam-5638	7	6	(	(	PUNCT
ejpam-5638	7	7	x(t	x(t	PROPN
ejpam-5638	7	8	)	)	PUNCT
ejpam-5638	7	9	)	)	PUNCT
ejpam-5638	8	1	=	=	PUNCT
ejpam-5638	8	2	a	a	DET
ejpam-5638	8	3	d	d	X
ejpam-5638	8	4	dt	dt	X
ejpam-5638	8	5	(	(	PUNCT
ejpam-5638	8	6	x(t	x(t	PROPN
ejpam-5638	8	7	)	)	PUNCT
ejpam-5638	8	8	)	)	PUNCT
ejpam-5638	9	1	+	+	VERB
ejpam-5638	9	2	bx	bx	X
ejpam-5638	9	3	,	,	PUNCT
ejpam-5638	9	4	x	x	SYM
ejpam-5638	9	5	∈	∈	PROPN
ejpam-5638	9	6	rn,1	rn,1	PROPN
ejpam-5638	9	7	,	,	PUNCT
ejpam-5638	9	8	with	with	ADP
ejpam-5638	9	9	matrices	matrix	NOUN
ejpam-5638	9	10	a	a	PRON
ejpam-5638	9	11	,	,	PUNCT
ejpam-5638	9	12	b	b	PROPN
ejpam-5638	9	13	∈	∈	PROPN
ejpam-5638	9	14	rn	rn	PROPN
ejpam-5638	9	15	,	,	PUNCT
ejpam-5638	9	16	n.	n.	PROPN
ejpam-5638	9	17	new	new	ADJ
ejpam-5638	9	18	results	result	NOUN
ejpam-5638	9	19	are	be	AUX
ejpam-5638	9	20	developed	develop	VERB
ejpam-5638	9	21	with	with	ADP
ejpam-5638	9	22	the	the	DET
ejpam-5638	9	23	necessary	necessary	ADJ
ejpam-5638	9	24	conditions	condition	NOUN
ejpam-5638	9	25	for	for	ADP
ejpam-5638	9	26	interconnection	interconnection	NOUN
ejpam-5638	9	27	among	among	ADP
ejpam-5638	9	28	stable	stable	ADJ
ejpam-5638	9	29	,	,	PUNCT
ejpam-5638	9	30	structured	structured	ADJ
ejpam-5638	9	31	d	d	ADJ
ejpam-5638	9	32	-	-	ADJ
ejpam-5638	9	33	stable	stable	ADJ
ejpam-5638	9	34	matrices	matrix	NOUN
ejpam-5638	9	35	and	and	CCONJ
ejpam-5638	9	36	structured	structure	VERB
ejpam-5638	9	37	singular	singular	ADJ
ejpam-5638	9	38	values	value	NOUN
ejpam-5638	9	39	.	.	PUNCT
ejpam-5638	10	1	the	the	DET
ejpam-5638	10	2	numerical	numerical	PROPN
ejpam-5638	10	3	experimentation	experimentation	NOUN
ejpam-5638	10	4	show	show	VERB
ejpam-5638	10	5	how	how	SCONJ
ejpam-5638	10	6	structured	structured	ADJ
ejpam-5638	10	7	singular	singular	ADJ
ejpam-5638	10	8	values	value	NOUN
ejpam-5638	10	9	(	(	PUNCT
ejpam-5638	10	10	µ-values	µ-value	NOUN
ejpam-5638	10	11	)	)	PUNCT
ejpam-5638	10	12	behaves	behave	NOUN
ejpam-5638	10	13	.	.	PUNCT
ejpam-5638	11	1	the	the	DET
ejpam-5638	11	2	eigtool	eigtool	NOUN
ejpam-5638	11	3	is	be	AUX
ejpam-5638	11	4	used	use	VERB
ejpam-5638	11	5	to	to	PART
ejpam-5638	11	6	sketch	sketch	VERB
ejpam-5638	11	7	the	the	DET
ejpam-5638	11	8	behavior	behavior	NOUN
ejpam-5638	11	9	of	of	ADP
ejpam-5638	11	10	pseudo	pseudo	NOUN
ejpam-5638	11	11	-	-	NOUN
ejpam-5638	11	12	spectrum	spectrum	NOUN
ejpam-5638	11	13	.	.	PUNCT
ejpam-5638	12	1	2020	2020	NUM
ejpam-5638	12	2	mathematics	mathematics	PROPN
ejpam-5638	12	3	subject	subject	NOUN
ejpam-5638	12	4	classifications	classification	NOUN
ejpam-5638	12	5	:	:	PUNCT
ejpam-5638	12	6	15a18	15a18	NUM
ejpam-5638	12	7	,	,	PUNCT
ejpam-5638	12	8	15a16	15a16	NUM
ejpam-5638	12	9	,	,	PUNCT
ejpam-5638	12	10	15a23	15a23	NUM
ejpam-5638	12	11	key	key	ADJ
ejpam-5638	12	12	words	word	NOUN
ejpam-5638	12	13	and	and	CCONJ
ejpam-5638	12	14	phrases	phrase	NOUN
ejpam-5638	12	15	:	:	PUNCT
ejpam-5638	12	16	dynamic	dynamic	ADJ
ejpam-5638	12	17	stability	stability	NOUN
ejpam-5638	12	18	,	,	PUNCT
ejpam-5638	12	19	d	d	NOUN
ejpam-5638	12	20	-	-	PUNCT
ejpam-5638	12	21	stability	stability	NOUN
ejpam-5638	12	22	,	,	PUNCT
ejpam-5638	12	23	structured	structure	VERB
ejpam-5638	12	24	singular	singular	ADJ
ejpam-5638	12	25	values	value	NOUN
ejpam-5638	12	26	,	,	PUNCT
ejpam-5638	12	27	pseudospectrum	pseudospectrum	NOUN
ejpam-5638	12	28	∗corresponding	∗corresponde	VERB
ejpam-5638	12	29	author	author	NOUN
ejpam-5638	12	30	.	.	PUNCT
ejpam-5638	13	1	doi	doi	NOUN
ejpam-5638	13	2	:	:	PUNCT
ejpam-5638	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5638	https://doi.org/10.29020/nybg.ejpam.v18i2.5638	NOUN
ejpam-5638	13	4	email	email	NOUN
ejpam-5638	13	5	address	address	NOUN
ejpam-5638	13	6	:	:	PUNCT
ejpam-5638	13	7	aabhassan@uj.edu.sa	aabhassan@uj.edu.sa	PROPN
ejpam-5638	13	8	(	(	PUNCT
ejpam-5638	13	9	awad	awad	PROPN
ejpam-5638	13	10	a.	a.	PROPN
ejpam-5638	13	11	bakery	bakery	PROPN
ejpam-5638	13	12	)	)	PUNCT
ejpam-5638	13	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5638	14	1	1	1	NUM
ejpam-5638	14	2	copyright	copyright	NOUN
ejpam-5638	14	3	:	:	PUNCT
ejpam-5638	14	4	©	©	PROPN
ejpam-5638	14	5	2025	2025	NUM
ejpam-5638	14	6	the	the	DET
ejpam-5638	14	7	author(s	author(s	NOUN
ejpam-5638	14	8	)	)	PUNCT
ejpam-5638	14	9	.	.	PUNCT
ejpam-5638	15	1	(	(	PUNCT
ejpam-5638	15	2	cc	cc	NOUN
ejpam-5638	15	3	by	by	ADP
ejpam-5638	15	4	-	-	PUNCT
ejpam-5638	15	5	nc	nc	PROPN
ejpam-5638	15	6	4.0	4.0	NUM
ejpam-5638	15	7	)	)	PUNCT
ejpam-5638	15	8	m.u.r	m.u.r	NOUN
ejpam-5638	15	9	rehman	rehman	PROPN
ejpam-5638	15	10	et	et	PROPN
ejpam-5638	15	11	al	al	PROPN
ejpam-5638	15	12	.	.	PUNCT
ejpam-5638	15	13	/	/	SYM
ejpam-5638	15	14	eur	eur	PROPN
ejpam-5638	15	15	.	.	PUNCT
ejpam-5638	16	1	j.	j.	PROPN
ejpam-5638	16	2	pure	pure	PROPN
ejpam-5638	16	3	appl	appl	PROPN
ejpam-5638	16	4	.	.	PROPN
ejpam-5638	16	5	math	math	PROPN
ejpam-5638	16	6	,	,	PUNCT
ejpam-5638	16	7	18	18	NUM
ejpam-5638	16	8	(	(	PUNCT
ejpam-5638	16	9	2	2	NUM
ejpam-5638	16	10	)	)	PUNCT
ejpam-5638	16	11	(	(	PUNCT
ejpam-5638	16	12	2025	2025	NUM
ejpam-5638	16	13	)	)	PUNCT
ejpam-5638	16	14	,	,	PUNCT
ejpam-5638	16	15	5638	5638	NUM
ejpam-5638	16	16	2	2	NUM
ejpam-5638	16	17	of	of	ADP
ejpam-5638	16	18	23	23	NUM
ejpam-5638	16	19	1	1	NUM
ejpam-5638	16	20	.	.	PUNCT
ejpam-5638	17	1	introduction	introduction	NOUN
ejpam-5638	17	2	the	the	DET
ejpam-5638	17	3	concept	concept	NOUN
ejpam-5638	17	4	of	of	ADP
ejpam-5638	17	5	stable	stable	ADJ
ejpam-5638	17	6	and	and	CCONJ
ejpam-5638	17	7	d	d	ADJ
ejpam-5638	17	8	-	-	ADJ
ejpam-5638	17	9	stable	stable	ADJ
ejpam-5638	17	10	matrices	matrix	NOUN
ejpam-5638	17	11	play	play	VERB
ejpam-5638	17	12	a	a	DET
ejpam-5638	17	13	diverse	diverse	NOUN
ejpam-5638	17	14	and	and	CCONJ
ejpam-5638	17	15	a	a	DET
ejpam-5638	17	16	key	key	ADJ
ejpam-5638	17	17	role	role	NOUN
ejpam-5638	17	18	to	to	PART
ejpam-5638	17	19	analyze	analyze	VERB
ejpam-5638	17	20	behavior	behavior	NOUN
ejpam-5638	17	21	of	of	ADP
ejpam-5638	17	22	linear	linear	PROPN
ejpam-5638	17	23	,	,	PUNCT
ejpam-5638	17	24	non	non	ADJ
ejpam-5638	17	25	-	-	ADJ
ejpam-5638	17	26	linear	linear	ADJ
ejpam-5638	17	27	systems	system	NOUN
ejpam-5638	17	28	in	in	ADP
ejpam-5638	17	29	economies	economy	NOUN
ejpam-5638	17	30	models	model	NOUN
ejpam-5638	17	31	.	.	PUNCT
ejpam-5638	18	1	the	the	DET
ejpam-5638	18	2	stable	stable	ADJ
ejpam-5638	18	3	matrices	matrix	NOUN
ejpam-5638	18	4	characterize	characterize	VERB
ejpam-5638	18	5	and	and	CCONJ
ejpam-5638	18	6	analyze	analyze	VERB
ejpam-5638	18	7	the	the	DET
ejpam-5638	18	8	behavior	behavior	NOUN
ejpam-5638	18	9	of	of	ADP
ejpam-5638	18	10	dynamical	dynamical	ADJ
ejpam-5638	18	11	systems	system	NOUN
ejpam-5638	18	12	over	over	ADP
ejpam-5638	18	13	time	time	NOUN
ejpam-5638	18	14	.	.	PUNCT
ejpam-5638	19	1	the	the	DET
ejpam-5638	19	2	stability	stability	NOUN
ejpam-5638	19	3	of	of	ADP
ejpam-5638	19	4	structured	structured	ADJ
ejpam-5638	19	5	matrices	matrix	NOUN
ejpam-5638	19	6	in	in	ADP
ejpam-5638	19	7	such	such	ADJ
ejpam-5638	19	8	models	model	NOUN
ejpam-5638	19	9	indicates	indicate	VERB
ejpam-5638	19	10	that	that	SCONJ
ejpam-5638	19	11	the	the	DET
ejpam-5638	19	12	deviation	deviation	NOUN
ejpam-5638	19	13	from	from	ADP
ejpam-5638	19	14	an	an	DET
ejpam-5638	19	15	equilibrium	equilibrium	NOUN
ejpam-5638	19	16	point	point	NOUN
ejpam-5638	19	17	will	will	AUX
ejpam-5638	19	18	diminish	diminish	VERB
ejpam-5638	19	19	over	over	ADP
ejpam-5638	19	20	the	the	DET
ejpam-5638	19	21	period	period	NOUN
ejpam-5638	19	22	of	of	ADP
ejpam-5638	19	23	time	time	NOUN
ejpam-5638	19	24	.	.	PUNCT
ejpam-5638	20	1	this	this	PRON
ejpam-5638	20	2	helps	help	VERB
ejpam-5638	20	3	to	to	PART
ejpam-5638	20	4	model	model	VERB
ejpam-5638	20	5	the	the	DET
ejpam-5638	20	6	economies	economy	NOUN
ejpam-5638	20	7	system	system	NOUN
ejpam-5638	20	8	.	.	PUNCT
ejpam-5638	21	1	the	the	DET
ejpam-5638	21	2	stable	stable	ADJ
ejpam-5638	21	3	matrices	matrix	NOUN
ejpam-5638	21	4	are	be	AUX
ejpam-5638	21	5	particularly	particularly	ADV
ejpam-5638	21	6	valuable	valuable	ADJ
ejpam-5638	21	7	in	in	ADP
ejpam-5638	21	8	macroeconomic	macroeconomic	ADJ
ejpam-5638	21	9	models	model	NOUN
ejpam-5638	21	10	and	and	CCONJ
ejpam-5638	21	11	the	the	DET
ejpam-5638	21	12	dynamics	dynamic	NOUN
ejpam-5638	21	13	of	of	ADP
ejpam-5638	21	14	controller	controller	NOUN
ejpam-5638	21	15	.	.	PUNCT
ejpam-5638	22	1	the	the	DET
ejpam-5638	22	2	structured	structured	ADJ
ejpam-5638	22	3	d	d	ADJ
ejpam-5638	22	4	-	-	ADJ
ejpam-5638	22	5	stable	stable	ADJ
ejpam-5638	22	6	operators	operator	NOUN
ejpam-5638	22	7	provides	provide	VERB
ejpam-5638	22	8	a	a	DET
ejpam-5638	22	9	framework	framework	NOUN
ejpam-5638	22	10	for	for	ADP
ejpam-5638	22	11	the	the	DET
ejpam-5638	22	12	analysis	analysis	NOUN
ejpam-5638	22	13	,	,	PUNCT
ejpam-5638	22	14	performance	performance	NOUN
ejpam-5638	22	15	and	and	CCONJ
ejpam-5638	22	16	robustness	robustness	NOUN
ejpam-5638	22	17	of	of	ADP
ejpam-5638	22	18	the	the	DET
ejpam-5638	22	19	stability	stability	NOUN
ejpam-5638	22	20	.	.	PUNCT
ejpam-5638	23	1	the	the	DET
ejpam-5638	23	2	structured	structured	ADJ
ejpam-5638	23	3	d	d	NOUN
ejpam-5638	23	4	-	-	PUNCT
ejpam-5638	23	5	stability	stability	NOUN
ejpam-5638	23	6	play	play	VERB
ejpam-5638	23	7	a	a	DET
ejpam-5638	23	8	versatile	versatile	ADJ
ejpam-5638	23	9	and	and	CCONJ
ejpam-5638	23	10	important	important	ADJ
ejpam-5638	23	11	role	role	NOUN
ejpam-5638	23	12	once	once	SCONJ
ejpam-5638	23	13	the	the	DET
ejpam-5638	23	14	dynamical	dynamical	ADJ
ejpam-5638	23	15	system	system	NOUN
ejpam-5638	23	16	is	be	AUX
ejpam-5638	23	17	subject	subject	ADJ
ejpam-5638	23	18	to	to	ADP
ejpam-5638	23	19	some	some	DET
ejpam-5638	23	20	external	external	ADJ
ejpam-5638	23	21	perturbations	perturbation	NOUN
ejpam-5638	23	22	,	,	PUNCT
ejpam-5638	23	23	for	for	ADP
ejpam-5638	23	24	instance	instance	NOUN
ejpam-5638	23	25	,	,	PUNCT
ejpam-5638	23	26	perturbation	perturbation	NOUN
ejpam-5638	23	27	to	to	ADP
ejpam-5638	23	28	policy	policy	NOUN
ejpam-5638	23	29	of	of	ADP
ejpam-5638	23	30	adjustment	adjustment	NOUN
ejpam-5638	23	31	or	or	CCONJ
ejpam-5638	23	32	to	to	PART
ejpam-5638	23	33	vary	vary	VERB
ejpam-5638	23	34	consumer	consumer	NOUN
ejpam-5638	23	35	performance	performance	NOUN
ejpam-5638	23	36	.	.	PUNCT
ejpam-5638	24	1	we	we	PRON
ejpam-5638	24	2	address	address	VERB
ejpam-5638	24	3	the	the	DET
ejpam-5638	24	4	problem	problem	NOUN
ejpam-5638	24	5	of	of	ADP
ejpam-5638	24	6	discussing	discuss	VERB
ejpam-5638	24	7	structured	structured	ADJ
ejpam-5638	24	8	stability	stability	NOUN
ejpam-5638	24	9	and	and	CCONJ
ejpam-5638	24	10	structured	structure	VERB
ejpam-5638	24	11	d	d	X
ejpam-5638	24	12	-	-	NOUN
ejpam-5638	24	13	stability	stability	NOUN
ejpam-5638	24	14	of	of	ADP
ejpam-5638	24	15	first	first	ADJ
ejpam-5638	24	16	and	and	CCONJ
ejpam-5638	24	17	second	second	ADJ
ejpam-5638	24	18	order	order	NOUN
ejpam-5638	24	19	time	time	NOUN
ejpam-5638	24	20	varying	vary	VERB
ejpam-5638	24	21	dynamical	dynamical	ADJ
ejpam-5638	24	22	models	model	NOUN
ejpam-5638	24	23	ẋ	ẋ	PUNCT
ejpam-5638	25	1	=	=	NOUN
ejpam-5638	25	2	ax	ax	NOUN
ejpam-5638	25	3	,	,	PUNCT
ejpam-5638	25	4	and	and	CCONJ
ejpam-5638	25	5	ẍ	ẍ	X
ejpam-5638	25	6	=	=	PUNCT
ejpam-5638	26	1	aẋ+bx	aẋ+bx	PROPN
ejpam-5638	26	2	,	,	PUNCT
ejpam-5638	26	3	x	x	SYM
ejpam-5638	26	4	∈	∈	PROPN
ejpam-5638	26	5	rn,1	rn,1	PROPN
ejpam-5638	26	6	,	,	PUNCT
ejpam-5638	26	7	a	a	DET
ejpam-5638	26	8	,	,	PUNCT
ejpam-5638	26	9	b	b	PROPN
ejpam-5638	26	10	∈	∈	PROPN
ejpam-5638	26	11	rn	rn	PROPN
ejpam-5638	26	12	,	,	PUNCT
ejpam-5638	26	13	n.	n.	NOUN
ejpam-5638	26	14	we	we	PRON
ejpam-5638	26	15	make	make	VERB
ejpam-5638	26	16	use	use	VERB
ejpam-5638	26	17	various	various	ADJ
ejpam-5638	26	18	tools	tool	NOUN
ejpam-5638	26	19	from	from	ADP
ejpam-5638	26	20	linear	linear	PROPN
ejpam-5638	26	21	algebra	algebra	NOUN
ejpam-5638	26	22	,	,	PUNCT
ejpam-5638	26	23	matrix	matrix	NOUN
ejpam-5638	26	24	analysis	analysis	NOUN
ejpam-5638	26	25	,	,	PUNCT
ejpam-5638	26	26	and	and	CCONJ
ejpam-5638	26	27	system	system	NOUN
ejpam-5638	26	28	theory	theory	NOUN
ejpam-5638	26	29	to	to	PART
ejpam-5638	26	30	derive	derive	VERB
ejpam-5638	26	31	some	some	DET
ejpam-5638	26	32	novel	novel	ADJ
ejpam-5638	26	33	results	result	NOUN
ejpam-5638	26	34	.	.	PUNCT
ejpam-5638	27	1	the	the	DET
ejpam-5638	27	2	stability	stability	NOUN
ejpam-5638	27	3	of	of	ADP
ejpam-5638	27	4	ẋ	ẋ	PROPN
ejpam-5638	27	5	=	=	NOUN
ejpam-5638	27	6	ax	ax	NOUN
ejpam-5638	27	7	,	,	PUNCT
ejpam-5638	27	8	x	x	SYM
ejpam-5638	27	9	∈	∈	PROPN
ejpam-5638	27	10	rn,1	rn,1	NOUN
ejpam-5638	27	11	is	be	AUX
ejpam-5638	27	12	considered	consider	VERB
ejpam-5638	27	13	in	in	ADP
ejpam-5638	27	14	the	the	DET
ejpam-5638	27	15	sense	sense	NOUN
ejpam-5638	27	16	of	of	ADP
ejpam-5638	27	17	schur	schur	ADJ
ejpam-5638	27	18	stability	stability	PROPN
ejpam-5638	27	19	,	,	PUNCT
ejpam-5638	27	20	that	that	ADV
ejpam-5638	27	21	is	is	ADV
ejpam-5638	27	22	,	,	PUNCT
ejpam-5638	27	23	re(λi(da	re(λi(da	X
ejpam-5638	27	24	)	)	PUNCT
ejpam-5638	27	25	)	)	PUNCT
ejpam-5638	28	1	>	>	X
ejpam-5638	28	2	0	0	NUM
ejpam-5638	28	3	,	,	PUNCT
ejpam-5638	28	4	∀i	∀i	NOUN
ejpam-5638	28	5	.	.	PUNCT
ejpam-5638	29	1	the	the	DET
ejpam-5638	29	2	jordan	jordan	PROPN
ejpam-5638	29	3	canonical	canonical	ADJ
ejpam-5638	29	4	form	form	NOUN
ejpam-5638	29	5	of	of	ADP
ejpam-5638	29	6	matrix	matrix	NOUN
ejpam-5638	29	7	-	-	PUNCT
ejpam-5638	29	8	product	product	NOUN
ejpam-5638	29	9	da	da	NOUN
ejpam-5638	29	10	is	be	AUX
ejpam-5638	29	11	being	be	AUX
ejpam-5638	29	12	used	use	VERB
ejpam-5638	29	13	for	for	ADP
ejpam-5638	29	14	derivation	derivation	NOUN
ejpam-5638	29	15	of	of	ADP
ejpam-5638	29	16	novel	novel	ADJ
ejpam-5638	29	17	results	result	NOUN
ejpam-5638	29	18	.	.	PUNCT
ejpam-5638	30	1	furthermore	furthermore	ADV
ejpam-5638	30	2	,	,	PUNCT
ejpam-5638	30	3	new	new	ADJ
ejpam-5638	30	4	results	result	NOUN
ejpam-5638	30	5	are	be	AUX
ejpam-5638	30	6	established	establish	VERB
ejpam-5638	30	7	on	on	ADP
ejpam-5638	30	8	interconnections	interconnection	NOUN
ejpam-5638	30	9	between	between	ADP
ejpam-5638	30	10	structured	structured	ADJ
ejpam-5638	30	11	stable	stable	ADJ
ejpam-5638	30	12	matrices	matrix	NOUN
ejpam-5638	30	13	,	,	PUNCT
ejpam-5638	30	14	structured	structured	ADJ
ejpam-5638	30	15	d	d	ADJ
ejpam-5638	30	16	-	-	ADJ
ejpam-5638	30	17	stable	stable	ADJ
ejpam-5638	30	18	matrices	matrix	NOUN
ejpam-5638	30	19	,	,	PUNCT
ejpam-5638	30	20	and	and	CCONJ
ejpam-5638	30	21	µ-values	µ-value	VERB
ejpam-5638	30	22	.	.	PUNCT
ejpam-5638	31	1	for	for	ADP
ejpam-5638	31	2	matrices	matrix	NOUN
ejpam-5638	31	3	a	a	DET
ejpam-5638	31	4	,	,	PUNCT
ejpam-5638	31	5	b	b	PROPN
ejpam-5638	31	6	∈	∈	PROPN
ejpam-5638	31	7	rn	rn	PROPN
ejpam-5638	31	8	,	,	PUNCT
ejpam-5638	31	9	n	n	CCONJ
ejpam-5638	31	10	,	,	PUNCT
ejpam-5638	31	11	we	we	PRON
ejpam-5638	31	12	present	present	VERB
ejpam-5638	31	13	novel	novel	ADJ
ejpam-5638	31	14	results	result	NOUN
ejpam-5638	31	15	on	on	ADP
ejpam-5638	31	16	d	d	NOUN
ejpam-5638	31	17	-	-	NOUN
ejpam-5638	31	18	stability	stability	NOUN
ejpam-5638	31	19	of	of	ADP
ejpam-5638	31	20	second	second	ADJ
ejpam-5638	31	21	order	order	NOUN
ejpam-5638	31	22	dynamical	dynamical	ADJ
ejpam-5638	31	23	system	system	NOUN
ejpam-5638	31	24	ẍ	ẍ	X
ejpam-5638	32	1	=	=	PUNCT
ejpam-5638	32	2	aẋ	aẋ	NOUN
ejpam-5638	33	1	+	+	CCONJ
ejpam-5638	33	2	bx	bx	X
ejpam-5638	33	3	,	,	PUNCT
ejpam-5638	33	4	x	x	PROPN
ejpam-5638	33	5	∈	∈	PROPN
ejpam-5638	33	6	rn,1	rn,1	PROPN
ejpam-5638	33	7	.	.	PUNCT
ejpam-5638	34	1	here	here	ADV
ejpam-5638	34	2	ẍ	ẍ	PROPN
ejpam-5638	34	3	,	,	PUNCT
ejpam-5638	34	4	ẋ	ẋ	PROPN
ejpam-5638	34	5	denotes	denote	VERB
ejpam-5638	34	6	second	second	ADJ
ejpam-5638	34	7	,	,	PUNCT
ejpam-5638	34	8	and	and	CCONJ
ejpam-5638	34	9	first	first	ADJ
ejpam-5638	34	10	order	order	NOUN
ejpam-5638	34	11	time	time	NOUN
ejpam-5638	34	12	-	-	PUNCT
ejpam-5638	34	13	derivatives	derivative	NOUN
ejpam-5638	34	14	,	,	PUNCT
ejpam-5638	34	15	respectively	respectively	ADV
ejpam-5638	34	16	.	.	PUNCT
ejpam-5638	35	1	these	these	DET
ejpam-5638	35	2	dynamical	dynamical	ADJ
ejpam-5638	35	3	systems	system	NOUN
ejpam-5638	35	4	are	be	AUX
ejpam-5638	35	5	determined	determine	VERB
ejpam-5638	35	6	by	by	ADP
ejpam-5638	35	7	computing	compute	VERB
ejpam-5638	35	8	and	and	CCONJ
ejpam-5638	35	9	analyzing	analyze	VERB
ejpam-5638	35	10	spectrum	spectrum	NOUN
ejpam-5638	35	11	(	(	PUNCT
ejpam-5638	35	12	eigenvalues	eigenvalue	NOUN
ejpam-5638	35	13	)	)	PUNCT
ejpam-5638	35	14	of	of	ADP
ejpam-5638	35	15	2n×	2n×	ADJ
ejpam-5638	35	16	2n	2n	NUM
ejpam-5638	35	17	matrix	matrix	NOUN
ejpam-5638	35	18	(	(	PUNCT
ejpam-5638	35	19	a	a	DET
ejpam-5638	35	20	b	b	NOUN
ejpam-5638	35	21	in	in	ADP
ejpam-5638	35	22	o	o	PROPN
ejpam-5638	35	23	)	)	PUNCT
ejpam-5638	35	24	.	.	PUNCT
ejpam-5638	36	1	the	the	DET
ejpam-5638	36	2	above	above	ADV
ejpam-5638	36	3	structured	structured	ADJ
ejpam-5638	36	4	matrix	matrix	NOUN
ejpam-5638	36	5	can	can	AUX
ejpam-5638	36	6	be	be	AUX
ejpam-5638	36	7	obtained	obtain	VERB
ejpam-5638	36	8	by	by	ADP
ejpam-5638	36	9	reducing	reduce	VERB
ejpam-5638	36	10	second	second	ADJ
ejpam-5638	36	11	order	order	NOUN
ejpam-5638	36	12	system	system	NOUN
ejpam-5638	36	13	into	into	ADP
ejpam-5638	36	14	a	a	DET
ejpam-5638	36	15	first	first	ADJ
ejpam-5638	36	16	order	order	NOUN
ejpam-5638	36	17	system	system	NOUN
ejpam-5638	36	18	[	[	X
ejpam-5638	36	19	1	1	NUM
ejpam-5638	36	20	]	]	PUNCT
ejpam-5638	36	21	.	.	PUNCT
ejpam-5638	37	1	furthermore	furthermore	ADV
ejpam-5638	37	2	,	,	PUNCT
ejpam-5638	37	3	the	the	DET
ejpam-5638	37	4	stability	stability	NOUN
ejpam-5638	37	5	of	of	ADP
ejpam-5638	37	6	this	this	DET
ejpam-5638	37	7	matrix	matrix	NOUN
ejpam-5638	37	8	is	be	AUX
ejpam-5638	37	9	about	about	ADP
ejpam-5638	37	10	the	the	DET
ejpam-5638	37	11	computation	computation	NOUN
ejpam-5638	37	12	of	of	ADP
ejpam-5638	37	13	strictly	strictly	ADV
ejpam-5638	37	14	positive	positive	ADJ
ejpam-5638	37	15	real	real	ADJ
ejpam-5638	37	16	part	part	NOUN
ejpam-5638	37	17	of	of	ADP
ejpam-5638	37	18	the	the	DET
ejpam-5638	37	19	eigenvalues	eigenvalue	NOUN
ejpam-5638	37	20	.	.	PUNCT
ejpam-5638	38	1	on	on	ADP
ejpam-5638	38	2	the	the	DET
ejpam-5638	38	3	other	other	ADJ
ejpam-5638	38	4	hand	hand	NOUN
ejpam-5638	38	5	,	,	PUNCT
ejpam-5638	38	6	the	the	PRON
ejpam-5638	38	7	d	d	NOUN
ejpam-5638	38	8	-	-	NOUN
ejpam-5638	38	9	stability	stability	NOUN
ejpam-5638	38	10	demands	demand	VERB
ejpam-5638	38	11	the	the	DET
ejpam-5638	38	12	determination	determination	NOUN
ejpam-5638	38	13	of	of	ADP
ejpam-5638	38	14	the	the	DET
ejpam-5638	38	15	positive	positive	ADJ
ejpam-5638	38	16	(	(	PUNCT
ejpam-5638	38	17	in	in	ADP
ejpam-5638	38	18	the	the	DET
ejpam-5638	38	19	strict	strict	ADJ
ejpam-5638	38	20	sense	sense	NOUN
ejpam-5638	38	21	)	)	PUNCT
ejpam-5638	38	22	real	real	ADJ
ejpam-5638	38	23	part	part	NOUN
ejpam-5638	38	24	of	of	ADP
ejpam-5638	38	25	spectrum	spectrum	NOUN
ejpam-5638	38	26	of	of	ADP
ejpam-5638	38	27	(	(	PUNCT
ejpam-5638	38	28	p11	p11	ADJ
ejpam-5638	38	29	o	o	NOUN
ejpam-5638	38	30	0	0	NUM
ejpam-5638	38	31	p22	p22	NOUN
ejpam-5638	38	32	)	)	PUNCT
ejpam-5638	38	33	(	(	PUNCT
ejpam-5638	38	34	a	a	DET
ejpam-5638	38	35	b	b	NOUN
ejpam-5638	38	36	in	in	ADP
ejpam-5638	38	37	o	o	PROPN
ejpam-5638	38	38	)	)	PUNCT
ejpam-5638	38	39	.	.	PUNCT
ejpam-5638	39	1	the	the	DET
ejpam-5638	39	2	stability	stability	NOUN
ejpam-5638	39	3	further	far	ADV
ejpam-5638	39	4	means	mean	VERB
ejpam-5638	39	5	that	that	SCONJ
ejpam-5638	39	6	the	the	DET
ejpam-5638	39	7	solution	solution	NOUN
ejpam-5638	39	8	tends	tend	VERB
ejpam-5638	39	9	towards	towards	ADP
ejpam-5638	39	10	an	an	DET
ejpam-5638	39	11	equilibrium	equilibrium	NOUN
ejpam-5638	39	12	vector	vector	NOUN
ejpam-5638	39	13	having	have	VERB
ejpam-5638	39	14	all	all	DET
ejpam-5638	39	15	zero	zero	NUM
ejpam-5638	39	16	entries	entry	NOUN
ejpam-5638	39	17	[	[	X
ejpam-5638	39	18	2	2	NUM
ejpam-5638	39	19	]	]	PUNCT
ejpam-5638	39	20	.	.	PUNCT
ejpam-5638	40	1	the	the	DET
ejpam-5638	40	2	spectral	spectral	ADJ
ejpam-5638	40	3	properties	property	NOUN
ejpam-5638	40	4	of	of	ADP
ejpam-5638	40	5	above	above	ADP
ejpam-5638	40	6	2n	2n	NUM
ejpam-5638	40	7	×	×	PROPN
ejpam-5638	40	8	2n	2n	NUM
ejpam-5638	40	9	matrix	matrix	NOUN
ejpam-5638	40	10	were	be	AUX
ejpam-5638	40	11	studied	study	VERB
ejpam-5638	40	12	and	and	CCONJ
ejpam-5638	40	13	analyzed	analyze	VERB
ejpam-5638	40	14	in	in	ADP
ejpam-5638	40	15	[	[	X
ejpam-5638	40	16	3	3	NUM
ejpam-5638	40	17	]	]	X
ejpam-5638	40	18	putting	put	VERB
ejpam-5638	40	19	conditions	condition	NOUN
ejpam-5638	40	20	on	on	ADP
ejpam-5638	40	21	a	a	DET
ejpam-5638	40	22	,	,	PUNCT
ejpam-5638	40	23	b.	b.	PROPN
ejpam-5638	40	24	further	far	ADV
ejpam-5638	40	25	,	,	PUNCT
ejpam-5638	40	26	it	it	PRON
ejpam-5638	40	27	was	be	AUX
ejpam-5638	40	28	shown	show	VERB
ejpam-5638	40	29	that	that	SCONJ
ejpam-5638	40	30	2n	2n	NUM
ejpam-5638	40	31	×	×	NOUN
ejpam-5638	40	32	2n	2n	NUM
ejpam-5638	40	33	matrix	matrix	NOUN
ejpam-5638	40	34	have	have	VERB
ejpam-5638	40	35	sufficient	sufficient	ADJ
ejpam-5638	40	36	negative	negative	ADJ
ejpam-5638	40	37	dominant	dominant	ADJ
ejpam-5638	40	38	diagonal	diagonal	ADJ
ejpam-5638	40	39	elements	element	NOUN
ejpam-5638	40	40	which	which	PRON
ejpam-5638	40	41	implies	imply	VERB
ejpam-5638	40	42	its	its	PRON
ejpam-5638	40	43	stability	stability	NOUN
ejpam-5638	40	44	.	.	PUNCT
ejpam-5638	41	1	the	the	DET
ejpam-5638	41	2	µ-value	µ-value	NOUN
ejpam-5638	41	3	[	[	X
ejpam-5638	41	4	4	4	NUM
ejpam-5638	41	5	]	]	PUNCT
ejpam-5638	41	6	,	,	PUNCT
ejpam-5638	41	7	a	a	DET
ejpam-5638	41	8	well	well	ADV
ejpam-5638	41	9	-	-	PUNCT
ejpam-5638	41	10	known	know	VERB
ejpam-5638	41	11	mathematical	mathematical	ADJ
ejpam-5638	41	12	technique	technique	NOUN
ejpam-5638	41	13	to	to	PART
ejpam-5638	41	14	analyze	analyze	VERB
ejpam-5638	41	15	and	and	CCONJ
ejpam-5638	41	16	synthesize	synthesize	VERB
ejpam-5638	41	17	both	both	DET
ejpam-5638	41	18	robust	robust	ADJ
ejpam-5638	41	19	nature	nature	NOUN
ejpam-5638	41	20	and	and	CCONJ
ejpam-5638	41	21	the	the	DET
ejpam-5638	41	22	performance	performance	NOUN
ejpam-5638	41	23	of	of	ADP
ejpam-5638	41	24	linear	linear	PROPN
ejpam-5638	41	25	systems	system	NOUN
ejpam-5638	41	26	from	from	ADP
ejpam-5638	41	27	control	control	NOUN
ejpam-5638	41	28	.	.	PUNCT
ejpam-5638	42	1	the	the	DET
ejpam-5638	42	2	applications	application	NOUN
ejpam-5638	42	3	of	of	ADP
ejpam-5638	42	4	µvalues	µvalue	NOUN
ejpam-5638	42	5	includes	include	VERB
ejpam-5638	42	6	the	the	DET
ejpam-5638	42	7	study	study	NOUN
ejpam-5638	42	8	and	and	CCONJ
ejpam-5638	42	9	analysis	analysis	NOUN
ejpam-5638	42	10	of	of	ADP
ejpam-5638	42	11	d	d	NOUN
ejpam-5638	42	12	-	-	NOUN
ejpam-5638	42	13	stability	stability	NOUN
ejpam-5638	42	14	problem	problem	NOUN
ejpam-5638	42	15	[	[	X
ejpam-5638	42	16	5	5	NUM
ejpam-5638	42	17	]	]	PUNCT
ejpam-5638	42	18	.	.	PUNCT
ejpam-5638	43	1	an	an	DET
ejpam-5638	43	2	exact	exact	ADJ
ejpam-5638	43	3	determination	determination	NOUN
ejpam-5638	43	4	of	of	ADP
ejpam-5638	43	5	µ-values	µ-value	NOUN
ejpam-5638	43	6	is	be	AUX
ejpam-5638	43	7	a	a	DET
ejpam-5638	43	8	very	very	ADV
ejpam-5638	43	9	hard	hard	ADJ
ejpam-5638	43	10	problem	problem	NOUN
ejpam-5638	43	11	and	and	CCONJ
ejpam-5638	43	12	for	for	ADP
ejpam-5638	43	13	a	a	DET
ejpam-5638	43	14	class	class	NOUN
ejpam-5638	43	15	of	of	ADP
ejpam-5638	43	16	block	block	NOUN
ejpam-5638	43	17	structured	structure	VERB
ejpam-5638	43	18	perturbations	perturbation	NOUN
ejpam-5638	43	19	with	with	ADP
ejpam-5638	43	20	real	real	ADJ
ejpam-5638	43	21	parametric	parametric	ADJ
ejpam-5638	43	22	uncertainties	uncertainty	NOUN
ejpam-5638	43	23	it	it	PRON
ejpam-5638	43	24	becomes	become	VERB
ejpam-5638	43	25	an	an	DET
ejpam-5638	43	26	np	np	NOUN
ejpam-5638	43	27	-	-	PUNCT
ejpam-5638	43	28	hard	hard	ADJ
ejpam-5638	43	29	problem	problem	NOUN
ejpam-5638	44	1	[	[	X
ejpam-5638	44	2	6	6	NUM
ejpam-5638	44	3	]	]	PUNCT
ejpam-5638	44	4	.	.	PUNCT
ejpam-5638	45	1	there	there	PRON
ejpam-5638	45	2	are	be	VERB
ejpam-5638	45	3	various	various	ADJ
ejpam-5638	45	4	techniques	technique	NOUN
ejpam-5638	45	5	m.u.r	m.u.r	NOUN
ejpam-5638	45	6	rehman	rehman	PROPN
ejpam-5638	45	7	et	et	PROPN
ejpam-5638	45	8	al	al	PROPN
ejpam-5638	45	9	.	.	PUNCT
ejpam-5638	45	10	/	/	SYM
ejpam-5638	45	11	eur	eur	PROPN
ejpam-5638	45	12	.	.	PUNCT
ejpam-5638	46	1	j.	j.	PROPN
ejpam-5638	46	2	pure	pure	PROPN
ejpam-5638	46	3	appl	appl	PROPN
ejpam-5638	46	4	.	.	PROPN
ejpam-5638	46	5	math	math	PROPN
ejpam-5638	46	6	,	,	PUNCT
ejpam-5638	46	7	18	18	NUM
ejpam-5638	46	8	(	(	PUNCT
ejpam-5638	46	9	2	2	NUM
ejpam-5638	46	10	)	)	PUNCT
ejpam-5638	46	11	(	(	PUNCT
ejpam-5638	46	12	2025	2025	NUM
ejpam-5638	46	13	)	)	PUNCT
ejpam-5638	46	14	,	,	PUNCT
ejpam-5638	46	15	5638	5638	NUM
ejpam-5638	46	16	3	3	NUM
ejpam-5638	46	17	of	of	ADP
ejpam-5638	46	18	23	23	NUM
ejpam-5638	46	19	to	to	PART
ejpam-5638	46	20	compute	compute	VERB
ejpam-5638	46	21	structured	structure	VERB
ejpam-5638	46	22	singular	singular	ADJ
ejpam-5638	46	23	values	value	NOUN
ejpam-5638	46	24	in	in	ADP
ejpam-5638	46	25	the	the	DET
ejpam-5638	46	26	lower	lower	ADV
ejpam-5638	46	27	-	-	PUNCT
ejpam-5638	46	28	dimensional	dimensional	ADJ
ejpam-5638	46	29	problems	problem	NOUN
ejpam-5638	46	30	,	,	PUNCT
ejpam-5638	46	31	we	we	PRON
ejpam-5638	46	32	refer	refer	VERB
ejpam-5638	46	33	[	[	X
ejpam-5638	46	34	7	7	NUM
ejpam-5638	46	35	,	,	PUNCT
ejpam-5638	46	36	8	8	NUM
ejpam-5638	46	37	]	]	PUNCT
ejpam-5638	46	38	and	and	CCONJ
ejpam-5638	46	39	the	the	DET
ejpam-5638	46	40	references	reference	NOUN
ejpam-5638	46	41	therein	therein	ADV
ejpam-5638	46	42	.	.	PUNCT
ejpam-5638	47	1	computing	compute	VERB
ejpam-5638	47	2	exact	exact	ADJ
ejpam-5638	47	3	value	value	NOUN
ejpam-5638	47	4	of	of	ADP
ejpam-5638	47	5	structured	structured	ADJ
ejpam-5638	47	6	singular	singular	ADJ
ejpam-5638	47	7	values	value	NOUN
ejpam-5638	47	8	(	(	PUNCT
ejpam-5638	47	9	µvalue	µvalue	NOUN
ejpam-5638	47	10	)	)	PUNCT
ejpam-5638	47	11	for	for	ADP
ejpam-5638	47	12	large	large	ADJ
ejpam-5638	47	13	dimensional	dimensional	ADJ
ejpam-5638	47	14	problems	problem	NOUN
ejpam-5638	47	15	is	be	AUX
ejpam-5638	47	16	hard	hard	ADJ
ejpam-5638	47	17	and	and	CCONJ
ejpam-5638	47	18	this	this	PRON
ejpam-5638	47	19	motivates	motivate	VERB
ejpam-5638	47	20	to	to	PART
ejpam-5638	47	21	develop	develop	VERB
ejpam-5638	47	22	the	the	DET
ejpam-5638	47	23	numerical	numerical	ADJ
ejpam-5638	47	24	techniques	technique	NOUN
ejpam-5638	47	25	for	for	ADP
ejpam-5638	47	26	its	its	PRON
ejpam-5638	47	27	approximation	approximation	NOUN
ejpam-5638	47	28	from	from	ADP
ejpam-5638	47	29	above	above	ADP
ejpam-5638	47	30	and	and	CCONJ
ejpam-5638	47	31	below	below	ADV
ejpam-5638	47	32	.	.	PUNCT
ejpam-5638	48	1	in	in	ADP
ejpam-5638	48	2	[	[	X
ejpam-5638	48	3	9	9	NUM
ejpam-5638	48	4	,	,	PUNCT
ejpam-5638	48	5	10	10	NUM
ejpam-5638	48	6	]	]	PUNCT
ejpam-5638	48	7	,	,	PUNCT
ejpam-5638	48	8	a	a	DET
ejpam-5638	48	9	scheme	scheme	NOUN
ejpam-5638	48	10	was	be	AUX
ejpam-5638	48	11	developed	develop	VERB
ejpam-5638	48	12	to	to	PART
ejpam-5638	48	13	numerically	numerically	ADV
ejpam-5638	48	14	approximate	approximate	VERB
ejpam-5638	48	15	the	the	DET
ejpam-5638	48	16	bounds	bound	NOUN
ejpam-5638	48	17	of	of	ADP
ejpam-5638	48	18	µ-values	µ-value	NOUN
ejpam-5638	48	19	subject	subject	ADJ
ejpam-5638	48	20	to	to	ADP
ejpam-5638	48	21	mixed	mixed	ADJ
ejpam-5638	48	22	real	real	ADJ
ejpam-5638	48	23	and	and	CCONJ
ejpam-5638	48	24	complex	complex	ADJ
ejpam-5638	48	25	uncertainties	uncertainty	NOUN
ejpam-5638	48	26	.	.	PUNCT
ejpam-5638	49	1	the	the	DET
ejpam-5638	49	2	linear	linear	ADJ
ejpam-5638	49	3	matrix	matrix	NOUN
ejpam-5638	49	4	inequalities	inequality	NOUN
ejpam-5638	49	5	(	(	PUNCT
ejpam-5638	49	6	lmi	lmi	PROPN
ejpam-5638	49	7	)	)	PUNCT
ejpam-5638	49	8	based	base	VERB
ejpam-5638	49	9	techniques	technique	NOUN
ejpam-5638	49	10	were	be	AUX
ejpam-5638	49	11	developed	develop	VERB
ejpam-5638	49	12	[	[	PUNCT
ejpam-5638	49	13	11	11	NUM
ejpam-5638	49	14	]	]	PUNCT
ejpam-5638	49	15	to	to	PART
ejpam-5638	49	16	approximate	approximate	VERB
ejpam-5638	49	17	µ-values	µ-value	NOUN
ejpam-5638	49	18	from	from	ADP
ejpam-5638	49	19	above	above	ADP
ejpam-5638	49	20	and	and	CCONJ
ejpam-5638	49	21	below	below	ADV
ejpam-5638	49	22	.	.	PUNCT
ejpam-5638	50	1	in	in	ADP
ejpam-5638	50	2	[	[	X
ejpam-5638	50	3	12	12	NUM
ejpam-5638	50	4	]	]	PUNCT
ejpam-5638	50	5	,	,	PUNCT
ejpam-5638	50	6	some	some	DET
ejpam-5638	50	7	new	new	ADJ
ejpam-5638	50	8	results	result	NOUN
ejpam-5638	50	9	on	on	ADP
ejpam-5638	50	10	the	the	DET
ejpam-5638	50	11	interconnections	interconnection	NOUN
ejpam-5638	50	12	between	between	ADP
ejpam-5638	50	13	the	the	DET
ejpam-5638	50	14	notations	notation	NOUN
ejpam-5638	50	15	of	of	ADP
ejpam-5638	50	16	h	h	NOUN
ejpam-5638	50	17	-	-	PUNCT
ejpam-5638	50	18	stability	stability	NOUN
ejpam-5638	50	19	,	,	PUNCT
ejpam-5638	50	20	d(α)-stability	d(α)-stability	PROPN
ejpam-5638	50	21	,	,	PUNCT
ejpam-5638	50	22	a	a	DET
ejpam-5638	50	23	rank-1	rank-1	NUM
ejpam-5638	50	24	perturbation	perturbation	NOUN
ejpam-5638	50	25	to	to	ADP
ejpam-5638	50	26	d	d	ADJ
ejpam-5638	50	27	-	-	ADJ
ejpam-5638	50	28	semistable	semistable	ADJ
ejpam-5638	50	29	matrices	matrix	NOUN
ejpam-5638	50	30	,	,	PUNCT
ejpam-5638	50	31	and	and	CCONJ
ejpam-5638	50	32	the	the	DET
ejpam-5638	50	33	µ-values	µ-value	NOUN
ejpam-5638	50	34	were	be	AUX
ejpam-5638	50	35	presented	present	VERB
ejpam-5638	50	36	and	and	CCONJ
ejpam-5638	50	37	analyzed	analyze	VERB
ejpam-5638	50	38	.	.	PUNCT
ejpam-5638	51	1	a	a	DET
ejpam-5638	51	2	detailed	detailed	ADJ
ejpam-5638	51	3	review	review	NOUN
ejpam-5638	51	4	on	on	ADP
ejpam-5638	51	5	mathematical	mathematical	ADJ
ejpam-5638	51	6	methods	method	NOUN
ejpam-5638	51	7	to	to	PART
ejpam-5638	51	8	approximate	approximate	VERB
ejpam-5638	51	9	µvalues	µvalue	NOUN
ejpam-5638	51	10	is	be	AUX
ejpam-5638	51	11	presented	present	VERB
ejpam-5638	51	12	in	in	ADP
ejpam-5638	51	13	[	[	X
ejpam-5638	51	14	13	13	NUM
ejpam-5638	51	15	]	]	PUNCT
ejpam-5638	51	16	.	.	PUNCT
ejpam-5638	52	1	in	in	ADP
ejpam-5638	52	2	[	[	X
ejpam-5638	52	3	14	14	NUM
ejpam-5638	52	4	]	]	PUNCT
ejpam-5638	52	5	,	,	PUNCT
ejpam-5638	52	6	new	new	ADJ
ejpam-5638	52	7	results	result	NOUN
ejpam-5638	52	8	and	and	CCONJ
ejpam-5638	52	9	a	a	DET
ejpam-5638	52	10	detailed	detailed	ADJ
ejpam-5638	52	11	analysis	analysis	NOUN
ejpam-5638	52	12	was	be	AUX
ejpam-5638	52	13	presented	present	VERB
ejpam-5638	52	14	on	on	ADP
ejpam-5638	52	15	spectrum	spectrum	NOUN
ejpam-5638	52	16	and	and	CCONJ
ejpam-5638	52	17	pseudo	pseudo	NOUN
ejpam-5638	52	18	-	-	NOUN
ejpam-5638	52	19	spectrum	spectrum	NOUN
ejpam-5638	52	20	of	of	ADP
ejpam-5638	52	21	d	d	ADJ
ejpam-5638	52	22	-	-	ADJ
ejpam-5638	52	23	stable	stable	ADJ
ejpam-5638	52	24	matrices	matrix	NOUN
ejpam-5638	52	25	for	for	ADP
ejpam-5638	52	26	economic	economic	ADJ
ejpam-5638	52	27	models	model	NOUN
ejpam-5638	52	28	.	.	PUNCT
ejpam-5638	53	1	proposed	propose	VERB
ejpam-5638	53	2	technique	technique	NOUN
ejpam-5638	53	3	in	in	ADP
ejpam-5638	53	4	this	this	DET
ejpam-5638	53	5	article	article	NOUN
ejpam-5638	53	6	bridge	bridge	VERB
ejpam-5638	53	7	the	the	DET
ejpam-5638	53	8	links	link	NOUN
ejpam-5638	53	9	in	in	ADP
ejpam-5638	53	10	the	the	DET
ejpam-5638	53	11	sense	sense	NOUN
ejpam-5638	53	12	that	that	SCONJ
ejpam-5638	53	13	how	how	SCONJ
ejpam-5638	53	14	we	we	PRON
ejpam-5638	53	15	quantify	quantify	VERB
ejpam-5638	53	16	the	the	DET
ejpam-5638	53	17	interconnection	interconnection	NOUN
ejpam-5638	53	18	between	between	ADP
ejpam-5638	53	19	stable	stable	ADJ
ejpam-5638	53	20	matrices	matrix	NOUN
ejpam-5638	53	21	,	,	PUNCT
ejpam-5638	53	22	d	d	ADJ
ejpam-5638	53	23	-	-	ADJ
ejpam-5638	53	24	stable	stable	ADJ
ejpam-5638	53	25	matrices	matrix	NOUN
ejpam-5638	53	26	with	with	ADP
ejpam-5638	53	27	µ-values	µ-value	NOUN
ejpam-5638	53	28	subject	subject	ADJ
ejpam-5638	53	29	to	to	ADP
ejpam-5638	53	30	constraints	constraint	NOUN
ejpam-5638	53	31	.	.	PUNCT
ejpam-5638	54	1	according	accord	VERB
ejpam-5638	54	2	to	to	ADP
ejpam-5638	54	3	best	good	ADJ
ejpam-5638	54	4	of	of	ADP
ejpam-5638	54	5	our	our	PRON
ejpam-5638	54	6	knowledge	knowledge	NOUN
ejpam-5638	54	7	not	not	PART
ejpam-5638	54	8	a	a	DET
ejpam-5638	54	9	single	single	ADJ
ejpam-5638	54	10	technique	technique	NOUN
ejpam-5638	54	11	is	be	AUX
ejpam-5638	54	12	developed	develop	VERB
ejpam-5638	54	13	to	to	PART
ejpam-5638	54	14	give	give	VERB
ejpam-5638	54	15	the	the	DET
ejpam-5638	54	16	interconnections	interconnection	NOUN
ejpam-5638	54	17	of	of	ADP
ejpam-5638	54	18	stability	stability	NOUN
ejpam-5638	54	19	and	and	CCONJ
ejpam-5638	55	1	d	d	NOUN
ejpam-5638	55	2	-	-	NOUN
ejpam-5638	55	3	stability	stability	NOUN
ejpam-5638	55	4	of	of	ADP
ejpam-5638	55	5	structured	structured	ADJ
ejpam-5638	55	6	matrices	matrix	NOUN
ejpam-5638	55	7	across	across	ADP
ejpam-5638	55	8	first	first	ADJ
ejpam-5638	55	9	order	order	NOUN
ejpam-5638	55	10	and	and	CCONJ
ejpam-5638	55	11	second	second	ADJ
ejpam-5638	55	12	order	order	NOUN
ejpam-5638	55	13	dynamical	dynamical	ADJ
ejpam-5638	55	14	systems	system	NOUN
ejpam-5638	55	15	and	and	CCONJ
ejpam-5638	55	16	µ-values	µ-value	NOUN
ejpam-5638	55	17	.	.	PUNCT
ejpam-5638	56	1	the	the	DET
ejpam-5638	56	2	proposed	propose	VERB
ejpam-5638	56	3	methodology	methodology	NOUN
ejpam-5638	56	4	determines	determine	VERB
ejpam-5638	56	5	the	the	DET
ejpam-5638	56	6	novel	novel	ADJ
ejpam-5638	56	7	results	result	NOUN
ejpam-5638	56	8	to	to	PART
ejpam-5638	56	9	discuss	discuss	VERB
ejpam-5638	56	10	the	the	DET
ejpam-5638	56	11	stable	stable	ADJ
ejpam-5638	56	12	,	,	PUNCT
ejpam-5638	56	13	structured	structured	ADJ
ejpam-5638	56	14	d	d	NOUN
ejpam-5638	56	15	-	-	ADJ
ejpam-5638	56	16	stable	stable	ADJ
ejpam-5638	56	17	,	,	PUNCT
ejpam-5638	56	18	and	and	CCONJ
ejpam-5638	56	19	µ-values	µ-value	VERB
ejpam-5638	56	20	for	for	ADP
ejpam-5638	56	21	structured	structured	ADJ
ejpam-5638	56	22	class	class	NOUN
ejpam-5638	56	23	of	of	ADP
ejpam-5638	56	24	matrices	matrix	NOUN
ejpam-5638	56	25	appearing	appear	VERB
ejpam-5638	56	26	across	across	ADP
ejpam-5638	56	27	the	the	DET
ejpam-5638	56	28	economy	economy	NOUN
ejpam-5638	56	29	models	model	NOUN
ejpam-5638	56	30	.	.	PUNCT
ejpam-5638	57	1	the	the	DET
ejpam-5638	57	2	mathematical	mathematical	ADJ
ejpam-5638	57	3	technique	technique	NOUN
ejpam-5638	57	4	presented	present	VERB
ejpam-5638	57	5	in	in	ADP
ejpam-5638	57	6	this	this	DET
ejpam-5638	57	7	article	article	NOUN
ejpam-5638	57	8	is	be	AUX
ejpam-5638	57	9	applicable	applicable	ADJ
ejpam-5638	57	10	to	to	ADP
ejpam-5638	57	11	n	n	CCONJ
ejpam-5638	57	12	-	-	PUNCT
ejpam-5638	57	13	dimensional	dimensional	ADJ
ejpam-5638	57	14	complex	complex	NOUN
ejpam-5638	57	15	valued	value	VERB
ejpam-5638	57	16	,	,	PUNCT
ejpam-5638	57	17	and	and	CCONJ
ejpam-5638	57	18	real	real	ADV
ejpam-5638	57	19	valued	value	VERB
ejpam-5638	57	20	structured	structure	VERB
ejpam-5638	57	21	and	and	CCONJ
ejpam-5638	57	22	unstructured	unstructured	ADJ
ejpam-5638	57	23	matrices	matrix	NOUN
ejpam-5638	57	24	.	.	PUNCT
ejpam-5638	58	1	the	the	DET
ejpam-5638	58	2	use	use	NOUN
ejpam-5638	58	3	of	of	ADP
ejpam-5638	58	4	various	various	ADJ
ejpam-5638	58	5	tools	tool	NOUN
ejpam-5638	58	6	from	from	ADP
ejpam-5638	58	7	linear	linear	PROPN
ejpam-5638	58	8	algebra	algebra	NOUN
ejpam-5638	58	9	,	,	PUNCT
ejpam-5638	58	10	matrix	matrix	NOUN
ejpam-5638	58	11	analysis	analysis	NOUN
ejpam-5638	58	12	and	and	CCONJ
ejpam-5638	58	13	system	system	NOUN
ejpam-5638	58	14	theory	theory	NOUN
ejpam-5638	58	15	allow	allow	VERB
ejpam-5638	58	16	us	we	PRON
ejpam-5638	58	17	to	to	PART
ejpam-5638	58	18	develop	develop	VERB
ejpam-5638	58	19	a	a	DET
ejpam-5638	58	20	mathematical	mathematical	ADJ
ejpam-5638	58	21	technique	technique	NOUN
ejpam-5638	58	22	rather	rather	ADV
ejpam-5638	58	23	developing	develop	VERB
ejpam-5638	58	24	a	a	DET
ejpam-5638	58	25	complex	complex	ADJ
ejpam-5638	58	26	geometrical	geometrical	ADJ
ejpam-5638	58	27	based	base	VERB
ejpam-5638	58	28	approach	approach	NOUN
ejpam-5638	58	29	to	to	PART
ejpam-5638	58	30	discuss	discuss	VERB
ejpam-5638	58	31	the	the	DET
ejpam-5638	58	32	interconnections	interconnection	NOUN
ejpam-5638	58	33	among	among	ADP
ejpam-5638	58	34	structured	structured	ADJ
ejpam-5638	58	35	stability	stability	NOUN
ejpam-5638	58	36	,	,	PUNCT
ejpam-5638	58	37	structured	structured	ADJ
ejpam-5638	58	38	d	d	NOUN
ejpam-5638	58	39	-	-	NOUN
ejpam-5638	58	40	stability	stability	NOUN
ejpam-5638	58	41	,	,	PUNCT
ejpam-5638	58	42	and	and	CCONJ
ejpam-5638	58	43	the	the	DET
ejpam-5638	58	44	µ-values	µ-value	NOUN
ejpam-5638	58	45	.	.	PUNCT
ejpam-5638	59	1	the	the	DET
ejpam-5638	59	2	proposed	propose	VERB
ejpam-5638	59	3	mathematical	mathematical	ADJ
ejpam-5638	59	4	methodology	methodology	NOUN
ejpam-5638	59	5	guarantees	guarantee	VERB
ejpam-5638	59	6	that	that	SCONJ
ejpam-5638	59	7	all	all	DET
ejpam-5638	59	8	the	the	DET
ejpam-5638	59	9	equilibrium	equilibrium	NOUN
ejpam-5638	59	10	states	state	NOUN
ejpam-5638	59	11	of	of	ADP
ejpam-5638	59	12	an	an	DET
ejpam-5638	59	13	economy	economy	NOUN
ejpam-5638	59	14	models	model	NOUN
ejpam-5638	59	15	shall	shall	AUX
ejpam-5638	59	16	remains	remain	VERB
ejpam-5638	59	17	in	in	ADP
ejpam-5638	59	18	a	a	DET
ejpam-5638	59	19	stable	stable	ADJ
ejpam-5638	59	20	mood	mood	NOUN
ejpam-5638	59	21	subject	subject	ADJ
ejpam-5638	59	22	to	to	ADP
ejpam-5638	59	23	structured	structured	ADJ
ejpam-5638	59	24	or	or	CCONJ
ejpam-5638	59	25	unstructured	unstructured	ADJ
ejpam-5638	59	26	perturbations	perturbation	NOUN
ejpam-5638	59	27	.	.	PUNCT
ejpam-5638	60	1	our	our	PRON
ejpam-5638	60	2	technique	technique	NOUN
ejpam-5638	60	3	further	far	ADV
ejpam-5638	60	4	allows	allow	VERB
ejpam-5638	60	5	us	we	PRON
ejpam-5638	60	6	to	to	PART
ejpam-5638	60	7	analyze	analyze	VERB
ejpam-5638	60	8	both	both	CCONJ
ejpam-5638	60	9	robust	robust	ADJ
ejpam-5638	60	10	and	and	CCONJ
ejpam-5638	60	11	performance	performance	NOUN
ejpam-5638	60	12	of	of	ADP
ejpam-5638	60	13	economy	economy	NOUN
ejpam-5638	60	14	models	model	NOUN
ejpam-5638	60	15	subject	subject	ADJ
ejpam-5638	60	16	to	to	ADP
ejpam-5638	60	17	structured	structured	ADJ
ejpam-5638	60	18	or	or	CCONJ
ejpam-5638	60	19	unstructured	unstructured	ADJ
ejpam-5638	60	20	parametric	parametric	ADJ
ejpam-5638	60	21	uncertainties	uncertainty	NOUN
ejpam-5638	60	22	.	.	PUNCT
ejpam-5638	61	1	the	the	DET
ejpam-5638	61	2	economic	economic	ADJ
ejpam-5638	61	3	models	model	NOUN
ejpam-5638	61	4	based	base	VERB
ejpam-5638	61	5	on	on	ADP
ejpam-5638	61	6	linear	linear	ADJ
ejpam-5638	61	7	assumptions	assumption	NOUN
ejpam-5638	61	8	can	can	AUX
ejpam-5638	61	9	benefit	benefit	VERB
ejpam-5638	61	10	from	from	ADP
ejpam-5638	61	11	our	our	PRON
ejpam-5638	61	12	presented	present	VERB
ejpam-5638	61	13	methodology	methodology	NOUN
ejpam-5638	61	14	to	to	PART
ejpam-5638	61	15	study	study	VERB
ejpam-5638	61	16	stability	stability	NOUN
ejpam-5638	61	17	and	and	CCONJ
ejpam-5638	61	18	d	d	NOUN
ejpam-5638	61	19	-	-	PUNCT
ejpam-5638	61	20	stability	stability	NOUN
ejpam-5638	61	21	and	and	CCONJ
ejpam-5638	61	22	its	its	PRON
ejpam-5638	61	23	interconnection	interconnection	NOUN
ejpam-5638	61	24	with	with	ADP
ejpam-5638	61	25	structured	structured	ADJ
ejpam-5638	61	26	singular	singular	ADJ
ejpam-5638	61	27	values	value	NOUN
ejpam-5638	61	28	to	to	PART
ejpam-5638	61	29	ensure	ensure	VERB
ejpam-5638	61	30	that	that	SCONJ
ejpam-5638	61	31	a	a	DET
ejpam-5638	61	32	number	number	NOUN
ejpam-5638	61	33	of	of	ADP
ejpam-5638	61	34	economic	economic	ADJ
ejpam-5638	61	35	indicators	indicator	NOUN
ejpam-5638	61	36	will	will	AUX
ejpam-5638	61	37	remain	remain	VERB
ejpam-5638	61	38	within	within	ADP
ejpam-5638	61	39	considerable	considerable	ADJ
ejpam-5638	61	40	range	range	NOUN
ejpam-5638	61	41	.	.	PUNCT
ejpam-5638	62	1	we	we	PRON
ejpam-5638	62	2	organized	organize	VERB
ejpam-5638	62	3	our	our	PRON
ejpam-5638	62	4	paper	paper	NOUN
ejpam-5638	62	5	as	as	ADP
ejpam-5638	62	6	:	:	PUNCT
ejpam-5638	62	7	section	section	NOUN
ejpam-5638	62	8	2	2	NUM
ejpam-5638	62	9	is	be	AUX
ejpam-5638	62	10	on	on	ADP
ejpam-5638	62	11	conditions	condition	NOUN
ejpam-5638	62	12	for	for	ADP
ejpam-5638	62	13	stability	stability	NOUN
ejpam-5638	62	14	and	and	CCONJ
ejpam-5638	63	1	d	d	NOUN
ejpam-5638	63	2	-	-	NOUN
ejpam-5638	63	3	stability	stability	NOUN
ejpam-5638	63	4	,	,	PUNCT
ejpam-5638	63	5	where	where	SCONJ
ejpam-5638	63	6	we	we	PRON
ejpam-5638	63	7	have	have	AUX
ejpam-5638	63	8	recalled	recall	VERB
ejpam-5638	63	9	basic	basic	ADJ
ejpam-5638	63	10	notations	notation	NOUN
ejpam-5638	63	11	,	,	PUNCT
ejpam-5638	63	12	definitions	definition	NOUN
ejpam-5638	63	13	,	,	PUNCT
ejpam-5638	63	14	and	and	CCONJ
ejpam-5638	63	15	results	result	NOUN
ejpam-5638	63	16	concerning	concern	VERB
ejpam-5638	63	17	our	our	PRON
ejpam-5638	63	18	proposed	propose	VERB
ejpam-5638	63	19	study	study	NOUN
ejpam-5638	63	20	.	.	PUNCT
ejpam-5638	64	1	the	the	DET
ejpam-5638	64	2	novel	novel	ADJ
ejpam-5638	64	3	results	result	NOUN
ejpam-5638	64	4	on	on	ADP
ejpam-5638	64	5	structured	structured	ADJ
ejpam-5638	64	6	stable	stable	ADJ
ejpam-5638	64	7	matrices	matrix	NOUN
ejpam-5638	64	8	,	,	PUNCT
ejpam-5638	64	9	and	and	CCONJ
ejpam-5638	64	10	structured	structure	VERB
ejpam-5638	64	11	d	d	ADJ
ejpam-5638	64	12	-	-	ADJ
ejpam-5638	64	13	stable	stable	ADJ
ejpam-5638	64	14	matrices	matrix	NOUN
ejpam-5638	64	15	corresponding	correspond	VERB
ejpam-5638	64	16	to	to	ADP
ejpam-5638	64	17	first	first	ADJ
ejpam-5638	64	18	order	order	NOUN
ejpam-5638	64	19	dynamical	dynamical	ADJ
ejpam-5638	64	20	systems	system	NOUN
ejpam-5638	64	21	are	be	AUX
ejpam-5638	64	22	analyzed	analyze	VERB
ejpam-5638	64	23	in	in	ADP
ejpam-5638	64	24	section	section	NOUN
ejpam-5638	64	25	3	3	NUM
ejpam-5638	64	26	.	.	PUNCT
ejpam-5638	64	27	in	in	ADP
ejpam-5638	64	28	the	the	DET
ejpam-5638	64	29	section	section	NOUN
ejpam-5638	64	30	4	4	NUM
ejpam-5638	64	31	,	,	PUNCT
ejpam-5638	64	32	we	we	PRON
ejpam-5638	64	33	present	present	VERB
ejpam-5638	64	34	the	the	DET
ejpam-5638	64	35	numeric	numeric	ADJ
ejpam-5638	64	36	experimentation	experimentation	NOUN
ejpam-5638	64	37	’s	’s	PART
ejpam-5638	64	38	and	and	CCONJ
ejpam-5638	64	39	comparison	comparison	NOUN
ejpam-5638	64	40	on	on	ADP
ejpam-5638	64	41	computation	computation	NOUN
ejpam-5638	64	42	and	and	CCONJ
ejpam-5638	64	43	approximation	approximation	NOUN
ejpam-5638	64	44	of	of	ADP
ejpam-5638	64	45	lower	low	ADJ
ejpam-5638	64	46	bounds	bound	NOUN
ejpam-5638	64	47	to	to	ADP
ejpam-5638	64	48	µ-values	µ-value	NOUN
ejpam-5638	64	49	for	for	ADP
ejpam-5638	64	50	structured	structured	ADJ
ejpam-5638	64	51	matrices	matrix	NOUN
ejpam-5638	64	52	corresponding	correspond	VERB
ejpam-5638	64	53	to	to	ADP
ejpam-5638	64	54	dynamical	dynamical	ADJ
ejpam-5638	64	55	systems	system	NOUN
ejpam-5638	64	56	under	under	ADP
ejpam-5638	64	57	consideration	consideration	NOUN
ejpam-5638	64	58	.	.	PUNCT
ejpam-5638	65	1	finally	finally	ADV
ejpam-5638	65	2	,	,	PUNCT
ejpam-5638	65	3	the	the	DET
ejpam-5638	65	4	conclusion	conclusion	NOUN
ejpam-5638	65	5	is	be	AUX
ejpam-5638	65	6	presented	present	VERB
ejpam-5638	65	7	in	in	ADP
ejpam-5638	65	8	the	the	DET
ejpam-5638	65	9	section	section	NOUN
ejpam-5638	65	10	5	5	NUM
ejpam-5638	65	11	of	of	ADP
ejpam-5638	65	12	this	this	DET
ejpam-5638	65	13	article	article	NOUN
ejpam-5638	65	14	.	.	PUNCT
ejpam-5638	66	1	m.u.r	m.u.r	PROPN
ejpam-5638	66	2	rehman	rehman	PROPN
ejpam-5638	66	3	et	et	PROPN
ejpam-5638	66	4	al	al	PROPN
ejpam-5638	66	5	.	.	PUNCT
ejpam-5638	66	6	/	/	SYM
ejpam-5638	66	7	eur	eur	PROPN
ejpam-5638	66	8	.	.	PUNCT
ejpam-5638	67	1	j.	j.	PROPN
ejpam-5638	67	2	pure	pure	PROPN
ejpam-5638	67	3	appl	appl	PROPN
ejpam-5638	67	4	.	.	PROPN
ejpam-5638	67	5	math	math	PROPN
ejpam-5638	67	6	,	,	PUNCT
ejpam-5638	67	7	18	18	NUM
ejpam-5638	67	8	(	(	PUNCT
ejpam-5638	67	9	2	2	NUM
ejpam-5638	67	10	)	)	PUNCT
ejpam-5638	67	11	(	(	PUNCT
ejpam-5638	67	12	2025	2025	NUM
ejpam-5638	67	13	)	)	PUNCT
ejpam-5638	67	14	,	,	PUNCT
ejpam-5638	67	15	5638	5638	NUM
ejpam-5638	67	16	4	4	NUM
ejpam-5638	67	17	of	of	ADP
ejpam-5638	67	18	23	23	NUM
ejpam-5638	67	19	2	2	NUM
ejpam-5638	67	20	.	.	PUNCT
ejpam-5638	67	21	conditions	condition	NOUN
ejpam-5638	67	22	for	for	ADP
ejpam-5638	67	23	stability	stability	NOUN
ejpam-5638	67	24	and	and	CCONJ
ejpam-5638	68	1	d	d	NOUN
ejpam-5638	68	2	-	-	PUNCT
ejpam-5638	68	3	stability	stability	NOUN
ejpam-5638	68	4	let	let	VERB
ejpam-5638	68	5	⃗̂x	⃗̂x	PROPN
ejpam-5638	68	6	=	=	SYM
ejpam-5638	68	7	(	(	PUNCT
ejpam-5638	68	8	x̂1	x̂1	PROPN
ejpam-5638	68	9	,	,	PUNCT
ejpam-5638	68	10	x̂2	x̂2	NOUN
ejpam-5638	68	11	,	,	PUNCT
ejpam-5638	68	12	.	.	PUNCT
ejpam-5638	68	13	.	.	PUNCT
ejpam-5638	69	1	.	.	PUNCT
ejpam-5638	70	1	,	,	PUNCT
ejpam-5638	70	2	x̂n	x̂n	NUM
ejpam-5638	70	3	)	)	PUNCT
ejpam-5638	70	4	denotes	denote	VERB
ejpam-5638	70	5	steady	steady	ADJ
ejpam-5638	70	6	state	state	NOUN
ejpam-5638	70	7	of	of	ADP
ejpam-5638	70	8	dynamical	dynamical	ADJ
ejpam-5638	70	9	system	system	NOUN
ejpam-5638	70	10	,	,	PUNCT
ejpam-5638	70	11	and	and	CCONJ
ejpam-5638	70	12	fi,∀i	fi,∀i	PROPN
ejpam-5638	70	13	,	,	PUNCT
ejpam-5638	70	14	continuously	continuously	ADV
ejpam-5638	70	15	differentiable	differentiable	ADJ
ejpam-5638	70	16	functions	function	NOUN
ejpam-5638	70	17	,	,	PUNCT
ejpam-5638	70	18	then	then	ADV
ejpam-5638	70	19	the	the	DET
ejpam-5638	70	20	n	n	ADV
ejpam-5638	70	21	-	-	PUNCT
ejpam-5638	70	22	dimensional	dimensional	ADJ
ejpam-5638	70	23	continuous	continuous	ADJ
ejpam-5638	70	24	(	(	PUNCT
ejpam-5638	70	25	in	in	ADP
ejpam-5638	70	26	time	time	NOUN
ejpam-5638	70	27	)	)	PUNCT
ejpam-5638	70	28	dynamical	dynamical	ADJ
ejpam-5638	70	29	system	system	NOUN
ejpam-5638	70	30	may	may	AUX
ejpam-5638	70	31	be	be	AUX
ejpam-5638	70	32	written	write	VERB
ejpam-5638	70	33	mathematically	mathematically	ADV
ejpam-5638	70	34	as	as	ADP
ejpam-5638	70	35	d	d	X
ejpam-5638	70	36	dt	dt	NOUN
ejpam-5638	70	37	xi(t	xi(t	PUNCT
ejpam-5638	70	38	)	)	PUNCT
ejpam-5638	71	1	=	=	SYM
ejpam-5638	71	2	fi	fi	NOUN
ejpam-5638	71	3	(	(	PUNCT
ejpam-5638	71	4	x1(t	x1(t	PROPN
ejpam-5638	71	5	)	)	PUNCT
ejpam-5638	71	6	,	,	PUNCT
ejpam-5638	71	7	x2(t	x2(t	PROPN
ejpam-5638	71	8	)	)	PUNCT
ejpam-5638	71	9	,	,	PUNCT
ejpam-5638	71	10	.	.	PUNCT
ejpam-5638	71	11	.	.	PUNCT
ejpam-5638	71	12	.	.	PUNCT
ejpam-5638	72	1	,	,	PUNCT
ejpam-5638	72	2	xn(t	xn(t	NUM
ejpam-5638	72	3	)	)	PUNCT
ejpam-5638	72	4	)	)	PUNCT
ejpam-5638	72	5	,	,	PUNCT
ejpam-5638	72	6	∀i	∀i	NOUN
ejpam-5638	72	7	=	=	SYM
ejpam-5638	72	8	1	1	NUM
ejpam-5638	72	9	:	:	PUNCT
ejpam-5638	72	10	n.	n.	NOUN
ejpam-5638	72	11	linearized	linearize	VERB
ejpam-5638	72	12	version	version	NOUN
ejpam-5638	72	13	of	of	ADP
ejpam-5638	72	14	above	above	ADP
ejpam-5638	72	15	dynamical	dynamical	ADJ
ejpam-5638	72	16	model	model	NOUN
ejpam-5638	72	17	is	be	AUX
ejpam-5638	72	18	rewritten	rewrite	VERB
ejpam-5638	72	19	as	as	ADP
ejpam-5638	72	20	follow	follow	NOUN
ejpam-5638	72	21	:	:	PUNCT
ejpam-5638	73	1	d	d	X
ejpam-5638	73	2	dt	dt	X
ejpam-5638	73	3	xiβ(t	xiβ(t	PROPN
ejpam-5638	73	4	)	)	PUNCT
ejpam-5638	74	1	=	=	PUNCT
ejpam-5638	74	2	∑	∑	PUNCT
ejpam-5638	74	3	j	j	PROPN
ejpam-5638	74	4	∂fi(x	∂fi(x	NOUN
ejpam-5638	74	5	)	)	PUNCT
ejpam-5638	74	6	∂xj	∂xj	PROPN
ejpam-5638	74	7	xiβ(t	xiβ(t	PROPN
ejpam-5638	74	8	)	)	PUNCT
ejpam-5638	74	9	,	,	PUNCT
ejpam-5638	74	10	where	where	SCONJ
ejpam-5638	74	11	xiβ(t	xiβ(t	NOUN
ejpam-5638	74	12	)	)	PUNCT
ejpam-5638	74	13	=	=	PUNCT
ejpam-5638	74	14	xi(t)−	xi(t)−	PROPN
ejpam-5638	74	15	x̂i	x̂i	PROPN
ejpam-5638	74	16	,	,	PUNCT
ejpam-5638	74	17	∀i	∀i	NOUN
ejpam-5638	74	18	.	.	PUNCT
ejpam-5638	74	19	remark	remark	PROPN
ejpam-5638	74	20	1	1	NUM
ejpam-5638	74	21	.	.	PUNCT
ejpam-5638	75	1	if	if	SCONJ
ejpam-5638	75	2	all	all	DET
ejpam-5638	75	3	the	the	DET
ejpam-5638	75	4	eigenvalues	eigenvalue	NOUN
ejpam-5638	75	5	corresponding	correspond	VERB
ejpam-5638	75	6	to	to	ADP
ejpam-5638	75	7	coefficient	coefficient	NOUN
ejpam-5638	75	8	matrix	matrix	NOUN
ejpam-5638	75	9	have	have	VERB
ejpam-5638	75	10	strictly	strictly	ADV
ejpam-5638	75	11	positive	positive	ADJ
ejpam-5638	75	12	real	real	ADJ
ejpam-5638	75	13	parts	part	NOUN
ejpam-5638	75	14	,	,	PUNCT
ejpam-5638	75	15	that	that	ADV
ejpam-5638	75	16	is	is	ADV
ejpam-5638	75	17	,	,	PUNCT
ejpam-5638	75	18	re(λi(t	re(λi(t	NOUN
ejpam-5638	75	19	)	)	PUNCT
ejpam-5638	75	20	)	)	PUNCT
ejpam-5638	76	1	>	>	X
ejpam-5638	76	2	0,∀t	0,∀t	NUM
ejpam-5638	76	3	,	,	PUNCT
ejpam-5638	76	4	then	then	ADV
ejpam-5638	76	5	linear	linear	PROPN
ejpam-5638	76	6	dynamical	dynamical	ADJ
ejpam-5638	76	7	system	system	NOUN
ejpam-5638	76	8	is	be	AUX
ejpam-5638	76	9	stable	stable	ADJ
ejpam-5638	76	10	.	.	PUNCT
ejpam-5638	77	1	it	it	PRON
ejpam-5638	77	2	is	be	AUX
ejpam-5638	77	3	well	well	ADV
ejpam-5638	77	4	-	-	PUNCT
ejpam-5638	77	5	known	know	VERB
ejpam-5638	77	6	that	that	SCONJ
ejpam-5638	77	7	coefficient	coefficient	NOUN
ejpam-5638	77	8	matrix	matrix	NOUN
ejpam-5638	77	9	is	be	AUX
ejpam-5638	77	10	jacobian	jacobian	ADJ
ejpam-5638	77	11	of	of	ADP
ejpam-5638	77	12	system	system	NOUN
ejpam-5638	77	13	d	d	NOUN
ejpam-5638	77	14	dt	dt	NOUN
ejpam-5638	77	15	xi(t	xi(t	PUNCT
ejpam-5638	77	16	)	)	PUNCT
ejpam-5638	77	17	=	=	SYM
ejpam-5638	77	18	fi(x1(t	fi(x1(t	PROPN
ejpam-5638	77	19	)	)	PUNCT
ejpam-5638	77	20	,	,	PUNCT
ejpam-5638	77	21	x2(t	x2(t	PROPN
ejpam-5638	77	22	)	)	PUNCT
ejpam-5638	77	23	,	,	PUNCT
ejpam-5638	77	24	.	.	PUNCT
ejpam-5638	77	25	.	.	PUNCT
ejpam-5638	77	26	.	.	PUNCT
ejpam-5638	78	1	xn(t	xn(t	NUM
ejpam-5638	78	2	)	)	PUNCT
ejpam-5638	78	3	)	)	PUNCT
ejpam-5638	79	1	,	,	PUNCT
ejpam-5638	79	2	∀i	∀i	NOUN
ejpam-5638	79	3	=	=	SYM
ejpam-5638	79	4	1	1	NUM
ejpam-5638	79	5	:	:	PUNCT
ejpam-5638	79	6	n	n	CCONJ
ejpam-5638	79	7	,	,	PUNCT
ejpam-5638	79	8	and	and	CCONJ
ejpam-5638	79	9	is	be	AUX
ejpam-5638	79	10	presented	present	VERB
ejpam-5638	79	11	by	by	ADP
ejpam-5638	79	12	jc	jc	PROPN
ejpam-5638	79	13	=	=	PROPN
ejpam-5638	79	14			NOUN
ejpam-5638	79	15	∂f1(x̂	∂f1(x̂	NOUN
ejpam-5638	79	16	)	)	PUNCT
ejpam-5638	79	17	∂x1	∂x1	NOUN
ejpam-5638	79	18	∂f1(x̂	∂f1(x̂	NOUN
ejpam-5638	79	19	)	)	PUNCT
ejpam-5638	79	20	∂xn	∂xn	PROPN
ejpam-5638	79	21	∂fn(x̂	∂fn(x̂	NOUN
ejpam-5638	79	22	)	)	PUNCT
ejpam-5638	79	23	∂x1	∂x1	PROPN
ejpam-5638	79	24	∂fn(x̂	∂fn(x̂	NOUN
ejpam-5638	79	25	)	)	PUNCT
ejpam-5638	79	26	∂xn	∂xn	PUNCT
ejpam-5638	79	27			NOUN
ejpam-5638	79	28	.	.	PUNCT
ejpam-5638	80	1	if	if	SCONJ
ejpam-5638	80	2	re(λi(jc	re(λi(jc	ADJ
ejpam-5638	80	3	)	)	PUNCT
ejpam-5638	80	4	)	)	PUNCT
ejpam-5638	81	1	>	>	X
ejpam-5638	81	2	0	0	NUM
ejpam-5638	82	1	∀i	∀i	NOUN
ejpam-5638	82	2	,	,	PUNCT
ejpam-5638	82	3	then	then	ADV
ejpam-5638	82	4	system	system	NOUN
ejpam-5638	82	5	is	be	AUX
ejpam-5638	82	6	stable	stable	ADJ
ejpam-5638	82	7	.	.	PUNCT
ejpam-5638	83	1	the	the	DET
ejpam-5638	83	2	continuous	continuous	ADJ
ejpam-5638	83	3	-	-	PUNCT
ejpam-5638	83	4	time	time	NOUN
ejpam-5638	83	5	linear	linear	PROPN
ejpam-5638	83	6	dynamic	dynamic	ADJ
ejpam-5638	83	7	model	model	NOUN
ejpam-5638	83	8	d	d	X
ejpam-5638	83	9	dt	dt	X
ejpam-5638	83	10	x(t	x(t	PROPN
ejpam-5638	83	11	)	)	PUNCT
ejpam-5638	83	12	=	=	SYM
ejpam-5638	83	13	ax(t	ax(t	NUM
ejpam-5638	83	14	)	)	PUNCT
ejpam-5638	83	15	,	,	PUNCT
ejpam-5638	83	16	x(0	x(0	PROPN
ejpam-5638	83	17	)	)	PUNCT
ejpam-5638	84	1	=	=	PUNCT
ejpam-5638	84	2	x0	x0	PROPN
ejpam-5638	84	3	,	,	PUNCT
ejpam-5638	84	4	with	with	ADP
ejpam-5638	84	5	x(t	x(t	PROPN
ejpam-5638	84	6	)	)	PUNCT
ejpam-5638	84	7	∈	∈	PROPN
ejpam-5638	84	8	rn,1	rn,1	NOUN
ejpam-5638	84	9	be	be	VERB
ejpam-5638	84	10	a	a	DET
ejpam-5638	84	11	state	state	NOUN
ejpam-5638	84	12	variable	variable	NOUN
ejpam-5638	84	13	,	,	PUNCT
ejpam-5638	84	14	the	the	DET
ejpam-5638	84	15	initial	initial	ADJ
ejpam-5638	84	16	condition	condition	NOUN
ejpam-5638	84	17	is	be	AUX
ejpam-5638	84	18	x0	x0	PROPN
ejpam-5638	84	19	∈	∈	PROPN
ejpam-5638	84	20	rn,1	rn,1	PROPN
ejpam-5638	84	21	,	,	PUNCT
ejpam-5638	84	22	and	and	CCONJ
ejpam-5638	84	23	a	a	DET
ejpam-5638	84	24	∈	∈	PROPN
ejpam-5638	84	25	rn	rn	PROPN
ejpam-5638	84	26	,	,	PUNCT
ejpam-5638	84	27	n	n	PRON
ejpam-5638	84	28	matrix	matrix	NOUN
ejpam-5638	84	29	.	.	PUNCT
ejpam-5638	85	1	an	an	DET
ejpam-5638	85	2	optimal	optimal	ADJ
ejpam-5638	85	3	and	and	CCONJ
ejpam-5638	85	4	feasible	feasible	ADJ
ejpam-5638	85	5	solution	solution	NOUN
ejpam-5638	85	6	to	to	ADP
ejpam-5638	85	7	an	an	DET
ejpam-5638	85	8	optimization	optimization	NOUN
ejpam-5638	85	9	problem	problem	NOUN
ejpam-5638	85	10	a	a	DET
ejpam-5638	85	11	∈	∈	PROPN
ejpam-5638	85	12	rn	rn	PROPN
ejpam-5638	85	13	,	,	PUNCT
ejpam-5638	85	14	n	n	PROPN
ejpam-5638	85	15	is	be	AUX
ejpam-5638	85	16	obtain	obtain	ADJ
ejpam-5638	85	17	as	as	ADP
ejpam-5638	85	18	a	a	DET
ejpam-5638	85	19	=	=	SYM
ejpam-5638	85	20	arg	arg	NOUN
ejpam-5638	85	21	min	min	PROPN
ejpam-5638	85	22	dx	dx	PROPN
ejpam-5638	85	23	dt	dt	PROPN
ejpam-5638	85	24	−	−	PROPN
ejpam-5638	85	25	âx	âx	PROPN
ejpam-5638	85	26	f	f	PROPN
ejpam-5638	85	27	,	,	PUNCT
ejpam-5638	85	28	where	where	SCONJ
ejpam-5638	85	29	∥	∥	X
ejpam-5638	85	30	·	·	PUNCT
ejpam-5638	86	1	∥f	∥f	PROPN
ejpam-5638	86	2	denotes	denote	VERB
ejpam-5638	86	3	frobenius	frobenius	VERB
ejpam-5638	86	4	matrix	matrix	NOUN
ejpam-5638	86	5	-	-	PUNCT
ejpam-5638	86	6	norm	norm	NOUN
ejpam-5638	86	7	,	,	PUNCT
ejpam-5638	86	8	and	and	CCONJ
ejpam-5638	86	9	the	the	DET
ejpam-5638	86	10	min	min	NOUN
ejpam-5638	86	11	is	be	AUX
ejpam-5638	86	12	taken	take	VERB
ejpam-5638	86	13	over	over	ADP
ejpam-5638	86	14	â	â	PROPN
ejpam-5638	86	15	∈	∈	PROPN
ejpam-5638	86	16	rn	rn	PROPN
ejpam-5638	86	17	,	,	PUNCT
ejpam-5638	86	18	n	n	CCONJ
ejpam-5638	86	19	,	,	PUNCT
ejpam-5638	86	20	and	and	CCONJ
ejpam-5638	86	21	arg	arg	NOUN
ejpam-5638	86	22	means	mean	VERB
ejpam-5638	86	23	the	the	DET
ejpam-5638	86	24	argument	argument	NOUN
ejpam-5638	86	25	.	.	PUNCT
ejpam-5638	87	1	furthermore	furthermore	ADV
ejpam-5638	87	2	,	,	PUNCT
ejpam-5638	87	3	a	a	DET
ejpam-5638	87	4	minimal	minimal	ADJ
ejpam-5638	87	5	-	-	PUNCT
ejpam-5638	87	6	norm	norm	NOUN
ejpam-5638	87	7	solution	solution	NOUN
ejpam-5638	87	8	obtained	obtain	VERB
ejpam-5638	87	9	[	[	X
ejpam-5638	87	10	15	15	NUM
ejpam-5638	87	11	]	]	PUNCT
ejpam-5638	87	12	to	to	ADP
ejpam-5638	87	13	the	the	DET
ejpam-5638	87	14	dynamical	dynamical	ADJ
ejpam-5638	87	15	system	system	NOUN
ejpam-5638	87	16	has	have	VERB
ejpam-5638	87	17	the	the	DET
ejpam-5638	87	18	form	form	NOUN
ejpam-5638	87	19	a	a	PRON
ejpam-5638	87	20	=	=	SYM
ejpam-5638	87	21	x+	x+	PROPN
ejpam-5638	87	22	dx	dx	PROPN
ejpam-5638	87	23	dt	dt	X
ejpam-5638	87	24	,	,	PUNCT
ejpam-5638	87	25	with	with	ADP
ejpam-5638	87	26	x+	x+	ADJ
ejpam-5638	87	27	,	,	PUNCT
ejpam-5638	87	28	the	the	DET
ejpam-5638	87	29	pseudo	pseudo	NOUN
ejpam-5638	87	30	-	-	NOUN
ejpam-5638	87	31	inverse	inverse	NOUN
ejpam-5638	87	32	to	to	PART
ejpam-5638	87	33	matrix	matrix	VERB
ejpam-5638	87	34	x.	x.	NOUN
ejpam-5638	87	35	remark	remark	NOUN
ejpam-5638	87	36	2	2	NUM
ejpam-5638	87	37	.	.	PUNCT
ejpam-5638	88	1	the	the	DET
ejpam-5638	88	2	dynamical	dynamical	ADJ
ejpam-5638	88	3	system	system	NOUN
ejpam-5638	88	4	d	d	NOUN
ejpam-5638	88	5	dt	dt	NOUN
ejpam-5638	88	6	x(t	x(t	PROPN
ejpam-5638	88	7	)	)	PUNCT
ejpam-5638	88	8	=	=	SYM
ejpam-5638	88	9	ax(t	ax(t	NUM
ejpam-5638	88	10	)	)	PUNCT
ejpam-5638	88	11	,	,	PUNCT
ejpam-5638	88	12	x(0	x(0	PROPN
ejpam-5638	88	13	)	)	PUNCT
ejpam-5638	89	1	=	=	SYM
ejpam-5638	89	2	x0	x0	PROPN
ejpam-5638	89	3	m.u.r	m.u.r	PROPN
ejpam-5638	89	4	rehman	rehman	NOUN
ejpam-5638	89	5	et	et	PROPN
ejpam-5638	89	6	al	al	PROPN
ejpam-5638	89	7	.	.	PUNCT
ejpam-5638	89	8	/	/	SYM
ejpam-5638	89	9	eur	eur	PROPN
ejpam-5638	89	10	.	.	PUNCT
ejpam-5638	90	1	j.	j.	PROPN
ejpam-5638	90	2	pure	pure	PROPN
ejpam-5638	90	3	appl	appl	PROPN
ejpam-5638	90	4	.	.	PROPN
ejpam-5638	90	5	math	math	PROPN
ejpam-5638	90	6	,	,	PUNCT
ejpam-5638	90	7	18	18	NUM
ejpam-5638	90	8	(	(	PUNCT
ejpam-5638	90	9	2	2	NUM
ejpam-5638	90	10	)	)	PUNCT
ejpam-5638	90	11	(	(	PUNCT
ejpam-5638	90	12	2025	2025	NUM
ejpam-5638	90	13	)	)	PUNCT
ejpam-5638	90	14	,	,	PUNCT
ejpam-5638	90	15	5638	5638	NUM
ejpam-5638	90	16	5	5	NUM
ejpam-5638	90	17	of	of	ADP
ejpam-5638	90	18	23	23	NUM
ejpam-5638	90	19	may	may	AUX
ejpam-5638	90	20	not	not	PART
ejpam-5638	90	21	be	be	AUX
ejpam-5638	90	22	a	a	DET
ejpam-5638	90	23	stable	stable	ADJ
ejpam-5638	90	24	dynamical	dynamical	ADJ
ejpam-5638	90	25	system	system	NOUN
ejpam-5638	90	26	means	mean	VERB
ejpam-5638	90	27	that	that	SCONJ
ejpam-5638	90	28	the	the	DET
ejpam-5638	90	29	solution	solution	NOUN
ejpam-5638	90	30	matrix	matrix	NOUN
ejpam-5638	90	31	has	have	VERB
ejpam-5638	90	32	the	the	DET
ejpam-5638	90	33	form	form	NOUN
ejpam-5638	90	34	a	a	DET
ejpam-5638	90	35	=	=	NOUN
ejpam-5638	90	36	arg	arg	NOUN
ejpam-5638	90	37	min	min	PROPN
ejpam-5638	90	38	dx	dx	PROPN
ejpam-5638	90	39	dt	dt	PROPN
ejpam-5638	90	40	−	−	PROPN
ejpam-5638	90	41	âx	âx	PROPN
ejpam-5638	90	42	f	f	PROPN
ejpam-5638	90	43	,	,	PUNCT
ejpam-5638	90	44	where	where	SCONJ
ejpam-5638	90	45	min	min	NOUN
ejpam-5638	90	46	is	be	AUX
ejpam-5638	90	47	taken	take	VERB
ejpam-5638	90	48	over	over	ADP
ejpam-5638	90	49	â	â	PROPN
ejpam-5638	90	50	∈	∈	PROPN
ejpam-5638	90	51	rn	rn	PROPN
ejpam-5638	90	52	,	,	PUNCT
ejpam-5638	90	53	n	n	PROPN
ejpam-5638	90	54	and	and	CCONJ
ejpam-5638	90	55	arg	arg	NOUN
ejpam-5638	90	56	means	mean	VERB
ejpam-5638	90	57	the	the	DET
ejpam-5638	90	58	argument	argument	NOUN
ejpam-5638	90	59	.	.	PUNCT
ejpam-5638	91	1	for	for	ADP
ejpam-5638	91	2	the	the	DET
ejpam-5638	91	3	structured	structured	ADJ
ejpam-5638	91	4	stability	stability	NOUN
ejpam-5638	91	5	of	of	ADP
ejpam-5638	91	6	dynamical	dynamical	ADJ
ejpam-5638	91	7	model	model	NOUN
ejpam-5638	91	8	(	(	PUNCT
ejpam-5638	91	9	linear	linear	PROPN
ejpam-5638	91	10	)	)	PUNCT
ejpam-5638	91	11	,	,	PUNCT
ejpam-5638	91	12	the	the	DET
ejpam-5638	91	13	eigenvalues	eigenvalue	NOUN
ejpam-5638	91	14	of	of	ADP
ejpam-5638	91	15	a	a	DET
ejpam-5638	91	16	∈	∈	PROPN
ejpam-5638	91	17	rn	rn	PROPN
ejpam-5638	91	18	,	,	PUNCT
ejpam-5638	91	19	n	n	PRON
ejpam-5638	91	20	must	must	AUX
ejpam-5638	91	21	lie	lie	VERB
ejpam-5638	91	22	in	in	ADP
ejpam-5638	91	23	right	right	ADJ
ejpam-5638	91	24	hand	hand	NOUN
ejpam-5638	91	25	side	side	NOUN
ejpam-5638	91	26	of	of	ADP
ejpam-5638	91	27	the	the	DET
ejpam-5638	91	28	complex	complex	ADJ
ejpam-5638	91	29	plane	plane	NOUN
ejpam-5638	91	30	c.	c.	NOUN
ejpam-5638	91	31	the	the	DET
ejpam-5638	91	32	n	n	CCONJ
ejpam-5638	91	33	-	-	PUNCT
ejpam-5638	91	34	dimensional	dimensional	ADJ
ejpam-5638	91	35	real	real	ADJ
ejpam-5638	91	36	and	and	CCONJ
ejpam-5638	91	37	complex	complex	ADJ
ejpam-5638	91	38	valued	value	VERB
ejpam-5638	91	39	matrices	matrix	NOUN
ejpam-5638	91	40	are	be	AUX
ejpam-5638	91	41	dented	dent	VERB
ejpam-5638	91	42	with	with	ADP
ejpam-5638	91	43	a	a	DET
ejpam-5638	91	44	∈	∈	PROPN
ejpam-5638	91	45	rn	rn	PROPN
ejpam-5638	91	46	,	,	PUNCT
ejpam-5638	91	47	n	n	CCONJ
ejpam-5638	91	48	,	,	PUNCT
ejpam-5638	91	49	and	and	CCONJ
ejpam-5638	91	50	a	a	DET
ejpam-5638	91	51	∈	∈	PROPN
ejpam-5638	91	52	cn	cn	PROPN
ejpam-5638	91	53	,	,	PUNCT
ejpam-5638	91	54	n	n	PRON
ejpam-5638	91	55	respectively	respectively	ADV
ejpam-5638	91	56	.	.	PUNCT
ejpam-5638	92	1	the	the	DET
ejpam-5638	92	2	given	give	VERB
ejpam-5638	92	3	matrix	matrix	NOUN
ejpam-5638	92	4	a	a	DET
ejpam-5638	92	5	∈	∈	PROPN
ejpam-5638	92	6	cn	cn	PROPN
ejpam-5638	92	7	,	,	PUNCT
ejpam-5638	92	8	n	n	PRON
ejpam-5638	92	9	is	be	AUX
ejpam-5638	92	10	called	call	VERB
ejpam-5638	92	11	a	a	DET
ejpam-5638	92	12	structured	structured	ADJ
ejpam-5638	92	13	d	d	ADJ
ejpam-5638	92	14	-	-	ADJ
ejpam-5638	92	15	stable	stable	ADJ
ejpam-5638	92	16	matrix	matrix	NOUN
ejpam-5638	92	17	if	if	SCONJ
ejpam-5638	92	18	matrix	matrix	NOUN
ejpam-5638	92	19	product	product	NOUN
ejpam-5638	92	20	da	da	PROPN
ejpam-5638	92	21	appears	appear	VERB
ejpam-5638	92	22	to	to	PART
ejpam-5638	92	23	be	be	AUX
ejpam-5638	92	24	a	a	DET
ejpam-5638	92	25	stable	stable	ADJ
ejpam-5638	92	26	matrix	matrix	NOUN
ejpam-5638	92	27	for	for	ADP
ejpam-5638	92	28	all	all	DET
ejpam-5638	92	29	d	d	PROPN
ejpam-5638	92	30	∈	∈	PROPN
ejpam-5638	93	1	d̂	d̂	NOUN
ejpam-5638	93	2	,	,	PUNCT
ejpam-5638	93	3	where	where	SCONJ
ejpam-5638	93	4	d̂	d̂	PROPN
ejpam-5638	93	5	denotes	denote	NOUN
ejpam-5638	93	6	set	set	VERB
ejpam-5638	93	7	of	of	ADP
ejpam-5638	93	8	positive	positive	ADJ
ejpam-5638	93	9	diagonal	diagonal	ADJ
ejpam-5638	93	10	structured	structured	ADJ
ejpam-5638	93	11	matrices	matrix	NOUN
ejpam-5638	93	12	.	.	PUNCT
ejpam-5638	94	1	remark	remark	PROPN
ejpam-5638	94	2	3	3	NUM
ejpam-5638	94	3	.	.	PUNCT
ejpam-5638	95	1	the	the	DET
ejpam-5638	95	2	matrix	matrix	NOUN
ejpam-5638	95	3	products	product	NOUN
ejpam-5638	95	4	da	da	NOUN
ejpam-5638	95	5	,	,	PUNCT
ejpam-5638	95	6	and	and	CCONJ
ejpam-5638	95	7	ad	ad	NOUN
ejpam-5638	95	8	are	be	AUX
ejpam-5638	95	9	similar	similar	ADJ
ejpam-5638	95	10	which	which	PRON
ejpam-5638	95	11	implies	imply	VERB
ejpam-5638	95	12	that	that	SCONJ
ejpam-5638	95	13	λi(da	λi(da	NOUN
ejpam-5638	95	14	)	)	PUNCT
ejpam-5638	95	15	∀i	∀i	NOUN
ejpam-5638	95	16	are	be	AUX
ejpam-5638	95	17	the	the	DET
ejpam-5638	95	18	eigenvalues	eigenvalue	NOUN
ejpam-5638	95	19	of	of	ADP
ejpam-5638	95	20	ad	ad	NOUN
ejpam-5638	95	21	,	,	PUNCT
ejpam-5638	95	22	because	because	SCONJ
ejpam-5638	95	23	da	da	NOUN
ejpam-5638	95	24	=	=	SYM
ejpam-5638	95	25	d(ad)d−1	d(ad)d−1	NOUN
ejpam-5638	95	26	.	.	PUNCT
ejpam-5638	96	1	some	some	DET
ejpam-5638	96	2	simple	simple	ADJ
ejpam-5638	96	3	observations	observation	NOUN
ejpam-5638	96	4	[	[	X
ejpam-5638	96	5	16	16	NUM
ejpam-5638	96	6	]	]	PUNCT
ejpam-5638	96	7	to	to	ADP
ejpam-5638	96	8	d	d	NOUN
ejpam-5638	96	9	-	-	PUNCT
ejpam-5638	96	10	stability	stability	NOUN
ejpam-5638	96	11	of	of	ADP
ejpam-5638	96	12	a	a	DET
ejpam-5638	96	13	∈	∈	PROPN
ejpam-5638	96	14	cn	cn	PROPN
ejpam-5638	96	15	,	,	PUNCT
ejpam-5638	96	16	n	n	PRON
ejpam-5638	96	17	are	be	AUX
ejpam-5638	96	18	:	:	PUNCT
ejpam-5638	96	19	1	1	X
ejpam-5638	96	20	.	.	X
ejpam-5638	97	1	it	it	PRON
ejpam-5638	97	2	is	be	AUX
ejpam-5638	97	3	a	a	DET
ejpam-5638	97	4	condition	condition	NOUN
ejpam-5638	97	5	which	which	PRON
ejpam-5638	97	6	imply	imply	VERB
ejpam-5638	97	7	stabilization	stabilization	NOUN
ejpam-5638	97	8	,	,	PUNCT
ejpam-5638	97	9	and	and	CCONJ
ejpam-5638	97	10	is	be	AUX
ejpam-5638	97	11	preserved	preserve	VERB
ejpam-5638	97	12	under	under	ADP
ejpam-5638	97	13	matrix	matrix	NOUN
ejpam-5638	97	14	multiplication	multiplication	NOUN
ejpam-5638	97	15	of	of	ADP
ejpam-5638	97	16	positive	positive	ADJ
ejpam-5638	97	17	structured	structured	ADJ
ejpam-5638	97	18	diagonal	diagonal	ADJ
ejpam-5638	97	19	matrices	matrix	NOUN
ejpam-5638	97	20	.	.	PUNCT
ejpam-5638	98	1	2	2	X
ejpam-5638	98	2	.	.	X
ejpam-5638	98	3	for	for	ADP
ejpam-5638	98	4	a	a	DET
ejpam-5638	98	5	d	d	ADJ
ejpam-5638	98	6	-	-	ADJ
ejpam-5638	98	7	stable	stable	ADJ
ejpam-5638	98	8	matrix	matrix	NOUN
ejpam-5638	98	9	a	a	DET
ejpam-5638	98	10	∈	∈	PROPN
ejpam-5638	98	11	cn	cn	PROPN
ejpam-5638	98	12	,	,	PUNCT
ejpam-5638	98	13	n	n	PRON
ejpam-5638	98	14	such	such	ADJ
ejpam-5638	98	15	that	that	DET
ejpam-5638	98	16	det(a	det(a	NOUN
ejpam-5638	98	17	)	)	PUNCT
ejpam-5638	98	18	̸=	̸=	PROPN
ejpam-5638	98	19	0	0	NUM
ejpam-5638	98	20	,	,	PUNCT
ejpam-5638	98	21	then	then	ADV
ejpam-5638	98	22	(	(	PUNCT
ejpam-5638	98	23	a	a	X
ejpam-5638	98	24	)	)	PUNCT
ejpam-5638	98	25	the	the	DET
ejpam-5638	98	26	inversion	inversion	NOUN
ejpam-5638	98	27	a−1	a−1	PROPN
ejpam-5638	98	28	is	be	AUX
ejpam-5638	98	29	d	d	ADJ
ejpam-5638	98	30	-	-	ADJ
ejpam-5638	98	31	stable	stable	ADJ
ejpam-5638	98	32	matrix	matrix	NOUN
ejpam-5638	98	33	.	.	PUNCT
ejpam-5638	99	1	(	(	PUNCT
ejpam-5638	99	2	b	b	X
ejpam-5638	99	3	)	)	PUNCT
ejpam-5638	99	4	for	for	ADP
ejpam-5638	99	5	p	p	NOUN
ejpam-5638	99	6	(	(	PUNCT
ejpam-5638	99	7	permutation	permutation	NOUN
ejpam-5638	99	8	matrix	matrix	NOUN
ejpam-5638	99	9	)	)	PUNCT
ejpam-5638	99	10	,	,	PUNCT
ejpam-5638	99	11	the	the	DET
ejpam-5638	99	12	matrix	matrix	NOUN
ejpam-5638	99	13	p	p	NOUN
ejpam-5638	99	14	tap	tap	NOUN
ejpam-5638	99	15	be	be	AUX
ejpam-5638	99	16	a	a	DET
ejpam-5638	99	17	d	d	ADJ
ejpam-5638	99	18	-	-	ADJ
ejpam-5638	99	19	stable	stable	ADJ
ejpam-5638	99	20	matrix	matrix	NOUN
ejpam-5638	99	21	.	.	PUNCT
ejpam-5638	100	1	(	(	PUNCT
ejpam-5638	100	2	c	c	X
ejpam-5638	100	3	)	)	PUNCT
ejpam-5638	100	4	for	for	ADP
ejpam-5638	100	5	d	d	PROPN
ejpam-5638	100	6	,	,	PUNCT
ejpam-5638	100	7	e	e	PROPN
ejpam-5638	100	8	∈	∈	PROPN
ejpam-5638	100	9	d̂	d̂	PROPN
ejpam-5638	100	10	,	,	PUNCT
ejpam-5638	100	11	matrix	matrix	NOUN
ejpam-5638	100	12	-	-	PUNCT
ejpam-5638	100	13	product	product	NOUN
ejpam-5638	100	14	dae	dae	NOUN
ejpam-5638	100	15	is	be	AUX
ejpam-5638	100	16	a	a	DET
ejpam-5638	100	17	d	d	ADJ
ejpam-5638	100	18	-	-	ADJ
ejpam-5638	100	19	stable	stable	ADJ
ejpam-5638	100	20	structured	structured	ADJ
ejpam-5638	100	21	matrix	matrix	NOUN
ejpam-5638	100	22	.	.	PUNCT
ejpam-5638	101	1	(	(	PUNCT
ejpam-5638	101	2	d	d	X
ejpam-5638	101	3	)	)	PUNCT
ejpam-5638	101	4	for	for	ADP
ejpam-5638	101	5	a	a	PRON
ejpam-5638	101	6	,	,	PUNCT
ejpam-5638	101	7	a∗	a∗	PROPN
ejpam-5638	101	8	is	be	AUX
ejpam-5638	101	9	a	a	DET
ejpam-5638	101	10	structured	structured	ADJ
ejpam-5638	101	11	d	d	ADJ
ejpam-5638	101	12	-	-	ADJ
ejpam-5638	101	13	stable	stable	ADJ
ejpam-5638	101	14	matrix	matrix	NOUN
ejpam-5638	101	15	where	where	SCONJ
ejpam-5638	101	16	∗	∗	NOUN
ejpam-5638	101	17	is	be	AUX
ejpam-5638	101	18	complex	complex	ADJ
ejpam-5638	101	19	conjugate	conjugate	ADJ
ejpam-5638	101	20	transpose	transpose	NOUN
ejpam-5638	101	21	of	of	ADP
ejpam-5638	101	22	a	a	DET
ejpam-5638	101	23	matrix	matrix	NOUN
ejpam-5638	101	24	.	.	PUNCT
ejpam-5638	102	1	3	3	X
ejpam-5638	102	2	.	.	X
ejpam-5638	102	3	for	for	ADP
ejpam-5638	102	4	a	a	DET
ejpam-5638	102	5	d	d	ADJ
ejpam-5638	102	6	-	-	ADJ
ejpam-5638	102	7	stable	stable	ADJ
ejpam-5638	102	8	matrix	matrix	NOUN
ejpam-5638	102	9	a	a	DET
ejpam-5638	102	10	∈	∈	PROPN
ejpam-5638	102	11	rn	rn	PROPN
ejpam-5638	102	12	,	,	PUNCT
ejpam-5638	102	13	n	n	CCONJ
ejpam-5638	102	14	,	,	PUNCT
ejpam-5638	102	15	the	the	DET
ejpam-5638	102	16	m	m	PROPN
ejpam-5638	102	17	×	×	NOUN
ejpam-5638	102	18	m	m	NOUN
ejpam-5638	102	19	principal	principal	ADJ
ejpam-5638	102	20	sub	sub	NOUN
ejpam-5638	102	21	-	-	NOUN
ejpam-5638	102	22	matrix	matrix	NOUN
ejpam-5638	102	23	is	be	AUX
ejpam-5638	102	24	in	in	ADP
ejpam-5638	102	25	euclidean	euclidean	ADJ
ejpam-5638	102	26	closure	closure	NOUN
ejpam-5638	102	27	of	of	ADP
ejpam-5638	102	28	m×m	m×m	ADJ
ejpam-5638	102	29	d	d	ADJ
ejpam-5638	102	30	-	-	ADJ
ejpam-5638	102	31	stable	stable	ADJ
ejpam-5638	102	32	structured	structured	ADJ
ejpam-5638	102	33	matrices	matrix	NOUN
ejpam-5638	102	34	[	[	X
ejpam-5638	102	35	17	17	NUM
ejpam-5638	102	36	]	]	PUNCT
ejpam-5638	102	37	.	.	PUNCT
ejpam-5638	103	1	remark	remark	PROPN
ejpam-5638	103	2	4	4	NUM
ejpam-5638	103	3	.	.	PUNCT
ejpam-5638	104	1	for	for	ADP
ejpam-5638	104	2	a	a	DET
ejpam-5638	104	3	∈	∈	PROPN
ejpam-5638	104	4	rn	rn	PROPN
ejpam-5638	104	5	,	,	PUNCT
ejpam-5638	104	6	n	n	CCONJ
ejpam-5638	104	7	,	,	PUNCT
ejpam-5638	104	8	structured	structured	ADJ
ejpam-5638	104	9	d	d	NOUN
ejpam-5638	104	10	-	-	ADJ
ejpam-5638	104	11	stable	stable	ADJ
ejpam-5638	104	12	,	,	PUNCT
ejpam-5638	104	13	a	a	DET
ejpam-5638	104	14	necessary	necessary	ADJ
ejpam-5638	104	15	condition	condition	NOUN
ejpam-5638	104	16	is	be	AUX
ejpam-5638	104	17	that	that	SCONJ
ejpam-5638	104	18	each	each	PRON
ejpam-5638	104	19	of	of	ADP
ejpam-5638	104	20	the	the	DET
ejpam-5638	104	21	principal	principal	ADJ
ejpam-5638	104	22	minor	minor	NOUN
ejpam-5638	104	23	of	of	ADP
ejpam-5638	104	24	a	a	PRON
ejpam-5638	104	25	is	be	AUX
ejpam-5638	104	26	such	such	ADJ
ejpam-5638	104	27	that	that	SCONJ
ejpam-5638	104	28	their	their	PRON
ejpam-5638	104	29	determinants	determinant	NOUN
ejpam-5638	104	30	are	be	AUX
ejpam-5638	104	31	non	non	ADJ
ejpam-5638	104	32	-	-	ADJ
ejpam-5638	104	33	negative	negative	ADJ
ejpam-5638	104	34	.	.	PUNCT
ejpam-5638	105	1	for	for	ADP
ejpam-5638	105	2	complete	complete	ADJ
ejpam-5638	105	3	discussion	discussion	NOUN
ejpam-5638	105	4	,	,	PUNCT
ejpam-5638	105	5	we	we	PRON
ejpam-5638	105	6	refer	refer	VERB
ejpam-5638	105	7	[	[	X
ejpam-5638	105	8	18	18	NUM
ejpam-5638	105	9	,	,	PUNCT
ejpam-5638	105	10	19	19	NUM
ejpam-5638	105	11	]	]	PUNCT
ejpam-5638	105	12	and	and	CCONJ
ejpam-5638	105	13	the	the	DET
ejpam-5638	105	14	references	reference	NOUN
ejpam-5638	105	15	therein	therein	ADV
ejpam-5638	105	16	.	.	PUNCT
ejpam-5638	106	1	4	4	X
ejpam-5638	106	2	.	.	X
ejpam-5638	106	3	let	let	VERB
ejpam-5638	106	4	a	a	DET
ejpam-5638	106	5	∈	∈	PROPN
ejpam-5638	106	6	cn	cn	PROPN
ejpam-5638	106	7	,	,	PUNCT
ejpam-5638	106	8	n	n	CCONJ
ejpam-5638	106	9	,	,	PUNCT
ejpam-5638	106	10	and	and	CCONJ
ejpam-5638	106	11	∃	∃	PROPN
ejpam-5638	106	12	ã	ã	PROPN
ejpam-5638	106	13	∈	∈	PROPN
ejpam-5638	106	14	d̂	d̂	NOUN
ejpam-5638	106	15	such	such	ADJ
ejpam-5638	106	16	that	that	PRON
ejpam-5638	106	17	for	for	ADP
ejpam-5638	106	18	each	each	DET
ejpam-5638	106	19	re(λi(ãa	re(λi(ãa	PROPN
ejpam-5638	106	20	)	)	PUNCT
ejpam-5638	106	21	)	)	PUNCT
ejpam-5638	107	1	>	>	X
ejpam-5638	108	1	0	0	X
ejpam-5638	108	2	.	.	PUNCT
ejpam-5638	109	1	then	then	ADV
ejpam-5638	109	2	,	,	PUNCT
ejpam-5638	109	3	a	a	PRON
ejpam-5638	109	4	is	be	AUX
ejpam-5638	109	5	a	a	DET
ejpam-5638	109	6	structured	structured	ADJ
ejpam-5638	109	7	d	d	ADJ
ejpam-5638	109	8	-	-	ADJ
ejpam-5638	109	9	stable	stable	ADJ
ejpam-5638	109	10	matrix	matrix	NOUN
ejpam-5638	109	11	if	if	SCONJ
ejpam-5638	109	12	and	and	CCONJ
ejpam-5638	109	13	only	only	ADV
ejpam-5638	109	14	if	if	SCONJ
ejpam-5638	109	15	det(a±d	det(a±d	NOUN
ejpam-5638	109	16	)	)	PUNCT
ejpam-5638	109	17	̸=	̸=	PROPN
ejpam-5638	109	18	0	0	NUM
ejpam-5638	109	19	∀d	∀d	PUNCT
ejpam-5638	110	1	∈	∈	PROPN
ejpam-5638	110	2	d̂.	d̂.	NOUN
ejpam-5638	110	3	a	a	DET
ejpam-5638	110	4	sufficient	sufficient	ADJ
ejpam-5638	110	5	condition	condition	NOUN
ejpam-5638	110	6	fora	fora	X
ejpam-5638	110	7	∈	∈	PROPN
ejpam-5638	110	8	cn	cn	PROPN
ejpam-5638	110	9	,	,	PUNCT
ejpam-5638	110	10	n	n	PRON
ejpam-5638	110	11	to	to	PART
ejpam-5638	110	12	be	be	AUX
ejpam-5638	110	13	ad	ad	NOUN
ejpam-5638	110	14	-	-	PUNCT
ejpam-5638	110	15	stable	stable	ADJ
ejpam-5638	110	16	matrix	matrix	NOUN
ejpam-5638	110	17	is	be	AUX
ejpam-5638	110	18	that	that	SCONJ
ejpam-5638	110	19	λi(da+a∗d	λi(da+a∗d	PROPN
ejpam-5638	110	20	)	)	PUNCT
ejpam-5638	110	21	>	>	X
ejpam-5638	110	22	0	0	NUM
ejpam-5638	111	1	∀i	∀i	NOUN
ejpam-5638	111	2	,	,	PUNCT
ejpam-5638	111	3	where	where	SCONJ
ejpam-5638	111	4	d	d	PROPN
ejpam-5638	111	5	∈	∈	PROPN
ejpam-5638	111	6	d̂.	d̂.	NOUN
ejpam-5638	111	7	for	for	ADP
ejpam-5638	111	8	more	more	ADJ
ejpam-5638	111	9	details	detail	NOUN
ejpam-5638	111	10	,	,	PUNCT
ejpam-5638	111	11	we	we	PRON
ejpam-5638	111	12	refer	refer	VERB
ejpam-5638	111	13	[	[	X
ejpam-5638	111	14	20–22	20–22	NUM
ejpam-5638	111	15	]	]	PUNCT
ejpam-5638	111	16	and	and	CCONJ
ejpam-5638	111	17	references	reference	NOUN
ejpam-5638	111	18	therein	therein	ADV
ejpam-5638	111	19	.	.	PUNCT
ejpam-5638	112	1	the	the	DET
ejpam-5638	112	2	another	another	DET
ejpam-5638	112	3	sufficient	sufficient	ADJ
ejpam-5638	112	4	condition	condition	NOUN
ejpam-5638	112	5	for	for	ADP
ejpam-5638	112	6	a	a	DET
ejpam-5638	112	7	∈	∈	PROPN
ejpam-5638	112	8	cn	cn	PROPN
ejpam-5638	112	9	,	,	PUNCT
ejpam-5638	112	10	n	n	PRON
ejpam-5638	112	11	to	to	PART
ejpam-5638	112	12	be	be	AUX
ejpam-5638	112	13	structured	structure	VERB
ejpam-5638	112	14	d	d	ADJ
ejpam-5638	112	15	-	-	ADJ
ejpam-5638	112	16	stable	stable	ADJ
ejpam-5638	112	17	matrix	matrix	NOUN
ejpam-5638	112	18	is	be	AUX
ejpam-5638	112	19	that	that	SCONJ
ejpam-5638	112	20	given	give	VERB
ejpam-5638	112	21	matrix	matrix	NOUN
ejpam-5638	112	22	a	a	PRON
ejpam-5638	112	23	is	be	AUX
ejpam-5638	112	24	an	an	DET
ejpam-5638	112	25	m	m	NOUN
ejpam-5638	112	26	-matrix	-matrix	NOUN
ejpam-5638	112	27	.	.	PUNCT
ejpam-5638	113	1	for	for	ADP
ejpam-5638	113	2	a	a	DET
ejpam-5638	113	3	∈	∈	PROPN
ejpam-5638	113	4	rn	rn	PROPN
ejpam-5638	113	5	,	,	PUNCT
ejpam-5638	113	6	n	n	PRON
ejpam-5638	113	7	to	to	PART
ejpam-5638	113	8	be	be	AUX
ejpam-5638	113	9	a	a	DET
ejpam-5638	113	10	class	class	NOUN
ejpam-5638	113	11	of	of	ADP
ejpam-5638	113	12	an	an	DET
ejpam-5638	113	13	m	m	NOUN
ejpam-5638	113	14	-matrix	-matrix	NOUN
ejpam-5638	113	15	,	,	PUNCT
ejpam-5638	113	16	all	all	PRON
ejpam-5638	113	17	of	of	ADP
ejpam-5638	113	18	its	its	PRON
ejpam-5638	113	19	off	off	ADV
ejpam-5638	113	20	-	-	PUNCT
ejpam-5638	113	21	diagonal	diagonal	ADJ
ejpam-5638	113	22	elements	element	NOUN
ejpam-5638	113	23	must	must	AUX
ejpam-5638	113	24	be	be	AUX
ejpam-5638	113	25	less	less	ADJ
ejpam-5638	113	26	than	than	ADP
ejpam-5638	113	27	or	or	CCONJ
ejpam-5638	113	28	equal	equal	ADJ
ejpam-5638	113	29	to	to	ADP
ejpam-5638	113	30	zero	zero	NUM
ejpam-5638	113	31	while	while	SCONJ
ejpam-5638	113	32	all	all	PRON
ejpam-5638	113	33	of	of	ADP
ejpam-5638	113	34	the	the	DET
ejpam-5638	113	35	principal	principal	ADJ
ejpam-5638	113	36	minors	minor	NOUN
ejpam-5638	113	37	to	to	PART
ejpam-5638	113	38	be	be	AUX
ejpam-5638	113	39	strictly	strictly	ADV
ejpam-5638	113	40	positive	positive	ADJ
ejpam-5638	113	41	.	.	PUNCT
ejpam-5638	114	1	the	the	DET
ejpam-5638	114	2	structured	structured	ADJ
ejpam-5638	114	3	m	m	NOUN
ejpam-5638	114	4	-matrices	-matrice	NOUN
ejpam-5638	114	5	are	be	AUX
ejpam-5638	114	6	a	a	DET
ejpam-5638	114	7	class	class	NOUN
ejpam-5638	114	8	of	of	ADP
ejpam-5638	114	9	structured	structured	ADJ
ejpam-5638	114	10	stable	stable	ADJ
ejpam-5638	114	11	-	-	PUNCT
ejpam-5638	114	12	matrices	matrix	NOUN
ejpam-5638	114	13	[	[	X
ejpam-5638	114	14	23	23	NUM
ejpam-5638	114	15	]	]	PUNCT
ejpam-5638	114	16	.	.	PUNCT
ejpam-5638	115	1	for	for	ADP
ejpam-5638	115	2	a	a	DET
ejpam-5638	115	3	positive	positive	ADJ
ejpam-5638	115	4	structured	structured	ADJ
ejpam-5638	115	5	diagonal	diagonal	ADJ
ejpam-5638	115	6	matrix	matrix	NOUN
ejpam-5638	115	7	d	d	X
ejpam-5638	115	8	∈	∈	PROPN
ejpam-5638	115	9	d̂	d̂	NOUN
ejpam-5638	115	10	such	such	ADJ
ejpam-5638	115	11	that	that	PRON
ejpam-5638	115	12	ad	ad	NOUN
ejpam-5638	115	13	=	=	SYM
ejpam-5638	115	14	b	b	NOUN
ejpam-5638	115	15	=	=	SYM
ejpam-5638	115	16	(	(	PUNCT
ejpam-5638	115	17	bij	bij	NOUN
ejpam-5638	115	18	)	)	PUNCT
ejpam-5638	115	19	satisfies	satisfy	VERB
ejpam-5638	115	20	the	the	DET
ejpam-5638	115	21	strict	strict	ADJ
ejpam-5638	115	22	inequality	inequality	NOUN
ejpam-5638	115	23	condition	condition	NOUN
ejpam-5638	115	24	.	.	PUNCT
ejpam-5638	116	1	re(bii	re(bii	NOUN
ejpam-5638	116	2	)	)	PUNCT
ejpam-5638	116	3	>	>	X
ejpam-5638	117	1	n∑	n∑	INTJ
ejpam-5638	118	1	j=1,j	j=1,j	NOUN
ejpam-5638	118	2	̸=i	̸=i	PROPN
ejpam-5638	118	3	|bij	|bij	VERB
ejpam-5638	118	4	|	|	ADV
ejpam-5638	118	5	,	,	PUNCT
ejpam-5638	118	6	∀i	∀i	X
ejpam-5638	118	7	=	=	SYM
ejpam-5638	118	8	1	1	NUM
ejpam-5638	118	9	:	:	PUNCT
ejpam-5638	118	10	n.	n.	NOUN
ejpam-5638	118	11	m.u.r	m.u.r	PROPN
ejpam-5638	119	1	rehman	rehman	PROPN
ejpam-5638	119	2	et	et	PROPN
ejpam-5638	119	3	al	al	PROPN
ejpam-5638	119	4	.	.	PUNCT
ejpam-5638	119	5	/	/	SYM
ejpam-5638	119	6	eur	eur	PROPN
ejpam-5638	119	7	.	.	PUNCT
ejpam-5638	120	1	j.	j.	PROPN
ejpam-5638	120	2	pure	pure	PROPN
ejpam-5638	120	3	appl	appl	PROPN
ejpam-5638	120	4	.	.	PROPN
ejpam-5638	120	5	math	math	PROPN
ejpam-5638	120	6	,	,	PUNCT
ejpam-5638	120	7	18	18	NUM
ejpam-5638	120	8	(	(	PUNCT
ejpam-5638	120	9	2	2	NUM
ejpam-5638	120	10	)	)	PUNCT
ejpam-5638	120	11	(	(	PUNCT
ejpam-5638	120	12	2025	2025	NUM
ejpam-5638	120	13	)	)	PUNCT
ejpam-5638	120	14	,	,	PUNCT
ejpam-5638	120	15	5638	5638	NUM
ejpam-5638	120	16	6	6	NUM
ejpam-5638	120	17	of	of	ADP
ejpam-5638	120	18	23	23	NUM
ejpam-5638	120	19	structured	structured	ADJ
ejpam-5638	120	20	matrix	matrix	NOUN
ejpam-5638	120	21	a	a	DET
ejpam-5638	120	22	∈	∈	PROPN
ejpam-5638	120	23	cn	cn	PROPN
ejpam-5638	120	24	,	,	PUNCT
ejpam-5638	120	25	n	n	PRON
ejpam-5638	120	26	satisfying	satisfy	VERB
ejpam-5638	120	27	above	above	ADP
ejpam-5638	120	28	strict	strict	ADJ
ejpam-5638	120	29	inequality	inequality	NOUN
ejpam-5638	120	30	condition	condition	NOUN
ejpam-5638	120	31	is	be	AUX
ejpam-5638	120	32	known	know	VERB
ejpam-5638	120	33	as	as	ADP
ejpam-5638	120	34	the	the	DET
ejpam-5638	120	35	quasi	quasi	ADJ
ejpam-5638	120	36	-	-	ADJ
ejpam-5638	120	37	dominant	dominant	ADJ
ejpam-5638	120	38	diagonal	diagonal	ADJ
ejpam-5638	120	39	matrix	matrix	NOUN
ejpam-5638	120	40	[	[	X
ejpam-5638	120	41	24	24	NUM
ejpam-5638	120	42	]	]	PUNCT
ejpam-5638	120	43	.	.	PUNCT
ejpam-5638	121	1	the	the	DET
ejpam-5638	121	2	given	give	VERB
ejpam-5638	121	3	matrix	matrix	NOUN
ejpam-5638	121	4	a	a	DET
ejpam-5638	121	5	∈	∈	PROPN
ejpam-5638	121	6	rn	rn	PROPN
ejpam-5638	121	7	,	,	PUNCT
ejpam-5638	121	8	n	n	PRON
ejpam-5638	121	9	is	be	AUX
ejpam-5638	121	10	structured	structure	VERB
ejpam-5638	121	11	d	d	ADJ
ejpam-5638	121	12	-	-	ADJ
ejpam-5638	121	13	stable	stable	ADJ
ejpam-5638	121	14	if	if	SCONJ
ejpam-5638	121	15	a	a	DET
ejpam-5638	121	16	=	=	SYM
ejpam-5638	121	17	bd−1	bd−1	PROPN
ejpam-5638	121	18	.	.	PROPN
ejpam-5638	121	19	remark	remark	PROPN
ejpam-5638	121	20	5	5	NUM
ejpam-5638	121	21	.	.	PUNCT
ejpam-5638	122	1	the	the	DET
ejpam-5638	122	2	matrix	matrix	NOUN
ejpam-5638	122	3	b	b	NOUN
ejpam-5638	122	4	=	=	SYM
ejpam-5638	122	5	ad	ad	NOUN
ejpam-5638	122	6	for	for	ADP
ejpam-5638	122	7	d	d	PROPN
ejpam-5638	122	8	∈	∈	PROPN
ejpam-5638	122	9	d̂	d̂	X
ejpam-5638	122	10	is	be	AUX
ejpam-5638	122	11	such	such	ADJ
ejpam-5638	122	12	that	that	SCONJ
ejpam-5638	122	13	re(λi(b	re(λi(b	PROPN
ejpam-5638	122	14	)	)	PUNCT
ejpam-5638	122	15	)	)	PUNCT
ejpam-5638	122	16	>	>	X
ejpam-5638	123	1	0,∀i	0,∀i	X
ejpam-5638	123	2	.	.	PUNCT
ejpam-5638	124	1	one	one	PRON
ejpam-5638	124	2	can	can	AUX
ejpam-5638	124	3	prove	prove	VERB
ejpam-5638	124	4	this	this	DET
ejpam-5638	124	5	result	result	NOUN
ejpam-5638	124	6	by	by	ADP
ejpam-5638	124	7	using	use	VERB
ejpam-5638	124	8	gersgorin	gersgorin	PROPN
ejpam-5638	124	9	’s	’s	PART
ejpam-5638	124	10	circle	circle	NOUN
ejpam-5638	124	11	theorem	theorem	NOUN
ejpam-5638	124	12	[	[	X
ejpam-5638	124	13	21	21	NUM
ejpam-5638	124	14	,	,	PUNCT
ejpam-5638	124	15	25	25	NUM
ejpam-5638	124	16	]	]	PUNCT
ejpam-5638	124	17	.	.	PUNCT
ejpam-5638	125	1	a	a	DET
ejpam-5638	125	2	sufficient	sufficient	ADJ
ejpam-5638	125	3	condition	condition	NOUN
ejpam-5638	125	4	to	to	ADP
ejpam-5638	125	5	d−stability	d−stability	PRON
ejpam-5638	125	6	to	to	ADP
ejpam-5638	125	7	a	a	DET
ejpam-5638	125	8	∈	∈	PROPN
ejpam-5638	125	9	cn	cn	PROPN
ejpam-5638	125	10	,	,	PUNCT
ejpam-5638	125	11	n	n	PRON
ejpam-5638	125	12	is	be	AUX
ejpam-5638	125	13	that	that	SCONJ
ejpam-5638	125	14	a	a	PRON
ejpam-5638	125	15	is	be	AUX
ejpam-5638	125	16	a	a	DET
ejpam-5638	125	17	triangular	triangular	NOUN
ejpam-5638	125	18	matrix	matrix	NOUN
ejpam-5638	125	19	and	and	CCONJ
ejpam-5638	125	20	further	far	ADV
ejpam-5638	125	21	the	the	DET
ejpam-5638	125	22	real	real	ADJ
ejpam-5638	125	23	part	part	NOUN
ejpam-5638	125	24	of	of	ADP
ejpam-5638	125	25	all	all	DET
ejpam-5638	125	26	elements	element	NOUN
ejpam-5638	125	27	of	of	ADP
ejpam-5638	125	28	a	a	PRON
ejpam-5638	125	29	is	be	AUX
ejpam-5638	125	30	strictly	strictly	ADV
ejpam-5638	125	31	positive	positive	ADJ
ejpam-5638	125	32	,	,	PUNCT
ejpam-5638	125	33	that	that	ADV
ejpam-5638	125	34	is	is	ADV
ejpam-5638	125	35	,	,	PUNCT
ejpam-5638	125	36	re(aii	re(aii	X
ejpam-5638	125	37	)	)	PUNCT
ejpam-5638	125	38	>	>	X
ejpam-5638	125	39	0	0	NUM
ejpam-5638	125	40	,	,	PUNCT
ejpam-5638	125	41	∀i	∀i	NOUN
ejpam-5638	125	42	=	=	SYM
ejpam-5638	125	43	1	1	NUM
ejpam-5638	125	44	:	:	PUNCT
ejpam-5638	125	45	n.	n.	NOUN
ejpam-5638	125	46	theorem	theorem	NOUN
ejpam-5638	125	47	1	1	NUM
ejpam-5638	125	48	.	.	PUNCT
ejpam-5638	126	1	[	[	X
ejpam-5638	126	2	16	16	NUM
ejpam-5638	126	3	]	]	PUNCT
ejpam-5638	126	4	any	any	DET
ejpam-5638	126	5	condition	condition	NOUN
ejpam-5638	126	6	to	to	ADP
ejpam-5638	126	7	a	a	DET
ejpam-5638	126	8	class	class	NOUN
ejpam-5638	126	9	of	of	ADP
ejpam-5638	126	10	structured	structured	ADJ
ejpam-5638	126	11	matrices	matrix	NOUN
ejpam-5638	126	12	implying	imply	VERB
ejpam-5638	126	13	structured	structured	ADJ
ejpam-5638	126	14	stability	stability	NOUN
ejpam-5638	126	15	,	,	PUNCT
ejpam-5638	126	16	and	and	CCONJ
ejpam-5638	126	17	remain	remain	VERB
ejpam-5638	126	18	preserve	preserve	VERB
ejpam-5638	126	19	under	under	ADP
ejpam-5638	126	20	multiplication	multiplication	NOUN
ejpam-5638	126	21	of	of	ADP
ejpam-5638	126	22	structured	structured	ADJ
ejpam-5638	126	23	positive	positive	ADJ
ejpam-5638	126	24	diagonal	diagonal	ADJ
ejpam-5638	126	25	matrices	matrix	NOUN
ejpam-5638	126	26	is	be	AUX
ejpam-5638	126	27	a	a	DET
ejpam-5638	126	28	sufficient	sufficient	ADJ
ejpam-5638	126	29	condition	condition	NOUN
ejpam-5638	126	30	to	to	ADP
ejpam-5638	126	31	structured	structured	ADJ
ejpam-5638	126	32	d	d	ADJ
ejpam-5638	126	33	-	-	ADJ
ejpam-5638	126	34	stable	stable	ADJ
ejpam-5638	126	35	matrices	matrix	NOUN
ejpam-5638	126	36	.	.	PUNCT
ejpam-5638	127	1	following	follow	VERB
ejpam-5638	127	2	theorem	theorem	VERB
ejpam-5638	127	3	[	[	X
ejpam-5638	127	4	16	16	NUM
ejpam-5638	127	5	]	]	PUNCT
ejpam-5638	127	6	guarantees	guarantee	VERB
ejpam-5638	127	7	that	that	SCONJ
ejpam-5638	127	8	not	not	PART
ejpam-5638	127	9	a	a	DET
ejpam-5638	127	10	single	single	ADJ
ejpam-5638	127	11	condition	condition	NOUN
ejpam-5638	127	12	is	be	AUX
ejpam-5638	127	13	the	the	DET
ejpam-5638	127	14	necessary	necessary	ADJ
ejpam-5638	127	15	condition	condition	NOUN
ejpam-5638	127	16	for	for	ADP
ejpam-5638	127	17	the	the	DET
ejpam-5638	127	18	structured	structured	ADJ
ejpam-5638	127	19	d	d	NOUN
ejpam-5638	127	20	-	-	NOUN
ejpam-5638	127	21	stability	stability	NOUN
ejpam-5638	127	22	of	of	ADP
ejpam-5638	127	23	matrices	matrix	NOUN
ejpam-5638	127	24	.	.	PUNCT
ejpam-5638	128	1	theorem	theorem	NOUN
ejpam-5638	128	2	2	2	NUM
ejpam-5638	128	3	.	.	PUNCT
ejpam-5638	129	1	each	each	PRON
ejpam-5638	129	2	of	of	ADP
ejpam-5638	129	3	below	below	ADP
ejpam-5638	129	4	class	class	NOUN
ejpam-5638	129	5	of	of	ADP
ejpam-5638	129	6	structured	structured	ADJ
ejpam-5638	129	7	matrices	matrix	NOUN
ejpam-5638	129	8	is	be	AUX
ejpam-5638	129	9	a	a	DET
ejpam-5638	129	10	structured	structured	ADJ
ejpam-5638	129	11	d	d	ADJ
ejpam-5638	129	12	-	-	ADJ
ejpam-5638	129	13	stable	stable	ADJ
ejpam-5638	129	14	matrix	matrix	NOUN
ejpam-5638	129	15	.	.	PUNCT
ejpam-5638	130	1	1	1	X
ejpam-5638	130	2	.	.	X
ejpam-5638	130	3	the	the	DET
ejpam-5638	130	4	diagonally	diagonally	ADV
ejpam-5638	130	5	stable	stable	ADJ
ejpam-5638	130	6	structured	structured	ADJ
ejpam-5638	130	7	matrices	matrix	NOUN
ejpam-5638	130	8	are	be	AUX
ejpam-5638	130	9	structured	structure	VERB
ejpam-5638	130	10	d	d	ADJ
ejpam-5638	130	11	-	-	ADJ
ejpam-5638	130	12	stable	stable	ADJ
ejpam-5638	130	13	matrices	matrix	NOUN
ejpam-5638	130	14	.	.	PUNCT
ejpam-5638	131	1	2	2	X
ejpam-5638	131	2	.	.	X
ejpam-5638	131	3	the	the	DET
ejpam-5638	131	4	structured	structured	ADJ
ejpam-5638	131	5	m	m	NOUN
ejpam-5638	131	6	-matrices	-matrice	NOUN
ejpam-5638	131	7	are	be	AUX
ejpam-5638	131	8	structured	structure	VERB
ejpam-5638	131	9	d	d	ADJ
ejpam-5638	131	10	-	-	ADJ
ejpam-5638	131	11	stable	stable	ADJ
ejpam-5638	131	12	matrices	matrix	NOUN
ejpam-5638	131	13	.	.	PUNCT
ejpam-5638	132	1	3	3	X
ejpam-5638	132	2	.	.	X
ejpam-5638	132	3	the	the	DET
ejpam-5638	132	4	strictly	strictly	ADV
ejpam-5638	132	5	diagonally	diagonally	ADV
ejpam-5638	132	6	dominant	dominant	ADJ
ejpam-5638	132	7	matrices	matrix	NOUN
ejpam-5638	132	8	having	have	VERB
ejpam-5638	132	9	principal	principal	ADJ
ejpam-5638	132	10	diagonal	diagonal	ADJ
ejpam-5638	132	11	positive	positive	ADJ
ejpam-5638	132	12	are	be	AUX
ejpam-5638	132	13	d−stable	d−stable	ADJ
ejpam-5638	132	14	matrices	matrix	NOUN
ejpam-5638	132	15	.	.	PUNCT
ejpam-5638	133	1	4	4	X
ejpam-5638	133	2	.	.	X
ejpam-5638	133	3	the	the	DET
ejpam-5638	133	4	triangular	triangular	NOUN
ejpam-5638	133	5	matrices	matrice	VERB
ejpam-5638	133	6	with	with	ADP
ejpam-5638	133	7	main	main	ADJ
ejpam-5638	133	8	(	(	PUNCT
ejpam-5638	133	9	principal	principal	NOUN
ejpam-5638	133	10	)	)	PUNCT
ejpam-5638	133	11	diagonal	diagonal	ADJ
ejpam-5638	133	12	entries	entry	NOUN
ejpam-5638	133	13	to	to	PART
ejpam-5638	133	14	be	be	AUX
ejpam-5638	133	15	positive	positive	ADJ
ejpam-5638	133	16	are	be	AUX
ejpam-5638	133	17	structured	structure	VERB
ejpam-5638	133	18	d	d	ADJ
ejpam-5638	133	19	-	-	ADJ
ejpam-5638	133	20	stable	stable	ADJ
ejpam-5638	133	21	matrices	matrix	NOUN
ejpam-5638	133	22	.	.	PUNCT
ejpam-5638	134	1	5	5	X
ejpam-5638	134	2	.	.	PUNCT
ejpam-5638	134	3	the	the	DET
ejpam-5638	134	4	sign	sign	NOUN
ejpam-5638	134	5	-	-	PUNCT
ejpam-5638	134	6	stable	stable	ADJ
ejpam-5638	134	7	matrices	matrix	NOUN
ejpam-5638	134	8	are	be	AUX
ejpam-5638	134	9	d−stable	d−stable	ADJ
ejpam-5638	134	10	matrices	matrix	NOUN
ejpam-5638	134	11	.	.	PUNCT
ejpam-5638	135	1	6	6	X
ejpam-5638	135	2	.	.	X
ejpam-5638	135	3	the	the	DET
ejpam-5638	135	4	tri	tri	ADJ
ejpam-5638	135	5	-	-	ADJ
ejpam-5638	135	6	diagonal	diagonal	ADJ
ejpam-5638	135	7	structured	structured	ADJ
ejpam-5638	135	8	p	p	NOUN
ejpam-5638	135	9	-matrices	-matrice	NOUN
ejpam-5638	135	10	are	be	AUX
ejpam-5638	135	11	structured	structure	VERB
ejpam-5638	135	12	d	d	ADJ
ejpam-5638	135	13	-	-	ADJ
ejpam-5638	135	14	stable	stable	ADJ
ejpam-5638	135	15	.	.	PUNCT
ejpam-5638	136	1	7	7	X
ejpam-5638	136	2	.	.	X
ejpam-5638	136	3	the	the	DET
ejpam-5638	136	4	oscillatory	oscillatory	ADJ
ejpam-5638	136	5	matrices	matrix	NOUN
ejpam-5638	136	6	are	be	AUX
ejpam-5638	136	7	structured	structure	VERB
ejpam-5638	136	8	d	d	ADJ
ejpam-5638	136	9	-	-	ADJ
ejpam-5638	136	10	stable	stable	ADJ
ejpam-5638	136	11	matrices	matrix	NOUN
ejpam-5638	136	12	.	.	PUNCT
ejpam-5638	137	1	8	8	X
ejpam-5638	137	2	.	.	PUNCT
ejpam-5638	138	1	the	the	DET
ejpam-5638	138	2	hadamard	hadamard	ADJ
ejpam-5638	138	3	h	h	ADJ
ejpam-5638	138	4	-	-	PUNCT
ejpam-5638	138	5	stable	stable	ADJ
ejpam-5638	138	6	structured	structured	ADJ
ejpam-5638	138	7	matrices	matrix	NOUN
ejpam-5638	138	8	are	be	AUX
ejpam-5638	138	9	structured	structure	VERB
ejpam-5638	138	10	d	d	ADJ
ejpam-5638	138	11	-	-	ADJ
ejpam-5638	138	12	stable	stable	ADJ
ejpam-5638	138	13	.	.	PUNCT
ejpam-5638	139	1	9	9	X
ejpam-5638	139	2	.	.	X
ejpam-5638	139	3	the	the	DET
ejpam-5638	139	4	structured	structured	ADJ
ejpam-5638	139	5	p	p	NOUN
ejpam-5638	139	6	-matrices	-matrice	NOUN
ejpam-5638	139	7	(	(	PUNCT
ejpam-5638	139	8	sign	sign	NOUN
ejpam-5638	139	9	symmetric	symmetric	ADJ
ejpam-5638	139	10	)	)	PUNCT
ejpam-5638	139	11	are	be	AUX
ejpam-5638	139	12	structured	structure	VERB
ejpam-5638	139	13	d	d	ADJ
ejpam-5638	139	14	-	-	ADJ
ejpam-5638	139	15	stable	stable	ADJ
ejpam-5638	139	16	matrices	matrix	NOUN
ejpam-5638	139	17	.	.	PUNCT
ejpam-5638	140	1	2.1	2.1	NUM
ejpam-5638	140	2	.	.	PUNCT
ejpam-5638	141	1	the	the	DET
ejpam-5638	141	2	µ-values	µ-value	NOUN
ejpam-5638	141	3	and	and	CCONJ
ejpam-5638	141	4	d	d	NOUN
ejpam-5638	141	5	-	-	NOUN
ejpam-5638	141	6	stability	stability	NOUN
ejpam-5638	141	7	:	:	PUNCT
ejpam-5638	141	8	the	the	DET
ejpam-5638	141	9	stability	stability	NOUN
ejpam-5638	141	10	of	of	ADP
ejpam-5638	141	11	a	a	DET
ejpam-5638	141	12	dynamical	dynamical	ADJ
ejpam-5638	141	13	system	system	NOUN
ejpam-5638	141	14	ẋ	ẋ	PUNCT
ejpam-5638	142	1	=	=	NOUN
ejpam-5638	142	2	ax	ax	NOUN
ejpam-5638	142	3	,	,	PUNCT
ejpam-5638	142	4	x	x	SYM
ejpam-5638	142	5	∈	∈	PROPN
ejpam-5638	142	6	rn,1	rn,1	PROPN
ejpam-5638	142	7	,	,	PUNCT
ejpam-5638	142	8	a	a	DET
ejpam-5638	142	9	∈	∈	PROPN
ejpam-5638	142	10	km	km	NOUN
ejpam-5638	142	11	,	,	PUNCT
ejpam-5638	142	12	n	n	CCONJ
ejpam-5638	142	13	,	,	PUNCT
ejpam-5638	142	14	k	k	PROPN
ejpam-5638	142	15	=	=	SYM
ejpam-5638	142	16	r(or	r(or	PROPN
ejpam-5638	142	17	c	c	NOUN
ejpam-5638	142	18	)	)	PUNCT
ejpam-5638	142	19	,	,	PUNCT
ejpam-5638	142	20	demands	demand	VERB
ejpam-5638	142	21	that	that	SCONJ
ejpam-5638	142	22	for	for	ADP
ejpam-5638	142	23	given	give	VERB
ejpam-5638	142	24	a	a	PRON
ejpam-5638	142	25	,	,	PUNCT
ejpam-5638	142	26	and	and	CCONJ
ejpam-5638	142	27	for	for	ADP
ejpam-5638	142	28	all	all	DET
ejpam-5638	142	29	∆	∆	X
ejpam-5638	142	30	∈	∈	PROPN
ejpam-5638	142	31	∆̂	∆̂	NOUN
ejpam-5638	142	32	,	,	PUNCT
ejpam-5638	142	33	λi(in+m∆	λi(in+m∆	NOUN
ejpam-5638	142	34	)	)	PUNCT
ejpam-5638	142	35	̸=	̸=	PROPN
ejpam-5638	142	36	0	0	NUM
ejpam-5638	142	37	,	,	PUNCT
ejpam-5638	142	38	∀i	∀i	NOUN
ejpam-5638	142	39	.	.	PUNCT
ejpam-5638	143	1	the	the	DET
ejpam-5638	143	2	notation	notation	NOUN
ejpam-5638	143	3	∆̂	∆̂	PUNCT
ejpam-5638	143	4	denotes	denote	VERB
ejpam-5638	143	5	a	a	DET
ejpam-5638	143	6	set	set	NOUN
ejpam-5638	143	7	of	of	ADP
ejpam-5638	143	8	block	block	NOUN
ejpam-5638	143	9	-	-	PUNCT
ejpam-5638	143	10	diagonal	diagonal	ADJ
ejpam-5638	143	11	matrices	matrix	NOUN
ejpam-5638	143	12	,	,	PUNCT
ejpam-5638	143	13	∆̂	∆̂	PUNCT
ejpam-5638	143	14	=	=	PUNCT
ejpam-5638	143	15	{	{	PUNCT
ejpam-5638	143	16	diag(δ1ir1	diag(δ1ir1	PROPN
ejpam-5638	143	17	,	,	PUNCT
ejpam-5638	143	18	δ2ir2	δ2ir2	NOUN
ejpam-5638	143	19	,	,	PUNCT
ejpam-5638	143	20	.	.	PUNCT
ejpam-5638	143	21	.	.	PUNCT
ejpam-5638	144	1	.	.	PUNCT
ejpam-5638	145	1	,	,	PUNCT
ejpam-5638	145	2	δsirs	δsir	NOUN
ejpam-5638	145	3	;	;	PUNCT
ejpam-5638	145	4	∆1,∆2	∆1,∆2	NOUN
ejpam-5638	145	5	,	,	PUNCT
ejpam-5638	145	6	.	.	PUNCT
ejpam-5638	145	7	.	.	PUNCT
ejpam-5638	145	8	.	.	PUNCT
ejpam-5638	146	1	,	,	PUNCT
ejpam-5638	146	2	∆f	∆f	PROPN
ejpam-5638	146	3	)	)	PUNCT
ejpam-5638	146	4	:	:	PUNCT
ejpam-5638	147	1	δi	δi	ADP
ejpam-5638	147	2	∈	∈	NOUN
ejpam-5638	147	3	k	k	NOUN
ejpam-5638	147	4	∀i	∀i	NOUN
ejpam-5638	147	5	=	=	SYM
ejpam-5638	147	6	1	1	NUM
ejpam-5638	147	7	:	:	SYM
ejpam-5638	147	8	s	s	X
ejpam-5638	147	9	;	;	PUNCT
ejpam-5638	147	10	∆j	∆j	PROPN
ejpam-5638	147	11	∈	∈	PROPN
ejpam-5638	147	12	kmj	kmj	NOUN
ejpam-5638	147	13	,	,	PUNCT
ejpam-5638	147	14	mj	mj	NOUN
ejpam-5638	147	15	∀j	∀j	NOUN
ejpam-5638	147	16	=	=	SYM
ejpam-5638	147	17	1	1	NUM
ejpam-5638	147	18	:	:	SYM
ejpam-5638	147	19	f	f	X
ejpam-5638	147	20	}	}	PUNCT
ejpam-5638	147	21	.	.	PUNCT
ejpam-5638	148	1	the	the	DET
ejpam-5638	148	2	matrix	matrix	NOUN
ejpam-5638	148	3	problem	problem	NOUN
ejpam-5638	148	4	to	to	PART
ejpam-5638	148	5	determine	determine	VERB
ejpam-5638	148	6	the	the	DET
ejpam-5638	148	7	necessary	necessary	ADJ
ejpam-5638	148	8	and	and	CCONJ
ejpam-5638	148	9	sufficient	sufficient	ADJ
ejpam-5638	148	10	conditions	condition	NOUN
ejpam-5638	148	11	so	so	SCONJ
ejpam-5638	148	12	that	that	SCONJ
ejpam-5638	148	13	λi(in+	λi(in+	PROPN
ejpam-5638	148	14	m∆	m∆	X
ejpam-5638	148	15	)	)	PUNCT
ejpam-5638	148	16	̸=	̸=	PROPN
ejpam-5638	148	17	0,∀i	0,∀i	NUM
ejpam-5638	149	1	=	=	SYM
ejpam-5638	149	2	1	1	NUM
ejpam-5638	149	3	:	:	PUNCT
ejpam-5638	149	4	n	n	PRON
ejpam-5638	149	5	is	be	AUX
ejpam-5638	149	6	a	a	DET
ejpam-5638	149	7	key	key	ADJ
ejpam-5638	149	8	problem	problem	NOUN
ejpam-5638	149	9	in	in	ADP
ejpam-5638	149	10	control	control	NOUN
ejpam-5638	149	11	engineering	engineering	NOUN
ejpam-5638	149	12	.	.	PUNCT
ejpam-5638	150	1	these	these	DET
ejpam-5638	150	2	discussions	discussion	NOUN
ejpam-5638	150	3	leads	lead	VERB
ejpam-5638	150	4	us	we	PRON
ejpam-5638	150	5	to	to	ADP
ejpam-5638	150	6	the	the	DET
ejpam-5638	150	7	definition	definition	NOUN
ejpam-5638	150	8	of	of	ADP
ejpam-5638	150	9	structured	structured	ADJ
ejpam-5638	150	10	singular	singular	ADJ
ejpam-5638	150	11	value	value	NOUN
ejpam-5638	150	12	.	.	PUNCT
ejpam-5638	151	1	m.u.r	m.u.r	PROPN
ejpam-5638	151	2	rehman	rehman	PROPN
ejpam-5638	151	3	et	et	PROPN
ejpam-5638	151	4	al	al	PROPN
ejpam-5638	151	5	.	.	PUNCT
ejpam-5638	151	6	/	/	SYM
ejpam-5638	151	7	eur	eur	PROPN
ejpam-5638	151	8	.	.	PUNCT
ejpam-5638	152	1	j.	j.	PROPN
ejpam-5638	152	2	pure	pure	PROPN
ejpam-5638	152	3	appl	appl	PROPN
ejpam-5638	152	4	.	.	PROPN
ejpam-5638	152	5	math	math	PROPN
ejpam-5638	152	6	,	,	PUNCT
ejpam-5638	152	7	18	18	NUM
ejpam-5638	152	8	(	(	PUNCT
ejpam-5638	152	9	2	2	NUM
ejpam-5638	152	10	)	)	PUNCT
ejpam-5638	152	11	(	(	PUNCT
ejpam-5638	152	12	2025	2025	NUM
ejpam-5638	152	13	)	)	PUNCT
ejpam-5638	152	14	,	,	PUNCT
ejpam-5638	152	15	5638	5638	NUM
ejpam-5638	152	16	7	7	NUM
ejpam-5638	152	17	of	of	ADP
ejpam-5638	152	18	23	23	NUM
ejpam-5638	152	19	definition	definition	NOUN
ejpam-5638	152	20	1	1	NUM
ejpam-5638	152	21	.	.	PUNCT
ejpam-5638	153	1	[	[	X
ejpam-5638	153	2	26	26	NUM
ejpam-5638	153	3	]	]	PUNCT
ejpam-5638	153	4	the	the	DET
ejpam-5638	153	5	structured	structured	ADJ
ejpam-5638	153	6	singular	singular	ADJ
ejpam-5638	153	7	value	value	NOUN
ejpam-5638	153	8	(	(	PUNCT
ejpam-5638	153	9	µ−value	µ−value	NOUN
ejpam-5638	153	10	)	)	PUNCT
ejpam-5638	153	11	of	of	ADP
ejpam-5638	153	12	m	m	PROPN
ejpam-5638	153	13	∈	∈	PROPN
ejpam-5638	153	14	km	km	PROPN
ejpam-5638	153	15	,	,	PUNCT
ejpam-5638	153	16	n	n	CCONJ
ejpam-5638	153	17	,	,	PUNCT
ejpam-5638	153	18	m	m	VERB
ejpam-5638	153	19	=	=	NOUN
ejpam-5638	153	20	n	n	ADJ
ejpam-5638	153	21	with	with	ADP
ejpam-5638	153	22	respect	respect	NOUN
ejpam-5638	153	23	to	to	ADP
ejpam-5638	153	24	∆̂	∆̂	NOUN
ejpam-5638	153	25	the	the	DET
ejpam-5638	153	26	set	set	NOUN
ejpam-5638	153	27	of	of	ADP
ejpam-5638	153	28	block	block	NOUN
ejpam-5638	153	29	-	-	PUNCT
ejpam-5638	153	30	diagonal	diagonal	ADJ
ejpam-5638	153	31	matrices	matrix	NOUN
ejpam-5638	153	32	is	be	AUX
ejpam-5638	153	33	defined	define	VERB
ejpam-5638	153	34	as	as	ADP
ejpam-5638	153	35	µ∆̂(m	µ∆̂(m	NUM
ejpam-5638	153	36	)	)	PUNCT
ejpam-5638	153	37	:	:	PUNCT
ejpam-5638	153	38	=	=	SYM
ejpam-5638	153	39	{	{	PUNCT
ejpam-5638	153	40	0	0	NUM
ejpam-5638	153	41	,	,	PUNCT
ejpam-5638	153	42	if	if	SCONJ
ejpam-5638	153	43	det(in	det(in	ADJ
ejpam-5638	153	44	−m∆	−m∆	NOUN
ejpam-5638	153	45	)	)	PUNCT
ejpam-5638	153	46	̸=	̸=	NOUN
ejpam-5638	153	47	0	0	NUM
ejpam-5638	153	48	∀∆	∀∆	NOUN
ejpam-5638	153	49	∈	∈	NOUN
ejpam-5638	153	50	∆̂	∆̂	NOUN
ejpam-5638	153	51	1	1	NUM
ejpam-5638	153	52	min{∥∆∥2:∆∈∆̂	min{∥∆∥2:∆∈∆̂	ADJ
ejpam-5638	153	53	,	,	PUNCT
ejpam-5638	153	54	det(in−m∆)=0	det(in−m∆)=0	ADJ
ejpam-5638	153	55	}	}	PUNCT
ejpam-5638	153	56	,	,	PUNCT
ejpam-5638	153	57	else	else	ADV
ejpam-5638	153	58	where	where	SCONJ
ejpam-5638	153	59	min	min	NOUN
ejpam-5638	153	60	is	be	AUX
ejpam-5638	153	61	taken	take	VERB
ejpam-5638	153	62	over	over	ADP
ejpam-5638	153	63	∆	∆	PROPN
ejpam-5638	153	64	∈	∈	PROPN
ejpam-5638	153	65	∆̂	∆̂	NOUN
ejpam-5638	153	66	,	,	PUNCT
ejpam-5638	153	67	∥	∥	X
ejpam-5638	153	68	·	·	PUNCT
ejpam-5638	153	69	∥2	∥2	PRON
ejpam-5638	153	70	represent	represent	VERB
ejpam-5638	153	71	maximum	maximum	ADJ
ejpam-5638	153	72	singular	singular	ADJ
ejpam-5638	153	73	value	value	NOUN
ejpam-5638	153	74	,	,	PUNCT
ejpam-5638	153	75	that	that	ADV
ejpam-5638	153	76	is	is	ADV
ejpam-5638	153	77	,	,	PUNCT
ejpam-5638	153	78	σmax	σmax	NOUN
ejpam-5638	153	79	.	.	PUNCT
ejpam-5638	154	1	2.1.1	2.1.1	X
ejpam-5638	154	2	.	.	PUNCT
ejpam-5638	154	3	properties	property	NOUN
ejpam-5638	154	4	of	of	ADP
ejpam-5638	154	5	µ-values	µ-value	VERB
ejpam-5638	154	6	the	the	DET
ejpam-5638	154	7	following	follow	VERB
ejpam-5638	154	8	properties	property	NOUN
ejpam-5638	154	9	of	of	ADP
ejpam-5638	154	10	µ−values	µ−value	NOUN
ejpam-5638	154	11	are	be	AUX
ejpam-5638	154	12	easily	easily	ADV
ejpam-5638	154	13	proven	prove	VERB
ejpam-5638	154	14	and	and	CCONJ
ejpam-5638	154	15	the	the	DET
ejpam-5638	154	16	proofs	proof	NOUN
ejpam-5638	154	17	are	be	AUX
ejpam-5638	154	18	available	available	ADJ
ejpam-5638	154	19	in	in	ADP
ejpam-5638	154	20	literature	literature	NOUN
ejpam-5638	154	21	.	.	PUNCT
ejpam-5638	155	1	1	1	X
ejpam-5638	155	2	.	.	X
ejpam-5638	155	3	for	for	ADP
ejpam-5638	155	4	α	α	PRON
ejpam-5638	155	5	∈	∈	PROPN
ejpam-5638	155	6	c	c	X
ejpam-5638	155	7	,	,	PUNCT
ejpam-5638	155	8	µ∆̂(αm	µ∆̂(αm	ADJ
ejpam-5638	155	9	)	)	PUNCT
ejpam-5638	155	10	=	=	SYM
ejpam-5638	155	11	|α|µ∆̂(m	|α|µ∆̂(m	NOUN
ejpam-5638	155	12	)	)	PUNCT
ejpam-5638	155	13	.	.	PUNCT
ejpam-5638	156	1	2	2	X
ejpam-5638	156	2	.	.	X
ejpam-5638	156	3	for	for	ADP
ejpam-5638	156	4	an	an	DET
ejpam-5638	156	5	identity	identity	NOUN
ejpam-5638	156	6	matrix	matrix	NOUN
ejpam-5638	156	7	in	in	ADP
ejpam-5638	156	8	,	,	PUNCT
ejpam-5638	156	9	µ∆̂(in	µ∆̂(in	ADJ
ejpam-5638	156	10	)	)	PUNCT
ejpam-5638	156	11	=	=	SYM
ejpam-5638	156	12	1	1	NUM
ejpam-5638	156	13	.	.	NOUN
ejpam-5638	156	14	3	3	X
ejpam-5638	156	15	.	.	X
ejpam-5638	157	1	for	for	ADP
ejpam-5638	157	2	given	give	VERB
ejpam-5638	157	3	matrices	matrix	NOUN
ejpam-5638	157	4	a	a	DET
ejpam-5638	157	5	,	,	PUNCT
ejpam-5638	157	6	b	b	NOUN
ejpam-5638	157	7	,	,	PUNCT
ejpam-5638	157	8	µ∆̂(ab	µ∆̂(ab	PROPN
ejpam-5638	157	9	)	)	PUNCT
ejpam-5638	157	10	≤	≤	NUM
ejpam-5638	157	11	∥a∥2	∥a∥2	VERB
ejpam-5638	157	12	µ∆̂(b	µ∆̂(b	NOUN
ejpam-5638	157	13	)	)	PUNCT
ejpam-5638	157	14	.	.	PUNCT
ejpam-5638	158	1	4	4	X
ejpam-5638	158	2	.	.	X
ejpam-5638	158	3	µ(∆	µ(∆	NUM
ejpam-5638	158	4	)	)	PUNCT
ejpam-5638	158	5	=	=	SYM
ejpam-5638	158	6	∥∆∥2	∥∆∥2	NUM
ejpam-5638	158	7	,	,	PUNCT
ejpam-5638	158	8	∀∆	∀∆	PROPN
ejpam-5638	158	9	∈	∈	PROPN
ejpam-5638	158	10	∆̂.	∆̂.	VERB
ejpam-5638	158	11	an	an	DET
ejpam-5638	158	12	alternative	alternative	ADJ
ejpam-5638	158	13	expression	expression	NOUN
ejpam-5638	158	14	to	to	ADP
ejpam-5638	158	15	µ−values	µ−values	PUNCT
ejpam-5638	158	16	can	can	AUX
ejpam-5638	158	17	be	be	AUX
ejpam-5638	158	18	easily	easily	ADV
ejpam-5638	158	19	follows	follow	VERB
ejpam-5638	158	20	from	from	ADP
ejpam-5638	158	21	the	the	DET
ejpam-5638	158	22	definition	definition	NOUN
ejpam-5638	158	23	.	.	PUNCT
ejpam-5638	159	1	lemma	lemma	PROPN
ejpam-5638	159	2	1	1	NUM
ejpam-5638	159	3	.	.	PUNCT
ejpam-5638	160	1	[	[	X
ejpam-5638	160	2	26	26	NUM
ejpam-5638	160	3	]	]	PUNCT
ejpam-5638	160	4	for	for	ADP
ejpam-5638	160	5	m	m	PROPN
ejpam-5638	160	6	∈	∈	PROPN
ejpam-5638	160	7	kn	kn	PROPN
ejpam-5638	160	8	,	,	PUNCT
ejpam-5638	160	9	n	n	CCONJ
ejpam-5638	160	10	,	,	PUNCT
ejpam-5638	160	11	µ∆̂1	µ∆̂1	PROPN
ejpam-5638	160	12	(	(	PUNCT
ejpam-5638	160	13	m	m	NOUN
ejpam-5638	160	14	)	)	PUNCT
ejpam-5638	160	15	=	=	SYM
ejpam-5638	160	16	max	max	PROPN
ejpam-5638	160	17	ρ(∆m	ρ(∆m	PROPN
ejpam-5638	160	18	)	)	PUNCT
ejpam-5638	160	19	,	,	PUNCT
ejpam-5638	160	20	where	where	SCONJ
ejpam-5638	160	21	max	max	PROPN
ejpam-5638	160	22	is	be	AUX
ejpam-5638	160	23	taken	take	VERB
ejpam-5638	160	24	over	over	ADP
ejpam-5638	160	25	∆	∆	PROPN
ejpam-5638	160	26	∈	∈	PROPN
ejpam-5638	160	27	∆̂1	∆̂1	ADV
ejpam-5638	160	28	with	with	ADP
ejpam-5638	160	29	∆̂1	∆̂1	NOUN
ejpam-5638	160	30	:	:	PUNCT
ejpam-5638	160	31	=	=	SYM
ejpam-5638	160	32	{	{	PUNCT
ejpam-5638	160	33	∆	∆	PROPN
ejpam-5638	160	34	∈	∈	PROPN
ejpam-5638	160	35	∆̂	∆̂	NOUN
ejpam-5638	160	36	:	:	PUNCT
ejpam-5638	160	37	σmax(∆	σmax(∆	PROPN
ejpam-5638	160	38	)	)	PUNCT
ejpam-5638	160	39	≤	≤	NOUN
ejpam-5638	160	40	1	1	NUM
ejpam-5638	160	41	}	}	PUNCT
ejpam-5638	160	42	,	,	PUNCT
ejpam-5638	160	43	and	and	CCONJ
ejpam-5638	160	44	the	the	DET
ejpam-5638	160	45	mathematical	mathematical	ADJ
ejpam-5638	160	46	notation	notation	PROPN
ejpam-5638	160	47	ρ	ρ	PROPN
ejpam-5638	160	48	(	(	PUNCT
ejpam-5638	160	49	·	·	PUNCT
ejpam-5638	160	50	)	)	PUNCT
ejpam-5638	160	51	represents	represent	VERB
ejpam-5638	160	52	spectral	spectral	ADJ
ejpam-5638	160	53	radius	radius	NOUN
ejpam-5638	160	54	(	(	PUNCT
ejpam-5638	160	55	max	max	PROPN
ejpam-5638	160	56	of	of	ADP
ejpam-5638	160	57	absolute	absolute	ADJ
ejpam-5638	160	58	value	value	NOUN
ejpam-5638	160	59	of	of	ADP
ejpam-5638	160	60	an	an	DET
ejpam-5638	160	61	eigenvalue	eigenvalue	NOUN
ejpam-5638	160	62	)	)	PUNCT
ejpam-5638	160	63	of	of	ADP
ejpam-5638	160	64	a	a	DET
ejpam-5638	160	65	matrix	matrix	NOUN
ejpam-5638	160	66	.	.	PUNCT
ejpam-5638	161	1	remark	remark	NOUN
ejpam-5638	161	2	6	6	NUM
ejpam-5638	161	3	.	.	PUNCT
ejpam-5638	162	1	the	the	DET
ejpam-5638	162	2	above	above	ADJ
ejpam-5638	162	3	lemma	lemma	PROPN
ejpam-5638	162	4	applies	apply	VERB
ejpam-5638	162	5	the	the	DET
ejpam-5638	162	6	continuity	continuity	NOUN
ejpam-5638	162	7	of	of	ADP
ejpam-5638	162	8	µ	µ	NOUN
ejpam-5638	162	9	:	:	PUNCT
ejpam-5638	162	10	cn	cn	PROPN
ejpam-5638	162	11	,	,	PUNCT
ejpam-5638	162	12	n	n	NOUN
ejpam-5638	162	13	→	→	SYM
ejpam-5638	162	14	r	r	NOUN
ejpam-5638	162	15	which	which	PRON
ejpam-5638	162	16	encompass	encompass	VERB
ejpam-5638	162	17	the	the	DET
ejpam-5638	162	18	continuity	continuity	NOUN
ejpam-5638	162	19	property	property	NOUN
ejpam-5638	162	20	of	of	ADP
ejpam-5638	162	21	spectral	spectral	ADJ
ejpam-5638	162	22	radius	radius	NOUN
ejpam-5638	162	23	as	as	ADV
ejpam-5638	162	24	well	well	ADV
ejpam-5638	162	25	as	as	ADP
ejpam-5638	162	26	the	the	DET
ejpam-5638	162	27	max	max	PROPN
ejpam-5638	162	28	functions	function	NOUN
ejpam-5638	162	29	.	.	PUNCT
ejpam-5638	163	1	it	it	PRON
ejpam-5638	163	2	can	can	AUX
ejpam-5638	163	3	be	be	AUX
ejpam-5638	163	4	shown	show	VERB
ejpam-5638	163	5	that	that	SCONJ
ejpam-5638	163	6	for	for	ADP
ejpam-5638	163	7	s	s	NOUN
ejpam-5638	163	8	=	=	SYM
ejpam-5638	163	9	1	1	NUM
ejpam-5638	163	10	,	,	PUNCT
ejpam-5638	163	11	f	f	PROPN
ejpam-5638	163	12	=	=	SYM
ejpam-5638	163	13	0	0	PROPN
ejpam-5638	163	14	,	,	PUNCT
ejpam-5638	163	15	r1	r1	NOUN
ejpam-5638	163	16	=	=	SYM
ejpam-5638	163	17	n	n	CCONJ
ejpam-5638	163	18	,	,	PUNCT
ejpam-5638	163	19	µ∆̂(m	µ∆̂(m	ADP
ejpam-5638	163	20	)	)	PUNCT
ejpam-5638	163	21	=	=	SYM
ejpam-5638	163	22	ρ(m	ρ(m	NUM
ejpam-5638	163	23	)	)	PUNCT
ejpam-5638	163	24	,	,	PUNCT
ejpam-5638	163	25	where	where	SCONJ
ejpam-5638	163	26	∆̂	∆̂	PUNCT
ejpam-5638	163	27	=	=	PRON
ejpam-5638	163	28	{	{	PUNCT
ejpam-5638	163	29	δin	δin	NOUN
ejpam-5638	163	30	:	:	PUNCT
ejpam-5638	163	31	δ	δ	PROPN
ejpam-5638	163	32	∈	∈	PROPN
ejpam-5638	163	33	c	c	AUX
ejpam-5638	163	34	}	}	PUNCT
ejpam-5638	163	35	.	.	PUNCT
ejpam-5638	164	1	furthermore	furthermore	ADV
ejpam-5638	164	2	,	,	PUNCT
ejpam-5638	164	3	if	if	SCONJ
ejpam-5638	164	4	s	s	VERB
ejpam-5638	164	5	=	=	NOUN
ejpam-5638	164	6	0	0	PROPN
ejpam-5638	164	7	,	,	PUNCT
ejpam-5638	164	8	f	f	PROPN
ejpam-5638	164	9	=	=	SYM
ejpam-5638	164	10	1	1	NUM
ejpam-5638	164	11	,	,	PUNCT
ejpam-5638	164	12	then	then	ADV
ejpam-5638	164	13	µ∆̂(m	µ∆̂(m	VERB
ejpam-5638	164	14	)	)	PUNCT
ejpam-5638	164	15	=	=	SYM
ejpam-5638	164	16	σmax(m	σmax(m	PROPN
ejpam-5638	164	17	)	)	PUNCT
ejpam-5638	164	18	.	.	PUNCT
ejpam-5638	165	1	the	the	DET
ejpam-5638	165	2	interconnection	interconnection	NOUN
ejpam-5638	165	3	between	between	ADP
ejpam-5638	165	4	structured	structured	ADJ
ejpam-5638	165	5	singular	singular	ADJ
ejpam-5638	165	6	values	value	NOUN
ejpam-5638	165	7	,	,	PUNCT
ejpam-5638	165	8	the	the	DET
ejpam-5638	165	9	largest	large	ADJ
ejpam-5638	165	10	singular	singular	ADJ
ejpam-5638	165	11	value	value	NOUN
ejpam-5638	165	12	,	,	PUNCT
ejpam-5638	165	13	and	and	CCONJ
ejpam-5638	165	14	the	the	DET
ejpam-5638	165	15	spectral	spectral	ADJ
ejpam-5638	165	16	radius	radius	NOUN
ejpam-5638	165	17	of	of	ADP
ejpam-5638	165	18	m	m	PROPN
ejpam-5638	165	19	∈	∈	PROPN
ejpam-5638	165	20	kn	kn	PROPN
ejpam-5638	165	21	,	,	PUNCT
ejpam-5638	165	22	n	n	PRON
ejpam-5638	165	23	is	be	AUX
ejpam-5638	165	24	given	give	VERB
ejpam-5638	165	25	by	by	ADP
ejpam-5638	165	26	ρ(m	ρ(m	NUM
ejpam-5638	165	27	)	)	PUNCT
ejpam-5638	165	28	≤	≤	NOUN
ejpam-5638	165	29	µ∆̂(m	µ∆̂(m	ADP
ejpam-5638	165	30	)	)	PUNCT
ejpam-5638	165	31	≤	≤	NUM
ejpam-5638	165	32	σmax(m	σmax(m	NOUN
ejpam-5638	165	33	)	)	PUNCT
ejpam-5638	165	34	.	.	PUNCT
ejpam-5638	166	1	m.u.r	m.u.r	PROPN
ejpam-5638	166	2	rehman	rehman	PROPN
ejpam-5638	166	3	et	et	PROPN
ejpam-5638	166	4	al	al	PROPN
ejpam-5638	166	5	.	.	PUNCT
ejpam-5638	166	6	/	/	SYM
ejpam-5638	166	7	eur	eur	PROPN
ejpam-5638	166	8	.	.	PUNCT
ejpam-5638	167	1	j.	j.	PROPN
ejpam-5638	167	2	pure	pure	PROPN
ejpam-5638	167	3	appl	appl	PROPN
ejpam-5638	167	4	.	.	PROPN
ejpam-5638	167	5	math	math	PROPN
ejpam-5638	167	6	,	,	PUNCT
ejpam-5638	167	7	18	18	NUM
ejpam-5638	167	8	(	(	PUNCT
ejpam-5638	167	9	2	2	NUM
ejpam-5638	167	10	)	)	PUNCT
ejpam-5638	167	11	(	(	PUNCT
ejpam-5638	167	12	2025	2025	NUM
ejpam-5638	167	13	)	)	PUNCT
ejpam-5638	167	14	,	,	PUNCT
ejpam-5638	167	15	5638	5638	NUM
ejpam-5638	167	16	8	8	NUM
ejpam-5638	167	17	of	of	ADP
ejpam-5638	167	18	23	23	NUM
ejpam-5638	167	19	3	3	NUM
ejpam-5638	167	20	.	.	PUNCT
ejpam-5638	168	1	new	new	ADJ
ejpam-5638	168	2	results	result	NOUN
ejpam-5638	168	3	for	for	ADP
ejpam-5638	168	4	stability	stability	NOUN
ejpam-5638	168	5	analysis	analysis	NOUN
ejpam-5638	168	6	,	,	PUNCT
ejpam-5638	168	7	and	and	CCONJ
ejpam-5638	168	8	d	d	X
ejpam-5638	168	9	-	-	NOUN
ejpam-5638	168	10	stability	stability	NOUN
ejpam-5638	168	11	analysis	analysis	NOUN
ejpam-5638	168	12	of	of	ADP
ejpam-5638	168	13	first	first	ADJ
ejpam-5638	168	14	and	and	CCONJ
ejpam-5638	168	15	second	second	ADJ
ejpam-5638	168	16	order	order	NOUN
ejpam-5638	168	17	dynamical	dynamical	ADJ
ejpam-5638	168	18	systems	system	NOUN
ejpam-5638	168	19	in	in	ADP
ejpam-5638	168	20	this	this	DET
ejpam-5638	168	21	particular	particular	ADJ
ejpam-5638	168	22	section	section	NOUN
ejpam-5638	168	23	of	of	ADP
ejpam-5638	168	24	the	the	DET
ejpam-5638	168	25	paper	paper	NOUN
ejpam-5638	168	26	,	,	PUNCT
ejpam-5638	168	27	we	we	PRON
ejpam-5638	168	28	present	present	VERB
ejpam-5638	168	29	new	new	ADJ
ejpam-5638	168	30	results	result	NOUN
ejpam-5638	168	31	for	for	ADP
ejpam-5638	168	32	structured	structured	ADJ
ejpam-5638	168	33	stability	stability	NOUN
ejpam-5638	168	34	,	,	PUNCT
ejpam-5638	168	35	and	and	CCONJ
ejpam-5638	168	36	structured	structure	VERB
ejpam-5638	168	37	d	d	X
ejpam-5638	168	38	-	-	PUNCT
ejpam-5638	168	39	stability	stability	NOUN
ejpam-5638	168	40	analysis	analysis	NOUN
ejpam-5638	168	41	of	of	ADP
ejpam-5638	168	42	first	first	ADJ
ejpam-5638	168	43	and	and	CCONJ
ejpam-5638	168	44	second	second	ADJ
ejpam-5638	168	45	order	order	NOUN
ejpam-5638	168	46	dynamical	dynamical	ADJ
ejpam-5638	168	47	systems	system	NOUN
ejpam-5638	168	48	.	.	PUNCT
ejpam-5638	169	1	furthermore	furthermore	ADV
ejpam-5638	169	2	,	,	PUNCT
ejpam-5638	169	3	we	we	PRON
ejpam-5638	169	4	establish	establish	VERB
ejpam-5638	169	5	the	the	DET
ejpam-5638	169	6	necessary	necessary	ADJ
ejpam-5638	169	7	conditions	condition	NOUN
ejpam-5638	169	8	on	on	ADP
ejpam-5638	169	9	the	the	DET
ejpam-5638	169	10	interconnection	interconnection	NOUN
ejpam-5638	169	11	among	among	ADP
ejpam-5638	169	12	the	the	DET
ejpam-5638	169	13	structured	structured	ADJ
ejpam-5638	169	14	stability	stability	NOUN
ejpam-5638	169	15	,	,	PUNCT
ejpam-5638	169	16	structured	structured	ADJ
ejpam-5638	169	17	d	d	NOUN
ejpam-5638	169	18	-	-	NOUN
ejpam-5638	169	19	stability	stability	NOUN
ejpam-5638	169	20	,	,	PUNCT
ejpam-5638	169	21	and	and	CCONJ
ejpam-5638	169	22	µ-values	µ-value	VERB
ejpam-5638	169	23	.	.	PUNCT
ejpam-5638	170	1	we	we	PRON
ejpam-5638	170	2	make	make	VERB
ejpam-5638	170	3	use	use	NOUN
ejpam-5638	170	4	of	of	ADP
ejpam-5638	170	5	various	various	ADJ
ejpam-5638	170	6	tools	tool	NOUN
ejpam-5638	170	7	from	from	ADP
ejpam-5638	170	8	linear	linear	PROPN
ejpam-5638	170	9	algebra	algebra	NOUN
ejpam-5638	170	10	,	,	PUNCT
ejpam-5638	170	11	matrix	matrix	NOUN
ejpam-5638	170	12	analysis	analysis	NOUN
ejpam-5638	170	13	and	and	CCONJ
ejpam-5638	170	14	system	system	NOUN
ejpam-5638	170	15	theory	theory	NOUN
ejpam-5638	170	16	to	to	PART
ejpam-5638	170	17	derive	derive	VERB
ejpam-5638	170	18	new	new	ADJ
ejpam-5638	170	19	results	result	NOUN
ejpam-5638	170	20	.	.	PUNCT
ejpam-5638	171	1	3.1	3.1	NUM
ejpam-5638	171	2	.	.	PUNCT
ejpam-5638	171	3	stability	stability	NOUN
ejpam-5638	171	4	and	and	CCONJ
ejpam-5638	171	5	d	d	NOUN
ejpam-5638	171	6	-	-	NOUN
ejpam-5638	171	7	stability	stability	NOUN
ejpam-5638	171	8	of	of	ADP
ejpam-5638	171	9	first	first	ADJ
ejpam-5638	171	10	order	order	NOUN
ejpam-5638	171	11	dynamical	dynamical	ADJ
ejpam-5638	171	12	systems	system	NOUN
ejpam-5638	171	13	first	first	ADV
ejpam-5638	171	14	,	,	PUNCT
ejpam-5638	171	15	we	we	PRON
ejpam-5638	171	16	discuss	discuss	VERB
ejpam-5638	171	17	and	and	CCONJ
ejpam-5638	171	18	provide	provide	VERB
ejpam-5638	171	19	results	result	NOUN
ejpam-5638	171	20	on	on	ADP
ejpam-5638	171	21	the	the	DET
ejpam-5638	171	22	stability	stability	NOUN
ejpam-5638	171	23	of	of	ADP
ejpam-5638	171	24	ẋ	ẋ	PROPN
ejpam-5638	171	25	=	=	NOUN
ejpam-5638	171	26	ax	ax	NOUN
ejpam-5638	171	27	,	,	PUNCT
ejpam-5638	171	28	x	x	SYM
ejpam-5638	171	29	∈	∈	PROPN
ejpam-5638	171	30	rn,1	rn,1	PROPN
ejpam-5638	171	31	,	,	PUNCT
ejpam-5638	171	32	a	a	DET
ejpam-5638	171	33	∈	∈	PROPN
ejpam-5638	171	34	rn	rn	PROPN
ejpam-5638	171	35	,	,	PUNCT
ejpam-5638	171	36	n.	n.	PROPN
ejpam-5638	171	37	assumption	assumption	NOUN
ejpam-5638	171	38	1	1	X
ejpam-5638	171	39	.	.	PUNCT
ejpam-5638	172	1	the	the	DET
ejpam-5638	172	2	given	give	VERB
ejpam-5638	172	3	matrix	matrix	NOUN
ejpam-5638	172	4	a	a	DET
ejpam-5638	172	5	∈	∈	PROPN
ejpam-5638	172	6	rn	rn	PROPN
ejpam-5638	172	7	,	,	PUNCT
ejpam-5638	172	8	n	n	PRON
ejpam-5638	172	9	is	be	AUX
ejpam-5638	172	10	a	a	DET
ejpam-5638	172	11	symmetric	symmetric	ADJ
ejpam-5638	172	12	matrix	matrix	NOUN
ejpam-5638	172	13	,	,	PUNCT
ejpam-5638	172	14	that	that	ADV
ejpam-5638	172	15	is	is	ADV
ejpam-5638	172	16	,	,	PUNCT
ejpam-5638	172	17	at	at	ADP
ejpam-5638	172	18	=	=	NOUN
ejpam-5638	172	19	a.	a.	NOUN
ejpam-5638	172	20	theorem	theorem	NOUN
ejpam-5638	172	21	3	3	NUM
ejpam-5638	172	22	provides	provide	VERB
ejpam-5638	172	23	mathematical	mathematical	ADJ
ejpam-5638	172	24	results	result	NOUN
ejpam-5638	172	25	on	on	ADP
ejpam-5638	172	26	structured	structured	ADJ
ejpam-5638	172	27	stability	stability	NOUN
ejpam-5638	172	28	dynamical	dynamical	ADJ
ejpam-5638	172	29	system	system	NOUN
ejpam-5638	172	30	which	which	PRON
ejpam-5638	172	31	means	mean	VERB
ejpam-5638	172	32	that	that	SCONJ
ejpam-5638	172	33	the	the	DET
ejpam-5638	172	34	real	real	ADJ
ejpam-5638	172	35	part	part	NOUN
ejpam-5638	172	36	of	of	ADP
ejpam-5638	172	37	its	its	PRON
ejpam-5638	172	38	largest	large	ADJ
ejpam-5638	172	39	eigenvalue	eigenvalue	NOUN
ejpam-5638	172	40	is	be	AUX
ejpam-5638	172	41	strictly	strictly	ADV
ejpam-5638	172	42	greater	great	ADJ
ejpam-5638	172	43	than	than	ADP
ejpam-5638	172	44	real	real	ADJ
ejpam-5638	172	45	part	part	NOUN
ejpam-5638	172	46	of	of	ADP
ejpam-5638	172	47	the	the	DET
ejpam-5638	172	48	eigenvalues	eigenvalue	NOUN
ejpam-5638	172	49	of	of	ADP
ejpam-5638	172	50	all	all	DET
ejpam-5638	172	51	remaining	remain	VERB
ejpam-5638	172	52	eigenvalues	eigenvalue	NOUN
ejpam-5638	172	53	.	.	PUNCT
ejpam-5638	173	1	theorem	theorem	NOUN
ejpam-5638	173	2	3	3	NUM
ejpam-5638	173	3	.	.	PUNCT
ejpam-5638	174	1	the	the	DET
ejpam-5638	174	2	first	first	ADJ
ejpam-5638	174	3	order	order	NOUN
ejpam-5638	174	4	dynamic	dynamic	ADJ
ejpam-5638	174	5	model	model	NOUN
ejpam-5638	174	6	ẋ	ẋ	PROPN
ejpam-5638	175	1	=	=	NOUN
ejpam-5638	175	2	ax	ax	NOUN
ejpam-5638	175	3	,	,	PUNCT
ejpam-5638	175	4	x	x	SYM
ejpam-5638	175	5	∈	∈	PROPN
ejpam-5638	175	6	rn,1	rn,1	NOUN
ejpam-5638	175	7	is	be	AUX
ejpam-5638	175	8	stable	stable	ADJ
ejpam-5638	175	9	if	if	SCONJ
ejpam-5638	175	10	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	175	11	)	)	PUNCT
ejpam-5638	175	12	)	)	PUNCT
ejpam-5638	175	13	>	>	X
ejpam-5638	176	1	|re(µi(a))|	|re(µi(a))|	PROPN
ejpam-5638	176	2	>	>	X
ejpam-5638	176	3	0	0	NUM
ejpam-5638	176	4	,	,	PUNCT
ejpam-5638	176	5	∀i	∀i	NOUN
ejpam-5638	176	6	,	,	PUNCT
ejpam-5638	176	7	with	with	ADP
ejpam-5638	176	8	λ1(a	λ1(a	NOUN
ejpam-5638	176	9	)	)	PUNCT
ejpam-5638	176	10	,	,	PUNCT
ejpam-5638	176	11	the	the	DET
ejpam-5638	176	12	largest	large	ADJ
ejpam-5638	176	13	eigenvalue	eigenvalue	NOUN
ejpam-5638	176	14	,	,	PUNCT
ejpam-5638	176	15	and	and	CCONJ
ejpam-5638	176	16	µi(a),∀i	µi(a),∀i	PROPN
ejpam-5638	176	17	are	be	AUX
ejpam-5638	176	18	the	the	DET
ejpam-5638	176	19	eigenvalues	eigenvalue	NOUN
ejpam-5638	176	20	other	other	ADJ
ejpam-5638	176	21	than	than	ADP
ejpam-5638	176	22	λ1(a	λ1(a	PROPN
ejpam-5638	176	23	)	)	PUNCT
ejpam-5638	176	24	.	.	PUNCT
ejpam-5638	177	1	proof	proof	NOUN
ejpam-5638	177	2	.	.	PUNCT
ejpam-5638	178	1	the	the	DET
ejpam-5638	178	2	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	178	3	)	)	PUNCT
ejpam-5638	178	4	)	)	PUNCT
ejpam-5638	179	1	>	>	X
ejpam-5638	179	2	0	0	PUNCT
ejpam-5638	180	1	because	because	SCONJ
ejpam-5638	180	2	λi(a	λi(a	NOUN
ejpam-5638	180	3	)	)	PUNCT
ejpam-5638	180	4	∈	∈	PROPN
ejpam-5638	180	5	r,∀i	r,∀i	PROPN
ejpam-5638	180	6	and	and	CCONJ
ejpam-5638	180	7	∑	∑	ADV
ejpam-5638	180	8	i	i	PROPN
ejpam-5638	180	9	(	(	PUNCT
ejpam-5638	180	10	λi(a	λi(a	PROPN
ejpam-5638	180	11	)	)	PUNCT
ejpam-5638	180	12	)	)	PUNCT
ejpam-5638	180	13	=	=	SYM
ejpam-5638	180	14	trace(a	trace(a	NUM
ejpam-5638	180	15	)	)	PUNCT
ejpam-5638	180	16	>	>	X
ejpam-5638	180	17	0	0	NUM
ejpam-5638	180	18	,	,	PUNCT
ejpam-5638	180	19	and	and	CCONJ
ejpam-5638	180	20	hence	hence	ADV
ejpam-5638	180	21	it	it	PRON
ejpam-5638	180	22	follows	follow	VERB
ejpam-5638	180	23	that	that	PRON
ejpam-5638	180	24	λ1(a	λ1(a	VERB
ejpam-5638	180	25	)	)	PUNCT
ejpam-5638	180	26	>	>	X
ejpam-5638	180	27	0	0	X
ejpam-5638	180	28	.	.	PUNCT
ejpam-5638	181	1	now	now	ADV
ejpam-5638	181	2	,	,	PUNCT
ejpam-5638	181	3	we	we	PRON
ejpam-5638	181	4	aim	aim	VERB
ejpam-5638	181	5	to	to	PART
ejpam-5638	181	6	show	show	VERB
ejpam-5638	181	7	that	that	SCONJ
ejpam-5638	181	8	µi(a	µi(a	PUNCT
ejpam-5638	181	9	)	)	PUNCT
ejpam-5638	181	10	̸=	̸=	PROPN
ejpam-5638	181	11	λ1(a	λ1(a	NUM
ejpam-5638	181	12	)	)	PUNCT
ejpam-5638	181	13	,	,	PUNCT
ejpam-5638	181	14	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	181	15	)	)	PUNCT
ejpam-5638	181	16	)	)	PUNCT
ejpam-5638	181	17	>	>	X
ejpam-5638	182	1	|re(µi(a))|	|re(µi(a))|	PROPN
ejpam-5638	182	2	>	>	X
ejpam-5638	182	3	0	0	NUM
ejpam-5638	182	4	,	,	PUNCT
ejpam-5638	182	5	∀i	∀i	NOUN
ejpam-5638	182	6	.	.	PUNCT
ejpam-5638	183	1	let	let	VERB
ejpam-5638	183	2	v⃗j	v⃗j	NOUN
ejpam-5638	183	3	be	be	AUX
ejpam-5638	183	4	the	the	DET
ejpam-5638	183	5	normalized	normalize	VERB
ejpam-5638	183	6	eigenvector	eigenvector	NOUN
ejpam-5638	183	7	for	for	ADP
ejpam-5638	183	8	λ1	λ1	PROPN
ejpam-5638	183	9	>	>	X
ejpam-5638	183	10	µi,∀i	µi,∀i	PROPN
ejpam-5638	183	11	,	,	PUNCT
ejpam-5638	183	12	then,∑	then,∑	X
ejpam-5638	184	1	i	i	PRON
ejpam-5638	184	2	aij	aij	VERB
ejpam-5638	184	3	v⃗j	v⃗j	NOUN
ejpam-5638	184	4	=	=	SYM
ejpam-5638	184	5	µiv⃗j	µiv⃗j	PROPN
ejpam-5638	184	6	,	,	PUNCT
ejpam-5638	184	7	∀i	∀i	NOUN
ejpam-5638	184	8	.	.	PUNCT
ejpam-5638	185	1	we	we	PRON
ejpam-5638	185	2	set	set	VERB
ejpam-5638	185	3	|vj	|vj	ADV
ejpam-5638	185	4	|	|	ADV
ejpam-5638	185	5	=	=	SYM
ejpam-5638	185	6	xj	xj	PROPN
ejpam-5638	185	7	,	,	PUNCT
ejpam-5638	185	8	then	then	ADV
ejpam-5638	185	9	0	0	NUM
ejpam-5638	185	10	<	<	X
ejpam-5638	185	11	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	185	12	)	)	PUNCT
ejpam-5638	185	13	)	)	PUNCT
ejpam-5638	186	1	=	=	PUNCT
ejpam-5638	186	2	∑	∑	PUNCT
ejpam-5638	186	3	ij	ij	INTJ
ejpam-5638	186	4	aij	aij	PROPN
ejpam-5638	186	5	v⃗iv⃗j	v⃗iv⃗j	NOUN
ejpam-5638	186	6	=	=	PUNCT
ejpam-5638	187	1	|	|	ADV
ejpam-5638	187	2	∑	∑	PUNCT
ejpam-5638	187	3	ij	ij	INTJ
ejpam-5638	187	4	aij	aij	PROPN
ejpam-5638	187	5	v⃗iv⃗j	v⃗iv⃗j	NOUN
ejpam-5638	187	6	|	|	ADV
ejpam-5638	187	7	≤	≤	NUM
ejpam-5638	187	8	∑	∑	PUNCT
ejpam-5638	187	9	ij	ij	PROPN
ejpam-5638	187	10	aijxixj	aijxixj	PROPN
ejpam-5638	187	11	.	.	PUNCT
ejpam-5638	188	1	let	let	VERB
ejpam-5638	188	2	xj	xj	NOUN
ejpam-5638	188	3	be	be	AUX
ejpam-5638	188	4	an	an	DET
ejpam-5638	188	5	eigenvector	eigenvector	NOUN
ejpam-5638	188	6	for	for	ADP
ejpam-5638	188	7	λ1(a	λ1(a	NOUN
ejpam-5638	188	8	)	)	PUNCT
ejpam-5638	188	9	,	,	PUNCT
ejpam-5638	188	10	then∑	then∑	NOUN
ejpam-5638	188	11	j	j	NOUN
ejpam-5638	188	12	aijxj	aijxj	NOUN
ejpam-5638	188	13	=	=	SYM
ejpam-5638	188	14	λ1xi	λ1xi	NOUN
ejpam-5638	188	15	,	,	PUNCT
ejpam-5638	188	16	∀i	∀i	NOUN
ejpam-5638	188	17	.	.	PUNCT
ejpam-5638	189	1	if	if	SCONJ
ejpam-5638	189	2	we	we	PRON
ejpam-5638	189	3	take	take	VERB
ejpam-5638	189	4	xi	xi	NOUN
ejpam-5638	189	5	=	=	SYM
ejpam-5638	189	6	0	0	NUM
ejpam-5638	189	7	,	,	PUNCT
ejpam-5638	189	8	for	for	ADP
ejpam-5638	189	9	some	some	DET
ejpam-5638	189	10	i	i	PROPN
ejpam-5638	189	11	,	,	PUNCT
ejpam-5638	189	12	then	then	ADV
ejpam-5638	189	13	aij	aij	PROPN
ejpam-5638	189	14	>	>	X
ejpam-5638	189	15	0,∀j	0,∀j	PROPN
ejpam-5638	189	16	.	.	PUNCT
ejpam-5638	190	1	from	from	ADP
ejpam-5638	190	2	this	this	PRON
ejpam-5638	190	3	we	we	PRON
ejpam-5638	190	4	have	have	VERB
ejpam-5638	190	5	that	that	SCONJ
ejpam-5638	190	6	each	each	PRON
ejpam-5638	190	7	of	of	ADP
ejpam-5638	190	8	xj	xj	PROPN
ejpam-5638	190	9	=	=	SYM
ejpam-5638	190	10	0	0	PROPN
ejpam-5638	190	11	,	,	PUNCT
ejpam-5638	190	12	this	this	PRON
ejpam-5638	190	13	is	be	AUX
ejpam-5638	190	14	not	not	PART
ejpam-5638	190	15	possible	possible	ADJ
ejpam-5638	190	16	,	,	PUNCT
ejpam-5638	190	17	and	and	CCONJ
ejpam-5638	190	18	hence	hence	ADV
ejpam-5638	190	19	each	each	DET
ejpam-5638	190	20	xj	xj	PROPN
ejpam-5638	190	21	>	>	X
ejpam-5638	190	22	0	0	PROPN
ejpam-5638	190	23	,	,	PUNCT
ejpam-5638	190	24	the	the	DET
ejpam-5638	190	25	non	non	ADJ
ejpam-5638	190	26	-	-	ADJ
ejpam-5638	190	27	decreasing	decrease	VERB
ejpam-5638	190	28	condition	condition	NOUN
ejpam-5638	190	29	of	of	ADP
ejpam-5638	190	30	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	190	31	)	)	PUNCT
ejpam-5638	190	32	)	)	PUNCT
ejpam-5638	190	33	.	.	PUNCT
ejpam-5638	191	1	the	the	DET
ejpam-5638	191	2	non	non	ADJ
ejpam-5638	191	3	-	-	ADJ
ejpam-5638	191	4	decreasing	decrease	VERB
ejpam-5638	191	5	condition	condition	NOUN
ejpam-5638	191	6	allows	allow	VERB
ejpam-5638	191	7	us	we	PRON
ejpam-5638	191	8	to	to	PART
ejpam-5638	191	9	have	have	VERB
ejpam-5638	191	10	that	that	DET
ejpam-5638	191	11	re(λ1(a	re(λ1(a	PROPN
ejpam-5638	191	12	)	)	PUNCT
ejpam-5638	191	13	)	)	PUNCT
ejpam-5638	191	14	>	>	PUNCT
ejpam-5638	192	1	∑	∑	PUNCT
ejpam-5638	192	2	ij	ij	INTJ
ejpam-5638	192	3	aij	aij	PROPN
ejpam-5638	192	4	|vi||vj	|vi||vj	PROPN
ejpam-5638	192	5	|	|	ADV
ejpam-5638	192	6	≥	≥	NOUN
ejpam-5638	192	7	|	|	ADV
ejpam-5638	192	8	∑	∑	ADP
ejpam-5638	192	9	ij	ij	PROPN
ejpam-5638	192	10	aijv	aijv	PROPN
ejpam-5638	192	11	∗	∗	VERB
ejpam-5638	193	1	i	i	PRON
ejpam-5638	193	2	vj	vj	VERB
ejpam-5638	194	1	|	|	ADV
ejpam-5638	194	2	=	=	SYM
ejpam-5638	194	3	|µi(a)|	|µi(a)|	X
ejpam-5638	194	4	=	=	SYM
ejpam-5638	194	5	|re(µi(a))|	|re(µi(a))|	X
ejpam-5638	194	6	>	>	X
ejpam-5638	194	7	0	0	X
ejpam-5638	194	8	.	.	PUNCT
ejpam-5638	195	1	m.u.r	m.u.r	PROPN
ejpam-5638	195	2	rehman	rehman	PROPN
ejpam-5638	195	3	et	et	PROPN
ejpam-5638	195	4	al	al	PROPN
ejpam-5638	195	5	.	.	PUNCT
ejpam-5638	195	6	/	/	SYM
ejpam-5638	195	7	eur	eur	PROPN
ejpam-5638	195	8	.	.	PUNCT
ejpam-5638	196	1	j.	j.	PROPN
ejpam-5638	196	2	pure	pure	PROPN
ejpam-5638	196	3	appl	appl	PROPN
ejpam-5638	196	4	.	.	PROPN
ejpam-5638	196	5	math	math	PROPN
ejpam-5638	196	6	,	,	PUNCT
ejpam-5638	196	7	18	18	NUM
ejpam-5638	196	8	(	(	PUNCT
ejpam-5638	196	9	2	2	NUM
ejpam-5638	196	10	)	)	PUNCT
ejpam-5638	196	11	(	(	PUNCT
ejpam-5638	196	12	2025	2025	NUM
ejpam-5638	196	13	)	)	PUNCT
ejpam-5638	196	14	,	,	PUNCT
ejpam-5638	196	15	5638	5638	NUM
ejpam-5638	196	16	9	9	NUM
ejpam-5638	196	17	of	of	ADP
ejpam-5638	196	18	23	23	NUM
ejpam-5638	196	19	theorem	theorem	ADJ
ejpam-5638	196	20	4	4	NUM
ejpam-5638	196	21	shows	show	VERB
ejpam-5638	196	22	that	that	SCONJ
ejpam-5638	196	23	first	first	ADJ
ejpam-5638	196	24	order	order	NOUN
ejpam-5638	196	25	dynamical	dynamical	ADJ
ejpam-5638	196	26	system	system	NOUN
ejpam-5638	196	27	is	be	AUX
ejpam-5638	196	28	stable	stable	ADJ
ejpam-5638	196	29	if	if	SCONJ
ejpam-5638	196	30	the	the	DET
ejpam-5638	196	31	quadratic	quadratic	ADJ
ejpam-5638	196	32	form	form	NOUN
ejpam-5638	196	33	xtax	xtax	NOUN
ejpam-5638	196	34	is	be	AUX
ejpam-5638	196	35	strictly	strictly	ADV
ejpam-5638	196	36	positive	positive	ADJ
ejpam-5638	196	37	if	if	SCONJ
ejpam-5638	196	38	and	and	CCONJ
ejpam-5638	196	39	only	only	ADV
ejpam-5638	196	40	if	if	SCONJ
ejpam-5638	196	41	re(λi	re(λi	NOUN
ejpam-5638	196	42	)	)	PUNCT
ejpam-5638	196	43	,	,	PUNCT
ejpam-5638	196	44	that	that	ADV
ejpam-5638	196	45	is	is	ADV
ejpam-5638	196	46	,	,	PUNCT
ejpam-5638	196	47	real	real	ADJ
ejpam-5638	196	48	part	part	NOUN
ejpam-5638	196	49	of	of	ADP
ejpam-5638	196	50	all	all	DET
ejpam-5638	196	51	the	the	DET
ejpam-5638	196	52	eigenvalues	eigenvalue	NOUN
ejpam-5638	196	53	of	of	ADP
ejpam-5638	196	54	a	a	DET
ejpam-5638	196	55	real	real	ADV
ejpam-5638	196	56	valued	value	VERB
ejpam-5638	196	57	matrix	matrix	NOUN
ejpam-5638	196	58	a	a	PRON
ejpam-5638	196	59	be	be	VERB
ejpam-5638	196	60	strictly	strictly	ADV
ejpam-5638	196	61	positive	positive	ADJ
ejpam-5638	196	62	.	.	PUNCT
ejpam-5638	197	1	here	here	ADV
ejpam-5638	197	2	,	,	PUNCT
ejpam-5638	197	3	x	x	SYM
ejpam-5638	197	4	∈	∈	PROPN
ejpam-5638	197	5	rn,1	rn,1	NOUN
ejpam-5638	197	6	is	be	AUX
ejpam-5638	197	7	a	a	DET
ejpam-5638	197	8	non	non	ADJ
ejpam-5638	197	9	-	-	ADJ
ejpam-5638	197	10	zero	zero	NUM
ejpam-5638	197	11	vector	vector	NOUN
ejpam-5638	197	12	.	.	PUNCT
ejpam-5638	198	1	theorem	theorem	NOUN
ejpam-5638	198	2	4	4	NUM
ejpam-5638	198	3	.	.	PUNCT
ejpam-5638	199	1	let	let	VERB
ejpam-5638	199	2	dynamical	dynamical	ADJ
ejpam-5638	199	3	system	system	NOUN
ejpam-5638	199	4	ẋ	ẋ	PUNCT
ejpam-5638	200	1	=	=	NOUN
ejpam-5638	200	2	ax	ax	NOUN
ejpam-5638	200	3	,	,	PUNCT
ejpam-5638	200	4	x	x	SYM
ejpam-5638	200	5	∈	∈	PROPN
ejpam-5638	200	6	rn,1	rn,1	NOUN
ejpam-5638	200	7	is	be	AUX
ejpam-5638	200	8	stable	stable	ADJ
ejpam-5638	200	9	,	,	PUNCT
ejpam-5638	200	10	then	then	ADV
ejpam-5638	200	11	xtax	xtax	VERB
ejpam-5638	200	12	>	>	X
ejpam-5638	200	13	0	0	NUM
ejpam-5638	200	14	,	,	PUNCT
ejpam-5638	200	15	∀x	∀x	X
ejpam-5638	200	16	∈	∈	PROPN
ejpam-5638	200	17	rn,1	rn,1	PROPN
ejpam-5638	200	18	iff	iff	PROPN
ejpam-5638	200	19	re(λi(a	re(λi(a	PROPN
ejpam-5638	200	20	)	)	PUNCT
ejpam-5638	200	21	)	)	PUNCT
ejpam-5638	201	1	>	>	X
ejpam-5638	201	2	0,∀i	0,∀i	X
ejpam-5638	201	3	.	.	PUNCT
ejpam-5638	202	1	proof	proof	NOUN
ejpam-5638	202	2	.	.	PUNCT
ejpam-5638	203	1	for	for	ADP
ejpam-5638	203	2	the	the	DET
ejpam-5638	203	3	stability	stability	NOUN
ejpam-5638	203	4	of	of	ADP
ejpam-5638	203	5	dynamical	dynamical	ADJ
ejpam-5638	203	6	system	system	NOUN
ejpam-5638	203	7	ẋ	ẋ	PUNCT
ejpam-5638	203	8	=	=	NOUN
ejpam-5638	203	9	ax	ax	NOUN
ejpam-5638	203	10	,	,	PUNCT
ejpam-5638	203	11	x	x	SYM
ejpam-5638	203	12	∈	∈	PROPN
ejpam-5638	203	13	rn,1	rn,1	PROPN
ejpam-5638	203	14	,	,	PUNCT
ejpam-5638	203	15	we	we	PRON
ejpam-5638	203	16	aim	aim	VERB
ejpam-5638	203	17	to	to	PART
ejpam-5638	203	18	show	show	VERB
ejpam-5638	203	19	that	that	SCONJ
ejpam-5638	203	20	for	for	ADP
ejpam-5638	203	21	z	z	NOUN
ejpam-5638	203	22	=	=	SYM
ejpam-5638	203	23	x	x	PROPN
ejpam-5638	203	24	+	+	NUM
ejpam-5638	203	25	iy	iy	INTJ
ejpam-5638	203	26	,	,	PUNCT
ejpam-5638	203	27	x	x	X
ejpam-5638	203	28	,	,	PUNCT
ejpam-5638	203	29	y	y	PROPN
ejpam-5638	203	30	∈	∈	PROPN
ejpam-5638	203	31	rn,1	rn,1	PROPN
ejpam-5638	203	32	,	,	PUNCT
ejpam-5638	203	33	the	the	DET
ejpam-5638	203	34	quantity	quantity	NOUN
ejpam-5638	203	35	z∗az	z∗az	X
ejpam-5638	203	36	>	>	X
ejpam-5638	203	37	0	0	PROPN
ejpam-5638	203	38	,	,	PUNCT
ejpam-5638	203	39	z	z	PROPN
ejpam-5638	203	40	∈	∈	PROPN
ejpam-5638	203	41	cn,1	cn,1	PROPN
ejpam-5638	203	42	.	.	PUNCT
ejpam-5638	204	1	now	now	ADV
ejpam-5638	204	2	,	,	PUNCT
ejpam-5638	204	3	we	we	PRON
ejpam-5638	204	4	take	take	VERB
ejpam-5638	204	5	(	(	PUNCT
ejpam-5638	204	6	ytax)t	ytax)t	NOUN
ejpam-5638	204	7	=	=	SYM
ejpam-5638	204	8	xtay	xtay	PROPN
ejpam-5638	204	9	,	,	PUNCT
ejpam-5638	204	10	at	at	ADP
ejpam-5638	204	11	=	=	NOUN
ejpam-5638	204	12	a.	a.	NOUN
ejpam-5638	204	13	furthermore	furthermore	ADV
ejpam-5638	204	14	,	,	PUNCT
ejpam-5638	204	15	z∗az	z∗az	X
ejpam-5638	204	16	=	=	SYM
ejpam-5638	204	17	(	(	PUNCT
ejpam-5638	204	18	x+	x+	X
ejpam-5638	204	19	iy)∗a(x+	iy)∗a(x+	NOUN
ejpam-5638	204	20	iy	iy	PROPN
ejpam-5638	204	21	)	)	PUNCT
ejpam-5638	204	22	=	=	PUNCT
ejpam-5638	205	1	xtax+	xtax+	NOUN
ejpam-5638	205	2	ytay	ytay	NOUN
ejpam-5638	205	3	+	+	CCONJ
ejpam-5638	205	4	i(xtay	i(xtay	NOUN
ejpam-5638	205	5	−	−	NOUN
ejpam-5638	205	6	ytax	ytax	NOUN
ejpam-5638	205	7	)	)	PUNCT
ejpam-5638	205	8	=	=	PUNCT
ejpam-5638	206	1	xtax+	xtax+	NOUN
ejpam-5638	206	2	ytay	ytay	VERB
ejpam-5638	206	3	>	>	X
ejpam-5638	206	4	0	0	X
ejpam-5638	206	5	.	.	PUNCT
ejpam-5638	207	1	the	the	DET
ejpam-5638	207	2	strict	strict	ADJ
ejpam-5638	207	3	inequality	inequality	NOUN
ejpam-5638	207	4	holds	hold	VERB
ejpam-5638	207	5	true	true	ADJ
ejpam-5638	207	6	if	if	SCONJ
ejpam-5638	207	7	one	one	NUM
ejpam-5638	207	8	of	of	ADP
ejpam-5638	207	9	x	x	PUNCT
ejpam-5638	207	10	and	and	CCONJ
ejpam-5638	207	11	y	y	PROPN
ejpam-5638	207	12	be	be	AUX
ejpam-5638	207	13	non	non	ADJ
ejpam-5638	207	14	-	-	ADJ
ejpam-5638	207	15	zero	zero	NUM
ejpam-5638	207	16	.	.	PUNCT
ejpam-5638	208	1	this	this	PRON
ejpam-5638	208	2	imply	imply	VERB
ejpam-5638	208	3	that	that	SCONJ
ejpam-5638	208	4	re(λi(a	re(λi(a	PROPN
ejpam-5638	208	5	)	)	PUNCT
ejpam-5638	208	6	)	)	PUNCT
ejpam-5638	208	7	>	>	X
ejpam-5638	209	1	0	0	NUM
ejpam-5638	209	2	,	,	PUNCT
ejpam-5638	209	3	∀i	∀i	NOUN
ejpam-5638	209	4	.	.	PUNCT
ejpam-5638	209	5	theorem	theorem	NOUN
ejpam-5638	209	6	5	5	NUM
ejpam-5638	209	7	shows	show	VERB
ejpam-5638	209	8	that	that	SCONJ
ejpam-5638	209	9	first	first	ADJ
ejpam-5638	209	10	order	order	NOUN
ejpam-5638	209	11	dynamical	dynamical	ADJ
ejpam-5638	209	12	system	system	NOUN
ejpam-5638	209	13	is	be	AUX
ejpam-5638	209	14	stable	stable	ADJ
ejpam-5638	209	15	if	if	SCONJ
ejpam-5638	209	16	the	the	DET
ejpam-5638	209	17	quadratic	quadratic	ADJ
ejpam-5638	209	18	form	form	NOUN
ejpam-5638	209	19	xtax	xtax	NOUN
ejpam-5638	209	20	is	be	AUX
ejpam-5638	209	21	strictly	strictly	ADV
ejpam-5638	209	22	positive	positive	ADJ
ejpam-5638	209	23	if	if	SCONJ
ejpam-5638	209	24	and	and	CCONJ
ejpam-5638	209	25	only	only	ADV
ejpam-5638	209	26	if	if	SCONJ
ejpam-5638	209	27	re(λi	re(λi	NOUN
ejpam-5638	209	28	)	)	PUNCT
ejpam-5638	209	29	,	,	PUNCT
ejpam-5638	209	30	that	that	ADV
ejpam-5638	209	31	is	is	ADV
ejpam-5638	209	32	,	,	PUNCT
ejpam-5638	209	33	real	real	ADJ
ejpam-5638	209	34	part	part	NOUN
ejpam-5638	209	35	of	of	ADP
ejpam-5638	209	36	all	all	DET
ejpam-5638	209	37	the	the	DET
ejpam-5638	209	38	eigenvalues	eigenvalue	NOUN
ejpam-5638	209	39	of	of	ADP
ejpam-5638	209	40	a	a	DET
ejpam-5638	209	41	complex	complex	ADJ
ejpam-5638	209	42	valued	value	VERB
ejpam-5638	209	43	matrix	matrix	NOUN
ejpam-5638	209	44	a	a	PRON
ejpam-5638	209	45	is	be	AUX
ejpam-5638	209	46	strictly	strictly	ADV
ejpam-5638	209	47	positive	positive	ADJ
ejpam-5638	209	48	.	.	PUNCT
ejpam-5638	210	1	here	here	ADV
ejpam-5638	210	2	x	x	X
ejpam-5638	210	3	∈	∈	PROPN
ejpam-5638	210	4	cn,1	cn,1	PROPN
ejpam-5638	210	5	is	be	AUX
ejpam-5638	210	6	a	a	DET
ejpam-5638	210	7	non	non	ADJ
ejpam-5638	210	8	-	-	ADJ
ejpam-5638	210	9	zero	zero	NUM
ejpam-5638	210	10	vector	vector	NOUN
ejpam-5638	210	11	corresponding	correspond	VERB
ejpam-5638	210	12	to	to	ADP
ejpam-5638	210	13	the	the	DET
ejpam-5638	210	14	eigenvalues	eigenvalue	NOUN
ejpam-5638	210	15	of	of	ADP
ejpam-5638	210	16	a.	a.	NOUN
ejpam-5638	210	17	theorem	theorem	NOUN
ejpam-5638	210	18	5	5	NUM
ejpam-5638	210	19	.	.	PUNCT
ejpam-5638	211	1	the	the	DET
ejpam-5638	211	2	dynamical	dynamical	ADJ
ejpam-5638	211	3	system	system	NOUN
ejpam-5638	211	4	ẋ	ẋ	PUNCT
ejpam-5638	212	1	=	=	NOUN
ejpam-5638	212	2	ax	ax	NOUN
ejpam-5638	212	3	,	,	PUNCT
ejpam-5638	212	4	x	x	SYM
ejpam-5638	212	5	∈	∈	PROPN
ejpam-5638	212	6	cn,1	cn,1	PROPN
ejpam-5638	212	7	is	be	AUX
ejpam-5638	212	8	stable	stable	ADJ
ejpam-5638	212	9	,	,	PUNCT
ejpam-5638	212	10	then	then	ADV
ejpam-5638	212	11	x∗ax	x∗ax	PROPN
ejpam-5638	212	12	>	>	X
ejpam-5638	212	13	0	0	NUM
ejpam-5638	213	1	⇔	⇔	X
ejpam-5638	213	2	re(λi(a	re(λi(a	PROPN
ejpam-5638	213	3	)	)	PUNCT
ejpam-5638	213	4	)	)	PUNCT
ejpam-5638	214	1	>	>	X
ejpam-5638	214	2	0	0	NUM
ejpam-5638	214	3	,	,	PUNCT
ejpam-5638	214	4	∀i	∀i	NOUN
ejpam-5638	214	5	.	.	PUNCT
ejpam-5638	215	1	proof	proof	NOUN
ejpam-5638	215	2	.	.	PUNCT
ejpam-5638	216	1	the	the	DET
ejpam-5638	216	2	quantity	quantity	NOUN
ejpam-5638	216	3	x∗ax	x∗ax	PROPN
ejpam-5638	216	4	is	be	AUX
ejpam-5638	216	5	a	a	DET
ejpam-5638	216	6	real	real	ADV
ejpam-5638	216	7	valued	value	VERB
ejpam-5638	216	8	and	and	CCONJ
ejpam-5638	216	9	positive	positive	ADJ
ejpam-5638	216	10	,	,	PUNCT
ejpam-5638	216	11	then	then	ADV
ejpam-5638	216	12	for	for	ADP
ejpam-5638	216	13	all	all	DET
ejpam-5638	216	14	x	x	SYM
ejpam-5638	216	15	∈	∈	PROPN
ejpam-5638	216	16	cn,1	cn,1	PROPN
ejpam-5638	216	17	,	,	PUNCT
ejpam-5638	216	18	x∗ax	x∗ax	PROPN
ejpam-5638	216	19	is	be	AUX
ejpam-5638	216	20	real	real	ADV
ejpam-5638	216	21	valued	value	VERB
ejpam-5638	216	22	.	.	PUNCT
ejpam-5638	217	1	furthermore	furthermore	ADV
ejpam-5638	217	2	,	,	PUNCT
ejpam-5638	217	3	re(λi(a	re(λi(a	PROPN
ejpam-5638	217	4	)	)	PUNCT
ejpam-5638	217	5	)	)	PUNCT
ejpam-5638	218	1	=	=	PRON
ejpam-5638	218	2	v∗i	v∗i	X
ejpam-5638	218	3	(	(	PUNCT
ejpam-5638	218	4	λivi	λivi	ADJ
ejpam-5638	218	5	)	)	PUNCT
ejpam-5638	218	6	=	=	SYM
ejpam-5638	218	7	v∗iavi	v∗iavi	ADJ
ejpam-5638	218	8	,	,	PUNCT
ejpam-5638	218	9	vi	vi	PROPN
ejpam-5638	218	10	∈	∈	PROPN
ejpam-5638	218	11	cn,1,∀i	cn,1,∀i	PROPN
ejpam-5638	218	12	being	being	NOUN
ejpam-5638	218	13	unit	unit	NOUN
ejpam-5638	218	14	eigenvectors	eigenvector	NOUN
ejpam-5638	218	15	corresponding	correspond	VERB
ejpam-5638	218	16	to	to	ADP
ejpam-5638	218	17	λi	λi	PROPN
ejpam-5638	218	18	of	of	ADP
ejpam-5638	218	19	a.	a.	NOUN
ejpam-5638	218	20	this	this	PRON
ejpam-5638	218	21	ensures	ensure	VERB
ejpam-5638	218	22	that	that	SCONJ
ejpam-5638	218	23	re(λi(a	re(λi(a	PROPN
ejpam-5638	218	24	)	)	PUNCT
ejpam-5638	218	25	)	)	PUNCT
ejpam-5638	218	26	>	>	X
ejpam-5638	219	1	0	0	NUM
ejpam-5638	219	2	,	,	PUNCT
ejpam-5638	219	3	∀i	∀i	NOUN
ejpam-5638	219	4	.	.	PUNCT
ejpam-5638	220	1	on	on	ADP
ejpam-5638	220	2	the	the	DET
ejpam-5638	220	3	other	other	ADJ
ejpam-5638	220	4	hand	hand	NOUN
ejpam-5638	220	5	if	if	SCONJ
ejpam-5638	220	6	we	we	PRON
ejpam-5638	220	7	take	take	VERB
ejpam-5638	220	8	a	a	PRON
ejpam-5638	220	9	has	have	VERB
ejpam-5638	220	10	only	only	ADV
ejpam-5638	220	11	one	one	NUM
ejpam-5638	220	12	eigenvalue	eigenvalue	NOUN
ejpam-5638	220	13	to	to	PART
ejpam-5638	220	14	be	be	AUX
ejpam-5638	220	15	positive	positive	ADJ
ejpam-5638	220	16	,	,	PUNCT
ejpam-5638	220	17	then	then	ADV
ejpam-5638	220	18	a	a	DET
ejpam-5638	220	19	=	=	X
ejpam-5638	220	20	uλu∗	uλu∗	ADJ
ejpam-5638	220	21	,	,	PUNCT
ejpam-5638	220	22	with	with	ADP
ejpam-5638	220	23	u	u	NOUN
ejpam-5638	220	24	being	be	AUX
ejpam-5638	220	25	a	a	DET
ejpam-5638	220	26	unitary	unitary	ADJ
ejpam-5638	220	27	matrix	matrix	NOUN
ejpam-5638	220	28	,	,	PUNCT
ejpam-5638	220	29	u∗u	u∗u	SYM
ejpam-5638	220	30	=	=	PUNCT
ejpam-5638	220	31	in	in	ADP
ejpam-5638	220	32	and	and	CCONJ
ejpam-5638	220	33	λ	λ	X
ejpam-5638	220	34	=	=	SYM
ejpam-5638	220	35	diag(λ1	diag(λ1	NOUN
ejpam-5638	220	36	,	,	PUNCT
ejpam-5638	220	37	λ2	λ2	NOUN
ejpam-5638	220	38	,	,	PUNCT
ejpam-5638	220	39	.	.	PUNCT
ejpam-5638	220	40	.	.	PUNCT
ejpam-5638	221	1	.	.	PUNCT
ejpam-5638	222	1	,	,	PUNCT
ejpam-5638	222	2	λn	λn	NOUN
ejpam-5638	222	3	)	)	PUNCT
ejpam-5638	222	4	.	.	PUNCT
ejpam-5638	223	1	from	from	ADP
ejpam-5638	223	2	this	this	PRON
ejpam-5638	223	3	we	we	PRON
ejpam-5638	223	4	have	have	VERB
ejpam-5638	223	5	that	that	PRON
ejpam-5638	223	6	x∗ax	x∗ax	PROPN
ejpam-5638	224	1	=	=	PUNCT
ejpam-5638	225	1	x∗uλu∗x	x∗uλu∗x	PROPN
ejpam-5638	226	1	=	=	PRON
ejpam-5638	227	1	(	(	PUNCT
ejpam-5638	227	2	u∗x)∗λ(u∗x	u∗x)∗λ(u∗x	INTJ
ejpam-5638	227	3	)	)	PUNCT
ejpam-5638	228	1	=	=	PUNCT
ejpam-5638	228	2	∑	∑	PUNCT
ejpam-5638	228	3	i	i	PRON
ejpam-5638	228	4	re(λi)|v∗i	re(λi)|v∗i	VERB
ejpam-5638	228	5	x|2	x|2	PROPN
ejpam-5638	228	6	≥	≥	PROPN
ejpam-5638	228	7	0	0	NUM
ejpam-5638	228	8	,	,	PUNCT
ejpam-5638	228	9	for	for	ADP
ejpam-5638	228	10	re(λi(a	re(λi(a	PROPN
ejpam-5638	228	11	)	)	PUNCT
ejpam-5638	228	12	)	)	PUNCT
ejpam-5638	228	13	>	>	X
ejpam-5638	229	1	0	0	NUM
ejpam-5638	229	2	,	,	PUNCT
ejpam-5638	229	3	and	and	CCONJ
ejpam-5638	229	4	for	for	ADP
ejpam-5638	229	5	some	some	DET
ejpam-5638	229	6	non	non	ADJ
ejpam-5638	229	7	-	-	ADJ
ejpam-5638	229	8	zero	zero	ADJ
ejpam-5638	229	9	v∗i	v∗i	NOUN
ejpam-5638	229	10	x	x	PUNCT
ejpam-5638	229	11	for	for	ADP
ejpam-5638	229	12	a	a	DET
ejpam-5638	229	13	non	non	ADJ
ejpam-5638	229	14	-	-	ADJ
ejpam-5638	229	15	zero	zero	NUM
ejpam-5638	229	16	x.	x.	NOUN
ejpam-5638	229	17	this	this	PRON
ejpam-5638	229	18	complete	complete	VERB
ejpam-5638	229	19	the	the	DET
ejpam-5638	229	20	proof	proof	NOUN
ejpam-5638	229	21	.	.	PUNCT
ejpam-5638	230	1	theorem	theorem	ADJ
ejpam-5638	230	2	6	6	NUM
ejpam-5638	230	3	shows	show	NOUN
ejpam-5638	230	4	structured	structure	VERB
ejpam-5638	230	5	d	d	NOUN
ejpam-5638	230	6	-	-	PUNCT
ejpam-5638	230	7	stability	stability	NOUN
ejpam-5638	230	8	analysis	analysis	NOUN
ejpam-5638	230	9	of	of	ADP
ejpam-5638	230	10	the	the	DET
ejpam-5638	230	11	first	first	ADJ
ejpam-5638	230	12	order	order	NOUN
ejpam-5638	230	13	dynamical	dynamical	ADJ
ejpam-5638	230	14	model	model	NOUN
ejpam-5638	230	15	.	.	PUNCT
ejpam-5638	231	1	for	for	ADP
ejpam-5638	231	2	this	this	PRON
ejpam-5638	231	3	,	,	PUNCT
ejpam-5638	231	4	we	we	PRON
ejpam-5638	231	5	aim	aim	VERB
ejpam-5638	231	6	to	to	PART
ejpam-5638	231	7	prove	prove	VERB
ejpam-5638	231	8	that	that	SCONJ
ejpam-5638	231	9	a	a	PRON
ejpam-5638	231	10	is	be	AUX
ejpam-5638	231	11	structured	structure	VERB
ejpam-5638	232	1	d	d	ADJ
ejpam-5638	232	2	-	-	ADJ
ejpam-5638	232	3	stable	stable	ADJ
ejpam-5638	232	4	if	if	SCONJ
ejpam-5638	232	5	for	for	ADP
ejpam-5638	232	6	each	each	DET
ejpam-5638	232	7	positive	positive	ADJ
ejpam-5638	232	8	structured	structured	ADJ
ejpam-5638	232	9	diagonal	diagonal	ADJ
ejpam-5638	232	10	matrix	matrix	NOUN
ejpam-5638	232	11	d	d	NOUN
ejpam-5638	232	12	,	,	PUNCT
ejpam-5638	232	13	the	the	DET
ejpam-5638	232	14	matrix	matrix	NOUN
ejpam-5638	232	15	-	-	PUNCT
ejpam-5638	232	16	product	product	NOUN
ejpam-5638	232	17	da	da	NOUN
ejpam-5638	232	18	is	be	AUX
ejpam-5638	232	19	structured	structure	VERB
ejpam-5638	232	20	stable	stable	ADJ
ejpam-5638	232	21	,	,	PUNCT
ejpam-5638	232	22	that	that	ADV
ejpam-5638	232	23	is	is	ADV
ejpam-5638	232	24	,	,	PUNCT
ejpam-5638	232	25	the	the	DET
ejpam-5638	232	26	real	real	ADJ
ejpam-5638	232	27	part	part	NOUN
ejpam-5638	232	28	of	of	ADP
ejpam-5638	232	29	each	each	PRON
ejpam-5638	232	30	of	of	ADP
ejpam-5638	232	31	the	the	DET
ejpam-5638	232	32	eigenvalue	eigenvalue	PROPN
ejpam-5638	232	33	(	(	PUNCT
ejpam-5638	232	34	spectrum	spectrum	NOUN
ejpam-5638	232	35	)	)	PUNCT
ejpam-5638	232	36	of	of	ADP
ejpam-5638	232	37	da	da	PROPN
ejpam-5638	232	38	is	be	AUX
ejpam-5638	232	39	strictly	strictly	ADV
ejpam-5638	232	40	positive	positive	ADJ
ejpam-5638	232	41	.	.	PUNCT
ejpam-5638	233	1	theorem	theorem	ADJ
ejpam-5638	233	2	6	6	NUM
ejpam-5638	233	3	.	.	PUNCT
ejpam-5638	234	1	the	the	DET
ejpam-5638	234	2	dynamical	dynamical	ADJ
ejpam-5638	234	3	system	system	NOUN
ejpam-5638	234	4	ẋ	ẋ	PUNCT
ejpam-5638	235	1	=	=	NOUN
ejpam-5638	235	2	ax	ax	NOUN
ejpam-5638	235	3	,	,	PUNCT
ejpam-5638	235	4	x	x	SYM
ejpam-5638	235	5	∈	∈	NOUN
ejpam-5638	235	6	rn,1	rn,1	NOUN
ejpam-5638	235	7	is	be	AUX
ejpam-5638	235	8	structured	structure	VERB
ejpam-5638	235	9	d	d	ADJ
ejpam-5638	235	10	-	-	ADJ
ejpam-5638	235	11	stable	stable	ADJ
ejpam-5638	235	12	if	if	SCONJ
ejpam-5638	235	13	da	da	PROPN
ejpam-5638	235	14	is	be	AUX
ejpam-5638	235	15	structured	structure	VERB
ejpam-5638	235	16	stable	stable	ADJ
ejpam-5638	235	17	matrix	matrix	NOUN
ejpam-5638	235	18	for	for	ADP
ejpam-5638	235	19	each	each	DET
ejpam-5638	235	20	d	d	PROPN
ejpam-5638	235	21	=	=	SYM
ejpam-5638	235	22	diag(dii	diag(dii	PROPN
ejpam-5638	235	23	)	)	PUNCT
ejpam-5638	235	24	,	,	PUNCT
ejpam-5638	235	25	dii	dii	INTJ
ejpam-5638	235	26	>	>	X
ejpam-5638	235	27	0	0	NUM
ejpam-5638	235	28	,	,	PUNCT
ejpam-5638	235	29	∀	∀	VERB
ejpam-5638	236	1	i	i	NOUN
ejpam-5638	236	2	=	=	NOUN
ejpam-5638	236	3	1	1	X
ejpam-5638	236	4	:	:	PUNCT
ejpam-5638	236	5	n.	n.	NOUN
ejpam-5638	236	6	m.u.r	m.u.r	PROPN
ejpam-5638	236	7	rehman	rehman	PROPN
ejpam-5638	236	8	et	et	PROPN
ejpam-5638	236	9	al	al	PROPN
ejpam-5638	236	10	.	.	PUNCT
ejpam-5638	236	11	/	/	SYM
ejpam-5638	236	12	eur	eur	PROPN
ejpam-5638	236	13	.	.	PUNCT
ejpam-5638	237	1	j.	j.	PROPN
ejpam-5638	237	2	pure	pure	PROPN
ejpam-5638	237	3	appl	appl	PROPN
ejpam-5638	237	4	.	.	PROPN
ejpam-5638	237	5	math	math	PROPN
ejpam-5638	237	6	,	,	PUNCT
ejpam-5638	237	7	18	18	NUM
ejpam-5638	237	8	(	(	PUNCT
ejpam-5638	237	9	2	2	NUM
ejpam-5638	237	10	)	)	PUNCT
ejpam-5638	237	11	(	(	PUNCT
ejpam-5638	237	12	2025	2025	NUM
ejpam-5638	237	13	)	)	PUNCT
ejpam-5638	237	14	,	,	PUNCT
ejpam-5638	237	15	5638	5638	NUM
ejpam-5638	237	16	10	10	NUM
ejpam-5638	237	17	of	of	ADP
ejpam-5638	237	18	23	23	NUM
ejpam-5638	237	19	proof	proof	NOUN
ejpam-5638	237	20	.	.	PUNCT
ejpam-5638	238	1	we	we	PRON
ejpam-5638	238	2	aim	aim	VERB
ejpam-5638	238	3	to	to	PART
ejpam-5638	238	4	show	show	VERB
ejpam-5638	238	5	that	that	PRON
ejpam-5638	238	6	re(λi(da	re(λi(da	PUNCT
ejpam-5638	238	7	)	)	PUNCT
ejpam-5638	238	8	)	)	PUNCT
ejpam-5638	238	9	>	>	X
ejpam-5638	239	1	0,∀	0,∀	PUNCT
ejpam-5638	239	2	i	i	NOUN
ejpam-5638	239	3	=	=	NOUN
ejpam-5638	239	4	1	1	NUM
ejpam-5638	239	5	:	:	PUNCT
ejpam-5638	239	6	n.	n.	VERB
ejpam-5638	239	7	in	in	ADP
ejpam-5638	239	8	turn	turn	NOUN
ejpam-5638	239	9	this	this	PRON
ejpam-5638	239	10	will	will	AUX
ejpam-5638	239	11	imply	imply	VERB
ejpam-5638	239	12	that	that	DET
ejpam-5638	239	13	dynamical	dynamical	ADJ
ejpam-5638	239	14	system	system	NOUN
ejpam-5638	239	15	ẋ	ẋ	PUNCT
ejpam-5638	240	1	=	=	NOUN
ejpam-5638	240	2	ax	ax	NOUN
ejpam-5638	240	3	,	,	PUNCT
ejpam-5638	240	4	x	x	SYM
ejpam-5638	240	5	∈	∈	NOUN
ejpam-5638	240	6	rn,1	rn,1	NOUN
ejpam-5638	240	7	is	be	AUX
ejpam-5638	240	8	d	d	ADJ
ejpam-5638	240	9	-	-	ADJ
ejpam-5638	240	10	stable	stable	ADJ
ejpam-5638	240	11	.	.	PUNCT
ejpam-5638	241	1	the	the	DET
ejpam-5638	241	2	jordan	jordan	PROPN
ejpam-5638	241	3	canonical	canonical	ADJ
ejpam-5638	241	4	form	form	NOUN
ejpam-5638	241	5	of	of	ADP
ejpam-5638	241	6	da	da	PROPN
ejpam-5638	241	7	is	be	AUX
ejpam-5638	241	8	d̂−1dad̂	d̂−1dad̂	PROPN
ejpam-5638	241	9	=	=	SYM
ejpam-5638	241	10	j.	j.	PROPN
ejpam-5638	241	11	let	let	VERB
ejpam-5638	241	12	λi	λi	AUX
ejpam-5638	241	13	be	be	AUX
ejpam-5638	241	14	an	an	DET
ejpam-5638	241	15	eigenvalues	eigenvalue	NOUN
ejpam-5638	241	16	of	of	ADP
ejpam-5638	241	17	da	da	NOUN
ejpam-5638	241	18	,	,	PUNCT
ejpam-5638	241	19	then	then	ADV
ejpam-5638	241	20	j	j	PROPN
ejpam-5638	241	21	=	=	PUNCT
ejpam-5638	241	22	j1	j1	ADJ
ejpam-5638	241	23	0	0	NUM
ejpam-5638	241	24	0	0	NUM
ejpam-5638	242	1	jm	jm	PROPN
ejpam-5638	242	2			PROPN
ejpam-5638	242	3	,	,	PUNCT
ejpam-5638	242	4	with	with	ADP
ejpam-5638	242	5	jj	jj	PROPN
ejpam-5638	242	6	=	=	PUNCT
ejpam-5638	242	7			NOUN
ejpam-5638	242	8	λi	λi	ADP
ejpam-5638	242	9	1	1	NUM
ejpam-5638	242	10	0	0	NUM
ejpam-5638	242	11	0	0	NUM
ejpam-5638	242	12	0	0	NUM
ejpam-5638	242	13	λi	λi	CCONJ
ejpam-5638	242	14	1	1	NUM
ejpam-5638	242	15	0	0	NUM
ejpam-5638	242	16	0	0	NUM
ejpam-5638	242	17	λi	λi	NOUN
ejpam-5638	242	18	0	0	NUM
ejpam-5638	242	19	1	1	NUM
ejpam-5638	242	20	0	0	NUM
ejpam-5638	242	21	0	0	NUM
ejpam-5638	242	22	0	0	NUM
ejpam-5638	242	23	λi	λi	ADP
ejpam-5638	242	24			PROPN
ejpam-5638	242	25	.	.	PUNCT
ejpam-5638	243	1	let	let	VERB
ejpam-5638	243	2	x	x	SYM
ejpam-5638	243	3	=	=	SYM
ejpam-5638	243	4	d̂y	d̂y	NOUN
ejpam-5638	243	5	,	,	PUNCT
ejpam-5638	243	6	then	then	ADV
ejpam-5638	243	7	ẋ	ẋ	PUNCT
ejpam-5638	244	1	=	=	NOUN
ejpam-5638	244	2	ax	ax	NOUN
ejpam-5638	244	3	,	,	PUNCT
ejpam-5638	244	4	x	x	SYM
ejpam-5638	244	5	∈	∈	NOUN
ejpam-5638	244	6	rn,1	rn,1	NOUN
ejpam-5638	244	7	becomes	become	VERB
ejpam-5638	244	8	ẏ	ẏ	PROPN
ejpam-5638	244	9	=	=	SYM
ejpam-5638	244	10	jy	jy	PROPN
ejpam-5638	244	11	.	.	PROPN
ejpam-5638	245	1	for	for	ADP
ejpam-5638	245	2	y0	y0	PROPN
ejpam-5638	245	3	being	be	AUX
ejpam-5638	245	4	an	an	DET
ejpam-5638	245	5	initial	initial	ADJ
ejpam-5638	245	6	condition	condition	NOUN
ejpam-5638	245	7	,	,	PUNCT
ejpam-5638	245	8	we	we	PRON
ejpam-5638	245	9	have	have	VERB
ejpam-5638	245	10	that	that	PRON
ejpam-5638	245	11	,	,	PUNCT
ejpam-5638	245	12	y(t	y(t	NUM
ejpam-5638	245	13	)	)	PUNCT
ejpam-5638	246	1	=	=	SYM
ejpam-5638	246	2	ejty0	ejty0	PROPN
ejpam-5638	246	3	.	.	PUNCT
ejpam-5638	247	1	now	now	ADV
ejpam-5638	247	2	,	,	PUNCT
ejpam-5638	247	3	ej̇t	ej̇t	ADV
ejpam-5638	247	4	=	=	SYM
ejpam-5638	247	5	ej1	ej1	NOUN
ejpam-5638	247	6	t	t	NOUN
ejpam-5638	247	7	0	0	NUM
ejpam-5638	247	8	0	0	NUM
ejpam-5638	247	9	ejmt	ejmt	ADJ
ejpam-5638	247	10			PROPN
ejpam-5638	247	11	.	.	PUNCT
ejpam-5638	248	1	the	the	DET
ejpam-5638	248	2	jordan	jordan	PROPN
ejpam-5638	248	3	blocks	blocks	PROPN
ejpam-5638	248	4	jj	jj	PROPN
ejpam-5638	248	5	,	,	PUNCT
ejpam-5638	248	6	j	j	PROPN
ejpam-5638	248	7	=	=	NOUN
ejpam-5638	248	8	1	1	NUM
ejpam-5638	248	9	:	:	PUNCT
ejpam-5638	248	10	m	m	VERB
ejpam-5638	248	11	can	can	AUX
ejpam-5638	248	12	be	be	AUX
ejpam-5638	248	13	written	write	VERB
ejpam-5638	248	14	as	as	ADP
ejpam-5638	248	15	jj	jj	PROPN
ejpam-5638	248	16	=	=	PUNCT
ejpam-5638	248	17	λiiµi	λiiµi	PROPN
ejpam-5638	248	18	+	+	NOUN
ejpam-5638	248	19	mµi	mµi	NOUN
ejpam-5638	248	20	,	,	PUNCT
ejpam-5638	248	21	where	where	SCONJ
ejpam-5638	248	22	mµi	mµi	NOUN
ejpam-5638	248	23	=	=	SYM
ejpam-5638	248	24			VERB
ejpam-5638	248	25	0	0	NUM
ejpam-5638	249	1	1	1	NUM
ejpam-5638	249	2	0	0	NUM
ejpam-5638	249	3	0	0	NUM
ejpam-5638	249	4	0	0	NUM
ejpam-5638	249	5	0	0	NUM
ejpam-5638	249	6	1	1	NUM
ejpam-5638	249	7	0	0	NUM
ejpam-5638	249	8	0	0	NUM
ejpam-5638	249	9	0	0	NUM
ejpam-5638	249	10	0	0	NUM
ejpam-5638	249	11	1	1	NUM
ejpam-5638	249	12	0	0	NUM
ejpam-5638	249	13	0	0	NUM
ejpam-5638	249	14	0	0	NUM
ejpam-5638	249	15	0	0	NUM
ejpam-5638	249	16			PROPN
ejpam-5638	249	17	,	,	PUNCT
ejpam-5638	249	18	with	with	ADP
ejpam-5638	249	19	iµi	iµi	NOUN
ejpam-5638	249	20	,	,	PUNCT
ejpam-5638	249	21	an	an	DET
ejpam-5638	249	22	identity	identity	NOUN
ejpam-5638	249	23	matrix	matrix	NOUN
ejpam-5638	249	24	with	with	ADP
ejpam-5638	249	25	order	order	NOUN
ejpam-5638	249	26	µi	µi	ADP
ejpam-5638	249	27	,	,	PUNCT
ejpam-5638	249	28	i	i	PRON
ejpam-5638	249	29	=	=	NOUN
ejpam-5638	249	30	1	1	X
ejpam-5638	249	31	:	:	PUNCT
ejpam-5638	249	32	m.	m.	NOUN
ejpam-5638	249	33	since	since	ADV
ejpam-5638	249	34	,	,	PUNCT
ejpam-5638	249	35	eλiiµi	eλiiµi	PROPN
ejpam-5638	249	36	t	t	NOUN
ejpam-5638	249	37	=	=	PUNCT
ejpam-5638	249	38	eλitiµi	eλitiµi	NOUN
ejpam-5638	249	39	,	,	PUNCT
ejpam-5638	249	40	which	which	PRON
ejpam-5638	249	41	can	can	AUX
ejpam-5638	249	42	be	be	AUX
ejpam-5638	249	43	rewritten	rewrite	VERB
ejpam-5638	249	44	as	as	ADP
ejpam-5638	249	45	ejit	ejit	NOUN
ejpam-5638	249	46	=	=	PUNCT
ejpam-5638	249	47	eλitemµi	eλitemµi	NOUN
ejpam-5638	249	48	t.	t.	PROPN
ejpam-5638	249	49	thus	thus	ADV
ejpam-5638	249	50	,	,	PUNCT
ejpam-5638	249	51	ej̇it	ej̇it	PROPN
ejpam-5638	249	52	=	=	SYM
ejpam-5638	249	53	ere(λi)teimg(λi)tr	ere(λi)teimg(λi)tr	PROPN
ejpam-5638	249	54	,	,	PUNCT
ejpam-5638	249	55	where	where	SCONJ
ejpam-5638	249	56	r	r	NOUN
ejpam-5638	249	57	=	=	PUNCT
ejpam-5638	249	58			ADJ
ejpam-5638	249	59	1	1	NUM
ejpam-5638	249	60	t	t	NOUN
ejpam-5638	249	61	t2	t2	NOUN
ejpam-5638	249	62	2	2	NUM
ejpam-5638	249	63	!	!	PUNCT
ejpam-5638	250	1	tµi−1	tµi−1	PROPN
ejpam-5638	250	2	(	(	PUNCT
ejpam-5638	250	3	µi−1	µi−1	PROPN
ejpam-5638	250	4	)	)	PUNCT
ejpam-5638	250	5	t2	t2	NOUN
ejpam-5638	250	6	2	2	NUM
ejpam-5638	250	7	!	!	PUNCT
ejpam-5638	250	8	t	t	PROPN
ejpam-5638	250	9	1	1	NUM
ejpam-5638	250	10			PROPN
ejpam-5638	250	11	.	.	PUNCT
ejpam-5638	251	1	m.u.r	m.u.r	PROPN
ejpam-5638	251	2	rehman	rehman	PROPN
ejpam-5638	251	3	et	et	PROPN
ejpam-5638	251	4	al	al	PROPN
ejpam-5638	251	5	.	.	PUNCT
ejpam-5638	251	6	/	/	SYM
ejpam-5638	251	7	eur	eur	PROPN
ejpam-5638	251	8	.	.	PUNCT
ejpam-5638	252	1	j.	j.	PROPN
ejpam-5638	252	2	pure	pure	PROPN
ejpam-5638	252	3	appl	appl	PROPN
ejpam-5638	252	4	.	.	PROPN
ejpam-5638	252	5	math	math	PROPN
ejpam-5638	252	6	,	,	PUNCT
ejpam-5638	252	7	18	18	NUM
ejpam-5638	252	8	(	(	PUNCT
ejpam-5638	252	9	2	2	NUM
ejpam-5638	252	10	)	)	PUNCT
ejpam-5638	252	11	(	(	PUNCT
ejpam-5638	252	12	2025	2025	NUM
ejpam-5638	252	13	)	)	PUNCT
ejpam-5638	252	14	,	,	PUNCT
ejpam-5638	252	15	5638	5638	NUM
ejpam-5638	252	16	11	11	NUM
ejpam-5638	252	17	of	of	ADP
ejpam-5638	252	18	23	23	NUM
ejpam-5638	252	19	define	define	NOUN
ejpam-5638	252	20	βi	βi	NOUN
ejpam-5638	252	21	=	=	PUNCT
ejpam-5638	252	22	∑	∑	PUNCT
ejpam-5638	252	23	i	i	PRON
ejpam-5638	252	24	µi	µi	VERB
ejpam-5638	252	25	;	;	PUNCT
ejpam-5638	252	26	β̂i	β̂i	PUNCT
ejpam-5638	252	27	=	=	SYM
ejpam-5638	252	28	{	{	PUNCT
ejpam-5638	252	29	βi−1	βi−1	PROPN
ejpam-5638	252	30	+	+	PROPN
ejpam-5638	252	31	t	t	PROPN
ejpam-5638	252	32	,	,	PUNCT
ejpam-5638	252	33	.	.	PUNCT
ejpam-5638	252	34	.	.	PUNCT
ejpam-5638	252	35	.	.	PUNCT
ejpam-5638	253	1	,	,	PUNCT
ejpam-5638	253	2	βi	βi	X
ejpam-5638	253	3	}	}	PUNCT
ejpam-5638	253	4	,	,	PUNCT
ejpam-5638	253	5	then	then	ADV
ejpam-5638	253	6	we	we	PRON
ejpam-5638	253	7	have	have	VERB
ejpam-5638	253	8	that	that	DET
ejpam-5638	253	9	yk(t	yk(t	NUM
ejpam-5638	253	10	)	)	PUNCT
ejpam-5638	253	11	=	=	PUNCT
ejpam-5638	254	1	ere(λi)teimg(λi)t	ere(λi)teimg(λi)t	NOUN
ejpam-5638	254	2	∑	∑	PUNCT
ejpam-5638	254	3	q̂	q̂	X
ejpam-5638	254	4	mp̃k	mp̃k	PROPN
ejpam-5638	254	5	q̂(µi	q̂(µi	PROPN
ejpam-5638	254	6	,	,	PUNCT
ejpam-5638	254	7	t)y	t)y	ADJ
ejpam-5638	254	8	◦	◦	NOUN
ejpam-5638	254	9	q̂	q̂	NUM
ejpam-5638	254	10	where	where	SCONJ
ejpam-5638	254	11	p̃k	p̃k	NOUN
ejpam-5638	254	12	=	=	SYM
ejpam-5638	254	13	k	k	PROPN
ejpam-5638	254	14	−	−	PROPN
ejpam-5638	254	15	βi−1	βi−1	PROPN
ejpam-5638	254	16	.	.	PUNCT
ejpam-5638	255	1	consider	consider	VERB
ejpam-5638	255	2	that	that	DET
ejpam-5638	255	3	µ	µ	X
ejpam-5638	255	4	:	:	PUNCT
ejpam-5638	255	5	=	=	SYM
ejpam-5638	255	6	maxµi	maxµi	NOUN
ejpam-5638	255	7	,	,	PUNCT
ejpam-5638	255	8	i	i	PRON
ejpam-5638	255	9	=	=	NOUN
ejpam-5638	255	10	1	1	NUM
ejpam-5638	255	11	:	:	PUNCT
ejpam-5638	255	12	m	m	X
ejpam-5638	255	13	,	,	PUNCT
ejpam-5638	255	14	then	then	ADV
ejpam-5638	255	15	we	we	PRON
ejpam-5638	255	16	have	have	VERB
ejpam-5638	255	17	that	that	DET
ejpam-5638	255	18	yk(t	yk(t	NUM
ejpam-5638	255	19	)	)	PUNCT
ejpam-5638	255	20	=	=	PUNCT
ejpam-5638	255	21	ere(λi)teimg(λi)ttµ	ere(λi)teimg(λi)ttµ	NOUN
ejpam-5638	255	22	∑	∑	PUNCT
ejpam-5638	255	23	q̂	q̂	X
ejpam-5638	255	24	mp̃k	mp̃k	PROPN
ejpam-5638	255	25	q̂(µi	q̂(µi	PROPN
ejpam-5638	255	26	,	,	PUNCT
ejpam-5638	255	27	t)t	t)t	X
ejpam-5638	255	28	−µy	−µy	PROPN
ejpam-5638	255	29	◦	◦	NOUN
ejpam-5638	255	30	q̂.	q̂.	NOUN
ejpam-5638	255	31	thus	thus	ADV
ejpam-5638	255	32	,	,	PUNCT
ejpam-5638	255	33	|yk(t)|	|yk(t)|	ADJ
ejpam-5638	255	34	=	=	SYM
ejpam-5638	255	35	ere(λi)ttµ|	ere(λi)ttµ|	NOUN
ejpam-5638	255	36	∑	∑	PUNCT
ejpam-5638	255	37	q̂	q̂	X
ejpam-5638	255	38	mp̃k	mp̃k	PROPN
ejpam-5638	255	39	q̂(µi	q̂(µi	PROPN
ejpam-5638	255	40	,	,	PUNCT
ejpam-5638	255	41	t)t	t)t	X
ejpam-5638	255	42	−µy	−µy	PROPN
ejpam-5638	255	43	◦	◦	NOUN
ejpam-5638	255	44	q̂|	q̂|	NOUN
ejpam-5638	255	45	.	.	PUNCT
ejpam-5638	256	1	for	for	ADP
ejpam-5638	256	2	t	t	PROPN
ejpam-5638	256	3	→	→	SYM
ejpam-5638	256	4	∞	∞	PROPN
ejpam-5638	256	5	,	,	PUNCT
ejpam-5638	256	6	|	|	ADV
ejpam-5638	256	7	∑̂	∑̂	VERB
ejpam-5638	256	8	q	q	NOUN
ejpam-5638	256	9	mp̃k	mp̃k	PROPN
ejpam-5638	256	10	q̂(µi	q̂(µi	PROPN
ejpam-5638	256	11	,	,	PUNCT
ejpam-5638	256	12	t)t	t)t	X
ejpam-5638	256	13	−µy	−µy	PROPN
ejpam-5638	256	14	◦	◦	NOUN
ejpam-5638	256	15	q̂|	q̂|	PROPN
ejpam-5638	256	16	<	<	X
ejpam-5638	256	17	ϵ	ϵ	X
ejpam-5638	256	18	,	,	PUNCT
ejpam-5638	256	19	ϵ	ϵ	X
ejpam-5638	256	20	>	>	X
ejpam-5638	256	21	0	0	X
ejpam-5638	256	22	.	.	PUNCT
ejpam-5638	257	1	since	since	ADV
ejpam-5638	257	2	,	,	PUNCT
ejpam-5638	257	3	re(λi	re(λi	PROPN
ejpam-5638	257	4	)	)	PUNCT
ejpam-5638	257	5	>	>	X
ejpam-5638	257	6	0	0	NUM
ejpam-5638	257	7	,	,	PUNCT
ejpam-5638	257	8	∀i	∀i	NOUN
ejpam-5638	257	9	,	,	PUNCT
ejpam-5638	257	10	then	then	ADV
ejpam-5638	257	11	we	we	PRON
ejpam-5638	257	12	have	have	VERB
ejpam-5638	257	13	that	that	DET
ejpam-5638	257	14	e−re(λi)t	e−re(λi)t	PROPN
ejpam-5638	257	15	>	>	X
ejpam-5638	257	16	tµ	tµ	NOUN
ejpam-5638	257	17	,	,	PUNCT
ejpam-5638	257	18	i	i	PRON
ejpam-5638	257	19	=	=	NOUN
ejpam-5638	257	20	1	1	NUM
ejpam-5638	257	21	:	:	PUNCT
ejpam-5638	257	22	m.	m.	NOUN
ejpam-5638	258	1	this	this	PRON
ejpam-5638	258	2	further	far	ADV
ejpam-5638	258	3	implies	imply	VERB
ejpam-5638	258	4	that	that	SCONJ
ejpam-5638	258	5	yk(t	yk(t	NUM
ejpam-5638	258	6	)	)	PUNCT
ejpam-5638	258	7	→	→	SYM
ejpam-5638	258	8	0	0	NUM
ejpam-5638	258	9	as	as	ADP
ejpam-5638	258	10	t	t	PROPN
ejpam-5638	258	11	→	→	SYM
ejpam-5638	258	12	∞.	∞.	PROPN
ejpam-5638	258	13	further	far	ADV
ejpam-5638	258	14	,	,	PUNCT
ejpam-5638	258	15	consider	consider	VERB
ejpam-5638	258	16	that	that	PRON
ejpam-5638	258	17	λi	λi	ADP
ejpam-5638	258	18	◦	◦	NOUN
ejpam-5638	258	19	=	=	SYM
ejpam-5638	258	20	re(λi	re(λi	NOUN
ejpam-5638	258	21	◦	◦	NOUN
ejpam-5638	258	22	)	)	PUNCT
ejpam-5638	258	23	>	>	X
ejpam-5638	259	1	0	0	X
ejpam-5638	259	2	.	.	PUNCT
ejpam-5638	260	1	the	the	DET
ejpam-5638	260	2	initial	initial	ADJ
ejpam-5638	260	3	state	state	NOUN
ejpam-5638	260	4	ŷ0	ŷ0	NOUN
ejpam-5638	260	5	so	so	SCONJ
ejpam-5638	260	6	that	that	PRON
ejpam-5638	260	7	ŷ	ŷ	NUM
ejpam-5638	260	8	◦	◦	NOUN
ejpam-5638	260	9	q̂	q̂	PUNCT
ejpam-5638	260	10	=	=	SYM
ejpam-5638	260	11	α	α	X
ejpam-5638	260	12	>	>	X
ejpam-5638	260	13	0	0	NUM
ejpam-5638	260	14	,	,	PUNCT
ejpam-5638	260	15	ŷ	ŷ	X
ejpam-5638	260	16	◦	◦	NOUN
ejpam-5638	260	17	γ	γ	X
ejpam-5638	260	18	=	=	SYM
ejpam-5638	260	19	0	0	NUM
ejpam-5638	260	20	,	,	PUNCT
ejpam-5638	260	21	γ	γ	PROPN
ejpam-5638	260	22	̸=	̸=	PROPN
ejpam-5638	260	23	q̂.	q̂.	NOUN
ejpam-5638	260	24	if	if	SCONJ
ejpam-5638	260	25	re(λi	re(λi	NOUN
ejpam-5638	260	26	◦	◦	NOUN
ejpam-5638	260	27	)	)	PUNCT
ejpam-5638	260	28	>	>	X
ejpam-5638	260	29	0	0	X
ejpam-5638	260	30	.	.	PUNCT
ejpam-5638	261	1	then	then	ADV
ejpam-5638	261	2	|yk(t)|	|yk(t)|	ADJ
ejpam-5638	261	3	=	=	NOUN
ejpam-5638	261	4	ere(λi	ere(λi	PRON
ejpam-5638	261	5	◦	◦	NOUN
ejpam-5638	261	6	)t|	)t|	PUNCT
ejpam-5638	261	7	∑	∑	PUNCT
ejpam-5638	261	8	q̂	q̂	X
ejpam-5638	261	9	mp̃k	mp̃k	PROPN
ejpam-5638	261	10	q̂(µi	q̂(µi	PROPN
ejpam-5638	261	11	◦	◦	NOUN
ejpam-5638	261	12	,	,	PUNCT
ejpam-5638	261	13	t)ŷ	t)ŷ	PROPN
ejpam-5638	261	14	◦	◦	NOUN
ejpam-5638	261	15	q̂|	q̂|	PROPN
ejpam-5638	261	16	→	→	SYM
ejpam-5638	261	17	∞	∞	PROPN
ejpam-5638	261	18	,	,	PUNCT
ejpam-5638	261	19	as	as	ADP
ejpam-5638	261	20	t	t	PROPN
ejpam-5638	261	21	→	→	SYM
ejpam-5638	261	22	0	0	NUM
ejpam-5638	261	23	.	.	PUNCT
ejpam-5638	262	1	this	this	PRON
ejpam-5638	262	2	ensure	ensure	VERB
ejpam-5638	262	3	that	that	SCONJ
ejpam-5638	262	4	|yk(t)|	|yk(t)|	ADJ
ejpam-5638	262	5	=	=	SYM
ejpam-5638	262	6	ŷ	ŷ	NUM
ejpam-5638	262	7	◦	◦	NOUN
ejpam-5638	262	8	k	k	NOUN
ejpam-5638	262	9	=	=	PUNCT
ejpam-5638	262	10	α	α	X
ejpam-5638	262	11	>	>	X
ejpam-5638	262	12	0	0	PROPN
ejpam-5638	262	13	.	.	PUNCT
ejpam-5638	263	1	thus	thus	ADV
ejpam-5638	263	2	,	,	PUNCT
ejpam-5638	263	3	this	this	PRON
ejpam-5638	263	4	concludes	conclude	VERB
ejpam-5638	263	5	that	that	SCONJ
ejpam-5638	263	6	re(λi	re(λi	VERB
ejpam-5638	263	7	)	)	PUNCT
ejpam-5638	263	8	>	>	X
ejpam-5638	263	9	0	0	X
ejpam-5638	263	10	.	.	PUNCT
ejpam-5638	263	11	theorem	theorem	VERB
ejpam-5638	263	12	7	7	NUM
ejpam-5638	263	13	.	.	PUNCT
ejpam-5638	264	1	the	the	DET
ejpam-5638	264	2	linear	linear	PROPN
ejpam-5638	264	3	dynamical	dynamical	ADJ
ejpam-5638	264	4	model	model	NOUN
ejpam-5638	264	5	ẋ	ẋ	PROPN
ejpam-5638	265	1	=	=	NOUN
ejpam-5638	265	2	ax	ax	NOUN
ejpam-5638	265	3	,	,	PUNCT
ejpam-5638	265	4	x	x	SYM
ejpam-5638	265	5	∈	∈	NOUN
ejpam-5638	265	6	rn,1	rn,1	NOUN
ejpam-5638	265	7	is	be	AUX
ejpam-5638	265	8	structured	structure	VERB
ejpam-5638	265	9	d	d	ADJ
ejpam-5638	265	10	-	-	ADJ
ejpam-5638	265	11	stable	stable	ADJ
ejpam-5638	265	12	if	if	SCONJ
ejpam-5638	265	13	λj(a+	λj(a+	PROPN
ejpam-5638	265	14	i	i	PROPN
ejpam-5638	265	15	d	d	PROPN
ejpam-5638	265	16	)	)	PUNCT
ejpam-5638	265	17	̸=	̸=	PROPN
ejpam-5638	265	18	0	0	NUM
ejpam-5638	265	19	,	,	PUNCT
ejpam-5638	265	20	d	d	NOUN
ejpam-5638	265	21	=	=	SYM
ejpam-5638	265	22	diag(dii	diag(dii	PROPN
ejpam-5638	265	23	)	)	PUNCT
ejpam-5638	265	24	>	>	X
ejpam-5638	265	25	0	0	NUM
ejpam-5638	265	26	,	,	PUNCT
ejpam-5638	265	27	∀	∀	X
ejpam-5638	265	28	j	j	NOUN
ejpam-5638	265	29	=	=	NOUN
ejpam-5638	265	30	1	1	NUM
ejpam-5638	265	31	:	:	PUNCT
ejpam-5638	265	32	n.	n.	NOUN
ejpam-5638	265	33	proof	proof	NOUN
ejpam-5638	265	34	.	.	PUNCT
ejpam-5638	266	1	consider	consider	VERB
ejpam-5638	266	2	that	that	SCONJ
ejpam-5638	266	3	a	a	PRON
ejpam-5638	266	4	in	in	ADP
ejpam-5638	266	5	ẋ	ẋ	PROPN
ejpam-5638	267	1	=	=	NOUN
ejpam-5638	267	2	ax	ax	NOUN
ejpam-5638	267	3	is	be	AUX
ejpam-5638	267	4	d	d	ADJ
ejpam-5638	267	5	-	-	ADJ
ejpam-5638	267	6	stable	stable	ADJ
ejpam-5638	267	7	,	,	PUNCT
ejpam-5638	267	8	means	mean	VERB
ejpam-5638	267	9	that	that	SCONJ
ejpam-5638	267	10	,	,	PUNCT
ejpam-5638	267	11	for	for	ADP
ejpam-5638	267	12	all	all	DET
ejpam-5638	267	13	positive	positive	ADJ
ejpam-5638	267	14	diagonal	diagonal	ADJ
ejpam-5638	267	15	matrices	matrix	NOUN
ejpam-5638	267	16	p	p	NOUN
ejpam-5638	267	17	,	,	PUNCT
ejpam-5638	267	18	re(λj(pa	re(λj(pa	NOUN
ejpam-5638	267	19	)	)	PUNCT
ejpam-5638	267	20	)	)	PUNCT
ejpam-5638	267	21	>	>	PUNCT
ejpam-5638	268	1	0,∀j	0,∀j	X
ejpam-5638	268	2	.	.	PUNCT
ejpam-5638	269	1	the	the	DET
ejpam-5638	269	2	matrix	matrix	NOUN
ejpam-5638	269	3	-	-	PUNCT
ejpam-5638	269	4	product	product	NOUN
ejpam-5638	269	5	pa	pa	NOUN
ejpam-5638	269	6	does	do	AUX
ejpam-5638	269	7	not	not	PART
ejpam-5638	269	8	have	have	VERB
ejpam-5638	269	9	i	i	PRON
ejpam-5638	269	10	=	=	PUNCT
ejpam-5638	269	11	√	√	NUM
ejpam-5638	270	1	−1	−1	NOUN
ejpam-5638	271	1	as	as	SCONJ
ejpam-5638	271	2	it	it	PRON
ejpam-5638	271	3	’s	’	VERB
ejpam-5638	271	4	one	one	NUM
ejpam-5638	271	5	of	of	ADP
ejpam-5638	271	6	eigenvalue	eigenvalue	PROPN
ejpam-5638	271	7	.	.	PUNCT
ejpam-5638	272	1	also	also	ADV
ejpam-5638	272	2	,	,	PUNCT
ejpam-5638	272	3	we	we	PRON
ejpam-5638	272	4	have	have	VERB
ejpam-5638	272	5	that	that	PRON
ejpam-5638	272	6	a+	a+	PUNCT
ejpam-5638	272	7	i	i	PROPN
ejpam-5638	272	8	d	d	NOUN
ejpam-5638	272	9	=	=	SYM
ejpam-5638	272	10	d(d−1a+	d(d−1a+	ADJ
ejpam-5638	272	11	iin	iin	NOUN
ejpam-5638	272	12	)	)	PUNCT
ejpam-5638	272	13	,	,	PUNCT
ejpam-5638	272	14	such	such	ADJ
ejpam-5638	272	15	that	that	SCONJ
ejpam-5638	272	16	λj(d(d−1a+	λj(d(d−1a+	PROPN
ejpam-5638	272	17	iin	iin	NOUN
ejpam-5638	272	18	)	)	PUNCT
ejpam-5638	272	19	)	)	PUNCT
ejpam-5638	273	1	̸=	̸=	PROPN
ejpam-5638	273	2	0	0	NUM
ejpam-5638	273	3	,	,	PUNCT
ejpam-5638	273	4	∀j	∀j	NOUN
ejpam-5638	273	5	,	,	PUNCT
ejpam-5638	273	6	where	where	SCONJ
ejpam-5638	273	7	in	in	ADP
ejpam-5638	273	8	being	be	AUX
ejpam-5638	273	9	n×	n×	PRON
ejpam-5638	273	10	n	n	PRON
ejpam-5638	273	11	identity	identity	NOUN
ejpam-5638	273	12	matrix	matrix	NOUN
ejpam-5638	273	13	.	.	PUNCT
ejpam-5638	274	1	on	on	ADP
ejpam-5638	274	2	the	the	DET
ejpam-5638	274	3	other	other	ADJ
ejpam-5638	274	4	hand	hand	NOUN
ejpam-5638	274	5	,	,	PUNCT
ejpam-5638	274	6	let	let	VERB
ejpam-5638	274	7	a	a	PRON
ejpam-5638	274	8	is	be	AUX
ejpam-5638	274	9	not	not	PART
ejpam-5638	274	10	structured	structure	VERB
ejpam-5638	274	11	d	d	ADJ
ejpam-5638	274	12	-	-	ADJ
ejpam-5638	274	13	stable	stable	ADJ
ejpam-5638	274	14	.	.	PUNCT
ejpam-5638	275	1	this	this	DET
ejpam-5638	275	2	further	far	ADV
ejpam-5638	275	3	implies	imply	VERB
ejpam-5638	275	4	that	that	SCONJ
ejpam-5638	275	5	re(λj(pa	re(λj(pa	NOUN
ejpam-5638	275	6	)	)	PUNCT
ejpam-5638	275	7	)	)	PUNCT
ejpam-5638	275	8	≤	≤	NUM
ejpam-5638	275	9	0,∀j	0,∀j	NUM
ejpam-5638	275	10	.	.	PUNCT
ejpam-5638	276	1	then	then	ADV
ejpam-5638	276	2	for	for	ADP
ejpam-5638	276	3	a	a	DET
ejpam-5638	276	4	positive	positive	ADJ
ejpam-5638	276	5	structured	structured	ADJ
ejpam-5638	276	6	diagonal	diagonal	ADJ
ejpam-5638	276	7	matrix	matrix	NOUN
ejpam-5638	276	8	d̂	d̂	NOUN
ejpam-5638	276	9	,	,	PUNCT
ejpam-5638	276	10	d̂pa	d̂pa	PROPN
ejpam-5638	276	11	is	be	AUX
ejpam-5638	276	12	not	not	PART
ejpam-5638	276	13	structured	structure	VERB
ejpam-5638	276	14	stable	stable	ADJ
ejpam-5638	276	15	but	but	CCONJ
ejpam-5638	276	16	d̂a	d̂a	NOUN
ejpam-5638	276	17	is	be	AUX
ejpam-5638	276	18	stable	stable	ADJ
ejpam-5638	276	19	,	,	PUNCT
ejpam-5638	276	20	that	that	ADV
ejpam-5638	276	21	is	is	ADV
ejpam-5638	276	22	,	,	PUNCT
ejpam-5638	276	23	re(λj(d̂a	re(λj(d̂a	PROPN
ejpam-5638	276	24	)	)	PUNCT
ejpam-5638	276	25	)	)	PUNCT
ejpam-5638	277	1	>	>	X
ejpam-5638	278	1	0,∀j	0,∀j	X
ejpam-5638	278	2	.	.	PUNCT
ejpam-5638	279	1	this	this	PRON
ejpam-5638	279	2	follows	follow	VERB
ejpam-5638	279	3	form	form	VERB
ejpam-5638	279	4	the	the	DET
ejpam-5638	279	5	fact	fact	NOUN
ejpam-5638	279	6	that	that	SCONJ
ejpam-5638	279	7	for	for	ADP
ejpam-5638	279	8	0	0	NUM
ejpam-5638	279	9	<	<	X
ejpam-5638	279	10	t	t	X
ejpam-5638	279	11	≤	≤	NUM
ejpam-5638	279	12	1	1	NUM
ejpam-5638	279	13	,	,	PUNCT
ejpam-5638	279	14	and	and	CCONJ
ejpam-5638	279	15	for	for	ADP
ejpam-5638	279	16	some	some	DET
ejpam-5638	279	17	β	β	X
ejpam-5638	279	18	>	>	X
ejpam-5638	279	19	0	0	NUM
ejpam-5638	279	20	,	,	PUNCT
ejpam-5638	279	21	i	i	PRON
ejpam-5638	279	22	=	=	PUNCT
ejpam-5638	279	23	√	√	NUM
ejpam-5638	280	1	−1	−1	NOUN
ejpam-5638	280	2	is	be	AUX
ejpam-5638	280	3	an	an	DET
ejpam-5638	280	4	eigenvalue	eigenvalue	NOUN
ejpam-5638	280	5	of	of	ADP
ejpam-5638	280	6	1	1	NUM
ejpam-5638	280	7	β	β	X
ejpam-5638	280	8	(	(	PUNCT
ejpam-5638	280	9	tp	tp	X
ejpam-5638	280	10	+	+	X
ejpam-5638	280	11	(	(	PUNCT
ejpam-5638	280	12	1−	1−	NUM
ejpam-5638	280	13	t)in)d̂a	t)in)d̂a	NOUN
ejpam-5638	280	14	,	,	PUNCT
ejpam-5638	280	15	where	where	SCONJ
ejpam-5638	280	16	d	d	NOUN
ejpam-5638	280	17	=	=	SYM
ejpam-5638	280	18	β(tp	β(tp	PROPN
ejpam-5638	280	19	+	+	CCONJ
ejpam-5638	280	20	(	(	PUNCT
ejpam-5638	280	21	1−	1−	NUM
ejpam-5638	280	22	t)in	t)in	PROPN
ejpam-5638	280	23	)	)	PUNCT
ejpam-5638	280	24	−1	−1	NOUN
ejpam-5638	280	25	.	.	PUNCT
ejpam-5638	281	1	m.u.r	m.u.r	PROPN
ejpam-5638	282	1	rehman	rehman	PROPN
ejpam-5638	282	2	et	et	PROPN
ejpam-5638	282	3	al	al	PROPN
ejpam-5638	282	4	.	.	PUNCT
ejpam-5638	282	5	/	/	SYM
ejpam-5638	282	6	eur	eur	PROPN
ejpam-5638	282	7	.	.	PUNCT
ejpam-5638	283	1	j.	j.	PROPN
ejpam-5638	283	2	pure	pure	PROPN
ejpam-5638	283	3	appl	appl	PROPN
ejpam-5638	283	4	.	.	PROPN
ejpam-5638	283	5	math	math	PROPN
ejpam-5638	283	6	,	,	PUNCT
ejpam-5638	283	7	18	18	NUM
ejpam-5638	283	8	(	(	PUNCT
ejpam-5638	283	9	2	2	NUM
ejpam-5638	283	10	)	)	PUNCT
ejpam-5638	283	11	(	(	PUNCT
ejpam-5638	283	12	2025	2025	NUM
ejpam-5638	283	13	)	)	PUNCT
ejpam-5638	283	14	,	,	PUNCT
ejpam-5638	283	15	5638	5638	NUM
ejpam-5638	283	16	12	12	NUM
ejpam-5638	283	17	of	of	ADP
ejpam-5638	283	18	23	23	NUM
ejpam-5638	283	19	theorem	theorem	NOUN
ejpam-5638	283	20	8	8	NUM
ejpam-5638	283	21	.	.	PUNCT
ejpam-5638	284	1	the	the	DET
ejpam-5638	284	2	dynamical	dynamical	ADJ
ejpam-5638	284	3	system	system	NOUN
ejpam-5638	284	4	ẋ	ẋ	PUNCT
ejpam-5638	285	1	=	=	NOUN
ejpam-5638	285	2	ax	ax	NOUN
ejpam-5638	285	3	,	,	PUNCT
ejpam-5638	285	4	x	x	SYM
ejpam-5638	285	5	∈	∈	NOUN
ejpam-5638	285	6	rn,1	rn,1	NOUN
ejpam-5638	285	7	is	be	AUX
ejpam-5638	285	8	d	d	ADJ
ejpam-5638	285	9	-	-	ADJ
ejpam-5638	285	10	stable	stable	ADJ
ejpam-5638	285	11	if	if	SCONJ
ejpam-5638	285	12	n∏	n∏	NOUN
ejpam-5638	285	13	k=1	k=1	PROPN
ejpam-5638	286	1	(	(	PUNCT
ejpam-5638	286	2	λk(ad	λk(ad	PROPN
ejpam-5638	286	3	−1	−1	NOUN
ejpam-5638	286	4	+	+	NOUN
ejpam-5638	286	5	da−1	da−1	NOUN
ejpam-5638	286	6	)	)	PUNCT
ejpam-5638	286	7	)	)	PUNCT
ejpam-5638	286	8	>	>	X
ejpam-5638	286	9	0	0	NUM
ejpam-5638	286	10	,	,	PUNCT
ejpam-5638	286	11	∀k	∀k	X
ejpam-5638	286	12	.	.	PUNCT
ejpam-5638	287	1	proof	proof	NOUN
ejpam-5638	287	2	.	.	PUNCT
ejpam-5638	288	1	consider	consider	VERB
ejpam-5638	288	2	the	the	DET
ejpam-5638	288	3	partitioned	partition	VERB
ejpam-5638	288	4	matrix	matrix	NOUN
ejpam-5638	288	5	(	(	PUNCT
ejpam-5638	288	6	a	a	DET
ejpam-5638	288	7	−d	−d	PROPN
ejpam-5638	288	8	d	d	NOUN
ejpam-5638	288	9	a	a	PRON
ejpam-5638	288	10	)	)	PUNCT
ejpam-5638	288	11	.	.	PUNCT
ejpam-5638	289	1	the	the	DET
ejpam-5638	289	2	schur	schur	PROPN
ejpam-5638	289	3	complement	complement	NOUN
ejpam-5638	289	4	of	of	ADP
ejpam-5638	289	5	the	the	DET
ejpam-5638	289	6	partitioned	partition	VERB
ejpam-5638	289	7	matrix	matrix	NOUN
ejpam-5638	289	8	is	be	AUX
ejpam-5638	289	9	a+da−1d	a+da−1d	NOUN
ejpam-5638	289	10	=	=	PUNCT
ejpam-5638	289	11	ad−1d	ad−1d	NOUN
ejpam-5638	290	1	+	+	ADJ
ejpam-5638	290	2	da−1d	da−1d	X
ejpam-5638	290	3	=	=	SYM
ejpam-5638	290	4	(	(	PUNCT
ejpam-5638	290	5	ad−1	ad−1	PROPN
ejpam-5638	290	6	+	+	PROPN
ejpam-5638	290	7	da−1)d	da−1)d	PROPN
ejpam-5638	290	8	.	.	PUNCT
ejpam-5638	291	1	by	by	ADP
ejpam-5638	291	2	computing	compute	VERB
ejpam-5638	291	3	the	the	DET
ejpam-5638	291	4	kth	kth	PROPN
ejpam-5638	291	5	eigenvalue	eigenvalue	PROPN
ejpam-5638	291	6	of	of	ADP
ejpam-5638	291	7	(	(	PUNCT
ejpam-5638	291	8	a+da−1d	a+da−1d	PROPN
ejpam-5638	291	9	)	)	PUNCT
ejpam-5638	291	10	,	,	PUNCT
ejpam-5638	291	11	we	we	PRON
ejpam-5638	291	12	have	have	VERB
ejpam-5638	291	13	that	that	PRON
ejpam-5638	291	14	n∏	n∏	PROPN
ejpam-5638	292	1	k=1	k=1	PROPN
ejpam-5638	292	2	(	(	PUNCT
ejpam-5638	292	3	λk(a+da−1d	λk(a+da−1d	PROPN
ejpam-5638	292	4	)	)	PUNCT
ejpam-5638	292	5	)	)	PUNCT
ejpam-5638	293	1	=	=	PUNCT
ejpam-5638	293	2	n∏	n∏	NOUN
ejpam-5638	293	3	k=1	k=1	PUNCT
ejpam-5638	294	1	λk((ad	λk((ad	PUNCT
ejpam-5638	294	2	−1	−1	NOUN
ejpam-5638	294	3	+	+	NOUN
ejpam-5638	294	4	da−1)d	da−1)d	NOUN
ejpam-5638	294	5	)	)	PUNCT
ejpam-5638	295	1	=	=	NOUN
ejpam-5638	295	2	=	=	SYM
ejpam-5638	295	3	n∏	n∏	PROPN
ejpam-5638	295	4	k=1	k=1	NOUN
ejpam-5638	295	5	λk(a	λk(a	NOUN
ejpam-5638	295	6	)	)	PUNCT
ejpam-5638	295	7	n∏	n∏	NOUN
ejpam-5638	295	8	k=1	k=1	PUNCT
ejpam-5638	296	1	λk(ad	λk(ad	PROPN
ejpam-5638	296	2	−1	−1	NOUN
ejpam-5638	296	3	+	+	NOUN
ejpam-5638	296	4	da−1	da−1	NOUN
ejpam-5638	296	5	)	)	PUNCT
ejpam-5638	296	6	n∏	n∏	PROPN
ejpam-5638	296	7	k=1	k=1	PROPN
ejpam-5638	296	8	λk(d	λk(d	PROPN
ejpam-5638	296	9	)	)	PUNCT
ejpam-5638	296	10	.	.	PUNCT
ejpam-5638	297	1	since	since	SCONJ
ejpam-5638	297	2	,	,	PUNCT
ejpam-5638	297	3	n∏	n∏	PROPN
ejpam-5638	297	4	k=1	k=1	PROPN
ejpam-5638	297	5	λk(a+da−1d	λk(a+da−1d	PROPN
ejpam-5638	297	6	)	)	PUNCT
ejpam-5638	297	7	>	>	X
ejpam-5638	297	8	0	0	NUM
ejpam-5638	298	1	⇔	⇔	PROPN
ejpam-5638	298	2	n∏	n∏	PROPN
ejpam-5638	298	3	k=1	k=1	PUNCT
ejpam-5638	299	1	λk(ad	λk(ad	PROPN
ejpam-5638	299	2	−1	−1	NOUN
ejpam-5638	299	3	+	+	PROPN
ejpam-5638	299	4	da−1	da−1	NOUN
ejpam-5638	299	5	)	)	PUNCT
ejpam-5638	299	6	>	>	X
ejpam-5638	300	1	0	0	X
ejpam-5638	300	2	.	.	PUNCT
ejpam-5638	301	1	as	as	ADP
ejpam-5638	301	2	λk(a	λk(a	NOUN
ejpam-5638	301	3	)	)	PUNCT
ejpam-5638	301	4	≤	≤	NUM
ejpam-5638	301	5	0	0	NUM
ejpam-5638	301	6	,	,	PUNCT
ejpam-5638	301	7	λk(d	λk(d	ADJ
ejpam-5638	301	8	)	)	PUNCT
ejpam-5638	301	9	≤	≤	NUM
ejpam-5638	301	10	0	0	NUM
ejpam-5638	301	11	,	,	PUNCT
ejpam-5638	301	12	∀	∀	X
ejpam-5638	301	13	k	k	X
ejpam-5638	301	14	,	,	PUNCT
ejpam-5638	301	15	and	and	CCONJ
ejpam-5638	301	16	hence	hence	ADV
ejpam-5638	301	17	λk(ad	λk(ad	PROPN
ejpam-5638	301	18	−1	−1	NOUN
ejpam-5638	301	19	)	)	PUNCT
ejpam-5638	301	20	≤	≤	NOUN
ejpam-5638	301	21	0	0	NUM
ejpam-5638	301	22	,	,	PUNCT
ejpam-5638	301	23	λk(da−1	λk(da−1	NOUN
ejpam-5638	301	24	)	)	PUNCT
ejpam-5638	301	25	≤	≤	NOUN
ejpam-5638	301	26	0	0	NUM
ejpam-5638	301	27	.	.	PROPN
ejpam-5638	301	28	3.2	3.2	NUM
ejpam-5638	301	29	.	.	PUNCT
ejpam-5638	302	1	stability	stability	NOUN
ejpam-5638	302	2	and	and	CCONJ
ejpam-5638	302	3	d	d	NOUN
ejpam-5638	302	4	-	-	NOUN
ejpam-5638	302	5	stability	stability	NOUN
ejpam-5638	302	6	of	of	ADP
ejpam-5638	302	7	second	second	ADJ
ejpam-5638	302	8	order	order	NOUN
ejpam-5638	302	9	dynamical	dynamical	ADJ
ejpam-5638	302	10	systems	system	NOUN
ejpam-5638	302	11	in	in	ADP
ejpam-5638	302	12	[	[	X
ejpam-5638	302	13	27	27	NUM
ejpam-5638	302	14	]	]	PUNCT
ejpam-5638	302	15	,	,	PUNCT
ejpam-5638	302	16	some	some	DET
ejpam-5638	302	17	close	close	ADJ
ejpam-5638	302	18	interconnections	interconnection	NOUN
ejpam-5638	302	19	between	between	ADP
ejpam-5638	302	20	µ-values	µ-value	NOUN
ejpam-5638	302	21	and	and	CCONJ
ejpam-5638	302	22	structured	structure	VERB
ejpam-5638	302	23	d	d	X
ejpam-5638	302	24	-	-	NOUN
ejpam-5638	302	25	stability	stability	NOUN
ejpam-5638	302	26	of	of	ADP
ejpam-5638	302	27	real	real	ADJ
ejpam-5638	302	28	squared	squared	ADJ
ejpam-5638	302	29	matrices	matrix	NOUN
ejpam-5638	302	30	were	be	AUX
ejpam-5638	302	31	developed	develop	VERB
ejpam-5638	302	32	.	.	PUNCT
ejpam-5638	303	1	it	it	PRON
ejpam-5638	303	2	was	be	AUX
ejpam-5638	303	3	further	far	ADV
ejpam-5638	303	4	shown	show	VERB
ejpam-5638	303	5	that	that	SCONJ
ejpam-5638	303	6	real	real	ADV
ejpam-5638	303	7	-	-	PUNCT
ejpam-5638	303	8	valued	value	VERB
ejpam-5638	303	9	square	square	ADJ
ejpam-5638	303	10	matrix	matrix	NOUN
ejpam-5638	303	11	is	be	AUX
ejpam-5638	303	12	structured	structure	VERB
ejpam-5638	304	1	d	d	ADJ
ejpam-5638	304	2	-	-	ADJ
ejpam-5638	304	3	stable	stable	ADJ
ejpam-5638	304	4	if	if	SCONJ
ejpam-5638	304	5	and	and	CCONJ
ejpam-5638	304	6	only	only	ADV
ejpam-5638	304	7	if	if	SCONJ
ejpam-5638	304	8	µ∆̂(m	µ∆̂(m	ADP
ejpam-5638	304	9	)	)	PUNCT
ejpam-5638	304	10	<	<	X
ejpam-5638	304	11	1	1	NUM
ejpam-5638	304	12	for	for	ADP
ejpam-5638	304	13	a	a	DET
ejpam-5638	304	14	given	give	VERB
ejpam-5638	304	15	m	m	PRON
ejpam-5638	304	16	∈	∈	PROPN
ejpam-5638	304	17	cn	cn	PROPN
ejpam-5638	304	18	,	,	PUNCT
ejpam-5638	304	19	n.	n.	NOUN
ejpam-5638	304	20	the	the	DET
ejpam-5638	304	21	following	follow	VERB
ejpam-5638	304	22	theorem	theorem	NOUN
ejpam-5638	304	23	gives	give	VERB
ejpam-5638	304	24	an	an	DET
ejpam-5638	304	25	interconnection	interconnection	NOUN
ejpam-5638	304	26	between	between	ADP
ejpam-5638	304	27	µ−value	µ−value	NOUN
ejpam-5638	304	28	and	and	CCONJ
ejpam-5638	304	29	d−stability	d−stability	PROPN
ejpam-5638	304	30	.	.	PUNCT
ejpam-5638	305	1	theorem	theorem	VERB
ejpam-5638	305	2	9	9	NUM
ejpam-5638	305	3	.	.	PUNCT
ejpam-5638	306	1	[	[	X
ejpam-5638	306	2	27	27	NUM
ejpam-5638	306	3	]	]	PUNCT
ejpam-5638	306	4	consider	consider	VERB
ejpam-5638	306	5	m	m	PROPN
ejpam-5638	306	6	∈	∈	PROPN
ejpam-5638	306	7	rn	rn	PROPN
ejpam-5638	306	8	,	,	PUNCT
ejpam-5638	306	9	n.	n.	PROPN
ejpam-5638	306	10	then	then	ADV
ejpam-5638	306	11	structured	structure	VERB
ejpam-5638	306	12	matrix	matrix	NOUN
ejpam-5638	306	13	m	m	NOUN
ejpam-5638	306	14	is	be	AUX
ejpam-5638	306	15	structured	structure	VERB
ejpam-5638	306	16	d	d	ADJ
ejpam-5638	306	17	-	-	ADJ
ejpam-5638	306	18	stable	stable	ADJ
ejpam-5638	306	19	matrix	matrix	NOUN
ejpam-5638	306	20	⇔	⇔	PROPN
ejpam-5638	306	21	m	m	VERB
ejpam-5638	306	22	is	be	AUX
ejpam-5638	306	23	structured	structure	VERB
ejpam-5638	306	24	stable	stable	ADJ
ejpam-5638	306	25	matrix	matrix	NOUN
ejpam-5638	306	26	and	and	CCONJ
ejpam-5638	306	27	0	0	NUM
ejpam-5638	306	28	≤	≤	NOUN
ejpam-5638	306	29	µ∆̂((iin	µ∆̂((iin	NOUN
ejpam-5638	306	30	+	+	SYM
ejpam-5638	306	31	m)−1(iin	m)−1(iin	NOUN
ejpam-5638	306	32	−m	−m	NOUN
ejpam-5638	306	33	)	)	PUNCT
ejpam-5638	306	34	)	)	PUNCT
ejpam-5638	307	1	<	<	X
ejpam-5638	308	1	1	1	X
ejpam-5638	308	2	.	.	PUNCT
ejpam-5638	308	3	an	an	DET
ejpam-5638	308	4	extension	extension	NOUN
ejpam-5638	308	5	to	to	ADP
ejpam-5638	308	6	strong	strong	ADJ
ejpam-5638	308	7	structured	structured	ADJ
ejpam-5638	308	8	d	d	NOUN
ejpam-5638	308	9	-	-	PUNCT
ejpam-5638	308	10	stability	stability	NOUN
ejpam-5638	308	11	condition	condition	NOUN
ejpam-5638	308	12	for	for	ADP
ejpam-5638	308	13	a	a	DET
ejpam-5638	308	14	given	give	VERB
ejpam-5638	308	15	structured	structured	ADJ
ejpam-5638	308	16	matrix	matrix	NOUN
ejpam-5638	308	17	was	be	AUX
ejpam-5638	308	18	derived	derive	VERB
ejpam-5638	308	19	in	in	ADP
ejpam-5638	308	20	[	[	X
ejpam-5638	308	21	27	27	NUM
ejpam-5638	308	22	]	]	PUNCT
ejpam-5638	308	23	.	.	PUNCT
ejpam-5638	309	1	theorem	theorem	ADJ
ejpam-5638	309	2	10	10	NUM
ejpam-5638	309	3	.	.	PUNCT
ejpam-5638	310	1	[	[	X
ejpam-5638	310	2	27	27	NUM
ejpam-5638	310	3	]	]	PUNCT
ejpam-5638	310	4	let	let	VERB
ejpam-5638	310	5	m	m	PROPN
ejpam-5638	310	6	∈	∈	PROPN
ejpam-5638	310	7	rn	rn	PROPN
ejpam-5638	310	8	,	,	PUNCT
ejpam-5638	310	9	n	n	CCONJ
ejpam-5638	310	10	,	,	PUNCT
ejpam-5638	310	11	and	and	CCONJ
ejpam-5638	310	12	let	let	VERB
ejpam-5638	310	13	µ∆̂	µ∆̂	PROPN
ejpam-5638	310	14	(	(	PUNCT
ejpam-5638	310	15	·	·	PUNCT
ejpam-5638	310	16	)	)	PUNCT
ejpam-5638	310	17	is	be	AUX
ejpam-5638	310	18	the	the	DET
ejpam-5638	310	19	µ-value	µ-value	NOUN
ejpam-5638	310	20	of	of	ADP
ejpam-5638	310	21	a	a	DET
ejpam-5638	310	22	matrix	matrix	NOUN
ejpam-5638	310	23	.	.	PUNCT
ejpam-5638	311	1	then	then	ADV
ejpam-5638	311	2	structured	structure	VERB
ejpam-5638	311	3	matrix	matrix	NOUN
ejpam-5638	311	4	m	m	NOUN
ejpam-5638	311	5	is	be	AUX
ejpam-5638	311	6	strongly	strongly	ADV
ejpam-5638	311	7	d	d	ADJ
ejpam-5638	311	8	-	-	ADJ
ejpam-5638	311	9	stable	stable	ADJ
ejpam-5638	311	10	iff	iff	PROPN
ejpam-5638	311	11	re(λi(m	re(λi(m	NOUN
ejpam-5638	311	12	)	)	PUNCT
ejpam-5638	311	13	)	)	PUNCT
ejpam-5638	312	1	>	>	X
ejpam-5638	312	2	0	0	NUM
ejpam-5638	312	3	,	,	PUNCT
ejpam-5638	312	4	∀i	∀i	NOUN
ejpam-5638	312	5	and	and	CCONJ
ejpam-5638	312	6	∃	∃	PROPN
ejpam-5638	312	7	ε	ε	PROPN
ejpam-5638	312	8	>	>	PUNCT
ejpam-5638	312	9	0	0	PUNCT
ejpam-5638	313	1	so	so	SCONJ
ejpam-5638	313	2	that	that	SCONJ
ejpam-5638	313	3	0	0	NUM
ejpam-5638	313	4	≤	≤	NUM
ejpam-5638	313	5	µ∆̂(m	µ∆̂(m	ADP
ejpam-5638	313	6	)	)	PUNCT
ejpam-5638	313	7	<	<	X
ejpam-5638	313	8	1	1	NUM
ejpam-5638	313	9	,	,	PUNCT
ejpam-5638	313	10	where	where	SCONJ
ejpam-5638	313	11	m	m	VERB
ejpam-5638	313	12	=	=	PUNCT
ejpam-5638	313	13	(	(	PUNCT
ejpam-5638	313	14	(	(	PUNCT
ejpam-5638	313	15	iin	iin	NOUN
ejpam-5638	313	16	+	+	NOUN
ejpam-5638	313	17	m)−1(iin	m)−1(iin	NOUN
ejpam-5638	313	18	−m	−m	NOUN
ejpam-5638	313	19	)	)	PUNCT
ejpam-5638	314	1	2i(iin	2i(iin	NOUN
ejpam-5638	315	1	+	+	NOUN
ejpam-5638	315	2	m)−1	m)−1	NOUN
ejpam-5638	315	3	ε(iin	ε(iin	NOUN
ejpam-5638	315	4	+	+	ADP
ejpam-5638	315	5	m)−1	m)−1	NOUN
ejpam-5638	315	6	−ε(iin	−ε(iin	PROPN
ejpam-5638	315	7	+	+	PROPN
ejpam-5638	315	8	m)−1	m)−1	NOUN
ejpam-5638	315	9	)	)	PUNCT
ejpam-5638	315	10	.	.	PUNCT
ejpam-5638	316	1	m.u.r	m.u.r	PROPN
ejpam-5638	316	2	rehman	rehman	PROPN
ejpam-5638	316	3	et	et	PROPN
ejpam-5638	316	4	al	al	PROPN
ejpam-5638	316	5	.	.	PUNCT
ejpam-5638	316	6	/	/	SYM
ejpam-5638	316	7	eur	eur	PROPN
ejpam-5638	316	8	.	.	PUNCT
ejpam-5638	317	1	j.	j.	PROPN
ejpam-5638	317	2	pure	pure	PROPN
ejpam-5638	317	3	appl	appl	PROPN
ejpam-5638	317	4	.	.	PROPN
ejpam-5638	317	5	math	math	PROPN
ejpam-5638	317	6	,	,	PUNCT
ejpam-5638	317	7	18	18	NUM
ejpam-5638	317	8	(	(	PUNCT
ejpam-5638	317	9	2	2	NUM
ejpam-5638	317	10	)	)	PUNCT
ejpam-5638	317	11	(	(	PUNCT
ejpam-5638	317	12	2025	2025	NUM
ejpam-5638	317	13	)	)	PUNCT
ejpam-5638	317	14	,	,	PUNCT
ejpam-5638	317	15	5638	5638	NUM
ejpam-5638	317	16	13	13	NUM
ejpam-5638	317	17	of	of	ADP
ejpam-5638	317	18	23	23	NUM
ejpam-5638	317	19	lemma	lemma	PROPN
ejpam-5638	317	20	2	2	NUM
ejpam-5638	317	21	.	.	PUNCT
ejpam-5638	318	1	[	[	X
ejpam-5638	318	2	28	28	NUM
ejpam-5638	318	3	]	]	X
ejpam-5638	318	4	let	let	VERB
ejpam-5638	318	5	m	m	VERB
ejpam-5638	318	6	=	=	PUNCT
ejpam-5638	318	7	(	(	PUNCT
ejpam-5638	318	8	m11	m11	PROPN
ejpam-5638	318	9	m12	m12	PROPN
ejpam-5638	318	10	m21	m21	PROPN
ejpam-5638	318	11	m22	m22	PROPN
ejpam-5638	318	12	)	)	PUNCT
ejpam-5638	318	13	.	.	PUNCT
ejpam-5638	319	1	if	if	SCONJ
ejpam-5638	319	2	m	m	NOUN
ejpam-5638	319	3	is	be	AUX
ejpam-5638	319	4	strongly	strongly	ADV
ejpam-5638	319	5	d	d	ADJ
ejpam-5638	319	6	-	-	ADJ
ejpam-5638	319	7	stable	stable	ADJ
ejpam-5638	319	8	matrix	matrix	NOUN
ejpam-5638	319	9	,	,	PUNCT
ejpam-5638	319	10	m22	m22	PROPN
ejpam-5638	319	11	and	and	CCONJ
ejpam-5638	319	12	m	m	PROPN
ejpam-5638	319	13	c	c	NOUN
ejpam-5638	319	14	22	22	NUM
ejpam-5638	319	15	are	be	AUX
ejpam-5638	319	16	both	both	PRON
ejpam-5638	319	17	strongly	strongly	ADV
ejpam-5638	319	18	d	d	ADJ
ejpam-5638	319	19	-	-	ADJ
ejpam-5638	319	20	stable	stable	ADJ
ejpam-5638	319	21	matrices	matrix	NOUN
ejpam-5638	319	22	,	,	PUNCT
ejpam-5638	319	23	that	that	ADV
ejpam-5638	319	24	is	is	ADV
ejpam-5638	319	25	,	,	PUNCT
ejpam-5638	319	26	for	for	ADP
ejpam-5638	319	27	m22	m22	PROPN
ejpam-5638	319	28	or	or	CCONJ
ejpam-5638	319	29	m	m	PROPN
ejpam-5638	319	30	c	c	NOUN
ejpam-5638	319	31	22	22	NUM
ejpam-5638	319	32	,	,	PUNCT
ejpam-5638	319	33	∃	∃	PROPN
ejpam-5638	319	34	δ	δ	PROPN
ejpam-5638	319	35	>	>	X
ejpam-5638	319	36	0	0	PROPN
ejpam-5638	319	37	,	,	PUNCT
ejpam-5638	319	38	such	such	ADJ
ejpam-5638	319	39	that	that	SCONJ
ejpam-5638	319	40	,	,	PUNCT
ejpam-5638	319	41	to	to	ADP
ejpam-5638	319	42	each	each	DET
ejpam-5638	319	43	em	em	PROPN
ejpam-5638	319	44	∈	∈	PROPN
ejpam-5638	319	45	rm	rm	PROPN
ejpam-5638	319	46	,	,	PUNCT
ejpam-5638	319	47	m	m	PROPN
ejpam-5638	319	48	,	,	PUNCT
ejpam-5638	319	49	∥em∥	∥em∥	ADP
ejpam-5638	319	50	<	<	X
ejpam-5638	319	51	δ	δ	PROPN
ejpam-5638	319	52	,	,	PUNCT
ejpam-5638	319	53	λi(in	λi(in	NOUN
ejpam-5638	319	54	−	−	PROPN
ejpam-5638	319	55	(	(	PUNCT
ejpam-5638	319	56	iin	iin	NOUN
ejpam-5638	320	1	+	+	NOUN
ejpam-5638	320	2	m	m	NOUN
ejpam-5638	320	3	c	c	NOUN
ejpam-5638	320	4	22	22	NUM
ejpam-5638	321	1	+	+	CCONJ
ejpam-5638	321	2	em)−1(iin	em)−1(iin	PROPN
ejpam-5638	321	3	−m	−m	NOUN
ejpam-5638	321	4	c	c	PROPN
ejpam-5638	321	5	22	22	NUM
ejpam-5638	321	6	−	−	NOUN
ejpam-5638	321	7	em)qm	em)qm	NUM
ejpam-5638	321	8	)	)	PUNCT
ejpam-5638	321	9	̸=	̸=	PROPN
ejpam-5638	321	10	0	0	NUM
ejpam-5638	321	11	,	,	PUNCT
ejpam-5638	321	12	for	for	ADP
ejpam-5638	321	13	qm	qm	PROPN
ejpam-5638	321	14	∈	∈	PROPN
ejpam-5638	321	15	∆̂.	∆̂.	PROPN
ejpam-5638	321	16	remark	remark	NOUN
ejpam-5638	321	17	7	7	NUM
ejpam-5638	321	18	.	.	PUNCT
ejpam-5638	322	1	the	the	DET
ejpam-5638	322	2	matrix	matrix	NOUN
ejpam-5638	322	3	m	m	VERB
ejpam-5638	322	4	c	c	NOUN
ejpam-5638	322	5	22	22	NUM
ejpam-5638	322	6	is	be	AUX
ejpam-5638	322	7	defined	define	VERB
ejpam-5638	322	8	by	by	ADP
ejpam-5638	322	9	schur	schur	PROPN
ejpam-5638	322	10	complement	complement	PROPN
ejpam-5638	322	11	,	,	PUNCT
ejpam-5638	322	12	that	that	ADV
ejpam-5638	322	13	is	be	AUX
ejpam-5638	322	14	,	,	PUNCT
ejpam-5638	322	15	m	m	PROPN
ejpam-5638	322	16	c	c	NOUN
ejpam-5638	322	17	22	22	NUM
ejpam-5638	322	18	=	=	SYM
ejpam-5638	322	19	m22	m22	PROPN
ejpam-5638	322	20	−	−	PROPN
ejpam-5638	322	21	m21	m21	PROPN
ejpam-5638	322	22	m	m	PROPN
ejpam-5638	322	23	−1	−1	NOUN
ejpam-5638	322	24	11	11	NUM
ejpam-5638	322	25	m12	m12	NOUN
ejpam-5638	322	26	with	with	ADP
ejpam-5638	322	27	m11	m11	NOUN
ejpam-5638	322	28	such	such	ADJ
ejpam-5638	322	29	that	that	PRON
ejpam-5638	322	30	λi(m11	λi(m11	PROPN
ejpam-5638	322	31	)	)	PUNCT
ejpam-5638	322	32	̸=	̸=	PROPN
ejpam-5638	322	33	0	0	NUM
ejpam-5638	322	34	∀i	∀i	NOUN
ejpam-5638	322	35	.	.	PUNCT
ejpam-5638	323	1	remark	remark	PROPN
ejpam-5638	323	2	8	8	NUM
ejpam-5638	323	3	.	.	PUNCT
ejpam-5638	324	1	a	a	DET
ejpam-5638	324	2	sufficient	sufficient	ADJ
ejpam-5638	324	3	condition	condition	NOUN
ejpam-5638	324	4	[	[	X
ejpam-5638	324	5	29	29	NUM
ejpam-5638	324	6	,	,	PUNCT
ejpam-5638	324	7	30	30	NUM
ejpam-5638	324	8	]	]	PUNCT
ejpam-5638	324	9	for	for	ADP
ejpam-5638	324	10	structured	structured	ADJ
ejpam-5638	324	11	matrix	matrix	NOUN
ejpam-5638	324	12	m	m	VERB
ejpam-5638	324	13	to	to	PART
ejpam-5638	324	14	be	be	AUX
ejpam-5638	324	15	strong	strong	ADJ
ejpam-5638	324	16	d	d	ADJ
ejpam-5638	324	17	-	-	ADJ
ejpam-5638	324	18	stable	stable	ADJ
ejpam-5638	324	19	structured	structured	ADJ
ejpam-5638	324	20	matrix	matrix	NOUN
ejpam-5638	324	21	is	be	AUX
ejpam-5638	324	22	that	that	DET
ejpam-5638	324	23	inf	inf	NOUN
ejpam-5638	324	24	σ1(d(in	σ1(d(in	X
ejpam-5638	325	1	+	+	NOUN
ejpam-5638	325	2	m)−1(in	m)−1(in	NOUN
ejpam-5638	325	3	−m)d−1	−m)d−1	NOUN
ejpam-5638	325	4	)	)	PUNCT
ejpam-5638	325	5	<	<	X
ejpam-5638	325	6	1	1	NUM
ejpam-5638	325	7	,	,	PUNCT
ejpam-5638	325	8	where	where	SCONJ
ejpam-5638	325	9	inf	inf	NOUN
ejpam-5638	325	10	is	be	AUX
ejpam-5638	325	11	taken	take	VERB
ejpam-5638	325	12	over	over	ADP
ejpam-5638	325	13	d	d	PROPN
ejpam-5638	325	14	∈	∈	PROPN
ejpam-5638	325	15	d̂.	d̂.	NOUN
ejpam-5638	325	16	theorem	theorem	VERB
ejpam-5638	325	17	11	11	NUM
ejpam-5638	325	18	shows	show	VERB
ejpam-5638	325	19	that	that	SCONJ
ejpam-5638	325	20	second	second	ADJ
ejpam-5638	325	21	order	order	NOUN
ejpam-5638	325	22	dynamical	dynamical	ADJ
ejpam-5638	325	23	system	system	NOUN
ejpam-5638	325	24	is	be	AUX
ejpam-5638	325	25	structured	structure	VERB
ejpam-5638	326	1	d	d	ADJ
ejpam-5638	326	2	-	-	ADJ
ejpam-5638	326	3	stable	stable	ADJ
ejpam-5638	326	4	for	for	ADP
ejpam-5638	326	5	matrices	matrix	NOUN
ejpam-5638	326	6	a	a	PRON
ejpam-5638	326	7	,	,	PUNCT
ejpam-5638	326	8	b	b	X
ejpam-5638	326	9	such	such	ADJ
ejpam-5638	326	10	that	that	SCONJ
ejpam-5638	326	11	(	(	PUNCT
ejpam-5638	326	12	a	a	DET
ejpam-5638	326	13	b	b	NOUN
ejpam-5638	326	14	in	in	ADP
ejpam-5638	326	15	o	o	PROPN
ejpam-5638	326	16	)	)	PUNCT
ejpam-5638	326	17	is	be	AUX
ejpam-5638	326	18	stable	stable	ADJ
ejpam-5638	326	19	,	,	PUNCT
ejpam-5638	326	20	and	and	CCONJ
ejpam-5638	326	21	its	its	PRON
ejpam-5638	326	22	non	non	ADJ
ejpam-5638	326	23	-	-	ADJ
ejpam-5638	326	24	negative	negative	ADJ
ejpam-5638	326	25	structured	structured	ADJ
ejpam-5638	326	26	singular	singular	ADJ
ejpam-5638	326	27	value	value	NOUN
ejpam-5638	326	28	is	be	AUX
ejpam-5638	326	29	bounded	bound	VERB
ejpam-5638	326	30	by	by	ADP
ejpam-5638	326	31	1	1	NUM
ejpam-5638	326	32	.	.	PUNCT
ejpam-5638	327	1	theorem	theorem	VERB
ejpam-5638	327	2	11	11	NUM
ejpam-5638	327	3	.	.	PUNCT
ejpam-5638	328	1	the	the	DET
ejpam-5638	328	2	dynamical	dynamical	ADJ
ejpam-5638	328	3	system	system	NOUN
ejpam-5638	328	4	ẍ	ẍ	X
ejpam-5638	328	5	=	=	SYM
ejpam-5638	328	6	aẋ+	aẋ+	PUNCT
ejpam-5638	329	1	bx	bx	NOUN
ejpam-5638	329	2	,	,	PUNCT
ejpam-5638	329	3	x	x	SYM
ejpam-5638	329	4	∈	∈	PROPN
ejpam-5638	329	5	rn,1	rn,1	PROPN
ejpam-5638	329	6	with	with	ADP
ejpam-5638	329	7	a	a	DET
ejpam-5638	329	8	,	,	PUNCT
ejpam-5638	329	9	b	b	PROPN
ejpam-5638	329	10	∈	∈	PROPN
ejpam-5638	329	11	rn	rn	PROPN
ejpam-5638	329	12	,	,	PUNCT
ejpam-5638	329	13	n	n	CCONJ
ejpam-5638	329	14	,	,	PUNCT
ejpam-5638	329	15	is	be	AUX
ejpam-5638	329	16	structured	structure	VERB
ejpam-5638	329	17	d	d	ADJ
ejpam-5638	329	18	-	-	ADJ
ejpam-5638	329	19	stable	stable	ADJ
ejpam-5638	329	20	if	if	SCONJ
ejpam-5638	329	21	the	the	DET
ejpam-5638	329	22	matrix	matrix	NOUN
ejpam-5638	329	23	(	(	PUNCT
ejpam-5638	329	24	a	a	DET
ejpam-5638	329	25	b	b	NOUN
ejpam-5638	329	26	in	in	ADP
ejpam-5638	329	27	o	o	PROPN
ejpam-5638	329	28	)	)	PUNCT
ejpam-5638	329	29	is	be	AUX
ejpam-5638	329	30	structured	structure	VERB
ejpam-5638	329	31	stable	stable	ADJ
ejpam-5638	329	32	and	and	CCONJ
ejpam-5638	329	33	0	0	NUM
ejpam-5638	329	34	≤	≤	NUM
ejpam-5638	329	35	µ∆̂	µ∆̂	PROPN
ejpam-5638	329	36	(	(	PUNCT
ejpam-5638	329	37	(	(	PUNCT
ejpam-5638	329	38	a	a	DET
ejpam-5638	329	39	b	b	NOUN
ejpam-5638	329	40	in	in	ADP
ejpam-5638	329	41	o	o	NOUN
ejpam-5638	329	42	)	)	PUNCT
ejpam-5638	329	43	−2	−2	NOUN
ejpam-5638	329	44	)	)	PUNCT
ejpam-5638	329	45	<	<	X
ejpam-5638	330	1	1	1	X
ejpam-5638	330	2	.	.	PUNCT
ejpam-5638	330	3	proof	proof	NOUN
ejpam-5638	330	4	.	.	PUNCT
ejpam-5638	331	1	we	we	PRON
ejpam-5638	331	2	assume	assume	VERB
ejpam-5638	331	3	that	that	SCONJ
ejpam-5638	331	4	(	(	PUNCT
ejpam-5638	331	5	a	a	DET
ejpam-5638	331	6	b	b	NOUN
ejpam-5638	331	7	in	in	ADP
ejpam-5638	331	8	o	o	PROPN
ejpam-5638	331	9	)	)	PUNCT
ejpam-5638	331	10	is	be	AUX
ejpam-5638	331	11	stable	stable	ADJ
ejpam-5638	331	12	matrix	matrix	NOUN
ejpam-5638	331	13	and	and	CCONJ
ejpam-5638	331	14	aim	aim	VERB
ejpam-5638	331	15	to	to	PART
ejpam-5638	331	16	show	show	VERB
ejpam-5638	331	17	that	that	SCONJ
ejpam-5638	331	18	0	0	NUM
ejpam-5638	331	19	≤	≤	NUM
ejpam-5638	331	20	µ∆̂	µ∆̂	PROPN
ejpam-5638	331	21	(	(	PUNCT
ejpam-5638	331	22	(	(	PUNCT
ejpam-5638	331	23	a	a	DET
ejpam-5638	331	24	b	b	NOUN
ejpam-5638	331	25	in	in	ADP
ejpam-5638	331	26	o	o	PROPN
ejpam-5638	331	27	)	)	PUNCT
ejpam-5638	331	28	)	)	PUNCT
ejpam-5638	332	1	<	<	X
ejpam-5638	332	2	1	1	X
ejpam-5638	332	3	.	.	PUNCT
ejpam-5638	332	4	from	from	ADP
ejpam-5638	332	5	[	[	X
ejpam-5638	332	6	31	31	NUM
ejpam-5638	332	7	]	]	PUNCT
ejpam-5638	332	8	it	it	PRON
ejpam-5638	332	9	follows	follow	VERB
ejpam-5638	332	10	that	that	SCONJ
ejpam-5638	332	11	(	(	PUNCT
ejpam-5638	332	12	a	a	DET
ejpam-5638	332	13	b	b	NOUN
ejpam-5638	332	14	in	in	ADP
ejpam-5638	332	15	o	o	PROPN
ejpam-5638	332	16	)	)	PUNCT
ejpam-5638	332	17	is	be	AUX
ejpam-5638	332	18	d	d	NOUN
ejpam-5638	332	19	-	-	ADJ
ejpam-5638	332	20	stable	stable	ADJ
ejpam-5638	332	21	if	if	SCONJ
ejpam-5638	332	22	and	and	CCONJ
ejpam-5638	332	23	only	only	ADV
ejpam-5638	332	24	if	if	SCONJ
ejpam-5638	332	25	re	re	X
ejpam-5638	332	26	(	(	PUNCT
ejpam-5638	332	27	λi	λi	X
ejpam-5638	332	28	(	(	PUNCT
ejpam-5638	332	29	a	a	DET
ejpam-5638	332	30	b	b	NOUN
ejpam-5638	332	31	in	in	ADP
ejpam-5638	332	32	o	o	PROPN
ejpam-5638	332	33	)	)	PUNCT
ejpam-5638	332	34	)	)	PUNCT
ejpam-5638	332	35	>	>	X
ejpam-5638	332	36	0	0	NUM
ejpam-5638	332	37	∀i	∀i	NOUN
ejpam-5638	332	38	and	and	CCONJ
ejpam-5638	332	39	n∏	n∏	PROPN
ejpam-5638	332	40	i=1	i=1	PROPN
ejpam-5638	333	1	λi	λi	X
ejpam-5638	333	2	(	(	PUNCT
ejpam-5638	333	3	(	(	PUNCT
ejpam-5638	333	4	x	x	SYM
ejpam-5638	333	5	−p	−p	NOUN
ejpam-5638	333	6	p	p	NOUN
ejpam-5638	333	7	x	x	PROPN
ejpam-5638	333	8	)	)	PUNCT
ejpam-5638	333	9	)	)	PUNCT
ejpam-5638	334	1	̸=	̸=	NOUN
ejpam-5638	334	2	0	0	NUM
ejpam-5638	334	3	∀i	∀i	NOUN
ejpam-5638	334	4	,	,	PUNCT
ejpam-5638	334	5	∀p	∀p	NOUN
ejpam-5638	334	6	∈	∈	PROPN
ejpam-5638	334	7	d̂	d̂	NOUN
ejpam-5638	334	8	,	,	PUNCT
ejpam-5638	334	9	wherex	wherex	PROPN
ejpam-5638	334	10	=	=	PUNCT
ejpam-5638	334	11	(	(	PUNCT
ejpam-5638	334	12	a	a	DET
ejpam-5638	334	13	b	b	NOUN
ejpam-5638	334	14	in	in	ADP
ejpam-5638	334	15	o	o	PROPN
ejpam-5638	334	16	)	)	PUNCT
ejpam-5638	334	17	.	.	PUNCT
ejpam-5638	335	1	thus	thus	ADV
ejpam-5638	335	2	,	,	PUNCT
ejpam-5638	335	3	n∏	n∏	PROPN
ejpam-5638	335	4	i=1	i=1	PROPN
ejpam-5638	336	1	λi	λi	X
ejpam-5638	336	2	(	(	PUNCT
ejpam-5638	336	3	(	(	PUNCT
ejpam-5638	336	4	x	x	SYM
ejpam-5638	336	5	−p	−p	NOUN
ejpam-5638	336	6	p	p	NOUN
ejpam-5638	336	7	x	x	PROPN
ejpam-5638	336	8	)	)	PUNCT
ejpam-5638	336	9	)	)	PUNCT
ejpam-5638	337	1	̸=	̸=	NOUN
ejpam-5638	337	2	0	0	NUM
ejpam-5638	338	1	=	=	NOUN
ejpam-5638	338	2	⇒	⇒	PROPN
ejpam-5638	338	3	n∏	n∏	PROPN
ejpam-5638	338	4	i=1	i=1	PROPN
ejpam-5638	338	5	λi(x	λi(x	X
ejpam-5638	338	6	2	2	NUM
ejpam-5638	338	7	−	−	NOUN
ejpam-5638	338	8	px−1px	px−1px	NUM
ejpam-5638	338	9	)	)	PUNCT
ejpam-5638	338	10	̸=	̸=	PROPN
ejpam-5638	338	11	0	0	NUM
ejpam-5638	338	12	,	,	PUNCT
ejpam-5638	338	13	∀i	∀i	NOUN
ejpam-5638	338	14	.	.	PUNCT
ejpam-5638	339	1	m.u.r	m.u.r	PROPN
ejpam-5638	339	2	rehman	rehman	PROPN
ejpam-5638	339	3	et	et	PROPN
ejpam-5638	339	4	al	al	PROPN
ejpam-5638	339	5	.	.	PUNCT
ejpam-5638	339	6	/	/	SYM
ejpam-5638	339	7	eur	eur	PROPN
ejpam-5638	339	8	.	.	PUNCT
ejpam-5638	340	1	j.	j.	PROPN
ejpam-5638	340	2	pure	pure	PROPN
ejpam-5638	340	3	appl	appl	PROPN
ejpam-5638	340	4	.	.	PROPN
ejpam-5638	340	5	math	math	PROPN
ejpam-5638	340	6	,	,	PUNCT
ejpam-5638	340	7	18	18	NUM
ejpam-5638	340	8	(	(	PUNCT
ejpam-5638	340	9	2	2	NUM
ejpam-5638	340	10	)	)	PUNCT
ejpam-5638	340	11	(	(	PUNCT
ejpam-5638	340	12	2025	2025	NUM
ejpam-5638	340	13	)	)	PUNCT
ejpam-5638	340	14	,	,	PUNCT
ejpam-5638	340	15	5638	5638	NUM
ejpam-5638	340	16	14	14	NUM
ejpam-5638	340	17	of	of	ADP
ejpam-5638	340	18	23	23	NUM
ejpam-5638	340	19	furthermore	furthermore	ADV
ejpam-5638	340	20	,	,	PUNCT
ejpam-5638	340	21	we	we	PRON
ejpam-5638	340	22	have	have	VERB
ejpam-5638	340	23	that	that	DET
ejpam-5638	340	24	n∏	n∏	PROPN
ejpam-5638	340	25	i=1	i=1	PROPN
ejpam-5638	340	26	λi(x	λi(x	X
ejpam-5638	340	27	2	2	NUM
ejpam-5638	340	28	−	−	NOUN
ejpam-5638	340	29	px−1px	px−1px	NUM
ejpam-5638	340	30	)	)	PUNCT
ejpam-5638	340	31	̸=	̸=	PROPN
ejpam-5638	340	32	0	0	NUM
ejpam-5638	341	1	=	=	NOUN
ejpam-5638	341	2	⇒	⇒	PRON
ejpam-5638	341	3	n∏	n∏	PROPN
ejpam-5638	341	4	i=1	i=1	PROPN
ejpam-5638	341	5	λi(in	λi(in	NOUN
ejpam-5638	341	6	−x−2p̂	−x−2p̂	X
ejpam-5638	341	7	)	)	PUNCT
ejpam-5638	342	1	̸=	̸=	NOUN
ejpam-5638	342	2	0	0	NUM
ejpam-5638	342	3	,	,	PUNCT
ejpam-5638	342	4	where	where	SCONJ
ejpam-5638	342	5	p̂	p̂	X
ejpam-5638	342	6	=	=	PUNCT
ejpam-5638	342	7	p	p	X
ejpam-5638	342	8	∈	∈	PROPN
ejpam-5638	342	9	d̂	d̂	PROPN
ejpam-5638	342	10	,	,	PUNCT
ejpam-5638	342	11	a	a	DET
ejpam-5638	342	12	positive	positive	ADJ
ejpam-5638	342	13	diagonal	diagonal	ADJ
ejpam-5638	342	14	matrix	matrix	NOUN
ejpam-5638	342	15	.	.	PUNCT
ejpam-5638	343	1	thus	thus	ADV
ejpam-5638	343	2	,	,	PUNCT
ejpam-5638	343	3	finally	finally	ADV
ejpam-5638	343	4	we	we	PRON
ejpam-5638	343	5	have	have	VERB
ejpam-5638	343	6	that	that	DET
ejpam-5638	343	7	n∏	n∏	PROPN
ejpam-5638	343	8	i=1	i=1	PROPN
ejpam-5638	343	9	λi(in	λi(in	NOUN
ejpam-5638	343	10	−x−2p̂	−x−2p̂	X
ejpam-5638	343	11	)	)	PUNCT
ejpam-5638	344	1	̸=	̸=	NOUN
ejpam-5638	344	2	0	0	NUM
ejpam-5638	345	1	=	=	NOUN
ejpam-5638	345	2	⇒	⇒	NOUN
ejpam-5638	345	3	0	0	NUM
ejpam-5638	345	4	≤	≤	NUM
ejpam-5638	345	5	µ∆̂	µ∆̂	PROPN
ejpam-5638	345	6	(	(	PUNCT
ejpam-5638	345	7	(	(	PUNCT
ejpam-5638	345	8	a	a	DET
ejpam-5638	345	9	b	b	NOUN
ejpam-5638	345	10	in	in	ADP
ejpam-5638	345	11	o	o	NOUN
ejpam-5638	345	12	)	)	PUNCT
ejpam-5638	345	13	−2	−2	NOUN
ejpam-5638	345	14	)	)	PUNCT
ejpam-5638	345	15	<	<	X
ejpam-5638	346	1	1	1	X
ejpam-5638	346	2	.	.	PUNCT
ejpam-5638	346	3	lemma	lemma	PROPN
ejpam-5638	346	4	3	3	X
ejpam-5638	346	5	.	.	PUNCT
ejpam-5638	347	1	let	let	VERB
ejpam-5638	347	2	dynamical	dynamical	ADJ
ejpam-5638	347	3	system	system	NOUN
ejpam-5638	347	4	ẍ	ẍ	X
ejpam-5638	348	1	=	=	PUNCT
ejpam-5638	348	2	aẋ	aẋ	NOUN
ejpam-5638	349	1	+	+	CCONJ
ejpam-5638	349	2	bx	bx	X
ejpam-5638	349	3	,	,	PUNCT
ejpam-5638	349	4	x	x	PROPN
ejpam-5638	349	5	∈	∈	PROPN
ejpam-5638	349	6	rn,1	rn,1	PROPN
ejpam-5638	349	7	,	,	PUNCT
ejpam-5638	349	8	with	with	ADP
ejpam-5638	349	9	a	a	DET
ejpam-5638	349	10	∈	∈	PROPN
ejpam-5638	349	11	rn	rn	PROPN
ejpam-5638	349	12	,	,	PUNCT
ejpam-5638	349	13	n	n	PRON
ejpam-5638	349	14	such	such	ADJ
ejpam-5638	349	15	that	that	SCONJ
ejpam-5638	349	16	aii	aii	PROPN
ejpam-5638	349	17	<	<	X
ejpam-5638	349	18	0	0	NUM
ejpam-5638	349	19	,	,	PUNCT
ejpam-5638	349	20	∀i	∀i	NOUN
ejpam-5638	349	21	=	=	SYM
ejpam-5638	349	22	1	1	NUM
ejpam-5638	349	23	:	:	PUNCT
ejpam-5638	349	24	n.	n.	NOUN
ejpam-5638	349	25	then	then	ADV
ejpam-5638	349	26	dynamical	dynamical	ADJ
ejpam-5638	349	27	system	system	NOUN
ejpam-5638	349	28	is	be	AUX
ejpam-5638	349	29	structured	structure	VERB
ejpam-5638	349	30	d	d	ADJ
ejpam-5638	349	31	-	-	ADJ
ejpam-5638	349	32	stable	stable	ADJ
ejpam-5638	349	33	if	if	SCONJ
ejpam-5638	349	34	(	(	PUNCT
ejpam-5638	349	35	a	a	DET
ejpam-5638	349	36	bin	bin	NOUN
ejpam-5638	349	37	in	in	ADP
ejpam-5638	349	38	o	o	PROPN
ejpam-5638	349	39	)	)	PUNCT
ejpam-5638	349	40	is	be	AUX
ejpam-5638	349	41	stable	stable	ADJ
ejpam-5638	349	42	for	for	ADP
ejpam-5638	349	43	b	b	NOUN
ejpam-5638	349	44	<	<	X
ejpam-5638	349	45	0	0	NUM
ejpam-5638	349	46	and	and	CCONJ
ejpam-5638	349	47	0	0	NUM
ejpam-5638	349	48	≤	≤	NUM
ejpam-5638	350	1	µ∆̂	µ∆̂	PROPN
ejpam-5638	350	2	(	(	PUNCT
ejpam-5638	350	3	(	(	PUNCT
ejpam-5638	350	4	a	a	DET
ejpam-5638	350	5	b	b	NOUN
ejpam-5638	350	6	in	in	ADP
ejpam-5638	350	7	o	o	PROPN
ejpam-5638	350	8	)	)	PUNCT
ejpam-5638	350	9	)	)	PUNCT
ejpam-5638	351	1	<	<	X
ejpam-5638	351	2	1	1	X
ejpam-5638	351	3	.	.	PUNCT
ejpam-5638	351	4	proof	proof	NOUN
ejpam-5638	351	5	.	.	PUNCT
ejpam-5638	352	1	assume	assume	VERB
ejpam-5638	352	2	(	(	PUNCT
ejpam-5638	352	3	a	a	DET
ejpam-5638	352	4	bin	bin	NOUN
ejpam-5638	352	5	in	in	ADP
ejpam-5638	352	6	o	o	PROPN
ejpam-5638	352	7	)	)	PUNCT
ejpam-5638	352	8	is	be	AUX
ejpam-5638	352	9	structured	structure	VERB
ejpam-5638	352	10	stable	stable	ADJ
ejpam-5638	352	11	,	,	PUNCT
ejpam-5638	352	12	and	and	CCONJ
ejpam-5638	352	13	we	we	PRON
ejpam-5638	352	14	aim	aim	VERB
ejpam-5638	352	15	to	to	PART
ejpam-5638	352	16	show	show	VERB
ejpam-5638	352	17	that	that	SCONJ
ejpam-5638	352	18	0	0	NUM
ejpam-5638	352	19	≤	≤	NUM
ejpam-5638	352	20	µ∆̂	µ∆̂	PROPN
ejpam-5638	352	21	(	(	PUNCT
ejpam-5638	352	22	(	(	PUNCT
ejpam-5638	352	23	a	a	DET
ejpam-5638	352	24	bin	bin	NOUN
ejpam-5638	352	25	in	in	ADP
ejpam-5638	352	26	o	o	PROPN
ejpam-5638	352	27	)	)	PUNCT
ejpam-5638	352	28	)	)	PUNCT
ejpam-5638	352	29	<	<	X
ejpam-5638	353	1	1	1	X
ejpam-5638	353	2	.	.	PUNCT
ejpam-5638	353	3	the	the	DET
ejpam-5638	353	4	matrix	matrix	NOUN
ejpam-5638	353	5	(	(	PUNCT
ejpam-5638	353	6	a	a	DET
ejpam-5638	353	7	bin	bin	NOUN
ejpam-5638	353	8	in	in	ADP
ejpam-5638	353	9	o	o	PROPN
ejpam-5638	353	10	)	)	PUNCT
ejpam-5638	353	11	is	be	AUX
ejpam-5638	353	12	d	d	ADJ
ejpam-5638	353	13	-	-	ADJ
ejpam-5638	353	14	stable	stable	ADJ
ejpam-5638	353	15	⇔	⇔	X
ejpam-5638	353	16	re	re	X
ejpam-5638	353	17	(	(	PUNCT
ejpam-5638	353	18	λi	λi	X
ejpam-5638	353	19	(	(	PUNCT
ejpam-5638	353	20	a	a	DET
ejpam-5638	353	21	bin	bin	NOUN
ejpam-5638	353	22	in	in	ADP
ejpam-5638	353	23	o	o	PROPN
ejpam-5638	353	24	)	)	PUNCT
ejpam-5638	353	25	)	)	PUNCT
ejpam-5638	353	26	>	>	X
ejpam-5638	353	27	0	0	NUM
ejpam-5638	353	28	,	,	PUNCT
ejpam-5638	353	29	and	and	CCONJ
ejpam-5638	353	30	n∏	n∏	PROPN
ejpam-5638	353	31	i=1	i=1	PROPN
ejpam-5638	353	32	λi	λi	X
ejpam-5638	353	33	(	(	PUNCT
ejpam-5638	353	34	(	(	PUNCT
ejpam-5638	353	35	x	x	SYM
ejpam-5638	353	36	−p	−p	NOUN
ejpam-5638	353	37	p	p	NOUN
ejpam-5638	353	38	x	x	PROPN
ejpam-5638	353	39	)	)	PUNCT
ejpam-5638	353	40	)	)	PUNCT
ejpam-5638	354	1	̸=	̸=	PROPN
ejpam-5638	354	2	0,∀i	0,∀i	NUM
ejpam-5638	354	3	,	,	PUNCT
ejpam-5638	354	4	∀p	∀p	X
ejpam-5638	354	5	∈	∈	PROPN
ejpam-5638	354	6	d̂	d̂	NOUN
ejpam-5638	354	7	,	,	PUNCT
ejpam-5638	354	8	wherex	wherex	PROPN
ejpam-5638	354	9	=	=	SYM
ejpam-5638	354	10	(	(	PUNCT
ejpam-5638	354	11	a	a	DET
ejpam-5638	354	12	bin	bin	NOUN
ejpam-5638	354	13	in	in	ADP
ejpam-5638	354	14	o	o	PROPN
ejpam-5638	354	15	)	)	PUNCT
ejpam-5638	354	16	.	.	PUNCT
ejpam-5638	355	1	thus	thus	ADV
ejpam-5638	355	2	,	,	PUNCT
ejpam-5638	355	3	n∏	n∏	PROPN
ejpam-5638	355	4	i=1	i=1	PROPN
ejpam-5638	356	1	λi	λi	X
ejpam-5638	356	2	(	(	PUNCT
ejpam-5638	356	3	(	(	PUNCT
ejpam-5638	356	4	x	x	SYM
ejpam-5638	356	5	−p	−p	NOUN
ejpam-5638	356	6	p	p	NOUN
ejpam-5638	356	7	x	x	PROPN
ejpam-5638	356	8	)	)	PUNCT
ejpam-5638	356	9	)	)	PUNCT
ejpam-5638	357	1	̸=	̸=	NOUN
ejpam-5638	357	2	0	0	NUM
ejpam-5638	358	1	=	=	NOUN
ejpam-5638	358	2	⇒	⇒	PROPN
ejpam-5638	358	3	n∏	n∏	PROPN
ejpam-5638	358	4	i=1	i=1	PROPN
ejpam-5638	358	5	λi(x	λi(x	X
ejpam-5638	358	6	2	2	NUM
ejpam-5638	358	7	−	−	NOUN
ejpam-5638	358	8	px−1px	px−1px	NUM
ejpam-5638	358	9	)	)	PUNCT
ejpam-5638	358	10	̸=	̸=	PROPN
ejpam-5638	358	11	0	0	NUM
ejpam-5638	358	12	,	,	PUNCT
ejpam-5638	358	13	∀i	∀i	NOUN
ejpam-5638	358	14	,	,	PUNCT
ejpam-5638	358	15	∀p	∀p	NOUN
ejpam-5638	358	16	∈	∈	NOUN
ejpam-5638	358	17	d̂.	d̂.	NOUN
ejpam-5638	358	18	also	also	ADV
ejpam-5638	358	19	,	,	PUNCT
ejpam-5638	358	20	n∏	n∏	PROPN
ejpam-5638	358	21	i=1	i=1	PROPN
ejpam-5638	358	22	λi(x	λi(x	X
ejpam-5638	358	23	2	2	NUM
ejpam-5638	358	24	−	−	NOUN
ejpam-5638	358	25	px−1px	px−1px	NUM
ejpam-5638	358	26	)	)	PUNCT
ejpam-5638	358	27	̸=	̸=	PROPN
ejpam-5638	358	28	0	0	NUM
ejpam-5638	358	29	=	=	NOUN
ejpam-5638	358	30	⇒	⇒	PRON
ejpam-5638	358	31	n∏	n∏	PROPN
ejpam-5638	358	32	i=1	i=1	PROPN
ejpam-5638	358	33	λi(in	λi(in	NOUN
ejpam-5638	358	34	−x−2p̂	−x−2p̂	X
ejpam-5638	358	35	)	)	PUNCT
ejpam-5638	359	1	̸=	̸=	NOUN
ejpam-5638	359	2	0	0	NUM
ejpam-5638	359	3	,	,	PUNCT
ejpam-5638	359	4	where	where	SCONJ
ejpam-5638	359	5	p̂	p̂	X
ejpam-5638	359	6	=	=	PUNCT
ejpam-5638	359	7	p	p	X
ejpam-5638	359	8	∈	∈	PROPN
ejpam-5638	359	9	d̂	d̂	PROPN
ejpam-5638	359	10	,	,	PUNCT
ejpam-5638	359	11	a	a	DET
ejpam-5638	359	12	positive	positive	ADJ
ejpam-5638	359	13	diagonal	diagonal	ADJ
ejpam-5638	359	14	matrix	matrix	NOUN
ejpam-5638	359	15	.	.	PUNCT
ejpam-5638	360	1	so	so	ADV
ejpam-5638	360	2	,	,	PUNCT
ejpam-5638	360	3	finally	finally	ADV
ejpam-5638	360	4	we	we	PRON
ejpam-5638	360	5	have	have	VERB
ejpam-5638	360	6	that	that	DET
ejpam-5638	360	7	n∏	n∏	PROPN
ejpam-5638	360	8	i=1	i=1	PROPN
ejpam-5638	361	1	λi	λi	X
ejpam-5638	361	2	(	(	PUNCT
ejpam-5638	361	3	in	in	ADP
ejpam-5638	361	4	−	−	PROPN
ejpam-5638	361	5	(	(	PUNCT
ejpam-5638	361	6	a	a	DET
ejpam-5638	361	7	bin	bin	NOUN
ejpam-5638	361	8	in	in	ADP
ejpam-5638	361	9	o	o	PROPN
ejpam-5638	361	10	)	)	PUNCT
ejpam-5638	361	11	−2	−2	NOUN
ejpam-5638	361	12	p̂	p̂	NOUN
ejpam-5638	361	13	)	)	PUNCT
ejpam-5638	362	1	̸=	̸=	NOUN
ejpam-5638	362	2	0	0	NUM
ejpam-5638	363	1	=	=	NOUN
ejpam-5638	363	2	⇒	⇒	NOUN
ejpam-5638	363	3	0	0	NUM
ejpam-5638	363	4	≤	≤	NUM
ejpam-5638	363	5	µ∆̂	µ∆̂	PROPN
ejpam-5638	363	6	(	(	PUNCT
ejpam-5638	363	7	(	(	PUNCT
ejpam-5638	363	8	a	a	DET
ejpam-5638	363	9	bin	bin	NOUN
ejpam-5638	363	10	in	in	ADP
ejpam-5638	363	11	o	o	PROPN
ejpam-5638	363	12	)	)	PUNCT
ejpam-5638	363	13	−2	−2	NOUN
ejpam-5638	363	14	)	)	PUNCT
ejpam-5638	363	15	<	<	X
ejpam-5638	363	16	1	1	X
ejpam-5638	363	17	.	.	PUNCT
ejpam-5638	363	18	theorem	theorem	VERB
ejpam-5638	363	19	12	12	NUM
ejpam-5638	363	20	shows	show	VERB
ejpam-5638	363	21	that	that	SCONJ
ejpam-5638	363	22	second	second	ADJ
ejpam-5638	363	23	order	order	NOUN
ejpam-5638	363	24	dynamical	dynamical	ADJ
ejpam-5638	363	25	system	system	NOUN
ejpam-5638	363	26	is	be	AUX
ejpam-5638	363	27	d	d	NOUN
ejpam-5638	363	28	-	-	ADJ
ejpam-5638	363	29	stable	stable	ADJ
ejpam-5638	363	30	for	for	ADP
ejpam-5638	363	31	matrices	matrix	NOUN
ejpam-5638	363	32	a	a	PRON
ejpam-5638	363	33	,	,	PUNCT
ejpam-5638	363	34	b	b	X
ejpam-5638	363	35	such	such	ADJ
ejpam-5638	363	36	that	that	PRON
ejpam-5638	363	37	(	(	PUNCT
ejpam-5638	363	38	ain	ain	PROPN
ejpam-5638	363	39	b	b	PROPN
ejpam-5638	363	40	in	in	ADP
ejpam-5638	363	41	o	o	PROPN
ejpam-5638	363	42	)	)	PUNCT
ejpam-5638	363	43	is	be	AUX
ejpam-5638	363	44	stable	stable	ADJ
ejpam-5638	363	45	for	for	ADP
ejpam-5638	363	46	a	a	DET
ejpam-5638	363	47	<	<	X
ejpam-5638	363	48	0	0	NUM
ejpam-5638	363	49	,	,	PUNCT
ejpam-5638	363	50	and	and	CCONJ
ejpam-5638	363	51	the	the	DET
ejpam-5638	363	52	non	non	ADJ
ejpam-5638	363	53	-	-	ADJ
ejpam-5638	363	54	negative	negative	ADJ
ejpam-5638	363	55	structured	structured	ADJ
ejpam-5638	363	56	singular	singular	ADJ
ejpam-5638	363	57	value	value	NOUN
ejpam-5638	363	58	is	be	AUX
ejpam-5638	363	59	bounded	bound	VERB
ejpam-5638	363	60	by	by	ADP
ejpam-5638	363	61	1	1	NUM
ejpam-5638	363	62	.	.	PUNCT
ejpam-5638	364	1	m.u.r	m.u.r	PROPN
ejpam-5638	364	2	rehman	rehman	PROPN
ejpam-5638	364	3	et	et	PROPN
ejpam-5638	364	4	al	al	PROPN
ejpam-5638	364	5	.	.	PUNCT
ejpam-5638	364	6	/	/	SYM
ejpam-5638	364	7	eur	eur	PROPN
ejpam-5638	364	8	.	.	PUNCT
ejpam-5638	365	1	j.	j.	PROPN
ejpam-5638	365	2	pure	pure	PROPN
ejpam-5638	365	3	appl	appl	PROPN
ejpam-5638	365	4	.	.	PROPN
ejpam-5638	365	5	math	math	PROPN
ejpam-5638	365	6	,	,	PUNCT
ejpam-5638	365	7	18	18	NUM
ejpam-5638	365	8	(	(	PUNCT
ejpam-5638	365	9	2	2	NUM
ejpam-5638	365	10	)	)	PUNCT
ejpam-5638	365	11	(	(	PUNCT
ejpam-5638	365	12	2025	2025	NUM
ejpam-5638	365	13	)	)	PUNCT
ejpam-5638	365	14	,	,	PUNCT
ejpam-5638	365	15	5638	5638	NUM
ejpam-5638	365	16	15	15	NUM
ejpam-5638	365	17	of	of	ADP
ejpam-5638	365	18	23	23	NUM
ejpam-5638	365	19	theorem	theorem	NOUN
ejpam-5638	365	20	12	12	NUM
ejpam-5638	365	21	.	.	PUNCT
ejpam-5638	366	1	the	the	DET
ejpam-5638	366	2	dynamical	dynamical	ADJ
ejpam-5638	366	3	system	system	NOUN
ejpam-5638	366	4	ẍ	ẍ	X
ejpam-5638	366	5	=	=	PUNCT
ejpam-5638	367	1	aẋ	aẋ	NOUN
ejpam-5638	368	1	+	+	CCONJ
ejpam-5638	368	2	bx	bx	X
ejpam-5638	368	3	,	,	PUNCT
ejpam-5638	368	4	x	x	SYM
ejpam-5638	368	5	∈	∈	PROPN
ejpam-5638	368	6	rn,1	rn,1	PROPN
ejpam-5638	368	7	,	,	PUNCT
ejpam-5638	368	8	is	be	AUX
ejpam-5638	368	9	structured	structure	VERB
ejpam-5638	368	10	d	d	ADJ
ejpam-5638	368	11	-	-	ADJ
ejpam-5638	368	12	stable	stable	ADJ
ejpam-5638	368	13	if	if	SCONJ
ejpam-5638	368	14	(	(	PUNCT
ejpam-5638	368	15	ain	ain	PROPN
ejpam-5638	368	16	b	b	PROPN
ejpam-5638	368	17	in	in	ADP
ejpam-5638	368	18	o	o	PROPN
ejpam-5638	368	19	)	)	PUNCT
ejpam-5638	368	20	,	,	PUNCT
ejpam-5638	368	21	a	a	DET
ejpam-5638	368	22	<	<	X
ejpam-5638	368	23	0	0	NUM
ejpam-5638	368	24	is	be	AUX
ejpam-5638	368	25	stable	stable	ADJ
ejpam-5638	368	26	and	and	CCONJ
ejpam-5638	368	27	0	0	NUM
ejpam-5638	368	28	≤	≤	NOUN
ejpam-5638	368	29	µ∆̂(x	µ∆̂(x	NOUN
ejpam-5638	368	30	)	)	PUNCT
ejpam-5638	368	31	<	<	X
ejpam-5638	368	32	1	1	NUM
ejpam-5638	368	33	,	,	PUNCT
ejpam-5638	368	34	where	where	SCONJ
ejpam-5638	368	35	x	x	X
ejpam-5638	368	36	=	=	PUNCT
ejpam-5638	368	37	(	(	PUNCT
ejpam-5638	368	38	(	(	PUNCT
ejpam-5638	368	39	iin	iin	NOUN
ejpam-5638	368	40	o	o	NOUN
ejpam-5638	368	41	o	o	X
ejpam-5638	368	42	iin	iin	NOUN
ejpam-5638	368	43	)	)	PUNCT
ejpam-5638	369	1	+	+	CCONJ
ejpam-5638	369	2	(	(	PUNCT
ejpam-5638	369	3	p11	p11	ADJ
ejpam-5638	369	4	o	o	NOUN
ejpam-5638	369	5	o	o	NOUN
ejpam-5638	369	6	p22	p22	NOUN
ejpam-5638	369	7	)	)	PUNCT
ejpam-5638	369	8	(	(	PUNCT
ejpam-5638	369	9	ain	ain	PROPN
ejpam-5638	369	10	b	b	PROPN
ejpam-5638	369	11	in	in	ADP
ejpam-5638	369	12	o	o	PROPN
ejpam-5638	369	13	)	)	PUNCT
ejpam-5638	370	1	+	+	CCONJ
ejpam-5638	370	2	(	(	PUNCT
ejpam-5638	370	3	ain	ain	PROPN
ejpam-5638	370	4	b	b	PROPN
ejpam-5638	370	5	in	in	ADP
ejpam-5638	370	6	o	o	PROPN
ejpam-5638	370	7	)	)	PUNCT
ejpam-5638	370	8	t	t	PROPN
ejpam-5638	370	9	(	(	PUNCT
ejpam-5638	370	10	p11	p11	VERB
ejpam-5638	370	11	o	o	NOUN
ejpam-5638	370	12	o	o	NOUN
ejpam-5638	370	13	p22	p22	NOUN
ejpam-5638	370	14	)	)	PUNCT
ejpam-5638	370	15	)	)	PUNCT
ejpam-5638	370	16	−1	−1	NOUN
ejpam-5638	370	17	(	(	PUNCT
ejpam-5638	370	18	(	(	PUNCT
ejpam-5638	370	19	iin	iin	NOUN
ejpam-5638	370	20	o	o	NOUN
ejpam-5638	370	21	o	o	X
ejpam-5638	370	22	iin	iin	NOUN
ejpam-5638	370	23	)	)	PUNCT
ejpam-5638	370	24	−	−	PROPN
ejpam-5638	371	1	(	(	PUNCT
ejpam-5638	371	2	p11	p11	NOUN
ejpam-5638	371	3	o	o	NOUN
ejpam-5638	371	4	o	o	NOUN
ejpam-5638	371	5	p22	p22	NOUN
ejpam-5638	371	6	)	)	PUNCT
ejpam-5638	371	7	(	(	PUNCT
ejpam-5638	371	8	ain	ain	PROPN
ejpam-5638	371	9	b	b	PROPN
ejpam-5638	371	10	in	in	ADP
ejpam-5638	371	11	o	o	PROPN
ejpam-5638	371	12	)	)	PUNCT
ejpam-5638	372	1	(	(	PUNCT
ejpam-5638	372	2	ain	ain	PROPN
ejpam-5638	372	3	b	b	PROPN
ejpam-5638	372	4	in	in	ADP
ejpam-5638	372	5	o	o	PROPN
ejpam-5638	372	6	)	)	PUNCT
ejpam-5638	373	1	t	t	PROPN
ejpam-5638	373	2	(	(	PUNCT
ejpam-5638	373	3	p11	p11	VERB
ejpam-5638	373	4	o	o	NOUN
ejpam-5638	373	5	o	o	NOUN
ejpam-5638	373	6	p22	p22	NOUN
ejpam-5638	373	7	)	)	PUNCT
ejpam-5638	373	8	.	.	PUNCT
ejpam-5638	374	1	proof	proof	NOUN
ejpam-5638	374	2	.	.	PUNCT
ejpam-5638	375	1	to	to	PART
ejpam-5638	375	2	show	show	VERB
ejpam-5638	375	3	that	that	SCONJ
ejpam-5638	375	4	(	(	PUNCT
ejpam-5638	375	5	ain	ain	PROPN
ejpam-5638	375	6	b	b	PROPN
ejpam-5638	375	7	in	in	ADP
ejpam-5638	375	8	o	o	PROPN
ejpam-5638	375	9	)	)	PUNCT
ejpam-5638	375	10	is	be	AUX
ejpam-5638	375	11	d	d	ADJ
ejpam-5638	375	12	-	-	ADJ
ejpam-5638	375	13	stable	stable	ADJ
ejpam-5638	375	14	matrix	matrix	NOUN
ejpam-5638	375	15	iff	iff	PROPN
ejpam-5638	375	16	re	re	ADP
ejpam-5638	375	17	(	(	PUNCT
ejpam-5638	375	18	λi	λi	X
ejpam-5638	375	19	(	(	PUNCT
ejpam-5638	375	20	(	(	PUNCT
ejpam-5638	375	21	p11	p11	NOUN
ejpam-5638	375	22	o	o	NOUN
ejpam-5638	375	23	o	o	NOUN
ejpam-5638	375	24	p22	p22	NOUN
ejpam-5638	375	25	)	)	PUNCT
ejpam-5638	375	26	(	(	PUNCT
ejpam-5638	375	27	ain	ain	PROPN
ejpam-5638	375	28	b	b	PROPN
ejpam-5638	375	29	in	in	ADP
ejpam-5638	375	30	o	o	PROPN
ejpam-5638	375	31	)	)	PUNCT
ejpam-5638	376	1	+	+	CCONJ
ejpam-5638	376	2	(	(	PUNCT
ejpam-5638	376	3	ain	ain	PROPN
ejpam-5638	376	4	b	b	PROPN
ejpam-5638	376	5	in	in	ADP
ejpam-5638	376	6	o	o	PROPN
ejpam-5638	376	7	)	)	PUNCT
ejpam-5638	376	8	t	t	PROPN
ejpam-5638	376	9	(	(	PUNCT
ejpam-5638	376	10	p11	p11	VERB
ejpam-5638	376	11	o	o	NOUN
ejpam-5638	376	12	o	o	NOUN
ejpam-5638	376	13	p22	p22	NOUN
ejpam-5638	376	14	)	)	PUNCT
ejpam-5638	376	15	)	)	PUNCT
ejpam-5638	376	16	)	)	PUNCT
ejpam-5638	377	1	>	>	X
ejpam-5638	377	2	0	0	NUM
ejpam-5638	377	3	,	,	PUNCT
ejpam-5638	377	4	∀i	∀i	NOUN
ejpam-5638	377	5	,	,	PUNCT
ejpam-5638	377	6	p	p	PROPN
ejpam-5638	377	7	∈	∈	PROPN
ejpam-5638	377	8	d̂	d̂	X
ejpam-5638	377	9	a	a	DET
ejpam-5638	377	10	positive	positive	ADJ
ejpam-5638	377	11	diagonal	diagonal	ADJ
ejpam-5638	377	12	matrix	matrix	NOUN
ejpam-5638	377	13	,	,	PUNCT
ejpam-5638	377	14	one	one	PRON
ejpam-5638	377	15	can	can	AUX
ejpam-5638	377	16	follow	follow	VERB
ejpam-5638	377	17	theorem-1	theorem-1	NUM
ejpam-5638	377	18	of	of	ADP
ejpam-5638	377	19	[	[	X
ejpam-5638	377	20	31	31	NUM
ejpam-5638	377	21	]	]	PUNCT
ejpam-5638	377	22	.	.	PUNCT
ejpam-5638	378	1	to	to	PART
ejpam-5638	378	2	prove	prove	VERB
ejpam-5638	378	3	that	that	SCONJ
ejpam-5638	378	4	(	(	PUNCT
ejpam-5638	378	5	ain	ain	PROPN
ejpam-5638	378	6	b	b	PROPN
ejpam-5638	378	7	in	in	ADP
ejpam-5638	378	8	o	o	PROPN
ejpam-5638	378	9	)	)	PUNCT
ejpam-5638	378	10	is	be	AUX
ejpam-5638	378	11	d	d	ADJ
ejpam-5638	378	12	-	-	ADJ
ejpam-5638	378	13	stable	stable	ADJ
ejpam-5638	378	14	iff	iff	NOUN
ejpam-5638	379	1	it	it	PRON
ejpam-5638	379	2	’s	’	VERB
ejpam-5638	379	3	structured	structure	VERB
ejpam-5638	379	4	singular	singular	ADJ
ejpam-5638	379	5	values	value	NOUN
ejpam-5638	379	6	are	be	AUX
ejpam-5638	379	7	non	non	ADJ
ejpam-5638	379	8	-	-	ADJ
ejpam-5638	379	9	negative	negative	ADJ
ejpam-5638	379	10	and	and	CCONJ
ejpam-5638	379	11	bounded	bound	VERB
ejpam-5638	379	12	by	by	ADP
ejpam-5638	379	13	1	1	NUM
ejpam-5638	379	14	,	,	PUNCT
ejpam-5638	379	15	we	we	PRON
ejpam-5638	379	16	let	let	VERB
ejpam-5638	379	17	∆	∆	PROPN
ejpam-5638	379	18	,	,	PUNCT
ejpam-5638	379	19	a	a	DET
ejpam-5638	379	20	block	block	NOUN
ejpam-5638	379	21	-	-	PUNCT
ejpam-5638	379	22	diagonal	diagonal	ADJ
ejpam-5638	379	23	structure	structure	NOUN
ejpam-5638	379	24	as	as	ADP
ejpam-5638	379	25	∆	∆	PROPN
ejpam-5638	379	26	=	=	PUNCT
ejpam-5638	379	27	(	(	PUNCT
ejpam-5638	379	28	(	(	PUNCT
ejpam-5638	379	29	iin	iin	NOUN
ejpam-5638	379	30	o	o	NOUN
ejpam-5638	380	1	o	o	X
ejpam-5638	380	2	iin	iin	NOUN
ejpam-5638	380	3	)	)	PUNCT
ejpam-5638	380	4	−	−	PROPN
ejpam-5638	381	1	(	(	PUNCT
ejpam-5638	381	2	p11	p11	NOUN
ejpam-5638	381	3	o	o	NOUN
ejpam-5638	381	4	o	o	NOUN
ejpam-5638	381	5	p22	p22	NOUN
ejpam-5638	381	6	)	)	PUNCT
ejpam-5638	381	7	)	)	PUNCT
ejpam-5638	382	1	(	(	PUNCT
ejpam-5638	382	2	(	(	PUNCT
ejpam-5638	382	3	iin	iin	NOUN
ejpam-5638	382	4	o	o	NOUN
ejpam-5638	382	5	o	o	X
ejpam-5638	382	6	iin	iin	NOUN
ejpam-5638	382	7	)	)	PUNCT
ejpam-5638	383	1	+	+	CCONJ
ejpam-5638	383	2	(	(	PUNCT
ejpam-5638	383	3	p11	p11	ADJ
ejpam-5638	383	4	o	o	NOUN
ejpam-5638	383	5	o	o	NOUN
ejpam-5638	383	6	p22	p22	NOUN
ejpam-5638	383	7	)	)	PUNCT
ejpam-5638	383	8	)	)	PUNCT
ejpam-5638	383	9	−1	−1	NOUN
ejpam-5638	383	10	,	,	PUNCT
ejpam-5638	383	11	∆	∆	PROPN
ejpam-5638	383	12	∈	∈	PROPN
ejpam-5638	383	13	∆̂	∆̂	PUNCT
ejpam-5638	383	14	since	since	ADV
ejpam-5638	383	15	,	,	PUNCT
ejpam-5638	383	16	λi	λi	X
ejpam-5638	383	17	(	(	PUNCT
ejpam-5638	383	18	(	(	PUNCT
ejpam-5638	383	19	p11	p11	NOUN
ejpam-5638	383	20	o	o	NOUN
ejpam-5638	383	21	o	o	NOUN
ejpam-5638	383	22	p22	p22	NOUN
ejpam-5638	383	23	)	)	PUNCT
ejpam-5638	383	24	(	(	PUNCT
ejpam-5638	383	25	ain	ain	PROPN
ejpam-5638	383	26	b	b	PROPN
ejpam-5638	383	27	in	in	ADP
ejpam-5638	383	28	o	o	PROPN
ejpam-5638	383	29	)	)	PUNCT
ejpam-5638	384	1	+	+	CCONJ
ejpam-5638	384	2	(	(	PUNCT
ejpam-5638	384	3	ain	ain	PROPN
ejpam-5638	384	4	b	b	PROPN
ejpam-5638	384	5	in	in	ADP
ejpam-5638	384	6	o	o	PROPN
ejpam-5638	384	7	)	)	PUNCT
ejpam-5638	384	8	t	t	PROPN
ejpam-5638	384	9	(	(	PUNCT
ejpam-5638	384	10	p11	p11	VERB
ejpam-5638	384	11	o	o	NOUN
ejpam-5638	384	12	o	o	NOUN
ejpam-5638	384	13	p22	p22	NOUN
ejpam-5638	384	14	)	)	PUNCT
ejpam-5638	384	15	)	)	PUNCT
ejpam-5638	385	1	̸=	̸=	PROPN
ejpam-5638	385	2	0	0	NUM
ejpam-5638	385	3	,	,	PUNCT
ejpam-5638	385	4	∀p	∀p	NOUN
ejpam-5638	385	5	∈	∈	NOUN
ejpam-5638	385	6	d̂.	d̂.	NOUN
ejpam-5638	385	7	this	this	PRON
ejpam-5638	385	8	implies	imply	VERB
ejpam-5638	385	9	that	that	SCONJ
ejpam-5638	385	10	λi	λi	ADP
ejpam-5638	385	11	(	(	PUNCT
ejpam-5638	385	12	(	(	PUNCT
ejpam-5638	385	13	p11	p11	NOUN
ejpam-5638	385	14	o	o	NOUN
ejpam-5638	385	15	o	o	NOUN
ejpam-5638	385	16	p22	p22	NOUN
ejpam-5638	385	17	)	)	PUNCT
ejpam-5638	385	18	(	(	PUNCT
ejpam-5638	385	19	ain	ain	PROPN
ejpam-5638	385	20	b	b	PROPN
ejpam-5638	385	21	in	in	ADP
ejpam-5638	385	22	o	o	PROPN
ejpam-5638	385	23	)	)	PUNCT
ejpam-5638	386	1	+	+	CCONJ
ejpam-5638	386	2	(	(	PUNCT
ejpam-5638	386	3	ain	ain	PROPN
ejpam-5638	386	4	b	b	PROPN
ejpam-5638	386	5	in	in	ADP
ejpam-5638	386	6	o	o	PROPN
ejpam-5638	386	7	)	)	PUNCT
ejpam-5638	386	8	t	t	PROPN
ejpam-5638	386	9	(	(	PUNCT
ejpam-5638	386	10	p11	p11	VERB
ejpam-5638	386	11	o	o	NOUN
ejpam-5638	386	12	o	o	NOUN
ejpam-5638	386	13	p22	p22	NOUN
ejpam-5638	386	14	)	)	PUNCT
ejpam-5638	387	1	+	+	CCONJ
ejpam-5638	387	2	(	(	PUNCT
ejpam-5638	387	3	ip11	ip11	PROPN
ejpam-5638	387	4	o	o	NOUN
ejpam-5638	387	5	o	o	X
ejpam-5638	387	6	ip22	ip22	PROPN
ejpam-5638	387	7	)	)	PUNCT
ejpam-5638	387	8	)	)	PUNCT
ejpam-5638	388	1	̸=	̸=	PROPN
ejpam-5638	388	2	0	0	NUM
ejpam-5638	388	3	,	,	PUNCT
ejpam-5638	388	4	∀i	∀i	NOUN
ejpam-5638	388	5	iff	iff	PROPN
ejpam-5638	388	6	λi(y	λi(y	X
ejpam-5638	388	7	)	)	PUNCT
ejpam-5638	388	8	̸=	̸=	PROPN
ejpam-5638	388	9	0	0	NUM
ejpam-5638	388	10	,	,	PUNCT
ejpam-5638	388	11	∀i	∀i	NOUN
ejpam-5638	388	12	,	,	PUNCT
ejpam-5638	388	13	∀∆	∀∆	X
ejpam-5638	388	14	∈	∈	NOUN
ejpam-5638	388	15	∆̂	∆̂	NOUN
ejpam-5638	388	16	,	,	PUNCT
ejpam-5638	388	17	where	where	SCONJ
ejpam-5638	388	18	y	y	PROPN
ejpam-5638	388	19	=	=	SYM
ejpam-5638	388	20	(	(	PUNCT
ejpam-5638	388	21	(	(	PUNCT
ejpam-5638	388	22	p11	p11	NOUN
ejpam-5638	388	23	o	o	NOUN
ejpam-5638	388	24	o	o	NOUN
ejpam-5638	388	25	p22	p22	NOUN
ejpam-5638	388	26	)	)	PUNCT
ejpam-5638	388	27	(	(	PUNCT
ejpam-5638	388	28	ain	ain	PROPN
ejpam-5638	388	29	b	b	PROPN
ejpam-5638	388	30	in	in	ADP
ejpam-5638	388	31	o	o	PROPN
ejpam-5638	388	32	)	)	PUNCT
ejpam-5638	389	1	+	+	CCONJ
ejpam-5638	389	2	(	(	PUNCT
ejpam-5638	389	3	ain	ain	PROPN
ejpam-5638	389	4	b	b	PROPN
ejpam-5638	389	5	in	in	ADP
ejpam-5638	389	6	o	o	PROPN
ejpam-5638	389	7	)	)	PUNCT
ejpam-5638	389	8	t	t	PROPN
ejpam-5638	389	9	(	(	PUNCT
ejpam-5638	389	10	p11	p11	VERB
ejpam-5638	389	11	o	o	NOUN
ejpam-5638	389	12	o	o	NOUN
ejpam-5638	389	13	p22	p22	NOUN
ejpam-5638	389	14	)	)	PUNCT
ejpam-5638	390	1	+	+	CCONJ
ejpam-5638	390	2	i	i	PRON
ejpam-5638	391	1	[	[	X
ejpam-5638	391	2	(	(	PUNCT
ejpam-5638	391	3	iin	iin	NOUN
ejpam-5638	391	4	o	o	NOUN
ejpam-5638	391	5	o	o	X
ejpam-5638	391	6	iin	iin	NOUN
ejpam-5638	391	7	)	)	PUNCT
ejpam-5638	392	1	+	+	CCONJ
ejpam-5638	392	2	(	(	PUNCT
ejpam-5638	392	3	∆11	∆11	X
ejpam-5638	392	4	o	o	X
ejpam-5638	392	5	o	o	X
ejpam-5638	392	6	∆22	∆22	CCONJ
ejpam-5638	392	7	)	)	PUNCT
ejpam-5638	392	8	]	]	X
ejpam-5638	392	9	)	)	PUNCT
ejpam-5638	392	10	−1	−1	NOUN
ejpam-5638	392	11	(	(	PUNCT
ejpam-5638	392	12	(	(	PUNCT
ejpam-5638	392	13	iin	iin	NOUN
ejpam-5638	392	14	o	o	NOUN
ejpam-5638	392	15	o	o	X
ejpam-5638	392	16	iin	iin	NOUN
ejpam-5638	392	17	)	)	PUNCT
ejpam-5638	392	18	−	−	PROPN
ejpam-5638	393	1	(	(	PUNCT
ejpam-5638	393	2	∆11	∆11	X
ejpam-5638	393	3	o	o	X
ejpam-5638	393	4	o	o	X
ejpam-5638	393	5	∆22	∆22	PROPN
ejpam-5638	393	6	)	)	PUNCT
ejpam-5638	393	7	)	)	PUNCT
ejpam-5638	393	8	.	.	PUNCT
ejpam-5638	394	1	also	also	ADV
ejpam-5638	394	2	,	,	PUNCT
ejpam-5638	394	3	λi(z	λi(z	X
ejpam-5638	394	4	)	)	PUNCT
ejpam-5638	394	5	̸=	̸=	PROPN
ejpam-5638	394	6	0	0	NUM
ejpam-5638	394	7	,	,	PUNCT
ejpam-5638	394	8	∀∆	∀∆	NOUN
ejpam-5638	394	9	∈	∈	NOUN
ejpam-5638	394	10	∆̂	∆̂	NOUN
ejpam-5638	394	11	,	,	PUNCT
ejpam-5638	394	12	where	where	SCONJ
ejpam-5638	394	13	z	z	NOUN
ejpam-5638	394	14	=	=	PUNCT
ejpam-5638	394	15	(	(	PUNCT
ejpam-5638	394	16	iin	iin	NOUN
ejpam-5638	394	17	o	o	NOUN
ejpam-5638	394	18	o	o	X
ejpam-5638	394	19	iin	iin	NOUN
ejpam-5638	394	20	)	)	PUNCT
ejpam-5638	395	1	+	+	CCONJ
ejpam-5638	395	2	(	(	PUNCT
ejpam-5638	395	3	p11	p11	ADJ
ejpam-5638	395	4	o	o	NOUN
ejpam-5638	395	5	o	o	NOUN
ejpam-5638	395	6	p22	p22	NOUN
ejpam-5638	395	7	)	)	PUNCT
ejpam-5638	395	8	(	(	PUNCT
ejpam-5638	395	9	ain	ain	PROPN
ejpam-5638	395	10	b	b	PROPN
ejpam-5638	395	11	in	in	ADP
ejpam-5638	395	12	o	o	PROPN
ejpam-5638	395	13	)	)	PUNCT
ejpam-5638	396	1	+	+	CCONJ
ejpam-5638	396	2	(	(	PUNCT
ejpam-5638	396	3	ain	ain	PROPN
ejpam-5638	396	4	b	b	PROPN
ejpam-5638	396	5	in	in	ADP
ejpam-5638	396	6	o	o	PROPN
ejpam-5638	396	7	)	)	PUNCT
ejpam-5638	396	8	t	t	PROPN
ejpam-5638	396	9	(	(	PUNCT
ejpam-5638	396	10	p11	p11	VERB
ejpam-5638	396	11	o	o	NOUN
ejpam-5638	396	12	o	o	NOUN
ejpam-5638	396	13	p22	p22	NOUN
ejpam-5638	396	14	)	)	PUNCT
ejpam-5638	396	15	−	−	PROPN
ejpam-5638	397	1	(	(	PUNCT
ejpam-5638	397	2	i	i	PRON
ejpam-5638	397	3	(	(	PUNCT
ejpam-5638	397	4	iin	iin	NOUN
ejpam-5638	397	5	o	o	NOUN
ejpam-5638	397	6	o	o	X
ejpam-5638	397	7	iin	iin	NOUN
ejpam-5638	397	8	)	)	PUNCT
ejpam-5638	397	9	−	−	PROPN
ejpam-5638	398	1	(	(	PUNCT
ejpam-5638	398	2	p11	p11	NOUN
ejpam-5638	398	3	o	o	NOUN
ejpam-5638	398	4	o	o	NOUN
ejpam-5638	398	5	p22	p22	NOUN
ejpam-5638	398	6	)	)	PUNCT
ejpam-5638	398	7	m.u.r	m.u.r	PROPN
ejpam-5638	398	8	rehman	rehman	PROPN
ejpam-5638	398	9	et	et	PROPN
ejpam-5638	398	10	al	al	PROPN
ejpam-5638	398	11	.	.	PUNCT
ejpam-5638	398	12	/	/	SYM
ejpam-5638	398	13	eur	eur	PROPN
ejpam-5638	398	14	.	.	PUNCT
ejpam-5638	399	1	j.	j.	PROPN
ejpam-5638	399	2	pure	pure	PROPN
ejpam-5638	399	3	appl	appl	PROPN
ejpam-5638	399	4	.	.	PROPN
ejpam-5638	399	5	math	math	PROPN
ejpam-5638	399	6	,	,	PUNCT
ejpam-5638	399	7	18	18	NUM
ejpam-5638	399	8	(	(	PUNCT
ejpam-5638	399	9	2	2	NUM
ejpam-5638	399	10	)	)	PUNCT
ejpam-5638	399	11	(	(	PUNCT
ejpam-5638	399	12	2025	2025	NUM
ejpam-5638	399	13	)	)	PUNCT
ejpam-5638	399	14	,	,	PUNCT
ejpam-5638	399	15	5638	5638	NUM
ejpam-5638	399	16	16	16	NUM
ejpam-5638	399	17	of	of	ADP
ejpam-5638	399	18	23	23	NUM
ejpam-5638	399	19	(	(	PUNCT
ejpam-5638	399	20	ain	ain	PROPN
ejpam-5638	399	21	b	b	PROPN
ejpam-5638	399	22	in	in	ADP
ejpam-5638	399	23	o	o	PROPN
ejpam-5638	399	24	)	)	PUNCT
ejpam-5638	400	1	(	(	PUNCT
ejpam-5638	400	2	ain	ain	PROPN
ejpam-5638	400	3	b	b	PROPN
ejpam-5638	400	4	in	in	ADP
ejpam-5638	400	5	o	o	PROPN
ejpam-5638	400	6	)	)	PUNCT
ejpam-5638	401	1	t	t	PROPN
ejpam-5638	401	2	(	(	PUNCT
ejpam-5638	401	3	p11	p11	VERB
ejpam-5638	401	4	o	o	NOUN
ejpam-5638	401	5	o	o	NOUN
ejpam-5638	401	6	p22	p22	NOUN
ejpam-5638	401	7	)	)	PUNCT
ejpam-5638	401	8	(	(	PUNCT
ejpam-5638	401	9	∆11	∆11	X
ejpam-5638	401	10	o	o	X
ejpam-5638	401	11	o	o	X
ejpam-5638	401	12	∆22	∆22	CCONJ
ejpam-5638	401	13	)	)	PUNCT
ejpam-5638	401	14	.	.	PUNCT
ejpam-5638	402	1	finally	finally	ADV
ejpam-5638	402	2	,	,	PUNCT
ejpam-5638	402	3	λi(w	λi(w	PUNCT
ejpam-5638	402	4	)	)	PUNCT
ejpam-5638	403	1	̸=	̸=	PROPN
ejpam-5638	403	2	0	0	NUM
ejpam-5638	403	3	,	,	PUNCT
ejpam-5638	403	4	∀i	∀i	NOUN
ejpam-5638	403	5	,	,	PUNCT
ejpam-5638	403	6	∀∆	∀∆	X
ejpam-5638	403	7	∈	∈	NOUN
ejpam-5638	403	8	∆̂	∆̂	NOUN
ejpam-5638	403	9	,	,	PUNCT
ejpam-5638	403	10	where	where	SCONJ
ejpam-5638	403	11	w	w	NOUN
ejpam-5638	403	12	=	=	PUNCT
ejpam-5638	403	13	(	(	PUNCT
ejpam-5638	403	14	in	in	ADP
ejpam-5638	403	15	o	o	NOUN
ejpam-5638	403	16	o	o	NOUN
ejpam-5638	403	17	in	in	ADP
ejpam-5638	403	18	)	)	PUNCT
ejpam-5638	403	19	−	−	PROPN
ejpam-5638	404	1	(	(	PUNCT
ejpam-5638	404	2	(	(	PUNCT
ejpam-5638	404	3	iin	iin	NOUN
ejpam-5638	404	4	o	o	NOUN
ejpam-5638	404	5	o	o	X
ejpam-5638	404	6	iin	iin	NOUN
ejpam-5638	404	7	)	)	PUNCT
ejpam-5638	405	1	+	+	CCONJ
ejpam-5638	405	2	(	(	PUNCT
ejpam-5638	405	3	p11	p11	ADJ
ejpam-5638	405	4	o	o	NOUN
ejpam-5638	405	5	o	o	NOUN
ejpam-5638	405	6	p22	p22	NOUN
ejpam-5638	405	7	)	)	PUNCT
ejpam-5638	405	8	(	(	PUNCT
ejpam-5638	405	9	in	in	ADP
ejpam-5638	405	10	o	o	NOUN
ejpam-5638	405	11	o	o	NOUN
ejpam-5638	405	12	in	in	ADP
ejpam-5638	405	13	)	)	PUNCT
ejpam-5638	406	1	+	+	CCONJ
ejpam-5638	406	2	(	(	PUNCT
ejpam-5638	406	3	ain	ain	PROPN
ejpam-5638	406	4	b	b	PROPN
ejpam-5638	406	5	in	in	ADP
ejpam-5638	406	6	o	o	PROPN
ejpam-5638	406	7	)	)	PUNCT
ejpam-5638	406	8	t	t	PROPN
ejpam-5638	406	9	(	(	PUNCT
ejpam-5638	406	10	p11	p11	VERB
ejpam-5638	406	11	o	o	NOUN
ejpam-5638	406	12	o	o	NOUN
ejpam-5638	406	13	p22	p22	NOUN
ejpam-5638	406	14	)	)	PUNCT
ejpam-5638	406	15	)	)	PUNCT
ejpam-5638	406	16	−1	−1	NOUN
ejpam-5638	406	17	(	(	PUNCT
ejpam-5638	406	18	(	(	PUNCT
ejpam-5638	406	19	iin	iin	NOUN
ejpam-5638	406	20	o	o	NOUN
ejpam-5638	406	21	o	o	X
ejpam-5638	406	22	iin	iin	NOUN
ejpam-5638	406	23	)	)	PUNCT
ejpam-5638	406	24	−	−	PROPN
ejpam-5638	407	1	(	(	PUNCT
ejpam-5638	407	2	p11	p11	NOUN
ejpam-5638	407	3	o	o	NOUN
ejpam-5638	407	4	o	o	NOUN
ejpam-5638	407	5	p22	p22	NOUN
ejpam-5638	407	6	)	)	PUNCT
ejpam-5638	407	7	(	(	PUNCT
ejpam-5638	407	8	ain	ain	PROPN
ejpam-5638	407	9	b	b	PROPN
ejpam-5638	407	10	in	in	ADP
ejpam-5638	407	11	o	o	PROPN
ejpam-5638	407	12	)	)	PUNCT
ejpam-5638	408	1	(	(	PUNCT
ejpam-5638	408	2	ain	ain	PROPN
ejpam-5638	408	3	b	b	PROPN
ejpam-5638	408	4	in	in	ADP
ejpam-5638	408	5	o	o	PROPN
ejpam-5638	408	6	)	)	PUNCT
ejpam-5638	409	1	t	t	PROPN
ejpam-5638	409	2	(	(	PUNCT
ejpam-5638	409	3	p11	p11	VERB
ejpam-5638	409	4	o	o	NOUN
ejpam-5638	409	5	o	o	NOUN
ejpam-5638	409	6	p22	p22	NOUN
ejpam-5638	409	7	)	)	PUNCT
ejpam-5638	409	8	(	(	PUNCT
ejpam-5638	409	9	∆11	∆11	X
ejpam-5638	409	10	o	o	X
ejpam-5638	409	11	o	o	X
ejpam-5638	409	12	∆22	∆22	CCONJ
ejpam-5638	409	13	)	)	PUNCT
ejpam-5638	409	14	.	.	PUNCT
ejpam-5638	410	1	this	this	PRON
ejpam-5638	410	2	is	be	AUX
ejpam-5638	410	3	necessary	necessary	ADJ
ejpam-5638	410	4	condition	condition	NOUN
ejpam-5638	410	5	for	for	SCONJ
ejpam-5638	410	6	µ−value	µ−value	NOUN
ejpam-5638	410	7	to	to	PART
ejpam-5638	410	8	be	be	AUX
ejpam-5638	410	9	less	less	ADJ
ejpam-5638	410	10	than	than	ADP
ejpam-5638	410	11	1	1	NUM
ejpam-5638	410	12	.	.	PUNCT
ejpam-5638	411	1	this	this	PRON
ejpam-5638	411	2	complete	complete	ADJ
ejpam-5638	411	3	the	the	DET
ejpam-5638	411	4	proof	proof	NOUN
ejpam-5638	411	5	.	.	PUNCT
ejpam-5638	412	1	theorem	theorem	VERB
ejpam-5638	412	2	13	13	NUM
ejpam-5638	412	3	.	.	PUNCT
ejpam-5638	413	1	the	the	DET
ejpam-5638	413	2	dynamical	dynamical	ADJ
ejpam-5638	413	3	system	system	NOUN
ejpam-5638	413	4	ẍ	ẍ	X
ejpam-5638	413	5	=	=	PUNCT
ejpam-5638	413	6	aẋ+bx	aẋ+bx	PROPN
ejpam-5638	413	7	,	,	PUNCT
ejpam-5638	413	8	x	x	SYM
ejpam-5638	413	9	∈	∈	PROPN
ejpam-5638	413	10	rn,1	rn,1	PROPN
ejpam-5638	413	11	,	,	PUNCT
ejpam-5638	413	12	with	with	ADP
ejpam-5638	413	13	a	a	DET
ejpam-5638	413	14	,	,	PUNCT
ejpam-5638	413	15	b	b	PROPN
ejpam-5638	413	16	∈	∈	PROPN
ejpam-5638	413	17	rn	rn	PROPN
ejpam-5638	413	18	,	,	PUNCT
ejpam-5638	413	19	m	m	VERB
ejpam-5638	413	20	is	be	AUX
ejpam-5638	413	21	d	d	ADJ
ejpam-5638	413	22	-	-	ADJ
ejpam-5638	413	23	stable	stable	ADJ
ejpam-5638	413	24	if	if	SCONJ
ejpam-5638	413	25	(	(	PUNCT
ejpam-5638	413	26	ain	ain	PROPN
ejpam-5638	413	27	b	b	PROPN
ejpam-5638	413	28	in	in	ADP
ejpam-5638	413	29	o	o	PROPN
ejpam-5638	413	30	)	)	PUNCT
ejpam-5638	413	31	is	be	AUX
ejpam-5638	413	32	stable	stable	ADJ
ejpam-5638	413	33	and	and	CCONJ
ejpam-5638	413	34	0	0	NUM
ejpam-5638	413	35	≤	≤	NOUN
ejpam-5638	413	36	µ∆̂(x	µ∆̂(x	NOUN
ejpam-5638	413	37	)	)	PUNCT
ejpam-5638	413	38	<	<	X
ejpam-5638	413	39	1	1	NUM
ejpam-5638	413	40	,	,	PUNCT
ejpam-5638	413	41	where	where	SCONJ
ejpam-5638	413	42	x	x	X
ejpam-5638	413	43	=	=	PUNCT
ejpam-5638	413	44	(	(	PUNCT
ejpam-5638	413	45	(	(	PUNCT
ejpam-5638	413	46	iin	iin	NOUN
ejpam-5638	413	47	o	o	NOUN
ejpam-5638	413	48	o	o	X
ejpam-5638	413	49	iin	iin	NOUN
ejpam-5638	413	50	)	)	PUNCT
ejpam-5638	414	1	+	+	CCONJ
ejpam-5638	414	2	(	(	PUNCT
ejpam-5638	414	3	ain	ain	PROPN
ejpam-5638	414	4	b	b	PROPN
ejpam-5638	414	5	in	in	ADP
ejpam-5638	414	6	o	o	PROPN
ejpam-5638	414	7	)	)	PUNCT
ejpam-5638	414	8	)	)	PUNCT
ejpam-5638	414	9	−1	−1	NOUN
ejpam-5638	414	10	(	(	PUNCT
ejpam-5638	414	11	(	(	PUNCT
ejpam-5638	414	12	iin	iin	NOUN
ejpam-5638	414	13	o	o	NOUN
ejpam-5638	414	14	o	o	X
ejpam-5638	414	15	iin	iin	NOUN
ejpam-5638	414	16	)	)	PUNCT
ejpam-5638	414	17	−	−	PROPN
ejpam-5638	415	1	(	(	PUNCT
ejpam-5638	415	2	ain	ain	PROPN
ejpam-5638	415	3	b	b	PROPN
ejpam-5638	415	4	in	in	ADP
ejpam-5638	415	5	o	o	PROPN
ejpam-5638	415	6	)	)	PUNCT
ejpam-5638	415	7	)	)	PUNCT
ejpam-5638	415	8	.	.	PUNCT
ejpam-5638	416	1	proof	proof	NOUN
ejpam-5638	416	2	.	.	PUNCT
ejpam-5638	417	1	the	the	DET
ejpam-5638	417	2	matrix	matrix	NOUN
ejpam-5638	417	3	(	(	PUNCT
ejpam-5638	417	4	ain	ain	PROPN
ejpam-5638	417	5	b	b	PROPN
ejpam-5638	417	6	in	in	ADP
ejpam-5638	417	7	o	o	PROPN
ejpam-5638	417	8	)	)	PUNCT
ejpam-5638	417	9	is	be	AUX
ejpam-5638	417	10	d	d	ADJ
ejpam-5638	417	11	-	-	ADJ
ejpam-5638	417	12	stable	stable	ADJ
ejpam-5638	417	13	iff	iff	PROPN
ejpam-5638	417	14	(	(	PUNCT
ejpam-5638	417	15	ain	ain	PROPN
ejpam-5638	417	16	b	b	PROPN
ejpam-5638	417	17	in	in	ADP
ejpam-5638	417	18	o	o	PROPN
ejpam-5638	417	19	)	)	PUNCT
ejpam-5638	417	20	is	be	AUX
ejpam-5638	417	21	stable	stable	ADJ
ejpam-5638	417	22	and	and	CCONJ
ejpam-5638	417	23	λi	λi	INTJ
ejpam-5638	417	24	(	(	PUNCT
ejpam-5638	417	25	(	(	PUNCT
ejpam-5638	417	26	ain	ain	PROPN
ejpam-5638	417	27	b	b	PROPN
ejpam-5638	417	28	in	in	ADP
ejpam-5638	417	29	o	o	PROPN
ejpam-5638	417	30	)	)	PUNCT
ejpam-5638	418	1	+	+	CCONJ
ejpam-5638	418	2	i	i	PRON
ejpam-5638	418	3	(	(	PUNCT
ejpam-5638	418	4	p11	p11	ADJ
ejpam-5638	418	5	o	o	NOUN
ejpam-5638	418	6	o	o	NOUN
ejpam-5638	418	7	p22	p22	NOUN
ejpam-5638	418	8	)	)	PUNCT
ejpam-5638	418	9	)	)	PUNCT
ejpam-5638	418	10	̸=	̸=	PROPN
ejpam-5638	418	11	0	0	NUM
ejpam-5638	418	12	,	,	PUNCT
ejpam-5638	418	13	∀i	∀i	NOUN
ejpam-5638	418	14	,	,	PUNCT
ejpam-5638	418	15	for	for	ADP
ejpam-5638	418	16	any	any	DET
ejpam-5638	418	17	p	p	NOUN
ejpam-5638	418	18	=	=	PUNCT
ejpam-5638	418	19	(	(	PUNCT
ejpam-5638	418	20	p11	p11	NOUN
ejpam-5638	418	21	o	o	NOUN
ejpam-5638	418	22	o	o	NOUN
ejpam-5638	418	23	p22	p22	NOUN
ejpam-5638	418	24	)	)	PUNCT
ejpam-5638	418	25	positive	positive	ADJ
ejpam-5638	418	26	diagonal	diagonal	ADJ
ejpam-5638	418	27	matrix	matrix	NOUN
ejpam-5638	418	28	.	.	PUNCT
ejpam-5638	419	1	consider	consider	VERB
ejpam-5638	419	2	that	that	PRON
ejpam-5638	419	3	(	(	PUNCT
ejpam-5638	419	4	ain	ain	PROPN
ejpam-5638	419	5	b	b	PROPN
ejpam-5638	419	6	in	in	ADP
ejpam-5638	419	7	o	o	PROPN
ejpam-5638	419	8	)	)	PUNCT
ejpam-5638	419	9	is	be	AUX
ejpam-5638	419	10	d	d	ADJ
ejpam-5638	419	11	-	-	ADJ
ejpam-5638	419	12	stable	stable	ADJ
ejpam-5638	419	13	,	,	PUNCT
ejpam-5638	419	14	that	that	PRON
ejpam-5638	419	15	is	be	AUX
ejpam-5638	419	16	λi	λi	ADP
ejpam-5638	419	17	(	(	PUNCT
ejpam-5638	419	18	(	(	PUNCT
ejpam-5638	419	19	ain	ain	PROPN
ejpam-5638	419	20	b	b	PROPN
ejpam-5638	419	21	in	in	ADP
ejpam-5638	419	22	o	o	PROPN
ejpam-5638	419	23	)	)	PUNCT
ejpam-5638	420	1	+	+	CCONJ
ejpam-5638	420	2	i	i	PRON
ejpam-5638	420	3	(	(	PUNCT
ejpam-5638	420	4	p11	p11	ADJ
ejpam-5638	420	5	o	o	NOUN
ejpam-5638	420	6	o	o	NOUN
ejpam-5638	420	7	p22	p22	NOUN
ejpam-5638	420	8	)	)	PUNCT
ejpam-5638	420	9	)	)	PUNCT
ejpam-5638	420	10	̸=	̸=	PROPN
ejpam-5638	420	11	0	0	NUM
ejpam-5638	420	12	,	,	PUNCT
ejpam-5638	420	13	∀i	∀i	NOUN
ejpam-5638	420	14	.	.	PUNCT
ejpam-5638	421	1	let	let	VERB
ejpam-5638	421	2	∆	∆	PROPN
ejpam-5638	421	3	=	=	PUNCT
ejpam-5638	421	4	(	(	PUNCT
ejpam-5638	421	5	(	(	PUNCT
ejpam-5638	421	6	iin	iin	NOUN
ejpam-5638	421	7	o	o	NOUN
ejpam-5638	421	8	o	o	X
ejpam-5638	421	9	iin	iin	NOUN
ejpam-5638	421	10	)	)	PUNCT
ejpam-5638	421	11	−	−	PROPN
ejpam-5638	422	1	(	(	PUNCT
ejpam-5638	422	2	p11	p11	NOUN
ejpam-5638	422	3	o	o	NOUN
ejpam-5638	422	4	o	o	NOUN
ejpam-5638	422	5	p22	p22	NOUN
ejpam-5638	422	6	)	)	PUNCT
ejpam-5638	422	7	)	)	PUNCT
ejpam-5638	423	1	(	(	PUNCT
ejpam-5638	423	2	(	(	PUNCT
ejpam-5638	423	3	iin	iin	NOUN
ejpam-5638	423	4	o	o	NOUN
ejpam-5638	423	5	o	o	X
ejpam-5638	423	6	iin	iin	NOUN
ejpam-5638	423	7	)	)	PUNCT
ejpam-5638	424	1	+	+	CCONJ
ejpam-5638	424	2	(	(	PUNCT
ejpam-5638	424	3	p11	p11	ADJ
ejpam-5638	424	4	o	o	NOUN
ejpam-5638	424	5	o	o	NOUN
ejpam-5638	424	6	p22	p22	NOUN
ejpam-5638	424	7	)	)	PUNCT
ejpam-5638	424	8	)	)	PUNCT
ejpam-5638	424	9	−1	−1	NOUN
ejpam-5638	424	10	be	be	AUX
ejpam-5638	424	11	a	a	DET
ejpam-5638	424	12	diagonal	diagonal	ADJ
ejpam-5638	424	13	matrix	matrix	NOUN
ejpam-5638	424	14	and	and	CCONJ
ejpam-5638	424	15	∆	∆	PROPN
ejpam-5638	424	16	∈	∈	PROPN
ejpam-5638	424	17	∆̂.	∆̂.	VERB
ejpam-5638	424	18	then	then	ADV
ejpam-5638	424	19	,	,	PUNCT
ejpam-5638	424	20	(	(	PUNCT
ejpam-5638	424	21	p11	p11	NOUN
ejpam-5638	424	22	o	o	NOUN
ejpam-5638	424	23	o	o	NOUN
ejpam-5638	424	24	p22	p22	NOUN
ejpam-5638	424	25	)	)	PUNCT
ejpam-5638	424	26	=	=	PUNCT
ejpam-5638	425	1	(	(	PUNCT
ejpam-5638	425	2	(	(	PUNCT
ejpam-5638	425	3	iin	iin	NOUN
ejpam-5638	425	4	o	o	NOUN
ejpam-5638	425	5	o	o	X
ejpam-5638	425	6	iin	iin	NOUN
ejpam-5638	425	7	)	)	PUNCT
ejpam-5638	426	1	+	+	CCONJ
ejpam-5638	426	2	(	(	PUNCT
ejpam-5638	426	3	∆11	∆11	X
ejpam-5638	426	4	o	o	X
ejpam-5638	426	5	o	o	X
ejpam-5638	426	6	∆22	∆22	CCONJ
ejpam-5638	426	7	)	)	PUNCT
ejpam-5638	426	8	)	)	PUNCT
ejpam-5638	426	9	−1	−1	NOUN
ejpam-5638	426	10	(	(	PUNCT
ejpam-5638	426	11	(	(	PUNCT
ejpam-5638	426	12	iin	iin	NOUN
ejpam-5638	426	13	o	o	NOUN
ejpam-5638	426	14	o	o	X
ejpam-5638	426	15	iin	iin	NOUN
ejpam-5638	426	16	)	)	PUNCT
ejpam-5638	426	17	−	−	PROPN
ejpam-5638	427	1	(	(	PUNCT
ejpam-5638	427	2	∆11	∆11	X
ejpam-5638	427	3	o	o	X
ejpam-5638	427	4	o	o	X
ejpam-5638	427	5	∆22	∆22	CCONJ
ejpam-5638	427	6	)	)	PUNCT
ejpam-5638	427	7	)	)	PUNCT
ejpam-5638	427	8	is	be	AUX
ejpam-5638	427	9	positive	positive	ADJ
ejpam-5638	427	10	diagonal	diagonal	ADJ
ejpam-5638	427	11	matrix	matrix	NOUN
ejpam-5638	427	12	if	if	SCONJ
ejpam-5638	427	13	∆	∆	PROPN
ejpam-5638	427	14	∈	∈	PROPN
ejpam-5638	427	15	∆̂.	∆̂.	VERB
ejpam-5638	427	16	as	as	ADP
ejpam-5638	427	17	,	,	PUNCT
ejpam-5638	427	18	λi	λi	X
ejpam-5638	427	19	(	(	PUNCT
ejpam-5638	427	20	(	(	PUNCT
ejpam-5638	427	21	ain	ain	PROPN
ejpam-5638	427	22	b	b	PROPN
ejpam-5638	427	23	in	in	ADP
ejpam-5638	427	24	o	o	PROPN
ejpam-5638	427	25	)	)	PUNCT
ejpam-5638	428	1	+	+	CCONJ
ejpam-5638	428	2	i	i	PRON
ejpam-5638	428	3	(	(	PUNCT
ejpam-5638	428	4	p11	p11	ADJ
ejpam-5638	428	5	o	o	NOUN
ejpam-5638	428	6	o	o	NOUN
ejpam-5638	428	7	p22	p22	NOUN
ejpam-5638	428	8	)	)	PUNCT
ejpam-5638	428	9	)	)	PUNCT
ejpam-5638	428	10	̸=	̸=	PROPN
ejpam-5638	428	11	0	0	NUM
ejpam-5638	428	12	,	,	PUNCT
ejpam-5638	428	13	m.u.r	m.u.r	NOUN
ejpam-5638	428	14	rehman	rehman	PROPN
ejpam-5638	428	15	et	et	PROPN
ejpam-5638	428	16	al	al	PROPN
ejpam-5638	428	17	.	.	PUNCT
ejpam-5638	428	18	/	/	SYM
ejpam-5638	428	19	eur	eur	PROPN
ejpam-5638	428	20	.	.	PUNCT
ejpam-5638	429	1	j.	j.	PROPN
ejpam-5638	429	2	pure	pure	PROPN
ejpam-5638	429	3	appl	appl	PROPN
ejpam-5638	429	4	.	.	PROPN
ejpam-5638	429	5	math	math	PROPN
ejpam-5638	429	6	,	,	PUNCT
ejpam-5638	429	7	18	18	NUM
ejpam-5638	429	8	(	(	PUNCT
ejpam-5638	429	9	2	2	NUM
ejpam-5638	429	10	)	)	PUNCT
ejpam-5638	429	11	(	(	PUNCT
ejpam-5638	429	12	2025	2025	NUM
ejpam-5638	429	13	)	)	PUNCT
ejpam-5638	429	14	,	,	PUNCT
ejpam-5638	429	15	5638	5638	NUM
ejpam-5638	429	16	17	17	NUM
ejpam-5638	429	17	of	of	ADP
ejpam-5638	429	18	23	23	NUM
ejpam-5638	429	19	in	in	ADP
ejpam-5638	429	20	turn	turn	NOUN
ejpam-5638	429	21	this	this	PRON
ejpam-5638	429	22	imples	imple	VERB
ejpam-5638	429	23	that	that	PRON
ejpam-5638	429	24	λi(x	λi(x	X
ejpam-5638	429	25	)	)	PUNCT
ejpam-5638	429	26	̸=	̸=	PROPN
ejpam-5638	429	27	0,∀∆	0,∀∆	PROPN
ejpam-5638	429	28	∈	∈	PROPN
ejpam-5638	429	29	∆̂	∆̂	NOUN
ejpam-5638	429	30	,	,	PUNCT
ejpam-5638	429	31	where	where	SCONJ
ejpam-5638	429	32	x	x	PUNCT
ejpam-5638	429	33	=	=	PRON
ejpam-5638	429	34	(	(	PUNCT
ejpam-5638	429	35	ain	ain	PROPN
ejpam-5638	429	36	b	b	PROPN
ejpam-5638	429	37	in	in	ADP
ejpam-5638	429	38	o	o	PROPN
ejpam-5638	429	39	)	)	PUNCT
ejpam-5638	430	1	+	+	CCONJ
ejpam-5638	430	2	i	i	PRON
ejpam-5638	430	3	(	(	PUNCT
ejpam-5638	430	4	(	(	PUNCT
ejpam-5638	430	5	iin	iin	NOUN
ejpam-5638	430	6	o	o	NOUN
ejpam-5638	430	7	o	o	X
ejpam-5638	430	8	iin	iin	NOUN
ejpam-5638	430	9	)	)	PUNCT
ejpam-5638	431	1	+	+	CCONJ
ejpam-5638	431	2	(	(	PUNCT
ejpam-5638	431	3	∆11	∆11	X
ejpam-5638	431	4	o	o	X
ejpam-5638	431	5	o	o	X
ejpam-5638	431	6	∆22	∆22	CCONJ
ejpam-5638	431	7	)	)	PUNCT
ejpam-5638	431	8	)	)	PUNCT
ejpam-5638	431	9	−1	−1	NOUN
ejpam-5638	431	10	(	(	PUNCT
ejpam-5638	431	11	(	(	PUNCT
ejpam-5638	431	12	iin	iin	NOUN
ejpam-5638	431	13	o	o	NOUN
ejpam-5638	431	14	o	o	X
ejpam-5638	431	15	iin	iin	NOUN
ejpam-5638	431	16	)	)	PUNCT
ejpam-5638	431	17	−	−	PROPN
ejpam-5638	432	1	(	(	PUNCT
ejpam-5638	432	2	∆11	∆11	X
ejpam-5638	432	3	o	o	X
ejpam-5638	432	4	o	o	X
ejpam-5638	432	5	∆22	∆22	PROPN
ejpam-5638	432	6	)	)	PUNCT
ejpam-5638	432	7	)	)	PUNCT
ejpam-5638	432	8	.	.	PUNCT
ejpam-5638	433	1	the	the	DET
ejpam-5638	433	2	rank	rank	NOUN
ejpam-5638	433	3	of	of	ADP
ejpam-5638	433	4	(	(	PUNCT
ejpam-5638	433	5	ain	ain	PROPN
ejpam-5638	433	6	b	b	PROPN
ejpam-5638	433	7	in	in	ADP
ejpam-5638	433	8	o	o	PROPN
ejpam-5638	433	9	)	)	PUNCT
ejpam-5638	434	1	+	+	CCONJ
ejpam-5638	434	2	i	i	PRON
ejpam-5638	434	3	(	(	PUNCT
ejpam-5638	434	4	(	(	PUNCT
ejpam-5638	434	5	iin	iin	NOUN
ejpam-5638	434	6	o	o	NOUN
ejpam-5638	434	7	o	o	X
ejpam-5638	434	8	iin	iin	NOUN
ejpam-5638	434	9	)	)	PUNCT
ejpam-5638	435	1	+	+	CCONJ
ejpam-5638	435	2	(	(	PUNCT
ejpam-5638	435	3	∆11	∆11	X
ejpam-5638	435	4	o	o	X
ejpam-5638	435	5	o	o	X
ejpam-5638	435	6	∆22	∆22	CCONJ
ejpam-5638	435	7	)	)	PUNCT
ejpam-5638	435	8	)	)	PUNCT
ejpam-5638	435	9	−1	−1	NOUN
ejpam-5638	435	10	(	(	PUNCT
ejpam-5638	435	11	(	(	PUNCT
ejpam-5638	435	12	iin	iin	NOUN
ejpam-5638	435	13	o	o	NOUN
ejpam-5638	435	14	o	o	X
ejpam-5638	435	15	iin	iin	NOUN
ejpam-5638	435	16	)	)	PUNCT
ejpam-5638	435	17	−	−	PROPN
ejpam-5638	436	1	(	(	PUNCT
ejpam-5638	436	2	∆11	∆11	X
ejpam-5638	436	3	o	o	X
ejpam-5638	436	4	o	o	X
ejpam-5638	436	5	∆22	∆22	PROPN
ejpam-5638	436	6	)	)	PUNCT
ejpam-5638	436	7	)	)	PUNCT
ejpam-5638	436	8	.	.	PUNCT
ejpam-5638	437	1	implies	imply	VERB
ejpam-5638	437	2	that	that	SCONJ
ejpam-5638	437	3	λi(y	λi(y	X
ejpam-5638	437	4	)	)	PUNCT
ejpam-5638	437	5	̸=	̸=	PROPN
ejpam-5638	437	6	0	0	NUM
ejpam-5638	437	7	,	,	PUNCT
ejpam-5638	437	8	∀∆	∀∆	NOUN
ejpam-5638	437	9	∈	∈	NOUN
ejpam-5638	437	10	∆̂	∆̂	NOUN
ejpam-5638	437	11	,	,	PUNCT
ejpam-5638	437	12	where	where	SCONJ
ejpam-5638	437	13	y	y	PROPN
ejpam-5638	437	14	=	=	PUNCT
ejpam-5638	437	15	(	(	PUNCT
ejpam-5638	437	16	in	in	ADP
ejpam-5638	437	17	o	o	NOUN
ejpam-5638	437	18	o	o	NOUN
ejpam-5638	437	19	in	in	ADP
ejpam-5638	437	20	)	)	PUNCT
ejpam-5638	437	21	−	−	PROPN
ejpam-5638	438	1	(	(	PUNCT
ejpam-5638	438	2	(	(	PUNCT
ejpam-5638	438	3	iin	iin	NOUN
ejpam-5638	438	4	o	o	NOUN
ejpam-5638	438	5	o	o	X
ejpam-5638	438	6	iin	iin	NOUN
ejpam-5638	438	7	)	)	PUNCT
ejpam-5638	439	1	+	+	CCONJ
ejpam-5638	439	2	(	(	PUNCT
ejpam-5638	439	3	ain	ain	PROPN
ejpam-5638	439	4	b	b	PROPN
ejpam-5638	439	5	in	in	ADP
ejpam-5638	439	6	o	o	PROPN
ejpam-5638	439	7	)	)	PUNCT
ejpam-5638	439	8	)	)	PUNCT
ejpam-5638	439	9	−1	−1	NOUN
ejpam-5638	439	10	(	(	PUNCT
ejpam-5638	439	11	(	(	PUNCT
ejpam-5638	439	12	iin	iin	NOUN
ejpam-5638	439	13	o	o	NOUN
ejpam-5638	439	14	o	o	X
ejpam-5638	439	15	iin	iin	NOUN
ejpam-5638	439	16	)	)	PUNCT
ejpam-5638	439	17	−	−	PROPN
ejpam-5638	440	1	(	(	PUNCT
ejpam-5638	440	2	ain	ain	PROPN
ejpam-5638	440	3	b	b	PROPN
ejpam-5638	440	4	in	in	ADP
ejpam-5638	440	5	o	o	PROPN
ejpam-5638	440	6	)	)	PUNCT
ejpam-5638	440	7	)	)	PUNCT
ejpam-5638	441	1	(	(	PUNCT
ejpam-5638	441	2	∆11	∆11	X
ejpam-5638	441	3	o	o	X
ejpam-5638	441	4	o	o	X
ejpam-5638	441	5	∆22	∆22	CCONJ
ejpam-5638	441	6	)	)	PUNCT
ejpam-5638	441	7	.	.	PUNCT
ejpam-5638	442	1	finally	finally	ADV
ejpam-5638	442	2	,	,	PUNCT
ejpam-5638	442	3	this	this	DET
ejpam-5638	442	4	necessary	necessary	ADJ
ejpam-5638	442	5	condition	condition	NOUN
ejpam-5638	442	6	guaratness	guaratness	NOUN
ejpam-5638	442	7	that	that	PRON
ejpam-5638	442	8	µ-value	µ-value	NOUN
ejpam-5638	442	9	is	be	AUX
ejpam-5638	442	10	less	less	ADJ
ejpam-5638	442	11	than	than	ADP
ejpam-5638	442	12	1	1	NUM
ejpam-5638	442	13	.	.	ADP
ejpam-5638	442	14	3.3	3.3	NUM
ejpam-5638	442	15	.	.	PUNCT
ejpam-5638	443	1	pseudo	pseudo	NOUN
ejpam-5638	443	2	-	-	NOUN
ejpam-5638	443	3	spectrum	spectrum	NOUN
ejpam-5638	443	4	:	:	PUNCT
ejpam-5638	443	5	the	the	DET
ejpam-5638	443	6	pseudo	pseudo	NOUN
ejpam-5638	443	7	-	-	NOUN
ejpam-5638	443	8	spectrum	spectrum	NOUN
ejpam-5638	443	9	of	of	ADP
ejpam-5638	443	10	a	a	DET
ejpam-5638	443	11	matrix	matrix	NOUN
ejpam-5638	443	12	a	a	PRON
ejpam-5638	443	13	is	be	AUX
ejpam-5638	443	14	the	the	DET
ejpam-5638	443	15	set	set	NOUN
ejpam-5638	443	16	of	of	ADP
ejpam-5638	443	17	which	which	PRON
ejpam-5638	443	18	contains	contain	VERB
ejpam-5638	443	19	the	the	DET
ejpam-5638	443	20	spectrum	spectrum	NOUN
ejpam-5638	443	21	of	of	ADP
ejpam-5638	443	22	matrix	matrix	NOUN
ejpam-5638	443	23	a.	a.	NOUN
ejpam-5638	443	24	the	the	DET
ejpam-5638	443	25	important	important	ADJ
ejpam-5638	443	26	question	question	NOUN
ejpam-5638	443	27	one	one	PRON
ejpam-5638	443	28	can	can	AUX
ejpam-5638	443	29	raise	raise	VERB
ejpam-5638	443	30	is	be	AUX
ejpam-5638	443	31	about	about	ADP
ejpam-5638	443	32	the	the	DET
ejpam-5638	443	33	singularity	singularity	NOUN
ejpam-5638	443	34	of	of	ADP
ejpam-5638	443	35	a	a	PRON
ejpam-5638	443	36	which	which	PRON
ejpam-5638	443	37	does	do	AUX
ejpam-5638	443	38	not	not	PART
ejpam-5638	443	39	appear	appear	VERB
ejpam-5638	443	40	as	as	ADP
ejpam-5638	443	41	a	a	DET
ejpam-5638	443	42	robust	robust	ADJ
ejpam-5638	443	43	in	in	ADP
ejpam-5638	443	44	the	the	DET
ejpam-5638	443	45	sense	sense	NOUN
ejpam-5638	443	46	that	that	SCONJ
ejpam-5638	443	47	a	a	DET
ejpam-5638	443	48	small	small	ADJ
ejpam-5638	443	49	perturbation	perturbation	NOUN
ejpam-5638	443	50	ϵ	ϵ	X
ejpam-5638	443	51	may	may	AUX
ejpam-5638	443	52	vary	vary	VERB
ejpam-5638	443	53	the	the	DET
ejpam-5638	443	54	answer	answer	NOUN
ejpam-5638	443	55	from	from	ADP
ejpam-5638	443	56	yes	yes	INTJ
ejpam-5638	443	57	to	to	ADP
ejpam-5638	443	58	no	no	PRON
ejpam-5638	443	59	in	in	ADP
ejpam-5638	443	60	a	a	DET
ejpam-5638	443	61	dramatic	dramatic	ADJ
ejpam-5638	443	62	way	way	NOUN
ejpam-5638	443	63	.	.	PUNCT
ejpam-5638	444	1	this	this	PRON
ejpam-5638	444	2	helps	help	VERB
ejpam-5638	444	3	to	to	PART
ejpam-5638	444	4	think	think	VERB
ejpam-5638	444	5	that	that	SCONJ
ejpam-5638	444	6	either	either	CCONJ
ejpam-5638	444	7	||a−1||	||a−1||	PRON
ejpam-5638	444	8	is	be	AUX
ejpam-5638	444	9	large	large	ADJ
ejpam-5638	444	10	enough	enough	ADV
ejpam-5638	444	11	or	or	CCONJ
ejpam-5638	444	12	not	not	PART
ejpam-5638	444	13	?	?	PUNCT
ejpam-5638	445	1	for	for	ADP
ejpam-5638	445	2	λ	λ	PROPN
ejpam-5638	445	3	,	,	PUNCT
ejpam-5638	445	4	an	an	DET
ejpam-5638	445	5	eigenvalue	eigenvalue	NOUN
ejpam-5638	445	6	of	of	ADP
ejpam-5638	445	7	a	a	DET
ejpam-5638	445	8	,	,	PUNCT
ejpam-5638	445	9	a	a	DET
ejpam-5638	445	10	much	much	ADV
ejpam-5638	445	11	better	well	ADJ
ejpam-5638	445	12	question	question	NOUN
ejpam-5638	445	13	is	be	AUX
ejpam-5638	445	14	to	to	PART
ejpam-5638	445	15	ask	ask	VERB
ejpam-5638	445	16	:	:	PUNCT
ejpam-5638	445	17	does	do	AUX
ejpam-5638	445	18	||(λin	||(λin	PROPN
ejpam-5638	446	1	−	−	PROPN
ejpam-5638	446	2	a)−1||	a)−1||	NOUN
ejpam-5638	446	3	is	be	AUX
ejpam-5638	446	4	large	large	ADJ
ejpam-5638	446	5	or	or	CCONJ
ejpam-5638	446	6	not	not	PART
ejpam-5638	446	7	?	?	PUNCT
ejpam-5638	447	1	such	such	DET
ejpam-5638	447	2	a	a	DET
ejpam-5638	447	3	pattern	pattern	NOUN
ejpam-5638	447	4	allows	allow	VERB
ejpam-5638	447	5	following	follow	VERB
ejpam-5638	447	6	definitions	definition	NOUN
ejpam-5638	447	7	and	and	CCONJ
ejpam-5638	447	8	results	result	NOUN
ejpam-5638	447	9	[	[	X
ejpam-5638	447	10	32	32	NUM
ejpam-5638	447	11	]	]	PUNCT
ejpam-5638	447	12	of	of	ADP
ejpam-5638	447	13	pseudo	pseudo	NOUN
ejpam-5638	447	14	-	-	NOUN
ejpam-5638	447	15	spectrum	spectrum	NOUN
ejpam-5638	447	16	.	.	PUNCT
ejpam-5638	448	1	definition	definition	NOUN
ejpam-5638	448	2	2	2	NUM
ejpam-5638	448	3	.	.	PUNCT
ejpam-5638	448	4	let	let	VERB
ejpam-5638	448	5	a	a	DET
ejpam-5638	448	6	∈	∈	PROPN
ejpam-5638	448	7	rn	rn	PROPN
ejpam-5638	448	8	,	,	PUNCT
ejpam-5638	448	9	n	n	CCONJ
ejpam-5638	448	10	,	,	PUNCT
ejpam-5638	448	11	ϵ	ϵ	X
ejpam-5638	448	12	>	>	X
ejpam-5638	448	13	0	0	PROPN
ejpam-5638	448	14	,	,	PUNCT
ejpam-5638	448	15	a	a	DET
ejpam-5638	448	16	small	small	ADJ
ejpam-5638	448	17	perturbation	perturbation	NOUN
ejpam-5638	448	18	.	.	PUNCT
ejpam-5638	449	1	the	the	DET
ejpam-5638	449	2	ϵ-pseudo	ϵ-pseudo	NOUN
ejpam-5638	449	3	-	-	PUNCT
ejpam-5638	449	4	spectrum	spectrum	NOUN
ejpam-5638	449	5	σϵ(a	σϵ(a	NOUN
ejpam-5638	449	6	)	)	PUNCT
ejpam-5638	449	7	which	which	PRON
ejpam-5638	449	8	is	be	AUX
ejpam-5638	449	9	set	set	VERB
ejpam-5638	449	10	of	of	ADP
ejpam-5638	449	11	eigenvalues	eigenvalue	NOUN
ejpam-5638	449	12	(	(	PUNCT
ejpam-5638	449	13	the	the	DET
ejpam-5638	449	14	spectrum	spectrum	NOUN
ejpam-5638	449	15	)	)	PUNCT
ejpam-5638	450	1	λ	λ	PROPN
ejpam-5638	450	2	∈	∈	NOUN
ejpam-5638	450	3	c	c	NOUN
ejpam-5638	450	4	such	such	ADJ
ejpam-5638	450	5	that	that	PRON
ejpam-5638	450	6	||(λin	||(λin	PROPN
ejpam-5638	450	7	−a)−1||	−a)−1||	PROPN
ejpam-5638	450	8	>	>	SYM
ejpam-5638	450	9	1	1	NUM
ejpam-5638	450	10	ϵ	ϵ	NOUN
ejpam-5638	450	11	.	.	PUNCT
ejpam-5638	451	1	remark	remark	PROPN
ejpam-5638	451	2	4	4	NUM
ejpam-5638	451	3	.	.	PUNCT
ejpam-5638	452	1	for	for	ADP
ejpam-5638	452	2	λ	λ	PROPN
ejpam-5638	452	3	∈	∈	PROPN
ejpam-5638	452	4	σ(a	σ(a	PROPN
ejpam-5638	452	5	)	)	PUNCT
ejpam-5638	452	6	,	,	PUNCT
ejpam-5638	452	7	σ(a	σ(a	PROPN
ejpam-5638	452	8	)	)	PUNCT
ejpam-5638	452	9	being	be	AUX
ejpam-5638	452	10	as	as	ADP
ejpam-5638	452	11	the	the	DET
ejpam-5638	452	12	set	set	NOUN
ejpam-5638	452	13	of	of	ADP
ejpam-5638	452	14	eigenvalues	eigenvalue	NOUN
ejpam-5638	452	15	of	of	ADP
ejpam-5638	452	16	a	a	PRON
ejpam-5638	452	17	,	,	PUNCT
ejpam-5638	452	18	||(λin−a)−1||	||(λin−a)−1||	PROPN
ejpam-5638	452	19	=	=	SYM
ejpam-5638	452	20	∞.	∞.	PROPN
ejpam-5638	452	21	the	the	DET
ejpam-5638	452	22	second	second	ADJ
ejpam-5638	452	23	definition	definition	NOUN
ejpam-5638	452	24	of	of	ADP
ejpam-5638	452	25	pseudo	pseudo	NOUN
ejpam-5638	452	26	-	-	NOUN
ejpam-5638	452	27	spectrum	spectrum	NOUN
ejpam-5638	452	28	is	be	AUX
ejpam-5638	452	29	given	give	VERB
ejpam-5638	452	30	as	as	SCONJ
ejpam-5638	452	31	follows	follow	VERB
ejpam-5638	452	32	.	.	PUNCT
ejpam-5638	453	1	definition	definition	NOUN
ejpam-5638	453	2	3	3	NUM
ejpam-5638	453	3	.	.	PUNCT
ejpam-5638	454	1	let	let	VERB
ejpam-5638	454	2	a	a	DET
ejpam-5638	454	3	∈	∈	PROPN
ejpam-5638	454	4	rn	rn	PROPN
ejpam-5638	454	5	,	,	PUNCT
ejpam-5638	454	6	n	n	CCONJ
ejpam-5638	454	7	,	,	PUNCT
ejpam-5638	454	8	ϵ	ϵ	X
ejpam-5638	454	9	>	>	X
ejpam-5638	454	10	0	0	PROPN
ejpam-5638	454	11	,	,	PUNCT
ejpam-5638	454	12	a	a	DET
ejpam-5638	454	13	small	small	ADJ
ejpam-5638	454	14	perturbation	perturbation	NOUN
ejpam-5638	454	15	.	.	PUNCT
ejpam-5638	455	1	the	the	DET
ejpam-5638	455	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5638	455	3	σϵ(a	σϵ(a	PROPN
ejpam-5638	455	4	)	)	PUNCT
ejpam-5638	455	5	which	which	PRON
ejpam-5638	455	6	is	be	AUX
ejpam-5638	455	7	set	set	VERB
ejpam-5638	455	8	of	of	ADP
ejpam-5638	455	9	eigenvalues	eigenvalue	NOUN
ejpam-5638	455	10	(	(	PUNCT
ejpam-5638	455	11	the	the	DET
ejpam-5638	455	12	spectrum	spectrum	NOUN
ejpam-5638	455	13	)	)	PUNCT
ejpam-5638	456	1	λ	λ	PROPN
ejpam-5638	456	2	∈	∈	NOUN
ejpam-5638	456	3	c	c	NOUN
ejpam-5638	456	4	such	such	ADJ
ejpam-5638	456	5	that	that	SCONJ
ejpam-5638	456	6	λ	λ	PROPN
ejpam-5638	456	7	∈	∈	PROPN
ejpam-5638	456	8	σ(a+	σ(a+	PROPN
ejpam-5638	456	9	e	e	NOUN
ejpam-5638	456	10	)	)	PUNCT
ejpam-5638	456	11	,	,	PUNCT
ejpam-5638	456	12	to	to	ADP
ejpam-5638	456	13	some	some	DET
ejpam-5638	456	14	e	e	NOUN
ejpam-5638	456	15	having	have	VERB
ejpam-5638	456	16	||e||	||e||	PROPN
ejpam-5638	456	17	<	<	X
ejpam-5638	456	18	ϵ.	ϵ.	NOUN
ejpam-5638	456	19	the	the	DET
ejpam-5638	456	20	third	third	ADJ
ejpam-5638	456	21	characterization	characterization	NOUN
ejpam-5638	456	22	of	of	ADP
ejpam-5638	456	23	pseudo	pseudo	NOUN
ejpam-5638	456	24	-	-	NOUN
ejpam-5638	456	25	spectrum	spectrum	NOUN
ejpam-5638	456	26	is	be	AUX
ejpam-5638	456	27	given	give	VERB
ejpam-5638	456	28	as	as	ADP
ejpam-5638	456	29	bellow	bellow	ADJ
ejpam-5638	456	30	.	.	PUNCT
ejpam-5638	457	1	definition	definition	NOUN
ejpam-5638	457	2	4	4	NUM
ejpam-5638	457	3	.	.	PUNCT
ejpam-5638	458	1	let	let	VERB
ejpam-5638	458	2	a	a	DET
ejpam-5638	458	3	∈	∈	PROPN
ejpam-5638	458	4	rn	rn	PROPN
ejpam-5638	458	5	,	,	PUNCT
ejpam-5638	458	6	n	n	CCONJ
ejpam-5638	458	7	,	,	PUNCT
ejpam-5638	458	8	ϵ	ϵ	X
ejpam-5638	458	9	>	>	X
ejpam-5638	458	10	0	0	PROPN
ejpam-5638	458	11	,	,	PUNCT
ejpam-5638	458	12	a	a	DET
ejpam-5638	458	13	small	small	ADJ
ejpam-5638	458	14	perturbation	perturbation	NOUN
ejpam-5638	458	15	.	.	PUNCT
ejpam-5638	459	1	the	the	DET
ejpam-5638	459	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5638	459	3	σϵ(a	σϵ(a	PROPN
ejpam-5638	459	4	)	)	PUNCT
ejpam-5638	459	5	which	which	PRON
ejpam-5638	459	6	is	be	AUX
ejpam-5638	459	7	the	the	PRON
ejpam-5638	459	8	of	of	ADP
ejpam-5638	459	9	eigenvalues	eigenvalue	NOUN
ejpam-5638	459	10	(	(	PUNCT
ejpam-5638	459	11	the	the	DET
ejpam-5638	459	12	spectrum	spectrum	NOUN
ejpam-5638	459	13	)	)	PUNCT
ejpam-5638	460	1	λ	λ	PROPN
ejpam-5638	460	2	∈	∈	NOUN
ejpam-5638	460	3	c	c	NOUN
ejpam-5638	460	4	such	such	ADJ
ejpam-5638	460	5	that	that	PRON
ejpam-5638	460	6	||(λin	||(λin	PROPN
ejpam-5638	460	7	−a)v||	−a)v||	PROPN
ejpam-5638	460	8	<	<	X
ejpam-5638	460	9	ϵ	ϵ	X
ejpam-5638	460	10	for	for	ADP
ejpam-5638	460	11	some	some	DET
ejpam-5638	460	12	v	v	NOUN
ejpam-5638	460	13	∈	∈	NOUN
ejpam-5638	460	14	cn,1	cn,1	PROPN
ejpam-5638	460	15	having	have	VERB
ejpam-5638	460	16	||v||	||v||	PROPN
ejpam-5638	460	17	=	=	SYM
ejpam-5638	460	18	1	1	X
ejpam-5638	460	19	.	.	PUNCT
ejpam-5638	460	20	m.u.r	m.u.r	PROPN
ejpam-5638	461	1	rehman	rehman	PROPN
ejpam-5638	461	2	et	et	PROPN
ejpam-5638	461	3	al	al	PROPN
ejpam-5638	461	4	.	.	PUNCT
ejpam-5638	461	5	/	/	SYM
ejpam-5638	461	6	eur	eur	PROPN
ejpam-5638	461	7	.	.	PUNCT
ejpam-5638	462	1	j.	j.	PROPN
ejpam-5638	462	2	pure	pure	PROPN
ejpam-5638	462	3	appl	appl	PROPN
ejpam-5638	462	4	.	.	PROPN
ejpam-5638	462	5	math	math	PROPN
ejpam-5638	462	6	,	,	PUNCT
ejpam-5638	462	7	18	18	NUM
ejpam-5638	462	8	(	(	PUNCT
ejpam-5638	462	9	2	2	NUM
ejpam-5638	462	10	)	)	PUNCT
ejpam-5638	462	11	(	(	PUNCT
ejpam-5638	462	12	2025	2025	NUM
ejpam-5638	462	13	)	)	PUNCT
ejpam-5638	462	14	,	,	PUNCT
ejpam-5638	462	15	5638	5638	NUM
ejpam-5638	462	16	18	18	NUM
ejpam-5638	462	17	of	of	ADP
ejpam-5638	462	18	23	23	NUM
ejpam-5638	462	19	4	4	NUM
ejpam-5638	462	20	.	.	PUNCT
ejpam-5638	462	21	numerical	numerical	ADJ
ejpam-5638	462	22	experimentation	experimentation	NOUN
ejpam-5638	462	23	we	we	PRON
ejpam-5638	462	24	present	present	VERB
ejpam-5638	462	25	a	a	DET
ejpam-5638	462	26	detailed	detailed	ADJ
ejpam-5638	462	27	comparison	comparison	NOUN
ejpam-5638	462	28	on	on	ADP
ejpam-5638	462	29	the	the	DET
ejpam-5638	462	30	approximation	approximation	NOUN
ejpam-5638	462	31	of	of	ADP
ejpam-5638	462	32	the	the	DET
ejpam-5638	462	33	bounds	bound	NOUN
ejpam-5638	462	34	(	(	PUNCT
ejpam-5638	462	35	from	from	ADP
ejpam-5638	462	36	below	below	ADV
ejpam-5638	462	37	)	)	PUNCT
ejpam-5638	462	38	to	to	PART
ejpam-5638	462	39	µ-values	µ-value	NOUN
ejpam-5638	462	40	.	.	PUNCT
ejpam-5638	463	1	we	we	PRON
ejpam-5638	463	2	consider	consider	VERB
ejpam-5638	463	3	some	some	DET
ejpam-5638	463	4	well	well	ADV
ejpam-5638	463	5	-	-	PUNCT
ejpam-5638	463	6	known	know	VERB
ejpam-5638	463	7	algorithm	algorithm	NOUN
ejpam-5638	463	8	for	for	ADP
ejpam-5638	463	9	the	the	DET
ejpam-5638	463	10	approximation	approximation	NOUN
ejpam-5638	463	11	of	of	ADP
ejpam-5638	463	12	µ-values	µ-value	NOUN
ejpam-5638	463	13	:	:	PUNCT
ejpam-5638	463	14	the	the	DET
ejpam-5638	463	15	mussv	mussv	PROPN
ejpam-5638	463	16	function	function	PROPN
ejpam-5638	463	17	mussv	mussv	PROPN
ejpam-5638	463	18	,	,	PUNCT
ejpam-5638	463	19	power	power	NOUN
ejpam-5638	463	20	algorithm	algorithm	NOUN
ejpam-5638	463	21	(	(	PUNCT
ejpam-5638	463	22	pa	pa	PROPN
ejpam-5638	463	23	)	)	PUNCT
ejpam-5638	464	1	[	[	X
ejpam-5638	464	2	33	33	NUM
ejpam-5638	464	3	]	]	PUNCT
ejpam-5638	464	4	,	,	PUNCT
ejpam-5638	464	5	gain	gain	VERB
ejpam-5638	464	6	based	base	VERB
ejpam-5638	464	7	algorithm	algorithm	NOUN
ejpam-5638	464	8	(	(	PUNCT
ejpam-5638	464	9	gba	gba	NOUN
ejpam-5638	464	10	)	)	PUNCT
ejpam-5638	465	1	[	[	X
ejpam-5638	465	2	34	34	NUM
ejpam-5638	465	3	]	]	PUNCT
ejpam-5638	465	4	,	,	PUNCT
ejpam-5638	465	5	poles	pole	NOUN
ejpam-5638	465	6	migration	migration	NOUN
ejpam-5638	465	7	algorithm	algorithm	NOUN
ejpam-5638	465	8	(	(	PUNCT
ejpam-5638	465	9	pma	pma	NOUN
ejpam-5638	465	10	)	)	PUNCT
ejpam-5638	466	1	[	[	X
ejpam-5638	466	2	35	35	NUM
ejpam-5638	466	3	]	]	PUNCT
ejpam-5638	466	4	,	,	PUNCT
ejpam-5638	466	5	non	non	ADJ
ejpam-5638	466	6	-	-	ADJ
ejpam-5638	466	7	linear	linear	ADJ
ejpam-5638	466	8	optimization	optimization	NOUN
ejpam-5638	466	9	algorithm	algorithm	NOUN
ejpam-5638	466	10	(	(	PUNCT
ejpam-5638	466	11	nla	nla	NOUN
ejpam-5638	466	12	)	)	PUNCT
ejpam-5638	467	1	[	[	X
ejpam-5638	467	2	36	36	NUM
ejpam-5638	467	3	]	]	PUNCT
ejpam-5638	467	4	,	,	PUNCT
ejpam-5638	467	5	and	and	CCONJ
ejpam-5638	467	6	low	low	ADJ
ejpam-5638	467	7	-	-	PUNCT
ejpam-5638	467	8	rank	rank	NOUN
ejpam-5638	467	9	ode	ode	PROPN
ejpam-5638	467	10	’s	’s	PART
ejpam-5638	467	11	based	base	VERB
ejpam-5638	467	12	algorithm	algorithm	NOUN
ejpam-5638	467	13	(	(	PUNCT
ejpam-5638	467	14	lra	lra	NOUN
ejpam-5638	467	15	)	)	PUNCT
ejpam-5638	467	16	given	give	VERB
ejpam-5638	467	17	by	by	ADP
ejpam-5638	467	18	first	first	ADJ
ejpam-5638	467	19	author	author	NOUN
ejpam-5638	467	20	[	[	X
ejpam-5638	467	21	37	37	NUM
ejpam-5638	467	22	]	]	PUNCT
ejpam-5638	467	23	.	.	PUNCT
ejpam-5638	468	1	the	the	DET
ejpam-5638	468	2	structured	structured	ADJ
ejpam-5638	468	3	matrices	matrix	NOUN
ejpam-5638	468	4	are	be	AUX
ejpam-5638	468	5	taken	take	VERB
ejpam-5638	468	6	from	from	ADP
ejpam-5638	468	7	various	various	ADJ
ejpam-5638	468	8	economics	economic	NOUN
ejpam-5638	468	9	models	model	NOUN
ejpam-5638	468	10	.	.	PUNCT
ejpam-5638	469	1	we	we	PRON
ejpam-5638	469	2	make	make	VERB
ejpam-5638	469	3	use	use	NOUN
ejpam-5638	469	4	of	of	ADP
ejpam-5638	469	5	eigtool	eigtool	NOUN
ejpam-5638	469	6	[	[	X
ejpam-5638	469	7	38	38	NUM
ejpam-5638	469	8	]	]	PUNCT
ejpam-5638	469	9	to	to	PART
ejpam-5638	469	10	compute	compute	VERB
ejpam-5638	469	11	and	and	CCONJ
ejpam-5638	469	12	display	display	VERB
ejpam-5638	469	13	pseudo	pseudo	NOUN
ejpam-5638	469	14	-	-	NOUN
ejpam-5638	469	15	spectrum	spectrum	NOUN
ejpam-5638	469	16	and	and	CCONJ
ejpam-5638	469	17	eigenvalues	eigenvalue	NOUN
ejpam-5638	469	18	.	.	PUNCT
ejpam-5638	470	1	the	the	DET
ejpam-5638	470	2	function	function	NOUN
ejpam-5638	470	3	mussv	mussv	NOUN
ejpam-5638	470	4	is	be	AUX
ejpam-5638	470	5	being	be	AUX
ejpam-5638	470	6	freely	freely	ADV
ejpam-5638	470	7	available	available	ADJ
ejpam-5638	470	8	in	in	ADP
ejpam-5638	470	9	the	the	DET
ejpam-5638	470	10	matlab	matlab	PROPN
ejpam-5638	470	11	control	control	PROPN
ejpam-5638	470	12	toolbox	toolbox	PROPN
ejpam-5638	470	13	.	.	PUNCT
ejpam-5638	471	1	this	this	DET
ejpam-5638	471	2	tool	tool	NOUN
ejpam-5638	471	3	provides	provide	VERB
ejpam-5638	471	4	results	result	NOUN
ejpam-5638	471	5	on	on	ADP
ejpam-5638	471	6	the	the	DET
ejpam-5638	471	7	numerical	numerical	ADJ
ejpam-5638	471	8	computation	computation	NOUN
ejpam-5638	471	9	of	of	ADP
ejpam-5638	471	10	bounds	bound	NOUN
ejpam-5638	471	11	of	of	ADP
ejpam-5638	471	12	µ-values	µ-value	NOUN
ejpam-5638	471	13	.	.	PUNCT
ejpam-5638	472	1	the	the	DET
ejpam-5638	472	2	proposed	propose	VERB
ejpam-5638	472	3	mathematical	mathematical	ADJ
ejpam-5638	472	4	methodology	methodology	NOUN
ejpam-5638	472	5	give	give	VERB
ejpam-5638	472	6	results	result	NOUN
ejpam-5638	472	7	on	on	ADP
ejpam-5638	472	8	the	the	DET
ejpam-5638	472	9	numerics	numeric	NOUN
ejpam-5638	472	10	of	of	ADP
ejpam-5638	472	11	bounds	bound	NOUN
ejpam-5638	472	12	(	(	PUNCT
ejpam-5638	472	13	from	from	ADP
ejpam-5638	472	14	below	below	ADV
ejpam-5638	472	15	)	)	PUNCT
ejpam-5638	472	16	of	of	ADP
ejpam-5638	472	17	µ-values	µ-value	NOUN
ejpam-5638	472	18	of	of	ADP
ejpam-5638	472	19	structured	structured	ADJ
ejpam-5638	472	20	matrices	matrix	NOUN
ejpam-5638	472	21	from	from	ADP
ejpam-5638	472	22	various	various	ADJ
ejpam-5638	472	23	economic	economic	ADJ
ejpam-5638	472	24	models	model	NOUN
ejpam-5638	472	25	.	.	PUNCT
ejpam-5638	473	1	the	the	DET
ejpam-5638	473	2	reasons	reason	NOUN
ejpam-5638	473	3	for	for	ADP
ejpam-5638	473	4	our	our	PRON
ejpam-5638	473	5	results	result	NOUN
ejpam-5638	473	6	closer	close	ADV
ejpam-5638	473	7	to	to	ADP
ejpam-5638	473	8	the	the	DET
ejpam-5638	473	9	one	one	NOUN
ejpam-5638	473	10	obtained	obtain	VERB
ejpam-5638	473	11	by	by	ADP
ejpam-5638	473	12	existing	exist	VERB
ejpam-5638	473	13	methodologies	methodology	NOUN
ejpam-5638	473	14	are	be	AUX
ejpam-5638	473	15	:	:	PUNCT
ejpam-5638	473	16	(	(	PUNCT
ejpam-5638	473	17	i	i	NOUN
ejpam-5638	473	18	)	)	PUNCT
ejpam-5638	473	19	our	our	PRON
ejpam-5638	473	20	mathematical	mathematical	ADJ
ejpam-5638	473	21	methodology	methodology	NOUN
ejpam-5638	473	22	uses	use	VERB
ejpam-5638	473	23	an	an	DET
ejpam-5638	473	24	approximation	approximation	NOUN
ejpam-5638	473	25	of	of	ADP
ejpam-5638	473	26	singular	singular	ADJ
ejpam-5638	473	27	values	value	NOUN
ejpam-5638	473	28	rather	rather	ADV
ejpam-5638	473	29	than	than	ADP
ejpam-5638	473	30	computing	compute	VERB
ejpam-5638	473	31	eigenvalues	eigenvalue	NOUN
ejpam-5638	473	32	for	for	ADP
ejpam-5638	473	33	the	the	DET
ejpam-5638	473	34	structured	structured	ADJ
ejpam-5638	473	35	matrices	matrix	NOUN
ejpam-5638	473	36	.	.	PUNCT
ejpam-5638	474	1	(	(	PUNCT
ejpam-5638	474	2	ii	ii	NOUN
ejpam-5638	474	3	)	)	PUNCT
ejpam-5638	474	4	the	the	DET
ejpam-5638	474	5	approximation	approximation	NOUN
ejpam-5638	474	6	to	to	ADP
ejpam-5638	474	7	singular	singular	ADJ
ejpam-5638	474	8	values	value	NOUN
ejpam-5638	474	9	is	be	AUX
ejpam-5638	474	10	obtained	obtain	VERB
ejpam-5638	474	11	with	with	ADP
ejpam-5638	474	12	singular	singular	ADJ
ejpam-5638	474	13	value	value	NOUN
ejpam-5638	474	14	decomposition	decomposition	NOUN
ejpam-5638	474	15	tool	tool	NOUN
ejpam-5638	474	16	.	.	PUNCT
ejpam-5638	475	1	the	the	DET
ejpam-5638	475	2	matlab	matlab	PROPN
ejpam-5638	475	3	routine	routine	ADJ
ejpam-5638	475	4	svd	svd	PROPN
ejpam-5638	475	5	computes	compute	VERB
ejpam-5638	475	6	the	the	DET
ejpam-5638	475	7	singular	singular	ADJ
ejpam-5638	475	8	values	value	NOUN
ejpam-5638	475	9	.	.	PUNCT
ejpam-5638	476	1	(	(	PUNCT
ejpam-5638	476	2	iii	iii	X
ejpam-5638	476	3	)	)	PUNCT
ejpam-5638	476	4	the	the	DET
ejpam-5638	476	5	approximation	approximation	NOUN
ejpam-5638	476	6	to	to	ADP
ejpam-5638	476	7	largest	large	ADJ
ejpam-5638	476	8	singular	singular	ADJ
ejpam-5638	476	9	value	value	NOUN
ejpam-5638	476	10	of	of	ADP
ejpam-5638	476	11	structured	structured	ADJ
ejpam-5638	476	12	matrices	matrix	NOUN
ejpam-5638	476	13	in	in	ADP
ejpam-5638	476	14	the	the	DET
ejpam-5638	476	15	sense	sense	NOUN
ejpam-5638	476	16	of	of	ADP
ejpam-5638	476	17	low	low	ADJ
ejpam-5638	476	18	-	-	PUNCT
ejpam-5638	476	19	rank	rank	NOUN
ejpam-5638	476	20	provides	provide	VERB
ejpam-5638	476	21	the	the	DET
ejpam-5638	476	22	sharper	sharp	ADJ
ejpam-5638	476	23	bounds	bound	NOUN
ejpam-5638	476	24	(	(	PUNCT
ejpam-5638	476	25	from	from	ADP
ejpam-5638	476	26	below	below	ADV
ejpam-5638	476	27	)	)	PUNCT
ejpam-5638	476	28	to	to	PART
ejpam-5638	476	29	µ-values	µ-value	NOUN
ejpam-5638	476	30	.	.	PUNCT
ejpam-5638	477	1	the	the	DET
ejpam-5638	477	2	computational	computational	ADJ
ejpam-5638	477	3	cost	cost	NOUN
ejpam-5638	477	4	is	be	AUX
ejpam-5638	477	5	not	not	PART
ejpam-5638	477	6	high	high	ADJ
ejpam-5638	477	7	as	as	SCONJ
ejpam-5638	477	8	compared	compare	VERB
ejpam-5638	477	9	with	with	ADP
ejpam-5638	477	10	exiting	exit	VERB
ejpam-5638	477	11	techniques	technique	NOUN
ejpam-5638	477	12	.	.	PUNCT
ejpam-5638	478	1	we	we	PRON
ejpam-5638	478	2	give	give	VERB
ejpam-5638	478	3	a	a	DET
ejpam-5638	478	4	number	number	NOUN
ejpam-5638	478	5	of	of	ADP
ejpam-5638	478	6	numerical	numerical	ADJ
ejpam-5638	478	7	examples	example	NOUN
ejpam-5638	478	8	for	for	ADP
ejpam-5638	478	9	economy	economy	NOUN
ejpam-5638	478	10	models	model	NOUN
ejpam-5638	478	11	on	on	ADP
ejpam-5638	478	12	the	the	DET
ejpam-5638	478	13	numerical	numerical	ADJ
ejpam-5638	478	14	approximation	approximation	NOUN
ejpam-5638	478	15	of	of	ADP
ejpam-5638	478	16	bounds	bound	NOUN
ejpam-5638	478	17	of	of	ADP
ejpam-5638	478	18	µ-values	µ-value	NOUN
ejpam-5638	478	19	.	.	PUNCT
ejpam-5638	479	1	the	the	DET
ejpam-5638	479	2	obtained	obtain	VERB
ejpam-5638	479	3	results	result	NOUN
ejpam-5638	479	4	on	on	ADP
ejpam-5638	479	5	the	the	DET
ejpam-5638	479	6	computation	computation	NOUN
ejpam-5638	479	7	of	of	ADP
ejpam-5638	479	8	µ-values	µ-value	NOUN
ejpam-5638	479	9	demonstrates	demonstrate	VERB
ejpam-5638	479	10	the	the	DET
ejpam-5638	479	11	effectiveness	effectiveness	NOUN
ejpam-5638	479	12	of	of	ADP
ejpam-5638	479	13	proposed	propose	VERB
ejpam-5638	479	14	methodology	methodology	NOUN
ejpam-5638	479	15	and	and	CCONJ
ejpam-5638	479	16	existing	exist	VERB
ejpam-5638	479	17	techniques	technique	NOUN
ejpam-5638	479	18	.	.	PUNCT
ejpam-5638	480	1	example	example	NOUN
ejpam-5638	481	1	1	1	X
ejpam-5638	481	2	.	.	X
ejpam-5638	481	3	we	we	PRON
ejpam-5638	481	4	consider	consider	VERB
ejpam-5638	481	5	a	a	DET
ejpam-5638	481	6	first	first	ADJ
ejpam-5638	481	7	order	order	NOUN
ejpam-5638	481	8	dynamical	dynamical	ADJ
ejpam-5638	481	9	model	model	NOUN
ejpam-5638	481	10	ẋ	ẋ	PROPN
ejpam-5638	482	1	=	=	NOUN
ejpam-5638	482	2	ax	ax	NOUN
ejpam-5638	482	3	,	,	PUNCT
ejpam-5638	482	4	with	with	ADP
ejpam-5638	482	5	the	the	DET
ejpam-5638	482	6	coefficient	coefficient	NOUN
ejpam-5638	482	7	matrix	matrix	NOUN
ejpam-5638	482	8	a	a	PRON
ejpam-5638	482	9	,	,	PUNCT
ejpam-5638	482	10	a	a	DET
ejpam-5638	482	11	4	4	NUM
ejpam-5638	482	12	-	-	PUNCT
ejpam-5638	482	13	dimensional	dimensional	ADJ
ejpam-5638	482	14	real	real	ADJ
ejpam-5638	482	15	valued	value	VERB
ejpam-5638	482	16	matrix	matrix	NOUN
ejpam-5638	482	17	taken	take	VERB
ejpam-5638	482	18	from	from	ADP
ejpam-5638	482	19	[	[	X
ejpam-5638	482	20	39	39	NUM
ejpam-5638	482	21	]	]	PUNCT
ejpam-5638	482	22	.	.	PUNCT
ejpam-5638	483	1	a	a	DET
ejpam-5638	483	2	=	=	NOUN
ejpam-5638	483	3			NOUN
ejpam-5638	483	4	−8	−8	X
ejpam-5638	484	1	2	2	NUM
ejpam-5638	484	2	2	2	NUM
ejpam-5638	484	3	1	1	NUM
ejpam-5638	484	4	0	0	NUM
ejpam-5638	484	5	−1	−1	NOUN
ejpam-5638	484	6	1	1	NUM
ejpam-5638	484	7	0	0	NUM
ejpam-5638	484	8	0	0	NUM
ejpam-5638	484	9	2	2	NUM
ejpam-5638	484	10	−2	−2	NOUN
ejpam-5638	484	11	0	0	NUM
ejpam-5638	484	12	1	1	NUM
ejpam-5638	484	13	1	1	NUM
ejpam-5638	484	14	1	1	NUM
ejpam-5638	484	15	−5	−5	NOUN
ejpam-5638	484	16			NOUN
ejpam-5638	484	17	.	.	PUNCT
ejpam-5638	485	1	the	the	DET
ejpam-5638	485	2	comparison	comparison	NOUN
ejpam-5638	485	3	on	on	ADP
ejpam-5638	485	4	approximation	approximation	NOUN
ejpam-5638	485	5	to	to	ADP
ejpam-5638	485	6	the	the	DET
ejpam-5638	485	7	bounds	bound	NOUN
ejpam-5638	485	8	from	from	ADP
ejpam-5638	485	9	below	below	ADP
ejpam-5638	485	10	to	to	ADP
ejpam-5638	485	11	µ-values	µ-value	NOUN
ejpam-5638	485	12	is	be	AUX
ejpam-5638	485	13	given	give	VERB
ejpam-5638	485	14	in	in	ADP
ejpam-5638	485	15	the	the	DET
ejpam-5638	485	16	following	follow	VERB
ejpam-5638	485	17	table	table	NOUN
ejpam-5638	485	18	1	1	NUM
ejpam-5638	485	19	.	.	PUNCT
ejpam-5638	486	1	the	the	DET
ejpam-5638	486	2	approximated	approximate	VERB
ejpam-5638	486	3	µ-values	µ-value	VERB
ejpam-5638	486	4	mussv	mussv	PROPN
ejpam-5638	486	5	pa	pa	PROPN
ejpam-5638	486	6	gba	gba	PROPN
ejpam-5638	486	7	pma	pma	PROPN
ejpam-5638	486	8	nla	nla	PROPN
ejpam-5638	486	9	lra	lra	PROPN
ejpam-5638	486	10	8.6448	8.6448	NUM
ejpam-5638	486	11	8.6421	8.6421	NUM
ejpam-5638	486	12	8.6430	8.6430	NUM
ejpam-5638	486	13	8.6442	8.6442	NUM
ejpam-5638	486	14	8.6439	8.6439	NUM
ejpam-5638	486	15	8.6448	8.6448	NUM
ejpam-5638	486	16	example	example	NOUN
ejpam-5638	486	17	2	2	X
ejpam-5638	486	18	.	.	X
ejpam-5638	486	19	we	we	PRON
ejpam-5638	486	20	consider	consider	VERB
ejpam-5638	486	21	a	a	DET
ejpam-5638	486	22	first	first	ADJ
ejpam-5638	486	23	order	order	NOUN
ejpam-5638	486	24	dynamical	dynamical	ADJ
ejpam-5638	486	25	system	system	NOUN
ejpam-5638	486	26	ẋ	ẋ	PUNCT
ejpam-5638	487	1	=	=	SYM
ejpam-5638	487	2	ax	ax	NOUN
ejpam-5638	487	3	,	,	PUNCT
ejpam-5638	487	4	with	with	ADP
ejpam-5638	487	5	the	the	DET
ejpam-5638	487	6	coefficient	coefficient	NOUN
ejpam-5638	487	7	(	(	PUNCT
ejpam-5638	487	8	d	d	NOUN
ejpam-5638	487	9	-	-	ADJ
ejpam-5638	487	10	stable	stable	ADJ
ejpam-5638	487	11	)	)	PUNCT
ejpam-5638	487	12	matrix	matrix	NOUN
ejpam-5638	487	13	a	a	PRON
ejpam-5638	487	14	,	,	PUNCT
ejpam-5638	487	15	a	a	DET
ejpam-5638	487	16	3	3	NUM
ejpam-5638	487	17	-	-	PUNCT
ejpam-5638	487	18	dimensional	dimensional	ADJ
ejpam-5638	487	19	real	real	ADJ
ejpam-5638	487	20	valued	value	VERB
ejpam-5638	487	21	matrix	matrix	NOUN
ejpam-5638	487	22	taken	take	VERB
ejpam-5638	487	23	from	from	ADP
ejpam-5638	487	24	[	[	X
ejpam-5638	487	25	39	39	NUM
ejpam-5638	487	26	]	]	PUNCT
ejpam-5638	487	27	.	.	PUNCT
ejpam-5638	488	1	a	a	DET
ejpam-5638	488	2	=	=	NOUN
ejpam-5638	488	3	−1	−1	NOUN
ejpam-5638	488	4	−1	−1	NOUN
ejpam-5638	488	5	0	0	NUM
ejpam-5638	488	6	1	1	NUM
ejpam-5638	488	7	−2	−2	NOUN
ejpam-5638	488	8	1	1	NUM
ejpam-5638	488	9	0	0	NUM
ejpam-5638	488	10	2	2	NUM
ejpam-5638	488	11	−1	−1	NOUN
ejpam-5638	488	12			NOUN
ejpam-5638	488	13	.	.	PUNCT
ejpam-5638	489	1	m.u.r	m.u.r	PROPN
ejpam-5638	489	2	rehman	rehman	PROPN
ejpam-5638	489	3	et	et	PROPN
ejpam-5638	489	4	al	al	PROPN
ejpam-5638	489	5	.	.	PUNCT
ejpam-5638	489	6	/	/	SYM
ejpam-5638	489	7	eur	eur	PROPN
ejpam-5638	489	8	.	.	PUNCT
ejpam-5638	490	1	j.	j.	PROPN
ejpam-5638	490	2	pure	pure	PROPN
ejpam-5638	490	3	appl	appl	PROPN
ejpam-5638	490	4	.	.	PROPN
ejpam-5638	490	5	math	math	PROPN
ejpam-5638	490	6	,	,	PUNCT
ejpam-5638	490	7	18	18	NUM
ejpam-5638	490	8	(	(	PUNCT
ejpam-5638	490	9	2	2	NUM
ejpam-5638	490	10	)	)	PUNCT
ejpam-5638	490	11	(	(	PUNCT
ejpam-5638	490	12	2025	2025	NUM
ejpam-5638	490	13	)	)	PUNCT
ejpam-5638	490	14	,	,	PUNCT
ejpam-5638	490	15	5638	5638	NUM
ejpam-5638	490	16	19	19	NUM
ejpam-5638	490	17	of	of	ADP
ejpam-5638	490	18	23	23	NUM
ejpam-5638	490	19	the	the	DET
ejpam-5638	490	20	comparison	comparison	NOUN
ejpam-5638	490	21	on	on	ADP
ejpam-5638	490	22	approximation	approximation	NOUN
ejpam-5638	490	23	to	to	ADP
ejpam-5638	490	24	the	the	DET
ejpam-5638	490	25	lower	low	ADJ
ejpam-5638	490	26	bounds	bound	NOUN
ejpam-5638	490	27	from	from	ADP
ejpam-5638	490	28	below	below	ADP
ejpam-5638	490	29	to	to	ADP
ejpam-5638	490	30	µ-values	µ-value	NOUN
ejpam-5638	490	31	is	be	AUX
ejpam-5638	490	32	given	give	VERB
ejpam-5638	490	33	in	in	ADP
ejpam-5638	490	34	the	the	DET
ejpam-5638	490	35	following	follow	VERB
ejpam-5638	490	36	table	table	NOUN
ejpam-5638	490	37	2	2	NUM
ejpam-5638	490	38	.	.	PUNCT
ejpam-5638	491	1	the	the	DET
ejpam-5638	491	2	approximated	approximate	VERB
ejpam-5638	491	3	µ-values	µ-value	VERB
ejpam-5638	491	4	mussv	mussv	PROPN
ejpam-5638	491	5	pa	pa	PROPN
ejpam-5638	491	6	gba	gba	PROPN
ejpam-5638	491	7	pma	pma	PROPN
ejpam-5638	491	8	nla	nla	PROPN
ejpam-5638	491	9	lra	lra	PROPN
ejpam-5638	491	10	3.3181	3.3181	NUM
ejpam-5638	491	11	3.3145	3.3145	NUM
ejpam-5638	491	12	3.3167	3.3167	NUM
ejpam-5638	491	13	3.3177	3.3177	NUM
ejpam-5638	491	14	3.3120	3.3120	NUM
ejpam-5638	491	15	3.3180	3.3180	NUM
ejpam-5638	491	16	example	example	NOUN
ejpam-5638	491	17	3	3	X
ejpam-5638	491	18	.	.	X
ejpam-5638	492	1	we	we	PRON
ejpam-5638	492	2	consider	consider	VERB
ejpam-5638	492	3	a	a	DET
ejpam-5638	492	4	second	second	ADJ
ejpam-5638	492	5	order	order	NOUN
ejpam-5638	492	6	dynamical	dynamical	ADJ
ejpam-5638	492	7	system	system	NOUN
ejpam-5638	492	8	ẍ	ẍ	X
ejpam-5638	493	1	=	=	SYM
ejpam-5638	493	2	aẋ+	aẋ+	PUNCT
ejpam-5638	494	1	bx	bx	NOUN
ejpam-5638	494	2	,	,	PUNCT
ejpam-5638	494	3	with	with	ADP
ejpam-5638	494	4	a	a	DET
ejpam-5638	494	5	,	,	PUNCT
ejpam-5638	494	6	b	b	PROPN
ejpam-5638	494	7	taken	take	VERB
ejpam-5638	494	8	from	from	ADP
ejpam-5638	494	9	[	[	X
ejpam-5638	494	10	3	3	NUM
ejpam-5638	494	11	]	]	PUNCT
ejpam-5638	494	12	.	.	PUNCT
ejpam-5638	495	1	a	a	DET
ejpam-5638	495	2	=	=	NOUN
ejpam-5638	495	3	−1	−1	VERB
ejpam-5638	495	4	1	1	NUM
ejpam-5638	495	5	−1	−1	NOUN
ejpam-5638	495	6	8	8	NUM
ejpam-5638	495	7	−3	−3	NOUN
ejpam-5638	495	8	2	2	NUM
ejpam-5638	495	9	2	2	NUM
ejpam-5638	495	10	2	2	NUM
ejpam-5638	495	11	−2	−2	NOUN
ejpam-5638	495	12			NOUN
ejpam-5638	495	13	,	,	PUNCT
ejpam-5638	495	14	b	b	X
ejpam-5638	495	15	=	=	NOUN
ejpam-5638	495	16	−1	−1	VERB
ejpam-5638	495	17	0	0	NUM
ejpam-5638	495	18	0	0	NUM
ejpam-5638	495	19	0	0	NUM
ejpam-5638	496	1	−0.1	−0.1	NOUN
ejpam-5638	496	2	0	0	NUM
ejpam-5638	496	3	0	0	NUM
ejpam-5638	496	4	0	0	NUM
ejpam-5638	496	5	−0.1	−0.1	ADJ
ejpam-5638	496	6			NOUN
ejpam-5638	496	7	.	.	PUNCT
ejpam-5638	497	1	the	the	DET
ejpam-5638	497	2	matrix	matrix	NOUN
ejpam-5638	497	3	m	m	VERB
ejpam-5638	497	4	is	be	AUX
ejpam-5638	497	5	:	:	PUNCT
ejpam-5638	497	6	m	m	VERB
ejpam-5638	497	7	=	=	PUNCT
ejpam-5638	497	8	[	[	PUNCT
ejpam-5638	497	9	a	a	DET
ejpam-5638	497	10	b	b	NOUN
ejpam-5638	497	11	i3	i3	NOUN
ejpam-5638	497	12	0	0	NUM
ejpam-5638	497	13	]	]	PUNCT
ejpam-5638	497	14	=	=	PUNCT
ejpam-5638	497	15			NOUN
ejpam-5638	497	16	−1	−1	NOUN
ejpam-5638	497	17	1	1	NUM
ejpam-5638	497	18	−1	−1	NOUN
ejpam-5638	497	19	0	0	NUM
ejpam-5638	497	20	0	0	NUM
ejpam-5638	497	21	0	0	NUM
ejpam-5638	497	22	8	8	NUM
ejpam-5638	497	23	−3	−3	NOUN
ejpam-5638	497	24	2	2	NUM
ejpam-5638	497	25	0	0	NUM
ejpam-5638	497	26	−0.1	−0.1	NOUN
ejpam-5638	497	27	0	0	NUM
ejpam-5638	497	28	2	2	NUM
ejpam-5638	497	29	2	2	NUM
ejpam-5638	497	30	−2	−2	NOUN
ejpam-5638	497	31	0	0	NUM
ejpam-5638	497	32	0	0	NUM
ejpam-5638	498	1	−0.1	−0.1	NOUN
ejpam-5638	498	2	1	1	NUM
ejpam-5638	498	3	0	0	NUM
ejpam-5638	498	4	0	0	NUM
ejpam-5638	498	5	0	0	NUM
ejpam-5638	498	6	0	0	NUM
ejpam-5638	498	7	0	0	NUM
ejpam-5638	498	8	0	0	NUM
ejpam-5638	498	9	1	1	NUM
ejpam-5638	498	10	0	0	NUM
ejpam-5638	498	11	0	0	NUM
ejpam-5638	498	12	0	0	NUM
ejpam-5638	498	13	0	0	NUM
ejpam-5638	498	14	0	0	NUM
ejpam-5638	498	15	0	0	NUM
ejpam-5638	498	16	1	1	NUM
ejpam-5638	498	17	0	0	NUM
ejpam-5638	498	18	0	0	NUM
ejpam-5638	498	19	0	0	NUM
ejpam-5638	498	20			NUM
ejpam-5638	498	21	.	.	PUNCT
ejpam-5638	499	1	the	the	DET
ejpam-5638	499	2	comparison	comparison	NOUN
ejpam-5638	499	3	on	on	ADP
ejpam-5638	499	4	approximation	approximation	NOUN
ejpam-5638	499	5	to	to	ADP
ejpam-5638	499	6	bounds	bound	NOUN
ejpam-5638	499	7	from	from	ADP
ejpam-5638	499	8	below	below	ADP
ejpam-5638	499	9	to	to	ADP
ejpam-5638	499	10	µ-values	µ-value	NOUN
ejpam-5638	499	11	is	be	AUX
ejpam-5638	499	12	given	give	VERB
ejpam-5638	499	13	in	in	ADP
ejpam-5638	499	14	the	the	DET
ejpam-5638	499	15	following	follow	VERB
ejpam-5638	499	16	table	table	NOUN
ejpam-5638	499	17	3	3	NUM
ejpam-5638	499	18	.	.	PUNCT
ejpam-5638	500	1	the	the	DET
ejpam-5638	500	2	approximated	approximate	VERB
ejpam-5638	500	3	µ-values	µ-value	NOUN
ejpam-5638	500	4	of	of	ADP
ejpam-5638	500	5	matrix	matrix	NOUN
ejpam-5638	500	6	m	m	NOUN
ejpam-5638	500	7	mussv	mussv	ADJ
ejpam-5638	500	8	pa	pa	PROPN
ejpam-5638	500	9	gba	gba	PROPN
ejpam-5638	500	10	pma	pma	PROPN
ejpam-5638	500	11	nla	nla	PROPN
ejpam-5638	500	12	lra	lra	PROPN
ejpam-5638	500	13	8.9841	8.9841	NUM
ejpam-5638	500	14	8.4940	8.4940	NUM
ejpam-5638	500	15	8.2361	8.2361	NUM
ejpam-5638	500	16	8.2391	8.2391	NUM
ejpam-5638	500	17	8.9821	8.9821	NUM
ejpam-5638	500	18	9.9838	9.9838	NUM
ejpam-5638	500	19	example	example	NOUN
ejpam-5638	500	20	4	4	NUM
ejpam-5638	500	21	.	.	PUNCT
ejpam-5638	501	1	we	we	PRON
ejpam-5638	501	2	consider	consider	VERB
ejpam-5638	501	3	a	a	DET
ejpam-5638	501	4	second	second	ADJ
ejpam-5638	501	5	order	order	NOUN
ejpam-5638	501	6	dynamical	dynamical	ADJ
ejpam-5638	501	7	system	system	NOUN
ejpam-5638	501	8	ẍ	ẍ	X
ejpam-5638	502	1	=	=	SYM
ejpam-5638	502	2	aẋ+	aẋ+	PUNCT
ejpam-5638	503	1	bx	bx	NOUN
ejpam-5638	503	2	,	,	PUNCT
ejpam-5638	503	3	with	with	ADP
ejpam-5638	503	4	a	a	DET
ejpam-5638	503	5	,	,	PUNCT
ejpam-5638	503	6	b	b	PROPN
ejpam-5638	503	7	taken	take	VERB
ejpam-5638	503	8	from	from	ADP
ejpam-5638	503	9	[	[	X
ejpam-5638	503	10	3	3	NUM
ejpam-5638	503	11	]	]	PUNCT
ejpam-5638	503	12	.	.	PUNCT
ejpam-5638	504	1	a	a	DET
ejpam-5638	504	2	=	=	NOUN
ejpam-5638	504	3	−1	−1	VERB
ejpam-5638	504	4	0.9	0.9	NUM
ejpam-5638	504	5	0.2	0.2	NUM
ejpam-5638	504	6	0.6	0.6	NUM
ejpam-5638	504	7	−1.5	−1.5	NOUN
ejpam-5638	504	8	0.9	0.9	NUM
ejpam-5638	504	9	1	1	NUM
ejpam-5638	504	10	1	1	NUM
ejpam-5638	504	11	−2	−2	NOUN
ejpam-5638	504	12			NOUN
ejpam-5638	504	13	,	,	PUNCT
ejpam-5638	504	14	b	b	X
ejpam-5638	504	15	=	=	SYM
ejpam-5638	504	16	−2	−2	NOUN
ejpam-5638	504	17	0	0	NUM
ejpam-5638	504	18	0	0	NUM
ejpam-5638	504	19	0	0	NUM
ejpam-5638	504	20	−1	−1	NOUN
ejpam-5638	504	21	0	0	NUM
ejpam-5638	504	22	0	0	NUM
ejpam-5638	504	23	0	0	NUM
ejpam-5638	504	24	−2	−2	NOUN
ejpam-5638	504	25			NOUN
ejpam-5638	504	26	.	.	PUNCT
ejpam-5638	505	1	the	the	DET
ejpam-5638	505	2	matrix	matrix	NOUN
ejpam-5638	505	3	m	m	VERB
ejpam-5638	505	4	is	be	AUX
ejpam-5638	505	5	:	:	PUNCT
ejpam-5638	505	6	n	n	PROPN
ejpam-5638	505	7	=	=	PRON
ejpam-5638	505	8	[	[	PUNCT
ejpam-5638	505	9	a	a	DET
ejpam-5638	505	10	b	b	NOUN
ejpam-5638	505	11	i3	i3	NOUN
ejpam-5638	505	12	0	0	NUM
ejpam-5638	505	13	]	]	PUNCT
ejpam-5638	505	14	=	=	PUNCT
ejpam-5638	505	15			NOUN
ejpam-5638	505	16	−1	−1	NOUN
ejpam-5638	505	17	0.9	0.9	NUM
ejpam-5638	505	18	0.2	0.2	NUM
ejpam-5638	505	19	−2	−2	NOUN
ejpam-5638	505	20	0	0	NUM
ejpam-5638	505	21	0	0	NUM
ejpam-5638	505	22	0.6	0.6	NUM
ejpam-5638	505	23	−1.5	−1.5	PROPN
ejpam-5638	505	24	0.9	0.9	NUM
ejpam-5638	505	25	0	0	NUM
ejpam-5638	505	26	−1	−1	NOUN
ejpam-5638	505	27	0	0	NUM
ejpam-5638	505	28	1	1	NUM
ejpam-5638	505	29	1	1	NUM
ejpam-5638	505	30	−2	−2	NOUN
ejpam-5638	505	31	0	0	NUM
ejpam-5638	505	32	0	0	NUM
ejpam-5638	506	1	−2	−2	NOUN
ejpam-5638	506	2	1	1	NUM
ejpam-5638	506	3	0	0	NUM
ejpam-5638	506	4	0	0	NUM
ejpam-5638	506	5	0	0	NUM
ejpam-5638	506	6	0	0	NUM
ejpam-5638	506	7	0	0	NUM
ejpam-5638	506	8	0	0	NUM
ejpam-5638	506	9	1	1	NUM
ejpam-5638	506	10	0	0	NUM
ejpam-5638	506	11	0	0	NUM
ejpam-5638	506	12	0	0	NUM
ejpam-5638	506	13	0	0	NUM
ejpam-5638	506	14	0	0	NUM
ejpam-5638	506	15	0	0	NUM
ejpam-5638	506	16	1	1	NUM
ejpam-5638	506	17	0	0	NUM
ejpam-5638	506	18	0	0	NUM
ejpam-5638	506	19	0	0	NUM
ejpam-5638	506	20			NUM
ejpam-5638	506	21	.	.	PUNCT
ejpam-5638	507	1	the	the	DET
ejpam-5638	507	2	comparison	comparison	NOUN
ejpam-5638	507	3	on	on	ADP
ejpam-5638	507	4	approximation	approximation	NOUN
ejpam-5638	507	5	to	to	ADP
ejpam-5638	507	6	bounds	bound	NOUN
ejpam-5638	507	7	from	from	ADP
ejpam-5638	507	8	below	below	ADP
ejpam-5638	507	9	to	to	ADP
ejpam-5638	507	10	µ-values	µ-value	NOUN
ejpam-5638	507	11	is	be	AUX
ejpam-5638	507	12	given	give	VERB
ejpam-5638	507	13	in	in	ADP
ejpam-5638	507	14	the	the	DET
ejpam-5638	507	15	following	follow	VERB
ejpam-5638	507	16	table	table	NOUN
ejpam-5638	507	17	4	4	NUM
ejpam-5638	507	18	.	.	PUNCT
ejpam-5638	508	1	m.u.r	m.u.r	PROPN
ejpam-5638	508	2	rehman	rehman	PROPN
ejpam-5638	508	3	et	et	PROPN
ejpam-5638	508	4	al	al	PROPN
ejpam-5638	508	5	.	.	PUNCT
ejpam-5638	508	6	/	/	SYM
ejpam-5638	508	7	eur	eur	PROPN
ejpam-5638	508	8	.	.	PUNCT
ejpam-5638	509	1	j.	j.	PROPN
ejpam-5638	509	2	pure	pure	PROPN
ejpam-5638	509	3	appl	appl	PROPN
ejpam-5638	509	4	.	.	PROPN
ejpam-5638	509	5	math	math	PROPN
ejpam-5638	509	6	,	,	PUNCT
ejpam-5638	509	7	18	18	NUM
ejpam-5638	509	8	(	(	PUNCT
ejpam-5638	509	9	2	2	NUM
ejpam-5638	509	10	)	)	PUNCT
ejpam-5638	509	11	(	(	PUNCT
ejpam-5638	509	12	2025	2025	NUM
ejpam-5638	509	13	)	)	PUNCT
ejpam-5638	509	14	,	,	PUNCT
ejpam-5638	509	15	5638	5638	NUM
ejpam-5638	509	16	20	20	NUM
ejpam-5638	509	17	of	of	ADP
ejpam-5638	509	18	23	23	NUM
ejpam-5638	509	19	the	the	DET
ejpam-5638	509	20	approximated	approximated	ADJ
ejpam-5638	509	21	µ-values	µ-value	NOUN
ejpam-5638	509	22	of	of	ADP
ejpam-5638	509	23	matrix	matrix	NOUN
ejpam-5638	509	24	m	m	NOUN
ejpam-5638	509	25	mussv	mussv	ADJ
ejpam-5638	509	26	pa	pa	PROPN
ejpam-5638	509	27	gba	gba	PROPN
ejpam-5638	509	28	pma	pma	PROPN
ejpam-5638	509	29	nla	nla	PROPN
ejpam-5638	509	30	lra	lra	PROPN
ejpam-5638	509	31	3.4352	3.4352	NUM
ejpam-5638	509	32	3.4189	3.4189	NUM
ejpam-5638	509	33	3.4310	3.4310	NUM
ejpam-5638	509	34	3.4329	3.4329	NUM
ejpam-5638	509	35	3.4155	3.4155	NUM
ejpam-5638	509	36	3.4350	3.4350	NUM
ejpam-5638	509	37	5	5	NUM
ejpam-5638	509	38	.	.	PUNCT
ejpam-5638	510	1	conclusion	conclusion	NOUN
ejpam-5638	510	2	this	this	DET
ejpam-5638	510	3	article	article	NOUN
ejpam-5638	510	4	considers	consider	VERB
ejpam-5638	510	5	a	a	DET
ejpam-5638	510	6	mathematical	mathematical	ADJ
ejpam-5638	510	7	problem	problem	NOUN
ejpam-5638	510	8	related	relate	VERB
ejpam-5638	510	9	with	with	ADP
ejpam-5638	510	10	an	an	DET
ejpam-5638	510	11	interconnections	interconnection	NOUN
ejpam-5638	510	12	among	among	ADP
ejpam-5638	510	13	the	the	DET
ejpam-5638	510	14	notations	notation	NOUN
ejpam-5638	510	15	of	of	ADP
ejpam-5638	510	16	structured	structured	ADJ
ejpam-5638	510	17	stability	stability	NOUN
ejpam-5638	510	18	,	,	PUNCT
ejpam-5638	510	19	structured	structured	ADJ
ejpam-5638	510	20	d	d	X
ejpam-5638	510	21	-	-	PUNCT
ejpam-5638	510	22	stability	stability	NOUN
ejpam-5638	510	23	analysis	analysis	NOUN
ejpam-5638	510	24	,	,	PUNCT
ejpam-5638	510	25	and	and	CCONJ
ejpam-5638	510	26	µ-values	µ-value	VERB
ejpam-5638	510	27	.	.	PUNCT
ejpam-5638	511	1	the	the	DET
ejpam-5638	511	2	novel	novel	ADJ
ejpam-5638	511	3	mathematical	mathematical	ADJ
ejpam-5638	511	4	results	result	NOUN
ejpam-5638	511	5	are	be	AUX
ejpam-5638	511	6	developed	develop	VERB
ejpam-5638	511	7	to	to	PART
ejpam-5638	511	8	link	link	VERB
ejpam-5638	511	9	the	the	DET
ejpam-5638	511	10	bridge	bridge	NOUN
ejpam-5638	511	11	between	between	ADP
ejpam-5638	511	12	stability	stability	NOUN
ejpam-5638	511	13	,	,	PUNCT
ejpam-5638	511	14	structured	structured	ADJ
ejpam-5638	511	15	d	d	X
ejpam-5638	511	16	-	-	PUNCT
ejpam-5638	511	17	stability	stability	NOUN
ejpam-5638	511	18	analysis	analysis	NOUN
ejpam-5638	511	19	,	,	PUNCT
ejpam-5638	511	20	and	and	CCONJ
ejpam-5638	511	21	µ-values	µ-value	VERB
ejpam-5638	511	22	.	.	PUNCT
ejpam-5638	512	1	the	the	DET
ejpam-5638	512	2	numerical	numerical	PROPN
ejpam-5638	512	3	experimentation	experimentation	NOUN
ejpam-5638	512	4	show	show	VERB
ejpam-5638	512	5	the	the	DET
ejpam-5638	512	6	dynamic	dynamic	NOUN
ejpam-5638	512	7	of	of	ADP
ejpam-5638	512	8	the	the	DET
ejpam-5638	512	9	spectrum	spectrum	NOUN
ejpam-5638	512	10	of	of	ADP
ejpam-5638	512	11	structured	structured	ADJ
ejpam-5638	512	12	matrices	matrix	NOUN
ejpam-5638	512	13	.	.	PUNCT
ejpam-5638	513	1	the	the	DET
ejpam-5638	513	2	matlab	matlab	PROPN
ejpam-5638	513	3	eigtool	eigtool	NOUN
ejpam-5638	513	4	is	be	AUX
ejpam-5638	513	5	used	use	VERB
ejpam-5638	513	6	for	for	ADP
ejpam-5638	513	7	the	the	DET
ejpam-5638	513	8	computation	computation	NOUN
ejpam-5638	513	9	of	of	ADP
ejpam-5638	513	10	pseud	pseud	NOUN
ejpam-5638	513	11	-	-	PUNCT
ejpam-5638	513	12	spectrum	spectrum	NOUN
ejpam-5638	513	13	of	of	ADP
ejpam-5638	513	14	structured	structured	ADJ
ejpam-5638	513	15	matrices	matrix	NOUN
ejpam-5638	513	16	across	across	ADP
ejpam-5638	513	17	first	first	ADJ
ejpam-5638	513	18	,	,	PUNCT
ejpam-5638	513	19	and	and	CCONJ
ejpam-5638	513	20	second	second	ADJ
ejpam-5638	513	21	order	order	NOUN
ejpam-5638	513	22	dynamical	dynamical	ADJ
ejpam-5638	513	23	models	model	NOUN
ejpam-5638	513	24	.	.	PUNCT
ejpam-5638	514	1	the	the	DET
ejpam-5638	514	2	advantages	advantage	NOUN
ejpam-5638	514	3	and	and	CCONJ
ejpam-5638	514	4	limitations	limitation	NOUN
ejpam-5638	514	5	of	of	ADP
ejpam-5638	514	6	the	the	DET
ejpam-5638	514	7	proposed	propose	VERB
ejpam-5638	514	8	mathematical	mathematical	ADJ
ejpam-5638	514	9	work	work	NOUN
ejpam-5638	514	10	are	be	AUX
ejpam-5638	514	11	listed	list	VERB
ejpam-5638	514	12	below	below	ADP
ejpam-5638	514	13	.	.	PUNCT
ejpam-5638	515	1	advantages	advantage	NOUN
ejpam-5638	515	2	of	of	ADP
ejpam-5638	515	3	proposed	propose	VERB
ejpam-5638	515	4	work	work	NOUN
ejpam-5638	515	5	:	:	PUNCT
ejpam-5638	515	6	the	the	DET
ejpam-5638	515	7	proposed	propose	VERB
ejpam-5638	515	8	mathematical	mathematical	ADJ
ejpam-5638	515	9	technique	technique	NOUN
ejpam-5638	515	10	provides	provide	VERB
ejpam-5638	515	11	an	an	DET
ejpam-5638	515	12	interesting	interesting	ADJ
ejpam-5638	515	13	interconnections	interconnection	NOUN
ejpam-5638	515	14	between	between	ADP
ejpam-5638	515	15	stability	stability	NOUN
ejpam-5638	515	16	,	,	PUNCT
ejpam-5638	515	17	d	d	NOUN
ejpam-5638	515	18	-	-	PUNCT
ejpam-5638	515	19	stability	stability	NOUN
ejpam-5638	515	20	of	of	ADP
ejpam-5638	515	21	structured	structured	ADJ
ejpam-5638	515	22	matrices	matrix	NOUN
ejpam-5638	515	23	and	and	CCONJ
ejpam-5638	515	24	their	their	PRON
ejpam-5638	515	25	structured	structured	ADJ
ejpam-5638	515	26	singular	singular	ADJ
ejpam-5638	515	27	values	value	NOUN
ejpam-5638	515	28	.	.	PUNCT
ejpam-5638	516	1	the	the	DET
ejpam-5638	516	2	new	new	ADJ
ejpam-5638	516	3	results	result	NOUN
ejpam-5638	516	4	on	on	ADP
ejpam-5638	516	5	structured	structured	ADJ
ejpam-5638	516	6	stability	stability	NOUN
ejpam-5638	516	7	,	,	PUNCT
ejpam-5638	516	8	and	and	CCONJ
ejpam-5638	516	9	structured	structure	VERB
ejpam-5638	516	10	d	d	X
ejpam-5638	516	11	-	-	PUNCT
ejpam-5638	516	12	stability	stability	NOUN
ejpam-5638	516	13	may	may	AUX
ejpam-5638	516	14	be	be	AUX
ejpam-5638	516	15	applicable	applicable	ADJ
ejpam-5638	516	16	for	for	ADP
ejpam-5638	516	17	robust	robust	ADJ
ejpam-5638	516	18	analysis	analysis	NOUN
ejpam-5638	516	19	of	of	ADP
ejpam-5638	516	20	nonlinear	nonlinear	ADJ
ejpam-5638	516	21	models	model	NOUN
ejpam-5638	516	22	which	which	PRON
ejpam-5638	516	23	are	be	AUX
ejpam-5638	516	24	subject	subject	ADJ
ejpam-5638	516	25	to	to	ADP
ejpam-5638	516	26	lyapunov	lyapunov	NOUN
ejpam-5638	516	27	functions	function	NOUN
ejpam-5638	516	28	.	.	PUNCT
ejpam-5638	517	1	the	the	DET
ejpam-5638	517	2	results	result	NOUN
ejpam-5638	517	3	on	on	ADP
ejpam-5638	517	4	d	d	NOUN
ejpam-5638	517	5	-	-	NOUN
ejpam-5638	517	6	stability	stability	NOUN
ejpam-5638	517	7	ensure	ensure	VERB
ejpam-5638	517	8	the	the	DET
ejpam-5638	517	9	stable	stable	ADJ
ejpam-5638	517	10	equilibrium	equilibrium	NOUN
ejpam-5638	517	11	points	point	NOUN
ejpam-5638	517	12	subject	subject	ADJ
ejpam-5638	517	13	to	to	ADP
ejpam-5638	517	14	various	various	ADJ
ejpam-5638	517	15	different	different	ADJ
ejpam-5638	517	16	constraints	constraint	NOUN
ejpam-5638	517	17	.	.	PUNCT
ejpam-5638	518	1	the	the	DET
ejpam-5638	518	2	economic	economic	ADJ
ejpam-5638	518	3	models	model	NOUN
ejpam-5638	518	4	involves	involve	VERB
ejpam-5638	518	5	structured	structure	VERB
ejpam-5638	518	6	or	or	CCONJ
ejpam-5638	518	7	unstructured	unstructured	ADJ
ejpam-5638	518	8	uncertainties	uncertainty	NOUN
ejpam-5638	518	9	among	among	ADP
ejpam-5638	518	10	the	the	DET
ejpam-5638	518	11	tax	tax	NOUN
ejpam-5638	518	12	policies	policy	NOUN
ejpam-5638	518	13	,	,	PUNCT
ejpam-5638	518	14	the	the	DET
ejpam-5638	518	15	rates	rate	NOUN
ejpam-5638	518	16	of	of	ADP
ejpam-5638	518	17	interest	interest	NOUN
ejpam-5638	518	18	.	.	PUNCT
ejpam-5638	519	1	the	the	DET
ejpam-5638	519	2	study	study	NOUN
ejpam-5638	519	3	of	of	ADP
ejpam-5638	519	4	µ-values	µ-value	NOUN
ejpam-5638	519	5	enable	enable	VERB
ejpam-5638	519	6	to	to	PART
ejpam-5638	519	7	identify	identify	VERB
ejpam-5638	519	8	the	the	DET
ejpam-5638	519	9	amount	amount	NOUN
ejpam-5638	519	10	of	of	ADP
ejpam-5638	519	11	structured	structured	ADJ
ejpam-5638	519	12	or	or	CCONJ
ejpam-5638	519	13	unstructured	unstructured	ADJ
ejpam-5638	519	14	uncertainties	uncertainty	NOUN
ejpam-5638	519	15	affecting	affect	VERB
ejpam-5638	519	16	overall	overall	ADJ
ejpam-5638	519	17	economy	economy	NOUN
ejpam-5638	519	18	while	while	SCONJ
ejpam-5638	519	19	allowing	allow	VERB
ejpam-5638	519	20	policymakers	policymaker	NOUN
ejpam-5638	519	21	to	to	PART
ejpam-5638	519	22	design	design	VERB
ejpam-5638	519	23	more	more	ADV
ejpam-5638	519	24	robust	robust	ADJ
ejpam-5638	519	25	policies	policy	NOUN
ejpam-5638	519	26	.	.	PUNCT
ejpam-5638	520	1	limitations	limitation	NOUN
ejpam-5638	520	2	of	of	ADP
ejpam-5638	520	3	proposed	propose	VERB
ejpam-5638	520	4	work	work	NOUN
ejpam-5638	520	5	:	:	PUNCT
ejpam-5638	520	6	the	the	DET
ejpam-5638	520	7	d	d	NOUN
ejpam-5638	520	8	-	-	NOUN
ejpam-5638	520	9	stability	stability	NOUN
ejpam-5638	520	10	,	,	PUNCT
ejpam-5638	520	11	and	and	CCONJ
ejpam-5638	520	12	numerical	numerical	ADJ
ejpam-5638	520	13	computation	computation	NOUN
ejpam-5638	520	14	of	of	ADP
ejpam-5638	520	15	µvalues	µvalue	NOUN
ejpam-5638	520	16	has	have	VERB
ejpam-5638	520	17	limitations	limitation	NOUN
ejpam-5638	520	18	in	in	ADP
ejpam-5638	520	19	the	the	DET
ejpam-5638	520	20	sense	sense	NOUN
ejpam-5638	520	21	that	that	SCONJ
ejpam-5638	520	22	the	the	DET
ejpam-5638	520	23	dynamic	dynamic	ADJ
ejpam-5638	520	24	models	model	NOUN
ejpam-5638	520	25	subject	subject	ADJ
ejpam-5638	520	26	to	to	ADP
ejpam-5638	520	27	consideration	consideration	NOUN
ejpam-5638	520	28	are	be	AUX
ejpam-5638	520	29	most	most	ADV
ejpam-5638	520	30	often	often	ADV
ejpam-5638	520	31	time	time	NOUN
ejpam-5638	520	32	linear	linear	ADJ
ejpam-5638	520	33	or	or	CCONJ
ejpam-5638	520	34	linear	linear	ADJ
ejpam-5638	520	35	time	time	NOUN
ejpam-5638	520	36	varying	vary	VERB
ejpam-5638	520	37	in	in	ADP
ejpam-5638	520	38	their	their	PRON
ejpam-5638	520	39	nature	nature	NOUN
ejpam-5638	520	40	.	.	PUNCT
ejpam-5638	521	1	the	the	DET
ejpam-5638	521	2	application	application	NOUN
ejpam-5638	521	3	of	of	ADP
ejpam-5638	521	4	stability	stability	NOUN
ejpam-5638	521	5	,	,	PUNCT
ejpam-5638	521	6	and	and	CCONJ
ejpam-5638	521	7	d	d	X
ejpam-5638	521	8	-	-	NOUN
ejpam-5638	521	9	stability	stability	VERB
ejpam-5638	521	10	the	the	DET
ejpam-5638	521	11	nonlinear	nonlinear	ADJ
ejpam-5638	521	12	systems	system	NOUN
ejpam-5638	521	13	may	may	AUX
ejpam-5638	521	14	be	be	AUX
ejpam-5638	521	15	overly	overly	ADV
ejpam-5638	521	16	simplistic	simplistic	ADJ
ejpam-5638	521	17	.	.	PUNCT
ejpam-5638	522	1	in	in	ADP
ejpam-5638	522	2	general	general	ADJ
ejpam-5638	522	3	,	,	PUNCT
ejpam-5638	522	4	the	the	DET
ejpam-5638	522	5	results	result	NOUN
ejpam-5638	522	6	for	for	ADP
ejpam-5638	522	7	stability	stability	NOUN
ejpam-5638	522	8	,	,	PUNCT
ejpam-5638	522	9	and	and	CCONJ
ejpam-5638	522	10	d	d	X
ejpam-5638	522	11	-	-	PUNCT
ejpam-5638	522	12	stability	stability	NOUN
ejpam-5638	522	13	may	may	AUX
ejpam-5638	522	14	not	not	PART
ejpam-5638	522	15	capture	capture	VERB
ejpam-5638	522	16	the	the	DET
ejpam-5638	522	17	true	true	ADJ
ejpam-5638	522	18	dynamics	dynamic	NOUN
ejpam-5638	522	19	of	of	ADP
ejpam-5638	522	20	the	the	DET
ejpam-5638	522	21	economy	economy	NOUN
ejpam-5638	522	22	models	model	NOUN
ejpam-5638	522	23	.	.	PUNCT
ejpam-5638	523	1	the	the	DET
ejpam-5638	523	2	µ-analysis	µ-analysis	NOUN
ejpam-5638	523	3	is	be	AUX
ejpam-5638	523	4	not	not	PART
ejpam-5638	523	5	cheap	cheap	ADJ
ejpam-5638	523	6	and	and	CCONJ
ejpam-5638	523	7	is	be	AUX
ejpam-5638	523	8	very	very	ADV
ejpam-5638	523	9	costly	costly	ADJ
ejpam-5638	523	10	.	.	PUNCT
ejpam-5638	524	1	on	on	ADP
ejpam-5638	524	2	the	the	DET
ejpam-5638	524	3	other	other	ADJ
ejpam-5638	524	4	hand	hand	NOUN
ejpam-5638	524	5	,	,	PUNCT
ejpam-5638	524	6	an	an	DET
ejpam-5638	524	7	exact	exact	ADJ
ejpam-5638	524	8	determination	determination	NOUN
ejpam-5638	524	9	of	of	ADP
ejpam-5638	524	10	µ-values	µ-value	NOUN
ejpam-5638	524	11	is	be	AUX
ejpam-5638	524	12	infect	infect	VERB
ejpam-5638	524	13	an	an	DET
ejpam-5638	524	14	np	np	NOUN
ejpam-5638	524	15	-	-	PUNCT
ejpam-5638	524	16	hard	hard	ADJ
ejpam-5638	524	17	problem	problem	NOUN
ejpam-5638	524	18	.	.	PUNCT
ejpam-5638	525	1	the	the	DET
ejpam-5638	525	2	economics	economics	NOUN
ejpam-5638	525	3	models	model	NOUN
ejpam-5638	525	4	most	most	ADV
ejpam-5638	525	5	often	often	ADV
ejpam-5638	525	6	involves	involve	VERB
ejpam-5638	525	7	a	a	DET
ejpam-5638	525	8	large	large	ADJ
ejpam-5638	525	9	amount	amount	NOUN
ejpam-5638	525	10	of	of	ADP
ejpam-5638	525	11	parameters	parameter	NOUN
ejpam-5638	525	12	and	and	CCONJ
ejpam-5638	525	13	hence	hence	ADV
ejpam-5638	525	14	it	it	PRON
ejpam-5638	525	15	demands	demand	VERB
ejpam-5638	525	16	very	very	ADV
ejpam-5638	525	17	high	high	ADJ
ejpam-5638	525	18	computational	computational	ADJ
ejpam-5638	525	19	requirements	requirement	NOUN
ejpam-5638	525	20	for	for	ADP
ejpam-5638	525	21	the	the	DET
ejpam-5638	525	22	analysis	analysis	NOUN
ejpam-5638	525	23	of	of	ADP
ejpam-5638	525	24	robustness	robustness	NOUN
ejpam-5638	525	25	and	and	CCONJ
ejpam-5638	525	26	performance	performance	NOUN
ejpam-5638	525	27	.	.	PUNCT
ejpam-5638	526	1	this	this	PRON
ejpam-5638	526	2	leads	lead	VERB
ejpam-5638	526	3	the	the	DET
ejpam-5638	526	4	practical	practical	ADJ
ejpam-5638	526	5	difficulties	difficulty	NOUN
ejpam-5638	526	6	and	and	CCONJ
ejpam-5638	526	7	complexities	complexity	NOUN
ejpam-5638	526	8	to	to	PART
ejpam-5638	526	9	scale	scale	VERB
ejpam-5638	526	10	µ-analysis	µ-analysis	NOUN
ejpam-5638	526	11	to	to	ADP
ejpam-5638	526	12	large	large	ADJ
ejpam-5638	526	13	dimensional	dimensional	ADJ
ejpam-5638	526	14	macroeconomic	macroeconomic	ADJ
ejpam-5638	526	15	models	model	NOUN
ejpam-5638	526	16	.	.	PUNCT
ejpam-5638	527	1	acknowledgements	acknowledgement	NOUN
ejpam-5638	527	2	the	the	DET
ejpam-5638	527	3	authors	author	NOUN
ejpam-5638	527	4	thank	thank	VERB
ejpam-5638	527	5	the	the	DET
ejpam-5638	527	6	anonymous	anonymous	ADJ
ejpam-5638	527	7	referees	referee	NOUN
ejpam-5638	527	8	for	for	ADP
ejpam-5638	527	9	their	their	PRON
ejpam-5638	527	10	crucial	crucial	ADJ
ejpam-5638	527	11	and	and	CCONJ
ejpam-5638	527	12	valuable	valuable	ADJ
ejpam-5638	527	13	comments	comment	NOUN
ejpam-5638	527	14	and	and	CCONJ
ejpam-5638	527	15	suggestions	suggestion	NOUN
ejpam-5638	527	16	,	,	PUNCT
ejpam-5638	527	17	which	which	PRON
ejpam-5638	527	18	are	be	AUX
ejpam-5638	527	19	essential	essential	ADJ
ejpam-5638	527	20	for	for	ADP
ejpam-5638	527	21	improving	improve	VERB
ejpam-5638	527	22	the	the	DET
ejpam-5638	527	23	manuscript	manuscript	NOUN
ejpam-5638	527	24	.	.	PUNCT
ejpam-5638	528	1	conflict	conflict	NOUN
ejpam-5638	528	2	of	of	ADP
ejpam-5638	528	3	interest	interest	NOUN
ejpam-5638	528	4	statement	statement	NOUN
ejpam-5638	528	5	the	the	DET
ejpam-5638	528	6	authors	author	NOUN
ejpam-5638	528	7	declare	declare	VERB
ejpam-5638	528	8	that	that	SCONJ
ejpam-5638	528	9	they	they	PRON
ejpam-5638	528	10	have	have	VERB
ejpam-5638	528	11	no	no	DET
ejpam-5638	528	12	conflict	conflict	NOUN
ejpam-5638	528	13	of	of	ADP
ejpam-5638	528	14	interest	interest	NOUN
ejpam-5638	528	15	.	.	PUNCT
ejpam-5638	529	1	m.u.r	m.u.r	PROPN
ejpam-5638	529	2	rehman	rehman	PROPN
ejpam-5638	529	3	et	et	PROPN
ejpam-5638	529	4	al	al	PROPN
ejpam-5638	529	5	.	.	PUNCT
ejpam-5638	529	6	/	/	SYM
ejpam-5638	529	7	eur	eur	PROPN
ejpam-5638	529	8	.	.	PUNCT
ejpam-5638	530	1	j.	j.	PROPN
ejpam-5638	530	2	pure	pure	PROPN
ejpam-5638	530	3	appl	appl	PROPN
ejpam-5638	530	4	.	.	PROPN
ejpam-5638	530	5	math	math	PROPN
ejpam-5638	530	6	,	,	PUNCT
ejpam-5638	530	7	18	18	NUM
ejpam-5638	530	8	(	(	PUNCT
ejpam-5638	530	9	2	2	NUM
ejpam-5638	530	10	)	)	PUNCT
ejpam-5638	530	11	(	(	PUNCT
ejpam-5638	530	12	2025	2025	NUM
ejpam-5638	530	13	)	)	PUNCT
ejpam-5638	530	14	,	,	PUNCT
ejpam-5638	530	15	5638	5638	NUM
ejpam-5638	530	16	21	21	NUM
ejpam-5638	530	17	of	of	ADP
ejpam-5638	530	18	23	23	NUM
ejpam-5638	530	19	authors	author	NOUN
ejpam-5638	530	20	contributions	contribution	NOUN
ejpam-5638	530	21	all	all	DET
ejpam-5638	530	22	authors	author	NOUN
ejpam-5638	530	23	contributed	contribute	VERB
ejpam-5638	530	24	equally	equally	ADV
ejpam-5638	530	25	to	to	ADP
ejpam-5638	530	26	the	the	DET
ejpam-5638	530	27	writing	writing	NOUN
ejpam-5638	530	28	of	of	ADP
ejpam-5638	530	29	this	this	DET
ejpam-5638	530	30	paper	paper	NOUN
ejpam-5638	530	31	.	.	PUNCT
ejpam-5638	531	1	all	all	DET
ejpam-5638	531	2	authors	author	NOUN
ejpam-5638	531	3	read	read	VERB
ejpam-5638	531	4	and	and	CCONJ
ejpam-5638	531	5	approved	approve	VERB
ejpam-5638	531	6	the	the	DET
ejpam-5638	531	7	final	final	ADJ
ejpam-5638	531	8	manuscript	manuscript	NOUN
ejpam-5638	531	9	.	.	PUNCT
ejpam-5638	532	1	references	reference	NOUN
ejpam-5638	532	2	[	[	X
ejpam-5638	532	3	1	1	NUM
ejpam-5638	532	4	]	]	PUNCT
ejpam-5638	532	5	herman	herman	PROPN
ejpam-5638	532	6	j.	j.	PROPN
ejpam-5638	532	7	nieuwenhuis	nieuwenhuis	PROPN
ejpam-5638	532	8	and	and	CCONJ
ejpam-5638	532	9	lambert	lambert	PROPN
ejpam-5638	532	10	schoonbeek	schoonbeek	PROPN
ejpam-5638	532	11	.	.	PUNCT
ejpam-5638	533	1	stability	stability	NOUN
ejpam-5638	533	2	of	of	ADP
ejpam-5638	533	3	matrices	matrix	NOUN
ejpam-5638	533	4	with	with	ADP
ejpam-5638	533	5	negative	negative	ADJ
ejpam-5638	533	6	diagonal	diagonal	ADJ
ejpam-5638	533	7	submatrices	submatrice	NOUN
ejpam-5638	533	8	.	.	PUNCT
ejpam-5638	534	1	linear	linear	PROPN
ejpam-5638	534	2	algebra	algebra	PROPN
ejpam-5638	534	3	and	and	CCONJ
ejpam-5638	534	4	its	its	PRON
ejpam-5638	534	5	applications	application	NOUN
ejpam-5638	534	6	,	,	PUNCT
ejpam-5638	534	7	353(1	353(1	NUM
ejpam-5638	534	8	-	-	SYM
ejpam-5638	534	9	3):183–196	3):183–196	NUM
ejpam-5638	534	10	,	,	PUNCT
ejpam-5638	534	11	2002	2002	NUM
ejpam-5638	534	12	.	.	PUNCT
ejpam-5638	535	1	[	[	X
ejpam-5638	535	2	2	2	X
ejpam-5638	535	3	]	]	X
ejpam-5638	535	4	y.	y.	NOUN
ejpam-5638	535	5	murata	murata	PROPN
ejpam-5638	535	6	.	.	PUNCT
ejpam-5638	536	1	mathematics	mathematic	NOUN
ejpam-5638	536	2	for	for	ADP
ejpam-5638	536	3	stability	stability	NOUN
ejpam-5638	536	4	and	and	CCONJ
ejpam-5638	536	5	optimization	optimization	NOUN
ejpam-5638	536	6	of	of	ADP
ejpam-5638	536	7	economic	economic	ADJ
ejpam-5638	536	8	systems	system	NOUN
ejpam-5638	536	9	.	.	PUNCT
ejpam-5638	537	1	academic	academic	ADJ
ejpam-5638	537	2	press	press	NOUN
ejpam-5638	537	3	,	,	PUNCT
ejpam-5638	537	4	new	new	PROPN
ejpam-5638	537	5	york	york	PROPN
ejpam-5638	537	6	,	,	PUNCT
ejpam-5638	537	7	1977	1977	NUM
ejpam-5638	537	8	.	.	PUNCT
ejpam-5638	538	1	[	[	X
ejpam-5638	538	2	3	3	X
ejpam-5638	538	3	]	]	X
ejpam-5638	538	4	h.	h.	PROPN
ejpam-5638	538	5	j.	j.	PROPN
ejpam-5638	538	6	nieuwenhuis	nieuwenhuis	PROPN
ejpam-5638	538	7	and	and	CCONJ
ejpam-5638	538	8	l.	l.	PROPN
ejpam-5638	538	9	schoonbeek	schoonbeek	PROPN
ejpam-5638	538	10	.	.	PUNCT
ejpam-5638	539	1	stability	stability	NOUN
ejpam-5638	539	2	of	of	ADP
ejpam-5638	539	3	matrices	matrix	NOUN
ejpam-5638	539	4	with	with	ADP
ejpam-5638	539	5	sufficiently	sufficiently	ADV
ejpam-5638	539	6	strong	strong	ADJ
ejpam-5638	539	7	negative	negative	ADJ
ejpam-5638	539	8	-	-	PUNCT
ejpam-5638	539	9	dominant	dominant	ADJ
ejpam-5638	539	10	diagonal	diagonal	ADJ
ejpam-5638	539	11	submatrices	submatrice	NOUN
ejpam-5638	539	12	.	.	PUNCT
ejpam-5638	540	1	linear	linear	PROPN
ejpam-5638	540	2	algebra	algebra	PROPN
ejpam-5638	540	3	and	and	CCONJ
ejpam-5638	540	4	its	its	PRON
ejpam-5638	540	5	applications	application	NOUN
ejpam-5638	540	6	,	,	PUNCT
ejpam-5638	540	7	258:195–217	258:195–217	NUM
ejpam-5638	540	8	,	,	PUNCT
ejpam-5638	540	9	1997	1997	NUM
ejpam-5638	540	10	.	.	PUNCT
ejpam-5638	541	1	[	[	X
ejpam-5638	541	2	4	4	X
ejpam-5638	541	3	]	]	X
ejpam-5638	541	4	john	john	PROPN
ejpam-5638	541	5	doyle	doyle	PROPN
ejpam-5638	541	6	.	.	PUNCT
ejpam-5638	542	1	analysis	analysis	NOUN
ejpam-5638	542	2	of	of	ADP
ejpam-5638	542	3	feedback	feedback	NOUN
ejpam-5638	542	4	systems	system	NOUN
ejpam-5638	542	5	with	with	ADP
ejpam-5638	542	6	structured	structured	ADJ
ejpam-5638	542	7	uncertainties	uncertainty	NOUN
ejpam-5638	542	8	.	.	PUNCT
ejpam-5638	543	1	iee	iee	PROPN
ejpam-5638	543	2	proceedings	proceeding	NOUN
ejpam-5638	543	3	d	d	X
ejpam-5638	543	4	(	(	PUNCT
ejpam-5638	543	5	control	control	NOUN
ejpam-5638	543	6	theory	theory	NOUN
ejpam-5638	543	7	and	and	CCONJ
ejpam-5638	543	8	applications	application	NOUN
ejpam-5638	543	9	)	)	PUNCT
ejpam-5638	543	10	,	,	PUNCT
ejpam-5638	543	11	129(6):242–250	129(6):242–250	NUM
ejpam-5638	543	12	,	,	PUNCT
ejpam-5638	543	13	1982	1982	NUM
ejpam-5638	543	14	.	.	PUNCT
ejpam-5638	544	1	[	[	X
ejpam-5638	544	2	5	5	X
ejpam-5638	544	3	]	]	PUNCT
ejpam-5638	544	4	j.	j.	PROPN
ejpam-5638	544	5	lee	lee	PROPN
ejpam-5638	544	6	and	and	CCONJ
ejpam-5638	544	7	t.	t.	PROPN
ejpam-5638	544	8	f.	f.	PROPN
ejpam-5638	544	9	edgar	edgar	PROPN
ejpam-5638	544	10	.	.	PUNCT
ejpam-5638	545	1	real	real	ADJ
ejpam-5638	545	2	structured	structure	VERB
ejpam-5638	545	3	singular	singular	ADJ
ejpam-5638	545	4	value	value	NOUN
ejpam-5638	545	5	conditions	condition	NOUN
ejpam-5638	545	6	for	for	ADP
ejpam-5638	545	7	the	the	DET
ejpam-5638	545	8	strong	strong	ADJ
ejpam-5638	545	9	d	d	NOUN
ejpam-5638	545	10	-	-	NOUN
ejpam-5638	545	11	stability	stability	NOUN
ejpam-5638	545	12	.	.	PUNCT
ejpam-5638	546	1	systems	system	NOUN
ejpam-5638	546	2	and	and	CCONJ
ejpam-5638	546	3	control	control	NOUN
ejpam-5638	546	4	letters	letter	NOUN
ejpam-5638	546	5	,	,	PUNCT
ejpam-5638	546	6	44(4):273–277	44(4):273–277	PROPN
ejpam-5638	546	7	,	,	PUNCT
ejpam-5638	546	8	2001	2001	NUM
ejpam-5638	546	9	.	.	PUNCT
ejpam-5638	547	1	[	[	X
ejpam-5638	547	2	6	6	NUM
ejpam-5638	547	3	]	]	PUNCT
ejpam-5638	547	4	r.	r.	PROPN
ejpam-5638	547	5	d.	d.	PROPN
ejpam-5638	547	6	braatz	braatz	PROPN
ejpam-5638	547	7	,	,	PUNCT
ejpam-5638	547	8	p.	p.	PROPN
ejpam-5638	547	9	m.	m.	PROPN
ejpam-5638	547	10	young	young	PROPN
ejpam-5638	547	11	,	,	PUNCT
ejpam-5638	547	12	j.	j.	PROPN
ejpam-5638	547	13	c.	c.	PROPN
ejpam-5638	547	14	doyle	doyle	PROPN
ejpam-5638	547	15	,	,	PUNCT
ejpam-5638	547	16	and	and	CCONJ
ejpam-5638	547	17	m.	m.	NOUN
ejpam-5638	547	18	morari	morari	PROPN
ejpam-5638	547	19	.	.	PUNCT
ejpam-5638	548	1	computational	computational	ADJ
ejpam-5638	548	2	complexity	complexity	NOUN
ejpam-5638	548	3	of	of	ADP
ejpam-5638	548	4	µ	µ	DET
ejpam-5638	548	5	calculation	calculation	NOUN
ejpam-5638	548	6	.	.	PUNCT
ejpam-5638	549	1	ieee	ieee	NOUN
ejpam-5638	549	2	transactions	transaction	NOUN
ejpam-5638	549	3	on	on	ADP
ejpam-5638	549	4	automatic	automatic	ADJ
ejpam-5638	549	5	control	control	NOUN
ejpam-5638	549	6	,	,	PUNCT
ejpam-5638	549	7	39(5):1000–1002	39(5):1000–1002	NUM
ejpam-5638	549	8	,	,	PUNCT
ejpam-5638	549	9	1994	1994	NUM
ejpam-5638	549	10	.	.	PUNCT
ejpam-5638	550	1	[	[	X
ejpam-5638	550	2	7	7	X
ejpam-5638	550	3	]	]	X
ejpam-5638	550	4	r.	r.	PROPN
ejpam-5638	550	5	r.	r.	PROPN
ejpam-5638	550	6	e.	e.	PROPN
ejpam-5638	550	7	de	de	PROPN
ejpam-5638	550	8	gaston	gaston	PROPN
ejpam-5638	550	9	and	and	CCONJ
ejpam-5638	550	10	m.	m.	PROPN
ejpam-5638	550	11	g.	g.	PROPN
ejpam-5638	550	12	safonov	safonov	PROPN
ejpam-5638	550	13	.	.	PUNCT
ejpam-5638	551	1	exact	exact	ADJ
ejpam-5638	551	2	computation	computation	NOUN
ejpam-5638	551	3	of	of	ADP
ejpam-5638	551	4	the	the	DET
ejpam-5638	551	5	multivariable	multivariable	ADJ
ejpam-5638	551	6	stability	stability	NOUN
ejpam-5638	551	7	margin	margin	NOUN
ejpam-5638	551	8	.	.	PUNCT
ejpam-5638	552	1	ieee	ieee	NOUN
ejpam-5638	552	2	transactions	transaction	NOUN
ejpam-5638	552	3	on	on	ADP
ejpam-5638	552	4	automatic	automatic	ADJ
ejpam-5638	552	5	control	control	NOUN
ejpam-5638	552	6	,	,	PUNCT
ejpam-5638	552	7	33(2):156–171	33(2):156–171	PROPN
ejpam-5638	552	8	,	,	PUNCT
ejpam-5638	552	9	1988	1988	NUM
ejpam-5638	552	10	.	.	PUNCT
ejpam-5638	553	1	[	[	X
ejpam-5638	553	2	8	8	NUM
ejpam-5638	553	3	]	]	PUNCT
ejpam-5638	553	4	m.	m.	NOUN
ejpam-5638	553	5	p.	p.	PROPN
ejpam-5638	553	6	newlin	newlin	PROPN
ejpam-5638	553	7	and	and	CCONJ
ejpam-5638	553	8	p.	p.	PROPN
ejpam-5638	553	9	m.	m.	PROPN
ejpam-5638	553	10	young	young	PROPN
ejpam-5638	553	11	.	.	PUNCT
ejpam-5638	554	1	mixed	mixed	ADJ
ejpam-5638	554	2	µ	µ	PRON
ejpam-5638	554	3	problems	problem	NOUN
ejpam-5638	554	4	and	and	CCONJ
ejpam-5638	554	5	branch	branch	NOUN
ejpam-5638	554	6	and	and	CCONJ
ejpam-5638	554	7	bound	bound	ADJ
ejpam-5638	554	8	techniques	technique	NOUN
ejpam-5638	554	9	.	.	PUNCT
ejpam-5638	555	1	international	international	ADJ
ejpam-5638	555	2	journal	journal	NOUN
ejpam-5638	555	3	of	of	ADP
ejpam-5638	555	4	robust	robust	ADJ
ejpam-5638	555	5	and	and	CCONJ
ejpam-5638	555	6	nonlinear	nonlinear	ADJ
ejpam-5638	555	7	control	control	NOUN
ejpam-5638	555	8	,	,	PUNCT
ejpam-5638	555	9	7(2):145–164	7(2):145–164	NOUN
ejpam-5638	555	10	,	,	PUNCT
ejpam-5638	555	11	1997	1997	NUM
ejpam-5638	555	12	.	.	PUNCT
ejpam-5638	556	1	[	[	X
ejpam-5638	556	2	9	9	NUM
ejpam-5638	556	3	]	]	PUNCT
ejpam-5638	556	4	m.	m.	NOUN
ejpam-5638	556	5	k.	k.	PROPN
ejpam-5638	556	6	h.	h.	PROPN
ejpam-5638	556	7	fan	fan	PROPN
ejpam-5638	556	8	,	,	PUNCT
ejpam-5638	556	9	a.	a.	PROPN
ejpam-5638	556	10	l.	l.	PROPN
ejpam-5638	556	11	tits	tits	PROPN
ejpam-5638	556	12	,	,	PUNCT
ejpam-5638	556	13	and	and	CCONJ
ejpam-5638	556	14	j.	j.	PROPN
ejpam-5638	556	15	c.	c.	PROPN
ejpam-5638	556	16	doyle	doyle	PROPN
ejpam-5638	556	17	.	.	PUNCT
ejpam-5638	557	1	robustness	robustness	NOUN
ejpam-5638	557	2	in	in	ADP
ejpam-5638	557	3	the	the	DET
ejpam-5638	557	4	presence	presence	NOUN
ejpam-5638	557	5	of	of	ADP
ejpam-5638	557	6	mixed	mixed	ADJ
ejpam-5638	557	7	parametric	parametric	ADJ
ejpam-5638	557	8	uncertainty	uncertainty	NOUN
ejpam-5638	557	9	and	and	CCONJ
ejpam-5638	557	10	unmodeled	unmodeled	ADJ
ejpam-5638	557	11	dynamics	dynamic	NOUN
ejpam-5638	557	12	.	.	PUNCT
ejpam-5638	558	1	ieee	ieee	NOUN
ejpam-5638	558	2	transactions	transaction	NOUN
ejpam-5638	558	3	on	on	ADP
ejpam-5638	558	4	automatic	automatic	ADJ
ejpam-5638	558	5	control	control	NOUN
ejpam-5638	558	6	,	,	PUNCT
ejpam-5638	558	7	36(1):25–38	36(1):25–38	NUM
ejpam-5638	558	8	,	,	PUNCT
ejpam-5638	558	9	1991	1991	NUM
ejpam-5638	558	10	.	.	PUNCT
ejpam-5638	559	1	[	[	X
ejpam-5638	559	2	10	10	NUM
ejpam-5638	559	3	]	]	X
ejpam-5638	559	4	g.	g.	PROPN
ejpam-5638	559	5	j.	j.	PROPN
ejpam-5638	559	6	balas	balas	PROPN
ejpam-5638	559	7	,	,	PUNCT
ejpam-5638	559	8	j.	j.	PROPN
ejpam-5638	559	9	c.	c.	PROPN
ejpam-5638	559	10	doyle	doyle	PROPN
ejpam-5638	559	11	,	,	PUNCT
ejpam-5638	559	12	k.	k.	PROPN
ejpam-5638	559	13	glover	glover	PROPN
ejpam-5638	559	14	,	,	PUNCT
ejpam-5638	559	15	a.	a.	NOUN
ejpam-5638	559	16	packard	packard	PROPN
ejpam-5638	559	17	,	,	PUNCT
ejpam-5638	559	18	and	and	CCONJ
ejpam-5638	559	19	r.	r.	PROPN
ejpam-5638	559	20	smith	smith	PROPN
ejpam-5638	559	21	.	.	PUNCT
ejpam-5638	560	1	µ-analysis	µ-analysis	NOUN
ejpam-5638	560	2	and	and	CCONJ
ejpam-5638	560	3	synthesis	synthesis	NOUN
ejpam-5638	560	4	toolbox	toolbox	NOUN
ejpam-5638	560	5	.	.	PUNCT
ejpam-5638	561	1	mathworks	mathworks	PROPN
ejpam-5638	561	2	,	,	PUNCT
ejpam-5638	561	3	natick	natick	PROPN
ejpam-5638	561	4	,	,	PUNCT
ejpam-5638	561	5	ma	ma	PROPN
ejpam-5638	561	6	,	,	PUNCT
ejpam-5638	561	7	1995	1995	NUM
ejpam-5638	561	8	.	.	PUNCT
ejpam-5638	562	1	[	[	X
ejpam-5638	562	2	11	11	NUM
ejpam-5638	562	3	]	]	X
ejpam-5638	562	4	p.	p.	NOUN
ejpam-5638	562	5	m.	m.	PROPN
ejpam-5638	562	6	young	young	PROPN
ejpam-5638	562	7	,	,	PUNCT
ejpam-5638	562	8	m.	m.	NOUN
ejpam-5638	562	9	p.	p.	PROPN
ejpam-5638	562	10	newlin	newlin	PROPN
ejpam-5638	562	11	,	,	PUNCT
ejpam-5638	562	12	and	and	CCONJ
ejpam-5638	562	13	j.	j.	PROPN
ejpam-5638	562	14	c.	c.	PROPN
ejpam-5638	562	15	doyle	doyle	PROPN
ejpam-5638	562	16	.	.	PUNCT
ejpam-5638	563	1	practical	practical	ADJ
ejpam-5638	563	2	computation	computation	NOUN
ejpam-5638	563	3	of	of	ADP
ejpam-5638	563	4	the	the	DET
ejpam-5638	563	5	mixed	mixed	ADJ
ejpam-5638	563	6	µ	µ	PROPN
ejpam-5638	563	7	problem	problem	NOUN
ejpam-5638	563	8	.	.	PUNCT
ejpam-5638	564	1	proceedings	proceeding	NOUN
ejpam-5638	564	2	of	of	ADP
ejpam-5638	564	3	the	the	DET
ejpam-5638	564	4	american	american	PROPN
ejpam-5638	564	5	control	control	PROPN
ejpam-5638	564	6	conference	conference	PROPN
ejpam-5638	564	7	,	,	PUNCT
ejpam-5638	564	8	pages	page	NOUN
ejpam-5638	564	9	2190–2194	2190–2194	NUM
ejpam-5638	564	10	,	,	PUNCT
ejpam-5638	564	11	1992	1992	NUM
ejpam-5638	564	12	.	.	PUNCT
ejpam-5638	565	1	[	[	X
ejpam-5638	565	2	12	12	NUM
ejpam-5638	565	3	]	]	X
ejpam-5638	565	4	mutti	mutti	PROPN
ejpam-5638	565	5	-	-	PUNCT
ejpam-5638	565	6	ur	ur	PROPN
ejpam-5638	565	7	rehman	rehman	PROPN
ejpam-5638	565	8	and	and	CCONJ
ejpam-5638	565	9	alisher	alisher	PROPN
ejpam-5638	565	10	shadiyev	shadiyev	PROPN
ejpam-5638	565	11	.	.	PUNCT
ejpam-5638	566	1	interconnection	interconnection	NOUN
ejpam-5638	566	2	between	between	ADP
ejpam-5638	566	3	h	h	NOUN
ejpam-5638	566	4	-	-	PUNCT
ejpam-5638	566	5	stable	stable	ADJ
ejpam-5638	566	6	,	,	PUNCT
ejpam-5638	566	7	d(α)stable	d(α)stable	ADJ
ejpam-5638	566	8	,	,	PUNCT
ejpam-5638	566	9	d	d	ADJ
ejpam-5638	566	10	-	-	ADJ
ejpam-5638	566	11	semistable	semistable	ADJ
ejpam-5638	566	12	matrices	matrix	NOUN
ejpam-5638	566	13	,	,	PUNCT
ejpam-5638	566	14	and	and	CCONJ
ejpam-5638	566	15	µ-values	µ-value	VERB
ejpam-5638	566	16	.	.	PUNCT
ejpam-5638	567	1	asia	asia	PROPN
ejpam-5638	567	2	pacific	pacific	PROPN
ejpam-5638	567	3	journal	journal	PROPN
ejpam-5638	567	4	of	of	ADP
ejpam-5638	567	5	mathematics	mathematic	NOUN
ejpam-5638	567	6	,	,	PUNCT
ejpam-5638	567	7	11:102	11:102	NUM
ejpam-5638	567	8	,	,	PUNCT
ejpam-5638	567	9	2024	2024	NUM
ejpam-5638	567	10	.	.	PUNCT
ejpam-5638	568	1	[	[	X
ejpam-5638	568	2	13	13	NUM
ejpam-5638	568	3	]	]	X
ejpam-5638	568	4	mutti	mutti	PROPN
ejpam-5638	568	5	-	-	PUNCT
ejpam-5638	568	6	ur	ur	PROPN
ejpam-5638	568	7	rehman	rehman	PROPN
ejpam-5638	568	8	and	and	CCONJ
ejpam-5638	568	9	sukhrob	sukhrob	PROPN
ejpam-5638	568	10	babaev	babaev	PROPN
ejpam-5638	568	11	.	.	PUNCT
ejpam-5638	569	1	a	a	DET
ejpam-5638	569	2	review	review	NOUN
ejpam-5638	569	3	on	on	ADP
ejpam-5638	569	4	mathematical	mathematical	ADJ
ejpam-5638	569	5	methods	method	NOUN
ejpam-5638	569	6	to	to	PART
ejpam-5638	569	7	approximate	approximate	VERB
ejpam-5638	569	8	µ-values	µ-value	NOUN
ejpam-5638	569	9	.	.	PUNCT
ejpam-5638	570	1	international	international	ADJ
ejpam-5638	570	2	journal	journal	NOUN
ejpam-5638	570	3	of	of	ADP
ejpam-5638	570	4	analysis	analysis	NOUN
ejpam-5638	570	5	and	and	CCONJ
ejpam-5638	570	6	applications	application	NOUN
ejpam-5638	570	7	,	,	PUNCT
ejpam-5638	570	8	22:232	22:232	NOUN
ejpam-5638	570	9	,	,	PUNCT
ejpam-5638	570	10	2024	2024	NUM
ejpam-5638	570	11	.	.	PUNCT
ejpam-5638	571	1	[	[	X
ejpam-5638	571	2	14	14	NUM
ejpam-5638	571	3	]	]	X
ejpam-5638	571	4	mutti	mutti	PROPN
ejpam-5638	571	5	-	-	PUNCT
ejpam-5638	571	6	ur	ur	PROPN
ejpam-5638	571	7	rehman	rehman	PROPN
ejpam-5638	571	8	et	et	PROPN
ejpam-5638	571	9	al	al	PROPN
ejpam-5638	571	10	.	.	PROPN
ejpam-5638	571	11	spectrum	spectrum	PROPN
ejpam-5638	571	12	and	and	CCONJ
ejpam-5638	571	13	pseudspectrum	pseudspectrum	NOUN
ejpam-5638	571	14	of	of	ADP
ejpam-5638	571	15	d	d	ADJ
ejpam-5638	571	16	-	-	ADJ
ejpam-5638	571	17	stable	stable	ADJ
ejpam-5638	571	18	matrices	matrix	NOUN
ejpam-5638	571	19	of	of	ADP
ejpam-5638	571	20	economy	economy	NOUN
ejpam-5638	571	21	models	model	NOUN
ejpam-5638	571	22	.	.	PUNCT
ejpam-5638	572	1	journal	journal	NOUN
ejpam-5638	572	2	of	of	ADP
ejpam-5638	572	3	mathematics	mathematic	NOUN
ejpam-5638	572	4	and	and	CCONJ
ejpam-5638	572	5	computer	computer	NOUN
ejpam-5638	572	6	science	science	NOUN
ejpam-5638	572	7	,	,	PUNCT
ejpam-5638	572	8	38(3):298–312	38(3):298–312	NUM
ejpam-5638	572	9	,	,	PUNCT
ejpam-5638	572	10	2025	2025	NUM
ejpam-5638	572	11	.	.	PUNCT
ejpam-5638	573	1	[	[	X
ejpam-5638	573	2	15	15	NUM
ejpam-5638	573	3	]	]	X
ejpam-5638	573	4	pawan	pawan	PROPN
ejpam-5638	573	5	goyal	goyal	PROPN
ejpam-5638	573	6	,	,	PUNCT
ejpam-5638	573	7	igor	igor	PROPN
ejpam-5638	573	8	pontes	pontes	PROPN
ejpam-5638	573	9	duff	duff	PROPN
ejpam-5638	573	10	,	,	PUNCT
ejpam-5638	573	11	and	and	CCONJ
ejpam-5638	573	12	peter	peter	PROPN
ejpam-5638	573	13	benner	benner	PROPN
ejpam-5638	573	14	.	.	PUNCT
ejpam-5638	574	1	inference	inference	NOUN
ejpam-5638	574	2	of	of	ADP
ejpam-5638	574	3	continuous	continuous	ADJ
ejpam-5638	574	4	linear	linear	PROPN
ejpam-5638	574	5	systems	system	NOUN
ejpam-5638	574	6	from	from	ADP
ejpam-5638	574	7	data	datum	NOUN
ejpam-5638	574	8	with	with	ADP
ejpam-5638	574	9	guaranteed	guarantee	VERB
ejpam-5638	574	10	stability	stability	NOUN
ejpam-5638	574	11	.	.	PUNCT
ejpam-5638	575	1	arxiv	arxiv	PROPN
ejpam-5638	575	2	preprint	preprint	NOUN
ejpam-5638	575	3	arxiv:2301.10060	arxiv:2301.10060	NOUN
ejpam-5638	575	4	,	,	PUNCT
ejpam-5638	575	5	2023	2023	NUM
ejpam-5638	575	6	.	.	PUNCT
ejpam-5638	576	1	[	[	X
ejpam-5638	576	2	16	16	NUM
ejpam-5638	576	3	]	]	X
ejpam-5638	576	4	charles	charles	PROPN
ejpam-5638	576	5	r.	r.	PROPN
ejpam-5638	576	6	johnson	johnson	PROPN
ejpam-5638	576	7	.	.	PUNCT
ejpam-5638	577	1	sufficient	sufficient	ADJ
ejpam-5638	577	2	conditions	condition	NOUN
ejpam-5638	577	3	for	for	ADP
ejpam-5638	577	4	d	d	NOUN
ejpam-5638	577	5	-	-	NOUN
ejpam-5638	577	6	stability	stability	NOUN
ejpam-5638	577	7	.	.	PUNCT
ejpam-5638	578	1	journal	journal	NOUN
ejpam-5638	578	2	of	of	ADP
ejpam-5638	578	3	economic	economic	ADJ
ejpam-5638	578	4	theory	theory	NOUN
ejpam-5638	578	5	,	,	PUNCT
ejpam-5638	578	6	9(1):53–62	9(1):53–62	NUM
ejpam-5638	578	7	,	,	PUNCT
ejpam-5638	578	8	1974	1974	NUM
ejpam-5638	578	9	.	.	PUNCT
ejpam-5638	579	1	m.u.r	m.u.r	PROPN
ejpam-5638	579	2	rehman	rehman	PROPN
ejpam-5638	579	3	et	et	PROPN
ejpam-5638	579	4	al	al	PROPN
ejpam-5638	579	5	.	.	PUNCT
ejpam-5638	579	6	/	/	SYM
ejpam-5638	579	7	eur	eur	PROPN
ejpam-5638	579	8	.	.	PUNCT
ejpam-5638	580	1	j.	j.	PROPN
ejpam-5638	580	2	pure	pure	PROPN
ejpam-5638	580	3	appl	appl	PROPN
ejpam-5638	580	4	.	.	PROPN
ejpam-5638	580	5	math	math	PROPN
ejpam-5638	580	6	,	,	PUNCT
ejpam-5638	580	7	18	18	NUM
ejpam-5638	580	8	(	(	PUNCT
ejpam-5638	580	9	2	2	NUM
ejpam-5638	580	10	)	)	PUNCT
ejpam-5638	580	11	(	(	PUNCT
ejpam-5638	580	12	2025	2025	NUM
ejpam-5638	580	13	)	)	PUNCT
ejpam-5638	580	14	,	,	PUNCT
ejpam-5638	580	15	5638	5638	NUM
ejpam-5638	580	16	22	22	NUM
ejpam-5638	580	17	of	of	ADP
ejpam-5638	580	18	23	23	NUM
ejpam-5638	581	1	[	[	SYM
ejpam-5638	581	2	17	17	NUM
ejpam-5638	581	3	]	]	X
ejpam-5638	581	4	charles	charles	PROPN
ejpam-5638	581	5	johnson	johnson	PROPN
ejpam-5638	581	6	.	.	PUNCT
ejpam-5638	582	1	hadamard	hadamard	ADJ
ejpam-5638	582	2	products	product	NOUN
ejpam-5638	582	3	of	of	ADP
ejpam-5638	582	4	matrices	matrix	NOUN
ejpam-5638	582	5	.	.	PUNCT
ejpam-5638	583	1	linear	linear	ADJ
ejpam-5638	583	2	and	and	CCONJ
ejpam-5638	583	3	multilinear	multilinear	PROPN
ejpam-5638	583	4	algebra	algebra	NOUN
ejpam-5638	583	5	,	,	PUNCT
ejpam-5638	583	6	1(4):295–307	1(4):295–307	NUM
ejpam-5638	583	7	,	,	PUNCT
ejpam-5638	583	8	1974	1974	NUM
ejpam-5638	583	9	.	.	PUNCT
ejpam-5638	584	1	[	[	X
ejpam-5638	584	2	18	18	NUM
ejpam-5638	584	3	]	]	X
ejpam-5638	584	4	charles	charles	PROPN
ejpam-5638	584	5	r.	r.	PROPN
ejpam-5638	584	6	johnson	johnson	PROPN
ejpam-5638	584	7	.	.	PUNCT
ejpam-5638	585	1	d	d	X
ejpam-5638	585	2	-	-	PUNCT
ejpam-5638	585	3	stability	stability	NOUN
ejpam-5638	585	4	and	and	CCONJ
ejpam-5638	585	5	real	real	ADJ
ejpam-5638	585	6	and	and	CCONJ
ejpam-5638	585	7	complex	complex	ADJ
ejpam-5638	585	8	quadratic	quadratic	ADJ
ejpam-5638	585	9	forms	form	NOUN
ejpam-5638	585	10	.	.	PUNCT
ejpam-5638	586	1	linear	linear	ADJ
ejpam-5638	586	2	algebra	algebra	NOUN
ejpam-5638	586	3	and	and	CCONJ
ejpam-5638	586	4	its	its	PRON
ejpam-5638	586	5	applications	application	NOUN
ejpam-5638	586	6	,	,	PUNCT
ejpam-5638	586	7	9:89–94	9:89–94	NUM
ejpam-5638	586	8	,	,	PUNCT
ejpam-5638	586	9	1974	1974	NUM
ejpam-5638	586	10	.	.	PUNCT
ejpam-5638	587	1	[	[	X
ejpam-5638	587	2	19	19	NUM
ejpam-5638	587	3	]	]	X
ejpam-5638	587	4	james	james	PROPN
ejpam-5638	587	5	quirk	quirk	PROPN
ejpam-5638	587	6	and	and	CCONJ
ejpam-5638	587	7	richard	richard	PROPN
ejpam-5638	587	8	ruppert	ruppert	PROPN
ejpam-5638	587	9	.	.	PUNCT
ejpam-5638	588	1	qualitative	qualitative	ADJ
ejpam-5638	588	2	economics	economic	NOUN
ejpam-5638	588	3	and	and	CCONJ
ejpam-5638	588	4	the	the	DET
ejpam-5638	588	5	stability	stability	NOUN
ejpam-5638	588	6	of	of	ADP
ejpam-5638	588	7	equilibrium	equilibrium	NOUN
ejpam-5638	588	8	.	.	PUNCT
ejpam-5638	589	1	the	the	DET
ejpam-5638	589	2	review	review	NOUN
ejpam-5638	589	3	of	of	ADP
ejpam-5638	589	4	economic	economic	ADJ
ejpam-5638	589	5	studies	study	NOUN
ejpam-5638	589	6	,	,	PUNCT
ejpam-5638	589	7	32(4):311–326	32(4):311–326	NUM
ejpam-5638	589	8	,	,	PUNCT
ejpam-5638	589	9	1965	1965	NUM
ejpam-5638	589	10	.	.	PUNCT
ejpam-5638	590	1	[	[	X
ejpam-5638	590	2	20	20	NUM
ejpam-5638	590	3	]	]	PUNCT
ejpam-5638	590	4	kenneth	kenneth	PROPN
ejpam-5638	590	5	j.	j.	PROPN
ejpam-5638	590	6	arrow	arrow	PROPN
ejpam-5638	590	7	and	and	CCONJ
ejpam-5638	590	8	maurice	maurice	PROPN
ejpam-5638	590	9	mcmanus	mcmanus	PROPN
ejpam-5638	590	10	.	.	PUNCT
ejpam-5638	591	1	a	a	DET
ejpam-5638	591	2	note	note	NOUN
ejpam-5638	591	3	on	on	ADP
ejpam-5638	591	4	dynamic	dynamic	ADJ
ejpam-5638	591	5	stability	stability	NOUN
ejpam-5638	591	6	.	.	PUNCT
ejpam-5638	592	1	econometrica	econometrica	PROPN
ejpam-5638	592	2	,	,	PUNCT
ejpam-5638	592	3	26(3):448–454	26(3):448–454	PROPN
ejpam-5638	592	4	,	,	PUNCT
ejpam-5638	592	5	1958	1958	NUM
ejpam-5638	592	6	.	.	PUNCT
ejpam-5638	593	1	[	[	X
ejpam-5638	593	2	21	21	NUM
ejpam-5638	593	3	]	]	X
ejpam-5638	593	4	charles	charles	PROPN
ejpam-5638	593	5	royal	royal	PROPN
ejpam-5638	593	6	johnson	johnson	PROPN
ejpam-5638	593	7	.	.	PUNCT
ejpam-5638	594	1	matrices	matrix	NOUN
ejpam-5638	594	2	whose	whose	DET
ejpam-5638	594	3	hermitian	hermitian	ADJ
ejpam-5638	594	4	part	part	NOUN
ejpam-5638	594	5	is	be	AUX
ejpam-5638	594	6	positive	positive	ADJ
ejpam-5638	594	7	definite	definite	ADJ
ejpam-5638	594	8	.	.	PUNCT
ejpam-5638	595	1	phd	phd	NOUN
ejpam-5638	595	2	thesis	thesis	PROPN
ejpam-5638	595	3	,	,	PUNCT
ejpam-5638	595	4	california	california	PROPN
ejpam-5638	595	5	institute	institute	PROPN
ejpam-5638	595	6	of	of	ADP
ejpam-5638	595	7	technology	technology	PROPN
ejpam-5638	595	8	,	,	PUNCT
ejpam-5638	595	9	1972	1972	NUM
ejpam-5638	595	10	.	.	PUNCT
ejpam-5638	596	1	[	[	X
ejpam-5638	596	2	22	22	NUM
ejpam-5638	596	3	]	]	X
ejpam-5638	596	4	stephen	stephen	PROPN
ejpam-5638	596	5	barnett	barnett	PROPN
ejpam-5638	596	6	and	and	CCONJ
ejpam-5638	596	7	colin	colin	PROPN
ejpam-5638	596	8	storey	storey	PROPN
ejpam-5638	596	9	.	.	PUNCT
ejpam-5638	597	1	matrix	matrix	NOUN
ejpam-5638	597	2	methods	method	NOUN
ejpam-5638	597	3	in	in	ADP
ejpam-5638	597	4	stability	stability	NOUN
ejpam-5638	597	5	theory	theory	NOUN
ejpam-5638	597	6	.	.	PUNCT
ejpam-5638	598	1	nelson	nelson	PROPN
ejpam-5638	598	2	,	,	PUNCT
ejpam-5638	598	3	london	london	PROPN
ejpam-5638	598	4	,	,	PUNCT
ejpam-5638	598	5	1970	1970	NUM
ejpam-5638	598	6	.	.	PUNCT
ejpam-5638	599	1	[	[	X
ejpam-5638	599	2	23	23	NUM
ejpam-5638	599	3	]	]	PUNCT
ejpam-5638	599	4	miroslav	miroslav	ADJ
ejpam-5638	599	5	fiedler	fiedler	NOUN
ejpam-5638	599	6	and	and	CCONJ
ejpam-5638	599	7	vlastimil	vlastimil	VERB
ejpam-5638	599	8	pták	pták	NOUN
ejpam-5638	599	9	.	.	PUNCT
ejpam-5638	600	1	on	on	ADP
ejpam-5638	600	2	matrices	matrix	NOUN
ejpam-5638	600	3	with	with	ADP
ejpam-5638	600	4	non	non	ADJ
ejpam-5638	600	5	-	-	ADJ
ejpam-5638	600	6	positive	positive	ADJ
ejpam-5638	600	7	off	off	ADJ
ejpam-5638	600	8	-	-	PUNCT
ejpam-5638	600	9	diagonal	diagonal	ADJ
ejpam-5638	600	10	elements	element	NOUN
ejpam-5638	600	11	and	and	CCONJ
ejpam-5638	600	12	positive	positive	ADJ
ejpam-5638	600	13	principal	principal	ADJ
ejpam-5638	600	14	minors	minor	NOUN
ejpam-5638	600	15	.	.	PUNCT
ejpam-5638	601	1	czechoslovak	czechoslovak	ADJ
ejpam-5638	601	2	mathematical	mathematical	PROPN
ejpam-5638	601	3	journal	journal	NOUN
ejpam-5638	601	4	,	,	PUNCT
ejpam-5638	601	5	12(3):382	12(3):382	NUM
ejpam-5638	601	6	–	–	PUNCT
ejpam-5638	601	7	400	400	NUM
ejpam-5638	601	8	,	,	PUNCT
ejpam-5638	601	9	1962	1962	NUM
ejpam-5638	601	10	.	.	PUNCT
ejpam-5638	602	1	[	[	X
ejpam-5638	602	2	24	24	NUM
ejpam-5638	602	3	]	]	X
ejpam-5638	602	4	james	james	PROPN
ejpam-5638	602	5	p.	p.	PROPN
ejpam-5638	602	6	quirk	quirk	PROPN
ejpam-5638	602	7	and	and	CCONJ
ejpam-5638	602	8	rubin	rubin	PROPN
ejpam-5638	602	9	saposnik	saposnik	PROPN
ejpam-5638	602	10	.	.	PUNCT
ejpam-5638	603	1	introduction	introduction	NOUN
ejpam-5638	603	2	to	to	ADP
ejpam-5638	603	3	general	general	ADJ
ejpam-5638	603	4	equilibrium	equilibrium	NOUN
ejpam-5638	603	5	theory	theory	NOUN
ejpam-5638	603	6	and	and	CCONJ
ejpam-5638	603	7	welfare	welfare	NOUN
ejpam-5638	603	8	economics	economic	NOUN
ejpam-5638	603	9	.	.	PUNCT
ejpam-5638	604	1	1968	1968	NUM
ejpam-5638	604	2	.	.	PUNCT
ejpam-5638	605	1	[	[	X
ejpam-5638	605	2	25	25	NUM
ejpam-5638	605	3	]	]	X
ejpam-5638	605	4	olga	olga	PROPN
ejpam-5638	605	5	taussky	taussky	PROPN
ejpam-5638	605	6	.	.	PUNCT
ejpam-5638	606	1	a	a	DET
ejpam-5638	606	2	recurring	recur	VERB
ejpam-5638	606	3	theorem	theorem	NOUN
ejpam-5638	606	4	on	on	ADP
ejpam-5638	606	5	determinants	determinant	NOUN
ejpam-5638	606	6	.	.	PUNCT
ejpam-5638	607	1	the	the	DET
ejpam-5638	607	2	american	american	PROPN
ejpam-5638	607	3	mathematical	mathematical	PROPN
ejpam-5638	607	4	monthly	monthly	ADV
ejpam-5638	607	5	,	,	PUNCT
ejpam-5638	607	6	56(10):672–676	56(10):672–676	NUM
ejpam-5638	607	7	,	,	PUNCT
ejpam-5638	607	8	1949	1949	NUM
ejpam-5638	607	9	.	.	PUNCT
ejpam-5638	608	1	[	[	X
ejpam-5638	608	2	26	26	NUM
ejpam-5638	608	3	]	]	X
ejpam-5638	608	4	andrew	andrew	PROPN
ejpam-5638	608	5	packard	packard	PROPN
ejpam-5638	608	6	and	and	CCONJ
ejpam-5638	608	7	john	john	PROPN
ejpam-5638	608	8	doyle	doyle	PROPN
ejpam-5638	608	9	.	.	PUNCT
ejpam-5638	609	1	the	the	DET
ejpam-5638	609	2	complex	complex	ADJ
ejpam-5638	609	3	structured	structured	ADJ
ejpam-5638	609	4	singular	singular	ADJ
ejpam-5638	609	5	value	value	NOUN
ejpam-5638	609	6	.	.	PUNCT
ejpam-5638	610	1	automatica	automatica	PROPN
ejpam-5638	610	2	,	,	PUNCT
ejpam-5638	610	3	29(1):71–109	29(1):71–109	NUM
ejpam-5638	610	4	,	,	PUNCT
ejpam-5638	610	5	1993	1993	NUM
ejpam-5638	610	6	.	.	PUNCT
ejpam-5638	611	1	[	[	X
ejpam-5638	611	2	27	27	NUM
ejpam-5638	611	3	]	]	X
ejpam-5638	611	4	jie	jie	PROPN
ejpam-5638	611	5	chen	chen	PROPN
ejpam-5638	611	6	,	,	PUNCT
ejpam-5638	611	7	michael	michael	PROPN
ejpam-5638	611	8	k.	k.	PROPN
ejpam-5638	611	9	h.	h.	PROPN
ejpam-5638	611	10	fan	fan	PROPN
ejpam-5638	611	11	,	,	PUNCT
ejpam-5638	611	12	and	and	CCONJ
ejpam-5638	611	13	cheng	cheng	PROPN
ejpam-5638	611	14	-	-	PUNCT
ejpam-5638	611	15	ching	ching	PROPN
ejpam-5638	611	16	yu	yu	PROPN
ejpam-5638	611	17	.	.	PUNCT
ejpam-5638	612	1	on	on	ADP
ejpam-5638	612	2	d	d	NOUN
ejpam-5638	612	3	-	-	NOUN
ejpam-5638	612	4	stability	stability	NOUN
ejpam-5638	612	5	and	and	CCONJ
ejpam-5638	612	6	structured	structure	VERB
ejpam-5638	612	7	singular	singular	ADJ
ejpam-5638	612	8	values	value	NOUN
ejpam-5638	612	9	.	.	PUNCT
ejpam-5638	613	1	systems	system	NOUN
ejpam-5638	613	2	and	and	CCONJ
ejpam-5638	613	3	control	control	NOUN
ejpam-5638	613	4	letters	letter	NOUN
ejpam-5638	613	5	,	,	PUNCT
ejpam-5638	613	6	24(1):19–24	24(1):19–24	NUM
ejpam-5638	613	7	,	,	PUNCT
ejpam-5638	613	8	1995	1995	NUM
ejpam-5638	613	9	.	.	PUNCT
ejpam-5638	614	1	[	[	X
ejpam-5638	614	2	28	28	NUM
ejpam-5638	614	3	]	]	X
ejpam-5638	614	4	jietae	jietae	PROPN
ejpam-5638	614	5	lee	lee	PROPN
ejpam-5638	614	6	and	and	CCONJ
ejpam-5638	614	7	thomas	thomas	PROPN
ejpam-5638	614	8	f.	f.	PROPN
ejpam-5638	614	9	edgar	edgar	PROPN
ejpam-5638	614	10	.	.	PUNCT
ejpam-5638	615	1	real	real	ADJ
ejpam-5638	615	2	structured	structure	VERB
ejpam-5638	615	3	singular	singular	ADJ
ejpam-5638	615	4	value	value	NOUN
ejpam-5638	615	5	conditions	condition	NOUN
ejpam-5638	615	6	for	for	ADP
ejpam-5638	615	7	the	the	DET
ejpam-5638	615	8	strong	strong	ADJ
ejpam-5638	615	9	d	d	NOUN
ejpam-5638	615	10	-	-	NOUN
ejpam-5638	615	11	stability	stability	NOUN
ejpam-5638	615	12	.	.	PUNCT
ejpam-5638	616	1	systems	system	NOUN
ejpam-5638	616	2	and	and	CCONJ
ejpam-5638	616	3	control	control	NOUN
ejpam-5638	616	4	letters	letter	NOUN
ejpam-5638	616	5	,	,	PUNCT
ejpam-5638	616	6	44(4):273–277	44(4):273–277	PROPN
ejpam-5638	616	7	,	,	PUNCT
ejpam-5638	616	8	2001	2001	NUM
ejpam-5638	616	9	.	.	PUNCT
ejpam-5638	617	1	[	[	X
ejpam-5638	617	2	29	29	NUM
ejpam-5638	617	3	]	]	PUNCT
ejpam-5638	617	4	p.	p.	NOUN
ejpam-5638	617	5	j.	j.	PROPN
ejpam-5638	617	6	campo	campo	PROPN
ejpam-5638	617	7	and	and	CCONJ
ejpam-5638	617	8	m.	m.	NOUN
ejpam-5638	617	9	morari	morari	PROPN
ejpam-5638	617	10	.	.	PUNCT
ejpam-5638	618	1	achievable	achievable	ADJ
ejpam-5638	618	2	closed	closed	ADJ
ejpam-5638	618	3	-	-	PUNCT
ejpam-5638	618	4	loop	loop	NOUN
ejpam-5638	618	5	properties	property	NOUN
ejpam-5638	618	6	of	of	ADP
ejpam-5638	618	7	systems	system	NOUN
ejpam-5638	618	8	under	under	ADP
ejpam-5638	618	9	decentralized	decentralized	ADJ
ejpam-5638	618	10	control	control	NOUN
ejpam-5638	618	11	:	:	PUNCT
ejpam-5638	618	12	conditions	condition	NOUN
ejpam-5638	618	13	involving	involve	VERB
ejpam-5638	618	14	the	the	DET
ejpam-5638	618	15	steady	steady	ADJ
ejpam-5638	618	16	-	-	PUNCT
ejpam-5638	618	17	state	state	NOUN
ejpam-5638	618	18	gain	gain	NOUN
ejpam-5638	618	19	.	.	PUNCT
ejpam-5638	619	1	ieee	ieee	NOUN
ejpam-5638	619	2	transactions	transaction	NOUN
ejpam-5638	619	3	on	on	ADP
ejpam-5638	619	4	automatic	automatic	ADJ
ejpam-5638	619	5	control	control	NOUN
ejpam-5638	619	6	,	,	PUNCT
ejpam-5638	619	7	39(5):932–943	39(5):932–943	PROPN
ejpam-5638	619	8	,	,	PUNCT
ejpam-5638	619	9	1994	1994	NUM
ejpam-5638	619	10	.	.	PUNCT
ejpam-5638	620	1	[	[	X
ejpam-5638	620	2	30	30	NUM
ejpam-5638	620	3	]	]	X
ejpam-5638	620	4	jie	jie	PROPN
ejpam-5638	620	5	chen	chen	PROPN
ejpam-5638	620	6	,	,	PUNCT
ejpam-5638	620	7	michael	michael	PROPN
ejpam-5638	620	8	k.	k.	PROPN
ejpam-5638	620	9	h.	h.	PROPN
ejpam-5638	620	10	fan	fan	PROPN
ejpam-5638	620	11	,	,	PUNCT
ejpam-5638	620	12	and	and	CCONJ
ejpam-5638	620	13	cheng	cheng	PROPN
ejpam-5638	620	14	-	-	PUNCT
ejpam-5638	620	15	ching	ching	PROPN
ejpam-5638	620	16	yu	yu	PROPN
ejpam-5638	620	17	.	.	PUNCT
ejpam-5638	621	1	on	on	ADP
ejpam-5638	621	2	d	d	NOUN
ejpam-5638	621	3	-	-	NOUN
ejpam-5638	621	4	stability	stability	NOUN
ejpam-5638	621	5	and	and	CCONJ
ejpam-5638	621	6	structured	structure	VERB
ejpam-5638	621	7	singular	singular	ADJ
ejpam-5638	621	8	values	value	NOUN
ejpam-5638	621	9	.	.	PUNCT
ejpam-5638	622	1	systems	system	NOUN
ejpam-5638	622	2	and	and	CCONJ
ejpam-5638	622	3	control	control	NOUN
ejpam-5638	622	4	letters	letter	NOUN
ejpam-5638	622	5	,	,	PUNCT
ejpam-5638	622	6	24(1):19–24	24(1):19–24	NUM
ejpam-5638	622	7	,	,	PUNCT
ejpam-5638	622	8	1995	1995	NUM
ejpam-5638	622	9	.	.	PUNCT
ejpam-5638	623	1	[	[	X
ejpam-5638	623	2	31	31	NUM
ejpam-5638	623	3	]	]	X
ejpam-5638	623	4	mutti	mutti	PROPN
ejpam-5638	623	5	-	-	PUNCT
ejpam-5638	623	6	ur	ur	PROPN
ejpam-5638	623	7	rehman	rehman	PROPN
ejpam-5638	623	8	,	,	PUNCT
ejpam-5638	623	9	tulkin	tulkin	PROPN
ejpam-5638	623	10	h.	h.	PROPN
ejpam-5638	623	11	rasulov	rasulov	PROPN
ejpam-5638	623	12	,	,	PUNCT
ejpam-5638	623	13	and	and	CCONJ
ejpam-5638	623	14	fouzia	fouzia	AUX
ejpam-5638	623	15	amir	amir	X
ejpam-5638	623	16	.	.	PUNCT
ejpam-5638	624	1	d	d	X
ejpam-5638	624	2	-	-	PUNCT
ejpam-5638	624	3	stability	stability	NOUN
ejpam-5638	624	4	,	,	PUNCT
ejpam-5638	624	5	strong	strong	ADJ
ejpam-5638	624	6	dstability	dstability	NOUN
ejpam-5638	624	7	and	and	CCONJ
ejpam-5638	624	8	µ-values	µ-value	NOUN
ejpam-5638	624	9	.	.	PUNCT
ejpam-5638	625	1	lobachevskii	lobachevskii	PROPN
ejpam-5638	625	2	journal	journal	PROPN
ejpam-5638	625	3	of	of	ADP
ejpam-5638	625	4	mathematics	mathematic	NOUN
ejpam-5638	625	5	,	,	PUNCT
ejpam-5638	625	6	45(3):1227–1233	45(3):1227–1233	NUM
ejpam-5638	625	7	,	,	PUNCT
ejpam-5638	625	8	2024	2024	NUM
ejpam-5638	625	9	.	.	PUNCT
ejpam-5638	626	1	[	[	X
ejpam-5638	626	2	32	32	NUM
ejpam-5638	626	3	]	]	PUNCT
ejpam-5638	626	4	nicholas	nicholas	PROPN
ejpam-5638	626	5	l.	l.	PROPN
ejpam-5638	626	6	trefethen	trefethen	PROPN
ejpam-5638	626	7	.	.	PUNCT
ejpam-5638	627	1	spectra	spectra	PROPN
ejpam-5638	627	2	and	and	CCONJ
ejpam-5638	627	3	pseudospectra	pseudospectra	PROPN
ejpam-5638	627	4	:	:	PUNCT
ejpam-5638	627	5	the	the	DET
ejpam-5638	627	6	behavior	behavior	NOUN
ejpam-5638	627	7	of	of	ADP
ejpam-5638	627	8	non	non	ADJ
ejpam-5638	627	9	-	-	ADJ
ejpam-5638	627	10	normal	normal	ADJ
ejpam-5638	627	11	matrices	matrix	NOUN
ejpam-5638	627	12	and	and	CCONJ
ejpam-5638	627	13	operators	operator	NOUN
ejpam-5638	627	14	.	.	PUNCT
ejpam-5638	628	1	princeton	princeton	PROPN
ejpam-5638	628	2	university	university	PROPN
ejpam-5638	628	3	press	press	PROPN
ejpam-5638	628	4	,	,	PUNCT
ejpam-5638	628	5	princeton	princeton	PROPN
ejpam-5638	628	6	,	,	PUNCT
ejpam-5638	628	7	nj	nj	PROPN
ejpam-5638	628	8	,	,	PUNCT
ejpam-5638	628	9	2005	2005	NUM
ejpam-5638	628	10	.	.	PUNCT
ejpam-5638	629	1	[	[	X
ejpam-5638	629	2	33	33	NUM
ejpam-5638	629	3	]	]	PUNCT
ejpam-5638	629	4	a.	a.	NOUN
ejpam-5638	629	5	zackard	zackard	PROPN
ejpam-5638	629	6	,	,	PUNCT
ejpam-5638	629	7	michael	michael	PROPN
ejpam-5638	629	8	k.	k.	PROPN
ejpam-5638	629	9	h.	h.	PROPN
ejpam-5638	629	10	fan	fan	PROPN
ejpam-5638	629	11	,	,	PUNCT
ejpam-5638	629	12	and	and	CCONJ
ejpam-5638	629	13	john	john	PROPN
ejpam-5638	629	14	doyle	doyle	PROPN
ejpam-5638	629	15	.	.	PUNCT
ejpam-5638	630	1	a	a	DET
ejpam-5638	630	2	power	power	NOUN
ejpam-5638	630	3	method	method	NOUN
ejpam-5638	630	4	for	for	ADP
ejpam-5638	630	5	the	the	DET
ejpam-5638	630	6	structured	structured	ADJ
ejpam-5638	630	7	singular	singular	NOUN
ejpam-5638	630	8	value	value	NOUN
ejpam-5638	630	9	,	,	PUNCT
ejpam-5638	630	10	1988	1988	NUM
ejpam-5638	630	11	.	.	PUNCT
ejpam-5638	631	1	[	[	X
ejpam-5638	631	2	34	34	NUM
ejpam-5638	631	3	]	]	X
ejpam-5638	631	4	p.	p.	NOUN
ejpam-5638	631	5	seiler	seiler	PROPN
ejpam-5638	631	6	,	,	PUNCT
ejpam-5638	631	7	g.	g.	PROPN
ejpam-5638	631	8	balas	balas	PROPN
ejpam-5638	631	9	,	,	PUNCT
ejpam-5638	631	10	and	and	CCONJ
ejpam-5638	631	11	a.	a.	NOUN
ejpam-5638	631	12	packard	packard	PROPN
ejpam-5638	631	13	.	.	PUNCT
ejpam-5638	632	1	a	a	DET
ejpam-5638	632	2	gain	gain	NOUN
ejpam-5638	632	3	-	-	PUNCT
ejpam-5638	632	4	based	base	VERB
ejpam-5638	632	5	lower	low	ADJ
ejpam-5638	632	6	bound	bind	VERB
ejpam-5638	632	7	algorithm	algorithm	NOUN
ejpam-5638	632	8	for	for	ADP
ejpam-5638	632	9	real	real	ADJ
ejpam-5638	632	10	and	and	CCONJ
ejpam-5638	632	11	mixed	mixed	ADJ
ejpam-5638	632	12	µ-problems	µ-problem	NOUN
ejpam-5638	632	13	.	.	PUNCT
ejpam-5638	633	1	proceedings	proceeding	NOUN
ejpam-5638	633	2	of	of	ADP
ejpam-5638	633	3	the	the	DET
ejpam-5638	633	4	45th	45th	ADJ
ejpam-5638	633	5	ieee	ieee	NOUN
ejpam-5638	633	6	conference	conference	NOUN
ejpam-5638	633	7	on	on	ADP
ejpam-5638	633	8	decision	decision	NOUN
ejpam-5638	633	9	and	and	CCONJ
ejpam-5638	633	10	control	control	NOUN
ejpam-5638	633	11	,	,	PUNCT
ejpam-5638	633	12	pages	page	NOUN
ejpam-5638	633	13	3548–3553	3548–3553	NUM
ejpam-5638	633	14	,	,	PUNCT
ejpam-5638	633	15	2006	2006	NUM
ejpam-5638	633	16	.	.	PUNCT
ejpam-5638	634	1	[	[	X
ejpam-5638	634	2	35	35	NUM
ejpam-5638	634	3	]	]	PUNCT
ejpam-5638	634	4	j.	j.	PROPN
ejpam-5638	634	5	f.	f.	PROPN
ejpam-5638	634	6	magni	magni	PROPN
ejpam-5638	634	7	,	,	PUNCT
ejpam-5638	634	8	c.	c.	PROPN
ejpam-5638	634	9	döll	döll	PROPN
ejpam-5638	634	10	,	,	PUNCT
ejpam-5638	634	11	c.	c.	PROPN
ejpam-5638	634	12	chiappa	chiappa	PROPN
ejpam-5638	634	13	,	,	PUNCT
ejpam-5638	634	14	b.	b.	PROPN
ejpam-5638	634	15	frappard	frappard	PROPN
ejpam-5638	634	16	,	,	PUNCT
ejpam-5638	634	17	and	and	CCONJ
ejpam-5638	634	18	b.	b.	PROPN
ejpam-5638	634	19	girouart	girouart	NOUN
ejpam-5638	634	20	.	.	PUNCT
ejpam-5638	635	1	mixed	mix	VERB
ejpam-5638	635	2	µ-analysis	µ-analysis	NOUN
ejpam-5638	635	3	for	for	ADP
ejpam-5638	635	4	flexible	flexible	ADJ
ejpam-5638	635	5	systems	system	NOUN
ejpam-5638	635	6	.	.	PUNCT
ejpam-5638	636	1	part	part	NOUN
ejpam-5638	636	2	1	1	NUM
ejpam-5638	636	3	:	:	PUNCT
ejpam-5638	636	4	theory	theory	NOUN
ejpam-5638	636	5	.	.	PUNCT
ejpam-5638	637	1	proceedings	proceeding	NOUN
ejpam-5638	637	2	of	of	ADP
ejpam-5638	637	3	the	the	DET
ejpam-5638	637	4	14th	14th	ADJ
ejpam-5638	637	5	ifac	ifac	NOUN
ejpam-5638	637	6	world	world	PROPN
ejpam-5638	637	7	congress	congress	PROPN
ejpam-5638	637	8	,	,	PUNCT
ejpam-5638	637	9	5:325–360	5:325–360	NUM
ejpam-5638	637	10	,	,	PUNCT
ejpam-5638	637	11	1999	1999	NUM
ejpam-5638	637	12	.	.	PUNCT
ejpam-5638	638	1	[	[	X
ejpam-5638	638	2	36	36	NUM
ejpam-5638	638	3	]	]	PUNCT
ejpam-5638	638	4	m.	m.	PROPN
ejpam-5638	638	5	halton	halton	PROPN
ejpam-5638	638	6	,	,	PUNCT
ejpam-5638	638	7	m.	m.	NOUN
ejpam-5638	638	8	hayes	hayes	PROPN
ejpam-5638	638	9	,	,	PUNCT
ejpam-5638	638	10	and	and	CCONJ
ejpam-5638	638	11	p.	p.	NOUN
ejpam-5638	638	12	iordanov	iordanov	PROPN
ejpam-5638	638	13	.	.	PUNCT
ejpam-5638	639	1	state	state	NOUN
ejpam-5638	639	2	-	-	PUNCT
ejpam-5638	639	3	space	space	NOUN
ejpam-5638	639	4	µ-analysis	µ-analysis	NOUN
ejpam-5638	639	5	for	for	ADP
ejpam-5638	639	6	an	an	DET
ejpam-5638	639	7	experimenm.u.r	experimenm.u.r	PROPN
ejpam-5638	639	8	rehman	rehman	PROPN
ejpam-5638	639	9	et	et	PROPN
ejpam-5638	639	10	al	al	PROPN
ejpam-5638	639	11	.	.	PUNCT
ejpam-5638	639	12	/	/	SYM
ejpam-5638	639	13	eur	eur	PROPN
ejpam-5638	639	14	.	.	PUNCT
ejpam-5638	640	1	j.	j.	PROPN
ejpam-5638	640	2	pure	pure	PROPN
ejpam-5638	640	3	appl	appl	PROPN
ejpam-5638	640	4	.	.	PROPN
ejpam-5638	640	5	math	math	PROPN
ejpam-5638	640	6	,	,	PUNCT
ejpam-5638	640	7	18	18	NUM
ejpam-5638	640	8	(	(	PUNCT
ejpam-5638	640	9	2	2	NUM
ejpam-5638	640	10	)	)	PUNCT
ejpam-5638	640	11	(	(	PUNCT
ejpam-5638	640	12	2025	2025	NUM
ejpam-5638	640	13	)	)	PUNCT
ejpam-5638	640	14	,	,	PUNCT
ejpam-5638	640	15	5638	5638	NUM
ejpam-5638	640	16	23	23	NUM
ejpam-5638	640	17	of	of	ADP
ejpam-5638	640	18	23	23	NUM
ejpam-5638	640	19	tal	tal	ADJ
ejpam-5638	640	20	drive	drive	NOUN
ejpam-5638	640	21	-	-	PUNCT
ejpam-5638	640	22	by	by	ADP
ejpam-5638	640	23	-	-	PUNCT
ejpam-5638	640	24	wire	wire	NOUN
ejpam-5638	640	25	vehicle	vehicle	NOUN
ejpam-5638	640	26	.	.	PUNCT
ejpam-5638	641	1	international	international	ADJ
ejpam-5638	641	2	journal	journal	PROPN
ejpam-5638	641	3	of	of	ADP
ejpam-5638	641	4	robust	robust	ADJ
ejpam-5638	641	5	and	and	CCONJ
ejpam-5638	641	6	nonlinear	nonlinear	ADJ
ejpam-5638	641	7	control	control	NOUN
ejpam-5638	641	8	,	,	PUNCT
ejpam-5638	641	9	18(9):975–992	18(9):975–992	NUM
ejpam-5638	641	10	,	,	PUNCT
ejpam-5638	641	11	2008	2008	NUM
ejpam-5638	641	12	.	.	PUNCT
ejpam-5638	642	1	[	[	X
ejpam-5638	642	2	37	37	NUM
ejpam-5638	642	3	]	]	X
ejpam-5638	642	4	n.	n.	NOUN
ejpam-5638	642	5	guglielmi	guglielmi	PROPN
ejpam-5638	642	6	,	,	PUNCT
ejpam-5638	642	7	mutti	mutti	PROPN
ejpam-5638	642	8	-	-	PUNCT
ejpam-5638	642	9	ur	ur	PROPN
ejpam-5638	642	10	rehman	rehman	PROPN
ejpam-5638	642	11	,	,	PUNCT
ejpam-5638	642	12	and	and	CCONJ
ejpam-5638	642	13	daniel	daniel	PROPN
ejpam-5638	642	14	kressner	kressner	PROPN
ejpam-5638	642	15	.	.	PUNCT
ejpam-5638	643	1	a	a	DET
ejpam-5638	643	2	novel	novel	ADJ
ejpam-5638	643	3	iterative	iterative	NOUN
ejpam-5638	643	4	method	method	NOUN
ejpam-5638	643	5	to	to	PART
ejpam-5638	643	6	approximate	approximate	VERB
ejpam-5638	643	7	structured	structured	ADJ
ejpam-5638	643	8	singular	singular	ADJ
ejpam-5638	643	9	values	value	NOUN
ejpam-5638	643	10	.	.	PUNCT
ejpam-5638	644	1	siam	siam	PROPN
ejpam-5638	644	2	journal	journal	PROPN
ejpam-5638	644	3	on	on	ADP
ejpam-5638	644	4	matrix	matrix	NOUN
ejpam-5638	644	5	analysis	analysis	NOUN
ejpam-5638	644	6	and	and	CCONJ
ejpam-5638	644	7	applications	application	NOUN
ejpam-5638	644	8	,	,	PUNCT
ejpam-5638	644	9	38(2):361–386	38(2):361–386	NUM
ejpam-5638	644	10	,	,	PUNCT
ejpam-5638	644	11	2017	2017	NUM
ejpam-5638	644	12	.	.	PUNCT
ejpam-5638	645	1	[	[	X
ejpam-5638	645	2	38	38	NUM
ejpam-5638	645	3	]	]	PUNCT
ejpam-5638	645	4	g.	g.	PROPN
ejpam-5638	645	5	w.	w.	PROPN
ejpam-5638	645	6	thomas	thomas	PROPN
ejpam-5638	645	7	.	.	PUNCT
ejpam-5638	646	1	eigtool	eigtool	PROPN
ejpam-5638	646	2	.	.	PUNCT
ejpam-5638	647	1	http://www.comlab.ox.ac.uk/pseudospectra/eigtool/	http://www.comlab.ox.ac.uk/pseudospectra/eigtool/	NOUN
ejpam-5638	647	2	,	,	PUNCT
ejpam-5638	647	3	2002	2002	NUM
ejpam-5638	647	4	.	.	PUNCT
ejpam-5638	648	1	[	[	X
ejpam-5638	648	2	39	39	NUM
ejpam-5638	648	3	]	]	PUNCT
ejpam-5638	648	4	giorgio	giorgio	PROPN
ejpam-5638	648	5	giorgi	giorgi	PROPN
ejpam-5638	648	6	.	.	PUNCT
ejpam-5638	649	1	stable	stable	ADJ
ejpam-5638	649	2	and	and	CCONJ
ejpam-5638	649	3	related	related	ADJ
ejpam-5638	649	4	matrices	matrix	NOUN
ejpam-5638	649	5	in	in	ADP
ejpam-5638	649	6	economic	economic	ADJ
ejpam-5638	649	7	theory	theory	NOUN
ejpam-5638	649	8	.	.	PUNCT
ejpam-5638	650	1	control	control	NOUN
ejpam-5638	650	2	and	and	CCONJ
ejpam-5638	650	3	cybernetics	cybernetic	NOUN
ejpam-5638	650	4	,	,	PUNCT
ejpam-5638	650	5	32(2):397–410	32(2):397–410	NUM
ejpam-5638	650	6	,	,	PUNCT
ejpam-5638	650	7	2003	2003	NUM
ejpam-5638	650	8	.	.	PUNCT