id	sid	tid	token	lemma	pos
ejpam-5657	1	1	european	european	PROPN
ejpam-5657	1	2	journal	journal	PROPN
ejpam-5657	1	3	of	of	ADP
ejpam-5657	1	4	pure	pure	ADJ
ejpam-5657	1	5	and	and	CCONJ
ejpam-5657	1	6	applied	applied	ADJ
ejpam-5657	1	7	mathematics	mathematic	NOUN
ejpam-5657	1	8	2025	2025	NUM
ejpam-5657	1	9	,	,	PUNCT
ejpam-5657	1	10	vol	vol	NOUN
ejpam-5657	1	11	.	.	PROPN
ejpam-5657	1	12	18	18	NUM
ejpam-5657	1	13	,	,	PUNCT
ejpam-5657	1	14	issue	issue	NOUN
ejpam-5657	1	15	1	1	NUM
ejpam-5657	1	16	,	,	PUNCT
ejpam-5657	1	17	article	article	NOUN
ejpam-5657	1	18	number	number	NOUN
ejpam-5657	1	19	5657	5657	NUM
ejpam-5657	1	20	issn	issn	VERB
ejpam-5657	1	21	1307	1307	NUM
ejpam-5657	1	22	-	-	SYM
ejpam-5657	1	23	5543	5543	NUM
ejpam-5657	1	24	–	–	PUNCT
ejpam-5657	1	25	ejpam.com	ejpam.com	X
ejpam-5657	1	26	published	publish	VERB
ejpam-5657	1	27	by	by	ADP
ejpam-5657	1	28	new	new	PROPN
ejpam-5657	1	29	york	york	PROPN
ejpam-5657	1	30	business	business	PROPN
ejpam-5657	1	31	global	global	ADJ
ejpam-5657	1	32	analysis	analysis	NOUN
ejpam-5657	1	33	of	of	ADP
ejpam-5657	1	34	stability	stability	NOUN
ejpam-5657	1	35	,	,	PUNCT
ejpam-5657	1	36	d	d	NOUN
ejpam-5657	1	37	-	-	NOUN
ejpam-5657	1	38	stability	stability	NOUN
ejpam-5657	1	39	,	,	PUNCT
ejpam-5657	1	40	and	and	CCONJ
ejpam-5657	1	41	pseudospectra	pseudospectra	PROPN
ejpam-5657	1	42	in	in	ADP
ejpam-5657	1	43	economic	economic	ADJ
ejpam-5657	1	44	modeling	modeling	NOUN
ejpam-5657	1	45	mutti	mutti	PROPN
ejpam-5657	1	46	-	-	PUNCT
ejpam-5657	1	47	ur	ur	PROPN
ejpam-5657	1	48	rehman1	rehman1	NOUN
ejpam-5657	1	49	,	,	PUNCT
ejpam-5657	1	50	sakeena	sakeena	PROPN
ejpam-5657	1	51	e.	e.	PROPN
ejpam-5657	1	52	m.	m.	PROPN
ejpam-5657	1	53	hamed3	hamed3	PROPN
ejpam-5657	1	54	,	,	PUNCT
ejpam-5657	1	55	nidal	nidal	PROPN
ejpam-5657	1	56	e.	e.	PROPN
ejpam-5657	1	57	taha2	taha2	PROPN
ejpam-5657	1	58	,	,	PUNCT
ejpam-5657	1	59	arafa	arafa	PROPN
ejpam-5657	1	60	o.	o.	PROPN
ejpam-5657	1	61	mustafa3,∗	mustafa3,∗	PROPN
ejpam-5657	1	62	,	,	PUNCT
ejpam-5657	1	63	khurshidbek	khurshidbek	PROPN
ejpam-5657	1	64	dilmurodov1	dilmurodov1	PROPN
ejpam-5657	1	65	,	,	PUNCT
ejpam-5657	1	66	hala	hala	PROPN
ejpam-5657	1	67	s.	s.	PROPN
ejpam-5657	1	68	mahgoub3	mahgoub3	PROPN
ejpam-5657	1	69	,	,	PUNCT
ejpam-5657	1	70	mona	mona	PROPN
ejpam-5657	1	71	magzoub4	magzoub4	PROPN
ejpam-5657	1	72	,	,	PUNCT
ejpam-5657	1	73	runda	runda	PROPN
ejpam-5657	1	74	a.	a.	PROPN
ejpam-5657	1	75	a.	a.	PROPN
ejpam-5657	1	76	bashir5	bashir5	PROPN
ejpam-5657	1	77	,	,	PUNCT
ejpam-5657	1	78	mustafa	mustafa	PROPN
ejpam-5657	1	79	m.	m.	PROPN
ejpam-5657	1	80	mohammed5,∗	mohammed5,∗	PROPN
ejpam-5657	1	81	,	,	PUNCT
ejpam-5657	1	82	awad	awad	PROPN
ejpam-5657	1	83	a.	a.	NOUN
ejpam-5657	1	84	bakery5,6	bakery5,6	PROPN
ejpam-5657	1	85	1	1	NUM
ejpam-5657	1	86	center	center	NOUN
ejpam-5657	1	87	of	of	ADP
ejpam-5657	1	88	research	research	NOUN
ejpam-5657	1	89	and	and	CCONJ
ejpam-5657	1	90	innovation	innovation	NOUN
ejpam-5657	1	91	,	,	PUNCT
ejpam-5657	1	92	asia	asia	PROPN
ejpam-5657	1	93	international	international	PROPN
ejpam-5657	1	94	university	university	PROPN
ejpam-5657	1	95	,	,	PUNCT
ejpam-5657	1	96	yangiobod	yangiobod	ADJ
ejpam-5657	1	97	mfy	mfy	NOUN
ejpam-5657	1	98	,	,	PUNCT
ejpam-5657	1	99	g‘ijduvon	g‘ijduvon	PROPN
ejpam-5657	1	100	street	street	PROPN
ejpam-5657	1	101	,	,	PUNCT
ejpam-5657	1	102	house	house	NOUN
ejpam-5657	1	103	74	74	NUM
ejpam-5657	1	104	,	,	PUNCT
ejpam-5657	1	105	bukhara	bukhara	PROPN
ejpam-5657	1	106	,	,	PUNCT
ejpam-5657	1	107	uzbekistan	uzbekistan	PROPN
ejpam-5657	1	108	2	2	NUM
ejpam-5657	1	109	department	department	NOUN
ejpam-5657	1	110	of	of	ADP
ejpam-5657	1	111	mathematics	mathematic	NOUN
ejpam-5657	1	112	,	,	PUNCT
ejpam-5657	1	113	college	college	NOUN
ejpam-5657	1	114	of	of	ADP
ejpam-5657	1	115	science	science	NOUN
ejpam-5657	1	116	,	,	PUNCT
ejpam-5657	1	117	qassim	qassim	PROPN
ejpam-5657	1	118	university	university	PROPN
ejpam-5657	1	119	,	,	PUNCT
ejpam-5657	1	120	buraidah	buraidah	NOUN
ejpam-5657	1	121	51452	51452	NUM
ejpam-5657	1	122	,	,	PUNCT
ejpam-5657	1	123	saudi	saudi	PROPN
ejpam-5657	1	124	arabia	arabia	PROPN
ejpam-5657	1	125	3	3	NUM
ejpam-5657	1	126	university	university	NOUN
ejpam-5657	1	127	of	of	ADP
ejpam-5657	1	128	jeddah	jeddah	PROPN
ejpam-5657	1	129	,	,	PUNCT
ejpam-5657	1	130	college	college	NOUN
ejpam-5657	1	131	of	of	ADP
ejpam-5657	1	132	business	business	NOUN
ejpam-5657	1	133	at	at	ADP
ejpam-5657	1	134	khulis	khulis	PROPN
ejpam-5657	1	135	,	,	PUNCT
ejpam-5657	1	136	jeddah	jeddah	PROPN
ejpam-5657	1	137	,	,	PUNCT
ejpam-5657	1	138	saudi	saudi	PROPN
ejpam-5657	1	139	arabia	arabia	PROPN
ejpam-5657	1	140	4	4	NUM
ejpam-5657	1	141	mathematics	mathematics	PROPN
ejpam-5657	1	142	department	department	NOUN
ejpam-5657	1	143	,	,	PUNCT
ejpam-5657	1	144	applied	apply	VERB
ejpam-5657	1	145	college	college	NOUN
ejpam-5657	1	146	at	at	ADP
ejpam-5657	1	147	alkamil	alkamil	NOUN
ejpam-5657	1	148	,	,	PUNCT
ejpam-5657	1	149	university	university	NOUN
ejpam-5657	1	150	of	of	ADP
ejpam-5657	1	151	jeddah	jeddah	PROPN
ejpam-5657	1	152	,	,	PUNCT
ejpam-5657	1	153	saudi	saudi	PROPN
ejpam-5657	1	154	arabia	arabia	PROPN
ejpam-5657	1	155	5	5	NUM
ejpam-5657	1	156	university	university	NOUN
ejpam-5657	1	157	of	of	ADP
ejpam-5657	1	158	jeddah	jeddah	PROPN
ejpam-5657	1	159	,	,	PUNCT
ejpam-5657	1	160	applied	apply	VERB
ejpam-5657	1	161	college	college	NOUN
ejpam-5657	1	162	at	at	ADP
ejpam-5657	1	163	khulis	khulis	PROPN
ejpam-5657	1	164	,	,	PUNCT
ejpam-5657	1	165	department	department	NOUN
ejpam-5657	1	166	of	of	ADP
ejpam-5657	1	167	mathematics	mathematics	PROPN
ejpam-5657	1	168	,	,	PUNCT
ejpam-5657	1	169	jeddah	jeddah	PROPN
ejpam-5657	1	170	,	,	PUNCT
ejpam-5657	1	171	saudi	saudi	PROPN
ejpam-5657	1	172	arabia	arabia	PROPN
ejpam-5657	1	173	6	6	NUM
ejpam-5657	1	174	department	department	NOUN
ejpam-5657	1	175	of	of	ADP
ejpam-5657	1	176	mathematics	mathematic	NOUN
ejpam-5657	1	177	,	,	PUNCT
ejpam-5657	1	178	faculty	faculty	NOUN
ejpam-5657	1	179	of	of	ADP
ejpam-5657	1	180	science	science	NOUN
ejpam-5657	1	181	,	,	PUNCT
ejpam-5657	1	182	ain	ain	PROPN
ejpam-5657	1	183	shams	shams	PROPN
ejpam-5657	1	184	university	university	PROPN
ejpam-5657	1	185	,	,	PUNCT
ejpam-5657	1	186	p.o	p.o	PROPN
ejpam-5657	1	187	.	.	PROPN
ejpam-5657	1	188	box	box	PROPN
ejpam-5657	1	189	1156	1156	NUM
ejpam-5657	1	190	,	,	PUNCT
ejpam-5657	1	191	abbassia	abbassia	PROPN
ejpam-5657	1	192	,	,	PUNCT
ejpam-5657	1	193	cairo	cairo	PROPN
ejpam-5657	1	194	11566	11566	NUM
ejpam-5657	1	195	,	,	PUNCT
ejpam-5657	1	196	egypt	egypt	PROPN
ejpam-5657	1	197	abstract	abstract	PROPN
ejpam-5657	1	198	.	.	PUNCT
ejpam-5657	2	1	the	the	DET
ejpam-5657	2	2	analysis	analysis	NOUN
ejpam-5657	2	3	of	of	ADP
ejpam-5657	2	4	dynamic	dynamic	ADJ
ejpam-5657	2	5	stability	stability	NOUN
ejpam-5657	2	6	is	be	AUX
ejpam-5657	2	7	a	a	DET
ejpam-5657	2	8	fundamental	fundamental	ADJ
ejpam-5657	2	9	and	and	CCONJ
ejpam-5657	2	10	an	an	DET
ejpam-5657	2	11	important	important	ADJ
ejpam-5657	2	12	concept	concept	NOUN
ejpam-5657	2	13	in	in	ADP
ejpam-5657	2	14	system	system	NOUN
ejpam-5657	2	15	dynamics	dynamic	NOUN
ejpam-5657	2	16	.	.	PUNCT
ejpam-5657	3	1	its	its	PRON
ejpam-5657	3	2	focus	focus	NOUN
ejpam-5657	3	3	is	be	AUX
ejpam-5657	3	4	on	on	ADP
ejpam-5657	3	5	the	the	DET
ejpam-5657	3	6	ability	ability	NOUN
ejpam-5657	3	7	of	of	ADP
ejpam-5657	3	8	a	a	DET
ejpam-5657	3	9	dynamical	dynamical	ADJ
ejpam-5657	3	10	system	system	NOUN
ejpam-5657	3	11	to	to	PART
ejpam-5657	3	12	return	return	VERB
ejpam-5657	3	13	to	to	ADP
ejpam-5657	3	14	an	an	DET
ejpam-5657	3	15	equilibrium	equilibrium	NOUN
ejpam-5657	3	16	state	state	NOUN
ejpam-5657	3	17	under	under	ADP
ejpam-5657	3	18	structured	structured	ADJ
ejpam-5657	3	19	perturbations	perturbation	NOUN
ejpam-5657	3	20	.	.	PUNCT
ejpam-5657	4	1	the	the	DET
ejpam-5657	4	2	study	study	NOUN
ejpam-5657	4	3	of	of	ADP
ejpam-5657	4	4	dynamic	dynamic	ADJ
ejpam-5657	4	5	stability	stability	NOUN
ejpam-5657	4	6	plays	play	VERB
ejpam-5657	4	7	critical	critical	ADJ
ejpam-5657	4	8	role	role	NOUN
ejpam-5657	4	9	in	in	ADP
ejpam-5657	4	10	various	various	ADJ
ejpam-5657	4	11	fields	field	NOUN
ejpam-5657	4	12	,	,	PUNCT
ejpam-5657	4	13	for	for	ADP
ejpam-5657	4	14	instance	instance	NOUN
ejpam-5657	4	15	,	,	PUNCT
ejpam-5657	4	16	engineering	engineering	NOUN
ejpam-5657	4	17	,	,	PUNCT
ejpam-5657	4	18	control	control	NOUN
ejpam-5657	4	19	theory	theory	NOUN
ejpam-5657	4	20	,	,	PUNCT
ejpam-5657	4	21	and	and	CCONJ
ejpam-5657	4	22	economics	economic	NOUN
ejpam-5657	4	23	.	.	PUNCT
ejpam-5657	5	1	the	the	DET
ejpam-5657	5	2	analysis	analysis	NOUN
ejpam-5657	5	3	on	on	ADP
ejpam-5657	5	4	the	the	DET
ejpam-5657	5	5	dynamic	dynamic	ADJ
ejpam-5657	5	6	stability	stability	NOUN
ejpam-5657	5	7	mostly	mostly	ADV
ejpam-5657	5	8	involves	involve	VERB
ejpam-5657	5	9	computation	computation	NOUN
ejpam-5657	5	10	of	of	ADP
ejpam-5657	5	11	the	the	DET
ejpam-5657	5	12	eigenvalues	eigenvalue	NOUN
ejpam-5657	5	13	of	of	ADP
ejpam-5657	5	14	a	a	DET
ejpam-5657	5	15	system	system	NOUN
ejpam-5657	5	16	’s	’s	PART
ejpam-5657	5	17	state	state	NOUN
ejpam-5657	5	18	matrix	matrix	NOUN
ejpam-5657	5	19	.	.	PUNCT
ejpam-5657	6	1	the	the	DET
ejpam-5657	6	2	d	d	NOUN
ejpam-5657	6	3	-	-	NOUN
ejpam-5657	6	4	stability	stability	NOUN
ejpam-5657	6	5	is	be	AUX
ejpam-5657	6	6	a	a	DET
ejpam-5657	6	7	particular	particular	ADJ
ejpam-5657	6	8	and	and	CCONJ
ejpam-5657	6	9	specialized	specialized	ADJ
ejpam-5657	6	10	form	form	NOUN
ejpam-5657	6	11	of	of	ADP
ejpam-5657	6	12	dynamic	dynamic	ADJ
ejpam-5657	6	13	stability	stability	NOUN
ejpam-5657	6	14	,	,	PUNCT
ejpam-5657	6	15	and	and	CCONJ
ejpam-5657	6	16	its	its	PRON
ejpam-5657	6	17	mainly	mainly	ADV
ejpam-5657	6	18	focus	focus	VERB
ejpam-5657	6	19	dynamical	dynamical	ADJ
ejpam-5657	6	20	systems	system	NOUN
ejpam-5657	6	21	subject	subject	ADJ
ejpam-5657	6	22	to	to	ADP
ejpam-5657	6	23	structured	structured	ADJ
ejpam-5657	6	24	perturbations	perturbation	NOUN
ejpam-5657	6	25	.	.	PUNCT
ejpam-5657	7	1	in	in	ADP
ejpam-5657	7	2	this	this	DET
ejpam-5657	7	3	paper	paper	NOUN
ejpam-5657	7	4	,	,	PUNCT
ejpam-5657	7	5	we	we	PRON
ejpam-5657	7	6	present	present	VERB
ejpam-5657	7	7	new	new	ADJ
ejpam-5657	7	8	results	result	NOUN
ejpam-5657	7	9	on	on	ADP
ejpam-5657	7	10	dynamic	dynamic	ADJ
ejpam-5657	7	11	stability	stability	NOUN
ejpam-5657	7	12	,	,	PUNCT
ejpam-5657	7	13	and	and	CCONJ
ejpam-5657	7	14	d	d	X
ejpam-5657	7	15	-	-	NOUN
ejpam-5657	7	16	stability	stability	NOUN
ejpam-5657	7	17	of	of	ADP
ejpam-5657	7	18	a	a	DET
ejpam-5657	7	19	class	class	NOUN
ejpam-5657	7	20	of	of	ADP
ejpam-5657	7	21	linear	linear	ADJ
ejpam-5657	7	22	economic	economic	ADJ
ejpam-5657	7	23	model	model	NOUN
ejpam-5657	7	24	in	in	ADP
ejpam-5657	7	25	the	the	DET
ejpam-5657	7	26	mathematical	mathematical	ADJ
ejpam-5657	7	27	form	form	NOUN
ejpam-5657	7	28	yt	yt	X
ejpam-5657	7	29	=	=	PUNCT
ejpam-5657	7	30	ayt	ayt	PROPN
ejpam-5657	7	31	+	+	SYM
ejpam-5657	7	32	byt−1	byt−1	NOUN
ejpam-5657	7	33	+	+	CCONJ
ejpam-5657	7	34	cxt	cxt	PROPN
ejpam-5657	7	35	,	,	PUNCT
ejpam-5657	7	36	with	with	ADP
ejpam-5657	7	37	yt	yt	PROPN
ejpam-5657	7	38	,	,	PUNCT
ejpam-5657	7	39	a	a	DET
ejpam-5657	7	40	vector	vector	NOUN
ejpam-5657	7	41	of	of	ADP
ejpam-5657	7	42	the	the	DET
ejpam-5657	7	43	endogenous	endogenous	ADJ
ejpam-5657	7	44	variables	variable	NOUN
ejpam-5657	7	45	,	,	PUNCT
ejpam-5657	7	46	xt	xt	PROPN
ejpam-5657	7	47	is	be	AUX
ejpam-5657	7	48	a	a	DET
ejpam-5657	7	49	vector	vector	NOUN
ejpam-5657	7	50	of	of	ADP
ejpam-5657	7	51	exogenous	exogenous	ADJ
ejpam-5657	7	52	variables	variable	NOUN
ejpam-5657	7	53	,	,	PUNCT
ejpam-5657	7	54	and	and	CCONJ
ejpam-5657	7	55	a	a	DET
ejpam-5657	7	56	,	,	PUNCT
ejpam-5657	7	57	b	b	NOUN
ejpam-5657	7	58	,	,	PUNCT
ejpam-5657	7	59	and	and	CCONJ
ejpam-5657	7	60	c	c	NOUN
ejpam-5657	7	61	are	be	AUX
ejpam-5657	7	62	the	the	DET
ejpam-5657	7	63	matrices	matrix	NOUN
ejpam-5657	7	64	having	have	VERB
ejpam-5657	7	65	an	an	DET
ejpam-5657	7	66	appropriate	appropriate	ADJ
ejpam-5657	7	67	dimensions	dimension	NOUN
ejpam-5657	7	68	.	.	PUNCT
ejpam-5657	8	1	the	the	DET
ejpam-5657	8	2	new	new	ADJ
ejpam-5657	8	3	results	result	NOUN
ejpam-5657	8	4	are	be	AUX
ejpam-5657	8	5	developed	develop	VERB
ejpam-5657	8	6	on	on	ADP
ejpam-5657	8	7	both	both	CCONJ
ejpam-5657	8	8	necessary	necessary	ADJ
ejpam-5657	8	9	and	and	CCONJ
ejpam-5657	8	10	sufficient	sufficient	ADJ
ejpam-5657	8	11	conditions	condition	NOUN
ejpam-5657	8	12	on	on	ADP
ejpam-5657	8	13	the	the	DET
ejpam-5657	8	14	interconnection	interconnection	NOUN
ejpam-5657	8	15	between	between	ADP
ejpam-5657	8	16	d	d	ADJ
ejpam-5657	8	17	-	-	ADJ
ejpam-5657	8	18	stable	stable	ADJ
ejpam-5657	8	19	matrices	matrix	NOUN
ejpam-5657	8	20	and	and	CCONJ
ejpam-5657	8	21	structured	structure	VERB
ejpam-5657	8	22	singular	singular	ADJ
ejpam-5657	8	23	values	value	NOUN
ejpam-5657	8	24	.	.	PUNCT
ejpam-5657	9	1	the	the	DET
ejpam-5657	9	2	numerical	numerical	PROPN
ejpam-5657	9	3	experimentation	experimentation	NOUN
ejpam-5657	9	4	show	show	VERB
ejpam-5657	9	5	the	the	DET
ejpam-5657	9	6	behaviour	behaviour	NOUN
ejpam-5657	9	7	of	of	ADP
ejpam-5657	9	8	structured	structured	ADJ
ejpam-5657	9	9	singular	singular	ADJ
ejpam-5657	9	10	values	value	NOUN
ejpam-5657	9	11	for	for	ADP
ejpam-5657	9	12	matrices	matrix	NOUN
ejpam-5657	9	13	appearing	appear	VERB
ejpam-5657	9	14	across	across	ADP
ejpam-5657	9	15	linear	linear	ADJ
ejpam-5657	9	16	dynamic	dynamic	ADJ
ejpam-5657	9	17	model	model	NOUN
ejpam-5657	9	18	.	.	PUNCT
ejpam-5657	10	1	2020	2020	NUM
ejpam-5657	10	2	mathematics	mathematics	PROPN
ejpam-5657	10	3	subject	subject	NOUN
ejpam-5657	10	4	classifications	classification	NOUN
ejpam-5657	10	5	:	:	PUNCT
ejpam-5657	10	6	15a18	15a18	NUM
ejpam-5657	10	7	,	,	PUNCT
ejpam-5657	10	8	15a16	15a16	NUM
ejpam-5657	10	9	,	,	PUNCT
ejpam-5657	10	10	15a23	15a23	NUM
ejpam-5657	10	11	key	key	ADJ
ejpam-5657	10	12	words	word	NOUN
ejpam-5657	10	13	and	and	CCONJ
ejpam-5657	10	14	phrases	phrase	NOUN
ejpam-5657	10	15	:	:	PUNCT
ejpam-5657	10	16	dynamic	dynamic	ADJ
ejpam-5657	10	17	stability	stability	NOUN
ejpam-5657	10	18	,	,	PUNCT
ejpam-5657	10	19	d	d	NOUN
ejpam-5657	10	20	-	-	PUNCT
ejpam-5657	10	21	stability	stability	NOUN
ejpam-5657	10	22	,	,	PUNCT
ejpam-5657	10	23	structured	structure	VERB
ejpam-5657	10	24	singular	singular	ADJ
ejpam-5657	10	25	values	value	NOUN
ejpam-5657	10	26	,	,	PUNCT
ejpam-5657	10	27	pseudospectrum	pseudospectrum	NOUN
ejpam-5657	10	28	∗corresponding	∗corresponde	VERB
ejpam-5657	10	29	author	author	NOUN
ejpam-5657	10	30	.	.	PUNCT
ejpam-5657	11	1	∗corresponding	∗corresponde	VERB
ejpam-5657	11	2	author	author	NOUN
ejpam-5657	11	3	.	.	PUNCT
ejpam-5657	12	1	doi	doi	NOUN
ejpam-5657	12	2	:	:	PUNCT
ejpam-5657	12	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5657	https://doi.org/10.29020/nybg.ejpam.v18i1.5657	PROPN
ejpam-5657	12	4	email	email	NOUN
ejpam-5657	12	5	addresses	address	VERB
ejpam-5657	12	6	:	:	PUNCT
ejpam-5657	12	7	mustasta@yahoo.com	mustasta@yahoo.com	X
ejpam-5657	12	8	and	and	CCONJ
ejpam-5657	12	9	mmibrahim@uj.edu.sa	mmibrahim@uj.edu.sa	PROPN
ejpam-5657	12	10	(	(	PUNCT
ejpam-5657	12	11	mustafa	mustafa	PROPN
ejpam-5657	12	12	m.	m.	PROPN
ejpam-5657	12	13	mohammed	mohammed	PROPN
ejpam-5657	12	14	)	)	PUNCT
ejpam-5657	12	15	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5657	13	1	1	1	NUM
ejpam-5657	13	2	copyright	copyright	NOUN
ejpam-5657	13	3	:	:	PUNCT
ejpam-5657	13	4	©	©	PROPN
ejpam-5657	13	5	2025	2025	NUM
ejpam-5657	13	6	the	the	DET
ejpam-5657	13	7	author(s	author(s	NOUN
ejpam-5657	13	8	)	)	PUNCT
ejpam-5657	13	9	.	.	PUNCT
ejpam-5657	14	1	(	(	PUNCT
ejpam-5657	14	2	cc	cc	NOUN
ejpam-5657	14	3	by	by	ADP
ejpam-5657	14	4	-	-	PUNCT
ejpam-5657	14	5	nc	nc	PROPN
ejpam-5657	14	6	4.0	4.0	NUM
ejpam-5657	14	7	)	)	PUNCT
ejpam-5657	14	8	m.u.r	m.u.r	NOUN
ejpam-5657	14	9	et	et	PROPN
ejpam-5657	14	10	al	al	PROPN
ejpam-5657	14	11	.	.	PUNCT
ejpam-5657	14	12	/	/	SYM
ejpam-5657	14	13	eur	eur	PROPN
ejpam-5657	14	14	.	.	PUNCT
ejpam-5657	15	1	j.	j.	PROPN
ejpam-5657	15	2	pure	pure	PROPN
ejpam-5657	15	3	appl	appl	PROPN
ejpam-5657	15	4	.	.	PROPN
ejpam-5657	15	5	math	math	PROPN
ejpam-5657	15	6	,	,	PUNCT
ejpam-5657	15	7	18	18	NUM
ejpam-5657	15	8	(	(	PUNCT
ejpam-5657	15	9	1	1	NUM
ejpam-5657	15	10	)	)	PUNCT
ejpam-5657	15	11	(	(	PUNCT
ejpam-5657	15	12	2025	2025	NUM
ejpam-5657	15	13	)	)	PUNCT
ejpam-5657	15	14	,	,	PUNCT
ejpam-5657	15	15	5657	5657	NUM
ejpam-5657	15	16	2	2	NUM
ejpam-5657	15	17	of	of	ADP
ejpam-5657	15	18	17	17	NUM
ejpam-5657	15	19	1	1	NUM
ejpam-5657	15	20	.	.	PUNCT
ejpam-5657	16	1	introduction	introduction	NOUN
ejpam-5657	16	2	a	a	DET
ejpam-5657	16	3	vast	vast	ADJ
ejpam-5657	16	4	amount	amount	NOUN
ejpam-5657	16	5	of	of	ADP
ejpam-5657	16	6	literature	literature	NOUN
ejpam-5657	16	7	has	have	AUX
ejpam-5657	16	8	been	be	AUX
ejpam-5657	16	9	written	write	VERB
ejpam-5657	16	10	on	on	ADP
ejpam-5657	16	11	the	the	DET
ejpam-5657	16	12	problem	problem	NOUN
ejpam-5657	16	13	related	relate	VERB
ejpam-5657	16	14	to	to	ADP
ejpam-5657	16	15	the	the	DET
ejpam-5657	16	16	control	control	NOUN
ejpam-5657	16	17	of	of	ADP
ejpam-5657	16	18	economics	economic	NOUN
ejpam-5657	16	19	.	.	PUNCT
ejpam-5657	17	1	the	the	DET
ejpam-5657	17	2	main	main	ADJ
ejpam-5657	17	3	concentration	concentration	NOUN
ejpam-5657	17	4	was	be	AUX
ejpam-5657	17	5	given	give	VERB
ejpam-5657	17	6	to	to	PART
ejpam-5657	17	7	study	study	VERB
ejpam-5657	17	8	and	and	CCONJ
ejpam-5657	17	9	analyze	analyze	VERB
ejpam-5657	17	10	the	the	DET
ejpam-5657	17	11	static	static	ADJ
ejpam-5657	17	12	economic	economic	ADJ
ejpam-5657	17	13	models	model	NOUN
ejpam-5657	17	14	.	.	PUNCT
ejpam-5657	18	1	the	the	DET
ejpam-5657	18	2	most	most	ADJ
ejpam-5657	18	3	of	of	ADP
ejpam-5657	18	4	the	the	DET
ejpam-5657	18	5	economics	economics	NOUN
ejpam-5657	18	6	models	model	NOUN
ejpam-5657	18	7	are	be	AUX
ejpam-5657	18	8	dynamic	dynamic	ADJ
ejpam-5657	18	9	in	in	ADP
ejpam-5657	18	10	their	their	PRON
ejpam-5657	18	11	nature	nature	NOUN
ejpam-5657	18	12	.	.	PUNCT
ejpam-5657	19	1	the	the	DET
ejpam-5657	19	2	study	study	NOUN
ejpam-5657	19	3	on	on	ADP
ejpam-5657	19	4	the	the	DET
ejpam-5657	19	5	current	current	ADJ
ejpam-5657	19	6	state	state	NOUN
ejpam-5657	19	7	of	of	ADP
ejpam-5657	19	8	an	an	DET
ejpam-5657	19	9	economic	economic	ADJ
ejpam-5657	19	10	system	system	NOUN
ejpam-5657	19	11	involving	involve	VERB
ejpam-5657	19	12	a	a	DET
ejpam-5657	19	13	vast	vast	ADJ
ejpam-5657	19	14	amount	amount	NOUN
ejpam-5657	19	15	of	of	ADP
ejpam-5657	19	16	policies	policy	NOUN
ejpam-5657	19	17	are	be	AUX
ejpam-5657	19	18	being	be	AUX
ejpam-5657	19	19	used	use	VERB
ejpam-5657	19	20	to	to	PART
ejpam-5657	19	21	shift	shift	VERB
ejpam-5657	19	22	system	system	NOUN
ejpam-5657	19	23	from	from	ADP
ejpam-5657	19	24	current	current	ADJ
ejpam-5657	19	25	status	status	NOUN
ejpam-5657	19	26	to	to	ADP
ejpam-5657	19	27	future	future	ADJ
ejpam-5657	19	28	state	state	NOUN
ejpam-5657	19	29	while	while	SCONJ
ejpam-5657	19	30	dealing	deal	VERB
ejpam-5657	19	31	with	with	ADP
ejpam-5657	19	32	such	such	ADJ
ejpam-5657	19	33	dynamic	dynamic	ADJ
ejpam-5657	19	34	systems	system	NOUN
ejpam-5657	19	35	.	.	PUNCT
ejpam-5657	20	1	for	for	ADP
ejpam-5657	20	2	the	the	DET
ejpam-5657	20	3	input	input	NOUN
ejpam-5657	20	4	-	-	PUNCT
ejpam-5657	20	5	output	output	NOUN
ejpam-5657	20	6	economics	economic	NOUN
ejpam-5657	20	7	,	,	PUNCT
ejpam-5657	20	8	a	a	DET
ejpam-5657	20	9	vast	vast	ADJ
ejpam-5657	20	10	amount	amount	NOUN
ejpam-5657	20	11	of	of	ADP
ejpam-5657	20	12	literature	literature	NOUN
ejpam-5657	20	13	has	have	AUX
ejpam-5657	20	14	been	be	AUX
ejpam-5657	20	15	written	write	VERB
ejpam-5657	20	16	in	in	ADP
ejpam-5657	20	17	order	order	NOUN
ejpam-5657	20	18	to	to	PART
ejpam-5657	20	19	describe	describe	VERB
ejpam-5657	20	20	the	the	DET
ejpam-5657	20	21	real	real	ADJ
ejpam-5657	20	22	economics	economic	NOUN
ejpam-5657	20	23	[	[	X
ejpam-5657	20	24	25	25	NUM
ejpam-5657	20	25	,	,	PUNCT
ejpam-5657	20	26	31	31	NUM
ejpam-5657	20	27	]	]	PUNCT
ejpam-5657	20	28	.	.	PUNCT
ejpam-5657	21	1	the	the	DET
ejpam-5657	21	2	general	general	ADJ
ejpam-5657	21	3	linear	linear	PROPN
ejpam-5657	21	4	dynamic	dynamic	ADJ
ejpam-5657	21	5	systems	system	NOUN
ejpam-5657	21	6	are	be	AUX
ejpam-5657	21	7	much	much	ADV
ejpam-5657	21	8	easier	easy	ADJ
ejpam-5657	21	9	to	to	PART
ejpam-5657	21	10	deal	deal	VERB
ejpam-5657	21	11	with	with	ADP
ejpam-5657	21	12	compare	compare	NOUN
ejpam-5657	21	13	to	to	ADP
ejpam-5657	21	14	singular	singular	ADJ
ejpam-5657	21	15	dynamic	dynamic	ADJ
ejpam-5657	21	16	systems	system	NOUN
ejpam-5657	21	17	such	such	ADJ
ejpam-5657	21	18	as	as	ADP
ejpam-5657	21	19	implicit	implicit	ADJ
ejpam-5657	21	20	dynamic	dynamic	ADJ
ejpam-5657	21	21	systems	system	NOUN
ejpam-5657	21	22	,	,	PUNCT
ejpam-5657	21	23	generalized	generalize	VERB
ejpam-5657	21	24	dynamic	dynamic	ADJ
ejpam-5657	21	25	systems	system	NOUN
ejpam-5657	21	26	,	,	PUNCT
ejpam-5657	21	27	generalized	generalize	VERB
ejpam-5657	21	28	state	state	NOUN
ejpam-5657	21	29	-	-	PUNCT
ejpam-5657	21	30	space	space	NOUN
ejpam-5657	21	31	dynamic	dynamic	ADJ
ejpam-5657	21	32	systems	system	NOUN
ejpam-5657	21	33	,	,	PUNCT
ejpam-5657	21	34	semi	semi	ADJ
ejpam-5657	21	35	-	-	ADJ
ejpam-5657	21	36	state	state	ADJ
ejpam-5657	21	37	dynamic	dynamic	ADJ
ejpam-5657	21	38	systems	system	NOUN
ejpam-5657	21	39	[	[	X
ejpam-5657	21	40	9	9	NUM
ejpam-5657	21	41	,	,	PUNCT
ejpam-5657	21	42	24	24	NUM
ejpam-5657	21	43	]	]	PUNCT
ejpam-5657	21	44	.	.	PUNCT
ejpam-5657	22	1	a	a	DET
ejpam-5657	22	2	vast	vast	ADJ
ejpam-5657	22	3	amount	amount	NOUN
ejpam-5657	22	4	of	of	ADP
ejpam-5657	22	5	literature	literature	NOUN
ejpam-5657	22	6	has	have	AUX
ejpam-5657	22	7	been	be	AUX
ejpam-5657	22	8	written	write	VERB
ejpam-5657	22	9	on	on	ADP
ejpam-5657	22	10	regular	regular	ADJ
ejpam-5657	22	11	dynamic	dynamic	ADJ
ejpam-5657	22	12	systems	system	NOUN
ejpam-5657	22	13	and	and	CCONJ
ejpam-5657	22	14	descriptor	descriptor	NOUN
ejpam-5657	22	15	systems	system	NOUN
ejpam-5657	22	16	,	,	PUNCT
ejpam-5657	22	17	we	we	PRON
ejpam-5657	22	18	refer	refer	VERB
ejpam-5657	22	19	interested	interested	ADJ
ejpam-5657	22	20	reader	reader	NOUN
ejpam-5657	22	21	to	to	PART
ejpam-5657	22	22	see	see	VERB
ejpam-5657	22	23	[	[	X
ejpam-5657	22	24	14	14	NUM
ejpam-5657	22	25	,	,	PUNCT
ejpam-5657	22	26	15	15	NUM
ejpam-5657	22	27	,	,	PUNCT
ejpam-5657	22	28	42	42	NUM
ejpam-5657	22	29	]	]	PUNCT
ejpam-5657	22	30	and	and	CCONJ
ejpam-5657	22	31	references	reference	NOUN
ejpam-5657	22	32	therein	therein	ADV
ejpam-5657	22	33	.	.	PUNCT
ejpam-5657	23	1	the	the	DET
ejpam-5657	23	2	linear	linear	ADJ
ejpam-5657	23	3	matrix	matrix	NOUN
ejpam-5657	23	4	inequalities	inequality	NOUN
ejpam-5657	23	5	techniques	technique	NOUN
ejpam-5657	23	6	were	be	AUX
ejpam-5657	23	7	developed	develop	VERB
ejpam-5657	23	8	to	to	PART
ejpam-5657	23	9	study	study	VERB
ejpam-5657	23	10	the	the	DET
ejpam-5657	23	11	singular	singular	ADJ
ejpam-5657	23	12	dynamic	dynamic	ADJ
ejpam-5657	23	13	system	system	NOUN
ejpam-5657	23	14	in	in	ADP
ejpam-5657	23	15	economics	economic	NOUN
ejpam-5657	23	16	,	,	PUNCT
ejpam-5657	23	17	see	see	VERB
ejpam-5657	23	18	[	[	X
ejpam-5657	23	19	10	10	NUM
ejpam-5657	23	20	,	,	PUNCT
ejpam-5657	23	21	35	35	NUM
ejpam-5657	23	22	,	,	PUNCT
ejpam-5657	23	23	36	36	NUM
ejpam-5657	23	24	,	,	PUNCT
ejpam-5657	23	25	43	43	NUM
ejpam-5657	23	26	,	,	PUNCT
ejpam-5657	23	27	45	45	NUM
ejpam-5657	23	28	]	]	PUNCT
ejpam-5657	23	29	.	.	PUNCT
ejpam-5657	24	1	the	the	DET
ejpam-5657	24	2	new	new	ADJ
ejpam-5657	24	3	results	result	NOUN
ejpam-5657	24	4	on	on	ADP
ejpam-5657	24	5	the	the	DET
ejpam-5657	24	6	interconnections	interconnection	NOUN
ejpam-5657	24	7	between	between	ADP
ejpam-5657	24	8	dynamic	dynamic	ADJ
ejpam-5657	24	9	behavior	behavior	NOUN
ejpam-5657	24	10	of	of	ADP
ejpam-5657	24	11	macroeconomics	macroeconomic	NOUN
ejpam-5657	24	12	,	,	PUNCT
ejpam-5657	24	13	continuous	continuous	ADJ
ejpam-5657	24	14	-	-	PUNCT
ejpam-5657	24	15	time	time	NOUN
ejpam-5657	24	16	dynamical	dynamical	ADJ
ejpam-5657	24	17	models	model	NOUN
ejpam-5657	24	18	and	and	CCONJ
ejpam-5657	24	19	relationships	relationship	NOUN
ejpam-5657	24	20	between	between	ADP
ejpam-5657	24	21	dynamic	dynamic	ADJ
ejpam-5657	24	22	stability	stability	NOUN
ejpam-5657	24	23	and	and	CCONJ
ejpam-5657	24	24	dominant	dominant	ADJ
ejpam-5657	24	25	-	-	PUNCT
ejpam-5657	24	26	diagonal	diagonal	ADJ
ejpam-5657	24	27	structure	structure	NOUN
ejpam-5657	24	28	was	be	AUX
ejpam-5657	24	29	studied	study	VERB
ejpam-5657	24	30	and	and	CCONJ
ejpam-5657	24	31	analyzed	analyze	VERB
ejpam-5657	24	32	in	in	ADP
ejpam-5657	24	33	[	[	X
ejpam-5657	24	34	30	30	NUM
ejpam-5657	24	35	]	]	PUNCT
ejpam-5657	24	36	.	.	PUNCT
ejpam-5657	25	1	the	the	DET
ejpam-5657	25	2	most	most	ADJ
ejpam-5657	25	3	of	of	ADP
ejpam-5657	25	4	macroeconomics	macroeconomic	NOUN
ejpam-5657	25	5	continuous	continuous	ADJ
ejpam-5657	25	6	-	-	PUNCT
ejpam-5657	25	7	time	time	NOUN
ejpam-5657	25	8	dynamic	dynamic	ADJ
ejpam-5657	25	9	models	model	NOUN
ejpam-5657	25	10	appears	appear	VERB
ejpam-5657	25	11	to	to	PART
ejpam-5657	25	12	be	be	AUX
ejpam-5657	25	13	non	non	ADJ
ejpam-5657	25	14	-	-	ADJ
ejpam-5657	25	15	stable	stable	ADJ
ejpam-5657	25	16	.	.	PUNCT
ejpam-5657	26	1	in	in	ADP
ejpam-5657	26	2	[	[	X
ejpam-5657	26	3	5	5	NUM
ejpam-5657	26	4	,	,	PUNCT
ejpam-5657	26	5	6	6	NUM
ejpam-5657	26	6	,	,	PUNCT
ejpam-5657	26	7	11	11	NUM
ejpam-5657	26	8	,	,	PUNCT
ejpam-5657	26	9	37	37	NUM
ejpam-5657	26	10	]	]	PUNCT
ejpam-5657	26	11	it	it	PRON
ejpam-5657	26	12	was	be	AUX
ejpam-5657	26	13	shown	show	VERB
ejpam-5657	26	14	that	that	SCONJ
ejpam-5657	26	15	macro	macro	ADJ
ejpam-5657	26	16	-	-	ADJ
ejpam-5657	26	17	economic	economic	ADJ
ejpam-5657	26	18	continuous	continuous	ADJ
ejpam-5657	26	19	-	-	PUNCT
ejpam-5657	26	20	time	time	NOUN
ejpam-5657	26	21	models	model	NOUN
ejpam-5657	26	22	are	be	AUX
ejpam-5657	26	23	unstable	unstable	ADJ
ejpam-5657	26	24	.	.	PUNCT
ejpam-5657	27	1	for	for	ADP
ejpam-5657	27	2	general	general	ADJ
ejpam-5657	27	3	discrete	discrete	ADJ
ejpam-5657	27	4	-	-	PUNCT
ejpam-5657	27	5	time	time	NOUN
ejpam-5657	27	6	dynamical	dynamical	ADJ
ejpam-5657	27	7	models	model	NOUN
ejpam-5657	27	8	appearing	appear	VERB
ejpam-5657	27	9	in	in	ADP
ejpam-5657	27	10	economics	economic	NOUN
ejpam-5657	27	11	,	,	PUNCT
ejpam-5657	27	12	the	the	DET
ejpam-5657	27	13	relationship	relationship	NOUN
ejpam-5657	27	14	between	between	ADP
ejpam-5657	27	15	the	the	DET
ejpam-5657	27	16	dominant	dominant	ADJ
ejpam-5657	27	17	diagonals	diagonal	NOUN
ejpam-5657	27	18	and	and	CCONJ
ejpam-5657	27	19	the	the	DET
ejpam-5657	27	20	stability	stability	NOUN
ejpam-5657	27	21	was	be	AUX
ejpam-5657	27	22	developed	develop	VERB
ejpam-5657	27	23	by	by	ADP
ejpam-5657	27	24	[	[	X
ejpam-5657	27	25	16	16	NUM
ejpam-5657	27	26	,	,	PUNCT
ejpam-5657	27	27	21	21	NUM
ejpam-5657	27	28	,	,	PUNCT
ejpam-5657	27	29	26	26	NUM
ejpam-5657	27	30	,	,	PUNCT
ejpam-5657	27	31	27	27	NUM
ejpam-5657	27	32	,	,	PUNCT
ejpam-5657	27	33	41	41	NUM
ejpam-5657	27	34	]	]	PUNCT
ejpam-5657	27	35	.	.	PUNCT
ejpam-5657	28	1	the	the	DET
ejpam-5657	28	2	d	d	NOUN
ejpam-5657	28	3	-	-	NOUN
ejpam-5657	28	4	stability	stability	NOUN
ejpam-5657	28	5	for	for	ADP
ejpam-5657	28	6	a	a	DET
ejpam-5657	28	7	class	class	NOUN
ejpam-5657	28	8	of	of	ADP
ejpam-5657	28	9	real	real	ADV
ejpam-5657	28	10	valued	value	VERB
ejpam-5657	28	11	matrices	matrix	NOUN
ejpam-5657	28	12	to	to	PART
ejpam-5657	28	13	study	study	VERB
ejpam-5657	28	14	the	the	DET
ejpam-5657	28	15	equilibrium	equilibrium	NOUN
ejpam-5657	28	16	in	in	ADP
ejpam-5657	28	17	dynamic	dynamic	ADJ
ejpam-5657	28	18	models	model	NOUN
ejpam-5657	28	19	of	of	ADP
ejpam-5657	28	20	competitive	competitive	ADJ
ejpam-5657	28	21	market	market	NOUN
ejpam-5657	28	22	for	for	ADP
ejpam-5657	28	23	the	the	DET
ejpam-5657	28	24	first	first	ADJ
ejpam-5657	28	25	time	time	NOUN
ejpam-5657	28	26	was	be	AUX
ejpam-5657	28	27	studied	study	VERB
ejpam-5657	28	28	by	by	ADP
ejpam-5657	28	29	arrow	arrow	NOUN
ejpam-5657	28	30	and	and	CCONJ
ejpam-5657	28	31	mcmanus	mcmanus	PROPN
ejpam-5657	29	1	[	[	X
ejpam-5657	29	2	2	2	NUM
ejpam-5657	29	3	]	]	PUNCT
ejpam-5657	29	4	,	,	PUNCT
ejpam-5657	29	5	and	and	CCONJ
ejpam-5657	29	6	enthoven	enthoven	ADV
ejpam-5657	29	7	and	and	CCONJ
ejpam-5657	29	8	arrow	arrow	NOUN
ejpam-5657	29	9	in	in	ADP
ejpam-5657	29	10	[	[	X
ejpam-5657	29	11	13	13	NUM
ejpam-5657	29	12	]	]	PUNCT
ejpam-5657	29	13	.	.	PUNCT
ejpam-5657	30	1	the	the	DET
ejpam-5657	30	2	study	study	NOUN
ejpam-5657	30	3	of	of	ADP
ejpam-5657	30	4	dynamic	dynamic	ADJ
ejpam-5657	30	5	stability	stability	NOUN
ejpam-5657	30	6	of	of	ADP
ejpam-5657	30	7	tatonnement	tatonnement	ADJ
ejpam-5657	30	8	process	process	NOUN
ejpam-5657	30	9	for	for	ADP
ejpam-5657	30	10	walrsian	walrsian	ADJ
ejpam-5657	30	11	model	model	NOUN
ejpam-5657	30	12	of	of	ADP
ejpam-5657	30	13	general	general	ADJ
ejpam-5657	30	14	equilibrium	equilibrium	NOUN
ejpam-5657	30	15	attracted	attract	VERB
ejpam-5657	30	16	a	a	DET
ejpam-5657	30	17	major	major	ADJ
ejpam-5657	30	18	community	community	NOUN
ejpam-5657	30	19	of	of	ADP
ejpam-5657	30	20	economists	economist	NOUN
ejpam-5657	30	21	.	.	PUNCT
ejpam-5657	31	1	the	the	DET
ejpam-5657	31	2	classical	classical	ADJ
ejpam-5657	31	3	approach	approach	NOUN
ejpam-5657	31	4	developed	develop	VERB
ejpam-5657	31	5	by	by	ADP
ejpam-5657	31	6	sanuelson	sanuelson	NOUN
ejpam-5657	31	7	describes	describe	VERB
ejpam-5657	31	8	the	the	DET
ejpam-5657	31	9	dynamic	dynamic	ADJ
ejpam-5657	31	10	behaviour	behaviour	NOUN
ejpam-5657	31	11	of	of	ADP
ejpam-5657	31	12	the	the	DET
ejpam-5657	31	13	economic	economic	ADJ
ejpam-5657	31	14	models	model	NOUN
ejpam-5657	31	15	.	.	PUNCT
ejpam-5657	32	1	the	the	DET
ejpam-5657	32	2	new	new	ADJ
ejpam-5657	32	3	results	result	NOUN
ejpam-5657	32	4	on	on	ADP
ejpam-5657	32	5	d	d	NOUN
ejpam-5657	32	6	-	-	NOUN
ejpam-5657	32	7	stability	stability	NOUN
ejpam-5657	32	8	,	,	PUNCT
ejpam-5657	32	9	strong	strong	ADJ
ejpam-5657	32	10	d	d	NOUN
ejpam-5657	32	11	-	-	NOUN
ejpam-5657	32	12	stability	stability	NOUN
ejpam-5657	32	13	and	and	CCONJ
ejpam-5657	32	14	structured	structure	VERB
ejpam-5657	32	15	singular	singular	ADJ
ejpam-5657	32	16	values	value	NOUN
ejpam-5657	32	17	were	be	AUX
ejpam-5657	32	18	developed	develop	VERB
ejpam-5657	32	19	by	by	ADP
ejpam-5657	32	20	using	use	VERB
ejpam-5657	32	21	various	various	ADJ
ejpam-5657	32	22	tools	tool	NOUN
ejpam-5657	32	23	from	from	ADP
ejpam-5657	32	24	linear	linear	PROPN
ejpam-5657	32	25	algebra	algebra	NOUN
ejpam-5657	32	26	,	,	PUNCT
ejpam-5657	32	27	matrix	matrix	NOUN
ejpam-5657	32	28	analysis	analysis	NOUN
ejpam-5657	32	29	,	,	PUNCT
ejpam-5657	32	30	and	and	CCONJ
ejpam-5657	32	31	system	system	NOUN
ejpam-5657	32	32	theory	theory	NOUN
ejpam-5657	32	33	,	,	PUNCT
ejpam-5657	32	34	see	see	VERB
ejpam-5657	32	35	[	[	X
ejpam-5657	32	36	34	34	NUM
ejpam-5657	32	37	]	]	PUNCT
ejpam-5657	32	38	.	.	PUNCT
ejpam-5657	33	1	in	in	ADP
ejpam-5657	33	2	[	[	X
ejpam-5657	33	3	22	22	NUM
ejpam-5657	33	4	]	]	PUNCT
ejpam-5657	33	5	,	,	PUNCT
ejpam-5657	33	6	the	the	DET
ejpam-5657	33	7	most	most	ADV
ejpam-5657	33	8	general	general	ADJ
ejpam-5657	33	9	general	general	ADJ
ejpam-5657	33	10	relationships	relationship	NOUN
ejpam-5657	33	11	between	between	ADP
ejpam-5657	33	12	performance	performance	NOUN
ejpam-5657	33	13	and	and	CCONJ
ejpam-5657	33	14	robustness	robustness	NOUN
ejpam-5657	33	15	of	of	ADP
ejpam-5657	33	16	dynamical	dynamical	ADJ
ejpam-5657	33	17	system	system	NOUN
ejpam-5657	33	18	,	,	PUNCT
ejpam-5657	33	19	and	and	CCONJ
ejpam-5657	33	20	special	special	ADJ
ejpam-5657	33	21	type	type	NOUN
ejpam-5657	33	22	of	of	ADP
ejpam-5657	33	23	matrix	matrix	NOUN
ejpam-5657	33	24	stabilities	stability	NOUN
ejpam-5657	33	25	,	,	PUNCT
ejpam-5657	33	26	that	that	ADV
ejpam-5657	33	27	is	is	ADV
ejpam-5657	33	28	,	,	PUNCT
ejpam-5657	33	29	d	d	ADP
ejpam-5657	33	30	stability	stability	NOUN
ejpam-5657	33	31	and	and	CCONJ
ejpam-5657	33	32	diagonal	diagonal	ADJ
ejpam-5657	33	33	stability	stability	NOUN
ejpam-5657	33	34	were	be	AUX
ejpam-5657	33	35	studied	study	VERB
ejpam-5657	33	36	and	and	CCONJ
ejpam-5657	33	37	analyzed	analyze	VERB
ejpam-5657	33	38	.	.	PUNCT
ejpam-5657	34	1	the	the	DET
ejpam-5657	34	2	results	result	NOUN
ejpam-5657	34	3	on	on	ADP
ejpam-5657	34	4	new	new	ADJ
ejpam-5657	34	5	stability	stability	NOUN
ejpam-5657	34	6	conditions	condition	NOUN
ejpam-5657	34	7	for	for	ADP
ejpam-5657	34	8	second	second	ADJ
ejpam-5657	34	9	-	-	PUNCT
ejpam-5657	34	10	order	order	NOUN
ejpam-5657	34	11	dynamical	dynamical	ADJ
ejpam-5657	34	12	systems	system	NOUN
ejpam-5657	34	13	were	be	AUX
ejpam-5657	34	14	presented	present	VERB
ejpam-5657	34	15	and	and	CCONJ
ejpam-5657	34	16	analyzed	analyze	VERB
ejpam-5657	34	17	.	.	PUNCT
ejpam-5657	35	1	an	an	DET
ejpam-5657	35	2	extension	extension	NOUN
ejpam-5657	35	3	to	to	ADP
ejpam-5657	35	4	d	d	NOUN
ejpam-5657	35	5	-	-	NOUN
ejpam-5657	35	6	stability	stability	NOUN
ejpam-5657	35	7	for	for	ADP
ejpam-5657	35	8	non	non	ADJ
ejpam-5657	35	9	-	-	ADJ
ejpam-5657	35	10	square	square	ADJ
ejpam-5657	35	11	matrices	matrix	NOUN
ejpam-5657	35	12	which	which	PRON
ejpam-5657	35	13	are	be	AUX
ejpam-5657	35	14	applicable	applicable	ADJ
ejpam-5657	35	15	to	to	AUX
ejpam-5657	35	16	distributed	distribute	VERB
ejpam-5657	35	17	and	and	CCONJ
ejpam-5657	35	18	decentralized	decentralize	VERB
ejpam-5657	35	19	controllability	controllability	NOUN
ejpam-5657	35	20	analysis	analysis	NOUN
ejpam-5657	35	21	was	be	AUX
ejpam-5657	35	22	recently	recently	ADV
ejpam-5657	35	23	studied	study	VERB
ejpam-5657	35	24	in	in	ADP
ejpam-5657	35	25	[	[	X
ejpam-5657	35	26	40	40	NUM
ejpam-5657	35	27	]	]	PUNCT
ejpam-5657	35	28	.	.	PUNCT
ejpam-5657	36	1	the	the	DET
ejpam-5657	36	2	µ-values	µ-value	NOUN
ejpam-5657	36	3	or	or	CCONJ
ejpam-5657	36	4	structured	structure	VERB
ejpam-5657	36	5	singular	singular	ADJ
ejpam-5657	36	6	values	value	NOUN
ejpam-5657	36	7	first	first	ADV
ejpam-5657	36	8	introduced	introduce	VERB
ejpam-5657	36	9	and	and	CCONJ
ejpam-5657	36	10	analyzed	analyze	VERB
ejpam-5657	36	11	by	by	ADP
ejpam-5657	36	12	j.	j.	PROPN
ejpam-5657	36	13	c.	c.	PROPN
ejpam-5657	36	14	doyel	doyel	PROPN
ejpam-5657	36	15	[	[	X
ejpam-5657	36	16	12	12	NUM
ejpam-5657	36	17	]	]	PUNCT
ejpam-5657	36	18	and	and	CCONJ
ejpam-5657	36	19	safonov	safonov	VERB
ejpam-5657	36	20	[	[	X
ejpam-5657	36	21	38	38	NUM
ejpam-5657	36	22	]	]	PUNCT
ejpam-5657	36	23	is	be	AUX
ejpam-5657	36	24	a	a	DET
ejpam-5657	36	25	mathematical	mathematical	ADJ
ejpam-5657	36	26	technique	technique	NOUN
ejpam-5657	36	27	in	in	ADP
ejpam-5657	36	28	order	order	NOUN
ejpam-5657	36	29	to	to	PART
ejpam-5657	36	30	investigate	investigate	VERB
ejpam-5657	36	31	and	and	CCONJ
ejpam-5657	36	32	test	test	VERB
ejpam-5657	36	33	the	the	DET
ejpam-5657	36	34	stability	stability	NOUN
ejpam-5657	36	35	of	of	ADP
ejpam-5657	36	36	linear	linear	PROPN
ejpam-5657	36	37	dynamical	dynamical	ADJ
ejpam-5657	36	38	systems	system	NOUN
ejpam-5657	36	39	.	.	PUNCT
ejpam-5657	37	1	in	in	ADP
ejpam-5657	37	2	general	general	ADJ
ejpam-5657	37	3	problem	problem	NOUN
ejpam-5657	37	4	aiming	aim	VERB
ejpam-5657	37	5	the	the	DET
ejpam-5657	37	6	determination	determination	NOUN
ejpam-5657	37	7	of	of	ADP
ejpam-5657	37	8	stability	stability	NOUN
ejpam-5657	37	9	in	in	ADP
ejpam-5657	37	10	the	the	DET
ejpam-5657	37	11	presence	presence	NOUN
ejpam-5657	37	12	of	of	ADP
ejpam-5657	37	13	structured	structured	ADJ
ejpam-5657	37	14	or	or	CCONJ
ejpam-5657	37	15	unstructured	unstructured	ADJ
ejpam-5657	37	16	uncertainties	uncertainty	NOUN
ejpam-5657	37	17	is	be	AUX
ejpam-5657	37	18	most	most	ADV
ejpam-5657	37	19	fundamental	fundamental	ADJ
ejpam-5657	37	20	issue	issue	NOUN
ejpam-5657	37	21	in	in	ADP
ejpam-5657	37	22	control	control	NOUN
ejpam-5657	37	23	and	and	CCONJ
ejpam-5657	37	24	has	have	AUX
ejpam-5657	37	25	attracted	attract	VERB
ejpam-5657	37	26	researchers	researcher	NOUN
ejpam-5657	37	27	from	from	ADP
ejpam-5657	37	28	almost	almost	ADV
ejpam-5657	37	29	last	last	ADJ
ejpam-5657	37	30	three	three	NUM
ejpam-5657	37	31	decades	decade	NOUN
ejpam-5657	37	32	.	.	PUNCT
ejpam-5657	38	1	in	in	ADP
ejpam-5657	38	2	this	this	DET
ejpam-5657	38	3	article	article	NOUN
ejpam-5657	38	4	,	,	PUNCT
ejpam-5657	38	5	we	we	PRON
ejpam-5657	38	6	present	present	VERB
ejpam-5657	38	7	new	new	ADJ
ejpam-5657	38	8	results	result	NOUN
ejpam-5657	38	9	on	on	ADP
ejpam-5657	38	10	stability	stability	NOUN
ejpam-5657	38	11	and	and	CCONJ
ejpam-5657	38	12	d	d	NOUN
ejpam-5657	38	13	-	-	NOUN
ejpam-5657	38	14	stability	stability	NOUN
ejpam-5657	38	15	of	of	ADP
ejpam-5657	38	16	linear	linear	ADJ
ejpam-5657	38	17	dynamic	dynamic	ADJ
ejpam-5657	38	18	models	model	NOUN
ejpam-5657	38	19	that	that	PRON
ejpam-5657	38	20	appears	appear	VERB
ejpam-5657	38	21	in	in	ADP
ejpam-5657	38	22	economics	economic	NOUN
ejpam-5657	38	23	.	.	PUNCT
ejpam-5657	39	1	we	we	PRON
ejpam-5657	39	2	also	also	ADV
ejpam-5657	39	3	present	present	VERB
ejpam-5657	39	4	new	new	ADJ
ejpam-5657	39	5	results	result	NOUN
ejpam-5657	39	6	on	on	ADP
ejpam-5657	39	7	necessary	necessary	ADJ
ejpam-5657	39	8	and	and	CCONJ
ejpam-5657	39	9	sufficient	sufficient	ADJ
ejpam-5657	39	10	m.u.r	m.u.r	NOUN
ejpam-5657	39	11	et	et	PROPN
ejpam-5657	39	12	al	al	PROPN
ejpam-5657	39	13	.	.	PUNCT
ejpam-5657	39	14	/	/	SYM
ejpam-5657	39	15	eur	eur	PROPN
ejpam-5657	39	16	.	.	PUNCT
ejpam-5657	40	1	j.	j.	PROPN
ejpam-5657	40	2	pure	pure	PROPN
ejpam-5657	40	3	appl	appl	PROPN
ejpam-5657	40	4	.	.	PROPN
ejpam-5657	40	5	math	math	PROPN
ejpam-5657	40	6	,	,	PUNCT
ejpam-5657	40	7	18	18	NUM
ejpam-5657	40	8	(	(	PUNCT
ejpam-5657	40	9	1	1	NUM
ejpam-5657	40	10	)	)	PUNCT
ejpam-5657	40	11	(	(	PUNCT
ejpam-5657	40	12	2025	2025	NUM
ejpam-5657	40	13	)	)	PUNCT
ejpam-5657	40	14	,	,	PUNCT
ejpam-5657	40	15	5657	5657	NUM
ejpam-5657	40	16	3	3	NUM
ejpam-5657	40	17	of	of	ADP
ejpam-5657	40	18	17	17	NUM
ejpam-5657	40	19	conditions	condition	NOUN
ejpam-5657	40	20	on	on	ADP
ejpam-5657	40	21	interconnections	interconnection	NOUN
ejpam-5657	40	22	between	between	ADP
ejpam-5657	40	23	d	d	NOUN
ejpam-5657	40	24	-	-	NOUN
ejpam-5657	40	25	stability	stability	NOUN
ejpam-5657	40	26	and	and	CCONJ
ejpam-5657	40	27	structured	structure	VERB
ejpam-5657	40	28	singular	singular	ADJ
ejpam-5657	40	29	values	value	NOUN
ejpam-5657	40	30	of	of	ADP
ejpam-5657	40	31	matrices	matrix	NOUN
ejpam-5657	40	32	appearing	appear	VERB
ejpam-5657	40	33	across	across	ADP
ejpam-5657	40	34	dynamic	dynamic	ADJ
ejpam-5657	40	35	models	model	NOUN
ejpam-5657	40	36	.	.	PUNCT
ejpam-5657	41	1	the	the	DET
ejpam-5657	41	2	numerical	numerical	PROPN
ejpam-5657	41	3	experimentation	experimentation	NOUN
ejpam-5657	41	4	shows	show	VERB
ejpam-5657	41	5	the	the	DET
ejpam-5657	41	6	comparison	comparison	NOUN
ejpam-5657	41	7	of	of	ADP
ejpam-5657	41	8	structured	structured	ADJ
ejpam-5657	41	9	singular	singular	ADJ
ejpam-5657	41	10	values	value	NOUN
ejpam-5657	41	11	for	for	ADP
ejpam-5657	41	12	matrices	matrix	NOUN
ejpam-5657	41	13	with	with	ADP
ejpam-5657	41	14	various	various	ADJ
ejpam-5657	41	15	dimensions	dimension	NOUN
ejpam-5657	41	16	from	from	ADP
ejpam-5657	41	17	dynamic	dynamic	ADJ
ejpam-5657	41	18	models	model	NOUN
ejpam-5657	41	19	.	.	PUNCT
ejpam-5657	42	1	finally	finally	ADV
ejpam-5657	42	2	,	,	PUNCT
ejpam-5657	42	3	the	the	DET
ejpam-5657	42	4	pseudo	pseudo	NOUN
ejpam-5657	42	5	-	-	NOUN
ejpam-5657	42	6	spectrum	spectrum	NOUN
ejpam-5657	42	7	of	of	ADP
ejpam-5657	42	8	matrices	matrix	NOUN
ejpam-5657	42	9	across	across	ADP
ejpam-5657	42	10	dynamic	dynamic	ADJ
ejpam-5657	42	11	models	model	NOUN
ejpam-5657	42	12	is	be	AUX
ejpam-5657	42	13	presented	present	VERB
ejpam-5657	42	14	while	while	SCONJ
ejpam-5657	42	15	making	make	VERB
ejpam-5657	42	16	use	use	NOUN
ejpam-5657	42	17	of	of	ADP
ejpam-5657	42	18	eigtool	eigtool	NOUN
ejpam-5657	42	19	[	[	X
ejpam-5657	42	20	28	28	NUM
ejpam-5657	42	21	]	]	PUNCT
ejpam-5657	42	22	.	.	PUNCT
ejpam-5657	43	1	overview	overview	NOUN
ejpam-5657	43	2	of	of	ADP
ejpam-5657	43	3	article	article	NOUN
ejpam-5657	43	4	:	:	PUNCT
ejpam-5657	43	5	in	in	ADP
ejpam-5657	43	6	subsection	subsection	NOUN
ejpam-5657	43	7	1.1	1.1	NUM
ejpam-5657	43	8	,	,	PUNCT
ejpam-5657	43	9	we	we	PRON
ejpam-5657	43	10	give	give	VERB
ejpam-5657	43	11	the	the	DET
ejpam-5657	43	12	preliminaries	preliminary	NOUN
ejpam-5657	43	13	to	to	PART
ejpam-5657	43	14	recall	recall	VERB
ejpam-5657	43	15	important	important	ADJ
ejpam-5657	43	16	concepts	concept	NOUN
ejpam-5657	43	17	,	,	PUNCT
ejpam-5657	43	18	and	and	CCONJ
ejpam-5657	43	19	definition	definition	NOUN
ejpam-5657	43	20	to	to	PART
ejpam-5657	43	21	be	be	AUX
ejpam-5657	43	22	used	use	VERB
ejpam-5657	43	23	in	in	ADP
ejpam-5657	43	24	this	this	DET
ejpam-5657	43	25	article	article	NOUN
ejpam-5657	43	26	.	.	PUNCT
ejpam-5657	44	1	in	in	ADP
ejpam-5657	44	2	section	section	NOUN
ejpam-5657	44	3	2	2	NUM
ejpam-5657	44	4	,	,	PUNCT
ejpam-5657	44	5	we	we	PRON
ejpam-5657	44	6	provide	provide	VERB
ejpam-5657	44	7	new	new	ADJ
ejpam-5657	44	8	results	result	NOUN
ejpam-5657	44	9	to	to	PART
ejpam-5657	44	10	study	study	VERB
ejpam-5657	44	11	dynamic	dynamic	ADJ
ejpam-5657	44	12	stability	stability	NOUN
ejpam-5657	44	13	and	and	CCONJ
ejpam-5657	44	14	d	d	NOUN
ejpam-5657	44	15	-	-	NOUN
ejpam-5657	44	16	stability	stability	NOUN
ejpam-5657	44	17	of	of	ADP
ejpam-5657	44	18	economic	economic	ADJ
ejpam-5657	44	19	models	model	NOUN
ejpam-5657	44	20	.	.	PUNCT
ejpam-5657	45	1	we	we	PRON
ejpam-5657	45	2	make	make	VERB
ejpam-5657	45	3	use	use	NOUN
ejpam-5657	45	4	of	of	ADP
ejpam-5657	45	5	various	various	ADJ
ejpam-5657	45	6	tools	tool	NOUN
ejpam-5657	45	7	from	from	ADP
ejpam-5657	45	8	linear	linear	ADJ
ejpam-5657	45	9	algebra	algebra	NOUN
ejpam-5657	45	10	,	,	PUNCT
ejpam-5657	45	11	system	system	NOUN
ejpam-5657	45	12	theory	theory	NOUN
ejpam-5657	45	13	to	to	PART
ejpam-5657	45	14	derive	derive	VERB
ejpam-5657	45	15	these	these	DET
ejpam-5657	45	16	new	new	ADJ
ejpam-5657	45	17	results	result	NOUN
ejpam-5657	45	18	.	.	PUNCT
ejpam-5657	46	1	in	in	ADP
ejpam-5657	46	2	section	section	NOUN
ejpam-5657	46	3	3	3	NUM
ejpam-5657	46	4	,	,	PUNCT
ejpam-5657	46	5	necessary	necessary	ADJ
ejpam-5657	46	6	and	and	CCONJ
ejpam-5657	46	7	sufficient	sufficient	ADJ
ejpam-5657	46	8	conditions	condition	NOUN
ejpam-5657	46	9	are	be	AUX
ejpam-5657	46	10	derived	derive	VERB
ejpam-5657	46	11	for	for	ADP
ejpam-5657	46	12	the	the	DET
ejpam-5657	46	13	d	d	NOUN
ejpam-5657	46	14	-	-	NOUN
ejpam-5657	46	15	stability	stability	NOUN
ejpam-5657	46	16	of	of	ADP
ejpam-5657	46	17	dynamical	dynamical	ADJ
ejpam-5657	46	18	system	system	NOUN
ejpam-5657	46	19	.	.	PUNCT
ejpam-5657	47	1	the	the	DET
ejpam-5657	47	2	numerical	numerical	ADJ
ejpam-5657	47	3	experimentation	experimentation	NOUN
ejpam-5657	47	4	to	to	PART
ejpam-5657	47	5	support	support	VERB
ejpam-5657	47	6	new	new	ADJ
ejpam-5657	47	7	results	result	NOUN
ejpam-5657	47	8	are	be	AUX
ejpam-5657	47	9	presented	present	VERB
ejpam-5657	47	10	in	in	ADP
ejpam-5657	47	11	section	section	NOUN
ejpam-5657	47	12	4	4	NUM
ejpam-5657	47	13	.	.	PUNCT
ejpam-5657	48	1	we	we	PRON
ejpam-5657	48	2	have	have	AUX
ejpam-5657	48	3	made	make	VERB
ejpam-5657	48	4	use	use	NOUN
ejpam-5657	48	5	of	of	ADP
ejpam-5657	48	6	eigtool	eigtool	NOUN
ejpam-5657	48	7	to	to	PART
ejpam-5657	48	8	visualize	visualize	VERB
ejpam-5657	48	9	the	the	DET
ejpam-5657	48	10	pseudo	pseudo	NOUN
ejpam-5657	48	11	-	-	NOUN
ejpam-5657	48	12	spectrum	spectrum	NOUN
ejpam-5657	48	13	of	of	ADP
ejpam-5657	48	14	structured	structured	ADJ
ejpam-5657	48	15	matrices	matrix	NOUN
ejpam-5657	48	16	across	across	ADP
ejpam-5657	48	17	the	the	DET
ejpam-5657	48	18	dynamical	dynamical	ADJ
ejpam-5657	48	19	systems	system	NOUN
ejpam-5657	48	20	.	.	PUNCT
ejpam-5657	49	1	finally	finally	ADV
ejpam-5657	49	2	,	,	PUNCT
ejpam-5657	49	3	in	in	ADP
ejpam-5657	49	4	section	section	NOUN
ejpam-5657	49	5	5	5	NUM
ejpam-5657	49	6	,	,	PUNCT
ejpam-5657	49	7	we	we	PRON
ejpam-5657	49	8	conclude	conclude	VERB
ejpam-5657	49	9	our	our	PRON
ejpam-5657	49	10	paper	paper	NOUN
ejpam-5657	49	11	.	.	PUNCT
ejpam-5657	50	1	1.1	1.1	NUM
ejpam-5657	50	2	.	.	PUNCT
ejpam-5657	50	3	preliminaries	preliminary	NOUN
ejpam-5657	50	4	.	.	PUNCT
ejpam-5657	51	1	for	for	ADP
ejpam-5657	51	2	m	m	PROPN
ejpam-5657	51	3	∈	∈	PROPN
ejpam-5657	51	4	cn	cn	PROPN
ejpam-5657	51	5	,	,	PUNCT
ejpam-5657	51	6	n	n	CCONJ
ejpam-5657	51	7	,	,	PUNCT
ejpam-5657	51	8	the	the	DET
ejpam-5657	51	9	largest	large	ADJ
ejpam-5657	51	10	singular	singular	ADJ
ejpam-5657	51	11	value	value	NOUN
ejpam-5657	51	12	is	be	AUX
ejpam-5657	51	13	denoted	denote	VERB
ejpam-5657	51	14	by	by	ADP
ejpam-5657	51	15	σmax	σmax	NOUN
ejpam-5657	51	16	,	,	PUNCT
ejpam-5657	51	17	and	and	CCONJ
ejpam-5657	51	18	is	be	AUX
ejpam-5657	51	19	a	a	DET
ejpam-5657	51	20	non	non	ADJ
ejpam-5657	51	21	-	-	ADJ
ejpam-5657	51	22	negative	negative	ADJ
ejpam-5657	51	23	real	real	ADJ
ejpam-5657	51	24	number	number	NOUN
ejpam-5657	51	25	.	.	PUNCT
ejpam-5657	52	1	the	the	DET
ejpam-5657	52	2	smallest	small	ADJ
ejpam-5657	52	3	singular	singular	ADJ
ejpam-5657	52	4	value	value	NOUN
ejpam-5657	52	5	is	be	AUX
ejpam-5657	52	6	denoted	denote	VERB
ejpam-5657	52	7	by	by	ADP
ejpam-5657	52	8	σmin	σmin	NOUN
ejpam-5657	52	9	.	.	PUNCT
ejpam-5657	53	1	the	the	DET
ejpam-5657	53	2	notation	notation	PROPN
ejpam-5657	53	3	mt	mt	PROPN
ejpam-5657	53	4	denotes	denote	VERB
ejpam-5657	53	5	the	the	DET
ejpam-5657	53	6	transpose	transpose	NOUN
ejpam-5657	53	7	of	of	ADP
ejpam-5657	53	8	a	a	DET
ejpam-5657	53	9	matrix	matrix	NOUN
ejpam-5657	53	10	,	,	PUNCT
ejpam-5657	53	11	λi(m	λi(m	NUM
ejpam-5657	53	12	)	)	PUNCT
ejpam-5657	53	13	denotes	denote	VERB
ejpam-5657	53	14	all	all	DET
ejpam-5657	53	15	the	the	DET
ejpam-5657	53	16	eigenvalues	eigenvalue	NOUN
ejpam-5657	53	17	of	of	ADP
ejpam-5657	53	18	the	the	DET
ejpam-5657	53	19	matrixm	matrixm	NOUN
ejpam-5657	53	20	.	.	PUNCT
ejpam-5657	54	1	form	form	VERB
ejpam-5657	54	2	>	>	X
ejpam-5657	54	3	0(m	0(m	NUM
ejpam-5657	54	4	≥	≥	NOUN
ejpam-5657	54	5	0	0	NUM
ejpam-5657	54	6	)	)	PUNCT
ejpam-5657	54	7	means	mean	VERB
ejpam-5657	54	8	that	that	SCONJ
ejpam-5657	54	9	matrix	matrix	NOUN
ejpam-5657	54	10	m	m	VERB
ejpam-5657	54	11	is	be	AUX
ejpam-5657	54	12	positive	positive	ADJ
ejpam-5657	54	13	definite	definite	ADJ
ejpam-5657	54	14	,	,	PUNCT
ejpam-5657	54	15	and	and	CCONJ
ejpam-5657	54	16	positive	positive	ADJ
ejpam-5657	54	17	semi	semi	ADJ
ejpam-5657	54	18	-	-	ADJ
ejpam-5657	54	19	definite	definite	ADJ
ejpam-5657	54	20	,	,	PUNCT
ejpam-5657	54	21	respectively	respectively	ADV
ejpam-5657	54	22	.	.	PUNCT
ejpam-5657	55	1	for	for	ADP
ejpam-5657	55	2	m	m	PROPN
ejpam-5657	55	3	<	<	X
ejpam-5657	55	4	0	0	PUNCT
ejpam-5657	55	5	(	(	PUNCT
ejpam-5657	55	6	m	m	VERB
ejpam-5657	55	7	≤	≤	NUM
ejpam-5657	55	8	0	0	NUM
ejpam-5657	55	9	)	)	PUNCT
ejpam-5657	55	10	means	mean	VERB
ejpam-5657	55	11	that	that	SCONJ
ejpam-5657	55	12	matrix	matrix	NOUN
ejpam-5657	55	13	m	m	VERB
ejpam-5657	55	14	is	be	AUX
ejpam-5657	55	15	negative	negative	ADJ
ejpam-5657	55	16	definite	definite	ADJ
ejpam-5657	55	17	,	,	PUNCT
ejpam-5657	55	18	and	and	CCONJ
ejpam-5657	55	19	negative	negative	ADJ
ejpam-5657	55	20	semi	semi	ADJ
ejpam-5657	55	21	-	-	ADJ
ejpam-5657	55	22	definite	definite	ADJ
ejpam-5657	55	23	,	,	PUNCT
ejpam-5657	55	24	respectively	respectively	ADV
ejpam-5657	55	25	.	.	PUNCT
ejpam-5657	56	1	the	the	DET
ejpam-5657	56	2	symbol	symbol	NOUN
ejpam-5657	56	3	c+	c+	VERB
ejpam-5657	56	4	.	.	PUNCT
ejpam-5657	57	1	definition	definition	NOUN
ejpam-5657	57	2	1	1	NUM
ejpam-5657	57	3	.	.	PUNCT
ejpam-5657	58	1	a	a	DET
ejpam-5657	58	2	block	block	NOUN
ejpam-5657	58	3	diagonal	diagonal	ADJ
ejpam-5657	58	4	matrix	matrix	NOUN
ejpam-5657	58	5	d	d	NOUN
ejpam-5657	58	6	is	be	AUX
ejpam-5657	58	7	defined	define	VERB
ejpam-5657	58	8	as	as	ADP
ejpam-5657	58	9	d	d	PROPN
ejpam-5657	58	10	=	=	PROPN
ejpam-5657	58	11	diag(d11	diag(d11	PROPN
ejpam-5657	58	12	,	,	PUNCT
ejpam-5657	58	13	d22	d22	PROPN
ejpam-5657	58	14	,	,	PUNCT
ejpam-5657	58	15	·	·	PUNCT
ejpam-5657	58	16	·	·	PUNCT
ejpam-5657	58	17	·	·	SYM
ejpam-5657	58	18	,	,	PUNCT
ejpam-5657	58	19	dnn	dnn	PROPN
ejpam-5657	58	20	)	)	PUNCT
ejpam-5657	58	21	,	,	PUNCT
ejpam-5657	58	22	where	where	SCONJ
ejpam-5657	58	23	d11	d11	PROPN
ejpam-5657	58	24	,	,	PUNCT
ejpam-5657	58	25	·	·	PUNCT
ejpam-5657	58	26	·	·	PUNCT
ejpam-5657	58	27	·	·	PUNCT
ejpam-5657	58	28	,	,	PUNCT
ejpam-5657	58	29	dnn	dnn	PROPN
ejpam-5657	58	30	,	,	PUNCT
ejpam-5657	58	31	are	be	AUX
ejpam-5657	58	32	the	the	DET
ejpam-5657	58	33	matrices	matrix	NOUN
ejpam-5657	58	34	.	.	PUNCT
ejpam-5657	59	1	definition	definition	NOUN
ejpam-5657	59	2	2	2	NUM
ejpam-5657	59	3	.	.	PUNCT
ejpam-5657	60	1	the	the	DET
ejpam-5657	60	2	block	block	NOUN
ejpam-5657	60	3	-	-	PUNCT
ejpam-5657	60	4	diagonal	diagonal	ADJ
ejpam-5657	60	5	structure	structure	NOUN
ejpam-5657	60	6	∆	∆	PROPN
ejpam-5657	60	7	represents	represent	VERB
ejpam-5657	60	8	the	the	DET
ejpam-5657	60	9	uncertainty	uncertainty	NOUN
ejpam-5657	60	10	set	set	VERB
ejpam-5657	60	11	and	and	CCONJ
ejpam-5657	60	12	is	be	AUX
ejpam-5657	60	13	defined	define	VERB
ejpam-5657	60	14	as	as	ADP
ejpam-5657	60	15	∆	∆	PROPN
ejpam-5657	60	16	=	=	NOUN
ejpam-5657	60	17	:	:	PUNCT
ejpam-5657	60	18	{	{	PUNCT
ejpam-5657	60	19	d	d	X
ejpam-5657	60	20	=	=	PUNCT
ejpam-5657	60	21	diag(d11	diag(d11	PROPN
ejpam-5657	60	22	,	,	PUNCT
ejpam-5657	60	23	d22	d22	PROPN
ejpam-5657	60	24	,	,	PUNCT
ejpam-5657	60	25	·	·	PUNCT
ejpam-5657	60	26	·	·	PUNCT
ejpam-5657	61	1	·	·	PUNCT
ejpam-5657	61	2	,	,	PUNCT
ejpam-5657	61	3	dnn	dnn	PROPN
ejpam-5657	61	4	)	)	PUNCT
ejpam-5657	61	5	}	}	PUNCT
ejpam-5657	61	6	,	,	PUNCT
ejpam-5657	61	7	d	d	PROPN
ejpam-5657	61	8	∈	∈	PROPN
ejpam-5657	61	9	rn	rn	PROPN
ejpam-5657	61	10	,	,	PUNCT
ejpam-5657	61	11	n.	n.	ADJ
ejpam-5657	61	12	definition	definition	NOUN
ejpam-5657	61	13	3	3	X
ejpam-5657	61	14	.	.	PUNCT
ejpam-5657	62	1	the	the	DET
ejpam-5657	62	2	set	set	NOUN
ejpam-5657	62	3	∆+	∆+	NUM
ejpam-5657	62	4	is	be	AUX
ejpam-5657	62	5	defined	define	VERB
ejpam-5657	62	6	as	as	ADP
ejpam-5657	62	7	∆+	∆+	NUM
ejpam-5657	62	8	=	=	NOUN
ejpam-5657	62	9	:	:	PUNCT
ejpam-5657	62	10	{	{	PUNCT
ejpam-5657	62	11	d	d	PUNCT
ejpam-5657	62	12	∈	∈	PRON
ejpam-5657	62	13	∆	∆	PROPN
ejpam-5657	62	14	:	:	PUNCT
ejpam-5657	63	1	dii	dii	NOUN
ejpam-5657	63	2	>	>	X
ejpam-5657	63	3	0	0	NUM
ejpam-5657	63	4	,	,	PUNCT
ejpam-5657	63	5	∀i	∀i	NOUN
ejpam-5657	63	6	=	=	SYM
ejpam-5657	63	7	1	1	NUM
ejpam-5657	63	8	:	:	PUNCT
ejpam-5657	63	9	n	n	CCONJ
ejpam-5657	63	10	}	}	PUNCT
ejpam-5657	63	11	.	.	PUNCT
ejpam-5657	64	1	definition	definition	NOUN
ejpam-5657	64	2	4	4	NUM
ejpam-5657	64	3	.	.	PUNCT
ejpam-5657	65	1	the	the	DET
ejpam-5657	65	2	singular	singular	PROPN
ejpam-5657	65	3	values	value	VERB
ejpam-5657	65	4	σi	σi	PRON
ejpam-5657	65	5	∀	∀	PUNCT
ejpam-5657	66	1	i	i	NOUN
ejpam-5657	66	2	=	=	NOUN
ejpam-5657	66	3	1	1	NUM
ejpam-5657	66	4	:	:	PUNCT
ejpam-5657	66	5	n	n	X
ejpam-5657	66	6	are	be	AUX
ejpam-5657	66	7	the	the	DET
ejpam-5657	66	8	non	non	ADJ
ejpam-5657	66	9	-	-	ADJ
ejpam-5657	66	10	negative	negative	ADJ
ejpam-5657	66	11	numbers	number	NOUN
ejpam-5657	66	12	appearing	appear	VERB
ejpam-5657	66	13	in	in	ADP
ejpam-5657	66	14	the	the	DET
ejpam-5657	66	15	diagonal	diagonal	ADJ
ejpam-5657	66	16	matrix	matrix	NOUN
ejpam-5657	66	17	σ	σ	NOUN
ejpam-5657	66	18	in	in	ADP
ejpam-5657	66	19	the	the	DET
ejpam-5657	66	20	singular	singular	ADJ
ejpam-5657	66	21	value	value	NOUN
ejpam-5657	66	22	decomposition	decomposition	NOUN
ejpam-5657	66	23	of	of	ADP
ejpam-5657	66	24	a	a	DET
ejpam-5657	66	25	matrix	matrix	NOUN
ejpam-5657	66	26	m	m	NOUN
ejpam-5657	66	27	=	=	SYM
ejpam-5657	66	28	uσv	uσv	X
ejpam-5657	66	29	t	t	PROPN
ejpam-5657	66	30	,	,	PUNCT
ejpam-5657	66	31	with	with	ADP
ejpam-5657	66	32	u	u	NOUN
ejpam-5657	66	33	,	,	PUNCT
ejpam-5657	66	34	v	v	ADP
ejpam-5657	66	35	being	be	AUX
ejpam-5657	66	36	as	as	ADP
ejpam-5657	66	37	real	real	ADJ
ejpam-5657	66	38	orthogonal	orthogonal	ADJ
ejpam-5657	66	39	matrices	matrix	NOUN
ejpam-5657	66	40	.	.	PUNCT
ejpam-5657	67	1	definition	definition	NOUN
ejpam-5657	67	2	5	5	NUM
ejpam-5657	67	3	.	.	PUNCT
ejpam-5657	68	1	for	for	ADP
ejpam-5657	68	2	a	a	DET
ejpam-5657	68	3	given	give	VERB
ejpam-5657	68	4	matrix	matrix	NOUN
ejpam-5657	68	5	m	m	NOUN
ejpam-5657	68	6	∈	∈	PROPN
ejpam-5657	68	7	cn	cn	PROPN
ejpam-5657	68	8	,	,	PUNCT
ejpam-5657	68	9	n	n	CCONJ
ejpam-5657	68	10	,	,	PUNCT
ejpam-5657	68	11	and	and	CCONJ
ejpam-5657	68	12	an	an	DET
ejpam-5657	68	13	underlying	underlie	VERB
ejpam-5657	68	14	set	set	NOUN
ejpam-5657	68	15	∆	∆	PROPN
ejpam-5657	68	16	,	,	PUNCT
ejpam-5657	68	17	the	the	DET
ejpam-5657	68	18	structured	structured	ADJ
ejpam-5657	68	19	singular	singular	ADJ
ejpam-5657	68	20	value	value	NOUN
ejpam-5657	68	21	is	be	AUX
ejpam-5657	68	22	defined	define	VERB
ejpam-5657	68	23	[	[	PUNCT
ejpam-5657	68	24	33	33	NUM
ejpam-5657	68	25	]	]	PUNCT
ejpam-5657	68	26	as	as	ADP
ejpam-5657	68	27	µ∆(m	µ∆(m	NOUN
ejpam-5657	68	28	)	)	PUNCT
ejpam-5657	68	29	:	:	PUNCT
ejpam-5657	68	30	=	=	SYM
ejpam-5657	68	31	1	1	NUM
ejpam-5657	68	32	min{||∆̂||	min{||∆̂||	NOUN
ejpam-5657	68	33	:	:	PUNCT
ejpam-5657	68	34	det(in	det(in	ADJ
ejpam-5657	68	35	−m∆̂	−m∆̂	NOUN
ejpam-5657	68	36	)	)	PUNCT
ejpam-5657	68	37	=	=	SYM
ejpam-5657	68	38	0	0	NUM
ejpam-5657	68	39	,	,	PUNCT
ejpam-5657	68	40	∀∆̂	∀∆̂	PROPN
ejpam-5657	68	41	∈	∈	NOUN
ejpam-5657	68	42	∆	∆	PROPN
ejpam-5657	68	43	}	}	PUNCT
ejpam-5657	68	44	,	,	PUNCT
ejpam-5657	68	45	otherwise	otherwise	ADV
ejpam-5657	68	46	µ∆(m	µ∆(m	PUNCT
ejpam-5657	68	47	)	)	PUNCT
ejpam-5657	69	1	=	=	SYM
ejpam-5657	69	2	0	0	PUNCT
ejpam-5657	69	3	if	if	SCONJ
ejpam-5657	69	4	det(in	det(in	NOUN
ejpam-5657	69	5	−m∆̂	−m∆̂	NOUN
ejpam-5657	69	6	)	)	PUNCT
ejpam-5657	69	7	̸=	̸=	PROPN
ejpam-5657	69	8	0	0	NUM
ejpam-5657	69	9	,	,	PUNCT
ejpam-5657	69	10	∀∆̂	∀∆̂	PROPN
ejpam-5657	69	11	∈	∈	PROPN
ejpam-5657	70	1	∆.	∆.	ADJ
ejpam-5657	70	2	m.u.r	m.u.r	NOUN
ejpam-5657	70	3	et	et	PROPN
ejpam-5657	70	4	al	al	PROPN
ejpam-5657	70	5	.	.	PUNCT
ejpam-5657	70	6	/	/	SYM
ejpam-5657	70	7	eur	eur	PROPN
ejpam-5657	70	8	.	.	PUNCT
ejpam-5657	71	1	j.	j.	PROPN
ejpam-5657	71	2	pure	pure	PROPN
ejpam-5657	71	3	appl	appl	PROPN
ejpam-5657	71	4	.	.	PROPN
ejpam-5657	71	5	math	math	PROPN
ejpam-5657	71	6	,	,	PUNCT
ejpam-5657	71	7	18	18	NUM
ejpam-5657	71	8	(	(	PUNCT
ejpam-5657	71	9	1	1	NUM
ejpam-5657	71	10	)	)	PUNCT
ejpam-5657	71	11	(	(	PUNCT
ejpam-5657	71	12	2025	2025	NUM
ejpam-5657	71	13	)	)	PUNCT
ejpam-5657	71	14	,	,	PUNCT
ejpam-5657	71	15	5657	5657	NUM
ejpam-5657	71	16	4	4	NUM
ejpam-5657	71	17	of	of	ADP
ejpam-5657	71	18	17	17	NUM
ejpam-5657	71	19	note	note	NOUN
ejpam-5657	71	20	that	that	SCONJ
ejpam-5657	71	21	min	min	NOUN
ejpam-5657	71	22	is	be	AUX
ejpam-5657	71	23	taken	take	VERB
ejpam-5657	71	24	over	over	ADP
ejpam-5657	71	25	∆̂	∆̂	NOUN
ejpam-5657	71	26	∈	∈	NOUN
ejpam-5657	71	27	∆	∆	PROPN
ejpam-5657	71	28	,	,	PUNCT
ejpam-5657	71	29	and	and	CCONJ
ejpam-5657	71	30	min	min	NOUN
ejpam-5657	71	31	over	over	ADP
ejpam-5657	71	32	an	an	DET
ejpam-5657	71	33	empty	empty	ADJ
ejpam-5657	71	34	set	set	NOUN
ejpam-5657	71	35	is	be	AUX
ejpam-5657	71	36	+	+	NOUN
ejpam-5657	71	37	∞.	∞.	PROPN
ejpam-5657	71	38	definition	definition	NOUN
ejpam-5657	71	39	6	6	NUM
ejpam-5657	71	40	.	.	PUNCT
ejpam-5657	72	1	[	[	X
ejpam-5657	72	2	4	4	NUM
ejpam-5657	72	3	,	,	PUNCT
ejpam-5657	72	4	17	17	NUM
ejpam-5657	72	5	]	]	PUNCT
ejpam-5657	72	6	.	.	PUNCT
ejpam-5657	73	1	the	the	DET
ejpam-5657	73	2	n	n	ADV
ejpam-5657	73	3	-	-	PUNCT
ejpam-5657	73	4	dimensional	dimensional	ADJ
ejpam-5657	73	5	real	real	ADJ
ejpam-5657	73	6	valued	value	VERB
ejpam-5657	73	7	matrix	matrix	NOUN
ejpam-5657	73	8	a	a	DET
ejpam-5657	73	9	∈	∈	PROPN
ejpam-5657	73	10	rn	rn	PROPN
ejpam-5657	73	11	,	,	PUNCT
ejpam-5657	73	12	n	n	PRON
ejpam-5657	73	13	is	be	AUX
ejpam-5657	73	14	continuous	continuous	ADJ
ejpam-5657	73	15	-	-	PUNCT
ejpam-5657	73	16	time	time	NOUN
ejpam-5657	73	17	stable	stable	ADJ
ejpam-5657	73	18	if	if	SCONJ
ejpam-5657	73	19	∃	∃	PROPN
ejpam-5657	73	20	d	d	PROPN
ejpam-5657	73	21	∈	∈	PROPN
ejpam-5657	73	22	∆+	∆+	NUM
ejpam-5657	73	23	such	such	ADJ
ejpam-5657	73	24	that	that	SCONJ
ejpam-5657	73	25	(	(	PUNCT
ejpam-5657	73	26	atda−d	atda−d	PROPN
ejpam-5657	73	27	)	)	PUNCT
ejpam-5657	73	28	<	<	X
ejpam-5657	73	29	0	0	X
ejpam-5657	73	30	.	.	PUNCT
ejpam-5657	73	31	theorem	theorem	NOUN
ejpam-5657	73	32	1	1	NUM
ejpam-5657	73	33	.	.	PUNCT
ejpam-5657	74	1	[	[	X
ejpam-5657	74	2	23	23	NUM
ejpam-5657	74	3	]	]	PUNCT
ejpam-5657	74	4	the	the	DET
ejpam-5657	74	5	continuous	continuous	ADJ
ejpam-5657	74	6	-	-	PUNCT
ejpam-5657	74	7	time	time	NOUN
ejpam-5657	74	8	linear	linear	PROPN
ejpam-5657	74	9	system	system	NOUN
ejpam-5657	74	10	dx(t	dx(t	NOUN
ejpam-5657	74	11	)	)	PUNCT
ejpam-5657	74	12	dt	dt	NOUN
ejpam-5657	74	13	=	=	SYM
ejpam-5657	74	14	ax(t	ax(t	NUM
ejpam-5657	74	15	)	)	PUNCT
ejpam-5657	74	16	,	,	PUNCT
ejpam-5657	74	17	x(t	x(t	PROPN
ejpam-5657	74	18	)	)	PUNCT
ejpam-5657	74	19	∈	∈	PROPN
ejpam-5657	74	20	rn,1	rn,1	NOUN
ejpam-5657	74	21	is	be	AUX
ejpam-5657	74	22	asymptotically	asymptotically	ADV
ejpam-5657	74	23	stable	stable	ADJ
ejpam-5657	74	24	iff	iff	PROPN
ejpam-5657	74	25	re(λi	re(λi	PROPN
ejpam-5657	74	26	)	)	PUNCT
ejpam-5657	74	27	<	<	X
ejpam-5657	74	28	0	0	NUM
ejpam-5657	74	29	⇔	⇔	X
ejpam-5657	74	30	π	π	PROPN
ejpam-5657	74	31	2	2	NUM
ejpam-5657	74	32	<	<	X
ejpam-5657	74	33	ϕ	ϕ	X
ejpam-5657	74	34	<	<	X
ejpam-5657	74	35	3π	3π	NUM
ejpam-5657	74	36	2	2	NUM
ejpam-5657	74	37	,	,	PUNCT
ejpam-5657	74	38	∀	∀	VERB
ejpam-5657	75	1	i	i	NOUN
ejpam-5657	75	2	=	=	NOUN
ejpam-5657	75	3	1	1	NUM
ejpam-5657	75	4	:	:	SYM
ejpam-5657	75	5	n	n	CCONJ
ejpam-5657	75	6	,	,	PUNCT
ejpam-5657	75	7	with	with	ADP
ejpam-5657	75	8	λi	λi	NOUN
ejpam-5657	75	9	=	=	NOUN
ejpam-5657	75	10	|λi|eιϕi	|λi|eιϕi	PROPN
ejpam-5657	75	11	,	,	PUNCT
ejpam-5657	75	12	∀	∀	VERB
ejpam-5657	76	1	i	i	NOUN
ejpam-5657	76	2	=	=	NOUN
ejpam-5657	76	3	1	1	NUM
ejpam-5657	76	4	:	:	SYM
ejpam-5657	76	5	n	n	CCONJ
ejpam-5657	76	6	,	,	PUNCT
ejpam-5657	76	7	the	the	DET
ejpam-5657	76	8	eigenvalues	eigenvalue	NOUN
ejpam-5657	76	9	of	of	ADP
ejpam-5657	76	10	a.	a.	NOUN
ejpam-5657	76	11	note	note	NOUN
ejpam-5657	76	12	that	that	SCONJ
ejpam-5657	76	13	the	the	DET
ejpam-5657	76	14	matrix	matrix	NOUN
ejpam-5657	76	15	â	â	ADP
ejpam-5657	76	16	∈	∈	PROPN
ejpam-5657	76	17	rn	rn	PROPN
ejpam-5657	76	18	,	,	PUNCT
ejpam-5657	76	19	n	n	PROPN
ejpam-5657	76	20	is	be	AUX
ejpam-5657	76	21	discrete	discrete	ADJ
ejpam-5657	76	22	-	-	PUNCT
ejpam-5657	76	23	time	time	NOUN
ejpam-5657	76	24	diagonal	diagonal	ADJ
ejpam-5657	76	25	stable	stable	NOUN
ejpam-5657	76	26	if	if	SCONJ
ejpam-5657	76	27	∃	∃	PROPN
ejpam-5657	76	28	d	d	PROPN
ejpam-5657	76	29	∈	∈	PROPN
ejpam-5657	76	30	∆+	∆+	NUM
ejpam-5657	76	31	such	such	ADJ
ejpam-5657	76	32	that	that	SCONJ
ejpam-5657	76	33	(	(	PUNCT
ejpam-5657	76	34	âtdâ−d	âtdâ−d	PROPN
ejpam-5657	76	35	)	)	PUNCT
ejpam-5657	76	36	<	<	X
ejpam-5657	76	37	0	0	X
ejpam-5657	76	38	.	.	PUNCT
ejpam-5657	76	39	definition	definition	NOUN
ejpam-5657	76	40	7	7	NUM
ejpam-5657	76	41	.	.	PUNCT
ejpam-5657	77	1	[	[	X
ejpam-5657	77	2	8	8	NUM
ejpam-5657	77	3	,	,	PUNCT
ejpam-5657	77	4	44	44	NUM
ejpam-5657	77	5	]	]	PUNCT
ejpam-5657	77	6	.	.	PUNCT
ejpam-5657	78	1	the	the	DET
ejpam-5657	78	2	n	n	ADV
ejpam-5657	78	3	-	-	PUNCT
ejpam-5657	78	4	dimensional	dimensional	ADJ
ejpam-5657	78	5	real	real	ADJ
ejpam-5657	78	6	valued	value	VERB
ejpam-5657	78	7	matrix	matrix	NOUN
ejpam-5657	78	8	a	a	DET
ejpam-5657	78	9	∈	∈	PROPN
ejpam-5657	78	10	rn	rn	PROPN
ejpam-5657	78	11	,	,	PUNCT
ejpam-5657	78	12	n	n	PRON
ejpam-5657	78	13	is	be	AUX
ejpam-5657	78	14	continuous	continuous	ADJ
ejpam-5657	78	15	-	-	PUNCT
ejpam-5657	78	16	time	time	NOUN
ejpam-5657	78	17	d	d	NOUN
ejpam-5657	78	18	-	-	NOUN
ejpam-5657	78	19	stable	stable	ADJ
ejpam-5657	78	20	if	if	SCONJ
ejpam-5657	78	21	the	the	DET
ejpam-5657	78	22	product	product	NOUN
ejpam-5657	78	23	da	da	NOUN
ejpam-5657	78	24	is	be	AUX
ejpam-5657	78	25	such	such	ADJ
ejpam-5657	78	26	that	that	SCONJ
ejpam-5657	78	27	re(λi(da	re(λi(da	NOUN
ejpam-5657	78	28	)	)	PUNCT
ejpam-5657	78	29	)	)	PUNCT
ejpam-5657	79	1	<	<	X
ejpam-5657	79	2	0	0	NUM
ejpam-5657	79	3	,	,	PUNCT
ejpam-5657	79	4	∀i	∀i	NOUN
ejpam-5657	79	5	,	,	PUNCT
ejpam-5657	79	6	d	d	PROPN
ejpam-5657	79	7	∈	∈	PROPN
ejpam-5657	79	8	∆+	∆+	NOUN
ejpam-5657	79	9	,	,	PUNCT
ejpam-5657	79	10	a	a	DET
ejpam-5657	79	11	positive	positive	ADJ
ejpam-5657	79	12	diagonal	diagonal	ADJ
ejpam-5657	79	13	matrix	matrix	NOUN
ejpam-5657	79	14	.	.	PUNCT
ejpam-5657	80	1	definition	definition	NOUN
ejpam-5657	80	2	8	8	NUM
ejpam-5657	80	3	.	.	PUNCT
ejpam-5657	81	1	[	[	X
ejpam-5657	81	2	3	3	NUM
ejpam-5657	81	3	]	]	PUNCT
ejpam-5657	81	4	.	.	PUNCT
ejpam-5657	82	1	the	the	DET
ejpam-5657	82	2	n	n	ADV
ejpam-5657	82	3	-	-	PUNCT
ejpam-5657	82	4	dimensional	dimensional	ADJ
ejpam-5657	82	5	real	real	ADJ
ejpam-5657	82	6	valued	value	VERB
ejpam-5657	82	7	matrix	matrix	NOUN
ejpam-5657	82	8	â	â	ADP
ejpam-5657	82	9	∈	∈	PROPN
ejpam-5657	82	10	rn	rn	PROPN
ejpam-5657	82	11	,	,	PUNCT
ejpam-5657	82	12	n	n	PROPN
ejpam-5657	82	13	is	be	AUX
ejpam-5657	82	14	discrete	discrete	ADJ
ejpam-5657	82	15	-	-	PUNCT
ejpam-5657	82	16	time	time	NOUN
ejpam-5657	82	17	dstable	dstable	ADJ
ejpam-5657	82	18	if	if	SCONJ
ejpam-5657	82	19	the	the	DET
ejpam-5657	82	20	product	product	NOUN
ejpam-5657	82	21	dâ	dâ	PROPN
ejpam-5657	82	22	is	be	AUX
ejpam-5657	82	23	such	such	ADJ
ejpam-5657	82	24	that	that	SCONJ
ejpam-5657	82	25	ρ(dâ	ρ(dâ	NOUN
ejpam-5657	82	26	)	)	PUNCT
ejpam-5657	82	27	<	<	X
ejpam-5657	82	28	1	1	NUM
ejpam-5657	82	29	,	,	PUNCT
ejpam-5657	82	30	for	for	SCONJ
ejpam-5657	82	31	all	all	PRON
ejpam-5657	82	32	real	real	ADV
ejpam-5657	82	33	valued	value	VERB
ejpam-5657	82	34	diagonal	diagonal	ADJ
ejpam-5657	82	35	and	and	CCONJ
ejpam-5657	82	36	norm	norm	NOUN
ejpam-5657	82	37	bounded	bound	VERB
ejpam-5657	82	38	matrices	matrix	NOUN
ejpam-5657	82	39	d.	d.	PROPN
ejpam-5657	82	40	theorem	theorem	VERB
ejpam-5657	82	41	2	2	NUM
ejpam-5657	82	42	.	.	PUNCT
ejpam-5657	83	1	[	[	X
ejpam-5657	83	2	23	23	NUM
ejpam-5657	83	3	]	]	PUNCT
ejpam-5657	83	4	the	the	DET
ejpam-5657	83	5	discrete	discrete	ADJ
ejpam-5657	83	6	-	-	PUNCT
ejpam-5657	83	7	time	time	NOUN
ejpam-5657	83	8	linear	linear	ADJ
ejpam-5657	83	9	system	system	NOUN
ejpam-5657	83	10	xi+1	xi+1	X
ejpam-5657	84	1	=	=	SYM
ejpam-5657	84	2	āxi	āxi	PROPN
ejpam-5657	84	3	,	,	PUNCT
ejpam-5657	84	4	xi	xi	PROPN
ejpam-5657	84	5	∈	∈	PROPN
ejpam-5657	84	6	rn,1	rn,1	PROPN
ejpam-5657	84	7	,	,	PUNCT
ejpam-5657	84	8	i	i	PRON
ejpam-5657	84	9	=	=	NOUN
ejpam-5657	84	10	z+	z+	NUM
ejpam-5657	84	11	is	be	AUX
ejpam-5657	84	12	asymptotically	asymptotically	ADV
ejpam-5657	84	13	stable	stable	ADJ
ejpam-5657	84	14	iff	iff	PROPN
ejpam-5657	84	15	|λi|	|λi|	PROPN
ejpam-5657	84	16	<	<	X
ejpam-5657	84	17	1	1	NUM
ejpam-5657	84	18	with	with	ADP
ejpam-5657	84	19	λi	λi	ADP
ejpam-5657	84	20	,	,	PUNCT
ejpam-5657	84	21	∀	∀	VERB
ejpam-5657	84	22	i	i	NOUN
ejpam-5657	84	23	=	=	NOUN
ejpam-5657	84	24	1	1	NUM
ejpam-5657	84	25	:	:	SYM
ejpam-5657	84	26	n	n	CCONJ
ejpam-5657	84	27	,	,	PUNCT
ejpam-5657	84	28	are	be	AUX
ejpam-5657	84	29	the	the	DET
ejpam-5657	84	30	eigenvalues	eigenvalue	NOUN
ejpam-5657	84	31	of	of	ADP
ejpam-5657	84	32	ā.	ā.	NOUN
ejpam-5657	84	33	2	2	NUM
ejpam-5657	84	34	.	.	X
ejpam-5657	84	35	dynamic	dynamic	ADJ
ejpam-5657	84	36	stability	stability	NOUN
ejpam-5657	84	37	and	and	CCONJ
ejpam-5657	84	38	d	d	NOUN
ejpam-5657	84	39	-	-	NOUN
ejpam-5657	84	40	stability	stability	NOUN
ejpam-5657	84	41	of	of	ADP
ejpam-5657	84	42	economic	economic	ADJ
ejpam-5657	84	43	models	model	NOUN
ejpam-5657	84	44	in	in	ADP
ejpam-5657	84	45	the	the	DET
ejpam-5657	84	46	section	section	NOUN
ejpam-5657	84	47	,	,	PUNCT
ejpam-5657	84	48	we	we	PRON
ejpam-5657	84	49	present	present	VERB
ejpam-5657	84	50	new	new	ADJ
ejpam-5657	84	51	results	result	NOUN
ejpam-5657	84	52	to	to	PART
ejpam-5657	84	53	study	study	VERB
ejpam-5657	84	54	the	the	DET
ejpam-5657	84	55	dynamic	dynamic	ADJ
ejpam-5657	84	56	stability	stability	NOUN
ejpam-5657	84	57	and	and	CCONJ
ejpam-5657	84	58	d	d	NOUN
ejpam-5657	84	59	-	-	NOUN
ejpam-5657	84	60	stability	stability	NOUN
ejpam-5657	84	61	of	of	ADP
ejpam-5657	84	62	a	a	DET
ejpam-5657	84	63	class	class	NOUN
ejpam-5657	84	64	of	of	ADP
ejpam-5657	84	65	linear	linear	ADJ
ejpam-5657	84	66	economic	economic	ADJ
ejpam-5657	84	67	model	model	NOUN
ejpam-5657	84	68	given	give	VERB
ejpam-5657	84	69	in	in	ADP
ejpam-5657	84	70	the	the	DET
ejpam-5657	84	71	mathematical	mathematical	ADJ
ejpam-5657	84	72	form	form	NOUN
ejpam-5657	84	73	yt	yt	X
ejpam-5657	84	74	=	=	PUNCT
ejpam-5657	84	75	ayt	ayt	PROPN
ejpam-5657	84	76	+	+	SYM
ejpam-5657	84	77	byt−1	byt−1	NOUN
ejpam-5657	84	78	+	+	CCONJ
ejpam-5657	84	79	cxt	cxt	PROPN
ejpam-5657	84	80	.	.	PUNCT
ejpam-5657	85	1	here	here	ADV
ejpam-5657	85	2	,	,	PUNCT
ejpam-5657	85	3	yt	yt	PROPN
ejpam-5657	85	4	is	be	AUX
ejpam-5657	85	5	a	a	DET
ejpam-5657	85	6	vector	vector	NOUN
ejpam-5657	85	7	of	of	ADP
ejpam-5657	85	8	the	the	DET
ejpam-5657	85	9	endogenous	endogenous	ADJ
ejpam-5657	85	10	variables	variable	NOUN
ejpam-5657	85	11	,	,	PUNCT
ejpam-5657	85	12	and	and	CCONJ
ejpam-5657	85	13	xt	xt	PROPN
ejpam-5657	85	14	is	be	AUX
ejpam-5657	85	15	a	a	DET
ejpam-5657	85	16	vector	vector	NOUN
ejpam-5657	85	17	of	of	ADP
ejpam-5657	85	18	exogenous	exogenous	ADJ
ejpam-5657	85	19	variables	variable	NOUN
ejpam-5657	85	20	.	.	PUNCT
ejpam-5657	86	1	a	a	DET
ejpam-5657	86	2	,	,	PUNCT
ejpam-5657	86	3	b	b	NOUN
ejpam-5657	86	4	,	,	PUNCT
ejpam-5657	86	5	and	and	CCONJ
ejpam-5657	86	6	c	c	NOUN
ejpam-5657	86	7	are	be	AUX
ejpam-5657	86	8	the	the	DET
ejpam-5657	86	9	matrices	matrix	NOUN
ejpam-5657	86	10	having	have	VERB
ejpam-5657	86	11	an	an	DET
ejpam-5657	86	12	appropriate	appropriate	ADJ
ejpam-5657	86	13	dimensions	dimension	NOUN
ejpam-5657	86	14	.	.	PUNCT
ejpam-5657	87	1	the	the	DET
ejpam-5657	87	2	reduced	reduce	VERB
ejpam-5657	87	3	mathematical	mathematical	ADJ
ejpam-5657	87	4	form	form	NOUN
ejpam-5657	87	5	of	of	ADP
ejpam-5657	87	6	the	the	DET
ejpam-5657	87	7	above	above	ADJ
ejpam-5657	87	8	dynamic	dynamic	ADJ
ejpam-5657	87	9	model	model	NOUN
ejpam-5657	87	10	is	be	AUX
ejpam-5657	87	11	given	give	VERB
ejpam-5657	87	12	as	as	ADP
ejpam-5657	87	13	yt	yt	NOUN
ejpam-5657	87	14	=	=	PUNCT
ejpam-5657	87	15	(	(	PUNCT
ejpam-5657	87	16	in	in	ADP
ejpam-5657	87	17	−a)−1byt−1	−a)−1byt−1	NOUN
ejpam-5657	87	18	+	+	CCONJ
ejpam-5657	87	19	ext	ext	NOUN
ejpam-5657	87	20	.	.	PUNCT
ejpam-5657	88	1	if	if	SCONJ
ejpam-5657	88	2	the	the	DET
ejpam-5657	88	3	spectral	spectral	ADJ
ejpam-5657	88	4	radius	radius	NOUN
ejpam-5657	88	5	,	,	PUNCT
ejpam-5657	88	6	that	that	ADV
ejpam-5657	88	7	is	be	AUX
ejpam-5657	88	8	,	,	PUNCT
ejpam-5657	88	9	ρ((in	ρ((in	NUM
ejpam-5657	88	10	−	−	PROPN
ejpam-5657	88	11	a)−1b	a)−1b	PROPN
ejpam-5657	88	12	)	)	PUNCT
ejpam-5657	88	13	<	<	X
ejpam-5657	88	14	1	1	NUM
ejpam-5657	88	15	,	,	PUNCT
ejpam-5657	88	16	then	then	ADV
ejpam-5657	88	17	dynamic	dynamic	ADJ
ejpam-5657	88	18	model	model	NOUN
ejpam-5657	88	19	is	be	AUX
ejpam-5657	88	20	said	say	VERB
ejpam-5657	88	21	to	to	PART
ejpam-5657	88	22	be	be	AUX
ejpam-5657	88	23	dynamically	dynamically	ADV
ejpam-5657	88	24	stable	stable	ADJ
ejpam-5657	88	25	.	.	PUNCT
ejpam-5657	89	1	the	the	DET
ejpam-5657	89	2	following	follow	VERB
ejpam-5657	89	3	theorem	theorem	VERB
ejpam-5657	89	4	3	3	NUM
ejpam-5657	89	5	show	show	VERB
ejpam-5657	89	6	that	that	SCONJ
ejpam-5657	89	7	the	the	DET
ejpam-5657	89	8	reduced	reduced	ADJ
ejpam-5657	89	9	dynamic	dynamic	ADJ
ejpam-5657	89	10	model	model	NOUN
ejpam-5657	89	11	is	be	AUX
ejpam-5657	89	12	dynamically	dynamically	ADV
ejpam-5657	89	13	stable	stable	ADJ
ejpam-5657	89	14	.	.	PUNCT
ejpam-5657	90	1	m.u.r	m.u.r	NOUN
ejpam-5657	90	2	et	et	PROPN
ejpam-5657	90	3	al	al	PROPN
ejpam-5657	90	4	.	.	PUNCT
ejpam-5657	90	5	/	/	SYM
ejpam-5657	90	6	eur	eur	PROPN
ejpam-5657	90	7	.	.	PUNCT
ejpam-5657	91	1	j.	j.	PROPN
ejpam-5657	91	2	pure	pure	PROPN
ejpam-5657	91	3	appl	appl	PROPN
ejpam-5657	91	4	.	.	PROPN
ejpam-5657	91	5	math	math	PROPN
ejpam-5657	91	6	,	,	PUNCT
ejpam-5657	91	7	18	18	NUM
ejpam-5657	91	8	(	(	PUNCT
ejpam-5657	91	9	1	1	NUM
ejpam-5657	91	10	)	)	PUNCT
ejpam-5657	91	11	(	(	PUNCT
ejpam-5657	91	12	2025	2025	NUM
ejpam-5657	91	13	)	)	PUNCT
ejpam-5657	91	14	,	,	PUNCT
ejpam-5657	91	15	5657	5657	NUM
ejpam-5657	91	16	5	5	NUM
ejpam-5657	91	17	of	of	ADP
ejpam-5657	91	18	17	17	NUM
ejpam-5657	91	19	theorem	theorem	NOUN
ejpam-5657	91	20	3	3	X
ejpam-5657	91	21	.	.	PUNCT
ejpam-5657	92	1	let	let	VERB
ejpam-5657	92	2	a	a	DET
ejpam-5657	92	3	,	,	PUNCT
ejpam-5657	92	4	b	b	PROPN
ejpam-5657	92	5	∈	∈	PROPN
ejpam-5657	92	6	rn	rn	PROPN
ejpam-5657	92	7	,	,	PUNCT
ejpam-5657	92	8	n.	n.	PROPN
ejpam-5657	92	9	then	then	ADV
ejpam-5657	92	10	dynamical	dynamical	ADJ
ejpam-5657	92	11	model	model	NOUN
ejpam-5657	92	12	yt	yt	PROPN
ejpam-5657	93	1	=	=	PUNCT
ejpam-5657	93	2	(	(	PUNCT
ejpam-5657	93	3	in	in	ADP
ejpam-5657	93	4	−	−	PROPN
ejpam-5657	93	5	a)−1byt−1	a)−1byt−1	PROPN
ejpam-5657	94	1	+	+	CCONJ
ejpam-5657	94	2	ext	ext	NOUN
ejpam-5657	94	3	is	be	AUX
ejpam-5657	94	4	dynamically	dynamically	ADV
ejpam-5657	94	5	stable	stable	ADJ
ejpam-5657	94	6	if	if	SCONJ
ejpam-5657	94	7	ρ((in	ρ((in	NUM
ejpam-5657	94	8	−a)−1b	−a)−1b	NOUN
ejpam-5657	94	9	)	)	PUNCT
ejpam-5657	94	10	<	<	X
ejpam-5657	94	11	1	1	X
ejpam-5657	94	12	.	.	PUNCT
ejpam-5657	94	13	proof	proof	NOUN
ejpam-5657	94	14	.	.	PUNCT
ejpam-5657	95	1	we	we	PRON
ejpam-5657	95	2	aim	aim	VERB
ejpam-5657	95	3	to	to	PART
ejpam-5657	95	4	prove	prove	VERB
ejpam-5657	95	5	that	that	SCONJ
ejpam-5657	95	6	ρ(in	ρ(in	NOUN
ejpam-5657	95	7	−a)−1b	−a)−1b	NOUN
ejpam-5657	95	8	)	)	PUNCT
ejpam-5657	95	9	<	<	X
ejpam-5657	95	10	1	1	NUM
ejpam-5657	95	11	by	by	ADP
ejpam-5657	95	12	using	use	VERB
ejpam-5657	95	13	inequality	inequality	NOUN
ejpam-5657	95	14	ρ((in	ρ((in	NUM
ejpam-5657	95	15	−a)−1b	−a)−1b	NOUN
ejpam-5657	95	16	)	)	PUNCT
ejpam-5657	95	17	)	)	PUNCT
ejpam-5657	95	18	≤	≤	NOUN
ejpam-5657	95	19	||(in	||(in	NOUN
ejpam-5657	95	20	−a)−1b)||2	−a)−1b)||2	PROPN
ejpam-5657	95	21	.	.	PUNCT
ejpam-5657	96	1	in	in	ADP
ejpam-5657	96	2	order	order	NOUN
ejpam-5657	96	3	to	to	PART
ejpam-5657	96	4	prove	prove	VERB
ejpam-5657	96	5	our	our	PRON
ejpam-5657	96	6	result	result	NOUN
ejpam-5657	96	7	,	,	PUNCT
ejpam-5657	96	8	we	we	PRON
ejpam-5657	96	9	assume	assume	VERB
ejpam-5657	96	10	that	that	SCONJ
ejpam-5657	96	11	inequality	inequality	NOUN
ejpam-5657	96	12	holds	hold	VERB
ejpam-5657	96	13	true	true	ADJ
ejpam-5657	96	14	for	for	ADP
ejpam-5657	96	15	strict	strict	ADJ
ejpam-5657	96	16	inequality	inequality	NOUN
ejpam-5657	96	17	,	,	PUNCT
ejpam-5657	96	18	that	that	ADV
ejpam-5657	96	19	is	be	AUX
ejpam-5657	96	20	,	,	PUNCT
ejpam-5657	96	21	ρ((in	ρ((in	NOUN
ejpam-5657	96	22	−a)−1b	−a)−1b	NOUN
ejpam-5657	96	23	)	)	PUNCT
ejpam-5657	96	24	)	)	PUNCT
ejpam-5657	97	1	<	<	X
ejpam-5657	97	2	||(in	||(in	X
ejpam-5657	97	3	−a)−1b||2	−a)−1b||2	NOUN
ejpam-5657	97	4	.	.	PUNCT
ejpam-5657	98	1	for	for	ADP
ejpam-5657	98	2	the	the	DET
ejpam-5657	98	3	matrix	matrix	NOUN
ejpam-5657	98	4	(	(	PUNCT
ejpam-5657	98	5	in	in	ADP
ejpam-5657	98	6	−a)−1b	−a)−1b	NOUN
ejpam-5657	98	7	,	,	PUNCT
ejpam-5657	98	8	there	there	PRON
ejpam-5657	98	9	exists	exist	VERB
ejpam-5657	98	10	unitary	unitary	ADJ
ejpam-5657	98	11	matrices	matrix	NOUN
ejpam-5657	98	12	u	u	NOUN
ejpam-5657	98	13	∈	∈	NOUN
ejpam-5657	98	14	cm	cm	NOUN
ejpam-5657	98	15	,	,	PUNCT
ejpam-5657	98	16	n	n	CCONJ
ejpam-5657	98	17	,	,	PUNCT
ejpam-5657	98	18	v	v	NOUN
ejpam-5657	98	19	∈	∈	NOUN
ejpam-5657	98	20	cm	cm	NOUN
ejpam-5657	98	21	,	,	PUNCT
ejpam-5657	98	22	n	n	PRON
ejpam-5657	98	23	such	such	ADJ
ejpam-5657	98	24	that	that	SCONJ
ejpam-5657	98	25	(	(	PUNCT
ejpam-5657	98	26	in	in	ADP
ejpam-5657	98	27	−a)−1b	−a)−1b	PUNCT
ejpam-5657	98	28	=	=	SYM
ejpam-5657	98	29	u	u	PROPN
ejpam-5657	98	30	(	(	PUNCT
ejpam-5657	98	31	σ1	σ1	NOUN
ejpam-5657	98	32	0	0	NUM
ejpam-5657	98	33	0	0	NUM
ejpam-5657	98	34	t	t	PROPN
ejpam-5657	98	35	)	)	PUNCT
ejpam-5657	98	36	v	v	ADP
ejpam-5657	98	37	h	h	NOUN
ejpam-5657	98	38	.	.	PUNCT
ejpam-5657	99	1	next	next	ADV
ejpam-5657	99	2	,	,	PUNCT
ejpam-5657	99	3	we	we	PRON
ejpam-5657	99	4	consider	consider	VERB
ejpam-5657	99	5	σ1	σ1	NOUN
ejpam-5657	99	6	and	and	CCONJ
ejpam-5657	99	7	θ1	θ1	NOUN
ejpam-5657	99	8	∈	∈	PROPN
ejpam-5657	99	9	cn,1	cn,1	PROPN
ejpam-5657	99	10	so	so	SCONJ
ejpam-5657	99	11	that	that	SCONJ
ejpam-5657	99	12	σ1	σ1	NOUN
ejpam-5657	99	13	=	=	PUNCT
ejpam-5657	99	14	∥(in	∥(in	ADP
ejpam-5657	99	15	−a)−1bθ1∥2	−a)−1bθ1∥2	NOUN
ejpam-5657	99	16	=	=	SYM
ejpam-5657	99	17	∥(in	∥(in	NOUN
ejpam-5657	99	18	−a)−1b∥2	−a)−1b∥2	ADJ
ejpam-5657	99	19	,	,	PUNCT
ejpam-5657	99	20	while	while	SCONJ
ejpam-5657	99	21	∥θ1∥2	∥θ1∥2	PROPN
ejpam-5657	99	22	=	=	SYM
ejpam-5657	99	23	1	1	NUM
ejpam-5657	99	24	.	.	PUNCT
ejpam-5657	99	25	further	far	ADV
ejpam-5657	99	26	,	,	PUNCT
ejpam-5657	99	27	we	we	PRON
ejpam-5657	99	28	let	let	VERB
ejpam-5657	99	29	u1	u1	NOUN
ejpam-5657	99	30	=	=	SYM
ejpam-5657	100	1	(	(	PUNCT
ejpam-5657	100	2	in−a)−1bθ1	in−a)−1bθ1	PROPN
ejpam-5657	100	3	σ1	σ1	PROPN
ejpam-5657	100	4	such	such	ADJ
ejpam-5657	100	5	that	that	SCONJ
ejpam-5657	100	6	∥u1∥2	∥u1∥2	ADJ
ejpam-5657	101	1	=	=	NOUN
ejpam-5657	102	1	∥(in	∥(in	ADP
ejpam-5657	102	2	−a)−1bθ1∥2	−a)−1bθ1∥2	NOUN
ejpam-5657	102	3	σ1	σ1	NOUN
ejpam-5657	102	4	=	=	PUNCT
ejpam-5657	102	5	∥(in	∥(in	ADP
ejpam-5657	102	6	−a)−1bθ1∥2	−a)−1bθ1∥2	NOUN
ejpam-5657	102	7	∥(in	∥(in	NOUN
ejpam-5657	102	8	−a)−1b∥2	−a)−1b∥2	NOUN
ejpam-5657	102	9	=	=	NOUN
ejpam-5657	102	10	1	1	X
ejpam-5657	102	11	.	.	X
ejpam-5657	103	1	consider	consider	VERB
ejpam-5657	103	2	that	that	DET
ejpam-5657	103	3	u2	u2	PROPN
ejpam-5657	103	4	∈	∈	PROPN
ejpam-5657	103	5	cm	cm	NOUN
ejpam-5657	103	6	,	,	PUNCT
ejpam-5657	103	7	m−1	m−1	PROPN
ejpam-5657	103	8	,	,	PUNCT
ejpam-5657	103	9	v2	v2	PROPN
ejpam-5657	103	10	∈	∈	PROPN
ejpam-5657	103	11	cn	cn	PROPN
ejpam-5657	103	12	,	,	PUNCT
ejpam-5657	103	13	n−1	n−1	PROPN
ejpam-5657	103	14	.	.	PUNCT
ejpam-5657	104	1	thus	thus	ADV
ejpam-5657	104	2	,	,	PUNCT
ejpam-5657	104	3	u	u	NOUN
ejpam-5657	104	4	and	and	CCONJ
ejpam-5657	104	5	v	v	NOUN
ejpam-5657	104	6	takes	take	VERB
ejpam-5657	104	7	the	the	DET
ejpam-5657	104	8	form	form	NOUN
ejpam-5657	104	9	u	u	NOUN
ejpam-5657	104	10	=	=	X
ejpam-5657	104	11	(	(	PUNCT
ejpam-5657	104	12	u1|u2	u1|u2	PROPN
ejpam-5657	104	13	)	)	PUNCT
ejpam-5657	104	14	,	,	PUNCT
ejpam-5657	104	15	and	and	CCONJ
ejpam-5657	104	16	v	v	X
ejpam-5657	104	17	=	=	SYM
ejpam-5657	104	18	(	(	PUNCT
ejpam-5657	104	19	v1|v2	v1|v2	X
ejpam-5657	104	20	)	)	PUNCT
ejpam-5657	104	21	with	with	ADP
ejpam-5657	104	22	u	u	NOUN
ejpam-5657	104	23	,	,	PUNCT
ejpam-5657	104	24	v	v	ADP
ejpam-5657	104	25	being	be	AUX
ejpam-5657	104	26	unitary	unitary	ADJ
ejpam-5657	104	27	matrices	matrix	NOUN
ejpam-5657	104	28	.	.	PUNCT
ejpam-5657	105	1	the	the	DET
ejpam-5657	105	2	matrix	matrix	NOUN
ejpam-5657	105	3	product	product	NOUN
ejpam-5657	105	4	uh(in−a)−1bv	uh(in−a)−1bv	NOUN
ejpam-5657	105	5	can	can	AUX
ejpam-5657	105	6	be	be	AUX
ejpam-5657	105	7	rewritten	rewrite	VERB
ejpam-5657	105	8	as	as	ADP
ejpam-5657	105	9	(	(	PUNCT
ejpam-5657	105	10	u1|u2)(in	u1|u2)(in	NUM
ejpam-5657	105	11	−a)−1b(v1|v2	−a)−1b(v1|v2	NOUN
ejpam-5657	105	12	)	)	PUNCT
ejpam-5657	105	13	=(	=(	NOUN
ejpam-5657	105	14	uh1	uh1	NOUN
ejpam-5657	105	15	(	(	PUNCT
ejpam-5657	105	16	in	in	ADP
ejpam-5657	105	17	−a)−1bθ1	−a)−1bθ1	NUM
ejpam-5657	105	18	uh1	uh1	NOUN
ejpam-5657	105	19	(	(	PUNCT
ejpam-5657	105	20	in	in	ADP
ejpam-5657	105	21	−a)−1bv2	−a)−1bv2	NUM
ejpam-5657	105	22	u2(in	u2(in	SYM
ejpam-5657	105	23	−a)−1bθ1	−a)−1bθ1	PUNCT
ejpam-5657	105	24	uh	uh	INTJ
ejpam-5657	105	25	2	2	NUM
ejpam-5657	105	26	(	(	PUNCT
ejpam-5657	105	27	in	in	ADP
ejpam-5657	105	28	−a)−1bv2	−a)−1bv2	NUM
ejpam-5657	105	29	)	)	PUNCT
ejpam-5657	105	30	=	=	SYM
ejpam-5657	106	1	(	(	PUNCT
ejpam-5657	106	2	σ1u	σ1u	NOUN
ejpam-5657	106	3	h	h	NOUN
ejpam-5657	106	4	1	1	NUM
ejpam-5657	106	5	u1	u1	NOUN
ejpam-5657	106	6	uh1	uh1	NOUN
ejpam-5657	106	7	(	(	PUNCT
ejpam-5657	106	8	in	in	ADP
ejpam-5657	106	9	−a)−1bv2	−a)−1bv2	NUM
ejpam-5657	106	10	σ1u	σ1u	NOUN
ejpam-5657	106	11	h	h	NOUN
ejpam-5657	106	12	2	2	NUM
ejpam-5657	106	13	u1	u1	NOUN
ejpam-5657	106	14	uh	uh	INTJ
ejpam-5657	106	15	2	2	NUM
ejpam-5657	106	16	(	(	PUNCT
ejpam-5657	106	17	in	in	ADP
ejpam-5657	106	18	−a)−1bv2	−a)−1bv2	NUM
ejpam-5657	106	19	)	)	PUNCT
ejpam-5657	106	20	=	=	SYM
ejpam-5657	107	1	(	(	PUNCT
ejpam-5657	107	2	σ1	σ1	NOUN
ejpam-5657	107	3	wh	wh	VERB
ejpam-5657	107	4	0	0	NUM
ejpam-5657	107	5	b	b	PROPN
ejpam-5657	107	6	)	)	PUNCT
ejpam-5657	107	7	,	,	PUNCT
ejpam-5657	107	8	where	where	SCONJ
ejpam-5657	107	9	uh1	uh1	NOUN
ejpam-5657	107	10	u1	u1	NOUN
ejpam-5657	107	11	=	=	SYM
ejpam-5657	107	12	1	1	NUM
ejpam-5657	107	13	,	,	PUNCT
ejpam-5657	107	14	uh	uh	INTJ
ejpam-5657	107	15	2	2	NUM
ejpam-5657	107	16	u1	u1	NOUN
ejpam-5657	107	17	=	=	SYM
ejpam-5657	107	18	0	0	NUM
ejpam-5657	107	19	,	,	PUNCT
ejpam-5657	107	20	w	w	NOUN
ejpam-5657	107	21	=	=	SYM
ejpam-5657	107	22	v	v	NOUN
ejpam-5657	107	23	h	h	NOUN
ejpam-5657	107	24	2	2	NUM
ejpam-5657	107	25	(	(	PUNCT
ejpam-5657	107	26	(	(	PUNCT
ejpam-5657	107	27	in	in	ADP
ejpam-5657	107	28	−a)−1b)hu1	−a)−1b)hu1	PROPN
ejpam-5657	107	29	,	,	PUNCT
ejpam-5657	107	30	and	and	CCONJ
ejpam-5657	107	31	c	c	X
ejpam-5657	107	32	=	=	SYM
ejpam-5657	107	33	uh	uh	INTJ
ejpam-5657	107	34	2	2	NUM
ejpam-5657	107	35	(	(	PUNCT
ejpam-5657	107	36	in	in	ADP
ejpam-5657	107	37	−a)−1bv2	−a)−1bv2	NOUN
ejpam-5657	107	38	.	.	PUNCT
ejpam-5657	108	1	let	let	VERB
ejpam-5657	108	2	w	w	NOUN
ejpam-5657	108	3	=	=	SYM
ejpam-5657	108	4	0	0	NUM
ejpam-5657	108	5	,	,	PUNCT
ejpam-5657	108	6	we	we	PRON
ejpam-5657	108	7	get	get	VERB
ejpam-5657	108	8	σ2	σ2	NOUN
ejpam-5657	108	9	1	1	NUM
ejpam-5657	108	10	=	=	SYM
ejpam-5657	109	1	∥(in−a)−1b∥22	∥(in−a)−1b∥22	PROPN
ejpam-5657	109	2	=	=	PUNCT
ejpam-5657	109	3	∥uh(in−a)−1bv	∥uh(in−a)−1bv	PROPN
ejpam-5657	109	4	∥22	∥22	PROPN
ejpam-5657	109	5	=	=	SYM
ejpam-5657	109	6	max	max	PROPN
ejpam-5657	109	7	x	x	X
ejpam-5657	109	8	̸=0	̸=0	ADV
ejpam-5657	109	9	∥uh(in	∥uh(in	ADP
ejpam-5657	109	10	−a)−1bv	−a)−1bv	NUM
ejpam-5657	109	11	x∥22	x∥22	PROPN
ejpam-5657	109	12	∥x∥22	∥x∥22	PROPN
ejpam-5657	110	1	=	=	NUM
ejpam-5657	110	2	max	max	PROPN
ejpam-5657	110	3	x	x	X
ejpam-5657	110	4	̸=0	̸=0	ADV
ejpam-5657	110	5	∥	∥	X
ejpam-5657	110	6	(	(	PUNCT
ejpam-5657	110	7	σ1	σ1	NOUN
ejpam-5657	110	8	uh	uh	INTJ
ejpam-5657	110	9	0	0	NUM
ejpam-5657	110	10	c	c	NOUN
ejpam-5657	110	11	)	)	PUNCT
ejpam-5657	111	1	x∥22	x∥22	PROPN
ejpam-5657	111	2	∥x∥22	∥x∥22	PROPN
ejpam-5657	111	3	.	.	PUNCT
ejpam-5657	112	1	take	take	VERB
ejpam-5657	112	2	x	x	PRON
ejpam-5657	112	3	−→	−→	NOUN
ejpam-5657	112	4	w	w	NOUN
ejpam-5657	112	5	,	,	PUNCT
ejpam-5657	112	6	we	we	PRON
ejpam-5657	112	7	have	have	VERB
ejpam-5657	112	8	that	that	DET
ejpam-5657	112	9	σ2	σ2	NOUN
ejpam-5657	112	10	1	1	NUM
ejpam-5657	112	11	>	>	X
ejpam-5657	112	12	(	(	PUNCT
ejpam-5657	112	13	σ2	σ2	NOUN
ejpam-5657	112	14	1	1	NUM
ejpam-5657	112	15	+	+	CCONJ
ejpam-5657	113	1	whw)2	whw)2	PROPN
ejpam-5657	113	2	(	(	PUNCT
ejpam-5657	113	3	σ2	σ2	NOUN
ejpam-5657	113	4	1	1	NUM
ejpam-5657	113	5	+	+	NUM
ejpam-5657	113	6	whw	whw	NOUN
ejpam-5657	113	7	)	)	PUNCT
ejpam-5657	114	1	=	=	SYM
ejpam-5657	114	2	σ2	σ2	NOUN
ejpam-5657	114	3	1	1	NUM
ejpam-5657	114	4	+	+	NUM
ejpam-5657	114	5	whw	whw	PROPN
ejpam-5657	114	6	.	.	PUNCT
ejpam-5657	115	1	thus	thus	ADV
ejpam-5657	115	2	,	,	PUNCT
ejpam-5657	115	3	this	this	PRON
ejpam-5657	115	4	yield	yield	NOUN
ejpam-5657	115	5	that	that	PRON
ejpam-5657	115	6	w	w	NOUN
ejpam-5657	115	7	=	=	SYM
ejpam-5657	115	8	0	0	NUM
ejpam-5657	115	9	,	,	PUNCT
ejpam-5657	115	10	and	and	CCONJ
ejpam-5657	115	11	uh(in	uh(in	PRON
ejpam-5657	115	12	−a)−1bv	−a)−1bv	NOUN
ejpam-5657	116	1	=	=	PUNCT
ejpam-5657	117	1	(	(	PUNCT
ejpam-5657	117	2	σ1	σ1	NOUN
ejpam-5657	117	3	0	0	NUM
ejpam-5657	117	4	0	0	NUM
ejpam-5657	117	5	c	c	NOUN
ejpam-5657	117	6	)	)	PUNCT
ejpam-5657	117	7	or	or	CCONJ
ejpam-5657	117	8	(	(	PUNCT
ejpam-5657	117	9	in	in	ADP
ejpam-5657	117	10	−a)−1b	−a)−1b	X
ejpam-5657	117	11	=	=	SYM
ejpam-5657	117	12	u	u	PROPN
ejpam-5657	117	13	(	(	PUNCT
ejpam-5657	117	14	σ1	σ1	NOUN
ejpam-5657	117	15	0	0	NUM
ejpam-5657	117	16	0	0	NUM
ejpam-5657	117	17	c	c	NOUN
ejpam-5657	117	18	)	)	PUNCT
ejpam-5657	117	19	v	v	NUM
ejpam-5657	117	20	h	h	NOUN
ejpam-5657	117	21	.	.	PUNCT
ejpam-5657	118	1	m.u.r	m.u.r	PROPN
ejpam-5657	118	2	et	et	PROPN
ejpam-5657	118	3	al	al	PROPN
ejpam-5657	118	4	.	.	PUNCT
ejpam-5657	118	5	/	/	SYM
ejpam-5657	118	6	eur	eur	PROPN
ejpam-5657	118	7	.	.	PUNCT
ejpam-5657	119	1	j.	j.	PROPN
ejpam-5657	119	2	pure	pure	PROPN
ejpam-5657	119	3	appl	appl	PROPN
ejpam-5657	119	4	.	.	PROPN
ejpam-5657	119	5	math	math	PROPN
ejpam-5657	119	6	,	,	PUNCT
ejpam-5657	119	7	18	18	NUM
ejpam-5657	119	8	(	(	PUNCT
ejpam-5657	119	9	1	1	NUM
ejpam-5657	119	10	)	)	PUNCT
ejpam-5657	119	11	(	(	PUNCT
ejpam-5657	119	12	2025	2025	NUM
ejpam-5657	119	13	)	)	PUNCT
ejpam-5657	119	14	,	,	PUNCT
ejpam-5657	119	15	5657	5657	NUM
ejpam-5657	119	16	6	6	NUM
ejpam-5657	119	17	of	of	ADP
ejpam-5657	119	18	17	17	NUM
ejpam-5657	119	19	we	we	PRON
ejpam-5657	119	20	see	see	VERB
ejpam-5657	119	21	that	that	PRON
ejpam-5657	119	22	µs((in	µs((in	PUNCT
ejpam-5657	119	23	−a)−1b	−a)−1b	X
ejpam-5657	119	24	)	)	PUNCT
ejpam-5657	119	25	<	<	X
ejpam-5657	119	26	σ1((in	σ1((in	NOUN
ejpam-5657	119	27	−a)−1b	−a)−1b	NOUN
ejpam-5657	119	28	)	)	PUNCT
ejpam-5657	120	1	,	,	PUNCT
ejpam-5657	120	2	we	we	PRON
ejpam-5657	120	3	have	have	VERB
ejpam-5657	120	4	that	that	PRON
ejpam-5657	120	5	(	(	PUNCT
ejpam-5657	120	6	in	in	ADP
ejpam-5657	120	7	−a)−1b	−a)−1b	X
ejpam-5657	120	8	:	:	PUNCT
ejpam-5657	120	9	=	=	SYM
ejpam-5657	120	10	s−1(in	s−1(in	NOUN
ejpam-5657	120	11	−a)−1b	−a)−1b	NOUN
ejpam-5657	120	12	=	=	PUNCT
ejpam-5657	120	13	(	(	PUNCT
ejpam-5657	120	14	(	(	PUNCT
ejpam-5657	120	15	(	(	PUNCT
ejpam-5657	120	16	in	in	ADP
ejpam-5657	120	17	−a)−1b)11	−a)−1b)11	PROPN
ejpam-5657	120	18	(	(	PUNCT
ejpam-5657	120	19	(	(	PUNCT
ejpam-5657	120	20	in	in	ADP
ejpam-5657	120	21	−a)−1b)12	−a)−1b)12	PROPN
ejpam-5657	120	22	1	1	NUM
ejpam-5657	120	23	ν	ν	NOUN
ejpam-5657	120	24	(	(	PUNCT
ejpam-5657	120	25	(	(	PUNCT
ejpam-5657	120	26	in	in	ADP
ejpam-5657	120	27	−a)−1b)21	−a)−1b)21	PROPN
ejpam-5657	120	28	1	1	NUM
ejpam-5657	120	29	ν	ν	NOUN
ejpam-5657	120	30	(	(	PUNCT
ejpam-5657	120	31	(	(	PUNCT
ejpam-5657	120	32	in	in	ADP
ejpam-5657	120	33	−a)−1b)22	−a)−1b)22	PROPN
ejpam-5657	120	34	)	)	PUNCT
ejpam-5657	120	35	.	.	PUNCT
ejpam-5657	121	1	furthermore	furthermore	ADV
ejpam-5657	121	2	,	,	PUNCT
ejpam-5657	121	3	(	(	PUNCT
ejpam-5657	121	4	i	i	PRON
ejpam-5657	121	5	(	(	PUNCT
ejpam-5657	121	6	in	in	ADP
ejpam-5657	121	7	−a)−1b	−a)−1b	X
ejpam-5657	121	8	(	(	PUNCT
ejpam-5657	121	9	(	(	PUNCT
ejpam-5657	121	10	in	in	ADP
ejpam-5657	121	11	−a)−1b)h	−a)−1b)h	PROPN
ejpam-5657	121	12	i	i	PROPN
ejpam-5657	121	13	)	)	PUNCT
ejpam-5657	121	14	>	>	X
ejpam-5657	121	15	0	0	PUNCT
ejpam-5657	121	16	⇐	⇐	ADJ
ejpam-5657	121	17	⇒	⇒	NOUN
ejpam-5657	121	18	i	i	PRON
ejpam-5657	121	19	−	−	PROPN
ejpam-5657	121	20	(	(	PUNCT
ejpam-5657	121	21	in	in	ADP
ejpam-5657	121	22	−a)−1bi−1((in	−a)−1bi−1((in	NUM
ejpam-5657	121	23	−a)−1b)h	−a)−1b)h	X
ejpam-5657	121	24	>	>	X
ejpam-5657	121	25	0	0	NUM
ejpam-5657	121	26	.	.	PUNCT
ejpam-5657	121	27	from	from	ADP
ejpam-5657	121	28	this	this	PRON
ejpam-5657	121	29	we	we	PRON
ejpam-5657	121	30	follow	follow	VERB
ejpam-5657	121	31	that	that	PRON
ejpam-5657	121	32	λi(i	λi(i	PRON
ejpam-5657	121	33	−	−	PROPN
ejpam-5657	121	34	(	(	PUNCT
ejpam-5657	121	35	in	in	ADP
ejpam-5657	121	36	−a)−1b((in	−a)−1b((in	NOUN
ejpam-5657	121	37	−a)−1b)h(ν	−a)−1b)h(ν	NOUN
ejpam-5657	121	38	)	)	PUNCT
ejpam-5657	121	39	)	)	PUNCT
ejpam-5657	121	40	>	>	X
ejpam-5657	122	1	0	0	NUM
ejpam-5657	122	2	,	,	PUNCT
ejpam-5657	122	3	∀i	∀i	NOUN
ejpam-5657	122	4	or	or	CCONJ
ejpam-5657	122	5	1−	1−	NUM
ejpam-5657	122	6	λi((in	λi((in	PUNCT
ejpam-5657	122	7	−a)−1b((in	−a)−1b((in	NOUN
ejpam-5657	122	8	−a)−1b)h(ν	−a)−1b)h(ν	NOUN
ejpam-5657	122	9	)	)	PUNCT
ejpam-5657	122	10	>	>	X
ejpam-5657	122	11	0,∀i	0,∀i	PUNCT
ejpam-5657	122	12	or	or	CCONJ
ejpam-5657	122	13	λi((in	λi((in	ADP
ejpam-5657	122	14	−a)−1b((in	−a)−1b((in	NOUN
ejpam-5657	122	15	−a)−1b)h(ν	−a)−1b)h(ν	NOUN
ejpam-5657	122	16	)	)	PUNCT
ejpam-5657	122	17	)	)	PUNCT
ejpam-5657	123	1	<	<	X
ejpam-5657	123	2	1	1	NUM
ejpam-5657	123	3	,	,	PUNCT
ejpam-5657	123	4	∀i	∀i	NOUN
ejpam-5657	123	5	.	.	PUNCT
ejpam-5657	124	1	thus	thus	ADV
ejpam-5657	124	2	finally	finally	ADV
ejpam-5657	124	3	,	,	PUNCT
ejpam-5657	124	4	we	we	PRON
ejpam-5657	124	5	get	get	VERB
ejpam-5657	124	6	σ1((in	σ1((in	NOUN
ejpam-5657	124	7	−a)−1b	−a)−1b	NOUN
ejpam-5657	124	8	)	)	PUNCT
ejpam-5657	124	9	<	<	X
ejpam-5657	124	10	1	1	NUM
ejpam-5657	124	11	⇒	⇒	PROPN
ejpam-5657	124	12	||(in	||(in	NOUN
ejpam-5657	124	13	−a)−1b||2	−a)−1b||2	NOUN
ejpam-5657	124	14	<	<	X
ejpam-5657	124	15	1	1	NUM
ejpam-5657	124	16	⇒	⇒	NOUN
ejpam-5657	124	17	ρ((in	ρ((in	NUM
ejpam-5657	124	18	−a)−1b	−a)−1b	NOUN
ejpam-5657	124	19	)	)	PUNCT
ejpam-5657	124	20	)	)	PUNCT
ejpam-5657	124	21	<	<	X
ejpam-5657	125	1	1	1	X
ejpam-5657	125	2	.	.	PUNCT
ejpam-5657	125	3	theorem	theorem	NOUN
ejpam-5657	125	4	4	4	NUM
ejpam-5657	125	5	gives	give	VERB
ejpam-5657	125	6	the	the	DET
ejpam-5657	125	7	dynamic	dynamic	ADJ
ejpam-5657	125	8	d	d	NOUN
ejpam-5657	125	9	-	-	NOUN
ejpam-5657	125	10	stability	stability	NOUN
ejpam-5657	125	11	of	of	ADP
ejpam-5657	125	12	dynamical	dynamical	ADJ
ejpam-5657	125	13	model	model	NOUN
ejpam-5657	125	14	yt	yt	PROPN
ejpam-5657	126	1	=	=	PUNCT
ejpam-5657	126	2	(	(	PUNCT
ejpam-5657	126	3	in−a)−1b+ext	in−a)−1b+ext	PROPN
ejpam-5657	126	4	.	.	PUNCT
ejpam-5657	127	1	we	we	PRON
ejpam-5657	127	2	make	make	VERB
ejpam-5657	127	3	use	use	NOUN
ejpam-5657	127	4	of	of	ADP
ejpam-5657	127	5	results	result	NOUN
ejpam-5657	127	6	on	on	ADP
ejpam-5657	127	7	interconnection	interconnection	NOUN
ejpam-5657	127	8	between	between	ADP
ejpam-5657	127	9	structured	structure	VERB
ejpam-5657	127	10	singular	singular	ADJ
ejpam-5657	127	11	value	value	NOUN
ejpam-5657	127	12	,	,	PUNCT
ejpam-5657	127	13	and	and	CCONJ
ejpam-5657	127	14	dstability	dstability	NOUN
ejpam-5657	127	15	.	.	PUNCT
ejpam-5657	128	1	theorem	theorem	VERB
ejpam-5657	128	2	4	4	NUM
ejpam-5657	128	3	.	.	PUNCT
ejpam-5657	129	1	let	let	VERB
ejpam-5657	129	2	the	the	DET
ejpam-5657	129	3	dynamical	dynamical	ADJ
ejpam-5657	129	4	system	system	NOUN
ejpam-5657	129	5	be	be	AUX
ejpam-5657	129	6	yt	yt	NOUN
ejpam-5657	129	7	=	=	PUNCT
ejpam-5657	129	8	(	(	PUNCT
ejpam-5657	129	9	in−a)−1b+ext	in−a)−1b+ext	PROPN
ejpam-5657	129	10	.	.	PUNCT
ejpam-5657	130	1	then	then	ADV
ejpam-5657	130	2	,	,	PUNCT
ejpam-5657	130	3	for	for	ADP
ejpam-5657	130	4	dynamic	dynamic	ADJ
ejpam-5657	130	5	dstability	dstability	NOUN
ejpam-5657	130	6	the	the	DET
ejpam-5657	130	7	matrix	matrix	NOUN
ejpam-5657	130	8	(	(	PUNCT
ejpam-5657	130	9	in−a)−1b	in−a)−1b	ADJ
ejpam-5657	130	10	is	be	AUX
ejpam-5657	130	11	d	d	ADJ
ejpam-5657	130	12	-	-	ADJ
ejpam-5657	130	13	stable	stable	ADJ
ejpam-5657	130	14	iff	iff	PROPN
ejpam-5657	130	15	(	(	PUNCT
ejpam-5657	130	16	in−a)−1b	in−a)−1b	ADJ
ejpam-5657	130	17	is	be	AUX
ejpam-5657	130	18	stable	stable	ADJ
ejpam-5657	130	19	,	,	PUNCT
ejpam-5657	130	20	and	and	CCONJ
ejpam-5657	130	21	0	0	NUM
ejpam-5657	130	22	≤	≤	NUM
ejpam-5657	130	23	µ∆(m	µ∆(m	NOUN
ejpam-5657	130	24	)	)	PUNCT
ejpam-5657	130	25	<	<	X
ejpam-5657	130	26	1	1	NUM
ejpam-5657	130	27	,	,	PUNCT
ejpam-5657	130	28	where	where	SCONJ
ejpam-5657	130	29	m	m	VERB
ejpam-5657	130	30	:	:	PUNCT
ejpam-5657	130	31	=	=	SYM
ejpam-5657	130	32	(	(	PUNCT
ejpam-5657	130	33	iin	iin	NOUN
ejpam-5657	130	34	+	+	CCONJ
ejpam-5657	130	35	(	(	PUNCT
ejpam-5657	130	36	in	in	ADP
ejpam-5657	130	37	−a)−1b	−a)−1b	NOUN
ejpam-5657	130	38	)	)	PUNCT
ejpam-5657	130	39	−1	−1	NOUN
ejpam-5657	130	40	(	(	PUNCT
ejpam-5657	130	41	iin	iin	PROPN
ejpam-5657	130	42	−	−	PROPN
ejpam-5657	130	43	(	(	PUNCT
ejpam-5657	130	44	in	in	ADP
ejpam-5657	130	45	−a)−1b	−a)−1b	X
ejpam-5657	130	46	)	)	PUNCT
ejpam-5657	130	47	.	.	PUNCT
ejpam-5657	131	1	proof	proof	NOUN
ejpam-5657	131	2	.	.	PUNCT
ejpam-5657	132	1	the	the	DET
ejpam-5657	132	2	matrix	matrix	NOUN
ejpam-5657	132	3	(	(	PUNCT
ejpam-5657	132	4	in	in	ADP
ejpam-5657	132	5	−	−	PROPN
ejpam-5657	132	6	a)−1b	a)−1b	PROPN
ejpam-5657	132	7	is	be	AUX
ejpam-5657	132	8	d	d	ADJ
ejpam-5657	132	9	-	-	ADJ
ejpam-5657	132	10	stable	stable	ADJ
ejpam-5657	132	11	iff	iff	PROPN
ejpam-5657	132	12	0	0	NUM
ejpam-5657	132	13	≤	≤	NUM
ejpam-5657	132	14	µ∆(m	µ∆(m	NOUN
ejpam-5657	132	15	)	)	PUNCT
ejpam-5657	132	16	<	<	X
ejpam-5657	132	17	1	1	X
ejpam-5657	132	18	.	.	X
ejpam-5657	132	19	assume	assume	VERB
ejpam-5657	132	20	that	that	SCONJ
ejpam-5657	132	21	matrix	matrix	NOUN
ejpam-5657	132	22	m	m	VERB
ejpam-5657	132	23	is	be	AUX
ejpam-5657	132	24	d	d	ADJ
ejpam-5657	132	25	-	-	ADJ
ejpam-5657	132	26	stable	stable	ADJ
ejpam-5657	132	27	,	,	PUNCT
ejpam-5657	132	28	means	mean	VERB
ejpam-5657	132	29	that	that	SCONJ
ejpam-5657	132	30	,	,	PUNCT
ejpam-5657	132	31	λi	λi	ADP
ejpam-5657	132	32	(	(	PUNCT
ejpam-5657	132	33	in	in	ADP
ejpam-5657	132	34	−	−	PROPN
ejpam-5657	132	35	(	(	PUNCT
ejpam-5657	132	36	in	in	ADP
ejpam-5657	132	37	−a)−1b	−a)−1b	X
ejpam-5657	132	38	+	+	CCONJ
ejpam-5657	132	39	ip	ip	NOUN
ejpam-5657	132	40	)	)	PUNCT
ejpam-5657	132	41	̸=	̸=	PROPN
ejpam-5657	132	42	0	0	NUM
ejpam-5657	132	43	,	,	PUNCT
ejpam-5657	132	44	∀	∀	PUNCT
ejpam-5657	133	1	i	i	NOUN
ejpam-5657	133	2	=	=	NOUN
ejpam-5657	133	3	1	1	NUM
ejpam-5657	133	4	:	:	PUNCT
ejpam-5657	133	5	n	n	CCONJ
ejpam-5657	133	6	,	,	PUNCT
ejpam-5657	133	7	and	and	CCONJ
ejpam-5657	133	8	for	for	ADP
ejpam-5657	133	9	some	some	DET
ejpam-5657	133	10	p	p	NOUN
ejpam-5657	133	11	=	=	SYM
ejpam-5657	133	12	diag(re(pii	diag(re(pii	NOUN
ejpam-5657	133	13	)	)	PUNCT
ejpam-5657	133	14	)	)	PUNCT
ejpam-5657	134	1	>	>	X
ejpam-5657	134	2	0	0	NUM
ejpam-5657	134	3	,	,	PUNCT
ejpam-5657	134	4	∀	∀	VERB
ejpam-5657	135	1	i	i	NOUN
ejpam-5657	135	2	=	=	NOUN
ejpam-5657	135	3	1	1	X
ejpam-5657	135	4	:	:	PUNCT
ejpam-5657	135	5	n.	n.	NOUN
ejpam-5657	135	6	in	in	ADP
ejpam-5657	135	7	order	order	NOUN
ejpam-5657	135	8	to	to	PART
ejpam-5657	135	9	prove	prove	VERB
ejpam-5657	135	10	that	that	SCONJ
ejpam-5657	135	11	(	(	PUNCT
ejpam-5657	135	12	in	in	ADP
ejpam-5657	135	13	−	−	PROPN
ejpam-5657	135	14	a)−1b	a)−1b	PROPN
ejpam-5657	135	15	is	be	AUX
ejpam-5657	135	16	d	d	ADJ
ejpam-5657	135	17	-	-	ADJ
ejpam-5657	135	18	stable	stable	ADJ
ejpam-5657	135	19	matrix	matrix	NOUN
ejpam-5657	135	20	iff	iff	NOUN
ejpam-5657	135	21	0	0	NUM
ejpam-5657	135	22	≤	≤	NUM
ejpam-5657	135	23	µ∆(m	µ∆(m	NOUN
ejpam-5657	135	24	)	)	PUNCT
ejpam-5657	135	25	<	<	X
ejpam-5657	135	26	1	1	NUM
ejpam-5657	135	27	,	,	PUNCT
ejpam-5657	135	28	we	we	PRON
ejpam-5657	135	29	let	let	VERB
ejpam-5657	135	30	(	(	PUNCT
ejpam-5657	135	31	in	in	ADP
ejpam-5657	135	32	−a)−1b	−a)−1b	X
ejpam-5657	135	33	is	be	AUX
ejpam-5657	135	34	d	d	ADJ
ejpam-5657	135	35	-	-	ADJ
ejpam-5657	135	36	stable	stable	ADJ
ejpam-5657	135	37	matrix	matrix	NOUN
ejpam-5657	135	38	,	,	PUNCT
ejpam-5657	135	39	that	that	ADV
ejpam-5657	135	40	is	is	ADV
ejpam-5657	135	41	,	,	PUNCT
ejpam-5657	135	42	λi	λi	ADP
ejpam-5657	135	43	(	(	PUNCT
ejpam-5657	135	44	(	(	PUNCT
ejpam-5657	135	45	in	in	ADP
ejpam-5657	135	46	−a)−1b	−a)−1b	X
ejpam-5657	135	47	+	+	CCONJ
ejpam-5657	135	48	ip	ip	NOUN
ejpam-5657	135	49	)	)	PUNCT
ejpam-5657	135	50	̸=	̸=	PROPN
ejpam-5657	135	51	0	0	NUM
ejpam-5657	135	52	,	,	PUNCT
ejpam-5657	135	53	∀	∀	PUNCT
ejpam-5657	136	1	i	i	NOUN
ejpam-5657	136	2	=	=	NOUN
ejpam-5657	136	3	1	1	X
ejpam-5657	136	4	:	:	PUNCT
ejpam-5657	136	5	n.	n.	NOUN
ejpam-5657	136	6	consider	consider	VERB
ejpam-5657	136	7	a	a	DET
ejpam-5657	136	8	block	block	NOUN
ejpam-5657	136	9	-	-	PUNCT
ejpam-5657	136	10	diagonal	diagonal	ADJ
ejpam-5657	136	11	matrix	matrix	NOUN
ejpam-5657	136	12	∆̂	∆̂	NOUN
ejpam-5657	137	1	=	=	SYM
ejpam-5657	137	2	(	(	PUNCT
ejpam-5657	137	3	iin	iin	NOUN
ejpam-5657	137	4	−	−	PROPN
ejpam-5657	137	5	p	p	NOUN
ejpam-5657	137	6	)	)	PUNCT
ejpam-5657	137	7	(	(	PUNCT
ejpam-5657	137	8	iin	iin	NOUN
ejpam-5657	137	9	+	+	CCONJ
ejpam-5657	137	10	p	p	NOUN
ejpam-5657	137	11	)	)	PUNCT
ejpam-5657	137	12	−1	−1	NOUN
ejpam-5657	137	13	,	,	PUNCT
ejpam-5657	137	14	∆̂	∆̂	PUNCT
ejpam-5657	137	15	∈	∈	PROPN
ejpam-5657	138	1	∆.	∆.	X
ejpam-5657	138	2	this	this	PRON
ejpam-5657	138	3	allow	allow	VERB
ejpam-5657	138	4	us	we	PRON
ejpam-5657	138	5	p	p	NOUN
ejpam-5657	138	6	=	=	X
ejpam-5657	138	7	(	(	PUNCT
ejpam-5657	138	8	iin+∆̂)−1(iin−∆̂	iin+∆̂)−1(iin−∆̂	NOUN
ejpam-5657	138	9	)	)	PUNCT
ejpam-5657	138	10	is	be	AUX
ejpam-5657	138	11	a	a	DET
ejpam-5657	138	12	positive	positive	ADJ
ejpam-5657	138	13	diagonal	diagonal	ADJ
ejpam-5657	138	14	matrix	matrix	NOUN
ejpam-5657	138	15	if	if	SCONJ
ejpam-5657	138	16	∆̂	∆̂	PUNCT
ejpam-5657	138	17	∈	∈	PROPN
ejpam-5657	138	18	∆.	∆.	X
ejpam-5657	138	19	since	since	ADV
ejpam-5657	138	20	,	,	PUNCT
ejpam-5657	138	21	λi	λi	X
ejpam-5657	138	22	(	(	PUNCT
ejpam-5657	138	23	(	(	PUNCT
ejpam-5657	138	24	in	in	ADP
ejpam-5657	138	25	−a)−1b	−a)−1b	X
ejpam-5657	138	26	+	+	CCONJ
ejpam-5657	138	27	ip	ip	NOUN
ejpam-5657	138	28	)	)	PUNCT
ejpam-5657	138	29	̸=	̸=	PROPN
ejpam-5657	138	30	0	0	NUM
ejpam-5657	138	31	,	,	PUNCT
ejpam-5657	138	32	∀	∀	PUNCT
ejpam-5657	139	1	i	i	NOUN
ejpam-5657	139	2	=	=	NOUN
ejpam-5657	139	3	1	1	X
ejpam-5657	139	4	:	:	PUNCT
ejpam-5657	139	5	n.	n.	PROPN
ejpam-5657	139	6	thus	thus	ADV
ejpam-5657	139	7	,	,	PUNCT
ejpam-5657	139	8	it	it	PRON
ejpam-5657	139	9	shows	show	VERB
ejpam-5657	139	10	that	that	SCONJ
ejpam-5657	139	11	λi	λi	ADP
ejpam-5657	139	12	(	(	PUNCT
ejpam-5657	139	13	(	(	PUNCT
ejpam-5657	139	14	in	in	ADP
ejpam-5657	139	15	−a)−1b	−a)−1b	NOUN
ejpam-5657	140	1	+	+	CCONJ
ejpam-5657	140	2	i(iin	i(iin	NOUN
ejpam-5657	140	3	+	+	NOUN
ejpam-5657	140	4	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5657	140	5	−	−	NUM
ejpam-5657	140	6	∆̂	∆̂	NOUN
ejpam-5657	140	7	)	)	PUNCT
ejpam-5657	140	8	)	)	PUNCT
ejpam-5657	141	1	̸=	̸=	PROPN
ejpam-5657	141	2	0	0	NUM
ejpam-5657	141	3	,	,	PUNCT
ejpam-5657	141	4	∀	∀	PUNCT
ejpam-5657	142	1	i	i	NOUN
ejpam-5657	142	2	=	=	NOUN
ejpam-5657	142	3	1	1	NUM
ejpam-5657	142	4	:	:	SYM
ejpam-5657	142	5	n	n	CCONJ
ejpam-5657	142	6	,	,	PUNCT
ejpam-5657	142	7	∀	∀	X
ejpam-5657	142	8	∆̂	∆̂	NOUN
ejpam-5657	143	1	∈	∈	PROPN
ejpam-5657	144	1	∆.	∆.	INTJ
ejpam-5657	144	2	m.u.r	m.u.r	NOUN
ejpam-5657	144	3	et	et	PROPN
ejpam-5657	144	4	al	al	PROPN
ejpam-5657	144	5	.	.	PUNCT
ejpam-5657	144	6	/	/	SYM
ejpam-5657	144	7	eur	eur	PROPN
ejpam-5657	144	8	.	.	PUNCT
ejpam-5657	145	1	j.	j.	PROPN
ejpam-5657	145	2	pure	pure	PROPN
ejpam-5657	145	3	appl	appl	PROPN
ejpam-5657	145	4	.	.	PROPN
ejpam-5657	145	5	math	math	PROPN
ejpam-5657	145	6	,	,	PUNCT
ejpam-5657	145	7	18	18	NUM
ejpam-5657	145	8	(	(	PUNCT
ejpam-5657	145	9	1	1	NUM
ejpam-5657	145	10	)	)	PUNCT
ejpam-5657	145	11	(	(	PUNCT
ejpam-5657	145	12	2025	2025	NUM
ejpam-5657	145	13	)	)	PUNCT
ejpam-5657	145	14	,	,	PUNCT
ejpam-5657	145	15	5657	5657	NUM
ejpam-5657	145	16	7	7	NUM
ejpam-5657	145	17	of	of	ADP
ejpam-5657	145	18	17	17	NUM
ejpam-5657	145	19	as	as	ADP
ejpam-5657	145	20	,	,	PUNCT
ejpam-5657	145	21	the	the	DET
ejpam-5657	145	22	rank	rank	NOUN
ejpam-5657	145	23	of	of	ADP
ejpam-5657	145	24	matrix	matrix	NOUN
ejpam-5657	145	25	(	(	PUNCT
ejpam-5657	145	26	(	(	PUNCT
ejpam-5657	145	27	in	in	ADP
ejpam-5657	145	28	−a)−1b	−a)−1b	NOUN
ejpam-5657	145	29	+	+	CCONJ
ejpam-5657	145	30	i(iin	i(iin	NOUN
ejpam-5657	145	31	+	+	NOUN
ejpam-5657	145	32	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5657	145	33	−	−	NUM
ejpam-5657	145	34	∆̂	∆̂	NOUN
ejpam-5657	145	35	)	)	PUNCT
ejpam-5657	145	36	)	)	PUNCT
ejpam-5657	145	37	is	be	AUX
ejpam-5657	145	38	exactly	exactly	ADV
ejpam-5657	145	39	equal	equal	ADJ
ejpam-5657	145	40	to	to	ADP
ejpam-5657	145	41	the	the	DET
ejpam-5657	145	42	rank	rank	NOUN
ejpam-5657	145	43	of	of	ADP
ejpam-5657	145	44	matrix	matrix	NOUN
ejpam-5657	145	45	(	(	PUNCT
ejpam-5657	145	46	(	(	PUNCT
ejpam-5657	145	47	iin	iin	NOUN
ejpam-5657	145	48	+	+	CCONJ
ejpam-5657	145	49	(	(	PUNCT
ejpam-5657	145	50	in	in	ADP
ejpam-5657	145	51	−a)−1b)−	−a)−1b)−	PROPN
ejpam-5657	145	52	(	(	PUNCT
ejpam-5657	145	53	iin	iin	PROPN
ejpam-5657	145	54	−	−	PROPN
ejpam-5657	145	55	(	(	PUNCT
ejpam-5657	145	56	in	in	ADP
ejpam-5657	145	57	−a)−1b)∆̂	−a)−1b)∆̂	PROPN
ejpam-5657	145	58	)	)	PUNCT
ejpam-5657	145	59	,	,	PUNCT
ejpam-5657	145	60	∀	∀	X
ejpam-5657	145	61	∆̂	∆̂	NOUN
ejpam-5657	146	1	∈	∈	PROPN
ejpam-5657	146	2	∆.	∆.	X
ejpam-5657	146	3	also	also	ADV
ejpam-5657	146	4	,	,	PUNCT
ejpam-5657	146	5	(	(	PUNCT
ejpam-5657	146	6	(	(	PUNCT
ejpam-5657	146	7	in	in	ADP
ejpam-5657	146	8	−a)−1b	−a)−1b	NOUN
ejpam-5657	146	9	+	+	CCONJ
ejpam-5657	146	10	i(iin	i(iin	NOUN
ejpam-5657	146	11	+	+	NOUN
ejpam-5657	146	12	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5657	146	13	−	−	NUM
ejpam-5657	146	14	∆̂	∆̂	NOUN
ejpam-5657	146	15	)	)	PUNCT
ejpam-5657	146	16	)	)	PUNCT
ejpam-5657	146	17	∼	∼	NOUN
ejpam-5657	146	18	(	(	PUNCT
ejpam-5657	146	19	(	(	PUNCT
ejpam-5657	146	20	iin	iin	NOUN
ejpam-5657	146	21	+	+	CCONJ
ejpam-5657	146	22	(	(	PUNCT
ejpam-5657	146	23	in	in	ADP
ejpam-5657	146	24	−a)−1b)−	−a)−1b)−	PROPN
ejpam-5657	146	25	(	(	PUNCT
ejpam-5657	146	26	iin	iin	PROPN
ejpam-5657	146	27	−	−	PROPN
ejpam-5657	146	28	(	(	PUNCT
ejpam-5657	146	29	in	in	ADP
ejpam-5657	146	30	−a)−1b)∆̂	−a)−1b)∆̂	PROPN
ejpam-5657	146	31	)	)	PUNCT
ejpam-5657	146	32	,	,	PUNCT
ejpam-5657	146	33	∀	∀	X
ejpam-5657	146	34	∆̂	∆̂	NOUN
ejpam-5657	147	1	∈	∈	PROPN
ejpam-5657	147	2	∆.	∆.	X
ejpam-5657	147	3	furthermore	furthermore	ADV
ejpam-5657	147	4	,	,	PUNCT
ejpam-5657	147	5	λi	λi	X
ejpam-5657	147	6	(	(	PUNCT
ejpam-5657	147	7	in	in	ADP
ejpam-5657	147	8	−	−	PROPN
ejpam-5657	147	9	(	(	PUNCT
ejpam-5657	147	10	iin	iin	NOUN
ejpam-5657	147	11	+	+	CCONJ
ejpam-5657	147	12	(	(	PUNCT
ejpam-5657	147	13	in	in	ADP
ejpam-5657	147	14	−a)−1b)−1(iin	−a)−1b)−1(iin	NOUN
ejpam-5657	147	15	−	−	PROPN
ejpam-5657	148	1	(	(	PUNCT
ejpam-5657	148	2	in	in	ADP
ejpam-5657	148	3	−a)−1b)∆̂	−a)−1b)∆̂	NOUN
ejpam-5657	148	4	)	)	PUNCT
ejpam-5657	148	5	̸=	̸=	PROPN
ejpam-5657	148	6	0	0	NUM
ejpam-5657	148	7	,	,	PUNCT
ejpam-5657	148	8	∀∆̂	∀∆̂	PROPN
ejpam-5657	148	9	∈	∈	PROPN
ejpam-5657	149	1	∆.	∆.	X
ejpam-5657	149	2	this	this	PRON
ejpam-5657	149	3	is	be	AUX
ejpam-5657	149	4	a	a	DET
ejpam-5657	149	5	necessary	necessary	ADJ
ejpam-5657	149	6	condition	condition	NOUN
ejpam-5657	149	7	that	that	SCONJ
ejpam-5657	149	8	0	0	NUM
ejpam-5657	149	9	≤	≤	NUM
ejpam-5657	149	10	µ∆(m	µ∆(m	NOUN
ejpam-5657	149	11	)	)	PUNCT
ejpam-5657	149	12	<	<	X
ejpam-5657	150	1	1	1	X
ejpam-5657	150	2	.	.	PUNCT
ejpam-5657	150	3	since	since	ADV
ejpam-5657	150	4	,	,	PUNCT
ejpam-5657	150	5	our	our	PRON
ejpam-5657	150	6	aim	aim	NOUN
ejpam-5657	150	7	is	be	AUX
ejpam-5657	150	8	to	to	PART
ejpam-5657	150	9	show	show	VERB
ejpam-5657	150	10	that	that	SCONJ
ejpam-5657	150	11	(	(	PUNCT
ejpam-5657	150	12	in	in	ADP
ejpam-5657	150	13	−a)−1b	−a)−1b	INTJ
ejpam-5657	150	14	is	be	AUX
ejpam-5657	150	15	d	d	ADJ
ejpam-5657	150	16	-	-	ADJ
ejpam-5657	150	17	stable	stable	ADJ
ejpam-5657	150	18	matrix	matrix	NOUN
ejpam-5657	150	19	.	.	PUNCT
ejpam-5657	151	1	this	this	PRON
ejpam-5657	151	2	means	mean	VERB
ejpam-5657	151	3	that	that	SCONJ
ejpam-5657	151	4	we	we	PRON
ejpam-5657	151	5	need	need	VERB
ejpam-5657	151	6	to	to	PART
ejpam-5657	151	7	show	show	VERB
ejpam-5657	151	8	λi	λi	INTJ
ejpam-5657	151	9	(	(	PUNCT
ejpam-5657	151	10	(	(	PUNCT
ejpam-5657	151	11	in	in	ADP
ejpam-5657	151	12	−a)−1b	−a)−1b	X
ejpam-5657	151	13	+	+	CCONJ
ejpam-5657	151	14	ip	ip	NOUN
ejpam-5657	151	15	)	)	PUNCT
ejpam-5657	151	16	̸=	̸=	PROPN
ejpam-5657	151	17	0	0	NUM
ejpam-5657	151	18	,	,	PUNCT
ejpam-5657	151	19	∀	∀	PUNCT
ejpam-5657	152	1	i	i	NOUN
ejpam-5657	152	2	=	=	NOUN
ejpam-5657	152	3	1	1	X
ejpam-5657	152	4	:	:	PUNCT
ejpam-5657	152	5	n.	n.	VERB
ejpam-5657	152	6	since	since	SCONJ
ejpam-5657	152	7	,	,	PUNCT
ejpam-5657	152	8	0	0	NUM
ejpam-5657	152	9	≤	≤	NUM
ejpam-5657	152	10	µ∆(m	µ∆(m	NOUN
ejpam-5657	152	11	)	)	PUNCT
ejpam-5657	152	12	<	<	X
ejpam-5657	152	13	1	1	NUM
ejpam-5657	152	14	,	,	PUNCT
ejpam-5657	152	15	means	mean	VERB
ejpam-5657	152	16	that	that	SCONJ
ejpam-5657	152	17	λi(iin	λi(iin	PRON
ejpam-5657	152	18	−	−	PUNCT
ejpam-5657	152	19	m∆̂	m∆̂	PROPN
ejpam-5657	152	20	)	)	PUNCT
ejpam-5657	152	21	̸=	̸=	PROPN
ejpam-5657	152	22	0	0	NUM
ejpam-5657	152	23	,	,	PUNCT
ejpam-5657	152	24	∀	∀	X
ejpam-5657	152	25	∆̂	∆̂	NOUN
ejpam-5657	153	1	∈	∈	PROPN
ejpam-5657	153	2	∆.	∆.	X
ejpam-5657	153	3	in	in	ADP
ejpam-5657	153	4	turn	turn	NOUN
ejpam-5657	153	5	this	this	PRON
ejpam-5657	153	6	implies	imply	VERB
ejpam-5657	153	7	that	that	SCONJ
ejpam-5657	153	8	λi	λi	ADP
ejpam-5657	153	9	(	(	PUNCT
ejpam-5657	153	10	in	in	ADP
ejpam-5657	153	11	−	−	PROPN
ejpam-5657	153	12	(	(	PUNCT
ejpam-5657	153	13	iin	iin	NOUN
ejpam-5657	153	14	+	+	CCONJ
ejpam-5657	153	15	(	(	PUNCT
ejpam-5657	153	16	in	in	ADP
ejpam-5657	153	17	−a)−1b)−1(iin	−a)−1b)−1(iin	NOUN
ejpam-5657	153	18	−	−	PROPN
ejpam-5657	154	1	(	(	PUNCT
ejpam-5657	154	2	in	in	ADP
ejpam-5657	154	3	−a)−1b)∆̂	−a)−1b)∆̂	NOUN
ejpam-5657	154	4	)	)	PUNCT
ejpam-5657	154	5	̸=	̸=	PROPN
ejpam-5657	154	6	0	0	NUM
ejpam-5657	154	7	,	,	PUNCT
ejpam-5657	154	8	∀∆̂	∀∆̂	PROPN
ejpam-5657	154	9	∈	∈	PROPN
ejpam-5657	154	10	∆	∆	PROPN
ejpam-5657	154	11	which	which	PRON
ejpam-5657	154	12	further	far	ADV
ejpam-5657	154	13	reduces	reduce	VERB
ejpam-5657	154	14	to	to	ADP
ejpam-5657	154	15	the	the	DET
ejpam-5657	154	16	fact	fact	NOUN
ejpam-5657	154	17	that	that	SCONJ
ejpam-5657	154	18	λi	λi	ADP
ejpam-5657	154	19	(	(	PUNCT
ejpam-5657	154	20	(	(	PUNCT
ejpam-5657	154	21	in	in	ADP
ejpam-5657	154	22	−a)−1b	−a)−1b	X
ejpam-5657	154	23	+	+	CCONJ
ejpam-5657	154	24	ip	ip	NOUN
ejpam-5657	154	25	)	)	PUNCT
ejpam-5657	154	26	̸=	̸=	PROPN
ejpam-5657	154	27	0	0	NUM
ejpam-5657	154	28	,	,	PUNCT
ejpam-5657	154	29	and	and	CCONJ
ejpam-5657	154	30	this	this	PRON
ejpam-5657	154	31	shows	show	VERB
ejpam-5657	154	32	that	that	SCONJ
ejpam-5657	154	33	(	(	PUNCT
ejpam-5657	154	34	in	in	ADP
ejpam-5657	154	35	−a)−1b	−a)−1b	INTJ
ejpam-5657	154	36	is	be	AUX
ejpam-5657	154	37	a	a	DET
ejpam-5657	154	38	d	d	ADJ
ejpam-5657	154	39	-	-	ADJ
ejpam-5657	154	40	stable	stable	ADJ
ejpam-5657	154	41	matrix	matrix	NOUN
ejpam-5657	154	42	.	.	PUNCT
ejpam-5657	155	1	theorem	theorem	NOUN
ejpam-5657	155	2	5	5	NUM
ejpam-5657	155	3	.	.	PUNCT
ejpam-5657	156	1	let	let	VERB
ejpam-5657	156	2	the	the	DET
ejpam-5657	156	3	dynamical	dynamical	ADJ
ejpam-5657	156	4	system	system	NOUN
ejpam-5657	156	5	be	be	AUX
ejpam-5657	156	6	yt	yt	NOUN
ejpam-5657	156	7	=	=	PUNCT
ejpam-5657	156	8	(	(	PUNCT
ejpam-5657	156	9	in−a)−1b+ext	in−a)−1b+ext	PROPN
ejpam-5657	156	10	.	.	PUNCT
ejpam-5657	157	1	then	then	ADV
ejpam-5657	157	2	,	,	PUNCT
ejpam-5657	157	3	for	for	ADP
ejpam-5657	157	4	dynamic	dynamic	ADJ
ejpam-5657	157	5	dstability	dstability	NOUN
ejpam-5657	157	6	the	the	DET
ejpam-5657	157	7	matrix	matrix	NOUN
ejpam-5657	157	8	(	(	PUNCT
ejpam-5657	157	9	in−a)−1b	in−a)−1b	ADJ
ejpam-5657	157	10	is	be	AUX
ejpam-5657	157	11	d	d	ADJ
ejpam-5657	157	12	-	-	ADJ
ejpam-5657	157	13	stable	stable	ADJ
ejpam-5657	157	14	iff	iff	PROPN
ejpam-5657	157	15	re	re	X
ejpam-5657	157	16	(	(	PUNCT
ejpam-5657	157	17	λi(p	λi(p	X
ejpam-5657	157	18	(	(	PUNCT
ejpam-5657	157	19	in	in	ADP
ejpam-5657	157	20	−a)−1b	−a)−1b	X
ejpam-5657	157	21	+	+	CCONJ
ejpam-5657	157	22	(	(	PUNCT
ejpam-5657	157	23	(	(	PUNCT
ejpam-5657	157	24	in	in	ADP
ejpam-5657	157	25	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	157	26	)	)	PUNCT
ejpam-5657	157	27	)	)	PUNCT
ejpam-5657	158	1	>	>	X
ejpam-5657	158	2	0	0	NUM
ejpam-5657	158	3	,	,	PUNCT
ejpam-5657	158	4	∀	∀	VERB
ejpam-5657	159	1	i	i	NOUN
ejpam-5657	159	2	=	=	NOUN
ejpam-5657	159	3	1	1	NUM
ejpam-5657	159	4	:	:	PUNCT
ejpam-5657	159	5	n	n	CCONJ
ejpam-5657	159	6	,	,	PUNCT
ejpam-5657	159	7	and	and	CCONJ
ejpam-5657	159	8	0	0	NUM
ejpam-5657	159	9	≤	≤	NUM
ejpam-5657	159	10	µ∆(m	µ∆(m	NOUN
ejpam-5657	159	11	)	)	PUNCT
ejpam-5657	159	12	<	<	X
ejpam-5657	159	13	1	1	NUM
ejpam-5657	159	14	,	,	PUNCT
ejpam-5657	159	15	with	with	ADP
ejpam-5657	159	16	m	m	PRON
ejpam-5657	159	17	:	:	PUNCT
ejpam-5657	159	18	=	=	SYM
ejpam-5657	159	19	(	(	PUNCT
ejpam-5657	159	20	iin	iin	NOUN
ejpam-5657	160	1	+	+	CCONJ
ejpam-5657	160	2	p	p	X
ejpam-5657	160	3	(	(	PUNCT
ejpam-5657	160	4	in	in	ADP
ejpam-5657	160	5	−a)−1b	−a)−1b	X
ejpam-5657	160	6	+	+	CCONJ
ejpam-5657	160	7	(	(	PUNCT
ejpam-5657	160	8	(	(	PUNCT
ejpam-5657	160	9	in	in	ADP
ejpam-5657	160	10	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	160	11	)	)	PUNCT
ejpam-5657	160	12	−1	−1	NOUN
ejpam-5657	160	13	(	(	PUNCT
ejpam-5657	160	14	iin	iin	NOUN
ejpam-5657	160	15	−	−	PROPN
ejpam-5657	160	16	p	p	X
ejpam-5657	160	17	(	(	PUNCT
ejpam-5657	160	18	in	in	ADP
ejpam-5657	160	19	−a)−1b	−a)−1b	INTJ
ejpam-5657	160	20	−	−	PROPN
ejpam-5657	160	21	(	(	PUNCT
ejpam-5657	160	22	(	(	PUNCT
ejpam-5657	160	23	in	in	ADP
ejpam-5657	160	24	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	160	25	)	)	PUNCT
ejpam-5657	160	26	.	.	PUNCT
ejpam-5657	161	1	proof	proof	NOUN
ejpam-5657	161	2	.	.	PUNCT
ejpam-5657	162	1	we	we	PRON
ejpam-5657	162	2	follow	follow	VERB
ejpam-5657	162	3	the	the	DET
ejpam-5657	162	4	same	same	ADJ
ejpam-5657	162	5	procedure	procedure	NOUN
ejpam-5657	162	6	as	as	SCONJ
ejpam-5657	162	7	given	give	VERB
ejpam-5657	162	8	in	in	ADP
ejpam-5657	162	9	theorem	theorem	NOUN
ejpam-5657	162	10	4	4	NUM
ejpam-5657	162	11	to	to	PART
ejpam-5657	162	12	prove	prove	VERB
ejpam-5657	162	13	theorem	theorem	VERB
ejpam-5657	162	14	5	5	X
ejpam-5657	162	15	.	.	PUNCT
ejpam-5657	163	1	we	we	PRON
ejpam-5657	163	2	aim	aim	VERB
ejpam-5657	163	3	to	to	PART
ejpam-5657	163	4	show	show	VERB
ejpam-5657	163	5	that	that	SCONJ
ejpam-5657	163	6	(	(	PUNCT
ejpam-5657	163	7	in−a)−1b	in−a)−1b	ADJ
ejpam-5657	163	8	isd	isd	PROPN
ejpam-5657	163	9	-	-	PUNCT
ejpam-5657	163	10	stable	stable	ADJ
ejpam-5657	163	11	iffre	iffre	NOUN
ejpam-5657	163	12	(	(	PUNCT
ejpam-5657	163	13	λi(p	λi(p	X
ejpam-5657	163	14	(	(	PUNCT
ejpam-5657	163	15	in	in	ADP
ejpam-5657	163	16	−a)−1b	−a)−1b	X
ejpam-5657	163	17	+	+	CCONJ
ejpam-5657	163	18	(	(	PUNCT
ejpam-5657	163	19	(	(	PUNCT
ejpam-5657	163	20	in	in	ADP
ejpam-5657	163	21	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	163	22	)	)	PUNCT
ejpam-5657	163	23	)	)	PUNCT
ejpam-5657	163	24	>	>	X
ejpam-5657	164	1	0	0	NUM
ejpam-5657	164	2	,	,	PUNCT
ejpam-5657	164	3	∀	∀	VERB
ejpam-5657	165	1	i	i	NOUN
ejpam-5657	165	2	=	=	NOUN
ejpam-5657	165	3	1	1	X
ejpam-5657	165	4	:	:	PUNCT
ejpam-5657	165	5	n.	n.	NOUN
ejpam-5657	165	6	let	let	VERB
ejpam-5657	165	7	∆̂	∆̂	PUNCT
ejpam-5657	165	8	∈	∈	PROPN
ejpam-5657	165	9	∆	∆	PROPN
ejpam-5657	165	10	be	be	VERB
ejpam-5657	165	11	a	a	DET
ejpam-5657	165	12	block	block	NOUN
ejpam-5657	165	13	-	-	PUNCT
ejpam-5657	165	14	diagonal	diagonal	ADJ
ejpam-5657	165	15	structure	structure	NOUN
ejpam-5657	165	16	,	,	PUNCT
ejpam-5657	165	17	and	and	CCONJ
ejpam-5657	165	18	defined	define	VERB
ejpam-5657	165	19	as	as	ADP
ejpam-5657	165	20	∆̂	∆̂	PUNCT
ejpam-5657	165	21	:	:	PUNCT
ejpam-5657	165	22	=	=	SYM
ejpam-5657	165	23	(	(	PUNCT
ejpam-5657	165	24	iin	iin	NOUN
ejpam-5657	165	25	−	−	PROPN
ejpam-5657	165	26	p	p	NOUN
ejpam-5657	165	27	)	)	PUNCT
ejpam-5657	165	28	(	(	PUNCT
ejpam-5657	165	29	iin	iin	NOUN
ejpam-5657	165	30	+	+	CCONJ
ejpam-5657	165	31	p	p	NOUN
ejpam-5657	165	32	)	)	PUNCT
ejpam-5657	165	33	−1	−1	NOUN
ejpam-5657	165	34	,	,	PUNCT
ejpam-5657	165	35	a	a	DET
ejpam-5657	165	36	diagonal	diagonal	ADJ
ejpam-5657	165	37	matrix	matrix	NOUN
ejpam-5657	165	38	.	.	PUNCT
ejpam-5657	166	1	as	as	ADP
ejpam-5657	166	2	λi(p	λi(p	X
ejpam-5657	166	3	(	(	PUNCT
ejpam-5657	166	4	in	in	ADP
ejpam-5657	166	5	−	−	PROPN
ejpam-5657	166	6	a)−1b	a)−1b	PROPN
ejpam-5657	166	7	+	+	CCONJ
ejpam-5657	166	8	(	(	PUNCT
ejpam-5657	166	9	(	(	PUNCT
ejpam-5657	166	10	in	in	ADP
ejpam-5657	166	11	−	−	PROPN
ejpam-5657	166	12	a)−1b)tp	a)−1b)tp	NOUN
ejpam-5657	166	13	)	)	PUNCT
ejpam-5657	166	14	̸=	̸=	PROPN
ejpam-5657	166	15	0	0	NUM
ejpam-5657	166	16	,	,	PUNCT
ejpam-5657	166	17	∀i	∀i	NOUN
ejpam-5657	166	18	=	=	SYM
ejpam-5657	166	19	1	1	NUM
ejpam-5657	166	20	:	:	PUNCT
ejpam-5657	166	21	n.	n.	NOUN
ejpam-5657	166	22	this	this	PRON
ejpam-5657	166	23	implies	imply	VERB
ejpam-5657	166	24	that	that	SCONJ
ejpam-5657	166	25	λi(p	λi(p	VERB
ejpam-5657	166	26	(	(	PUNCT
ejpam-5657	166	27	in	in	ADP
ejpam-5657	166	28	−	−	PROPN
ejpam-5657	166	29	a)−1b	a)−1b	PROPN
ejpam-5657	167	1	+	+	CCONJ
ejpam-5657	167	2	(	(	PUNCT
ejpam-5657	167	3	(	(	PUNCT
ejpam-5657	167	4	in	in	ADP
ejpam-5657	167	5	−	−	PROPN
ejpam-5657	167	6	a)−1b)tp	a)−1b)tp	NOUN
ejpam-5657	167	7	+	+	CCONJ
ejpam-5657	167	8	ip	ip	NOUN
ejpam-5657	167	9	)	)	PUNCT
ejpam-5657	167	10	̸=	̸=	PROPN
ejpam-5657	167	11	0	0	NUM
ejpam-5657	167	12	,	,	PUNCT
ejpam-5657	167	13	∀i	∀i	NOUN
ejpam-5657	167	14	=	=	SYM
ejpam-5657	167	15	1	1	NUM
ejpam-5657	167	16	:	:	PUNCT
ejpam-5657	167	17	n	n	CCONJ
ejpam-5657	167	18	iff	iff	VERB
ejpam-5657	167	19	λi(p	λi(p	NOUN
ejpam-5657	167	20	(	(	PUNCT
ejpam-5657	167	21	in−a)−1b+((in−a)−1b)tp	in−a)−1b+((in−a)−1b)tp	X
ejpam-5657	167	22	+	+	CCONJ
ejpam-5657	167	23	i(iin+∆̂)−1(iin−∆̂	i(iin+∆̂)−1(iin−∆̂	NUM
ejpam-5657	167	24	)	)	PUNCT
ejpam-5657	167	25	)	)	PUNCT
ejpam-5657	168	1	̸=	̸=	PROPN
ejpam-5657	168	2	0	0	NUM
ejpam-5657	168	3	,	,	PUNCT
ejpam-5657	168	4	∀i	∀i	NOUN
ejpam-5657	168	5	=	=	SYM
ejpam-5657	168	6	1	1	NUM
ejpam-5657	168	7	:	:	PUNCT
ejpam-5657	168	8	n.	n.	NOUN
ejpam-5657	168	9	this	this	PRON
ejpam-5657	168	10	further	far	ADV
ejpam-5657	168	11	reduces	reduce	VERB
ejpam-5657	168	12	to	to	PART
ejpam-5657	168	13	λi	λi	ADP
ejpam-5657	168	14	(	(	PUNCT
ejpam-5657	168	15	iin	iin	NOUN
ejpam-5657	168	16	+	+	CCONJ
ejpam-5657	168	17	p	p	X
ejpam-5657	168	18	(	(	PUNCT
ejpam-5657	168	19	in	in	ADP
ejpam-5657	168	20	−a)−1b	−a)−1b	X
ejpam-5657	168	21	+	+	CCONJ
ejpam-5657	168	22	(	(	PUNCT
ejpam-5657	168	23	(	(	PUNCT
ejpam-5657	168	24	in	in	ADP
ejpam-5657	168	25	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	168	26	)	)	PUNCT
ejpam-5657	168	27	−	−	PROPN
ejpam-5657	169	1	(	(	PUNCT
ejpam-5657	169	2	iin	iin	NOUN
ejpam-5657	169	3	−	−	PROPN
ejpam-5657	169	4	p	p	X
ejpam-5657	169	5	(	(	PUNCT
ejpam-5657	169	6	in	in	ADP
ejpam-5657	169	7	−a)−1b	−a)−1b	INTJ
ejpam-5657	169	8	−	−	PROPN
ejpam-5657	169	9	(	(	PUNCT
ejpam-5657	169	10	(	(	PUNCT
ejpam-5657	169	11	in	in	ADP
ejpam-5657	169	12	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	169	13	)	)	PUNCT
ejpam-5657	169	14	∆̂	∆̂	PUNCT
ejpam-5657	169	15	)	)	PUNCT
ejpam-5657	169	16	̸=	̸=	PROPN
ejpam-5657	169	17	0	0	NUM
ejpam-5657	169	18	.	.	PUNCT
ejpam-5657	170	1	this	this	PRON
ejpam-5657	170	2	,	,	PUNCT
ejpam-5657	170	3	finally	finally	ADV
ejpam-5657	170	4	we	we	PRON
ejpam-5657	170	5	have	have	VERB
ejpam-5657	170	6	that	that	DET
ejpam-5657	170	7	λi	λi	ADP
ejpam-5657	170	8	(	(	PUNCT
ejpam-5657	170	9	in	in	ADP
ejpam-5657	170	10	−	−	PROPN
ejpam-5657	170	11	(	(	PUNCT
ejpam-5657	170	12	iin	iin	NOUN
ejpam-5657	170	13	+	+	CCONJ
ejpam-5657	170	14	p	p	X
ejpam-5657	170	15	(	(	PUNCT
ejpam-5657	170	16	in	in	ADP
ejpam-5657	170	17	−a)−1b	−a)−1b	X
ejpam-5657	170	18	+	+	CCONJ
ejpam-5657	170	19	(	(	PUNCT
ejpam-5657	170	20	(	(	PUNCT
ejpam-5657	170	21	in	in	ADP
ejpam-5657	170	22	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	170	23	)	)	PUNCT
ejpam-5657	171	1	−1(iin	−1(iin	PROPN
ejpam-5657	172	1	−	−	PROPN
ejpam-5657	172	2	p	p	X
ejpam-5657	172	3	(	(	PUNCT
ejpam-5657	172	4	in	in	ADP
ejpam-5657	172	5	−a)−1b	−a)−1b	INTJ
ejpam-5657	172	6	−	−	PROPN
ejpam-5657	172	7	(	(	PUNCT
ejpam-5657	172	8	(	(	PUNCT
ejpam-5657	172	9	in	in	ADP
ejpam-5657	172	10	−a)−1b)tp	−a)−1b)tp	NOUN
ejpam-5657	172	11	)	)	PUNCT
ejpam-5657	172	12	∆̂	∆̂	PUNCT
ejpam-5657	172	13	)	)	PUNCT
ejpam-5657	172	14	̸=	̸=	PROPN
ejpam-5657	172	15	0	0	NUM
ejpam-5657	172	16	.	.	PUNCT
ejpam-5657	173	1	this	this	DET
ejpam-5657	173	2	last	last	ADJ
ejpam-5657	173	3	inequality	inequality	NOUN
ejpam-5657	173	4	is	be	AUX
ejpam-5657	173	5	the	the	DET
ejpam-5657	173	6	necessary	necessary	ADJ
ejpam-5657	173	7	condition	condition	NOUN
ejpam-5657	173	8	that	that	SCONJ
ejpam-5657	173	9	structured	structure	VERB
ejpam-5657	173	10	singular	singular	ADJ
ejpam-5657	173	11	values	value	NOUN
ejpam-5657	173	12	is	be	AUX
ejpam-5657	173	13	strictly	strictly	ADV
ejpam-5657	173	14	less	less	ADJ
ejpam-5657	173	15	than	than	ADP
ejpam-5657	173	16	1	1	NUM
ejpam-5657	173	17	,	,	PUNCT
ejpam-5657	173	18	means	mean	VERB
ejpam-5657	173	19	that	that	SCONJ
ejpam-5657	173	20	,	,	PUNCT
ejpam-5657	173	21	0	0	NUM
ejpam-5657	173	22	≤	≤	NUM
ejpam-5657	173	23	µ∆(m	µ∆(m	NOUN
ejpam-5657	173	24	)	)	PUNCT
ejpam-5657	173	25	<	<	X
ejpam-5657	174	1	1	1	X
ejpam-5657	174	2	.	.	PUNCT
ejpam-5657	174	3	m.u.r	m.u.r	NOUN
ejpam-5657	174	4	et	et	PROPN
ejpam-5657	174	5	al	al	PROPN
ejpam-5657	174	6	.	.	PUNCT
ejpam-5657	174	7	/	/	SYM
ejpam-5657	174	8	eur	eur	PROPN
ejpam-5657	174	9	.	.	PUNCT
ejpam-5657	175	1	j.	j.	PROPN
ejpam-5657	175	2	pure	pure	PROPN
ejpam-5657	175	3	appl	appl	PROPN
ejpam-5657	175	4	.	.	PROPN
ejpam-5657	175	5	math	math	PROPN
ejpam-5657	175	6	,	,	PUNCT
ejpam-5657	175	7	18	18	NUM
ejpam-5657	175	8	(	(	PUNCT
ejpam-5657	175	9	1	1	NUM
ejpam-5657	175	10	)	)	PUNCT
ejpam-5657	175	11	(	(	PUNCT
ejpam-5657	175	12	2025	2025	NUM
ejpam-5657	175	13	)	)	PUNCT
ejpam-5657	175	14	,	,	PUNCT
ejpam-5657	175	15	5657	5657	NUM
ejpam-5657	175	16	8	8	NUM
ejpam-5657	175	17	of	of	ADP
ejpam-5657	175	18	17	17	NUM
ejpam-5657	175	19	3	3	NUM
ejpam-5657	175	20	.	.	NOUN
ejpam-5657	175	21	necessary	necessary	ADJ
ejpam-5657	175	22	and	and	CCONJ
ejpam-5657	175	23	sufficient	sufficient	ADJ
ejpam-5657	175	24	conditions	condition	NOUN
ejpam-5657	175	25	for	for	ADP
ejpam-5657	175	26	d	d	NOUN
ejpam-5657	175	27	-	-	NOUN
ejpam-5657	175	28	stability	stability	NOUN
ejpam-5657	175	29	in	in	ADP
ejpam-5657	175	30	this	this	DET
ejpam-5657	175	31	section	section	NOUN
ejpam-5657	175	32	,	,	PUNCT
ejpam-5657	175	33	we	we	PRON
ejpam-5657	175	34	present	present	VERB
ejpam-5657	175	35	some	some	DET
ejpam-5657	175	36	new	new	ADJ
ejpam-5657	175	37	results	result	NOUN
ejpam-5657	175	38	on	on	ADP
ejpam-5657	175	39	necessary	necessary	ADJ
ejpam-5657	175	40	and	and	CCONJ
ejpam-5657	175	41	sufficient	sufficient	ADJ
ejpam-5657	175	42	conditions	condition	NOUN
ejpam-5657	175	43	for	for	ADP
ejpam-5657	175	44	d	d	NOUN
ejpam-5657	175	45	-	-	NOUN
ejpam-5657	175	46	stability	stability	NOUN
ejpam-5657	175	47	of	of	ADP
ejpam-5657	175	48	a	a	DET
ejpam-5657	175	49	given	give	VERB
ejpam-5657	175	50	matrix	matrix	NOUN
ejpam-5657	175	51	in	in	ADP
ejpam-5657	175	52	term	term	NOUN
ejpam-5657	175	53	of	of	ADP
ejpam-5657	175	54	its	its	PRON
ejpam-5657	175	55	structured	structured	ADJ
ejpam-5657	175	56	singular	singular	ADJ
ejpam-5657	175	57	values	value	NOUN
ejpam-5657	175	58	.	.	PUNCT
ejpam-5657	176	1	lemma	lemma	PROPN
ejpam-5657	176	2	1	1	NUM
ejpam-5657	176	3	.	.	PUNCT
ejpam-5657	177	1	[	[	X
ejpam-5657	177	2	20	20	NUM
ejpam-5657	177	3	]	]	PUNCT
ejpam-5657	177	4	.	.	PUNCT
ejpam-5657	178	1	a	a	DET
ejpam-5657	178	2	∈	∈	PROPN
ejpam-5657	178	3	rn	rn	PROPN
ejpam-5657	178	4	,	,	PUNCT
ejpam-5657	178	5	n	n	NUM
ejpam-5657	178	6	which	which	PRON
ejpam-5657	178	7	is	be	AUX
ejpam-5657	178	8	continuous	continuous	ADJ
ejpam-5657	178	9	-	-	PUNCT
ejpam-5657	178	10	time	time	NOUN
ejpam-5657	178	11	diagonal	diagonal	ADJ
ejpam-5657	178	12	stable	stable	ADJ
ejpam-5657	178	13	matrix	matrix	NOUN
ejpam-5657	178	14	is	be	AUX
ejpam-5657	178	15	a	a	DET
ejpam-5657	178	16	d	d	ADJ
ejpam-5657	178	17	-	-	ADJ
ejpam-5657	178	18	stable	stable	ADJ
ejpam-5657	178	19	matrix	matrix	NOUN
ejpam-5657	178	20	.	.	PUNCT
ejpam-5657	179	1	lemma	lemma	PROPN
ejpam-5657	179	2	2	2	NUM
ejpam-5657	179	3	.	.	PUNCT
ejpam-5657	180	1	[	[	X
ejpam-5657	180	2	20	20	NUM
ejpam-5657	180	3	]	]	PUNCT
ejpam-5657	180	4	.	.	PUNCT
ejpam-5657	181	1	a	a	DET
ejpam-5657	181	2	∈	∈	PROPN
ejpam-5657	181	3	rn	rn	PROPN
ejpam-5657	181	4	,	,	PUNCT
ejpam-5657	181	5	n	n	NUM
ejpam-5657	181	6	which	which	PRON
ejpam-5657	181	7	is	be	AUX
ejpam-5657	181	8	discrete	discrete	ADJ
ejpam-5657	181	9	-	-	PUNCT
ejpam-5657	181	10	time	time	NOUN
ejpam-5657	181	11	diagonal	diagonal	ADJ
ejpam-5657	181	12	stable	stable	ADJ
ejpam-5657	181	13	matrix	matrix	NOUN
ejpam-5657	181	14	is	be	AUX
ejpam-5657	181	15	a	a	DET
ejpam-5657	181	16	d	d	ADJ
ejpam-5657	181	17	-	-	ADJ
ejpam-5657	181	18	stable	stable	ADJ
ejpam-5657	181	19	matrix	matrix	NOUN
ejpam-5657	181	20	.	.	PUNCT
ejpam-5657	182	1	the	the	DET
ejpam-5657	182	2	following	follow	VERB
ejpam-5657	182	3	theorem	theorem	VERB
ejpam-5657	182	4	6	6	NUM
ejpam-5657	182	5	show	show	NOUN
ejpam-5657	182	6	that	that	SCONJ
ejpam-5657	182	7	hurwitz	hurwitz	NOUN
ejpam-5657	182	8	-	-	PUNCT
ejpam-5657	182	9	stable	stable	ADJ
ejpam-5657	182	10	matrix	matrix	NOUN
ejpam-5657	182	11	is	be	AUX
ejpam-5657	182	12	also	also	ADV
ejpam-5657	182	13	a	a	DET
ejpam-5657	182	14	continuous	continuous	ADJ
ejpam-5657	182	15	-	-	PUNCT
ejpam-5657	182	16	time	time	NOUN
ejpam-5657	182	17	d	d	ADJ
ejpam-5657	182	18	-	-	ADJ
ejpam-5657	182	19	stable	stable	ADJ
ejpam-5657	182	20	matrix	matrix	NOUN
ejpam-5657	182	21	matrix	matrix	NOUN
ejpam-5657	182	22	.	.	PUNCT
ejpam-5657	183	1	theorem	theorem	VERB
ejpam-5657	183	2	6	6	NUM
ejpam-5657	183	3	.	.	PUNCT
ejpam-5657	184	1	[	[	X
ejpam-5657	184	2	20	20	NUM
ejpam-5657	184	3	]	]	PUNCT
ejpam-5657	184	4	.	.	PUNCT
ejpam-5657	185	1	let	let	VERB
ejpam-5657	185	2	a	a	DET
ejpam-5657	185	3	∈	∈	PROPN
ejpam-5657	185	4	rn	rn	PROPN
ejpam-5657	185	5	,	,	PUNCT
ejpam-5657	185	6	n	n	PRON
ejpam-5657	185	7	be	be	VERB
ejpam-5657	185	8	a	a	DET
ejpam-5657	185	9	hurwitz	hurwitz	NOUN
ejpam-5657	185	10	-	-	PUNCT
ejpam-5657	185	11	stable	stable	ADJ
ejpam-5657	185	12	matrix	matrix	NOUN
ejpam-5657	185	13	.	.	PUNCT
ejpam-5657	186	1	then	then	ADV
ejpam-5657	186	2	a	a	PRON
ejpam-5657	186	3	is	be	AUX
ejpam-5657	186	4	continuous	continuous	ADJ
ejpam-5657	186	5	-	-	PUNCT
ejpam-5657	186	6	time	time	NOUN
ejpam-5657	186	7	d	d	NOUN
ejpam-5657	186	8	-	-	NOUN
ejpam-5657	186	9	stable	stable	ADJ
ejpam-5657	186	10	only	only	ADV
ejpam-5657	186	11	if	if	SCONJ
ejpam-5657	186	12	0	0	NUM
ejpam-5657	186	13	≤	≤	NUM
ejpam-5657	186	14	µ∆	µ∆	NOUN
ejpam-5657	186	15	(	(	PUNCT
ejpam-5657	186	16	(	(	PUNCT
ejpam-5657	186	17	sin	sin	NOUN
ejpam-5657	186	18	+	+	NOUN
ejpam-5657	186	19	a)(sin	a)(sin	NOUN
ejpam-5657	186	20	−a)−1	−a)−1	NOUN
ejpam-5657	186	21	)	)	PUNCT
ejpam-5657	186	22	≤	≤	NUM
ejpam-5657	186	23	1	1	NUM
ejpam-5657	186	24	,	,	PUNCT
ejpam-5657	186	25	∀	∀	NOUN
ejpam-5657	186	26	s	s	NOUN
ejpam-5657	186	27	∈	∈	NOUN
ejpam-5657	186	28	c+	c+	NOUN
ejpam-5657	186	29	.	.	PUNCT
ejpam-5657	187	1	from	from	ADP
ejpam-5657	187	2	above	above	ADP
ejpam-5657	187	3	theorem	theorem	NOUN
ejpam-5657	187	4	6	6	NUM
ejpam-5657	187	5	,	,	PUNCT
ejpam-5657	187	6	it	it	PRON
ejpam-5657	187	7	is	be	AUX
ejpam-5657	187	8	clear	clear	ADJ
ejpam-5657	187	9	that	that	SCONJ
ejpam-5657	187	10	the	the	DET
ejpam-5657	187	11	definition	definition	NOUN
ejpam-5657	187	12	of	of	ADP
ejpam-5657	187	13	structured	structure	VERB
ejpam-5657	187	14	singular	singular	ADJ
ejpam-5657	187	15	value	value	NOUN
ejpam-5657	187	16	holds	hold	VERB
ejpam-5657	187	17	true	true	ADJ
ejpam-5657	187	18	for	for	ADP
ejpam-5657	187	19	all	all	DET
ejpam-5657	187	20	the	the	DET
ejpam-5657	187	21	values	value	NOUN
ejpam-5657	187	22	of	of	ADP
ejpam-5657	187	23	parameter	parameter	NOUN
ejpam-5657	187	24	s	s	PROPN
ejpam-5657	187	25	∈	∈	PROPN
ejpam-5657	187	26	c+	c+	NOUN
ejpam-5657	187	27	,	,	PUNCT
ejpam-5657	187	28	that	that	ADV
ejpam-5657	187	29	is	is	ADV
ejpam-5657	187	30	,	,	PUNCT
ejpam-5657	187	31	in	in	ADP
ejpam-5657	187	32	closed	closed	ADJ
ejpam-5657	187	33	right	right	ADJ
ejpam-5657	187	34	-	-	PUNCT
ejpam-5657	187	35	half	half	NOUN
ejpam-5657	187	36	of	of	ADP
ejpam-5657	187	37	complex	complex	ADJ
ejpam-5657	187	38	plane	plane	NOUN
ejpam-5657	187	39	.	.	PUNCT
ejpam-5657	188	1	the	the	DET
ejpam-5657	188	2	following	follow	VERB
ejpam-5657	188	3	lemma	lemma	PROPN
ejpam-5657	188	4	show	show	VERB
ejpam-5657	188	5	that	that	SCONJ
ejpam-5657	188	6	structured	structured	ADJ
ejpam-5657	188	7	singular	singular	ADJ
ejpam-5657	188	8	value	value	NOUN
ejpam-5657	188	9	can	can	AUX
ejpam-5657	188	10	be	be	AUX
ejpam-5657	188	11	determined	determine	VERB
ejpam-5657	188	12	at	at	ADP
ejpam-5657	188	13	a	a	DET
ejpam-5657	188	14	single	single	ADJ
ejpam-5657	188	15	value	value	NOUN
ejpam-5657	188	16	of	of	ADP
ejpam-5657	188	17	s	s	NOUN
ejpam-5657	188	18	∈	∈	NOUN
ejpam-5657	188	19	c+	c+	VERB
ejpam-5657	188	20	rather	rather	ADV
ejpam-5657	188	21	than	than	ADP
ejpam-5657	188	22	evaluating	evaluate	VERB
ejpam-5657	188	23	at	at	ADP
ejpam-5657	188	24	entire	entire	ADJ
ejpam-5657	188	25	closed	closed	ADJ
ejpam-5657	188	26	right	right	ADJ
ejpam-5657	188	27	-	-	PUNCT
ejpam-5657	188	28	half	half	NOUN
ejpam-5657	188	29	of	of	ADP
ejpam-5657	188	30	complex	complex	ADJ
ejpam-5657	188	31	plane	plane	NOUN
ejpam-5657	188	32	.	.	PUNCT
ejpam-5657	189	1	lemma	lemma	PROPN
ejpam-5657	189	2	3	3	NUM
ejpam-5657	189	3	.	.	PUNCT
ejpam-5657	190	1	[	[	X
ejpam-5657	190	2	20	20	NUM
ejpam-5657	190	3	]	]	PUNCT
ejpam-5657	190	4	.	.	PUNCT
ejpam-5657	191	1	let	let	VERB
ejpam-5657	191	2	a	a	DET
ejpam-5657	191	3	∈	∈	PROPN
ejpam-5657	191	4	rn	rn	PROPN
ejpam-5657	191	5	,	,	PUNCT
ejpam-5657	191	6	n	n	PRON
ejpam-5657	191	7	be	be	VERB
ejpam-5657	191	8	a	a	DET
ejpam-5657	191	9	hurwitz	hurwitz	NOUN
ejpam-5657	191	10	-	-	PUNCT
ejpam-5657	191	11	stable	stable	ADJ
ejpam-5657	191	12	matrix	matrix	NOUN
ejpam-5657	191	13	.	.	PUNCT
ejpam-5657	192	1	then	then	ADV
ejpam-5657	192	2	,	,	PUNCT
ejpam-5657	192	3	a	a	PRON
ejpam-5657	192	4	is	be	AUX
ejpam-5657	192	5	continuous	continuous	ADJ
ejpam-5657	192	6	-	-	PUNCT
ejpam-5657	192	7	time	time	NOUN
ejpam-5657	192	8	d	d	ADJ
ejpam-5657	192	9	-	-	ADJ
ejpam-5657	192	10	stable	stable	ADJ
ejpam-5657	192	11	matrix	matrix	NOUN
ejpam-5657	192	12	iff	iff	NOUN
ejpam-5657	192	13	0	0	NUM
ejpam-5657	192	14	≤	≤	NUM
ejpam-5657	192	15	µ∆	µ∆	NOUN
ejpam-5657	192	16	(	(	PUNCT
ejpam-5657	192	17	(	(	PUNCT
ejpam-5657	192	18	iin	iin	PROPN
ejpam-5657	192	19	+	+	NOUN
ejpam-5657	192	20	a)(iin	a)(iin	NOUN
ejpam-5657	192	21	−a)−1	−a)−1	NOUN
ejpam-5657	192	22	)	)	PUNCT
ejpam-5657	192	23	≤	≤	NUM
ejpam-5657	192	24	1	1	NUM
ejpam-5657	192	25	,	,	PUNCT
ejpam-5657	192	26	i	i	PRON
ejpam-5657	192	27	=	=	PUNCT
ejpam-5657	192	28	√	√	NUM
ejpam-5657	192	29	−1	−1	NOUN
ejpam-5657	192	30	.	.	PUNCT
ejpam-5657	193	1	theorem	theorem	VERB
ejpam-5657	193	2	7	7	NUM
ejpam-5657	193	3	present	present	NOUN
ejpam-5657	193	4	an	an	DET
ejpam-5657	193	5	interesting	interesting	ADJ
ejpam-5657	193	6	relation	relation	NOUN
ejpam-5657	193	7	between	between	ADP
ejpam-5657	193	8	a	a	DET
ejpam-5657	193	9	continuous	continuous	ADJ
ejpam-5657	193	10	-	-	PUNCT
ejpam-5657	193	11	time	time	NOUN
ejpam-5657	193	12	d	d	NOUN
ejpam-5657	193	13	-	-	ADJ
ejpam-5657	193	14	stable	stable	ADJ
ejpam-5657	193	15	matrix	matrix	NOUN
ejpam-5657	193	16	a	a	DET
ejpam-5657	193	17	∈	∈	PROPN
ejpam-5657	193	18	rn	rn	PROPN
ejpam-5657	193	19	,	,	PUNCT
ejpam-5657	193	20	n	n	PROPN
ejpam-5657	193	21	and	and	CCONJ
ejpam-5657	193	22	structured	structure	VERB
ejpam-5657	193	23	singular	singular	ADJ
ejpam-5657	193	24	values	value	NOUN
ejpam-5657	193	25	of	of	ADP
ejpam-5657	193	26	a	a	DET
ejpam-5657	193	27	perturbed	perturb	VERB
ejpam-5657	193	28	matrix	matrix	NOUN
ejpam-5657	193	29	obtained	obtain	VERB
ejpam-5657	193	30	from	from	ADP
ejpam-5657	193	31	a	a	DET
ejpam-5657	193	32	∈	∈	PROPN
ejpam-5657	193	33	rn	rn	PROPN
ejpam-5657	193	34	,	,	PUNCT
ejpam-5657	193	35	n.	n.	PROPN
ejpam-5657	193	36	theorem	theorem	VERB
ejpam-5657	193	37	7	7	NUM
ejpam-5657	193	38	.	.	PUNCT
ejpam-5657	194	1	let	let	VERB
ejpam-5657	194	2	a	a	DET
ejpam-5657	194	3	∈	∈	PROPN
ejpam-5657	194	4	rn	rn	PROPN
ejpam-5657	194	5	,	,	PUNCT
ejpam-5657	194	6	n	n	PRON
ejpam-5657	194	7	such	such	ADJ
ejpam-5657	194	8	that	that	SCONJ
ejpam-5657	194	9	re(λi(a	re(λi(a	PROPN
ejpam-5657	194	10	)	)	PUNCT
ejpam-5657	194	11	)	)	PUNCT
ejpam-5657	195	1	>	>	X
ejpam-5657	195	2	0	0	NUM
ejpam-5657	195	3	,	,	PUNCT
ejpam-5657	195	4	∀	∀	VERB
ejpam-5657	196	1	i	i	PRON
ejpam-5657	196	2	and	and	CCONJ
ejpam-5657	196	3	is	be	AUX
ejpam-5657	196	4	continuous	continuous	ADJ
ejpam-5657	196	5	-	-	PUNCT
ejpam-5657	196	6	time	time	NOUN
ejpam-5657	196	7	d	d	ADJ
ejpam-5657	196	8	-	-	ADJ
ejpam-5657	196	9	stable	stable	ADJ
ejpam-5657	196	10	matrix	matrix	NOUN
ejpam-5657	196	11	,	,	PUNCT
ejpam-5657	196	12	then	then	ADV
ejpam-5657	196	13	0	0	NUM
ejpam-5657	196	14	≤	≤	NUM
ejpam-5657	196	15	µ∆	µ∆	NOUN
ejpam-5657	196	16	(	(	PUNCT
ejpam-5657	196	17	(	(	PUNCT
ejpam-5657	196	18	αin	αin	NOUN
ejpam-5657	196	19	+	+	ADJ
ejpam-5657	196	20	a)−1(αin	a)−1(αin	NOUN
ejpam-5657	196	21	−a	−a	ADJ
ejpam-5657	196	22	)	)	PUNCT
ejpam-5657	196	23	)	)	PUNCT
ejpam-5657	196	24	≤	≤	NUM
ejpam-5657	196	25	1	1	NUM
ejpam-5657	196	26	,	,	PUNCT
ejpam-5657	196	27	α	α	PROPN
ejpam-5657	196	28	∈	∈	PROPN
ejpam-5657	196	29	c+	c+	NOUN
ejpam-5657	196	30	.	.	PUNCT
ejpam-5657	197	1	proof	proof	NOUN
ejpam-5657	197	2	.	.	PUNCT
ejpam-5657	198	1	let	let	VERB
ejpam-5657	198	2	a	a	PRON
ejpam-5657	198	3	=	=	AUX
ejpam-5657	198	4	eh	eh	INTJ
ejpam-5657	198	5	be	be	AUX
ejpam-5657	198	6	a	a	DET
ejpam-5657	198	7	stable	stable	ADJ
ejpam-5657	198	8	matrix	matrix	NOUN
ejpam-5657	198	9	.	.	PUNCT
ejpam-5657	199	1	the	the	DET
ejpam-5657	199	2	matrix	matrix	NOUN
ejpam-5657	199	3	h	h	NOUN
ejpam-5657	199	4	≥	≥	PROPN
ejpam-5657	199	5	0	0	NUM
ejpam-5657	199	6	,	,	PUNCT
ejpam-5657	199	7	a	a	DET
ejpam-5657	199	8	positive	positive	ADJ
ejpam-5657	199	9	semi	semi	ADJ
ejpam-5657	199	10	-	-	ADJ
ejpam-5657	199	11	definite	definite	ADJ
ejpam-5657	199	12	matrix	matrix	NOUN
ejpam-5657	199	13	.	.	PUNCT
ejpam-5657	200	1	let	let	VERB
ejpam-5657	200	2	p	p	PRON
ejpam-5657	200	3	>	>	X
ejpam-5657	200	4	0	0	PROPN
ejpam-5657	200	5	,	,	PUNCT
ejpam-5657	200	6	a	a	DET
ejpam-5657	200	7	positive	positive	ADJ
ejpam-5657	200	8	definite	definite	ADJ
ejpam-5657	200	9	such	such	ADJ
ejpam-5657	200	10	that	that	SCONJ
ejpam-5657	200	11	λi(αin	λi(αin	NOUN
ejpam-5657	200	12	+	+	CCONJ
ejpam-5657	200	13	ehp	ehp	NOUN
ejpam-5657	200	14	)	)	PUNCT
ejpam-5657	200	15	̸=	̸=	PROPN
ejpam-5657	200	16	0	0	NUM
ejpam-5657	200	17	,	,	PUNCT
ejpam-5657	200	18	∀i	∀i	NOUN
ejpam-5657	200	19	,	,	PUNCT
ejpam-5657	200	20	and	and	CCONJ
ejpam-5657	200	21	p	p	NOUN
ejpam-5657	200	22	=	=	PUNCT
ejpam-5657	200	23	(	(	PUNCT
ejpam-5657	200	24	αin	αin	NOUN
ejpam-5657	200	25	+	+	CCONJ
ejpam-5657	200	26	∆̂)−1(αin	∆̂)−1(αin	DET
ejpam-5657	200	27	−	−	NOUN
ejpam-5657	200	28	∆̂	∆̂	NOUN
ejpam-5657	200	29	)	)	PUNCT
ejpam-5657	200	30	for	for	ADP
ejpam-5657	200	31	all	all	PRON
ejpam-5657	200	32	∆̂	∆̂	PUNCT
ejpam-5657	200	33	∈	∈	PROPN
ejpam-5657	200	34	∆.	∆.	NOUN
ejpam-5657	200	35	this	this	DET
ejpam-5657	200	36	formulation	formulation	NOUN
ejpam-5657	200	37	allows	allow	VERB
ejpam-5657	200	38	as	as	SCONJ
ejpam-5657	200	39	to	to	PART
ejpam-5657	200	40	have	have	VERB
ejpam-5657	200	41	that	that	PRON
ejpam-5657	200	42	λi	λi	ADP
ejpam-5657	200	43	(	(	PUNCT
ejpam-5657	200	44	αin	αin	NOUN
ejpam-5657	200	45	+	+	CCONJ
ejpam-5657	200	46	eh(αin	eh(αin	ADJ
ejpam-5657	200	47	+	+	ADJ
ejpam-5657	200	48	∆̂)−1(αin	∆̂)−1(αin	DET
ejpam-5657	200	49	−	−	NOUN
ejpam-5657	200	50	∆̂	∆̂	NOUN
ejpam-5657	200	51	)	)	PUNCT
ejpam-5657	200	52	)	)	PUNCT
ejpam-5657	201	1	̸=	̸=	NOUN
ejpam-5657	201	2	0	0	NUM
ejpam-5657	201	3	∀i	∀i	NOUN
ejpam-5657	201	4	,	,	PUNCT
ejpam-5657	201	5	∀∆̂	∀∆̂	PROPN
ejpam-5657	201	6	∈	∈	PROPN
ejpam-5657	202	1	∆.	∆.	ADP
ejpam-5657	202	2	the	the	DET
ejpam-5657	202	3	above	above	ADJ
ejpam-5657	202	4	expression	expression	NOUN
ejpam-5657	202	5	for	for	ADP
ejpam-5657	202	6	λi	λi	INTJ
ejpam-5657	202	7	reduces	reduce	VERB
ejpam-5657	202	8	to	to	PART
ejpam-5657	202	9	λi	λi	X
ejpam-5657	202	10	(	(	PUNCT
ejpam-5657	202	11	(	(	PUNCT
ejpam-5657	202	12	αin	αin	NOUN
ejpam-5657	202	13	+	+	CCONJ
ejpam-5657	202	14	eh)−1(αin	eh)−1(αin	ADJ
ejpam-5657	202	15	−	−	PROPN
ejpam-5657	202	16	eh)∆̂	eh)∆̂	PROPN
ejpam-5657	202	17	)	)	PUNCT
ejpam-5657	203	1	̸=	̸=	NOUN
ejpam-5657	203	2	0	0	NUM
ejpam-5657	203	3	∀i	∀i	NOUN
ejpam-5657	203	4	,	,	PUNCT
ejpam-5657	203	5	∀∆̂	∀∆̂	PROPN
ejpam-5657	203	6	∈	∈	PROPN
ejpam-5657	204	1	∆.	∆.	X
ejpam-5657	204	2	in	in	ADP
ejpam-5657	204	3	turn	turn	NOUN
ejpam-5657	204	4	this	this	DET
ejpam-5657	204	5	yields	yield	NOUN
ejpam-5657	204	6	λi	λi	INTJ
ejpam-5657	204	7	(	(	PUNCT
ejpam-5657	204	8	(	(	PUNCT
ejpam-5657	204	9	αin	αin	NOUN
ejpam-5657	204	10	+	+	PROPN
ejpam-5657	204	11	a)−1(αin	a)−1(αin	ADJ
ejpam-5657	204	12	−a)∆̂	−a)∆̂	PROPN
ejpam-5657	204	13	)	)	PUNCT
ejpam-5657	204	14	̸=	̸=	PROPN
ejpam-5657	204	15	0	0	NUM
ejpam-5657	204	16	∀i	∀i	NOUN
ejpam-5657	204	17	,	,	PUNCT
ejpam-5657	204	18	∀∆̂	∀∆̂	PROPN
ejpam-5657	204	19	∈	∈	PROPN
ejpam-5657	205	1	∆.	∆.	ADJ
ejpam-5657	205	2	m.u.r	m.u.r	NOUN
ejpam-5657	205	3	et	et	PROPN
ejpam-5657	205	4	al	al	PROPN
ejpam-5657	205	5	.	.	PUNCT
ejpam-5657	205	6	/	/	SYM
ejpam-5657	205	7	eur	eur	PROPN
ejpam-5657	205	8	.	.	PUNCT
ejpam-5657	206	1	j.	j.	PROPN
ejpam-5657	206	2	pure	pure	PROPN
ejpam-5657	206	3	appl	appl	PROPN
ejpam-5657	206	4	.	.	PROPN
ejpam-5657	206	5	math	math	PROPN
ejpam-5657	206	6	,	,	PUNCT
ejpam-5657	206	7	18	18	NUM
ejpam-5657	206	8	(	(	PUNCT
ejpam-5657	206	9	1	1	NUM
ejpam-5657	206	10	)	)	PUNCT
ejpam-5657	206	11	(	(	PUNCT
ejpam-5657	206	12	2025	2025	NUM
ejpam-5657	206	13	)	)	PUNCT
ejpam-5657	206	14	,	,	PUNCT
ejpam-5657	206	15	5657	5657	NUM
ejpam-5657	206	16	9	9	NUM
ejpam-5657	206	17	of	of	ADP
ejpam-5657	206	18	17	17	NUM
ejpam-5657	206	19	finally	finally	ADV
ejpam-5657	206	20	,	,	PUNCT
ejpam-5657	206	21	we	we	PRON
ejpam-5657	206	22	conclude	conclude	VERB
ejpam-5657	206	23	that	that	SCONJ
ejpam-5657	206	24	0	0	NUM
ejpam-5657	206	25	≤	≤	NUM
ejpam-5657	206	26	µ∆	µ∆	NOUN
ejpam-5657	206	27	(	(	PUNCT
ejpam-5657	206	28	(	(	PUNCT
ejpam-5657	206	29	αin	αin	NOUN
ejpam-5657	206	30	+	+	ADJ
ejpam-5657	206	31	a)−1(αin	a)−1(αin	NOUN
ejpam-5657	206	32	−a	−a	ADJ
ejpam-5657	206	33	)	)	PUNCT
ejpam-5657	206	34	)	)	PUNCT
ejpam-5657	206	35	≤	≤	NUM
ejpam-5657	206	36	1	1	NUM
ejpam-5657	206	37	.	.	PUNCT
ejpam-5657	207	1	the	the	DET
ejpam-5657	207	2	following	follow	VERB
ejpam-5657	207	3	theorem	theorem	NOUN
ejpam-5657	207	4	8	8	NUM
ejpam-5657	207	5	gives	give	VERB
ejpam-5657	207	6	an	an	DET
ejpam-5657	207	7	interconnection	interconnection	NOUN
ejpam-5657	207	8	between	between	ADP
ejpam-5657	207	9	continuous	continuous	ADJ
ejpam-5657	207	10	-	-	PUNCT
ejpam-5657	207	11	time	time	NOUN
ejpam-5657	207	12	d	d	NOUN
ejpam-5657	207	13	-	-	ADJ
ejpam-5657	207	14	stable	stable	ADJ
ejpam-5657	207	15	matrix	matrix	NOUN
ejpam-5657	207	16	and	and	CCONJ
ejpam-5657	207	17	structured	structure	VERB
ejpam-5657	207	18	singular	singular	ADJ
ejpam-5657	207	19	values	value	NOUN
ejpam-5657	207	20	of	of	ADP
ejpam-5657	207	21	a	a	DET
ejpam-5657	207	22	perturbed	perturb	VERB
ejpam-5657	207	23	matrix	matrix	NOUN
ejpam-5657	207	24	.	.	PUNCT
ejpam-5657	208	1	theorem	theorem	VERB
ejpam-5657	208	2	8	8	NUM
ejpam-5657	208	3	.	.	PUNCT
ejpam-5657	209	1	let	let	VERB
ejpam-5657	209	2	a	a	DET
ejpam-5657	209	3	∈	∈	PROPN
ejpam-5657	209	4	rn	rn	PROPN
ejpam-5657	209	5	,	,	PUNCT
ejpam-5657	209	6	n	n	PRON
ejpam-5657	209	7	such	such	ADJ
ejpam-5657	209	8	that	that	SCONJ
ejpam-5657	209	9	re(λi(a	re(λi(a	PROPN
ejpam-5657	209	10	)	)	PUNCT
ejpam-5657	209	11	)	)	PUNCT
ejpam-5657	210	1	>	>	X
ejpam-5657	210	2	0	0	NUM
ejpam-5657	210	3	,	,	PUNCT
ejpam-5657	210	4	∀	∀	VERB
ejpam-5657	211	1	i	i	PRON
ejpam-5657	211	2	and	and	CCONJ
ejpam-5657	211	3	is	be	AUX
ejpam-5657	211	4	continuous	continuous	ADJ
ejpam-5657	211	5	-	-	PUNCT
ejpam-5657	211	6	time	time	NOUN
ejpam-5657	211	7	d	d	ADJ
ejpam-5657	211	8	-	-	ADJ
ejpam-5657	211	9	stable	stable	ADJ
ejpam-5657	211	10	matrix	matrix	NOUN
ejpam-5657	211	11	,	,	PUNCT
ejpam-5657	211	12	then	then	ADV
ejpam-5657	211	13	0	0	NUM
ejpam-5657	211	14	≤	≤	NUM
ejpam-5657	211	15	µ∆	µ∆	NOUN
ejpam-5657	211	16	(	(	PUNCT
ejpam-5657	211	17	(	(	PUNCT
ejpam-5657	211	18	iin	iin	NOUN
ejpam-5657	211	19	+	+	NOUN
ejpam-5657	211	20	a)−1(iin	a)−1(iin	NOUN
ejpam-5657	211	21	−a	−a	NOUN
ejpam-5657	211	22	)	)	PUNCT
ejpam-5657	211	23	)	)	PUNCT
ejpam-5657	212	1	<	<	X
ejpam-5657	212	2	1	1	NUM
ejpam-5657	212	3	,	,	PUNCT
ejpam-5657	212	4	i	i	PRON
ejpam-5657	212	5	=	=	PUNCT
ejpam-5657	212	6	√	√	NUM
ejpam-5657	212	7	−1	−1	NOUN
ejpam-5657	212	8	.	.	PUNCT
ejpam-5657	213	1	proof	proof	NOUN
ejpam-5657	213	2	.	.	PUNCT
ejpam-5657	214	1	we	we	PRON
ejpam-5657	214	2	aim	aim	VERB
ejpam-5657	214	3	to	to	PART
ejpam-5657	214	4	show	show	VERB
ejpam-5657	214	5	that	that	SCONJ
ejpam-5657	214	6	re(λi(a	re(λi(a	PROPN
ejpam-5657	214	7	)	)	PUNCT
ejpam-5657	214	8	)	)	PUNCT
ejpam-5657	215	1	>	>	X
ejpam-5657	215	2	0,∀i	0,∀i	PUNCT
ejpam-5657	216	1	if	if	SCONJ
ejpam-5657	216	2	re(λi(ah	re(λi(ah	X
ejpam-5657	216	3	)	)	PUNCT
ejpam-5657	216	4	)	)	PUNCT
ejpam-5657	217	1	=	=	SYM
ejpam-5657	217	2	re(λi(h)),∀i,∀h	re(λi(h)),∀i,∀h	PROPN
ejpam-5657	217	3	≥	≥	NOUN
ejpam-5657	217	4	0	0	NUM
ejpam-5657	217	5	.	.	PUNCT
ejpam-5657	218	1	if	if	SCONJ
ejpam-5657	218	2	re(λi(a	re(λi(a	PROPN
ejpam-5657	218	3	)	)	PUNCT
ejpam-5657	218	4	)	)	PUNCT
ejpam-5657	219	1	≥	≥	NOUN
ejpam-5657	219	2	0	0	NUM
ejpam-5657	219	3	,	,	PUNCT
ejpam-5657	219	4	∀i	∀i	NOUN
ejpam-5657	219	5	and	and	CCONJ
ejpam-5657	219	6	a	a	DET
ejpam-5657	219	7	∈	∈	PROPN
ejpam-5657	219	8	cn×n	cn×n	NOUN
ejpam-5657	219	9	is	be	AUX
ejpam-5657	219	10	n	n	NUM
ejpam-5657	219	11	×	×	NOUN
ejpam-5657	219	12	n	n	CCONJ
ejpam-5657	219	13	-	-	PUNCT
ejpam-5657	219	14	singular	singular	ADJ
ejpam-5657	219	15	matrix	matrix	NOUN
ejpam-5657	219	16	,	,	PUNCT
ejpam-5657	219	17	then	then	ADV
ejpam-5657	219	18	there	there	PRON
ejpam-5657	219	19	exists	exist	VERB
ejpam-5657	219	20	a	a	DET
ejpam-5657	219	21	unitary	unitary	ADJ
ejpam-5657	219	22	matrix	matrix	NOUN
ejpam-5657	219	23	u	u	NOUN
ejpam-5657	219	24	such	such	ADJ
ejpam-5657	219	25	that	that	SCONJ
ejpam-5657	219	26	u∗au	u∗au	PROPN
ejpam-5657	220	1	=	=	PRON
ejpam-5657	220	2	(	(	PUNCT
ejpam-5657	220	3	m11	m11	NOUN
ejpam-5657	220	4	+	+	CCONJ
ejpam-5657	220	5	in11	in11	PROPN
ejpam-5657	220	6	in12	in12	PROPN
ejpam-5657	220	7	in21	in21	PROPN
ejpam-5657	220	8	·	·	PUNCT
ejpam-5657	220	9	)	)	PUNCT
ejpam-5657	220	10	,	,	PUNCT
ejpam-5657	220	11	with	with	ADP
ejpam-5657	220	12	m11	m11	PROPN
ejpam-5657	220	13	>	>	X
ejpam-5657	220	14	0	0	NUM
ejpam-5657	220	15	,	,	PUNCT
ejpam-5657	220	16	and	and	CCONJ
ejpam-5657	220	17	for	for	ADP
ejpam-5657	220	18	u∗au	u∗au	PROPN
ejpam-5657	220	19	=	=	SYM
ejpam-5657	220	20	(	(	PUNCT
ejpam-5657	220	21	·	·	PUNCT
ejpam-5657	220	22	·	·	PUNCT
ejpam-5657	220	23	·	·	PUNCT
ejpam-5657	220	24	in	in	ADP
ejpam-5657	220	25	)	)	PUNCT
ejpam-5657	220	26	≥	≥	NOUN
ejpam-5657	220	27	0	0	NUM
ejpam-5657	220	28	.	.	PUNCT
ejpam-5657	221	1	in	in	ADP
ejpam-5657	221	2	turn	turn	NOUN
ejpam-5657	221	3	,	,	PUNCT
ejpam-5657	221	4	this	this	DET
ejpam-5657	221	5	yields	yield	NOUN
ejpam-5657	221	6	re(λi(ah	re(λi(ah	NOUN
ejpam-5657	221	7	)	)	PUNCT
ejpam-5657	221	8	)	)	PUNCT
ejpam-5657	222	1	=	=	SYM
ejpam-5657	222	2	re(λi(h	re(λi(h	NOUN
ejpam-5657	222	3	)	)	PUNCT
ejpam-5657	222	4	)	)	PUNCT
ejpam-5657	222	5	,	,	PUNCT
ejpam-5657	222	6	∀i	∀i	NOUN
ejpam-5657	222	7	.	.	PUNCT
ejpam-5657	223	1	secondly	secondly	ADV
ejpam-5657	223	2	,	,	PUNCT
ejpam-5657	223	3	we	we	PRON
ejpam-5657	223	4	prove	prove	VERB
ejpam-5657	223	5	that	that	SCONJ
ejpam-5657	223	6	0	0	NUM
ejpam-5657	223	7	≤	≤	NUM
ejpam-5657	223	8	µ∆	µ∆	NOUN
ejpam-5657	223	9	(	(	PUNCT
ejpam-5657	223	10	(	(	PUNCT
ejpam-5657	223	11	iin	iin	NOUN
ejpam-5657	223	12	+	+	NOUN
ejpam-5657	223	13	a)−1(iin	a)−1(iin	NOUN
ejpam-5657	223	14	−a	−a	NOUN
ejpam-5657	223	15	)	)	PUNCT
ejpam-5657	223	16	)	)	PUNCT
ejpam-5657	223	17	<	<	X
ejpam-5657	224	1	1	1	X
ejpam-5657	224	2	.	.	PUNCT
ejpam-5657	224	3	to	to	PART
ejpam-5657	224	4	prove	prove	VERB
ejpam-5657	224	5	the	the	DET
ejpam-5657	224	6	above	above	ADJ
ejpam-5657	224	7	result	result	NOUN
ejpam-5657	224	8	,	,	PUNCT
ejpam-5657	224	9	we	we	PRON
ejpam-5657	224	10	take	take	VERB
ejpam-5657	224	11	the	the	DET
ejpam-5657	224	12	given	give	VERB
ejpam-5657	224	13	matrix	matrix	NOUN
ejpam-5657	224	14	a	a	DET
ejpam-5657	224	15	=	=	X
ejpam-5657	224	16	eh	eh	INTJ
ejpam-5657	224	17	,	,	PUNCT
ejpam-5657	224	18	a	a	DET
ejpam-5657	224	19	stable	stable	ADJ
ejpam-5657	224	20	matrix	matrix	NOUN
ejpam-5657	224	21	where	where	SCONJ
ejpam-5657	224	22	h	h	PROPN
ejpam-5657	224	23	≥	≥	NOUN
ejpam-5657	224	24	0	0	NUM
ejpam-5657	224	25	,	,	PUNCT
ejpam-5657	224	26	a	a	DET
ejpam-5657	224	27	positive	positive	ADJ
ejpam-5657	224	28	semi	semi	ADJ
ejpam-5657	224	29	-	-	ADJ
ejpam-5657	224	30	definite	definite	ADJ
ejpam-5657	224	31	matrix	matrix	NOUN
ejpam-5657	224	32	.	.	PUNCT
ejpam-5657	225	1	let	let	VERB
ejpam-5657	225	2	p	p	PRON
ejpam-5657	225	3	>	>	X
ejpam-5657	225	4	0	0	PROPN
ejpam-5657	225	5	,	,	PUNCT
ejpam-5657	225	6	a	a	DET
ejpam-5657	225	7	positive	positive	ADJ
ejpam-5657	225	8	definite	definite	ADJ
ejpam-5657	225	9	such	such	ADJ
ejpam-5657	225	10	that	that	DET
ejpam-5657	225	11	λi(iin+ehp	λi(iin+ehp	NOUN
ejpam-5657	225	12	)	)	PUNCT
ejpam-5657	225	13	̸=	̸=	PROPN
ejpam-5657	225	14	0	0	NUM
ejpam-5657	225	15	,	,	PUNCT
ejpam-5657	225	16	∀i	∀i	NOUN
ejpam-5657	225	17	where	where	SCONJ
ejpam-5657	225	18	p	p	NOUN
ejpam-5657	225	19	=	=	X
ejpam-5657	225	20	(	(	PUNCT
ejpam-5657	225	21	iin	iin	NOUN
ejpam-5657	225	22	+	+	CCONJ
ejpam-5657	225	23	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5657	225	24	−	−	NUM
ejpam-5657	225	25	∆̂	∆̂	NOUN
ejpam-5657	225	26	)	)	PUNCT
ejpam-5657	225	27	for	for	ADP
ejpam-5657	225	28	all	all	PRON
ejpam-5657	225	29	∆̂	∆̂	PUNCT
ejpam-5657	225	30	∈	∈	PROPN
ejpam-5657	226	1	∆.	∆.	NOUN
ejpam-5657	226	2	this	this	PRON
ejpam-5657	226	3	allows	allow	VERB
ejpam-5657	226	4	as	as	SCONJ
ejpam-5657	226	5	to	to	PART
ejpam-5657	226	6	have	have	VERB
ejpam-5657	226	7	that	that	PRON
ejpam-5657	226	8	λi	λi	ADP
ejpam-5657	226	9	(	(	PUNCT
ejpam-5657	226	10	iin	iin	NOUN
ejpam-5657	226	11	+	+	CCONJ
ejpam-5657	226	12	eh(iin	eh(iin	NOUN
ejpam-5657	226	13	+	+	NOUN
ejpam-5657	226	14	∆̂)−1(iin	∆̂)−1(iin	NOUN
ejpam-5657	226	15	−	−	NUM
ejpam-5657	226	16	∆̂	∆̂	NOUN
ejpam-5657	226	17	)	)	PUNCT
ejpam-5657	226	18	)	)	PUNCT
ejpam-5657	227	1	̸=	̸=	NOUN
ejpam-5657	227	2	0	0	NUM
ejpam-5657	228	1	∀i,∀∆̂	∀i,∀∆̂	PROPN
ejpam-5657	228	2	∈	∈	PROPN
ejpam-5657	229	1	∆.	∆.	NOUN
ejpam-5657	229	2	the	the	DET
ejpam-5657	229	3	above	above	ADJ
ejpam-5657	229	4	expression	expression	NOUN
ejpam-5657	229	5	takes	take	VERB
ejpam-5657	229	6	the	the	DET
ejpam-5657	229	7	form	form	NOUN
ejpam-5657	229	8	λi	λi	INTJ
ejpam-5657	229	9	(	(	PUNCT
ejpam-5657	229	10	(	(	PUNCT
ejpam-5657	229	11	iin	iin	PROPN
ejpam-5657	229	12	+	+	CCONJ
ejpam-5657	229	13	eh)−1(iin	eh)−1(iin	VERB
ejpam-5657	229	14	−	−	PROPN
ejpam-5657	229	15	eh)∆̂	eh)∆̂	PROPN
ejpam-5657	229	16	)	)	PUNCT
ejpam-5657	230	1	̸=	̸=	PROPN
ejpam-5657	230	2	0	0	NUM
ejpam-5657	231	1	∀i,∀∆̂	∀i,∀∆̂	PROPN
ejpam-5657	231	2	∈	∈	PROPN
ejpam-5657	232	1	∆.	∆.	X
ejpam-5657	232	2	finally	finally	ADV
ejpam-5657	232	3	,	,	PUNCT
ejpam-5657	232	4	this	this	PRON
ejpam-5657	232	5	implies	imply	VERB
ejpam-5657	232	6	that	that	SCONJ
ejpam-5657	232	7	λi	λi	ADP
ejpam-5657	232	8	(	(	PUNCT
ejpam-5657	232	9	(	(	PUNCT
ejpam-5657	232	10	iin	iin	NOUN
ejpam-5657	232	11	+	+	PROPN
ejpam-5657	232	12	a)−1(iin	a)−1(iin	PROPN
ejpam-5657	232	13	−a)∆̂	−a)∆̂	PROPN
ejpam-5657	232	14	)	)	PUNCT
ejpam-5657	232	15	̸=	̸=	PROPN
ejpam-5657	232	16	0	0	NUM
ejpam-5657	233	1	∀i,∀∆̂	∀i,∀∆̂	PROPN
ejpam-5657	233	2	∈	∈	PROPN
ejpam-5657	233	3	∆.	∆.	X
ejpam-5657	233	4	thus	thus	ADV
ejpam-5657	233	5	,	,	PUNCT
ejpam-5657	233	6	0	0	NUM
ejpam-5657	233	7	≤	≤	NUM
ejpam-5657	233	8	µb	µb	VERB
ejpam-5657	233	9	(	(	PUNCT
ejpam-5657	233	10	(	(	PUNCT
ejpam-5657	233	11	iin	iin	NOUN
ejpam-5657	233	12	+	+	NOUN
ejpam-5657	233	13	a)−1(iin	a)−1(iin	NOUN
ejpam-5657	233	14	−a	−a	NOUN
ejpam-5657	233	15	)	)	PUNCT
ejpam-5657	233	16	)	)	PUNCT
ejpam-5657	234	1	<	<	X
ejpam-5657	234	2	1	1	X
ejpam-5657	234	3	.	.	PUNCT
ejpam-5657	234	4	theorem	theorem	NOUN
ejpam-5657	234	5	9	9	NUM
ejpam-5657	234	6	.	.	PUNCT
ejpam-5657	235	1	let	let	VERB
ejpam-5657	235	2	a	a	DET
ejpam-5657	235	3	∈	∈	ADJ
ejpam-5657	235	4	cn×n	cn×n	ADJ
ejpam-5657	235	5	satisfies	satisfie	NOUN
ejpam-5657	235	6	re(λi(a	re(λi(a	PROPN
ejpam-5657	235	7	)	)	PUNCT
ejpam-5657	235	8	)	)	PUNCT
ejpam-5657	236	1	>	>	X
ejpam-5657	236	2	0	0	NUM
ejpam-5657	236	3	,	,	PUNCT
ejpam-5657	236	4	∀	∀	NUM
ejpam-5657	236	5	i	i	PRON
ejpam-5657	236	6	is	be	AUX
ejpam-5657	236	7	a	a	DET
ejpam-5657	236	8	continuous	continuous	ADJ
ejpam-5657	236	9	-	-	PUNCT
ejpam-5657	236	10	time	time	NOUN
ejpam-5657	236	11	diagonal	diagonal	ADJ
ejpam-5657	236	12	stable	stable	ADJ
ejpam-5657	236	13	matrix	matrix	NOUN
ejpam-5657	236	14	and	and	CCONJ
ejpam-5657	236	15	its	its	PRON
ejpam-5657	236	16	dual	dual	ADJ
ejpam-5657	236	17	matrix	matrix	NOUN
ejpam-5657	236	18	â	â	PUNCT
ejpam-5657	236	19	:	:	PUNCT
ejpam-5657	236	20	=	=	SYM
ejpam-5657	236	21	(	(	PUNCT
ejpam-5657	236	22	a−	a−	PROPN
ejpam-5657	236	23	i)−1(a+	i)−1(a+	NOUN
ejpam-5657	236	24	i	i	PROPN
ejpam-5657	236	25	)	)	PUNCT
ejpam-5657	236	26	is	be	AUX
ejpam-5657	236	27	discrete	discrete	ADJ
ejpam-5657	236	28	-	-	PUNCT
ejpam-5657	236	29	time	time	NOUN
ejpam-5657	236	30	diagonal	diagonal	ADJ
ejpam-5657	236	31	stable	stable	NOUN
ejpam-5657	236	32	,	,	PUNCT
ejpam-5657	236	33	then	then	ADV
ejpam-5657	236	34	σmax(â1	σmax(â1	NUM
ejpam-5657	236	35	)	)	PUNCT
ejpam-5657	236	36	<	<	X
ejpam-5657	236	37	1	1	NUM
ejpam-5657	236	38	,	,	PUNCT
ejpam-5657	236	39	with	with	ADP
ejpam-5657	236	40	â1	â1	PRON
ejpam-5657	236	41	:	:	PUNCT
ejpam-5657	237	1	=	=	SYM
ejpam-5657	237	2	d	d	SYM
ejpam-5657	237	3	1	1	NUM
ejpam-5657	237	4	2	2	NUM
ejpam-5657	237	5	âd	âd	NOUN
ejpam-5657	237	6	−1	−1	NOUN
ejpam-5657	237	7	2	2	NUM
ejpam-5657	237	8	.	.	PUNCT
ejpam-5657	238	1	m.u.r	m.u.r	NOUN
ejpam-5657	238	2	et	et	PROPN
ejpam-5657	238	3	al	al	PROPN
ejpam-5657	238	4	.	.	PUNCT
ejpam-5657	238	5	/	/	SYM
ejpam-5657	238	6	eur	eur	PROPN
ejpam-5657	238	7	.	.	PUNCT
ejpam-5657	239	1	j.	j.	PROPN
ejpam-5657	239	2	pure	pure	PROPN
ejpam-5657	239	3	appl	appl	PROPN
ejpam-5657	239	4	.	.	PROPN
ejpam-5657	239	5	math	math	PROPN
ejpam-5657	239	6	,	,	PUNCT
ejpam-5657	239	7	18	18	NUM
ejpam-5657	239	8	(	(	PUNCT
ejpam-5657	239	9	1	1	NUM
ejpam-5657	239	10	)	)	PUNCT
ejpam-5657	239	11	(	(	PUNCT
ejpam-5657	239	12	2025	2025	NUM
ejpam-5657	239	13	)	)	PUNCT
ejpam-5657	239	14	,	,	PUNCT
ejpam-5657	239	15	5657	5657	NUM
ejpam-5657	239	16	10	10	NUM
ejpam-5657	239	17	of	of	ADP
ejpam-5657	239	18	17	17	NUM
ejpam-5657	239	19	proof	proof	NOUN
ejpam-5657	239	20	.	.	PUNCT
ejpam-5657	240	1	the	the	DET
ejpam-5657	240	2	matrix	matrix	NOUN
ejpam-5657	240	3	a	a	DET
ejpam-5657	240	4	∈	∈	ADJ
ejpam-5657	240	5	cn×n	cn×n	NOUN
ejpam-5657	240	6	is	be	AUX
ejpam-5657	240	7	continuous	continuous	ADJ
ejpam-5657	240	8	-	-	PUNCT
ejpam-5657	240	9	time	time	NOUN
ejpam-5657	240	10	diagonal	diagonal	ADJ
ejpam-5657	240	11	matrix	matrix	NOUN
ejpam-5657	240	12	.	.	PUNCT
ejpam-5657	241	1	this	this	PRON
ejpam-5657	241	2	means	mean	VERB
ejpam-5657	241	3	that	that	SCONJ
ejpam-5657	241	4	for	for	ADP
ejpam-5657	241	5	a	a	DET
ejpam-5657	241	6	positive	positive	ADJ
ejpam-5657	241	7	diagonal	diagonal	ADJ
ejpam-5657	241	8	matrix	matrix	NOUN
ejpam-5657	241	9	d	d	NOUN
ejpam-5657	241	10	,	,	PUNCT
ejpam-5657	241	11	the	the	DET
ejpam-5657	241	12	matrix	matrix	NOUN
ejpam-5657	241	13	da+atd	da+atd	NOUN
ejpam-5657	241	14	is	be	AUX
ejpam-5657	241	15	negative	negative	ADJ
ejpam-5657	241	16	definite	definite	ADJ
ejpam-5657	241	17	,	,	PUNCT
ejpam-5657	241	18	that	that	ADV
ejpam-5657	241	19	is	is	ADV
ejpam-5657	241	20	,	,	PUNCT
ejpam-5657	241	21	da+atd	da+atd	VERB
ejpam-5657	241	22	<	<	X
ejpam-5657	241	23	0	0	NUM
ejpam-5657	241	24	⇐	⇐	ADJ
ejpam-5657	241	25	⇒	⇒	NOUN
ejpam-5657	241	26	d(â+	d(â+	VERB
ejpam-5657	241	27	i)(â−	i)(â−	VERB
ejpam-5657	241	28	i)−1	i)−1	NOUN
ejpam-5657	241	29	+	+	CCONJ
ejpam-5657	241	30	(	(	PUNCT
ejpam-5657	241	31	(	(	PUNCT
ejpam-5657	241	32	â+	â+	PROPN
ejpam-5657	241	33	i)(â−	i)(â−	NOUN
ejpam-5657	241	34	i)−1)td	i)−1)td	NOUN
ejpam-5657	241	35	<	<	X
ejpam-5657	241	36	0	0	NUM
ejpam-5657	241	37	⇐	⇐	ADJ
ejpam-5657	241	38	⇒	⇒	NOUN
ejpam-5657	241	39	d	d	PROPN
ejpam-5657	241	40	1	1	NUM
ejpam-5657	241	41	2	2	NUM
ejpam-5657	241	42	(	(	PUNCT
ejpam-5657	241	43	â+	â+	PROPN
ejpam-5657	241	44	i)(â−	i)(â−	NOUN
ejpam-5657	241	45	i)−1d	i)−1d	X
ejpam-5657	241	46	−1	−1	NOUN
ejpam-5657	241	47	2	2	NUM
ejpam-5657	241	48	+	+	CCONJ
ejpam-5657	241	49	(	(	PUNCT
ejpam-5657	241	50	(	(	PUNCT
ejpam-5657	241	51	â+	â+	PROPN
ejpam-5657	241	52	i)(â−	i)(â−	NOUN
ejpam-5657	241	53	i)−1)td	i)−1)td	NOUN
ejpam-5657	241	54	<	<	X
ejpam-5657	241	55	0	0	NUM
ejpam-5657	241	56	⇐	⇐	ADJ
ejpam-5657	241	57	⇒	⇒	NOUN
ejpam-5657	241	58	(	(	PUNCT
ejpam-5657	241	59	â1	â1	VERB
ejpam-5657	242	1	+	+	CCONJ
ejpam-5657	242	2	i)(â1	i)(â1	NUM
ejpam-5657	242	3	−	−	NOUN
ejpam-5657	243	1	i)−1	i)−1	NOUN
ejpam-5657	243	2	+	+	X
ejpam-5657	243	3	(	(	PUNCT
ejpam-5657	243	4	(	(	PUNCT
ejpam-5657	243	5	â+	â+	PROPN
ejpam-5657	243	6	i)(â−	i)(â−	VERB
ejpam-5657	243	7	i))−1d	i))−1d	PROPN
ejpam-5657	243	8	<	<	X
ejpam-5657	243	9	0	0	NUM
ejpam-5657	243	10	⇐	⇐	ADJ
ejpam-5657	243	11	⇒	⇒	PROPN
ejpam-5657	243	12	â1	â1	PROPN
ejpam-5657	243	13	t	t	PROPN
ejpam-5657	243	14	â1−i	â1−i	NOUN
ejpam-5657	243	15	<	<	X
ejpam-5657	243	16	0	0	NUM
ejpam-5657	244	1	⇐	⇐	ADJ
ejpam-5657	244	2	⇒	⇒	PROPN
ejpam-5657	244	3	λmax((â1	λmax((â1	X
ejpam-5657	244	4	t	t	NOUN
ejpam-5657	244	5	)	)	PUNCT
ejpam-5657	244	6	â1−i	â1−i	NOUN
ejpam-5657	244	7	)	)	PUNCT
ejpam-5657	244	8	<	<	X
ejpam-5657	244	9	0	0	NUM
ejpam-5657	244	10	⇐	⇐	ADJ
ejpam-5657	244	11	⇒	⇒	PROPN
ejpam-5657	244	12	ρ((â1	ρ((â1	PROPN
ejpam-5657	244	13	t	t	NOUN
ejpam-5657	244	14	)	)	PUNCT
ejpam-5657	244	15	â1	â1	PUNCT
ejpam-5657	244	16	)	)	PUNCT
ejpam-5657	245	1	<	<	X
ejpam-5657	245	2	1	1	NUM
ejpam-5657	245	3	⇐	⇐	ADJ
ejpam-5657	245	4	⇒	⇒	NOUN
ejpam-5657	245	5	σmax(â1	σmax(â1	NUM
ejpam-5657	245	6	)	)	PUNCT
ejpam-5657	245	7	<	<	X
ejpam-5657	245	8	1	1	NUM
ejpam-5657	245	9	.	.	SYM
ejpam-5657	245	10	3.1	3.1	NUM
ejpam-5657	245	11	.	.	PUNCT
ejpam-5657	246	1	pseudo	pseudo	NOUN
ejpam-5657	246	2	-	-	NOUN
ejpam-5657	246	3	spectrum	spectrum	VERB
ejpam-5657	246	4	the	the	DET
ejpam-5657	246	5	computation	computation	NOUN
ejpam-5657	246	6	of	of	ADP
ejpam-5657	246	7	pseudo	pseudo	NOUN
ejpam-5657	246	8	-	-	NOUN
ejpam-5657	246	9	spectrum	spectrum	NOUN
ejpam-5657	246	10	for	for	ADP
ejpam-5657	246	11	a	a	DET
ejpam-5657	246	12	given	give	VERB
ejpam-5657	246	13	matrix	matrix	NOUN
ejpam-5657	246	14	(	(	PUNCT
ejpam-5657	246	15	say	say	INTJ
ejpam-5657	246	16	)	)	PUNCT
ejpam-5657	247	1	m	m	VERB
ejpam-5657	247	2	is	be	AUX
ejpam-5657	247	3	the	the	DET
ejpam-5657	247	4	set	set	NOUN
ejpam-5657	247	5	containing	contain	VERB
ejpam-5657	247	6	the	the	DET
ejpam-5657	247	7	all	all	DET
ejpam-5657	247	8	eigenvalues	eigenvalue	NOUN
ejpam-5657	247	9	of	of	ADP
ejpam-5657	247	10	m	m	PROPN
ejpam-5657	247	11	.	.	PUNCT
ejpam-5657	248	1	one	one	PRON
ejpam-5657	248	2	may	may	AUX
ejpam-5657	248	3	raise	raise	VERB
ejpam-5657	248	4	an	an	DET
ejpam-5657	248	5	important	important	ADJ
ejpam-5657	248	6	question	question	NOUN
ejpam-5657	248	7	about	about	ADP
ejpam-5657	248	8	the	the	DET
ejpam-5657	248	9	singularity	singularity	NOUN
ejpam-5657	248	10	of	of	ADP
ejpam-5657	248	11	given	give	VERB
ejpam-5657	248	12	matrix	matrix	NOUN
ejpam-5657	248	13	m	m	NOUN
ejpam-5657	248	14	as	as	SCONJ
ejpam-5657	248	15	it	it	PRON
ejpam-5657	248	16	does	do	AUX
ejpam-5657	248	17	not	not	PART
ejpam-5657	248	18	appear	appear	VERB
ejpam-5657	248	19	as	as	ADP
ejpam-5657	248	20	a	a	DET
ejpam-5657	248	21	small	small	ADJ
ejpam-5657	248	22	perturbation	perturbation	NOUN
ejpam-5657	248	23	ϵ	ϵ	X
ejpam-5657	248	24	which	which	PRON
ejpam-5657	248	25	may	may	AUX
ejpam-5657	248	26	completely	completely	ADV
ejpam-5657	248	27	change	change	VERB
ejpam-5657	248	28	the	the	DET
ejpam-5657	248	29	answer	answer	NOUN
ejpam-5657	248	30	from	from	ADP
ejpam-5657	248	31	a	a	DET
ejpam-5657	248	32	yes	yes	NOUN
ejpam-5657	248	33	to	to	ADP
ejpam-5657	248	34	a	a	DET
ejpam-5657	248	35	no	no	NOUN
ejpam-5657	248	36	.	.	PUNCT
ejpam-5657	249	1	this	this	DET
ejpam-5657	249	2	further	far	ADV
ejpam-5657	249	3	implies	imply	VERB
ejpam-5657	249	4	that	that	SCONJ
ejpam-5657	249	5	either	either	CCONJ
ejpam-5657	249	6	matrix	matrix	NOUN
ejpam-5657	249	7	-	-	PUNCT
ejpam-5657	249	8	norm	norm	NOUN
ejpam-5657	249	9	||m−1||	||m−1||	NOUN
ejpam-5657	249	10	is	be	AUX
ejpam-5657	249	11	large	large	ADJ
ejpam-5657	249	12	enough	enough	ADV
ejpam-5657	249	13	or	or	CCONJ
ejpam-5657	249	14	not	not	PART
ejpam-5657	249	15	?	?	PUNCT
ejpam-5657	250	1	for	for	ADP
ejpam-5657	250	2	an	an	DET
ejpam-5657	250	3	eigenvalue	eigenvalue	PROPN
ejpam-5657	250	4	λ	λ	NOUN
ejpam-5657	250	5	corresponding	correspond	VERB
ejpam-5657	250	6	to	to	ADP
ejpam-5657	250	7	given	give	VERB
ejpam-5657	250	8	matrix	matrix	NOUN
ejpam-5657	250	9	m	m	NOUN
ejpam-5657	250	10	,	,	PUNCT
ejpam-5657	250	11	a	a	DET
ejpam-5657	250	12	much	much	ADV
ejpam-5657	250	13	important	important	ADJ
ejpam-5657	250	14	question	question	NOUN
ejpam-5657	250	15	one	one	PRON
ejpam-5657	250	16	may	may	AUX
ejpam-5657	250	17	ask	ask	VERB
ejpam-5657	250	18	:	:	PUNCT
ejpam-5657	250	19	is	be	AUX
ejpam-5657	250	20	the	the	DET
ejpam-5657	250	21	matrix	matrix	NOUN
ejpam-5657	250	22	||(λin	||(λin	PROPN
ejpam-5657	251	1	−	−	PROPN
ejpam-5657	252	1	m)−1||	m)−1||	NOUN
ejpam-5657	252	2	is	be	AUX
ejpam-5657	252	3	large	large	ADJ
ejpam-5657	252	4	or	or	CCONJ
ejpam-5657	252	5	not	not	PART
ejpam-5657	252	6	?	?	PUNCT
ejpam-5657	253	1	this	this	DET
ejpam-5657	253	2	pattern	pattern	NOUN
ejpam-5657	253	3	allows	allow	VERB
ejpam-5657	253	4	to	to	PART
ejpam-5657	253	5	have	have	VERB
ejpam-5657	253	6	definitions	definition	NOUN
ejpam-5657	253	7	and	and	CCONJ
ejpam-5657	253	8	results	result	NOUN
ejpam-5657	253	9	of	of	ADP
ejpam-5657	253	10	pseudo	pseudo	NOUN
ejpam-5657	253	11	-	-	NOUN
ejpam-5657	253	12	spectrum	spectrum	NOUN
ejpam-5657	253	13	given	give	VERB
ejpam-5657	253	14	as	as	ADP
ejpam-5657	253	15	below	below	ADV
ejpam-5657	253	16	:	:	PUNCT
ejpam-5657	253	17	definition	definition	NOUN
ejpam-5657	253	18	9	9	NUM
ejpam-5657	253	19	.	.	PUNCT
ejpam-5657	254	1	for	for	ADP
ejpam-5657	254	2	matrix	matrix	NOUN
ejpam-5657	254	3	n	n	CCONJ
ejpam-5657	254	4	-	-	PUNCT
ejpam-5657	254	5	dimensional	dimensional	ADJ
ejpam-5657	254	6	matrix	matrix	NOUN
ejpam-5657	254	7	m	m	NOUN
ejpam-5657	254	8	,	,	PUNCT
ejpam-5657	254	9	and	and	CCONJ
ejpam-5657	254	10	for	for	ADP
ejpam-5657	254	11	ϵ	ϵ	PROPN
ejpam-5657	254	12	>	>	X
ejpam-5657	254	13	0	0	PROPN
ejpam-5657	254	14	,	,	PUNCT
ejpam-5657	254	15	a	a	DET
ejpam-5657	254	16	small	small	ADJ
ejpam-5657	254	17	perturbation	perturbation	NOUN
ejpam-5657	254	18	level	level	NOUN
ejpam-5657	254	19	.	.	PUNCT
ejpam-5657	255	1	the	the	DET
ejpam-5657	255	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5657	255	3	σϵ(m	σϵ(m	ADV
ejpam-5657	255	4	)	)	PUNCT
ejpam-5657	255	5	is	be	AUX
ejpam-5657	255	6	the	the	DET
ejpam-5657	255	7	set	set	NOUN
ejpam-5657	255	8	of	of	ADP
ejpam-5657	255	9	eigenvalues	eigenvalue	NOUN
ejpam-5657	255	10	λ	λ	X
ejpam-5657	255	11	∈	∈	NOUN
ejpam-5657	255	12	c	c	AUX
ejpam-5657	256	1	so	so	SCONJ
ejpam-5657	256	2	that	that	SCONJ
ejpam-5657	256	3	||(λin	||(λin	PROPN
ejpam-5657	256	4	−m)−1||	−m)−1||	PROPN
ejpam-5657	256	5	>	>	ADP
ejpam-5657	256	6	1	1	NUM
ejpam-5657	256	7	ϵ	ϵ	NOUN
ejpam-5657	256	8	.	.	PUNCT
ejpam-5657	257	1	remark	remark	PROPN
ejpam-5657	257	2	1	1	NUM
ejpam-5657	257	3	.	.	PUNCT
ejpam-5657	258	1	for	for	ADP
ejpam-5657	258	2	quantity	quantity	NOUN
ejpam-5657	258	3	λ	λ	PROPN
ejpam-5657	258	4	∈	∈	PROPN
ejpam-5657	258	5	σ(m	σ(m	NOUN
ejpam-5657	258	6	)	)	PUNCT
ejpam-5657	258	7	,	,	PUNCT
ejpam-5657	258	8	σ(m	σ(m	NOUN
ejpam-5657	258	9	)	)	PUNCT
ejpam-5657	258	10	,	,	PUNCT
ejpam-5657	258	11	denotes	denote	VERB
ejpam-5657	258	12	the	the	DET
ejpam-5657	258	13	set	set	NOUN
ejpam-5657	258	14	of	of	ADP
ejpam-5657	258	15	eigenvalues	eigenvalue	NOUN
ejpam-5657	258	16	of	of	ADP
ejpam-5657	258	17	m	m	PROPN
ejpam-5657	258	18	,	,	PUNCT
ejpam-5657	258	19	||(λin	||(λin	PROPN
ejpam-5657	258	20	−	−	PROPN
ejpam-5657	258	21	m)−1||	m)−1||	NOUN
ejpam-5657	258	22	=	=	PROPN
ejpam-5657	258	23	∞.	∞.	PROPN
ejpam-5657	258	24	the	the	DET
ejpam-5657	258	25	second	second	ADJ
ejpam-5657	258	26	definition	definition	NOUN
ejpam-5657	258	27	of	of	ADP
ejpam-5657	258	28	pseudo	pseudo	NOUN
ejpam-5657	258	29	-	-	NOUN
ejpam-5657	258	30	spectrum	spectrum	NOUN
ejpam-5657	258	31	is	be	AUX
ejpam-5657	258	32	given	give	VERB
ejpam-5657	258	33	as	as	SCONJ
ejpam-5657	258	34	follows	follow	VERB
ejpam-5657	258	35	.	.	PUNCT
ejpam-5657	259	1	definition	definition	NOUN
ejpam-5657	259	2	10	10	NUM
ejpam-5657	259	3	.	.	PUNCT
ejpam-5657	260	1	for	for	ADP
ejpam-5657	260	2	an	an	DET
ejpam-5657	260	3	n	n	ADV
ejpam-5657	260	4	-	-	PUNCT
ejpam-5657	260	5	dimensional	dimensional	ADJ
ejpam-5657	260	6	matrix	matrix	NOUN
ejpam-5657	260	7	,	,	PUNCT
ejpam-5657	260	8	and	and	CCONJ
ejpam-5657	260	9	for	for	ADP
ejpam-5657	260	10	a	a	DET
ejpam-5657	260	11	given	give	VERB
ejpam-5657	260	12	ϵ	ϵ	PROPN
ejpam-5657	260	13	>	>	X
ejpam-5657	260	14	0	0	PROPN
ejpam-5657	260	15	,	,	PUNCT
ejpam-5657	260	16	a	a	DET
ejpam-5657	260	17	small	small	ADJ
ejpam-5657	260	18	perturbation	perturbation	NOUN
ejpam-5657	260	19	level	level	NOUN
ejpam-5657	260	20	.	.	PUNCT
ejpam-5657	261	1	the	the	DET
ejpam-5657	261	2	ϵ-pseudospectrum	ϵ-pseudospectrum	PROPN
ejpam-5657	261	3	σϵ(m	σϵ(m	ADV
ejpam-5657	261	4	)	)	PUNCT
ejpam-5657	261	5	is	be	AUX
ejpam-5657	261	6	the	the	DET
ejpam-5657	261	7	set	set	NOUN
ejpam-5657	261	8	of	of	ADP
ejpam-5657	261	9	eigenvalues	eigenvalue	NOUN
ejpam-5657	261	10	λ	λ	X
ejpam-5657	261	11	∈	∈	NOUN
ejpam-5657	261	12	c	c	AUX
ejpam-5657	262	1	so	so	SCONJ
ejpam-5657	262	2	that	that	SCONJ
ejpam-5657	262	3	λ	λ	PROPN
ejpam-5657	262	4	∈	∈	PRON
ejpam-5657	262	5	σ(m	σ(m	NOUN
ejpam-5657	262	6	+	+	CCONJ
ejpam-5657	262	7	e	e	NOUN
ejpam-5657	262	8	)	)	PUNCT
ejpam-5657	262	9	,	,	PUNCT
ejpam-5657	262	10	for	for	ADP
ejpam-5657	262	11	some	some	DET
ejpam-5657	262	12	e	e	NOUN
ejpam-5657	262	13	having	have	VERB
ejpam-5657	262	14	||e||	||e||	PROPN
ejpam-5657	262	15	<	<	X
ejpam-5657	262	16	ϵ.	ϵ.	NOUN
ejpam-5657	263	1	the	the	DET
ejpam-5657	263	2	third	third	ADJ
ejpam-5657	263	3	characterization	characterization	NOUN
ejpam-5657	263	4	of	of	ADP
ejpam-5657	263	5	the	the	DET
ejpam-5657	263	6	computation	computation	NOUN
ejpam-5657	263	7	of	of	ADP
ejpam-5657	263	8	pseudo	pseudo	NOUN
ejpam-5657	263	9	-	-	NOUN
ejpam-5657	263	10	spectrum	spectrum	NOUN
ejpam-5657	263	11	for	for	ADP
ejpam-5657	263	12	given	give	VERB
ejpam-5657	263	13	matrix	matrix	NOUN
ejpam-5657	263	14	m	m	VERB
ejpam-5657	263	15	is	be	AUX
ejpam-5657	263	16	given	give	VERB
ejpam-5657	263	17	as	as	ADP
ejpam-5657	263	18	bellow	bellow	ADJ
ejpam-5657	263	19	.	.	PUNCT
ejpam-5657	264	1	definition	definition	NOUN
ejpam-5657	264	2	11	11	NUM
ejpam-5657	264	3	.	.	PUNCT
ejpam-5657	265	1	for	for	ADP
ejpam-5657	265	2	a	a	DET
ejpam-5657	265	3	given	give	VERB
ejpam-5657	265	4	n	n	CCONJ
ejpam-5657	265	5	-	-	PUNCT
ejpam-5657	265	6	dimensional	dimensional	ADJ
ejpam-5657	265	7	matrix	matrix	NOUN
ejpam-5657	265	8	m	m	NOUN
ejpam-5657	265	9	,	,	PUNCT
ejpam-5657	265	10	and	and	CCONJ
ejpam-5657	265	11	ϵ	ϵ	X
ejpam-5657	265	12	>	>	X
ejpam-5657	265	13	0	0	PROPN
ejpam-5657	265	14	,	,	PUNCT
ejpam-5657	265	15	a	a	DET
ejpam-5657	265	16	small	small	ADJ
ejpam-5657	265	17	perturbation	perturbation	NOUN
ejpam-5657	265	18	level	level	NOUN
ejpam-5657	265	19	.	.	PUNCT
ejpam-5657	266	1	the	the	DET
ejpam-5657	266	2	ϵ-pseudo	ϵ-pseudo	PROPN
ejpam-5657	266	3	spectrum	spectrum	NOUN
ejpam-5657	266	4	σϵ(m	σϵ(m	ADV
ejpam-5657	266	5	)	)	PUNCT
ejpam-5657	266	6	is	be	AUX
ejpam-5657	266	7	the	the	DET
ejpam-5657	266	8	set	set	NOUN
ejpam-5657	266	9	of	of	ADP
ejpam-5657	266	10	eigenvalues	eigenvalue	NOUN
ejpam-5657	266	11	λ	λ	X
ejpam-5657	266	12	∈	∈	NOUN
ejpam-5657	266	13	c	c	AUX
ejpam-5657	267	1	so	so	SCONJ
ejpam-5657	267	2	that	that	SCONJ
ejpam-5657	267	3	||(λin	||(λin	AUX
ejpam-5657	267	4	−m)v||	−m)v||	PROPN
ejpam-5657	267	5	<	<	X
ejpam-5657	267	6	ϵ	ϵ	NOUN
ejpam-5657	267	7	for	for	ADP
ejpam-5657	267	8	some	some	DET
ejpam-5657	267	9	v	v	ADP
ejpam-5657	267	10	∈	∈	PROPN
ejpam-5657	267	11	cn,1	cn,1	PROPN
ejpam-5657	267	12	,	,	PUNCT
ejpam-5657	267	13	||v||	||v||	PROPN
ejpam-5657	267	14	=	=	SYM
ejpam-5657	267	15	1	1	X
ejpam-5657	267	16	.	.	PUNCT
ejpam-5657	267	17	m.u.r	m.u.r	NOUN
ejpam-5657	267	18	et	et	PROPN
ejpam-5657	267	19	al	al	PROPN
ejpam-5657	267	20	.	.	PUNCT
ejpam-5657	267	21	/	/	SYM
ejpam-5657	267	22	eur	eur	PROPN
ejpam-5657	267	23	.	.	PUNCT
ejpam-5657	268	1	j.	j.	PROPN
ejpam-5657	268	2	pure	pure	PROPN
ejpam-5657	268	3	appl	appl	PROPN
ejpam-5657	268	4	.	.	PROPN
ejpam-5657	268	5	math	math	PROPN
ejpam-5657	268	6	,	,	PUNCT
ejpam-5657	268	7	18	18	NUM
ejpam-5657	268	8	(	(	PUNCT
ejpam-5657	268	9	1	1	NUM
ejpam-5657	268	10	)	)	PUNCT
ejpam-5657	268	11	(	(	PUNCT
ejpam-5657	268	12	2025	2025	NUM
ejpam-5657	268	13	)	)	PUNCT
ejpam-5657	268	14	,	,	PUNCT
ejpam-5657	268	15	5657	5657	NUM
ejpam-5657	268	16	11	11	NUM
ejpam-5657	268	17	of	of	ADP
ejpam-5657	268	18	17	17	NUM
ejpam-5657	268	19	the	the	DET
ejpam-5657	268	20	following	follow	VERB
ejpam-5657	268	21	theorem	theorem	NOUN
ejpam-5657	268	22	gives	give	VERB
ejpam-5657	268	23	an	an	DET
ejpam-5657	268	24	equivalence	equivalence	NOUN
ejpam-5657	268	25	of	of	ADP
ejpam-5657	268	26	all	all	DET
ejpam-5657	268	27	above	above	ADJ
ejpam-5657	268	28	definitions	definition	NOUN
ejpam-5657	268	29	of	of	ADP
ejpam-5657	268	30	pseudo	pseudo	NOUN
ejpam-5657	268	31	-	-	NOUN
ejpam-5657	268	32	spectrum	spectrum	NOUN
ejpam-5657	268	33	.	.	PUNCT
ejpam-5657	269	1	theorem	theorem	ADJ
ejpam-5657	269	2	10	10	NUM
ejpam-5657	269	3	.	.	PUNCT
ejpam-5657	270	1	consider	consider	VERB
ejpam-5657	270	2	that	that	PRON
ejpam-5657	270	3	||	||	PUNCT
ejpam-5657	271	1	·	·	PUNCT
ejpam-5657	271	2	||	||	NUM
ejpam-5657	271	3	denotes	denote	VERB
ejpam-5657	271	4	a	a	DET
ejpam-5657	271	5	matrix	matrix	NOUN
ejpam-5657	271	6	norm	norm	NOUN
ejpam-5657	271	7	for	for	ADP
ejpam-5657	271	8	a	a	DET
ejpam-5657	271	9	given	give	VERB
ejpam-5657	271	10	matrix	matrix	NOUN
ejpam-5657	271	11	m	m	NOUN
ejpam-5657	271	12	.	.	PUNCT
ejpam-5657	272	1	following	follow	VERB
ejpam-5657	272	2	statement	statement	NOUN
ejpam-5657	272	3	are	be	AUX
ejpam-5657	272	4	equivalent	equivalent	ADJ
ejpam-5657	272	5	:	:	PUNCT
ejpam-5657	272	6	(	(	PUNCT
ejpam-5657	272	7	i	i	NOUN
ejpam-5657	272	8	)	)	PUNCT
ejpam-5657	272	9	λϵ(m	λϵ(m	PUNCT
ejpam-5657	272	10	)	)	PUNCT
ejpam-5657	273	1	=	=	PRON
ejpam-5657	273	2	{	{	PUNCT
ejpam-5657	273	3	z	z	NOUN
ejpam-5657	273	4	∈	∈	PROPN
ejpam-5657	273	5	c	c	NOUN
ejpam-5657	273	6	:	:	PUNCT
ejpam-5657	273	7	||(zin	||(zin	ADP
ejpam-5657	273	8	−m)−1||	−m)−1||	PROPN
ejpam-5657	273	9	≥	≥	NUM
ejpam-5657	273	10	1	1	NUM
ejpam-5657	273	11	ϵ	ϵ	NOUN
ejpam-5657	273	12	}	}	PUNCT
ejpam-5657	273	13	.	.	PUNCT
ejpam-5657	274	1	(	(	PUNCT
ejpam-5657	274	2	ii	ii	NOUN
ejpam-5657	274	3	)	)	PUNCT
ejpam-5657	274	4	λϵ(m	λϵ(m	PUNCT
ejpam-5657	274	5	)	)	PUNCT
ejpam-5657	275	1	=	=	PRON
ejpam-5657	275	2	{	{	PUNCT
ejpam-5657	275	3	z	z	NOUN
ejpam-5657	275	4	∈	∈	PROPN
ejpam-5657	275	5	c	c	NOUN
ejpam-5657	275	6	:	:	PUNCT
ejpam-5657	275	7	z	z	PROPN
ejpam-5657	275	8	∈	∈	PROPN
ejpam-5657	276	1	λ(m	λ(m	PROPN
ejpam-5657	276	2	+	+	CCONJ
ejpam-5657	276	3	e	e	NOUN
ejpam-5657	276	4	)	)	PUNCT
ejpam-5657	276	5	,	,	PUNCT
ejpam-5657	276	6	||e||	||e||	VERB
ejpam-5657	276	7	≤	≤	NOUN
ejpam-5657	276	8	ϵ	ϵ	X
ejpam-5657	276	9	}	}	PUNCT
ejpam-5657	276	10	.	.	PUNCT
ejpam-5657	277	1	(	(	PUNCT
ejpam-5657	277	2	iii	iii	NOUN
ejpam-5657	277	3	)	)	PUNCT
ejpam-5657	277	4	λϵ(m	λϵ(m	PUNCT
ejpam-5657	277	5	)	)	PUNCT
ejpam-5657	278	1	=	=	PRON
ejpam-5657	278	2	{	{	PUNCT
ejpam-5657	278	3	z	z	NOUN
ejpam-5657	278	4	∈	∈	PROPN
ejpam-5657	278	5	c	c	NOUN
ejpam-5657	278	6	:	:	PUNCT
ejpam-5657	278	7	∃	∃	PROPN
ejpam-5657	278	8	v	v	NOUN
ejpam-5657	278	9	∈	∈	PROPN
ejpam-5657	278	10	cn,1	cn,1	PROPN
ejpam-5657	278	11	s.t	s.t	PROPN
ejpam-5657	278	12	||(m	||(m	NOUN
ejpam-5657	278	13	−	−	PROPN
ejpam-5657	279	1	zin)v||	zin)v||	PROPN
ejpam-5657	279	2	≤	≤	NOUN
ejpam-5657	279	3	ϵ	ϵ	X
ejpam-5657	279	4	}	}	PUNCT
ejpam-5657	279	5	.	.	PUNCT
ejpam-5657	280	1	remark	remark	PROPN
ejpam-5657	280	2	2	2	NUM
ejpam-5657	280	3	.	.	PUNCT
ejpam-5657	281	1	the	the	DET
ejpam-5657	281	2	second	second	ADJ
ejpam-5657	281	3	statement	statement	NOUN
ejpam-5657	281	4	in	in	ADP
ejpam-5657	281	5	the	the	DET
ejpam-5657	281	6	above	above	ADJ
ejpam-5657	281	7	theorem	theorem	NOUN
ejpam-5657	281	8	is	be	AUX
ejpam-5657	281	9	true	true	ADJ
ejpam-5657	281	10	for	for	ADP
ejpam-5657	281	11	some	some	DET
ejpam-5657	281	12	matrix	matrix	NOUN
ejpam-5657	281	13	e.	e.	PROPN
ejpam-5657	281	14	furthermore	furthermore	ADV
ejpam-5657	281	15	,	,	PUNCT
ejpam-5657	281	16	in	in	ADP
ejpam-5657	281	17	last	last	ADJ
ejpam-5657	281	18	statement	statement	NOUN
ejpam-5657	281	19	the	the	DET
ejpam-5657	281	20	column	column	PROPN
ejpam-5657	281	21	vector	vector	NOUN
ejpam-5657	281	22	v	v	PROPN
ejpam-5657	281	23	has	have	VERB
ejpam-5657	281	24	a	a	DET
ejpam-5657	281	25	unit	unit	NOUN
ejpam-5657	281	26	2	2	NUM
ejpam-5657	281	27	-	-	PUNCT
ejpam-5657	281	28	norm	norm	NOUN
ejpam-5657	281	29	,	,	PUNCT
ejpam-5657	281	30	that	that	ADV
ejpam-5657	281	31	is	is	ADV
ejpam-5657	281	32	,	,	PUNCT
ejpam-5657	281	33	||v||2	||v||2	ADJ
ejpam-5657	281	34	=	=	SYM
ejpam-5657	281	35	1	1	NUM
ejpam-5657	281	36	.	.	NOUN
ejpam-5657	281	37	4	4	NUM
ejpam-5657	281	38	.	.	NOUN
ejpam-5657	281	39	numerical	numerical	ADJ
ejpam-5657	281	40	experimentation	experimentation	NOUN
ejpam-5657	281	41	in	in	ADP
ejpam-5657	281	42	this	this	DET
ejpam-5657	281	43	section	section	NOUN
ejpam-5657	281	44	,	,	PUNCT
ejpam-5657	281	45	we	we	PRON
ejpam-5657	281	46	a	a	DET
ejpam-5657	281	47	present	present	NOUN
ejpam-5657	281	48	a	a	DET
ejpam-5657	281	49	comparison	comparison	NOUN
ejpam-5657	281	50	on	on	ADP
ejpam-5657	281	51	the	the	DET
ejpam-5657	281	52	numerical	numerical	ADJ
ejpam-5657	281	53	computation	computation	NOUN
ejpam-5657	281	54	of	of	ADP
ejpam-5657	281	55	lower	low	ADJ
ejpam-5657	281	56	bounds	bound	NOUN
ejpam-5657	281	57	of	of	ADP
ejpam-5657	281	58	structured	structured	ADJ
ejpam-5657	281	59	singular	singular	ADJ
ejpam-5657	281	60	values	value	NOUN
ejpam-5657	281	61	.	.	PUNCT
ejpam-5657	282	1	the	the	DET
ejpam-5657	282	2	numerical	numerical	ADJ
ejpam-5657	282	3	algorithms	algorithm	NOUN
ejpam-5657	282	4	under	under	ADP
ejpam-5657	282	5	consideration	consideration	NOUN
ejpam-5657	282	6	for	for	ADP
ejpam-5657	282	7	approximation	approximation	NOUN
ejpam-5657	282	8	of	of	ADP
ejpam-5657	282	9	lower	low	ADJ
ejpam-5657	282	10	bounds	bound	NOUN
ejpam-5657	282	11	of	of	ADP
ejpam-5657	282	12	structured	structured	ADJ
ejpam-5657	282	13	singular	singular	ADJ
ejpam-5657	282	14	values	value	NOUN
ejpam-5657	282	15	are	be	AUX
ejpam-5657	282	16	:	:	PUNCT
ejpam-5657	282	17	the	the	DET
ejpam-5657	282	18	matlab	matlab	PROPN
ejpam-5657	282	19	function	function	PROPN
ejpam-5657	282	20	mussv	mussv	PROPN
ejpam-5657	282	21	,	,	PUNCT
ejpam-5657	282	22	the	the	DET
ejpam-5657	282	23	power	power	NOUN
ejpam-5657	282	24	algorithm	algorithm	NOUN
ejpam-5657	282	25	(	(	PUNCT
ejpam-5657	282	26	pa	pa	PROPN
ejpam-5657	282	27	)	)	PUNCT
ejpam-5657	283	1	[	[	X
ejpam-5657	283	2	32	32	NUM
ejpam-5657	283	3	]	]	PUNCT
ejpam-5657	283	4	,	,	PUNCT
ejpam-5657	283	5	gain	gain	VERB
ejpam-5657	283	6	based	base	VERB
ejpam-5657	283	7	algorithm	algorithm	NOUN
ejpam-5657	283	8	(	(	PUNCT
ejpam-5657	283	9	gba	gba	NOUN
ejpam-5657	283	10	)	)	PUNCT
ejpam-5657	284	1	[	[	X
ejpam-5657	284	2	39	39	NUM
ejpam-5657	284	3	]	]	PUNCT
ejpam-5657	284	4	,	,	PUNCT
ejpam-5657	284	5	poles	pole	NOUN
ejpam-5657	284	6	migration	migration	NOUN
ejpam-5657	284	7	algorithm	algorithm	NOUN
ejpam-5657	284	8	(	(	PUNCT
ejpam-5657	284	9	pma	pma	NOUN
ejpam-5657	284	10	)	)	PUNCT
ejpam-5657	285	1	[	[	X
ejpam-5657	285	2	29	29	NUM
ejpam-5657	285	3	]	]	PUNCT
ejpam-5657	285	4	,	,	PUNCT
ejpam-5657	285	5	non	non	ADJ
ejpam-5657	285	6	-	-	ADJ
ejpam-5657	285	7	linear	linear	ADJ
ejpam-5657	285	8	optimization	optimization	NOUN
ejpam-5657	285	9	algorithm	algorithm	NOUN
ejpam-5657	285	10	(	(	PUNCT
ejpam-5657	285	11	nla	nla	NOUN
ejpam-5657	285	12	)	)	PUNCT
ejpam-5657	286	1	[	[	X
ejpam-5657	286	2	19	19	NUM
ejpam-5657	286	3	]	]	PUNCT
ejpam-5657	286	4	,	,	PUNCT
ejpam-5657	286	5	and	and	CCONJ
ejpam-5657	286	6	the	the	DET
ejpam-5657	286	7	low	low	ADJ
ejpam-5657	286	8	-	-	PUNCT
ejpam-5657	286	9	rank	rank	NOUN
ejpam-5657	286	10	ode	ode	PROPN
ejpam-5657	286	11	’s	’s	PART
ejpam-5657	286	12	based	base	VERB
ejpam-5657	286	13	algorithm	algorithm	NOUN
ejpam-5657	286	14	(	(	PUNCT
ejpam-5657	286	15	lra	lra	NOUN
ejpam-5657	286	16	)	)	PUNCT
ejpam-5657	286	17	given	give	VERB
ejpam-5657	286	18	by	by	ADP
ejpam-5657	286	19	first	first	ADJ
ejpam-5657	286	20	author	author	NOUN
ejpam-5657	286	21	[	[	X
ejpam-5657	286	22	18	18	NUM
ejpam-5657	286	23	]	]	PUNCT
ejpam-5657	286	24	.	.	PUNCT
ejpam-5657	287	1	the	the	DET
ejpam-5657	287	2	matrices	matrix	NOUN
ejpam-5657	287	3	are	be	AUX
ejpam-5657	287	4	taken	take	VERB
ejpam-5657	287	5	from	from	ADP
ejpam-5657	287	6	various	various	ADJ
ejpam-5657	287	7	models	model	NOUN
ejpam-5657	287	8	of	of	ADP
ejpam-5657	287	9	economy	economy	NOUN
ejpam-5657	287	10	and	and	CCONJ
ejpam-5657	287	11	finance	finance	NOUN
ejpam-5657	287	12	.	.	PUNCT
ejpam-5657	288	1	furthermore	furthermore	ADV
ejpam-5657	288	2	,	,	PUNCT
ejpam-5657	288	3	we	we	PRON
ejpam-5657	288	4	use	use	VERB
ejpam-5657	288	5	eigtool	eigtool	NOUN
ejpam-5657	288	6	[	[	X
ejpam-5657	288	7	28	28	NUM
ejpam-5657	288	8	]	]	PUNCT
ejpam-5657	288	9	for	for	ADP
ejpam-5657	288	10	the	the	DET
ejpam-5657	288	11	computation	computation	NOUN
ejpam-5657	288	12	of	of	ADP
ejpam-5657	288	13	the	the	DET
ejpam-5657	288	14	pseudo	pseudo	NOUN
ejpam-5657	288	15	-	-	NOUN
ejpam-5657	288	16	spectrum	spectrum	NOUN
ejpam-5657	288	17	of	of	ADP
ejpam-5657	288	18	each	each	DET
ejpam-5657	288	19	matrix	matrix	NOUN
ejpam-5657	288	20	.	.	PUNCT
ejpam-5657	289	1	example	example	NOUN
ejpam-5657	290	1	1	1	X
ejpam-5657	290	2	.	.	X
ejpam-5657	290	3	consider	consider	VERB
ejpam-5657	290	4	macroeconomic	macroeconomic	ADJ
ejpam-5657	290	5	model	model	NOUN
ejpam-5657	290	6	of	of	ADP
ejpam-5657	290	7	the	the	DET
ejpam-5657	290	8	trade	trade	NOUN
ejpam-5657	290	9	cycle	cycle	NOUN
ejpam-5657	291	1	[	[	X
ejpam-5657	291	2	7]	7]	NUM
ejpam-5657	291	3	dk	dk	NOUN
ejpam-5657	291	4	=	=	SYM
ejpam-5657	291	5	γ1(k̂	γ1(k̂	NOUN
ejpam-5657	291	6	−k)with	−k)with	X
ejpam-5657	291	7	k̂	k̂	NOUN
ejpam-5657	292	1	=	=	PUNCT
ejpam-5657	292	2	β1y	β1y	VERB
ejpam-5657	292	3	dc	dc	PROPN
ejpam-5657	292	4	=	=	SYM
ejpam-5657	292	5	γ2(ĉ	γ2(ĉ	PROPN
ejpam-5657	292	6	−	−	NOUN
ejpam-5657	292	7	c)with	c)with	NOUN
ejpam-5657	292	8	ĉ	ĉ	VERB
ejpam-5657	292	9	=	=	X
ejpam-5657	292	10	β2y	β2y	PUNCT
ejpam-5657	292	11	+	+	NUM
ejpam-5657	292	12	β3	β3	ADJ
ejpam-5657	292	13	dy	dy	X
ejpam-5657	292	14	=	=	SYM
ejpam-5657	293	1	γ3(ŷ	γ3(ŷ	PROPN
ejpam-5657	293	2	−	−	PUNCT
ejpam-5657	294	1	y	y	PROPN
ejpam-5657	294	2	)	)	PUNCT
ejpam-5657	294	3	with	with	ADP
ejpam-5657	294	4	ŷ	ŷ	NUM
ejpam-5657	294	5	=	=	SYM
ejpam-5657	295	1	c	c	X
ejpam-5657	296	1	+	+	NOUN
ejpam-5657	296	2	dk	dk	PROPN
ejpam-5657	296	3	here	here	ADV
ejpam-5657	296	4	,	,	PUNCT
ejpam-5657	296	5	k	k	PROPN
ejpam-5657	296	6	,	,	PUNCT
ejpam-5657	296	7	c	c	X
ejpam-5657	296	8	,	,	PUNCT
ejpam-5657	296	9	y	y	PROPN
ejpam-5657	296	10	denotes	denote	VERB
ejpam-5657	296	11	stock	stock	NOUN
ejpam-5657	296	12	of	of	ADP
ejpam-5657	296	13	capital	capital	NOUN
ejpam-5657	296	14	,	,	PUNCT
ejpam-5657	296	15	consumption	consumption	NOUN
ejpam-5657	296	16	,	,	PUNCT
ejpam-5657	296	17	and	and	CCONJ
ejpam-5657	296	18	output	output	NOUN
ejpam-5657	296	19	less	less	ADJ
ejpam-5657	296	20	replacement	replacement	NOUN
ejpam-5657	296	21	,	,	PUNCT
ejpam-5657	296	22	respectively	respectively	ADV
ejpam-5657	296	23	.	.	PUNCT
ejpam-5657	297	1	case	case	NOUN
ejpam-5657	297	2	-	-	PUNCT
ejpam-5657	297	3	i	i	PRON
ejpam-5657	297	4	:	:	PUNCT
ejpam-5657	297	5	for	for	ADP
ejpam-5657	297	6	γ1	γ1	PROPN
ejpam-5657	297	7	<	<	X
ejpam-5657	297	8	0.0625	0.0625	NUM
ejpam-5657	297	9	,	,	PUNCT
ejpam-5657	297	10	γ2	γ2	NOUN
ejpam-5657	297	11	=	=	SYM
ejpam-5657	297	12	0.6	0.6	NUM
ejpam-5657	297	13	,	,	PUNCT
ejpam-5657	297	14	γ3	γ3	NOUN
ejpam-5657	297	15	=	=	NOUN
ejpam-5657	297	16	4.0	4.0	NUM
ejpam-5657	297	17	,	,	PUNCT
ejpam-5657	297	18	β1	β1	PROPN
ejpam-5657	297	19	=	=	SYM
ejpam-5657	297	20	2.0	2.0	NUM
ejpam-5657	297	21	,	,	PUNCT
ejpam-5657	297	22	β2	β2	NOUN
ejpam-5657	297	23	=	=	NOUN
ejpam-5657	297	24	0.75	0.75	NUM
ejpam-5657	297	25	,	,	PUNCT
ejpam-5657	297	26	the	the	DET
ejpam-5657	297	27	matrix	matrix	NOUN
ejpam-5657	297	28	c	c	NOUN
ejpam-5657	297	29	has	have	VERB
ejpam-5657	297	30	the	the	DET
ejpam-5657	297	31	structure	structure	NOUN
ejpam-5657	297	32	:	:	PUNCT
ejpam-5657	297	33	c	c	X
ejpam-5657	297	34	=	=	SYM
ejpam-5657	297	35	−0.05	−0.05	NUM
ejpam-5657	297	36	0	0	NUM
ejpam-5657	297	37	0.1	0.1	NUM
ejpam-5657	297	38	0	0	NUM
ejpam-5657	297	39	−0.6	−0.6	PROPN
ejpam-5657	297	40	0.45	0.45	NUM
ejpam-5657	297	41	−0.2	−0.2	PROPN
ejpam-5657	297	42	4.0	4.0	NUM
ejpam-5657	297	43	−3.6	−3.6	NOUN
ejpam-5657	297	44			NOUN
ejpam-5657	297	45	.	.	PUNCT
ejpam-5657	298	1	we	we	PRON
ejpam-5657	298	2	present	present	VERB
ejpam-5657	298	3	the	the	DET
ejpam-5657	298	4	comparison	comparison	NOUN
ejpam-5657	298	5	on	on	ADP
ejpam-5657	298	6	numerical	numerical	ADJ
ejpam-5657	298	7	approximation	approximation	NOUN
ejpam-5657	298	8	of	of	ADP
ejpam-5657	298	9	the	the	DET
ejpam-5657	298	10	lower	low	ADJ
ejpam-5657	298	11	bounds	bound	NOUN
ejpam-5657	298	12	of	of	ADP
ejpam-5657	298	13	structured	structured	ADJ
ejpam-5657	298	14	singular	singular	ADJ
ejpam-5657	298	15	values	value	NOUN
ejpam-5657	298	16	in	in	ADP
ejpam-5657	298	17	following	follow	VERB
ejpam-5657	298	18	table	table	NOUN
ejpam-5657	298	19	1	1	NUM
ejpam-5657	298	20	.	.	PUNCT
ejpam-5657	299	1	the	the	DET
ejpam-5657	299	2	numerical	numerical	ADJ
ejpam-5657	299	3	approximation	approximation	NOUN
ejpam-5657	299	4	of	of	ADP
ejpam-5657	299	5	lower	low	ADJ
ejpam-5657	299	6	bounds	bound	NOUN
ejpam-5657	299	7	of	of	ADP
ejpam-5657	299	8	structured	structured	ADJ
ejpam-5657	299	9	singular	singular	ADJ
ejpam-5657	299	10	values	value	NOUN
ejpam-5657	299	11	mussv	mussv	VERB
ejpam-5657	299	12	pa	pa	PROPN
ejpam-5657	299	13	gba	gba	PROPN
ejpam-5657	299	14	pma	pma	PROPN
ejpam-5657	299	15	nla	nla	PROPN
ejpam-5657	299	16	lra	lra	PROPN
ejpam-5657	299	17	5.4369	5.4369	NUM
ejpam-5657	299	18	5.4369	5.4369	NUM
ejpam-5657	299	19	5.4389	5.4389	NUM
ejpam-5657	299	20	5.4391	5.4391	NUM
ejpam-5657	299	21	5.4371	5.4371	NUM
ejpam-5657	299	22	5.4370	5.4370	NUM
ejpam-5657	299	23	case	case	NOUN
ejpam-5657	299	24	-	-	PUNCT
ejpam-5657	299	25	ii	ii	NOUN
ejpam-5657	299	26	:	:	PUNCT
ejpam-5657	299	27	for	for	ADP
ejpam-5657	299	28	γ1	γ1	NOUN
ejpam-5657	299	29	=	=	PROPN
ejpam-5657	299	30	0.4	0.4	NUM
ejpam-5657	299	31	,	,	PUNCT
ejpam-5657	299	32	the	the	DET
ejpam-5657	299	33	matrix	matrix	NOUN
ejpam-5657	299	34	c	c	NOUN
ejpam-5657	299	35	has	have	VERB
ejpam-5657	299	36	the	the	DET
ejpam-5657	299	37	structure	structure	NOUN
ejpam-5657	299	38	:	:	PUNCT
ejpam-5657	299	39	m.u.r	m.u.r	PROPN
ejpam-5657	299	40	et	et	PROPN
ejpam-5657	299	41	al	al	PROPN
ejpam-5657	299	42	.	.	PUNCT
ejpam-5657	299	43	/	/	SYM
ejpam-5657	299	44	eur	eur	PROPN
ejpam-5657	299	45	.	.	PUNCT
ejpam-5657	300	1	j.	j.	PROPN
ejpam-5657	300	2	pure	pure	PROPN
ejpam-5657	300	3	appl	appl	PROPN
ejpam-5657	300	4	.	.	PROPN
ejpam-5657	300	5	math	math	PROPN
ejpam-5657	300	6	,	,	PUNCT
ejpam-5657	300	7	18	18	NUM
ejpam-5657	300	8	(	(	PUNCT
ejpam-5657	300	9	1	1	NUM
ejpam-5657	300	10	)	)	PUNCT
ejpam-5657	300	11	(	(	PUNCT
ejpam-5657	300	12	2025	2025	NUM
ejpam-5657	300	13	)	)	PUNCT
ejpam-5657	300	14	,	,	PUNCT
ejpam-5657	300	15	5657	5657	NUM
ejpam-5657	300	16	12	12	NUM
ejpam-5657	300	17	of	of	ADP
ejpam-5657	300	18	17	17	NUM
ejpam-5657	300	19	figure	figure	NOUN
ejpam-5657	300	20	1	1	NUM
ejpam-5657	300	21	:	:	PUNCT
ejpam-5657	300	22	the	the	DET
ejpam-5657	300	23	graphs	graph	NOUN
ejpam-5657	300	24	of	of	ADP
ejpam-5657	300	25	singular	singular	ADJ
ejpam-5657	300	26	values	value	NOUN
ejpam-5657	300	27	and	and	CCONJ
ejpam-5657	300	28	pseudo	pseudo	NOUN
ejpam-5657	300	29	-	-	NOUN
ejpam-5657	300	30	inverse	inverse	NOUN
ejpam-5657	300	31	of	of	ADP
ejpam-5657	300	32	m	m	PROPN
ejpam-5657	300	33	in	in	ADP
ejpam-5657	300	34	example-1	example-1	PROPN
ejpam-5657	300	35	(	(	PUNCT
ejpam-5657	300	36	case	case	NOUN
ejpam-5657	300	37	-	-	PUNCT
ejpam-5657	300	38	i	i	NOUN
ejpam-5657	300	39	)	)	PUNCT
ejpam-5657	300	40	figure	figure	NOUN
ejpam-5657	300	41	2	2	NUM
ejpam-5657	300	42	:	:	PUNCT
ejpam-5657	300	43	the	the	DET
ejpam-5657	300	44	graphs	graph	NOUN
ejpam-5657	300	45	of	of	ADP
ejpam-5657	300	46	singular	singular	ADJ
ejpam-5657	300	47	values	value	NOUN
ejpam-5657	300	48	and	and	CCONJ
ejpam-5657	300	49	pseudo	pseudo	NOUN
ejpam-5657	300	50	-	-	NOUN
ejpam-5657	300	51	inverse	inverse	NOUN
ejpam-5657	300	52	of	of	ADP
ejpam-5657	300	53	m	m	PROPN
ejpam-5657	300	54	in	in	ADP
ejpam-5657	300	55	example-1	example-1	PROPN
ejpam-5657	300	56	(	(	PUNCT
ejpam-5657	300	57	case	case	NOUN
ejpam-5657	300	58	-	-	PUNCT
ejpam-5657	300	59	ii	ii	NOUN
ejpam-5657	300	60	)	)	PUNCT
ejpam-5657	300	61	c	c	NOUN
ejpam-5657	301	1	=	=	PUNCT
ejpam-5657	301	2	−0.4	−0.4	PROPN
ejpam-5657	301	3	0	0	NUM
ejpam-5657	301	4	0.8	0.8	NUM
ejpam-5657	301	5	0	0	NUM
ejpam-5657	301	6	−0.6	−0.6	PROPN
ejpam-5657	301	7	0.45	0.45	NUM
ejpam-5657	301	8	−1.6	−1.6	NOUN
ejpam-5657	301	9	4.0	4.0	NUM
ejpam-5657	301	10	−0.8	−0.8	ADJ
ejpam-5657	301	11			NOUN
ejpam-5657	301	12	.	.	PUNCT
ejpam-5657	302	1	we	we	PRON
ejpam-5657	302	2	present	present	VERB
ejpam-5657	302	3	the	the	DET
ejpam-5657	302	4	comparison	comparison	NOUN
ejpam-5657	302	5	on	on	ADP
ejpam-5657	302	6	numerical	numerical	ADJ
ejpam-5657	302	7	approximation	approximation	NOUN
ejpam-5657	302	8	of	of	ADP
ejpam-5657	302	9	the	the	DET
ejpam-5657	302	10	lower	low	ADJ
ejpam-5657	302	11	bounds	bound	NOUN
ejpam-5657	302	12	of	of	ADP
ejpam-5657	302	13	structured	structured	ADJ
ejpam-5657	302	14	singular	singular	ADJ
ejpam-5657	302	15	values	value	NOUN
ejpam-5657	302	16	in	in	ADP
ejpam-5657	302	17	following	follow	VERB
ejpam-5657	302	18	table	table	NOUN
ejpam-5657	302	19	2	2	NUM
ejpam-5657	302	20	.	.	PUNCT
ejpam-5657	303	1	the	the	DET
ejpam-5657	303	2	numerical	numerical	ADJ
ejpam-5657	303	3	approximation	approximation	NOUN
ejpam-5657	303	4	of	of	ADP
ejpam-5657	303	5	lower	low	ADJ
ejpam-5657	303	6	bounds	bound	NOUN
ejpam-5657	303	7	of	of	ADP
ejpam-5657	303	8	structured	structured	ADJ
ejpam-5657	303	9	singular	singular	ADJ
ejpam-5657	303	10	values	value	NOUN
ejpam-5657	303	11	mussv	mussv	VERB
ejpam-5657	303	12	pa	pa	PROPN
ejpam-5657	303	13	gba	gba	PROPN
ejpam-5657	303	14	pma	pma	PROPN
ejpam-5657	303	15	nla	nla	PROPN
ejpam-5657	303	16	lra	lra	PROPN
ejpam-5657	303	17	4.4272	4.4272	NUM
ejpam-5657	303	18	4.4274	4.4274	NUM
ejpam-5657	303	19	4.4285	4.4285	NUM
ejpam-5657	303	20	4.4293	4.4293	NUM
ejpam-5657	303	21	4.4290	4.4290	NUM
ejpam-5657	303	22	4.4272	4.4272	NUM
ejpam-5657	303	23	example	example	NOUN
ejpam-5657	303	24	2	2	NUM
ejpam-5657	303	25	.	.	X
ejpam-5657	303	26	consider	consider	VERB
ejpam-5657	303	27	linear	linear	ADJ
ejpam-5657	303	28	dynamical	dynamical	ADJ
ejpam-5657	303	29	model	model	NOUN
ejpam-5657	303	30	yt	yt	PROPN
ejpam-5657	304	1	=	=	PUNCT
ejpam-5657	304	2	(	(	PUNCT
ejpam-5657	304	3	in	in	ADP
ejpam-5657	304	4	−a)−1b	−a)−1b	X
ejpam-5657	304	5	+	+	CCONJ
ejpam-5657	304	6	ext	ext	NOUN
ejpam-5657	304	7	.	.	PUNCT
ejpam-5657	305	1	for	for	ADP
ejpam-5657	305	2	a	a	PRON
ejpam-5657	305	3	=	=	X
ejpam-5657	305	4	[	[	PUNCT
ejpam-5657	305	5	0	0	NUM
ejpam-5657	305	6	1	1	NUM
ejpam-5657	305	7	0	0	NUM
ejpam-5657	305	8	0	0	NUM
ejpam-5657	305	9	]	]	PUNCT
ejpam-5657	305	10	,	,	PUNCT
ejpam-5657	305	11	b	b	X
ejpam-5657	305	12	=	=	PUNCT
ejpam-5657	305	13	[	[	PUNCT
ejpam-5657	305	14	0	0	NUM
ejpam-5657	305	15	0.5	0.5	NUM
ejpam-5657	305	16	0	0	NUM
ejpam-5657	305	17	0	0	NUM
ejpam-5657	305	18	]	]	PUNCT
ejpam-5657	305	19	.	.	PUNCT
ejpam-5657	306	1	the	the	DET
ejpam-5657	306	2	matrix	matrix	NOUN
ejpam-5657	306	3	(	(	PUNCT
ejpam-5657	306	4	in	in	ADP
ejpam-5657	306	5	−a)−1b	−a)−1b	X
ejpam-5657	306	6	for	for	ADP
ejpam-5657	306	7	n	n	NOUN
ejpam-5657	306	8	=	=	SYM
ejpam-5657	306	9	2	2	NUM
ejpam-5657	306	10	,	,	PUNCT
ejpam-5657	306	11	has	have	VERB
ejpam-5657	306	12	the	the	DET
ejpam-5657	306	13	following	follow	VERB
ejpam-5657	306	14	structure	structure	NOUN
ejpam-5657	306	15	:	:	PUNCT
ejpam-5657	306	16	(	(	PUNCT
ejpam-5657	306	17	i2	i2	PROPN
ejpam-5657	306	18	−a)−1b	−a)−1b	X
ejpam-5657	307	1	=	=	PUNCT
ejpam-5657	308	1	[	[	PUNCT
ejpam-5657	308	2	0	0	NUM
ejpam-5657	308	3	0.5	0.5	NUM
ejpam-5657	308	4	0	0	NUM
ejpam-5657	308	5	0	0	NUM
ejpam-5657	308	6	]	]	PUNCT
ejpam-5657	308	7	.	.	PUNCT
ejpam-5657	309	1	we	we	PRON
ejpam-5657	309	2	present	present	VERB
ejpam-5657	309	3	the	the	DET
ejpam-5657	309	4	comparison	comparison	NOUN
ejpam-5657	309	5	on	on	ADP
ejpam-5657	309	6	numerical	numerical	ADJ
ejpam-5657	309	7	approximation	approximation	NOUN
ejpam-5657	309	8	of	of	ADP
ejpam-5657	309	9	the	the	DET
ejpam-5657	309	10	lower	low	ADJ
ejpam-5657	309	11	bounds	bound	NOUN
ejpam-5657	309	12	of	of	ADP
ejpam-5657	309	13	structured	structured	ADJ
ejpam-5657	309	14	singular	singular	ADJ
ejpam-5657	309	15	values	value	NOUN
ejpam-5657	309	16	in	in	ADP
ejpam-5657	309	17	following	follow	VERB
ejpam-5657	309	18	table	table	NOUN
ejpam-5657	309	19	3	3	NUM
ejpam-5657	309	20	.	.	PUNCT
ejpam-5657	310	1	m.u.r	m.u.r	NOUN
ejpam-5657	310	2	et	et	PROPN
ejpam-5657	310	3	al	al	PROPN
ejpam-5657	310	4	.	.	PUNCT
ejpam-5657	310	5	/	/	SYM
ejpam-5657	310	6	eur	eur	PROPN
ejpam-5657	310	7	.	.	PUNCT
ejpam-5657	311	1	j.	j.	PROPN
ejpam-5657	311	2	pure	pure	PROPN
ejpam-5657	311	3	appl	appl	PROPN
ejpam-5657	311	4	.	.	PROPN
ejpam-5657	311	5	math	math	PROPN
ejpam-5657	311	6	,	,	PUNCT
ejpam-5657	311	7	18	18	NUM
ejpam-5657	311	8	(	(	PUNCT
ejpam-5657	311	9	1	1	NUM
ejpam-5657	311	10	)	)	PUNCT
ejpam-5657	311	11	(	(	PUNCT
ejpam-5657	311	12	2025	2025	NUM
ejpam-5657	311	13	)	)	PUNCT
ejpam-5657	311	14	,	,	PUNCT
ejpam-5657	311	15	5657	5657	NUM
ejpam-5657	311	16	13	13	NUM
ejpam-5657	311	17	of	of	ADP
ejpam-5657	311	18	17	17	NUM
ejpam-5657	311	19	figure	figure	NOUN
ejpam-5657	311	20	3	3	NUM
ejpam-5657	311	21	:	:	PUNCT
ejpam-5657	311	22	matlab	matlab	PROPN
ejpam-5657	311	23	interface	interface	NOUN
ejpam-5657	311	24	for	for	ADP
ejpam-5657	311	25	computing	compute	VERB
ejpam-5657	311	26	pseudo	pseudo	NOUN
ejpam-5657	311	27	-	-	NOUN
ejpam-5657	311	28	spectrum	spectrum	NOUN
ejpam-5657	311	29	of	of	ADP
ejpam-5657	311	30	matrix	matrix	NOUN
ejpam-5657	311	31	(	(	PUNCT
ejpam-5657	311	32	i2	i2	PROPN
ejpam-5657	311	33	−a)−1b	−a)−1b	PROPN
ejpam-5657	311	34	.	.	PUNCT
ejpam-5657	312	1	the	the	DET
ejpam-5657	312	2	numerical	numerical	ADJ
ejpam-5657	312	3	approximation	approximation	NOUN
ejpam-5657	312	4	of	of	ADP
ejpam-5657	312	5	lower	low	ADJ
ejpam-5657	312	6	bounds	bound	NOUN
ejpam-5657	312	7	of	of	ADP
ejpam-5657	312	8	structured	structured	ADJ
ejpam-5657	312	9	singular	singular	ADJ
ejpam-5657	312	10	values	value	NOUN
ejpam-5657	312	11	mussv	mussv	VERB
ejpam-5657	312	12	pa	pa	PROPN
ejpam-5657	312	13	gba	gba	PROPN
ejpam-5657	312	14	pma	pma	PROPN
ejpam-5657	312	15	nla	nla	PROPN
ejpam-5657	312	16	lra	lra	PROPN
ejpam-5657	312	17	0.5000	0.5000	NUM
ejpam-5657	313	1	0.5123	0.5123	NUM
ejpam-5657	313	2	0.5341	0.5341	NUM
ejpam-5657	313	3	0.5001	0.5001	NUM
ejpam-5657	313	4	0.5012	0.5012	NUM
ejpam-5657	313	5	0.5000	0.5000	NUM
ejpam-5657	313	6	example	example	NOUN
ejpam-5657	313	7	3	3	X
ejpam-5657	313	8	.	.	X
ejpam-5657	313	9	consider	consider	VERB
ejpam-5657	313	10	the	the	DET
ejpam-5657	313	11	non	non	ADJ
ejpam-5657	313	12	-	-	ADJ
ejpam-5657	313	13	linear	linear	ADJ
ejpam-5657	313	14	model	model	NOUN
ejpam-5657	313	15	of	of	ADP
ejpam-5657	313	16	macro	macro	NOUN
ejpam-5657	313	17	-	-	NOUN
ejpam-5657	313	18	econometrics	econometric	NOUN
ejpam-5657	313	19	presented	present	VERB
ejpam-5657	313	20	in	in	ADP
ejpam-5657	313	21	[	[	X
ejpam-5657	313	22	6	6	NUM
ejpam-5657	313	23	]	]	PUNCT
ejpam-5657	313	24	.	.	PUNCT
ejpam-5657	314	1	the	the	DET
ejpam-5657	314	2	matrix	matrix	NOUN
ejpam-5657	314	3	c	c	NOUN
ejpam-5657	314	4	=	=	PUNCT
ejpam-5657	315	1	(	(	PUNCT
ejpam-5657	315	2	in	in	ADP
ejpam-5657	315	3	−a)−1b	−a)−1b	X
ejpam-5657	315	4	and	and	CCONJ
ejpam-5657	315	5	has	have	VERB
ejpam-5657	315	6	the	the	DET
ejpam-5657	315	7	following	follow	VERB
ejpam-5657	315	8	structure	structure	NOUN
ejpam-5657	315	9	for	for	ADP
ejpam-5657	315	10	n	n	NOUN
ejpam-5657	315	11	=	=	SYM
ejpam-5657	315	12	13:	13:	NUM
ejpam-5657	316	1	−0.08	−0.08	ADJ
ejpam-5657	316	2	0	0	NUM
ejpam-5657	316	3	0	0	NUM
ejpam-5657	316	4	0	0	NUM
ejpam-5657	316	5	0	0	NUM
ejpam-5657	316	6	0	0	NUM
ejpam-5657	316	7	0	0	NUM
ejpam-5657	317	1	−0.01	−0.01	DET
ejpam-5657	317	2	0.01	0.01	NUM
ejpam-5657	317	3	0	0	NUM
ejpam-5657	317	4	0	0	NUM
ejpam-5657	317	5	0	0	NUM
ejpam-5657	317	6	0	0	NUM
ejpam-5657	318	1	−1.27	−1.27	PRON
ejpam-5657	318	2	0	0	NUM
ejpam-5657	318	3	0	0	NUM
ejpam-5657	318	4	0	0	NUM
ejpam-5657	318	5	0	0	NUM
ejpam-5657	318	6	0	0	NUM
ejpam-5657	318	7	0	0	NUM
ejpam-5657	319	1	−0.01	−0.01	PRON
ejpam-5657	319	2	0.01	0.01	NUM
ejpam-5657	319	3	0	0	NUM
ejpam-5657	319	4	0	0	NUM
ejpam-5657	319	5	0	0	NUM
ejpam-5657	319	6	0	0	NUM
ejpam-5657	319	7	0	0	NUM
ejpam-5657	319	8	0	0	NUM
ejpam-5657	320	1	−0.24	−0.24	NOUN
ejpam-5657	320	2	0	0	NUM
ejpam-5657	320	3	0.24	0.24	NUM
ejpam-5657	320	4	0	0	NUM
ejpam-5657	320	5	0	0	NUM
ejpam-5657	320	6	0	0	NUM
ejpam-5657	320	7	0	0	NUM
ejpam-5657	320	8	0	0	NUM
ejpam-5657	320	9	0	0	NUM
ejpam-5657	320	10	0	0	NUM
ejpam-5657	320	11	0	0	NUM
ejpam-5657	320	12	0	0	NUM
ejpam-5657	320	13	0	0	NUM
ejpam-5657	320	14	0	0	NUM
ejpam-5657	320	15	−0.09	−0.09	PROPN
ejpam-5657	320	16	0.10	0.10	NUM
ejpam-5657	320	17	0	0	NUM
ejpam-5657	320	18	0	0	NUM
ejpam-5657	320	19	0	0	NUM
ejpam-5657	320	20	0	0	NUM
ejpam-5657	320	21	0	0	NUM
ejpam-5657	320	22	0	0	NUM
ejpam-5657	320	23	0	0	NUM
ejpam-5657	320	24	0	0	NUM
ejpam-5657	320	25	7.63	7.63	NUM
ejpam-5657	320	26	0	0	NUM
ejpam-5657	320	27	0.48	0.48	NUM
ejpam-5657	320	28	0	0	NUM
ejpam-5657	321	1	−0.65	−0.65	ADP
ejpam-5657	321	2	0	0	NUM
ejpam-5657	322	1	0.11	0.11	NUM
ejpam-5657	322	2	0	0	NUM
ejpam-5657	322	3	0	0	NUM
ejpam-5657	322	4	0	0	NUM
ejpam-5657	322	5	0	0	NUM
ejpam-5657	322	6	0.05	0.05	NUM
ejpam-5657	322	7	0	0	NUM
ejpam-5657	322	8	8.14	8.14	NUM
ejpam-5657	322	9	0	0	NUM
ejpam-5657	323	1	0.51	0.51	NUM
ejpam-5657	323	2	0	0	NUM
ejpam-5657	323	3	0	0	NUM
ejpam-5657	324	1	−0.35	−0.35	NOUN
ejpam-5657	324	2	0.12	0.12	NUM
ejpam-5657	324	3	0	0	NUM
ejpam-5657	324	4	0	0	NUM
ejpam-5657	324	5	0	0	NUM
ejpam-5657	325	1	−0.33	−0.33	NOUN
ejpam-5657	325	2	0.05	0.05	NUM
ejpam-5657	325	3	0	0	NUM
ejpam-5657	325	4	0	0	NUM
ejpam-5657	325	5	0	0	NUM
ejpam-5657	325	6	0	0	NUM
ejpam-5657	325	7	0	0	NUM
ejpam-5657	325	8	0	0	NUM
ejpam-5657	325	9	0	0	X
ejpam-5657	326	1	−0.29	−0.29	PRON
ejpam-5657	326	2	−0.29	−0.29	NOUN
ejpam-5657	326	3	0	0	NUM
ejpam-5657	326	4	0	0	NUM
ejpam-5657	326	5	0	0	NUM
ejpam-5657	326	6	0	0	NUM
ejpam-5657	326	7	0	0	NUM
ejpam-5657	326	8	0	0	NUM
ejpam-5657	326	9	0	0	NUM
ejpam-5657	326	10	0	0	NUM
ejpam-5657	326	11	0	0	NUM
ejpam-5657	326	12	0.02	0.02	NUM
ejpam-5657	326	13	0	0	NUM
ejpam-5657	326	14	0	0	NUM
ejpam-5657	327	1	−0.13	−0.13	NOUN
ejpam-5657	327	2	0.13	0.13	NUM
ejpam-5657	327	3	0	0	NUM
ejpam-5657	327	4	0	0	NUM
ejpam-5657	328	1	−0.02	−0.02	NOUN
ejpam-5657	328	2	0	0	NUM
ejpam-5657	328	3	0	0	NUM
ejpam-5657	328	4	0	0	NUM
ejpam-5657	328	5	0	0	NUM
ejpam-5657	328	6	0	0	NUM
ejpam-5657	329	1	0.11	0.11	NUM
ejpam-5657	329	2	0	0	NUM
ejpam-5657	329	3	0	0	NUM
ejpam-5657	329	4	0	0	NUM
ejpam-5657	329	5	0	0	NUM
ejpam-5657	329	6	0	0	NUM
ejpam-5657	329	7	0	0	NUM
ejpam-5657	330	1	−0.01	−0.01	PRON
ejpam-5657	330	2	0	0	NUM
ejpam-5657	330	3	0	0	NUM
ejpam-5657	330	4	0	0	NUM
ejpam-5657	330	5	0	0	NUM
ejpam-5657	330	6	0	0	NUM
ejpam-5657	330	7	0.19	0.19	NUM
ejpam-5657	330	8	0	0	NUM
ejpam-5657	330	9	0	0	NUM
ejpam-5657	330	10	0.19	0.19	NUM
ejpam-5657	330	11	0	0	NUM
ejpam-5657	331	1	−0.16	−0.16	NOUN
ejpam-5657	331	2	0	0	NUM
ejpam-5657	331	3	0	0	NUM
ejpam-5657	331	4	−0.19	−0.19	PROPN
ejpam-5657	332	1	−8.60	−8.60	INTJ
ejpam-5657	332	2	0	0	PUNCT
ejpam-5657	333	1	−0.54	−0.54	X
ejpam-5657	333	2	0	0	NUM
ejpam-5657	333	3	0.60	0.60	NUM
ejpam-5657	333	4	0.13	0.13	NUM
ejpam-5657	333	5	−0.13	−0.13	NOUN
ejpam-5657	333	6	0	0	NUM
ejpam-5657	333	7	0	0	NUM
ejpam-5657	333	8	0	0	NUM
ejpam-5657	333	9	0	0	NUM
ejpam-5657	334	1	−0.05	−0.05	NOUN
ejpam-5657	334	2	0	0	NUM
ejpam-5657	334	3	1.00	1.00	NUM
ejpam-5657	334	4	0	0	NUM
ejpam-5657	334	5	0	0	NUM
ejpam-5657	334	6	0	0	NUM
ejpam-5657	334	7	−0	−0	NOUN
ejpam-5657	334	8	0	0	NUM
ejpam-5657	334	9	0	0	NUM
ejpam-5657	334	10	0	0	NUM
ejpam-5657	334	11	0	0	NUM
ejpam-5657	334	12	0	0	NUM
ejpam-5657	334	13	0	0	NUM
ejpam-5657	334	14	0	0	NUM
ejpam-5657	334	15	0	0	NUM
ejpam-5657	334	16			NUM
ejpam-5657	334	17	.	.	PUNCT
ejpam-5657	335	1	we	we	PRON
ejpam-5657	335	2	present	present	VERB
ejpam-5657	335	3	the	the	DET
ejpam-5657	335	4	comparison	comparison	NOUN
ejpam-5657	335	5	on	on	ADP
ejpam-5657	335	6	numerical	numerical	ADJ
ejpam-5657	335	7	approximation	approximation	NOUN
ejpam-5657	335	8	of	of	ADP
ejpam-5657	335	9	the	the	DET
ejpam-5657	335	10	lower	low	ADJ
ejpam-5657	335	11	bounds	bound	NOUN
ejpam-5657	335	12	of	of	ADP
ejpam-5657	335	13	structured	structured	ADJ
ejpam-5657	335	14	m.u.r	m.u.r	PROPN
ejpam-5657	335	15	et	et	PROPN
ejpam-5657	335	16	al	al	PROPN
ejpam-5657	335	17	.	.	PUNCT
ejpam-5657	335	18	/	/	SYM
ejpam-5657	335	19	eur	eur	PROPN
ejpam-5657	335	20	.	.	PUNCT
ejpam-5657	336	1	j.	j.	PROPN
ejpam-5657	336	2	pure	pure	PROPN
ejpam-5657	336	3	appl	appl	PROPN
ejpam-5657	336	4	.	.	PROPN
ejpam-5657	336	5	math	math	PROPN
ejpam-5657	336	6	,	,	PUNCT
ejpam-5657	336	7	18	18	NUM
ejpam-5657	336	8	(	(	PUNCT
ejpam-5657	336	9	1	1	NUM
ejpam-5657	336	10	)	)	PUNCT
ejpam-5657	336	11	(	(	PUNCT
ejpam-5657	336	12	2025	2025	NUM
ejpam-5657	336	13	)	)	PUNCT
ejpam-5657	336	14	,	,	PUNCT
ejpam-5657	336	15	5657	5657	NUM
ejpam-5657	336	16	14	14	NUM
ejpam-5657	336	17	of	of	ADP
ejpam-5657	336	18	17	17	NUM
ejpam-5657	336	19	figure	figure	NOUN
ejpam-5657	336	20	4	4	NUM
ejpam-5657	336	21	:	:	PUNCT
ejpam-5657	336	22	matlab	matlab	PROPN
ejpam-5657	336	23	interface	interface	NOUN
ejpam-5657	336	24	for	for	ADP
ejpam-5657	336	25	computing	compute	VERB
ejpam-5657	336	26	pseudo	pseudo	NOUN
ejpam-5657	336	27	-	-	NOUN
ejpam-5657	336	28	spectrum	spectrum	NOUN
ejpam-5657	336	29	of	of	ADP
ejpam-5657	336	30	matrix	matrix	NOUN
ejpam-5657	336	31	(	(	PUNCT
ejpam-5657	336	32	i2	i2	PROPN
ejpam-5657	336	33	−a)−1b	−a)−1b	PROPN
ejpam-5657	336	34	.	.	PUNCT
ejpam-5657	337	1	singular	singular	ADJ
ejpam-5657	337	2	values	value	NOUN
ejpam-5657	337	3	in	in	ADP
ejpam-5657	337	4	following	follow	VERB
ejpam-5657	337	5	table	table	NOUN
ejpam-5657	337	6	4	4	NUM
ejpam-5657	337	7	.	.	PUNCT
ejpam-5657	338	1	the	the	DET
ejpam-5657	338	2	numerical	numerical	ADJ
ejpam-5657	338	3	approximation	approximation	NOUN
ejpam-5657	338	4	of	of	ADP
ejpam-5657	338	5	lower	low	ADJ
ejpam-5657	338	6	bounds	bound	NOUN
ejpam-5657	338	7	of	of	ADP
ejpam-5657	338	8	structured	structured	ADJ
ejpam-5657	338	9	singular	singular	ADJ
ejpam-5657	338	10	values	value	NOUN
ejpam-5657	338	11	mussv	mussv	VERB
ejpam-5657	338	12	pa	pa	PROPN
ejpam-5657	338	13	gba	gba	PROPN
ejpam-5657	338	14	pma	pma	PROPN
ejpam-5657	338	15	nla	nla	PROPN
ejpam-5657	338	16	lra	lra	PROPN
ejpam-5657	338	17	14.2303	14.2303	NUM
ejpam-5657	338	18	14.2309	14.2309	NUM
ejpam-5657	338	19	14.2312	14.2312	NUM
ejpam-5657	338	20	14.2332	14.2332	NUM
ejpam-5657	338	21	14.2398	14.2398	NUM
ejpam-5657	338	22	14.2306	14.2306	NUM
ejpam-5657	338	23	5	5	NUM
ejpam-5657	338	24	.	.	PUNCT
ejpam-5657	338	25	conclusion	conclusion	NOUN
ejpam-5657	338	26	in	in	ADP
ejpam-5657	338	27	this	this	DET
ejpam-5657	338	28	article	article	NOUN
ejpam-5657	338	29	,	,	PUNCT
ejpam-5657	338	30	we	we	PRON
ejpam-5657	338	31	have	have	AUX
ejpam-5657	338	32	developed	develop	VERB
ejpam-5657	338	33	new	new	ADJ
ejpam-5657	338	34	results	result	NOUN
ejpam-5657	338	35	on	on	ADP
ejpam-5657	338	36	stability	stability	NOUN
ejpam-5657	338	37	,	,	PUNCT
ejpam-5657	338	38	and	and	CCONJ
ejpam-5657	338	39	d	d	X
ejpam-5657	338	40	-	-	NOUN
ejpam-5657	338	41	stability	stability	NOUN
ejpam-5657	338	42	of	of	ADP
ejpam-5657	338	43	linear	linear	ADJ
ejpam-5657	338	44	economic	economic	ADJ
ejpam-5657	338	45	models	model	NOUN
ejpam-5657	338	46	.	.	PUNCT
ejpam-5657	339	1	the	the	DET
ejpam-5657	339	2	new	new	ADJ
ejpam-5657	339	3	results	result	NOUN
ejpam-5657	339	4	are	be	AUX
ejpam-5657	339	5	obtained	obtain	VERB
ejpam-5657	339	6	by	by	ADP
ejpam-5657	339	7	using	use	VERB
ejpam-5657	339	8	tools	tool	NOUN
ejpam-5657	339	9	from	from	ADP
ejpam-5657	339	10	linear	linear	PROPN
ejpam-5657	339	11	algebra	algebra	NOUN
ejpam-5657	339	12	,	,	PUNCT
ejpam-5657	339	13	matrix	matrix	NOUN
ejpam-5657	339	14	analysis	analysis	NOUN
ejpam-5657	339	15	,	,	PUNCT
ejpam-5657	339	16	and	and	CCONJ
ejpam-5657	339	17	system	system	NOUN
ejpam-5657	339	18	theory	theory	NOUN
ejpam-5657	339	19	.	.	PUNCT
ejpam-5657	340	1	some	some	DET
ejpam-5657	340	2	novel	novel	ADJ
ejpam-5657	340	3	results	result	NOUN
ejpam-5657	340	4	are	be	AUX
ejpam-5657	340	5	also	also	ADV
ejpam-5657	340	6	presented	present	VERB
ejpam-5657	340	7	on	on	ADP
ejpam-5657	340	8	necessary	necessary	ADJ
ejpam-5657	340	9	and	and	CCONJ
ejpam-5657	340	10	sufficient	sufficient	ADJ
ejpam-5657	340	11	conditions	condition	NOUN
ejpam-5657	340	12	on	on	ADP
ejpam-5657	340	13	the	the	DET
ejpam-5657	340	14	interconnection	interconnection	NOUN
ejpam-5657	340	15	between	between	ADP
ejpam-5657	340	16	d	d	ADJ
ejpam-5657	340	17	-	-	ADJ
ejpam-5657	340	18	stable	stable	ADJ
ejpam-5657	340	19	matrices	matrix	NOUN
ejpam-5657	340	20	and	and	CCONJ
ejpam-5657	340	21	structured	structure	VERB
ejpam-5657	340	22	singular	singular	ADJ
ejpam-5657	340	23	values	value	NOUN
ejpam-5657	340	24	.	.	PUNCT
ejpam-5657	341	1	the	the	DET
ejpam-5657	341	2	numerical	numerical	PROPN
ejpam-5657	341	3	experimentation	experimentation	NOUN
ejpam-5657	341	4	show	show	VERB
ejpam-5657	341	5	the	the	DET
ejpam-5657	341	6	comparison	comparison	NOUN
ejpam-5657	341	7	of	of	ADP
ejpam-5657	341	8	structured	structured	ADJ
ejpam-5657	341	9	singular	singular	ADJ
ejpam-5657	341	10	values	value	NOUN
ejpam-5657	341	11	by	by	ADP
ejpam-5657	341	12	various	various	ADJ
ejpam-5657	341	13	numerical	numerical	ADJ
ejpam-5657	341	14	techniques	technique	NOUN
ejpam-5657	341	15	,	,	PUNCT
ejpam-5657	341	16	the	the	DET
ejpam-5657	341	17	eigtool	eigtool	NOUN
ejpam-5657	341	18	is	be	AUX
ejpam-5657	341	19	used	use	VERB
ejpam-5657	341	20	to	to	PART
ejpam-5657	341	21	present	present	VERB
ejpam-5657	341	22	the	the	DET
ejpam-5657	341	23	pseudo	pseudo	NOUN
ejpam-5657	341	24	-	-	NOUN
ejpam-5657	341	25	spectrum	spectrum	NOUN
ejpam-5657	341	26	of	of	ADP
ejpam-5657	341	27	matrices	matrix	NOUN
ejpam-5657	341	28	across	across	ADP
ejpam-5657	341	29	linear	linear	ADJ
ejpam-5657	341	30	dynamic	dynamic	ADJ
ejpam-5657	341	31	models	model	NOUN
ejpam-5657	341	32	.	.	PUNCT
ejpam-5657	342	1	the	the	DET
ejpam-5657	342	2	main	main	ADJ
ejpam-5657	342	3	advantages	advantage	NOUN
ejpam-5657	342	4	of	of	ADP
ejpam-5657	342	5	the	the	DET
ejpam-5657	342	6	proposed	propose	VERB
ejpam-5657	342	7	methodology	methodology	NOUN
ejpam-5657	342	8	in	in	ADP
ejpam-5657	342	9	the	the	DET
ejpam-5657	342	10	present	present	ADJ
ejpam-5657	342	11	study	study	NOUN
ejpam-5657	342	12	:	:	PUNCT
ejpam-5657	342	13	1	1	X
ejpam-5657	342	14	.	.	PUNCT
ejpam-5657	343	1	the	the	DET
ejpam-5657	343	2	proposed	propose	VERB
ejpam-5657	343	3	methodology	methodology	NOUN
ejpam-5657	343	4	helps	help	VERB
ejpam-5657	343	5	to	to	PART
ejpam-5657	343	6	study	study	VERB
ejpam-5657	343	7	and	and	CCONJ
ejpam-5657	343	8	analyze	analyze	VERB
ejpam-5657	343	9	many	many	ADJ
ejpam-5657	343	10	spectral	spectral	ADJ
ejpam-5657	343	11	properties	property	NOUN
ejpam-5657	343	12	of	of	ADP
ejpam-5657	343	13	structured	structured	ADJ
ejpam-5657	343	14	matrices	matrix	NOUN
ejpam-5657	343	15	.	.	PUNCT
ejpam-5657	344	1	it	it	PRON
ejpam-5657	344	2	contains	contain	VERB
ejpam-5657	344	3	the	the	DET
ejpam-5657	344	4	properties	property	NOUN
ejpam-5657	344	5	like	like	ADP
ejpam-5657	344	6	eigenvalues	eigenvalue	NOUN
ejpam-5657	344	7	,	,	PUNCT
ejpam-5657	344	8	singular	singular	ADJ
ejpam-5657	344	9	values	value	NOUN
ejpam-5657	344	10	,	,	PUNCT
ejpam-5657	344	11	structured	structure	VERB
ejpam-5657	344	12	singular	singular	ADJ
ejpam-5657	344	13	values	value	NOUN
ejpam-5657	344	14	.	.	PUNCT
ejpam-5657	345	1	2	2	X
ejpam-5657	345	2	.	.	X
ejpam-5657	345	3	the	the	DET
ejpam-5657	345	4	proposed	propose	VERB
ejpam-5657	345	5	methodology	methodology	NOUN
ejpam-5657	345	6	based	base	VERB
ejpam-5657	345	7	on	on	ADP
ejpam-5657	345	8	theoretical	theoretical	ADJ
ejpam-5657	345	9	results	result	NOUN
ejpam-5657	345	10	link	link	VERB
ejpam-5657	345	11	the	the	DET
ejpam-5657	345	12	bridge	bridge	NOUN
ejpam-5657	345	13	between	between	ADP
ejpam-5657	345	14	stability	stability	NOUN
ejpam-5657	345	15	,	,	PUNCT
ejpam-5657	345	16	d	d	NOUN
ejpam-5657	345	17	-	-	NOUN
ejpam-5657	345	18	stability	stability	NOUN
ejpam-5657	345	19	,	,	PUNCT
ejpam-5657	345	20	and	and	CCONJ
ejpam-5657	345	21	structured	structure	VERB
ejpam-5657	345	22	singular	singular	ADJ
ejpam-5657	345	23	values	value	NOUN
ejpam-5657	345	24	for	for	ADP
ejpam-5657	345	25	structured	structured	ADJ
ejpam-5657	345	26	matrices	matrix	NOUN
ejpam-5657	345	27	corresponding	correspond	VERB
ejpam-5657	345	28	to	to	ADP
ejpam-5657	345	29	dynamical	dynamical	ADJ
ejpam-5657	345	30	systems	system	NOUN
ejpam-5657	345	31	.	.	PUNCT
ejpam-5657	346	1	3	3	X
ejpam-5657	346	2	.	.	X
ejpam-5657	346	3	the	the	DET
ejpam-5657	346	4	geometrical	geometrical	ADJ
ejpam-5657	346	5	interpretation	interpretation	NOUN
ejpam-5657	346	6	gives	give	VERB
ejpam-5657	346	7	an	an	DET
ejpam-5657	346	8	advantage	advantage	NOUN
ejpam-5657	346	9	to	to	PART
ejpam-5657	346	10	exploit	exploit	VERB
ejpam-5657	346	11	the	the	DET
ejpam-5657	346	12	hidden	hidden	ADJ
ejpam-5657	346	13	structures	structure	NOUN
ejpam-5657	346	14	of	of	ADP
ejpam-5657	346	15	structured	structured	ADJ
ejpam-5657	346	16	matrices	matrix	NOUN
ejpam-5657	346	17	.	.	PUNCT
ejpam-5657	347	1	4	4	X
ejpam-5657	347	2	.	.	X
ejpam-5657	347	3	the	the	DET
ejpam-5657	347	4	proposed	propose	VERB
ejpam-5657	347	5	methodology	methodology	NOUN
ejpam-5657	347	6	has	have	VERB
ejpam-5657	347	7	strong	strong	ADJ
ejpam-5657	347	8	theoretical	theoretical	ADJ
ejpam-5657	347	9	foundations	foundation	NOUN
ejpam-5657	347	10	and	and	CCONJ
ejpam-5657	347	11	also	also	ADV
ejpam-5657	347	12	numerical	numerical	ADJ
ejpam-5657	347	13	experimentation	experimentation	NOUN
ejpam-5657	347	14	to	to	PART
ejpam-5657	347	15	support	support	VERB
ejpam-5657	347	16	the	the	DET
ejpam-5657	347	17	theoretical	theoretical	ADJ
ejpam-5657	347	18	construction	construction	NOUN
ejpam-5657	347	19	.	.	PUNCT
ejpam-5657	348	1	acknowledgements	acknowledgement	NOUN
ejpam-5657	348	2	this	this	DET
ejpam-5657	348	3	work	work	NOUN
ejpam-5657	348	4	was	be	AUX
ejpam-5657	348	5	funded	fund	VERB
ejpam-5657	348	6	by	by	ADP
ejpam-5657	348	7	the	the	DET
ejpam-5657	348	8	university	university	PROPN
ejpam-5657	348	9	of	of	ADP
ejpam-5657	348	10	jeddah	jeddah	PROPN
ejpam-5657	348	11	,	,	PUNCT
ejpam-5657	348	12	jeddah	jeddah	PROPN
ejpam-5657	348	13	,	,	PUNCT
ejpam-5657	348	14	saudi	saudi	PROPN
ejpam-5657	348	15	arabia	arabia	PROPN
ejpam-5657	348	16	,	,	PUNCT
ejpam-5657	348	17	under	under	ADP
ejpam-5657	348	18	grant	grant	NOUN
ejpam-5657	348	19	no	no	NOUN
ejpam-5657	348	20	.	.	PUNCT
ejpam-5657	349	1	(	(	PUNCT
ejpam-5657	349	2	uj-23	uj-23	NOUN
ejpam-5657	349	3	-	-	PUNCT
ejpam-5657	349	4	dr-128	dr-128	NOUN
ejpam-5657	349	5	)	)	PUNCT
ejpam-5657	349	6	.	.	PUNCT
ejpam-5657	350	1	therefore	therefore	ADV
ejpam-5657	350	2	,	,	PUNCT
ejpam-5657	350	3	the	the	DET
ejpam-5657	350	4	authors	author	NOUN
ejpam-5657	350	5	thank	thank	VERB
ejpam-5657	350	6	the	the	DET
ejpam-5657	350	7	university	university	NOUN
ejpam-5657	350	8	of	of	ADP
ejpam-5657	350	9	jeddah	jeddah	PROPN
ejpam-5657	350	10	for	for	ADP
ejpam-5657	350	11	its	its	PRON
ejpam-5657	350	12	technical	technical	ADJ
ejpam-5657	350	13	and	and	CCONJ
ejpam-5657	350	14	financial	financial	ADJ
ejpam-5657	350	15	support	support	NOUN
ejpam-5657	350	16	.	.	PUNCT
ejpam-5657	351	1	m.u.r	m.u.r	NOUN
ejpam-5657	351	2	et	et	PROPN
ejpam-5657	351	3	al	al	PROPN
ejpam-5657	351	4	.	.	PUNCT
ejpam-5657	351	5	/	/	SYM
ejpam-5657	351	6	eur	eur	PROPN
ejpam-5657	351	7	.	.	PUNCT
ejpam-5657	352	1	j.	j.	PROPN
ejpam-5657	352	2	pure	pure	PROPN
ejpam-5657	352	3	appl	appl	PROPN
ejpam-5657	352	4	.	.	PROPN
ejpam-5657	352	5	math	math	PROPN
ejpam-5657	352	6	,	,	PUNCT
ejpam-5657	352	7	18	18	NUM
ejpam-5657	352	8	(	(	PUNCT
ejpam-5657	352	9	1	1	NUM
ejpam-5657	352	10	)	)	PUNCT
ejpam-5657	352	11	(	(	PUNCT
ejpam-5657	352	12	2025	2025	NUM
ejpam-5657	352	13	)	)	PUNCT
ejpam-5657	352	14	,	,	PUNCT
ejpam-5657	352	15	5657	5657	NUM
ejpam-5657	352	16	15	15	NUM
ejpam-5657	352	17	of	of	ADP
ejpam-5657	352	18	17	17	NUM
ejpam-5657	352	19	references	reference	NOUN
ejpam-5657	352	20	[	[	X
ejpam-5657	352	21	1	1	NUM
ejpam-5657	352	22	]	]	PUNCT
ejpam-5657	352	23	aneya	aneya	NOUN
ejpam-5657	352	24	,	,	PUNCT
ejpam-5657	352	25	y.p	y.p	PROPN
ejpam-5657	352	26	.	.	PROPN
ejpam-5657	352	27	;	;	PUNCT
ejpam-5657	352	28	nair	nair	PROPN
ejpam-5657	352	29	,	,	PUNCT
ejpam-5657	352	30	k.p.k	k.p.k	PROPN
ejpam-5657	352	31	.	.	PUNCT
ejpam-5657	353	1	bi	bi	ADJ
ejpam-5657	353	2	-	-	PUNCT
ejpam-5657	353	3	criteria	criterion	NOUN
ejpam-5657	353	4	transportation	transportation	NOUN
ejpam-5657	353	5	problem	problem	NOUN
ejpam-5657	353	6	.	.	PUNCT
ejpam-5657	354	1	manag	manag	PROPN
ejpam-5657	354	2	.	.	PUNCT
ejpam-5657	355	1	sci	sci	PROPN
ejpam-5657	355	2	.	.	PROPN
ejpam-5657	355	3	1979	1979	NUM
ejpam-5657	355	4	,	,	PUNCT
ejpam-5657	355	5	25	25	NUM
ejpam-5657	355	6	,	,	PUNCT
ejpam-5657	355	7	73–78	73–78	NUM
ejpam-5657	355	8	.	.	PUNCT
ejpam-5657	356	1	[	[	X
ejpam-5657	356	2	2	2	NUM
ejpam-5657	356	3	]	]	PUNCT
ejpam-5657	356	4	arrow	arrow	NOUN
ejpam-5657	356	5	,	,	PUNCT
ejpam-5657	356	6	k.	k.	PROPN
ejpam-5657	356	7	j.	j.	PROPN
ejpam-5657	356	8	and	and	CCONJ
ejpam-5657	356	9	mcmanus	mcmanus	PROPN
ejpam-5657	356	10	,	,	PUNCT
ejpam-5657	356	11	m.	m.	NOUN
ejpam-5657	356	12	(	(	PUNCT
ejpam-5657	356	13	1958	1958	NUM
ejpam-5657	356	14	)	)	PUNCT
ejpam-5657	356	15	,	,	PUNCT
ejpam-5657	356	16	a	a	DET
ejpam-5657	356	17	note	note	NOUN
ejpam-5657	356	18	on	on	ADP
ejpam-5657	356	19	dynamic	dynamic	ADJ
ejpam-5657	356	20	stability	stability	NOUN
ejpam-5657	356	21	,	,	PUNCT
ejpam-5657	356	22	econometrica	econometrica	PROPN
ejpam-5657	356	23	,	,	PUNCT
ejpam-5657	356	24	26	26	NUM
ejpam-5657	356	25	,	,	PUNCT
ejpam-5657	356	26	448	448	NUM
ejpam-5657	356	27	-	-	SYM
ejpam-5657	356	28	454	454	NUM
ejpam-5657	356	29	.	.	PUNCT
ejpam-5657	357	1	[	[	X
ejpam-5657	357	2	3	3	NUM
ejpam-5657	357	3	]	]	PUNCT
ejpam-5657	357	4	a.	a.	NOUN
ejpam-5657	357	5	bhaya	bhaya	NOUN
ejpam-5657	357	6	and	and	CCONJ
ejpam-5657	357	7	e.	e.	PROPN
ejpam-5657	357	8	kaszkurewicz	kaszkurewicz	PROPN
ejpam-5657	357	9	,	,	PUNCT
ejpam-5657	357	10	linear	linear	PROPN
ejpam-5657	357	11	algebra	algebra	PROPN
ejpam-5657	357	12	&	&	CCONJ
ejpam-5657	357	13	its	its	PRON
ejpam-5657	357	14	applications	application	NOUN
ejpam-5657	357	15	,	,	PUNCT
ejpam-5657	357	16	vol	vol	NOUN
ejpam-5657	357	17	.	.	PROPN
ejpam-5657	357	18	187	187	NUM
ejpam-5657	357	19	,	,	PUNCT
ejpam-5657	357	20	pp	pp	ADJ
ejpam-5657	357	21	.	.	PUNCT
ejpam-5657	358	1	87–104	87–104	PROPN
ejpam-5657	358	2	,	,	PUNCT
ejpam-5657	358	3	1993	1993	NUM
ejpam-5657	358	4	.	.	PUNCT
ejpam-5657	359	1	[	[	X
ejpam-5657	359	2	4	4	NUM
ejpam-5657	359	3	]	]	PUNCT
ejpam-5657	359	4	a.	a.	NOUN
ejpam-5657	359	5	berman	berman	PROPN
ejpam-5657	359	6	and	and	CCONJ
ejpam-5657	359	7	d.	d.	PROPN
ejpam-5657	359	8	hershkowitz	hershkowitz	PROPN
ejpam-5657	359	9	,	,	PUNCT
ejpam-5657	359	10	siam	siam	PROPN
ejpam-5657	359	11	j.	j.	PROPN
ejpam-5657	359	12	on	on	ADP
ejpam-5657	359	13	algebra	algebra	PROPN
ejpam-5657	359	14	&	&	CCONJ
ejpam-5657	359	15	discrete	discrete	ADJ
ejpam-5657	359	16	methods	method	NOUN
ejpam-5657	359	17	,	,	PUNCT
ejpam-5657	359	18	vol	vol	NOUN
ejpam-5657	359	19	.	.	PROPN
ejpam-5657	359	20	4	4	NUM
ejpam-5657	359	21	,	,	PUNCT
ejpam-5657	359	22	pp	pp	ADJ
ejpam-5657	359	23	.	.	PUNCT
ejpam-5657	360	1	377–382	377–382	NUM
ejpam-5657	360	2	,	,	PUNCT
ejpam-5657	360	3	1983	1983	NUM
ejpam-5657	360	4	.	.	PUNCT
ejpam-5657	361	1	[	[	X
ejpam-5657	361	2	5	5	NUM
ejpam-5657	361	3	]	]	SYM
ejpam-5657	361	4	bergstrom	bergstrom	PROPN
ejpam-5657	361	5	,	,	PUNCT
ejpam-5657	361	6	a.r	a.r	PROPN
ejpam-5657	361	7	.	.	PROPN
ejpam-5657	361	8	,	,	PUNCT
ejpam-5657	361	9	k.b	k.b	PROPN
ejpam-5657	361	10	.	.	PROPN
ejpam-5657	361	11	nowman	nowman	PROPN
ejpam-5657	361	12	and	and	CCONJ
ejpam-5657	361	13	c.r	c.r	PROPN
ejpam-5657	361	14	.	.	PROPN
ejpam-5657	361	15	wymer	wym	ADJ
ejpam-5657	361	16	,	,	PUNCT
ejpam-5657	361	17	1992	1992	NUM
ejpam-5657	361	18	,	,	PUNCT
ejpam-5657	361	19	gaussian	gaussian	ADJ
ejpam-5657	361	20	estimation	estimation	NOUN
ejpam-5657	361	21	of	of	ADP
ejpam-5657	361	22	a	a	DET
ejpam-5657	361	23	second	second	ADJ
ejpam-5657	361	24	order	order	NOUN
ejpam-5657	361	25	continuous	continuous	ADJ
ejpam-5657	361	26	time	time	NOUN
ejpam-5657	361	27	macroeconometric	macroeconometric	ADJ
ejpam-5657	361	28	model	model	NOUN
ejpam-5657	361	29	of	of	ADP
ejpam-5657	361	30	the	the	DET
ejpam-5657	361	31	uk	uk	PROPN
ejpam-5657	361	32	,	,	PUNCT
ejpam-5657	361	33	economic	economic	ADJ
ejpam-5657	361	34	modelling	modelling	NOUN
ejpam-5657	361	35	9	9	NUM
ejpam-5657	361	36	,	,	PUNCT
ejpam-5657	361	37	313	313	NUM
ejpam-5657	361	38	-	-	SYM
ejpam-5657	361	39	351	351	NUM
ejpam-5657	361	40	.	.	PUNCT
ejpam-5657	362	1	[	[	X
ejpam-5657	362	2	6	6	NUM
ejpam-5657	362	3	]	]	X
ejpam-5657	362	4	bergstrom	bergstrom	PROPN
ejpam-5657	362	5	,	,	PUNCT
ejpam-5657	362	6	a.r	a.r	PROPN
ejpam-5657	362	7	.	.	PROPN
ejpam-5657	362	8	and	and	CCONJ
ejpam-5657	362	9	c.r	c.r	PROPN
ejpam-5657	362	10	.	.	PROPN
ejpam-5657	362	11	wymer	wym	ADJ
ejpam-5657	362	12	,	,	PUNCT
ejpam-5657	362	13	1976	1976	NUM
ejpam-5657	362	14	,	,	PUNCT
ejpam-5657	362	15	a	a	DET
ejpam-5657	362	16	model	model	NOUN
ejpam-5657	362	17	of	of	ADP
ejpam-5657	362	18	disequilibrium	disequilibrium	NOUN
ejpam-5657	362	19	neoclassical	neoclassical	ADJ
ejpam-5657	362	20	growth	growth	NOUN
ejpam-5657	362	21	and	and	CCONJ
ejpam-5657	362	22	its	its	PRON
ejpam-5657	362	23	application	application	NOUN
ejpam-5657	362	24	to	to	ADP
ejpam-5657	362	25	the	the	DET
ejpam-5657	362	26	united	united	ADJ
ejpam-5657	362	27	kingdom	kingdom	PROPN
ejpam-5657	362	28	,	,	PUNCT
ejpam-5657	362	29	in	in	ADP
ejpam-5657	362	30	:	:	PUNCT
ejpam-5657	362	31	a.r	a.r	PROPN
ejpam-5657	362	32	.	.	PROPN
ejpam-5657	362	33	bergstrom	bergstrom	PROPN
ejpam-5657	362	34	,	,	PUNCT
ejpam-5657	362	35	ed	ed	NOUN
ejpam-5657	362	36	.	.	PROPN
ejpam-5657	362	37	,	,	PUNCT
ejpam-5657	362	38	statistical	statistical	ADJ
ejpam-5657	362	39	inference	inference	NOUN
ejpam-5657	362	40	in	in	ADP
ejpam-5657	362	41	continuous	continuous	ADJ
ejpam-5657	362	42	time	time	NOUN
ejpam-5657	362	43	economic	economic	ADJ
ejpam-5657	362	44	models	model	NOUN
ejpam-5657	362	45	(	(	PUNCT
ejpam-5657	362	46	north	north	NOUN
ejpam-5657	362	47	-	-	PUNCT
ejpam-5657	362	48	holland	holland	PROPN
ejpam-5657	362	49	,	,	PUNCT
ejpam-5657	362	50	amsterdam	amsterdam	PROPN
ejpam-5657	362	51	)	)	PUNCT
ejpam-5657	362	52	267	267	NUM
ejpam-5657	362	53	-	-	SYM
ejpam-5657	362	54	327	327	NUM
ejpam-5657	362	55	.	.	PUNCT
ejpam-5657	363	1	[	[	X
ejpam-5657	363	2	7	7	X
ejpam-5657	363	3	]	]	SYM
ejpam-5657	363	4	bergstrom	bergstrom	PROPN
ejpam-5657	363	5	,	,	PUNCT
ejpam-5657	363	6	albert	albert	PROPN
ejpam-5657	363	7	r.	r.	PROPN
ejpam-5657	363	8	continuous	continuous	ADJ
ejpam-5657	363	9	time	time	NOUN
ejpam-5657	363	10	stochastic	stochastic	NOUN
ejpam-5657	363	11	models	model	NOUN
ejpam-5657	363	12	and	and	CCONJ
ejpam-5657	363	13	issues	issue	NOUN
ejpam-5657	363	14	of	of	ADP
ejpam-5657	363	15	aggregation	aggregation	NOUN
ejpam-5657	363	16	over	over	ADP
ejpam-5657	363	17	time	time	NOUN
ejpam-5657	363	18	.	.	PUNCT
ejpam-5657	364	1	handbook	handbook	NOUN
ejpam-5657	364	2	of	of	ADP
ejpam-5657	364	3	econometrics	econometrics	NOUN
ejpam-5657	364	4	2	2	NUM
ejpam-5657	364	5	(	(	PUNCT
ejpam-5657	364	6	1984	1984	NUM
ejpam-5657	364	7	):	):	PUNCT
ejpam-5657	364	8	1145	1145	NUM
ejpam-5657	364	9	-	-	SYM
ejpam-5657	364	10	1212	1212	NUM
ejpam-5657	364	11	.	.	PUNCT
ejpam-5657	365	1	[	[	X
ejpam-5657	365	2	8	8	NUM
ejpam-5657	365	3	]	]	X
ejpam-5657	365	4	c.	c.	PROPN
ejpam-5657	365	5	r.	r.	PROPN
ejpam-5657	365	6	johnson	johnson	PROPN
ejpam-5657	365	7	,	,	PUNCT
ejpam-5657	365	8	j.	j.	PROPN
ejpam-5657	365	9	of	of	ADP
ejpam-5657	365	10	econ	econ	PROPN
ejpam-5657	365	11	.	.	PUNCT
ejpam-5657	366	1	theory	theory	NOUN
ejpam-5657	366	2	,	,	PUNCT
ejpam-5657	366	3	vol	vol	NOUN
ejpam-5657	366	4	.	.	PROPN
ejpam-5657	366	5	9	9	NUM
ejpam-5657	366	6	,	,	PUNCT
ejpam-5657	366	7	pp	pp	ADJ
ejpam-5657	366	8	.	.	PUNCT
ejpam-5657	367	1	53–62	53–62	NUM
ejpam-5657	367	2	,	,	PUNCT
ejpam-5657	367	3	1974	1974	NUM
ejpam-5657	367	4	.	.	PUNCT
ejpam-5657	368	1	[	[	X
ejpam-5657	368	2	9	9	NUM
ejpam-5657	368	3	]	]	X
ejpam-5657	368	4	dai	dai	PROPN
ejpam-5657	368	5	,	,	PUNCT
ejpam-5657	368	6	liyi	liyi	PROPN
ejpam-5657	368	7	,	,	PUNCT
ejpam-5657	368	8	ed	ed	NOUN
ejpam-5657	368	9	.	.	PROPN
ejpam-5657	368	10	singular	singular	PROPN
ejpam-5657	368	11	control	control	PROPN
ejpam-5657	368	12	systems	system	NOUN
ejpam-5657	368	13	.	.	PUNCT
ejpam-5657	369	1	berlin	berlin	PROPN
ejpam-5657	369	2	,	,	PUNCT
ejpam-5657	369	3	heidelberg	heidelberg	PROPN
ejpam-5657	369	4	:	:	PUNCT
ejpam-5657	369	5	springer	springer	PROPN
ejpam-5657	369	6	berlin	berlin	PROPN
ejpam-5657	369	7	heidelberg	heidelberg	PROPN
ejpam-5657	369	8	,	,	PUNCT
ejpam-5657	369	9	1989	1989	NUM
ejpam-5657	369	10	.	.	PUNCT
ejpam-5657	370	1	[	[	X
ejpam-5657	370	2	10	10	NUM
ejpam-5657	370	3	]	]	X
ejpam-5657	370	4	d.	d.	PROPN
ejpam-5657	370	5	yue	yue	PROPN
ejpam-5657	370	6	and	and	CCONJ
ejpam-5657	370	7	q.	q.	PROPN
ejpam-5657	370	8	han	han	PROPN
ejpam-5657	370	9	,	,	PUNCT
ejpam-5657	370	10	delay	delay	NOUN
ejpam-5657	370	11	-	-	PUNCT
ejpam-5657	370	12	dependent	dependent	ADJ
ejpam-5657	370	13	exponential	exponential	ADJ
ejpam-5657	370	14	stability	stability	NOUN
ejpam-5657	370	15	of	of	ADP
ejpam-5657	370	16	stochastic	stochastic	ADJ
ejpam-5657	370	17	systems	system	NOUN
ejpam-5657	370	18	with	with	ADP
ejpam-5657	370	19	time	time	NOUN
ejpam-5657	370	20	-	-	PUNCT
ejpam-5657	370	21	varying	vary	VERB
ejpam-5657	370	22	delay	delay	NOUN
ejpam-5657	370	23	,	,	PUNCT
ejpam-5657	370	24	nonlinearity	nonlinearity	NOUN
ejpam-5657	370	25	,	,	PUNCT
ejpam-5657	370	26	and	and	CCONJ
ejpam-5657	370	27	markovian	markovian	PROPN
ejpam-5657	370	28	switching	switching	NOUN
ejpam-5657	370	29	,	,	PUNCT
ejpam-5657	370	30	ieee	ieee	NOUN
ejpam-5657	370	31	trans	trans	PROPN
ejpam-5657	370	32	.	.	PROPN
ejpam-5657	371	1	automat	automat	PROPN
ejpam-5657	371	2	.	.	PUNCT
ejpam-5657	372	1	control	control	PROPN
ejpam-5657	372	2	,	,	PUNCT
ejpam-5657	372	3	vol	vol	NOUN
ejpam-5657	372	4	.	.	PROPN
ejpam-5657	372	5	50	50	NUM
ejpam-5657	372	6	,	,	PUNCT
ejpam-5657	372	7	pp	pp	ADJ
ejpam-5657	372	8	.	.	PUNCT
ejpam-5657	373	1	217	217	NUM
ejpam-5657	373	2	-	-	SYM
ejpam-5657	373	3	222	222	NUM
ejpam-5657	373	4	,	,	PUNCT
ejpam-5657	373	5	feb	feb	PROPN
ejpam-5657	373	6	.	.	PROPN
ejpam-5657	373	7	2005	2005	NUM
ejpam-5657	373	8	.	.	PUNCT
ejpam-5657	374	1	[	[	X
ejpam-5657	374	2	11	11	NUM
ejpam-5657	374	3	]	]	X
ejpam-5657	374	4	donaghy	donaghy	PROPN
ejpam-5657	374	5	,	,	PUNCT
ejpam-5657	374	6	k.p	k.p	PROPN
ejpam-5657	374	7	.	.	PROPN
ejpam-5657	374	8	,	,	PUNCT
ejpam-5657	374	9	1993	1993	NUM
ejpam-5657	374	10	,	,	PUNCT
ejpam-5657	374	11	a	a	DET
ejpam-5657	374	12	continuous	continuous	ADJ
ejpam-5657	374	13	-	-	PUNCT
ejpam-5657	374	14	time	time	NOUN
ejpam-5657	374	15	model	model	NOUN
ejpam-5657	374	16	of	of	ADP
ejpam-5657	374	17	the	the	DET
ejpam-5657	374	18	united	united	PROPN
ejpam-5657	374	19	states	states	PROPN
ejpam-5657	374	20	economy	economy	NOUN
ejpam-5657	374	21	,	,	PUNCT
ejpam-5657	374	22	in	in	ADP
ejpam-5657	374	23	:	:	PUNCT
ejpam-5657	374	24	(	(	PUNCT
ejpam-5657	374	25	3	3	X
ejpam-5657	374	26	.	.	X
ejpam-5657	374	27	gandoifo	gandoifo	PROPN
ejpam-5657	374	28	,	,	PUNCT
ejpam-5657	374	29	ed	ed	NOUN
ejpam-5657	374	30	.	.	PROPN
ejpam-5657	374	31	,	,	PUNCT
ejpam-5657	374	32	continuous	continuous	ADJ
ejpam-5657	374	33	time	time	NOUN
ejpam-5657	374	34	econometrics	econometric	NOUN
ejpam-5657	374	35	;	;	PUNCT
ejpam-5657	374	36	theory	theory	NOUN
ejpam-5657	374	37	and	and	CCONJ
ejpam-5657	374	38	applications	application	NOUN
ejpam-5657	374	39	(	(	PUNCT
ejpam-5657	374	40	chapman	chapman	PROPN
ejpam-5657	374	41	&	&	CCONJ
ejpam-5657	374	42	hall	hall	PROPN
ejpam-5657	374	43	,	,	PUNCT
ejpam-5657	374	44	london	london	PROPN
ejpam-5657	374	45	)	)	PUNCT
ejpam-5657	374	46	151	151	NUM
ejpam-5657	374	47	-	-	SYM
ejpam-5657	374	48	193	193	NUM
ejpam-5657	374	49	.	.	PUNCT
ejpam-5657	375	1	[	[	X
ejpam-5657	375	2	12	12	NUM
ejpam-5657	375	3	]	]	X
ejpam-5657	375	4	doyle	doyle	NOUN
ejpam-5657	375	5	,	,	PUNCT
ejpam-5657	375	6	j.	j.	PROPN
ejpam-5657	375	7	analysis	analysis	NOUN
ejpam-5657	375	8	of	of	ADP
ejpam-5657	375	9	feedback	feedback	NOUN
ejpam-5657	375	10	systems	system	NOUN
ejpam-5657	375	11	with	with	ADP
ejpam-5657	375	12	structured	structured	ADJ
ejpam-5657	375	13	uncertainties	uncertainty	NOUN
ejpam-5657	375	14	.	.	PUNCT
ejpam-5657	376	1	iee	iee	PROPN
ejpam-5657	376	2	proc	proc	PROPN
ejpam-5657	376	3	.	.	PUNCT
ejpam-5657	377	1	dcontrol	dcontrol	NOUN
ejpam-5657	377	2	theory	theory	PROPN
ejpam-5657	377	3	appl	appl	PROPN
ejpam-5657	377	4	.	.	PROPN
ejpam-5657	378	1	1982	1982	NUM
ejpam-5657	378	2	,	,	PUNCT
ejpam-5657	378	3	129	129	NUM
ejpam-5657	378	4	,	,	PUNCT
ejpam-5657	378	5	242–250	242–250	NUM
ejpam-5657	378	6	.	.	PUNCT
ejpam-5657	379	1	[	[	X
ejpam-5657	379	2	13	13	NUM
ejpam-5657	379	3	]	]	PUNCT
ejpam-5657	379	4	enthoven	enthoven	ADJ
ejpam-5657	379	5	,	,	PUNCT
ejpam-5657	379	6	a.	a.	NOUN
ejpam-5657	379	7	c.	c.	PROPN
ejpam-5657	379	8	and	and	CCONJ
ejpam-5657	379	9	arrow	arrow	NOUN
ejpam-5657	379	10	,	,	PUNCT
ejpam-5657	379	11	k.	k.	PROPN
ejpam-5657	379	12	j.	j.	PROPN
ejpam-5657	379	13	(	(	PUNCT
ejpam-5657	379	14	1956	1956	NUM
ejpam-5657	379	15	)	)	PUNCT
ejpam-5657	379	16	,	,	PUNCT
ejpam-5657	379	17	a	a	DET
ejpam-5657	379	18	theorem	theorem	NOUN
ejpam-5657	379	19	on	on	ADP
ejpam-5657	379	20	expectations	expectation	NOUN
ejpam-5657	379	21	and	and	CCONJ
ejpam-5657	379	22	the	the	DET
ejpam-5657	379	23	stability	stability	NOUN
ejpam-5657	379	24	of	of	ADP
ejpam-5657	379	25	equilibrium	equilibrium	NOUN
ejpam-5657	379	26	,	,	PUNCT
ejpam-5657	379	27	econometrica	econometrica	PROPN
ejpam-5657	379	28	,	,	PUNCT
ejpam-5657	379	29	24	24	NUM
ejpam-5657	379	30	,	,	PUNCT
ejpam-5657	379	31	288	288	NUM
ejpam-5657	379	32	-	-	SYM
ejpam-5657	379	33	293	293	NUM
ejpam-5657	379	34	.	.	PUNCT
ejpam-5657	380	1	[	[	X
ejpam-5657	380	2	14	14	NUM
ejpam-5657	380	3	]	]	X
ejpam-5657	380	4	fang	fang	X
ejpam-5657	380	5	,	,	PUNCT
ejpam-5657	380	6	chun	chun	PROPN
ejpam-5657	380	7	-	-	PUNCT
ejpam-5657	380	8	hsiung	hsiung	PROPN
ejpam-5657	380	9	,	,	PUNCT
ejpam-5657	380	10	and	and	CCONJ
ejpam-5657	380	11	fan	fan	PROPN
ejpam-5657	380	12	-	-	PUNCT
ejpam-5657	380	13	ren	ren	PROPN
ejpam-5657	380	14	chang	chang	PROPN
ejpam-5657	380	15	.	.	PUNCT
ejpam-5657	381	1	analysis	analysis	NOUN
ejpam-5657	381	2	of	of	ADP
ejpam-5657	381	3	stability	stability	NOUN
ejpam-5657	381	4	robustness	robustness	NOUN
ejpam-5657	381	5	for	for	ADP
ejpam-5657	381	6	generalized	generalized	ADJ
ejpam-5657	381	7	state	state	NOUN
ejpam-5657	381	8	-	-	PUNCT
ejpam-5657	381	9	space	space	NOUN
ejpam-5657	381	10	systems	system	NOUN
ejpam-5657	381	11	with	with	ADP
ejpam-5657	381	12	structured	structured	ADJ
ejpam-5657	381	13	perturbations	perturbation	NOUN
ejpam-5657	381	14	.	.	PUNCT
ejpam-5657	382	1	systems	system	NOUN
ejpam-5657	382	2	&	&	CCONJ
ejpam-5657	382	3	control	control	PROPN
ejpam-5657	382	4	letters	letter	NOUN
ejpam-5657	382	5	21	21	NUM
ejpam-5657	382	6	,	,	PUNCT
ejpam-5657	382	7	no	no	INTJ
ejpam-5657	382	8	.	.	NOUN
ejpam-5657	382	9	2	2	NUM
ejpam-5657	382	10	(	(	PUNCT
ejpam-5657	382	11	1993	1993	NUM
ejpam-5657	382	12	):	):	PUNCT
ejpam-5657	382	13	109	109	NUM
ejpam-5657	382	14	-	-	SYM
ejpam-5657	382	15	114	114	NUM
ejpam-5657	382	16	.	.	PUNCT
ejpam-5657	383	1	[	[	X
ejpam-5657	383	2	15	15	NUM
ejpam-5657	383	3	]	]	X
ejpam-5657	383	4	fang	fang	X
ejpam-5657	383	5	,	,	PUNCT
ejpam-5657	383	6	chun	chun	PROPN
ejpam-5657	383	7	-	-	PUNCT
ejpam-5657	383	8	hsiung	hsiung	PROPN
ejpam-5657	383	9	,	,	PUNCT
ejpam-5657	383	10	li	li	PROPN
ejpam-5657	383	11	lee	lee	PROPN
ejpam-5657	383	12	,	,	PUNCT
ejpam-5657	383	13	and	and	CCONJ
ejpam-5657	383	14	fan	fan	PROPN
ejpam-5657	383	15	-	-	PUNCT
ejpam-5657	383	16	ren	ren	PROPN
ejpam-5657	383	17	chang	chang	PROPN
ejpam-5657	383	18	.	.	PUNCT
ejpam-5657	384	1	robust	robust	ADJ
ejpam-5657	384	2	control	control	NOUN
ejpam-5657	384	3	analysis	analysis	NOUN
ejpam-5657	384	4	and	and	CCONJ
ejpam-5657	384	5	design	design	NOUN
ejpam-5657	384	6	for	for	ADP
ejpam-5657	384	7	discrete	discrete	ADJ
ejpam-5657	384	8	-	-	PUNCT
ejpam-5657	384	9	time	time	NOUN
ejpam-5657	384	10	singular	singular	PROPN
ejpam-5657	384	11	systems	system	NOUN
ejpam-5657	384	12	.	.	PUNCT
ejpam-5657	385	1	automatica	automatica	PROPN
ejpam-5657	385	2	30	30	NUM
ejpam-5657	385	3	,	,	PUNCT
ejpam-5657	385	4	no	no	INTJ
ejpam-5657	385	5	.	.	NOUN
ejpam-5657	385	6	11	11	NUM
ejpam-5657	385	7	(	(	PUNCT
ejpam-5657	385	8	1994	1994	NUM
ejpam-5657	385	9	):	):	PUNCT
ejpam-5657	385	10	1741	1741	NUM
ejpam-5657	385	11	-	-	SYM
ejpam-5657	385	12	1750	1750	NUM
ejpam-5657	385	13	.	.	PUNCT
ejpam-5657	386	1	[	[	X
ejpam-5657	386	2	16	16	NUM
ejpam-5657	386	3	]	]	X
ejpam-5657	386	4	fisher	fisher	PROPN
ejpam-5657	386	5	,	,	PUNCT
ejpam-5657	386	6	f.m	f.m	PROPN
ejpam-5657	386	7	.	.	PROPN
ejpam-5657	386	8	,	,	PUNCT
ejpam-5657	386	9	1965	1965	NUM
ejpam-5657	386	10	,	,	PUNCT
ejpam-5657	386	11	choice	choice	NOUN
ejpam-5657	386	12	of	of	ADP
ejpam-5657	386	13	units	unit	NOUN
ejpam-5657	386	14	,	,	PUNCT
ejpam-5657	386	15	column	column	NOUN
ejpam-5657	386	16	sums	sum	NOUN
ejpam-5657	386	17	,	,	PUNCT
ejpam-5657	386	18	and	and	CCONJ
ejpam-5657	386	19	stability	stability	NOUN
ejpam-5657	386	20	in	in	ADP
ejpam-5657	386	21	linear	linear	ADJ
ejpam-5657	386	22	dynamic	dynamic	ADJ
ejpam-5657	386	23	systems	system	NOUN
ejpam-5657	386	24	with	with	ADP
ejpam-5657	386	25	nonnegative	nonnegative	ADJ
ejpam-5657	386	26	square	square	ADJ
ejpam-5657	386	27	matrices	matrix	NOUN
ejpam-5657	386	28	,	,	PUNCT
ejpam-5657	386	29	econometrica	econometrica	PROPN
ejpam-5657	386	30	33	33	NUM
ejpam-5657	386	31	,	,	PUNCT
ejpam-5657	386	32	445	445	NUM
ejpam-5657	386	33	-	-	SYM
ejpam-5657	386	34	450	450	NUM
ejpam-5657	386	35	.	.	PUNCT
ejpam-5657	387	1	[	[	X
ejpam-5657	387	2	17	17	NUM
ejpam-5657	387	3	]	]	X
ejpam-5657	387	4	g.	g.	PROPN
ejpam-5657	387	5	p.	p.	PROPN
ejpam-5657	387	6	barker	barker	PROPN
ejpam-5657	387	7	,	,	PUNCT
ejpam-5657	387	8	a.	a.	NOUN
ejpam-5657	387	9	berman	berman	PROPN
ejpam-5657	387	10	,	,	PUNCT
ejpam-5657	387	11	and	and	CCONJ
ejpam-5657	387	12	r.	r.	PROPN
ejpam-5657	387	13	j.	j.	PROPN
ejpam-5657	387	14	plemmons	plemmons	PROPN
ejpam-5657	387	15	,	,	PUNCT
ejpam-5657	387	16	linear	linear	PROPN
ejpam-5657	387	17	&	&	CCONJ
ejpam-5657	387	18	multilinear	multilinear	PROPN
ejpam-5657	387	19	algebra	algebra	PROPN
ejpam-5657	387	20	,	,	PUNCT
ejpam-5657	387	21	vol	vol	NOUN
ejpam-5657	387	22	.	.	PROPN
ejpam-5657	387	23	5	5	NUM
ejpam-5657	387	24	,	,	PUNCT
ejpam-5657	387	25	pp	pp	ADJ
ejpam-5657	387	26	.	.	PUNCT
ejpam-5657	388	1	249–256	249–256	NUM
ejpam-5657	388	2	,	,	PUNCT
ejpam-5657	388	3	1978	1978	NUM
ejpam-5657	388	4	.	.	PUNCT
ejpam-5657	389	1	[	[	X
ejpam-5657	389	2	18	18	NUM
ejpam-5657	389	3	]	]	X
ejpam-5657	389	4	guglielmi	guglielmi	NOUN
ejpam-5657	389	5	,	,	PUNCT
ejpam-5657	389	6	nicola	nicola	PROPN
ejpam-5657	389	7	,	,	PUNCT
ejpam-5657	389	8	mutti	mutti	PROPN
ejpam-5657	389	9	-	-	PUNCT
ejpam-5657	389	10	ur	ur	PROPN
ejpam-5657	389	11	rehman	rehman	PROPN
ejpam-5657	389	12	,	,	PUNCT
ejpam-5657	389	13	and	and	CCONJ
ejpam-5657	389	14	daniel	daniel	PROPN
ejpam-5657	389	15	kressner	kressner	PROPN
ejpam-5657	389	16	.	.	PUNCT
ejpam-5657	390	1	a	a	DET
ejpam-5657	390	2	novel	novel	ADJ
ejpam-5657	390	3	iterative	iterative	NOUN
ejpam-5657	390	4	method	method	NOUN
ejpam-5657	390	5	to	to	PART
ejpam-5657	390	6	approximate	approximate	VERB
ejpam-5657	390	7	structured	structured	ADJ
ejpam-5657	390	8	singular	singular	ADJ
ejpam-5657	390	9	values	value	NOUN
ejpam-5657	390	10	.	.	PUNCT
ejpam-5657	391	1	siam	siam	PROPN
ejpam-5657	391	2	journal	journal	PROPN
ejpam-5657	391	3	on	on	ADP
ejpam-5657	391	4	matrix	matrix	NOUN
ejpam-5657	391	5	analysis	analysis	NOUN
ejpam-5657	391	6	and	and	CCONJ
ejpam-5657	391	7	m.u.r	m.u.r	NOUN
ejpam-5657	391	8	et	et	PROPN
ejpam-5657	391	9	al	al	PROPN
ejpam-5657	391	10	.	.	PUNCT
ejpam-5657	391	11	/	/	SYM
ejpam-5657	391	12	eur	eur	PROPN
ejpam-5657	391	13	.	.	PUNCT
ejpam-5657	392	1	j.	j.	PROPN
ejpam-5657	392	2	pure	pure	PROPN
ejpam-5657	392	3	appl	appl	PROPN
ejpam-5657	392	4	.	.	PROPN
ejpam-5657	392	5	math	math	PROPN
ejpam-5657	392	6	,	,	PUNCT
ejpam-5657	392	7	18	18	NUM
ejpam-5657	392	8	(	(	PUNCT
ejpam-5657	392	9	1	1	NUM
ejpam-5657	392	10	)	)	PUNCT
ejpam-5657	392	11	(	(	PUNCT
ejpam-5657	392	12	2025	2025	NUM
ejpam-5657	392	13	)	)	PUNCT
ejpam-5657	392	14	,	,	PUNCT
ejpam-5657	392	15	5657	5657	NUM
ejpam-5657	392	16	16	16	NUM
ejpam-5657	392	17	of	of	ADP
ejpam-5657	392	18	17	17	NUM
ejpam-5657	392	19	applications	application	NOUN
ejpam-5657	392	20	38.2	38.2	NUM
ejpam-5657	392	21	(	(	PUNCT
ejpam-5657	392	22	2017	2017	NUM
ejpam-5657	392	23	)	)	PUNCT
ejpam-5657	392	24	,	,	PUNCT
ejpam-5657	392	25	361	361	NUM
ejpam-5657	392	26	-	-	SYM
ejpam-5657	392	27	386	386	NUM
ejpam-5657	392	28	.	.	PUNCT
ejpam-5657	393	1	[	[	X
ejpam-5657	393	2	19	19	NUM
ejpam-5657	393	3	]	]	X
ejpam-5657	393	4	halton	halton	PROPN
ejpam-5657	393	5	,	,	PUNCT
ejpam-5657	393	6	m.	m.	NOUN
ejpam-5657	393	7	,	,	PUNCT
ejpam-5657	393	8	hayes	hayes	PROPN
ejpam-5657	393	9	,	,	PUNCT
ejpam-5657	393	10	m.	m.	NOUN
ejpam-5657	393	11	,	,	PUNCT
ejpam-5657	393	12	&	&	CCONJ
ejpam-5657	393	13	iordanov	iordanov	PROPN
ejpam-5657	393	14	,	,	PUNCT
ejpam-5657	393	15	p.	p.	NOUN
ejpam-5657	393	16	state	state	NOUN
ejpam-5657	393	17	-	-	PUNCT
ejpam-5657	393	18	space	space	NOUN
ejpam-5657	393	19	µ	µ	NOUN
ejpam-5657	393	20	analysis	analysis	NOUN
ejpam-5657	393	21	for	for	ADP
ejpam-5657	393	22	an	an	DET
ejpam-5657	393	23	experimental	experimental	ADJ
ejpam-5657	393	24	drive	drive	NOUN
ejpam-5657	393	25	-	-	PUNCT
ejpam-5657	393	26	by	by	ADP
ejpam-5657	393	27	-	-	PUNCT
ejpam-5657	393	28	wire	wire	NOUN
ejpam-5657	393	29	vehicle	vehicle	NOUN
ejpam-5657	393	30	.	.	PUNCT
ejpam-5657	394	1	international	international	ADJ
ejpam-5657	394	2	journal	journal	PROPN
ejpam-5657	394	3	of	of	ADP
ejpam-5657	394	4	robust	robust	ADJ
ejpam-5657	394	5	and	and	CCONJ
ejpam-5657	394	6	non	non	ADJ
ejpam-5657	394	7	-	-	ADJ
ejpam-5657	394	8	linear	linear	ADJ
ejpam-5657	394	9	control	control	NOUN
ejpam-5657	394	10	,	,	PUNCT
ejpam-5657	394	11	18(9	18(9	NOUN
ejpam-5657	394	12	)	)	PUNCT
ejpam-5657	394	13	(	(	PUNCT
ejpam-5657	394	14	2008	2008	NUM
ejpam-5657	394	15	)	)	PUNCT
ejpam-5657	394	16	975–992	975–992	NUM
ejpam-5657	394	17	.	.	PUNCT
ejpam-5657	395	1	[	[	X
ejpam-5657	395	2	20	20	NUM
ejpam-5657	395	3	]	]	X
ejpam-5657	395	4	kim	kim	PROPN
ejpam-5657	395	5	,	,	PUNCT
ejpam-5657	395	6	kwang	kwang	PROPN
ejpam-5657	395	7	-	-	PUNCT
ejpam-5657	395	8	ki	ki	PROPN
ejpam-5657	395	9	k.	k.	PROPN
ejpam-5657	395	10	,	,	PUNCT
ejpam-5657	395	11	and	and	CCONJ
ejpam-5657	395	12	richard	richard	PROPN
ejpam-5657	395	13	d.	d.	PROPN
ejpam-5657	395	14	braatz	braatz	PROPN
ejpam-5657	395	15	.	.	PUNCT
ejpam-5657	396	1	continuous	continuous	ADJ
ejpam-5657	396	2	-	-	PUNCT
ejpam-5657	396	3	and	and	CCONJ
ejpam-5657	396	4	discrete	discrete	ADJ
ejpam-5657	396	5	-	-	PUNCT
ejpam-5657	396	6	time	time	NOUN
ejpam-5657	396	7	d	d	NOUN
ejpam-5657	396	8	-	-	NOUN
ejpam-5657	396	9	stability	stability	NOUN
ejpam-5657	396	10	,	,	PUNCT
ejpam-5657	396	11	joint	joint	ADJ
ejpam-5657	396	12	d	d	NOUN
ejpam-5657	396	13	-	-	NOUN
ejpam-5657	396	14	stability	stability	NOUN
ejpam-5657	396	15	,	,	PUNCT
ejpam-5657	396	16	and	and	CCONJ
ejpam-5657	396	17	their	their	PRON
ejpam-5657	396	18	applications	application	NOUN
ejpam-5657	396	19	:	:	PUNCT
ejpam-5657	396	20	µ	µ	DET
ejpam-5657	396	21	theory	theory	NOUN
ejpam-5657	396	22	and	and	CCONJ
ejpam-5657	396	23	diagonal	diagonal	ADJ
ejpam-5657	396	24	stability	stability	NOUN
ejpam-5657	396	25	approaches	approach	NOUN
ejpam-5657	396	26	.	.	PUNCT
ejpam-5657	397	1	2012	2012	NUM
ejpam-5657	397	2	ieee	ieee	PROPN
ejpam-5657	397	3	51st	51st	ADJ
ejpam-5657	397	4	ieee	ieee	NOUN
ejpam-5657	397	5	conference	conference	NOUN
ejpam-5657	397	6	on	on	ADP
ejpam-5657	397	7	decision	decision	NOUN
ejpam-5657	397	8	and	and	CCONJ
ejpam-5657	397	9	control	control	NOUN
ejpam-5657	397	10	(	(	PUNCT
ejpam-5657	397	11	cdc	cdc	PROPN
ejpam-5657	397	12	)	)	PUNCT
ejpam-5657	397	13	.	.	PUNCT
ejpam-5657	398	1	ieee	ieee	PROPN
ejpam-5657	398	2	,	,	PUNCT
ejpam-5657	398	3	2012	2012	NUM
ejpam-5657	398	4	.	.	PUNCT
ejpam-5657	399	1	[	[	X
ejpam-5657	399	2	21	21	NUM
ejpam-5657	399	3	]	]	X
ejpam-5657	399	4	kemp	kemp	PROPN
ejpam-5657	399	5	,	,	PUNCT
ejpam-5657	399	6	m.c	m.c	PROPN
ejpam-5657	399	7	.	.	PROPN
ejpam-5657	399	8	and	and	CCONJ
ejpam-5657	399	9	y.	y.	PROPN
ejpam-5657	399	10	kimura	kimura	PROPN
ejpam-5657	399	11	,	,	PUNCT
ejpam-5657	399	12	1978	1978	NUM
ejpam-5657	399	13	,	,	PUNCT
ejpam-5657	399	14	introduction	introduction	NOUN
ejpam-5657	399	15	to	to	ADP
ejpam-5657	399	16	mathematical	mathematical	ADJ
ejpam-5657	399	17	economics	economic	NOUN
ejpam-5657	399	18	(	(	PUNCT
ejpam-5657	399	19	springer	springer	NOUN
ejpam-5657	399	20	-	-	PUNCT
ejpam-5657	399	21	verlag	verlag	PROPN
ejpam-5657	399	22	,	,	PUNCT
ejpam-5657	399	23	new	new	PROPN
ejpam-5657	399	24	york	york	PROPN
ejpam-5657	399	25	)	)	PUNCT
ejpam-5657	399	26	.	.	PUNCT
ejpam-5657	400	1	[	[	X
ejpam-5657	400	2	22	22	NUM
ejpam-5657	400	3	]	]	SYM
ejpam-5657	400	4	kushel	kushel	PROPN
ejpam-5657	400	5	,	,	PUNCT
ejpam-5657	400	6	o.y	o.y	PROPN
ejpam-5657	400	7	.	.	PROPN
ejpam-5657	400	8	,	,	PUNCT
ejpam-5657	400	9	pavani	pavani	PROPN
ejpam-5657	400	10	,	,	PUNCT
ejpam-5657	400	11	r.	r.	PROPN
ejpam-5657	400	12	novel	novel	ADJ
ejpam-5657	400	13	versions	version	NOUN
ejpam-5657	400	14	of	of	ADP
ejpam-5657	400	15	d	d	NOUN
ejpam-5657	400	16	-	-	NOUN
ejpam-5657	400	17	stability	stability	NOUN
ejpam-5657	400	18	in	in	ADP
ejpam-5657	400	19	matrices	matrix	NOUN
ejpam-5657	400	20	provide	provide	VERB
ejpam-5657	400	21	new	new	ADJ
ejpam-5657	400	22	insights	insight	NOUN
ejpam-5657	400	23	into	into	ADP
ejpam-5657	400	24	ode	ode	ADJ
ejpam-5657	400	25	dynamics	dynamic	NOUN
ejpam-5657	400	26	.	.	PUNCT
ejpam-5657	401	1	mediterr	mediterr	PROPN
ejpam-5657	401	2	.	.	PUNCT
ejpam-5657	402	1	j.	j.	PROPN
ejpam-5657	402	2	math	math	PROPN
ejpam-5657	402	3	.	.	PROPN
ejpam-5657	403	1	20	20	NUM
ejpam-5657	403	2	,	,	PUNCT
ejpam-5657	403	3	225	225	NUM
ejpam-5657	403	4	(	(	PUNCT
ejpam-5657	403	5	2023	2023	NUM
ejpam-5657	403	6	)	)	PUNCT
ejpam-5657	403	7	.	.	PUNCT
ejpam-5657	404	1	[	[	X
ejpam-5657	404	2	23	23	NUM
ejpam-5657	404	3	]	]	X
ejpam-5657	404	4	kaczorek	kaczorek	NOUN
ejpam-5657	404	5	,	,	PUNCT
ejpam-5657	404	6	tadeusz	tadeusz	PROPN
ejpam-5657	404	7	.	.	PUNCT
ejpam-5657	405	1	analysis	analysis	NOUN
ejpam-5657	405	2	and	and	CCONJ
ejpam-5657	405	3	comparison	comparison	NOUN
ejpam-5657	405	4	of	of	ADP
ejpam-5657	405	5	the	the	DET
ejpam-5657	405	6	stability	stability	NOUN
ejpam-5657	405	7	of	of	ADP
ejpam-5657	405	8	discrete	discrete	ADJ
ejpam-5657	405	9	-	-	PUNCT
ejpam-5657	405	10	time	time	NOUN
ejpam-5657	405	11	and	and	CCONJ
ejpam-5657	405	12	continuous	continuous	ADJ
ejpam-5657	405	13	-	-	PUNCT
ejpam-5657	405	14	time	time	NOUN
ejpam-5657	405	15	linear	linear	PROPN
ejpam-5657	405	16	systems	system	NOUN
ejpam-5657	405	17	.	.	PUNCT
ejpam-5657	406	1	archives	archive	NOUN
ejpam-5657	406	2	of	of	ADP
ejpam-5657	406	3	control	control	PROPN
ejpam-5657	406	4	sciences	science	NOUN
ejpam-5657	406	5	26	26	NUM
ejpam-5657	406	6	,	,	PUNCT
ejpam-5657	406	7	no	no	INTJ
ejpam-5657	406	8	.	.	NOUN
ejpam-5657	406	9	4	4	NUM
ejpam-5657	406	10	(	(	PUNCT
ejpam-5657	406	11	2016	2016	NUM
ejpam-5657	406	12	)	)	PUNCT
ejpam-5657	406	13	.	.	PUNCT
ejpam-5657	407	1	[	[	X
ejpam-5657	407	2	24	24	NUM
ejpam-5657	407	3	]	]	SYM
ejpam-5657	407	4	lewis	lewis	PROPN
ejpam-5657	407	5	,	,	PUNCT
ejpam-5657	407	6	frank	frank	PROPN
ejpam-5657	407	7	l.	l.	PROPN
ejpam-5657	407	8	a	a	DET
ejpam-5657	407	9	tutorial	tutorial	NOUN
ejpam-5657	407	10	on	on	ADP
ejpam-5657	407	11	the	the	DET
ejpam-5657	407	12	geometric	geometric	ADJ
ejpam-5657	407	13	analysis	analysis	NOUN
ejpam-5657	407	14	of	of	ADP
ejpam-5657	407	15	linear	linear	ADJ
ejpam-5657	407	16	time	time	NOUN
ejpam-5657	407	17	-	-	PUNCT
ejpam-5657	407	18	invariant	invariant	ADJ
ejpam-5657	407	19	implicit	implicit	ADJ
ejpam-5657	407	20	systems	system	NOUN
ejpam-5657	407	21	.	.	PUNCT
ejpam-5657	408	1	automatica	automatica	PROPN
ejpam-5657	408	2	28	28	NUM
ejpam-5657	408	3	,	,	PUNCT
ejpam-5657	408	4	no	no	INTJ
ejpam-5657	408	5	.	.	NOUN
ejpam-5657	408	6	1	1	NUM
ejpam-5657	408	7	(	(	PUNCT
ejpam-5657	408	8	1992	1992	NUM
ejpam-5657	408	9	):	):	PUNCT
ejpam-5657	408	10	119	119	NUM
ejpam-5657	408	11	-	-	SYM
ejpam-5657	408	12	137	137	NUM
ejpam-5657	408	13	.	.	PUNCT
ejpam-5657	409	1	[	[	X
ejpam-5657	409	2	25	25	NUM
ejpam-5657	409	3	]	]	PUNCT
ejpam-5657	409	4	leontief	leontief	NOUN
ejpam-5657	409	5	,	,	PUNCT
ejpam-5657	409	6	w.	w.	PROPN
ejpam-5657	409	7	input	input	PROPN
ejpam-5657	409	8	-	-	PUNCT
ejpam-5657	409	9	output	output	NOUN
ejpam-5657	409	10	economics	economic	NOUN
ejpam-5657	409	11	.	.	PUNCT
ejpam-5657	410	1	(	(	PUNCT
ejpam-5657	410	2	1986	1986	NUM
ejpam-5657	410	3	)	)	PUNCT
ejpam-5657	410	4	.	.	PUNCT
ejpam-5657	411	1	[	[	X
ejpam-5657	411	2	26	26	NUM
ejpam-5657	411	3	]	]	X
ejpam-5657	411	4	mckenzie	mckenzie	PROPN
ejpam-5657	411	5	,	,	PUNCT
ejpam-5657	411	6	l.	l.	PROPN
ejpam-5657	411	7	,	,	PUNCT
ejpam-5657	411	8	1960	1960	NUM
ejpam-5657	411	9	,	,	PUNCT
ejpam-5657	411	10	matrices	matrix	NOUN
ejpam-5657	411	11	with	with	ADP
ejpam-5657	411	12	dominant	dominant	ADJ
ejpam-5657	411	13	diagonals	diagonal	NOUN
ejpam-5657	411	14	and	and	CCONJ
ejpam-5657	411	15	economic	economic	ADJ
ejpam-5657	411	16	theory	theory	NOUN
ejpam-5657	411	17	,	,	PUNCT
ejpam-5657	411	18	in	in	ADP
ejpam-5657	411	19	:	:	PUNCT
ejpam-5657	411	20	k.j	k.j	PROPN
ejpam-5657	411	21	.	.	PROPN
ejpam-5657	411	22	arrow	arrow	PROPN
ejpam-5657	411	23	,	,	PUNCT
ejpam-5657	411	24	s.	s.	PROPN
ejpam-5657	411	25	karlin	karlin	PROPN
ejpam-5657	411	26	and	and	CCONJ
ejpam-5657	411	27	p.	p.	PROPN
ejpam-5657	411	28	suppes	suppe	NOUN
ejpam-5657	411	29	,	,	PUNCT
ejpam-5657	411	30	eds	eds	PROPN
ejpam-5657	411	31	.	.	PROPN
ejpam-5657	411	32	,	,	PUNCT
ejpam-5657	411	33	mathematical	mathematical	ADJ
ejpam-5657	411	34	methods	method	NOUN
ejpam-5657	411	35	in	in	ADP
ejpam-5657	411	36	the	the	DET
ejpam-5657	411	37	social	social	ADJ
ejpam-5657	411	38	sciences	science	NOUN
ejpam-5657	411	39	,	,	PUNCT
ejpam-5657	411	40	1959	1959	NUM
ejpam-5657	411	41	(	(	PUNCT
ejpam-5657	411	42	stanford	stanford	PROPN
ejpam-5657	411	43	university	university	PROPN
ejpam-5657	411	44	press	press	PROPN
ejpam-5657	411	45	,	,	PUNCT
ejpam-5657	411	46	stanford	stanford	PROPN
ejpam-5657	411	47	)	)	PUNCT
ejpam-5657	411	48	47	47	NUM
ejpam-5657	411	49	-	-	SYM
ejpam-5657	411	50	62	62	NUM
ejpam-5657	411	51	.	.	PUNCT
ejpam-5657	412	1	[	[	X
ejpam-5657	412	2	27	27	NUM
ejpam-5657	412	3	]	]	X
ejpam-5657	412	4	murata	murata	PROPN
ejpam-5657	412	5	,	,	PUNCT
ejpam-5657	412	6	y.	y.	PROPN
ejpam-5657	412	7	,	,	PUNCT
ejpam-5657	412	8	1977	1977	NUM
ejpam-5657	412	9	,	,	PUNCT
ejpam-5657	412	10	mathematics	mathematic	NOUN
ejpam-5657	412	11	for	for	ADP
ejpam-5657	412	12	stability	stability	NOUN
ejpam-5657	412	13	and	and	CCONJ
ejpam-5657	412	14	optimization	optimization	NOUN
ejpam-5657	412	15	of	of	ADP
ejpam-5657	412	16	economic	economic	ADJ
ejpam-5657	412	17	systems	system	NOUN
ejpam-5657	412	18	(	(	PUNCT
ejpam-5657	412	19	academic	academic	ADJ
ejpam-5657	412	20	press	press	NOUN
ejpam-5657	412	21	,	,	PUNCT
ejpam-5657	412	22	new	new	PROPN
ejpam-5657	412	23	york	york	PROPN
ejpam-5657	412	24	)	)	PUNCT
ejpam-5657	412	25	.	.	PUNCT
ejpam-5657	413	1	[	[	X
ejpam-5657	413	2	28	28	NUM
ejpam-5657	413	3	]	]	X
ejpam-5657	413	4	mark	mark	PROPN
ejpam-5657	413	5	embree	embree	PROPN
ejpam-5657	413	6	and	and	CCONJ
ejpam-5657	413	7	lloyd	lloyd	PROPN
ejpam-5657	413	8	n.	n.	PROPN
ejpam-5657	413	9	trefethen	trefethen	PROPN
ejpam-5657	413	10	.	.	PUNCT
ejpam-5657	414	1	pseudospectra	pseudospectra	PROPN
ejpam-5657	414	2	gateway	gateway	PROPN
ejpam-5657	414	3	.	.	PUNCT
ejpam-5657	415	1	[	[	X
ejpam-5657	415	2	29	29	NUM
ejpam-5657	415	3	]	]	X
ejpam-5657	415	4	magni	magni	X
ejpam-5657	415	5	,	,	PUNCT
ejpam-5657	415	6	j.	j.	PROPN
ejpam-5657	415	7	,	,	PUNCT
ejpam-5657	415	8	döll	döll	PROPN
ejpam-5657	415	9	,	,	PUNCT
ejpam-5657	415	10	c.	c.	PROPN
ejpam-5657	415	11	,	,	PUNCT
ejpam-5657	415	12	chiappa	chiappa	PROPN
ejpam-5657	415	13	,	,	PUNCT
ejpam-5657	415	14	c.	c.	PROPN
ejpam-5657	415	15	,	,	PUNCT
ejpam-5657	415	16	frappard	frappard	NOUN
ejpam-5657	415	17	,	,	PUNCT
ejpam-5657	415	18	b.	b.	PROPN
ejpam-5657	415	19	,	,	PUNCT
ejpam-5657	415	20	&	&	CCONJ
ejpam-5657	415	21	girouart	girouart	PROPN
ejpam-5657	415	22	,	,	PUNCT
ejpam-5657	415	23	b.	b.	PROPN
ejpam-5657	415	24	mixed	mix	VERB
ejpam-5657	415	25	µ-analysis	µ-analysis	NOUN
ejpam-5657	415	26	for	for	ADP
ejpam-5657	415	27	flexible	flexible	ADJ
ejpam-5657	415	28	systems	system	NOUN
ejpam-5657	415	29	.	.	PUNCT
ejpam-5657	416	1	part	part	NOUN
ejpam-5657	416	2	1	1	NUM
ejpam-5657	416	3	:	:	PUNCT
ejpam-5657	416	4	theory	theory	NOUN
ejpam-5657	416	5	.	.	PUNCT
ejpam-5657	417	1	in	in	ADP
ejpam-5657	417	2	proceedings	proceeding	NOUN
ejpam-5657	417	3	of	of	ADP
ejpam-5657	417	4	the	the	DET
ejpam-5657	417	5	14th	14th	ADJ
ejpam-5657	417	6	ifac	ifac	NOUN
ejpam-5657	417	7	world	world	PROPN
ejpam-5657	417	8	congress	congress	PROPN
ejpam-5657	417	9	,	,	PUNCT
ejpam-5657	417	10	beijing	beijing	PROPN
ejpam-5657	417	11	,	,	PUNCT
ejpam-5657	417	12	china	china	PROPN
ejpam-5657	417	13	,	,	PUNCT
ejpam-5657	417	14	(	(	PUNCT
ejpam-5657	417	15	1999	1999	NUM
ejpam-5657	417	16	)	)	PUNCT
ejpam-5657	417	17	,	,	PUNCT
ejpam-5657	417	18	325–360	325–360	NUM
ejpam-5657	417	19	.	.	PUNCT
ejpam-5657	418	1	[	[	X
ejpam-5657	418	2	30	30	NUM
ejpam-5657	418	3	]	]	X
ejpam-5657	418	4	nieuwenhuis	nieuwenhuis	PROPN
ejpam-5657	418	5	,	,	PUNCT
ejpam-5657	418	6	herman	herman	PROPN
ejpam-5657	418	7	j.	j.	PROPN
ejpam-5657	418	8	,	,	PUNCT
ejpam-5657	418	9	and	and	CCONJ
ejpam-5657	418	10	lambert	lambert	PROPN
ejpam-5657	418	11	schoonbeek	schoonbeek	PROPN
ejpam-5657	418	12	.	.	PUNCT
ejpam-5657	419	1	stability	stability	NOUN
ejpam-5657	419	2	and	and	CCONJ
ejpam-5657	419	3	the	the	DET
ejpam-5657	419	4	structure	structure	NOUN
ejpam-5657	419	5	of	of	ADP
ejpam-5657	419	6	continuous	continuous	ADJ
ejpam-5657	419	7	-	-	PUNCT
ejpam-5657	419	8	time	time	NOUN
ejpam-5657	419	9	economic	economic	ADJ
ejpam-5657	419	10	models	model	NOUN
ejpam-5657	419	11	.	.	PUNCT
ejpam-5657	420	1	economic	economic	ADJ
ejpam-5657	420	2	modelling	modelling	NOUN
ejpam-5657	420	3	14	14	NUM
ejpam-5657	420	4	,	,	PUNCT
ejpam-5657	420	5	no	no	INTJ
ejpam-5657	420	6	.	.	NOUN
ejpam-5657	420	7	3	3	NUM
ejpam-5657	420	8	(	(	PUNCT
ejpam-5657	420	9	1997	1997	NUM
ejpam-5657	420	10	):	):	PUNCT
ejpam-5657	420	11	311	311	NUM
ejpam-5657	420	12	-	-	SYM
ejpam-5657	420	13	340	340	NUM
ejpam-5657	420	14	.	.	PUNCT
ejpam-5657	421	1	[	[	X
ejpam-5657	421	2	31	31	NUM
ejpam-5657	421	3	]	]	PUNCT
ejpam-5657	421	4	o’connor	o’connor	ADV
ejpam-5657	421	5	,	,	PUNCT
ejpam-5657	421	6	robert	robert	PROPN
ejpam-5657	421	7	,	,	PUNCT
ejpam-5657	421	8	and	and	CCONJ
ejpam-5657	421	9	edmund	edmund	PROPN
ejpam-5657	421	10	w.	w.	PROPN
ejpam-5657	421	11	henry	henry	PROPN
ejpam-5657	421	12	.	.	PUNCT
ejpam-5657	421	13	input	input	NOUN
ejpam-5657	421	14	-	-	PUNCT
ejpam-5657	421	15	output	output	NOUN
ejpam-5657	421	16	analysis	analysis	NOUN
ejpam-5657	421	17	and	and	CCONJ
ejpam-5657	421	18	its	its	PRON
ejpam-5657	421	19	applications	application	NOUN
ejpam-5657	421	20	.	.	PUNCT
ejpam-5657	422	1	(	(	PUNCT
ejpam-5657	422	2	1975	1975	NUM
ejpam-5657	422	3	)	)	PUNCT
ejpam-5657	422	4	.	.	PUNCT
ejpam-5657	423	1	[	[	X
ejpam-5657	423	2	32	32	NUM
ejpam-5657	423	3	]	]	X
ejpam-5657	423	4	packard	packard	NOUN
ejpam-5657	423	5	,	,	PUNCT
ejpam-5657	423	6	andy	andy	PROPN
ejpam-5657	423	7	,	,	PUNCT
ejpam-5657	423	8	michael	michael	PROPN
ejpam-5657	423	9	kh	kh	PROPN
ejpam-5657	423	10	fan	fan	PROPN
ejpam-5657	423	11	,	,	PUNCT
ejpam-5657	423	12	and	and	CCONJ
ejpam-5657	423	13	john	john	PROPN
ejpam-5657	423	14	doyle	doyle	PROPN
ejpam-5657	423	15	.	.	PUNCT
ejpam-5657	424	1	a	a	DET
ejpam-5657	424	2	power	power	NOUN
ejpam-5657	424	3	method	method	NOUN
ejpam-5657	424	4	for	for	ADP
ejpam-5657	424	5	the	the	DET
ejpam-5657	424	6	structured	structured	ADJ
ejpam-5657	424	7	singular	singular	NOUN
ejpam-5657	424	8	value	value	NOUN
ejpam-5657	424	9	.	.	PUNCT
ejpam-5657	425	1	ieee	ieee	NOUN
ejpam-5657	425	2	conf	conf	NOUN
ejpam-5657	425	3	.	.	PUNCT
ejpam-5657	426	1	on	on	ADP
ejpam-5657	426	2	decision	decision	NOUN
ejpam-5657	426	3	and	and	CCONJ
ejpam-5657	426	4	control	control	NOUN
ejpam-5657	426	5	,	,	PUNCT
ejpam-5657	426	6	(	(	PUNCT
ejpam-5657	426	7	1988	1988	NUM
ejpam-5657	426	8	)	)	PUNCT
ejpam-5657	426	9	.	.	PUNCT
ejpam-5657	427	1	[	[	X
ejpam-5657	427	2	33	33	NUM
ejpam-5657	427	3	]	]	X
ejpam-5657	427	4	packard	packard	PROPN
ejpam-5657	427	5	,	,	PUNCT
ejpam-5657	427	6	andrew	andrew	PROPN
ejpam-5657	427	7	,	,	PUNCT
ejpam-5657	427	8	and	and	CCONJ
ejpam-5657	427	9	john	john	PROPN
ejpam-5657	427	10	doyle	doyle	PROPN
ejpam-5657	427	11	.	.	PUNCT
ejpam-5657	428	1	the	the	DET
ejpam-5657	428	2	complex	complex	ADJ
ejpam-5657	428	3	structured	structured	ADJ
ejpam-5657	428	4	singular	singular	ADJ
ejpam-5657	428	5	value	value	NOUN
ejpam-5657	428	6	.	.	PUNCT
ejpam-5657	429	1	automatica	automatica	PROPN
ejpam-5657	429	2	29.1	29.1	NUM
ejpam-5657	429	3	(	(	PUNCT
ejpam-5657	429	4	1993	1993	NUM
ejpam-5657	429	5	):	):	PUNCT
ejpam-5657	429	6	71	71	NUM
ejpam-5657	429	7	-	-	SYM
ejpam-5657	429	8	109	109	NUM
ejpam-5657	429	9	.	.	PUNCT
ejpam-5657	430	1	[	[	X
ejpam-5657	430	2	34	34	NUM
ejpam-5657	430	3	]	]	X
ejpam-5657	430	4	rehman	rehman	PROPN
ejpam-5657	430	5	,	,	PUNCT
ejpam-5657	430	6	mu	mu	PROPN
ejpam-5657	430	7	.	.	PROPN
ejpam-5657	430	8	,	,	PUNCT
ejpam-5657	430	9	rasulov	rasulov	PROPN
ejpam-5657	430	10	,	,	PUNCT
ejpam-5657	430	11	t.h	t.h	PROPN
ejpam-5657	430	12	.	.	PROPN
ejpam-5657	430	13	&	&	CCONJ
ejpam-5657	430	14	amir	amir	PROPN
ejpam-5657	430	15	,	,	PUNCT
ejpam-5657	430	16	f.	f.	PROPN
ejpam-5657	430	17	d	d	PROPN
ejpam-5657	430	18	-	-	PUNCT
ejpam-5657	430	19	stability	stability	NOUN
ejpam-5657	430	20	,	,	PUNCT
ejpam-5657	430	21	strong	strong	ADJ
ejpam-5657	430	22	d	d	NOUN
ejpam-5657	430	23	-	-	NOUN
ejpam-5657	430	24	stability	stability	NOUN
ejpam-5657	430	25	and	and	CCONJ
ejpam-5657	430	26	µvalues	µvalue	NOUN
ejpam-5657	430	27	.	.	PUNCT
ejpam-5657	431	1	lobachevskii	lobachevskii	VERB
ejpam-5657	431	2	j	j	PROPN
ejpam-5657	431	3	math	math	PROPN
ejpam-5657	431	4	45	45	NUM
ejpam-5657	431	5	,	,	PUNCT
ejpam-5657	431	6	1227–1233	1227–1233	NUM
ejpam-5657	431	7	(	(	PUNCT
ejpam-5657	431	8	2024	2024	NUM
ejpam-5657	431	9	)	)	PUNCT
ejpam-5657	431	10	.	.	PUNCT
ejpam-5657	432	1	[	[	X
ejpam-5657	432	2	35	35	NUM
ejpam-5657	432	3	]	]	X
ejpam-5657	432	4	s.	s.	PROPN
ejpam-5657	432	5	xu	xu	PROPN
ejpam-5657	432	6	,	,	PUNCT
ejpam-5657	432	7	p.	p.	PROPN
ejpam-5657	432	8	van	van	PROPN
ejpam-5657	432	9	dooren	dooren	PROPN
ejpam-5657	432	10	,	,	PUNCT
ejpam-5657	432	11	r.	r.	PROPN
ejpam-5657	432	12	stefan	stefan	PROPN
ejpam-5657	432	13	and	and	CCONJ
ejpam-5657	432	14	j.	j.	PROPN
ejpam-5657	432	15	lam	lam	PROPN
ejpam-5657	432	16	,	,	PUNCT
ejpam-5657	432	17	robust	robust	ADJ
ejpam-5657	432	18	stability	stability	NOUN
ejpam-5657	432	19	and	and	CCONJ
ejpam-5657	432	20	stabilization	stabilization	NOUN
ejpam-5657	432	21	for	for	ADP
ejpam-5657	432	22	singular	singular	ADJ
ejpam-5657	432	23	systems	system	NOUN
ejpam-5657	432	24	with	with	ADP
ejpam-5657	432	25	state	state	NOUN
ejpam-5657	432	26	delay	delay	NOUN
ejpam-5657	432	27	and	and	CCONJ
ejpam-5657	432	28	parameter	parameter	NOUN
ejpam-5657	432	29	uncertainty	uncertainty	NOUN
ejpam-5657	432	30	,	,	PUNCT
ejpam-5657	432	31	ieee	ieee	NOUN
ejpam-5657	432	32	trans	trans	PROPN
ejpam-5657	432	33	.	.	PROPN
ejpam-5657	433	1	automat	automat	PROPN
ejpam-5657	433	2	.	.	PUNCT
ejpam-5657	434	1	control	control	PROPN
ejpam-5657	434	2	,	,	PUNCT
ejpam-5657	434	3	vol	vol	NOUN
ejpam-5657	434	4	.	.	PROPN
ejpam-5657	435	1	47	47	NUM
ejpam-5657	435	2	,	,	PUNCT
ejpam-5657	435	3	pp	pp	ADJ
ejpam-5657	435	4	.	.	PUNCT
ejpam-5657	436	1	1122	1122	NUM
ejpam-5657	436	2	-	-	SYM
ejpam-5657	436	3	1128	1128	NUM
ejpam-5657	436	4	,	,	PUNCT
ejpam-5657	436	5	july	july	PROPN
ejpam-5657	436	6	2002	2002	NUM
ejpam-5657	436	7	.	.	PUNCT
ejpam-5657	437	1	[	[	X
ejpam-5657	437	2	36	36	NUM
ejpam-5657	437	3	]	]	PUNCT
ejpam-5657	437	4	s.	s.	PROPN
ejpam-5657	437	5	xu	xu	PROPN
ejpam-5657	437	6	and	and	CCONJ
ejpam-5657	437	7	c.	c.	PROPN
ejpam-5657	437	8	yang	yang	PROPN
ejpam-5657	437	9	,	,	PUNCT
ejpam-5657	437	10	stabilization	stabilization	NOUN
ejpam-5657	437	11	of	of	ADP
ejpam-5657	437	12	discrete	discrete	ADJ
ejpam-5657	437	13	-	-	PUNCT
ejpam-5657	437	14	time	time	NOUN
ejpam-5657	437	15	singular	singular	ADJ
ejpam-5657	437	16	systems	system	NOUN
ejpam-5657	437	17	:	:	PUNCT
ejpam-5657	437	18	a	a	DET
ejpam-5657	437	19	matrix	matrix	NOUN
ejpam-5657	437	20	inequalities	inequality	NOUN
ejpam-5657	437	21	approach	approach	NOUN
ejpam-5657	437	22	,	,	PUNCT
ejpam-5657	437	23	automatica	automatica	PROPN
ejpam-5657	437	24	,	,	PUNCT
ejpam-5657	437	25	vol	vol	NOUN
ejpam-5657	437	26	.	.	PROPN
ejpam-5657	437	27	35	35	NUM
ejpam-5657	437	28	,	,	PUNCT
ejpam-5657	437	29	pp	pp	ADJ
ejpam-5657	437	30	.	.	PUNCT
ejpam-5657	438	1	1613	1613	NUM
ejpam-5657	438	2	-	-	SYM
ejpam-5657	438	3	1617	1617	NUM
ejpam-5657	438	4	,	,	PUNCT
ejpam-5657	438	5	1999	1999	NUM
ejpam-5657	438	6	.	.	PUNCT
ejpam-5657	439	1	[	[	X
ejpam-5657	439	2	37	37	NUM
ejpam-5657	439	3	]	]	X
ejpam-5657	439	4	sjoo	sjoo	PROPN
ejpam-5657	439	5	b.	b.	PROPN
ejpam-5657	439	6	,	,	PUNCT
ejpam-5657	439	7	1993	1993	NUM
ejpam-5657	439	8	,	,	PUNCT
ejpam-5657	439	9	a	a	DET
ejpam-5657	439	10	continuous	continuous	ADJ
ejpam-5657	439	11	-	-	PUNCT
ejpam-5657	439	12	time	time	NOUN
ejpam-5657	439	13	econometric	econometric	ADJ
ejpam-5657	439	14	model	model	NOUN
ejpam-5657	439	15	for	for	ADP
ejpam-5657	439	16	sweden	sweden	PROPN
ejpam-5657	439	17	based	base	VERB
ejpam-5657	439	18	on	on	ADP
ejpam-5657	439	19	monthly	monthly	ADJ
ejpam-5657	439	20	data	datum	NOUN
ejpam-5657	439	21	,	,	PUNCT
ejpam-5657	439	22	in	in	ADP
ejpam-5657	439	23	:	:	PUNCT
ejpam-5657	439	24	(	(	PUNCT
ejpam-5657	439	25	3	3	X
ejpam-5657	439	26	.	.	X
ejpam-5657	439	27	gandolfo	gandolfo	PROPN
ejpam-5657	439	28	,	,	PUNCT
ejpam-5657	439	29	ed	ed	NOUN
ejpam-5657	439	30	.	.	PROPN
ejpam-5657	439	31	,	,	PUNCT
ejpam-5657	439	32	continuous	continuous	ADJ
ejpam-5657	439	33	time	time	NOUN
ejpam-5657	439	34	econometrics	econometric	NOUN
ejpam-5657	439	35	;	;	PUNCT
ejpam-5657	439	36	theory	theory	NOUN
ejpam-5657	439	37	and	and	CCONJ
ejpam-5657	439	38	applications	application	NOUN
ejpam-5657	439	39	(	(	PUNCT
ejpam-5657	439	40	chapman	chapman	PROPN
ejpam-5657	439	41	&	&	CCONJ
ejpam-5657	439	42	hall	hall	PROPN
ejpam-5657	439	43	,	,	PUNCT
ejpam-5657	439	44	london	london	PROPN
ejpam-5657	439	45	)	)	PUNCT
ejpam-5657	439	46	195	195	NUM
ejpam-5657	439	47	-	-	SYM
ejpam-5657	439	48	227	227	NUM
ejpam-5657	439	49	.	.	PUNCT
ejpam-5657	439	50	m.u.r	m.u.r	NOUN
ejpam-5657	439	51	et	et	PROPN
ejpam-5657	439	52	al	al	PROPN
ejpam-5657	439	53	.	.	PUNCT
ejpam-5657	439	54	/	/	SYM
ejpam-5657	439	55	eur	eur	PROPN
ejpam-5657	439	56	.	.	PUNCT
ejpam-5657	440	1	j.	j.	PROPN
ejpam-5657	440	2	pure	pure	PROPN
ejpam-5657	440	3	appl	appl	PROPN
ejpam-5657	440	4	.	.	PROPN
ejpam-5657	440	5	math	math	PROPN
ejpam-5657	440	6	,	,	PUNCT
ejpam-5657	440	7	18	18	NUM
ejpam-5657	440	8	(	(	PUNCT
ejpam-5657	440	9	1	1	NUM
ejpam-5657	440	10	)	)	PUNCT
ejpam-5657	440	11	(	(	PUNCT
ejpam-5657	440	12	2025	2025	NUM
ejpam-5657	440	13	)	)	PUNCT
ejpam-5657	440	14	,	,	PUNCT
ejpam-5657	440	15	5657	5657	NUM
ejpam-5657	440	16	17	17	NUM
ejpam-5657	440	17	of	of	ADP
ejpam-5657	440	18	17	17	NUM
ejpam-5657	440	19	[	[	SYM
ejpam-5657	440	20	38	38	NUM
ejpam-5657	440	21	]	]	PUNCT
ejpam-5657	440	22	safonov	safonov	PROPN
ejpam-5657	440	23	,	,	PUNCT
ejpam-5657	440	24	m.g	m.g	PROPN
ejpam-5657	440	25	.	.	PROPN
ejpam-5657	440	26	stability	stability	NOUN
ejpam-5657	440	27	margins	margin	NOUN
ejpam-5657	440	28	of	of	ADP
ejpam-5657	440	29	diagonally	diagonally	ADV
ejpam-5657	440	30	perturbed	perturb	VERB
ejpam-5657	440	31	multivariable	multivariable	ADJ
ejpam-5657	440	32	feedback	feedback	NOUN
ejpam-5657	440	33	systems	system	NOUN
ejpam-5657	440	34	.	.	PUNCT
ejpam-5657	441	1	iee	iee	PROPN
ejpam-5657	441	2	proc	proc	PROPN
ejpam-5657	441	3	.	.	PUNCT
ejpam-5657	442	1	d	d	X
ejpam-5657	442	2	(	(	PUNCT
ejpam-5657	442	3	control	control	NOUN
ejpam-5657	442	4	theory	theory	NOUN
ejpam-5657	442	5	appl	appl	PROPN
ejpam-5657	442	6	.	.	PUNCT
ejpam-5657	442	7	)	)	PUNCT
ejpam-5657	442	8	1982	1982	NUM
ejpam-5657	442	9	,	,	PUNCT
ejpam-5657	442	10	129	129	NUM
ejpam-5657	442	11	,	,	PUNCT
ejpam-5657	442	12	251–256	251–256	NUM
ejpam-5657	442	13	.	.	PUNCT
ejpam-5657	443	1	[	[	X
ejpam-5657	443	2	39	39	NUM
ejpam-5657	443	3	]	]	X
ejpam-5657	443	4	seiler	seiler	NOUN
ejpam-5657	443	5	,	,	PUNCT
ejpam-5657	443	6	p.	p.	PROPN
ejpam-5657	443	7	,	,	PUNCT
ejpam-5657	443	8	balas	balas	PROPN
ejpam-5657	443	9	,	,	PUNCT
ejpam-5657	443	10	g.	g.	PROPN
ejpam-5657	443	11	,	,	PUNCT
ejpam-5657	443	12	&	&	CCONJ
ejpam-5657	443	13	packard	packard	PROPN
ejpam-5657	443	14	,	,	PUNCT
ejpam-5657	443	15	a.	a.	NOUN
ejpam-5657	443	16	a	a	DET
ejpam-5657	443	17	gain	gain	NOUN
ejpam-5657	443	18	-	-	PUNCT
ejpam-5657	443	19	based	base	VERB
ejpam-5657	443	20	lower	low	ADJ
ejpam-5657	443	21	bound	bind	VERB
ejpam-5657	443	22	algorithm	algorithm	NOUN
ejpam-5657	443	23	for	for	ADP
ejpam-5657	443	24	real	real	ADJ
ejpam-5657	443	25	and	and	CCONJ
ejpam-5657	443	26	mixed	mixed	ADJ
ejpam-5657	443	27	µ	µ	PRON
ejpam-5657	443	28	problems	problem	NOUN
ejpam-5657	443	29	.	.	PUNCT
ejpam-5657	444	1	in	in	ADP
ejpam-5657	444	2	proceedings	proceeding	NOUN
ejpam-5657	444	3	of	of	ADP
ejpam-5657	444	4	the	the	DET
ejpam-5657	444	5	45th	45th	ADJ
ejpam-5657	444	6	ieee	ieee	NOUN
ejpam-5657	444	7	conference	conference	NOUN
ejpam-5657	444	8	on	on	ADP
ejpam-5657	444	9	decision	decision	NOUN
ejpam-5657	444	10	and	and	CCONJ
ejpam-5657	444	11	control	control	NOUN
ejpam-5657	444	12	,	,	PUNCT
ejpam-5657	444	13	san	san	PROPN
ejpam-5657	444	14	diego	diego	PROPN
ejpam-5657	444	15	,	,	PUNCT
ejpam-5657	444	16	california	california	PROPN
ejpam-5657	444	17	,	,	PUNCT
ejpam-5657	444	18	(	(	PUNCT
ejpam-5657	444	19	2006	2006	NUM
ejpam-5657	444	20	)	)	PUNCT
ejpam-5657	444	21	,	,	PUNCT
ejpam-5657	444	22	3548–3553	3548–3553	NUM
ejpam-5657	444	23	.	.	PUNCT
ejpam-5657	445	1	[	[	X
ejpam-5657	445	2	40	40	NUM
ejpam-5657	445	3	]	]	X
ejpam-5657	445	4	tong	tong	PROPN
ejpam-5657	445	5	,	,	PUNCT
ejpam-5657	445	6	yuhao	yuhao	NOUN
ejpam-5657	445	7	,	,	PUNCT
ejpam-5657	445	8	and	and	CCONJ
ejpam-5657	445	9	steven	steven	PROPN
ejpam-5657	445	10	w.	w.	PROPN
ejpam-5657	445	11	su	su	PROPN
ejpam-5657	445	12	.	.	PROPN
ejpam-5657	445	13	sufficient	sufficient	ADJ
ejpam-5657	445	14	d	d	ADJ
ejpam-5657	445	15	-	-	NOUN
ejpam-5657	445	16	stability	stability	NOUN
ejpam-5657	445	17	conditions	condition	NOUN
ejpam-5657	445	18	for	for	ADP
ejpam-5657	445	19	non	non	ADJ
ejpam-5657	445	20	-	-	ADJ
ejpam-5657	445	21	square	square	ADJ
ejpam-5657	445	22	matrices	matrix	NOUN
ejpam-5657	445	23	.	.	PUNCT
ejpam-5657	446	1	arxiv	arxiv	PROPN
ejpam-5657	446	2	preprint	preprint	VERB
ejpam-5657	446	3	arxiv:2406.15440	arxiv:2406.15440	NOUN
ejpam-5657	446	4	(	(	PUNCT
ejpam-5657	446	5	2024	2024	NUM
ejpam-5657	446	6	)	)	PUNCT
ejpam-5657	446	7	.	.	PUNCT
ejpam-5657	447	1	[	[	X
ejpam-5657	447	2	41	41	NUM
ejpam-5657	447	3	]	]	X
ejpam-5657	447	4	woods	wood	NOUN
ejpam-5657	447	5	,	,	PUNCT
ejpam-5657	447	6	j.e	j.e	PROPN
ejpam-5657	447	7	.	.	PROPN
ejpam-5657	447	8	,	,	PUNCT
ejpam-5657	447	9	1978	1978	NUM
ejpam-5657	447	10	,	,	PUNCT
ejpam-5657	447	11	mathematical	mathematical	ADJ
ejpam-5657	447	12	economics	economic	NOUN
ejpam-5657	447	13	(	(	PUNCT
ejpam-5657	447	14	longman	longman	NOUN
ejpam-5657	447	15	,	,	PUNCT
ejpam-5657	447	16	new	new	PROPN
ejpam-5657	447	17	york	york	PROPN
ejpam-5657	447	18	)	)	PUNCT
ejpam-5657	447	19	.	.	PUNCT
ejpam-5657	448	1	[	[	X
ejpam-5657	448	2	42	42	NUM
ejpam-5657	448	3	]	]	PUNCT
ejpam-5657	448	4	xu	xu	PROPN
ejpam-5657	448	5	,	,	PUNCT
ejpam-5657	448	6	shengyuan	shengyuan	PROPN
ejpam-5657	448	7	,	,	PUNCT
ejpam-5657	448	8	and	and	CCONJ
ejpam-5657	448	9	james	james	PROPN
ejpam-5657	448	10	lam	lam	PROPN
ejpam-5657	448	11	.	.	PUNCT
ejpam-5657	448	12	robust	robust	ADJ
ejpam-5657	448	13	stability	stability	NOUN
ejpam-5657	448	14	and	and	CCONJ
ejpam-5657	448	15	stabilization	stabilization	NOUN
ejpam-5657	448	16	of	of	ADP
ejpam-5657	448	17	discrete	discrete	ADJ
ejpam-5657	448	18	singular	singular	NOUN
ejpam-5657	448	19	systems	system	NOUN
ejpam-5657	448	20	:	:	PUNCT
ejpam-5657	448	21	an	an	DET
ejpam-5657	448	22	equivalent	equivalent	ADJ
ejpam-5657	448	23	characterization	characterization	NOUN
ejpam-5657	448	24	.	.	PUNCT
ejpam-5657	449	1	ieee	ieee	NOUN
ejpam-5657	449	2	transactions	transaction	NOUN
ejpam-5657	449	3	on	on	ADP
ejpam-5657	449	4	automatic	automatic	ADJ
ejpam-5657	449	5	control	control	NOUN
ejpam-5657	449	6	49	49	NUM
ejpam-5657	449	7	,	,	PUNCT
ejpam-5657	449	8	no	no	INTJ
ejpam-5657	449	9	.	.	NOUN
ejpam-5657	449	10	4	4	NUM
ejpam-5657	449	11	(	(	PUNCT
ejpam-5657	449	12	2004	2004	NUM
ejpam-5657	449	13	):	):	PUNCT
ejpam-5657	449	14	568	568	NUM
ejpam-5657	449	15	-	-	SYM
ejpam-5657	449	16	574	574	NUM
ejpam-5657	449	17	.	.	PUNCT
ejpam-5657	450	1	[	[	X
ejpam-5657	450	2	43	43	NUM
ejpam-5657	450	3	]	]	PUNCT
ejpam-5657	450	4	x.	x.	NOUN
ejpam-5657	450	5	mao	mao	PROPN
ejpam-5657	450	6	,	,	PUNCT
ejpam-5657	450	7	robustness	robustness	NOUN
ejpam-5657	450	8	of	of	ADP
ejpam-5657	450	9	exponential	exponential	ADJ
ejpam-5657	450	10	stability	stability	NOUN
ejpam-5657	450	11	of	of	ADP
ejpam-5657	450	12	stochastic	stochastic	ADJ
ejpam-5657	450	13	differential	differential	ADJ
ejpam-5657	450	14	delay	delay	NOUN
ejpam-5657	450	15	equation	equation	NOUN
ejpam-5657	450	16	,	,	PUNCT
ejpam-5657	450	17	ieee	ieee	NOUN
ejpam-5657	450	18	trans	trans	PROPN
ejpam-5657	450	19	.	.	PUNCT
ejpam-5657	451	1	autom	autom	PROPN
ejpam-5657	451	2	.	.	PUNCT
ejpam-5657	452	1	control	control	PROPN
ejpam-5657	452	2	,	,	PUNCT
ejpam-5657	452	3	vol	vol	NOUN
ejpam-5657	452	4	.	.	PROPN
ejpam-5657	452	5	41	41	NUM
ejpam-5657	452	6	,	,	PUNCT
ejpam-5657	452	7	no	no	INTJ
ejpam-5657	452	8	.	.	NOUN
ejpam-5657	452	9	9	9	NUM
ejpam-5657	452	10	,	,	PUNCT
ejpam-5657	452	11	pp	pp	ADJ
ejpam-5657	452	12	.	.	PUNCT
ejpam-5657	453	1	442	442	NUM
ejpam-5657	453	2	-	-	SYM
ejpam-5657	453	3	447	447	NUM
ejpam-5657	453	4	,	,	PUNCT
ejpam-5657	453	5	mar	mar	PROPN
ejpam-5657	453	6	.	.	PROPN
ejpam-5657	453	7	1996	1996	NUM
ejpam-5657	453	8	.	.	PUNCT
ejpam-5657	454	1	[	[	X
ejpam-5657	454	2	44	44	NUM
ejpam-5657	454	3	]	]	X
ejpam-5657	454	4	y.	y.	PROPN
ejpam-5657	454	5	kimura	kimura	PROPN
ejpam-5657	454	6	,	,	PUNCT
ejpam-5657	454	7	j.	j.	PROPN
ejpam-5657	454	8	of	of	ADP
ejpam-5657	454	9	math	math	PROPN
ejpam-5657	454	10	.	.	PUNCT
ejpam-5657	455	1	econ	econ	PROPN
ejpam-5657	455	2	.	.	PROPN
ejpam-5657	455	3	,	,	PUNCT
ejpam-5657	455	4	vol	vol	NOUN
ejpam-5657	455	5	.	.	PROPN
ejpam-5657	455	6	8	8	NUM
ejpam-5657	455	7	,	,	PUNCT
ejpam-5657	455	8	pp	pp	ADJ
ejpam-5657	455	9	.	.	PUNCT
ejpam-5657	456	1	113–120	113–120	NUM
ejpam-5657	456	2	,	,	PUNCT
ejpam-5657	456	3	1981	1981	NUM
ejpam-5657	456	4	.	.	PUNCT
ejpam-5657	457	1	[	[	X
ejpam-5657	457	2	45	45	NUM
ejpam-5657	457	3	]	]	PUNCT
ejpam-5657	457	4	z.	z.	PROPN
ejpam-5657	457	5	wang	wang	PROPN
ejpam-5657	457	6	,	,	PUNCT
ejpam-5657	457	7	h.	h.	PROPN
ejpam-5657	457	8	qiao	qiao	PROPN
ejpam-5657	457	9	,	,	PUNCT
ejpam-5657	457	10	and	and	CCONJ
ejpam-5657	457	11	k.	k.	PROPN
ejpam-5657	457	12	j.	j.	PROPN
ejpam-5657	457	13	burnham	burnham	PROPN
ejpam-5657	457	14	,	,	PUNCT
ejpam-5657	457	15	on	on	ADP
ejpam-5657	457	16	stabilization	stabilization	NOUN
ejpam-5657	457	17	of	of	ADP
ejpam-5657	457	18	bilinear	bilinear	ADJ
ejpam-5657	457	19	uncertain	uncertain	ADJ
ejpam-5657	457	20	timedelay	timedelay	ADJ
ejpam-5657	457	21	stochastic	stochastic	NOUN
ejpam-5657	457	22	systems	system	NOUN
ejpam-5657	457	23	with	with	ADP
ejpam-5657	457	24	markovian	markovian	ADJ
ejpam-5657	457	25	jumping	jumping	NOUN
ejpam-5657	457	26	parameters	parameter	NOUN
ejpam-5657	457	27	,	,	PUNCT
ejpam-5657	457	28	ieee	ieee	PROPN
ejpam-5657	457	29	trans	trans	PROPN
ejpam-5657	457	30	.	.	PROPN
ejpam-5657	457	31	automat	automat	PROPN
ejpam-5657	457	32	.	.	PUNCT
ejpam-5657	457	33	control	control	PROPN
ejpam-5657	457	34	,	,	PUNCT
ejpam-5657	457	35	vol	vol	NOUN
ejpam-5657	457	36	.	.	PROPN
ejpam-5657	458	1	47	47	NUM
ejpam-5657	458	2	,	,	PUNCT
ejpam-5657	458	3	pp	pp	ADJ
ejpam-5657	458	4	.	.	PUNCT
ejpam-5657	459	1	640	640	NUM
ejpam-5657	459	2	-	-	SYM
ejpam-5657	459	3	646	646	NUM
ejpam-5657	459	4	,	,	PUNCT
ejpam-5657	459	5	april	april	PROPN
ejpam-5657	459	6	2002	2002	NUM
ejpam-5657	459	7	.	.	PUNCT