id	sid	tid	token	lemma	pos
ejpam-6111	1	1	european	european	PROPN
ejpam-6111	1	2	journal	journal	PROPN
ejpam-6111	1	3	of	of	ADP
ejpam-6111	1	4	pure	pure	ADJ
ejpam-6111	1	5	and	and	CCONJ
ejpam-6111	1	6	applied	applied	ADJ
ejpam-6111	1	7	mathematics	mathematic	NOUN
ejpam-6111	1	8	2025	2025	NUM
ejpam-6111	1	9	,	,	PUNCT
ejpam-6111	1	10	vol	vol	NOUN
ejpam-6111	1	11	.	.	PROPN
ejpam-6111	1	12	18	18	NUM
ejpam-6111	1	13	,	,	PUNCT
ejpam-6111	1	14	issue	issue	NOUN
ejpam-6111	1	15	2	2	NUM
ejpam-6111	1	16	,	,	PUNCT
ejpam-6111	1	17	article	article	NOUN
ejpam-6111	1	18	number	number	NOUN
ejpam-6111	1	19	6111	6111	NUM
ejpam-6111	1	20	issn	issn	PROPN
ejpam-6111	1	21	1307	1307	NUM
ejpam-6111	1	22	-	-	SYM
ejpam-6111	1	23	5543	5543	NUM
ejpam-6111	1	24	–	–	PUNCT
ejpam-6111	1	25	ejpam.com	ejpam.com	X
ejpam-6111	1	26	published	publish	VERB
ejpam-6111	1	27	by	by	ADP
ejpam-6111	1	28	new	new	PROPN
ejpam-6111	1	29	york	york	PROPN
ejpam-6111	1	30	business	business	PROPN
ejpam-6111	1	31	global	global	PROPN
ejpam-6111	1	32	haar	haar	PROPN
ejpam-6111	1	33	wavelets	wavelet	NOUN
ejpam-6111	1	34	and	and	CCONJ
ejpam-6111	2	1	d	d	NOUN
ejpam-6111	2	2	-	-	NOUN
ejpam-6111	2	3	stability	stability	NOUN
ejpam-6111	2	4	of	of	ADP
ejpam-6111	2	5	lumped	lump	VERB
ejpam-6111	2	6	-	-	PUNCT
ejpam-6111	2	7	parameter	parameter	NOUN
ejpam-6111	2	8	dynamical	dynamical	ADJ
ejpam-6111	2	9	systems	system	NOUN
ejpam-6111	2	10	siddiqua	siddiqua	NOUN
ejpam-6111	2	11	mazhar1	mazhar1	PROPN
ejpam-6111	2	12	,	,	PUNCT
ejpam-6111	2	13	mutti	mutti	PROPN
ejpam-6111	2	14	-	-	PUNCT
ejpam-6111	2	15	ur	ur	PROPN
ejpam-6111	2	16	rehman2,∗	rehman2,∗	VERB
ejpam-6111	2	17	1	1	NUM
ejpam-6111	2	18	university	university	PROPN
ejpam-6111	2	19	of	of	ADP
ejpam-6111	2	20	pittsburgh	pittsburgh	PROPN
ejpam-6111	2	21	,	,	PUNCT
ejpam-6111	2	22	div	div	PROPN
ejpam-6111	2	23	.	.	PROPN
ejpam-6111	2	24	of	of	ADP
ejpam-6111	2	25	phys	phy	NOUN
ejpam-6111	2	26	.	.	PUNCT
ejpam-6111	3	1	comp	comp	PROPN
ejpam-6111	3	2	.	.	PUNCT
ejpam-6111	4	1	sci	sci	PROPN
ejpam-6111	4	2	,	,	PUNCT
ejpam-6111	4	3	300	300	NUM
ejpam-6111	4	4	campus	campus	NOUN
ejpam-6111	4	5	drive	drive	NOUN
ejpam-6111	4	6	,	,	PUNCT
ejpam-6111	4	7	bradford	bradford	NOUN
ejpam-6111	4	8	,	,	PUNCT
ejpam-6111	4	9	pa	pa	PROPN
ejpam-6111	4	10	16701	16701	NUM
ejpam-6111	4	11	,	,	PUNCT
ejpam-6111	4	12	usa	usa	PROPN
ejpam-6111	4	13	2	2	NUM
ejpam-6111	4	14	center	center	NOUN
ejpam-6111	4	15	of	of	ADP
ejpam-6111	4	16	research	research	NOUN
ejpam-6111	4	17	and	and	CCONJ
ejpam-6111	4	18	innovation	innovation	NOUN
ejpam-6111	4	19	,	,	PUNCT
ejpam-6111	4	20	asia	asia	PROPN
ejpam-6111	4	21	international	international	PROPN
ejpam-6111	4	22	university	university	PROPN
ejpam-6111	4	23	,	,	PUNCT
ejpam-6111	4	24	yangiobod	yangiobod	ADJ
ejpam-6111	4	25	mfy	mfy	NOUN
ejpam-6111	4	26	,	,	PUNCT
ejpam-6111	4	27	g‘ijduvon	g‘ijduvon	PROPN
ejpam-6111	4	28	street	street	PROPN
ejpam-6111	4	29	,	,	PUNCT
ejpam-6111	4	30	house	house	NOUN
ejpam-6111	4	31	74	74	NUM
ejpam-6111	4	32	,	,	PUNCT
ejpam-6111	4	33	bukhara	bukhara	PROPN
ejpam-6111	4	34	,	,	PUNCT
ejpam-6111	4	35	uzbekistan	uzbekistan	PROPN
ejpam-6111	4	36	abstract	abstract	NOUN
ejpam-6111	4	37	.	.	PUNCT
ejpam-6111	5	1	d	d	X
ejpam-6111	5	2	-	-	PUNCT
ejpam-6111	5	3	stability	stability	NOUN
ejpam-6111	5	4	is	be	AUX
ejpam-6111	5	5	a	a	DET
ejpam-6111	5	6	well	well	ADV
ejpam-6111	5	7	-	-	PUNCT
ejpam-6111	5	8	known	know	VERB
ejpam-6111	5	9	mathematical	mathematical	ADJ
ejpam-6111	5	10	tool	tool	NOUN
ejpam-6111	5	11	used	use	VERB
ejpam-6111	5	12	to	to	PART
ejpam-6111	5	13	analyze	analyze	VERB
ejpam-6111	5	14	and	and	CCONJ
ejpam-6111	5	15	characterize	characterize	VERB
ejpam-6111	5	16	dynamical	dynamical	ADJ
ejpam-6111	5	17	systems	system	NOUN
ejpam-6111	5	18	.	.	PUNCT
ejpam-6111	6	1	it	it	PRON
ejpam-6111	6	2	plays	play	VERB
ejpam-6111	6	3	an	an	DET
ejpam-6111	6	4	important	important	ADJ
ejpam-6111	6	5	role	role	NOUN
ejpam-6111	6	6	in	in	ADP
ejpam-6111	6	7	the	the	DET
ejpam-6111	6	8	stability	stability	NOUN
ejpam-6111	6	9	analysis	analysis	NOUN
ejpam-6111	6	10	of	of	ADP
ejpam-6111	6	11	dynamical	dynamical	ADJ
ejpam-6111	6	12	systems	system	NOUN
ejpam-6111	6	13	,	,	PUNCT
ejpam-6111	6	14	particularly	particularly	ADV
ejpam-6111	6	15	in	in	ADP
ejpam-6111	6	16	cases	case	NOUN
ejpam-6111	6	17	where	where	SCONJ
ejpam-6111	6	18	stability	stability	NOUN
ejpam-6111	6	19	is	be	AUX
ejpam-6111	6	20	preserved	preserve	VERB
ejpam-6111	6	21	under	under	ADP
ejpam-6111	6	22	various	various	ADJ
ejpam-6111	6	23	types	type	NOUN
ejpam-6111	6	24	of	of	ADP
ejpam-6111	6	25	perturbation	perturbation	NOUN
ejpam-6111	6	26	,	,	PUNCT
ejpam-6111	6	27	especially	especially	ADV
ejpam-6111	6	28	those	those	PRON
ejpam-6111	6	29	involving	involve	VERB
ejpam-6111	6	30	positive	positive	ADJ
ejpam-6111	6	31	diagonal	diagonal	ADJ
ejpam-6111	6	32	scaling	scaling	NOUN
ejpam-6111	6	33	.	.	PUNCT
ejpam-6111	7	1	the	the	DET
ejpam-6111	7	2	analysis	analysis	NOUN
ejpam-6111	7	3	of	of	ADP
ejpam-6111	7	4	d	d	NOUN
ejpam-6111	7	5	-	-	NOUN
ejpam-6111	7	6	stability	stability	NOUN
ejpam-6111	7	7	ensures	ensure	VERB
ejpam-6111	7	8	the	the	DET
ejpam-6111	7	9	stability	stability	NOUN
ejpam-6111	7	10	of	of	ADP
ejpam-6111	7	11	dynamical	dynamical	ADJ
ejpam-6111	7	12	systems	system	NOUN
ejpam-6111	7	13	.	.	PUNCT
ejpam-6111	8	1	in	in	ADP
ejpam-6111	8	2	this	this	DET
ejpam-6111	8	3	paper	paper	NOUN
ejpam-6111	8	4	,	,	PUNCT
ejpam-6111	8	5	we	we	PRON
ejpam-6111	8	6	present	present	VERB
ejpam-6111	8	7	new	new	ADJ
ejpam-6111	8	8	results	result	NOUN
ejpam-6111	8	9	on	on	ADP
ejpam-6111	8	10	the	the	DET
ejpam-6111	8	11	characterization	characterization	NOUN
ejpam-6111	8	12	of	of	ADP
ejpam-6111	8	13	d	d	NOUN
ejpam-6111	8	14	-	-	NOUN
ejpam-6111	8	15	stability	stability	NOUN
ejpam-6111	8	16	and	and	CCONJ
ejpam-6111	8	17	strong	strong	ADJ
ejpam-6111	8	18	d	d	NOUN
ejpam-6111	8	19	-	-	NOUN
ejpam-6111	8	20	stability	stability	NOUN
ejpam-6111	8	21	for	for	ADP
ejpam-6111	8	22	structured	structured	ADJ
ejpam-6111	8	23	matrices	matrix	NOUN
ejpam-6111	8	24	of	of	ADP
ejpam-6111	8	25	the	the	DET
ejpam-6111	8	26	form	form	NOUN
ejpam-6111	8	27	(	(	PUNCT
ejpam-6111	8	28	in	in	ADP
ejpam-6111	8	29	−	−	PROPN
ejpam-6111	8	30	a	a	DET
ejpam-6111	8	31	⊗	⊗	PROPN
ejpam-6111	8	32	p	p	PROPN
ejpam-6111	8	33	t	t	PROPN
ejpam-6111	8	34	)	)	PUNCT
ejpam-6111	8	35	,	,	PUNCT
ejpam-6111	8	36	where	where	SCONJ
ejpam-6111	8	37	in	in	ADP
ejpam-6111	8	38	is	be	AUX
ejpam-6111	8	39	an	an	DET
ejpam-6111	8	40	n	n	NUM
ejpam-6111	8	41	×	×	NOUN
ejpam-6111	8	42	n	n	CCONJ
ejpam-6111	8	43	identity	identity	NOUN
ejpam-6111	8	44	matrix	matrix	NOUN
ejpam-6111	8	45	and	and	CCONJ
ejpam-6111	8	46	the	the	DET
ejpam-6111	8	47	matrices	matrix	NOUN
ejpam-6111	8	48	a	a	PRON
ejpam-6111	8	49	and	and	CCONJ
ejpam-6111	8	50	p	p	NOUN
ejpam-6111	8	51	associated	associate	VERB
ejpam-6111	8	52	with	with	ADP
ejpam-6111	8	53	a	a	DET
ejpam-6111	8	54	lumped	lump	VERB
ejpam-6111	8	55	-	-	PUNCT
ejpam-6111	8	56	parameter	parameter	NOUN
ejpam-6111	8	57	dynamical	dynamical	ADJ
ejpam-6111	8	58	system	system	NOUN
ejpam-6111	8	59	{	{	PUNCT
ejpam-6111	8	60	x(t	x(t	PROPN
ejpam-6111	8	61	)	)	PUNCT
ejpam-6111	8	62	=	=	PUNCT
ejpam-6111	8	63	a	a	DET
ejpam-6111	8	64	x(t	x(t	PROPN
ejpam-6111	8	65	)	)	PUNCT
ejpam-6111	9	1	+	+	NOUN
ejpam-6111	9	2	b	b	NOUN
ejpam-6111	9	3	u(t	u(t	NOUN
ejpam-6111	9	4	)	)	PUNCT
ejpam-6111	9	5	,	,	PUNCT
ejpam-6111	9	6	x(0	x(0	PROPN
ejpam-6111	9	7	)	)	PUNCT
ejpam-6111	10	1	=	=	PUNCT
ejpam-6111	11	1	x0	x0	PROPN
ejpam-6111	11	2	y(t	y(t	NUM
ejpam-6111	11	3	)	)	PUNCT
ejpam-6111	12	1	=	=	SYM
ejpam-6111	12	2	c	c	NOUN
ejpam-6111	12	3	x(t	x(t	PROPN
ejpam-6111	12	4	)	)	PUNCT
ejpam-6111	13	1	+	+	ADP
ejpam-6111	13	2	d	d	NOUN
ejpam-6111	13	3	u(t	u(t	NOUN
ejpam-6111	13	4	)	)	PUNCT
ejpam-6111	13	5	.	.	PUNCT
ejpam-6111	14	1	the	the	DET
ejpam-6111	14	2	results	result	NOUN
ejpam-6111	14	3	on	on	ADP
ejpam-6111	14	4	d	d	NOUN
ejpam-6111	14	5	-	-	NOUN
ejpam-6111	14	6	stability	stability	NOUN
ejpam-6111	14	7	and	and	CCONJ
ejpam-6111	14	8	strong	strong	ADJ
ejpam-6111	14	9	d	d	NOUN
ejpam-6111	14	10	-	-	NOUN
ejpam-6111	14	11	stability	stability	NOUN
ejpam-6111	14	12	are	be	AUX
ejpam-6111	14	13	obtained	obtain	VERB
ejpam-6111	14	14	using	use	VERB
ejpam-6111	14	15	mathematical	mathematical	ADJ
ejpam-6111	14	16	tools	tool	NOUN
ejpam-6111	14	17	from	from	ADP
ejpam-6111	14	18	linear	linear	PROPN
ejpam-6111	14	19	algebra	algebra	NOUN
ejpam-6111	14	20	,	,	PUNCT
ejpam-6111	14	21	matrix	matrix	NOUN
ejpam-6111	14	22	analysis	analysis	NOUN
ejpam-6111	14	23	,	,	PUNCT
ejpam-6111	14	24	system	system	NOUN
ejpam-6111	14	25	theory	theory	NOUN
ejpam-6111	14	26	and	and	CCONJ
ejpam-6111	14	27	their	their	PRON
ejpam-6111	14	28	interactions	interaction	NOUN
ejpam-6111	14	29	with	with	ADP
ejpam-6111	14	30	the	the	DET
ejpam-6111	14	31	computation	computation	NOUN
ejpam-6111	14	32	of	of	ADP
ejpam-6111	14	33	structured	structured	ADJ
ejpam-6111	14	34	singular	singular	ADJ
ejpam-6111	14	35	values	value	NOUN
ejpam-6111	14	36	.	.	PUNCT
ejpam-6111	15	1	furthermore	furthermore	ADV
ejpam-6111	15	2	,	,	PUNCT
ejpam-6111	15	3	we	we	PRON
ejpam-6111	15	4	present	present	VERB
ejpam-6111	15	5	the	the	DET
ejpam-6111	15	6	numerical	numerical	ADJ
ejpam-6111	15	7	approximations	approximation	NOUN
ejpam-6111	15	8	to	to	ADP
ejpam-6111	15	9	singular	singular	ADJ
ejpam-6111	15	10	values	value	NOUN
ejpam-6111	15	11	and	and	CCONJ
ejpam-6111	15	12	pseudo	pseudo	NOUN
ejpam-6111	15	13	-	-	NOUN
ejpam-6111	15	14	spectrum	spectrum	NOUN
ejpam-6111	15	15	of	of	ADP
ejpam-6111	15	16	haar	haar	PROPN
ejpam-6111	15	17	wavelet	wavelet	NOUN
ejpam-6111	15	18	matrices	matrix	NOUN
ejpam-6111	15	19	associated	associate	VERB
ejpam-6111	15	20	with	with	ADP
ejpam-6111	15	21	a	a	DET
ejpam-6111	15	22	lumped	lump	VERB
ejpam-6111	15	23	-	-	PUNCT
ejpam-6111	15	24	parameter	parameter	NOUN
ejpam-6111	15	25	dynamical	dynamical	ADJ
ejpam-6111	15	26	system	system	NOUN
ejpam-6111	15	27	.	.	PUNCT
ejpam-6111	16	1	2020	2020	NUM
ejpam-6111	16	2	mathematics	mathematic	NOUN
ejpam-6111	16	3	subject	subject	NOUN
ejpam-6111	16	4	classifications	classification	NOUN
ejpam-6111	16	5	:	:	PUNCT
ejpam-6111	16	6	15a18	15a18	NUM
ejpam-6111	16	7	,	,	PUNCT
ejpam-6111	16	8	65k05	65k05	NUM
ejpam-6111	16	9	key	key	ADJ
ejpam-6111	16	10	words	word	NOUN
ejpam-6111	16	11	and	and	CCONJ
ejpam-6111	16	12	phrases	phrase	NOUN
ejpam-6111	16	13	:	:	PUNCT
ejpam-6111	16	14	haar	haar	PROPN
ejpam-6111	16	15	wavelets	wavelet	NOUN
ejpam-6111	16	16	,	,	PUNCT
ejpam-6111	16	17	structured	structure	VERB
ejpam-6111	16	18	singular	singular	ADJ
ejpam-6111	16	19	value	value	NOUN
ejpam-6111	16	20	,	,	PUNCT
ejpam-6111	16	21	block	block	NOUN
ejpam-6111	16	22	diagonal	diagonal	ADJ
ejpam-6111	16	23	perturbations	perturbation	NOUN
ejpam-6111	16	24	,	,	PUNCT
ejpam-6111	16	25	d	d	NOUN
ejpam-6111	16	26	-	-	PUNCT
ejpam-6111	16	27	stability	stability	NOUN
ejpam-6111	16	28	,	,	PUNCT
ejpam-6111	16	29	pseudo	pseudo	NOUN
ejpam-6111	16	30	-	-	NOUN
ejpam-6111	16	31	spectrum	spectrum	ADJ
ejpam-6111	16	32	1	1	NUM
ejpam-6111	16	33	.	.	PUNCT
ejpam-6111	17	1	introduction	introduction	NOUN
ejpam-6111	17	2	haar	haar	PROPN
ejpam-6111	17	3	wavelets	wavelet	NOUN
ejpam-6111	17	4	are	be	AUX
ejpam-6111	17	5	an	an	DET
ejpam-6111	17	6	excellent	excellent	ADJ
ejpam-6111	17	7	mathematical	mathematical	ADJ
ejpam-6111	17	8	tool	tool	NOUN
ejpam-6111	17	9	for	for	ADP
ejpam-6111	17	10	studying	study	VERB
ejpam-6111	17	11	and	and	CCONJ
ejpam-6111	17	12	analyzinglyzing	analyzinglyze	VERB
ejpam-6111	17	13	signal	signal	NOUN
ejpam-6111	17	14	processing	processing	NOUN
ejpam-6111	17	15	and	and	CCONJ
ejpam-6111	17	16	optimal	optimal	ADJ
ejpam-6111	17	17	control	control	NOUN
ejpam-6111	17	18	of	of	ADP
ejpam-6111	17	19	linear	linear	ADJ
ejpam-6111	17	20	time	time	NOUN
ejpam-6111	17	21	-	-	PUNCT
ejpam-6111	17	22	varying	vary	VERB
ejpam-6111	17	23	systems	system	NOUN
ejpam-6111	17	24	.	.	PUNCT
ejpam-6111	18	1	regarding	regard	VERB
ejpam-6111	18	2	system	system	NOUN
ejpam-6111	18	3	analysis	analysis	NOUN
ejpam-6111	18	4	via	via	ADP
ejpam-6111	18	5	haar	haar	PROPN
ejpam-6111	18	6	wavelets	wavelet	NOUN
ejpam-6111	18	7	,	,	PUNCT
ejpam-6111	18	8	the	the	DET
ejpam-6111	18	9	classical	classical	ADJ
ejpam-6111	18	10	work	work	NOUN
ejpam-6111	18	11	was	be	AUX
ejpam-6111	18	12	done	do	VERB
ejpam-6111	18	13	by	by	ADP
ejpam-6111	18	14	[	[	X
ejpam-6111	18	15	1	1	NUM
ejpam-6111	18	16	]	]	PUNCT
ejpam-6111	18	17	.	.	PUNCT
ejpam-6111	19	1	in	in	ADP
ejpam-6111	19	2	their	their	PRON
ejpam-6111	19	3	classical	classical	ADJ
ejpam-6111	19	4	paper	paper	NOUN
ejpam-6111	19	5	,	,	PUNCT
ejpam-6111	19	6	chen	chen	PROPN
ejpam-6111	19	7	and	and	CCONJ
ejpam-6111	19	8	hasiao	hasiao	VERB
ejpam-6111	19	9	[	[	X
ejpam-6111	19	10	1	1	NUM
ejpam-6111	19	11	]	]	PUNCT
ejpam-6111	19	12	constructed	construct	VERB
ejpam-6111	19	13	and	and	CCONJ
ejpam-6111	19	14	analyzed	analyze	VERB
ejpam-6111	19	15	a	a	DET
ejpam-6111	19	16	haar	haar	NOUN
ejpam-6111	19	17	operation	operation	NOUN
ejpam-6111	19	18	matrix	matrix	NOUN
ejpam-6111	19	19	for	for	ADP
ejpam-6111	19	20	the	the	DET
ejpam-6111	19	21	integrals	integral	NOUN
ejpam-6111	19	22	of	of	ADP
ejpam-6111	19	23	∗corresponding	∗corresponde	VERB
ejpam-6111	19	24	author	author	NOUN
ejpam-6111	19	25	.	.	PUNCT
ejpam-6111	20	1	doi	doi	NOUN
ejpam-6111	20	2	:	:	PUNCT
ejpam-6111	20	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6111	https://doi.org/10.29020/nybg.ejpam.v18i2.6111	ADJ
ejpam-6111	20	4	email	email	NOUN
ejpam-6111	20	5	addresses	address	VERB
ejpam-6111	20	6	:	:	PUNCT
ejpam-6111	20	7	smazhar@pitt.edu	smazhar@pitt.edu	PROPN
ejpam-6111	20	8	(	(	PUNCT
ejpam-6111	20	9	s.	s.	PROPN
ejpam-6111	20	10	mazhar	mazhar	PROPN
ejpam-6111	20	11	)	)	PUNCT
ejpam-6111	20	12	,	,	PUNCT
ejpam-6111	20	13	muttiur.abbasi@oxu.uz	muttiur.abbasi@oxu.uz	PROPN
ejpam-6111	20	14	(	(	PUNCT
ejpam-6111	20	15	m.	m.	NOUN
ejpam-6111	20	16	u.	u.	PROPN
ejpam-6111	20	17	rehman	rehman	PROPN
ejpam-6111	20	18	)	)	PUNCT
ejpam-6111	20	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6111	21	1	1	1	NUM
ejpam-6111	21	2	copyright	copyright	NOUN
ejpam-6111	21	3	:	:	PUNCT
ejpam-6111	21	4	©	©	PROPN
ejpam-6111	21	5	2025	2025	NUM
ejpam-6111	21	6	the	the	DET
ejpam-6111	21	7	author(s	author(s	NOUN
ejpam-6111	21	8	)	)	PUNCT
ejpam-6111	21	9	.	.	PUNCT
ejpam-6111	22	1	(	(	PUNCT
ejpam-6111	22	2	cc	cc	NOUN
ejpam-6111	22	3	by	by	ADP
ejpam-6111	22	4	-	-	PUNCT
ejpam-6111	22	5	nc	nc	PROPN
ejpam-6111	22	6	4.0	4.0	NUM
ejpam-6111	22	7	)	)	PUNCT
ejpam-6111	22	8	s.	s.	PROPN
ejpam-6111	22	9	mazhar	mazhar	PROPN
ejpam-6111	22	10	,	,	PUNCT
ejpam-6111	22	11	m.	m.	NOUN
ejpam-6111	22	12	u.	u.	PROPN
ejpam-6111	22	13	rehman	rehman	PROPN
ejpam-6111	22	14	/	/	SYM
ejpam-6111	22	15	eur	eur	PROPN
ejpam-6111	22	16	.	.	PUNCT
ejpam-6111	23	1	j.	j.	PROPN
ejpam-6111	23	2	pure	pure	PROPN
ejpam-6111	23	3	appl	appl	PROPN
ejpam-6111	23	4	.	.	PROPN
ejpam-6111	23	5	math	math	PROPN
ejpam-6111	23	6	,	,	PUNCT
ejpam-6111	23	7	18	18	NUM
ejpam-6111	23	8	(	(	PUNCT
ejpam-6111	23	9	2	2	NUM
ejpam-6111	23	10	)	)	PUNCT
ejpam-6111	23	11	(	(	PUNCT
ejpam-6111	23	12	2025	2025	NUM
ejpam-6111	23	13	)	)	PUNCT
ejpam-6111	23	14	,	,	PUNCT
ejpam-6111	23	15	6111	6111	NUM
ejpam-6111	23	16	2	2	NUM
ejpam-6111	23	17	of	of	ADP
ejpam-6111	23	18	25	25	NUM
ejpam-6111	23	19	haar	haar	PROPN
ejpam-6111	23	20	wavelets	wavelet	NOUN
ejpam-6111	23	21	vector	vector	NOUN
ejpam-6111	23	22	.	.	PUNCT
ejpam-6111	24	1	the	the	DET
ejpam-6111	24	2	haar	haar	PROPN
ejpam-6111	24	3	product	product	NOUN
ejpam-6111	24	4	matrix	matrix	NOUN
ejpam-6111	24	5	was	be	AUX
ejpam-6111	24	6	constructed	construct	VERB
ejpam-6111	24	7	and	and	CCONJ
ejpam-6111	24	8	analyzed	analyze	VERB
ejpam-6111	24	9	by	by	ADP
ejpam-6111	24	10	hasiao	hasiao	NOUN
ejpam-6111	24	11	[	[	X
ejpam-6111	24	12	2	2	NUM
ejpam-6111	24	13	]	]	PUNCT
ejpam-6111	24	14	to	to	PART
ejpam-6111	24	15	study	study	VERB
ejpam-6111	24	16	problems	problem	NOUN
ejpam-6111	24	17	such	such	ADJ
ejpam-6111	24	18	as	as	ADP
ejpam-6111	24	19	state	state	NOUN
ejpam-6111	24	20	analysis	analysis	NOUN
ejpam-6111	24	21	of	of	ADP
ejpam-6111	24	22	linear	linear	ADJ
ejpam-6111	24	23	time	time	NOUN
ejpam-6111	24	24	-	-	PUNCT
ejpam-6111	24	25	delayed	delay	VERB
ejpam-6111	24	26	systems	system	NOUN
ejpam-6111	24	27	.	.	PUNCT
ejpam-6111	25	1	haar	haar	PROPN
ejpam-6111	25	2	wavelets	wavelet	NOUN
ejpam-6111	25	3	hi(t	hi(t	NOUN
ejpam-6111	25	4	)	)	PUNCT
ejpam-6111	25	5	denote	denote	VERB
ejpam-6111	25	6	the	the	DET
ejpam-6111	25	7	group	group	NOUN
ejpam-6111	25	8	of	of	ADP
ejpam-6111	25	9	square	square	ADJ
ejpam-6111	25	10	waves	wave	NOUN
ejpam-6111	25	11	having	have	VERB
ejpam-6111	25	12	the	the	DET
ejpam-6111	25	13	magnitude	magnitude	NOUN
ejpam-6111	25	14	±1	±1	VERB
ejpam-6111	25	15	in	in	ADP
ejpam-6111	25	16	some	some	DET
ejpam-6111	25	17	given	give	VERB
ejpam-6111	25	18	intervals	interval	NOUN
ejpam-6111	25	19	and	and	CCONJ
ejpam-6111	25	20	0	0	NUM
ejpam-6111	25	21	,	,	PUNCT
ejpam-6111	25	22	elsewhere	elsewhere	ADV
ejpam-6111	25	23	.	.	PUNCT
ejpam-6111	26	1	the	the	DET
ejpam-6111	26	2	zeros	zero	NOUN
ejpam-6111	26	3	make	make	VERB
ejpam-6111	26	4	haar	haar	NOUN
ejpam-6111	26	5	transformation	transformation	NOUN
ejpam-6111	26	6	faster	fast	ADV
ejpam-6111	26	7	compared	compare	VERB
ejpam-6111	26	8	with	with	ADP
ejpam-6111	26	9	transformations	transformation	NOUN
ejpam-6111	26	10	associated	associate	VERB
ejpam-6111	26	11	with	with	ADP
ejpam-6111	26	12	square	square	ADJ
ejpam-6111	26	13	functions	function	NOUN
ejpam-6111	26	14	.	.	PUNCT
ejpam-6111	27	1	the	the	DET
ejpam-6111	27	2	scaling	scale	VERB
ejpam-6111	27	3	function	function	NOUN
ejpam-6111	27	4	is	be	AUX
ejpam-6111	27	5	a	a	DET
ejpam-6111	27	6	line	line	NOUN
ejpam-6111	27	7	h0(t	h0(t	NOUN
ejpam-6111	27	8	)	)	PUNCT
ejpam-6111	27	9	=	=	SYM
ejpam-6111	27	10	1	1	NUM
ejpam-6111	27	11	,	,	PUNCT
ejpam-6111	27	12	0	0	NUM
ejpam-6111	27	13	≤	≤	NUM
ejpam-6111	27	14	t	t	X
ejpam-6111	27	15	<	<	X
ejpam-6111	27	16	1	1	NUM
ejpam-6111	27	17	.	.	PUNCT
ejpam-6111	28	1	in	in	ADP
ejpam-6111	28	2	general	general	ADJ
ejpam-6111	28	3	,	,	PUNCT
ejpam-6111	28	4	the	the	DET
ejpam-6111	28	5	haar	haar	NOUN
ejpam-6111	28	6	wavelets	wavelet	NOUN
ejpam-6111	28	7	as	as	ADP
ejpam-6111	28	8	a	a	DET
ejpam-6111	28	9	family	family	NOUN
ejpam-6111	28	10	of	of	ADP
ejpam-6111	28	11	single	single	ADJ
ejpam-6111	28	12	square	square	ADJ
ejpam-6111	28	13	wavelets	wavelet	NOUN
ejpam-6111	28	14	can	can	AUX
ejpam-6111	28	15	be	be	AUX
ejpam-6111	28	16	written	write	VERB
ejpam-6111	28	17	as	as	ADP
ejpam-6111	28	18	hn(t	hn(t	NUM
ejpam-6111	28	19	)	)	PUNCT
ejpam-6111	29	1	=	=	SYM
ejpam-6111	29	2	h1	h1	NOUN
ejpam-6111	29	3	(	(	PUNCT
ejpam-6111	29	4	2it−	2it−	NUM
ejpam-6111	29	5	k	k	PROPN
ejpam-6111	29	6	)	)	PUNCT
ejpam-6111	29	7	;	;	PUNCT
ejpam-6111	29	8	n	n	NOUN
ejpam-6111	29	9	=	=	SYM
ejpam-6111	29	10	2i	2i	NUM
ejpam-6111	30	1	+	+	CCONJ
ejpam-6111	30	2	k	k	X
ejpam-6111	30	3	,	,	PUNCT
ejpam-6111	30	4	i	i	PRON
ejpam-6111	30	5	≥	≥	VERB
ejpam-6111	30	6	0	0	NUM
ejpam-6111	30	7	,	,	PUNCT
ejpam-6111	30	8	0	0	NUM
ejpam-6111	31	1	≤	≤	NUM
ejpam-6111	32	1	k	k	X
ejpam-6111	32	2	<	<	X
ejpam-6111	32	3	2i	2i	NUM
ejpam-6111	32	4	.	.	PUNCT
ejpam-6111	33	1	the	the	DET
ejpam-6111	33	2	operational	operational	ADJ
ejpam-6111	33	3	matrices	matrix	NOUN
ejpam-6111	33	4	used	use	VERB
ejpam-6111	33	5	to	to	PART
ejpam-6111	33	6	solve	solve	VERB
ejpam-6111	33	7	the	the	DET
ejpam-6111	33	8	optimization	optimization	NOUN
ejpam-6111	33	9	and	and	CCONJ
ejpam-6111	33	10	identification	identification	NOUN
ejpam-6111	33	11	problems	problem	NOUN
ejpam-6111	33	12	from	from	ADP
ejpam-6111	33	13	the	the	DET
ejpam-6111	33	14	dynamic	dynamic	ADJ
ejpam-6111	33	15	systems	system	NOUN
ejpam-6111	33	16	were	be	AUX
ejpam-6111	33	17	constructed	construct	VERB
ejpam-6111	33	18	by	by	ADP
ejpam-6111	33	19	using	use	VERB
ejpam-6111	33	20	orthogonal	orthogonal	ADJ
ejpam-6111	33	21	functions	function	NOUN
ejpam-6111	33	22	,	,	PUNCT
ejpam-6111	33	23	see	see	VERB
ejpam-6111	33	24	[	[	X
ejpam-6111	33	25	3	3	NUM
ejpam-6111	33	26	]	]	PUNCT
ejpam-6111	33	27	.	.	PUNCT
ejpam-6111	34	1	many	many	ADJ
ejpam-6111	34	2	operational	operational	ADJ
ejpam-6111	34	3	matrices	matrix	NOUN
ejpam-6111	34	4	were	be	AUX
ejpam-6111	34	5	constructed	construct	VERB
ejpam-6111	34	6	using	use	VERB
ejpam-6111	34	7	orthogonal	orthogonal	ADJ
ejpam-6111	34	8	functions	function	NOUN
ejpam-6111	34	9	,	,	PUNCT
ejpam-6111	34	10	such	such	ADJ
ejpam-6111	34	11	as	as	ADP
ejpam-6111	34	12	block	block	NOUN
ejpam-6111	34	13	pulse	pulse	NOUN
ejpam-6111	35	1	[	[	X
ejpam-6111	35	2	4	4	NUM
ejpam-6111	35	3	]	]	PUNCT
ejpam-6111	35	4	,	,	PUNCT
ejpam-6111	35	5	lagurre	lagurre	PROPN
ejpam-6111	35	6	[	[	X
ejpam-6111	35	7	5	5	NUM
ejpam-6111	35	8	,	,	PUNCT
ejpam-6111	35	9	6	6	NUM
ejpam-6111	35	10	]	]	PUNCT
ejpam-6111	35	11	,	,	PUNCT
ejpam-6111	35	12	legendre	legendre	PROPN
ejpam-6111	36	1	[	[	X
ejpam-6111	36	2	7	7	NUM
ejpam-6111	36	3	]	]	PUNCT
ejpam-6111	36	4	,	,	PUNCT
ejpam-6111	36	5	chebyshev	chebyshev	X
ejpam-6111	37	1	[	[	X
ejpam-6111	37	2	8	8	NUM
ejpam-6111	37	3	]	]	PUNCT
ejpam-6111	37	4	,	,	PUNCT
ejpam-6111	37	5	and	and	CCONJ
ejpam-6111	37	6	fourier	fourier	NOUN
ejpam-6111	38	1	[	[	X
ejpam-6111	38	2	9	9	NUM
ejpam-6111	38	3	]	]	PUNCT
ejpam-6111	38	4	.	.	PUNCT
ejpam-6111	39	1	in	in	ADP
ejpam-6111	39	2	[	[	X
ejpam-6111	39	3	1	1	NUM
ejpam-6111	39	4	]	]	PUNCT
ejpam-6111	39	5	,	,	PUNCT
ejpam-6111	39	6	an	an	DET
ejpam-6111	39	7	operational	operational	ADJ
ejpam-6111	39	8	matrix	matrix	NOUN
ejpam-6111	39	9	was	be	AUX
ejpam-6111	39	10	constructed	construct	VERB
ejpam-6111	39	11	for	for	ADP
ejpam-6111	39	12	integration	integration	NOUN
ejpam-6111	39	13	using	use	VERB
ejpam-6111	39	14	haar	haar	PROPN
ejpam-6111	39	15	wavelets	wavelet	NOUN
ejpam-6111	39	16	.	.	PUNCT
ejpam-6111	40	1	furthermore	furthermore	ADV
ejpam-6111	40	2	,	,	PUNCT
ejpam-6111	40	3	this	this	DET
ejpam-6111	40	4	operational	operational	ADJ
ejpam-6111	40	5	matrix	matrix	NOUN
ejpam-6111	40	6	was	be	AUX
ejpam-6111	40	7	used	use	VERB
ejpam-6111	40	8	to	to	PART
ejpam-6111	40	9	study	study	VERB
ejpam-6111	40	10	and	and	CCONJ
ejpam-6111	40	11	analyze	analyze	VERB
ejpam-6111	40	12	lumped	lump	VERB
ejpam-6111	40	13	-	-	PUNCT
ejpam-6111	40	14	parameter	parameter	NOUN
ejpam-6111	40	15	and	and	CCONJ
ejpam-6111	40	16	distributed	distribute	VERB
ejpam-6111	40	17	-	-	PUNCT
ejpam-6111	40	18	parameter	parameter	NOUN
ejpam-6111	40	19	systems	system	NOUN
ejpam-6111	40	20	.	.	PUNCT
ejpam-6111	41	1	the	the	DET
ejpam-6111	41	2	structural	structural	ADJ
ejpam-6111	41	3	stability	stability	NOUN
ejpam-6111	41	4	scheme	scheme	NOUN
ejpam-6111	41	5	with	with	ADP
ejpam-6111	41	6	in	in	ADP
ejpam-6111	41	7	-	-	PUNCT
ejpam-6111	41	8	plane	plane	NOUN
ejpam-6111	41	9	forces	force	NOUN
ejpam-6111	41	10	as	as	SCONJ
ejpam-6111	41	11	the	the	DET
ejpam-6111	41	12	discretized	discretized	ADJ
ejpam-6111	41	13	parameters	parameter	NOUN
ejpam-6111	41	14	was	be	AUX
ejpam-6111	41	15	studied	study	VERB
ejpam-6111	41	16	and	and	CCONJ
ejpam-6111	41	17	analyzed	analyze	VERB
ejpam-6111	41	18	in	in	ADP
ejpam-6111	41	19	[	[	X
ejpam-6111	41	20	10–12	10–12	NUM
ejpam-6111	41	21	]	]	PUNCT
ejpam-6111	41	22	.	.	PUNCT
ejpam-6111	42	1	a	a	DET
ejpam-6111	42	2	more	more	ADV
ejpam-6111	42	3	general	general	ADJ
ejpam-6111	42	4	methodology	methodology	NOUN
ejpam-6111	42	5	was	be	AUX
ejpam-6111	42	6	presented	present	VERB
ejpam-6111	42	7	to	to	PART
ejpam-6111	42	8	construct	construct	VERB
ejpam-6111	42	9	the	the	DET
ejpam-6111	42	10	lumped	lump	VERB
ejpam-6111	42	11	-	-	PUNCT
ejpam-6111	42	12	parameter	parameter	NOUN
ejpam-6111	42	13	force	force	NOUN
ejpam-6111	42	14	stiffness	stiffness	NOUN
ejpam-6111	42	15	matrices	matrix	NOUN
ejpam-6111	42	16	for	for	ADP
ejpam-6111	42	17	elements	element	NOUN
ejpam-6111	42	18	such	such	ADJ
ejpam-6111	42	19	as	as	ADP
ejpam-6111	42	20	beams	beam	NOUN
ejpam-6111	42	21	,	,	PUNCT
ejpam-6111	42	22	curved	curved	ADJ
ejpam-6111	42	23	beams	beam	NOUN
ejpam-6111	42	24	,	,	PUNCT
ejpam-6111	42	25	shells	shell	NOUN
ejpam-6111	42	26	and	and	CCONJ
ejpam-6111	42	27	circular	circular	ADJ
ejpam-6111	42	28	plates	plate	NOUN
ejpam-6111	42	29	.	.	PUNCT
ejpam-6111	43	1	the	the	DET
ejpam-6111	43	2	numerical	numerical	ADJ
ejpam-6111	43	3	experiments	experiment	NOUN
ejpam-6111	43	4	were	be	AUX
ejpam-6111	43	5	performed	perform	VERB
ejpam-6111	43	6	to	to	PART
ejpam-6111	43	7	compare	compare	VERB
ejpam-6111	43	8	the	the	DET
ejpam-6111	43	9	results	result	NOUN
ejpam-6111	43	10	with	with	ADP
ejpam-6111	43	11	exact	exact	ADJ
ejpam-6111	43	12	and	and	CCONJ
ejpam-6111	43	13	various	various	ADJ
ejpam-6111	43	14	other	other	ADJ
ejpam-6111	43	15	solutions	solution	NOUN
ejpam-6111	43	16	,	,	PUNCT
ejpam-6111	43	17	for	for	ADP
ejpam-6111	43	18	instance	instance	NOUN
ejpam-6111	43	19	,	,	PUNCT
ejpam-6111	43	20	the	the	DET
ejpam-6111	43	21	consistent	consistent	ADJ
ejpam-6111	43	22	geometric	geometric	ADJ
ejpam-6111	43	23	stiffness	stiffness	NOUN
ejpam-6111	43	24	matrix	matrix	NOUN
ejpam-6111	43	25	solutions	solution	NOUN
ejpam-6111	43	26	.	.	PUNCT
ejpam-6111	44	1	a	a	DET
ejpam-6111	44	2	transfer	transfer	NOUN
ejpam-6111	44	3	matrix	matrix	NOUN
ejpam-6111	44	4	with	with	ADP
ejpam-6111	44	5	in	in	ADP
ejpam-6111	44	6	-	-	PUNCT
ejpam-6111	44	7	plane	plane	NOUN
ejpam-6111	44	8	forces	force	NOUN
ejpam-6111	44	9	in	in	ADP
ejpam-6111	44	10	the	the	DET
ejpam-6111	44	11	form	form	NOUN
ejpam-6111	44	12	of	of	ADP
ejpam-6111	44	13	a	a	DET
ejpam-6111	44	14	lumped	lump	VERB
ejpam-6111	44	15	-	-	PUNCT
ejpam-6111	44	16	parameters	parameter	NOUN
ejpam-6111	44	17	was	be	AUX
ejpam-6111	44	18	constructed	construct	VERB
ejpam-6111	44	19	by	by	ADP
ejpam-6111	44	20	[	[	X
ejpam-6111	44	21	13	13	NUM
ejpam-6111	44	22	]	]	PUNCT
ejpam-6111	44	23	,	,	PUNCT
ejpam-6111	44	24	and	and	CCONJ
ejpam-6111	44	25	[	[	X
ejpam-6111	44	26	14	14	NUM
ejpam-6111	44	27	]	]	PUNCT
ejpam-6111	44	28	.	.	PUNCT
ejpam-6111	45	1	the	the	DET
ejpam-6111	45	2	computation	computation	NOUN
ejpam-6111	45	3	of	of	ADP
ejpam-6111	45	4	structured	structured	ADJ
ejpam-6111	45	5	singular	singular	ADJ
ejpam-6111	45	6	values	value	NOUN
ejpam-6111	45	7	(	(	PUNCT
ejpam-6111	45	8	µ-values	µ-value	NOUN
ejpam-6111	45	9	)	)	PUNCT
ejpam-6111	46	1	[	[	X
ejpam-6111	46	2	15	15	NUM
ejpam-6111	46	3	]	]	X
ejpam-6111	46	4	is	be	AUX
ejpam-6111	46	5	a	a	DET
ejpam-6111	46	6	well	well	ADV
ejpam-6111	46	7	-	-	PUNCT
ejpam-6111	46	8	known	know	VERB
ejpam-6111	46	9	mathematical	mathematical	ADJ
ejpam-6111	46	10	tool	tool	NOUN
ejpam-6111	46	11	for	for	ADP
ejpam-6111	46	12	addressing	address	VERB
ejpam-6111	46	13	an	an	DET
ejpam-6111	46	14	important	important	ADJ
ejpam-6111	46	15	problem	problem	NOUN
ejpam-6111	46	16	in	in	ADP
ejpam-6111	46	17	the	the	DET
ejpam-6111	46	18	analysis	analysis	NOUN
ejpam-6111	46	19	of	of	ADP
ejpam-6111	46	20	linear	linear	ADJ
ejpam-6111	46	21	time	time	NOUN
ejpam-6111	46	22	-	-	PUNCT
ejpam-6111	46	23	invariant	invariant	ADJ
ejpam-6111	46	24	systems	system	NOUN
ejpam-6111	46	25	.	.	PUNCT
ejpam-6111	47	1	the	the	DET
ejpam-6111	47	2	µ-value	µ-value	NOUN
ejpam-6111	47	3	also	also	ADV
ejpam-6111	47	4	quantifies	quantify	VERB
ejpam-6111	47	5	the	the	DET
ejpam-6111	47	6	stability	stability	NOUN
ejpam-6111	47	7	analysis	analysis	NOUN
ejpam-6111	47	8	of	of	ADP
ejpam-6111	47	9	linear	linear	PROPN
ejpam-6111	47	10	systems	system	NOUN
ejpam-6111	47	11	subject	subject	ADJ
ejpam-6111	47	12	to	to	ADP
ejpam-6111	47	13	structured	structured	ADJ
ejpam-6111	47	14	perturbations	perturbation	NOUN
ejpam-6111	47	15	.	.	PUNCT
ejpam-6111	48	1	the	the	DET
ejpam-6111	48	2	computation	computation	NOUN
ejpam-6111	48	3	of	of	ADP
ejpam-6111	48	4	the	the	DET
ejpam-6111	48	5	µ-value	µ-value	NOUN
ejpam-6111	48	6	is	be	AUX
ejpam-6111	48	7	possible	possible	ADJ
ejpam-6111	48	8	with	with	ADP
ejpam-6111	48	9	respect	respect	NOUN
ejpam-6111	48	10	to	to	ADP
ejpam-6111	48	11	all	all	DET
ejpam-6111	48	12	kind	kind	NOUN
ejpam-6111	48	13	of	of	ADP
ejpam-6111	48	14	perturbations	perturbation	NOUN
ejpam-6111	48	15	and	and	CCONJ
ejpam-6111	48	16	this	this	PRON
ejpam-6111	48	17	includes	include	VERB
ejpam-6111	48	18	,	,	PUNCT
ejpam-6111	48	19	real	real	ADJ
ejpam-6111	48	20	,	,	PUNCT
ejpam-6111	48	21	complex	complex	ADJ
ejpam-6111	48	22	,	,	PUNCT
ejpam-6111	48	23	and	and	CCONJ
ejpam-6111	48	24	a	a	DET
ejpam-6111	48	25	mixture	mixture	NOUN
ejpam-6111	48	26	of	of	ADP
ejpam-6111	48	27	both	both	PRON
ejpam-6111	48	28	.	.	PUNCT
ejpam-6111	49	1	the	the	DET
ejpam-6111	49	2	exact	exact	ADJ
ejpam-6111	49	3	computation	computation	NOUN
ejpam-6111	49	4	of	of	ADP
ejpam-6111	49	5	the	the	DET
ejpam-6111	49	6	µ-value	µ-value	NOUN
ejpam-6111	49	7	is	be	AUX
ejpam-6111	49	8	an	an	DET
ejpam-6111	49	9	np	np	NOUN
ejpam-6111	49	10	-	-	PUNCT
ejpam-6111	49	11	hard	hard	ADJ
ejpam-6111	49	12	problem	problem	NOUN
ejpam-6111	49	13	[	[	X
ejpam-6111	49	14	16	16	NUM
ejpam-6111	49	15	]	]	PUNCT
ejpam-6111	49	16	.	.	PUNCT
ejpam-6111	50	1	the	the	DET
ejpam-6111	50	2	np	np	INTJ
ejpam-6111	50	3	-	-	PUNCT
ejpam-6111	50	4	hard	hard	ADJ
ejpam-6111	50	5	nature	nature	NOUN
ejpam-6111	50	6	of	of	ADP
ejpam-6111	50	7	computing	compute	VERB
ejpam-6111	50	8	µ-value	µ-value	NOUN
ejpam-6111	50	9	motivates	motivate	VERB
ejpam-6111	50	10	the	the	DET
ejpam-6111	50	11	development	development	NOUN
ejpam-6111	50	12	of	of	ADP
ejpam-6111	50	13	iterative	iterative	ADJ
ejpam-6111	50	14	methods	method	NOUN
ejpam-6111	50	15	and	and	CCONJ
ejpam-6111	50	16	numerical	numerical	ADJ
ejpam-6111	50	17	algorithms	algorithm	NOUN
ejpam-6111	50	18	for	for	ADP
ejpam-6111	50	19	computing	compute	VERB
ejpam-6111	50	20	upper	upper	ADJ
ejpam-6111	50	21	and	and	CCONJ
ejpam-6111	50	22	lower	lower	ADV
ejpam-6111	50	23	bound	bind	VERB
ejpam-6111	50	24	.	.	PUNCT
ejpam-6111	51	1	for	for	ADP
ejpam-6111	51	2	upper	upper	ADJ
ejpam-6111	51	3	bounds	bound	NOUN
ejpam-6111	51	4	see	see	VERB
ejpam-6111	51	5	[	[	X
ejpam-6111	51	6	17	17	NUM
ejpam-6111	51	7	,	,	PUNCT
ejpam-6111	51	8	18	18	NUM
ejpam-6111	51	9	]	]	PUNCT
ejpam-6111	51	10	and	and	CCONJ
ejpam-6111	51	11	the	the	DET
ejpam-6111	51	12	references	reference	NOUN
ejpam-6111	51	13	therein	therein	ADV
ejpam-6111	51	14	.	.	PUNCT
ejpam-6111	52	1	for	for	ADP
ejpam-6111	52	2	lower	low	ADJ
ejpam-6111	52	3	bounds	bound	NOUN
ejpam-6111	52	4	,	,	PUNCT
ejpam-6111	52	5	see	see	VERB
ejpam-6111	52	6	[	[	X
ejpam-6111	52	7	19	19	NUM
ejpam-6111	52	8	,	,	PUNCT
ejpam-6111	52	9	20	20	NUM
ejpam-6111	52	10	]	]	PUNCT
ejpam-6111	52	11	and	and	CCONJ
ejpam-6111	52	12	references	reference	NOUN
ejpam-6111	52	13	therein	therein	ADV
ejpam-6111	52	14	.	.	PUNCT
ejpam-6111	53	1	for	for	ADP
ejpam-6111	53	2	applications	application	NOUN
ejpam-6111	53	3	of	of	ADP
ejpam-6111	53	4	µ-values	µ-value	NOUN
ejpam-6111	53	5	in	in	ADP
ejpam-6111	53	6	various	various	ADJ
ejpam-6111	53	7	research	research	NOUN
ejpam-6111	53	8	directions	direction	NOUN
ejpam-6111	53	9	,	,	PUNCT
ejpam-6111	53	10	see	see	VERB
ejpam-6111	53	11	[	[	X
ejpam-6111	53	12	15	15	NUM
ejpam-6111	53	13	,	,	PUNCT
ejpam-6111	53	14	21–28	21–28	NUM
ejpam-6111	53	15	]	]	PUNCT
ejpam-6111	53	16	.	.	PUNCT
ejpam-6111	54	1	the	the	DET
ejpam-6111	54	2	d	d	NOUN
ejpam-6111	54	3	-	-	NOUN
ejpam-6111	54	4	stability	stability	NOUN
ejpam-6111	54	5	or	or	CCONJ
ejpam-6111	54	6	diagonal	diagonal	ADJ
ejpam-6111	54	7	stability	stability	NOUN
ejpam-6111	54	8	was	be	AUX
ejpam-6111	54	9	introduced	introduce	VERB
ejpam-6111	54	10	in	in	ADP
ejpam-6111	54	11	a	a	DET
ejpam-6111	54	12	classical	classical	ADJ
ejpam-6111	54	13	paper	paper	NOUN
ejpam-6111	54	14	by	by	ADP
ejpam-6111	54	15	arrow	arrow	NOUN
ejpam-6111	54	16	and	and	CCONJ
ejpam-6111	54	17	mcmanus	mcmanus	PROPN
ejpam-6111	55	1	[	[	X
ejpam-6111	55	2	29	29	NUM
ejpam-6111	55	3	]	]	PUNCT
ejpam-6111	55	4	,	,	PUNCT
ejpam-6111	55	5	and	and	CCONJ
ejpam-6111	55	6	then	then	ADV
ejpam-6111	55	7	by	by	ADP
ejpam-6111	55	8	enthoven	enthoven	ADV
ejpam-6111	55	9	and	and	CCONJ
ejpam-6111	55	10	arrow	arrow	NOUN
ejpam-6111	55	11	[	[	X
ejpam-6111	55	12	30	30	NUM
ejpam-6111	55	13	]	]	PUNCT
ejpam-6111	55	14	in	in	ADP
ejpam-6111	55	15	the	the	DET
ejpam-6111	55	16	study	study	NOUN
ejpam-6111	55	17	of	of	ADP
ejpam-6111	55	18	equilibrium	equilibrium	NOUN
ejpam-6111	55	19	.	.	PUNCT
ejpam-6111	56	1	dynamics	dynamic	NOUN
ejpam-6111	56	2	.	.	PUNCT
ejpam-6111	57	1	a	a	DET
ejpam-6111	57	2	given	give	VERB
ejpam-6111	57	3	matrix	matrix	NOUN
ejpam-6111	57	4	a	a	PRON
ejpam-6111	57	5	is	be	AUX
ejpam-6111	57	6	d	d	NOUN
ejpam-6111	57	7	-	-	ADJ
ejpam-6111	57	8	stable	stable	ADJ
ejpam-6111	57	9	if	if	SCONJ
ejpam-6111	58	1	and	and	CCONJ
ejpam-6111	58	2	only	only	ADV
ejpam-6111	58	3	if	if	SCONJ
ejpam-6111	58	4	for	for	ADP
ejpam-6111	58	5	every	every	DET
ejpam-6111	58	6	positive	positive	ADJ
ejpam-6111	58	7	diagonal	diagonal	ADJ
ejpam-6111	58	8	matrix	matrix	NOUN
ejpam-6111	59	1	d	d	NOUN
ejpam-6111	59	2	,	,	PUNCT
ejpam-6111	59	3	the	the	DET
ejpam-6111	59	4	matrix	matrix	NOUN
ejpam-6111	59	5	product	product	NOUN
ejpam-6111	59	6	da	da	NOUN
ejpam-6111	59	7	or	or	CCONJ
ejpam-6111	59	8	ad	ad	NOUN
ejpam-6111	59	9	has	have	AUX
ejpam-6111	59	10	all	all	PRON
ejpam-6111	59	11	eigenvalues	eigenvalue	NOUN
ejpam-6111	59	12	in	in	ADP
ejpam-6111	59	13	the	the	DET
ejpam-6111	59	14	left	left	ADJ
ejpam-6111	59	15	half	half	NOUN
ejpam-6111	59	16	of	of	ADP
ejpam-6111	59	17	the	the	DET
ejpam-6111	59	18	complex	complex	ADJ
ejpam-6111	59	19	plane	plane	NOUN
ejpam-6111	59	20	.	.	PUNCT
ejpam-6111	60	1	the	the	DET
ejpam-6111	60	2	characterization	characterization	NOUN
ejpam-6111	60	3	of	of	ADP
ejpam-6111	60	4	d	d	NOUN
ejpam-6111	60	5	-	-	NOUN
ejpam-6111	60	6	stability	stability	NOUN
ejpam-6111	60	7	for	for	ADP
ejpam-6111	60	8	various	various	ADJ
ejpam-6111	60	9	class	class	NOUN
ejpam-6111	60	10	of	of	ADP
ejpam-6111	60	11	matrices	matrix	NOUN
ejpam-6111	60	12	have	have	AUX
ejpam-6111	60	13	been	be	AUX
ejpam-6111	60	14	extensively	extensively	ADV
ejpam-6111	60	15	studied	study	VERB
ejpam-6111	60	16	in	in	ADP
ejpam-6111	60	17	[	[	X
ejpam-6111	60	18	31–34	31–34	NUM
ejpam-6111	60	19	]	]	PUNCT
ejpam-6111	60	20	.	.	PUNCT
ejpam-6111	61	1	the	the	DET
ejpam-6111	61	2	concepts	concept	NOUN
ejpam-6111	61	3	of	of	ADP
ejpam-6111	61	4	d	d	NOUN
ejpam-6111	61	5	-	-	NOUN
ejpam-6111	61	6	stability	stability	NOUN
ejpam-6111	61	7	and	and	CCONJ
ejpam-6111	61	8	µ-values	µ-value	NOUN
ejpam-6111	61	9	are	be	AUX
ejpam-6111	61	10	closely	closely	ADV
ejpam-6111	61	11	interconnected	interconnect	VERB
ejpam-6111	61	12	.	.	PUNCT
ejpam-6111	62	1	in	in	ADP
ejpam-6111	62	2	[	[	X
ejpam-6111	62	3	35	35	NUM
ejpam-6111	62	4	]	]	PUNCT
ejpam-6111	62	5	,	,	PUNCT
ejpam-6111	62	6	the	the	DET
ejpam-6111	62	7	novel	novel	ADJ
ejpam-6111	62	8	results	result	NOUN
ejpam-6111	62	9	were	be	AUX
ejpam-6111	62	10	analyzed	analyze	VERB
ejpam-6111	62	11	and	and	CCONJ
ejpam-6111	62	12	proposed	propose	VERB
ejpam-6111	62	13	on	on	ADP
ejpam-6111	62	14	the	the	DET
ejpam-6111	62	15	relationship	relationship	NOUN
ejpam-6111	62	16	between	between	ADP
ejpam-6111	62	17	d	d	NOUN
ejpam-6111	62	18	-	-	NOUN
ejpam-6111	62	19	stability	stability	NOUN
ejpam-6111	62	20	of	of	ADP
ejpam-6111	62	21	real	real	ADV
ejpam-6111	62	22	-	-	PUNCT
ejpam-6111	62	23	valued	value	VERB
ejpam-6111	62	24	square	square	ADJ
ejpam-6111	62	25	matrices	matrix	NOUN
ejpam-6111	62	26	and	and	CCONJ
ejpam-6111	62	27	structured	structure	VERB
ejpam-6111	62	28	singular	singular	ADJ
ejpam-6111	62	29	values	value	NOUN
ejpam-6111	62	30	.	.	PUNCT
ejpam-6111	63	1	it	it	PRON
ejpam-6111	63	2	was	be	AUX
ejpam-6111	63	3	shown	show	VERB
ejpam-6111	63	4	that	that	SCONJ
ejpam-6111	63	5	a	a	DET
ejpam-6111	63	6	given	give	VERB
ejpam-6111	63	7	n	n	CCONJ
ejpam-6111	63	8	-	-	PUNCT
ejpam-6111	63	9	dimensional	dimensional	ADJ
ejpam-6111	63	10	real	real	ADV
ejpam-6111	63	11	-	-	PUNCT
ejpam-6111	63	12	valued	value	VERB
ejpam-6111	63	13	matrix	matrix	NOUN
ejpam-6111	63	14	is	be	AUX
ejpam-6111	63	15	d	d	NOUN
ejpam-6111	63	16	-	-	ADJ
ejpam-6111	63	17	stable	stable	ADJ
ejpam-6111	63	18	if	if	SCONJ
ejpam-6111	63	19	and	and	CCONJ
ejpam-6111	63	20	only	only	ADV
ejpam-6111	63	21	if	if	SCONJ
ejpam-6111	63	22	its	its	PRON
ejpam-6111	63	23	real	real	ADV
ejpam-6111	63	24	-	-	PUNCT
ejpam-6111	63	25	valued	value	VERB
ejpam-6111	63	26	µ-value	µ-value	NOUN
ejpam-6111	63	27	is	be	AUX
ejpam-6111	63	28	greater	great	ADJ
ejpam-6111	63	29	than	than	ADP
ejpam-6111	63	30	or	or	CCONJ
ejpam-6111	63	31	equal	equal	ADJ
ejpam-6111	63	32	to	to	ADP
ejpam-6111	63	33	0	0	NUM
ejpam-6111	63	34	,	,	PUNCT
ejpam-6111	63	35	and	and	CCONJ
ejpam-6111	63	36	strictly	strictly	ADV
ejpam-6111	63	37	less	less	ADJ
ejpam-6111	63	38	than	than	ADP
ejpam-6111	63	39	1	1	NUM
ejpam-6111	63	40	.	.	PUNCT
ejpam-6111	64	1	furthermore	furthermore	ADV
ejpam-6111	64	2	,	,	PUNCT
ejpam-6111	64	3	some	some	DET
ejpam-6111	64	4	new	new	ADJ
ejpam-6111	64	5	results	result	NOUN
ejpam-6111	64	6	were	be	AUX
ejpam-6111	64	7	presented	present	VERB
ejpam-6111	64	8	on	on	ADP
ejpam-6111	64	9	conditions	condition	NOUN
ejpam-6111	64	10	s.	s.	PROPN
ejpam-6111	64	11	mazhar	mazhar	PROPN
ejpam-6111	64	12	,	,	PUNCT
ejpam-6111	64	13	m.	m.	NOUN
ejpam-6111	64	14	u.	u.	PROPN
ejpam-6111	64	15	rehman	rehman	PROPN
ejpam-6111	64	16	/	/	SYM
ejpam-6111	64	17	eur	eur	PROPN
ejpam-6111	64	18	.	.	PUNCT
ejpam-6111	65	1	j.	j.	PROPN
ejpam-6111	65	2	pure	pure	PROPN
ejpam-6111	65	3	appl	appl	PROPN
ejpam-6111	65	4	.	.	PROPN
ejpam-6111	65	5	math	math	PROPN
ejpam-6111	65	6	,	,	PUNCT
ejpam-6111	65	7	18	18	NUM
ejpam-6111	65	8	(	(	PUNCT
ejpam-6111	65	9	2	2	NUM
ejpam-6111	65	10	)	)	PUNCT
ejpam-6111	65	11	(	(	PUNCT
ejpam-6111	65	12	2025	2025	NUM
ejpam-6111	65	13	)	)	PUNCT
ejpam-6111	65	14	,	,	PUNCT
ejpam-6111	65	15	6111	6111	NUM
ejpam-6111	65	16	3	3	NUM
ejpam-6111	65	17	of	of	ADP
ejpam-6111	65	18	25	25	NUM
ejpam-6111	65	19	to	to	ADP
ejpam-6111	65	20	strong	strong	ADJ
ejpam-6111	65	21	d	d	NOUN
ejpam-6111	65	22	-	-	NOUN
ejpam-6111	65	23	stability	stability	NOUN
ejpam-6111	65	24	in	in	ADP
ejpam-6111	65	25	terms	term	NOUN
ejpam-6111	65	26	of	of	ADP
ejpam-6111	65	27	µ-values	µ-value	NOUN
ejpam-6111	65	28	,	,	PUNCT
ejpam-6111	65	29	see	see	VERB
ejpam-6111	65	30	[	[	X
ejpam-6111	65	31	36	36	NUM
ejpam-6111	65	32	]	]	PUNCT
ejpam-6111	65	33	.	.	PUNCT
ejpam-6111	66	1	additional	additional	ADJ
ejpam-6111	66	2	results	result	NOUN
ejpam-6111	66	3	on	on	ADP
ejpam-6111	66	4	the	the	DET
ejpam-6111	66	5	relationships	relationship	NOUN
ejpam-6111	66	6	between	between	ADP
ejpam-6111	66	7	d	d	NOUN
ejpam-6111	66	8	-	-	NOUN
ejpam-6111	66	9	stability	stability	NOUN
ejpam-6111	66	10	,	,	PUNCT
ejpam-6111	66	11	strong	strong	ADJ
ejpam-6111	66	12	d	d	NOUN
ejpam-6111	66	13	-	-	NOUN
ejpam-6111	66	14	stability	stability	NOUN
ejpam-6111	66	15	and	and	CCONJ
ejpam-6111	66	16	real	real	ADV
ejpam-6111	66	17	-	-	PUNCT
ejpam-6111	66	18	valued	value	VERB
ejpam-6111	66	19	µ-values	µ-value	NOUN
ejpam-6111	66	20	were	be	AUX
ejpam-6111	66	21	presented	present	VERB
ejpam-6111	66	22	in	in	ADP
ejpam-6111	66	23	[	[	X
ejpam-6111	66	24	37	37	NUM
ejpam-6111	66	25	]	]	PUNCT
ejpam-6111	66	26	.	.	PUNCT
ejpam-6111	67	1	in	in	ADP
ejpam-6111	67	2	[	[	X
ejpam-6111	67	3	38	38	NUM
ejpam-6111	67	4	]	]	PUNCT
ejpam-6111	67	5	,	,	PUNCT
ejpam-6111	67	6	new	new	ADJ
ejpam-6111	67	7	results	result	NOUN
ejpam-6111	67	8	on	on	ADP
ejpam-6111	67	9	the	the	DET
ejpam-6111	67	10	interconnections	interconnection	NOUN
ejpam-6111	67	11	between	between	ADP
ejpam-6111	67	12	h	h	NOUN
ejpam-6111	67	13	-	-	PUNCT
ejpam-6111	67	14	stable	stable	ADJ
ejpam-6111	67	15	,	,	PUNCT
ejpam-6111	67	16	d(α)-stable	d(α)-stable	ADJ
ejpam-6111	67	17	,	,	PUNCT
ejpam-6111	67	18	semi	semi	ADJ
ejpam-6111	67	19	-	-	ADJ
ejpam-6111	67	20	stable	stable	ADJ
ejpam-6111	67	21	matrices	matrix	NOUN
ejpam-6111	67	22	and	and	CCONJ
ejpam-6111	67	23	structured	structure	VERB
ejpam-6111	67	24	singular	singular	ADJ
ejpam-6111	67	25	values	value	NOUN
ejpam-6111	67	26	were	be	AUX
ejpam-6111	67	27	analyzed	analyze	VERB
ejpam-6111	67	28	and	and	CCONJ
ejpam-6111	67	29	presented	present	VERB
ejpam-6111	67	30	.	.	PUNCT
ejpam-6111	68	1	spectra	spectra	NOUN
ejpam-6111	68	2	and	and	CCONJ
ejpam-6111	68	3	pseudo	pseudo	NOUN
ejpam-6111	68	4	-	-	NOUN
ejpam-6111	68	5	spectra	spectra	NOUN
ejpam-6111	68	6	of	of	ADP
ejpam-6111	68	7	structured	structured	ADJ
ejpam-6111	68	8	matrices	matrix	NOUN
ejpam-6111	68	9	play	play	VERB
ejpam-6111	68	10	an	an	DET
ejpam-6111	68	11	important	important	ADJ
ejpam-6111	68	12	role	role	NOUN
ejpam-6111	68	13	to	to	PART
ejpam-6111	68	14	study	study	VERB
ejpam-6111	68	15	and	and	CCONJ
ejpam-6111	68	16	analyze	analyze	VERB
ejpam-6111	68	17	system	system	NOUN
ejpam-6111	68	18	of	of	ADP
ejpam-6111	68	19	linear	linear	ADJ
ejpam-6111	68	20	equations	equation	NOUN
ejpam-6111	68	21	appearing	appear	VERB
ejpam-6111	68	22	across	across	ADP
ejpam-6111	68	23	various	various	ADJ
ejpam-6111	68	24	research	research	NOUN
ejpam-6111	68	25	disciplines	discipline	NOUN
ejpam-6111	68	26	.	.	PUNCT
ejpam-6111	69	1	recently	recently	ADV
ejpam-6111	69	2	,	,	PUNCT
ejpam-6111	69	3	novel	novel	ADJ
ejpam-6111	69	4	results	result	NOUN
ejpam-6111	69	5	on	on	ADP
ejpam-6111	69	6	the	the	DET
ejpam-6111	69	7	spectral	spectral	ADJ
ejpam-6111	69	8	,	,	PUNCT
ejpam-6111	69	9	pseudo	pseudo	NOUN
ejpam-6111	69	10	-	-	NOUN
ejpam-6111	69	11	spectrum	spectrum	NOUN
ejpam-6111	69	12	of	of	ADP
ejpam-6111	69	13	d	d	ADJ
ejpam-6111	69	14	-	-	ADJ
ejpam-6111	69	15	stable	stable	ADJ
ejpam-6111	69	16	matrices	matrix	NOUN
ejpam-6111	69	17	in	in	ADP
ejpam-6111	69	18	economic	economic	ADJ
ejpam-6111	69	19	models	model	NOUN
ejpam-6111	69	20	were	be	AUX
ejpam-6111	69	21	presented	present	VERB
ejpam-6111	69	22	in	in	ADP
ejpam-6111	69	23	[	[	X
ejpam-6111	69	24	39	39	NUM
ejpam-6111	69	25	]	]	PUNCT
ejpam-6111	69	26	.	.	PUNCT
ejpam-6111	70	1	spectral	spectral	ADJ
ejpam-6111	70	2	properties	property	NOUN
ejpam-6111	70	3	ofd	ofd	ADJ
ejpam-6111	70	4	-	-	PUNCT
ejpam-6111	70	5	stable	stable	ADJ
ejpam-6111	70	6	matrices	matrix	NOUN
ejpam-6111	70	7	in	in	ADP
ejpam-6111	70	8	transportation	transportation	NOUN
ejpam-6111	70	9	problems	problem	NOUN
ejpam-6111	70	10	were	be	AUX
ejpam-6111	70	11	studied	study	VERB
ejpam-6111	70	12	and	and	CCONJ
ejpam-6111	70	13	analyzed	analyze	VERB
ejpam-6111	70	14	in	in	ADP
ejpam-6111	70	15	[	[	X
ejpam-6111	70	16	40	40	NUM
ejpam-6111	70	17	]	]	PUNCT
ejpam-6111	70	18	.	.	PUNCT
ejpam-6111	71	1	a	a	DET
ejpam-6111	71	2	detailed	detailed	ADJ
ejpam-6111	71	3	analysis	analysis	NOUN
ejpam-6111	71	4	of	of	ADP
ejpam-6111	71	5	stability	stability	NOUN
ejpam-6111	71	6	,	,	PUNCT
ejpam-6111	71	7	d	d	NOUN
ejpam-6111	71	8	-	-	PUNCT
ejpam-6111	71	9	stability	stability	NOUN
ejpam-6111	71	10	and	and	CCONJ
ejpam-6111	71	11	the	the	DET
ejpam-6111	71	12	pseudo	pseudo	NOUN
ejpam-6111	71	13	-	-	NOUN
ejpam-6111	71	14	spectrum	spectrum	NOUN
ejpam-6111	71	15	for	for	ADP
ejpam-6111	71	16	economic	economic	ADJ
ejpam-6111	71	17	models	model	NOUN
ejpam-6111	71	18	was	be	AUX
ejpam-6111	71	19	presented	present	VERB
ejpam-6111	71	20	in	in	ADP
ejpam-6111	71	21	[	[	X
ejpam-6111	71	22	41	41	NUM
ejpam-6111	71	23	]	]	PUNCT
ejpam-6111	71	24	.	.	PUNCT
ejpam-6111	72	1	in	in	ADP
ejpam-6111	72	2	[	[	X
ejpam-6111	72	3	42	42	NUM
ejpam-6111	72	4	]	]	PUNCT
ejpam-6111	72	5	,	,	PUNCT
ejpam-6111	72	6	the	the	DET
ejpam-6111	72	7	interconnection	interconnection	NOUN
ejpam-6111	72	8	between	between	ADP
ejpam-6111	72	9	schur	schur	PROPN
ejpam-6111	72	10	stability	stability	NOUN
ejpam-6111	72	11	and	and	CCONJ
ejpam-6111	72	12	µ-values	µ-value	NOUN
ejpam-6111	72	13	were	be	AUX
ejpam-6111	72	14	analyzed	analyze	VERB
ejpam-6111	72	15	,	,	PUNCT
ejpam-6111	72	16	leading	lead	VERB
ejpam-6111	72	17	to	to	ADP
ejpam-6111	72	18	new	new	ADJ
ejpam-6111	72	19	results	result	NOUN
ejpam-6111	72	20	.	.	PUNCT
ejpam-6111	73	1	in	in	ADP
ejpam-6111	73	2	this	this	DET
ejpam-6111	73	3	article	article	NOUN
ejpam-6111	73	4	,	,	PUNCT
ejpam-6111	73	5	we	we	PRON
ejpam-6111	73	6	present	present	VERB
ejpam-6111	73	7	new	new	ADJ
ejpam-6111	73	8	results	result	NOUN
ejpam-6111	73	9	on	on	ADP
ejpam-6111	73	10	d	d	NOUN
ejpam-6111	73	11	-	-	NOUN
ejpam-6111	73	12	stability	stability	NOUN
ejpam-6111	73	13	,	,	PUNCT
ejpam-6111	73	14	and	and	CCONJ
ejpam-6111	73	15	strong	strong	ADJ
ejpam-6111	73	16	d	d	NOUN
ejpam-6111	73	17	-	-	NOUN
ejpam-6111	73	18	stability	stability	NOUN
ejpam-6111	73	19	for	for	ADP
ejpam-6111	73	20	the	the	DET
ejpam-6111	73	21	structured	structured	ADJ
ejpam-6111	73	22	matrix	matrix	NOUN
ejpam-6111	73	23	of	of	ADP
ejpam-6111	73	24	the	the	DET
ejpam-6111	73	25	form	form	NOUN
ejpam-6111	73	26	(	(	PUNCT
ejpam-6111	73	27	in	in	ADP
ejpam-6111	73	28	−a⊗p	−a⊗p	PROPN
ejpam-6111	73	29	t	t	PROPN
ejpam-6111	73	30	)	)	PUNCT
ejpam-6111	73	31	,	,	PUNCT
ejpam-6111	73	32	where	where	SCONJ
ejpam-6111	73	33	in	in	ADP
ejpam-6111	73	34	is	be	AUX
ejpam-6111	73	35	an	an	DET
ejpam-6111	73	36	n×n	n×n	PROPN
ejpam-6111	73	37	identity	identity	NOUN
ejpam-6111	73	38	matrix	matrix	NOUN
ejpam-6111	73	39	and	and	CCONJ
ejpam-6111	73	40	the	the	DET
ejpam-6111	73	41	matrices	matrix	NOUN
ejpam-6111	73	42	a	a	PRON
ejpam-6111	73	43	and	and	CCONJ
ejpam-6111	73	44	p	p	NOUN
ejpam-6111	73	45	are	be	AUX
ejpam-6111	73	46	from	from	ADP
ejpam-6111	73	47	the	the	DET
ejpam-6111	73	48	following	follow	VERB
ejpam-6111	73	49	lumped	lump	VERB
ejpam-6111	73	50	-	-	PUNCT
ejpam-6111	73	51	parameter	parameter	NOUN
ejpam-6111	73	52	dynamical	dynamical	ADJ
ejpam-6111	73	53	system	system	NOUN
ejpam-6111	73	54	{	{	PUNCT
ejpam-6111	73	55	x(t	x(t	PROPN
ejpam-6111	73	56	)	)	PUNCT
ejpam-6111	73	57	=	=	PUNCT
ejpam-6111	73	58	a	a	DET
ejpam-6111	73	59	x(t	x(t	PROPN
ejpam-6111	73	60	)	)	PUNCT
ejpam-6111	74	1	+	+	NOUN
ejpam-6111	74	2	b	b	NOUN
ejpam-6111	74	3	u(t	u(t	NOUN
ejpam-6111	74	4	)	)	PUNCT
ejpam-6111	74	5	,	,	PUNCT
ejpam-6111	74	6	x(0	x(0	PROPN
ejpam-6111	74	7	)	)	PUNCT
ejpam-6111	75	1	=	=	PUNCT
ejpam-6111	76	1	x0	x0	PROPN
ejpam-6111	76	2	y(t	y(t	NUM
ejpam-6111	76	3	)	)	PUNCT
ejpam-6111	77	1	=	=	SYM
ejpam-6111	77	2	c	c	NOUN
ejpam-6111	77	3	x(t	x(t	PROPN
ejpam-6111	77	4	)	)	PUNCT
ejpam-6111	78	1	+	+	ADP
ejpam-6111	78	2	d	d	NOUN
ejpam-6111	78	3	u(t	u(t	NOUN
ejpam-6111	78	4	)	)	PUNCT
ejpam-6111	78	5	.	.	PUNCT
ejpam-6111	79	1	we	we	PRON
ejpam-6111	79	2	use	use	VERB
ejpam-6111	79	3	an	an	DET
ejpam-6111	79	4	idea	idea	NOUN
ejpam-6111	79	5	of	of	ADP
ejpam-6111	79	6	interconnection	interconnection	NOUN
ejpam-6111	79	7	between	between	ADP
ejpam-6111	79	8	d	d	NOUN
ejpam-6111	79	9	-	-	NOUN
ejpam-6111	79	10	stability	stability	NOUN
ejpam-6111	79	11	and	and	CCONJ
ejpam-6111	79	12	µ-values	µ-value	VERB
ejpam-6111	79	13	to	to	PART
ejpam-6111	79	14	construct	construct	VERB
ejpam-6111	79	15	our	our	PRON
ejpam-6111	79	16	results	result	NOUN
ejpam-6111	79	17	.	.	PUNCT
ejpam-6111	80	1	for	for	ADP
ejpam-6111	80	2	d	d	NOUN
ejpam-6111	80	3	-	-	NOUN
ejpam-6111	80	4	stability	stability	NOUN
ejpam-6111	80	5	,	,	PUNCT
ejpam-6111	80	6	we	we	PRON
ejpam-6111	80	7	aim	aim	VERB
ejpam-6111	80	8	to	to	PART
ejpam-6111	80	9	show	show	VERB
ejpam-6111	80	10	that	that	SCONJ
ejpam-6111	80	11	a	a	DET
ejpam-6111	80	12	given	give	VERB
ejpam-6111	80	13	matrix	matrix	NOUN
ejpam-6111	80	14	is	be	AUX
ejpam-6111	80	15	d	d	NOUN
ejpam-6111	80	16	-	-	ADJ
ejpam-6111	80	17	stable	stable	ADJ
ejpam-6111	80	18	if	if	SCONJ
ejpam-6111	80	19	its	its	PRON
ejpam-6111	80	20	structured	structured	ADJ
ejpam-6111	80	21	singular	singular	ADJ
ejpam-6111	80	22	values	value	NOUN
ejpam-6111	80	23	belong	belong	VERB
ejpam-6111	80	24	to	to	ADP
ejpam-6111	80	25	[	[	X
ejpam-6111	80	26	0	0	NUM
ejpam-6111	80	27	,	,	PUNCT
ejpam-6111	80	28	1	1	NUM
ejpam-6111	80	29	)	)	PUNCT
ejpam-6111	80	30	.	.	PUNCT
ejpam-6111	81	1	overview	overview	NOUN
ejpam-6111	81	2	of	of	ADP
ejpam-6111	81	3	article	article	NOUN
ejpam-6111	81	4	:	:	PUNCT
ejpam-6111	81	5	in	in	ADP
ejpam-6111	81	6	section	section	NOUN
ejpam-6111	81	7	2	2	NUM
ejpam-6111	81	8	,	,	PUNCT
ejpam-6111	81	9	we	we	PRON
ejpam-6111	81	10	give	give	VERB
ejpam-6111	81	11	basic	basic	ADJ
ejpam-6111	81	12	concepts	concept	NOUN
ejpam-6111	81	13	,	,	PUNCT
ejpam-6111	81	14	definitions	definition	NOUN
ejpam-6111	81	15	,	,	PUNCT
ejpam-6111	81	16	and	and	CCONJ
ejpam-6111	81	17	observations	observation	NOUN
ejpam-6111	81	18	on	on	ADP
ejpam-6111	81	19	structured	structured	ADJ
ejpam-6111	81	20	singular	singular	ADJ
ejpam-6111	81	21	values	value	NOUN
ejpam-6111	81	22	,	,	PUNCT
ejpam-6111	81	23	d	d	NOUN
ejpam-6111	81	24	-	-	NOUN
ejpam-6111	81	25	stability	stability	NOUN
ejpam-6111	81	26	,	,	PUNCT
ejpam-6111	81	27	and	and	CCONJ
ejpam-6111	81	28	strong	strong	ADJ
ejpam-6111	81	29	d	d	NOUN
ejpam-6111	81	30	-	-	NOUN
ejpam-6111	81	31	stability	stability	NOUN
ejpam-6111	81	32	.	.	PUNCT
ejpam-6111	82	1	the	the	DET
ejpam-6111	82	2	problem	problem	NOUN
ejpam-6111	82	3	statement	statement	NOUN
ejpam-6111	82	4	is	be	AUX
ejpam-6111	82	5	formulated	formulate	VERB
ejpam-6111	82	6	in	in	ADP
ejpam-6111	82	7	section	section	NOUN
ejpam-6111	82	8	3	3	NUM
ejpam-6111	82	9	of	of	ADP
ejpam-6111	82	10	the	the	DET
ejpam-6111	82	11	article	article	NOUN
ejpam-6111	82	12	.	.	PUNCT
ejpam-6111	83	1	in	in	ADP
ejpam-6111	83	2	section	section	NOUN
ejpam-6111	83	3	4	4	NUM
ejpam-6111	83	4	,	,	PUNCT
ejpam-6111	83	5	we	we	PRON
ejpam-6111	83	6	recall	recall	VERB
ejpam-6111	83	7	sufficient	sufficient	ADJ
ejpam-6111	83	8	conditions	condition	NOUN
ejpam-6111	83	9	for	for	ADP
ejpam-6111	83	10	d	d	NOUN
ejpam-6111	83	11	-	-	NOUN
ejpam-6111	83	12	stability	stability	NOUN
ejpam-6111	83	13	and	and	CCONJ
ejpam-6111	83	14	strong	strong	ADJ
ejpam-6111	83	15	d	d	NOUN
ejpam-6111	83	16	-	-	NOUN
ejpam-6111	83	17	stability	stability	NOUN
ejpam-6111	83	18	of	of	ADP
ejpam-6111	83	19	an	an	DET
ejpam-6111	83	20	n	n	ADV
ejpam-6111	83	21	-	-	PUNCT
ejpam-6111	83	22	dimensional	dimensional	ADJ
ejpam-6111	83	23	real	real	ADV
ejpam-6111	83	24	-	-	PUNCT
ejpam-6111	83	25	valued	value	VERB
ejpam-6111	83	26	matrix	matrix	NOUN
ejpam-6111	83	27	.	.	PUNCT
ejpam-6111	84	1	we	we	PRON
ejpam-6111	84	2	provide	provide	VERB
ejpam-6111	84	3	new	new	ADJ
ejpam-6111	84	4	results	result	NOUN
ejpam-6111	84	5	for	for	ADP
ejpam-6111	84	6	d	d	NOUN
ejpam-6111	84	7	-	-	ADJ
ejpam-6111	84	8	stable	stable	ADJ
ejpam-6111	84	9	,	,	PUNCT
ejpam-6111	84	10	and	and	CCONJ
ejpam-6111	84	11	strong	strong	ADJ
ejpam-6111	84	12	d	d	ADJ
ejpam-6111	84	13	-	-	ADJ
ejpam-6111	84	14	stable	stable	ADJ
ejpam-6111	84	15	matrices	matrix	NOUN
ejpam-6111	84	16	in	in	ADP
ejpam-6111	84	17	section	section	NOUN
ejpam-6111	84	18	5	5	NUM
ejpam-6111	84	19	.	.	PUNCT
ejpam-6111	85	1	the	the	DET
ejpam-6111	85	2	main	main	ADJ
ejpam-6111	85	3	idea	idea	NOUN
ejpam-6111	85	4	to	to	PART
ejpam-6111	85	5	construct	construct	VERB
ejpam-6111	85	6	and	and	CCONJ
ejpam-6111	85	7	prove	prove	VERB
ejpam-6111	85	8	new	new	ADJ
ejpam-6111	85	9	results	result	NOUN
ejpam-6111	85	10	is	be	AUX
ejpam-6111	85	11	based	base	VERB
ejpam-6111	85	12	on	on	ADP
ejpam-6111	85	13	the	the	DET
ejpam-6111	85	14	computation	computation	NOUN
ejpam-6111	85	15	of	of	ADP
ejpam-6111	85	16	eigenvalues	eigenvalue	NOUN
ejpam-6111	85	17	,	,	PUNCT
ejpam-6111	85	18	singular	singular	ADJ
ejpam-6111	85	19	values	value	NOUN
ejpam-6111	85	20	and	and	CCONJ
ejpam-6111	85	21	structured	structure	VERB
ejpam-6111	85	22	singular	singular	ADJ
ejpam-6111	85	23	values	value	NOUN
ejpam-6111	85	24	and	and	CCONJ
ejpam-6111	85	25	their	their	PRON
ejpam-6111	85	26	interaction	interaction	NOUN
ejpam-6111	85	27	with	with	ADP
ejpam-6111	85	28	d	d	NOUN
ejpam-6111	85	29	-	-	NOUN
ejpam-6111	85	30	stability	stability	NOUN
ejpam-6111	85	31	and	and	CCONJ
ejpam-6111	85	32	strong	strong	ADJ
ejpam-6111	85	33	d	d	NOUN
ejpam-6111	85	34	-	-	NOUN
ejpam-6111	85	35	stability	stability	NOUN
ejpam-6111	85	36	.	.	PUNCT
ejpam-6111	86	1	numerical	numerical	ADJ
ejpam-6111	86	2	tests	test	NOUN
ejpam-6111	86	3	for	for	ADP
ejpam-6111	86	4	structured	structured	ADJ
ejpam-6111	86	5	matrices	matrix	NOUN
ejpam-6111	86	6	,	,	PUNCT
ejpam-6111	86	7	for	for	ADP
ejpam-6111	86	8	instance	instance	NOUN
ejpam-6111	86	9	,	,	PUNCT
ejpam-6111	86	10	haar	haar	PROPN
ejpam-6111	86	11	matrices	matrix	NOUN
ejpam-6111	86	12	and	and	CCONJ
ejpam-6111	86	13	haar	haar	PROPN
ejpam-6111	86	14	wavelet	wavelet	NOUN
ejpam-6111	86	15	operational	operational	ADJ
ejpam-6111	86	16	matrices	matrix	NOUN
ejpam-6111	86	17	,	,	PUNCT
ejpam-6111	86	18	are	be	AUX
ejpam-6111	86	19	presented	present	VERB
ejpam-6111	86	20	in	in	ADP
ejpam-6111	86	21	section	section	NOUN
ejpam-6111	86	22	6	6	NUM
ejpam-6111	86	23	,	,	PUNCT
ejpam-6111	86	24	and	and	CCONJ
ejpam-6111	86	25	finally	finally	ADV
ejpam-6111	86	26	we	we	PRON
ejpam-6111	86	27	conclude	conclude	VERB
ejpam-6111	86	28	in	in	ADP
ejpam-6111	86	29	section	section	NOUN
ejpam-6111	86	30	7	7	NUM
ejpam-6111	86	31	.	.	NOUN
ejpam-6111	86	32	2	2	NUM
ejpam-6111	86	33	.	.	NUM
ejpam-6111	86	34	preliminaries	preliminary	NOUN
ejpam-6111	86	35	in	in	ADP
ejpam-6111	86	36	this	this	DET
ejpam-6111	86	37	section	section	NOUN
ejpam-6111	86	38	,	,	PUNCT
ejpam-6111	86	39	we	we	PRON
ejpam-6111	86	40	recall	recall	VERB
ejpam-6111	86	41	the	the	DET
ejpam-6111	86	42	definitions	definition	NOUN
ejpam-6111	86	43	and	and	CCONJ
ejpam-6111	86	44	present	present	ADJ
ejpam-6111	86	45	well	well	ADV
ejpam-6111	86	46	-	-	PUNCT
ejpam-6111	86	47	known	know	VERB
ejpam-6111	86	48	results	result	NOUN
ejpam-6111	86	49	to	to	PART
ejpam-6111	86	50	provide	provide	VERB
ejpam-6111	86	51	a	a	DET
ejpam-6111	86	52	background	background	NOUN
ejpam-6111	86	53	on	on	ADP
ejpam-6111	86	54	d	d	NOUN
ejpam-6111	86	55	-	-	ADJ
ejpam-6111	86	56	stable	stable	ADJ
ejpam-6111	86	57	and	and	CCONJ
ejpam-6111	86	58	strong	strong	ADJ
ejpam-6111	86	59	d	d	ADJ
ejpam-6111	86	60	-	-	ADJ
ejpam-6111	86	61	stable	stable	ADJ
ejpam-6111	86	62	matrices	matrix	NOUN
ejpam-6111	86	63	and	and	CCONJ
ejpam-6111	86	64	the	the	DET
ejpam-6111	86	65	computation	computation	NOUN
ejpam-6111	86	66	of	of	ADP
ejpam-6111	86	67	µ-values	µ-value	NOUN
ejpam-6111	86	68	.	.	PUNCT
ejpam-6111	87	1	we	we	PRON
ejpam-6111	87	2	also	also	ADV
ejpam-6111	87	3	recall	recall	VERB
ejpam-6111	87	4	some	some	DET
ejpam-6111	87	5	existing	exist	VERB
ejpam-6111	87	6	and	and	CCONJ
ejpam-6111	87	7	fundamental	fundamental	ADJ
ejpam-6111	87	8	results	result	NOUN
ejpam-6111	87	9	on	on	ADP
ejpam-6111	87	10	the	the	DET
ejpam-6111	87	11	interconnections	interconnection	NOUN
ejpam-6111	87	12	between	between	ADP
ejpam-6111	87	13	d	d	NOUN
ejpam-6111	87	14	-	-	ADJ
ejpam-6111	87	15	stable	stable	ADJ
ejpam-6111	87	16	,	,	PUNCT
ejpam-6111	87	17	strong	strong	ADJ
ejpam-6111	87	18	d	d	ADJ
ejpam-6111	87	19	-	-	ADJ
ejpam-6111	87	20	stable	stable	ADJ
ejpam-6111	87	21	matrices	matrix	NOUN
ejpam-6111	87	22	and	and	CCONJ
ejpam-6111	87	23	structured	structure	VERB
ejpam-6111	87	24	singular	singular	ADJ
ejpam-6111	87	25	values	value	NOUN
ejpam-6111	87	26	.	.	PUNCT
ejpam-6111	88	1	in	in	ADP
ejpam-6111	88	2	the	the	DET
ejpam-6111	88	3	µ-theory	µ-theory	NOUN
ejpam-6111	88	4	the	the	DET
ejpam-6111	88	5	uncertainties	uncertainty	NOUN
ejpam-6111	88	6	across	across	ADP
ejpam-6111	88	7	the	the	DET
ejpam-6111	88	8	system	system	NOUN
ejpam-6111	88	9	are	be	AUX
ejpam-6111	88	10	presented	present	VERB
ejpam-6111	88	11	with	with	ADP
ejpam-6111	88	12	the	the	DET
ejpam-6111	88	13	set	set	NOUN
ejpam-6111	88	14	of	of	ADP
ejpam-6111	88	15	blockdiagonal	blockdiagonal	ADJ
ejpam-6111	88	16	matrices	matrix	NOUN
ejpam-6111	88	17	.	.	PUNCT
ejpam-6111	89	1	there	there	PRON
ejpam-6111	89	2	are	be	VERB
ejpam-6111	89	3	three	three	NUM
ejpam-6111	89	4	possible	possible	ADJ
ejpam-6111	89	5	types	type	NOUN
ejpam-6111	89	6	of	of	ADP
ejpam-6111	89	7	uncertainties	uncertainty	NOUN
ejpam-6111	89	8	,	,	PUNCT
ejpam-6111	89	9	that	that	ADV
ejpam-6111	89	10	is	is	ADV
ejpam-6111	89	11	,	,	PUNCT
ejpam-6111	89	12	repeated	repeat	VERB
ejpam-6111	89	13	real	real	ADJ
ejpam-6111	89	14	scalar	scalar	ADJ
ejpam-6111	89	15	blocks	block	NOUN
ejpam-6111	89	16	,	,	PUNCT
ejpam-6111	89	17	repeated	repeat	VERB
ejpam-6111	89	18	complex	complex	ADJ
ejpam-6111	89	19	scalar	scalar	ADJ
ejpam-6111	89	20	blocks	block	NOUN
ejpam-6111	89	21	,	,	PUNCT
ejpam-6111	89	22	and	and	CCONJ
ejpam-6111	89	23	real	real	ADJ
ejpam-6111	89	24	or	or	CCONJ
ejpam-6111	89	25	complex	complex	ADJ
ejpam-6111	89	26	full	full	ADJ
ejpam-6111	89	27	blocks	block	NOUN
ejpam-6111	89	28	.	.	PUNCT
ejpam-6111	90	1	the	the	DET
ejpam-6111	90	2	following	follow	VERB
ejpam-6111	90	3	definition	definition	NOUN
ejpam-6111	90	4	1	1	NUM
ejpam-6111	90	5	is	be	AUX
ejpam-6111	90	6	about	about	ADP
ejpam-6111	90	7	the	the	DET
ejpam-6111	90	8	set	set	NOUN
ejpam-6111	90	9	of	of	ADP
ejpam-6111	90	10	block	block	NOUN
ejpam-6111	90	11	-	-	PUNCT
ejpam-6111	90	12	diagonal	diagonal	ADJ
ejpam-6111	90	13	matrices	matrix	NOUN
ejpam-6111	90	14	.	.	PUNCT
ejpam-6111	91	1	s.	s.	PROPN
ejpam-6111	91	2	mazhar	mazhar	PROPN
ejpam-6111	91	3	,	,	PUNCT
ejpam-6111	91	4	m.	m.	NOUN
ejpam-6111	91	5	u.	u.	PROPN
ejpam-6111	91	6	rehman	rehman	PROPN
ejpam-6111	91	7	/	/	SYM
ejpam-6111	91	8	eur	eur	PROPN
ejpam-6111	91	9	.	.	PUNCT
ejpam-6111	92	1	j.	j.	PROPN
ejpam-6111	92	2	pure	pure	PROPN
ejpam-6111	92	3	appl	appl	PROPN
ejpam-6111	92	4	.	.	PROPN
ejpam-6111	92	5	math	math	PROPN
ejpam-6111	92	6	,	,	PUNCT
ejpam-6111	92	7	18	18	NUM
ejpam-6111	92	8	(	(	PUNCT
ejpam-6111	92	9	2	2	NUM
ejpam-6111	92	10	)	)	PUNCT
ejpam-6111	92	11	(	(	PUNCT
ejpam-6111	92	12	2025	2025	NUM
ejpam-6111	92	13	)	)	PUNCT
ejpam-6111	92	14	,	,	PUNCT
ejpam-6111	92	15	6111	6111	NUM
ejpam-6111	92	16	4	4	NUM
ejpam-6111	92	17	of	of	ADP
ejpam-6111	92	18	25	25	NUM
ejpam-6111	92	19	definition	definition	NOUN
ejpam-6111	92	20	1	1	NUM
ejpam-6111	92	21	.	.	PUNCT
ejpam-6111	93	1	the	the	DET
ejpam-6111	93	2	set	set	NOUN
ejpam-6111	93	3	b1	b1	NOUN
ejpam-6111	93	4	is	be	AUX
ejpam-6111	93	5	the	the	DET
ejpam-6111	93	6	set	set	NOUN
ejpam-6111	93	7	of	of	ADP
ejpam-6111	93	8	block	block	NOUN
ejpam-6111	93	9	-	-	PUNCT
ejpam-6111	93	10	diagonal	diagonal	ADJ
ejpam-6111	93	11	matrices	matrix	NOUN
ejpam-6111	93	12	and	and	CCONJ
ejpam-6111	93	13	is	be	AUX
ejpam-6111	93	14	defined	define	VERB
ejpam-6111	93	15	as	as	ADP
ejpam-6111	93	16	b1	b1	NOUN
ejpam-6111	93	17	:	:	PUNCT
ejpam-6111	93	18	=	=	SYM
ejpam-6111	93	19	{	{	PUNCT
ejpam-6111	93	20	diag	diag	X
ejpam-6111	93	21	(	(	PUNCT
ejpam-6111	93	22	δ1ir1	δ1ir1	ADJ
ejpam-6111	93	23	,	,	PUNCT
ejpam-6111	93	24	δ2ir2	δ2ir2	NOUN
ejpam-6111	93	25	,	,	PUNCT
ejpam-6111	93	26	·	·	PUNCT
ejpam-6111	93	27	·	·	PUNCT
ejpam-6111	93	28	·	·	PUNCT
ejpam-6111	93	29	,	,	PUNCT
ejpam-6111	93	30	δsirs	δsir	NOUN
ejpam-6111	93	31	;	;	PUNCT
ejpam-6111	93	32	∆1,∆2	∆1,∆2	NOUN
ejpam-6111	93	33	,	,	PUNCT
ejpam-6111	93	34	·	·	PUNCT
ejpam-6111	93	35	·	·	PUNCT
ejpam-6111	93	36	·	·	PUNCT
ejpam-6111	93	37	,	,	PUNCT
ejpam-6111	93	38	∆f	∆f	PROPN
ejpam-6111	93	39	)	)	PUNCT
ejpam-6111	93	40	:	:	PUNCT
ejpam-6111	93	41	δi	δi	ADP
ejpam-6111	93	42	∈	∈	PROPN
ejpam-6111	93	43	k	k	PROPN
ejpam-6111	93	44	,	,	PUNCT
ejpam-6111	93	45	∆j	∆j	PROPN
ejpam-6111	93	46	∈	∈	PROPN
ejpam-6111	93	47	kmj	kmj	NOUN
ejpam-6111	93	48	,	,	PUNCT
ejpam-6111	93	49	mj	mj	INTJ
ejpam-6111	93	50	,	,	PUNCT
ejpam-6111	93	51	i	i	PRON
ejpam-6111	93	52	=	=	NOUN
ejpam-6111	93	53	1	1	NUM
ejpam-6111	93	54	:	:	SYM
ejpam-6111	93	55	s	s	X
ejpam-6111	93	56	,	,	PUNCT
ejpam-6111	93	57	j	j	PROPN
ejpam-6111	93	58	=	=	SYM
ejpam-6111	93	59	1	1	NUM
ejpam-6111	93	60	:	:	SYM
ejpam-6111	93	61	f	f	X
ejpam-6111	93	62	}	}	PUNCT
ejpam-6111	93	63	,	,	PUNCT
ejpam-6111	93	64	where	where	SCONJ
ejpam-6111	93	65	k	k	PROPN
ejpam-6111	93	66	=	=	SYM
ejpam-6111	93	67	r	r	NOUN
ejpam-6111	93	68	or	or	CCONJ
ejpam-6111	93	69	c.	c.	NOUN
ejpam-6111	93	70	the	the	DET
ejpam-6111	93	71	computation	computation	NOUN
ejpam-6111	93	72	of	of	ADP
ejpam-6111	93	73	structured	structured	ADJ
ejpam-6111	93	74	singular	singular	ADJ
ejpam-6111	93	75	values	value	NOUN
ejpam-6111	93	76	or	or	CCONJ
ejpam-6111	93	77	µ-values	µ-value	NOUN
ejpam-6111	93	78	involve	involve	VERB
ejpam-6111	93	79	the	the	DET
ejpam-6111	93	80	computation	computation	NOUN
ejpam-6111	93	81	of	of	ADP
ejpam-6111	93	82	eigenvalues	eigenvalue	NOUN
ejpam-6111	93	83	and	and	CCONJ
ejpam-6111	93	84	singular	singular	ADJ
ejpam-6111	93	85	values	value	NOUN
ejpam-6111	93	86	.	.	PUNCT
ejpam-6111	94	1	it	it	PRON
ejpam-6111	94	2	demands	demand	VERB
ejpam-6111	94	3	the	the	DET
ejpam-6111	94	4	computation	computation	NOUN
ejpam-6111	94	5	of	of	ADP
ejpam-6111	94	6	the	the	DET
ejpam-6111	94	7	largest	large	ADJ
ejpam-6111	94	8	singular	singular	ADJ
ejpam-6111	94	9	value	value	NOUN
ejpam-6111	94	10	of	of	ADP
ejpam-6111	94	11	an	an	DET
ejpam-6111	94	12	admissible	admissible	ADJ
ejpam-6111	94	13	perturbation	perturbation	NOUN
ejpam-6111	94	14	∆	∆	PUNCT
ejpam-6111	94	15	from	from	ADP
ejpam-6111	94	16	the	the	DET
ejpam-6111	94	17	set	set	NOUN
ejpam-6111	94	18	of	of	ADP
ejpam-6111	94	19	block	block	NOUN
ejpam-6111	94	20	-	-	PUNCT
ejpam-6111	94	21	diagonal	diagonal	ADJ
ejpam-6111	94	22	matrices	matrix	NOUN
ejpam-6111	94	23	such	such	ADJ
ejpam-6111	94	24	that	that	SCONJ
ejpam-6111	94	25	the	the	DET
ejpam-6111	94	26	modified	modify	VERB
ejpam-6111	94	27	matrix	matrix	NOUN
ejpam-6111	94	28	i	i	PRON
ejpam-6111	94	29	−	−	PROPN
ejpam-6111	94	30	m∆	m∆	ADJ
ejpam-6111	94	31	for	for	ADP
ejpam-6111	94	32	a	a	DET
ejpam-6111	94	33	given	give	VERB
ejpam-6111	94	34	system	system	NOUN
ejpam-6111	94	35	matrix	matrix	NOUN
ejpam-6111	94	36	m	m	VERB
ejpam-6111	94	37	has	have	AUX
ejpam-6111	94	38	atleast	atleast	VERB
ejpam-6111	94	39	one	one	NUM
ejpam-6111	94	40	of	of	ADP
ejpam-6111	94	41	its	its	PRON
ejpam-6111	94	42	eigenvalue	eigenvalue	NOUN
ejpam-6111	94	43	to	to	PART
ejpam-6111	94	44	be	be	AUX
ejpam-6111	94	45	exactly	exactly	ADV
ejpam-6111	94	46	equal	equal	ADJ
ejpam-6111	94	47	to	to	ADP
ejpam-6111	94	48	zero	zero	NUM
ejpam-6111	94	49	.	.	PUNCT
ejpam-6111	95	1	the	the	DET
ejpam-6111	95	2	following	follow	VERB
ejpam-6111	95	3	is	be	AUX
ejpam-6111	95	4	the	the	DET
ejpam-6111	95	5	definition	definition	NOUN
ejpam-6111	95	6	of	of	ADP
ejpam-6111	95	7	µ-value	µ-value	NOUN
ejpam-6111	95	8	for	for	ADP
ejpam-6111	95	9	a	a	DET
ejpam-6111	95	10	given	give	VERB
ejpam-6111	95	11	m	m	PRON
ejpam-6111	95	12	with	with	ADP
ejpam-6111	95	13	respect	respect	NOUN
ejpam-6111	95	14	to	to	ADP
ejpam-6111	95	15	set	set	NOUN
ejpam-6111	95	16	of	of	ADP
ejpam-6111	95	17	block	block	NOUN
ejpam-6111	95	18	-	-	PUNCT
ejpam-6111	95	19	diagonal	diagonal	ADJ
ejpam-6111	95	20	matrices	matrix	NOUN
ejpam-6111	95	21	b1	b1	NOUN
ejpam-6111	95	22	.	.	PUNCT
ejpam-6111	96	1	definition	definition	NOUN
ejpam-6111	96	2	2	2	NUM
ejpam-6111	96	3	.	.	PUNCT
ejpam-6111	97	1	[	[	X
ejpam-6111	97	2	15	15	NUM
ejpam-6111	97	3	]	]	X
ejpam-6111	97	4	for	for	ADP
ejpam-6111	97	5	a	a	DET
ejpam-6111	97	6	given	give	VERB
ejpam-6111	97	7	m	m	PRON
ejpam-6111	97	8	∈	∈	PROPN
ejpam-6111	97	9	cn	cn	PROPN
ejpam-6111	97	10	,	,	PUNCT
ejpam-6111	97	11	n	n	CCONJ
ejpam-6111	97	12	,	,	PUNCT
ejpam-6111	97	13	the	the	DET
ejpam-6111	97	14	structured	structured	ADJ
ejpam-6111	97	15	singular	singular	ADJ
ejpam-6111	97	16	value	value	NOUN
ejpam-6111	97	17	is	be	AUX
ejpam-6111	97	18	denoted	denote	VERB
ejpam-6111	97	19	by	by	ADP
ejpam-6111	97	20	µb1(m	µb1(m	PROPN
ejpam-6111	97	21	)	)	PUNCT
ejpam-6111	97	22	and	and	CCONJ
ejpam-6111	97	23	is	be	AUX
ejpam-6111	97	24	defined	define	VERB
ejpam-6111	97	25	by	by	ADP
ejpam-6111	97	26	µb1(m	µb1(m	PROPN
ejpam-6111	97	27	)	)	PUNCT
ejpam-6111	97	28	:	:	PUNCT
ejpam-6111	97	29	=	=	SYM
ejpam-6111	97	30	{	{	PUNCT
ejpam-6111	97	31	0	0	NUM
ejpam-6111	97	32	,	,	PUNCT
ejpam-6111	97	33	if	if	SCONJ
ejpam-6111	97	34	det(i	det(i	PROPN
ejpam-6111	97	35	−m∆	−m∆	AUX
ejpam-6111	97	36	)	)	PUNCT
ejpam-6111	97	37	̸=	̸=	PROPN
ejpam-6111	97	38	0	0	NUM
ejpam-6111	97	39	,	,	PUNCT
ejpam-6111	97	40	∀∆	∀∆	NOUN
ejpam-6111	97	41	∈	∈	PROPN
ejpam-6111	97	42	b1	b1	NOUN
ejpam-6111	97	43	(	(	PUNCT
ejpam-6111	97	44	min{||∆||2	min{||∆||2	NOUN
ejpam-6111	97	45	:	:	PUNCT
ejpam-6111	97	46	det(i	det(i	PROPN
ejpam-6111	97	47	−m∆	−m∆	ADJ
ejpam-6111	97	48	)	)	PUNCT
ejpam-6111	97	49	=	=	SYM
ejpam-6111	97	50	0	0	NUM
ejpam-6111	97	51	,	,	PUNCT
ejpam-6111	97	52	∀∆	∀∆	NOUN
ejpam-6111	97	53	∈	∈	PROPN
ejpam-6111	97	54	b1	b1	PROPN
ejpam-6111	97	55	}	}	PUNCT
ejpam-6111	97	56	)	)	PUNCT
ejpam-6111	97	57	,	,	PUNCT
ejpam-6111	97	58	−1	−1	NOUN
ejpam-6111	97	59	else	else	ADV
ejpam-6111	97	60	where	where	SCONJ
ejpam-6111	97	61	min	min	NOUN
ejpam-6111	97	62	is	be	AUX
ejpam-6111	97	63	taken	take	VERB
ejpam-6111	97	64	over	over	ADP
ejpam-6111	97	65	all	all	DET
ejpam-6111	97	66	∆	∆	PROPN
ejpam-6111	97	67	∈	∈	PROPN
ejpam-6111	97	68	b1	b1	NOUN
ejpam-6111	97	69	.	.	PUNCT
ejpam-6111	98	1	remark	remark	PROPN
ejpam-6111	98	2	1	1	NUM
ejpam-6111	98	3	.	.	PUNCT
ejpam-6111	99	1	[	[	X
ejpam-6111	99	2	15	15	NUM
ejpam-6111	99	3	]	]	PUNCT
ejpam-6111	99	4	the	the	DET
ejpam-6111	99	5	set	set	NOUN
ejpam-6111	99	6	b1	b1	NOUN
ejpam-6111	99	7	represents	represent	VERB
ejpam-6111	99	8	a	a	DET
ejpam-6111	99	9	multi	multi	ADJ
ejpam-6111	99	10	-	-	NOUN
ejpam-6111	99	11	index	index	NOUN
ejpam-6111	99	12	of	of	ADP
ejpam-6111	99	13	integers	integer	NOUN
ejpam-6111	99	14	.	.	PUNCT
ejpam-6111	100	1	hence	hence	ADV
ejpam-6111	100	2	,	,	PUNCT
ejpam-6111	100	3	it	it	PRON
ejpam-6111	100	4	does	do	AUX
ejpam-6111	100	5	make	make	VERB
ejpam-6111	100	6	sense	sense	NOUN
ejpam-6111	100	7	to	to	PART
ejpam-6111	100	8	identify	identify	VERB
ejpam-6111	100	9	as	as	ADP
ejpam-6111	100	10	one	one	NUM
ejpam-6111	100	11	of	of	ADP
ejpam-6111	100	12	the	the	DET
ejpam-6111	100	13	valid	valid	ADJ
ejpam-6111	100	14	candidate	candidate	NOUN
ejpam-6111	100	15	from	from	ADP
ejpam-6111	100	16	the	the	DET
ejpam-6111	100	17	set	set	NOUN
ejpam-6111	100	18	.	.	PUNCT
ejpam-6111	101	1	this	this	PRON
ejpam-6111	101	2	implies	imply	VERB
ejpam-6111	101	3	that	that	SCONJ
ejpam-6111	101	4	the	the	DET
ejpam-6111	101	5	computation	computation	NOUN
ejpam-6111	101	6	of	of	ADP
ejpam-6111	101	7	µ-value	µ-value	NOUN
ejpam-6111	101	8	depends	depend	VERB
ejpam-6111	101	9	on	on	ADP
ejpam-6111	101	10	a	a	DET
ejpam-6111	101	11	given	give	VERB
ejpam-6111	101	12	matrix	matrix	NOUN
ejpam-6111	101	13	and	and	CCONJ
ejpam-6111	101	14	the	the	DET
ejpam-6111	101	15	set	set	NOUN
ejpam-6111	101	16	of	of	ADP
ejpam-6111	101	17	block	block	NOUN
ejpam-6111	101	18	-	-	PUNCT
ejpam-6111	101	19	diagonal	diagonal	ADJ
ejpam-6111	101	20	matrices	matrix	NOUN
ejpam-6111	101	21	.	.	PUNCT
ejpam-6111	102	1	remark	remark	NOUN
ejpam-6111	102	2	2	2	NUM
ejpam-6111	102	3	.	.	PUNCT
ejpam-6111	103	1	[	[	X
ejpam-6111	103	2	15	15	NUM
ejpam-6111	103	3	]	]	PUNCT
ejpam-6111	103	4	in	in	ADP
ejpam-6111	103	5	the	the	DET
ejpam-6111	103	6	set	set	NOUN
ejpam-6111	103	7	b1	b1	NOUN
ejpam-6111	103	8	,	,	PUNCT
ejpam-6111	103	9	the	the	DET
ejpam-6111	103	10	full	full	ADJ
ejpam-6111	103	11	blocks	block	NOUN
ejpam-6111	103	12	can	can	AUX
ejpam-6111	103	13	be	be	AUX
ejpam-6111	103	14	taken	take	VERB
ejpam-6111	103	15	as	as	ADP
ejpam-6111	103	16	the	the	DET
ejpam-6111	103	17	rank-1	rank-1	NUM
ejpam-6111	103	18	matrices	matrix	NOUN
ejpam-6111	103	19	,	,	PUNCT
ejpam-6111	103	20	that	that	ADV
ejpam-6111	103	21	is	be	AUX
ejpam-6111	103	22	,	,	PUNCT
ejpam-6111	103	23	dyads	dyad	NOUN
ejpam-6111	103	24	.	.	PUNCT
ejpam-6111	104	1	remark	remark	PROPN
ejpam-6111	104	2	3	3	NUM
ejpam-6111	104	3	.	.	PUNCT
ejpam-6111	105	1	[	[	X
ejpam-6111	105	2	15	15	NUM
ejpam-6111	105	3	]	]	PUNCT
ejpam-6111	105	4	from	from	ADP
ejpam-6111	105	5	the	the	DET
ejpam-6111	105	6	definition	definition	NOUN
ejpam-6111	105	7	of	of	ADP
ejpam-6111	105	8	µ-value	µ-value	PROPN
ejpam-6111	105	9	,	,	PUNCT
ejpam-6111	105	10	one	one	PRON
ejpam-6111	105	11	can	can	AUX
ejpam-6111	105	12	easily	easily	ADV
ejpam-6111	105	13	verify	verify	VERB
ejpam-6111	105	14	that	that	SCONJ
ejpam-6111	105	15	for	for	ADP
ejpam-6111	105	16	any	any	DET
ejpam-6111	105	17	α	α	NOUN
ejpam-6111	105	18	∈	∈	ADJ
ejpam-6111	105	19	c	c	X
ejpam-6111	105	20	,	,	PUNCT
ejpam-6111	105	21	we	we	PRON
ejpam-6111	105	22	have	have	VERB
ejpam-6111	105	23	that	that	PRON
ejpam-6111	105	24	µb1(αm	µb1(αm	X
ejpam-6111	105	25	)	)	PUNCT
ejpam-6111	105	26	=	=	PUNCT
ejpam-6111	105	27	αµb1(m	αµb1(m	NUM
ejpam-6111	105	28	)	)	PUNCT
ejpam-6111	105	29	.	.	PUNCT
ejpam-6111	106	1	an	an	DET
ejpam-6111	106	2	alternative	alternative	ADJ
ejpam-6111	106	3	expression	expression	NOUN
ejpam-6111	106	4	for	for	ADP
ejpam-6111	106	5	the	the	DET
ejpam-6111	106	6	computation	computation	NOUN
ejpam-6111	106	7	of	of	ADP
ejpam-6111	106	8	µb1(m	µb1(m	PROPN
ejpam-6111	106	9	)	)	PUNCT
ejpam-6111	106	10	can	can	AUX
ejpam-6111	106	11	be	be	AUX
ejpam-6111	106	12	followed	follow	VERB
ejpam-6111	106	13	from	from	ADP
ejpam-6111	106	14	the	the	DET
ejpam-6111	106	15	following	follow	VERB
ejpam-6111	106	16	lemma	lemma	PROPN
ejpam-6111	106	17	1	1	NUM
ejpam-6111	106	18	.	.	PUNCT
ejpam-6111	107	1	lemma	lemma	PROPN
ejpam-6111	107	2	1	1	NUM
ejpam-6111	107	3	.	.	PUNCT
ejpam-6111	108	1	[	[	X
ejpam-6111	108	2	15	15	NUM
ejpam-6111	108	3	]	]	PUNCT
ejpam-6111	108	4	for	for	ADP
ejpam-6111	108	5	given	give	VERB
ejpam-6111	108	6	m	m	PRON
ejpam-6111	108	7	∈	∈	PROPN
ejpam-6111	108	8	cn	cn	PROPN
ejpam-6111	108	9	,	,	PUNCT
ejpam-6111	108	10	n	n	PROPN
ejpam-6111	108	11	and	and	CCONJ
ejpam-6111	108	12	for	for	ADP
ejpam-6111	108	13	all	all	DET
ejpam-6111	108	14	∆	∆	CCONJ
ejpam-6111	108	15	∈	∈	PROPN
ejpam-6111	108	16	b1	b1	NOUN
ejpam-6111	108	17	,	,	PUNCT
ejpam-6111	108	18	we	we	PRON
ejpam-6111	108	19	have	have	VERB
ejpam-6111	108	20	µb1(m	µb1(m	PROPN
ejpam-6111	108	21	)	)	PUNCT
ejpam-6111	108	22	=	=	SYM
ejpam-6111	108	23	max	max	PROPN
ejpam-6111	108	24	ρ(∆m	ρ(∆m	PROPN
ejpam-6111	108	25	)	)	PUNCT
ejpam-6111	108	26	,	,	PUNCT
ejpam-6111	108	27	where	where	SCONJ
ejpam-6111	108	28	ρ	ρ	PROPN
ejpam-6111	108	29	(	(	PUNCT
ejpam-6111	108	30	·	·	PUNCT
ejpam-6111	108	31	)	)	PUNCT
ejpam-6111	108	32	denotes	denote	VERB
ejpam-6111	108	33	the	the	DET
ejpam-6111	108	34	spectral	spectral	ADJ
ejpam-6111	108	35	radius	radius	NOUN
ejpam-6111	108	36	of	of	ADP
ejpam-6111	108	37	a	a	DET
ejpam-6111	108	38	matrix	matrix	NOUN
ejpam-6111	108	39	,	,	PUNCT
ejpam-6111	108	40	and	and	CCONJ
ejpam-6111	108	41	max	max	PROPN
ejpam-6111	108	42	is	be	AUX
ejpam-6111	108	43	taken	take	VERB
ejpam-6111	108	44	over	over	ADP
ejpam-6111	108	45	all	all	DET
ejpam-6111	108	46	∆	∆	PROPN
ejpam-6111	108	47	∈	∈	PROPN
ejpam-6111	108	48	b1	b1	NOUN
ejpam-6111	108	49	.	.	PUNCT
ejpam-6111	109	1	the	the	DET
ejpam-6111	109	2	concept	concept	NOUN
ejpam-6111	109	3	of	of	ADP
ejpam-6111	109	4	d	d	NOUN
ejpam-6111	109	5	-	-	NOUN
ejpam-6111	109	6	stability	stability	NOUN
ejpam-6111	109	7	or	or	CCONJ
ejpam-6111	109	8	some	some	DET
ejpam-6111	109	9	time	time	NOUN
ejpam-6111	109	10	known	know	VERB
ejpam-6111	109	11	as	as	ADP
ejpam-6111	109	12	diagonal	diagonal	ADJ
ejpam-6111	109	13	stability	stability	NOUN
ejpam-6111	109	14	in	in	ADP
ejpam-6111	109	15	the	the	DET
ejpam-6111	109	16	literature	literature	NOUN
ejpam-6111	109	17	,	,	PUNCT
ejpam-6111	109	18	of	of	ADP
ejpam-6111	109	19	a	a	DET
ejpam-6111	109	20	given	give	VERB
ejpam-6111	109	21	matrix	matrix	NOUN
ejpam-6111	109	22	is	be	AUX
ejpam-6111	109	23	a	a	DET
ejpam-6111	109	24	play	play	NOUN
ejpam-6111	109	25	an	an	DET
ejpam-6111	109	26	important	important	ADJ
ejpam-6111	109	27	and	and	CCONJ
ejpam-6111	109	28	role	role	NOUN
ejpam-6111	109	29	in	in	ADP
ejpam-6111	109	30	matrix	matrix	NOUN
ejpam-6111	109	31	theory	theory	NOUN
ejpam-6111	109	32	and	and	CCONJ
ejpam-6111	109	33	control	control	NOUN
ejpam-6111	109	34	theory	theory	NOUN
ejpam-6111	109	35	,	,	PUNCT
ejpam-6111	109	36	particularly	particularly	ADV
ejpam-6111	109	37	when	when	SCONJ
ejpam-6111	109	38	analyzing	analyze	VERB
ejpam-6111	109	39	the	the	DET
ejpam-6111	109	40	stability	stability	NOUN
ejpam-6111	109	41	of	of	ADP
ejpam-6111	109	42	linear	linear	ADJ
ejpam-6111	109	43	time	time	NOUN
ejpam-6111	109	44	invariant	invariant	ADJ
ejpam-6111	109	45	dynamical	dynamical	ADJ
ejpam-6111	109	46	systems	system	NOUN
ejpam-6111	109	47	.	.	PUNCT
ejpam-6111	110	1	definition	definition	NOUN
ejpam-6111	110	2	3	3	NUM
ejpam-6111	110	3	.	.	PUNCT
ejpam-6111	111	1	[	[	X
ejpam-6111	111	2	34	34	NUM
ejpam-6111	111	3	]	]	X
ejpam-6111	111	4	a	a	DET
ejpam-6111	111	5	given	give	VERB
ejpam-6111	111	6	n	n	CCONJ
ejpam-6111	111	7	-	-	PUNCT
ejpam-6111	111	8	dimensional	dimensional	ADJ
ejpam-6111	111	9	matrix	matrix	NOUN
ejpam-6111	111	10	m	m	NOUN
ejpam-6111	111	11	is	be	AUX
ejpam-6111	111	12	said	say	VERB
ejpam-6111	111	13	to	to	PART
ejpam-6111	111	14	be	be	AUX
ejpam-6111	111	15	a	a	DET
ejpam-6111	111	16	d	d	ADJ
ejpam-6111	111	17	-	-	ADJ
ejpam-6111	111	18	stable	stable	ADJ
ejpam-6111	111	19	matrix	matrix	NOUN
ejpam-6111	111	20	if	if	SCONJ
ejpam-6111	111	21	for	for	ADP
ejpam-6111	111	22	every	every	DET
ejpam-6111	111	23	positive	positive	ADJ
ejpam-6111	111	24	diagonal	diagonal	ADJ
ejpam-6111	111	25	matrix	matrix	NOUN
ejpam-6111	111	26	d	d	NOUN
ejpam-6111	111	27	,	,	PUNCT
ejpam-6111	111	28	the	the	DET
ejpam-6111	111	29	matrix	matrix	NOUN
ejpam-6111	111	30	product	product	NOUN
ejpam-6111	111	31	dm	dm	PROPN
ejpam-6111	111	32	or	or	CCONJ
ejpam-6111	111	33	md	md	PROPN
ejpam-6111	111	34	has	have	VERB
ejpam-6111	111	35	all	all	PRON
ejpam-6111	111	36	of	of	ADP
ejpam-6111	111	37	its	its	PRON
ejpam-6111	111	38	eigenvalues	eigenvalue	NOUN
ejpam-6111	111	39	in	in	ADP
ejpam-6111	111	40	the	the	DET
ejpam-6111	111	41	left	left	ADJ
ejpam-6111	111	42	half	half	NOUN
ejpam-6111	111	43	of	of	ADP
ejpam-6111	111	44	the	the	DET
ejpam-6111	111	45	complex	complex	ADJ
ejpam-6111	111	46	plane	plane	NOUN
ejpam-6111	111	47	.	.	PUNCT
ejpam-6111	112	1	remark	remark	PROPN
ejpam-6111	112	2	4	4	NUM
ejpam-6111	112	3	.	.	PUNCT
ejpam-6111	113	1	the	the	DET
ejpam-6111	113	2	matrix	matrix	NOUN
ejpam-6111	113	3	products	product	NOUN
ejpam-6111	113	4	dm	dm	PROPN
ejpam-6111	113	5	and	and	CCONJ
ejpam-6111	113	6	md	md	PROPN
ejpam-6111	113	7	are	be	AUX
ejpam-6111	113	8	the	the	DET
ejpam-6111	113	9	similar	similar	ADJ
ejpam-6111	113	10	matrices	matrix	NOUN
ejpam-6111	113	11	and	and	CCONJ
ejpam-6111	113	12	their	their	PRON
ejpam-6111	113	13	dstability	dstability	NOUN
ejpam-6111	113	14	remains	remain	VERB
ejpam-6111	113	15	preserved	preserve	VERB
ejpam-6111	113	16	under	under	ADP
ejpam-6111	113	17	perturbations	perturbation	NOUN
ejpam-6111	113	18	subject	subject	ADJ
ejpam-6111	113	19	to	to	ADP
ejpam-6111	113	20	both	both	DET
ejpam-6111	113	21	rows	row	NOUN
ejpam-6111	113	22	and	and	CCONJ
ejpam-6111	113	23	columns	column	NOUN
ejpam-6111	113	24	.	.	PUNCT
ejpam-6111	114	1	s.	s.	PROPN
ejpam-6111	114	2	mazhar	mazhar	PROPN
ejpam-6111	114	3	,	,	PUNCT
ejpam-6111	114	4	m.	m.	NOUN
ejpam-6111	114	5	u.	u.	PROPN
ejpam-6111	114	6	rehman	rehman	PROPN
ejpam-6111	114	7	/	/	SYM
ejpam-6111	114	8	eur	eur	PROPN
ejpam-6111	114	9	.	.	PUNCT
ejpam-6111	115	1	j.	j.	PROPN
ejpam-6111	115	2	pure	pure	PROPN
ejpam-6111	115	3	appl	appl	PROPN
ejpam-6111	115	4	.	.	PROPN
ejpam-6111	115	5	math	math	PROPN
ejpam-6111	115	6	,	,	PUNCT
ejpam-6111	115	7	18	18	NUM
ejpam-6111	115	8	(	(	PUNCT
ejpam-6111	115	9	2	2	NUM
ejpam-6111	115	10	)	)	PUNCT
ejpam-6111	115	11	(	(	PUNCT
ejpam-6111	115	12	2025	2025	NUM
ejpam-6111	115	13	)	)	PUNCT
ejpam-6111	115	14	,	,	PUNCT
ejpam-6111	115	15	6111	6111	NUM
ejpam-6111	115	16	5	5	NUM
ejpam-6111	115	17	of	of	ADP
ejpam-6111	115	18	25	25	NUM
ejpam-6111	115	19	the	the	DET
ejpam-6111	115	20	following	follow	VERB
ejpam-6111	115	21	four	four	NUM
ejpam-6111	115	22	observations	observation	NOUN
ejpam-6111	115	23	given	give	VERB
ejpam-6111	115	24	in	in	ADP
ejpam-6111	115	25	[	[	PUNCT
ejpam-6111	115	26	34	34	NUM
ejpam-6111	115	27	]	]	PUNCT
ejpam-6111	115	28	holds	hold	VERB
ejpam-6111	115	29	true	true	ADJ
ejpam-6111	115	30	for	for	ADP
ejpam-6111	115	31	d	d	NOUN
ejpam-6111	115	32	-	-	ADJ
ejpam-6111	115	33	stable	stable	ADJ
ejpam-6111	115	34	matrices	matrix	NOUN
ejpam-6111	115	35	.	.	PUNCT
ejpam-6111	116	1	observation	observation	NOUN
ejpam-6111	116	2	1	1	NUM
ejpam-6111	116	3	.	.	PUNCT
ejpam-6111	117	1	the	the	DET
ejpam-6111	117	2	condition	condition	NOUN
ejpam-6111	117	3	which	which	PRON
ejpam-6111	117	4	holds	hold	VERB
ejpam-6111	117	5	true	true	ADJ
ejpam-6111	117	6	for	for	ADP
ejpam-6111	117	7	matrices	matrix	NOUN
ejpam-6111	117	8	under	under	ADP
ejpam-6111	117	9	consideration	consideration	NOUN
ejpam-6111	117	10	that	that	SCONJ
ejpam-6111	117	11	implying	imply	VERB
ejpam-6111	117	12	stability	stability	NOUN
ejpam-6111	117	13	and	and	CCONJ
ejpam-6111	117	14	remains	remain	VERB
ejpam-6111	117	15	preserved	preserve	VERB
ejpam-6111	117	16	under	under	ADP
ejpam-6111	117	17	positive	positive	ADJ
ejpam-6111	117	18	diagonal	diagonal	ADJ
ejpam-6111	117	19	multiplication	multiplication	NOUN
ejpam-6111	117	20	is	be	AUX
ejpam-6111	117	21	a	a	DET
ejpam-6111	117	22	sufficient	sufficient	ADJ
ejpam-6111	117	23	condition	condition	NOUN
ejpam-6111	117	24	for	for	ADP
ejpam-6111	117	25	d	d	NOUN
ejpam-6111	117	26	-	-	NOUN
ejpam-6111	117	27	stability	stability	NOUN
ejpam-6111	117	28	of	of	ADP
ejpam-6111	117	29	matrices	matrix	NOUN
ejpam-6111	117	30	.	.	PUNCT
ejpam-6111	118	1	observation	observation	NOUN
ejpam-6111	118	2	2	2	NUM
ejpam-6111	118	3	.	.	PUNCT
ejpam-6111	119	1	if	if	SCONJ
ejpam-6111	119	2	given	give	VERB
ejpam-6111	119	3	m	m	PRON
ejpam-6111	119	4	∈	∈	PROPN
ejpam-6111	119	5	cn	cn	PROPN
ejpam-6111	119	6	,	,	PUNCT
ejpam-6111	119	7	n	n	PRON
ejpam-6111	119	8	such	such	ADJ
ejpam-6111	119	9	that	that	SCONJ
ejpam-6111	119	10	dm	dm	PROPN
ejpam-6111	119	11	is	be	AUX
ejpam-6111	119	12	stable	stable	ADJ
ejpam-6111	119	13	for	for	ADP
ejpam-6111	119	14	a	a	DET
ejpam-6111	119	15	positive	positive	ADJ
ejpam-6111	119	16	diagonal	diagonal	ADJ
ejpam-6111	119	17	matrix	matrix	NOUN
ejpam-6111	119	18	d	d	NOUN
ejpam-6111	119	19	,	,	PUNCT
ejpam-6111	119	20	then	then	ADV
ejpam-6111	119	21	non	non	PROPN
ejpam-6111	119	22	of	of	ADP
ejpam-6111	119	23	the	the	DET
ejpam-6111	119	24	eigenvalue	eigenvalue	NOUN
ejpam-6111	119	25	of	of	ADP
ejpam-6111	119	26	m	m	PROPN
ejpam-6111	119	27	is	be	AUX
ejpam-6111	119	28	exactly	exactly	ADV
ejpam-6111	119	29	equal	equal	ADJ
ejpam-6111	119	30	to	to	ADP
ejpam-6111	119	31	0	0	NUM
ejpam-6111	119	32	,	,	PUNCT
ejpam-6111	119	33	and	and	CCONJ
ejpam-6111	119	34	hence	hence	ADV
ejpam-6111	119	35	m	m	VERB
ejpam-6111	119	36	-1	-1	VERB
ejpam-6111	119	37	is	be	AUX
ejpam-6111	119	38	invertible	invertible	ADJ
ejpam-6111	119	39	,	,	PUNCT
ejpam-6111	119	40	d̂tmd̂	d̂tmd̂	PROPN
ejpam-6111	119	41	,	,	PUNCT
ejpam-6111	119	42	d̂md	d̂md	PROPN
ejpam-6111	119	43	,	,	PUNCT
ejpam-6111	119	44	mt	mt	PROPN
ejpam-6111	119	45	are	be	AUX
ejpam-6111	119	46	all	all	PRON
ejpam-6111	119	47	d	d	ADJ
ejpam-6111	119	48	-	-	ADJ
ejpam-6111	119	49	stable	stable	ADJ
ejpam-6111	119	50	matrices	matrix	NOUN
ejpam-6111	119	51	,	,	PUNCT
ejpam-6111	119	52	with	with	ADP
ejpam-6111	119	53	d̂	d̂	NUM
ejpam-6111	119	54	having	have	VERB
ejpam-6111	119	55	a	a	DET
ejpam-6111	119	56	positive	positive	ADJ
ejpam-6111	119	57	diagonal	diagonal	ADJ
ejpam-6111	119	58	structure	structure	NOUN
ejpam-6111	119	59	.	.	PUNCT
ejpam-6111	120	1	observation	observation	NOUN
ejpam-6111	120	2	3	3	NUM
ejpam-6111	120	3	.	.	PUNCT
ejpam-6111	121	1	if	if	SCONJ
ejpam-6111	121	2	given	give	VERB
ejpam-6111	121	3	m	m	PRON
ejpam-6111	121	4	∈	∈	PROPN
ejpam-6111	121	5	cn	cn	PROPN
ejpam-6111	121	6	,	,	PUNCT
ejpam-6111	121	7	n	n	PRON
ejpam-6111	121	8	such	such	ADJ
ejpam-6111	121	9	that	that	SCONJ
ejpam-6111	121	10	dm	dm	PROPN
ejpam-6111	121	11	is	be	AUX
ejpam-6111	121	12	stable	stable	ADJ
ejpam-6111	121	13	for	for	ADP
ejpam-6111	121	14	a	a	DET
ejpam-6111	121	15	positive	positive	ADJ
ejpam-6111	121	16	diagonal	diagonal	ADJ
ejpam-6111	121	17	matrix	matrix	NOUN
ejpam-6111	121	18	d	d	NOUN
ejpam-6111	121	19	,	,	PUNCT
ejpam-6111	121	20	then	then	ADV
ejpam-6111	121	21	k	k	PROPN
ejpam-6111	121	22	×	×	PROPN
ejpam-6111	121	23	k	k	PROPN
ejpam-6111	121	24	principal	principal	ADJ
ejpam-6111	121	25	sub	sub	NOUN
ejpam-6111	121	26	-	-	NOUN
ejpam-6111	121	27	matrix	matrix	NOUN
ejpam-6111	121	28	of	of	ADP
ejpam-6111	121	29	m	m	VERB
ejpam-6111	121	30	belongs	belong	VERB
ejpam-6111	121	31	to	to	PART
ejpam-6111	121	32	euclidean	euclidean	VERB
ejpam-6111	121	33	closure	closure	NOUN
ejpam-6111	121	34	of	of	ADP
ejpam-6111	121	35	k	k	PROPN
ejpam-6111	121	36	×	×	PROPN
ejpam-6111	121	37	k	k	PROPN
ejpam-6111	122	1	d	d	ADJ
ejpam-6111	122	2	-	-	ADJ
ejpam-6111	122	3	stable	stable	ADJ
ejpam-6111	122	4	matrices	matrix	NOUN
ejpam-6111	122	5	.	.	PUNCT
ejpam-6111	123	1	observation	observation	NOUN
ejpam-6111	123	2	4	4	NUM
ejpam-6111	123	3	.	.	PUNCT
ejpam-6111	124	1	let	let	VERB
ejpam-6111	124	2	m	m	VERB
ejpam-6111	124	3	∈	∈	PROPN
ejpam-6111	124	4	cn	cn	PROPN
ejpam-6111	124	5	,	,	PUNCT
ejpam-6111	124	6	n	n	PRON
ejpam-6111	124	7	such	such	ADJ
ejpam-6111	124	8	that	that	SCONJ
ejpam-6111	124	9	dm	dm	PROPN
ejpam-6111	124	10	is	be	AUX
ejpam-6111	124	11	stable	stable	ADJ
ejpam-6111	124	12	for	for	ADP
ejpam-6111	124	13	a	a	DET
ejpam-6111	124	14	positive	positive	ADJ
ejpam-6111	124	15	diagonal	diagonal	ADJ
ejpam-6111	124	16	matrix	matrix	NOUN
ejpam-6111	125	1	d	d	NOUN
ejpam-6111	125	2	,	,	PUNCT
ejpam-6111	125	3	then	then	ADV
ejpam-6111	125	4	m	m	VERB
ejpam-6111	125	5	is	be	AUX
ejpam-6111	125	6	a	a	DET
ejpam-6111	125	7	d	d	ADJ
ejpam-6111	125	8	-	-	ADJ
ejpam-6111	125	9	stable	stable	ADJ
ejpam-6111	125	10	matrix	matrix	NOUN
ejpam-6111	125	11	if	if	SCONJ
ejpam-6111	125	12	and	and	CCONJ
ejpam-6111	125	13	only	only	ADV
ejpam-6111	126	1	if	if	SCONJ
ejpam-6111	126	2	det(m	det(m	PROPN
ejpam-6111	126	3	±	±	NUM
ejpam-6111	126	4	i	i	NOUN
ejpam-6111	126	5	d	d	NOUN
ejpam-6111	126	6	)	)	PUNCT
ejpam-6111	126	7	̸=	̸=	PROPN
ejpam-6111	126	8	0	0	NUM
ejpam-6111	126	9	,	,	PUNCT
ejpam-6111	126	10	for	for	ADP
ejpam-6111	126	11	all	all	DET
ejpam-6111	126	12	positive	positive	ADJ
ejpam-6111	126	13	diagonal	diagonal	ADJ
ejpam-6111	126	14	matrices	matrix	NOUN
ejpam-6111	126	15	d.	d.	PROPN
ejpam-6111	126	16	definition	definition	NOUN
ejpam-6111	126	17	4	4	NUM
ejpam-6111	126	18	.	.	PUNCT
ejpam-6111	127	1	[	[	X
ejpam-6111	127	2	43	43	NUM
ejpam-6111	127	3	]	]	X
ejpam-6111	127	4	a	a	DET
ejpam-6111	127	5	given	give	VERB
ejpam-6111	127	6	m	m	PRON
ejpam-6111	127	7	∈	∈	PROPN
ejpam-6111	127	8	cn	cn	PROPN
ejpam-6111	127	9	,	,	PUNCT
ejpam-6111	127	10	n	n	PRON
ejpam-6111	127	11	is	be	AUX
ejpam-6111	127	12	said	say	VERB
ejpam-6111	127	13	to	to	PART
ejpam-6111	127	14	be	be	AUX
ejpam-6111	127	15	strongly	strongly	ADV
ejpam-6111	127	16	d	d	NOUN
ejpam-6111	127	17	-	-	ADJ
ejpam-6111	127	18	stable	stable	ADJ
ejpam-6111	127	19	if	if	SCONJ
ejpam-6111	127	20	there	there	PRON
ejpam-6111	127	21	exists	exist	VERB
ejpam-6111	127	22	γ	γ	X
ejpam-6111	127	23	>	>	X
ejpam-6111	127	24	0	0	NUM
ejpam-6111	127	25	such	such	ADJ
ejpam-6111	127	26	that	that	SCONJ
ejpam-6111	127	27	m	m	VERB
ejpam-6111	127	28	+	+	ADJ
ejpam-6111	127	29	m̂	m̂	NOUN
ejpam-6111	127	30	is	be	AUX
ejpam-6111	127	31	a	a	DET
ejpam-6111	127	32	d	d	ADJ
ejpam-6111	127	33	-	-	ADJ
ejpam-6111	127	34	stable	stable	ADJ
ejpam-6111	127	35	matrix	matrix	NOUN
ejpam-6111	127	36	for	for	ADP
ejpam-6111	127	37	each	each	DET
ejpam-6111	127	38	m̂	m̂	PROPN
ejpam-6111	127	39	∈	∈	PROPN
ejpam-6111	127	40	rn	rn	PROPN
ejpam-6111	127	41	,	,	PUNCT
ejpam-6111	127	42	n	n	PROPN
ejpam-6111	127	43	with	with	ADP
ejpam-6111	127	44	σmax(m̂	σmax(m̂	NUM
ejpam-6111	127	45	)	)	PUNCT
ejpam-6111	127	46	<	<	X
ejpam-6111	127	47	γ	γ	PROPN
ejpam-6111	127	48	.	.	PROPN
ejpam-6111	127	49	remark	remark	PROPN
ejpam-6111	127	50	5	5	NUM
ejpam-6111	127	51	.	.	PUNCT
ejpam-6111	128	1	all	all	DET
ejpam-6111	128	2	the	the	DET
ejpam-6111	128	3	13	13	NUM
ejpam-6111	128	4	sufficient	sufficient	ADJ
ejpam-6111	128	5	conditions	condition	NOUN
ejpam-6111	128	6	to	to	ADP
ejpam-6111	128	7	d	d	NOUN
ejpam-6111	128	8	-	-	PUNCT
ejpam-6111	128	9	stability	stability	NOUN
ejpam-6111	128	10	[	[	X
ejpam-6111	128	11	34	34	NUM
ejpam-6111	128	12	]	]	PUNCT
ejpam-6111	128	13	satisfies	satisfie	NOUN
ejpam-6111	128	14	are	be	AUX
ejpam-6111	128	15	extended	extend	VERB
ejpam-6111	128	16	to	to	ADP
ejpam-6111	128	17	strong	strong	ADJ
ejpam-6111	128	18	d	d	NOUN
ejpam-6111	128	19	-	-	NOUN
ejpam-6111	128	20	stability	stability	NOUN
ejpam-6111	128	21	,	,	PUNCT
ejpam-6111	128	22	and	and	CCONJ
ejpam-6111	128	23	the	the	DET
ejpam-6111	128	24	simpler	simple	ADJ
ejpam-6111	128	25	conditions	condition	NOUN
ejpam-6111	128	26	which	which	PRON
ejpam-6111	128	27	holds	hold	VERB
ejpam-6111	128	28	true	true	ADJ
ejpam-6111	128	29	for	for	ADP
ejpam-6111	128	30	strong	strong	ADJ
ejpam-6111	128	31	d	d	NOUN
ejpam-6111	128	32	-	-	NOUN
ejpam-6111	128	33	stability	stability	NOUN
ejpam-6111	128	34	are	be	AUX
ejpam-6111	128	35	constructed	construct	VERB
ejpam-6111	128	36	and	and	CCONJ
ejpam-6111	128	37	analyzed	analyze	VERB
ejpam-6111	128	38	in	in	ADP
ejpam-6111	128	39	[	[	X
ejpam-6111	128	40	36	36	NUM
ejpam-6111	128	41	]	]	PUNCT
ejpam-6111	128	42	and	and	CCONJ
ejpam-6111	128	43	compare	compare	VERB
ejpam-6111	128	44	with	with	ADP
ejpam-6111	128	45	the	the	DET
ejpam-6111	128	46	one	one	NOUN
ejpam-6111	128	47	which	which	PRON
ejpam-6111	128	48	are	be	AUX
ejpam-6111	128	49	presented	present	VERB
ejpam-6111	128	50	in	in	ADP
ejpam-6111	128	51	[	[	X
ejpam-6111	128	52	35	35	NUM
ejpam-6111	128	53	]	]	SYM
ejpam-6111	128	54	.	.	PUNCT
ejpam-6111	129	1	3	3	X
ejpam-6111	129	2	.	.	X
ejpam-6111	129	3	problem	problem	NOUN
ejpam-6111	129	4	statement	statement	NOUN
ejpam-6111	129	5	we	we	PRON
ejpam-6111	129	6	consider	consider	VERB
ejpam-6111	129	7	lumped	lump	VERB
ejpam-6111	129	8	-	-	PUNCT
ejpam-6111	129	9	parameter	parameter	NOUN
ejpam-6111	129	10	dynamical	dynamical	ADJ
ejpam-6111	129	11	system	system	NOUN
ejpam-6111	129	12	with	with	ADP
ejpam-6111	129	13	x(t	x(t	PROPN
ejpam-6111	129	14	)	)	PUNCT
ejpam-6111	129	15	representing	represent	VERB
ejpam-6111	129	16	the	the	DET
ejpam-6111	129	17	n	n	PRON
ejpam-6111	129	18	number	number	NOUN
ejpam-6111	129	19	of	of	ADP
ejpam-6111	129	20	states	state	NOUN
ejpam-6111	129	21	;	;	PUNCT
ejpam-6111	129	22	u(t	u(t	NOUN
ejpam-6111	129	23	)	)	PUNCT
ejpam-6111	129	24	,	,	PUNCT
ejpam-6111	129	25	the	the	DET
ejpam-6111	129	26	input	input	NOUN
ejpam-6111	129	27	data	datum	NOUN
ejpam-6111	129	28	;	;	PUNCT
ejpam-6111	129	29	y(t	y(t	NUM
ejpam-6111	129	30	)	)	PUNCT
ejpam-6111	129	31	,	,	PUNCT
ejpam-6111	129	32	the	the	DET
ejpam-6111	129	33	output	output	NOUN
ejpam-6111	129	34	data	datum	NOUN
ejpam-6111	129	35	.	.	PUNCT
ejpam-6111	130	1	the	the	DET
ejpam-6111	130	2	lumped	lump	VERB
ejpam-6111	130	3	-	-	PUNCT
ejpam-6111	130	4	parameter	parameter	NOUN
ejpam-6111	130	5	linear	linear	NOUN
ejpam-6111	130	6	system	system	NOUN
ejpam-6111	130	7	,	,	PUNCT
ejpam-6111	130	8	with	with	ADP
ejpam-6111	130	9	its	its	PRON
ejpam-6111	130	10	state	state	NOUN
ejpam-6111	130	11	equation	equation	NOUN
ejpam-6111	130	12	and	and	CCONJ
ejpam-6111	130	13	output	output	NOUN
ejpam-6111	130	14	equation	equation	NOUN
ejpam-6111	130	15	has	have	VERB
ejpam-6111	130	16	the	the	DET
ejpam-6111	130	17	following	follow	VERB
ejpam-6111	130	18	mathematical	mathematical	ADJ
ejpam-6111	130	19	formulation	formulation	NOUN
ejpam-6111	130	20	:	:	PUNCT
ejpam-6111	130	21	{	{	PUNCT
ejpam-6111	130	22	x(t	x(t	PROPN
ejpam-6111	130	23	)	)	PUNCT
ejpam-6111	130	24	=	=	PUNCT
ejpam-6111	130	25	a	a	DET
ejpam-6111	130	26	x(t	x(t	PROPN
ejpam-6111	130	27	)	)	PUNCT
ejpam-6111	131	1	+	+	NOUN
ejpam-6111	131	2	b	b	NOUN
ejpam-6111	131	3	u(t	u(t	NOUN
ejpam-6111	131	4	)	)	PUNCT
ejpam-6111	131	5	,	,	PUNCT
ejpam-6111	131	6	x(0	x(0	PROPN
ejpam-6111	131	7	)	)	PUNCT
ejpam-6111	132	1	=	=	PUNCT
ejpam-6111	133	1	x0	x0	PROPN
ejpam-6111	133	2	y(t	y(t	NUM
ejpam-6111	133	3	)	)	PUNCT
ejpam-6111	134	1	=	=	SYM
ejpam-6111	134	2	c	c	NOUN
ejpam-6111	134	3	x(t	x(t	PROPN
ejpam-6111	134	4	)	)	PUNCT
ejpam-6111	135	1	+	+	ADP
ejpam-6111	135	2	d	d	NOUN
ejpam-6111	135	3	u(t	u(t	NOUN
ejpam-6111	135	4	)	)	PUNCT
ejpam-6111	135	5	.	.	PUNCT
ejpam-6111	136	1	assumption	assumption	NOUN
ejpam-6111	136	2	1	1	NUM
ejpam-6111	136	3	.	.	PUNCT
ejpam-6111	137	1	for	for	ADP
ejpam-6111	137	2	0	0	NUM
ejpam-6111	137	3	≤	≤	NOUN
ejpam-6111	137	4	t	t	NOUN
ejpam-6111	137	5	<	<	X
ejpam-6111	137	6	1	1	NUM
ejpam-6111	137	7	,	,	PUNCT
ejpam-6111	137	8	assume	assume	VERB
ejpam-6111	137	9	that	that	SCONJ
ejpam-6111	137	10	u(t	u(t	NOUN
ejpam-6111	137	11	)	)	PUNCT
ejpam-6111	137	12	is	be	AUX
ejpam-6111	137	13	a	a	DET
ejpam-6111	137	14	square	square	ADJ
ejpam-6111	137	15	integrable	integrable	ADJ
ejpam-6111	137	16	function	function	NOUN
ejpam-6111	137	17	.	.	PUNCT
ejpam-6111	138	1	the	the	DET
ejpam-6111	138	2	haar	haar	PROPN
ejpam-6111	138	3	series	series	PROPN
ejpam-6111	138	4	expansion	expansion	NOUN
ejpam-6111	138	5	of	of	ADP
ejpam-6111	138	6	square	square	ADJ
ejpam-6111	138	7	integrable	integrable	ADJ
ejpam-6111	138	8	function	function	NOUN
ejpam-6111	138	9	u(t	u(t	NOUN
ejpam-6111	138	10	)	)	PUNCT
ejpam-6111	138	11	can	can	AUX
ejpam-6111	138	12	be	be	AUX
ejpam-6111	138	13	written	write	VERB
ejpam-6111	138	14	as	as	ADP
ejpam-6111	138	15	u(t	u(t	NOUN
ejpam-6111	138	16	)	)	PUNCT
ejpam-6111	139	1	=	=	SYM
ejpam-6111	140	1	ã	ã	PROPN
ejpam-6111	140	2	h(t	h(t	PROPN
ejpam-6111	140	3	)	)	PUNCT
ejpam-6111	140	4	,	,	PUNCT
ejpam-6111	140	5	where	where	SCONJ
ejpam-6111	140	6	ã	ã	PROPN
ejpam-6111	140	7	is	be	AUX
ejpam-6111	140	8	a	a	DET
ejpam-6111	140	9	structured	structured	ADJ
ejpam-6111	140	10	matrix	matrix	NOUN
ejpam-6111	140	11	,	,	PUNCT
ejpam-6111	140	12	and	and	CCONJ
ejpam-6111	140	13	h(t	h(t	NUM
ejpam-6111	140	14	)	)	PUNCT
ejpam-6111	140	15	is	be	AUX
ejpam-6111	140	16	the	the	DET
ejpam-6111	140	17	matrix	matrix	NOUN
ejpam-6111	140	18	of	of	ADP
ejpam-6111	140	19	haar	haar	PROPN
ejpam-6111	140	20	functions	function	NOUN
ejpam-6111	140	21	.	.	PUNCT
ejpam-6111	141	1	remark	remark	PROPN
ejpam-6111	141	2	6	6	NUM
ejpam-6111	141	3	.	.	PUNCT
ejpam-6111	142	1	the	the	DET
ejpam-6111	142	2	haar	haar	PROPN
ejpam-6111	142	3	series	series	PROPN
ejpam-6111	142	4	of	of	ADP
ejpam-6111	142	5	state	state	NOUN
ejpam-6111	142	6	variable	variable	ADJ
ejpam-6111	142	7	vector	vector	NOUN
ejpam-6111	142	8	is	be	AUX
ejpam-6111	142	9	dx(t	dx(t	NOUN
ejpam-6111	142	10	)	)	PUNCT
ejpam-6111	142	11	dt	dt	NOUN
ejpam-6111	142	12	=	=	PUNCT
ejpam-6111	142	13	fh(t	fh(t	PROPN
ejpam-6111	142	14	)	)	PUNCT
ejpam-6111	142	15	.	.	PUNCT
ejpam-6111	143	1	the	the	DET
ejpam-6111	143	2	integration	integration	NOUN
ejpam-6111	143	3	of	of	ADP
ejpam-6111	143	4	dx(t	dx(t	NOUN
ejpam-6111	143	5	)	)	PUNCT
ejpam-6111	143	6	dt	dt	PUNCT
ejpam-6111	143	7	yields	yield	VERB
ejpam-6111	143	8	x(t	x(t	PROPN
ejpam-6111	143	9	)	)	PUNCT
ejpam-6111	143	10	as	as	ADP
ejpam-6111	143	11	,	,	PUNCT
ejpam-6111	143	12	x(t	x(t	PROPN
ejpam-6111	143	13	)	)	PUNCT
ejpam-6111	143	14	=	=	SYM
ejpam-6111	144	1	∫	∫	PROPN
ejpam-6111	144	2	t	t	PROPN
ejpam-6111	144	3	0	0	NUM
ejpam-6111	144	4	(	(	PUNCT
ejpam-6111	144	5	dx(t	dx(t	PROPN
ejpam-6111	144	6	)	)	PUNCT
ejpam-6111	144	7	dt	dt	PUNCT
ejpam-6111	145	1	+	+	CCONJ
ejpam-6111	145	2	x0	x0	PROPN
ejpam-6111	145	3	)	)	PUNCT
ejpam-6111	145	4	dt	dt	X
ejpam-6111	146	1	=	=	SYM
ejpam-6111	146	2	f	f	X
ejpam-6111	146	3	∫	∫	PROPN
ejpam-6111	146	4	t	t	PROPN
ejpam-6111	146	5	0	0	NUM
ejpam-6111	146	6	h(r	h(r	PROPN
ejpam-6111	146	7	)	)	PUNCT
ejpam-6111	146	8	dr	dr	PROPN
ejpam-6111	147	1	+	+	NUM
ejpam-6111	147	2	x0	x0	PROPN
ejpam-6111	147	3	=	=	SYM
ejpam-6111	147	4	fph(t	fph(t	PROPN
ejpam-6111	147	5	)	)	PUNCT
ejpam-6111	148	1	+	+	CCONJ
ejpam-6111	148	2	x0	x0	PROPN
ejpam-6111	148	3	.	.	PUNCT
ejpam-6111	149	1	s.	s.	PROPN
ejpam-6111	149	2	mazhar	mazhar	PROPN
ejpam-6111	149	3	,	,	PUNCT
ejpam-6111	149	4	m.	m.	NOUN
ejpam-6111	149	5	u.	u.	PROPN
ejpam-6111	149	6	rehman	rehman	PROPN
ejpam-6111	149	7	/	/	SYM
ejpam-6111	149	8	eur	eur	PROPN
ejpam-6111	149	9	.	.	PUNCT
ejpam-6111	150	1	j.	j.	PROPN
ejpam-6111	150	2	pure	pure	PROPN
ejpam-6111	150	3	appl	appl	PROPN
ejpam-6111	150	4	.	.	PROPN
ejpam-6111	150	5	math	math	PROPN
ejpam-6111	150	6	,	,	PUNCT
ejpam-6111	150	7	18	18	NUM
ejpam-6111	150	8	(	(	PUNCT
ejpam-6111	150	9	2	2	NUM
ejpam-6111	150	10	)	)	PUNCT
ejpam-6111	150	11	(	(	PUNCT
ejpam-6111	150	12	2025	2025	NUM
ejpam-6111	150	13	)	)	PUNCT
ejpam-6111	150	14	,	,	PUNCT
ejpam-6111	150	15	6111	6111	NUM
ejpam-6111	150	16	6	6	NUM
ejpam-6111	150	17	of	of	ADP
ejpam-6111	150	18	25	25	NUM
ejpam-6111	150	19	in	in	ADP
ejpam-6111	150	20	view	view	NOUN
ejpam-6111	150	21	of	of	ADP
ejpam-6111	150	22	u(t	u(t	NOUN
ejpam-6111	150	23	)	)	PUNCT
ejpam-6111	150	24	,	,	PUNCT
ejpam-6111	150	25	and	and	CCONJ
ejpam-6111	150	26	x(t	x(t	PROPN
ejpam-6111	150	27	)	)	PUNCT
ejpam-6111	150	28	,	,	PUNCT
ejpam-6111	150	29	one	one	PRON
ejpam-6111	150	30	may	may	AUX
ejpam-6111	150	31	obtain	obtain	VERB
ejpam-6111	150	32	the	the	DET
ejpam-6111	150	33	following	follow	VERB
ejpam-6111	150	34	matrix	matrix	NOUN
ejpam-6111	150	35	equation	equation	NOUN
ejpam-6111	150	36	,	,	PUNCT
ejpam-6111	150	37	f	f	PROPN
ejpam-6111	150	38	=	=	PUNCT
ejpam-6111	150	39	(	(	PUNCT
ejpam-6111	150	40	in	in	ADP
ejpam-6111	150	41	−a⊗	−a⊗	PROPN
ejpam-6111	150	42	p	p	NOUN
ejpam-6111	150	43	t)q	t)q	PRON
ejpam-6111	150	44	,	,	PUNCT
ejpam-6111	150	45	where	where	SCONJ
ejpam-6111	150	46	f	f	NOUN
ejpam-6111	150	47	=	=	PRON
ejpam-6111	150	48			PROPN
ejpam-6111	150	49	f0	f0	PROPN
ejpam-6111	150	50	f1	f1	PROPN
ejpam-6111	150	51	...	...	PUNCT
ejpam-6111	150	52	fm−1	fm−1	PROPN
ejpam-6111	150	53			NOUN
ejpam-6111	150	54	;	;	PUNCT
ejpam-6111	150	55	q	q	SYM
ejpam-6111	150	56	=	=	PUNCT
ejpam-6111	150	57			PROPN
ejpam-6111	150	58	q0	q0	PROPN
ejpam-6111	150	59	q1	q1	PROPN
ejpam-6111	150	60	...	...	PUNCT
ejpam-6111	150	61	qm−1	qm−1	NOUN
ejpam-6111	150	62			NOUN
ejpam-6111	150	63	,	,	PUNCT
ejpam-6111	150	64	and	and	CCONJ
ejpam-6111	150	65	⊗	⊗	PROPN
ejpam-6111	150	66	denotes	denotes	PROPN
ejpam-6111	150	67	kronecker	kronecker	NOUN
ejpam-6111	150	68	-	-	PUNCT
ejpam-6111	150	69	product	product	NOUN
ejpam-6111	150	70	,	,	PUNCT
ejpam-6111	150	71	that	that	ADV
ejpam-6111	150	72	is	is	ADV
ejpam-6111	150	73	,	,	PUNCT
ejpam-6111	150	74	a⊗	a⊗	NOUN
ejpam-6111	150	75	p	p	PROPN
ejpam-6111	150	76	t	t	PROPN
ejpam-6111	150	77	=	=	PUNCT
ejpam-6111	150	78			NOUN
ejpam-6111	150	79	p11a	p11a	PROPN
ejpam-6111	150	80	p12a	p12a	ADJ
ejpam-6111	150	81	.	.	PUNCT
ejpam-6111	150	82	.	.	PUNCT
ejpam-6111	150	83	.	.	PUNCT
ejpam-6111	151	1	p1ma	p1ma	VERB
ejpam-6111	151	2	p11a	p11a	PROPN
ejpam-6111	151	3	p22a	p22a	VERB
ejpam-6111	151	4	.	.	PUNCT
ejpam-6111	151	5	.	.	PUNCT
ejpam-6111	151	6	.	.	PUNCT
ejpam-6111	152	1	p2ma	p2ma	PROPN
ejpam-6111	152	2	...	...	PUNCT
ejpam-6111	152	3	...	...	PUNCT
ejpam-6111	152	4	.	.	PUNCT
ejpam-6111	152	5	.	.	PUNCT
ejpam-6111	152	6	.	.	PUNCT
ejpam-6111	153	1	...	...	PUNCT
ejpam-6111	153	2	p1ma	p1ma	VERB
ejpam-6111	153	3	p2ma	p2ma	PROPN
ejpam-6111	153	4	.	.	PUNCT
ejpam-6111	153	5	.	.	PUNCT
ejpam-6111	153	6	.	.	PUNCT
ejpam-6111	154	1	pmma	pmma	PROPN
ejpam-6111	154	2			PROPN
ejpam-6111	154	3	.	.	PUNCT
ejpam-6111	155	1	in	in	ADP
ejpam-6111	155	2	this	this	DET
ejpam-6111	155	3	article	article	NOUN
ejpam-6111	155	4	,	,	PUNCT
ejpam-6111	155	5	we	we	PRON
ejpam-6111	155	6	study	study	VERB
ejpam-6111	155	7	and	and	CCONJ
ejpam-6111	155	8	analyze	analyze	VERB
ejpam-6111	155	9	the	the	DET
ejpam-6111	155	10	lumped	lump	VERB
ejpam-6111	155	11	-	-	PUNCT
ejpam-6111	155	12	parameter	parameter	NOUN
ejpam-6111	155	13	linear	linear	NOUN
ejpam-6111	155	14	system	system	NOUN
ejpam-6111	155	15	by	by	ADP
ejpam-6111	155	16	characterizing	characterize	VERB
ejpam-6111	155	17	the	the	DET
ejpam-6111	155	18	spectral	spectral	ADJ
ejpam-6111	155	19	properties	property	NOUN
ejpam-6111	155	20	of	of	ADP
ejpam-6111	155	21	(	(	PUNCT
ejpam-6111	155	22	in	in	ADP
ejpam-6111	155	23	−	−	PROPN
ejpam-6111	155	24	a	a	DET
ejpam-6111	155	25	⊗	⊗	PROPN
ejpam-6111	155	26	p	p	PROPN
ejpam-6111	155	27	t	t	PROPN
ejpam-6111	155	28	)	)	PUNCT
ejpam-6111	155	29	.	.	PUNCT
ejpam-6111	156	1	furthermore	furthermore	ADV
ejpam-6111	156	2	,	,	PUNCT
ejpam-6111	156	3	our	our	PRON
ejpam-6111	156	4	results	result	NOUN
ejpam-6111	156	5	are	be	AUX
ejpam-6111	156	6	primiraly	primiraly	NOUN
ejpam-6111	156	7	based	base	VERB
ejpam-6111	156	8	on	on	ADP
ejpam-6111	156	9	the	the	DET
ejpam-6111	156	10	analysis	analysis	NOUN
ejpam-6111	156	11	of	of	ADP
ejpam-6111	156	12	interconnection	interconnection	NOUN
ejpam-6111	156	13	between	between	ADP
ejpam-6111	156	14	µ-theory	µ-theory	ADJ
ejpam-6111	156	15	and	and	CCONJ
ejpam-6111	156	16	theory	theory	NOUN
ejpam-6111	156	17	of	of	ADP
ejpam-6111	156	18	matrix	matrix	NOUN
ejpam-6111	156	19	stability	stability	NOUN
ejpam-6111	156	20	.	.	PUNCT
ejpam-6111	157	1	4	4	X
ejpam-6111	157	2	.	.	X
ejpam-6111	157	3	sufficient	sufficient	ADJ
ejpam-6111	157	4	conditions	condition	NOUN
ejpam-6111	157	5	for	for	ADP
ejpam-6111	157	6	d	d	NOUN
ejpam-6111	157	7	-	-	NOUN
ejpam-6111	157	8	stability	stability	NOUN
ejpam-6111	157	9	,	,	PUNCT
ejpam-6111	157	10	and	and	CCONJ
ejpam-6111	157	11	strong	strong	ADJ
ejpam-6111	157	12	d	d	NOUN
ejpam-6111	157	13	-	-	NOUN
ejpam-6111	157	14	stability	stability	NOUN
ejpam-6111	157	15	in	in	ADP
ejpam-6111	157	16	this	this	DET
ejpam-6111	157	17	section	section	NOUN
ejpam-6111	157	18	,	,	PUNCT
ejpam-6111	157	19	we	we	PRON
ejpam-6111	157	20	provide	provide	VERB
ejpam-6111	157	21	a	a	DET
ejpam-6111	157	22	number	number	NOUN
ejpam-6111	157	23	of	of	ADP
ejpam-6111	157	24	sufficient	sufficient	ADJ
ejpam-6111	157	25	conditions	condition	NOUN
ejpam-6111	157	26	for	for	ADP
ejpam-6111	157	27	d	d	NOUN
ejpam-6111	157	28	-	-	NOUN
ejpam-6111	157	29	stability	stability	NOUN
ejpam-6111	157	30	and	and	CCONJ
ejpam-6111	157	31	strong	strong	ADJ
ejpam-6111	157	32	d	d	NOUN
ejpam-6111	157	33	-	-	NOUN
ejpam-6111	157	34	stability	stability	NOUN
ejpam-6111	157	35	of	of	ADP
ejpam-6111	157	36	a	a	DET
ejpam-6111	157	37	given	give	VERB
ejpam-6111	157	38	n	n	CCONJ
ejpam-6111	157	39	-	-	PUNCT
ejpam-6111	157	40	dimensional	dimensional	ADJ
ejpam-6111	157	41	real	real	ADV
ejpam-6111	157	42	-	-	PUNCT
ejpam-6111	157	43	valued	value	VERB
ejpam-6111	157	44	matrix	matrix	NOUN
ejpam-6111	157	45	m	m	NOUN
ejpam-6111	157	46	.	.	PUNCT
ejpam-6111	158	1	these	these	DET
ejpam-6111	158	2	sufficient	sufficient	ADJ
ejpam-6111	158	3	conditions	condition	NOUN
ejpam-6111	158	4	are	be	AUX
ejpam-6111	158	5	provided	provide	VERB
ejpam-6111	158	6	by	by	ADP
ejpam-6111	158	7	c.r	c.r	PROPN
ejpam-6111	158	8	.	.	PROPN
ejpam-6111	158	9	johnson	johnson	PROPN
ejpam-6111	159	1	[	[	X
ejpam-6111	159	2	34	34	NUM
ejpam-6111	159	3	]	]	PUNCT
ejpam-6111	159	4	and	and	CCONJ
ejpam-6111	159	5	w.s	w.s	PROPN
ejpam-6111	159	6	.	.	PROPN
ejpam-6111	159	7	kafri	kafri	PROPN
ejpam-6111	160	1	[	[	X
ejpam-6111	160	2	44	44	NUM
ejpam-6111	160	3	]	]	PUNCT
ejpam-6111	160	4	,	,	PUNCT
ejpam-6111	160	5	respectively	respectively	ADV
ejpam-6111	160	6	.	.	PUNCT
ejpam-6111	161	1	one	one	PRON
ejpam-6111	161	2	may	may	AUX
ejpam-6111	161	3	have	have	VERB
ejpam-6111	161	4	a	a	DET
ejpam-6111	161	5	look	look	NOUN
ejpam-6111	161	6	at	at	ADP
ejpam-6111	161	7	these	these	DET
ejpam-6111	161	8	classical	classical	ADJ
ejpam-6111	161	9	papers	paper	NOUN
ejpam-6111	161	10	by	by	ADP
ejpam-6111	161	11	johnson	johnson	PROPN
ejpam-6111	161	12	and	and	CCONJ
ejpam-6111	161	13	kafri	kafri	ADJ
ejpam-6111	161	14	to	to	PART
ejpam-6111	161	15	get	get	VERB
ejpam-6111	161	16	the	the	DET
ejpam-6111	161	17	proof	proof	NOUN
ejpam-6111	161	18	of	of	ADP
ejpam-6111	161	19	each	each	DET
ejpam-6111	161	20	and	and	CCONJ
ejpam-6111	161	21	every	every	DET
ejpam-6111	161	22	sufficient	sufficient	ADJ
ejpam-6111	161	23	condition	condition	NOUN
ejpam-6111	161	24	for	for	ADP
ejpam-6111	161	25	d	d	NOUN
ejpam-6111	161	26	-	-	NOUN
ejpam-6111	161	27	stability	stability	NOUN
ejpam-6111	161	28	and	and	CCONJ
ejpam-6111	161	29	strong	strong	ADJ
ejpam-6111	161	30	d	d	NOUN
ejpam-6111	161	31	-	-	NOUN
ejpam-6111	161	32	stability	stability	NOUN
ejpam-6111	161	33	.	.	PUNCT
ejpam-6111	162	1	4.1	4.1	NUM
ejpam-6111	162	2	.	.	PUNCT
ejpam-6111	162	3	sufficient	sufficient	ADJ
ejpam-6111	162	4	condition	condition	NOUN
ejpam-6111	162	5	for	for	ADP
ejpam-6111	162	6	d	d	NOUN
ejpam-6111	162	7	-	-	NOUN
ejpam-6111	162	8	stability	stability	NOUN
ejpam-6111	162	9	:	:	PUNCT
ejpam-6111	162	10	for	for	ADP
ejpam-6111	162	11	a	a	DET
ejpam-6111	162	12	given	give	VERB
ejpam-6111	162	13	m	m	PROPN
ejpam-6111	162	14	∈	∈	PROPN
ejpam-6111	162	15	rn	rn	PROPN
ejpam-6111	162	16	,	,	PUNCT
ejpam-6111	162	17	n	n	CCONJ
ejpam-6111	162	18	,	,	PUNCT
ejpam-6111	162	19	the	the	DET
ejpam-6111	162	20	sufficient	sufficient	ADJ
ejpam-6111	162	21	conditions	condition	NOUN
ejpam-6111	162	22	for	for	ADP
ejpam-6111	162	23	d	d	NOUN
ejpam-6111	162	24	-	-	NOUN
ejpam-6111	162	25	stability	stability	NOUN
ejpam-6111	162	26	are	be	AUX
ejpam-6111	162	27	:	:	PUNCT
ejpam-6111	162	28	c1	c1	NOUN
ejpam-6111	162	29	:	:	PUNCT
ejpam-6111	162	30	all	all	DET
ejpam-6111	162	31	the	the	DET
ejpam-6111	162	32	eigenvalues	eigenvalues	PROPN
ejpam-6111	162	33	λi	λi	INTJ
ejpam-6111	162	34	(	(	PUNCT
ejpam-6111	162	35	dm	dm	PROPN
ejpam-6111	162	36	+	+	NOUN
ejpam-6111	162	37	m	m	NOUN
ejpam-6111	162	38	td	td	NOUN
ejpam-6111	162	39	)	)	PUNCT
ejpam-6111	162	40	>	>	X
ejpam-6111	162	41	0	0	NUM
ejpam-6111	162	42	,	,	PUNCT
ejpam-6111	162	43	∀i	∀i	NOUN
ejpam-6111	162	44	,	,	PUNCT
ejpam-6111	162	45	d	d	PRON
ejpam-6111	162	46	is	be	AUX
ejpam-6111	162	47	a	a	DET
ejpam-6111	162	48	positive	positive	ADJ
ejpam-6111	162	49	diagonal	diagonal	ADJ
ejpam-6111	162	50	matrix	matrix	NOUN
ejpam-6111	162	51	.	.	PUNCT
ejpam-6111	163	1	c2	c2	PROPN
ejpam-6111	163	2	:	:	PUNCT
ejpam-6111	163	3	given	give	VERB
ejpam-6111	163	4	m	m	PROPN
ejpam-6111	163	5	∈	∈	PROPN
ejpam-6111	163	6	rn	rn	PROPN
ejpam-6111	163	7	,	,	PUNCT
ejpam-6111	163	8	n	n	PRON
ejpam-6111	163	9	is	be	AUX
ejpam-6111	163	10	an	an	DET
ejpam-6111	163	11	m	m	NOUN
ejpam-6111	163	12	-matrix	-matrix	NOUN
ejpam-6111	163	13	,	,	PUNCT
ejpam-6111	163	14	that	that	ADV
ejpam-6111	163	15	is	is	ADV
ejpam-6111	163	16	,	,	PUNCT
ejpam-6111	163	17	all	all	DET
ejpam-6111	163	18	the	the	DET
ejpam-6111	163	19	off	off	ADJ
ejpam-6111	163	20	-	-	PUNCT
ejpam-6111	163	21	diagonal	diagonal	ADJ
ejpam-6111	163	22	entries	entry	NOUN
ejpam-6111	163	23	are	be	AUX
ejpam-6111	163	24	non	non	ADJ
ejpam-6111	163	25	-	-	ADJ
ejpam-6111	163	26	positive	positive	ADJ
ejpam-6111	163	27	and	and	CCONJ
ejpam-6111	163	28	all	all	DET
ejpam-6111	163	29	the	the	DET
ejpam-6111	163	30	principal	principal	ADJ
ejpam-6111	163	31	minors	minor	NOUN
ejpam-6111	163	32	are	be	AUX
ejpam-6111	163	33	positive	positive	ADJ
ejpam-6111	163	34	.	.	PUNCT
ejpam-6111	164	1	c3	c3	NOUN
ejpam-6111	164	2	:	:	PUNCT
ejpam-6111	164	3	there	there	PRON
ejpam-6111	164	4	exists	exist	VERB
ejpam-6111	164	5	a	a	DET
ejpam-6111	164	6	positive	positive	ADJ
ejpam-6111	164	7	diagonal	diagonal	ADJ
ejpam-6111	164	8	matrix	matrix	NOUN
ejpam-6111	164	9	d	d	ADP
ejpam-6111	164	10	such	such	ADJ
ejpam-6111	164	11	that	that	PRON
ejpam-6111	164	12	md	md	PROPN
ejpam-6111	164	13	=	=	SYM
ejpam-6111	164	14	b	b	PROPN
ejpam-6111	164	15	=	=	SYM
ejpam-6111	164	16	(	(	PUNCT
ejpam-6111	164	17	bij	bij	NOUN
ejpam-6111	164	18	)	)	PUNCT
ejpam-6111	164	19	which	which	PRON
ejpam-6111	164	20	satisfies	satisfy	VERB
ejpam-6111	164	21	the	the	DET
ejpam-6111	164	22	condition	condition	NOUN
ejpam-6111	164	23	that	that	SCONJ
ejpam-6111	164	24	re(bii	re(bii	NOUN
ejpam-6111	164	25	)	)	PUNCT
ejpam-6111	164	26	>	>	PUNCT
ejpam-6111	165	1	n∑	n∑	PUNCT
ejpam-6111	165	2	j=1	j=1	PROPN
ejpam-6111	165	3	|bij	|bij	VERB
ejpam-6111	165	4	|	|	ADV
ejpam-6111	165	5	;	;	PUNCT
ejpam-6111	165	6	i	i	NOUN
ejpam-6111	165	7	=	=	NOUN
ejpam-6111	165	8	1	1	NUM
ejpam-6111	165	9	:	:	SYM
ejpam-6111	165	10	n	n	CCONJ
ejpam-6111	165	11	,	,	PUNCT
ejpam-6111	165	12	j	j	PROPN
ejpam-6111	165	13	̸=	̸=	PROPN
ejpam-6111	165	14	i.	i.	NOUN
ejpam-6111	165	15	c4	c4	NOUN
ejpam-6111	165	16	:	:	PUNCT
ejpam-6111	165	17	given	give	VERB
ejpam-6111	165	18	m	m	PROPN
ejpam-6111	165	19	∈	∈	PROPN
ejpam-6111	165	20	rn	rn	PROPN
ejpam-6111	165	21	,	,	PUNCT
ejpam-6111	165	22	n	n	PRON
ejpam-6111	165	23	is	be	AUX
ejpam-6111	165	24	a	a	DET
ejpam-6111	165	25	triangular	triangular	NOUN
ejpam-6111	165	26	matrix	matrix	NOUN
ejpam-6111	165	27	and	and	CCONJ
ejpam-6111	165	28	the	the	DET
ejpam-6111	165	29	real	real	ADJ
ejpam-6111	165	30	part	part	NOUN
ejpam-6111	165	31	of	of	ADP
ejpam-6111	165	32	all	all	DET
ejpam-6111	165	33	the	the	DET
ejpam-6111	165	34	off	off	ADJ
ejpam-6111	165	35	-	-	PUNCT
ejpam-6111	165	36	diagonal	diagonal	ADJ
ejpam-6111	165	37	entries	entry	NOUN
ejpam-6111	165	38	mii	mii	PRON
ejpam-6111	165	39	is	be	AUX
ejpam-6111	165	40	strictly	strictly	ADV
ejpam-6111	165	41	positive	positive	ADJ
ejpam-6111	165	42	.	.	PUNCT
ejpam-6111	166	1	c5	c5	PROPN
ejpam-6111	166	2	:	:	PUNCT
ejpam-6111	166	3	given	give	VERB
ejpam-6111	166	4	m	m	PROPN
ejpam-6111	166	5	∈	∈	PROPN
ejpam-6111	166	6	rn	rn	PROPN
ejpam-6111	166	7	,	,	PUNCT
ejpam-6111	166	8	n	n	PRON
ejpam-6111	166	9	is	be	AUX
ejpam-6111	166	10	a	a	DET
ejpam-6111	166	11	sign	sign	ADJ
ejpam-6111	166	12	stable	stable	ADJ
ejpam-6111	166	13	matrix	matrix	NOUN
ejpam-6111	166	14	.	.	PUNCT
ejpam-6111	167	1	c6	c6	PROPN
ejpam-6111	167	2	:	:	PUNCT
ejpam-6111	167	3	for	for	SCONJ
ejpam-6111	167	4	given	give	VERB
ejpam-6111	167	5	m	m	PROPN
ejpam-6111	167	6	∈	∈	PROPN
ejpam-6111	167	7	rn	rn	PROPN
ejpam-6111	167	8	,	,	PUNCT
ejpam-6111	167	9	n	n	CCONJ
ejpam-6111	167	10	,	,	PUNCT
ejpam-6111	167	11	each	each	DET
ejpam-6111	167	12	principal	principal	ADJ
ejpam-6111	167	13	minor	minor	ADJ
ejpam-6111	167	14	is	be	AUX
ejpam-6111	167	15	positive	positive	ADJ
ejpam-6111	167	16	and	and	CCONJ
ejpam-6111	167	17	m	m	VERB
ejpam-6111	167	18	is	be	AUX
ejpam-6111	167	19	a	a	DET
ejpam-6111	167	20	tri	tri	ADJ
ejpam-6111	167	21	-	-	ADJ
ejpam-6111	167	22	diagonal	diagonal	ADJ
ejpam-6111	167	23	matrix	matrix	NOUN
ejpam-6111	167	24	.	.	PUNCT
ejpam-6111	168	1	s.	s.	PROPN
ejpam-6111	168	2	mazhar	mazhar	PROPN
ejpam-6111	168	3	,	,	PUNCT
ejpam-6111	168	4	m.	m.	NOUN
ejpam-6111	168	5	u.	u.	PROPN
ejpam-6111	168	6	rehman	rehman	PROPN
ejpam-6111	168	7	/	/	SYM
ejpam-6111	168	8	eur	eur	PROPN
ejpam-6111	168	9	.	.	PUNCT
ejpam-6111	169	1	j.	j.	PROPN
ejpam-6111	169	2	pure	pure	PROPN
ejpam-6111	169	3	appl	appl	PROPN
ejpam-6111	169	4	.	.	PROPN
ejpam-6111	169	5	math	math	PROPN
ejpam-6111	169	6	,	,	PUNCT
ejpam-6111	169	7	18	18	NUM
ejpam-6111	169	8	(	(	PUNCT
ejpam-6111	169	9	2	2	NUM
ejpam-6111	169	10	)	)	PUNCT
ejpam-6111	169	11	(	(	PUNCT
ejpam-6111	169	12	2025	2025	NUM
ejpam-6111	169	13	)	)	PUNCT
ejpam-6111	169	14	,	,	PUNCT
ejpam-6111	169	15	6111	6111	NUM
ejpam-6111	169	16	7	7	NUM
ejpam-6111	169	17	of	of	ADP
ejpam-6111	169	18	25	25	NUM
ejpam-6111	169	19	c7	c7	NOUN
ejpam-6111	169	20	:	:	PUNCT
ejpam-6111	169	21	given	give	VERB
ejpam-6111	169	22	m	m	PROPN
ejpam-6111	169	23	∈	∈	PROPN
ejpam-6111	169	24	rn	rn	PROPN
ejpam-6111	169	25	,	,	PUNCT
ejpam-6111	169	26	n	n	PRON
ejpam-6111	169	27	is	be	AUX
ejpam-6111	169	28	an	an	DET
ejpam-6111	169	29	oscillatory	oscillatory	ADJ
ejpam-6111	169	30	matrix	matrix	NOUN
ejpam-6111	169	31	,	,	PUNCT
ejpam-6111	169	32	that	that	ADV
ejpam-6111	169	33	is	is	ADV
ejpam-6111	169	34	,	,	PUNCT
ejpam-6111	169	35	m	m	VERB
ejpam-6111	169	36	is	be	AUX
ejpam-6111	169	37	totally	totally	ADV
ejpam-6111	169	38	non	non	ADJ
ejpam-6111	169	39	-	-	ADJ
ejpam-6111	169	40	negative	negative	ADJ
ejpam-6111	169	41	matrix	matrix	NOUN
ejpam-6111	169	42	.	.	PUNCT
ejpam-6111	170	1	c8	c8	NOUN
ejpam-6111	170	2	:	:	PUNCT
ejpam-6111	170	3	for	for	ADP
ejpam-6111	170	4	each	each	DET
ejpam-6111	170	5	x	x	SYM
ejpam-6111	170	6	∈	∈	PROPN
ejpam-6111	170	7	rn,1	rn,1	PROPN
ejpam-6111	170	8	,	,	PUNCT
ejpam-6111	170	9	x	x	X
ejpam-6111	170	10	̸=	̸=	PROPN
ejpam-6111	170	11	0	0	NUM
ejpam-6111	170	12	,	,	PUNCT
ejpam-6111	170	13	there	there	PRON
ejpam-6111	170	14	exists	exist	VERB
ejpam-6111	170	15	a	a	DET
ejpam-6111	170	16	positive	positive	ADJ
ejpam-6111	170	17	diagonal	diagonal	ADJ
ejpam-6111	170	18	matrix	matrix	NOUN
ejpam-6111	170	19	d	d	SCONJ
ejpam-6111	170	20	such	such	ADJ
ejpam-6111	170	21	that	that	DET
ejpam-6111	170	22	real	real	ADJ
ejpam-6111	170	23	part	part	NOUN
ejpam-6111	170	24	of	of	ADP
ejpam-6111	170	25	xtdmx	xtdmx	NOUN
ejpam-6111	170	26	is	be	AUX
ejpam-6111	170	27	strictly	strictly	ADV
ejpam-6111	170	28	positive	positive	ADJ
ejpam-6111	170	29	.	.	PUNCT
ejpam-6111	171	1	c9	c9	NOUN
ejpam-6111	171	2	:	:	PUNCT
ejpam-6111	171	3	for	for	ADP
ejpam-6111	171	4	given	give	VERB
ejpam-6111	171	5	m	m	PROPN
ejpam-6111	171	6	∈	∈	PROPN
ejpam-6111	171	7	rn	rn	PROPN
ejpam-6111	171	8	,	,	PUNCT
ejpam-6111	171	9	n	n	CCONJ
ejpam-6111	171	10	,	,	PUNCT
ejpam-6111	171	11	the	the	DET
ejpam-6111	171	12	hadamard	hadamard	ADJ
ejpam-6111	171	13	product	product	NOUN
ejpam-6111	171	14	of	of	ADP
ejpam-6111	171	15	p	p	PROPN
ejpam-6111	171	16	and	and	CCONJ
ejpam-6111	171	17	m	m	PROPN
ejpam-6111	171	18	is	be	AUX
ejpam-6111	171	19	a	a	DET
ejpam-6111	171	20	stable	stable	ADJ
ejpam-6111	171	21	matrix	matrix	NOUN
ejpam-6111	171	22	for	for	ADP
ejpam-6111	171	23	each	each	DET
ejpam-6111	171	24	positive	positive	ADJ
ejpam-6111	171	25	definite	definite	ADJ
ejpam-6111	171	26	matrix	matrix	NOUN
ejpam-6111	171	27	p.	p.	NOUN
ejpam-6111	171	28	c10	c10	VERB
ejpam-6111	171	29	:	:	PUNCT
ejpam-6111	171	30	for	for	SCONJ
ejpam-6111	171	31	given	give	VERB
ejpam-6111	171	32	m	m	PROPN
ejpam-6111	171	33	∈	∈	PROPN
ejpam-6111	171	34	rn	rn	PROPN
ejpam-6111	171	35	,	,	PUNCT
ejpam-6111	171	36	n	n	CCONJ
ejpam-6111	171	37	each	each	DET
ejpam-6111	171	38	principal	principal	ADJ
ejpam-6111	171	39	minor	minor	ADJ
ejpam-6111	171	40	is	be	AUX
ejpam-6111	171	41	positive	positive	ADJ
ejpam-6111	171	42	and	and	CCONJ
ejpam-6111	171	43	m	m	VERB
ejpam-6111	171	44	is	be	AUX
ejpam-6111	171	45	strictly	strictly	ADV
ejpam-6111	171	46	sign	sign	VERB
ejpam-6111	171	47	symmetric	symmetric	ADJ
ejpam-6111	171	48	matrix	matrix	NOUN
ejpam-6111	171	49	.	.	PUNCT
ejpam-6111	172	1	c11	c11	NOUN
ejpam-6111	172	2	:	:	PUNCT
ejpam-6111	172	3	given	give	VERB
ejpam-6111	172	4	m	m	PROPN
ejpam-6111	172	5	∈	∈	PROPN
ejpam-6111	172	6	rn	rn	PROPN
ejpam-6111	172	7	,	,	PUNCT
ejpam-6111	172	8	n	n	PRON
ejpam-6111	172	9	such	such	ADJ
ejpam-6111	172	10	that	that	SCONJ
ejpam-6111	172	11	m	m	PROPN
ejpam-6111	172	12	∈	∈	PROPN
ejpam-6111	172	13	r2,2	r2,2	PROPN
ejpam-6111	172	14	∩	∩	NOUN
ejpam-6111	172	15	p+	p+	VERB
ejpam-6111	172	16	0	0	NUM
ejpam-6111	172	17	.	.	PUNCT
ejpam-6111	173	1	c12	c12	PROPN
ejpam-6111	173	2	:	:	PUNCT
ejpam-6111	173	3	given	give	VERB
ejpam-6111	173	4	m	m	PROPN
ejpam-6111	173	5	∈	∈	PROPN
ejpam-6111	173	6	rn	rn	PROPN
ejpam-6111	173	7	,	,	PUNCT
ejpam-6111	173	8	n	n	PRON
ejpam-6111	173	9	such	such	ADJ
ejpam-6111	173	10	that	that	SCONJ
ejpam-6111	173	11	m	m	PROPN
ejpam-6111	173	12	∈	∈	PROPN
ejpam-6111	173	13	r3,3	r3,3	PROPN
ejpam-6111	173	14	∩	∩	NOUN
ejpam-6111	173	15	p+	p+	VERB
ejpam-6111	173	16	0	0	NUM
ejpam-6111	173	17	,	,	PUNCT
ejpam-6111	173	18	and	and	CCONJ
ejpam-6111	173	19	m	m	PROPN
ejpam-6111	173	20	=	=	X
ejpam-6111	173	21	x	x	PUNCT
ejpam-6111	173	22	a	a	DET
ejpam-6111	173	23	b	b	NOUN
ejpam-6111	173	24	α	α	NOUN
ejpam-6111	173	25	y	y	NOUN
ejpam-6111	173	26	c	c	NOUN
ejpam-6111	173	27	β	β	X
ejpam-6111	173	28	α	α	X
ejpam-6111	173	29	z	z	PROPN
ejpam-6111	173	30			PROPN
ejpam-6111	173	31	.	.	PUNCT
ejpam-6111	174	1	c13	c13	NOUN
ejpam-6111	174	2	:	:	PUNCT
ejpam-6111	174	3	given	give	VERB
ejpam-6111	174	4	given	give	VERB
ejpam-6111	174	5	m	m	PRON
ejpam-6111	174	6	∈	∈	PROPN
ejpam-6111	174	7	rn	rn	PROPN
ejpam-6111	174	8	,	,	PUNCT
ejpam-6111	174	9	n	n	PRON
ejpam-6111	174	10	such	such	ADJ
ejpam-6111	174	11	that	that	SCONJ
ejpam-6111	174	12	m	m	PROPN
ejpam-6111	174	13	∈	∈	PROPN
ejpam-6111	174	14	rn	rn	PROPN
ejpam-6111	174	15	,	,	PUNCT
ejpam-6111	174	16	n	n	PRON
ejpam-6111	174	17	∩	∩	NOUN
ejpam-6111	174	18	p+	p+	PART
ejpam-6111	174	19	0	0	NUM
ejpam-6111	174	20	satisfies	satisfy	VERB
ejpam-6111	174	21	gkk	gkk	PROPN
ejpam-6111	174	22	condition	condition	NOUN
ejpam-6111	174	23	with	with	ADP
ejpam-6111	174	24	n	n	PRON
ejpam-6111	174	25	≤	≤	NUM
ejpam-6111	174	26	4	4	NUM
ejpam-6111	174	27	.	.	X
ejpam-6111	174	28	4.2	4.2	NUM
ejpam-6111	174	29	.	.	PUNCT
ejpam-6111	175	1	sufficient	sufficient	ADJ
ejpam-6111	175	2	condition	condition	NOUN
ejpam-6111	175	3	for	for	ADP
ejpam-6111	175	4	strong	strong	ADJ
ejpam-6111	175	5	d	d	NOUN
ejpam-6111	175	6	-	-	NOUN
ejpam-6111	175	7	stability	stability	NOUN
ejpam-6111	175	8	:	:	PUNCT
ejpam-6111	175	9	for	for	ADP
ejpam-6111	175	10	a	a	DET
ejpam-6111	175	11	given	give	VERB
ejpam-6111	175	12	m	m	PROPN
ejpam-6111	175	13	∈	∈	PROPN
ejpam-6111	175	14	rn	rn	PROPN
ejpam-6111	175	15	,	,	PUNCT
ejpam-6111	175	16	n	n	CCONJ
ejpam-6111	175	17	,	,	PUNCT
ejpam-6111	175	18	the	the	DET
ejpam-6111	175	19	sufficient	sufficient	ADJ
ejpam-6111	175	20	conditions	condition	NOUN
ejpam-6111	175	21	for	for	ADP
ejpam-6111	175	22	the	the	DET
ejpam-6111	175	23	strong	strong	ADJ
ejpam-6111	175	24	d	d	NOUN
ejpam-6111	175	25	-	-	NOUN
ejpam-6111	175	26	stability	stability	NOUN
ejpam-6111	175	27	are	be	AUX
ejpam-6111	175	28	:	:	PUNCT
ejpam-6111	175	29	c1	c1	NOUN
ejpam-6111	175	30	:	:	PUNCT
ejpam-6111	175	31	for	for	ADP
ejpam-6111	175	32	a	a	DET
ejpam-6111	175	33	positive	positive	ADJ
ejpam-6111	175	34	diagonal	diagonal	ADJ
ejpam-6111	175	35	matrix	matrix	NOUN
ejpam-6111	175	36	d	d	NOUN
ejpam-6111	175	37	,	,	PUNCT
ejpam-6111	175	38	all	all	DET
ejpam-6111	175	39	the	the	DET
ejpam-6111	175	40	eigenvalues	eigenvalue	NOUN
ejpam-6111	175	41	λi	λi	INTJ
ejpam-6111	175	42	(	(	PUNCT
ejpam-6111	175	43	dm	dm	PROPN
ejpam-6111	176	1	+	+	NOUN
ejpam-6111	176	2	m	m	NOUN
ejpam-6111	176	3	td	td	NOUN
ejpam-6111	176	4	)	)	PUNCT
ejpam-6111	176	5	<	<	X
ejpam-6111	176	6	0	0	NUM
ejpam-6111	176	7	,	,	PUNCT
ejpam-6111	176	8	∀i	∀i	NOUN
ejpam-6111	176	9	.	.	PUNCT
ejpam-6111	177	1	c2	c2	PROPN
ejpam-6111	177	2	:	:	PUNCT
ejpam-6111	177	3	given	give	VERB
ejpam-6111	177	4	m	m	PROPN
ejpam-6111	177	5	∈	∈	PROPN
ejpam-6111	177	6	rn	rn	PROPN
ejpam-6111	177	7	,	,	PUNCT
ejpam-6111	177	8	n	n	PRON
ejpam-6111	177	9	is	be	AUX
ejpam-6111	177	10	an	an	DET
ejpam-6111	177	11	m	m	NOUN
ejpam-6111	177	12	-matrix	-matrix	NOUN
ejpam-6111	177	13	,	,	PUNCT
ejpam-6111	177	14	that	that	ADV
ejpam-6111	177	15	is	is	ADV
ejpam-6111	177	16	,	,	PUNCT
ejpam-6111	177	17	all	all	DET
ejpam-6111	177	18	the	the	DET
ejpam-6111	177	19	off	off	ADJ
ejpam-6111	177	20	-	-	PUNCT
ejpam-6111	177	21	diagonal	diagonal	ADJ
ejpam-6111	177	22	entries	entry	NOUN
ejpam-6111	177	23	are	be	AUX
ejpam-6111	177	24	non	non	ADJ
ejpam-6111	177	25	-	-	ADJ
ejpam-6111	177	26	positive	positive	ADJ
ejpam-6111	177	27	and	and	CCONJ
ejpam-6111	177	28	all	all	DET
ejpam-6111	177	29	the	the	DET
ejpam-6111	177	30	principal	principal	ADJ
ejpam-6111	177	31	minors	minor	NOUN
ejpam-6111	177	32	are	be	AUX
ejpam-6111	177	33	positive	positive	ADJ
ejpam-6111	177	34	.	.	PUNCT
ejpam-6111	178	1	c3	c3	NOUN
ejpam-6111	178	2	:	:	PUNCT
ejpam-6111	178	3	there	there	PRON
ejpam-6111	178	4	exists	exist	VERB
ejpam-6111	178	5	a	a	DET
ejpam-6111	178	6	positive	positive	ADJ
ejpam-6111	178	7	diagonal	diagonal	ADJ
ejpam-6111	178	8	matrix	matrix	NOUN
ejpam-6111	178	9	d	d	ADP
ejpam-6111	178	10	such	such	ADJ
ejpam-6111	178	11	that	that	PRON
ejpam-6111	178	12	md	md	PROPN
ejpam-6111	178	13	=	=	SYM
ejpam-6111	178	14	b	b	PROPN
ejpam-6111	178	15	=	=	SYM
ejpam-6111	178	16	(	(	PUNCT
ejpam-6111	178	17	bij	bij	NOUN
ejpam-6111	178	18	)	)	PUNCT
ejpam-6111	178	19	which	which	PRON
ejpam-6111	178	20	satisfies	satisfy	VERB
ejpam-6111	178	21	the	the	DET
ejpam-6111	178	22	condition	condition	NOUN
ejpam-6111	178	23	that	that	SCONJ
ejpam-6111	178	24	re(bii	re(bii	NOUN
ejpam-6111	178	25	)	)	PUNCT
ejpam-6111	178	26	<	<	X
ejpam-6111	178	27	−	−	PROPN
ejpam-6111	178	28	n∑	n∑	PROPN
ejpam-6111	178	29	1≤j≤n	1≤j≤n	NUM
ejpam-6111	178	30	|bij	|bij	NOUN
ejpam-6111	178	31	|	|	ADV
ejpam-6111	178	32	;	;	PUNCT
ejpam-6111	178	33	1	1	NUM
ejpam-6111	178	34	≤	≤	NUM
ejpam-6111	178	35	i	i	PRON
ejpam-6111	178	36	≤	≤	PROPN
ejpam-6111	178	37	n	n	CCONJ
ejpam-6111	178	38	,	,	PUNCT
ejpam-6111	178	39	j	j	PROPN
ejpam-6111	178	40	̸=	̸=	PROPN
ejpam-6111	178	41	i.	i.	NOUN
ejpam-6111	178	42	c4	c4	NOUN
ejpam-6111	178	43	:	:	PUNCT
ejpam-6111	178	44	given	give	VERB
ejpam-6111	178	45	m	m	PROPN
ejpam-6111	178	46	∈	∈	PROPN
ejpam-6111	178	47	rn	rn	PROPN
ejpam-6111	178	48	,	,	PUNCT
ejpam-6111	178	49	n	n	PRON
ejpam-6111	178	50	is	be	AUX
ejpam-6111	178	51	a	a	DET
ejpam-6111	178	52	sign	sign	NOUN
ejpam-6111	178	53	triangular	triangular	NOUN
ejpam-6111	178	54	matrix	matrix	NOUN
ejpam-6111	178	55	,	,	PUNCT
ejpam-6111	178	56	and	and	CCONJ
ejpam-6111	178	57	mii	mii	PRON
ejpam-6111	178	58	<	<	X
ejpam-6111	178	59	0	0	PROPN
ejpam-6111	178	60	,	,	PUNCT
ejpam-6111	178	61	i	i	PRON
ejpam-6111	178	62	=	=	NOUN
ejpam-6111	178	63	1	1	NUM
ejpam-6111	178	64	:	:	PUNCT
ejpam-6111	178	65	n	n	CCONJ
ejpam-6111	178	66	..	..	PUNCT
ejpam-6111	178	67	c5	c5	PROPN
ejpam-6111	178	68	:	:	PUNCT
ejpam-6111	178	69	given	give	VERB
ejpam-6111	178	70	m	m	PROPN
ejpam-6111	178	71	∈	∈	PROPN
ejpam-6111	178	72	rn	rn	PROPN
ejpam-6111	178	73	,	,	PUNCT
ejpam-6111	178	74	n	n	PRON
ejpam-6111	178	75	is	be	AUX
ejpam-6111	178	76	a	a	DET
ejpam-6111	178	77	sign	sign	ADJ
ejpam-6111	178	78	stable	stable	ADJ
ejpam-6111	178	79	matrix	matrix	NOUN
ejpam-6111	178	80	without	without	ADP
ejpam-6111	178	81	having	have	VERB
ejpam-6111	178	82	a	a	DET
ejpam-6111	178	83	any	any	PRON
ejpam-6111	178	84	of	of	ADP
ejpam-6111	178	85	non	non	ADJ
ejpam-6111	178	86	-	-	ADJ
ejpam-6111	178	87	zero	zero	NUM
ejpam-6111	178	88	entry	entry	NOUN
ejpam-6111	178	89	.	.	PUNCT
ejpam-6111	179	1	c6	c6	PROPN
ejpam-6111	179	2	:	:	PUNCT
ejpam-6111	179	3	for	for	SCONJ
ejpam-6111	179	4	given	give	VERB
ejpam-6111	179	5	m	m	PROPN
ejpam-6111	179	6	∈	∈	PROPN
ejpam-6111	179	7	rn	rn	PROPN
ejpam-6111	179	8	,	,	PUNCT
ejpam-6111	179	9	n	n	PRON
ejpam-6111	179	10	is	be	AUX
ejpam-6111	179	11	a	a	DET
ejpam-6111	179	12	jocabi	jocabi	NOUN
ejpam-6111	179	13	matrix	matrix	NOUN
ejpam-6111	179	14	,	,	PUNCT
ejpam-6111	179	15	and	and	CCONJ
ejpam-6111	179	16	each	each	PRON
ejpam-6111	179	17	of	of	ADP
ejpam-6111	179	18	jth	jth	PROPN
ejpam-6111	179	19	-	-	PUNCT
ejpam-6111	179	20	order	order	NOUN
ejpam-6111	179	21	principal	principal	ADJ
ejpam-6111	179	22	minor	minor	ADJ
ejpam-6111	179	23	is	be	AUX
ejpam-6111	179	24	of	of	ADP
ejpam-6111	179	25	sign	sign	NOUN
ejpam-6111	179	26	(	(	PUNCT
ejpam-6111	179	27	−1)j	−1)j	X
ejpam-6111	179	28	.	.	PUNCT
ejpam-6111	180	1	c7	c7	PROPN
ejpam-6111	180	2	:	:	PUNCT
ejpam-6111	180	3	given	give	VERB
ejpam-6111	180	4	m	m	PROPN
ejpam-6111	180	5	∈	∈	PROPN
ejpam-6111	180	6	rn	rn	PROPN
ejpam-6111	180	7	,	,	PUNCT
ejpam-6111	180	8	n	n	PRON
ejpam-6111	180	9	is	be	AUX
ejpam-6111	180	10	an	an	DET
ejpam-6111	180	11	oscillatory	oscillatory	ADJ
ejpam-6111	180	12	matrix	matrix	NOUN
ejpam-6111	180	13	,	,	PUNCT
ejpam-6111	180	14	that	that	ADV
ejpam-6111	180	15	is	is	ADV
ejpam-6111	180	16	,	,	PUNCT
ejpam-6111	180	17	m	m	VERB
ejpam-6111	180	18	is	be	AUX
ejpam-6111	180	19	totally	totally	ADV
ejpam-6111	180	20	non	non	ADJ
ejpam-6111	180	21	-	-	ADJ
ejpam-6111	180	22	negative	negative	ADJ
ejpam-6111	180	23	matrix	matrix	NOUN
ejpam-6111	180	24	.	.	PUNCT
ejpam-6111	181	1	c8	c8	NOUN
ejpam-6111	181	2	:	:	PUNCT
ejpam-6111	181	3	for	for	ADP
ejpam-6111	181	4	each	each	DET
ejpam-6111	181	5	x	x	SYM
ejpam-6111	181	6	∈	∈	PROPN
ejpam-6111	181	7	rn,1	rn,1	PROPN
ejpam-6111	181	8	,	,	PUNCT
ejpam-6111	181	9	x	x	X
ejpam-6111	181	10	̸=	̸=	PROPN
ejpam-6111	181	11	0	0	NUM
ejpam-6111	181	12	,	,	PUNCT
ejpam-6111	181	13	there	there	PRON
ejpam-6111	181	14	exists	exist	VERB
ejpam-6111	181	15	a	a	DET
ejpam-6111	181	16	positive	positive	ADJ
ejpam-6111	181	17	diagonal	diagonal	ADJ
ejpam-6111	181	18	matrix	matrix	NOUN
ejpam-6111	181	19	d	d	SCONJ
ejpam-6111	181	20	such	such	ADJ
ejpam-6111	181	21	that	that	DET
ejpam-6111	181	22	real	real	ADJ
ejpam-6111	181	23	part	part	NOUN
ejpam-6111	181	24	of	of	ADP
ejpam-6111	181	25	xtdmx	xtdmx	NOUN
ejpam-6111	181	26	is	be	AUX
ejpam-6111	181	27	strictly	strictly	ADV
ejpam-6111	181	28	positive	positive	ADJ
ejpam-6111	181	29	.	.	PUNCT
ejpam-6111	182	1	c9	c9	NOUN
ejpam-6111	182	2	:	:	PUNCT
ejpam-6111	182	3	for	for	ADP
ejpam-6111	182	4	given	give	VERB
ejpam-6111	182	5	m	m	PROPN
ejpam-6111	182	6	∈	∈	PROPN
ejpam-6111	182	7	rn	rn	PROPN
ejpam-6111	182	8	,	,	PUNCT
ejpam-6111	182	9	n	n	CCONJ
ejpam-6111	182	10	,	,	PUNCT
ejpam-6111	182	11	the	the	DET
ejpam-6111	182	12	hadamard	hadamard	ADJ
ejpam-6111	182	13	product	product	NOUN
ejpam-6111	182	14	(	(	PUNCT
ejpam-6111	182	15	h	h	NOUN
ejpam-6111	182	16	◦	◦	NOUN
ejpam-6111	182	17	(	(	PUNCT
ejpam-6111	182	18	m	m	VERB
ejpam-6111	182	19	+	+	NOUN
ejpam-6111	182	20	g	g	NOUN
ejpam-6111	182	21	)	)	PUNCT
ejpam-6111	182	22	)	)	PUNCT
ejpam-6111	182	23	is	be	AUX
ejpam-6111	182	24	schur	schur	ADJ
ejpam-6111	182	25	stable	stable	ADJ
ejpam-6111	182	26	matrix	matrix	NOUN
ejpam-6111	182	27	for	for	ADP
ejpam-6111	182	28	each	each	DET
ejpam-6111	182	29	positive	positive	ADJ
ejpam-6111	182	30	definite	definite	ADJ
ejpam-6111	182	31	symmetric	symmetric	ADJ
ejpam-6111	182	32	matrix	matrix	NOUN
ejpam-6111	182	33	h	h	NOUN
ejpam-6111	182	34	,	,	PUNCT
ejpam-6111	182	35	and	and	CCONJ
ejpam-6111	182	36	a	a	DET
ejpam-6111	182	37	perturbation	perturbation	NOUN
ejpam-6111	182	38	matrix	matrix	NOUN
ejpam-6111	182	39	g	g	ADP
ejpam-6111	182	40	such	such	ADJ
ejpam-6111	182	41	that	that	DET
ejpam-6111	182	42	||g||2	||g||2	PROPN
ejpam-6111	182	43	<	<	X
ejpam-6111	182	44	α	α	PROPN
ejpam-6111	182	45	,	,	PUNCT
ejpam-6111	182	46	α	α	PROPN
ejpam-6111	182	47	∈	∈	PROPN
ejpam-6111	182	48	r.	r.	PROPN
ejpam-6111	182	49	c10	c10	VERB
ejpam-6111	182	50	:	:	PUNCT
ejpam-6111	182	51	for	for	ADP
ejpam-6111	182	52	given	give	VERB
ejpam-6111	182	53	m	m	PROPN
ejpam-6111	182	54	∈	∈	PROPN
ejpam-6111	182	55	rn	rn	PROPN
ejpam-6111	182	56	,	,	PUNCT
ejpam-6111	182	57	n	n	PRON
ejpam-6111	182	58	each	each	DET
ejpam-6111	182	59	jth	jth	PROPN
ejpam-6111	182	60	-	-	PUNCT
ejpam-6111	182	61	order	order	NOUN
ejpam-6111	182	62	principal	principal	ADJ
ejpam-6111	182	63	minor	minor	ADJ
ejpam-6111	182	64	is	be	AUX
ejpam-6111	182	65	of	of	ADP
ejpam-6111	182	66	sign	sign	NOUN
ejpam-6111	182	67	(	(	PUNCT
ejpam-6111	182	68	−1)j	−1)j	X
ejpam-6111	182	69	.	.	PUNCT
ejpam-6111	183	1	c11	c11	NOUN
ejpam-6111	183	2	:	:	PUNCT
ejpam-6111	183	3	given	give	VERB
ejpam-6111	183	4	m	m	PRON
ejpam-6111	183	5	∈	∈	PROPN
ejpam-6111	183	6	r2,2	r2,2	PROPN
ejpam-6111	183	7	is	be	AUX
ejpam-6111	183	8	strongly	strongly	ADV
ejpam-6111	183	9	d	d	ADJ
ejpam-6111	183	10	-	-	ADJ
ejpam-6111	183	11	stable	stable	ADJ
ejpam-6111	183	12	iff	iff	NOUN
ejpam-6111	183	13	its	its	PRON
ejpam-6111	183	14	jth	jth	PROPN
ejpam-6111	183	15	-	-	PUNCT
ejpam-6111	183	16	order	order	NOUN
ejpam-6111	183	17	principal	principal	ADJ
ejpam-6111	183	18	minors	minor	NOUN
ejpam-6111	183	19	are	be	AUX
ejpam-6111	183	20	of	of	ADP
ejpam-6111	183	21	sign	sign	NOUN
ejpam-6111	183	22	(	(	PUNCT
ejpam-6111	183	23	−1)j	−1)j	X
ejpam-6111	183	24	.	.	PUNCT
ejpam-6111	184	1	c12	c12	PROPN
ejpam-6111	184	2	:	:	PUNCT
ejpam-6111	184	3	given	give	VERB
ejpam-6111	184	4	m	m	PRON
ejpam-6111	184	5	∈	∈	NOUN
ejpam-6111	184	6	r3,3	r3,3	NOUN
ejpam-6111	184	7	with	with	ADP
ejpam-6111	184	8	all	all	PRON
ejpam-6111	184	9	of	of	ADP
ejpam-6111	184	10	its	its	PRON
ejpam-6111	184	11	jth	jth	ADJ
ejpam-6111	184	12	-	-	PUNCT
ejpam-6111	184	13	order	order	NOUN
ejpam-6111	184	14	principal	principal	ADJ
ejpam-6111	184	15	minors	minor	NOUN
ejpam-6111	184	16	are	be	AUX
ejpam-6111	184	17	with	with	ADP
ejpam-6111	184	18	sign	sign	NOUN
ejpam-6111	184	19	(	(	PUNCT
ejpam-6111	184	20	−1)j	−1)j	X
ejpam-6111	184	21	,	,	PUNCT
ejpam-6111	184	22	and	and	CCONJ
ejpam-6111	184	23	m11m22m33	m11m22m33	NOUN
ejpam-6111	184	24	<	<	X
ejpam-6111	184	25	m12m23m31	m12m23m31	PROPN
ejpam-6111	185	1	+	+	NOUN
ejpam-6111	185	2	m21m32m13	m21m32m13	NOUN
ejpam-6111	185	3	2	2	NUM
ejpam-6111	185	4	.	.	PUNCT
ejpam-6111	186	1	c13	c13	NOUN
ejpam-6111	186	2	:	:	PUNCT
ejpam-6111	186	3	given	give	VERB
ejpam-6111	186	4	given	give	VERB
ejpam-6111	186	5	m	m	PRON
ejpam-6111	186	6	∈	∈	PROPN
ejpam-6111	186	7	rn	rn	PROPN
ejpam-6111	186	8	,	,	PUNCT
ejpam-6111	186	9	n	n	PRON
ejpam-6111	186	10	is	be	AUX
ejpam-6111	186	11	strongly	strongly	ADV
ejpam-6111	186	12	d	d	ADJ
ejpam-6111	186	13	-	-	ADJ
ejpam-6111	186	14	stable	stable	ADJ
ejpam-6111	186	15	matrix	matrix	NOUN
ejpam-6111	186	16	if	if	SCONJ
ejpam-6111	186	17	for	for	ADP
ejpam-6111	186	18	n	n	DET
ejpam-6111	186	19	≤	≤	NUM
ejpam-6111	186	20	4	4	NUM
ejpam-6111	186	21	,	,	PUNCT
ejpam-6111	186	22	and	and	CCONJ
ejpam-6111	186	23	m	m	NOUN
ejpam-6111	186	24	satisfies	satisfy	VERB
ejpam-6111	186	25	gkk	gkk	PROPN
ejpam-6111	186	26	condition	condition	NOUN
ejpam-6111	186	27	.	.	PUNCT
ejpam-6111	187	1	s.	s.	PROPN
ejpam-6111	187	2	mazhar	mazhar	PROPN
ejpam-6111	187	3	,	,	PUNCT
ejpam-6111	187	4	m.	m.	NOUN
ejpam-6111	187	5	u.	u.	PROPN
ejpam-6111	187	6	rehman	rehman	PROPN
ejpam-6111	187	7	/	/	SYM
ejpam-6111	187	8	eur	eur	PROPN
ejpam-6111	187	9	.	.	PUNCT
ejpam-6111	188	1	j.	j.	PROPN
ejpam-6111	188	2	pure	pure	PROPN
ejpam-6111	188	3	appl	appl	PROPN
ejpam-6111	188	4	.	.	PROPN
ejpam-6111	188	5	math	math	PROPN
ejpam-6111	188	6	,	,	PUNCT
ejpam-6111	188	7	18	18	NUM
ejpam-6111	188	8	(	(	PUNCT
ejpam-6111	188	9	2	2	NUM
ejpam-6111	188	10	)	)	PUNCT
ejpam-6111	188	11	(	(	PUNCT
ejpam-6111	188	12	2025	2025	NUM
ejpam-6111	188	13	)	)	PUNCT
ejpam-6111	188	14	,	,	PUNCT
ejpam-6111	188	15	6111	6111	NUM
ejpam-6111	188	16	8	8	NUM
ejpam-6111	188	17	of	of	ADP
ejpam-6111	188	18	25	25	NUM
ejpam-6111	188	19	5	5	NUM
ejpam-6111	188	20	.	.	PUNCT
ejpam-6111	189	1	new	new	ADJ
ejpam-6111	189	2	results	result	NOUN
ejpam-6111	189	3	in	in	ADP
ejpam-6111	189	4	this	this	DET
ejpam-6111	189	5	section	section	NOUN
ejpam-6111	189	6	,	,	PUNCT
ejpam-6111	189	7	we	we	PRON
ejpam-6111	189	8	present	present	VERB
ejpam-6111	189	9	new	new	ADJ
ejpam-6111	189	10	results	result	NOUN
ejpam-6111	189	11	on	on	ADP
ejpam-6111	189	12	d	d	NOUN
ejpam-6111	189	13	-	-	NOUN
ejpam-6111	189	14	stability	stability	NOUN
ejpam-6111	189	15	and	and	CCONJ
ejpam-6111	189	16	strong	strong	ADJ
ejpam-6111	189	17	d	d	NOUN
ejpam-6111	189	18	-	-	NOUN
ejpam-6111	189	19	stability	stability	NOUN
ejpam-6111	189	20	for	for	ADP
ejpam-6111	189	21	structured	structured	ADJ
ejpam-6111	189	22	matrices	matrix	NOUN
ejpam-6111	189	23	associated	associate	VERB
ejpam-6111	189	24	with	with	ADP
ejpam-6111	189	25	lumped	lump	VERB
ejpam-6111	189	26	-	-	PUNCT
ejpam-6111	189	27	parameter	parameter	NOUN
ejpam-6111	189	28	dynamical	dynamical	ADJ
ejpam-6111	189	29	systems	system	NOUN
ejpam-6111	189	30	,	,	PUNCT
ejpam-6111	189	31	as	as	SCONJ
ejpam-6111	189	32	described	describe	VERB
ejpam-6111	189	33	in	in	ADP
ejpam-6111	189	34	the	the	DET
ejpam-6111	189	35	section	section	NOUN
ejpam-6111	189	36	on	on	ADP
ejpam-6111	189	37	problem	problem	NOUN
ejpam-6111	189	38	statement	statement	NOUN
ejpam-6111	189	39	.	.	PUNCT
ejpam-6111	190	1	we	we	PRON
ejpam-6111	190	2	make	make	VERB
ejpam-6111	190	3	use	use	NOUN
ejpam-6111	190	4	of	of	ADP
ejpam-6111	190	5	various	various	ADJ
ejpam-6111	190	6	mathematical	mathematical	ADJ
ejpam-6111	190	7	tools	tool	NOUN
ejpam-6111	190	8	from	from	ADP
ejpam-6111	190	9	linear	linear	PROPN
ejpam-6111	190	10	algebra	algebra	NOUN
ejpam-6111	190	11	,	,	PUNCT
ejpam-6111	190	12	matrix	matrix	NOUN
ejpam-6111	190	13	analysis	analysis	NOUN
ejpam-6111	190	14	and	and	CCONJ
ejpam-6111	190	15	system	system	NOUN
ejpam-6111	190	16	theory	theory	NOUN
ejpam-6111	190	17	to	to	PART
ejpam-6111	190	18	construct	construct	VERB
ejpam-6111	190	19	and	and	CCONJ
ejpam-6111	190	20	present	present	VERB
ejpam-6111	190	21	our	our	PRON
ejpam-6111	190	22	results	result	NOUN
ejpam-6111	190	23	.	.	PUNCT
ejpam-6111	191	1	the	the	DET
ejpam-6111	191	2	main	main	ADJ
ejpam-6111	191	3	ideas	idea	NOUN
ejpam-6111	191	4	involve	involve	VERB
ejpam-6111	191	5	the	the	DET
ejpam-6111	191	6	computation	computation	NOUN
ejpam-6111	191	7	of	of	ADP
ejpam-6111	191	8	the	the	DET
ejpam-6111	191	9	spectrum	spectrum	NOUN
ejpam-6111	191	10	and	and	CCONJ
ejpam-6111	191	11	the	the	DET
ejpam-6111	191	12	analysis	analysis	NOUN
ejpam-6111	191	13	of	of	ADP
ejpam-6111	191	14	the	the	DET
ejpam-6111	191	15	interconnections	interconnection	NOUN
ejpam-6111	191	16	between	between	ADP
ejpam-6111	191	17	d	d	NOUN
ejpam-6111	191	18	-	-	NOUN
ejpam-6111	191	19	stability	stability	NOUN
ejpam-6111	191	20	and	and	CCONJ
ejpam-6111	191	21	structured	structure	VERB
ejpam-6111	191	22	singular	singular	ADJ
ejpam-6111	191	23	values	value	NOUN
ejpam-6111	191	24	.	.	PUNCT
ejpam-6111	192	1	the	the	DET
ejpam-6111	192	2	characterization	characterization	NOUN
ejpam-6111	192	3	of	of	ADP
ejpam-6111	192	4	d	d	NOUN
ejpam-6111	192	5	-	-	NOUN
ejpam-6111	192	6	stability	stability	NOUN
ejpam-6111	192	7	[	[	X
ejpam-6111	192	8	35	35	NUM
ejpam-6111	192	9	]	]	X
ejpam-6111	192	10	for	for	ADP
ejpam-6111	192	11	a	a	DET
ejpam-6111	192	12	given	give	VERB
ejpam-6111	192	13	real	real	ADV
ejpam-6111	192	14	-	-	PUNCT
ejpam-6111	192	15	valued	value	VERB
ejpam-6111	192	16	n	n	CCONJ
ejpam-6111	192	17	-	-	PUNCT
ejpam-6111	192	18	dimensional	dimensional	ADJ
ejpam-6111	192	19	matrix	matrix	NOUN
ejpam-6111	192	20	m	m	VERB
ejpam-6111	192	21	in	in	ADP
ejpam-6111	192	22	terms	term	NOUN
ejpam-6111	192	23	of	of	ADP
ejpam-6111	192	24	the	the	DET
ejpam-6111	192	25	real	real	ADV
ejpam-6111	192	26	structured	structured	ADJ
ejpam-6111	192	27	singular	singular	ADJ
ejpam-6111	192	28	values	value	NOUN
ejpam-6111	192	29	is	be	AUX
ejpam-6111	192	30	given	give	VERB
ejpam-6111	192	31	by	by	ADP
ejpam-6111	192	32	the	the	DET
ejpam-6111	192	33	following	follow	VERB
ejpam-6111	192	34	theorem	theorem	NOUN
ejpam-6111	192	35	1	1	NUM
ejpam-6111	192	36	.	.	PUNCT
ejpam-6111	192	37	theorem	theorem	NOUN
ejpam-6111	192	38	1	1	NUM
ejpam-6111	192	39	.	.	PUNCT
ejpam-6111	193	1	let	let	VERB
ejpam-6111	193	2	m	m	PROPN
ejpam-6111	193	3	∈	∈	PROPN
ejpam-6111	193	4	rn	rn	PROPN
ejpam-6111	193	5	,	,	PUNCT
ejpam-6111	193	6	n	n	CCONJ
ejpam-6111	193	7	be	be	VERB
ejpam-6111	193	8	the	the	DET
ejpam-6111	193	9	given	give	VERB
ejpam-6111	193	10	matrix	matrix	NOUN
ejpam-6111	193	11	.	.	PUNCT
ejpam-6111	194	1	then	then	ADV
ejpam-6111	194	2	m	m	PROPN
ejpam-6111	194	3	is	be	AUX
ejpam-6111	194	4	a	a	DET
ejpam-6111	194	5	d	d	ADJ
ejpam-6111	194	6	-	-	ADJ
ejpam-6111	194	7	stable	stable	ADJ
ejpam-6111	194	8	matrix	matrix	NOUN
ejpam-6111	194	9	if	if	SCONJ
ejpam-6111	194	10	and	and	CCONJ
ejpam-6111	194	11	only	only	ADV
ejpam-6111	194	12	if	if	SCONJ
ejpam-6111	194	13	it	it	PRON
ejpam-6111	194	14	is	be	AUX
ejpam-6111	194	15	stable	stable	ADJ
ejpam-6111	194	16	and	and	CCONJ
ejpam-6111	194	17	none	none	NOUN
ejpam-6111	194	18	of	of	ADP
ejpam-6111	194	19	the	the	DET
ejpam-6111	194	20	eigenvalues	eigenvalue	NOUN
ejpam-6111	194	21	of	of	ADP
ejpam-6111	194	22	m	m	PROPN
ejpam-6111	194	23	±	±	NUM
ejpam-6111	194	24	i	i	NOUN
ejpam-6111	194	25	d	d	PROPN
ejpam-6111	194	26	is	be	AUX
ejpam-6111	194	27	exactly	exactly	ADV
ejpam-6111	194	28	equal	equal	ADJ
ejpam-6111	194	29	to	to	ADP
ejpam-6111	194	30	zero	zero	NUM
ejpam-6111	194	31	,	,	PUNCT
ejpam-6111	194	32	and	and	CCONJ
ejpam-6111	194	33	0	0	NUM
ejpam-6111	194	34	≤	≤	NUM
ejpam-6111	194	35	µb1	µb1	VERB
ejpam-6111	194	36	(	(	PUNCT
ejpam-6111	194	37	(	(	PUNCT
ejpam-6111	194	38	ii	ii	X
ejpam-6111	194	39	+	+	NOUN
ejpam-6111	194	40	m)−1(ii	m)−1(ii	ADJ
ejpam-6111	194	41	−m	−m	NOUN
ejpam-6111	194	42	)	)	PUNCT
ejpam-6111	194	43	)	)	PUNCT
ejpam-6111	194	44	<	<	X
ejpam-6111	195	1	1	1	X
ejpam-6111	195	2	.	.	PUNCT
ejpam-6111	195	3	the	the	DET
ejpam-6111	195	4	following	follow	VERB
ejpam-6111	195	5	theorem	theorem	ADJ
ejpam-6111	195	6	2	2	NUM
ejpam-6111	195	7	shows	show	VERB
ejpam-6111	195	8	that	that	SCONJ
ejpam-6111	195	9	(	(	PUNCT
ejpam-6111	195	10	in	in	ADP
ejpam-6111	195	11	−a⊗	−a⊗	PROPN
ejpam-6111	195	12	p	p	PROPN
ejpam-6111	195	13	t	t	PROPN
ejpam-6111	195	14	)	)	PUNCT
ejpam-6111	195	15	∈	∈	PROPN
ejpam-6111	195	16	rn	rn	PROPN
ejpam-6111	195	17	,	,	PUNCT
ejpam-6111	195	18	n	n	PRON
ejpam-6111	195	19	is	be	AUX
ejpam-6111	195	20	a	a	DET
ejpam-6111	195	21	d	d	ADJ
ejpam-6111	195	22	-	-	ADJ
ejpam-6111	195	23	stable	stable	ADJ
ejpam-6111	195	24	matrix	matrix	NOUN
ejpam-6111	195	25	if	if	SCONJ
ejpam-6111	195	26	it	it	PRON
ejpam-6111	195	27	is	be	AUX
ejpam-6111	195	28	stable	stable	ADJ
ejpam-6111	195	29	and	and	CCONJ
ejpam-6111	195	30	the	the	DET
ejpam-6111	195	31	structured	structured	ADJ
ejpam-6111	195	32	singular	singular	ADJ
ejpam-6111	195	33	values	value	NOUN
ejpam-6111	195	34	of	of	ADP
ejpam-6111	195	35	(	(	PUNCT
ejpam-6111	195	36	in	in	ADP
ejpam-6111	195	37	−	−	PROPN
ejpam-6111	195	38	a⊗	a⊗	NOUN
ejpam-6111	195	39	p	p	NOUN
ejpam-6111	195	40	t)−1	t)−1	NOUN
ejpam-6111	195	41	are	be	AUX
ejpam-6111	195	42	greater	great	ADJ
ejpam-6111	195	43	than	than	ADP
ejpam-6111	195	44	or	or	CCONJ
ejpam-6111	195	45	equal	equal	ADJ
ejpam-6111	195	46	to	to	ADP
ejpam-6111	195	47	zero	zero	NUM
ejpam-6111	195	48	and	and	CCONJ
ejpam-6111	195	49	strictly	strictly	ADV
ejpam-6111	195	50	less	less	ADJ
ejpam-6111	195	51	than	than	ADP
ejpam-6111	195	52	one	one	NUM
ejpam-6111	195	53	.	.	PUNCT
ejpam-6111	196	1	theorem	theorem	NOUN
ejpam-6111	196	2	2	2	NUM
ejpam-6111	196	3	.	.	X
ejpam-6111	197	1	let	let	VERB
ejpam-6111	197	2	(	(	PUNCT
ejpam-6111	197	3	in	in	ADP
ejpam-6111	197	4	−a⊗	−a⊗	PROPN
ejpam-6111	197	5	p	p	PROPN
ejpam-6111	197	6	t	t	PROPN
ejpam-6111	197	7	)	)	PUNCT
ejpam-6111	197	8	∈	∈	PROPN
ejpam-6111	197	9	rn	rn	PROPN
ejpam-6111	197	10	,	,	PUNCT
ejpam-6111	197	11	n.	n.	PROPN
ejpam-6111	197	12	then	then	ADV
ejpam-6111	197	13	(	(	PUNCT
ejpam-6111	197	14	in	in	ADP
ejpam-6111	197	15	−a⊗	−a⊗	PROPN
ejpam-6111	197	16	p	p	PROPN
ejpam-6111	197	17	t	t	PROPN
ejpam-6111	197	18	)	)	PUNCT
ejpam-6111	197	19	is	be	AUX
ejpam-6111	197	20	d	d	NOUN
ejpam-6111	197	21	-	-	ADJ
ejpam-6111	197	22	stable	stable	ADJ
ejpam-6111	197	23	if	if	SCONJ
ejpam-6111	197	24	(	(	PUNCT
ejpam-6111	197	25	in	in	ADP
ejpam-6111	197	26	−a⊗	−a⊗	PROPN
ejpam-6111	197	27	p	p	PROPN
ejpam-6111	197	28	t	t	PROPN
ejpam-6111	197	29	)	)	PUNCT
ejpam-6111	197	30	is	be	AUX
ejpam-6111	197	31	stable	stable	ADJ
ejpam-6111	197	32	,	,	PUNCT
ejpam-6111	197	33	and	and	CCONJ
ejpam-6111	197	34	0	0	NUM
ejpam-6111	197	35	≤	≤	NUM
ejpam-6111	197	36	µb1	µb1	NOUN
ejpam-6111	197	37	(	(	PUNCT
ejpam-6111	197	38	1	1	NUM
ejpam-6111	197	39	(	(	PUNCT
ejpam-6111	197	40	in−a⊗p	in−a⊗p	ADV
ejpam-6111	197	41	t)2	t)2	NOUN
ejpam-6111	197	42	)	)	PUNCT
ejpam-6111	197	43	<	<	X
ejpam-6111	198	1	1	1	X
ejpam-6111	198	2	.	.	PUNCT
ejpam-6111	198	3	proof	proof	NOUN
ejpam-6111	198	4	.	.	PUNCT
ejpam-6111	199	1	the	the	DET
ejpam-6111	199	2	matrix	matrix	NOUN
ejpam-6111	199	3	(	(	PUNCT
ejpam-6111	199	4	in	in	ADP
ejpam-6111	199	5	−a⊗p	−a⊗p	PROPN
ejpam-6111	199	6	t	t	PROPN
ejpam-6111	199	7	)	)	PUNCT
ejpam-6111	199	8	is	be	AUX
ejpam-6111	199	9	d	d	NOUN
ejpam-6111	199	10	-	-	ADJ
ejpam-6111	199	11	stable	stable	ADJ
ejpam-6111	199	12	if	if	SCONJ
ejpam-6111	199	13	and	and	CCONJ
ejpam-6111	199	14	only	only	ADV
ejpam-6111	199	15	if	if	SCONJ
ejpam-6111	199	16	(	(	PUNCT
ejpam-6111	199	17	in	in	ADP
ejpam-6111	199	18	−a⊗p	−a⊗p	PROPN
ejpam-6111	199	19	t	t	PROPN
ejpam-6111	199	20	)	)	PUNCT
ejpam-6111	199	21	is	be	AUX
ejpam-6111	199	22	stable	stable	ADJ
ejpam-6111	199	23	,	,	PUNCT
ejpam-6111	199	24	and	and	CCONJ
ejpam-6111	199	25	satisfy	satisfy	VERB
ejpam-6111	199	26	the	the	DET
ejpam-6111	199	27	condition	condition	NOUN
ejpam-6111	199	28	that∏	that∏	VERB
ejpam-6111	200	1	i	i	PRON
ejpam-6111	200	2	λi	λi	VERB
ejpam-6111	200	3	(	(	PUNCT
ejpam-6111	200	4	[	[	PUNCT
ejpam-6111	200	5	in	in	ADP
ejpam-6111	200	6	−a⊗	−a⊗	PROPN
ejpam-6111	200	7	p	p	X
ejpam-6111	200	8	t	t	X
ejpam-6111	200	9	−p	−p	NOUN
ejpam-6111	200	10	p	p	NOUN
ejpam-6111	200	11	in	in	ADP
ejpam-6111	200	12	−a⊗	−a⊗	PROPN
ejpam-6111	200	13	p	p	PROPN
ejpam-6111	200	14	t	t	PROPN
ejpam-6111	200	15	]	]	PUNCT
ejpam-6111	200	16	)	)	PUNCT
ejpam-6111	200	17	̸=	̸=	NOUN
ejpam-6111	200	18	0	0	NUM
ejpam-6111	200	19	∀i	∀i	NOUN
ejpam-6111	200	20	.	.	PUNCT
ejpam-6111	201	1	to	to	PART
ejpam-6111	201	2	show	show	VERB
ejpam-6111	201	3	that	that	SCONJ
ejpam-6111	201	4	0	0	NUM
ejpam-6111	201	5	≤	≤	NUM
ejpam-6111	201	6	µb1	µb1	NOUN
ejpam-6111	201	7	(	(	PUNCT
ejpam-6111	201	8	1	1	NUM
ejpam-6111	201	9	(	(	PUNCT
ejpam-6111	201	10	in−a⊗p	in−a⊗p	ADV
ejpam-6111	201	11	t)2	t)2	NOUN
ejpam-6111	201	12	)	)	PUNCT
ejpam-6111	201	13	<	<	X
ejpam-6111	201	14	1	1	NUM
ejpam-6111	201	15	,	,	PUNCT
ejpam-6111	201	16	it	it	PRON
ejpam-6111	201	17	is	be	AUX
ejpam-6111	201	18	enough	enough	ADJ
ejpam-6111	201	19	to	to	PART
ejpam-6111	201	20	show	show	VERB
ejpam-6111	201	21	that	that	SCONJ
ejpam-6111	201	22	∏	∏	PROPN
ejpam-6111	201	23	i	i	PRON
ejpam-6111	201	24	λi	λi	X
ejpam-6111	201	25	(	(	PUNCT
ejpam-6111	201	26	[	[	PUNCT
ejpam-6111	201	27	in	in	ADP
ejpam-6111	201	28	−a⊗	−a⊗	PROPN
ejpam-6111	201	29	p	p	X
ejpam-6111	201	30	t	t	X
ejpam-6111	201	31	−p	−p	NOUN
ejpam-6111	201	32	p	p	NOUN
ejpam-6111	201	33	in	in	ADP
ejpam-6111	201	34	−a⊗	−a⊗	PROPN
ejpam-6111	201	35	p	p	PROPN
ejpam-6111	201	36	t	t	PROPN
ejpam-6111	201	37	]	]	PUNCT
ejpam-6111	201	38	)	)	PUNCT
ejpam-6111	201	39	̸=	̸=	NOUN
ejpam-6111	201	40	0	0	NUM
ejpam-6111	201	41	∀i,∀p	∀i,∀p	PROPN
ejpam-6111	201	42	∈	∈	PROPN
ejpam-6111	201	43	ω	ω	PROPN
ejpam-6111	201	44	,	,	PUNCT
ejpam-6111	201	45	where	where	SCONJ
ejpam-6111	201	46	ω	ω	X
ejpam-6111	201	47	=	=	PRON
ejpam-6111	201	48	{	{	PUNCT
ejpam-6111	201	49	p	p	X
ejpam-6111	201	50	∈	∈	PROPN
ejpam-6111	201	51	rn	rn	PROPN
ejpam-6111	201	52	,	,	PUNCT
ejpam-6111	201	53	n	n	NUM
ejpam-6111	201	54	:	:	PUNCT
ejpam-6111	201	55	diag(pii	diag(pii	NOUN
ejpam-6111	201	56	)	)	PUNCT
ejpam-6111	201	57	>	>	X
ejpam-6111	201	58	0	0	NUM
ejpam-6111	201	59	∀i	∀i	NOUN
ejpam-6111	201	60	}	}	PUNCT
ejpam-6111	201	61	.	.	PUNCT
ejpam-6111	202	1	since	since	SCONJ
ejpam-6111	202	2	we	we	PRON
ejpam-6111	202	3	know	know	VERB
ejpam-6111	202	4	that	that	SCONJ
ejpam-6111	202	5	∏	∏	NUM
ejpam-6111	202	6	i	i	PRON
ejpam-6111	202	7	λi	λi	VERB
ejpam-6111	202	8	(	(	PUNCT
ejpam-6111	202	9	[	[	PUNCT
ejpam-6111	202	10	in	in	ADP
ejpam-6111	202	11	−a⊗	−a⊗	PROPN
ejpam-6111	202	12	p	p	X
ejpam-6111	202	13	t	t	X
ejpam-6111	202	14	−p	−p	NOUN
ejpam-6111	202	15	p	p	NOUN
ejpam-6111	202	16	in	in	ADP
ejpam-6111	202	17	−a⊗	−a⊗	PROPN
ejpam-6111	202	18	p	p	PROPN
ejpam-6111	202	19	t	t	PROPN
ejpam-6111	202	20	]	]	PUNCT
ejpam-6111	202	21	)	)	PUNCT
ejpam-6111	202	22	̸=	̸=	PROPN
ejpam-6111	202	23	0	0	NUM
ejpam-6111	202	24	.	.	PUNCT
ejpam-6111	203	1	in	in	ADP
ejpam-6111	203	2	turn	turn	NOUN
ejpam-6111	203	3	this	this	PRON
ejpam-6111	203	4	implies	imply	VERB
ejpam-6111	203	5	that∏	that∏	VERB
ejpam-6111	204	1	i	i	PRON
ejpam-6111	204	2	λi	λi	VERB
ejpam-6111	204	3	[	[	X
ejpam-6111	204	4	(	(	PUNCT
ejpam-6111	204	5	in	in	ADP
ejpam-6111	204	6	−a⊗	−a⊗	PROPN
ejpam-6111	204	7	p	p	PROPN
ejpam-6111	204	8	t	t	PROPN
ejpam-6111	204	9	)	)	PUNCT
ejpam-6111	204	10	2	2	NUM
ejpam-6111	204	11	−	−	NOUN
ejpam-6111	204	12	p	p	NOUN
ejpam-6111	204	13	(	(	PUNCT
ejpam-6111	204	14	1	1	NUM
ejpam-6111	204	15	(	(	PUNCT
ejpam-6111	204	16	in	in	ADP
ejpam-6111	204	17	−a⊗	−a⊗	PROPN
ejpam-6111	204	18	p	p	PROPN
ejpam-6111	204	19	t	t	PROPN
ejpam-6111	204	20	)	)	PUNCT
ejpam-6111	204	21	)	)	PUNCT
ejpam-6111	205	1	p	p	X
ejpam-6111	205	2	(	(	PUNCT
ejpam-6111	205	3	in	in	ADP
ejpam-6111	205	4	−a⊗	−a⊗	PROPN
ejpam-6111	205	5	p	p	PROPN
ejpam-6111	205	6	t	t	PROPN
ejpam-6111	205	7	)	)	PUNCT
ejpam-6111	205	8	]	]	PUNCT
ejpam-6111	206	1	̸=	̸=	PROPN
ejpam-6111	206	2	0	0	NUM
ejpam-6111	206	3	.	.	PUNCT
ejpam-6111	207	1	s.	s.	PROPN
ejpam-6111	207	2	mazhar	mazhar	PROPN
ejpam-6111	207	3	,	,	PUNCT
ejpam-6111	207	4	m.	m.	NOUN
ejpam-6111	207	5	u.	u.	PROPN
ejpam-6111	207	6	rehman	rehman	PROPN
ejpam-6111	207	7	/	/	SYM
ejpam-6111	207	8	eur	eur	PROPN
ejpam-6111	207	9	.	.	PUNCT
ejpam-6111	208	1	j.	j.	PROPN
ejpam-6111	208	2	pure	pure	PROPN
ejpam-6111	208	3	appl	appl	PROPN
ejpam-6111	208	4	.	.	PROPN
ejpam-6111	208	5	math	math	PROPN
ejpam-6111	208	6	,	,	PUNCT
ejpam-6111	208	7	18	18	NUM
ejpam-6111	208	8	(	(	PUNCT
ejpam-6111	208	9	2	2	NUM
ejpam-6111	208	10	)	)	PUNCT
ejpam-6111	208	11	(	(	PUNCT
ejpam-6111	208	12	2025	2025	NUM
ejpam-6111	208	13	)	)	PUNCT
ejpam-6111	208	14	,	,	PUNCT
ejpam-6111	208	15	6111	6111	NUM
ejpam-6111	208	16	9	9	NUM
ejpam-6111	208	17	of	of	ADP
ejpam-6111	208	18	25	25	NUM
ejpam-6111	208	19	also	also	ADV
ejpam-6111	208	20	,	,	PUNCT
ejpam-6111	208	21	∏	∏	PROPN
ejpam-6111	208	22	i	i	PRON
ejpam-6111	208	23	λi	λi	VERB
ejpam-6111	208	24	(	(	PUNCT
ejpam-6111	208	25	in	in	ADP
ejpam-6111	208	26	−	−	NUM
ejpam-6111	208	27	1	1	NUM
ejpam-6111	208	28	(	(	PUNCT
ejpam-6111	208	29	in−a⊗p	in−a⊗p	ADV
ejpam-6111	208	30	t)2	t)2	PROPN
ejpam-6111	208	31	p̃	p̃	PROPN
ejpam-6111	208	32	)	)	PUNCT
ejpam-6111	208	33	̸=	̸=	PROPN
ejpam-6111	208	34	0	0	NUM
ejpam-6111	208	35	,	,	PUNCT
ejpam-6111	208	36	where	where	SCONJ
ejpam-6111	208	37	p̃	p̃	PROPN
ejpam-6111	208	38	=	=	SYM
ejpam-6111	208	39	diag(p̃ii	diag(p̃ii	PROPN
ejpam-6111	208	40	)	)	PUNCT
ejpam-6111	209	1	=	=	SYM
ejpam-6111	210	1	p	p	X
ejpam-6111	210	2	,	,	PUNCT
ejpam-6111	210	3	a	a	DET
ejpam-6111	210	4	positive	positive	ADJ
ejpam-6111	210	5	diagonal	diagonal	ADJ
ejpam-6111	210	6	matrix	matrix	NOUN
ejpam-6111	210	7	from	from	ADP
ejpam-6111	210	8	ω	ω	PROPN
ejpam-6111	210	9	.	.	PUNCT
ejpam-6111	211	1	further	far	ADV
ejpam-6111	211	2	,	,	PUNCT
ejpam-6111	211	3	we	we	PRON
ejpam-6111	211	4	have∏	have∏	VERB
ejpam-6111	211	5	i	i	PRON
ejpam-6111	211	6	λi	λi	VERB
ejpam-6111	211	7	(	(	PUNCT
ejpam-6111	211	8	in	in	ADP
ejpam-6111	211	9	−	−	PROPN
ejpam-6111	211	10	1	1	NUM
ejpam-6111	211	11	(	(	PUNCT
ejpam-6111	211	12	in	in	ADP
ejpam-6111	211	13	−a⊗	−a⊗	PROPN
ejpam-6111	211	14	p	p	PRON
ejpam-6111	211	15	t)2	t)2	PROPN
ejpam-6111	211	16	p̃	p̃	PROPN
ejpam-6111	211	17	)	)	PUNCT
ejpam-6111	211	18	̸=	̸=	PROPN
ejpam-6111	211	19	0	0	NUM
ejpam-6111	211	20	.	.	PUNCT
ejpam-6111	212	1	thus	thus	ADV
ejpam-6111	212	2	,	,	PUNCT
ejpam-6111	212	3	finally	finally	ADV
ejpam-6111	212	4	we	we	PRON
ejpam-6111	212	5	have	have	VERB
ejpam-6111	212	6	that	that	DET
ejpam-6111	212	7	0	0	NUM
ejpam-6111	212	8	≤	≤	NUM
ejpam-6111	212	9	µb1	µb1	NOUN
ejpam-6111	212	10	(	(	PUNCT
ejpam-6111	212	11	1	1	NUM
ejpam-6111	212	12	(	(	PUNCT
ejpam-6111	212	13	in−a⊗p	in−a⊗p	ADV
ejpam-6111	212	14	t)2	t)2	NOUN
ejpam-6111	212	15	)	)	PUNCT
ejpam-6111	212	16	<	<	X
ejpam-6111	213	1	1	1	X
ejpam-6111	213	2	.	.	PUNCT
ejpam-6111	214	1	the	the	DET
ejpam-6111	214	2	following	follow	VERB
ejpam-6111	214	3	theorem	theorem	VERB
ejpam-6111	214	4	3	3	NUM
ejpam-6111	214	5	shows	show	VERB
ejpam-6111	214	6	d	d	NOUN
ejpam-6111	214	7	-	-	NOUN
ejpam-6111	214	8	stability	stability	NOUN
ejpam-6111	214	9	of	of	ADP
ejpam-6111	214	10	(	(	PUNCT
ejpam-6111	214	11	in	in	ADP
ejpam-6111	214	12	−a⊗	−a⊗	PROPN
ejpam-6111	214	13	p	p	PROPN
ejpam-6111	214	14	t	t	PROPN
ejpam-6111	214	15	)	)	PUNCT
ejpam-6111	214	16	∈	∈	PROPN
ejpam-6111	214	17	rn	rn	PROPN
ejpam-6111	214	18	,	,	PUNCT
ejpam-6111	214	19	n	n	CCONJ
ejpam-6111	214	20	if	if	SCONJ
ejpam-6111	214	21	the	the	DET
ejpam-6111	214	22	real	real	ADJ
ejpam-6111	214	23	part	part	NOUN
ejpam-6111	214	24	of	of	ADP
ejpam-6111	214	25	all	all	DET
ejpam-6111	214	26	the	the	DET
ejpam-6111	214	27	eigenvalues	eigenvalue	NOUN
ejpam-6111	214	28	of	of	ADP
ejpam-6111	214	29	p	p	NOUN
ejpam-6111	214	30	(	(	PUNCT
ejpam-6111	214	31	in	in	ADP
ejpam-6111	214	32	−a⊗	−a⊗	PROPN
ejpam-6111	214	33	p	p	PROPN
ejpam-6111	214	34	t	t	PROPN
ejpam-6111	214	35	)	)	PUNCT
ejpam-6111	214	36	+	+	CCONJ
ejpam-6111	214	37	(	(	PUNCT
ejpam-6111	214	38	in	in	ADP
ejpam-6111	214	39	−a⊗	−a⊗	PROPN
ejpam-6111	214	40	p	p	PROPN
ejpam-6111	215	1	t)tp	t)tp	PROPN
ejpam-6111	216	1	is	be	AUX
ejpam-6111	216	2	strictly	strictly	ADV
ejpam-6111	216	3	positive	positive	ADJ
ejpam-6111	216	4	.	.	PUNCT
ejpam-6111	217	1	theorem	theorem	NOUN
ejpam-6111	217	2	3	3	X
ejpam-6111	217	3	.	.	PUNCT
ejpam-6111	218	1	let	let	VERB
ejpam-6111	218	2	(	(	PUNCT
ejpam-6111	218	3	in	in	ADP
ejpam-6111	218	4	−a⊗	−a⊗	PROPN
ejpam-6111	218	5	p	p	PROPN
ejpam-6111	218	6	t	t	PROPN
ejpam-6111	218	7	)	)	PUNCT
ejpam-6111	218	8	∈	∈	PROPN
ejpam-6111	218	9	rn	rn	PROPN
ejpam-6111	218	10	,	,	PUNCT
ejpam-6111	218	11	n.	n.	PROPN
ejpam-6111	218	12	then	then	ADV
ejpam-6111	218	13	(	(	PUNCT
ejpam-6111	218	14	in	in	ADP
ejpam-6111	218	15	−a⊗	−a⊗	PROPN
ejpam-6111	218	16	p	p	PROPN
ejpam-6111	218	17	t	t	PROPN
ejpam-6111	218	18	)	)	PUNCT
ejpam-6111	218	19	is	be	AUX
ejpam-6111	218	20	d	d	NOUN
ejpam-6111	218	21	-	-	ADJ
ejpam-6111	218	22	stable	stable	ADJ
ejpam-6111	218	23	if	if	SCONJ
ejpam-6111	218	24	re	re	ADP
ejpam-6111	218	25	[	[	PUNCT
ejpam-6111	218	26	λi(p	λi(p	X
ejpam-6111	218	27	(	(	PUNCT
ejpam-6111	218	28	in	in	ADP
ejpam-6111	218	29	−a⊗	−a⊗	PROPN
ejpam-6111	218	30	p	p	PROPN
ejpam-6111	218	31	t	t	PROPN
ejpam-6111	218	32	)	)	PUNCT
ejpam-6111	219	1	+	+	CCONJ
ejpam-6111	219	2	(	(	PUNCT
ejpam-6111	219	3	in	in	ADP
ejpam-6111	219	4	−a⊗	−a⊗	PROPN
ejpam-6111	219	5	p	p	PROPN
ejpam-6111	219	6	t)tp	t)tp	PROPN
ejpam-6111	219	7	)	)	PUNCT
ejpam-6111	219	8	]	]	PUNCT
ejpam-6111	220	1	>	>	X
ejpam-6111	220	2	0	0	NUM
ejpam-6111	220	3	,	,	PUNCT
ejpam-6111	220	4	∀i	∀i	NOUN
ejpam-6111	220	5	,	,	PUNCT
ejpam-6111	220	6	∀p	∀p	PROPN
ejpam-6111	220	7	∈	∈	NOUN
ejpam-6111	220	8	ω	ω	NOUN
ejpam-6111	220	9	,	,	PUNCT
ejpam-6111	220	10	where	where	SCONJ
ejpam-6111	220	11	ω	ω	X
ejpam-6111	220	12	:	:	PUNCT
ejpam-6111	220	13	=	=	SYM
ejpam-6111	220	14	{	{	PUNCT
ejpam-6111	220	15	p	p	X
ejpam-6111	220	16	∈	∈	PROPN
ejpam-6111	220	17	rn	rn	PROPN
ejpam-6111	220	18	,	,	PUNCT
ejpam-6111	220	19	n	n	NUM
ejpam-6111	220	20	:	:	PUNCT
ejpam-6111	220	21	diag(pii	diag(pii	NOUN
ejpam-6111	220	22	)	)	PUNCT
ejpam-6111	220	23	>	>	X
ejpam-6111	220	24	0	0	NUM
ejpam-6111	220	25	,	,	PUNCT
ejpam-6111	220	26	∀i	∀i	NOUN
ejpam-6111	220	27	}	}	PUNCT
ejpam-6111	220	28	,	,	PUNCT
ejpam-6111	220	29	and	and	CCONJ
ejpam-6111	220	30	0	0	NUM
ejpam-6111	220	31	≤	≤	NUM
ejpam-6111	220	32	µb1	µb1	VERB
ejpam-6111	220	33	[	[	X
ejpam-6111	220	34	(	(	PUNCT
ejpam-6111	220	35	iin+p	iin+p	PROPN
ejpam-6111	220	36	(	(	PUNCT
ejpam-6111	220	37	in−a⊗p	in−a⊗p	ADV
ejpam-6111	220	38	t)+(in−a⊗p	t)+(in−a⊗p	NOUN
ejpam-6111	220	39	t)t	t)t	X
ejpam-6111	220	40	p	p	NOUN
ejpam-6111	220	41	)	)	PUNCT
ejpam-6111	220	42	−1	−1	NOUN
ejpam-6111	220	43	(	(	PUNCT
ejpam-6111	220	44	iin−p	iin−p	X
ejpam-6111	220	45	(	(	PUNCT
ejpam-6111	220	46	in−a⊗p	in−a⊗p	ADV
ejpam-6111	220	47	t)−(in−a⊗p	t)−(in−a⊗p	X
ejpam-6111	220	48	t)t	t)t	X
ejpam-6111	220	49	p	p	NOUN
ejpam-6111	220	50	)	)	PUNCT
ejpam-6111	220	51	]	]	PUNCT
ejpam-6111	221	1	<	<	X
ejpam-6111	221	2	1	1	X
ejpam-6111	221	3	.	.	PUNCT
ejpam-6111	221	4	proof	proof	NOUN
ejpam-6111	221	5	.	.	PUNCT
ejpam-6111	222	1	we	we	PRON
ejpam-6111	222	2	aim	aim	VERB
ejpam-6111	222	3	to	to	PART
ejpam-6111	222	4	show	show	VERB
ejpam-6111	222	5	that	that	SCONJ
ejpam-6111	222	6	(	(	PUNCT
ejpam-6111	222	7	in	in	ADP
ejpam-6111	222	8	−a⊗	−a⊗	PROPN
ejpam-6111	222	9	p	p	PROPN
ejpam-6111	222	10	t	t	PROPN
ejpam-6111	222	11	)	)	PUNCT
ejpam-6111	222	12	is	be	AUX
ejpam-6111	222	13	d	d	ADJ
ejpam-6111	222	14	-	-	ADJ
ejpam-6111	222	15	stable	stable	ADJ
ejpam-6111	222	16	matrix	matrix	NOUN
ejpam-6111	222	17	if	if	SCONJ
ejpam-6111	222	18	re	re	VERB
ejpam-6111	222	19	[	[	PUNCT
ejpam-6111	222	20	λi	λi	X
ejpam-6111	222	21	(	(	PUNCT
ejpam-6111	222	22	p	p	X
ejpam-6111	222	23	(	(	PUNCT
ejpam-6111	222	24	in	in	ADP
ejpam-6111	222	25	−a⊗	−a⊗	PROPN
ejpam-6111	222	26	p	p	PROPN
ejpam-6111	222	27	t	t	PROPN
ejpam-6111	222	28	)	)	PUNCT
ejpam-6111	222	29	+	+	CCONJ
ejpam-6111	222	30	(	(	PUNCT
ejpam-6111	222	31	in	in	ADP
ejpam-6111	222	32	−a⊗	−a⊗	PROPN
ejpam-6111	222	33	p	p	PROPN
ejpam-6111	222	34	t)tp	t)tp	PROPN
ejpam-6111	222	35	)	)	PUNCT
ejpam-6111	222	36	]	]	PUNCT
ejpam-6111	223	1	>	>	X
ejpam-6111	223	2	0	0	NUM
ejpam-6111	223	3	,	,	PUNCT
ejpam-6111	223	4	∀i	∀i	NOUN
ejpam-6111	223	5	,	,	PUNCT
ejpam-6111	223	6	∀p	∀p	PROPN
ejpam-6111	223	7	∈	∈	PROPN
ejpam-6111	223	8	ω	ω	NOUN
ejpam-6111	223	9	.	.	PUNCT
ejpam-6111	223	10	to	to	PART
ejpam-6111	223	11	prove	prove	VERB
ejpam-6111	223	12	we	we	PRON
ejpam-6111	223	13	have	have	VERB
ejpam-6111	223	14	to	to	PART
ejpam-6111	223	15	follow	follow	VERB
ejpam-6111	223	16	all	all	DET
ejpam-6111	223	17	steps	step	NOUN
ejpam-6111	223	18	of	of	ADP
ejpam-6111	223	19	theorem	theorem	NOUN
ejpam-6111	223	20	1	1	NUM
ejpam-6111	223	21	.	.	PUNCT
ejpam-6111	224	1	next	next	ADV
ejpam-6111	224	2	,	,	PUNCT
ejpam-6111	224	3	we	we	PRON
ejpam-6111	224	4	aim	aim	VERB
ejpam-6111	224	5	to	to	PART
ejpam-6111	224	6	prove	prove	VERB
ejpam-6111	224	7	that	that	SCONJ
ejpam-6111	224	8	(	(	PUNCT
ejpam-6111	224	9	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	224	10	t	t	NOUN
ejpam-6111	224	11	)	)	PUNCT
ejpam-6111	224	12	is	be	AUX
ejpam-6111	224	13	d	d	ADJ
ejpam-6111	224	14	-	-	ADJ
ejpam-6111	224	15	stable	stable	ADJ
ejpam-6111	224	16	matrix	matrix	NOUN
ejpam-6111	224	17	if	if	SCONJ
ejpam-6111	224	18	it	it	PRON
ejpam-6111	224	19	’s	’	VERB
ejpam-6111	224	20	structured	structure	VERB
ejpam-6111	224	21	singular	singular	ADJ
ejpam-6111	224	22	value	value	NOUN
ejpam-6111	224	23	is	be	AUX
ejpam-6111	224	24	strictly	strictly	ADV
ejpam-6111	224	25	less	less	ADJ
ejpam-6111	224	26	than	than	ADP
ejpam-6111	224	27	1	1	NUM
ejpam-6111	224	28	.	.	PUNCT
ejpam-6111	225	1	for	for	ADP
ejpam-6111	225	2	this	this	PRON
ejpam-6111	225	3	,	,	PUNCT
ejpam-6111	225	4	we	we	PRON
ejpam-6111	225	5	consider	consider	VERB
ejpam-6111	225	6	∆	∆	PROPN
ejpam-6111	225	7	∈	∈	PROPN
ejpam-6111	225	8	b1	b1	NOUN
ejpam-6111	225	9	,	,	PUNCT
ejpam-6111	225	10	a	a	DET
ejpam-6111	225	11	block	block	NOUN
ejpam-6111	225	12	diagonal	diagonal	ADJ
ejpam-6111	225	13	structured	structure	VERB
ejpam-6111	225	14	matrix	matrix	NOUN
ejpam-6111	225	15	.	.	PUNCT
ejpam-6111	226	1	let	let	VERB
ejpam-6111	226	2	∆	∆	PROPN
ejpam-6111	227	1	=	=	PRON
ejpam-6111	228	1	(	(	PUNCT
ejpam-6111	228	2	i	i	PRON
ejpam-6111	228	3	in	in	ADP
ejpam-6111	228	4	−	−	PROPN
ejpam-6111	228	5	p	p	NOUN
ejpam-6111	228	6	)	)	PUNCT
ejpam-6111	228	7	(	(	PUNCT
ejpam-6111	228	8	i	i	PRON
ejpam-6111	228	9	in	in	ADP
ejpam-6111	228	10	+	+	CCONJ
ejpam-6111	228	11	p	p	NOUN
ejpam-6111	228	12	)	)	PUNCT
ejpam-6111	228	13	−1	−1	NOUN
ejpam-6111	228	14	.	.	PUNCT
ejpam-6111	229	1	as	as	ADP
ejpam-6111	229	2	,	,	PUNCT
ejpam-6111	229	3	we	we	PRON
ejpam-6111	229	4	know	know	VERB
ejpam-6111	229	5	that	that	PRON
ejpam-6111	229	6	for	for	ADP
ejpam-6111	229	7	p	p	PROPN
ejpam-6111	229	8	∈	∈	PROPN
ejpam-6111	229	9	ω	ω	PROPN
ejpam-6111	229	10	,	,	PUNCT
ejpam-6111	229	11	and	and	CCONJ
ejpam-6111	229	12	for	for	ADP
ejpam-6111	229	13	given	give	VERB
ejpam-6111	229	14	(	(	PUNCT
ejpam-6111	229	15	in	in	ADP
ejpam-6111	229	16	−a⊗	−a⊗	PROPN
ejpam-6111	229	17	p	p	PROPN
ejpam-6111	229	18	t	t	PROPN
ejpam-6111	229	19	)	)	PUNCT
ejpam-6111	229	20	,	,	PUNCT
ejpam-6111	229	21	we	we	PRON
ejpam-6111	229	22	have	have	VERB
ejpam-6111	229	23	that	that	PRON
ejpam-6111	229	24	λi	λi	ADP
ejpam-6111	229	25	[	[	PUNCT
ejpam-6111	229	26	p	p	X
ejpam-6111	229	27	(	(	PUNCT
ejpam-6111	229	28	in	in	ADP
ejpam-6111	229	29	−a⊗	−a⊗	PROPN
ejpam-6111	229	30	p	p	PROPN
ejpam-6111	229	31	t	t	PROPN
ejpam-6111	229	32	)	)	PUNCT
ejpam-6111	230	1	+	+	CCONJ
ejpam-6111	230	2	(	(	PUNCT
ejpam-6111	230	3	in	in	ADP
ejpam-6111	230	4	−a⊗	−a⊗	PROPN
ejpam-6111	230	5	p	p	PROPN
ejpam-6111	230	6	t)tp	t)tp	PROPN
ejpam-6111	230	7	]	]	PUNCT
ejpam-6111	230	8	̸=	̸=	PROPN
ejpam-6111	230	9	0	0	NUM
ejpam-6111	230	10	.	.	PUNCT
ejpam-6111	231	1	this	this	DET
ejpam-6111	231	2	yields	yield	NOUN
ejpam-6111	231	3	that	that	PRON
ejpam-6111	231	4	λi	λi	ADP
ejpam-6111	231	5	[	[	PUNCT
ejpam-6111	231	6	p	p	X
ejpam-6111	231	7	(	(	PUNCT
ejpam-6111	231	8	in	in	ADP
ejpam-6111	231	9	−a⊗	−a⊗	PROPN
ejpam-6111	231	10	p	p	PROPN
ejpam-6111	231	11	t	t	PROPN
ejpam-6111	231	12	)	)	PUNCT
ejpam-6111	231	13	+	+	CCONJ
ejpam-6111	231	14	(	(	PUNCT
ejpam-6111	231	15	in	in	ADP
ejpam-6111	231	16	−a⊗	−a⊗	PROPN
ejpam-6111	231	17	p	p	PROPN
ejpam-6111	231	18	t)tp	t)tp	PROPN
ejpam-6111	231	19	+	+	CCONJ
ejpam-6111	231	20	ip	ip	NOUN
ejpam-6111	231	21	]	]	X
ejpam-6111	231	22	̸=	̸=	PROPN
ejpam-6111	231	23	0	0	NUM
ejpam-6111	231	24	,	,	PUNCT
ejpam-6111	231	25	∀i	∀i	X
ejpam-6111	231	26	if	if	SCONJ
ejpam-6111	231	27	λi	λi	ADP
ejpam-6111	231	28	[	[	PUNCT
ejpam-6111	231	29	p	p	X
ejpam-6111	231	30	(	(	PUNCT
ejpam-6111	231	31	in	in	ADP
ejpam-6111	231	32	−a⊗	−a⊗	PROPN
ejpam-6111	231	33	p	p	PROPN
ejpam-6111	231	34	t	t	PROPN
ejpam-6111	231	35	)	)	PUNCT
ejpam-6111	231	36	+	+	CCONJ
ejpam-6111	231	37	(	(	PUNCT
ejpam-6111	231	38	in	in	ADP
ejpam-6111	231	39	−a⊗	−a⊗	PROPN
ejpam-6111	231	40	p	p	PROPN
ejpam-6111	231	41	t)tp	t)tp	PROPN
ejpam-6111	231	42	+	+	CCONJ
ejpam-6111	231	43	i(i	i(i	PROPN
ejpam-6111	231	44	in	in	ADP
ejpam-6111	231	45	+	+	NOUN
ejpam-6111	231	46	∆)−1(i	∆)−1(i	NOUN
ejpam-6111	231	47	in	in	ADP
ejpam-6111	231	48	−∆	−∆	NOUN
ejpam-6111	231	49	)	)	PUNCT
ejpam-6111	231	50	]	]	PUNCT
ejpam-6111	232	1	̸=	̸=	PROPN
ejpam-6111	232	2	0	0	NUM
ejpam-6111	232	3	.	.	PUNCT
ejpam-6111	233	1	s.	s.	PROPN
ejpam-6111	233	2	mazhar	mazhar	PROPN
ejpam-6111	233	3	,	,	PUNCT
ejpam-6111	233	4	m.	m.	NOUN
ejpam-6111	233	5	u.	u.	PROPN
ejpam-6111	233	6	rehman	rehman	PROPN
ejpam-6111	233	7	/	/	SYM
ejpam-6111	233	8	eur	eur	PROPN
ejpam-6111	233	9	.	.	PUNCT
ejpam-6111	234	1	j.	j.	PROPN
ejpam-6111	234	2	pure	pure	PROPN
ejpam-6111	234	3	appl	appl	PROPN
ejpam-6111	234	4	.	.	PROPN
ejpam-6111	234	5	math	math	PROPN
ejpam-6111	234	6	,	,	PUNCT
ejpam-6111	234	7	18	18	NUM
ejpam-6111	234	8	(	(	PUNCT
ejpam-6111	234	9	2	2	NUM
ejpam-6111	234	10	)	)	PUNCT
ejpam-6111	234	11	(	(	PUNCT
ejpam-6111	234	12	2025	2025	NUM
ejpam-6111	234	13	)	)	PUNCT
ejpam-6111	234	14	,	,	PUNCT
ejpam-6111	234	15	6111	6111	NUM
ejpam-6111	234	16	10	10	NUM
ejpam-6111	234	17	of	of	ADP
ejpam-6111	234	18	25	25	NUM
ejpam-6111	234	19	in	in	ADP
ejpam-6111	234	20	turn	turn	NOUN
ejpam-6111	234	21	this	this	PRON
ejpam-6111	234	22	implies	imply	VERB
ejpam-6111	234	23	that	that	SCONJ
ejpam-6111	234	24	λi	λi	ADP
ejpam-6111	234	25	[	[	X
ejpam-6111	234	26	(	(	PUNCT
ejpam-6111	234	27	i	i	PRON
ejpam-6111	234	28	in+p	in+p	PROPN
ejpam-6111	234	29	(	(	PUNCT
ejpam-6111	234	30	in−a⊗p	in−a⊗p	NOUN
ejpam-6111	234	31	t)+(in−a⊗p	t)+(in−a⊗p	PROPN
ejpam-6111	234	32	t)tp	t)tp	PROPN
ejpam-6111	234	33	)	)	PUNCT
ejpam-6111	234	34	−	−	PROPN
ejpam-6111	235	1	(	(	PUNCT
ejpam-6111	235	2	i	i	PRON
ejpam-6111	235	3	in−p	in−p	VERB
ejpam-6111	235	4	(	(	PUNCT
ejpam-6111	235	5	in−a⊗p	in−a⊗p	NOUN
ejpam-6111	235	6	t)−(in−a⊗p	t)−(in−a⊗p	PROPN
ejpam-6111	235	7	t)tp	t)tp	NOUN
ejpam-6111	235	8	)	)	PUNCT
ejpam-6111	235	9	∆	∆	PROPN
ejpam-6111	235	10	]	]	PUNCT
ejpam-6111	236	1	̸=	̸=	PROPN
ejpam-6111	236	2	0	0	NUM
ejpam-6111	236	3	,	,	PUNCT
ejpam-6111	236	4	∀∆	∀∆	NOUN
ejpam-6111	236	5	∈	∈	PROPN
ejpam-6111	236	6	b1	b1	NOUN
ejpam-6111	236	7	.	.	PUNCT
ejpam-6111	237	1	thus	thus	ADV
ejpam-6111	237	2	final	final	ADJ
ejpam-6111	237	3	we	we	PRON
ejpam-6111	237	4	have	have	VERB
ejpam-6111	237	5	that	that	PRON
ejpam-6111	237	6	λi	λi	ADP
ejpam-6111	237	7	[	[	X
ejpam-6111	237	8	(	(	PUNCT
ejpam-6111	237	9	in−(i	in−(i	ADJ
ejpam-6111	237	10	in+p	in+p	PROPN
ejpam-6111	237	11	(	(	PUNCT
ejpam-6111	237	12	in−a⊗p	in−a⊗p	NOUN
ejpam-6111	237	13	t)+(in−a⊗p	t)+(in−a⊗p	NOUN
ejpam-6111	237	14	t)t)p	t)t)p	NOUN
ejpam-6111	237	15	)	)	PUNCT
ejpam-6111	237	16	(	(	PUNCT
ejpam-6111	237	17	i	i	PRON
ejpam-6111	237	18	in−p	in−p	VERB
ejpam-6111	237	19	(	(	PUNCT
ejpam-6111	237	20	in−a⊗p	in−a⊗p	NOUN
ejpam-6111	237	21	t)−(in−a⊗p	t)−(in−a⊗p	PROPN
ejpam-6111	237	22	t)tp	t)tp	NOUN
ejpam-6111	237	23	)	)	PUNCT
ejpam-6111	237	24	∆	∆	PROPN
ejpam-6111	237	25	]	]	PUNCT
ejpam-6111	238	1	̸=	̸=	PROPN
ejpam-6111	238	2	0	0	NUM
ejpam-6111	238	3	,	,	PUNCT
ejpam-6111	238	4	∀∆	∀∆	NOUN
ejpam-6111	238	5	∈	∈	PROPN
ejpam-6111	238	6	b1	b1	NOUN
ejpam-6111	238	7	.	.	PUNCT
ejpam-6111	239	1	the	the	DET
ejpam-6111	239	2	last	last	ADJ
ejpam-6111	239	3	expression	expression	NOUN
ejpam-6111	239	4	for	for	ADP
ejpam-6111	239	5	λi	λi	SYM
ejpam-6111	239	6	(	(	PUNCT
ejpam-6111	239	7	·	·	PUNCT
ejpam-6111	239	8	)	)	PUNCT
ejpam-6111	239	9	implies	imply	VERB
ejpam-6111	239	10	that	that	SCONJ
ejpam-6111	239	11	0	0	NUM
ejpam-6111	239	12	≤	≤	NUM
ejpam-6111	239	13	µb1	µb1	VERB
ejpam-6111	239	14	[	[	X
ejpam-6111	239	15	(	(	PUNCT
ejpam-6111	239	16	i	i	PRON
ejpam-6111	239	17	in+p	in+p	PROPN
ejpam-6111	239	18	(	(	PUNCT
ejpam-6111	239	19	in−a⊗p	in−a⊗p	NOUN
ejpam-6111	239	20	t)+(in−a⊗p	t)+(in−a⊗p	NOUN
ejpam-6111	239	21	t)t)p	t)t)p	NOUN
ejpam-6111	239	22	)	)	PUNCT
ejpam-6111	239	23	−1	−1	NOUN
ejpam-6111	239	24	(	(	PUNCT
ejpam-6111	239	25	i	i	PRON
ejpam-6111	239	26	in−p	in−p	VERB
ejpam-6111	239	27	(	(	PUNCT
ejpam-6111	239	28	in−a⊗p	in−a⊗p	ADV
ejpam-6111	239	29	t)−(i	t)−(i	X
ejpam-6111	239	30	in−a⊗p	in−a⊗p	ADJ
ejpam-6111	239	31	t)tp	t)tp	PROPN
ejpam-6111	239	32	)	)	PUNCT
ejpam-6111	239	33	]	]	PUNCT
ejpam-6111	240	1	<	<	X
ejpam-6111	240	2	1	1	X
ejpam-6111	240	3	.	.	PUNCT
ejpam-6111	241	1	the	the	DET
ejpam-6111	241	2	following	follow	VERB
ejpam-6111	241	3	theorem	theorem	VERB
ejpam-6111	241	4	4	4	NUM
ejpam-6111	241	5	shows	show	VERB
ejpam-6111	241	6	that	that	SCONJ
ejpam-6111	241	7	given	give	VERB
ejpam-6111	241	8	(	(	PUNCT
ejpam-6111	241	9	in	in	ADP
ejpam-6111	241	10	−	−	PROPN
ejpam-6111	241	11	a⊗	a⊗	NOUN
ejpam-6111	241	12	p	p	PROPN
ejpam-6111	241	13	t	t	PROPN
ejpam-6111	241	14	)	)	PUNCT
ejpam-6111	241	15	∈	∈	PROPN
ejpam-6111	241	16	rn	rn	PROPN
ejpam-6111	241	17	,	,	PUNCT
ejpam-6111	241	18	n	n	PRON
ejpam-6111	241	19	is	be	AUX
ejpam-6111	241	20	a	a	DET
ejpam-6111	241	21	d	d	ADJ
ejpam-6111	241	22	-	-	ADJ
ejpam-6111	241	23	stable	stable	ADJ
ejpam-6111	241	24	matrix	matrix	NOUN
ejpam-6111	241	25	if	if	SCONJ
ejpam-6111	241	26	it	it	PRON
ejpam-6111	241	27	is	be	AUX
ejpam-6111	241	28	stable	stable	ADJ
ejpam-6111	241	29	,	,	PUNCT
ejpam-6111	241	30	and	and	CCONJ
ejpam-6111	241	31	(	(	PUNCT
ejpam-6111	241	32	i	i	PRON
ejpam-6111	241	33	in	in	ADP
ejpam-6111	241	34	+	+	CCONJ
ejpam-6111	241	35	(	(	PUNCT
ejpam-6111	241	36	in	in	ADP
ejpam-6111	241	37	−	−	PROPN
ejpam-6111	241	38	a	a	DET
ejpam-6111	241	39	⊗	⊗	PROPN
ejpam-6111	241	40	p	p	PROPN
ejpam-6111	241	41	t	t	PROPN
ejpam-6111	241	42	)	)	PUNCT
ejpam-6111	241	43	)	)	PUNCT
ejpam-6111	241	44	−1	−1	NOUN
ejpam-6111	242	1	(	(	PUNCT
ejpam-6111	242	2	i	i	PRON
ejpam-6111	242	3	in	in	ADP
ejpam-6111	242	4	−	−	PROPN
ejpam-6111	242	5	a	a	DET
ejpam-6111	242	6	⊗	⊗	PROPN
ejpam-6111	242	7	p	p	PROPN
ejpam-6111	242	8	t	t	PROPN
ejpam-6111	242	9	)	)	PUNCT
ejpam-6111	242	10	are	be	AUX
ejpam-6111	242	11	greater	great	ADJ
ejpam-6111	242	12	than	than	ADP
ejpam-6111	242	13	or	or	CCONJ
ejpam-6111	242	14	equal	equal	ADJ
ejpam-6111	242	15	to	to	ADP
ejpam-6111	242	16	zero	zero	NUM
ejpam-6111	242	17	and	and	CCONJ
ejpam-6111	242	18	strictly	strictly	ADV
ejpam-6111	242	19	less	less	ADJ
ejpam-6111	242	20	than	than	ADP
ejpam-6111	242	21	one	one	NUM
ejpam-6111	242	22	.	.	PUNCT
ejpam-6111	243	1	theorem	theorem	ADJ
ejpam-6111	243	2	4	4	NUM
ejpam-6111	243	3	.	.	PUNCT
ejpam-6111	244	1	let	let	VERB
ejpam-6111	244	2	(	(	PUNCT
ejpam-6111	244	3	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	244	4	t	t	NOUN
ejpam-6111	244	5	)	)	PUNCT
ejpam-6111	244	6	∈	∈	PROPN
ejpam-6111	244	7	rn	rn	PROPN
ejpam-6111	244	8	,	,	PUNCT
ejpam-6111	244	9	n.	n.	PROPN
ejpam-6111	244	10	then	then	ADV
ejpam-6111	244	11	(	(	PUNCT
ejpam-6111	244	12	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	244	13	t	t	NOUN
ejpam-6111	244	14	)	)	PUNCT
ejpam-6111	244	15	is	be	AUX
ejpam-6111	244	16	d	d	ADJ
ejpam-6111	244	17	-	-	ADJ
ejpam-6111	244	18	stable	stable	ADJ
ejpam-6111	244	19	matrix	matrix	NOUN
ejpam-6111	244	20	if	if	SCONJ
ejpam-6111	244	21	(	(	PUNCT
ejpam-6111	244	22	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	244	23	t	t	NOUN
ejpam-6111	244	24	)	)	PUNCT
ejpam-6111	244	25	is	be	AUX
ejpam-6111	244	26	stable	stable	ADJ
ejpam-6111	244	27	,	,	PUNCT
ejpam-6111	244	28	and	and	CCONJ
ejpam-6111	245	1	0	0	NUM
ejpam-6111	245	2	≤	≤	NUM
ejpam-6111	245	3	µb1	µb1	VERB
ejpam-6111	245	4	[	[	X
ejpam-6111	245	5	(	(	PUNCT
ejpam-6111	245	6	i	i	PRON
ejpam-6111	245	7	in	in	ADP
ejpam-6111	245	8	+	+	CCONJ
ejpam-6111	245	9	(	(	PUNCT
ejpam-6111	245	10	in	in	ADP
ejpam-6111	245	11	−a⊗	−a⊗	PROPN
ejpam-6111	245	12	p	p	PROPN
ejpam-6111	245	13	t	t	PROPN
ejpam-6111	245	14	)	)	PUNCT
ejpam-6111	245	15	)	)	PUNCT
ejpam-6111	245	16	−1	−1	NOUN
ejpam-6111	246	1	(	(	PUNCT
ejpam-6111	246	2	i	i	PRON
ejpam-6111	246	3	in	in	ADP
ejpam-6111	246	4	−a⊗	−a⊗	PROPN
ejpam-6111	246	5	p	p	PROPN
ejpam-6111	246	6	t	t	PROPN
ejpam-6111	246	7	)	)	PUNCT
ejpam-6111	246	8	]	]	PUNCT
ejpam-6111	246	9	<	<	X
ejpam-6111	246	10	1	1	NUM
ejpam-6111	246	11	,	,	PUNCT
ejpam-6111	246	12	∀p	∀p	PROPN
ejpam-6111	246	13	∈	∈	PROPN
ejpam-6111	246	14	ω	ω	NOUN
ejpam-6111	246	15	.	.	PUNCT
ejpam-6111	247	1	proof	proof	NOUN
ejpam-6111	247	2	.	.	PUNCT
ejpam-6111	248	1	the	the	DET
ejpam-6111	248	2	matrix	matrix	NOUN
ejpam-6111	248	3	(	(	PUNCT
ejpam-6111	248	4	in	in	ADP
ejpam-6111	248	5	−	−	PROPN
ejpam-6111	248	6	a	a	DET
ejpam-6111	248	7	⊗	⊗	PROPN
ejpam-6111	248	8	p	p	PROPN
ejpam-6111	248	9	t	t	PROPN
ejpam-6111	248	10	)	)	PUNCT
ejpam-6111	248	11	is	be	AUX
ejpam-6111	248	12	d	d	NOUN
ejpam-6111	248	13	-	-	NOUN
ejpam-6111	248	14	stable	stable	ADJ
ejpam-6111	248	15	if	if	SCONJ
ejpam-6111	248	16	it	it	PRON
ejpam-6111	248	17	is	be	AUX
ejpam-6111	248	18	stable	stable	ADJ
ejpam-6111	248	19	and	and	CCONJ
ejpam-6111	248	20	λi	λi	INTJ
ejpam-6111	248	21	(	(	PUNCT
ejpam-6111	248	22	(	(	PUNCT
ejpam-6111	248	23	in	in	ADP
ejpam-6111	248	24	−	−	PROPN
ejpam-6111	248	25	a	a	DET
ejpam-6111	248	26	⊗	⊗	PROPN
ejpam-6111	248	27	p	p	PROPN
ejpam-6111	248	28	t	t	PROPN
ejpam-6111	248	29	)	)	PUNCT
ejpam-6111	249	1	+	+	CCONJ
ejpam-6111	250	1	i	i	PRON
ejpam-6111	250	2	p	p	NOUN
ejpam-6111	250	3	)	)	PUNCT
ejpam-6111	250	4	̸=	̸=	PROPN
ejpam-6111	250	5	0	0	NUM
ejpam-6111	250	6	,	,	PUNCT
ejpam-6111	250	7	∀p	∀p	PROPN
ejpam-6111	250	8	∈	∈	NOUN
ejpam-6111	250	9	ω	ω	NOUN
ejpam-6111	250	10	.	.	PUNCT
ejpam-6111	251	1	we	we	PRON
ejpam-6111	251	2	aim	aim	VERB
ejpam-6111	251	3	to	to	PART
ejpam-6111	251	4	prove	prove	VERB
ejpam-6111	251	5	that	that	SCONJ
ejpam-6111	251	6	(	(	PUNCT
ejpam-6111	251	7	in	in	ADP
ejpam-6111	251	8	−a⊗p	−a⊗p	PROPN
ejpam-6111	251	9	t	t	PROPN
ejpam-6111	251	10	)	)	PUNCT
ejpam-6111	251	11	is	be	AUX
ejpam-6111	251	12	d	d	NOUN
ejpam-6111	251	13	-	-	NOUN
ejpam-6111	251	14	stable	stable	ADJ
ejpam-6111	251	15	if	if	SCONJ
ejpam-6111	251	16	it	it	PRON
ejpam-6111	251	17	is	be	AUX
ejpam-6111	251	18	structured	structured	ADJ
ejpam-6111	251	19	singular	singular	ADJ
ejpam-6111	251	20	value	value	NOUN
ejpam-6111	251	21	is	be	AUX
ejpam-6111	251	22	strictly	strictly	ADV
ejpam-6111	251	23	less	less	ADJ
ejpam-6111	251	24	than	than	ADP
ejpam-6111	251	25	1	1	NUM
ejpam-6111	251	26	.	.	PUNCT
ejpam-6111	252	1	for	for	ADP
ejpam-6111	252	2	this	this	PRON
ejpam-6111	252	3	we	we	PRON
ejpam-6111	252	4	assume	assume	VERB
ejpam-6111	252	5	that	that	SCONJ
ejpam-6111	252	6	(	(	PUNCT
ejpam-6111	252	7	in	in	ADP
ejpam-6111	252	8	−	−	PROPN
ejpam-6111	252	9	a	a	DET
ejpam-6111	252	10	⊗	⊗	PROPN
ejpam-6111	252	11	p	p	PROPN
ejpam-6111	252	12	t	t	PROPN
ejpam-6111	252	13	)	)	PUNCT
ejpam-6111	252	14	is	be	AUX
ejpam-6111	252	15	d	d	NOUN
ejpam-6111	252	16	-	-	ADJ
ejpam-6111	252	17	stable	stable	ADJ
ejpam-6111	252	18	.	.	PUNCT
ejpam-6111	253	1	let	let	VERB
ejpam-6111	253	2	∆	∆	PROPN
ejpam-6111	253	3	∈	∈	PROPN
ejpam-6111	253	4	b1	b1	NOUN
ejpam-6111	253	5	with	with	ADP
ejpam-6111	253	6	block	block	NOUN
ejpam-6111	253	7	diagonal	diagonal	ADJ
ejpam-6111	253	8	structure	structure	NOUN
ejpam-6111	253	9	,	,	PUNCT
ejpam-6111	253	10	∆	∆	PROPN
ejpam-6111	253	11	=	=	PUNCT
ejpam-6111	254	1	(	(	PUNCT
ejpam-6111	254	2	i	i	PRON
ejpam-6111	254	3	in	in	ADP
ejpam-6111	254	4	−	−	PROPN
ejpam-6111	254	5	p	p	NOUN
ejpam-6111	254	6	)	)	PUNCT
ejpam-6111	254	7	(	(	PUNCT
ejpam-6111	254	8	i	i	PRON
ejpam-6111	254	9	in	in	ADP
ejpam-6111	254	10	+	+	CCONJ
ejpam-6111	254	11	p	p	NOUN
ejpam-6111	254	12	)	)	PUNCT
ejpam-6111	254	13	−1	−1	NOUN
ejpam-6111	254	14	,	,	PUNCT
ejpam-6111	254	15	∀p	∀p	PROPN
ejpam-6111	254	16	∈	∈	PROPN
ejpam-6111	254	17	ω	ω	NOUN
ejpam-6111	254	18	.	.	PUNCT
ejpam-6111	255	1	then	then	ADV
ejpam-6111	255	2	,	,	PUNCT
ejpam-6111	255	3	p	p	PROPN
ejpam-6111	255	4	∈	∈	PROPN
ejpam-6111	255	5	ω	ω	X
ejpam-6111	255	6	in	in	ADP
ejpam-6111	255	7	terms	term	NOUN
ejpam-6111	255	8	of	of	ADP
ejpam-6111	255	9	∆	∆	PROPN
ejpam-6111	255	10	can	can	AUX
ejpam-6111	255	11	be	be	AUX
ejpam-6111	255	12	re	re	VERB
ejpam-6111	255	13	-	-	VERB
ejpam-6111	255	14	written	write	VERB
ejpam-6111	255	15	as	as	ADP
ejpam-6111	255	16	p	p	NOUN
ejpam-6111	255	17	=	=	PUNCT
ejpam-6111	255	18	(	(	PUNCT
ejpam-6111	255	19	i	i	PRON
ejpam-6111	255	20	in+∆)−1(i	in+∆)−1(i	PROPN
ejpam-6111	255	21	in−∆	in−∆	PROPN
ejpam-6111	255	22	)	)	PUNCT
ejpam-6111	255	23	,	,	PUNCT
ejpam-6111	255	24	∀∆	∀∆	PROPN
ejpam-6111	255	25	∈	∈	PROPN
ejpam-6111	255	26	b1	b1	NOUN
ejpam-6111	255	27	.	.	PUNCT
ejpam-6111	256	1	since	since	ADV
ejpam-6111	256	2	,	,	PUNCT
ejpam-6111	256	3	λi	λi	X
ejpam-6111	256	4	(	(	PUNCT
ejpam-6111	256	5	(	(	PUNCT
ejpam-6111	256	6	in−a⊗p	in−a⊗p	ADV
ejpam-6111	256	7	t)+i	t)+i	PROPN
ejpam-6111	256	8	p	p	NOUN
ejpam-6111	256	9	)	)	PUNCT
ejpam-6111	256	10	̸=	̸=	PROPN
ejpam-6111	256	11	0	0	NUM
ejpam-6111	256	12	,	,	PUNCT
ejpam-6111	256	13	for	for	ADP
ejpam-6111	256	14	some	some	DET
ejpam-6111	256	15	p	p	PROPN
ejpam-6111	256	16	∈	∈	PROPN
ejpam-6111	256	17	ω	ω	NOUN
ejpam-6111	256	18	.	.	PUNCT
ejpam-6111	257	1	this	this	DET
ejpam-6111	257	2	yields	yield	NOUN
ejpam-6111	257	3	λi	λi	X
ejpam-6111	257	4	[	[	PUNCT
ejpam-6111	257	5	(	(	PUNCT
ejpam-6111	257	6	in	in	ADP
ejpam-6111	257	7	−a⊗	−a⊗	PROPN
ejpam-6111	257	8	p	p	PROPN
ejpam-6111	257	9	t	t	PROPN
ejpam-6111	257	10	)	)	PUNCT
ejpam-6111	258	1	+	+	CCONJ
ejpam-6111	258	2	i(i	i(i	PROPN
ejpam-6111	258	3	in	in	ADP
ejpam-6111	258	4	+	+	NOUN
ejpam-6111	258	5	∆)−1(i	∆)−1(i	NOUN
ejpam-6111	258	6	in	in	ADP
ejpam-6111	258	7	−∆	−∆	NOUN
ejpam-6111	258	8	)	)	PUNCT
ejpam-6111	258	9	]	]	PUNCT
ejpam-6111	259	1	̸=	̸=	PROPN
ejpam-6111	259	2	0	0	NUM
ejpam-6111	259	3	,	,	PUNCT
ejpam-6111	259	4	∀i	∀i	NOUN
ejpam-6111	259	5	,	,	PUNCT
ejpam-6111	259	6	∀∆	∀∆	NOUN
ejpam-6111	259	7	∈	∈	PROPN
ejpam-6111	259	8	b1	b1	NOUN
ejpam-6111	259	9	.	.	PUNCT
ejpam-6111	260	1	by	by	ADP
ejpam-6111	260	2	making	make	VERB
ejpam-6111	260	3	use	use	NOUN
ejpam-6111	260	4	of	of	ADP
ejpam-6111	260	5	singular	singular	ADJ
ejpam-6111	260	6	value	value	NOUN
ejpam-6111	260	7	decomposition	decomposition	NOUN
ejpam-6111	260	8	,	,	PUNCT
ejpam-6111	260	9	we	we	PRON
ejpam-6111	260	10	have	have	VERB
ejpam-6111	260	11	σi	σi	PRON
ejpam-6111	260	12	[	[	PUNCT
ejpam-6111	260	13	(	(	PUNCT
ejpam-6111	260	14	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	260	15	t)+i(i	t)+i(i	NOUN
ejpam-6111	260	16	in+∆)−1(i	in+∆)−1(i	PROPN
ejpam-6111	260	17	in−∆	in−∆	PROPN
ejpam-6111	260	18	)	)	PUNCT
ejpam-6111	260	19	]	]	PUNCT
ejpam-6111	261	1	=	=	PUNCT
ejpam-6111	261	2	σi	σi	X
ejpam-6111	262	1	[	[	X
ejpam-6111	262	2	(	(	PUNCT
ejpam-6111	262	3	i	i	PRON
ejpam-6111	262	4	in+(in−a⊗p	in+(in−a⊗p	PROPN
ejpam-6111	262	5	t	t	NOUN
ejpam-6111	262	6	)	)	PUNCT
ejpam-6111	262	7	)	)	PUNCT
ejpam-6111	262	8	−	−	PROPN
ejpam-6111	263	1	(	(	PUNCT
ejpam-6111	263	2	i	i	PRON
ejpam-6111	263	3	in−(in−a⊗p	in−(in−a⊗p	PROPN
ejpam-6111	263	4	t	t	PROPN
ejpam-6111	263	5	)	)	PUNCT
ejpam-6111	263	6	)	)	PUNCT
ejpam-6111	264	1	∆	∆	PROPN
ejpam-6111	264	2	]	]	PUNCT
ejpam-6111	264	3	,	,	PUNCT
ejpam-6111	264	4	∀∆	∀∆	PROPN
ejpam-6111	264	5	∈	∈	PROPN
ejpam-6111	264	6	b1	b1	NOUN
ejpam-6111	264	7	.	.	PUNCT
ejpam-6111	265	1	the	the	DET
ejpam-6111	265	2	σi	σi	X
ejpam-6111	265	3	(	(	PUNCT
ejpam-6111	265	4	·	·	PUNCT
ejpam-6111	265	5	)	)	PUNCT
ejpam-6111	265	6	denotes	denote	VERB
ejpam-6111	265	7	that	that	SCONJ
ejpam-6111	265	8	number	number	NOUN
ejpam-6111	265	9	of	of	ADP
ejpam-6111	265	10	non	non	ADJ
ejpam-6111	265	11	-	-	ADJ
ejpam-6111	265	12	zero	zero	ADJ
ejpam-6111	265	13	singular	singular	NOUN
ejpam-6111	265	14	-	-	PUNCT
ejpam-6111	265	15	value	value	NOUN
ejpam-6111	265	16	of	of	ADP
ejpam-6111	265	17	a	a	DET
ejpam-6111	265	18	matrix	matrix	NOUN
ejpam-6111	265	19	.	.	PUNCT
ejpam-6111	266	1	from	from	ADP
ejpam-6111	266	2	this	this	PRON
ejpam-6111	266	3	,	,	PUNCT
ejpam-6111	266	4	we	we	PRON
ejpam-6111	266	5	have	have	VERB
ejpam-6111	266	6	(	(	PUNCT
ejpam-6111	266	7	i	i	PRON
ejpam-6111	266	8	in+(in−a⊗p	in+(in−a⊗p	NOUN
ejpam-6111	266	9	t	t	NOUN
ejpam-6111	266	10	)	)	PUNCT
ejpam-6111	266	11	)	)	PUNCT
ejpam-6111	267	1	−	−	PROPN
ejpam-6111	268	1	(	(	PUNCT
ejpam-6111	268	2	i	i	PRON
ejpam-6111	268	3	in−(in−a⊗p	in−(in−a⊗p	PROPN
ejpam-6111	268	4	t	t	PROPN
ejpam-6111	268	5	)	)	PUNCT
ejpam-6111	268	6	)	)	PUNCT
ejpam-6111	269	1	∆	∆	PROPN
ejpam-6111	270	1	=	=	PRON
ejpam-6111	270	2	(	(	PUNCT
ejpam-6111	270	3	in−(i	in−(i	PROPN
ejpam-6111	270	4	in+(in−a⊗p	in+(in−a⊗p	NOUN
ejpam-6111	270	5	t)−1(i	t)−1(i	NOUN
ejpam-6111	270	6	in−(in−a⊗p	in−(in−a⊗p	ADV
ejpam-6111	270	7	t))∆	t))∆	PROPN
ejpam-6111	270	8	)	)	PUNCT
ejpam-6111	270	9	.	.	PUNCT
ejpam-6111	271	1	s.	s.	PROPN
ejpam-6111	271	2	mazhar	mazhar	PROPN
ejpam-6111	271	3	,	,	PUNCT
ejpam-6111	271	4	m.	m.	NOUN
ejpam-6111	271	5	u.	u.	PROPN
ejpam-6111	271	6	rehman	rehman	PROPN
ejpam-6111	271	7	/	/	SYM
ejpam-6111	271	8	eur	eur	PROPN
ejpam-6111	271	9	.	.	PUNCT
ejpam-6111	272	1	j.	j.	PROPN
ejpam-6111	272	2	pure	pure	PROPN
ejpam-6111	272	3	appl	appl	PROPN
ejpam-6111	272	4	.	.	PROPN
ejpam-6111	272	5	math	math	PROPN
ejpam-6111	272	6	,	,	PUNCT
ejpam-6111	272	7	18	18	NUM
ejpam-6111	272	8	(	(	PUNCT
ejpam-6111	272	9	2	2	NUM
ejpam-6111	272	10	)	)	PUNCT
ejpam-6111	272	11	(	(	PUNCT
ejpam-6111	272	12	2025	2025	NUM
ejpam-6111	272	13	)	)	PUNCT
ejpam-6111	272	14	,	,	PUNCT
ejpam-6111	272	15	6111	6111	NUM
ejpam-6111	272	16	11	11	NUM
ejpam-6111	272	17	of	of	ADP
ejpam-6111	272	18	25	25	NUM
ejpam-6111	272	19	this	this	DET
ejpam-6111	272	20	further	further	ADJ
ejpam-6111	272	21	yields	yield	NOUN
ejpam-6111	272	22	λi	λi	ADP
ejpam-6111	272	23	[	[	PUNCT
ejpam-6111	272	24	in	in	ADP
ejpam-6111	272	25	−	−	PROPN
ejpam-6111	272	26	(	(	PUNCT
ejpam-6111	272	27	i	i	PRON
ejpam-6111	272	28	in	in	ADP
ejpam-6111	272	29	+	+	CCONJ
ejpam-6111	272	30	(	(	PUNCT
ejpam-6111	272	31	in	in	ADP
ejpam-6111	272	32	−a⊗	−a⊗	PROPN
ejpam-6111	272	33	p	p	PROPN
ejpam-6111	272	34	t	t	PROPN
ejpam-6111	272	35	)	)	PUNCT
ejpam-6111	272	36	)	)	PUNCT
ejpam-6111	273	1	−1	−1	NOUN
ejpam-6111	273	2	(	(	PUNCT
ejpam-6111	273	3	i	i	PRON
ejpam-6111	273	4	in	in	ADP
ejpam-6111	273	5	−	−	PROPN
ejpam-6111	273	6	(	(	PUNCT
ejpam-6111	273	7	in	in	ADP
ejpam-6111	273	8	−a⊗	−a⊗	PROPN
ejpam-6111	273	9	p	p	PROPN
ejpam-6111	273	10	t	t	PROPN
ejpam-6111	273	11	)	)	PUNCT
ejpam-6111	273	12	)	)	PUNCT
ejpam-6111	273	13	∆	∆	PROPN
ejpam-6111	273	14	]	]	PUNCT
ejpam-6111	274	1	̸=	̸=	PROPN
ejpam-6111	274	2	0	0	NUM
ejpam-6111	274	3	,	,	PUNCT
ejpam-6111	274	4	∀∆	∀∆	NOUN
ejpam-6111	274	5	∈	∈	PROPN
ejpam-6111	274	6	b1	b1	NOUN
ejpam-6111	274	7	,	,	PUNCT
ejpam-6111	274	8	and	and	CCONJ
ejpam-6111	274	9	hence	hence	ADV
ejpam-6111	274	10	0	0	NUM
ejpam-6111	274	11	≤	≤	NUM
ejpam-6111	274	12	µb1	µb1	VERB
ejpam-6111	275	1	[	[	X
ejpam-6111	275	2	(	(	PUNCT
ejpam-6111	275	3	i	i	PRON
ejpam-6111	275	4	in	in	ADP
ejpam-6111	275	5	+	+	CCONJ
ejpam-6111	275	6	(	(	PUNCT
ejpam-6111	275	7	in	in	ADP
ejpam-6111	275	8	−a⊗	−a⊗	PROPN
ejpam-6111	275	9	p	p	PROPN
ejpam-6111	275	10	t	t	PROPN
ejpam-6111	275	11	)	)	PUNCT
ejpam-6111	275	12	)	)	PUNCT
ejpam-6111	275	13	−1	−1	NOUN
ejpam-6111	275	14	(	(	PUNCT
ejpam-6111	275	15	i	i	PRON
ejpam-6111	275	16	in	in	ADP
ejpam-6111	275	17	−a⊗	−a⊗	PROPN
ejpam-6111	275	18	p	p	PROPN
ejpam-6111	275	19	t	t	PROPN
ejpam-6111	275	20	)	)	PUNCT
ejpam-6111	275	21	]	]	PUNCT
ejpam-6111	275	22	<	<	X
ejpam-6111	275	23	1	1	NUM
ejpam-6111	275	24	,	,	PUNCT
ejpam-6111	275	25	∀p	∀p	PROPN
ejpam-6111	275	26	∈	∈	PROPN
ejpam-6111	275	27	ω	ω	NOUN
ejpam-6111	275	28	.	.	PUNCT
ejpam-6111	276	1	the	the	DET
ejpam-6111	276	2	following	follow	VERB
ejpam-6111	276	3	theorem	theorem	NOUN
ejpam-6111	276	4	5	5	NUM
ejpam-6111	276	5	is	be	AUX
ejpam-6111	276	6	to	to	PART
ejpam-6111	276	7	give	give	VERB
ejpam-6111	276	8	the	the	DET
ejpam-6111	276	9	necessary	necessary	ADJ
ejpam-6111	276	10	condition	condition	NOUN
ejpam-6111	276	11	for	for	ADP
ejpam-6111	276	12	the	the	DET
ejpam-6111	276	13	d	d	NOUN
ejpam-6111	276	14	-	-	NOUN
ejpam-6111	276	15	stability	stability	NOUN
ejpam-6111	276	16	of	of	ADP
ejpam-6111	276	17	(	(	PUNCT
ejpam-6111	276	18	in	in	ADP
ejpam-6111	276	19	−a⊗p	−a⊗p	PROPN
ejpam-6111	276	20	t	t	PROPN
ejpam-6111	276	21	)	)	PUNCT
ejpam-6111	276	22	∈	∈	PROPN
ejpam-6111	276	23	rn	rn	PROPN
ejpam-6111	276	24	,	,	PUNCT
ejpam-6111	276	25	n.	n.	NOUN
ejpam-6111	276	26	it	it	PRON
ejpam-6111	276	27	is	be	AUX
ejpam-6111	276	28	shown	show	VERB
ejpam-6111	276	29	that	that	SCONJ
ejpam-6111	276	30	this	this	DET
ejpam-6111	276	31	given	give	VERB
ejpam-6111	276	32	matrix	matrix	NOUN
ejpam-6111	276	33	is	be	AUX
ejpam-6111	276	34	d	d	NOUN
ejpam-6111	276	35	-	-	ADJ
ejpam-6111	276	36	stable	stable	ADJ
ejpam-6111	276	37	if	if	SCONJ
ejpam-6111	276	38	we	we	PRON
ejpam-6111	276	39	can	can	AUX
ejpam-6111	276	40	express	express	VERB
ejpam-6111	276	41	it	it	PRON
ejpam-6111	276	42	in	in	ADP
ejpam-6111	276	43	matrix	matrix	NOUN
ejpam-6111	276	44	series	series	NOUN
ejpam-6111	276	45	for	for	ADP
ejpam-6111	276	46	such	such	DET
ejpam-6111	276	47	the	the	DET
ejpam-6111	276	48	structured	structured	ADJ
ejpam-6111	276	49	singular	singular	ADJ
ejpam-6111	276	50	value	value	NOUN
ejpam-6111	276	51	of	of	ADP
ejpam-6111	276	52	(	(	PUNCT
ejpam-6111	276	53	in+(in+a+	in+(in+a+	PROPN
ejpam-6111	276	54	a2	a2	PROPN
ejpam-6111	276	55	2	2	NUM
ejpam-6111	276	56	!	!	PUNCT
ejpam-6111	277	1	+	+	CCONJ
ejpam-6111	277	2	.	.	PUNCT
ejpam-6111	277	3	.	.	PUNCT
ejpam-6111	277	4	.	.	PUNCT
ejpam-6111	277	5	)	)	PUNCT
ejpam-6111	277	6	)	)	PUNCT
ejpam-6111	278	1	−1	−1	NOUN
ejpam-6111	278	2	(	(	PUNCT
ejpam-6111	278	3	in−	in−	PROPN
ejpam-6111	278	4	(	(	PUNCT
ejpam-6111	278	5	in	in	ADP
ejpam-6111	278	6	+	+	PROPN
ejpam-6111	278	7	a+	a+	X
ejpam-6111	278	8	a2	a2	PROPN
ejpam-6111	278	9	2	2	NUM
ejpam-6111	278	10	!	!	PUNCT
ejpam-6111	279	1	+	+	CCONJ
ejpam-6111	279	2	.	.	PUNCT
ejpam-6111	279	3	.	.	PUNCT
ejpam-6111	279	4	.	.	PUNCT
ejpam-6111	279	5	)	)	PUNCT
ejpam-6111	280	1	)	)	PUNCT
ejpam-6111	280	2	is	be	AUX
ejpam-6111	280	3	greater	great	ADJ
ejpam-6111	280	4	than	than	ADP
ejpam-6111	280	5	and	and	CCONJ
ejpam-6111	280	6	equal	equal	ADJ
ejpam-6111	280	7	to	to	ADP
ejpam-6111	280	8	zero	zero	NUM
ejpam-6111	280	9	and	and	CCONJ
ejpam-6111	280	10	strictly	strictly	ADV
ejpam-6111	280	11	less	less	ADJ
ejpam-6111	280	12	than	than	ADP
ejpam-6111	280	13	one	one	NUM
ejpam-6111	280	14	.	.	PUNCT
ejpam-6111	281	1	theorem	theorem	NOUN
ejpam-6111	281	2	5	5	NUM
ejpam-6111	281	3	.	.	PUNCT
ejpam-6111	282	1	let	let	AUX
ejpam-6111	282	2	(	(	PUNCT
ejpam-6111	282	3	in	in	ADP
ejpam-6111	282	4	−a⊗p	−a⊗p	PROPN
ejpam-6111	282	5	t	t	PROPN
ejpam-6111	282	6	)	)	PUNCT
ejpam-6111	282	7	∈	∈	PROPN
ejpam-6111	282	8	rn	rn	PROPN
ejpam-6111	282	9	,	,	PUNCT
ejpam-6111	282	10	n.	n.	VERB
ejpam-6111	282	11	the	the	DET
ejpam-6111	282	12	necessary	necessary	ADJ
ejpam-6111	282	13	condition	condition	NOUN
ejpam-6111	282	14	for	for	ADP
ejpam-6111	282	15	(	(	PUNCT
ejpam-6111	282	16	in	in	ADP
ejpam-6111	282	17	−a⊗p	−a⊗p	PROPN
ejpam-6111	282	18	t	t	PROPN
ejpam-6111	282	19	)	)	PUNCT
ejpam-6111	282	20	to	to	PART
ejpam-6111	282	21	be	be	AUX
ejpam-6111	282	22	a	a	DET
ejpam-6111	282	23	d	d	ADJ
ejpam-6111	282	24	-	-	ADJ
ejpam-6111	282	25	stable	stable	ADJ
ejpam-6111	282	26	matrix	matrix	NOUN
ejpam-6111	282	27	i	i	PRON
ejpam-6111	282	28	s	s	VERB
ejpam-6111	282	29	that	that	PRON
ejpam-6111	282	30	for	for	ADP
ejpam-6111	282	31	a	a	DET
ejpam-6111	282	32	∈	∈	PROPN
ejpam-6111	282	33	rn	rn	PROPN
ejpam-6111	282	34	,	,	PUNCT
ejpam-6111	282	35	n	n	CCONJ
ejpam-6111	282	36	,	,	PUNCT
ejpam-6111	282	37	(	(	PUNCT
ejpam-6111	282	38	in	in	ADP
ejpam-6111	282	39	−a⊗	−a⊗	PROPN
ejpam-6111	282	40	p	p	PROPN
ejpam-6111	282	41	t	t	PROPN
ejpam-6111	282	42	)	)	PUNCT
ejpam-6111	282	43	can	can	AUX
ejpam-6111	282	44	be	be	AUX
ejpam-6111	282	45	expressed	express	VERB
ejpam-6111	282	46	as	as	ADP
ejpam-6111	282	47	(	(	PUNCT
ejpam-6111	282	48	in	in	ADP
ejpam-6111	282	49	−a⊗	−a⊗	PROPN
ejpam-6111	282	50	p	p	PROPN
ejpam-6111	282	51	t	t	PROPN
ejpam-6111	282	52	)	)	PUNCT
ejpam-6111	282	53	=	=	PUNCT
ejpam-6111	282	54	in	in	ADP
ejpam-6111	282	55	+	+	PROPN
ejpam-6111	282	56	a+	a+	X
ejpam-6111	282	57	a2	a2	PROPN
ejpam-6111	282	58	2	2	NUM
ejpam-6111	282	59	!	!	PUNCT
ejpam-6111	283	1	+	+	CCONJ
ejpam-6111	283	2	.	.	PUNCT
ejpam-6111	283	3	.	.	PUNCT
ejpam-6111	284	1	.	.	PUNCT
ejpam-6111	285	1	,	,	PUNCT
ejpam-6111	285	2	and	and	CCONJ
ejpam-6111	285	3	0	0	NUM
ejpam-6111	285	4	≤	≤	NUM
ejpam-6111	285	5	µb1	µb1	VERB
ejpam-6111	285	6	[	[	X
ejpam-6111	285	7	(	(	PUNCT
ejpam-6111	285	8	in	in	ADP
ejpam-6111	285	9	+	+	CCONJ
ejpam-6111	285	10	(	(	PUNCT
ejpam-6111	285	11	in	in	ADP
ejpam-6111	285	12	+	+	PROPN
ejpam-6111	285	13	a+	a+	X
ejpam-6111	285	14	a2	a2	PROPN
ejpam-6111	285	15	2	2	NUM
ejpam-6111	285	16	!	!	PUNCT
ejpam-6111	286	1	+	+	CCONJ
ejpam-6111	286	2	.	.	PUNCT
ejpam-6111	286	3	.	.	PUNCT
ejpam-6111	286	4	.	.	PUNCT
ejpam-6111	286	5	)	)	PUNCT
ejpam-6111	286	6	)	)	PUNCT
ejpam-6111	287	1	−1	−1	NOUN
ejpam-6111	287	2	(	(	PUNCT
ejpam-6111	287	3	in	in	ADP
ejpam-6111	287	4	−	−	PROPN
ejpam-6111	287	5	(	(	PUNCT
ejpam-6111	287	6	in	in	ADP
ejpam-6111	287	7	+	+	PROPN
ejpam-6111	287	8	a+	a+	X
ejpam-6111	287	9	a2	a2	PROPN
ejpam-6111	287	10	2	2	NUM
ejpam-6111	287	11	!	!	PUNCT
ejpam-6111	288	1	+	+	CCONJ
ejpam-6111	288	2	.	.	PUNCT
ejpam-6111	288	3	.	.	PUNCT
ejpam-6111	288	4	.	.	PUNCT
ejpam-6111	288	5	)	)	PUNCT
ejpam-6111	289	1	)	)	PUNCT
ejpam-6111	289	2	]	]	PUNCT
ejpam-6111	289	3	<	<	X
ejpam-6111	289	4	1	1	X
ejpam-6111	289	5	.	.	PUNCT
ejpam-6111	289	6	proof	proof	NOUN
ejpam-6111	289	7	.	.	PUNCT
ejpam-6111	290	1	for	for	SCONJ
ejpam-6111	290	2	the	the	DET
ejpam-6111	290	3	necessary	necessary	ADJ
ejpam-6111	290	4	condition	condition	NOUN
ejpam-6111	290	5	of	of	ADP
ejpam-6111	290	6	(	(	PUNCT
ejpam-6111	290	7	in	in	ADP
ejpam-6111	290	8	−	−	PROPN
ejpam-6111	290	9	a	a	DET
ejpam-6111	290	10	⊗	⊗	PROPN
ejpam-6111	290	11	p	p	PROPN
ejpam-6111	290	12	t	t	PROPN
ejpam-6111	290	13	)	)	PUNCT
ejpam-6111	290	14	to	to	PART
ejpam-6111	290	15	be	be	AUX
ejpam-6111	290	16	a	a	DET
ejpam-6111	290	17	d	d	ADJ
ejpam-6111	290	18	-	-	ADJ
ejpam-6111	290	19	stable	stable	ADJ
ejpam-6111	290	20	matrix	matrix	NOUN
ejpam-6111	290	21	,	,	PUNCT
ejpam-6111	290	22	we	we	PRON
ejpam-6111	290	23	aim	aim	VERB
ejpam-6111	290	24	to	to	PART
ejpam-6111	290	25	show	show	VERB
ejpam-6111	290	26	that	that	PRON
ejpam-6111	290	27	λi	λi	ADP
ejpam-6111	290	28	[	[	PUNCT
ejpam-6111	290	29	i	i	PRON
ejpam-6111	290	30	in	in	ADP
ejpam-6111	290	31	+	+	CCONJ
ejpam-6111	290	32	(	(	PUNCT
ejpam-6111	290	33	in	in	ADP
ejpam-6111	290	34	+	+	PROPN
ejpam-6111	290	35	a+	a+	X
ejpam-6111	290	36	a2	a2	PROPN
ejpam-6111	290	37	2	2	NUM
ejpam-6111	290	38	!	!	PUNCT
ejpam-6111	291	1	+	+	CCONJ
ejpam-6111	291	2	.	.	PUNCT
ejpam-6111	291	3	.	.	PUNCT
ejpam-6111	292	1	.)p	.)p	NUM
ejpam-6111	292	2	]	]	X
ejpam-6111	293	1	̸=	̸=	PROPN
ejpam-6111	293	2	0	0	NUM
ejpam-6111	293	3	,	,	PUNCT
ejpam-6111	293	4	∀i	∀i	NOUN
ejpam-6111	293	5	,	,	PUNCT
ejpam-6111	293	6	∀p	∀p	PROPN
ejpam-6111	293	7	∈	∈	PROPN
ejpam-6111	293	8	ω	ω	NOUN
ejpam-6111	293	9	.	.	PUNCT
ejpam-6111	294	1	let	let	VERB
ejpam-6111	294	2	∆	∆	PROPN
ejpam-6111	294	3	∈	∈	PROPN
ejpam-6111	294	4	b1	b1	NOUN
ejpam-6111	294	5	with	with	ADP
ejpam-6111	294	6	a	a	DET
ejpam-6111	294	7	block	block	NOUN
ejpam-6111	294	8	-	-	PUNCT
ejpam-6111	294	9	diagonal	diagonal	ADJ
ejpam-6111	294	10	structure	structure	NOUN
ejpam-6111	294	11	,	,	PUNCT
ejpam-6111	294	12	and	and	CCONJ
ejpam-6111	294	13	∆	∆	X
ejpam-6111	295	1	=	=	SYM
ejpam-6111	295	2	(	(	PUNCT
ejpam-6111	295	3	in	in	ADP
ejpam-6111	295	4	−	−	PROPN
ejpam-6111	295	5	p	p	NOUN
ejpam-6111	295	6	)	)	PUNCT
ejpam-6111	295	7	(	(	PUNCT
ejpam-6111	295	8	in	in	ADP
ejpam-6111	295	9	+	+	CCONJ
ejpam-6111	295	10	p	p	NOUN
ejpam-6111	295	11	)	)	PUNCT
ejpam-6111	295	12	−1	−1	NOUN
ejpam-6111	295	13	such	such	ADJ
ejpam-6111	295	14	that	that	SCONJ
ejpam-6111	295	15	p	p	NOUN
ejpam-6111	295	16	=	=	X
ejpam-6111	295	17	(	(	PUNCT
ejpam-6111	295	18	in	in	ADP
ejpam-6111	295	19	+	+	NOUN
ejpam-6111	295	20	∆)−1(in	∆)−1(in	X
ejpam-6111	295	21	−∆	−∆	NOUN
ejpam-6111	295	22	)	)	PUNCT
ejpam-6111	295	23	.	.	PUNCT
ejpam-6111	296	1	this	this	DET
ejpam-6111	296	2	further	further	ADJ
ejpam-6111	296	3	yields	yield	NOUN
ejpam-6111	296	4	that	that	PRON
ejpam-6111	296	5	λi	λi	ADP
ejpam-6111	296	6	[	[	PUNCT
ejpam-6111	296	7	i	i	PRON
ejpam-6111	296	8	in	in	ADP
ejpam-6111	296	9	+	+	CCONJ
ejpam-6111	296	10	(	(	PUNCT
ejpam-6111	296	11	in	in	ADP
ejpam-6111	296	12	+	+	PROPN
ejpam-6111	296	13	a+	a+	X
ejpam-6111	296	14	a2	a2	PROPN
ejpam-6111	296	15	2	2	NUM
ejpam-6111	296	16	!	!	PUNCT
ejpam-6111	297	1	+	+	CCONJ
ejpam-6111	297	2	.	.	PUNCT
ejpam-6111	297	3	.	.	PUNCT
ejpam-6111	298	1	.)(in	.)(in	PUNCT
ejpam-6111	299	1	+	+	ADP
ejpam-6111	299	2	∆)−1(in	∆)−1(in	X
ejpam-6111	299	3	−∆	−∆	NOUN
ejpam-6111	299	4	)	)	PUNCT
ejpam-6111	299	5	]	]	PUNCT
ejpam-6111	300	1	̸=	̸=	PROPN
ejpam-6111	300	2	0	0	NUM
ejpam-6111	300	3	,	,	PUNCT
ejpam-6111	300	4	∀i	∀i	NOUN
ejpam-6111	300	5	,	,	PUNCT
ejpam-6111	300	6	∀∆	∀∆	NOUN
ejpam-6111	300	7	∈	∈	PROPN
ejpam-6111	300	8	b1	b1	NOUN
ejpam-6111	300	9	.	.	PUNCT
ejpam-6111	301	1	furthermore	furthermore	ADV
ejpam-6111	301	2	,	,	PUNCT
ejpam-6111	301	3	λi	λi	X
ejpam-6111	301	4	[	[	X
ejpam-6111	301	5	(	(	PUNCT
ejpam-6111	301	6	i	i	PRON
ejpam-6111	301	7	in	in	ADP
ejpam-6111	301	8	+	+	CCONJ
ejpam-6111	301	9	(	(	PUNCT
ejpam-6111	301	10	in	in	ADP
ejpam-6111	301	11	+	+	PROPN
ejpam-6111	301	12	a+	a+	X
ejpam-6111	301	13	a2	a2	PROPN
ejpam-6111	301	14	2	2	NUM
ejpam-6111	301	15	!	!	PUNCT
ejpam-6111	302	1	+	+	CCONJ
ejpam-6111	302	2	.	.	PUNCT
ejpam-6111	302	3	.	.	PUNCT
ejpam-6111	302	4	.	.	PUNCT
ejpam-6111	302	5	)	)	PUNCT
ejpam-6111	302	6	)	)	PUNCT
ejpam-6111	303	1	−1	−1	NOUN
ejpam-6111	303	2	(	(	PUNCT
ejpam-6111	303	3	i	i	PRON
ejpam-6111	303	4	in	in	ADP
ejpam-6111	303	5	−	−	PROPN
ejpam-6111	303	6	(	(	PUNCT
ejpam-6111	303	7	in	in	ADP
ejpam-6111	303	8	+	+	PROPN
ejpam-6111	303	9	a+	a+	X
ejpam-6111	303	10	a2	a2	PROPN
ejpam-6111	303	11	2	2	NUM
ejpam-6111	303	12	!	!	PUNCT
ejpam-6111	304	1	+	+	CCONJ
ejpam-6111	304	2	.	.	PUNCT
ejpam-6111	304	3	.	.	PUNCT
ejpam-6111	304	4	.	.	PUNCT
ejpam-6111	304	5	)	)	PUNCT
ejpam-6111	304	6	)	)	PUNCT
ejpam-6111	305	1	∆	∆	PROPN
ejpam-6111	305	2	]	]	PUNCT
ejpam-6111	306	1	̸=	̸=	PROPN
ejpam-6111	306	2	0	0	NUM
ejpam-6111	306	3	,	,	PUNCT
ejpam-6111	306	4	∀i	∀i	NOUN
ejpam-6111	306	5	,	,	PUNCT
ejpam-6111	306	6	∀∆	∀∆	NOUN
ejpam-6111	306	7	∈	∈	PROPN
ejpam-6111	306	8	b1	b1	NOUN
ejpam-6111	306	9	.	.	PUNCT
ejpam-6111	307	1	finally	finally	ADV
ejpam-6111	307	2	,	,	PUNCT
ejpam-6111	307	3	we	we	PRON
ejpam-6111	307	4	conclude	conclude	VERB
ejpam-6111	307	5	that	that	SCONJ
ejpam-6111	307	6	0	0	NUM
ejpam-6111	307	7	≤	≤	NUM
ejpam-6111	307	8	µb1	µb1	VERB
ejpam-6111	308	1	[	[	X
ejpam-6111	308	2	(	(	PUNCT
ejpam-6111	308	3	in	in	ADP
ejpam-6111	308	4	+	+	CCONJ
ejpam-6111	308	5	(	(	PUNCT
ejpam-6111	308	6	in	in	ADP
ejpam-6111	308	7	+	+	PROPN
ejpam-6111	308	8	a+	a+	X
ejpam-6111	308	9	a2	a2	PROPN
ejpam-6111	308	10	2	2	NUM
ejpam-6111	308	11	!	!	PUNCT
ejpam-6111	309	1	+	+	CCONJ
ejpam-6111	309	2	.	.	PUNCT
ejpam-6111	309	3	.	.	PUNCT
ejpam-6111	309	4	.	.	PUNCT
ejpam-6111	309	5	)	)	PUNCT
ejpam-6111	309	6	)	)	PUNCT
ejpam-6111	310	1	−1	−1	NOUN
ejpam-6111	310	2	(	(	PUNCT
ejpam-6111	310	3	in	in	ADP
ejpam-6111	310	4	−	−	PROPN
ejpam-6111	310	5	(	(	PUNCT
ejpam-6111	310	6	in	in	ADP
ejpam-6111	310	7	+	+	PROPN
ejpam-6111	310	8	a+	a+	X
ejpam-6111	310	9	a2	a2	PROPN
ejpam-6111	310	10	2	2	NUM
ejpam-6111	310	11	!	!	PUNCT
ejpam-6111	311	1	+	+	CCONJ
ejpam-6111	311	2	.	.	PUNCT
ejpam-6111	311	3	.	.	PUNCT
ejpam-6111	311	4	.	.	PUNCT
ejpam-6111	311	5	)	)	PUNCT
ejpam-6111	311	6	)	)	PUNCT
ejpam-6111	312	1	]	]	PUNCT
ejpam-6111	312	2	<	<	X
ejpam-6111	312	3	1	1	X
ejpam-6111	312	4	.	.	PUNCT
ejpam-6111	312	5	s.	s.	PROPN
ejpam-6111	312	6	mazhar	mazhar	PROPN
ejpam-6111	312	7	,	,	PUNCT
ejpam-6111	312	8	m.	m.	NOUN
ejpam-6111	312	9	u.	u.	PROPN
ejpam-6111	312	10	rehman	rehman	PROPN
ejpam-6111	312	11	/	/	SYM
ejpam-6111	312	12	eur	eur	PROPN
ejpam-6111	312	13	.	.	PUNCT
ejpam-6111	313	1	j.	j.	PROPN
ejpam-6111	313	2	pure	pure	PROPN
ejpam-6111	313	3	appl	appl	PROPN
ejpam-6111	313	4	.	.	PROPN
ejpam-6111	313	5	math	math	PROPN
ejpam-6111	313	6	,	,	PUNCT
ejpam-6111	313	7	18	18	NUM
ejpam-6111	313	8	(	(	PUNCT
ejpam-6111	313	9	2	2	NUM
ejpam-6111	313	10	)	)	PUNCT
ejpam-6111	313	11	(	(	PUNCT
ejpam-6111	313	12	2025	2025	NUM
ejpam-6111	313	13	)	)	PUNCT
ejpam-6111	313	14	,	,	PUNCT
ejpam-6111	313	15	6111	6111	NUM
ejpam-6111	313	16	12	12	NUM
ejpam-6111	313	17	of	of	ADP
ejpam-6111	313	18	25	25	NUM
ejpam-6111	313	19	5.1	5.1	NUM
ejpam-6111	313	20	.	.	PUNCT
ejpam-6111	314	1	strong	strong	ADJ
ejpam-6111	314	2	d	d	NOUN
ejpam-6111	314	3	-	-	NOUN
ejpam-6111	314	4	stability	stability	NOUN
ejpam-6111	314	5	:	:	PUNCT
ejpam-6111	314	6	in	in	ADP
ejpam-6111	314	7	this	this	DET
ejpam-6111	314	8	subsection	subsection	NOUN
ejpam-6111	314	9	,	,	PUNCT
ejpam-6111	314	10	we	we	PRON
ejpam-6111	314	11	provide	provide	VERB
ejpam-6111	314	12	new	new	ADJ
ejpam-6111	314	13	results	result	NOUN
ejpam-6111	314	14	on	on	ADP
ejpam-6111	314	15	strong	strong	ADJ
ejpam-6111	314	16	d	d	NOUN
ejpam-6111	314	17	-	-	NOUN
ejpam-6111	314	18	stability	stability	NOUN
ejpam-6111	314	19	of	of	ADP
ejpam-6111	314	20	(	(	PUNCT
ejpam-6111	314	21	in	in	ADP
ejpam-6111	314	22	−	−	PROPN
ejpam-6111	314	23	a	a	DET
ejpam-6111	314	24	⊗	⊗	PROPN
ejpam-6111	314	25	p	p	PROPN
ejpam-6111	314	26	t	t	PROPN
ejpam-6111	314	27	)	)	PUNCT
ejpam-6111	314	28	,	,	PUNCT
ejpam-6111	314	29	which	which	PRON
ejpam-6111	314	30	is	be	AUX
ejpam-6111	314	31	a	a	DET
ejpam-6111	314	32	n	n	CCONJ
ejpam-6111	314	33	-	-	PUNCT
ejpam-6111	314	34	dimensional	dimensional	ADJ
ejpam-6111	314	35	real	real	ADV
ejpam-6111	314	36	-	-	PUNCT
ejpam-6111	314	37	valued	value	VERB
ejpam-6111	314	38	matrix	matrix	NOUN
ejpam-6111	314	39	.	.	PUNCT
ejpam-6111	315	1	the	the	DET
ejpam-6111	315	2	following	follow	VERB
ejpam-6111	315	3	theorem	theorem	VERB
ejpam-6111	315	4	6	6	NUM
ejpam-6111	315	5	shows	show	VERB
ejpam-6111	315	6	the	the	DET
ejpam-6111	315	7	strong	strong	ADJ
ejpam-6111	315	8	d	d	NOUN
ejpam-6111	315	9	-	-	NOUN
ejpam-6111	315	10	stability	stability	NOUN
ejpam-6111	315	11	and	and	CCONJ
ejpam-6111	315	12	we	we	PRON
ejpam-6111	315	13	have	have	AUX
ejpam-6111	315	14	made	make	VERB
ejpam-6111	315	15	use	use	NOUN
ejpam-6111	315	16	of	of	ADP
ejpam-6111	315	17	the	the	DET
ejpam-6111	315	18	eigenvalue	eigenvalue	ADJ
ejpam-6111	315	19	perturbation	perturbation	NOUN
ejpam-6111	315	20	result	result	NOUN
ejpam-6111	315	21	to	to	ADP
ejpam-6111	315	22	the	the	DET
ejpam-6111	315	23	largest	large	ADJ
ejpam-6111	315	24	and	and	CCONJ
ejpam-6111	315	25	simple	simple	ADJ
ejpam-6111	315	26	eigenvalue	eigenvalue	NOUN
ejpam-6111	315	27	to	to	PART
ejpam-6111	315	28	analyze	analyze	VERB
ejpam-6111	315	29	its	its	PRON
ejpam-6111	315	30	behaviour	behaviour	NOUN
ejpam-6111	315	31	,	,	PUNCT
ejpam-6111	315	32	which	which	PRON
ejpam-6111	315	33	in	in	ADP
ejpam-6111	315	34	turn	turn	NOUN
ejpam-6111	315	35	helps	help	VERB
ejpam-6111	315	36	us	we	PRON
ejpam-6111	315	37	to	to	PART
ejpam-6111	315	38	conclude	conclude	VERB
ejpam-6111	315	39	our	our	PRON
ejpam-6111	315	40	results	result	NOUN
ejpam-6111	315	41	for	for	ADP
ejpam-6111	315	42	d	d	NOUN
ejpam-6111	315	43	-	-	NOUN
ejpam-6111	315	44	stability	stability	NOUN
ejpam-6111	315	45	.	.	PUNCT
ejpam-6111	316	1	theorem	theorem	VERB
ejpam-6111	316	2	6	6	NUM
ejpam-6111	316	3	.	.	PUNCT
ejpam-6111	317	1	let	let	AUX
ejpam-6111	317	2	(	(	PUNCT
ejpam-6111	317	3	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	317	4	t	t	NOUN
ejpam-6111	317	5	)	)	PUNCT
ejpam-6111	317	6	be	be	AUX
ejpam-6111	317	7	a	a	DET
ejpam-6111	317	8	n	n	CCONJ
ejpam-6111	317	9	-	-	PUNCT
ejpam-6111	317	10	dimensional	dimensional	ADJ
ejpam-6111	317	11	real	real	ADV
ejpam-6111	317	12	-	-	PUNCT
ejpam-6111	317	13	valued	value	VERB
ejpam-6111	317	14	matrix	matrix	NOUN
ejpam-6111	317	15	.	.	PUNCT
ejpam-6111	318	1	then	then	ADV
ejpam-6111	318	2	(	(	PUNCT
ejpam-6111	318	3	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	318	4	t	t	NOUN
ejpam-6111	318	5	)	)	PUNCT
ejpam-6111	318	6	is	be	AUX
ejpam-6111	318	7	strongly	strongly	ADV
ejpam-6111	318	8	d	d	NOUN
ejpam-6111	318	9	-	-	ADJ
ejpam-6111	318	10	stable	stable	ADJ
ejpam-6111	318	11	if	if	SCONJ
ejpam-6111	318	12	for	for	ADP
ejpam-6111	318	13	n	n	CCONJ
ejpam-6111	318	14	-	-	PUNCT
ejpam-6111	318	15	dimensional	dimensional	ADJ
ejpam-6111	318	16	matrices	matrix	NOUN
ejpam-6111	318	17	a1	a1	NOUN
ejpam-6111	318	18	,	,	PUNCT
ejpam-6111	318	19	a2	a2	PROPN
ejpam-6111	318	20	,	,	PUNCT
ejpam-6111	318	21	·	·	PUNCT
ejpam-6111	318	22	·	·	PUNCT
ejpam-6111	318	23	·	·	PUNCT
ejpam-6111	318	24	,	,	PUNCT
ejpam-6111	318	25	ar	ar	PROPN
ejpam-6111	318	26	,	,	PUNCT
ejpam-6111	318	27	the	the	DET
ejpam-6111	318	28	matrix	matrix	NOUN
ejpam-6111	318	29	log(in−a⊗	log(in−a⊗	NOUN
ejpam-6111	318	30	p	p	PROPN
ejpam-6111	318	31	t	t	PROPN
ejpam-6111	318	32	)	)	PUNCT
ejpam-6111	318	33	+	+	CCONJ
ejpam-6111	319	1	[	[	X
ejpam-6111	319	2	(	(	PUNCT
ejpam-6111	319	3	log(in−a⊗p	log(in−a⊗p	NOUN
ejpam-6111	319	4	t)⊗	t)⊗	PRON
ejpam-6111	319	5	(	(	PUNCT
ejpam-6111	319	6	a1+α2a2	a1+α2a2	NOUN
ejpam-6111	319	7	+	+	X
ejpam-6111	319	8	·	·	PUNCT
ejpam-6111	319	9	·	·	PUNCT
ejpam-6111	319	10	·	·	PUNCT
ejpam-6111	319	11	+	+	PROPN
ejpam-6111	319	12	αr	αr	NUM
ejpam-6111	319	13	ar	ar	NOUN
ejpam-6111	319	14	)	)	PUNCT
ejpam-6111	319	15	)	)	PUNCT
ejpam-6111	319	16	t	t	PROPN
ejpam-6111	319	17	∆+∆	∆+∆	PROPN
ejpam-6111	319	18	(	(	PUNCT
ejpam-6111	319	19	log(in−a⊗p	log(in−a⊗p	NOUN
ejpam-6111	319	20	t)⊗	t)⊗	X
ejpam-6111	319	21	(	(	PUNCT
ejpam-6111	319	22	a1	a1	NOUN
ejpam-6111	319	23	+	+	SYM
ejpam-6111	319	24	α2a2	α2a2	NOUN
ejpam-6111	319	25	+	+	CCONJ
ejpam-6111	319	26	·	·	PUNCT
ejpam-6111	319	27	·	·	PUNCT
ejpam-6111	319	28	·	·	PUNCT
ejpam-6111	319	29	+	+	NOUN
ejpam-6111	319	30	α2ar	α2ar	X
ejpam-6111	319	31	)	)	PUNCT
ejpam-6111	319	32	)	)	PUNCT
ejpam-6111	319	33	]	]	PUNCT
ejpam-6111	319	34	is	be	AUX
ejpam-6111	319	35	a	a	DET
ejpam-6111	319	36	d	d	ADJ
ejpam-6111	319	37	-	-	ADJ
ejpam-6111	319	38	stable	stable	ADJ
ejpam-6111	319	39	matrix	matrix	NOUN
ejpam-6111	319	40	for	for	ADP
ejpam-6111	319	41	all	all	DET
ejpam-6111	319	42	∆	∆	X
ejpam-6111	319	43	∈	∈	PROPN
ejpam-6111	319	44	b1	b1	NOUN
ejpam-6111	319	45	,	,	PUNCT
ejpam-6111	319	46	here	here	ADV
ejpam-6111	319	47	⊗	⊗	PROPN
ejpam-6111	319	48	denotes	denote	VERB
ejpam-6111	319	49	the	the	DET
ejpam-6111	319	50	entry	entry	NOUN
ejpam-6111	319	51	-	-	PUNCT
ejpam-6111	319	52	wise	wise	ADJ
ejpam-6111	319	53	product	product	NOUN
ejpam-6111	319	54	of	of	ADP
ejpam-6111	319	55	matrices	matrix	NOUN
ejpam-6111	319	56	,	,	PUNCT
ejpam-6111	319	57	and	and	CCONJ
ejpam-6111	319	58	αi	αi	ADP
ejpam-6111	319	59	∈	∈	PROPN
ejpam-6111	319	60	r	r	NOUN
ejpam-6111	319	61	,	,	PUNCT
ejpam-6111	319	62	αi	αi	VERB
ejpam-6111	319	63	>	>	X
ejpam-6111	319	64	0	0	NUM
ejpam-6111	319	65	∀i	∀i	NOUN
ejpam-6111	319	66	.	.	PUNCT
ejpam-6111	320	1	proof	proof	NOUN
ejpam-6111	320	2	.	.	PUNCT
ejpam-6111	321	1	suppose	suppose	VERB
ejpam-6111	321	2	that	that	SCONJ
ejpam-6111	321	3	∆	∆	PROPN
ejpam-6111	321	4	∈	∈	PROPN
ejpam-6111	321	5	b1	b1	NOUN
ejpam-6111	321	6	has	have	VERB
ejpam-6111	321	7	a	a	DET
ejpam-6111	321	8	block	block	NOUN
ejpam-6111	321	9	-	-	PUNCT
ejpam-6111	321	10	diagonal	diagonal	ADJ
ejpam-6111	321	11	structure	structure	NOUN
ejpam-6111	321	12	,	,	PUNCT
ejpam-6111	321	13	whereas	whereas	SCONJ
ejpam-6111	321	14	the	the	DET
ejpam-6111	321	15	set	set	NOUN
ejpam-6111	321	16	b1	b1	NOUN
ejpam-6111	321	17	can	can	AUX
ejpam-6111	321	18	have	have	VERB
ejpam-6111	321	19	a	a	DET
ejpam-6111	321	20	matrix	matrix	NOUN
ejpam-6111	321	21	of	of	ADP
ejpam-6111	321	22	real	real	ADJ
ejpam-6111	321	23	and	and	CCONJ
ejpam-6111	321	24	complex	complex	ADJ
ejpam-6111	321	25	uncertainties	uncertainty	NOUN
ejpam-6111	321	26	.	.	PUNCT
ejpam-6111	322	1	for	for	ADP
ejpam-6111	322	2	0	0	NUM
ejpam-6111	322	3	<	<	X
ejpam-6111	322	4	θ	θ	X
ejpam-6111	322	5	≤	≤	ADJ
ejpam-6111	322	6	2π	2π	NOUN
ejpam-6111	322	7	,	,	PUNCT
ejpam-6111	322	8	let	let	VERB
ejpam-6111	322	9	λ(t	λ(t	PRON
ejpam-6111	322	10	)	)	PUNCT
ejpam-6111	322	11	=	=	PRON
ejpam-6111	322	12	|λ(t)|eiθ	|λ(t)|eiθ	PRON
ejpam-6111	322	13	be	be	VERB
ejpam-6111	322	14	the	the	DET
ejpam-6111	322	15	simple	simple	ADJ
ejpam-6111	322	16	and	and	CCONJ
ejpam-6111	322	17	largest	large	ADJ
ejpam-6111	322	18	eigenvalue	eigenvalue	NOUN
ejpam-6111	322	19	.	.	PUNCT
ejpam-6111	323	1	assume	assume	VERB
ejpam-6111	323	2	that	that	SCONJ
ejpam-6111	323	3	x(t	x(t	PROPN
ejpam-6111	323	4	)	)	PUNCT
ejpam-6111	323	5	,	,	PUNCT
ejpam-6111	323	6	y(t	y(t	NUM
ejpam-6111	323	7	)	)	PUNCT
ejpam-6111	323	8	have	have	VERB
ejpam-6111	323	9	structure	structure	NOUN
ejpam-6111	323	10	and	and	CCONJ
ejpam-6111	323	11	size	size	NOUN
ejpam-6111	323	12	similar	similar	ADJ
ejpam-6111	323	13	to	to	ADP
ejpam-6111	323	14	given	give	VERB
ejpam-6111	323	15	matrix	matrix	NOUN
ejpam-6111	323	16	(	(	PUNCT
ejpam-6111	323	17	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	323	18	t	t	NOUN
ejpam-6111	323	19	)	)	PUNCT
ejpam-6111	323	20	,	,	PUNCT
ejpam-6111	323	21	and	and	CCONJ
ejpam-6111	323	22	are	be	AUX
ejpam-6111	323	23	the	the	DET
ejpam-6111	323	24	right	right	ADJ
ejpam-6111	323	25	hand	hand	NOUN
ejpam-6111	323	26	and	and	CCONJ
ejpam-6111	323	27	left	leave	VERB
ejpam-6111	323	28	hand	hand	NOUN
ejpam-6111	323	29	eigen	eigen	NOUN
ejpam-6111	323	30	-	-	PUNCT
ejpam-6111	323	31	vectors	vector	NOUN
ejpam-6111	323	32	.	.	PUNCT
ejpam-6111	324	1	consider	consider	VERB
ejpam-6111	324	2	that	that	PRON
ejpam-6111	324	3	x̃(t	x̃(t	PROPN
ejpam-6111	324	4	)	)	PUNCT
ejpam-6111	324	5	of	of	ADP
ejpam-6111	324	6	the	the	DET
ejpam-6111	324	7	form	form	NOUN
ejpam-6111	324	8	(	(	PUNCT
ejpam-6111	324	9	log(in−a⊗p	log(in−a⊗p	NOUN
ejpam-6111	324	10	t)⊗	t)⊗	PRON
ejpam-6111	324	11	(	(	PUNCT
ejpam-6111	324	12	a1+α2a2	a1+α2a2	PROPN
ejpam-6111	324	13	+	+	NOUN
ejpam-6111	324	14	·	·	PUNCT
ejpam-6111	324	15	·	·	PUNCT
ejpam-6111	324	16	·	·	PUNCT
ejpam-6111	324	17	+	+	PROPN
ejpam-6111	324	18	αr	αr	NUM
ejpam-6111	324	19	ar	ar	NOUN
ejpam-6111	324	20	)	)	PUNCT
ejpam-6111	324	21	)	)	PUNCT
ejpam-6111	324	22	t	t	NOUN
ejpam-6111	324	23	∆	∆	X
ejpam-6111	325	1	+	+	CCONJ
ejpam-6111	326	1	∆	∆	PROPN
ejpam-6111	326	2	(	(	PUNCT
ejpam-6111	326	3	log(in−a⊗p	log(in−a⊗p	NOUN
ejpam-6111	326	4	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	326	5	+	+	PROPN
ejpam-6111	326	6	·	·	PUNCT
ejpam-6111	326	7	·	·	PUNCT
ejpam-6111	326	8	·	·	PUNCT
ejpam-6111	326	9	+	+	NOUN
ejpam-6111	326	10	α2ar	α2ar	X
ejpam-6111	326	11	)	)	PUNCT
ejpam-6111	326	12	)	)	PUNCT
ejpam-6111	326	13	y(t	y(t	NUM
ejpam-6111	326	14	)	)	PUNCT
ejpam-6111	326	15	the	the	DET
ejpam-6111	326	16	eigenvalue	eigenvalue	PROPN
ejpam-6111	326	17	perturbation	perturbation	NOUN
ejpam-6111	326	18	result	result	NOUN
ejpam-6111	326	19	by	by	ADP
ejpam-6111	326	20	kato	kato	PROPN
ejpam-6111	326	21	to	to	ADP
ejpam-6111	326	22	λ(t	λ(t	PROPN
ejpam-6111	326	23	)	)	PUNCT
ejpam-6111	326	24	which	which	PRON
ejpam-6111	326	25	yields	yield	VERB
ejpam-6111	326	26	d	d	NOUN
ejpam-6111	326	27	dt	dt	NOUN
ejpam-6111	326	28	|λ(t)|2	|λ(t)|2	NOUN
ejpam-6111	326	29	=	=	SYM
ejpam-6111	326	30	2ϵ	2ϵ	NUM
ejpam-6111	327	1	|λ(t)|	|λ(t)|	VERB
ejpam-6111	327	2	r	r	NOUN
ejpam-6111	327	3	re	re	X
ejpam-6111	327	4	(	(	PUNCT
ejpam-6111	327	5	x̃t(t)∆̇(t)x(t	x̃t(t)∆̇(t)x(t	PROPN
ejpam-6111	327	6	)	)	PUNCT
ejpam-6111	327	7	)	)	PUNCT
ejpam-6111	327	8	;	;	PUNCT
ejpam-6111	327	9	r	r	NOUN
ejpam-6111	327	10	=	=	SYM
ejpam-6111	327	11	eiθ	eiθ	PROPN
ejpam-6111	327	12	yt(t)x(t	yt(t)x(t	PROPN
ejpam-6111	327	13	)	)	PUNCT
ejpam-6111	327	14	,	,	PUNCT
ejpam-6111	327	15	ϵ	ϵ	X
ejpam-6111	327	16	>	>	X
ejpam-6111	327	17	0	0	X
ejpam-6111	327	18	.	.	PUNCT
ejpam-6111	328	1	this	this	DET
ejpam-6111	328	2	further	far	ADV
ejpam-6111	328	3	implies	imply	VERB
ejpam-6111	328	4	that	that	SCONJ
ejpam-6111	328	5	(	(	PUNCT
ejpam-6111	328	6	log(in−a⊗p	log(in−a⊗p	NOUN
ejpam-6111	328	7	t)⊗	t)⊗	PRON
ejpam-6111	328	8	(	(	PUNCT
ejpam-6111	328	9	a1+α2a2	a1+α2a2	PROPN
ejpam-6111	328	10	+	+	NOUN
ejpam-6111	328	11	·	·	PUNCT
ejpam-6111	328	12	·	·	PUNCT
ejpam-6111	328	13	·	·	PUNCT
ejpam-6111	328	14	+	+	PROPN
ejpam-6111	328	15	αr	αr	NUM
ejpam-6111	328	16	ar	ar	NOUN
ejpam-6111	328	17	)	)	PUNCT
ejpam-6111	328	18	)	)	PUNCT
ejpam-6111	329	1	t	t	NOUN
ejpam-6111	329	2	∆	∆	X
ejpam-6111	330	1	+	+	PRON
ejpam-6111	330	2	∆	∆	PROPN
ejpam-6111	330	3	(	(	PUNCT
ejpam-6111	330	4	log(in−a⊗p	log(in−a⊗p	PROPN
ejpam-6111	330	5	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	330	6	+	+	PROPN
ejpam-6111	330	7	·	·	PUNCT
ejpam-6111	330	8	·	·	PUNCT
ejpam-6111	330	9	·	·	PUNCT
ejpam-6111	330	10	+	+	NOUN
ejpam-6111	330	11	α2ar	α2ar	X
ejpam-6111	330	12	)	)	PUNCT
ejpam-6111	330	13	)	)	PUNCT
ejpam-6111	330	14	>	>	X
ejpam-6111	331	1	0	0	X
ejpam-6111	331	2	.	.	PUNCT
ejpam-6111	332	1	in	in	ADP
ejpam-6111	332	2	turn	turn	NOUN
ejpam-6111	332	3	,	,	PUNCT
ejpam-6111	332	4	this	this	DET
ejpam-6111	332	5	further	further	ADJ
ejpam-6111	332	6	yields	yield	NOUN
ejpam-6111	332	7	log(in	log(in	NOUN
ejpam-6111	332	8	−	−	PROPN
ejpam-6111	332	9	a	a	DET
ejpam-6111	332	10	⊗	⊗	PROPN
ejpam-6111	332	11	p	p	PROPN
ejpam-6111	332	12	t	t	PROPN
ejpam-6111	332	13	)	)	PUNCT
ejpam-6111	332	14	+	+	CCONJ
ejpam-6111	333	1	[	[	X
ejpam-6111	333	2	(	(	PUNCT
ejpam-6111	333	3	log(in	log(in	NOUN
ejpam-6111	333	4	−	−	PROPN
ejpam-6111	333	5	a	a	DET
ejpam-6111	333	6	⊗	⊗	PROPN
ejpam-6111	333	7	p	p	PROPN
ejpam-6111	333	8	t	t	PROPN
ejpam-6111	333	9	)	)	PUNCT
ejpam-6111	333	10	⊗	⊗	PROPN
ejpam-6111	333	11	(	(	PUNCT
ejpam-6111	333	12	a1	a1	NOUN
ejpam-6111	333	13	+	+	CCONJ
ejpam-6111	333	14	α2a2	α2a2	PUNCT
ejpam-6111	333	15	+	+	CCONJ
ejpam-6111	333	16	·	·	PUNCT
ejpam-6111	333	17	·	·	PUNCT
ejpam-6111	333	18	·	·	PUNCT
ejpam-6111	334	1	+	+	CCONJ
ejpam-6111	334	2	αr	αr	NUM
ejpam-6111	334	3	ar	ar	NOUN
ejpam-6111	334	4	)	)	PUNCT
ejpam-6111	334	5	)	)	PUNCT
ejpam-6111	335	1	t	t	PROPN
ejpam-6111	335	2	∆+∆	∆+∆	PROPN
ejpam-6111	335	3	(	(	PUNCT
ejpam-6111	335	4	log(in	log(in	NOUN
ejpam-6111	335	5	−	−	NOUN
ejpam-6111	335	6	a⊗	a⊗	NOUN
ejpam-6111	335	7	p	p	NOUN
ejpam-6111	335	8	t)⊗	t)⊗	PRON
ejpam-6111	335	9	(	(	PUNCT
ejpam-6111	335	10	a1	a1	NOUN
ejpam-6111	335	11	+	+	CCONJ
ejpam-6111	335	12	α2a2	α2a2	PUNCT
ejpam-6111	335	13	+	+	CCONJ
ejpam-6111	335	14	·	·	PUNCT
ejpam-6111	335	15	·	·	PUNCT
ejpam-6111	335	16	·	·	PUNCT
ejpam-6111	335	17	+	+	X
ejpam-6111	335	18	α2ar	α2ar	X
ejpam-6111	335	19	)	)	PUNCT
ejpam-6111	335	20	)	)	PUNCT
ejpam-6111	335	21	]	]	PUNCT
ejpam-6111	335	22	is	be	AUX
ejpam-6111	335	23	a	a	DET
ejpam-6111	335	24	d	d	ADJ
ejpam-6111	335	25	-	-	ADJ
ejpam-6111	335	26	stable	stable	ADJ
ejpam-6111	335	27	matrix	matrix	NOUN
ejpam-6111	335	28	.	.	PUNCT
ejpam-6111	336	1	in	in	ADP
ejpam-6111	336	2	theorem	theorem	NOUN
ejpam-6111	336	3	7	7	NUM
ejpam-6111	336	4	,	,	PUNCT
ejpam-6111	336	5	we	we	PRON
ejpam-6111	336	6	show	show	VERB
ejpam-6111	336	7	the	the	DET
ejpam-6111	336	8	d	d	NOUN
ejpam-6111	336	9	-	-	NOUN
ejpam-6111	336	10	stability	stability	NOUN
ejpam-6111	336	11	of	of	ADP
ejpam-6111	336	12	a	a	DET
ejpam-6111	336	13	2	2	NUM
ejpam-6111	336	14	-	-	PUNCT
ejpam-6111	336	15	dimensional	dimensional	ADJ
ejpam-6111	336	16	real	real	ADV
ejpam-6111	336	17	-	-	PUNCT
ejpam-6111	336	18	valued	value	VERB
ejpam-6111	336	19	matrix	matrix	NOUN
ejpam-6111	336	20	,	,	PUNCT
ejpam-6111	336	21	that	that	ADV
ejpam-6111	336	22	is	is	ADV
ejpam-6111	336	23	,	,	PUNCT
ejpam-6111	336	24	(	(	PUNCT
ejpam-6111	336	25	i2	i2	PROPN
ejpam-6111	336	26	−	−	PROPN
ejpam-6111	336	27	(	(	PUNCT
ejpam-6111	336	28	a⊗	a⊗	PROPN
ejpam-6111	336	29	p	p	PROPN
ejpam-6111	336	30	t	t	PROPN
ejpam-6111	336	31	)	)	PUNCT
ejpam-6111	336	32	)	)	PUNCT
ejpam-6111	337	1	∈	∈	PROPN
ejpam-6111	337	2	r2,2	r2,2	PROPN
ejpam-6111	337	3	.	.	PUNCT
ejpam-6111	338	1	we	we	PRON
ejpam-6111	338	2	again	again	ADV
ejpam-6111	338	3	make	make	VERB
ejpam-6111	338	4	use	use	NOUN
ejpam-6111	338	5	of	of	ADP
ejpam-6111	338	6	the	the	DET
ejpam-6111	338	7	eigenvalue	eigenvalue	ADJ
ejpam-6111	338	8	perturbation	perturbation	NOUN
ejpam-6111	338	9	result	result	NOUN
ejpam-6111	338	10	for	for	ADP
ejpam-6111	338	11	the	the	DET
ejpam-6111	338	12	largest	large	ADJ
ejpam-6111	338	13	and	and	CCONJ
ejpam-6111	338	14	simple	simple	ADJ
ejpam-6111	338	15	eigenvalue	eigenvalue	NOUN
ejpam-6111	338	16	to	to	PART
ejpam-6111	338	17	analyze	analyze	VERB
ejpam-6111	338	18	its	its	PRON
ejpam-6111	338	19	behaviour	behaviour	NOUN
ejpam-6111	338	20	,	,	PUNCT
ejpam-6111	338	21	which	which	PRON
ejpam-6111	338	22	in	in	ADP
ejpam-6111	338	23	turn	turn	NOUN
ejpam-6111	338	24	helps	help	VERB
ejpam-6111	338	25	us	we	PRON
ejpam-6111	338	26	to	to	PART
ejpam-6111	338	27	conclude	conclude	VERB
ejpam-6111	338	28	our	our	PRON
ejpam-6111	338	29	results	result	NOUN
ejpam-6111	338	30	for	for	ADP
ejpam-6111	338	31	d	d	NOUN
ejpam-6111	338	32	-	-	NOUN
ejpam-6111	338	33	stability	stability	NOUN
ejpam-6111	338	34	.	.	PUNCT
ejpam-6111	339	1	s.	s.	PROPN
ejpam-6111	339	2	mazhar	mazhar	PROPN
ejpam-6111	339	3	,	,	PUNCT
ejpam-6111	339	4	m.	m.	NOUN
ejpam-6111	339	5	u.	u.	PROPN
ejpam-6111	339	6	rehman	rehman	PROPN
ejpam-6111	339	7	/	/	SYM
ejpam-6111	339	8	eur	eur	PROPN
ejpam-6111	339	9	.	.	PUNCT
ejpam-6111	340	1	j.	j.	PROPN
ejpam-6111	340	2	pure	pure	PROPN
ejpam-6111	340	3	appl	appl	PROPN
ejpam-6111	340	4	.	.	PROPN
ejpam-6111	340	5	math	math	PROPN
ejpam-6111	340	6	,	,	PUNCT
ejpam-6111	340	7	18	18	NUM
ejpam-6111	340	8	(	(	PUNCT
ejpam-6111	340	9	2	2	NUM
ejpam-6111	340	10	)	)	PUNCT
ejpam-6111	340	11	(	(	PUNCT
ejpam-6111	340	12	2025	2025	NUM
ejpam-6111	340	13	)	)	PUNCT
ejpam-6111	340	14	,	,	PUNCT
ejpam-6111	340	15	6111	6111	NUM
ejpam-6111	340	16	13	13	NUM
ejpam-6111	340	17	of	of	ADP
ejpam-6111	340	18	25	25	NUM
ejpam-6111	340	19	theorem	theorem	NOUN
ejpam-6111	340	20	7	7	NUM
ejpam-6111	340	21	.	.	PUNCT
ejpam-6111	341	1	let	let	VERB
ejpam-6111	341	2	(	(	PUNCT
ejpam-6111	341	3	i2	i2	PROPN
ejpam-6111	341	4	−	−	PROPN
ejpam-6111	342	1	(	(	PUNCT
ejpam-6111	342	2	a⊗	a⊗	PROPN
ejpam-6111	342	3	p	p	PROPN
ejpam-6111	342	4	t	t	PROPN
ejpam-6111	342	5	)	)	PUNCT
ejpam-6111	342	6	)	)	PUNCT
ejpam-6111	343	1	∈	∈	PROPN
ejpam-6111	343	2	r2,2	r2,2	PROPN
ejpam-6111	343	3	such	such	ADJ
ejpam-6111	343	4	that	that	DET
ejpam-6111	343	5	i2	i2	PROPN
ejpam-6111	343	6	−	−	PROPN
ejpam-6111	344	1	(	(	PUNCT
ejpam-6111	344	2	a⊗	a⊗	PROPN
ejpam-6111	344	3	p	p	PROPN
ejpam-6111	344	4	t	t	PROPN
ejpam-6111	344	5	)	)	PUNCT
ejpam-6111	345	1	=	=	VERB
ejpam-6111	346	1	cos(a1	cos(a1	PROPN
ejpam-6111	346	2	+	+	CCONJ
ejpam-6111	346	3	α2a2	α2a2	PUNCT
ejpam-6111	346	4	+	+	CCONJ
ejpam-6111	346	5	·	·	PUNCT
ejpam-6111	346	6	·	·	PUNCT
ejpam-6111	346	7	·	·	PUNCT
ejpam-6111	346	8	+	+	NUM
ejpam-6111	346	9	αr	αr	NUM
ejpam-6111	346	10	ar	ar	NOUN
ejpam-6111	346	11	)	)	PUNCT
ejpam-6111	346	12	+	+	CCONJ
ejpam-6111	346	13	i	i	PRON
ejpam-6111	346	14	sin(a1	sin(a1	VERB
ejpam-6111	346	15	+	+	X
ejpam-6111	346	16	α2a2	α2a2	PUNCT
ejpam-6111	346	17	+	+	CCONJ
ejpam-6111	346	18	·	·	PUNCT
ejpam-6111	346	19	·	·	PUNCT
ejpam-6111	346	20	·	·	PUNCT
ejpam-6111	346	21	+	+	NUM
ejpam-6111	346	22	αr	αr	NUM
ejpam-6111	346	23	ar	ar	NOUN
ejpam-6111	346	24	)	)	PUNCT
ejpam-6111	346	25	where	where	SCONJ
ejpam-6111	346	26	a1	a1	NOUN
ejpam-6111	346	27	,	,	PUNCT
ejpam-6111	346	28	a2	a2	PROPN
ejpam-6111	346	29	,	,	PUNCT
ejpam-6111	346	30	·	·	PUNCT
ejpam-6111	346	31	·	·	PUNCT
ejpam-6111	346	32	·	·	PUNCT
ejpam-6111	346	33	,	,	PUNCT
ejpam-6111	346	34	ar	ar	PROPN
ejpam-6111	346	35	are	be	AUX
ejpam-6111	346	36	2	2	NUM
ejpam-6111	346	37	-	-	PUNCT
ejpam-6111	346	38	dimensional	dimensional	ADJ
ejpam-6111	346	39	matrices	matrix	NOUN
ejpam-6111	346	40	.	.	PUNCT
ejpam-6111	347	1	then	then	ADV
ejpam-6111	347	2	(	(	PUNCT
ejpam-6111	347	3	i2−a⊗p	i2−a⊗p	NOUN
ejpam-6111	347	4	t	t	NOUN
ejpam-6111	347	5	)	)	PUNCT
ejpam-6111	347	6	is	be	AUX
ejpam-6111	347	7	strongly	strongly	ADV
ejpam-6111	347	8	d	d	ADJ
ejpam-6111	347	9	-	-	ADJ
ejpam-6111	347	10	stable	stable	ADJ
ejpam-6111	347	11	matrix	matrix	NOUN
ejpam-6111	347	12	if	if	SCONJ
ejpam-6111	347	13	it	it	PRON
ejpam-6111	347	14	is	be	AUX
ejpam-6111	347	15	stable	stable	ADJ
ejpam-6111	347	16	,	,	PUNCT
ejpam-6111	347	17	and	and	CCONJ
ejpam-6111	347	18	for	for	ADP
ejpam-6111	347	19	some	some	DET
ejpam-6111	347	20	α̃	α̃	PROPN
ejpam-6111	347	21	>	>	X
ejpam-6111	347	22	0	0	NUM
ejpam-6111	347	23	,	,	PUNCT
ejpam-6111	347	24	(	(	PUNCT
ejpam-6111	347	25	i2	i2	PROPN
ejpam-6111	347	26	−	−	PROPN
ejpam-6111	347	27	a	a	DET
ejpam-6111	347	28	⊗	⊗	PROPN
ejpam-6111	347	29	p	p	PROPN
ejpam-6111	347	30	t	t	PROPN
ejpam-6111	347	31	)	)	PUNCT
ejpam-6111	348	1	+	+	CCONJ
ejpam-6111	348	2	m	m	VERB
ejpam-6111	348	3	is	be	AUX
ejpam-6111	348	4	a	a	DET
ejpam-6111	348	5	d	d	ADJ
ejpam-6111	348	6	-	-	ADJ
ejpam-6111	348	7	stable	stable	ADJ
ejpam-6111	348	8	matrix	matrix	NOUN
ejpam-6111	348	9	with	with	ADP
ejpam-6111	348	10	||m	||m	ADJ
ejpam-6111	348	11	||	||	NOUN
ejpam-6111	349	1	<	<	X
ejpam-6111	349	2	γ	γ	X
ejpam-6111	349	3	,	,	PUNCT
ejpam-6111	349	4	where	where	SCONJ
ejpam-6111	349	5	m	m	VERB
ejpam-6111	349	6	:	:	PUNCT
ejpam-6111	349	7	=	=	SYM
ejpam-6111	349	8	(	(	PUNCT
ejpam-6111	349	9	(	(	PUNCT
ejpam-6111	349	10	i2−a⊗p	i2−a⊗p	ADV
ejpam-6111	349	11	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	349	12	+	+	PROPN
ejpam-6111	349	13	·	·	PUNCT
ejpam-6111	349	14	·	·	PUNCT
ejpam-6111	349	15	·	·	PUNCT
ejpam-6111	349	16	+	+	PROPN
ejpam-6111	349	17	αr	αr	NUM
ejpam-6111	349	18	ar	ar	NOUN
ejpam-6111	349	19	)	)	PUNCT
ejpam-6111	349	20	)	)	PUNCT
ejpam-6111	349	21	t	t	PROPN
ejpam-6111	349	22	∆+∆	∆+∆	PROPN
ejpam-6111	349	23	(	(	PUNCT
ejpam-6111	349	24	log(i2−a⊗p	log(i2−a⊗p	NOUN
ejpam-6111	349	25	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	349	26	+	+	PROPN
ejpam-6111	349	27	·	·	PUNCT
ejpam-6111	349	28	·	·	PUNCT
ejpam-6111	349	29	·	·	PUNCT
ejpam-6111	349	30	+	+	NOUN
ejpam-6111	349	31	α2ar	α2ar	X
ejpam-6111	349	32	)	)	PUNCT
ejpam-6111	349	33	)	)	PUNCT
ejpam-6111	349	34	.	.	PUNCT
ejpam-6111	350	1	proof	proof	NOUN
ejpam-6111	350	2	.	.	PUNCT
ejpam-6111	351	1	let	let	VERB
ejpam-6111	351	2	∆	∆	PROPN
ejpam-6111	351	3	∈	∈	PROPN
ejpam-6111	351	4	b1	b1	NOUN
ejpam-6111	351	5	,	,	PUNCT
ejpam-6111	351	6	λ(t	λ(t	PROPN
ejpam-6111	351	7	)	)	PUNCT
ejpam-6111	351	8	,	,	PUNCT
ejpam-6111	351	9	x(t	x(t	PROPN
ejpam-6111	351	10	)	)	PUNCT
ejpam-6111	351	11	,	,	PUNCT
ejpam-6111	351	12	y(t	y(t	PROPN
ejpam-6111	351	13	)	)	PUNCT
ejpam-6111	351	14	be	be	AUX
ejpam-6111	351	15	same	same	ADJ
ejpam-6111	351	16	as	as	SCONJ
ejpam-6111	351	17	described	describe	VERB
ejpam-6111	351	18	in	in	ADP
ejpam-6111	351	19	the	the	DET
ejpam-6111	351	20	proof	proof	NOUN
ejpam-6111	351	21	of	of	ADP
ejpam-6111	351	22	theorem-5	theorem-5	PROPN
ejpam-6111	351	23	.	.	PUNCT
ejpam-6111	352	1	let	let	VERB
ejpam-6111	352	2	x̃(t	x̃(t	PRON
ejpam-6111	352	3	)	)	PUNCT
ejpam-6111	353	1	=	=	PUNCT
ejpam-6111	354	1	m	m	NOUN
ejpam-6111	354	2	ty(t	ty(t	NUM
ejpam-6111	354	3	)	)	PUNCT
ejpam-6111	354	4	.	.	PUNCT
ejpam-6111	355	1	we	we	PRON
ejpam-6111	355	2	use	use	VERB
ejpam-6111	355	3	eigenvalue	eigenvalue	NOUN
ejpam-6111	355	4	perturbation	perturbation	NOUN
ejpam-6111	355	5	result	result	NOUN
ejpam-6111	355	6	by	by	ADP
ejpam-6111	355	7	kato	kato	PROPN
ejpam-6111	355	8	on	on	ADP
ejpam-6111	355	9	simple	simple	ADJ
ejpam-6111	355	10	and	and	CCONJ
ejpam-6111	355	11	largest	large	ADJ
ejpam-6111	355	12	eigenvalue	eigenvalue	NOUN
ejpam-6111	355	13	λ(t	λ(t	NOUN
ejpam-6111	355	14	)	)	PUNCT
ejpam-6111	355	15	to	to	PART
ejpam-6111	355	16	have	have	VERB
ejpam-6111	355	17	d	d	NOUN
ejpam-6111	355	18	dt	dt	NOUN
ejpam-6111	355	19	|λ(t)|2	|λ(t)|2	NOUN
ejpam-6111	355	20	=	=	SYM
ejpam-6111	355	21	2ϵ	2ϵ	NUM
ejpam-6111	356	1	|λ(t)|	|λ(t)|	VERB
ejpam-6111	356	2	r	r	NOUN
ejpam-6111	356	3	re	re	X
ejpam-6111	356	4	(	(	PUNCT
ejpam-6111	356	5	x̃t(t)∆̇(t)x(t	x̃t(t)∆̇(t)x(t	PROPN
ejpam-6111	356	6	)	)	PUNCT
ejpam-6111	356	7	)	)	PUNCT
ejpam-6111	356	8	;	;	PUNCT
ejpam-6111	356	9	r	r	NOUN
ejpam-6111	356	10	=	=	SYM
ejpam-6111	356	11	eiθ	eiθ	PROPN
ejpam-6111	356	12	yt(t)x(t	yt(t)x(t	PROPN
ejpam-6111	356	13	)	)	PUNCT
ejpam-6111	356	14	,	,	PUNCT
ejpam-6111	356	15	ϵ	ϵ	X
ejpam-6111	356	16	>	>	X
ejpam-6111	356	17	0	0	X
ejpam-6111	356	18	.	.	PUNCT
ejpam-6111	357	1	since	since	ADV
ejpam-6111	357	2	,	,	PUNCT
ejpam-6111	357	3	we	we	PRON
ejpam-6111	357	4	know	know	VERB
ejpam-6111	357	5	that	that	SCONJ
ejpam-6111	357	6	re	re	ADP
ejpam-6111	357	7	(	(	PUNCT
ejpam-6111	357	8	x̃t(t)∆̇(t)x(t	x̃t(t)∆̇(t)x(t	PROPN
ejpam-6111	357	9	)	)	PUNCT
ejpam-6111	357	10	)	)	PUNCT
ejpam-6111	357	11	>	>	X
ejpam-6111	358	1	0	0	NUM
ejpam-6111	358	2	,	,	PUNCT
ejpam-6111	358	3	thus	thus	ADV
ejpam-6111	358	4	(	(	PUNCT
ejpam-6111	358	5	(	(	PUNCT
ejpam-6111	358	6	i2−a⊗p	i2−a⊗p	ADV
ejpam-6111	358	7	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	358	8	+	+	PROPN
ejpam-6111	358	9	·	·	PUNCT
ejpam-6111	358	10	·	·	PUNCT
ejpam-6111	358	11	·	·	PUNCT
ejpam-6111	358	12	+	+	PROPN
ejpam-6111	358	13	αr	αr	NUM
ejpam-6111	358	14	ar	ar	NOUN
ejpam-6111	358	15	)	)	PUNCT
ejpam-6111	358	16	)	)	PUNCT
ejpam-6111	358	17	t	t	PROPN
ejpam-6111	358	18	∆(t)+∆(t	∆(t)+∆(t	PROPN
ejpam-6111	358	19	)	)	PUNCT
ejpam-6111	358	20	(	(	PUNCT
ejpam-6111	358	21	(	(	PUNCT
ejpam-6111	358	22	i2−a⊗p	i2−a⊗p	ADV
ejpam-6111	358	23	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	358	24	+	+	PROPN
ejpam-6111	358	25	·	·	PUNCT
ejpam-6111	358	26	·	·	PUNCT
ejpam-6111	358	27	·	·	PUNCT
ejpam-6111	358	28	+	+	NOUN
ejpam-6111	358	29	α2ar	α2ar	X
ejpam-6111	358	30	)	)	PUNCT
ejpam-6111	358	31	)	)	PUNCT
ejpam-6111	358	32	is	be	AUX
ejpam-6111	358	33	such	such	ADJ
ejpam-6111	358	34	that	that	SCONJ
ejpam-6111	358	35	all	all	PRON
ejpam-6111	358	36	of	of	ADP
ejpam-6111	358	37	its	its	PRON
ejpam-6111	358	38	eigenvalues	eigenvalue	NOUN
ejpam-6111	358	39	are	be	AUX
ejpam-6111	358	40	strictly	strictly	ADV
ejpam-6111	358	41	positive	positive	ADJ
ejpam-6111	358	42	.	.	PUNCT
ejpam-6111	359	1	next	next	ADV
ejpam-6111	359	2	,	,	PUNCT
ejpam-6111	359	3	for	for	ADP
ejpam-6111	359	4	d	d	PROPN
ejpam-6111	359	5	=	=	SYM
ejpam-6111	359	6	(	(	PUNCT
ejpam-6111	359	7	d1	d1	PROPN
ejpam-6111	359	8	0	0	NUM
ejpam-6111	359	9	0	0	NUM
ejpam-6111	359	10	d2	d2	PROPN
ejpam-6111	359	11	)	)	PUNCT
ejpam-6111	359	12	;	;	PUNCT
ejpam-6111	359	13	d1	d1	PROPN
ejpam-6111	359	14	,	,	PUNCT
ejpam-6111	359	15	d2	d2	PROPN
ejpam-6111	359	16	>	>	X
ejpam-6111	359	17	0	0	PROPN
ejpam-6111	359	18	,	,	PUNCT
ejpam-6111	359	19	the	the	DET
ejpam-6111	359	20	matrix	matrix	NOUN
ejpam-6111	359	21	(	(	PUNCT
ejpam-6111	359	22	d1	d1	PROPN
ejpam-6111	359	23	0	0	NUM
ejpam-6111	359	24	0	0	NUM
ejpam-6111	359	25	d2	d2	PROPN
ejpam-6111	359	26	)	)	PUNCT
ejpam-6111	359	27	cos(a1	cos(a1	PROPN
ejpam-6111	359	28	+	+	CCONJ
ejpam-6111	359	29	α2a2	α2a2	PUNCT
ejpam-6111	359	30	+	+	CCONJ
ejpam-6111	359	31	·	·	PUNCT
ejpam-6111	359	32	·	·	PUNCT
ejpam-6111	359	33	·	·	PUNCT
ejpam-6111	359	34	+	+	X
ejpam-6111	359	35	α2ar	α2ar	X
ejpam-6111	359	36	)	)	PUNCT
ejpam-6111	360	1	+	+	CCONJ
ejpam-6111	360	2	i	i	PRON
ejpam-6111	360	3	sin(a1	sin(a1	VERB
ejpam-6111	360	4	+	+	X
ejpam-6111	360	5	α2a2	α2a2	PUNCT
ejpam-6111	360	6	+	+	CCONJ
ejpam-6111	360	7	·	·	PUNCT
ejpam-6111	360	8	·	·	PUNCT
ejpam-6111	360	9	·	·	PUNCT
ejpam-6111	360	10	+	+	NUM
ejpam-6111	360	11	α2ar	α2ar	X
ejpam-6111	360	12	)	)	PUNCT
ejpam-6111	361	1	+	+	NOUN
ejpam-6111	361	2	m	m	NOUN
ejpam-6111	361	3	allows	allow	VERB
ejpam-6111	361	4	us	we	PRON
ejpam-6111	361	5	to	to	PART
ejpam-6111	361	6	have	have	VERB
ejpam-6111	361	7	log(i2−a⊗p	log(i2−a⊗p	PROPN
ejpam-6111	361	8	t)+m	t)+m	PROPN
ejpam-6111	361	9	=	=	PUNCT
ejpam-6111	362	1	log(i2−a⊗p	log(i2−a⊗p	NOUN
ejpam-6111	362	2	t)+	t)+	NOUN
ejpam-6111	362	3	(	(	PUNCT
ejpam-6111	362	4	log(i2−a⊗p	log(i2−a⊗p	NOUN
ejpam-6111	362	5	t)⊗(a1+α2a2	t)⊗(a1+α2a2	PROPN
ejpam-6111	362	6	+	+	PROPN
ejpam-6111	362	7	·	·	PUNCT
ejpam-6111	362	8	·	·	PUNCT
ejpam-6111	362	9	·	·	PUNCT
ejpam-6111	362	10	+	+	PROPN
ejpam-6111	362	11	αr	αr	NUM
ejpam-6111	362	12	ar	ar	NOUN
ejpam-6111	362	13	)	)	PUNCT
ejpam-6111	362	14	)	)	PUNCT
ejpam-6111	362	15	t	t	PROPN
ejpam-6111	362	16	∆+	∆+	NUM
ejpam-6111	362	17	∆	∆	X
ejpam-6111	362	18	(	(	PUNCT
ejpam-6111	362	19	log(i2	log(i2	PROPN
ejpam-6111	362	20	−a⊗	−a⊗	PROPN
ejpam-6111	362	21	p	p	NOUN
ejpam-6111	362	22	t)⊗	t)⊗	PRON
ejpam-6111	362	23	(	(	PUNCT
ejpam-6111	362	24	a1	a1	NOUN
ejpam-6111	362	25	+	+	CCONJ
ejpam-6111	362	26	α2a2	α2a2	PUNCT
ejpam-6111	362	27	+	+	CCONJ
ejpam-6111	362	28	·	·	PUNCT
ejpam-6111	362	29	·	·	PUNCT
ejpam-6111	362	30	·	·	PUNCT
ejpam-6111	362	31	+	+	X
ejpam-6111	362	32	α2ar	α2ar	X
ejpam-6111	362	33	)	)	PUNCT
ejpam-6111	362	34	)	)	PUNCT
ejpam-6111	362	35	as	as	ADP
ejpam-6111	362	36	a	a	DET
ejpam-6111	362	37	d	d	ADJ
ejpam-6111	362	38	-	-	ADJ
ejpam-6111	362	39	stable	stable	ADJ
ejpam-6111	362	40	matrix	matrix	NOUN
ejpam-6111	362	41	.	.	PUNCT
ejpam-6111	363	1	theorem	theorem	ADJ
ejpam-6111	363	2	8	8	NUM
ejpam-6111	363	3	shows	show	VERB
ejpam-6111	363	4	that	that	SCONJ
ejpam-6111	363	5	given	give	VERB
ejpam-6111	363	6	(	(	PUNCT
ejpam-6111	363	7	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	363	8	t	t	NOUN
ejpam-6111	363	9	)	)	PUNCT
ejpam-6111	363	10	∈	∈	PROPN
ejpam-6111	363	11	rn	rn	PROPN
ejpam-6111	363	12	,	,	PUNCT
ejpam-6111	363	13	n	n	PRON
ejpam-6111	363	14	is	be	AUX
ejpam-6111	363	15	a	a	DET
ejpam-6111	363	16	d	d	ADJ
ejpam-6111	363	17	-	-	ADJ
ejpam-6111	363	18	stable	stable	ADJ
ejpam-6111	363	19	matrix	matrix	NOUN
ejpam-6111	363	20	iff	iff	NOUN
ejpam-6111	363	21	it	it	PRON
ejpam-6111	363	22	is	be	AUX
ejpam-6111	363	23	a	a	DET
ejpam-6111	363	24	stable	stable	ADJ
ejpam-6111	363	25	matrix	matrix	NOUN
ejpam-6111	363	26	and	and	CCONJ
ejpam-6111	363	27	the	the	DET
ejpam-6111	363	28	structured	structured	ADJ
ejpam-6111	363	29	singular	singular	ADJ
ejpam-6111	363	30	value	value	NOUN
ejpam-6111	363	31	of	of	ADP
ejpam-6111	363	32	ã	ã	PROPN
ejpam-6111	363	33	is	be	AUX
ejpam-6111	363	34	greater	great	ADJ
ejpam-6111	363	35	than	than	ADP
ejpam-6111	363	36	or	or	CCONJ
ejpam-6111	363	37	equal	equal	ADJ
ejpam-6111	363	38	to	to	ADP
ejpam-6111	363	39	zero	zero	NUM
ejpam-6111	363	40	and	and	CCONJ
ejpam-6111	363	41	strictly	strictly	ADV
ejpam-6111	363	42	less	less	ADJ
ejpam-6111	363	43	than	than	ADP
ejpam-6111	363	44	one	one	NUM
ejpam-6111	363	45	.	.	PUNCT
ejpam-6111	364	1	theorem	theorem	ADJ
ejpam-6111	364	2	8	8	NUM
ejpam-6111	364	3	.	.	PUNCT
ejpam-6111	365	1	let	let	VERB
ejpam-6111	365	2	(	(	PUNCT
ejpam-6111	365	3	in	in	ADP
ejpam-6111	365	4	−	−	PROPN
ejpam-6111	365	5	a	a	DET
ejpam-6111	365	6	⊗	⊗	PROPN
ejpam-6111	365	7	p	p	PROPN
ejpam-6111	365	8	t	t	PROPN
ejpam-6111	365	9	)	)	PUNCT
ejpam-6111	365	10	∈	∈	PROPN
ejpam-6111	365	11	rn	rn	PROPN
ejpam-6111	365	12	,	,	PUNCT
ejpam-6111	365	13	n.	n.	PROPN
ejpam-6111	365	14	then	then	ADV
ejpam-6111	365	15	(	(	PUNCT
ejpam-6111	365	16	in	in	ADP
ejpam-6111	365	17	−	−	PROPN
ejpam-6111	365	18	a	a	DET
ejpam-6111	365	19	⊗	⊗	PROPN
ejpam-6111	365	20	p	p	PROPN
ejpam-6111	365	21	t	t	PROPN
ejpam-6111	365	22	)	)	PUNCT
ejpam-6111	365	23	is	be	AUX
ejpam-6111	365	24	strongly	strongly	ADV
ejpam-6111	365	25	d	d	NOUN
ejpam-6111	365	26	-	-	ADJ
ejpam-6111	365	27	stable	stable	ADJ
ejpam-6111	365	28	if	if	SCONJ
ejpam-6111	365	29	and	and	CCONJ
ejpam-6111	365	30	only	only	ADV
ejpam-6111	365	31	if	if	SCONJ
ejpam-6111	365	32	(	(	PUNCT
ejpam-6111	365	33	in	in	ADP
ejpam-6111	365	34	−a⊗	−a⊗	PROPN
ejpam-6111	365	35	p	p	PROPN
ejpam-6111	365	36	t	t	PROPN
ejpam-6111	365	37	)	)	PUNCT
ejpam-6111	365	38	is	be	AUX
ejpam-6111	365	39	stable	stable	ADJ
ejpam-6111	365	40	and	and	CCONJ
ejpam-6111	366	1	∃	∃	PROPN
ejpam-6111	366	2	ϵ	ϵ	X
ejpam-6111	366	3	>	>	X
ejpam-6111	366	4	0	0	NUM
ejpam-6111	367	1	such	such	ADJ
ejpam-6111	367	2	that	that	SCONJ
ejpam-6111	367	3	0	0	NUM
ejpam-6111	367	4	≤	≤	NUM
ejpam-6111	367	5	µb1(ã	µb1(ã	NOUN
ejpam-6111	367	6	)	)	PUNCT
ejpam-6111	367	7	<	<	X
ejpam-6111	367	8	1	1	NUM
ejpam-6111	367	9	,	,	PUNCT
ejpam-6111	367	10	where	where	SCONJ
ejpam-6111	367	11	ã	ã	PROPN
ejpam-6111	367	12	:	:	PUNCT
ejpam-6111	367	13	=	=	SYM
ejpam-6111	367	14			PROPN
ejpam-6111	367	15	(	(	PUNCT
ejpam-6111	367	16	i	i	PRON
ejpam-6111	367	17	in	in	ADP
ejpam-6111	367	18	+	+	CCONJ
ejpam-6111	367	19	(	(	PUNCT
ejpam-6111	367	20	in	in	ADP
ejpam-6111	367	21	−a⊗	−a⊗	PROPN
ejpam-6111	367	22	p	p	PROPN
ejpam-6111	367	23	t	t	PROPN
ejpam-6111	367	24	)	)	PUNCT
ejpam-6111	367	25	)	)	PUNCT
ejpam-6111	367	26	−1	−1	NOUN
ejpam-6111	367	27	(	(	PUNCT
ejpam-6111	367	28	i	i	PRON
ejpam-6111	367	29	in	in	ADP
ejpam-6111	367	30	−	−	PROPN
ejpam-6111	367	31	(	(	PUNCT
ejpam-6111	367	32	in	in	ADP
ejpam-6111	367	33	−a⊗	−a⊗	PROPN
ejpam-6111	367	34	p	p	PROPN
ejpam-6111	367	35	t	t	PROPN
ejpam-6111	367	36	)	)	PUNCT
ejpam-6111	367	37	)	)	PUNCT
ejpam-6111	367	38	2i	2i	NOUN
ejpam-6111	367	39	(	(	PUNCT
ejpam-6111	367	40	i	i	PRON
ejpam-6111	367	41	in	in	ADP
ejpam-6111	367	42	+	+	CCONJ
ejpam-6111	367	43	(	(	PUNCT
ejpam-6111	367	44	in	in	ADP
ejpam-6111	367	45	−a⊗	−a⊗	PROPN
ejpam-6111	367	46	p	p	PROPN
ejpam-6111	367	47	t	t	PROPN
ejpam-6111	367	48	)	)	PUNCT
ejpam-6111	367	49	)	)	PUNCT
ejpam-6111	367	50	−1	−1	NOUN
ejpam-6111	368	1	ϵ	ϵ	NOUN
ejpam-6111	368	2	(	(	PUNCT
ejpam-6111	368	3	i	i	PRON
ejpam-6111	368	4	in	in	ADP
ejpam-6111	368	5	+	+	CCONJ
ejpam-6111	368	6	(	(	PUNCT
ejpam-6111	368	7	in	in	ADP
ejpam-6111	368	8	−a⊗	−a⊗	PROPN
ejpam-6111	368	9	p	p	PROPN
ejpam-6111	368	10	t	t	PROPN
ejpam-6111	368	11	)	)	PUNCT
ejpam-6111	368	12	)	)	PUNCT
ejpam-6111	368	13	−1	−1	NOUN
ejpam-6111	369	1	−ϵ	−ϵ	NOUN
ejpam-6111	369	2	(	(	PUNCT
ejpam-6111	369	3	i	i	PRON
ejpam-6111	369	4	in	in	ADP
ejpam-6111	369	5	+	+	CCONJ
ejpam-6111	369	6	(	(	PUNCT
ejpam-6111	369	7	in	in	ADP
ejpam-6111	369	8	−a⊗	−a⊗	PROPN
ejpam-6111	369	9	p	p	PROPN
ejpam-6111	369	10	t	t	PROPN
ejpam-6111	369	11	)	)	PUNCT
ejpam-6111	369	12	)	)	PUNCT
ejpam-6111	369	13	−1	−1	NOUN
ejpam-6111	369	14			NOUN
ejpam-6111	369	15	.	.	PUNCT
ejpam-6111	370	1	s.	s.	PROPN
ejpam-6111	370	2	mazhar	mazhar	PROPN
ejpam-6111	370	3	,	,	PUNCT
ejpam-6111	370	4	m.	m.	NOUN
ejpam-6111	370	5	u.	u.	PROPN
ejpam-6111	370	6	rehman	rehman	PROPN
ejpam-6111	370	7	/	/	SYM
ejpam-6111	370	8	eur	eur	PROPN
ejpam-6111	370	9	.	.	PUNCT
ejpam-6111	371	1	j.	j.	PROPN
ejpam-6111	371	2	pure	pure	PROPN
ejpam-6111	371	3	appl	appl	PROPN
ejpam-6111	371	4	.	.	PROPN
ejpam-6111	371	5	math	math	PROPN
ejpam-6111	371	6	,	,	PUNCT
ejpam-6111	371	7	18	18	NUM
ejpam-6111	371	8	(	(	PUNCT
ejpam-6111	371	9	2	2	NUM
ejpam-6111	371	10	)	)	PUNCT
ejpam-6111	371	11	(	(	PUNCT
ejpam-6111	371	12	2025	2025	NUM
ejpam-6111	371	13	)	)	PUNCT
ejpam-6111	371	14	,	,	PUNCT
ejpam-6111	371	15	6111	6111	NUM
ejpam-6111	371	16	14	14	NUM
ejpam-6111	371	17	of	of	ADP
ejpam-6111	371	18	25	25	NUM
ejpam-6111	371	19	proof	proof	NOUN
ejpam-6111	371	20	.	.	PUNCT
ejpam-6111	372	1	as	as	SCONJ
ejpam-6111	372	2	(	(	PUNCT
ejpam-6111	372	3	in	in	ADP
ejpam-6111	372	4	−a⊗	−a⊗	PROPN
ejpam-6111	372	5	p	p	PROPN
ejpam-6111	372	6	t	t	PROPN
ejpam-6111	372	7	)	)	PUNCT
ejpam-6111	372	8	is	be	AUX
ejpam-6111	372	9	strongly	strongly	ADV
ejpam-6111	372	10	d	d	NOUN
ejpam-6111	372	11	-	-	ADJ
ejpam-6111	372	12	stable	stable	ADJ
ejpam-6111	372	13	if	if	SCONJ
ejpam-6111	372	14	and	and	CCONJ
ejpam-6111	372	15	only	only	ADV
ejpam-6111	372	16	if	if	SCONJ
ejpam-6111	372	17	(	(	PUNCT
ejpam-6111	372	18	in	in	ADP
ejpam-6111	372	19	−a⊗	−a⊗	PROPN
ejpam-6111	372	20	p	p	PROPN
ejpam-6111	372	21	t	t	PROPN
ejpam-6111	372	22	)	)	PUNCT
ejpam-6111	372	23	is	be	AUX
ejpam-6111	372	24	stable	stable	ADJ
ejpam-6111	372	25	and	and	CCONJ
ejpam-6111	373	1	∃	∃	PROPN
ejpam-6111	373	2	ϵ	ϵ	X
ejpam-6111	373	3	>	>	X
ejpam-6111	373	4	0	0	NUM
ejpam-6111	374	1	such	such	ADJ
ejpam-6111	374	2	that	that	SCONJ
ejpam-6111	374	3	∆(in−a⊗p	∆(in−a⊗p	PROPN
ejpam-6111	374	4	t	t	PROPN
ejpam-6111	374	5	)	)	PUNCT
ejpam-6111	374	6	∈	∈	PROPN
ejpam-6111	374	7	rn	rn	PROPN
ejpam-6111	374	8	,	,	PUNCT
ejpam-6111	374	9	n	n	CCONJ
ejpam-6111	374	10	having	have	VERB
ejpam-6111	374	11	σmax	σmax	NOUN
ejpam-6111	374	12	(	(	PUNCT
ejpam-6111	374	13	∆(in−a⊗p	∆(in−a⊗p	PROPN
ejpam-6111	374	14	t	t	PROPN
ejpam-6111	374	15	)	)	PUNCT
ejpam-6111	374	16	)	)	PUNCT
ejpam-6111	375	1	<	<	X
ejpam-6111	375	2	ϵ	ϵ	X
ejpam-6111	375	3	,	,	PUNCT
ejpam-6111	375	4	the	the	DET
ejpam-6111	375	5	inequality	inequality	NOUN
ejpam-6111	375	6	0	0	NUM
ejpam-6111	375	7	≤	≤	NUM
ejpam-6111	375	8	µb1	µb1	VERB
ejpam-6111	376	1	[	[	X
ejpam-6111	376	2	(	(	PUNCT
ejpam-6111	376	3	i	i	PRON
ejpam-6111	376	4	in+(in−a⊗p	in+(in−a⊗p	VERB
ejpam-6111	376	5	t)+∆(in−a⊗p	t)+∆(in−a⊗p	PROPN
ejpam-6111	376	6	t	t	PROPN
ejpam-6111	376	7	)	)	PUNCT
ejpam-6111	376	8	)	)	PUNCT
ejpam-6111	376	9	−1	−1	NOUN
ejpam-6111	376	10	(	(	PUNCT
ejpam-6111	376	11	i	i	PRON
ejpam-6111	376	12	in−(in−a⊗p	in−(in−a⊗p	VERB
ejpam-6111	376	13	t)−∆(in−a⊗p	t)−∆(in−a⊗p	PROPN
ejpam-6111	376	14	t	t	PROPN
ejpam-6111	376	15	)	)	PUNCT
ejpam-6111	376	16	)	)	PUNCT
ejpam-6111	376	17	]	]	PUNCT
ejpam-6111	377	1	<	<	X
ejpam-6111	377	2	1	1	NUM
ejpam-6111	377	3	holds	hold	VERB
ejpam-6111	377	4	true	true	ADJ
ejpam-6111	377	5	.	.	PUNCT
ejpam-6111	378	1	consider	consider	VERB
ejpam-6111	378	2	,	,	PUNCT
ejpam-6111	378	3	ã	ã	PROPN
ejpam-6111	378	4	(	(	PUNCT
ejpam-6111	378	5	∆(in−a⊗p	∆(in−a⊗p	PROPN
ejpam-6111	378	6	t	t	PROPN
ejpam-6111	378	7	)	)	PUNCT
ejpam-6111	378	8	)	)	PUNCT
ejpam-6111	379	1	=	=	PUNCT
ejpam-6111	379	2	(	(	PUNCT
ejpam-6111	379	3	i	i	PRON
ejpam-6111	379	4	in+(in−a⊗p	in+(in−a⊗p	VERB
ejpam-6111	379	5	t)+∆(in−a⊗p	t)+∆(in−a⊗p	PROPN
ejpam-6111	379	6	t	t	PROPN
ejpam-6111	379	7	)	)	PUNCT
ejpam-6111	379	8	)	)	PUNCT
ejpam-6111	380	1	−1	−1	NOUN
ejpam-6111	380	2	(	(	PUNCT
ejpam-6111	380	3	i	i	PRON
ejpam-6111	380	4	in−(in−a⊗p	in−(in−a⊗p	VERB
ejpam-6111	380	5	t)−∆(in−a⊗p	t)−∆(in−a⊗p	PROPN
ejpam-6111	380	6	t	t	NOUN
ejpam-6111	380	7	)	)	PUNCT
ejpam-6111	380	8	)	)	PUNCT
ejpam-6111	381	1	=	=	SYM
ejpam-6111	381	2	2i	2i	NOUN
ejpam-6111	381	3	(	(	PUNCT
ejpam-6111	381	4	in	in	ADP
ejpam-6111	381	5	+	+	CCONJ
ejpam-6111	381	6	(	(	PUNCT
ejpam-6111	381	7	in	in	ADP
ejpam-6111	381	8	−a⊗	−a⊗	PROPN
ejpam-6111	381	9	p	p	PROPN
ejpam-6111	381	10	t	t	PROPN
ejpam-6111	381	11	)	)	PUNCT
ejpam-6111	381	12	+	+	NUM
ejpam-6111	381	13	∆(in	∆(in	NOUN
ejpam-6111	381	14	−a⊗	−a⊗	PROPN
ejpam-6111	381	15	p	p	PROPN
ejpam-6111	381	16	t	t	PROPN
ejpam-6111	381	17	)	)	PUNCT
ejpam-6111	381	18	)	)	PUNCT
ejpam-6111	381	19	−1	−1	NOUN
ejpam-6111	381	20	−	−	NOUN
ejpam-6111	381	21	in	in	ADP
ejpam-6111	381	22	=	=	PUNCT
ejpam-6111	381	23	(	(	PUNCT
ejpam-6111	381	24	i	i	PRON
ejpam-6111	381	25	in	in	ADP
ejpam-6111	381	26	+	+	CCONJ
ejpam-6111	381	27	(	(	PUNCT
ejpam-6111	381	28	in	in	ADP
ejpam-6111	381	29	−a⊗	−a⊗	PROPN
ejpam-6111	381	30	p	p	PROPN
ejpam-6111	381	31	t	t	PROPN
ejpam-6111	381	32	)	)	PUNCT
ejpam-6111	381	33	)	)	PUNCT
ejpam-6111	382	1	−1	−1	NOUN
ejpam-6111	382	2	(	(	PUNCT
ejpam-6111	382	3	i	i	PRON
ejpam-6111	382	4	in	in	ADP
ejpam-6111	382	5	−	−	PROPN
ejpam-6111	382	6	(	(	PUNCT
ejpam-6111	382	7	in	in	ADP
ejpam-6111	382	8	−a⊗	−a⊗	PROPN
ejpam-6111	382	9	p	p	PROPN
ejpam-6111	382	10	t	t	PROPN
ejpam-6111	382	11	)	)	PUNCT
ejpam-6111	382	12	)	)	PUNCT
ejpam-6111	383	1	−	−	PROPN
ejpam-6111	383	2	2i	2i	NOUN
ejpam-6111	383	3	(	(	PUNCT
ejpam-6111	383	4	i	i	PRON
ejpam-6111	383	5	in	in	ADP
ejpam-6111	383	6	+	+	CCONJ
ejpam-6111	383	7	(	(	PUNCT
ejpam-6111	383	8	in	in	ADP
ejpam-6111	383	9	−a⊗	−a⊗	PROPN
ejpam-6111	383	10	p	p	PROPN
ejpam-6111	383	11	t	t	PROPN
ejpam-6111	383	12	)	)	PUNCT
ejpam-6111	383	13	)	)	PUNCT
ejpam-6111	383	14	−1	−1	NOUN
ejpam-6111	383	15	where	where	SCONJ
ejpam-6111	383	16	x	x	X
ejpam-6111	383	17	=	=	PUNCT
ejpam-6111	383	18	∆(in	∆(in	NOUN
ejpam-6111	383	19	−a⊗	−a⊗	PROPN
ejpam-6111	383	20	p	p	PROPN
ejpam-6111	383	21	t	t	PROPN
ejpam-6111	383	22	)	)	PUNCT
ejpam-6111	383	23	ϵ	ϵ	X
ejpam-6111	383	24	[	[	PUNCT
ejpam-6111	383	25	in+ϵ	in+ϵ	PROPN
ejpam-6111	383	26	(	(	PUNCT
ejpam-6111	383	27	i	i	PRON
ejpam-6111	383	28	in+(in−a⊗p	in+(in−a⊗p	NOUN
ejpam-6111	383	29	t	t	NOUN
ejpam-6111	383	30	)	)	PUNCT
ejpam-6111	383	31	)	)	PUNCT
ejpam-6111	383	32	−1∆(in	−1∆(in	PROPN
ejpam-6111	383	33	−a⊗	−a⊗	PROPN
ejpam-6111	383	34	p	p	PROPN
ejpam-6111	383	35	t	t	PROPN
ejpam-6111	383	36	)	)	PUNCT
ejpam-6111	383	37	ϵ	ϵ	X
ejpam-6111	383	38	]	]	X
ejpam-6111	383	39	−1	−1	NOUN
ejpam-6111	383	40	ϵ	ϵ	X
ejpam-6111	383	41	(	(	PUNCT
ejpam-6111	383	42	i	i	PRON
ejpam-6111	383	43	in+(in−a⊗p	in+(in−a⊗p	NOUN
ejpam-6111	383	44	t	t	NOUN
ejpam-6111	383	45	)	)	PUNCT
ejpam-6111	383	46	)	)	PUNCT
ejpam-6111	383	47	−1	−1	NOUN
ejpam-6111	383	48	.	.	PUNCT
ejpam-6111	384	1	from	from	ADP
ejpam-6111	384	2	[	[	X
ejpam-6111	384	3	35	35	NUM
ejpam-6111	384	4	]	]	PUNCT
ejpam-6111	384	5	,	,	PUNCT
ejpam-6111	384	6	it	it	PRON
ejpam-6111	384	7	follows	follow	VERB
ejpam-6111	384	8	that	that	SCONJ
ejpam-6111	384	9	0	0	NUM
ejpam-6111	384	10	≤	≤	NUM
ejpam-6111	384	11	µb1	µb1	VERB
ejpam-6111	384	12	[	[	PUNCT
ejpam-6111	384	13	ã	ã	PROPN
ejpam-6111	384	14	(	(	PUNCT
ejpam-6111	384	15	∆(in	∆(in	NOUN
ejpam-6111	384	16	−a⊗	−a⊗	PROPN
ejpam-6111	384	17	p	p	PROPN
ejpam-6111	384	18	t	t	PROPN
ejpam-6111	384	19	)	)	PUNCT
ejpam-6111	384	20	]	]	PUNCT
ejpam-6111	384	21	<	<	X
ejpam-6111	384	22	1	1	NUM
ejpam-6111	384	23	,	,	PUNCT
ejpam-6111	384	24	∀∆	∀∆	NOUN
ejpam-6111	384	25	∈	∈	PROPN
ejpam-6111	384	26	b1	b1	NOUN
ejpam-6111	384	27	and	and	CCONJ
ejpam-6111	384	28	for	for	ADP
ejpam-6111	384	29	all	all	DET
ejpam-6111	384	30	σmax	σmax	NOUN
ejpam-6111	384	31	(	(	PUNCT
ejpam-6111	384	32	∆(in	∆(in	NOUN
ejpam-6111	384	33	−a⊗	−a⊗	PROPN
ejpam-6111	384	34	p	p	PROPN
ejpam-6111	384	35	t	t	PROPN
ejpam-6111	384	36	)	)	PUNCT
ejpam-6111	384	37	)	)	PUNCT
ejpam-6111	385	1	<	<	X
ejpam-6111	386	1	ϵ	ϵ	X
ejpam-6111	386	2	if	if	SCONJ
ejpam-6111	386	3	and	and	CCONJ
ejpam-6111	386	4	only	only	ADV
ejpam-6111	386	5	if	if	SCONJ
ejpam-6111	386	6	0	0	NUM
ejpam-6111	386	7	≤	≤	NOUN
ejpam-6111	386	8	µb1	µb1	VERB
ejpam-6111	387	1	[	[	X
ejpam-6111	387	2	(	(	PUNCT
ejpam-6111	387	3	i	i	PRON
ejpam-6111	387	4	in	in	ADP
ejpam-6111	387	5	+	+	CCONJ
ejpam-6111	387	6	(	(	PUNCT
ejpam-6111	387	7	in	in	ADP
ejpam-6111	387	8	−a⊗	−a⊗	PROPN
ejpam-6111	387	9	p	p	PROPN
ejpam-6111	387	10	t	t	PROPN
ejpam-6111	387	11	)	)	PUNCT
ejpam-6111	387	12	)	)	PUNCT
ejpam-6111	387	13	−1	−1	NOUN
ejpam-6111	387	14	(	(	PUNCT
ejpam-6111	387	15	i	i	PRON
ejpam-6111	387	16	in	in	ADP
ejpam-6111	387	17	−	−	PROPN
ejpam-6111	387	18	(	(	PUNCT
ejpam-6111	387	19	in	in	ADP
ejpam-6111	387	20	−a⊗	−a⊗	PROPN
ejpam-6111	387	21	p	p	PROPN
ejpam-6111	387	22	t	t	PROPN
ejpam-6111	387	23	)	)	PUNCT
ejpam-6111	387	24	)	)	PUNCT
ejpam-6111	387	25	]	]	PUNCT
ejpam-6111	388	1	<	<	X
ejpam-6111	388	2	1	1	NUM
ejpam-6111	388	3	,	,	PUNCT
ejpam-6111	388	4	and	and	CCONJ
ejpam-6111	388	5	thus	thus	ADV
ejpam-6111	388	6	implying	imply	VERB
ejpam-6111	388	7	that	that	SCONJ
ejpam-6111	388	8	0	0	NUM
ejpam-6111	388	9	≤	≤	NUM
ejpam-6111	388	10	µb1(ã	µb1(ã	NOUN
ejpam-6111	388	11	)	)	PUNCT
ejpam-6111	388	12	<	<	X
ejpam-6111	388	13	1	1	NUM
ejpam-6111	388	14	.	.	NOUN
ejpam-6111	388	15	6	6	NUM
ejpam-6111	388	16	.	.	PUNCT
ejpam-6111	388	17	numerical	numerical	ADJ
ejpam-6111	388	18	experimentation	experimentation	NOUN
ejpam-6111	388	19	this	this	DET
ejpam-6111	388	20	section	section	NOUN
ejpam-6111	388	21	is	be	AUX
ejpam-6111	388	22	about	about	ADP
ejpam-6111	388	23	the	the	DET
ejpam-6111	388	24	numerical	numerical	ADJ
ejpam-6111	388	25	experimentation	experimentation	NOUN
ejpam-6111	388	26	for	for	ADP
ejpam-6111	388	27	the	the	DET
ejpam-6111	388	28	approximation	approximation	NOUN
ejpam-6111	388	29	and	and	CCONJ
ejpam-6111	388	30	visualization	visualization	NOUN
ejpam-6111	388	31	of	of	ADP
ejpam-6111	388	32	eigenvalues	eigenvalue	NOUN
ejpam-6111	388	33	,	,	PUNCT
ejpam-6111	388	34	singular	singular	ADJ
ejpam-6111	388	35	values	value	NOUN
ejpam-6111	388	36	,	,	PUNCT
ejpam-6111	388	37	structured	structure	VERB
ejpam-6111	388	38	singular	singular	ADJ
ejpam-6111	388	39	values	value	NOUN
ejpam-6111	388	40	,	,	PUNCT
ejpam-6111	388	41	and	and	CCONJ
ejpam-6111	388	42	pseudo	pseudo	NOUN
ejpam-6111	388	43	-	-	NOUN
ejpam-6111	388	44	spectra	spectra	NOUN
ejpam-6111	388	45	for	for	ADP
ejpam-6111	388	46	haar	haar	NOUN
ejpam-6111	388	47	matrices	matrix	NOUN
ejpam-6111	388	48	and	and	CCONJ
ejpam-6111	388	49	structured	structured	ADJ
ejpam-6111	388	50	matrices	matrix	NOUN
ejpam-6111	388	51	corresponding	correspond	VERB
ejpam-6111	388	52	to	to	ADP
ejpam-6111	388	53	lumped	lump	VERB
ejpam-6111	388	54	-	-	PUNCT
ejpam-6111	388	55	parameter	parameter	NOUN
ejpam-6111	388	56	dynamical	dynamical	ADJ
ejpam-6111	388	57	systems	system	NOUN
ejpam-6111	388	58	.	.	PUNCT
ejpam-6111	389	1	for	for	ADP
ejpam-6111	389	2	pseudo	pseudo	NOUN
ejpam-6111	389	3	-	-	NOUN
ejpam-6111	389	4	spectrum	spectrum	NOUN
ejpam-6111	389	5	in	in	ADP
ejpam-6111	389	6	the	the	DET
ejpam-6111	389	7	complex	complex	ADJ
ejpam-6111	389	8	plane	plane	NOUN
ejpam-6111	389	9	,	,	PUNCT
ejpam-6111	389	10	we	we	PRON
ejpam-6111	389	11	display	display	VERB
ejpam-6111	389	12	the	the	DET
ejpam-6111	389	13	level	level	NOUN
ejpam-6111	389	14	sets	set	NOUN
ejpam-6111	389	15	corresponding	correspond	VERB
ejpam-6111	389	16	to	to	ADP
ejpam-6111	389	17	resolvent	resolvent	ADJ
ejpam-6111	389	18	norm	norm	NOUN
ejpam-6111	389	19	||(a−	||(a−	PROPN
ejpam-6111	389	20	zin	zin	NOUN
ejpam-6111	389	21	)	)	PUNCT
ejpam-6111	389	22	−1||	−1||	PROPN
ejpam-6111	389	23	,	,	PUNCT
ejpam-6111	389	24	for	for	ADP
ejpam-6111	389	25	a	a	DET
ejpam-6111	389	26	given	give	VERB
ejpam-6111	389	27	matrix	matrix	NOUN
ejpam-6111	389	28	a.	a.	NOUN
ejpam-6111	389	29	s.	s.	PROPN
ejpam-6111	389	30	mazhar	mazhar	PROPN
ejpam-6111	389	31	,	,	PUNCT
ejpam-6111	389	32	m.	m.	NOUN
ejpam-6111	389	33	u.	u.	PROPN
ejpam-6111	389	34	rehman	rehman	PROPN
ejpam-6111	389	35	/	/	SYM
ejpam-6111	389	36	eur	eur	PROPN
ejpam-6111	389	37	.	.	PUNCT
ejpam-6111	390	1	j.	j.	PROPN
ejpam-6111	390	2	pure	pure	PROPN
ejpam-6111	390	3	appl	appl	PROPN
ejpam-6111	390	4	.	.	PROPN
ejpam-6111	390	5	math	math	PROPN
ejpam-6111	390	6	,	,	PUNCT
ejpam-6111	390	7	18	18	NUM
ejpam-6111	390	8	(	(	PUNCT
ejpam-6111	390	9	2	2	NUM
ejpam-6111	390	10	)	)	PUNCT
ejpam-6111	390	11	(	(	PUNCT
ejpam-6111	390	12	2025	2025	NUM
ejpam-6111	390	13	)	)	PUNCT
ejpam-6111	390	14	,	,	PUNCT
ejpam-6111	390	15	6111	6111	NUM
ejpam-6111	390	16	15	15	NUM
ejpam-6111	390	17	of	of	ADP
ejpam-6111	390	18	25	25	NUM
ejpam-6111	390	19	example	example	NOUN
ejpam-6111	390	20	1	1	NUM
ejpam-6111	390	21	.	.	X
ejpam-6111	391	1	for	for	ADP
ejpam-6111	391	2	the	the	DET
ejpam-6111	391	3	family	family	NOUN
ejpam-6111	391	4	of	of	ADP
ejpam-6111	391	5	haar	haar	PROPN
ejpam-6111	391	6	wavelets	wavelet	NOUN
ejpam-6111	391	7	,	,	PUNCT
ejpam-6111	391	8	the	the	DET
ejpam-6111	391	9	scaling	scaling	NOUN
ejpam-6111	391	10	function	function	NOUN
ejpam-6111	391	11	h1(x	h1(x	NOUN
ejpam-6111	391	12	)	)	PUNCT
ejpam-6111	391	13	is	be	AUX
ejpam-6111	391	14	defined	define	VERB
ejpam-6111	391	15	as	as	ADP
ejpam-6111	391	16	h1(x	h1(x	NOUN
ejpam-6111	391	17	)	)	PUNCT
ejpam-6111	391	18	=	=	NOUN
ejpam-6111	391	19	{	{	PUNCT
ejpam-6111	391	20	1	1	NUM
ejpam-6111	391	21	for	for	ADP
ejpam-6111	391	22	x	x	PROPN
ejpam-6111	391	23	∈	∈	PROPN
ejpam-6111	392	1	[	[	X
ejpam-6111	392	2	0	0	NUM
ejpam-6111	392	3	,	,	PUNCT
ejpam-6111	392	4	1	1	NUM
ejpam-6111	392	5	)	)	PUNCT
ejpam-6111	392	6	0	0	NUM
ejpam-6111	392	7	,	,	PUNCT
ejpam-6111	392	8	else	else	ADV
ejpam-6111	392	9	.	.	PUNCT
ejpam-6111	393	1	the	the	DET
ejpam-6111	393	2	haar	haar	NOUN
ejpam-6111	393	3	wavelets	wavelet	NOUN
ejpam-6111	393	4	for	for	ADP
ejpam-6111	393	5	[	[	X
ejpam-6111	393	6	0	0	NUM
ejpam-6111	393	7	,	,	PUNCT
ejpam-6111	393	8	1	1	NUM
ejpam-6111	393	9	)	)	PUNCT
ejpam-6111	393	10	maybe	maybe	ADV
ejpam-6111	393	11	defined	define	VERB
ejpam-6111	393	12	as	as	ADP
ejpam-6111	393	13	hi(x	hi(x	NOUN
ejpam-6111	393	14	)	)	PUNCT
ejpam-6111	394	1	=	=	PUNCT
ejpam-6111	394	2			NOUN
ejpam-6111	394	3	1	1	NUM
ejpam-6111	394	4	for	for	ADP
ejpam-6111	394	5	x	x	PROPN
ejpam-6111	394	6	∈	∈	PROPN
ejpam-6111	394	7	[	[	X
ejpam-6111	394	8	α	α	X
ejpam-6111	394	9	,	,	PUNCT
ejpam-6111	394	10	β	β	NOUN
ejpam-6111	394	11	)	)	PUNCT
ejpam-6111	394	12	−1	−1	NOUN
ejpam-6111	394	13	,	,	PUNCT
ejpam-6111	394	14	for	for	ADP
ejpam-6111	394	15	x	x	PROPN
ejpam-6111	394	16	∈	∈	PROPN
ejpam-6111	394	17	[	[	X
ejpam-6111	394	18	β	β	X
ejpam-6111	394	19	,	,	PUNCT
ejpam-6111	394	20	γ	γ	NOUN
ejpam-6111	394	21	)	)	PUNCT
ejpam-6111	394	22	0	0	NUM
ejpam-6111	394	23	,	,	PUNCT
ejpam-6111	394	24	else	else	ADV
ejpam-6111	394	25	,	,	PUNCT
ejpam-6111	394	26	where	where	SCONJ
ejpam-6111	394	27	α	α	NOUN
ejpam-6111	394	28	=	=	PUNCT
ejpam-6111	394	29	k	k	PROPN
ejpam-6111	394	30	m	m	PROPN
ejpam-6111	394	31	,	,	PUNCT
ejpam-6111	394	32	β	β	X
ejpam-6111	394	33	=	=	PUNCT
ejpam-6111	395	1	k+5	k+5	NOUN
ejpam-6111	395	2	m	m	X
ejpam-6111	395	3	,	,	PUNCT
ejpam-6111	395	4	γ	γ	X
ejpam-6111	395	5	=	=	SYM
ejpam-6111	395	6	k+1	k+1	PROPN
ejpam-6111	395	7	m	m	PROPN
ejpam-6111	395	8	,	,	PUNCT
ejpam-6111	395	9	m	m	VERB
ejpam-6111	395	10	=	=	NOUN
ejpam-6111	395	11	2l	2l	NUM
ejpam-6111	395	12	,	,	PUNCT
ejpam-6111	395	13	l	l	NOUN
ejpam-6111	395	14	=	=	SYM
ejpam-6111	395	15	1	1	X
ejpam-6111	395	16	:	:	PUNCT
ejpam-6111	395	17	j	j	NOUN
ejpam-6111	395	18	,	,	PUNCT
ejpam-6111	395	19	k	k	PROPN
ejpam-6111	396	1	=	=	NOUN
ejpam-6111	396	2	0	0	NUM
ejpam-6111	396	3	:	:	PUNCT
ejpam-6111	396	4	m−	m−	PROPN
ejpam-6111	396	5	1	1	NUM
ejpam-6111	396	6	.	.	PUNCT
ejpam-6111	397	1	here	here	ADV
ejpam-6111	397	2	,	,	PUNCT
ejpam-6111	397	3	l	l	PROPN
ejpam-6111	397	4	and	and	CCONJ
ejpam-6111	397	5	k	k	PROPN
ejpam-6111	397	6	are	be	AUX
ejpam-6111	397	7	the	the	DET
ejpam-6111	397	8	level	level	NOUN
ejpam-6111	397	9	of	of	ADP
ejpam-6111	397	10	resolution	resolution	NOUN
ejpam-6111	397	11	and	and	CCONJ
ejpam-6111	397	12	translation	translation	NOUN
ejpam-6111	397	13	parameters	parameter	NOUN
ejpam-6111	397	14	,	,	PUNCT
ejpam-6111	397	15	respectively	respectively	ADV
ejpam-6111	397	16	.	.	PUNCT
ejpam-6111	398	1	for	for	ADP
ejpam-6111	398	2	j	j	PROPN
ejpam-6111	398	3	=	=	SYM
ejpam-6111	398	4	3	3	NUM
ejpam-6111	398	5	,	,	PUNCT
ejpam-6111	398	6	and	and	CCONJ
ejpam-6111	398	7	n	n	CCONJ
ejpam-6111	398	8	=	=	SYM
ejpam-6111	398	9	16	16	NUM
ejpam-6111	398	10	(	(	PUNCT
ejpam-6111	398	11	the	the	DET
ejpam-6111	398	12	size	size	NOUN
ejpam-6111	398	13	of	of	ADP
ejpam-6111	398	14	matrix	matrix	NOUN
ejpam-6111	398	15	)	)	PUNCT
ejpam-6111	398	16	,	,	PUNCT
ejpam-6111	398	17	the	the	DET
ejpam-6111	398	18	haar	haar	NOUN
ejpam-6111	398	19	matrix	matrix	NOUN
ejpam-6111	398	20	h	h	NOUN
ejpam-6111	398	21	=	=	SYM
ejpam-6111	398	22	h(i	h(i	PROPN
ejpam-6111	398	23	,	,	PUNCT
ejpam-6111	398	24	j	j	NOUN
ejpam-6111	398	25	)	)	PUNCT
ejpam-6111	398	26	=	=	SYM
ejpam-6111	398	27	hi(xj	hi(xj	NOUN
ejpam-6111	398	28	)	)	PUNCT
ejpam-6111	398	29	taken	take	VERB
ejpam-6111	398	30	from	from	ADP
ejpam-6111	398	31	[	[	X
ejpam-6111	398	32	45	45	NUM
ejpam-6111	398	33	]	]	PUNCT
ejpam-6111	398	34	is	be	AUX
ejpam-6111	398	35	:	:	PUNCT
ejpam-6111	398	36	h	h	PROPN
ejpam-6111	398	37	=	=	SYM
ejpam-6111	398	38	h(i	h(i	PROPN
ejpam-6111	398	39	,	,	PUNCT
ejpam-6111	398	40	j	j	NOUN
ejpam-6111	398	41	)	)	PUNCT
ejpam-6111	398	42	=	=	NOUN
ejpam-6111	399	1			NOUN
ejpam-6111	399	2	1	1	NUM
ejpam-6111	399	3	1	1	NUM
ejpam-6111	399	4	1	1	NUM
ejpam-6111	399	5	1	1	NUM
ejpam-6111	399	6	1	1	NUM
ejpam-6111	399	7	1	1	NUM
ejpam-6111	399	8	1	1	NUM
ejpam-6111	399	9	1	1	NUM
ejpam-6111	399	10	1	1	NUM
ejpam-6111	399	11	1	1	NUM
ejpam-6111	399	12	1	1	NUM
ejpam-6111	399	13	1	1	NUM
ejpam-6111	399	14	1	1	NUM
ejpam-6111	399	15	1	1	NUM
ejpam-6111	399	16	1	1	NUM
ejpam-6111	399	17	1	1	NUM
ejpam-6111	399	18	1	1	NUM
ejpam-6111	399	19	1	1	NUM
ejpam-6111	399	20	1	1	NUM
ejpam-6111	399	21	1	1	NUM
ejpam-6111	399	22	1	1	NUM
ejpam-6111	399	23	1	1	NUM
ejpam-6111	399	24	1	1	NUM
ejpam-6111	399	25	1	1	NUM
ejpam-6111	399	26	−1	−1	NOUN
ejpam-6111	399	27	−1	−1	NOUN
ejpam-6111	399	28	−1	−1	NOUN
ejpam-6111	399	29	−1	−1	NOUN
ejpam-6111	399	30	−1	−1	NOUN
ejpam-6111	399	31	−1	−1	NOUN
ejpam-6111	399	32	−1	−1	NOUN
ejpam-6111	399	33	−1	−1	NOUN
ejpam-6111	399	34	1	1	NUM
ejpam-6111	399	35	1	1	NUM
ejpam-6111	399	36	1	1	NUM
ejpam-6111	399	37	1	1	NUM
ejpam-6111	399	38	−1	−1	NOUN
ejpam-6111	399	39	−1	−1	NOUN
ejpam-6111	399	40	−1	−1	NOUN
ejpam-6111	399	41	−1	−1	NOUN
ejpam-6111	399	42	0	0	NUM
ejpam-6111	399	43	0	0	NUM
ejpam-6111	399	44	0	0	NUM
ejpam-6111	399	45	0	0	NUM
ejpam-6111	399	46	0	0	NUM
ejpam-6111	399	47	0	0	NUM
ejpam-6111	399	48	0	0	NUM
ejpam-6111	399	49	0	0	NUM
ejpam-6111	399	50	0	0	NUM
ejpam-6111	399	51	0	0	NUM
ejpam-6111	399	52	0	0	NUM
ejpam-6111	399	53	0	0	NUM
ejpam-6111	399	54	0	0	NUM
ejpam-6111	399	55	0	0	NUM
ejpam-6111	399	56	0	0	NUM
ejpam-6111	399	57	0	0	NUM
ejpam-6111	399	58	1	1	NUM
ejpam-6111	399	59	1	1	NUM
ejpam-6111	399	60	1	1	NUM
ejpam-6111	399	61	1	1	NUM
ejpam-6111	399	62	−1	−1	NOUN
ejpam-6111	399	63	−1	−1	NOUN
ejpam-6111	399	64	−1	−1	NOUN
ejpam-6111	399	65	−1	−1	NOUN
ejpam-6111	399	66	1	1	NUM
ejpam-6111	399	67	1	1	NUM
ejpam-6111	399	68	−1	−1	NOUN
ejpam-6111	399	69	−1	−1	NOUN
ejpam-6111	399	70	0	0	NUM
ejpam-6111	399	71	0	0	NUM
ejpam-6111	399	72	0	0	NUM
ejpam-6111	399	73	0	0	NUM
ejpam-6111	399	74	0	0	NUM
ejpam-6111	399	75	0	0	NUM
ejpam-6111	399	76	0	0	NUM
ejpam-6111	399	77	0	0	NUM
ejpam-6111	399	78	0	0	NUM
ejpam-6111	399	79	0	0	NUM
ejpam-6111	399	80	0	0	NUM
ejpam-6111	399	81	0	0	NUM
ejpam-6111	399	82	0	0	NUM
ejpam-6111	399	83	0	0	NUM
ejpam-6111	399	84	0	0	NUM
ejpam-6111	399	85	0	0	NUM
ejpam-6111	399	86	1	1	NUM
ejpam-6111	399	87	1	1	NUM
ejpam-6111	399	88	−1	−1	NOUN
ejpam-6111	399	89	−1	−1	NOUN
ejpam-6111	399	90	0	0	NUM
ejpam-6111	399	91	0	0	NUM
ejpam-6111	399	92	0	0	NUM
ejpam-6111	399	93	0	0	NUM
ejpam-6111	399	94	0	0	NUM
ejpam-6111	399	95	0	0	NUM
ejpam-6111	399	96	0	0	NUM
ejpam-6111	399	97	0	0	NUM
ejpam-6111	399	98	0	0	NUM
ejpam-6111	399	99	0	0	NUM
ejpam-6111	399	100	0	0	NUM
ejpam-6111	399	101	0	0	NUM
ejpam-6111	399	102	0	0	NUM
ejpam-6111	399	103	0	0	NUM
ejpam-6111	399	104	0	0	NUM
ejpam-6111	399	105	0	0	NUM
ejpam-6111	399	106	1	1	NUM
ejpam-6111	399	107	1	1	NUM
ejpam-6111	399	108	−1	−1	NOUN
ejpam-6111	399	109	−1	−1	NOUN
ejpam-6111	399	110	0	0	NUM
ejpam-6111	399	111	0	0	NUM
ejpam-6111	399	112	0	0	NUM
ejpam-6111	399	113	0	0	NUM
ejpam-6111	399	114	0	0	NUM
ejpam-6111	399	115	0	0	NUM
ejpam-6111	399	116	0	0	NUM
ejpam-6111	399	117	0	0	NUM
ejpam-6111	399	118	0	0	NUM
ejpam-6111	399	119	0	0	NUM
ejpam-6111	399	120	0	0	NUM
ejpam-6111	399	121	0	0	NUM
ejpam-6111	399	122	0	0	NUM
ejpam-6111	399	123	0	0	NUM
ejpam-6111	399	124	0	0	NUM
ejpam-6111	399	125	0	0	NUM
ejpam-6111	399	126	1	1	NUM
ejpam-6111	399	127	1	1	NUM
ejpam-6111	399	128	1	1	NUM
ejpam-6111	399	129	1	1	NUM
ejpam-6111	399	130	1	1	NUM
ejpam-6111	399	131	1	1	NUM
ejpam-6111	399	132	0	0	NUM
ejpam-6111	399	133	0	0	NUM
ejpam-6111	399	134	0	0	NUM
ejpam-6111	399	135	0	0	NUM
ejpam-6111	399	136	0	0	NUM
ejpam-6111	399	137	0	0	NUM
ejpam-6111	399	138	0	0	NUM
ejpam-6111	399	139	0	0	NUM
ejpam-6111	399	140	0	0	NUM
ejpam-6111	399	141	0	0	NUM
ejpam-6111	399	142	0	0	NUM
ejpam-6111	399	143	0	0	NUM
ejpam-6111	399	144	0	0	NUM
ejpam-6111	399	145	0	0	NUM
ejpam-6111	399	146	0	0	NUM
ejpam-6111	399	147	0	0	NUM
ejpam-6111	399	148	1	1	NUM
ejpam-6111	399	149	1	1	NUM
ejpam-6111	399	150	0	0	NUM
ejpam-6111	399	151	0	0	NUM
ejpam-6111	399	152	0	0	NUM
ejpam-6111	399	153	0	0	NUM
ejpam-6111	399	154	0	0	NUM
ejpam-6111	399	155	0	0	NUM
ejpam-6111	399	156	0	0	NUM
ejpam-6111	399	157	0	0	NUM
ejpam-6111	399	158	0	0	NUM
ejpam-6111	399	159	0	0	NUM
ejpam-6111	399	160	0	0	NUM
ejpam-6111	399	161	0	0	NUM
ejpam-6111	399	162	0	0	NUM
ejpam-6111	399	163	0	0	NUM
ejpam-6111	399	164	0	0	NUM
ejpam-6111	399	165	0	0	NUM
ejpam-6111	399	166	1	1	NUM
ejpam-6111	399	167	1	1	NUM
ejpam-6111	399	168	0	0	NUM
ejpam-6111	399	169	0	0	NUM
ejpam-6111	399	170	0	0	NUM
ejpam-6111	399	171	0	0	NUM
ejpam-6111	399	172	0	0	NUM
ejpam-6111	399	173	0	0	NUM
ejpam-6111	399	174	0	0	NUM
ejpam-6111	399	175	0	0	NUM
ejpam-6111	399	176	0	0	NUM
ejpam-6111	399	177	0	0	NUM
ejpam-6111	399	178	0	0	NUM
ejpam-6111	399	179	0	0	NUM
ejpam-6111	399	180	0	0	NUM
ejpam-6111	399	181	0	0	NUM
ejpam-6111	399	182	0	0	NUM
ejpam-6111	399	183	0	0	NUM
ejpam-6111	399	184	1	1	NUM
ejpam-6111	399	185	1	1	NUM
ejpam-6111	399	186	0	0	NUM
ejpam-6111	399	187	0	0	NUM
ejpam-6111	399	188	0	0	NUM
ejpam-6111	399	189	0	0	NUM
ejpam-6111	399	190	0	0	NUM
ejpam-6111	399	191	0	0	NUM
ejpam-6111	399	192	0	0	NUM
ejpam-6111	399	193	0	0	NUM
ejpam-6111	399	194	0	0	NUM
ejpam-6111	399	195	0	0	NUM
ejpam-6111	399	196	0	0	NUM
ejpam-6111	399	197	0	0	NUM
ejpam-6111	399	198	0	0	NUM
ejpam-6111	399	199	0	0	NUM
ejpam-6111	399	200	0	0	NUM
ejpam-6111	399	201	0	0	NUM
ejpam-6111	399	202	1	1	NUM
ejpam-6111	399	203	1	1	NUM
ejpam-6111	399	204	0	0	NUM
ejpam-6111	399	205	0	0	NUM
ejpam-6111	399	206	0	0	NUM
ejpam-6111	399	207	0	0	NUM
ejpam-6111	399	208	0	0	NUM
ejpam-6111	399	209	0	0	NUM
ejpam-6111	399	210	0	0	NUM
ejpam-6111	399	211	0	0	NUM
ejpam-6111	399	212	0	0	NUM
ejpam-6111	399	213	0	0	NUM
ejpam-6111	399	214	0	0	NUM
ejpam-6111	399	215	0	0	NUM
ejpam-6111	399	216	0	0	NUM
ejpam-6111	399	217	0	0	NUM
ejpam-6111	399	218	0	0	NUM
ejpam-6111	399	219	0	0	NUM
ejpam-6111	399	220	1	1	NUM
ejpam-6111	399	221	1	1	NUM
ejpam-6111	399	222	0	0	NUM
ejpam-6111	399	223	0	0	NUM
ejpam-6111	399	224	0	0	NUM
ejpam-6111	399	225	0	0	NUM
ejpam-6111	399	226	0	0	NUM
ejpam-6111	399	227	0	0	NUM
ejpam-6111	399	228	0	0	NUM
ejpam-6111	399	229	0	0	NUM
ejpam-6111	399	230	0	0	NUM
ejpam-6111	399	231	0	0	NUM
ejpam-6111	399	232	0	0	NUM
ejpam-6111	399	233	0	0	NUM
ejpam-6111	399	234	0	0	NUM
ejpam-6111	399	235	0	0	NUM
ejpam-6111	399	236	0	0	NUM
ejpam-6111	399	237	0	0	NUM
ejpam-6111	399	238	1	1	NUM
ejpam-6111	399	239	1	1	NUM
ejpam-6111	399	240	0	0	NUM
ejpam-6111	399	241	0	0	NUM
ejpam-6111	399	242	0	0	NUM
ejpam-6111	399	243	0	0	NUM
ejpam-6111	399	244	0	0	NUM
ejpam-6111	399	245	0	0	NUM
ejpam-6111	399	246	0	0	NUM
ejpam-6111	399	247	0	0	NUM
ejpam-6111	399	248	0	0	NUM
ejpam-6111	399	249	0	0	NUM
ejpam-6111	399	250	0	0	NUM
ejpam-6111	399	251	0	0	NUM
ejpam-6111	399	252	0	0	NUM
ejpam-6111	399	253	0	0	NUM
ejpam-6111	399	254	0	0	NUM
ejpam-6111	399	255	0	0	NUM
ejpam-6111	399	256	1	1	NUM
ejpam-6111	399	257	1	1	NUM
ejpam-6111	399	258			NOUN
ejpam-6111	399	259	.	.	PUNCT
ejpam-6111	400	1	the	the	DET
ejpam-6111	400	2	spectral	spectral	ADJ
ejpam-6111	400	3	properties	property	NOUN
ejpam-6111	400	4	such	such	ADJ
ejpam-6111	400	5	as	as	ADP
ejpam-6111	400	6	the	the	DET
ejpam-6111	400	7	computation	computation	NOUN
ejpam-6111	400	8	of	of	ADP
ejpam-6111	400	9	spectrum	spectrum	NOUN
ejpam-6111	400	10	,	,	PUNCT
ejpam-6111	400	11	singular	singular	ADJ
ejpam-6111	400	12	values	value	NOUN
ejpam-6111	400	13	,	,	PUNCT
ejpam-6111	400	14	structured	structure	VERB
ejpam-6111	400	15	singular	singular	ADJ
ejpam-6111	400	16	values	value	NOUN
ejpam-6111	400	17	,	,	PUNCT
ejpam-6111	400	18	and	and	CCONJ
ejpam-6111	400	19	pseudo	pseudo	NOUN
ejpam-6111	400	20	-	-	NOUN
ejpam-6111	400	21	spectrum	spectrum	NOUN
ejpam-6111	400	22	of	of	ADP
ejpam-6111	400	23	h(i	h(i	PROPN
ejpam-6111	400	24	,	,	PUNCT
ejpam-6111	400	25	j	j	NOUN
ejpam-6111	400	26	)	)	PUNCT
ejpam-6111	400	27	are	be	AUX
ejpam-6111	400	28	presented	present	VERB
ejpam-6111	400	29	in	in	ADP
ejpam-6111	400	30	figure	figure	NOUN
ejpam-6111	400	31	1	1	NUM
ejpam-6111	400	32	.	.	PUNCT
ejpam-6111	401	1	in	in	ADP
ejpam-6111	401	2	figure	figure	NOUN
ejpam-6111	401	3	2	2	NUM
ejpam-6111	401	4	,	,	PUNCT
ejpam-6111	401	5	we	we	PRON
ejpam-6111	401	6	plot	plot	VERB
ejpam-6111	401	7	the	the	DET
ejpam-6111	401	8	eigenmode	eigenmode	PROPN
ejpam-6111	401	9	corresponding	corresponding	NOUN
ejpam-6111	401	10	to	to	ADP
ejpam-6111	401	11	the	the	DET
ejpam-6111	401	12	eigenvalues	eigenvalue	NOUN
ejpam-6111	401	13	.	.	PUNCT
ejpam-6111	402	1	the	the	DET
ejpam-6111	402	2	top	top	ADJ
ejpam-6111	402	3	plot	plot	NOUN
ejpam-6111	402	4	in	in	ADP
ejpam-6111	402	5	the	the	DET
ejpam-6111	402	6	figure	figure	NOUN
ejpam-6111	402	7	shows	show	VERB
ejpam-6111	402	8	an	an	DET
ejpam-6111	402	9	envelope	envelope	NOUN
ejpam-6111	402	10	which	which	PRON
ejpam-6111	402	11	is	be	AUX
ejpam-6111	402	12	produced	produce	VERB
ejpam-6111	402	13	by	by	ADP
ejpam-6111	402	14	plotting	plot	VERB
ejpam-6111	402	15	the	the	DET
ejpam-6111	402	16	absolute	absolute	ADJ
ejpam-6111	402	17	value	value	NOUN
ejpam-6111	402	18	of	of	ADP
ejpam-6111	402	19	an	an	DET
ejpam-6111	402	20	eigenmode	eigenmode	NOUN
ejpam-6111	402	21	minus	minus	ADP
ejpam-6111	402	22	the	the	DET
ejpam-6111	402	23	absolute	absolute	ADJ
ejpam-6111	402	24	value	value	NOUN
ejpam-6111	402	25	.	.	PUNCT
ejpam-6111	403	1	the	the	DET
ejpam-6111	403	2	real	real	ADJ
ejpam-6111	403	3	part	part	NOUN
ejpam-6111	403	4	is	be	AUX
ejpam-6111	403	5	shown	show	VERB
ejpam-6111	403	6	with	with	ADP
ejpam-6111	403	7	a	a	DET
ejpam-6111	403	8	cyan	cyan	ADJ
ejpam-6111	403	9	line	line	NOUN
ejpam-6111	403	10	.	.	PUNCT
ejpam-6111	404	1	the	the	DET
ejpam-6111	404	2	plot	plot	NOUN
ejpam-6111	404	3	at	at	ADP
ejpam-6111	404	4	the	the	DET
ejpam-6111	404	5	bottom	bottom	ADJ
ejpam-6111	404	6	level	level	NOUN
ejpam-6111	404	7	shows	show	VERB
ejpam-6111	404	8	absolute	absolute	ADJ
ejpam-6111	404	9	value	value	NOUN
ejpam-6111	404	10	of	of	ADP
ejpam-6111	404	11	eigenmode	eigenmode	ADJ
ejpam-6111	404	12	being	be	AUX
ejpam-6111	404	13	plotted	plot	VERB
ejpam-6111	404	14	at	at	ADP
ejpam-6111	404	15	a	a	DET
ejpam-6111	404	16	log	log	NOUN
ejpam-6111	404	17	scale	scale	NOUN
ejpam-6111	404	18	.	.	PUNCT
ejpam-6111	405	1	further	far	ADV
ejpam-6111	405	2	it	it	PRON
ejpam-6111	405	3	shows	show	VERB
ejpam-6111	405	4	how	how	SCONJ
ejpam-6111	405	5	quickly	quickly	ADV
ejpam-6111	405	6	an	an	DET
ejpam-6111	405	7	eigenmode	eigenmode	NOUN
ejpam-6111	405	8	is	be	AUX
ejpam-6111	405	9	decaying	decay	VERB
ejpam-6111	405	10	with	with	ADP
ejpam-6111	405	11	the	the	DET
ejpam-6111	405	12	time	time	NOUN
ejpam-6111	405	13	.	.	PUNCT
ejpam-6111	406	1	the	the	DET
ejpam-6111	406	2	condition	condition	NOUN
ejpam-6111	406	3	number	number	NOUN
ejpam-6111	406	4	computed	compute	VERB
ejpam-6111	406	5	for	for	ADP
ejpam-6111	406	6	an	an	DET
ejpam-6111	406	7	eigenvalue	eigenvalue	NOUN
ejpam-6111	406	8	is	be	AUX
ejpam-6111	406	9	shown	show	VERB
ejpam-6111	406	10	in	in	ADP
ejpam-6111	406	11	the	the	DET
ejpam-6111	406	12	top	top	ADJ
ejpam-6111	406	13	plot	plot	NOUN
ejpam-6111	406	14	.	.	PUNCT
ejpam-6111	407	1	the	the	DET
ejpam-6111	407	2	large	large	ADJ
ejpam-6111	407	3	condition	condition	NOUN
ejpam-6111	407	4	number	number	NOUN
ejpam-6111	407	5	means	mean	VERB
ejpam-6111	407	6	that	that	SCONJ
ejpam-6111	407	7	eigenvalue	eigenvalue	NOUN
ejpam-6111	407	8	is	be	AUX
ejpam-6111	407	9	sensitive	sensitive	ADJ
ejpam-6111	407	10	to	to	ADP
ejpam-6111	407	11	perturbations	perturbation	NOUN
ejpam-6111	407	12	.	.	PUNCT
ejpam-6111	408	1	in	in	ADP
ejpam-6111	408	2	figure	figure	NOUN
ejpam-6111	408	3	2	2	NUM
ejpam-6111	408	4	,	,	PUNCT
ejpam-6111	408	5	we	we	PRON
ejpam-6111	408	6	plot	plot	VERB
ejpam-6111	408	7	the	the	DET
ejpam-6111	408	8	value	value	NOUN
ejpam-6111	408	9	of	of	ADP
ejpam-6111	408	10	the	the	DET
ejpam-6111	408	11	inverse	inverse	NOUN
ejpam-6111	408	12	of	of	ADP
ejpam-6111	408	13	the	the	DET
ejpam-6111	408	14	resolvent	resolvent	ADJ
ejpam-6111	408	15	norm	norm	NOUN
ejpam-6111	408	16	.	.	PUNCT
ejpam-6111	409	1	we	we	PRON
ejpam-6111	409	2	show	show	VERB
ejpam-6111	409	3	the	the	DET
ejpam-6111	409	4	real	real	ADJ
ejpam-6111	409	5	part	part	NOUN
ejpam-6111	409	6	of	of	ADP
ejpam-6111	409	7	the	the	DET
ejpam-6111	409	8	pseudomode	pseudomode	NOUN
ejpam-6111	409	9	in	in	ADP
ejpam-6111	409	10	magenta	magenta	NOUN
ejpam-6111	409	11	.	.	PUNCT
ejpam-6111	410	1	the	the	DET
ejpam-6111	410	2	right	right	ADJ
ejpam-6111	410	3	singular	singular	PROPN
ejpam-6111	410	4	vector	vector	NOUN
ejpam-6111	410	5	corresponding	correspond	VERB
ejpam-6111	410	6	to	to	ADP
ejpam-6111	410	7	the	the	DET
ejpam-6111	410	8	s.	s.	PROPN
ejpam-6111	410	9	mazhar	mazhar	PROPN
ejpam-6111	410	10	,	,	PUNCT
ejpam-6111	410	11	m.	m.	NOUN
ejpam-6111	410	12	u.	u.	PROPN
ejpam-6111	410	13	rehman	rehman	PROPN
ejpam-6111	410	14	/	/	SYM
ejpam-6111	410	15	eur	eur	PROPN
ejpam-6111	410	16	.	.	PUNCT
ejpam-6111	411	1	j.	j.	PROPN
ejpam-6111	411	2	pure	pure	PROPN
ejpam-6111	411	3	appl	appl	PROPN
ejpam-6111	411	4	.	.	PROPN
ejpam-6111	411	5	math	math	PROPN
ejpam-6111	411	6	,	,	PUNCT
ejpam-6111	411	7	18	18	NUM
ejpam-6111	411	8	(	(	PUNCT
ejpam-6111	411	9	2	2	NUM
ejpam-6111	411	10	)	)	PUNCT
ejpam-6111	411	11	(	(	PUNCT
ejpam-6111	411	12	2025	2025	NUM
ejpam-6111	411	13	)	)	PUNCT
ejpam-6111	411	14	,	,	PUNCT
ejpam-6111	411	15	6111	6111	NUM
ejpam-6111	411	16	16	16	NUM
ejpam-6111	411	17	of	of	ADP
ejpam-6111	411	18	25	25	NUM
ejpam-6111	411	19	figure	figure	NOUN
ejpam-6111	411	20	1	1	NUM
ejpam-6111	411	21	:	:	PUNCT
ejpam-6111	411	22	spectral	spectral	ADJ
ejpam-6111	411	23	properties	property	NOUN
ejpam-6111	411	24	of	of	ADP
ejpam-6111	411	25	matrix	matrix	NOUN
ejpam-6111	411	26	h	h	NOUN
ejpam-6111	411	27	=	=	SYM
ejpam-6111	412	1	h(i	h(i	PROPN
ejpam-6111	412	2	,	,	PUNCT
ejpam-6111	412	3	j	j	NOUN
ejpam-6111	412	4	)	)	PUNCT
ejpam-6111	412	5	in	in	ADP
ejpam-6111	412	6	example-1	example-1	PROPN
ejpam-6111	412	7	.	.	PUNCT
ejpam-6111	413	1	smallest	small	ADJ
ejpam-6111	413	2	singular	singular	ADJ
ejpam-6111	413	3	value	value	NOUN
ejpam-6111	413	4	of	of	ADP
ejpam-6111	413	5	the	the	DET
ejpam-6111	413	6	matrix	matrix	NOUN
ejpam-6111	413	7	(	(	PUNCT
ejpam-6111	413	8	zi16	zi16	PROPN
ejpam-6111	413	9	−h(i	−h(i	PROPN
ejpam-6111	413	10	,	,	PUNCT
ejpam-6111	413	11	j	j	NOUN
ejpam-6111	413	12	)	)	PUNCT
ejpam-6111	413	13	)	)	PUNCT
ejpam-6111	413	14	,	,	PUNCT
ejpam-6111	413	15	is	be	AUX
ejpam-6111	413	16	shown	show	VERB
ejpam-6111	413	17	in	in	ADP
ejpam-6111	413	18	pseudomode	pseudomode	NOUN
ejpam-6111	413	19	.	.	PUNCT
ejpam-6111	414	1	example	example	NOUN
ejpam-6111	415	1	2	2	NUM
ejpam-6111	415	2	.	.	PUNCT
ejpam-6111	415	3	the	the	DET
ejpam-6111	415	4	integration	integration	NOUN
ejpam-6111	415	5	of	of	ADP
ejpam-6111	415	6	hm(t	hm(t	ADJ
ejpam-6111	415	7	)	)	PUNCT
ejpam-6111	416	1	=	=	PUNCT
ejpam-6111	417	1	[	[	X
ejpam-6111	417	2	ho(t	ho(t	X
ejpam-6111	417	3	)	)	PUNCT
ejpam-6111	417	4	,	,	PUNCT
ejpam-6111	417	5	h1(t	h1(t	PROPN
ejpam-6111	417	6	)	)	PUNCT
ejpam-6111	417	7	,	,	PUNCT
ejpam-6111	417	8	·	·	PUNCT
ejpam-6111	417	9	·	·	PUNCT
ejpam-6111	417	10	·	·	PUNCT
ejpam-6111	417	11	,	,	PUNCT
ejpam-6111	417	12	hm−1(t	hm−1(t	PROPN
ejpam-6111	417	13	)	)	PUNCT
ejpam-6111	417	14	]	]	PUNCT
ejpam-6111	418	1	t	t	PROPN
ejpam-6111	418	2	maybe	maybe	ADV
ejpam-6111	418	3	approximated	approximate	VERB
ejpam-6111	418	4	as	as	ADP
ejpam-6111	418	5	∫	∫	PROPN
ejpam-6111	418	6	t	t	PROPN
ejpam-6111	418	7	0	0	NUM
ejpam-6111	418	8	hm(τ)dτ	hm(τ)dτ	PROPN
ejpam-6111	419	1	≈	≈	PROPN
ejpam-6111	419	2	qhm(t	qhm(t	PROPN
ejpam-6111	419	3	)	)	PUNCT
ejpam-6111	419	4	,	,	PUNCT
ejpam-6111	419	5	where	where	SCONJ
ejpam-6111	419	6	q	q	NOUN
ejpam-6111	419	7	is	be	AUX
ejpam-6111	419	8	haar	haar	PROPN
ejpam-6111	419	9	wavelet	wavelet	PROPN
ejpam-6111	419	10	operational	operational	ADJ
ejpam-6111	419	11	matrix	matrix	NOUN
ejpam-6111	419	12	with	with	ADP
ejpam-6111	419	13	order	order	NOUN
ejpam-6111	419	14	n.	n.	VERB
ejpam-6111	419	15	the	the	DET
ejpam-6111	419	16	haar	haar	PROPN
ejpam-6111	419	17	wavelet	wavelet	PROPN
ejpam-6111	419	18	operational	operational	ADJ
ejpam-6111	419	19	matrix	matrix	NOUN
ejpam-6111	419	20	of	of	ADP
ejpam-6111	419	21	fractional	fractional	ADJ
ejpam-6111	419	22	order	order	NOUN
ejpam-6111	419	23	integration	integration	NOUN
ejpam-6111	419	24	qα	qα	PROPN
ejpam-6111	419	25	and	and	CCONJ
ejpam-6111	419	26	is	be	AUX
ejpam-6111	419	27	given	give	VERB
ejpam-6111	419	28	by	by	ADP
ejpam-6111	419	29	qαhm(t	qαhm(t	NOUN
ejpam-6111	419	30	)	)	PUNCT
ejpam-6111	419	31	=	=	SYM
ejpam-6111	419	32	jαhm(t	jαhm(t	NOUN
ejpam-6111	419	33	)	)	PUNCT
ejpam-6111	419	34	=	=	PUNCT
ejpam-6111	420	1	[	[	X
ejpam-6111	420	2	qh0(t	qh0(t	PROPN
ejpam-6111	420	3	)	)	PUNCT
ejpam-6111	420	4	,	,	PUNCT
ejpam-6111	420	5	qh0(t	qh0(t	PROPN
ejpam-6111	420	6	)	)	PUNCT
ejpam-6111	420	7	,	,	PUNCT
ejpam-6111	420	8	·	·	PUNCT
ejpam-6111	420	9	·	·	PUNCT
ejpam-6111	420	10	·	·	PUNCT
ejpam-6111	420	11	,	,	PUNCT
ejpam-6111	420	12	qhm−1(t	qhm−1(t	NUM
ejpam-6111	420	13	)	)	PUNCT
ejpam-6111	420	14	]	]	PUNCT
ejpam-6111	420	15	.	.	PUNCT
ejpam-6111	421	1	t	t	PROPN
ejpam-6111	421	2	figure	figure	NOUN
ejpam-6111	421	3	2	2	NUM
ejpam-6111	421	4	:	:	PUNCT
ejpam-6111	421	5	eigenmode	eigenmode	ADJ
ejpam-6111	421	6	(	(	PUNCT
ejpam-6111	421	7	left	left	ADJ
ejpam-6111	421	8	)	)	PUNCT
ejpam-6111	421	9	and	and	CCONJ
ejpam-6111	421	10	inverse	inverse	NOUN
ejpam-6111	421	11	of	of	ADP
ejpam-6111	421	12	resolvent	resolvent	ADJ
ejpam-6111	421	13	norm	norm	NOUN
ejpam-6111	421	14	(	(	PUNCT
ejpam-6111	421	15	right	right	NOUN
ejpam-6111	421	16	)	)	PUNCT
ejpam-6111	421	17	of	of	ADP
ejpam-6111	421	18	matrix	matrix	NOUN
ejpam-6111	421	19	h	h	NOUN
ejpam-6111	421	20	in	in	ADP
ejpam-6111	421	21	example-1	example-1	NUM
ejpam-6111	421	22	s.	s.	PROPN
ejpam-6111	421	23	mazhar	mazhar	PROPN
ejpam-6111	421	24	,	,	PUNCT
ejpam-6111	421	25	m.	m.	NOUN
ejpam-6111	421	26	u.	u.	PROPN
ejpam-6111	421	27	rehman	rehman	PROPN
ejpam-6111	421	28	/	/	SYM
ejpam-6111	421	29	eur	eur	PROPN
ejpam-6111	421	30	.	.	PUNCT
ejpam-6111	422	1	j.	j.	PROPN
ejpam-6111	422	2	pure	pure	PROPN
ejpam-6111	422	3	appl	appl	PROPN
ejpam-6111	422	4	.	.	PROPN
ejpam-6111	422	5	math	math	PROPN
ejpam-6111	422	6	,	,	PUNCT
ejpam-6111	422	7	18	18	NUM
ejpam-6111	422	8	(	(	PUNCT
ejpam-6111	422	9	2	2	NUM
ejpam-6111	422	10	)	)	PUNCT
ejpam-6111	422	11	(	(	PUNCT
ejpam-6111	422	12	2025	2025	NUM
ejpam-6111	422	13	)	)	PUNCT
ejpam-6111	422	14	,	,	PUNCT
ejpam-6111	422	15	6111	6111	NUM
ejpam-6111	422	16	17	17	NUM
ejpam-6111	422	17	of	of	ADP
ejpam-6111	422	18	25	25	NUM
ejpam-6111	422	19	here	here	ADV
ejpam-6111	422	20	,	,	PUNCT
ejpam-6111	422	21	qh0(t	qh0(t	PROPN
ejpam-6111	422	22	)	)	PUNCT
ejpam-6111	422	23	=	=	SYM
ejpam-6111	422	24	1√	1√	PROPN
ejpam-6111	422	25	m	m	VERB
ejpam-6111	422	26	tα	tα	NOUN
ejpam-6111	422	27	γ(1+α	γ(1+α	PROPN
ejpam-6111	422	28	)	)	PUNCT
ejpam-6111	422	29	,	,	PUNCT
ejpam-6111	422	30	qhi(t	qhi(t	PROPN
ejpam-6111	422	31	)	)	PUNCT
ejpam-6111	422	32	=	=	SYM
ejpam-6111	423	1	1√	1√	NUM
ejpam-6111	423	2	m	m	VERB
ejpam-6111	423	3			NOUN
ejpam-6111	423	4	0	0	NUM
ejpam-6111	423	5	,	,	PUNCT
ejpam-6111	423	6	0	0	NUM
ejpam-6111	423	7	≤	≤	NUM
ejpam-6111	423	8	t	t	X
ejpam-6111	423	9	<	<	X
ejpam-6111	423	10	k−1	k−1	PROPN
ejpam-6111	423	11	2j	2j	NUM
ejpam-6111	423	12	2	2	NUM
ejpam-6111	423	13	j	j	PROPN
ejpam-6111	423	14	2ϕ1(t	2ϕ1(t	NUM
ejpam-6111	423	15	)	)	PUNCT
ejpam-6111	423	16	,	,	PUNCT
ejpam-6111	423	17	k−1	k−1	PROPN
ejpam-6111	423	18	2j	2j	PROPN
ejpam-6111	423	19	≤	≤	PROPN
ejpam-6111	423	20	t	t	X
ejpam-6111	423	21	<	<	X
ejpam-6111	423	22	k−0.5	k−0.5	PUNCT
ejpam-6111	423	23	2j	2j	NUM
ejpam-6111	423	24	2	2	NUM
ejpam-6111	423	25	j	j	PROPN
ejpam-6111	423	26	2ϕ2(t	2ϕ2(t	NUM
ejpam-6111	423	27	)	)	PUNCT
ejpam-6111	423	28	,	,	PUNCT
ejpam-6111	423	29	k−0.5	k−0.5	PUNCT
ejpam-6111	423	30	2j	2j	PROPN
ejpam-6111	423	31	≤	≤	PROPN
ejpam-6111	423	32	t	t	PROPN
ejpam-6111	423	33	<	<	X
ejpam-6111	423	34	k	k	X
ejpam-6111	423	35	2j	2j	NUM
ejpam-6111	423	36	2	2	NUM
ejpam-6111	423	37	j	j	PROPN
ejpam-6111	423	38	2ϕ3(t	2ϕ3(t	NUM
ejpam-6111	423	39	)	)	PUNCT
ejpam-6111	423	40	,	,	PUNCT
ejpam-6111	424	1	k	k	PROPN
ejpam-6111	424	2	2j	2j	PROPN
ejpam-6111	424	3	≤	≤	PROPN
ejpam-6111	424	4	t	t	X
ejpam-6111	424	5	<	<	X
ejpam-6111	424	6	1	1	NUM
ejpam-6111	424	7	,	,	PUNCT
ejpam-6111	424	8	ϕ1(t	ϕ1(t	NUM
ejpam-6111	424	9	)	)	PUNCT
ejpam-6111	424	10	=	=	SYM
ejpam-6111	424	11	1	1	NUM
ejpam-6111	424	12	γ(α+1	γ(α+1	NOUN
ejpam-6111	424	13	)	)	PUNCT
ejpam-6111	424	14	(	(	PUNCT
ejpam-6111	424	15	t−	t−	PROPN
ejpam-6111	424	16	k−1	k−1	PROPN
ejpam-6111	424	17	2j	2j	PROPN
ejpam-6111	424	18	)	)	PUNCT
ejpam-6111	424	19	α	α	NOUN
ejpam-6111	424	20	,	,	PUNCT
ejpam-6111	424	21	ϕ2(t	ϕ2(t	PROPN
ejpam-6111	424	22	)	)	PUNCT
ejpam-6111	424	23	=	=	NOUN
ejpam-6111	424	24	1	1	NUM
ejpam-6111	424	25	γ(α+1	γ(α+1	NOUN
ejpam-6111	424	26	)	)	PUNCT
ejpam-6111	424	27	(	(	PUNCT
ejpam-6111	424	28	t−	t−	PROPN
ejpam-6111	424	29	k−1	k−1	PROPN
ejpam-6111	424	30	2j	2j	PROPN
ejpam-6111	424	31	)	)	PUNCT
ejpam-6111	425	1	α	α	NOUN
ejpam-6111	425	2	−	−	NOUN
ejpam-6111	425	3	2	2	NUM
ejpam-6111	425	4	γ(α+1	γ(α+1	NOUN
ejpam-6111	425	5	)	)	PUNCT
ejpam-6111	425	6	(	(	PUNCT
ejpam-6111	425	7	t−	t−	PROPN
ejpam-6111	425	8	k−0.5	k−0.5	PROPN
ejpam-6111	425	9	2j	2j	X
ejpam-6111	425	10	)	)	PUNCT
ejpam-6111	425	11	α	α	NOUN
ejpam-6111	425	12	,	,	PUNCT
ejpam-6111	425	13	ϕ3(t	ϕ3(t	PROPN
ejpam-6111	425	14	)	)	PUNCT
ejpam-6111	425	15	=	=	NOUN
ejpam-6111	425	16	1	1	NUM
ejpam-6111	425	17	γ(α+1	γ(α+1	NOUN
ejpam-6111	425	18	)	)	PUNCT
ejpam-6111	425	19	(	(	PUNCT
ejpam-6111	425	20	t−	t−	PROPN
ejpam-6111	425	21	k−1	k−1	PROPN
ejpam-6111	425	22	2j	2j	PROPN
ejpam-6111	425	23	)	)	PUNCT
ejpam-6111	426	1	α	α	NOUN
ejpam-6111	426	2	−	−	NOUN
ejpam-6111	426	3	2	2	NUM
ejpam-6111	426	4	γ(α+1	γ(α+1	NOUN
ejpam-6111	426	5	)	)	PUNCT
ejpam-6111	426	6	(	(	PUNCT
ejpam-6111	427	1	t−	t−	PROPN
ejpam-6111	427	2	k−0.5	k−0.5	PROPN
ejpam-6111	427	3	2j	2j	X
ejpam-6111	427	4	)	)	PUNCT
ejpam-6111	427	5	α	α	PROPN
ejpam-6111	428	1	+	+	NOUN
ejpam-6111	428	2	1	1	NUM
ejpam-6111	428	3	γ(α+1)(t−	γ(α+1)(t−	PROPN
ejpam-6111	428	4	k	k	X
ejpam-6111	428	5	2j	2j	X
ejpam-6111	428	6	)	)	PUNCT
ejpam-6111	428	7	α	α	X
ejpam-6111	428	8	.	.	PUNCT
ejpam-6111	429	1	for	for	ADP
ejpam-6111	429	2	α	α	NOUN
ejpam-6111	429	3	=	=	SYM
ejpam-6111	429	4	1.5	1.5	NUM
ejpam-6111	429	5	and	and	CCONJ
ejpam-6111	429	6	m	m	PROPN
ejpam-6111	429	7	=	=	ADJ
ejpam-6111	429	8	8	8	NUM
ejpam-6111	429	9	,	,	PUNCT
ejpam-6111	429	10	the	the	DET
ejpam-6111	429	11	haar	haar	PROPN
ejpam-6111	429	12	wavelet	wavelet	PROPN
ejpam-6111	429	13	operational	operational	ADJ
ejpam-6111	429	14	matrix	matrix	NOUN
ejpam-6111	429	15	[	[	X
ejpam-6111	429	16	46	46	NUM
ejpam-6111	429	17	]	]	PUNCT
ejpam-6111	429	18	is	be	AUX
ejpam-6111	429	19	:	:	PUNCT
ejpam-6111	429	20	qαh8	qαh8	PROPN
ejpam-6111	429	21	=	=	PUNCT
ejpam-6111	429	22			NOUN
ejpam-6111	429	23	0.0042	0.0042	NUM
ejpam-6111	429	24	0.0216	0.0216	NUM
ejpam-6111	429	25	0.0465	0.0465	NUM
ejpam-6111	429	26	0.0770	0.0770	NUM
ejpam-6111	429	27	0.1122	0.1122	NUM
ejpam-6111	429	28	0.1516	0.1516	NUM
ejpam-6111	429	29	0.1948	0.1948	NUM
ejpam-6111	429	30	0.2414	0.2414	NUM
ejpam-6111	429	31	0.0042	0.0042	NUM
ejpam-6111	429	32	0.0216	0.0216	NUM
ejpam-6111	429	33	0.0465	0.0465	NUM
ejpam-6111	429	34	0.0770	0.0770	NUM
ejpam-6111	429	35	0.1039	0.1039	NUM
ejpam-6111	429	36	0.1084	0.1084	NUM
ejpam-6111	430	1	0.1019	0.1019	NUM
ejpam-6111	430	2	0.0875	0.0875	NUM
ejpam-6111	430	3	0.0059	0.0059	NUM
ejpam-6111	430	4	0.0305	0.0305	NUM
ejpam-6111	430	5	0.0540	0.0540	NUM
ejpam-6111	430	6	0.0478	0.0478	NUM
ejpam-6111	430	7	0.0331	0.0331	NUM
ejpam-6111	430	8	0.0273	0.0273	NUM
ejpam-6111	430	9	0.0238	0.0238	NUM
ejpam-6111	430	10	0.0214	0.0214	NUM
ejpam-6111	430	11	0	0	NUM
ejpam-6111	430	12	0	0	NUM
ejpam-6111	430	13	0	0	NUM
ejpam-6111	430	14	0	0	NUM
ejpam-6111	430	15	0.0059	0.0059	NUM
ejpam-6111	430	16	0.0305	0.0305	NUM
ejpam-6111	430	17	0.0540	0.0540	NUM
ejpam-6111	430	18	0.0478	0.0478	NUM
ejpam-6111	430	19	0.0083	0.0083	NUM
ejpam-6111	430	20	0.0266	0.0266	NUM
ejpam-6111	430	21	0.0149	0.0149	NUM
ejpam-6111	430	22	0.0113	0.0113	NUM
ejpam-6111	430	23	0.0095	0.0095	NUM
ejpam-6111	430	24	0.0083	0.0083	NUM
ejpam-6111	430	25	0.0075	0.0075	NUM
ejpam-6111	430	26	0.0069	0.0069	NUM
ejpam-6111	430	27	0	0	NUM
ejpam-6111	430	28	0	0	NUM
ejpam-6111	430	29	0.0083	0.0083	NUM
ejpam-6111	430	30	0.0266	0.0266	NUM
ejpam-6111	430	31	0.0149	0.0149	NUM
ejpam-6111	430	32	0.0113	0.0113	NUM
ejpam-6111	430	33	0.0095	0.0095	NUM
ejpam-6111	430	34	0.0083	0.0083	NUM
ejpam-6111	430	35	0	0	NUM
ejpam-6111	430	36	0	0	NUM
ejpam-6111	430	37	0	0	NUM
ejpam-6111	430	38	0	0	NUM
ejpam-6111	430	39	0.0083	0.0083	NUM
ejpam-6111	430	40	0.0266	0.0266	NUM
ejpam-6111	430	41	0.0149	0.0149	NUM
ejpam-6111	430	42	0.0113	0.0113	NUM
ejpam-6111	430	43	0	0	NUM
ejpam-6111	430	44	0	0	NUM
ejpam-6111	430	45	0	0	NUM
ejpam-6111	430	46	0	0	NUM
ejpam-6111	430	47	0	0	NUM
ejpam-6111	430	48	0	0	NUM
ejpam-6111	430	49	0.0083	0.0083	NUM
ejpam-6111	430	50	0.0266	0.0266	NUM
ejpam-6111	430	51			NUM
ejpam-6111	430	52	.	.	PUNCT
ejpam-6111	431	1	the	the	DET
ejpam-6111	431	2	spectral	spectral	ADJ
ejpam-6111	431	3	properties	property	NOUN
ejpam-6111	431	4	such	such	ADJ
ejpam-6111	431	5	as	as	ADP
ejpam-6111	431	6	the	the	DET
ejpam-6111	431	7	computation	computation	NOUN
ejpam-6111	431	8	of	of	ADP
ejpam-6111	431	9	spectrum	spectrum	NOUN
ejpam-6111	431	10	,	,	PUNCT
ejpam-6111	431	11	singular	singular	ADJ
ejpam-6111	431	12	values	value	NOUN
ejpam-6111	431	13	,	,	PUNCT
ejpam-6111	431	14	structured	structure	VERB
ejpam-6111	431	15	singular	singular	ADJ
ejpam-6111	431	16	values	value	NOUN
ejpam-6111	431	17	,	,	PUNCT
ejpam-6111	431	18	and	and	CCONJ
ejpam-6111	431	19	pseudo	pseudo	NOUN
ejpam-6111	431	20	-	-	NOUN
ejpam-6111	431	21	spectrum	spectrum	NOUN
ejpam-6111	431	22	of	of	ADP
ejpam-6111	431	23	h(i	h(i	PROPN
ejpam-6111	431	24	,	,	PUNCT
ejpam-6111	431	25	j	j	NOUN
ejpam-6111	431	26	)	)	PUNCT
ejpam-6111	431	27	are	be	AUX
ejpam-6111	431	28	presented	present	VERB
ejpam-6111	431	29	in	in	ADP
ejpam-6111	431	30	figure	figure	NOUN
ejpam-6111	431	31	3	3	NUM
ejpam-6111	431	32	.	.	PUNCT
ejpam-6111	432	1	in	in	ADP
ejpam-6111	432	2	figure	figure	NOUN
ejpam-6111	432	3	4	4	NUM
ejpam-6111	432	4	,	,	PUNCT
ejpam-6111	432	5	we	we	PRON
ejpam-6111	432	6	plot	plot	VERB
ejpam-6111	432	7	the	the	DET
ejpam-6111	432	8	eigenmode	eigenmode	PROPN
ejpam-6111	432	9	corresponding	corresponding	NOUN
ejpam-6111	432	10	to	to	ADP
ejpam-6111	432	11	the	the	DET
ejpam-6111	432	12	eigenvalues	eigenvalue	NOUN
ejpam-6111	432	13	.	.	PUNCT
ejpam-6111	433	1	the	the	DET
ejpam-6111	433	2	top	top	ADJ
ejpam-6111	433	3	plot	plot	NOUN
ejpam-6111	433	4	in	in	ADP
ejpam-6111	433	5	the	the	DET
ejpam-6111	433	6	figure	figure	NOUN
ejpam-6111	433	7	shows	show	VERB
ejpam-6111	433	8	an	an	DET
ejpam-6111	433	9	envelope	envelope	NOUN
ejpam-6111	433	10	which	which	PRON
ejpam-6111	433	11	is	be	AUX
ejpam-6111	433	12	produced	produce	VERB
ejpam-6111	433	13	by	by	ADP
ejpam-6111	433	14	plotting	plot	VERB
ejpam-6111	433	15	the	the	DET
ejpam-6111	433	16	absolute	absolute	ADJ
ejpam-6111	433	17	value	value	NOUN
ejpam-6111	433	18	of	of	ADP
ejpam-6111	433	19	an	an	DET
ejpam-6111	433	20	eigenmode	eigenmode	NOUN
ejpam-6111	433	21	and	and	CCONJ
ejpam-6111	433	22	minus	minus	ADP
ejpam-6111	433	23	the	the	DET
ejpam-6111	433	24	absolute	absolute	ADJ
ejpam-6111	433	25	value	value	NOUN
ejpam-6111	433	26	.	.	PUNCT
ejpam-6111	434	1	the	the	DET
ejpam-6111	434	2	real	real	ADJ
ejpam-6111	434	3	part	part	NOUN
ejpam-6111	434	4	is	be	AUX
ejpam-6111	434	5	shown	show	VERB
ejpam-6111	434	6	with	with	ADP
ejpam-6111	434	7	a	a	DET
ejpam-6111	434	8	cyan	cyan	ADJ
ejpam-6111	434	9	line	line	NOUN
ejpam-6111	434	10	.	.	PUNCT
ejpam-6111	435	1	the	the	DET
ejpam-6111	435	2	plot	plot	NOUN
ejpam-6111	435	3	at	at	ADP
ejpam-6111	435	4	the	the	DET
ejpam-6111	435	5	bottom	bottom	ADJ
ejpam-6111	435	6	level	level	NOUN
ejpam-6111	435	7	shows	show	VERB
ejpam-6111	435	8	the	the	DET
ejpam-6111	435	9	absolute	absolute	ADJ
ejpam-6111	435	10	value	value	NOUN
ejpam-6111	435	11	of	of	ADP
ejpam-6111	435	12	eigenmode	eigenmode	ADJ
ejpam-6111	435	13	being	be	AUX
ejpam-6111	435	14	plotted	plot	VERB
ejpam-6111	435	15	at	at	ADP
ejpam-6111	435	16	a	a	DET
ejpam-6111	435	17	log	log	NOUN
ejpam-6111	435	18	scale	scale	NOUN
ejpam-6111	435	19	.	.	PUNCT
ejpam-6111	436	1	further	far	ADV
ejpam-6111	436	2	,	,	PUNCT
ejpam-6111	436	3	it	it	PRON
ejpam-6111	436	4	shows	show	VERB
ejpam-6111	436	5	that	that	SCONJ
ejpam-6111	436	6	how	how	SCONJ
ejpam-6111	436	7	quickly	quickly	ADV
ejpam-6111	436	8	an	an	DET
ejpam-6111	436	9	eigenmode	eigenmode	NOUN
ejpam-6111	436	10	is	be	AUX
ejpam-6111	436	11	decaying	decay	VERB
ejpam-6111	436	12	with	with	ADP
ejpam-6111	436	13	the	the	DET
ejpam-6111	436	14	time	time	NOUN
ejpam-6111	436	15	.	.	PUNCT
ejpam-6111	437	1	the	the	DET
ejpam-6111	437	2	condition	condition	NOUN
ejpam-6111	437	3	number	number	NOUN
ejpam-6111	437	4	computed	compute	VERB
ejpam-6111	437	5	for	for	ADP
ejpam-6111	437	6	an	an	DET
ejpam-6111	437	7	eigenvalue	eigenvalue	NOUN
ejpam-6111	437	8	is	be	AUX
ejpam-6111	437	9	shown	show	VERB
ejpam-6111	437	10	in	in	ADP
ejpam-6111	437	11	the	the	DET
ejpam-6111	437	12	top	top	ADJ
ejpam-6111	437	13	plot	plot	NOUN
ejpam-6111	437	14	.	.	PUNCT
ejpam-6111	438	1	a	a	DET
ejpam-6111	438	2	large	large	ADJ
ejpam-6111	438	3	condition	condition	NOUN
ejpam-6111	438	4	number	number	NOUN
ejpam-6111	438	5	means	mean	VERB
ejpam-6111	438	6	that	that	SCONJ
ejpam-6111	438	7	the	the	DET
ejpam-6111	438	8	eigenvalue	eigenvalue	NOUN
ejpam-6111	438	9	is	be	AUX
ejpam-6111	438	10	sensitive	sensitive	ADJ
ejpam-6111	438	11	to	to	ADP
ejpam-6111	438	12	perturbations	perturbation	NOUN
ejpam-6111	438	13	.	.	PUNCT
ejpam-6111	439	1	in	in	ADP
ejpam-6111	439	2	figure	figure	NOUN
ejpam-6111	439	3	4	4	NUM
ejpam-6111	439	4	,	,	PUNCT
ejpam-6111	439	5	we	we	PRON
ejpam-6111	439	6	plot	plot	VERB
ejpam-6111	439	7	the	the	DET
ejpam-6111	439	8	value	value	NOUN
ejpam-6111	439	9	of	of	ADP
ejpam-6111	439	10	the	the	DET
ejpam-6111	439	11	inverse	inverse	NOUN
ejpam-6111	439	12	of	of	ADP
ejpam-6111	439	13	the	the	DET
ejpam-6111	439	14	resolvent	resolvent	ADJ
ejpam-6111	439	15	norm	norm	NOUN
ejpam-6111	439	16	.	.	PUNCT
ejpam-6111	440	1	we	we	PRON
ejpam-6111	440	2	show	show	VERB
ejpam-6111	440	3	real	real	ADJ
ejpam-6111	440	4	part	part	NOUN
ejpam-6111	440	5	of	of	ADP
ejpam-6111	440	6	pseudomode	pseudomode	NOUN
ejpam-6111	440	7	in	in	ADP
ejpam-6111	440	8	magenta	magenta	NOUN
ejpam-6111	440	9	.	.	PUNCT
ejpam-6111	441	1	the	the	DET
ejpam-6111	441	2	right	right	ADJ
ejpam-6111	441	3	singular	singular	PROPN
ejpam-6111	441	4	vector	vector	NOUN
ejpam-6111	441	5	corresponding	correspond	VERB
ejpam-6111	441	6	to	to	ADP
ejpam-6111	441	7	the	the	DET
ejpam-6111	441	8	smallest	small	ADJ
ejpam-6111	441	9	singular	singular	ADJ
ejpam-6111	441	10	value	value	NOUN
ejpam-6111	441	11	to	to	ADP
ejpam-6111	441	12	the	the	DET
ejpam-6111	441	13	matrix	matrix	NOUN
ejpam-6111	441	14	(	(	PUNCT
ejpam-6111	441	15	zi16	zi16	PROPN
ejpam-6111	441	16	−h(i	−h(i	PROPN
ejpam-6111	441	17	,	,	PUNCT
ejpam-6111	441	18	j	j	NOUN
ejpam-6111	441	19	)	)	PUNCT
ejpam-6111	441	20	)	)	PUNCT
ejpam-6111	441	21	,	,	PUNCT
ejpam-6111	441	22	is	be	AUX
ejpam-6111	441	23	shown	show	VERB
ejpam-6111	441	24	in	in	ADP
ejpam-6111	441	25	pseudomode	pseudomode	NOUN
ejpam-6111	441	26	.	.	PUNCT
ejpam-6111	442	1	example	example	NOUN
ejpam-6111	443	1	3	3	X
ejpam-6111	443	2	.	.	X
ejpam-6111	443	3	we	we	PRON
ejpam-6111	443	4	consider	consider	VERB
ejpam-6111	443	5	50	50	NUM
ejpam-6111	443	6	,	,	PUNCT
ejpam-6111	443	7	100	100	NUM
ejpam-6111	443	8	and	and	CCONJ
ejpam-6111	443	9	200	200	NUM
ejpam-6111	443	10	dimensional	dimensional	ADJ
ejpam-6111	443	11	haar	haar	NOUN
ejpam-6111	443	12	matrices	matrix	NOUN
ejpam-6111	443	13	which	which	PRON
ejpam-6111	443	14	are	be	AUX
ejpam-6111	443	15	generated	generate	VERB
ejpam-6111	443	16	by	by	ADP
ejpam-6111	443	17	matlab	matlab	PROPN
ejpam-6111	443	18	command	command	PROPN
ejpam-6111	443	19	haarmtx(n	haarmtx(n	PROPN
ejpam-6111	443	20	)	)	PUNCT
ejpam-6111	443	21	.	.	PUNCT
ejpam-6111	444	1	the	the	DET
ejpam-6111	444	2	spectral	spectral	ADJ
ejpam-6111	444	3	properties	property	NOUN
ejpam-6111	444	4	like	like	ADP
ejpam-6111	444	5	the	the	DET
ejpam-6111	444	6	computation	computation	NOUN
ejpam-6111	444	7	of	of	ADP
ejpam-6111	444	8	spectrum	spectrum	NOUN
ejpam-6111	444	9	,	,	PUNCT
ejpam-6111	444	10	singular	singular	ADJ
ejpam-6111	444	11	values	value	NOUN
ejpam-6111	444	12	,	,	PUNCT
ejpam-6111	444	13	structured	structure	VERB
ejpam-6111	444	14	singular	singular	ADJ
ejpam-6111	444	15	values	value	NOUN
ejpam-6111	444	16	,	,	PUNCT
ejpam-6111	444	17	and	and	CCONJ
ejpam-6111	444	18	pseudo	pseudo	NOUN
ejpam-6111	444	19	-	-	NOUN
ejpam-6111	444	20	spectrum	spectrum	NOUN
ejpam-6111	444	21	of	of	ADP
ejpam-6111	444	22	50	50	NUM
ejpam-6111	444	23	,	,	PUNCT
ejpam-6111	444	24	100	100	NUM
ejpam-6111	444	25	and	and	CCONJ
ejpam-6111	444	26	200	200	NUM
ejpam-6111	444	27	dimensional	dimensional	ADJ
ejpam-6111	444	28	haar	haar	NOUN
ejpam-6111	444	29	matrices	matrix	NOUN
ejpam-6111	444	30	are	be	AUX
ejpam-6111	444	31	presented	present	VERB
ejpam-6111	444	32	in	in	ADP
ejpam-6111	444	33	figure	figure	NOUN
ejpam-6111	444	34	5	5	NUM
ejpam-6111	444	35	.	.	PUNCT
ejpam-6111	445	1	in	in	ADP
ejpam-6111	445	2	figures	figure	NOUN
ejpam-6111	445	3	6	6	NUM
ejpam-6111	445	4	-	-	SYM
ejpam-6111	445	5	8	8	NUM
ejpam-6111	445	6	,	,	PUNCT
ejpam-6111	445	7	we	we	PRON
ejpam-6111	445	8	plot	plot	VERB
ejpam-6111	445	9	the	the	DET
ejpam-6111	445	10	eigenmode	eigenmode	PROPN
ejpam-6111	445	11	corresponding	corresponding	NOUN
ejpam-6111	445	12	to	to	ADP
ejpam-6111	445	13	the	the	DET
ejpam-6111	445	14	eigenvalues	eigenvalue	NOUN
ejpam-6111	445	15	.	.	PUNCT
ejpam-6111	446	1	the	the	DET
ejpam-6111	446	2	top	top	ADJ
ejpam-6111	446	3	plot	plot	NOUN
ejpam-6111	446	4	in	in	ADP
ejpam-6111	446	5	each	each	DET
ejpam-6111	446	6	figure	figure	NOUN
ejpam-6111	446	7	shows	show	VERB
ejpam-6111	446	8	an	an	DET
ejpam-6111	446	9	envelope	envelope	NOUN
ejpam-6111	446	10	which	which	PRON
ejpam-6111	446	11	is	be	AUX
ejpam-6111	446	12	produced	produce	VERB
ejpam-6111	446	13	by	by	ADP
ejpam-6111	446	14	plotting	plot	VERB
ejpam-6111	446	15	the	the	DET
ejpam-6111	446	16	absolute	absolute	ADJ
ejpam-6111	446	17	value	value	NOUN
ejpam-6111	446	18	of	of	ADP
ejpam-6111	446	19	an	an	DET
ejpam-6111	446	20	eigenmode	eigenmode	NOUN
ejpam-6111	446	21	and	and	CCONJ
ejpam-6111	446	22	minus	minus	ADP
ejpam-6111	446	23	the	the	DET
ejpam-6111	446	24	absolute	absolute	ADJ
ejpam-6111	446	25	value	value	NOUN
ejpam-6111	446	26	.	.	PUNCT
ejpam-6111	447	1	the	the	DET
ejpam-6111	447	2	real	real	ADJ
ejpam-6111	447	3	part	part	NOUN
ejpam-6111	447	4	is	be	AUX
ejpam-6111	447	5	shown	show	VERB
ejpam-6111	447	6	with	with	ADP
ejpam-6111	447	7	a	a	DET
ejpam-6111	447	8	cyan	cyan	ADJ
ejpam-6111	447	9	line	line	NOUN
ejpam-6111	447	10	.	.	PUNCT
ejpam-6111	448	1	the	the	DET
ejpam-6111	448	2	s.	s.	PROPN
ejpam-6111	448	3	mazhar	mazhar	PROPN
ejpam-6111	448	4	,	,	PUNCT
ejpam-6111	448	5	m.	m.	NOUN
ejpam-6111	448	6	u.	u.	PROPN
ejpam-6111	448	7	rehman	rehman	PROPN
ejpam-6111	448	8	/	/	SYM
ejpam-6111	448	9	eur	eur	PROPN
ejpam-6111	448	10	.	.	PUNCT
ejpam-6111	449	1	j.	j.	PROPN
ejpam-6111	449	2	pure	pure	PROPN
ejpam-6111	449	3	appl	appl	PROPN
ejpam-6111	449	4	.	.	PROPN
ejpam-6111	449	5	math	math	PROPN
ejpam-6111	449	6	,	,	PUNCT
ejpam-6111	449	7	18	18	NUM
ejpam-6111	449	8	(	(	PUNCT
ejpam-6111	449	9	2	2	NUM
ejpam-6111	449	10	)	)	PUNCT
ejpam-6111	449	11	(	(	PUNCT
ejpam-6111	449	12	2025	2025	NUM
ejpam-6111	449	13	)	)	PUNCT
ejpam-6111	449	14	,	,	PUNCT
ejpam-6111	449	15	6111	6111	NUM
ejpam-6111	449	16	18	18	NUM
ejpam-6111	449	17	of	of	ADP
ejpam-6111	449	18	25	25	NUM
ejpam-6111	449	19	figure	figure	NOUN
ejpam-6111	449	20	3	3	NUM
ejpam-6111	449	21	:	:	PUNCT
ejpam-6111	449	22	spectral	spectral	ADJ
ejpam-6111	449	23	properties	property	NOUN
ejpam-6111	449	24	of	of	ADP
ejpam-6111	449	25	matrix	matrix	NOUN
ejpam-6111	449	26	qαh8	qαh8	NOUN
ejpam-6111	449	27	in	in	ADP
ejpam-6111	449	28	example-2	example-2	PROPN
ejpam-6111	449	29	.	.	PUNCT
ejpam-6111	449	30	plot	plot	NOUN
ejpam-6111	449	31	at	at	ADP
ejpam-6111	449	32	the	the	DET
ejpam-6111	449	33	bottom	bottom	ADJ
ejpam-6111	449	34	level	level	NOUN
ejpam-6111	449	35	in	in	ADP
ejpam-6111	449	36	each	each	DET
ejpam-6111	449	37	figure	figure	NOUN
ejpam-6111	449	38	show	show	VERB
ejpam-6111	449	39	absolute	absolute	ADJ
ejpam-6111	449	40	value	value	NOUN
ejpam-6111	449	41	of	of	ADP
ejpam-6111	449	42	eigenmode	eigenmode	ADJ
ejpam-6111	449	43	being	be	AUX
ejpam-6111	449	44	ploted	plot	VERB
ejpam-6111	449	45	at	at	ADP
ejpam-6111	449	46	a	a	DET
ejpam-6111	449	47	log	log	NOUN
ejpam-6111	449	48	scale	scale	NOUN
ejpam-6111	449	49	.	.	PUNCT
ejpam-6111	450	1	further	far	ADV
ejpam-6111	450	2	it	it	PRON
ejpam-6111	450	3	shows	show	VERB
ejpam-6111	450	4	that	that	SCONJ
ejpam-6111	450	5	how	how	SCONJ
ejpam-6111	450	6	quickly	quickly	ADV
ejpam-6111	450	7	an	an	DET
ejpam-6111	450	8	eigenmode	eigenmode	NOUN
ejpam-6111	450	9	is	be	AUX
ejpam-6111	450	10	decaying	decay	VERB
ejpam-6111	450	11	with	with	ADP
ejpam-6111	450	12	the	the	DET
ejpam-6111	450	13	time	time	NOUN
ejpam-6111	450	14	.	.	PUNCT
ejpam-6111	451	1	the	the	DET
ejpam-6111	451	2	condition	condition	NOUN
ejpam-6111	451	3	number	number	NOUN
ejpam-6111	451	4	computed	compute	VERB
ejpam-6111	451	5	for	for	ADP
ejpam-6111	451	6	an	an	DET
ejpam-6111	451	7	eigenvalue	eigenvalue	NOUN
ejpam-6111	451	8	is	be	AUX
ejpam-6111	451	9	shown	show	VERB
ejpam-6111	451	10	in	in	ADP
ejpam-6111	451	11	the	the	DET
ejpam-6111	451	12	top	top	ADJ
ejpam-6111	451	13	plot	plot	NOUN
ejpam-6111	451	14	.	.	PUNCT
ejpam-6111	452	1	the	the	DET
ejpam-6111	452	2	large	large	ADJ
ejpam-6111	452	3	condition	condition	NOUN
ejpam-6111	452	4	number	number	NOUN
ejpam-6111	452	5	means	mean	VERB
ejpam-6111	452	6	that	that	SCONJ
ejpam-6111	452	7	eigenvalue	eigenvalue	NOUN
ejpam-6111	452	8	is	be	AUX
ejpam-6111	452	9	sensitive	sensitive	ADJ
ejpam-6111	452	10	to	to	ADP
ejpam-6111	452	11	perturbations	perturbation	NOUN
ejpam-6111	452	12	.	.	PUNCT
ejpam-6111	453	1	further	far	ADV
ejpam-6111	453	2	,	,	PUNCT
ejpam-6111	453	3	we	we	PRON
ejpam-6111	453	4	present	present	VERB
ejpam-6111	453	5	the	the	DET
ejpam-6111	453	6	plot	plot	NOUN
ejpam-6111	453	7	of	of	ADP
ejpam-6111	453	8	the	the	DET
ejpam-6111	453	9	value	value	NOUN
ejpam-6111	453	10	of	of	ADP
ejpam-6111	453	11	inverse	inverse	NOUN
ejpam-6111	453	12	of	of	ADP
ejpam-6111	453	13	the	the	DET
ejpam-6111	453	14	resolvent	resolvent	ADJ
ejpam-6111	453	15	norm	norm	NOUN
ejpam-6111	453	16	.	.	PUNCT
ejpam-6111	454	1	we	we	PRON
ejpam-6111	454	2	show	show	VERB
ejpam-6111	454	3	real	real	ADJ
ejpam-6111	454	4	part	part	NOUN
ejpam-6111	454	5	of	of	ADP
ejpam-6111	454	6	pseudomode	pseudomode	NOUN
ejpam-6111	454	7	in	in	ADP
ejpam-6111	454	8	magenta	magenta	NOUN
ejpam-6111	454	9	.	.	PUNCT
ejpam-6111	455	1	the	the	DET
ejpam-6111	455	2	right	right	ADJ
ejpam-6111	455	3	singular	singular	PROPN
ejpam-6111	455	4	vector	vector	NOUN
ejpam-6111	455	5	corresponding	correspond	VERB
ejpam-6111	455	6	to	to	ADP
ejpam-6111	455	7	the	the	DET
ejpam-6111	455	8	smallest	small	ADJ
ejpam-6111	455	9	singular	singular	ADJ
ejpam-6111	455	10	value	value	NOUN
ejpam-6111	455	11	corresponding	correspond	VERB
ejpam-6111	455	12	to	to	PART
ejpam-6111	455	13	matrix	matrix	VERB
ejpam-6111	455	14	zi	zi	NOUN
ejpam-6111	455	15	−m	−m	PROPN
ejpam-6111	455	16	,	,	PUNCT
ejpam-6111	455	17	is	be	AUX
ejpam-6111	455	18	shown	show	VERB
ejpam-6111	455	19	in	in	ADP
ejpam-6111	455	20	pseudomde	pseudomde	NOUN
ejpam-6111	455	21	.	.	PUNCT
ejpam-6111	456	1	s.	s.	PROPN
ejpam-6111	456	2	mazhar	mazhar	PROPN
ejpam-6111	456	3	,	,	PUNCT
ejpam-6111	456	4	m.	m.	NOUN
ejpam-6111	456	5	u.	u.	PROPN
ejpam-6111	456	6	rehman	rehman	PROPN
ejpam-6111	456	7	/	/	SYM
ejpam-6111	456	8	eur	eur	PROPN
ejpam-6111	456	9	.	.	PUNCT
ejpam-6111	457	1	j.	j.	PROPN
ejpam-6111	457	2	pure	pure	PROPN
ejpam-6111	457	3	appl	appl	PROPN
ejpam-6111	457	4	.	.	PROPN
ejpam-6111	457	5	math	math	PROPN
ejpam-6111	457	6	,	,	PUNCT
ejpam-6111	457	7	18	18	NUM
ejpam-6111	457	8	(	(	PUNCT
ejpam-6111	457	9	2	2	NUM
ejpam-6111	457	10	)	)	PUNCT
ejpam-6111	457	11	(	(	PUNCT
ejpam-6111	457	12	2025	2025	NUM
ejpam-6111	457	13	)	)	PUNCT
ejpam-6111	457	14	,	,	PUNCT
ejpam-6111	457	15	6111	6111	NUM
ejpam-6111	457	16	19	19	NUM
ejpam-6111	457	17	of	of	ADP
ejpam-6111	457	18	25	25	NUM
ejpam-6111	457	19	figure	figure	NOUN
ejpam-6111	457	20	4	4	NUM
ejpam-6111	457	21	:	:	PUNCT
ejpam-6111	457	22	eigenmode	eigenmode	ADJ
ejpam-6111	457	23	(	(	PUNCT
ejpam-6111	457	24	left	left	ADJ
ejpam-6111	457	25	)	)	PUNCT
ejpam-6111	457	26	and	and	CCONJ
ejpam-6111	457	27	inverse	inverse	NOUN
ejpam-6111	457	28	of	of	ADP
ejpam-6111	457	29	resolvent	resolvent	ADJ
ejpam-6111	457	30	norm	norm	NOUN
ejpam-6111	457	31	(	(	PUNCT
ejpam-6111	457	32	right	right	NOUN
ejpam-6111	457	33	)	)	PUNCT
ejpam-6111	457	34	of	of	ADP
ejpam-6111	457	35	matrix	matrix	NOUN
ejpam-6111	457	36	qαh8	qαh8	NOUN
ejpam-6111	457	37	in	in	ADP
ejpam-6111	457	38	example-2	example-2	NUM
ejpam-6111	457	39	s.	s.	PROPN
ejpam-6111	457	40	mazhar	mazhar	PROPN
ejpam-6111	457	41	,	,	PUNCT
ejpam-6111	457	42	m.	m.	NOUN
ejpam-6111	457	43	u.	u.	PROPN
ejpam-6111	457	44	rehman	rehman	PROPN
ejpam-6111	457	45	/	/	SYM
ejpam-6111	457	46	eur	eur	PROPN
ejpam-6111	457	47	.	.	PUNCT
ejpam-6111	458	1	j.	j.	PROPN
ejpam-6111	458	2	pure	pure	PROPN
ejpam-6111	458	3	appl	appl	PROPN
ejpam-6111	458	4	.	.	PROPN
ejpam-6111	458	5	math	math	PROPN
ejpam-6111	458	6	,	,	PUNCT
ejpam-6111	458	7	18	18	NUM
ejpam-6111	458	8	(	(	PUNCT
ejpam-6111	458	9	2	2	NUM
ejpam-6111	458	10	)	)	PUNCT
ejpam-6111	458	11	(	(	PUNCT
ejpam-6111	458	12	2025	2025	NUM
ejpam-6111	458	13	)	)	PUNCT
ejpam-6111	458	14	,	,	PUNCT
ejpam-6111	458	15	6111	6111	NUM
ejpam-6111	458	16	20	20	NUM
ejpam-6111	458	17	of	of	ADP
ejpam-6111	458	18	25	25	NUM
ejpam-6111	458	19	figure	figure	NOUN
ejpam-6111	458	20	5	5	NUM
ejpam-6111	458	21	:	:	PUNCT
ejpam-6111	458	22	spectral	spectral	ADJ
ejpam-6111	458	23	properties	property	NOUN
ejpam-6111	458	24	of	of	ADP
ejpam-6111	458	25	50	50	NUM
ejpam-6111	458	26	,	,	PUNCT
ejpam-6111	458	27	100	100	NUM
ejpam-6111	458	28	and	and	CCONJ
ejpam-6111	458	29	200	200	NUM
ejpam-6111	458	30	haar	haar	NOUN
ejpam-6111	458	31	matrices	matrix	NOUN
ejpam-6111	458	32	in	in	ADP
ejpam-6111	458	33	example-3	example-3	PROPN
ejpam-6111	458	34	.	.	PUNCT
ejpam-6111	459	1	s.	s.	PROPN
ejpam-6111	459	2	mazhar	mazhar	PROPN
ejpam-6111	459	3	,	,	PUNCT
ejpam-6111	459	4	m.	m.	NOUN
ejpam-6111	459	5	u.	u.	PROPN
ejpam-6111	459	6	rehman	rehman	PROPN
ejpam-6111	459	7	/	/	SYM
ejpam-6111	459	8	eur	eur	PROPN
ejpam-6111	459	9	.	.	PUNCT
ejpam-6111	460	1	j.	j.	PROPN
ejpam-6111	460	2	pure	pure	PROPN
ejpam-6111	460	3	appl	appl	PROPN
ejpam-6111	460	4	.	.	PROPN
ejpam-6111	460	5	math	math	PROPN
ejpam-6111	460	6	,	,	PUNCT
ejpam-6111	460	7	18	18	NUM
ejpam-6111	460	8	(	(	PUNCT
ejpam-6111	460	9	2	2	NUM
ejpam-6111	460	10	)	)	PUNCT
ejpam-6111	460	11	(	(	PUNCT
ejpam-6111	460	12	2025	2025	NUM
ejpam-6111	460	13	)	)	PUNCT
ejpam-6111	460	14	,	,	PUNCT
ejpam-6111	460	15	6111	6111	NUM
ejpam-6111	460	16	21	21	NUM
ejpam-6111	460	17	of	of	ADP
ejpam-6111	460	18	25	25	NUM
ejpam-6111	460	19	figure	figure	NOUN
ejpam-6111	460	20	6	6	NUM
ejpam-6111	460	21	:	:	PUNCT
ejpam-6111	460	22	eigenmode	eigenmode	ADJ
ejpam-6111	460	23	(	(	PUNCT
ejpam-6111	460	24	left	left	ADJ
ejpam-6111	460	25	)	)	PUNCT
ejpam-6111	460	26	and	and	CCONJ
ejpam-6111	460	27	inverse	inverse	NOUN
ejpam-6111	460	28	of	of	ADP
ejpam-6111	460	29	resolvent	resolvent	ADJ
ejpam-6111	460	30	norm	norm	NOUN
ejpam-6111	460	31	(	(	PUNCT
ejpam-6111	460	32	right	right	NOUN
ejpam-6111	460	33	)	)	PUNCT
ejpam-6111	460	34	of	of	ADP
ejpam-6111	460	35	50	50	NUM
ejpam-6111	460	36	dimensional	dimensional	ADJ
ejpam-6111	460	37	haar	haar	NOUN
ejpam-6111	460	38	matrix	matrix	NOUN
ejpam-6111	460	39	in	in	ADP
ejpam-6111	460	40	example-3	example-3	NUM
ejpam-6111	460	41	figure	figure	NOUN
ejpam-6111	460	42	7	7	NUM
ejpam-6111	460	43	:	:	PUNCT
ejpam-6111	460	44	eigenmode	eigenmode	ADJ
ejpam-6111	460	45	(	(	PUNCT
ejpam-6111	460	46	left	left	ADJ
ejpam-6111	460	47	)	)	PUNCT
ejpam-6111	460	48	and	and	CCONJ
ejpam-6111	460	49	inverse	inverse	NOUN
ejpam-6111	460	50	of	of	ADP
ejpam-6111	460	51	resolvent	resolvent	ADJ
ejpam-6111	460	52	norm	norm	NOUN
ejpam-6111	460	53	(	(	PUNCT
ejpam-6111	460	54	right	right	NOUN
ejpam-6111	460	55	)	)	PUNCT
ejpam-6111	460	56	of	of	ADP
ejpam-6111	460	57	100	100	NUM
ejpam-6111	460	58	dimensional	dimensional	ADJ
ejpam-6111	460	59	haar	haar	NOUN
ejpam-6111	460	60	matrix	matrix	NOUN
ejpam-6111	460	61	in	in	ADP
ejpam-6111	460	62	example-3	example-3	NUM
ejpam-6111	460	63	figure	figure	NOUN
ejpam-6111	460	64	8	8	NUM
ejpam-6111	460	65	:	:	PUNCT
ejpam-6111	460	66	eigenmode	eigenmode	PROPN
ejpam-6111	460	67	(	(	PUNCT
ejpam-6111	460	68	left	left	ADJ
ejpam-6111	460	69	)	)	PUNCT
ejpam-6111	460	70	and	and	CCONJ
ejpam-6111	460	71	inverse	inverse	NOUN
ejpam-6111	460	72	of	of	ADP
ejpam-6111	460	73	resolvent	resolvent	ADJ
ejpam-6111	460	74	norm	norm	NOUN
ejpam-6111	460	75	(	(	PUNCT
ejpam-6111	460	76	right	right	NOUN
ejpam-6111	460	77	)	)	PUNCT
ejpam-6111	460	78	of	of	ADP
ejpam-6111	460	79	200	200	NUM
ejpam-6111	460	80	dimensional	dimensional	ADJ
ejpam-6111	460	81	haar	haar	NOUN
ejpam-6111	460	82	matrix	matrix	NOUN
ejpam-6111	460	83	in	in	ADP
ejpam-6111	460	84	example-3	example-3	PROPN
ejpam-6111	460	85	s.	s.	PROPN
ejpam-6111	460	86	mazhar	mazhar	PROPN
ejpam-6111	460	87	,	,	PUNCT
ejpam-6111	460	88	m.	m.	NOUN
ejpam-6111	460	89	u.	u.	PROPN
ejpam-6111	460	90	rehman	rehman	PROPN
ejpam-6111	460	91	/	/	SYM
ejpam-6111	460	92	eur	eur	PROPN
ejpam-6111	460	93	.	.	PUNCT
ejpam-6111	461	1	j.	j.	PROPN
ejpam-6111	461	2	pure	pure	PROPN
ejpam-6111	461	3	appl	appl	PROPN
ejpam-6111	461	4	.	.	PROPN
ejpam-6111	461	5	math	math	PROPN
ejpam-6111	461	6	,	,	PUNCT
ejpam-6111	461	7	18	18	NUM
ejpam-6111	461	8	(	(	PUNCT
ejpam-6111	461	9	2	2	NUM
ejpam-6111	461	10	)	)	PUNCT
ejpam-6111	461	11	(	(	PUNCT
ejpam-6111	461	12	2025	2025	NUM
ejpam-6111	461	13	)	)	PUNCT
ejpam-6111	461	14	,	,	PUNCT
ejpam-6111	461	15	6111	6111	NUM
ejpam-6111	461	16	22	22	NUM
ejpam-6111	461	17	of	of	ADP
ejpam-6111	461	18	25	25	NUM
ejpam-6111	461	19	7	7	NUM
ejpam-6111	461	20	.	.	PUNCT
ejpam-6111	461	21	conclusion	conclusion	NOUN
ejpam-6111	461	22	in	in	ADP
ejpam-6111	461	23	this	this	DET
ejpam-6111	461	24	article	article	NOUN
ejpam-6111	462	1	,	,	PUNCT
ejpam-6111	462	2	we	we	PRON
ejpam-6111	462	3	have	have	AUX
ejpam-6111	462	4	presented	present	VERB
ejpam-6111	462	5	new	new	ADJ
ejpam-6111	462	6	results	result	NOUN
ejpam-6111	462	7	on	on	ADP
ejpam-6111	462	8	d	d	NOUN
ejpam-6111	462	9	-	-	NOUN
ejpam-6111	462	10	stability	stability	NOUN
ejpam-6111	462	11	and	and	CCONJ
ejpam-6111	462	12	strong	strong	ADJ
ejpam-6111	462	13	d	d	NOUN
ejpam-6111	462	14	-	-	NOUN
ejpam-6111	462	15	stability	stability	NOUN
ejpam-6111	462	16	for	for	ADP
ejpam-6111	462	17	the	the	DET
ejpam-6111	462	18	structured	structured	ADJ
ejpam-6111	462	19	matrix	matrix	NOUN
ejpam-6111	462	20	of	of	ADP
ejpam-6111	462	21	the	the	DET
ejpam-6111	462	22	form	form	NOUN
ejpam-6111	462	23	(	(	PUNCT
ejpam-6111	462	24	in−a⊗p	in−a⊗p	PROPN
ejpam-6111	462	25	t	t	NOUN
ejpam-6111	462	26	)	)	PUNCT
ejpam-6111	462	27	,	,	PUNCT
ejpam-6111	462	28	where	where	SCONJ
ejpam-6111	462	29	in	in	ADP
ejpam-6111	462	30	is	be	AUX
ejpam-6111	462	31	an	an	DET
ejpam-6111	462	32	n×n	n×n	PROPN
ejpam-6111	462	33	identity	identity	NOUN
ejpam-6111	462	34	matrix	matrix	NOUN
ejpam-6111	462	35	and	and	CCONJ
ejpam-6111	462	36	the	the	DET
ejpam-6111	462	37	matrices	matrix	NOUN
ejpam-6111	462	38	a	a	PRON
ejpam-6111	462	39	and	and	CCONJ
ejpam-6111	462	40	p	p	NOUN
ejpam-6111	462	41	correspond	correspond	NOUN
ejpam-6111	462	42	to	to	ADP
ejpam-6111	462	43	the	the	DET
ejpam-6111	462	44	following	follow	VERB
ejpam-6111	462	45	lumped	lump	VERB
ejpam-6111	462	46	-	-	PUNCT
ejpam-6111	462	47	parameter	parameter	NOUN
ejpam-6111	462	48	dynamical	dynamical	ADJ
ejpam-6111	462	49	system	system	NOUN
ejpam-6111	462	50	.	.	PUNCT
ejpam-6111	463	1	our	our	PRON
ejpam-6111	463	2	proposed	propose	VERB
ejpam-6111	463	3	methodology	methodology	NOUN
ejpam-6111	463	4	is	be	AUX
ejpam-6111	463	5	based	base	VERB
ejpam-6111	463	6	on	on	ADP
ejpam-6111	463	7	the	the	DET
ejpam-6111	463	8	collection	collection	NOUN
ejpam-6111	463	9	of	of	ADP
ejpam-6111	463	10	various	various	ADJ
ejpam-6111	463	11	tools	tool	NOUN
ejpam-6111	463	12	from	from	ADP
ejpam-6111	463	13	linear	linear	PROPN
ejpam-6111	463	14	algebra	algebra	NOUN
ejpam-6111	463	15	,	,	PUNCT
ejpam-6111	463	16	matrix	matrix	NOUN
ejpam-6111	463	17	analysis	analysis	NOUN
ejpam-6111	463	18	and	and	CCONJ
ejpam-6111	463	19	system	system	NOUN
ejpam-6111	463	20	theory	theory	NOUN
ejpam-6111	463	21	.	.	PUNCT
ejpam-6111	464	1	the	the	DET
ejpam-6111	464	2	analytical	analytical	ADJ
ejpam-6111	464	3	and	and	CCONJ
ejpam-6111	464	4	numerical	numerical	ADJ
ejpam-6111	464	5	results	result	NOUN
ejpam-6111	464	6	on	on	ADP
ejpam-6111	464	7	d	d	NOUN
ejpam-6111	464	8	-	-	NOUN
ejpam-6111	464	9	stability	stability	NOUN
ejpam-6111	464	10	,	,	PUNCT
ejpam-6111	464	11	strong	strong	ADJ
ejpam-6111	464	12	d	d	NOUN
ejpam-6111	464	13	-	-	NOUN
ejpam-6111	464	14	stability	stability	NOUN
ejpam-6111	464	15	,	,	PUNCT
ejpam-6111	464	16	spectrum	spectrum	NOUN
ejpam-6111	464	17	and	and	CCONJ
ejpam-6111	464	18	pseudo	pseudo	NOUN
ejpam-6111	464	19	-	-	NOUN
ejpam-6111	464	20	spectrum	spectrum	NOUN
ejpam-6111	464	21	are	be	AUX
ejpam-6111	464	22	obtained	obtain	VERB
ejpam-6111	464	23	by	by	ADP
ejpam-6111	464	24	interconnecting	interconnect	VERB
ejpam-6111	464	25	the	the	DET
ejpam-6111	464	26	concepts	concept	NOUN
ejpam-6111	464	27	from	from	ADP
ejpam-6111	464	28	d	d	ADJ
ejpam-6111	464	29	-	-	PUNCT
ejpam-6111	464	30	stability	stability	NOUN
ejpam-6111	464	31	theory	theory	NOUN
ejpam-6111	464	32	and	and	CCONJ
ejpam-6111	464	33	µ-theory	µ-theory	NOUN
ejpam-6111	464	34	.	.	PUNCT
ejpam-6111	465	1	in	in	ADP
ejpam-6111	465	2	order	order	NOUN
ejpam-6111	465	3	to	to	PART
ejpam-6111	465	4	further	far	ADV
ejpam-6111	465	5	advance	advance	VERB
ejpam-6111	465	6	the	the	DET
ejpam-6111	465	7	understanding	understanding	NOUN
ejpam-6111	465	8	of	of	ADP
ejpam-6111	465	9	d	d	ADJ
ejpam-6111	465	10	-	-	NOUN
ejpam-6111	465	11	stability	stability	NOUN
ejpam-6111	465	12	analysis	analysis	NOUN
ejpam-6111	465	13	for	for	ADP
ejpam-6111	465	14	the	the	DET
ejpam-6111	465	15	lumped	lump	VERB
ejpam-6111	465	16	parameter	parameter	NOUN
ejpam-6111	465	17	dynamical	dynamical	ADJ
ejpam-6111	465	18	systems	system	NOUN
ejpam-6111	465	19	,	,	PUNCT
ejpam-6111	465	20	our	our	PRON
ejpam-6111	465	21	future	future	ADJ
ejpam-6111	465	22	research	research	NOUN
ejpam-6111	465	23	aim	aim	NOUN
ejpam-6111	465	24	is	be	AUX
ejpam-6111	465	25	to	to	PART
ejpam-6111	465	26	develop	develop	VERB
ejpam-6111	465	27	a	a	DET
ejpam-6111	465	28	comprehensive	comprehensive	ADJ
ejpam-6111	465	29	lumped	lump	VERB
ejpam-6111	465	30	-	-	PUNCT
ejpam-6111	465	31	parameter	parameter	NOUN
ejpam-6111	465	32	models	model	NOUN
ejpam-6111	465	33	for	for	ADP
ejpam-6111	465	34	the	the	DET
ejpam-6111	465	35	stability	stability	NOUN
ejpam-6111	465	36	,	,	PUNCT
ejpam-6111	465	37	h	h	NOUN
ejpam-6111	465	38	-	-	PUNCT
ejpam-6111	465	39	stable	stable	ADJ
ejpam-6111	465	40	,	,	PUNCT
ejpam-6111	465	41	d(α)-stable	d(α)-stable	PROPN
ejpam-6111	465	42	,	,	PUNCT
ejpam-6111	465	43	and	and	CCONJ
ejpam-6111	465	44	d	d	ADJ
ejpam-6111	465	45	-	-	ADJ
ejpam-6111	465	46	semistable	semistable	ADJ
ejpam-6111	465	47	matrices	matrix	NOUN
ejpam-6111	465	48	.	.	PUNCT
ejpam-6111	466	1	conflicts	conflict	NOUN
ejpam-6111	466	2	of	of	ADP
ejpam-6111	466	3	interest	interest	NOUN
ejpam-6111	466	4	the	the	DET
ejpam-6111	466	5	authors	author	NOUN
ejpam-6111	466	6	declare	declare	VERB
ejpam-6111	466	7	that	that	SCONJ
ejpam-6111	466	8	there	there	PRON
ejpam-6111	466	9	are	be	VERB
ejpam-6111	466	10	no	no	DET
ejpam-6111	466	11	conflicts	conflict	NOUN
ejpam-6111	466	12	of	of	ADP
ejpam-6111	466	13	interest	interest	NOUN
ejpam-6111	466	14	regarding	regard	VERB
ejpam-6111	466	15	the	the	DET
ejpam-6111	466	16	publication	publication	NOUN
ejpam-6111	466	17	of	of	ADP
ejpam-6111	466	18	this	this	DET
ejpam-6111	466	19	paper	paper	NOUN
ejpam-6111	466	20	.	.	PUNCT
ejpam-6111	467	1	references	reference	NOUN
ejpam-6111	467	2	[	[	X
ejpam-6111	467	3	1	1	NUM
ejpam-6111	467	4	]	]	X
ejpam-6111	467	5	chi	chi	PROPN
ejpam-6111	467	6	fan	fan	PROPN
ejpam-6111	467	7	chen	chen	PROPN
ejpam-6111	467	8	and	and	CCONJ
ejpam-6111	467	9	chi	chi	PROPN
ejpam-6111	467	10	-	-	PUNCT
ejpam-6111	467	11	huang	huang	PROPN
ejpam-6111	467	12	hsiao	hsiao	PROPN
ejpam-6111	467	13	.	.	PROPN
ejpam-6111	467	14	haar	haar	PROPN
ejpam-6111	467	15	wavelet	wavelet	PROPN
ejpam-6111	467	16	method	method	NOUN
ejpam-6111	467	17	for	for	ADP
ejpam-6111	467	18	solving	solve	VERB
ejpam-6111	467	19	lumped	lump	VERB
ejpam-6111	467	20	and	and	CCONJ
ejpam-6111	467	21	distributed	distribute	VERB
ejpam-6111	467	22	-	-	PUNCT
ejpam-6111	467	23	parameter	parameter	NOUN
ejpam-6111	467	24	systems	system	NOUN
ejpam-6111	467	25	.	.	PUNCT
ejpam-6111	468	1	iee	iee	PROPN
ejpam-6111	468	2	proceedings	proceedings	PROPN
ejpam-6111	468	3	-	-	PUNCT
ejpam-6111	468	4	control	control	NOUN
ejpam-6111	468	5	theory	theory	NOUN
ejpam-6111	468	6	and	and	CCONJ
ejpam-6111	468	7	applications	application	NOUN
ejpam-6111	468	8	,	,	PUNCT
ejpam-6111	468	9	144(1):87–94	144(1):87–94	NOUN
ejpam-6111	468	10	,	,	PUNCT
ejpam-6111	468	11	1997	1997	NUM
ejpam-6111	468	12	.	.	PUNCT
ejpam-6111	469	1	[	[	X
ejpam-6111	469	2	2	2	NUM
ejpam-6111	469	3	]	]	X
ejpam-6111	469	4	chun	chun	PROPN
ejpam-6111	469	5	-	-	PUNCT
ejpam-6111	469	6	hui	hui	PROPN
ejpam-6111	469	7	hsiao	hsiao	PROPN
ejpam-6111	469	8	.	.	PUNCT
ejpam-6111	470	1	state	state	NOUN
ejpam-6111	470	2	analysis	analysis	NOUN
ejpam-6111	470	3	of	of	ADP
ejpam-6111	470	4	linear	linear	ADJ
ejpam-6111	470	5	time	time	NOUN
ejpam-6111	470	6	delayed	delay	VERB
ejpam-6111	470	7	systems	system	NOUN
ejpam-6111	470	8	via	via	ADP
ejpam-6111	470	9	haar	haar	PROPN
ejpam-6111	470	10	wavelets	wavelet	NOUN
ejpam-6111	470	11	.	.	PUNCT
ejpam-6111	471	1	mathematics	mathematic	NOUN
ejpam-6111	471	2	and	and	CCONJ
ejpam-6111	471	3	computers	computer	NOUN
ejpam-6111	471	4	in	in	ADP
ejpam-6111	471	5	simulation	simulation	NOUN
ejpam-6111	471	6	,	,	PUNCT
ejpam-6111	471	7	44(5):457–470	44(5):457–470	PROPN
ejpam-6111	471	8	,	,	PUNCT
ejpam-6111	471	9	1997	1997	NUM
ejpam-6111	471	10	.	.	PUNCT
ejpam-6111	472	1	[	[	X
ejpam-6111	472	2	3	3	X
ejpam-6111	472	3	]	]	X
ejpam-6111	472	4	cf	cf	NOUN
ejpam-6111	472	5	chen	chen	PROPN
ejpam-6111	472	6	and	and	CCONJ
ejpam-6111	472	7	ch	ch	PROPN
ejpam-6111	472	8	hsiao	hsiao	PROPN
ejpam-6111	472	9	.	.	PUNCT
ejpam-6111	473	1	a	a	DET
ejpam-6111	473	2	state	state	NOUN
ejpam-6111	473	3	-	-	PUNCT
ejpam-6111	473	4	space	space	NOUN
ejpam-6111	473	5	approach	approach	NOUN
ejpam-6111	473	6	to	to	ADP
ejpam-6111	473	7	walsh	walsh	PROPN
ejpam-6111	473	8	series	series	PROPN
ejpam-6111	473	9	solution	solution	NOUN
ejpam-6111	473	10	of	of	ADP
ejpam-6111	473	11	linear	linear	PROPN
ejpam-6111	473	12	systems	system	NOUN
ejpam-6111	473	13	.	.	PUNCT
ejpam-6111	474	1	international	international	ADJ
ejpam-6111	474	2	journal	journal	PROPN
ejpam-6111	474	3	of	of	ADP
ejpam-6111	474	4	systems	system	NOUN
ejpam-6111	474	5	science	science	NOUN
ejpam-6111	474	6	,	,	PUNCT
ejpam-6111	474	7	6(9):833–858	6(9):833–858	NOUN
ejpam-6111	474	8	,	,	PUNCT
ejpam-6111	474	9	1975	1975	NUM
ejpam-6111	474	10	.	.	PUNCT
ejpam-6111	475	1	[	[	X
ejpam-6111	475	2	4	4	X
ejpam-6111	475	3	]	]	X
ejpam-6111	475	4	cf	cf	NOUN
ejpam-6111	475	5	cheng	cheng	PROPN
ejpam-6111	475	6	,	,	PUNCT
ejpam-6111	475	7	yt	yt	PROPN
ejpam-6111	475	8	tsay	tsay	PROPN
ejpam-6111	475	9	,	,	PUNCT
ejpam-6111	475	10	and	and	CCONJ
ejpam-6111	475	11	tt	tt	PROPN
ejpam-6111	475	12	wu	wu	PROPN
ejpam-6111	475	13	.	.	PUNCT
ejpam-6111	476	1	walsh	walsh	PROPN
ejpam-6111	476	2	operational	operational	ADJ
ejpam-6111	476	3	matrices	matrix	NOUN
ejpam-6111	476	4	for	for	ADP
ejpam-6111	476	5	fractional	fractional	ADJ
ejpam-6111	476	6	calculus	calculus	NOUN
ejpam-6111	476	7	and	and	CCONJ
ejpam-6111	476	8	their	their	PRON
ejpam-6111	476	9	application	application	NOUN
ejpam-6111	476	10	to	to	ADP
ejpam-6111	476	11	distributed	distribute	VERB
ejpam-6111	476	12	systems	system	NOUN
ejpam-6111	476	13	.	.	PUNCT
ejpam-6111	477	1	journal	journal	NOUN
ejpam-6111	477	2	of	of	ADP
ejpam-6111	477	3	the	the	DET
ejpam-6111	477	4	franklin	franklin	PROPN
ejpam-6111	477	5	institute	institute	PROPN
ejpam-6111	477	6	,	,	PUNCT
ejpam-6111	477	7	303(3):267–284	303(3):267–284	PROPN
ejpam-6111	477	8	,	,	PUNCT
ejpam-6111	477	9	1977	1977	NUM
ejpam-6111	477	10	.	.	PUNCT
ejpam-6111	478	1	[	[	X
ejpam-6111	478	2	5	5	X
ejpam-6111	478	3	]	]	X
ejpam-6111	478	4	chyi	chyi	PROPN
ejpam-6111	478	5	hwang	hwang	PROPN
ejpam-6111	478	6	and	and	CCONJ
ejpam-6111	478	7	yen	yen	NOUN
ejpam-6111	478	8	-	-	PUNCT
ejpam-6111	478	9	ping	ping	NOUN
ejpam-6111	478	10	shih	shih	NOUN
ejpam-6111	478	11	.	.	PUNCT
ejpam-6111	479	1	laguerre	laguerre	PROPN
ejpam-6111	479	2	operational	operational	ADJ
ejpam-6111	479	3	matrices	matrix	NOUN
ejpam-6111	479	4	for	for	ADP
ejpam-6111	479	5	fractional	fractional	ADJ
ejpam-6111	479	6	calculus	calculus	NOUN
ejpam-6111	479	7	and	and	CCONJ
ejpam-6111	479	8	applications	application	NOUN
ejpam-6111	479	9	.	.	PUNCT
ejpam-6111	480	1	international	international	ADJ
ejpam-6111	480	2	journal	journal	PROPN
ejpam-6111	480	3	of	of	ADP
ejpam-6111	480	4	control	control	PROPN
ejpam-6111	480	5	,	,	PUNCT
ejpam-6111	480	6	34(3):577–584	34(3):577–584	PROPN
ejpam-6111	480	7	,	,	PUNCT
ejpam-6111	480	8	1981	1981	NUM
ejpam-6111	480	9	.	.	PUNCT
ejpam-6111	481	1	[	[	X
ejpam-6111	481	2	6	6	NUM
ejpam-6111	481	3	]	]	SYM
ejpam-6111	481	4	re	re	ADP
ejpam-6111	481	5	king	king	NOUN
ejpam-6111	481	6	and	and	CCONJ
ejpam-6111	481	7	pn	pn	PROPN
ejpam-6111	481	8	paraskevopoulos	paraskevopoulo	NOUN
ejpam-6111	481	9	.	.	PUNCT
ejpam-6111	482	1	parametric	parametric	ADJ
ejpam-6111	482	2	identification	identification	NOUN
ejpam-6111	482	3	of	of	ADP
ejpam-6111	482	4	discrete	discrete	ADJ
ejpam-6111	482	5	-	-	PUNCT
ejpam-6111	482	6	time	time	NOUN
ejpam-6111	482	7	siso	siso	NOUN
ejpam-6111	482	8	systems	system	NOUN
ejpam-6111	482	9	.	.	PUNCT
ejpam-6111	483	1	international	international	ADJ
ejpam-6111	483	2	journal	journal	PROPN
ejpam-6111	483	3	of	of	ADP
ejpam-6111	483	4	control	control	PROPN
ejpam-6111	483	5	,	,	PUNCT
ejpam-6111	483	6	30(6):1023–1029	30(6):1023–1029	PROPN
ejpam-6111	483	7	,	,	PUNCT
ejpam-6111	483	8	1979	1979	NUM
ejpam-6111	483	9	.	.	PUNCT
ejpam-6111	484	1	[	[	X
ejpam-6111	484	2	7	7	X
ejpam-6111	484	3	]	]	X
ejpam-6111	484	4	rong	rong	PROPN
ejpam-6111	484	5	-	-	PUNCT
ejpam-6111	484	6	yeu	yeu	PROPN
ejpam-6111	484	7	chang	chang	PROPN
ejpam-6111	484	8	and	and	CCONJ
ejpam-6111	484	9	maw	maw	NOUN
ejpam-6111	484	10	-	-	PUNCT
ejpam-6111	484	11	ling	ling	PROPN
ejpam-6111	484	12	wang	wang	PROPN
ejpam-6111	484	13	.	.	PUNCT
ejpam-6111	485	1	legendre	legendre	PROPN
ejpam-6111	485	2	polynomials	polynomials	PROPN
ejpam-6111	485	3	approximation	approximation	NOUN
ejpam-6111	485	4	to	to	ADP
ejpam-6111	485	5	dynamic	dynamic	ADJ
ejpam-6111	485	6	linear	linear	ADJ
ejpam-6111	485	7	state	state	NOUN
ejpam-6111	485	8	equations	equation	NOUN
ejpam-6111	485	9	with	with	ADP
ejpam-6111	485	10	initial	initial	ADJ
ejpam-6111	485	11	or	or	CCONJ
ejpam-6111	485	12	boundary	boundary	ADJ
ejpam-6111	485	13	value	value	NOUN
ejpam-6111	485	14	conditions	condition	NOUN
ejpam-6111	485	15	.	.	PUNCT
ejpam-6111	486	1	international	international	ADJ
ejpam-6111	486	2	journal	journal	PROPN
ejpam-6111	486	3	of	of	ADP
ejpam-6111	486	4	control	control	PROPN
ejpam-6111	486	5	,	,	PUNCT
ejpam-6111	486	6	40(1):215–232	40(1):215–232	PROPN
ejpam-6111	486	7	,	,	PUNCT
ejpam-6111	486	8	1984	1984	NUM
ejpam-6111	486	9	.	.	PUNCT
ejpam-6111	487	1	[	[	X
ejpam-6111	487	2	8	8	NUM
ejpam-6111	487	3	]	]	X
ejpam-6111	487	4	pn	pn	NOUN
ejpam-6111	487	5	paraskevopoulos	paraskevopoulo	NOUN
ejpam-6111	487	6	.	.	PUNCT
ejpam-6111	488	1	chebyshev	chebyshev	PROPN
ejpam-6111	488	2	series	series	PROPN
ejpam-6111	488	3	approach	approach	NOUN
ejpam-6111	488	4	to	to	ADP
ejpam-6111	488	5	system	system	NOUN
ejpam-6111	488	6	identification	identification	NOUN
ejpam-6111	488	7	,	,	PUNCT
ejpam-6111	488	8	analysis	analysis	NOUN
ejpam-6111	488	9	and	and	CCONJ
ejpam-6111	488	10	optimal	optimal	ADJ
ejpam-6111	488	11	control	control	NOUN
ejpam-6111	488	12	.	.	PUNCT
ejpam-6111	489	1	journal	journal	NOUN
ejpam-6111	489	2	of	of	ADP
ejpam-6111	489	3	the	the	DET
ejpam-6111	489	4	franklin	franklin	PROPN
ejpam-6111	489	5	institute	institute	PROPN
ejpam-6111	489	6	,	,	PUNCT
ejpam-6111	489	7	316(2):135–157	316(2):135–157	PROPN
ejpam-6111	489	8	,	,	PUNCT
ejpam-6111	489	9	1983	1983	NUM
ejpam-6111	489	10	.	.	PUNCT
ejpam-6111	490	1	[	[	X
ejpam-6111	490	2	9	9	NUM
ejpam-6111	490	3	]	]	X
ejpam-6111	490	4	pn	pn	NOUN
ejpam-6111	490	5	paraskevopoulos	paraskevopoulos	PROPN
ejpam-6111	490	6	,	,	PUNCT
ejpam-6111	490	7	pd	pd	PROPN
ejpam-6111	490	8	sparis	sparis	NOUN
ejpam-6111	490	9	,	,	PUNCT
ejpam-6111	490	10	and	and	CCONJ
ejpam-6111	490	11	sg	sg	ADP
ejpam-6111	490	12	mouroutsos	mouroutsos	NOUN
ejpam-6111	490	13	.	.	PUNCT
ejpam-6111	491	1	the	the	DET
ejpam-6111	491	2	fourier	fourier	PROPN
ejpam-6111	491	3	series	series	PROPN
ejpam-6111	491	4	operational	operational	ADJ
ejpam-6111	491	5	matrix	matrix	NOUN
ejpam-6111	491	6	of	of	ADP
ejpam-6111	491	7	integration	integration	NOUN
ejpam-6111	491	8	.	.	PUNCT
ejpam-6111	492	1	international	international	ADJ
ejpam-6111	492	2	journal	journal	PROPN
ejpam-6111	492	3	of	of	ADP
ejpam-6111	492	4	systems	system	NOUN
ejpam-6111	492	5	science	science	NOUN
ejpam-6111	492	6	,	,	PUNCT
ejpam-6111	492	7	16(2):171–176	16(2):171–176	PROPN
ejpam-6111	492	8	,	,	PUNCT
ejpam-6111	492	9	1985	1985	NUM
ejpam-6111	492	10	.	.	PUNCT
ejpam-6111	493	1	[	[	X
ejpam-6111	493	2	10	10	NUM
ejpam-6111	493	3	]	]	X
ejpam-6111	493	4	sudhir	sudhir	PROPN
ejpam-6111	493	5	j	j	PROPN
ejpam-6111	493	6	shah	shah	PROPN
ejpam-6111	493	7	andwalter	andwalter	PROPN
ejpam-6111	493	8	d	d	X
ejpam-6111	493	9	pilkey	pilkey	PROPN
ejpam-6111	493	10	.	.	PUNCT
ejpam-6111	493	11	lumped	lump	VERB
ejpam-6111	493	12	-	-	PUNCT
ejpam-6111	493	13	parameter	parameter	NOUN
ejpam-6111	493	14	approach	approach	NOUN
ejpam-6111	493	15	to	to	ADP
ejpam-6111	493	16	stability	stability	NOUN
ejpam-6111	493	17	analysis	analysis	NOUN
ejpam-6111	493	18	.	.	PUNCT
ejpam-6111	494	1	journal	journal	NOUN
ejpam-6111	494	2	of	of	ADP
ejpam-6111	494	3	engineering	engineering	NOUN
ejpam-6111	494	4	mechanics	mechanic	NOUN
ejpam-6111	494	5	,	,	PUNCT
ejpam-6111	494	6	119(10):2109–2129	119(10):2109–2129	NUM
ejpam-6111	494	7	,	,	PUNCT
ejpam-6111	494	8	1993	1993	NUM
ejpam-6111	494	9	.	.	PUNCT
ejpam-6111	495	1	s.	s.	PROPN
ejpam-6111	495	2	mazhar	mazhar	PROPN
ejpam-6111	495	3	,	,	PUNCT
ejpam-6111	495	4	m.	m.	NOUN
ejpam-6111	495	5	u.	u.	PROPN
ejpam-6111	495	6	rehman	rehman	PROPN
ejpam-6111	495	7	/	/	SYM
ejpam-6111	495	8	eur	eur	PROPN
ejpam-6111	495	9	.	.	PUNCT
ejpam-6111	496	1	j.	j.	PROPN
ejpam-6111	496	2	pure	pure	PROPN
ejpam-6111	496	3	appl	appl	PROPN
ejpam-6111	496	4	.	.	PROPN
ejpam-6111	496	5	math	math	PROPN
ejpam-6111	496	6	,	,	PUNCT
ejpam-6111	496	7	18	18	NUM
ejpam-6111	496	8	(	(	PUNCT
ejpam-6111	496	9	2	2	NUM
ejpam-6111	496	10	)	)	PUNCT
ejpam-6111	496	11	(	(	PUNCT
ejpam-6111	496	12	2025	2025	NUM
ejpam-6111	496	13	)	)	PUNCT
ejpam-6111	496	14	,	,	PUNCT
ejpam-6111	496	15	6111	6111	NUM
ejpam-6111	496	16	23	23	NUM
ejpam-6111	496	17	of	of	ADP
ejpam-6111	496	18	25	25	NUM
ejpam-6111	497	1	[	[	SYM
ejpam-6111	497	2	11	11	NUM
ejpam-6111	497	3	]	]	X
ejpam-6111	497	4	farah	farah	PROPN
ejpam-6111	497	5	m	m	PROPN
ejpam-6111	497	6	al	al	PROPN
ejpam-6111	497	7	-	-	PUNCT
ejpam-6111	497	8	askar	askar	PROPN
ejpam-6111	497	9	,	,	PUNCT
ejpam-6111	497	10	clemente	clemente	PROPN
ejpam-6111	497	11	cesarano	cesarano	PROPN
ejpam-6111	497	12	,	,	PUNCT
ejpam-6111	497	13	and	and	CCONJ
ejpam-6111	497	14	wael	wael	PROPN
ejpam-6111	497	15	w	w	PROPN
ejpam-6111	497	16	mohammed	mohammed	PROPN
ejpam-6111	497	17	.	.	PUNCT
ejpam-6111	498	1	multiplicative	multiplicative	ADJ
ejpam-6111	498	2	brownian	brownian	ADJ
ejpam-6111	498	3	motion	motion	NOUN
ejpam-6111	498	4	stabilizes	stabilize	VERB
ejpam-6111	498	5	the	the	DET
ejpam-6111	498	6	exact	exact	ADJ
ejpam-6111	498	7	stochastic	stochastic	ADJ
ejpam-6111	498	8	solutions	solution	NOUN
ejpam-6111	498	9	of	of	ADP
ejpam-6111	498	10	the	the	DET
ejpam-6111	498	11	davey	davey	NOUN
ejpam-6111	498	12	–	–	PUNCT
ejpam-6111	498	13	stewartson	stewartson	NOUN
ejpam-6111	498	14	equations	equation	NOUN
ejpam-6111	498	15	.	.	PUNCT
ejpam-6111	499	1	symmetry	symmetry	PROPN
ejpam-6111	499	2	,	,	PUNCT
ejpam-6111	499	3	14(10):2176	14(10):2176	NUM
ejpam-6111	499	4	,	,	PUNCT
ejpam-6111	499	5	2022	2022	NUM
ejpam-6111	499	6	.	.	PUNCT
ejpam-6111	500	1	[	[	X
ejpam-6111	500	2	12	12	NUM
ejpam-6111	500	3	]	]	X
ejpam-6111	500	4	wael	wael	PROPN
ejpam-6111	500	5	w	w	PROPN
ejpam-6111	500	6	mohammed	mohammed	PROPN
ejpam-6111	500	7	,	,	PUNCT
ejpam-6111	500	8	clemente	clemente	PROPN
ejpam-6111	500	9	cesarano	cesarano	PROPN
ejpam-6111	500	10	,	,	PUNCT
ejpam-6111	500	11	and	and	CCONJ
ejpam-6111	500	12	farah	farah	PROPN
ejpam-6111	500	13	m	m	PROPN
ejpam-6111	500	14	al	al	PROPN
ejpam-6111	500	15	-	-	PUNCT
ejpam-6111	500	16	askar	askar	NOUN
ejpam-6111	500	17	.	.	PUNCT
ejpam-6111	501	1	solutions	solution	NOUN
ejpam-6111	501	2	to	to	ADP
ejpam-6111	501	3	the	the	DET
ejpam-6111	501	4	(	(	PUNCT
ejpam-6111	501	5	4	4	NUM
ejpam-6111	501	6	+	+	NUM
ejpam-6111	501	7	1)-dimensional	1)-dimensional	NUM
ejpam-6111	501	8	time	time	NOUN
ejpam-6111	501	9	-	-	PUNCT
ejpam-6111	501	10	fractional	fractional	ADJ
ejpam-6111	501	11	fokas	fokas	ADJ
ejpam-6111	501	12	equation	equation	NOUN
ejpam-6111	501	13	with	with	ADP
ejpam-6111	501	14	m	m	ADJ
ejpam-6111	501	15	-	-	PUNCT
ejpam-6111	501	16	truncated	truncate	VERB
ejpam-6111	501	17	derivative	derivative	NOUN
ejpam-6111	501	18	.	.	PUNCT
ejpam-6111	502	1	mathematics	mathematic	NOUN
ejpam-6111	502	2	,	,	PUNCT
ejpam-6111	502	3	11(1):194	11(1):194	NUM
ejpam-6111	502	4	,	,	PUNCT
ejpam-6111	502	5	2022	2022	NUM
ejpam-6111	502	6	.	.	PUNCT
ejpam-6111	503	1	[	[	X
ejpam-6111	503	2	13	13	NUM
ejpam-6111	503	3	]	]	X
ejpam-6111	503	4	walter	walter	NOUN
ejpam-6111	503	5	d	d	PROPN
ejpam-6111	503	6	pilkey	pilkey	PROPN
ejpam-6111	503	7	and	and	CCONJ
ejpam-6111	503	8	kevin	kevin	PROPN
ejpam-6111	503	9	j	j	PROPN
ejpam-6111	503	10	o’connor	o’connor	ADV
ejpam-6111	503	11	.	.	PUNCT
ejpam-6111	504	1	lumped	lump	VERB
ejpam-6111	504	2	parameter	parameter	NOUN
ejpam-6111	504	3	model	model	NOUN
ejpam-6111	504	4	for	for	ADP
ejpam-6111	504	5	stability	stability	NOUN
ejpam-6111	504	6	analysis	analysis	NOUN
ejpam-6111	504	7	.	.	PUNCT
ejpam-6111	505	1	journal	journal	NOUN
ejpam-6111	505	2	of	of	ADP
ejpam-6111	505	3	the	the	DET
ejpam-6111	505	4	structural	structural	ADJ
ejpam-6111	505	5	division	division	NOUN
ejpam-6111	505	6	,	,	PUNCT
ejpam-6111	505	7	99(7):1702–1707	99(7):1702–1707	PROPN
ejpam-6111	505	8	,	,	PUNCT
ejpam-6111	505	9	1973	1973	NUM
ejpam-6111	505	10	.	.	PUNCT
ejpam-6111	506	1	[	[	X
ejpam-6111	506	2	14	14	NUM
ejpam-6111	506	3	]	]	X
ejpam-6111	506	4	george	george	PROPN
ejpam-6111	506	5	johnson	johnson	PROPN
ejpam-6111	506	6	and	and	CCONJ
ejpam-6111	506	7	walter	walter	PROPN
ejpam-6111	506	8	pilkey	pilkey	PROPN
ejpam-6111	506	9	.	.	PUNCT
ejpam-6111	507	1	lumped	lump	VERB
ejpam-6111	507	2	parameter	parameter	NOUN
ejpam-6111	507	3	circular	circular	ADJ
ejpam-6111	507	4	plate	plate	NOUN
ejpam-6111	507	5	stability	stability	NOUN
ejpam-6111	507	6	analysis	analysis	NOUN
ejpam-6111	507	7	.	.	PUNCT
ejpam-6111	508	1	journal	journal	NOUN
ejpam-6111	508	2	of	of	ADP
ejpam-6111	508	3	the	the	DET
ejpam-6111	508	4	structural	structural	ADJ
ejpam-6111	508	5	division	division	NOUN
ejpam-6111	508	6	,	,	PUNCT
ejpam-6111	508	7	102(5):1135–1140	102(5):1135–1140	NUM
ejpam-6111	508	8	,	,	PUNCT
ejpam-6111	508	9	1976	1976	NUM
ejpam-6111	508	10	.	.	PUNCT
ejpam-6111	509	1	[	[	X
ejpam-6111	509	2	15	15	NUM
ejpam-6111	509	3	]	]	X
ejpam-6111	509	4	andrew	andrew	PROPN
ejpam-6111	509	5	packard	packard	PROPN
ejpam-6111	509	6	and	and	CCONJ
ejpam-6111	509	7	john	john	PROPN
ejpam-6111	509	8	doyle	doyle	PROPN
ejpam-6111	509	9	.	.	PUNCT
ejpam-6111	510	1	the	the	DET
ejpam-6111	510	2	complex	complex	ADJ
ejpam-6111	510	3	structured	structured	ADJ
ejpam-6111	510	4	singular	singular	ADJ
ejpam-6111	510	5	value	value	NOUN
ejpam-6111	510	6	.	.	PUNCT
ejpam-6111	511	1	automatica	automatica	PROPN
ejpam-6111	511	2	,	,	PUNCT
ejpam-6111	511	3	29(1):71–109	29(1):71–109	NUM
ejpam-6111	511	4	,	,	PUNCT
ejpam-6111	511	5	1993	1993	NUM
ejpam-6111	511	6	.	.	PUNCT
ejpam-6111	512	1	[	[	X
ejpam-6111	512	2	16	16	NUM
ejpam-6111	512	3	]	]	X
ejpam-6111	512	4	richard	richard	PROPN
ejpam-6111	512	5	p	p	PROPN
ejpam-6111	512	6	braatz	braatz	PROPN
ejpam-6111	512	7	,	,	PUNCT
ejpam-6111	512	8	peter	peter	PROPN
ejpam-6111	512	9	michael	michael	PROPN
ejpam-6111	512	10	young	young	PROPN
ejpam-6111	512	11	,	,	PUNCT
ejpam-6111	512	12	john	john	PROPN
ejpam-6111	512	13	c	c	PROPN
ejpam-6111	512	14	doyle	doyle	PROPN
ejpam-6111	512	15	,	,	PUNCT
ejpam-6111	512	16	and	and	CCONJ
ejpam-6111	512	17	manfred	manfre	VERB
ejpam-6111	512	18	morari	morari	PROPN
ejpam-6111	512	19	.	.	PUNCT
ejpam-6111	513	1	computational	computational	ADJ
ejpam-6111	513	2	complexity	complexity	NOUN
ejpam-6111	513	3	of	of	ADP
ejpam-6111	513	4	/	/	SYM
ejpam-6111	513	5	spl	spl	PROPN
ejpam-6111	513	6	mu	mu	PROPN
ejpam-6111	513	7	/	/	SYM
ejpam-6111	513	8	calculation	calculation	NOUN
ejpam-6111	513	9	.	.	PUNCT
ejpam-6111	514	1	ieee	ieee	NOUN
ejpam-6111	514	2	transactions	transaction	NOUN
ejpam-6111	514	3	on	on	ADP
ejpam-6111	514	4	automatic	automatic	ADJ
ejpam-6111	514	5	control	control	NOUN
ejpam-6111	514	6	,	,	PUNCT
ejpam-6111	514	7	39(5):1000–1002	39(5):1000–1002	NUM
ejpam-6111	514	8	,	,	PUNCT
ejpam-6111	514	9	1994	1994	NUM
ejpam-6111	514	10	.	.	PUNCT
ejpam-6111	515	1	[	[	X
ejpam-6111	515	2	17	17	NUM
ejpam-6111	515	3	]	]	X
ejpam-6111	515	4	michael	michael	PROPN
ejpam-6111	515	5	kh	kh	PROPN
ejpam-6111	515	6	fan	fan	PROPN
ejpam-6111	515	7	,	,	PUNCT
ejpam-6111	515	8	andré	andré	ADJ
ejpam-6111	515	9	l	l	NOUN
ejpam-6111	515	10	tits	tit	NOUN
ejpam-6111	515	11	,	,	PUNCT
ejpam-6111	515	12	and	and	CCONJ
ejpam-6111	515	13	john	john	PROPN
ejpam-6111	515	14	c	c	PROPN
ejpam-6111	515	15	doyle	doyle	PROPN
ejpam-6111	515	16	.	.	PUNCT
ejpam-6111	516	1	robustness	robustness	NOUN
ejpam-6111	516	2	in	in	ADP
ejpam-6111	516	3	the	the	DET
ejpam-6111	516	4	presence	presence	NOUN
ejpam-6111	516	5	of	of	ADP
ejpam-6111	516	6	joint	joint	ADJ
ejpam-6111	516	7	parametric	parametric	ADJ
ejpam-6111	516	8	uncertainty	uncertainty	NOUN
ejpam-6111	516	9	and	and	CCONJ
ejpam-6111	516	10	unmodeled	unmodeled	ADJ
ejpam-6111	516	11	dynamics	dynamic	NOUN
ejpam-6111	516	12	.	.	PUNCT
ejpam-6111	517	1	in	in	ADP
ejpam-6111	517	2	1988	1988	NUM
ejpam-6111	517	3	american	american	PROPN
ejpam-6111	517	4	control	control	PROPN
ejpam-6111	517	5	conference	conference	PROPN
ejpam-6111	517	6	,	,	PUNCT
ejpam-6111	517	7	pages	page	NOUN
ejpam-6111	517	8	1195–1200	1195–1200	NUM
ejpam-6111	517	9	.	.	PUNCT
ejpam-6111	518	1	ieee	ieee	PROPN
ejpam-6111	518	2	,	,	PUNCT
ejpam-6111	518	3	1988	1988	NUM
ejpam-6111	518	4	.	.	PUNCT
ejpam-6111	519	1	[	[	X
ejpam-6111	519	2	18	18	NUM
ejpam-6111	519	3	]	]	X
ejpam-6111	519	4	peter	peter	PROPN
ejpam-6111	519	5	m	m	PROPN
ejpam-6111	519	6	young	young	PROPN
ejpam-6111	519	7	,	,	PUNCT
ejpam-6111	519	8	matthew	matthew	PROPN
ejpam-6111	519	9	p	p	PROPN
ejpam-6111	519	10	newlin	newlin	PROPN
ejpam-6111	519	11	,	,	PUNCT
ejpam-6111	519	12	and	and	CCONJ
ejpam-6111	519	13	john	john	PROPN
ejpam-6111	519	14	c	c	PROPN
ejpam-6111	519	15	doyle	doyle	PROPN
ejpam-6111	519	16	.	.	PUNCT
ejpam-6111	520	1	practical	practical	ADJ
ejpam-6111	520	2	computation	computation	NOUN
ejpam-6111	520	3	of	of	ADP
ejpam-6111	520	4	the	the	DET
ejpam-6111	520	5	mixed	mixed	ADJ
ejpam-6111	520	6	µ	µ	PROPN
ejpam-6111	520	7	problem	problem	NOUN
ejpam-6111	520	8	.	.	PUNCT
ejpam-6111	521	1	in	in	ADP
ejpam-6111	521	2	1992	1992	NUM
ejpam-6111	521	3	american	american	PROPN
ejpam-6111	521	4	control	control	PROPN
ejpam-6111	521	5	conference	conference	PROPN
ejpam-6111	521	6	,	,	PUNCT
ejpam-6111	521	7	pages	page	NOUN
ejpam-6111	521	8	2190–2194	2190–2194	NUM
ejpam-6111	521	9	.	.	PUNCT
ejpam-6111	521	10	ieee	ieee	PROPN
ejpam-6111	521	11	,	,	PUNCT
ejpam-6111	521	12	1992	1992	NUM
ejpam-6111	521	13	.	.	PUNCT
ejpam-6111	522	1	[	[	X
ejpam-6111	522	2	19	19	NUM
ejpam-6111	522	3	]	]	X
ejpam-6111	522	4	andy	andy	PROPN
ejpam-6111	522	5	packard	packard	PROPN
ejpam-6111	522	6	,	,	PUNCT
ejpam-6111	522	7	michael	michael	PROPN
ejpam-6111	522	8	kh	kh	PROPN
ejpam-6111	522	9	fan	fan	PROPN
ejpam-6111	522	10	,	,	PUNCT
ejpam-6111	522	11	and	and	CCONJ
ejpam-6111	522	12	john	john	PROPN
ejpam-6111	522	13	doyle	doyle	PROPN
ejpam-6111	522	14	.	.	PUNCT
ejpam-6111	523	1	a	a	DET
ejpam-6111	523	2	power	power	NOUN
ejpam-6111	523	3	method	method	NOUN
ejpam-6111	523	4	for	for	ADP
ejpam-6111	523	5	the	the	DET
ejpam-6111	523	6	structured	structured	ADJ
ejpam-6111	523	7	singular	singular	NOUN
ejpam-6111	523	8	value	value	NOUN
ejpam-6111	523	9	.	.	PUNCT
ejpam-6111	524	1	in	in	ADP
ejpam-6111	524	2	ieee	ieee	NOUN
ejpam-6111	524	3	conf	conf	NOUN
ejpam-6111	524	4	.	.	PUNCT
ejpam-6111	525	1	on	on	ADP
ejpam-6111	525	2	decision	decision	NOUN
ejpam-6111	525	3	and	and	CCONJ
ejpam-6111	525	4	control	control	NOUN
ejpam-6111	525	5	,	,	PUNCT
ejpam-6111	525	6	pages	page	NOUN
ejpam-6111	525	7	2132–2137	2132–2137	NUM
ejpam-6111	525	8	,	,	PUNCT
ejpam-6111	525	9	1988	1988	NUM
ejpam-6111	525	10	.	.	PUNCT
ejpam-6111	526	1	[	[	X
ejpam-6111	526	2	20	20	NUM
ejpam-6111	526	3	]	]	X
ejpam-6111	526	4	peter	peter	PROPN
ejpam-6111	526	5	m	m	PROPN
ejpam-6111	526	6	young	young	PROPN
ejpam-6111	526	7	.	.	PUNCT
ejpam-6111	527	1	theoretical	theoretical	ADJ
ejpam-6111	527	2	and	and	CCONJ
ejpam-6111	527	3	computational	computational	ADJ
ejpam-6111	527	4	aspects	aspect	NOUN
ejpam-6111	527	5	of	of	ADP
ejpam-6111	527	6	the	the	DET
ejpam-6111	527	7	structured	structured	ADJ
ejpam-6111	527	8	singular	singular	NOUN
ejpam-6111	527	9	value	value	NOUN
ejpam-6111	527	10	.	.	PUNCT
ejpam-6111	528	1	systems	system	NOUN
ejpam-6111	528	2	,	,	PUNCT
ejpam-6111	528	3	control	control	NOUN
ejpam-6111	528	4	and	and	CCONJ
ejpam-6111	528	5	information	information	NOUN
ejpam-6111	528	6	,	,	PUNCT
ejpam-6111	528	7	38(3):p129–138	38(3):p129–138	PROPN
ejpam-6111	528	8	,	,	PUNCT
ejpam-6111	528	9	1994	1994	NUM
ejpam-6111	528	10	.	.	PUNCT
ejpam-6111	529	1	[	[	X
ejpam-6111	529	2	21	21	NUM
ejpam-6111	529	3	]	]	X
ejpam-6111	529	4	bo	bo	PROPN
ejpam-6111	529	5	bernhardsson	bernhardsson	PROPN
ejpam-6111	529	6	,	,	PUNCT
ejpam-6111	529	7	anders	anders	PROPN
ejpam-6111	529	8	rantzer	rantzer	VERB
ejpam-6111	529	9	,	,	PUNCT
ejpam-6111	529	10	and	and	CCONJ
ejpam-6111	529	11	li	li	PROPN
ejpam-6111	529	12	qiu	qiu	PROPN
ejpam-6111	529	13	.	.	PUNCT
ejpam-6111	530	1	real	real	ADJ
ejpam-6111	530	2	perturbation	perturbation	NOUN
ejpam-6111	530	3	values	value	NOUN
ejpam-6111	530	4	and	and	CCONJ
ejpam-6111	530	5	real	real	ADJ
ejpam-6111	530	6	quadratic	quadratic	ADJ
ejpam-6111	530	7	forms	form	NOUN
ejpam-6111	530	8	in	in	ADP
ejpam-6111	530	9	a	a	DET
ejpam-6111	530	10	complex	complex	ADJ
ejpam-6111	530	11	vector	vector	NOUN
ejpam-6111	530	12	space	space	NOUN
ejpam-6111	530	13	.	.	PUNCT
ejpam-6111	531	1	linear	linear	ADJ
ejpam-6111	531	2	algebra	algebra	NOUN
ejpam-6111	531	3	and	and	CCONJ
ejpam-6111	531	4	its	its	PRON
ejpam-6111	531	5	applications	application	NOUN
ejpam-6111	531	6	,	,	PUNCT
ejpam-6111	531	7	270(13):131–154	270(13):131–154	NUM
ejpam-6111	531	8	,	,	PUNCT
ejpam-6111	531	9	1998	1998	NUM
ejpam-6111	531	10	.	.	PUNCT
ejpam-6111	532	1	[	[	X
ejpam-6111	532	2	22	22	NUM
ejpam-6111	532	3	]	]	X
ejpam-6111	532	4	jie	jie	PROPN
ejpam-6111	532	5	chen	chen	PROPN
ejpam-6111	532	6	,	,	PUNCT
ejpam-6111	532	7	michael	michael	PROPN
ejpam-6111	532	8	kh	kh	PROPN
ejpam-6111	532	9	fan	fan	PROPN
ejpam-6111	532	10	,	,	PUNCT
ejpam-6111	532	11	and	and	CCONJ
ejpam-6111	532	12	carl	carl	PROPN
ejpam-6111	532	13	n	n	PROPN
ejpam-6111	532	14	nett	nett	PROPN
ejpam-6111	532	15	.	.	PUNCT
ejpam-6111	533	1	structured	structure	VERB
ejpam-6111	533	2	singular	singular	ADJ
ejpam-6111	533	3	values	value	NOUN
ejpam-6111	533	4	with	with	ADP
ejpam-6111	533	5	nondiagonal	nondiagonal	ADJ
ejpam-6111	533	6	structures	structure	NOUN
ejpam-6111	533	7	.	.	PUNCT
ejpam-6111	534	1	i.	i.	PROPN
ejpam-6111	534	2	characterizations	characterizations	PROPN
ejpam-6111	534	3	.	.	PUNCT
ejpam-6111	535	1	ieee	ieee	NOUN
ejpam-6111	535	2	transactions	transaction	NOUN
ejpam-6111	535	3	on	on	ADP
ejpam-6111	535	4	automatic	automatic	ADJ
ejpam-6111	535	5	control	control	NOUN
ejpam-6111	535	6	,	,	PUNCT
ejpam-6111	535	7	41(10):1507–1511	41(10):1507–1511	NUM
ejpam-6111	535	8	,	,	PUNCT
ejpam-6111	535	9	1996	1996	NUM
ejpam-6111	535	10	.	.	PUNCT
ejpam-6111	536	1	[	[	X
ejpam-6111	536	2	23	23	NUM
ejpam-6111	536	3	]	]	X
ejpam-6111	536	4	jie	jie	PROPN
ejpam-6111	536	5	chen	chen	PROPN
ejpam-6111	536	6	,	,	PUNCT
ejpam-6111	536	7	michael	michael	PROPN
ejpam-6111	536	8	kh	kh	PROPN
ejpam-6111	536	9	fan	fan	PROPN
ejpam-6111	536	10	,	,	PUNCT
ejpam-6111	536	11	and	and	CCONJ
ejpam-6111	536	12	carl	carl	PROPN
ejpam-6111	536	13	n	n	PROPN
ejpam-6111	536	14	nett	nett	PROPN
ejpam-6111	536	15	.	.	PUNCT
ejpam-6111	537	1	structured	structure	VERB
ejpam-6111	537	2	singular	singular	ADJ
ejpam-6111	537	3	values	value	NOUN
ejpam-6111	537	4	with	with	ADP
ejpam-6111	537	5	nondiagonal	nondiagonal	ADJ
ejpam-6111	537	6	structures	structure	NOUN
ejpam-6111	537	7	.	.	PUNCT
ejpam-6111	538	1	ii	ii	PROPN
ejpam-6111	538	2	.	.	PUNCT
ejpam-6111	538	3	computation	computation	NOUN
ejpam-6111	538	4	.	.	PUNCT
ejpam-6111	539	1	ieee	ieee	NOUN
ejpam-6111	539	2	transactions	transaction	NOUN
ejpam-6111	539	3	on	on	ADP
ejpam-6111	539	4	automatic	automatic	ADJ
ejpam-6111	539	5	control	control	NOUN
ejpam-6111	539	6	,	,	PUNCT
ejpam-6111	539	7	41(10):1511–1516	41(10):1511–1516	NUM
ejpam-6111	539	8	,	,	PUNCT
ejpam-6111	539	9	1996	1996	NUM
ejpam-6111	539	10	.	.	PUNCT
ejpam-6111	540	1	[	[	X
ejpam-6111	540	2	24	24	NUM
ejpam-6111	540	3	]	]	PUNCT
ejpam-6111	540	4	diederich	diederich	NOUN
ejpam-6111	540	5	hinrichsen	hinrichsen	PROPN
ejpam-6111	540	6	and	and	CCONJ
ejpam-6111	540	7	anthony	anthony	PROPN
ejpam-6111	540	8	j	j	PROPN
ejpam-6111	540	9	pritchard	pritchard	PROPN
ejpam-6111	540	10	.	.	PUNCT
ejpam-6111	541	1	texts	text	NOUN
ejpam-6111	541	2	in	in	ADP
ejpam-6111	541	3	applied	applied	ADJ
ejpam-6111	541	4	mathematics	mathematic	NOUN
ejpam-6111	541	5	.	.	PUNCT
ejpam-6111	542	1	2005	2005	NUM
ejpam-6111	542	2	.	.	PUNCT
ejpam-6111	543	1	[	[	X
ejpam-6111	543	2	25	25	NUM
ejpam-6111	543	3	]	]	PUNCT
ejpam-6111	543	4	michael	michael	PROPN
ejpam-6111	543	5	karow	karow	PROPN
ejpam-6111	543	6	.	.	PUNCT
ejpam-6111	544	1	µ-values	µ-value	VERB
ejpam-6111	544	2	and	and	CCONJ
ejpam-6111	544	3	spectral	spectral	ADJ
ejpam-6111	544	4	value	value	NOUN
ejpam-6111	544	5	sets	set	NOUN
ejpam-6111	544	6	for	for	ADP
ejpam-6111	544	7	linear	linear	ADJ
ejpam-6111	544	8	perturbation	perturbation	NOUN
ejpam-6111	544	9	classes	class	NOUN
ejpam-6111	544	10	defined	define	VERB
ejpam-6111	544	11	by	by	ADP
ejpam-6111	544	12	a	a	DET
ejpam-6111	544	13	scalar	scalar	ADJ
ejpam-6111	544	14	product	product	NOUN
ejpam-6111	544	15	.	.	PUNCT
ejpam-6111	545	1	siam	siam	PROPN
ejpam-6111	545	2	journal	journal	PROPN
ejpam-6111	545	3	on	on	ADP
ejpam-6111	545	4	matrix	matrix	NOUN
ejpam-6111	545	5	analysis	analysis	NOUN
ejpam-6111	545	6	and	and	CCONJ
ejpam-6111	545	7	applications	application	NOUN
ejpam-6111	545	8	,	,	PUNCT
ejpam-6111	545	9	32(3):845	32(3):845	NUM
ejpam-6111	545	10	–	–	PUNCT
ejpam-6111	545	11	865	865	NUM
ejpam-6111	545	12	,	,	PUNCT
ejpam-6111	545	13	2011	2011	NUM
ejpam-6111	545	14	.	.	PUNCT
ejpam-6111	546	1	[	[	X
ejpam-6111	546	2	26	26	NUM
ejpam-6111	546	3	]	]	X
ejpam-6111	546	4	michael	michael	PROPN
ejpam-6111	546	5	karow	karow	PROPN
ejpam-6111	546	6	,	,	PUNCT
ejpam-6111	546	7	diederich	diederich	PROPN
ejpam-6111	546	8	hinrichsen	hinrichsen	PROPN
ejpam-6111	546	9	,	,	PUNCT
ejpam-6111	546	10	and	and	CCONJ
ejpam-6111	546	11	anthony	anthony	PROPN
ejpam-6111	546	12	j	j	PROPN
ejpam-6111	546	13	pritchard	pritchard	PROPN
ejpam-6111	546	14	.	.	PUNCT
ejpam-6111	547	1	interconnected	interconnected	ADJ
ejpam-6111	547	2	systems	system	NOUN
ejpam-6111	547	3	with	with	ADP
ejpam-6111	547	4	uncertain	uncertain	ADJ
ejpam-6111	547	5	couplings	coupling	NOUN
ejpam-6111	547	6	:	:	PUNCT
ejpam-6111	547	7	explicit	explicit	ADJ
ejpam-6111	547	8	formulae	formulae	NOUN
ejpam-6111	547	9	for	for	ADP
ejpam-6111	547	10	mu	mu	NOUN
ejpam-6111	547	11	-	-	PUNCT
ejpam-6111	547	12	values	value	NOUN
ejpam-6111	547	13	,	,	PUNCT
ejpam-6111	547	14	spectral	spectral	ADJ
ejpam-6111	547	15	value	value	NOUN
ejpam-6111	547	16	sets	set	NOUN
ejpam-6111	547	17	,	,	PUNCT
ejpam-6111	547	18	and	and	CCONJ
ejpam-6111	547	19	stability	stability	NOUN
ejpam-6111	547	20	radii	radii	VERB
ejpam-6111	547	21	.	.	PUNCT
ejpam-6111	548	1	siam	siam	PROPN
ejpam-6111	548	2	journal	journal	PROPN
ejpam-6111	548	3	on	on	ADP
ejpam-6111	548	4	control	control	NOUN
ejpam-6111	548	5	and	and	CCONJ
ejpam-6111	548	6	optimization	optimization	NOUN
ejpam-6111	548	7	,	,	PUNCT
ejpam-6111	548	8	45(3):856–884	45(3):856–884	PROPN
ejpam-6111	548	9	,	,	PUNCT
ejpam-6111	548	10	2006	2006	NUM
ejpam-6111	548	11	.	.	PUNCT
ejpam-6111	549	1	[	[	X
ejpam-6111	549	2	27	27	NUM
ejpam-6111	549	3	]	]	X
ejpam-6111	549	4	li	li	PROPN
ejpam-6111	549	5	qiu	qiu	PROPN
ejpam-6111	549	6	,	,	PUNCT
ejpam-6111	549	7	bo	bo	PROPN
ejpam-6111	549	8	bernhardsson	bernhardsson	PROPN
ejpam-6111	549	9	,	,	PUNCT
ejpam-6111	549	10	anders	anders	PROPN
ejpam-6111	549	11	rantzer	rantzer	PROPN
ejpam-6111	549	12	,	,	PUNCT
ejpam-6111	549	13	edward	edward	PROPN
ejpam-6111	549	14	j	j	PROPN
ejpam-6111	549	15	davison	davison	PROPN
ejpam-6111	549	16	,	,	PUNCT
ejpam-6111	549	17	and	and	CCONJ
ejpam-6111	549	18	jc	jc	PROPN
ejpam-6111	549	19	doyle	doyle	PROPN
ejpam-6111	549	20	.	.	PUNCT
ejpam-6111	550	1	a	a	DET
ejpam-6111	550	2	formula	formula	NOUN
ejpam-6111	550	3	for	for	ADP
ejpam-6111	550	4	computation	computation	NOUN
ejpam-6111	550	5	of	of	ADP
ejpam-6111	550	6	the	the	DET
ejpam-6111	550	7	real	real	ADJ
ejpam-6111	550	8	stability	stability	NOUN
ejpam-6111	550	9	radius	radius	NOUN
ejpam-6111	550	10	.	.	PUNCT
ejpam-6111	550	11	1993	1993	NUM
ejpam-6111	550	12	.	.	PUNCT
ejpam-6111	551	1	s.	s.	PROPN
ejpam-6111	551	2	mazhar	mazhar	PROPN
ejpam-6111	551	3	,	,	PUNCT
ejpam-6111	551	4	m.	m.	NOUN
ejpam-6111	551	5	u.	u.	PROPN
ejpam-6111	551	6	rehman	rehman	PROPN
ejpam-6111	551	7	/	/	SYM
ejpam-6111	551	8	eur	eur	PROPN
ejpam-6111	551	9	.	.	PUNCT
ejpam-6111	552	1	j.	j.	PROPN
ejpam-6111	552	2	pure	pure	PROPN
ejpam-6111	552	3	appl	appl	PROPN
ejpam-6111	552	4	.	.	PROPN
ejpam-6111	552	5	math	math	PROPN
ejpam-6111	552	6	,	,	PUNCT
ejpam-6111	552	7	18	18	NUM
ejpam-6111	552	8	(	(	PUNCT
ejpam-6111	552	9	2	2	NUM
ejpam-6111	552	10	)	)	PUNCT
ejpam-6111	552	11	(	(	PUNCT
ejpam-6111	552	12	2025	2025	NUM
ejpam-6111	552	13	)	)	PUNCT
ejpam-6111	552	14	,	,	PUNCT
ejpam-6111	552	15	6111	6111	NUM
ejpam-6111	552	16	24	24	NUM
ejpam-6111	552	17	of	of	ADP
ejpam-6111	552	18	25	25	NUM
ejpam-6111	553	1	[	[	SYM
ejpam-6111	553	2	28	28	NUM
ejpam-6111	553	3	]	]	X
ejpam-6111	553	4	is	be	AUX
ejpam-6111	553	5	khalil	khalil	PROPN
ejpam-6111	553	6	,	,	PUNCT
ejpam-6111	553	7	jc	jc	PROPN
ejpam-6111	553	8	doyle	doyle	PROPN
ejpam-6111	553	9	,	,	PUNCT
ejpam-6111	553	10	and	and	CCONJ
ejpam-6111	553	11	k	k	PROPN
ejpam-6111	553	12	glover	glover	PROPN
ejpam-6111	553	13	.	.	PUNCT
ejpam-6111	554	1	robust	robust	ADJ
ejpam-6111	554	2	and	and	CCONJ
ejpam-6111	554	3	optimal	optimal	ADJ
ejpam-6111	554	4	control	control	NOUN
ejpam-6111	554	5	,	,	PUNCT
ejpam-6111	554	6	volume	volume	NOUN
ejpam-6111	554	7	2	2	NUM
ejpam-6111	554	8	.	.	PUNCT
ejpam-6111	554	9	prentice	prentice	PROPN
ejpam-6111	554	10	hall	hall	PROPN
ejpam-6111	554	11	new	new	PROPN
ejpam-6111	554	12	york	york	PROPN
ejpam-6111	554	13	,	,	PUNCT
ejpam-6111	554	14	1996	1996	NUM
ejpam-6111	554	15	.	.	PUNCT
ejpam-6111	555	1	[	[	X
ejpam-6111	555	2	29	29	NUM
ejpam-6111	555	3	]	]	X
ejpam-6111	555	4	kenneth	kenneth	PROPN
ejpam-6111	555	5	j	j	PROPN
ejpam-6111	555	6	arrow	arrow	NOUN
ejpam-6111	555	7	and	and	CCONJ
ejpam-6111	555	8	maurice	maurice	PROPN
ejpam-6111	555	9	mcmanus	mcmanus	PROPN
ejpam-6111	555	10	.	.	PUNCT
ejpam-6111	556	1	a	a	DET
ejpam-6111	556	2	note	note	NOUN
ejpam-6111	556	3	on	on	ADP
ejpam-6111	556	4	dynamic	dynamic	ADJ
ejpam-6111	556	5	stability	stability	NOUN
ejpam-6111	556	6	.	.	PUNCT
ejpam-6111	557	1	econometrica	econometrica	PROPN
ejpam-6111	557	2	:	:	PUNCT
ejpam-6111	557	3	journal	journal	NOUN
ejpam-6111	557	4	of	of	ADP
ejpam-6111	557	5	the	the	DET
ejpam-6111	557	6	econometric	econometric	ADJ
ejpam-6111	557	7	society	society	NOUN
ejpam-6111	557	8	,	,	PUNCT
ejpam-6111	557	9	pages	page	NOUN
ejpam-6111	557	10	448–454	448–454	NUM
ejpam-6111	557	11	,	,	PUNCT
ejpam-6111	557	12	1958	1958	NUM
ejpam-6111	557	13	.	.	PUNCT
ejpam-6111	558	1	[	[	X
ejpam-6111	558	2	30	30	NUM
ejpam-6111	558	3	]	]	X
ejpam-6111	558	4	david	david	PROPN
ejpam-6111	558	5	carlson	carlson	PROPN
ejpam-6111	558	6	.	.	PUNCT
ejpam-6111	559	1	a	a	DET
ejpam-6111	559	2	class	class	NOUN
ejpam-6111	559	3	of	of	ADP
ejpam-6111	559	4	positive	positive	ADJ
ejpam-6111	559	5	stable	stable	ADJ
ejpam-6111	559	6	matrices	matrix	NOUN
ejpam-6111	559	7	.	.	PUNCT
ejpam-6111	560	1	j.	j.	PROPN
ejpam-6111	560	2	res	res	PROPN
ejpam-6111	560	3	.	.	PUNCT
ejpam-6111	561	1	nat	nat	PROPN
ejpam-6111	561	2	.	.	PUNCT
ejpam-6111	562	1	bur	bur	PROPN
ejpam-6111	562	2	.	.	PROPN
ejpam-6111	563	1	standards	standard	NOUN
ejpam-6111	563	2	sect	sect	NOUN
ejpam-6111	563	3	.	.	PUNCT
ejpam-6111	564	1	b	b	X
ejpam-6111	564	2	,	,	PUNCT
ejpam-6111	564	3	78:1–2	78:1–2	NUM
ejpam-6111	564	4	,	,	PUNCT
ejpam-6111	564	5	1974	1974	NUM
ejpam-6111	564	6	.	.	PUNCT
ejpam-6111	565	1	[	[	X
ejpam-6111	565	2	31	31	NUM
ejpam-6111	565	3	]	]	PUNCT
ejpam-6111	565	4	christina	christina	PROPN
ejpam-6111	565	5	a	a	DET
ejpam-6111	565	6	bahl	bahl	PROPN
ejpam-6111	565	7	and	and	CCONJ
ejpam-6111	565	8	bryan	bryan	PROPN
ejpam-6111	565	9	e	e	PROPN
ejpam-6111	565	10	cain	cain	PROPN
ejpam-6111	565	11	.	.	PUNCT
ejpam-6111	566	1	the	the	DET
ejpam-6111	566	2	inertia	inertia	NOUN
ejpam-6111	566	3	of	of	ADP
ejpam-6111	566	4	diagonal	diagonal	ADJ
ejpam-6111	566	5	multiples	multiple	NOUN
ejpam-6111	566	6	of	of	ADP
ejpam-6111	566	7	3×	3×	NUM
ejpam-6111	566	8	3	3	NUM
ejpam-6111	566	9	real	real	ADJ
ejpam-6111	566	10	matrices	matrix	NOUN
ejpam-6111	566	11	.	.	PUNCT
ejpam-6111	567	1	linear	linear	ADJ
ejpam-6111	567	2	algebra	algebra	NOUN
ejpam-6111	567	3	and	and	CCONJ
ejpam-6111	567	4	its	its	PRON
ejpam-6111	567	5	applications	application	NOUN
ejpam-6111	567	6	,	,	PUNCT
ejpam-6111	567	7	18(3):267–280	18(3):267–280	PROPN
ejpam-6111	567	8	,	,	PUNCT
ejpam-6111	567	9	1977	1977	NUM
ejpam-6111	567	10	.	.	PUNCT
ejpam-6111	568	1	[	[	X
ejpam-6111	568	2	32	32	NUM
ejpam-6111	568	3	]	]	PUNCT
ejpam-6111	568	4	bryan	bryan	PROPN
ejpam-6111	568	5	e	e	PROPN
ejpam-6111	568	6	cain	cain	PROPN
ejpam-6111	568	7	.	.	PUNCT
ejpam-6111	569	1	real	real	ADJ
ejpam-6111	569	2	,	,	PUNCT
ejpam-6111	569	3	3×	3×	NUM
ejpam-6111	569	4	3	3	NUM
ejpam-6111	569	5	,	,	PUNCT
ejpam-6111	569	6	d	d	ADJ
ejpam-6111	569	7	-	-	ADJ
ejpam-6111	569	8	stable	stable	ADJ
ejpam-6111	569	9	matrices	matrix	NOUN
ejpam-6111	569	10	.	.	PUNCT
ejpam-6111	570	1	j.	j.	PROPN
ejpam-6111	570	2	res	res	PROPN
ejpam-6111	570	3	.	.	PUNCT
ejpam-6111	571	1	nat	nat	PROPN
ejpam-6111	571	2	.	.	PUNCT
ejpam-6111	572	1	bur	bur	PROPN
ejpam-6111	572	2	.	.	PROPN
ejpam-6111	573	1	standards	standard	NOUN
ejpam-6111	573	2	sect	sect	NOUN
ejpam-6111	573	3	.	.	PUNCT
ejpam-6111	574	1	b	b	X
ejpam-6111	574	2	,	,	PUNCT
ejpam-6111	574	3	80:75–77	80:75–77	PROPN
ejpam-6111	574	4	,	,	PUNCT
ejpam-6111	574	5	1976	1976	NUM
ejpam-6111	574	6	.	.	PUNCT
ejpam-6111	575	1	[	[	X
ejpam-6111	575	2	33	33	NUM
ejpam-6111	575	3	]	]	X
ejpam-6111	575	4	daniel	daniel	PROPN
ejpam-6111	575	5	hershkowitz	hershkowitz	PROPN
ejpam-6111	575	6	.	.	PUNCT
ejpam-6111	576	1	recent	recent	ADJ
ejpam-6111	576	2	directions	direction	NOUN
ejpam-6111	576	3	in	in	ADP
ejpam-6111	576	4	matrix	matrix	NOUN
ejpam-6111	576	5	stability	stability	NOUN
ejpam-6111	576	6	.	.	PUNCT
ejpam-6111	577	1	linear	linear	ADJ
ejpam-6111	577	2	algebra	algebra	NOUN
ejpam-6111	577	3	and	and	CCONJ
ejpam-6111	577	4	its	its	PRON
ejpam-6111	577	5	applications	application	NOUN
ejpam-6111	577	6	,	,	PUNCT
ejpam-6111	577	7	171:161–186	171:161–186	NUM
ejpam-6111	577	8	,	,	PUNCT
ejpam-6111	577	9	1992	1992	NUM
ejpam-6111	577	10	.	.	PUNCT
ejpam-6111	578	1	[	[	X
ejpam-6111	578	2	34	34	NUM
ejpam-6111	578	3	]	]	X
ejpam-6111	578	4	charles	charles	PROPN
ejpam-6111	578	5	r	r	PROPN
ejpam-6111	578	6	johnson	johnson	PROPN
ejpam-6111	578	7	.	.	PUNCT
ejpam-6111	579	1	sufficient	sufficient	ADJ
ejpam-6111	579	2	conditions	condition	NOUN
ejpam-6111	579	3	for	for	ADP
ejpam-6111	579	4	d	d	NOUN
ejpam-6111	579	5	-	-	NOUN
ejpam-6111	579	6	stability	stability	NOUN
ejpam-6111	579	7	.	.	PUNCT
ejpam-6111	580	1	journal	journal	NOUN
ejpam-6111	580	2	of	of	ADP
ejpam-6111	580	3	economic	economic	ADJ
ejpam-6111	580	4	theory	theory	NOUN
ejpam-6111	580	5	,	,	PUNCT
ejpam-6111	580	6	9(1):53–62	9(1):53–62	NUM
ejpam-6111	580	7	,	,	PUNCT
ejpam-6111	580	8	1974	1974	NUM
ejpam-6111	580	9	.	.	PUNCT
ejpam-6111	581	1	[	[	X
ejpam-6111	581	2	35	35	NUM
ejpam-6111	581	3	]	]	X
ejpam-6111	581	4	jie	jie	PROPN
ejpam-6111	581	5	chen	chen	PROPN
ejpam-6111	581	6	,	,	PUNCT
ejpam-6111	581	7	michael	michael	PROPN
ejpam-6111	581	8	kh	kh	PROPN
ejpam-6111	581	9	fan	fan	PROPN
ejpam-6111	581	10	,	,	PUNCT
ejpam-6111	581	11	and	and	CCONJ
ejpam-6111	581	12	cheng	cheng	PROPN
ejpam-6111	581	13	-	-	PUNCT
ejpam-6111	581	14	ching	ching	PROPN
ejpam-6111	581	15	yu	yu	PROPN
ejpam-6111	581	16	.	.	PUNCT
ejpam-6111	582	1	on	on	ADP
ejpam-6111	582	2	d	d	NOUN
ejpam-6111	582	3	-	-	NOUN
ejpam-6111	582	4	stability	stability	NOUN
ejpam-6111	582	5	and	and	CCONJ
ejpam-6111	582	6	structured	structure	VERB
ejpam-6111	582	7	singular	singular	ADJ
ejpam-6111	582	8	values	value	NOUN
ejpam-6111	582	9	.	.	PUNCT
ejpam-6111	583	1	systems	system	NOUN
ejpam-6111	583	2	&	&	CCONJ
ejpam-6111	583	3	control	control	PROPN
ejpam-6111	583	4	letters	letter	NOUN
ejpam-6111	583	5	,	,	PUNCT
ejpam-6111	583	6	24(1):19–24	24(1):19–24	NUM
ejpam-6111	583	7	,	,	PUNCT
ejpam-6111	583	8	1995	1995	NUM
ejpam-6111	583	9	.	.	PUNCT
ejpam-6111	584	1	[	[	X
ejpam-6111	584	2	36	36	NUM
ejpam-6111	584	3	]	]	X
ejpam-6111	584	4	jietae	jietae	PROPN
ejpam-6111	584	5	lee	lee	PROPN
ejpam-6111	584	6	and	and	CCONJ
ejpam-6111	584	7	thomas	thomas	PROPN
ejpam-6111	584	8	f	f	PROPN
ejpam-6111	584	9	edgar	edgar	PROPN
ejpam-6111	584	10	.	.	PUNCT
ejpam-6111	585	1	real	real	ADJ
ejpam-6111	585	2	structured	structure	VERB
ejpam-6111	585	3	singular	singular	ADJ
ejpam-6111	585	4	value	value	NOUN
ejpam-6111	585	5	conditions	condition	NOUN
ejpam-6111	585	6	for	for	ADP
ejpam-6111	585	7	the	the	DET
ejpam-6111	585	8	strong	strong	ADJ
ejpam-6111	585	9	d	d	NOUN
ejpam-6111	585	10	-	-	NOUN
ejpam-6111	585	11	stability	stability	NOUN
ejpam-6111	585	12	.	.	PUNCT
ejpam-6111	586	1	systems	system	NOUN
ejpam-6111	586	2	&	&	CCONJ
ejpam-6111	586	3	control	control	PROPN
ejpam-6111	586	4	letters	letter	NOUN
ejpam-6111	586	5	,	,	PUNCT
ejpam-6111	586	6	44(4):273–277	44(4):273–277	PROPN
ejpam-6111	586	7	,	,	PUNCT
ejpam-6111	586	8	2001	2001	NUM
ejpam-6111	586	9	.	.	PUNCT
ejpam-6111	587	1	[	[	X
ejpam-6111	587	2	37	37	NUM
ejpam-6111	587	3	]	]	X
ejpam-6111	587	4	mutti	mutti	PROPN
ejpam-6111	587	5	-	-	PUNCT
ejpam-6111	587	6	ur	ur	PROPN
ejpam-6111	587	7	rehman	rehman	PROPN
ejpam-6111	587	8	,	,	PUNCT
ejpam-6111	587	9	tulkin	tulkin	PROPN
ejpam-6111	587	10	h	h	PROPN
ejpam-6111	587	11	rasulov	rasulov	PROPN
ejpam-6111	587	12	,	,	PUNCT
ejpam-6111	587	13	and	and	CCONJ
ejpam-6111	587	14	fouzia	fouzia	AUX
ejpam-6111	587	15	amir	amir	X
ejpam-6111	587	16	.	.	PUNCT
ejpam-6111	588	1	d	d	X
ejpam-6111	588	2	-	-	PUNCT
ejpam-6111	588	3	stability	stability	NOUN
ejpam-6111	588	4	,	,	PUNCT
ejpam-6111	588	5	strong	strong	ADJ
ejpam-6111	588	6	d	d	NOUN
ejpam-6111	588	7	-	-	NOUN
ejpam-6111	588	8	stability	stability	NOUN
ejpam-6111	588	9	and	and	CCONJ
ejpam-6111	588	10	-	-	PUNCT
ejpam-6111	588	11	values	value	NOUN
ejpam-6111	588	12	.	.	PUNCT
ejpam-6111	589	1	lobachevskii	lobachevskii	PROPN
ejpam-6111	589	2	journal	journal	PROPN
ejpam-6111	589	3	of	of	ADP
ejpam-6111	589	4	mathematics	mathematic	NOUN
ejpam-6111	589	5	,	,	PUNCT
ejpam-6111	589	6	45(3):1227–1233	45(3):1227–1233	NUM
ejpam-6111	589	7	,	,	PUNCT
ejpam-6111	589	8	2024	2024	NUM
ejpam-6111	589	9	.	.	PUNCT
ejpam-6111	590	1	[	[	X
ejpam-6111	590	2	38	38	NUM
ejpam-6111	590	3	]	]	PUNCT
ejpam-6111	590	4	alisher	alisher	PROPN
ejpam-6111	590	5	shadiyev	shadiyev	PROPN
ejpam-6111	590	6	mutti	mutti	PROPN
ejpam-6111	590	7	-	-	PUNCT
ejpam-6111	590	8	ur	ur	PROPN
ejpam-6111	590	9	rehman	rehman	PROPN
ejpam-6111	590	10	.	.	PUNCT
ejpam-6111	590	11	interconnection	interconnection	NOUN
ejpam-6111	590	12	between	between	ADP
ejpam-6111	590	13	h	h	NOUN
ejpam-6111	590	14	-	-	PUNCT
ejpam-6111	590	15	stable	stable	ADJ
ejpam-6111	590	16	,	,	PUNCT
ejpam-6111	590	17	d(alpha)stable	d(alpha)stable	ADJ
ejpam-6111	590	18	,	,	PUNCT
ejpam-6111	590	19	d	d	ADJ
ejpam-6111	590	20	-	-	ADJ
ejpam-6111	590	21	semistable	semistable	ADJ
ejpam-6111	590	22	matrices	matrix	NOUN
ejpam-6111	590	23	,	,	PUNCT
ejpam-6111	590	24	and	and	CCONJ
ejpam-6111	590	25	µ-values	µ-value	VERB
ejpam-6111	590	26	.	.	PUNCT
ejpam-6111	591	1	asia	asia	PROPN
ejpam-6111	591	2	pac	pac	PROPN
ejpam-6111	591	3	.	.	PUNCT
ejpam-6111	591	4	j.	j.	PROPN
ejpam-6111	591	5	math	math	PROPN
ejpam-6111	591	6	,	,	PUNCT
ejpam-6111	591	7	(	(	PUNCT
ejpam-6111	591	8	11):102	11):102	NUM
ejpam-6111	591	9	.	.	PUNCT
ejpam-6111	592	1	[	[	X
ejpam-6111	592	2	39	39	NUM
ejpam-6111	592	3	]	]	PUNCT
ejpam-6111	592	4	mutti	mutti	PROPN
ejpam-6111	592	5	-	-	PUNCT
ejpam-6111	592	6	ur	ur	PROPN
ejpam-6111	592	7	rehman	rehman	PROPN
ejpam-6111	592	8	et	et	PROPN
ejpam-6111	592	9	al	al	PROPN
ejpam-6111	592	10	.	.	PROPN
ejpam-6111	592	11	spectrum	spectrum	PROPN
ejpam-6111	592	12	and	and	CCONJ
ejpam-6111	592	13	pseudspectrum	pseudspectrum	NOUN
ejpam-6111	592	14	of	of	ADP
ejpam-6111	592	15	d	d	ADJ
ejpam-6111	592	16	-	-	ADJ
ejpam-6111	592	17	stable	stable	ADJ
ejpam-6111	592	18	matrices	matrix	NOUN
ejpam-6111	592	19	of	of	ADP
ejpam-6111	592	20	economy	economy	NOUN
ejpam-6111	592	21	models	model	NOUN
ejpam-6111	592	22	.	.	PUNCT
ejpam-6111	593	1	j.	j.	PROPN
ejpam-6111	593	2	math	math	PROPN
ejpam-6111	593	3	.	.	PUNCT
ejpam-6111	594	1	computer	computer	PROPN
ejpam-6111	594	2	sci	sci	PROPN
ejpam-6111	594	3	,	,	PUNCT
ejpam-6111	594	4	38:298–312	38:298–312	NUM
ejpam-6111	594	5	,	,	PUNCT
ejpam-6111	594	6	2025	2025	NUM
ejpam-6111	594	7	.	.	PUNCT
ejpam-6111	595	1	[	[	X
ejpam-6111	595	2	40	40	NUM
ejpam-6111	595	3	]	]	X
ejpam-6111	595	4	mutti	mutti	PROPN
ejpam-6111	595	5	-	-	PUNCT
ejpam-6111	595	6	ur	ur	PROPN
ejpam-6111	595	7	rehman	rehman	PROPN
ejpam-6111	595	8	,	,	PUNCT
ejpam-6111	595	9	behkzod	behkzod	PROPN
ejpam-6111	595	10	aminov	aminov	PROPN
ejpam-6111	595	11	,	,	PUNCT
ejpam-6111	595	12	mohammed	mohammed	PROPN
ejpam-6111	595	13	n	n	PROPN
ejpam-6111	595	14	alshehri	alshehri	PROPN
ejpam-6111	595	15	,	,	PUNCT
ejpam-6111	595	16	mustafa	mustafa	PROPN
ejpam-6111	595	17	m	m	PROPN
ejpam-6111	595	18	mohammed	mohammed	PROPN
ejpam-6111	595	19	,	,	PUNCT
ejpam-6111	595	20	arafa	arafa	NOUN
ejpam-6111	595	21	o	o	PROPN
ejpam-6111	595	22	mustafa	mustafa	PROPN
ejpam-6111	595	23	,	,	PUNCT
ejpam-6111	595	24	nhla	nhla	VERB
ejpam-6111	595	25	a	a	DET
ejpam-6111	595	26	abdalrahman	abdalrahman	NOUN
ejpam-6111	595	27	,	,	PUNCT
ejpam-6111	595	28	mona	mona	PROPN
ejpam-6111	595	29	magzoub	magzoub	PROPN
ejpam-6111	595	30	,	,	PUNCT
ejpam-6111	595	31	hala	hala	PROPN
ejpam-6111	595	32	s	s	PART
ejpam-6111	595	33	mahgoub	mahgoub	NOUN
ejpam-6111	595	34	,	,	PUNCT
ejpam-6111	595	35	sakeena	sakeena	PRON
ejpam-6111	595	36	em	em	PRON
ejpam-6111	595	37	hamed	hamed	PROPN
ejpam-6111	595	38	,	,	PUNCT
ejpam-6111	595	39	runda	runda	PROPN
ejpam-6111	595	40	aa	aa	PROPN
ejpam-6111	595	41	bashir	bashir	PROPN
ejpam-6111	595	42	,	,	PUNCT
ejpam-6111	595	43	et	et	PROPN
ejpam-6111	595	44	al	al	PROPN
ejpam-6111	595	45	.	.	PUNCT
ejpam-6111	596	1	spectral	spectral	ADJ
ejpam-6111	596	2	properties	property	NOUN
ejpam-6111	596	3	of	of	ADP
ejpam-6111	596	4	structured	structured	ADJ
ejpam-6111	596	5	matrices	matrix	NOUN
ejpam-6111	596	6	in	in	ADP
ejpam-6111	596	7	transportation	transportation	NOUN
ejpam-6111	596	8	problems	problem	NOUN
ejpam-6111	596	9	.	.	PUNCT
ejpam-6111	597	1	european	european	ADJ
ejpam-6111	597	2	journal	journal	PROPN
ejpam-6111	597	3	of	of	ADP
ejpam-6111	597	4	pure	pure	ADJ
ejpam-6111	597	5	and	and	CCONJ
ejpam-6111	597	6	applied	applied	ADJ
ejpam-6111	597	7	mathematics	mathematic	NOUN
ejpam-6111	597	8	,	,	PUNCT
ejpam-6111	597	9	18(1):5637–5637	18(1):5637–5637	NUM
ejpam-6111	597	10	,	,	PUNCT
ejpam-6111	597	11	2025	2025	NUM
ejpam-6111	597	12	.	.	PUNCT
ejpam-6111	598	1	[	[	X
ejpam-6111	598	2	41	41	NUM
ejpam-6111	598	3	]	]	X
ejpam-6111	598	4	mutti	mutti	PROPN
ejpam-6111	598	5	-	-	PUNCT
ejpam-6111	598	6	ur	ur	PROPN
ejpam-6111	598	7	rehman	rehman	PROPN
ejpam-6111	598	8	,	,	PUNCT
ejpam-6111	598	9	sakeena	sakeena	PRON
ejpam-6111	598	10	em	em	PRON
ejpam-6111	598	11	hamed	hamed	ADJ
ejpam-6111	598	12	,	,	PUNCT
ejpam-6111	598	13	nidal	nidal	PROPN
ejpam-6111	598	14	e	e	PROPN
ejpam-6111	598	15	taha	taha	PROPN
ejpam-6111	598	16	,	,	PUNCT
ejpam-6111	598	17	arafa	arafa	NOUN
ejpam-6111	598	18	o	o	PROPN
ejpam-6111	598	19	mustafa	mustafa	PROPN
ejpam-6111	598	20	,	,	PUNCT
ejpam-6111	598	21	khurshidbek	khurshidbek	PROPN
ejpam-6111	598	22	dilmurodov	dilmurodov	PROPN
ejpam-6111	598	23	,	,	PUNCT
ejpam-6111	598	24	hala	hala	PROPN
ejpam-6111	598	25	s	s	PART
ejpam-6111	598	26	mahgoub	mahgoub	NOUN
ejpam-6111	598	27	,	,	PUNCT
ejpam-6111	598	28	mona	mona	PROPN
ejpam-6111	598	29	magzoub	magzoub	PROPN
ejpam-6111	598	30	,	,	PUNCT
ejpam-6111	598	31	runda	runda	PROPN
ejpam-6111	598	32	aa	aa	PROPN
ejpam-6111	598	33	bashir	bashir	PROPN
ejpam-6111	598	34	,	,	PUNCT
ejpam-6111	598	35	mustafa	mustafa	PROPN
ejpam-6111	598	36	m	m	PROPN
ejpam-6111	598	37	mohammed	mohammed	PROPN
ejpam-6111	598	38	,	,	PUNCT
ejpam-6111	598	39	and	and	CCONJ
ejpam-6111	598	40	awad	awad	VERB
ejpam-6111	598	41	a	a	DET
ejpam-6111	598	42	bakery	bakery	NOUN
ejpam-6111	598	43	.	.	PUNCT
ejpam-6111	599	1	analysis	analysis	NOUN
ejpam-6111	599	2	of	of	ADP
ejpam-6111	599	3	stability	stability	NOUN
ejpam-6111	599	4	,	,	PUNCT
ejpam-6111	599	5	d	d	NOUN
ejpam-6111	599	6	-	-	NOUN
ejpam-6111	599	7	stability	stability	NOUN
ejpam-6111	599	8	,	,	PUNCT
ejpam-6111	599	9	and	and	CCONJ
ejpam-6111	599	10	pseudospectra	pseudospectra	PROPN
ejpam-6111	599	11	in	in	ADP
ejpam-6111	599	12	economic	economic	ADJ
ejpam-6111	599	13	modeling	modeling	NOUN
ejpam-6111	599	14	.	.	PUNCT
ejpam-6111	600	1	european	european	ADJ
ejpam-6111	600	2	journal	journal	PROPN
ejpam-6111	600	3	of	of	ADP
ejpam-6111	600	4	pure	pure	ADJ
ejpam-6111	600	5	and	and	CCONJ
ejpam-6111	600	6	applied	applied	ADJ
ejpam-6111	600	7	mathematics	mathematic	NOUN
ejpam-6111	600	8	,	,	PUNCT
ejpam-6111	600	9	18(1):5657–5657	18(1):5657–5657	NUM
ejpam-6111	600	10	,	,	PUNCT
ejpam-6111	600	11	2025	2025	NUM
ejpam-6111	600	12	.	.	PUNCT
ejpam-6111	601	1	[	[	X
ejpam-6111	601	2	42	42	NUM
ejpam-6111	601	3	]	]	X
ejpam-6111	601	4	m	m	VERB
ejpam-6111	601	5	rehman	rehman	PROPN
ejpam-6111	601	6	,	,	PUNCT
ejpam-6111	601	7	j	j	PROPN
ejpam-6111	601	8	alzabut	alzabut	PROPN
ejpam-6111	601	9	,	,	PUNCT
ejpam-6111	601	10	m	m	PROPN
ejpam-6111	601	11	tayyab	tayyab	NOUN
ejpam-6111	601	12	,	,	PUNCT
ejpam-6111	601	13	and	and	CCONJ
ejpam-6111	601	14	f	f	PROPN
ejpam-6111	601	15	amir	amir	X
ejpam-6111	601	16	.	.	PUNCT
ejpam-6111	602	1	interconnection	interconnection	NOUN
ejpam-6111	602	2	between	between	ADP
ejpam-6111	602	3	schur	schur	PROPN
ejpam-6111	602	4	stability	stability	NOUN
ejpam-6111	602	5	and	and	CCONJ
ejpam-6111	602	6	structured	structure	VERB
ejpam-6111	602	7	singular	singular	ADJ
ejpam-6111	602	8	values	value	NOUN
ejpam-6111	602	9	.	.	PUNCT
ejpam-6111	603	1	contemporary	contemporary	ADJ
ejpam-6111	603	2	mathematics	mathematic	NOUN
ejpam-6111	603	3	,	,	PUNCT
ejpam-6111	603	4	pages	page	NOUN
ejpam-6111	603	5	63–72	63–72	NUM
ejpam-6111	603	6	,	,	PUNCT
ejpam-6111	603	7	2025	2025	NUM
ejpam-6111	603	8	.	.	PUNCT
ejpam-6111	604	1	[	[	X
ejpam-6111	604	2	43	43	NUM
ejpam-6111	604	3	]	]	X
ejpam-6111	604	4	eyad	eyad	NOUN
ejpam-6111	604	5	h	h	NOUN
ejpam-6111	604	6	abed	abe	VERB
ejpam-6111	604	7	.	.	PUNCT
ejpam-6111	605	1	strong	strong	ADJ
ejpam-6111	605	2	d	d	NOUN
ejpam-6111	605	3	-	-	NOUN
ejpam-6111	605	4	stability	stability	NOUN
ejpam-6111	605	5	.	.	PUNCT
ejpam-6111	606	1	systems	system	NOUN
ejpam-6111	606	2	&	&	CCONJ
ejpam-6111	606	3	control	control	PROPN
ejpam-6111	606	4	letters	letter	NOUN
ejpam-6111	606	5	,	,	PUNCT
ejpam-6111	606	6	7(3):207–212	7(3):207–212	NUM
ejpam-6111	606	7	,	,	PUNCT
ejpam-6111	606	8	1986	1986	NUM
ejpam-6111	606	9	.	.	PUNCT
ejpam-6111	607	1	[	[	X
ejpam-6111	607	2	44	44	NUM
ejpam-6111	607	3	]	]	PUNCT
ejpam-6111	607	4	wasfi	wasfi	NOUN
ejpam-6111	607	5	kafri	kafri	PROPN
ejpam-6111	607	6	.	.	PUNCT
ejpam-6111	608	1	robust	robust	ADJ
ejpam-6111	608	2	d	d	NOUN
ejpam-6111	608	3	-	-	NOUN
ejpam-6111	608	4	stability	stability	NOUN
ejpam-6111	608	5	.	.	PUNCT
ejpam-6111	609	1	2001	2001	NUM
ejpam-6111	609	2	.	.	PUNCT
ejpam-6111	610	1	[	[	X
ejpam-6111	610	2	45	45	NUM
ejpam-6111	610	3	]	]	PUNCT
ejpam-6111	610	4	siddu	siddu	NOUN
ejpam-6111	610	5	shiralasetti	shiralasetti	NOUN
ejpam-6111	610	6	et	et	PROPN
ejpam-6111	610	7	al	al	PROPN
ejpam-6111	610	8	.	.	PUNCT
ejpam-6111	611	1	some	some	DET
ejpam-6111	611	2	results	result	NOUN
ejpam-6111	611	3	on	on	ADP
ejpam-6111	611	4	haar	haar	NOUN
ejpam-6111	611	5	wavelets	wavelet	NOUN
ejpam-6111	611	6	matrix	matrix	NOUN
ejpam-6111	611	7	through	through	ADP
ejpam-6111	611	8	linear	linear	PROPN
ejpam-6111	611	9	algebra	algebra	PROPN
ejpam-6111	611	10	.	.	PUNCT
ejpam-6111	612	1	wavelet	wavelet	NOUN
ejpam-6111	612	2	and	and	CCONJ
ejpam-6111	612	3	linear	linear	PROPN
ejpam-6111	612	4	algebra	algebra	PROPN
ejpam-6111	612	5	,	,	PUNCT
ejpam-6111	612	6	4(2):49–59	4(2):49–59	NUM
ejpam-6111	612	7	,	,	PUNCT
ejpam-6111	612	8	2017	2017	NUM
ejpam-6111	612	9	.	.	PUNCT
ejpam-6111	613	1	[	[	X
ejpam-6111	613	2	46	46	NUM
ejpam-6111	613	3	]	]	X
ejpam-6111	613	4	firdous	firdous	ADJ
ejpam-6111	613	5	a	a	DET
ejpam-6111	613	6	shah	shah	NOUN
ejpam-6111	613	7	and	and	CCONJ
ejpam-6111	613	8	r	r	NOUN
ejpam-6111	613	9	abbas	abbas	NOUN
ejpam-6111	613	10	.	.	PUNCT
ejpam-6111	614	1	haar	haar	PROPN
ejpam-6111	614	2	wavelet	wavelet	PROPN
ejpam-6111	614	3	operational	operational	ADJ
ejpam-6111	614	4	matrix	matrix	NOUN
ejpam-6111	614	5	method	method	NOUN
ejpam-6111	614	6	for	for	ADP
ejpam-6111	614	7	the	the	DET
ejpam-6111	614	8	numerical	numerical	ADJ
ejpam-6111	614	9	solution	solution	NOUN
ejpam-6111	614	10	of	of	ADP
ejpam-6111	614	11	fractional	fractional	ADJ
ejpam-6111	614	12	order	order	NOUN
ejpam-6111	614	13	differential	differential	NOUN
ejpam-6111	614	14	equations	equation	NOUN
ejpam-6111	614	15	.	.	PUNCT
ejpam-6111	615	1	nonlinear	nonlinear	ADJ
ejpam-6111	615	2	engineering	engineering	PROPN
ejpam-6111	615	3	,	,	PUNCT
ejpam-6111	615	4	s.	s.	PROPN
ejpam-6111	615	5	mazhar	mazhar	PROPN
ejpam-6111	615	6	,	,	PUNCT
ejpam-6111	615	7	m.	m.	NOUN
ejpam-6111	615	8	u.	u.	PROPN
ejpam-6111	615	9	rehman	rehman	PROPN
ejpam-6111	615	10	/	/	SYM
ejpam-6111	615	11	eur	eur	PROPN
ejpam-6111	615	12	.	.	PUNCT
ejpam-6111	616	1	j.	j.	PROPN
ejpam-6111	616	2	pure	pure	PROPN
ejpam-6111	616	3	appl	appl	PROPN
ejpam-6111	616	4	.	.	PROPN
ejpam-6111	616	5	math	math	PROPN
ejpam-6111	616	6	,	,	PUNCT
ejpam-6111	616	7	18	18	NUM
ejpam-6111	616	8	(	(	PUNCT
ejpam-6111	616	9	2	2	NUM
ejpam-6111	616	10	)	)	PUNCT
ejpam-6111	616	11	(	(	PUNCT
ejpam-6111	616	12	2025	2025	NUM
ejpam-6111	616	13	)	)	PUNCT
ejpam-6111	616	14	,	,	PUNCT
ejpam-6111	616	15	6111	6111	NUM
ejpam-6111	616	16	25	25	NUM
ejpam-6111	616	17	of	of	ADP
ejpam-6111	616	18	25	25	NUM
ejpam-6111	616	19	4(4):203–213	4(4):203–213	NUM
ejpam-6111	616	20	,	,	PUNCT
ejpam-6111	616	21	2015	2015	NUM
ejpam-6111	616	22	.	.	PUNCT