id	sid	tid	token	lemma	pos
ejpam-3258	1	1	european	european	PROPN
ejpam-3258	1	2	journal	journal	PROPN
ejpam-3258	1	3	of	of	ADP
ejpam-3258	1	4	pure	pure	ADJ
ejpam-3258	1	5	and	and	CCONJ
ejpam-3258	1	6	applied	apply	VERB
ejpam-3258	1	7	mathematics	mathematic	NOUN
ejpam-3258	1	8	vol	vol	NOUN
ejpam-3258	1	9	.	.	PUNCT
ejpam-3258	2	1	11	11	NUM
ejpam-3258	2	2	,	,	PUNCT
ejpam-3258	2	3	no	no	INTJ
ejpam-3258	2	4	.	.	NOUN
ejpam-3258	2	5	3	3	NUM
ejpam-3258	2	6	,	,	PUNCT
ejpam-3258	2	7	2018	2018	NUM
ejpam-3258	2	8	,	,	PUNCT
ejpam-3258	2	9	774	774	NUM
ejpam-3258	2	10	-	-	SYM
ejpam-3258	2	11	792	792	NUM
ejpam-3258	2	12	issn	issn	PROPN
ejpam-3258	2	13	1307	1307	NUM
ejpam-3258	2	14	-	-	SYM
ejpam-3258	2	15	5543	5543	NUM
ejpam-3258	2	16	–	–	PUNCT
ejpam-3258	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3258	2	18	published	publish	VERB
ejpam-3258	2	19	by	by	ADP
ejpam-3258	2	20	new	new	PROPN
ejpam-3258	2	21	york	york	PROPN
ejpam-3258	2	22	business	business	PROPN
ejpam-3258	2	23	global	global	ADJ
ejpam-3258	2	24	computing	computing	NOUN
ejpam-3258	2	25	µ-values	µ-value	VERB
ejpam-3258	2	26	for	for	ADP
ejpam-3258	2	27	representations	representation	NOUN
ejpam-3258	2	28	of	of	ADP
ejpam-3258	2	29	symmetric	symmetric	ADJ
ejpam-3258	2	30	groups	group	NOUN
ejpam-3258	2	31	in	in	ADP
ejpam-3258	2	32	engineering	engineering	NOUN
ejpam-3258	2	33	systems	system	NOUN
ejpam-3258	2	34	mutti	mutti	PROPN
ejpam-3258	2	35	-	-	PUNCT
ejpam-3258	2	36	ur	ur	PROPN
ejpam-3258	2	37	rehman1,∗	rehman1,∗	NOUN
ejpam-3258	2	38	,	,	PUNCT
ejpam-3258	2	39	m.	m.	NOUN
ejpam-3258	2	40	fazeel	fazeel	NOUN
ejpam-3258	2	41	anwar1	anwar1	PROPN
ejpam-3258	2	42	1	1	NUM
ejpam-3258	2	43	department	department	NOUN
ejpam-3258	2	44	of	of	ADP
ejpam-3258	2	45	mathematics	mathematic	NOUN
ejpam-3258	2	46	,	,	PUNCT
ejpam-3258	2	47	sukkur	sukkur	PROPN
ejpam-3258	2	48	iba	iba	PROPN
ejpam-3258	2	49	university	university	PROPN
ejpam-3258	2	50	,	,	PUNCT
ejpam-3258	2	51	65200	65200	NUM
ejpam-3258	2	52	sukkur	sukkur	PROPN
ejpam-3258	2	53	,	,	PUNCT
ejpam-3258	2	54	pakistan	pakistan	PROPN
ejpam-3258	2	55	abstract	abstract	NOUN
ejpam-3258	2	56	.	.	PUNCT
ejpam-3258	3	1	in	in	ADP
ejpam-3258	3	2	this	this	DET
ejpam-3258	3	3	article	article	NOUN
ejpam-3258	3	4	we	we	PRON
ejpam-3258	3	5	consider	consider	VERB
ejpam-3258	3	6	the	the	DET
ejpam-3258	3	7	matrix	matrix	NOUN
ejpam-3258	3	8	representations	representation	NOUN
ejpam-3258	3	9	of	of	ADP
ejpam-3258	3	10	finite	finite	ADJ
ejpam-3258	3	11	symmetric	symmetric	ADJ
ejpam-3258	3	12	groups	group	NOUN
ejpam-3258	3	13	sn	sn	INTJ
ejpam-3258	3	14	over	over	ADP
ejpam-3258	3	15	the	the	DET
ejpam-3258	3	16	filed	file	VERB
ejpam-3258	3	17	of	of	ADP
ejpam-3258	3	18	complex	complex	ADJ
ejpam-3258	3	19	numbers	number	NOUN
ejpam-3258	3	20	.	.	PUNCT
ejpam-3258	4	1	these	these	DET
ejpam-3258	4	2	groups	group	NOUN
ejpam-3258	4	3	and	and	CCONJ
ejpam-3258	4	4	their	their	PRON
ejpam-3258	4	5	representations	representation	NOUN
ejpam-3258	4	6	also	also	ADV
ejpam-3258	4	7	appear	appear	VERB
ejpam-3258	4	8	as	as	ADP
ejpam-3258	4	9	symmetries	symmetry	NOUN
ejpam-3258	4	10	of	of	ADP
ejpam-3258	4	11	certain	certain	ADJ
ejpam-3258	4	12	linear	linear	PROPN
ejpam-3258	4	13	control	control	NOUN
ejpam-3258	4	14	systems	system	NOUN
ejpam-3258	4	15	[	[	X
ejpam-3258	4	16	5	5	NUM
ejpam-3258	4	17	]	]	PUNCT
ejpam-3258	4	18	.	.	PUNCT
ejpam-3258	5	1	we	we	PRON
ejpam-3258	5	2	compute	compute	VERB
ejpam-3258	5	3	the	the	DET
ejpam-3258	5	4	structure	structure	NOUN
ejpam-3258	5	5	singular	singular	ADJ
ejpam-3258	5	6	values	value	NOUN
ejpam-3258	5	7	(	(	PUNCT
ejpam-3258	5	8	ssv	ssv	NOUN
ejpam-3258	5	9	)	)	PUNCT
ejpam-3258	5	10	of	of	ADP
ejpam-3258	5	11	the	the	DET
ejpam-3258	5	12	matrices	matrix	NOUN
ejpam-3258	5	13	arising	arise	VERB
ejpam-3258	5	14	from	from	ADP
ejpam-3258	5	15	these	these	DET
ejpam-3258	5	16	representations	representation	NOUN
ejpam-3258	5	17	.	.	PUNCT
ejpam-3258	6	1	the	the	DET
ejpam-3258	6	2	obtained	obtain	VERB
ejpam-3258	6	3	results	result	NOUN
ejpam-3258	6	4	of	of	ADP
ejpam-3258	6	5	ssv	ssv	NOUN
ejpam-3258	6	6	are	be	AUX
ejpam-3258	6	7	compared	compare	VERB
ejpam-3258	6	8	with	with	ADP
ejpam-3258	6	9	well	well	ADV
ejpam-3258	6	10	-	-	PUNCT
ejpam-3258	6	11	known	know	VERB
ejpam-3258	6	12	matlab	matlab	PROPN
ejpam-3258	6	13	routine	routine	PROPN
ejpam-3258	6	14	mussv	mussv	PROPN
ejpam-3258	6	15	.	.	PUNCT
ejpam-3258	7	1	2010	2010	NUM
ejpam-3258	7	2	mathematics	mathematic	NOUN
ejpam-3258	7	3	subject	subject	NOUN
ejpam-3258	7	4	classifications	classification	NOUN
ejpam-3258	7	5	:	:	PUNCT
ejpam-3258	7	6	49n25	49n25	NUM
ejpam-3258	7	7	,	,	PUNCT
ejpam-3258	7	8	15a18	15a18	NUM
ejpam-3258	7	9	,	,	PUNCT
ejpam-3258	7	10	20c30	20c30	NUM
ejpam-3258	7	11	key	key	ADJ
ejpam-3258	7	12	words	word	NOUN
ejpam-3258	7	13	and	and	CCONJ
ejpam-3258	7	14	phrases	phrase	NOUN
ejpam-3258	7	15	:	:	PUNCT
ejpam-3258	7	16	group	group	NOUN
ejpam-3258	7	17	representations	representation	NOUN
ejpam-3258	7	18	,	,	PUNCT
ejpam-3258	7	19	symmetric	symmetric	ADJ
ejpam-3258	7	20	groups	group	NOUN
ejpam-3258	7	21	,	,	PUNCT
ejpam-3258	7	22	µ-values	µ-value	VERB
ejpam-3258	7	23	,	,	PUNCT
ejpam-3258	7	24	spectral	spectral	ADJ
ejpam-3258	7	25	radius	radius	NOUN
ejpam-3258	7	26	,	,	PUNCT
ejpam-3258	7	27	family	family	NOUN
ejpam-3258	7	28	of	of	ADP
ejpam-3258	7	29	block	block	NOUN
ejpam-3258	7	30	diagonal	diagonal	ADJ
ejpam-3258	7	31	perturbations	perturbation	NOUN
ejpam-3258	7	32	.	.	PUNCT
ejpam-3258	8	1	1	1	X
ejpam-3258	8	2	.	.	X
ejpam-3258	8	3	introduction	introduction	NOUN
ejpam-3258	8	4	in	in	ADP
ejpam-3258	8	5	[	[	X
ejpam-3258	8	6	5	5	NUM
ejpam-3258	8	7	]	]	PUNCT
ejpam-3258	8	8	,	,	PUNCT
ejpam-3258	8	9	danielson	danielson	PROPN
ejpam-3258	8	10	used	use	VERB
ejpam-3258	8	11	symmetric	symmetric	ADJ
ejpam-3258	8	12	groups	group	NOUN
ejpam-3258	8	13	to	to	PART
ejpam-3258	8	14	design	design	VERB
ejpam-3258	8	15	model	model	NOUN
ejpam-3258	8	16	predictive	predictive	ADJ
ejpam-3258	8	17	controllers	controller	NOUN
ejpam-3258	8	18	with	with	ADP
ejpam-3258	8	19	reduced	reduced	ADJ
ejpam-3258	8	20	complexity	complexity	NOUN
ejpam-3258	8	21	for	for	ADP
ejpam-3258	8	22	constrained	constrain	VERB
ejpam-3258	8	23	linear	linear	PROPN
ejpam-3258	8	24	control	control	NOUN
ejpam-3258	8	25	systems	system	NOUN
ejpam-3258	8	26	.	.	PUNCT
ejpam-3258	9	1	in	in	ADP
ejpam-3258	9	2	model	model	NOUN
ejpam-3258	9	3	predictive	predictive	PROPN
ejpam-3258	9	4	control	control	PROPN
ejpam-3258	9	5	,	,	PUNCT
ejpam-3258	9	6	the	the	DET
ejpam-3258	9	7	control	control	NOUN
ejpam-3258	9	8	input	input	NOUN
ejpam-3258	9	9	is	be	AUX
ejpam-3258	9	10	obtained	obtain	VERB
ejpam-3258	9	11	by	by	ADP
ejpam-3258	9	12	solving	solve	VERB
ejpam-3258	9	13	a	a	DET
ejpam-3258	9	14	constrained	constrain	VERB
ejpam-3258	9	15	finite	finite	ADJ
ejpam-3258	9	16	time	time	NOUN
ejpam-3258	9	17	optimal	optimal	ADJ
ejpam-3258	9	18	control	control	NOUN
ejpam-3258	9	19	problem	problem	NOUN
ejpam-3258	9	20	.	.	PUNCT
ejpam-3258	10	1	for	for	ADP
ejpam-3258	10	2	a	a	DET
ejpam-3258	10	3	piecewise	piecewise	NOUN
ejpam-3258	10	4	affine	affine	NOUN
ejpam-3258	10	5	control	control	PROPN
ejpam-3258	10	6	law	law	PROPN
ejpam-3258	10	7	symmetries	symmetry	NOUN
ejpam-3258	10	8	are	be	AUX
ejpam-3258	10	9	state	state	NOUN
ejpam-3258	10	10	-	-	PUNCT
ejpam-3258	10	11	space	space	NOUN
ejpam-3258	10	12	and	and	CCONJ
ejpam-3258	10	13	input	input	NOUN
ejpam-3258	10	14	-	-	PUNCT
ejpam-3258	10	15	space	space	NOUN
ejpam-3258	10	16	transformations	transformation	NOUN
ejpam-3258	10	17	that	that	PRON
ejpam-3258	10	18	relate	relate	VERB
ejpam-3258	10	19	controller	controller	NOUN
ejpam-3258	10	20	pieces	piece	NOUN
ejpam-3258	10	21	.	.	PUNCT
ejpam-3258	11	1	using	use	VERB
ejpam-3258	11	2	symmetry	symmetry	NOUN
ejpam-3258	11	3	he	he	PRON
ejpam-3258	11	4	could	could	AUX
ejpam-3258	11	5	discard	discard	VERB
ejpam-3258	11	6	some	some	PRON
ejpam-3258	11	7	of	of	ADP
ejpam-3258	11	8	the	the	DET
ejpam-3258	11	9	pieces	piece	NOUN
ejpam-3258	11	10	of	of	ADP
ejpam-3258	11	11	a	a	DET
ejpam-3258	11	12	given	give	VERB
ejpam-3258	11	13	controller	controller	NOUN
ejpam-3258	11	14	.	.	PUNCT
ejpam-3258	12	1	these	these	DET
ejpam-3258	12	2	discarded	discard	VERB
ejpam-3258	12	3	pieces	piece	NOUN
ejpam-3258	12	4	can	can	AUX
ejpam-3258	12	5	also	also	ADV
ejpam-3258	12	6	be	be	AUX
ejpam-3258	12	7	reconstructed	reconstruct	VERB
ejpam-3258	12	8	using	use	VERB
ejpam-3258	12	9	symmetry	symmetry	NOUN
ejpam-3258	12	10	.	.	PUNCT
ejpam-3258	13	1	using	use	VERB
ejpam-3258	13	2	symmetries	symmetry	NOUN
ejpam-3258	13	3	of	of	ADP
ejpam-3258	13	4	the	the	DET
ejpam-3258	13	5	control	control	NOUN
ejpam-3258	13	6	system	system	NOUN
ejpam-3258	13	7	he	he	PRON
ejpam-3258	13	8	was	be	AUX
ejpam-3258	13	9	able	able	ADJ
ejpam-3258	13	10	to	to	PART
ejpam-3258	13	11	reduce	reduce	VERB
ejpam-3258	13	12	the	the	DET
ejpam-3258	13	13	complexity	complexity	NOUN
ejpam-3258	13	14	of	of	ADP
ejpam-3258	13	15	the	the	DET
ejpam-3258	13	16	controller	controller	NOUN
ejpam-3258	13	17	and	and	CCONJ
ejpam-3258	13	18	save	save	VERB
ejpam-3258	13	19	memory	memory	NOUN
ejpam-3258	13	20	without	without	ADP
ejpam-3258	13	21	sacrificing	sacrifice	VERB
ejpam-3258	13	22	performance	performance	NOUN
ejpam-3258	13	23	.	.	PUNCT
ejpam-3258	14	1	it	it	PRON
ejpam-3258	14	2	was	be	AUX
ejpam-3258	14	3	also	also	ADV
ejpam-3258	14	4	noted	note	VERB
ejpam-3258	14	5	that	that	SCONJ
ejpam-3258	14	6	the	the	DET
ejpam-3258	14	7	amount	amount	NOUN
ejpam-3258	14	8	of	of	ADP
ejpam-3258	14	9	reduction	reduction	NOUN
ejpam-3258	14	10	in	in	ADP
ejpam-3258	14	11	complexity	complexity	NOUN
ejpam-3258	14	12	depends	depend	VERB
ejpam-3258	14	13	on	on	ADP
ejpam-3258	14	14	the	the	DET
ejpam-3258	14	15	number	number	NOUN
ejpam-3258	14	16	of	of	ADP
ejpam-3258	14	17	symmetries	symmetry	NOUN
ejpam-3258	14	18	possessed	possess	VERB
ejpam-3258	14	19	by	by	ADP
ejpam-3258	14	20	the	the	DET
ejpam-3258	14	21	system	system	NOUN
ejpam-3258	14	22	.	.	PUNCT
ejpam-3258	15	1	for	for	ADP
ejpam-3258	15	2	systems	system	NOUN
ejpam-3258	15	3	with	with	ADP
ejpam-3258	15	4	large	large	ADJ
ejpam-3258	15	5	symmetry	symmetry	NOUN
ejpam-3258	15	6	groups	group	NOUN
ejpam-3258	15	7	the	the	DET
ejpam-3258	15	8	techniques	technique	NOUN
ejpam-3258	15	9	presented	present	VERB
ejpam-3258	15	10	in	in	ADP
ejpam-3258	15	11	[	[	X
ejpam-3258	15	12	5	5	NUM
ejpam-3258	15	13	]	]	PUNCT
ejpam-3258	15	14	can	can	AUX
ejpam-3258	15	15	significantly	significantly	ADV
ejpam-3258	15	16	reduce	reduce	VERB
ejpam-3258	15	17	the	the	DET
ejpam-3258	15	18	complexity	complexity	NOUN
ejpam-3258	15	19	of	of	ADP
ejpam-3258	15	20	the	the	DET
ejpam-3258	15	21	piecewise	piecewise	NOUN
ejpam-3258	15	22	affine	affine	NOUN
ejpam-3258	15	23	control	control	NOUN
ejpam-3258	15	24	-	-	PUNCT
ejpam-3258	15	25	law	law	NOUN
ejpam-3258	15	26	produced	produce	VERB
ejpam-3258	15	27	using	use	VERB
ejpam-3258	15	28	explicit	explicit	ADJ
ejpam-3258	15	29	model	model	NOUN
ejpam-3258	15	30	predictive	predictive	ADJ
ejpam-3258	15	31	control	control	NOUN
ejpam-3258	15	32	.	.	PUNCT
ejpam-3258	16	1	in	in	ADP
ejpam-3258	16	2	this	this	DET
ejpam-3258	16	3	paper	paper	NOUN
ejpam-3258	16	4	we	we	PRON
ejpam-3258	16	5	consider	consider	VERB
ejpam-3258	16	6	the	the	DET
ejpam-3258	16	7	characters	character	NOUN
ejpam-3258	16	8	of	of	ADP
ejpam-3258	16	9	the	the	DET
ejpam-3258	16	10	groups	group	NOUN
ejpam-3258	16	11	of	of	ADP
ejpam-3258	16	12	finite	finite	ADJ
ejpam-3258	16	13	number	number	NOUN
ejpam-3258	16	14	of	of	ADP
ejpam-3258	16	15	symmetries	symmetry	NOUN
ejpam-3258	16	16	and	and	CCONJ
ejpam-3258	16	17	construct	construct	VERB
ejpam-3258	16	18	their	their	PRON
ejpam-3258	16	19	representations	representation	NOUN
ejpam-3258	16	20	.	.	PUNCT
ejpam-3258	17	1	these	these	DET
ejpam-3258	17	2	representations	representation	NOUN
ejpam-3258	17	3	in	in	ADP
ejpam-3258	17	4	particular	particular	ADJ
ejpam-3258	17	5	give	give	VERB
ejpam-3258	17	6	us	we	PRON
ejpam-3258	17	7	matrix	matrix	NOUN
ejpam-3258	17	8	generators	generator	NOUN
ejpam-3258	17	9	for	for	ADP
ejpam-3258	17	10	these	these	DET
ejpam-3258	17	11	groups	group	NOUN
ejpam-3258	17	12	.	.	PUNCT
ejpam-3258	18	1	we	we	PRON
ejpam-3258	18	2	then	then	ADV
ejpam-3258	18	3	compute	compute	VERB
ejpam-3258	18	4	the	the	DET
ejpam-3258	18	5	µ-values	µ-value	NOUN
ejpam-3258	18	6	(	(	PUNCT
ejpam-3258	18	7	structured	structured	ADJ
ejpam-3258	18	8	singular	singular	ADJ
ejpam-3258	18	9	values	value	NOUN
ejpam-3258	18	10	)	)	PUNCT
ejpam-3258	18	11	∗corresponding	∗corresponde	VERB
ejpam-3258	18	12	author	author	NOUN
ejpam-3258	18	13	.	.	PUNCT
ejpam-3258	19	1	doi	doi	NOUN
ejpam-3258	19	2	:	:	PUNCT
ejpam-3258	19	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3258	https://doi.org/10.29020/nybg.ejpam.v11i3.3258	NOUN
ejpam-3258	19	4	email	email	NOUN
ejpam-3258	19	5	addresses	address	NOUN
ejpam-3258	19	6	:	:	PUNCT
ejpam-3258	19	7	mutti.rehman@iba-suk.edu.pk	mutti.rehman@iba-suk.edu.pk	PROPN
ejpam-3258	19	8	(	(	PUNCT
ejpam-3258	19	9	m.	m.	PROPN
ejpam-3258	19	10	rehman	rehman	PROPN
ejpam-3258	19	11	)	)	PUNCT
ejpam-3258	19	12	,	,	PUNCT
ejpam-3258	19	13	fazeel.anwar@iba-suk.edu.pk	fazeel.anwar@iba-suk.edu.pk	NOUN
ejpam-3258	19	14	(	(	PUNCT
ejpam-3258	19	15	m.	m.	PROPN
ejpam-3258	19	16	f.	f.	PROPN
ejpam-3258	19	17	anwar	anwar	PROPN
ejpam-3258	19	18	)	)	PUNCT
ejpam-3258	19	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3258	20	1	774	774	NUM
ejpam-3258	21	1	c	c	NOUN
ejpam-3258	21	2	©	©	PROPN
ejpam-3258	21	3	2018	2018	NUM
ejpam-3258	21	4	ejpam	ejpam	VERB
ejpam-3258	21	5	all	all	DET
ejpam-3258	21	6	rights	right	NOUN
ejpam-3258	21	7	reserved	reserve	VERB
ejpam-3258	21	8	.	.	PUNCT
ejpam-3258	22	1	m.	m.	PROPN
ejpam-3258	22	2	rehman	rehman	PROPN
ejpam-3258	22	3	,	,	PUNCT
ejpam-3258	22	4	m.	m.	PROPN
ejpam-3258	22	5	f.	f.	PROPN
ejpam-3258	22	6	anwar	anwar	PROPN
ejpam-3258	22	7	/	/	PUNCT
ejpam-3258	22	8	eur	eur	PROPN
ejpam-3258	22	9	.	.	PUNCT
ejpam-3258	23	1	j.	j.	PROPN
ejpam-3258	23	2	pure	pure	PROPN
ejpam-3258	23	3	appl	appl	PROPN
ejpam-3258	23	4	.	.	PROPN
ejpam-3258	23	5	math	math	PROPN
ejpam-3258	23	6	,	,	PUNCT
ejpam-3258	23	7	11	11	NUM
ejpam-3258	23	8	(	(	PUNCT
ejpam-3258	23	9	3	3	NUM
ejpam-3258	23	10	)	)	PUNCT
ejpam-3258	23	11	(	(	PUNCT
ejpam-3258	23	12	2018	2018	NUM
ejpam-3258	23	13	)	)	PUNCT
ejpam-3258	23	14	,	,	PUNCT
ejpam-3258	23	15	774	774	NUM
ejpam-3258	23	16	-	-	SYM
ejpam-3258	23	17	792	792	NUM
ejpam-3258	23	18	775	775	NUM
ejpam-3258	23	19	for	for	ADP
ejpam-3258	23	20	these	these	DET
ejpam-3258	23	21	matrices	matrix	NOUN
ejpam-3258	23	22	.	.	PUNCT
ejpam-3258	24	1	the	the	DET
ejpam-3258	24	2	structured	structured	ADJ
ejpam-3258	24	3	singular	singular	ADJ
ejpam-3258	24	4	value	value	NOUN
ejpam-3258	24	5	[	[	X
ejpam-3258	24	6	11	11	NUM
ejpam-3258	24	7	]	]	PUNCT
ejpam-3258	24	8	is	be	AUX
ejpam-3258	24	9	very	very	ADV
ejpam-3258	24	10	important	important	ADJ
ejpam-3258	24	11	tool	tool	NOUN
ejpam-3258	24	12	being	be	AUX
ejpam-3258	24	13	used	use	VERB
ejpam-3258	24	14	in	in	ADP
ejpam-3258	24	15	linear	linear	PROPN
ejpam-3258	24	16	control	control	NOUN
ejpam-3258	24	17	theory	theory	NOUN
ejpam-3258	24	18	which	which	PRON
ejpam-3258	24	19	allows	allow	VERB
ejpam-3258	24	20	to	to	PART
ejpam-3258	24	21	discuss	discuss	VERB
ejpam-3258	24	22	mathematical	mathematical	ADJ
ejpam-3258	24	23	problems	problem	NOUN
ejpam-3258	24	24	related	relate	VERB
ejpam-3258	24	25	to	to	ADP
ejpam-3258	24	26	both	both	DET
ejpam-3258	24	27	stability	stability	NOUN
ejpam-3258	24	28	and	and	CCONJ
ejpam-3258	24	29	instability	instability	NOUN
ejpam-3258	24	30	analysis	analysis	NOUN
ejpam-3258	24	31	of	of	ADP
ejpam-3258	24	32	feedback	feedback	NOUN
ejpam-3258	24	33	systems	system	NOUN
ejpam-3258	24	34	subject	subject	ADJ
ejpam-3258	24	35	to	to	ADP
ejpam-3258	24	36	a	a	DET
ejpam-3258	24	37	certain	certain	ADJ
ejpam-3258	24	38	class	class	NOUN
ejpam-3258	24	39	of	of	ADP
ejpam-3258	24	40	perturbations	perturbation	NOUN
ejpam-3258	24	41	.	.	PUNCT
ejpam-3258	25	1	a	a	DET
ejpam-3258	25	2	well	well	ADV
ejpam-3258	25	3	defined	define	VERB
ejpam-3258	25	4	complex	complex	ADJ
ejpam-3258	25	5	/	/	SYM
ejpam-3258	25	6	real	real	ADJ
ejpam-3258	25	7	linear	linear	ADJ
ejpam-3258	25	8	fractional	fractional	ADJ
ejpam-3258	25	9	transformation	transformation	NOUN
ejpam-3258	25	10	lft	lft	PROPN
ejpam-3258	25	11	’s	’s	PART
ejpam-3258	25	12	can	can	AUX
ejpam-3258	25	13	be	be	AUX
ejpam-3258	25	14	used	use	VERB
ejpam-3258	25	15	to	to	PART
ejpam-3258	25	16	cover	cover	VERB
ejpam-3258	25	17	parametric	parametric	ADJ
ejpam-3258	25	18	perturbations	perturbation	NOUN
ejpam-3258	25	19	addressed	address	VERB
ejpam-3258	25	20	by	by	ADP
ejpam-3258	25	21	ssv	ssv	NOUN
ejpam-3258	25	22	incorporated	incorporate	VERB
ejpam-3258	25	23	into	into	ADP
ejpam-3258	25	24	feedback	feedback	NOUN
ejpam-3258	25	25	systems	system	NOUN
ejpam-3258	25	26	.	.	PUNCT
ejpam-3258	26	1	we	we	PRON
ejpam-3258	26	2	suggest	suggest	VERB
ejpam-3258	26	3	to	to	PART
ejpam-3258	26	4	read	read	VERB
ejpam-3258	26	5	[	[	X
ejpam-3258	26	6	1	1	NUM
ejpam-3258	26	7	,	,	PUNCT
ejpam-3258	26	8	3	3	NUM
ejpam-3258	26	9	,	,	PUNCT
ejpam-3258	26	10	8–11	8–11	NOUN
ejpam-3258	26	11	,	,	PUNCT
ejpam-3258	26	12	13	13	NUM
ejpam-3258	26	13	]	]	PUNCT
ejpam-3258	26	14	on	on	ADP
ejpam-3258	26	15	more	more	ADJ
ejpam-3258	26	16	about	about	ADP
ejpam-3258	26	17	ssv	ssv	NOUN
ejpam-3258	26	18	and	and	CCONJ
ejpam-3258	26	19	its	its	PRON
ejpam-3258	26	20	application	application	NOUN
ejpam-3258	26	21	in	in	ADP
ejpam-3258	26	22	system	system	NOUN
ejpam-3258	26	23	theory	theory	NOUN
ejpam-3258	26	24	.	.	PUNCT
ejpam-3258	27	1	the	the	DET
ejpam-3258	27	2	exact	exact	ADJ
ejpam-3258	27	3	computation	computation	NOUN
ejpam-3258	27	4	of	of	ADP
ejpam-3258	27	5	the	the	DET
ejpam-3258	27	6	ssv	ssv	NOUN
ejpam-3258	27	7	,	,	PUNCT
ejpam-3258	27	8	especially	especially	ADV
ejpam-3258	27	9	in	in	ADP
ejpam-3258	27	10	higher	high	ADJ
ejpam-3258	27	11	dimensions	dimension	NOUN
ejpam-3258	27	12	is	be	AUX
ejpam-3258	27	13	notoriously	notoriously	ADV
ejpam-3258	27	14	hard	hard	ADJ
ejpam-3258	27	15	,	,	PUNCT
ejpam-3258	27	16	in	in	ADP
ejpam-3258	27	17	fact	fact	NOUN
ejpam-3258	27	18	non	non	ADJ
ejpam-3258	27	19	-	-	ADJ
ejpam-3258	27	20	deterministic	deterministic	ADJ
ejpam-3258	27	21	polynomial	polynomial	ADJ
ejpam-3258	27	22	time	time	NOUN
ejpam-3258	27	23	that	that	PRON
ejpam-3258	27	24	is	be	AUX
ejpam-3258	27	25	np	np	INTJ
ejpam-3258	27	26	hard	hard	ADJ
ejpam-3258	27	27	[	[	X
ejpam-3258	27	28	2	2	X
ejpam-3258	27	29	]	]	PUNCT
ejpam-3258	27	30	to	to	PART
ejpam-3258	27	31	investigate	investigate	VERB
ejpam-3258	27	32	.	.	PUNCT
ejpam-3258	28	1	the	the	DET
ejpam-3258	28	2	numerical	numerical	ADJ
ejpam-3258	28	3	methods	method	NOUN
ejpam-3258	28	4	available	available	ADJ
ejpam-3258	28	5	in	in	ADP
ejpam-3258	28	6	literature	literature	NOUN
ejpam-3258	28	7	provides	provide	VERB
ejpam-3258	28	8	the	the	DET
ejpam-3258	28	9	approximation	approximation	NOUN
ejpam-3258	28	10	of	of	ADP
ejpam-3258	28	11	both	both	CCONJ
ejpam-3258	28	12	upper	upper	ADJ
ejpam-3258	28	13	and	and	CCONJ
ejpam-3258	28	14	lower	low	ADJ
ejpam-3258	28	15	bounds	bound	NOUN
ejpam-3258	28	16	of	of	ADP
ejpam-3258	28	17	structured	structured	ADJ
ejpam-3258	28	18	singiular	singiular	ADJ
ejpam-3258	28	19	values	value	NOUN
ejpam-3258	28	20	.	.	PUNCT
ejpam-3258	29	1	the	the	DET
ejpam-3258	29	2	message	message	NOUN
ejpam-3258	29	3	from	from	ADP
ejpam-3258	29	4	upper	upper	ADJ
ejpam-3258	29	5	bound	bind	VERB
ejpam-3258	29	6	is	be	AUX
ejpam-3258	29	7	to	to	PART
ejpam-3258	29	8	provide	provide	VERB
ejpam-3258	29	9	the	the	DET
ejpam-3258	29	10	conditions	condition	NOUN
ejpam-3258	29	11	which	which	PRON
ejpam-3258	29	12	guarantee	guarantee	VERB
ejpam-3258	29	13	stability	stability	NOUN
ejpam-3258	29	14	of	of	ADP
ejpam-3258	29	15	linear	linear	PROPN
ejpam-3258	29	16	systems	system	NOUN
ejpam-3258	29	17	,	,	PUNCT
ejpam-3258	29	18	while	while	SCONJ
ejpam-3258	29	19	on	on	ADP
ejpam-3258	29	20	the	the	DET
ejpam-3258	29	21	other	other	ADJ
ejpam-3258	29	22	hand	hand	NOUN
ejpam-3258	29	23	the	the	DET
ejpam-3258	29	24	message	message	NOUN
ejpam-3258	29	25	from	from	ADP
ejpam-3258	29	26	a	a	DET
ejpam-3258	29	27	lower	low	ADJ
ejpam-3258	29	28	bound	bind	VERB
ejpam-3258	29	29	is	be	AUX
ejpam-3258	29	30	to	to	PART
ejpam-3258	29	31	provide	provide	VERB
ejpam-3258	29	32	sufficient	sufficient	ADJ
ejpam-3258	29	33	conditions	condition	NOUN
ejpam-3258	29	34	for	for	ADP
ejpam-3258	29	35	instability	instability	NOUN
ejpam-3258	29	36	analysis	analysis	NOUN
ejpam-3258	29	37	of	of	ADP
ejpam-3258	29	38	the	the	DET
ejpam-3258	29	39	feedback	feedback	NOUN
ejpam-3258	29	40	systems	system	NOUN
ejpam-3258	29	41	in	in	ADP
ejpam-3258	29	42	the	the	DET
ejpam-3258	29	43	linear	linear	PROPN
ejpam-3258	29	44	control	control	PROPN
ejpam-3258	29	45	theory	theory	NOUN
ejpam-3258	29	46	.	.	PUNCT
ejpam-3258	30	1	the	the	DET
ejpam-3258	30	2	well	well	ADV
ejpam-3258	30	3	-	-	PUNCT
ejpam-3258	30	4	known	know	VERB
ejpam-3258	30	5	matlab	matlab	PROPN
ejpam-3258	30	6	function	function	NOUN
ejpam-3258	30	7	mussv	mussv	PROPN
ejpam-3258	30	8	available	available	ADJ
ejpam-3258	30	9	in	in	ADP
ejpam-3258	30	10	the	the	DET
ejpam-3258	30	11	matlab	matlab	PROPN
ejpam-3258	30	12	control	control	NOUN
ejpam-3258	30	13	toolbox	toolbox	NOUN
ejpam-3258	30	14	can	can	AUX
ejpam-3258	30	15	be	be	AUX
ejpam-3258	30	16	used	use	VERB
ejpam-3258	30	17	to	to	PART
ejpam-3258	30	18	approximate	approximate	VERB
ejpam-3258	30	19	an	an	DET
ejpam-3258	30	20	upper	upper	ADJ
ejpam-3258	30	21	bounds	bound	NOUN
ejpam-3258	30	22	of	of	ADP
ejpam-3258	30	23	ssv	ssv	NOUN
ejpam-3258	30	24	by	by	ADP
ejpam-3258	30	25	help	help	NOUN
ejpam-3258	30	26	of	of	ADP
ejpam-3258	30	27	both	both	CCONJ
ejpam-3258	30	28	diagonal	diagonal	ADJ
ejpam-3258	30	29	balancing	balancing	NOUN
ejpam-3258	30	30	and	and	CCONJ
ejpam-3258	30	31	linear	linear	ADJ
ejpam-3258	30	32	matrix	matrix	NOUN
ejpam-3258	30	33	inequlaity	inequlaity	NOUN
ejpam-3258	30	34	techniques	technique	NOUN
ejpam-3258	30	35	[	[	X
ejpam-3258	30	36	6	6	NUM
ejpam-3258	30	37	]	]	PUNCT
ejpam-3258	30	38	.	.	PUNCT
ejpam-3258	31	1	while	while	SCONJ
ejpam-3258	31	2	the	the	DET
ejpam-3258	31	3	computation	computation	NOUN
ejpam-3258	31	4	of	of	ADP
ejpam-3258	31	5	lower	low	ADJ
ejpam-3258	31	6	bound	bind	VERB
ejpam-3258	31	7	is	be	AUX
ejpam-3258	31	8	quite	quite	ADV
ejpam-3258	31	9	possible	possible	ADJ
ejpam-3258	31	10	by	by	ADP
ejpam-3258	31	11	help	help	NOUN
ejpam-3258	31	12	of	of	ADP
ejpam-3258	31	13	generalized	generalized	ADJ
ejpam-3258	31	14	version	version	NOUN
ejpam-3258	31	15	of	of	ADP
ejpam-3258	31	16	power	power	NOUN
ejpam-3258	31	17	method	method	NOUN
ejpam-3258	31	18	,	,	PUNCT
ejpam-3258	31	19	see	see	VERB
ejpam-3258	31	20	in	in	ADP
ejpam-3258	31	21	[	[	X
ejpam-3258	31	22	12	12	NUM
ejpam-3258	31	23	]	]	PUNCT
ejpam-3258	31	24	for	for	ADP
ejpam-3258	31	25	more	more	ADJ
ejpam-3258	31	26	detail	detail	NOUN
ejpam-3258	31	27	.	.	PUNCT
ejpam-3258	32	1	in	in	ADP
ejpam-3258	32	2	this	this	DET
ejpam-3258	32	3	paper	paper	NOUN
ejpam-3258	32	4	the	the	DET
ejpam-3258	32	5	main	main	ADJ
ejpam-3258	32	6	contribution	contribution	NOUN
ejpam-3258	32	7	is	be	AUX
ejpam-3258	32	8	towards	towards	ADP
ejpam-3258	32	9	the	the	DET
ejpam-3258	32	10	comparison	comparison	NOUN
ejpam-3258	32	11	of	of	ADP
ejpam-3258	32	12	both	both	CCONJ
ejpam-3258	32	13	lower	low	ADJ
ejpam-3258	32	14	and	and	CCONJ
ejpam-3258	32	15	upper	upper	ADJ
ejpam-3258	32	16	bounds	bound	NOUN
ejpam-3258	32	17	of	of	ADP
ejpam-3258	32	18	ssv	ssv	NOUN
ejpam-3258	32	19	subject	subject	ADJ
ejpam-3258	32	20	to	to	ADP
ejpam-3258	32	21	class	class	NOUN
ejpam-3258	32	22	of	of	ADP
ejpam-3258	32	23	mixed	mixed	ADJ
ejpam-3258	32	24	real	real	ADJ
ejpam-3258	32	25	and	and	CCONJ
ejpam-3258	32	26	complex	complex	ADJ
ejpam-3258	32	27	uncertainties	uncertainty	NOUN
ejpam-3258	32	28	.	.	PUNCT
ejpam-3258	33	1	we	we	PRON
ejpam-3258	33	2	also	also	ADV
ejpam-3258	33	3	consider	consider	VERB
ejpam-3258	33	4	the	the	DET
ejpam-3258	33	5	case	case	NOUN
ejpam-3258	33	6	when	when	SCONJ
ejpam-3258	33	7	pure	pure	ADJ
ejpam-3258	33	8	real	real	ADJ
ejpam-3258	33	9	and	and	CCONJ
ejpam-3258	33	10	pure	pure	ADJ
ejpam-3258	33	11	complex	complex	ADJ
ejpam-3258	33	12	uncertainties	uncertainty	NOUN
ejpam-3258	33	13	are	be	AUX
ejpam-3258	33	14	under	under	ADP
ejpam-3258	33	15	consideration	consideration	NOUN
ejpam-3258	33	16	.	.	PUNCT
ejpam-3258	34	1	1.1	1.1	NUM
ejpam-3258	34	2	.	.	PUNCT
ejpam-3258	35	1	group	group	NOUN
ejpam-3258	35	2	representations	representation	NOUN
ejpam-3258	35	3	let	let	VERB
ejpam-3258	35	4	g	g	NOUN
ejpam-3258	35	5	be	be	AUX
ejpam-3258	35	6	a	a	DET
ejpam-3258	35	7	group	group	NOUN
ejpam-3258	35	8	,	,	PUNCT
ejpam-3258	35	9	k	k	X
ejpam-3258	35	10	be	be	VERB
ejpam-3258	35	11	a	a	DET
ejpam-3258	35	12	field	field	NOUN
ejpam-3258	35	13	and	and	CCONJ
ejpam-3258	35	14	gl(n	gl(n	X
ejpam-3258	35	15	,	,	PUNCT
ejpam-3258	35	16	k	k	X
ejpam-3258	35	17	)	)	PUNCT
ejpam-3258	35	18	be	be	VERB
ejpam-3258	35	19	the	the	DET
ejpam-3258	35	20	group	group	NOUN
ejpam-3258	35	21	of	of	ADP
ejpam-3258	35	22	invertible	invertible	ADJ
ejpam-3258	35	23	n×	n×	PROPN
ejpam-3258	35	24	n	n	NOUN
ejpam-3258	35	25	matrices	matrix	NOUN
ejpam-3258	35	26	.	.	PUNCT
ejpam-3258	36	1	a	a	DET
ejpam-3258	36	2	representation	representation	NOUN
ejpam-3258	36	3	ρ	ρ	NOUN
ejpam-3258	36	4	of	of	ADP
ejpam-3258	36	5	g	g	PROPN
ejpam-3258	36	6	is	be	AUX
ejpam-3258	36	7	a	a	DET
ejpam-3258	36	8	homomorphism	homomorphism	NOUN
ejpam-3258	36	9	from	from	ADP
ejpam-3258	36	10	g	g	PRON
ejpam-3258	36	11	to	to	ADP
ejpam-3258	36	12	gl(n	gl(n	NUM
ejpam-3258	36	13	,	,	PUNCT
ejpam-3258	36	14	k	k	NOUN
ejpam-3258	36	15	)	)	PUNCT
ejpam-3258	36	16	.	.	PUNCT
ejpam-3258	37	1	let	let	VERB
ejpam-3258	37	2	v	v	VERB
ejpam-3258	37	3	=	=	SYM
ejpam-3258	37	4	kn	kn	PROPN
ejpam-3258	37	5	(	(	PUNCT
ejpam-3258	37	6	n−	n−	NOUN
ejpam-3258	37	7	dimensional	dimensional	ADJ
ejpam-3258	37	8	vector	vector	NOUN
ejpam-3258	37	9	space	space	NOUN
ejpam-3258	37	10	over	over	ADP
ejpam-3258	37	11	k	k	NOUN
ejpam-3258	37	12	)	)	PUNCT
ejpam-3258	37	13	then	then	ADV
ejpam-3258	37	14	we	we	PRON
ejpam-3258	37	15	can	can	AUX
ejpam-3258	37	16	make	make	VERB
ejpam-3258	37	17	v	v	NOUN
ejpam-3258	37	18	into	into	ADP
ejpam-3258	37	19	a	a	DET
ejpam-3258	37	20	kg−module	kg−module	NOUN
ejpam-3258	37	21	by	by	ADP
ejpam-3258	37	22	defining	define	VERB
ejpam-3258	37	23	g	g	PROPN
ejpam-3258	37	24	·	·	PUNCT
ejpam-3258	37	25	v	v	NOUN
ejpam-3258	37	26	=	=	SYM
ejpam-3258	37	27	ρ(g)v	ρ(g)v	NOUN
ejpam-3258	37	28	.	.	PUNCT
ejpam-3258	38	1	equivalently	equivalently	ADV
ejpam-3258	38	2	every	every	DET
ejpam-3258	38	3	kg−module	kg−module	NOUN
ejpam-3258	38	4	v	v	NOUN
ejpam-3258	38	5	gives	give	VERB
ejpam-3258	38	6	rise	rise	NOUN
ejpam-3258	38	7	to	to	ADP
ejpam-3258	38	8	a	a	DET
ejpam-3258	38	9	representation	representation	NOUN
ejpam-3258	38	10	σ	σ	NOUN
ejpam-3258	38	11	of	of	ADP
ejpam-3258	38	12	g.	g.	PROPN
ejpam-3258	38	13	in	in	ADP
ejpam-3258	38	14	this	this	DET
ejpam-3258	38	15	paper	paper	NOUN
ejpam-3258	38	16	we	we	PRON
ejpam-3258	38	17	will	will	AUX
ejpam-3258	38	18	write	write	VERB
ejpam-3258	38	19	g−module	g−module	PROPN
ejpam-3258	38	20	instead	instead	ADV
ejpam-3258	38	21	of	of	ADP
ejpam-3258	38	22	kg−module	kg−module	NOUN
ejpam-3258	38	23	.	.	PUNCT
ejpam-3258	39	1	we	we	PRON
ejpam-3258	39	2	will	will	AUX
ejpam-3258	39	3	say	say	VERB
ejpam-3258	39	4	that	that	SCONJ
ejpam-3258	39	5	a	a	DET
ejpam-3258	39	6	g−module	g−module	NOUN
ejpam-3258	39	7	is	be	AUX
ejpam-3258	39	8	irreducible	irreducible	ADJ
ejpam-3258	39	9	if	if	SCONJ
ejpam-3258	39	10	it	it	PRON
ejpam-3258	39	11	has	have	VERB
ejpam-3258	39	12	no	no	DET
ejpam-3258	39	13	nontrivial	nontrivial	ADJ
ejpam-3258	39	14	g−submodules	g−submodule	NOUN
ejpam-3258	39	15	.	.	PUNCT
ejpam-3258	40	1	a	a	DET
ejpam-3258	40	2	g−module	g−module	NOUN
ejpam-3258	40	3	is	be	AUX
ejpam-3258	40	4	said	say	VERB
ejpam-3258	40	5	to	to	PART
ejpam-3258	40	6	be	be	AUX
ejpam-3258	40	7	completely	completely	ADV
ejpam-3258	40	8	reducible	reducible	ADJ
ejpam-3258	40	9	if	if	SCONJ
ejpam-3258	40	10	it	it	PRON
ejpam-3258	40	11	can	can	AUX
ejpam-3258	40	12	be	be	AUX
ejpam-3258	40	13	written	write	VERB
ejpam-3258	40	14	as	as	ADP
ejpam-3258	40	15	a	a	DET
ejpam-3258	40	16	direct	direct	ADJ
ejpam-3258	40	17	sum	sum	NOUN
ejpam-3258	40	18	of	of	ADP
ejpam-3258	40	19	irreducible	irreducible	ADJ
ejpam-3258	40	20	g−submodules	g−submodule	NOUN
ejpam-3258	40	21	.	.	PUNCT
ejpam-3258	41	1	moreover	moreover	ADV
ejpam-3258	41	2	a	a	DET
ejpam-3258	41	3	representation	representation	NOUN
ejpam-3258	41	4	is	be	AUX
ejpam-3258	41	5	irreducible	irreducible	ADJ
ejpam-3258	41	6	(	(	PUNCT
ejpam-3258	41	7	completely	completely	ADV
ejpam-3258	41	8	reducible	reducible	ADJ
ejpam-3258	41	9	)	)	PUNCT
ejpam-3258	41	10	if	if	SCONJ
ejpam-3258	41	11	the	the	DET
ejpam-3258	41	12	corresponding	correspond	VERB
ejpam-3258	41	13	g−module	g−module	NOUN
ejpam-3258	41	14	is	be	AUX
ejpam-3258	41	15	irreducible	irreducible	ADJ
ejpam-3258	41	16	(	(	PUNCT
ejpam-3258	41	17	completely	completely	ADV
ejpam-3258	41	18	reducible	reducible	ADJ
ejpam-3258	41	19	)	)	PUNCT
ejpam-3258	41	20	.	.	PUNCT
ejpam-3258	42	1	it	it	PRON
ejpam-3258	42	2	is	be	AUX
ejpam-3258	42	3	an	an	DET
ejpam-3258	42	4	important	important	ADJ
ejpam-3258	42	5	problem	problem	NOUN
ejpam-3258	42	6	in	in	ADP
ejpam-3258	42	7	representation	representation	NOUN
ejpam-3258	42	8	theory	theory	NOUN
ejpam-3258	42	9	of	of	ADP
ejpam-3258	42	10	groups	group	NOUN
ejpam-3258	42	11	to	to	PART
ejpam-3258	42	12	classify	classify	VERB
ejpam-3258	42	13	all	all	DET
ejpam-3258	42	14	possible	possible	ADJ
ejpam-3258	42	15	irreducible	irreducible	ADJ
ejpam-3258	42	16	representations	representation	NOUN
ejpam-3258	42	17	of	of	ADP
ejpam-3258	42	18	a	a	DET
ejpam-3258	42	19	given	give	VERB
ejpam-3258	42	20	group	group	NOUN
ejpam-3258	42	21	g.	g.	NOUN
ejpam-3258	42	22	for	for	ADP
ejpam-3258	42	23	a	a	DET
ejpam-3258	42	24	detailed	detailed	ADJ
ejpam-3258	42	25	account	account	NOUN
ejpam-3258	42	26	on	on	ADP
ejpam-3258	42	27	representation	representation	NOUN
ejpam-3258	42	28	theory	theory	NOUN
ejpam-3258	42	29	see	see	VERB
ejpam-3258	42	30	[	[	X
ejpam-3258	42	31	15	15	NUM
ejpam-3258	42	32	]	]	PUNCT
ejpam-3258	42	33	.	.	PUNCT
ejpam-3258	43	1	for	for	ADP
ejpam-3258	43	2	the	the	DET
ejpam-3258	43	3	rest	rest	NOUN
ejpam-3258	43	4	of	of	ADP
ejpam-3258	43	5	this	this	DET
ejpam-3258	43	6	paper	paper	NOUN
ejpam-3258	43	7	let	let	VERB
ejpam-3258	43	8	k	k	NOUN
ejpam-3258	43	9	=	=	SYM
ejpam-3258	43	10	c	c	PROPN
ejpam-3258	43	11	,	,	PUNCT
ejpam-3258	43	12	the	the	DET
ejpam-3258	43	13	field	field	NOUN
ejpam-3258	43	14	of	of	ADP
ejpam-3258	43	15	complex	complex	ADJ
ejpam-3258	43	16	numbers	number	NOUN
ejpam-3258	43	17	and	and	CCONJ
ejpam-3258	43	18	g	g	NOUN
ejpam-3258	43	19	be	be	AUX
ejpam-3258	43	20	a	a	DET
ejpam-3258	43	21	finite	finite	ADJ
ejpam-3258	43	22	group	group	NOUN
ejpam-3258	43	23	.	.	PUNCT
ejpam-3258	44	1	the	the	DET
ejpam-3258	44	2	mashke	mashke	NOUN
ejpam-3258	44	3	’s	’s	PART
ejpam-3258	44	4	theorem	theorem	ADJ
ejpam-3258	44	5	states	state	NOUN
ejpam-3258	44	6	that	that	SCONJ
ejpam-3258	44	7	every	every	DET
ejpam-3258	44	8	nonzero	nonzero	NOUN
ejpam-3258	44	9	g−module	g−module	NOUN
ejpam-3258	44	10	is	be	AUX
ejpam-3258	44	11	completely	completely	ADV
ejpam-3258	44	12	reducible	reducible	ADJ
ejpam-3258	44	13	.	.	PUNCT
ejpam-3258	45	1	this	this	PRON
ejpam-3258	45	2	theorem	theorem	VERB
ejpam-3258	45	3	guarantees	guarantee	NOUN
ejpam-3258	45	4	that	that	SCONJ
ejpam-3258	45	5	finding	find	VERB
ejpam-3258	45	6	the	the	DET
ejpam-3258	45	7	irreducible	irreducible	ADJ
ejpam-3258	45	8	representations	representation	NOUN
ejpam-3258	45	9	of	of	ADP
ejpam-3258	45	10	g	g	PROPN
ejpam-3258	45	11	gives	give	VERB
ejpam-3258	45	12	us	we	PRON
ejpam-3258	45	13	all	all	DET
ejpam-3258	45	14	possible	possible	ADJ
ejpam-3258	45	15	representations	representation	NOUN
ejpam-3258	45	16	of	of	ADP
ejpam-3258	45	17	g.	g.	PROPN
ejpam-3258	45	18	it	it	PRON
ejpam-3258	45	19	is	be	AUX
ejpam-3258	45	20	worth	worth	ADJ
ejpam-3258	45	21	mentioning	mention	VERB
ejpam-3258	45	22	here	here	ADV
ejpam-3258	45	23	that	that	SCONJ
ejpam-3258	45	24	in	in	ADP
ejpam-3258	45	25	general	general	ADJ
ejpam-3258	45	26	mashke	mashke	NOUN
ejpam-3258	45	27	’s	’s	PART
ejpam-3258	45	28	theorem	theorem	NOUN
ejpam-3258	45	29	does	do	AUX
ejpam-3258	45	30	not	not	PART
ejpam-3258	45	31	hold	hold	VERB
ejpam-3258	45	32	for	for	ADP
ejpam-3258	45	33	infinite	infinite	ADJ
ejpam-3258	45	34	group	group	NOUN
ejpam-3258	45	35	or	or	CCONJ
ejpam-3258	45	36	for	for	ADP
ejpam-3258	45	37	fields	field	NOUN
ejpam-3258	45	38	other	other	ADJ
ejpam-3258	45	39	then	then	ADV
ejpam-3258	45	40	the	the	DET
ejpam-3258	45	41	field	field	NOUN
ejpam-3258	45	42	of	of	ADP
ejpam-3258	45	43	complex	complex	ADJ
ejpam-3258	45	44	numbers	number	NOUN
ejpam-3258	45	45	.	.	PUNCT
ejpam-3258	46	1	also	also	ADV
ejpam-3258	46	2	note	note	VERB
ejpam-3258	46	3	that	that	SCONJ
ejpam-3258	46	4	writing	write	VERB
ejpam-3258	46	5	down	down	ADP
ejpam-3258	46	6	all	all	DET
ejpam-3258	46	7	possible	possible	ADJ
ejpam-3258	46	8	irreducible	irreducible	ADJ
ejpam-3258	46	9	representations	representation	NOUN
ejpam-3258	46	10	of	of	ADP
ejpam-3258	46	11	g	g	NOUN
ejpam-3258	46	12	is	be	AUX
ejpam-3258	46	13	not	not	PART
ejpam-3258	46	14	always	always	ADV
ejpam-3258	46	15	easy	easy	ADJ
ejpam-3258	46	16	.	.	PUNCT
ejpam-3258	47	1	let	let	VERB
ejpam-3258	47	2	ρ	ρ	NOUN
ejpam-3258	47	3	:	:	PUNCT
ejpam-3258	47	4	g	g	NOUN
ejpam-3258	47	5	→	→	SYM
ejpam-3258	47	6	gl(n	gl(n	X
ejpam-3258	47	7	,	,	PUNCT
ejpam-3258	47	8	k	k	NOUN
ejpam-3258	47	9	)	)	PUNCT
ejpam-3258	47	10	be	be	AUX
ejpam-3258	47	11	a	a	DET
ejpam-3258	47	12	representation	representation	NOUN
ejpam-3258	47	13	of	of	ADP
ejpam-3258	47	14	g.	g.	PROPN
ejpam-3258	47	15	a	a	DET
ejpam-3258	47	16	function	function	NOUN
ejpam-3258	48	1	χ	χ	X
ejpam-3258	48	2	:	:	PUNCT
ejpam-3258	48	3	g	g	PROPN
ejpam-3258	48	4	→	→	SYM
ejpam-3258	48	5	k	k	PROPN
ejpam-3258	48	6	defined	define	VERB
ejpam-3258	48	7	by	by	ADP
ejpam-3258	48	8	m.	m.	PROPN
ejpam-3258	48	9	rehman	rehman	PROPN
ejpam-3258	48	10	,	,	PUNCT
ejpam-3258	48	11	m.	m.	PROPN
ejpam-3258	48	12	f.	f.	PROPN
ejpam-3258	48	13	anwar	anwar	PROPN
ejpam-3258	48	14	/	/	PUNCT
ejpam-3258	48	15	eur	eur	PROPN
ejpam-3258	48	16	.	.	PUNCT
ejpam-3258	49	1	j.	j.	PROPN
ejpam-3258	49	2	pure	pure	PROPN
ejpam-3258	49	3	appl	appl	PROPN
ejpam-3258	49	4	.	.	PROPN
ejpam-3258	49	5	math	math	PROPN
ejpam-3258	49	6	,	,	PUNCT
ejpam-3258	49	7	11	11	NUM
ejpam-3258	49	8	(	(	PUNCT
ejpam-3258	49	9	3	3	NUM
ejpam-3258	49	10	)	)	PUNCT
ejpam-3258	49	11	(	(	PUNCT
ejpam-3258	49	12	2018	2018	NUM
ejpam-3258	49	13	)	)	PUNCT
ejpam-3258	49	14	,	,	PUNCT
ejpam-3258	49	15	774	774	NUM
ejpam-3258	49	16	-	-	SYM
ejpam-3258	49	17	792	792	NUM
ejpam-3258	49	18	776	776	NUM
ejpam-3258	49	19	gi	gi	NOUN
ejpam-3258	49	20	1	1	NUM
ejpam-3258	49	21	(	(	PUNCT
ejpam-3258	49	22	12	12	NUM
ejpam-3258	49	23	)	)	PUNCT
ejpam-3258	49	24	(	(	PUNCT
ejpam-3258	49	25	123	123	NUM
ejpam-3258	49	26	)	)	PUNCT
ejpam-3258	49	27	|cg(gi)|	|cg(gi)|	NOUN
ejpam-3258	49	28	6	6	NUM
ejpam-3258	49	29	2	2	NUM
ejpam-3258	49	30	3	3	NUM
ejpam-3258	49	31	χ1	χ1	NOUN
ejpam-3258	49	32	1	1	NUM
ejpam-3258	49	33	1	1	NUM
ejpam-3258	49	34	1	1	NUM
ejpam-3258	49	35	χ2	χ2	NOUN
ejpam-3258	49	36	1	1	NUM
ejpam-3258	49	37	−1	−1	NOUN
ejpam-3258	49	38	1	1	NUM
ejpam-3258	49	39	χ3	χ3	NOUN
ejpam-3258	49	40	2	2	NUM
ejpam-3258	49	41	0	0	NUM
ejpam-3258	49	42	−1	−1	NOUN
ejpam-3258	49	43	gi	gi	NOUN
ejpam-3258	49	44	1	1	NUM
ejpam-3258	49	45	(	(	PUNCT
ejpam-3258	49	46	12	12	NUM
ejpam-3258	49	47	)	)	PUNCT
ejpam-3258	49	48	(	(	PUNCT
ejpam-3258	49	49	123	123	NUM
ejpam-3258	49	50	)	)	PUNCT
ejpam-3258	49	51	(	(	PUNCT
ejpam-3258	49	52	12)(34	12)(34	NUM
ejpam-3258	49	53	)	)	PUNCT
ejpam-3258	49	54	(	(	PUNCT
ejpam-3258	49	55	1234	1234	NUM
ejpam-3258	49	56	)	)	PUNCT
ejpam-3258	49	57	|cg(gi)|	|cg(gi)|	NOUN
ejpam-3258	49	58	24	24	NUM
ejpam-3258	49	59	4	4	NUM
ejpam-3258	49	60	3	3	NUM
ejpam-3258	49	61	8	8	NUM
ejpam-3258	49	62	4	4	NUM
ejpam-3258	49	63	χ1	χ1	NOUN
ejpam-3258	49	64	1	1	NUM
ejpam-3258	49	65	1	1	NUM
ejpam-3258	49	66	1	1	NUM
ejpam-3258	49	67	1	1	NUM
ejpam-3258	49	68	1	1	NUM
ejpam-3258	49	69	χ2	χ2	NOUN
ejpam-3258	49	70	1	1	NUM
ejpam-3258	49	71	−1	−1	NOUN
ejpam-3258	49	72	1	1	NUM
ejpam-3258	49	73	1	1	NUM
ejpam-3258	49	74	−1	−1	NOUN
ejpam-3258	49	75	χ3	χ3	NOUN
ejpam-3258	49	76	2	2	NUM
ejpam-3258	49	77	0	0	NUM
ejpam-3258	49	78	−1	−1	NOUN
ejpam-3258	49	79	2	2	NUM
ejpam-3258	49	80	0	0	NUM
ejpam-3258	49	81	χ4	χ4	NOUN
ejpam-3258	49	82	3	3	NUM
ejpam-3258	49	83	1	1	NUM
ejpam-3258	49	84	0	0	NUM
ejpam-3258	49	85	−1	−1	NOUN
ejpam-3258	49	86	−1	−1	NOUN
ejpam-3258	49	87	χ5	χ5	NOUN
ejpam-3258	49	88	3	3	NUM
ejpam-3258	49	89	−1	−1	NOUN
ejpam-3258	49	90	0	0	NUM
ejpam-3258	49	91	−1	−1	NOUN
ejpam-3258	49	92	1	1	NUM
ejpam-3258	49	93	χ(g	χ(g	PROPN
ejpam-3258	49	94	)	)	PUNCT
ejpam-3258	49	95	=	=	SYM
ejpam-3258	49	96	trace(ρ(g	trace(ρ(g	NOUN
ejpam-3258	49	97	)	)	PUNCT
ejpam-3258	49	98	)	)	PUNCT
ejpam-3258	49	99	is	be	AUX
ejpam-3258	49	100	called	call	VERB
ejpam-3258	49	101	the	the	DET
ejpam-3258	49	102	character	character	NOUN
ejpam-3258	49	103	of	of	ADP
ejpam-3258	49	104	the	the	DET
ejpam-3258	49	105	representation	representation	NOUN
ejpam-3258	49	106	ρ	ρ	NOUN
ejpam-3258	49	107	.	.	PUNCT
ejpam-3258	50	1	the	the	DET
ejpam-3258	50	2	characters	character	NOUN
ejpam-3258	50	3	of	of	ADP
ejpam-3258	50	4	a	a	DET
ejpam-3258	50	5	group	group	NOUN
ejpam-3258	50	6	g	g	NOUN
ejpam-3258	50	7	are	be	AUX
ejpam-3258	50	8	the	the	DET
ejpam-3258	50	9	characters	character	NOUN
ejpam-3258	50	10	of	of	ADP
ejpam-3258	50	11	its	its	PRON
ejpam-3258	50	12	representations	representation	NOUN
ejpam-3258	50	13	.	.	PUNCT
ejpam-3258	51	1	a	a	DET
ejpam-3258	51	2	character	character	NOUN
ejpam-3258	51	3	χ	χ	NOUN
ejpam-3258	51	4	is	be	AUX
ejpam-3258	51	5	said	say	VERB
ejpam-3258	51	6	to	to	PART
ejpam-3258	51	7	be	be	AUX
ejpam-3258	51	8	irreducible	irreducible	ADJ
ejpam-3258	51	9	if	if	SCONJ
ejpam-3258	51	10	it	it	PRON
ejpam-3258	51	11	corresponds	correspond	VERB
ejpam-3258	51	12	to	to	ADP
ejpam-3258	51	13	an	an	DET
ejpam-3258	51	14	irreducible	irreducible	ADJ
ejpam-3258	51	15	representation	representation	NOUN
ejpam-3258	51	16	.	.	PUNCT
ejpam-3258	52	1	it	it	PRON
ejpam-3258	52	2	is	be	AUX
ejpam-3258	52	3	true	true	ADJ
ejpam-3258	52	4	in	in	ADP
ejpam-3258	52	5	general	general	ADJ
ejpam-3258	52	6	that	that	SCONJ
ejpam-3258	52	7	the	the	DET
ejpam-3258	52	8	number	number	NOUN
ejpam-3258	52	9	of	of	ADP
ejpam-3258	52	10	irreducible	irreducible	ADJ
ejpam-3258	52	11	representations	representation	NOUN
ejpam-3258	52	12	of	of	ADP
ejpam-3258	52	13	g	g	NOUN
ejpam-3258	52	14	is	be	AUX
ejpam-3258	52	15	equal	equal	ADJ
ejpam-3258	52	16	to	to	ADP
ejpam-3258	52	17	number	number	NOUN
ejpam-3258	52	18	of	of	ADP
ejpam-3258	52	19	conjugacy	conjugacy	ADJ
ejpam-3258	52	20	classes	class	NOUN
ejpam-3258	52	21	of	of	ADP
ejpam-3258	52	22	g	g	PROPN
ejpam-3258	52	23	(	(	PUNCT
ejpam-3258	52	24	finite	finite	PROPN
ejpam-3258	52	25	)	)	PUNCT
ejpam-3258	52	26	.	.	PUNCT
ejpam-3258	53	1	for	for	ADP
ejpam-3258	53	2	characters	character	NOUN
ejpam-3258	53	3	χ	χ	NOUN
ejpam-3258	53	4	and	and	CCONJ
ejpam-3258	53	5	ψ	ψ	X
ejpam-3258	53	6	of	of	ADP
ejpam-3258	53	7	g	g	NOUN
ejpam-3258	53	8	we	we	PRON
ejpam-3258	53	9	can	can	AUX
ejpam-3258	53	10	define	define	VERB
ejpam-3258	53	11	an	an	DET
ejpam-3258	53	12	inner	inner	ADJ
ejpam-3258	53	13	product	product	NOUN
ejpam-3258	53	14	of	of	ADP
ejpam-3258	53	15	character	character	NOUN
ejpam-3258	53	16	of	of	ADP
ejpam-3258	53	17	g	g	NOUN
ejpam-3258	53	18	by	by	ADP
ejpam-3258	53	19	〈	〈	PROPN
ejpam-3258	53	20	χ	χ	PART
ejpam-3258	53	21	,	,	PUNCT
ejpam-3258	53	22	ψ	ψ	VERB
ejpam-3258	53	23	〉	〉	NOUN
ejpam-3258	53	24	=	=	SYM
ejpam-3258	53	25	1	1	NUM
ejpam-3258	53	26	|g|	|g|	PROPN
ejpam-3258	53	27	σg∈gχ(g)ψ(g	σg∈gχ(g)ψ(g	NOUN
ejpam-3258	53	28	)	)	PUNCT
ejpam-3258	53	29	.	.	PUNCT
ejpam-3258	54	1	suppose	suppose	VERB
ejpam-3258	54	2	χ	χ	PRON
ejpam-3258	54	3	is	be	AUX
ejpam-3258	54	4	a	a	DET
ejpam-3258	54	5	character	character	NOUN
ejpam-3258	54	6	of	of	ADP
ejpam-3258	54	7	a	a	DET
ejpam-3258	54	8	g−module	g−module	NOUN
ejpam-3258	54	9	v	v	ADP
ejpam-3258	54	10	then	then	ADV
ejpam-3258	54	11	v	v	NOUN
ejpam-3258	54	12	is	be	AUX
ejpam-3258	54	13	irreducible	irreducible	ADJ
ejpam-3258	54	14	if	if	SCONJ
ejpam-3258	54	15	and	and	CCONJ
ejpam-3258	54	16	only	only	ADV
ejpam-3258	54	17	if	if	SCONJ
ejpam-3258	54	18	〈	〈	PROPN
ejpam-3258	54	19	χ	χ	PRON
ejpam-3258	54	20	,	,	PUNCT
ejpam-3258	54	21	χ	χ	PRON
ejpam-3258	54	22	〉	〉	NOUN
ejpam-3258	54	23	=	=	SYM
ejpam-3258	54	24	1	1	X
ejpam-3258	54	25	.	.	X
ejpam-3258	54	26	we	we	PRON
ejpam-3258	54	27	can	can	AUX
ejpam-3258	54	28	classify	classify	VERB
ejpam-3258	54	29	all	all	DET
ejpam-3258	54	30	possible	possible	ADJ
ejpam-3258	54	31	irreducible	irreducible	ADJ
ejpam-3258	54	32	characters	character	NOUN
ejpam-3258	54	33	of	of	ADP
ejpam-3258	54	34	g	g	PROPN
ejpam-3258	54	35	and	and	CCONJ
ejpam-3258	54	36	this	this	PRON
ejpam-3258	54	37	in	in	ADP
ejpam-3258	54	38	turn	turn	NOUN
ejpam-3258	54	39	gives	give	VERB
ejpam-3258	54	40	us	we	PRON
ejpam-3258	54	41	a	a	DET
ejpam-3258	54	42	classification	classification	NOUN
ejpam-3258	54	43	of	of	ADP
ejpam-3258	54	44	irreducible	irreducible	ADJ
ejpam-3258	54	45	representations	representation	NOUN
ejpam-3258	54	46	of	of	ADP
ejpam-3258	54	47	g.	g.	PROPN
ejpam-3258	54	48	a	a	DET
ejpam-3258	54	49	character	character	NOUN
ejpam-3258	54	50	table	table	NOUN
ejpam-3258	54	51	of	of	ADP
ejpam-3258	54	52	g	g	PROPN
ejpam-3258	54	53	is	be	AUX
ejpam-3258	54	54	a	a	DET
ejpam-3258	54	55	table	table	NOUN
ejpam-3258	54	56	which	which	PRON
ejpam-3258	54	57	lists	list	VERB
ejpam-3258	54	58	character	character	NOUN
ejpam-3258	54	59	values	value	NOUN
ejpam-3258	54	60	for	for	ADP
ejpam-3258	54	61	all	all	DET
ejpam-3258	54	62	irreducible	irreducible	ADJ
ejpam-3258	54	63	characters	character	NOUN
ejpam-3258	54	64	of	of	ADP
ejpam-3258	54	65	g.	g.	PROPN
ejpam-3258	54	66	we	we	PRON
ejpam-3258	54	67	now	now	ADV
ejpam-3258	54	68	turn	turn	VERB
ejpam-3258	54	69	our	our	PRON
ejpam-3258	54	70	attention	attention	NOUN
ejpam-3258	54	71	to	to	ADP
ejpam-3258	54	72	the	the	DET
ejpam-3258	54	73	special	special	ADJ
ejpam-3258	54	74	case	case	NOUN
ejpam-3258	54	75	when	when	SCONJ
ejpam-3258	54	76	g	g	PROPN
ejpam-3258	54	77	=	=	SYM
ejpam-3258	54	78	sn	sn	PROPN
ejpam-3258	54	79	,	,	PUNCT
ejpam-3258	54	80	the	the	DET
ejpam-3258	54	81	symmetric	symmetric	ADJ
ejpam-3258	54	82	group	group	NOUN
ejpam-3258	54	83	on	on	ADP
ejpam-3258	54	84	n	n	DET
ejpam-3258	54	85	letters	letter	NOUN
ejpam-3258	54	86	.	.	PUNCT
ejpam-3258	55	1	the	the	DET
ejpam-3258	55	2	symmetric	symmetric	ADJ
ejpam-3258	55	3	group	group	NOUN
ejpam-3258	55	4	s3	s3	PROPN
ejpam-3258	55	5	has	have	VERB
ejpam-3258	55	6	three	three	NUM
ejpam-3258	55	7	conjugacy	conjugacy	ADJ
ejpam-3258	55	8	classes	class	NOUN
ejpam-3258	55	9	and	and	CCONJ
ejpam-3258	55	10	hence	hence	ADV
ejpam-3258	55	11	three	three	NUM
ejpam-3258	55	12	irreducible	irreducible	ADJ
ejpam-3258	55	13	characters	character	NOUN
ejpam-3258	55	14	.	.	PUNCT
ejpam-3258	56	1	the	the	DET
ejpam-3258	56	2	character	character	NOUN
ejpam-3258	56	3	table	table	NOUN
ejpam-3258	56	4	for	for	ADP
ejpam-3258	56	5	s3	s3	PROPN
ejpam-3258	56	6	is	be	AUX
ejpam-3258	56	7	given	give	VERB
ejpam-3258	56	8	below	below	ADP
ejpam-3258	56	9	in	in	ADP
ejpam-3258	56	10	this	this	DET
ejpam-3258	56	11	table	table	NOUN
ejpam-3258	56	12	the	the	DET
ejpam-3258	56	13	character	character	NOUN
ejpam-3258	56	14	χ3	χ3	NOUN
ejpam-3258	56	15	can	can	AUX
ejpam-3258	56	16	be	be	AUX
ejpam-3258	56	17	obtained	obtain	VERB
ejpam-3258	56	18	from	from	ADP
ejpam-3258	56	19	the	the	DET
ejpam-3258	56	20	permutation	permutation	NOUN
ejpam-3258	56	21	representation	representation	NOUN
ejpam-3258	56	22	and	and	CCONJ
ejpam-3258	56	23	the	the	DET
ejpam-3258	56	24	two	two	NUM
ejpam-3258	56	25	linear	linear	ADJ
ejpam-3258	56	26	characters	character	NOUN
ejpam-3258	56	27	correspond	correspond	VERB
ejpam-3258	56	28	to	to	ADP
ejpam-3258	56	29	the	the	DET
ejpam-3258	56	30	abelian	abelian	ADJ
ejpam-3258	56	31	group	group	NOUN
ejpam-3258	57	1	g	g	PROPN
ejpam-3258	57	2	/	/	SYM
ejpam-3258	57	3	g	g	NOUN
ejpam-3258	57	4	′	′	NOUN
ejpam-3258	57	5	,	,	PUNCT
ejpam-3258	57	6	where	where	SCONJ
ejpam-3258	57	7	g	g	PROPN
ejpam-3258	57	8	′	′	NUM
ejpam-3258	57	9	is	be	AUX
ejpam-3258	57	10	the	the	DET
ejpam-3258	57	11	derived	derived	ADJ
ejpam-3258	57	12	subgroup	subgroup	NOUN
ejpam-3258	57	13	of	of	ADP
ejpam-3258	57	14	g.	g.	PROPN
ejpam-3258	58	1	the	the	DET
ejpam-3258	58	2	symmetric	symmetric	PROPN
ejpam-3258	58	3	group	group	NOUN
ejpam-3258	58	4	s4	s4	PROPN
ejpam-3258	58	5	has	have	VERB
ejpam-3258	58	6	five	five	NUM
ejpam-3258	58	7	conjugacy	conjugacy	ADJ
ejpam-3258	58	8	classes	class	NOUN
ejpam-3258	58	9	and	and	CCONJ
ejpam-3258	58	10	the	the	DET
ejpam-3258	58	11	character	character	NOUN
ejpam-3258	58	12	table	table	NOUN
ejpam-3258	58	13	of	of	ADP
ejpam-3258	58	14	s4	s4	PROPN
ejpam-3258	58	15	is	be	AUX
ejpam-3258	58	16	given	give	VERB
ejpam-3258	58	17	below	below	ADV
ejpam-3258	58	18	in	in	ADP
ejpam-3258	58	19	the	the	DET
ejpam-3258	58	20	above	above	ADJ
ejpam-3258	58	21	table	table	NOUN
ejpam-3258	58	22	linear	linear	NOUN
ejpam-3258	58	23	characters	character	NOUN
ejpam-3258	58	24	correspond	correspond	VERB
ejpam-3258	58	25	to	to	ADP
ejpam-3258	58	26	the	the	DET
ejpam-3258	58	27	abelian	abelian	ADJ
ejpam-3258	58	28	group	group	NOUN
ejpam-3258	58	29	g	g	PROPN
ejpam-3258	58	30	/	/	SYM
ejpam-3258	58	31	g	g	NOUN
ejpam-3258	58	32	′	′	NOUN
ejpam-3258	58	33	and	and	CCONJ
ejpam-3258	58	34	the	the	DET
ejpam-3258	58	35	character	character	NOUN
ejpam-3258	58	36	χ4	χ4	NOUN
ejpam-3258	58	37	can	can	AUX
ejpam-3258	58	38	be	be	AUX
ejpam-3258	58	39	obtained	obtain	VERB
ejpam-3258	58	40	from	from	ADP
ejpam-3258	58	41	the	the	DET
ejpam-3258	58	42	permutation	permutation	NOUN
ejpam-3258	58	43	character	character	NOUN
ejpam-3258	58	44	of	of	ADP
ejpam-3258	58	45	g.	g.	PROPN
ejpam-3258	58	46	more	more	ADV
ejpam-3258	58	47	over	over	ADP
ejpam-3258	58	48	χ5	χ5	NOUN
ejpam-3258	58	49	is	be	AUX
ejpam-3258	58	50	the	the	DET
ejpam-3258	58	51	product	product	NOUN
ejpam-3258	58	52	of	of	ADP
ejpam-3258	58	53	irreducible	irreducible	ADJ
ejpam-3258	58	54	characters	character	NOUN
ejpam-3258	58	55	χ2	χ2	PROPN
ejpam-3258	58	56	and	and	CCONJ
ejpam-3258	58	57	χ4	χ4	NOUN
ejpam-3258	58	58	.	.	PUNCT
ejpam-3258	59	1	moreover	moreover	ADV
ejpam-3258	59	2	the	the	DET
ejpam-3258	59	3	character	character	NOUN
ejpam-3258	59	4	χ3	χ3	NOUN
ejpam-3258	59	5	of	of	ADP
ejpam-3258	59	6	g	g	NOUN
ejpam-3258	59	7	can	can	AUX
ejpam-3258	59	8	be	be	AUX
ejpam-3258	59	9	obtained	obtain	VERB
ejpam-3258	59	10	by	by	ADP
ejpam-3258	59	11	lifting	lift	VERB
ejpam-3258	59	12	the	the	DET
ejpam-3258	59	13	character	character	NOUN
ejpam-3258	59	14	of	of	ADP
ejpam-3258	59	15	the	the	DET
ejpam-3258	59	16	subgroup	subgroup	NOUN
ejpam-3258	59	17	of	of	ADP
ejpam-3258	59	18	s4	s4	PROPN
ejpam-3258	59	19	generated	generate	VERB
ejpam-3258	59	20	by	by	ADP
ejpam-3258	59	21	the	the	DET
ejpam-3258	59	22	permutation	permutation	NOUN
ejpam-3258	59	23	(	(	PUNCT
ejpam-3258	59	24	12)(34	12)(34	NUM
ejpam-3258	59	25	)	)	PUNCT
ejpam-3258	59	26	.	.	PUNCT
ejpam-3258	60	1	m.	m.	PROPN
ejpam-3258	60	2	rehman	rehman	PROPN
ejpam-3258	60	3	,	,	PUNCT
ejpam-3258	60	4	m.	m.	PROPN
ejpam-3258	60	5	f.	f.	PROPN
ejpam-3258	60	6	anwar	anwar	PROPN
ejpam-3258	60	7	/	/	PUNCT
ejpam-3258	60	8	eur	eur	PROPN
ejpam-3258	60	9	.	.	PUNCT
ejpam-3258	61	1	j.	j.	PROPN
ejpam-3258	61	2	pure	pure	PROPN
ejpam-3258	61	3	appl	appl	PROPN
ejpam-3258	61	4	.	.	PROPN
ejpam-3258	61	5	math	math	PROPN
ejpam-3258	61	6	,	,	PUNCT
ejpam-3258	61	7	11	11	NUM
ejpam-3258	61	8	(	(	PUNCT
ejpam-3258	61	9	3	3	NUM
ejpam-3258	61	10	)	)	PUNCT
ejpam-3258	61	11	(	(	PUNCT
ejpam-3258	61	12	2018	2018	NUM
ejpam-3258	61	13	)	)	PUNCT
ejpam-3258	61	14	,	,	PUNCT
ejpam-3258	61	15	774	774	NUM
ejpam-3258	61	16	-	-	SYM
ejpam-3258	61	17	792	792	NUM
ejpam-3258	61	18	777	777	NUM
ejpam-3258	61	19	1.2	1.2	NUM
ejpam-3258	61	20	.	.	PUNCT
ejpam-3258	62	1	from	from	ADP
ejpam-3258	62	2	characters	character	NOUN
ejpam-3258	62	3	to	to	ADP
ejpam-3258	62	4	representations	representation	NOUN
ejpam-3258	62	5	finding	find	VERB
ejpam-3258	62	6	an	an	DET
ejpam-3258	62	7	irreducible	irreducible	ADJ
ejpam-3258	62	8	representation	representation	NOUN
ejpam-3258	62	9	corresponding	correspond	VERB
ejpam-3258	62	10	to	to	ADP
ejpam-3258	62	11	a	a	DET
ejpam-3258	62	12	given	give	VERB
ejpam-3258	62	13	character	character	NOUN
ejpam-3258	62	14	is	be	AUX
ejpam-3258	62	15	a	a	DET
ejpam-3258	62	16	historical	historical	ADJ
ejpam-3258	62	17	problem	problem	NOUN
ejpam-3258	62	18	which	which	PRON
ejpam-3258	62	19	has	have	AUX
ejpam-3258	62	20	been	be	AUX
ejpam-3258	62	21	around	around	ADV
ejpam-3258	62	22	since	since	SCONJ
ejpam-3258	62	23	late	late	ADJ
ejpam-3258	62	24	eighteenth	eighteenth	ADJ
ejpam-3258	62	25	century	century	NOUN
ejpam-3258	62	26	.	.	PUNCT
ejpam-3258	63	1	for	for	ADP
ejpam-3258	63	2	a	a	DET
ejpam-3258	63	3	detailed	detailed	ADJ
ejpam-3258	63	4	history	history	NOUN
ejpam-3258	63	5	of	of	ADP
ejpam-3258	63	6	the	the	DET
ejpam-3258	63	7	problem	problem	NOUN
ejpam-3258	63	8	see	see	VERB
ejpam-3258	63	9	[	[	X
ejpam-3258	63	10	4	4	NUM
ejpam-3258	63	11	]	]	PUNCT
ejpam-3258	63	12	.	.	PUNCT
ejpam-3258	64	1	it	it	PRON
ejpam-3258	64	2	is	be	AUX
ejpam-3258	64	3	not	not	PART
ejpam-3258	64	4	always	always	ADV
ejpam-3258	64	5	straight	straight	ADV
ejpam-3258	64	6	forward	forward	ADV
ejpam-3258	64	7	to	to	PART
ejpam-3258	64	8	come	come	VERB
ejpam-3258	64	9	up	up	ADP
ejpam-3258	64	10	with	with	ADP
ejpam-3258	64	11	the	the	DET
ejpam-3258	64	12	right	right	ADJ
ejpam-3258	64	13	representation	representation	NOUN
ejpam-3258	64	14	although	although	SCONJ
ejpam-3258	64	15	it	it	PRON
ejpam-3258	64	16	always	always	ADV
ejpam-3258	64	17	exists	exist	VERB
ejpam-3258	64	18	.	.	PUNCT
ejpam-3258	65	1	several	several	ADJ
ejpam-3258	65	2	methods	method	NOUN
ejpam-3258	65	3	has	have	AUX
ejpam-3258	65	4	been	be	AUX
ejpam-3258	65	5	proposed	propose	VERB
ejpam-3258	65	6	to	to	PART
ejpam-3258	65	7	construct	construct	VERB
ejpam-3258	65	8	these	these	DET
ejpam-3258	65	9	representations	representation	NOUN
ejpam-3258	65	10	with	with	ADP
ejpam-3258	65	11	various	various	ADJ
ejpam-3258	65	12	limitations	limitation	NOUN
ejpam-3258	65	13	.	.	PUNCT
ejpam-3258	66	1	in	in	ADP
ejpam-3258	66	2	this	this	DET
ejpam-3258	66	3	paper	paper	NOUN
ejpam-3258	66	4	we	we	PRON
ejpam-3258	66	5	use	use	VERB
ejpam-3258	66	6	an	an	DET
ejpam-3258	66	7	algorithm	algorithm	NOUN
ejpam-3258	66	8	given	give	VERB
ejpam-3258	66	9	by	by	ADP
ejpam-3258	66	10	[	[	X
ejpam-3258	66	11	4	4	X
ejpam-3258	66	12	]	]	PUNCT
ejpam-3258	66	13	to	to	PART
ejpam-3258	66	14	compute	compute	VERB
ejpam-3258	66	15	the	the	DET
ejpam-3258	66	16	representations	representation	NOUN
ejpam-3258	66	17	of	of	ADP
ejpam-3258	66	18	sn	sn	NOUN
ejpam-3258	66	19	for	for	ADP
ejpam-3258	66	20	n	n	NOUN
ejpam-3258	66	21	=	=	SYM
ejpam-3258	66	22	3	3	NUM
ejpam-3258	66	23	,	,	PUNCT
ejpam-3258	66	24	4	4	NUM
ejpam-3258	66	25	.	.	PUNCT
ejpam-3258	67	1	his	his	PRON
ejpam-3258	67	2	algorithm	algorithm	NOUN
ejpam-3258	67	3	has	have	AUX
ejpam-3258	67	4	been	be	AUX
ejpam-3258	67	5	implemented	implement	VERB
ejpam-3258	67	6	in	in	ADP
ejpam-3258	67	7	the	the	DET
ejpam-3258	67	8	gap	gap	NOUN
ejpam-3258	67	9	[	[	X
ejpam-3258	67	10	7	7	NUM
ejpam-3258	67	11	]	]	X
ejpam-3258	67	12	package	package	NOUN
ejpam-3258	67	13	”	"	PUNCT
ejpam-3258	67	14	repsn	repsn	NOUN
ejpam-3258	67	15	”	"	PUNCT
ejpam-3258	67	16	.	.	PUNCT
ejpam-3258	68	1	for	for	ADP
ejpam-3258	68	2	the	the	DET
ejpam-3258	68	3	group	group	NOUN
ejpam-3258	68	4	s3	s3	PROPN
ejpam-3258	68	5	the	the	DET
ejpam-3258	68	6	only	only	ADJ
ejpam-3258	68	7	representation	representation	NOUN
ejpam-3258	68	8	we	we	PRON
ejpam-3258	68	9	have	have	VERB
ejpam-3258	68	10	to	to	PART
ejpam-3258	68	11	compute	compute	VERB
ejpam-3258	68	12	is	be	AUX
ejpam-3258	68	13	for	for	ADP
ejpam-3258	68	14	the	the	DET
ejpam-3258	68	15	character	character	NOUN
ejpam-3258	68	16	χ3	χ3	NOUN
ejpam-3258	68	17	.	.	PUNCT
ejpam-3258	69	1	the	the	DET
ejpam-3258	69	2	matrix	matrix	NOUN
ejpam-3258	69	3	representation	representation	NOUN
ejpam-3258	69	4	is	be	AUX
ejpam-3258	69	5	given	give	VERB
ejpam-3258	69	6	by	by	ADP
ejpam-3258	69	7	the	the	DET
ejpam-3258	69	8	matrices	matrix	NOUN
ejpam-3258	69	9	a	a	PRON
ejpam-3258	69	10	and	and	CCONJ
ejpam-3258	69	11	b	b	NOUN
ejpam-3258	69	12	where	where	SCONJ
ejpam-3258	69	13	a	a	DET
ejpam-3258	69	14	=	=	X
ejpam-3258	69	15	[	[	PUNCT
ejpam-3258	69	16	−1	−1	NOUN
ejpam-3258	69	17	2	2	NUM
ejpam-3258	69	18	−	−	NOUN
ejpam-3258	69	19	√	√	NUM
ejpam-3258	69	20	3	3	NUM
ejpam-3258	69	21	2	2	NUM
ejpam-3258	69	22	i	i	NOUN
ejpam-3258	69	23	0	0	NUM
ejpam-3258	69	24	0	0	NUM
ejpam-3258	69	25	−1	−1	NOUN
ejpam-3258	69	26	2	2	NUM
ejpam-3258	69	27	+	+	CCONJ
ejpam-3258	69	28	√	√	NUM
ejpam-3258	69	29	3	3	NUM
ejpam-3258	69	30	2	2	NUM
ejpam-3258	69	31	i	i	NOUN
ejpam-3258	69	32	]	]	PUNCT
ejpam-3258	69	33	;	;	PUNCT
ejpam-3258	69	34	b	b	X
ejpam-3258	69	35	=	=	SYM
ejpam-3258	69	36	[	[	PUNCT
ejpam-3258	69	37	0	0	NUM
ejpam-3258	69	38	1	1	NUM
ejpam-3258	69	39	2	2	NUM
ejpam-3258	69	40	+	+	CCONJ
ejpam-3258	69	41	√	√	NUM
ejpam-3258	69	42	3	3	NUM
ejpam-3258	69	43	2	2	NUM
ejpam-3258	69	44	i	i	PRON
ejpam-3258	69	45	−1	−1	NOUN
ejpam-3258	69	46	2	2	NUM
ejpam-3258	69	47	−	−	NOUN
ejpam-3258	69	48	√	√	NUM
ejpam-3258	69	49	3	3	NUM
ejpam-3258	69	50	2	2	NUM
ejpam-3258	69	51	i	i	NOUN
ejpam-3258	69	52	0	0	NUM
ejpam-3258	69	53	]	]	PUNCT
ejpam-3258	69	54	.	.	PUNCT
ejpam-3258	70	1	it	it	PRON
ejpam-3258	70	2	is	be	AUX
ejpam-3258	70	3	worth	worth	ADJ
ejpam-3258	70	4	mentioning	mention	VERB
ejpam-3258	70	5	here	here	ADV
ejpam-3258	70	6	that	that	SCONJ
ejpam-3258	70	7	a	a	PRON
ejpam-3258	70	8	and	and	CCONJ
ejpam-3258	70	9	b	b	NOUN
ejpam-3258	70	10	are	be	AUX
ejpam-3258	70	11	matrices	matrix	NOUN
ejpam-3258	70	12	of	of	ADP
ejpam-3258	70	13	order	order	NOUN
ejpam-3258	70	14	3	3	NUM
ejpam-3258	70	15	and	and	CCONJ
ejpam-3258	70	16	2	2	NUM
ejpam-3258	70	17	respectively	respectively	ADV
ejpam-3258	70	18	and	and	CCONJ
ejpam-3258	70	19	therefore	therefore	ADV
ejpam-3258	70	20	are	be	AUX
ejpam-3258	70	21	matrix	matrix	NOUN
ejpam-3258	70	22	generators	generator	NOUN
ejpam-3258	70	23	for	for	ADP
ejpam-3258	70	24	s3	s3	PROPN
ejpam-3258	70	25	.	.	PUNCT
ejpam-3258	71	1	for	for	ADP
ejpam-3258	71	2	the	the	DET
ejpam-3258	71	3	group	group	NOUN
ejpam-3258	71	4	s4	s4	NOUN
ejpam-3258	71	5	we	we	PRON
ejpam-3258	71	6	need	need	VERB
ejpam-3258	71	7	to	to	PART
ejpam-3258	71	8	construct	construct	VERB
ejpam-3258	71	9	representations	representation	NOUN
ejpam-3258	71	10	for	for	ADP
ejpam-3258	71	11	χ3	χ3	NOUN
ejpam-3258	71	12	,	,	PUNCT
ejpam-3258	71	13	χ4	χ4	NOUN
ejpam-3258	71	14	and	and	CCONJ
ejpam-3258	71	15	χ5	χ5	NOUN
ejpam-3258	71	16	.	.	PUNCT
ejpam-3258	72	1	the	the	DET
ejpam-3258	72	2	matrix	matrix	NOUN
ejpam-3258	72	3	representation	representation	NOUN
ejpam-3258	72	4	for	for	ADP
ejpam-3258	72	5	χ3	χ3	NOUN
ejpam-3258	72	6	is	be	AUX
ejpam-3258	72	7	given	give	VERB
ejpam-3258	72	8	by	by	ADP
ejpam-3258	72	9	the	the	DET
ejpam-3258	72	10	matrices	matrix	NOUN
ejpam-3258	72	11	a1	a1	NOUN
ejpam-3258	72	12	and	and	CCONJ
ejpam-3258	72	13	b1	b1	NOUN
ejpam-3258	72	14	where	where	SCONJ
ejpam-3258	72	15	a1	a1	NOUN
ejpam-3258	72	16	=	=	PUNCT
ejpam-3258	72	17	[	[	PUNCT
ejpam-3258	72	18	0	0	NUM
ejpam-3258	72	19	−1	−1	NOUN
ejpam-3258	72	20	2	2	NUM
ejpam-3258	72	21	+	+	CCONJ
ejpam-3258	72	22	√	√	NUM
ejpam-3258	72	23	3	3	NUM
ejpam-3258	72	24	2	2	NUM
ejpam-3258	72	25	i	i	PRON
ejpam-3258	72	26	−1	−1	NOUN
ejpam-3258	73	1	2	2	NUM
ejpam-3258	73	2	−	−	NOUN
ejpam-3258	73	3	√	√	NUM
ejpam-3258	73	4	3	3	NUM
ejpam-3258	73	5	2	2	NUM
ejpam-3258	73	6	i	i	NOUN
ejpam-3258	73	7	0	0	NUM
ejpam-3258	73	8	]	]	PUNCT
ejpam-3258	73	9	;	;	PUNCT
ejpam-3258	73	10	b1	b1	NOUN
ejpam-3258	73	11	=	=	PUNCT
ejpam-3258	73	12	[	[	PUNCT
ejpam-3258	73	13	0	0	NUM
ejpam-3258	73	14	1	1	NUM
ejpam-3258	73	15	1	1	NUM
ejpam-3258	73	16	0	0	NUM
ejpam-3258	73	17	]	]	PUNCT
ejpam-3258	73	18	.	.	PUNCT
ejpam-3258	74	1	these	these	PRON
ejpam-3258	74	2	are	be	AUX
ejpam-3258	74	3	matrix	matrix	NOUN
ejpam-3258	74	4	generators	generator	NOUN
ejpam-3258	74	5	of	of	ADP
ejpam-3258	74	6	s4	s4	PROPN
ejpam-3258	74	7	.	.	PUNCT
ejpam-3258	75	1	for	for	ADP
ejpam-3258	75	2	χ4	χ4	NOUN
ejpam-3258	75	3	we	we	PRON
ejpam-3258	75	4	get	get	VERB
ejpam-3258	75	5	a2	a2	NOUN
ejpam-3258	75	6	=	=	PUNCT
ejpam-3258	75	7	0	0	PROPN
ejpam-3258	75	8	0	0	NUM
ejpam-3258	75	9	−1	−1	NOUN
ejpam-3258	75	10	0	0	NUM
ejpam-3258	75	11	1	1	NUM
ejpam-3258	75	12	0	0	NUM
ejpam-3258	75	13	1	1	NUM
ejpam-3258	75	14	0	0	NUM
ejpam-3258	75	15	0	0	NUM
ejpam-3258	75	16			NOUN
ejpam-3258	75	17	;	;	PUNCT
ejpam-3258	75	18	b2	b2	NOUN
ejpam-3258	75	19	=	=	SYM
ejpam-3258	75	20			PROPN
ejpam-3258	75	21	0	0	NUM
ejpam-3258	75	22	−1	−1	NOUN
ejpam-3258	75	23	0	0	NUM
ejpam-3258	75	24	−1	−1	NOUN
ejpam-3258	75	25	0	0	NUM
ejpam-3258	75	26	0	0	NUM
ejpam-3258	75	27	0	0	NUM
ejpam-3258	75	28	0	0	NUM
ejpam-3258	75	29	−1	−1	NOUN
ejpam-3258	75	30			NOUN
ejpam-3258	75	31	.	.	PUNCT
ejpam-3258	76	1	similarly	similarly	ADV
ejpam-3258	76	2	for	for	ADP
ejpam-3258	76	3	χ5	χ5	NOUN
ejpam-3258	76	4	the	the	DET
ejpam-3258	76	5	matrix	matrix	NOUN
ejpam-3258	76	6	representation	representation	NOUN
ejpam-3258	76	7	of	of	ADP
ejpam-3258	76	8	s5	s5	PROPN
ejpam-3258	76	9	is	be	AUX
ejpam-3258	76	10	given	give	VERB
ejpam-3258	76	11	by	by	ADP
ejpam-3258	76	12	the	the	DET
ejpam-3258	76	13	matrices	matrix	NOUN
ejpam-3258	76	14	a3	a3	NOUN
ejpam-3258	76	15	and	and	CCONJ
ejpam-3258	76	16	b3	b3	PROPN
ejpam-3258	76	17	where	where	SCONJ
ejpam-3258	76	18	a3	a3	NOUN
ejpam-3258	76	19	=	=	SYM
ejpam-3258	76	20			PROPN
ejpam-3258	76	21	0	0	NUM
ejpam-3258	76	22	0	0	NUM
ejpam-3258	76	23	1	1	NUM
ejpam-3258	76	24	0	0	NUM
ejpam-3258	76	25	−1	−1	NOUN
ejpam-3258	76	26	0	0	NUM
ejpam-3258	76	27	−1	−1	NOUN
ejpam-3258	76	28	0	0	NUM
ejpam-3258	76	29	0	0	NUM
ejpam-3258	76	30			NOUN
ejpam-3258	76	31	;	;	PUNCT
ejpam-3258	76	32	b3	b3	PROPN
ejpam-3258	76	33	=	=	SYM
ejpam-3258	76	34			PROPN
ejpam-3258	76	35	0	0	NUM
ejpam-3258	76	36	−1	−1	NOUN
ejpam-3258	76	37	0	0	NUM
ejpam-3258	76	38	−1	−1	NOUN
ejpam-3258	76	39	0	0	NUM
ejpam-3258	76	40	0	0	NUM
ejpam-3258	76	41	0	0	NUM
ejpam-3258	76	42	0	0	NUM
ejpam-3258	76	43	−1	−1	NOUN
ejpam-3258	76	44			NOUN
ejpam-3258	76	45	.	.	PUNCT
ejpam-3258	77	1	in	in	ADP
ejpam-3258	77	2	this	this	DET
ejpam-3258	77	3	paper	paper	NOUN
ejpam-3258	77	4	we	we	PRON
ejpam-3258	77	5	will	will	AUX
ejpam-3258	77	6	compute	compute	VERB
ejpam-3258	77	7	the	the	DET
ejpam-3258	77	8	µ−values	µ−value	NOUN
ejpam-3258	77	9	for	for	ADP
ejpam-3258	77	10	the	the	DET
ejpam-3258	77	11	matrices	matrix	NOUN
ejpam-3258	77	12	obtained	obtain	VERB
ejpam-3258	77	13	from	from	ADP
ejpam-3258	77	14	the	the	DET
ejpam-3258	77	15	representations	representation	NOUN
ejpam-3258	77	16	of	of	ADP
ejpam-3258	77	17	symmetric	symmetric	ADJ
ejpam-3258	77	18	group	group	NOUN
ejpam-3258	77	19	sn	sn	PROPN
ejpam-3258	77	20	for	for	ADP
ejpam-3258	77	21	n	n	NOUN
ejpam-3258	77	22	=	=	SYM
ejpam-3258	77	23	3	3	NUM
ejpam-3258	77	24	,	,	PUNCT
ejpam-3258	77	25	4	4	NUM
ejpam-3258	77	26	.	.	PUNCT
ejpam-3258	78	1	in	in	ADP
ejpam-3258	78	2	the	the	DET
ejpam-3258	78	3	following	follow	VERB
ejpam-3258	78	4	subsection	subsection	NOUN
ejpam-3258	78	5	we	we	PRON
ejpam-3258	78	6	give	give	VERB
ejpam-3258	78	7	definition	definition	NOUN
ejpam-3258	78	8	of	of	ADP
ejpam-3258	78	9	ssv	ssv	NOUN
ejpam-3258	78	10	.	.	PUNCT
ejpam-3258	79	1	in	in	ADP
ejpam-3258	79	2	the	the	DET
ejpam-3258	79	3	subsequent	subsequent	ADJ
ejpam-3258	79	4	sections	section	NOUN
ejpam-3258	79	5	we	we	PRON
ejpam-3258	79	6	present	present	VERB
ejpam-3258	79	7	the	the	DET
ejpam-3258	79	8	algorithm	algorithm	NOUN
ejpam-3258	79	9	for	for	ADP
ejpam-3258	79	10	ssv	ssv	NOUN
ejpam-3258	79	11	and	and	CCONJ
ejpam-3258	79	12	discuss	discuss	VERB
ejpam-3258	79	13	our	our	PRON
ejpam-3258	79	14	main	main	ADJ
ejpam-3258	79	15	results	result	NOUN
ejpam-3258	79	16	.	.	PUNCT
ejpam-3258	80	1	consider	consider	VERB
ejpam-3258	80	2	n	n	CCONJ
ejpam-3258	80	3	-	-	PUNCT
ejpam-3258	80	4	dimensional	dimensional	ADJ
ejpam-3258	80	5	real	real	ADJ
ejpam-3258	80	6	(	(	PUNCT
ejpam-3258	80	7	or	or	CCONJ
ejpam-3258	80	8	complex	complex	ADJ
ejpam-3258	80	9	)	)	PUNCT
ejpam-3258	80	10	matrix	matrix	NOUN
ejpam-3258	80	11	m	m	NOUN
ejpam-3258	80	12	and	and	CCONJ
ejpam-3258	80	13	a	a	DET
ejpam-3258	80	14	set	set	NOUN
ejpam-3258	80	15	of	of	ADP
ejpam-3258	80	16	block	block	NOUN
ejpam-3258	80	17	diagonal	diagonal	ADJ
ejpam-3258	80	18	matrices	matrix	NOUN
ejpam-3258	80	19	∆b	∆b	PROPN
ejpam-3258	80	20	,	,	PUNCT
ejpam-3258	80	21	where	where	SCONJ
ejpam-3258	80	22	∆b	∆b	PROPN
ejpam-3258	80	23	=	=	SYM
ejpam-3258	80	24	{	{	PUNCT
ejpam-3258	80	25	diag(γi	diag(γi	NOUN
ejpam-3258	80	26	,	,	PUNCT
ejpam-3258	80	27	αjij	αjij	NOUN
ejpam-3258	80	28	)	)	PUNCT
ejpam-3258	80	29	:	:	PUNCT
ejpam-3258	81	1	γi	γi	PROPN
ejpam-3258	81	2	∈	∈	PROPN
ejpam-3258	81	3	cmi	cmi	PROPN
ejpam-3258	81	4	,	,	PUNCT
ejpam-3258	81	5	mi(rmi	mi(rmi	PROPN
ejpam-3258	81	6	,	,	PUNCT
ejpam-3258	81	7	mi	mi	PROPN
ejpam-3258	81	8	)	)	PUNCT
ejpam-3258	81	9	,	,	PUNCT
ejpam-3258	81	10	αj	αj	PROPN
ejpam-3258	81	11	∈	∈	PROPN
ejpam-3258	81	12	c(r	c(r	NOUN
ejpam-3258	81	13	)	)	PUNCT
ejpam-3258	81	14	}	}	PUNCT
ejpam-3258	81	15	,	,	PUNCT
ejpam-3258	81	16	where	where	SCONJ
ejpam-3258	81	17	ij	ij	NOUN
ejpam-3258	81	18	denotes	denote	VERB
ejpam-3258	81	19	the	the	DET
ejpam-3258	81	20	identity	identity	NOUN
ejpam-3258	81	21	matrix	matrix	NOUN
ejpam-3258	81	22	with	with	ADP
ejpam-3258	81	23	the	the	DET
ejpam-3258	81	24	dimension	dimension	NOUN
ejpam-3258	81	25	j.	j.	PROPN
ejpam-3258	81	26	we	we	PRON
ejpam-3258	81	27	give	give	VERB
ejpam-3258	81	28	following	follow	VERB
ejpam-3258	81	29	definition	definition	NOUN
ejpam-3258	81	30	of	of	ADP
ejpam-3258	81	31	ssv	ssv	PROPN
ejpam-3258	81	32	.	.	PROPN
ejpam-3258	81	33	m.	m.	PROPN
ejpam-3258	81	34	rehman	rehman	PROPN
ejpam-3258	81	35	,	,	PUNCT
ejpam-3258	81	36	m.	m.	PROPN
ejpam-3258	81	37	f.	f.	PROPN
ejpam-3258	81	38	anwar	anwar	PROPN
ejpam-3258	81	39	/	/	PUNCT
ejpam-3258	81	40	eur	eur	PROPN
ejpam-3258	81	41	.	.	PUNCT
ejpam-3258	82	1	j.	j.	PROPN
ejpam-3258	82	2	pure	pure	PROPN
ejpam-3258	82	3	appl	appl	PROPN
ejpam-3258	82	4	.	.	PROPN
ejpam-3258	82	5	math	math	PROPN
ejpam-3258	82	6	,	,	PUNCT
ejpam-3258	82	7	11	11	NUM
ejpam-3258	82	8	(	(	PUNCT
ejpam-3258	82	9	3	3	NUM
ejpam-3258	82	10	)	)	PUNCT
ejpam-3258	82	11	(	(	PUNCT
ejpam-3258	82	12	2018	2018	NUM
ejpam-3258	82	13	)	)	PUNCT
ejpam-3258	82	14	,	,	PUNCT
ejpam-3258	82	15	774	774	NUM
ejpam-3258	82	16	-	-	SYM
ejpam-3258	82	17	792	792	NUM
ejpam-3258	82	18	778	778	NUM
ejpam-3258	82	19	definition	definition	NOUN
ejpam-3258	82	20	1.2	1.2	NUM
ejpam-3258	82	21	[	[	X
ejpam-3258	82	22	11	11	NUM
ejpam-3258	82	23	]	]	PUNCT
ejpam-3258	82	24	.	.	PUNCT
ejpam-3258	83	1	for	for	ADP
ejpam-3258	83	2	a	a	DET
ejpam-3258	83	3	n×	n×	ADV
ejpam-3258	83	4	n	n	CCONJ
ejpam-3258	83	5	dimensional	dimensional	ADJ
ejpam-3258	83	6	real	real	ADJ
ejpam-3258	83	7	or	or	CCONJ
ejpam-3258	83	8	complex	complex	ADJ
ejpam-3258	83	9	matrix	matrix	NOUN
ejpam-3258	83	10	m	m	NOUN
ejpam-3258	83	11	and	and	CCONJ
ejpam-3258	83	12	consider	consider	VERB
ejpam-3258	83	13	a	a	DET
ejpam-3258	83	14	family	family	NOUN
ejpam-3258	83	15	of	of	ADP
ejpam-3258	83	16	block	block	NOUN
ejpam-3258	83	17	diagonal	diagonal	ADJ
ejpam-3258	83	18	matrices	matrix	NOUN
ejpam-3258	83	19	∆b	∆b	PROPN
ejpam-3258	83	20	.	.	PUNCT
ejpam-3258	84	1	then	then	ADV
ejpam-3258	84	2	the	the	DET
ejpam-3258	84	3	structured	structured	ADJ
ejpam-3258	84	4	singular	singular	ADJ
ejpam-3258	84	5	value	value	NOUN
ejpam-3258	84	6	denoted	denote	VERB
ejpam-3258	84	7	by	by	ADP
ejpam-3258	84	8	µ∆b(m	µ∆b(m	NOUN
ejpam-3258	84	9	)	)	PUNCT
ejpam-3258	84	10	is	be	AUX
ejpam-3258	84	11	given	give	VERB
ejpam-3258	84	12	as	as	ADP
ejpam-3258	84	13	µ∆b(m	µ∆b(m	ADV
ejpam-3258	84	14	)	)	PUNCT
ejpam-3258	84	15	:	:	PUNCT
ejpam-3258	84	16	=	=	SYM
ejpam-3258	84	17	1	1	NUM
ejpam-3258	84	18	min	min	NOUN
ejpam-3258	84	19	{	{	PUNCT
ejpam-3258	84	20	‖∆‖2	‖∆‖2	NOUN
ejpam-3258	84	21	:	:	PUNCT
ejpam-3258	84	22	∆	∆	PROPN
ejpam-3258	84	23	∈	∈	PROPN
ejpam-3258	84	24	∆b	∆b	PROPN
ejpam-3258	84	25	,	,	PUNCT
ejpam-3258	84	26	|(i	|(i	NUM
ejpam-3258	84	27	−m∆)|	−m∆)|	NOUN
ejpam-3258	84	28	=	=	SYM
ejpam-3258	84	29	0	0	NUM
ejpam-3258	84	30	}	}	PUNCT
ejpam-3258	84	31	.	.	PUNCT
ejpam-3258	85	1	(	(	PUNCT
ejpam-3258	85	2	1	1	X
ejpam-3258	85	3	)	)	PUNCT
ejpam-3258	85	4	in	in	ADP
ejpam-3258	85	5	definition	definition	NOUN
ejpam-3258	85	6	1.2	1.2	NUM
ejpam-3258	85	7	,	,	PUNCT
ejpam-3258	85	8	|	|	ADV
ejpam-3258	85	9	·	·	PUNCT
ejpam-3258	85	10	|	|	ADV
ejpam-3258	85	11	denotes	denote	VERB
ejpam-3258	85	12	the	the	DET
ejpam-3258	85	13	determinant	determinant	NOUN
ejpam-3258	85	14	of	of	ADP
ejpam-3258	85	15	a	a	DET
ejpam-3258	85	16	matrix	matrix	NOUN
ejpam-3258	85	17	while	while	SCONJ
ejpam-3258	85	18	matrix	matrix	NOUN
ejpam-3258	85	19	2	2	NUM
ejpam-3258	85	20	-	-	PUNCT
ejpam-3258	85	21	norm	norm	NOUN
ejpam-3258	85	22	is	be	AUX
ejpam-3258	85	23	give	give	VERB
ejpam-3258	85	24	by	by	ADP
ejpam-3258	85	25	‖	‖	PROPN
ejpam-3258	85	26	·	·	PUNCT
ejpam-3258	85	27	‖.	‖.	X
ejpam-3258	85	28	from	from	ADP
ejpam-3258	85	29	above	above	ADP
ejpam-3258	85	30	definition	definition	NOUN
ejpam-3258	85	31	of	of	ADP
ejpam-3258	85	32	ssv	ssv	NOUN
ejpam-3258	85	33	,	,	PUNCT
ejpam-3258	85	34	its	its	PRON
ejpam-3258	85	35	clear	clear	ADJ
ejpam-3258	85	36	that	that	SCONJ
ejpam-3258	85	37	µ∆b(m	µ∆b(m	VERB
ejpam-3258	85	38	)	)	PUNCT
ejpam-3258	86	1	=	=	SYM
ejpam-3258	86	2	0	0	PUNCT
ejpam-3258	87	1	if	if	SCONJ
ejpam-3258	87	2	|(i	|(i	PROPN
ejpam-3258	87	3	−m∆)|	−m∆)|	PROPN
ejpam-3258	87	4	6=	6=	ADP
ejpam-3258	87	5	0	0	NUM
ejpam-3258	87	6	for	for	ADP
ejpam-3258	87	7	all	all	DET
ejpam-3258	87	8	∆	∆	PROPN
ejpam-3258	87	9	∈	∈	PROPN
ejpam-3258	87	10	∆b	∆b	PROPN
ejpam-3258	87	11	.	.	PUNCT
ejpam-3258	88	1	the	the	DET
ejpam-3258	88	2	most	most	ADV
ejpam-3258	88	3	important	important	ADJ
ejpam-3258	88	4	case	case	NOUN
ejpam-3258	88	5	under	under	ADP
ejpam-3258	88	6	consideration	consideration	NOUN
ejpam-3258	88	7	is	be	AUX
ejpam-3258	88	8	when	when	SCONJ
ejpam-3258	88	9	∆b	∆b	PROPN
ejpam-3258	88	10	allows	allow	VERB
ejpam-3258	88	11	only	only	ADV
ejpam-3258	88	12	pure	pure	ADJ
ejpam-3258	88	13	complex	complex	ADJ
ejpam-3258	88	14	uncertainties	uncertainty	NOUN
ejpam-3258	88	15	.	.	PUNCT
ejpam-3258	89	1	in	in	ADP
ejpam-3258	89	2	this	this	DET
ejpam-3258	89	3	case	case	NOUN
ejpam-3258	89	4	we	we	PRON
ejpam-3258	89	5	write	write	VERB
ejpam-3258	89	6	∆∗b	∆∗b	NOUN
ejpam-3258	89	7	instead	instead	ADV
ejpam-3258	89	8	of	of	ADP
ejpam-3258	89	9	∆b	∆b	PROPN
ejpam-3258	89	10	.	.	PUNCT
ejpam-3258	90	1	the	the	DET
ejpam-3258	90	2	pure	pure	ADJ
ejpam-3258	90	3	complex	complex	ADJ
ejpam-3258	90	4	uncertainties	uncertainty	NOUN
ejpam-3258	90	5	∆	∆	X
ejpam-3258	90	6	∈	∈	NOUN
ejpam-3258	90	7	∆∗b	∆∗b	NOUN
ejpam-3258	90	8	gives	give	VERB
ejpam-3258	90	9	exp(iϕ)∆	exp(iϕ)∆	NOUN
ejpam-3258	90	10	∈	∈	NOUN
ejpam-3258	90	11	∆∗b	∆∗b	NOUN
ejpam-3258	90	12	for	for	ADP
ejpam-3258	90	13	any	any	DET
ejpam-3258	90	14	ϕ	ϕ	PROPN
ejpam-3258	90	15	∈	∈	PROPN
ejpam-3258	90	16	r.	r.	PROPN
ejpam-3258	90	17	as	as	ADP
ejpam-3258	90	18	a	a	DET
ejpam-3258	90	19	result	result	NOUN
ejpam-3258	90	20	,	,	PUNCT
ejpam-3258	90	21	this	this	PRON
ejpam-3258	90	22	gives	give	VERB
ejpam-3258	90	23	us	we	PRON
ejpam-3258	90	24	a	a	DET
ejpam-3258	90	25	suitable	suitable	ADJ
ejpam-3258	90	26	choice	choice	NOUN
ejpam-3258	90	27	of	of	ADP
ejpam-3258	90	28	∆	∆	X
ejpam-3258	90	29	∈	∈	PROPN
ejpam-3258	90	30	∆∗b	∆∗b	NOUN
ejpam-3258	90	31	such	such	ADJ
ejpam-3258	90	32	that	that	SCONJ
ejpam-3258	90	33	spectral	spectral	ADJ
ejpam-3258	90	34	radius	radius	NOUN
ejpam-3258	90	35	attains	attain	VERB
ejpam-3258	90	36	the	the	DET
ejpam-3258	90	37	maximum	maximum	ADJ
ejpam-3258	90	38	value	value	NOUN
ejpam-3258	90	39	1	1	NUM
ejpam-3258	90	40	that	that	PRON
ejpam-3258	90	41	is	be	AUX
ejpam-3258	90	42	ρ(m∆	ρ(m∆	NOUN
ejpam-3258	90	43	)	)	PUNCT
ejpam-3258	91	1	=	=	SYM
ejpam-3258	91	2	1	1	NUM
ejpam-3258	91	3	iff	iff	NOUN
ejpam-3258	91	4	there	there	PRON
ejpam-3258	91	5	is	be	VERB
ejpam-3258	91	6	∆′	∆′	PROPN
ejpam-3258	91	7	∈	∈	PROPN
ejpam-3258	91	8	∆∗b	∆∗b	NOUN
ejpam-3258	91	9	,	,	PUNCT
ejpam-3258	91	10	which	which	PRON
ejpam-3258	91	11	possesses	possess	VERB
ejpam-3258	91	12	the	the	DET
ejpam-3258	91	13	same	same	ADJ
ejpam-3258	91	14	matrix	matrix	NOUN
ejpam-3258	91	15	2	2	NUM
ejpam-3258	91	16	-	-	PUNCT
ejpam-3258	91	17	norm	norm	NOUN
ejpam-3258	91	18	so	so	SCONJ
ejpam-3258	91	19	that	that	SCONJ
ejpam-3258	91	20	m∆′	m∆′	NUM
ejpam-3258	91	21	posses	posse	VERB
ejpam-3258	91	22	an	an	DET
ejpam-3258	91	23	eigenvalue	eigenvalue	PROPN
ejpam-3258	91	24	1	1	NUM
ejpam-3258	91	25	,	,	PUNCT
ejpam-3258	91	26	this	this	PRON
ejpam-3258	91	27	in	in	ADP
ejpam-3258	91	28	turn	turn	NOUN
ejpam-3258	91	29	implies	imply	VERB
ejpam-3258	91	30	that	that	SCONJ
ejpam-3258	91	31	the	the	DET
ejpam-3258	91	32	matrix	matrix	NOUN
ejpam-3258	91	33	(	(	PUNCT
ejpam-3258	91	34	i	i	NOUN
ejpam-3258	91	35	−m∆′	−m∆′	NOUN
ejpam-3258	91	36	)	)	PUNCT
ejpam-3258	91	37	is	be	AUX
ejpam-3258	91	38	singular	singular	ADJ
ejpam-3258	91	39	.	.	PUNCT
ejpam-3258	92	1	from	from	ADP
ejpam-3258	92	2	above	above	ADP
ejpam-3258	92	3	discussion	discussion	NOUN
ejpam-3258	92	4	on	on	ADP
ejpam-3258	92	5	pure	pure	ADJ
ejpam-3258	92	6	complex	complex	ADJ
ejpam-3258	92	7	uncertainties	uncertainty	NOUN
ejpam-3258	92	8	we	we	PRON
ejpam-3258	92	9	have	have	AUX
ejpam-3258	92	10	following	follow	VERB
ejpam-3258	92	11	alternative	alternative	ADJ
ejpam-3258	92	12	expression	expression	NOUN
ejpam-3258	92	13	for	for	ADP
ejpam-3258	92	14	ssv	ssv	NOUN
ejpam-3258	92	15	:	:	PUNCT
ejpam-3258	92	16	∆∗b	∆∗b	NOUN
ejpam-3258	92	17	=	=	SYM
ejpam-3258	92	18	1	1	NUM
ejpam-3258	92	19	min	min	NOUN
ejpam-3258	92	20	{	{	PUNCT
ejpam-3258	92	21	‖∆‖2	‖∆‖2	NOUN
ejpam-3258	92	22	:	:	PUNCT
ejpam-3258	93	1	∆	∆	PROPN
ejpam-3258	93	2	∈	∈	PROPN
ejpam-3258	93	3	∆∗b	∆∗b	NOUN
ejpam-3258	93	4	,	,	PUNCT
ejpam-3258	93	5	ρ(m∆	ρ(m∆	NOUN
ejpam-3258	93	6	)	)	PUNCT
ejpam-3258	93	7	=	=	SYM
ejpam-3258	93	8	1	1	X
ejpam-3258	93	9	}	}	PUNCT
ejpam-3258	93	10	,	,	PUNCT
ejpam-3258	93	11	(	(	PUNCT
ejpam-3258	93	12	2	2	X
ejpam-3258	93	13	)	)	PUNCT
ejpam-3258	93	14	where	where	SCONJ
ejpam-3258	93	15	ρ	ρ	PROPN
ejpam-3258	93	16	(	(	PUNCT
ejpam-3258	93	17	·	·	PUNCT
ejpam-3258	93	18	)	)	PUNCT
ejpam-3258	93	19	is	be	AUX
ejpam-3258	93	20	the	the	DET
ejpam-3258	93	21	spectral	spectral	ADJ
ejpam-3258	93	22	radius	radius	NOUN
ejpam-3258	93	23	of	of	ADP
ejpam-3258	93	24	a	a	DET
ejpam-3258	93	25	matrix	matrix	NOUN
ejpam-3258	93	26	m∆	m∆	NUM
ejpam-3258	93	27	,	,	PUNCT
ejpam-3258	93	28	that	that	ADV
ejpam-3258	93	29	is	is	ADV
ejpam-3258	93	30	,	,	PUNCT
ejpam-3258	93	31	maximum	maximum	ADJ
ejpam-3258	93	32	absolute	absolute	ADJ
ejpam-3258	93	33	value	value	NOUN
ejpam-3258	93	34	of	of	ADP
ejpam-3258	93	35	eigenvalue	eigenvalue	PROPN
ejpam-3258	93	36	of	of	ADP
ejpam-3258	93	37	m∆.	m∆.	PROPN
ejpam-3258	93	38	2	2	NUM
ejpam-3258	93	39	.	.	X
ejpam-3258	93	40	ssv	ssv	NOUN
ejpam-3258	93	41	based	base	VERB
ejpam-3258	93	42	on	on	ADP
ejpam-3258	93	43	structured	structured	ADJ
ejpam-3258	93	44	spectral	spectral	ADJ
ejpam-3258	93	45	sets	set	NOUN
ejpam-3258	93	46	structured	structure	VERB
ejpam-3258	93	47	spectral	spectral	ADJ
ejpam-3258	93	48	value	value	NOUN
ejpam-3258	93	49	set	set	NOUN
ejpam-3258	93	50	of	of	ADP
ejpam-3258	93	51	a	a	DET
ejpam-3258	93	52	given	give	VERB
ejpam-3258	93	53	n	n	CCONJ
ejpam-3258	93	54	dimensional	dimensional	ADJ
ejpam-3258	93	55	complex	complex	ADJ
ejpam-3258	93	56	m	m	NOUN
ejpam-3258	93	57	with	with	ADP
ejpam-3258	93	58	respect	respect	NOUN
ejpam-3258	93	59	to	to	ADP
ejpam-3258	93	60	ε0	ε0	PROPN
ejpam-3258	93	61	,	,	PUNCT
ejpam-3258	93	62	the	the	DET
ejpam-3258	93	63	perturbation	perturbation	NOUN
ejpam-3258	93	64	level	level	NOUN
ejpam-3258	93	65	is	be	AUX
ejpam-3258	93	66	given	give	VERB
ejpam-3258	93	67	as	as	ADP
ejpam-3258	93	68	λ∆b	λ∆b	ADJ
ejpam-3258	93	69	ε0	ε0	PROPN
ejpam-3258	93	70	(	(	PUNCT
ejpam-3258	93	71	m	m	NOUN
ejpam-3258	93	72	)	)	PUNCT
ejpam-3258	93	73	=	=	SYM
ejpam-3258	93	74	{	{	PUNCT
ejpam-3258	93	75	λ	λ	X
ejpam-3258	93	76	∈	∈	PROPN
ejpam-3258	93	77	λ(ε0m∆	λ(ε0m∆	PROPN
ejpam-3258	93	78	)	)	PUNCT
ejpam-3258	93	79	:	:	PUNCT
ejpam-3258	94	1	∆	∆	PROPN
ejpam-3258	94	2	∈	∈	PROPN
ejpam-3258	94	3	∆b	∆b	PROPN
ejpam-3258	94	4	}	}	PUNCT
ejpam-3258	94	5	,	,	PUNCT
ejpam-3258	94	6	(	(	PUNCT
ejpam-3258	94	7	3	3	X
ejpam-3258	94	8	)	)	PUNCT
ejpam-3258	94	9	where	where	SCONJ
ejpam-3258	94	10	λ	λ	X
ejpam-3258	94	11	(	(	PUNCT
ejpam-3258	94	12	·	·	PUNCT
ejpam-3258	94	13	)	)	PUNCT
ejpam-3258	94	14	contains	contain	VERB
ejpam-3258	94	15	all	all	DET
ejpam-3258	94	16	eigenvalues	eigenvalue	NOUN
ejpam-3258	94	17	of	of	ADP
ejpam-3258	94	18	a	a	DET
ejpam-3258	94	19	matrix	matrix	NOUN
ejpam-3258	94	20	while	while	SCONJ
ejpam-3258	94	21	∆	∆	PROPN
ejpam-3258	94	22	has	have	VERB
ejpam-3258	94	23	a	a	DET
ejpam-3258	94	24	unit	unit	NOUN
ejpam-3258	94	25	2	2	NUM
ejpam-3258	94	26	-	-	PUNCT
ejpam-3258	94	27	norm	norm	NOUN
ejpam-3258	94	28	.	.	PUNCT
ejpam-3258	95	1	the	the	DET
ejpam-3258	95	2	above	above	ADV
ejpam-3258	95	3	set	set	ADJ
ejpam-3258	95	4	λ∆b	λ∆b	ADJ
ejpam-3258	95	5	ε0	ε0	PROPN
ejpam-3258	95	6	(	(	PUNCT
ejpam-3258	95	7	m	m	NOUN
ejpam-3258	95	8	)	)	PUNCT
ejpam-3258	95	9	is	be	AUX
ejpam-3258	95	10	simply	simply	ADV
ejpam-3258	95	11	a	a	DET
ejpam-3258	95	12	disk	disk	NOUN
ejpam-3258	95	13	centered	center	VERB
ejpam-3258	95	14	at	at	ADP
ejpam-3258	95	15	the	the	DET
ejpam-3258	95	16	origin	origin	NOUN
ejpam-3258	95	17	say	say	VERB
ejpam-3258	95	18	o	o	NOUN
ejpam-3258	95	19	when	when	SCONJ
ejpam-3258	95	20	∆∗b	∆∗b	NOUN
ejpam-3258	95	21	contains	contain	VERB
ejpam-3258	95	22	only	only	ADV
ejpam-3258	95	23	pure	pure	ADJ
ejpam-3258	95	24	complex	complex	ADJ
ejpam-3258	95	25	uncertainties	uncertainty	NOUN
ejpam-3258	95	26	.	.	PUNCT
ejpam-3258	96	1	the	the	DET
ejpam-3258	96	2	structured	structured	ADJ
ejpam-3258	96	3	spectral	spectral	ADJ
ejpam-3258	96	4	values	value	NOUN
ejpam-3258	96	5	set	set	VERB
ejpam-3258	96	6	σ∆b	σ∆b	ADJ
ejpam-3258	96	7	ε	ε	PROPN
ejpam-3258	96	8	(	(	PUNCT
ejpam-3258	96	9	m	m	NOUN
ejpam-3258	96	10	)	)	PUNCT
ejpam-3258	96	11	=	=	PRON
ejpam-3258	96	12	{	{	PUNCT
ejpam-3258	96	13	ξ	ξ	X
ejpam-3258	96	14	=	=	SYM
ejpam-3258	96	15	1−	1−	NUM
ejpam-3258	96	16	λ	λ	NOUN
ejpam-3258	96	17	:	:	PUNCT
ejpam-3258	96	18	λ	λ	X
ejpam-3258	96	19	∈	∈	PROPN
ejpam-3258	96	20	λ∆b	λ∆b	NOUN
ejpam-3258	96	21	ε0	ε0	PROPN
ejpam-3258	96	22	(	(	PUNCT
ejpam-3258	96	23	m	m	NOUN
ejpam-3258	96	24	)	)	PUNCT
ejpam-3258	96	25	}	}	PUNCT
ejpam-3258	96	26	,	,	PUNCT
ejpam-3258	96	27	(	(	PUNCT
ejpam-3258	96	28	4	4	X
ejpam-3258	96	29	)	)	PUNCT
ejpam-3258	96	30	allows	allow	VERB
ejpam-3258	96	31	us	we	PRON
ejpam-3258	96	32	to	to	PART
ejpam-3258	96	33	write	write	VERB
ejpam-3258	96	34	down	down	ADP
ejpam-3258	96	35	the	the	DET
ejpam-3258	96	36	structured	structured	ADJ
ejpam-3258	96	37	singular	singular	ADJ
ejpam-3258	96	38	values	value	NOUN
ejpam-3258	96	39	defined	define	VERB
ejpam-3258	96	40	in	in	ADP
ejpam-3258	96	41	equ	equ	PROPN
ejpam-3258	96	42	.	.	PUNCT
ejpam-3258	97	1	(	(	PUNCT
ejpam-3258	97	2	2	2	X
ejpam-3258	97	3	)	)	PUNCT
ejpam-3258	97	4	as	as	ADP
ejpam-3258	97	5	below	below	ADV
ejpam-3258	97	6	when	when	SCONJ
ejpam-3258	97	7	both	both	DET
ejpam-3258	97	8	real	real	ADJ
ejpam-3258	97	9	and	and	CCONJ
ejpam-3258	97	10	complex	complex	ADJ
ejpam-3258	97	11	uncertainties	uncertainty	NOUN
ejpam-3258	97	12	are	be	AUX
ejpam-3258	97	13	under	under	ADP
ejpam-3258	97	14	consideration	consideration	NOUN
ejpam-3258	97	15	µ∆b(m	µ∆b(m	ADJ
ejpam-3258	97	16	)	)	PUNCT
ejpam-3258	97	17	=	=	SYM
ejpam-3258	97	18	1	1	NUM
ejpam-3258	97	19	arg	arg	NOUN
ejpam-3258	97	20	min{0	min{0	PROPN
ejpam-3258	97	21	∈	∈	PROPN
ejpam-3258	97	22	σ∆b	σ∆b	ADJ
ejpam-3258	97	23	ε0	ε0	NOUN
ejpam-3258	97	24	(	(	PUNCT
ejpam-3258	97	25	m	m	NOUN
ejpam-3258	97	26	)	)	PUNCT
ejpam-3258	97	27	}	}	PUNCT
ejpam-3258	97	28	,	,	PUNCT
ejpam-3258	97	29	(	(	PUNCT
ejpam-3258	97	30	5	5	X
ejpam-3258	97	31	)	)	PUNCT
ejpam-3258	97	32	for	for	ADP
ejpam-3258	97	33	a	a	DET
ejpam-3258	97	34	purely	purely	ADV
ejpam-3258	97	35	complex	complex	ADJ
ejpam-3258	97	36	uncertainties	uncertainty	NOUN
ejpam-3258	97	37	∆∗b	∆∗b	NOUN
ejpam-3258	97	38	,	,	PUNCT
ejpam-3258	97	39	one	one	PRON
ejpam-3258	97	40	can	can	AUX
ejpam-3258	97	41	rewrite	rewrite	VERB
ejpam-3258	97	42	equ	equ	PROPN
ejpam-3258	97	43	.	.	PUNCT
ejpam-3258	98	1	(	(	PUNCT
ejpam-3258	98	2	3)to	3)to	ADJ
ejpam-3258	98	3	express	express	NOUN
ejpam-3258	98	4	ssv	ssv	NOUN
ejpam-3258	98	5	as	as	ADP
ejpam-3258	98	6	µ∆∗b	µ∆∗b	PROPN
ejpam-3258	98	7	(	(	PUNCT
ejpam-3258	98	8	m	m	NOUN
ejpam-3258	98	9	)	)	PUNCT
ejpam-3258	98	10	=	=	SYM
ejpam-3258	98	11	1	1	NUM
ejpam-3258	98	12	arg	arg	NOUN
ejpam-3258	98	13	min{max	min{max	NOUN
ejpam-3258	98	14	|λ|	|λ|	PROPN
ejpam-3258	98	15	=	=	PUNCT
ejpam-3258	98	16	1	1	NUM
ejpam-3258	98	17	}	}	PUNCT
ejpam-3258	98	18	,	,	PUNCT
ejpam-3258	98	19	(	(	PUNCT
ejpam-3258	98	20	6	6	X
ejpam-3258	98	21	)	)	PUNCT
ejpam-3258	98	22	m.	m.	NOUN
ejpam-3258	98	23	rehman	rehman	PROPN
ejpam-3258	98	24	,	,	PUNCT
ejpam-3258	98	25	m.	m.	PROPN
ejpam-3258	98	26	f.	f.	PROPN
ejpam-3258	98	27	anwar	anwar	PROPN
ejpam-3258	98	28	/	/	PUNCT
ejpam-3258	98	29	eur	eur	PROPN
ejpam-3258	98	30	.	.	PUNCT
ejpam-3258	99	1	j.	j.	PROPN
ejpam-3258	99	2	pure	pure	PROPN
ejpam-3258	99	3	appl	appl	PROPN
ejpam-3258	99	4	.	.	PROPN
ejpam-3258	99	5	math	math	PROPN
ejpam-3258	99	6	,	,	PUNCT
ejpam-3258	99	7	11	11	NUM
ejpam-3258	99	8	(	(	PUNCT
ejpam-3258	99	9	3	3	NUM
ejpam-3258	99	10	)	)	PUNCT
ejpam-3258	99	11	(	(	PUNCT
ejpam-3258	99	12	2018	2018	NUM
ejpam-3258	99	13	)	)	PUNCT
ejpam-3258	99	14	,	,	PUNCT
ejpam-3258	99	15	774	774	NUM
ejpam-3258	99	16	-	-	SYM
ejpam-3258	99	17	792	792	NUM
ejpam-3258	99	18	779	779	NUM
ejpam-3258	99	19	where	where	SCONJ
ejpam-3258	99	20	λ	λ	PROPN
ejpam-3258	99	21	∈	∈	PROPN
ejpam-3258	99	22	λ	λ	PROPN
ejpam-3258	99	23	∆∗b	∆∗b	NOUN
ejpam-3258	99	24	ε0	ε0	PROPN
ejpam-3258	99	25	(	(	PUNCT
ejpam-3258	99	26	m	m	NOUN
ejpam-3258	99	27	)	)	PUNCT
ejpam-3258	99	28	.	.	PUNCT
ejpam-3258	100	1	2.1	2.1	NUM
ejpam-3258	100	2	.	.	PUNCT
ejpam-3258	100	3	mathematical	mathematical	ADJ
ejpam-3258	100	4	problem	problem	NOUN
ejpam-3258	100	5	consider	consider	VERB
ejpam-3258	100	6	the	the	DET
ejpam-3258	100	7	following	follow	VERB
ejpam-3258	100	8	optimization	optimization	NOUN
ejpam-3258	100	9	problem	problem	NOUN
ejpam-3258	100	10	ξ(ε0	ξ(ε0	NOUN
ejpam-3258	100	11	)	)	PUNCT
ejpam-3258	101	1	=	=	SYM
ejpam-3258	101	2	arg	arg	NOUN
ejpam-3258	101	3	min	min	PROPN
ejpam-3258	101	4	|ξ|	|ξ|	PROPN
ejpam-3258	101	5	.	.	PUNCT
ejpam-3258	102	1	(	(	PUNCT
ejpam-3258	102	2	7	7	NUM
ejpam-3258	102	3	)	)	PUNCT
ejpam-3258	102	4	in	in	ADP
ejpam-3258	102	5	equ	equ	PROPN
ejpam-3258	102	6	.	.	PUNCT
ejpam-3258	103	1	(	(	PUNCT
ejpam-3258	103	2	7	7	NUM
ejpam-3258	103	3	)	)	PUNCT
ejpam-3258	103	4	,	,	PUNCT
ejpam-3258	103	5	ξ	ξ	PROPN
ejpam-3258	103	6	∈	∈	PROPN
ejpam-3258	103	7	σ∆b	σ∆b	ADJ
ejpam-3258	103	8	ε0	ε0	NOUN
ejpam-3258	103	9	(	(	PUNCT
ejpam-3258	103	10	m	m	NOUN
ejpam-3258	103	11	)	)	PUNCT
ejpam-3258	103	12	.	.	PUNCT
ejpam-3258	104	1	from	from	ADP
ejpam-3258	104	2	above	above	ADP
ejpam-3258	104	3	discussion	discussion	NOUN
ejpam-3258	104	4	we	we	PRON
ejpam-3258	104	5	obtain	obtain	VERB
ejpam-3258	104	6	a	a	DET
ejpam-3258	104	7	fact	fact	NOUN
ejpam-3258	104	8	that	that	SCONJ
ejpam-3258	104	9	ssv	ssv	NOUN
ejpam-3258	104	10	µ∆b(m	µ∆b(m	ADV
ejpam-3258	104	11	)	)	PUNCT
ejpam-3258	104	12	is	be	AUX
ejpam-3258	104	13	the	the	DET
ejpam-3258	104	14	reciprocal	reciprocal	NOUN
ejpam-3258	104	15	of	of	ADP
ejpam-3258	104	16	the	the	DET
ejpam-3258	104	17	minimum	minimum	ADJ
ejpam-3258	104	18	value	value	NOUN
ejpam-3258	104	19	of	of	ADP
ejpam-3258	104	20	perturbation	perturbation	NOUN
ejpam-3258	104	21	level	level	NOUN
ejpam-3258	104	22	for	for	ADP
ejpam-3258	104	23	which	which	PRON
ejpam-3258	104	24	ξ(ε0	ξ(ε0	NOUN
ejpam-3258	104	25	)	)	PUNCT
ejpam-3258	104	26	=	=	SYM
ejpam-3258	104	27	0	0	X
ejpam-3258	104	28	.	.	PUNCT
ejpam-3258	105	1	in	in	ADP
ejpam-3258	105	2	order	order	NOUN
ejpam-3258	105	3	to	to	PART
ejpam-3258	105	4	overcome	overcome	VERB
ejpam-3258	105	5	this	this	DET
ejpam-3258	105	6	difficulty	difficulty	NOUN
ejpam-3258	105	7	we	we	PRON
ejpam-3258	105	8	give	give	VERB
ejpam-3258	105	9	a	a	DET
ejpam-3258	105	10	two	two	NUM
ejpam-3258	105	11	-	-	PUNCT
ejpam-3258	105	12	level	level	NOUN
ejpam-3258	105	13	algorithm	algorithm	NOUN
ejpam-3258	105	14	,	,	PUNCT
ejpam-3258	105	15	that	that	PRON
ejpam-3258	105	16	is	be	AUX
ejpam-3258	105	17	inner	inner	ADJ
ejpam-3258	105	18	and	and	CCONJ
ejpam-3258	105	19	outer	outer	ADJ
ejpam-3258	105	20	algorithm	algorithm	NOUN
ejpam-3258	105	21	:	:	PUNCT
ejpam-3258	105	22	by	by	ADP
ejpam-3258	105	23	the	the	DET
ejpam-3258	105	24	help	help	NOUN
ejpam-3258	105	25	of	of	ADP
ejpam-3258	105	26	inner	inner	ADJ
ejpam-3258	105	27	algorithm	algorithm	NOUN
ejpam-3258	105	28	,	,	PUNCT
ejpam-3258	105	29	we	we	PRON
ejpam-3258	105	30	obtain	obtain	VERB
ejpam-3258	105	31	a	a	DET
ejpam-3258	105	32	solution	solution	NOUN
ejpam-3258	105	33	corresponding	correspond	VERB
ejpam-3258	105	34	to	to	ADP
ejpam-3258	105	35	the	the	DET
ejpam-3258	105	36	optimization	optimization	NOUN
ejpam-3258	105	37	problem	problem	NOUN
ejpam-3258	105	38	as	as	SCONJ
ejpam-3258	105	39	addressed	address	VERB
ejpam-3258	105	40	in	in	ADP
ejpam-3258	105	41	equ	equ	PROPN
ejpam-3258	105	42	.	.	PUNCT
ejpam-3258	106	1	(	(	PUNCT
ejpam-3258	106	2	7	7	X
ejpam-3258	106	3	)	)	PUNCT
ejpam-3258	106	4	while	while	SCONJ
ejpam-3258	106	5	outer	outer	ADJ
ejpam-3258	106	6	algorithm	algorithm	NOUN
ejpam-3258	106	7	helps	help	VERB
ejpam-3258	106	8	to	to	PART
ejpam-3258	106	9	vary	vary	VERB
ejpam-3258	106	10	the	the	DET
ejpam-3258	106	11	perturbation	perturbation	NOUN
ejpam-3258	106	12	level	level	NOUN
ejpam-3258	106	13	by	by	ADP
ejpam-3258	106	14	using	use	VERB
ejpam-3258	106	15	fast	fast	ADJ
ejpam-3258	106	16	newton	newton	PROPN
ejpam-3258	106	17	iteration	iteration	NOUN
ejpam-3258	106	18	.	.	PUNCT
ejpam-3258	107	1	we	we	PRON
ejpam-3258	107	2	first	first	ADV
ejpam-3258	107	3	construct	construct	VERB
ejpam-3258	107	4	a	a	DET
ejpam-3258	107	5	gradient	gradient	ADJ
ejpam-3258	107	6	system	system	NOUN
ejpam-3258	107	7	of	of	ADP
ejpam-3258	107	8	ordinary	ordinary	ADJ
ejpam-3258	107	9	differential	differential	ADJ
ejpam-3258	107	10	equations	equation	NOUN
ejpam-3258	107	11	(	(	PUNCT
ejpam-3258	107	12	ode	ode	PROPN
ejpam-3258	107	13	’s	’s	NOUN
ejpam-3258	107	14	)	)	PUNCT
ejpam-3258	107	15	and	and	CCONJ
ejpam-3258	107	16	then	then	ADV
ejpam-3258	107	17	solve	solve	VERB
ejpam-3258	107	18	it	it	PRON
ejpam-3258	107	19	.	.	PUNCT
ejpam-3258	108	1	this	this	DET
ejpam-3258	108	2	gradient	gradient	ADJ
ejpam-3258	108	3	system	system	NOUN
ejpam-3258	108	4	of	of	ADP
ejpam-3258	108	5	ode	ode	PROPN
ejpam-3258	108	6	’s	’s	NOUN
ejpam-3258	108	7	in	in	ADP
ejpam-3258	108	8	turn	turn	NOUN
ejpam-3258	108	9	solve	solve	VERB
ejpam-3258	108	10	the	the	DET
ejpam-3258	108	11	optimization	optimization	NOUN
ejpam-3258	108	12	problem	problem	NOUN
ejpam-3258	108	13	addressed	address	VERB
ejpam-3258	108	14	in	in	ADP
ejpam-3258	108	15	equ	equ	PROPN
ejpam-3258	108	16	.	.	PUNCT
ejpam-3258	109	1	(	(	PUNCT
ejpam-3258	109	2	7	7	NUM
ejpam-3258	109	3	)	)	PUNCT
ejpam-3258	109	4	.	.	PUNCT
ejpam-3258	110	1	while	while	SCONJ
ejpam-3258	110	2	the	the	DET
ejpam-3258	110	3	case	case	NOUN
ejpam-3258	110	4	of	of	ADP
ejpam-3258	110	5	a	a	DET
ejpam-3258	110	6	purely	purely	ADV
ejpam-3258	110	7	complex	complex	ADJ
ejpam-3258	110	8	uncertainties	uncertainty	NOUN
ejpam-3258	110	9	∆∗b	∆∗b	NOUN
ejpam-3258	110	10	can	can	AUX
ejpam-3258	110	11	be	be	AUX
ejpam-3258	110	12	addressed	address	VERB
ejpam-3258	110	13	by	by	ADP
ejpam-3258	110	14	taking	take	VERB
ejpam-3258	110	15	an	an	DET
ejpam-3258	110	16	inner	inner	ADJ
ejpam-3258	110	17	algorithm	algorithm	NOUN
ejpam-3258	110	18	to	to	PART
ejpam-3258	110	19	compute	compute	VERB
ejpam-3258	110	20	a	a	DET
ejpam-3258	110	21	local	local	ADJ
ejpam-3258	110	22	optima	optima	NOUN
ejpam-3258	110	23	for	for	ADP
ejpam-3258	110	24	the	the	DET
ejpam-3258	110	25	following	follow	VERB
ejpam-3258	110	26	maximization	maximization	NOUN
ejpam-3258	110	27	problem	problem	NOUN
ejpam-3258	110	28	λ(ε0	λ(ε0	NOUN
ejpam-3258	110	29	)	)	PUNCT
ejpam-3258	111	1	=	=	SYM
ejpam-3258	111	2	arg	arg	NOUN
ejpam-3258	111	3	max	max	PROPN
ejpam-3258	111	4	|λ|	|λ|	PROPN
ejpam-3258	111	5	,	,	PUNCT
ejpam-3258	111	6	(	(	PUNCT
ejpam-3258	111	7	8)	8)	NUM
ejpam-3258	111	8	where	where	SCONJ
ejpam-3258	111	9	λ	λ	PROPN
ejpam-3258	111	10	∈	∈	PROPN
ejpam-3258	111	11	λ	λ	PROPN
ejpam-3258	111	12	∆∗b	∆∗b	NOUN
ejpam-3258	111	13	ε0	ε0	PROPN
ejpam-3258	111	14	(	(	PUNCT
ejpam-3258	111	15	m	m	NOUN
ejpam-3258	111	16	)	)	PUNCT
ejpam-3258	111	17	this	this	PRON
ejpam-3258	111	18	produces	produce	VERB
ejpam-3258	111	19	a	a	DET
ejpam-3258	111	20	lower	low	ADJ
ejpam-3258	111	21	bound	bind	VERB
ejpam-3258	111	22	for	for	ADP
ejpam-3258	111	23	µ∆∗b	µ∆∗b	PROPN
ejpam-3258	111	24	(	(	PUNCT
ejpam-3258	111	25	m	m	NOUN
ejpam-3258	111	26	)	)	PUNCT
ejpam-3258	111	27	.	.	PUNCT
ejpam-3258	112	1	3	3	X
ejpam-3258	112	2	.	.	X
ejpam-3258	112	3	purely	purely	ADV
ejpam-3258	112	4	complex	complex	ADJ
ejpam-3258	112	5	uncertainties	uncertainty	NOUN
ejpam-3258	112	6	[	[	X
ejpam-3258	112	7	14	14	NUM
ejpam-3258	112	8	]	]	PUNCT
ejpam-3258	112	9	this	this	DET
ejpam-3258	112	10	section	section	NOUN
ejpam-3258	112	11	is	be	AUX
ejpam-3258	112	12	devoted	devote	VERB
ejpam-3258	112	13	to	to	ADP
ejpam-3258	112	14	the	the	DET
ejpam-3258	112	15	case	case	NOUN
ejpam-3258	112	16	of	of	ADP
ejpam-3258	112	17	pure	pure	ADJ
ejpam-3258	112	18	complex	complex	ADJ
ejpam-3258	112	19	perturbations	perturbation	NOUN
ejpam-3258	112	20	.	.	PUNCT
ejpam-3258	113	1	we	we	PRON
ejpam-3258	113	2	estimate	estimate	VERB
ejpam-3258	113	3	ssv	ssv	NOUN
ejpam-3258	113	4	µ∆∗b	µ∆∗b	PROPN
ejpam-3258	113	5	(	(	PUNCT
ejpam-3258	113	6	m	m	NOUN
ejpam-3258	113	7	)	)	PUNCT
ejpam-3258	113	8	for	for	ADP
ejpam-3258	113	9	the	the	DET
ejpam-3258	113	10	given	give	VERB
ejpam-3258	113	11	n	n	CCONJ
ejpam-3258	113	12	-	-	PUNCT
ejpam-3258	113	13	dimensional	dimensional	ADJ
ejpam-3258	113	14	complex	complex	ADJ
ejpam-3258	113	15	matrix	matrix	NOUN
ejpam-3258	113	16	m	m	VERB
ejpam-3258	113	17	while	while	SCONJ
ejpam-3258	113	18	taking	take	VERB
ejpam-3258	113	19	inner	inner	ADJ
ejpam-3258	113	20	problem	problem	NOUN
ejpam-3258	113	21	discussed	discuss	VERB
ejpam-3258	113	22	in	in	ADP
ejpam-3258	113	23	equ	equ	PROPN
ejpam-3258	113	24	.	.	PUNCT
ejpam-3258	114	1	(	(	PUNCT
ejpam-3258	114	2	8)	8)	NUM
ejpam-3258	114	3	into	into	ADP
ejpam-3258	114	4	account	account	NOUN
ejpam-3258	114	5	.	.	PUNCT
ejpam-3258	115	1	the	the	DET
ejpam-3258	115	2	set	set	NOUN
ejpam-3258	115	3	of	of	ADP
ejpam-3258	115	4	purely	purely	ADV
ejpam-3258	115	5	complex	complex	ADJ
ejpam-3258	115	6	perturbations	perturbation	NOUN
ejpam-3258	115	7	is	be	AUX
ejpam-3258	115	8	defined	define	VERB
ejpam-3258	115	9	as	as	ADP
ejpam-3258	115	10	∆∗b	∆∗b	NOUN
ejpam-3258	115	11	=	=	PUNCT
ejpam-3258	115	12	{	{	PUNCT
ejpam-3258	115	13	diag(α1i1	diag(α1i1	PROPN
ejpam-3258	115	14	,	,	PUNCT
ejpam-3258	115	15	...	...	PUNCT
ejpam-3258	115	16	,	,	PUNCT
ejpam-3258	115	17	αnin	αnin	ADJ
ejpam-3258	115	18	;	;	PUNCT
ejpam-3258	115	19	∆1	∆1	NUM
ejpam-3258	115	20	,	,	PUNCT
ejpam-3258	115	21	...	...	PUNCT
ejpam-3258	115	22	,	,	PUNCT
ejpam-3258	115	23	∆f	∆f	PROPN
ejpam-3258	115	24	)	)	PUNCT
ejpam-3258	115	25	:	:	PUNCT
ejpam-3258	115	26	αi	αi	PROPN
ejpam-3258	115	27	∈	∈	PROPN
ejpam-3258	115	28	c,∆j	c,∆j	PROPN
ejpam-3258	115	29	∈	∈	PROPN
ejpam-3258	115	30	cmj	cmj	NOUN
ejpam-3258	115	31	,	,	PUNCT
ejpam-3258	115	32	mj	mj	NOUN
ejpam-3258	115	33	}	}	PUNCT
ejpam-3258	115	34	.	.	PUNCT
ejpam-3258	116	1	(	(	PUNCT
ejpam-3258	116	2	9	9	X
ejpam-3258	116	3	)	)	PUNCT
ejpam-3258	116	4	we	we	PRON
ejpam-3258	116	5	make	make	VERB
ejpam-3258	116	6	use	use	NOUN
ejpam-3258	116	7	of	of	ADP
ejpam-3258	116	8	the	the	DET
ejpam-3258	116	9	following	follow	VERB
ejpam-3258	116	10	eigenvalue	eigenvalue	ADJ
ejpam-3258	116	11	perturbation	perturbation	NOUN
ejpam-3258	116	12	result	result	NOUN
ejpam-3258	116	13	in	in	ADP
ejpam-3258	116	14	order	order	NOUN
ejpam-3258	116	15	to	to	PART
ejpam-3258	116	16	compute	compute	VERB
ejpam-3258	116	17	the	the	DET
ejpam-3258	116	18	derivative	derivative	NOUN
ejpam-3258	116	19	of	of	ADP
ejpam-3258	116	20	an	an	DET
ejpam-3258	116	21	eigenvalue	eigenvalue	PROPN
ejpam-3258	116	22	λ(t	λ(t	NOUN
ejpam-3258	116	23	)	)	PUNCT
ejpam-3258	116	24	.	.	PUNCT
ejpam-3258	117	1	lemma	lemma	PROPN
ejpam-3258	117	2	3.1	3.1	NUM
ejpam-3258	117	3	.	.	PUNCT
ejpam-3258	118	1	let	let	VERB
ejpam-3258	118	2	τ	τ	PROPN
ejpam-3258	118	3	:	:	PUNCT
ejpam-3258	118	4	r	r	X
ejpam-3258	118	5	→	→	SYM
ejpam-3258	118	6	cn	cn	PROPN
ejpam-3258	118	7	,	,	PUNCT
ejpam-3258	118	8	n	n	PROPN
ejpam-3258	118	9	and	and	CCONJ
ejpam-3258	118	10	consider	consider	VERB
ejpam-3258	118	11	that	that	PRON
ejpam-3258	118	12	λ(t	λ(t	NOUN
ejpam-3258	118	13	)	)	PUNCT
ejpam-3258	118	14	is	be	AUX
ejpam-3258	118	15	an	an	DET
ejpam-3258	118	16	eigenvalue	eigenvalue	NOUN
ejpam-3258	118	17	of	of	ADP
ejpam-3258	118	18	τ(t	τ(t	NOUN
ejpam-3258	118	19	)	)	PUNCT
ejpam-3258	118	20	which	which	PRON
ejpam-3258	118	21	converges	converge	VERB
ejpam-3258	118	22	towards	towards	ADP
ejpam-3258	118	23	a	a	DET
ejpam-3258	118	24	simple	simple	ADJ
ejpam-3258	118	25	eigenvalue	eigenvalue	NOUN
ejpam-3258	118	26	λ0	λ0	NOUN
ejpam-3258	118	27	of	of	ADP
ejpam-3258	118	28	τ0	τ0	NOUN
ejpam-3258	118	29	=	=	SYM
ejpam-3258	118	30	τ(0	τ(0	NUM
ejpam-3258	118	31	)	)	PUNCT
ejpam-3258	118	32	as	as	ADP
ejpam-3258	118	33	t→	t→	X
ejpam-3258	118	34	0	0	X
ejpam-3258	118	35	.	.	PUNCT
ejpam-3258	119	1	then	then	ADV
ejpam-3258	119	2	the	the	DET
ejpam-3258	119	3	simple	simple	ADJ
ejpam-3258	119	4	eigenvalue	eigenvalue	PROPN
ejpam-3258	119	5	λ(t	λ(t	NOUN
ejpam-3258	119	6	)	)	PUNCT
ejpam-3258	119	7	is	be	AUX
ejpam-3258	119	8	analytic	analytic	ADJ
ejpam-3258	119	9	near	near	ADP
ejpam-3258	119	10	t	t	PROPN
ejpam-3258	119	11	=	=	SYM
ejpam-3258	119	12	0	0	PUNCT
ejpam-3258	119	13	with	with	ADP
ejpam-3258	119	14	λ̇(t)|t=0	λ̇(t)|t=0	X
ejpam-3258	119	15	=	=	PUNCT
ejpam-3258	119	16	w∗0τ1v0	w∗0τ1v0	PROPN
ejpam-3258	119	17	w∗0v0	w∗0v0	NOUN
ejpam-3258	119	18	,	,	PUNCT
ejpam-3258	119	19	where	where	SCONJ
ejpam-3258	119	20	τ1	τ1	NOUN
ejpam-3258	119	21	=	=	SYM
ejpam-3258	119	22	τ̇(0	τ̇(0	X
ejpam-3258	119	23	)	)	PUNCT
ejpam-3258	119	24	and	and	CCONJ
ejpam-3258	119	25	v0	v0	PROPN
ejpam-3258	119	26	,	,	PUNCT
ejpam-3258	119	27	w0	w0	PROPN
ejpam-3258	119	28	are	be	AUX
ejpam-3258	119	29	right	right	ADJ
ejpam-3258	119	30	and	and	CCONJ
ejpam-3258	119	31	left	leave	VERB
ejpam-3258	119	32	eigenvectors	eigenvector	NOUN
ejpam-3258	119	33	of	of	ADP
ejpam-3258	119	34	τ0	τ0	NOUN
ejpam-3258	119	35	associated	associate	VERB
ejpam-3258	119	36	to	to	ADP
ejpam-3258	119	37	λ0	λ0	NOUN
ejpam-3258	119	38	,	,	PUNCT
ejpam-3258	119	39	that	that	ADV
ejpam-3258	119	40	is	is	ADV
ejpam-3258	119	41	,	,	PUNCT
ejpam-3258	119	42	(	(	PUNCT
ejpam-3258	119	43	τ0−λ0i)v0	τ0−λ0i)v0	NOUN
ejpam-3258	119	44	=	=	SYM
ejpam-3258	119	45	0	0	NUM
ejpam-3258	119	46	and	and	CCONJ
ejpam-3258	119	47	w∗0(τ0−λ0i	w∗0(τ0−λ0i	NOUN
ejpam-3258	119	48	)	)	PUNCT
ejpam-3258	119	49	=	=	SYM
ejpam-3258	120	1	0	0	X
ejpam-3258	120	2	.	.	PUNCT
ejpam-3258	121	1	since	since	SCONJ
ejpam-3258	121	2	our	our	PRON
ejpam-3258	121	3	main	main	ADJ
ejpam-3258	121	4	objective	objective	NOUN
ejpam-3258	121	5	is	be	AUX
ejpam-3258	121	6	to	to	PART
ejpam-3258	121	7	solve	solve	VERB
ejpam-3258	121	8	the	the	DET
ejpam-3258	121	9	optimization	optimization	NOUN
ejpam-3258	121	10	problem	problem	NOUN
ejpam-3258	121	11	as	as	SCONJ
ejpam-3258	121	12	discussed	discuss	VERB
ejpam-3258	121	13	in	in	ADP
ejpam-3258	121	14	equ	equ	PROPN
ejpam-3258	121	15	.	.	PUNCT
ejpam-3258	122	1	(	(	PUNCT
ejpam-3258	122	2	8)	8)	NUM
ejpam-3258	122	3	.	.	PUNCT
ejpam-3258	123	1	for	for	ADP
ejpam-3258	123	2	this	this	PRON
ejpam-3258	123	3	we	we	PRON
ejpam-3258	123	4	need	need	VERB
ejpam-3258	123	5	to	to	PART
ejpam-3258	123	6	compute	compute	VERB
ejpam-3258	123	7	a	a	DET
ejpam-3258	123	8	perturbation	perturbation	NOUN
ejpam-3258	123	9	∆local	∆local	ADJ
ejpam-3258	123	10	so	so	SCONJ
ejpam-3258	123	11	that	that	SCONJ
ejpam-3258	123	12	ρ(εa∆local	ρ(εa∆local	NOUN
ejpam-3258	123	13	)	)	PUNCT
ejpam-3258	123	14	has	have	VERB
ejpam-3258	123	15	the	the	DET
ejpam-3258	123	16	maximum	maximum	ADJ
ejpam-3258	123	17	growth	growth	NOUN
ejpam-3258	123	18	among	among	ADP
ejpam-3258	123	19	all	all	DET
ejpam-3258	123	20	∆	∆	X
ejpam-3258	123	21	∈	∈	NOUN
ejpam-3258	123	22	∆∗b	∆∗b	NOUN
ejpam-3258	123	23	while	while	SCONJ
ejpam-3258	123	24	‖∆‖	‖∆‖	PROPN
ejpam-3258	123	25	posses	posse	NOUN
ejpam-3258	123	26	a	a	DET
ejpam-3258	123	27	unit	unit	NOUN
ejpam-3258	123	28	a	a	DET
ejpam-3258	123	29	m.	m.	NOUN
ejpam-3258	123	30	rehman	rehman	PROPN
ejpam-3258	123	31	,	,	PUNCT
ejpam-3258	123	32	m.	m.	PROPN
ejpam-3258	123	33	f.	f.	PROPN
ejpam-3258	123	34	anwar	anwar	PROPN
ejpam-3258	123	35	/	/	PUNCT
ejpam-3258	123	36	eur	eur	PROPN
ejpam-3258	123	37	.	.	PUNCT
ejpam-3258	124	1	j.	j.	PROPN
ejpam-3258	124	2	pure	pure	PROPN
ejpam-3258	124	3	appl	appl	PROPN
ejpam-3258	124	4	.	.	PROPN
ejpam-3258	124	5	math	math	PROPN
ejpam-3258	124	6	,	,	PUNCT
ejpam-3258	124	7	11	11	NUM
ejpam-3258	124	8	(	(	PUNCT
ejpam-3258	124	9	3	3	NUM
ejpam-3258	124	10	)	)	PUNCT
ejpam-3258	124	11	(	(	PUNCT
ejpam-3258	124	12	2018	2018	NUM
ejpam-3258	124	13	)	)	PUNCT
ejpam-3258	124	14	,	,	PUNCT
ejpam-3258	124	15	774	774	NUM
ejpam-3258	124	16	-	-	SYM
ejpam-3258	124	17	792	792	NUM
ejpam-3258	124	18	780	780	NUM
ejpam-3258	124	19	unit	unit	NOUN
ejpam-3258	124	20	2	2	NUM
ejpam-3258	124	21	-	-	PUNCT
ejpam-3258	124	22	norm	norm	NOUN
ejpam-3258	124	23	.	.	PUNCT
ejpam-3258	125	1	in	in	ADP
ejpam-3258	125	2	the	the	DET
ejpam-3258	125	3	following	following	NOUN
ejpam-3258	125	4	we	we	PRON
ejpam-3258	125	5	give	give	VERB
ejpam-3258	125	6	definition	definition	NOUN
ejpam-3258	125	7	of	of	ADP
ejpam-3258	125	8	local	local	ADJ
ejpam-3258	125	9	extremizer	extremizer	NOUN
ejpam-3258	125	10	of	of	ADP
ejpam-3258	125	11	a	a	DET
ejpam-3258	125	12	structured	structured	ADJ
ejpam-3258	125	13	spectral	spectral	ADJ
ejpam-3258	125	14	value	value	NOUN
ejpam-3258	125	15	set	set	NOUN
ejpam-3258	125	16	.	.	PUNCT
ejpam-3258	126	1	definition	definition	NOUN
ejpam-3258	126	2	3.2	3.2	NUM
ejpam-3258	126	3	[	[	X
ejpam-3258	126	4	14	14	NUM
ejpam-3258	126	5	]	]	PUNCT
ejpam-3258	126	6	.	.	PUNCT
ejpam-3258	127	1	a	a	DET
ejpam-3258	127	2	matrix	matrix	NOUN
ejpam-3258	127	3	∆	∆	X
ejpam-3258	127	4	∈	∈	NOUN
ejpam-3258	127	5	∆∗b	∆∗b	NOUN
ejpam-3258	127	6	so	so	SCONJ
ejpam-3258	127	7	that	that	SCONJ
ejpam-3258	127	8	‖∆‖	‖∆‖	PROPN
ejpam-3258	127	9	possesses	possess	VERB
ejpam-3258	127	10	a	a	DET
ejpam-3258	127	11	unit	unit	NOUN
ejpam-3258	127	12	2	2	NUM
ejpam-3258	127	13	-	-	PUNCT
ejpam-3258	127	14	norm	norm	NOUN
ejpam-3258	127	15	while	while	SCONJ
ejpam-3258	127	16	(	(	PUNCT
ejpam-3258	127	17	ε0m∆	ε0m∆	NOUN
ejpam-3258	127	18	)	)	PUNCT
ejpam-3258	127	19	has	have	VERB
ejpam-3258	127	20	a	a	DET
ejpam-3258	127	21	maximum	maximum	ADJ
ejpam-3258	127	22	eigenvalue	eigenvalue	NOUN
ejpam-3258	127	23	which	which	PRON
ejpam-3258	127	24	maximizes	maximize	VERB
ejpam-3258	127	25	(	(	PUNCT
ejpam-3258	127	26	locally	locally	ADV
ejpam-3258	127	27	)	)	PUNCT
ejpam-3258	127	28	λ	λ	PROPN
ejpam-3258	127	29	∆∗b	∆∗b	NOUN
ejpam-3258	127	30	ε0	ε0	PROPN
ejpam-3258	127	31	(	(	PUNCT
ejpam-3258	127	32	m	m	NOUN
ejpam-3258	127	33	)	)	PUNCT
ejpam-3258	127	34	is	be	AUX
ejpam-3258	127	35	known	know	VERB
ejpam-3258	127	36	a	a	DET
ejpam-3258	127	37	local	local	ADJ
ejpam-3258	127	38	extremizer	extremizer	NOUN
ejpam-3258	127	39	of	of	ADP
ejpam-3258	127	40	structured	structured	ADJ
ejpam-3258	127	41	spectral	spectral	ADJ
ejpam-3258	127	42	value	value	NOUN
ejpam-3258	127	43	set	set	VERB
ejpam-3258	127	44	.	.	PUNCT
ejpam-3258	128	1	we	we	PRON
ejpam-3258	128	2	give	give	VERB
ejpam-3258	128	3	following	follow	VERB
ejpam-3258	128	4	theorem	theorem	NOUN
ejpam-3258	128	5	in	in	ADP
ejpam-3258	128	6	order	order	NOUN
ejpam-3258	128	7	to	to	PART
ejpam-3258	128	8	compute	compute	VERB
ejpam-3258	128	9	the	the	DET
ejpam-3258	128	10	local	local	ADJ
ejpam-3258	128	11	extremizer	extremizer	NOUN
ejpam-3258	128	12	of	of	ADP
ejpam-3258	128	13	structured	structured	ADJ
ejpam-3258	128	14	spectral	spectral	ADJ
ejpam-3258	128	15	value	value	NOUN
ejpam-3258	128	16	set	set	NOUN
ejpam-3258	128	17	.	.	PUNCT
ejpam-3258	129	1	theorem	theorem	VERB
ejpam-3258	129	2	3.3	3.3	NUM
ejpam-3258	129	3	[	[	X
ejpam-3258	129	4	14	14	NUM
ejpam-3258	129	5	]	]	PUNCT
ejpam-3258	129	6	.	.	PUNCT
ejpam-3258	130	1	let	let	VERB
ejpam-3258	130	2	’s	’s	NOUN
ejpam-3258	130	3	suppose	suppose	VERB
ejpam-3258	130	4	that	that	SCONJ
ejpam-3258	130	5	∆local	∆local	ADJ
ejpam-3258	130	6	=	=	SYM
ejpam-3258	130	7	diag(α1i1	diag(α1i1	PROPN
ejpam-3258	130	8	,	,	PUNCT
ejpam-3258	130	9	...	...	PUNCT
ejpam-3258	130	10	,	,	PUNCT
ejpam-3258	130	11	αnin	αnin	ADJ
ejpam-3258	130	12	;	;	PUNCT
ejpam-3258	130	13	∆1	∆1	NUM
ejpam-3258	130	14	,	,	PUNCT
ejpam-3258	130	15	...	...	PUNCT
ejpam-3258	130	16	,	,	PUNCT
ejpam-3258	130	17	∆f	∆f	PROPN
ejpam-3258	130	18	)	)	PUNCT
ejpam-3258	130	19	,	,	PUNCT
ejpam-3258	131	1	‖∆local‖2	‖∆local‖2	NOUN
ejpam-3258	131	2	=	=	SYM
ejpam-3258	131	3	1	1	NUM
ejpam-3258	131	4	,	,	PUNCT
ejpam-3258	131	5	is	be	AUX
ejpam-3258	131	6	an	an	DET
ejpam-3258	131	7	extremizer	extremizer	NOUN
ejpam-3258	131	8	of	of	ADP
ejpam-3258	131	9	structured	structured	ADJ
ejpam-3258	131	10	epsilon	epsilon	PROPN
ejpam-3258	131	11	spectral	spectral	ADJ
ejpam-3258	131	12	value	value	NOUN
ejpam-3258	131	13	set	set	VERB
ejpam-3258	131	14	λ	λ	PROPN
ejpam-3258	131	15	∆∗b	∆∗b	NOUN
ejpam-3258	131	16	ε	ε	PROPN
ejpam-3258	131	17	(	(	PUNCT
ejpam-3258	131	18	a	a	NOUN
ejpam-3258	131	19	)	)	PUNCT
ejpam-3258	131	20	.	.	PUNCT
ejpam-3258	132	1	further	far	ADV
ejpam-3258	132	2	consider	consider	VERB
ejpam-3258	132	3	that	that	SCONJ
ejpam-3258	132	4	ε0m∆local	ε0m∆local	ADJ
ejpam-3258	132	5	possesses	possesse	NOUN
ejpam-3258	132	6	a	a	DET
ejpam-3258	132	7	simple	simple	ADJ
ejpam-3258	132	8	greatest	great	ADJ
ejpam-3258	132	9	eigenvalue	eigenvalue	PROPN
ejpam-3258	132	10	λ	λ	NOUN
ejpam-3258	132	11	=	=	PRON
ejpam-3258	132	12	|λ|eiθ	|λ|eiθ	ADP
ejpam-3258	132	13	having	have	VERB
ejpam-3258	132	14	v	v	NOUN
ejpam-3258	132	15	and	and	CCONJ
ejpam-3258	132	16	w	w	NOUN
ejpam-3258	132	17	as	as	ADV
ejpam-3258	132	18	right	right	ADV
ejpam-3258	132	19	and	and	CCONJ
ejpam-3258	132	20	left	leave	VERB
ejpam-3258	132	21	eigenvectors	eigenvector	NOUN
ejpam-3258	132	22	which	which	PRON
ejpam-3258	132	23	are	be	AUX
ejpam-3258	132	24	scaled	scale	VERB
ejpam-3258	132	25	as	as	ADP
ejpam-3258	132	26	s	s	NOUN
ejpam-3258	132	27	=	=	PUNCT
ejpam-3258	132	28	eiθw∗v	eiθw∗v	NOUN
ejpam-3258	132	29	>	>	X
ejpam-3258	132	30	0	0	X
ejpam-3258	132	31	.	.	PUNCT
ejpam-3258	133	1	upon	upon	SCONJ
ejpam-3258	133	2	the	the	DET
ejpam-3258	133	3	partitioning	partitioning	NOUN
ejpam-3258	133	4	,	,	PUNCT
ejpam-3258	133	5	we	we	PRON
ejpam-3258	133	6	have	have	VERB
ejpam-3258	133	7	v	v	NOUN
ejpam-3258	133	8	=	=	SYM
ejpam-3258	133	9	(	(	PUNCT
ejpam-3258	133	10	vt	vt	PROPN
ejpam-3258	133	11	1	1	NUM
ejpam-3258	133	12	,	,	PUNCT
ejpam-3258	133	13	.	.	PUNCT
ejpam-3258	133	14	.	.	PUNCT
ejpam-3258	134	1	.	.	PUNCT
ejpam-3258	135	1	,	,	PUNCT
ejpam-3258	135	2	v	v	ADP
ejpam-3258	135	3	t	t	PROPN
ejpam-3258	135	4	n	n	PROPN
ejpam-3258	135	5	,	,	PUNCT
ejpam-3258	135	6	v	v	ADP
ejpam-3258	135	7	t	t	NOUN
ejpam-3258	135	8	n+1	n+1	PROPN
ejpam-3258	135	9	,	,	PUNCT
ejpam-3258	135	10	.	.	PUNCT
ejpam-3258	135	11	.	.	PUNCT
ejpam-3258	136	1	.	.	PUNCT
ejpam-3258	137	1	,	,	PUNCT
ejpam-3258	137	2	v	v	ADP
ejpam-3258	137	3	t	t	NOUN
ejpam-3258	137	4	n+f	n+f	PUNCT
ejpam-3258	137	5	)	)	PUNCT
ejpam-3258	137	6	t	t	PROPN
ejpam-3258	137	7	;	;	PUNCT
ejpam-3258	137	8	u	u	NOUN
ejpam-3258	137	9	=	=	NOUN
ejpam-3258	137	10	a∗w	a∗w	NUM
ejpam-3258	137	11	=	=	SYM
ejpam-3258	137	12	(	(	PUNCT
ejpam-3258	137	13	ut	ut	PROPN
ejpam-3258	137	14	1	1	NUM
ejpam-3258	137	15	,	,	PUNCT
ejpam-3258	137	16	.	.	PUNCT
ejpam-3258	137	17	.	.	PUNCT
ejpam-3258	137	18	.	.	PUNCT
ejpam-3258	138	1	,	,	PUNCT
ejpam-3258	138	2	u	u	NOUN
ejpam-3258	138	3	t	t	NOUN
ejpam-3258	138	4	n	n	NOUN
ejpam-3258	138	5	,	,	PUNCT
ejpam-3258	138	6	u	u	X
ejpam-3258	138	7	t	t	PROPN
ejpam-3258	138	8	n+1	n+1	PROPN
ejpam-3258	138	9	,	,	PUNCT
ejpam-3258	138	10	.	.	PUNCT
ejpam-3258	138	11	.	.	PUNCT
ejpam-3258	139	1	.	.	PUNCT
ejpam-3258	140	1	,	,	PUNCT
ejpam-3258	140	2	u	u	NOUN
ejpam-3258	140	3	t	t	PROPN
ejpam-3258	140	4	n+f	n+f	PUNCT
ejpam-3258	140	5	)	)	PUNCT
ejpam-3258	140	6	t	t	PROPN
ejpam-3258	140	7	,	,	PUNCT
ejpam-3258	140	8	(	(	PUNCT
ejpam-3258	140	9	10	10	NUM
ejpam-3258	140	10	)	)	PUNCT
ejpam-3258	140	11	also	also	ADV
ejpam-3258	140	12	consider	consider	VERB
ejpam-3258	140	13	that	that	PRON
ejpam-3258	140	14	,	,	PUNCT
ejpam-3258	140	15	u∗kvk	u∗kvk	PROPN
ejpam-3258	140	16	6=	6=	ADP
ejpam-3258	140	17	0	0	NUM
ejpam-3258	140	18	∀	∀	NOUN
ejpam-3258	140	19	k	k	NOUN
ejpam-3258	141	1	=	=	SYM
ejpam-3258	141	2	1	1	NUM
ejpam-3258	141	3	,	,	PUNCT
ejpam-3258	141	4	.	.	PUNCT
ejpam-3258	141	5	.	.	PUNCT
ejpam-3258	142	1	.	.	PUNCT
ejpam-3258	143	1	,	,	PUNCT
ejpam-3258	143	2	n	n	X
ejpam-3258	143	3	(	(	PUNCT
ejpam-3258	143	4	11	11	NUM
ejpam-3258	143	5	)	)	PUNCT
ejpam-3258	143	6	‖un+l‖2	‖un+l‖2	X
ejpam-3258	143	7	·	·	PUNCT
ejpam-3258	143	8	‖vn+l‖2	‖vn+l‖2	PUNCT
ejpam-3258	143	9	6=	6=	NUM
ejpam-3258	143	10	0	0	NUM
ejpam-3258	143	11	∀	∀	NOUN
ejpam-3258	143	12	l	l	NOUN
ejpam-3258	143	13	=	=	SYM
ejpam-3258	143	14	1	1	NUM
ejpam-3258	143	15	,	,	PUNCT
ejpam-3258	143	16	.	.	PUNCT
ejpam-3258	143	17	.	.	PUNCT
ejpam-3258	143	18	.	.	PUNCT
ejpam-3258	144	1	,	,	PUNCT
ejpam-3258	144	2	f.	f.	PROPN
ejpam-3258	144	3	(	(	PUNCT
ejpam-3258	144	4	12	12	NUM
ejpam-3258	144	5	)	)	PUNCT
ejpam-3258	144	6	then	then	ADV
ejpam-3258	144	7	|sk|	|sk|	NOUN
ejpam-3258	144	8	=	=	SYM
ejpam-3258	144	9	1	1	NUM
ejpam-3258	144	10	∀	∀	NOUN
ejpam-3258	144	11	k	k	X
ejpam-3258	144	12	=	=	SYM
ejpam-3258	144	13	1	1	NUM
ejpam-3258	144	14	,	,	PUNCT
ejpam-3258	144	15	.	.	PUNCT
ejpam-3258	144	16	.	.	PUNCT
ejpam-3258	145	1	.	.	PUNCT
ejpam-3258	146	1	,	,	PUNCT
ejpam-3258	146	2	n	n	PROPN
ejpam-3258	146	3	and	and	CCONJ
ejpam-3258	146	4	‖∆l‖2	‖∆l‖2	NOUN
ejpam-3258	146	5	=	=	SYM
ejpam-3258	146	6	1	1	NUM
ejpam-3258	146	7	∀l	∀l	NOUN
ejpam-3258	146	8	=	=	NOUN
ejpam-3258	146	9	1	1	NUM
ejpam-3258	146	10	,	,	PUNCT
ejpam-3258	146	11	.	.	PUNCT
ejpam-3258	146	12	.	.	PUNCT
ejpam-3258	147	1	.	.	PUNCT
ejpam-3258	148	1	,	,	PUNCT
ejpam-3258	148	2	f	f	X
ejpam-3258	148	3	,	,	PUNCT
ejpam-3258	148	4	this	this	PRON
ejpam-3258	148	5	means	mean	VERB
ejpam-3258	148	6	that	that	SCONJ
ejpam-3258	148	7	all	all	DET
ejpam-3258	148	8	blocks	block	NOUN
ejpam-3258	148	9	of	of	ADP
ejpam-3258	148	10	∆local	∆local	ADJ
ejpam-3258	148	11	possesses	possesse	NOUN
ejpam-3258	148	12	unit	unit	NOUN
ejpam-3258	148	13	2	2	NUM
ejpam-3258	148	14	-	-	PUNCT
ejpam-3258	148	15	norm	norm	NOUN
ejpam-3258	148	16	.	.	PUNCT
ejpam-3258	149	1	in	in	ADP
ejpam-3258	149	2	following	follow	VERB
ejpam-3258	149	3	theorem	theorem	NOUN
ejpam-3258	149	4	we	we	PRON
ejpam-3258	149	5	replace	replace	VERB
ejpam-3258	149	6	full	full	ADJ
ejpam-3258	149	7	blocks	block	NOUN
ejpam-3258	149	8	in	in	ADP
ejpam-3258	149	9	local	local	ADJ
ejpam-3258	149	10	extremizer	extremizer	NOUN
ejpam-3258	149	11	with	with	ADP
ejpam-3258	149	12	rank-1	rank-1	NUM
ejpam-3258	149	13	matrices	matrix	NOUN
ejpam-3258	149	14	,	,	PUNCT
ejpam-3258	149	15	in	in	ADP
ejpam-3258	149	16	turn	turn	NOUN
ejpam-3258	149	17	,	,	PUNCT
ejpam-3258	149	18	this	this	PRON
ejpam-3258	149	19	allow	allow	VERB
ejpam-3258	149	20	us	we	PRON
ejpam-3258	149	21	to	to	PART
ejpam-3258	149	22	work	work	VERB
ejpam-3258	149	23	to	to	ADP
ejpam-3258	149	24	forbenius	forbenius	PROPN
ejpam-3258	149	25	norm	norm	NOUN
ejpam-3258	149	26	instead	instead	ADV
ejpam-3258	149	27	with	with	ADP
ejpam-3258	149	28	matrix	matrix	NOUN
ejpam-3258	149	29	2	2	NUM
ejpam-3258	149	30	-	-	PUNCT
ejpam-3258	149	31	norm	norm	NOUN
ejpam-3258	149	32	.	.	PUNCT
ejpam-3258	150	1	theorem	theorem	VERB
ejpam-3258	150	2	3.4	3.4	NUM
ejpam-3258	150	3	[	[	X
ejpam-3258	150	4	14	14	NUM
ejpam-3258	150	5	]	]	PUNCT
ejpam-3258	150	6	.	.	PUNCT
ejpam-3258	151	1	let	let	VERB
ejpam-3258	151	2	’s	’s	NOUN
ejpam-3258	151	3	suppose	suppose	VERB
ejpam-3258	151	4	that	that	SCONJ
ejpam-3258	151	5	∆local	∆local	ADJ
ejpam-3258	151	6	=	=	SYM
ejpam-3258	151	7	diag(α1i1	diag(α1i1	PROPN
ejpam-3258	151	8	,	,	PUNCT
ejpam-3258	151	9	...	...	PUNCT
ejpam-3258	151	10	,	,	PUNCT
ejpam-3258	151	11	αnin,∆1	αnin,∆1	NOUN
ejpam-3258	151	12	,	,	PUNCT
ejpam-3258	151	13	...	...	PUNCT
ejpam-3258	151	14	,	,	PUNCT
ejpam-3258	151	15	∆f	∆f	PROPN
ejpam-3258	151	16	)	)	PUNCT
ejpam-3258	151	17	is	be	AUX
ejpam-3258	151	18	a	a	DET
ejpam-3258	151	19	local	local	ADJ
ejpam-3258	151	20	maximizer	maximizer	NOUN
ejpam-3258	151	21	and	and	CCONJ
ejpam-3258	151	22	also	also	ADV
ejpam-3258	151	23	consider	consider	VERB
ejpam-3258	151	24	that	that	DET
ejpam-3258	151	25	λ	λ	NOUN
ejpam-3258	151	26	,	,	PUNCT
ejpam-3258	151	27	v	v	NOUN
ejpam-3258	151	28	,	,	PUNCT
ejpam-3258	151	29	u	u	NOUN
ejpam-3258	151	30	as	as	ADV
ejpam-3258	151	31	defined	define	VERB
ejpam-3258	151	32	and	and	CCONJ
ejpam-3258	151	33	partitioned	partition	VERB
ejpam-3258	151	34	in	in	ADP
ejpam-3258	151	35	the	the	DET
ejpam-3258	151	36	previous	previous	ADJ
ejpam-3258	151	37	given	give	VERB
ejpam-3258	151	38	theorem	theorem	VERB
ejpam-3258	151	39	.	.	PUNCT
ejpam-3258	151	40	further	further	PROPN
ejpam-3258	151	41	assume	assume	VERB
ejpam-3258	151	42	that	that	SCONJ
ejpam-3258	151	43	equ	equ	PROPN
ejpam-3258	151	44	.	.	PUNCT
ejpam-3258	152	1	(	(	PUNCT
ejpam-3258	152	2	12	12	NUM
ejpam-3258	152	3	)	)	PUNCT
ejpam-3258	152	4	holds	hold	VERB
ejpam-3258	152	5	true	true	ADJ
ejpam-3258	152	6	and	and	CCONJ
ejpam-3258	152	7	every	every	DET
ejpam-3258	152	8	single	single	ADJ
ejpam-3258	152	9	block	block	NOUN
ejpam-3258	152	10	∆h	∆h	PROPN
ejpam-3258	152	11	possesses	possess	VERB
ejpam-3258	152	12	a	a	DET
ejpam-3258	152	13	singular	singular	ADJ
ejpam-3258	152	14	value	value	NOUN
ejpam-3258	152	15	1	1	NUM
ejpam-3258	152	16	which	which	PRON
ejpam-3258	152	17	having	have	VERB
ejpam-3258	152	18	the	the	DET
ejpam-3258	152	19	singular	singular	ADJ
ejpam-3258	152	20	vectors	vector	NOUN
ejpam-3258	152	21	ql	ql	X
ejpam-3258	152	22	=	=	SYM
ejpam-3258	152	23	γlwn+l/‖wn+l‖2	γlwn+l/‖wn+l‖2	NOUN
ejpam-3258	152	24	and	and	CCONJ
ejpam-3258	152	25	rl	rl	X
ejpam-3258	152	26	=	=	PUNCT
ejpam-3258	152	27	γlun+l/‖un+l‖2	γlun+l/‖un+l‖2	PROPN
ejpam-3258	152	28	for	for	ADP
ejpam-3258	152	29	|γl|	|γl|	PROPN
ejpam-3258	152	30	=	=	SYM
ejpam-3258	152	31	1	1	X
ejpam-3258	152	32	.	.	PUNCT
ejpam-3258	153	1	furthermore	furthermore	ADV
ejpam-3258	153	2	,	,	PUNCT
ejpam-3258	153	3	the	the	DET
ejpam-3258	153	4	matrix	matrix	NOUN
ejpam-3258	153	5	∆̂	∆̂	NOUN
ejpam-3258	153	6	=	=	SYM
ejpam-3258	153	7	diag(α1i1	diag(α1i1	PROPN
ejpam-3258	153	8	,	,	PUNCT
ejpam-3258	153	9	...	...	PUNCT
ejpam-3258	153	10	,	,	PUNCT
ejpam-3258	153	11	αnin	αnin	NOUN
ejpam-3258	153	12	,	,	PUNCT
ejpam-3258	153	13	a1b	a1b	PROPN
ejpam-3258	153	14	∗	∗	VERB
ejpam-3258	153	15	1	1	NUM
ejpam-3258	153	16	,	,	PUNCT
ejpam-3258	153	17	...	...	PUNCT
ejpam-3258	153	18	,	,	PUNCT
ejpam-3258	153	19	af	af	PROPN
ejpam-3258	153	20	b	b	PROPN
ejpam-3258	153	21	∗	∗	X
ejpam-3258	153	22	f	f	PROPN
ejpam-3258	153	23	)	)	PUNCT
ejpam-3258	153	24	is	be	AUX
ejpam-3258	153	25	also	also	ADV
ejpam-3258	153	26	a	a	DET
ejpam-3258	153	27	maximizer	maximizer	NOUN
ejpam-3258	153	28	,	,	PUNCT
ejpam-3258	153	29	that	that	PRON
ejpam-3258	153	30	is	be	AUX
ejpam-3258	153	31	ρ(εm∆local	ρ(εm∆local	ADJ
ejpam-3258	153	32	)	)	PUNCT
ejpam-3258	154	1	=	=	SYM
ejpam-3258	154	2	ρ(εm	ρ(εm	NUM
ejpam-3258	154	3	∆̂	∆̂	NOUN
ejpam-3258	154	4	)	)	PUNCT
ejpam-3258	154	5	.	.	PUNCT
ejpam-3258	155	1	m.	m.	PROPN
ejpam-3258	155	2	rehman	rehman	PROPN
ejpam-3258	155	3	,	,	PUNCT
ejpam-3258	155	4	m.	m.	PROPN
ejpam-3258	155	5	f.	f.	PROPN
ejpam-3258	155	6	anwar	anwar	PROPN
ejpam-3258	155	7	/	/	PUNCT
ejpam-3258	155	8	eur	eur	PROPN
ejpam-3258	155	9	.	.	PUNCT
ejpam-3258	156	1	j.	j.	PROPN
ejpam-3258	156	2	pure	pure	PROPN
ejpam-3258	156	3	appl	appl	PROPN
ejpam-3258	156	4	.	.	PROPN
ejpam-3258	156	5	math	math	PROPN
ejpam-3258	156	6	,	,	PUNCT
ejpam-3258	156	7	11	11	NUM
ejpam-3258	156	8	(	(	PUNCT
ejpam-3258	156	9	3	3	NUM
ejpam-3258	156	10	)	)	PUNCT
ejpam-3258	156	11	(	(	PUNCT
ejpam-3258	156	12	2018	2018	NUM
ejpam-3258	156	13	)	)	PUNCT
ejpam-3258	156	14	,	,	PUNCT
ejpam-3258	156	15	774	774	NUM
ejpam-3258	156	16	-	-	SYM
ejpam-3258	156	17	792	792	NUM
ejpam-3258	156	18	781	781	NUM
ejpam-3258	156	19	3.1	3.1	NUM
ejpam-3258	156	20	.	.	PUNCT
ejpam-3258	157	1	a	a	DET
ejpam-3258	157	2	system	system	NOUN
ejpam-3258	157	3	of	of	ADP
ejpam-3258	157	4	odes	ode	NOUN
ejpam-3258	157	5	to	to	PART
ejpam-3258	157	6	approximate	approximate	VERB
ejpam-3258	157	7	the	the	DET
ejpam-3258	157	8	extremal	extremal	ADJ
ejpam-3258	157	9	points	point	NOUN
ejpam-3258	157	10	of	of	ADP
ejpam-3258	157	11	structured	structured	ADJ
ejpam-3258	157	12	spectral	spectral	ADJ
ejpam-3258	157	13	values	value	NOUN
ejpam-3258	157	14	set	set	VERB
ejpam-3258	157	15	.	.	PUNCT
ejpam-3258	158	1	first	first	ADV
ejpam-3258	158	2	of	of	ADP
ejpam-3258	158	3	all	all	PRON
ejpam-3258	158	4	we	we	PRON
ejpam-3258	158	5	compute	compute	VERB
ejpam-3258	158	6	a	a	DET
ejpam-3258	158	7	matrix	matrix	NOUN
ejpam-3258	158	8	valued	value	VERB
ejpam-3258	158	9	function	function	NOUN
ejpam-3258	158	10	denoted	denote	VERB
ejpam-3258	158	11	as	as	ADP
ejpam-3258	158	12	∆(t	∆(t	NOUN
ejpam-3258	158	13	)	)	PUNCT
ejpam-3258	158	14	.	.	PUNCT
ejpam-3258	159	1	this	this	DET
ejpam-3258	159	2	matrix	matrix	NOUN
ejpam-3258	159	3	valued	value	VERB
ejpam-3258	159	4	function	function	NOUN
ejpam-3258	159	5	will	will	AUX
ejpam-3258	159	6	help	help	VERB
ejpam-3258	159	7	to	to	PART
ejpam-3258	159	8	have	have	VERB
ejpam-3258	159	9	a	a	DET
ejpam-3258	159	10	maximum	maximum	ADJ
ejpam-3258	159	11	growth	growth	NOUN
ejpam-3258	159	12	for	for	ADP
ejpam-3258	159	13	the	the	DET
ejpam-3258	159	14	largest	large	ADJ
ejpam-3258	159	15	eigenvalue	eigenvalue	NOUN
ejpam-3258	159	16	|λ(t)|	|λ(t)|	VERB
ejpam-3258	159	17	,	,	PUNCT
ejpam-3258	159	18	with	with	ADP
ejpam-3258	159	19	λ(t	λ(t	NOUN
ejpam-3258	159	20	)	)	PUNCT
ejpam-3258	159	21	∈	∈	PROPN
ejpam-3258	159	22	λ∆b∗	λ∆b∗	VERB
ejpam-3258	159	23	ε0	ε0	PROPN
ejpam-3258	159	24	(	(	PUNCT
ejpam-3258	159	25	m	m	NOUN
ejpam-3258	159	26	)	)	PUNCT
ejpam-3258	159	27	and	and	CCONJ
ejpam-3258	159	28	then	then	ADV
ejpam-3258	159	29	finally	finally	ADV
ejpam-3258	159	30	we	we	PRON
ejpam-3258	159	31	construct	construct	VERB
ejpam-3258	159	32	and	and	CCONJ
ejpam-3258	159	33	solve	solve	VERB
ejpam-3258	159	34	a	a	DET
ejpam-3258	159	35	system	system	NOUN
ejpam-3258	159	36	of	of	ADP
ejpam-3258	159	37	ordinary	ordinary	ADJ
ejpam-3258	159	38	differential	differential	ADJ
ejpam-3258	159	39	equations	equation	NOUN
ejpam-3258	159	40	.	.	PUNCT
ejpam-3258	160	1	for	for	ADP
ejpam-3258	160	2	this	this	DET
ejpam-3258	160	3	system	system	NOUN
ejpam-3258	160	4	of	of	ADP
ejpam-3258	160	5	ode	ode	PROPN
ejpam-3258	160	6	’s	’s	PART
ejpam-3258	160	7	the	the	DET
ejpam-3258	160	8	matrix	matrix	NOUN
ejpam-3258	160	9	valued	value	VERB
ejpam-3258	160	10	function	function	NOUN
ejpam-3258	160	11	∆(t	∆(t	NOUN
ejpam-3258	160	12	)	)	PUNCT
ejpam-3258	160	13	acts	act	VERB
ejpam-3258	160	14	as	as	ADP
ejpam-3258	160	15	the	the	DET
ejpam-3258	160	16	initial	initial	ADJ
ejpam-3258	160	17	approximation	approximation	NOUN
ejpam-3258	160	18	.	.	PUNCT
ejpam-3258	161	1	3.2	3.2	NUM
ejpam-3258	161	2	.	.	PUNCT
ejpam-3258	162	1	the	the	DET
ejpam-3258	162	2	local	local	ADJ
ejpam-3258	162	3	optimization	optimization	NOUN
ejpam-3258	162	4	problem	problem	NOUN
ejpam-3258	162	5	.	.	PUNCT
ejpam-3258	162	6	consider	consider	VERB
ejpam-3258	162	7	that	that	DET
ejpam-3258	162	8	λ	λ	NOUN
ejpam-3258	162	9	=	=	PRON
ejpam-3258	162	10	|λ|eiθ	|λ|eiθ	PUNCT
ejpam-3258	162	11	is	be	AUX
ejpam-3258	162	12	eigenvalue	eigenvalue	VERB
ejpam-3258	162	13	with	with	ADP
ejpam-3258	162	14	algebraic	algebraic	ADJ
ejpam-3258	162	15	multiplicity	multiplicity	NOUN
ejpam-3258	162	16	1	1	NUM
ejpam-3258	162	17	and	and	CCONJ
ejpam-3258	162	18	having	have	VERB
ejpam-3258	162	19	the	the	DET
ejpam-3258	162	20	eigenvectors	eigenvector	NOUN
ejpam-3258	162	21	v	v	ADP
ejpam-3258	162	22	,	,	PUNCT
ejpam-3258	162	23	w	w	ADP
ejpam-3258	162	24	which	which	PRON
ejpam-3258	162	25	are	be	AUX
ejpam-3258	162	26	normalized	normalize	VERB
ejpam-3258	162	27	such	such	ADJ
ejpam-3258	162	28	that	that	SCONJ
ejpam-3258	162	29	‖w‖	‖w‖	PROPN
ejpam-3258	162	30	=	=	SYM
ejpam-3258	162	31	‖v‖	‖v‖	PUNCT
ejpam-3258	162	32	=	=	SYM
ejpam-3258	162	33	1	1	NUM
ejpam-3258	162	34	,	,	PUNCT
ejpam-3258	162	35	w∗v	w∗v	NOUN
ejpam-3258	162	36	=	=	SYM
ejpam-3258	162	37	|w∗v|e−iθ	|w∗v|e−iθ	NOUN
ejpam-3258	162	38	.	.	PUNCT
ejpam-3258	163	1	(	(	PUNCT
ejpam-3258	163	2	13	13	NUM
ejpam-3258	163	3	)	)	PUNCT
ejpam-3258	163	4	as	as	ADP
ejpam-3258	163	5	a	a	DET
ejpam-3258	163	6	result	result	NOUN
ejpam-3258	163	7	of	of	ADP
ejpam-3258	163	8	the	the	DET
ejpam-3258	163	9	previous	previous	ADJ
ejpam-3258	163	10	lemma	lemma	PROPN
ejpam-3258	163	11	3.1	3.1	NUM
ejpam-3258	163	12	,	,	PUNCT
ejpam-3258	163	13	we	we	PRON
ejpam-3258	163	14	have	have	VERB
ejpam-3258	163	15	d	d	NOUN
ejpam-3258	163	16	dt	dt	ADP
ejpam-3258	163	17	|λ|2	|λ|2	PROPN
ejpam-3258	163	18	=	=	SYM
ejpam-3258	163	19	2|λ|re	2|λ|re	NUM
ejpam-3258	163	20	(	(	PUNCT
ejpam-3258	163	21	u∗∆̇v	u∗∆̇v	NOUN
ejpam-3258	163	22	eiθw∗v	eiθw∗v	ADJ
ejpam-3258	163	23	)	)	PUNCT
ejpam-3258	164	1	=	=	SYM
ejpam-3258	164	2	2|λ|	2|λ|	NUM
ejpam-3258	164	3	|w∗v|	|w∗v|	PROPN
ejpam-3258	164	4	re(u∗∆̇v	re(u∗∆̇v	NOUN
ejpam-3258	164	5	)	)	PUNCT
ejpam-3258	164	6	,	,	PUNCT
ejpam-3258	164	7	(	(	PUNCT
ejpam-3258	164	8	14	14	NUM
ejpam-3258	164	9	)	)	PUNCT
ejpam-3258	164	10	where	where	SCONJ
ejpam-3258	164	11	u	u	NOUN
ejpam-3258	164	12	=	=	PUNCT
ejpam-3258	164	13	m∗w	m∗w	PROPN
ejpam-3258	164	14	.	.	PUNCT
ejpam-3258	165	1	in	in	ADP
ejpam-3258	165	2	fact	fact	NOUN
ejpam-3258	165	3	the	the	DET
ejpam-3258	165	4	dependence	dependence	NOUN
ejpam-3258	165	5	on	on	ADP
ejpam-3258	165	6	t	t	PROPN
ejpam-3258	165	7	is	be	AUX
ejpam-3258	165	8	intentionally	intentionally	ADV
ejpam-3258	165	9	omitted	omit	VERB
ejpam-3258	165	10	.	.	PUNCT
ejpam-3258	166	1	now	now	ADV
ejpam-3258	166	2	we	we	PRON
ejpam-3258	166	3	consider	consider	VERB
ejpam-3258	166	4	∆	∆	PROPN
ejpam-3258	166	5	∈	∈	PROPN
ejpam-3258	166	6	∆b	∆b	PROPN
ejpam-3258	166	7	and	and	CCONJ
ejpam-3258	166	8	we	we	PRON
ejpam-3258	166	9	aim	aim	VERB
ejpam-3258	166	10	to	to	PART
ejpam-3258	166	11	compute	compute	VERB
ejpam-3258	166	12	∆̇	∆̇	NOUN
ejpam-3258	166	13	=	=	SYM
ejpam-3258	166	14	u	u	NOUN
ejpam-3258	166	15	.	.	PUNCT
ejpam-3258	167	1	this	this	DET
ejpam-3258	167	2	direction	direction	NOUN
ejpam-3258	167	3	will	will	AUX
ejpam-3258	167	4	locally	locally	ADV
ejpam-3258	167	5	maximizes	maximize	VERB
ejpam-3258	167	6	the	the	DET
ejpam-3258	167	7	growth	growth	NOUN
ejpam-3258	167	8	of	of	ADP
ejpam-3258	167	9	trajectory	trajectory	NOUN
ejpam-3258	167	10	of	of	ADP
ejpam-3258	167	11	the	the	DET
ejpam-3258	167	12	modulus	modulus	NOUN
ejpam-3258	167	13	of	of	ADP
ejpam-3258	167	14	λ(t	λ(t	NOUN
ejpam-3258	167	15	)	)	PUNCT
ejpam-3258	167	16	.	.	PUNCT
ejpam-3258	168	1	as	as	ADP
ejpam-3258	168	2	a	a	DET
ejpam-3258	168	3	result	result	NOUN
ejpam-3258	168	4	,	,	PUNCT
ejpam-3258	168	5	finally	finally	ADV
ejpam-3258	168	6	we	we	PRON
ejpam-3258	168	7	get	get	VERB
ejpam-3258	168	8	u	u	NOUN
ejpam-3258	168	9	=	=	PROPN
ejpam-3258	168	10	diag(ω1ir1	diag(ω1ir1	PROPN
ejpam-3258	168	11	,	,	PUNCT
ejpam-3258	168	12	.	.	PUNCT
ejpam-3258	168	13	.	.	PUNCT
ejpam-3258	169	1	.	.	PUNCT
ejpam-3258	170	1	,	,	PUNCT
ejpam-3258	170	2	ωsirn	ωsirn	NOUN
ejpam-3258	170	3	,	,	PUNCT
ejpam-3258	170	4	ω1	ω1	PROPN
ejpam-3258	170	5	,	,	PUNCT
ejpam-3258	170	6	.	.	PUNCT
ejpam-3258	170	7	.	.	PUNCT
ejpam-3258	171	1	.	.	PUNCT
ejpam-3258	172	1	,	,	PUNCT
ejpam-3258	172	2	ωf	ωf	PROPN
ejpam-3258	172	3	)	)	PUNCT
ejpam-3258	172	4	.	.	PUNCT
ejpam-3258	173	1	(	(	PUNCT
ejpam-3258	173	2	15	15	NUM
ejpam-3258	173	3	)	)	PUNCT
ejpam-3258	173	4	the	the	DET
ejpam-3258	173	5	result	result	NOUN
ejpam-3258	173	6	as	as	SCONJ
ejpam-3258	173	7	given	give	VERB
ejpam-3258	173	8	in	in	ADP
ejpam-3258	173	9	equ	equ	PROPN
ejpam-3258	173	10	.	.	PUNCT
ejpam-3258	174	1	(	(	PUNCT
ejpam-3258	174	2	15	15	NUM
ejpam-3258	174	3	)	)	PUNCT
ejpam-3258	174	4	is	be	AUX
ejpam-3258	174	5	the	the	DET
ejpam-3258	174	6	solution	solution	NOUN
ejpam-3258	174	7	of	of	ADP
ejpam-3258	174	8	the	the	DET
ejpam-3258	174	9	following	follow	VERB
ejpam-3258	174	10	maximization	maximization	NOUN
ejpam-3258	174	11	problem	problem	NOUN
ejpam-3258	174	12	u∗	u∗	NOUN
ejpam-3258	174	13	=	=	PUNCT
ejpam-3258	174	14	arg	arg	NOUN
ejpam-3258	174	15	max{re(u∗ux	max{re(u∗ux	NOUN
ejpam-3258	174	16	)	)	PUNCT
ejpam-3258	174	17	}	}	PUNCT
ejpam-3258	174	18	subject	subject	ADJ
ejpam-3258	174	19	to	to	ADP
ejpam-3258	174	20	re(δiωi	re(δiωi	NOUN
ejpam-3258	174	21	)	)	PUNCT
ejpam-3258	174	22	=	=	SYM
ejpam-3258	175	1	0	0	NUM
ejpam-3258	175	2	,	,	PUNCT
ejpam-3258	175	3	i	i	PRON
ejpam-3258	175	4	=	=	NOUN
ejpam-3258	175	5	1	1	NUM
ejpam-3258	175	6	:	:	PUNCT
ejpam-3258	175	7	n	n	CCONJ
ejpam-3258	175	8	,	,	PUNCT
ejpam-3258	175	9	and	and	CCONJ
ejpam-3258	175	10	re〈∆j	re〈∆j	NOUN
ejpam-3258	175	11	,	,	PUNCT
ejpam-3258	175	12	ωj	ωj	ADP
ejpam-3258	175	13	〉	〉	NOUN
ejpam-3258	175	14	=	=	SYM
ejpam-3258	175	15	0	0	NUM
ejpam-3258	175	16	,	,	PUNCT
ejpam-3258	175	17	j	j	X
ejpam-3258	175	18	=	=	NOUN
ejpam-3258	175	19	1	1	NUM
ejpam-3258	175	20	:	:	PUNCT
ejpam-3258	175	21	f.	f.	PROPN
ejpam-3258	175	22	(	(	PUNCT
ejpam-3258	175	23	16	16	NUM
ejpam-3258	175	24	)	)	PUNCT
ejpam-3258	175	25	we	we	PRON
ejpam-3258	175	26	give	give	VERB
ejpam-3258	175	27	following	follow	VERB
ejpam-3258	175	28	lemma	lemma	PROPN
ejpam-3258	175	29	3.5	3.5	NUM
ejpam-3258	175	30	in	in	ADP
ejpam-3258	175	31	order	order	NOUN
ejpam-3258	175	32	to	to	PART
ejpam-3258	175	33	solve	solve	VERB
ejpam-3258	175	34	the	the	DET
ejpam-3258	175	35	maximization	maximization	NOUN
ejpam-3258	175	36	problem	problem	NOUN
ejpam-3258	175	37	as	as	SCONJ
ejpam-3258	175	38	discussed	discuss	VERB
ejpam-3258	175	39	in	in	ADP
ejpam-3258	175	40	above	above	ADP
ejpam-3258	175	41	equ	equ	PROPN
ejpam-3258	175	42	.	.	PUNCT
ejpam-3258	176	1	(	(	PUNCT
ejpam-3258	176	2	8)	8)	NUM
ejpam-3258	176	3	.	.	PUNCT
ejpam-3258	177	1	lemma	lemma	PROPN
ejpam-3258	177	2	3.5	3.5	NUM
ejpam-3258	177	3	.	.	PUNCT
ejpam-3258	178	1	we	we	PRON
ejpam-3258	178	2	make	make	VERB
ejpam-3258	178	3	use	use	NOUN
ejpam-3258	178	4	of	of	ADP
ejpam-3258	178	5	the	the	DET
ejpam-3258	178	6	notation	notation	NOUN
ejpam-3258	178	7	as	as	SCONJ
ejpam-3258	178	8	already	already	ADV
ejpam-3258	178	9	introduced	introduce	VERB
ejpam-3258	178	10	in	in	ADP
ejpam-3258	178	11	above	above	ADP
ejpam-3258	178	12	theorem	theorem	NOUN
ejpam-3258	178	13	and	and	CCONJ
ejpam-3258	178	14	partitioning	partitioning	NOUN
ejpam-3258	178	15	of	of	ADP
ejpam-3258	178	16	the	the	DET
ejpam-3258	178	17	v	v	NOUN
ejpam-3258	178	18	,	,	PUNCT
ejpam-3258	178	19	u	u	NOUN
ejpam-3258	178	20	as	as	ADP
ejpam-3258	178	21	earlier	early	ADV
ejpam-3258	178	22	,	,	PUNCT
ejpam-3258	178	23	a	a	DET
ejpam-3258	178	24	solution	solution	NOUN
ejpam-3258	178	25	of	of	ADP
ejpam-3258	178	26	the	the	DET
ejpam-3258	178	27	maximization	maximization	NOUN
ejpam-3258	178	28	problem	problem	NOUN
ejpam-3258	178	29	discussed	discuss	VERB
ejpam-3258	178	30	in	in	ADP
ejpam-3258	178	31	equ	equ	PROPN
ejpam-3258	178	32	.	.	PUNCT
ejpam-3258	179	1	(	(	PUNCT
ejpam-3258	179	2	15	15	NUM
ejpam-3258	179	3	)	)	PUNCT
ejpam-3258	179	4	is	be	AUX
ejpam-3258	179	5	given	give	VERB
ejpam-3258	179	6	by	by	ADP
ejpam-3258	179	7	u∗	u∗	NOUN
ejpam-3258	179	8	=	=	SYM
ejpam-3258	179	9	diag(ω1ir1	diag(ω1ir1	PROPN
ejpam-3258	179	10	,	,	PUNCT
ejpam-3258	179	11	.	.	PUNCT
ejpam-3258	179	12	.	.	PUNCT
ejpam-3258	179	13	.	.	PUNCT
ejpam-3258	180	1	,	,	PUNCT
ejpam-3258	180	2	ωnirn	ωnirn	NOUN
ejpam-3258	180	3	,	,	PUNCT
ejpam-3258	180	4	ω1	ω1	PROPN
ejpam-3258	180	5	,	,	PUNCT
ejpam-3258	180	6	.	.	PUNCT
ejpam-3258	180	7	.	.	PUNCT
ejpam-3258	181	1	.	.	PUNCT
ejpam-3258	182	1	,	,	PUNCT
ejpam-3258	182	2	ωf	ωf	PROPN
ejpam-3258	182	3	)	)	PUNCT
ejpam-3258	182	4	,	,	PUNCT
ejpam-3258	182	5	(	(	PUNCT
ejpam-3258	182	6	17	17	NUM
ejpam-3258	182	7	)	)	PUNCT
ejpam-3258	182	8	with	with	ADP
ejpam-3258	182	9	m.	m.	NOUN
ejpam-3258	182	10	rehman	rehman	PROPN
ejpam-3258	182	11	,	,	PUNCT
ejpam-3258	182	12	m.	m.	PROPN
ejpam-3258	182	13	f.	f.	PROPN
ejpam-3258	182	14	anwar	anwar	PROPN
ejpam-3258	182	15	/	/	PUNCT
ejpam-3258	182	16	eur	eur	PROPN
ejpam-3258	182	17	.	.	PUNCT
ejpam-3258	183	1	j.	j.	PROPN
ejpam-3258	183	2	pure	pure	PROPN
ejpam-3258	183	3	appl	appl	PROPN
ejpam-3258	183	4	.	.	PROPN
ejpam-3258	183	5	math	math	PROPN
ejpam-3258	183	6	,	,	PUNCT
ejpam-3258	183	7	11	11	NUM
ejpam-3258	183	8	(	(	PUNCT
ejpam-3258	183	9	3	3	NUM
ejpam-3258	183	10	)	)	PUNCT
ejpam-3258	183	11	(	(	PUNCT
ejpam-3258	183	12	2018	2018	NUM
ejpam-3258	183	13	)	)	PUNCT
ejpam-3258	183	14	,	,	PUNCT
ejpam-3258	183	15	774	774	NUM
ejpam-3258	183	16	-	-	SYM
ejpam-3258	183	17	792	792	NUM
ejpam-3258	183	18	782	782	NUM
ejpam-3258	183	19	ωi	ωi	NOUN
ejpam-3258	183	20	=	=	PUNCT
ejpam-3258	183	21	νi	νi	PRON
ejpam-3258	183	22	(	(	PUNCT
ejpam-3258	183	23	v∗i	v∗i	X
ejpam-3258	183	24	ui	ui	PROPN
ejpam-3258	183	25	−re	−re	PROPN
ejpam-3258	183	26	(	(	PUNCT
ejpam-3258	183	27	v∗i	v∗i	X
ejpam-3258	183	28	uisi	uisi	ADJ
ejpam-3258	183	29	)	)	PUNCT
ejpam-3258	183	30	si	si	NOUN
ejpam-3258	183	31	)	)	PUNCT
ejpam-3258	183	32	,	,	PUNCT
ejpam-3258	183	33	i	i	PRON
ejpam-3258	183	34	=	=	NOUN
ejpam-3258	183	35	1	1	NUM
ejpam-3258	183	36	,	,	PUNCT
ejpam-3258	183	37	.	.	PUNCT
ejpam-3258	183	38	.	.	PUNCT
ejpam-3258	184	1	.	.	PUNCT
ejpam-3258	185	1	,	,	PUNCT
ejpam-3258	185	2	n	n	X
ejpam-3258	185	3	(	(	PUNCT
ejpam-3258	185	4	18	18	NUM
ejpam-3258	185	5	)	)	PUNCT
ejpam-3258	185	6	ωj	ωj	ADP
ejpam-3258	185	7	=	=	VERB
ejpam-3258	185	8	ζj	ζj	PROPN
ejpam-3258	185	9	(	(	PUNCT
ejpam-3258	185	10	un+jv	un+jv	ADP
ejpam-3258	185	11	∗	∗	NOUN
ejpam-3258	185	12	n+j	n+j	PROPN
ejpam-3258	185	13	−re〈∆j	−re〈∆j	PROPN
ejpam-3258	185	14	,	,	PUNCT
ejpam-3258	185	15	un+jv	un+jv	ADP
ejpam-3258	185	16	∗	∗	NOUN
ejpam-3258	185	17	n+j〉∆j	n+j〉∆j	NOUN
ejpam-3258	185	18	)	)	PUNCT
ejpam-3258	185	19	,	,	PUNCT
ejpam-3258	185	20	j	j	PROPN
ejpam-3258	185	21	=	=	SYM
ejpam-3258	185	22	1	1	NUM
ejpam-3258	185	23	,	,	PUNCT
ejpam-3258	185	24	.	.	PUNCT
ejpam-3258	185	25	.	.	PUNCT
ejpam-3258	185	26	.	.	PUNCT
ejpam-3258	186	1	,	,	PUNCT
ejpam-3258	186	2	f.	f.	PROPN
ejpam-3258	186	3	(	(	PUNCT
ejpam-3258	186	4	19	19	NUM
ejpam-3258	186	5	)	)	PUNCT
ejpam-3258	186	6	the	the	DET
ejpam-3258	186	7	coefficient	coefficient	NOUN
ejpam-3258	186	8	νi	νi	PRON
ejpam-3258	186	9	is	be	AUX
ejpam-3258	186	10	strictly	strictly	ADV
ejpam-3258	186	11	positive	positive	ADJ
ejpam-3258	186	12	.	.	PUNCT
ejpam-3258	187	1	the	the	DET
ejpam-3258	187	2	νi	νi	NOUN
ejpam-3258	187	3	is	be	AUX
ejpam-3258	187	4	the	the	DET
ejpam-3258	187	5	reciprocal	reciprocal	NOUN
ejpam-3258	187	6	of	of	ADP
ejpam-3258	187	7	the	the	DET
ejpam-3258	187	8	absolute	absolute	ADJ
ejpam-3258	187	9	value	value	NOUN
ejpam-3258	187	10	of	of	ADP
ejpam-3258	187	11	the	the	DET
ejpam-3258	187	12	right	right	ADJ
ejpam-3258	187	13	-	-	PUNCT
ejpam-3258	187	14	hand	hand	NOUN
ejpam-3258	187	15	side	side	NOUN
ejpam-3258	187	16	in	in	ADP
ejpam-3258	187	17	equ	equ	PROPN
ejpam-3258	187	18	.	.	PUNCT
ejpam-3258	188	1	(	(	PUNCT
ejpam-3258	188	2	18	18	NUM
ejpam-3258	188	3	)	)	PUNCT
ejpam-3258	188	4	,	,	PUNCT
ejpam-3258	188	5	if	if	SCONJ
ejpam-3258	188	6	this	this	PRON
ejpam-3258	188	7	is	be	AUX
ejpam-3258	188	8	different	different	ADJ
ejpam-3258	188	9	from	from	ADP
ejpam-3258	188	10	zero	zero	NUM
ejpam-3258	188	11	,	,	PUNCT
ejpam-3258	188	12	and	and	CCONJ
ejpam-3258	188	13	νi	νi	DET
ejpam-3258	188	14	=	=	SYM
ejpam-3258	188	15	1	1	NUM
ejpam-3258	188	16	otherwise	otherwise	ADV
ejpam-3258	188	17	.	.	PUNCT
ejpam-3258	189	1	in	in	ADP
ejpam-3258	189	2	a	a	DET
ejpam-3258	189	3	similar	similar	ADJ
ejpam-3258	189	4	fashion	fashion	NOUN
ejpam-3258	189	5	,	,	PUNCT
ejpam-3258	189	6	ζj	ζj	PROPN
ejpam-3258	189	7	is	be	AUX
ejpam-3258	189	8	also	also	ADV
ejpam-3258	189	9	obtained	obtain	VERB
ejpam-3258	189	10	as	as	ADP
ejpam-3258	189	11	strictly	strictly	ADV
ejpam-3258	189	12	positive	positive	ADJ
ejpam-3258	189	13	and	and	CCONJ
ejpam-3258	189	14	is	be	AUX
ejpam-3258	189	15	the	the	DET
ejpam-3258	189	16	reciprocal	reciprocal	NOUN
ejpam-3258	189	17	of	of	ADP
ejpam-3258	189	18	the	the	DET
ejpam-3258	189	19	frobenius	frobenius	ADJ
ejpam-3258	189	20	norm	norm	NOUN
ejpam-3258	189	21	of	of	ADP
ejpam-3258	189	22	the	the	DET
ejpam-3258	189	23	matrix	matrix	NOUN
ejpam-3258	189	24	on	on	ADP
ejpam-3258	189	25	the	the	DET
ejpam-3258	189	26	right	right	ADJ
ejpam-3258	189	27	hand	hand	NOUN
ejpam-3258	189	28	side	side	NOUN
ejpam-3258	189	29	in	in	ADP
ejpam-3258	189	30	equ	equ	PROPN
ejpam-3258	189	31	.	.	PUNCT
ejpam-3258	190	1	(	(	PUNCT
ejpam-3258	190	2	19	19	NUM
ejpam-3258	190	3	)	)	PUNCT
ejpam-3258	190	4	,	,	PUNCT
ejpam-3258	190	5	if	if	SCONJ
ejpam-3258	190	6	this	this	PRON
ejpam-3258	190	7	is	be	AUX
ejpam-3258	190	8	different	different	ADJ
ejpam-3258	190	9	from	from	ADP
ejpam-3258	190	10	zero	zero	NUM
ejpam-3258	190	11	,	,	PUNCT
ejpam-3258	190	12	and	and	CCONJ
ejpam-3258	190	13	ζj	ζj	X
ejpam-3258	190	14	=	=	NOUN
ejpam-3258	190	15	1	1	NUM
ejpam-3258	190	16	otherwise	otherwise	ADV
ejpam-3258	190	17	.	.	PUNCT
ejpam-3258	191	1	the	the	DET
ejpam-3258	191	2	result	result	NOUN
ejpam-3258	191	3	of	of	ADP
ejpam-3258	191	4	previous	previous	ADJ
ejpam-3258	191	5	lemma	lemma	PROPN
ejpam-3258	191	6	3.5	3.5	NUM
ejpam-3258	191	7	can	can	AUX
ejpam-3258	191	8	be	be	AUX
ejpam-3258	191	9	expressed	express	VERB
ejpam-3258	191	10	as	as	ADP
ejpam-3258	191	11	u∗	u∗	NOUN
ejpam-3258	191	12	=	=	SYM
ejpam-3258	191	13	d1p∆∗b	d1p∆∗b	NOUN
ejpam-3258	191	14	(	(	PUNCT
ejpam-3258	191	15	uv∗)−d2∆.	uv∗)−d2∆.	PROPN
ejpam-3258	191	16	(	(	PUNCT
ejpam-3258	191	17	20	20	NUM
ejpam-3258	191	18	)	)	PUNCT
ejpam-3258	191	19	in	in	ADP
ejpam-3258	191	20	equ	equ	PROPN
ejpam-3258	191	21	.	.	PUNCT
ejpam-3258	192	1	(	(	PUNCT
ejpam-3258	192	2	20	20	NUM
ejpam-3258	192	3	)	)	PUNCT
ejpam-3258	192	4	,	,	PUNCT
ejpam-3258	192	5	p∆∗b	p∆∗b	PROPN
ejpam-3258	192	6	(	(	PUNCT
ejpam-3258	192	7	·	·	PUNCT
ejpam-3258	192	8	)	)	PUNCT
ejpam-3258	192	9	,	,	PUNCT
ejpam-3258	192	10	denotes	denote	VERB
ejpam-3258	192	11	the	the	DET
ejpam-3258	192	12	orthogonal	orthogonal	ADJ
ejpam-3258	192	13	projection	projection	NOUN
ejpam-3258	192	14	while	while	SCONJ
ejpam-3258	192	15	the	the	DET
ejpam-3258	192	16	matrices	matrix	NOUN
ejpam-3258	192	17	d1	d1	NOUN
ejpam-3258	192	18	,	,	PUNCT
ejpam-3258	192	19	d2	d2	PROPN
ejpam-3258	192	20	∈	∈	PROPN
ejpam-3258	192	21	∆∗b	∆∗b	NOUN
ejpam-3258	192	22	are	be	AUX
ejpam-3258	192	23	diagonal	diagonal	ADJ
ejpam-3258	192	24	matrices	matrix	NOUN
ejpam-3258	192	25	with	with	ADP
ejpam-3258	192	26	d1	d1	NOUN
ejpam-3258	192	27	having	have	VERB
ejpam-3258	192	28	structure	structure	NOUN
ejpam-3258	192	29	such	such	ADJ
ejpam-3258	192	30	that	that	SCONJ
ejpam-3258	192	31	all	all	PRON
ejpam-3258	192	32	of	of	ADP
ejpam-3258	192	33	its	its	PRON
ejpam-3258	192	34	eigenvalues	eigenvalue	NOUN
ejpam-3258	192	35	are	be	AUX
ejpam-3258	192	36	positive	positive	ADJ
ejpam-3258	192	37	.	.	PUNCT
ejpam-3258	193	1	4	4	X
ejpam-3258	193	2	.	.	X
ejpam-3258	193	3	system	system	NOUN
ejpam-3258	193	4	of	of	ADP
ejpam-3258	193	5	ordinary	ordinary	ADJ
ejpam-3258	193	6	differential	differential	ADJ
ejpam-3258	193	7	equation	equation	NOUN
ejpam-3258	193	8	’s	’	VERB
ejpam-3258	193	9	the	the	DET
ejpam-3258	193	10	lemma	lemma	PROPN
ejpam-3258	193	11	3.5	3.5	NUM
ejpam-3258	193	12	,	,	PUNCT
ejpam-3258	193	13	as	as	SCONJ
ejpam-3258	193	14	discussed	discuss	VERB
ejpam-3258	193	15	previously	previously	ADV
ejpam-3258	193	16	suggest	suggest	VERB
ejpam-3258	193	17	us	we	PRON
ejpam-3258	193	18	to	to	PART
ejpam-3258	193	19	consider	consider	VERB
ejpam-3258	193	20	the	the	DET
ejpam-3258	193	21	differential	differential	ADJ
ejpam-3258	193	22	equation	equation	NOUN
ejpam-3258	193	23	∆̇(t	∆̇(t	NOUN
ejpam-3258	193	24	)	)	PUNCT
ejpam-3258	193	25	on	on	ADP
ejpam-3258	193	26	the	the	DET
ejpam-3258	193	27	manifold	manifold	ADJ
ejpam-3258	193	28	∆∗b	∆∗b	NOUN
ejpam-3258	193	29	:	:	PUNCT
ejpam-3258	193	30	∆̇(t	∆̇(t	NOUN
ejpam-3258	193	31	)	)	PUNCT
ejpam-3258	193	32	=	=	PUNCT
ejpam-3258	193	33	d1p∆∗b	d1p∆∗b	NOUN
ejpam-3258	193	34	(	(	PUNCT
ejpam-3258	193	35	uv∗)−d2∆(t	uv∗)−d2∆(t	ADJ
ejpam-3258	193	36	)	)	PUNCT
ejpam-3258	193	37	.	.	PUNCT
ejpam-3258	194	1	(	(	PUNCT
ejpam-3258	194	2	21	21	NUM
ejpam-3258	194	3	)	)	PUNCT
ejpam-3258	194	4	in	in	ADP
ejpam-3258	194	5	equ	equ	PROPN
ejpam-3258	194	6	.	.	PUNCT
ejpam-3258	195	1	(	(	PUNCT
ejpam-3258	195	2	21	21	NUM
ejpam-3258	195	3	)	)	PUNCT
ejpam-3258	195	4	,	,	PUNCT
ejpam-3258	195	5	v(t	v(t	NOUN
ejpam-3258	195	6	)	)	PUNCT
ejpam-3258	195	7	is	be	AUX
ejpam-3258	195	8	an	an	DET
ejpam-3258	195	9	eigenvector	eigenvector	NOUN
ejpam-3258	195	10	possesses	possess	VERB
ejpam-3258	195	11	the	the	DET
ejpam-3258	195	12	unit	unit	NOUN
ejpam-3258	195	13	2	2	NUM
ejpam-3258	195	14	-	-	PUNCT
ejpam-3258	195	15	norm	norm	NOUN
ejpam-3258	195	16	and	and	CCONJ
ejpam-3258	195	17	is	be	AUX
ejpam-3258	195	18	associated	associate	VERB
ejpam-3258	195	19	to	to	ADP
ejpam-3258	195	20	the	the	DET
ejpam-3258	195	21	simple	simple	ADJ
ejpam-3258	195	22	eigenvalue	eigenvalue	PROPN
ejpam-3258	195	23	λ(t	λ(t	PROPN
ejpam-3258	195	24	)	)	PUNCT
ejpam-3258	195	25	of	of	ADP
ejpam-3258	195	26	ε0m∆(t	ε0m∆(t	NOUN
ejpam-3258	195	27	)	)	PUNCT
ejpam-3258	195	28	.	.	PUNCT
ejpam-3258	196	1	here	here	ADV
ejpam-3258	196	2	we	we	PRON
ejpam-3258	196	3	also	also	ADV
ejpam-3258	196	4	note	note	VERB
ejpam-3258	196	5	that	that	DET
ejpam-3258	196	6	fact	fact	NOUN
ejpam-3258	196	7	that	that	SCONJ
ejpam-3258	196	8	u(t	u(t	NOUN
ejpam-3258	196	9	)	)	PUNCT
ejpam-3258	196	10	,	,	PUNCT
ejpam-3258	196	11	d1(t	d1(t	PROPN
ejpam-3258	196	12	)	)	PUNCT
ejpam-3258	196	13	,	,	PUNCT
ejpam-3258	196	14	d2(t	d2(t	PROPN
ejpam-3258	196	15	)	)	PUNCT
ejpam-3258	196	16	depend	depend	VERB
ejpam-3258	196	17	on	on	ADP
ejpam-3258	196	18	∆(t	∆(t	NOUN
ejpam-3258	196	19	)	)	PUNCT
ejpam-3258	196	20	.	.	PUNCT
ejpam-3258	197	1	the	the	DET
ejpam-3258	197	2	differential	differential	ADJ
ejpam-3258	197	3	equation	equation	NOUN
ejpam-3258	197	4	as	as	SCONJ
ejpam-3258	197	5	obtained	obtain	VERB
ejpam-3258	197	6	in	in	ADP
ejpam-3258	197	7	equ	equ	PROPN
ejpam-3258	197	8	.	.	PUNCT
ejpam-3258	198	1	(	(	PUNCT
ejpam-3258	198	2	21	21	NUM
ejpam-3258	198	3	)	)	PUNCT
ejpam-3258	198	4	generates	generate	VERB
ejpam-3258	198	5	a	a	DET
ejpam-3258	198	6	system	system	NOUN
ejpam-3258	198	7	of	of	ADP
ejpam-3258	198	8	ode	ode	PROPN
ejpam-3258	198	9	’s	’s	NOUN
ejpam-3258	198	10	.	.	PUNCT
ejpam-3258	199	1	this	this	DET
ejpam-3258	199	2	system	system	NOUN
ejpam-3258	199	3	of	of	ADP
ejpam-3258	199	4	ode	ode	PROPN
ejpam-3258	199	5	’s	’s	PART
ejpam-3258	199	6	is	be	AUX
ejpam-3258	199	7	a	a	DET
ejpam-3258	199	8	gradient	gradient	ADJ
ejpam-3258	199	9	system	system	NOUN
ejpam-3258	199	10	of	of	ADP
ejpam-3258	199	11	ode	ode	PROPN
ejpam-3258	199	12	’s	’s	PART
ejpam-3258	199	13	because	because	SCONJ
ejpam-3258	199	14	,	,	PUNCT
ejpam-3258	199	15	by	by	ADP
ejpam-3258	199	16	definition	definition	NOUN
ejpam-3258	199	17	,	,	PUNCT
ejpam-3258	199	18	the	the	DET
ejpam-3258	199	19	right	right	ADJ
ejpam-3258	199	20	-	-	PUNCT
ejpam-3258	199	21	hand	hand	NOUN
ejpam-3258	199	22	side	side	NOUN
ejpam-3258	199	23	is	be	AUX
ejpam-3258	199	24	nothing	nothing	PRON
ejpam-3258	199	25	but	but	SCONJ
ejpam-3258	199	26	the	the	DET
ejpam-3258	199	27	projected	project	VERB
ejpam-3258	199	28	gradient	gradient	NOUN
ejpam-3258	199	29	of	of	ADP
ejpam-3258	199	30	u	u	PROPN
ejpam-3258	199	31	7→	7→	PROPN
ejpam-3258	199	32	re(u∗uv	re(u∗uv	NOUN
ejpam-3258	199	33	)	)	PUNCT
ejpam-3258	199	34	.	.	PUNCT
ejpam-3258	200	1	4.1	4.1	NUM
ejpam-3258	200	2	.	.	PUNCT
ejpam-3258	200	3	computation	computation	NOUN
ejpam-3258	200	4	of	of	ADP
ejpam-3258	200	5	initial	initial	ADJ
ejpam-3258	200	6	value	value	NOUN
ejpam-3258	200	7	matrix	matrix	NOUN
ejpam-3258	200	8	∆(t	∆(t	NOUN
ejpam-3258	200	9	)	)	PUNCT
ejpam-3258	200	10	and	and	CCONJ
ejpam-3258	200	11	ε1	ε1	VERB
ejpam-3258	200	12	[	[	X
ejpam-3258	200	13	14	14	NUM
ejpam-3258	200	14	]	]	PUNCT
ejpam-3258	200	15	.	.	PUNCT
ejpam-3258	201	1	in	in	ADP
ejpam-3258	201	2	order	order	NOUN
ejpam-3258	201	3	to	to	PART
ejpam-3258	201	4	obtain	obtain	VERB
ejpam-3258	201	5	a	a	DET
ejpam-3258	201	6	suitable	suitable	ADJ
ejpam-3258	201	7	choice	choice	NOUN
ejpam-3258	201	8	for	for	ADP
ejpam-3258	201	9	the	the	DET
ejpam-3258	201	10	initial	initial	ADJ
ejpam-3258	201	11	valued	value	VERB
ejpam-3258	201	12	matrix	matrix	NOUN
ejpam-3258	201	13	function	function	NOUN
ejpam-3258	201	14	∆0(t	∆0(t	PROPN
ejpam-3258	201	15	)	)	PUNCT
ejpam-3258	201	16	which	which	PRON
ejpam-3258	201	17	acts	act	VERB
ejpam-3258	201	18	as	as	SCONJ
ejpam-3258	201	19	the	the	DET
ejpam-3258	201	20	initial	initial	ADJ
ejpam-3258	201	21	value	value	NOUN
ejpam-3258	201	22	to	to	PART
ejpam-3258	201	23	solve	solve	VERB
ejpam-3258	201	24	the	the	DET
ejpam-3258	201	25	gradient	gradient	ADJ
ejpam-3258	201	26	system	system	NOUN
ejpam-3258	201	27	of	of	ADP
ejpam-3258	201	28	ode	ode	PROPN
ejpam-3258	201	29	’s	’s	PART
ejpam-3258	201	30	is	be	AUX
ejpam-3258	201	31	given	give	VERB
ejpam-3258	201	32	as	as	ADP
ejpam-3258	201	33	below	below	ADV
ejpam-3258	201	34	.	.	PUNCT
ejpam-3258	202	1	∆0	∆0	VERB
ejpam-3258	202	2	=	=	PUNCT
ejpam-3258	202	3	dp∆b(wv∗	dp∆b(wv∗	X
ejpam-3258	202	4	)	)	PUNCT
ejpam-3258	202	5	,	,	PUNCT
ejpam-3258	202	6	(	(	PUNCT
ejpam-3258	202	7	22	22	NUM
ejpam-3258	202	8	)	)	PUNCT
ejpam-3258	202	9	where	where	SCONJ
ejpam-3258	202	10	d	d	NOUN
ejpam-3258	202	11	is	be	AUX
ejpam-3258	202	12	positive	positive	ADJ
ejpam-3258	202	13	diagonal	diagonal	ADJ
ejpam-3258	202	14	matrix	matrix	NOUN
ejpam-3258	202	15	.	.	PUNCT
ejpam-3258	203	1	the	the	DET
ejpam-3258	203	2	matrix	matrix	NOUN
ejpam-3258	203	3	d	d	NOUN
ejpam-3258	203	4	is	be	AUX
ejpam-3258	203	5	chosen	choose	VERB
ejpam-3258	203	6	so	so	SCONJ
ejpam-3258	203	7	that	that	SCONJ
ejpam-3258	203	8	∆0	∆0	NUM
ejpam-3258	203	9	∈	∈	PROPN
ejpam-3258	203	10	∆b	∆b	PROPN
ejpam-3258	203	11	.	.	PROPN
ejpam-3258	204	1	on	on	ADP
ejpam-3258	204	2	the	the	DET
ejpam-3258	204	3	other	other	ADJ
ejpam-3258	204	4	hand	hand	NOUN
ejpam-3258	204	5	,	,	PUNCT
ejpam-3258	204	6	a	a	DET
ejpam-3258	204	7	straight	straight	ADJ
ejpam-3258	204	8	forward	forward	ADV
ejpam-3258	204	9	but	but	CCONJ
ejpam-3258	204	10	a	a	DET
ejpam-3258	204	11	very	very	ADV
ejpam-3258	204	12	natural	natural	ADJ
ejpam-3258	204	13	choice	choice	NOUN
ejpam-3258	204	14	for	for	ADP
ejpam-3258	204	15	ε0	ε0	PROPN
ejpam-3258	204	16	is	be	AUX
ejpam-3258	204	17	given	give	VERB
ejpam-3258	204	18	by	by	ADP
ejpam-3258	204	19	just	just	ADV
ejpam-3258	204	20	computing	compute	VERB
ejpam-3258	204	21	the	the	DET
ejpam-3258	204	22	reciprocal	reciprocal	NOUN
ejpam-3258	204	23	of	of	ADP
ejpam-3258	204	24	the	the	DET
ejpam-3258	204	25	upper	upper	ADJ
ejpam-3258	204	26	bound	bind	VERB
ejpam-3258	204	27	µ̂∆b(m	µ̂∆b(m	NOUN
ejpam-3258	204	28	)	)	PUNCT
ejpam-3258	204	29	of	of	ADP
ejpam-3258	204	30	ssv	ssv	NOUN
ejpam-3258	204	31	by	by	ADP
ejpam-3258	204	32	using	use	VERB
ejpam-3258	204	33	mussv	mussv	ADJ
ejpam-3258	204	34	function	function	NOUN
ejpam-3258	204	35	.	.	PUNCT
ejpam-3258	205	1	that	that	PRON
ejpam-3258	205	2	is	be	AUX
ejpam-3258	205	3	,	,	PUNCT
ejpam-3258	205	4	ε0	ε0	PROPN
ejpam-3258	205	5	=	=	NOUN
ejpam-3258	205	6	1	1	NUM
ejpam-3258	205	7	µ̂∆b(m	µ̂∆b(m	ADV
ejpam-3258	205	8	)	)	PUNCT
ejpam-3258	205	9	(	(	PUNCT
ejpam-3258	205	10	23	23	X
ejpam-3258	205	11	)	)	PUNCT
ejpam-3258	205	12	m.	m.	NOUN
ejpam-3258	205	13	rehman	rehman	PROPN
ejpam-3258	205	14	,	,	PUNCT
ejpam-3258	205	15	m.	m.	PROPN
ejpam-3258	205	16	f.	f.	PROPN
ejpam-3258	205	17	anwar	anwar	PROPN
ejpam-3258	205	18	/	/	PUNCT
ejpam-3258	205	19	eur	eur	PROPN
ejpam-3258	205	20	.	.	PUNCT
ejpam-3258	206	1	j.	j.	PROPN
ejpam-3258	206	2	pure	pure	PROPN
ejpam-3258	206	3	appl	appl	PROPN
ejpam-3258	206	4	.	.	PROPN
ejpam-3258	206	5	math	math	PROPN
ejpam-3258	206	6	,	,	PUNCT
ejpam-3258	206	7	11	11	NUM
ejpam-3258	206	8	(	(	PUNCT
ejpam-3258	206	9	3	3	NUM
ejpam-3258	206	10	)	)	PUNCT
ejpam-3258	206	11	(	(	PUNCT
ejpam-3258	206	12	2018	2018	NUM
ejpam-3258	206	13	)	)	PUNCT
ejpam-3258	206	14	,	,	PUNCT
ejpam-3258	206	15	774	774	NUM
ejpam-3258	206	16	-	-	SYM
ejpam-3258	206	17	792	792	NUM
ejpam-3258	206	18	783	783	NUM
ejpam-3258	206	19	4.2	4.2	NUM
ejpam-3258	206	20	.	.	PUNCT
ejpam-3258	207	1	outer	outer	ADJ
ejpam-3258	207	2	algorithm	algorithm	NOUN
ejpam-3258	207	3	to	to	PART
ejpam-3258	207	4	compute	compute	VERB
ejpam-3258	207	5	ssv	ssv	NOUN
ejpam-3258	207	6	in	in	ADP
ejpam-3258	207	7	this	this	DET
ejpam-3258	207	8	section	section	NOUN
ejpam-3258	207	9	of	of	ADP
ejpam-3258	207	10	the	the	DET
ejpam-3258	207	11	article	article	NOUN
ejpam-3258	207	12	,	,	PUNCT
ejpam-3258	207	13	we	we	PRON
ejpam-3258	207	14	give	give	VERB
ejpam-3258	207	15	a	a	DET
ejpam-3258	207	16	brief	brief	ADJ
ejpam-3258	207	17	discussion	discussion	NOUN
ejpam-3258	207	18	on	on	ADP
ejpam-3258	207	19	the	the	DET
ejpam-3258	207	20	outer	outer	ADJ
ejpam-3258	207	21	algorithm	algorithm	NOUN
ejpam-3258	207	22	.	.	PUNCT
ejpam-3258	208	1	as	as	SCONJ
ejpam-3258	208	2	the	the	DET
ejpam-3258	208	3	principles	principle	NOUN
ejpam-3258	208	4	are	be	AUX
ejpam-3258	208	5	the	the	DET
ejpam-3258	208	6	same	same	ADJ
ejpam-3258	208	7	,	,	PUNCT
ejpam-3258	208	8	one	one	PRON
ejpam-3258	208	9	can	can	AUX
ejpam-3258	208	10	deal	deal	VERB
ejpam-3258	208	11	with	with	ADP
ejpam-3258	208	12	the	the	DET
ejpam-3258	208	13	purely	purely	ADV
ejpam-3258	208	14	complex	complex	ADJ
ejpam-3258	208	15	perturbations	perturbation	NOUN
ejpam-3258	208	16	in	in	ADP
ejpam-3258	208	17	a	a	DET
ejpam-3258	208	18	great	great	ADJ
ejpam-3258	208	19	.	.	PUNCT
ejpam-3258	209	1	the	the	DET
ejpam-3258	209	2	same	same	ADJ
ejpam-3258	209	3	discussion	discussion	NOUN
ejpam-3258	209	4	is	be	AUX
ejpam-3258	209	5	true	true	ADJ
ejpam-3258	209	6	for	for	ADP
ejpam-3258	209	7	the	the	PRON
ejpam-3258	209	8	when	when	SCONJ
ejpam-3258	209	9	we	we	PRON
ejpam-3258	209	10	have	have	AUX
ejpam-3258	209	11	mixed	mix	VERB
ejpam-3258	209	12	real	real	ADJ
ejpam-3258	209	13	and	and	CCONJ
ejpam-3258	209	14	complex	complex	ADJ
ejpam-3258	209	15	uncertainties	uncertainty	NOUN
ejpam-3258	209	16	.	.	PUNCT
ejpam-3258	210	1	5	5	X
ejpam-3258	210	2	.	.	X
ejpam-3258	210	3	numerical	numerical	ADJ
ejpam-3258	210	4	experimentation	experimentation	NOUN
ejpam-3258	210	5	in	in	ADP
ejpam-3258	210	6	this	this	DET
ejpam-3258	210	7	section	section	NOUN
ejpam-3258	210	8	,	,	PUNCT
ejpam-3258	210	9	we	we	PRON
ejpam-3258	210	10	give	give	VERB
ejpam-3258	210	11	the	the	DET
ejpam-3258	210	12	main	main	ADJ
ejpam-3258	210	13	contribution	contribution	NOUN
ejpam-3258	210	14	towards	towards	ADP
ejpam-3258	210	15	our	our	PRON
ejpam-3258	210	16	article	article	NOUN
ejpam-3258	210	17	.	.	PUNCT
ejpam-3258	211	1	we	we	PRON
ejpam-3258	211	2	establish	establish	VERB
ejpam-3258	211	3	the	the	DET
ejpam-3258	211	4	numerical	numerical	ADJ
ejpam-3258	211	5	results	result	NOUN
ejpam-3258	211	6	for	for	ADP
ejpam-3258	211	7	the	the	DET
ejpam-3258	211	8	approximation	approximation	NOUN
ejpam-3258	211	9	of	of	ADP
ejpam-3258	211	10	both	both	CCONJ
ejpam-3258	211	11	lower	low	ADJ
ejpam-3258	211	12	and	and	CCONJ
ejpam-3258	211	13	upper	upper	ADJ
ejpam-3258	211	14	bounds	bound	NOUN
ejpam-3258	211	15	of	of	ADP
ejpam-3258	211	16	ssv	ssv	NOUN
ejpam-3258	211	17	for	for	ADP
ejpam-3258	211	18	a	a	DET
ejpam-3258	211	19	set	set	NOUN
ejpam-3258	211	20	of	of	ADP
ejpam-3258	211	21	matrices	matrix	NOUN
ejpam-3258	211	22	obtianed	obtiane	VERB
ejpam-3258	211	23	by	by	ADP
ejpam-3258	211	24	the	the	DET
ejpam-3258	211	25	representation	representation	NOUN
ejpam-3258	211	26	of	of	ADP
ejpam-3258	211	27	symmetric	symmetric	ADJ
ejpam-3258	211	28	groups	group	NOUN
ejpam-3258	211	29	sn	sn	INTJ
ejpam-3258	211	30	for	for	ADP
ejpam-3258	211	31	n	n	NOUN
ejpam-3258	211	32	=	=	SYM
ejpam-3258	211	33	3.4	3.4	NUM
ejpam-3258	211	34	.	.	PUNCT
ejpam-3258	212	1	finally	finally	ADV
ejpam-3258	212	2	,	,	PUNCT
ejpam-3258	212	3	we	we	PRON
ejpam-3258	212	4	compare	compare	VERB
ejpam-3258	212	5	our	our	PRON
ejpam-3258	212	6	obtained	obtain	VERB
ejpam-3258	212	7	results	result	NOUN
ejpam-3258	212	8	with	with	ADP
ejpam-3258	212	9	the	the	DET
ejpam-3258	212	10	one	one	NOUN
ejpam-3258	212	11	ontained	ontaine	VERB
ejpam-3258	212	12	by	by	ADP
ejpam-3258	212	13	matlab	matlab	PROPN
ejpam-3258	212	14	function	function	PROPN
ejpam-3258	212	15	mussv	mussv	PROPN
ejpam-3258	212	16	.	.	PUNCT
ejpam-3258	212	17	example	example	NOUN
ejpam-3258	213	1	1	1	NUM
ejpam-3258	213	2	.	.	X
ejpam-3258	213	3	consider	consider	VERB
ejpam-3258	213	4	the	the	DET
ejpam-3258	213	5	following	follow	VERB
ejpam-3258	213	6	two	two	NUM
ejpam-3258	213	7	dimensional	dimensional	ADJ
ejpam-3258	213	8	complex	complex	ADJ
ejpam-3258	213	9	matrix	matrix	NOUN
ejpam-3258	213	10	a.	a.	NOUN
ejpam-3258	213	11	a	a	NOUN
ejpam-3258	213	12	=	=	X
ejpam-3258	213	13	[	[	PUNCT
ejpam-3258	213	14	−1	−1	NOUN
ejpam-3258	213	15	2	2	NUM
ejpam-3258	213	16	−	−	NOUN
ejpam-3258	213	17	√	√	NUM
ejpam-3258	213	18	3	3	NUM
ejpam-3258	213	19	2	2	NUM
ejpam-3258	213	20	i	i	NOUN
ejpam-3258	213	21	0	0	NUM
ejpam-3258	213	22	0	0	NUM
ejpam-3258	213	23	−1	−1	NOUN
ejpam-3258	213	24	2	2	NUM
ejpam-3258	213	25	+	+	CCONJ
ejpam-3258	213	26	√	√	NUM
ejpam-3258	213	27	3	3	NUM
ejpam-3258	213	28	2	2	NUM
ejpam-3258	213	29	i	i	NOUN
ejpam-3258	213	30	]	]	PUNCT
ejpam-3258	213	31	.	.	PUNCT
ejpam-3258	214	1	we	we	PRON
ejpam-3258	214	2	take	take	VERB
ejpam-3258	214	3	the	the	DET
ejpam-3258	214	4	perturbation	perturbation	NOUN
ejpam-3258	214	5	set	set	VERB
ejpam-3258	214	6	as	as	ADP
ejpam-3258	214	7	,	,	PUNCT
ejpam-3258	214	8	∆b	∆b	PROPN
ejpam-3258	214	9	=	=	SYM
ejpam-3258	214	10	{	{	PUNCT
ejpam-3258	214	11	diag(∆1	diag(∆1	PROPN
ejpam-3258	214	12	)	)	PUNCT
ejpam-3258	214	13	:	:	PUNCT
ejpam-3258	215	1	∆1	∆1	PUNCT
ejpam-3258	215	2	∈	∈	NOUN
ejpam-3258	215	3	c2,2	c2,2	NOUN
ejpam-3258	215	4	}	}	PUNCT
ejpam-3258	215	5	.	.	PUNCT
ejpam-3258	216	1	first	first	ADV
ejpam-3258	216	2	,	,	PUNCT
ejpam-3258	216	3	by	by	ADP
ejpam-3258	216	4	using	use	VERB
ejpam-3258	216	5	mussv	mussv	ADJ
ejpam-3258	216	6	function	function	NOUN
ejpam-3258	216	7	,	,	PUNCT
ejpam-3258	216	8	we	we	PRON
ejpam-3258	216	9	obtain	obtain	VERB
ejpam-3258	216	10	the	the	DET
ejpam-3258	216	11	perturbation	perturbation	NOUN
ejpam-3258	216	12	structure	structure	NOUN
ejpam-3258	216	13	∆̂	∆̂	PUNCT
ejpam-3258	216	14	with	with	ADP
ejpam-3258	216	15	∆̂	∆̂	NOUN
ejpam-3258	216	16	=	=	PUNCT
ejpam-3258	217	1	[	[	PUNCT
ejpam-3258	217	2	0	0	NUM
ejpam-3258	217	3	0	0	NUM
ejpam-3258	217	4	0	0	NUM
ejpam-3258	218	1	−0.5000−	−0.5000−	PROPN
ejpam-3258	218	2	0.8660i	0.8660i	NOUN
ejpam-3258	218	3	]	]	PUNCT
ejpam-3258	218	4	.	.	PUNCT
ejpam-3258	219	1	here	here	ADV
ejpam-3258	219	2	,	,	PUNCT
ejpam-3258	219	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	219	4	=	=	NOUN
ejpam-3258	219	5	1	1	X
ejpam-3258	219	6	.	.	PUNCT
ejpam-3258	220	1	the	the	DET
ejpam-3258	220	2	value	value	NOUN
ejpam-3258	220	3	of	of	ADP
ejpam-3258	220	4	upper	upper	ADJ
ejpam-3258	220	5	bound	bind	VERB
ejpam-3258	220	6	is	be	AUX
ejpam-3258	220	7	obtained	obtain	VERB
ejpam-3258	220	8	as	as	ADP
ejpam-3258	220	9	,	,	PUNCT
ejpam-3258	220	10	that	that	PRON
ejpam-3258	220	11	is	is	ADV
ejpam-3258	220	12	,	,	PUNCT
ejpam-3258	220	13	µupperpd	µupperpd	PROPN
ejpam-3258	220	14	=	=	SYM
ejpam-3258	220	15	1.0000	1.0000	NUM
ejpam-3258	220	16	while	while	SCONJ
ejpam-3258	220	17	the	the	DET
ejpam-3258	220	18	same	same	ADJ
ejpam-3258	220	19	lower	low	ADJ
ejpam-3258	220	20	bound	bind	VERB
ejpam-3258	220	21	is	be	AUX
ejpam-3258	220	22	obtained	obtain	VERB
ejpam-3258	220	23	,	,	PUNCT
ejpam-3258	220	24	that	that	ADV
ejpam-3258	220	25	is	is	ADV
ejpam-3258	220	26	,	,	PUNCT
ejpam-3258	220	27	µlowerpd	µlowerpd	NOUN
ejpam-3258	220	28	=	=	SYM
ejpam-3258	220	29	1.0000	1.0000	NUM
ejpam-3258	220	30	.	.	PUNCT
ejpam-3258	221	1	now	now	ADV
ejpam-3258	221	2	,	,	PUNCT
ejpam-3258	221	3	by	by	ADP
ejpam-3258	221	4	using	use	VERB
ejpam-3258	221	5	algorithm	algorithm	NOUN
ejpam-3258	221	6	[	[	X
ejpam-3258	221	7	14	14	NUM
ejpam-3258	221	8	]	]	PUNCT
ejpam-3258	221	9	,	,	PUNCT
ejpam-3258	221	10	we	we	PRON
ejpam-3258	221	11	obtain	obtain	VERB
ejpam-3258	221	12	the	the	DET
ejpam-3258	221	13	perturbation	perturbation	NOUN
ejpam-3258	221	14	structure	structure	NOUN
ejpam-3258	221	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	221	16	with	with	ADP
ejpam-3258	221	17	∆∗	∆∗	NOUN
ejpam-3258	221	18	=	=	PUNCT
ejpam-3258	222	1	[	[	PUNCT
ejpam-3258	222	2	0	0	NUM
ejpam-3258	222	3	0	0	NUM
ejpam-3258	222	4	0	0	NUM
ejpam-3258	223	1	−0.5000−	−0.5000−	PROPN
ejpam-3258	223	2	0.8660i	0.8660i	NOUN
ejpam-3258	223	3	]	]	PUNCT
ejpam-3258	223	4	.	.	PUNCT
ejpam-3258	224	1	here	here	ADV
ejpam-3258	224	2	,	,	PUNCT
ejpam-3258	224	3	ε∗	ε∗	PROPN
ejpam-3258	224	4	=	=	SYM
ejpam-3258	224	5	1.0000	1.0000	NUM
ejpam-3258	224	6	and	and	CCONJ
ejpam-3258	224	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	224	8	=	=	SYM
ejpam-3258	224	9	1	1	NUM
ejpam-3258	224	10	,	,	PUNCT
ejpam-3258	224	11	we	we	PRON
ejpam-3258	224	12	got	get	VERB
ejpam-3258	224	13	the	the	DET
ejpam-3258	224	14	same	same	ADJ
ejpam-3258	224	15	lower	lower	ADV
ejpam-3258	224	16	bound	bind	VERB
ejpam-3258	224	17	,	,	PUNCT
ejpam-3258	224	18	that	that	ADV
ejpam-3258	224	19	is	is	ADV
ejpam-3258	224	20	,	,	PUNCT
ejpam-3258	224	21	µlowernew	µlowernew	ADJ
ejpam-3258	224	22	=	=	NOUN
ejpam-3258	224	23	1.0000	1.0000	NUM
ejpam-3258	224	24	.	.	PUNCT
ejpam-3258	225	1	the	the	DET
ejpam-3258	225	2	bounds	bound	NOUN
ejpam-3258	225	3	of	of	ADP
ejpam-3258	225	4	structured	structured	ADJ
ejpam-3258	225	5	singular	singular	ADJ
ejpam-3258	225	6	value	value	NOUN
ejpam-3258	225	7	for	for	ADP
ejpam-3258	225	8	above	above	ADJ
ejpam-3258	225	9	matrix	matrix	NOUN
ejpam-3258	225	10	a	a	PRON
ejpam-3258	225	11	when	when	SCONJ
ejpam-3258	225	12	the	the	DET
ejpam-3258	225	13	perturbation	perturbation	NOUN
ejpam-3258	225	14	set	set	NOUN
ejpam-3258	225	15	is	be	AUX
ejpam-3258	225	16	considered	consider	VERB
ejpam-3258	225	17	as	as	ADP
ejpam-3258	225	18	,	,	PUNCT
ejpam-3258	225	19	∆b	∆b	PROPN
ejpam-3258	225	20	=	=	SYM
ejpam-3258	225	21	{	{	PUNCT
ejpam-3258	225	22	diag(δ1i2	diag(δ1i2	PROPN
ejpam-3258	225	23	)	)	PUNCT
ejpam-3258	225	24	:	:	PUNCT
ejpam-3258	225	25	δ1	δ1	NOUN
ejpam-3258	225	26	∈	∈	PROPN
ejpam-3258	225	27	c	c	X
ejpam-3258	225	28	}	}	PUNCT
ejpam-3258	225	29	,	,	PUNCT
ejpam-3258	225	30	are	be	AUX
ejpam-3258	225	31	as	as	SCONJ
ejpam-3258	225	32	follows	follow	VERB
ejpam-3258	225	33	.	.	PUNCT
ejpam-3258	226	1	first	first	ADV
ejpam-3258	226	2	,	,	PUNCT
ejpam-3258	226	3	we	we	PRON
ejpam-3258	226	4	apply	apply	VERB
ejpam-3258	226	5	the	the	DET
ejpam-3258	226	6	mussv	mussv	ADJ
ejpam-3258	226	7	function	function	NOUN
ejpam-3258	226	8	and	and	CCONJ
ejpam-3258	226	9	we	we	PRON
ejpam-3258	226	10	obtain	obtain	VERB
ejpam-3258	226	11	the	the	DET
ejpam-3258	226	12	perturbation	perturbation	NOUN
ejpam-3258	226	13	∆̂	∆̂	PUNCT
ejpam-3258	226	14	with	with	ADP
ejpam-3258	226	15	∆̂	∆̂	NOUN
ejpam-3258	227	1	=	=	PUNCT
ejpam-3258	227	2	[	[	PUNCT
ejpam-3258	227	3	−0.5000	−0.5000	NOUN
ejpam-3258	227	4	+	+	NOUN
ejpam-3258	227	5	0.8660i	0.8660i	NOUN
ejpam-3258	227	6	0	0	NUM
ejpam-3258	227	7	0	0	NUM
ejpam-3258	228	1	−0.5000	−0.5000	NUM
ejpam-3258	229	1	+	+	NOUN
ejpam-3258	229	2	0.8660i	0.8660i	NOUN
ejpam-3258	229	3	]	]	PUNCT
ejpam-3258	229	4	.	.	PUNCT
ejpam-3258	230	1	m.	m.	PROPN
ejpam-3258	230	2	rehman	rehman	PROPN
ejpam-3258	230	3	,	,	PUNCT
ejpam-3258	230	4	m.	m.	PROPN
ejpam-3258	230	5	f.	f.	PROPN
ejpam-3258	230	6	anwar	anwar	PROPN
ejpam-3258	230	7	/	/	PUNCT
ejpam-3258	230	8	eur	eur	PROPN
ejpam-3258	230	9	.	.	PUNCT
ejpam-3258	231	1	j.	j.	PROPN
ejpam-3258	231	2	pure	pure	PROPN
ejpam-3258	231	3	appl	appl	PROPN
ejpam-3258	231	4	.	.	PROPN
ejpam-3258	231	5	math	math	PROPN
ejpam-3258	231	6	,	,	PUNCT
ejpam-3258	231	7	11	11	NUM
ejpam-3258	231	8	(	(	PUNCT
ejpam-3258	231	9	3	3	NUM
ejpam-3258	231	10	)	)	PUNCT
ejpam-3258	231	11	(	(	PUNCT
ejpam-3258	231	12	2018	2018	NUM
ejpam-3258	231	13	)	)	PUNCT
ejpam-3258	231	14	,	,	PUNCT
ejpam-3258	231	15	774	774	NUM
ejpam-3258	231	16	-	-	SYM
ejpam-3258	231	17	792	792	NUM
ejpam-3258	231	18	784	784	NUM
ejpam-3258	231	19	here	here	ADV
ejpam-3258	231	20	,	,	PUNCT
ejpam-3258	231	21	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	231	22	=	=	NOUN
ejpam-3258	231	23	1	1	X
ejpam-3258	231	24	.	.	X
ejpam-3258	232	1	for	for	ADP
ejpam-3258	232	2	this	this	DET
ejpam-3258	232	3	particular	particular	ADJ
ejpam-3258	232	4	example	example	NOUN
ejpam-3258	232	5	,	,	PUNCT
ejpam-3258	232	6	we	we	PRON
ejpam-3258	232	7	obtain	obtain	VERB
ejpam-3258	232	8	the	the	DET
ejpam-3258	232	9	upper	upper	ADJ
ejpam-3258	232	10	bound	bind	VERB
ejpam-3258	232	11	µupperpd	µupperpd	NOUN
ejpam-3258	232	12	=	=	PROPN
ejpam-3258	232	13	1.0000	1.0000	NUM
ejpam-3258	232	14	.	.	PUNCT
ejpam-3258	233	1	the	the	DET
ejpam-3258	233	2	value	value	NOUN
ejpam-3258	233	3	of	of	ADP
ejpam-3258	233	4	lower	low	ADJ
ejpam-3258	233	5	bound	bind	VERB
ejpam-3258	233	6	also	also	ADV
ejpam-3258	233	7	remain	remain	VERB
ejpam-3258	233	8	same	same	ADJ
ejpam-3258	233	9	,	,	PUNCT
ejpam-3258	233	10	that	that	SCONJ
ejpam-3258	233	11	is,µlowerpd	is,µlowerpd	PROPN
ejpam-3258	233	12	=	=	SYM
ejpam-3258	233	13	1.0000	1.0000	NUM
ejpam-3258	233	14	.	.	PUNCT
ejpam-3258	234	1	now	now	ADV
ejpam-3258	234	2	,	,	PUNCT
ejpam-3258	234	3	by	by	ADP
ejpam-3258	234	4	using	use	VERB
ejpam-3258	234	5	algorithm	algorithm	NOUN
ejpam-3258	234	6	[	[	X
ejpam-3258	234	7	14	14	NUM
ejpam-3258	234	8	]	]	PUNCT
ejpam-3258	234	9	,	,	PUNCT
ejpam-3258	234	10	we	we	PRON
ejpam-3258	234	11	obtain	obtain	VERB
ejpam-3258	234	12	the	the	DET
ejpam-3258	234	13	perturbation	perturbation	NOUN
ejpam-3258	234	14	structure	structure	NOUN
ejpam-3258	234	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	234	16	with	with	ADP
ejpam-3258	234	17	∆∗	∆∗	NOUN
ejpam-3258	234	18	=	=	PUNCT
ejpam-3258	235	1	[	[	PUNCT
ejpam-3258	235	2	−0.5000−	−0.5000−	PROPN
ejpam-3258	235	3	0.8660i	0.8660i	NOUN
ejpam-3258	235	4	0	0	NUM
ejpam-3258	235	5	0	0	NUM
ejpam-3258	236	1	−0.5000−	−0.5000−	PROPN
ejpam-3258	236	2	0.8660i	0.8660i	NOUN
ejpam-3258	236	3	]	]	PUNCT
ejpam-3258	236	4	.	.	PUNCT
ejpam-3258	237	1	here	here	ADV
ejpam-3258	237	2	,	,	PUNCT
ejpam-3258	237	3	ε∗	ε∗	PROPN
ejpam-3258	237	4	=	=	SYM
ejpam-3258	237	5	1.0000	1.0000	NUM
ejpam-3258	237	6	and	and	CCONJ
ejpam-3258	237	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	237	8	=	=	SYM
ejpam-3258	237	9	1	1	X
ejpam-3258	237	10	.	.	PUNCT
ejpam-3258	238	1	the	the	DET
ejpam-3258	238	2	same	same	ADJ
ejpam-3258	238	3	lower	low	ADJ
ejpam-3258	238	4	bound	bind	VERB
ejpam-3258	238	5	is	be	AUX
ejpam-3258	238	6	obtained	obtain	VERB
ejpam-3258	238	7	for	for	ADP
ejpam-3258	238	8	this	this	DET
ejpam-3258	238	9	particular	particular	ADJ
ejpam-3258	238	10	example	example	NOUN
ejpam-3258	238	11	,	,	PUNCT
ejpam-3258	238	12	that	that	ADV
ejpam-3258	238	13	is	is	ADV
ejpam-3258	238	14	,	,	PUNCT
ejpam-3258	238	15	µlowernew	µlowernew	ADJ
ejpam-3258	238	16	=	=	NOUN
ejpam-3258	238	17	1.0000	1.0000	NUM
ejpam-3258	238	18	,	,	PUNCT
ejpam-3258	238	19	the	the	DET
ejpam-3258	238	20	one	one	NOUN
ejpam-3258	238	21	approximated	approximate	VERB
ejpam-3258	238	22	by	by	ADP
ejpam-3258	238	23	matlab	matlab	PROPN
ejpam-3258	238	24	function	function	PROPN
ejpam-3258	238	25	mussv	mussv	PROPN
ejpam-3258	238	26	.	.	PUNCT
ejpam-3258	238	27	example	example	NOUN
ejpam-3258	239	1	2	2	NUM
ejpam-3258	239	2	.	.	X
ejpam-3258	239	3	in	in	ADP
ejpam-3258	239	4	figure	figure	NOUN
ejpam-3258	239	5	1	1	NUM
ejpam-3258	239	6	,	,	PUNCT
ejpam-3258	239	7	we	we	PRON
ejpam-3258	239	8	show	show	VERB
ejpam-3258	239	9	the	the	DET
ejpam-3258	239	10	comparison	comparison	NOUN
ejpam-3258	239	11	of	of	ADP
ejpam-3258	239	12	lower	low	ADJ
ejpam-3258	239	13	bounds	bound	NOUN
ejpam-3258	239	14	computed	compute	VERB
ejpam-3258	239	15	by	by	ADP
ejpam-3258	239	16	algorithm	algorithm	NOUN
ejpam-3258	239	17	[	[	X
ejpam-3258	239	18	14	14	NUM
ejpam-3258	239	19	]	]	PUNCT
ejpam-3258	239	20	with	with	ADP
ejpam-3258	239	21	the	the	DET
ejpam-3258	239	22	bounds	bound	NOUN
ejpam-3258	239	23	(	(	PUNCT
ejpam-3258	239	24	lower	low	ADJ
ejpam-3258	239	25	and	and	CCONJ
ejpam-3258	239	26	upper	upper	ADJ
ejpam-3258	239	27	)	)	PUNCT
ejpam-3258	239	28	computed	compute	VERB
ejpam-3258	239	29	by	by	ADP
ejpam-3258	239	30	mussv	mussv	ADJ
ejpam-3258	239	31	function	function	NOUN
ejpam-3258	239	32	for	for	ADP
ejpam-3258	239	33	matrix	matrix	NOUN
ejpam-3258	239	34	valued	value	VERB
ejpam-3258	239	35	function	function	NOUN
ejpam-3258	239	36	b(w	b(w	NOUN
ejpam-3258	239	37	)	)	PUNCT
ejpam-3258	239	38	for	for	ADP
ejpam-3258	239	39	w	w	NOUN
ejpam-3258	239	40	=	=	SYM
ejpam-3258	239	41	1	1	NUM
ejpam-3258	239	42	:	:	SYM
ejpam-3258	239	43	4	4	NUM
ejpam-3258	239	44	,	,	PUNCT
ejpam-3258	239	45	where	where	SCONJ
ejpam-3258	239	46	w	w	PROPN
ejpam-3258	239	47	∈	∈	PROPN
ejpam-3258	239	48	ω	ω	PROPN
ejpam-3258	239	49	and	and	CCONJ
ejpam-3258	239	50	ω	ω	PROPN
ejpam-3258	239	51	denotes	denote	VERB
ejpam-3258	239	52	the	the	DET
ejpam-3258	239	53	frequency	frequency	NOUN
ejpam-3258	239	54	range	range	NOUN
ejpam-3258	239	55	of	of	ADP
ejpam-3258	239	56	interest	interest	NOUN
ejpam-3258	239	57	which	which	PRON
ejpam-3258	239	58	is	be	AUX
ejpam-3258	239	59	usually	usually	ADV
ejpam-3258	239	60	r+	r+	X
ejpam-3258	239	61	.	.	PUNCT
ejpam-3258	240	1	the	the	DET
ejpam-3258	240	2	frequency	frequency	NOUN
ejpam-3258	240	3	response	response	NOUN
ejpam-3258	240	4	w	w	NOUN
ejpam-3258	240	5	is	be	AUX
ejpam-3258	240	6	the	the	DET
ejpam-3258	240	7	quantitative	quantitative	ADJ
ejpam-3258	240	8	measure	measure	NOUN
ejpam-3258	240	9	of	of	ADP
ejpam-3258	240	10	output	output	NOUN
ejpam-3258	240	11	of	of	ADP
ejpam-3258	240	12	(	(	PUNCT
ejpam-3258	240	13	m−∆	m−∆	NOUN
ejpam-3258	240	14	)	)	PUNCT
ejpam-3258	240	15	system	system	NOUN
ejpam-3258	240	16	.	.	PUNCT
ejpam-3258	241	1	we	we	PRON
ejpam-3258	241	2	use	use	VERB
ejpam-3258	241	3	mussv	mussv	ADJ
ejpam-3258	241	4	function	function	NOUN
ejpam-3258	241	5	to	to	PART
ejpam-3258	241	6	compute	compute	VERB
ejpam-3258	241	7	µ	µ	PRON
ejpam-3258	241	8	as	as	ADP
ejpam-3258	241	9	a	a	DET
ejpam-3258	241	10	function	function	NOUN
ejpam-3258	241	11	of	of	ADP
ejpam-3258	241	12	frequency	frequency	NOUN
ejpam-3258	241	13	response	response	NOUN
ejpam-3258	241	14	.	.	PUNCT
ejpam-3258	242	1	example	example	NOUN
ejpam-3258	243	1	3	3	X
ejpam-3258	243	2	.	.	X
ejpam-3258	243	3	consider	consider	VERB
ejpam-3258	243	4	the	the	DET
ejpam-3258	243	5	following	follow	VERB
ejpam-3258	243	6	two	two	NUM
ejpam-3258	243	7	dimensional	dimensional	ADJ
ejpam-3258	243	8	complex	complex	ADJ
ejpam-3258	243	9	matrix	matrix	NOUN
ejpam-3258	243	10	a1	a1	NOUN
ejpam-3258	243	11	.	.	PUNCT
ejpam-3258	243	12	a1	a1	NOUN
ejpam-3258	243	13	=	=	PUNCT
ejpam-3258	243	14	[	[	PUNCT
ejpam-3258	243	15	0	0	NUM
ejpam-3258	243	16	−1	−1	NOUN
ejpam-3258	243	17	2	2	NUM
ejpam-3258	243	18	+	+	CCONJ
ejpam-3258	243	19	√	√	NUM
ejpam-3258	243	20	3	3	NUM
ejpam-3258	243	21	2	2	NUM
ejpam-3258	243	22	i	i	PRON
ejpam-3258	243	23	−1	−1	NOUN
ejpam-3258	243	24	2	2	NUM
ejpam-3258	243	25	−	−	NOUN
ejpam-3258	243	26	√	√	NUM
ejpam-3258	243	27	3	3	NUM
ejpam-3258	243	28	2	2	NUM
ejpam-3258	243	29	i	i	NOUN
ejpam-3258	243	30	0	0	NUM
ejpam-3258	243	31	]	]	PUNCT
ejpam-3258	243	32	.	.	PUNCT
ejpam-3258	244	1	we	we	PRON
ejpam-3258	244	2	take	take	VERB
ejpam-3258	244	3	the	the	DET
ejpam-3258	244	4	perturbation	perturbation	NOUN
ejpam-3258	244	5	set	set	VERB
ejpam-3258	244	6	as	as	ADP
ejpam-3258	244	7	,	,	PUNCT
ejpam-3258	244	8	∆b	∆b	PROPN
ejpam-3258	244	9	=	=	SYM
ejpam-3258	244	10	{	{	PUNCT
ejpam-3258	244	11	diag(∆1	diag(∆1	PROPN
ejpam-3258	244	12	)	)	PUNCT
ejpam-3258	244	13	:	:	PUNCT
ejpam-3258	245	1	∆1	∆1	PUNCT
ejpam-3258	245	2	∈	∈	NOUN
ejpam-3258	245	3	c2,2	c2,2	NOUN
ejpam-3258	245	4	}	}	PUNCT
ejpam-3258	245	5	.	.	PUNCT
ejpam-3258	246	1	first	first	ADV
ejpam-3258	246	2	,	,	PUNCT
ejpam-3258	246	3	by	by	ADP
ejpam-3258	246	4	using	use	VERB
ejpam-3258	246	5	mussv	mussv	ADJ
ejpam-3258	246	6	function	function	NOUN
ejpam-3258	246	7	,	,	PUNCT
ejpam-3258	246	8	we	we	PRON
ejpam-3258	246	9	obtain	obtain	VERB
ejpam-3258	246	10	the	the	DET
ejpam-3258	246	11	perturbation	perturbation	NOUN
ejpam-3258	246	12	structure	structure	NOUN
ejpam-3258	246	13	∆̂	∆̂	PUNCT
ejpam-3258	246	14	with	with	ADP
ejpam-3258	246	15	∆̂	∆̂	NOUN
ejpam-3258	247	1	=	=	PUNCT
ejpam-3258	247	2	[	[	PUNCT
ejpam-3258	247	3	0	0	NUM
ejpam-3258	247	4	0	0	NUM
ejpam-3258	248	1	−0.5000−	−0.5000−	PROPN
ejpam-3258	248	2	0.8660i	0.8660i	NOUN
ejpam-3258	248	3	0	0	NUM
ejpam-3258	248	4	]	]	PUNCT
ejpam-3258	248	5	.	.	PUNCT
ejpam-3258	249	1	here	here	ADV
ejpam-3258	249	2	,	,	PUNCT
ejpam-3258	249	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	249	4	=	=	NOUN
ejpam-3258	249	5	1	1	X
ejpam-3258	249	6	.	.	PUNCT
ejpam-3258	250	1	the	the	DET
ejpam-3258	250	2	value	value	NOUN
ejpam-3258	250	3	of	of	ADP
ejpam-3258	250	4	upper	upper	ADJ
ejpam-3258	250	5	bound	bind	VERB
ejpam-3258	250	6	is	be	AUX
ejpam-3258	250	7	obtained	obtain	VERB
ejpam-3258	250	8	as	as	ADP
ejpam-3258	250	9	µupperpd	µupperpd	NOUN
ejpam-3258	250	10	=	=	NOUN
ejpam-3258	250	11	1.0000	1.0000	NUM
ejpam-3258	250	12	while	while	SCONJ
ejpam-3258	250	13	the	the	DET
ejpam-3258	250	14	same	same	ADJ
ejpam-3258	250	15	lower	lower	ADV
ejpam-3258	250	16	bound	bind	VERB
ejpam-3258	250	17	as	as	ADP
ejpam-3258	250	18	obtained	obtain	VERB
ejpam-3258	250	19	,	,	PUNCT
ejpam-3258	250	20	that	that	ADV
ejpam-3258	250	21	is	is	ADV
ejpam-3258	250	22	,	,	PUNCT
ejpam-3258	250	23	µlowerpd	µlowerpd	NOUN
ejpam-3258	250	24	=	=	SYM
ejpam-3258	250	25	1.0000	1.0000	NUM
ejpam-3258	250	26	.	.	PUNCT
ejpam-3258	251	1	now	now	ADV
ejpam-3258	251	2	,	,	PUNCT
ejpam-3258	251	3	by	by	ADP
ejpam-3258	251	4	using	use	VERB
ejpam-3258	251	5	algorithm	algorithm	NOUN
ejpam-3258	251	6	[	[	X
ejpam-3258	251	7	14	14	NUM
ejpam-3258	251	8	]	]	PUNCT
ejpam-3258	251	9	,	,	PUNCT
ejpam-3258	251	10	we	we	PRON
ejpam-3258	251	11	obtain	obtain	VERB
ejpam-3258	251	12	the	the	DET
ejpam-3258	251	13	perturbation	perturbation	NOUN
ejpam-3258	251	14	structure	structure	NOUN
ejpam-3258	251	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	251	16	with	with	ADP
ejpam-3258	251	17	∆∗	∆∗	NOUN
ejpam-3258	251	18	=	=	PUNCT
ejpam-3258	252	1	[	[	PUNCT
ejpam-3258	252	2	−0.5000−	−0.5000−	PROPN
ejpam-3258	252	3	0.0000i	0.0000i	NOUN
ejpam-3258	252	4	−0.2500	−0.2500	NOUN
ejpam-3258	253	1	+	+	CCONJ
ejpam-3258	253	2	0.4330i	0.4330i	ADP
ejpam-3258	253	3	−0.2500−	−0.2500−	PROPN
ejpam-3258	253	4	0.4330i	0.4330i	PROPN
ejpam-3258	253	5	−0.5000−	−0.5000−	PROPN
ejpam-3258	253	6	0.0000i	0.0000i	NOUN
ejpam-3258	253	7	]	]	PUNCT
ejpam-3258	253	8	.	.	PUNCT
ejpam-3258	254	1	here	here	ADV
ejpam-3258	254	2	,	,	PUNCT
ejpam-3258	254	3	ε∗	ε∗	PROPN
ejpam-3258	254	4	=	=	SYM
ejpam-3258	254	5	1.0000	1.0000	NUM
ejpam-3258	254	6	and	and	CCONJ
ejpam-3258	254	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	254	8	=	=	SYM
ejpam-3258	254	9	1	1	X
ejpam-3258	254	10	.	.	X
ejpam-3258	255	1	for	for	ADP
ejpam-3258	255	2	this	this	DET
ejpam-3258	255	3	particular	particular	ADJ
ejpam-3258	255	4	example	example	NOUN
ejpam-3258	255	5	,	,	PUNCT
ejpam-3258	255	6	we	we	PRON
ejpam-3258	255	7	got	get	VERB
ejpam-3258	255	8	the	the	DET
ejpam-3258	255	9	same	same	ADJ
ejpam-3258	255	10	lower	lower	ADV
ejpam-3258	255	11	bound	bind	VERB
ejpam-3258	255	12	,	,	PUNCT
ejpam-3258	255	13	that	that	ADV
ejpam-3258	255	14	is	is	ADV
ejpam-3258	255	15	,	,	PUNCT
ejpam-3258	255	16	µlowernew	µlowernew	ADJ
ejpam-3258	255	17	=	=	NOUN
ejpam-3258	255	18	1.0000	1.0000	NUM
ejpam-3258	255	19	.	.	PUNCT
ejpam-3258	256	1	the	the	DET
ejpam-3258	256	2	bounds	bound	NOUN
ejpam-3258	256	3	of	of	ADP
ejpam-3258	256	4	structured	structured	ADJ
ejpam-3258	256	5	singular	singular	ADJ
ejpam-3258	256	6	value	value	NOUN
ejpam-3258	256	7	for	for	ADP
ejpam-3258	256	8	above	above	ADJ
ejpam-3258	256	9	matrix	matrix	NOUN
ejpam-3258	256	10	a1	a1	NOUN
ejpam-3258	256	11	when	when	SCONJ
ejpam-3258	256	12	the	the	DET
ejpam-3258	256	13	perturbation	perturbation	NOUN
ejpam-3258	256	14	set	set	NOUN
ejpam-3258	256	15	is	be	AUX
ejpam-3258	256	16	considered	consider	VERB
ejpam-3258	256	17	as	as	ADP
ejpam-3258	256	18	,	,	PUNCT
ejpam-3258	256	19	∆b	∆b	PROPN
ejpam-3258	256	20	=	=	SYM
ejpam-3258	256	21	{	{	PUNCT
ejpam-3258	256	22	diag(δ1i2	diag(δ1i2	PROPN
ejpam-3258	256	23	)	)	PUNCT
ejpam-3258	256	24	:	:	PUNCT
ejpam-3258	256	25	δ1	δ1	NOUN
ejpam-3258	256	26	∈	∈	PROPN
ejpam-3258	256	27	c	c	NOUN
ejpam-3258	256	28	}	}	PUNCT
ejpam-3258	256	29	,	,	PUNCT
ejpam-3258	256	30	m.	m.	NOUN
ejpam-3258	256	31	rehman	rehman	PROPN
ejpam-3258	256	32	,	,	PUNCT
ejpam-3258	256	33	m.	m.	PROPN
ejpam-3258	256	34	f.	f.	PROPN
ejpam-3258	256	35	anwar	anwar	PROPN
ejpam-3258	256	36	/	/	PUNCT
ejpam-3258	256	37	eur	eur	PROPN
ejpam-3258	256	38	.	.	PUNCT
ejpam-3258	257	1	j.	j.	PROPN
ejpam-3258	257	2	pure	pure	PROPN
ejpam-3258	257	3	appl	appl	PROPN
ejpam-3258	257	4	.	.	PROPN
ejpam-3258	257	5	math	math	PROPN
ejpam-3258	257	6	,	,	PUNCT
ejpam-3258	257	7	11	11	NUM
ejpam-3258	257	8	(	(	PUNCT
ejpam-3258	257	9	3	3	NUM
ejpam-3258	257	10	)	)	PUNCT
ejpam-3258	257	11	(	(	PUNCT
ejpam-3258	257	12	2018	2018	NUM
ejpam-3258	257	13	)	)	PUNCT
ejpam-3258	257	14	,	,	PUNCT
ejpam-3258	257	15	774	774	NUM
ejpam-3258	257	16	-	-	SYM
ejpam-3258	257	17	792	792	NUM
ejpam-3258	257	18	785	785	NUM
ejpam-3258	257	19	are	be	AUX
ejpam-3258	257	20	as	as	SCONJ
ejpam-3258	257	21	follows	follow	VERB
ejpam-3258	257	22	.	.	PUNCT
ejpam-3258	258	1	first	first	ADV
ejpam-3258	258	2	,	,	PUNCT
ejpam-3258	258	3	we	we	PRON
ejpam-3258	258	4	apply	apply	VERB
ejpam-3258	258	5	the	the	DET
ejpam-3258	258	6	mussv	mussv	ADJ
ejpam-3258	258	7	function	function	NOUN
ejpam-3258	258	8	and	and	CCONJ
ejpam-3258	258	9	we	we	PRON
ejpam-3258	258	10	obtain	obtain	VERB
ejpam-3258	258	11	the	the	DET
ejpam-3258	258	12	perturbation	perturbation	NOUN
ejpam-3258	258	13	∆̂	∆̂	PUNCT
ejpam-3258	258	14	with	with	ADP
ejpam-3258	258	15	∆̂	∆̂	NOUN
ejpam-3258	259	1	=	=	PUNCT
ejpam-3258	259	2	[	[	PUNCT
ejpam-3258	259	3	−0.2000	−0.2000	X
ejpam-3258	259	4	+	+	CCONJ
ejpam-3258	259	5	0.8660i	0.8660i	NOUN
ejpam-3258	259	6	0	0	NUM
ejpam-3258	259	7	0	0	NUM
ejpam-3258	260	1	−0.2000	−0.2000	NUM
ejpam-3258	261	1	+	+	CCONJ
ejpam-3258	261	2	0.8660i	0.8660i	NOUN
ejpam-3258	261	3	]	]	PUNCT
ejpam-3258	261	4	.	.	PUNCT
ejpam-3258	262	1	here	here	ADV
ejpam-3258	262	2	‖∆̂‖2	‖∆̂‖2	X
ejpam-3258	262	3	=	=	NOUN
ejpam-3258	262	4	1	1	X
ejpam-3258	262	5	.	.	X
ejpam-3258	262	6	for	for	ADP
ejpam-3258	262	7	this	this	DET
ejpam-3258	262	8	particular	particular	ADJ
ejpam-3258	262	9	example	example	NOUN
ejpam-3258	262	10	,	,	PUNCT
ejpam-3258	262	11	we	we	PRON
ejpam-3258	262	12	obtain	obtain	VERB
ejpam-3258	262	13	the	the	DET
ejpam-3258	262	14	upper	upper	ADJ
ejpam-3258	262	15	bound	bind	VERB
ejpam-3258	262	16	µupperpd	µupperpd	NOUN
ejpam-3258	262	17	=	=	PROPN
ejpam-3258	262	18	1.0000	1.0000	NUM
ejpam-3258	262	19	.	.	PUNCT
ejpam-3258	263	1	the	the	DET
ejpam-3258	263	2	value	value	NOUN
ejpam-3258	263	3	of	of	ADP
ejpam-3258	263	4	lower	low	ADJ
ejpam-3258	263	5	bound	bind	VERB
ejpam-3258	263	6	remains	remain	NOUN
ejpam-3258	263	7	same	same	ADJ
ejpam-3258	263	8	,	,	PUNCT
ejpam-3258	263	9	that	that	ADV
ejpam-3258	263	10	is	is	ADV
ejpam-3258	263	11	,	,	PUNCT
ejpam-3258	263	12	µlowerpd	µlowerpd	NOUN
ejpam-3258	263	13	=	=	SYM
ejpam-3258	263	14	1.0000	1.0000	NUM
ejpam-3258	263	15	.	.	PUNCT
ejpam-3258	264	1	now	now	ADV
ejpam-3258	264	2	,	,	PUNCT
ejpam-3258	264	3	by	by	ADP
ejpam-3258	264	4	using	use	VERB
ejpam-3258	264	5	algorithm	algorithm	NOUN
ejpam-3258	264	6	[	[	X
ejpam-3258	264	7	14	14	NUM
ejpam-3258	264	8	]	]	PUNCT
ejpam-3258	264	9	,	,	PUNCT
ejpam-3258	264	10	we	we	PRON
ejpam-3258	264	11	obtain	obtain	VERB
ejpam-3258	264	12	the	the	DET
ejpam-3258	264	13	perturbation	perturbation	NOUN
ejpam-3258	264	14	structure	structure	NOUN
ejpam-3258	264	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	264	16	with	with	ADP
ejpam-3258	264	17	∆∗	∆∗	NOUN
ejpam-3258	264	18	=	=	PUNCT
ejpam-3258	265	1	[	[	PUNCT
ejpam-3258	265	2	−0.4000−	−0.4000−	PROPN
ejpam-3258	265	3	0.8660i	0.8660i	NOUN
ejpam-3258	265	4	0	0	NUM
ejpam-3258	265	5	0	0	NUM
ejpam-3258	265	6	−0.4000−	−0.4000−	PROPN
ejpam-3258	265	7	0.8660i	0.8660i	NOUN
ejpam-3258	265	8	]	]	PUNCT
ejpam-3258	265	9	.	.	PUNCT
ejpam-3258	266	1	here	here	ADV
ejpam-3258	266	2	,	,	PUNCT
ejpam-3258	266	3	ε∗	ε∗	PROPN
ejpam-3258	266	4	=	=	SYM
ejpam-3258	266	5	1.0000	1.0000	NUM
ejpam-3258	266	6	and	and	CCONJ
ejpam-3258	266	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	266	8	=	=	SYM
ejpam-3258	266	9	1	1	X
ejpam-3258	266	10	.	.	PUNCT
ejpam-3258	267	1	the	the	DET
ejpam-3258	267	2	same	same	ADJ
ejpam-3258	267	3	lower	low	ADJ
ejpam-3258	267	4	bound	bind	VERB
ejpam-3258	267	5	is	be	AUX
ejpam-3258	267	6	obtained	obtain	VERB
ejpam-3258	267	7	for	for	ADP
ejpam-3258	267	8	this	this	DET
ejpam-3258	267	9	particular	particular	ADJ
ejpam-3258	267	10	example	example	NOUN
ejpam-3258	267	11	,	,	PUNCT
ejpam-3258	267	12	that	that	ADV
ejpam-3258	267	13	is	is	ADV
ejpam-3258	267	14	,	,	PUNCT
ejpam-3258	267	15	µlowernew	µlowernew	ADJ
ejpam-3258	267	16	=	=	NOUN
ejpam-3258	267	17	1.0000	1.0000	NUM
ejpam-3258	267	18	,	,	PUNCT
ejpam-3258	267	19	the	the	DET
ejpam-3258	267	20	one	one	NOUN
ejpam-3258	267	21	approximated	approximate	VERB
ejpam-3258	267	22	by	by	ADP
ejpam-3258	267	23	matlab	matlab	PROPN
ejpam-3258	267	24	function	function	PROPN
ejpam-3258	267	25	mussv	mussv	PROPN
ejpam-3258	267	26	.	.	PUNCT
ejpam-3258	267	27	example	example	NOUN
ejpam-3258	268	1	4	4	NUM
ejpam-3258	268	2	.	.	PUNCT
ejpam-3258	269	1	in	in	ADP
ejpam-3258	269	2	figure	figure	NOUN
ejpam-3258	269	3	2	2	NUM
ejpam-3258	269	4	,	,	PUNCT
ejpam-3258	269	5	we	we	PRON
ejpam-3258	269	6	show	show	VERB
ejpam-3258	269	7	the	the	DET
ejpam-3258	269	8	comparison	comparison	NOUN
ejpam-3258	269	9	of	of	ADP
ejpam-3258	269	10	lower	low	ADJ
ejpam-3258	269	11	bounds	bound	NOUN
ejpam-3258	269	12	computed	compute	VERB
ejpam-3258	269	13	by	by	ADP
ejpam-3258	269	14	algorithm	algorithm	NOUN
ejpam-3258	269	15	[	[	X
ejpam-3258	269	16	14	14	NUM
ejpam-3258	269	17	]	]	PUNCT
ejpam-3258	269	18	with	with	ADP
ejpam-3258	269	19	the	the	DET
ejpam-3258	269	20	bounds	bound	NOUN
ejpam-3258	269	21	(	(	PUNCT
ejpam-3258	269	22	lower	low	ADJ
ejpam-3258	269	23	and	and	CCONJ
ejpam-3258	269	24	upper	upper	ADJ
ejpam-3258	269	25	)	)	PUNCT
ejpam-3258	269	26	computed	compute	VERB
ejpam-3258	269	27	by	by	ADP
ejpam-3258	269	28	mussv	mussv	ADJ
ejpam-3258	269	29	function	function	NOUN
ejpam-3258	269	30	for	for	ADP
ejpam-3258	269	31	matrix	matrix	NOUN
ejpam-3258	269	32	valued	value	VERB
ejpam-3258	269	33	function	function	NOUN
ejpam-3258	269	34	b1(w	b1(w	NOUN
ejpam-3258	269	35	)	)	PUNCT
ejpam-3258	269	36	for	for	ADP
ejpam-3258	269	37	w	w	NOUN
ejpam-3258	269	38	=	=	SYM
ejpam-3258	269	39	1	1	NUM
ejpam-3258	269	40	:	:	SYM
ejpam-3258	269	41	7	7	NUM
ejpam-3258	269	42	,	,	PUNCT
ejpam-3258	269	43	where	where	SCONJ
ejpam-3258	269	44	w	w	PROPN
ejpam-3258	269	45	∈	∈	PROPN
ejpam-3258	269	46	ω	ω	PROPN
ejpam-3258	269	47	and	and	CCONJ
ejpam-3258	269	48	ω	ω	PROPN
ejpam-3258	269	49	denotes	denote	VERB
ejpam-3258	269	50	the	the	DET
ejpam-3258	269	51	frequency	frequency	NOUN
ejpam-3258	269	52	range	range	NOUN
ejpam-3258	269	53	of	of	ADP
ejpam-3258	269	54	interest	interest	NOUN
ejpam-3258	269	55	which	which	PRON
ejpam-3258	269	56	is	be	AUX
ejpam-3258	269	57	usually	usually	ADV
ejpam-3258	269	58	r+	r+	X
ejpam-3258	269	59	.	.	PUNCT
ejpam-3258	270	1	the	the	DET
ejpam-3258	270	2	frequency	frequency	NOUN
ejpam-3258	270	3	response	response	NOUN
ejpam-3258	270	4	w	w	NOUN
ejpam-3258	270	5	is	be	AUX
ejpam-3258	270	6	the	the	DET
ejpam-3258	270	7	quantitative	quantitative	ADJ
ejpam-3258	270	8	measure	measure	NOUN
ejpam-3258	270	9	of	of	ADP
ejpam-3258	270	10	output	output	NOUN
ejpam-3258	270	11	of	of	ADP
ejpam-3258	270	12	(	(	PUNCT
ejpam-3258	270	13	m−∆	m−∆	NOUN
ejpam-3258	270	14	)	)	PUNCT
ejpam-3258	270	15	system	system	NOUN
ejpam-3258	270	16	.	.	PUNCT
ejpam-3258	271	1	we	we	PRON
ejpam-3258	271	2	use	use	VERB
ejpam-3258	271	3	mussv	mussv	ADJ
ejpam-3258	271	4	function	function	NOUN
ejpam-3258	271	5	to	to	PART
ejpam-3258	271	6	compute	compute	VERB
ejpam-3258	271	7	µ	µ	PRON
ejpam-3258	271	8	as	as	ADP
ejpam-3258	271	9	a	a	DET
ejpam-3258	271	10	function	function	NOUN
ejpam-3258	271	11	of	of	ADP
ejpam-3258	271	12	frequency	frequency	NOUN
ejpam-3258	271	13	response	response	NOUN
ejpam-3258	271	14	.	.	PUNCT
ejpam-3258	272	1	example	example	NOUN
ejpam-3258	272	2	5	5	NUM
ejpam-3258	272	3	.	.	PUNCT
ejpam-3258	273	1	consider	consider	VERB
ejpam-3258	273	2	the	the	DET
ejpam-3258	273	3	following	follow	VERB
ejpam-3258	273	4	three	three	NUM
ejpam-3258	273	5	dimensional	dimensional	ADJ
ejpam-3258	273	6	real	real	ADJ
ejpam-3258	273	7	valued	value	VERB
ejpam-3258	273	8	matrix	matrix	NOUN
ejpam-3258	273	9	a2	a2	PROPN
ejpam-3258	273	10	.	.	PUNCT
ejpam-3258	274	1	a2	a2	PROPN
ejpam-3258	274	2	=	=	SYM
ejpam-3258	274	3	0	0	PROPN
ejpam-3258	274	4	0	0	NUM
ejpam-3258	274	5	−1	−1	NOUN
ejpam-3258	274	6	0	0	NUM
ejpam-3258	274	7	1	1	NUM
ejpam-3258	274	8	0	0	NUM
ejpam-3258	274	9	1	1	NUM
ejpam-3258	274	10	0	0	NUM
ejpam-3258	274	11	0	0	NUM
ejpam-3258	274	12			NOUN
ejpam-3258	274	13	.	.	PUNCT
ejpam-3258	275	1	we	we	PRON
ejpam-3258	275	2	take	take	VERB
ejpam-3258	275	3	the	the	DET
ejpam-3258	275	4	perturbation	perturbation	NOUN
ejpam-3258	275	5	set	set	VERB
ejpam-3258	275	6	as	as	ADP
ejpam-3258	275	7	,	,	PUNCT
ejpam-3258	275	8	∆b	∆b	PROPN
ejpam-3258	275	9	=	=	SYM
ejpam-3258	275	10	{	{	PUNCT
ejpam-3258	275	11	diag(δ1i1	diag(δ1i1	PROPN
ejpam-3258	275	12	,	,	PUNCT
ejpam-3258	275	13	δ2i1	δ2i1	NOUN
ejpam-3258	275	14	,	,	PUNCT
ejpam-3258	275	15	δ3i1	δ3i1	NOUN
ejpam-3258	275	16	)	)	PUNCT
ejpam-3258	275	17	:	:	PUNCT
ejpam-3258	275	18	δ1	δ1	NOUN
ejpam-3258	275	19	,	,	PUNCT
ejpam-3258	275	20	δ2	δ2	VERB
ejpam-3258	275	21	,	,	PUNCT
ejpam-3258	275	22	δ3	δ3	PROPN
ejpam-3258	275	23	∈	∈	PROPN
ejpam-3258	275	24	r	r	NOUN
ejpam-3258	275	25	}	}	PUNCT
ejpam-3258	275	26	.	.	PUNCT
ejpam-3258	276	1	first	first	ADV
ejpam-3258	276	2	,	,	PUNCT
ejpam-3258	276	3	by	by	ADP
ejpam-3258	276	4	using	use	VERB
ejpam-3258	276	5	mussv	mussv	ADJ
ejpam-3258	276	6	function	function	NOUN
ejpam-3258	276	7	,	,	PUNCT
ejpam-3258	276	8	we	we	PRON
ejpam-3258	276	9	obtain	obtain	VERB
ejpam-3258	276	10	the	the	DET
ejpam-3258	276	11	perturbation	perturbation	NOUN
ejpam-3258	276	12	structure	structure	NOUN
ejpam-3258	276	13	∆̂	∆̂	PUNCT
ejpam-3258	276	14	with	with	ADP
ejpam-3258	276	15	∆̂	∆̂	NOUN
ejpam-3258	276	16	=	=	SYM
ejpam-3258	276	17	1.0e+	1.0e+	NUM
ejpam-3258	276	18	050	050	NUM
ejpam-3258	276	19			NOUN
ejpam-3258	276	20	5.0000	5.0000	NUM
ejpam-3258	276	21	0.0000	0.0000	NUM
ejpam-3258	276	22	0.0000	0.0000	NUM
ejpam-3258	276	23	0.00000	0.00000	NUM
ejpam-3258	276	24	5.0000	5.0000	NUM
ejpam-3258	276	25	0.00000	0.00000	NUM
ejpam-3258	276	26	0.0000	0.0000	NUM
ejpam-3258	276	27	0.0000	0.0000	NUM
ejpam-3258	276	28	5.00000	5.00000	NUM
ejpam-3258	276	29			NOUN
ejpam-3258	276	30	.	.	PUNCT
ejpam-3258	277	1	here	here	ADV
ejpam-3258	277	2	,	,	PUNCT
ejpam-3258	277	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	277	4	=	=	SYM
ejpam-3258	277	5	5.0000e+050	5.0000e+050	PROPN
ejpam-3258	277	6	.	.	PUNCT
ejpam-3258	278	1	for	for	ADP
ejpam-3258	278	2	this	this	DET
ejpam-3258	278	3	particular	particular	ADJ
ejpam-3258	278	4	example	example	NOUN
ejpam-3258	278	5	,	,	PUNCT
ejpam-3258	278	6	we	we	PRON
ejpam-3258	278	7	obtain	obtain	VERB
ejpam-3258	278	8	the	the	DET
ejpam-3258	278	9	upper	upper	ADJ
ejpam-3258	278	10	bound	bind	VERB
ejpam-3258	278	11	,	,	PUNCT
ejpam-3258	278	12	that	that	ADV
ejpam-3258	278	13	is	is	ADV
ejpam-3258	278	14	,	,	PUNCT
ejpam-3258	278	15	µupperpd	µupperpd	PROPN
ejpam-3258	278	16	=	=	SYM
ejpam-3258	278	17	1.0000	1.0000	NUM
ejpam-3258	278	18	.	.	PUNCT
ejpam-3258	279	1	in	in	ADP
ejpam-3258	279	2	this	this	DET
ejpam-3258	279	3	case	case	NOUN
ejpam-3258	279	4	the	the	DET
ejpam-3258	279	5	obtained	obtain	VERB
ejpam-3258	279	6	lower	lower	ADV
ejpam-3258	279	7	bound	bind	VERB
ejpam-3258	279	8	is	be	AUX
ejpam-3258	279	9	µlowerpd	µlowerpd	ADJ
ejpam-3258	279	10	=	=	SYM
ejpam-3258	279	11	0.0000	0.0000	NUM
ejpam-3258	279	12	.	.	PUNCT
ejpam-3258	280	1	now	now	ADV
ejpam-3258	280	2	,	,	PUNCT
ejpam-3258	280	3	by	by	ADP
ejpam-3258	280	4	using	use	VERB
ejpam-3258	280	5	algorithm	algorithm	NOUN
ejpam-3258	280	6	[	[	X
ejpam-3258	280	7	14	14	NUM
ejpam-3258	280	8	]	]	PUNCT
ejpam-3258	280	9	,	,	PUNCT
ejpam-3258	280	10	we	we	PRON
ejpam-3258	280	11	obtain	obtain	VERB
ejpam-3258	280	12	the	the	DET
ejpam-3258	280	13	perturbation	perturbation	NOUN
ejpam-3258	280	14	structure	structure	NOUN
ejpam-3258	280	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	280	16	with	with	ADP
ejpam-3258	280	17	∆∗	∆∗	NOUN
ejpam-3258	280	18	=	=	SYM
ejpam-3258	280	19	−1.0000	−1.0000	PROPN
ejpam-3258	281	1	0.0000	0.0000	NUM
ejpam-3258	282	1	0.0000	0.0000	NUM
ejpam-3258	282	2	0.0000	0.0000	NUM
ejpam-3258	282	3	−1.0000	−1.0000	NUM
ejpam-3258	282	4	0.0000	0.0000	NUM
ejpam-3258	282	5	0.0000	0.0000	NUM
ejpam-3258	282	6	0.0000	0.0000	NUM
ejpam-3258	282	7	−1.0000	−1.0000	NUM
ejpam-3258	282	8			NOUN
ejpam-3258	282	9	.	.	PUNCT
ejpam-3258	283	1	m.	m.	PROPN
ejpam-3258	283	2	rehman	rehman	PROPN
ejpam-3258	283	3	,	,	PUNCT
ejpam-3258	283	4	m.	m.	PROPN
ejpam-3258	283	5	f.	f.	PROPN
ejpam-3258	283	6	anwar	anwar	PROPN
ejpam-3258	283	7	/	/	PUNCT
ejpam-3258	283	8	eur	eur	PROPN
ejpam-3258	283	9	.	.	PUNCT
ejpam-3258	284	1	j.	j.	PROPN
ejpam-3258	284	2	pure	pure	PROPN
ejpam-3258	284	3	appl	appl	PROPN
ejpam-3258	284	4	.	.	PROPN
ejpam-3258	284	5	math	math	PROPN
ejpam-3258	284	6	,	,	PUNCT
ejpam-3258	284	7	11	11	NUM
ejpam-3258	284	8	(	(	PUNCT
ejpam-3258	284	9	3	3	NUM
ejpam-3258	284	10	)	)	PUNCT
ejpam-3258	284	11	(	(	PUNCT
ejpam-3258	284	12	2018	2018	NUM
ejpam-3258	284	13	)	)	PUNCT
ejpam-3258	284	14	,	,	PUNCT
ejpam-3258	284	15	774	774	NUM
ejpam-3258	284	16	-	-	SYM
ejpam-3258	284	17	792	792	NUM
ejpam-3258	284	18	786	786	NUM
ejpam-3258	284	19	here	here	ADV
ejpam-3258	284	20	ε∗	ε∗	PROPN
ejpam-3258	284	21	=	=	PUNCT
ejpam-3258	284	22	1.0000	1.0000	NUM
ejpam-3258	284	23	and	and	CCONJ
ejpam-3258	284	24	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	284	25	=	=	SYM
ejpam-3258	284	26	1.0000	1.0000	NUM
ejpam-3258	284	27	.	.	PUNCT
ejpam-3258	285	1	in	in	ADP
ejpam-3258	285	2	this	this	DET
ejpam-3258	285	3	case	case	NOUN
ejpam-3258	285	4	,	,	PUNCT
ejpam-3258	285	5	same	same	ADJ
ejpam-3258	285	6	lower	lower	ADV
ejpam-3258	285	7	bound	bind	VERB
ejpam-3258	285	8	is	be	AUX
ejpam-3258	285	9	obtained	obtain	VERB
ejpam-3258	285	10	,	,	PUNCT
ejpam-3258	285	11	that	that	ADV
ejpam-3258	285	12	is	is	ADV
ejpam-3258	285	13	,	,	PUNCT
ejpam-3258	285	14	µlowernew	µlowernew	ADJ
ejpam-3258	285	15	=	=	NOUN
ejpam-3258	285	16	1.0000	1.0000	NUM
ejpam-3258	285	17	,	,	PUNCT
ejpam-3258	285	18	as	as	ADP
ejpam-3258	285	19	the	the	DET
ejpam-3258	285	20	one	one	NOUN
ejpam-3258	285	21	obtained	obtain	VERB
ejpam-3258	285	22	by	by	ADP
ejpam-3258	285	23	mussv	mussv	ADJ
ejpam-3258	285	24	function	function	PROPN
ejpam-3258	285	25	.	.	PUNCT
ejpam-3258	286	1	example	example	NOUN
ejpam-3258	286	2	6	6	NUM
ejpam-3258	286	3	.	.	PUNCT
ejpam-3258	287	1	consider	consider	VERB
ejpam-3258	287	2	the	the	DET
ejpam-3258	287	3	following	follow	VERB
ejpam-3258	287	4	three	three	NUM
ejpam-3258	287	5	dimensional	dimensional	ADJ
ejpam-3258	287	6	real	real	ADJ
ejpam-3258	287	7	valued	value	VERB
ejpam-3258	287	8	matrix	matrix	NOUN
ejpam-3258	287	9	b2	b2	NOUN
ejpam-3258	287	10	.	.	PUNCT
ejpam-3258	287	11	b2	b2	NOUN
ejpam-3258	287	12	=	=	SYM
ejpam-3258	287	13			PROPN
ejpam-3258	287	14	0	0	NUM
ejpam-3258	287	15	−1	−1	NOUN
ejpam-3258	287	16	0	0	NUM
ejpam-3258	287	17	−1	−1	NOUN
ejpam-3258	287	18	0	0	NUM
ejpam-3258	287	19	0	0	NUM
ejpam-3258	287	20	0	0	NUM
ejpam-3258	287	21	0	0	NUM
ejpam-3258	287	22	−1	−1	NOUN
ejpam-3258	287	23			NOUN
ejpam-3258	287	24	.	.	PUNCT
ejpam-3258	288	1	we	we	PRON
ejpam-3258	288	2	take	take	VERB
ejpam-3258	288	3	the	the	DET
ejpam-3258	288	4	perturbation	perturbation	NOUN
ejpam-3258	288	5	set	set	VERB
ejpam-3258	288	6	as	as	ADP
ejpam-3258	288	7	,	,	PUNCT
ejpam-3258	288	8	∆b	∆b	PROPN
ejpam-3258	288	9	=	=	SYM
ejpam-3258	288	10	{	{	PUNCT
ejpam-3258	288	11	diag(δ1i1,∆1	diag(δ1i1,∆1	NOUN
ejpam-3258	288	12	)	)	PUNCT
ejpam-3258	288	13	:	:	PUNCT
ejpam-3258	288	14	δ1	δ1	NOUN
ejpam-3258	288	15	∈	∈	PROPN
ejpam-3258	288	16	r,∆2	r,∆2	PROPN
ejpam-3258	288	17	∈	∈	PROPN
ejpam-3258	288	18	c2,2	c2,2	NOUN
ejpam-3258	288	19	}	}	PUNCT
ejpam-3258	288	20	.	.	PUNCT
ejpam-3258	289	1	first	first	ADV
ejpam-3258	289	2	,	,	PUNCT
ejpam-3258	289	3	by	by	ADP
ejpam-3258	289	4	using	use	VERB
ejpam-3258	289	5	mussv	mussv	ADJ
ejpam-3258	289	6	function	function	NOUN
ejpam-3258	289	7	,	,	PUNCT
ejpam-3258	289	8	we	we	PRON
ejpam-3258	289	9	obtain	obtain	VERB
ejpam-3258	289	10	the	the	DET
ejpam-3258	289	11	perturbation	perturbation	NOUN
ejpam-3258	289	12	structure	structure	NOUN
ejpam-3258	289	13	∆̂	∆̂	PUNCT
ejpam-3258	289	14	with	with	ADP
ejpam-3258	289	15	∆̂	∆̂	NOUN
ejpam-3258	289	16	=	=	SYM
ejpam-3258	289	17	1.0e+	1.0e+	NUM
ejpam-3258	289	18	050	050	NUM
ejpam-3258	289	19			NOUN
ejpam-3258	290	1	0.0000	0.0000	NUM
ejpam-3258	290	2	0.0000	0.0000	NUM
ejpam-3258	290	3	0.0000	0.0000	NUM
ejpam-3258	290	4	0.00000	0.00000	NUM
ejpam-3258	290	5	0.0000	0.0000	NUM
ejpam-3258	290	6	0.00000	0.00000	NUM
ejpam-3258	290	7	0.0000	0.0000	NUM
ejpam-3258	290	8	0.0000	0.0000	NUM
ejpam-3258	290	9	−1.00000	−1.00000	NOUN
ejpam-3258	290	10			NOUN
ejpam-3258	290	11	.	.	PUNCT
ejpam-3258	291	1	here	here	ADV
ejpam-3258	291	2	,	,	PUNCT
ejpam-3258	291	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	291	4	=	=	SYM
ejpam-3258	291	5	1.0000	1.0000	NUM
ejpam-3258	291	6	.	.	PUNCT
ejpam-3258	292	1	for	for	ADP
ejpam-3258	292	2	this	this	DET
ejpam-3258	292	3	particular	particular	ADJ
ejpam-3258	292	4	example	example	NOUN
ejpam-3258	292	5	,	,	PUNCT
ejpam-3258	292	6	we	we	PRON
ejpam-3258	292	7	obtain	obtain	VERB
ejpam-3258	292	8	the	the	DET
ejpam-3258	292	9	upper	upper	ADJ
ejpam-3258	292	10	bound	bind	VERB
ejpam-3258	292	11	µupperpd	µupperpd	NOUN
ejpam-3258	292	12	=	=	PROPN
ejpam-3258	292	13	1.0000	1.0000	NUM
ejpam-3258	292	14	while	while	SCONJ
ejpam-3258	292	15	a	a	DET
ejpam-3258	292	16	same	same	ADJ
ejpam-3258	292	17	lower	low	ADJ
ejpam-3258	292	18	bound	bind	VERB
ejpam-3258	292	19	is	be	AUX
ejpam-3258	292	20	obtained	obtain	VERB
ejpam-3258	292	21	,	,	PUNCT
ejpam-3258	292	22	that	that	ADV
ejpam-3258	292	23	is	is	ADV
ejpam-3258	292	24	,	,	PUNCT
ejpam-3258	292	25	µlowerpd	µlowerpd	NOUN
ejpam-3258	292	26	=	=	SYM
ejpam-3258	292	27	1.0000	1.0000	NUM
ejpam-3258	292	28	.	.	PUNCT
ejpam-3258	293	1	now	now	ADV
ejpam-3258	293	2	,	,	PUNCT
ejpam-3258	293	3	by	by	ADP
ejpam-3258	293	4	algorithm	algorithm	NOUN
ejpam-3258	293	5	[	[	X
ejpam-3258	293	6	14	14	NUM
ejpam-3258	293	7	]	]	PUNCT
ejpam-3258	293	8	,	,	PUNCT
ejpam-3258	293	9	we	we	PRON
ejpam-3258	293	10	have	have	AUX
ejpam-3258	293	11	obtained	obtain	VERB
ejpam-3258	293	12	the	the	DET
ejpam-3258	293	13	perturbation	perturbation	NOUN
ejpam-3258	293	14	structure	structure	NOUN
ejpam-3258	293	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	293	16	with	with	ADP
ejpam-3258	293	17	∆∗	∆∗	NOUN
ejpam-3258	293	18	=	=	SYM
ejpam-3258	293	19	−1.0000	−1.0000	PROPN
ejpam-3258	294	1	0.0000	0.0000	NUM
ejpam-3258	294	2	0.0000	0.0000	NUM
ejpam-3258	294	3	0.0000	0.0000	NUM
ejpam-3258	294	4	−1.0000	−1.0000	NUM
ejpam-3258	295	1	0.0000	0.0000	NUM
ejpam-3258	295	2	0.0000	0.0000	NUM
ejpam-3258	295	3	0.0000	0.0000	NUM
ejpam-3258	295	4	0.0000	0.0000	NUM
ejpam-3258	295	5			NOUN
ejpam-3258	295	6	.	.	PUNCT
ejpam-3258	296	1	here	here	ADV
ejpam-3258	296	2	,	,	PUNCT
ejpam-3258	296	3	ε∗	ε∗	PROPN
ejpam-3258	296	4	=	=	SYM
ejpam-3258	296	5	1.0000	1.0000	NUM
ejpam-3258	296	6	and	and	CCONJ
ejpam-3258	296	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	296	8	=	=	SYM
ejpam-3258	296	9	1.0000	1.0000	NUM
ejpam-3258	296	10	.	.	PUNCT
ejpam-3258	297	1	in	in	ADP
ejpam-3258	297	2	this	this	DET
ejpam-3258	297	3	case	case	NOUN
ejpam-3258	297	4	,	,	PUNCT
ejpam-3258	297	5	the	the	DET
ejpam-3258	297	6	same	same	ADJ
ejpam-3258	297	7	lower	low	ADJ
ejpam-3258	297	8	bound	bind	VERB
ejpam-3258	297	9	is	be	AUX
ejpam-3258	297	10	obtained	obtain	VERB
ejpam-3258	297	11	µlowernew	µlowernew	ADV
ejpam-3258	297	12	=	=	NOUN
ejpam-3258	297	13	1.0000	1.0000	NUM
ejpam-3258	297	14	as	as	ADP
ejpam-3258	297	15	the	the	DET
ejpam-3258	297	16	one	one	NOUN
ejpam-3258	297	17	obtained	obtain	VERB
ejpam-3258	297	18	by	by	ADP
ejpam-3258	297	19	mussv	mussv	ADJ
ejpam-3258	297	20	function	function	NOUN
ejpam-3258	297	21	.	.	PUNCT
ejpam-3258	298	1	the	the	DET
ejpam-3258	298	2	obtained	obtain	VERB
ejpam-3258	298	3	bounds	bound	NOUN
ejpam-3258	298	4	for	for	ADP
ejpam-3258	298	5	ssv	ssv	NOUN
ejpam-3258	298	6	for	for	ADP
ejpam-3258	298	7	above	above	ADJ
ejpam-3258	298	8	matrix	matrix	NOUN
ejpam-3258	298	9	m	m	VERB
ejpam-3258	298	10	when	when	SCONJ
ejpam-3258	298	11	the	the	DET
ejpam-3258	298	12	perturbation	perturbation	NOUN
ejpam-3258	298	13	structure	structure	NOUN
ejpam-3258	298	14	takes	take	VERB
ejpam-3258	298	15	the	the	DET
ejpam-3258	298	16	form	form	NOUN
ejpam-3258	298	17	,	,	PUNCT
ejpam-3258	298	18	∆b	∆b	PROPN
ejpam-3258	298	19	=	=	SYM
ejpam-3258	298	20	{	{	PUNCT
ejpam-3258	298	21	diag(∆1	diag(∆1	PROPN
ejpam-3258	298	22	)	)	PUNCT
ejpam-3258	298	23	:	:	PUNCT
ejpam-3258	299	1	∆1	∆1	PUNCT
ejpam-3258	299	2	∈	∈	PROPN
ejpam-3258	299	3	c3,3	c3,3	PROPN
ejpam-3258	299	4	}	}	PUNCT
ejpam-3258	299	5	,	,	PUNCT
ejpam-3258	299	6	are	be	AUX
ejpam-3258	299	7	as	as	SCONJ
ejpam-3258	299	8	follows	follow	VERB
ejpam-3258	299	9	.	.	PUNCT
ejpam-3258	300	1	applying	apply	VERB
ejpam-3258	300	2	the	the	DET
ejpam-3258	300	3	mussv	mussv	ADJ
ejpam-3258	300	4	function	function	NOUN
ejpam-3258	300	5	,	,	PUNCT
ejpam-3258	300	6	we	we	PRON
ejpam-3258	300	7	obtain	obtain	VERB
ejpam-3258	300	8	the	the	DET
ejpam-3258	300	9	perturbation	perturbation	NOUN
ejpam-3258	300	10	structure	structure	NOUN
ejpam-3258	300	11	∆̂	∆̂	PUNCT
ejpam-3258	300	12	with	with	ADP
ejpam-3258	300	13	∆̂	∆̂	NOUN
ejpam-3258	300	14	=	=	SYM
ejpam-3258	300	15	0.0000	0.0000	NUM
ejpam-3258	300	16	0.0000	0.0000	NUM
ejpam-3258	300	17	0.0000	0.0000	NUM
ejpam-3258	301	1	0.0000	0.0000	NUM
ejpam-3258	301	2	0.0000	0.0000	NUM
ejpam-3258	301	3	0.0000	0.0000	NUM
ejpam-3258	301	4	0.0000	0.0000	NUM
ejpam-3258	301	5	0.0000	0.0000	NUM
ejpam-3258	301	6	−1.0000	−1.0000	NUM
ejpam-3258	301	7			NOUN
ejpam-3258	301	8	.	.	PUNCT
ejpam-3258	302	1	here	here	ADV
ejpam-3258	302	2	,	,	PUNCT
ejpam-3258	302	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	302	4	=	=	NOUN
ejpam-3258	302	5	1	1	X
ejpam-3258	302	6	.	.	X
ejpam-3258	303	1	for	for	ADP
ejpam-3258	303	2	this	this	DET
ejpam-3258	303	3	particular	particular	ADJ
ejpam-3258	303	4	example	example	NOUN
ejpam-3258	303	5	,	,	PUNCT
ejpam-3258	303	6	we	we	PRON
ejpam-3258	303	7	have	have	AUX
ejpam-3258	303	8	obtained	obtain	VERB
ejpam-3258	303	9	an	an	DET
ejpam-3258	303	10	upper	upper	ADJ
ejpam-3258	303	11	bound	bind	VERB
ejpam-3258	303	12	µupperpd	µupperpd	NOUN
ejpam-3258	303	13	=	=	PROPN
ejpam-3258	303	14	1.0000	1.0000	NUM
ejpam-3258	303	15	.	.	PUNCT
ejpam-3258	304	1	the	the	DET
ejpam-3258	304	2	same	same	ADJ
ejpam-3258	304	3	lower	low	ADJ
ejpam-3258	304	4	bound	bind	VERB
ejpam-3258	304	5	is	be	AUX
ejpam-3258	304	6	obtained	obtain	VERB
ejpam-3258	304	7	,	,	PUNCT
ejpam-3258	304	8	that	that	PRON
ejpam-3258	304	9	is	be	AUX
ejpam-3258	304	10	µlowerpd	µlowerpd	ADJ
ejpam-3258	304	11	=	=	ADJ
ejpam-3258	304	12	1.0000	1.0000	NUM
ejpam-3258	304	13	,	,	PUNCT
ejpam-3258	304	14	while	while	SCONJ
ejpam-3258	304	15	applying	apply	VERB
ejpam-3258	304	16	mussv	mussv	ADJ
ejpam-3258	304	17	function	function	NOUN
ejpam-3258	304	18	.	.	PUNCT
ejpam-3258	305	1	now	now	ADV
ejpam-3258	305	2	,	,	PUNCT
ejpam-3258	305	3	by	by	ADP
ejpam-3258	305	4	applying	apply	VERB
ejpam-3258	305	5	algorithm	algorithm	NOUN
ejpam-3258	305	6	[	[	X
ejpam-3258	305	7	14	14	NUM
ejpam-3258	305	8	]	]	PUNCT
ejpam-3258	305	9	,	,	PUNCT
ejpam-3258	305	10	we	we	PRON
ejpam-3258	305	11	obtain	obtain	VERB
ejpam-3258	305	12	the	the	DET
ejpam-3258	305	13	perturbation	perturbation	NOUN
ejpam-3258	305	14	structure	structure	NOUN
ejpam-3258	305	15	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	305	16	with	with	ADP
ejpam-3258	305	17	∆∗	∆∗	NOUN
ejpam-3258	305	18	=	=	SYM
ejpam-3258	305	19	−0.5000	−0.5000	ADJ
ejpam-3258	305	20	−0.5000	−0.5000	NUM
ejpam-3258	305	21	0.0000	0.0000	NUM
ejpam-3258	306	1	−0.5000	−0.5000	NUM
ejpam-3258	307	1	−0.5000	−0.5000	NUM
ejpam-3258	307	2	0.0000	0.0000	NUM
ejpam-3258	307	3	0.0000	0.0000	NUM
ejpam-3258	307	4	0.0000	0.0000	NUM
ejpam-3258	307	5	0.0000	0.0000	NUM
ejpam-3258	307	6			NOUN
ejpam-3258	307	7	.	.	PUNCT
ejpam-3258	308	1	m.	m.	PROPN
ejpam-3258	308	2	rehman	rehman	PROPN
ejpam-3258	308	3	,	,	PUNCT
ejpam-3258	308	4	m.	m.	PROPN
ejpam-3258	308	5	f.	f.	PROPN
ejpam-3258	308	6	anwar	anwar	PROPN
ejpam-3258	308	7	/	/	PUNCT
ejpam-3258	308	8	eur	eur	PROPN
ejpam-3258	308	9	.	.	PUNCT
ejpam-3258	309	1	j.	j.	PROPN
ejpam-3258	309	2	pure	pure	PROPN
ejpam-3258	309	3	appl	appl	PROPN
ejpam-3258	309	4	.	.	PROPN
ejpam-3258	309	5	math	math	PROPN
ejpam-3258	309	6	,	,	PUNCT
ejpam-3258	309	7	11	11	NUM
ejpam-3258	309	8	(	(	PUNCT
ejpam-3258	309	9	3	3	NUM
ejpam-3258	309	10	)	)	PUNCT
ejpam-3258	309	11	(	(	PUNCT
ejpam-3258	309	12	2018	2018	NUM
ejpam-3258	309	13	)	)	PUNCT
ejpam-3258	309	14	,	,	PUNCT
ejpam-3258	309	15	774	774	NUM
ejpam-3258	309	16	-	-	SYM
ejpam-3258	309	17	792	792	NUM
ejpam-3258	309	18	787	787	NUM
ejpam-3258	309	19	here	here	ADV
ejpam-3258	309	20	,	,	PUNCT
ejpam-3258	309	21	ε∗	ε∗	PROPN
ejpam-3258	309	22	=	=	SYM
ejpam-3258	309	23	1.0000	1.0000	NUM
ejpam-3258	309	24	and	and	CCONJ
ejpam-3258	309	25	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	309	26	=	=	SYM
ejpam-3258	309	27	1	1	NUM
ejpam-3258	309	28	,	,	PUNCT
ejpam-3258	309	29	while	while	SCONJ
ejpam-3258	309	30	same	same	ADJ
ejpam-3258	309	31	lower	low	ADJ
ejpam-3258	309	32	bound	bind	VERB
ejpam-3258	309	33	is	be	AUX
ejpam-3258	309	34	obtained	obtain	VERB
ejpam-3258	309	35	µlowernew	µlowernew	ADV
ejpam-3258	309	36	=	=	NOUN
ejpam-3258	309	37	1.0000	1.0000	NUM
ejpam-3258	309	38	as	as	ADP
ejpam-3258	309	39	the	the	DET
ejpam-3258	309	40	one	one	NOUN
ejpam-3258	309	41	obtained	obtain	VERB
ejpam-3258	309	42	by	by	ADP
ejpam-3258	309	43	mussv	mussv	ADJ
ejpam-3258	309	44	function	function	PROPN
ejpam-3258	309	45	.	.	PUNCT
ejpam-3258	310	1	example	example	NOUN
ejpam-3258	310	2	7	7	NUM
ejpam-3258	310	3	.	.	PUNCT
ejpam-3258	311	1	consider	consider	VERB
ejpam-3258	311	2	the	the	DET
ejpam-3258	311	3	following	follow	VERB
ejpam-3258	311	4	three	three	NUM
ejpam-3258	311	5	dimensional	dimensional	ADJ
ejpam-3258	311	6	real	real	ADJ
ejpam-3258	311	7	valued	value	VERB
ejpam-3258	311	8	matrix	matrix	NOUN
ejpam-3258	311	9	b3	b3	NOUN
ejpam-3258	311	10	.	.	PUNCT
ejpam-3258	312	1	b3	b3	PROPN
ejpam-3258	312	2	=	=	SYM
ejpam-3258	312	3			PROPN
ejpam-3258	312	4	0	0	NUM
ejpam-3258	312	5	−1	−1	NOUN
ejpam-3258	312	6	0	0	NUM
ejpam-3258	312	7	−1	−1	NOUN
ejpam-3258	312	8	0	0	NUM
ejpam-3258	312	9	0	0	NUM
ejpam-3258	312	10	0	0	NUM
ejpam-3258	312	11	0	0	NUM
ejpam-3258	312	12	−1	−1	NOUN
ejpam-3258	312	13			NOUN
ejpam-3258	312	14	.	.	PUNCT
ejpam-3258	313	1	we	we	PRON
ejpam-3258	313	2	take	take	VERB
ejpam-3258	313	3	the	the	DET
ejpam-3258	313	4	perturbation	perturbation	NOUN
ejpam-3258	313	5	set	set	VERB
ejpam-3258	313	6	as	as	ADP
ejpam-3258	313	7	,	,	PUNCT
ejpam-3258	313	8	∆b	∆b	PROPN
ejpam-3258	313	9	=	=	SYM
ejpam-3258	313	10	{	{	PUNCT
ejpam-3258	313	11	diag(δ1i1,∆1	diag(δ1i1,∆1	NOUN
ejpam-3258	313	12	)	)	PUNCT
ejpam-3258	313	13	:	:	PUNCT
ejpam-3258	313	14	δ1	δ1	NOUN
ejpam-3258	313	15	∈	∈	PROPN
ejpam-3258	313	16	r,∆2	r,∆2	PROPN
ejpam-3258	313	17	∈	∈	PROPN
ejpam-3258	313	18	c2,2	c2,2	NOUN
ejpam-3258	313	19	}	}	PUNCT
ejpam-3258	313	20	.	.	PUNCT
ejpam-3258	314	1	first	first	ADV
ejpam-3258	314	2	,	,	PUNCT
ejpam-3258	314	3	by	by	ADP
ejpam-3258	314	4	making	make	VERB
ejpam-3258	314	5	use	use	NOUN
ejpam-3258	314	6	of	of	ADP
ejpam-3258	314	7	the	the	DET
ejpam-3258	314	8	well	well	ADV
ejpam-3258	314	9	-	-	PUNCT
ejpam-3258	314	10	known	know	VERB
ejpam-3258	314	11	matlab	matlab	PROPN
ejpam-3258	314	12	routine	routine	PROPN
ejpam-3258	314	13	mussv	mussv	PROPN
ejpam-3258	314	14	,	,	PUNCT
ejpam-3258	314	15	we	we	PRON
ejpam-3258	314	16	have	have	AUX
ejpam-3258	314	17	obtained	obtain	VERB
ejpam-3258	314	18	the	the	DET
ejpam-3258	314	19	perturbation	perturbation	NOUN
ejpam-3258	314	20	structure	structure	NOUN
ejpam-3258	314	21	∆̂	∆̂	PUNCT
ejpam-3258	314	22	with	with	ADP
ejpam-3258	314	23	∆̂	∆̂	NOUN
ejpam-3258	314	24	=	=	SYM
ejpam-3258	314	25	1.0e+	1.0e+	NUM
ejpam-3258	314	26	050	050	NUM
ejpam-3258	315	1			NOUN
ejpam-3258	315	2	0.0000	0.0000	NUM
ejpam-3258	315	3	0.0000	0.0000	NUM
ejpam-3258	315	4	0.0000	0.0000	NUM
ejpam-3258	316	1	0.00000	0.00000	NUM
ejpam-3258	316	2	0.0000	0.0000	NUM
ejpam-3258	316	3	0.00000	0.00000	NUM
ejpam-3258	316	4	0.0000	0.0000	NUM
ejpam-3258	316	5	0.0000	0.0000	NUM
ejpam-3258	316	6	−1.00000	−1.00000	NOUN
ejpam-3258	316	7			NOUN
ejpam-3258	316	8	.	.	PUNCT
ejpam-3258	317	1	here	here	ADV
ejpam-3258	317	2	,	,	PUNCT
ejpam-3258	317	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	317	4	=	=	SYM
ejpam-3258	317	5	1.0000	1.0000	NUM
ejpam-3258	317	6	.	.	PUNCT
ejpam-3258	318	1	for	for	ADP
ejpam-3258	318	2	this	this	DET
ejpam-3258	318	3	particular	particular	ADJ
ejpam-3258	318	4	example	example	NOUN
ejpam-3258	318	5	,	,	PUNCT
ejpam-3258	318	6	we	we	PRON
ejpam-3258	318	7	have	have	AUX
ejpam-3258	318	8	obtained	obtain	VERB
ejpam-3258	318	9	an	an	DET
ejpam-3258	318	10	upper	upper	ADJ
ejpam-3258	318	11	bound	bind	VERB
ejpam-3258	318	12	µupperpd	µupperpd	NOUN
ejpam-3258	318	13	=	=	PROPN
ejpam-3258	318	14	1.0000	1.0000	NUM
ejpam-3258	318	15	,	,	PUNCT
ejpam-3258	318	16	while	while	SCONJ
ejpam-3258	318	17	a	a	DET
ejpam-3258	318	18	same	same	ADJ
ejpam-3258	318	19	lower	low	ADJ
ejpam-3258	318	20	bound	bind	VERB
ejpam-3258	318	21	is	be	AUX
ejpam-3258	318	22	obtained	obtain	VERB
ejpam-3258	318	23	,	,	PUNCT
ejpam-3258	318	24	that	that	ADV
ejpam-3258	318	25	is	is	ADV
ejpam-3258	318	26	,	,	PUNCT
ejpam-3258	318	27	µlowerpd	µlowerpd	NOUN
ejpam-3258	318	28	=	=	SYM
ejpam-3258	318	29	1.0000	1.0000	NUM
ejpam-3258	318	30	.	.	PUNCT
ejpam-3258	319	1	now	now	ADV
ejpam-3258	319	2	,	,	PUNCT
ejpam-3258	319	3	by	by	ADP
ejpam-3258	319	4	making	make	VERB
ejpam-3258	319	5	use	use	NOUN
ejpam-3258	319	6	of	of	ADP
ejpam-3258	319	7	algorithm	algorithm	NOUN
ejpam-3258	319	8	[	[	X
ejpam-3258	319	9	14	14	NUM
ejpam-3258	319	10	]	]	PUNCT
ejpam-3258	319	11	,	,	PUNCT
ejpam-3258	319	12	we	we	PRON
ejpam-3258	319	13	obtain	obtain	VERB
ejpam-3258	319	14	perturbation	perturbation	NOUN
ejpam-3258	319	15	structure	structure	NOUN
ejpam-3258	319	16	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	319	17	with	with	ADP
ejpam-3258	319	18	∆∗	∆∗	NOUN
ejpam-3258	319	19	=	=	SYM
ejpam-3258	319	20	−1.0000	−1.0000	PROPN
ejpam-3258	320	1	0.0000	0.0000	NUM
ejpam-3258	321	1	0.0000	0.0000	NUM
ejpam-3258	321	2	0.0000	0.0000	NUM
ejpam-3258	321	3	−1.0000	−1.0000	NUM
ejpam-3258	322	1	0.0000	0.0000	NUM
ejpam-3258	322	2	0.0000	0.0000	NUM
ejpam-3258	322	3	0.0000	0.0000	NUM
ejpam-3258	322	4	0.0000	0.0000	NUM
ejpam-3258	322	5			NOUN
ejpam-3258	322	6	.	.	PUNCT
ejpam-3258	323	1	here	here	ADV
ejpam-3258	323	2	,	,	PUNCT
ejpam-3258	323	3	ε∗	ε∗	PROPN
ejpam-3258	323	4	=	=	SYM
ejpam-3258	323	5	1.0000	1.0000	NUM
ejpam-3258	323	6	and	and	CCONJ
ejpam-3258	323	7	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	323	8	=	=	SYM
ejpam-3258	323	9	1.0000	1.0000	NUM
ejpam-3258	323	10	,	,	PUNCT
ejpam-3258	323	11	while	while	SCONJ
ejpam-3258	323	12	a	a	DET
ejpam-3258	323	13	same	same	ADJ
ejpam-3258	323	14	lower	low	ADJ
ejpam-3258	323	15	bound	bind	VERB
ejpam-3258	323	16	is	be	AUX
ejpam-3258	323	17	achieved	achieve	VERB
ejpam-3258	323	18	,	,	PUNCT
ejpam-3258	323	19	that	that	ADV
ejpam-3258	323	20	is	is	ADV
ejpam-3258	323	21	,	,	PUNCT
ejpam-3258	323	22	µlowernew	µlowernew	ADJ
ejpam-3258	323	23	=	=	NOUN
ejpam-3258	323	24	1.0000	1.0000	NUM
ejpam-3258	323	25	as	as	ADP
ejpam-3258	323	26	the	the	DET
ejpam-3258	323	27	one	one	NOUN
ejpam-3258	323	28	obtained	obtain	VERB
ejpam-3258	323	29	by	by	ADP
ejpam-3258	323	30	mussv	mussv	ADJ
ejpam-3258	323	31	function	function	NOUN
ejpam-3258	323	32	.	.	PUNCT
ejpam-3258	324	1	the	the	DET
ejpam-3258	324	2	obtained	obtain	VERB
ejpam-3258	324	3	bounds	bound	NOUN
ejpam-3258	324	4	of	of	ADP
ejpam-3258	324	5	ssv	ssv	NOUN
ejpam-3258	324	6	for	for	ADP
ejpam-3258	324	7	above	above	ADV
ejpam-3258	324	8	given	give	VERB
ejpam-3258	324	9	matrix	matrix	NOUN
ejpam-3258	324	10	m	m	VERB
ejpam-3258	324	11	when	when	SCONJ
ejpam-3258	324	12	the	the	DET
ejpam-3258	324	13	perturbation	perturbation	NOUN
ejpam-3258	324	14	set	set	NOUN
ejpam-3258	324	15	takes	take	VERB
ejpam-3258	324	16	the	the	DET
ejpam-3258	324	17	form	form	NOUN
ejpam-3258	324	18	,	,	PUNCT
ejpam-3258	324	19	∆b	∆b	PROPN
ejpam-3258	324	20	=	=	SYM
ejpam-3258	324	21	{	{	PUNCT
ejpam-3258	324	22	diag(∆1	diag(∆1	PROPN
ejpam-3258	324	23	)	)	PUNCT
ejpam-3258	324	24	:	:	PUNCT
ejpam-3258	325	1	∆1	∆1	PUNCT
ejpam-3258	325	2	∈	∈	PROPN
ejpam-3258	325	3	c3,3	c3,3	PROPN
ejpam-3258	325	4	}	}	PUNCT
ejpam-3258	325	5	,	,	PUNCT
ejpam-3258	325	6	are	be	AUX
ejpam-3258	325	7	as	as	SCONJ
ejpam-3258	325	8	follows	follow	VERB
ejpam-3258	325	9	.	.	PUNCT
ejpam-3258	326	1	first	first	ADV
ejpam-3258	326	2	,	,	PUNCT
ejpam-3258	326	3	by	by	ADP
ejpam-3258	326	4	using	use	VERB
ejpam-3258	326	5	mussv	mussv	ADJ
ejpam-3258	326	6	function	function	NOUN
ejpam-3258	326	7	,	,	PUNCT
ejpam-3258	326	8	we	we	PRON
ejpam-3258	326	9	obtain	obtain	VERB
ejpam-3258	326	10	the	the	DET
ejpam-3258	326	11	perturbation	perturbation	NOUN
ejpam-3258	326	12	structure	structure	NOUN
ejpam-3258	326	13	∆̂	∆̂	PUNCT
ejpam-3258	326	14	with	with	ADP
ejpam-3258	326	15	∆̂	∆̂	NOUN
ejpam-3258	326	16	=	=	SYM
ejpam-3258	326	17	0.0000	0.0000	NUM
ejpam-3258	326	18	0.0000	0.0000	NUM
ejpam-3258	326	19	0.0000	0.0000	NUM
ejpam-3258	327	1	0.0000	0.0000	NUM
ejpam-3258	327	2	0.0000	0.0000	NUM
ejpam-3258	327	3	0.0000	0.0000	NUM
ejpam-3258	327	4	0.0000	0.0000	NUM
ejpam-3258	327	5	0.0000	0.0000	NUM
ejpam-3258	327	6	−1.0000	−1.0000	NUM
ejpam-3258	327	7			NOUN
ejpam-3258	327	8	.	.	PUNCT
ejpam-3258	328	1	here	here	ADV
ejpam-3258	328	2	,	,	PUNCT
ejpam-3258	328	3	‖∆̂‖2	‖∆̂‖2	NOUN
ejpam-3258	328	4	=	=	NOUN
ejpam-3258	328	5	1	1	X
ejpam-3258	328	6	.	.	X
ejpam-3258	329	1	for	for	ADP
ejpam-3258	329	2	this	this	DET
ejpam-3258	329	3	particular	particular	ADJ
ejpam-3258	329	4	example	example	NOUN
ejpam-3258	329	5	,	,	PUNCT
ejpam-3258	329	6	we	we	PRON
ejpam-3258	329	7	have	have	AUX
ejpam-3258	329	8	obtained	obtain	VERB
ejpam-3258	329	9	an	an	DET
ejpam-3258	329	10	upper	upper	ADJ
ejpam-3258	329	11	bound	bind	VERB
ejpam-3258	329	12	µupperpd	µupperpd	NOUN
ejpam-3258	329	13	=	=	NOUN
ejpam-3258	329	14	1.0000	1.0000	NUM
ejpam-3258	329	15	while	while	SCONJ
ejpam-3258	329	16	lower	low	ADJ
ejpam-3258	329	17	bound	bound	ADJ
ejpam-3258	329	18	is	be	AUX
ejpam-3258	329	19	approximated	approximate	VERB
ejpam-3258	329	20	,	,	PUNCT
ejpam-3258	329	21	that	that	ADV
ejpam-3258	329	22	is	is	ADV
ejpam-3258	329	23	,	,	PUNCT
ejpam-3258	329	24	µlowerpd	µlowerpd	NOUN
ejpam-3258	329	25	=	=	SYM
ejpam-3258	329	26	1.0000	1.0000	NUM
ejpam-3258	329	27	.	.	PUNCT
ejpam-3258	330	1	now	now	ADV
ejpam-3258	330	2	,	,	PUNCT
ejpam-3258	330	3	by	by	ADP
ejpam-3258	330	4	making	make	VERB
ejpam-3258	330	5	use	use	NOUN
ejpam-3258	330	6	of	of	ADP
ejpam-3258	330	7	algorithm	algorithm	NOUN
ejpam-3258	330	8	[	[	X
ejpam-3258	330	9	14	14	NUM
ejpam-3258	330	10	]	]	PUNCT
ejpam-3258	330	11	,	,	PUNCT
ejpam-3258	330	12	we	we	PRON
ejpam-3258	330	13	have	have	AUX
ejpam-3258	330	14	obtained	obtain	VERB
ejpam-3258	330	15	obtain	obtain	VERB
ejpam-3258	330	16	the	the	DET
ejpam-3258	330	17	perturbation	perturbation	NOUN
ejpam-3258	330	18	structure	structure	NOUN
ejpam-3258	330	19	ε∗∆∗	ε∗∆∗	NOUN
ejpam-3258	330	20	with	with	ADP
ejpam-3258	330	21	∆∗	∆∗	NOUN
ejpam-3258	330	22	=	=	SYM
ejpam-3258	330	23	−0.5000	−0.5000	ADJ
ejpam-3258	330	24	−0.5000	−0.5000	NUM
ejpam-3258	330	25	0.0000	0.0000	NUM
ejpam-3258	331	1	−0.5000	−0.5000	NUM
ejpam-3258	332	1	−0.5000	−0.5000	NUM
ejpam-3258	332	2	0.0000	0.0000	NUM
ejpam-3258	332	3	0.0000	0.0000	NUM
ejpam-3258	332	4	0.0000	0.0000	NUM
ejpam-3258	332	5	0.0000	0.0000	NUM
ejpam-3258	332	6			NOUN
ejpam-3258	332	7	.	.	PUNCT
ejpam-3258	333	1	references	reference	NOUN
ejpam-3258	333	2	788	788	NUM
ejpam-3258	333	3	here	here	ADV
ejpam-3258	333	4	,	,	PUNCT
ejpam-3258	333	5	ε∗	ε∗	PROPN
ejpam-3258	333	6	=	=	SYM
ejpam-3258	333	7	1.0000	1.0000	NUM
ejpam-3258	333	8	and	and	CCONJ
ejpam-3258	333	9	‖∆∗‖2	‖∆∗‖2	NOUN
ejpam-3258	333	10	=	=	SYM
ejpam-3258	333	11	1	1	NUM
ejpam-3258	333	12	,	,	PUNCT
ejpam-3258	333	13	while	while	SCONJ
ejpam-3258	333	14	a	a	DET
ejpam-3258	333	15	same	same	ADJ
ejpam-3258	333	16	lower	low	ADJ
ejpam-3258	333	17	bound	bind	VERB
ejpam-3258	333	18	is	be	AUX
ejpam-3258	333	19	approximated	approximate	VERB
ejpam-3258	333	20	,	,	PUNCT
ejpam-3258	333	21	that	that	ADV
ejpam-3258	333	22	is	is	ADV
ejpam-3258	333	23	,	,	PUNCT
ejpam-3258	333	24	µlowernew	µlowernew	ADJ
ejpam-3258	333	25	=	=	NOUN
ejpam-3258	333	26	1.0000	1.0000	NUM
ejpam-3258	333	27	as	as	ADP
ejpam-3258	333	28	the	the	DET
ejpam-3258	333	29	one	one	NOUN
ejpam-3258	333	30	obtained	obtain	VERB
ejpam-3258	333	31	by	by	ADP
ejpam-3258	333	32	mussv	mussv	ADJ
ejpam-3258	333	33	function	function	PROPN
ejpam-3258	333	34	.	.	PUNCT
ejpam-3258	334	1	example	example	NOUN
ejpam-3258	334	2	8	8	NUM
ejpam-3258	334	3	.	.	PUNCT
ejpam-3258	335	1	in	in	ADP
ejpam-3258	335	2	figure	figure	NOUN
ejpam-3258	335	3	3	3	NUM
ejpam-3258	335	4	,	,	PUNCT
ejpam-3258	335	5	we	we	PRON
ejpam-3258	335	6	show	show	VERB
ejpam-3258	335	7	the	the	DET
ejpam-3258	335	8	comparison	comparison	NOUN
ejpam-3258	335	9	of	of	ADP
ejpam-3258	335	10	lower	low	ADJ
ejpam-3258	335	11	bounds	bound	NOUN
ejpam-3258	335	12	computed	compute	VERB
ejpam-3258	335	13	by	by	ADP
ejpam-3258	335	14	algorithm	algorithm	NOUN
ejpam-3258	335	15	algorithm	algorithm	NOUN
ejpam-3258	336	1	[	[	X
ejpam-3258	336	2	14	14	NUM
ejpam-3258	336	3	]	]	PUNCT
ejpam-3258	336	4	with	with	ADP
ejpam-3258	336	5	the	the	DET
ejpam-3258	336	6	bounds	bound	NOUN
ejpam-3258	336	7	(	(	PUNCT
ejpam-3258	336	8	lower	low	ADJ
ejpam-3258	336	9	and	and	CCONJ
ejpam-3258	336	10	upper	upper	ADJ
ejpam-3258	336	11	)	)	PUNCT
ejpam-3258	336	12	computed	compute	VERB
ejpam-3258	336	13	by	by	ADP
ejpam-3258	336	14	mussv	mussv	ADJ
ejpam-3258	336	15	function	function	NOUN
ejpam-3258	336	16	for	for	ADP
ejpam-3258	336	17	matrix	matrix	NOUN
ejpam-3258	336	18	valued	value	VERB
ejpam-3258	336	19	function	function	NOUN
ejpam-3258	336	20	a3(w	a3(w	NOUN
ejpam-3258	336	21	)	)	PUNCT
ejpam-3258	336	22	for	for	ADP
ejpam-3258	336	23	w	w	NOUN
ejpam-3258	336	24	=	=	SYM
ejpam-3258	336	25	1	1	NUM
ejpam-3258	336	26	:	:	SYM
ejpam-3258	336	27	5	5	NUM
ejpam-3258	336	28	,	,	PUNCT
ejpam-3258	336	29	where	where	SCONJ
ejpam-3258	336	30	w	w	PROPN
ejpam-3258	336	31	∈	∈	PROPN
ejpam-3258	336	32	ω	ω	PROPN
ejpam-3258	336	33	and	and	CCONJ
ejpam-3258	336	34	ω	ω	PROPN
ejpam-3258	336	35	denotes	denote	VERB
ejpam-3258	336	36	the	the	DET
ejpam-3258	336	37	frequency	frequency	NOUN
ejpam-3258	336	38	range	range	NOUN
ejpam-3258	336	39	of	of	ADP
ejpam-3258	336	40	interest	interest	NOUN
ejpam-3258	336	41	which	which	PRON
ejpam-3258	336	42	is	be	AUX
ejpam-3258	336	43	usually	usually	ADV
ejpam-3258	336	44	r+	r+	X
ejpam-3258	336	45	.	.	PUNCT
ejpam-3258	337	1	the	the	DET
ejpam-3258	337	2	frequency	frequency	NOUN
ejpam-3258	337	3	response	response	NOUN
ejpam-3258	337	4	w	w	NOUN
ejpam-3258	337	5	is	be	AUX
ejpam-3258	337	6	the	the	DET
ejpam-3258	337	7	quantitative	quantitative	ADJ
ejpam-3258	337	8	measure	measure	NOUN
ejpam-3258	337	9	of	of	ADP
ejpam-3258	337	10	output	output	NOUN
ejpam-3258	337	11	of	of	ADP
ejpam-3258	337	12	(	(	PUNCT
ejpam-3258	337	13	m	m	PROPN
ejpam-3258	337	14	−∆	−∆	NOUN
ejpam-3258	337	15	)	)	PUNCT
ejpam-3258	337	16	system	system	NOUN
ejpam-3258	337	17	.	.	PUNCT
ejpam-3258	338	1	we	we	PRON
ejpam-3258	338	2	use	use	VERB
ejpam-3258	338	3	mussv	mussv	ADJ
ejpam-3258	338	4	function	function	NOUN
ejpam-3258	338	5	to	to	PART
ejpam-3258	338	6	compute	compute	VERB
ejpam-3258	338	7	µ	µ	PRON
ejpam-3258	338	8	as	as	ADP
ejpam-3258	338	9	a	a	DET
ejpam-3258	338	10	function	function	NOUN
ejpam-3258	338	11	of	of	ADP
ejpam-3258	338	12	frequency	frequency	NOUN
ejpam-3258	338	13	response	response	NOUN
ejpam-3258	338	14	.	.	PUNCT
ejpam-3258	339	1	6	6	X
ejpam-3258	339	2	.	.	X
ejpam-3258	339	3	conclusion	conclusion	NOUN
ejpam-3258	339	4	we	we	PRON
ejpam-3258	339	5	have	have	AUX
ejpam-3258	339	6	considered	consider	VERB
ejpam-3258	339	7	the	the	DET
ejpam-3258	339	8	approximation	approximation	NOUN
ejpam-3258	339	9	of	of	ADP
ejpam-3258	339	10	ssv	ssv	NOUN
ejpam-3258	339	11	for	for	ADP
ejpam-3258	339	12	the	the	DET
ejpam-3258	339	13	matrix	matrix	NOUN
ejpam-3258	339	14	representations	representation	NOUN
ejpam-3258	339	15	of	of	ADP
ejpam-3258	339	16	finite	finite	ADJ
ejpam-3258	339	17	symmetric	symmetric	ADJ
ejpam-3258	339	18	groups	group	NOUN
ejpam-3258	339	19	s3	s3	PROPN
ejpam-3258	339	20	and	and	CCONJ
ejpam-3258	339	21	s4	s4	PROPN
ejpam-3258	339	22	over	over	ADP
ejpam-3258	339	23	the	the	DET
ejpam-3258	339	24	filed	file	VERB
ejpam-3258	339	25	of	of	ADP
ejpam-3258	339	26	complex	complex	ADJ
ejpam-3258	339	27	numbers	number	NOUN
ejpam-3258	339	28	.	.	PUNCT
ejpam-3258	340	1	for	for	ADP
ejpam-3258	340	2	the	the	DET
ejpam-3258	340	3	comparison	comparison	NOUN
ejpam-3258	340	4	of	of	ADP
ejpam-3258	340	5	bounds	bound	NOUN
ejpam-3258	340	6	of	of	ADP
ejpam-3258	340	7	ssv	ssv	NOUN
ejpam-3258	340	8	,	,	PUNCT
ejpam-3258	340	9	we	we	PRON
ejpam-3258	340	10	have	have	AUX
ejpam-3258	340	11	done	do	VERB
ejpam-3258	340	12	experiments	experiment	NOUN
ejpam-3258	340	13	on	on	ADP
ejpam-3258	340	14	family	family	NOUN
ejpam-3258	340	15	of	of	ADP
ejpam-3258	340	16	matrices	matrix	NOUN
ejpam-3258	340	17	.	.	PUNCT
ejpam-3258	341	1	the	the	DET
ejpam-3258	341	2	experimental	experimental	ADJ
ejpam-3258	341	3	results	result	NOUN
ejpam-3258	341	4	shows	show	VERB
ejpam-3258	341	5	the	the	DET
ejpam-3258	341	6	comparison	comparison	NOUN
ejpam-3258	341	7	of	of	ADP
ejpam-3258	341	8	both	both	CCONJ
ejpam-3258	341	9	lower	low	ADJ
ejpam-3258	341	10	and	and	CCONJ
ejpam-3258	341	11	upper	upper	ADJ
ejpam-3258	341	12	bounds	bound	NOUN
ejpam-3258	341	13	with	with	ADP
ejpam-3258	341	14	once	once	ADV
ejpam-3258	341	15	computed	compute	VERB
ejpam-3258	341	16	by	by	ADP
ejpam-3258	341	17	matlab	matlab	PROPN
ejpam-3258	341	18	funtion	funtion	PROPN
ejpam-3258	341	19	mussv	mussv	NOUN
ejpam-3258	341	20	and	and	CCONJ
ejpam-3258	341	21	our	our	PRON
ejpam-3258	341	22	numerical	numerical	ADJ
ejpam-3258	341	23	alogorithm	alogorithm	NOUN
ejpam-3258	342	1	[	[	X
ejpam-3258	342	2	14	14	NUM
ejpam-3258	342	3	]	]	PUNCT
ejpam-3258	342	4	.	.	PUNCT
ejpam-3258	343	1	references	reference	NOUN
ejpam-3258	343	2	[	[	X
ejpam-3258	343	3	1	1	NUM
ejpam-3258	343	4	]	]	PUNCT
ejpam-3258	343	5	bernhardsson	bernhardsson	NOUN
ejpam-3258	343	6	,	,	PUNCT
ejpam-3258	343	7	bo	bo	PROPN
ejpam-3258	343	8	and	and	CCONJ
ejpam-3258	343	9	rantzer	rantzer	VERB
ejpam-3258	343	10	,	,	PUNCT
ejpam-3258	343	11	anders	ander	NOUN
ejpam-3258	343	12	and	and	CCONJ
ejpam-3258	343	13	qiu	qiu	PROPN
ejpam-3258	343	14	,	,	PUNCT
ejpam-3258	343	15	li	li	PROPN
ejpam-3258	343	16	.	.	PROPN
ejpam-3258	343	17	real	real	ADJ
ejpam-3258	343	18	perturbation	perturbation	NOUN
ejpam-3258	343	19	values	value	NOUN
ejpam-3258	343	20	and	and	CCONJ
ejpam-3258	343	21	real	real	ADJ
ejpam-3258	343	22	quadratic	quadratic	ADJ
ejpam-3258	343	23	forms	form	NOUN
ejpam-3258	343	24	in	in	ADP
ejpam-3258	343	25	a	a	DET
ejpam-3258	343	26	complex	complex	ADJ
ejpam-3258	343	27	vector	vector	NOUN
ejpam-3258	343	28	space	space	NOUN
ejpam-3258	343	29	.	.	PUNCT
ejpam-3258	344	1	linear	linear	ADJ
ejpam-3258	344	2	algebra	algebra	NOUN
ejpam-3258	344	3	and	and	CCONJ
ejpam-3258	344	4	its	its	PRON
ejpam-3258	344	5	applications	application	NOUN
ejpam-3258	344	6	,	,	PUNCT
ejpam-3258	344	7	volume	volume	NOUN
ejpam-3258	344	8	1	1	NUM
ejpam-3258	344	9	:	:	PUNCT
ejpam-3258	344	10	131	131	NUM
ejpam-3258	344	11	-	-	SYM
ejpam-3258	344	12	154	154	NUM
ejpam-3258	344	13	,	,	PUNCT
ejpam-3258	344	14	1994	1994	NUM
ejpam-3258	344	15	.	.	PUNCT
ejpam-3258	345	1	[	[	X
ejpam-3258	345	2	2	2	NUM
ejpam-3258	345	3	]	]	PUNCT
ejpam-3258	345	4	braatz	braatz	PROPN
ejpam-3258	345	5	,	,	PUNCT
ejpam-3258	345	6	richard	richard	PROPN
ejpam-3258	345	7	p	p	PROPN
ejpam-3258	345	8	and	and	CCONJ
ejpam-3258	345	9	young	young	ADJ
ejpam-3258	345	10	,	,	PUNCT
ejpam-3258	345	11	peter	peter	PROPN
ejpam-3258	345	12	m	m	PROPN
ejpam-3258	345	13	and	and	CCONJ
ejpam-3258	345	14	doyle	doyle	PROPN
ejpam-3258	345	15	,	,	PUNCT
ejpam-3258	345	16	john	john	PROPN
ejpam-3258	345	17	c	c	PROPN
ejpam-3258	345	18	and	and	CCONJ
ejpam-3258	345	19	morari	morari	PROPN
ejpam-3258	345	20	,	,	PUNCT
ejpam-3258	345	21	manfred	manfre	VERB
ejpam-3258	345	22	.	.	PUNCT
ejpam-3258	346	1	computational	computational	ADJ
ejpam-3258	346	2	complexity	complexity	NOUN
ejpam-3258	346	3	of	of	ADP
ejpam-3258	346	4	µ	µ	DET
ejpam-3258	346	5	calculation	calculation	NOUN
ejpam-3258	346	6	.	.	PUNCT
ejpam-3258	347	1	automatic	automatic	ADJ
ejpam-3258	347	2	control	control	NOUN
ejpam-3258	347	3	,	,	PUNCT
ejpam-3258	347	4	ieee	ieee	NOUN
ejpam-3258	347	5	transactions	transaction	NOUN
ejpam-3258	347	6	on	on	ADP
ejpam-3258	347	7	,	,	PUNCT
ejpam-3258	347	8	volume	volume	NOUN
ejpam-3258	347	9	39	39	NUM
ejpam-3258	347	10	:	:	PUNCT
ejpam-3258	347	11	1000	1000	NUM
ejpam-3258	347	12	-	-	SYM
ejpam-3258	347	13	1002	1002	NUM
ejpam-3258	347	14	,	,	PUNCT
ejpam-3258	347	15	1994	1994	NUM
ejpam-3258	347	16	.	.	PUNCT
ejpam-3258	348	1	[	[	X
ejpam-3258	348	2	3	3	NUM
ejpam-3258	348	3	]	]	X
ejpam-3258	348	4	chen	chen	PROPN
ejpam-3258	348	5	,	,	PUNCT
ejpam-3258	348	6	jie	jie	PROPN
ejpam-3258	348	7	and	and	CCONJ
ejpam-3258	348	8	fan	fan	PROPN
ejpam-3258	348	9	,	,	PUNCT
ejpam-3258	348	10	michael	michael	PROPN
ejpam-3258	348	11	kh	kh	PROPN
ejpam-3258	348	12	and	and	CCONJ
ejpam-3258	348	13	nett	nett	PROPN
ejpam-3258	348	14	,	,	PUNCT
ejpam-3258	348	15	carl	carl	PROPN
ejpam-3258	348	16	n.	n.	PROPN
ejpam-3258	348	17	structured	structure	VERB
ejpam-3258	348	18	singular	singular	ADJ
ejpam-3258	348	19	values	value	NOUN
ejpam-3258	348	20	with	with	ADP
ejpam-3258	348	21	nondiagonal	nondiagonal	ADJ
ejpam-3258	348	22	structures	structure	NOUN
ejpam-3258	348	23	.	.	PUNCT
ejpam-3258	349	1	i.	i.	PROPN
ejpam-3258	349	2	characterizations	characterization	NOUN
ejpam-3258	349	3	.	.	PUNCT
ejpam-3258	350	1	automatic	automatic	ADJ
ejpam-3258	350	2	control	control	NOUN
ejpam-3258	350	3	,	,	PUNCT
ejpam-3258	350	4	ieee	ieee	NOUN
ejpam-3258	350	5	transactions	transaction	NOUN
ejpam-3258	350	6	on	on	ADP
ejpam-3258	350	7	,	,	PUNCT
ejpam-3258	350	8	volume	volume	NOUN
ejpam-3258	350	9	41	41	NUM
ejpam-3258	350	10	:	:	PUNCT
ejpam-3258	350	11	1507	1507	NUM
ejpam-3258	350	12	-	-	SYM
ejpam-3258	350	13	1511	1511	NUM
ejpam-3258	350	14	,	,	PUNCT
ejpam-3258	350	15	1996	1996	NUM
ejpam-3258	350	16	.	.	PUNCT
ejpam-3258	351	1	[	[	X
ejpam-3258	351	2	4	4	NUM
ejpam-3258	351	3	]	]	X
ejpam-3258	351	4	dabbaghian	dabbaghian	ADJ
ejpam-3258	351	5	-	-	PUNCT
ejpam-3258	351	6	abdoly	abdoly	ADJ
ejpam-3258	351	7	,	,	PUNCT
ejpam-3258	351	8	vahid	vahid	PROPN
ejpam-3258	351	9	.	.	PUNCT
ejpam-3258	352	1	an	an	DET
ejpam-3258	352	2	algorithm	algorithm	NOUN
ejpam-3258	352	3	for	for	ADP
ejpam-3258	352	4	constructing	construct	VERB
ejpam-3258	352	5	representations	representation	NOUN
ejpam-3258	352	6	of	of	ADP
ejpam-3258	352	7	finite	finite	ADJ
ejpam-3258	352	8	groups	group	NOUN
ejpam-3258	352	9	.	.	PUNCT
ejpam-3258	353	1	journal	journal	PROPN
ejpam-3258	353	2	of	of	ADP
ejpam-3258	353	3	symbolic	symbolic	ADJ
ejpam-3258	353	4	computation	computation	NOUN
ejpam-3258	353	5	39.6	39.6	NUM
ejpam-3258	353	6	(	(	PUNCT
ejpam-3258	353	7	2005	2005	NUM
ejpam-3258	353	8	):	):	PUNCT
ejpam-3258	353	9	671	671	NUM
ejpam-3258	353	10	-	-	SYM
ejpam-3258	353	11	688	688	NUM
ejpam-3258	353	12	.	.	PUNCT
ejpam-3258	354	1	[	[	X
ejpam-3258	354	2	5	5	NUM
ejpam-3258	354	3	]	]	X
ejpam-3258	354	4	danielson	danielson	NOUN
ejpam-3258	354	5	,	,	PUNCT
ejpam-3258	354	6	claus	claus	PROPN
ejpam-3258	354	7	robert	robert	PROPN
ejpam-3258	354	8	.	.	PROPN
ejpam-3258	354	9	symmetric	symmetric	PROPN
ejpam-3258	354	10	constrained	constrain	VERB
ejpam-3258	354	11	optimal	optimal	ADJ
ejpam-3258	354	12	control	control	NOUN
ejpam-3258	354	13	:	:	PUNCT
ejpam-3258	354	14	theory	theory	NOUN
ejpam-3258	354	15	,	,	PUNCT
ejpam-3258	354	16	algorithms	algorithm	NOUN
ejpam-3258	354	17	,	,	PUNCT
ejpam-3258	354	18	and	and	CCONJ
ejpam-3258	354	19	applications	application	NOUN
ejpam-3258	354	20	.	.	PUNCT
ejpam-3258	355	1	university	university	PROPN
ejpam-3258	355	2	of	of	ADP
ejpam-3258	355	3	california	california	PROPN
ejpam-3258	355	4	,	,	PUNCT
ejpam-3258	355	5	berkeley	berkeley	PROPN
ejpam-3258	355	6	,	,	PUNCT
ejpam-3258	355	7	2014	2014	NUM
ejpam-3258	355	8	.	.	PUNCT
ejpam-3258	356	1	[	[	X
ejpam-3258	356	2	6	6	NUM
ejpam-3258	356	3	]	]	SYM
ejpam-3258	356	4	fan	fan	PROPN
ejpam-3258	356	5	,	,	PUNCT
ejpam-3258	356	6	michael	michael	PROPN
ejpam-3258	356	7	kh	kh	PROPN
ejpam-3258	356	8	and	and	CCONJ
ejpam-3258	356	9	tits	tit	NOUN
ejpam-3258	356	10	,	,	PUNCT
ejpam-3258	356	11	andré	andré	ADJ
ejpam-3258	356	12	l	l	NOUN
ejpam-3258	356	13	and	and	CCONJ
ejpam-3258	356	14	doyle	doyle	NOUN
ejpam-3258	356	15	,	,	PUNCT
ejpam-3258	356	16	john	john	PROPN
ejpam-3258	356	17	c.	c.	PROPN
ejpam-3258	356	18	robustness	robustness	NOUN
ejpam-3258	356	19	in	in	ADP
ejpam-3258	356	20	the	the	DET
ejpam-3258	356	21	presence	presence	NOUN
ejpam-3258	356	22	of	of	ADP
ejpam-3258	356	23	mixed	mixed	ADJ
ejpam-3258	356	24	parametric	parametric	ADJ
ejpam-3258	356	25	uncertainty	uncertainty	NOUN
ejpam-3258	356	26	and	and	CCONJ
ejpam-3258	356	27	unmodeled	unmodeled	ADJ
ejpam-3258	356	28	dynamics	dynamic	NOUN
ejpam-3258	356	29	.	.	PUNCT
ejpam-3258	357	1	automatic	automatic	ADJ
ejpam-3258	357	2	control	control	NOUN
ejpam-3258	357	3	,	,	PUNCT
ejpam-3258	357	4	ieee	ieee	NOUN
ejpam-3258	357	5	transactions	transaction	NOUN
ejpam-3258	357	6	on	on	ADP
ejpam-3258	357	7	,	,	PUNCT
ejpam-3258	357	8	volume	volume	NOUN
ejpam-3258	357	9	36	36	NUM
ejpam-3258	357	10	:	:	PUNCT
ejpam-3258	357	11	25	25	NUM
ejpam-3258	357	12	-	-	SYM
ejpam-3258	357	13	38	38	NUM
ejpam-3258	357	14	,	,	PUNCT
ejpam-3258	357	15	1991	1991	NUM
ejpam-3258	357	16	.	.	PUNCT
ejpam-3258	358	1	[	[	X
ejpam-3258	358	2	7	7	X
ejpam-3258	358	3	]	]	PUNCT
ejpam-3258	358	4	the	the	DET
ejpam-3258	358	5	gap	gap	NOUN
ejpam-3258	358	6	group	group	NOUN
ejpam-3258	358	7	,	,	PUNCT
ejpam-3258	358	8	gap	gap	NOUN
ejpam-3258	358	9	–	–	PUNCT
ejpam-3258	358	10	groups	group	NOUN
ejpam-3258	358	11	,	,	PUNCT
ejpam-3258	358	12	algorithms	algorithm	NOUN
ejpam-3258	358	13	,	,	PUNCT
ejpam-3258	358	14	and	and	CCONJ
ejpam-3258	358	15	programming	programming	NOUN
ejpam-3258	358	16	,	,	PUNCT
ejpam-3258	358	17	version	version	NOUN
ejpam-3258	358	18	4.8.10	4.8.10	NUM
ejpam-3258	358	19	;	;	PUNCT
ejpam-3258	358	20	2018	2018	NUM
ejpam-3258	358	21	,	,	PUNCT
ejpam-3258	358	22	(	(	PUNCT
ejpam-3258	358	23	https://www.gap-system.org	https://www.gap-system.org	ADJ
ejpam-3258	358	24	)	)	PUNCT
ejpam-3258	358	25	.	.	PUNCT
ejpam-3258	359	1	appendix	appendix	VERB
ejpam-3258	359	2	789	789	NUM
ejpam-3258	359	3	[	[	SYM
ejpam-3258	359	4	8	8	NUM
ejpam-3258	359	5	]	]	X
ejpam-3258	359	6	hinrichsen	hinrichsen	NOUN
ejpam-3258	359	7	,	,	PUNCT
ejpam-3258	359	8	d	d	NOUN
ejpam-3258	359	9	and	and	CCONJ
ejpam-3258	359	10	pritchard	pritchard	PROPN
ejpam-3258	359	11	,	,	PUNCT
ejpam-3258	359	12	aj	aj	PROPN
ejpam-3258	359	13	.	.	PROPN
ejpam-3258	359	14	mathematical	mathematical	PROPN
ejpam-3258	359	15	systems	systems	PROPN
ejpam-3258	359	16	theory	theory	NOUN
ejpam-3258	359	17	i	i	PRON
ejpam-3258	359	18	,	,	PUNCT
ejpam-3258	359	19	vol	vol	NOUN
ejpam-3258	359	20	.	.	PROPN
ejpam-3258	359	21	48	48	NUM
ejpam-3258	359	22	of	of	ADP
ejpam-3258	359	23	texts	text	NOUN
ejpam-3258	359	24	in	in	ADP
ejpam-3258	359	25	applied	applied	ADJ
ejpam-3258	359	26	mathematics	mathematic	NOUN
ejpam-3258	359	27	.	.	PUNCT
ejpam-3258	360	1	springer	springer	NOUN
ejpam-3258	360	2	-	-	PUNCT
ejpam-3258	360	3	verlag	verlag	PROPN
ejpam-3258	360	4	,	,	PUNCT
ejpam-3258	360	5	berlin	berlin	PROPN
ejpam-3258	360	6	volume	volume	NOUN
ejpam-3258	360	7	48	48	NUM
ejpam-3258	360	8	:	:	SYM
ejpam-3258	360	9	2005	2005	NUM
ejpam-3258	360	10	.	.	PUNCT
ejpam-3258	361	1	[	[	X
ejpam-3258	361	2	9	9	NUM
ejpam-3258	361	3	]	]	SYM
ejpam-3258	361	4	karow	karow	PROPN
ejpam-3258	361	5	,	,	PUNCT
ejpam-3258	361	6	michael	michael	PROPN
ejpam-3258	361	7	and	and	CCONJ
ejpam-3258	361	8	kokiopoulou	kokiopoulou	PROPN
ejpam-3258	361	9	,	,	PUNCT
ejpam-3258	361	10	effrosyni	effrosyni	NOUN
ejpam-3258	361	11	and	and	CCONJ
ejpam-3258	361	12	kressner	kressner	NOUN
ejpam-3258	361	13	,	,	PUNCT
ejpam-3258	361	14	daniel	daniel	PROPN
ejpam-3258	361	15	.	.	PUNCT
ejpam-3258	362	1	on	on	ADP
ejpam-3258	362	2	the	the	DET
ejpam-3258	362	3	computation	computation	NOUN
ejpam-3258	362	4	of	of	ADP
ejpam-3258	362	5	structured	structured	ADJ
ejpam-3258	362	6	singular	singular	ADJ
ejpam-3258	362	7	values	value	NOUN
ejpam-3258	362	8	and	and	CCONJ
ejpam-3258	362	9	pseudospectra	pseudospectra	NOUN
ejpam-3258	362	10	.	.	PUNCT
ejpam-3258	363	1	systems	system	NOUN
ejpam-3258	363	2	&	&	CCONJ
ejpam-3258	363	3	control	control	PROPN
ejpam-3258	363	4	letters	letter	NOUN
ejpam-3258	363	5	volume	volume	VERB
ejpam-3258	363	6	59	59	NUM
ejpam-3258	363	7	:	:	SYM
ejpam-3258	363	8	122	122	NUM
ejpam-3258	363	9	-	-	SYM
ejpam-3258	363	10	129	129	NUM
ejpam-3258	363	11	,	,	PUNCT
ejpam-3258	363	12	2010	2010	NUM
ejpam-3258	363	13	.	.	PUNCT
ejpam-3258	364	1	[	[	X
ejpam-3258	364	2	10	10	NUM
ejpam-3258	364	3	]	]	SYM
ejpam-3258	364	4	karow	karow	PROPN
ejpam-3258	364	5	,	,	PUNCT
ejpam-3258	364	6	michael	michael	PROPN
ejpam-3258	364	7	and	and	CCONJ
ejpam-3258	364	8	kressner	kressner	PROPN
ejpam-3258	364	9	,	,	PUNCT
ejpam-3258	364	10	daniel	daniel	PROPN
ejpam-3258	364	11	and	and	CCONJ
ejpam-3258	364	12	tisseur	tisseur	PROPN
ejpam-3258	364	13	,	,	PUNCT
ejpam-3258	364	14	françoise	françoise	PROPN
ejpam-3258	364	15	.	.	PUNCT
ejpam-3258	365	1	structured	structure	VERB
ejpam-3258	365	2	eigenvalue	eigenvalue	NOUN
ejpam-3258	365	3	condition	condition	NOUN
ejpam-3258	365	4	numbers	number	NOUN
ejpam-3258	365	5	.	.	PUNCT
ejpam-3258	366	1	siam	siam	PROPN
ejpam-3258	366	2	journal	journal	PROPN
ejpam-3258	366	3	on	on	ADP
ejpam-3258	366	4	matrix	matrix	NOUN
ejpam-3258	366	5	analysis	analysis	NOUN
ejpam-3258	366	6	and	and	CCONJ
ejpam-3258	366	7	applications	application	NOUN
ejpam-3258	366	8	volume	volume	NOUN
ejpam-3258	366	9	28	28	NUM
ejpam-3258	366	10	:	:	SYM
ejpam-3258	366	11	1052	1052	NUM
ejpam-3258	366	12	-	-	SYM
ejpam-3258	366	13	1068	1068	NUM
ejpam-3258	366	14	,	,	PUNCT
ejpam-3258	366	15	2006	2006	NUM
ejpam-3258	366	16	.	.	PUNCT
ejpam-3258	367	1	[	[	X
ejpam-3258	367	2	11	11	NUM
ejpam-3258	367	3	]	]	X
ejpam-3258	367	4	packard	packard	NOUN
ejpam-3258	367	5	,	,	PUNCT
ejpam-3258	367	6	andrew	andrew	PROPN
ejpam-3258	367	7	and	and	CCONJ
ejpam-3258	367	8	doyle	doyle	PROPN
ejpam-3258	367	9	,	,	PUNCT
ejpam-3258	367	10	john	john	PROPN
ejpam-3258	367	11	.	.	PUNCT
ejpam-3258	368	1	the	the	DET
ejpam-3258	368	2	complex	complex	ADJ
ejpam-3258	368	3	structured	structured	ADJ
ejpam-3258	368	4	singular	singular	ADJ
ejpam-3258	368	5	value	value	NOUN
ejpam-3258	368	6	.	.	PUNCT
ejpam-3258	369	1	automatica	automatica	PROPN
ejpam-3258	369	2	volume	volume	NOUN
ejpam-3258	369	3	29	29	NUM
ejpam-3258	369	4	:	:	PUNCT
ejpam-3258	369	5	71	71	NUM
ejpam-3258	369	6	-	-	SYM
ejpam-3258	369	7	109	109	NUM
ejpam-3258	369	8	,	,	PUNCT
ejpam-3258	369	9	1993	1993	NUM
ejpam-3258	369	10	.	.	PUNCT
ejpam-3258	370	1	[	[	X
ejpam-3258	370	2	12	12	NUM
ejpam-3258	370	3	]	]	X
ejpam-3258	370	4	packard	packard	NOUN
ejpam-3258	370	5	,	,	PUNCT
ejpam-3258	370	6	andy	andy	PROPN
ejpam-3258	370	7	and	and	CCONJ
ejpam-3258	370	8	fan	fan	PROPN
ejpam-3258	370	9	,	,	PUNCT
ejpam-3258	370	10	michael	michael	PROPN
ejpam-3258	370	11	kh	kh	PROPN
ejpam-3258	370	12	and	and	CCONJ
ejpam-3258	370	13	doyle	doyle	PROPN
ejpam-3258	370	14	,	,	PUNCT
ejpam-3258	370	15	john	john	PROPN
ejpam-3258	370	16	.	.	PUNCT
ejpam-3258	371	1	a	a	DET
ejpam-3258	371	2	power	power	NOUN
ejpam-3258	371	3	method	method	NOUN
ejpam-3258	371	4	for	for	ADP
ejpam-3258	371	5	the	the	DET
ejpam-3258	371	6	structured	structured	ADJ
ejpam-3258	371	7	singular	singular	NOUN
ejpam-3258	371	8	value	value	NOUN
ejpam-3258	371	9	.	.	PUNCT
ejpam-3258	372	1	decision	decision	NOUN
ejpam-3258	372	2	and	and	CCONJ
ejpam-3258	372	3	control	control	NOUN
ejpam-3258	372	4	,	,	PUNCT
ejpam-3258	372	5	1988	1988	NUM
ejpam-3258	372	6	.	.	PUNCT
ejpam-3258	373	1	,	,	PUNCT
ejpam-3258	373	2	proceedings	proceeding	NOUN
ejpam-3258	373	3	of	of	ADP
ejpam-3258	373	4	the	the	DET
ejpam-3258	373	5	27th	27th	ADJ
ejpam-3258	373	6	ieee	ieee	NOUN
ejpam-3258	373	7	conference	conference	NOUN
ejpam-3258	373	8	on	on	ADP
ejpam-3258	373	9	,	,	PUNCT
ejpam-3258	373	10	2132	2132	NUM
ejpam-3258	373	11	-	-	SYM
ejpam-3258	373	12	2137	2137	NUM
ejpam-3258	373	13	,	,	PUNCT
ejpam-3258	373	14	1998	1998	NUM
ejpam-3258	373	15	.	.	PUNCT
ejpam-3258	374	1	[	[	X
ejpam-3258	374	2	13	13	NUM
ejpam-3258	374	3	]	]	X
ejpam-3258	374	4	qiu	qiu	PROPN
ejpam-3258	374	5	,	,	PUNCT
ejpam-3258	374	6	li	li	PROPN
ejpam-3258	374	7	and	and	CCONJ
ejpam-3258	374	8	bernhardsson	bernhardsson	PROPN
ejpam-3258	374	9	,	,	PUNCT
ejpam-3258	374	10	bo	bo	PROPN
ejpam-3258	374	11	and	and	CCONJ
ejpam-3258	374	12	rantzer	rantzer	VERB
ejpam-3258	374	13	,	,	PUNCT
ejpam-3258	374	14	anders	ander	NOUN
ejpam-3258	374	15	and	and	CCONJ
ejpam-3258	374	16	davison	davison	PROPN
ejpam-3258	374	17	,	,	PUNCT
ejpam-3258	374	18	ej	ej	PROPN
ejpam-3258	374	19	and	and	CCONJ
ejpam-3258	374	20	young	young	ADJ
ejpam-3258	374	21	,	,	PUNCT
ejpam-3258	374	22	pm	pm	NOUN
ejpam-3258	374	23	and	and	CCONJ
ejpam-3258	374	24	doyle	doyle	NOUN
ejpam-3258	374	25	,	,	PUNCT
ejpam-3258	374	26	jc	jc	PROPN
ejpam-3258	374	27	.	.	PROPN
ejpam-3258	375	1	a	a	DET
ejpam-3258	375	2	formula	formula	NOUN
ejpam-3258	375	3	for	for	ADP
ejpam-3258	375	4	computation	computation	NOUN
ejpam-3258	375	5	of	of	ADP
ejpam-3258	375	6	the	the	DET
ejpam-3258	375	7	real	real	ADJ
ejpam-3258	375	8	stability	stability	NOUN
ejpam-3258	375	9	radius	radius	NOUN
ejpam-3258	375	10	.	.	PUNCT
ejpam-3258	376	1	automatica	automatica	PROPN
ejpam-3258	376	2	,	,	PUNCT
ejpam-3258	376	3	879	879	NUM
ejpam-3258	376	4	-	-	SYM
ejpam-3258	376	5	890	890	NUM
ejpam-3258	376	6	,	,	PUNCT
ejpam-3258	376	7	1995	1995	NUM
ejpam-3258	376	8	.	.	PUNCT
ejpam-3258	377	1	[	[	X
ejpam-3258	377	2	14	14	NUM
ejpam-3258	377	3	]	]	X
ejpam-3258	377	4	rehman	rehman	PROPN
ejpam-3258	377	5	,	,	PUNCT
ejpam-3258	377	6	mutti	mutti	PROPN
ejpam-3258	377	7	-	-	PUNCT
ejpam-3258	377	8	ur	ur	PROPN
ejpam-3258	377	9	and	and	CCONJ
ejpam-3258	377	10	tabassum	tabassum	NOUN
ejpam-3258	377	11	,	,	PUNCT
ejpam-3258	377	12	shabana	shabana	PROPN
ejpam-3258	377	13	numerical	numerical	PROPN
ejpam-3258	377	14	computation	computation	PROPN
ejpam-3258	377	15	of	of	ADP
ejpam-3258	377	16	structured	structured	ADJ
ejpam-3258	377	17	singular	singular	ADJ
ejpam-3258	377	18	values	value	NOUN
ejpam-3258	377	19	for	for	ADP
ejpam-3258	377	20	companion	companion	NOUN
ejpam-3258	377	21	matrices	matrix	NOUN
ejpam-3258	377	22	.	.	PUNCT
ejpam-3258	378	1	journal	journal	NOUN
ejpam-3258	378	2	of	of	ADP
ejpam-3258	378	3	applied	apply	VERB
ejpam-3258	378	4	mathematics	mathematic	NOUN
ejpam-3258	378	5	and	and	CCONJ
ejpam-3258	378	6	physics	physics	NOUN
ejpam-3258	378	7	volume	volume	NOUN
ejpam-3258	378	8	.	.	PUNCT
ejpam-3258	379	1	5	5	NUM
ejpam-3258	379	2	,	,	PUNCT
ejpam-3258	379	3	number	number	NOUN
ejpam-3258	379	4	.	.	PUNCT
ejpam-3258	379	5	5	5	NUM
ejpam-3258	379	6	,	,	PUNCT
ejpam-3258	379	7	pages	page	NOUN
ejpam-3258	379	8	.	.	PUNCT
ejpam-3258	379	9	1057	1057	NUM
ejpam-3258	379	10	,	,	PUNCT
ejpam-3258	379	11	year	year	NOUN
ejpam-3258	379	12	.	.	PUNCT
ejpam-3258	380	1	2017	2017	NUM
ejpam-3258	380	2	.	.	PUNCT
ejpam-3258	381	1	[	[	X
ejpam-3258	381	2	15	15	NUM
ejpam-3258	381	3	]	]	X
ejpam-3258	381	4	serre	serre	X
ejpam-3258	381	5	,	,	PUNCT
ejpam-3258	381	6	jean	jean	NOUN
ejpam-3258	381	7	-	-	PUNCT
ejpam-3258	381	8	pierre	pierre	PROPN
ejpam-3258	381	9	linear	linear	ADJ
ejpam-3258	381	10	representations	representation	NOUN
ejpam-3258	381	11	of	of	ADP
ejpam-3258	381	12	finite	finite	ADJ
ejpam-3258	381	13	groups	group	NOUN
ejpam-3258	381	14	.	.	PUNCT
ejpam-3258	382	1	vol	vol	NOUN
ejpam-3258	382	2	.	.	PUNCT
ejpam-3258	383	1	42	42	NUM
ejpam-3258	383	2	.	.	PUNCT
ejpam-3258	384	1	springer	springer	PROPN
ejpam-3258	384	2	science	science	PROPN
ejpam-3258	384	3	&	&	CCONJ
ejpam-3258	384	4	business	business	NOUN
ejpam-3258	384	5	media	medium	NOUN
ejpam-3258	384	6	,	,	PUNCT
ejpam-3258	384	7	2012	2012	NUM
ejpam-3258	384	8	.	.	PUNCT
ejpam-3258	385	1	appendix	appendix	NOUN
ejpam-3258	385	2	appendix	appendix	VERB
ejpam-3258	385	3	790	790	NUM
ejpam-3258	385	4	0	0	NUM
ejpam-3258	385	5	0.5	0.5	NUM
ejpam-3258	385	6	1	1	NUM
ejpam-3258	385	7	1.5	1.5	NUM
ejpam-3258	385	8	2	2	NUM
ejpam-3258	385	9	2.5	2.5	NUM
ejpam-3258	385	10	3	3	NUM
ejpam-3258	385	11	0.2	0.2	NUM
ejpam-3258	385	12	0.4	0.4	NUM
ejpam-3258	385	13	0.6	0.6	NUM
ejpam-3258	385	14	0.8	0.8	NUM
ejpam-3258	385	15	1	1	NUM
ejpam-3258	385	16	1.2	1.2	NUM
ejpam-3258	385	17	1.4	1.4	NUM
ejpam-3258	385	18	1.6	1.6	NUM
ejpam-3258	385	19	1.8	1.8	NUM
ejpam-3258	385	20	frequency(rad	frequency(rad	PROPN
ejpam-3258	385	21	/	/	SYM
ejpam-3258	385	22	sec	sec	PROPN
ejpam-3258	385	23	)	)	PUNCT
ejpam-3258	385	24	u	u	NOUN
ejpam-3258	385	25	pp	pp	ADV
ejpam-3258	386	1	er	er	INTJ
ejpam-3258	386	2	/l	/l	PUNCT
ejpam-3258	387	1	ow	ow	INTJ
ejpam-3258	387	2	er	er	INTJ
ejpam-3258	387	3	b	b	PROPN
ejpam-3258	387	4	ou	ou	ADP
ejpam-3258	387	5	nd	nd	NOUN
ejpam-3258	387	6	s	s	NOUN
ejpam-3258	387	7	ssv	ssv	NOUN
ejpam-3258	387	8	upper	upper	ADJ
ejpam-3258	387	9	bounds	bound	NOUN
ejpam-3258	387	10	by	by	ADP
ejpam-3258	387	11	mussv	mussv	ADJ
ejpam-3258	387	12	ssv	ssv	NOUN
ejpam-3258	387	13	lower	low	ADJ
ejpam-3258	387	14	bounds	bound	NOUN
ejpam-3258	387	15	by	by	ADP
ejpam-3258	387	16	mussv	mussv	ADJ
ejpam-3258	387	17	ssv	ssv	NOUN
ejpam-3258	387	18	lower	low	ADJ
ejpam-3258	387	19	bounds	bound	NOUN
ejpam-3258	387	20	by	by	ADP
ejpam-3258	387	21	newalgo	newalgo	NOUN
ejpam-3258	387	22	figure	figure	NOUN
ejpam-3258	387	23	1	1	NUM
ejpam-3258	387	24	:	:	PUNCT
ejpam-3258	387	25	comparison	comparison	NOUN
ejpam-3258	387	26	of	of	ADP
ejpam-3258	387	27	bounds	bound	NOUN
ejpam-3258	387	28	of	of	ADP
ejpam-3258	387	29	ssv	ssv	NOUN
ejpam-3258	387	30	appendix	appendix	VERB
ejpam-3258	387	31	791	791	NUM
ejpam-3258	387	32	0	0	NUM
ejpam-3258	387	33	1	1	NUM
ejpam-3258	387	34	2	2	NUM
ejpam-3258	387	35	3	3	NUM
ejpam-3258	387	36	4	4	NUM
ejpam-3258	387	37	5	5	NUM
ejpam-3258	387	38	6	6	NUM
ejpam-3258	387	39	0.4	0.4	NUM
ejpam-3258	387	40	0.6	0.6	NUM
ejpam-3258	387	41	0.8	0.8	NUM
ejpam-3258	387	42	1	1	NUM
ejpam-3258	387	43	1.2	1.2	NUM
ejpam-3258	387	44	1.4	1.4	NUM
ejpam-3258	387	45	1.6	1.6	NUM
ejpam-3258	387	46	1.8	1.8	NUM
ejpam-3258	387	47	2	2	NUM
ejpam-3258	387	48	2.2	2.2	NUM
ejpam-3258	387	49	2.4	2.4	NUM
ejpam-3258	387	50	frequency(rad	frequency(rad	NOUN
ejpam-3258	387	51	/	/	SYM
ejpam-3258	387	52	sec	sec	PROPN
ejpam-3258	387	53	)	)	PUNCT
ejpam-3258	387	54	u	u	NOUN
ejpam-3258	387	55	pp	pp	ADV
ejpam-3258	388	1	er	er	INTJ
ejpam-3258	388	2	/l	/l	PUNCT
ejpam-3258	389	1	ow	ow	INTJ
ejpam-3258	389	2	er	er	INTJ
ejpam-3258	389	3	b	b	PROPN
ejpam-3258	389	4	ou	ou	ADP
ejpam-3258	389	5	nd	nd	NOUN
ejpam-3258	389	6	s	s	NOUN
ejpam-3258	389	7	ssv	ssv	NOUN
ejpam-3258	389	8	upper	upper	ADJ
ejpam-3258	389	9	bounds	bound	NOUN
ejpam-3258	389	10	by	by	ADP
ejpam-3258	389	11	mussv	mussv	ADJ
ejpam-3258	389	12	ssv	ssv	NOUN
ejpam-3258	389	13	lower	low	ADJ
ejpam-3258	389	14	bounds	bound	NOUN
ejpam-3258	389	15	by	by	ADP
ejpam-3258	389	16	mussv	mussv	ADJ
ejpam-3258	389	17	ssv	ssv	NOUN
ejpam-3258	389	18	lower	low	ADJ
ejpam-3258	389	19	bounds	bound	NOUN
ejpam-3258	389	20	by	by	ADP
ejpam-3258	389	21	newalgo	newalgo	NOUN
ejpam-3258	389	22	figure	figure	NOUN
ejpam-3258	389	23	2	2	NUM
ejpam-3258	389	24	:	:	PUNCT
ejpam-3258	389	25	comparison	comparison	NOUN
ejpam-3258	389	26	of	of	ADP
ejpam-3258	389	27	bounds	bound	NOUN
ejpam-3258	389	28	of	of	ADP
ejpam-3258	389	29	ssv	ssv	NOUN
ejpam-3258	389	30	appendix	appendix	VERB
ejpam-3258	389	31	792	792	NUM
ejpam-3258	389	32	0	0	NUM
ejpam-3258	389	33	0.5	0.5	NUM
ejpam-3258	389	34	1	1	NUM
ejpam-3258	389	35	1.5	1.5	NUM
ejpam-3258	389	36	2	2	NUM
ejpam-3258	389	37	2.5	2.5	NUM
ejpam-3258	389	38	3	3	NUM
ejpam-3258	389	39	3.5	3.5	NUM
ejpam-3258	389	40	4	4	NUM
ejpam-3258	389	41	0	0	NUM
ejpam-3258	389	42	0.5	0.5	NUM
ejpam-3258	389	43	1	1	NUM
ejpam-3258	389	44	1.5	1.5	NUM
ejpam-3258	389	45	2	2	NUM
ejpam-3258	389	46	2.5	2.5	NUM
ejpam-3258	389	47	3	3	NUM
ejpam-3258	389	48	frequency(rad	frequency(rad	PROPN
ejpam-3258	389	49	/	/	SYM
ejpam-3258	389	50	sec	sec	PROPN
ejpam-3258	389	51	)	)	PUNCT
ejpam-3258	389	52	u	u	NOUN
ejpam-3258	389	53	pp	pp	ADV
ejpam-3258	390	1	er	er	INTJ
ejpam-3258	390	2	/l	/l	PUNCT
ejpam-3258	391	1	ow	ow	INTJ
ejpam-3258	391	2	er	er	INTJ
ejpam-3258	391	3	b	b	PROPN
ejpam-3258	391	4	ou	ou	ADP
ejpam-3258	391	5	nd	nd	NOUN
ejpam-3258	391	6	s	s	NOUN
ejpam-3258	391	7	ssv	ssv	NOUN
ejpam-3258	391	8	upper	upper	ADJ
ejpam-3258	391	9	bounds	bound	NOUN
ejpam-3258	391	10	by	by	ADP
ejpam-3258	391	11	mussv	mussv	ADJ
ejpam-3258	391	12	ssv	ssv	NOUN
ejpam-3258	391	13	lower	low	ADJ
ejpam-3258	391	14	bounds	bound	NOUN
ejpam-3258	391	15	by	by	ADP
ejpam-3258	391	16	mussv	mussv	ADJ
ejpam-3258	391	17	ssv	ssv	NOUN
ejpam-3258	391	18	lower	low	ADJ
ejpam-3258	391	19	bounds	bound	NOUN
ejpam-3258	391	20	by	by	ADP
ejpam-3258	391	21	newalgo	newalgo	NOUN
ejpam-3258	391	22	figure	figure	NOUN
ejpam-3258	391	23	3	3	NUM
ejpam-3258	391	24	:	:	PUNCT
ejpam-3258	391	25	comparison	comparison	NOUN
ejpam-3258	391	26	of	of	ADP
ejpam-3258	391	27	bounds	bound	NOUN
ejpam-3258	391	28	of	of	ADP
ejpam-3258	391	29	ssv	ssv	NOUN